LMFDB - Embedded newform 546.2.z.b.131.12

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			131.12
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.0921101 + 1.72960i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.890016 - 1.54155i) q^{5} +(-0.944570 + 1.45182i) q^{6} +(-1.51727 + 2.16746i) q^{7} +1.00000i q^{8} +(-2.98303 - 0.318627i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0921101 + 1.72960i) 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} +(-2.98303 - 0.318627i) q^{9} +(1.54155 - 0.890016i) q^{10} +(-3.61827 + 2.08901i) q^{11} +(-1.54393 + 0.785030i) 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} +(-2.42407 - 1.76746i) q^{18} +(-2.62640 - 1.51635i) q^{19} +1.78003 q^{20} +(-3.60909 - 2.82391i) q^{21} -4.17801 q^{22} +(6.70577 + 3.87158i) q^{23} +(-1.72960 - 0.0921101i) 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} +(1.39738 + 2.74825i) q^{30} +(-1.78918 + 1.03299i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.27987 - 6.45057i) 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} +(-1.72960 - 0.0921101i) q^{39} +(1.54155 + 0.890016i) q^{40} +2.69649 q^{41} +(-1.71361 - 4.25012i) q^{42} +0.322841 q^{43} +(-3.61827 - 2.08901i) q^{44} +(-3.14613 + 4.31492i) 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} +(-11.7730 + 5.98614i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(10.2425 - 5.91349i) q^{53} +(3.28027 - 4.02987i) 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} +(-0.163959 + 3.07874i) q^{60} +(-7.38934 - 4.26624i) q^{61} -2.06597 q^{62} +(5.21667 - 5.98217i) q^{63} -1.00000 q^{64} +(1.54155 + 0.890016i) q^{65} +(0.384837 - 7.22629i) 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} +(0.318627 - 2.98303i) q^{72} +(1.14565 - 0.661439i) q^{73} +(6.84960 - 3.95462i) q^{74} +(-2.82769 + 1.43777i) 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} +(8.79695 + 1.90095i) q^{81} +(2.33523 + 1.34825i) q^{82} -3.38793 q^{83} +(0.641031 - 4.53752i) q^{84} +13.5734 q^{85} +(0.279589 + 0.161421i) q^{86} +(13.2334 + 0.704745i) 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} +(-1.62185 - 3.18972i) q^{93} +(-3.54688 + 2.04779i) q^{94} +(-4.67508 + 2.69916i) q^{95} +(-0.785030 - 1.54393i) 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} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 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} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 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} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.0921101	+	1.72960i	−0.0531798	+	0.998585i
$3$	−0.0921101	+	1.72960i	−0.0531798	+	0.998585i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.890016	−	1.54155i	0.398027	−	0.689404i	−0.595455	−	0.803389i	$-0.703028\pi$
$5$	0.890016	−	1.54155i	0.398027	−	0.689404i	0.993482	+	0.113985i	$0.0363616\pi$
$6$	−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
$9$	−2.98303	−	0.318627i	−0.994344	−	0.106209i
$10$	1.54155	−	0.890016i	0.487482	−	0.281448i
$11$	−3.61827	+	2.08901i	−1.09095	+	0.629859i	−0.933829	−	0.357720i	$-0.883554\pi$
$11$	−3.61827	+	2.08901i	−1.09095	+	0.629859i	−0.157119	+	0.987580i	$0.550221\pi$
$12$	−1.54393	+	0.785030i	−0.445695	+	0.226619i
$13$			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	0.792025	+	0.610489i	$0.209027\pi$
$17$	3.81268	+	6.60376i	0.924711	+	1.60165i	0.132686	+	0.991158i	$0.457640\pi$
$18$	−2.42407	−	1.76746i	−0.571358	−	0.416593i
$19$	−2.62640	−	1.51635i	−0.602538	−	0.347875i	0.167502	−	0.985872i	$-0.446430\pi$
$19$	−2.62640	−	1.51635i	−0.602538	−	0.347875i	−0.770039	+	0.637996i	$0.779763\pi$
$20$	1.78003			0.398027
$21$	−3.60909	−	2.82391i	−0.787568	−	0.616227i
$22$	−4.17801			−0.890755
$23$	6.70577	+	3.87158i	1.39825	+	0.807279i	0.994209	−	0.107462i	$-0.0342724\pi$
$23$	6.70577	+	3.87158i	1.39825	+	0.807279i	0.404040	+	0.914741i	$0.367606\pi$
$24$	−1.72960	−	0.0921101i	−0.353053	−	0.0188019i
$25$	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	$-0.251481\pi$
$30$	1.39738	+	2.74825i	0.255125	+	0.501760i
$31$	−1.78918	+	1.03299i	−0.321347	+	0.185530i	−0.651993	−	0.758225i	$-0.726067\pi$
$31$	−1.78918	+	1.03299i	−0.321347	+	0.185530i	0.330646	+	0.943755i	$0.392733\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.27987	−	6.45057i	−0.570951	−	1.12290i
$34$			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	−0.332955	−	0.942943i	$-0.608046\pi$
$37$	3.95462	−	6.84960i	0.650135	−	1.12607i	0.983090	−	0.183124i	$-0.0586209\pi$
$38$	−1.51635	−	2.62640i	−0.245985	−	0.426059i
$39$	−1.72960	−	0.0921101i	−0.276958	−	0.0147494i
$40$	1.54155	+	0.890016i	0.243741	+	0.140724i
$41$	2.69649			0.421121			0.210561	−	0.977581i	$-0.432471\pi$
$41$	2.69649			0.421121			0.210561	+	0.977581i	$0.432471\pi$
$42$	−1.71361	−	4.25012i	−0.264416	−	0.655808i
$43$	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
$45$	−3.14613	+	4.31492i	−0.468997	+	0.643230i
$46$	3.87158	+	6.70577i	0.570833	+	0.988711i
$47$	−2.04779	+	3.54688i	−0.298701	+	0.517366i	−0.975839	−	0.218490i	$-0.929887\pi$
$47$	−2.04779	+	3.54688i	−0.298701	+	0.517366i	0.677138	+	0.735856i	$0.263220\pi$
$48$	−1.45182	−	0.944570i	−0.209553	−	0.136337i
$49$	−2.39581	−	6.57724i	−0.342258	−	0.939606i
$50$			1.83148i			0.259011i
$51$	−11.7730	+	5.98614i	−1.64856	+	0.838227i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	10.2425	−	5.91349i	1.40691	−	0.812281i	0.411822	−	0.911264i	$-0.364892\pi$
$53$	10.2425	−	5.91349i	1.40691	−	0.812281i	0.995089	+	0.0989835i	$0.0315591\pi$
$54$	3.28027	−	4.02987i	0.446388	−	0.548395i
$55$			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	0.835629	+	0.549294i	$0.185103\pi$
$59$	6.86324	+	11.8875i	0.893517	+	1.54762i	0.0578885	+	0.998323i	$0.481563\pi$
$60$	−0.163959	+	3.07874i	−0.0211670	+	0.397464i
$61$	−7.38934	−	4.26624i	−0.946108	−	0.546236i	−0.0542381	−	0.998528i	$-0.517273\pi$
$61$	−7.38934	−	4.26624i	−0.946108	−	0.546236i	−0.891870	+	0.452292i	$0.850606\pi$
$62$	−2.06597			−0.262379
$63$	5.21667	−	5.98217i	0.657238	−	0.753683i
$64$	−1.00000			−0.125000
$65$	1.54155	+	0.890016i	0.191206	+	0.110393i
$66$	0.384837	−	7.22629i	0.0473702	−	0.889495i
$67$	−6.25392	−	10.8321i	−0.764037	−	1.32335i	−0.940754	−	0.339090i	$-0.889881\pi$
$67$	−6.25392	−	10.8321i	−0.764037	−	1.32335i	0.176716	−	0.984262i	$-0.443452\pi$
$68$	−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	$0.925349\pi$
$72$	0.318627	−	2.98303i	0.0375506	−	0.351554i
$73$	1.14565	−	0.661439i	0.134088	−	0.0774155i	−0.431456	−	0.902134i	$-0.642000\pi$
$73$	1.14565	−	0.661439i	0.134088	−	0.0774155i	0.565543	+	0.824719i	$0.308667\pi$
$74$	6.84960	−	3.95462i	0.796249	−	0.459715i
$75$	−2.82769	+	1.43777i	−0.326513	+	0.166019i
$76$		−	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	−0.351266	−	0.936276i	$-0.614249\pi$
$79$	5.64583	−	9.77886i	0.635205	−	1.10021i	0.986472	−	0.163932i	$-0.0524179\pi$
$80$	0.890016	+	1.54155i	0.0995068	+	0.172351i
$81$	8.79695	+	1.90095i	0.977439	+	0.211217i
$82$	2.33523	+	1.34825i	0.257883	+	0.148889i
$83$	−3.38793			−0.371874			−0.185937	−	0.982562i	$-0.559532\pi$
$83$	−3.38793			−0.371874			−0.185937	+	0.982562i	$0.559532\pi$
$84$	0.641031	−	4.53752i	0.0699422	−	0.495084i
$85$	13.5734			1.47224
$86$	0.279589	+	0.161421i	0.0301488	+	0.0174064i
$87$	13.2334	+	0.704745i	1.41877	+	0.0755566i
$88$	−2.08901	−	3.61827i	−0.222689	−	0.385708i
$89$	−1.23778	+	2.14390i	−0.131205	+	0.227253i	−0.924141	−	0.382051i	$-0.875218\pi$
$89$	−1.23778	+	2.14390i	−0.131205	+	0.227253i	0.792937	+	0.609304i	$0.208551\pi$
$90$	−4.88209	+	2.16377i	−0.514617	+	0.228081i
$91$	−2.16746	−	1.51727i	−0.227212	−	0.159053i
$92$			7.74315i			0.807279i
$93$	−1.62185	−	3.18972i	−0.168178	−	0.330759i
$94$	−3.54688	+	2.04779i	−0.365833	+	0.211214i
$95$	−4.67508	+	2.69916i	−0.479653	+	0.276928i
$96$	−0.785030	−	1.54393i	−0.0801218	−	0.157577i
$97$			6.52429i			0.662442i	0.943553	+	0.331221i	$0.107460\pi$
$97$			6.52429i			0.662442i	−0.943553	+	0.331221i	$0.892540\pi$
$98$	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	$-0.169800\pi$
$101$	−0.0989242	−	0.171342i	−0.00984333	−	0.0170491i	−0.870905	+	0.491451i	$0.836467\pi$
$102$	−13.1888	−	0.702373i	−1.30589	−	0.0695453i
$103$	5.71582	+	3.30003i	0.563196	+	0.325161i	0.754427	−	0.656384i	$-0.227915\pi$
$103$	5.71582	+	3.30003i	0.563196	+	0.325161i	−0.191231	+	0.981545i	$0.561248\pi$
$104$	−1.00000			−0.0980581
$105$	−7.56536	+	3.05028i	−0.738303	+	0.297677i
$106$	11.8270			1.14874
$107$	9.96012	+	5.75048i	0.962882	+	0.555920i	0.897059	−	0.441911i	$-0.145699\pi$
$107$	9.96012	+	5.75048i	0.962882	+	0.555920i	0.0658228	+	0.997831i	$0.479033\pi$
$108$	4.85573	−	1.84983i	0.467243	−	0.178000i
$109$	5.16177	+	8.94045i	0.494408	+	0.856340i	0.999979	−	0.00644502i	$-0.00205153\pi$
$109$	5.16177	+	8.94045i	0.494408	+	0.856340i	−0.505571	+	0.862785i	$0.668718\pi$
$110$	−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	$0.994574\pi$
$114$	4.68229	−	2.38077i	0.438537	−	0.222979i
$115$	11.9365	−	6.89153i	1.11308	−	0.642639i
$116$	6.62606	−	3.82556i	0.615214	−	0.355194i
$117$	0.318627	−	2.98303i	0.0294571	−	0.275781i
$118$			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
$123$	−0.248374	+	4.66385i	−0.0223951	+	0.420525i
$124$	−1.78918	−	1.03299i	−0.160674	−	0.0927649i
$125$	12.1603			1.08765
$126$	7.50885	−	2.57238i	0.668942	−	0.229166i
$127$	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
$129$	−0.0297369	+	0.558386i	−0.00261819	+	0.0491631i
$130$	0.890016	+	1.54155i	0.0780596	+	0.135203i
$131$	4.34750	−	7.53010i	0.379843	−	0.657908i	−0.611196	−	0.791479i	$-0.709311\pi$
$131$	4.34750	−	7.53010i	0.379843	−	0.657908i	0.991039	+	0.133572i	$0.0426446\pi$
$132$	3.94642	−	6.06573i	0.343492	−	0.527954i
$133$	7.27159	−	3.39192i	0.630527	−	0.294117i
$134$		−	12.5078i		−	1.08051i
$135$	−7.17329	−	5.83899i	−0.617379	−	0.502540i
$136$	−6.60376	+	3.81268i	−0.566268	+	0.326935i
$137$	−7.42752	+	4.28828i	−0.634576	+	0.366373i	−0.782522	−	0.622623i	$-0.786067\pi$
$137$	−7.42752	+	4.28828i	−0.634576	+	0.366373i	0.147946	+	0.988995i	$0.452734\pi$
$138$	−11.9549	+	6.07861i	−1.01767	+	0.517445i
$139$			0.761522i			0.0645915i	0.999478	+	0.0322957i	$0.0102818\pi$
$139$			0.761522i			0.0645915i	−0.999478	+	0.0322957i	$0.989718\pi$
$140$	−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
$144$	1.76746	−	2.42407i	0.147288	−	0.202006i
$145$	−11.7946	−	6.80962i	−0.979489	−	0.565508i
$146$	1.32288			0.109482
$147$	11.5967	−	3.53796i	0.956478	−	0.291806i
$148$	7.90923			0.650135
$149$	−1.22069	−	0.704767i	−0.100003	−	0.0577368i	0.449164	−	0.893449i	$-0.351722\pi$
$149$	−1.22069	−	0.704767i	−0.100003	−	0.0577368i	−0.549167	+	0.835712i	$0.685055\pi$
$150$	−3.16773	−	0.168698i	−0.258644	−	0.0137742i
$151$	−7.33631	−	12.7069i	−0.597020	−	1.03407i	−0.993258	−	0.115922i	$-0.963018\pi$
$151$	−7.33631	−	12.7069i	−0.597020	−	1.03407i	0.396238	−	0.918148i	$-0.370316\pi$
$152$	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
$156$	−0.785030	−	1.54393i	−0.0628527	−	0.123614i
$157$	−18.1677	+	10.4891i	−1.44994	+	0.837121i	−0.998477	−	0.0551705i	$-0.982430\pi$
$157$	−18.1677	+	10.4891i	−1.44994	+	0.837121i	−0.451459	+	0.892292i	$0.649096\pi$
$158$	9.77886	−	5.64583i	0.777965	−	0.449158i
$159$	9.28454	+	18.2601i	0.736312	+	1.44812i
$160$			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	−0.0636510	+	0.997972i	$0.520274\pi$
$163$	−11.4406	+	19.8157i	−0.896095	+	1.55208i	−0.832444	+	0.554109i	$0.813059\pi$
$164$	1.34825	+	2.33523i	0.105280	+	0.182351i
$165$	−12.8630	−	0.685023i	−1.00139	−	0.0533290i
$166$	−2.93403	−	1.69397i	−0.227725	−	0.131477i
$167$	−0.927408			−0.0717650			−0.0358825	−	0.999356i	$-0.511424\pi$
$167$	−0.927408			−0.0717650			−0.0358825	+	0.999356i	$0.511424\pi$
$168$	2.82391	−	3.60909i	0.217869	−	0.278447i
$169$	−1.00000			−0.0769231
$170$	11.7549	+	6.78670i	0.901560	+	0.520516i
$171$	7.35149	+	5.36017i	0.562182	+	0.409903i
$172$	0.161421	+	0.279589i	0.0123082	+	0.0213184i
$173$	1.98619	−	3.44018i	0.151007	−	0.261552i	−0.780591	−	0.625042i	$-0.785082\pi$
$173$	1.98619	−	3.44018i	0.151007	−	0.261552i	0.931598	+	0.363490i	$0.118415\pi$
$174$	11.1081	+	7.22701i	0.842100	+	0.547878i
$175$	−4.82727	−	0.421715i	−0.364907	−	0.0318787i
$176$		−	4.17801i		−	0.314930i
$177$	−21.1928	+	10.7757i	−1.59294	+	0.809951i
$178$	−2.14390	+	1.23778i	−0.160692	+	0.0927757i
$179$	12.3345	−	7.12132i	0.921923	−	0.532273i	0.0376751	−	0.999290i	$-0.488005\pi$
$179$	12.3345	−	7.12132i	0.921923	−	0.532273i	0.884248	+	0.467017i	$0.154671\pi$
$180$	−5.30989	−	0.567167i	−0.395776	−	0.0422741i
$181$			8.17371i			0.607547i	0.952744	+	0.303774i	$0.0982467\pi$
$181$			8.17371i			0.607547i	−0.952744	+	0.303774i	$0.901753\pi$
$182$	−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
$186$	0.190297	−	3.57331i	0.0139532	−	0.262007i
$187$	−27.5906	−	15.9294i	−2.01762	−	1.16488i
$188$	−4.09559			−0.298701
$189$	9.86626	+	9.57376i	0.717665	+	0.696389i
$190$	−5.39832			−0.391635
$191$	−21.0081	−	12.1290i	−1.52009	−	0.877627i	−0.999719	−	0.0236888i	$-0.992459\pi$
$191$	−21.0081	−	12.1290i	−1.52009	−	0.877627i	−0.520375	−	0.853938i	$-0.674208\pi$
$192$	0.0921101	−	1.72960i	0.00664747	−	0.124823i
$193$	−9.38887	−	16.2620i	−0.675826	−	1.17056i	−0.976227	−	0.216751i	$-0.930454\pi$
$193$	−9.38887	−	16.2620i	−0.675826	−	1.17056i	0.300401	−	0.953813i	$-0.402879\pi$
$194$	−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	$0.930036\pi$
$198$	12.4631	+	1.33123i	0.885717	+	0.0946063i
$199$	−2.20348	+	1.27218i	−0.156200	+	0.0901824i	−0.576063	−	0.817405i	$-0.695412\pi$
$199$	−2.20348	+	1.27218i	−0.156200	+	0.0901824i	0.419862	+	0.907588i	$0.362078\pi$
$200$	−1.58611	+	0.915742i	−0.112155	+	0.0647527i
$201$	19.3112	−	9.81903i	1.36211	−	0.692581i
$202$		−	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
$207$	−18.7699	−	13.6857i	−1.30460	−	0.951220i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	12.6707			0.876450
$210$	−8.07693	−	1.14106i	−0.557361	−	0.0787404i
$211$	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
$213$	−6.77332	−	0.360714i	−0.464100	−	0.0247157i
$214$	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
$219$	1.03850	+	2.04243i	0.0701752	+	0.138015i
$220$	−6.44063	+	3.71850i	−0.434227	+	0.250701i
$221$	−6.60376	+	3.81268i	−0.444217	+	0.256469i
$222$	6.20899	+	12.2113i	0.416720	+	0.819570i
$223$			16.6396i			1.11427i	0.830423	+	0.557134i	$0.188099\pi$
$223$			16.6396i			1.11427i	−0.830423	+	0.557134i	$0.811901\pi$
$224$	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	$-0.329544\pi$
$227$	−7.37740	−	12.7780i	−0.489655	−	0.848108i	−0.999929	+	0.0119039i	$0.996211\pi$
$228$	5.24537	+	0.279343i	0.347383	+	0.0184999i
$229$	18.7792	+	10.8422i	1.24097	+	0.716473i	0.969291	−	0.245916i	$-0.0790888\pi$
$229$	18.7792	+	10.8422i	1.24097	+	0.716473i	0.271676	+	0.962389i	$0.412422\pi$
$230$	13.7831			0.908828
$231$	18.9578	+	2.67824i	1.24733	+	0.176215i
$232$	7.65112			0.502320
$233$	−6.74565	−	3.89460i	−0.441922	−	0.255144i	0.262490	−	0.964935i	$-0.415456\pi$
$233$	−6.74565	−	3.89460i	−0.441922	−	0.255144i	−0.704413	+	0.709791i	$0.748790\pi$
$234$	1.76746	−	2.42407i	0.115542	−	0.158466i
$235$	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	$0.872369\pi$
$240$	−2.74825	+	1.39738i	−0.177399	+	0.0902005i
$241$	13.9929	−	8.07879i	0.901360	−	0.520400i	0.0237187	−	0.999719i	$-0.492449\pi$
$241$	13.9929	−	8.07879i	0.901360	−	0.520400i	0.877641	+	0.479318i	$0.159116\pi$
$242$	5.59088	−	3.22790i	0.359395	−	0.207497i
$243$	−4.09817	+	15.0401i	−0.262898	+	0.964824i
$244$		−	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
$249$	0.312063	−	5.85976i	0.0197762	−	0.371347i
$250$	10.5311	+	6.08013i	0.666045	+	0.384541i
$251$	−0.0295982			−0.00186822			−0.000934112	−	1.00000i	$-0.500297\pi$
$251$	−0.0295982			−0.00186822			−0.000934112		1.00000i	$0.500297\pi$
$252$	7.78905	+	1.52668i	0.490664	+	0.0961717i
$253$	−32.3510			−2.03389
$254$	15.3533	+	8.86422i	0.963350	+	0.556190i
$255$	−1.25025	+	23.4765i	−0.0782935	+	1.47016i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.68113	+	13.3041i	−0.479136	+	0.829887i	−0.999714	−	0.0239268i	$-0.992383\pi$
$257$	−7.68113	+	13.3041i	−0.479136	+	0.829887i	0.520578	+	0.853814i	$0.325716\pi$
$258$	−0.304946	+	0.468708i	−0.0189851	+	0.0291805i
$259$	8.84605	+	18.9641i	0.549667	+	1.17837i
$260$			1.78003i			0.110393i
$261$	−2.43785	+	22.8235i	−0.150899	+	1.41274i
$262$	7.53010	−	4.34750i	0.465211	−	0.268590i
$263$	16.8894	−	9.75108i	1.04144	−	0.601277i	0.121201	−	0.992628i	$-0.461325\pi$
$263$	16.8894	−	9.75108i	1.04144	−	0.601277i	0.920242	+	0.391351i	$0.127992\pi$
$264$	6.45057	−	3.27987i	0.397005	−	0.201862i
$265$		−	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	$-0.199553\pi$
$269$	−1.69151	−	2.92978i	−0.103133	−	0.178632i	−0.912974	+	0.408018i	$0.866220\pi$
$270$	−3.29276	−	8.64336i	−0.200391	−	0.526018i
$271$	−27.5354	−	15.8975i	−1.67265	−	0.965707i	−0.966144	−	0.258004i	$-0.916935\pi$
$271$	−27.5354	−	15.8975i	−1.67265	−	0.965707i	−0.706510	−	0.707703i	$-0.749732\pi$
$272$	−7.62536			−0.462356
$273$	2.82391	−	3.60909i	0.170911	−	0.218432i
$274$	−8.57657			−0.518129
$275$	−6.62680	−	3.82598i	−0.399611	−	0.230715i
$276$	−13.3926	−	0.713223i	−0.806137	−	0.0429310i
$277$	−0.205326	−	0.355636i	−0.0123369	−	0.0213681i	0.859791	−	0.510646i	$-0.170594\pi$
$277$	−0.205326	−	0.355636i	−0.0123369	−	0.0213681i	−0.872128	+	0.489278i	$0.837260\pi$
$278$	−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	$-0.224087\pi$
$282$	−3.21516	−	6.32331i	−0.191460	−	0.376547i
$283$	−9.90407	+	5.71812i	−0.588736	+	0.339907i	−0.764598	−	0.644508i	$-0.777062\pi$
$283$	−9.90407	+	5.71812i	−0.588736	+	0.339907i	0.175861	+	0.984415i	$0.443729\pi$
$284$	−3.39146	+	1.95806i	−0.201246	+	0.116189i
$285$	−4.23784	−	8.33464i	−0.251028	−	0.493701i
$286$		−	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
$291$	−11.2844	−	0.600953i	−0.661504	−	0.0352285i
$292$	1.14565	+	0.661439i	0.0670438	+	0.0387078i
$293$	10.6232			0.620616			0.310308	−	0.950636i	$-0.399568\pi$
$293$	10.6232			0.620616			0.310308	+	0.950636i	$0.399568\pi$
$294$	11.8120	+	2.73438i	0.688889	+	0.159472i
$295$	24.4336			1.42258
$296$	6.84960	+	3.95462i	0.398125	+	0.229857i
$297$	7.72862	+	20.2873i	0.448460	+	1.17719i
$298$	−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
$303$	0.305465	−	0.155317i	0.0175485	−	0.00892273i
$304$	2.62640	−	1.51635i	0.150634	−	0.0869688i
$305$	−13.1533	+	7.59404i	−0.753154	+	0.434833i
$306$	2.42965	−	22.7467i	0.138894	−	1.30034i
$307$		−	30.4761i		−	1.73936i	−0.493615	−	0.869680i	$-0.664325\pi$
$307$		−	30.4761i		−	1.73936i	0.493615	−	0.869680i	$-0.335675\pi$
$308$	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	$-0.100133\pi$
$311$	3.65935	+	6.33818i	0.207503	+	0.359405i	−0.743425	+	0.668820i	$0.766800\pi$
$312$	0.0921101	−	1.72960i	0.00521471	−	0.0979193i
$313$	−3.28061	−	1.89406i	−0.185431	−	0.107059i	0.404411	−	0.914577i	$-0.367477\pi$
$313$	−3.28061	−	1.89406i	−0.185431	−	0.107059i	−0.589842	+	0.807519i	$0.700810\pi$
$314$	−20.9782			−1.18387
$315$	−4.57892	−	13.3660i	−0.257993	−	0.753089i
$316$	11.2917			0.635205
$317$	4.69062	+	2.70813i	0.263452	+	0.152104i	0.625908	−	0.779897i	$-0.284728\pi$
$317$	4.69062	+	2.70813i	0.263452	+	0.152104i	−0.362456	+	0.932001i	$0.618062\pi$
$318$	−1.08938	+	20.4560i	−0.0610897	+	1.14711i
$319$	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
$324$	2.75221	+	8.56886i	0.152900	+	0.476048i
$325$	−1.58611	+	0.915742i	−0.0879816	+	0.0507962i
$326$	−19.8157	+	11.4406i	−1.09749	+	0.633635i
$327$	−15.9389	+	8.10429i	−0.881421	+	0.448168i
$328$			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	−0.378625	−	0.925550i	$-0.623603\pi$
$331$	11.1387	−	19.2928i	0.612237	−	1.06043i	0.990862	−	0.134876i	$-0.0430636\pi$
$332$	−1.69397	−	2.93403i	−0.0929684	−	0.161026i
$333$	−13.9792	+	19.1725i	−0.766056	+	1.05065i
$334$	−0.803159	−	0.463704i	−0.0439469	−	0.0253728i
$335$	−22.2643			−1.21643
$336$	4.25012	−	1.71361i	0.231863	−	0.0934851i
$337$	−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
$339$	−0.626777	−	0.0333791i	−0.0340418	−	0.00181290i
$340$	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
$345$	10.8201	+	21.2801i	0.582536	+	1.14568i
$346$	3.44018	−	1.98619i	0.184945	−	0.106778i
$347$	7.46932	−	4.31241i	0.400974	−	0.231502i	−0.285930	−	0.958250i	$-0.592303\pi$
$347$	7.46932	−	4.31241i	0.400974	−	0.231502i	0.686904	+	0.726748i	$0.258969\pi$
$348$	6.00636	+	11.8128i	0.321975	+	0.633233i
$349$			0.237322i			0.0127035i	0.999980	+	0.00635177i	$0.00202184\pi$
$349$			0.237322i			0.0127035i	−0.999980	+	0.00635177i	$0.997978\pi$
$350$	−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	$-0.131863\pi$
$353$	2.05021	+	3.55106i	0.109121	+	0.189004i	−0.806293	+	0.591516i	$0.798530\pi$
$354$	−23.7413	−	1.26435i	−1.26184	−	0.0671993i
$355$	6.03690	+	3.48541i	0.320406	+	0.184986i
$356$	−2.47557			−0.131205
$357$	4.88810	−	34.6002i	0.258705	−	1.83124i
$358$	14.2426			0.752747
$359$	5.27567	+	3.04591i	0.278439	+	0.160757i	0.632717	−	0.774383i	$-0.281940\pi$
$359$	5.27567	+	3.04591i	0.278439	+	0.160757i	−0.354277	+	0.935140i	$0.615273\pi$
$360$	−4.31492	−	3.14613i	−0.227416	−	0.165815i
$361$	−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
$366$	13.1736	−	6.69825i	0.688593	−	0.350123i
$367$	−18.0027	+	10.3939i	−0.939734	+	0.542556i	−0.889877	−	0.456201i	$-0.849210\pi$
$367$	−18.0027	+	10.3939i	−0.939734	+	0.542556i	−0.0498569	+	0.998756i	$0.515877\pi$
$368$	−6.70577	+	3.87158i	−0.349562	+	0.201820i
$369$	−8.04372	−	0.859176i	−0.418739	−	0.0447269i
$370$		−	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	−0.763045	−	0.646345i	$-0.776297\pi$
$373$	3.44216	−	5.96200i	0.178228	−	0.308701i	0.941274	+	0.337644i	$0.109630\pi$
$374$	−15.9294	−	27.5906i	−0.823691	−	1.42668i
$375$	−1.12008	+	21.0324i	−0.0578409	+	1.08611i
$376$	−3.54688	−	2.04779i	−0.182916	−	0.105607i
$377$	7.65112			0.394053
$378$	3.75755	+	13.2243i	0.193267	+	0.680182i
$379$	−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
$381$	−1.63297	+	30.6631i	−0.0836595	+	1.57092i
$382$	−12.1290	−	21.0081i	−0.620576	−	1.07487i
$383$	10.9702	−	19.0009i	0.560550	−	0.970900i	−0.436899	−	0.899511i	$-0.643923\pi$
$383$	10.9702	−	19.0009i	0.560550	−	0.970900i	0.997448	−	0.0713898i	$-0.0227434\pi$
$384$	0.944570	−	1.45182i	0.0482024	−	0.0740880i
$385$	−16.1194	−	11.2839i	−0.821522	−	0.575081i
$386$		−	18.7777i		−	0.955762i
$387$	−0.963045	−	0.102866i	−0.0489543	−	0.00522897i
$388$	−5.65020	+	3.26215i	−0.286846	+	0.165610i
$389$	19.8429	−	11.4563i	1.00608	−	0.580858i	0.0960352	−	0.995378i	$-0.469384\pi$
$389$	19.8429	−	11.4563i	1.00608	−	0.580858i	0.910040	+	0.414520i	$0.136051\pi$
$390$	−2.74825	+	1.39738i	−0.139163	+	0.0707591i
$391$			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
$396$	10.1278	+	7.38445i	0.508940	+	0.371083i
$397$	−3.67578	−	2.12221i	−0.184482	−	0.106511i	0.404915	−	0.914354i	$-0.367301\pi$
$397$	−3.67578	−	2.12221i	−0.184482	−	0.106511i	−0.589397	+	0.807844i	$0.700635\pi$
$398$	−2.54436			−0.127537
$399$	5.19688	+	12.8894i	0.260169	+	0.645276i
$400$	−1.83148			−0.0915742
$401$	−12.9346	−	7.46782i	−0.645925	−	0.372925i	0.140968	−	0.990014i	$-0.454978\pi$
$401$	−12.9346	−	7.46782i	−0.645925	−	0.372925i	−0.786893	+	0.617089i	$0.788312\pi$
$402$	21.6335	+	1.15210i	1.07898	+	0.0574614i
$403$	−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
$408$	−5.98614	−	11.7730i	−0.296358	−	0.582853i
$409$	28.2564	−	16.3138i	1.39719	−	0.806666i	0.403090	−	0.915160i	$-0.367936\pi$
$409$	28.2564	−	16.3138i	1.39719	−	0.806666i	0.994097	+	0.108494i	$0.0346028\pi$
$410$	4.15679	−	2.39992i	0.205289	−	0.118524i
$411$	−6.73286	−	13.2416i	−0.332108	−	0.653162i
$412$			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
$417$	−1.31713	−	0.0701439i	−0.0645001	−	0.00343496i
$418$	10.9731	+	6.33534i	0.536714	+	0.309872i
$419$	27.4096			1.33905			0.669524	−	0.742790i	$-0.266498\pi$
$419$	27.4096			1.33905			0.669524	+	0.742790i	$0.266498\pi$
$420$	−6.42430	−	5.02665i	−0.313474	−	0.245275i
$421$	−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
$423$	7.23876	−	9.92798i	0.351961	−	0.482715i
$424$	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
$429$	6.45057	−	3.27987i	0.311436	−	0.158353i
$430$	0.497677	−	0.287334i	0.0240001	−	0.0138565i
$431$	4.24835	−	2.45278i	0.204636	−	0.118146i	−0.394180	−	0.919033i	$-0.628971\pi$
$431$	4.24835	−	2.45278i	0.204636	−	0.118146i	0.598816	+	0.800887i	$0.295638\pi$
$432$	4.02987	+	3.28027i	0.193887	+	0.157822i
$433$			1.02650i			0.0493306i	0.999696	+	0.0246653i	$0.00785201\pi$
$433$			1.02650i			0.0493306i	−0.999696	+	0.0246653i	$0.992148\pi$
$434$	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
$438$	−0.121850	+	2.28805i	−0.00582224	+	0.109327i
$439$	1.98357	+	1.14522i	0.0946708	+	0.0546582i	0.546588	−	0.837402i	$-0.315926\pi$
$439$	1.98357	+	1.14522i	0.0946708	+	0.0546582i	−0.451917	+	0.892060i	$0.649260\pi$
$440$	−7.43700			−0.354545
$441$	5.05108	+	20.3835i	0.240528	+	0.970642i
$442$	−7.62536			−0.362702
$443$	−23.5109	−	13.5740i	−1.11704	−	0.644922i	−0.176395	−	0.984319i	$-0.556444\pi$
$443$	−23.5109	−	13.5740i	−1.11704	−	0.644922i	−0.940643	+	0.339397i	$0.889777\pi$
$444$	−0.728520	+	13.6798i	−0.0345740	+	0.649215i
$445$	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	$0.961042\pi$
$450$	0.583561	−	5.46337i	0.0275093	−	0.257546i
$451$	−9.75662	+	5.63299i	−0.459421	+	0.265247i
$452$	−0.313832	+	0.181191i	−0.0147614	+	0.00852252i
$453$	22.6535	−	11.5185i	1.06436	−	0.541184i
$454$		−	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	−0.485638	−	0.874160i	$-0.661413\pi$
$457$	10.9929	−	19.0402i	0.514225	−	0.890664i	0.999864	−	0.0165046i	$-0.00525381\pi$
$458$	10.8422	+	18.7792i	0.506623	+	0.877496i
$459$	37.0267	−	14.1056i	1.72826	−	0.658395i
$460$	11.9365	+	6.89153i	0.556541	+	0.321319i
$461$	−11.9652			−0.557276			−0.278638	−	0.960396i	$-0.589883\pi$
$461$	−11.9652			−0.557276			−0.278638	+	0.960396i	$0.589883\pi$
$462$	15.0788	+	11.7983i	0.701531	+	0.548908i
$463$	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
$465$	−6.36060	−	0.338735i	−0.294966	−	0.0157084i
$466$	−3.89460	−	6.74565i	−0.180414	−	0.312486i
$467$	12.6840	−	21.9693i	0.586943	−	1.01662i	−0.407687	−	0.913122i	$-0.633664\pi$
$467$	12.6840	−	21.9693i	0.586943	−	1.01662i	0.994630	−	0.103494i	$-0.0330022\pi$
$468$	2.74269	−	1.21558i	0.126781	−	0.0561900i
$469$	32.9671	+	2.88004i	1.52228	+	0.132988i
$470$			7.29028i			0.336275i
$471$	−16.4685	−	32.3889i	−0.758829	−	1.49240i
$472$	−11.8875	+	6.86324i	−0.547165	+	0.315906i
$473$	−1.16812	+	0.674417i	−0.0537104	+	0.0310097i
$474$	8.86429	+	17.4336i	0.407151	+	0.800750i
$475$		−	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	$-0.0779022\pi$
$479$	6.02439	+	10.4346i	0.275261	+	0.476767i	−0.694940	+	0.719068i	$0.744569\pi$
$480$	−3.07874	−	0.163959i	−0.140525	−	0.00748367i
$481$	6.84960	+	3.95462i	0.312315	+	0.180315i
$482$	16.1576			0.735957
$483$	−13.2687	−	32.9093i	−0.603749	−	1.49743i
$484$	6.45579			0.293445
$485$	10.0575	+	5.80673i	0.456690	+	0.263670i
$486$	−11.0692	+	10.9760i	−0.502108	+	0.497883i
$487$	3.26366	+	5.65282i	0.147890	+	0.256154i	0.930448	−	0.366425i	$-0.119418\pi$
$487$	3.26366	+	5.65282i	0.147890	+	0.256154i	−0.782557	+	0.622579i	$0.786085\pi$
$488$	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	$0.782366\pi$
$492$	−4.16320	+	2.11683i	−0.187692	+	0.0954340i
$493$	50.5261	−	29.1713i	2.27558	−	1.31381i
$494$	2.62640	−	1.51635i	0.118167	−	0.0682240i
$495$	2.36963	−	22.1848i	0.106507	−	0.997133i
$496$		−	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	−0.395038	−	0.918665i	$-0.629268\pi$
$499$	13.3598	−	23.1399i	0.598068	−	1.03588i	0.993106	−	0.117220i	$-0.0373982\pi$
$500$	6.08013	+	10.5311i	0.271912	+	0.470965i
$501$	0.0854237	−	1.60404i	0.00381645	−	0.0716634i
$502$	−0.0256328	−	0.0147991i	−0.00114405	−	0.000660517i
$503$	5.93142			0.264469			0.132234	−	0.991218i	$-0.457785\pi$
$503$	5.93142			0.264469			0.132234	+	0.991218i	$0.457785\pi$
$504$	5.98217	+	5.21667i	0.266467	+	0.232369i
$505$	−0.352177			−0.0156717
$506$	−28.0168	−	16.1755i	−1.24550	−	0.719088i
$507$	0.0921101	−	1.72960i	0.00409075	−	0.0768142i
$508$	8.86422	+	15.3533i	0.393286	+	0.681191i
$509$	0.579080	−	1.00300i	0.0256673	−	0.0444570i	−0.852906	−	0.522064i	$-0.825162\pi$
$509$	0.579080	−	1.00300i	0.0256673	−	0.0444570i	0.878574	+	0.477607i	$0.158496\pi$
$510$	−12.8210	+	19.7062i	−0.567724	+	0.872603i
$511$	−0.304604	+	3.48672i	−0.0134749	+	0.154244i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.94810	+	12.2214i	−0.439219	+	0.539588i
$514$	−13.3041	+	7.68113i	−0.586819	+	0.338800i
$515$	10.1743	−	5.87416i	0.448335	−	0.258846i
$516$	−0.498445	+	0.253440i	−0.0219428	+	0.0111571i
$517$		−	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	$-0.323772\pi$
$521$	−10.8139	−	18.7301i	−0.473764	−	0.820583i	−0.999549	+	0.0300347i	$0.990438\pi$
$522$	−13.5230	+	18.5468i	−0.591886	+	0.811772i
$523$	7.93704	+	4.58245i	0.347062	+	0.200377i	0.663391	−	0.748273i	$-0.269117\pi$
$523$	7.93704	+	4.58245i	0.347062	+	0.200377i	−0.316328	+	0.948650i	$0.602450\pi$
$524$	8.69501			0.379843
$525$	1.17404	−	8.31039i	0.0512392	−	0.362695i
$526$	19.5022			0.850334
$527$	−13.6432	−	7.87690i	−0.594306	−	0.343123i
$528$	7.22629	+	0.384837i	0.314484	+	0.0167479i
$529$	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
$534$	−1.94339	−	3.82211i	−0.0840989	−	0.165399i
$535$	17.7293	−	10.2360i	0.766506	−	0.442543i
$536$	10.8321	−	6.25392i	0.467875	−	0.270128i
$537$	11.1809	+	21.9897i	0.482492	+	0.948925i
$538$		−	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	−0.779093	−	0.626909i	$-0.784320\pi$
$541$	3.56736	−	6.17885i	0.153373	−	0.265649i	0.932465	+	0.361260i	$0.117653\pi$
$542$	−15.8975	−	27.5354i	−0.682858	−	1.18274i
$543$	−14.1373	−	0.752882i	−0.606688	−	0.0323092i
$544$	−6.60376	−	3.81268i	−0.283134	−	0.163467i
$545$	18.3762			0.787152
$546$	4.25012	−	1.71361i	0.181888	−	0.0733357i
$547$	−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
$549$	20.6833	+	15.0808i	0.882741	+	0.643631i
$550$	−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
$555$	21.7365	−	11.0522i	0.922665	−	0.469140i
$556$	−0.659498	+	0.380761i	−0.0279689	+	0.0161479i
$557$	−16.3293	+	9.42770i	−0.691893	+	0.399464i	−0.804321	−	0.594195i	$-0.797471\pi$
$557$	−16.3293	+	9.42770i	−0.691893	+	0.399464i	0.112428	+	0.993660i	$0.464137\pi$
$558$	6.16286	+	0.658275i	0.260895	+	0.0278670i
$559$			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	−0.962008	−	0.273020i	$-0.911977\pi$
$563$	−17.0233	−	29.4852i	−0.717446	−	1.24265i	0.244562	−	0.969634i	$-0.421356\pi$
$564$	0.377245	−	7.08372i	0.0158849	−	0.298279i
$565$	0.558632	+	0.322526i	0.0235018	+	0.0135688i
$566$	−11.4362			−0.480701
$567$	−17.4676	+	16.1828i	−0.733569	+	0.679615i
$568$	−3.91612			−0.164317
$569$	9.68078	+	5.58920i	0.405839	+	0.234311i	0.689000	−	0.724761i	$-0.258050\pi$
$569$	9.68078	+	5.58920i	0.405839	+	0.234311i	−0.283161	+	0.959072i	$0.591383\pi$
$570$	0.497240	−	9.33693i	0.0208271	−	0.391081i
$571$	−8.44767	−	14.6318i	−0.353524	−	0.612322i	0.633340	−	0.773874i	$-0.281683\pi$
$571$	−8.44767	−	14.6318i	−0.353524	−	0.612322i	−0.986864	+	0.161552i	$0.948350\pi$
$572$	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
$576$	2.98303	+	0.318627i	0.124293	+	0.0132761i
$577$	5.63256	−	3.25196i	0.234487	−	0.135381i	−0.378154	−	0.925743i	$-0.623441\pi$
$577$	5.63256	−	3.25196i	0.234487	−	0.135381i	0.612640	+	0.790362i	$0.290108\pi$
$578$	−35.6336	+	20.5731i	−1.48216	+	0.855728i
$579$	28.9916	−	14.7411i	1.20485	−	0.612619i
$580$		−	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
$585$	−4.31492	−	3.14613i	−0.178400	−	0.130076i
$586$	9.19999	+	5.31162i	0.380048	+	0.219421i
$587$	−22.5985			−0.932741			−0.466370	−	0.884590i	$-0.654439\pi$
$587$	−22.5985			−0.932741			−0.466370	+	0.884590i	$0.654439\pi$
$588$	8.86230	+	8.27404i	0.365475	+	0.341216i
$589$	6.26549			0.258165
$590$	21.1601	+	12.2168i	0.871147	+	0.502957i
$591$	−10.5860	−	0.563758i	−0.435449	−	0.0231899i
$592$	3.95462	+	6.84960i	0.162534	+	0.281517i
$593$	15.5467	−	26.9276i	0.638425	−	1.10578i	−0.347354	−	0.937734i	$-0.612920\pi$
$593$	15.5467	−	26.9276i	0.638425	−	1.10578i	0.985779	−	0.168050i	$-0.0537470\pi$
$594$	−3.45047	+	21.4336i	−0.141575	+	0.879433i
$595$	−20.5945	+	29.4199i	−0.844290	+	1.20610i
$596$		−	1.40953i		−	0.0577368i
$597$	−1.99740	−	3.92832i	−0.0817480	−	0.160775i
$598$	−6.70577	+	3.87158i	−0.274219	+	0.158321i
$599$	19.9056	−	11.4925i	0.813321	−	0.469571i	−0.0347868	−	0.999395i	$-0.511075\pi$
$599$	19.9056	−	11.4925i	0.813321	−	0.469571i	0.848108	+	0.529824i	$0.177742\pi$
$600$	−1.43777	−	2.82769i	−0.0586967	−	0.115440i
$601$			3.44036i			0.140335i	0.997535	+	0.0701675i	$0.0223534\pi$
$601$			3.44036i			0.140335i	−0.997535	+	0.0701675i	$0.977647\pi$
$602$	−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
$606$	0.342199	+	0.0182238i	0.0139009	+	0.000740293i
$607$	6.79228	+	3.92152i	0.275690	+	0.159170i	0.631471	−	0.775400i	$-0.282452\pi$
$607$	6.79228	+	3.92152i	0.275690	+	0.159170i	−0.355781	+	0.934570i	$0.615785\pi$
$608$	3.03271			0.122993
$609$	−21.6061	+	27.6136i	−0.875521	+	1.11896i
$610$	−15.1881			−0.614947
$611$	−3.54688	−	2.04779i	−0.143491	−	0.0828448i
$612$	13.4775	−	18.4844i	0.544795	−	0.747187i
$613$	−3.03080	−	5.24950i	−0.122413	−	0.212025i	0.798306	−	0.602252i	$-0.205730\pi$
$613$	−3.03080	−	5.24950i	−0.122413	−	0.212025i	−0.920719	+	0.390227i	$0.872397\pi$
$614$	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	$0.952876\pi$
$618$	−10.1900	+	5.18124i	−0.409904	+	0.208420i
$619$	−14.1166	+	8.15023i	−0.567394	+	0.327585i	−0.756108	−	0.654447i	$-0.772902\pi$
$619$	−14.1166	+	8.15023i	−0.567394	+	0.327585i	0.188714	+	0.982032i	$0.439568\pi$
$620$	−3.18481	+	1.83875i	−0.127905	+	0.0738459i
$621$	25.3996	−	31.2039i	1.01925	−	1.25217i
$622$			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
$627$	−1.16710	+	21.9152i	−0.0466094	+	0.875210i
$628$	−18.1677	−	10.4891i	−0.724968	−	0.418561i
$629$	60.3108			2.40475
$630$	2.71754	−	13.8648i	0.108269	−	0.552385i
$631$	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
$633$	−0.257350	+	4.83240i	−0.0102288	+	0.192071i
$634$	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
$639$	1.24778	−	11.6819i	0.0493615	−	0.462129i
$640$	−1.54155	+	0.890016i	−0.0609352	+	0.0351810i
$641$	−11.6157	+	6.70635i	−0.458794	+	0.264885i	−0.711537	−	0.702648i	$-0.752001\pi$
$641$	−11.6157	+	6.70635i	−0.458794	+	0.264885i	0.252743	+	0.967534i	$0.418667\pi$
$642$	−17.7567	+	9.02860i	−0.700801	+	0.356330i
$643$			13.1234i			0.517536i	0.965939	+	0.258768i	$0.0833165\pi$
$643$			13.1234i			0.517536i	−0.965939	+	0.258768i	$0.916683\pi$
$644$	−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	$-0.226511\pi$
$647$	−4.75405	−	8.23425i	−0.186901	−	0.323722i	−0.944215	+	0.329328i	$0.893178\pi$
$648$	−1.90095	+	8.79695i	−0.0746764	+	0.345577i
$649$	−49.6660	−	28.6747i	−1.94956	−	1.12558i
$650$	−1.83148			−0.0718367
$651$	9.37439	+	1.32435i	0.367411	+	0.0519055i
$652$	−22.8811			−0.896095
$653$	37.9647	+	21.9189i	1.48567	+	0.857753i	0.999867	−	0.0163145i	$-0.00519331\pi$
$653$	37.9647	+	21.9189i	1.48567	+	0.857753i	0.485805	+	0.874067i	$0.338527\pi$
$654$	−17.8556	−	0.950903i	−0.698209	−	0.0371832i
$655$	−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	$-0.00363682\pi$
$660$	−5.83827	−	11.4822i	−0.227254	−	0.446945i
$661$	22.3525	−	12.9052i	0.869412	−	0.501955i	0.00225925	−	0.999997i	$-0.499281\pi$
$661$	22.3525	−	12.9052i	0.869412	−	0.501955i	0.867153	+	0.498042i	$0.165948\pi$
$662$	19.2928	−	11.1387i	0.749835	−	0.432917i
$663$	−5.98614	−	11.7730i	−0.232482	−	0.457227i
$664$		−	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
$669$	−28.7798	−	1.53267i	−1.11269	−	0.0592565i
$670$	−19.2815	−	11.1322i	−0.744909	−	0.430073i
$671$	35.6488			1.37621
$672$	4.53752	+	0.641031i	0.175039	+	0.0247283i
$673$	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
$675$	8.89319	−	3.38794i	0.342299	−	0.130402i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−1.34288	+	2.32594i	−0.0516110	+	0.0893929i	−0.890677	−	0.454637i	$-0.849769\pi$
$677$	−1.34288	+	2.32594i	−0.0516110	+	0.0893929i	0.839066	+	0.544030i	$0.183102\pi$
$678$	−0.526115	−	0.342296i	−0.0202053	−	0.0131458i
$679$	−14.1412	−	9.89909i	−0.542688	−	0.379892i
$680$			13.5734i			0.520516i
$681$	22.7804	−	11.5830i	0.872948	−	0.443860i
$682$	7.47524	−	4.31583i	0.286242	−	0.165262i
$683$	20.6264	−	11.9087i	0.789249	−	0.455673i	−0.0504493	−	0.998727i	$-0.516065\pi$
$683$	20.6264	−	11.9087i	0.789249	−	0.455673i	0.839698	+	0.543054i	$0.182732\pi$
$684$	−0.966303	+	9.04666i	−0.0369475	+	0.345908i
$685$			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
$690$	−1.26956	+	23.8392i	−0.0483313	+	0.907542i
$691$	−19.1284	−	11.0438i	−0.727680	−	0.420126i	0.0898926	−	0.995951i	$-0.471348\pi$
$691$	−19.1284	−	11.0438i	−0.727680	−	0.420126i	−0.817573	+	0.575825i	$0.804681\pi$
$692$	3.97238			0.151007
$693$	−6.37848	+	32.5427i	−0.242299	+	1.23620i
$694$	8.62482			0.327394
$695$	1.17393	+	0.677767i	0.0445296	+	0.0257092i
$696$	−0.704745	+	13.2334i	−0.0267133	+	0.501610i
$697$	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	$0.712318\pi$
$702$	4.02987	+	3.28027i	0.152097	+	0.123806i
$703$	−20.7728	+	11.9932i	−0.783462	+	0.452332i
$704$	3.61827	−	2.08901i	0.136369	−	0.0787324i
$705$	−11.2557	+	5.72309i	−0.423914	+	0.215544i
$706$			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	−0.980180	−	0.198111i	$-0.936519\pi$
$709$	−8.48128	+	14.6900i	−0.318521	+	0.551695i	0.661659	+	0.749805i	$0.269853\pi$
$710$	3.48541	+	6.03690i	0.130805	+	0.226561i
$711$	−19.9575	+	27.3717i	−0.748465	+	1.02652i
$712$	−2.14390	−	1.23778i	−0.0803461	−	0.0463879i
$713$	−15.9971			−0.599098
$714$	21.5333	−	27.5206i	0.805865	−	1.02993i
$715$	−7.43700			−0.278128
$716$	12.3345	+	7.12132i	0.460962	+	0.266136i
$717$	−20.8728	−	1.11159i	−0.779510	−	0.0415130i
$718$	3.04591	+	5.27567i	0.113672	+	0.196886i
$719$	−16.5688	+	28.6980i	−0.617912	+	1.07025i	0.371954	+	0.928251i	$0.378688\pi$
$719$	−16.5688	+	28.6980i	−0.617912	+	1.07025i	−0.989866	+	0.142003i	$0.954646\pi$
$720$	−2.16377	−	4.88209i	−0.0806388	−	0.181945i
$721$	−15.8251	+	7.38181i	−0.589358	+	0.274913i
$722$		−	9.80269i		−	0.364818i
$723$	12.6842	+	24.9462i	0.471730	+	0.927759i
$724$	−7.07864	+	4.08686i	−0.263076	+	0.151887i
$725$	12.1355	−	7.00645i	0.450702	−	0.260213i
$726$	5.06799	+	9.96731i	0.188091	+	0.369921i
$727$		−	21.4992i		−	0.797361i	−0.917090	−	0.398680i	$-0.869468\pi$
$727$		−	21.4992i		−	0.797361i	0.917090	−	0.398680i	$-0.130532\pi$
$728$	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
$732$	14.7578	+	0.785927i	0.545463	+	0.0290487i
$733$	23.1346	+	13.3568i	0.854497	+	0.493344i	0.862166	−	0.506626i	$-0.169108\pi$
$733$	23.1346	+	13.3568i	0.854497	+	0.493344i	−0.00766847	+	0.999971i	$0.502441\pi$
$734$	−20.7877			−0.767289
$735$	4.86728	−	21.0257i	0.179532	−	0.775546i
$736$	−7.74315			−0.285416
$737$	45.2567	+	26.1289i	1.66705	+	0.962472i
$738$	−6.53648	−	4.76593i	−0.240611	−	0.175436i
$739$	−3.52025	−	6.09726i	−0.129495	−	0.224291i	0.793986	−	0.607936i	$-0.208002\pi$
$739$	−3.52025	−	6.09726i	−0.129495	−	0.224291i	−0.923481	+	0.383644i	$0.874669\pi$
$740$	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	$-0.0656821\pi$
$744$	3.18972	−	1.62185i	0.116941	−	0.0594599i
$745$	−2.17287	+	1.25451i	−0.0796079	+	0.0459616i
$746$	5.96200	−	3.44216i	0.218284	−	0.126027i
$747$	10.1063	+	1.07949i	0.369770	+	0.0394964i
$748$		−	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	0.185844	+	0.982579i	$0.440498\pi$
$751$	−20.7730	+	35.9798i	−0.758017	+	1.31292i	−0.943861	+	0.330344i	$0.892835\pi$
$752$	−2.04779	−	3.54688i	−0.0746753	−	0.129341i
$753$	0.00272630	−	0.0511931i	9.93518e−5	−	0.00186558i
$754$	6.62606	+	3.82556i	0.241307	+	0.139319i
$755$	−26.1177			−0.950522
$756$	−3.35799	+	13.3313i	−0.122129	+	0.484855i
$757$	−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
$759$	2.97985	−	55.9543i	0.108162	−	2.03101i
$760$	−2.69916	−	4.67508i	−0.0979088	−	0.169583i
$761$	−25.7381	+	44.5797i	−0.933006	+	1.61601i	−0.154853	+	0.987937i	$0.549490\pi$
$761$	−25.7381	+	44.5797i	−0.933006	+	1.61601i	−0.778152	+	0.628076i	$0.783843\pi$
$762$	−16.7457	+	25.7385i	−0.606634	+	0.932409i
$763$	−27.2099	−	2.37709i	−0.985064	−	0.0860563i
$764$		−	24.2581i		−	0.877627i
$765$	−40.4899	−	4.32485i	−1.46391	−	0.156365i
$766$	19.0009	−	10.9702i	0.686530	−	0.396368i
$767$	−11.8875	+	6.86324i	−0.429232	+	0.247817i
$768$	1.54393	−	0.785030i	0.0557119	−	0.0283273i
$769$			1.33310i			0.0480730i	0.999711	+	0.0240365i	$0.00765179\pi$
$769$			1.33310i			0.0480730i	−0.999711	+	0.0240365i	$0.992348\pi$
$770$	−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	$-0.177497\pi$
$773$	−0.945780	−	1.63814i	−0.0340173	−	0.0589198i	−0.882533	+	0.470251i	$0.844163\pi$
$774$	−0.782589	−	0.570607i	−0.0281296	−	0.0205100i
$775$	−3.27686	−	1.89190i	−0.117708	−	0.0679590i
$776$	−6.52429			−0.234208
$777$	−33.6152	+	13.5533i	−1.20594	+	0.486223i
$778$	22.9126			0.821457
$779$	−7.08207	−	4.08884i	−0.253741	−	0.146498i
$780$	−3.07874	−	0.163959i	−0.110237	−	0.00587067i
$781$	−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
$786$	6.82584	+	13.4245i	0.243470	+	0.478836i
$787$	−20.5239	+	11.8495i	−0.731598	+	0.422388i	−0.819007	−	0.573784i	$-0.805475\pi$
$787$	−20.5239	+	11.8495i	−0.731598	+	0.422388i	0.0874084	+	0.996173i	$0.472141\pi$
$788$	−5.30049	+	3.06024i	−0.188822	+	0.109016i
$789$	15.3098	+	30.1100i	0.545043	+	1.07194i
$790$		−	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
$795$	36.4123	+	1.93914i	1.29141	+	0.0687742i
$796$	−2.20348	−	1.27218i	−0.0781002	−	0.0450912i
$797$	−37.0409			−1.31205			−0.656027	−	0.754737i	$-0.727764\pi$
$797$	−37.0409			−1.31205			−0.656027	+	0.754737i	$0.727764\pi$
$798$	−1.94406	+	13.7610i	−0.0688190	+	0.487133i
$799$	−31.2303			−1.10485
$800$	−1.58611	−	0.915742i	−0.0560775	−	0.0323764i
$801$	4.37545	−	6.00094i	0.154599	−	0.212033i
$802$	−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
$807$	5.22316	−	2.65577i	0.183864	−	0.0934877i
$808$	0.171342	−	0.0989242i	0.00602778	−	0.00348014i
$809$	32.3735	−	18.6908i	1.13819	−	0.657135i	0.192209	−	0.981354i	$-0.438435\pi$
$809$	32.3735	−	18.6908i	1.13819	−	0.657135i	0.945982	+	0.324219i	$0.105102\pi$
$810$	15.2529	−	4.89902i	0.535931	−	0.172134i
$811$			45.1640i			1.58592i	0.609272	+	0.792961i	$0.291462\pi$
$811$			45.1640i			1.58592i	−0.609272	+	0.792961i	$0.708538\pi$
$812$	−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
$816$	0.702373	−	13.1888i	0.0245880	−	0.461701i
$817$	−0.847910	−	0.489541i	−0.0296646	−	0.0171269i
$818$	32.6276			1.14080
$819$	5.98217	+	5.21667i	0.209034	+	0.182285i
$820$	4.79984			0.167618
$821$	6.52016	+	3.76442i	0.227555	+	0.131379i	0.609444	−	0.792829i	$-0.291393\pi$
$821$	6.52016	+	3.76442i	0.227555	+	0.131379i	−0.381889	+	0.924208i	$0.624726\pi$
$822$	0.789989	−	14.8340i	0.0275540	−	0.517396i
$823$	−5.65277	−	9.79088i	−0.197043	−	0.341289i	0.750525	−	0.660842i	$-0.229801\pi$
$823$	−5.65277	−	9.79088i	−0.197043	−	0.341289i	−0.947568	+	0.319553i	$0.896467\pi$
$824$	−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	$-0.0922304\pi$
$828$	2.46718	−	23.0981i	0.0857404	−	0.802713i
$829$	−9.26281	+	5.34789i	−0.321711	+	0.185740i	−0.652155	−	0.758086i	$-0.726135\pi$
$829$	−9.26281	+	5.34789i	−0.321711	+	0.185740i	0.330444	+	0.943826i	$0.392801\pi$
$830$	−5.22268	+	3.01531i	−0.181282	+	0.104663i
$831$	0.634020	−	0.322375i	0.0219939	−	0.0111831i
$832$		−	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
$837$	3.82170	+	10.0318i	0.132097	+	0.346750i
$838$	23.7375	+	13.7048i	0.819997	+	0.473425i
$839$	−37.6696			−1.30050			−0.650250	−	0.759721i	$-0.725336\pi$
$839$	−37.6696			−1.30050			−0.650250	+	0.759721i	$0.725336\pi$
$840$	−3.05028	−	7.56536i	−0.105245	−	0.261030i
$841$	−29.5396			−1.01861
$842$	−16.3735	−	9.45326i	−0.564269	−	0.325781i
$843$	37.5328	+	1.99881i	1.29270	+	0.0688428i
$844$	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
$849$	−8.97779	−	17.6568i	−0.308117	−	0.605979i
$850$	−12.0947	+	6.98287i	−0.414844	+	0.239510i
$851$	53.0375	−	30.6212i	1.81810	−	1.04968i
$852$	−3.07427	−	6.04622i	−0.105323	−	0.207140i
$853$		−	20.1209i		−	0.688926i	−0.938800	−	0.344463i	$-0.888061\pi$
$853$		−	20.1209i		−	0.688926i	0.938800	−	0.344463i	$-0.111939\pi$
$854$	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	0.984177	+	0.177188i	$0.0567001\pi$
$857$	18.8978	+	32.7320i	0.645538	+	1.11810i	−0.338639	+	0.940916i	$0.609967\pi$
$858$	7.22629	+	0.384837i	0.246701	+	0.0131381i
$859$	3.63139	+	2.09658i	0.123901	+	0.0715345i	0.560670	−	0.828040i	$-0.310544\pi$
$859$	3.63139	+	2.09658i	0.123901	+	0.0715345i	−0.436768	+	0.899574i	$0.643877\pi$
$860$	0.574668			0.0195960
$861$	−9.73189	−	7.61465i	−0.331662	−	0.259506i
$862$	4.90557			0.167084
$863$	−17.3613	−	10.0235i	−0.590984	−	0.341205i	0.174503	−	0.984657i	$-0.444168\pi$
$863$	−17.3613	−	10.0235i	−0.590984	−	0.341205i	−0.765486	+	0.643452i	$0.777502\pi$
$864$	1.84983	+	4.85573i	0.0629325	+	0.165195i
$865$	−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
$870$	21.0272	−	10.6915i	0.712888	−	0.362476i
$871$	10.8321	−	6.25392i	0.367032	−	0.211906i
$872$	−8.94045	+	5.16177i	−0.302762	+	0.174800i
$873$	2.07882	−	19.4622i	0.0703573	−	0.658695i
$874$		−	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	−0.787914	−	0.615785i	$-0.788839\pi$
$877$	4.12611	−	7.14663i	0.139329	−	0.241325i	0.927243	+	0.374461i	$0.122172\pi$
$878$	1.14522	+	1.98357i	0.0386492	+	0.0669423i
$879$	−0.978507	+	18.3739i	−0.0330042	+	0.619738i
$880$	−6.44063	−	3.71850i	−0.217114	−	0.125351i
$881$	−20.8084			−0.701052			−0.350526	−	0.936553i	$-0.613997\pi$
$881$	−20.8084			−0.701052			−0.350526	+	0.936553i	$0.613997\pi$
$882$	−5.81738	+	20.1782i	−0.195881	+	0.679434i
$883$	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
$885$	−2.25058	+	42.2603i	−0.0756524	+	1.42056i
$886$	−13.5740	−	23.5109i	−0.456029	−	0.789865i
$887$	−8.46183	+	14.6563i	−0.284120	+	0.492111i	−0.972396	−	0.233339i	$-0.925035\pi$
$887$	−8.46183	+	14.6563i	−0.284120	+	0.492111i	0.688275	+	0.725450i	$0.258368\pi$
$888$	−7.47082	+	11.4828i	−0.250704	+	0.385338i
$889$	−26.8988	+	38.4258i	−0.902155	+	1.28876i
$890$			4.40659i			0.147709i
$891$	−35.8008	+	11.4987i	−1.19937	+	0.385223i
$892$	−14.4103	+	8.31978i	−0.482492	+	0.278567i
$893$	10.7567	−	6.21036i	0.359958	−	0.207822i
$894$	2.17623	−	1.10653i	0.0727839	−	0.0370078i
$895$		−	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
$900$	3.23707	−	4.43964i	0.107902	−	0.147988i
$901$	78.1026	+	45.0925i	2.60197	+	1.50225i
$902$	−11.2660			−0.375116
$903$	−1.16516	−	0.911674i	−0.0387742	−	0.0303386i
$904$	−0.362383			−0.0120527
$905$	12.6002	+	7.27474i	0.418845	+	0.241820i
$906$	25.3778	+	1.35150i	0.843120	+	0.0449005i
$907$	13.6532	+	23.6481i	0.453349	+	0.785223i	0.998592	−	0.0530552i	$-0.0168959\pi$
$907$	13.6532	+	23.6481i	0.453349	+	0.785223i	−0.545243	+	0.838278i	$0.683563\pi$
$908$	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	$0.739711\pi$
$912$	2.38077	+	4.68229i	0.0788351	+	0.155046i
$913$	12.2584	−	7.07741i	0.405695	−	0.234228i
$914$	19.0402	−	10.9929i	0.629795	−	0.363612i
$915$	−11.9231	−	23.4494i	−0.394166	−	0.775212i
$916$			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	−0.296405	−	0.955062i	$-0.595788\pi$
$919$	20.5810	−	35.6474i	0.678906	−	1.17590i	0.975311	−	0.220837i	$-0.0708790\pi$
$920$	6.89153	+	11.9365i	0.227207	+	0.393534i
$921$	52.7114	+	2.80715i	1.73690	+	0.0924989i
$922$	−10.3622	−	5.98261i	−0.341260	−	0.197027i
$923$	−3.91612			−0.128901
$924$	7.15949	+	17.7571i	0.235530	+	0.584165i
$925$	14.4856			0.476285
$926$	13.9816	+	8.07226i	0.459463	+	0.265271i
$927$	−15.9990	−	11.6653i	−0.525476	−	0.383139i
$928$	3.82556	+	6.62606i	0.125580	+	0.217511i
$929$	−12.9117	+	22.3637i	−0.423619	+	0.733730i	−0.996290	−	0.0860551i	$-0.972574\pi$
$929$	−12.9117	+	22.3637i	−0.423619	+	0.733730i	0.572671	+	0.819785i	$0.305907\pi$
$930$	−5.33907	−	3.47365i	−0.175075	−	0.113906i
$931$	−3.68107	+	20.9074i	−0.120642	+	0.685211i
$932$		−	7.78921i		−	0.255144i
$933$	−11.2996	+	5.74540i	−0.369931	+	0.188096i
$934$	21.9693	−	12.6840i	0.718856	−	0.415032i
$935$	−49.1121	+	28.3549i	−1.60614	+	0.927305i
$936$	2.98303	+	0.318627i	0.0975034	+	0.0104147i
$937$		−	34.6955i		−	1.13345i	−0.823906	−	0.566726i	$-0.808210\pi$
$937$		−	34.6955i		−	1.13345i	0.823906	−	0.566726i	$-0.191790\pi$
$938$	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	$-0.291551\pi$
$941$	−11.7288	−	20.3148i	−0.382347	−	0.662245i	−0.991397	+	0.130887i	$0.958218\pi$
$942$	1.93230	−	36.2839i	0.0629579	−	1.18219i
$943$	18.0820	+	10.4397i	0.588832	+	0.339963i
$944$	−13.7265			−0.446759
$945$	23.5396	−	6.68856i	0.765743	−	0.217579i
$946$	−1.34883			−0.0438544
$947$	21.8287	+	12.6028i	0.709337	+	0.409536i	0.810815	−	0.585302i	$-0.199024\pi$
$947$	21.8287	+	12.6028i	0.709337	+	0.409536i	−0.101479	+	0.994838i	$0.532357\pi$
$948$	−1.04008	+	19.5301i	−0.0337801	+	0.634307i
$949$	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	$0.762282\pi$
$954$	−35.2803	−	3.76840i	−1.14224	−	0.122006i
$955$	−37.3951	+	21.5901i	−1.21008	+	0.698639i
$956$	−10.4512	+	6.03401i	−0.338016	+	0.195154i
$957$	−49.3541	+	25.0946i	−1.59539	+	0.811194i
$958$			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
$963$	−27.8791	−	20.3274i	−0.898392	−	0.655042i
$964$	13.9929	+	8.07879i	0.450680	+	0.260200i
$965$	−33.4250			−1.07599
$966$	4.96360	−	35.1347i	0.159701	−	1.13044i
$967$	−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
$969$	39.9979	+	2.13009i	1.28492	+	0.0684284i
$970$	5.80673	+	10.0575i	0.186443	+	0.322928i
$971$	16.5100	−	28.5961i	0.529830	−	0.917692i	−0.469565	−	0.882898i	$-0.655589\pi$
$971$	16.5100	−	28.5961i	0.529830	−	0.917692i	0.999395	−	0.0347938i	$-0.0110774\pi$
$972$	−15.0742	+	3.97094i	−0.483505	+	0.127368i
$973$	−1.65057	−	1.15543i	−0.0529149	−	0.0370414i
$974$			6.52731i			0.209149i
$975$	−1.43777	−	2.82769i	−0.0460455	−	0.0905585i
$976$	7.38934	−	4.26624i	0.236527	−	0.136559i
$977$	6.63023	−	3.82796i	0.212120	−	0.122467i	−0.390176	−	0.920740i	$-0.627586\pi$
$977$	6.63023	−	3.82796i	0.212120	−	0.122467i	0.602296	+	0.798273i	$0.294253\pi$
$978$	−17.9624	−	35.3269i	−0.574374	−	1.12963i
$979$		−	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	−0.976780	−	0.214244i	$-0.931271\pi$
$983$	−21.1296	−	36.5976i	−0.673931	−	1.16728i	0.302850	−	0.953038i	$-0.402062\pi$
$984$	−4.66385	−	0.248374i	−0.148678	−	0.00791788i
$985$	9.43504	+	5.44732i	0.300625	+	0.173566i
$986$	58.3425			1.85801
$987$	17.4067	−	7.01824i	0.554063	−	0.223393i
$988$	3.03271			0.0964833
$989$	2.16490	+	1.24990i	0.0688397	+	0.0397446i
$990$	13.1446	−	18.0278i	0.417762	−	0.572961i
$991$	−6.94512	−	12.0293i	−0.220619	−	0.382124i	0.734377	−	0.678742i	$-0.237474\pi$
$991$	−6.94512	−	12.0293i	−0.220619	−	0.382124i	−0.954996	+	0.296618i	$0.904141\pi$
$992$	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
$996$	5.23074	−	2.65963i	0.165742	−	0.0842735i
$997$	38.9188	−	22.4698i	1.23257	−	0.711626i	0.265007	−	0.964247i	$-0.414626\pi$
$997$	38.9188	−	22.4698i	1.23257	−	0.711626i	0.967565	+	0.252621i	$0.0812925\pi$
$998$	23.1399	−	13.3598i	0.732481	−	0.422898i
$999$	−31.8731	−	25.9444i	−1.00842	−	0.820845i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.2	✓	32	3.2	odd	2
546.2.z.a.521.2	yes	32	7.3	odd	6
546.2.z.b.131.12	yes	32	1.1	even	1	trivial
546.2.z.b.521.12	yes	32	21.17	even	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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0921101 + 1.72960i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.890016 - 1.54155i) q^{5} +(-0.944570 + 1.45182i) q^{6} +(-1.51727 + 2.16746i) q^{7} +1.00000i q^{8} +(-2.98303 - 0.318627i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0921101 + 1.72960i) 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} +(-2.98303 - 0.318627i) q^{9} +(1.54155 - 0.890016i) q^{10} +(-3.61827 + 2.08901i) q^{11} +(-1.54393 + 0.785030i) 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} +(-2.42407 - 1.76746i) q^{18} +(-2.62640 - 1.51635i) q^{19} +1.78003 q^{20} +(-3.60909 - 2.82391i) q^{21} -4.17801 q^{22} +(6.70577 + 3.87158i) q^{23} +(-1.72960 - 0.0921101i) 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} +(1.39738 + 2.74825i) q^{30} +(-1.78918 + 1.03299i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.27987 - 6.45057i) 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} +(-1.72960 - 0.0921101i) q^{39} +(1.54155 + 0.890016i) q^{40} +2.69649 q^{41} +(-1.71361 - 4.25012i) q^{42} +0.322841 q^{43} +(-3.61827 - 2.08901i) q^{44} +(-3.14613 + 4.31492i) 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} +(-11.7730 + 5.98614i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(10.2425 - 5.91349i) q^{53} +(3.28027 - 4.02987i) 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} +(-0.163959 + 3.07874i) q^{60} +(-7.38934 - 4.26624i) q^{61} -2.06597 q^{62} +(5.21667 - 5.98217i) q^{63} -1.00000 q^{64} +(1.54155 + 0.890016i) q^{65} +(0.384837 - 7.22629i) 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} +(0.318627 - 2.98303i) q^{72} +(1.14565 - 0.661439i) q^{73} +(6.84960 - 3.95462i) q^{74} +(-2.82769 + 1.43777i) 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} +(8.79695 + 1.90095i) q^{81} +(2.33523 + 1.34825i) q^{82} -3.38793 q^{83} +(0.641031 - 4.53752i) q^{84} +13.5734 q^{85} +(0.279589 + 0.161421i) q^{86} +(13.2334 + 0.704745i) 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} +(-1.62185 - 3.18972i) q^{93} +(-3.54688 + 2.04779i) q^{94} +(-4.67508 + 2.69916i) q^{95} +(-0.785030 - 1.54393i) 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	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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