LMFDB - Embedded newform 930.2.s.c.439.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.2
Character	$\chi$	$=$	930.439
Dual form			930.2.s.c.769.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.968769 + 2.01531i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-3.61895 - 2.08940i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.968769 + 2.01531i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-3.61895 - 2.08940i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.01531 + 0.968769i) q^{10} +(-0.324354 - 0.561798i) q^{11} +(0.866025 + 0.500000i) q^{12} +(1.99676 - 1.15283i) q^{13} +(-2.08940 + 3.61895i) q^{14} +(1.84664 - 1.26093i) q^{15} +1.00000 q^{16} +(0.894833 + 0.516632i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.12885 + 3.68728i) q^{19} +(0.968769 - 2.01531i) q^{20} +(2.08940 + 3.61895i) q^{21} +(-0.561798 + 0.324354i) q^{22} +4.34823i q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.12297 - 3.90475i) q^{25} +(-1.15283 - 1.99676i) q^{26} -1.00000i q^{27} +(3.61895 + 2.08940i) q^{28} +9.24924 q^{29} +(-1.26093 - 1.84664i) q^{30} +(2.68393 - 4.87817i) q^{31} -1.00000i q^{32} +0.648708i q^{33} +(0.516632 - 0.894833i) q^{34} +(7.71672 - 5.26917i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.55416 + 5.51609i) q^{37} +(3.68728 + 2.12885i) q^{38} -2.30565 q^{39} +(-2.01531 - 0.968769i) q^{40} +(2.04726 + 3.54596i) q^{41} +(3.61895 - 2.08940i) q^{42} +(5.09983 + 2.94439i) q^{43} +(0.324354 + 0.561798i) q^{44} +(-2.22970 + 0.168678i) q^{45} +4.34823 q^{46} -3.42912i q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.23119 + 9.06069i) q^{49} +(-3.90475 + 3.12297i) q^{50} +(-0.516632 - 0.894833i) q^{51} +(-1.99676 + 1.15283i) q^{52} +(5.52654 - 3.19075i) q^{53} -1.00000 q^{54} +(1.44642 - 0.109423i) q^{55} +(2.08940 - 3.61895i) q^{56} +(3.68728 - 2.12885i) q^{57} -9.24924i q^{58} +(0.574671 - 0.995359i) q^{59} +(-1.84664 + 1.26093i) q^{60} -8.11415 q^{61} +(-4.87817 - 2.68393i) q^{62} -4.17880i q^{63} -1.00000 q^{64} +(0.388912 + 5.14091i) q^{65} +0.648708 q^{66} +(-9.53716 + 5.50628i) q^{67} +(-0.894833 - 0.516632i) q^{68} +(2.17412 - 3.76568i) q^{69} +(-5.26917 - 7.71672i) q^{70} +(-1.71256 - 2.96624i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.38014 - 4.26093i) q^{73} +(5.51609 - 9.55416i) q^{74} +(0.752200 + 4.94310i) q^{75} +(2.12885 - 3.68728i) q^{76} +2.71082i q^{77} +2.30565i q^{78} +(-8.47707 + 14.6827i) q^{79} +(-0.968769 + 2.01531i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.54596 - 2.04726i) q^{82} +(2.43251 - 1.40441i) q^{83} +(-2.08940 - 3.61895i) q^{84} +(-1.90806 + 1.30287i) q^{85} +(2.94439 - 5.09983i) q^{86} +(-8.01008 - 4.62462i) q^{87} +(0.561798 - 0.324354i) q^{88} +13.8500 q^{89} +(0.168678 + 2.22970i) q^{90} -9.63487 q^{91} -4.34823i q^{92} +(-4.76343 + 2.88265i) q^{93} -3.42912 q^{94} +(-5.36865 - 7.86242i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.0488039i q^{97} +(9.06069 - 5.23119i) q^{98} +(0.324354 - 0.561798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	−0.968769	+	2.01531i	−0.433247	+	0.901275i
$5$	−0.968769	+	2.01531i	−0.433247	+	0.901275i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−3.61895	−	2.08940i	−1.36783	−	0.789719i	−0.377183	−	0.926139i	$-0.623107\pi$
$7$	−3.61895	−	2.08940i	−1.36783	−	0.789719i	−0.990651	+	0.136420i	$0.956440\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.01531	+	0.968769i	0.637298	+	0.306352i
$11$	−0.324354	−	0.561798i	−0.0977964	−	0.169388i	0.812976	−	0.582297i	$-0.197846\pi$
$11$	−0.324354	−	0.561798i	−0.0977964	−	0.169388i	−0.910772	+	0.412909i	$0.864513\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	1.99676	−	1.15283i	0.553800	−	0.319737i	−0.196853	−	0.980433i	$-0.563072\pi$
$13$	1.99676	−	1.15283i	0.553800	−	0.319737i	0.750653	+	0.660696i	$0.229739\pi$
$14$	−2.08940	+	3.61895i	−0.558416	+	0.967205i
$15$	1.84664	−	1.26093i	0.476799	−	0.325570i
$16$	1.00000			0.250000
$17$	0.894833	+	0.516632i	0.217029	+	0.125302i	0.604574	−	0.796549i	$-0.293343\pi$
$17$	0.894833	+	0.516632i	0.217029	+	0.125302i	−0.387545	+	0.921851i	$0.626677\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.12885	+	3.68728i	−0.488392	+	0.845920i	−0.999911	−	0.0133523i	$-0.995750\pi$
$19$	−2.12885	+	3.68728i	−0.488392	+	0.845920i	0.511519	+	0.859272i	$0.329083\pi$
$20$	0.968769	−	2.01531i	0.216623	−	0.450638i
$21$	2.08940	+	3.61895i	0.455945	+	0.789719i
$22$	−0.561798	+	0.324354i	−0.119776	+	0.0691525i
$23$			4.34823i			0.906669i	0.891340	+	0.453335i	$0.149766\pi$
$23$			4.34823i			0.906669i	−0.891340	+	0.453335i	$0.850234\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−3.12297	−	3.90475i	−0.624594	−	0.780949i
$26$	−1.15283	−	1.99676i	−0.226088	−	0.391596i
$27$		−	1.00000i		−	0.192450i
$28$	3.61895	+	2.08940i	0.683917	+	0.394860i
$29$	9.24924			1.71754			0.858771	−	0.512360i	$-0.171229\pi$
$29$	9.24924			1.71754			0.858771	+	0.512360i	$0.171229\pi$
$30$	−1.26093	−	1.84664i	−0.230213	−	0.337148i
$31$	2.68393	−	4.87817i	0.482048	−	0.876145i
$31$	2.68393	−	4.87817i	0.482048	−	0.876145i
$32$		−	1.00000i		−	0.176777i
$33$			0.648708i			0.112926i
$34$	0.516632	−	0.894833i	0.0886017	−	0.153463i
$35$	7.71672	−	5.26917i	1.30436	−	0.890652i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.55416	+	5.51609i	1.57069	+	0.906840i	0.996084	+	0.0884127i	$0.0281794\pi$
$37$	9.55416	+	5.51609i	1.57069	+	0.906840i	0.574610	+	0.818428i	$0.305154\pi$
$38$	3.68728	+	2.12885i	0.598156	+	0.345345i
$39$	−2.30565			−0.369200
$40$	−2.01531	−	0.968769i	−0.318649	−	0.153176i
$41$	2.04726	+	3.54596i	0.319729	+	0.553786i	0.980431	−	0.196861i	$-0.0630749\pi$
$41$	2.04726	+	3.54596i	0.319729	+	0.553786i	−0.660703	+	0.750648i	$0.729742\pi$
$42$	3.61895	−	2.08940i	0.558416	−	0.322402i
$43$	5.09983	+	2.94439i	0.777716	+	0.449015i	0.835620	−	0.549308i	$-0.185108\pi$
$43$	5.09983	+	2.94439i	0.777716	+	0.449015i	−0.0579041	+	0.998322i	$0.518442\pi$
$44$	0.324354	+	0.561798i	0.0488982	+	0.0846942i
$45$	−2.22970	+	0.168678i	−0.332384	+	0.0251450i
$46$	4.34823			0.641112
$47$		−	3.42912i		−	0.500188i	−0.968222	−	0.250094i	$-0.919538\pi$
$47$		−	3.42912i		−	0.500188i	0.968222	−	0.250094i	$-0.0804616\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	5.23119	+	9.06069i	0.747313	+	1.29438i
$50$	−3.90475	+	3.12297i	−0.552215	+	0.441655i
$51$	−0.516632	−	0.894833i	−0.0723430	−	0.125302i
$52$	−1.99676	+	1.15283i	−0.276900	+	0.159868i
$53$	5.52654	−	3.19075i	0.759128	−	0.438283i	−0.0698544	−	0.997557i	$-0.522253\pi$
$53$	5.52654	−	3.19075i	0.759128	−	0.438283i	0.828983	+	0.559274i	$0.188920\pi$
$54$	−1.00000			−0.136083
$55$	1.44642	−	0.109423i	0.195036	−	0.0147545i
$56$	2.08940	−	3.61895i	0.279208	−	0.483602i
$57$	3.68728	−	2.12885i	0.488392	−	0.281973i
$58$		−	9.24924i		−	1.21448i
$59$	0.574671	−	0.995359i	0.0748158	−	0.129585i	−0.826190	−	0.563391i	$-0.809496\pi$
$59$	0.574671	−	0.995359i	0.0748158	−	0.129585i	0.901006	+	0.433806i	$0.142830\pi$
$60$	−1.84664	+	1.26093i	−0.238400	+	0.162785i
$61$	−8.11415			−1.03891			−0.519455	−	0.854498i	$-0.673865\pi$
$61$	−8.11415			−1.03891			−0.519455	+	0.854498i	$0.673865\pi$
$62$	−4.87817	−	2.68393i	−0.619528	−	0.340859i
$63$		−	4.17880i		−	0.526480i
$64$	−1.00000			−0.125000
$65$	0.388912	+	5.14091i	0.0482386	+	0.637651i
$66$	0.648708			0.0798504
$67$	−9.53716	+	5.50628i	−1.16515	+	0.672699i	−0.952533	−	0.304436i	$-0.901532\pi$
$67$	−9.53716	+	5.50628i	−1.16515	+	0.672699i	−0.212617	+	0.977136i	$0.568199\pi$
$68$	−0.894833	−	0.516632i	−0.108514	−	0.0626508i
$69$	2.17412	−	3.76568i	0.261733	−	0.453335i
$70$	−5.26917	−	7.71672i	−0.629786	−	0.922325i
$71$	−1.71256	−	2.96624i	−0.203244	−	0.352028i	0.746328	−	0.665578i	$-0.231815\pi$
$71$	−1.71256	−	2.96624i	−0.203244	−	0.352028i	−0.949572	+	0.313550i	$0.898482\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	7.38014	−	4.26093i	0.863780	−	0.498704i	−0.00149602	−	0.999999i	$-0.500476\pi$
$73$	7.38014	−	4.26093i	0.863780	−	0.498704i	0.865276	+	0.501295i	$0.167143\pi$
$74$	5.51609	−	9.55416i	0.641233	−	1.11065i
$75$	0.752200	+	4.94310i	0.0868566	+	0.570780i
$76$	2.12885	−	3.68728i	0.244196	−	0.422960i
$77$			2.71082i			0.308927i
$78$			2.30565i			0.261064i
$79$	−8.47707	+	14.6827i	−0.953745	+	1.65193i	−0.216530	+	0.976276i	$0.569474\pi$
$79$	−8.47707	+	14.6827i	−0.953745	+	1.65193i	−0.737215	+	0.675659i	$0.763859\pi$
$80$	−0.968769	+	2.01531i	−0.108312	+	0.225319i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.54596	−	2.04726i	0.391586	−	0.226082i
$83$	2.43251	−	1.40441i	0.267003	−	0.154154i	−0.360522	−	0.932751i	$-0.617401\pi$
$83$	2.43251	−	1.40441i	0.267003	−	0.154154i	0.627525	+	0.778596i	$0.284068\pi$
$84$	−2.08940	−	3.61895i	−0.227972	−	0.394860i
$85$	−1.90806	+	1.30287i	−0.206958	+	0.141316i
$86$	2.94439	−	5.09983i	0.317501	−	0.549928i
$87$	−8.01008	−	4.62462i	−0.858771	−	0.495811i
$88$	0.561798	−	0.324354i	0.0598878	−	0.0345763i
$89$	13.8500			1.46810			0.734048	−	0.679097i	$-0.237628\pi$
$89$	13.8500			1.46810			0.734048	+	0.679097i	$0.237628\pi$
$90$	0.168678	+	2.22970i	0.0177802	+	0.235031i
$91$	−9.63487			−1.01001
$92$		−	4.34823i		−	0.453335i
$93$	−4.76343	+	2.88265i	−0.493945	+	0.298917i
$94$	−3.42912			−0.353687
$95$	−5.36865	−	7.86242i	−0.550812	−	0.806668i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	0.0488039i		−	0.00495528i	−0.999997	−	0.00247764i	$-0.999211\pi$
$97$		−	0.0488039i		−	0.00495528i	0.999997	−	0.00247764i	$-0.000788659\pi$
$98$	9.06069	−	5.23119i	0.915268	−	0.528430i
$99$	0.324354	−	0.561798i	0.0325988	−	0.0564628i
$100$	3.12297	+	3.90475i	0.312297	+	0.390475i
$101$	10.9441			1.08898			0.544490	−	0.838767i	$-0.316723\pi$
$101$	10.9441			1.08898			0.544490	+	0.838767i	$0.316723\pi$
$102$	−0.894833	+	0.516632i	−0.0886017	+	0.0511542i
$103$	−9.21554	+	5.32059i	−0.908034	+	0.524254i	−0.879798	−	0.475348i	$-0.842322\pi$
$103$	−9.21554	+	5.32059i	−0.908034	+	0.524254i	−0.0282357	+	0.999601i	$0.508989\pi$
$104$	1.15283	+	1.99676i	0.113044	+	0.195798i
$105$	−9.31746	+	0.704870i	−0.909291	+	0.0687883i
$106$	−3.19075	−	5.52654i	−0.309913	−	0.536785i
$107$	15.2553	+	8.80765i	1.47479	+	0.851468i	0.999596	−	0.0284155i	$-0.00904615\pi$
$107$	15.2553	+	8.80765i	1.47479	+	0.851468i	0.475190	+	0.879883i	$0.342379\pi$
$108$			1.00000i			0.0962250i
$109$	−10.5792			−1.01330			−0.506652	−	0.862151i	$-0.669117\pi$
$109$	−10.5792			−1.01330			−0.506652	+	0.862151i	$0.669117\pi$
$110$	−0.109423	−	1.44642i	−0.0104330	−	0.137911i
$111$	−5.51609	−	9.55416i	−0.523565	−	0.906840i
$112$	−3.61895	−	2.08940i	−0.341958	−	0.197430i
$113$	−4.88133	+	2.81823i	−0.459197	+	0.265117i	−0.711706	−	0.702477i	$-0.752077\pi$
$113$	−4.88133	+	2.81823i	−0.459197	+	0.265117i	0.252510	+	0.967594i	$0.418744\pi$
$114$	−2.12885	−	3.68728i	−0.199385	−	0.345345i
$115$	−8.76305	−	4.21243i	−0.817158	−	0.392811i
$116$	−9.24924			−0.858771
$117$	1.99676	+	1.15283i	0.184600	+	0.106579i
$118$	−0.995359	−	0.574671i	−0.0916302	−	0.0529027i
$119$	−2.15890	−	3.73933i	−0.197906	−	0.342784i
$120$	1.26093	+	1.84664i	0.115106	+	0.168574i
$121$	5.28959	−	9.16184i	0.480872	−	0.832894i
$122$			8.11415i			0.734621i
$123$		−	4.09453i		−	0.369191i
$124$	−2.68393	+	4.87817i	−0.241024	+	0.438072i
$125$	10.8947	−	2.51097i	0.974454	−	0.224588i
$126$	−4.17880			−0.372277
$127$	9.67454	+	5.58560i	0.858476	+	0.495642i	0.863502	−	0.504346i	$-0.168266\pi$
$127$	9.67454	+	5.58560i	0.858476	+	0.495642i	−0.00502544	+	0.999987i	$0.501600\pi$
$128$			1.00000i			0.0883883i
$129$	−2.94439	−	5.09983i	−0.259239	−	0.449015i
$130$	5.14091	−	0.388912i	0.450888	−	0.0341099i
$131$	10.5535	−	18.2793i	0.922068	−	1.59707i	0.125857	−	0.992048i	$-0.459832\pi$
$131$	10.5535	−	18.2793i	0.922068	−	1.59707i	0.796211	−	0.605019i	$-0.206835\pi$
$132$		−	0.648708i		−	0.0564628i
$133$	15.4084	−	8.89605i	1.33608	−	0.771385i
$134$	5.50628	+	9.53716i	0.475670	+	0.823885i
$135$	2.01531	+	0.968769i	0.173451	+	0.0833784i
$136$	−0.516632	+	0.894833i	−0.0443008	+	0.0767313i
$137$	−11.7209	+	6.76705i	−1.00138	+	0.578148i	−0.908657	−	0.417544i	$-0.862891\pi$
$137$	−11.7209	+	6.76705i	−1.00138	+	0.578148i	−0.0927245	+	0.995692i	$0.529558\pi$
$138$	−3.76568	−	2.17412i	−0.320556	−	0.185073i
$139$	−9.33859			−0.792089			−0.396044	−	0.918231i	$-0.629617\pi$
$139$	−9.33859			−0.792089			−0.396044	+	0.918231i	$0.629617\pi$
$140$	−7.71672	+	5.26917i	−0.652182	+	0.445326i
$141$	−1.71456	+	2.96970i	−0.144392	+	0.250094i
$142$	−2.96624	+	1.71256i	−0.248922	+	0.143715i
$143$	−1.29531	−	0.747848i	−0.108319	−	0.0625382i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−8.96038	+	18.6401i	−0.744119	+	1.54798i
$146$	−4.26093	−	7.38014i	−0.352637	−	0.610785i
$147$		−	10.4624i		−	0.862923i
$148$	−9.55416	−	5.51609i	−0.785347	−	0.453420i
$149$	−6.75564	+	11.7011i	−0.553443	+	0.958592i	0.444580	+	0.895739i	$0.353353\pi$
$149$	−6.75564	+	11.7011i	−0.553443	+	0.958592i	−0.998023	+	0.0628524i	$0.979980\pi$
$150$	4.94310	−	0.752200i	0.403602	−	0.0614169i
$151$	−0.0704403			−0.00573235			−0.00286618	−	0.999996i	$-0.500912\pi$
$151$	−0.0704403			−0.00573235			−0.00286618	+	0.999996i	$0.500912\pi$
$152$	−3.68728	−	2.12885i	−0.299078	−	0.172673i
$153$			1.03326i			0.0835344i
$154$	2.71082			0.218444
$155$	7.23093	+	10.1348i	0.580802	+	0.814045i
$156$	2.30565			0.184600
$157$			7.12272i			0.568455i	0.958757	+	0.284227i	$0.0917371\pi$
$157$			7.12272i			0.568455i	−0.958757	+	0.284227i	$0.908263\pi$
$158$	14.6827	+	8.47707i	1.16809	+	0.674399i
$159$	−6.38150			−0.506086
$160$	2.01531	+	0.968769i	0.159324	+	0.0765879i
$161$	9.08520	−	15.7360i	0.716014	−	1.24017i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	3.73585i		−	0.292614i	−0.989239	−	0.146307i	$-0.953261\pi$
$163$		−	3.73585i		−	0.292614i	0.989239	−	0.146307i	$-0.0467388\pi$
$164$	−2.04726	−	3.54596i	−0.159864	−	0.276893i
$165$	−1.30735	−	0.628448i	−0.101777	−	0.0489246i
$166$	−1.40441	−	2.43251i	−0.109004	−	0.188800i
$167$	12.6906	+	7.32694i	0.982031	+	0.566976i	0.902883	−	0.429887i	$-0.141447\pi$
$167$	12.6906	+	7.32694i	0.982031	+	0.566976i	0.0791483	+	0.996863i	$0.474780\pi$
$168$	−3.61895	+	2.08940i	−0.279208	+	0.161201i
$169$	−3.84198	+	6.65450i	−0.295537	+	0.511885i
$170$	1.30287	+	1.90806i	0.0999256	+	0.146342i
$171$	−4.25770			−0.325595
$172$	−5.09983	−	2.94439i	−0.388858	−	0.224507i
$173$	−19.7420	+	11.3980i	−1.50096	+	0.866577i	−0.500957	+	0.865472i	$0.667018\pi$
$173$	−19.7420	+	11.3980i	−1.50096	+	0.866577i	−0.999999	+	0.00110508i	$0.999648\pi$
$174$	−4.62462	+	8.01008i	−0.350592	+	0.607242i
$175$	3.14329	+	20.6562i	0.237611	+	1.56146i
$176$	−0.324354	−	0.561798i	−0.0244491	−	0.0423471i
$177$	−0.995359	+	0.574671i	−0.0748158	+	0.0431949i
$178$		−	13.8500i		−	1.03810i
$179$	2.17099	−	3.76026i	0.162267	−	0.281055i	−0.773414	−	0.633901i	$-0.781453\pi$
$179$	2.17099	−	3.76026i	0.162267	−	0.281055i	0.935681	+	0.352846i	$0.114786\pi$
$180$	2.22970	−	0.168678i	0.166192	−	0.0125725i
$181$	2.85456	+	4.94424i	0.212178	+	0.367503i	0.952396	−	0.304864i	$-0.0986111\pi$
$181$	2.85456	+	4.94424i	0.212178	+	0.367503i	−0.740218	+	0.672367i	$0.765278\pi$
$182$			9.63487i			0.714184i
$183$	7.02706	+	4.05708i	0.519455	+	0.299908i
$184$	−4.34823			−0.320556
$185$	−20.3724	+	13.9108i	−1.49781	+	1.02274i
$186$	2.88265	+	4.76343i	0.211366	+	0.349272i
$187$		−	0.670287i		−	0.0490162i
$188$			3.42912i			0.250094i
$189$	−2.08940	+	3.61895i	−0.151982	+	0.263240i
$190$	−7.86242	+	5.36865i	−0.570400	+	0.389483i
$191$	−1.70884	−	2.95980i	−0.123648	−	0.214164i	0.797556	−	0.603245i	$-0.206126\pi$
$191$	−1.70884	−	2.95980i	−0.123648	−	0.214164i	−0.921203	+	0.389081i	$0.872793\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−7.24575	−	4.18334i	−0.521561	−	0.301123i	0.216012	−	0.976391i	$-0.430695\pi$
$193$	−7.24575	−	4.18334i	−0.521561	−	0.301123i	−0.737573	+	0.675267i	$0.764028\pi$
$194$	−0.0488039			−0.00350391
$195$	2.23365	−	4.64662i	0.159955	−	0.332751i
$196$	−5.23119	−	9.06069i	−0.373657	−	0.647192i
$197$	−6.05411	+	3.49534i	−0.431338	+	0.249033i	−0.699916	−	0.714225i	$-0.746779\pi$
$197$	−6.05411	+	3.49534i	−0.431338	+	0.249033i	0.268579	+	0.963258i	$0.413446\pi$
$198$	−0.561798	−	0.324354i	−0.0399252	−	0.0230508i
$199$	9.69109	+	16.7855i	0.686983	+	1.18989i	0.972809	+	0.231608i	$0.0743988\pi$
$199$	9.69109	+	16.7855i	0.686983	+	1.18989i	−0.285826	+	0.958282i	$0.592268\pi$
$200$	3.90475	−	3.12297i	0.276107	−	0.220827i
$201$	11.0126			0.776766
$202$		−	10.9441i		−	0.770025i
$203$	−33.4725	−	19.3254i	−2.34931	−	1.35638i
$204$	0.516632	+	0.894833i	0.0361715	+	0.0626508i
$205$	−9.12955	+	0.690655i	−0.637636	+	0.0482374i
$206$	5.32059	+	9.21554i	0.370703	+	0.642077i
$207$	−3.76568	+	2.17412i	−0.261733	+	0.151112i
$208$	1.99676	−	1.15283i	0.138450	−	0.0799342i
$209$	2.76201			0.191052
$210$	0.704870	+	9.31746i	0.0486407	+	0.642966i
$211$	−2.42712	+	4.20389i	−0.167090	+	0.289408i	−0.937395	−	0.348267i	$-0.886770\pi$
$211$	−2.42712	+	4.20389i	−0.167090	+	0.289408i	0.770306	+	0.637675i	$0.220104\pi$
$212$	−5.52654	+	3.19075i	−0.379564	+	0.219141i
$213$			3.42512i			0.234685i
$214$	8.80765	−	15.2553i	0.602079	−	1.04283i
$215$	−10.8744	+	7.42531i	−0.741629	+	0.506402i
$216$	1.00000			0.0680414
$217$	−19.9054	+	12.0460i	−1.35127	+	0.817738i
$218$			10.5792i			0.716514i
$219$	−8.52186			−0.575854
$220$	−1.44642	+	0.109423i	−0.0975178	+	0.00737727i
$221$	2.38235			0.160254
$222$	−9.55416	+	5.51609i	−0.641233	+	0.370216i
$223$	19.9058	+	11.4926i	1.33299	+	0.769604i	0.985757	−	0.168174i	$-0.0537869\pi$
$223$	19.9058	+	11.4926i	1.33299	+	0.769604i	0.347236	+	0.937778i	$0.387120\pi$
$224$	−2.08940	+	3.61895i	−0.139604	+	0.241801i
$225$	1.82012	−	4.65695i	0.121342	−	0.310463i
$226$	2.81823	+	4.88133i	0.187466	+	0.324701i
$227$	24.7366	−	14.2817i	1.64182	−	0.947907i	0.661639	−	0.749823i	$-0.269861\pi$
$227$	24.7366	−	14.2817i	1.64182	−	0.947907i	0.980185	−	0.198084i	$-0.0634720\pi$
$228$	−3.68728	+	2.12885i	−0.244196	+	0.140987i
$229$	9.84097	−	17.0451i	0.650310	−	1.12637i	−0.332738	−	0.943019i	$-0.607972\pi$
$229$	9.84097	−	17.0451i	0.650310	−	1.12637i	0.983048	−	0.183350i	$-0.0586942\pi$
$230$	−4.21243	+	8.76305i	−0.277760	+	0.577818i
$231$	1.35541	−	2.34764i	0.0891795	−	0.154463i
$232$			9.24924i			0.607242i
$233$			18.3751i			1.20379i	0.798574	+	0.601897i	$0.205588\pi$
$233$			18.3751i			1.20379i	−0.798574	+	0.601897i	$0.794412\pi$
$234$	1.15283	−	1.99676i	0.0753627	−	0.130532i
$235$	6.91075	+	3.32202i	0.450807	+	0.216705i
$236$	−0.574671	+	0.995359i	−0.0374079	+	0.0647924i
$237$	14.6827	−	8.47707i	0.953745	−	0.550645i
$238$	−3.73933	+	2.15890i	−0.242385	+	0.139941i
$239$	−4.25215	−	7.36494i	−0.275049	−	0.476399i	0.695099	−	0.718914i	$-0.255361\pi$
$239$	−4.25215	−	7.36494i	−0.275049	−	0.476399i	−0.970147	+	0.242516i	$0.922027\pi$
$240$	1.84664	−	1.26093i	0.119200	−	0.0813925i
$241$	5.82911	−	10.0963i	0.375486	−	0.650360i	−0.614914	−	0.788594i	$-0.710809\pi$
$241$	5.82911	−	10.0963i	0.375486	−	0.650360i	0.990400	+	0.138234i	$0.0441426\pi$
$242$	−9.16184	−	5.28959i	−0.588945	−	0.340028i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	8.11415			0.519455
$245$	−23.3279	+	1.76477i	−1.49037	+	0.112747i
$246$	−4.09453			−0.261057
$247$			9.81679i			0.624628i
$248$	4.87817	+	2.68393i	0.309764	+	0.170430i
$249$	−2.80883			−0.178002
$250$	−2.51097	−	10.8947i	−0.158808	−	0.689043i
$251$	4.00518	−	6.93717i	0.252805	−	0.437870i	−0.711492	−	0.702694i	$-0.751980\pi$
$251$	4.00518	−	6.93717i	0.252805	−	0.437870i	0.964297	+	0.264823i	$0.0853137\pi$
$252$			4.17880i			0.263240i
$253$	2.44283	−	1.41037i	0.153579	−	0.0886690i
$254$	5.58560	−	9.67454i	0.350471	−	0.607034i
$255$	2.30387	−	0.174289i	0.144274	−	0.0109144i
$256$	1.00000			0.0625000
$257$	6.23230	−	3.59822i	0.388760	−	0.224451i	−0.292863	−	0.956155i	$-0.594608\pi$
$257$	6.23230	−	3.59822i	0.388760	−	0.224451i	0.681623	+	0.731704i	$0.261275\pi$
$258$	−5.09983	+	2.94439i	−0.317501	+	0.183309i
$259$	−23.0507	−	39.9249i	−1.43230	−	2.48081i
$260$	−0.388912	−	5.14091i	−0.0241193	−	0.318826i
$261$	4.62462	+	8.01008i	0.286257	+	0.495811i
$262$	−18.2793	−	10.5535i	−1.12930	−	0.652000i
$263$			18.2533i			1.12554i	0.826612	+	0.562772i	$0.190265\pi$
$263$			18.2533i			1.12554i	−0.826612	+	0.562772i	$0.809735\pi$
$264$	−0.648708			−0.0399252
$265$	1.07642	+	14.2288i	0.0661237	+	0.874068i
$266$	−8.89605	−	15.4084i	−0.545452	−	0.944750i
$267$	−11.9945	−	6.92500i	−0.734048	−	0.423803i
$268$	9.53716	−	5.50628i	0.582575	−	0.336350i
$269$	9.53009	+	16.5066i	0.581060	+	1.00643i	0.995354	+	0.0962824i	$0.0306952\pi$
$269$	9.53009	+	16.5066i	0.581060	+	1.00643i	−0.414294	+	0.910143i	$0.635971\pi$
$270$	0.968769	−	2.01531i	0.0589574	−	0.122648i
$271$	14.8981			0.904998			0.452499	−	0.891765i	$-0.350533\pi$
$271$	14.8981			0.904998			0.452499	+	0.891765i	$0.350533\pi$
$272$	0.894833	+	0.516632i	0.0542572	+	0.0313254i
$273$	8.34404	+	4.81744i	0.505005	+	0.291565i
$274$	6.76705	+	11.7209i	0.408812	+	0.708083i
$275$	−1.18073	+	3.02100i	−0.0712006	+	0.182173i
$276$	−2.17412	+	3.76568i	−0.130866	+	0.226667i
$277$		−	7.33247i		−	0.440565i	−0.975436	−	0.220283i	$-0.929302\pi$
$277$		−	7.33247i		−	0.440565i	0.975436	−	0.220283i	$-0.0706980\pi$
$278$			9.33859i			0.560091i
$279$	5.56658	−	0.114734i	0.333263	−	0.00686896i
$280$	5.26917	+	7.71672i	0.314893	+	0.461162i
$281$	−1.99248			−0.118861			−0.0594306	−	0.998232i	$-0.518928\pi$
$281$	−1.99248			−0.118861			−0.0594306	+	0.998232i	$0.518928\pi$
$282$	2.96970	+	1.71456i	0.176843	+	0.102101i
$283$		−	15.2151i		−	0.904443i	−0.891906	−	0.452222i	$-0.850632\pi$
$283$		−	15.2151i		−	0.904443i	0.891906	−	0.452222i	$-0.149368\pi$
$284$	1.71256	+	2.96624i	0.101622	+	0.176014i
$285$	0.718179	+	9.49339i	0.0425413	+	0.562340i
$286$	−0.747848	+	1.29531i	−0.0442212	+	0.0765934i
$287$		−	17.1102i		−	1.00998i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−7.96618	−	13.7978i	−0.468599	−	0.811637i
$290$	18.6401	+	8.96038i	1.09459	+	0.526172i
$291$	−0.0244019	+	0.0422654i	−0.00143047	+	0.00247764i
$292$	−7.38014	+	4.26093i	−0.431890	+	0.249352i
$293$	10.2543	+	5.92034i	0.599065	+	0.345870i	0.768673	−	0.639641i	$-0.220917\pi$
$293$	10.2543	+	5.92034i	0.599065	+	0.345870i	−0.169609	+	0.985511i	$0.554250\pi$
$294$	−10.4624			−0.610179
$295$	1.44924	+	2.12241i	0.0843778	+	0.123572i
$296$	−5.51609	+	9.55416i	−0.320616	+	0.555324i
$297$	−0.561798	+	0.324354i	−0.0325988	+	0.0188209i
$298$	11.7011	+	6.75564i	0.677827	+	0.391343i
$299$	5.01276	+	8.68236i	0.289895	+	0.502114i
$300$	−0.752200	−	4.94310i	−0.0434283	−	0.285390i
$301$	−12.3040	−	21.3112i	−0.709191	−	1.22835i
$302$			0.0704403i			0.00405338i
$303$	−9.47788	−	5.47205i	−0.544490	−	0.314361i
$304$	−2.12885	+	3.68728i	−0.122098	+	0.211480i
$305$	7.86074	−	16.3526i	0.450105	−	0.936344i
$306$	1.03326			0.0590678
$307$	1.51794	+	0.876385i	0.0866336	+	0.0500179i	0.542691	−	0.839932i	$-0.317405\pi$
$307$	1.51794	+	0.876385i	0.0866336	+	0.0500179i	−0.456057	+	0.889950i	$0.650739\pi$
$308$		−	2.71082i		−	0.154463i
$309$	10.6412			0.605356
$310$	10.1348	−	7.23093i	0.575617	−	0.410689i
$311$	−1.47310			−0.0835318			−0.0417659	−	0.999127i	$-0.513298\pi$
$311$	−1.47310			−0.0835318			−0.0417659	+	0.999127i	$0.513298\pi$
$312$		−	2.30565i		−	0.130532i
$313$	1.13158	+	0.653321i	0.0639610	+	0.0369279i	0.531639	−	0.846971i	$-0.321576\pi$
$313$	1.13158	+	0.653321i	0.0639610	+	0.0369279i	−0.467678	+	0.883899i	$0.654909\pi$
$314$	7.12272			0.401958
$315$	8.42159	+	4.04829i	0.474503	+	0.228096i
$316$	8.47707	−	14.6827i	0.476872	−	0.825967i
$317$	−17.9723	−	10.3763i	−1.00942	−	0.582791i	−0.0984010	−	0.995147i	$-0.531373\pi$
$317$	−17.9723	−	10.3763i	−1.00942	−	0.582791i	−0.911023	+	0.412356i	$0.864706\pi$
$318$			6.38150i			0.357857i
$319$	−3.00003	−	5.19620i	−0.167969	−	0.290931i
$320$	0.968769	−	2.01531i	0.0541558	−	0.112659i
$321$	−8.80765	−	15.2553i	−0.491595	−	0.851468i
$322$	−15.7360	−	9.08520i	−0.876934	−	0.506298i
$323$	−3.80993	+	2.19967i	−0.211990	+	0.122393i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−10.7373	−	4.19658i	−0.595599	−	0.232784i
$326$	−3.73585			−0.206909
$327$	9.16186	+	5.28960i	0.506652	+	0.292516i
$328$	−3.54596	+	2.04726i	−0.195793	+	0.113041i
$329$	−7.16480	+	12.4098i	−0.395008	+	0.684175i
$330$	−0.628448	+	1.30735i	−0.0345949	+	0.0719672i
$331$	−15.3523	−	26.5910i	−0.843839	−	1.46157i	−0.886625	−	0.462488i	$-0.846957\pi$
$331$	−15.3523	−	26.5910i	−0.843839	−	1.46157i	0.0427860	−	0.999084i	$-0.486377\pi$
$332$	−2.43251	+	1.40441i	−0.133502	+	0.0770772i
$333$			11.0322i			0.604560i
$334$	7.32694	−	12.6906i	0.400912	−	0.694401i
$335$	−1.85757	−	24.5547i	−0.101490	−	1.34157i
$336$	2.08940	+	3.61895i	0.113986	+	0.197430i
$337$		−	12.3498i		−	0.672734i	−0.941731	−	0.336367i	$-0.890802\pi$
$337$		−	12.3498i		−	0.672734i	0.941731	−	0.336367i	$-0.109198\pi$
$338$	6.65450	+	3.84198i	0.361957	+	0.208976i
$339$	5.63647			0.306131
$340$	1.90806	−	1.30287i	0.103479	−	0.0706581i
$341$	−3.61109	+	0.0744291i	−0.195551	+	0.00403056i
$342$			4.25770i			0.230230i
$343$		−	14.4686i		−	0.781231i
$344$	−2.94439	+	5.09983i	−0.158751	+	0.274964i
$345$	5.48281	+	8.02960i	0.295184	+	0.432299i
$346$	11.3980	+	19.7420i	0.612763	+	1.06134i
$347$	14.7477	+	8.51459i	0.791699	+	0.457087i	0.840560	−	0.541718i	$-0.182226\pi$
$347$	14.7477	+	8.51459i	0.791699	+	0.457087i	−0.0488616	+	0.998806i	$0.515559\pi$
$348$	8.01008	+	4.62462i	0.429385	+	0.247906i
$349$	9.90842			0.530386			0.265193	−	0.964195i	$-0.414564\pi$
$349$	9.90842			0.530386			0.265193	+	0.964195i	$0.414564\pi$
$350$	20.6562	−	3.14329i	1.10412	−	0.168016i
$351$	−1.15283	−	1.99676i	−0.0615334	−	0.106579i
$352$	−0.561798	+	0.324354i	−0.0299439	+	0.0172881i
$353$	−11.5562	−	6.67200i	−0.615076	−	0.355114i	0.159873	−	0.987138i	$-0.448891\pi$
$353$	−11.5562	−	6.67200i	−0.615076	−	0.355114i	−0.774950	+	0.632023i	$0.782225\pi$
$354$	0.574671	+	0.995359i	0.0305434	+	0.0529027i
$355$	7.63698	−	0.577741i	0.405329	−	0.0306633i
$356$	−13.8500			−0.734048
$357$			4.31781i			0.228522i
$358$	−3.76026	−	2.17099i	−0.198736	−	0.114740i
$359$	7.38297	+	12.7877i	0.389658	+	0.674908i	0.992403	−	0.123026i	$-0.0392598\pi$
$359$	7.38297	+	12.7877i	0.389658	+	0.674908i	−0.602745	+	0.797934i	$0.705926\pi$
$360$	−0.168678	−	2.22970i	−0.00889009	−	0.117515i
$361$	0.435983	+	0.755144i	0.0229465	+	0.0397444i
$362$	4.94424	−	2.85456i	0.259864	−	0.150032i
$363$	−9.16184	+	5.28959i	−0.480872	+	0.277631i
$364$	9.63487			0.505005
$365$	1.43745	+	19.0012i	0.0752394	+	0.994566i
$366$	4.05708	−	7.02706i	0.212067	−	0.367310i
$367$	−10.3817	+	5.99388i	−0.541921	+	0.312878i	−0.745857	−	0.666106i	$-0.767960\pi$
$367$	−10.3817	+	5.99388i	−0.541921	+	0.312878i	0.203936	+	0.978984i	$0.434626\pi$
$368$			4.34823i			0.226667i
$369$	−2.04726	+	3.54596i	−0.106576	+	0.184595i
$370$	13.9108	+	20.3724i	0.723188	+	1.05911i
$371$	−26.6670			−1.38448
$372$	4.76343	−	2.88265i	0.246973	−	0.149459i
$373$			25.4624i			1.31840i	0.751970	+	0.659198i	$0.229104\pi$
$373$			25.4624i			1.31840i	−0.751970	+	0.659198i	$0.770896\pi$
$374$	−0.670287			−0.0346597
$375$	−10.6906	−	3.27280i	−0.552060	−	0.169007i
$376$	3.42912			0.176843
$377$	18.4685	−	10.6628i	0.951175	−	0.549161i
$378$	3.61895	+	2.08940i	0.186139	+	0.107467i
$379$	−13.0590	+	22.6189i	−0.670797	+	1.16185i	0.306882	+	0.951748i	$0.400714\pi$
$379$	−13.0590	+	22.6189i	−0.670797	+	1.16185i	−0.977679	+	0.210106i	$0.932619\pi$
$380$	5.36865	+	7.86242i	0.275406	+	0.403334i
$381$	−5.58560	−	9.67454i	−0.286159	−	0.495642i
$382$	−2.95980	+	1.70884i	−0.151437	+	0.0874320i
$383$	3.64393	−	2.10383i	0.186196	−	0.107500i	−0.404004	−	0.914757i	$-0.632382\pi$
$383$	3.64393	−	2.10383i	0.186196	−	0.107500i	0.590201	+	0.807257i	$0.299049\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−5.46316	−	2.62616i	−0.278428	−	0.133842i
$386$	−4.18334	+	7.24575i	−0.212926	+	0.368799i
$387$			5.88877i			0.299343i
$388$			0.0488039i			0.00247764i
$389$	1.92719	−	3.33799i	0.0977123	−	0.169243i	−0.813025	−	0.582229i	$-0.802181\pi$
$389$	1.92719	−	3.33799i	0.0977123	−	0.169243i	0.910737	+	0.412986i	$0.135514\pi$
$390$	−4.64662	−	2.23365i	−0.235291	−	0.113105i
$391$	−2.24644	+	3.89094i	−0.113607	+	0.196773i
$392$	−9.06069	+	5.23119i	−0.457634	+	0.264215i
$393$	−18.2793	+	10.5535i	−0.922068	+	0.532356i
$394$	3.49534	+	6.05411i	0.176093	+	0.305002i
$395$	−21.3779	−	31.3081i	−1.07564	−	1.57528i
$396$	−0.324354	+	0.561798i	−0.0162994	+	0.0282314i
$397$	8.02719	+	4.63450i	0.402873	+	0.232599i	0.687723	−	0.725973i	$-0.258610\pi$
$397$	8.02719	+	4.63450i	0.402873	+	0.232599i	−0.284850	+	0.958572i	$0.591944\pi$
$398$	16.7855	−	9.69109i	0.841379	−	0.485771i
$399$	−17.7921			−0.890719
$400$	−3.12297	−	3.90475i	−0.156149	−	0.195237i
$401$	28.2958			1.41302			0.706512	−	0.707701i	$-0.250268\pi$
$401$	28.2958			1.41302			0.706512	+	0.707701i	$0.250268\pi$
$402$		−	11.0126i		−	0.549257i
$403$	−0.264538	−	12.8346i	−0.0131776	−	0.639338i
$404$	−10.9441			−0.544490
$405$	−1.26093	−	1.84664i	−0.0626560	−	0.0917600i
$406$	−19.3254	+	33.4725i	−0.959102	+	1.66121i
$407$		−	7.15667i		−	0.354743i
$408$	0.894833	−	0.516632i	0.0443008	−	0.0255771i
$409$	−5.75084	+	9.96074i	−0.284361	+	0.492527i	−0.972454	−	0.233095i	$-0.925115\pi$
$409$	−5.75084	+	9.96074i	−0.284361	+	0.492527i	0.688093	+	0.725622i	$0.258448\pi$
$410$	0.690655	+	9.12955i	0.0341090	+	0.450876i
$411$	13.5341			0.667587
$412$	9.21554	−	5.32059i	0.454017	−	0.262127i
$413$	−4.15941	+	2.40144i	−0.204671	+	0.118167i
$414$	2.17412	+	3.76568i	0.106852	+	0.185073i
$415$	0.473786	+	6.26283i	0.0232572	+	0.307430i
$416$	−1.15283	−	1.99676i	−0.0565220	−	0.0978990i
$417$	8.08746	+	4.66929i	0.396044	+	0.228656i
$418$		−	2.76201i		−	0.135094i
$419$	−8.65168			−0.422662			−0.211331	−	0.977415i	$-0.567780\pi$
$419$	−8.65168			−0.422662			−0.211331	+	0.977415i	$0.567780\pi$
$420$	9.31746	−	0.704870i	0.454646	−	0.0343942i
$421$	5.50713	+	9.53864i	0.268401	+	0.464885i	0.968449	−	0.249211i	$-0.0801713\pi$
$421$	5.50713	+	9.53864i	0.268401	+	0.464885i	−0.700048	+	0.714096i	$0.746838\pi$
$422$	4.20389	+	2.42712i	0.204642	+	0.118150i
$423$	2.96970	−	1.71456i	0.144392	−	0.0833647i
$424$	3.19075	+	5.52654i	0.154956	+	0.268392i
$425$	−0.777221	−	5.10752i	−0.0377008	−	0.247751i
$426$	3.42512			0.165948
$427$	29.3647	+	16.9537i	1.42106	+	0.820448i
$428$	−15.2553	−	8.80765i	−0.737393	−	0.425734i
$429$	0.747848	+	1.29531i	0.0361065	+	0.0625382i
$430$	7.42531	+	10.8744i	0.358080	+	0.524411i
$431$	4.47725	−	7.75482i	0.215661	−	0.373537i	−0.737816	−	0.675002i	$-0.764143\pi$
$431$	4.47725	−	7.75482i	0.215661	−	0.373537i	0.953477	+	0.301466i	$0.0974759\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	19.2723i		−	0.926170i	−0.886314	−	0.463085i	$-0.846743\pi$
$433$		−	19.2723i		−	0.926170i	0.886314	−	0.463085i	$-0.153257\pi$
$434$	12.0460	+	19.9054i	0.578228	+	0.955492i
$435$	17.0800	−	11.6626i	0.818922	−	0.559180i
$436$	10.5792			0.506652
$437$	−16.0331	−	9.25674i	−0.766969	−	0.442810i
$438$			8.52186i			0.407190i
$439$	−11.1568	−	19.3241i	−0.532483	−	0.922288i	−0.999281	−	0.0379234i	$-0.987926\pi$
$439$	−11.1568	−	19.3241i	−0.532483	−	0.922288i	0.466798	−	0.884364i	$-0.345408\pi$
$440$	0.109423	+	1.44642i	0.00521652	+	0.0689555i
$441$	−5.23119	+	9.06069i	−0.249104	+	0.431461i
$442$		−	2.38235i		−	0.113317i
$443$	30.8361	−	17.8033i	1.46507	−	0.845858i	0.465831	−	0.884874i	$-0.345756\pi$
$443$	30.8361	−	17.8033i	1.46507	−	0.845858i	0.999239	+	0.0390156i	$0.0124222\pi$
$444$	5.51609	+	9.55416i	0.261782	+	0.453420i
$445$	−13.4175	+	27.9121i	−0.636048	+	1.32316i
$446$	11.4926	−	19.9058i	0.544192	−	0.942569i
$447$	11.7011	−	6.75564i	0.553443	−	0.319531i
$448$	3.61895	+	2.08940i	0.170979	+	0.0987149i
$449$	−13.1892			−0.622437			−0.311218	−	0.950338i	$-0.600737\pi$
$449$	−13.1892			−0.622437			−0.311218	+	0.950338i	$0.600737\pi$
$450$	−4.65695	−	1.82012i	−0.219531	−	0.0858014i
$451$	1.32808	−	2.30030i	0.0625367	−	0.108317i
$452$	4.88133	−	2.81823i	0.229598	−	0.132559i
$453$	0.0610031	+	0.0352202i	0.00286618	+	0.00165479i
$454$	−14.2817	−	24.7366i	−0.670272	−	1.16094i
$455$	9.33397	−	19.4173i	0.437583	−	0.910296i
$456$	2.12885	+	3.68728i	0.0996926	+	0.172673i
$457$		−	33.3758i		−	1.56125i	−0.624997	−	0.780627i	$-0.714900\pi$
$457$		−	33.3758i		−	1.56125i	0.624997	−	0.780627i	$-0.285100\pi$
$458$	−17.0451	−	9.84097i	−0.796463	−	0.459838i
$459$	0.516632	−	0.894833i	0.0241143	−	0.0417672i
$460$	8.76305	+	4.21243i	0.408579	+	0.196406i
$461$	−6.63396			−0.308974			−0.154487	−	0.987995i	$-0.549373\pi$
$461$	−6.63396			−0.308974			−0.154487	+	0.987995i	$0.549373\pi$
$462$	−2.34764	−	1.35541i	−0.109222	−	0.0630594i
$463$			2.20118i			0.102298i	0.998691	+	0.0511488i	$0.0162883\pi$
$463$			2.20118i			0.102298i	−0.998691	+	0.0511488i	$0.983712\pi$
$464$	9.24924			0.429385
$465$	−1.19478	−	12.3924i	−0.0554066	−	0.574686i
$466$	18.3751			0.851210
$467$		−	29.5855i		−	1.36905i	−0.728988	−	0.684526i	$-0.760009\pi$
$467$		−	29.5855i		−	1.36905i	0.728988	−	0.684526i	$-0.239991\pi$
$468$	−1.99676	−	1.15283i	−0.0923001	−	0.0532895i
$469$	46.0193			2.12497
$470$	3.32202	−	6.91075i	0.153234	−	0.318769i
$471$	3.56136	−	6.16845i	0.164099	−	0.284227i
$472$	0.995359	+	0.574671i	0.0458151	+	0.0264514i
$473$		−	3.82009i		−	0.175648i
$474$	−8.47707	−	14.6827i	−0.389365	−	0.674399i
$475$	21.0462	−	3.20264i	0.965667	−	0.146947i
$476$	2.15890	+	3.73933i	0.0989531	+	0.171392i
$477$	5.52654	+	3.19075i	0.253043	+	0.146094i
$478$	−7.36494	+	4.25215i	−0.336865	+	0.194489i
$479$	−11.8221	+	20.4764i	−0.540163	+	0.935590i	0.458731	+	0.888575i	$0.348304\pi$
$479$	−11.8221	+	20.4764i	−0.540163	+	0.935590i	−0.998894	+	0.0470152i	$0.985029\pi$
$480$	−1.26093	−	1.84664i	−0.0575532	−	0.0842870i
$481$	25.4364			1.15980
$482$	−10.0963	−	5.82911i	−0.459874	−	0.265509i
$483$	−15.7360	+	9.08520i	−0.716014	+	0.413391i
$484$	−5.28959	+	9.16184i	−0.240436	+	0.416447i
$485$	0.0983551	+	0.0472797i	0.00446607	+	0.00214686i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	12.2265	−	7.05898i	0.554036	−	0.319873i	−0.196712	−	0.980461i	$-0.563026\pi$
$487$	12.2265	−	7.05898i	0.554036	−	0.319873i	0.750748	+	0.660588i	$0.229693\pi$
$488$		−	8.11415i		−	0.367310i
$489$	−1.86792	+	3.23534i	−0.0844704	+	0.146307i
$490$	1.76477	+	23.3279i	0.0797242	+	1.05385i
$491$	9.07404	+	15.7167i	0.409506	+	0.709284i	0.994834	−	0.101512i	$-0.0323679\pi$
$491$	9.07404	+	15.7167i	0.409506	+	0.709284i	−0.585329	+	0.810796i	$0.699035\pi$
$492$			4.09453i			0.184595i
$493$	8.27653	+	4.77845i	0.372756	+	0.215211i
$494$	9.81679			0.441678
$495$	0.817974	+	1.19793i	0.0367652	+	0.0538428i
$496$	2.68393	−	4.87817i	0.120512	−	0.219036i
$497$			14.3129i			0.642021i
$498$			2.80883i			0.125866i
$499$	13.7827	−	23.8724i	0.617000	−	1.06868i	−0.373030	−	0.927819i	$-0.621681\pi$
$499$	13.7827	−	23.8724i	0.617000	−	1.06868i	0.990030	−	0.140856i	$-0.0449855\pi$
$500$	−10.8947	+	2.51097i	−0.487227	+	0.112294i
$501$	−7.32694	−	12.6906i	−0.327344	−	0.566976i
$502$	−6.93717	−	4.00518i	−0.309621	−	0.178760i
$503$	−10.4212	−	6.01669i	−0.464659	−	0.268271i	0.249342	−	0.968415i	$-0.419786\pi$
$503$	−10.4212	−	6.01669i	−0.464659	−	0.268271i	−0.714001	+	0.700145i	$0.753119\pi$
$504$	4.17880			0.186139
$505$	−10.6023	+	22.0558i	−0.471797	+	0.981470i
$506$	−1.41037	−	2.44283i	−0.0626984	−	0.108597i
$507$	6.65450	−	3.84198i	0.295537	−	0.170628i
$508$	−9.67454	−	5.58560i	−0.429238	−	0.247821i
$509$	−13.9571	−	24.1744i	−0.618637	−	1.07151i	−0.989735	−	0.142917i	$-0.954352\pi$
$509$	−13.9571	−	24.1744i	−0.618637	−	1.07151i	0.371098	−	0.928594i	$-0.378982\pi$
$510$	−0.174289	−	2.30387i	−0.00771763	−	0.102017i
$511$	−35.6111			−1.57534
$512$		−	1.00000i		−	0.0441942i
$513$	3.68728	+	2.12885i	0.162797	+	0.0939911i
$514$	−3.59822	−	6.23230i	−0.158711	−	0.274895i
$515$	−1.79493	−	23.7266i	−0.0790941	−	1.04552i
$516$	2.94439	+	5.09983i	0.129619	+	0.224507i
$517$	−1.92647	+	1.11225i	−0.0847261	+	0.0489166i
$518$	−39.9249	+	23.0507i	−1.75420	+	1.01279i
$519$	22.7961			1.00064
$520$	−5.14091	+	0.388912i	−0.225444	+	0.0170549i
$521$	−4.12893	+	7.15152i	−0.180892	+	0.313314i	−0.942185	−	0.335095i	$-0.891232\pi$
$521$	−4.12893	+	7.15152i	−0.180892	+	0.313314i	0.761293	+	0.648408i	$0.224565\pi$
$522$	8.01008	−	4.62462i	0.350592	−	0.202414i
$523$		−	36.0699i		−	1.57723i	−0.614888	−	0.788614i	$-0.710799\pi$
$523$		−	36.0699i		−	1.57723i	0.614888	−	0.788614i	$-0.289201\pi$
$524$	−10.5535	+	18.2793i	−0.461034	+	0.798534i
$525$	7.60593	−	19.4605i	0.331950	−	0.849324i
$526$	18.2533			0.795880
$527$	4.92189	−	2.97854i	0.214401	−	0.129747i
$528$			0.648708i			0.0282314i
$529$	4.09288			0.177951
$530$	14.2288	−	1.07642i	0.618060	−	0.0467565i
$531$	1.14934			0.0498772
$532$	−15.4084	+	8.89605i	−0.668039	+	0.385693i
$533$	8.17577	+	4.72028i	0.354132	+	0.204458i
$534$	−6.92500	+	11.9945i	−0.299674	+	0.519051i
$535$	−32.5290	+	22.2116i	−1.40635	+	0.960292i
$536$	−5.50628	−	9.53716i	−0.237835	−	0.411943i
$537$	−3.76026	+	2.17099i	−0.162267	+	0.0936851i
$538$	16.5066	−	9.53009i	0.711650	−	0.410872i
$539$	3.39352	−	5.87774i	0.146169	−	0.253172i
$540$	−2.01531	−	0.968769i	−0.0867253	−	0.0416892i
$541$	−10.3222	+	17.8785i	−0.443785	+	0.768657i	−0.997967	−	0.0637381i	$-0.979698\pi$
$541$	−10.3222	+	17.8785i	−0.443785	+	0.768657i	0.554182	+	0.832395i	$0.313031\pi$
$542$		−	14.8981i		−	0.639930i
$543$		−	5.70912i		−	0.245002i
$544$	0.516632	−	0.894833i	0.0221504	−	0.0383656i
$545$	10.2488	−	21.3204i	0.439011	−	0.913266i
$546$	4.81744	−	8.34404i	0.206167	−	0.357092i
$547$	27.7806	−	16.0391i	1.18781	−	0.685785i	0.230004	−	0.973190i	$-0.426126\pi$
$547$	27.7806	−	16.0391i	1.18781	−	0.685785i	0.957809	+	0.287405i	$0.0927926\pi$
$548$	11.7209	−	6.76705i	0.500691	−	0.289074i
$549$	−4.05708	−	7.02706i	−0.173152	−	0.299908i
$550$	3.02100	+	1.18073i	0.128816	+	0.0503464i
$551$	−19.6903	+	34.1045i	−0.838833	+	1.45290i
$552$	3.76568	+	2.17412i	0.160278	+	0.0925365i
$553$	61.3562	−	35.4240i	2.60913	−	1.50638i
$554$	−7.33247			−0.311527
$555$	24.5984	−	1.86088i	1.04415	−	0.0789901i
$556$	9.33859			0.396044
$557$		−	10.3555i		−	0.438776i	−0.975638	−	0.219388i	$-0.929594\pi$
$557$		−	10.3555i		−	0.438776i	0.975638	−	0.219388i	$-0.0704060\pi$
$558$	−0.114734	−	5.56658i	−0.00485709	−	0.235652i
$559$	13.5775			0.574266
$560$	7.71672	−	5.26917i	0.326091	−	0.222663i
$561$	−0.335143	+	0.580485i	−0.0141498	+	0.0245081i
$562$			1.99248i			0.0840475i
$563$	−17.8622	+	10.3128i	−0.752802	+	0.434631i	−0.826706	−	0.562635i	$-0.809788\pi$
$563$	−17.8622	+	10.3128i	−0.752802	+	0.434631i	0.0739033	+	0.997265i	$0.476454\pi$
$564$	1.71456	−	2.96970i	0.0721960	−	0.125047i
$565$	−0.950746	−	12.5676i	−0.0399982	−	0.528724i
$566$	−15.2151			−0.639538
$567$	3.61895	−	2.08940i	0.151982	−	0.0877466i
$568$	2.96624	−	1.71256i	0.124461	−	0.0718575i
$569$	3.75336	+	6.50101i	0.157349	+	0.272537i	0.933912	−	0.357503i	$-0.116372\pi$
$569$	3.75336	+	6.50101i	0.157349	+	0.272537i	−0.776563	+	0.630040i	$0.783039\pi$
$570$	9.49339	−	0.718179i	0.397634	−	0.0300812i
$571$	2.16134	+	3.74355i	0.0904494	+	0.156663i	0.907700	−	0.419619i	$-0.137836\pi$
$571$	2.16134	+	3.74355i	0.0904494	+	0.156663i	−0.817251	+	0.576282i	$0.804503\pi$
$572$	1.29531	+	0.747848i	0.0541597	+	0.0312691i
$573$			3.41769i			0.142776i
$574$	−17.1102			−0.714166
$575$	16.9787	−	13.5794i	0.708063	−	0.566300i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	29.0282	+	16.7594i	1.20846	+	0.697703i	0.962422	−	0.271557i	$-0.0875387\pi$
$577$	29.0282	+	16.7594i	1.20846	+	0.697703i	0.246036	+	0.969261i	$0.420872\pi$
$578$	−13.7978	+	7.96618i	−0.573914	+	0.331350i
$579$	4.18334	+	7.24575i	0.173854	+	0.301123i
$580$	8.96038	−	18.6401i	0.372060	−	0.773989i
$581$	−11.7375			−0.486954
$582$	0.0422654	+	0.0244019i	0.00175196	+	0.00101149i
$583$	−3.58511	−	2.06986i	−0.148480	−	0.0857250i
$584$	4.26093	+	7.38014i	0.176318	+	0.305392i
$585$	−4.25770	+	2.90726i	−0.176034	+	0.120201i
$586$	5.92034	−	10.2543i	0.244567	−	0.423603i
$587$			25.3249i			1.04527i	0.852556	+	0.522636i	$0.175051\pi$
$587$			25.3249i			1.04527i	−0.852556	+	0.522636i	$0.824949\pi$
$588$			10.4624i			0.431461i
$589$	12.2735	+	20.2813i	0.505720	+	0.835676i
$590$	2.12241	−	1.44924i	0.0873784	−	0.0596641i
$591$	6.99069			0.287558
$592$	9.55416	+	5.51609i	0.392673	+	0.226710i
$593$		−	43.7536i		−	1.79674i	−0.439236	−	0.898372i	$-0.644751\pi$
$593$		−	43.7536i		−	1.79674i	0.439236	−	0.898372i	$-0.355249\pi$
$594$	0.324354	+	0.561798i	0.0133084	+	0.0230508i
$595$	9.62740	−	0.728317i	0.394685	−	0.0298581i
$596$	6.75564	−	11.7011i	0.276722	−	0.479296i
$597$		−	19.3822i		−	0.793260i
$598$	8.68236	−	5.01276i	0.355048	−	0.204987i
$599$	6.30871	+	10.9270i	0.257767	+	0.446466i	0.965643	−	0.259871i	$-0.0836799\pi$
$599$	6.30871	+	10.9270i	0.257767	+	0.446466i	−0.707876	+	0.706336i	$0.750347\pi$
$600$	−4.94310	+	0.752200i	−0.201801	+	0.0307084i
$601$	−11.6962	+	20.2584i	−0.477099	+	0.826359i	−0.999656	−	0.0262453i	$-0.991645\pi$
$601$	−11.6962	+	20.2584i	−0.477099	+	0.826359i	0.522557	+	0.852604i	$0.324978\pi$
$602$	−21.3112	+	12.3040i	−0.868578	+	0.501474i
$603$	−9.53716	−	5.50628i	−0.388383	−	0.224233i
$604$	0.0704403			0.00286618
$605$	13.3396	+	19.5359i	0.542331	+	0.794247i
$606$	−5.47205	+	9.47788i	−0.222287	+	0.385012i
$607$	−5.97216	+	3.44803i	−0.242402	+	0.139951i	−0.616280	−	0.787527i	$-0.711361\pi$
$607$	−5.97216	+	3.44803i	−0.242402	+	0.139951i	0.373878	+	0.927478i	$0.378028\pi$
$608$	3.68728	+	2.12885i	0.149539	+	0.0863363i
$609$	19.3254	+	33.4725i	0.783104	+	1.35638i
$610$	−16.3526	−	7.86074i	−0.662095	−	0.318272i
$611$	−3.95318	−	6.84711i	−0.159929	−	0.277004i
$612$		−	1.03326i		−	0.0417672i
$613$	−39.7312	−	22.9388i	−1.60473	−	0.926491i	−0.990523	−	0.137346i	$-0.956143\pi$
$613$	−39.7312	−	22.9388i	−1.60473	−	0.926491i	−0.614207	−	0.789145i	$-0.710524\pi$
$614$	0.876385	−	1.51794i	0.0353680	−	0.0612592i
$615$	8.25175	+	3.96665i	0.332743	+	0.159951i
$616$	−2.71082			−0.109222
$617$	34.0005	+	19.6302i	1.36881	+	0.790282i	0.990776	−	0.135511i	$-0.0432676\pi$
$617$	34.0005	+	19.6302i	1.36881	+	0.790282i	0.378032	+	0.925793i	$0.376601\pi$
$618$		−	10.6412i		−	0.428051i
$619$	−34.9125			−1.40325			−0.701625	−	0.712546i	$-0.747542\pi$
$619$	−34.9125			−1.40325			−0.701625	+	0.712546i	$0.747542\pi$
$620$	−7.23093	−	10.1348i	−0.290401	−	0.407022i
$621$	4.34823			0.174489
$622$			1.47310i			0.0590659i
$623$	−50.1224	−	28.9382i	−2.00811	−	1.15938i
$624$	−2.30565			−0.0923001
$625$	−5.49409	+	24.3888i	−0.219764	+	0.975553i
$626$	0.653321	−	1.13158i	0.0261120	−	0.0452272i
$627$	−2.39197	−	1.38100i	−0.0955260	−	0.0551520i
$628$		−	7.12272i		−	0.284227i
$629$	5.69958	+	9.87197i	0.227257	+	0.393621i
$630$	4.04829	−	8.42159i	0.161288	−	0.335524i
$631$	3.03740	+	5.26093i	0.120917	+	0.209434i	0.920129	−	0.391614i	$-0.128083\pi$
$631$	3.03740	+	5.26093i	0.120917	+	0.209434i	−0.799213	+	0.601048i	$0.794750\pi$
$632$	−14.6827	−	8.47707i	−0.584047	−	0.337200i
$633$	4.20389	−	2.42712i	0.167090	−	0.0964694i
$634$	−10.3763	+	17.9723i	−0.412096	+	0.713770i
$635$	−20.6291	+	14.0861i	−0.818642	+	0.558988i
$636$	6.38150			0.253043
$637$	20.8908	+	12.0613i	0.827724	+	0.477887i
$638$	−5.19620	+	3.00003i	−0.205720	+	0.118772i
$639$	1.71256	−	2.96624i	0.0677479	−	0.117343i
$640$	−2.01531	−	0.968769i	−0.0796622	−	0.0382940i
$641$	10.9294	+	18.9303i	0.431686	+	0.747702i	0.997019	−	0.0771613i	$-0.0245856\pi$
$641$	10.9294	+	18.9303i	0.431686	+	0.747702i	−0.565333	+	0.824863i	$0.691252\pi$
$642$	−15.2553	+	8.80765i	−0.602079	+	0.347610i
$643$		−	2.08828i		−	0.0823536i	−0.999152	−	0.0411768i	$-0.986889\pi$
$643$		−	2.08828i		−	0.0823536i	0.999152	−	0.0411768i	$-0.0131107\pi$
$644$	−9.08520	+	15.7360i	−0.358007	+	0.620086i
$645$	13.1302	−	0.993304i	0.517000	−	0.0391113i
$646$	2.19967	+	3.80993i	0.0865447	+	0.149900i
$647$		−	3.06699i		−	0.120576i	−0.998181	−	0.0602880i	$-0.980798\pi$
$647$		−	3.06699i		−	0.120576i	0.998181	−	0.0602880i	$-0.0192019\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−0.745587			−0.0292669
$650$	−4.19658	+	10.7373i	−0.164603	+	0.421152i
$651$	23.2616	−	0.479452i	0.911696	−	0.0187912i
$652$			3.73585i			0.146307i
$653$			11.1514i			0.436389i	0.975905	+	0.218195i	$0.0700167\pi$
$653$			11.1514i			0.436389i	−0.975905	+	0.218195i	$0.929983\pi$
$654$	5.28960	−	9.16186i	0.206840	−	0.358257i
$655$	26.6145	+	38.9771i	1.03992	+	1.52296i
$656$	2.04726	+	3.54596i	0.0799322	+	0.138447i
$657$	7.38014	+	4.26093i	0.287927	+	0.166235i
$658$	12.4098	+	7.16480i	0.483784	+	0.279313i
$659$	11.9822			0.466761			0.233381	−	0.972385i	$-0.425021\pi$
$659$	11.9822			0.466761			0.233381	+	0.972385i	$0.425021\pi$
$660$	1.30735	+	0.628448i	0.0508885	+	0.0244623i
$661$	−3.61059	−	6.25373i	−0.140436	−	0.243242i	0.787225	−	0.616666i	$-0.211517\pi$
$661$	−3.61059	−	6.25373i	−0.140436	−	0.243242i	−0.927661	+	0.373424i	$0.878184\pi$
$662$	−26.5910	+	15.3523i	−1.03349	+	0.596685i
$663$	−2.06318	−	1.19117i	−0.0801271	−	0.0462614i
$664$	1.40441	+	2.43251i	0.0545018	+	0.0943998i
$665$	3.00113	+	39.6710i	0.116379	+	1.53837i
$666$	11.0322			0.427489
$667$			40.2178i			1.55724i
$668$	−12.6906	−	7.32694i	−0.491016	−	0.283488i
$669$	−11.4926	−	19.9058i	−0.444331	−	0.769604i
$670$	−24.5547	+	1.85757i	−0.948630	+	0.0717643i
$671$	2.63186	+	4.55851i	0.101602	+	0.175979i
$672$	3.61895	−	2.08940i	0.139604	−	0.0806004i
$673$	−32.7278	+	18.8954i	−1.26156	+	0.728364i	−0.973377	−	0.229210i	$-0.926386\pi$
$673$	−32.7278	+	18.8954i	−1.26156	+	0.728364i	−0.288187	+	0.957574i	$0.593052\pi$
$674$	−12.3498			−0.475695
$675$	−3.90475	+	3.12297i	−0.150294	+	0.120203i
$676$	3.84198	−	6.65450i	0.147768	−	0.255942i
$677$	−3.31758	+	1.91541i	−0.127505	+	0.0736150i	−0.562396	−	0.826868i	$-0.690120\pi$
$677$	−3.31758	+	1.91541i	−0.127505	+	0.0736150i	0.434891	+	0.900483i	$0.356787\pi$
$678$		−	5.63647i		−	0.216467i
$679$	−0.101971	+	0.176619i	−0.00391328	+	0.00677800i
$680$	−1.30287	−	1.90806i	−0.0499628	−	0.0731708i
$681$	−28.5633			−1.09455
$682$	0.0744291	+	3.61109i	0.00285004	+	0.138276i
$683$			42.6921i			1.63357i	0.576942	+	0.816785i	$0.304246\pi$
$683$			42.6921i			1.63357i	−0.576942	+	0.816785i	$0.695754\pi$
$684$	4.25770			0.162797
$685$	−2.28290	−	30.1769i	−0.0872251	−	1.15300i
$686$	−14.4686			−0.552414
$687$	−17.0451	+	9.84097i	−0.650310	+	0.375456i
$688$	5.09983	+	2.94439i	0.194429	+	0.112254i
$689$	7.35676	−	12.7423i	0.280270	−	0.485442i
$690$	8.02960	−	5.48281i	0.305682	−	0.208727i
$691$	−0.275837	−	0.477763i	−0.0104933	−	0.0181750i	0.860731	−	0.509060i	$-0.170007\pi$
$691$	−0.275837	−	0.477763i	−0.0104933	−	0.0181750i	−0.871224	+	0.490885i	$0.836674\pi$
$692$	19.7420	−	11.3980i	0.750478	−	0.433289i
$693$	−2.34764	+	1.35541i	−0.0891795	+	0.0514878i
$694$	8.51459	−	14.7477i	0.323210	−	0.559815i
$695$	9.04694	−	18.8202i	0.343170	−	0.713890i
$696$	4.62462	−	8.01008i	0.175296	−	0.303621i
$697$			4.23073i			0.160250i
$698$		−	9.90842i		−	0.375039i
$699$	9.18755	−	15.9133i	0.347505	−	0.601897i
$700$	−3.14329	−	20.6562i	−0.118805	−	0.780732i
$701$	−6.66772	+	11.5488i	−0.251836	+	0.436193i	−0.964031	−	0.265788i	$-0.914368\pi$
$701$	−6.66772	+	11.5488i	−0.251836	+	0.436193i	0.712195	+	0.701982i	$0.247701\pi$
$702$	−1.99676	+	1.15283i	−0.0753627	+	0.0435107i
$703$	−40.6788	+	23.4859i	−1.53423	+	0.885787i
$704$	0.324354	+	0.561798i	0.0122246	+	0.0211735i
$705$	−4.32387	−	6.33233i	−0.162846	−	0.238489i
$706$	−6.67200	+	11.5562i	−0.251104	+	0.434925i
$707$	−39.6062	−	22.8666i	−1.48954	−	0.859988i
$708$	0.995359	−	0.574671i	0.0374079	−	0.0215975i
$709$	47.9257			1.79989			0.899943	−	0.436007i	$-0.143608\pi$
$709$	47.9257			1.79989			0.899943	+	0.436007i	$0.143608\pi$
$710$	−0.577741	−	7.63698i	−0.0216823	−	0.286611i
$711$	−16.9541			−0.635830
$712$			13.8500i			0.519051i
$713$	21.2114	+	11.6703i	0.794373	+	0.437058i
$714$	4.31781			0.161590
$715$	2.76201	−	1.88597i	0.103293	−	0.0705311i
$716$	−2.17099	+	3.76026i	−0.0811337	+	0.140528i
$717$			8.50430i			0.317599i
$718$	12.7877	−	7.38297i	0.477232	−	0.275530i
$719$	3.15928	−	5.47203i	0.117821	−	0.204072i	−0.801083	−	0.598553i	$-0.795742\pi$
$719$	3.15928	−	5.47203i	0.117821	−	0.204072i	0.918904	+	0.394481i	$0.129076\pi$
$720$	−2.22970	+	0.168678i	−0.0830959	+	0.00628625i
$721$	44.4674			1.65605
$722$	0.755144	−	0.435983i	0.0281036	−	0.0162256i
$723$	−10.0963	+	5.82911i	−0.375486	+	0.216787i
$724$	−2.85456	−	4.94424i	−0.106089	−	0.183751i
$725$	−28.8851	−	36.1159i	−1.07277	−	1.34131i
$726$	5.28959	+	9.16184i	0.196315	+	0.340028i
$727$	43.2003	+	24.9417i	1.60221	+	0.925037i	0.991044	+	0.133535i	$0.0426329\pi$
$727$	43.2003	+	24.9417i	1.60221	+	0.925037i	0.611167	+	0.791502i	$0.290700\pi$
$728$		−	9.63487i		−	0.357092i
$729$	−1.00000			−0.0370370
$730$	19.0012	−	1.43745i	0.703264	−	0.0532023i
$731$	3.04233	+	5.26947i	0.112525	+	0.194898i
$732$	−7.02706	−	4.05708i	−0.259728	−	0.149954i
$733$	−4.50464	+	2.60076i	−0.166383	+	0.0960611i	−0.580879	−	0.813990i	$-0.697291\pi$
$733$	−4.50464	+	2.60076i	−0.166383	+	0.0960611i	0.414496	+	0.910051i	$0.363958\pi$
$734$	5.99388	+	10.3817i	0.221238	+	0.383196i
$735$	21.0850	+	10.1356i	0.777731	+	0.373859i
$736$	4.34823			0.160278
$737$	6.18683	+	3.57197i	0.227895	+	0.131575i
$738$	3.54596	+	2.04726i	0.130529	+	0.0753608i
$739$	−11.0996	−	19.2251i	−0.408305	−	0.707205i	0.586395	−	0.810025i	$-0.300547\pi$
$739$	−11.0996	−	19.2251i	−0.408305	−	0.707205i	−0.994700	+	0.102820i	$0.967213\pi$
$740$	20.3724	−	13.9108i	0.748905	−	0.511371i
$741$	4.90840	−	8.50159i	0.180314	−	0.312314i
$742$			26.6670i			0.978977i
$743$		−	1.61481i		−	0.0592417i	−0.999561	−	0.0296208i	$-0.990570\pi$
$743$		−	1.61481i		−	0.0592417i	0.999561	−	0.0296208i	$-0.00942999\pi$
$744$	−2.88265	−	4.76343i	−0.105683	−	0.174636i
$745$	−17.0367	−	24.9504i	−0.624178	−	0.914112i
$746$	25.4624			0.932246
$747$	2.43251	+	1.40441i	0.0890010	+	0.0513848i
$748$			0.670287i			0.0245081i
$749$	−36.8054	−	63.7489i	−1.34484	−	2.32933i
$750$	−3.27280	+	10.6906i	−0.119506	+	0.390365i
$751$	−20.9612	+	36.3059i	−0.764885	+	1.32482i	0.175423	+	0.984493i	$0.443871\pi$
$751$	−20.9612	+	36.3059i	−0.764885	+	1.32482i	−0.940307	+	0.340326i	$0.889463\pi$
$752$		−	3.42912i		−	0.125047i
$753$	−6.93717	+	4.00518i	−0.252805	+	0.145957i
$754$	−10.6628	−	18.4685i	−0.388315	−	0.672582i
$755$	0.0682404	−	0.141959i	0.00248352	−	0.00516643i
$756$	2.08940	−	3.61895i	0.0759908	−	0.131620i
$757$	−40.1491	+	23.1801i	−1.45924	+	0.842494i	−0.998974	−	0.0452857i	$-0.985580\pi$
$757$	−40.1491	+	23.1801i	−1.45924	+	0.842494i	−0.460268	+	0.887780i	$0.652247\pi$
$758$	22.6189	+	13.0590i	0.821555	+	0.474325i
$759$	−2.82073			−0.102386
$760$	7.86242	−	5.36865i	0.285200	−	0.194742i
$761$	14.5814	−	25.2557i	0.528574	−	0.915517i	−0.470871	−	0.882202i	$-0.656060\pi$
$761$	14.5814	−	25.2557i	0.528574	−	0.915517i	0.999445	−	0.0333149i	$-0.0106064\pi$
$762$	−9.67454	+	5.58560i	−0.350471	+	0.202345i
$763$	38.2856	+	22.1042i	1.38603	+	0.800226i
$764$	1.70884	+	2.95980i	0.0618238	+	0.107082i
$765$	−2.08235	−	1.00099i	−0.0752875	−	0.0361910i
$766$	−2.10383	−	3.64393i	−0.0760143	−	0.131661i
$767$		−	2.64998i		−	0.0956854i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−9.10847	+	15.7763i	−0.328460	+	0.568909i	−0.982206	−	0.187804i	$-0.939863\pi$
$769$	−9.10847	+	15.7763i	−0.328460	+	0.568909i	0.653747	+	0.756714i	$0.273196\pi$
$770$	−2.62616	+	5.46316i	−0.0946403	+	0.196878i
$771$	−7.19644			−0.259173
$772$	7.24575	+	4.18334i	0.260780	+	0.150562i
$773$		−	5.29041i		−	0.190283i	−0.995464	−	0.0951415i	$-0.969670\pi$
$773$		−	5.29041i		−	0.190283i	0.995464	−	0.0951415i	$-0.0303303\pi$
$774$	5.88877			0.211668
$775$	−27.4298	+	4.75433i	−0.985309	+	0.170780i
$776$	0.0488039			0.00175196
$777$			46.1013i			1.65388i
$778$	−3.33799	−	1.92719i	−0.119673	−	0.0690930i
$779$	−17.4333			−0.624612
$780$	−2.23365	+	4.64662i	−0.0799774	+	0.166376i
$781$	−1.11095	+	1.92423i	−0.0397530	+	0.0688542i
$782$	3.89094	+	2.24644i	0.139140	+	0.0803324i
$783$		−	9.24924i		−	0.330541i
$784$	5.23119	+	9.06069i	0.186828	+	0.323596i
$785$	−14.3545	−	6.90027i	−0.512334	−	0.246281i
$786$	10.5535	+	18.2793i	0.376432	+	0.652000i
$787$	−23.3470	−	13.4794i	−0.832229	−	0.480488i	0.0223862	−	0.999749i	$-0.492874\pi$
$787$	−23.3470	−	13.4794i	−0.832229	−	0.480488i	−0.854615	+	0.519262i	$0.826207\pi$
$788$	6.05411	−	3.49534i	0.215669	−	0.124516i
$789$	9.12663	−	15.8078i	0.324917	−	0.562772i
$790$	−31.3081	+	21.3779i	−1.11389	+	0.760593i
$791$	23.5537			0.837473
$792$	0.561798	+	0.324354i	0.0199626	+	0.0115254i
$793$	−16.2020	+	9.35421i	−0.575349	+	0.332178i
$794$	4.63450	−	8.02719i	0.164472	−	0.284874i
$795$	6.18220	−	12.8607i	0.219260	−	0.456122i
$796$	−9.69109	−	16.7855i	−0.343492	−	0.594945i
$797$	16.0648	−	9.27502i	0.569045	−	0.328538i	−0.187723	−	0.982222i	$-0.560111\pi$
$797$	16.0648	−	9.27502i	0.569045	−	0.328538i	0.756768	+	0.653684i	$0.226777\pi$
$798$			17.7921i			0.629833i
$799$	1.77159	−	3.06849i	0.0626744	−	0.108555i
$800$	−3.90475	+	3.12297i	−0.138054	+	0.110414i
$801$	6.92500	+	11.9945i	0.244683	+	0.423803i
$802$		−	28.2958i		−	0.999159i
$803$	−4.78756	−	2.76410i	−0.168949	−	0.0975429i
$804$	−11.0126			−0.388383
$805$	22.9116	+	33.5541i	0.807526	+	1.18263i
$806$	−12.8346	+	0.264538i	−0.452080	+	0.00931794i
$807$		−	19.0602i		−	0.670950i
$808$			10.9441i			0.385012i
$809$	−18.2757	+	31.6544i	−0.642538	+	1.11291i	0.342326	+	0.939581i	$0.388785\pi$
$809$	−18.2757	+	31.6544i	−0.642538	+	1.11291i	−0.984864	+	0.173328i	$0.944548\pi$
$810$	−1.84664	+	1.26093i	−0.0648841	+	0.0443045i
$811$	−25.2274	−	43.6952i	−0.885854	−	1.53434i	−0.844731	−	0.535191i	$-0.820240\pi$
$811$	−25.2274	−	43.6952i	−0.885854	−	1.53434i	−0.0411230	−	0.999154i	$-0.513094\pi$
$812$	33.4725	+	19.3254i	1.17466	+	0.678188i
$813$	−12.9022	−	7.44907i	−0.452499	−	0.261250i
$814$	−7.15667			−0.250841
$815$	7.52890	+	3.61917i	0.263726	+	0.126774i
$816$	−0.516632	−	0.894833i	−0.0180857	−	0.0313254i
$817$	−21.7135	+	12.5363i	−0.759661	+	0.438590i
$818$	9.96074	+	5.75084i	0.348269	+	0.201073i
$819$	−4.81744	−	8.34404i	−0.168335	−	0.291565i
$820$	9.12955	−	0.690655i	0.318818	−	0.0241187i
$821$	−37.4675			−1.30763			−0.653813	−	0.756657i	$-0.726832\pi$
$821$	−37.4675			−1.30763			−0.653813	+	0.756657i	$0.726832\pi$
$822$		−	13.5341i		−	0.472056i
$823$	25.2288	+	14.5658i	0.879420	+	0.507733i	0.870467	−	0.492227i	$-0.163817\pi$
$823$	25.2288	+	14.5658i	0.879420	+	0.507733i	0.00895262	+	0.999960i	$0.497150\pi$
$824$	−5.32059	−	9.21554i	−0.185352	−	0.321038i
$825$	2.53304	−	2.02590i	0.0881892	−	0.0705327i
$826$	2.40144	+	4.15941i	0.0835566	+	0.144724i
$827$	33.5228	−	19.3544i	1.16570	−	0.673018i	0.213037	−	0.977044i	$-0.431664\pi$
$827$	33.5228	−	19.3544i	1.16570	−	0.673018i	0.952664	+	0.304026i	$0.0983311\pi$
$828$	3.76568	−	2.17412i	0.130866	−	0.0755558i
$829$	−26.1448			−0.908045			−0.454023	−	0.890990i	$-0.650011\pi$
$829$	−26.1448			−0.908045			−0.454023	+	0.890990i	$0.650011\pi$
$830$	6.26283	−	0.473786i	0.217386	−	0.0164454i
$831$	−3.66623	+	6.35010i	−0.127180	+	0.220283i
$832$	−1.99676	+	1.15283i	−0.0692250	+	0.0399671i
$833$			10.8104i			0.374558i
$834$	4.66929	−	8.08746i	0.161684	−	0.280046i
$835$	−27.0604	+	18.4775i	−0.936463	+	0.639440i
$836$	−2.76201			−0.0955260
$837$	−4.87817	−	2.68393i	−0.168614	−	0.0927701i
$838$			8.65168i			0.298867i
$839$	30.8280			1.06430			0.532151	−	0.846650i	$-0.321384\pi$
$839$	30.8280			1.06430			0.532151	+	0.846650i	$0.321384\pi$
$840$	−0.704870	−	9.31746i	−0.0243203	−	0.321483i
$841$	56.5485			1.94995
$842$	9.53864	−	5.50713i	0.328723	−	0.189788i
$843$	1.72553	+	0.996238i	0.0594306	+	0.0343123i
$844$	2.42712	−	4.20389i	0.0835449	−	0.144704i
$845$	−9.68891	−	14.1895i	−0.333309	−	0.488132i
$846$	−1.71456	−	2.96970i	−0.0589478	−	0.102101i
$847$	−38.2855	+	22.1041i	−1.31551	+	0.759507i
$848$	5.52654	−	3.19075i	0.189782	−	0.109571i
$849$	−7.60755	+	13.1767i	−0.261090	+	0.452222i
$850$	−5.10752	+	0.777221i	−0.175187	+	0.0266585i
$851$	−23.9853	+	41.5437i	−0.822204	+	1.42410i
$852$		−	3.42512i		−	0.117343i
$853$		−	51.4472i		−	1.76152i	−0.473565	−	0.880759i	$-0.657033\pi$
$853$		−	51.4472i		−	1.76152i	0.473565	−	0.880759i	$-0.342967\pi$
$854$	16.9537	−	29.3647i	0.580144	−	1.00484i
$855$	4.12473	−	8.58060i	0.141063	−	0.293450i
$856$	−8.80765	+	15.2553i	−0.301039	+	0.521416i
$857$	−23.4617	+	13.5456i	−0.801436	+	0.462709i	−0.843973	−	0.536386i	$-0.819789\pi$
$857$	−23.4617	+	13.5456i	−0.801436	+	0.462709i	0.0425371	+	0.999095i	$0.486456\pi$
$858$	1.29531	−	0.747848i	0.0442212	−	0.0255311i
$859$	20.0650	+	34.7535i	0.684608	+	1.18578i	0.973560	+	0.228432i	$0.0733599\pi$
$859$	20.0650	+	34.7535i	0.684608	+	1.18578i	−0.288952	+	0.957344i	$0.593307\pi$
$860$	10.8744	−	7.42531i	0.370814	−	0.253201i
$861$	−8.55511	+	14.8179i	−0.291557	+	0.504992i
$862$	−7.75482	−	4.47725i	−0.264130	−	0.152496i
$863$	−13.9376	+	8.04690i	−0.474443	+	0.273920i	−0.718098	−	0.695942i	$-0.754987\pi$
$863$	−13.9376	+	8.04690i	−0.474443	+	0.273920i	0.243655	+	0.969862i	$0.421654\pi$
$864$	−1.00000			−0.0340207
$865$	−3.84519	−	50.8284i	−0.130740	−	1.72822i
$866$	−19.2723			−0.654901
$867$			15.9324i			0.541092i
$868$	19.9054	−	12.0460i	0.675635	−	0.408869i
$869$	10.9983			0.373091
$870$	−11.6626	−	17.0800i	−0.395400	−	0.579065i
$871$	−12.6956	+	21.9894i	−0.430173	+	0.745082i
$872$		−	10.5792i		−	0.358257i
$873$	0.0422654	−	0.0244019i	0.00143047	−	0.000825880i
$874$	−9.25674	+	16.0331i	−0.313114	+	0.542329i
$875$	−44.6739	−	13.6764i	−1.51025	−	0.462346i
$876$	8.52186			0.287927
$877$	26.9478	−	15.5583i	0.909962	−	0.525367i	0.0295428	−	0.999564i	$-0.490595\pi$
$877$	26.9478	−	15.5583i	0.909962	−	0.525367i	0.880419	+	0.474197i	$0.157262\pi$
$878$	−19.3241	+	11.1568i	−0.652156	+	0.376522i
$879$	−5.92034	−	10.2543i	−0.199688	−	0.345870i
$880$	1.44642	−	0.109423i	0.0487589	−	0.00368863i
$881$	16.4059	+	28.4159i	0.552730	+	0.957357i	0.998076	+	0.0619982i	$0.0197473\pi$
$881$	16.4059	+	28.4159i	0.552730	+	0.957357i	−0.445346	+	0.895358i	$0.646919\pi$
$882$	9.06069	+	5.23119i	0.305089	+	0.176143i
$883$		−	18.7969i		−	0.632566i	−0.948665	−	0.316283i	$-0.897565\pi$
$883$		−	18.7969i		−	0.632566i	0.948665	−	0.316283i	$-0.102435\pi$
$884$	−2.38235			−0.0801271
$885$	−0.193868	−	2.56268i	−0.00651681	−	0.0861437i
$886$	−17.8033	−	30.8361i	−0.598112	−	1.03596i
$887$	22.2796	+	12.8631i	0.748076	+	0.431902i	0.824998	−	0.565135i	$-0.191176\pi$
$887$	22.2796	+	12.8631i	0.748076	+	0.431902i	−0.0769225	+	0.997037i	$0.524509\pi$
$888$	9.55416	−	5.51609i	0.320616	−	0.185108i
$889$	−23.3411	−	40.4280i	−0.782835	−	1.35591i
$890$	27.9121	+	13.4175i	0.935615	+	0.449754i
$891$	0.648708			0.0217325
$892$	−19.9058	−	11.4926i	−0.666497	−	0.384802i
$893$	12.6441	+	7.30008i	0.423119	+	0.244288i
$894$	−6.75564	−	11.7011i	−0.225942	−	0.391343i
$895$	5.47492	+	8.01805i	0.183006	+	0.268014i
$896$	2.08940	−	3.61895i	0.0698020	−	0.120901i
$897$		−	10.0255i		−	0.334742i
$898$			13.1892i			0.440129i
$899$	24.8243	−	45.1194i	0.827937	−	1.50481i
$900$	−1.82012	+	4.65695i	−0.0606708	+	0.155232i
$901$	6.59377			0.219670
$902$	−2.30030	−	1.32808i	−0.0765914	−	0.0442201i
$903$			24.6080i			0.818903i
$904$	−2.81823	−	4.88133i	−0.0937331	−	0.162350i
$905$	−12.7296	+	0.963001i	−0.423146	+	0.0320112i
$906$	0.0352202	−	0.0610031i	0.00117011	−	0.00202669i
$907$		−	28.3313i		−	0.940727i	−0.882473	−	0.470363i	$-0.844123\pi$
$907$		−	28.3313i		−	0.940727i	0.882473	−	0.470363i	$-0.155877\pi$
$908$	−24.7366	+	14.2817i	−0.820912	+	0.473954i
$909$	5.47205	+	9.47788i	0.181497	+	0.314361i
$910$	−19.4173	−	9.33397i	−0.643677	−	0.309418i
$911$	−24.9501	+	43.2148i	−0.826633	+	1.43177i	0.0740320	+	0.997256i	$0.476413\pi$
$911$	−24.9501	+	43.2148i	−0.826633	+	1.43177i	−0.900665	+	0.434514i	$0.856920\pi$
$912$	3.68728	−	2.12885i	0.122098	−	0.0704933i
$913$	−1.57799	−	0.911054i	−0.0522239	−	0.0301515i
$914$	−33.3758			−1.10397
$915$	−14.9839	+	10.2314i	−0.495352	+	0.338238i
$916$	−9.84097	+	17.0451i	−0.325155	+	0.563185i
$917$	−76.3855	+	44.1012i	−2.52247	+	1.45635i
$918$	−0.894833	−	0.516632i	−0.0295339	−	0.0170514i
$919$	22.2482	+	38.5351i	0.733901	+	1.27115i	0.955204	+	0.295949i	$0.0956358\pi$
$919$	22.2482	+	38.5351i	0.733901	+	1.27115i	−0.221303	+	0.975205i	$0.571031\pi$
$920$	4.21243	−	8.76305i	0.138880	−	0.288909i
$921$	−0.876385	−	1.51794i	−0.0288779	−	0.0500179i
$922$			6.63396i			0.218478i
$923$	−6.83913	−	3.94857i	−0.225113	−	0.129969i
$924$	−1.35541	+	2.34764i	−0.0445898	+	0.0772317i
$925$	−8.29841	−	54.5332i	−0.272850	−	1.79304i
$926$	2.20118			0.0723353
$927$	−9.21554	−	5.32059i	−0.302678	−	0.174751i
$928$		−	9.24924i		−	0.303621i
$929$	−45.5312			−1.49383			−0.746916	−	0.664919i	$-0.768466\pi$
$929$	−45.5312			−1.49383			−0.746916	+	0.664919i	$0.768466\pi$
$930$	−12.3924	+	1.19478i	−0.406364	+	0.0391784i
$931$	−44.5457			−1.45993
$932$		−	18.3751i		−	0.601897i
$933$	1.27574	+	0.736550i	0.0417659	+	0.0241136i
$934$	−29.5855			−0.968067
$935$	1.35084	+	0.649353i	0.0441771	+	0.0212361i
$936$	−1.15283	+	1.99676i	−0.0376813	+	0.0652660i
$937$	−38.5767	−	22.2723i	−1.26025	−	0.727604i	−0.287125	−	0.957893i	$-0.592699\pi$
$937$	−38.5767	−	22.2723i	−1.26025	−	0.727604i	−0.973122	+	0.230289i	$0.926033\pi$
$938$		−	46.0193i		−	1.50258i
$939$	−0.653321	−	1.13158i	−0.0213203	−	0.0369279i
$940$	−6.91075	−	3.32202i	−0.225404	−	0.108352i
$941$	8.22945	+	14.2538i	0.268273	+	0.464662i	0.968416	−	0.249341i	$-0.0802139\pi$
$941$	8.22945	+	14.2538i	0.268273	+	0.464662i	−0.700143	+	0.714002i	$0.746881\pi$
$942$	−6.16845	−	3.56136i	−0.200979	−	0.116035i
$943$	−15.4187	+	8.90197i	−0.502101	+	0.289888i
$944$	0.574671	−	0.995359i	0.0187039	−	0.0323962i
$945$	−5.26917	−	7.71672i	−0.171406	−	0.251025i
$946$	−3.82009			−0.124202
$947$	31.4105	+	18.1349i	1.02070	+	0.589304i	0.914308	−	0.405020i	$-0.132735\pi$
$947$	31.4105	+	18.1349i	1.02070	+	0.589304i	0.106397	+	0.994324i	$0.466069\pi$
$948$	−14.6827	+	8.47707i	−0.476872	+	0.275322i
$949$	9.82423	−	17.0161i	0.318908	−	0.552365i
$950$	−3.20264	−	21.0462i	−0.103908	−	0.682830i
$951$	10.3763	+	17.9723i	0.336475	+	0.582791i
$952$	3.73933	−	2.15890i	0.121192	−	0.0699704i
$953$			32.2234i			1.04382i	0.853001	+	0.521910i	$0.174780\pi$
$953$			32.2234i			1.04382i	−0.853001	+	0.521910i	$0.825220\pi$
$954$	3.19075	−	5.52654i	0.103304	−	0.178928i
$955$	7.62040	−	0.576487i	0.246591	−	0.0186547i
$956$	4.25215	+	7.36494i	0.137524	+	0.238199i
$957$			6.00006i			0.193954i
$958$	20.4764	+	11.8221i	0.661562	+	0.381953i
$959$	56.5563			1.82630
$960$	−1.84664	+	1.26093i	−0.0595999	+	0.0406963i
$961$	−16.5931	−	26.1853i	−0.535260	−	0.844687i
$962$		−	25.4364i		−	0.820103i
$963$			17.6153i			0.567645i
$964$	−5.82911	+	10.0963i	−0.187743	+	0.325180i
$965$	15.4502	−	10.5498i	0.497359	−	0.339609i
$966$	9.08520	+	15.7360i	0.292311	+	0.506298i
$967$	−9.42857	−	5.44359i	−0.303202	−	0.175054i	0.340678	−	0.940180i	$-0.389343\pi$
$967$	−9.42857	−	5.44359i	−0.303202	−	0.175054i	−0.643881	+	0.765126i	$0.722677\pi$
$968$	9.16184	+	5.28959i	0.294473	+	0.170014i
$969$	4.39933			0.141327
$970$	0.0472797	−	0.0983551i	0.00151806	−	0.00315799i
$971$	−1.12529	−	1.94907i	−0.0361124	−	0.0625485i	0.847404	−	0.530948i	$-0.178164\pi$
$971$	−1.12529	−	1.94907i	−0.0361124	−	0.0625485i	−0.883517	+	0.468400i	$0.844831\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	33.7959	+	19.5121i	1.08345	+	0.625528i
$974$	−7.05898	−	12.2265i	−0.226184	−	0.391763i
$975$	7.20050	+	9.00300i	0.230600	+	0.288327i
$976$	−8.11415			−0.259728
$977$		−	28.2024i		−	0.902276i	−0.892454	−	0.451138i	$-0.851018\pi$
$977$		−	28.2024i		−	0.902276i	0.892454	−	0.451138i	$-0.148982\pi$
$978$	3.23534	+	1.86792i	0.103455	+	0.0597296i
$979$	−4.49230	−	7.78090i	−0.143575	−	0.248679i
$980$	23.3279	−	1.76477i	0.745184	−	0.0563735i
$981$	−5.28960	−	9.16186i	−0.168884	−	0.292516i
$982$	15.7167	−	9.07404i	0.501540	−	0.289564i
$983$	−30.2842	+	17.4846i	−0.965917	+	0.557672i	−0.897989	−	0.440018i	$-0.854972\pi$
$983$	−30.2842	+	17.4846i	−0.965917	+	0.557672i	−0.0679278	+	0.997690i	$0.521639\pi$
$984$	4.09453			0.130529
$985$	−1.17917	−	15.5871i	−0.0375716	−	0.496647i
$986$	4.77845	−	8.27653i	0.152177	−	0.263578i
$987$	12.4098	−	7.16480i	0.395008	−	0.228058i
$988$		−	9.81679i		−	0.312314i
$989$	−12.8029	+	22.1752i	−0.407108	+	0.705131i
$990$	1.19793	−	0.817974i	0.0380726	−	0.0259969i
$991$	43.5255			1.38263			0.691316	−	0.722552i	$-0.257031\pi$
$991$	43.5255			1.38263			0.691316	+	0.722552i	$0.257031\pi$
$992$	−4.87817	−	2.68393i	−0.154882	−	0.0852148i
$993$			30.7046i			0.974382i
$994$	14.3129			0.453978
$995$	−43.2164	+	3.26934i	−1.37005	+	0.103645i
$996$	2.80883			0.0890010
$997$	−16.6835	+	9.63223i	−0.528372	+	0.305056i	−0.740353	−	0.672218i	$-0.765342\pi$
$997$	−16.6835	+	9.63223i	−0.528372	+	0.305056i	0.211981	+	0.977274i	$0.432008\pi$
$998$	−23.8724	−	13.7827i	−0.755668	−	0.436285i
$999$	5.51609	−	9.55416i	0.174522	−	0.302280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.c.439.2	✓	24
5.4	even	2	inner	930.2.s.c.439.12	yes	24
31.25	even	3	inner	930.2.s.c.769.6	yes	24
155.149	even	6	inner	930.2.s.c.769.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.c.439.2	✓	24	1.1	even	1	trivial
930.2.s.c.439.12	yes	24	5.4	even	2	inner
930.2.s.c.769.6	yes	24	31.25	even	3	inner
930.2.s.c.769.8	yes	24	155.149	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.968769 + 2.01531i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-3.61895 - 2.08940i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.968769 + 2.01531i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-3.61895 - 2.08940i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.01531 + 0.968769i) q^{10} +(-0.324354 - 0.561798i) q^{11} +(0.866025 + 0.500000i) q^{12} +(1.99676 - 1.15283i) q^{13} +(-2.08940 + 3.61895i) q^{14} +(1.84664 - 1.26093i) q^{15} +1.00000 q^{16} +(0.894833 + 0.516632i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.12885 + 3.68728i) q^{19} +(0.968769 - 2.01531i) q^{20} +(2.08940 + 3.61895i) q^{21} +(-0.561798 + 0.324354i) q^{22} +4.34823i q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.12297 - 3.90475i) q^{25} +(-1.15283 - 1.99676i) q^{26} -1.00000i q^{27} +(3.61895 + 2.08940i) q^{28} +9.24924 q^{29} +(-1.26093 - 1.84664i) q^{30} +(2.68393 - 4.87817i) q^{31} -1.00000i q^{32} +0.648708i q^{33} +(0.516632 - 0.894833i) q^{34} +(7.71672 - 5.26917i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.55416 + 5.51609i) q^{37} +(3.68728 + 2.12885i) q^{38} -2.30565 q^{39} +(-2.01531 - 0.968769i) q^{40} +(2.04726 + 3.54596i) q^{41} +(3.61895 - 2.08940i) q^{42} +(5.09983 + 2.94439i) q^{43} +(0.324354 + 0.561798i) q^{44} +(-2.22970 + 0.168678i) q^{45} +4.34823 q^{46} -3.42912i q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.23119 + 9.06069i) q^{49} +(-3.90475 + 3.12297i) q^{50} +(-0.516632 - 0.894833i) q^{51} +(-1.99676 + 1.15283i) q^{52} +(5.52654 - 3.19075i) q^{53} -1.00000 q^{54} +(1.44642 - 0.109423i) q^{55} +(2.08940 - 3.61895i) q^{56} +(3.68728 - 2.12885i) q^{57} -9.24924i q^{58} +(0.574671 - 0.995359i) q^{59} +(-1.84664 + 1.26093i) q^{60} -8.11415 q^{61} +(-4.87817 - 2.68393i) q^{62} -4.17880i q^{63} -1.00000 q^{64} +(0.388912 + 5.14091i) q^{65} +0.648708 q^{66} +(-9.53716 + 5.50628i) q^{67} +(-0.894833 - 0.516632i) q^{68} +(2.17412 - 3.76568i) q^{69} +(-5.26917 - 7.71672i) q^{70} +(-1.71256 - 2.96624i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.38014 - 4.26093i) q^{73} +(5.51609 - 9.55416i) q^{74} +(0.752200 + 4.94310i) q^{75} +(2.12885 - 3.68728i) q^{76} +2.71082i q^{77} +2.30565i q^{78} +(-8.47707 + 14.6827i) q^{79} +(-0.968769 + 2.01531i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.54596 - 2.04726i) q^{82} +(2.43251 - 1.40441i) q^{83} +(-2.08940 - 3.61895i) q^{84} +(-1.90806 + 1.30287i) q^{85} +(2.94439 - 5.09983i) q^{86} +(-8.01008 - 4.62462i) q^{87} +(0.561798 - 0.324354i) q^{88} +13.8500 q^{89} +(0.168678 + 2.22970i) q^{90} -9.63487 q^{91} -4.34823i q^{92} +(-4.76343 + 2.88265i) q^{93} -3.42912 q^{94} +(-5.36865 - 7.86242i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.0488039i q^{97} +(9.06069 - 5.23119i) q^{98} +(0.324354 - 0.561798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

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