LMFDB - Embedded newform 930.2.s.d.439.6

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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.6
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.02320 + 1.98823i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.02320 + 1.98823i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.98823 - 1.02320i) q^{10} +(1.12401 + 1.94684i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.52471 + 2.61234i) q^{13} +(-2.28961 + 3.96572i) q^{14} +(-0.107998 + 2.23346i) q^{15} +1.00000 q^{16} +(1.87651 + 1.08340i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.884673 - 1.53230i) q^{19} +(-1.02320 - 1.98823i) q^{20} +(-2.28961 - 3.96572i) q^{21} +(1.94684 - 1.12401i) q^{22} +7.60749i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.90612 + 4.06872i) q^{25} +(2.61234 + 4.52471i) q^{26} +1.00000i q^{27} +(3.96572 + 2.28961i) q^{28} -3.56764 q^{29} +(2.23346 + 0.107998i) q^{30} +(1.86454 + 5.24628i) q^{31} -1.00000i q^{32} +2.24801i q^{33} +(1.08340 - 1.87651i) q^{34} +(0.494547 - 10.2275i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.84176 - 1.64069i) q^{37} +(-1.53230 - 0.884673i) q^{38} -5.22469 q^{39} +(-1.98823 + 1.02320i) q^{40} +(1.66046 + 2.87600i) q^{41} +(-3.96572 + 2.28961i) q^{42} +(-0.967335 - 0.558491i) q^{43} +(-1.12401 - 1.94684i) q^{44} +(-1.21026 + 1.88023i) q^{45} +7.60749 q^{46} -1.34764i q^{47} +(0.866025 + 0.500000i) q^{48} +(6.98462 + 12.0977i) q^{49} +(4.06872 + 2.90612i) q^{50} +(1.08340 + 1.87651i) q^{51} +(4.52471 - 2.61234i) q^{52} +(-4.54951 + 2.62666i) q^{53} +1.00000 q^{54} +(-2.72068 + 4.22679i) q^{55} +(2.28961 - 3.96572i) q^{56} +(1.53230 - 0.884673i) q^{57} +3.56764i q^{58} +(-2.77594 + 4.80807i) q^{59} +(0.107998 - 2.23346i) q^{60} -5.98443 q^{61} +(5.24628 - 1.86454i) q^{62} -4.57922i q^{63} -1.00000 q^{64} +(-9.82363 - 6.32322i) q^{65} +2.24801 q^{66} +(7.84436 - 4.52894i) q^{67} +(-1.87651 - 1.08340i) q^{68} +(-3.80374 + 6.58828i) q^{69} +(-10.2275 - 0.494547i) q^{70} +(-5.71934 - 9.90618i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-13.9615 + 8.06069i) q^{73} +(-1.64069 + 2.84176i) q^{74} +(-4.55113 + 2.07055i) q^{75} +(-0.884673 + 1.53230i) q^{76} -10.2941i q^{77} +5.22469i q^{78} +(-1.15794 + 2.00561i) q^{79} +(1.02320 + 1.98823i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.87600 - 1.66046i) q^{82} +(15.1446 - 8.74371i) q^{83} +(2.28961 + 3.96572i) q^{84} +(-0.234011 + 4.83946i) q^{85} +(-0.558491 + 0.967335i) q^{86} +(-3.08967 - 1.78382i) q^{87} +(-1.94684 + 1.12401i) q^{88} +0.683694 q^{89} +(1.88023 + 1.21026i) q^{90} +23.9250 q^{91} -7.60749i q^{92} +(-1.00840 + 5.47569i) q^{93} -1.34764 q^{94} +(3.95176 + 0.191086i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.66751i q^{97} +(12.0977 - 6.98462i) q^{98} +(-1.12401 + 1.94684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * 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
$5$	1.02320	+	1.98823i	0.457589	+	0.889164i
$5$	1.02320	+	1.98823i	0.457589	+	0.889164i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−3.96572	−	2.28961i	−1.49890	−	0.865391i	−0.498902	−	0.866659i	$-0.666263\pi$
$7$	−3.96572	−	2.28961i	−1.49890	−	0.865391i	−0.999999	+	0.00126771i	$0.999596\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.98823	−	1.02320i	0.628734	−	0.323564i
$11$	1.12401	+	1.94684i	0.338901	+	0.586994i	0.984226	−	0.176914i	$-0.0566115\pi$
$11$	1.12401	+	1.94684i	0.338901	+	0.586994i	−0.645325	+	0.763908i	$0.723278\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−4.52471	+	2.61234i	−1.25493	+	0.724534i	−0.972084	−	0.234632i	$-0.924612\pi$
$13$	−4.52471	+	2.61234i	−1.25493	+	0.724534i	−0.282845	+	0.959166i	$0.591278\pi$
$14$	−2.28961	+	3.96572i	−0.611924	+	1.05988i
$15$	−0.107998	+	2.23346i	−0.0278850	+	0.576676i
$16$	1.00000			0.250000
$17$	1.87651	+	1.08340i	0.455119	+	0.262763i	0.709990	−	0.704212i	$-0.248699\pi$
$17$	1.87651	+	1.08340i	0.455119	+	0.262763i	−0.254870	+	0.966975i	$0.582033\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	0.884673	−	1.53230i	0.202958	−	0.351534i	−0.746522	−	0.665361i	$-0.768278\pi$
$19$	0.884673	−	1.53230i	0.202958	−	0.351534i	0.949480	+	0.313827i	$0.101611\pi$
$20$	−1.02320	−	1.98823i	−0.228794	−	0.444582i
$21$	−2.28961	−	3.96572i	−0.499634	−	0.865391i
$22$	1.94684	−	1.12401i	0.415067	−	0.239639i
$23$			7.60749i			1.58627i	0.609046	+	0.793135i	$0.291553\pi$
$23$			7.60749i			1.58627i	−0.609046	+	0.793135i	$0.708447\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.90612	+	4.06872i	−0.581225	+	0.813743i
$26$	2.61234	+	4.52471i	0.512323	+	0.887369i
$27$			1.00000i			0.192450i
$28$	3.96572	+	2.28961i	0.749450	+	0.432695i
$29$	−3.56764			−0.662494			−0.331247	−	0.943544i	$-0.607469\pi$
$29$	−3.56764			−0.662494			−0.331247	+	0.943544i	$0.607469\pi$
$30$	2.23346	+	0.107998i	0.407772	+	0.0197177i
$31$	1.86454	+	5.24628i	0.334882	+	0.942260i
$31$	1.86454	+	5.24628i	0.334882	+	0.942260i
$32$		−	1.00000i		−	0.176777i
$33$			2.24801i			0.391329i
$34$	1.08340	−	1.87651i	0.185802	−	0.321818i
$35$	0.494547	−	10.2275i	0.0835937	−	1.72876i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.84176	−	1.64069i	−0.467183	−	0.269728i	0.247877	−	0.968792i	$-0.420267\pi$
$37$	−2.84176	−	1.64069i	−0.467183	−	0.269728i	−0.715060	+	0.699063i	$0.753600\pi$
$38$	−1.53230	−	0.884673i	−0.248572	−	0.143513i
$39$	−5.22469			−0.836620
$40$	−1.98823	+	1.02320i	−0.314367	+	0.161782i
$41$	1.66046	+	2.87600i	0.259321	+	0.449156i	0.966060	−	0.258318i	$-0.0831681\pi$
$41$	1.66046	+	2.87600i	0.259321	+	0.449156i	−0.706740	+	0.707474i	$0.749835\pi$
$42$	−3.96572	+	2.28961i	−0.611924	+	0.353294i
$43$	−0.967335	−	0.558491i	−0.147517	−	0.0851691i	0.424425	−	0.905463i	$-0.360476\pi$
$43$	−0.967335	−	0.558491i	−0.147517	−	0.0851691i	−0.571942	+	0.820294i	$0.693810\pi$
$44$	−1.12401	−	1.94684i	−0.169450	−	0.293497i
$45$	−1.21026	+	1.88023i	−0.180415	+	0.280289i
$46$	7.60749			1.12166
$47$		−	1.34764i		−	0.196573i	−0.995158	−	0.0982864i	$-0.968664\pi$
$47$		−	1.34764i		−	0.196573i	0.995158	−	0.0982864i	$-0.0313361\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	6.98462	+	12.0977i	0.997803	+	1.72824i
$50$	4.06872	+	2.90612i	0.575403	+	0.410988i
$51$	1.08340	+	1.87651i	0.151706	+	0.262763i
$52$	4.52471	−	2.61234i	0.627465	−	0.362267i
$53$	−4.54951	+	2.62666i	−0.624923	+	0.360800i	−0.778783	−	0.627293i	$-0.784163\pi$
$53$	−4.54951	+	2.62666i	−0.624923	+	0.360800i	0.153860	+	0.988093i	$0.450829\pi$
$54$	1.00000			0.136083
$55$	−2.72068	+	4.22679i	−0.366856	+	0.569940i
$56$	2.28961	−	3.96572i	0.305962	−	0.529942i
$57$	1.53230	−	0.884673i	0.202958	−	0.117178i
$58$			3.56764i			0.468454i
$59$	−2.77594	+	4.80807i	−0.361397	+	0.625957i	−0.988191	−	0.153227i	$-0.951033\pi$
$59$	−2.77594	+	4.80807i	−0.361397	+	0.625957i	0.626794	+	0.779185i	$0.284367\pi$
$60$	0.107998	−	2.23346i	0.0139425	−	0.288338i
$61$	−5.98443			−0.766228			−0.383114	−	0.923701i	$-0.625148\pi$
$61$	−5.98443			−0.766228			−0.383114	+	0.923701i	$0.625148\pi$
$62$	5.24628	−	1.86454i	0.666279	−	0.236797i
$63$		−	4.57922i		−	0.576927i
$64$	−1.00000			−0.125000
$65$	−9.82363	−	6.32322i	−1.21847	−	0.784299i
$66$	2.24801			0.276711
$67$	7.84436	−	4.52894i	0.958341	−	0.553298i	0.0626790	−	0.998034i	$-0.480036\pi$
$67$	7.84436	−	4.52894i	0.958341	−	0.553298i	0.895662	+	0.444735i	$0.146702\pi$
$68$	−1.87651	−	1.08340i	−0.227560	−	0.131382i
$69$	−3.80374	+	6.58828i	−0.457917	+	0.793135i
$70$	−10.2275	−	0.494547i	−1.22242	−	0.0591097i
$71$	−5.71934	−	9.90618i	−0.678760	−	1.17565i	−0.975355	−	0.220644i	$-0.929184\pi$
$71$	−5.71934	−	9.90618i	−0.678760	−	1.17565i	0.296594	−	0.955004i	$-0.404149\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−13.9615	+	8.06069i	−1.63407	+	0.943433i	−0.651254	+	0.758860i	$0.725757\pi$
$73$	−13.9615	+	8.06069i	−1.63407	+	0.943433i	−0.982819	+	0.184573i	$0.940910\pi$
$74$	−1.64069	+	2.84176i	−0.190727	+	0.330348i
$75$	−4.55113	+	2.07055i	−0.525520	+	0.239086i
$76$	−0.884673	+	1.53230i	−0.101479	+	0.175767i
$77$		−	10.2941i		−	1.17313i
$78$			5.22469i			0.591579i
$79$	−1.15794	+	2.00561i	−0.130278	+	0.225648i	−0.923784	−	0.382914i	$-0.874920\pi$
$79$	−1.15794	+	2.00561i	−0.130278	+	0.225648i	0.793506	+	0.608563i	$0.208254\pi$
$80$	1.02320	+	1.98823i	0.114397	+	0.222291i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.87600	−	1.66046i	0.317601	−	0.183367i
$83$	15.1446	−	8.74371i	1.66233	−	0.959747i	0.690733	−	0.723110i	$-0.257288\pi$
$83$	15.1446	−	8.74371i	1.66233	−	0.959747i	0.971598	−	0.236637i	$-0.0760452\pi$
$84$	2.28961	+	3.96572i	0.249817	+	0.432695i
$85$	−0.234011	+	4.83946i	−0.0253820	+	0.524913i
$86$	−0.558491	+	0.967335i	−0.0602237	+	0.104310i
$87$	−3.08967	−	1.78382i	−0.331247	−	0.191246i
$88$	−1.94684	+	1.12401i	−0.207534	+	0.119820i
$89$	0.683694			0.0724714			0.0362357	−	0.999343i	$-0.488463\pi$
$89$	0.683694			0.0724714			0.0362357	+	0.999343i	$0.488463\pi$
$90$	1.88023	+	1.21026i	0.198194	+	0.127572i
$91$	23.9250			2.50802
$92$		−	7.60749i		−	0.793135i
$93$	−1.00840	+	5.47569i	−0.104566	+	0.567802i
$94$	−1.34764			−0.138998
$95$	3.95176	+	0.191086i	0.405442	+	0.0196050i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			7.66751i			0.778518i	0.921128	+	0.389259i	$0.127269\pi$
$97$			7.66751i			0.778518i	−0.921128	+	0.389259i	$0.872731\pi$
$98$	12.0977	−	6.98462i	1.22205	−	0.705553i
$99$	−1.12401	+	1.94684i	−0.112967	+	0.195665i
$100$	2.90612	−	4.06872i	0.290612	−	0.406872i
$101$	−5.98825			−0.595853			−0.297927	−	0.954589i	$-0.596295\pi$
$101$	−5.98825			−0.595853			−0.297927	+	0.954589i	$0.596295\pi$
$102$	1.87651	−	1.08340i	0.185802	−	0.107273i
$103$	14.5737	−	8.41412i	1.43599	−	0.829068i	0.438420	−	0.898770i	$-0.355538\pi$
$103$	14.5737	−	8.41412i	1.43599	−	0.829068i	0.997568	+	0.0697018i	$0.0222048\pi$
$104$	−2.61234	−	4.52471i	−0.256161	−	0.443685i
$105$	5.54204	−	8.61000i	0.540847	−	0.840249i
$106$	2.62666	+	4.54951i	0.255124	+	0.441887i
$107$	0.423967	+	0.244777i	0.0409864	+	0.0236635i	0.520353	−	0.853951i	$-0.325800\pi$
$107$	0.423967	+	0.244777i	0.0409864	+	0.0236635i	−0.479367	+	0.877615i	$0.659134\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	20.0620			1.92159			0.960794	−	0.277264i	$-0.0894277\pi$
$109$	20.0620			1.92159			0.960794	+	0.277264i	$0.0894277\pi$
$110$	4.22679	+	2.72068i	0.403009	+	0.259407i
$111$	−1.64069	−	2.84176i	−0.155728	−	0.269728i
$112$	−3.96572	−	2.28961i	−0.374725	−	0.216348i
$113$	11.0431	−	6.37573i	1.03885	−	0.599778i	0.119340	−	0.992853i	$-0.461922\pi$
$113$	11.0431	−	6.37573i	1.03885	−	0.599778i	0.919506	+	0.393075i	$0.128589\pi$
$114$	−0.884673	−	1.53230i	−0.0828573	−	0.143513i
$115$	−15.1254	+	7.78398i	−1.41045	+	0.725860i
$116$	3.56764			0.331247
$117$	−4.52471	−	2.61234i	−0.418310	−	0.241511i
$118$	4.80807	+	2.77594i	0.442619	+	0.255546i
$119$	−4.96113	−	8.59293i	−0.454786	−	0.787712i
$120$	−2.23346	−	0.107998i	−0.203886	−	0.00985884i
$121$	2.97321	−	5.14976i	0.270292	−	0.468160i
$122$			5.98443i			0.541805i
$123$			3.32092i			0.299438i
$124$	−1.86454	−	5.24628i	−0.167441	−	0.471130i
$125$	−11.0631	−	1.61493i	−0.989513	−	0.144444i
$126$	−4.57922			−0.407949
$127$	15.5973	+	9.00509i	1.38403	+	0.799073i	0.992634	−	0.121148i	$-0.0386575\pi$
$127$	15.5973	+	9.00509i	1.38403	+	0.799073i	0.391400	+	0.920221i	$0.371991\pi$
$128$			1.00000i			0.0883883i
$129$	−0.558491	−	0.967335i	−0.0491724	−	0.0851691i
$130$	−6.32322	+	9.82363i	−0.554583	+	0.861589i
$131$	7.30917	−	12.6598i	0.638605	−	1.10610i	−0.347134	−	0.937815i	$-0.612845\pi$
$131$	7.30917	−	12.6598i	0.638605	−	1.10610i	0.985739	−	0.168280i	$-0.0538214\pi$
$132$		−	2.24801i		−	0.195665i
$133$	−7.01673	+	4.05111i	−0.608428	+	0.351276i
$134$	−4.52894	−	7.84436i	−0.391241	−	0.677649i
$135$	−1.98823	+	1.02320i	−0.171120	+	0.0880630i
$136$	−1.08340	+	1.87651i	−0.0929009	+	0.160909i
$137$	1.60457	−	0.926398i	0.137087	−	0.0791475i	−0.429888	−	0.902882i	$-0.641447\pi$
$137$	1.60457	−	0.926398i	0.137087	−	0.0791475i	0.566975	+	0.823735i	$0.308114\pi$
$138$	6.58828	+	3.80374i	0.560831	+	0.323796i
$139$	−2.99572			−0.254094			−0.127047	−	0.991897i	$-0.540550\pi$
$139$	−2.99572			−0.254094			−0.127047	+	0.991897i	$0.540550\pi$
$140$	−0.494547	+	10.2275i	−0.0417969	+	0.864381i
$141$	0.673818	−	1.16709i	0.0567457	−	0.0982864i
$142$	−9.90618	+	5.71934i	−0.831308	+	0.479956i
$143$	−10.1716	−	5.87259i	−0.850594	−	0.491090i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−3.65041	−	7.09330i	−0.303150	−	0.589066i
$146$	8.06069	+	13.9615i	0.667108	+	1.15546i
$147$			13.9692i			1.15216i
$148$	2.84176	+	1.64069i	0.233591	+	0.134864i
$149$	−0.824610	+	1.42827i	−0.0675547	+	0.117008i	−0.897824	−	0.440354i	$-0.854853\pi$
$149$	−0.824610	+	1.42827i	−0.0675547	+	0.117008i	0.830270	+	0.557362i	$0.188186\pi$
$150$	2.07055	+	4.55113i	0.169060	+	0.371599i
$151$	−6.63717			−0.540125			−0.270063	−	0.962843i	$-0.587044\pi$
$151$	−6.63717			−0.540125			−0.270063	+	0.962843i	$0.587044\pi$
$152$	1.53230	+	0.884673i	0.124286	+	0.0717565i
$153$			2.16680i			0.175176i
$154$	−10.2941			−0.829526
$155$	−8.52302	+	9.07514i	−0.684586	+	0.728932i
$156$	5.22469			0.418310
$157$			20.2828i			1.61874i	0.587299	+	0.809370i	$0.300191\pi$
$157$			20.2828i			1.61874i	−0.587299	+	0.809370i	$0.699809\pi$
$158$	2.00561	+	1.15794i	0.159558	+	0.0921206i
$159$	−5.25332			−0.416615
$160$	1.98823	−	1.02320i	0.157183	−	0.0808911i
$161$	17.4182	−	30.1692i	1.37274	−	2.37766i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			3.89243i			0.304879i	0.988313	+	0.152440i	$0.0487129\pi$
$163$			3.89243i			0.304879i	−0.988313	+	0.152440i	$0.951287\pi$
$164$	−1.66046	−	2.87600i	−0.129660	−	0.224578i
$165$	−4.46957	+	2.30017i	−0.347956	+	0.179068i
$166$	−8.74371	−	15.1446i	−0.678644	−	1.17545i
$167$	−10.6533	−	6.15070i	−0.824379	−	0.475956i	0.0275450	−	0.999621i	$-0.491231\pi$
$167$	−10.6533	−	6.15070i	−0.824379	−	0.475956i	−0.851924	+	0.523665i	$0.824564\pi$
$168$	3.96572	−	2.28961i	0.305962	−	0.176647i
$169$	7.14868	−	12.3819i	0.549898	−	0.952452i
$170$	4.83946	+	0.234011i	0.371170	+	0.0179478i
$171$	1.76935			0.135305
$172$	0.967335	+	0.558491i	0.0737586	+	0.0425846i
$173$	12.1122	−	6.99295i	0.920870	−	0.531664i	0.0369573	−	0.999317i	$-0.488233\pi$
$173$	12.1122	−	6.99295i	0.920870	−	0.531664i	0.883912	+	0.467652i	$0.154900\pi$
$174$	−1.78382	+	3.08967i	−0.135231	+	0.234227i
$175$	20.8406	−	9.48150i	1.57540	−	0.716734i
$176$	1.12401	+	1.94684i	0.0847252	+	0.146748i
$177$	−4.80807	+	2.77594i	−0.361397	+	0.208652i
$178$		−	0.683694i		−	0.0512450i
$179$	−1.89187	+	3.27682i	−0.141405	+	0.244921i	−0.928026	−	0.372515i	$-0.878495\pi$
$179$	−1.89187	+	3.27682i	−0.141405	+	0.244921i	0.786621	+	0.617436i	$0.211829\pi$
$180$	1.21026	−	1.88023i	0.0902073	−	0.140144i
$181$	−11.4105	−	19.7635i	−0.848133	−	1.46901i	−0.882872	−	0.469613i	$-0.844393\pi$
$181$	−11.4105	−	19.7635i	−0.848133	−	1.46901i	0.0347392	−	0.999396i	$-0.488940\pi$
$182$		−	23.9250i		−	1.77344i
$183$	−5.18267	−	2.99222i	−0.383114	−	0.221191i
$184$	−7.60749			−0.560831
$185$	0.354383	−	7.32883i	0.0260548	−	0.538827i
$186$	5.47569	+	1.00840i	0.401497	+	0.0739396i
$187$			4.87100i			0.356203i
$188$			1.34764i			0.0982864i
$189$	2.28961	−	3.96572i	0.166545	−	0.288464i
$190$	0.191086	−	3.95176i	0.0138628	−	0.286691i
$191$	12.2567	+	21.2293i	0.886867	+	1.53610i	0.843559	+	0.537037i	$0.180457\pi$
$191$	12.2567	+	21.2293i	0.886867	+	1.53610i	0.0433086	+	0.999062i	$0.486210\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−18.7716	−	10.8378i	−1.35121	−	0.780119i	−0.362788	−	0.931872i	$-0.618175\pi$
$193$	−18.7716	−	10.8378i	−1.35121	−	0.780119i	−0.988419	+	0.151752i	$0.951508\pi$
$194$	7.66751			0.550495
$195$	−5.34590	−	10.3879i	−0.382828	−	0.743892i
$196$	−6.98462	−	12.0977i	−0.498901	−	0.864122i
$197$	−17.3417	+	10.0122i	−1.23554	+	0.713341i	−0.968180	−	0.250255i	$-0.919485\pi$
$197$	−17.3417	+	10.0122i	−1.23554	+	0.713341i	−0.267362	+	0.963596i	$0.586152\pi$
$198$	1.94684	+	1.12401i	0.138356	+	0.0798797i
$199$	−2.41549	−	4.18375i	−0.171230	−	0.296578i	0.767620	−	0.640905i	$-0.221441\pi$
$199$	−2.41549	−	4.18375i	−0.171230	−	0.296578i	−0.938850	+	0.344326i	$0.888107\pi$
$200$	−4.06872	−	2.90612i	−0.287702	−	0.205494i
$201$	9.05789			0.638894
$202$			5.98825i			0.421332i
$203$	14.1483	+	8.16850i	0.993014	+	0.573317i
$204$	−1.08340	−	1.87651i	−0.0758532	−	0.131382i
$205$	−4.01917	+	6.24411i	−0.280711	+	0.436107i
$206$	−8.41412	−	14.5737i	−0.586240	−	1.01540i
$207$	−6.58828	+	3.80374i	−0.457917	+	0.264378i
$208$	−4.52471	+	2.61234i	−0.313732	+	0.181133i
$209$	3.97752			0.275131
$210$	−8.61000	−	5.54204i	−0.594146	−	0.382437i
$211$	−3.78481	+	6.55549i	−0.260557	+	0.451299i	−0.966390	−	0.257080i	$-0.917240\pi$
$211$	−3.78481	+	6.55549i	−0.260557	+	0.451299i	0.705833	+	0.708378i	$0.250573\pi$
$212$	4.54951	−	2.62666i	0.312462	−	0.180400i
$213$		−	11.4387i		−	0.783765i
$214$	0.244777	−	0.423967i	0.0167326	−	0.0289818i
$215$	0.120632	−	2.49473i	0.00822704	−	0.170139i
$216$	−1.00000			−0.0680414
$217$	4.61769	−	25.0744i	0.313469	−	1.70216i
$218$		−	20.0620i		−	1.35877i
$219$	−16.1214			−1.08938
$220$	2.72068	−	4.22679i	0.183428	−	0.284970i
$221$	−11.3209			−0.761524
$222$	−2.84176	+	1.64069i	−0.190727	+	0.110116i
$223$	−4.93546	−	2.84949i	−0.330503	−	0.190816i	0.325561	−	0.945521i	$-0.394447\pi$
$223$	−4.93546	−	2.84949i	−0.330503	−	0.190816i	−0.656064	+	0.754705i	$0.727780\pi$
$224$	−2.28961	+	3.96572i	−0.152981	+	0.264971i
$225$	−4.97667	−	0.482419i	−0.331778	−	0.0321612i
$226$	−6.37573	−	11.0431i	−0.424107	−	0.734576i
$227$	6.67585	−	3.85430i	0.443092	−	0.255819i	−0.261817	−	0.965118i	$-0.584322\pi$
$227$	6.67585	−	3.85430i	0.443092	−	0.255819i	0.704908	+	0.709299i	$0.250988\pi$
$228$	−1.53230	+	0.884673i	−0.101479	+	0.0585889i
$229$	−7.10263	+	12.3021i	−0.469355	+	0.812947i	−0.999386	−	0.0350314i	$-0.988847\pi$
$229$	−7.10263	+	12.3021i	−0.469355	+	0.812947i	0.530031	+	0.847978i	$0.322180\pi$
$230$	7.78398	+	15.1254i	0.513260	+	0.997342i
$231$	5.14707	−	8.91499i	0.338653	−	0.586564i
$232$		−	3.56764i		−	0.234227i
$233$			9.15400i			0.599699i	0.953987	+	0.299849i	$0.0969364\pi$
$233$			9.15400i			0.599699i	−0.953987	+	0.299849i	$0.903064\pi$
$234$	−2.61234	+	4.52471i	−0.170774	+	0.295790i
$235$	2.67941	−	1.37890i	0.174785	−	0.0899496i
$236$	2.77594	−	4.80807i	0.180698	−	0.312979i
$237$	−2.00561	+	1.15794i	−0.130278	+	0.0752162i
$238$	−8.59293	+	4.96113i	−0.556997	+	0.321582i
$239$	−11.2096	−	19.4156i	−0.725087	−	1.25589i	−0.958938	−	0.283615i	$-0.908466\pi$
$239$	−11.2096	−	19.4156i	−0.725087	−	1.25589i	0.233851	−	0.972272i	$-0.424867\pi$
$240$	−0.107998	+	2.23346i	−0.00697125	+	0.144169i
$241$	12.4504	−	21.5647i	0.802000	−	1.38910i	−0.116298	−	0.993214i	$-0.537103\pi$
$241$	12.4504	−	21.5647i	0.802000	−	1.38910i	0.918298	−	0.395890i	$-0.129564\pi$
$242$	−5.14976	−	2.97321i	−0.331039	−	0.191125i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.98443			0.383114
$245$	−16.9064	+	26.2654i	−1.08011	+	1.67804i
$246$	3.32092			0.211734
$247$			9.24428i			0.588200i
$248$	−5.24628	+	1.86454i	−0.333139	+	0.118398i
$249$	17.4874			1.10822
$250$	−1.61493	+	11.0631i	−0.102137	+	0.699691i
$251$	−5.08411	+	8.80594i	−0.320906	+	0.555826i	−0.980675	−	0.195643i	$-0.937321\pi$
$251$	−5.08411	+	8.80594i	−0.320906	+	0.555826i	0.659769	+	0.751468i	$0.270654\pi$
$252$			4.57922i			0.288464i
$253$	−14.8105	+	8.55087i	−0.931131	+	0.537589i
$254$	9.00509	−	15.5973i	0.565030	−	0.978660i
$255$	−2.62239	+	4.07409i	−0.164220	+	0.255129i
$256$	1.00000			0.0625000
$257$	−21.1909	+	12.2346i	−1.32185	+	0.763170i	−0.984024	−	0.178038i	$-0.943025\pi$
$257$	−21.1909	+	12.2346i	−1.32185	+	0.763170i	−0.337826	+	0.941208i	$0.609692\pi$
$258$	−0.967335	+	0.558491i	−0.0602237	+	0.0347701i
$259$	7.51309	+	13.0130i	0.466840	+	0.808591i
$260$	9.82363	+	6.32322i	0.609236	+	0.392150i
$261$	−1.78382	−	3.08967i	−0.110416	−	0.191246i
$262$	−12.6598	−	7.30917i	−0.782128	−	0.451562i
$263$			3.43008i			0.211508i	0.994392	+	0.105754i	$0.0337256\pi$
$263$			3.43008i			0.211508i	−0.994392	+	0.105754i	$0.966274\pi$
$264$	−2.24801			−0.138356
$265$	−9.87747	−	6.35788i	−0.606768	−	0.390561i
$266$	4.05111	+	7.01673i	0.248390	+	0.430223i
$267$	0.592096	+	0.341847i	0.0362357	+	0.0209207i
$268$	−7.84436	+	4.52894i	−0.479171	+	0.276649i
$269$	10.3450	+	17.9181i	0.630746	+	1.09248i	0.987399	+	0.158248i	$0.0505844\pi$
$269$	10.3450	+	17.9181i	0.630746	+	1.09248i	−0.356653	+	0.934237i	$0.616082\pi$
$270$	1.02320	+	1.98823i	0.0622700	+	0.121000i
$271$	20.3964			1.23899			0.619496	−	0.785000i	$-0.287337\pi$
$271$	20.3964			1.23899			0.619496	+	0.785000i	$0.287337\pi$
$272$	1.87651	+	1.08340i	0.113780	+	0.0656908i
$273$	20.7196	+	11.9625i	1.25401	+	0.724003i
$274$	−0.926398	−	1.60457i	−0.0559657	−	0.0969355i
$275$	−11.1876	−	1.08448i	−0.674640	−	0.0653969i
$276$	3.80374	−	6.58828i	0.228958	−	0.396568i
$277$		−	2.94909i		−	0.177193i	−0.996068	−	0.0885967i	$-0.971762\pi$
$277$		−	2.94909i		−	0.177193i	0.996068	−	0.0885967i	$-0.0282382\pi$
$278$			2.99572i			0.179672i
$279$	−3.61114	+	4.23788i	−0.216194	+	0.253715i
$280$	10.2275	+	0.494547i	0.611210	+	0.0295548i
$281$	23.5294			1.40365			0.701823	−	0.712351i	$-0.252370\pi$
$281$	23.5294			1.40365			0.701823	+	0.712351i	$0.252370\pi$
$282$	−1.16709	−	0.673818i	−0.0694990	−	0.0401253i
$283$			23.0945i			1.37282i	0.727213	+	0.686412i	$0.240815\pi$
$283$			23.0945i			1.37282i	−0.727213	+	0.686412i	$0.759185\pi$
$284$	5.71934	+	9.90618i	0.339380	+	0.587824i
$285$	3.32678	+	2.14137i	0.197062	+	0.126844i
$286$	−5.87259	+	10.1716i	−0.347253	+	0.601460i
$287$		−	15.2072i		−	0.897654i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−6.15249	−	10.6564i	−0.361911	−	0.626848i
$290$	−7.09330	+	3.65041i	−0.416533	+	0.214360i
$291$	−3.83376	+	6.64026i	−0.224739	+	0.389259i
$292$	13.9615	−	8.06069i	0.817037	−	0.471716i
$293$	2.22022	+	1.28185i	0.129707	+	0.0748863i	0.563449	−	0.826151i	$-0.309474\pi$
$293$	2.22022	+	1.28185i	0.129707	+	0.0748863i	−0.433743	+	0.901037i	$0.642807\pi$
$294$	13.9692			0.814702
$295$	−12.3999	−	0.599593i	−0.721950	−	0.0349096i
$296$	1.64069	−	2.84176i	0.0953633	−	0.165174i
$297$	−1.94684	+	1.12401i	−0.112967	+	0.0652215i
$298$	1.42827	+	0.824610i	0.0827373	+	0.0477684i
$299$	−19.8734	−	34.4217i	−1.14931	−	1.99066i
$300$	4.55113	−	2.07055i	0.262760	−	0.119543i
$301$	2.55745	+	4.42964i	0.147409	+	0.255320i
$302$			6.63717i			0.381926i
$303$	−5.18598	−	2.99412i	−0.297927	−	0.172008i
$304$	0.884673	−	1.53230i	0.0507395	−	0.0878834i
$305$	−6.12327	−	11.8984i	−0.350618	−	0.681302i
$306$	2.16680			0.123868
$307$	23.6615	+	13.6610i	1.35043	+	0.779673i	0.988310	−	0.152457i	$-0.0487186\pi$
$307$	23.6615	+	13.6610i	1.35043	+	0.779673i	0.362123	+	0.932130i	$0.382052\pi$
$308$			10.2941i			0.586564i
$309$	16.8282			0.957326
$310$	9.07514	+	8.52302i	0.515433	+	0.484075i
$311$	−5.87643			−0.333222			−0.166611	−	0.986023i	$-0.553282\pi$
$311$	−5.87643			−0.333222			−0.166611	+	0.986023i	$0.553282\pi$
$312$		−	5.22469i		−	0.295790i
$313$	−17.9705	−	10.3753i	−1.01575	−	0.586445i	−0.102881	−	0.994694i	$-0.532806\pi$
$313$	−17.9705	−	10.3753i	−1.01575	−	0.586445i	−0.912871	+	0.408249i	$0.866140\pi$
$314$	20.2828			1.14462
$315$	9.10454	−	4.68546i	0.512983	−	0.263996i
$316$	1.15794	−	2.00561i	0.0651391	−	0.112824i
$317$	23.6450	+	13.6514i	1.32803	+	0.766741i	0.984995	−	0.172580i	$-0.0552104\pi$
$317$	23.6450	+	13.6514i	1.32803	+	0.766741i	0.343039	+	0.939321i	$0.388544\pi$
$318$			5.25332i			0.294592i
$319$	−4.01006	−	6.94562i	−0.224520	−	0.388880i
$320$	−1.02320	−	1.98823i	−0.0571986	−	0.111145i
$321$	0.244777	+	0.423967i	0.0136621	+	0.0236635i
$322$	−30.1692	−	17.4182i	−1.68126	−	0.970677i
$323$	3.32019	−	1.91691i	0.184740	−	0.106660i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	2.52049	−	26.0016i	0.139811	−	1.44231i
$326$	3.89243			0.215582
$327$	17.3742	+	10.0310i	0.960794	+	0.554715i
$328$	−2.87600	+	1.66046i	−0.158801	+	0.0916836i
$329$	−3.08556	+	5.34434i	−0.170112	+	0.294643i
$330$	2.30017	+	4.46957i	0.126620	+	0.246042i
$331$	−1.32818	−	2.30048i	−0.0730034	−	0.126446i	0.827213	−	0.561889i	$-0.189925\pi$
$331$	−1.32818	−	2.30048i	−0.0730034	−	0.126446i	−0.900216	+	0.435443i	$0.856592\pi$
$332$	−15.1446	+	8.74371i	−0.831165	+	0.479874i
$333$		−	3.28138i		−	0.179819i
$334$	−6.15070	+	10.6533i	−0.336551	+	0.582924i
$335$	17.0309	+	10.9624i	0.930499	+	0.598939i
$336$	−2.28961	−	3.96572i	−0.124908	−	0.216348i
$337$		−	22.1976i		−	1.20918i	−0.796537	−	0.604590i	$-0.793337\pi$
$337$		−	22.1976i		−	1.20918i	0.796537	−	0.604590i	$-0.206663\pi$
$338$	−12.3819	−	7.14868i	−0.673485	−	0.388837i
$339$	12.7515			0.692565
$340$	0.234011	−	4.83946i	0.0126910	−	0.262457i
$341$	−8.11790	+	9.52682i	−0.439609	+	0.515906i
$342$		−	1.76935i		−	0.0956753i
$343$		−	31.9137i		−	1.72318i
$344$	0.558491	−	0.967335i	0.0301118	−	0.0521552i
$345$	−16.9910	−	0.821594i	−0.914765	−	0.0442332i
$346$	−6.99295	−	12.1122i	−0.375944	−	0.651153i
$347$	20.4631	+	11.8144i	1.09852	+	0.634229i	0.935831	−	0.352449i	$-0.114651\pi$
$347$	20.4631	+	11.8144i	1.09852	+	0.634229i	0.162686	+	0.986678i	$0.447984\pi$
$348$	3.08967	+	1.78382i	0.165624	+	0.0956228i
$349$	−9.12158			−0.488267			−0.244134	−	0.969742i	$-0.578504\pi$
$349$	−9.12158			−0.488267			−0.244134	+	0.969742i	$0.578504\pi$
$350$	−9.48150	−	20.8406i	−0.506807	−	1.11398i
$351$	−2.61234	−	4.52471i	−0.139437	−	0.241511i
$352$	1.94684	−	1.12401i	0.103767	−	0.0599098i
$353$	0.761294	+	0.439533i	0.0405196	+	0.0233940i	0.520123	−	0.854091i	$-0.325886\pi$
$353$	0.761294	+	0.439533i	0.0405196	+	0.0233940i	−0.479603	+	0.877485i	$0.659219\pi$
$354$	2.77594	+	4.80807i	0.147540	+	0.255546i
$355$	13.8437	−	21.5074i	0.734750	−	1.14149i
$356$	−0.683694			−0.0362357
$357$		−	9.92226i		−	0.525142i
$358$	3.27682	+	1.89187i	0.173185	+	0.0999885i
$359$	−4.63407	−	8.02644i	−0.244577	−	0.423619i	0.717436	−	0.696625i	$-0.245316\pi$
$359$	−4.63407	−	8.02644i	−0.244577	−	0.423619i	−0.962013	+	0.273005i	$0.911982\pi$
$360$	−1.88023	−	1.21026i	−0.0990970	−	0.0637862i
$361$	7.93471	+	13.7433i	0.417616	+	0.723332i
$362$	−19.7635	+	11.4105i	−1.03875	+	0.599721i
$363$	5.14976	−	2.97321i	0.270292	−	0.156053i
$364$	−23.9250			−1.25401
$365$	−30.3119	−	19.5110i	−1.58660	−	1.02125i
$366$	−2.99222	+	5.18267i	−0.156406	+	0.270903i
$367$	−12.7486	+	7.36040i	−0.665471	+	0.384210i	−0.794358	−	0.607449i	$-0.792193\pi$
$367$	−12.7486	+	7.36040i	−0.665471	+	0.384210i	0.128887	+	0.991659i	$0.458859\pi$
$368$			7.60749i			0.396568i
$369$	−1.66046	+	2.87600i	−0.0864402	+	0.149719i
$370$	−7.32883	−	0.354383i	−0.381008	−	0.0184235i
$371$	24.0561			1.24893
$372$	1.00840	−	5.47569i	0.0522832	−	0.283901i
$373$		−	4.99754i		−	0.258763i	−0.991595	−	0.129382i	$-0.958701\pi$
$373$		−	4.99754i		−	0.258763i	0.991595	−	0.129382i	$-0.0412992\pi$
$374$	4.87100			0.251874
$375$	−8.77345	−	6.93012i	−0.453059	−	0.357870i
$376$	1.34764			0.0694990
$377$	16.1426	−	9.31991i	0.831384	−	0.480000i
$378$	−3.96572	−	2.28961i	−0.203975	−	0.117765i
$379$	−13.4275	+	23.2571i	−0.689724	+	1.19464i	0.282202	+	0.959355i	$0.408935\pi$
$379$	−13.4275	+	23.2571i	−0.689724	+	1.19464i	−0.971927	+	0.235283i	$0.924398\pi$
$380$	−3.95176	−	0.191086i	−0.202721	−	0.00980251i
$381$	9.00509	+	15.5973i	0.461345	+	0.799073i
$382$	21.2293	−	12.2567i	1.08619	−	0.627110i
$383$	−16.5663	+	9.56453i	−0.846496	+	0.488725i	−0.859467	−	0.511191i	$-0.829204\pi$
$383$	−16.5663	+	9.56453i	−0.846496	+	0.488725i	0.0129708	+	0.999916i	$0.495871\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	20.4671	−	10.5330i	1.04310	−	0.536810i
$386$	−10.8378	+	18.7716i	−0.551628	+	0.955447i
$387$		−	1.11698i		−	0.0567794i
$388$		−	7.66751i		−	0.389259i
$389$	6.52925	−	11.3090i	0.331046	−	0.573389i	−0.651671	−	0.758502i	$-0.725932\pi$
$389$	6.52925	−	11.3090i	0.331046	−	0.573389i	0.982717	+	0.185113i	$0.0592651\pi$
$390$	−10.3879	+	5.34590i	−0.526011	+	0.270700i
$391$	−8.24196	+	14.2755i	−0.416814	+	0.721942i
$392$	−12.0977	+	6.98462i	−0.611027	+	0.352777i
$393$	12.6598	−	7.30917i	0.638605	−	0.368699i
$394$	10.0122	+	17.3417i	0.504408	+	0.873660i
$395$	−5.17241	−	0.250110i	−0.260252	−	0.0125844i
$396$	1.12401	−	1.94684i	0.0564835	−	0.0978323i
$397$	22.8280	+	13.1797i	1.14570	+	0.661472i	0.947836	−	0.318757i	$-0.103265\pi$
$397$	22.8280	+	13.1797i	1.14570	+	0.661472i	0.197866	+	0.980229i	$0.436599\pi$
$398$	−4.18375	+	2.41549i	−0.209713	+	0.121078i
$399$	−8.10223			−0.405619
$400$	−2.90612	+	4.06872i	−0.145306	+	0.203436i
$401$	−3.14261			−0.156934			−0.0784672	−	0.996917i	$-0.525003\pi$
$401$	−3.14261			−0.156934			−0.0784672	+	0.996917i	$0.525003\pi$
$402$		−	9.05789i		−	0.451766i
$403$	−22.1416	−	18.8671i	−1.10295	−	0.939837i
$404$	5.98825			0.297927
$405$	−2.23346	−	0.107998i	−0.110981	−	0.00536647i
$406$	8.16850	−	14.1483i	0.405396	−	0.702167i
$407$		−	7.37660i		−	0.365644i
$408$	−1.87651	+	1.08340i	−0.0929009	+	0.0536363i
$409$	−4.10458	+	7.10934i	−0.202958	+	0.351534i	−0.949480	−	0.313827i	$-0.898389\pi$
$409$	−4.10458	+	7.10934i	−0.202958	+	0.351534i	0.746522	+	0.665361i	$0.231722\pi$
$410$	6.24411	+	4.01917i	0.308375	+	0.198493i
$411$	1.85280			0.0913917
$412$	−14.5737	+	8.41412i	−0.717994	+	0.414534i
$413$	22.0172	−	12.7116i	1.08340	−	0.625499i
$414$	3.80374	+	6.58828i	0.186944	+	0.323796i
$415$	32.8804	+	21.1643i	1.61404	+	1.03891i
$416$	2.61234	+	4.52471i	0.128081	+	0.221842i
$417$	−2.59437	−	1.49786i	−0.127047	−	0.0733506i
$418$		−	3.97752i		−	0.194547i
$419$	23.9498			1.17002			0.585012	−	0.811025i	$-0.301090\pi$
$419$	23.9498			1.17002			0.585012	+	0.811025i	$0.301090\pi$
$420$	−5.54204	+	8.61000i	−0.270424	+	0.420125i
$421$	7.61707	+	13.1932i	0.371233	+	0.642995i	0.989756	−	0.142772i	$-0.0456017\pi$
$421$	7.61707	+	13.1932i	0.371233	+	0.642995i	−0.618522	+	0.785767i	$0.712268\pi$
$422$	6.55549	+	3.78481i	0.319116	+	0.184242i
$423$	1.16709	−	0.673818i	0.0567457	−	0.0327621i
$424$	−2.62666	−	4.54951i	−0.127562	−	0.220944i
$425$	−9.86141	+	4.48647i	−0.478348	+	0.217626i
$426$	−11.4387			−0.554205
$427$	23.7326	+	13.7020i	1.14850	+	0.663087i
$428$	−0.423967	−	0.244777i	−0.0204932	−	0.0118318i
$429$	−5.87259	−	10.1716i	−0.283531	−	0.491090i
$430$	−2.49473	−	0.120632i	−0.120307	−	0.00581739i
$431$	15.8379	−	27.4321i	0.762886	−	1.32136i	−0.178471	−	0.983945i	$-0.557115\pi$
$431$	15.8379	−	27.4321i	0.762886	−	1.32136i	0.941357	−	0.337412i	$-0.109551\pi$
$432$			1.00000i			0.0481125i
$433$			29.2353i			1.40496i	0.711705	+	0.702478i	$0.247923\pi$
$433$			29.2353i			1.40496i	−0.711705	+	0.702478i	$0.752077\pi$
$434$	−25.0744	−	4.61769i	−1.20361	−	0.221656i
$435$	0.385299	−	7.96818i	0.0184737	−	0.382045i
$436$	−20.0620			−0.960794
$437$	11.6569	+	6.73014i	0.557627	+	0.321946i
$438$			16.1214i			0.770309i
$439$	14.3217	+	24.8060i	0.683539	+	1.18392i	0.973894	+	0.227005i	$0.0728934\pi$
$439$	14.3217	+	24.8060i	0.683539	+	1.18392i	−0.290355	+	0.956919i	$0.593773\pi$
$440$	−4.22679	−	2.72068i	−0.201504	−	0.129703i
$441$	−6.98462	+	12.0977i	−0.332601	+	0.576082i
$442$			11.3209i			0.538478i
$443$	−4.43797	+	2.56226i	−0.210854	+	0.121737i	−0.601708	−	0.798716i	$-0.705513\pi$
$443$	−4.43797	+	2.56226i	−0.210854	+	0.121737i	0.390854	+	0.920453i	$0.372180\pi$
$444$	1.64069	+	2.84176i	0.0778638	+	0.134864i
$445$	0.699556	+	1.35934i	0.0331621	+	0.0644390i
$446$	−2.84949	+	4.93546i	−0.134927	+	0.233701i
$447$	−1.42827	+	0.824610i	−0.0675547	+	0.0390027i
$448$	3.96572	+	2.28961i	0.187363	+	0.108174i
$449$	−13.2500			−0.625308			−0.312654	−	0.949867i	$-0.601218\pi$
$449$	−13.2500			−0.625308			−0.312654	+	0.949867i	$0.601218\pi$
$450$	−0.482419	+	4.97667i	−0.0227414	+	0.234603i
$451$	−3.73274	+	6.46530i	−0.175768	+	0.304439i
$452$	−11.0431	+	6.37573i	−0.519423	+	0.299889i
$453$	−5.74796	−	3.31858i	−0.270063	−	0.155921i
$454$	−3.85430	−	6.67585i	−0.180891	−	0.313313i
$455$	24.4800	+	47.5684i	1.14764	+	2.23004i
$456$	0.884673	+	1.53230i	0.0414286	+	0.0717565i
$457$			25.2874i			1.18289i	0.806344	+	0.591446i	$0.201443\pi$
$457$			25.2874i			1.18289i	−0.806344	+	0.591446i	$0.798557\pi$
$458$	12.3021	+	7.10263i	0.574840	+	0.331884i
$459$	−1.08340	+	1.87651i	−0.0505688	+	0.0875878i
$460$	15.1254	−	7.78398i	0.705227	−	0.362930i
$461$	−17.5310			−0.816499			−0.408249	−	0.912870i	$-0.633861\pi$
$461$	−17.5310			−0.816499			−0.408249	+	0.912870i	$0.633861\pi$
$462$	−8.91499	−	5.14707i	−0.414763	−	0.239464i
$463$		−	7.42744i		−	0.345183i	−0.984994	−	0.172591i	$-0.944786\pi$
$463$		−	7.42744i		−	0.345183i	0.984994	−	0.172591i	$-0.0552140\pi$
$464$	−3.56764			−0.165624
$465$	−11.9187	+	3.59779i	−0.552717	+	0.166843i
$466$	9.15400			0.424051
$467$			9.59245i			0.443886i	0.975060	+	0.221943i	$0.0712399\pi$
$467$			9.59245i			0.443886i	−0.975060	+	0.221943i	$0.928760\pi$
$468$	4.52471	+	2.61234i	0.209155	+	0.120756i
$469$	−41.4780			−1.91528
$470$	−1.37890	−	2.67941i	−0.0636039	−	0.123592i
$471$	−10.1414	+	17.5654i	−0.467290	+	0.809370i
$472$	−4.80807	−	2.77594i	−0.221309	−	0.127773i
$473$		−	2.51099i		−	0.115456i
$474$	1.15794	+	2.00561i	0.0531859	+	0.0921206i
$475$	3.66352	+	8.05254i	0.168094	+	0.369476i
$476$	4.96113	+	8.59293i	0.227393	+	0.393856i
$477$	−4.54951	−	2.62666i	−0.208308	−	0.120267i
$478$	−19.4156	+	11.2096i	−0.888047	+	0.512714i
$479$	5.61817	−	9.73096i	0.256701	−	0.444619i	−0.708655	−	0.705555i	$-0.750698\pi$
$479$	5.61817	−	9.73096i	0.256701	−	0.444619i	0.965356	+	0.260936i	$0.0840311\pi$
$480$	2.23346	+	0.107998i	0.101943	+	0.00492942i
$481$	17.1442			0.781708
$482$	−21.5647	−	12.4504i	−0.982245	−	0.567100i
$483$	30.1692	−	17.4182i	1.37274	−	0.792554i
$484$	−2.97321	+	5.14976i	−0.135146	+	0.234080i
$485$	−15.2448	+	7.84540i	−0.692230	+	0.356241i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	23.8828	−	13.7887i	1.08223	−	0.624827i	0.150734	−	0.988574i	$-0.451836\pi$
$487$	23.8828	−	13.7887i	1.08223	−	0.624827i	0.931498	+	0.363747i	$0.118503\pi$
$488$		−	5.98443i		−	0.270903i
$489$	−1.94622	+	3.37095i	−0.0880110	+	0.152440i
$490$	26.2654	+	16.9064i	1.18655	+	0.763753i
$491$	−10.0918	−	17.4796i	−0.455438	−	0.788842i	0.543275	−	0.839555i	$-0.317184\pi$
$491$	−10.0918	−	17.4796i	−0.455438	−	0.788842i	−0.998713	+	0.0507127i	$0.983851\pi$
$492$		−	3.32092i		−	0.149719i
$493$	−6.69470	−	3.86519i	−0.301514	−	0.174079i
$494$	9.24428			0.415920
$495$	−5.02085	−	0.242781i	−0.225670	−	0.0109122i
$496$	1.86454	+	5.24628i	0.0837204	+	0.235565i
$497$			52.3802i			2.34957i
$498$		−	17.4874i		−	0.783630i
$499$	−1.60065	+	2.77241i	−0.0716550	+	0.124110i	−0.899627	−	0.436660i	$-0.856161\pi$
$499$	−1.60065	+	2.77241i	−0.0716550	+	0.124110i	0.827972	+	0.560770i	$0.189495\pi$
$500$	11.0631	+	1.61493i	0.494756	+	0.0722220i
$501$	−6.15070	−	10.6533i	−0.274793	−	0.475956i
$502$	8.80594	+	5.08411i	0.393028	+	0.226915i
$503$	20.0408	+	11.5706i	0.893576	+	0.515907i	0.875111	−	0.483923i	$-0.160789\pi$
$503$	20.0408	+	11.5706i	0.893576	+	0.515907i	0.0184657	+	0.999829i	$0.494122\pi$
$504$	4.57922			0.203975
$505$	−6.12718	−	11.9060i	−0.272656	−	0.529811i
$506$	8.55087	+	14.8105i	0.380133	+	0.658409i
$507$	12.3819	−	7.14868i	0.549898	−	0.317484i
$508$	−15.5973	−	9.00509i	−0.692017	−	0.399536i
$509$	12.4928	+	21.6382i	0.553733	+	0.959094i	0.998001	+	0.0632002i	$0.0201307\pi$
$509$	12.4928	+	21.6382i	0.553733	+	0.959094i	−0.444267	+	0.895894i	$0.646536\pi$
$510$	4.07409	+	2.62239i	0.180404	+	0.116121i
$511$	73.8233			3.26575
$512$		−	1.00000i		−	0.0441942i
$513$	1.53230	+	0.884673i	0.0676527	+	0.0390593i
$514$	12.2346	+	21.1909i	0.539643	+	0.934689i
$515$	31.6410	+	20.3665i	1.39427	+	0.897456i
$516$	0.558491	+	0.967335i	0.0245862	+	0.0425846i
$517$	2.62363	−	1.51475i	0.115387	−	0.0666187i
$518$	13.0130	−	7.51309i	0.571760	−	0.330106i
$519$	13.9859			0.613913
$520$	6.32322	−	9.82363i	0.277292	−	0.430795i
$521$	4.93903	−	8.55465i	0.216383	−	0.374786i	−0.737317	−	0.675547i	$-0.763907\pi$
$521$	4.93903	−	8.55465i	0.216383	−	0.374786i	0.953699	+	0.300761i	$0.0972407\pi$
$522$	−3.08967	+	1.78382i	−0.135231	+	0.0780757i
$523$		−	7.67657i		−	0.335673i	−0.985815	−	0.167836i	$-0.946322\pi$
$523$		−	7.67657i		−	0.335673i	0.985815	−	0.167836i	$-0.0536780\pi$
$524$	−7.30917	+	12.6598i	−0.319302	+	0.553048i
$525$	22.7893	+	2.20910i	0.994605	+	0.0964130i
$526$	3.43008			0.149559
$527$	−2.18501	+	11.8647i	−0.0951803	+	0.516835i
$528$			2.24801i			0.0978323i
$529$	−34.8738			−1.51625
$530$	−6.35788	+	9.87747i	−0.276168	+	0.429050i
$531$	−5.55188			−0.240931
$532$	7.01673	−	4.05111i	0.304214	−	0.175638i
$533$	−15.0262	−	8.67539i	−0.650858	−	0.375773i
$534$	0.341847	−	0.592096i	0.0147932	−	0.0256225i
$535$	−0.0528710	+	1.09340i	−0.00228581	+	0.0472718i
$536$	4.52894	+	7.84436i	0.195621	+	0.338825i
$537$	−3.27682	+	1.89187i	−0.141405	+	0.0816403i
$538$	17.9181	−	10.3450i	0.772503	−	0.446005i
$539$	−15.7015	+	27.1958i	−0.676313	+	1.17141i
$540$	1.98823	−	1.02320i	0.0855598	−	0.0440315i
$541$	−4.71567	+	8.16778i	−0.202742	+	0.351160i	−0.949411	−	0.314036i	$-0.898319\pi$
$541$	−4.71567	+	8.16778i	−0.202742	+	0.351160i	0.746669	+	0.665196i	$0.231652\pi$
$542$		−	20.3964i		−	0.876099i
$543$		−	22.8209i		−	0.979340i
$544$	1.08340	−	1.87651i	0.0464504	−	0.0804545i
$545$	20.5274	+	39.8878i	0.879297	+	1.70861i
$546$	11.9625	−	20.7196i	0.511947	−	0.886719i
$547$	−9.05133	+	5.22579i	−0.387007	+	0.223439i	−0.680862	−	0.732411i	$-0.738395\pi$
$547$	−9.05133	+	5.22579i	−0.387007	+	0.223439i	0.293856	+	0.955850i	$0.405062\pi$
$548$	−1.60457	+	0.926398i	−0.0685437	+	0.0395737i
$549$	−2.99222	−	5.18267i	−0.127705	−	0.221191i
$550$	−1.08448	+	11.1876i	−0.0462426	+	0.477042i
$551$	−3.15620	+	5.46670i	−0.134459	+	0.232889i
$552$	−6.58828	−	3.80374i	−0.280416	−	0.161898i
$553$	9.18411	−	5.30245i	0.390548	−	0.225483i
$554$	−2.94909			−0.125295
$555$	3.97132	−	6.16977i	0.168573	−	0.261892i
$556$	2.99572			0.127047
$557$			7.72066i			0.327135i	0.986532	+	0.163568i	$0.0523002\pi$
$557$			7.72066i			0.327135i	−0.986532	+	0.163568i	$0.947700\pi$
$558$	4.23788	+	3.61114i	0.179404	+	0.152872i
$559$	5.83588			0.246832
$560$	0.494547	−	10.2275i	0.0208984	−	0.432190i
$561$	−2.43550	+	4.21841i	−0.102827	+	0.178101i
$562$		−	23.5294i		−	0.992528i
$563$	−3.52753	+	2.03662i	−0.148668	+	0.0858334i	−0.572489	−	0.819913i	$-0.694022\pi$
$563$	−3.52753	+	2.03662i	−0.148668	+	0.0858334i	0.423821	+	0.905746i	$0.360689\pi$
$564$	−0.673818	+	1.16709i	−0.0283728	+	0.0491432i
$565$	23.9757	+	15.4326i	1.00867	+	0.649253i
$566$	23.0945			0.970734
$567$	3.96572	−	2.28961i	0.166545	−	0.0961545i
$568$	9.90618	−	5.71934i	0.415654	−	0.239978i
$569$	15.8405	+	27.4365i	0.664068	+	1.15020i	0.979537	+	0.201263i	$0.0645046\pi$
$569$	15.8405	+	27.4365i	0.664068	+	1.15020i	−0.315470	+	0.948936i	$0.602162\pi$
$570$	2.14137	−	3.32678i	0.0896920	−	0.139344i
$571$	−7.46257	−	12.9256i	−0.312299	−	0.540918i	0.666561	−	0.745451i	$-0.267766\pi$
$571$	−7.46257	−	12.9256i	−0.312299	−	0.540918i	−0.978860	+	0.204533i	$0.934432\pi$
$572$	10.1716	+	5.87259i	0.425297	+	0.245545i
$573$			24.5135i			1.02407i
$574$	−15.2072			−0.634738
$575$	−30.9527	−	22.1083i	−1.29082	−	0.921979i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	4.05944	+	2.34372i	0.168997	+	0.0975703i	0.582113	−	0.813108i	$-0.302226\pi$
$577$	4.05944	+	2.34372i	0.168997	+	0.0975703i	−0.413116	+	0.910678i	$0.635560\pi$
$578$	−10.6564	+	6.15249i	−0.443249	+	0.255910i
$579$	−10.8378	−	18.7716i	−0.450402	−	0.780119i
$580$	3.65041	+	7.09330i	0.151575	+	0.294533i
$581$	−80.0787			−3.32223
$582$	6.64026	+	3.83376i	0.275248	+	0.158914i
$583$	−10.2274	−	5.90477i	−0.423574	−	0.244551i
$584$	−8.06069	−	13.9615i	−0.333554	−	0.577732i
$585$	0.564257	−	11.6691i	0.0233291	−	0.482459i
$586$	1.28185	−	2.22022i	0.0529526	−	0.0917166i
$587$			13.3196i			0.549757i	0.961479	+	0.274879i	$0.0886376\pi$
$587$			13.3196i			0.549757i	−0.961479	+	0.274879i	$0.911362\pi$
$588$		−	13.9692i		−	0.576082i
$589$	9.68839	+	1.78421i	0.399203	+	0.0735172i
$590$	−0.599593	+	12.3999i	−0.0246848	+	0.510496i
$591$	−20.0244			−0.823695
$592$	−2.84176	−	1.64069i	−0.116796	−	0.0674320i
$593$		−	17.8086i		−	0.731310i	−0.930750	−	0.365655i	$-0.880845\pi$
$593$		−	17.8086i		−	0.731310i	0.930750	−	0.365655i	$-0.119155\pi$
$594$	1.12401	+	1.94684i	0.0461186	+	0.0798797i
$595$	12.0085	−	18.6562i	0.492300	−	0.764828i
$596$	0.824610	−	1.42827i	0.0337774	−	0.0585041i
$597$		−	4.83098i		−	0.197719i
$598$	−34.4217	+	19.8734i	−1.40761	+	0.812682i
$599$	12.4267	+	21.5237i	0.507742	+	0.879435i	0.999960	+	0.00896281i	$0.00285299\pi$
$599$	12.4267	+	21.5237i	0.507742	+	0.879435i	−0.492218	+	0.870472i	$0.663814\pi$
$600$	−2.07055	−	4.55113i	−0.0845298	−	0.185799i
$601$	−21.4721	+	37.1908i	−0.875866	+	1.51704i	−0.0200293	+	0.999799i	$0.506376\pi$
$601$	−21.4721	+	37.1908i	−0.875866	+	1.51704i	−0.855837	+	0.517246i	$0.826957\pi$
$602$	4.42964	−	2.55745i	0.180539	−	0.104234i
$603$	7.84436	+	4.52894i	0.319447	+	0.184433i
$604$	6.63717			0.270063
$605$	13.2811	+	0.642203i	0.539954	+	0.0261093i
$606$	−2.99412	+	5.18598i	−0.121628	+	0.210666i
$607$	−19.6820	+	11.3634i	−0.798868	+	0.461226i	−0.843075	−	0.537796i	$-0.819257\pi$
$607$	−19.6820	+	11.3634i	−0.798868	+	0.461226i	0.0442074	+	0.999022i	$0.485924\pi$
$608$	−1.53230	−	0.884673i	−0.0621429	−	0.0358782i
$609$	8.16850	+	14.1483i	0.331005	+	0.573317i
$610$	−11.8984	+	6.12327i	−0.481754	+	0.247924i
$611$	3.52049	+	6.09766i	0.142424	+	0.246685i
$612$		−	2.16680i		−	0.0875878i
$613$	22.5114	+	12.9970i	0.909227	+	0.524943i	0.880182	−	0.474636i	$-0.157420\pi$
$613$	22.5114	+	12.9970i	0.909227	+	0.524943i	0.0290448	+	0.999578i	$0.490753\pi$
$614$	13.6610	−	23.6615i	0.551312	−	0.954901i
$615$	−6.60276	+	3.39797i	−0.266249	+	0.137019i
$616$	10.2941			0.414763
$617$	−18.4464	−	10.6500i	−0.742625	−	0.428755i	0.0803979	−	0.996763i	$-0.474381\pi$
$617$	−18.4464	−	10.6500i	−0.742625	−	0.428755i	−0.823023	+	0.568008i	$0.807714\pi$
$618$		−	16.8282i		−	0.676931i
$619$	30.4829			1.22521			0.612606	−	0.790389i	$-0.290121\pi$
$619$	30.4829			1.22521			0.612606	+	0.790389i	$0.290121\pi$
$620$	8.52302	−	9.07514i	0.342293	−	0.364466i
$621$	−7.60749			−0.305278
$622$			5.87643i			0.235623i
$623$	−2.71134	−	1.56539i	−0.108627	−	0.0627161i
$624$	−5.22469			−0.209155
$625$	−8.10890	−	23.6484i	−0.324356	−	0.945935i
$626$	−10.3753	+	17.9705i	−0.414679	+	0.718245i
$627$	3.44463	+	1.98876i	0.137565	+	0.0794234i
$628$		−	20.2828i		−	0.809370i
$629$	−3.55505	−	6.15753i	−0.141749	−	0.245517i
$630$	−4.68546	−	9.10454i	−0.186673	−	0.362734i
$631$	2.44079	+	4.22757i	0.0971662	+	0.168297i	0.910511	−	0.413486i	$-0.135689\pi$
$631$	2.44079	+	4.22757i	0.0971662	+	0.168297i	−0.813344	+	0.581782i	$0.802355\pi$
$632$	−2.00561	−	1.15794i	−0.0797788	−	0.0460603i
$633$	−6.55549	+	3.78481i	−0.260557	+	0.150433i
$634$	13.6514	−	23.6450i	0.542168	−	0.939062i
$635$	−1.94507	+	40.2250i	−0.0771876	+	1.59628i
$636$	5.25332			0.208308
$637$	−63.2068	−	36.4925i	−2.50434	−	1.44588i
$638$	−6.94562	+	4.01006i	−0.274980	+	0.158760i
$639$	5.71934	−	9.90618i	0.226253	−	0.391882i
$640$	−1.98823	+	1.02320i	−0.0785917	+	0.0404455i
$641$	13.0766	+	22.6493i	0.516493	+	0.894592i	0.999817	+	0.0191506i	$0.00609620\pi$
$641$	13.0766	+	22.6493i	0.516493	+	0.894592i	−0.483323	+	0.875442i	$0.660570\pi$
$642$	0.423967	−	0.244777i	0.0167326	−	0.00966059i
$643$		−	17.2516i		−	0.680338i	−0.940364	−	0.340169i	$-0.889516\pi$
$643$		−	17.2516i		−	0.680338i	0.940364	−	0.340169i	$-0.110484\pi$
$644$	−17.4182	+	30.1692i	−0.686372	+	1.18883i
$645$	1.35184	−	2.10019i	0.0532285	−	0.0826948i
$646$	−1.91691	−	3.32019i	−0.0754199	−	0.130631i
$647$		−	12.7703i		−	0.502053i	−0.967980	−	0.251026i	$-0.919232\pi$
$647$		−	12.7703i		−	0.502053i	0.967980	−	0.251026i	$-0.0807681\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−12.4807			−0.489911
$650$	−26.0016	−	2.52049i	−1.01987	−	0.0988616i
$651$	16.5362	−	19.4062i	0.648105	−	0.760588i
$652$		−	3.89243i		−	0.152440i
$653$		−	31.9917i		−	1.25193i	−0.779850	−	0.625966i	$-0.784705\pi$
$653$		−	31.9917i		−	1.25193i	0.779850	−	0.625966i	$-0.215295\pi$
$654$	10.0310	−	17.3742i	0.392242	−	0.679384i
$655$	32.6494	+	1.57875i	1.27572	+	0.0616870i
$656$	1.66046	+	2.87600i	0.0648301	+	0.112289i
$657$	−13.9615	−	8.06069i	−0.544691	−	0.314478i
$658$	5.34434	+	3.08556i	0.208344	+	0.120288i
$659$	−21.8281			−0.850304			−0.425152	−	0.905122i	$-0.639779\pi$
$659$	−21.8281			−0.850304			−0.425152	+	0.905122i	$0.639779\pi$
$660$	4.46957	−	2.30017i	0.173978	−	0.0895339i
$661$	6.16568	+	10.6793i	0.239817	+	0.415376i	0.960662	−	0.277721i	$-0.0895791\pi$
$661$	6.16568	+	10.6793i	0.239817	+	0.415376i	−0.720844	+	0.693097i	$0.756246\pi$
$662$	−2.30048	+	1.32818i	−0.0894106	+	0.0516212i
$663$	−9.80415	−	5.66043i	−0.380762	−	0.219833i
$664$	8.74371	+	15.1446i	0.339322	+	0.587723i
$665$	−15.2341	−	9.80579i	−0.590752	−	0.380252i
$666$	−3.28138			−0.127151
$667$		−	27.1408i		−	1.05090i
$668$	10.6533	+	6.15070i	0.412190	+	0.237978i
$669$	−2.84949	−	4.93546i	−0.110168	−	0.190816i
$670$	10.9624	−	17.0309i	0.423514	−	0.657962i
$671$	−6.72655	−	11.6507i	−0.259675	−	0.449771i
$672$	−3.96572	+	2.28961i	−0.152981	+	0.0883236i
$673$	−17.6318	+	10.1797i	−0.679654	+	0.392399i	−0.799725	−	0.600367i	$-0.795021\pi$
$673$	−17.6318	+	10.1797i	−0.679654	+	0.392399i	0.120070	+	0.992765i	$0.461688\pi$
$674$	−22.1976			−0.855019
$675$	−4.06872	−	2.90612i	−0.156605	−	0.111857i
$676$	−7.14868	+	12.3819i	−0.274949	+	0.476226i
$677$	−35.2392	+	20.3454i	−1.35435	+	0.781936i	−0.988856	−	0.148877i	$-0.952434\pi$
$677$	−35.2392	+	20.3454i	−1.35435	+	0.781936i	−0.365497	+	0.930813i	$0.619101\pi$
$678$		−	12.7515i		−	0.489717i
$679$	17.5556	−	30.4072i	0.673722	−	1.16692i
$680$	−4.83946	−	0.234011i	−0.185585	−	0.00897390i
$681$	7.70861			0.295394
$682$	9.52682	+	8.11790i	0.364801	+	0.310851i
$683$		−	41.8596i		−	1.60171i	−0.598856	−	0.800857i	$-0.704378\pi$
$683$		−	41.8596i		−	1.60171i	0.598856	−	0.800857i	$-0.295622\pi$
$684$	−1.76935			−0.0676527
$685$	3.48369	+	2.24236i	0.133105	+	0.0856762i
$686$	−31.9137			−1.21847
$687$	−12.3021	+	7.10263i	−0.469355	+	0.270982i
$688$	−0.967335	−	0.558491i	−0.0368793	−	0.0212923i
$689$	13.7235	−	23.7698i	0.522823	−	0.905556i
$690$	−0.821594	+	16.9910i	−0.0312776	+	0.646836i
$691$	−15.7349	−	27.2537i	−0.598586	−	1.03678i	−0.993030	−	0.117861i	$-0.962396\pi$
$691$	−15.7349	−	27.2537i	−0.598586	−	1.03678i	0.394444	−	0.918920i	$-0.370937\pi$
$692$	−12.1122	+	6.99295i	−0.460435	+	0.265832i
$693$	8.91499	−	5.14707i	0.338653	−	0.195521i
$694$	11.8144	−	20.4631i	0.448468	−	0.776769i
$695$	−3.06523	−	5.95619i	−0.116271	−	0.225931i
$696$	1.78382	−	3.08967i	0.0676156	−	0.117114i
$697$			7.19578i			0.272560i
$698$			9.12158i			0.345257i
$699$	−4.57700	+	7.92760i	−0.173118	+	0.299849i
$700$	−20.8406	+	9.48150i	−0.787702	+	0.358367i
$701$	14.6158	−	25.3154i	0.552032	−	0.956148i	−0.446096	−	0.894985i	$-0.647186\pi$
$701$	14.6158	−	25.3154i	0.552032	−	0.956148i	0.998128	−	0.0611625i	$-0.0194808\pi$
$702$	−4.52471	+	2.61234i	−0.170774	+	0.0985966i
$703$	−5.02806	+	2.90295i	−0.189637	+	0.109487i
$704$	−1.12401	−	1.94684i	−0.0423626	−	0.0733742i
$705$	3.00989	+	0.145542i	0.113359	+	0.00548143i
$706$	0.439533	−	0.761294i	0.0165421	−	0.0286517i
$707$	23.7477	+	13.7107i	0.893125	+	0.515646i
$708$	4.80807	−	2.77594i	0.180698	−	0.104326i
$709$	13.9582			0.524211			0.262106	−	0.965039i	$-0.415583\pi$
$709$	13.9582			0.524211			0.262106	+	0.965039i	$0.415583\pi$
$710$	−21.5074	−	13.8437i	−0.807157	−	0.519547i
$711$	−2.31588			−0.0868521
$712$			0.683694i			0.0256225i
$713$	−39.9110	+	14.1845i	−1.49468	+	0.531213i
$714$	−9.92226			−0.371331
$715$	1.26846	−	26.2324i	0.0474376	−	0.981035i
$716$	1.89187	−	3.27682i	0.0707026	−	0.122460i
$717$		−	22.4192i		−	0.837259i
$718$	−8.02644	+	4.63407i	−0.299544	+	0.172942i
$719$	23.3673	−	40.4733i	0.871452	−	1.50940i	0.0109563	−	0.999940i	$-0.496512\pi$
$719$	23.3673	−	40.4733i	0.871452	−	1.50940i	0.860495	−	0.509458i	$-0.170154\pi$
$720$	−1.21026	+	1.88023i	−0.0451037	+	0.0700721i
$721$	−77.0602			−2.86987
$722$	13.7433	−	7.93471i	0.511473	−	0.295299i
$723$	21.5647	−	12.4504i	0.802000	−	0.463035i
$724$	11.4105	+	19.7635i	0.424067	+	0.734505i
$725$	10.3680	−	14.5157i	0.385058	−	0.539100i
$726$	−2.97321	−	5.14976i	−0.110346	−	0.191125i
$727$	14.9196	+	8.61386i	0.553339	+	0.319470i	0.750468	−	0.660907i	$-0.229828\pi$
$727$	14.9196	+	8.61386i	0.553339	+	0.319470i	−0.197129	+	0.980378i	$0.563162\pi$
$728$			23.9250i			0.886719i
$729$	−1.00000			−0.0370370
$730$	−19.5110	+	30.3119i	−0.722136	+	1.12190i
$731$	−1.21014	−	2.09602i	−0.0447586	−	0.0775242i
$732$	5.18267	+	2.99222i	0.191557	+	0.110596i
$733$	16.1048	−	9.29809i	0.594843	−	0.343433i	−0.172167	−	0.985068i	$-0.555077\pi$
$733$	16.1048	−	9.29809i	0.594843	−	0.343433i	0.767010	+	0.641635i	$0.221744\pi$
$734$	7.36040	+	12.7486i	0.271677	+	0.470559i
$735$	−27.7741	+	14.2933i	−1.02446	+	0.527217i
$736$	7.60749			0.280416
$737$	17.6342	+	10.1811i	0.649565	+	0.375027i
$738$	2.87600	+	1.66046i	0.105867	+	0.0611224i
$739$	9.98401	+	17.2928i	0.367268	+	0.636126i	0.989137	−	0.146994i	$-0.0469599\pi$
$739$	9.98401	+	17.2928i	0.367268	+	0.636126i	−0.621870	+	0.783121i	$0.713627\pi$
$740$	−0.354383	+	7.32883i	−0.0130274	+	0.269413i
$741$	−4.62214	+	8.00579i	−0.169799	+	0.294100i
$742$		−	24.0561i		−	0.883127i
$743$			16.7463i			0.614363i	0.951651	+	0.307182i	$0.0993859\pi$
$743$			16.7463i			0.614363i	−0.951651	+	0.307182i	$0.900614\pi$
$744$	−5.47569	−	1.00840i	−0.200748	−	0.0369698i
$745$	−3.68347	−	0.178113i	−0.134952	−	0.00652555i
$746$	−4.99754			−0.182973
$747$	15.1446	+	8.74371i	0.554110	+	0.319916i
$748$		−	4.87100i		−	0.178101i
$749$	−1.12089	−	1.94144i	−0.0409564	−	0.0709386i
$750$	−6.93012	+	8.77345i	−0.253052	+	0.320361i
$751$	1.04640	−	1.81242i	0.0381838	−	0.0661362i	−0.846302	−	0.532703i	$-0.821176\pi$
$751$	1.04640	−	1.81242i	0.0381838	−	0.0661362i	0.884486	+	0.466567i	$0.154509\pi$
$752$		−	1.34764i		−	0.0491432i
$753$	−8.80594	+	5.08411i	−0.320906	+	0.185275i
$754$	−9.31991	−	16.1426i	−0.339411	−	0.587877i
$755$	−6.79115	−	13.1962i	−0.247155	−	0.480260i
$756$	−2.28961	+	3.96572i	−0.0832723	+	0.144232i
$757$	21.3724	−	12.3394i	0.776794	−	0.448482i	−0.0584989	−	0.998287i	$-0.518631\pi$
$757$	21.3724	−	12.3394i	0.776794	−	0.448482i	0.835293	+	0.549805i	$0.185298\pi$
$758$	23.2571	+	13.4275i	0.844736	+	0.487709i
$759$	−17.1017			−0.620754
$760$	−0.191086	+	3.95176i	−0.00693142	+	0.143345i
$761$	15.7293	−	27.2439i	0.570185	−	0.987590i	−0.426361	−	0.904553i	$-0.640205\pi$
$761$	15.7293	−	27.2439i	0.570185	−	0.987590i	0.996546	−	0.0830369i	$-0.0264619\pi$
$762$	15.5973	−	9.00509i	0.565030	−	0.326220i
$763$	−79.5601	−	45.9340i	−2.88027	−	1.66292i
$764$	−12.2567	−	21.2293i	−0.443434	−	0.768049i
$765$	−4.30810	+	2.21707i	−0.155760	+	0.0801584i
$766$	9.56453	+	16.5663i	0.345581	+	0.598563i
$767$		−	29.0068i		−	1.04738i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−2.63572	+	4.56520i	−0.0950465	+	0.164625i	−0.909628	−	0.415424i	$-0.863633\pi$
$769$	−2.63572	+	4.56520i	−0.0950465	+	0.164625i	0.814582	+	0.580049i	$0.196967\pi$
$770$	−10.5330	−	20.4671i	−0.379582	−	0.737585i
$771$	−24.4691			−0.881233
$772$	18.7716	+	10.8378i	0.675603	+	0.390060i
$773$			52.3668i			1.88350i	0.336310	+	0.941751i	$0.390821\pi$
$773$			52.3668i			1.88350i	−0.336310	+	0.941751i	$0.609179\pi$
$774$	−1.11698			−0.0401491
$775$	−26.7642	−	7.66006i	−0.961399	−	0.275157i
$776$	−7.66751			−0.275248
$777$			15.0262i			0.539061i
$778$	−11.3090	−	6.52925i	−0.405447	−	0.234085i
$779$	5.87586			0.210525
$780$	5.34590	+	10.3879i	0.191414	+	0.371946i
$781$	12.8571	−	22.2692i	0.460065	−	0.796856i
$782$	14.2755	+	8.24196i	0.510490	+	0.294732i
$783$		−	3.56764i		−	0.127497i
$784$	6.98462	+	12.0977i	0.249451	+	0.432061i
$785$	−40.3268	+	20.7533i	−1.43933	+	0.740718i
$786$	−7.30917	−	12.6598i	−0.260709	−	0.451562i
$787$	46.2559	+	26.7058i	1.64884	+	0.951961i	0.977532	+	0.210785i	$0.0676021\pi$
$787$	46.2559	+	26.7058i	1.64884	+	0.951961i	0.671312	+	0.741175i	$0.265731\pi$
$788$	17.3417	−	10.0122i	0.617771	−	0.356670i
$789$	−1.71504	+	2.97054i	−0.0610570	+	0.105754i
$790$	−0.250110	+	5.17241i	−0.00889853	+	0.184026i
$791$	−58.3917			−2.07617
$792$	−1.94684	−	1.12401i	−0.0691779	−	0.0399399i
$793$	27.0778	−	15.6334i	0.961562	−	0.555158i
$794$	13.1797	−	22.8280i	0.467731	−	0.810134i
$795$	−5.37520	−	10.4448i	−0.190639	−	0.370439i
$796$	2.41549	+	4.18375i	0.0856148	+	0.148289i
$797$	−0.407042	+	0.235006i	−0.0144182	+	0.00832433i	−0.507192	−	0.861833i	$-0.669316\pi$
$797$	−0.407042	+	0.235006i	−0.0144182	+	0.00832433i	0.492774	+	0.870158i	$0.335983\pi$
$798$			8.10223i			0.286816i
$799$	1.46003	−	2.52885i	0.0516521	−	0.0894641i
$800$	4.06872	+	2.90612i	0.143851	+	0.102747i
$801$	0.341847	+	0.592096i	0.0120786	+	0.0209207i
$802$			3.14261i			0.110969i
$803$	−31.3857	−	18.1206i	−1.10758	−	0.639460i
$804$	−9.05789			−0.319447
$805$	77.8055	+	3.76226i	2.74228	+	0.132602i
$806$	−18.8671	+	22.1416i	−0.664565	+	0.779905i
$807$			20.6900i			0.728323i
$808$		−	5.98825i		−	0.210666i
$809$	6.94156	−	12.0231i	0.244052	−	0.422711i	−0.717812	−	0.696237i	$-0.754856\pi$
$809$	6.94156	−	12.0231i	0.244052	−	0.422711i	0.961865	+	0.273525i	$0.0881898\pi$
$810$	−0.107998	+	2.23346i	−0.00379467	+	0.0784757i
$811$	−0.616245	−	1.06737i	−0.0216393	−	0.0374803i	0.855003	−	0.518623i	$-0.173555\pi$
$811$	−0.616245	−	1.06737i	−0.0216393	−	0.0374803i	−0.876642	+	0.481143i	$0.840222\pi$
$812$	−14.1483	−	8.16850i	−0.496507	−	0.286658i
$813$	17.6638	+	10.1982i	0.619496	+	0.357666i
$814$	−7.37660			−0.258550
$815$	−7.73906	+	3.98274i	−0.271087	+	0.139509i
$816$	1.08340	+	1.87651i	0.0379266	+	0.0656908i
$817$	−1.71155	+	0.988165i	−0.0598796	+	0.0345715i
$818$	7.10934	+	4.10458i	0.248572	+	0.143513i
$819$	11.9625	+	20.7196i	0.418003	+	0.724003i
$820$	4.01917	−	6.24411i	0.140356	−	0.218054i
$821$	10.7435			0.374950			0.187475	−	0.982269i	$-0.439970\pi$
$821$	10.7435			0.374950			0.187475	+	0.982269i	$0.439970\pi$
$822$		−	1.85280i		−	0.0646237i
$823$	−14.5741	−	8.41438i	−0.508023	−	0.293307i	0.223998	−	0.974590i	$-0.428089\pi$
$823$	−14.5741	−	8.41438i	−0.508023	−	0.293307i	−0.732020	+	0.681283i	$0.761422\pi$
$824$	8.41412	+	14.5737i	0.293120	+	0.507699i
$825$	−9.14653	−	6.53301i	−0.318441	−	0.227450i
$826$	−12.7116	−	22.0172i	−0.442294	−	0.766076i
$827$	22.4763	−	12.9767i	0.781578	−	0.451244i	−0.0554110	−	0.998464i	$-0.517647\pi$
$827$	22.4763	−	12.9767i	0.781578	−	0.451244i	0.836989	+	0.547219i	$0.184314\pi$
$828$	6.58828	−	3.80374i	0.228958	−	0.132189i
$829$	−1.52019			−0.0527985			−0.0263992	−	0.999651i	$-0.508404\pi$
$829$	−1.52019			−0.0527985			−0.0263992	+	0.999651i	$0.508404\pi$
$830$	21.1643	−	32.8804i	0.734624	−	1.14130i
$831$	1.47454	−	2.55398i	0.0511513	−	0.0885967i
$832$	4.52471	−	2.61234i	0.156866	−	0.0905667i
$833$			30.2686i			1.04874i
$834$	−1.49786	+	2.59437i	−0.0518667	+	0.0898358i
$835$	1.32853	−	27.4747i	0.0459756	−	0.950800i
$836$	−3.97752			−0.137565
$837$	−5.24628	+	1.86454i	−0.181338	+	0.0644480i
$838$		−	23.9498i		−	0.827332i
$839$	−25.9498			−0.895888			−0.447944	−	0.894062i	$-0.647844\pi$
$839$	−25.9498			−0.895888			−0.447944	+	0.894062i	$0.647844\pi$
$840$	8.61000	+	5.54204i	0.297073	+	0.191218i
$841$	−16.2719			−0.561101
$842$	13.1932	−	7.61707i	0.454666	−	0.262502i
$843$	20.3771	+	11.7647i	0.701823	+	0.405198i
$844$	3.78481	−	6.55549i	0.130279	−	0.225649i
$845$	31.9326	+	1.54409i	1.09851	+	0.0531183i
$846$	−0.673818	−	1.16709i	−0.0231663	−	0.0401253i
$847$	−23.5819	+	13.6150i	−0.810283	+	0.467817i
$848$	−4.54951	+	2.62666i	−0.156231	+	0.0901999i
$849$	−11.5472	+	20.0004i	−0.396300	+	0.686412i
$850$	4.48647	+	9.86141i	0.153885	+	0.338243i
$851$	12.4815	−	21.6187i	0.427862	−	0.741078i
$852$			11.4387i			0.391882i
$853$			25.7525i			0.881749i	0.897569	+	0.440874i	$0.145332\pi$
$853$			25.7525i			0.881749i	−0.897569	+	0.440874i	$0.854668\pi$
$854$	13.7020	−	23.7326i	0.468873	−	0.812112i
$855$	1.81040	+	3.51787i	0.0619142	+	0.120309i
$856$	−0.244777	+	0.423967i	−0.00836632	+	0.0144909i
$857$	41.3791	−	23.8903i	1.41348	−	0.816075i	0.417769	−	0.908553i	$-0.362812\pi$
$857$	41.3791	−	23.8903i	1.41348	−	0.816075i	0.995715	+	0.0924776i	$0.0294787\pi$
$858$	−10.1716	+	5.87259i	−0.347253	+	0.200487i
$859$	26.3736	+	45.6805i	0.899857	+	1.55860i	0.827676	+	0.561206i	$0.189663\pi$
$859$	26.3736	+	45.6805i	0.899857	+	1.55860i	0.0721811	+	0.997392i	$0.477004\pi$
$860$	−0.120632	+	2.49473i	−0.00411352	+	0.0850697i
$861$	7.60362	−	13.1698i	0.259131	−	0.448827i
$862$	−27.4321	−	15.8379i	−0.934340	−	0.539442i
$863$	−33.7489	+	19.4849i	−1.14883	+	0.663275i	−0.948601	−	0.316475i	$-0.897501\pi$
$863$	−33.7489	+	19.4849i	−1.14883	+	0.663275i	−0.200225	+	0.979750i	$0.564167\pi$
$864$	1.00000			0.0340207
$865$	26.2968	+	16.9266i	0.894117	+	0.575520i
$866$	29.2353			0.993454
$867$		−	12.3050i		−	0.417899i
$868$	−4.61769	+	25.0744i	−0.156735	+	0.851079i
$869$	−5.20612			−0.176606
$870$	−7.96818	−	0.385299i	−0.270147	−	0.0130628i
$871$	−23.6623	+	40.9843i	−0.801767	+	1.38870i
$872$			20.0620i			0.679384i
$873$	−6.64026	+	3.83376i	−0.224739	+	0.129753i
$874$	6.73014	−	11.6569i	0.227650	−	0.394302i
$875$	40.1755	+	31.7345i	1.35818	+	1.07282i
$876$	16.1214			0.544691
$877$	19.6976	−	11.3724i	0.665141	−	0.384019i	−0.129092	−	0.991633i	$-0.541206\pi$
$877$	19.6976	−	11.3724i	0.665141	−	0.384019i	0.794233	+	0.607613i	$0.207873\pi$
$878$	24.8060	−	14.3217i	0.837161	−	0.483335i
$879$	1.28185	+	2.22022i	0.0432356	+	0.0748863i
$880$	−2.72068	+	4.22679i	−0.0917141	+	0.142485i
$881$	5.05432	+	8.75433i	0.170284	+	0.294941i	0.938519	−	0.345227i	$-0.112198\pi$
$881$	5.05432	+	8.75433i	0.170284	+	0.294941i	−0.768235	+	0.640168i	$0.778865\pi$
$882$	12.0977	+	6.98462i	0.407351	+	0.235184i
$883$			9.80566i			0.329987i	0.986295	+	0.164993i	$0.0527603\pi$
$883$			9.80566i			0.329987i	−0.986295	+	0.164993i	$0.947240\pi$
$884$	11.3209			0.380762
$885$	−10.4388	−	6.71921i	−0.350897	−	0.225864i
$886$	2.56226	+	4.43797i	0.0860809	+	0.149096i
$887$	−27.2955	−	15.7590i	−0.916492	−	0.529137i	−0.0339775	−	0.999423i	$-0.510817\pi$
$887$	−27.2955	−	15.7590i	−0.916492	−	0.529137i	−0.882514	+	0.470286i	$0.844151\pi$
$888$	2.84176	−	1.64069i	0.0953633	−	0.0550580i
$889$	−41.2363	−	71.4233i	−1.38302	−	2.39546i
$890$	1.35934	−	0.699556i	0.0455652	−	0.0234492i
$891$	−2.24801			−0.0753113
$892$	4.93546	+	2.84949i	0.165251	+	0.0954080i
$893$	−2.06498	−	1.19222i	−0.0691020	−	0.0398960i
$894$	0.824610	+	1.42827i	0.0275791	+	0.0477684i
$895$	−8.45083	−	0.408637i	−0.282480	−	0.0136592i
$896$	2.28961	−	3.96572i	0.0764905	−	0.132485i
$897$		−	39.7467i		−	1.32710i
$898$			13.2500i			0.442160i
$899$	−6.65202	−	18.7169i	−0.221857	−	0.624242i
$900$	4.97667	+	0.482419i	0.165889	+	0.0160806i
$901$	−11.3829			−0.379220
$902$	6.46530	+	3.73274i	0.215271	+	0.124287i
$903$			5.11491i			0.170213i
$904$	6.37573	+	11.0431i	0.212054	+	0.367288i
$905$	27.6192	−	42.9087i	0.918094	−	1.42633i
$906$	−3.31858	+	5.74796i	−0.110253	+	0.190963i
$907$		−	8.68452i		−	0.288365i	−0.989551	−	0.144182i	$-0.953945\pi$
$907$		−	8.68452i		−	0.288365i	0.989551	−	0.144182i	$-0.0460552\pi$
$908$	−6.67585	+	3.85430i	−0.221546	+	0.127910i
$909$	−2.99412	−	5.18598i	−0.0993088	−	0.172008i
$910$	47.5684	−	24.4800i	1.57688	−	0.811506i
$911$	6.71051	−	11.6229i	0.222329	−	0.385085i	−0.733186	−	0.680028i	$-0.761967\pi$
$911$	6.71051	−	11.6229i	0.222329	−	0.385085i	0.955515	+	0.294943i	$0.0953007\pi$
$912$	1.53230	−	0.884673i	0.0507395	−	0.0292945i
$913$	34.0452	+	19.6560i	1.12673	+	0.650518i
$914$	25.2874			0.836431
$915$	0.646308	−	13.3660i	0.0213663	−	0.441866i
$916$	7.10263	−	12.3021i	0.234677	−	0.406473i
$917$	−57.9722	+	33.4703i	−1.91441	+	1.10529i
$918$	1.87651	+	1.08340i	0.0619339	+	0.0357576i
$919$	−10.8210	−	18.7426i	−0.356953	−	0.618260i	0.630498	−	0.776191i	$-0.282851\pi$
$919$	−10.8210	−	18.7426i	−0.356953	−	0.618260i	−0.987450	+	0.157931i	$0.949518\pi$
$920$	−7.78398	−	15.1254i	−0.256630	−	0.498671i
$921$	13.6610	+	23.6615i	0.450144	+	0.779673i
$922$			17.5310i			0.577352i
$923$	51.7567	+	29.8817i	1.70359	+	0.983569i
$924$	−5.14707	+	8.91499i	−0.169326	+	0.293282i
$925$	14.9340	−	6.79427i	0.491028	−	0.223394i
$926$	−7.42744			−0.244081
$927$	14.5737	+	8.41412i	0.478663	+	0.276356i
$928$			3.56764i			0.117114i
$929$	26.8753			0.881750			0.440875	−	0.897569i	$-0.354668\pi$
$929$	26.8753			0.881750			0.440875	+	0.897569i	$0.354668\pi$
$930$	3.59779	+	11.9187i	0.117976	+	0.390830i
$931$	24.7164			0.810048
$932$		−	9.15400i		−	0.299849i
$933$	−5.08913	−	2.93821i	−0.166611	−	0.0961928i
$934$	9.59245			0.313875
$935$	−9.68468	+	4.98401i	−0.316723	+	0.162995i
$936$	2.61234	−	4.52471i	0.0853871	−	0.147895i
$937$	−8.27722	−	4.77886i	−0.270405	−	0.156118i	0.358667	−	0.933466i	$-0.383231\pi$
$937$	−8.27722	−	4.77886i	−0.270405	−	0.156118i	−0.629072	+	0.777347i	$0.716565\pi$
$938$			41.4780i			1.35431i
$939$	−10.3753	−	17.9705i	−0.338584	−	0.586445i
$940$	−2.67941	+	1.37890i	−0.0873927	+	0.0449748i
$941$	−5.91795	−	10.2502i	−0.192920	−	0.334147i	0.753297	−	0.657681i	$-0.228462\pi$
$941$	−5.91795	−	10.2502i	−0.192920	−	0.334147i	−0.946217	+	0.323534i	$0.895129\pi$
$942$	17.5654	+	10.1414i	0.572311	+	0.330424i
$943$	−21.8792	+	12.6319i	−0.712483	+	0.411352i
$944$	−2.77594	+	4.80807i	−0.0903492	+	0.156489i
$945$	10.2275	+	0.494547i	0.332700	+	0.0160876i
$946$	−2.51099			−0.0816394
$947$	−19.7297	−	11.3909i	−0.641129	−	0.370156i	0.143920	−	0.989589i	$-0.454029\pi$
$947$	−19.7297	−	11.3909i	−0.641129	−	0.370156i	−0.785049	+	0.619433i	$0.787362\pi$
$948$	2.00561	−	1.15794i	0.0651391	−	0.0376081i
$949$	42.1146	−	72.9446i	1.36710	−	2.36788i
$950$	8.05254	−	3.66352i	0.261259	−	0.118860i
$951$	13.6514	+	23.6450i	0.442678	+	0.766741i
$952$	8.59293	−	4.96113i	0.278498	−	0.160791i
$953$		−	11.4336i		−	0.370371i	−0.982704	−	0.185185i	$-0.940711\pi$
$953$		−	11.4336i		−	0.370371i	0.982704	−	0.185185i	$-0.0592886\pi$
$954$	−2.62666	+	4.54951i	−0.0850413	+	0.147296i
$955$	−29.6677	+	46.0911i	−0.960023	+	1.49147i
$956$	11.2096	+	19.4156i	0.362544	+	0.627944i
$957$		−	8.02011i		−	0.259253i
$958$	−9.73096	−	5.61817i	−0.314393	−	0.181515i
$959$	−8.48435			−0.273974
$960$	0.107998	−	2.23346i	0.00348563	−	0.0720846i
$961$	−24.0470	+	19.5638i	−0.775709	+	0.631091i
$962$		−	17.1442i		−	0.552751i
$963$			0.489555i			0.0157757i
$964$	−12.4504	+	21.5647i	−0.401000	+	0.694552i
$965$	2.34092	−	48.4114i	0.0753568	−	1.55842i
$966$	−17.4182	−	30.1692i	−0.560420	−	0.970677i
$967$	−20.1896	−	11.6565i	−0.649253	−	0.374846i	0.138917	−	0.990304i	$-0.455638\pi$
$967$	−20.1896	−	11.6565i	−0.649253	−	0.374846i	−0.788170	+	0.615458i	$0.788971\pi$
$968$	5.14976	+	2.97321i	0.165520	+	0.0955627i
$969$	3.83382			0.123160
$970$	7.84540	+	15.2448i	0.251901	+	0.489481i
$971$	14.8820	+	25.7764i	0.477586	+	0.827203i	0.999670	−	0.0256911i	$-0.00817863\pi$
$971$	14.8820	+	25.7764i	0.477586	+	0.827203i	−0.522084	+	0.852894i	$0.674845\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	11.8802	+	6.85904i	0.380862	+	0.219891i
$974$	−13.7887	−	23.8828i	−0.441819	−	0.765254i
$975$	15.1836	−	21.2578i	0.486264	−	0.680793i
$976$	−5.98443			−0.191557
$977$		−	45.9107i		−	1.46881i	−0.678710	−	0.734407i	$-0.737460\pi$
$977$		−	45.9107i		−	1.46881i	0.678710	−	0.734407i	$-0.262540\pi$
$978$	3.37095	+	1.94622i	0.107791	+	0.0622332i
$979$	0.768477	+	1.33104i	0.0245606	+	0.0425403i
$980$	16.9064	−	26.2654i	0.540055	−	0.839018i
$981$	10.0310	+	17.3742i	0.320265	+	0.554715i
$982$	−17.4796	+	10.0918i	−0.557796	+	0.322043i
$983$	34.4273	−	19.8766i	1.09806	−	0.633965i	0.162349	−	0.986733i	$-0.448093\pi$
$983$	34.4273	−	19.8766i	1.09806	−	0.633965i	0.935711	+	0.352768i	$0.114760\pi$
$984$	−3.32092			−0.105867
$985$	−37.6506	−	24.2347i	−1.19965	−	0.772183i
$986$	−3.86519	+	6.69470i	−0.123093	+	0.213203i
$987$	−5.34434	+	3.08556i	−0.170112	+	0.0982144i
$988$		−	9.24428i		−	0.294100i
$989$	4.24871	−	7.35899i	0.135101	−	0.234002i
$990$	−0.242781	+	5.02085i	−0.00771610	+	0.159573i
$991$	−34.2199			−1.08703			−0.543515	−	0.839400i	$-0.682907\pi$
$991$	−34.2199			−1.08703			−0.543515	+	0.839400i	$0.682907\pi$
$992$	5.24628	−	1.86454i	0.166570	−	0.0591992i
$993$		−	2.65636i		−	0.0842971i
$994$	52.3802			1.66140
$995$	5.84674	−	9.08337i	0.185354	−	0.287962i
$996$	−17.4874			−0.554110
$997$	−17.1824	+	9.92028i	−0.544173	+	0.314178i	−0.746768	−	0.665084i	$-0.768396\pi$
$997$	−17.1824	+	9.92028i	−0.544173	+	0.314178i	0.202596	+	0.979262i	$0.435062\pi$
$998$	2.77241	+	1.60065i	0.0877591	+	0.0506677i
$999$	1.64069	−	2.84176i	0.0519092	−	0.0899094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.6	✓	28
5.4	even	2	inner	930.2.s.d.439.12	yes	28
31.25	even	3	inner	930.2.s.d.769.5	yes	28
155.149	even	6	inner	930.2.s.d.769.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.6	✓	28	1.1	even	1	trivial
930.2.s.d.439.12	yes	28	5.4	even	2	inner
930.2.s.d.769.5	yes	28	31.25	even	3	inner
930.2.s.d.769.13	yes	28	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.02320 + 1.98823i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.02320 + 1.98823i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-3.96572 - 2.28961i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.98823 - 1.02320i) q^{10} +(1.12401 + 1.94684i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-4.52471 + 2.61234i) q^{13} +(-2.28961 + 3.96572i) q^{14} +(-0.107998 + 2.23346i) q^{15} +1.00000 q^{16} +(1.87651 + 1.08340i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.884673 - 1.53230i) q^{19} +(-1.02320 - 1.98823i) q^{20} +(-2.28961 - 3.96572i) q^{21} +(1.94684 - 1.12401i) q^{22} +7.60749i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.90612 + 4.06872i) q^{25} +(2.61234 + 4.52471i) q^{26} +1.00000i q^{27} +(3.96572 + 2.28961i) q^{28} -3.56764 q^{29} +(2.23346 + 0.107998i) q^{30} +(1.86454 + 5.24628i) q^{31} -1.00000i q^{32} +2.24801i q^{33} +(1.08340 - 1.87651i) q^{34} +(0.494547 - 10.2275i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.84176 - 1.64069i) q^{37} +(-1.53230 - 0.884673i) q^{38} -5.22469 q^{39} +(-1.98823 + 1.02320i) q^{40} +(1.66046 + 2.87600i) q^{41} +(-3.96572 + 2.28961i) q^{42} +(-0.967335 - 0.558491i) q^{43} +(-1.12401 - 1.94684i) q^{44} +(-1.21026 + 1.88023i) q^{45} +7.60749 q^{46} -1.34764i q^{47} +(0.866025 + 0.500000i) q^{48} +(6.98462 + 12.0977i) q^{49} +(4.06872 + 2.90612i) q^{50} +(1.08340 + 1.87651i) q^{51} +(4.52471 - 2.61234i) q^{52} +(-4.54951 + 2.62666i) q^{53} +1.00000 q^{54} +(-2.72068 + 4.22679i) q^{55} +(2.28961 - 3.96572i) q^{56} +(1.53230 - 0.884673i) q^{57} +3.56764i q^{58} +(-2.77594 + 4.80807i) q^{59} +(0.107998 - 2.23346i) q^{60} -5.98443 q^{61} +(5.24628 - 1.86454i) q^{62} -4.57922i q^{63} -1.00000 q^{64} +(-9.82363 - 6.32322i) q^{65} +2.24801 q^{66} +(7.84436 - 4.52894i) q^{67} +(-1.87651 - 1.08340i) q^{68} +(-3.80374 + 6.58828i) q^{69} +(-10.2275 - 0.494547i) q^{70} +(-5.71934 - 9.90618i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-13.9615 + 8.06069i) q^{73} +(-1.64069 + 2.84176i) q^{74} +(-4.55113 + 2.07055i) q^{75} +(-0.884673 + 1.53230i) q^{76} -10.2941i q^{77} +5.22469i q^{78} +(-1.15794 + 2.00561i) q^{79} +(1.02320 + 1.98823i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.87600 - 1.66046i) q^{82} +(15.1446 - 8.74371i) q^{83} +(2.28961 + 3.96572i) q^{84} +(-0.234011 + 4.83946i) q^{85} +(-0.558491 + 0.967335i) q^{86} +(-3.08967 - 1.78382i) q^{87} +(-1.94684 + 1.12401i) q^{88} +0.683694 q^{89} +(1.88023 + 1.21026i) q^{90} +23.9250 q^{91} -7.60749i q^{92} +(-1.00840 + 5.47569i) q^{93} -1.34764 q^{94} +(3.95176 + 0.191086i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.66751i q^{97} +(12.0977 - 6.98462i) q^{98} +(-1.12401 + 1.94684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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