LMFDB - Embedded newform 384.2.w.a.131.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(11,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 21, 16]))

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

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

chi := DirichletCharacter("384.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.w (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	384.131
Dual form			384.2.w.a.299.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38248 + 0.297929i) q^{2} +(0.428384 - 1.67824i) q^{3} +(1.82248 - 0.823758i) q^{4} +(0.606287 - 1.99866i) q^{5} +(-0.0922344 + 2.44775i) q^{6} +(-0.441862 - 2.22139i) q^{7} +(-2.27411 + 1.68179i) q^{8} +(-2.63298 - 1.43786i) q^{9} +O(q^{10})$	\(q+(-1.38248 + 0.297929i) q^{2} +(0.428384 - 1.67824i) q^{3} +(1.82248 - 0.823758i) q^{4} +(0.606287 - 1.99866i) q^{5} +(-0.0922344 + 2.44775i) q^{6} +(-0.441862 - 2.22139i) q^{7} +(-2.27411 + 1.68179i) q^{8} +(-2.63298 - 1.43786i) q^{9} +(-0.242719 + 2.94373i) q^{10} +(4.48085 - 0.441325i) q^{11} +(-0.601743 - 3.41144i) q^{12} +(-0.494698 - 1.63080i) q^{13} +(1.27268 + 2.93938i) q^{14} +(-3.09451 - 1.87369i) q^{15} +(2.64285 - 3.00256i) q^{16} +(-2.01633 - 0.835190i) q^{17} +(4.06840 + 1.20337i) q^{18} +(-4.00951 + 7.50127i) q^{19} +(-0.541468 - 4.14195i) q^{20} +(-3.91731 - 0.210057i) q^{21} +(-6.06318 + 1.94509i) q^{22} +(-0.408269 - 0.611018i) q^{23} +(1.84826 + 4.53695i) q^{24} +(0.530287 + 0.354326i) q^{25} +(1.16977 + 2.10716i) q^{26} +(-3.54100 + 3.80281i) q^{27} +(-2.63517 - 3.68445i) q^{28} +(5.82767 + 0.573975i) q^{29} +(4.83631 + 1.66839i) q^{30} +(0.361193 + 0.361193i) q^{31} +(-2.75912 + 4.93834i) q^{32} +(1.17887 - 7.70900i) q^{33} +(3.03635 + 0.553909i) q^{34} +(-4.70770 - 0.463668i) q^{35} +(-5.98299 - 0.451534i) q^{36} +(-3.66025 - 6.84785i) q^{37} +(3.30821 - 11.5649i) q^{38} +(-2.94879 + 0.131613i) q^{39} +(1.98257 + 5.56482i) q^{40} +(-5.77154 - 8.63772i) q^{41} +(5.47817 - 0.876681i) q^{42} +(-8.33382 - 6.83939i) q^{43} +(7.80270 - 4.49544i) q^{44} +(-4.47013 + 4.39067i) q^{45} +(0.746462 + 0.723082i) q^{46} +(11.8375 + 4.90324i) q^{47} +(-3.90686 - 5.72158i) q^{48} +(1.72782 - 0.715687i) q^{49} +(-0.838672 - 0.331860i) q^{50} +(-2.26541 + 3.02610i) q^{51} +(-2.24496 - 2.56459i) q^{52} +(0.630753 - 0.0621237i) q^{53} +(3.76238 - 6.31225i) q^{54} +(1.83462 - 9.22327i) q^{55} +(4.74076 + 4.30857i) q^{56} +(10.8713 + 9.94234i) q^{57} +(-8.22761 + 0.942722i) q^{58} +(-1.27573 + 4.20552i) q^{59} +(-7.18314 - 0.865630i) q^{60} +(3.02027 - 2.47867i) q^{61} +(-0.606951 - 0.391731i) q^{62} +(-2.03064 + 6.48420i) q^{63} +(2.34315 - 7.64916i) q^{64} -3.55935 q^{65} +(0.666966 + 11.0087i) q^{66} +(3.91840 + 4.77459i) q^{67} +(-4.36271 + 0.138850i) q^{68} +(-1.20033 + 0.423423i) q^{69} +(6.64642 - 0.761549i) q^{70} +(-1.06553 - 5.35680i) q^{71} +(8.40586 - 1.15827i) q^{72} +(6.32314 + 1.25775i) q^{73} +(7.10038 + 8.37649i) q^{74} +(0.821810 - 0.738160i) q^{75} +(-1.12802 + 16.9738i) q^{76} +(-2.96027 - 9.75872i) q^{77} +(4.03742 - 1.06048i) q^{78} +(4.60085 + 11.1074i) q^{79} +(-4.39877 - 7.10257i) q^{80} +(4.86512 + 7.57170i) q^{81} +(10.5524 + 10.2219i) q^{82} +(-3.39275 + 6.34740i) q^{83} +(-7.31225 + 2.84409i) q^{84} +(-2.89174 + 3.52359i) q^{85} +(13.5589 + 6.97240i) q^{86} +(3.45975 - 9.53434i) q^{87} +(-9.44773 + 8.53948i) q^{88} +(1.07081 + 0.715491i) q^{89} +(4.87175 - 7.40177i) q^{90} +(-3.40406 + 1.81951i) q^{91} +(-1.24739 - 0.777251i) q^{92} +(0.760899 - 0.451440i) q^{93} +(-17.8258 - 3.25189i) q^{94} +(12.5616 + 12.5616i) q^{95} +(7.10576 + 6.74597i) q^{96} +(-0.135186 + 0.135186i) q^{97} +(-2.17545 + 1.50419i) q^{98} +(-12.4325 - 5.28084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{32}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.38248	+	0.297929i	−0.977558	+	0.210667i
$2$	−1.38248	+	0.297929i	−0.977558	+	0.210667i
$3$	0.428384	−	1.67824i	0.247327	−	0.968932i
$3$	0.428384	−	1.67824i	0.247327	−	0.968932i
$4$	1.82248	−	0.823758i	0.911239	−	0.411879i
$5$	0.606287	−	1.99866i	0.271140	−	0.893828i	−0.710599	−	0.703597i	$-0.751576\pi$
$5$	0.606287	−	1.99866i	0.271140	−	0.893828i	0.981739	−	0.190232i	$-0.0609239\pi$
$6$	−0.0922344	+	2.44775i	−0.0376545	+	0.999291i
$7$	−0.441862	−	2.22139i	−0.167008	−	0.839607i	−0.969904	−	0.243488i	$-0.921709\pi$
$7$	−0.441862	−	2.22139i	−0.167008	−	0.839607i	0.802896	−	0.596119i	$-0.203291\pi$
$8$	−2.27411	+	1.68179i	−0.804019	+	0.594604i
$9$	−2.63298	−	1.43786i	−0.877658	−	0.479287i
$10$	−0.242719	+	2.94373i	−0.0767545	+	0.930889i
$11$	4.48085	−	0.441325i	1.35103	−	0.133065i	0.603536	−	0.797336i	$-0.293758\pi$
$11$	4.48085	−	0.441325i	1.35103	−	0.133065i	0.747491	+	0.664271i	$0.231258\pi$
$12$	−0.601743	−	3.41144i	−0.173708	−	0.984797i
$13$	−0.494698	−	1.63080i	−0.137205	−	0.452303i	0.861231	−	0.508213i	$-0.169694\pi$
$13$	−0.494698	−	1.63080i	−0.137205	−	0.452303i	−0.998436	+	0.0559106i	$0.982194\pi$
$14$	1.27268	+	2.93938i	0.340138	+	0.785581i
$15$	−3.09451	−	1.87369i	−0.798999	−	0.483784i
$16$	2.64285	−	3.00256i	0.660712	−	0.750640i
$17$	−2.01633	−	0.835190i	−0.489031	−	0.202563i	0.124522	−	0.992217i	$-0.460260\pi$
$17$	−2.01633	−	0.835190i	−0.489031	−	0.202563i	−0.613553	+	0.789653i	$0.710260\pi$
$18$	4.06840	+	1.20337i	0.958932	+	0.283637i
$19$	−4.00951	+	7.50127i	−0.919845	+	1.72091i	−0.266522	+	0.963829i	$0.585875\pi$
$19$	−4.00951	+	7.50127i	−0.919845	+	1.72091i	−0.653323	+	0.757080i	$0.726625\pi$
$20$	−0.541468	−	4.14195i	−0.121076	−	0.926168i
$21$	−3.91731	−	0.210057i	−0.854828	−	0.0458382i
$22$	−6.06318	+	1.94509i	−1.29267	+	0.414696i
$23$	−0.408269	−	0.611018i	−0.0851300	−	0.127406i	0.786461	−	0.617640i	$-0.211911\pi$
$23$	−0.408269	−	0.611018i	−0.0851300	−	0.127406i	−0.871591	+	0.490234i	$0.836911\pi$
$24$	1.84826	+	4.53695i	0.377275	+	0.926101i
$25$	0.530287	+	0.354326i	0.106057	+	0.0708652i
$26$	1.16977	+	2.10716i	0.229411	+	0.413248i
$27$	−3.54100	+	3.80281i	−0.681465	+	0.731851i
$28$	−2.63517	−	3.68445i	−0.498001	−	0.696295i
$29$	5.82767	+	0.573975i	1.08217	+	0.106585i	0.623349	−	0.781944i	$-0.285772\pi$
$29$	5.82767	+	0.573975i	1.08217	+	0.106585i	0.458822	+	0.888528i	$0.348272\pi$
$30$	4.83631	+	1.66839i	0.882985	+	0.304604i
$31$	0.361193	+	0.361193i	0.0648723	+	0.0648723i	0.738799	−	0.673926i	$-0.235393\pi$
$31$	0.361193	+	0.361193i	0.0648723	+	0.0648723i	−0.673926	+	0.738799i	$0.735393\pi$
$32$	−2.75912	+	4.93834i	−0.487749	+	0.872984i
$33$	1.17887	−	7.70900i	0.205215	−	1.34196i
$34$	3.03635	+	0.553909i	0.520730	+	0.0949946i
$35$	−4.70770	−	0.463668i	−0.795747	−	0.0783742i
$36$	−5.98299	−	0.451534i	−0.997164	−	0.0752557i
$37$	−3.66025	−	6.84785i	−0.601742	−	1.12578i	−0.979797	−	0.199996i	$-0.935907\pi$
$37$	−3.66025	−	6.84785i	−0.601742	−	1.12578i	0.378055	−	0.925783i	$-0.376593\pi$
$38$	3.30821	−	11.5649i	0.536662	−	1.87607i
$39$	−2.94879	+	0.131613i	−0.472185	+	0.0210750i
$40$	1.98257	+	5.56482i	0.313472	+	0.879876i
$41$	−5.77154	−	8.63772i	−0.901363	−	1.34898i	−0.936893	−	0.349616i	$-0.886312\pi$
$41$	−5.77154	−	8.63772i	−0.901363	−	1.34898i	0.0355305	−	0.999369i	$-0.488688\pi$
$42$	5.47817	−	0.876681i	0.845300	−	0.135275i
$43$	−8.33382	−	6.83939i	−1.27090	−	1.04300i	−0.996688	−	0.0813264i	$-0.974084\pi$
$43$	−8.33382	−	6.83939i	−1.27090	−	1.04300i	−0.274208	−	0.961670i	$-0.588416\pi$
$44$	7.80270	−	4.49544i	1.17630	−	0.677713i
$45$	−4.47013	+	4.39067i	−0.666368	+	0.654522i
$46$	0.746462	+	0.723082i	0.110060	+	0.106613i
$47$	11.8375	+	4.90324i	1.72667	+	0.715211i	0.999589	+	0.0286610i	$0.00912431\pi$
$47$	11.8375	+	4.90324i	1.72667	+	0.715211i	0.727083	+	0.686550i	$0.240876\pi$
$48$	−3.90686	−	5.72158i	−0.563907	−	0.825838i
$49$	1.72782	−	0.715687i	0.246832	−	0.102241i
$50$	−0.838672	−	0.331860i	−0.118606	−	0.0469321i
$51$	−2.26541	+	3.02610i	−0.317221	+	0.423739i
$52$	−2.24496	−	2.56459i	−0.311320	−	0.355644i
$53$	0.630753	−	0.0621237i	0.0866406	−	0.00853335i	−0.0546039	−	0.998508i	$-0.517390\pi$
$53$	0.630753	−	0.0621237i	0.0866406	−	0.00853335i	0.141245	+	0.989975i	$0.454890\pi$
$54$	3.76238	−	6.31225i	0.511995	−	0.858989i
$55$	1.83462	−	9.22327i	0.247380	−	1.24367i
$56$	4.74076	+	4.30857i	0.633511	+	0.575756i
$57$	10.8713	+	9.94234i	1.43994	+	1.31689i
$58$	−8.22761	+	0.942722i	−1.08034	+	0.123785i
$59$	−1.27573	+	4.20552i	−0.166086	+	0.547512i	−0.999990	−	0.00439698i	$-0.998600\pi$
$59$	−1.27573	+	4.20552i	−0.166086	+	0.547512i	0.833904	+	0.551909i	$0.186100\pi$
$60$	−7.18314	−	0.865630i	−0.927339	−	0.111752i
$61$	3.02027	−	2.47867i	0.386706	−	0.317362i	−0.420874	−	0.907119i	$-0.638277\pi$
$61$	3.02027	−	2.47867i	0.386706	−	0.317362i	0.807581	+	0.589757i	$0.200777\pi$
$62$	−0.606951	−	0.391731i	−0.0770829	−	0.0497499i
$63$	−2.03064	+	6.48420i	−0.255836	+	0.816933i
$64$	2.34315	−	7.64916i	0.292893	−	0.956145i
$65$	−3.55935			−0.441483
$66$	0.666966	+	11.0087i	0.0820979	+	1.35508i
$67$	3.91840	+	4.77459i	0.478709	+	0.583308i	0.955234	−	0.295853i	$-0.0956037\pi$
$67$	3.91840	+	4.77459i	0.478709	+	0.583308i	−0.476525	+	0.879161i	$0.658104\pi$
$68$	−4.36271	+	0.138850i	−0.529056	+	0.0168381i
$69$	−1.20033	+	0.423423i	−0.144503	+	0.0509742i
$70$	6.64642	−	0.761549i	0.794400	−	0.0910225i
$71$	−1.06553	−	5.35680i	−0.126456	−	0.635735i	−0.991075	−	0.133307i	$-0.957440\pi$
$71$	−1.06553	−	5.35680i	−0.126456	−	0.635735i	0.864619	−	0.502428i	$-0.167560\pi$
$72$	8.40586	−	1.15827i	0.990640	−	0.136503i
$73$	6.32314	+	1.25775i	0.740068	+	0.147209i	0.550707	−	0.834699i	$-0.314358\pi$
$73$	6.32314	+	1.25775i	0.740068	+	0.147209i	0.189361	+	0.981908i	$0.439358\pi$
$74$	7.10038	+	8.37649i	0.825402	+	0.973747i
$75$	0.821810	−	0.738160i	0.0948945	−	0.0852354i
$76$	−1.12802	+	16.9738i	−0.129392	+	1.94702i
$77$	−2.96027	−	9.75872i	−0.337355	−	1.11211i
$78$	4.03742	−	1.06048i	0.457148	−	0.120076i
$79$	4.60085	+	11.1074i	0.517636	+	1.24968i	0.939351	+	0.342956i	$0.111428\pi$
$79$	4.60085	+	11.1074i	0.517636	+	1.24968i	−0.421715	+	0.906728i	$0.638572\pi$
$80$	−4.39877	−	7.10257i	−0.491798	−	0.794091i
$81$	4.86512	+	7.57170i	0.540568	+	0.841300i
$82$	10.5524	+	10.2219i	1.16532	+	1.12882i
$83$	−3.39275	+	6.34740i	−0.372403	+	0.696717i	−0.996406	−	0.0847047i	$-0.973005\pi$
$83$	−3.39275	+	6.34740i	−0.372403	+	0.696717i	0.624003	+	0.781422i	$0.285505\pi$
$84$	−7.31225	+	2.84409i	−0.797832	+	0.310316i
$85$	−2.89174	+	3.52359i	−0.313653	+	0.382187i
$86$	13.5589	+	6.97240i	1.46210	+	0.751854i
$87$	3.45975	−	9.53434i	0.370924	−	1.02219i
$88$	−9.44773	+	8.53948i	−1.00713	+	0.910312i
$89$	1.07081	+	0.715491i	0.113505	+	0.0758419i	0.611027	−	0.791610i	$-0.290757\pi$
$89$	1.07081	+	0.715491i	0.113505	+	0.0758419i	−0.497522	+	0.867451i	$0.665757\pi$
$90$	4.87175	−	7.40177i	0.513527	−	0.780215i
$91$	−3.40406	+	1.81951i	−0.356842	+	0.190736i
$92$	−1.24739	−	0.777251i	−0.130050	−	0.0810341i
$93$	0.760899	−	0.451440i	0.0789015	−	0.0468121i
$94$	−17.8258	−	3.25189i	−1.83859	−	0.335407i
$95$	12.5616	+	12.5616i	1.28879	+	1.28879i
$96$	7.10576	+	6.74597i	0.725229	+	0.688508i
$97$	−0.135186	+	0.135186i	−0.0137261	+	0.0137261i	−0.713937	−	0.700210i	$-0.753089\pi$
$97$	−0.135186	+	0.135186i	−0.0137261	+	0.0137261i	0.700210	+	0.713937i	$0.253089\pi$
$98$	−2.17545	+	1.50419i	−0.219753	+	0.151946i
$99$	−12.4325	−	5.28084i	−1.24952	−	0.530744i
$100$	1.25831	+	0.208924i	0.125831	+	0.0208924i
$101$	−3.33403	−	6.23753i	−0.331748	−	0.620658i	0.659644	−	0.751578i	$-0.270707\pi$
$101$	−3.33403	−	6.23753i	−0.331748	−	0.620658i	−0.991393	+	0.130920i	$0.958207\pi$
$102$	2.23031	−	4.85844i	0.220834	−	0.481057i
$103$	7.37896	−	11.0434i	0.727070	−	1.08814i	−0.265218	−	0.964188i	$-0.585444\pi$
$103$	7.37896	−	11.0434i	0.727070	−	1.08814i	0.992289	−	0.123949i	$-0.0395561\pi$
$104$	3.86767	+	2.87664i	0.379256	+	0.282078i
$105$	−2.79485	+	7.70202i	−0.272749	+	0.751641i
$106$	−0.853492	+	0.273804i	−0.0828985	+	0.0265942i
$107$	1.76765	+	1.45067i	0.170885	+	0.140242i	0.715948	−	0.698153i	$-0.245995\pi$
$107$	1.76765	+	1.45067i	0.170885	+	0.140242i	−0.545064	+	0.838395i	$0.683495\pi$
$108$	−3.32079	+	9.84745i	−0.319544	+	0.947572i
$109$	9.83631	+	5.25761i	0.942147	+	0.503588i	0.869589	−	0.493776i	$-0.164384\pi$
$109$	9.83631	+	5.25761i	0.942147	+	0.503588i	0.0725580	+	0.997364i	$0.476884\pi$
$110$	0.211554	+	13.2975i	0.0201709	+	1.26787i
$111$	−13.0603	+	3.20927i	−1.23963	+	0.304611i
$112$	−7.83763	−	4.54408i	−0.740587	−	0.429375i
$113$	1.31346	−	0.544052i	0.123560	−	0.0511801i	−0.320047	−	0.947402i	$-0.603699\pi$
$113$	1.31346	−	0.544052i	0.123560	−	0.0511801i	0.443607	+	0.896222i	$0.353699\pi$
$114$	−17.9914	−	10.5062i	−1.68505	−	0.983992i
$115$	−1.46875	+	0.445539i	−0.136961	+	0.0415468i
$116$	11.0936	−	3.75453i	1.03002	−	0.348599i
$117$	−1.04234	+	5.00516i	−0.0963640	+	0.462728i
$118$	0.510722	−	6.19410i	0.0470158	−	0.570213i
$119$	−0.964345	+	4.84809i	−0.0884014	+	0.444424i
$120$	10.1884	−	0.943349i	0.930070	−	0.0861156i
$121$	9.09461	−	1.80903i	0.826783	−	0.164457i
$122$	−3.43699	+	4.32653i	−0.311170	+	0.391706i
$123$	−16.9686	+	5.98577i	−1.53001	+	0.539718i
$124$	0.955803	+	0.360731i	0.0858336	+	0.0323946i
$125$	9.10221	−	7.46999i	0.814127	−	0.668137i
$126$	0.875478	−	9.56924i	0.0779938	−	0.852495i
$127$		−	5.83827i		−	0.518062i	−0.965869	−	0.259031i	$-0.916597\pi$
$127$		−	5.83827i		−	0.518062i	0.965869	−	0.259031i	$-0.0834033\pi$
$128$	−0.960439	+	11.2729i	−0.0848916	+	0.996390i
$129$	−15.0482	+	11.0563i	−1.32492	+	0.973449i
$130$	4.92071	−	1.06043i	0.431575	−	0.0930059i
$131$	7.43762	+	9.06277i	0.649828	+	0.791818i	0.988843	−	0.148963i	$-0.0475937\pi$
$131$	7.43762	+	9.06277i	0.649828	+	0.791818i	−0.339015	+	0.940781i	$0.610094\pi$
$132$	−4.20188	−	15.0206i	−0.365726	−	1.30737i
$133$	18.4349	+	5.59216i	1.59851	+	0.484902i
$134$	−6.83958	−	5.43334i	−0.590850	−	0.469369i
$135$	5.45366	+	9.38285i	0.469376	+	0.807547i
$136$	5.98997	−	1.49173i	0.513635	−	0.127915i
$137$	5.89641	+	1.17287i	0.503765	+	0.100205i	0.440429	−	0.897787i	$-0.354826\pi$
$137$	5.89641	+	1.17287i	0.503765	+	0.100205i	0.0633353	+	0.997992i	$0.479826\pi$
$138$	1.53328	−	0.942985i	0.130521	−	0.0802722i
$139$	1.84963	+	18.7796i	0.156883	+	1.59286i	0.675174	+	0.737659i	$0.264069\pi$
$139$	1.84963	+	18.7796i	0.156883	+	1.59286i	−0.518290	+	0.855205i	$0.673431\pi$
$140$	−8.96163	+	3.03298i	−0.757396	+	0.256334i
$141$	13.2998	−	17.7656i	1.12004	−	1.49614i
$142$	3.06902	+	7.08819i	0.257546	+	0.594828i
$143$	−2.93638	−	7.08905i	−0.245553	−	0.592816i
$144$	−11.2758	+	4.10562i	−0.939651	+	0.342135i
$145$	4.68042	−	11.2995i	0.388688	−	0.938376i
$146$	−9.11631	+	0.145034i	−0.754471	+	0.0120031i
$147$	−0.460924	−	3.20629i	−0.0380164	−	0.264450i
$148$	−12.3117	−	9.46489i	−1.01201	−	0.778009i
$149$	5.01985	−	6.11670i	0.411242	−	0.501100i	−0.525659	−	0.850696i	$-0.676181\pi$
$149$	5.01985	−	6.11670i	0.411242	−	0.501100i	0.936901	+	0.349596i	$0.113681\pi$
$150$	−0.916213	+	1.26533i	−0.0748085	+	0.103314i
$151$	0.147234	−	0.0983783i	0.0119817	−	0.00800591i	−0.549565	−	0.835451i	$-0.685207\pi$
$151$	0.147234	−	0.0983783i	0.0119817	−	0.00800591i	0.561547	+	0.827445i	$0.310207\pi$
$152$	−3.49751	−	23.8019i	−0.283686	−	1.93059i
$153$	4.10805	+	5.09823i	0.332116	+	0.412168i
$154$	6.99991	+	12.6092i	0.564068	+	1.01608i
$155$	0.940890	−	0.502916i	0.0755741	−	0.0403952i
$156$	−5.26569	+	2.66895i	−0.421593	+	0.213687i
$157$	−0.626999	+	6.36603i	−0.0500400	+	0.508064i	0.937196	+	0.348802i	$0.113412\pi$
$157$	−0.626999	+	6.36603i	−0.0500400	+	0.508064i	−0.987236	+	0.159262i	$0.949088\pi$
$158$	−9.66979	−	13.9850i	−0.769287	−	1.11259i
$159$	0.165946	−	1.08517i	0.0131603	−	0.0860593i
$160$	8.19726	+	8.50861i	0.648050	+	0.672664i
$161$	−1.17691	+	1.17691i	−0.0927536	+	0.0927536i
$162$	−8.98173	−	9.01823i	−0.705671	−	0.708539i
$163$	1.84784	−	18.7615i	0.144734	−	1.46951i	−0.598846	−	0.800864i	$-0.704374\pi$
$163$	1.84784	−	18.7615i	0.144734	−	1.46951i	0.743580	−	0.668647i	$-0.233126\pi$
$164$	−17.6339	−	10.9877i	−1.37697	−	0.857995i
$165$	−14.6929	−	7.03003i	−1.14384	−	0.547287i
$166$	2.79933	−	9.78592i	0.217270	−	0.759535i
$167$	−4.62133	+	6.91630i	−0.357609	+	0.535200i	−0.966035	−	0.258411i	$-0.916801\pi$
$167$	−4.62133	+	6.91630i	−0.357609	+	0.535200i	0.608426	+	0.793610i	$0.291801\pi$
$168$	9.26167	−	6.11042i	0.714553	−	0.471429i
$169$	8.39432	−	5.60891i	0.645717	−	0.431454i
$170$	2.94798	−	5.73281i	0.226099	−	0.439686i
$171$	21.3427	−	13.9855i	1.63212	−	1.06950i
$172$	−20.8222	−	5.59958i	−1.58768	−	0.426964i
$173$	−12.8785	−	6.88369i	−0.979133	−	0.523357i	−0.0974705	−	0.995238i	$-0.531075\pi$
$173$	−12.8785	−	6.88369i	−0.979133	−	0.523357i	−0.881662	+	0.471881i	$0.843575\pi$
$174$	−1.94246	+	14.2118i	−0.147258	+	1.07739i
$175$	0.552783	−	1.33454i	0.0417865	−	0.100882i
$176$	10.5171	−	14.6204i	0.792756	−	1.10205i
$177$	6.51137	+	3.94256i	0.489424	+	0.296341i
$178$	−1.69353	−	0.670125i	−0.126936	−	0.0502280i
$179$	−16.1876	+	4.91046i	−1.20992	+	0.367025i	−0.829878	−	0.557944i	$-0.811590\pi$
$179$	−16.1876	+	4.91046i	−1.20992	+	0.367025i	−0.380042	+	0.924969i	$0.624090\pi$
$180$	−4.52987	+	11.6842i	−0.337637	+	0.870889i
$181$	−1.32032	−	13.4054i	−0.0981384	−	0.996415i	−0.910569	−	0.413357i	$-0.864356\pi$
$181$	−1.32032	−	13.4054i	−0.0981384	−	0.996415i	0.812431	−	0.583058i	$-0.198144\pi$
$182$	4.16394	−	3.52959i	0.308652	−	0.261631i
$183$	−2.86597	−	6.13057i	−0.211859	−	0.453184i
$184$	1.95605	+	0.702898i	0.144202	+	0.0518183i
$185$	−15.9057	+	3.16384i	−1.16941	+	0.232610i
$186$	−0.917427	+	0.850798i	−0.0672690	+	0.0623835i
$187$	−9.40345	−	2.85251i	−0.687649	−	0.208596i
$188$	25.6126	−	0.815163i	1.86799	−	0.0594519i
$189$	10.0122	+	6.18562i	0.728277	+	0.449938i
$190$	−21.1085	−	13.6236i	−1.53137	−	0.988361i
$191$			3.32321i			0.240459i	0.992746	+	0.120229i	$0.0383630\pi$
$191$			3.32321i			0.240459i	−0.992746	+	0.120229i	$0.961637\pi$
$192$	−11.8334	−	7.20913i	−0.853999	−	0.520274i
$193$			7.41555i			0.533783i	0.963727	+	0.266891i	$0.0859965\pi$
$193$			7.41555i			0.533783i	−0.963727	+	0.266891i	$0.914004\pi$
$194$	0.146616	−	0.227167i	0.0105264	−	0.0163097i
$195$	−1.52477	+	5.97344i	−0.109191	+	0.427767i
$196$	2.55936	−	2.72763i	0.182812	−	0.194831i
$197$	0.914483	+	0.277405i	0.0651542	+	0.0197643i	0.322694	−	0.946504i	$-0.395412\pi$
$197$	0.914483	+	0.277405i	0.0651542	+	0.0197643i	−0.257539	+	0.966268i	$0.582912\pi$
$198$	18.7610	+	3.59662i	1.33328	+	0.255601i
$199$	23.9554	−	4.76503i	1.69815	−	0.337784i	0.751426	−	0.659818i	$-0.229367\pi$
$199$	23.9554	−	4.76503i	1.69815	−	0.337784i	0.946728	+	0.322034i	$0.104367\pi$
$200$	−1.80183	+	0.0860558i	−0.127409	+	0.00608506i
$201$	9.69148	−	4.53066i	0.683584	−	0.319568i
$202$	6.46755	+	7.62993i	0.455056	+	0.536840i
$203$	−1.30000	−	13.1991i	−0.0912423	−	0.926399i
$204$	−1.63589	+	7.38115i	−0.114535	+	0.516784i
$205$	−20.7631	+	6.29841i	−1.45016	+	0.439900i
$206$	−6.91109	+	17.4656i	−0.481518	+	1.21689i
$207$	0.196404	+	2.19583i	0.0136510	+	0.152621i
$208$	−6.20399	−	2.82460i	−0.430169	−	0.195850i
$209$	−14.6555	+	35.3815i	−1.01374	+	2.44739i
$210$	1.56916	−	11.4805i	0.108282	−	0.792232i
$211$	−3.69542	−	1.97524i	−0.254403	−	0.135981i	0.339266	−	0.940690i	$-0.389821\pi$
$211$	−3.69542	−	1.97524i	−0.254403	−	0.135981i	−0.593669	+	0.804709i	$0.702321\pi$
$212$	1.09836	−	0.632807i	0.0754355	−	0.0434613i
$213$	−9.44645	−	0.506544i	−0.647260	−	0.0347078i
$214$	−2.87592	−	1.47888i	−0.196594	−	0.101094i
$215$	−18.7223	+	12.5098i	−1.27685	+	0.853164i
$216$	1.65708	−	14.6032i	0.112750	−	0.993623i
$217$	0.642754	−	0.961950i	0.0436330	−	0.0653014i
$218$	−15.1648	−	4.33801i	−1.02709	−	0.293807i
$219$	4.81954	−	10.0729i	0.325674	−	0.680666i
$220$	−4.25418	−	18.3205i	−0.286817	−	1.23517i
$221$	−0.364556	+	3.70140i	−0.0245227	+	0.248983i
$222$	17.0994	−	8.32778i	1.14764	−	0.558924i
$223$	7.69754	−	7.69754i	0.515466	−	0.515466i	−0.400730	−	0.916196i	$-0.631244\pi$
$223$	7.69754	−	7.69754i	0.515466	−	0.515466i	0.916196	+	0.400730i	$0.131244\pi$
$224$	12.1891	+	3.94702i	0.814422	+	0.263722i
$225$	−0.886760	−	1.69541i	−0.0591173	−	0.113027i
$226$	−1.65374	+	1.14346i	−0.110005	+	0.0760615i
$227$	0.251623	−	2.55477i	0.0167008	−	0.169566i	−0.983216	−	0.182444i	$-0.941599\pi$
$227$	0.251623	−	2.55477i	0.0167008	−	0.169566i	0.999917	+	0.0128777i	$0.00409921\pi$
$228$	28.0028	+	9.16435i	1.85453	+	0.606924i
$229$	−17.6495	+	9.43386i	−1.16631	+	0.623407i	−0.936789	−	0.349896i	$-0.886217\pi$
$229$	−17.6495	+	9.43386i	−1.16631	+	0.623407i	−0.229524	+	0.973303i	$0.573717\pi$
$230$	1.89777	−	1.05353i	0.125135	−	0.0694676i
$231$	−17.6456	+	0.787575i	−1.16099	+	0.0518187i
$232$	−14.2181	+	8.49565i	−0.933462	+	0.557767i
$233$	10.2627	−	6.85730i	0.672330	−	0.449237i	−0.171973	−	0.985102i	$-0.555014\pi$
$233$	10.2627	−	6.85730i	0.672330	−	0.449237i	0.844304	+	0.535865i	$0.180014\pi$
$234$	−0.0501770	−	7.23006i	−0.00328017	−	0.472644i
$235$	16.9768	−	20.6863i	1.10745	−	1.34943i
$236$	1.13934	+	8.71536i	0.0741647	+	0.567321i
$237$	20.6119	−	2.96309i	1.33888	−	0.192473i
$238$	−0.111201	−	6.98967i	−0.00720808	−	0.453073i
$239$	7.26738	−	17.5450i	0.470088	−	1.13489i	−0.494037	−	0.869441i	$-0.664479\pi$
$239$	7.26738	−	17.5450i	0.470088	−	1.13489i	0.964124	−	0.265451i	$-0.0855208\pi$
$240$	−13.8042	+	4.33957i	−0.891055	+	0.280118i
$241$	6.40309	+	15.4584i	0.412460	+	0.995765i	0.984475	+	0.175523i	$0.0561616\pi$
$241$	6.40309	+	15.4584i	0.412460	+	0.995765i	−0.572016	+	0.820243i	$0.693838\pi$
$242$	−12.0341	+	5.21049i	−0.773582	+	0.334943i
$243$	14.7913	−	4.92124i	0.948860	−	0.315698i
$244$	3.46255	−	7.00530i	0.221667	−	0.448468i
$245$	−0.382860	−	3.88724i	−0.0244600	−	0.248347i
$246$	21.6753	−	13.3306i	1.38197	−	0.849928i
$247$	14.2166	+	2.82785i	0.904578	+	0.179932i
$248$	−1.42885	−	0.213941i	−0.0907318	−	0.0135853i
$249$	9.19905	+	8.41297i	0.582966	+	0.533151i
$250$	−10.3581	+	13.0389i	−0.655101	+	0.824652i
$251$	18.1672	+	5.51096i	1.14670	+	0.347849i	0.805764	−	0.592236i	$-0.201755\pi$
$251$	18.1672	+	5.51096i	1.14670	+	0.347849i	0.340939	+	0.940085i	$0.389255\pi$
$252$	1.64062	+	13.4901i	0.103349	+	0.849794i
$253$	−2.09905	−	2.55770i	−0.131966	−	0.160801i
$254$	1.73939	+	8.07126i	0.109139	+	0.506436i
$255$	4.67466	+	6.36247i	0.292738	+	0.398434i
$256$	−2.03073	−	15.8706i	−0.126920	−	0.991913i
$257$			7.47451i			0.466247i	0.972447	+	0.233123i	$0.0748946\pi$
$257$			7.47451i			0.466247i	−0.972447	+	0.233123i	$0.925105\pi$
$258$	17.5098	−	19.7683i	1.09011	−	1.23072i
$259$	−13.5944	+	11.1567i	−0.844716	+	0.693241i
$260$	−6.48683	+	2.93204i	−0.402296	+	0.181837i
$261$	−14.5188	−	9.89064i	−0.898692	−	0.612215i
$262$	−12.9824	−	10.3132i	−0.802054	−	0.637150i
$263$	15.0942	−	3.00242i	0.930748	−	0.185137i	0.293644	−	0.955915i	$-0.405132\pi$
$263$	15.0942	−	3.00242i	0.930748	−	0.185137i	0.637104	+	0.770778i	$0.280132\pi$
$264$	10.2840	+	19.5137i	0.632939	+	1.20099i
$265$	0.258253	−	1.29833i	0.0158644	−	0.0797555i
$266$	−27.1519	−	2.23875i	−1.66479	−	0.137267i
$267$	1.65948	−	1.49057i	0.101559	−	0.0912213i
$268$	11.0743	+	5.47376i	0.676470	+	0.334363i
$269$	−27.5715	+	8.36372i	−1.68106	+	0.509945i	−0.979291	−	0.202456i	$-0.935108\pi$
$269$	−27.5715	+	8.36372i	−1.68106	+	0.509945i	−0.701773	+	0.712401i	$0.747608\pi$
$270$	−10.3350	−	11.3468i	−0.628966	−	0.690541i
$271$	−20.7899	+	8.61146i	−1.26290	+	0.523109i	−0.910797	−	0.412854i	$-0.864532\pi$
$271$	−20.7899	+	8.61146i	−1.26290	+	0.523109i	−0.352099	+	0.935963i	$0.614532\pi$
$272$	−7.83655	+	3.84686i	−0.475161	+	0.233250i
$273$	1.59533	+	6.49227i	0.0965535	+	0.392930i
$274$	−8.50108	+	0.135246i	−0.513569	+	0.00817052i
$275$	2.53251	+	1.35365i	0.152716	+	0.0816284i
$276$	−1.83878	+	1.76046i	−0.110681	+	0.105967i
$277$	−13.1187	−	10.7662i	−0.788227	−	0.646881i	0.151635	−	0.988437i	$-0.451546\pi$
$277$	−13.1187	−	10.7662i	−0.788227	−	0.646881i	−0.939862	+	0.341556i	$0.889046\pi$
$278$	−8.15204	−	25.4113i	−0.488927	−	1.52407i
$279$	−0.431668	−	1.47036i	−0.0258433	−	0.0880281i
$280$	11.4856	−	6.86295i	0.686397	−	0.410140i
$281$	0.771314	−	1.15435i	0.0460127	−	0.0688629i	−0.807750	−	0.589525i	$-0.799315\pi$
$281$	0.771314	−	1.15435i	0.0460127	−	0.0688629i	0.853763	+	0.520662i	$0.174315\pi$
$282$	−13.0937	+	28.5229i	−0.779721	+	1.69852i
$283$	11.2824	+	21.1080i	0.670671	+	1.25474i	0.955169	+	0.296061i	$0.0956733\pi$
$283$	11.2824	+	21.1080i	0.670671	+	1.25474i	−0.284498	+	0.958677i	$0.591827\pi$
$284$	−6.35461	−	8.88490i	−0.377077	−	0.527222i
$285$	26.4625	−	15.7002i	1.56750	−	0.929997i
$286$	6.17150	+	8.92561i	0.364929	+	0.527782i
$287$	−16.6375	+	16.6375i	−0.982082	+	0.982082i
$288$	14.3653	−	9.03530i	0.846486	−	0.532410i
$289$	−8.65278	−	8.65278i	−0.508987	−	0.508987i
$290$	−3.10411	+	17.0158i	−0.182280	+	0.999200i
$291$	0.168963	+	0.284786i	0.00990479	+	0.0166945i
$292$	12.5599	−	2.91651i	0.735010	−	0.170676i
$293$	−26.2591	+	14.0358i	−1.53407	+	0.819979i	−0.999681	−	0.0252586i	$-0.991959\pi$
$293$	−26.2591	+	14.0358i	−1.53407	+	0.819979i	−0.534391	+	0.845237i	$0.679459\pi$
$294$	1.59246	+	4.29529i	0.0928741	+	0.250506i
$295$	7.63195	+	5.09950i	0.444349	+	0.296905i
$296$	19.8405	+	9.41697i	1.15320	+	0.547350i
$297$	−14.1884	+	18.6025i	−0.823295	+	1.07943i
$298$	−5.11748	+	9.95175i	−0.296448	+	0.576489i
$299$	−0.794479	+	0.968075i	−0.0459459	+	0.0559852i
$300$	0.889665	−	2.02225i	0.0513648	−	0.116755i
$301$	−11.5106	+	21.5347i	−0.663457	+	1.24124i
$302$	−0.174237	+	0.179871i	−0.0100262	+	0.0103504i
$303$	−11.8963	+	2.92325i	−0.683426	+	0.167936i
$304$	11.9265	+	31.8635i	0.684030	+	1.82750i
$305$	−3.12288	−	7.53929i	−0.178815	−	0.431699i
$306$	−7.19819	−	5.82428i	−0.411493	−	0.332952i
$307$	2.94335	+	9.70292i	0.167986	+	0.553775i	1.00000		0.000980278i	$-0.000312032\pi$
$307$	2.94335	+	9.70292i	0.167986	+	0.553775i	−0.832014	+	0.554755i	$0.812812\pi$
$308$	−13.4338	−	15.3465i	−0.765465	−	0.874447i
$309$	−15.3724	−	17.1145i	−0.874507	−	0.973608i
$310$	−1.15092	+	0.975588i	−0.0653681	+	0.0554097i
$311$	−0.898623	−	0.178747i	−0.0509562	−	0.0101358i	0.169546	−	0.985522i	$-0.445770\pi$
$311$	−0.898623	−	0.178747i	−0.0509562	−	0.0101358i	−0.220503	+	0.975386i	$0.570770\pi$
$312$	6.48453	−	5.25856i	0.367114	−	0.297708i
$313$	0.543661	+	2.73317i	0.0307295	+	0.154488i	0.993104	−	0.117240i	$-0.0374048\pi$
$313$	0.543661	+	2.73317i	0.0307295	+	0.154488i	−0.962374	+	0.271728i	$0.912405\pi$
$314$	−1.02981	−	8.98768i	−0.0581156	−	0.507204i
$315$	11.7286	+	7.98985i	0.660830	+	0.450177i
$316$	17.5348	+	16.4531i	0.986409	+	0.925557i
$317$	9.98683	+	12.1690i	0.560916	+	0.683478i	0.973826	−	0.227293i	$-0.0729877\pi$
$317$	9.98683	+	12.1690i	0.560916	+	0.683478i	−0.412910	+	0.910772i	$0.635488\pi$
$318$	0.0938864	+	1.54966i	0.00526489	+	0.0869004i
$319$	26.3662			1.47622
$320$	−13.8675	−	9.32074i	−0.775215	−	0.521045i
$321$	3.19180	−	2.34509i	0.178149	−	0.130890i
$322$	1.27642	−	1.97769i	0.0711319	−	0.110212i
$323$	14.3495	−	11.7763i	0.798426	−	0.655251i
$324$	15.1038	+	9.79158i	0.839101	+	0.543976i
$325$	0.315504	−	1.04008i	0.0175010	−	0.0576930i
$326$	3.03498	+	26.4878i	0.168092	+	1.46702i
$327$	13.0372	−	14.2554i	0.720961	−	0.788325i
$328$	27.6520	+	9.93658i	1.52682	+	0.548656i
$329$	5.66148	−	28.4622i	0.312128	−	1.56917i
$330$	22.4071	+	5.34140i	1.23347	+	0.294035i
$331$	−8.53454	+	0.840579i	−0.469101	+	0.0462024i	−0.329806	−	0.944049i	$-0.606983\pi$
$331$	−8.53454	+	0.840579i	−0.469101	+	0.0462024i	−0.139295	+	0.990251i	$0.544483\pi$
$332$	−0.954500	+	14.3628i	−0.0523850	+	0.788261i
$333$	−0.208899	+	23.2931i	−0.0114476	+	1.27646i
$334$	4.32831	−	10.9384i	0.236834	−	0.598525i
$335$	11.9185	−	4.93679i	0.651175	−	0.269725i
$336$	−10.9836	+	11.2068i	−0.599203	+	0.611382i
$337$	−18.8067	−	7.79001i	−1.02447	−	0.424349i	−0.193756	−	0.981050i	$-0.562067\pi$
$337$	−18.8067	−	7.79001i	−1.02447	−	0.424349i	−0.830713	+	0.556701i	$0.812067\pi$
$338$	−9.93389	+	10.2551i	−0.540332	+	0.557803i
$339$	−0.350386	−	2.43736i	−0.0190304	−	0.132379i
$340$	−2.36754	+	8.80375i	−0.128398	+	0.477451i
$341$	1.77786	+	1.45905i	0.0962764	+	0.0790120i
$342$	−25.3391	+	25.6933i	−1.37018	+	1.38933i
$343$	−11.1615	−	16.7044i	−0.602664	−	0.901951i
$344$	30.4544	+	1.53776i	1.64199	+	0.0829104i
$345$	0.118535	+	2.65577i	0.00638170	+	0.142982i
$346$	19.8550	+	5.67967i	1.06741	+	0.305341i
$347$	−7.05157	−	13.1926i	−0.378548	−	0.708214i	0.618435	−	0.785836i	$-0.287767\pi$
$347$	−7.05157	−	13.1926i	−0.378548	−	0.708214i	−0.996983	+	0.0776225i	$0.975267\pi$
$348$	−1.54868	−	20.2261i	−0.0830180	−	1.08423i
$349$	3.76785	+	0.371101i	0.201688	+	0.0198646i	0.198357	−	0.980130i	$-0.436440\pi$
$349$	3.76785	+	0.371101i	0.201688	+	0.0198646i	0.00333156	+	0.999994i	$0.498940\pi$
$350$	−0.366613	+	2.00965i	−0.0195963	+	0.107421i
$351$	7.95334	+	3.89342i	0.424518	+	0.207815i
$352$	−10.1838	+	23.3457i	−0.542798	+	1.24433i
$353$	7.74148	+	7.74148i	0.412037	+	0.412037i	0.882448	−	0.470410i	$-0.155894\pi$
$353$	7.74148	+	7.74148i	0.412037	+	0.412037i	−0.470410	+	0.882448i	$0.655894\pi$
$354$	−10.1764	−	3.51057i	−0.540870	−	0.186584i
$355$	−11.3524	−	1.11812i	−0.602525	−	0.0593435i
$356$	2.54091	+	0.421880i	0.134668	+	0.0223596i
$357$	7.72315	+	3.69525i	0.408752	+	0.195573i
$358$	20.9160	−	11.6114i	1.10545	−	0.613679i
$359$	−0.213900	−	0.142923i	−0.0112892	−	0.00754321i	0.549913	−	0.835222i	$-0.314661\pi$
$359$	−0.213900	−	0.142923i	−0.0112892	−	0.00754321i	−0.561202	+	0.827679i	$0.689661\pi$
$360$	2.78138	−	17.5027i	0.146592	−	0.922473i
$361$	−29.6370	−	44.3549i	−1.55984	−	2.33447i
$362$	5.81916	+	18.1393i	0.305848	+	0.953379i
$363$	0.859995	−	16.0379i	0.0451380	−	0.841771i
$364$	−4.70498	+	6.12013i	−0.246608	+	0.320782i
$365$	6.34746	−	11.8753i	0.332241	−	0.621579i
$366$	5.78861	+	7.62150i	0.302575	+	0.398382i
$367$	−32.5777	−	13.4941i	−1.70054	−	0.704388i	−0.700585	−	0.713569i	$-0.747078\pi$
$367$	−32.5777	−	13.4941i	−1.70054	−	0.704388i	−0.999958	+	0.00918098i	$0.997078\pi$
$368$	−2.91361	−	0.388974i	−0.151882	−	0.0202767i
$369$	2.77649	+	31.0416i	0.144538	+	1.61596i
$370$	21.0466	−	9.11269i	1.09416	−	0.473746i
$371$	−0.416707	−	1.37370i	−0.0216343	−	0.0713189i
$372$	1.01484	−	1.44953i	0.0526172	−	0.0751549i
$373$	−6.91839	+	0.681402i	−0.358221	+	0.0352817i	−0.275527	−	0.961293i	$-0.588852\pi$
$373$	−6.91839	+	0.681402i	−0.358221	+	0.0352817i	−0.0826938	+	0.996575i	$0.526352\pi$
$374$	13.8499	+	1.14196i	0.716161	+	0.0590495i
$375$	−8.63720	−	18.4757i	−0.446023	−	0.954082i
$376$	−35.1659	+	8.75766i	−1.81354	+	0.451642i
$377$	−1.94690	−	9.78771i	−0.100270	−	0.504093i
$378$	−15.6844	−	5.56857i	−0.806720	−	0.286416i
$379$	−10.4501	+	34.4493i	−0.536785	+	1.76954i	0.0961801	+	0.995364i	$0.469338\pi$
$379$	−10.4501	+	34.4493i	−0.536785	+	1.76954i	−0.632965	+	0.774180i	$0.718162\pi$
$380$	33.2409	+	12.5455i	1.70522	+	0.643570i
$381$	−9.79801	−	2.50102i	−0.501967	−	0.128131i
$382$	−0.990078	−	4.59425i	−0.0506568	−	0.235062i
$383$	36.0538			1.84226			0.921132	−	0.389251i	$-0.127266\pi$
$383$	36.0538			1.84226			0.921132	+	0.389251i	$0.127266\pi$
$384$	18.5071	+	6.44096i	0.944438	+	0.328689i
$385$	−21.2991			−1.08550
$386$	−2.20930	−	10.2518i	−0.112451	−	0.521803i
$387$	12.1087	+	29.9908i	0.615517	+	1.52452i
$388$	−0.135013	+	0.357734i	−0.00685425	+	0.0181612i
$389$	2.79246	−	9.20549i	0.141583	−	0.466737i	−0.857257	−	0.514889i	$-0.827833\pi$
$389$	2.79246	−	9.20549i	0.141583	−	0.466737i	0.998840	+	0.0481519i	$0.0153332\pi$
$390$	0.328294	−	8.71240i	0.0166238	−	0.441170i
$391$	0.312888	+	1.57300i	0.0158234	+	0.0795498i
$392$	−2.72562	+	4.53339i	−0.137664	+	0.228971i
$393$	18.3956	−	8.59977i	0.927938	−	0.433801i
$394$	−1.34690	−	0.111056i	−0.0678557	−	0.00559490i
$395$	24.9894	−	2.46125i	1.25736	−	0.123839i
$396$	−27.0081	+	0.617186i	−1.35721	+	0.0310148i
$397$	6.20050	+	20.4403i	0.311194	+	1.02587i	0.963454	+	0.267874i	$0.0863212\pi$
$397$	6.20050	+	20.4403i	0.311194	+	1.02587i	−0.652260	+	0.757996i	$0.726179\pi$
$398$	−31.6981	+	13.7245i	−1.58888	+	0.687949i
$399$	17.2822	−	28.5426i	0.865192	−	1.42892i
$400$	2.46535	−	0.655787i	0.123268	−	0.0327894i
$401$	31.4199	+	13.0145i	1.56903	+	0.649915i	0.986629	−	0.162984i	$-0.0521119\pi$
$401$	31.4199	+	13.0145i	1.56903	+	0.649915i	0.582405	+	0.812899i	$0.302112\pi$
$402$	−12.0484	+	9.15090i	−0.600920	+	0.456405i
$403$	0.410353	−	0.767716i	0.0204411	−	0.0382427i
$404$	−11.2144	−	8.62133i	−0.557938	−	0.428927i
$405$	18.0829	−	5.13309i	0.898547	−	0.255065i
$406$	5.72962	+	17.8602i	0.284357	+	0.886386i
$407$	−19.4232	−	29.0688i	−0.962771	−	1.44089i
$408$	0.0625204	−	10.6916i	0.00309522	−	0.529315i
$409$	−5.84243	−	3.90379i	−0.288890	−	0.193030i	0.402678	−	0.915342i	$-0.368080\pi$
$409$	−5.84243	−	3.90379i	−0.288890	−	0.193030i	−0.691567	+	0.722312i	$0.743080\pi$
$410$	26.8280	−	14.8933i	1.32494	−	0.735528i
$411$	4.49428	−	9.39316i	0.221687	−	0.463330i
$412$	4.35090	−	26.2048i	0.214354	−	1.29102i
$413$	9.90580	+	0.975636i	0.487432	+	0.0480079i
$414$	−0.925724	−	2.97717i	−0.0454968	−	0.146320i
$415$	10.6293	+	10.6293i	0.521772	+	0.521772i
$416$	9.41839	+	2.05659i	0.461774	+	0.100833i
$417$	32.3090	+	4.94075i	1.58218	+	0.241949i
$418$	9.71972	−	53.2804i	0.475407	−	2.60603i
$419$	−31.3339	−	3.08612i	−1.53076	−	0.150767i	−0.702733	−	0.711454i	$-0.748037\pi$
$419$	−31.3339	−	3.08612i	−1.53076	−	0.150767i	−0.828028	+	0.560687i	$0.810537\pi$
$420$	1.25105	+	16.3390i	0.0610452	+	0.797264i
$421$	13.0885	+	24.4869i	0.637895	+	1.19342i	0.968350	+	0.249596i	$0.0802977\pi$
$421$	13.0885	+	24.4869i	0.637895	+	1.19342i	−0.330455	+	0.943822i	$0.607202\pi$
$422$	5.69731	+	1.62975i	0.277341	+	0.0793352i
$423$	−24.1176	−	29.9307i	−1.17264	−	1.45528i
$424$	−1.32992	+	1.20207i	−0.0645867	+	0.0583778i
$425$	−0.773302	−	1.15733i	−0.0375106	−	0.0561387i
$426$	13.2104	−	2.11408i	0.640046	−	0.102428i
$427$	−6.84065	−	5.61398i	−0.331042	−	0.271679i
$428$	4.41650	+	1.18770i	0.213479	+	0.0574097i
$429$	−13.1550	+	1.89112i	−0.635130	+	0.0913040i
$430$	22.1561	−	22.8725i	1.06846	−	1.10301i
$431$	−3.24275	−	1.34319i	−0.156198	−	0.0646992i	0.303215	−	0.952922i	$-0.401940\pi$
$431$	−3.24275	−	1.34319i	−0.156198	−	0.0646992i	−0.459413	+	0.888223i	$0.651940\pi$
$432$	2.05984	+	20.6823i	0.0991042	+	0.995077i
$433$	−7.07055	+	2.92872i	−0.339789	+	0.140745i	−0.546052	−	0.837751i	$-0.683870\pi$
$433$	−7.07055	+	2.92872i	−0.339789	+	0.140745i	0.206263	+	0.978497i	$0.433870\pi$
$434$	−0.602000	+	1.52137i	−0.0288969	+	0.0730279i
$435$	−16.9583	−	12.6954i	−0.813089	−	0.608698i
$436$	22.2574	+	1.47915i	1.06594	+	0.0708385i
$437$	6.22037	−	0.612653i	0.297561	−	0.0293072i
$438$	−3.66187	+	15.3615i	−0.174971	+	0.734000i
$439$	−1.50639	+	7.57313i	−0.0718960	+	0.361446i	−0.999939	−	0.0110269i	$-0.996490\pi$
$439$	−1.50639	+	7.57313i	−0.0718960	+	0.361446i	0.928043	+	0.372473i	$0.121490\pi$
$440$	11.3395	+	24.0602i	0.540589	+	1.14702i
$441$	−5.57837	−	0.599979i	−0.265637	−	0.0285704i
$442$	−0.598762	−	5.22570i	−0.0284802	−	0.248561i
$443$	4.18935	−	13.8104i	0.199042	−	0.656153i	−0.799423	−	0.600768i	$-0.794861\pi$
$443$	4.18935	−	13.8104i	0.199042	−	0.656153i	0.998465	−	0.0553848i	$-0.0176385\pi$
$444$	−21.1585	+	16.6074i	−1.00414	+	0.788151i
$445$	2.07924	−	1.70639i	0.0985655	−	0.0808906i
$446$	−8.34835	+	12.9350i	−0.395306	+	0.612489i
$447$	−8.11487	−	11.0448i	−0.383820	−	0.522401i
$448$	−18.0271	−	1.82517i	−0.851702	−	0.0862311i
$449$	−11.3667			−0.536430			−0.268215	−	0.963359i	$-0.586434\pi$
$449$	−11.3667			−0.536430			−0.268215	+	0.963359i	$0.586434\pi$
$450$	1.73103	+	2.07967i	0.0816018	+	0.0980367i
$451$	−29.6734	−	36.1572i	−1.39727	−	1.70258i
$452$	1.94558	−	2.07349i	0.0915124	−	0.0975290i
$453$	−0.102030	−	0.289237i	−0.00479379	−	0.0135895i
$454$	0.413277	+	3.60688i	0.0193960	+	0.169279i
$455$	1.57274	+	7.90670i	0.0737312	+	0.370672i
$456$	−41.4435	−	4.32667i	−1.94077	−	0.202615i
$457$	19.2993	+	3.83887i	0.902783	+	0.179575i	0.624592	−	0.780951i	$-0.285265\pi$
$457$	19.2993	+	3.83887i	0.902783	+	0.179575i	0.278191	+	0.960526i	$0.410265\pi$
$458$	21.5894	−	18.3004i	1.00881	−	0.855121i
$459$	10.3159	−	4.71030i	0.481504	−	0.219858i
$460$	−2.30974	+	2.02188i	−0.107692	+	0.0942705i
$461$	6.72733	+	22.1771i	0.313323	+	1.03289i	0.962280	+	0.272063i	$0.0877058\pi$
$461$	6.72733	+	22.1771i	0.313323	+	1.03289i	−0.648956	+	0.760826i	$0.724794\pi$
$462$	24.1600	−	6.34593i	1.12402	−	0.295239i
$463$	6.58740	+	15.9034i	0.306142	+	0.739093i	0.999823	+	0.0188103i	$0.00598785\pi$
$463$	6.58740	+	15.9034i	0.306142	+	0.739093i	−0.693681	+	0.720283i	$0.744012\pi$
$464$	17.1250	−	15.9810i	0.795009	−	0.741899i
$465$	−0.440952	−	1.79448i	−0.0204487	−	0.0832170i
$466$	−12.1449	+	12.5376i	−0.562602	+	0.580793i
$467$	0.821081	−	1.53613i	0.0379951	−	0.0710838i	−0.862207	−	0.506556i	$-0.830918\pi$
$467$	0.821081	−	1.53613i	0.0379951	−	0.0710838i	0.900202	+	0.435472i	$0.143418\pi$
$468$	2.22341	+	9.98043i	0.102777	+	0.461346i
$469$	8.87483	−	10.8140i	0.409801	−	0.499345i
$470$	−17.3070	+	33.6562i	−0.798312	+	1.55244i
$471$	10.4151	+	3.77936i	0.479904	+	0.174144i
$472$	−4.17166	−	11.7093i	−0.192016	−	0.538965i
$473$	−40.3610	−	26.9683i	−1.85580	−	1.24001i
$474$	−27.6126	+	10.2373i	−1.26829	+	0.470213i
$475$	−4.78408	+	2.55715i	−0.219509	+	0.117330i
$476$	2.23616	+	9.62992i	0.102494	+	0.441387i
$477$	−1.75008	−	0.743364i	−0.0801307	−	0.0340363i
$478$	−4.81982	+	26.4207i	−0.220453	+	1.20845i
$479$	−0.302945	−	0.302945i	−0.0138419	−	0.0138419i	0.700152	−	0.713994i	$-0.253116\pi$
$479$	−0.302945	−	0.302945i	−0.0138419	−	0.0138419i	−0.713994	+	0.700152i	$0.753116\pi$
$480$	17.7910	−	10.1120i	0.812046	−	0.461548i
$481$	−9.35676	+	9.35676i	−0.426631	+	0.426631i
$482$	−13.4576	−	19.4632i	−0.612978	−	0.886527i
$483$	1.47097	+	2.47931i	0.0669314	+	0.112812i
$484$	15.0845	−	10.7887i	0.685660	−	0.490394i
$485$	0.188230	+	0.352153i	0.00854706	+	0.0159904i
$486$	−18.9824	+	11.2102i	−0.861058	+	0.508506i
$487$	−17.7295	+	26.5341i	−0.803400	+	1.20237i	0.172683	+	0.984977i	$0.444756\pi$
$487$	−17.7295	+	26.5341i	−0.803400	+	1.20237i	−0.976083	+	0.217396i	$0.930244\pi$
$488$	−2.69982	+	10.7163i	−0.122215	+	0.485102i
$489$	−30.6946	−	11.1382i	−1.38806	−	0.503688i
$490$	1.68741	+	5.25995i	0.0762296	+	0.237620i
$491$	2.64852	+	2.17358i	0.119526	+	0.0980924i	0.692257	−	0.721651i	$-0.256616\pi$
$491$	2.64852	+	2.17358i	0.119526	+	0.0980924i	−0.572732	+	0.819743i	$0.694116\pi$
$492$	−25.9940	+	24.8869i	−1.17190	+	1.12199i
$493$	−11.2711	−	6.02454i	−0.507625	−	0.271331i
$494$	−20.4966	+	0.326086i	−0.922183	+	0.0146713i
$495$	−18.0923	+	21.6467i	−0.813188	+	0.972947i
$496$	2.03908	−	0.129926i	0.0915576	−	0.00583385i
$497$	−11.4287	+	4.73393i	−0.512648	+	0.212346i
$498$	−15.2239	−	8.89007i	−0.682200	−	0.398374i
$499$	1.49965	−	0.454912i	0.0671333	−	0.0203647i	−0.256539	−	0.966534i	$-0.582582\pi$
$499$	1.49965	−	0.454912i	0.0671333	−	0.0203647i	0.323673	+	0.946169i	$0.395082\pi$
$500$	10.4351	−	21.1119i	0.466672	−	0.944153i
$501$	9.62751	+	10.7185i	0.430126	+	0.478868i
$502$	−26.7576	−	2.20624i	−1.19425	−	0.0984693i
$503$	0.681969	−	3.42849i	0.0304075	−	0.152869i	−0.962599	−	0.270931i	$-0.912668\pi$
$503$	0.681969	−	3.42849i	0.0304075	−	0.152869i	0.993006	+	0.118063i	$0.0376684\pi$
$504$	−6.28719	−	18.1609i	−0.280054	−	0.808951i
$505$	−14.4881	+	2.88186i	−0.644712	+	0.128241i
$506$	3.66390	+	2.91059i	0.162880	+	0.129392i
$507$	−5.81710	−	16.4904i	−0.258346	−	0.732366i
$508$	−4.80932	−	10.6401i	−0.213379	−	0.472079i
$509$	−5.55580	+	4.55952i	−0.246256	+	0.202097i	−0.749422	−	0.662093i	$-0.769669\pi$
$509$	−5.55580	+	4.55952i	−0.246256	+	0.202097i	0.503166	+	0.864190i	$0.332169\pi$
$510$	−8.35816	−	7.40325i	−0.370106	−	0.327821i
$511$		−	14.6019i		−	0.645951i
$512$	7.53573	+	21.3357i	0.333036	+	0.942914i
$513$	−14.3282	−	41.8094i	−0.632606	−	1.84593i
$514$	−2.22687	−	10.3333i	−0.0982230	−	0.455783i
$515$	−17.5982	−	21.4435i	−0.775471	−	0.944914i
$516$	−18.3173	+	32.5459i	−0.806375	+	1.43275i
$517$	55.2058	+	16.7465i	2.42795	+	0.736511i
$518$	15.4701	−	19.4740i	0.679716	−	0.855637i
$519$	−17.0694	+	18.6643i	−0.749264	+	0.819272i
$520$	8.09434	−	5.98608i	0.354960	−	0.262507i
$521$	9.63765	+	1.91705i	0.422233	+	0.0839874i	0.401634	−	0.915800i	$-0.368443\pi$
$521$	9.63765	+	1.91705i	0.422233	+	0.0839874i	0.0205995	+	0.999788i	$0.493443\pi$
$522$	23.0186	+	9.34799i	1.00750	+	0.409151i
$523$	−0.568141	−	5.76843i	−0.0248431	−	0.252236i	−0.999583	−	0.0288911i	$-0.990802\pi$
$523$	−0.568141	−	5.76843i	−0.0248431	−	0.252236i	0.974739	−	0.223345i	$-0.0716976\pi$
$524$	21.0204	+	10.3899i	0.918281	+	0.453884i
$525$	−2.00287	−	1.49940i	−0.0874124	−	0.0654390i
$526$	−19.9729	+	8.64777i	−0.870858	+	0.377061i
$527$	−0.426619	−	1.02995i	−0.0185838	−	0.0448653i
$528$	−20.0311	−	23.9133i	−0.871743	−	1.04069i
$529$	8.59506	−	20.7503i	0.373698	−	0.902187i
$530$	0.0297797	+	1.87184i	0.00129355	+	0.0813077i
$531$	9.40591	−	9.23870i	0.408182	−	0.400926i
$532$	38.2038	−	4.99430i	1.65634	−	0.216530i
$533$	−11.2312	+	13.6853i	−0.486478	+	0.592776i
$534$	−1.85011	+	2.55508i	−0.0800621	+	0.110569i
$535$	3.97110	−	2.65340i	0.171686	−	0.114717i
$536$	−16.9407	−	4.26799i	−0.731728	−	0.184349i
$537$	1.30642	+	29.2703i	0.0563762	+	1.26311i
$538$	35.6251	−	19.7770i	1.53591	−	0.852646i
$539$	7.42626	−	3.96942i	0.319871	−	0.170975i
$540$	17.6684	+	12.6075i	0.760325	+	0.542542i
$541$	−2.99134	+	30.3716i	−0.128608	+	1.30578i	0.686781	+	0.726865i	$0.259023\pi$
$541$	−2.99134	+	30.3716i	−0.128608	+	1.30578i	−0.815389	+	0.578914i	$0.803477\pi$
$542$	26.1759	−	18.0990i	1.12435	−	0.777420i
$543$	−23.0631	−	3.52684i	−0.989731	−	0.151351i
$544$	9.68775	−	7.65293i	0.415359	−	0.328117i
$545$	16.4718	−	16.4718i	0.705575	−	0.705575i
$546$	−4.13973	−	8.50011i	−0.177164	−	0.363771i
$547$	2.21990	−	22.5390i	0.0949159	−	0.963697i	−0.823297	−	0.567611i	$-0.807868\pi$
$547$	2.21990	−	22.5390i	0.0949159	−	0.963697i	0.918213	−	0.396087i	$-0.129632\pi$
$548$	11.7122	−	2.71969i	0.500322	−	0.116179i
$549$	−11.5163	+	2.18356i	−0.491503	+	0.0931919i
$550$	−3.90442	−	1.11689i	−0.166485	−	0.0476242i
$551$	−27.6716	+	41.4135i	−1.17885	+	1.76428i
$552$	2.01757	−	2.98162i	0.0858736	−	0.126906i
$553$	22.6410	−	15.1282i	0.962794	−	0.643319i
$554$	21.3439	+	10.9756i	0.906814	+	0.466310i
$555$	−1.50406	+	28.0489i	−0.0638437	+	1.19061i
$556$	18.8407	+	32.7017i	0.799025	+	1.38686i
$557$	28.7399	+	15.3618i	1.21775	+	0.650901i	0.949898	−	0.312560i	$-0.101186\pi$
$557$	28.7399	+	15.3618i	1.21775	+	0.650901i	0.267851	+	0.963460i	$0.413686\pi$
$558$	1.03483	+	1.90413i	0.0438079	+	0.0806082i
$559$	−7.03095	+	16.9742i	−0.297378	+	0.717933i
$560$	−13.8339	+	12.9098i	−0.584590	+	0.545537i
$561$	−8.81547	+	14.5593i	−0.372190	+	0.614693i
$562$	−0.722408	+	1.82566i	−0.0304730	+	0.0770109i
$563$	−32.8460	+	9.96372i	−1.38429	+	0.419921i	−0.892601	−	0.450848i	$-0.851122\pi$
$563$	−32.8460	+	9.96372i	−1.38429	+	0.419921i	−0.491693	+	0.870769i	$0.663622\pi$
$564$	9.60397	−	43.3333i	0.404400	−	1.82466i
$565$	−0.291043	−	2.95501i	−0.0122443	−	0.124318i
$566$	−21.8864	−	25.8199i	−0.919952	−	1.08529i
$567$	14.6700	−	14.1530i	0.616082	−	0.594369i
$568$	11.4322	+	10.3899i	0.479683	+	0.435952i
$569$	5.03237	−	1.00100i	0.210968	−	0.0419641i	−0.0884748	−	0.996078i	$-0.528199\pi$
$569$	5.03237	−	1.00100i	0.210968	−	0.0419641i	0.299443	+	0.954114i	$0.403199\pi$
$570$	−31.9062	+	29.5890i	−1.33640	+	1.23935i
$571$	24.2801	+	7.36527i	1.01609	+	0.308227i	0.754041	−	0.656828i	$-0.228102\pi$
$571$	24.2801	+	7.36527i	1.01609	+	0.308227i	0.262048	+	0.965055i	$0.415602\pi$
$572$	−11.1911	−	10.5008i	−0.467925	−	0.439059i
$573$	5.57713	+	1.42361i	0.232988	+	0.0594720i
$574$	18.0442	−	27.9578i	0.753149	−	1.16693i
$575$		−	0.468675i		−	0.0195451i
$576$	−17.1679	+	16.7709i	−0.715328	+	0.698789i
$577$		−	6.78175i		−	0.282328i	−0.989986	−	0.141164i	$-0.954915\pi$
$577$		−	6.78175i		−	0.282328i	0.989986	−	0.141164i	$-0.0450845\pi$
$578$	14.5402	+	9.38435i	0.604791	+	0.390337i
$579$	12.4451	+	3.17670i	0.517199	+	0.132019i
$580$	−0.778120	−	24.4487i	−0.0323097	−	1.01518i
$581$	15.5992	+	4.73196i	0.647163	+	0.196315i
$582$	−0.318433	−	0.343371i	−0.0131995	−	0.0142332i
$583$	2.79889	−	0.556734i	0.115918	−	0.0230576i
$584$	−16.4948	+	7.77395i	−0.682559	+	0.321688i
$585$	9.37167	+	5.11784i	0.387471	+	0.211597i
$586$	32.1209	−	27.2274i	1.32690	−	1.12476i
$587$	4.51638	+	45.8555i	0.186411	+	1.89266i	0.401185	+	0.915997i	$0.368598\pi$
$587$	4.51638	+	45.8555i	0.186411	+	1.89266i	−0.214775	+	0.976664i	$0.568902\pi$
$588$	−3.48123	−	5.46369i	−0.143563	−	0.225319i
$589$	−4.15762	+	1.26120i	−0.171312	+	0.0519668i
$590$	−12.0703	−	4.77617i	−0.496925	−	0.196632i
$591$	0.857302	−	1.41589i	0.0352647	−	0.0582418i
$592$	−30.2346	−	7.10769i	−1.24263	−	0.292124i
$593$	1.88877	−	4.55989i	0.0775625	−	0.187252i	−0.880342	−	0.474339i	$-0.842687\pi$
$593$	1.88877	−	4.55989i	0.0775625	−	0.187252i	0.957904	+	0.287087i	$0.0926869\pi$
$594$	14.0729	−	29.9447i	0.577418	−	1.22865i
$595$	9.10502	+	4.86674i	0.373269	+	0.199517i
$596$	4.10988	−	15.2827i	0.168347	−	0.626003i
$597$	2.26525	−	42.2442i	0.0927103	−	1.72894i
$598$	0.809930	−	1.57504i	0.0331205	−	0.0644081i
$599$	35.2499	−	23.5532i	1.44027	−	0.962358i	0.442422	−	0.896807i	$-0.354119\pi$
$599$	35.2499	−	23.5532i	1.44027	−	0.962358i	0.997849	−	0.0655511i	$-0.0208805\pi$
$600$	−0.627453	+	3.06077i	−0.0256157	+	0.124955i
$601$	−13.4701	+	20.1594i	−0.549455	+	0.822318i	−0.997424	−	0.0717313i	$-0.977148\pi$
$601$	−13.4701	+	20.1594i	−0.549455	+	0.822318i	0.447969	+	0.894049i	$0.352148\pi$
$602$	9.49725	−	33.2006i	0.387079	−	1.35315i
$603$	−3.45187	−	18.2055i	−0.140571	−	0.741384i
$604$	0.187290	−	0.300577i	0.00762072	−	0.0122303i
$605$	1.89831	−	19.2738i	0.0771772	−	0.783593i
$606$	15.5754	−	7.58557i	0.632709	−	0.308143i
$607$	−14.8554	+	14.8554i	−0.602961	+	0.602961i	−0.941097	−	0.338136i	$-0.890203\pi$
$607$	−14.8554	+	14.8554i	−0.602961	+	0.602961i	0.338136	+	0.941097i	$0.390203\pi$
$608$	−25.9811	−	40.4973i	−1.05367	−	1.64238i
$609$	−22.7082	−	3.47258i	−0.920184	−	0.140716i
$610$	6.56347	+	9.49249i	0.265747	+	0.384340i
$611$	2.14023	−	21.7302i	0.0865846	−	0.879109i
$612$	11.6865	+	5.90737i	0.472401	+	0.238791i
$613$	26.2924	−	14.0536i	1.06194	−	0.567618i	0.154583	−	0.987980i	$-0.450597\pi$
$613$	26.2924	−	14.0536i	1.06194	−	0.567618i	0.907357	+	0.420361i	$0.138097\pi$
$614$	−6.95988	−	12.5371i	−0.280878	−	0.505958i
$615$	1.67568	+	37.5435i	0.0675699	+	1.51390i
$616$	23.1441	+	17.2138i	0.932503	+	0.693564i
$617$	8.16194	−	5.45364i	0.328587	−	0.219555i	−0.380323	−	0.924854i	$-0.624187\pi$
$617$	8.16194	−	5.45364i	0.328587	−	0.219555i	0.708910	+	0.705299i	$0.249187\pi$
$618$	26.3509	+	19.0804i	1.05999	+	0.767528i
$619$	14.7525	−	17.9760i	0.592953	−	0.722515i	−0.386925	−	0.922111i	$-0.626463\pi$
$619$	14.7525	−	17.9760i	0.592953	−	0.722515i	0.979878	+	0.199596i	$0.0639629\pi$
$620$	1.30047	−	1.69162i	0.0522281	−	0.0679371i
$621$	3.76926	+	0.611044i	0.151255	+	0.0245204i
$622$	1.29558	−	0.0206117i	0.0519480	−	0.000826455i
$623$	1.11624	−	2.69483i	0.0447210	−	0.107966i
$624$	−7.39803	+	9.20176i	−0.296158	+	0.368365i
$625$	−8.19111	−	19.7751i	−0.327644	−	0.791003i
$626$	−1.56589	−	3.61657i	−0.0625854	−	0.144547i
$627$	53.1005	+	39.7523i	2.12063	+	1.58756i
$628$	4.10137	+	12.1184i	0.163663	+	0.483578i
$629$	1.66101	+	16.8645i	0.0662288	+	0.672432i
$630$	−18.5949	−	7.55149i	−0.740837	−	0.300859i
$631$	−30.7309	−	6.11276i	−1.22338	−	0.243345i	−0.459190	−	0.888338i	$-0.651860\pi$
$631$	−30.7309	−	6.11276i	−1.22338	−	0.243345i	−0.764188	+	0.644993i	$0.776860\pi$
$632$	−29.1433	−	17.5219i	−1.15926	−	0.696982i
$633$	−4.89799	+	5.35564i	−0.194677	+	0.212867i
$634$	−17.4320	−	13.8480i	−0.692314	−	0.549973i
$635$	−11.6687	−	3.53967i	−0.463059	−	0.140467i
$636$	−0.591483	−	2.11439i	−0.0234538	−	0.0838411i
$637$	−2.02189	−	2.46368i	−0.0801103	−	0.0976147i
$638$	−36.4507	+	7.85525i	−1.44310	+	0.310992i
$639$	−4.89680	+	15.6364i	−0.193715	+	0.618566i
$640$	21.9483	+	8.75419i	0.867584	+	0.346040i
$641$			7.58378i			0.299541i	0.988721	+	0.149771i	$0.0478536\pi$
$641$			7.58378i			0.299541i	−0.988721	+	0.149771i	$0.952146\pi$
$642$	−3.71392	+	4.19296i	−0.146577	+	0.165483i
$643$	−25.9736	+	21.3160i	−1.02430	+	0.840620i	−0.987327	−	0.158697i	$-0.949271\pi$
$643$	−25.9736	+	21.3160i	−1.02430	+	0.840620i	−0.0369707	+	0.999316i	$0.511771\pi$
$644$	−1.17540	+	3.11438i	−0.0463174	+	0.122724i
$645$	12.9742	+	36.7795i	0.510858	+	1.44819i
$646$	−16.3293	+	20.5556i	−0.642468	+	0.808748i
$647$	−25.4805	+	5.06839i	−1.00174	+	0.199259i	−0.668603	−	0.743619i	$-0.733108\pi$
$647$	−25.4805	+	5.06839i	−1.00174	+	0.199259i	−0.333138	+	0.942878i	$0.608108\pi$
$648$	−23.7978	−	9.03676i	−0.934867	−	0.354997i
$649$	−3.86035	+	19.4073i	−0.151532	+	0.761804i
$650$	−0.126308	+	1.53188i	−0.00495420	+	0.0600852i
$651$	−1.33904	−	1.49078i	−0.0524810	−	0.0584282i
$652$	−12.0872	−	35.7145i	−0.473373	−	1.39869i
$653$	−23.9318	+	7.25964i	−0.936525	+	0.284092i	−0.721419	−	0.692499i	$-0.756510\pi$
$653$	−23.9318	+	7.25964i	−0.936525	+	0.284092i	−0.215106	+	0.976591i	$0.569010\pi$
$654$	−13.7766	+	23.5919i	−0.538707	+	0.922517i
$655$	22.6227	−	9.37064i	0.883943	−	0.366141i
$656$	−41.1885	−	5.49877i	−1.60814	−	0.214691i
$657$	−14.8402	−	12.4034i	−0.578971	−	0.483903i
$658$	0.652838	+	41.0350i	0.0254503	+	1.59971i
$659$	33.3013	+	17.7999i	1.29724	+	0.693387i	0.968021	−	0.250868i	$-0.0807161\pi$
$659$	33.3013	+	17.7999i	1.29724	+	0.693387i	0.329214	+	0.944255i	$0.393216\pi$
$660$	−32.5686	−	0.708657i	−1.26773	−	0.0275844i
$661$	−14.9900	−	12.3020i	−0.583042	−	0.478491i	0.296030	−	0.955179i	$-0.404337\pi$
$661$	−14.9900	−	12.3020i	−0.583042	−	0.478491i	−0.879073	+	0.476688i	$0.841837\pi$
$662$	11.5484	−	3.70476i	0.448840	−	0.143990i
$663$	6.05566	+	2.19743i	0.235182	+	0.0853411i
$664$	−2.95951	−	20.1406i	−0.114851	−	0.781606i
$665$	22.3537	−	33.4546i	0.866839	−	1.29732i
$666$	−6.65089	−	32.2644i	−0.257717	−	1.25022i
$667$	−2.02855	−	3.79515i	−0.0785457	−	0.146949i
$668$	−2.72490	+	16.4117i	−0.105430	+	0.634986i
$669$	−9.62082	−	16.2158i	−0.371962	−	0.626940i
$670$	−15.0062	+	10.3758i	−0.579739	+	0.400853i
$671$	12.4395	−	12.4395i	0.480221	−	0.480221i
$672$	11.8457	−	18.7655i	0.456957	−	0.723894i
$673$	14.5852	+	14.5852i	0.562217	+	0.562217i	0.929937	−	0.367720i	$-0.119861\pi$
$673$	14.5852	+	14.5852i	0.562217	+	0.562217i	−0.367720	+	0.929937i	$0.619861\pi$
$674$	28.3207	+	5.16643i	1.09087	+	0.199003i
$675$	−3.22518	+	0.761910i	−0.124137	+	0.0293259i
$676$	10.6781	−	17.1370i	0.410695	−	0.659115i
$677$	−15.1129	+	8.07801i	−0.580836	+	0.310463i	−0.735522	−	0.677500i	$-0.763063\pi$
$677$	−15.1129	+	8.07801i	−0.580836	+	0.310463i	0.154687	+	0.987964i	$0.450563\pi$
$678$	1.21056	+	3.26520i	0.0464912	+	0.125399i
$679$	0.360035	+	0.240568i	0.0138169	+	0.00923214i
$680$	0.650174	−	12.8763i	0.0249331	−	0.493785i
$681$	−4.17973	−	1.51671i	−0.160168	−	0.0581203i
$682$	−2.89254	−	1.48743i	−0.110761	−	0.0569565i
$683$	−28.2065	+	34.3697i	−1.07929	+	1.31512i	−0.133246	+	0.991083i	$0.542540\pi$
$683$	−28.2065	+	34.3697i	−1.07929	+	1.31512i	−0.946045	+	0.324036i	$0.894960\pi$
$684$	27.3759	−	43.0695i	1.04674	−	1.64680i
$685$	5.91909	−	11.0738i	0.226157	−	0.423110i
$686$	20.4072	+	19.7680i	0.779151	+	0.754747i
$687$	8.27152	+	33.6614i	0.315578	+	1.28426i
$688$	−42.5607	+	6.94733i	−1.62261	+	0.264865i
$689$	−0.413344	−	0.997900i	−0.0157471	−	0.0380169i
$690$	−0.955101	−	3.63622i	−0.0363601	−	0.138429i
$691$	−4.31723	−	14.2320i	−0.164235	−	0.541411i	0.835735	−	0.549133i	$-0.185042\pi$
$691$	−4.31723	−	14.2320i	−0.164235	−	0.541411i	−0.999970	+	0.00772216i	$0.997542\pi$
$692$	−29.1412	−	1.93662i	−1.10778	−	0.0736193i
$693$	−6.23734	+	29.9509i	−0.236937	+	1.13774i
$694$	13.6791	+	16.1375i	0.519250	+	0.612572i
$695$	38.6554	+	7.68904i	1.46628	+	0.291662i
$696$	8.16695	+	27.5007i	0.309567	+	1.04241i
$697$	4.42317	+	22.2368i	0.167540	+	0.842279i
$698$	−5.31952	+	0.609512i	−0.201347	+	0.0230704i
$699$	−7.11183	−	20.1608i	−0.268994	−	0.762551i
$700$	−0.0919002	−	2.88752i	−0.00347350	−	0.109138i
$701$	−31.5431	−	38.4353i	−1.19136	−	1.45168i	−0.861577	−	0.507627i	$-0.830523\pi$
$701$	−31.5431	−	38.4353i	−1.19136	−	1.45168i	−0.329788	−	0.944055i	$-0.606977\pi$
$702$	−12.1553	−	3.01303i	−0.458771	−	0.113719i
$703$	66.0433			2.49087
$704$	7.12352	−	35.3088i	0.268478	−	1.33075i
$705$	−27.4440	−	37.3528i	−1.03360	−	1.40679i
$706$	−13.0088	−	8.39600i	−0.489593	−	0.315987i
$707$	−12.3828	+	10.1623i	−0.465704	+	0.382193i
$708$	15.1145	+	1.82143i	0.568039	+	0.0684535i
$709$	−4.77893	+	15.7540i	−0.179476	+	0.591654i	0.820328	+	0.571893i	$0.193791\pi$
$709$	−4.77893	+	15.7540i	−0.179476	+	0.591654i	−0.999805	+	0.0197615i	$0.993709\pi$
$710$	16.0276	−	1.83645i	0.601505	−	0.0689206i
$711$	3.85702	−	35.8610i	0.144649	−	1.34489i
$712$	−3.63844	+	0.173772i	−0.136356	+	0.00651240i
$713$	0.0732316	−	0.368160i	0.00274254	−	0.0137877i
$714$	−11.7780	−	2.80764i	−0.440780	−	0.105073i
$715$	−15.9489	+	1.57083i	−0.596455	+	0.0587457i
$716$	−25.4565	+	22.2839i	−0.951356	+	0.832788i
$717$	−26.3315	−	19.7124i	−0.983367	−	0.736173i
$718$	0.338292	+	0.133861i	0.0126250	+	0.00499565i
$719$	−17.9803	+	7.44768i	−0.670551	+	0.277751i	−0.691871	−	0.722021i	$-0.743213\pi$
$719$	−17.9803	+	7.44768i	−0.670551	+	0.277751i	0.0213195	+	0.999773i	$0.493213\pi$
$720$	1.36936	+	25.0257i	0.0510332	+	0.932653i
$721$	−27.7922	−	11.5119i	−1.03503	−	0.428725i
$722$	54.1870	+	52.4898i	2.01663	+	1.95347i
$723$	28.6859	−	4.12379i	1.06684	−	0.153365i
$724$	−13.4490	−	23.3434i	−0.499830	−	0.867551i
$725$	2.88696	+	2.36927i	0.107219	+	0.0879924i
$726$	3.58922	+	22.4282i	0.133209	+	0.832389i
$727$	20.5730	+	30.7897i	0.763010	+	1.14192i	0.985941	+	0.167091i	$0.0534373\pi$
$727$	20.5730	+	30.7897i	0.763010	+	1.14192i	−0.222932	+	0.974834i	$0.571563\pi$
$728$	4.68117	−	9.86268i	0.173496	−	0.365535i
$729$	−1.92268	−	26.9315i	−0.0712104	−	0.997461i
$730$	−5.23723	+	18.3083i	−0.193838	+	0.677622i
$731$	11.0915	+	20.7508i	0.410235	+	0.767495i
$732$	−10.2733	−	8.81195i	−0.379711	−	0.325699i
$733$	52.5336	+	5.17411i	1.94037	+	0.191110i	0.992018	−	0.126097i	$-0.0402452\pi$
$733$	52.5336	+	5.17411i	1.94037	+	0.191110i	0.948356	+	0.317208i	$0.102745\pi$
$734$	49.0582	+	8.94948i	1.81077	+	0.330331i
$735$	−6.68773	−	1.02270i	−0.246681	−	0.0377228i
$736$	4.14388	−	0.330300i	0.152746	−	0.0121750i
$737$	19.6649	+	19.6649i	0.724366	+	0.724366i
$738$	−13.0866	−	42.0870i	−0.481724	−	1.54924i
$739$	13.7421	+	1.35348i	0.505511	+	0.0497885i	0.347559	−	0.937658i	$-0.387011\pi$
$739$	13.7421	+	1.35348i	0.505511	+	0.0497885i	0.157952	+	0.987447i	$0.449511\pi$
$740$	−26.3815	+	18.8685i	−0.969804	+	0.693618i
$741$	10.8360	−	22.6474i	0.398069	−	0.831973i
$742$	0.985351	+	1.77496i	0.0361734	+	0.0651607i
$743$	−31.4467	−	21.0120i	−1.15367	−	0.770856i	−0.176704	−	0.984264i	$-0.556544\pi$
$743$	−31.4467	−	21.0120i	−1.15367	−	0.770856i	−0.976963	+	0.213408i	$0.931544\pi$
$744$	−0.971138	+	2.30630i	−0.0356036	+	0.0845530i
$745$	−9.18175	−	13.7415i	−0.336393	−	0.503448i
$746$	9.36150	−	3.00321i	0.342749	−	0.109955i
$747$	18.0597	−	11.8342i	0.660770	−	0.432992i
$748$	−19.4874	+	2.54754i	−0.712528	+	0.0931473i
$749$	2.44145	−	4.56763i	0.0892086	−	0.166898i
$750$	17.4452	+	22.9690i	0.637007	+	0.838708i
$751$	−16.7817	−	6.95121i	−0.612373	−	0.253653i	0.0548697	−	0.998494i	$-0.482526\pi$
$751$	−16.7817	−	6.95121i	−0.612373	−	0.253653i	−0.667243	+	0.744840i	$0.732526\pi$
$752$	46.0069	−	22.5842i	1.67770	−	0.823561i
$753$	17.0312	−	28.1281i	0.620653	−	1.02505i
$754$	5.60757	+	12.9512i	0.204216	+	0.471656i
$755$	−0.107359	−	0.353916i	−0.00390720	−	0.0128803i
$756$	23.3424	+	3.02557i	0.848954	+	0.110039i
$757$	−44.3001	+	4.36318i	−1.61012	+	0.158583i	−0.862679	−	0.505751i	$-0.831215\pi$
$757$	−44.3001	+	4.36318i	−1.61012	+	0.158583i	−0.747436	+	0.664334i	$0.768715\pi$
$758$	4.18356	−	50.7388i	0.151954	−	1.84291i
$759$	−5.19163	+	2.42703i	−0.188444	+	0.0880957i
$760$	−49.6924	−	7.44043i	−1.80253	−	0.269893i
$761$	−1.53945	−	7.73933i	−0.0558049	−	0.280550i	0.942800	−	0.333360i	$-0.108182\pi$
$761$	−1.53945	−	7.73933i	−0.0558049	−	0.280550i	−0.998605	+	0.0528094i	$0.983182\pi$
$762$	14.2906	+	0.538489i	0.517695	+	0.0195074i
$763$	7.33293	−	24.1734i	0.265470	−	0.875137i
$764$	2.73752	+	6.05647i	0.0990399	+	0.219115i
$765$	12.6803	−	5.11961i	0.458457	−	0.185100i
$766$	−49.8435	+	10.7415i	−1.80092	+	0.388105i
$767$	7.48946			0.270429
$768$	−27.5046	−	3.39066i	−0.992487	−	0.122350i
$769$	−13.5739			−0.489486			−0.244743	−	0.969588i	$-0.578704\pi$
$769$	−13.5739			−0.489486			−0.244743	+	0.969588i	$0.578704\pi$
$770$	29.4455	−	6.34562i	1.06114	−	0.228680i
$771$	12.5440	+	3.20196i	0.451762	+	0.115316i
$772$	6.10861	+	13.5147i	0.219854	+	0.486403i
$773$	7.37384	−	24.3083i	0.265219	−	0.874309i	−0.718643	−	0.695379i	$-0.755236\pi$
$773$	7.37384	−	24.3083i	0.265219	−	0.874309i	0.983862	−	0.178930i	$-0.0572635\pi$
$774$	−25.6750	−	37.8540i	−0.922870	−	1.36064i
$775$	0.0635558	+	0.319516i	0.00228299	+	0.0114774i
$776$	0.0800729	−	0.534783i	0.00287445	−	0.0191976i
$777$	12.8999	+	27.5940i	0.462782	+	0.989930i
$778$	−1.11792	+	13.5583i	−0.0400795	+	0.486089i
$779$	87.9348	−	8.66083i	3.15059	−	0.310306i
$780$	2.14181	+	12.1425i	0.0766892	+	0.434771i
$781$	−7.13858	−	23.5328i	−0.255439	−	0.842068i
$782$	−0.901200	−	2.08141i	−0.0322269	−	0.0744310i
$783$	−22.8185	+	20.1291i	−0.815466	+	0.719354i
$784$	2.41747	−	7.07934i	0.0863383	−	0.252833i
$785$	12.3434	+	5.11280i	0.440555	+	0.182484i
$786$	−22.8694	+	17.3696i	−0.815725	+	0.619552i
$787$	−12.7472	+	23.8483i	−0.454388	+	0.850100i	0.545540	+	0.838085i	$0.316325\pi$
$787$	−12.7472	+	23.8483i	−0.454388	+	0.850100i	−0.999928	+	0.0120154i	$0.996175\pi$
$788$	1.89514	−	0.247748i	0.0675116	−	0.00882564i
$789$	1.42732	−	26.6179i	0.0508140	−	0.947621i
$790$	−33.8140	+	10.8477i	−1.20305	+	0.385943i
$791$	−1.78892	−	2.67731i	−0.0636067	−	0.0951941i
$792$	37.1542	−	8.89974i	1.32022	−	0.316238i
$793$	−5.53635	−	3.69927i	−0.196601	−	0.131365i
$794$	−14.6618	−	26.4109i	−0.520328	−	0.937289i
$795$	−2.06827	−	0.989592i	−0.0733540	−	0.0350972i
$796$	39.7330	−	28.4176i	1.40830	−	1.00724i
$797$	25.7272	+	2.53390i	0.911303	+	0.0897555i	0.542791	−	0.839868i	$-0.317367\pi$
$797$	25.7272	+	2.53390i	0.911303	+	0.0897555i	0.368512	+	0.929623i	$0.379867\pi$
$798$	−15.3886	+	44.6083i	−0.544749	+	1.57912i
$799$	−19.7731	−	19.7731i	−0.699521	−	0.699521i
$800$	−3.21291	+	1.64111i	−0.113594	+	0.0580219i
$801$	−1.79063	−	3.42354i	−0.0632690	−	0.120965i
$802$	−47.3146	−	8.63140i	−1.67074	−	0.304785i
$803$	28.8881	+	2.84523i	1.01944	+	0.100406i
$804$	13.9303	−	16.2405i	0.491285	−	0.572757i
$805$	1.63870	+	3.06579i	0.0577566	+	0.108055i
$806$	−0.338578	+	1.18360i	−0.0119259	+	0.0416907i
$807$	2.22515	+	49.8545i	0.0783291	+	1.75496i
$808$	18.0722	+	8.57768i	0.635777	+	0.301762i
$809$	24.9333	+	37.3154i	0.876610	+	1.31194i	0.949231	+	0.314580i	$0.101864\pi$
$809$	24.9333	+	37.3154i	0.876610	+	1.31194i	−0.0726214	+	0.997360i	$0.523136\pi$
$810$	−23.4699	+	12.4838i	−0.824648	+	0.438636i
$811$	−29.7632	−	24.4261i	−1.04513	−	0.857715i	−0.0550859	−	0.998482i	$-0.517543\pi$
$811$	−29.7632	−	24.4261i	−1.04513	−	0.857715i	−0.990043	+	0.140767i	$0.955043\pi$
$812$	−13.2421	−	22.9843i	−0.464708	−	0.806589i
$813$	5.54604	+	38.5794i	0.194508	+	1.35304i
$814$	35.5125	+	34.4002i	1.24471	+	1.20573i
$815$	−36.3775	−	15.0680i	−1.27425	−	0.527811i
$816$	3.09891	+	14.7995i	0.108484	+	0.518088i
$817$	84.7186	−	35.0916i	2.96393	−	1.22770i
$818$	9.24007	+	3.65626i	0.323071	+	0.127838i
$819$	11.5790	+	0.103843i	0.404603	+	0.00362858i
$820$	−32.6519	+	28.5824i	−1.14025	+	0.998142i
$821$	52.1619	−	5.13750i	1.82046	−	0.179300i	0.870606	−	0.491981i	$-0.163727\pi$
$821$	52.1619	−	5.13750i	1.82046	−	0.179300i	0.949858	+	0.312681i	$0.101227\pi$
$822$	−3.41475	+	14.3248i	−0.119103	+	0.499634i
$823$	−6.89824	+	34.6798i	−0.240458	+	1.20886i	0.652172	+	0.758071i	$0.273858\pi$
$823$	−6.89824	+	34.6798i	−0.240458	+	1.20886i	−0.892630	+	0.450791i	$0.851142\pi$
$824$	1.79214	+	37.5238i	0.0624321	+	1.30720i
$825$	3.35664	−	3.67027i	0.116863	−	0.127782i
$826$	−13.9852	+	1.60243i	−0.486607	+	0.0557556i
$827$	−9.72906	+	32.0724i	−0.338312	+	1.11527i	0.608520	+	0.793539i	$0.291764\pi$
$827$	−9.72906	+	32.0724i	−0.338312	+	1.11527i	−0.946832	+	0.321728i	$0.895736\pi$
$828$	2.16677	+	3.84006i	0.0753006	+	0.133451i
$829$	5.91232	−	4.85212i	0.205343	−	0.168521i	−0.526101	−	0.850422i	$-0.676347\pi$
$829$	5.91232	−	4.85212i	0.205343	−	0.168521i	0.731444	+	0.681901i	$0.238847\pi$
$830$	−17.8615	−	11.5280i	−0.619983	−	0.400142i
$831$	−23.6882	+	17.4042i	−0.821734	+	0.603747i
$832$	−13.6334	−	0.0371792i	−0.472653	−	0.00128896i
$833$	−4.08159			−0.141419
$834$	−46.1384	+	2.79531i	−1.59764	+	0.0967936i
$835$	11.0215	+	13.4297i	0.381415	+	0.464755i
$836$	2.43648	+	76.5547i	0.0842673	+	2.64770i
$837$	−2.65253	+	0.0945641i	−0.0916850	+	0.00326861i
$838$	44.2378	−	5.06877i	1.52817	−	0.175098i
$839$	3.51582	+	17.6752i	0.121379	+	0.610216i	0.992810	+	0.119698i	$0.0381925\pi$
$839$	3.51582	+	17.6752i	0.121379	+	0.610216i	−0.871431	+	0.490518i	$0.836808\pi$
$840$	−6.59742	−	22.2156i	−0.227633	−	0.766511i
$841$	5.18950	+	1.03226i	0.178948	+	0.0355951i
$842$	−25.3899	−	29.9531i	−0.874993	−	1.03225i
$843$	−1.60686	−	1.78896i	−0.0553433	−	0.0616149i
$844$	−8.36194	−	0.555705i	−0.287830	−	0.0191281i
$845$	−6.12093	−	20.1780i	−0.210566	−	0.694145i
$846$	42.2592	+	34.1932i	1.45290	+	1.17559i
$847$	−8.03713	−	19.4033i	−0.276159	−	0.666707i
$848$	1.48045	−	2.05806i	0.0508390	−	0.0706739i
$849$	40.2574	−	9.89233i	1.38163	−	0.339504i
$850$	1.41387	+	1.36959i	0.0484954	+	0.0469765i
$851$	−2.68979	+	5.03224i	−0.0922048	+	0.172503i
$852$	−17.6332	+	6.85842i	−0.604104	+	0.234966i
$853$	−27.4312	+	33.4250i	−0.939227	+	1.14445i	0.0501003	+	0.998744i	$0.484046\pi$
$853$	−27.4312	+	33.4250i	−0.939227	+	1.14445i	−0.989328	+	0.145708i	$0.953454\pi$
$854$	11.1296	+	5.72316i	0.380847	+	0.195843i
$855$	−15.0125	−	51.1361i	−0.513417	−	1.74882i
$856$	−6.45955	−	0.326167i	−0.220783	−	0.0111482i
$857$	−1.15066	−	0.768849i	−0.0393059	−	0.0262634i	0.535762	−	0.844369i	$-0.320024\pi$
$857$	−1.15066	−	0.768849i	−0.0393059	−	0.0262634i	−0.575068	+	0.818106i	$0.695024\pi$
$858$	17.6231	−	6.53368i	0.601642	−	0.223056i
$859$	−5.85221	+	3.12807i	−0.199675	+	0.106729i	−0.568204	−	0.822888i	$-0.692362\pi$
$859$	−5.85221	+	3.12807i	−0.199675	+	0.106729i	0.368529	+	0.929616i	$0.379862\pi$
$860$	−23.8159	+	38.2215i	−0.812115	+	1.30334i
$861$	20.7945	+	35.0490i	0.708675	+	1.19447i
$862$	4.88320	+	0.890821i	0.166322	+	0.0303415i
$863$	−22.3259	−	22.3259i	−0.759981	−	0.759981i	0.216337	−	0.976319i	$-0.430589\pi$
$863$	−22.3259	−	22.3259i	−0.759981	−	0.759981i	−0.976319	+	0.216337i	$0.930589\pi$
$864$	−9.00953	−	27.9791i	−0.306510	−	0.951867i
$865$	−21.5662	+	21.5662i	−0.733274	+	0.733274i
$866$	8.90232	−	6.15540i	0.302513	−	0.209169i
$867$	−18.2281	+	10.8147i	−0.619060	+	0.367287i
$868$	0.378991	−	2.28261i	0.0128638	−	0.0774767i
$869$	25.5177	+	47.7403i	0.865629	+	1.61948i
$870$	27.2268	+	12.4987i	0.923074	+	0.423746i
$871$	5.84797	−	8.75211i	0.198151	−	0.296554i
$872$	−31.2111	+	4.58624i	−1.05694	+	0.155310i
$873$	0.550320	−	0.161563i	0.0186255	−	0.00546808i
$874$	−8.41698	+	2.70020i	−0.284709	+	0.0913357i
$875$	−20.6157	−	16.9189i	−0.696938	−	0.571962i
$876$	0.485830	−	22.3278i	0.0164147	−	0.754388i
$877$	31.5743	+	16.8768i	1.06619	+	0.569890i	0.908622	−	0.417619i	$-0.137135\pi$
$877$	31.5743	+	16.8768i	1.06619	+	0.569890i	0.157566	+	0.987508i	$0.449635\pi$
$878$	−0.173705	−	10.9185i	−0.00586226	−	0.368480i
$879$	12.3064	+	50.0817i	0.415086	+	1.68921i
$880$	−22.8448	−	29.8842i	−0.770098	−	1.00740i
$881$	18.0420	−	7.47323i	0.607849	−	0.251779i	−0.0574594	−	0.998348i	$-0.518300\pi$
$881$	18.0420	−	7.47323i	0.607849	−	0.251779i	0.665309	+	0.746568i	$0.268300\pi$
$882$	7.89071	−	0.832498i	0.265694	−	0.0280317i
$883$	−8.49935	+	2.57825i	−0.286026	+	0.0867650i	−0.430038	−	0.902811i	$-0.641500\pi$
$883$	−8.49935	+	2.57825i	−0.286026	+	0.0867650i	0.144012	+	0.989576i	$0.454000\pi$
$884$	2.38466	+	7.04601i	0.0802048	+	0.236983i
$885$	11.8276	−	10.6237i	0.397580	−	0.357111i
$886$	−1.67715	+	20.3407i	−0.0563449	+	0.683359i
$887$	−1.33307	+	6.70179i	−0.0447601	+	0.225024i	−0.996690	−	0.0812903i	$-0.974096\pi$
$887$	−1.33307	+	6.70179i	−0.0447601	+	0.225024i	0.951930	+	0.306315i	$0.0990959\pi$
$888$	24.3033	−	29.2630i	0.815564	−	0.982002i
$889$	−12.9691	+	2.57971i	−0.434969	+	0.0865207i
$890$	−2.36612	+	2.97851i	−0.0793125	+	0.0998398i
$891$	25.1414	+	31.7806i	0.842270	+	1.06469i
$892$	7.68769	−	20.3695i	0.257403	−	0.682022i
$893$	−84.2429	+	69.1364i	−2.81908	+	2.31356i
$894$	14.5092	+	12.8515i	0.485259	+	0.429819i
$895$			35.3307i			1.18098i
$896$	25.4658	−	2.84754i	0.850754	−	0.0951298i
$897$	1.28432	+	1.74803i	0.0428822	+	0.0583651i
$898$	15.7142	−	3.38648i	0.524391	−	0.113008i
$899$	1.89760	+	2.31223i	0.0632885	+	0.0771173i
$900$	−3.01271	−	2.35937i	−0.100424	−	0.0786457i
$901$	−1.32369	−	0.401537i	−0.0440985	−	0.0133771i
$902$	51.7951	+	41.1459i	1.72459	+	1.37001i
$903$	31.2095	+	28.5426i	1.03859	+	0.949838i
$904$	−2.07196	+	3.44620i	−0.0689125	+	0.114619i
$905$	−27.5933	−	5.48866i	−0.917234	−	0.182449i
$906$	0.227226	+	0.369465i	0.00754907	+	0.0122747i
$907$	−0.656366	−	6.66419i	−0.0217943	−	0.221281i	−0.999912	−	0.0132310i	$-0.995788\pi$
$907$	−0.656366	−	6.66419i	−0.0217943	−	0.221281i	0.978118	−	0.208050i	$-0.0667117\pi$
$908$	−1.64594	−	4.86329i	−0.0546223	−	0.161394i
$909$	−0.190281	+	21.2171i	−0.00631121	+	0.703728i
$910$	−4.52991	−	10.4623i	−0.150165	−	0.346820i
$911$	−19.8276	−	47.8681i	−0.656918	−	1.58594i	−0.802539	−	0.596600i	$-0.796518\pi$
$911$	−19.8276	−	47.8681i	−0.656918	−	1.58594i	0.145621	−	0.989340i	$-0.453482\pi$
$912$	58.5837	−	6.36569i	1.93990	−	0.210789i
$913$	−12.4012	+	29.9390i	−0.410418	+	0.990838i
$914$	−27.8245	+	0.442668i	−0.920353	+	0.0146422i
$915$	−13.9905	+	2.01123i	−0.462513	+	0.0664891i
$916$	−24.3946	+	31.7319i	−0.806021	+	1.04845i
$917$	16.8455	−	20.5264i	0.556289	−	0.677840i
$918$	−12.8581	+	9.58527i	−0.424381	+	0.316361i
$919$	20.0460	−	13.3943i	0.661257	−	0.441838i	−0.179130	−	0.983825i	$-0.557328\pi$
$919$	20.0460	−	13.3943i	0.661257	−	0.441838i	0.840386	+	0.541988i	$0.182328\pi$
$920$	2.59078	−	3.48333i	0.0854156	−	0.114842i
$921$	17.5447	−	0.783072i	0.578117	−	0.0258031i
$922$	−15.9076	−	28.6550i	−0.523887	−	0.943701i
$923$	−8.20875	+	4.38767i	−0.270194	+	0.144422i
$924$	−31.5099	+	15.9710i	−1.03660	+	0.525408i
$925$	0.485390	−	4.92824i	0.0159595	−	0.162040i
$926$	−13.8450	−	20.0235i	−0.454974	−	0.658012i
$927$	−35.3075	+	18.4671i	−1.15965	+	0.606538i
$928$	−18.9137	+	27.1954i	−0.620874	+	0.892732i
$929$	−12.4363	+	12.4363i	−0.408023	+	0.408023i	−0.881049	−	0.473025i	$-0.843162\pi$
$929$	−12.4363	+	12.4363i	−0.408023	+	0.408023i	0.473025	+	0.881049i	$0.343162\pi$
$930$	1.14423	+	2.34945i	0.0375209	+	0.0770416i
$931$	−1.55916	+	15.8304i	−0.0510993	+	0.518820i
$932$	13.0547	−	20.9512i	0.427622	−	0.686281i
$933$	−0.684936	+	1.43153i	−0.0224238	+	0.0468663i
$934$	−0.677466	+	2.36829i	−0.0221674	+	0.0774929i
$935$	−11.4024	+	17.0649i	−0.372898	+	0.558081i
$936$	−6.04726	−	13.1353i	−0.197661	−	0.429340i
$937$	−13.3226	+	8.90187i	−0.435230	+	0.290811i	−0.753820	−	0.657081i	$-0.771791\pi$
$937$	−13.3226	+	8.90187i	−0.435230	+	0.290811i	0.318590	+	0.947893i	$0.396791\pi$
$938$	−9.04743	+	17.5942i	−0.295409	+	0.574470i
$939$	4.81981	+	0.258451i	0.157288	+	0.00843423i
$940$	13.8994	−	51.6851i	0.453347	−	1.68578i
$941$	−21.6865	−	11.5917i	−0.706961	−	0.377878i	0.0783955	−	0.996922i	$-0.475020\pi$
$941$	−21.6865	−	11.5917i	−0.706961	−	0.377878i	−0.785356	+	0.619044i	$0.787520\pi$
$942$	−15.5246	−	2.12191i	−0.505820	−	0.0691354i
$943$	−2.92146	+	7.05303i	−0.0951358	+	0.229678i
$944$	9.25576	+	14.9450i	0.301249	+	0.486418i
$945$	18.4332	−	16.2606i	0.599632	−	0.528959i
$946$	63.8327	+	25.2584i	2.07538	+	0.821221i
$947$	18.8464	−	5.71700i	0.612427	−	0.185778i	0.0311919	−	0.999513i	$-0.490070\pi$
$947$	18.8464	−	5.71700i	0.612427	−	0.185778i	0.581235	+	0.813736i	$0.302570\pi$
$948$	35.1238	−	22.3793i	1.14077	−	0.726847i
$949$	−1.07690	−	10.9340i	−0.0349578	−	0.354932i
$950$	5.85203	−	4.96051i	0.189865	−	0.160940i
$951$	24.7007	−	11.5473i	0.800974	−	0.374447i
$952$	−5.96046	−	12.6469i	−0.193180	−	0.409889i
$953$	20.3997	−	4.05776i	0.660812	−	0.131444i	0.146719	−	0.989178i	$-0.453129\pi$
$953$	20.3997	−	4.05776i	0.660812	−	0.131444i	0.514093	+	0.857735i	$0.328129\pi$
$954$	2.64091	+	0.506284i	0.0855028	+	0.0163915i
$955$	6.64196	+	2.01482i	0.214929	+	0.0651979i
$956$	−1.20820	−	37.9619i	−0.0390760	−	1.22778i
$957$	11.2949	−	44.2488i	0.365111	−	1.43036i
$958$	0.509070	+	0.328558i	0.0164473	+	0.0106152i
$959$		−	13.6165i		−	0.439699i
$960$	−21.5830	+	19.2801i	−0.696589	+	0.622261i
$961$		−	30.7391i		−	0.991583i
$962$	10.1478	−	15.7231i	0.327180	−	0.506934i
$963$	−2.56831	−	6.36121i	−0.0827626	−	0.204987i
$964$	24.4035	+	22.8980i	0.785984	+	0.737497i
$965$	14.8212	+	4.49595i	0.477110	+	0.144730i
$966$	−2.77224	−	2.98934i	−0.0891952	−	0.0961804i
$967$	−11.5446	+	2.29637i	−0.371250	+	0.0738462i	−0.377189	−	0.926136i	$-0.623109\pi$
$967$	−11.5446	+	2.29637i	−0.371250	+	0.0738462i	0.00593946	+	0.999982i	$0.498109\pi$
$968$	−17.6397	+	19.4092i	−0.566962	+	0.623835i
$969$	−13.6164	−	29.1266i	−0.437421	−	0.935682i
$970$	−0.365139	−	0.430764i	−0.0117239	−	0.0138310i
$971$	0.108838	+	1.10505i	0.00349279	+	0.0354629i	0.996773	−	0.0802701i	$-0.0255783\pi$
$971$	0.108838	+	1.10505i	0.00349279	+	0.0354629i	−0.993280	+	0.115733i	$0.963078\pi$
$972$	22.9028	−	21.1533i	0.734609	−	0.678491i
$973$	40.8995	−	12.4067i	1.31118	−	0.397742i
$974$	16.6053	−	41.9648i	0.532069	−	1.34464i
$975$	−1.61034	−	0.975042i	−0.0515722	−	0.0312263i
$976$	0.539752	−	15.6193i	0.0172770	−	0.499962i
$977$	−10.3661	+	25.0259i	−0.331641	+	0.800651i	0.666822	+	0.745217i	$0.267654\pi$
$977$	−10.3661	+	25.0259i	−0.331641	+	0.800651i	−0.998462	+	0.0554339i	$0.982346\pi$
$978$	45.7530	+	6.25351i	1.46302	+	0.199965i
$979$	5.11389	+	2.73343i	0.163441	+	0.0873609i
$980$	−3.89990	−	6.76902i	−0.124578	−	0.216228i
$981$	−18.3390	−	27.9864i	−0.585520	−	0.893537i
$982$	−4.30908	−	2.21586i	−0.137508	−	0.0707108i
$983$	−48.9712	+	32.7215i	−1.56194	+	1.04365i	−0.590300	+	0.807184i	$0.700990\pi$
$983$	−48.9712	+	32.7215i	−1.56194	+	1.04365i	−0.971639	+	0.236470i	$0.924010\pi$
$984$	28.5216	−	42.1499i	0.909235	−	1.34369i
$985$	1.10888	−	1.65955i	0.0353318	−	0.0528778i
$986$	17.3769	+	4.97079i	0.553394	+	0.158302i
$987$	−45.3411	−	21.6941i	−1.44322	−	0.690530i
$988$	28.2388	−	6.55731i	0.898397	−	0.208616i
$989$	−0.776548	+	7.88442i	−0.0246928	+	0.250710i
$990$	18.5630	−	35.3163i	0.589970	−	1.12242i
$991$	18.5148	−	18.5148i	0.588143	−	0.588143i	−0.348985	−	0.937128i	$-0.613474\pi$
$991$	18.5148	−	18.5148i	0.588143	−	0.588143i	0.937128	+	0.348985i	$0.113474\pi$
$992$	−2.78027	+	0.787121i	−0.0882738	+	0.0249911i
$993$	−2.24537	+	14.6831i	−0.0712545	+	0.465954i
$994$	14.3896	−	9.94949i	0.456409	−	0.315579i
$995$	5.00018	−	50.7677i	0.158516	−	1.60944i
$996$	23.6953	+	7.75466i	0.750815	+	0.245716i
$997$	−29.0408	+	15.5226i	−0.919731	+	0.491606i	−0.862104	−	0.506732i	$-0.830853\pi$
$997$	−29.0408	+	15.5226i	−0.919731	+	0.491606i	−0.0576271	+	0.998338i	$0.518353\pi$
$998$	−1.93769	+	1.07569i	−0.0613366	+	0.0340504i
$999$	39.0020	+	10.3290i	1.23397	+	0.326795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.w.a.131.4	✓	992
3.2	odd	2	inner	384.2.w.a.131.59	yes	992
128.43	odd	32	inner	384.2.w.a.299.59	yes	992
384.299	even	32	inner	384.2.w.a.299.4	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.w.a.131.4	✓	992	1.1	even	1	trivial
384.2.w.a.131.59	yes	992	3.2	odd	2	inner
384.2.w.a.299.4	yes	992	384.299	even	32	inner
384.2.w.a.299.59	yes	992	128.43	odd	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.w (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38248 + 0.297929i) q^{2} +(0.428384 - 1.67824i) q^{3} +(1.82248 - 0.823758i) q^{4} +(0.606287 - 1.99866i) q^{5} +(-0.0922344 + 2.44775i) q^{6} +(-0.441862 - 2.22139i) q^{7} +(-2.27411 + 1.68179i) q^{8} +(-2.63298 - 1.43786i) q^{9} +O(q^{10})\)	\(q+(-1.38248 + 0.297929i) q^{2} +(0.428384 - 1.67824i) q^{3} +(1.82248 - 0.823758i) q^{4} +(0.606287 - 1.99866i) q^{5} +(-0.0922344 + 2.44775i) q^{6} +(-0.441862 - 2.22139i) q^{7} +(-2.27411 + 1.68179i) q^{8} +(-2.63298 - 1.43786i) q^{9} +(-0.242719 + 2.94373i) q^{10} +(4.48085 - 0.441325i) q^{11} +(-0.601743 - 3.41144i) q^{12} +(-0.494698 - 1.63080i) q^{13} +(1.27268 + 2.93938i) q^{14} +(-3.09451 - 1.87369i) q^{15} +(2.64285 - 3.00256i) q^{16} +(-2.01633 - 0.835190i) q^{17} +(4.06840 + 1.20337i) q^{18} +(-4.00951 + 7.50127i) q^{19} +(-0.541468 - 4.14195i) q^{20} +(-3.91731 - 0.210057i) q^{21} +(-6.06318 + 1.94509i) q^{22} +(-0.408269 - 0.611018i) q^{23} +(1.84826 + 4.53695i) q^{24} +(0.530287 + 0.354326i) q^{25} +(1.16977 + 2.10716i) q^{26} +(-3.54100 + 3.80281i) q^{27} +(-2.63517 - 3.68445i) q^{28} +(5.82767 + 0.573975i) q^{29} +(4.83631 + 1.66839i) q^{30} +(0.361193 + 0.361193i) q^{31} +(-2.75912 + 4.93834i) q^{32} +(1.17887 - 7.70900i) q^{33} +(3.03635 + 0.553909i) q^{34} +(-4.70770 - 0.463668i) q^{35} +(-5.98299 - 0.451534i) q^{36} +(-3.66025 - 6.84785i) q^{37} +(3.30821 - 11.5649i) q^{38} +(-2.94879 + 0.131613i) q^{39} +(1.98257 + 5.56482i) q^{40} +(-5.77154 - 8.63772i) q^{41} +(5.47817 - 0.876681i) q^{42} +(-8.33382 - 6.83939i) q^{43} +(7.80270 - 4.49544i) q^{44} +(-4.47013 + 4.39067i) q^{45} +(0.746462 + 0.723082i) q^{46} +(11.8375 + 4.90324i) q^{47} +(-3.90686 - 5.72158i) q^{48} +(1.72782 - 0.715687i) q^{49} +(-0.838672 - 0.331860i) q^{50} +(-2.26541 + 3.02610i) q^{51} +(-2.24496 - 2.56459i) q^{52} +(0.630753 - 0.0621237i) q^{53} +(3.76238 - 6.31225i) q^{54} +(1.83462 - 9.22327i) q^{55} +(4.74076 + 4.30857i) q^{56} +(10.8713 + 9.94234i) q^{57} +(-8.22761 + 0.942722i) q^{58} +(-1.27573 + 4.20552i) q^{59} +(-7.18314 - 0.865630i) q^{60} +(3.02027 - 2.47867i) q^{61} +(-0.606951 - 0.391731i) q^{62} +(-2.03064 + 6.48420i) q^{63} +(2.34315 - 7.64916i) q^{64} -3.55935 q^{65} +(0.666966 + 11.0087i) q^{66} +(3.91840 + 4.77459i) q^{67} +(-4.36271 + 0.138850i) q^{68} +(-1.20033 + 0.423423i) q^{69} +(6.64642 - 0.761549i) q^{70} +(-1.06553 - 5.35680i) q^{71} +(8.40586 - 1.15827i) q^{72} +(6.32314 + 1.25775i) q^{73} +(7.10038 + 8.37649i) q^{74} +(0.821810 - 0.738160i) q^{75} +(-1.12802 + 16.9738i) q^{76} +(-2.96027 - 9.75872i) q^{77} +(4.03742 - 1.06048i) q^{78} +(4.60085 + 11.1074i) q^{79} +(-4.39877 - 7.10257i) q^{80} +(4.86512 + 7.57170i) q^{81} +(10.5524 + 10.2219i) q^{82} +(-3.39275 + 6.34740i) q^{83} +(-7.31225 + 2.84409i) q^{84} +(-2.89174 + 3.52359i) q^{85} +(13.5589 + 6.97240i) q^{86} +(3.45975 - 9.53434i) q^{87} +(-9.44773 + 8.53948i) q^{88} +(1.07081 + 0.715491i) q^{89} +(4.87175 - 7.40177i) q^{90} +(-3.40406 + 1.81951i) q^{91} +(-1.24739 - 0.777251i) q^{92} +(0.760899 - 0.451440i) q^{93} +(-17.8258 - 3.25189i) q^{94} +(12.5616 + 12.5616i) q^{95} +(7.10576 + 6.74597i) q^{96} +(-0.135186 + 0.135186i) q^{97} +(-2.17545 + 1.50419i) q^{98} +(-12.4325 - 5.28084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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