LMFDB - Embedded newform 462.2.bc.a.95.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.7
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(-0.611589 + 1.62048i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.684905 - 1.53832i) q^{5} +(1.54768 + 0.777625i) q^{6} +(1.54934 - 2.14465i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.25192 - 1.98214i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(-0.611589 + 1.62048i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.684905 - 1.53832i) q^{5} +(1.54768 + 0.777625i) q^{6} +(1.54934 - 2.14465i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.25192 - 1.98214i) q^{9} +(-1.45830 - 0.841952i) q^{10} +(-2.83081 + 1.72816i) q^{11} +(0.935142 - 1.45791i) q^{12} +(1.78780 - 2.46070i) q^{13} +(-1.97095 - 1.76503i) q^{14} +(2.07394 + 2.05070i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.447807 - 4.26060i) q^{17} +(-2.20667 + 2.03239i) q^{18} +(-0.153183 - 0.720668i) q^{19} +(-0.989774 + 1.36231i) q^{20} +(2.52781 + 3.82233i) q^{21} +(1.42279 + 2.99594i) q^{22} +(6.96058 - 4.01869i) q^{23} +(-1.35218 - 1.08241i) q^{24} +(1.44831 + 1.60851i) q^{25} +(-2.26034 - 2.03522i) q^{26} +(4.58927 - 2.43693i) q^{27} +(-1.96138 + 1.77566i) q^{28} +(-2.76393 - 8.50649i) q^{29} +(2.25625 - 1.84822i) q^{30} +(-5.99246 + 2.66801i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.06915 - 5.64419i) q^{33} -4.28407 q^{34} +(-2.23801 - 3.85227i) q^{35} +(1.79060 + 2.40702i) q^{36} +(4.23672 - 4.70535i) q^{37} +(-0.732732 + 0.0770132i) q^{38} +(2.89412 + 4.40204i) q^{39} +(1.25138 + 1.12675i) q^{40} +(-0.907773 + 2.79384i) q^{41} +(4.06562 - 2.11442i) q^{42} -6.89588i q^{43} +(3.12825 - 1.10184i) q^{44} +(-4.59152 + 2.10660i) q^{45} +(-3.26910 - 7.34252i) q^{46} +(2.33594 + 10.9898i) q^{47} +(-1.21782 + 1.23163i) q^{48} +(-2.19907 - 6.64561i) q^{49} +(1.75109 - 1.27224i) q^{50} +(7.17810 + 1.88008i) q^{51} +(-2.26034 + 2.03522i) q^{52} +(0.415379 + 0.932956i) q^{53} +(-1.94388 - 4.81885i) q^{54} +(0.719629 + 5.53832i) q^{55} +(1.56091 + 2.13625i) q^{56} +(1.26151 + 0.192523i) q^{57} +(-8.74880 + 1.85961i) q^{58} +(1.40444 - 6.60737i) q^{59} +(-1.60226 - 2.43708i) q^{60} +(-2.09528 + 4.70608i) q^{61} +(2.02702 + 6.23851i) q^{62} +(-7.73999 + 1.75857i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.56087 - 4.43556i) q^{65} +(-5.72503 + 0.473319i) q^{66} +(-2.70908 + 4.69227i) q^{67} +(-0.447807 + 4.26060i) q^{68} +(2.25520 + 13.7373i) q^{69} +(-4.06511 + 1.82308i) q^{70} +(9.86752 + 13.5815i) q^{71} +(2.58101 - 1.52919i) q^{72} +(-3.10170 + 14.5924i) q^{73} +(-4.23672 - 4.70535i) q^{74} +(-3.49234 + 1.36321i) q^{75} +0.736768i q^{76} +(-0.679594 + 8.74861i) q^{77} +(4.68044 - 2.41812i) q^{78} +(1.58877 + 0.166986i) q^{79} +(1.25138 - 1.12675i) q^{80} +(1.14226 + 8.92722i) q^{81} +(2.68364 + 1.19484i) q^{82} +(-0.791771 + 0.575255i) q^{83} +(-1.67786 - 4.26436i) q^{84} +(-6.86088 - 2.22924i) q^{85} +(-6.85811 - 0.720816i) q^{86} +(15.4750 + 0.723589i) q^{87} +(-0.768808 - 3.22629i) q^{88} +(-3.79817 + 2.19288i) q^{89} +(1.61511 + 4.78656i) q^{90} +(-2.50743 - 7.64668i) q^{91} +(-7.64401 + 2.48369i) q^{92} +(-0.658542 - 11.3424i) q^{93} +(11.1737 - 1.17441i) q^{94} +(-1.21354 - 0.257945i) q^{95} +(1.09758 + 1.33989i) q^{96} +(-11.6994 - 8.50013i) q^{97} +(-6.83907 + 1.49237i) q^{98} +(9.80019 + 1.71938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	−0.611589	+	1.62048i	−0.353101	+	0.935585i
$3$	−0.611589	+	1.62048i	−0.353101	+	0.935585i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	0.684905	−	1.53832i	0.306299	−	0.687959i	−0.693162	−	0.720782i	$-0.743783\pi$
$5$	0.684905	−	1.53832i	0.306299	−	0.687959i	0.999461	+	0.0328228i	$0.0104497\pi$
$6$	1.54768	+	0.777625i	0.631836	+	0.317464i
$7$	1.54934	−	2.14465i	0.585597	−	0.810603i
$7$	1.54934	−	2.14465i	0.585597	−	0.810603i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.25192	−	1.98214i	−0.750639	−	0.660713i
$10$	−1.45830	−	0.841952i	−0.461156	−	0.266249i
$11$	−2.83081	+	1.72816i	−0.853521	+	0.521059i
$11$	−2.83081	+	1.72816i	−0.853521	+	0.521059i
$12$	0.935142	−	1.45791i	0.269952	−	0.420863i
$13$	1.78780	−	2.46070i	0.495847	−	0.682475i	−0.485606	−	0.874178i	$-0.661401\pi$
$13$	1.78780	−	2.46070i	0.495847	−	0.682475i	0.981453	+	0.191703i	$0.0614009\pi$
$14$	−1.97095	−	1.76503i	−0.526760	−	0.471725i
$15$	2.07394	+	2.05070i	0.535489	+	0.529488i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.447807	−	4.26060i	−0.108609	−	1.03335i	−0.904082	−	0.427359i	$-0.859444\pi$
$17$	−0.447807	−	4.26060i	−0.108609	−	1.03335i	0.795473	−	0.605989i	$-0.207222\pi$
$18$	−2.20667	+	2.03239i	−0.520117	+	0.479039i
$19$	−0.153183	−	0.720668i	−0.0351425	−	0.165333i	0.957077	−	0.289834i	$-0.0936001\pi$
$19$	−0.153183	−	0.720668i	−0.0351425	−	0.165333i	−0.992219	+	0.124502i	$0.960267\pi$
$20$	−0.989774	+	1.36231i	−0.221320	+	0.304621i
$21$	2.52781	+	3.82233i	0.551613	+	0.834100i
$22$	1.42279	+	2.99594i	0.303340	+	0.638737i
$23$	6.96058	−	4.01869i	1.45138	−	0.837955i	0.452821	−	0.891601i	$-0.350418\pi$
$23$	6.96058	−	4.01869i	1.45138	−	0.837955i	0.998560	+	0.0536463i	$0.0170843\pi$
$24$	−1.35218	−	1.08241i	−0.276012	−	0.220946i
$25$	1.44831	+	1.60851i	0.289662	+	0.321703i
$26$	−2.26034	−	2.03522i	−0.443290	−	0.399140i
$27$	4.58927	−	2.43693i	0.883204	−	0.468988i
$28$	−1.96138	+	1.77566i	−0.370667	+	0.335568i
$29$	−2.76393	−	8.50649i	−0.513248	−	1.57962i	−0.786447	−	0.617658i	$-0.788082\pi$
$29$	−2.76393	−	8.50649i	−0.513248	−	1.57962i	0.273199	−	0.961958i	$-0.411918\pi$
$30$	2.25625	−	1.84822i	0.411933	−	0.337438i
$31$	−5.99246	+	2.66801i	−1.07628	+	0.479189i	−0.866816	−	0.498628i	$-0.833838\pi$
$31$	−5.99246	+	2.66801i	−1.07628	+	0.479189i	−0.209461	+	0.977817i	$0.567171\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.06915	−	5.64419i	−0.186116	−	0.982528i
$34$	−4.28407			−0.734712
$35$	−2.23801	−	3.85227i	−0.378294	−	0.651153i
$36$	1.79060	+	2.40702i	0.298433	+	0.401171i
$37$	4.23672	−	4.70535i	0.696512	−	0.773555i	−0.286304	−	0.958139i	$-0.592427\pi$
$37$	4.23672	−	4.70535i	0.696512	−	0.773555i	0.982817	+	0.184583i	$0.0590936\pi$
$38$	−0.732732	+	0.0770132i	−0.118865	+	0.0124932i
$39$	2.89412	+	4.40204i	0.463429	+	0.704890i
$40$	1.25138	+	1.12675i	0.197861	+	0.178155i
$41$	−0.907773	+	2.79384i	−0.141770	+	0.436324i	−0.996582	−	0.0826150i	$-0.973673\pi$
$41$	−0.907773	+	2.79384i	−0.141770	+	0.436324i	0.854811	+	0.518939i	$0.173673\pi$
$42$	4.06562	−	2.11442i	0.627338	−	0.326262i
$43$		−	6.89588i		−	1.05161i	−0.850604	−	0.525806i	$-0.823764\pi$
$43$		−	6.89588i		−	1.05161i	0.850604	−	0.525806i	$-0.176236\pi$
$44$	3.12825	−	1.10184i	0.471602	−	0.166108i
$45$	−4.59152	+	2.10660i	−0.684463	+	0.314033i
$46$	−3.26910	−	7.34252i	−0.482002	−	1.08259i
$47$	2.33594	+	10.9898i	0.340733	+	1.60302i	0.731039	+	0.682336i	$0.239036\pi$
$47$	2.33594	+	10.9898i	0.340733	+	1.60302i	−0.390306	+	0.920685i	$0.627631\pi$
$48$	−1.21782	+	1.23163i	−0.175778	+	0.177770i
$49$	−2.19907	−	6.64561i	−0.314153	−	0.949372i
$50$	1.75109	−	1.27224i	0.247642	−	0.179922i
$51$	7.17810	+	1.88008i	1.00513	+	0.263263i
$52$	−2.26034	+	2.03522i	−0.313453	+	0.282235i
$53$	0.415379	+	0.932956i	0.0570567	+	0.128151i	0.939824	−	0.341659i	$-0.110989\pi$
$53$	0.415379	+	0.932956i	0.0570567	+	0.128151i	−0.882767	+	0.469811i	$0.844322\pi$
$54$	−1.94388	−	4.81885i	−0.264528	−	0.655763i
$55$	0.719629	+	5.53832i	0.0970347	+	0.746787i
$56$	1.56091	+	2.13625i	0.208586	+	0.285468i
$57$	1.26151	+	0.192523i	0.167091	+	0.0255003i
$58$	−8.74880	+	1.85961i	−1.14877	+	0.244179i
$59$	1.40444	−	6.60737i	0.182843	−	0.860207i	−0.787091	−	0.616837i	$-0.788414\pi$
$59$	1.40444	−	6.60737i	0.182843	−	0.860207i	0.969934	−	0.243370i	$-0.0782528\pi$
$60$	−1.60226	−	2.43708i	−0.206851	−	0.314626i
$61$	−2.09528	+	4.70608i	−0.268273	+	0.602552i	−0.996574	−	0.0827059i	$-0.973644\pi$
$61$	−2.09528	+	4.70608i	−0.268273	+	0.602552i	0.728301	+	0.685258i	$0.240310\pi$
$62$	2.02702	+	6.23851i	0.257431	+	0.792292i
$63$	−7.73999	+	1.75857i	−0.975147	+	0.221559i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.56087	−	4.43556i	−0.317637	−	0.550164i
$66$	−5.72503	+	0.473319i	−0.704702	+	0.0582615i
$67$	−2.70908	+	4.69227i	−0.330967	+	0.573252i	−0.982702	−	0.185195i	$-0.940708\pi$
$67$	−2.70908	+	4.69227i	−0.330967	+	0.573252i	0.651735	+	0.758447i	$0.274042\pi$
$68$	−0.447807	+	4.26060i	−0.0543046	+	0.516674i
$69$	2.25520	+	13.7373i	0.271494	+	1.65377i
$70$	−4.06511	+	1.82308i	−0.485873	+	0.217900i
$71$	9.86752	+	13.5815i	1.17106	+	1.61182i	0.656338	+	0.754467i	$0.272104\pi$
$71$	9.86752	+	13.5815i	1.17106	+	1.61182i	0.514721	+	0.857358i	$0.327896\pi$
$72$	2.58101	−	1.52919i	0.304174	−	0.180216i
$73$	−3.10170	+	14.5924i	−0.363027	+	1.70791i	0.295493	+	0.955345i	$0.404516\pi$
$73$	−3.10170	+	14.5924i	−0.363027	+	1.70791i	−0.658520	+	0.752563i	$0.728817\pi$
$74$	−4.23672	−	4.70535i	−0.492509	−	0.546986i
$75$	−3.49234	+	1.36321i	−0.403260	+	0.157410i
$76$			0.736768i			0.0845131i
$77$	−0.679594	+	8.74861i	−0.0774469	+	0.996996i
$78$	4.68044	−	2.41812i	0.529956	−	0.273798i
$79$	1.58877	+	0.166986i	0.178750	+	0.0187874i	0.193481	−	0.981104i	$-0.438022\pi$
$79$	1.58877	+	0.166986i	0.178750	+	0.0187874i	−0.0147303	+	0.999892i	$0.504689\pi$
$80$	1.25138	−	1.12675i	0.139909	−	0.125975i
$81$	1.14226	+	8.92722i	0.126918	+	0.991913i
$82$	2.68364	+	1.19484i	0.296359	+	0.131947i
$83$	−0.791771	+	0.575255i	−0.0869081	+	0.0631424i	−0.630391	−	0.776278i	$-0.717105\pi$
$83$	−0.791771	+	0.575255i	−0.0869081	+	0.0631424i	0.543483	+	0.839420i	$0.317105\pi$
$84$	−1.67786	−	4.26436i	−0.183070	−	0.465280i
$85$	−6.86088	−	2.22924i	−0.744167	−	0.241795i
$86$	−6.85811	−	0.720816i	−0.739529	−	0.0777276i
$87$	15.4750	+	0.723589i	1.65909	+	0.0775769i
$88$	−0.768808	−	3.22629i	−0.0819552	−	0.343923i
$89$	−3.79817	+	2.19288i	−0.402605	+	0.232444i	−0.687608	−	0.726083i	$-0.741339\pi$
$89$	−3.79817	+	2.19288i	−0.402605	+	0.232444i	0.285002	+	0.958527i	$0.408006\pi$
$90$	1.61511	+	4.78656i	0.170248	+	0.504548i
$91$	−2.50743	−	7.64668i	−0.262850	−	0.801590i
$92$	−7.64401	+	2.48369i	−0.796943	+	0.258942i
$93$	−0.658542	−	11.3424i	−0.0682877	−	1.17615i
$94$	11.1737	−	1.17441i	1.15248	−	0.121131i
$95$	−1.21354	−	0.257945i	−0.124506	−	0.0264646i
$96$	1.09758	+	1.33989i	0.112022	+	0.136752i
$97$	−11.6994	−	8.50013i	−1.18790	−	0.863058i	−0.194857	−	0.980832i	$-0.562424\pi$
$97$	−11.6994	−	8.50013i	−1.18790	−	0.863058i	−0.993040	+	0.117774i	$0.962424\pi$
$98$	−6.83907	+	1.49237i	−0.690850	+	0.150752i
$99$	9.80019	+	1.71938i	0.984956	+	0.172805i
$100$	−1.08223	−	1.87448i	−0.108223	−	0.187448i
$101$	7.65077	−	3.40634i	0.761280	−	0.338944i	0.0108916	−	0.999941i	$-0.496533\pi$
$101$	7.65077	−	3.40634i	0.761280	−	0.338944i	0.750389	+	0.660997i	$0.229866\pi$
$102$	2.62009	−	6.94225i	0.259428	−	0.687385i
$103$	−9.09285	+	10.0986i	−0.895945	+	0.995048i	0.104055	+	0.994572i	$0.466818\pi$
$103$	−9.09285	+	10.0986i	−0.895945	+	0.995048i	−1.00000		0.000476377i	$0.999848\pi$
$104$	1.78780	+	2.46070i	0.175308	+	0.241291i
$105$	7.61128	−	1.27065i	0.742785	−	0.124003i
$106$	0.971264	−	0.315583i	0.0943375	−	0.0306521i
$107$	6.92688	−	1.47235i	0.669646	−	0.142338i	0.139472	−	0.990226i	$-0.455460\pi$
$107$	6.92688	−	1.47235i	0.669646	−	0.142338i	0.530175	+	0.847888i	$0.322126\pi$
$108$	−4.99565	+	1.42952i	−0.480706	+	0.137556i
$109$	0.286004	+	0.165125i	0.0273942	+	0.0158161i	0.513635	−	0.858009i	$-0.328299\pi$
$109$	0.286004	+	0.165125i	0.0273942	+	0.0158161i	−0.486240	+	0.873825i	$0.661632\pi$
$110$	5.58320	−	0.136775i	0.532337	−	0.0130409i
$111$	5.03380	+	9.74327i	0.477787	+	0.924790i
$112$	2.28770	−	1.32906i	0.216168	−	0.125585i
$113$	−1.12733	−	0.366290i	−0.106050	−	0.0344577i	0.255511	−	0.966806i	$-0.417756\pi$
$113$	−1.12733	−	0.366290i	−0.106050	−	0.0344577i	−0.361561	+	0.932348i	$0.617756\pi$
$114$	0.323333	−	1.23448i	0.0302829	−	0.115619i
$115$	−1.41471	−	13.4600i	−0.131922	−	1.25516i
$116$	0.934929	+	8.89526i	0.0868060	+	0.825904i
$117$	−8.90343	+	1.99762i	−0.823122	+	0.184680i
$118$	−6.42437	−	2.08740i	−0.591411	−	0.192161i
$119$	−9.83132	−	5.64074i	−0.901235	−	0.517086i
$120$	−2.59121	+	1.33874i	−0.236544	+	0.122209i
$121$	5.02694	−	9.78416i	0.456995	−	0.889469i
$122$	4.46128	+	2.57572i	0.403906	+	0.233195i
$123$	−3.97218	−	3.17971i	−0.358159	−	0.286705i
$124$	6.41622	−	1.36381i	0.576193	−	0.122474i
$125$	11.4738	−	3.72807i	1.02625	−	0.333448i
$126$	0.939885	+	7.88141i	0.0837316	+	0.702132i
$127$	10.5488	+	14.5192i	0.936053	+	1.28837i	0.957451	+	0.288596i	$0.0931884\pi$
$127$	10.5488	+	14.5192i	0.936053	+	1.28837i	−0.0213977	+	0.999771i	$0.506812\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	11.1746	+	4.21745i	0.983873	+	0.371326i
$130$	−4.67895	+	2.08320i	−0.410371	+	0.182709i
$131$	2.84964	+	4.93573i	0.248975	+	0.431237i	0.963242	−	0.268637i	$-0.0865731\pi$
$131$	2.84964	+	4.93573i	0.248975	+	0.431237i	−0.714267	+	0.699873i	$0.753240\pi$
$132$	−0.127702	+	5.74314i	−0.0111151	+	0.499876i
$133$	−1.78291	−	0.788038i	−0.154598	−	0.0683316i
$134$	4.38339	+	3.18472i	0.378667	+	0.275118i
$135$	−0.605578	−	8.72884i	−0.0521199	−	0.751259i
$136$	4.19045	+	0.890708i	0.359328	+	0.0763776i
$137$	−4.28222	+	0.450080i	−0.365855	+	0.0384529i	−0.285673	−	0.958327i	$-0.592217\pi$
$137$	−4.28222	+	0.450080i	−0.365855	+	0.0384529i	−0.0801825	+	0.996780i	$0.525550\pi$
$138$	13.8978	−	0.806907i	1.18306	−	0.0686885i
$139$	0.651788	−	0.211779i	0.0552839	−	0.0179628i	−0.281244	−	0.959636i	$-0.590747\pi$
$139$	0.651788	−	0.211779i	0.0552839	−	0.0179628i	0.336528	+	0.941673i	$0.390747\pi$
$140$	1.38818	+	4.23340i	0.117322	+	0.357788i
$141$	−19.2373	−	2.93586i	−1.62008	−	0.247244i
$142$	14.5385	−	8.39381i	1.22004	−	0.704393i
$143$	−0.808449	+	10.0554i	−0.0676059	+	0.840872i
$144$	−1.25102	−	2.72671i	−0.104252	−	0.227226i
$145$	−14.9788	−	1.57433i	−1.24392	−	0.130741i
$146$	14.1882	+	4.61003i	1.17422	+	0.381529i
$147$	12.1140	+	0.500829i	0.999146	+	0.0413077i
$148$	−5.12244	+	3.72167i	−0.421062	+	0.305919i
$149$	−2.19393	−	0.976799i	−0.179733	−	0.0800225i	0.314897	−	0.949126i	$-0.398030\pi$
$149$	−2.19393	−	0.976799i	−0.179733	−	0.0800225i	−0.494631	+	0.869103i	$0.664697\pi$
$150$	0.990695	+	3.61570i	0.0808899	+	0.295221i
$151$	11.5100	−	10.3637i	0.936671	−	0.843383i	−0.0511951	−	0.998689i	$-0.516303\pi$
$151$	11.5100	−	10.3637i	0.936671	−	0.843383i	0.987866	+	0.155306i	$0.0496364\pi$
$152$	0.732732	+	0.0770132i	0.0594324	+	0.00624660i
$153$	−7.43667	+	10.4821i	−0.601219	+	0.847430i
$154$	8.62965	+	1.59035i	0.695397	+	0.128154i
$155$			11.0457i			0.887210i
$156$	−1.91564	−	4.90756i	−0.153374	−	0.392920i
$157$	−8.81047	−	9.78501i	−0.703152	−	0.780929i	0.280723	−	0.959789i	$-0.409426\pi$
$157$	−8.81047	−	9.78501i	−0.703152	−	0.780929i	−0.983875	+	0.178860i	$0.942759\pi$
$158$	0.332143	−	1.56261i	0.0264239	−	0.124315i
$159$	−1.76588	+	0.102527i	−0.140043	+	0.00813095i
$160$	−0.989774	−	1.36231i	−0.0782485	−	0.107700i
$161$	2.16563	−	21.1544i	0.170675	−	1.66720i
$162$	8.99771	−	0.202853i	0.706927	−	0.0159376i
$163$	−0.707047	+	6.72710i	−0.0553802	+	0.526907i	0.931302	+	0.364248i	$0.118674\pi$
$163$	−0.707047	+	6.72710i	−0.0553802	+	0.526907i	−0.986682	+	0.162659i	$0.947993\pi$
$164$	1.46881	−	2.54405i	0.114695	−	0.198657i
$165$	−9.41486	−	2.22103i	−0.732946	−	0.172907i
$166$	0.489341	+	0.847564i	0.0379802	+	0.0657837i
$167$	−4.04114	−	2.93606i	−0.312713	−	0.227199i	0.420347	−	0.907363i	$-0.361908\pi$
$167$	−4.04114	−	2.93606i	−0.312713	−	0.227199i	−0.733060	+	0.680164i	$0.761908\pi$
$168$	−4.41639	+	1.22292i	−0.340732	+	0.0943506i
$169$	1.15842	+	3.56524i	0.0891091	+	0.274249i
$170$	−2.93418	+	6.59028i	−0.225042	+	0.505452i
$171$	−1.08351	+	1.92651i	−0.0828579	+	0.147324i
$172$	−1.43373	+	6.74519i	−0.109321	+	0.514316i
$173$	8.96840	−	1.90629i	0.681855	−	0.144933i	0.146054	−	0.989277i	$-0.453343\pi$
$173$	8.96840	−	1.90629i	0.681855	−	0.144933i	0.535802	+	0.844344i	$0.320009\pi$
$174$	2.33720	−	15.3146i	0.177183	−	1.16100i
$175$	5.69363	−	0.613987i	0.430398	−	0.0464130i
$176$	−3.28898	+	0.427357i	−0.247916	+	0.0322133i
$177$	9.84818	+	6.31687i	0.740234	+	0.474805i
$178$	1.78385	+	4.00658i	0.133705	+	0.300306i
$179$	2.77711	−	2.50052i	0.207571	−	0.186898i	−0.558788	−	0.829311i	$-0.688733\pi$
$179$	2.77711	−	2.50052i	0.207571	−	0.186898i	0.766358	+	0.642413i	$0.222067\pi$
$180$	4.92917	−	1.10593i	0.367399	−	0.0824314i
$181$	−15.4878	+	11.2525i	−1.15120	+	0.836393i	−0.988640	−	0.150306i	$-0.951974\pi$
$181$	−15.4878	+	11.2525i	−1.15120	+	0.836393i	−0.162557	+	0.986699i	$0.551974\pi$
$182$	−7.86689	+	1.69439i	−0.583133	+	0.125597i
$183$	−6.34466	−	6.27355i	−0.469011	−	0.463754i
$184$	1.67107	+	7.86175i	0.123193	+	0.579576i
$185$	−4.33660	−	9.74016i	−0.318833	−	0.716111i
$186$	−11.3491	−	0.530668i	−0.832156	−	0.0389105i
$187$	8.63065	+	11.2871i	0.631135	+	0.825392i
$188$		−	11.2353i		−	0.819417i
$189$	1.88397	−	13.6180i	0.137039	−	0.990566i
$190$	−0.383381	+	1.17992i	−0.0278134	+	0.0856007i
$191$	−0.211095	−	0.190071i	−0.0152743	−	0.0137531i	0.661458	−	0.749982i	$-0.269938\pi$
$191$	−0.211095	−	0.190071i	−0.0152743	−	0.0137531i	−0.676732	+	0.736229i	$0.736605\pi$
$192$	1.44728	−	0.951513i	0.104449	−	0.0686696i
$193$	13.2398	−	1.39156i	0.953023	−	0.100167i	0.384763	−	0.923016i	$-0.374283\pi$
$193$	13.2398	−	1.39156i	0.953023	−	0.100167i	0.568260	+	0.822849i	$0.307617\pi$
$194$	−9.67649	+	10.7468i	−0.694732	+	0.771578i
$195$	8.75395	−	1.43710i	0.626883	−	0.102913i
$196$	0.769317	+	6.95760i	0.0549512	+	0.496971i
$197$	6.13736			0.437269			0.218634	−	0.975807i	$-0.429840\pi$
$197$	6.13736			0.437269			0.218634	+	0.975807i	$0.429840\pi$
$198$	2.73436	−	9.56678i	0.194323	−	0.679881i
$199$	−1.40678	+	2.43661i	−0.0997238	+	0.172727i	−0.911570	−	0.411144i	$-0.865129\pi$
$199$	−1.40678	+	2.43661i	−0.0997238	+	0.172727i	0.811847	+	0.583871i	$0.198463\pi$
$200$	−1.97734	+	0.880368i	−0.139819	+	0.0622514i
$201$	−5.94689	−	7.25976i	−0.419461	−	0.512064i
$202$	−2.58796	−	7.96492i	−0.182088	−	0.560410i
$203$	−22.5257	−	7.25181i	−1.58100	−	0.508977i
$204$	−6.63035	−	3.33140i	−0.464217	−	0.233245i
$205$	3.67608	+	3.30996i	0.256749	+	0.231178i
$206$	9.09285	+	10.0986i	0.633529	+	0.703605i
$207$	−23.6402	−	4.74707i	−1.64311	−	0.329944i
$208$	2.63410	−	1.52080i	0.182642	−	0.105448i
$209$	1.67906	+	1.77535i	0.116143	+	0.122803i
$210$	−0.468094	−	7.70241i	−0.0323015	−	0.531517i
$211$	9.39063	−	12.9251i	0.646477	−	0.889800i	−0.352463	−	0.935826i	$-0.614656\pi$
$211$	9.39063	−	12.9251i	0.646477	−	0.889800i	0.998940	+	0.0460261i	$0.0146557\pi$
$212$	−0.212329	−	0.998931i	−0.0145828	−	0.0686068i
$213$	−28.0434	+	7.68384i	−1.92150	+	0.526488i
$214$	−0.740231	−	7.04283i	−0.0506012	−	0.481438i
$215$	−10.6081	−	4.72303i	−0.723466	−	0.322108i
$216$	0.899501	+	5.11770i	0.0612033	+	0.348216i
$217$	−3.56241	+	16.9854i	−0.241832	+	1.15304i
$218$	0.194116	−	0.267177i	0.0131472	−	0.0180955i
$219$	−21.7497	−	13.9508i	−1.46971	−	0.942707i
$220$	0.447578	−	5.56691i	0.0301757	−	0.375321i
$221$	−11.2846	−	6.51520i	−0.759088	−	0.438259i
$222$	10.2161	−	3.98778i	0.685658	−	0.267642i
$223$	5.91805	−	18.2139i	0.396302	−	1.21969i	−0.531641	−	0.846970i	$-0.678424\pi$
$223$	5.91805	−	18.2139i	0.396302	−	1.21969i	0.927943	−	0.372722i	$-0.121576\pi$
$224$	−1.08265	−	2.41410i	−0.0723377	−	0.161299i
$225$	−0.0731828	−	6.49299i	−0.00487885	−	0.432866i
$226$	−0.482121	+	1.08286i	−0.0320702	+	0.0720309i
$227$	−0.279265	−	0.0593597i	−0.0185355	−	0.00393984i	0.198635	−	0.980074i	$-0.436349\pi$
$227$	−0.279265	−	0.0593597i	−0.0185355	−	0.00393984i	−0.217170	+	0.976134i	$0.569683\pi$
$228$	−1.19392	−	0.450599i	−0.0790692	−	0.0298417i
$229$	−2.39377	+	22.7752i	−0.158185	+	1.50503i	0.571136	+	0.820855i	$0.306503\pi$
$229$	−2.39377	+	22.7752i	−0.158185	+	1.50503i	−0.729321	+	0.684172i	$0.760164\pi$
$230$	−13.5342			−0.892418
$231$	−13.7613	−	6.45183i	−0.905428	−	0.424499i
$232$	8.94425			0.587219
$233$	0.588320	−	5.59749i	0.0385421	−	0.366704i	−0.958203	−	0.286089i	$-0.907645\pi$
$233$	0.588320	−	5.59749i	0.0385421	−	0.366704i	0.996745	−	0.0806152i	$-0.0256885\pi$
$234$	1.05601	+	9.06346i	0.0690338	+	0.592497i
$235$	18.5057	+	3.93351i	1.20718	+	0.256594i
$236$	−2.74750	+	6.17099i	−0.178847	+	0.401697i
$237$	−1.24227	+	2.47244i	−0.0806943	+	0.160602i
$238$	−6.63749	+	9.18784i	−0.430245	+	0.595559i
$239$	5.44336	−	16.7529i	0.352101	−	1.08366i	−0.605570	−	0.795792i	$-0.707055\pi$
$239$	5.44336	−	16.7529i	0.352101	−	1.08366i	0.957671	−	0.287865i	$-0.0929453\pi$
$240$	1.06055	+	2.71695i	0.0684580	+	0.175379i
$241$	17.6831	+	10.2093i	1.13907	+	0.657641i	0.946200	−	0.323584i	$-0.104888\pi$
$241$	17.6831	+	10.2093i	1.13907	+	0.657641i	0.192868	+	0.981225i	$0.438221\pi$
$242$	−9.20511	−	6.02213i	−0.591727	−	0.387117i
$243$	−15.1650	−	3.60878i	−0.972834	−	0.231504i
$244$	3.02794	−	4.16761i	0.193844	−	0.266804i
$245$	−11.7292	−	1.16873i	−0.749354	−	0.0746674i
$246$	−3.57750	+	3.61804i	−0.228093	+	0.230678i
$247$	−2.04721	−	0.911475i	−0.130261	−	0.0579958i
$248$	−0.685661	−	6.52363i	−0.0435395	−	0.414251i
$249$	−0.447951	−	1.63487i	−0.0283878	−	0.103606i
$250$	−2.50830	−	11.8006i	−0.158639	−	0.746338i
$251$	2.59894	−	3.57713i	0.164043	−	0.225786i	−0.719080	−	0.694927i	$-0.755436\pi$
$251$	2.59894	−	3.57713i	0.164043	−	0.225786i	0.883123	+	0.469141i	$0.155436\pi$
$252$	7.93648	−	0.110905i	0.499951	−	0.00698634i
$253$	−12.7591	+	23.4051i	−0.802159	+	1.47147i
$254$	15.5423	−	8.97333i	0.975209	−	0.563037i
$255$	7.80848	−	9.75456i	0.488986	−	0.610854i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−4.34163	−	3.90922i	−0.270823	−	0.243850i	0.522517	−	0.852629i	$-0.324993\pi$
$257$	−4.34163	−	3.90922i	−0.270823	−	0.243850i	−0.793340	+	0.608779i	$0.791660\pi$
$258$	5.36241	−	10.6726i	0.333849	−	0.664446i
$259$	−3.52722	−	16.3765i	−0.219171	−	1.01759i
$260$	1.58271	+	4.87107i	0.0981553	+	0.302091i
$261$	−10.6369	+	24.6344i	−0.658408	+	1.52483i
$262$	5.20656	−	2.31811i	0.321662	−	0.143213i
$263$	−12.7571	+	22.0959i	−0.786634	+	1.36249i	0.141385	+	0.989955i	$0.454845\pi$
$263$	−12.7571	+	22.0959i	−0.786634	+	1.36249i	−0.928018	+	0.372535i	$0.878489\pi$
$264$	5.69833	+	0.727325i	0.350708	+	0.0447637i
$265$	1.71968			0.105639
$266$	−0.970086	+	1.69078i	−0.0594798	+	0.103668i
$267$	−1.23059	−	7.49600i	−0.0753110	−	0.458748i
$268$	3.62546	−	4.02648i	0.221460	−	0.245957i
$269$	27.1376	−	2.85228i	1.65461	−	0.173907i	0.769294	−	0.638895i	$-0.220608\pi$
$269$	27.1376	−	2.85228i	1.65461	−	0.173907i	0.885317	+	0.464989i	$0.153942\pi$
$270$	−8.74432	−	0.310151i	−0.532163	−	0.0188752i
$271$	−4.42176	−	3.98137i	−0.268603	−	0.241851i	0.523812	−	0.851834i	$-0.324510\pi$
$271$	−4.42176	−	3.98137i	−0.268603	−	0.241851i	−0.792414	+	0.609983i	$0.791176\pi$
$272$	1.32385	−	4.07439i	0.0802702	−	0.247046i
$273$	13.9248	+	0.613395i	0.842769	+	0.0371244i
$274$			4.30581i			0.260124i
$275$	−6.87965	−	2.05048i	−0.414859	−	0.123649i
$276$	0.650224	−	13.9060i	0.0391389	−	0.837041i
$277$	−5.47769	−	12.3031i	−0.329122	−	0.739221i	0.670875	−	0.741570i	$-0.265919\pi$
$277$	−5.47769	−	12.3031i	−0.329122	−	0.739221i	−0.999997	+	0.00234982i	$0.999252\pi$
$278$	−0.142488	−	0.670354i	−0.00854587	−	0.0402052i
$279$	18.7829	+	5.86973i	1.12450	+	0.351412i
$280$	4.35532	−	0.938060i	0.260280	−	0.0560598i
$281$	3.34114	−	2.42748i	0.199316	−	0.144811i	−0.483651	−	0.875261i	$-0.660690\pi$
$281$	3.34114	−	2.42748i	0.199316	−	0.144811i	0.682966	+	0.730450i	$0.260690\pi$
$282$	−4.93063	+	18.8251i	−0.293615	+	1.12102i
$283$	15.5805	−	14.0287i	0.926162	−	0.833920i	−0.0602544	−	0.998183i	$-0.519191\pi$
$283$	15.5805	−	14.0287i	0.926162	−	0.833920i	0.986417	+	0.164263i	$0.0525245\pi$
$284$	−6.82814	−	15.3363i	−0.405176	−	0.910040i
$285$	1.16018	−	1.80875i	0.0687231	−	0.107141i
$286$	9.91578	+	1.85509i	0.586332	+	0.109694i
$287$	4.58536	+	6.27547i	0.270665	+	0.370429i
$288$	−2.84254	+	0.959148i	−0.167498	+	0.0565184i
$289$	−1.32368	+	0.281357i	−0.0778634	+	0.0165504i
$290$	−3.13141	+	14.7321i	−0.183883	+	0.865101i
$291$	20.9296	−	13.7601i	1.22691	−	0.806632i
$292$	6.06785	−	13.6286i	0.355094	−	0.797554i
$293$	0.343411	+	1.05691i	0.0200623	+	0.0617453i	0.960586	−	0.277981i	$-0.0896654\pi$
$293$	0.343411	+	1.05691i	0.0200623	+	0.0617453i	−0.940524	+	0.339727i	$0.889665\pi$
$294$	1.76434	−	11.9953i	0.102899	−	0.699580i
$295$	−9.20236	−	6.68591i	−0.535782	−	0.389269i
$296$	3.16584	+	5.48339i	0.184011	+	0.318716i
$297$	−8.77992	+	14.8295i	−0.509463	+	0.860493i
$298$	−1.20078	+	2.07980i	−0.0695591	+	0.120480i
$299$	2.55535	−	24.3125i	0.147780	−	1.40603i
$300$	3.69945	−	0.607325i	0.213588	−	0.0350639i
$301$	−14.7893	−	10.6841i	−0.852440	−	0.615821i
$302$	−9.10376	−	12.5303i	−0.523863	−	0.721035i
$303$	0.840783	+	14.4812i	0.0483017	+	0.831924i
$304$	0.153183	−	0.720668i	0.00878563	−	0.0413331i
$305$	5.80440	+	6.44644i	0.332359	+	0.369122i
$306$	9.64737	+	8.49162i	0.551503	+	0.485433i
$307$			10.4908i			0.598744i	0.954136	+	0.299372i	$0.0967772\pi$
$307$			10.4908i			0.598744i	−0.954136	+	0.299372i	$0.903223\pi$
$308$	2.48368	−	8.41613i	0.141521	−	0.479554i
$309$	−10.8036	−	20.9110i	−0.614593	−	1.18959i
$310$	10.9852	+	1.15459i	0.623915	+	0.0655761i
$311$	0.329054	−	0.296281i	0.0186589	−	0.0168006i	−0.659748	−	0.751487i	$-0.729337\pi$
$311$	0.329054	−	0.296281i	0.0186589	−	0.0168006i	0.678407	+	0.734686i	$0.262670\pi$
$312$	−5.08092	+	1.39216i	−0.287650	+	0.0788157i
$313$	−1.88878	−	0.840939i	−0.106760	−	0.0475327i	0.352662	−	0.935751i	$-0.385277\pi$
$313$	−1.88878	−	0.840939i	−0.106760	−	0.0475327i	−0.459422	+	0.888218i	$0.651943\pi$
$314$	−10.6524	+	7.73939i	−0.601147	+	0.436759i
$315$	−2.59592	+	13.1111i	−0.146263	+	0.738724i
$316$	−1.51933	−	0.493661i	−0.0854691	−	0.0277706i
$317$	−7.32802	−	0.770206i	−0.411583	−	0.0432591i	−0.103525	−	0.994627i	$-0.533012\pi$
$317$	−7.32802	−	0.770206i	−0.411583	−	0.0432591i	−0.308058	+	0.951368i	$0.599679\pi$
$318$	−0.0826188	+	1.76692i	−0.00463303	+	0.0990840i
$319$	22.5247	+	19.3037i	1.26114	+	1.08080i
$320$	−1.45830	+	0.841952i	−0.0815216	+	0.0470665i
$321$	−1.85048	+	12.1253i	−0.103284	+	0.676771i
$322$	−20.8121	−	4.36499i	−1.15981	−	0.243252i
$323$	−3.00188	+	0.975370i	−0.167029	+	0.0542711i
$324$	0.738775	−	8.96963i	0.0410431	−	0.498313i
$325$	6.54736	−	0.688156i	0.363182	−	0.0381720i
$326$	6.61634	+	1.40635i	0.366445	+	0.0778904i
$327$	−0.442498	+	0.362476i	−0.0244702	+	0.0200450i
$328$	−2.37658	−	1.72669i	−0.131225	−	0.0953403i
$329$	27.1884	+	12.0171i	1.49894	+	0.662525i
$330$	−3.19299	+	9.13112i	−0.175768	+	0.502652i
$331$	1.40308	+	2.43021i	0.0771204	+	0.133576i	0.902006	−	0.431723i	$-0.142094\pi$
$331$	1.40308	+	2.43021i	0.0771204	+	0.133576i	−0.824886	+	0.565299i	$0.808761\pi$
$332$	0.894071	−	0.398066i	0.0490685	−	0.0218467i
$333$	−18.8674	+	2.19830i	−1.03393	+	0.120466i
$334$	−3.34239	+	3.71210i	−0.182887	+	0.203117i
$335$	5.36276	+	7.38120i	0.292999	+	0.403278i
$336$	0.754586	+	4.52002i	0.0411660	+	0.246587i
$337$	6.85817	−	2.22835i	0.373588	−	0.121386i	−0.116204	−	0.993225i	$-0.537073\pi$
$337$	6.85817	−	2.22835i	0.373588	−	0.121386i	0.489792	+	0.871839i	$0.337073\pi$
$338$	3.66680	−	0.779402i	0.199448	−	0.0423939i
$339$	1.28303	−	1.60279i	0.0696845	−	0.0870516i
$340$	6.24747	+	3.60698i	0.338817	+	0.195616i
$341$	12.3527	−	17.9085i	0.668939	−	0.969802i
$342$	1.80270	+	1.27895i	0.0974789	+	0.0691576i
$343$	−17.6596	−	5.58008i	−0.953531	−	0.301296i
$344$	6.55838	+	2.13095i	0.353604	+	0.114893i
$345$	22.6770	+	5.93951i	1.22089	+	0.319773i
$346$	−0.958397	−	9.11854i	−0.0515237	−	0.490216i
$347$	3.17224	+	30.1819i	0.170295	+	1.62025i	0.662013	+	0.749492i	$0.269702\pi$
$347$	3.17224	+	30.1819i	0.170295	+	1.62025i	−0.491718	+	0.870754i	$0.663631\pi$
$348$	−14.9864	−	3.92521i	−0.803355	−	0.210413i
$349$	8.05541	+	2.61736i	0.431196	+	0.140104i	0.516570	−	0.856245i	$-0.327208\pi$
$349$	8.05541	+	2.61736i	0.431196	+	0.140104i	−0.0853739	+	0.996349i	$0.527208\pi$
$350$	−0.0154767	−	5.72662i	−0.000827262	−	0.306101i
$351$	2.20814	−	15.6496i	0.117862	−	0.835312i
$352$	0.0812247	+	3.31563i	0.00432929	+	0.176724i
$353$	−2.65929	−	1.53534i	−0.141539	−	0.0817179i	0.427558	−	0.903988i	$-0.359374\pi$
$353$	−2.65929	−	1.53534i	−0.141539	−	0.0817179i	−0.569097	+	0.822270i	$0.692707\pi$
$354$	7.31168	−	9.13394i	0.388611	−	0.485463i
$355$	27.6510	−	5.87740i	1.46756	−	0.311940i
$356$	4.17110	−	1.35527i	0.221068	−	0.0718292i
$357$	15.1534	−	12.4816i	0.802005	−	0.660599i
$358$	−2.19653	−	3.02327i	−0.116090	−	0.159785i
$359$	−3.12050	+	3.46567i	−0.164694	+	0.182911i	−0.819843	−	0.572589i	$-0.805939\pi$
$359$	−3.12050	+	3.46567i	−0.164694	+	0.182911i	0.655149	+	0.755500i	$0.272606\pi$
$360$	−0.584637	−	5.01777i	−0.0308131	−	0.264460i
$361$	16.8615	−	7.50721i	0.887446	−	0.395116i
$362$	9.57196	+	16.5791i	0.503091	+	0.871380i
$363$	12.7806	+	14.1300i	0.670809	+	0.741630i
$364$	0.862798	+	8.00091i	0.0452229	+	0.419362i
$365$	20.3234	+	14.7658i	1.06378	+	0.772878i
$366$	−6.90238	+	5.65414i	−0.360793	+	0.295547i
$367$	15.8256	+	3.36383i	0.826089	+	0.175591i	0.601510	−	0.798865i	$-0.294566\pi$
$367$	15.8256	+	3.36383i	0.826089	+	0.175591i	0.224579	+	0.974456i	$0.427899\pi$
$368$	7.99335	−	0.840135i	0.416682	−	0.0437951i
$369$	7.58200	−	4.49216i	0.394703	−	0.233852i
$370$	−10.1401	+	3.29472i	−0.527159	+	0.171284i
$371$	2.64443	+	0.554626i	0.137292	+	0.0287947i
$372$	−1.71406	+	11.2315i	−0.0888701	+	0.582324i
$373$	6.68078	−	3.85715i	0.345918	−	0.199716i	−0.316968	−	0.948436i	$-0.602665\pi$
$373$	6.68078	−	3.85715i	0.345918	−	0.199716i	0.662886	+	0.748721i	$0.269332\pi$
$374$	12.1274	−	7.40355i	0.627092	−	0.382828i
$375$	−0.975999	+	20.8731i	−0.0504004	+	1.07788i
$376$	−11.1737	−	1.17441i	−0.576241	−	0.0605654i
$377$	−25.8733	−	8.40674i	−1.33254	−	0.432969i
$378$	−13.3465	−	3.29712i	−0.686470	−	0.169586i
$379$	−20.1495	+	14.6394i	−1.03501	+	0.751978i	−0.969305	−	0.245861i	$-0.920929\pi$
$379$	−20.1495	+	14.6394i	−1.03501	+	0.751978i	−0.0657038	+	0.997839i	$0.520929\pi$
$380$	1.13339	+	0.504616i	0.0581415	+	0.0258863i
$381$	−29.9795	+	8.21434i	−1.53590	+	0.420834i
$382$	−0.211095	+	0.190071i	−0.0108006	+	0.00972489i
$383$	4.63384	+	0.487037i	0.236778	+	0.0248864i	0.222174	−	0.975007i	$-0.428685\pi$
$383$	4.63384	+	0.487037i	0.236778	+	0.0248864i	0.0146040	+	0.999893i	$0.495351\pi$
$384$	−0.795019	−	1.53881i	−0.0405706	−	0.0785272i
$385$	12.9927	+	7.03740i	0.662171	+	0.358659i
$386$		−	13.3127i		−	0.677601i
$387$	−13.6686	+	15.5290i	−0.694814	+	0.789381i
$388$	9.67649	+	10.7468i	0.491249	+	0.545588i
$389$	6.97493	−	32.8144i	0.353643	−	1.66376i	−0.337717	−	0.941248i	$-0.609655\pi$
$389$	6.97493	−	32.8144i	0.353643	−	1.66376i	0.691360	−	0.722511i	$-0.257012\pi$
$390$	−0.514194	−	8.85621i	−0.0260372	−	0.448452i
$391$	−20.2390	−	27.8566i	−1.02353	−	1.40877i
$392$	6.99990	−	0.0378358i	0.353548	−	0.00191100i
$393$	−9.74107	+	1.59916i	−0.491372	+	0.0806667i
$394$	0.641528	−	6.10374i	0.0323197	−	0.307502i
$395$	1.34504	−	2.32967i	0.0676761	−	0.117218i
$396$	−9.22855	−	3.71938i	−0.463752	−	0.186906i
$397$	−11.1549	−	19.3208i	−0.559848	−	0.969685i	−0.997509	−	0.0705449i	$-0.977526\pi$
$397$	−11.1549	−	19.3208i	−0.559848	−	0.969685i	0.437661	−	0.899140i	$-0.355807\pi$
$398$	2.27621	+	1.65377i	0.114096	+	0.0828958i
$399$	2.36741	−	2.40722i	0.118519	−	0.120512i
$400$	0.668857	+	2.05853i	0.0334429	+	0.102927i
$401$	−12.8841	+	28.9381i	−0.643401	+	1.44510i	0.237304	+	0.971436i	$0.423736\pi$
$401$	−12.8841	+	28.9381i	−0.643401	+	1.44510i	−0.880704	+	0.473666i	$0.842930\pi$
$402$	−7.84161	+	5.15546i	−0.391104	+	0.257131i
$403$	−4.14815	+	19.5155i	−0.206634	+	0.972137i
$404$	−8.19180	+	1.74122i	−0.407557	+	0.0866290i
$405$	14.5153	+	4.35714i	0.721270	+	0.216508i
$406$	−9.56667	+	21.6443i	−0.474786	+	1.07419i
$407$	−3.86174	+	20.6417i	−0.191420	+	1.02317i
$408$	−4.00621	+	6.24580i	−0.198337	+	0.309213i
$409$	3.68655	+	8.28012i	0.182288	+	0.409426i	0.981457	−	0.191680i	$-0.0613936\pi$
$409$	3.68655	+	8.28012i	0.182288	+	0.409426i	−0.799169	+	0.601106i	$0.794727\pi$
$410$	3.67608	−	3.30996i	0.181549	−	0.163467i
$411$	1.88962	−	7.21453i	0.0932079	−	0.355866i
$412$	10.9938	−	7.98744i	0.541624	−	0.393513i
$413$	−11.9946	−	13.2491i	−0.590214	−	0.651947i
$414$	−7.19214	+	23.0145i	−0.353474	+	1.13110i
$415$	0.342640	+	1.61199i	0.0168195	+	0.0791297i
$416$	−1.23713	−	2.77863i	−0.0606551	−	0.136234i
$417$	−0.0554432	+	1.18573i	−0.00271506	+	0.0580655i
$418$	1.94113	−	1.48429i	0.0949438	−	0.0725988i
$419$			22.9780i			1.12255i	0.827630	+	0.561274i	$0.189688\pi$
$419$			22.9780i			1.12255i	−0.827630	+	0.561274i	$0.810312\pi$
$420$	−7.70914	−	0.339591i	−0.376168	−	0.0165704i
$421$	6.48091	−	19.9462i	0.315860	−	0.972118i	−0.659539	−	0.751671i	$-0.729248\pi$
$421$	6.48091	−	19.9462i	0.315860	−	0.972118i	0.975399	−	0.220447i	$-0.0707516\pi$
$422$	−11.8727	−	10.6902i	−0.577954	−	0.520392i
$423$	16.5229	−	29.3782i	0.803369	−	1.42842i
$424$	−1.01565	+	0.106749i	−0.0493245	+	0.00518421i
$425$	6.20467	−	6.89098i	0.300971	−	0.334262i
$426$	4.71042	+	28.6929i	0.228220	+	1.39018i
$427$	6.84660	+	11.7850i	0.331330	+	0.570315i
$428$	−7.08163			−0.342303
$429$	−15.8001	−	7.45983i	−0.762836	−	0.360164i
$430$	−5.80600	+	10.0563i	−0.279990	+	0.484957i
$431$	−16.8453	+	7.50001i	−0.811409	+	0.361263i	−0.770132	−	0.637885i	$-0.779809\pi$
$431$	−16.8453	+	7.50001i	−0.811409	+	0.361263i	−0.0412777	+	0.999148i	$0.513143\pi$
$432$	5.18369	−	0.359628i	0.249401	−	0.0173026i
$433$	7.67426	+	23.6190i	0.368802	+	1.13505i	0.947566	+	0.319560i	$0.103535\pi$
$433$	7.67426	+	23.6190i	0.368802	+	1.13505i	−0.578765	+	0.815495i	$0.696465\pi$
$434$	16.5200	+	5.31835i	0.792985	+	0.255289i
$435$	11.7120	−	23.3099i	0.561548	−	1.11763i
$436$	−0.245423	−	0.220980i	−0.0117536	−	0.0105830i
$437$	−3.96238	−	4.40067i	−0.189546	−	0.210513i
$438$	−16.1478	+	20.1723i	−0.771573	+	0.963869i
$439$	−29.7576	+	17.1806i	−1.42025	+	0.819984i	−0.996320	−	0.0857092i	$-0.972684\pi$
$439$	−29.7576	+	17.1806i	−1.42025	+	0.819984i	−0.423934	+	0.905693i	$0.639351\pi$
$440$	−5.48963	−	1.02703i	−0.261708	−	0.0489616i
$441$	−8.22038	+	19.3242i	−0.391447	+	0.920201i
$442$	−7.65907	+	10.5418i	−0.364305	+	0.501423i
$443$	−3.66851	−	17.2590i	−0.174296	−	0.819999i	−0.975221	−	0.221234i	$-0.928992\pi$
$443$	−3.66851	−	17.2590i	−0.174296	−	0.819999i	0.800925	−	0.598765i	$-0.204342\pi$
$444$	−2.89806	−	10.5769i	−0.137536	−	0.501959i
$445$	0.771962	+	7.34473i	0.0365945	+	0.348173i
$446$	−17.4955	−	7.78950i	−0.828436	−	0.368843i
$447$	2.92467	−	2.95782i	0.138332	−	0.139900i
$448$	−2.51404	+	0.824379i	−0.118777	+	0.0389483i
$449$	−8.09545	+	11.1424i	−0.382048	+	0.525844i	−0.956126	−	0.292957i	$-0.905361\pi$
$449$	−8.09545	+	11.1424i	−0.382048	+	0.525844i	0.574078	+	0.818801i	$0.305361\pi$
$450$	−6.46507	−	0.605920i	−0.304766	−	0.0285634i
$451$	−2.25846	−	9.47759i	−0.106347	−	0.446282i
$452$	1.02653	+	0.592670i	0.0482841	+	0.0278769i
$453$	9.75471	+	24.9901i	0.458316	+	1.17414i
$454$	−0.0882257	+	0.271531i	−0.00414064	+	0.0127436i
$455$	−13.4804	−	1.38003i	−0.631972	−	0.0646966i
$456$	−0.572929	+	1.14028i	−0.0268299	+	0.0533984i
$457$	2.68689	−	6.03485i	0.125687	−	0.282298i	−0.839732	−	0.543002i	$-0.817288\pi$
$457$	2.68689	−	6.03485i	0.125687	−	0.282298i	0.965419	+	0.260703i	$0.0839544\pi$
$458$	22.4002	+	4.76131i	1.04669	+	0.222481i
$459$	−12.4379	−	18.4617i	−0.580552	−	0.861721i
$460$	−1.41471	+	13.4600i	−0.0659611	+	0.627578i
$461$	5.54733			0.258365			0.129182	−	0.991621i	$-0.458765\pi$
$461$	5.54733			0.258365			0.129182	+	0.991621i	$0.458765\pi$
$462$	−7.85493	+	13.0115i	−0.365444	+	0.605351i
$463$	35.3665			1.64362			0.821811	−	0.569760i	$-0.192964\pi$
$463$	35.3665			1.64362			0.821811	+	0.569760i	$0.192964\pi$
$464$	0.934929	−	8.89526i	0.0434030	−	0.412952i
$465$	−17.8993	−	6.75541i	−0.830060	−	0.313275i
$466$	−5.50533	−	1.17019i	−0.255030	−	0.0542082i
$467$	−10.7784	+	24.2086i	−0.498764	+	1.12024i	0.472304	+	0.881436i	$0.343423\pi$
$467$	−10.7784	+	24.2086i	−0.498764	+	1.12024i	−0.971067	+	0.238806i	$0.923244\pi$
$468$	9.12420	−	0.102839i	0.421766	−	0.00475374i
$469$	5.86599	+	13.0800i	0.270866	+	0.603977i
$470$	5.84633	−	17.9932i	0.269671	−	0.829962i
$471$	21.2448	−	8.29278i	0.978909	−	0.382111i
$472$	5.84999	+	3.37749i	0.269268	+	0.155462i
$473$	11.9172	+	19.5209i	0.547952	+	0.897573i
$474$	2.32905	+	1.49391i	0.106977	+	0.0686175i
$475$	0.937347	−	1.29015i	0.0430084	−	0.0591960i
$476$	8.44370	+	7.56152i	0.387016	+	0.346582i
$477$	0.913849	−	2.92428i	0.0418423	−	0.133893i
$478$	−16.0922	−	7.16469i	−0.736039	−	0.327706i
$479$	−1.94812	−	18.5351i	−0.0890118	−	0.846891i	−0.944377	−	0.328865i	$-0.893334\pi$
$479$	−1.94812	−	18.5351i	−0.0890118	−	0.846891i	0.855365	−	0.518026i	$-0.173333\pi$
$480$	2.81293	−	0.770737i	0.128392	−	0.0351792i
$481$	−4.00404	−	18.8375i	−0.182569	−	0.858918i
$482$	12.0018	−	16.5191i	0.546667	−	0.752422i
$483$	32.9558	+	16.4471i	1.49954	+	0.748371i
$484$	−6.95133	+	8.52520i	−0.315970	+	0.387509i
$485$	−21.0890	+	12.1757i	−0.957600	+	0.552871i
$486$	−5.17419	+	14.7047i	−0.234706	+	0.667018i
$487$	8.87444	+	9.85606i	0.402139	+	0.446621i	0.909869	−	0.414896i	$-0.136182\pi$
$487$	8.87444	+	9.85606i	0.402139	+	0.446621i	−0.507730	+	0.861516i	$0.669515\pi$
$488$	−3.82827	−	3.44699i	−0.173298	−	0.156038i
$489$	−10.4687	−	5.25998i	−0.473412	−	0.237865i
$490$	−2.38837	+	11.5428i	−0.107895	+	0.521452i
$491$	−12.1208	−	37.3040i	−0.547004	−	1.68351i	−0.716176	−	0.697920i	$-0.754109\pi$
$491$	−12.1208	−	37.3040i	−0.547004	−	1.68351i	0.169172	−	0.985587i	$-0.445891\pi$
$492$	3.22427	+	3.93609i	0.145362	+	0.177452i
$493$	−35.0051	+	15.5853i	−1.57655	+	0.701925i
$494$	−1.12047	+	1.94072i	−0.0504125	+	0.0873170i
$495$	9.35717	−	13.8982i	0.420574	−	0.624679i
$496$	−6.55956			−0.294533
$497$	44.4157	−	0.120037i	1.99232	−	0.00538440i
$498$	−1.67274	+	0.274607i	−0.0749571	+	0.0123054i
$499$	−1.48350	+	1.64759i	−0.0664105	+	0.0737563i	−0.775434	−	0.631428i	$-0.782469\pi$
$499$	−1.48350	+	1.64759i	−0.0664105	+	0.0737563i	0.709024	+	0.705184i	$0.249136\pi$
$500$	−11.9982	+	1.26106i	−0.536575	+	0.0563963i
$501$	7.22934	−	4.75292i	0.322983	−	0.212345i
$502$	−3.28587	−	2.95861i	−0.146656	−	0.132049i
$503$	−2.73992	+	8.43261i	−0.122167	+	0.375991i	−0.993374	−	0.114924i	$-0.963338\pi$
$503$	−2.73992	+	8.43261i	−0.122167	+	0.375991i	0.871207	+	0.490915i	$0.163338\pi$
$504$	0.719291	−	7.90459i	0.0320398	−	0.352099i
$505$		−	14.1024i		−	0.627548i
$506$	21.9432	+	15.1357i	0.975495	+	0.672865i
$507$	−6.48588	−	0.303271i	−0.288048	−	0.0134687i
$508$	−7.29957	−	16.3951i	−0.323866	−	0.727415i
$509$	−4.97012	−	23.3826i	−0.220297	−	1.03642i	−0.939747	−	0.341871i	$-0.888939\pi$
$509$	−4.97012	−	23.3826i	−0.220297	−	1.03642i	0.719450	−	0.694544i	$-0.244394\pi$
$510$	−8.88491	−	8.78533i	−0.393430	−	0.389021i
$511$	26.4900	+	29.2607i	1.17185	+	1.29442i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.45922	−	2.93404i	−0.108577	−	0.129541i
$514$	−4.34163	+	3.90922i	−0.191501	+	0.172428i
$515$	9.30722	+	20.9043i	0.410125	+	0.921156i
$516$	−10.0536	−	6.44863i	−0.442585	−	0.283885i
$517$	−25.6046	−	27.0730i	−1.12609	−	1.19067i
$518$	−16.6555	+	1.79608i	−0.731800	+	0.0789154i
$519$	−2.39587	+	15.6990i	−0.105167	+	0.689109i
$520$	5.00983	−	1.06487i	0.219695	−	0.0466977i
$521$	−2.00086	+	9.41331i	−0.0876593	+	0.412405i	0.912336	+	0.409442i	$0.134276\pi$
$521$	−2.00086	+	9.41331i	−0.0876593	+	0.412405i	−0.999996	+	0.00296298i	$0.999057\pi$
$522$	23.3876	+	13.1536i	1.02365	+	0.575719i
$523$	−11.9719	+	26.8894i	−0.523496	+	1.17579i	0.437497	+	0.899220i	$0.355865\pi$
$523$	−11.9719	+	26.8894i	−0.523496	+	1.17579i	−0.960993	+	0.276572i	$0.910802\pi$
$524$	−1.76118	−	5.42035i	−0.0769374	−	0.236789i
$525$	−2.48721	+	9.60193i	−0.108551	+	0.419063i
$526$	20.6413	+	14.9968i	0.900005	+	0.653892i
$527$	14.0508	+	24.3367i	0.612063	+	1.06012i
$528$	1.31898	−	5.59109i	0.0574012	−	0.243321i
$529$	20.7998	−	36.0263i	0.904338	−	1.56636i
$530$	0.179756	−	1.71026i	0.00780809	−	0.0742890i
$531$	−16.2594	+	12.0955i	−0.705598	+	0.524898i
$532$	1.58011	+	1.14151i	0.0685065	+	0.0494906i
$533$	5.25187	+	7.22858i	0.227484	+	0.313105i
$534$	−7.58357	+	0.440304i	−0.328173	+	0.0190538i
$535$	2.47930	−	11.6642i	0.107190	−	0.504287i
$536$	−3.62546	−	4.02648i	−0.156596	−	0.173918i
$537$	2.35359	+	6.02954i	0.101565	+	0.260194i
$538$		−	27.2871i		−	1.17643i
$539$	17.7098	+	15.0121i	0.762815	+	0.646617i
$540$	−1.22248	+	8.66400i	−0.0526073	+	0.372839i
$541$	11.6192	+	1.22123i	0.499549	+	0.0525047i	0.350953	−	0.936393i	$-0.385858\pi$
$541$	11.6192	+	1.22123i	0.499549	+	0.0525047i	0.148596	+	0.988898i	$0.452524\pi$
$542$	−4.42176	+	3.98137i	−0.189931	+	0.171014i
$543$	−8.76234	−	31.9795i	−0.376028	−	1.37237i
$544$	−3.91369	−	1.74249i	−0.167798	−	0.0747086i
$545$	0.449901	−	0.326872i	0.0192716	−	0.0140017i
$546$	2.06558	−	13.7844i	0.0883985	−	0.589919i
$547$	−37.6447	−	12.2315i	−1.60957	−	0.522981i	−0.640122	−	0.768273i	$-0.721116\pi$
$547$	−37.6447	−	12.2315i	−1.60957	−	0.522981i	−0.969449	+	0.245292i	$0.921116\pi$
$548$	4.28222	+	0.450080i	0.182928	+	0.0192265i
$549$	14.0465	−	6.44456i	0.599490	−	0.275047i
$550$	−2.75837	+	6.62763i	−0.117617	+	0.282603i
$551$	−5.70697	+	3.29492i	−0.243125	+	0.140368i
$552$	−13.7618	−	2.10023i	−0.585742	−	0.0893918i
$553$	2.81968	−	3.14864i	0.119905	−	0.133894i
$554$	−12.8083	+	4.16166i	−0.544171	+	0.176812i
$555$	18.4360	−	1.07040i	0.782563	−	0.0454358i
$556$	−0.681576	+	0.0716365i	−0.0289053	+	0.00303806i
$557$	21.4025	+	4.54925i	0.906855	+	0.192758i	0.637651	−	0.770325i	$-0.279906\pi$
$557$	21.4025	+	4.54925i	0.906855	+	0.192758i	0.269204	+	0.963083i	$0.413239\pi$
$558$	7.80092	−	18.0664i	0.330239	−	0.764813i
$559$	−16.9687	−	12.3285i	−0.717699	−	0.521439i
$560$	−0.477667	−	4.42951i	−0.0201851	−	0.187181i
$561$	−23.5689	+	7.08275i	−0.995079	+	0.299034i
$562$	−2.06494	−	3.57658i	−0.0871041	−	0.150869i
$563$	−30.3916	+	13.5312i	−1.28085	+	0.570272i	−0.930481	−	0.366339i	$-0.880611\pi$
$563$	−30.3916	+	13.5312i	−1.28085	+	0.570272i	−0.350370	+	0.936611i	$0.613944\pi$
$564$	18.2065	+	6.87137i	0.766634	+	0.289337i
$565$	−1.33558	+	1.48332i	−0.0561885	+	0.0624036i
$566$	−12.3233	−	16.9615i	−0.517985	−	0.712945i
$567$	20.9155	+	11.3816i	0.878370	+	0.477981i
$568$	−15.9660	+	5.18766i	−0.669918	+	0.217669i
$569$	−12.7533	+	2.71079i	−0.534645	+	0.113642i	−0.467319	−	0.884089i	$-0.654780\pi$
$569$	−12.7533	+	2.71079i	−0.534645	+	0.113642i	−0.0673258	+	0.997731i	$0.521447\pi$
$570$	−1.67757	−	1.34289i	−0.0702658	−	0.0562475i
$571$	−24.9189	−	14.3869i	−1.04282	−	0.602074i	−0.122192	−	0.992507i	$-0.538992\pi$
$571$	−24.9189	−	14.3869i	−1.04282	−	0.602074i	−0.920632	+	0.390432i	$0.872326\pi$
$572$	2.88141	−	9.66755i	0.120478	−	0.404221i
$573$	0.437110	−	0.225831i	0.0182606	−	0.00943421i
$574$	6.72039	−	3.90427i	0.280504	−	0.162961i
$575$	16.5452	+	5.37586i	0.689983	+	0.224189i
$576$	0.656768	+	2.92723i	0.0273653	+	0.121968i
$577$	−0.247461	−	2.35443i	−0.0103019	−	0.0980162i	0.988163	−	0.153410i	$-0.0490254\pi$
$577$	−0.247461	−	2.35443i	−0.0103019	−	0.0980162i	−0.998465	+	0.0553934i	$0.982359\pi$
$578$	0.141453	+	1.34584i	0.00588368	+	0.0559794i
$579$	−5.84233	+	22.3059i	−0.242799	+	0.927003i
$580$	14.3241	+	4.65419i	0.594776	+	0.193255i
$581$	0.00699790	+	2.58934i	0.000290322	+	0.107424i
$582$	−11.4970	−	22.2532i	−0.476566	−	0.922426i
$583$	−2.78815	−	1.92318i	−0.115473	−	0.0796499i
$584$	−12.9197	−	7.45919i	−0.534621	−	0.308663i
$585$	−3.02502	+	15.0645i	−0.125069	+	0.622842i
$586$	1.08702	−	0.231052i	0.0449042	−	0.00954468i
$587$	−21.6789	+	7.04391i	−0.894785	+	0.290733i	−0.720083	−	0.693888i	$-0.755896\pi$
$587$	−21.6789	+	7.04391i	−0.894785	+	0.290733i	−0.174702	+	0.984621i	$0.555896\pi$
$588$	−11.7452	−	3.00853i	−0.484362	−	0.124070i
$589$	2.84069	+	3.90988i	0.117049	+	0.161104i
$590$	−7.61119	+	8.45308i	−0.313348	+	0.348008i
$591$	−3.75354	+	9.94547i	−0.154400	+	0.409102i
$592$	5.78428	−	2.57533i	0.237732	−	0.105845i
$593$	23.8150	+	41.2487i	0.977964	+	1.69388i	0.669786	+	0.742554i	$0.266386\pi$
$593$	23.8150	+	41.2487i	0.977964	+	1.69388i	0.308177	+	0.951329i	$0.400281\pi$
$594$	13.8305	+	10.2819i	0.567471	+	0.421872i
$595$	−15.4108	+	11.2604i	−0.631781	+	0.461630i
$596$	1.94290	+	1.41160i	0.0795841	+	0.0578212i
$597$	−3.08811	−	3.76986i	−0.126388	−	0.154290i
$598$	−23.9122	−	5.08270i	−0.977844	−	0.207847i
$599$	−18.9661	+	1.99342i	−0.774936	+	0.0814490i	−0.483737	−	0.875214i	$-0.660721\pi$
$599$	−18.9661	+	1.99342i	−0.774936	+	0.0814490i	−0.291199	+	0.956663i	$0.594054\pi$
$600$	−0.217300	−	3.74266i	−0.00887124	−	0.152794i
$601$	11.5061	−	3.73855i	0.469342	−	0.152498i	−0.0647911	−	0.997899i	$-0.520638\pi$
$601$	11.5061	−	3.73855i	0.469342	−	0.152498i	0.534133	+	0.845400i	$0.320638\pi$
$602$	−12.1715	+	13.5915i	−0.496072	+	0.553947i
$603$	15.4014	−	5.19682i	0.627192	−	0.211631i
$604$	−13.4132	+	7.74412i	−0.545776	+	0.315104i
$605$	−11.6082	−	14.4343i	−0.471941	−	0.586837i
$606$	14.4898	+	0.677522i	0.588607	+	0.0275224i
$607$	15.2038	+	1.59798i	0.617103	+	0.0648601i	0.407922	−	0.913017i	$-0.366254\pi$
$607$	15.2038	+	1.59798i	0.617103	+	0.0648601i	0.209181	+	0.977877i	$0.432920\pi$
$608$	−0.700708	−	0.227674i	−0.0284175	−	0.00923339i
$609$	25.5279	−	32.0674i	1.03444	−	1.29944i
$610$	7.01785	−	5.09877i	0.284144	−	0.206443i
$611$	31.2187	+	13.8995i	1.26297	+	0.562312i
$612$	9.45352	−	8.70690i	0.382136	−	0.351956i
$613$	19.1882	−	17.2772i	0.775005	−	0.697818i	−0.183460	−	0.983027i	$-0.558730\pi$
$613$	19.1882	−	17.2772i	0.775005	−	0.697818i	0.958465	+	0.285209i	$0.0920631\pi$
$614$	10.4334	+	1.09659i	0.421057	+	0.0442549i
$615$	−7.61198	+	3.93269i	−0.306945	+	0.158581i
$616$	−8.11042	−	3.34980i	−0.326778	−	0.134967i
$617$		−	17.6513i		−	0.710613i	−0.934750	−	0.355307i	$-0.884376\pi$
$617$		−	17.6513i		−	0.710613i	0.934750	−	0.355307i	$-0.115624\pi$
$618$	−21.9257	+	8.55857i	−0.881982	+	0.344276i
$619$	−3.76918	−	4.18610i	−0.151496	−	0.168254i	0.662620	−	0.748956i	$-0.269445\pi$
$619$	−3.76918	−	4.18610i	−0.151496	−	0.168254i	−0.814116	+	0.580702i	$0.802778\pi$
$620$	2.29652	−	10.8043i	0.0922306	−	0.433911i
$621$	22.1507	−	35.4053i	0.888875	−	1.42077i
$622$	−0.260263	−	0.358221i	−0.0104356	−	0.0143633i
$623$	−1.18171	+	11.5433i	−0.0473444	+	0.462472i
$624$	0.853436	+	5.19860i	0.0341648	+	0.208111i
$625$	0.992262	−	9.44074i	0.0396905	−	0.377630i
$626$	−1.03376	+	1.79053i	−0.0413175	+	0.0715640i
$627$	−3.90381	+	1.63510i	−0.155903	+	0.0652995i
$628$	6.58352	+	11.4030i	0.262711	+	0.455029i
$629$	−21.9449	−	15.9439i	−0.874999	−	0.635724i
$630$	12.7679	+	3.95217i	0.508685	+	0.157458i
$631$	5.09850	+	15.6916i	0.202968	+	0.624672i	0.999791	+	0.0204585i	$0.00651261\pi$
$631$	5.09850	+	15.6916i	0.202968	+	0.624672i	−0.796822	+	0.604214i	$0.793487\pi$
$632$	−0.649770	+	1.45941i	−0.0258465	+	0.0580521i
$633$	15.2017	+	23.1222i	0.604211	+	0.919024i
$634$	−1.53197	+	7.20737i	−0.0608425	+	0.286241i
$635$	29.5601	−	6.28319i	1.17306	−	0.249341i
$636$	1.74861	+	0.266860i	0.0693367	+	0.0105817i
$637$	−20.2843	−	6.46978i	−0.803695	−	0.256342i
$638$	21.5525	−	20.3835i	0.853270	−	0.806991i
$639$	4.69952	−	50.1431i	0.185910	−	1.98363i
$640$	0.684905	+	1.53832i	0.0270733	+	0.0608075i
$641$	15.7408	−	14.1731i	0.621723	−	0.559802i	−0.296914	−	0.954904i	$-0.595957\pi$
$641$	15.7408	−	14.1731i	0.621723	−	0.559802i	0.918637	+	0.395102i	$0.129291\pi$
$642$	11.8655	+	3.10779i	0.468294	+	0.122655i
$643$	30.1474	−	21.9033i	1.18890	−	0.863783i	0.195748	−	0.980654i	$-0.437286\pi$
$643$	30.1474	−	21.9033i	1.18890	−	0.863783i	0.993147	+	0.116871i	$0.0372864\pi$
$644$	−6.51654	+	20.2418i	−0.256788	+	0.797640i
$645$	14.1414	−	14.3017i	0.556816	−	0.563127i
$646$	0.656245	+	3.08739i	0.0258196	+	0.121472i
$647$	−14.4493	−	32.4536i	−0.568059	−	1.27588i	−0.937938	−	0.346802i	$-0.887268\pi$
$647$	−14.4493	−	32.4536i	−0.568059	−	1.27588i	0.369880	−	0.929080i	$-0.379399\pi$
$648$	−8.84327	−	1.67231i	−0.347396	−	0.0656945i
$649$	7.44288	+	21.1313i	0.292159	+	0.829476i
$650$		−	6.58343i		−	0.258223i
$651$	−25.3458	−	16.1609i	−0.993380	−	0.633396i
$652$	2.09024	−	6.43310i	0.0818601	−	0.251939i
$653$	10.1007	+	9.09469i	0.395270	+	0.355903i	0.842669	−	0.538432i	$-0.180983\pi$
$653$	10.1007	+	9.09469i	0.395270	+	0.355903i	−0.447399	+	0.894334i	$0.647650\pi$
$654$	0.314236	+	0.477963i	0.0122876	+	0.0186898i
$655$	9.54448	−	1.00317i	0.372934	−	0.0391969i
$656$	−1.96565	+	2.18307i	−0.0767456	+	0.0852347i
$657$	35.9089	−	26.7128i	1.40094	−	1.04217i
$658$	14.7932	−	25.7833i	0.576701	−	1.00514i
$659$	−3.19114			−0.124309			−0.0621546	−	0.998067i	$-0.519797\pi$
$659$	−3.19114			−0.124309			−0.0621546	+	0.998067i	$0.519797\pi$
$660$	8.74734	+	4.12996i	0.340490	+	0.160758i
$661$	−3.83242	+	6.63794i	−0.149064	+	0.258186i	−0.930882	−	0.365321i	$-0.880959\pi$
$661$	−3.83242	+	6.63794i	−0.149064	+	0.258186i	0.781818	+	0.623507i	$0.214293\pi$
$662$	2.56356	−	1.14137i	0.0996356	−	0.0443606i
$663$	17.4593	−	14.3019i	0.678064	−	0.555441i
$664$	−0.302429	−	0.930782i	−0.0117365	−	0.0361214i
$665$	−2.43338	+	2.20297i	−0.0943626	+	0.0854274i
$666$	0.214080	+	18.9938i	0.00829544	+	0.735996i
$667$	−53.4235	−	48.1027i	−2.06857	−	1.86255i
$668$	3.34239	+	3.71210i	0.129321	+	0.143625i
$669$	25.8958	+	20.7295i	1.00119	+	0.801449i
$670$	7.90133	−	4.56184i	0.305255	−	0.176239i
$671$	−2.20151	−	16.9430i	−0.0849883	−	0.654077i
$672$	4.57414	−	0.277981i	0.176451	−	0.0107234i
$673$	26.6253	−	36.6466i	1.02633	−	1.41262i	0.118660	−	0.992935i	$-0.462140\pi$
$673$	26.6253	−	36.6466i	1.02633	−	1.41262i	0.907669	−	0.419686i	$-0.137860\pi$
$674$	−1.49927	−	7.05353i	−0.0577498	−	0.271692i
$675$	10.5665	+	3.85245i	0.406706	+	0.148281i
$676$	−0.391848	−	3.72818i	−0.0150711	−	0.143392i
$677$	−18.5505	−	8.25924i	−0.712955	−	0.317428i	0.0180147	−	0.999838i	$-0.494265\pi$
$677$	−18.5505	−	8.25924i	−0.712955	−	0.317428i	−0.730970	+	0.682410i	$0.760932\pi$
$678$	−1.45990	−	1.44354i	−0.0560670	−	0.0554386i
$679$	−36.3563	+	11.9216i	−1.39523	+	0.457509i
$680$	4.24026	−	5.83622i	0.162607	−	0.223809i
$681$	0.266987	−	0.416241i	0.0102310	−	0.0159504i
$682$	−16.5192	−	14.1570i	−0.632554	−	0.542101i
$683$	30.8382	+	17.8045i	1.17999	+	0.681269i	0.956013	−	0.293325i	$-0.0947617\pi$
$683$	30.8382	+	17.8045i	1.17999	+	0.681269i	0.223980	+	0.974594i	$0.428095\pi$
$684$	1.46038	−	1.65914i	0.0558388	−	0.0634388i
$685$	−2.24055	+	6.89571i	−0.0856070	+	0.263471i
$686$	−7.39545	+	16.9796i	−0.282359	+	0.648285i
$687$	−35.4428	−	17.8081i	−1.35223	−	0.679422i
$688$	2.80481	−	6.29970i	0.106932	−	0.240174i
$689$	3.03834	+	0.645819i	0.115752	+	0.0246037i
$690$	8.27736	−	21.9319i	0.315114	−	0.834933i
$691$	−1.11922	+	10.6487i	−0.0425772	+	0.405095i	0.952389	+	0.304885i	$0.0986181\pi$
$691$	−1.11922	+	10.6487i	−0.0425772	+	0.405095i	−0.994966	+	0.100210i	$0.968049\pi$
$692$	−9.16876			−0.348544
$693$	18.8713	−	18.3541i	0.716863	−	0.697214i
$694$	30.3481			1.15200
$695$	0.120629	−	1.14771i	0.00457572	−	0.0435351i
$696$	−5.47021	+	14.4940i	−0.207348	+	0.549393i
$697$	12.3099	+	2.61656i	0.466272	+	0.0991091i
$698$	3.44504	−	7.73770i	0.130397	−	0.292876i
$699$	8.71082	+	4.37673i	0.329473	+	0.165543i
$700$	−5.69687	−	0.583203i	−0.215321	−	0.0220430i
$701$	−8.31361	+	25.5867i	−0.314001	+	0.966394i	0.662163	+	0.749360i	$0.269639\pi$
$701$	−8.31361	+	25.5867i	−0.314001	+	0.966394i	−0.976164	+	0.217035i	$0.930361\pi$
$702$	−15.3330	−	3.83187i	−0.578707	−	0.144625i
$703$	−4.03999	−	2.33249i	−0.152371	−	0.0879715i
$704$	3.30596	+	0.265798i	0.124598	+	0.0100176i
$705$	−17.6921	+	27.5824i	−0.666321	+	1.03881i
$706$	−1.80490	+	2.48423i	−0.0679283	+	0.0934953i
$707$	4.54825	−	21.6858i	0.171054	−	0.815580i
$708$	−8.31962	−	8.22638i	−0.312671	−	0.309166i
$709$	22.4624	+	10.0009i	0.843594	+	0.375592i	0.782584	−	0.622545i	$-0.213901\pi$
$709$	22.4624	+	10.0009i	0.843594	+	0.375592i	0.0610102	+	0.998137i	$0.480568\pi$
$710$	−2.95489	−	28.1139i	−0.110895	−	1.05510i
$711$	−3.24679	−	3.52520i	−0.121764	−	0.132205i
$712$	−0.911849	−	4.28991i	−0.0341730	−	0.160771i
$713$	−30.9890	+	42.6528i	−1.16055	+	1.59736i
$714$	−10.8293	−	16.3751i	−0.405276	−	0.612823i
$715$	14.9147	+	8.13063i	0.557778	+	0.304068i
$716$	−3.23631	+	1.86848i	−0.120947	+	0.0698285i
$717$	23.8187	+	19.0668i	0.889526	+	0.712061i
$718$	3.12050	+	3.46567i	0.116456	+	0.129338i
$719$	7.90862	+	7.12096i	0.294942	+	0.265567i	0.803294	−	0.595582i	$-0.203079\pi$
$719$	7.90862	+	7.12096i	0.294942	+	0.265567i	−0.508352	+	0.861149i	$0.669745\pi$
$720$	−5.05139	+	0.0569345i	−0.188254	+	0.00212182i
$721$	7.57012	+	35.1473i	0.281926	+	1.30895i
$722$	−5.70358	−	17.5538i	−0.212265	−	0.653285i
$723$	−27.3588	+	22.4112i	−1.01749	+	0.833481i
$724$	17.4888	−	7.78654i	0.649968	−	0.289384i
$725$	9.67977	−	16.7659i	0.359498	−	0.622668i
$726$	15.3885	−	11.2336i	0.571120	−	0.416919i
$727$	−2.10153			−0.0779416			−0.0389708	−	0.999240i	$-0.512408\pi$
$727$	−2.10153			−0.0779416			−0.0389708	+	0.999240i	$0.512408\pi$
$728$	8.04727	−	0.0217484i	0.298252	−	0.000806049i
$729$	15.1227	−	22.3675i	0.560100	−	0.828425i
$730$	16.8093	−	18.6686i	0.622140	−	0.690957i
$731$	−29.3806	+	3.08803i	−1.08668	+	0.114215i
$732$	4.90167	+	7.45559i	0.181171	+	0.275567i
$733$	15.7336	+	14.1666i	0.581133	+	0.523254i	0.906429	−	0.422358i	$-0.138797\pi$
$733$	15.7336	+	14.1666i	0.581133	+	0.523254i	−0.325296	+	0.945612i	$0.605464\pi$
$734$	4.99963	−	15.3873i	0.184540	−	0.567955i
$735$	9.06739	−	18.2922i	0.334456	−	0.674719i
$736$		−	8.03738i		−	0.296262i
$737$	−0.440089	−	17.9646i	−0.0162109	−	0.661736i
$738$	−3.67501	−	8.01002i	−0.135279	−	0.294853i
$739$	17.8861	+	40.1729i	0.657951	+	1.47778i	0.866195	+	0.499706i	$0.166559\pi$
$739$	17.8861	+	40.1729i	0.657951	+	1.47778i	−0.208244	+	0.978077i	$0.566775\pi$
$740$	2.21674	+	10.4289i	0.0814890	+	0.383376i
$741$	2.72908	−	2.76001i	0.100255	−	0.101392i
$742$	0.828006	−	2.57197i	0.0303970	−	0.0944200i
$743$	−36.2210	+	26.3161i	−1.32882	+	0.965445i	−0.329044	+	0.944315i	$0.606726\pi$
$743$	−36.2210	+	26.3161i	−1.32882	+	0.965445i	−0.999777	+	0.0211299i	$0.993274\pi$
$744$	10.9908	+	2.87868i	0.402941	+	0.105538i
$745$	−3.00526	+	2.70595i	−0.110104	+	0.0991384i
$746$	−3.13769	−	7.04736i	−0.114879	−	0.258022i
$747$	2.92324	+	0.273972i	0.106956	+	0.0100241i
$748$	−6.09533	−	12.8348i	−0.222867	−	0.469288i
$749$	7.57442	−	17.1369i	0.276763	−	0.626169i
$750$	20.6568	+	3.15249i	0.754278	+	0.115113i
$751$	−49.2241	+	10.4629i	−1.79621	+	0.381797i	−0.980478	−	0.196627i	$-0.937001\pi$
$751$	−49.2241	+	10.4629i	−1.79621	+	0.381797i	−0.815736	+	0.578424i	$0.803668\pi$
$752$	−2.33594	+	10.9898i	−0.0851831	+	0.400755i
$753$	4.20719	+	6.39926i	0.153318	+	0.233202i
$754$	−11.0652	+	24.8528i	−0.402970	+	0.905085i
$755$	−8.05939	−	24.8042i	−0.293311	−	0.902719i
$756$	−4.67415	+	12.9287i	−0.169997	+	0.470214i
$757$	1.26409	+	0.918418i	0.0459443	+	0.0333805i	0.610520	−	0.792001i	$-0.290960\pi$
$757$	1.26409	+	0.918418i	0.0459443	+	0.0333805i	−0.564576	+	0.825381i	$0.690960\pi$
$758$	12.4531	+	21.5693i	0.452315	+	0.783433i
$759$	−30.1242	−	34.9902i	−1.09344	−	1.27007i
$760$	0.620323	−	1.07443i	0.0225015	−	0.0389737i
$761$	3.28783	−	31.2816i	0.119184	−	1.13396i	−0.757481	−	0.652857i	$-0.773570\pi$
$761$	3.28783	−	31.2816i	0.119184	−	1.13396i	0.876665	−	0.481101i	$-0.159763\pi$
$762$	5.03563	+	30.6739i	0.182422	+	1.11120i
$763$	0.797253	−	0.357545i	0.0288625	−	0.0129440i
$764$	0.166964	+	0.229807i	0.00604056	+	0.00831412i
$765$	11.0315	+	18.6193i	0.398844	+	0.673181i
$766$	0.968737	−	4.55755i	0.0350019	−	0.164671i
$767$	−13.7479	−	15.2686i	−0.496408	−	0.551317i
$768$	−1.61349	+	0.629814i	−0.0582216	+	0.0227265i
$769$		−	1.65697i		−	0.0597518i	−0.999554	−	0.0298759i	$-0.990489\pi$
$769$		−	1.65697i		−	0.0597518i	0.999554	−	0.0298759i	$-0.00951121\pi$
$770$	8.35696	−	12.1859i	0.301164	−	0.439151i
$771$	8.99010	−	4.64469i	0.323771	−	0.167274i
$772$	−13.2398	−	1.39156i	−0.476512	−	0.0500834i
$773$	−38.6444	+	34.7955i	−1.38994	+	1.25151i	−0.457974	+	0.888966i	$0.651425\pi$
$773$	−38.6444	+	34.7955i	−1.38994	+	1.25151i	−0.931967	+	0.362542i	$0.881909\pi$
$774$	14.0151	+	15.2169i	0.503763	+	0.546961i
$775$	−12.9705	−	5.77483i	−0.465913	−	0.207438i
$776$	11.6994	−	8.50013i	0.419985	−	0.305137i
$777$	28.6950	+	4.29990i	1.02943	+	0.154258i
$778$	−31.9056	−	10.3668i	−1.14387	−	0.371666i
$779$	2.15248	+	0.226235i	0.0771207	+	0.00810571i
$780$	−8.86145	−	0.414349i	−0.317291	−	0.0148361i
$781$	−51.4040	−	21.3939i	−1.83938	−	0.765534i
$782$	−29.8196	+	17.2164i	−1.06635	+	0.615656i
$783$	−33.4141	−	32.3030i	−1.19412	−	1.15442i
$784$	0.694060	−	6.96551i	0.0247879	−	0.248768i
$785$	−21.0868	+	6.85153i	−0.752622	+	0.244542i
$786$	0.572176	+	9.85486i	0.0204088	+	0.351511i
$787$	1.84844	−	0.194278i	0.0658896	−	0.00692528i	−0.0715263	−	0.997439i	$-0.522787\pi$
$787$	1.84844	−	0.194278i	0.0658896	−	0.00692528i	0.137416	+	0.990513i	$0.456120\pi$
$788$	−6.00324	−	1.27603i	−0.213857	−	0.0454566i
$789$	−28.0038	−	34.1862i	−0.996963	−	1.21706i
$790$	−2.17631	−	1.58118i	−0.0774297	−	0.0562560i
$791$	−2.53218	+	1.85021i	−0.0900340	+	0.0657860i
$792$	−4.66366	+	8.78922i	−0.165716	+	0.312311i
$793$	7.83430	+	13.5694i	0.278204	+	0.481864i
$794$	−20.3810	+	9.07421i	−0.723295	+	0.322032i
$795$	−1.05174	+	2.78671i	−0.0373014	+	0.0988345i
$796$	1.88264	−	2.09088i	0.0667283	−	0.0741092i
$797$	17.6215	+	24.2539i	0.624185	+	0.859117i	0.997649	−	0.0685273i	$-0.0218300\pi$
$797$	17.6215	+	24.2539i	0.624185	+	0.859117i	−0.373464	+	0.927645i	$0.621830\pi$
$798$	−2.14657	−	2.60607i	−0.0759879	−	0.0922538i
$799$	45.7769	−	14.8738i	1.61947	−	0.526198i
$800$	2.11717	−	0.450018i	0.0748532	−	0.0159105i
$801$	12.8997	+	2.59033i	0.455790	+	0.0915247i
$802$	27.4329	+	15.8384i	0.968688	+	0.559272i
$803$	−16.4376	−	46.6684i	−0.580070	−	1.64689i
$804$	4.30754	+	8.33754i	0.151915	+	0.294042i
$805$	−31.0590	−	17.8202i	−1.09469	−	0.628078i
$806$	18.9750	+	6.16535i	0.668366	+	0.217165i
$807$	−11.9750	+	45.7204i	−0.421541	+	1.60944i
$808$	0.875406	+	8.32893i	0.0307967	+	0.293011i
$809$	−4.88242	−	46.4531i	−0.171657	−	1.63321i	−0.653485	−	0.756940i	$-0.726694\pi$
$809$	−4.88242	−	46.4531i	−0.171657	−	1.63321i	0.481828	−	0.876266i	$-0.339973\pi$
$810$	5.85053	−	13.9803i	0.205567	−	0.491218i
$811$	−16.8678	−	5.48067i	−0.592308	−	0.192452i	−0.00250090	−	0.999997i	$-0.500796\pi$
$811$	−16.8678	−	5.48067i	−0.592308	−	0.192452i	−0.589807	+	0.807544i	$0.700796\pi$
$812$	20.5258	+	11.7767i	0.720313	+	0.413281i
$813$	9.15603	−	4.73041i	0.321116	−	0.165903i
$814$	20.1249	+	5.99823i	0.705378	+	0.210238i
$815$	9.86419	+	5.69509i	0.345528	+	0.199490i
$816$	5.79282	+	4.63713i	0.202789	+	0.162332i
$817$	−4.96964	+	1.05633i	−0.173866	+	0.0369563i
$818$	8.62011	−	2.80084i	0.301395	−	0.0979292i
$819$	−9.51027	+	22.1898i	−0.332316	+	0.775373i
$820$	−2.90757	−	4.00193i	−0.101537	−	0.139754i
$821$	−2.30175	+	2.55636i	−0.0803317	+	0.0892174i	−0.781971	−	0.623315i	$-0.785785\pi$
$821$	−2.30175	+	2.55636i	−0.0803317	+	0.0892174i	0.701639	+	0.712533i	$0.252452\pi$
$822$	−6.97749	−	2.63339i	−0.243368	−	0.0918500i
$823$	−20.6887	+	9.21120i	−0.721163	+	0.321082i	−0.734294	−	0.678832i	$-0.762487\pi$
$823$	−20.6887	+	9.21120i	−0.721163	+	0.321082i	0.0131315	+	0.999914i	$0.495820\pi$
$824$	−6.79453	−	11.7685i	−0.236699	−	0.409974i
$825$	7.53029	−	9.89430i	0.262171	−	0.344475i
$826$	−14.4303	+	10.5439i	−0.502095	+	0.366871i
$827$	−11.1103	−	8.07211i	−0.386343	−	0.280695i	0.377612	−	0.925964i	$-0.376745\pi$
$827$	−11.1103	−	8.07211i	−0.386343	−	0.280695i	−0.763955	+	0.645269i	$0.776745\pi$
$828$	22.1367	+	9.55841i	0.769303	+	0.332178i
$829$	−50.7231	−	10.7815i	−1.76169	−	0.374458i	−0.790441	−	0.612538i	$-0.790149\pi$
$829$	−50.7231	−	10.7815i	−1.76169	−	0.374458i	−0.971246	+	0.238080i	$0.923482\pi$
$830$	1.63898	−	0.172264i	0.0568898	−	0.00597936i
$831$	23.2870	−	1.35205i	0.807817	−	0.0469021i
$832$	−2.89273	+	0.939904i	−0.100287	+	0.0325853i
$833$	−27.3295	+	12.3453i	−0.946912	+	0.427740i
$834$	1.17344	+	0.179082i	0.0406329	+	0.00620111i
$835$	−7.28440	+	4.20565i	−0.252087	+	0.145543i
$836$	−1.27325	−	2.08565i	−0.0440363	−	0.0721336i
$837$	−20.9992	+	26.8474i	−0.725839	+	0.927983i
$838$	22.8521	+	2.40185i	0.789412	+	0.0829706i
$839$	2.62044	+	0.851432i	0.0904676	+	0.0293947i	0.353901	−	0.935283i	$-0.384855\pi$
$839$	2.62044	+	0.851432i	0.0904676	+	0.0293947i	−0.263434	+	0.964678i	$0.584855\pi$
$840$	−1.14356	+	7.63141i	−0.0394564	+	0.263309i
$841$	−41.2596	+	29.9769i	−1.42275	+	1.03368i
$842$	−19.1595	−	8.53035i	−0.660279	−	0.293975i
$843$	1.89028	+	6.89887i	0.0651047	+	0.237610i
$844$	−11.8727	+	10.6902i	−0.408675	+	0.367973i
$845$	6.27790	+	0.659834i	0.215966	+	0.0226990i
$846$	−27.4901	−	19.5032i	−0.945130	−	0.670534i
$847$	−13.1952	−	25.9401i	−0.453392	−	0.891311i
$848$			1.02125i			0.0350698i
$849$	13.2044	+	33.8276i	0.453174	+	1.16096i
$850$	−6.20467	−	6.89098i	−0.212818	−	0.236359i
$851$	10.5807	−	49.7781i	0.362700	−	1.70637i
$852$	29.0281	−	1.68538i	0.994488	−	0.0577402i
$853$	−4.47516	−	6.15953i	−0.153227	−	0.210898i	0.725502	−	0.688220i	$-0.241608\pi$
$853$	−4.47516	−	6.15953i	−0.153227	−	0.210898i	−0.878729	+	0.477322i	$0.841608\pi$
$854$	12.4361	−	5.57722i	0.425554	−	0.190849i
$855$	2.22150	+	2.98626i	0.0759736	+	0.102128i
$856$	−0.740231	+	7.04283i	−0.0253006	+	0.240719i
$857$	−11.3163	+	19.6004i	−0.386557	+	0.669536i	−0.991984	−	0.126365i	$-0.959669\pi$
$857$	−11.3163	+	19.6004i	−0.386557	+	0.669536i	0.605427	+	0.795901i	$0.293002\pi$
$858$	−9.07053	+	14.9338i	−0.309663	+	0.509831i
$859$	−23.4573	−	40.6292i	−0.800353	−	1.38625i	−0.919384	−	0.393362i	$-0.871312\pi$
$859$	−23.4573	−	40.6292i	−0.800353	−	1.38625i	0.119031	−	0.992891i	$-0.462021\pi$
$860$	9.39431	+	6.82537i	0.320343	+	0.232743i
$861$	−12.9736	+	3.59248i	−0.442140	+	0.122431i
$862$	5.69811	+	17.5370i	0.194078	+	0.597312i
$863$	−14.4956	+	32.5577i	−0.493436	+	1.10828i	0.479572	+	0.877503i	$0.340792\pi$
$863$	−14.4956	+	32.5577i	−0.493436	+	1.10828i	−0.973008	+	0.230773i	$0.925875\pi$
$864$	0.184186	−	5.19289i	0.00626613	−	0.176666i
$865$	3.21001	−	15.1019i	0.109144	−	0.513481i
$866$	24.2917	−	5.16337i	0.825467	−	0.175458i
$867$	0.353615	−	2.31707i	0.0120094	−	0.0786918i
$868$	7.01603	−	15.8736i	0.238139	−	0.538784i
$869$	−4.78608	+	2.27294i	−0.162357	+	0.0771041i
$870$	−21.9580	−	14.0844i	−0.744446	−	0.477506i
$871$	6.70296	+	15.0551i	0.227121	+	0.510122i
$872$	−0.245423	+	0.220980i	−0.00831107	+	0.00748332i
$873$	9.49771	+	42.3315i	0.321449	+	1.43270i
$874$	−4.79074	+	3.48068i	−0.162049	+	0.117736i
$875$	9.78146	−	30.3834i	0.330674	−	1.02715i
$876$	18.3739	+	18.1679i	0.620796	+	0.613838i
$877$	3.50605	+	16.4946i	0.118391	+	0.556985i	0.996860	+	0.0791856i	$0.0252320\pi$
$877$	3.50605	+	16.4946i	0.118391	+	0.556985i	−0.878469	+	0.477799i	$0.841435\pi$
$878$	13.9759	+	31.3905i	0.471665	+	1.05938i
$879$	−1.92273	−	0.0899041i	−0.0648520	−	0.00303239i
$880$	−1.59522	+	5.35221i	−0.0537750	+	0.180423i
$881$		−	37.6729i		−	1.26923i	−0.772827	−	0.634616i	$-0.781158\pi$
$881$		−	37.6729i		−	1.26923i	0.772827	−	0.634616i	$-0.218842\pi$
$882$	18.3591	+	10.1953i	0.618183	+	0.343293i
$883$	−7.86328	+	24.2007i	−0.264620	+	0.814418i	0.727160	+	0.686468i	$0.240840\pi$
$883$	−7.86328	+	24.2007i	−0.264620	+	0.814418i	−0.991781	+	0.127950i	$0.959160\pi$
$884$	9.68347	+	8.71903i	0.325690	+	0.293253i
$885$	16.4625	−	10.8232i	0.553379	−	0.363819i
$886$	−17.5479	+	1.84436i	−0.589533	+	0.0619624i
$887$	18.0132	−	20.0057i	0.604825	−	0.671726i	−0.360505	−	0.932757i	$-0.617396\pi$
$887$	18.0132	−	20.0057i	0.604825	−	0.671726i	0.965330	+	0.261031i	$0.0840625\pi$
$888$	−10.8219	+	1.77660i	−0.363160	+	0.0596187i
$889$	47.4822	−	0.128325i	1.59250	−	0.00430387i
$890$	7.38518			0.247552
$891$	−18.6612	−	23.2972i	−0.625172	−	0.780487i
$892$	−9.57560	+	16.5854i	−0.320615	+	0.555321i
$893$	7.56214	−	3.36688i	0.253057	−	0.112668i
$894$	−2.63590	−	3.21782i	−0.0881577	−	0.107620i
$895$	−1.94455	−	5.98471i	−0.0649991	−	0.200047i
$896$	0.557075	+	2.58644i	0.0186106	+	0.0864069i
$897$	37.8352	+	19.0102i	1.26328	+	0.634731i
$898$	10.2352	+	9.21580i	0.341552	+	0.307535i
$899$	39.2581	+	43.6006i	1.30933	+	1.45416i
$900$	−1.27839	+	6.36632i	−0.0426128	+	0.212211i
$901$	3.78894	−	2.18755i	0.126228	−	0.0728778i
$902$	−9.66174	+	1.25541i	−0.321701	+	0.0418006i
$903$	26.3583	−	17.4315i	0.877150	−	0.580083i
$904$	0.696726	−	0.958960i	0.0231727	−	0.0318946i
$905$	6.70235	+	31.5321i	0.222794	+	1.04816i
$906$	25.8728	−	7.08910i	0.859566	−	0.235520i
$907$	1.72853	+	16.4459i	0.0573950	+	0.546077i	0.985005	+	0.172526i	$0.0551930\pi$
$907$	1.72853	+	16.4459i	0.0573950	+	0.546077i	−0.927610	+	0.373550i	$0.878140\pi$
$908$	0.260821	+	0.116125i	0.00865566	+	0.00385375i
$909$	−23.9807	−	7.49408i	−0.795391	−	0.248563i
$910$	−2.78155	+	13.2623i	−0.0922076	+	0.439642i
$911$	−15.8987	+	21.8827i	−0.526747	+	0.725005i	−0.986630	−	0.162974i	$-0.947891\pi$
$911$	−15.8987	+	21.8827i	−0.526747	+	0.725005i	0.459883	+	0.887979i	$0.347891\pi$
$912$	1.07414	+	0.688982i	0.0355684	+	0.0228145i
$913$	1.24722	−	2.99674i	0.0412769	−	0.0991776i
$914$	−5.72093	−	3.30298i	−0.189232	−	0.109253i
$915$	−13.9962	+	5.46335i	−0.462702	+	0.180613i
$916$	7.07669	−	21.7798i	0.233820	−	0.719625i
$917$	15.0005	+	1.53564i	0.495360	+	0.0507113i
$918$	−19.6607	+	10.4400i	−0.648901	+	0.344571i
$919$	0.831256	−	1.86703i	0.0274206	−	0.0615877i	−0.899316	−	0.437299i	$-0.855935\pi$
$919$	0.831256	−	1.86703i	0.0274206	−	0.0615877i	0.926737	+	0.375712i	$0.122602\pi$
$920$	13.2384	+	2.81391i	0.436458	+	0.0927720i
$921$	−17.0002	−	6.41609i	−0.560176	−	0.211417i
$922$	0.579854	−	5.51694i	0.0190965	−	0.181691i
$923$	51.0611			1.68070
$924$	12.1192	+	9.17198i	0.398692	+	0.301736i
$925$	13.7047			0.450608
$926$	3.69681	−	35.1728i	0.121485	−	1.15585i
$927$	40.4932	−	4.71800i	1.32997	−	0.154959i
$928$	−8.74880	−	1.85961i	−0.287193	−	0.0610449i
$929$	−4.70133	+	10.5594i	−0.154246	+	0.346442i	−0.974095	−	0.226137i	$-0.927390\pi$
$929$	−4.70133	+	10.5594i	−0.154246	+	0.346442i	0.819850	+	0.572579i	$0.194057\pi$
$930$	−8.58939	+	17.0951i	−0.281657	+	0.560571i
$931$	−4.45241	+	2.60279i	−0.145922	+	0.0853030i
$932$	−1.73925	+	5.35285i	−0.0569709	+	0.175339i
$933$	0.278872	+	0.714427i	0.00912987	+	0.0233893i
$934$	22.9494	+	13.2498i	0.750926	+	0.433547i
$935$	23.2743	−	5.54615i	0.761152	−	0.181379i
$936$	0.851462	−	9.08496i	0.0278309	−	0.296951i
$937$	0.365319	−	0.502818i	0.0119344	−	0.0164264i	−0.803008	−	0.595968i	$-0.796768\pi$
$937$	0.365319	−	0.502818i	0.0119344	−	0.0164264i	0.814943	+	0.579542i	$0.196768\pi$
$938$	13.6215	−	4.46662i	0.444757	−	0.145840i
$939$	2.51788	−	2.54642i	0.0821681	−	0.0830994i
$940$	−17.2835	−	7.69510i	−0.563725	−	0.250986i
$941$	−0.0251223	−	0.239023i	−0.000818965	−	0.00779193i	0.994105	−	0.108424i	$-0.0345803\pi$
$941$	−0.0251223	−	0.239023i	−0.000818965	−	0.00779193i	−0.994924	+	0.100632i	$0.967914\pi$
$942$	−6.02667	−	21.9953i	−0.196359	−	0.716645i
$943$	4.90895	+	23.0948i	0.159857	+	0.752069i
$944$	3.97048	−	5.46490i	0.129228	−	0.177867i
$945$	−19.6586	−	12.2252i	−0.639494	−	0.397686i
$946$	20.6597	−	9.81140i	0.671704	−	0.318996i
$947$	−16.9856	+	9.80662i	−0.551957	+	0.318672i	−0.749911	−	0.661539i	$-0.769904\pi$
$947$	−16.9856	+	9.80662i	−0.551957	+	0.318672i	0.197954	+	0.980211i	$0.436570\pi$
$948$	1.72918	−	2.16013i	0.0561610	−	0.0701578i
$949$	30.3622	+	33.7206i	0.985599	+	1.09462i
$950$	−1.18510	−	1.06707i	−0.0384497	−	0.0346203i
$951$	5.72985	−	11.4039i	0.185803	−	0.369796i
$952$	8.40271	−	7.60705i	0.272333	−	0.246546i
$953$	10.1199	+	31.1459i	0.327816	+	1.00891i	0.970153	+	0.242492i	$0.0779648\pi$
$953$	10.1199	+	31.1459i	0.327816	+	1.00891i	−0.642337	+	0.766422i	$0.722035\pi$
$954$	−2.81273	−	1.21451i	−0.0910656	−	0.0393213i
$955$	−0.436971	+	0.194552i	−0.0141401	+	0.00629556i
$956$	−8.80754	+	15.2551i	−0.284856	+	0.493385i
$957$	−45.0572	+	24.6949i	−1.45649	+	0.798272i
$958$	−18.6372			−0.602141
$959$	−5.66937	+	9.88121i	−0.183074	+	0.319081i
$960$	−0.472484	−	2.87808i	−0.0152494	−	0.0928897i
$961$	8.04820	−	8.93843i	0.259619	−	0.288336i
$962$	−19.1529	+	2.01305i	−0.617514	+	0.0649033i
$963$	−18.5172	−	10.4144i	−0.596707	−	0.335600i
$964$	−15.1740	−	13.6628i	−0.488723	−	0.440048i
$965$	6.92735	−	21.3202i	0.222999	−	0.686322i
$966$	19.8019	−	31.0560i	0.637114	−	0.999211i
$967$		−	1.44662i		−	0.0465203i	−0.999729	−	0.0232602i	$-0.992595\pi$
$967$		−	1.44662i		−	0.0465203i	0.999729	−	0.0232602i	$-0.00740461\pi$
$968$	7.75188	+	7.80438i	0.249155	+	0.250842i
$969$	0.255350	−	5.46102i	0.00820301	−	0.175433i
$970$	9.90462	+	22.2461i	0.318018	+	0.714280i
$971$	4.17496	+	19.6416i	0.133981	+	0.630330i	0.992973	+	0.118341i	$0.0377577\pi$
$971$	4.17496	+	19.6416i	0.133981	+	0.630330i	−0.858992	+	0.511989i	$0.828909\pi$
$972$	14.0833	+	6.68290i	0.451721	+	0.214354i
$973$	0.555651	−	1.72598i	0.0178134	−	0.0553323i
$974$	10.7297	−	7.79558i	0.343802	−	0.249787i
$975$	−2.88915	+	11.0307i	−0.0925270	+	0.353267i
$976$	−3.82827	+	3.44699i	−0.122540	+	0.110335i
$977$	7.31354	+	16.4265i	0.233981	+	0.525530i	0.991930	−	0.126784i	$-0.0404654\pi$
$977$	7.31354	+	16.4265i	0.233981	+	0.525530i	−0.757950	+	0.652313i	$0.773799\pi$
$978$	−6.32544	+	9.86155i	−0.202265	+	0.315338i
$979$	6.96226	−	12.7714i	0.222515	−	0.408177i
$980$	11.2299	+	3.58184i	0.358727	+	0.114418i
$981$	−0.316758	−	0.938746i	−0.0101133	−	0.0299719i
$982$	−38.3666	+	8.15508i	−1.22433	+	0.260239i
$983$	−3.73952	+	17.5931i	−0.119272	+	0.561131i	0.877410	+	0.479741i	$0.159269\pi$
$983$	−3.73952	+	17.5931i	−0.119272	+	0.561131i	−0.996682	+	0.0813904i	$0.974064\pi$
$984$	4.25155	−	2.79518i	0.135535	−	0.0891070i
$985$	4.20351	−	9.44124i	0.133935	−	0.300823i
$986$	11.8409	+	36.4424i	0.377090	+	1.16056i
$987$	−36.1016	+	36.7087i	−1.14913	+	1.16845i
$988$	1.81296	+	1.31720i	0.0576781	+	0.0419056i
$989$	−27.7124	−	47.9993i	−0.881204	−	1.52629i
$990$	−12.8440	−	10.7587i	−0.408210	−	0.341933i
$991$	−16.9398	+	29.3406i	−0.538110	+	0.932034i	0.460896	+	0.887454i	$0.347528\pi$
$991$	−16.9398	+	29.3406i	−0.538110	+	0.932034i	−0.999006	+	0.0445797i	$0.985805\pi$
$992$	−0.685661	+	6.52363i	−0.0217698	+	0.207125i
$993$	−4.79622	+	0.787378i	−0.152203	+	0.0249867i
$994$	4.52333	−	44.1850i	0.143471	−	1.40146i
$995$	2.78478	+	3.83293i	0.0882836	+	0.121512i
$996$	0.0982541	+	1.69228i	0.00311330	+	0.0536219i
$997$	12.9974	−	61.1480i	0.411632	−	1.93658i	0.0672837	−	0.997734i	$-0.478567\pi$
$997$	12.9974	−	61.1480i	0.411632	−	1.93658i	0.344348	−	0.938842i	$-0.388100\pi$
$998$	1.48350	+	1.64759i	0.0469593	+	0.0521536i
$999$	7.97679	−	31.9187i	0.252375	−	1.00986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.7	✓	128
3.2	odd	2		462.2.bc.b.95.16	yes	128
7.2	even	3	inner	462.2.bc.a.359.6	yes	128
11.8	odd	10		462.2.bc.b.305.6	yes	128
21.2	odd	6		462.2.bc.b.359.6	yes	128
33.8	even	10	inner	462.2.bc.a.305.6	yes	128
77.30	odd	30		462.2.bc.b.107.16	yes	128
231.107	even	30	inner	462.2.bc.a.107.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.7	✓	128	1.1	even	1	trivial
462.2.bc.a.107.7	yes	128	231.107	even	30	inner
462.2.bc.a.305.6	yes	128	33.8	even	10	inner
462.2.bc.a.359.6	yes	128	7.2	even	3	inner
462.2.bc.b.95.16	yes	128	3.2	odd	2
462.2.bc.b.107.16	yes	128	77.30	odd	30
462.2.bc.b.305.6	yes	128	11.8	odd	10
462.2.bc.b.359.6	yes	128	21.2	odd	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(-0.611589 + 1.62048i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.684905 - 1.53832i) q^{5} +(1.54768 + 0.777625i) q^{6} +(1.54934 - 2.14465i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.25192 - 1.98214i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(-0.611589 + 1.62048i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.684905 - 1.53832i) q^{5} +(1.54768 + 0.777625i) q^{6} +(1.54934 - 2.14465i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.25192 - 1.98214i) q^{9} +(-1.45830 - 0.841952i) q^{10} +(-2.83081 + 1.72816i) q^{11} +(0.935142 - 1.45791i) q^{12} +(1.78780 - 2.46070i) q^{13} +(-1.97095 - 1.76503i) q^{14} +(2.07394 + 2.05070i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.447807 - 4.26060i) q^{17} +(-2.20667 + 2.03239i) q^{18} +(-0.153183 - 0.720668i) q^{19} +(-0.989774 + 1.36231i) q^{20} +(2.52781 + 3.82233i) q^{21} +(1.42279 + 2.99594i) q^{22} +(6.96058 - 4.01869i) q^{23} +(-1.35218 - 1.08241i) q^{24} +(1.44831 + 1.60851i) q^{25} +(-2.26034 - 2.03522i) q^{26} +(4.58927 - 2.43693i) q^{27} +(-1.96138 + 1.77566i) q^{28} +(-2.76393 - 8.50649i) q^{29} +(2.25625 - 1.84822i) q^{30} +(-5.99246 + 2.66801i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.06915 - 5.64419i) q^{33} -4.28407 q^{34} +(-2.23801 - 3.85227i) q^{35} +(1.79060 + 2.40702i) q^{36} +(4.23672 - 4.70535i) q^{37} +(-0.732732 + 0.0770132i) q^{38} +(2.89412 + 4.40204i) q^{39} +(1.25138 + 1.12675i) q^{40} +(-0.907773 + 2.79384i) q^{41} +(4.06562 - 2.11442i) q^{42} -6.89588i q^{43} +(3.12825 - 1.10184i) q^{44} +(-4.59152 + 2.10660i) q^{45} +(-3.26910 - 7.34252i) q^{46} +(2.33594 + 10.9898i) q^{47} +(-1.21782 + 1.23163i) q^{48} +(-2.19907 - 6.64561i) q^{49} +(1.75109 - 1.27224i) q^{50} +(7.17810 + 1.88008i) q^{51} +(-2.26034 + 2.03522i) q^{52} +(0.415379 + 0.932956i) q^{53} +(-1.94388 - 4.81885i) q^{54} +(0.719629 + 5.53832i) q^{55} +(1.56091 + 2.13625i) q^{56} +(1.26151 + 0.192523i) q^{57} +(-8.74880 + 1.85961i) q^{58} +(1.40444 - 6.60737i) q^{59} +(-1.60226 - 2.43708i) q^{60} +(-2.09528 + 4.70608i) q^{61} +(2.02702 + 6.23851i) q^{62} +(-7.73999 + 1.75857i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.56087 - 4.43556i) q^{65} +(-5.72503 + 0.473319i) q^{66} +(-2.70908 + 4.69227i) q^{67} +(-0.447807 + 4.26060i) q^{68} +(2.25520 + 13.7373i) q^{69} +(-4.06511 + 1.82308i) q^{70} +(9.86752 + 13.5815i) q^{71} +(2.58101 - 1.52919i) q^{72} +(-3.10170 + 14.5924i) q^{73} +(-4.23672 - 4.70535i) q^{74} +(-3.49234 + 1.36321i) q^{75} +0.736768i q^{76} +(-0.679594 + 8.74861i) q^{77} +(4.68044 - 2.41812i) q^{78} +(1.58877 + 0.166986i) q^{79} +(1.25138 - 1.12675i) q^{80} +(1.14226 + 8.92722i) q^{81} +(2.68364 + 1.19484i) q^{82} +(-0.791771 + 0.575255i) q^{83} +(-1.67786 - 4.26436i) q^{84} +(-6.86088 - 2.22924i) q^{85} +(-6.85811 - 0.720816i) q^{86} +(15.4750 + 0.723589i) q^{87} +(-0.768808 - 3.22629i) q^{88} +(-3.79817 + 2.19288i) q^{89} +(1.61511 + 4.78656i) q^{90} +(-2.50743 - 7.64668i) q^{91} +(-7.64401 + 2.48369i) q^{92} +(-0.658542 - 11.3424i) q^{93} +(11.1737 - 1.17441i) q^{94} +(-1.21354 - 0.257945i) q^{95} +(1.09758 + 1.33989i) q^{96} +(-11.6994 - 8.50013i) q^{97} +(-6.83907 + 1.49237i) q^{98} +(9.80019 + 1.71938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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