LMFDB - Embedded newform 770.2.bv.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(-1.50590 + 0.977944i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.812068 + 2.08340i) q^{5} +(1.05542 - 1.45266i) q^{6} +(0.435551 - 2.60965i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0911544 - 0.204736i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(-1.50590 + 0.977944i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.812068 + 2.08340i) q^{5} +(1.05542 - 1.45266i) q^{6} +(0.435551 - 2.60965i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0911544 - 0.204736i) q^{9} +(0.0115077 - 2.23604i) q^{10} +(0.328001 + 3.30037i) q^{11} +(-0.464731 + 1.73440i) q^{12} +(0.129996 - 0.820762i) q^{13} +(0.528595 + 2.59241i) q^{14} +(-0.814552 - 3.93155i) q^{15} +(0.104528 - 0.994522i) q^{16} +(0.285343 + 0.109533i) q^{17} +(-0.0117291 + 0.223804i) q^{18} +(-4.95184 + 5.49958i) q^{19} +(0.790581 + 2.09165i) q^{20} +(1.89620 + 4.35583i) q^{21} +(-1.48896 - 2.96361i) q^{22} +(-0.598826 + 2.23485i) q^{23} +(-0.187689 - 1.78574i) q^{24} +(-3.68109 - 3.38372i) q^{25} +(0.172773 + 0.812834i) q^{26} +(-0.779721 - 4.92297i) q^{27} +(-1.42252 - 2.23079i) q^{28} +(-1.03617 - 0.336673i) q^{29} +(2.16939 + 3.37851i) q^{30} +(-2.82843 + 0.297280i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.72151 - 4.64926i) q^{33} -0.305644 q^{34} +(5.08325 + 3.02664i) q^{35} +(-0.0692543 - 0.213143i) q^{36} +(3.64113 - 5.60686i) q^{37} +(2.65207 - 6.90888i) q^{38} +(0.606898 + 1.36312i) q^{39} +(-1.48765 - 1.66940i) q^{40} +(2.48856 - 0.808583i) q^{41} +(-3.33124 - 3.38698i) q^{42} +(-1.41752 - 1.41752i) q^{43} +(2.45213 + 2.23317i) q^{44} +(0.352523 + 0.356170i) q^{45} +(-0.241846 - 2.30101i) q^{46} +(-4.65997 + 0.244219i) q^{47} +(0.815177 + 1.59987i) q^{48} +(-6.62059 - 2.27327i) q^{49} +(4.64921 + 1.83979i) q^{50} +(-0.536815 + 0.114104i) q^{51} +(-0.452591 - 0.696929i) q^{52} +(3.75707 - 4.63959i) q^{53} +(2.49217 + 4.31656i) q^{54} +(-7.14233 - 1.99676i) q^{55} +(2.12748 + 1.57284i) q^{56} +(2.07871 - 13.1244i) q^{57} +(1.08800 - 0.0570198i) q^{58} +(-1.90993 - 2.12119i) q^{59} +(-3.23605 - 2.37667i) q^{60} +(6.10517 + 0.641679i) q^{61} +(2.53403 - 1.29115i) q^{62} +(-0.494588 - 0.327054i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.60441 + 0.937348i) q^{65} +(5.14047 + 3.00679i) q^{66} +(-3.93608 - 14.6897i) q^{67} +(0.285343 - 0.109533i) q^{68} +(-1.28378 - 3.95108i) q^{69} +(-5.83027 - 1.00394i) q^{70} +(-9.66390 - 7.02124i) q^{71} +(0.141038 + 0.174167i) q^{72} +(-13.6351 - 0.714588i) q^{73} +(-1.38997 + 6.53932i) q^{74} +(8.85245 + 1.49565i) q^{75} +7.40041i q^{76} +(8.75568 + 0.581508i) q^{77} +(-1.05508 - 1.05508i) q^{78} +(2.30361 - 5.17399i) q^{79} +(1.98710 + 1.02539i) q^{80} +(6.43845 + 7.15062i) q^{81} +(-2.03350 + 1.64670i) q^{82} +(4.58045 - 0.725472i) q^{83} +(4.32377 + 1.96820i) q^{84} +(-0.459919 + 0.505535i) q^{85} +(1.83136 + 0.815375i) q^{86} +(1.88962 - 0.506322i) q^{87} +(-3.08956 - 1.20608i) q^{88} +(-0.908036 - 1.57276i) q^{89} +(-0.456749 - 0.206181i) q^{90} +(-2.08529 - 0.696728i) q^{91} +(1.05039 + 2.06151i) q^{92} +(3.96861 - 3.21372i) q^{93} +(4.26293 - 1.89798i) q^{94} +(-7.43657 - 14.7827i) q^{95} +(-1.33438 - 1.20148i) q^{96} +(-11.9252 - 1.88876i) q^{97} +(6.99552 - 0.250323i) q^{98} +(0.705603 + 0.233689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	−1.50590	+	0.977944i	−0.869432	+	0.564616i	−0.900478	−	0.434902i	$-0.856783\pi$
$3$	−1.50590	+	0.977944i	−0.869432	+	0.564616i	0.0310454	+	0.999518i	$0.490116\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	−0.812068	+	2.08340i	−0.363168	+	0.931724i
$5$	−0.812068	+	2.08340i	−0.363168	+	0.931724i
$6$	1.05542	−	1.45266i	0.430872	−	0.593044i
$7$	0.435551	−	2.60965i	0.164623	−	0.986357i
$7$	0.435551	−	2.60965i	0.164623	−	0.986357i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	0.0911544	−	0.204736i	0.0303848	−	0.0682453i
$10$	0.0115077	−	2.23604i	0.00363906	−	0.707097i
$11$	0.328001	+	3.30037i	0.0988961	+	0.995098i
$11$	0.328001	+	3.30037i	0.0988961	+	0.995098i
$12$	−0.464731	+	1.73440i	−0.134156	+	0.500678i
$13$	0.129996	−	0.820762i	0.0360544	−	0.227638i	−0.963081	−	0.269212i	$-0.913237\pi$
$13$	0.129996	−	0.820762i	0.0360544	−	0.227638i	0.999135	+	0.0415730i	$0.0132369\pi$
$14$	0.528595	+	2.59241i	0.141273	+	0.692851i
$15$	−0.814552	−	3.93155i	−0.210316	−	1.01512i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	0.285343	+	0.109533i	0.0692059	+	0.0265656i	0.392725	−	0.919656i	$-0.371533\pi$
$17$	0.285343	+	0.109533i	0.0692059	+	0.0265656i	−0.323519	+	0.946222i	$0.604866\pi$
$18$	−0.0117291	+	0.223804i	−0.00276457	+	0.0527512i
$19$	−4.95184	+	5.49958i	−1.13603	+	1.26169i	−0.175206	+	0.984532i	$0.556059\pi$
$19$	−4.95184	+	5.49958i	−1.13603	+	1.26169i	−0.960825	+	0.277157i	$0.910608\pi$
$20$	0.790581	+	2.09165i	0.176779	+	0.467706i
$21$	1.89620	+	4.35583i	0.413784	+	0.950519i
$22$	−1.48896	−	2.96361i	−0.317448	−	0.631844i
$23$	−0.598826	+	2.23485i	−0.124864	+	0.465998i	−0.999835	−	0.0181772i	$-0.994214\pi$
$23$	−0.598826	+	2.23485i	−0.124864	+	0.465998i	0.874971	+	0.484176i	$0.160880\pi$
$24$	−0.187689	−	1.78574i	−0.0383119	−	0.364514i
$25$	−3.68109	−	3.38372i	−0.736218	−	0.676744i
$26$	0.172773	+	0.812834i	0.0338836	+	0.159410i
$27$	−0.779721	−	4.92297i	−0.150057	−	0.947426i
$28$	−1.42252	−	2.23079i	−0.268831	−	0.421580i
$29$	−1.03617	−	0.336673i	−0.192412	−	0.0625186i	0.211226	−	0.977437i	$-0.432255\pi$
$29$	−1.03617	−	0.336673i	−0.192412	−	0.0625186i	−0.403638	+	0.914919i	$0.632255\pi$
$30$	2.16939	+	3.37851i	0.396075	+	0.616828i
$31$	−2.82843	+	0.297280i	−0.508000	+	0.0533930i	−0.355062	−	0.934843i	$-0.615540\pi$
$31$	−2.82843	+	0.297280i	−0.508000	+	0.0533930i	−0.152938	+	0.988236i	$0.548874\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−3.72151	−	4.64926i	−0.647832	−	0.809332i
$34$	−0.305644			−0.0524175
$35$	5.08325	+	3.02664i	0.859226	+	0.511596i
$36$	−0.0692543	−	0.213143i	−0.0115424	−	0.0355238i
$37$	3.64113	−	5.60686i	0.598599	−	0.921761i	−0.401384	−	0.915910i	$-0.631471\pi$
$37$	3.64113	−	5.60686i	0.598599	−	0.921761i	0.999983	−	0.00585148i	$-0.00186259\pi$
$38$	2.65207	−	6.90888i	0.430222	−	1.12077i
$39$	0.606898	+	1.36312i	0.0971815	+	0.218273i
$40$	−1.48765	−	1.66940i	−0.235218	−	0.263955i
$41$	2.48856	−	0.808583i	0.388648	−	0.126279i	−0.108174	−	0.994132i	$-0.534500\pi$
$41$	2.48856	−	0.808583i	0.388648	−	0.126279i	0.496822	+	0.867853i	$0.334500\pi$
$42$	−3.33124	−	3.38698i	−0.514022	−	0.522622i
$43$	−1.41752	−	1.41752i	−0.216170	−	0.216170i	0.590712	−	0.806882i	$-0.298847\pi$
$43$	−1.41752	−	1.41752i	−0.216170	−	0.216170i	−0.806882	+	0.590712i	$0.798847\pi$
$44$	2.45213	+	2.23317i	0.369672	+	0.336664i
$45$	0.352523	+	0.356170i	0.0525510	+	0.0530947i
$46$	−0.241846	−	2.30101i	−0.0356583	−	0.339266i
$47$	−4.65997	+	0.244219i	−0.679726	+	0.0356229i	−0.389075	−	0.921206i	$-0.627205\pi$
$47$	−4.65997	+	0.244219i	−0.679726	+	0.0356229i	−0.290651	+	0.956829i	$0.593872\pi$
$48$	0.815177	+	1.59987i	0.117661	+	0.230922i
$49$	−6.62059	−	2.27327i	−0.945799	−	0.324753i
$50$	4.64921	+	1.83979i	0.657498	+	0.260186i
$51$	−0.536815	+	0.114104i	−0.0751692	+	0.0159777i
$52$	−0.452591	−	0.696929i	−0.0627631	−	0.0966467i
$53$	3.75707	−	4.63959i	0.516073	−	0.637297i	−0.450779	−	0.892636i	$-0.648854\pi$
$53$	3.75707	−	4.63959i	0.516073	−	0.637297i	0.966852	+	0.255339i	$0.0821870\pi$
$54$	2.49217	+	4.31656i	0.339141	+	0.587409i
$55$	−7.14233	−	1.99676i	−0.963072	−	0.269244i
$56$	2.12748	+	1.57284i	0.284297	+	0.210179i
$57$	2.07871	−	13.1244i	0.275331	−	1.73837i
$58$	1.08800	−	0.0570198i	0.142862	−	0.00748707i
$59$	−1.90993	−	2.12119i	−0.248651	−	0.276155i	0.605879	−	0.795557i	$-0.292822\pi$
$59$	−1.90993	−	2.12119i	−0.248651	−	0.276155i	−0.854530	+	0.519402i	$0.826155\pi$
$60$	−3.23605	−	2.37667i	−0.417772	−	0.306826i
$61$	6.10517	+	0.641679i	0.781686	+	0.0821585i	0.486961	−	0.873424i	$-0.338105\pi$
$61$	6.10517	+	0.641679i	0.781686	+	0.0821585i	0.294725	+	0.955582i	$0.404772\pi$
$62$	2.53403	−	1.29115i	0.321822	−	0.163976i
$63$	−0.494588	−	0.327054i	−0.0623122	−	0.0412050i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	1.60441	+	0.937348i	0.199002	+	0.116264i
$66$	5.14047	+	3.00679i	0.632748	+	0.370110i
$67$	−3.93608	−	14.6897i	−0.480869	−	1.79463i	−0.597981	−	0.801510i	$-0.704030\pi$
$67$	−3.93608	−	14.6897i	−0.480869	−	1.79463i	0.117112	−	0.993119i	$-0.462636\pi$
$68$	0.285343	−	0.109533i	0.0346029	−	0.0132828i
$69$	−1.28378	−	3.95108i	−0.154549	−	0.475654i
$70$	−5.83027	−	1.00394i	−0.696851	−	0.119994i
$71$	−9.66390	−	7.02124i	−1.14689	−	0.833268i	−0.158830	−	0.987306i	$-0.550772\pi$
$71$	−9.66390	−	7.02124i	−1.14689	−	0.833268i	−0.988065	+	0.154038i	$0.950772\pi$
$72$	0.141038	+	0.174167i	0.0166215	+	0.0205258i
$73$	−13.6351	−	0.714588i	−1.59587	−	0.0836362i	−0.766468	−	0.642283i	$-0.777987\pi$
$73$	−13.6351	−	0.714588i	−1.59587	−	0.0836362i	−0.829406	+	0.558647i	$0.811321\pi$
$74$	−1.38997	+	6.53932i	−0.161581	+	0.760180i
$75$	8.85245	+	1.49565i	1.02219	+	0.172703i
$76$			7.40041i			0.848885i
$77$	8.75568	+	0.581508i	0.997802	+	0.0662689i
$78$	−1.05508	−	1.05508i	−0.119465	−	0.119465i
$79$	2.30361	−	5.17399i	0.259176	−	0.582119i	−0.736351	−	0.676600i	$-0.763453\pi$
$79$	2.30361	−	5.17399i	0.259176	−	0.582119i	0.995527	+	0.0944811i	$0.0301192\pi$
$80$	1.98710	+	1.02539i	0.222165	+	0.114642i
$81$	6.43845	+	7.15062i	0.715383	+	0.794513i
$82$	−2.03350	+	1.64670i	−0.224563	+	0.181847i
$83$	4.58045	−	0.725472i	0.502770	−	0.0796309i	0.100102	−	0.994977i	$-0.468083\pi$
$83$	4.58045	−	0.725472i	0.502770	−	0.0796309i	0.402668	+	0.915346i	$0.368083\pi$
$84$	4.32377	+	1.96820i	0.471762	+	0.214749i
$85$	−0.459919	+	0.505535i	−0.0498852	+	0.0548330i
$86$	1.83136	+	0.815375i	0.197481	+	0.0879242i
$87$	1.88962	−	0.506322i	0.202589	−	0.0542834i
$88$	−3.08956	−	1.20608i	−0.329348	−	0.128569i
$89$	−0.908036	−	1.57276i	−0.0962516	−	0.166713i	0.813879	−	0.581035i	$-0.197352\pi$
$89$	−0.908036	−	1.57276i	−0.0962516	−	0.166713i	−0.910130	+	0.414322i	$0.864019\pi$
$90$	−0.456749	−	0.206181i	−0.0481455	−	0.0217334i
$91$	−2.08529	−	0.696728i	−0.218597	−	0.0730370i
$92$	1.05039	+	2.06151i	0.109511	+	0.214927i
$93$	3.96861	−	3.21372i	0.411525	−	0.333247i
$94$	4.26293	−	1.89798i	0.439688	−	0.195762i
$95$	−7.43657	−	14.7827i	−0.762976	−	1.51667i
$96$	−1.33438	−	1.20148i	−0.136189	−	0.122625i
$97$	−11.9252	−	1.88876i	−1.21082	−	0.191775i	−0.481807	−	0.876278i	$-0.660019\pi$
$97$	−11.9252	−	1.88876i	−1.21082	−	0.191775i	−0.729010	+	0.684503i	$0.760019\pi$
$98$	6.99552	−	0.250323i	0.706655	−	0.0252865i
$99$	0.705603	+	0.233689i	0.0709157	+	0.0234866i
$100$	−4.99974	−	0.0514633i	−0.499974	−	0.00514633i
$101$	−10.9842	+	1.15448i	−1.09297	+	0.114875i	−0.633816	−	0.773484i	$-0.718512\pi$
$101$	−10.9842	+	1.15448i	−1.09297	+	0.114875i	−0.459149	+	0.888359i	$0.651846\pi$
$102$	0.460269	−	0.298902i	0.0455734	−	0.0295957i
$103$	−7.65464	+	11.7871i	−0.754234	+	1.16142i	0.227982	+	0.973665i	$0.426787\pi$
$103$	−7.65464	+	11.7871i	−0.754234	+	1.16142i	−0.982216	+	0.187753i	$0.939880\pi$
$104$	0.672288	+	0.488445i	0.0659232	+	0.0478960i
$105$	−10.6148	+	0.413309i	−1.03589	+	0.0403348i
$106$	−1.84484	+	5.67785i	−0.179187	+	0.551481i
$107$	0.772806	+	14.7460i	0.0747100	+	1.42555i	0.736792	+	0.676120i	$0.236340\pi$
$107$	0.772806	+	14.7460i	0.0747100	+	1.42555i	−0.662082	+	0.749432i	$0.730327\pi$
$108$	−3.87355	−	3.13674i	−0.372733	−	0.301833i
$109$	15.5164	+	8.95842i	1.48621	+	0.858061i	0.999877	−	0.0157152i	$-0.00500250\pi$
$109$	15.5164	+	8.95842i	1.48621	+	0.858061i	0.486329	+	0.873776i	$0.338336\pi$
$110$	7.38352	−	0.695444i	0.703991	−	0.0663079i
$111$			12.0042i			1.13939i
$112$	−2.54983	−	0.705948i	−0.240936	−	0.0667058i
$113$	2.94229	−	5.77456i	0.276787	−	0.543225i	−0.710205	−	0.703995i	$-0.751398\pi$
$113$	2.94229	−	5.77456i	0.276787	−	0.543225i	0.986992	+	0.160770i	$0.0513977\pi$
$114$	2.76274	+	12.9977i	0.258754	+	1.21734i
$115$	−4.16979	−	3.06244i	−0.388835	−	0.285574i
$116$	−0.995304	+	0.443138i	−0.0924117	+	0.0411443i
$117$	−0.156190	−	0.101431i	−0.0144398	−	0.00937729i
$118$	2.54324	+	1.29584i	0.234124	+	0.119292i
$119$	0.410125	−	0.696940i	0.0375961	−	0.0638883i
$120$	3.87283	+	1.05911i	0.353540	+	0.0966835i
$121$	−10.7848	+	2.16505i	−0.980439	+	0.196823i
$122$	−5.92962	+	1.58884i	−0.536843	+	0.143847i
$123$	−2.95678	+	3.65132i	−0.266604	+	0.329228i
$124$	−1.90301	+	2.11351i	−0.170895	+	0.189799i
$125$	10.0389	−	4.92137i	0.897909	−	0.440180i
$126$	0.578943	+	0.128087i	0.0515764	+	0.0114109i
$127$	−5.99086	+	0.948858i	−0.531603	+	0.0841976i	−0.416465	−	0.909152i	$-0.636731\pi$
$127$	−5.99086	+	0.948858i	−0.531603	+	0.0841976i	−0.115138	+	0.993350i	$0.536731\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	3.52090	+	0.748391i	0.309998	+	0.0658921i
$130$	−1.83376	−	0.300121i	−0.160831	−	0.0263224i
$131$	−18.6884	+	10.7897i	−1.63281	+	0.942704i	−0.649590	+	0.760285i	$0.725059\pi$
$131$	−18.6884	+	10.7897i	−1.63281	+	0.942704i	−0.983221	+	0.182419i	$0.941607\pi$
$132$	−5.87658	−	0.964896i	−0.511491	−	0.0839834i
$133$	12.1952	+	15.3179i	1.05746	+	1.32823i
$134$	8.93896	+	12.3034i	0.772208	+	1.06285i
$135$	10.8897	+	2.37331i	0.937235	+	0.204262i
$136$	−0.227138	+	0.204516i	−0.0194769	+	0.0175371i
$137$	2.14823	−	5.59634i	0.183536	−	0.478128i	−0.810685	−	0.585483i	$-0.800905\pi$
$137$	2.14823	−	5.59634i	0.183536	−	0.478128i	0.994221	+	0.107355i	$0.0342383\pi$
$138$	2.61446	+	3.22858i	0.222557	+	0.274835i
$139$	5.24545	−	16.1438i	0.444913	−	1.36930i	−0.437665	−	0.899138i	$-0.644195\pi$
$139$	5.24545	−	16.1438i	0.444913	−	1.36930i	0.882579	−	0.470165i	$-0.155805\pi$
$140$	5.80281	−	1.15213i	0.490427	−	0.0973724i
$141$	6.77862	−	4.92495i	0.570863	−	0.414756i
$142$	11.5382	+	3.09166i	0.968266	+	0.259446i
$143$	2.75145	+	0.159823i	0.230088	+	0.0133651i
$144$	−0.194086	−	0.112056i	−0.0161739	−	0.00933798i
$145$	1.54287	−	1.88536i	0.128128	−	0.156570i
$146$	12.9856	−	4.21927i	1.07470	−	0.349190i
$147$	12.1931	−	3.05124i	1.00567	−	0.251662i
$148$	−1.04583	−	6.60310i	−0.0859666	−	0.542771i
$149$	22.8167	+	2.39814i	1.86922	+	0.196463i	0.970342	−	0.241735i	$-0.0777165\pi$
$149$	22.8167	+	2.39814i	1.86922	+	0.196463i	0.898878	+	0.438198i	$0.144383\pi$
$150$	−8.80046	+	1.77613i	−0.718555	+	0.145020i
$151$	2.14706	+	0.456373i	0.174726	+	0.0371391i	0.294444	−	0.955669i	$-0.404866\pi$
$151$	2.14706	+	0.456373i	0.174726	+	0.0371391i	−0.119718	+	0.992808i	$0.538199\pi$
$152$	−2.65207	−	6.90888i	−0.215111	−	0.560384i
$153$	0.0484356	−	0.0484356i	0.00391579	−	0.00391579i
$154$	−8.38252	+	2.59487i	−0.675483	+	0.209101i
$155$	1.67752	−	6.13415i	0.134742	−	0.492707i
$156$	1.36312	+	0.606898i	0.109137	+	0.0485907i
$157$	8.61914	+	13.2723i	0.687882	+	1.05925i	0.994224	+	0.107324i	$0.0342282\pi$
$157$	8.61914	+	13.2723i	0.687882	+	1.05925i	−0.306342	+	0.951921i	$0.599105\pi$
$158$	−0.296412	+	5.65587i	−0.0235813	+	0.449957i
$159$	−1.12051	+	10.6610i	−0.0888624	+	0.845470i
$160$	−2.22259	−	0.245174i	−0.175711	−	0.0193827i
$161$	5.57137	+	2.53612i	0.439085	+	0.199874i
$162$	−8.57336	−	4.36835i	−0.673587	−	0.343210i
$163$	1.23210	+	3.20972i	0.0965052	+	0.251405i	0.973332	−	0.229402i	$-0.0736771\pi$
$163$	1.23210	+	3.20972i	0.0965052	+	0.251405i	−0.876827	+	0.480807i	$0.840344\pi$
$164$	1.30831	−	2.26607i	0.102162	−	0.176950i
$165$	12.7084	−	3.97787i	0.989345	−	0.309677i
$166$	−4.01623	+	2.31877i	−0.311720	+	0.179972i
$167$	−20.2529	−	3.20774i	−1.56722	−	0.248223i	−0.688382	−	0.725349i	$-0.741679\pi$
$167$	−20.2529	−	3.20774i	−1.56722	−	0.248223i	−0.878835	+	0.477126i	$0.841679\pi$
$168$	−4.74192	−	0.287978i	−0.365847	−	0.0222180i
$169$	11.7070	+	3.80383i	0.900537	+	0.292602i
$170$	0.248203	−	0.636778i	0.0190363	−	0.0488386i
$171$	0.674580	+	1.51513i	0.0515864	+	0.115865i
$172$	−2.00193	−	0.104917i	−0.152646	−	0.00799982i
$173$	0.512724	+	9.78335i	0.0389817	+	0.743815i	0.946284	+	0.323336i	$0.104804\pi$
$173$	0.512724	+	9.78335i	0.0389817	+	0.743815i	−0.907303	+	0.420478i	$0.861862\pi$
$174$	−1.58266	+	1.14987i	−0.119981	+	0.0871716i
$175$	−10.4336	+	8.13259i	−0.788709	+	0.614766i
$176$	3.31657	+	0.0187778i	0.249996	+	0.00141543i
$177$	4.95056	+	1.32650i	0.372107	+	0.0997058i
$178$	1.41135	+	1.14289i	0.105785	+	0.0856633i
$179$	2.65834	−	12.5065i	0.198694	−	0.934780i	−0.759908	−	0.650030i	$-0.774756\pi$
$179$	2.65834	−	12.5065i	0.198694	−	0.934780i	0.958602	−	0.284750i	$-0.0919106\pi$
$180$	0.500300	+	0.0288022i	0.0372902	+	0.00214679i
$181$	−7.08946	+	9.75780i	−0.526955	+	0.725292i	−0.986663	−	0.162779i	$-0.947954\pi$
$181$	−7.08946	+	9.75780i	−0.526955	+	0.725292i	0.459707	+	0.888070i	$0.347954\pi$
$182$	2.19647	−	0.0968477i	0.162813	−	0.00717883i
$183$	−9.82130	+	5.00420i	−0.726011	+	0.369921i
$184$	−1.71940	−	1.54816i	−0.126756	−	0.114132i
$185$	8.72446	+	12.1391i	0.641435	+	0.892483i
$186$	−2.55332	+	4.42248i	−0.187219	+	0.324272i
$187$	−0.267906	+	0.977663i	−0.0195912	+	0.0714938i
$188$	−3.29962	+	3.29962i	−0.240649	+	0.240649i
$189$	−13.1869	−	0.109399i	−0.959202	−	0.00795763i
$190$	12.2403	+	11.1358i	0.888003	+	0.807875i
$191$	−9.42835	+	2.00406i	−0.682212	+	0.145009i	−0.535966	−	0.844240i	$-0.680052\pi$
$191$	−9.42835	+	2.00406i	−0.682212	+	0.145009i	−0.146246	+	0.989248i	$0.546719\pi$
$192$	1.67632	+	0.643479i	0.120978	+	0.0464391i
$193$	−9.24312	−	3.54810i	−0.665334	−	0.255398i	0.00217693	−	0.999998i	$-0.499307\pi$
$193$	−9.24312	−	3.54810i	−0.665334	−	0.255398i	−0.667511	+	0.744600i	$0.732640\pi$
$194$	11.8100	−	2.51029i	0.847906	−	0.180228i
$195$	−3.33275	+	0.157468i	−0.238663	+	0.0112765i
$196$	−6.44118	+	2.74067i	−0.460084	+	0.195762i
$197$	−11.3172	+	11.3172i	−0.806320	+	0.806320i	−0.984075	−	0.177755i	$-0.943117\pi$
$197$	−11.3172	+	11.3172i	−0.806320	+	0.806320i	0.177755	+	0.984075i	$0.443117\pi$
$198$	−0.742483	+	0.0346978i	−0.0527660	+	0.00246587i
$199$	−4.89332	+	8.47548i	−0.346878	+	0.600811i	−0.985693	−	0.168550i	$-0.946092\pi$
$199$	−4.89332	+	8.47548i	−0.346878	+	0.600811i	0.638815	+	0.769360i	$0.279425\pi$
$200$	4.68610	−	1.74370i	0.331357	−	0.123298i
$201$	20.2930	+	18.2719i	1.43136	+	1.28880i
$202$	9.84087	−	5.01418i	0.692401	−	0.352796i
$203$	−1.32991	+	2.55741i	−0.0933411	+	0.179495i
$204$	−0.322581	+	0.443995i	−0.0225852	+	0.0310859i
$205$	−0.336282	+	5.84129i	−0.0234869	+	0.407973i
$206$	2.92210	−	13.7474i	0.203592	−	0.957826i
$207$	0.402969	+	0.326318i	0.0280083	+	0.0226806i
$208$	−0.802678	−	0.215077i	−0.0556557	−	0.0149129i
$209$	−19.7748	−	14.5390i	−1.36785	−	1.00568i
$210$	9.76161	−	4.18985i	0.673615	−	0.289127i
$211$	−19.1874	+	13.9405i	−1.32092	+	0.959702i	−0.320996	+	0.947080i	$0.604018\pi$
$211$	−19.1874	+	13.9405i	−1.32092	+	0.959702i	−0.999920	+	0.0126216i	$0.995982\pi$
$212$	−0.312448	−	5.96186i	−0.0214590	−	0.409462i
$213$	21.4193	+	1.12254i	1.46762	+	0.0769149i
$214$	−6.00598	−	13.4896i	−0.410560	−	0.922133i
$215$	4.10438	−	1.80214i	0.279917	−	0.122905i
$216$	4.74038	+	1.54024i	0.322542	+	0.104800i
$217$	−0.456127	+	7.51070i	−0.0309639	+	0.509859i
$218$	−17.6963	−	2.80281i	−1.19854	−	0.189830i
$219$	21.2320	−	12.2583i	1.43473	−	0.828340i
$220$	−6.64388	+	3.29527i	−0.447931	+	0.222167i
$221$	0.126994	−	0.219960i	0.00854254	−	0.0147961i
$222$	−4.30192	−	11.2069i	−0.288726	−	0.752156i
$223$	6.79358	+	3.46150i	0.454932	+	0.231799i	0.666413	−	0.745583i	$-0.267829\pi$
$223$	6.79358	+	3.46150i	0.454932	+	0.231799i	−0.211481	+	0.977382i	$0.567829\pi$
$224$	2.63346	−	0.254718i	0.175956	−	0.0170191i
$225$	−1.02832	+	0.445211i	−0.0685545	+	0.0296807i
$226$	−0.677443	+	6.44544i	−0.0450628	+	0.428744i
$227$	−0.736057	+	14.0448i	−0.0488538	+	0.932186i	0.858760	+	0.512379i	$0.171236\pi$
$227$	−0.736057	+	14.0448i	−0.0488538	+	0.932186i	−0.907613	+	0.419807i	$0.862098\pi$
$228$	−7.23718	−	11.1443i	−0.479294	−	0.738048i
$229$	−1.14082	−	0.507924i	−0.0753873	−	0.0335646i	0.368697	−	0.929550i	$-0.379804\pi$
$229$	−1.14082	−	0.507924i	−0.0753873	−	0.0335646i	−0.444084	+	0.895985i	$0.646471\pi$
$230$	4.99032	+	1.36472i	0.329052	+	0.0899867i
$231$	−13.7539	+	7.68686i	−0.904938	+	0.505758i
$232$	0.770390	−	0.770390i	0.0505786	−	0.0505786i
$233$	1.98995	+	5.18399i	0.130366	+	0.339615i	0.983190	−	0.182583i	$-0.0584458\pi$
$233$	1.98995	+	5.18399i	0.130366	+	0.339615i	−0.852825	+	0.522197i	$0.825112\pi$
$234$	0.182165	+	0.0387205i	0.0119085	+	0.00253124i
$235$	3.27541	−	9.90689i	0.213664	−	0.646254i
$236$	−2.83871	−	0.298360i	−0.184784	−	0.0194216i
$237$	1.59086	+	10.0443i	0.103338	+	0.652448i
$238$	−0.133123	+	0.797625i	−0.00862911	+	0.0517023i
$239$	12.5553	−	4.07946i	0.812134	−	0.263878i	0.126632	−	0.991950i	$-0.459583\pi$
$239$	12.5553	−	4.07946i	0.812134	−	0.263878i	0.685501	+	0.728071i	$0.259583\pi$
$240$	−3.99515	+	0.399131i	−0.257886	+	0.0257638i
$241$	20.2407	+	11.6859i	1.30382	+	0.752758i	0.981056	−	0.193723i	$-0.0620564\pi$
$241$	20.2407	+	11.6859i	1.30382	+	0.752758i	0.322759	+	0.946481i	$0.395390\pi$
$242$	9.29262	−	5.88618i	0.597352	−	0.378378i
$243$	−2.24508	−	0.601567i	−0.144022	−	0.0385906i
$244$	4.96639	−	3.60829i	0.317940	−	0.230997i
$245$	10.1125	−	11.9473i	0.646064	−	0.763283i
$246$	1.45188	−	4.46841i	0.0925682	−	0.284896i
$247$	3.87012	+	4.77921i	0.246250	+	0.304094i
$248$	1.01920	−	2.65511i	0.0647193	−	0.168600i
$249$	−6.18824	+	5.57191i	−0.392164	+	0.353106i
$250$	−7.60849	+	8.19212i	−0.481203	+	0.518115i
$251$	7.82203	+	10.7661i	0.493722	+	0.679550i	0.981069	−	0.193658i	$-0.0620353\pi$
$251$	7.82203	+	10.7661i	0.493722	+	0.679550i	−0.487347	+	0.873208i	$0.662035\pi$
$252$	−0.586392	+	0.0878952i	−0.0369393	+	0.00553688i
$253$	−7.57224	−	1.24331i	−0.476062	−	0.0781664i
$254$	5.25291	−	3.03277i	0.329597	−	0.190293i
$255$	0.198207	−	1.21106i	0.0124122	−	0.0758395i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−6.46284	−	4.19702i	−0.403141	−	0.261803i	0.327104	−	0.944988i	$-0.393927\pi$
$257$	−6.46284	−	4.19702i	−0.403141	−	0.261803i	−0.730245	+	0.683186i	$0.760594\pi$
$258$	−3.55524	+	0.563095i	−0.221340	+	0.0350568i
$259$	−13.0461	−	11.9442i	−0.810642	−	0.742175i
$260$	1.81952	−	0.376974i	0.112842	−	0.0233789i
$261$	−0.163381	+	0.181453i	−0.0101130	+	0.0112316i
$262$	13.5804	−	16.7704i	0.839000	−	1.03608i
$263$	−18.8400	+	5.04816i	−1.16172	+	0.311283i	−0.787654	−	0.616118i	$-0.788704\pi$
$263$	−18.8400	+	5.04816i	−1.16172	+	0.311283i	−0.374069	+	0.927401i	$0.622038\pi$
$264$	5.83205	−	1.20517i	0.358938	−	0.0741731i
$265$	6.61512	+	11.5951i	0.406364	+	0.712283i
$266$	−16.8747	−	9.93015i	−1.03465	−	0.608857i
$267$	2.90549	+	1.48042i	0.177813	+	0.0906002i
$268$	−12.7544	−	8.28280i	−0.779098	−	0.505952i
$269$	3.82398	−	1.70254i	0.233152	−	0.103806i	−0.286835	−	0.957980i	$-0.592603\pi$
$269$	3.82398	−	1.70254i	0.233152	−	0.103806i	0.519987	+	0.854174i	$0.325937\pi$
$270$	−11.0169	+	1.68684i	−0.670468	+	0.102658i
$271$	−4.93882	−	23.2353i	−0.300012	−	1.41145i	−0.827301	−	0.561759i	$-0.810125\pi$
$271$	−4.93882	−	23.2353i	−0.300012	−	1.41145i	0.527289	−	0.849686i	$-0.323209\pi$
$272$	0.138759	−	0.272331i	0.00841352	−	0.0165125i
$273$	3.82159	−	0.990088i	0.231293	−	0.0599229i
$274$			5.99449i			0.362140i
$275$	9.96011	−	13.2588i	0.600617	−	0.799537i
$276$	−3.59783	−	2.07721i	−0.216564	−	0.125033i
$277$	−14.2272	−	11.5209i	−0.854829	−	0.692227i	0.0981803	−	0.995169i	$-0.468698\pi$
$277$	−14.2272	−	11.5209i	−0.854829	−	0.692227i	−0.953009	+	0.302942i	$0.902031\pi$
$278$	0.888384	+	16.9514i	0.0532817	+	1.01668i
$279$	−0.196960	+	0.606179i	−0.0117917	+	0.0362910i
$280$	−5.00451	+	3.15514i	−0.299076	+	0.188556i
$281$	−0.0831910	−	0.0604418i	−0.00496276	−	0.00360565i	0.585301	−	0.810816i	$-0.300976\pi$
$281$	−0.0831910	−	0.0604418i	−0.00496276	−	0.00360565i	−0.590264	+	0.807210i	$0.700976\pi$
$282$	−4.56344	+	7.02708i	−0.271749	+	0.418457i
$283$	−2.58779	+	1.68053i	−0.153828	+	0.0998971i	−0.619258	−	0.785188i	$-0.712566\pi$
$283$	−2.58779	+	1.68053i	−0.153828	+	0.0998971i	0.465430	+	0.885085i	$0.345900\pi$
$284$	−11.8798	+	1.24862i	−0.704937	+	0.0740918i
$285$	25.6554	+	14.9887i	1.51969	+	0.887854i
$286$	−2.62598	+	0.836825i	−0.155277	+	0.0494825i
$287$	−1.02623	−	6.84646i	−0.0605762	−	0.404134i
$288$	0.221352	+	0.0350588i	0.0130433	+	0.00206586i
$289$	−12.5640	−	11.3127i	−0.739061	−	0.665454i
$290$	−0.764737	+	2.31305i	−0.0449069	+	0.135827i
$291$	19.8052	−	8.81785i	1.16100	−	0.516912i
$292$	−10.6110	+	8.59265i	−0.620964	+	0.502847i
$293$	−2.69622	−	5.29162i	−0.157515	−	0.309140i	0.798740	−	0.601677i	$-0.205501\pi$
$293$	−2.69622	−	5.29162i	−0.157515	−	0.309140i	−0.956254	+	0.292537i	$0.905501\pi$
$294$	−10.2898	+	7.21819i	−0.600111	+	0.420973i
$295$	5.97027	−	2.25659i	0.347603	−	0.131384i
$296$	3.34270	+	5.78973i	0.194291	+	0.336521i
$297$	15.9918	−	4.18811i	0.927941	−	0.243019i
$298$	−22.1607	+	5.93794i	−1.28373	+	0.343975i
$299$	1.75644	+	0.782015i	0.101577	+	0.0452251i
$300$	7.57943	−	4.81196i	0.437599	−	0.277819i
$301$	−4.31664	+	3.08184i	−0.248807	+	0.177634i
$302$	−2.16801	+	0.343379i	−0.124755	+	0.0197592i
$303$	15.4120	−	12.4804i	0.885399	−	0.716982i
$304$	4.95184	+	5.49958i	0.284008	+	0.315422i
$305$	−6.29468	+	12.1984i	−0.360432	+	0.698478i
$306$	−0.0278608	+	0.0625763i	−0.00159269	+	0.00357725i
$307$	2.62276	+	2.62276i	0.149689	+	0.149689i	0.777979	−	0.628290i	$-0.216245\pi$
$307$	2.62276	+	2.62276i	0.149689	+	0.149689i	−0.628290	+	0.777979i	$0.716245\pi$
$308$	6.89584	−	5.42655i	0.392927	−	0.309206i
$309$		−	25.2360i		−	1.43563i
$310$	0.632180	+	6.32789i	0.0359054	+	0.359400i
$311$	2.92099	−	13.7422i	0.165634	−	0.779246i	−0.814382	−	0.580329i	$-0.802924\pi$
$311$	2.92099	−	13.7422i	0.165634	−	0.779246i	0.980016	−	0.198918i	$-0.0637426\pi$
$312$	−1.49007	−	0.0780913i	−0.0843586	−	0.00442105i
$313$	10.2330	+	12.6367i	0.578404	+	0.714269i	0.979427	−	0.201799i	$-0.0646787\pi$
$313$	10.2330	+	12.6367i	0.578404	+	0.714269i	−0.401023	+	0.916068i	$0.631345\pi$
$314$	−12.8030	−	9.30194i	−0.722517	−	0.524939i
$315$	1.08302	−	0.764833i	0.0610214	−	0.0430935i
$316$	−1.75016	−	5.38644i	−0.0984542	−	0.303011i
$317$	13.8359	−	5.31111i	0.777103	−	0.298302i	0.0626963	−	0.998033i	$-0.480030\pi$
$317$	13.8359	−	5.31111i	0.777103	−	0.298302i	0.714407	+	0.699731i	$0.246697\pi$
$318$	−2.77446	−	10.3544i	−0.155584	−	0.580647i
$319$	0.771278	−	3.53018i	0.0431833	−	0.197652i
$320$	2.16283	−	0.567614i	0.120906	−	0.0317306i
$321$	−15.5845	−	21.4503i	−0.869844	−	1.19724i
$322$	−6.11018	−	0.371073i	−0.340507	−	0.0206791i
$323$	−2.01536	+	1.02688i	−0.112138	+	0.0571369i
$324$	9.56940	+	1.00578i	0.531633	+	0.0558769i
$325$	−3.25576	+	2.58143i	−0.180597	+	0.143192i
$326$	−2.30052	−	2.55499i	−0.127414	−	0.141508i
$327$	−32.1270	+	1.68371i	−1.77663	+	0.0931092i
$328$	−0.409331	+	2.58441i	−0.0226015	+	0.142700i
$329$	−1.39233	+	12.2673i	−0.0767615	+	0.676317i
$330$	−10.4387	+	8.26793i	−0.574634	+	0.455135i
$331$	−11.5982	−	20.0887i	−0.637497	−	1.10418i	−0.985980	−	0.166862i	$-0.946637\pi$
$331$	−11.5982	−	20.0887i	−0.637497	−	1.10418i	0.348484	−	0.937315i	$-0.386697\pi$
$332$	2.91850	−	3.60405i	0.160174	−	0.197798i
$333$	−0.816020	−	1.25656i	−0.0447176	−	0.0688591i
$334$	20.0573	−	4.26330i	1.09748	−	0.233278i
$335$	33.8008	+	3.72858i	1.84673	+	0.203714i
$336$	4.53017	−	1.43050i	0.247141	−	0.0780403i
$337$	−3.09618	−	6.07659i	−0.168660	−	0.331013i	0.791170	−	0.611596i	$-0.209472\pi$
$337$	−3.09618	−	6.07659i	−0.168660	−	0.331013i	−0.959830	+	0.280583i	$0.909472\pi$
$338$	−12.2926	+	0.644227i	−0.668628	+	0.0350413i
$339$	1.21640	+	11.5733i	0.0660660	+	0.628576i
$340$	−0.00351726	+	0.683431i	−0.000190750	+	0.0370643i
$341$	−1.90886	−	9.23733i	−0.103370	−	0.500230i
$342$	−1.17275	−	1.17275i	−0.0634150	−	0.0634150i
$343$	−8.81606	+	16.2873i	−0.476023	+	0.879433i
$344$	1.90656	−	0.619479i	0.102795	−	0.0334001i
$345$	9.27419	+	0.533913i	0.499306	+	0.0287449i
$346$	−3.98471	−	8.94980i	−0.214219	−	0.481144i
$347$	0.710577	−	1.85112i	0.0381458	−	0.0993732i	−0.913184	−	0.407547i	$-0.866384\pi$
$347$	0.710577	−	1.85112i	0.0381458	−	0.0993732i	0.951330	+	0.308173i	$0.0997177\pi$
$348$	1.06547	−	1.64067i	0.0571150	−	0.0879493i
$349$	−0.414956	−	1.27710i	−0.0222121	−	0.0683618i	0.939336	−	0.342998i	$-0.111442\pi$
$349$	−0.414956	−	1.27710i	−0.0222121	−	0.0683618i	−0.961548	+	0.274636i	$0.911442\pi$
$350$	6.82618	−	11.3315i	0.364875	−	0.605695i
$351$	−4.14195			−0.221081
$352$	−3.10302	+	1.17102i	−0.165391	+	0.0624157i
$353$	5.05947	+	18.8822i	0.269289	+	1.00500i	0.959573	+	0.281461i	$0.0908189\pi$
$353$	5.05947	+	18.8822i	0.269289	+	1.00500i	−0.690284	+	0.723538i	$0.742514\pi$
$354$	−5.09713	+	0.535729i	−0.270909	+	0.0284737i
$355$	22.4758	−	14.4320i	1.19289	−	0.765973i
$356$	−1.72719	−	0.561197i	−0.0915407	−	0.0297434i
$357$	0.0639606	+	1.45060i	0.00338516	+	0.0767739i
$358$	2.00016	+	12.6285i	0.105712	+	0.667437i
$359$	3.01754	+	14.1964i	0.159260	+	0.749258i	0.983193	+	0.182571i	$0.0584419\pi$
$359$	3.01754	+	14.1964i	0.159260	+	0.749258i	−0.823933	+	0.566687i	$0.808225\pi$
$360$	−0.477392	+	0.152402i	−0.0251608	+	0.00803231i
$361$	−3.73857	−	35.5701i	−0.196767	−	1.87211i
$362$	3.12170	−	11.6503i	0.164073	−	0.612328i
$363$	14.1236	−	13.8073i	0.741296	−	0.724695i
$364$	−2.01587	+	0.877559i	−0.105660	+	0.0459966i
$365$	12.5614	−	27.8271i	0.657496	−	1.45654i
$366$	7.37563	−	8.19146i	0.385530	−	0.428175i
$367$	1.41198	−	26.9422i	0.0737048	−	1.40637i	−0.672225	−	0.740347i	$-0.734661\pi$
$367$	1.41198	−	26.9422i	0.0737048	−	1.40637i	0.745930	−	0.666025i	$-0.232006\pi$
$368$	2.16001	+	0.829151i	0.112598	+	0.0432225i
$369$	0.0612972	−	0.583204i	0.00319101	−	0.0303604i
$370$	−12.4952	−	8.20624i	−0.649597	−	0.426622i
$371$	−10.4713	−	11.8254i	−0.543645	−	0.613946i
$372$	0.798855	−	5.04377i	0.0414187	−	0.261507i
$373$	1.50466	−	5.61547i	0.0779084	−	0.290758i	−0.915969	−	0.401250i	$-0.868576\pi$
$373$	1.50466	−	5.61547i	0.0779084	−	0.290758i	0.993877	+	0.110492i	$0.0352426\pi$
$374$	−0.100252	−	1.00874i	−0.00518388	−	0.0521605i
$375$	−10.3048	+	17.2286i	−0.532139	+	0.889681i
$376$	1.89798	−	4.26293i	0.0978809	−	0.219844i
$377$	−0.411027	+	0.806685i	−0.0211689	+	0.0415464i
$378$	12.3502	−	4.62361i	0.635225	−	0.237813i
$379$	−12.8102	+	17.6317i	−0.658015	+	0.905680i	−0.999414	−	0.0342389i	$-0.989099\pi$
$379$	−12.8102	+	17.6317i	−0.658015	+	0.905680i	0.341399	+	0.939918i	$0.389099\pi$
$380$	−15.4180	−	6.00963i	−0.790926	−	0.308288i
$381$	8.09371	−	7.28761i	0.414653	−	0.373355i
$382$	8.08393	−	5.24977i	0.413610	−	0.268602i
$383$	−9.69906	+	3.72312i	−0.495599	+	0.190243i	−0.593313	−	0.804972i	$-0.702180\pi$
$383$	−9.69906	+	3.72312i	−0.495599	+	0.190243i	0.0977140	+	0.995215i	$0.468847\pi$
$384$	−1.79558			−0.0916304
$385$	−8.32171	+	17.7693i	−0.424114	+	0.905609i
$386$	9.90072			0.503933
$387$	−0.419431	+	0.161004i	−0.0213209	+	0.00818431i
$388$	−10.1259	+	6.57587i	−0.514067	+	0.333839i
$389$	−22.9845	+	20.6954i	−1.16536	+	1.04930i	−0.167374	+	0.985893i	$0.553529\pi$
$389$	−22.9845	+	20.6954i	−1.16536	+	1.04930i	−0.997988	+	0.0634033i	$0.979805\pi$
$390$	3.05496	−	1.34136i	0.154694	−	0.0679225i
$391$	−0.415661	+	0.572108i	−0.0210209	+	0.0289327i
$392$	5.03119	−	4.86694i	0.254113	−	0.245818i
$393$	17.5911	−	34.5244i	0.887353	−	1.74153i
$394$	6.50982	−	14.6213i	0.327960	−	0.736610i
$395$	8.90879	+	9.00096i	0.448250	+	0.452888i
$396$	0.680733	−	0.298475i	0.0342081	−	0.0149990i
$397$	−1.91079	+	7.13117i	−0.0958998	+	0.357903i	−0.997154	−	0.0753870i	$-0.975981\pi$
$397$	−1.91079	+	7.13117i	−0.0958998	+	0.357903i	0.901255	+	0.433290i	$0.142647\pi$
$398$	1.53097	−	9.66615i	0.0767405	−	0.484520i
$399$	−33.3449	−	11.1411i	−1.66933	−	0.557751i
$400$	−3.74996	+	3.30723i	−0.187498	+	0.165362i
$401$	−1.91156	+	18.1872i	−0.0954585	+	0.908227i	0.837062	+	0.547109i	$0.184272\pi$
$401$	−1.91156	+	18.1872i	−0.0954585	+	0.908227i	−0.932520	+	0.361118i	$0.882395\pi$
$402$	−25.4932	−	9.78594i	−1.27149	−	0.488078i
$403$	−0.123688	+	2.36011i	−0.00616135	+	0.117565i
$404$	−7.39033	+	8.20779i	−0.367683	+	0.408353i
$405$	−20.1260	+	7.60706i	−1.00007	+	0.377998i
$406$	0.325079	−	2.86415i	0.0161334	−	0.142145i
$407$	19.6990	+	10.1780i	0.976442	+	0.504506i
$408$	0.142042	−	0.530108i	0.00703213	−	0.0262443i
$409$	−1.65224	−	15.7200i	−0.0816981	−	0.777306i	−0.956285	−	0.292437i	$-0.905534\pi$
$409$	−1.65224	−	15.7200i	−0.0816981	−	0.777306i	0.874587	−	0.484869i	$-0.161133\pi$
$410$	−1.77938	−	5.57382i	−0.0878775	−	0.275272i
$411$	2.23788	+	10.5284i	0.110386	+	0.519327i
$412$	2.19861	+	13.8815i	0.108318	+	0.683892i
$413$	−6.36744	+	4.06036i	−0.313321	+	0.199797i
$414$	−0.493145	−	0.160233i	−0.0242368	−	0.00787501i
$415$	−2.20819	+	10.1320i	−0.108396	+	0.497362i
$416$	0.826441	−	0.0868624i	0.0405196	−	0.00425878i
$417$	7.88863	+	29.4408i	0.386308	+	1.44172i
$418$	23.6717	+	6.48668i	1.15782	+	0.317274i
$419$	6.56853			0.320894			0.160447	−	0.987044i	$-0.448706\pi$
$419$	6.56853			0.320894			0.160447	+	0.987044i	$0.448706\pi$
$420$	−7.61174	+	7.40981i	−0.371415	+	0.361562i
$421$	−1.56572	−	4.81878i	−0.0763084	−	0.234853i	0.905625	−	0.424079i	$-0.139402\pi$
$421$	−1.56572	−	4.81878i	−0.0763084	−	0.234853i	−0.981934	+	0.189226i	$0.939402\pi$
$422$	12.9172	−	19.8907i	0.628799	−	0.968265i
$423$	−0.374776	+	0.976325i	−0.0182222	+	0.0474705i
$424$	2.42823	+	5.45390i	0.117925	+	0.264865i
$425$	−0.679745	−	1.36872i	−0.0329725	−	0.0663928i
$426$	−20.3989	+	6.62800i	−0.988329	+	0.321128i
$427$	4.33367	−	15.6529i	0.209721	−	0.757496i
$428$	10.4413	+	10.4413i	0.504700	+	0.504700i
$429$	−4.29972	+	2.45009i	−0.207592	+	0.118291i
$430$	−3.18594	+	3.15332i	−0.153640	+	0.152066i
$431$	3.23050	+	30.7361i	0.155608	+	1.48051i	0.741956	+	0.670448i	$0.233898\pi$
$431$	3.23050	+	30.7361i	0.155608	+	1.48051i	−0.586349	+	0.810059i	$0.699435\pi$
$432$	−4.97750	+	0.260860i	−0.239480	+	0.0125506i
$433$	−11.5374	−	22.6434i	−0.554451	−	1.08817i	−0.982820	−	0.184568i	$-0.940912\pi$
$433$	−11.5374	−	22.6434i	−0.554451	−	1.08817i	0.428369	−	0.903604i	$-0.359088\pi$
$434$	−2.26576	−	7.17530i	−0.108760	−	0.344425i
$435$	−0.479629	+	4.34800i	−0.0229965	+	0.208471i
$436$	17.5253	−	3.72512i	0.839310	−	0.178401i
$437$	−9.32543	−	14.3599i	−0.446096	−	0.686928i
$438$	−15.4288	+	19.0530i	−0.737217	+	0.910387i
$439$	11.0280	+	19.1010i	0.526336	+	0.911640i	0.999529	+	0.0306818i	$0.00976787\pi$
$439$	11.0280	+	19.1010i	0.526336	+	0.911640i	−0.473193	+	0.880959i	$0.656899\pi$
$440$	5.02168	−	5.45735i	0.239399	−	0.260169i
$441$	−1.06892	+	1.14825i	−0.0509008	+	0.0546788i
$442$	−0.0397325	+	0.250861i	−0.00188988	+	0.0119322i
$443$	−11.6708	+	0.611642i	−0.554497	+	0.0290600i	−0.327527	−	0.944842i	$-0.606215\pi$
$443$	−11.6708	+	0.611642i	−0.554497	+	0.0290600i	−0.226970	+	0.973902i	$0.572882\pi$
$444$	8.03237	+	8.92085i	0.381200	+	0.423365i
$445$	4.01408	−	0.614609i	0.190286	−	0.0291352i
$446$	−7.58284	−	0.796989i	−0.359058	−	0.0377385i
$447$	−36.7050	+	18.7021i	−1.73609	+	0.884581i
$448$	−2.36727	+	1.18155i	−0.111843	+	0.0558229i
$449$	−1.89148	−	2.60340i	−0.0892646	−	0.122862i	0.762049	−	0.647519i	$-0.224194\pi$
$449$	−1.89148	−	2.60340i	−0.0892646	−	0.122862i	−0.851314	+	0.524657i	$0.824194\pi$
$450$	0.800467	−	0.784156i	0.0377344	−	0.0369655i
$451$	3.48487	+	7.94795i	0.164096	+	0.374254i
$452$	−1.67739	−	6.26011i	−0.0788978	−	0.294451i
$453$	−3.67957	+	1.41246i	−0.172881	+	0.0663630i
$454$	−4.34604	−	13.3757i	−0.203970	−	0.627754i
$455$	3.14496	−	3.77869i	0.147438	−	0.177148i
$456$	10.7502	+	7.81051i	0.503426	+	0.365761i
$457$	3.38299	+	4.17764i	0.158250	+	0.195422i	0.850104	−	0.526615i	$-0.176539\pi$
$457$	3.38299	+	4.17764i	0.158250	+	0.195422i	−0.691854	+	0.722037i	$0.743206\pi$
$458$	1.24707	+	0.0653561i	0.0582717	+	0.00305389i
$459$	0.316739	−	1.49014i	0.0147841	−	0.0695538i
$460$	−5.14793	+	0.514298i	−0.240024	+	0.0239793i
$461$			0.181802i			0.00846736i	0.999991	+	0.00423368i	$0.00134763\pi$
$461$			0.181802i			0.00846736i	−0.999991	+	0.00423368i	$0.998652\pi$
$462$	10.0856	−	12.1052i	0.469225	−	0.563187i
$463$	−15.0897	−	15.0897i	−0.701280	−	0.701280i	0.263405	−	0.964685i	$-0.415154\pi$
$463$	−15.0897	−	15.0897i	−0.701280	−	0.701280i	−0.964685	+	0.263405i	$0.915154\pi$
$464$	−0.443138	+	0.995304i	−0.0205722	+	0.0462058i
$465$	3.47267	+	10.8779i	0.161041	+	0.504452i
$466$	−3.71555	−	4.12654i	−0.172120	−	0.191158i
$467$	−23.4195	+	18.9647i	−1.08372	+	0.877582i	−0.992979	−	0.118292i	$-0.962258\pi$
$467$	−23.4195	+	18.9647i	−1.08372	+	0.877582i	−0.0907449	+	0.995874i	$0.528925\pi$
$468$	−0.183942	+	0.0291336i	−0.00850273	+	0.00134670i
$469$	−40.0493	+	3.87372i	−1.84931	+	0.178872i
$470$	0.492457	+	10.4227i	0.0227153	+	0.480762i
$471$	−25.9591	−	11.5578i	−1.19613	−	0.532553i
$472$	2.75708	−	0.738758i	0.126905	−	0.0340041i
$473$	4.21339	−	5.14328i	0.193732	−	0.236488i
$474$	−5.08476	−	8.80706i	−0.233551	−	0.404522i
$475$	36.8372	−	3.48880i	1.69021	−	0.160077i
$476$	−0.161562	−	0.792354i	−0.00740517	−	0.0363175i
$477$	−0.607419	−	1.19213i	−0.0278118	−	0.0545837i
$478$	−10.2594	+	8.30791i	−0.469255	+	0.379995i
$479$	6.77410	−	3.01602i	0.309517	−	0.137806i	−0.246100	−	0.969245i	$-0.579149\pi$
$479$	6.77410	−	3.01602i	0.309517	−	0.137806i	0.555616	+	0.831439i	$0.312482\pi$
$480$	3.58676	−	1.80436i	0.163713	−	0.0823572i
$481$	−4.12856	−	3.71737i	−0.188246	−	0.169498i
$482$	−23.0841	−	3.65617i	−1.05145	−	0.166534i
$483$	−10.8701	+	1.62934i	−0.494607	+	0.0741373i
$484$	−6.56599	+	8.82540i	−0.298454	+	0.401155i
$485$	13.6191	−	23.3111i	0.618411	−	1.05850i
$486$	2.31154	−	0.242953i	0.104854	−	0.0110206i
$487$	21.3052	−	13.8358i	0.965431	−	0.626958i	0.0373361	−	0.999303i	$-0.488113\pi$
$487$	21.3052	−	13.8358i	0.965431	−	0.626958i	0.928094	+	0.372345i	$0.121446\pi$
$488$	−3.34343	+	5.14843i	−0.151350	+	0.233058i
$489$	−4.99434	−	3.62860i	−0.225852	−	0.164091i
$490$	−5.15932	+	14.7777i	−0.233074	+	0.667590i
$491$	−2.04562	+	6.29576i	−0.0923173	+	0.284123i	−0.986545	−	0.163488i	$-0.947725\pi$
$491$	−2.04562	+	6.29576i	−0.0923173	+	0.284123i	0.894228	+	0.447612i	$0.147725\pi$
$492$	0.245894	+	4.69193i	0.0110857	+	0.211529i
$493$	−0.258788	−	0.209562i	−0.0116552	−	0.00943821i
$494$	−5.32579	−	3.07484i	−0.239618	−	0.138344i
$495$	−1.05986	+	1.28028i	−0.0476374	+	0.0575443i
$496$			2.84401i			0.127700i
$497$	−22.5321	+	22.1613i	−1.01070	+	0.994072i
$498$	3.78042	−	7.41950i	0.169405	−	0.332476i
$499$	3.54053	+	16.6569i	0.158496	+	0.745664i	0.983554	+	0.180616i	$0.0578091\pi$
$499$	3.54053	+	16.6569i	0.158496	+	0.745664i	−0.825058	+	0.565048i	$0.808858\pi$
$500$	4.16734	−	10.3746i	0.186369	−	0.463968i
$501$	33.6359	−	14.9757i	1.50274	−	0.669063i
$502$	−11.1607	−	7.24785i	−0.498127	−	0.323488i
$503$	26.4960	+	13.5004i	1.18140	+	0.601953i	0.930583	−	0.366081i	$-0.119301\pi$
$503$	26.4960	+	13.5004i	1.18140	+	0.601953i	0.250817	+	0.968035i	$0.419301\pi$
$504$	0.515946	−	0.292202i	0.0229820	−	0.0130157i
$505$	6.51464	−	23.8219i	0.289898	−	1.06006i
$506$	7.51486	−	1.55292i	0.334076	−	0.0690355i
$507$	−21.3495	+	5.72058i	−0.948164	+	0.254060i
$508$	−3.81716	+	4.71380i	−0.169359	+	0.209141i
$509$	5.99796	−	6.66141i	0.265855	−	0.295262i	−0.595406	−	0.803425i	$-0.703009\pi$
$509$	5.99796	−	6.66141i	0.265855	−	0.295262i	0.861261	+	0.508163i	$0.169675\pi$
$510$	0.248963	+	1.20165i	0.0110242	+	0.0532101i
$511$	−7.80363	+	35.2718i	−0.345212	+	1.56033i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	30.9353	+	20.0896i	1.36583	+	0.886978i
$514$	7.53766	+	1.60218i	0.332472	+	0.0706691i
$515$	−18.3411	−	25.5196i	−0.808208	−	1.12453i
$516$	3.11731	−	1.79978i	0.137232	−	0.0792309i
$517$	−2.33449	−	15.2995i	−0.102671	−	0.672871i
$518$	16.4599	+	6.47556i	0.723209	+	0.284520i
$519$	−10.3397	−	14.2313i	−0.453861	−	0.624687i
$520$	−1.56357	+	1.00399i	−0.0685670	+	0.0440279i
$521$	13.0639	−	11.7628i	0.572341	−	0.515338i	−0.331359	−	0.943505i	$-0.607507\pi$
$521$	13.0639	−	11.7628i	0.572341	−	0.515338i	0.903700	+	0.428167i	$0.140840\pi$
$522$	0.0875022	−	0.227951i	0.00382987	−	0.00997715i
$523$	−7.40397	−	9.14314i	−0.323753	−	0.399802i	0.589120	−	0.808046i	$-0.299475\pi$
$523$	−7.40397	−	9.14314i	−0.323753	−	0.399802i	−0.912873	+	0.408244i	$0.866141\pi$
$524$	−6.66842	+	20.5233i	−0.291311	+	0.896564i
$525$	7.75882	−	22.4504i	0.338623	−	0.979816i
$526$	15.7795	−	11.4645i	0.688020	−	0.499876i
$527$	−0.839634	−	0.224979i	−0.0365750	−	0.00980025i
$528$	−5.01279	+	3.21514i	−0.218154	+	0.139921i
$529$	15.2826	+	8.82343i	0.664462	+	0.383627i
$530$	−10.3311	−	8.45434i	−0.448753	−	0.367233i
$531$	−0.608382	+	0.197675i	−0.0264015	+	0.00857838i
$532$	19.3125	+	3.22325i	0.837303	+	0.139746i
$533$	−0.340151	−	2.14763i	−0.0147336	−	0.0930242i
$534$	−3.24304	−	0.340857i	−0.140340	−	0.0147503i
$535$	−31.3494	−	10.3647i	−1.35535	−	0.448105i
$536$	14.8755	+	3.16189i	0.642525	+	0.136573i
$537$	8.22746	+	21.4333i	0.355041	+	0.924914i
$538$	−2.95985	+	2.95985i	−0.127608	+	0.127608i
$539$	5.33108	−	22.5960i	0.229626	−	0.973279i
$540$	9.68067	−	5.52291i	0.416590	−	0.237668i
$541$	−14.8341	−	6.60458i	−0.637769	−	0.283953i	0.0622683	−	0.998059i	$-0.480167\pi$
$541$	−14.8341	−	6.60458i	−0.637769	−	0.283953i	−0.700037	+	0.714106i	$0.746833\pi$
$542$	12.9376	+	19.9221i	0.555717	+	0.855729i
$543$	1.13344	−	21.6274i	0.0486407	−	0.928119i
$544$	−0.0319485	+	0.303969i	−0.00136978	+	0.0130326i
$545$	−31.2643	+	25.0521i	−1.33922	+	1.07311i
$546$	−3.21295	+	2.29386i	−0.137502	+	0.0981683i
$547$	36.4950	+	18.5951i	1.56041	+	0.795071i	0.999463	−	0.0327777i	$-0.0104353\pi$
$547$	36.4950	+	18.5951i	1.56041	+	0.795071i	0.560952	+	0.827849i	$0.310435\pi$
$548$	−2.14823	−	5.59634i	−0.0917680	−	0.239064i
$549$	0.687887	−	1.19146i	0.0293583	−	0.0508501i
$550$	−4.54703	+	15.9476i	−0.193886	+	0.680006i
$551$	6.98252	−	4.03136i	0.297465	−	0.171742i
$552$	4.10326	+	0.649893i	0.174647	+	0.0276613i
$553$	−12.4990	−	8.26516i	−0.531511	−	0.351470i
$554$	17.4110	+	5.65716i	0.739721	+	0.240350i
$555$	−25.0095	−	9.74822i	−1.06159	−	0.413789i
$556$	−6.90421	−	15.5071i	−0.292804	−	0.657648i
$557$	−2.31311	−	0.121225i	−0.0980098	−	0.00513648i	0.00326800	−	0.999995i	$-0.498960\pi$
$557$	−2.31311	−	0.121225i	−0.0980098	−	0.00513648i	−0.101278	+	0.994858i	$0.532293\pi$
$558$	−0.0333576	−	0.636501i	−0.00141214	−	0.0269452i
$559$	−1.34772	+	0.979175i	−0.0570024	+	0.0414147i
$560$	3.54141	−	4.73903i	0.149652	−	0.200261i
$561$	−0.552660	−	1.73426i	−0.0233333	−	0.0732206i
$562$	0.0993258	+	0.0266143i	0.00418981	+	0.00112266i
$563$	29.6966	+	24.0478i	1.25156	+	1.01349i	0.998945	+	0.0459277i	$0.0146244\pi$
$563$	29.6966	+	24.0478i	1.25156	+	1.01349i	0.252616	+	0.967567i	$0.418709\pi$
$564$	1.74206	−	8.19574i	0.0733538	−	0.345103i
$565$	9.64137	+	10.8193i	0.405616	+	0.455171i
$566$	1.81366	−	2.49629i	0.0762338	−	0.104927i
$567$	21.4649	−	13.6877i	0.901442	−	0.574828i
$568$	10.6433	−	5.42303i	0.446582	−	0.227545i
$569$	−23.2293	−	20.9157i	−0.973821	−	0.876833i	0.0185859	−	0.999827i	$-0.494084\pi$
$569$	−23.2293	−	20.9157i	−0.973821	−	0.876833i	−0.992407	+	0.122994i	$0.960750\pi$
$570$	−29.3228	−	4.79910i	−1.22820	−	0.201012i
$571$	−16.8854	+	29.2463i	−0.706631	+	1.22392i	0.259469	+	0.965751i	$0.416452\pi$
$571$	−16.8854	+	29.2463i	−0.706631	+	1.22392i	−0.966100	+	0.258169i	$0.916881\pi$
$572$	2.15167	−	1.72231i	0.0899659	−	0.0720134i
$573$	12.2383	−	12.2383i	0.511263	−	0.511263i
$574$	3.41162	+	6.02396i	0.142398	+	0.251435i
$575$	9.76644	−	6.20043i	0.407289	−	0.258576i
$576$	−0.219214	+	0.0465954i	−0.00913392	+	0.00194147i
$577$	5.72651	+	2.19820i	0.238398	+	0.0915123i	0.474634	−	0.880183i	$-0.342581\pi$
$577$	5.72651	+	2.19820i	0.238398	+	0.0915123i	−0.236236	+	0.971696i	$0.575914\pi$
$578$	15.7837	+	6.05878i	0.656513	+	0.252012i
$579$	17.3891	−	3.69616i	0.722665	−	0.153607i
$580$	−0.114978	−	2.43347i	−0.00477421	−	0.101044i
$581$	0.101788	−	12.2694i	0.00422287	−	0.509020i
$582$	−15.3297	+	15.3297i	−0.635438	+	0.635438i
$583$	16.5447	+	10.8779i	0.685210	+	0.450517i
$584$	6.82693	−	11.8246i	0.282500	−	0.489305i
$585$	0.338158	−	0.243037i	0.0139811	−	0.0100483i
$586$	4.41348	+	3.97392i	0.182319	+	0.164161i
$587$	32.3934	−	16.5053i	1.33702	−	0.681245i	0.368370	−	0.929679i	$-0.379916\pi$
$587$	32.3934	−	16.5053i	1.33702	−	0.681245i	0.968649	+	0.248434i	$0.0799159\pi$
$588$	7.01955	−	10.4263i	0.289482	−	0.429973i
$589$	12.3710	−	17.0272i	0.509738	−	0.701595i
$590$	−4.76504	+	4.24626i	−0.196174	+	0.174816i
$591$	5.97502	−	28.1103i	0.245780	−	1.15630i
$592$	−5.19554	−	4.20726i	−0.213535	−	0.172917i
$593$	−40.7528	−	10.9197i	−1.67352	−	0.448417i	−0.707461	−	0.706753i	$-0.750159\pi$
$593$	−40.7528	−	10.9197i	−1.67352	−	0.448417i	−0.966055	+	0.258336i	$0.916826\pi$
$594$	−13.4288	+	9.64090i	−0.550990	+	0.395571i
$595$	1.11895	+	1.42041i	0.0458726	+	0.0582313i
$596$	18.5608	−	13.4852i	0.760281	−	0.552376i
$597$	−0.919684	−	17.5486i	−0.0376402	−	0.718217i
$598$	−1.92002	−	0.100624i	−0.0785156	−	0.00411483i
$599$	13.5272	+	30.3826i	0.552707	+	1.24140i	0.946649	+	0.322266i	$0.104444\pi$
$599$	13.5272	+	30.3826i	0.552707	+	1.24140i	−0.393942	+	0.919135i	$0.628889\pi$
$600$	−5.35156	+	7.20858i	−0.218476	+	0.294289i
$601$	19.6352	+	6.37987i	0.800938	+	0.260240i	0.680755	−	0.732511i	$-0.261652\pi$
$601$	19.6352	+	6.37987i	0.800938	+	0.260240i	0.120183	+	0.992752i	$0.461652\pi$
$602$	2.92550	−	4.42409i	0.119234	−	0.180312i
$603$	−3.36630	−	0.533169i	−0.137086	−	0.0217123i
$604$	1.90095	−	1.09752i	0.0773487	−	0.0446573i
$605$	4.24736	−	24.2273i	0.172680	−	0.984978i
$606$	−9.91580	+	17.1747i	−0.402802	+	0.697673i
$607$	−1.62203	−	4.22553i	−0.0658361	−	0.171509i	0.896716	−	0.442607i	$-0.145946\pi$
$607$	−1.62203	−	4.22553i	−0.0658361	−	0.171509i	−0.962552	+	0.271098i	$0.912613\pi$
$608$	−6.59381	−	3.35972i	−0.267414	−	0.136254i
$609$	−0.498300	−	5.15178i	−0.0201921	−	0.208761i
$610$	1.50507	−	13.6440i	0.0609387	−	0.552429i
$611$	−0.405332	+	3.85647i	−0.0163980	+	0.156016i
$612$	0.00358492	−	0.0684044i	0.000144912	−	0.00276508i
$613$	−1.73487	−	2.67147i	−0.0700709	−	0.107900i	0.801898	−	0.597461i	$-0.203824\pi$
$613$	−1.73487	−	2.67147i	−0.0700709	−	0.107900i	−0.871969	+	0.489561i	$0.837157\pi$
$614$	−3.38847	−	1.50864i	−0.136747	−	0.0608839i
$615$	−5.20604	−	9.12527i	−0.209928	−	0.367966i
$616$	−4.49312	+	7.53736i	−0.181033	+	0.303689i
$617$	−1.26883	+	1.26883i	−0.0510813	+	0.0510813i	−0.732186	−	0.681105i	$-0.761500\pi$
$617$	−1.26883	+	1.26883i	−0.0510813	+	0.0510813i	0.681105	+	0.732186i	$0.261500\pi$
$618$	9.04378	+	23.5599i	0.363794	+	0.947716i
$619$	−0.862912	−	0.183418i	−0.0346834	−	0.00737218i	0.190537	−	0.981680i	$-0.438977\pi$
$619$	−0.862912	−	0.183418i	−0.0346834	−	0.00737218i	−0.225221	+	0.974308i	$0.572310\pi$
$620$	−2.85790	−	5.68104i	−0.114776	−	0.228156i
$621$	11.4690	+	1.20544i	0.460236	+	0.0483727i
$622$	2.19777	+	13.8762i	0.0881227	+	0.556385i
$623$	−4.49987	+	1.68464i	−0.180283	+	0.0674937i
$624$	1.41909	−	0.461089i	0.0568089	−	0.0184583i
$625$	2.10087	+	24.9116i	0.0840348	+	0.996463i
$626$	−14.0819	−	8.13021i	−0.562827	−	0.324948i
$627$	43.9973	+	2.55566i	1.75708	+	0.102063i
$628$	15.2862	+	4.09592i	0.609985	+	0.163445i
$629$	1.65311	−	1.20105i	0.0659137	−	0.0478891i
$630$	−0.736998	+	1.10215i	−0.0293627	+	0.0439109i
$631$	−9.11440	+	28.0512i	−0.362838	+	1.11670i	0.588485	+	0.808508i	$0.299725\pi$
$631$	−9.11440	+	28.0512i	−0.362838	+	1.11670i	−0.951324	+	0.308194i	$0.900275\pi$
$632$	3.56424	+	4.40147i	0.141778	+	0.175081i
$633$	15.2614	−	39.7572i	0.606585	−	1.58021i
$634$	−11.0136	+	9.91670i	−0.437407	+	0.393843i
$635$	2.88813	−	13.2519i	0.114612	−	0.525885i
$636$	6.30088	+	8.67241i	0.249846	+	0.343884i
$637$	−2.72647	+	5.13841i	−0.108027	+	0.203591i
$638$	0.545053	+	3.57211i	0.0215788	+	0.141421i
$639$	−2.31841	+	1.33853i	−0.0917148	+	0.0529515i
$640$	−1.81576	+	1.30500i	−0.0717741	+	0.0515847i
$641$	11.5093	+	2.44639i	0.454592	+	0.0966264i	0.429516	−	0.903059i	$-0.358684\pi$
$641$	11.5093	+	2.44639i	0.454592	+	0.0966264i	0.0250753	+	0.999686i	$0.492017\pi$
$642$	22.2365	+	14.4406i	0.877605	+	0.569924i
$643$	40.6043	−	6.43109i	1.60128	−	0.253617i	0.709034	−	0.705174i	$-0.249131\pi$
$643$	40.6043	−	6.43109i	1.60128	−	0.253617i	0.892242	+	0.451557i	$0.149131\pi$
$644$	5.83733	−	1.84327i	0.230023	−	0.0726349i
$645$	−4.41841	+	6.72769i	−0.173975	+	0.264903i
$646$	1.51350	−	1.68091i	0.0595478	−	0.0661346i
$647$	−29.8255	+	36.8315i	−1.17256	+	1.44799i	−0.303821	+	0.952729i	$0.598262\pi$
$647$	−29.8255	+	36.8315i	−1.17256	+	1.44799i	−0.868742	+	0.495265i	$0.835071\pi$
$648$	−9.29424	+	2.49038i	−0.365112	+	0.0978316i
$649$	6.37424	−	6.99921i	0.250211	−	0.274743i
$650$	2.11441	−	3.57673i	0.0829339	−	0.140291i
$651$	−6.65815	−	11.7564i	−0.260954	−	0.460771i
$652$	3.06335	+	1.56085i	0.119970	+	0.0611277i
$653$	−29.7635	−	19.3287i	−1.16474	−	0.756389i	−0.190449	−	0.981697i	$-0.560994\pi$
$653$	−29.7635	−	19.3287i	−1.16474	−	0.756389i	−0.974288	+	0.225308i	$0.927661\pi$
$654$	29.3898	−	13.0852i	1.14923	−	0.511671i
$655$	−7.30309	−	47.6973i	−0.285355	−	1.86369i
$656$	−0.544028	−	2.55945i	−0.0212407	−	0.0999297i
$657$	−1.38920	+	2.72647i	−0.0541980	+	0.106370i
$658$	−3.09635	−	11.9515i	−0.120708	−	0.465916i
$659$			39.0846i			1.52252i	0.648446	+	0.761261i	$0.275419\pi$
$659$			39.0846i			1.52252i	−0.648446	+	0.761261i	$0.724581\pi$
$660$	6.78245	−	11.4597i	0.264006	−	0.446068i
$661$	17.6935	+	10.2153i	0.688196	+	0.397330i	0.802936	−	0.596065i	$-0.203270\pi$
$661$	17.6935	+	10.2153i	0.688196	+	0.397330i	−0.114740	+	0.993396i	$0.536603\pi$
$662$	18.0270	+	14.5980i	0.700641	+	0.567368i
$663$	0.0238681	+	0.455431i	0.000926961	+	0.0176875i
$664$	−1.43308	+	4.41057i	−0.0556143	+	0.171163i
$665$	−41.8167	+	12.9683i	−1.62158	+	0.502888i
$666$	1.21213	+	0.880665i	0.0469691	+	0.0341251i
$667$	1.37290	−	2.11408i	0.0531589	−	0.0818576i
$668$	−17.1972	+	11.1680i	−0.665381	+	0.432104i
$669$	−13.6156	+	1.43106i	−0.526410	+	0.0553279i
$670$	−32.8920	+	8.63219i	−1.27073	+	0.333491i
$671$	−0.115273	+	20.3598i	−0.00445007	+	0.785979i
$672$	−3.71663	+	2.95896i	−0.143372	+	0.114144i
$673$	−0.812400	−	0.128672i	−0.0313157	−	0.00495992i	0.140757	−	0.990044i	$-0.455046\pi$
$673$	−0.812400	−	0.128672i	−0.0313157	−	0.00495992i	−0.172073	+	0.985084i	$0.555046\pi$
$674$	5.06819	+	4.56342i	0.195219	+	0.175776i
$675$	−13.7877	+	20.7603i	−0.530690	+	0.799063i
$676$	11.2452	−	5.00670i	0.432509	−	0.192566i
$677$	4.58752	−	3.71490i	0.176313	−	0.142775i	−0.537102	−	0.843517i	$-0.680481\pi$
$677$	4.58752	−	3.71490i	0.176313	−	0.142775i	0.713415	+	0.700742i	$0.247148\pi$
$678$	−5.28311	−	10.3687i	−0.202897	−	0.398207i
$679$	−10.1230	+	30.2979i	−0.388486	+	1.16273i
$680$	−0.241636	−	0.639298i	−0.00926633	−	0.0245160i
$681$	−12.6266	−	21.8699i	−0.483852	−	0.838056i
$682$	5.09244	+	7.93972i	0.195000	+	0.304028i
$683$	6.28024	−	1.68279i	0.240307	−	0.0643900i	−0.136655	−	0.990619i	$-0.543635\pi$
$683$	6.28024	−	1.68279i	0.240307	−	0.0643900i	0.376962	+	0.926229i	$0.376969\pi$
$684$	1.51513	+	0.674580i	0.0579325	+	0.0257932i
$685$	9.91489	+	9.02023i	0.378828	+	0.344645i
$686$	2.39365	−	18.3649i	0.0913900	−	0.701176i
$687$	2.21468	−	0.350771i	0.0844952	−	0.0133827i
$688$	−1.55793	+	1.26158i	−0.0593954	+	0.0480974i
$689$	−3.31960	−	3.68679i	−0.126467	−	0.140455i
$690$	−8.84954	+	2.82512i	−0.336896	+	0.107551i
$691$	4.01882	−	9.02642i	0.152883	−	0.343381i	−0.820825	−	0.571180i	$-0.806486\pi$
$691$	4.01882	−	9.02642i	0.152883	−	0.343381i	0.973708	+	0.227798i	$0.0731527\pi$
$692$	6.92737	+	6.92737i	0.263339	+	0.263339i
$693$	0.917173	−	1.73960i	0.0348405	−	0.0660818i
$694$			1.98281i			0.0752666i
$695$	29.3744	+	24.0383i	1.11423	+	0.911823i
$696$	−0.406733	+	1.91353i	−0.0154172	+	0.0725322i
$697$	0.798660	+	0.0418560i	0.0302514	+	0.00158541i
$698$	0.845068	+	1.04357i	0.0319863	+	0.0394998i
$699$	−8.06632	−	5.86052i	−0.305096	−	0.221665i
$700$	−2.31194	+	13.0252i	−0.0873831	+	0.492305i
$701$	7.34902	+	22.6180i	0.277569	+	0.854269i	0.988528	+	0.151036i	$0.0482609\pi$
$701$	7.34902	+	22.6180i	0.277569	+	0.854269i	−0.710959	+	0.703233i	$0.751739\pi$
$702$	3.86684	−	1.48434i	0.145944	−	0.0560228i
$703$	12.8050	+	47.7889i	0.482950	+	1.80239i
$704$	2.47726	−	2.20526i	0.0933652	−	0.0831140i
$705$	4.75594	+	18.1220i	0.179119	+	0.682512i
$706$	−11.4902	−	15.8149i	−0.432440	−	0.595202i
$707$	−1.77136	+	29.1677i	−0.0666190	+	1.09696i
$708$	4.56659	−	2.32679i	0.171623	−	0.0874462i
$709$	−42.5820	−	4.47555i	−1.59920	−	0.168083i	−0.737446	−	0.675406i	$-0.763968\pi$
$709$	−42.5820	−	4.47555i	−1.59920	−	0.168083i	−0.861756	+	0.507323i	$0.830635\pi$
$710$	−15.8110	+	21.5281i	−0.593375	+	0.807934i
$711$	−0.849318	−	0.943263i	−0.0318519	−	0.0353751i
$712$	1.81358	−	0.0950459i	0.0679669	−	0.00356199i
$713$	1.02936	−	6.49913i	0.0385499	−	0.243394i
$714$	−0.579561	−	1.33133i	−0.0216895	−	0.0498238i
$715$	−2.56734	+	5.60259i	−0.0960132	+	0.209525i
$716$	−6.39296	−	11.0729i	−0.238916	−	0.413815i
$717$	−14.9175	+	18.4216i	−0.557105	+	0.687968i
$718$	−7.90466	−	12.1721i	−0.294999	−	0.454259i
$719$	−46.5678	+	9.89828i	−1.73668	+	0.369144i	−0.964053	−	0.265711i	$-0.914393\pi$
$719$	−46.5678	+	9.89828i	−1.73668	+	0.369144i	−0.772632	+	0.634855i	$0.781060\pi$
$720$	0.391068	−	0.313362i	0.0145742	−	0.0116783i
$721$	27.4263	+	25.1098i	1.02141	+	0.935139i
$722$	16.2374	+	31.8678i	0.604295	+	1.18600i
$723$	−41.9086	+	2.19634i	−1.55860	+	0.0816827i
$724$	1.26075	+	11.9952i	0.0468554	+	0.445799i
$725$	2.67504	+	4.74544i	0.0993485	+	0.176241i
$726$	−8.23741	+	17.9517i	−0.305719	+	0.666249i
$727$	−25.5825	−	25.5825i	−0.948802	−	0.948802i	0.0499498	−	0.998752i	$-0.484094\pi$
$727$	−25.5825	−	25.5825i	−0.948802	−	0.948802i	−0.998752	+	0.0499498i	$0.984094\pi$
$728$	1.56749	−	1.54170i	0.0580950	−	0.0571390i
$729$	−23.4843	+	7.63052i	−0.869790	+	0.282612i
$730$	−1.75476	+	30.4805i	−0.0649464	+	1.12813i
$731$	−0.249214	−	0.559745i	−0.00921753	−	0.0207029i
$732$	−3.95018	+	10.2906i	−0.146003	+	0.380351i
$733$	−7.84304	+	12.0772i	−0.289689	+	0.446082i	−0.953313	−	0.301984i	$-0.902351\pi$
$733$	−7.84304	+	12.0772i	−0.289689	+	0.446082i	0.663624	+	0.748067i	$0.269018\pi$
$734$	8.33703	+	25.6587i	0.307725	+	0.947081i
$735$	−3.54467	+	27.8809i	−0.130747	+	1.02840i
$736$	−2.31369			−0.0852836
$737$	47.1902	−	17.8087i	1.73827	−	0.655994i
$738$	0.151776	+	0.566435i	0.00558694	+	0.0208508i
$739$	31.4304	−	3.30347i	1.15619	−	0.121520i	0.493038	−	0.870008i	$-0.335886\pi$
$739$	31.4304	−	3.30347i	1.15619	−	0.121520i	0.663149	+	0.748487i	$0.269220\pi$
$740$	14.6062	+	3.18329i	0.536933	+	0.117020i
$741$	−10.5018	−	3.41225i	−0.385794	−	0.125352i
$742$	14.0137	+	7.28739i	0.514459	+	0.267529i
$743$	3.03268	+	19.1476i	0.111258	+	0.702457i	0.978758	+	0.205019i	$0.0657256\pi$
$743$	3.03268	+	19.1476i	0.111258	+	0.702457i	−0.867500	+	0.497438i	$0.834274\pi$
$744$	1.06173	+	4.99505i	0.0389249	+	0.183127i
$745$	−23.5250	+	45.5889i	−0.861890	+	1.67025i
$746$	0.607683	+	5.78172i	0.0222489	+	0.211684i
$747$	0.268998	−	1.00391i	0.00984212	−	0.0367313i
$748$	0.455092	+	0.905810i	0.0166398	+	0.0331197i
$749$	38.8186	+	4.40589i	1.41840	+	0.160988i
$750$	3.44620	−	19.7772i	0.125837	−	0.722161i
$751$	21.7874	−	24.1974i	0.795034	−	0.882975i	−0.200273	−	0.979740i	$-0.564183\pi$
$751$	21.7874	−	24.1974i	0.795034	−	0.882975i	0.995307	+	0.0967650i	$0.0308495\pi$
$752$	−0.244219	+	4.65997i	−0.00890574	+	0.169932i
$753$	−22.3078	−	8.56318i	−0.812943	−	0.312060i
$754$	0.0946363	−	0.900404i	0.00344645	−	0.0327908i
$755$	−2.69437	+	4.10258i	−0.0980581	+	0.149308i
$756$	−9.87294	+	8.74243i	−0.359075	+	0.317959i
$757$	−6.73109	+	42.4984i	−0.244646	+	1.54463i	0.493353	+	0.869829i	$0.335771\pi$
$757$	−6.73109	+	42.4984i	−0.244646	+	1.54463i	−0.737999	+	0.674802i	$0.764229\pi$
$758$	5.64070	−	21.0514i	0.204879	−	0.764620i
$759$	12.6189	−	5.53292i	0.458038	−	0.200832i
$760$	16.5476	+	0.0851617i	0.600244	+	0.00308914i
$761$	9.14759	−	20.5458i	0.331600	−	0.744786i	−0.668399	−	0.743802i	$-0.733020\pi$
$761$	9.14759	−	20.5458i	0.331600	−	0.744786i	1.00000		0.000983377i	$-0.000313019\pi$
$762$	−4.94448	+	9.70409i	−0.179120	+	0.351542i
$763$	30.1366	−	36.5907i	1.09102	−	1.32467i
$764$	−5.66565	+	7.79810i	−0.204976	+	0.282125i
$765$	0.0615776	+	0.140244i	0.00222634	+	0.00507052i
$766$	7.72061	−	6.95166i	0.278957	−	0.251174i
$767$	−1.98927	+	1.29185i	−0.0718285	+	0.0466460i
$768$	1.67632	−	0.643479i	0.0604890	−	0.0232195i
$769$	−45.9046			−1.65536			−0.827682	−	0.561198i	$-0.810341\pi$
$769$	−45.9046			−1.65536			−0.827682	+	0.561198i	$0.810341\pi$
$770$	1.40103	−	19.5713i	0.0504897	−	0.705302i
$771$	13.8368			0.498322
$772$	−9.24312	+	3.54810i	−0.332667	+	0.127699i
$773$	−31.4436	+	20.4197i	−1.13095	+	0.734446i	−0.967691	−	0.252138i	$-0.918866\pi$
$773$	−31.4436	+	20.4197i	−1.13095	+	0.734446i	−0.163256	+	0.986584i	$0.552200\pi$
$774$	0.333873	−	0.300621i	0.0120008	−	0.0108056i
$775$	11.4176	+	8.47629i	0.410133	+	0.304477i
$776$	7.09681	−	9.76792i	0.254761	−	0.350648i
$777$	31.3268	+	5.22844i	1.12384	+	0.187569i
$778$	14.0414	−	27.5577i	0.503407	−	0.987992i
$779$	−7.87610	+	17.6900i	−0.282191	+	0.633810i
$780$	−2.37135	+	2.34707i	−0.0849080	+	0.0840385i
$781$	20.0029	−	34.1974i	0.715759	−	1.22368i
$782$	0.183027	−	0.683068i	0.00654505	−	0.0244265i
$783$	−0.849504	+	5.36355i	−0.0303588	+	0.191678i
$784$	−2.95286	+	6.34670i	−0.105459	+	0.226668i
$785$	−34.6508	+	7.17908i	−1.23674	+	0.256232i
$786$	−4.05024	+	38.5354i	−0.144467	+	1.37451i
$787$	−29.1469	−	11.1885i	−1.03898	−	0.398825i	−0.221726	−	0.975109i	$-0.571169\pi$
$787$	−29.1469	−	11.1885i	−1.03898	−	0.398825i	−0.817250	+	0.576284i	$0.804502\pi$
$788$	−0.837637	+	15.9831i	−0.0298396	+	0.569373i
$789$	23.4343	−	26.0265i	0.834284	−	0.926566i
$790$	−11.5427	−	5.21050i	−0.410672	−	0.185381i
$791$	−13.7881	−	10.1935i	−0.490248	−	0.362438i
$792$	−0.528555	+	0.522604i	−0.0187814	+	0.0185699i
$793$	1.32031	−	4.92747i	0.0468857	−	0.174980i
$794$	−0.771705	−	7.34228i	−0.0273868	−	0.260568i
$795$	−21.3011	−	10.9919i	−0.755472	−	0.389843i
$796$	2.03476	+	9.57278i	0.0721200	+	0.339298i
$797$	5.95075	+	37.5716i	0.210786	+	1.33085i	0.835281	+	0.549824i	$0.185305\pi$
$797$	5.95075	+	37.5716i	0.210786	+	1.33085i	−0.624494	+	0.781029i	$0.714695\pi$
$798$	35.1227	−	1.54865i	1.24333	−	0.0548216i
$799$	−1.35644	−	0.440734i	−0.0479874	−	0.0155920i
$800$	2.31569	−	4.43143i	0.0818719	−	0.156675i
$801$	−0.404773	+	0.0425434i	−0.0143019	+	0.00150320i
$802$	−4.73313	−	17.6643i	−0.167133	−	0.623748i
$803$	−2.11394	−	45.2354i	−0.0745994	−	1.59632i
$804$	27.3070			0.963042
$805$	−9.80807	+	9.54787i	−0.345689	+	0.336518i
$806$	−0.730315	−	2.24768i	−0.0257243	−	0.0791711i
$807$	−4.09354	+	6.30350i	−0.144099	+	0.221894i
$808$	3.95806	−	10.3111i	0.139244	−	0.362743i
$809$	19.7347	+	44.3248i	0.693834	+	1.55838i	0.823814	+	0.566860i	$0.191842\pi$
$809$	19.7347	+	44.3248i	0.693834	+	1.55838i	−0.129981	+	0.991517i	$0.541492\pi$
$810$	16.0632	−	14.3143i	0.564402	−	0.502954i
$811$	−30.6577	+	9.96128i	−1.07654	+	0.349788i	−0.793030	−	0.609183i	$-0.791498\pi$
$811$	−30.6577	+	9.96128i	−1.07654	+	0.349788i	−0.283506	+	0.958970i	$0.591498\pi$
$812$	0.722931	+	2.79041i	0.0253699	+	0.0979242i
$813$	30.1602	+	30.1602i	1.05777	+	1.05777i
$814$	−22.0380	−	2.44252i	−0.772433	−	0.0856103i
$815$	−7.68767	−	0.0395643i	−0.269287	−	0.00138588i
$816$	0.0573661	+	0.545802i	0.00200821	+	0.0191069i
$817$	14.8151	−	0.776426i	0.518315	−	0.0271637i
$818$	7.17606	+	14.0838i	0.250905	+	0.492429i
$819$	−0.332728	+	0.363423i	−0.0116265	+	0.0126990i
$820$	3.65868	+	4.56594i	0.127767	+	0.159450i
$821$	7.99530	−	1.69945i	0.279038	−	0.0593113i	−0.0662669	−	0.997802i	$-0.521109\pi$
$821$	7.99530	−	1.69945i	0.279038	−	0.0593113i	0.345305	+	0.938491i	$0.387776\pi$
$822$	−5.86227	−	9.02711i	−0.204470	−	0.314857i
$823$	33.0898	−	40.8625i	1.15344	−	1.42438i	0.265682	−	0.964061i	$-0.414403\pi$
$823$	33.0898	−	40.8625i	1.15344	−	1.42438i	0.887755	−	0.460316i	$-0.152264\pi$
$824$	−7.02726	−	12.1716i	−0.244806	−	0.424017i
$825$	−2.03257	+	29.7069i	−0.0707651	+	1.03426i
$826$	4.48941	−	6.07256i	0.156207	−	0.211292i
$827$	2.93037	−	18.5016i	0.101899	−	0.643365i	−0.882886	−	0.469588i	$-0.844403\pi$
$827$	2.93037	−	18.5016i	0.101899	−	0.643365i	0.984785	−	0.173778i	$-0.0555974\pi$
$828$	0.517813	−	0.0271374i	0.0179953	−	0.000943091i
$829$	16.1442	+	17.9299i	0.560711	+	0.622733i	0.955126	−	0.296200i	$-0.0957194\pi$
$829$	16.1442	+	17.9299i	0.560711	+	0.622733i	−0.394415	+	0.918932i	$0.629053\pi$
$830$	−1.56947	−	10.2504i	−0.0544772	−	0.355797i
$831$	32.6916	+	3.43602i	1.13406	+	0.119194i
$832$	−0.740420	+	0.377263i	−0.0256695	+	0.0130792i
$833$	−1.64014	−	1.37384i	−0.0568275	−	0.0476006i
$834$	−17.9153	−	24.6583i	−0.620356	−	0.853847i
$835$	23.1297	−	39.5899i	0.800438	−	1.37007i
$836$	−24.4241	+	2.42734i	−0.844724	+	0.0839514i
$837$	3.66888	+	13.6925i	0.126815	+	0.473281i
$838$	−6.13225	+	2.35395i	−0.211835	+	0.0813159i
$839$	−11.6519	−	35.8609i	−0.402269	−	1.23806i	−0.923154	−	0.384430i	$-0.874398\pi$
$839$	−11.6519	−	35.8609i	−0.402269	−	1.23806i	0.520885	−	0.853627i	$-0.325602\pi$
$840$	4.45074	−	9.64546i	0.153565	−	0.332800i
$841$	−22.5012	−	16.3481i	−0.775903	−	0.563727i
$842$	3.18862	+	3.93762i	0.109887	+	0.135699i
$843$	0.184386	+	0.00966326i	0.00635059	+	0.000332820i
$844$	−4.93103	+	23.1987i	−0.169733	+	0.798532i
$845$	−17.4318	+	21.3013i	−0.599671	+	0.732788i
$846$		−	1.04579i		−	0.0359548i
$847$	0.952684	+	29.0877i	0.0327346	+	0.999464i
$848$	−4.22146	−	4.22146i	−0.144965	−	0.144965i
$849$	2.25349	−	5.06142i	0.0773395	−	0.173707i
$850$	1.12510	+	1.03421i	0.0385907	+	0.0354732i
$851$	10.3501	+	11.4949i	0.354796	+	0.394041i
$852$	16.6687	−	13.4981i	0.571061	−	0.462436i
$853$	−2.37169	+	0.375639i	−0.0812051	+	0.0128616i	−0.196905	−	0.980423i	$-0.563089\pi$
$853$	−2.37169	+	0.375639i	−0.0812051	+	0.0128616i	0.115700	+	0.993284i	$0.463089\pi$
$854$	1.56366	+	16.1663i	0.0535075	+	0.553199i
$855$	−3.70442	+	0.175029i	−0.126689	+	0.00598586i
$856$	−13.4896	−	6.00598i	−0.461067	−	0.205280i
$857$	3.63643	−	0.974378i	0.124218	−	0.0332841i	−0.196174	−	0.980569i	$-0.562852\pi$
$857$	3.63643	−	0.974378i	0.124218	−	0.0332841i	0.320392	+	0.947285i	$0.396185\pi$
$858$	3.13610	−	3.82824i	0.107065	−	0.130694i
$859$	−16.5361	−	28.6414i	−0.564206	−	0.977233i	−0.997123	−	0.0757991i	$-0.975849\pi$
$859$	−16.5361	−	28.6414i	−0.564206	−	0.977233i	0.432918	−	0.901434i	$-0.357484\pi$
$860$	1.84429	−	4.08562i	0.0628896	−	0.139318i
$861$	8.24085	+	9.30651i	0.280847	+	0.317165i
$862$	−14.0308	−	27.5369i	−0.477890	−	0.937912i
$863$	−10.6640	+	8.63554i	−0.363007	+	0.293957i	−0.793420	−	0.608675i	$-0.791701\pi$
$863$	−10.6640	+	8.63554i	−0.363007	+	0.293957i	0.430413	+	0.902632i	$0.358368\pi$
$864$	4.55341	−	2.02731i	0.154910	−	0.0689705i
$865$	−20.7990	−	6.87654i	−0.707187	−	0.233809i
$866$	18.8857	+	17.0048i	0.641763	+	0.577846i
$867$	29.9834	+	4.74890i	1.01829	+	0.161281i
$868$	4.68667	+	5.88674i	0.159076	+	0.199809i
$869$	17.8316	+	5.90568i	0.604897	+	0.200336i
$870$	−1.11041	−	4.23109i	−0.0376465	−	0.143447i
$871$	−12.5684	+	1.32099i	−0.425864	+	0.0447601i
$872$	−15.0263	+	9.75821i	−0.508856	+	0.330455i
$873$	−1.47373	+	2.26934i	−0.0498781	+	0.0768056i
$874$	13.8522	+	10.0642i	0.468557	+	0.340426i
$875$	−8.47060	−	28.3416i	−0.286359	−	0.958123i
$876$	7.57605	−	23.3167i	0.255971	−	0.787798i
$877$	−1.24117	−	23.6830i	−0.0419114	−	0.799717i	−0.936037	−	0.351901i	$-0.885535\pi$
$877$	−1.24117	−	23.6830i	−0.0419114	−	0.799717i	0.894126	−	0.447816i	$-0.147798\pi$
$878$	−17.1407	−	13.8802i	−0.578470	−	0.468435i
$879$	9.23515	+	5.33191i	0.311494	+	0.179841i
$880$	−2.73240	+	6.89449i	−0.0921093	+	0.232413i
$881$			1.77859i			0.0599221i	0.999551	+	0.0299610i	$0.00953832\pi$
$881$			1.77859i			0.0599221i	−0.999551	+	0.0299610i	$0.990462\pi$
$882$	0.586422	−	1.45505i	0.0197459	−	0.0489942i
$883$	3.08604	−	6.05669i	0.103853	−	0.203824i	−0.833232	−	0.552923i	$-0.813512\pi$
$883$	3.08604	−	6.05669i	0.103853	−	0.203824i	0.937086	+	0.349099i	$0.113512\pi$
$884$	−0.0528070	−	0.248438i	−0.00177609	−	0.00835586i
$885$	−6.78382	+	9.23679i	−0.228036	+	0.310491i
$886$	10.6765	−	4.75346i	0.358682	−	0.159696i
$887$	−20.4271	−	13.2655i	−0.685874	−	0.445412i	0.154088	−	0.988057i	$-0.450756\pi$
$887$	−20.4271	−	13.2655i	−0.685874	−	0.445412i	−0.839962	+	0.542646i	$0.817423\pi$
$888$	−10.6958	−	5.44979i	−0.358928	−	0.182883i
$889$	−0.133130	+	16.0473i	−0.00446505	+	0.538210i
$890$	−3.52721	+	2.01230i	−0.118232	+	0.0674526i
$891$	−21.4878	+	23.5946i	−0.719870	+	0.790450i
$892$	7.36481	−	1.97340i	0.246592	−	0.0660742i
$893$	21.7323	−	26.8372i	0.727244	−	0.898072i
$894$	27.5648	−	30.6138i	0.921906	−	1.02388i
$895$	23.8973	+	15.6945i	0.798798	+	0.524610i
$896$	1.78660	−	1.95142i	0.0596862	−	0.0651924i
$897$	−3.40978	+	0.540057i	−0.113849	+	0.0180320i
$898$	2.69883	+	1.75264i	0.0900610	+	0.0584863i
$899$	3.03082	+	0.644221i	0.101084	+	0.0214860i
$900$	−0.466284	+	1.01893i	−0.0155428	+	0.0339645i
$901$	1.58024	−	0.912353i	0.0526455	−	0.0303949i
$902$	−6.10170	−	6.17118i	−0.203164	−	0.205478i
$903$	3.48657	−	8.86237i	0.116026	−	0.294921i
$904$	3.80940	+	5.24319i	0.126699	+	0.174386i
$905$	−14.5723	−	22.6942i	−0.484398	−	0.754379i
$906$	2.92900	−	2.63728i	0.0973095	−	0.0876179i
$907$	13.1614	−	34.2867i	0.437018	−	1.13847i	−0.521453	−	0.853280i	$-0.674610\pi$
$907$	13.1614	−	34.2867i	0.437018	−	1.13847i	0.958471	−	0.285191i	$-0.0920569\pi$
$908$	8.85081	+	10.9298i	0.293724	+	0.362719i
$909$	−0.764890	+	2.35409i	−0.0253698	+	0.0780803i
$910$	−1.58191	+	4.65476i	−0.0524397	+	0.154304i
$911$	23.5347	−	17.0989i	0.779739	−	0.566513i	−0.125162	−	0.992136i	$-0.539945\pi$
$911$	23.5347	−	17.0989i	0.779739	−	0.566513i	0.904901	+	0.425623i	$0.139945\pi$
$912$	−12.8353	−	3.43920i	−0.425018	−	0.113883i
$913$	3.89672	+	14.8792i	0.128963	+	0.492430i
$914$	−4.65543	−	2.68781i	−0.153988	−	0.0889049i
$915$	−2.45018	−	24.5254i	−0.0810005	−	0.810786i
$916$	−1.18766	+	0.385894i	−0.0392414	+	0.0127503i
$917$	20.0177	+	53.4697i	0.661044	+	1.76572i
$918$	0.238317	+	1.50467i	0.00786563	+	0.0496617i
$919$	28.4798	+	2.99335i	0.939462	+	0.0987414i	0.561865	−	0.827229i	$-0.310084\pi$
$919$	28.4798	+	2.99335i	0.939462	+	0.0987414i	0.377596	+	0.925970i	$0.376751\pi$
$920$	4.62170	−	2.32499i	0.152373	−	0.0766527i
$921$	−6.51453	−	1.38471i	−0.214661	−	0.0456276i
$922$	−0.0651520	−	0.169727i	−0.00214567	−	0.00558965i
$923$	−7.01903	+	7.01903i	−0.231034	+	0.231034i
$924$	−5.07760	+	14.9156i	−0.167041	+	0.490687i
$925$	−32.3754	+	8.31877i	−1.06450	+	0.273519i
$926$	19.4952	+	8.67981i	0.640651	+	0.285236i
$927$	1.71549	+	2.64163i	0.0563442	+	0.0867624i
$928$	0.0570198	−	1.08800i	0.00187177	−	0.0357155i
$929$	4.59394	−	43.7084i	0.150722	−	1.43403i	−0.613817	−	0.789448i	$-0.710367\pi$
$929$	4.59394	−	43.7084i	0.150722	−	1.43403i	0.764539	−	0.644577i	$-0.222967\pi$
$930$	−7.14032	−	8.91094i	−0.234140	−	0.292201i
$931$	45.2862	−	25.1535i	1.48419	−	0.824374i
$932$	4.94759	+	2.52092i	0.162064	+	0.0825755i
$933$	9.04034	+	23.5509i	0.295967	+	0.771022i
$934$	15.0676	−	26.0979i	0.493027	−	0.853948i
$935$	−1.81930	−	1.35208i	−0.0594976	−	0.0442179i
$936$	0.161284	−	0.0931176i	0.00527174	−	0.00304364i
$937$	−9.52394	−	1.50844i	−0.311134	−	0.0492787i	−0.00108491	−	0.999999i	$-0.500345\pi$
$937$	−9.52394	−	1.50844i	−0.311134	−	0.0492787i	−0.310049	+	0.950721i	$0.600345\pi$
$938$	36.0010	−	17.9688i	1.17548	−	0.586703i
$939$	−27.7679	−	9.02233i	−0.906171	−	0.294433i
$940$	−4.19490	−	9.55393i	−0.136823	−	0.311615i
$941$	−16.9267	−	38.0180i	−0.551795	−	1.23935i	−0.947141	−	0.320819i	$-0.896042\pi$
$941$	−16.9267	−	38.0180i	−0.551795	−	1.23935i	0.395346	−	0.918532i	$-0.370625\pi$
$942$	28.3769	+	1.48717i	0.924568	+	0.0484546i
$943$	0.316845	+	6.04576i	0.0103179	+	0.196877i
$944$	−2.30921	+	1.67774i	−0.0751584	+	0.0546058i
$945$	10.9365	−	27.3846i	0.355766	−	0.890822i
$946$	−2.09035	+	6.31161i	−0.0679631	+	0.205208i
$947$	−43.5931	−	11.6807i	−1.41659	−	0.379573i	−0.532315	−	0.846547i	$-0.678678\pi$
$947$	−43.5931	−	11.6807i	−1.41659	−	0.379573i	−0.884271	+	0.466974i	$0.845344\pi$
$948$	7.90320	+	6.39988i	0.256684	+	0.207859i
$949$	−2.35902	+	11.0983i	−0.0765771	+	0.360267i
$950$	−33.1402	+	16.4583i	−1.07521	+	0.533979i
$951$	−15.6416	+	21.5288i	−0.507212	+	0.698118i
$952$	0.434785	+	0.681828i	0.0140915	+	0.0220982i
$953$	−37.3985	+	19.0555i	−1.21146	+	0.617268i	−0.938674	−	0.344807i	$-0.887944\pi$
$953$	−37.3985	+	19.0555i	−1.21146	+	0.617268i	−0.272784	+	0.962075i	$0.587944\pi$
$954$	0.994294	+	0.895266i	0.0321915	+	0.0289853i
$955$	3.48121	−	21.2704i	0.112649	−	0.688295i
$956$	6.60070	−	11.4328i	0.213482	−	0.369762i
$957$	2.29085	+	6.07036i	0.0740525	+	0.196227i
$958$	−5.24332	+	5.24332i	−0.169404	+	0.169404i
$959$	−13.6688	−	8.04364i	−0.441390	−	0.259743i
$960$	−2.70191	+	2.96989i	−0.0872037	+	0.0958528i
$961$	−22.4110	+	4.76360i	−0.722934	+	0.153664i
$962$	5.18653	+	1.99092i	0.167221	+	0.0641899i
$963$	3.08949	+	1.18594i	0.0995573	+	0.0382165i
$964$	22.8612	−	4.85929i	0.736308	−	0.156507i
$965$	14.8981	−	16.3758i	0.479588	−	0.527155i
$966$	9.56422	−	5.41661i	0.307724	−	0.174277i
$967$	−16.1994	+	16.1994i	−0.520939	+	0.520939i	−0.917855	−	0.396916i	$-0.870080\pi$
$967$	−16.1994	+	16.1994i	−0.520939	+	0.520939i	0.396916	+	0.917855i	$0.370080\pi$
$968$	2.96714	−	10.5923i	0.0953675	−	0.340448i
$969$	2.03070	−	3.51728i	0.0652356	−	0.112991i
$970$	−4.36057	+	26.6434i	−0.140010	+	0.855468i
$971$	−38.1266	−	34.3294i	−1.22354	−	1.10168i	−0.991652	−	0.128940i	$-0.958842\pi$
$971$	−38.1266	−	34.3294i	−1.22354	−	1.10168i	−0.231890	−	0.972742i	$-0.574491\pi$
$972$	−2.07095	+	1.05520i	−0.0664256	+	0.0338456i
$973$	−39.8452	−	20.7203i	−1.27738	−	0.664262i
$974$	−14.9318	+	20.5519i	−0.478446	+	0.658525i
$975$	2.37835	−	7.07133i	0.0761683	−	0.226464i
$976$	1.27633	−	6.00465i	0.0408542	−	0.192204i
$977$	11.8745	+	9.61577i	0.379898	+	0.307636i	0.800182	−	0.599757i	$-0.204736\pi$
$977$	11.8745	+	9.61577i	0.379898	+	0.307636i	−0.420284	+	0.907393i	$0.638069\pi$
$978$	5.96299	+	1.59778i	0.190675	+	0.0510913i
$979$	4.89286	−	3.51272i	0.156377	−	0.112267i
$980$	−0.479230	−	15.6451i	−0.0153084	−	0.499766i
$981$	3.24850	−	2.36017i	0.103717	−	0.0753546i
$982$	−0.346451	−	6.61068i	−0.0110557	−	0.210955i
$983$	−57.5444	−	3.01577i	−1.83538	−	0.0961882i	−0.897050	−	0.441928i	$-0.854295\pi$
$983$	−57.5444	−	3.01577i	−1.83538	−	0.0961882i	−0.938330	+	0.345740i	$0.887628\pi$
$984$	−1.91100	−	4.29217i	−0.0609204	−	0.136830i
$985$	−14.3879	−	32.7687i	−0.458438	−	1.04410i
$986$	0.316700	+	0.102902i	0.0100858	+	0.00327707i
$987$	−9.90000	−	19.8349i	−0.315120	−	0.631352i
$988$	6.07398	+	0.962023i	0.193239	+	0.0306060i
$989$	4.01679	−	2.31910i	0.127727	−	0.0737430i
$990$	0.530658	−	1.57507i	0.0168654	−	0.0500589i
$991$	6.68477	−	11.5784i	0.212349	−	0.367799i	−0.740100	−	0.672496i	$-0.765222\pi$
$991$	6.68477	−	11.5784i	0.212349	−	0.367799i	0.952449	+	0.304698i	$0.0985554\pi$
$992$	−1.01920	−	2.65511i	−0.0323597	−	0.0842998i
$993$	37.1114	+	18.9092i	1.17770	+	0.600066i
$994$	13.0936	−	28.7642i	0.415305	−	0.912345i
$995$	−13.6841	−	17.0774i	−0.433815	−	0.541390i
$996$	−0.870418	+	8.28148i	−0.0275803	+	0.262409i
$997$	2.09160	−	39.9101i	0.0662416	−	1.26397i	−0.740092	−	0.672505i	$-0.765218\pi$
$997$	2.09160	−	39.9101i	0.0662416	−	1.26397i	0.806334	−	0.591461i	$-0.201448\pi$
$998$	−9.27466	−	14.2817i	−0.293584	−	0.452080i
$999$	−30.4414	−	13.5534i	−0.963124	−	0.428811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.6	✓	768
5.2	odd	4	inner	770.2.bv.a.157.19	yes	768
7.5	odd	6	inner	770.2.bv.a.663.43	yes	768
11.4	even	5	inner	770.2.bv.a.213.19	yes	768
35.12	even	12	inner	770.2.bv.a.47.19	yes	768
55.37	odd	20	inner	770.2.bv.a.367.43	yes	768
77.26	odd	30	inner	770.2.bv.a.103.19	yes	768
385.257	even	60	inner	770.2.bv.a.257.6	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.6	✓	768	1.1	even	1	trivial
770.2.bv.a.47.19	yes	768	35.12	even	12	inner
770.2.bv.a.103.19	yes	768	77.26	odd	30	inner
770.2.bv.a.157.19	yes	768	5.2	odd	4	inner
770.2.bv.a.213.19	yes	768	11.4	even	5	inner
770.2.bv.a.257.6	yes	768	385.257	even	60	inner
770.2.bv.a.367.43	yes	768	55.37	odd	20	inner
770.2.bv.a.663.43	yes	768	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-1.50590 + 0.977944i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.812068 + 2.08340i) q^{5} +(1.05542 - 1.45266i) q^{6} +(0.435551 - 2.60965i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0911544 - 0.204736i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-1.50590 + 0.977944i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.812068 + 2.08340i) q^{5} +(1.05542 - 1.45266i) q^{6} +(0.435551 - 2.60965i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0911544 - 0.204736i) q^{9} +(0.0115077 - 2.23604i) q^{10} +(0.328001 + 3.30037i) q^{11} +(-0.464731 + 1.73440i) q^{12} +(0.129996 - 0.820762i) q^{13} +(0.528595 + 2.59241i) q^{14} +(-0.814552 - 3.93155i) q^{15} +(0.104528 - 0.994522i) q^{16} +(0.285343 + 0.109533i) q^{17} +(-0.0117291 + 0.223804i) q^{18} +(-4.95184 + 5.49958i) q^{19} +(0.790581 + 2.09165i) q^{20} +(1.89620 + 4.35583i) q^{21} +(-1.48896 - 2.96361i) q^{22} +(-0.598826 + 2.23485i) q^{23} +(-0.187689 - 1.78574i) q^{24} +(-3.68109 - 3.38372i) q^{25} +(0.172773 + 0.812834i) q^{26} +(-0.779721 - 4.92297i) q^{27} +(-1.42252 - 2.23079i) q^{28} +(-1.03617 - 0.336673i) q^{29} +(2.16939 + 3.37851i) q^{30} +(-2.82843 + 0.297280i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.72151 - 4.64926i) q^{33} -0.305644 q^{34} +(5.08325 + 3.02664i) q^{35} +(-0.0692543 - 0.213143i) q^{36} +(3.64113 - 5.60686i) q^{37} +(2.65207 - 6.90888i) q^{38} +(0.606898 + 1.36312i) q^{39} +(-1.48765 - 1.66940i) q^{40} +(2.48856 - 0.808583i) q^{41} +(-3.33124 - 3.38698i) q^{42} +(-1.41752 - 1.41752i) q^{43} +(2.45213 + 2.23317i) q^{44} +(0.352523 + 0.356170i) q^{45} +(-0.241846 - 2.30101i) q^{46} +(-4.65997 + 0.244219i) q^{47} +(0.815177 + 1.59987i) q^{48} +(-6.62059 - 2.27327i) q^{49} +(4.64921 + 1.83979i) q^{50} +(-0.536815 + 0.114104i) q^{51} +(-0.452591 - 0.696929i) q^{52} +(3.75707 - 4.63959i) q^{53} +(2.49217 + 4.31656i) q^{54} +(-7.14233 - 1.99676i) q^{55} +(2.12748 + 1.57284i) q^{56} +(2.07871 - 13.1244i) q^{57} +(1.08800 - 0.0570198i) q^{58} +(-1.90993 - 2.12119i) q^{59} +(-3.23605 - 2.37667i) q^{60} +(6.10517 + 0.641679i) q^{61} +(2.53403 - 1.29115i) q^{62} +(-0.494588 - 0.327054i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.60441 + 0.937348i) q^{65} +(5.14047 + 3.00679i) q^{66} +(-3.93608 - 14.6897i) q^{67} +(0.285343 - 0.109533i) q^{68} +(-1.28378 - 3.95108i) q^{69} +(-5.83027 - 1.00394i) q^{70} +(-9.66390 - 7.02124i) q^{71} +(0.141038 + 0.174167i) q^{72} +(-13.6351 - 0.714588i) q^{73} +(-1.38997 + 6.53932i) q^{74} +(8.85245 + 1.49565i) q^{75} +7.40041i q^{76} +(8.75568 + 0.581508i) q^{77} +(-1.05508 - 1.05508i) q^{78} +(2.30361 - 5.17399i) q^{79} +(1.98710 + 1.02539i) q^{80} +(6.43845 + 7.15062i) q^{81} +(-2.03350 + 1.64670i) q^{82} +(4.58045 - 0.725472i) q^{83} +(4.32377 + 1.96820i) q^{84} +(-0.459919 + 0.505535i) q^{85} +(1.83136 + 0.815375i) q^{86} +(1.88962 - 0.506322i) q^{87} +(-3.08956 - 1.20608i) q^{88} +(-0.908036 - 1.57276i) q^{89} +(-0.456749 - 0.206181i) q^{90} +(-2.08529 - 0.696728i) q^{91} +(1.05039 + 2.06151i) q^{92} +(3.96861 - 3.21372i) q^{93} +(4.26293 - 1.89798i) q^{94} +(-7.43657 - 14.7827i) q^{95} +(-1.33438 - 1.20148i) q^{96} +(-11.9252 - 1.88876i) q^{97} +(6.99552 - 0.250323i) q^{98} +(0.705603 + 0.233689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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