LMFDB - Embedded newform 483.2.bf.a.61.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(10,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			61.14
Character	$\chi$	$=$	483.61
Dual form			483.2.bf.a.388.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.451440 - 0.355016i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(-0.393756 - 1.62309i) q^{4} +(0.598753 - 0.115400i) q^{5} +(0.161803 + 0.551049i) q^{6} +(-1.36900 + 2.26403i) q^{7} +(-0.875621 + 1.91734i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(-0.451440 - 0.355016i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(-0.393756 - 1.62309i) q^{4} +(0.598753 - 0.115400i) q^{5} +(0.161803 + 0.551049i) q^{6} +(-1.36900 + 2.26403i) q^{7} +(-0.875621 + 1.91734i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-0.311270 - 0.160471i) q^{10} +(-1.70470 - 2.16770i) q^{11} +(-0.620738 + 1.55053i) q^{12} +(-2.52621 - 3.93087i) q^{13} +(1.42179 - 0.536055i) q^{14} +(-0.554668 - 0.253308i) q^{15} +(-1.89303 + 0.975923i) q^{16} +(0.524184 + 0.499808i) q^{17} +(0.187839 - 0.542726i) q^{18} +(-3.03709 + 2.89586i) q^{19} +(-0.423067 - 0.926387i) q^{20} +(2.42842 - 1.05012i) q^{21} +1.58378i q^{22} +(-2.08493 + 4.31892i) q^{23} +(1.82543 - 1.05391i) q^{24} +(-4.29665 + 1.72012i) q^{25} +(-0.255088 + 2.67140i) q^{26} +(0.281733 - 0.959493i) q^{27} +(4.21377 + 1.33053i) q^{28} +(3.39452 - 0.996720i) q^{29} +(0.160471 + 0.311270i) q^{30} +(0.714409 + 7.48163i) q^{31} +(5.34052 + 1.02930i) q^{32} +(0.131217 + 2.75458i) q^{33} +(-0.0591975 - 0.411727i) q^{34} +(-0.558425 + 1.51358i) q^{35} +(1.40503 - 0.902959i) q^{36} +(-2.76488 + 0.956933i) q^{37} +(2.39914 - 0.229090i) q^{38} +(-0.222333 + 4.66734i) q^{39} +(-0.303019 + 1.24906i) q^{40} +(2.08159 - 1.80371i) q^{41} +(-1.46910 - 0.388062i) q^{42} +(-4.55925 + 2.08214i) q^{43} +(-2.84713 + 3.62042i) q^{44} +(0.304886 + 0.528078i) q^{45} +(2.47451 - 1.20955i) q^{46} +(2.68378 + 1.54948i) q^{47} +(2.10810 + 0.303100i) q^{48} +(-3.25166 - 6.19893i) q^{49} +(2.55035 + 0.748851i) q^{50} +(-0.137070 - 0.711188i) q^{51} +(-5.38542 + 5.64807i) q^{52} +(-11.5077 - 0.548179i) q^{53} +(-0.467821 + 0.333134i) q^{54} +(-1.27084 - 1.10119i) q^{55} +(-3.14219 - 4.60728i) q^{56} +(4.15370 - 0.597212i) q^{57} +(-1.88627 - 0.755149i) q^{58} +(4.15468 - 8.05896i) q^{59} +(-0.192737 + 1.00002i) q^{60} +(-4.87044 - 6.83957i) q^{61} +(2.33359 - 3.63114i) q^{62} +(-2.58727 - 0.553217i) q^{63} +(0.743917 + 0.858526i) q^{64} +(-1.96620 - 2.06209i) q^{65} +(0.918683 - 1.29011i) q^{66} +(0.189728 + 0.473918i) q^{67} +(0.604831 - 1.04760i) q^{68} +(4.20355 - 2.30871i) q^{69} +(0.789440 - 0.485039i) q^{70} +(0.444250 - 3.08983i) q^{71} +(-2.09828 - 0.200361i) q^{72} +(-8.90511 + 2.16036i) q^{73} +(1.58790 + 0.549578i) q^{74} +(4.49772 + 1.09113i) q^{75} +(5.89610 + 3.78919i) q^{76} +(7.24147 - 0.891900i) q^{77} +(1.75735 - 2.02809i) q^{78} +(-9.48527 + 0.451839i) q^{79} +(-1.02083 + 0.802792i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(-1.58006 + 0.0752674i) q^{82} +(5.91013 - 6.82065i) q^{83} +(-2.66065 - 3.52805i) q^{84} +(0.371534 + 0.238771i) q^{85} +(2.79742 + 0.678647i) q^{86} +(-3.34324 - 1.15711i) q^{87} +(5.64889 - 1.37041i) q^{88} +(7.15692 + 0.683403i) q^{89} +(0.0498386 - 0.346635i) q^{90} +(12.3580 - 0.338058i) q^{91} +(7.83093 + 1.68342i) q^{92} +(3.75783 - 6.50875i) q^{93} +(-0.661475 - 1.65229i) q^{94} +(-1.48428 + 2.08438i) q^{95} +(-3.75320 - 3.93625i) q^{96} +(-3.39838 - 3.92194i) q^{97} +(-0.732790 + 3.95284i) q^{98} +(1.49093 - 2.31993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.451440	−	0.355016i	−0.319216	−	0.251034i	0.445674	−	0.895196i	$-0.352964\pi$
$2$	−0.451440	−	0.355016i	−0.319216	−	0.251034i	−0.764890	+	0.644161i	$0.777207\pi$
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$4$	−0.393756	−	1.62309i	−0.196878	−	0.811543i
$5$	0.598753	−	0.115400i	0.267770	−	0.0516085i	−0.0535986	−	0.998563i	$-0.517069\pi$
$5$	0.598753	−	0.115400i	0.267770	−	0.0516085i	0.321369	+	0.946954i	$0.395857\pi$
$6$	0.161803	+	0.551049i	0.0660556	+	0.224965i
$7$	−1.36900	+	2.26403i	−0.517434	+	0.855723i
$7$	−1.36900	+	2.26403i	−0.517434	+	0.855723i
$8$	−0.875621	+	1.91734i	−0.309579	+	0.677883i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	−0.311270	−	0.160471i	−0.0984322	−	0.0507453i
$11$	−1.70470	−	2.16770i	−0.513986	−	0.653586i	0.457910	−	0.888999i	$-0.348598\pi$
$11$	−1.70470	−	2.16770i	−0.513986	−	0.653586i	−0.971895	+	0.235413i	$0.924356\pi$
$12$	−0.620738	+	1.55053i	−0.179192	+	0.447599i
$13$	−2.52621	−	3.93087i	−0.700646	−	1.09023i	−0.991072	−	0.133329i	$-0.957433\pi$
$13$	−2.52621	−	3.93087i	−0.700646	−	1.09023i	0.290426	−	0.956897i	$-0.406203\pi$
$14$	1.42179	−	0.536055i	0.379989	−	0.143267i
$15$	−0.554668	−	0.253308i	−0.143215	−	0.0654040i
$16$	−1.89303	+	0.975923i	−0.473257	+	0.243981i
$17$	0.524184	+	0.499808i	0.127133	+	0.121221i	0.750979	−	0.660326i	$-0.229582\pi$
$17$	0.524184	+	0.499808i	0.127133	+	0.121221i	−0.623845	+	0.781548i	$0.714431\pi$
$18$	0.187839	−	0.542726i	0.0442741	−	0.127922i
$19$	−3.03709	+	2.89586i	−0.696756	+	0.664355i	−0.953247	−	0.302191i	$-0.902282\pi$
$19$	−3.03709	+	2.89586i	−0.696756	+	0.664355i	0.256491	+	0.966547i	$0.417433\pi$
$20$	−0.423067	−	0.926387i	−0.0946007	−	0.207147i
$21$	2.42842	−	1.05012i	0.529925	−	0.229156i
$22$			1.58378i			0.337663i
$23$	−2.08493	+	4.31892i	−0.434738	+	0.900557i
$23$	−2.08493	+	4.31892i	−0.434738	+	0.900557i
$24$	1.82543	−	1.05391i	0.372614	−	0.215129i
$25$	−4.29665	+	1.72012i	−0.859330	+	0.344024i
$26$	−0.255088	+	2.67140i	−0.0500268	+	0.523904i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	4.21377	+	1.33053i	0.796327	+	0.251447i
$29$	3.39452	−	0.996720i	0.630346	−	0.185086i	0.0490732	−	0.998795i	$-0.484373\pi$
$29$	3.39452	−	0.996720i	0.630346	−	0.185086i	0.581272	+	0.813709i	$0.302555\pi$
$30$	0.160471	+	0.311270i	0.0292978	+	0.0568298i
$31$	0.714409	+	7.48163i	0.128312	+	1.34374i	0.798700	+	0.601730i	$0.205522\pi$
$31$	0.714409	+	7.48163i	0.128312	+	1.34374i	−0.670388	+	0.742011i	$0.733872\pi$
$32$	5.34052	+	1.02930i	0.944079	+	0.181956i
$33$	0.131217	+	2.75458i	0.0228419	+	0.479510i
$34$	−0.0591975	−	0.411727i	−0.0101523	−	0.0706107i
$35$	−0.558425	+	1.51358i	−0.0943910	+	0.255841i
$36$	1.40503	−	0.902959i	0.234172	−	0.150493i
$37$	−2.76488	+	0.956933i	−0.454543	+	0.157319i	−0.544740	−	0.838605i	$-0.683372\pi$
$37$	−2.76488	+	0.956933i	−0.454543	+	0.157319i	0.0901969	+	0.995924i	$0.471250\pi$
$38$	2.39914	−	0.229090i	0.389192	−	0.0371633i
$39$	−0.222333	+	4.66734i	−0.0356017	+	0.747372i
$40$	−0.303019	+	1.24906i	−0.0479115	+	0.197494i
$41$	2.08159	−	1.80371i	0.325089	−	0.281692i	−0.476990	−	0.878909i	$-0.658272\pi$
$41$	2.08159	−	1.80371i	0.325089	−	0.281692i	0.802080	+	0.597217i	$0.203727\pi$
$42$	−1.46910	−	0.388062i	−0.226687	−	0.0598792i
$43$	−4.55925	+	2.08214i	−0.695279	+	0.317523i	−0.731520	−	0.681820i	$-0.761189\pi$
$43$	−4.55925	+	2.08214i	−0.695279	+	0.317523i	0.0362413	+	0.999343i	$0.488462\pi$
$44$	−2.84713	+	3.62042i	−0.429220	+	0.545798i
$45$	0.304886	+	0.528078i	0.0454497	+	0.0787212i
$46$	2.47451	−	1.20955i	0.364846	−	0.178338i
$47$	2.68378	+	1.54948i	0.391470	+	0.226015i	0.682797	−	0.730608i	$-0.260763\pi$
$47$	2.68378	+	1.54948i	0.391470	+	0.226015i	−0.291327	+	0.956624i	$0.594097\pi$
$48$	2.10810	+	0.303100i	0.304279	+	0.0437487i
$49$	−3.25166	−	6.19893i	−0.464523	−	0.885561i
$50$	2.55035	+	0.748851i	0.360674	+	0.105903i
$51$	−0.137070	−	0.711188i	−0.0191937	−	0.0995863i
$52$	−5.38542	+	5.64807i	−0.746824	+	0.783246i
$53$	−11.5077	−	0.548179i	−1.58070	−	0.0752982i	−0.761256	−	0.648452i	$-0.775417\pi$
$53$	−11.5077	−	0.548179i	−1.58070	−	0.0752982i	−0.819448	+	0.573153i	$0.805720\pi$
$54$	−0.467821	+	0.333134i	−0.0636624	+	0.0453338i
$55$	−1.27084	−	1.10119i	−0.171361	−	0.148485i
$56$	−3.14219	−	4.60728i	−0.419893	−	0.615673i
$57$	4.15370	−	0.597212i	0.550171	−	0.0791027i
$58$	−1.88627	−	0.755149i	−0.247680	−	0.0991560i
$59$	4.15468	−	8.05896i	0.540894	−	1.04919i	−0.447070	−	0.894499i	$-0.647532\pi$
$59$	4.15468	−	8.05896i	0.540894	−	1.04919i	0.987963	−	0.154688i	$-0.0494373\pi$
$60$	−0.192737	+	1.00002i	−0.0248823	+	0.129101i
$61$	−4.87044	−	6.83957i	−0.623595	−	0.875717i	0.375089	−	0.926989i	$-0.377612\pi$
$61$	−4.87044	−	6.83957i	−0.623595	−	0.875717i	−0.998685	+	0.0512715i	$0.983673\pi$
$62$	2.33359	−	3.63114i	0.296366	−	0.461155i
$63$	−2.58727	−	0.553217i	−0.325965	−	0.0696988i
$64$	0.743917	+	0.858526i	0.0929896	+	0.107316i
$65$	−1.96620	−	2.06209i	−0.243877	−	0.255771i
$66$	0.918683	−	1.29011i	0.113082	−	0.158802i
$67$	0.189728	+	0.473918i	0.0231790	+	0.0578983i	0.939506	−	0.342533i	$-0.111285\pi$
$67$	0.189728	+	0.473918i	0.0231790	+	0.0578983i	−0.916327	+	0.400431i	$0.868860\pi$
$68$	0.604831	−	1.04760i	0.0733465	−	0.127040i
$69$	4.20355	−	2.30871i	0.506048	−	0.277936i
$70$	0.789440	−	0.485039i	0.0943561	−	0.0579733i
$71$	0.444250	−	3.08983i	0.0527228	−	0.366695i	−0.946331	−	0.323199i	$-0.895242\pi$
$71$	0.444250	−	3.08983i	0.0527228	−	0.366695i	0.999054	−	0.0434954i	$-0.0138494\pi$
$72$	−2.09828	−	0.200361i	−0.247284	−	0.0236128i
$73$	−8.90511	+	2.16036i	−1.04226	+	0.252851i	−0.720127	−	0.693842i	$-0.755917\pi$
$73$	−8.90511	+	2.16036i	−1.04226	+	0.252851i	−0.322138	+	0.946693i	$0.604401\pi$
$74$	1.58790	+	0.549578i	0.184590	+	0.0638872i
$75$	4.49772	+	1.09113i	0.519352	+	0.125993i
$76$	5.89610	+	3.78919i	0.676329	+	0.434650i
$77$	7.24147	−	0.891900i	0.825242	−	0.101641i
$78$	1.75735	−	2.02809i	0.198981	−	0.229636i
$79$	−9.48527	+	0.451839i	−1.06718	+	0.0508359i	−0.573812	−	0.818987i	$-0.694536\pi$
$79$	−9.48527	+	0.451839i	−1.06718	+	0.0508359i	−0.493364	+	0.869823i	$0.664233\pi$
$80$	−1.02083	+	0.802792i	−0.114133	+	0.0897548i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	−1.58006	+	0.0752674i	−0.174488	+	0.00831189i
$83$	5.91013	−	6.82065i	0.648721	−	0.748663i	−0.332171	−	0.943219i	$-0.607781\pi$
$83$	5.91013	−	6.82065i	0.648721	−	0.748663i	0.980891	+	0.194556i	$0.0623265\pi$
$84$	−2.66065	−	3.52805i	−0.290301	−	0.384941i
$85$	0.371534	+	0.238771i	0.0402986	+	0.0258983i
$86$	2.79742	+	0.678647i	0.301654	+	0.0731804i
$87$	−3.34324	−	1.15711i	−0.358433	−	0.124055i
$88$	5.64889	−	1.37041i	0.602173	−	0.146086i
$89$	7.15692	+	0.683403i	0.758632	+	0.0724405i	0.467201	−	0.884151i	$-0.345263\pi$
$89$	7.15692	+	0.683403i	0.758632	+	0.0724405i	0.291431	+	0.956592i	$0.405869\pi$
$90$	0.0498386	−	0.346635i	0.00525345	−	0.0365386i
$91$	12.3580	−	0.338058i	1.29547	−	0.0354381i
$92$	7.83093	+	1.68342i	0.816431	+	0.175509i
$93$	3.75783	−	6.50875i	0.389669	−	0.674926i
$94$	−0.661475	−	1.65229i	−0.0682260	−	0.170420i
$95$	−1.48428	+	2.08438i	−0.152284	+	0.213853i
$96$	−3.75320	−	3.93625i	−0.383060	−	0.401742i
$97$	−3.39838	−	3.92194i	−0.345053	−	0.398212i	0.556524	−	0.830832i	$-0.312135\pi$
$97$	−3.39838	−	3.92194i	−0.345053	−	0.398212i	−0.901577	+	0.432620i	$0.857589\pi$
$98$	−0.732790	+	3.95284i	−0.0740230	+	0.399297i
$99$	1.49093	−	2.31993i	0.149844	−	0.233161i
$100$	4.48374	+	6.29653i	0.448374	+	0.629653i
$101$	3.01312	−	15.6336i	0.299817	−	1.55560i	−0.449435	−	0.893313i	$-0.648375\pi$
$101$	3.01312	−	15.6336i	0.299817	−	1.55560i	0.749252	−	0.662285i	$-0.230413\pi$
$102$	−0.190604	+	0.369721i	−0.0188727	+	0.0366078i
$103$	−0.637115	−	0.255062i	−0.0627768	−	0.0251320i	0.340062	−	0.940403i	$-0.389552\pi$
$103$	−0.637115	−	0.255062i	−0.0627768	−	0.0251320i	−0.402838	+	0.915271i	$0.631976\pi$
$104$	9.74882	−	1.40167i	0.955951	−	0.137445i
$105$	1.33284	−	0.909005i	0.130072	−	0.0887098i
$106$	5.00042	+	4.33289i	0.485684	+	0.420848i
$107$	−7.26853	+	5.17590i	−0.702675	+	0.500373i	−0.874666	−	0.484726i	$-0.838919\pi$
$107$	−7.26853	+	5.17590i	−0.702675	+	0.500373i	0.171991	+	0.985099i	$0.444980\pi$
$108$	−1.66827	−	0.0794697i	−0.160530	−	0.00764697i
$109$	1.84207	−	1.93190i	0.176438	−	0.185043i	−0.629577	−	0.776938i	$-0.716772\pi$
$109$	1.84207	−	1.93190i	0.176438	−	0.185043i	0.806015	+	0.591895i	$0.201620\pi$
$110$	0.182769	+	0.948293i	0.0174263	+	0.0904162i
$111$	2.80728	+	0.824291i	0.266455	+	0.0782382i
$112$	0.382040	−	5.62191i	0.0360994	−	0.531220i
$113$	2.12063	+	0.304900i	0.199492	+	0.0286826i	0.241336	−	0.970442i	$-0.422414\pi$
$113$	2.12063	+	0.304900i	0.199492	+	0.0286826i	−0.0418445	+	0.999124i	$0.513323\pi$
$114$	−2.08717	−	1.20503i	−0.195481	−	0.112861i
$115$	−0.749954	+	2.82657i	−0.0699336	+	0.263579i
$116$	−2.95437	−	5.11712i	−0.274307	−	0.475113i
$117$	2.88843	−	3.67294i	0.267035	−	0.339563i
$118$	−4.73665	+	2.16316i	−0.436044	+	0.199135i
$119$	−1.84919	+	0.502529i	−0.169515	+	0.0460668i
$120$	0.971358	−	0.841686i	0.0886724	−	0.0768351i
$121$	0.800423	−	3.29939i	0.0727657	−	0.299944i
$122$	−0.229450	+	4.81674i	−0.0207734	+	0.436087i
$123$	−2.74186	+	0.261816i	−0.247225	+	0.0236072i
$124$	11.8620	−	4.10549i	1.06524	−	0.368684i
$125$	−4.93899	+	3.17410i	−0.441757	+	0.283900i
$126$	0.971595	+	1.16827i	0.0865565	+	0.104077i
$127$	1.87278	+	13.0255i	0.166182	+	1.15582i	0.886686	+	0.462373i	$0.153002\pi$
$127$	1.87278	+	13.0255i	0.166182	+	1.15582i	−0.720503	+	0.693452i	$0.756089\pi$
$128$	−0.548621	−	11.5170i	−0.0484917	−	1.01797i
$129$	4.92161	+	0.948563i	0.433324	+	0.0835163i
$130$	0.155545	+	1.62894i	0.0136422	+	0.142868i
$131$	−5.19518	−	10.0772i	−0.453905	−	0.880453i	−0.999111	−	0.0421509i	$-0.986579\pi$
$131$	−5.19518	−	10.0772i	−0.453905	−	0.880453i	0.545206	−	0.838302i	$-0.316451\pi$
$132$	4.41925	−	1.29761i	0.384646	−	0.112942i
$133$	−2.39853	−	10.8405i	−0.207979	−	0.939990i
$134$	0.0825978	−	0.281302i	0.00713536	−	0.0243008i
$135$	0.0579625	−	0.607011i	0.00498862	−	0.0522432i
$136$	−1.41729	+	0.567397i	−0.121532	+	0.0486539i
$137$	−8.78011	+	5.06920i	−0.750135	+	0.433091i	−0.825743	−	0.564047i	$-0.809244\pi$
$137$	−8.78011	+	5.06920i	−0.750135	+	0.433091i	0.0756076	+	0.997138i	$0.475910\pi$
$138$	−2.71728	−	0.450087i	−0.231310	−	0.0383139i
$139$		−	9.47105i		−	0.803324i	−0.915788	−	0.401662i	$-0.868433\pi$
$139$		−	9.47105i		−	0.803324i	0.915788	−	0.401662i	$-0.131567\pi$
$140$	2.67655	+	0.310391i	0.226210	+	0.0262328i
$141$	−1.28736	−	2.81892i	−0.108415	−	0.237396i
$142$	−1.29749	+	1.23716i	−0.108883	+	0.103820i
$143$	−4.21450	+	12.1770i	−0.352435	+	1.01829i
$144$	−1.54140	−	1.46972i	−0.128450	−	0.122477i
$145$	1.91745	−	0.988516i	0.159236	−	0.0820918i
$146$	4.78709	+	2.18619i	0.396182	+	0.180930i
$147$	−0.947004	+	6.93565i	−0.0781076	+	0.572042i
$148$	2.64187	+	4.11083i	0.217161	+	0.337908i
$149$	−5.91788	+	14.7822i	−0.484812	+	1.21100i	0.461324	+	0.887232i	$0.347375\pi$
$149$	−5.91788	+	14.7822i	−0.484812	+	1.21100i	−0.946136	+	0.323770i	$0.895050\pi$
$150$	−1.64308	−	2.08934i	−0.134157	−	0.170594i
$151$	1.76184	+	0.908292i	0.143377	+	0.0739158i	0.528422	−	0.848982i	$-0.322784\pi$
$151$	1.76184	+	0.908292i	0.143377	+	0.0739158i	−0.385045	+	0.922898i	$0.625814\pi$
$152$	−2.89301	−	8.35881i	−0.234654	−	0.677989i
$153$	−0.300876	+	0.658825i	−0.0243243	+	0.0532629i
$154$	−3.58573	−	2.16820i	−0.288946	−	0.174719i
$155$	1.29114	+	4.39720i	0.103706	+	0.353192i
$156$	7.66304	−	1.47693i	0.613534	−	0.118249i
$157$	−2.44128	−	10.0631i	−0.194836	−	0.803124i	−0.982384	−	0.186871i	$-0.940165\pi$
$157$	−2.44128	−	10.0631i	−0.194836	−	0.803124i	0.787549	−	0.616252i	$-0.211350\pi$
$158$	4.44244	+	3.16345i	0.353422	+	0.251670i
$159$	9.05592	+	7.12165i	0.718181	+	0.564784i
$160$	3.31643			0.262187
$161$	−6.92388	−	10.6330i	−0.545679	−	0.837995i
$162$	0.574312			0.0451222
$163$	−6.98599	−	5.49384i	−0.547185	−	0.430311i	0.305915	−	0.952059i	$-0.401038\pi$
$163$	−6.98599	−	5.49384i	−0.547185	−	0.430311i	−0.853100	+	0.521748i	$0.825280\pi$
$164$	−3.74721	−	2.66837i	−0.292608	−	0.208365i
$165$	0.396445	+	1.63417i	0.0308632	+	0.127220i
$166$	−5.08951	+	0.980923i	−0.395023	+	0.0761344i
$167$	2.41180	+	8.21382i	0.186630	+	0.635605i	0.998649	+	0.0519725i	$0.0165508\pi$
$167$	2.41180	+	8.21382i	0.186630	+	0.635605i	−0.812018	+	0.583632i	$0.801631\pi$
$168$	−0.112929	+	5.57563i	−0.00871268	+	0.430169i
$169$	−3.66956	+	8.03521i	−0.282274	+	0.618093i
$170$	−0.0829580	−	0.239691i	−0.00636259	−	0.0183835i
$171$	−3.72992	−	1.92291i	−0.285234	−	0.147049i
$172$	5.17472	+	6.58020i	0.394569	+	0.501735i
$173$	−4.41394	+	11.0255i	−0.335586	+	0.838253i	0.660579	+	0.750757i	$0.270311\pi$
$173$	−4.41394	+	11.0255i	−0.335586	+	0.838253i	−0.996165	+	0.0874965i	$0.972113\pi$
$174$	1.09848	+	1.70927i	0.0832757	+	0.129580i
$175$	1.98773	−	12.0826i	0.150258	−	0.913359i
$176$	5.34254	+	2.43986i	0.402709	+	0.183911i
$177$	−8.05896	+	4.15468i	−0.605749	+	0.312285i
$178$	−2.98830	−	2.84934i	−0.223983	−	0.213567i
$179$	−6.75622	+	19.5208i	−0.504984	+	1.45906i	0.348188	+	0.937425i	$0.386797\pi$
$179$	−6.75622	+	19.5208i	−0.504984	+	1.45906i	−0.853172	+	0.521630i	$0.825324\pi$
$180$	0.737065	−	0.702790i	0.0549376	−	0.0523829i
$181$	−9.64588	−	21.1215i	−0.716973	−	1.56995i	−0.818099	−	0.575077i	$-0.804972\pi$
$181$	−9.64588	−	21.1215i	−0.716973	−	1.56995i	0.101127	−	0.994874i	$-0.467755\pi$
$182$	−5.69891	−	4.23468i	−0.422431	−	0.313895i
$183$			8.39648i			0.620686i
$184$	−6.45524	−	7.77926i	−0.475886	−	0.573495i
$185$	−1.54505	+	0.892033i	−0.113594	+	0.0655836i
$186$	−4.00715	+	1.60422i	−0.293819	+	0.117627i
$187$	0.189859	−	1.98829i	0.0138839	−	0.145399i
$188$	1.45819	−	4.96613i	0.106349	−	0.362192i
$189$	1.78663	+	1.95140i	0.129958	+	0.141943i
$190$	1.41005	−	0.414029i	0.102296	−	0.0300369i
$191$	−8.66926	−	16.8160i	−0.627286	−	1.21676i	−0.961639	−	0.274317i	$-0.911548\pi$
$191$	−8.66926	−	16.8160i	−0.627286	−	1.21676i	0.334353	−	0.942448i	$-0.391482\pi$
$192$	−0.107983	−	1.13085i	−0.00779300	−	0.0816120i
$193$	20.9829	+	4.04413i	1.51039	+	0.291103i	0.876151	−	0.482038i	$-0.160103\pi$
$193$	20.9829	+	4.04413i	1.51039	+	0.291103i	0.634235	+	0.773141i	$0.281315\pi$
$194$	0.141812	+	2.97700i	0.0101815	+	0.213736i
$195$	0.405489	+	2.82024i	0.0290377	+	0.201961i
$196$	−8.78103	+	7.71859i	−0.627216	+	0.551328i
$197$	23.1276	−	14.8632i	1.64777	−	1.05896i	0.714596	−	0.699537i	$-0.246611\pi$
$197$	23.1276	−	14.8632i	1.64777	−	1.05896i	0.933175	−	0.359421i	$-0.117026\pi$
$198$	−1.49667	+	0.518004i	−0.106364	+	0.0368130i
$199$	23.1895	−	2.21433i	1.64386	−	0.156970i	0.768305	−	0.640084i	$-0.221100\pi$
$199$	23.1895	−	2.21433i	1.64386	−	0.156970i	0.875557	+	0.483114i	$0.160494\pi$
$200$	0.464179	−	9.74432i	0.0328224	−	0.689028i
$201$	0.120351	−	0.496096i	0.00848894	−	0.0349919i
$202$	−6.91042	+	5.98791i	−0.486215	+	0.421308i
$203$	−2.39050	+	9.04980i	−0.167780	+	0.635171i
$204$	−1.10035	+	0.502512i	−0.0770397	+	0.0351829i
$205$	1.03821	−	1.32019i	0.0725116	−	0.0922060i
$206$	0.197068	+	0.341331i	0.0137304	+	0.0237817i
$207$	−4.76330	−	0.557682i	−0.331072	−	0.0387616i
$208$	8.61841	+	4.97584i	0.597579	+	0.345013i
$209$	11.4547	+	1.64693i	0.792336	+	0.113921i
$210$	−0.924409	−	0.0628187i	−0.0637903	−	0.00433490i
$211$	−5.10111	−	1.49782i	−0.351175	−	0.103114i	0.101388	−	0.994847i	$-0.467672\pi$
$211$	−5.10111	−	1.49782i	−0.351175	−	0.103114i	−0.452562	+	0.891733i	$0.649490\pi$
$212$	3.64149	+	18.8938i	0.250098	+	1.29763i
$213$	−2.15415	+	2.25921i	−0.147600	+	0.154798i
$214$	5.11883	+	0.243840i	0.349916	+	0.0166686i
$215$	−2.48958	+	1.77282i	−0.169788	+	0.120906i
$216$	1.59299	+	1.38033i	0.108389	+	0.0939195i
$217$	−17.9167	−	8.62493i	−1.21626	−	0.585498i
$218$	−1.51744	+	0.218175i	−0.102774	+	0.0147767i
$219$	8.50702	+	3.40570i	0.574851	+	0.230136i
$220$	−1.28693	+	2.49629i	−0.0867647	+	0.168300i
$221$	0.640479	−	3.32312i	0.0430833	−	0.223537i
$222$	−0.974681	−	1.36875i	−0.0654163	−	0.0918643i
$223$	5.64500	−	8.78380i	0.378017	−	0.588207i	−0.599161	−	0.800629i	$-0.704499\pi$
$223$	5.64500	−	8.78380i	0.378017	−	0.588207i	0.977178	+	0.212422i	$0.0681353\pi$
$224$	−9.64155	+	10.6820i	−0.644203	+	0.713720i
$225$	−3.03081	−	3.49774i	−0.202054	−	0.233183i
$226$	−0.849091	−	0.890501i	−0.0564807	−	0.0592353i
$227$	−10.5690	+	14.8421i	−0.701488	+	0.985102i	0.298045	+	0.954552i	$0.403665\pi$
$227$	−10.5690	+	14.8421i	−0.701488	+	0.985102i	−0.999533	+	0.0305502i	$0.990274\pi$
$228$	−2.60487	−	6.50666i	−0.172512	−	0.430914i
$229$	−12.6269	+	21.8704i	−0.834408	+	1.44524i	0.0601027	+	0.998192i	$0.480857\pi$
$229$	−12.6269	+	21.8704i	−0.834408	+	1.44524i	−0.894511	+	0.447046i	$0.852476\pi$
$230$	1.34204	−	1.00978i	0.0884913	−	0.0665828i
$231$	−6.41608	−	3.47394i	−0.422147	−	0.228569i
$232$	−1.06126	+	7.38119i	−0.0696748	+	0.484599i
$233$	11.5088	+	1.09896i	0.753965	+	0.0719950i	0.464959	−	0.885332i	$-0.346069\pi$
$233$	11.5088	+	1.09896i	0.753965	+	0.0719950i	0.289006	+	0.957327i	$0.406675\pi$
$234$	−2.60790	+	0.632671i	−0.170484	+	0.0413590i
$235$	1.78573	+	0.618048i	0.116488	+	0.0403170i
$236$	−14.7163	−	3.57014i	−0.957951	−	0.232396i
$237$	7.98856	+	5.13394i	0.518913	+	0.333485i
$238$	1.01320	+	0.429631i	0.0656763	+	0.0278488i
$239$	−8.60813	+	9.93431i	−0.556814	+	0.642597i	−0.962457	−	0.271434i	$-0.912502\pi$
$239$	−8.60813	+	9.93431i	−0.556814	+	0.642597i	0.405643	+	0.914031i	$0.367048\pi$
$240$	1.29721	−	0.0617938i	0.0837346	−	0.00398877i
$241$	−3.21768	+	2.53041i	−0.207269	+	0.162998i	−0.716397	−	0.697692i	$-0.754210\pi$
$241$	−3.21768	+	2.53041i	−0.207269	+	0.162998i	0.509129	+	0.860691i	$0.329968\pi$
$242$	−1.53268	+	1.20531i	−0.0985243	+	0.0774804i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	−9.18344	+	10.5983i	−0.587910	+	0.678484i
$245$	−2.66230	−	3.33638i	−0.170088	−	0.213154i
$246$	1.33074	+	0.855212i	0.0848446	+	0.0545263i
$247$	19.0556	+	4.62283i	1.21248	+	0.294144i
$248$	−14.9704	−	5.18130i	−0.950621	−	0.329013i
$249$	−8.77061	+	2.12773i	−0.555815	+	0.134839i
$250$	3.35652	+	0.320509i	0.212285	+	0.0202707i
$251$	2.29326	−	15.9500i	0.144750	−	1.00676i	−0.779891	−	0.625915i	$-0.784726\pi$
$251$	2.29326	−	15.9500i	0.144750	−	1.00676i	0.924641	−	0.380840i	$-0.124365\pi$
$252$	0.120834	+	4.41719i	0.00761182	+	0.278257i
$253$	12.9163	−	2.84295i	0.812040	−	0.178735i
$254$	3.77881	−	6.54509i	0.237104	−	0.410675i
$255$	−0.164142	−	0.410008i	−0.0102790	−	0.0256757i
$256$	−2.52316	+	3.54328i	−0.157698	+	0.221455i
$257$	−3.59712	−	3.77255i	−0.224382	−	0.235325i	0.601914	−	0.798561i	$-0.294405\pi$
$257$	−3.59712	−	3.77255i	−0.224382	−	0.235325i	−0.826296	+	0.563235i	$0.809556\pi$
$258$	−1.88506	−	2.17547i	−0.117359	−	0.135439i
$259$	1.61860	−	7.56981i	0.100575	−	0.470365i
$260$	−2.57275	+	4.00327i	−0.159555	+	0.248273i
$261$	2.05214	+	2.88182i	0.127024	+	0.178380i
$262$	−1.23227	+	6.39365i	−0.0761301	+	0.395001i
$263$	−10.7985	+	20.9461i	−0.665861	+	1.29159i	0.277787	+	0.960643i	$0.410399\pi$
$263$	−10.7985	+	20.9461i	−0.665861	+	1.29159i	−0.943649	+	0.330948i	$0.892631\pi$
$264$	−5.39636	−	2.16038i	−0.332123	−	0.132962i
$265$	−6.95353	+	0.999766i	−0.427152	+	0.0614151i
$266$	−2.76576	+	5.74535i	−0.169580	+	0.352270i
$267$	−5.43344	−	4.70810i	−0.332521	−	0.288131i
$268$	0.694503	−	0.494554i	0.0424235	−	0.0302097i
$269$	22.6579	+	1.07933i	1.38148	+	0.0658078i	0.725109	−	0.688634i	$-0.241789\pi$
$269$	22.6579	+	1.07933i	1.38148	+	0.0658078i	0.656367	+	0.754442i	$0.272092\pi$
$270$	−0.241665	+	0.253451i	−0.0147073	+	0.0154246i
$271$	0.0312568	+	0.162176i	0.00189871	+	0.00985146i	0.982866	−	0.184323i	$-0.0590093\pi$
$271$	0.0312568	+	0.162176i	0.00189871	+	0.00985146i	−0.980967	+	0.194175i	$0.937797\pi$
$272$	−1.48007	−	0.434587i	−0.0897423	−	0.0263507i
$273$	−10.2626	−	6.89297i	−0.621122	−	0.417181i
$274$	5.76334	+	0.828643i	0.348176	+	0.0500602i
$275$	11.0532	+	6.38156i	0.666533	+	0.384823i
$276$	−5.40241	−	5.91366i	−0.325187	−	0.355960i
$277$	6.17734	+	10.6995i	0.371161	+	0.642869i	0.989744	−	0.142850i	$-0.0456266\pi$
$277$	6.17734	+	10.6995i	0.371161	+	0.642869i	−0.618584	+	0.785719i	$0.712293\pi$
$278$	−3.36238	+	4.27561i	−0.201662	+	0.256434i
$279$	−6.83649	+	3.12212i	−0.409290	+	0.186916i
$280$	−2.41308	−	2.39601i	−0.144209	−	0.143189i
$281$	−22.1138	+	19.1618i	−1.31920	+	1.14309i	−0.339950	+	0.940443i	$0.610410\pi$
$281$	−22.1138	+	19.1618i	−1.31920	+	1.14309i	−0.979251	+	0.202651i	$0.935044\pi$
$282$	−0.419598	+	1.72961i	−0.0249867	+	0.102996i
$283$	−1.11640	+	23.4362i	−0.0663633	+	1.39314i	0.682730	+	0.730671i	$0.260793\pi$
$283$	−1.11640	+	23.4362i	−0.0663633	+	1.39314i	−0.749093	+	0.662465i	$0.769510\pi$
$284$	−5.18998	+	0.495583i	−0.307969	+	0.0294074i
$285$	2.41812	−	0.836920i	0.143237	−	0.0495749i
$286$	6.22563	−	4.00097i	0.368130	−	0.236582i
$287$	1.23394	+	7.18206i	0.0728375	+	0.423943i
$288$	0.774022	+	5.38344i	0.0456097	+	0.317222i
$289$	−0.783932	−	16.4568i	−0.0461137	−	0.968045i
$290$	−1.21655	−	0.234472i	−0.0714385	−	0.0137687i
$291$	0.493290	+	5.16597i	0.0289172	+	0.302834i
$292$	7.01289	+	13.6031i	0.410398	+	0.796062i
$293$	13.7197	−	4.02848i	0.801516	−	0.235346i	0.144777	−	0.989464i	$-0.453753\pi$
$293$	13.7197	−	4.02848i	0.801516	−	0.235346i	0.656739	+	0.754118i	$0.271935\pi$
$294$	2.88978	−	2.79483i	0.168536	−	0.162998i
$295$	1.55762	−	5.30478i	0.0906883	−	0.308856i
$296$	0.586215	−	6.13912i	0.0340731	−	0.356829i
$297$	−2.56016	+	1.02493i	−0.148556	+	0.0594727i
$298$	7.91948	−	4.57231i	0.458763	−	0.264867i
$299$	22.2441	−	2.71493i	1.28641	−	0.157008i
$300$		−	7.72982i		−	0.446281i
$301$	1.52760	−	13.1727i	0.0880493	−	0.759263i
$302$	−0.472907	−	1.03552i	−0.0272127	−	0.0595876i
$303$	−11.5228	+	10.9869i	−0.661966	+	0.631184i
$304$	2.92315	−	8.44590i	0.167654	−	0.484406i
$305$	−3.70547	−	3.53316i	−0.212175	−	0.202308i
$306$	0.369721	−	0.190604i	0.0211355	−	0.0108961i
$307$	0.228480	+	0.104343i	0.0130400	+	0.00595518i	0.421924	−	0.906631i	$-0.361355\pi$
$307$	0.228480	+	0.104343i	0.0130400	+	0.00595518i	−0.408884	+	0.912586i	$0.634082\pi$
$308$	−4.29900	−	11.4023i	−0.244959	−	0.649708i
$309$	0.371028	+	0.577330i	0.0211070	+	0.0328432i
$310$	0.978209	−	2.44345i	0.0555585	−	0.138779i
$311$	9.68859	+	12.3200i	0.549389	+	0.698606i	0.978873	−	0.204469i	$-0.0655468\pi$
$311$	9.68859	+	12.3200i	0.549389	+	0.698606i	−0.429484	+	0.903075i	$0.641304\pi$
$312$	−8.75420	−	4.51311i	−0.495609	−	0.255504i
$313$	−3.35373	−	9.68997i	−0.189564	−	0.547709i	0.809668	−	0.586888i	$-0.199647\pi$
$313$	−3.35373	−	9.68997i	−0.189564	−	0.547709i	−0.999232	+	0.0391786i	$0.987526\pi$
$314$	−2.47048	+	5.40959i	−0.139417	+	0.305281i
$315$	−1.61297	−	0.0326693i	−0.0908808	−	0.00184071i
$316$	4.46826	+	15.2175i	0.251359	+	0.856051i
$317$	−34.0736	+	6.56714i	−1.91376	+	0.368847i	−0.999354	−	0.0359453i	$-0.988556\pi$
$317$	−34.0736	+	6.56714i	−1.91376	+	0.368847i	−0.914408	+	0.404793i	$0.867344\pi$
$318$	−1.55990	−	6.43000i	−0.0874749	−	0.360576i
$319$	−7.94721	−	5.65918i	−0.444958	−	0.316853i
$320$	0.544496	+	0.428196i	0.0304383	+	0.0239369i
$321$	8.92308			0.498038
$322$	−0.649156	+	7.25824i	−0.0361760	+	0.404486i
$323$	−3.03937			−0.169115
$324$	1.31284	+	1.03243i	0.0729355	+	0.0573571i
$325$	17.6158	+	12.5442i	0.977150	+	0.695826i
$326$	1.20335	+	4.96028i	0.0666474	+	0.274724i
$327$	−2.62112	+	0.505179i	−0.144948	+	0.0279365i
$328$	1.63564	+	5.57048i	0.0903131	+	0.307578i
$329$	−7.18218	+	3.95492i	−0.395966	+	0.218042i
$330$	0.401185	−	0.878473i	0.0220845	−	0.0483584i
$331$	−6.13510	−	17.7262i	−0.337216	−	0.974320i	−0.978362	−	0.206902i	$-0.933662\pi$
$331$	−6.13510	−	17.7262i	−0.337216	−	0.974320i	0.641146	−	0.767419i	$-0.278459\pi$
$332$	−13.3976	−	6.90697i	−0.735291	−	0.379069i
$333$	−1.80860	−	2.29983i	−0.0991109	−	0.126030i
$334$	1.82726	−	4.56428i	0.0999833	−	0.249746i
$335$	0.168291	+	0.261865i	0.00919469	+	0.0143072i
$336$	−3.57223	+	4.35787i	−0.194881	+	0.237741i
$337$	12.1771	+	5.56111i	0.663330	+	0.302933i	0.718482	−	0.695545i	$-0.244837\pi$
$337$	12.1771	+	5.56111i	0.663330	+	0.302933i	−0.0551522	+	0.998478i	$0.517564\pi$
$338$	4.50922	−	2.32466i	0.245269	−	0.126445i
$339$	−1.55055	−	1.47845i	−0.0842144	−	0.0802983i
$340$	0.241251	−	0.697050i	0.0130837	−	0.0378028i
$341$	15.0001	−	14.3025i	0.812299	−	0.774526i
$342$	1.00117	+	2.19226i	0.0541372	+	0.118544i
$343$	18.4861	+	1.12449i	0.998155	+	0.0607166i
$344$		−	10.5648i		−	0.569616i
$345$	2.25046	−	1.86744i	0.121161	−	0.100539i
$346$	5.90686	−	3.41033i	0.317555	−	0.183340i
$347$	20.0652	−	8.03289i	1.07716	−	0.431228i	0.235851	−	0.971789i	$-0.424212\pi$
$347$	20.0652	−	8.03289i	1.07716	−	0.431228i	0.841305	+	0.540561i	$0.181788\pi$
$348$	−0.561662	+	5.88199i	−0.0301082	+	0.315308i
$349$	−5.55908	+	18.9325i	−0.297571	+	1.01343i	0.665993	+	0.745958i	$0.268008\pi$
$349$	−5.55908	+	18.9325i	−0.297571	+	1.01343i	−0.963564	+	0.267476i	$0.913810\pi$
$350$	−5.18686	+	4.74889i	−0.277249	+	0.253839i
$351$	−4.48336	+	1.31643i	−0.239304	+	0.0702660i
$352$	−6.87275	−	13.3313i	−0.366319	−	0.710560i
$353$	−2.91299	−	30.5062i	−0.155043	−	1.62368i	−0.653611	−	0.756831i	$-0.726747\pi$
$353$	−2.91299	−	30.5062i	−0.155043	−	1.62368i	0.498568	−	0.866850i	$-0.333859\pi$
$354$	5.11312	+	0.985473i	0.271759	+	0.0523773i
$355$	−0.0905705	−	1.90131i	−0.00480698	−	0.100911i
$356$	−1.70886	−	11.8854i	−0.0905694	−	0.629924i
$357$	1.79780	+	0.663288i	0.0951497	+	0.0351049i
$358$	9.98024	−	6.41391i	0.527472	−	0.338986i
$359$	−16.0579	+	5.55771i	−0.847506	+	0.293325i	−0.716094	−	0.698003i	$-0.754072\pi$
$359$	−16.0579	+	5.55771i	−0.847506	+	0.293325i	−0.131411	+	0.991328i	$0.541951\pi$
$360$	−1.27947	+	0.122175i	−0.0674340	+	0.00643917i
$361$	−0.0661434	+	1.38852i	−0.00348123	+	0.0730800i
$362$	−3.14395	+	12.9595i	−0.165242	+	0.681139i
$363$	−2.56584	+	2.22331i	−0.134672	+	0.116694i
$364$	−5.41474	−	19.9250i	−0.283809	−	1.04435i
$365$	−5.08265	+	2.32117i	−0.266038	+	0.121496i
$366$	2.98089	−	3.79051i	0.155813	−	0.198133i
$367$	8.26826	+	14.3210i	0.431599	+	0.747552i	0.997011	−	0.0772566i	$-0.0246161\pi$
$367$	8.26826	+	14.3210i	0.431599	+	0.747552i	−0.565412	+	0.824809i	$0.691283\pi$
$368$	−0.268102	−	10.2106i	−0.0139758	−	0.532262i
$369$	2.38532	+	1.37717i	0.124175	+	0.0716925i
$370$	1.01418	+	0.145817i	0.0527248	+	0.00758069i
$371$	16.9952	−	25.3033i	0.882345	−	1.31368i
$372$	−12.0439	−	3.53642i	−0.624449	−	0.183355i
$373$	4.39905	+	22.8244i	0.227774	+	1.18180i	0.898119	+	0.439754i	$0.144934\pi$
$373$	4.39905	+	22.8244i	0.227774	+	1.18180i	−0.670345	+	0.742050i	$0.733854\pi$
$374$	−0.791587	+	0.830193i	−0.0409320	+	0.0429282i
$375$	5.86434	+	0.279353i	0.302833	+	0.0144257i
$376$	−5.32086	+	3.78897i	−0.274403	+	0.195401i
$377$	−12.4932	−	10.8255i	−0.643435	−	0.557540i
$378$	−0.113777	−	1.51522i	−0.00585204	−	0.0779346i
$379$	−23.6718	+	3.40349i	−1.21594	+	0.174826i	−0.720275	−	0.693688i	$-0.755985\pi$
$379$	−23.6718	+	3.40349i	−1.21594	+	0.174826i	−0.495665	+	0.868514i	$0.665075\pi$
$380$	3.96758	+	1.58838i	0.203533	+	0.0814821i
$381$	6.03000	−	11.6966i	0.308926	−	0.599233i
$382$	−2.05631	+	10.6692i	−0.105210	+	0.545882i
$383$	−5.87778	−	8.25419i	−0.300341	−	0.421769i	0.636634	−	0.771166i	$-0.280326\pi$
$383$	−5.87778	−	8.25419i	−0.300341	−	0.421769i	−0.936975	+	0.349396i	$0.886387\pi$
$384$	−6.23360	+	9.69967i	−0.318107	+	0.494984i
$385$	4.23292	−	1.36969i	0.215730	−	0.0698061i
$386$	−8.03681	−	9.27497i	−0.409063	−	0.472084i
$387$	−3.45881	−	3.62749i	−0.175821	−	0.184396i
$388$	−5.02751	+	7.06014i	−0.255233	+	0.358424i
$389$	−2.58595	−	6.45939i	−0.131113	−	0.327504i	0.848256	−	0.529587i	$-0.177653\pi$
$389$	−2.58595	−	6.45939i	−0.131113	−	0.327504i	−0.979368	+	0.202083i	$0.935229\pi$
$390$	0.818177	−	1.41712i	0.0414300	−	0.0717589i
$391$	−3.25152	+	1.22184i	−0.164436	+	0.0617912i
$392$	14.7327	−	0.806640i	0.744113	−	0.0407415i
$393$	−1.61351	+	11.2222i	−0.0813906	+	0.566084i
$394$	−15.7174	−	1.50083i	−0.791831	−	0.0756107i
$395$	−5.62719	+	1.36514i	−0.283134	+	0.0686877i
$396$	−4.35250	−	1.50641i	−0.218721	−	0.0757002i
$397$	26.9039	+	6.52683i	1.35027	+	0.327572i	0.844712	−	0.535221i	$-0.179772\pi$
$397$	26.9039	+	6.52683i	1.35027	+	0.327572i	0.505558	+	0.862793i	$0.331287\pi$
$398$	−11.2548	−	7.23303i	−0.564153	−	0.362559i
$399$	−4.33432	+	10.2217i	−0.216988	+	0.511725i
$400$	6.45497	−	7.44943i	0.322749	−	0.372472i
$401$	21.1555	−	1.00776i	1.05646	−	0.0503253i	0.487844	−	0.872931i	$-0.337783\pi$
$401$	21.1555	−	1.00776i	1.05646	−	0.0503253i	0.568613	+	0.822605i	$0.307480\pi$
$402$	−0.230454	+	0.181231i	−0.0114940	+	0.00903896i
$403$	27.6045	−	21.7085i	1.37508	−	1.08138i
$404$	−26.5611	+	1.26526i	−1.32146	+	0.0629490i
$405$	−0.399316	+	0.460835i	−0.0198422	+	0.0228991i
$406$	4.29199	−	3.23677i	0.213008	−	0.160638i
$407$	6.78762	+	4.36214i	0.336450	+	0.216223i
$408$	1.48361	+	0.359921i	0.0734498	+	0.0178187i
$409$	−16.5031	−	5.71176i	−0.816024	−	0.282429i	−0.113000	−	0.993595i	$-0.536046\pi$
$409$	−16.5031	−	5.71176i	−0.816024	−	0.282429i	−0.703024	+	0.711166i	$0.748167\pi$
$410$	−0.937378	+	0.227405i	−0.0462938	+	0.0112307i
$411$	10.0925	+	0.963716i	0.497826	+	0.0475366i
$412$	−0.163120	+	1.13452i	−0.00803634	+	0.0558940i
$413$	12.5580	+	20.4391i	0.617937	+	1.00574i
$414$	1.95236	+	1.94281i	0.0959531	+	0.0954838i
$415$	2.75160	−	4.76591i	0.135071	−	0.233949i
$416$	−9.44525	−	23.5931i	−0.463092	−	1.15675i
$417$	−5.49375	+	7.71489i	−0.269030	+	0.377800i
$418$	−4.58641	−	4.81009i	−0.224329	−	0.235269i
$419$	20.9851	+	24.2181i	1.02519	+	1.18313i	0.982922	+	0.184024i	$0.0589124\pi$
$419$	20.9851	+	24.2181i	1.02519	+	1.18313i	0.0422664	+	0.999106i	$0.486542\pi$
$420$	−2.00021	−	1.80539i	−0.0976002	−	0.0880939i
$421$	9.03446	−	14.0579i	0.440312	−	0.685140i	−0.548188	−	0.836355i	$-0.684682\pi$
$421$	9.03446	−	14.0579i	0.440312	−	0.685140i	0.988501	+	0.151215i	$0.0483187\pi$
$422$	1.77109	+	2.48715i	0.0862155	+	0.121073i
$423$	−0.586483	+	3.04296i	−0.0285158	+	0.147954i
$424$	11.1274	−	21.5842i	0.540396	−	1.04822i
$425$	−3.11197	−	1.24584i	−0.150953	−	0.0604323i
$426$	1.77453	−	0.255138i	0.0859760	−	0.0123615i
$427$	22.1526	−	1.66342i	1.07204	−	0.0804986i
$428$	11.2630	+	9.75940i	0.544415	+	0.471739i
$429$	10.4964	−	7.47445i	0.506771	−	0.360870i
$430$	1.75328	+	0.0835190i	0.0845506	+	0.00402764i
$431$	14.0484	−	14.7335i	0.676688	−	0.709690i	−0.292430	−	0.956287i	$-0.594464\pi$
$431$	14.0484	−	14.7335i	0.676688	−	0.709690i	0.969118	+	0.246597i	$0.0793124\pi$
$432$	0.403064	+	2.09129i	0.0193924	+	0.100617i
$433$	−12.7982	−	3.75788i	−0.615040	−	0.180592i	−0.0406495	−	0.999173i	$-0.512943\pi$
$433$	−12.7982	−	3.75788i	−0.615040	−	0.180592i	−0.574390	+	0.818581i	$0.694761\pi$
$434$	5.02631	+	10.2543i	0.241271	+	0.492225i
$435$	−2.13531	−	0.307011i	−0.102380	−	0.0147200i
$436$	−3.86097	−	2.22913i	−0.184907	−	0.106756i
$437$	−6.17486	−	19.1546i	−0.295383	−	0.916289i
$438$	−2.63133	−	4.55760i	−0.125730	−	0.217771i
$439$	−13.7653	+	17.5040i	−0.656982	+	0.835420i	−0.994372	−	0.105945i	$-0.966213\pi$
$439$	−13.7653	+	17.5040i	−0.656982	+	0.835420i	0.337390	+	0.941365i	$0.390456\pi$
$440$	3.22414	−	1.47242i	0.153705	−	0.0701947i
$441$	4.79448	−	5.10029i	0.228308	−	0.242871i
$442$	−1.46890	+	1.27281i	−0.0698685	+	0.0605414i
$443$	−2.13609	+	8.80509i	−0.101489	+	0.418342i	−0.999778	−	0.0210619i	$-0.993295\pi$
$443$	−2.13609	+	8.80509i	−0.101489	+	0.418342i	0.898289	+	0.439404i	$0.144810\pi$
$444$	0.232512	−	4.88102i	0.0110345	−	0.231643i
$445$	4.36409	−	0.416720i	0.206878	−	0.0197544i
$446$	−5.66677	+	1.96129i	−0.268329	+	0.0928697i
$447$	13.3951	−	8.60848i	0.633564	−	0.407167i
$448$	−2.96215	+	0.508926i	−0.139949	+	0.0240445i
$449$	−3.24341	−	22.5584i	−0.153066	−	1.06460i	−0.911042	−	0.412315i	$-0.864720\pi$
$449$	−3.24341	−	22.5584i	−0.153066	−	1.06460i	0.757975	−	0.652283i	$-0.226189\pi$
$450$	0.126474	+	2.65501i	0.00596203	+	0.125158i
$451$	−7.45837	−	1.43748i	−0.351201	−	0.0676884i
$452$	−0.340131	−	3.56202i	−0.0159984	−	0.167543i
$453$	−0.908292	−	1.76184i	−0.0426753	−	0.0827785i
$454$	10.0404	−	2.94814i	0.471221	−	0.138363i
$455$	7.36037	−	1.62853i	0.345060	−	0.0763465i
$456$	−2.49201	+	8.48700i	−0.116699	+	0.397440i
$457$	−0.607955	+	6.36679i	−0.0284389	+	0.297826i	0.970051	+	0.242899i	$0.0780985\pi$
$457$	−0.607955	+	6.36679i	−0.0284389	+	0.297826i	−0.998490	+	0.0549265i	$0.982508\pi$
$458$	13.4646	−	5.39043i	0.629161	−	0.251878i
$459$	0.627242	−	0.362138i	0.0292772	−	0.0169032i
$460$	4.88306	+	0.104262i	0.227674	+	0.00486125i
$461$			23.9955i			1.11758i	0.829309	+	0.558791i	$0.188735\pi$
$461$			23.9955i			1.11758i	−0.829309	+	0.558791i	$0.811265\pi$
$462$	1.66317	+	3.84609i	0.0773776	+	0.178936i
$463$	−13.6031	−	29.7865i	−0.632188	−	1.38430i	−0.906314	−	0.422604i	$-0.861116\pi$
$463$	−13.6031	−	29.7865i	−0.632188	−	1.38430i	0.274127	−	0.961694i	$-0.411611\pi$
$464$	−5.45318	+	5.19960i	−0.253158	+	0.241385i
$465$	1.49890	−	4.33079i	0.0695098	−	0.200836i
$466$	−4.80538	−	4.58192i	−0.222605	−	0.212253i
$467$	5.44530	−	2.80724i	0.251978	−	0.129904i	−0.327611	−	0.944813i	$-0.606243\pi$
$467$	5.44530	−	2.80724i	0.251978	−	0.129904i	0.579589	+	0.814909i	$0.303213\pi$
$468$	−7.09883	−	3.24193i	−0.328143	−	0.149858i
$469$	−1.33270	−	0.219245i	−0.0615385	−	0.0101238i
$470$	−0.586734	−	0.912976i	−0.0270640	−	0.0421124i
$471$	−3.84856	+	9.61325i	−0.177333	+	0.442955i
$472$	11.8139	+	15.0225i	0.543777	+	0.691469i
$473$	12.2856	+	6.33366i	0.564892	+	0.291222i
$474$	−1.78373	−	5.15374i	−0.0819292	−	0.236719i
$475$	8.06809	−	17.6667i	0.370189	−	0.810602i
$476$	1.54378	+	2.80352i	0.0707589	+	0.128499i
$477$	−3.24577	−	11.0541i	−0.148614	−	0.506131i
$478$	7.41290	−	1.42872i	0.339058	−	0.0653481i
$479$	−3.40211	−	14.0237i	−0.155446	−	0.640758i	−0.995206	−	0.0978001i	$-0.968819\pi$
$479$	−3.40211	−	14.0237i	−0.155446	−	0.640758i	0.839760	−	0.542958i	$-0.182696\pi$
$480$	−2.70148	−	1.92372i	−0.123305	−	0.0878053i
$481$	10.7462	+	8.45094i	0.489987	+	0.385330i
$482$	2.35093			0.107082
$483$	−0.527691	+	12.6776i	−0.0240108	+	0.576851i
$484$	−5.67036			−0.257744
$485$	−2.48738	−	1.95610i	−0.112946	−	0.0888217i
$486$	−0.467821	−	0.333134i	−0.0212208	−	0.0151113i
$487$	3.03225	+	12.4991i	0.137404	+	0.566389i	0.998336	+	0.0576679i	$0.0183664\pi$
$487$	3.03225	+	12.4991i	0.137404	+	0.566389i	−0.860931	+	0.508721i	$0.830118\pi$
$488$	17.3784	−	3.34942i	0.786685	−	0.151621i
$489$	2.50388	+	8.52742i	0.113229	+	0.385623i
$490$	0.0173980	+	2.45134i	0.000785962	+	0.110740i
$491$	−10.6782	+	23.3819i	−0.481898	+	1.05521i	0.500039	+	0.866003i	$0.333319\pi$
$491$	−10.6782	+	23.3819i	−0.481898	+	1.05521i	−0.981937	+	0.189207i	$0.939408\pi$
$492$	1.50458	+	4.34719i	0.0678315	+	0.195986i
$493$	2.27752	+	1.17414i	0.102574	+	0.0528807i
$494$	−6.96127	−	8.85197i	−0.313202	−	0.398269i
$495$	0.624976	−	1.56111i	0.0280906	−	0.0701669i
$496$	−8.65389	−	13.4657i	−0.388571	−	0.604628i
$497$	6.38728	+	5.23578i	0.286509	+	0.234857i
$498$	4.71478	+	2.15317i	0.211274	+	0.0964858i
$499$	−31.2082	+	16.0890i	−1.39707	+	0.720241i	−0.981882	−	0.189494i	$-0.939315\pi$
$499$	−31.2082	+	16.0890i	−1.39707	+	0.720241i	−0.415191	+	0.909734i	$0.636285\pi$
$500$	7.09660	+	6.76659i	0.317369	+	0.302611i
$501$	2.79989	−	8.08976i	0.125090	−	0.361424i
$502$	−6.69778	+	6.38632i	−0.298937	+	0.285036i
$503$	5.08868	+	11.1427i	0.226893	+	0.496826i	0.988501	−	0.151211i	$-0.0483173\pi$
$503$	5.08868	+	11.1427i	0.226893	+	0.496826i	−0.761609	+	0.648037i	$0.775590\pi$
$504$	3.32617	−	4.47627i	0.148159	−	0.199389i
$505$		−	9.70835i		−	0.432016i
$506$	−6.84022	−	3.30208i	−0.304085	−	0.146795i
$507$	7.65002	−	4.41674i	0.339749	−	0.196154i
$508$	20.4040	−	8.16855i	0.905283	−	0.362421i
$509$	2.95328	−	30.9282i	0.130902	−	1.37087i	−0.656452	−	0.754367i	$-0.727944\pi$
$509$	2.95328	−	30.9282i	0.130902	−	1.37087i	0.787354	−	0.616501i	$-0.211450\pi$
$510$	−0.0714591	+	0.243367i	−0.00316426	+	0.0107765i
$511$	7.30001	−	23.1190i	0.322934	−	1.02272i
$512$	−19.7290	+	5.79295i	−0.871906	+	0.256015i
$513$	1.92291	+	3.72992i	0.0848985	+	0.164680i
$514$	0.284567	+	2.98012i	0.0125517	+	0.131447i
$515$	−0.410908	−	0.0791961i	−0.0181068	−	0.00348980i
$516$	−0.398317	−	8.36170i	−0.0175349	−	0.368103i
$517$	−1.21623	−	8.45903i	−0.0534895	−	0.372028i
$518$	−3.41811	+	2.84268i	−0.150183	+	0.124900i
$519$	9.99091	−	6.42077i	0.438552	−	0.281840i
$520$	5.67538	−	1.96427i	0.248882	−	0.0861389i
$521$	35.5432	−	3.39397i	1.55718	−	0.148692i	0.719358	−	0.694640i	$-0.244436\pi$
$521$	35.5432	−	3.39397i	1.55718	−	0.148692i	0.837819	+	0.545947i	$0.183830\pi$
$522$	0.0966776	−	2.02951i	0.00423147	−	0.0888294i
$523$	0.729776	−	3.00818i	0.0319109	−	0.131538i	−0.953628	−	0.300988i	$-0.902684\pi$
$523$	0.729776	−	3.00818i	0.0319109	−	0.131538i	0.985539	+	0.169449i	$0.0541989\pi$
$524$	−14.3106	+	12.4002i	−0.625161	+	0.541705i
$525$	−8.62775	+	8.68920i	−0.376546	+	0.379228i
$526$	12.3111	−	5.62227i	0.536788	−	0.245143i
$527$	−3.36490	+	4.27882i	−0.146577	+	0.186388i
$528$	−2.93665	−	5.08643i	−0.127801	−	0.221358i
$529$	−14.3061	−	18.0093i	−0.622005	−	0.783013i
$530$	3.49403	+	2.01728i	0.151771	+	0.0876251i
$531$	8.97459	+	1.29035i	0.389464	+	0.0559965i
$532$	−16.6506	+	8.16153i	−0.721896	+	0.353847i
$533$	−12.3487	−	3.62590i	−0.534880	−	0.157055i
$534$	0.781419	+	4.05439i	0.0338153	+	0.175450i
$535$	−3.75475	+	3.93787i	−0.162332	+	0.170249i
$536$	−1.07479	−	0.0511987i	−0.0464240	−	0.00221145i
$537$	16.8267	−	11.9822i	0.726124	−	0.517070i
$538$	−9.84550	−	8.53117i	−0.424469	−	0.367805i
$539$	−7.89431	+	17.6159i	−0.340032	+	0.758771i
$540$	−1.00805	+	0.144936i	−0.0433797	+	0.00623706i
$541$	1.36779	+	0.547579i	0.0588057	+	0.0235423i	0.400879	−	0.916131i	$-0.368705\pi$
$541$	1.36779	+	0.547579i	0.0588057	+	0.0235423i	−0.342073	+	0.939673i	$0.611129\pi$
$542$	0.0434644	−	0.0843092i	0.00186696	−	0.00362139i
$543$	−4.39439	+	22.8002i	−0.188581	+	0.978452i
$544$	2.28496	+	3.20878i	0.0979669	+	0.137575i
$545$	0.880001	−	1.36931i	0.0376951	−	0.0586547i
$546$	2.18584	+	6.75516i	0.0935454	+	0.289094i
$547$	−13.3292	−	15.3827i	−0.569917	−	0.657719i	0.395489	−	0.918471i	$-0.370575\pi$
$547$	−13.3292	−	15.3827i	−0.569917	−	0.657719i	−0.965406	+	0.260752i	$0.916030\pi$
$548$	11.6850	+	12.2548i	0.499157	+	0.523501i
$549$	4.87044	−	6.83957i	0.207865	−	0.291906i
$550$	−2.72429	−	6.80496i	−0.116164	−	0.290164i
$551$	−7.42309	+	12.8572i	−0.316234	+	0.547733i
$552$	0.745866	+	10.0812i	0.0317461	+	0.429084i
$553$	11.9624	−	22.0935i	0.508692	−	0.939511i
$554$	1.00979	−	7.02323i	0.0429018	−	0.298388i
$555$	1.77599	+	0.169586i	0.0753865	+	0.00719854i
$556$	−15.3723	+	3.72929i	−0.651932	+	0.158157i
$557$	−8.77297	−	3.03635i	−0.371722	−	0.128654i	0.134818	−	0.990870i	$-0.456955\pi$
$557$	−8.77297	−	3.03635i	−0.371722	−	0.128654i	−0.506541	+	0.862216i	$0.669076\pi$
$558$	4.19467	+	1.01762i	0.177574	+	0.0430791i
$559$	19.7023	+	12.6619i	0.833316	+	0.535540i
$560$	−0.420022	−	3.41022i	−0.0177492	−	0.144108i
$561$	−1.30798	+	1.50949i	−0.0552229	+	0.0637306i
$562$	16.7858	−	0.799607i	0.708067	−	0.0337294i
$563$	−16.0662	+	12.6346i	−0.677111	+	0.532486i	−0.896440	−	0.443165i	$-0.853856\pi$
$563$	−16.0662	+	12.6346i	−0.677111	+	0.532486i	0.219329	+	0.975651i	$0.429613\pi$
$564$	−4.06844	+	3.19946i	−0.171312	+	0.134721i
$565$	1.30492	−	0.0621608i	0.0548982	−	0.00261513i
$566$	8.82422	−	10.1837i	0.370909	−	0.428052i
$567$	−0.323421	−	2.62591i	−0.0135824	−	0.110278i
$568$	5.53526	+	3.55729i	0.232254	+	0.149261i
$569$	35.1978	+	8.53888i	1.47557	+	0.357969i	0.891233	−	0.453545i	$-0.149841\pi$
$569$	35.1978	+	8.53888i	1.47557	+	0.357969i	0.584333	+	0.811514i	$0.301356\pi$
$570$	−1.38876	−	0.480654i	−0.0581686	−	0.0201324i
$571$	−13.9134	+	3.37535i	−0.582257	+	0.141254i	−0.516060	−	0.856553i	$-0.672602\pi$
$571$	−13.9134	+	3.37535i	−0.582257	+	0.141254i	−0.0661969	+	0.997807i	$0.521087\pi$
$572$	21.4238	+	2.04573i	0.895775	+	0.0855361i
$573$	−2.69248	+	18.7266i	−0.112480	+	0.782315i
$574$	1.99270	−	3.68034i	0.0831735	−	0.153614i
$575$	1.52917	−	22.1432i	0.0637706	−	0.923436i
$576$	−0.567996	+	0.983798i	−0.0236665	+	0.0409916i
$577$	11.0990	+	27.7241i	0.462059	+	1.15417i	0.958244	+	0.285951i	$0.0923096\pi$
$577$	11.0990	+	27.7241i	0.462059	+	1.15417i	−0.496185	+	0.868217i	$0.665266\pi$
$578$	−5.48852	+	7.70755i	−0.228292	+	0.320592i
$579$	−14.7464	−	15.4656i	−0.612838	−	0.642726i
$580$	−2.35946	−	2.72296i	−0.0979711	−	0.113065i
$581$	7.35117	+	22.7182i	0.304978	+	0.942509i
$582$	1.61131	−	2.50725i	0.0667910	−	0.103929i
$583$	18.4289	+	25.8797i	0.763245	+	1.07183i
$584$	3.65536	−	18.9658i	0.151260	−	0.784810i
$585$	1.30560	−	2.53251i	0.0539798	−	0.104706i
$586$	−7.62382	−	3.05212i	−0.314937	−	0.126082i
$587$	−30.2253	+	4.34574i	−1.24753	+	0.179368i	−0.734265	−	0.678862i	$-0.762473\pi$
$587$	−30.2253	+	4.34574i	−1.24753	+	0.179368i	−0.513265	+	0.858230i	$0.671564\pi$
$588$	11.6300	−	1.19389i	0.479615	−	0.0492350i
$589$	−23.8355	−	20.6536i	−0.982123	−	0.851015i
$590$	−2.58646	+	1.84181i	−0.106483	+	0.0758260i
$591$	−27.4607	−	1.30811i	−1.12958	−	0.0538086i
$592$	4.30009	−	4.50980i	0.176733	−	0.185352i
$593$	−1.11264	−	5.77295i	−0.0456908	−	0.237067i	0.951903	−	0.306401i	$-0.0991247\pi$
$593$	−1.11264	−	5.77295i	−0.0456908	−	0.237067i	−0.997593	+	0.0693340i	$0.977913\pi$
$594$	1.51963	+	0.446203i	0.0623511	+	0.0183079i
$595$	−1.04922	+	0.514287i	−0.0430136	+	0.0210837i
$596$	26.3229	+	3.78466i	1.07823	+	0.155026i
$597$	−20.1741	−	11.6475i	−0.825670	−	0.476701i
$598$	−11.0057	−	6.67139i	−0.450057	−	0.272813i
$599$	13.3350	+	23.0969i	0.544853	+	0.943713i	0.998616	+	0.0525909i	$0.0167479\pi$
$599$	13.3350	+	23.0969i	0.544853	+	0.943713i	−0.453763	+	0.891122i	$0.649919\pi$
$600$	−6.03037	+	7.66824i	−0.246189	+	0.313055i
$601$	−27.2630	+	12.4506i	−1.11208	+	0.507871i	−0.884806	−	0.465960i	$-0.845709\pi$
$601$	−27.2630	+	12.4506i	−1.11208	+	0.507871i	−0.227276	+	0.973830i	$0.572982\pi$
$602$	−5.36615	+	5.40437i	−0.218708	+	0.220266i
$603$	−0.385799	+	0.334297i	−0.0157110	+	0.0136136i
$604$	0.780500	−	3.21726i	0.0317581	−	0.130909i
$605$	0.0985055	−	2.06789i	0.00400482	−	0.0840715i
$606$	9.10239	−	0.869173i	0.369759	−	0.0353077i
$607$	−37.5805	+	13.0067i	−1.52535	+	0.527927i	−0.955796	−	0.294029i	$-0.905004\pi$
$607$	−37.5805	+	13.0067i	−1.52535	+	0.527927i	−0.569550	+	0.821957i	$0.692882\pi$
$608$	−19.2003	+	12.3393i	−0.778676	+	0.500425i
$609$	7.19664	−	5.98512i	0.291623	−	0.242529i
$610$	0.418469	+	2.91051i	0.0169433	+	0.117843i
$611$	−0.689001	−	14.4639i	−0.0278740	−	0.585148i
$612$	1.18780	+	0.228930i	0.0480140	+	0.00925395i
$613$	1.78523	+	18.6958i	0.0721047	+	0.755114i	0.957147	+	0.289603i	$0.0935234\pi$
$613$	1.78523	+	18.6958i	0.0721047	+	0.755114i	−0.885042	+	0.465511i	$0.845871\pi$
$614$	−0.0661014	−	0.128219i	−0.00266763	−	0.00517449i
$615$	−1.61148	+	0.473174i	−0.0649813	+	0.0190802i
$616$	−4.63070	+	14.6653i	−0.186576	+	0.590883i
$617$	0.533035	−	1.81535i	0.0214592	−	0.0730833i	−0.948067	−	0.318070i	$-0.896965\pi$
$617$	0.533035	−	1.81535i	0.0214592	−	0.0730833i	0.969526	+	0.244987i	$0.0787835\pi$
$618$	0.0374650	−	0.392351i	0.00150706	−	0.0157827i
$619$	32.1352	−	12.8650i	1.29162	−	0.517088i	0.378813	−	0.925473i	$-0.376332\pi$
$619$	32.1352	−	12.8650i	1.29162	−	0.517088i	0.912810	+	0.408385i	$0.133908\pi$
$620$	6.62865	−	3.82705i	0.266213	−	0.153698i
$621$	3.55658	+	3.21726i	0.142721	+	0.129104i
$622$		−	9.00137i		−	0.360922i
$623$	−11.3451	+	15.2679i	−0.454531	+	0.611695i
$624$	−4.13408	−	9.05237i	−0.165496	−	0.362385i
$625$	14.1569	−	13.4986i	0.566276	−	0.539943i
$626$	−1.92609	+	5.56507i	−0.0769820	+	0.222425i
$627$	−8.37538	−	7.98591i	−0.334481	−	0.318927i
$628$	−15.3720	+	7.92483i	−0.613410	+	0.316235i
$629$	−1.92759	−	0.880299i	−0.0768579	−	0.0350998i
$630$	0.716563	+	0.587381i	0.0285486	+	0.0234018i
$631$	−5.95816	−	9.27108i	−0.237191	−	0.369076i	0.702168	−	0.712011i	$-0.252215\pi$
$631$	−5.95816	−	9.27108i	−0.237191	−	0.369076i	−0.939359	+	0.342935i	$0.888579\pi$
$632$	7.43917	−	18.5821i	0.295914	−	0.739158i
$633$	3.28642	+	4.17902i	0.130623	+	0.166101i
$634$	17.7136	+	9.13200i	0.703498	+	0.362678i
$635$	2.62447	+	7.58292i	0.104149	+	0.300919i
$636$	7.99323	−	17.5027i	0.316952	−	0.694028i
$637$	−16.1528	+	28.4417i	−0.639996	+	1.12690i
$638$	1.57859	+	5.37617i	0.0624968	+	0.212845i
$639$	3.06519	−	0.590767i	0.121257	−	0.0233704i
$640$	−1.65755	−	6.83250i	−0.0655203	−	0.270078i
$641$	−34.0856	−	24.2722i	−1.34630	−	0.958696i	−0.999787	−	0.0206512i	$-0.993426\pi$
$641$	−34.0856	−	24.2722i	−1.34630	−	0.958696i	−0.346514	−	0.938045i	$-0.612635\pi$
$642$	−4.02824	−	3.16784i	−0.158982	−	0.125025i
$643$	−22.2909			−0.879069			−0.439534	−	0.898226i	$-0.644857\pi$
$643$	−22.2909			−0.879069			−0.439534	+	0.898226i	$0.644857\pi$
$644$	−14.5319	+	15.4249i	−0.572636	+	0.607824i
$645$	3.05629			0.120341
$646$	1.37209	+	1.07903i	0.0539842	+	0.0424537i
$647$	−9.83954	−	7.00671i	−0.386832	−	0.275462i	0.370052	−	0.929011i	$-0.379340\pi$
$647$	−9.83954	−	7.00671i	−0.386832	−	0.275462i	−0.756884	+	0.653549i	$0.773279\pi$
$648$	−0.496938	−	2.04841i	−0.0195216	−	0.0804690i
$649$	−24.5519	+	4.73199i	−0.963746	+	0.185747i
$650$	−3.49910	−	11.9169i	−0.137246	−	0.467417i
$651$	9.59153	+	17.4183i	0.375922	+	0.682679i
$652$	−6.16620	+	13.5021i	−0.241487	+	0.528783i
$653$	−8.44533	−	24.4012i	−0.330491	−	0.954892i	−0.980765	−	0.195192i	$-0.937467\pi$
$653$	−8.44533	−	24.4012i	−0.330491	−	0.954892i	0.650274	−	0.759700i	$-0.274654\pi$
$654$	1.36262	+	0.702482i	0.0532828	+	0.0274692i
$655$	−4.27354	−	5.43425i	−0.166981	−	0.212334i
$656$	−2.18022	+	5.44593i	−0.0851234	+	0.212628i
$657$	−4.95412	−	7.70876i	−0.193278	−	0.300747i
$658$	4.64638	+	0.764384i	0.181135	+	0.0297988i
$659$	−9.41429	−	4.29936i	−0.366729	−	0.167479i	0.223523	−	0.974699i	$-0.428244\pi$
$659$	−9.41429	−	4.29936i	−0.366729	−	0.167479i	−0.590252	+	0.807219i	$0.700971\pi$
$660$	2.49629	−	1.28693i	0.0971680	−	0.0500936i
$661$	21.8453	+	20.8294i	0.849682	+	0.810170i	0.983514	−	0.180834i	$-0.0578796\pi$
$661$	21.8453	+	20.8294i	0.849682	+	0.810170i	−0.133831	+	0.991004i	$0.542728\pi$
$662$	−3.52346	+	10.1804i	−0.136943	+	0.395672i
$663$	−2.44932	+	2.33542i	−0.0951236	+	0.0907002i
$664$	7.90249	+	17.3040i	0.306676	+	0.671527i
$665$	−2.68712	−	6.21399i	−0.104202	−	0.240968i
$666$			1.68032i			0.0651110i
$667$	−2.77258	+	16.7387i	−0.107355	+	0.648126i
$668$	12.3821	−	7.14880i	0.479077	−	0.276595i
$669$	−9.69339	+	3.88065i	−0.374768	+	0.150034i
$670$	0.0169933	−	0.177962i	0.000656510	−	0.00687528i
$671$	−6.52351	+	22.2170i	−0.251837	+	0.857679i
$672$	14.0499	−	3.10863i	0.541988	−	0.119918i
$673$	−22.3436	+	6.56066i	−0.861281	+	0.252895i	−0.682403	−	0.730976i	$-0.739065\pi$
$673$	−22.3436	+	6.56066i	−0.861281	+	0.252895i	−0.178878	+	0.983871i	$0.557247\pi$
$674$	−3.52296	−	6.83358i	−0.135699	−	0.263220i
$675$	0.439936	+	4.60722i	0.0169332	+	0.177332i
$676$	14.4868	+	2.79209i	0.557183	+	0.107388i
$677$	−1.12587	−	23.6350i	−0.0432709	−	0.908367i	−0.911272	−	0.411805i	$-0.864899\pi$
$677$	−1.12587	−	23.6350i	−0.0432709	−	0.908367i	0.868001	−	0.496562i	$-0.165405\pi$
$678$	0.175108	+	1.21790i	0.00672498	+	0.0467732i
$679$	13.5318	−	2.32488i	0.519301	−	0.0892209i
$680$	−0.783128	+	0.503286i	−0.0300316	+	0.0193001i
$681$	17.2185	−	5.95937i	0.659813	−	0.228364i
$682$	−11.8493	+	1.13147i	−0.453732	+	0.0433262i
$683$	0.269510	−	5.65771i	0.0103125	−	0.216486i	−0.987829	−	0.155545i	$-0.950287\pi$
$683$	0.269510	−	5.65771i	0.0103125	−	0.216486i	0.998141	−	0.0609414i	$-0.0194103\pi$
$684$	−1.65237	+	6.81114i	−0.0631798	+	0.260431i
$685$	−4.67213	+	4.04842i	−0.178513	+	0.154682i
$686$	−7.94615	−	7.07050i	−0.303385	−	0.269953i
$687$	22.9716	−	10.4908i	0.876423	−	0.400249i
$688$	6.59877	−	8.39102i	0.251576	−	0.319905i
$689$	26.9161	+	46.6201i	1.02542	+	1.77608i
$690$	−1.67892	+	0.0440840i	−0.0639154	+	0.00167825i
$691$	−27.5035	−	15.8792i	−1.04628	−	0.604072i	−0.124677	−	0.992197i	$-0.539790\pi$
$691$	−27.5035	−	15.8792i	−1.04628	−	0.604072i	−0.921607	+	0.388125i	$0.873123\pi$
$692$	19.6334	+	2.82285i	0.746348	+	0.107309i
$693$	3.21130	+	6.55148i	0.121987	+	0.248870i
$694$	−11.9100	−	3.49710i	−0.452099	−	0.132748i
$695$	−1.09296	−	5.67082i	−0.0414583	−	0.215106i
$696$	5.14599	−	5.39695i	0.195058	−	0.204571i
$697$	1.99264	+	0.0949212i	0.0754767	+	0.00359540i
$698$	9.23094	−	6.57332i	0.349396	−	0.248804i
$699$	−8.73732	−	7.57093i	−0.330476	−	0.286359i
$700$	−20.3938	+	1.53135i	−0.770812	+	0.0578796i
$701$	41.9940	−	6.03783i	1.58609	−	0.228046i	0.707885	−	0.706327i	$-0.249649\pi$
$701$	41.9940	−	6.03783i	1.58609	−	0.228046i	0.878206	+	0.478282i	$0.158740\pi$
$702$	2.49132	+	0.997375i	0.0940289	+	0.0376435i
$703$	5.62603	−	10.9130i	0.212190	−	0.411591i
$704$	0.592872	−	3.07611i	0.0223447	−	0.115935i
$705$	−1.09611	−	1.53927i	−0.0412820	−	0.0579724i
$706$	−9.51516	+	14.8059i	−0.358108	+	0.557227i
$707$	31.2699	+	28.2242i	1.17603	+	1.06148i
$708$	9.91668	+	11.4445i	0.372691	+	0.430109i
$709$	26.2885	+	27.5706i	0.987284	+	1.03543i	0.999369	+	0.0355070i	$0.0113046\pi$
$709$	26.2885	+	27.5706i	0.987284	+	1.03543i	−0.0120851	+	0.999927i	$0.503847\pi$
$710$	−0.634108	+	0.890481i	−0.0237977	+	0.0334191i
$711$	−3.52932	−	8.81580i	−0.132360	−	0.330618i
$712$	−7.57706	+	13.1239i	−0.283962	+	0.491837i
$713$	−33.8021	−	12.5132i	−1.26590	−	0.468623i
$714$	−0.576122	−	0.937683i	−0.0215608	−	0.0350919i
$715$	−1.11822	+	7.77737i	−0.0418190	+	0.290857i
$716$	34.3443	+	3.27948i	1.28351	+	0.122560i
$717$	12.7744	−	3.09905i	0.477070	−	0.115736i
$718$	9.22228	+	3.19186i	0.344172	+	0.119119i
$719$	−11.0695	−	2.68544i	−0.412823	−	0.100150i	0.0239680	−	0.999713i	$-0.492370\pi$
$719$	−11.0695	−	2.68544i	−0.412823	−	0.100150i	−0.436791	+	0.899563i	$0.643885\pi$
$720$	−1.09252	−	0.702120i	−0.0407158	−	0.0261665i
$721$	1.44968	−	1.09327i	0.0539889	−	0.0407153i
$722$	0.522807	−	0.603352i	0.0194569	−	0.0224544i
$723$	4.08883	−	0.194775i	0.152065	−	0.00724375i
$724$	−30.4839	+	23.9728i	−1.13293	+	0.890943i
$725$	−12.8706	+	10.1215i	−0.478001	+	0.375904i
$726$	1.94763	−	0.0927772i	0.0722835	−	0.00344329i
$727$	−24.5202	+	28.2978i	−0.909402	+	1.04951i	0.0891663	+	0.996017i	$0.471580\pi$
$727$	−24.5202	+	28.2978i	−0.909402	+	1.04951i	−0.998568	+	0.0534892i	$0.982966\pi$
$728$	−10.1727	+	23.9905i	−0.377027	+	0.889148i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	3.11857	+	0.756556i	0.115423	+	0.0280014i
$731$	−3.43055	−	1.18733i	−0.126884	−	0.0439149i
$732$	13.6282	−	3.30617i	0.503713	−	0.122199i
$733$	0.391693	+	0.0374022i	0.0144675	+	0.00138148i	0.102287	−	0.994755i	$-0.467384\pi$
$733$	0.391693	+	0.0374022i	0.0144675	+	0.00138148i	−0.0878198	+	0.996136i	$0.527990\pi$
$734$	1.35158	−	9.40046i	0.0498878	−	0.346977i
$735$	0.233353	+	4.26202i	0.00860736	+	0.157207i
$736$	−15.5801	+	20.9192i	−0.574289	+	0.771093i
$737$	0.703883	−	1.21916i	0.0259279	−	0.0449084i
$738$	−0.587914	−	1.46854i	−0.0216414	−	0.0540576i
$739$	1.95258	−	2.74201i	0.0718268	−	0.100867i	−0.777100	−	0.629377i	$-0.783310\pi$
$739$	1.95258	−	2.74201i	0.0718268	−	0.100867i	0.848927	+	0.528511i	$0.177249\pi$
$740$	2.05622	+	2.15650i	0.0755881	+	0.0792745i
$741$	−12.8407	−	14.8190i	−0.471715	−	0.544388i
$742$	−16.6554	+	5.38937i	−0.611439	+	0.197850i
$743$	4.45665	−	6.93469i	0.163499	−	0.254409i	−0.749831	−	0.661629i	$-0.769865\pi$
$743$	4.45665	−	6.93469i	0.163499	−	0.254409i	0.913330	+	0.407220i	$0.133502\pi$
$744$	9.18907	+	12.9042i	0.336888	+	0.473093i
$745$	−1.83749	+	9.53378i	−0.0673203	+	0.349291i
$746$	6.11714	−	11.8656i	0.223964	−	0.434430i
$747$	8.37853	+	3.35426i	0.306554	+	0.122726i
$748$	−3.30193	+	0.474746i	−0.120731	+	0.0173584i
$749$	−1.76775	−	23.5420i	−0.0645920	−	0.860205i
$750$	−2.54822	−	2.20805i	−0.0930480	−	0.0806266i
$751$	41.2789	−	29.3946i	1.50629	−	1.07262i	0.532158	−	0.846645i	$-0.321381\pi$
$751$	41.2789	−	29.3946i	1.50629	−	1.07262i	0.974132	−	0.225979i	$-0.0725582\pi$
$752$	−6.59265	−	0.314046i	−0.240409	−	0.0114521i
$753$	−11.1199	+	11.6623i	−0.405233	+	0.424996i
$754$	1.79674	+	9.32235i	0.0654333	+	0.339500i
$755$	1.15972	+	0.340526i	0.0422067	+	0.0123930i
$756$	2.46379	−	3.66823i	0.0896073	−	0.133412i
$757$	−23.6970	−	3.40711i	−0.861282	−	0.123834i	−0.302501	−	0.953149i	$-0.597822\pi$
$757$	−23.6970	−	3.40711i	−0.861282	−	0.123834i	−0.558781	+	0.829315i	$0.688731\pi$
$758$	11.8947	+	6.86741i	0.432035	+	0.249436i
$759$	−12.1704	−	5.17639i	−0.441757	−	0.187891i
$760$	−2.69681	−	4.67101i	−0.0978235	−	0.169435i
$761$	−2.14467	+	2.72717i	−0.0777443	+	0.0988600i	−0.823370	−	0.567506i	$-0.807909\pi$
$761$	−2.14467	+	2.72717i	−0.0777443	+	0.0988600i	0.745625	+	0.666366i	$0.232151\pi$
$762$	−6.87465	+	3.13955i	−0.249042	+	0.113734i
$763$	1.85209	+	6.81528i	0.0670503	+	0.246730i
$764$	−23.8803	+	20.6924i	−0.863958	+	0.748624i
$765$	−0.104121	+	0.429195i	−0.00376452	+	0.0155176i
$766$	−0.276906	+	5.81298i	−0.0100050	+	0.210032i
$767$	−42.1743	+	4.02716i	−1.52283	+	0.145412i
$768$	4.11061	−	1.42270i	0.148329	−	0.0513371i
$769$	0.494459	−	0.317770i	0.0178307	−	0.0114591i	−0.531695	−	0.846936i	$-0.678445\pi$
$769$	0.494459	−	0.317770i	0.0178307	−	0.0114591i	0.549526	+	0.835477i	$0.314808\pi$
$770$	−2.39718	−	0.884423i	−0.0863882	−	0.0318724i
$771$	0.741833	+	5.15956i	0.0267165	+	0.185817i
$772$	−1.69820	−	35.6495i	−0.0611194	−	1.28305i
$773$	21.4396	+	4.13214i	0.771128	+	0.148623i	0.559616	−	0.828752i	$-0.310949\pi$
$773$	21.4396	+	4.13214i	0.771128	+	0.148623i	0.211513	+	0.977375i	$0.432161\pi$
$774$	0.273625	+	2.86553i	0.00983524	+	0.102999i
$775$	−15.9389	−	30.9171i	−0.572541	−	1.11057i
$776$	10.4954	−	3.08172i	0.376762	−	0.110627i
$777$	−5.70939	+	5.22730i	−0.204823	+	0.187528i
$778$	−1.12579	+	3.83408i	−0.0403614	+	0.137458i
$779$	−1.09869	+	11.5060i	−0.0393646	+	0.412245i
$780$	4.41783	−	1.76863i	0.158184	−	0.0633271i
$781$	−7.45512	+	4.30422i	−0.266765	+	0.154017i
$782$	1.90164	+	0.602754i	0.0680025	+	0.0215544i
$783$		−	3.53782i		−	0.126431i
$784$	12.2052	+	8.56136i	0.435898	+	0.305763i
$785$	−2.62301	−	5.74359i	−0.0936192	−	0.204997i
$786$	4.71246	−	4.49332i	0.168088	−	0.160271i
$787$	−6.89211	+	19.9134i	−0.245677	+	0.709838i	0.752981	+	0.658043i	$0.228615\pi$
$787$	−6.89211	+	19.9134i	−0.245677	+	0.709838i	−0.998658	+	0.0517949i	$0.983506\pi$
$788$	−33.2309	−	31.6856i	−1.18380	−	1.12875i
$789$	20.9461	−	10.7985i	0.745700	−	0.384435i
$790$	3.02498	+	1.38146i	0.107624	+	0.0491503i
$791$	−3.59345	+	4.38375i	−0.127768	+	0.155868i
$792$	3.14260	+	4.88999i	0.111668	+	0.173758i
$793$	−14.5817	+	36.4233i	−0.517810	+	1.29343i
$794$	−9.82839	−	12.4978i	−0.348796	−	0.443531i
$795$	6.24410	+	3.21905i	0.221455	+	0.114168i
$796$	−12.7251	−	36.7667i	−0.451028	−	1.30316i
$797$	−22.2521	+	48.7252i	−0.788208	+	1.72594i	−0.106499	+	0.994313i	$0.533964\pi$
$797$	−22.2521	+	48.7252i	−0.788208	+	1.72594i	−0.681710	+	0.731623i	$0.738763\pi$
$798$	5.58556	−	3.07572i	0.197727	−	0.108879i
$799$	0.632351	+	2.15359i	0.0223710	+	0.0761886i
$800$	−24.7169	+	4.76379i	−0.873873	+	0.168425i
$801$	1.69498	+	6.98681i	0.0598892	+	0.246867i
$802$	−9.90823	−	7.05562i	−0.349872	−	0.249143i
$803$	19.8635	+	15.6208i	0.700969	+	0.551248i
$804$	−0.852595			−0.0300687
$805$	−5.37274	−	5.56750i	−0.189364	−	0.196228i
$806$	−20.1687			−0.710411
$807$	−17.8305	−	14.0221i	−0.627663	−	0.493600i
$808$	27.3365	+	19.4663i	0.961696	+	0.684821i
$809$	10.3774	+	42.7761i	0.364849	+	1.50393i	0.798028	+	0.602620i	$0.205876\pi$
$809$	10.3774	+	42.7761i	0.364849	+	1.50393i	−0.433179	+	0.901308i	$0.642608\pi$
$810$	0.343871	−	0.0662757i	0.0120824	−	0.00232869i
$811$	−4.88776	−	16.6462i	−0.171633	−	0.584527i	−0.999714	−	0.0239189i	$-0.992386\pi$
$811$	−4.88776	−	16.6462i	−0.171633	−	0.584527i	0.828081	−	0.560608i	$-0.189433\pi$
$812$	15.6299	+	0.316569i	0.548501	+	0.0111094i
$813$	0.0686100	−	0.150235i	0.00240626	−	0.00526897i
$814$	−1.51557	−	4.37896i	−0.0531208	−	0.153482i
$815$	−4.81687	−	2.48327i	−0.168728	−	0.0869851i
$816$	0.953543	+	1.21253i	0.0333807	+	0.0424470i
$817$	7.81726	−	19.5266i	0.273491	−	0.683148i
$818$	5.42237	+	8.43738i	0.189589	+	0.295006i
$819$	4.36137	+	11.5677i	0.152399	+	0.404210i
$820$	−2.55158	−	1.16527i	−0.0891051	−	0.0406929i
$821$	44.9120	−	23.1538i	1.56744	−	0.808071i	0.567556	−	0.823334i	$-0.307889\pi$
$821$	44.9120	−	23.1538i	1.56744	−	0.808071i	0.999884	+	0.0152630i	$0.00485855\pi$
$822$	−4.21402	−	4.01806i	−0.146981	−	0.140146i
$823$	9.98147	−	28.8396i	0.347932	−	1.00528i	−0.626270	−	0.779607i	$-0.715419\pi$
$823$	9.98147	−	28.8396i	0.347932	−	1.00528i	0.974202	−	0.225678i	$-0.0724597\pi$
$824$	1.04691	−	0.998229i	0.0364709	−	0.0347750i
$825$	−5.30200	−	11.6097i	−0.184592	−	0.404200i
$826$	1.58704	−	13.6853i	0.0552202	−	0.476172i
$827$		−	34.6092i		−	1.20348i	−0.798692	−	0.601740i	$-0.794474\pi$
$827$		−	34.6092i		−	1.20348i	0.798692	−	0.601740i	$-0.205526\pi$
$828$	0.970413	+	7.95083i	0.0337242	+	0.276310i
$829$	19.3915	−	11.1957i	0.673495	−	0.388842i	−0.123905	−	0.992294i	$-0.539542\pi$
$829$	19.3915	−	11.1957i	0.673495	−	0.388842i	0.797400	+	0.603452i	$0.206208\pi$
$830$	−2.93416	+	1.17466i	−0.101846	+	0.0407730i
$831$	1.17439	−	12.2987i	0.0407391	−	0.426639i
$832$	1.49546	−	5.09306i	0.0518456	−	0.176570i
$833$	1.39381	−	4.87459i	0.0482925	−	0.168894i
$834$	5.21901	−	1.53244i	0.180720	−	0.0530640i
$835$	2.39195	+	4.63973i	0.0827767	+	0.160564i
$836$	−1.83724	−	19.2404i	−0.0635421	−	0.665443i
$837$	7.37985	+	1.42235i	0.255085	+	0.0491636i
$838$	−0.875693	−	18.3831i	−0.0302503	−	0.635032i
$839$	−1.78552	−	12.4186i	−0.0616431	−	0.428737i	−0.997151	−	0.0754315i	$-0.975967\pi$
$839$	−1.78552	−	12.4186i	−0.0616431	−	0.428737i	0.935508	−	0.353306i	$-0.114943\pi$
$840$	0.575811	+	3.35145i	0.0198674	+	0.115636i
$841$	−13.8671	+	8.91182i	−0.478175	+	0.307304i
$842$	−9.06930	+	3.13891i	−0.312549	+	0.108174i
$843$	29.1283	−	2.78142i	1.00323	−	0.0957971i
$844$	−0.422497	+	8.86931i	−0.0145430	+	0.305294i
$845$	−1.26989	+	5.23457i	−0.0436857	+	0.180075i
$846$	1.34506	−	1.16550i	0.0462442	−	0.0400709i
$847$	6.37413	+	6.32905i	0.219018	+	0.217469i
$848$	22.3194	−	10.1929i	0.766450	−	0.350026i
$849$	14.5037	−	18.4430i	0.497766	−	0.632961i
$850$	0.962571	+	1.66722i	0.0330159	+	0.0571853i
$851$	1.63166	−	13.9364i	0.0559326	−	0.477734i
$852$	4.51510	+	2.60679i	0.154685	+	0.0893073i
$853$	5.50900	+	0.792075i	0.188625	+	0.0271201i	0.235980	−	0.971758i	$-0.424170\pi$
$853$	5.50900	+	0.792075i	0.188625	+	0.0271201i	−0.0473550	+	0.998878i	$0.515079\pi$
$854$	−10.5911	−	7.11361i	−0.362421	−	0.243423i
$855$	−2.45521	−	0.720913i	−0.0839662	−	0.0246547i
$856$	−3.55949	−	18.4684i	−0.121661	−	0.631236i
$857$	−8.15573	+	8.55348i	−0.278594	+	0.292181i	−0.848133	−	0.529783i	$-0.822273\pi$
$857$	−8.15573	+	8.55348i	−0.278594	+	0.292181i	0.569539	+	0.821964i	$0.307122\pi$
$858$	−7.39204	−	0.352126i	−0.252360	−	0.0120214i
$859$	−16.1910	+	11.5295i	−0.552428	+	0.393382i	−0.821905	−	0.569625i	$-0.807089\pi$
$859$	−16.1910	+	11.5295i	−0.552428	+	0.393382i	0.269477	+	0.963007i	$0.413149\pi$
$860$	3.85773	+	3.34275i	0.131548	+	0.113987i
$861$	3.16086	−	6.56609i	0.107722	−	0.223772i
$862$	−11.5727	+	1.66390i	−0.394167	+	0.0566726i
$863$	−4.80440	−	1.92339i	−0.163544	−	0.0654730i	0.288446	−	0.957496i	$-0.406861\pi$
$863$	−4.80440	−	1.92339i	−0.163544	−	0.0654730i	−0.451990	+	0.892023i	$0.649286\pi$
$864$	2.49220	−	4.83420i	0.0847865	−	0.164463i
$865$	−1.37052	+	7.11092i	−0.0465990	+	0.241778i
$866$	4.44349	+	6.24001i	0.150996	+	0.212044i
$867$	−8.90729	+	13.8600i	−0.302507	+	0.470711i
$868$	−6.94420	+	32.4764i	−0.235702	+	1.10232i
$869$	17.1490	+	19.7910i	0.581739	+	0.671362i
$870$	0.854969	+	0.896666i	0.0289862	+	0.0303998i
$871$	1.38362	−	1.94302i	0.0468820	−	0.0658366i
$872$	2.09117	+	5.22349i	0.0708159	+	0.176890i
$873$	2.59473	−	4.49421i	0.0878184	−	0.152106i
$874$	−4.01262	+	10.8393i	−0.135729	+	0.366646i
$875$	−0.424757	−	15.5274i	−0.0143594	−	0.524921i
$876$	2.17805	−	15.1486i	0.0735893	−	0.511825i
$877$	−43.1845	−	4.12362i	−1.45824	−	0.139245i	−0.664401	−	0.747377i	$-0.731313\pi$
$877$	−43.1845	−	4.12362i	−1.45824	−	0.139245i	−0.793836	+	0.608132i	$0.791919\pi$
$878$	12.4284	−	3.01510i	0.419439	−	0.101755i
$879$	−13.5125	−	4.67673i	−0.455766	−	0.157742i
$880$	3.48042	+	0.844341i	0.117325	+	0.0284627i
$881$	26.2620	+	16.8776i	0.884789	+	0.568619i	0.902243	−	0.431229i	$-0.141920\pi$
$881$	26.2620	+	16.8776i	0.884789	+	0.568619i	−0.0174541	+	0.999848i	$0.505556\pi$
$882$	−3.97511	+	0.600359i	−0.133849	+	0.0202152i
$883$	6.06261	−	6.99662i	0.204023	−	0.235455i	−0.644512	−	0.764594i	$-0.722940\pi$
$883$	6.06261	−	6.99662i	0.204023	−	0.235455i	0.848535	+	0.529139i	$0.177485\pi$
$884$	−5.64590	+	0.268947i	−0.189892	+	0.00904568i
$885$	−4.34587	+	3.41763i	−0.146085	+	0.114882i
$886$	4.09027	−	3.21662i	0.137415	−	0.108065i
$887$	0.767827	−	0.0365761i	0.0257811	−	0.00122811i	−0.0346874	−	0.999398i	$-0.511044\pi$
$887$	0.767827	−	0.0365761i	0.0257811	−	0.00122811i	0.0604685	+	0.998170i	$0.480741\pi$
$888$	−4.03856	+	4.66074i	−0.135525	+	0.156404i
$889$	−32.0539	−	13.5919i	−1.07505	−	0.455857i
$890$	−2.11807	−	1.36120i	−0.0709977	−	0.0456275i
$891$	2.67997	+	0.650152i	0.0897822	+	0.0217809i
$892$	−16.4796	−	5.70365i	−0.551778	−	0.190972i
$893$	−12.6380	+	3.06594i	−0.422913	+	0.102598i
$894$	−9.10322	−	0.869252i	−0.304457	−	0.0290721i
$895$	−1.79260	+	12.4678i	−0.0599201	+	0.416753i
$896$	26.8258	+	14.5247i	0.896187	+	0.485235i
$897$	−19.6943	−	10.6913i	−0.657574	−	0.356973i
$898$	−6.54440	+	11.3352i	−0.218390	+	0.378262i
$899$	9.88216	+	24.6844i	0.329589	+	0.823272i
$900$	−4.48374	+	6.29653i	−0.149458	+	0.209884i
$901$	−5.75817	−	6.03899i	−0.191832	−	0.201188i
$902$	2.85668	+	3.29678i	0.0951169	+	0.109771i
$903$	−8.88528	+	9.84409i	−0.295683	+	0.327591i
$904$	−2.44146	+	3.79899i	−0.0812018	+	0.126352i
$905$	−8.21292	−	11.5334i	−0.273007	−	0.383384i
$906$	−0.215443	+	1.11782i	−0.00715761	+	0.0371372i
$907$	−4.58480	+	8.89327i	−0.152236	+	0.295296i	−0.952604	−	0.304212i	$-0.901607\pi$
$907$	−4.58480	+	8.89327i	−0.152236	+	0.295296i	0.800369	+	0.599508i	$0.204637\pi$
$908$	28.2515	+	11.3102i	0.937560	+	0.375342i
$909$	15.7592	−	2.26584i	0.522701	−	0.0751530i
$910$	−3.90092	−	1.87787i	−0.129314	−	0.0622508i
$911$	−18.5671	−	16.0885i	−0.615155	−	0.533035i	0.290596	−	0.956846i	$-0.406147\pi$
$911$	−18.5671	−	16.0885i	−0.615155	−	0.533035i	−0.905751	+	0.423811i	$0.860692\pi$
$912$	−7.28023	+	5.18423i	−0.241073	+	0.171667i
$913$	−24.8601	−	1.18423i	−0.822749	−	0.0391924i
$914$	2.53477	−	2.65839i	0.0838428	−	0.0879318i
$915$	0.968955	+	5.02741i	0.0320326	+	0.166201i
$916$	40.4695	+	11.8829i	1.33715	+	0.392622i
$917$	29.9274	+	2.03373i	0.988290	+	0.0671597i
$918$	−0.411727	−	0.0591975i	−0.0135890	−	0.00195381i
$919$	−20.8999	−	12.0665i	−0.689423	−	0.398038i	0.113973	−	0.993484i	$-0.463642\pi$
$919$	−20.8999	−	12.0665i	−0.689423	−	0.398038i	−0.803396	+	0.595445i	$0.796976\pi$
$920$	−4.76282	−	3.91292i	−0.157025	−	0.129005i
$921$	−0.125589	−	0.217527i	−0.00413830	−	0.00716775i
$922$	8.51879	−	10.8325i	0.280552	−	0.356750i
$923$	−13.2680	+	6.05928i	−0.436720	+	0.199444i
$924$	−3.11214	+	11.7817i	−0.102382	+	0.387591i
$925$	10.2337	−	8.86753i	0.336481	−	0.291562i
$926$	−4.43375	+	18.2761i	−0.145702	+	0.600591i
$927$	0.0326542	−	0.685497i	0.00107251	−	0.0225147i
$928$	19.1544	−	1.82902i	0.628774	−	0.0600406i
$929$	−22.6218	+	7.82947i	−0.742196	+	0.256876i	−0.671892	−	0.740649i	$-0.734518\pi$
$929$	−22.6218	+	7.82947i	−0.742196	+	0.256876i	−0.0703038	+	0.997526i	$0.522397\pi$
$930$	−2.21416	+	1.42296i	−0.0726053	+	0.0466606i
$931$	27.8268	+	9.41034i	0.911987	+	0.308411i
$932$	−2.74796	−	19.1125i	−0.0900123	−	0.626049i
$933$	−0.745765	−	15.6555i	−0.0244153	−	0.512539i
$934$	−3.45484	−	0.665866i	−0.113046	−	0.0217878i
$935$	−0.115771	−	1.21241i	−0.00378611	−	0.0396499i
$936$	4.51311	+	8.75420i	0.147515	+	0.286140i
$937$	−27.1463	+	7.97088i	−0.886832	+	0.260397i	−0.693259	−	0.720689i	$-0.743826\pi$
$937$	−27.1463	+	7.97088i	−0.886832	+	0.260397i	−0.193573	+	0.981086i	$0.562008\pi$
$938$	0.523800	+	0.572108i	0.0171027	+	0.0186800i
$939$	−2.88886	+	9.83857i	−0.0942745	+	0.321070i
$940$	0.300001	−	3.14176i	0.00978497	−	0.102473i
$941$	9.90896	−	3.96695i	0.323023	−	0.129319i	−0.204483	−	0.978870i	$-0.565551\pi$
$941$	9.90896	−	3.96695i	0.323023	−	0.129319i	0.527506	+	0.849551i	$0.323127\pi$
$942$	5.15026	−	2.97350i	0.167804	−	0.0968820i
$943$	3.45009	+	12.7508i	0.112350	+	0.415224i
$944$			19.3105i			0.628502i
$945$	1.29494	+	0.962229i	0.0421244	+	0.0313013i
$946$	−3.29765	−	7.22085i	−0.107216	−	0.234770i
$947$	34.7146	−	33.1003i	1.12807	−	1.07562i	0.131634	−	0.991298i	$-0.457978\pi$
$947$	34.7146	−	33.1003i	1.12807	−	1.07562i	0.996439	−	0.0843174i	$-0.0268710\pi$
$948$	5.18727	−	14.9876i	0.168475	−	0.486776i
$949$	30.9883	+	29.5473i	1.00592	+	0.959146i
$950$	−9.91421	+	5.11113i	−0.321659	+	0.165827i
$951$	31.5648	+	14.4152i	1.02356	+	0.467444i
$952$	0.655669	−	3.98555i	0.0212504	−	0.129173i
$953$	−17.2116	−	26.7817i	−0.557538	−	0.867546i	0.442028	−	0.897001i	$-0.354259\pi$
$953$	−17.2116	−	26.7817i	−0.557538	−	0.867546i	−0.999566	+	0.0294553i	$0.990623\pi$
$954$	−2.45911	+	6.14255i	−0.0796166	+	0.198873i
$955$	−7.13132	−	9.06821i	−0.230764	−	0.293440i
$956$	19.5138	+	10.0600i	0.631120	+	0.325365i
$957$	3.19096	+	9.21967i	0.103149	+	0.298029i
$958$	−3.44279	+	7.53865i	−0.111231	+	0.243563i
$959$	0.543178	−	26.8182i	0.0175401	−	0.866004i
$960$	−0.195155	−	0.664637i	−0.00629860	−	0.0214511i
$961$	−25.0246	+	4.82310i	−0.807246	+	0.155584i
$962$	−1.85106	−	7.63019i	−0.0596807	−	0.246007i
$963$	−7.26853	−	5.17590i	−0.234225	−	0.166791i
$964$	5.37405	+	4.22620i	0.173087	+	0.136117i
$965$	13.0303			0.419460
$966$	4.73898	−	5.53584i	0.152474	−	0.178113i
$967$	41.0579			1.32033			0.660166	−	0.751119i	$-0.270486\pi$
$967$	41.0579			1.32033			0.660166	+	0.751119i	$0.270486\pi$
$968$	5.62519	+	4.42370i	0.180800	+	0.142183i
$969$	2.47580	+	1.76301i	0.0795340	+	0.0566359i
$970$	0.428456	+	1.76612i	0.0137569	+	0.0567067i
$971$	25.1864	−	4.85428i	0.808269	−	0.155781i	0.231655	−	0.972798i	$-0.425586\pi$
$971$	25.1864	−	4.85428i	0.808269	−	0.155781i	0.576614	+	0.817017i	$0.304374\pi$
$972$	−0.470540	−	1.60251i	−0.0150926	−	0.0514006i
$973$	21.4427	+	12.9659i	0.687423	+	0.415667i
$974$	3.06851	−	6.71910i	0.0983214	−	0.215294i
$975$	−7.07310	−	20.4364i	−0.226520	−	0.654488i
$976$	15.8948	+	8.19431i	0.508779	+	0.262294i
$977$	−16.6329	−	21.1505i	−0.532135	−	0.676664i	0.443447	−	0.896301i	$-0.353755\pi$
$977$	−16.6329	−	21.1505i	−0.532135	−	0.676664i	−0.975582	+	0.219636i	$0.929513\pi$
$978$	1.89702	−	4.73854i	0.0606601	−	0.151522i
$979$	−10.7190	−	16.6790i	−0.342580	−	0.533064i
$980$	−4.36694	+	5.63486i	−0.139497	+	0.179999i
$981$	2.42813	+	1.10889i	0.0775243	+	0.0354042i
$982$	13.1215	−	6.76461i	0.418724	−	0.215867i
$983$	−16.4856	−	15.7190i	−0.525810	−	0.501359i	0.380033	−	0.924973i	$-0.375913\pi$
$983$	−16.4856	−	15.7190i	−0.525810	−	0.501359i	−0.905843	+	0.423614i	$0.860761\pi$
$984$	1.89884	−	5.48634i	0.0605328	−	0.174898i
$985$	12.1325	−	11.5683i	0.386573	−	0.368597i
$986$	−0.611323	−	1.33861i	−0.0194685	−	0.0426301i
$987$	8.14451	+	0.944493i	0.259243	+	0.0300635i
$988$		−	32.7491i		−	1.04189i
$989$	0.513130	−	24.0321i	0.0163166	−	0.764178i
$990$	−0.836360	+	0.482873i	−0.0265813	+	0.0153467i
$991$	−32.8939	+	13.1687i	−1.04491	+	0.418318i	−0.829676	−	0.558245i	$-0.811475\pi$
$991$	−32.8939	+	13.1687i	−1.04491	+	0.418318i	−0.215232	+	0.976563i	$0.569051\pi$
$992$	−3.88553	+	40.6911i	−0.123366	+	1.29194i
$993$	−5.28470	+	17.9980i	−0.167705	+	0.571151i
$994$	−1.02469	−	4.63123i	−0.0325011	−	0.146894i
$995$	13.6293	−	4.00191i	0.432077	−	0.126869i
$996$	6.90697	+	13.3976i	0.218856	+	0.424521i
$997$	2.95346	+	30.9300i	0.0935370	+	0.979564i	0.913416	+	0.407027i	$0.133435\pi$
$997$	2.95346	+	30.9300i	0.0935370	+	0.979564i	−0.819879	+	0.572537i	$0.805959\pi$
$998$	19.8005	+	3.81623i	0.626774	+	0.120801i
$999$	0.139215	+	2.92248i	0.00440456	+	0.0924631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.61.14	✓	640
7.3	odd	6	inner	483.2.bf.a.199.19	yes	640
23.20	odd	22	inner	483.2.bf.a.250.19	yes	640
161.66	even	66	inner	483.2.bf.a.388.14	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.61.14	✓	640	1.1	even	1	trivial
483.2.bf.a.199.19	yes	640	7.3	odd	6	inner
483.2.bf.a.250.19	yes	640	23.20	odd	22	inner
483.2.bf.a.388.14	yes	640	161.66	even	66	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.451440 - 0.355016i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(-0.393756 - 1.62309i) q^{4} +(0.598753 - 0.115400i) q^{5} +(0.161803 + 0.551049i) q^{6} +(-1.36900 + 2.26403i) q^{7} +(-0.875621 + 1.91734i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(-0.451440 - 0.355016i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(-0.393756 - 1.62309i) q^{4} +(0.598753 - 0.115400i) q^{5} +(0.161803 + 0.551049i) q^{6} +(-1.36900 + 2.26403i) q^{7} +(-0.875621 + 1.91734i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-0.311270 - 0.160471i) q^{10} +(-1.70470 - 2.16770i) q^{11} +(-0.620738 + 1.55053i) q^{12} +(-2.52621 - 3.93087i) q^{13} +(1.42179 - 0.536055i) q^{14} +(-0.554668 - 0.253308i) q^{15} +(-1.89303 + 0.975923i) q^{16} +(0.524184 + 0.499808i) q^{17} +(0.187839 - 0.542726i) q^{18} +(-3.03709 + 2.89586i) q^{19} +(-0.423067 - 0.926387i) q^{20} +(2.42842 - 1.05012i) q^{21} +1.58378i q^{22} +(-2.08493 + 4.31892i) q^{23} +(1.82543 - 1.05391i) q^{24} +(-4.29665 + 1.72012i) q^{25} +(-0.255088 + 2.67140i) q^{26} +(0.281733 - 0.959493i) q^{27} +(4.21377 + 1.33053i) q^{28} +(3.39452 - 0.996720i) q^{29} +(0.160471 + 0.311270i) q^{30} +(0.714409 + 7.48163i) q^{31} +(5.34052 + 1.02930i) q^{32} +(0.131217 + 2.75458i) q^{33} +(-0.0591975 - 0.411727i) q^{34} +(-0.558425 + 1.51358i) q^{35} +(1.40503 - 0.902959i) q^{36} +(-2.76488 + 0.956933i) q^{37} +(2.39914 - 0.229090i) q^{38} +(-0.222333 + 4.66734i) q^{39} +(-0.303019 + 1.24906i) q^{40} +(2.08159 - 1.80371i) q^{41} +(-1.46910 - 0.388062i) q^{42} +(-4.55925 + 2.08214i) q^{43} +(-2.84713 + 3.62042i) q^{44} +(0.304886 + 0.528078i) q^{45} +(2.47451 - 1.20955i) q^{46} +(2.68378 + 1.54948i) q^{47} +(2.10810 + 0.303100i) q^{48} +(-3.25166 - 6.19893i) q^{49} +(2.55035 + 0.748851i) q^{50} +(-0.137070 - 0.711188i) q^{51} +(-5.38542 + 5.64807i) q^{52} +(-11.5077 - 0.548179i) q^{53} +(-0.467821 + 0.333134i) q^{54} +(-1.27084 - 1.10119i) q^{55} +(-3.14219 - 4.60728i) q^{56} +(4.15370 - 0.597212i) q^{57} +(-1.88627 - 0.755149i) q^{58} +(4.15468 - 8.05896i) q^{59} +(-0.192737 + 1.00002i) q^{60} +(-4.87044 - 6.83957i) q^{61} +(2.33359 - 3.63114i) q^{62} +(-2.58727 - 0.553217i) q^{63} +(0.743917 + 0.858526i) q^{64} +(-1.96620 - 2.06209i) q^{65} +(0.918683 - 1.29011i) q^{66} +(0.189728 + 0.473918i) q^{67} +(0.604831 - 1.04760i) q^{68} +(4.20355 - 2.30871i) q^{69} +(0.789440 - 0.485039i) q^{70} +(0.444250 - 3.08983i) q^{71} +(-2.09828 - 0.200361i) q^{72} +(-8.90511 + 2.16036i) q^{73} +(1.58790 + 0.549578i) q^{74} +(4.49772 + 1.09113i) q^{75} +(5.89610 + 3.78919i) q^{76} +(7.24147 - 0.891900i) q^{77} +(1.75735 - 2.02809i) q^{78} +(-9.48527 + 0.451839i) q^{79} +(-1.02083 + 0.802792i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(-1.58006 + 0.0752674i) q^{82} +(5.91013 - 6.82065i) q^{83} +(-2.66065 - 3.52805i) q^{84} +(0.371534 + 0.238771i) q^{85} +(2.79742 + 0.678647i) q^{86} +(-3.34324 - 1.15711i) q^{87} +(5.64889 - 1.37041i) q^{88} +(7.15692 + 0.683403i) q^{89} +(0.0498386 - 0.346635i) q^{90} +(12.3580 - 0.338058i) q^{91} +(7.83093 + 1.68342i) q^{92} +(3.75783 - 6.50875i) q^{93} +(-0.661475 - 1.65229i) q^{94} +(-1.48428 + 2.08438i) q^{95} +(-3.75320 - 3.93625i) q^{96} +(-3.39838 - 3.92194i) q^{97} +(-0.732790 + 3.95284i) q^{98} +(1.49093 - 2.31993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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