LMFDB - Embedded newform 71.2.g.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			15.3
Character	$\chi$	$=$	71.15
Dual form			71.2.g.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0758189 - 0.177387i) q^{2} +(-0.355633 - 0.0645379i) q^{3} +(1.35641 + 1.41869i) q^{4} +(-0.0139966 + 0.0430772i) q^{5} +(-0.0384119 + 0.0581915i) q^{6} +(1.74206 - 1.52199i) q^{7} +(0.715719 - 0.268614i) q^{8} +(-2.68639 - 1.00822i) q^{9} +O(q^{10})$	\(q+(0.0758189 - 0.177387i) q^{2} +(-0.355633 - 0.0645379i) q^{3} +(1.35641 + 1.41869i) q^{4} +(-0.0139966 + 0.0430772i) q^{5} +(-0.0384119 + 0.0581915i) q^{6} +(1.74206 - 1.52199i) q^{7} +(0.715719 - 0.268614i) q^{8} +(-2.68639 - 1.00822i) q^{9} +(0.00658013 + 0.00574888i) q^{10} +(-3.34669 + 0.923629i) q^{11} +(-0.390824 - 0.592073i) q^{12} +(0.0252193 + 0.00696008i) q^{13} +(-0.137900 - 0.424414i) q^{14} +(0.00775777 - 0.0144164i) q^{15} +(-0.169504 + 3.77429i) q^{16} +(-2.92807 + 2.12736i) q^{17} +(-0.382525 + 0.400090i) q^{18} +(-2.60396 - 4.83897i) q^{19} +(-0.0800983 + 0.0385733i) q^{20} +(-0.717759 + 0.428841i) q^{21} +(-0.0899027 + 0.663689i) q^{22} +(0.970016 - 4.24992i) q^{23} +(-0.271869 + 0.0493370i) q^{24} +(4.04343 + 2.93772i) q^{25} +(0.00314673 - 0.00394587i) q^{26} +(1.82114 + 1.08808i) q^{27} +(4.52217 + 0.407003i) q^{28} +(-0.203270 - 1.50060i) q^{29} +(-0.00196909 - 0.00246916i) q^{30} +(-0.112892 - 2.51375i) q^{31} +(2.03418 + 0.979608i) q^{32} +(1.24980 - 0.112484i) q^{33} +(0.155364 + 0.680695i) q^{34} +(0.0411801 + 0.0963456i) q^{35} +(-2.21349 - 5.17872i) q^{36} +(1.86910 + 8.18904i) q^{37} +(-1.05580 + 0.0950237i) q^{38} +(-0.00851962 - 0.00410283i) q^{39} +(0.00155348 + 0.0345908i) q^{40} +(2.11713 + 2.65479i) q^{41} +(0.0216512 + 0.159836i) q^{42} +(2.59195 + 0.233279i) q^{43} +(-5.84982 - 3.49511i) q^{44} +(0.0810318 - 0.101611i) q^{45} +(-0.680335 - 0.494292i) q^{46} +(11.6990 - 2.12306i) q^{47} +(0.303866 - 1.33132i) q^{48} +(-0.221321 + 1.63386i) q^{49} +(0.827682 - 0.494517i) q^{50} +(1.17861 - 0.567590i) q^{51} +(0.0243334 + 0.0452191i) q^{52} +(-5.80404 + 6.07055i) q^{53} +(0.331088 - 0.240550i) q^{54} +(0.00705509 - 0.157094i) q^{55} +(0.837996 - 1.55726i) q^{56} +(0.613758 + 1.88895i) q^{57} +(-0.281598 - 0.0777162i) q^{58} +(-4.95917 - 7.51282i) q^{59} +(0.0309751 - 0.00854857i) q^{60} +(-5.89639 - 5.15152i) q^{61} +(-0.454466 - 0.170564i) q^{62} +(-6.21436 + 2.33229i) q^{63} +(-5.36235 + 4.68495i) q^{64} +(-0.000652805 + 0.000988958i) q^{65} +(0.0748055 - 0.230228i) q^{66} +(3.75317 + 3.92550i) q^{67} +(-6.98972 - 1.26845i) q^{68} +(-0.619251 + 1.44881i) q^{69} +0.0202127 q^{70} +(-4.30467 + 7.24360i) q^{71} -2.19353 q^{72} +(2.56474 - 6.00050i) q^{73} +(1.59434 + 0.289331i) q^{74} +(-1.24838 - 1.30570i) q^{75} +(3.33297 - 10.2578i) q^{76} +(-4.42438 + 6.70265i) q^{77} +(-0.00137374 + 0.00120020i) q^{78} +(-1.04138 + 0.390838i) q^{79} +(-0.160213 - 0.0601291i) q^{80} +(5.90506 + 5.15910i) q^{81} +(0.631444 - 0.174267i) q^{82} +(-1.50101 - 2.27393i) q^{83} +(-1.58197 - 0.436595i) q^{84} +(-0.0506578 - 0.155909i) q^{85} +(0.237899 - 0.442091i) q^{86} +(-0.0245559 + 0.546781i) q^{87} +(-2.14719 + 1.56003i) q^{88} +(7.84268 - 8.20280i) q^{89} +(-0.0118807 - 0.0220780i) q^{90} +(0.0545266 - 0.0262586i) q^{91} +(7.34506 - 4.38847i) q^{92} +(-0.122084 + 0.901257i) q^{93} +(0.510403 - 2.23622i) q^{94} +(0.244896 - 0.0444420i) q^{95} +(-0.660199 - 0.479663i) q^{96} +(5.45671 - 6.84250i) q^{97} +(0.273045 + 0.163137i) q^{98} +(9.92176 + 0.892975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{27}{35}\right)$

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 $

$2$	0.0758189	−	0.177387i	0.0536120	−	0.125432i	−0.890581	−	0.454826i	$-0.849702\pi$
$2$	0.0758189	−	0.177387i	0.0536120	−	0.125432i	0.944193	+	0.329394i	$0.106844\pi$
$3$	−0.355633	−	0.0645379i	−0.205325	−	0.0372610i	0.0749198	−	0.997190i	$-0.476130\pi$
$3$	−0.355633	−	0.0645379i	−0.205325	−	0.0372610i	−0.280245	+	0.959929i	$0.590416\pi$
$4$	1.35641	+	1.41869i	0.678204	+	0.709346i
$5$	−0.0139966	+	0.0430772i	−0.00625948	+	0.0192647i	−0.954137	−	0.299369i	$-0.903224\pi$
$5$	−0.0139966	+	0.0430772i	−0.00625948	+	0.0192647i	0.947878	+	0.318633i	$0.103224\pi$
$6$	−0.0384119	+	0.0581915i	−0.0156816	+	0.0237566i
$7$	1.74206	−	1.52199i	0.658436	−	0.575258i	−0.262519	−	0.964927i	$-0.584553\pi$
$7$	1.74206	−	1.52199i	0.658436	−	0.575258i	0.920955	+	0.389669i	$0.127410\pi$
$8$	0.715719	−	0.268614i	0.253045	−	0.0949693i
$9$	−2.68639	−	1.00822i	−0.895465	−	0.336074i
$10$	0.00658013	+	0.00574888i	0.00208082	+	0.00181796i
$11$	−3.34669	+	0.923629i	−1.00907	+	0.278485i	−0.731220	−	0.682141i	$-0.761049\pi$
$11$	−3.34669	+	0.923629i	−1.00907	+	0.278485i	−0.277846	+	0.960626i	$0.589620\pi$
$12$	−0.390824	−	0.592073i	−0.112821	−	0.170917i
$13$	0.0252193	+	0.00696008i	0.00699457	+	0.00193038i	0.269532	−	0.962991i	$-0.413131\pi$
$13$	0.0252193	+	0.00696008i	0.00699457	+	0.00193038i	−0.262538	+	0.964922i	$0.584559\pi$
$14$	−0.137900	−	0.424414i	−0.0368555	−	0.113429i
$15$	0.00775777	−	0.0144164i	0.00200305	−	0.00372229i
$16$	−0.169504	+	3.77429i	−0.0423759	+	0.943573i
$17$	−2.92807	+	2.12736i	−0.710160	+	0.515962i	−0.883225	−	0.468949i	$-0.844633\pi$
$17$	−2.92807	+	2.12736i	−0.710160	+	0.515962i	0.173065	+	0.984910i	$0.444633\pi$
$18$	−0.382525	+	0.400090i	−0.0901620	+	0.0943020i
$19$	−2.60396	−	4.83897i	−0.597390	−	1.11014i	−0.982323	−	0.187192i	$-0.940061\pi$
$19$	−2.60396	−	4.83897i	−0.597390	−	1.11014i	0.384934	−	0.922944i	$-0.374224\pi$
$20$	−0.0800983	+	0.0385733i	−0.0179105	+	0.00862526i
$21$	−0.717759	+	0.428841i	−0.156628	+	0.0935808i
$22$	−0.0899027	+	0.663689i	−0.0191673	+	0.141499i
$23$	0.970016	−	4.24992i	0.202262	−	0.886169i	−0.767293	−	0.641297i	$-0.778397\pi$
$23$	0.970016	−	4.24992i	0.202262	−	0.886169i	0.969555	−	0.244872i	$-0.0787461\pi$
$24$	−0.271869	+	0.0493370i	−0.0554951	+	0.0100709i
$25$	4.04343	+	2.93772i	0.808685	+	0.587544i
$26$	0.00314673	−	0.00394587i	0.000617124	−	0.000773848i
$27$	1.82114	+	1.08808i	0.350479	+	0.209401i
$28$	4.52217	+	0.407003i	0.854610	+	0.0769163i
$29$	−0.203270	−	1.50060i	−0.0377462	−	0.278654i	−0.999979	−	0.00642708i	$-0.997954\pi$
$29$	−0.203270	−	1.50060i	−0.0377462	−	0.278654i	0.962233	−	0.272227i	$-0.0877601\pi$
$30$	−0.00196909	−	0.00246916i	−0.000359505	−	0.000450805i
$31$	−0.112892	−	2.51375i	−0.0202761	−	0.451482i	−0.983292	−	0.182037i	$-0.941731\pi$
$31$	−0.112892	−	2.51375i	−0.0202761	−	0.451482i	0.963016	−	0.269445i	$-0.0868404\pi$
$32$	2.03418	+	0.979608i	0.359595	+	0.173172i
$33$	1.24980	−	0.112484i	0.217563	−	0.0195810i
$34$	0.155364	+	0.680695i	0.0266448	+	0.116738i
$35$	0.0411801	+	0.0963456i	0.00696071	+	0.0162854i
$36$	−2.21349	−	5.17872i	−0.368915	−	0.863120i
$37$	1.86910	+	8.18904i	0.307277	+	1.34627i	0.858886	+	0.512167i	$0.171157\pi$
$37$	1.86910	+	8.18904i	0.307277	+	1.34627i	−0.551608	+	0.834103i	$0.685986\pi$
$38$	−1.05580	+	0.0950237i	−0.171273	+	0.0154149i
$39$	−0.00851962	−	0.00410283i	−0.00136423	−	0.000656979i
$40$	0.00155348	+	0.0345908i	0.000245626	+	0.00546929i
$41$	2.11713	+	2.65479i	0.330640	+	0.414609i	0.919167	−	0.393869i	$-0.128863\pi$
$41$	2.11713	+	2.65479i	0.330640	+	0.414609i	−0.588527	+	0.808477i	$0.700292\pi$
$42$	0.0216512	+	0.159836i	0.00334085	+	0.0246632i
$43$	2.59195	+	0.233279i	0.395268	+	0.0355748i	0.285491	−	0.958381i	$-0.407843\pi$
$43$	2.59195	+	0.233279i	0.395268	+	0.0355748i	0.109777	+	0.993956i	$0.464986\pi$
$44$	−5.84982	−	3.49511i	−0.881894	−	0.526907i
$45$	0.0810318	−	0.101611i	0.0120795	−	0.0151472i
$46$	−0.680335	−	0.494292i	−0.100310	−	0.0728794i
$47$	11.6990	−	2.12306i	1.70648	−	0.309680i	0.764317	−	0.644841i	$-0.223076\pi$
$47$	11.6990	−	2.12306i	1.70648	−	0.309680i	0.942161	+	0.335161i	$0.108791\pi$
$48$	0.303866	−	1.33132i	0.0438593	−	0.192160i
$49$	−0.221321	+	1.63386i	−0.0316174	+	0.233409i
$50$	0.827682	−	0.494517i	0.117052	−	0.0699352i
$51$	1.17861	−	0.567590i	0.165039	−	0.0794785i
$52$	0.0243334	+	0.0452191i	0.00337444	+	0.00627076i
$53$	−5.80404	+	6.07055i	−0.797246	+	0.833854i	−0.989050	−	0.147579i	$-0.952852\pi$
$53$	−5.80404	+	6.07055i	−0.797246	+	0.833854i	0.191804	+	0.981433i	$0.438566\pi$
$54$	0.331088	−	0.240550i	0.0450554	−	0.0327347i
$55$	0.00705509	−	0.157094i	0.000951308	−	0.0211825i
$56$	0.837996	−	1.55726i	0.111982	−	0.208097i
$57$	0.613758	+	1.88895i	0.0812942	+	0.250198i
$58$	−0.281598	−	0.0777162i	−0.0369757	−	0.0102046i
$59$	−4.95917	−	7.51282i	−0.645629	−	0.978086i	−0.999091	−	0.0426373i	$-0.986424\pi$
$59$	−4.95917	−	7.51282i	−0.645629	−	0.978086i	0.353461	−	0.935449i	$-0.385005\pi$
$60$	0.0309751	−	0.00854857i	0.00399886	−	0.00110362i
$61$	−5.89639	−	5.15152i	−0.754955	−	0.659585i	0.191838	−	0.981427i	$-0.438555\pi$
$61$	−5.89639	−	5.15152i	−0.754955	−	0.659585i	−0.946793	+	0.321842i	$0.895698\pi$
$62$	−0.454466	−	0.170564i	−0.0577172	−	0.0216616i
$63$	−6.21436	+	2.33229i	−0.782935	+	0.293841i
$64$	−5.36235	+	4.68495i	−0.670294	+	0.585619i
$65$	−0.000652805	0	0.000988958i	−8.09705e−5	0	0.000122665i
$66$	0.0748055	−	0.230228i	0.00920792	−	0.0283391i
$67$	3.75317	+	3.92550i	0.458522	+	0.479577i	0.911122	−	0.412137i	$-0.135218\pi$
$67$	3.75317	+	3.92550i	0.458522	+	0.479577i	−0.452600	+	0.891714i	$0.649503\pi$
$68$	−6.98972	−	1.26845i	−0.847628	−	0.153822i
$69$	−0.619251	+	1.44881i	−0.0745490	+	0.174416i
$70$	0.0202127			0.00241588
$71$	−4.30467	+	7.24360i	−0.510870	+	0.859658i
$71$	−4.30467	+	7.24360i	−0.510870	+	0.859658i
$72$	−2.19353			−0.258509
$73$	2.56474	−	6.00050i	0.300180	−	0.702306i	−0.699747	−	0.714391i	$-0.746704\pi$
$73$	2.56474	−	6.00050i	0.300180	−	0.702306i	0.999927	+	0.0120848i	$0.00384682\pi$
$74$	1.59434	+	0.289331i	0.185339	+	0.0336340i
$75$	−1.24838	−	1.30570i	−0.144151	−	0.150770i
$76$	3.33297	−	10.2578i	0.382318	−	1.17665i
$77$	−4.42438	+	6.70265i	−0.504205	+	0.763838i
$78$	−0.00137374	+	0.00120020i	−0.000155545	+	0.000135896i
$79$	−1.04138	+	0.390838i	−0.117165	+	0.0439727i	−0.409269	−	0.912414i	$-0.634216\pi$
$79$	−1.04138	+	0.390838i	−0.117165	+	0.0439727i	0.292104	+	0.956387i	$0.405645\pi$
$80$	−0.160213	−	0.0601291i	−0.0179124	−	0.00672264i
$81$	5.90506	+	5.15910i	0.656118	+	0.573233i
$82$	0.631444	−	0.174267i	0.0697313	−	0.0192446i
$83$	−1.50101	−	2.27393i	−0.164757	−	0.249596i	0.742811	−	0.669501i	$-0.233492\pi$
$83$	−1.50101	−	2.27393i	−0.164757	−	0.249596i	−0.907568	+	0.419905i	$0.862063\pi$
$84$	−1.58197	−	0.436595i	−0.172607	−	0.0476365i
$85$	−0.0506578	−	0.155909i	−0.00549461	−	0.0169107i
$86$	0.237899	−	0.442091i	0.0256533	−	0.0476719i
$87$	−0.0245559	+	0.546781i	−0.00263267	+	0.0586210i
$88$	−2.14719	+	1.56003i	−0.228891	+	0.166299i
$89$	7.84268	−	8.20280i	0.831322	−	0.869495i	−0.161771	−	0.986828i	$-0.551720\pi$
$89$	7.84268	−	8.20280i	0.831322	−	0.869495i	0.993093	+	0.117334i	$0.0374347\pi$
$90$	−0.0118807	−	0.0220780i	−0.00125233	−	0.00232722i
$91$	0.0545266	−	0.0262586i	0.00571594	−	0.00275265i
$92$	7.34506	−	4.38847i	0.765775	−	0.457529i
$93$	−0.122084	+	0.901257i	−0.0126595	+	0.0934560i
$94$	0.510403	−	2.23622i	0.0526441	−	0.230649i
$95$	0.244896	−	0.0444420i	0.0251258	−	0.00455966i
$96$	−0.660199	−	0.479663i	−0.0673813	−	0.0489554i
$97$	5.45671	−	6.84250i	0.554045	−	0.694750i	−0.423399	−	0.905943i	$-0.639163\pi$
$97$	5.45671	−	6.84250i	0.554045	−	0.694750i	0.977444	+	0.211193i	$0.0677347\pi$
$98$	0.273045	+	0.163137i	0.0275818	+	0.0164793i
$99$	9.92176	+	0.892975i	0.997175	+	0.0897473i
$100$	1.31681	+	9.72112i	0.131681	+	0.972112i
$101$	11.6065	+	14.5541i	1.15489	+	1.44818i	0.872318	+	0.488938i	$0.162616\pi$
$101$	11.6065	+	14.5541i	1.15489	+	1.44818i	0.282570	+	0.959247i	$0.408813\pi$
$102$	−0.0113220	−	0.252105i	−0.00112105	−	0.0249621i
$103$	−8.44462	−	4.06671i	−0.832073	−	0.400705i	−0.0311808	−	0.999514i	$-0.509927\pi$
$103$	−8.44462	−	4.06671i	−0.832073	−	0.400705i	−0.800892	+	0.598808i	$0.795641\pi$
$104$	0.0199195	−	0.00179279i	0.00195327	−	0.000175797i
$105$	−0.00842706	−	0.0369214i	−0.000822397	−	0.00360316i
$106$	0.636782	+	1.48982i	0.0618497	+	0.144705i
$107$	3.03380	+	7.09794i	0.293289	+	0.686183i	0.999768	−	0.0215507i	$-0.00686034\pi$
$107$	3.03380	+	7.09794i	0.293289	+	0.686183i	−0.706479	+	0.707734i	$0.749717\pi$
$108$	0.926558	+	4.05952i	0.0891581	+	0.390627i
$109$	−10.6593	+	0.959351i	−1.02097	+	0.0918892i	−0.587456	−	0.809256i	$-0.699870\pi$
$109$	−10.6593	+	0.959351i	−1.02097	+	0.0918892i	−0.433517	+	0.901146i	$0.642727\pi$
$110$	−0.0273315	−	0.0131622i	−0.00260596	−	0.00125496i
$111$	−0.136209	−	3.03292i	−0.0129284	−	0.287872i
$112$	5.44915	+	6.83302i	0.514896	+	0.645659i
$113$	−2.19390	−	16.1960i	−0.206385	−	1.52359i	−0.736948	−	0.675949i	$-0.763734\pi$
$113$	−2.19390	−	16.1960i	−0.206385	−	1.52359i	0.530564	−	0.847645i	$-0.321980\pi$
$114$	0.381610	+	0.0343455i	0.0357411	+	0.00321675i
$115$	0.169498	+	0.101270i	0.0158057	+	0.00944348i
$116$	1.85317	−	2.32380i	0.172062	−	0.215759i
$117$	−0.0607316	−	0.0441241i	−0.00561464	−	0.00407928i
$118$	−1.70868	+	0.310079i	−0.157296	+	0.0285451i
$119$	−1.86303	+	8.16248i	−0.170784	+	0.748253i
$120$	0.00167995	−	0.0124019i	0.000153358	−	0.00113213i
$121$	0.904331	−	0.540313i	0.0822120	−	0.0491194i
$122$	−1.36087	+	0.655361i	−0.123207	+	0.0593336i
$123$	−0.581585	−	1.08077i	−0.0524398	−	0.0974495i
$124$	3.41310	−	3.56982i	0.306506	−	0.320580i
$125$	−0.366361	+	0.266177i	−0.0327683	+	0.0238076i
$126$	−0.0574479	+	1.27918i	−0.00511787	+	0.113958i
$127$	8.77375	−	16.3044i	0.778544	−	1.44678i	−0.112881	−	0.993609i	$-0.536008\pi$
$127$	8.77375	−	16.3044i	0.778544	−	1.44678i	0.891425	−	0.453169i	$-0.149706\pi$
$128$	1.81986	+	5.60095i	0.160854	+	0.495059i
$129$	−0.906726	−	0.250241i	−0.0798328	−	0.0220325i
$130$	0.000125933	0	0.000190781i	1.10451e−5	0	1.67326e-5i
$131$	14.2744	−	3.93949i	1.24716	−	0.344195i	0.420707	−	0.907197i	$-0.361782\pi$
$131$	14.2744	−	3.93949i	1.24716	−	0.344195i	0.826456	+	0.563002i	$0.190354\pi$
$132$	1.85482	+	1.62051i	0.161442	+	0.141047i
$133$	−11.9011	−	4.46656i	−1.03196	−	0.387300i
$134$	0.980894	−	0.368136i	0.0847364	−	0.0318021i
$135$	−0.0723612	+	0.0632201i	−0.00622786	+	0.00544112i
$136$	−1.52423	+	2.30911i	−0.130702	+	0.198005i
$137$	−3.98148	+	12.2537i	−0.340161	+	1.04691i	0.623962	+	0.781454i	$0.285522\pi$
$137$	−3.98148	+	12.2537i	−0.340161	+	1.04691i	−0.964124	+	0.265454i	$0.914478\pi$
$138$	0.210049	+	0.219694i	0.0178806	+	0.0187016i
$139$	−20.3910	−	3.70042i	−1.72954	−	0.313866i	−0.779597	−	0.626281i	$-0.784576\pi$
$139$	−20.3910	−	3.70042i	−1.72954	−	0.313866i	−0.949946	+	0.312415i	$0.898862\pi$
$140$	−0.0808277	+	0.189106i	−0.00683119	+	0.0159824i
$141$	−4.29758			−0.361921
$142$	0.958547	+	1.31279i	0.0804394	+	0.110167i
$143$	−0.0908297			−0.00759556
$144$	4.26067	−	9.96834i	0.355056	−	0.830695i
$145$	0.0674866	+	0.0122470i	0.00560446	+	0.00101706i
$146$	−0.869956	−	0.909903i	−0.0719981	−	0.0753041i
$147$	0.184155	−	0.566771i	0.0151889	−	0.0467465i
$148$	−9.08247	+	13.7593i	−0.746574	+	1.13101i
$149$	2.02088	−	1.76559i	0.165557	−	0.144643i	−0.571173	−	0.820829i	$-0.693512\pi$
$149$	2.02088	−	1.76559i	0.165557	−	0.144643i	0.736730	+	0.676187i	$0.236369\pi$
$150$	−0.326266	+	0.122450i	−0.0266395	+	0.00999798i
$151$	−15.9993	−	6.00462i	−1.30200	−	0.488649i	−0.398474	−	0.917180i	$-0.630460\pi$
$151$	−15.9993	−	6.00462i	−1.30200	−	0.488649i	−0.903527	+	0.428530i	$0.859032\pi$
$152$	−3.16352	−	2.76388i	−0.256595	−	0.224181i
$153$	10.0108	−	2.76280i	0.809325	−	0.223359i
$154$	0.853512	+	1.29301i	0.0687779	+	0.104194i
$155$	0.109865	+	0.0303209i	0.00882459	+	0.00243543i
$156$	−0.00573543	−	0.0176518i	−0.000459202	−	0.00141328i
$157$	−8.13371	+	15.1150i	−0.649140	+	1.20630i	0.317034	+	0.948414i	$0.397313\pi$
$157$	−8.13371	+	15.1150i	−0.649140	+	1.20630i	−0.966174	+	0.257891i	$0.916973\pi$
$158$	−0.00962697	+	0.214361i	−0.000765880	+	0.0170537i
$159$	2.45589	−	1.78431i	0.194765	−	0.141505i
$160$	−0.0706704	+	0.0739154i	−0.00558698	+	0.00584353i
$161$	−4.77851	−	8.87996i	−0.376599	−	0.699839i
$162$	1.36287	−	0.656325i	0.107077	−	0.0515658i
$163$	−5.06336	+	3.02522i	−0.396593	+	0.236953i	−0.697324	−	0.716756i	$-0.745626\pi$
$163$	−5.06336	+	3.02522i	−0.396593	+	0.236953i	0.300732	+	0.953709i	$0.402769\pi$
$164$	−0.894644	+	6.60453i	−0.0698600	+	0.515727i
$165$	−0.0126475	+	0.0554124i	−0.000984609	+	0.00431385i
$166$	−0.517171	+	0.0938526i	−0.0401402	+	0.00728438i
$167$	−6.68902	−	4.85986i	−0.517612	−	0.376067i	0.298092	−	0.954537i	$-0.403650\pi$
$167$	−6.68902	−	4.85986i	−0.517612	−	0.376067i	−0.815704	+	0.578470i	$0.803650\pi$
$168$	−0.398521	+	0.499730i	−0.0307466	+	0.0385550i
$169$	−11.1592	−	6.66734i	−0.858404	−	0.512872i
$170$	−0.0314970	−	0.00283478i	−0.00241571	−	0.000217418i
$171$	2.11652	+	15.6248i	0.161854	+	1.19485i
$172$	3.18478	+	3.99359i	0.242837	+	0.304509i
$173$	−0.380857	−	8.48045i	−0.0289561	−	0.644757i	−0.960025	−	0.279914i	$-0.909694\pi$
$173$	−0.380857	−	8.48045i	−0.0289561	−	0.644757i	0.931069	−	0.364843i	$-0.118877\pi$
$174$	0.0951300	+	0.0458122i	0.00721179	+	0.00347301i
$175$	11.5151	−	1.03637i	0.870457	−	0.0783425i
$176$	−2.91877	−	12.7880i	−0.220010	−	0.963929i
$177$	1.27878	+	2.99186i	0.0961193	+	0.224882i
$178$	−0.860447	−	2.01312i	−0.0644932	−	0.150889i
$179$	1.77947	+	7.79635i	0.133004	+	0.582727i	0.996874	+	0.0790120i	$0.0251765\pi$
$179$	1.77947	+	7.79635i	0.133004	+	0.582727i	−0.863870	+	0.503715i	$0.831966\pi$
$180$	0.254066	−	0.0228664i	0.0189370	−	0.00170436i
$181$	−7.48265	−	3.60345i	−0.556181	−	0.267843i	0.134608	−	0.990899i	$-0.457022\pi$
$181$	−7.48265	−	3.60345i	−0.556181	−	0.267843i	−0.690789	+	0.723056i	$0.742737\pi$
$182$	−0.000523796	−	0.0116632i	−3.88263e−5	−	0.000864535i
$183$	1.76448	+	2.21259i	0.130434	+	0.163560i
$184$	−0.447328	−	3.30231i	−0.0329774	−	0.243449i
$185$	−0.378922	−	0.0341036i	−0.0278589	−	0.00250735i
$186$	0.150615	+	0.0899884i	0.0110436	+	0.00659827i
$187$	7.83444	−	9.82408i	0.572911	−	0.718408i
$188$	18.8806	+	13.7176i	1.37701	+	1.00046i
$189$	4.82858	−	0.876258i	0.351227	−	0.0637384i
$190$	0.0106843	−	0.0468109i	0.000775119	−	0.00339602i
$191$	−2.61027	+	19.2698i	−0.188873	+	1.39431i	0.609803	+	0.792553i	$0.291248\pi$
$191$	−2.61027	+	19.2698i	−0.188873	+	1.39431i	−0.798676	+	0.601761i	$0.794466\pi$
$192$	2.20939	−	1.32005i	0.159449	−	0.0952662i
$193$	19.4267	−	9.35542i	1.39837	−	0.673418i	0.425538	−	0.904941i	$-0.360085\pi$
$193$	19.4267	−	9.35542i	1.39837	−	0.673418i	0.972830	+	0.231523i	$0.0743707\pi$
$194$	−0.800049	−	1.48674i	−0.0574402	−	0.106742i
$195$	0.000295984	0	0.000309575i	2.11959e−5	0	2.21692e-5i
$196$	−2.61815	+	1.90219i	−0.187010	+	0.135871i
$197$	0.834541	−	18.5825i	0.0594586	−	1.32395i	−0.718453	−	0.695575i	$-0.755150\pi$
$197$	0.834541	−	18.5825i	0.0594586	−	1.32395i	0.777912	−	0.628373i	$-0.216279\pi$
$198$	0.910659	−	1.69229i	0.0647177	−	0.120266i
$199$	0.453767	+	1.39655i	0.0321667	+	0.0989989i	0.965851	−	0.259099i	$-0.0834255\pi$
$199$	0.453767	+	1.39655i	0.0321667	+	0.0989989i	−0.933684	+	0.358098i	$0.883426\pi$
$200$	3.68307	+	1.01646i	0.260432	+	0.0718747i
$201$	−1.08141	−	1.63826i	−0.0762765	−	0.115554i
$202$	3.46170	−	0.955367i	0.243564	−	0.0672194i
$203$	−2.63800	−	2.30475i	−0.185151	−	0.161762i
$204$	2.40391	+	0.902204i	0.168308	+	0.0631669i
$205$	−0.143994	+	0.0540417i	−0.0100569	+	0.00377444i
$206$	−1.36164	+	1.18963i	−0.0948702	+	0.0828856i
$207$	−6.89070	+	10.4390i	−0.478937	+	0.725558i
$208$	−0.0305441	+	0.0940052i	−0.00211785	+	0.00651809i
$209$	13.1841	+	13.7895i	0.911961	+	0.953837i
$210$	−0.00718831	−	0.00130449i	−0.000496040	−	9.00180e-5i
$211$	4.37254	−	10.2301i	0.301018	−	0.704267i	−0.698922	−	0.715198i	$-0.746337\pi$
$211$	4.37254	−	10.2301i	0.301018	−	0.704267i	0.999940	+	0.0109311i	$0.00347954\pi$
$212$	−16.4849			−1.13219
$213$	1.99837	−	2.29825i	0.136926	−	0.157474i
$214$	1.48910			0.101793
$215$	−0.0463275	+	0.108389i	−0.00315951	+	0.00739204i
$216$	1.59570	+	0.289576i	0.108573	+	0.0197032i
$217$	−4.02256	−	4.20727i	−0.273069	−	0.285608i
$218$	−0.637997	+	1.96355i	−0.0432106	+	0.132989i
$219$	−1.29937	+	1.96846i	−0.0878030	+	0.133016i
$220$	0.232437	−	0.203074i	0.0156709	−	0.0136913i
$221$	−0.0886503	+	0.0332710i	−0.00596327	+	0.00223805i
$222$	−0.548328	−	0.205791i	−0.0368014	−	0.0138118i
$223$	13.8823	+	12.1286i	0.929627	+	0.812190i	0.982472	−	0.186412i	$-0.0596860\pi$
$223$	13.8823	+	12.1286i	0.929627	+	0.812190i	−0.0528448	+	0.998603i	$0.516829\pi$
$224$	5.03461	−	1.38946i	0.336389	−	0.0928374i
$225$	−7.90037	−	11.9685i	−0.526691	−	0.797903i
$226$	−3.03931	−	0.838795i	−0.202172	−	0.0557958i
$227$	7.57980	+	23.3282i	0.503089	+	1.54835i	0.803960	+	0.594683i	$0.202723\pi$
$227$	7.57980	+	23.3282i	0.503089	+	1.54835i	−0.300871	+	0.953665i	$0.597277\pi$
$228$	−1.84733	+	3.43292i	−0.122343	+	0.227351i
$229$	−0.193993	+	4.31960i	−0.0128194	+	0.285447i	0.982336	+	0.187128i	$0.0599179\pi$
$229$	−0.193993	+	4.31960i	−0.0128194	+	0.285447i	−0.995155	+	0.0983188i	$0.968654\pi$
$230$	0.0308151	−	0.0223885i	0.00203189	−	0.00147625i
$231$	2.00603	−	2.09814i	0.131987	−	0.138048i
$232$	−0.548565	−	1.01940i	−0.0360151	−	0.0669272i
$233$	23.6856	−	11.4064i	1.55170	−	0.747258i	0.555267	−	0.831672i	$-0.312616\pi$
$233$	23.6856	−	11.4064i	1.55170	−	0.747258i	0.996431	+	0.0844136i	$0.0269017\pi$
$234$	−0.0124317	+	0.00742757i	−0.000812683	+	0.000485555i
$235$	−0.0722914	+	0.533677i	−0.00471577	+	0.0348132i
$236$	3.93172	−	17.2260i	0.255933	−	1.12132i
$237$	0.395575	−	0.0717862i	0.0256953	−	0.00466302i
$238$	1.30666	+	0.949348i	0.0846985	+	0.0615371i
$239$	−8.26856	+	10.3684i	−0.534849	+	0.670679i	−0.973688	−	0.227887i	$-0.926818\pi$
$239$	−8.26856	+	10.3684i	−0.534849	+	0.670679i	0.438839	+	0.898566i	$0.355390\pi$
$240$	0.0530966	+	0.0317237i	0.00342737	+	0.00204776i
$241$	13.0451	+	1.17408i	0.840306	+	0.0756290i	0.501426	−	0.865201i	$-0.332809\pi$
$241$	13.0451	+	1.17408i	0.840306	+	0.0756290i	0.338880	+	0.940829i	$0.389952\pi$
$242$	−0.0272791	−	0.201383i	−0.00175357	−	0.0129454i
$243$	−5.73515	−	7.19165i	−0.367910	−	0.461345i
$244$	−0.689491	−	15.3527i	−0.0441402	−	0.982857i
$245$	−0.0672844	−	0.0324024i	−0.00429864	−	0.00207012i
$246$	−0.235809	+	0.0212232i	−0.0150346	+	0.00135314i
$247$	−0.0319904	−	0.140159i	−0.00203550	−	0.00891811i
$248$	−0.756026	−	1.76881i	−0.0480077	−	0.112320i
$249$	0.387054	+	0.905557i	0.0245285	+	0.0573873i
$250$	0.0194393	+	0.0851690i	0.00122945	+	0.00538656i
$251$	−27.7044	+	2.49344i	−1.74869	+	0.157385i	−0.917271	−	0.398264i	$-0.869613\pi$
$251$	−27.7044	+	2.49344i	−1.74869	+	0.157385i	−0.831417	+	0.555648i	$0.812470\pi$
$252$	−11.7380	−	5.65272i	−0.739424	−	0.356088i
$253$	0.679000	+	15.1191i	0.0426884	+	0.950530i
$254$	−2.22697	−	2.79253i	−0.139732	−	0.175219i
$255$	0.00795358	+	0.0587156i	0.000498072	+	0.00367692i
$256$	−13.0524	−	1.17474i	−0.815778	−	0.0734213i
$257$	−22.7206	−	13.5749i	−1.41727	−	0.846782i	−0.419145	−	0.907919i	$-0.637670\pi$
$257$	−22.7206	−	13.5749i	−1.41727	−	0.846782i	−0.998129	+	0.0611373i	$0.980527\pi$
$258$	−0.113136	+	0.141869i	−0.00704357	+	0.00883235i
$259$	15.7197	+	11.4210i	0.976775	+	0.709669i
$260$	−0.00228850		0.000415301i	−0.000141926		2.57559e-5i
$261$	−0.966871	+	4.23614i	−0.0598478	+	0.262210i
$262$	0.383456	−	2.83079i	0.0236900	−	0.174887i
$263$	5.33958	−	3.19025i	0.329252	−	0.196719i	−0.338753	−	0.940875i	$-0.610005\pi$
$263$	5.33958	−	3.19025i	0.329252	−	0.196719i	0.668006	+	0.744156i	$0.267148\pi$
$264$	0.864294	−	0.416222i	0.0531936	−	0.0256167i
$265$	−0.180265	−	0.334989i	−0.0110736	−	0.0205782i
$266$	−1.69464	+	1.77245i	−0.103905	+	0.108676i
$267$	−3.31851	+	2.41104i	−0.203089	+	0.147553i
$268$	−0.478255	+	10.6492i	−0.0292140	+	0.650501i
$269$	1.91879	−	3.56571i	0.116991	−	0.217405i	−0.815365	−	0.578947i	$-0.803464\pi$
$269$	1.91879	−	3.56571i	0.116991	−	0.217405i	0.932356	+	0.361542i	$0.117750\pi$
$270$	0.00572808	+	0.0176292i	0.000348600	+	0.00107288i
$271$	16.2351	+	4.48061i	0.986213	+	0.272178i	0.721701	−	0.692205i	$-0.243361\pi$
$271$	16.2351	+	4.48061i	0.986213	+	0.272178i	0.264512	+	0.964382i	$0.414789\pi$
$272$	−7.53298	−	11.4120i	−0.456754	−	0.691952i
$273$	−0.0210861	+	0.00581941i	−0.00127619	+	0.000352206i
$274$	1.87178	+	1.63533i	0.113079	+	0.0987938i
$275$	−16.2455	−	6.09703i	−0.979639	−	0.367665i
$276$	−2.89537	+	1.08665i	−0.174281	+	0.0654086i
$277$	−13.2597	+	11.5846i	−0.796697	+	0.696053i	−0.956704	−	0.291063i	$-0.905991\pi$
$277$	−13.2597	+	11.5846i	−0.796697	+	0.696053i	0.160007	+	0.987116i	$0.448848\pi$
$278$	−2.20243	+	3.33654i	−0.132093	+	0.200112i
$279$	−2.23114	+	6.86674i	−0.133575	+	0.411101i
$280$	0.0553531	+	0.0578949i	0.00330798	+	0.00345988i
$281$	20.4989	+	3.72001i	1.22286	+	0.221917i	0.751328	−	0.659929i	$-0.229414\pi$
$281$	20.4989	+	3.72001i	1.22286	+	0.221917i	0.471537	+	0.881846i	$0.343699\pi$
$282$	−0.325838	+	0.762335i	−0.0194033	+	0.0453964i
$283$	−10.0691			−0.598546			−0.299273	−	0.954168i	$-0.596744\pi$
$283$	−10.0691			−0.598546			−0.299273	+	0.954168i	$0.596744\pi$
$284$	−16.1153	+	3.71828i	−0.956269	+	0.220639i
$285$	−0.0899613			−0.00532885
$286$	−0.00688661	+	0.0161120i	−0.000407214	+	0.000952724i
$287$	7.72872	+	1.40256i	0.456212	+	0.0827903i
$288$	−4.47694	−	4.68252i	−0.263806	−	0.275920i
$289$	−1.20540	+	3.70984i	−0.0709059	+	0.218226i
$290$	0.00728922	−	0.0110427i	0.000428038	−	0.000648449i
$291$	−2.38219	+	2.08125i	−0.139646	+	0.122005i
$292$	11.9917	−	4.50056i	0.701761	−	0.263375i
$293$	−24.3520	−	9.13944i	−1.42266	−	0.533932i	−0.482869	−	0.875692i	$-0.660405\pi$
$293$	−24.3520	−	9.13944i	−1.42266	−	0.533932i	−0.939787	+	0.341760i	$0.888977\pi$
$294$	−0.0865755	−	0.0756387i	−0.00504918	−	0.00441134i
$295$	0.393043	−	0.108473i	0.0228838	−	0.00631554i
$296$	3.53744	+	5.35899i	0.205609	+	0.311485i
$297$	−7.09978	−	1.95941i	−0.411971	−	0.113697i
$298$	−0.159972	−	0.492342i	−0.00926691	−	0.0285206i
$299$	0.0540429	−	0.100428i	0.00312538	−	0.00580793i
$300$	0.159078	−	3.54214i	0.00918434	−	0.204505i
$301$	4.87037	−	3.53853i	0.280723	−	0.203957i
$302$	−2.27819	+	2.38280i	−0.131095	+	0.137115i
$303$	−3.18836	−	5.92497i	−0.183167	−	0.340381i
$304$	18.7051	−	9.00789i	1.07281	−	0.516638i
$305$	0.304443	−	0.181896i	0.0174323	−	0.0104153i
$306$	0.268921	−	1.98526i	0.0153732	−	0.113490i
$307$	3.43931	−	15.0686i	0.196292	−	0.860010i	−0.776828	−	0.629712i	$-0.783173\pi$
$307$	3.43931	−	15.0686i	0.196292	−	0.860010i	0.973120	−	0.230298i	$-0.0739701\pi$
$308$	−15.5102	+	2.81470i	−0.883778	+	0.160382i
$309$	2.74073	+	1.99126i	0.155915	+	0.113279i
$310$	0.0137084	−	0.0171898i	0.000778584	−	0.000976314i
$311$	−14.3203	−	8.55597i	−0.812029	−	0.485165i	0.0458922	−	0.998946i	$-0.485387\pi$
$311$	−14.3203	−	8.55597i	−0.812029	−	0.485165i	−0.857921	+	0.513782i	$0.828244\pi$
$312$	−0.00719973		0.000647988i	−0.000407605		3.66851e-5i
$313$	2.17754	+	16.0753i	0.123082	+	0.908628i	0.942211	+	0.335019i	$0.108743\pi$
$313$	2.17754	+	16.0753i	0.123082	+	0.908628i	−0.819129	+	0.573609i	$0.805543\pi$
$314$	2.06451	+	2.58881i	0.116507	+	0.146095i
$315$	−0.0134883	−	0.300341i	−0.000759981	−	0.0169223i
$316$	−1.96702	−	0.947267i	−0.110654	−	0.0532879i
$317$	19.2477	−	1.73232i	1.08106	−	0.0972970i	0.465239	−	0.885185i	$-0.345968\pi$
$317$	19.2477	−	1.73232i	1.08106	−	0.0972970i	0.615819	+	0.787888i	$0.288825\pi$
$318$	−0.130310	−	0.570928i	−0.00730745	−	0.0320160i
$319$	2.06628	+	4.83429i	0.115689	+	0.270668i
$320$	−0.126759	−	0.296569i	−0.00708607	−	0.0165787i
$321$	−0.620835	−	2.72006i	−0.0346516	−	0.151819i
$322$	−1.93749	+	0.174377i	−0.107972	+	0.00971767i
$323$	17.9188	+	8.62925i	0.997030	+	0.480144i
$324$	0.690506	+	15.3753i	0.0383614	+	0.854184i
$325$	0.0815255	+	0.102230i	0.00452222	+	0.00567069i
$326$	0.152736	+	1.12754i	0.00845927	+	0.0624488i
$327$	3.85270	+	0.346749i	0.213055	+	0.0191753i
$328$	2.22838	+	1.33140i	0.123042	+	0.0735140i
$329$	17.1491	−	21.5043i	0.945460	−	1.18557i
$330$	0.00887053	+	0.00644482i	0.000488307	+	0.000354776i
$331$	17.2335	−	3.12742i	0.947238	−	0.171898i	0.317109	−	0.948389i	$-0.397288\pi$
$331$	17.2335	−	3.12742i	0.947238	−	0.171898i	0.630129	+	0.776491i	$0.283002\pi$
$332$	1.19003	−	5.21384i	0.0653112	−	0.286147i
$333$	3.23523	−	23.8835i	0.177290	−	1.30881i
$334$	−1.36923	+	0.818077i	−0.0749209	+	0.0447632i
$335$	−0.221631	+	0.106732i	−0.0121090	+	0.00583139i
$336$	−1.49691	−	2.78172i	−0.0816631	−	0.151755i
$337$	−4.85329	+	5.07615i	−0.264376	+	0.276515i	−0.841636	−	0.540045i	$-0.818407\pi$
$337$	−4.85329	+	5.07615i	−0.264376	+	0.276515i	0.577261	+	0.816560i	$0.304122\pi$
$338$	−2.02878	+	1.47400i	−0.110351	+	0.0801748i
$339$	−0.265034	+	5.90143i	−0.0143947	+	0.320522i
$340$	0.152474	−	0.283344i	0.00826905	−	0.0153665i
$341$	2.69959	+	8.30847i	0.146191	+	0.449929i
$342$	2.93210	+	0.809209i	0.158550	+	0.0437570i
$343$	11.0218	+	16.6973i	0.595120	+	0.901568i
$344$	1.91777	−	0.529270i	0.103399	−	0.0285363i
$345$	−0.0537432	−	0.0469540i	−0.00289344	−	0.00252792i
$346$	−1.53320	−	0.575419i	−0.0824253	−	0.0309347i
$347$	−2.57585	+	0.966734i	−0.138279	+	0.0518970i	−0.419555	−	0.907730i	$-0.637814\pi$
$347$	−2.57585	+	0.966734i	−0.138279	+	0.0518970i	0.281276	+	0.959627i	$0.409242\pi$
$348$	−0.809021	+	0.706820i	−0.0433681	+	0.0378895i
$349$	−14.5698	+	22.0724i	−0.779905	+	1.18151i	0.199558	+	0.979886i	$0.436049\pi$
$349$	−14.5698	+	22.0724i	−0.779905	+	1.18151i	−0.979464	+	0.201620i	$0.935379\pi$
$350$	0.689220	−	2.12120i	0.0368403	−	0.113383i
$351$	0.0383547	+	0.0401159i	0.00204722	+	0.00214123i
$352$	−7.71256	−	1.39962i	−0.411081	−	0.0746002i
$353$	0.00222673	−	0.00520969i	0.000118517	−	0.000277284i	−0.919469	−	0.393164i	$-0.871381\pi$
$353$	0.00222673	−	0.00520969i	0.000118517	−	0.000277284i	0.919587	+	0.392886i	$0.128523\pi$
$354$	0.627674			0.0333605
$355$	−0.251783	−	0.286819i	−0.0133633	−	0.0152228i
$356$	22.2751			1.18058
$357$	1.18934	−	2.78261i	0.0629468	−	0.147271i
$358$	1.51789	+	0.275456i	0.0802229	+	0.0145583i
$359$	4.06400	+	4.25061i	0.214490	+	0.224339i	0.821283	−	0.570521i	$-0.193259\pi$
$359$	4.06400	+	4.25061i	0.214490	+	0.224339i	−0.606793	+	0.794860i	$0.707544\pi$
$360$	0.0307020	−	0.0944909i	0.00161813	−	0.00498011i
$361$	−6.16798	+	9.34409i	−0.324631	+	0.491794i
$362$	−1.20653	+	1.05412i	−0.0634139	+	0.0554031i
$363$	−0.356481	+	0.133790i	−0.0187104	+	0.00702213i
$364$	0.111213	+	0.0417390i	0.00582915	+	0.00218772i
$365$	0.222587	+	0.194468i	0.0116507	+	0.0101789i
$366$	0.526266	−	0.145240i	0.0275084	−	0.00759183i
$367$	−13.2503	−	20.0734i	−0.691661	−	1.04782i	−0.995469	−	0.0950888i	$-0.969687\pi$
$367$	−13.2503	−	20.0734i	−0.691661	−	1.04782i	0.303807	−	0.952733i	$-0.401742\pi$
$368$	15.8760	+	4.38150i	0.827594	+	0.228402i
$369$	−3.01082	−	9.26635i	−0.156737	−	0.482387i
$370$	−0.0347790	+	0.0646301i	−0.00180807	+	0.00335996i
$371$	−0.871657	+	19.4089i	−0.0452542	+	1.00766i
$372$	−1.44420	+	1.04927i	−0.0748783	+	0.0544023i
$373$	12.0290	−	12.5813i	0.622837	−	0.651437i	−0.333825	−	0.942635i	$-0.608340\pi$
$373$	12.0290	−	12.5813i	0.622837	−	0.651437i	0.956663	+	0.291198i	$0.0940539\pi$
$374$	−1.14867	−	2.13458i	−0.0593961	−	0.110376i
$375$	0.147469	−	0.0710172i	0.00761525	−	0.00366731i
$376$	7.80293	−	4.66203i	0.402405	−	0.240426i
$377$	0.00531796	−	0.0392587i	0.000273889	−	0.00202193i
$378$	0.210661	−	0.922964i	0.0108352	−	0.0474722i
$379$	15.1864	−	2.75593i	0.780075	−	0.141563i	0.226109	−	0.974102i	$-0.427399\pi$
$379$	15.1864	−	2.75593i	0.780075	−	0.141563i	0.553966	+	0.832539i	$0.313114\pi$
$380$	0.395228	+	0.287150i	0.0202748	+	0.0147305i
$381$	−4.17248	+	5.23213i	−0.213763	+	0.268050i
$382$	3.22031	+	1.92404i	0.164765	+	0.0984426i
$383$	−2.91745	−	0.262575i	−0.149075	−	0.0134170i	0.0148506	−	0.999890i	$-0.495273\pi$
$383$	−2.91745	−	0.262575i	−0.149075	−	0.0134170i	−0.163925	+	0.986473i	$0.552416\pi$
$384$	−0.285729	−	2.10933i	−0.0145810	−	0.107641i
$385$	−0.226805	−	0.284404i	−0.0115590	−	0.0144946i
$386$	−0.186618	−	4.15537i	−0.00949860	−	0.211503i
$387$	−6.72779	−	3.23993i	−0.341993	−	0.164695i
$388$	17.1089	−	1.53983i	0.868574	−	0.0781730i
$389$	−4.22048	−	18.4911i	−0.213987	−	0.937539i	−0.961827	−	0.273659i	$-0.911766\pi$
$389$	−4.22048	−	18.4911i	−0.213987	−	0.937539i	0.747840	−	0.663879i	$-0.231091\pi$
$390$	−3.24735e−5	0	7.59755e-5i	−1.64436e−6	0	3.84717e-6i
$391$	6.20085	+	14.5076i	0.313591	+	0.733682i
$392$	0.280474	+	1.22884i	0.0141661	+	0.0620655i
$393$	−5.33071	+	0.479772i	−0.268899	+	0.0242013i
$394$	−3.23302	−	1.55694i	−0.162877	−	0.0784376i
$395$	−0.00226034	−	0.0503303i	−0.000113730	−	0.00253239i
$396$	12.1911	+	15.2872i	0.612626	+	0.768208i
$397$	−1.04167	−	7.68995i	−0.0522801	−	0.385947i	−0.998119	−	0.0613103i	$-0.980472\pi$
$397$	−1.04167	−	7.68995i	−0.0522801	−	0.385947i	0.945839	−	0.324637i	$-0.105242\pi$
$398$	0.282134	+	0.0253925i	0.0141421	+	0.00127281i
$399$	3.94417	+	2.35653i	0.197455	+	0.117974i
$400$	−11.7732	+	14.7631i	−0.588660	+	0.738156i
$401$	−14.8386	−	10.7809i	−0.741006	−	0.538373i	0.152020	−	0.988377i	$-0.451422\pi$
$401$	−14.8386	−	10.7809i	−0.741006	−	0.538373i	−0.893026	+	0.450005i	$0.851422\pi$
$402$	−0.372597	+	0.0676164i	−0.0185835	+	0.00337240i
$403$	0.0146488	−	0.0641806i	0.000729709	−	0.00319706i
$404$	−4.90461	+	36.2073i	−0.244013	+	1.80138i
$405$	−0.304890	+	0.182164i	−0.0151501	+	0.00905178i
$406$	−0.608844	+	0.293204i	−0.0302164	+	0.0145515i
$407$	−13.8189	−	25.6799i	−0.684979	−	1.27290i
$408$	0.691093	−	0.722827i	0.0342142	−	0.0357852i
$409$	21.0796	−	15.3152i	1.04232	−	0.757290i	0.0715826	−	0.997435i	$-0.477195\pi$
$409$	21.0796	−	15.3152i	1.04232	−	0.757290i	0.970737	+	0.240145i	$0.0771950\pi$
$410$	−0.00133113	+	0.0296400i	−6.57400e−5	+	0.00146381i
$411$	2.20678	−	4.10088i	0.108852	−	0.202282i
$412$	−5.68493	−	17.4964i	−0.280077	−	0.861987i
$413$	−20.0736	−	5.53996i	−0.987758	−	0.272604i
$414$	1.32929	+	2.01379i	0.0653312	+	0.0989725i
$415$	0.118964	−	0.0328319i	0.00583969	−	0.00161165i
$416$	0.0444823	+	0.0388631i	0.00218093	+	0.00190542i
$417$	7.01290	+	2.63199i	0.343423	+	0.128889i
$418$	3.44567	−	1.29318i	0.168533	−	0.0632516i
$419$	4.14152	−	3.61834i	0.202327	−	0.176768i	−0.550812	−	0.834629i	$-0.685682\pi$
$419$	4.14152	−	3.61834i	0.202327	−	0.176768i	0.753139	+	0.657862i	$0.228539\pi$
$420$	0.0409495	−	0.0620358i	0.00199813	−	0.00302704i
$421$	−5.19866	+	15.9998i	−0.253367	+	0.779785i	0.740780	+	0.671748i	$0.234456\pi$
$421$	−5.19866	+	15.9998i	−0.253367	+	0.779785i	−0.994147	+	0.108036i	$0.965544\pi$
$422$	−1.48316	−	1.55126i	−0.0721991	−	0.0755143i
$423$	−33.5687	−	6.09182i	−1.63217	−	0.296195i
$424$	−2.52343	+	5.90385i	−0.122549	+	0.286717i
$425$	−18.0890			−0.877446
$426$	−0.256166	−	0.528736i	−0.0124113	−	0.0256173i
$427$	−18.1124			−0.876521
$428$	−5.95470	+	13.9317i	−0.287832	+	0.673415i
$429$	0.0323021	+	0.00586196i	0.00155956	+	0.000283018i
$430$	0.0157142	+	0.0164358i	0.000757808	+	0.000792605i
$431$	3.24372	−	9.98315i	0.156245	−	0.480871i	−0.842040	−	0.539415i	$-0.818646\pi$
$431$	3.24372	−	9.98315i	0.156245	−	0.480871i	0.998285	+	0.0585432i	$0.0186455\pi$
$432$	−4.41542	+	6.68908i	−0.212437	+	0.321829i
$433$	−3.74802	+	3.27455i	−0.180118	+	0.157365i	−0.743276	−	0.668985i	$-0.766729\pi$
$433$	−3.74802	+	3.27455i	−0.180118	+	0.157365i	0.563158	+	0.826349i	$0.309586\pi$
$434$	−1.05130	+	0.394560i	−0.0504641	+	0.0189395i
$435$	−0.0232101	−	0.00871088i	−0.00111284	−	0.000417655i
$436$	−15.8193	−	13.8209i	−0.757608	−	0.661903i
$437$	−23.0911	+	6.37274i	−1.10460	+	0.304850i
$438$	0.250662	+	0.379737i	0.0119771	+	0.0181445i
$439$	0.151099	+	0.0417006i	0.00721154	+	0.00199026i	0.269641	−	0.962961i	$-0.413095\pi$
$439$	0.151099	+	0.0417006i	0.00721154	+	0.00199026i	−0.262429	+	0.964951i	$0.584524\pi$
$440$	−0.0371481	−	0.114330i	−0.00177097	−	0.00545047i
$441$	2.24185	−	4.16605i	0.106755	−	0.198384i
$442$	−0.000819518		0.0182480i	−3.89805e−5		0.000867968i
$443$	−2.21585	+	1.60991i	−0.105278	+	0.0764890i	−0.639179	−	0.769058i	$-0.720726\pi$
$443$	−2.21585	+	1.60991i	−0.105278	+	0.0764890i	0.533901	+	0.845547i	$0.320726\pi$
$444$	4.11803	−	4.30712i	0.195433	−	0.204407i
$445$	0.243582	+	0.452652i	0.0115469	+	0.0214578i
$446$	3.20399	−	1.54296i	0.151714	−	0.0730614i
$447$	−0.832638	+	0.497478i	−0.0393824	+	0.0235299i
$448$	−2.21109	+	16.3229i	−0.104464	+	0.771184i
$449$	−1.41979	+	6.22051i	−0.0670041	+	0.293564i	−0.997317	−	0.0732025i	$-0.976678\pi$
$449$	−1.41979	+	6.22051i	−0.0670041	+	0.293564i	0.930313	+	0.366767i	$0.119535\pi$
$450$	−2.72206	+	0.493981i	−0.128319	+	0.0232865i
$451$	−9.53741	−	6.92934i	−0.449099	−	0.326290i
$452$	20.0013	−	25.0809i	0.940784	−	1.17971i
$453$	5.30234	+	3.16800i	0.249126	+	0.148846i
$454$	4.71282	+	0.424161i	0.221183	+	0.0199069i
$455$	0.000367959		0.00271638i	1.72502e−5		0.000127346i
$456$	0.946677	+	1.18710i	0.0443322	+	0.0555908i
$457$	0.403353	+	8.98135i	0.0188680	+	0.420130i	0.986092	+	0.166203i	$0.0531507\pi$
$457$	0.403353	+	8.98135i	0.0188680	+	0.420130i	−0.967223	+	0.253927i	$0.918278\pi$
$458$	0.751532	+	0.361919i	0.0351168	+	0.0169114i
$459$	−7.64716	+	0.688257i	−0.356939	+	0.0321251i
$460$	0.0862368	+	0.377828i	0.00402081	+	0.0176163i
$461$	9.22087	+	21.5733i	0.429459	+	1.00477i	0.984886	+	0.173204i	$0.0554119\pi$
$461$	9.22087	+	21.5733i	0.429459	+	1.00477i	−0.555427	+	0.831565i	$0.687445\pi$
$462$	−0.220089	−	0.514923i	−0.0102394	−	0.0239564i
$463$	5.63459	+	24.6868i	0.261862	+	1.14729i	0.919230	+	0.393721i	$0.128812\pi$
$463$	5.63459	+	24.6868i	0.261862	+	1.14729i	−0.657368	+	0.753570i	$0.728330\pi$
$464$	5.69815	−	0.512843i	0.264530	−	0.0238081i
$465$	−0.0371149	−	0.0178736i	−0.00172116	−	0.000828867i
$466$	−0.227530	−	5.06635i	−0.0105401	−	0.234694i
$467$	−7.10336	−	8.90734i	−0.328704	−	0.412182i	0.589827	−	0.807529i	$-0.299196\pi$
$467$	−7.10336	−	8.90734i	−0.328704	−	0.412182i	−0.918532	+	0.395347i	$0.870624\pi$
$468$	−0.0197784	−	0.146010i	−0.000914255	−	0.00674930i
$469$	12.5128	+	1.12617i	0.577788	+	0.0520018i
$470$	0.0891863	+	0.0532863i	0.00411386	+	0.00245791i
$471$	3.86810	−	4.85045i	0.178233	−	0.223497i
$472$	−5.56742	−	4.04497i	−0.256261	−	0.186185i
$473$	−8.88991	+	1.61328i	−0.408759	+	0.0741787i
$474$	0.0172581	−	0.0756126i	0.000792690	−	0.00347300i
$475$	3.68662	−	27.2157i	0.169154	−	1.24874i
$476$	−14.1071	+	8.42858i	−0.646596	+	0.386323i
$477$	21.7124	−	10.4561i	0.994143	−	0.478754i
$478$	1.21232	+	2.25286i	0.0554500	+	0.103043i
$479$	−2.62594	+	2.74652i	−0.119982	+	0.125492i	−0.780057	−	0.625708i	$-0.784810\pi$
$479$	−2.62594	+	2.74652i	−0.119982	+	0.125492i	0.660075	+	0.751200i	$0.270524\pi$
$480$	0.0299031	−	0.0217259i	0.00136488	−	0.000991645i
$481$	−0.00985914	+	0.219531i	−0.000449538	+	0.0100097i
$482$	1.19733	−	2.22501i	0.0545368	−	0.101346i
$483$	1.12630	+	3.46640i	0.0512485	+	0.157727i
$484$	1.99318	+	0.550083i	0.0905991	+	0.0250038i
$485$	0.218380	+	0.330832i	0.00991612	+	0.0150223i
$486$	−1.71054	+	0.472079i	−0.0775916	+	0.0214139i
$487$	−3.95341	−	3.45399i	−0.179146	−	0.156515i	0.563695	−	0.825983i	$-0.309379\pi$
$487$	−3.95341	−	3.45399i	−0.179146	−	0.156515i	−0.742841	+	0.669468i	$0.766522\pi$
$488$	−5.60393	−	2.10319i	−0.253678	−	0.0952069i
$489$	1.99594	−	0.749088i	0.0902595	−	0.0338749i
$490$	−0.0108492	+	0.00947866i	−0.000490117	+	0.000428202i
$491$	13.4042	−	20.3065i	0.604924	−	0.916421i	−0.395073	−	0.918650i	$-0.629281\pi$
$491$	13.4042	−	20.3065i	0.604924	−	0.916421i	0.999998	+	0.00222861i	$0.000709388\pi$
$492$	0.744407	−	2.29105i	0.0335605	−	0.103289i
$493$	3.78750	+	3.96142i	0.170581	+	0.178413i
$494$	−0.0272879	−	0.00495202i	−0.00122774	−	0.000222802i
$495$	−0.177338	+	0.414903i	−0.00797075	+	0.0186485i
$496$	9.50675			0.426866
$497$	3.52571	+	19.1704i	0.158150	+	0.859912i
$498$	0.189980			0.00851321
$499$	8.65190	−	20.2421i	0.387312	−	0.906162i	−0.606500	−	0.795084i	$-0.707427\pi$
$499$	8.65190	−	20.2421i	0.387312	−	0.906162i	0.993812	−	0.111078i	$-0.0354303\pi$
$500$	−0.874558	−	0.158709i	−0.0391114	−	0.00709768i
$501$	2.06519	+	2.16002i	0.0922660	+	0.0965026i
$502$	−1.65821	+	5.10346i	−0.0740097	+	0.227779i
$503$	8.64861	−	13.1021i	0.385623	−	0.584193i	−0.588976	−	0.808150i	$-0.700469\pi$
$503$	8.64861	−	13.1021i	0.385623	−	0.584193i	0.974599	+	0.223957i	$0.0718975\pi$
$504$	−3.82125	+	3.33852i	−0.170212	+	0.148710i
$505$	−0.789400	+	0.296267i	−0.0351278	+	0.0131837i
$506$	2.73342	+	1.02587i	0.121515	+	0.0456054i
$507$	3.53830	+	3.09132i	0.157142	+	0.137290i
$508$	35.0316	−	9.66811i	1.55428	−	0.428953i
$509$	16.9552	+	25.6860i	0.751525	+	1.13851i	0.986058	+	0.166404i	$0.0532156\pi$
$509$	16.9552	+	25.6860i	0.751525	+	1.13851i	−0.234532	+	0.972108i	$0.575356\pi$
$510$	0.0110184	+	0.00304089i	0.000487904	+	0.000134653i
$511$	−4.66478	−	14.3567i	−0.206358	−	0.635104i
$512$	−6.77941	+	12.5982i	−0.299610	+	0.556769i
$513$	0.523012	−	11.6458i	0.0230915	−	0.514173i
$514$	−4.13067	+	3.00111i	−0.182196	+	0.132373i
$515$	0.293379	−	0.306850i	0.0129278	−	0.0135214i
$516$	−0.874876	−	1.62579i	−0.0385143	−	0.0715715i
$517$	−37.1921	+	17.9108i	−1.63571	+	0.787715i
$518$	3.21780	−	1.92254i	0.141382	−	0.0844717i
$519$	−0.411865	+	3.04051i	−0.0180789	+	0.133464i
$520$	−0.000201577	0	0.000883168i	−8.83975e−6	0	3.87295e-5i
$521$	28.6189	−	5.19357i	1.25382	−	0.227534i	0.489288	−	0.872122i	$-0.337257\pi$
$521$	28.6189	−	5.19357i	1.25382	−	0.227534i	0.764530	+	0.644588i	$0.222971\pi$
$522$	0.678129	+	0.492690i	0.0296809	+	0.0215644i
$523$	−8.61162	+	10.7986i	−0.376560	+	0.472191i	−0.933612	−	0.358287i	$-0.883361\pi$
$523$	−8.61162	+	10.7986i	−0.376560	+	0.472191i	0.557052	+	0.830478i	$0.311933\pi$
$524$	24.9509	+	14.9074i	1.08998	+	0.651235i
$525$	−4.16202	−	0.374589i	−0.181646	−	0.0163484i
$526$	−0.161068	−	1.18905i	−0.00702291	−	0.0518452i
$527$	5.67821	+	7.12025i	0.247347	+	0.310163i
$528$	0.212703	+	4.73619i	0.00925670	+	0.206116i
$529$	3.60141	+	1.73435i	0.156583	+	0.0754065i
$530$	−0.0730902	+	0.00657824i	−0.00317484	+	0.000285740i
$531$	5.74771	+	25.1824i	0.249429	+	1.09282i
$532$	−9.80609	−	22.9425i	−0.425148	−	0.994683i
$533$	0.0349148	+	0.0816873i	0.00151233	+	0.00353827i
$534$	0.176081	+	0.771462i	0.00761978	+	0.0333844i
$535$	−0.348222	+	0.0313406i	−0.0150550	+	0.00135497i
$536$	3.74066	+	1.80140i	0.161572	+	0.0778088i
$537$	−0.129677	−	2.88748i	−0.00559598	−	0.124604i
$538$	−0.487030	−	0.610716i	−0.0209974	−	0.0263299i
$539$	−0.768386	−	5.67245i	−0.0330967	−	0.244330i
$540$	−0.187841	−	0.0169060i	−0.00808340	−	0.000727519i
$541$	−1.08603	−	0.648873i	−0.0466921	−	0.0278972i	0.489364	−	0.872080i	$-0.337229\pi$
$541$	−1.08603	−	0.648873i	−0.0466921	−	0.0278972i	−0.536056	+	0.844183i	$0.680086\pi$
$542$	2.02573	−	2.54019i	0.0870126	−	0.109110i
$543$	2.42852	+	1.76442i	0.104218	+	0.0757186i
$544$	−8.04019	+	1.45908i	−0.344720	+	0.0625575i
$545$	0.107868	−	0.472599i	0.00462054	−	0.0202439i
$546$	−0.000566440		0.00418163i	−2.42414e−5		0.000178957i
$547$	20.7732	−	12.4114i	0.888199	−	0.530674i	0.00516684	−	0.999987i	$-0.498355\pi$
$547$	20.7732	−	12.4114i	0.888199	−	0.530674i	0.883032	+	0.469312i	$0.155498\pi$
$548$	−22.7848	+	10.9726i	−0.973318	+	0.468725i
$549$	10.6462	+	19.7839i	0.454367	+	0.844356i
$550$	−2.31325	+	2.41947i	−0.0986372	+	0.103166i
$551$	−6.73204	+	4.89111i	−0.286795	+	0.208368i
$552$	−0.0540393	+	1.20328i	−0.00230007	+	0.0512150i
$553$	−1.21930	+	2.26584i	−0.0518499	+	0.0963533i
$554$	1.04963	+	3.23043i	0.0445945	+	0.137248i
$555$	0.132556	+	0.0365832i	0.00562670	+	0.00155287i
$556$	−22.4088	−	33.9478i	−0.950343	−	1.43971i
$557$	19.6528	−	5.42383i	0.832717	−	0.229815i	0.176417	−	0.984316i	$-0.443549\pi$
$557$	19.6528	−	5.42383i	0.832717	−	0.229815i	0.656300	+	0.754500i	$0.272121\pi$
$558$	1.04891	+	0.916403i	0.0444038	+	0.0387944i
$559$	0.0637433	+	0.0239233i	0.00269606	+	0.00101185i
$560$	−0.370617	+	0.139095i	−0.0156614	+	0.00587783i
$561$	−3.42021	+	2.98815i	−0.144402	+	0.126160i
$562$	2.21409	−	3.35420i	0.0933957	−	0.141488i
$563$	8.46422	−	26.0502i	0.356724	−	1.09788i	−0.598279	−	0.801288i	$-0.704148\pi$
$563$	8.46422	−	26.0502i	0.356724	−	1.09788i	0.955003	−	0.296596i	$-0.0958516\pi$
$564$	−5.82927	−	6.09694i	−0.245456	−	0.256727i
$565$	0.728386	+	0.132183i	0.0306434	+	0.00556097i
$566$	−0.763428	+	1.78613i	−0.0320893	+	0.0750766i
$567$	18.1391			0.761769
$568$	−1.13520	+	6.34068i	−0.0476320	+	0.266049i
$569$	−20.5743			−0.862519			−0.431260	−	0.902228i	$-0.641931\pi$
$569$	−20.5743			−0.862519			−0.431260	+	0.902228i	$0.641931\pi$
$570$	−0.00682076	+	0.0159580i	−0.000285690	+	0.000668406i
$571$	−5.91796	−	1.07395i	−0.247659	−	0.0449435i	0.0533078	−	0.998578i	$-0.483024\pi$
$571$	−5.91796	−	1.07395i	−0.247659	−	0.0449435i	−0.300967	+	0.953635i	$0.597309\pi$
$572$	−0.123202	−	0.128859i	−0.00515134	−	0.00538788i
$573$	2.17193	−	6.68452i	0.0907337	−	0.279250i
$574$	0.834778	−	1.26464i	0.0348430	−	0.0527848i
$575$	16.4073	−	14.3346i	0.684230	−	0.597794i
$576$	19.1289	−	7.17918i	0.797036	−	0.299133i
$577$	13.9116	+	5.22113i	0.579149	+	0.217358i	0.623720	−	0.781648i	$-0.285621\pi$
$577$	13.9116	+	5.22113i	0.579149	+	0.217358i	−0.0445708	+	0.999006i	$0.514192\pi$
$578$	0.566685	+	0.495098i	0.0235710	+	0.0205934i
$579$	−7.51257	+	2.07334i	−0.312212	+	0.0861650i
$580$	0.0741646	+	0.112355i	0.00307952	+	0.00466527i
$581$	−6.07574	−	1.67680i	−0.252064	−	0.0695653i
$582$	0.188573	+	0.580368i	0.00781660	+	0.0240570i
$583$	13.8174	−	25.6771i	0.572259	−	1.06344i
$584$	0.223814	−	4.98360i	0.00926148	−	0.206223i
$585$	0.00275078	−	0.00199856i	0.000113731	−	8.26302e-5i
$586$	−3.46756	+	3.62678i	−0.143243	+	0.149821i
$587$	14.1172	+	26.2341i	0.582678	+	1.08280i	0.985843	+	0.167669i	$0.0536241\pi$
$587$	14.1172	+	26.2341i	0.582678	+	1.08280i	−0.403166	+	0.915127i	$0.632090\pi$
$588$	1.05386	−	0.507514i	0.0434606	−	0.0209295i
$589$	−11.8700	+	7.09198i	−0.489094	+	0.292220i
$590$	0.0105584	−	0.0779450i	0.000434681	−	0.00320895i
$591$	−1.49607	+	6.55469i	−0.0615399	+	0.269624i
$592$	−31.2247	+	5.66644i	−1.28333	+	0.232889i
$593$	18.3127	+	13.3049i	0.752011	+	0.546368i	0.896450	−	0.443146i	$-0.146138\pi$
$593$	18.3127	+	13.3049i	0.752011	+	0.546368i	−0.144438	+	0.989514i	$0.546138\pi$
$594$	−0.885872	+	1.11085i	−0.0363478	+	0.0455787i
$595$	−0.325540	−	0.194501i	−0.0133459	−	0.00797377i
$596$	5.24596	+	0.472145i	0.214883	+	0.0193398i
$597$	−0.0712441	−	0.525945i	−0.00291583	−	0.0215255i
$598$	−0.0137172	−	0.0172009i	−0.000560940	−	0.000703396i
$599$	0.768946	+	17.1219i	0.0314183	+	0.699583i	0.951462	+	0.307767i	$0.0995816\pi$
$599$	0.768946	+	17.1219i	0.0314183	+	0.699583i	−0.920044	+	0.391816i	$0.871847\pi$
$600$	−1.24422	−	0.599185i	−0.0507951	−	0.0244616i
$601$	−42.3611	+	3.81257i	−1.72795	+	0.155518i	−0.908569	−	0.417735i	$-0.862824\pi$
$601$	−42.3611	+	3.81257i	−1.72795	+	0.155518i	−0.819378	+	0.573253i	$0.805681\pi$
$602$	−0.258424	−	1.13223i	−0.0105326	−	0.0461461i
$603$	−6.12471	−	14.3295i	−0.249417	−	0.583541i
$604$	−13.1828	−	30.8427i	−0.536401	−	1.25497i
$605$	0.0106176	+	0.0465186i	0.000431666	+	0.00189125i
$606$	−1.29275	+	0.116350i	−0.0525144	+	0.00472638i
$607$	−8.26352	−	3.97950i	−0.335406	−	0.161523i	0.258598	−	0.965985i	$-0.416739\pi$
$607$	−8.26352	−	3.97950i	−0.335406	−	0.161523i	−0.594004	+	0.804462i	$0.702454\pi$
$608$	−0.556624	−	12.3942i	−0.0225741	−	0.502651i
$609$	0.789417	+	0.989897i	0.0319888	+	0.0401127i
$610$	−0.00918350	−	0.0677953i	−0.000371829	−	0.00274495i
$611$	0.309818	+	0.0278841i	0.0125339	+	0.00112807i
$612$	17.4983	+	10.4547i	0.707326	+	0.422608i
$613$	−20.2512	+	25.3942i	−0.817939	+	1.02566i	0.181169	+	0.983452i	$0.442012\pi$
$613$	−20.2512	+	25.3942i	−0.817939	+	1.02566i	−0.999109	+	0.0422114i	$0.986560\pi$
$614$	−2.41221	−	1.75257i	−0.0973489	−	0.0707281i
$615$	0.0546966	−	0.00992597i	0.00220558	−	0.000400254i
$616$	−1.36619	+	5.98566i	−0.0550453	+	0.241169i
$617$	−1.64654	+	12.1552i	−0.0662870	+	0.489350i	0.927125	+	0.374752i	$0.122272\pi$
$617$	−1.64654	+	12.1552i	−0.0662870	+	0.489350i	−0.993412	+	0.114598i	$0.963442\pi$
$618$	0.561022	−	0.335195i	0.0225676	−	0.0134835i
$619$	−12.3743	+	5.95916i	−0.497366	+	0.239519i	−0.665711	−	0.746209i	$-0.731872\pi$
$619$	−12.3743	+	5.95916i	−0.497366	+	0.239519i	0.168346	+	0.985728i	$0.446158\pi$
$620$	0.106006	+	0.196992i	0.00425731	+	0.00791140i
$621$	6.39079	−	6.68424i	0.256453	−	0.268229i
$622$	−2.60347	+	1.89153i	−0.104389	+	0.0758434i
$623$	1.17782	−	26.2262i	0.0471884	−	1.05073i
$624$	0.0169294	−	0.0314601i	0.000677718	−	0.00125941i
$625$	7.71592	+	23.7471i	0.308637	+	0.949886i
$626$	3.01664	+	0.832541i	0.120569	+	0.0332750i
$627$	−3.79875	−	5.75486i	−0.151707	−	0.229827i
$628$	−32.4761	+	8.96283i	−1.29594	+	0.357656i
$629$	−22.8939	−	20.0018i	−0.912840	−	0.797524i
$630$	−0.0542993	−	0.0203789i	−0.00216334	−	0.000811913i
$631$	−29.9470	+	11.2393i	−1.19217	+	0.447429i	−0.867039	−	0.498240i	$-0.833980\pi$
$631$	−29.9470	+	11.2393i	−1.19217	+	0.447429i	−0.325131	+	0.945669i	$0.605408\pi$
$632$	−0.640354	+	0.559461i	−0.0254719	+	0.0222541i
$633$	−2.21525	+	3.35595i	−0.0880481	+	0.133387i
$634$	1.15205	−	3.54563i	0.0457536	−	0.140815i
$635$	0.579543	+	0.606154i	0.0229984	+	0.0240545i
$636$	5.86257	+	1.06390i	0.232466	+	0.0421864i
$637$	−0.0169534	+	0.0396644i	−0.000671717	+	0.00157156i
$638$	1.01420			0.0401527
$639$	18.8672	−	15.1191i	0.746375	−	0.598103i
$640$	−0.266745			−0.0105440
$641$	−6.62707	+	15.5048i	−0.261754	+	0.612403i	−0.997925	−	0.0643926i	$-0.979489\pi$
$641$	−6.62707	+	15.5048i	−0.261754	+	0.612403i	0.736171	+	0.676795i	$0.236632\pi$
$642$	−0.529574	−	0.0961035i	−0.0209006	−	0.00379290i
$643$	0.794699	+	0.831190i	0.0313399	+	0.0327789i	0.738279	−	0.674496i	$-0.235639\pi$
$643$	0.794699	+	0.831190i	0.0313399	+	0.0327789i	−0.706939	+	0.707274i	$0.749925\pi$
$644$	6.11631	−	18.8241i	0.241016	−	0.741772i
$645$	0.0234708	−	0.0355567i	0.000924160	−	0.00140004i
$646$	2.88930	−	2.52431i	0.113678	−	0.0993175i
$647$	−41.1705	+	15.4516i	−1.61858	+	0.607463i	−0.985957	−	0.166996i	$-0.946593\pi$
$647$	−41.1705	+	15.4516i	−1.61858	+	0.607463i	−0.632623	+	0.774460i	$0.718022\pi$
$648$	5.61217	+	2.10628i	0.220467	+	0.0827426i
$649$	23.5359	+	20.5627i	0.923864	+	0.807156i
$650$	0.0243154	−	0.00671063i	0.000953729	−	0.000263212i
$651$	1.15903	+	1.75585i	0.0454259	+	0.0688173i
$652$	−11.1598	−	3.07992i	−0.437052	−	0.120619i
$653$	−1.17588	−	3.61898i	−0.0460156	−	0.141622i	0.925409	−	0.378970i	$-0.123722\pi$
$653$	−1.17588	−	3.61898i	−0.0460156	−	0.141622i	−0.971425	+	0.237349i	$0.923722\pi$
$654$	0.353616	−	0.657129i	0.0138275	−	0.0256958i
$655$	−0.0300916	+	0.670042i	−0.00117578	+	0.0261807i
$656$	−10.3788	+	7.54066i	−0.405225	+	0.294413i
$657$	−12.9397	+	13.5339i	−0.504827	+	0.528008i
$658$	−2.51436	−	4.67246i	−0.0980198	−	0.182151i
$659$	−9.50682	+	4.57824i	−0.370333	+	0.178343i	−0.609788	−	0.792564i	$-0.708746\pi$
$659$	−9.50682	+	4.57824i	−0.370333	+	0.178343i	0.239455	+	0.970907i	$0.423031\pi$
$660$	−0.0957683	+	0.0572189i	−0.00372778	+	0.00222724i
$661$	5.29328	−	39.0766i	0.205885	−	1.51990i	−0.533026	−	0.846099i	$-0.678945\pi$
$661$	5.29328	−	39.0766i	0.205885	−	1.51990i	0.738910	−	0.673804i	$-0.235341\pi$
$662$	0.751860	−	3.29411i	0.0292219	−	0.128029i
$663$	0.0336742	−	0.00611097i	0.00130780	−	0.000237330i
$664$	−1.68511	−	1.22430i	−0.0653949	−	0.0475122i
$665$	0.358982	−	0.450150i	0.0139207	−	0.0174561i
$666$	−3.99133	−	2.38471i	−0.154661	−	0.0924055i
$667$	−6.57459	−	0.591724i	−0.254569	−	0.0229116i
$668$	−2.17840	−	16.0816i	−0.0842849	−	0.622216i
$669$	−4.15425	−	5.20926i	−0.160613	−	0.201402i
$670$	0.00212904	+	0.0474068i	8.22521e−5	+	0.00183149i
$671$	24.4915	+	11.7945i	0.945484	+	0.455321i
$672$	−1.88015	+	0.169216i	−0.0725282	+	0.00652766i
$673$	6.64792	+	29.1264i	0.256258	+	1.12274i	0.925216	+	0.379441i	$0.123884\pi$
$673$	6.64792	+	29.1264i	0.256258	+	1.12274i	−0.668958	+	0.743301i	$0.733259\pi$
$674$	0.532472	+	1.24578i	0.0205100	+	0.0479856i
$675$	4.16717	+	9.74957i	0.160394	+	0.375261i
$676$	−5.67759	−	24.8752i	−0.218369	−	0.956737i
$677$	33.5837	−	3.02259i	1.29073	−	0.116168i	0.577089	−	0.816681i	$-0.304189\pi$
$677$	33.5837	−	3.02259i	1.29073	−	0.116168i	0.713639	+	0.700514i	$0.247046\pi$
$678$	1.02674	+	0.494454i	0.0394319	+	0.0189894i
$679$	−0.908310	−	20.2251i	−0.0348577	−	0.776167i
$680$	−0.0781360	−	0.0979794i	−0.00299638	−	0.00375734i
$681$	−1.19007	−	8.78547i	−0.0456037	−	0.336660i
$682$	1.67849	+	0.151067i	0.0642729	+	0.00578466i
$683$	−12.6710	−	7.57054i	−0.484841	−	0.289679i	0.249603	−	0.968348i	$-0.419700\pi$
$683$	−12.6710	−	7.57054i	−0.484841	−	0.289679i	−0.734444	+	0.678669i	$0.762557\pi$
$684$	−19.2958	+	24.1962i	−0.737795	+	0.925166i
$685$	−0.472129	−	0.343022i	−0.0180391	−	0.0131062i
$686$	3.79754	−	0.689152i	0.144991	−	0.0263119i
$687$	0.347768	−	1.52367i	0.0132682	−	0.0581317i
$688$	−1.31981	+	9.74322i	−0.0503172	+	0.371457i
$689$	−0.188625	+	0.112698i	−0.00718605	+	0.00429346i
$690$	−0.0124038	+	0.00597335i	−0.000472204	+	0.000227401i
$691$	17.3411	+	32.2252i	0.659687	+	1.22590i	0.962092	+	0.272725i	$0.0879248\pi$
$691$	17.3411	+	32.2252i	0.659687	+	1.22590i	−0.302405	+	0.953180i	$0.597789\pi$
$692$	11.5145	−	12.0433i	0.437717	−	0.457816i
$693$	18.6434	−	13.5452i	0.708203	−	0.514540i
$694$	−0.0238122	+	0.530220i	−0.000903899	+	0.0201269i
$695$	0.444809	−	0.826594i	0.0168726	−	0.0313545i
$696$	0.129298	+	0.397937i	0.00490102	+	0.0150838i
$697$	−11.8468	−	3.26951i	−0.448729	−	0.123841i
$698$	2.81068	+	4.25800i	0.106386	+	0.161168i
$699$	−9.15954	+	2.52787i	−0.346446	+	0.0956130i
$700$	17.0894	+	14.9306i	0.645919	+	0.564322i
$701$	13.2017	+	4.95466i	0.498620	+	0.187135i	0.587997	−	0.808863i	$-0.299916\pi$
$701$	13.2017	+	4.95466i	0.498620	+	0.187135i	−0.0893780	+	0.995998i	$0.528488\pi$
$702$	0.0100240	−	0.00376209i	0.000378333	−	0.000141991i
$703$	34.7595	−	30.3684i	1.31098	−	1.14537i
$704$	13.6190	−	20.6319i	0.513286	−	0.777594i
$705$	0.0601516	−	0.185128i	0.00226544	−	0.00697231i
$706$	−0.000755303	0	0.000789985i	−2.84262e−5	0	2.97315e-5i
$707$	42.3703	+	7.68908i	1.59350	+	0.289178i
$708$	−2.50998	+	5.87239i	−0.0943308	+	0.220698i
$709$	26.0264			0.977443			0.488721	−	0.872440i	$-0.337463\pi$
$709$	26.0264			0.977443			0.488721	+	0.872440i	$0.337463\pi$
$710$	−0.0699679	+	0.0229168i	−0.00262585	+	0.000860052i
$711$	3.19162			0.119695
$712$	3.40977	−	7.97755i	0.127786	−	0.298971i
$713$	−10.7927	−	1.95859i	−0.404191	−	0.0733498i
$714$	−0.403424	−	0.421949i	−0.0150978	−	0.0157910i
$715$	0.00127131	−	0.00391269i	4.75443e−5	−	0.000146326i
$716$	−8.64693	+	13.0995i	−0.323151	+	0.489553i
$717$	3.60973	−	3.15373i	0.134808	−	0.117778i
$718$	1.06213	−	0.398625i	0.0396384	−	0.0148765i
$719$	5.84774	+	2.19469i	0.218084	+	0.0818483i	0.458025	−	0.888939i	$-0.348557\pi$
$719$	5.84774	+	2.19469i	0.218084	+	0.0818483i	−0.239942	+	0.970787i	$0.577128\pi$
$720$	0.369773	+	0.323061i	0.0137806	+	0.0120398i
$721$	−20.9005	+	5.76817i	−0.778376	+	0.214818i
$722$	1.18987	+	1.80258i	0.0442824	+	0.0670850i
$723$	−4.56348	−	1.25944i	−0.169718	−	0.0468391i
$724$	−5.03733	−	15.5033i	−0.187211	−	0.576176i
$725$	3.58643	−	6.66470i	0.133197	−	0.247521i
$726$	−0.00329545	+	0.0733789i	−0.000122306	+	0.00272335i
$727$	−0.696919	+	0.506341i	−0.0258473	+	0.0187792i	−0.600634	−	0.799524i	$-0.705085\pi$
$727$	−0.696919	+	0.506341i	−0.0258473	+	0.0187792i	0.574787	+	0.818303i	$0.305085\pi$
$728$	0.0319723	−	0.0334404i	0.00118497	−	0.00123938i
$729$	−9.57177	−	17.7873i	−0.354510	−	0.658790i
$730$	0.0513725	−	0.0247397i	0.00190138	−	0.000915657i
$731$	−8.08566	+	4.83095i	−0.299059	+	0.178679i
$732$	−0.745626	+	5.50443i	−0.0275591	+	0.203450i
$733$	−7.70860	+	33.7736i	−0.284724	+	1.24746i	0.606936	+	0.794751i	$0.292398\pi$
$733$	−7.70860	+	33.7736i	−0.284724	+	1.24746i	−0.891660	+	0.452706i	$0.850459\pi$
$734$	−4.56538	+	0.828495i	−0.168511	+	0.0305803i
$735$	0.0218374	+	0.0158658i	0.000805483	+	0.000585218i
$736$	6.13644	−	7.69485i	0.226192	−	0.283636i
$737$	−16.1864	−	9.67093i	−0.596234	−	0.356233i
$738$	−1.87201	−	0.168484i	−0.0689096	−	0.00620197i
$739$	−3.46382	−	25.5709i	−0.127419	−	0.940642i	−0.935936	−	0.352170i	$-0.885444\pi$
$739$	−3.46382	−	25.5709i	−0.127419	−	0.940642i	0.808518	−	0.588472i	$-0.200270\pi$
$740$	−0.465590	−	0.583831i	−0.0171154	−	0.0214621i
$741$	0.00233127	+	0.0519098i	8.56414e−5	+	0.00190695i
$742$	3.37681	+	1.62618i	0.123967	+	0.0596991i
$743$	1.27895	−	0.115108i	0.0469201	−	0.00422289i	−0.0661544	−	0.997809i	$-0.521073\pi$
$743$	1.27895	−	0.115108i	0.0469201	−	0.00422289i	0.113074	+	0.993587i	$0.463930\pi$
$744$	0.154713	+	0.677840i	0.00567204	+	0.0248508i
$745$	0.0477711	+	0.111766i	0.00175020	+	0.00409479i
$746$	−1.31974	−	3.08769i	−0.0483192	−	0.113048i
$747$	1.73968	+	7.62202i	0.0636515	+	0.278875i
$748$	24.5640	−	2.21080i	0.898150	−	0.0808350i
$749$	16.0880	+	7.74759i	0.587844	+	0.283091i
$750$	−0.00141662	−	0.0315435i	−5.17276e−5	−	0.00115181i
$751$	0.473102	+	0.593252i	0.0172638	+	0.0216481i	0.790388	−	0.612606i	$-0.209879\pi$
$751$	0.473102	+	0.593252i	0.0172638	+	0.0216481i	−0.773125	+	0.634254i	$0.781307\pi$
$752$	6.03002	+	44.5154i	0.219892	+	1.62331i
$753$	10.0135	+	0.901235i	0.364914	+	0.0328428i
$754$	−0.00656079	−	0.00391989i	−0.000238930	−	0.000142754i
$755$	0.482598	−	0.605159i	0.0175635	−	0.0220240i
$756$	7.79266	+	5.66170i	0.283416	+	0.205914i
$757$	1.49421	−	0.271158i	0.0543079	−	0.00985542i	−0.151335	−	0.988483i	$-0.548357\pi$
$757$	1.49421	−	0.271158i	0.0543079	−	0.00985542i	0.205643	+	0.978627i	$0.434071\pi$
$758$	0.662552	−	2.90283i	0.0240650	−	0.105436i
$759$	0.734281	−	5.42068i	0.0266527	−	0.196758i
$760$	0.163339	−	0.0975904i	0.00592492	−	0.00353998i
$761$	−31.2817	+	15.0645i	−1.13396	+	0.546087i	−0.904179	−	0.427154i	$-0.859516\pi$
$761$	−31.2817	+	15.0645i	−1.13396	+	0.546087i	−0.229784	+	0.973242i	$0.573802\pi$
$762$	0.611759	+	1.13684i	0.0221617	+	0.0411833i
$763$	−17.1089	+	17.8945i	−0.619385	+	0.647826i
$764$	−30.8785	+	22.4345i	−1.11714	+	0.811653i
$765$	−0.0211035	+	0.469907i	−0.000763000	+	0.0169895i
$766$	−0.267775	+	0.497609i	−0.00967510	+	0.0179794i
$767$	−0.0727769	−	0.223984i	−0.00262782	−	0.00808760i
$768$	4.56607	+	1.26015i	0.164764	+	0.0454719i
$769$	10.7550	+	16.2931i	0.387835	+	0.587546i	0.975077	−	0.221866i	$-0.0712148\pi$
$769$	10.7550	+	16.2931i	0.387835	+	0.587546i	−0.587242	+	0.809412i	$0.699786\pi$
$770$	−0.0676457	+	0.0186690i	−0.00243778	+	0.000672785i
$771$	7.20411	+	6.29404i	0.259450	+	0.226674i
$772$	39.6230	+	14.8708i	1.42606	+	0.535211i
$773$	41.1879	−	15.4581i	1.48143	−	0.555989i	0.525810	−	0.850602i	$-0.323762\pi$
$773$	41.1879	−	15.4581i	1.48143	−	0.555989i	0.955616	+	0.294614i	$0.0951910\pi$
$774$	−1.08482	+	0.947775i	−0.0389929	+	0.0340671i
$775$	6.92821	−	10.4958i	0.248869	−	0.377020i
$776$	2.06748	−	6.36305i	0.0742183	−	0.228420i
$777$	−4.85336	−	5.07622i	−0.174113	−	0.182108i
$778$	−3.60008	−	0.653319i	−0.129069	−	0.0234226i
$779$	7.33355	−	17.1577i	0.262752	−	0.614738i
$780$	0.000840667	0		3.01007e−5	0
$781$	7.71601	−	28.2180i	0.276101	−	1.00972i
$782$	3.04361			0.108839
$783$	1.26259	−	2.95397i	0.0451212	−	0.105566i
$784$	−6.12915	−	1.11228i	−0.218898	−	0.0397242i
$785$	−0.537265	−	0.561935i	−0.0191758	−	0.0200563i
$786$	−0.319063	+	0.981974i	−0.0113806	+	0.0350259i
$787$	25.8172	−	39.1114i	0.920284	−	1.39417i	0.00124731	−	0.999999i	$-0.499603\pi$
$787$	25.8172	−	39.1114i	0.920284	−	1.39417i	0.919037	−	0.394172i	$-0.128968\pi$
$788$	27.4948	−	24.0215i	0.979462	−	0.855730i
$789$	−2.10482	+	0.789953i	−0.0749337	+	0.0281231i
$790$	−0.00909932	−	0.00341503i	−0.000323739	−	0.000121501i
$791$	−28.4721	−	24.8753i	−1.01235	−	0.884464i
$792$	7.34106	−	2.02600i	0.260853	−	0.0719909i
$793$	−0.112848	−	0.170957i	−0.00400734	−	0.00607086i
$794$	−1.44308	−	0.398264i	−0.0512129	−	0.0141339i
$795$	0.0424888	+	0.130767i	0.00150692	+	0.00463783i
$796$	−1.36578	+	2.53805i	−0.0484088	+	0.0899587i
$797$	−0.686234	+	15.2802i	−0.0243076	+	0.541252i	0.949485	+	0.313813i	$0.101607\pi$
$797$	−0.686234	+	15.2802i	−0.0243076	+	0.541252i	−0.973792	+	0.227439i	$0.926965\pi$
$798$	0.717060	−	0.520975i	0.0253837	−	0.0184423i
$799$	−29.7390	+	31.1045i	−1.05209	+	1.10040i
$800$	5.34723	+	9.93682i	0.189053	+	0.351320i
$801$	−29.3388	+	14.1288i	−1.03663	+	0.499217i
$802$	−3.03744	+	1.81479i	−0.107256	+	0.0640824i
$803$	−3.04116	+	22.4507i	−0.107320	+	0.792269i
$804$	0.857358	−	3.75633i	0.0302367	−	0.132476i
$805$	0.449406	−	0.0815552i	0.0158395	−	0.00287444i
$806$	−0.0102742	−	0.00746461i	−0.000361892	−	0.000262930i
$807$	−0.912508	+	1.14425i	−0.0321218	+	0.0402795i
$808$	12.2164	+	7.29897i	0.429772	+	0.256777i
$809$	−25.0752	−	2.25681i	−0.881598	−	0.0793453i	−0.360417	−	0.932791i	$-0.617366\pi$
$809$	−25.0752	−	2.25681i	−0.881598	−	0.0793453i	−0.521181	+	0.853446i	$0.674508\pi$
$810$	0.00919701	+	0.0678950i	0.000323150	+	0.00238559i
$811$	−2.44796	−	3.06965i	−0.0859597	−	0.107790i	0.736992	−	0.675902i	$-0.236246\pi$
$811$	−2.44796	−	3.06965i	−0.0859597	−	0.107790i	−0.822951	+	0.568112i	$0.807674\pi$
$812$	−0.308473	−	6.86869i	−0.0108253	−	0.241044i
$813$	−5.48458	−	2.64123i	−0.192352	−	0.0926321i
$814$	−5.60301	+	0.504280i	−0.196385	+	0.0176750i
$815$	−0.0594478	−	0.260458i	−0.00208237	−	0.00912344i
$816$	1.94247	+	4.54464i	0.0680001	+	0.159094i
$817$	−5.62049	−	13.1498i	−0.196636	−	0.460053i
$818$	−1.11849	−	4.90043i	−0.0391072	−	0.171340i
$819$	−0.172954	+	0.0155662i	−0.00604352	+	0.000543926i
$820$	−0.271982	−	0.130980i	−0.00949804	−	0.00457401i
$821$	−0.716042	−	15.9439i	−0.0249900	−	0.556447i	−0.971963	−	0.235134i	$-0.924447\pi$
$821$	−0.716042	−	15.9439i	−0.0249900	−	0.556447i	0.946973	−	0.321313i	$-0.104124\pi$
$822$	−0.560128	−	0.702378i	−0.0195367	−	0.0244983i
$823$	0.861934	+	6.36305i	0.0300451	+	0.221802i	0.999747	−	0.0224890i	$-0.00715908\pi$
$823$	0.861934	+	6.36305i	0.0300451	+	0.221802i	−0.969702	+	0.244291i	$0.921445\pi$
$824$	−7.13635	−	0.642283i	−0.248607	−	0.0223750i
$825$	5.38394	+	3.21675i	0.187445	+	0.111993i
$826$	−2.50468	+	3.14076i	−0.0871488	+	0.109281i
$827$	−37.7148	−	27.4014i	−1.31147	−	0.952840i	−0.999997	−	0.00258547i	$-0.999177\pi$
$827$	−37.7148	−	27.4014i	−1.31147	−	0.952840i	−0.311475	−	0.950254i	$-0.600823\pi$
$828$	−24.1563	+	4.38372i	−0.839488	+	0.152345i
$829$	1.97868	−	8.66918i	0.0687226	−	0.301093i	−0.928873	−	0.370399i	$-0.879221\pi$
$829$	1.97868	−	8.66918i	0.0687226	−	0.301093i	0.997595	+	0.0693053i	$0.0220783\pi$
$830$	0.00319574	−	0.0235919i	0.000110926	−	0.000818886i
$831$	5.46323	−	3.26413i	0.189517	−	0.113231i
$832$	−0.167842	+	0.0808286i	−0.00581889	+	0.00280223i
$833$	−2.82777	−	5.25488i	−0.0979765	−	0.182071i
$834$	0.998591	−	1.04444i	0.0345784	−	0.0361661i
$835$	0.302973	−	0.220122i	0.0104848	−	0.00761765i
$836$	−1.68001	+	37.4083i	−0.0581042	+	1.29379i
$837$	2.52957	−	4.70072i	0.0874346	−	0.162481i
$838$	−0.327841	−	1.00899i	−0.0113251	−	0.0348550i
$839$	−41.2895	−	11.3952i	−1.42547	−	0.393405i	−0.533616	−	0.845727i	$-0.679167\pi$
$839$	−41.2895	−	11.3952i	−1.42547	−	0.393405i	−0.891855	+	0.452322i	$0.850596\pi$
$840$	−0.0159490	−	0.0241617i	−0.000550293	−	0.000833658i
$841$	25.7444	−	7.10502i	0.887740	−	0.245001i
$842$	2.44401	+	2.13527i	0.0842261	+	0.0735861i
$843$	−7.05002	−	2.64592i	−0.242816	−	0.0911302i
$844$	20.4442	−	7.67285i	0.703720	−	0.264110i
$845$	0.443402	−	0.387389i	0.0152535	−	0.0133266i
$846$	−3.62575	+	5.49278i	−0.124656	+	0.188846i
$847$	0.753047	−	2.31764i	0.0258750	−	0.0796350i
$848$	−21.9282	−	22.9351i	−0.753019	−	0.787596i
$849$	3.58091	+	0.649839i	0.122896	+	0.0223024i
$850$	−1.37149	+	3.20876i	−0.0470417	+	0.110059i
$851$	36.6158			1.25517
$852$	5.97111	−	0.282295i	0.204567	−	0.00967128i
$853$	14.0928			0.482530			0.241265	−	0.970459i	$-0.422438\pi$
$853$	14.0928			0.482530			0.241265	+	0.970459i	$0.422438\pi$
$854$	−1.37326	+	3.21291i	−0.0469921	+	0.109943i
$855$	−0.702694	−	0.127520i	−0.0240316	−	0.00436110i
$856$	4.07795	+	4.26521i	0.139382	+	0.145782i
$857$	−14.7344	+	45.3477i	−0.503316	+	1.54905i	0.300267	+	0.953855i	$0.402924\pi$
$857$	−14.7344	+	45.3477i	−0.503316	+	1.54905i	−0.803583	+	0.595192i	$0.797076\pi$
$858$	0.00348894	−	0.00528552i	0.000119111	−	0.000180445i
$859$	−35.2075	+	30.7598i	−1.20126	+	1.04951i	−0.203751	+	0.979023i	$0.565313\pi$
$859$	−35.2075	+	30.7598i	−1.20126	+	1.04951i	−0.997513	+	0.0704897i	$0.977544\pi$
$860$	−0.216609	+	0.0812947i	−0.00738630	+	0.00277213i
$861$	−2.65807	−	0.997591i	−0.0905868	−	0.0339978i
$862$	−1.52495	−	1.33231i	−0.0519399	−	0.0453785i
$863$	−35.7390	+	9.86333i	−1.21657	+	0.335752i	−0.814666	−	0.579931i	$-0.803080\pi$
$863$	−35.7390	+	9.86333i	−1.21657	+	0.335752i	−0.401903	+	0.915682i	$0.631651\pi$
$864$	2.63863	+	3.99735i	0.0897680	+	0.135993i
$865$	0.370645	+	0.102291i	0.0126023	+	0.00347801i
$866$	0.296692	+	0.913123i	0.0100820	+	0.0310292i
$867$	0.668105	−	1.24155i	0.0226900	−	0.0421652i
$868$	0.512583	−	11.4135i	0.0173982	−	0.387401i
$869$	3.12421	−	2.26987i	0.105981	−	0.0770000i
$870$	−0.00330496	+	0.00345672i	−0.000112049	+	0.000117194i
$871$	0.0673303	+	0.125121i	0.00228140	+	0.00423955i
$872$	−7.37134	+	3.54985i	−0.249625	+	0.120213i
$873$	−21.5576	+	12.8801i	−0.729615	+	0.435925i
$874$	−0.620300	+	4.57924i	−0.0209820	+	0.154895i
$875$	−0.233104	+	1.02129i	−0.00788034	+	0.0345260i
$876$	−4.55510	+	0.826629i	−0.153903	+	0.0279292i
$877$	7.30065	+	5.30423i	0.246525	+	0.179111i	0.704186	−	0.710016i	$-0.251312\pi$
$877$	7.30065	+	5.30423i	0.246525	+	0.179111i	−0.457660	+	0.889127i	$0.651312\pi$
$878$	0.0188533	−	0.0236412i	0.000636267	−	0.000797854i
$879$	8.07052	+	4.82191i	0.272212	+	0.162639i
$880$	0.591722	+	0.0532560i	0.0199469	+	0.00179526i
$881$	−5.22857	−	38.5988i	−0.176155	−	1.30043i	−0.835876	−	0.548918i	$-0.815040\pi$
$881$	−5.22857	−	38.5988i	−0.176155	−	1.30043i	0.659721	−	0.751510i	$-0.270674\pi$
$882$	−0.569030	−	0.713541i	−0.0191602	−	0.0240262i
$883$	1.04227	+	23.2080i	0.0350752	+	0.781011i	0.937044	+	0.349210i	$0.113550\pi$
$883$	1.04227	+	23.2080i	0.0350752	+	0.781011i	−0.901969	+	0.431800i	$0.857878\pi$
$884$	−0.167447	−	0.0806383i	−0.00563186	−	0.00271216i
$885$	−0.146780	+	0.0132104i	−0.00493395	+	0.000444063i
$886$	0.117574	+	0.515124i	0.00394996	+	0.0173059i
$887$	9.44830	+	22.1054i	0.317243	+	0.742227i	0.999934	+	0.0115192i	$0.00366676\pi$
$887$	9.44830	+	22.1054i	0.317243	+	0.742227i	−0.682691	+	0.730707i	$0.739190\pi$
$888$	−0.912172	−	2.13413i	−0.0306105	−	0.0716168i
$889$	−9.53069	−	41.7567i	−0.319649	−	1.40047i
$890$	0.0987627	−	0.00888880i	0.00331053	−	0.000297953i
$891$	−24.5275	−	11.8118i	−0.821703	−	0.395711i
$892$	1.62332	+	36.1460i	0.0543527	+	1.21026i
$893$	−40.7372	−	51.0829i	−1.36322	−	1.70942i
$894$	0.0251165	+	0.185418i	0.000840022	+	0.00620129i
$895$	−0.360751	−	0.0324682i	−0.0120586	−	0.00108529i
$896$	11.6949	+	6.98737i	0.390699	+	0.233432i
$897$	−0.0257009	+	0.0322279i	−0.000858127	+	0.00107606i
$898$	0.995791	+	0.723485i	0.0332300	+	0.0241430i
$899$	−3.74917	+	0.680375i	−0.125042	+	0.0226918i
$900$	6.26355	−	27.4424i	0.208785	−	0.914747i
$901$	4.08034	−	30.1223i	0.135936	−	1.00352i
$902$	−1.95229	+	1.16644i	−0.0650042	+	0.0388382i
$903$	−1.96043	+	0.944095i	−0.0652391	+	0.0314175i
$904$	−5.92069	−	11.0025i	−0.196919	−	0.365937i
$905$	0.259958	−	0.271895i	0.00864131	−	0.00903810i
$906$	0.963980	−	0.700373i	0.0320261	−	0.0232683i
$907$	0.375825	−	8.36840i	0.0124791	−	0.277868i	−0.983045	−	0.183363i	$-0.941302\pi$
$907$	0.375825	−	8.36840i	0.0124791	−	0.277868i	0.995524	−	0.0945053i	$-0.0301269\pi$
$908$	−22.8142	+	42.3960i	−0.757117	+	1.40696i
$909$	−16.5059	−	50.7999i	−0.547466	−	1.68493i
$910$	0.000509750	0	0.000140682i	1.68980e−5	0	4.66356e-6i
$911$	27.2232	+	41.2414i	0.901946	+	1.36639i	0.930303	+	0.366792i	$0.119544\pi$
$911$	27.2232	+	41.2414i	0.901946	+	1.36639i	−0.0283567	+	0.999598i	$0.509027\pi$
$912$	−7.23349	+	1.99632i	−0.239525	+	0.0661047i
$913$	7.12368	+	6.22377i	0.235759	+	0.205977i
$914$	1.62376	+	0.609406i	0.0537091	+	0.0201574i
$915$	−0.120009	+	0.0450401i	−0.00396738	+	0.00148898i
$916$	−6.39131	+	5.58392i	−0.211175	+	0.184498i
$917$	18.8710	−	28.5884i	0.623176	−	0.944071i
$918$	−0.457711	+	1.40869i	−0.0151067	+	0.0464937i
$919$	−6.22932	−	6.51536i	−0.205486	−	0.214922i	0.612019	−	0.790843i	$-0.290358\pi$
$919$	−6.22932	−	6.51536i	−0.205486	−	0.214922i	−0.817505	+	0.575921i	$0.804643\pi$
$920$	0.148515	+	0.0269515i	0.00489640	+	0.000888565i
$921$	−2.19563	+	5.13693i	−0.0723484	+	0.169267i
$922$	4.52594			0.149054
$923$	−0.158977	+	0.152718i	−0.00523278	+	0.00502676i
$924$	5.69761			0.187438
$925$	−16.4996	+	38.6027i	−0.542502	+	1.26925i
$926$	4.80632	+	0.872218i	0.157945	+	0.0286629i
$927$	18.5854	+	19.4388i	0.610426	+	0.638455i
$928$	1.05651	−	3.25161i	0.0346817	−	0.106739i
$929$	11.0471	−	16.7357i	0.362445	−	0.549080i	−0.606902	−	0.794777i	$-0.707588\pi$
$929$	11.0471	−	16.7357i	0.362445	−	0.549080i	0.969347	+	0.245696i	$0.0790166\pi$
$930$	−0.00598455	+	0.00522854i	−0.000196241	+	0.000171451i
$931$	8.48252	−	3.18354i	0.278003	−	0.104336i
$932$	48.3096	+	18.1309i	1.58243	+	0.593897i
$933$	4.54058	+	3.96699i	0.148652	+	0.129873i
$934$	−2.11862	+	0.584701i	−0.0693232	+	0.0191320i
$935$	0.313538	+	0.474990i	0.0102538	+	0.0155338i
$936$	−0.0553191	−	0.0152671i	−0.00180816	−	0.000499021i
$937$	9.00833	+	27.7248i	0.294289	+	0.905729i	0.983459	+	0.181129i	$0.0579753\pi$
$937$	9.00833	+	27.7248i	0.294289	+	0.905729i	−0.689170	+	0.724600i	$0.742025\pi$
$938$	1.14848	−	2.13423i	0.0374991	−	0.0696849i
$939$	0.263058	−	5.85743i	0.00858456	−	0.191150i
$940$	−0.855179	+	0.621324i	−0.0278929	+	0.0202653i
$941$	26.3408	−	27.5503i	0.858684	−	0.898113i	−0.137033	−	0.990566i	$-0.543757\pi$
$941$	26.3408	−	27.5503i	0.858684	−	0.898113i	0.995717	+	0.0924533i	$0.0294709\pi$
$942$	−0.567132	−	1.05391i	−0.0184781	−	0.0343381i
$943$	13.3363	−	6.42242i	0.434289	−	0.209143i
$944$	29.1962	−	17.4439i	0.950255	−	0.567751i
$945$	−0.0298371	+	0.220266i	−0.000970600	+	0.00716526i
$946$	−0.387848	+	1.69927i	−0.0126100	+	0.0552481i
$947$	32.1039	−	5.82599i	1.04324	−	0.189319i	0.370217	−	0.928945i	$-0.379283\pi$
$947$	32.1039	−	5.82599i	1.04324	−	0.189319i	0.673018	+	0.739626i	$0.264998\pi$
$948$	0.638403	+	0.463827i	0.0207344	+	0.0150644i
$949$	0.106445	−	0.133478i	0.00345535	−	0.00433287i
$950$	−4.54820	−	2.71742i	−0.147563	−	0.0881649i
$951$	−6.95692	−	0.626134i	−0.225593	−	0.0203038i
$952$	0.859147	+	6.34247i	0.0278451	+	0.205561i
$953$	−26.0690	−	32.6895i	−0.844459	−	1.05892i	−0.997498	−	0.0706981i	$-0.977477\pi$
$953$	−26.0690	−	32.6895i	−0.844459	−	1.05892i	0.153039	−	0.988220i	$-0.451094\pi$
$954$	−0.208575	−	4.64427i	−0.00675285	−	0.150364i
$955$	−0.793554	−	0.382155i	−0.0256788	−	0.0123663i
$956$	−25.9252	+	2.33331i	−0.838480	+	0.0754645i
$957$	−0.422841	−	1.85259i	−0.0136685	−	0.0598857i
$958$	0.288101	+	0.674045i	0.00930811	+	0.0217774i
$959$	11.7141	+	27.4065i	0.378268	+	0.885002i
$960$	0.0259400	+	0.113650i	0.000837209	+	0.00366805i
$961$	24.5690	−	2.21125i	0.792549	−	0.0713307i
$962$	0.0381944	+	0.0183935i	0.00123144	+	0.000593029i
$963$	−0.993707	−	22.1266i	−0.0320218	−	0.713020i
$964$	16.0288	+	20.0994i	0.516252	+	0.647360i
$965$	0.131097	+	0.967793i	0.00422015	+	0.0311544i
$966$	0.700290	+	0.0630272i	0.0225315	+	0.00202787i
$967$	40.1082	+	23.9635i	1.28979	+	0.770615i	0.983428	−	0.181300i	$-0.0580305\pi$
$967$	40.1082	+	23.9635i	1.28979	+	0.770615i	0.306364	+	0.951915i	$0.400888\pi$
$968$	0.502112	−	0.629628i	0.0161385	−	0.0202370i
$969$	−5.81561	−	4.22529i	−0.186824	−	0.135736i
$970$	0.0752426	−	0.0136545i	0.00241589	−	0.000438420i
$971$	−3.99701	+	17.5120i	−0.128270	+	0.561988i	0.869421	+	0.494072i	$0.164492\pi$
$971$	−3.99701	+	17.5120i	−0.128270	+	0.561988i	−0.997691	+	0.0679159i	$0.978365\pi$
$972$	2.42353	−	17.8912i	0.0777348	−	0.573861i
$973$	−41.1543	+	24.5886i	−1.31935	+	0.788273i
$974$	−0.912435	+	0.439406i	−0.0292363	+	0.0140795i
$975$	−0.0223955	−	0.0416178i	−0.000717229	−	0.00133284i
$976$	20.4428	−	21.3815i	0.654358	−	0.684405i
$977$	−3.50909	+	2.54951i	−0.112266	+	0.0815659i	−0.642502	−	0.766284i	$-0.722103\pi$
$977$	−3.50909	+	2.54951i	−0.112266	+	0.0815659i	0.530236	+	0.847850i	$0.322103\pi$
$978$	0.0184512	−	0.410849i	0.000590006	−	0.0131375i
$979$	−18.6707	+	34.6960i	−0.596718	+	1.10889i
$980$	−0.0452960	−	0.139407i	−0.00144693	−	0.00445318i
$981$	29.6022	+	8.16970i	0.945126	+	0.260838i
$982$	−2.58582	−	3.91735i	−0.0825169	−	0.125008i
$983$	−49.7312	+	13.7249i	−1.58618	+	0.437757i	−0.944310	−	0.329057i	$-0.893269\pi$
$983$	−49.7312	+	13.7249i	−1.58618	+	0.437757i	−0.641868	+	0.766815i	$0.721840\pi$
$984$	−0.706561	−	0.617303i	−0.0225243	−	0.0196789i
$985$	0.788801	+	0.296042i	0.0251333	+	0.00943268i
$986$	0.989869	−	0.371504i	0.0315238	−	0.0118311i
$987$	−7.48663	+	6.54087i	−0.238302	+	0.208198i
$988$	0.155450	−	0.235497i	0.00494554	−	0.00749217i
$989$	3.50565	−	10.7893i	0.111473	−	0.343079i
$990$	0.0601528	+	0.0629149i	0.00191178	+	0.00199957i
$991$	40.8545	+	7.41400i	1.29779	+	0.235513i	0.783116	−	0.621875i	$-0.213629\pi$
$991$	40.8545	+	7.41400i	1.29779	+	0.235513i	0.514670	+	0.857389i	$0.327915\pi$
$992$	2.23284	−	5.22400i	0.0708929	−	0.165862i
$993$	−6.33063			−0.200897
$994$	3.66790	+	0.828066i	0.116339	+	0.0262647i
$995$	−0.0665107			−0.00210853
$996$	−0.759703	+	1.77741i	−0.0240721	+	0.0563195i
$997$	33.1552	+	6.01678i	1.05003	+	0.190553i	0.676030	−	0.736874i	$-0.263699\pi$
$997$	33.1552	+	6.01678i	1.05003	+	0.190553i	0.374004	+	0.927427i	$0.377985\pi$
$998$	−2.93471	−	3.06947i	−0.0928967	−	0.0971624i
$999$	−5.50645	+	16.9471i	−0.174216	+	0.536183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.15.3	✓	120
3.2	odd	2		639.2.v.a.370.3		120
71.19	even	35	inner	71.2.g.a.19.3	yes	120
71.27	even	35		5041.2.a.s.1.30		60
71.44	odd	70		5041.2.a.t.1.30		60
213.161	odd	70		639.2.v.a.19.3		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.15.3	✓	120	1.1	even	1	trivial
71.2.g.a.19.3	yes	120	71.19	even	35	inner
639.2.v.a.19.3		120	213.161	odd	70
639.2.v.a.370.3		120	3.2	odd	2
5041.2.a.s.1.30		60	71.27	even	35
5041.2.a.t.1.30		60	71.44	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0758189 - 0.177387i) q^{2} +(-0.355633 - 0.0645379i) q^{3} +(1.35641 + 1.41869i) q^{4} +(-0.0139966 + 0.0430772i) q^{5} +(-0.0384119 + 0.0581915i) q^{6} +(1.74206 - 1.52199i) q^{7} +(0.715719 - 0.268614i) q^{8} +(-2.68639 - 1.00822i) q^{9} +O(q^{10})\)	\(q+(0.0758189 - 0.177387i) q^{2} +(-0.355633 - 0.0645379i) q^{3} +(1.35641 + 1.41869i) q^{4} +(-0.0139966 + 0.0430772i) q^{5} +(-0.0384119 + 0.0581915i) q^{6} +(1.74206 - 1.52199i) q^{7} +(0.715719 - 0.268614i) q^{8} +(-2.68639 - 1.00822i) q^{9} +(0.00658013 + 0.00574888i) q^{10} +(-3.34669 + 0.923629i) q^{11} +(-0.390824 - 0.592073i) q^{12} +(0.0252193 + 0.00696008i) q^{13} +(-0.137900 - 0.424414i) q^{14} +(0.00775777 - 0.0144164i) q^{15} +(-0.169504 + 3.77429i) q^{16} +(-2.92807 + 2.12736i) q^{17} +(-0.382525 + 0.400090i) q^{18} +(-2.60396 - 4.83897i) q^{19} +(-0.0800983 + 0.0385733i) q^{20} +(-0.717759 + 0.428841i) q^{21} +(-0.0899027 + 0.663689i) q^{22} +(0.970016 - 4.24992i) q^{23} +(-0.271869 + 0.0493370i) q^{24} +(4.04343 + 2.93772i) q^{25} +(0.00314673 - 0.00394587i) q^{26} +(1.82114 + 1.08808i) q^{27} +(4.52217 + 0.407003i) q^{28} +(-0.203270 - 1.50060i) q^{29} +(-0.00196909 - 0.00246916i) q^{30} +(-0.112892 - 2.51375i) q^{31} +(2.03418 + 0.979608i) q^{32} +(1.24980 - 0.112484i) q^{33} +(0.155364 + 0.680695i) q^{34} +(0.0411801 + 0.0963456i) q^{35} +(-2.21349 - 5.17872i) q^{36} +(1.86910 + 8.18904i) q^{37} +(-1.05580 + 0.0950237i) q^{38} +(-0.00851962 - 0.00410283i) q^{39} +(0.00155348 + 0.0345908i) q^{40} +(2.11713 + 2.65479i) q^{41} +(0.0216512 + 0.159836i) q^{42} +(2.59195 + 0.233279i) q^{43} +(-5.84982 - 3.49511i) q^{44} +(0.0810318 - 0.101611i) q^{45} +(-0.680335 - 0.494292i) q^{46} +(11.6990 - 2.12306i) q^{47} +(0.303866 - 1.33132i) q^{48} +(-0.221321 + 1.63386i) q^{49} +(0.827682 - 0.494517i) q^{50} +(1.17861 - 0.567590i) q^{51} +(0.0243334 + 0.0452191i) q^{52} +(-5.80404 + 6.07055i) q^{53} +(0.331088 - 0.240550i) q^{54} +(0.00705509 - 0.157094i) q^{55} +(0.837996 - 1.55726i) q^{56} +(0.613758 + 1.88895i) q^{57} +(-0.281598 - 0.0777162i) q^{58} +(-4.95917 - 7.51282i) q^{59} +(0.0309751 - 0.00854857i) q^{60} +(-5.89639 - 5.15152i) q^{61} +(-0.454466 - 0.170564i) q^{62} +(-6.21436 + 2.33229i) q^{63} +(-5.36235 + 4.68495i) q^{64} +(-0.000652805 + 0.000988958i) q^{65} +(0.0748055 - 0.230228i) q^{66} +(3.75317 + 3.92550i) q^{67} +(-6.98972 - 1.26845i) q^{68} +(-0.619251 + 1.44881i) q^{69} +0.0202127 q^{70} +(-4.30467 + 7.24360i) q^{71} -2.19353 q^{72} +(2.56474 - 6.00050i) q^{73} +(1.59434 + 0.289331i) q^{74} +(-1.24838 - 1.30570i) q^{75} +(3.33297 - 10.2578i) q^{76} +(-4.42438 + 6.70265i) q^{77} +(-0.00137374 + 0.00120020i) q^{78} +(-1.04138 + 0.390838i) q^{79} +(-0.160213 - 0.0601291i) q^{80} +(5.90506 + 5.15910i) q^{81} +(0.631444 - 0.174267i) q^{82} +(-1.50101 - 2.27393i) q^{83} +(-1.58197 - 0.436595i) q^{84} +(-0.0506578 - 0.155909i) q^{85} +(0.237899 - 0.442091i) q^{86} +(-0.0245559 + 0.546781i) q^{87} +(-2.14719 + 1.56003i) q^{88} +(7.84268 - 8.20280i) q^{89} +(-0.0118807 - 0.0220780i) q^{90} +(0.0545266 - 0.0262586i) q^{91} +(7.34506 - 4.38847i) q^{92} +(-0.122084 + 0.901257i) q^{93} +(0.510403 - 2.23622i) q^{94} +(0.244896 - 0.0444420i) q^{95} +(-0.660199 - 0.479663i) q^{96} +(5.45671 - 6.84250i) q^{97} +(0.273045 + 0.163137i) q^{98} +(9.92176 + 0.892975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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