LMFDB - Embedded newform 138.2.f.a.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			65.3
Character	$\chi$	$=$	138.65
Dual form			138.2.f.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(0.322552 + 1.70175i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.12015 + 0.719874i) q^{5} +(-1.00034 - 1.41398i) q^{6} +(1.49094 - 0.214365i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.79192 + 1.09781i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(0.322552 + 1.70175i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.12015 + 0.719874i) q^{5} +(-1.00034 - 1.41398i) q^{6} +(1.49094 - 0.214365i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.79192 + 1.09781i) q^{9} +(-1.31797 - 0.189495i) q^{10} +(-1.00968 + 2.21088i) q^{11} +(1.49733 + 0.870642i) q^{12} +(-0.172574 + 1.20028i) q^{13} +(-1.26715 + 0.814351i) q^{14} +(-0.863741 + 2.13841i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-2.63441 - 3.04027i) q^{17} +(2.08357 - 2.15841i) q^{18} +(4.36347 + 3.78096i) q^{19} +(1.27758 - 0.375132i) q^{20} +(0.845700 + 2.46806i) q^{21} -2.43052i q^{22} +(2.02041 - 4.34948i) q^{23} +(-1.72369 - 0.169952i) q^{24} +(-1.34057 - 2.93543i) q^{25} +(-0.341634 - 1.16350i) q^{26} +(-2.76874 - 4.39706i) q^{27} +(0.814351 - 1.26715i) q^{28} +(1.94196 - 1.68271i) q^{29} +(-0.102640 - 2.30397i) q^{30} +(5.49153 + 1.61246i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-4.08805 - 1.00509i) q^{33} +(3.65932 + 1.67116i) q^{34} +(1.82438 + 0.833168i) q^{35} +(-0.998651 + 2.82890i) q^{36} +(-4.96610 - 7.72740i) q^{37} +(-5.53982 - 1.62664i) q^{38} +(-2.09824 + 0.0934742i) q^{39} +(-1.00630 + 0.871960i) q^{40} +(6.32320 - 9.83909i) q^{41} +(-1.79455 - 1.89371i) q^{42} +(-0.667960 - 2.27486i) q^{43} +(1.00968 + 2.21088i) q^{44} +(-3.91764 - 0.780126i) q^{45} +(-0.0309926 + 4.79573i) q^{46} +3.88490i q^{47} +(1.63853 - 0.561454i) q^{48} +(-4.53951 + 1.33292i) q^{49} +(2.43885 + 2.11327i) q^{50} +(4.32406 - 5.46376i) q^{51} +(0.794097 + 0.916437i) q^{52} +(1.06952 + 7.43870i) q^{53} +(4.34513 + 2.84953i) q^{54} +(-2.72254 + 1.74967i) q^{55} +(-0.214365 + 1.49094i) q^{56} +(-5.02682 + 8.64509i) q^{57} +(-1.06744 + 2.33737i) q^{58} +(1.80201 + 0.259090i) q^{59} +(1.05047 + 2.05313i) q^{60} +(-0.525376 + 1.78927i) q^{61} +(-5.66511 + 0.814520i) q^{62} +(-3.92725 + 2.23525i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-1.05736 + 1.22025i) q^{65} +(4.13615 - 0.783971i) q^{66} +(8.93253 - 4.07935i) q^{67} -4.02286 q^{68} +(8.05342 + 2.03531i) q^{69} -2.00563 q^{70} +(2.72650 - 1.24515i) q^{71} +(-0.266764 - 2.98812i) q^{72} +(-8.71102 + 10.0531i) q^{73} +(7.72740 + 4.96610i) q^{74} +(4.56298 - 3.22814i) q^{75} +(5.71492 - 0.821682i) q^{76} +(-1.03143 + 3.51273i) q^{77} +(1.86979 - 0.956667i) q^{78} +(-7.42390 - 1.06740i) q^{79} +(0.553133 - 1.21119i) q^{80} +(6.58964 - 6.12998i) q^{81} +(-1.66448 + 11.5767i) q^{82} +(-6.10459 + 3.92318i) q^{83} +(2.41905 + 0.977100i) q^{84} +(-0.762312 - 5.30199i) q^{85} +(1.55261 + 1.79181i) q^{86} +(3.48994 + 2.76196i) q^{87} +(-1.83687 - 1.59165i) q^{88} +(-7.87435 + 2.31212i) q^{89} +(3.88769 - 0.917819i) q^{90} +1.82653i q^{91} +(-1.96403 - 4.37523i) q^{92} +(-0.972700 + 9.86533i) q^{93} +(-1.61385 - 3.53383i) q^{94} +(2.16590 + 7.37638i) q^{95} +(-1.25722 + 1.19138i) q^{96} +(9.14934 - 14.2367i) q^{97} +(3.57557 - 3.09825i) q^{98} +(0.391811 - 7.28103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	0.322552	+	1.70175i	0.186226	+	0.982507i
$3$	0.322552	+	1.70175i	0.186226	+	0.982507i
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	1.12015	+	0.719874i	0.500944	+	0.321937i	0.766594	−	0.642132i	$-0.221950\pi$
$5$	1.12015	+	0.719874i	0.500944	+	0.321937i	−0.265649	+	0.964070i	$0.585586\pi$
$6$	−1.00034	−	1.41398i	−0.408386	−	0.577253i
$7$	1.49094	−	0.214365i	0.563522	−	0.0810222i	0.145334	−	0.989383i	$-0.453574\pi$
$7$	1.49094	−	0.214365i	0.563522	−	0.0810222i	0.418188	+	0.908361i	$0.362665\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	−2.79192	+	1.09781i	−0.930640	+	0.365936i
$10$	−1.31797	−	0.189495i	−0.416778	−	0.0599236i
$11$	−1.00968	+	2.21088i	−0.304429	+	0.666606i	−0.998583	−	0.0532206i	$-0.983051\pi$
$11$	−1.00968	+	2.21088i	−0.304429	+	0.666606i	0.694154	+	0.719826i	$0.255779\pi$
$12$	1.49733	+	0.870642i	0.432241	+	0.251333i
$13$	−0.172574	+	1.20028i	−0.0478634	+	0.332897i	0.951794	+	0.306737i	$0.0992371\pi$
$13$	−0.172574	+	1.20028i	−0.0478634	+	0.332897i	−0.999658	+	0.0261603i	$0.991672\pi$
$14$	−1.26715	+	0.814351i	−0.338661	+	0.217644i
$15$	−0.863741	+	2.13841i	−0.223017	+	0.552134i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−2.63441	−	3.04027i	−0.638939	−	0.737375i	0.340248	−	0.940336i	$-0.389489\pi$
$17$	−2.63441	−	3.04027i	−0.638939	−	0.737375i	−0.979187	+	0.202961i	$0.934944\pi$
$18$	2.08357	−	2.15841i	0.491103	−	0.508741i
$19$	4.36347	+	3.78096i	1.00105	+	0.867413i	0.991178	−	0.132539i	$-0.0423129\pi$
$19$	4.36347	+	3.78096i	1.00105	+	0.867413i	0.00986977	+	0.999951i	$0.496858\pi$
$20$	1.27758	−	0.375132i	0.285676	−	0.0838822i
$21$	0.845700	+	2.46806i	0.184547	+	0.538575i
$22$		−	2.43052i		−	0.518189i
$23$	2.02041	−	4.34948i	0.421285	−	0.906928i
$23$	2.02041	−	4.34948i	0.421285	−	0.906928i
$24$	−1.72369	−	0.169952i	−0.351847	−	0.0346914i
$25$	−1.34057	−	2.93543i	−0.268113	−	0.587087i
$26$	−0.341634	−	1.16350i	−0.0670000	−	0.228181i
$27$	−2.76874	−	4.39706i	−0.532844	−	0.846214i
$28$	0.814351	−	1.26715i	0.153898	−	0.239470i
$29$	1.94196	−	1.68271i	0.360612	−	0.312472i	−0.455644	−	0.890162i	$-0.650591\pi$
$29$	1.94196	−	1.68271i	0.360612	−	0.312472i	0.816256	+	0.577690i	$0.196046\pi$
$30$	−0.102640	−	2.30397i	−0.0187393	−	0.420646i
$31$	5.49153	+	1.61246i	0.986308	+	0.289606i	0.734826	−	0.678256i	$-0.237264\pi$
$31$	5.49153	+	1.61246i	0.986308	+	0.289606i	0.251482	+	0.967862i	$0.419082\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	−4.08805	−	1.00509i	−0.711637	−	0.174964i
$34$	3.65932	+	1.67116i	0.627569	+	0.286601i
$35$	1.82438	+	0.833168i	0.308377	+	0.140831i
$36$	−0.998651	+	2.82890i	−0.166442	+	0.471484i
$37$	−4.96610	−	7.72740i	−0.816421	−	1.27038i	−0.959793	−	0.280708i	$-0.909431\pi$
$37$	−4.96610	−	7.72740i	−0.816421	−	1.27038i	0.143372	−	0.989669i	$-0.454205\pi$
$38$	−5.53982	−	1.62664i	−0.898677	−	0.263875i
$39$	−2.09824	+	0.0934742i	−0.335987	+	0.0149679i
$40$	−1.00630	+	0.871960i	−0.159109	+	0.137869i
$41$	6.32320	−	9.83909i	0.987518	−	1.53661i	0.151098	−	0.988519i	$-0.451719\pi$
$41$	6.32320	−	9.83909i	0.987518	−	1.53661i	0.836420	−	0.548089i	$-0.184645\pi$
$42$	−1.79455	−	1.89371i	−0.276905	−	0.292206i
$43$	−0.667960	−	2.27486i	−0.101863	−	0.346913i	0.892753	−	0.450547i	$-0.148771\pi$
$43$	−0.667960	−	2.27486i	−0.101863	−	0.346913i	−0.994616	+	0.103634i	$0.966953\pi$
$44$	1.00968	+	2.21088i	0.152214	+	0.333303i
$45$	−3.91764	−	0.780126i	−0.584007	−	0.116294i
$46$	−0.0309926	+	4.79573i	−0.00456961	+	0.707092i
$47$			3.88490i			0.566671i	0.959021	+	0.283335i	$0.0914410\pi$
$47$			3.88490i			0.566671i	−0.959021	+	0.283335i	$0.908559\pi$
$48$	1.63853	−	0.561454i	0.236501	−	0.0810389i
$49$	−4.53951	+	1.33292i	−0.648501	+	0.190417i
$50$	2.43885	+	2.11327i	0.344905	+	0.298862i
$51$	4.32406	−	5.46376i	0.605489	−	0.765080i
$52$	0.794097	+	0.916437i	0.110121	+	0.127087i
$53$	1.06952	+	7.43870i	0.146910	+	1.02178i	0.921238	+	0.388999i	$0.127179\pi$
$53$	1.06952	+	7.43870i	0.146910	+	1.02178i	−0.774328	+	0.632785i	$0.781912\pi$
$54$	4.34513	+	2.84953i	0.591298	+	0.387772i
$55$	−2.72254	+	1.74967i	−0.367107	+	0.235925i
$56$	−0.214365	+	1.49094i	−0.0286457	+	0.199235i
$57$	−5.02682	+	8.64509i	−0.665818	+	1.14507i
$58$	−1.06744	+	2.33737i	−0.140162	+	0.306911i
$59$	1.80201	+	0.259090i	0.234602	+	0.0337306i	0.258613	−	0.965981i	$-0.416735\pi$
$59$	1.80201	+	0.259090i	0.234602	+	0.0337306i	−0.0240111	+	0.999712i	$0.507644\pi$
$60$	1.05047	+	2.05313i	0.135615	+	0.265058i
$61$	−0.525376	+	1.78927i	−0.0672675	+	0.229092i	−0.986265	−	0.165172i	$-0.947182\pi$
$61$	−0.525376	+	1.78927i	−0.0672675	+	0.229092i	0.918997	+	0.394264i	$0.129000\pi$
$62$	−5.66511	+	0.814520i	−0.719470	+	0.103444i
$63$	−3.92725	+	2.23525i	−0.494787	+	0.281615i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	−1.05736	+	1.22025i	−0.131149	+	0.151354i
$66$	4.13615	−	0.783971i	0.509125	−	0.0965001i
$67$	8.93253	−	4.07935i	1.09128	−	0.498372i	0.213262	−	0.976995i	$-0.431591\pi$
$67$	8.93253	−	4.07935i	1.09128	−	0.498372i	0.878020	+	0.478623i	$0.158864\pi$
$68$	−4.02286			−0.487843
$69$	8.05342	+	2.03531i	0.969518	+	0.245022i
$70$	−2.00563			−0.239718
$71$	2.72650	−	1.24515i	0.323576	−	0.147772i	−0.247004	−	0.969015i	$-0.579446\pi$
$71$	2.72650	−	1.24515i	0.323576	−	0.147772i	0.570579	+	0.821242i	$0.306719\pi$
$72$	−0.266764	−	2.98812i	−0.0314384	−	0.352153i
$73$	−8.71102	+	10.0531i	−1.01955	+	1.17662i	−0.0353814	+	0.999374i	$0.511265\pi$
$73$	−8.71102	+	10.0531i	−1.01955	+	1.17662i	−0.984166	+	0.177247i	$0.943281\pi$
$74$	7.72740	+	4.96610i	0.898292	+	0.577297i
$75$	4.56298	−	3.22814i	0.526887	−	0.372754i
$76$	5.71492	−	0.821682i	0.655547	−	0.0942534i
$77$	−1.03143	+	3.51273i	−0.117542	+	0.400312i
$78$	1.86979	−	0.956667i	0.211712	−	0.108321i
$79$	−7.42390	−	1.06740i	−0.835254	−	0.120091i	−0.288600	−	0.957450i	$-0.593190\pi$
$79$	−7.42390	−	1.06740i	−0.835254	−	0.120091i	−0.546654	+	0.837358i	$0.684099\pi$
$80$	0.553133	−	1.21119i	0.0618422	−	0.135415i
$81$	6.58964	−	6.12998i	0.732182	−	0.681109i
$82$	−1.66448	+	11.5767i	−0.183811	+	1.27843i
$83$	−6.10459	+	3.92318i	−0.670065	+	0.430625i	−0.830949	−	0.556348i	$-0.812202\pi$
$83$	−6.10459	+	3.92318i	−0.670065	+	0.430625i	0.160884	+	0.986973i	$0.448566\pi$
$84$	2.41905	+	0.977100i	0.263940	+	0.106610i
$85$	−0.762312	−	5.30199i	−0.0826843	−	0.575082i
$86$	1.55261	+	1.79181i	0.167422	+	0.193216i
$87$	3.48994	+	2.76196i	0.374161	+	0.296114i
$88$	−1.83687	−	1.59165i	−0.195811	−	0.169671i
$89$	−7.87435	+	2.31212i	−0.834679	+	0.245084i	−0.671026	−	0.741434i	$-0.734146\pi$
$89$	−7.87435	+	2.31212i	−0.834679	+	0.245084i	−0.163653	+	0.986518i	$0.552328\pi$
$90$	3.88769	−	0.917819i	0.409798	−	0.0967466i
$91$			1.82653i			0.191473i
$92$	−1.96403	−	4.37523i	−0.204764	−	0.456149i
$93$	−0.972700	+	9.86533i	−0.100864	+	1.02299i
$94$	−1.61385	−	3.53383i	−0.166455	−	0.364487i
$95$	2.16590	+	7.37638i	0.222217	+	0.756800i
$96$	−1.25722	+	1.19138i	−0.128314	+	0.121595i
$97$	9.14934	−	14.2367i	0.928975	−	1.44551i	0.0339871	−	0.999422i	$-0.489179\pi$
$97$	9.14934	−	14.2367i	0.928975	−	1.44551i	0.894988	−	0.446091i	$-0.147184\pi$
$98$	3.57557	−	3.09825i	0.361187	−	0.312970i
$99$	0.391811	−	7.28103i	0.0393785	−	0.731772i
$100$	−3.09634	−	0.909167i	−0.309634	−	0.0909167i
$101$	−0.785907	−	1.22290i	−0.0782007	−	0.121683i	0.799950	−	0.600066i	$-0.204859\pi$
$101$	−0.785907	−	1.22290i	−0.0782007	−	0.121683i	−0.878151	+	0.478384i	$0.841223\pi$
$102$	−1.66357	+	6.76629i	−0.164718	+	0.669963i
$103$	−11.4095	−	5.21054i	−1.12421	−	0.513410i	−0.235499	−	0.971875i	$-0.575672\pi$
$103$	−11.4095	−	5.21054i	−1.12421	−	0.513410i	−0.888713	+	0.458464i	$0.848400\pi$
$104$	−1.10304	−	0.503740i	−0.108162	−	0.0493958i
$105$	−0.829386	+	3.37339i	−0.0809398	+	0.329209i
$106$	−4.06302	−	6.32218i	−0.394635	−	0.614064i
$107$	−6.33498	−	1.86012i	−0.612426	−	0.179824i	−0.0392127	−	0.999231i	$-0.512485\pi$
$107$	−6.33498	−	1.86012i	−0.612426	−	0.179824i	−0.573213	+	0.819407i	$0.694303\pi$
$108$	−5.13621	−	0.786988i	−0.494232	−	0.0757279i
$109$	−14.0230	+	12.1510i	−1.34316	+	1.16385i	−0.371241	+	0.928537i	$0.621068\pi$
$109$	−14.0230	+	12.1510i	−1.34316	+	1.16385i	−0.971919	+	0.235317i	$0.924387\pi$
$110$	1.74967	−	2.72254i	0.166824	−	0.259584i
$111$	11.5483	−	10.9436i	1.09612	−	1.03872i
$112$	−0.424365	−	1.44526i	−0.0400987	−	0.136564i
$113$	−5.75929	−	12.6111i	−0.541788	−	1.18635i	−0.960512	−	0.278237i	$-0.910250\pi$
$113$	−5.75929	−	12.6111i	−0.541788	−	1.18635i	0.418724	−	0.908113i	$-0.362477\pi$
$114$	0.981253	−	9.95207i	0.0919027	−	0.932097i
$115$	5.39423	−	3.41761i	0.503014	−	0.318693i
$116$		−	2.56958i		−	0.238579i
$117$	−0.835861	−	3.54053i	−0.0772754	−	0.327322i
$118$	−1.74680	+	0.512906i	−0.160806	+	0.0472168i
$119$	−4.57947	−	3.96814i	−0.419800	−	0.363758i
$120$	−1.80844	−	1.43121i	−0.165087	−	0.130651i
$121$	3.33492	+	3.84870i	0.303174	+	0.349882i
$122$	−0.265389	−	1.84582i	−0.0240272	−	0.167113i
$123$	18.7833	+	7.58690i	1.69363	+	0.684088i
$124$	4.81480	−	3.09429i	0.432382	−	0.277875i
$125$	1.55899	−	10.8430i	0.139440	−	0.969826i
$126$	2.64379	−	3.66469i	0.235528	−	0.326477i
$127$	−7.59245	+	16.6251i	−0.673721	+	1.47524i	0.195441	+	0.980715i	$0.437386\pi$
$127$	−7.59245	+	16.6251i	−0.673721	+	1.47524i	−0.869162	+	0.494527i	$0.835341\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	3.65580	−	1.87046i	0.321875	−	0.164685i
$130$	0.454893	−	1.54922i	0.0398968	−	0.135876i
$131$	20.0087	−	2.87682i	1.74817	−	0.251349i	0.807306	−	0.590134i	$-0.200925\pi$
$131$	20.0087	−	2.87682i	1.74817	−	0.251349i	0.940864	+	0.338785i	$0.110016\pi$
$132$	−3.43670	+	2.43134i	−0.299126	+	0.211621i
$133$	7.31616	+	4.70181i	0.634392	+	0.407699i
$134$	−6.43069	+	7.42141i	−0.555527	+	0.641112i
$135$	0.0639374	−	6.91848i	0.00550286	−	0.595448i
$136$	3.65932	−	1.67116i	0.313784	−	0.143300i
$137$	−1.71701			−0.146694			−0.0733470	−	0.997306i	$-0.523368\pi$
$137$	−1.71701			−0.146694			−0.0733470	+	0.997306i	$0.523368\pi$
$138$	−8.17114	+	1.49413i	−0.695574	+	0.127189i
$139$	9.24109			0.783819			0.391909	−	0.920004i	$-0.371815\pi$
$139$	9.24109			0.783819			0.391909	+	0.920004i	$0.371815\pi$
$140$	1.82438	−	0.833168i	0.154188	−	0.0704155i
$141$	−6.61114	+	1.25308i	−0.556758	+	0.105529i
$142$	−1.96286	+	2.26526i	−0.164719	+	0.190096i
$143$	−2.47943	−	1.59343i	−0.207340	−	0.133249i
$144$	1.48397	+	2.60727i	0.123664	+	0.217272i
$145$	3.38662	−	0.486922i	0.281243	−	0.0404367i
$146$	3.74763	−	12.7633i	0.310156	−	1.05630i
$147$	−3.73253	−	7.29518i	−0.307854	−	0.601696i
$148$	−9.09208	−	1.30724i	−0.747364	−	0.107455i
$149$	−0.929742	+	2.03585i	−0.0761675	+	0.166783i	−0.943885	−	0.330274i	$-0.892859\pi$
$149$	−0.929742	+	2.03585i	−0.0761675	+	0.166783i	0.867718	+	0.497057i	$0.165586\pi$
$150$	−2.80961	+	4.83195i	−0.229404	+	0.394527i
$151$	−1.71974	+	11.9611i	−0.139951	+	0.973379i	0.791929	+	0.610613i	$0.209077\pi$
$151$	−1.71974	+	11.9611i	−0.139951	+	0.973379i	−0.931880	+	0.362766i	$0.881832\pi$
$152$	−4.85714	+	3.12149i	−0.393966	+	0.253187i
$153$	10.6927	+	5.59612i	0.864454	+	0.452420i
$154$	−0.521018	−	3.62376i	−0.0419848	−	0.292011i
$155$	4.99055	+	5.75940i	0.400850	+	0.462606i
$156$	−1.30341	+	1.64696i	−0.104356	+	0.131862i
$157$	7.39066	+	6.40404i	0.589839	+	0.511098i	0.897860	−	0.440281i	$-0.145121\pi$
$157$	7.39066	+	6.40404i	0.589839	+	0.511098i	−0.308021	+	0.951379i	$0.599667\pi$
$158$	7.19643	−	2.11306i	0.572517	−	0.168106i
$159$	−12.3138	+	4.21943i	−0.976551	+	0.334623i
$160$			1.33152i			0.105266i
$161$	2.07993	−	6.91790i	0.163922	−	0.545207i
$162$	−3.44766	+	8.31346i	−0.270874	+	0.653167i
$163$	−7.07658	−	15.4955i	−0.554280	−	1.21370i	−0.954754	−	0.297396i	$-0.903882\pi$
$163$	−7.07658	−	15.4955i	−0.554280	−	1.21370i	0.400474	−	0.916308i	$-0.368846\pi$
$164$	−3.29507	−	11.2220i	−0.257302	−	0.876290i
$165$	−3.85567	−	4.06873i	−0.300163	−	0.316750i
$166$	3.92318	−	6.10459i	0.304498	−	0.473808i
$167$	−17.5062	+	15.1692i	−1.35467	+	1.17383i	−0.386868	+	0.922135i	$0.626443\pi$
$167$	−17.5062	+	15.1692i	−1.35467	+	1.17383i	−0.967806	+	0.251696i	$0.919012\pi$
$168$	−2.60635	+	0.116110i	−0.201084	+	0.00895808i
$169$	11.0625	+	3.24825i	0.850963	+	0.249865i
$170$	2.89595	+	4.50619i	0.222109	+	0.345609i
$171$	−16.3332	−	5.76590i	−1.24903	−	0.440930i
$172$	−2.15665	−	0.984908i	−0.164443	−	0.0750985i
$173$	8.20959	+	3.74919i	0.624163	+	0.285046i	0.702283	−	0.711898i	$-0.252164\pi$
$173$	8.20959	+	3.74919i	0.624163	+	0.285046i	−0.0781193	+	0.996944i	$0.524892\pi$
$174$	−4.32193	−	1.06260i	−0.327644	−	0.0805552i
$175$	−2.62796	−	4.08918i	−0.198655	−	0.309113i
$176$	2.33207	+	0.684757i	0.175786	+	0.0516155i
$177$	0.140335	+	3.15014i	0.0105483	+	0.236779i
$178$	6.20227	−	5.37430i	0.464880	−	0.402821i
$179$	−11.9368	+	18.5740i	−0.892197	+	1.38829i	0.0291624	+	0.999575i	$0.490716\pi$
$179$	−11.9368	+	18.5740i	−0.892197	+	1.38829i	−0.921360	+	0.388711i	$0.872920\pi$
$180$	−3.15509	+	2.44988i	−0.235166	+	0.182603i
$181$	−0.799679	−	2.72345i	−0.0594396	−	0.202433i	0.924420	−	0.381377i	$-0.124550\pi$
$181$	−0.799679	−	2.72345i	−0.0594396	−	0.202433i	−0.983859	+	0.178944i	$0.942732\pi$
$182$	−0.758769	−	1.66147i	−0.0562437	−	0.123157i
$183$	−3.21435	−	0.316928i	−0.237612	−	0.0234280i
$184$	3.60408	+	3.16396i	0.265696	+	0.233250i
$185$		−	12.2308i		−	0.899225i
$186$	−3.21341	−	9.37789i	−0.235618	−	0.687620i
$187$	9.38159	−	2.75468i	0.686050	−	0.201442i
$188$	2.93601	+	2.54407i	0.214131	+	0.185545i
$189$	−5.07059	−	5.96222i	−0.368831	−	0.433688i
$190$	−5.03443	−	5.81004i	−0.365236	−	0.421505i
$191$	2.78216	+	19.3504i	0.201310	+	1.40014i	0.800402	+	0.599464i	$0.204619\pi$
$191$	2.78216	+	19.3504i	0.201310	+	1.40014i	−0.599092	+	0.800680i	$0.704472\pi$
$192$	0.648688	−	1.60599i	0.0468151	−	0.115902i
$193$	−1.97951	+	1.27215i	−0.142488	+	0.0915717i	−0.609943	−	0.792446i	$-0.708808\pi$
$193$	−1.97951	+	1.27215i	−0.142488	+	0.0915717i	0.467454	+	0.884017i	$0.345171\pi$
$194$	−2.40841	+	16.7509i	−0.172914	+	1.20264i
$195$	−2.41762	−	1.40576i	−0.173129	−	0.100669i
$196$	−1.96539	+	4.30361i	−0.140385	+	0.307401i
$197$	9.15698	+	1.31657i	0.652408	+	0.0938021i	0.460568	−	0.887624i	$-0.347646\pi$
$197$	9.15698	+	1.31657i	0.652408	+	0.0938021i	0.191839	+	0.981426i	$0.438555\pi$
$198$	2.66825	+	6.78583i	0.189624	+	0.482248i
$199$	−3.74392	+	12.7506i	−0.265399	+	0.903867i	0.713694	+	0.700457i	$0.247021\pi$
$199$	−3.74392	+	12.7506i	−0.265399	+	0.903867i	−0.979094	+	0.203410i	$0.934798\pi$
$200$	3.19421	−	0.459258i	0.225865	−	0.0324744i
$201$	9.82325	+	13.8851i	0.692878	+	0.979383i
$202$	1.22290	+	0.785907i	0.0860426	+	0.0552962i
$203$	2.53462	−	2.92511i	0.177896	−	0.205302i
$204$	−1.29758	−	6.84591i	−0.0908489	−	0.479310i
$205$	14.1658	−	6.46931i	0.989383	−	0.451836i
$206$	12.5430			0.873911
$207$	−0.865937	+	14.3614i	−0.0601868	+	0.998187i
$208$	1.21262			0.0840801
$209$	−12.7649	+	5.82956i	−0.882970	+	0.403239i
$210$	−0.646920	−	3.41308i	−0.0446417	−	0.235525i
$211$	4.41576	−	5.09606i	0.303994	−	0.350827i	−0.583114	−	0.812391i	$-0.698166\pi$
$211$	4.41576	−	5.09606i	0.303994	−	0.350827i	0.887107	+	0.461563i	$0.152711\pi$
$212$	6.32218	+	4.06302i	0.434209	+	0.279049i
$213$	2.99837	+	4.23820i	0.205445	+	0.290396i
$214$	6.53522	−	0.939623i	0.446738	−	0.0642313i
$215$	0.889402	−	3.02902i	0.0606567	−	0.206578i
$216$	4.99899	−	1.41779i	0.340138	−	0.0964684i
$217$	8.53318	+	1.22689i	0.579270	+	0.0832865i
$218$	7.70806	−	16.8783i	0.522056	−	1.14314i
$219$	−19.9176	−	11.5814i	−1.34590	−	0.782596i
$220$	−0.460572	+	3.20335i	−0.0310518	+	0.215970i
$221$	4.10380	−	2.63735i	0.276052	−	0.177408i
$222$	−5.95858	+	14.7519i	−0.399914	+	0.990086i
$223$	−3.94510	−	27.4388i	−0.264183	−	1.83744i	−0.500472	−	0.865753i	$-0.666840\pi$
$223$	−3.94510	−	27.4388i	−0.264183	−	1.83744i	0.236289	−	0.971683i	$-0.424069\pi$
$224$	0.986397	+	1.13836i	0.0659064	+	0.0760600i
$225$	6.96530	+	6.72381i	0.464353	+	0.448254i
$226$	10.4777	+	9.07895i	0.696964	+	0.603923i
$227$	−7.27118	+	2.13501i	−0.482605	+	0.141706i	−0.513980	−	0.857802i	$-0.671830\pi$
$227$	−7.27118	+	2.13501i	−0.482605	+	0.141706i	0.0313752	+	0.999508i	$0.490011\pi$
$228$	3.24166	+	9.46035i	0.214684	+	0.626527i
$229$		−	19.8565i		−	1.31215i	−0.754695	−	0.656076i	$-0.772215\pi$
$229$		−	19.8565i		−	1.31215i	0.754695	−	0.656076i	$-0.227785\pi$
$230$	−3.48704	+	5.34961i	−0.229928	+	0.352743i
$231$	−6.31048	−	0.622200i	−0.415199	−	0.0409377i
$232$	1.06744	+	2.33737i	0.0700809	+	0.153456i
$233$	4.48375	+	15.2703i	0.293740	+	1.00039i	0.965670	+	0.259773i	$0.0836476\pi$
$233$	4.48375	+	15.2703i	0.293740	+	1.00039i	−0.671929	+	0.740615i	$0.734534\pi$
$234$	2.23112	+	2.87335i	0.145853	+	0.187837i
$235$	−2.79664	+	4.35165i	−0.182433	+	0.283871i
$236$	1.37587	−	1.19220i	0.0895617	−	0.0776056i
$237$	−0.578153	−	12.9779i	−0.0375550	−	0.843007i
$238$	5.81406	+	1.70716i	0.376869	+	0.110659i
$239$	0.244516	+	0.380474i	0.0158164	+	0.0246108i	0.849072	−	0.528278i	$-0.177162\pi$
$239$	0.244516	+	0.380474i	0.0158164	+	0.0246108i	−0.833255	+	0.552888i	$0.813526\pi$
$240$	2.23956	+	0.550623i	0.144563	+	0.0355425i
$241$	0.138748	+	0.0633640i	0.00893754	+	0.00408164i	0.419879	−	0.907580i	$-0.362073\pi$
$241$	0.138748	+	0.0633640i	0.00893754	+	0.00408164i	−0.410941	+	0.911662i	$0.634800\pi$
$242$	−4.63235	−	2.11552i	−0.297779	−	0.135991i
$243$	12.5572	+	9.23669i	0.805546	+	0.592534i
$244$	1.00819	+	1.56877i	0.0645427	+	0.100430i
$245$	−6.04444	−	1.77481i	−0.386165	−	0.113388i
$246$	−20.2376	+	0.901561i	−1.29030	+	0.0574814i
$247$	−5.29122	+	4.58487i	−0.336673	+	0.291728i
$248$	−3.09429	+	4.81480i	−0.196487	+	0.305740i
$249$	−8.64533	−	9.12306i	−0.547875	−	0.578151i
$250$	3.08624	+	10.5108i	0.195191	+	0.664758i
$251$	−6.90784	−	15.1260i	−0.436019	−	0.954748i	−0.992312	−	0.123762i	$-0.960504\pi$
$251$	−6.90784	−	15.1260i	−0.436019	−	0.954748i	0.556293	−	0.830986i	$-0.312223\pi$
$252$	−0.882510	+	4.43179i	−0.0555929	+	0.279177i
$253$	7.57622	+	8.85845i	0.476313	+	0.556926i
$254$		−	18.2768i		−	1.14679i
$255$	8.77680	−	3.00744i	0.549624	−	0.188333i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	3.73058	+	3.23257i	0.232707	+	0.201642i	0.763407	−	0.645918i	$-0.223525\pi$
$257$	3.73058	+	3.23257i	0.232707	+	0.201642i	−0.530699	+	0.847560i	$0.678071\pi$
$258$	−2.54841	+	3.22011i	−0.158657	+	0.200475i
$259$	−9.06062	−	10.4565i	−0.563000	−	0.649736i
$260$	0.229785	+	1.59819i	0.0142507	+	0.0991157i
$261$	−3.57449	+	6.82990i	−0.221255	+	0.422760i
$262$	−17.0055	+	10.9288i	−1.05060	+	0.675181i
$263$	−1.27293	+	8.85339i	−0.0784920	+	0.545924i	0.912194	+	0.409758i	$0.134387\pi$
$263$	−1.27293	+	8.85339i	−0.0784920	+	0.545924i	−0.990686	+	0.136165i	$0.956522\pi$
$264$	2.11612	−	3.63928i	0.130238	−	0.223982i
$265$	−4.15690	+	9.10235i	−0.255356	+	0.559153i
$266$	−8.60822	−	1.23767i	−0.527804	−	0.0758867i
$267$	−6.47454	−	12.6544i	−0.396235	−	0.774437i
$268$	2.76660	−	9.42216i	0.168997	−	0.575550i
$269$	22.5063	−	3.23592i	1.37224	−	0.197298i	0.583542	−	0.812083i	$-0.301666\pi$
$269$	22.5063	−	3.23592i	1.37224	−	0.197298i	0.788695	+	0.614785i	$0.210757\pi$
$270$	2.81588	+	6.31983i	0.171369	+	0.384613i
$271$	−1.26973	−	0.816007i	−0.0771307	−	0.0495689i	0.501507	−	0.865154i	$-0.332779\pi$
$271$	−1.26973	−	0.816007i	−0.0771307	−	0.0495689i	−0.578638	+	0.815585i	$0.696415\pi$
$272$	−2.63441	+	3.04027i	−0.159735	+	0.184344i
$273$	−3.10830	+	0.589152i	−0.188123	+	0.0356571i
$274$	1.56185	−	0.713271i	0.0943546	−	0.0430903i
$275$	7.84343			0.472977
$276$	6.81205	−	4.75353i	0.410037	−	0.286129i
$277$	2.86203			0.171963			0.0859813	−	0.996297i	$-0.472597\pi$
$277$	2.86203			0.171963			0.0859813	+	0.996297i	$0.472597\pi$
$278$	−8.40599	+	3.83889i	−0.504158	+	0.230241i
$279$	−17.1021	+	1.52679i	−1.02388	+	0.0914064i
$280$	−1.31341	+	1.51575i	−0.0784911	+	0.0905835i
$281$	−13.5266	−	8.69300i	−0.806928	−	0.518581i	0.0709420	−	0.997480i	$-0.477399\pi$
$281$	−13.5266	−	8.69300i	−0.806928	−	0.518581i	−0.877870	+	0.478899i	$0.841036\pi$
$282$	5.49315	−	3.88621i	0.327112	−	0.231420i
$283$	−2.13160	+	0.306478i	−0.126711	+	0.0182182i	−0.205378	−	0.978683i	$-0.565842\pi$
$283$	−2.13160	+	0.306478i	−0.126711	+	0.0182182i	0.0786677	+	0.996901i	$0.474933\pi$
$284$	0.844455	−	2.87595i	0.0501092	−	0.170656i
$285$	−11.8541	+	6.06509i	−0.702179	+	0.359265i
$286$	2.91730	+	0.419445i	0.172504	+	0.0248023i
$287$	7.31835	−	16.0249i	0.431988	−	0.945923i
$288$	−2.43296	−	1.75519i	−0.143364	−	0.103426i
$289$	0.116214	−	0.808289i	0.00683615	−	0.0475464i
$290$	−2.87830	+	1.84977i	−0.169020	+	0.108622i
$291$	27.1784	+	10.9778i	1.59323	+	0.643533i
$292$	1.89309	+	13.1667i	0.110784	+	0.770523i
$293$	−18.9102	−	21.8236i	−1.10475	−	1.27495i	−0.958311	−	0.285727i	$-0.907765\pi$
$293$	−18.9102	−	21.8236i	−1.10475	−	1.27495i	−0.146437	−	0.989220i	$-0.546781\pi$
$294$	6.42575	+	5.08538i	0.374758	+	0.296585i
$295$	1.83200	+	1.58744i	0.106663	+	0.0924242i
$296$	8.81350	−	2.58788i	0.512274	−	0.150417i
$297$	12.5169	−	1.68175i	0.726304	−	0.0975849i
$298$		−	2.23810i		−	0.129650i
$299$	4.87191	+	3.17566i	0.281750	+	0.183653i
$300$	0.548446	−	5.56245i	0.0316645	−	0.321148i
$301$	−1.48354	−	3.24849i	−0.0855096	−	0.187240i
$302$	−3.40448	−	11.5946i	−0.195906	−	0.667194i
$303$	1.82757	−	1.73187i	0.104991	−	0.0994932i
$304$	3.12149	−	4.85714i	0.179030	−	0.278576i
$305$	−1.87654	+	1.62603i	−0.107451	+	0.0931065i
$306$	−12.0511	−	0.648503i	−0.688918	−	0.0370725i
$307$	−8.74066	−	2.56649i	−0.498856	−	0.146477i	0.0226186	−	0.999744i	$-0.492800\pi$
$307$	−8.74066	−	2.56649i	−0.498856	−	0.146477i	−0.521475	+	0.853267i	$0.674618\pi$
$308$	1.97930	+	3.07985i	0.112781	+	0.175491i
$309$	5.18690	−	21.0968i	0.295072	−	1.20016i
$310$	−6.93210	−	3.16578i	−0.393717	−	0.179804i
$311$	−10.6970	−	4.88517i	−0.606573	−	0.277013i	0.0883584	−	0.996089i	$-0.471838\pi$
$311$	−10.6970	−	4.88517i	−0.606573	−	0.277013i	−0.694931	+	0.719076i	$0.744565\pi$
$312$	0.501454	−	2.03958i	0.0283893	−	0.115468i
$313$	−2.30643	−	3.58887i	−0.130367	−	0.202855i	0.769933	−	0.638124i	$-0.220289\pi$
$313$	−2.30643	−	3.58887i	−0.130367	−	0.202855i	−0.900300	+	0.435269i	$0.856653\pi$
$314$	−9.38311	−	2.75513i	−0.529520	−	0.155481i
$315$	−6.00819	−	0.323316i	−0.338523	−	0.0182168i
$316$	−5.66831	+	4.91161i	−0.318867	+	0.276300i
$317$	−2.86723	+	4.46150i	−0.161040	+	0.250583i	−0.912391	−	0.409320i	$-0.865766\pi$
$317$	−2.86723	+	4.46150i	−0.161040	+	0.250583i	0.751351	+	0.659902i	$0.229402\pi$
$318$	9.44825	−	8.95348i	0.529831	−	0.502086i
$319$	1.75954	+	5.99243i	0.0985151	+	0.335512i
$320$	−0.553133	−	1.21119i	−0.0309211	−	0.0677077i
$321$	1.12210	−	11.3805i	0.0626294	−	0.635200i
$322$	0.981826	+	7.15678i	0.0547151	+	0.398832i
$323$		−	23.2268i		−	1.29237i
$324$	−0.317438	−	8.99440i	−0.0176354	−	0.499689i
$325$	3.75468	−	1.10247i	0.208272	−	0.0611542i
$326$	12.8742	+	11.1555i	0.713034	+	0.617847i
$327$	−25.2011	−	19.9443i	−1.39363	−	1.10292i
$328$	7.65909	+	8.83906i	0.422902	+	0.488055i
$329$	0.832785	+	5.79214i	0.0459129	+	0.319331i
$330$	5.19745	+	2.09934i	0.286110	+	0.115565i
$331$	10.3875	−	6.67562i	0.570947	−	0.366925i	−0.223087	−	0.974798i	$-0.571614\pi$
$331$	10.3875	−	6.67562i	0.570947	−	0.366925i	0.794034	+	0.607873i	$0.207977\pi$
$332$	−1.03271	+	7.18268i	−0.0566775	+	0.394201i
$333$	22.3481	+	16.1225i	1.22467	+	0.883505i
$334$	9.62271	−	21.0708i	0.526531	−	1.15294i
$335$	12.9423	+	1.86083i	0.707116	+	0.101668i
$336$	2.32259	−	1.18833i	0.126707	−	0.0648290i
$337$	5.36219	−	18.2619i	0.292097	−	0.994791i	−0.674454	−	0.738317i	$-0.735621\pi$
$337$	5.36219	−	18.2619i	0.292097	−	0.994791i	0.966551	−	0.256474i	$-0.0825609\pi$
$338$	−11.4122	+	1.64083i	−0.620742	+	0.0892492i
$339$	19.6033	−	13.8686i	1.06470	−	0.753240i
$340$	−4.50619	−	2.89595i	−0.244382	−	0.157055i
$341$	−9.10962	+	10.5131i	−0.493314	+	0.569314i
$342$	17.2525	−	1.54021i	0.932906	−	0.0832852i
$343$	−16.0734	+	7.34050i	−0.867885	+	0.396350i
$344$	2.37090			0.127830
$345$	7.55584	+	8.07728i	0.406793	+	0.434866i
$346$	−9.02518			−0.485196
$347$	−15.5113	+	7.08379i	−0.832692	+	0.380278i	−0.785693	−	0.618617i	$-0.787693\pi$
$347$	−15.5113	+	7.08379i	−0.832692	+	0.380278i	−0.0469997	+	0.998895i	$0.514966\pi$
$348$	4.37278	−	0.828822i	0.234406	−	0.0444295i
$349$	−17.1986	+	19.8483i	−0.920621	+	1.06245i	0.0772350	+	0.997013i	$0.475391\pi$
$349$	−17.1986	+	19.8483i	−0.920621	+	1.06245i	−0.997856	+	0.0654409i	$0.979155\pi$
$350$	4.08918	+	2.62796i	0.218576	+	0.140470i
$351$	5.75550	−	2.56443i	0.307206	−	0.136879i
$352$	−2.40578	+	0.345899i	−0.128229	+	0.0184365i
$353$	3.11065	−	10.5939i	0.165563	−	0.563856i	−0.834357	−	0.551224i	$-0.814161\pi$
$353$	3.11065	−	10.5939i	0.165563	−	0.563856i	0.999920	−	0.0126319i	$-0.00402096\pi$
$354$	−1.43627	−	2.80717i	−0.0763369	−	0.149200i
$355$	3.95043	+	0.567985i	0.209667	+	0.0301455i
$356$	−3.40922	+	7.46515i	−0.180688	+	0.395652i
$357$	5.27566	−	9.07306i	0.279218	−	0.480197i
$358$	3.14216	−	21.8542i	0.166068	−	1.15503i
$359$	18.5628	−	11.9296i	0.979705	−	0.629618i	0.0503215	−	0.998733i	$-0.483975\pi$
$359$	18.5628	−	11.9296i	0.979705	−	0.629618i	0.929384	+	0.369115i	$0.120339\pi$
$360$	1.85225	−	3.53916i	0.0976223	−	0.186530i
$361$	2.04016	+	14.1896i	0.107377	+	0.746821i
$362$	1.85878	+	2.14514i	0.0976952	+	0.112746i
$363$	−5.47385	+	6.91661i	−0.287302	+	0.363028i
$364$	1.38040	+	1.19612i	0.0723527	+	0.0626939i
$365$	−16.9945	+	4.99005i	−0.889535	+	0.261191i
$366$	3.05553	−	1.04700i	0.159715	−	0.0547276i
$367$			12.7528i			0.665692i	0.942981	+	0.332846i	$0.108009\pi$
$367$			12.7528i			0.665692i	−0.942981	+	0.332846i	$0.891991\pi$
$368$	−4.59274	−	1.38085i	−0.239413	−	0.0719818i
$369$	−6.85244	+	34.4116i	−0.356724	+	1.79140i
$370$	5.08085	+	11.1255i	0.264141	+	0.578387i
$371$	3.18919	+	10.8614i	0.165574	+	0.563894i
$372$	6.81873	+	7.19553i	0.353535	+	0.373071i
$373$	−1.34653	+	2.09524i	−0.0697206	+	0.108487i	−0.874363	−	0.485272i	$-0.838721\pi$
$373$	−1.34653	+	2.09524i	−0.0697206	+	0.108487i	0.804643	+	0.593759i	$0.202357\pi$
$374$	−7.38946	+	6.40300i	−0.382100	+	0.331091i
$375$	18.9549	−	0.844421i	0.978828	−	0.0436057i
$376$	−3.72753	−	1.09450i	−0.192233	−	0.0564447i
$377$	1.68459	+	2.62128i	0.0867609	+	0.135003i
$378$	7.08916	+	3.31703i	0.364627	+	0.170609i
$379$	4.75595	+	2.17197i	0.244297	+	0.111567i	0.533801	−	0.845610i	$-0.320763\pi$
$379$	4.75595	+	2.17197i	0.244297	+	0.111567i	−0.289504	+	0.957177i	$0.593490\pi$
$380$	6.99305	+	3.19362i	0.358736	+	0.163829i
$381$	−30.7408	−	7.55799i	−1.57490	−	0.387207i
$382$	−10.5692	−	16.4460i	−0.540766	−	0.841449i
$383$	8.76661	+	2.57411i	0.447953	+	0.131531i	0.497926	−	0.867220i	$-0.334095\pi$
$383$	8.76661	+	2.57411i	0.447953	+	0.131531i	−0.0499728	+	0.998751i	$0.515913\pi$
$384$	0.0770845	+	1.73033i	0.00393370	+	0.0883008i
$385$	−3.68407	+	3.19227i	−0.187758	+	0.162693i
$386$	1.27215	−	1.97951i	0.0647509	−	0.100754i
$387$	4.36225	+	5.61794i	0.221746	+	0.285576i
$388$	−4.76780	−	16.2376i	−0.242048	−	0.824341i
$389$	10.8067	+	23.6633i	0.547919	+	1.19978i	0.957747	+	0.287613i	$0.0928617\pi$
$389$	10.8067	+	23.6633i	0.547919	+	1.19978i	−0.409827	+	0.912163i	$0.634411\pi$
$390$	2.78312	+	0.274410i	0.140929	+	0.0138953i
$391$	−18.5462	+	5.31571i	−0.937921	+	0.268827i
$392$		−	4.73115i		−	0.238959i
$393$	11.3495	+	33.1219i	0.572506	+	1.67078i
$394$	−8.87641	+	2.60635i	−0.447187	+	0.131306i
$395$	−7.54746	−	6.53991i	−0.379754	−	0.329059i
$396$	−5.24606	−	5.06417i	−0.263624	−	0.254484i
$397$	3.14036	+	3.62417i	0.157610	+	0.181892i	0.829063	−	0.559156i	$-0.188875\pi$
$397$	3.14036	+	3.62417i	0.157610	+	0.181892i	−0.671452	+	0.741048i	$0.734329\pi$
$398$	−1.89121	−	13.1536i	−0.0947977	−	0.659333i
$399$	−5.64147	+	13.9669i	−0.282427	+	0.699218i
$400$	−2.71477	+	1.74468i	−0.135739	+	0.0872339i
$401$	1.11136	−	7.72970i	0.0554988	−	0.386003i	−0.943073	−	0.332585i	$-0.892079\pi$
$401$	1.11136	−	7.72970i	0.0554988	−	0.386003i	0.998572	−	0.0534182i	$-0.0170116\pi$
$402$	−14.7036	−	8.54965i	−0.733351	−	0.426418i
$403$	−2.88309	+	6.31309i	−0.143617	+	0.314477i
$404$	−1.43886	−	0.206877i	−0.0715861	−	0.0102925i
$405$	11.7942	−	2.12277i	0.586057	−	0.105481i
$406$	−1.09044	+	3.71369i	−0.0541176	+	0.184307i
$407$	22.0985	−	3.17729i	1.09538	−	0.157492i
$408$	4.02422	+	5.68822i	0.199228	+	0.281609i
$409$	−3.44698	−	2.21524i	−0.170442	−	0.109537i	0.452638	−	0.891694i	$-0.350483\pi$
$409$	−3.44698	−	2.21524i	−0.170442	−	0.109537i	−0.623081	+	0.782158i	$0.714119\pi$
$410$	−10.1982	+	11.7694i	−0.503655	+	0.581248i
$411$	−0.553825	−	2.92192i	−0.0273182	−	0.144128i
$412$	−11.4095	+	5.21054i	−0.562106	+	0.256705i
$413$	2.74222			0.134936
$414$	−5.17826	−	13.4233i	−0.254498	−	0.659720i
$415$	−9.66222			−0.474300
$416$	−1.10304	+	0.503740i	−0.0540809	+	0.0246979i
$417$	2.98073	+	15.7260i	0.145967	+	0.770107i
$418$	9.18972	−	10.6055i	0.449484	−	0.518732i
$419$	10.6842	+	6.86634i	0.521959	+	0.335443i	0.774946	−	0.632027i	$-0.217777\pi$
$419$	10.6842	+	6.86634i	0.521959	+	0.335443i	−0.252988	+	0.967470i	$0.581413\pi$
$420$	2.00630	+	2.83591i	0.0978976	+	0.138378i
$421$	−13.9088	+	1.99979i	−0.677874	+	0.0974636i	−0.472649	−	0.881251i	$-0.656702\pi$
$421$	−13.9088	+	1.99979i	−0.677874	+	0.0974636i	−0.205226	+	0.978715i	$0.565793\pi$
$422$	−1.89974	+	6.46992i	−0.0924778	+	0.314951i
$423$	−4.26487	−	10.8463i	−0.207365	−	0.527367i
$424$	−7.43870	−	1.06952i	−0.361255	−	0.0519406i
$425$	−5.39291	+	11.8088i	−0.261595	+	0.572813i
$426$	−4.48803	−	2.60963i	−0.217446	−	0.126437i
$427$	−0.399748	+	2.78031i	−0.0193452	+	0.134549i
$428$	−5.55431	+	3.56954i	−0.268478	+	0.172540i
$429$	1.91188	−	4.73333i	0.0923064	−	0.228528i
$430$	0.449274	+	3.12477i	0.0216659	+	0.150690i
$431$	2.00344	+	2.31209i	0.0965023	+	0.111370i	0.801946	−	0.597396i	$-0.203798\pi$
$431$	2.00344	+	2.31209i	0.0965023	+	0.111370i	−0.705444	+	0.708766i	$0.749252\pi$
$432$	−3.95827	+	3.36632i	−0.190442	+	0.161962i
$433$	−21.3204	−	18.4743i	−1.02459	−	0.887816i	−0.0308532	−	0.999524i	$-0.509822\pi$
$433$	−21.3204	−	18.4743i	−1.02459	−	0.887816i	−0.993741	+	0.111708i	$0.964368\pi$
$434$	−8.27172	+	2.42880i	−0.397055	+	0.116586i
$435$	1.92098	+	5.60612i	0.0921040	+	0.268793i
$436$			18.5551i			0.888627i
$437$	25.2612	−	11.3397i	1.20841	−	0.542451i
$438$	22.9287	+	2.26072i	1.09558	+	0.108022i
$439$	3.51792	+	7.70317i	0.167901	+	0.367652i	0.974814	−	0.223018i	$-0.0715908\pi$
$439$	3.51792	+	7.70317i	0.167901	+	0.367652i	−0.806913	+	0.590670i	$0.798864\pi$
$440$	−0.911768	−	3.10520i	−0.0434668	−	0.148034i
$441$	11.2107	−	8.70491i	0.533841	−	0.414520i
$442$	−2.63735	+	4.10380i	−0.125446	+	0.195198i
$443$	−14.7610	+	12.7905i	−0.701318	+	0.607695i	−0.930762	−	0.365627i	$-0.880855\pi$
$443$	−14.7610	+	12.7905i	−0.701318	+	0.607695i	0.229444	+	0.973322i	$0.426309\pi$
$444$	−0.708066	−	15.8941i	−0.0336033	−	0.754302i
$445$	−10.4849	−	3.07863i	−0.497030	−	0.145941i
$446$	14.9871	+	23.3203i	0.709658	+	1.10425i
$447$	−3.76441	−	0.925523i	−0.178050	−	0.0437757i
$448$	−1.37015	−	0.625727i	−0.0647335	−	0.0295628i
$449$	22.2546	+	10.1634i	1.05026	+	0.479638i	0.864330	−	0.502924i	$-0.167743\pi$
$449$	22.2546	+	10.1634i	1.05026	+	0.479638i	0.185931	+	0.982563i	$0.440470\pi$
$450$	−9.12903	−	3.22270i	−0.430347	−	0.151920i
$451$	15.3687	+	23.9141i	0.723683	+	1.12607i
$452$	−13.3024	−	3.90592i	−0.625690	−	0.183719i
$453$	−20.9095	+	0.931495i	−0.982414	+	0.0437655i
$454$	5.72718	−	4.96263i	0.268790	−	0.232908i
$455$	−1.31487	+	2.04598i	−0.0616422	+	0.0959171i
$456$	−6.87869	−	7.25880i	−0.322124	−	0.339925i
$457$	8.24801	+	28.0901i	0.385826	+	1.31400i	0.892182	+	0.451677i	$0.149174\pi$
$457$	8.24801	+	28.0901i	0.385826	+	1.31400i	−0.506356	+	0.862324i	$0.669008\pi$
$458$	8.24868	+	18.0621i	0.385435	+	0.843986i
$459$	−6.07426	+	20.0014i	−0.283522	+	0.933584i
$460$	0.949614	−	6.31474i	0.0442760	−	0.294426i
$461$		−	15.5646i		−	0.724916i	−0.932000	−	0.362458i	$-0.881938\pi$
$461$		−	15.5646i		−	0.724916i	0.932000	−	0.362458i	$-0.118062\pi$
$462$	5.99868	−	2.05549i	0.279084	−	0.0956303i
$463$	23.2934	−	6.83957i	1.08254	−	0.317862i	0.308645	−	0.951177i	$-0.400125\pi$
$463$	23.2934	−	6.83957i	1.08254	−	0.317862i	0.773894	+	0.633316i	$0.218306\pi$
$464$	−1.94196	−	1.68271i	−0.0901530	−	0.0781180i
$465$	−8.19136	+	10.3504i	−0.379865	+	0.479987i
$466$	−10.4221	−	12.0277i	−0.482792	−	0.557172i
$467$	0.00481759	+	0.0335070i	0.000222931	+	0.00155052i	0.989933	−	0.141540i	$-0.0452052\pi$
$467$	0.00481759	+	0.0335070i	0.000222931	+	0.00155052i	−0.989710	+	0.143090i	$0.954296\pi$
$468$	−3.22313	−	1.68685i	−0.148989	−	0.0779748i
$469$	12.4434	−	7.99687i	0.574582	−	0.369261i
$470$	0.736169	−	5.12017i	0.0339569	−	0.236176i
$471$	−8.51422	+	14.6427i	−0.392314	+	0.674700i
$472$	−0.756280	+	1.65602i	−0.0348106	+	0.0762246i
$473$	5.70387	+	0.820093i	0.262264	+	0.0377079i
$474$	5.91713	+	11.5650i	0.271783	+	0.531197i
$475$	5.24925	−	17.8773i	0.240852	−	0.820267i
$476$	−5.99783	+	0.862358i	−0.274910	+	0.0395261i
$477$	−11.1523	−	19.5941i	−0.510628	−	0.897153i
$478$	−0.380474	−	0.244516i	−0.0174025	−	0.0111839i
$479$	−1.37930	+	1.59179i	−0.0630217	+	0.0727309i	−0.786385	−	0.617737i	$-0.788050\pi$
$479$	−1.37930	+	1.59179i	−0.0630217	+	0.0727309i	0.723363	+	0.690468i	$0.242595\pi$
$480$	−2.26592	+	0.429485i	−0.103424	+	0.0196032i
$481$	10.1320	−	4.62715i	0.461981	−	0.210980i
$482$	−0.152532			−0.00694764
$483$	12.4434	+	1.30815i	0.566196	+	0.0595227i
$484$	5.09256			0.231480
$485$	20.4972	−	9.36075i	0.930729	−	0.425050i
$486$	−15.2595	−	3.18553i	−0.692185	−	0.144499i
$487$	21.6359	−	24.9691i	0.980415	−	1.13146i	−0.0108987	−	0.999941i	$-0.503469\pi$
$487$	21.6359	−	24.9691i	0.980415	−	1.13146i	0.991314	−	0.131519i	$-0.0419853\pi$
$488$	−1.56877	−	1.00819i	−0.0710150	−	0.0456386i
$489$	24.0870	−	17.0407i	1.08925	−	0.770607i
$490$	6.23550	−	0.896530i	0.281691	−	0.0405011i
$491$	7.31414	−	24.9097i	0.330082	−	1.12416i	−0.612580	−	0.790409i	$-0.709868\pi$
$491$	7.31414	−	24.9097i	0.330082	−	1.12416i	0.942662	−	0.333749i	$-0.108314\pi$
$492$	18.0342	−	9.22708i	0.813045	−	0.415989i
$493$	−10.2318	−	1.47111i	−0.460818	−	0.0662557i
$494$	2.90844	−	6.36860i	0.130857	−	0.286537i
$495$	5.68031	−	7.87376i	0.255311	−	0.353899i
$496$	0.814520	−	5.66511i	0.0365730	−	0.254371i
$497$	3.79812	−	2.44091i	0.170369	−	0.109490i
$498$	11.6539	+	4.70723i	0.522225	+	0.210936i
$499$	4.02510	+	27.9952i	0.180188	+	1.25324i	0.856316	+	0.516451i	$0.172747\pi$
$499$	4.02510	+	27.9952i	0.180188	+	1.25324i	−0.676128	+	0.736784i	$0.736344\pi$
$500$	−7.17366	−	8.27885i	−0.320816	−	0.370241i
$501$	−31.4610	−	24.8984i	−1.40557	−	1.11238i
$502$	12.5672	+	10.8895i	0.560901	+	0.486023i
$503$	−24.3923	+	7.16221i	−1.08760	+	0.319347i	−0.775914	−	0.630839i	$-0.782711\pi$
$503$	−24.3923	+	7.16221i	−1.08760	+	0.319347i	−0.311683	+	0.950186i	$0.600893\pi$
$504$	−1.03827	−	4.39791i	−0.0462484	−	0.195899i
$505$		−	1.93558i		−	0.0861320i
$506$	−10.5715	−	4.91065i	−0.469961	−	0.218305i
$507$	−1.95948	+	19.8734i	−0.0870234	+	0.882609i
$508$	7.59245	+	16.6251i	0.336860	+	0.737621i
$509$	0.266583	+	0.907898i	0.0118161	+	0.0402419i	0.965190	−	0.261550i	$-0.0842335\pi$
$509$	0.266583	+	0.907898i	0.0118161	+	0.0402419i	−0.953374	+	0.301792i	$0.902415\pi$
$510$	−6.73432	+	6.38167i	−0.298201	+	0.282585i
$511$	−10.8326	+	16.8558i	−0.479205	+	0.745657i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	4.54382	−	29.6549i	0.200615	−	1.30930i
$514$	−4.73632	−	1.39071i	−0.208910	−	0.0613415i
$515$	−9.02937	−	14.0500i	−0.397881	−	0.619116i
$516$	0.980437	−	3.98776i	0.0431614	−	0.175551i
$517$	−8.58905	−	3.92249i	−0.377746	−	0.172511i
$518$	12.5856	+	5.74766i	0.552981	+	0.252538i
$519$	−3.73218	+	15.1800i	−0.163824	+	0.666328i
$520$	−0.872933	−	1.35831i	−0.0382807	−	0.0595659i
$521$	−38.7495	−	11.3779i	−1.69765	−	0.498475i	−0.717470	−	0.696590i	$-0.754700\pi$
$521$	−38.7495	−	11.3779i	−1.69765	−	0.498475i	−0.980179	+	0.198115i	$0.936518\pi$
$522$	0.414227	−	7.69759i	0.0181302	−	0.336914i
$523$	20.4738	−	17.7406i	0.895256	−	0.775743i	−0.0800067	−	0.996794i	$-0.525494\pi$
$523$	20.4738	−	17.7406i	0.895256	−	0.775743i	0.975262	+	0.221051i	$0.0709487\pi$
$524$	10.9288	−	17.0055i	0.477425	−	0.742888i
$525$	6.11111	−	5.79110i	0.266711	−	0.252744i
$526$	−2.51994	−	8.58212i	−0.109875	−	0.374198i
$527$	−9.56464	−	20.9436i	−0.416642	−	0.912319i
$528$	−0.413073	+	4.18947i	−0.0179767	+	0.182323i
$529$	−14.8359	−	17.5755i	−0.645038	−	0.764150i
$530$		−	10.0066i		−	0.434660i
$531$	−5.31550	+	1.25490i	−0.230673	+	0.0544581i
$532$	8.34446	−	2.45015i	0.361778	−	0.106228i
$533$	10.7184	+	9.28756i	0.464266	+	0.402289i
$534$	11.1463	+	8.82124i	0.482347	+	0.381732i
$535$	−5.75705	−	6.64399i	−0.248899	−	0.287245i
$536$	1.39752	+	9.71998i	0.0603638	+	0.419839i
$537$	−35.4586	−	14.3224i	−1.53015	−	0.618056i
$538$	−19.1282	+	12.2930i	−0.824677	+	0.529988i
$539$	1.63650	−	11.3821i	0.0704892	−	0.490263i
$540$	−5.18677	−	4.57896i	−0.223203	−	0.197047i
$541$	3.24840	−	7.11301i	0.139660	−	0.305812i	−0.826859	−	0.562410i	$-0.809874\pi$
$541$	3.24840	−	7.11301i	0.139660	−	0.305812i	0.966518	+	0.256598i	$0.0826016\pi$
$542$	1.49397	+	0.214800i	0.0641715	+	0.00922646i
$543$	4.37671	−	2.23931i	0.187822	−	0.0960980i
$544$	1.13337	−	3.85991i	0.0485929	−	0.165492i
$545$	−24.4550	+	3.51609i	−1.04754	+	0.150613i
$546$	2.58267	−	1.82715i	0.110528	−	0.0781947i
$547$	−2.43890	−	1.56738i	−0.104280	−	0.0670165i	0.487462	−	0.873144i	$-0.337923\pi$
$547$	−2.43890	−	1.56738i	−0.104280	−	0.0670165i	−0.591741	+	0.806128i	$0.701559\pi$
$548$	−1.12440	+	1.29763i	−0.0480320	+	0.0554319i
$549$	−0.497463	−	5.57225i	−0.0212312	−	0.237818i
$550$	−7.13464	+	3.25828i	−0.304222	+	0.138934i
$551$	14.8359			0.632032
$552$	−4.22177	+	7.15379i	−0.179690	+	0.304485i
$553$	−11.2974			−0.480414
$554$	−2.60339	+	1.18893i	−0.110608	+	0.0505128i
$555$	20.8137	−	3.94506i	0.883494	−	0.167459i
$556$	6.05162	−	6.98395i	0.256646	−	0.296185i
$557$	34.8715	+	22.4106i	1.47755	+	0.949566i	0.997376	+	0.0723944i	$0.0230640\pi$
$557$	34.8715	+	22.4106i	1.47755	+	0.949566i	0.480177	+	0.877171i	$0.340572\pi$
$558$	14.9224	−	8.49328i	0.631714	−	0.359549i
$559$	2.84574	−	0.409155i	0.120362	−	0.0173054i
$560$	0.565051	−	1.92439i	0.0238777	−	0.0813201i
$561$	7.71384	+	15.0766i	0.325679	+	0.636535i
$562$	15.9154	+	2.28829i	0.671351	+	0.0965257i
$563$	1.33950	−	2.93310i	0.0564532	−	0.123615i	−0.879303	−	0.476263i	$-0.841991\pi$
$563$	1.33950	−	2.93310i	0.0564532	−	0.123615i	0.935756	+	0.352647i	$0.114718\pi$
$564$	−3.38236	+	5.81696i	−0.142423	+	0.244938i
$565$	2.62715	−	18.2722i	0.110525	−	0.768718i
$566$	1.81166	−	1.16428i	0.0761496	−	0.0489384i
$567$	8.51069	−	10.5520i	0.357415	−	0.443143i
$568$	0.426569	+	2.96685i	0.0178985	+	0.124486i
$569$	−22.2924	−	25.7268i	−0.934548	−	1.07853i	−0.996758	−	0.0804623i	$-0.974360\pi$
$569$	−22.2924	−	25.7268i	−0.934548	−	1.07853i	0.0622101	−	0.998063i	$-0.480185\pi$
$570$	8.26338	−	10.4414i	0.346115	−	0.437342i
$571$	−4.48979	−	3.89042i	−0.187892	−	0.162809i	0.555836	−	0.831292i	$-0.312398\pi$
$571$	−4.48979	−	3.89042i	−0.187892	−	0.162809i	−0.743727	+	0.668483i	$0.766944\pi$
$572$	−2.82791	+	0.830350i	−0.118241	+	0.0347187i
$573$	−32.0321	+	10.9761i	−1.33816	+	0.458531i
$574$			17.6170i			0.735317i
$575$	−15.4761	−	0.100015i	−0.645398	−	0.00417091i
$576$	2.94223	+	0.585891i	0.122593	+	0.0244121i
$577$	−7.37948	−	16.1588i	−0.307212	−	0.672700i	0.691556	−	0.722323i	$-0.256925\pi$
$577$	−7.37948	−	16.1588i	−0.307212	−	0.672700i	−0.998768	+	0.0496227i	$0.984198\pi$
$578$	0.230063	+	0.783523i	0.00956937	+	0.0325903i
$579$	−2.80339	−	2.95830i	−0.116505	−	0.122943i
$580$	1.84977	−	2.87830i	0.0768075	−	0.119515i
$581$	−8.26057	+	7.15782i	−0.342706	+	0.296957i
$582$	−29.2827	+	1.30451i	−1.21381	+	0.0540738i
$583$	−17.5259	−	5.14608i	−0.725851	−	0.213129i
$584$	−7.19166	−	11.1904i	−0.297593	−	0.463063i
$585$	1.61245	−	4.56762i	0.0666666	−	0.188848i
$586$	26.2672	+	11.9958i	1.08509	+	0.495543i
$587$	21.6172	+	9.87223i	0.892236	+	0.407471i	0.808142	−	0.588987i	$-0.200473\pi$
$587$	21.6172	+	9.87223i	0.892236	+	0.407471i	0.0840938	+	0.996458i	$0.473200\pi$
$588$	−7.95761	−	1.95647i	−0.328166	−	0.0806835i
$589$	17.8655	+	27.7992i	0.736133	+	1.14545i
$590$	−2.32589	−	0.682944i	−0.0957555	−	0.0281164i
$591$	0.713120	+	16.0076i	0.0293338	+	0.658463i
$592$	−6.94200	+	6.01527i	−0.285314	+	0.247226i
$593$	19.8367	−	30.8665i	0.814595	−	1.26754i	−0.145917	−	0.989297i	$-0.546613\pi$
$593$	19.8367	−	30.8665i	0.814595	−	1.26754i	0.960512	−	0.278238i	$-0.0897505\pi$
$594$	−10.6871	+	6.72948i	−0.438499	+	0.276114i
$595$	−2.27312	−	7.74153i	−0.0931888	−	0.317372i
$596$	0.929742	+	2.03585i	0.0380837	+	0.0833917i
$597$	−22.9060	−	2.25848i	−0.937480	−	0.0924335i
$598$	−5.75086	−	0.864817i	−0.235170	−	0.0353650i
$599$			3.46791i			0.141695i	0.997487	+	0.0708474i	$0.0225703\pi$
$599$			3.46791i			0.141695i	−0.997487	+	0.0708474i	$0.977430\pi$
$600$	1.81184	+	5.28762i	0.0739681	+	0.215866i
$601$	9.02985	−	2.65140i	0.368335	−	0.108153i	−0.0923264	−	0.995729i	$-0.529430\pi$
$601$	9.02985	−	2.65140i	0.368335	−	0.108153i	0.460662	+	0.887576i	$0.347612\pi$
$602$	2.69894	+	2.33865i	0.110001	+	0.0953162i
$603$	−20.4606	+	21.1954i	−0.833219	+	0.863144i
$604$	7.91339	+	9.13254i	0.321991	+	0.371598i
$605$	0.965014	+	6.71182i	0.0392334	+	0.272874i
$606$	−0.942972	+	2.33456i	−0.0383056	+	0.0948351i
$607$	29.7961	−	19.1488i	1.20939	−	0.777226i	0.228831	−	0.973466i	$-0.426510\pi$
$607$	29.7961	−	19.1488i	1.20939	−	0.777226i	0.980556	+	0.196240i	$0.0628732\pi$
$608$	−0.821682	+	5.71492i	−0.0333236	+	0.231771i
$609$	5.79536	+	3.36980i	0.234840	+	0.136551i
$610$	1.03149	−	2.25864i	0.0417636	−	0.0914496i
$611$	−4.66296	−	0.670432i	−0.188643	−	0.0271228i
$612$	11.2315	−	4.41633i	0.454007	−	0.178519i
$613$	−3.06093	+	10.4246i	−0.123630	+	0.421045i	−0.997928	−	0.0643452i	$-0.979504\pi$
$613$	−3.06093	+	10.4246i	−0.123630	+	0.421045i	0.874298	+	0.485390i	$0.161322\pi$
$614$	9.01695	−	1.29644i	0.363894	−	0.0523201i
$615$	15.5784	+	22.0200i	0.628181	+	0.887932i
$616$	−3.07985	−	1.97930i	−0.124091	−	0.0797482i
$617$	7.03315	−	8.11669i	0.283144	−	0.326765i	−0.596306	−	0.802757i	$-0.703365\pi$
$617$	7.03315	−	8.11669i	0.283144	−	0.326765i	0.879450	+	0.475992i	$0.157911\pi$
$618$	4.04577	+	21.3451i	0.162745	+	0.858624i
$619$	−25.0529	+	11.4413i	−1.00696	+	0.459864i	−0.849459	−	0.527655i	$-0.823071\pi$
$619$	−25.0529	+	11.4413i	−1.00696	+	0.459864i	−0.157502	+	0.987519i	$0.550344\pi$
$620$	7.62078			0.306058
$621$	−24.7189	+	3.15869i	−0.991934	+	0.126754i
$622$	11.7597			0.471522
$623$	−11.2445	+	5.13520i	−0.450503	+	0.205738i
$624$	0.391133	+	2.06358i	0.0156579	+	0.0826092i
$625$	−1.01449	+	1.17078i	−0.0405795	+	0.0468312i
$626$	3.58887	+	2.30643i	0.143440	+	0.0921833i
$627$	−14.0378	−	19.8424i	−0.560617	−	0.792431i
$628$	9.67970	−	1.39173i	0.386262	−	0.0555361i
$629$	−10.4107	+	35.4555i	−0.415100	+	1.41370i
$630$	5.59955	−	2.20179i	0.223091	−	0.0877215i
$631$	45.4113	+	6.52916i	1.80779	+	0.259922i	0.961895	−	0.273421i	$-0.0881551\pi$
$631$	45.4113	+	6.52916i	1.80779	+	0.259922i	0.845900	+	0.533342i	$0.179064\pi$
$632$	3.11571	−	6.82246i	0.123936	−	0.271383i
$633$	10.0966	+	5.87079i	0.401302	+	0.233343i
$634$	0.754752	−	5.24941i	0.0299750	−	0.208481i
$635$	−20.4727	+	13.1570i	−0.812432	+	0.522119i
$636$	−4.87502	+	12.0693i	−0.193307	+	0.478580i
$637$	−0.816473	−	5.67869i	−0.0323498	−	0.224998i
$638$	−4.08988	−	4.71997i	−0.161920	−	0.186865i
$639$	−6.24523	+	6.46953i	−0.247057	+	0.255931i
$640$	1.00630	+	0.871960i	0.0397773	+	0.0344672i
$641$	−36.5656	+	10.7366i	−1.44425	+	0.424071i	−0.907637	−	0.419755i	$-0.862116\pi$
$641$	−36.5656	+	10.7366i	−1.44425	+	0.424071i	−0.536616	+	0.843826i	$0.680298\pi$
$642$	3.70695	+	10.8182i	0.146302	+	0.426962i
$643$			11.1469i			0.439592i	0.975546	+	0.219796i	$0.0705392\pi$
$643$			11.1469i			0.439592i	−0.975546	+	0.219796i	$0.929461\pi$
$644$	−3.86614	−	6.10217i	−0.152347	−	0.240459i
$645$	5.44153	+	0.536523i	0.214260	+	0.0211256i
$646$	9.64874	+	21.1278i	0.379625	+	0.831262i
$647$	−10.3710	−	35.3203i	−0.407726	−	1.38859i	−0.866120	−	0.499837i	$-0.833393\pi$
$647$	−10.3710	−	35.3203i	−0.407726	−	1.38859i	0.458394	−	0.888749i	$-0.348425\pi$
$648$	4.02516	+	8.04973i	0.158123	+	0.316223i
$649$	−2.39226	+	3.72243i	−0.0939045	+	0.146118i
$650$	−2.95739	+	2.56260i	−0.115998	+	0.100513i
$651$	0.664540	+	14.9171i	0.0260454	+	0.584647i
$652$	−16.3449	−	4.79930i	−0.640117	−	0.187955i
$653$	20.3058	+	31.5964i	0.794627	+	1.23646i	0.967837	+	0.251579i	$0.0809499\pi$
$653$	20.3058	+	31.5964i	0.794627	+	1.23646i	−0.173209	+	0.984885i	$0.555414\pi$
$654$	31.2089	+	7.67307i	1.22037	+	0.300041i
$655$	24.4836	+	11.1813i	0.956654	+	0.436889i
$656$	−10.6388	−	4.85859i	−0.415377	−	0.189696i
$657$	13.2842	−	37.6303i	0.518264	−	1.46810i
$658$	−3.16367	−	4.92277i	−0.123333	−	0.191909i
$659$	−1.35956	−	0.399202i	−0.0529609	−	0.0155507i	0.255145	−	0.966903i	$-0.417877\pi$
$659$	−1.35956	−	0.399202i	−0.0529609	−	0.0155507i	−0.308106	+	0.951352i	$0.599695\pi$
$660$	−5.59986	+	0.249468i	−0.217974	+	0.00971052i
$661$	9.66401	−	8.37391i	0.375886	−	0.325707i	−0.446345	−	0.894861i	$-0.647274\pi$
$661$	9.66401	−	8.37391i	0.375886	−	0.325707i	0.822231	+	0.569154i	$0.192729\pi$
$662$	−6.67562	+	10.3875i	−0.259455	+	0.403720i
$663$	5.81181	+	6.13297i	0.225712	+	0.238185i
$664$	−2.04440	−	6.96260i	−0.0793382	−	0.270201i
$665$	4.81045	+	10.5334i	0.186541	+	0.408469i
$666$	−27.0261	−	5.38175i	−1.04724	−	0.208539i
$667$	−3.39538	−	11.8463i	−0.131470	−	0.458689i
$668$			23.1641i			0.896245i
$669$	45.4215	−	15.5640i	1.75610	−	0.601740i
$670$	−12.5458	+	3.68378i	−0.484686	+	0.142317i
$671$	−3.42540	−	2.96812i	−0.132236	−	0.114583i
$672$	−1.61905	+	2.04578i	−0.0624561	+	0.0789178i
$673$	10.6998	+	12.3482i	0.412446	+	0.475988i	0.923521	−	0.383548i	$-0.125298\pi$
$673$	10.6998	+	12.3482i	0.412446	+	0.475988i	−0.511075	+	0.859536i	$0.670753\pi$
$674$	2.70866	+	18.8392i	0.104334	+	0.725658i
$675$	−9.19558	+	14.0220i	−0.353938	+	0.539707i
$676$	9.69928	−	6.23335i	0.373049	−	0.239744i
$677$	−1.69449	+	11.7854i	−0.0651245	+	0.452951i	0.931002	+	0.365015i	$0.118936\pi$
$677$	−1.69449	+	11.7854i	−0.0651245	+	0.452951i	−0.996126	+	0.0879359i	$0.971973\pi$
$678$	−12.0705	+	20.7588i	−0.463566	+	0.797238i
$679$	10.5893	−	23.1873i	0.406379	−	0.889845i
$680$	5.30199	+	0.762312i	0.203322	+	0.0292333i
$681$	−5.97859	−	11.6851i	−0.229100	−	0.447774i
$682$	3.91912	−	13.3473i	0.150071	−	0.511094i
$683$	33.7209	−	4.84834i	1.29030	−	0.185517i	0.537215	−	0.843445i	$-0.319476\pi$
$683$	33.7209	−	4.84834i	1.29030	−	0.185517i	0.753080	+	0.657929i	$0.228567\pi$
$684$	−15.0536	+	8.56796i	−0.575587	+	0.327604i
$685$	−1.92330	−	1.23603i	−0.0734855	−	0.0472263i
$686$	11.5716	−	13.3543i	0.441805	−	0.509870i
$687$	33.7908	−	6.40475i	1.28920	−	0.244356i
$688$	−2.15665	+	0.984908i	−0.0822214	+	0.0375493i
$689$	−9.11307			−0.347180
$690$	−10.2285	−	4.20855i	−0.389391	−	0.160217i
$691$	9.58351			0.364574			0.182287	−	0.983245i	$-0.441650\pi$
$691$	9.58351			0.364574			0.182287	+	0.983245i	$0.441650\pi$
$692$	8.20959	−	3.74919i	0.312082	−	0.142523i
$693$	−0.976629	−	10.9396i	−0.0370991	−	0.415560i
$694$	11.1669	−	12.8873i	0.423890	−	0.489195i
$695$	10.3514	+	6.65242i	0.392650	+	0.252341i
$696$	−3.63332	+	2.57044i	−0.137720	+	0.0974324i
$697$	−46.5715	+	6.69597i	−1.76402	+	0.253628i
$698$	7.39915	−	25.1992i	0.280062	−	0.953804i
$699$	−24.5399	+	12.5557i	−0.928186	+	0.474900i
$700$	−4.81134	−	0.691766i	−0.181852	−	0.0261463i
$701$	−20.0434	+	43.8890i	−0.757030	+	1.65767i	−0.00372652	+	0.999993i	$0.501186\pi$
$701$	−20.0434	+	43.8890i	−0.757030	+	1.65767i	−0.753304	+	0.657672i	$0.771541\pi$
$702$	−4.17008	+	4.72361i	−0.157389	+	0.178281i
$703$	7.54762	−	52.4949i	0.284664	−	1.97988i
$704$	2.04469	−	1.31404i	0.0770620	−	0.0495247i
$705$	−8.30750	−	3.35555i	−0.312878	−	0.126377i
$706$	1.57132	+	10.9288i	0.0591373	+	0.411309i
$707$	−1.43388	−	1.65479i	−0.0539268	−	0.0622348i
$708$	2.47262	+	1.95685i	0.0929268	+	0.0735428i
$709$	−21.8638	−	18.9451i	−0.821111	−	0.711497i	0.139250	−	0.990257i	$-0.455531\pi$
$709$	−21.8638	−	18.9451i	−0.821111	−	0.711497i	−0.960361	+	0.278760i	$0.910076\pi$
$710$	−3.82938	+	1.12441i	−0.143714	+	0.0421983i
$711$	21.8987	−	5.16993i	0.821267	−	0.193888i
$712$		−	8.20678i		−	0.307562i
$713$	18.1085	−	20.6275i	0.678169	−	0.772504i
$714$	−1.02983	+	10.4447i	−0.0385404	+	0.390884i
$715$	−1.63025	−	3.56975i	−0.0609679	−	0.133501i
$716$	6.22036	+	21.1846i	0.232466	+	0.791706i
$717$	−0.568603	+	0.538828i	−0.0212349	+	0.0201229i
$718$	−11.9296	+	18.5628i	−0.445207	+	0.692756i
$719$	−0.924609	+	0.801178i	−0.0344821	+	0.0298789i	−0.671931	−	0.740613i	$-0.734535\pi$
$719$	−0.924609	+	0.801178i	−0.0344821	+	0.0298789i	0.637449	+	0.770492i	$0.279990\pi$
$720$	−0.214647	+	3.98879i	−0.00799942	+	0.148653i
$721$	−18.1278	−	5.32281i	−0.675115	−	0.198232i
$722$	−7.75037	−	12.0598i	−0.288439	−	0.448820i
$723$	−0.0630764	+	0.256553i	−0.00234584	+	0.00954130i
$724$	−2.58193	−	1.17913i	−0.0959566	−	0.0438219i
$725$	−7.54282	−	3.44469i	−0.280133	−	0.127933i
$726$	2.10592	−	8.56548i	0.0781581	−	0.317895i
$727$	19.6959	+	30.6474i	0.730480	+	1.13665i	0.985494	+	0.169711i	$0.0542835\pi$
$727$	19.6959	+	30.6474i	0.730480	+	1.13665i	−0.255014	+	0.966937i	$0.582080\pi$
$728$	−1.75254	−	0.514594i	−0.0649536	−	0.0190721i
$729$	−11.6682	+	24.3486i	−0.432155	+	0.901799i
$730$	13.3858	−	11.5989i	0.495432	−	0.429294i
$731$	−5.15652	+	8.02371i	−0.190721	+	0.296768i
$732$	−2.34447	+	2.22170i	−0.0866541	+	0.0821164i
$733$	5.61590	+	19.1260i	0.207428	+	0.706435i	0.995826	+	0.0912699i	$0.0290926\pi$
$733$	5.61590	+	19.1260i	0.207428	+	0.706435i	−0.788398	+	0.615165i	$0.789089\pi$
$734$	−5.29771	−	11.6004i	−0.195542	−	0.428178i
$735$	1.07064	−	10.8586i	0.0394910	−	0.400526i
$736$	4.75133	−	0.651827i	0.175136	−	0.0240266i
$737$			23.8676i			0.879174i
$738$	−8.06190	−	34.1485i	−0.296763	−	1.25702i
$739$	−3.64871	+	1.07136i	−0.134220	+	0.0394105i	−0.348153	−	0.937438i	$-0.613191\pi$
$739$	−3.64871	+	1.07136i	−0.134220	+	0.0394105i	0.213933	+	0.976848i	$0.431373\pi$
$740$	−9.24340	−	8.00945i	−0.339794	−	0.294433i
$741$	−9.50901	−	7.52549i	−0.349322	−	0.276456i
$742$	−7.41296	−	8.55501i	−0.272138	−	0.314064i
$743$	1.64081	+	11.4121i	0.0601953	+	0.418668i	0.997530	+	0.0702381i	$0.0223759\pi$
$743$	1.64081	+	11.4121i	0.0601953	+	0.418668i	−0.937335	+	0.348430i	$0.886715\pi$
$744$	−9.19167	−	3.71268i	−0.336983	−	0.136114i
$745$	−2.50700	+	1.61115i	−0.0918495	+	0.0590281i
$746$	0.354451	−	2.46526i	0.0129774	−	0.0902597i
$747$	12.7366	−	17.6549i	0.466009	−	0.645958i
$748$	4.06178	−	8.89407i	0.148514	−	0.325199i
$749$	−9.84380	−	1.41533i	−0.359685	−	0.0517149i
$750$	−16.8912	+	8.64227i	−0.616780	+	0.315571i
$751$	−9.22877	+	31.4303i	−0.336763	+	1.14691i	0.600889	+	0.799332i	$0.294813\pi$
$751$	−9.22877	+	31.4303i	−0.336763	+	1.14691i	−0.937652	+	0.347576i	$0.887005\pi$
$752$	3.84536	−	0.552879i	0.140226	−	0.0201614i
$753$	23.5126	−	16.6344i	0.856849	−	0.606190i
$754$	−2.62128	−	1.68459i	−0.0954613	−	0.0613492i
$755$	−10.5368	+	12.1602i	−0.383475	+	0.442553i
$756$	−7.82647	−	0.0723286i	−0.284646	−	0.00263057i
$757$	22.4650	−	10.2594i	0.816505	−	0.372885i	0.0370266	−	0.999314i	$-0.488211\pi$
$757$	22.4650	−	10.2594i	0.816505	−	0.372885i	0.779479	+	0.626429i	$0.215484\pi$
$758$	−5.22844			−0.189905
$759$	−12.6312	+	15.7502i	−0.458482	+	0.571694i
$760$	−7.68778			−0.278865
$761$	−29.5520	+	13.4959i	−1.07126	+	0.489228i	−0.871388	−	0.490594i	$-0.836780\pi$
$761$	−29.5520	+	13.4959i	−1.07126	+	0.489228i	−0.199871	+	0.979822i	$0.564052\pi$
$762$	31.1025	−	5.89521i	1.12673	−	0.213561i
$763$	−18.3027	+	21.1224i	−0.662601	+	0.764683i
$764$	16.4460	+	10.5692i	0.594994	+	0.382380i
$765$	7.94888	+	13.9659i	0.287393	+	0.504937i
$766$	−9.04371	+	1.30029i	−0.326763	+	0.0469814i
$767$	−0.621959	+	2.11820i	−0.0224577	+	0.0764837i
$768$	−0.788926	−	1.54195i	−0.0284679	−	0.0556402i
$769$	36.9236	+	5.30882i	1.33150	+	0.191441i	0.771064	−	0.636757i	$-0.219725\pi$
$769$	36.9236	+	5.30882i	1.33150	+	0.191441i	0.560436	+	0.828198i	$0.310634\pi$
$770$	2.02503	−	4.43420i	0.0729771	−	0.159798i
$771$	−4.29772	+	7.39120i	−0.154779	+	0.266188i
$772$	−0.334874	+	2.32910i	−0.0120524	+	0.0838261i
$773$	−7.59804	+	4.88296i	−0.273282	+	0.175628i	−0.670103	−	0.742268i	$-0.733750\pi$
$773$	−7.59804	+	4.88296i	−0.273282	+	0.175628i	0.396820	+	0.917896i	$0.370114\pi$
$774$	−6.30182	−	3.29812i	−0.226514	−	0.118548i
$775$	−2.62850	−	18.2816i	−0.0944186	−	0.656695i
$776$	11.0823	+	12.7897i	0.397831	+	0.459122i
$777$	14.8719	−	18.7917i	0.533526	−	0.674149i
$778$	−19.6602	−	17.0356i	−0.704851	−	0.610757i
$779$	64.7923	−	19.0247i	2.32143	−	0.681632i
$780$	−2.64561	+	0.906538i	−0.0947280	+	0.0324593i
$781$			7.28516i			0.260684i
$782$	14.6620	−	12.5397i	0.524312	−	0.448419i
$783$	−12.7758	−	3.87990i	−0.456568	−	0.138656i
$784$	1.96539	+	4.30361i	0.0701926	+	0.153700i
$785$	3.66851	+	12.4938i	0.130935	+	0.445923i
$786$	−24.0832	−	25.4140i	−0.859020	−	0.906489i
$787$	−28.2626	+	43.9774i	−1.00745	+	1.56763i	−0.198202	+	0.980161i	$0.563510\pi$
$787$	−28.2626	+	43.9774i	−1.00745	+	1.56763i	−0.809250	+	0.587464i	$0.800126\pi$
$788$	6.99155	−	6.05821i	0.249064	−	0.215815i
$789$	−15.4769	+	0.689477i	−0.550991	+	0.0245460i
$790$	9.58219	+	2.81358i	0.340919	+	0.100103i
$791$	−11.2901	−	17.5678i	−0.401430	−	0.624637i
$792$	6.87572	+	2.42724i	0.244318	+	0.0862484i
$793$	−2.05695	−	0.939377i	−0.0730444	−	0.0333583i
$794$	−4.36210	−	1.99211i	−0.154805	−	0.0706972i
$795$	−16.8308	−	4.13803i	−0.596925	−	0.146761i
$796$	7.18452	+	11.1793i	0.254649	+	0.396241i
$797$	−4.32636	−	1.27033i	−0.153247	−	0.0449975i	0.204209	−	0.978927i	$-0.434538\pi$
$797$	−4.32636	−	1.27033i	−0.153247	−	0.0449975i	−0.357456	+	0.933930i	$0.616356\pi$
$798$	−0.670384	−	15.0483i	−0.0237313	−	0.532703i
$799$	11.8112	−	10.2344i	0.417849	−	0.362068i
$800$	1.74468	−	2.71477i	0.0616837	−	0.0959817i
$801$	19.4463	−	15.0998i	0.687101	−	0.533524i
$802$	2.20010	+	7.49286i	0.0776883	+	0.264582i
$803$	−13.4308	−	29.4094i	−0.473963	−	1.03783i
$804$	16.9266	+	1.66892i	0.596953	+	0.0588583i
$805$	7.30985	−	6.25177i	0.257638	−	0.220346i
$806$		−	6.94027i		−	0.244461i
$807$	12.7662	+	37.2565i	0.449392	+	1.31149i
$808$	1.39478	−	0.409543i	0.0490680	−	0.0144077i
$809$	−10.3532	−	8.97113i	−0.364000	−	0.315408i	0.453588	−	0.891212i	$-0.350144\pi$
$809$	−10.3532	−	8.97113i	−0.364000	−	0.315408i	−0.817588	+	0.575804i	$0.804689\pi$
$810$	−9.84652	+	6.83041i	−0.345972	+	0.239996i
$811$	2.09191	+	2.41419i	0.0734568	+	0.0847737i	0.791288	−	0.611443i	$-0.209411\pi$
$811$	2.09191	+	2.41419i	0.0734568	+	0.0847737i	−0.717832	+	0.696217i	$0.754865\pi$
$812$	−0.550826	−	3.83108i	−0.0193302	−	0.134444i
$813$	0.979086	−	2.42397i	0.0343381	−	0.0850124i
$814$	−18.7816	+	12.0702i	−0.658295	+	0.423061i
$815$	3.22804	−	22.4515i	0.113073	−	0.786442i
$816$	−6.02353	−	3.50247i	−0.210866	−	0.122611i
$817$	5.68655	−	12.4518i	0.198947	−	0.435634i
$818$	4.05573	+	0.583126i	0.141805	+	0.0203885i
$819$	−2.00518	−	5.09953i	−0.0700667	−	0.178192i
$820$	4.38746	−	14.9423i	0.153217	−	0.521808i
$821$	7.79590	−	1.12088i	0.272079	−	0.0391190i	−0.00492485	−	0.999988i	$-0.501568\pi$
$821$	7.79590	−	1.12088i	0.272079	−	0.0391190i	0.277004	+	0.960869i	$0.410659\pi$
$822$	1.71759	+	2.42781i	0.0599077	+	0.0846795i
$823$	−5.83281	−	3.74852i	−0.203319	−	0.130665i	0.435019	−	0.900421i	$-0.356742\pi$
$823$	−5.83281	−	3.74852i	−0.203319	−	0.130665i	−0.638338	+	0.769756i	$0.720378\pi$
$824$	8.21391	−	9.47936i	0.286145	−	0.330229i
$825$	2.52992	+	13.3476i	0.0880804	+	0.464703i
$826$	−2.49442	+	1.13916i	−0.0867918	+	0.0396365i
$827$	4.30041			0.149540			0.0747700	−	0.997201i	$-0.476178\pi$
$827$	4.30041			0.149540			0.0747700	+	0.997201i	$0.476178\pi$
$828$	10.2866	+	10.0592i	0.357483	+	0.349580i
$829$	26.9212			0.935010			0.467505	−	0.883990i	$-0.345153\pi$
$829$	26.9212			0.935010			0.467505	+	0.883990i	$0.345153\pi$
$830$	8.78907	−	4.01383i	0.305073	−	0.139322i
$831$	0.923154	+	4.87046i	0.0320239	+	0.168955i
$832$	0.794097	−	0.916437i	0.0275304	−	0.0317717i
$833$	16.0114	+	10.2899i	0.554761	+	0.356523i
$834$	−9.24420	−	13.0667i	−0.320101	−	0.452462i
$835$	−30.5295	+	4.38948i	−1.05652	+	0.151904i
$836$	−3.95358	+	13.4647i	−0.136737	+	0.465685i
$837$	−8.11453	−	28.6110i	−0.280479	−	0.988942i
$838$	−12.5711	−	1.80745i	−0.434261	−	0.0624374i
$839$	13.7971	−	30.2114i	0.476329	−	1.04301i	−0.507128	−	0.861871i	$-0.669293\pi$
$839$	13.7971	−	30.2114i	0.476329	−	1.04301i	0.983457	−	0.181144i	$-0.0579800\pi$
$840$	−3.00308	−	1.74618i	−0.103616	−	0.0602490i
$841$	−3.18747	+	22.1693i	−0.109913	+	0.764459i
$842$	11.8212	−	7.59700i	0.407384	−	0.261810i
$843$	10.4303	−	25.8228i	0.359239	−	0.889385i
$844$	−0.959637	−	6.67442i	−0.0330321	−	0.229743i
$845$	10.0533	+	11.6021i	0.345844	+	0.399126i
$846$	8.38519	+	8.09448i	0.288289	+	0.278294i
$847$	5.79718	+	5.02328i	0.199193	+	0.172602i
$848$	7.21077	−	2.11727i	0.247619	−	0.0727075i
$849$	−1.20910	−	3.52860i	−0.0414963	−	0.121101i
$850$		−	12.9820i		−	0.445279i
$851$	−43.6437	+	5.98740i	−1.49609	+	0.205246i
$852$	5.16653	+	0.509409i	0.177003	+	0.0174521i
$853$	6.72238	+	14.7200i	0.230170	+	0.504002i	0.989113	−	0.147155i	$-0.0470115\pi$
$853$	6.72238	+	14.7200i	0.230170	+	0.504002i	−0.758944	+	0.651156i	$0.774284\pi$
$854$	−0.791358	−	2.69512i	−0.0270797	−	0.0922250i
$855$	−14.1449	−	18.2165i	−0.483744	−	0.622991i
$856$	3.56954	−	5.55431i	0.122004	−	0.189842i
$857$	18.2978	−	15.8551i	0.625040	−	0.541600i	−0.283726	−	0.958905i	$-0.591571\pi$
$857$	18.2978	−	15.8551i	0.625040	−	0.541600i	0.908767	+	0.417305i	$0.137025\pi$
$858$	0.227191	+	5.09982i	0.00775618	+	0.174105i
$859$	−16.4629	−	4.83395i	−0.561708	−	0.164932i	−0.0114610	−	0.999934i	$-0.503648\pi$
$859$	−16.4629	−	4.83395i	−0.561708	−	0.164932i	−0.550247	+	0.835002i	$0.685466\pi$
$860$	−1.70675	−	2.65575i	−0.0581997	−	0.0905605i
$861$	29.6310	+	7.28513i	1.00982	+	0.248277i
$862$	−2.78287	−	1.27090i	−0.0947850	−	0.0432869i
$863$	−37.9661	−	17.3386i	−1.29238	−	0.590211i	−0.353818	−	0.935314i	$-0.615117\pi$
$863$	−37.9661	−	17.3386i	−1.29238	−	0.590211i	−0.938565	+	0.345103i	$0.887844\pi$
$864$	2.20215	−	4.70644i	0.0749185	−	0.160116i
$865$	6.49699	+	10.1095i	0.220904	+	0.343734i
$866$	27.0682	+	7.94795i	0.919816	+	0.270082i
$867$	1.41299	−	0.0629473i	0.0479878	−	0.00213780i
$868$	6.51527	−	5.64551i	0.221143	−	0.191621i
$869$	9.85562	−	15.3356i	0.334329	−	0.520226i
$870$	−4.07625	−	4.30150i	−0.138198	−	0.145835i
$871$	3.35483	+	11.4255i	0.113674	+	0.387138i
$872$	−7.70806	−	16.8783i	−0.261028	−	0.571571i
$873$	−9.91512	+	49.7918i	−0.335576	+	1.68520i
$874$	−18.2677	+	20.8088i	−0.617915	+	0.703869i
$875$		−	16.5004i		−	0.557816i
$876$	−21.7958	+	7.46851i	−0.736413	+	0.252338i
$877$	−42.9657	+	12.6159i	−1.45085	+	0.426007i	−0.909822	−	0.414999i	$-0.863782\pi$
$877$	−42.9657	+	12.6159i	−1.45085	+	0.426007i	−0.541025	+	0.841006i	$0.681964\pi$
$878$	−6.40002	−	5.54565i	−0.215990	−	0.187157i
$879$	31.0388	−	39.2198i	1.04691	−	1.32285i
$880$	2.11932	+	2.44582i	0.0714422	+	0.0824487i
$881$	−1.12119	−	7.79802i	−0.0377737	−	0.262722i	0.962179	−	0.272417i	$-0.0878230\pi$
$881$	−1.12119	−	7.79802i	−0.0377737	−	0.262722i	−0.999953	+	0.00969504i	$0.996914\pi$
$882$	−6.58142	+	12.5753i	−0.221608	+	0.423434i
$883$	−16.5605	+	10.6428i	−0.557305	+	0.358158i	−0.788773	−	0.614684i	$-0.789283\pi$
$883$	−16.5605	+	10.6428i	−0.557305	+	0.358158i	0.231468	+	0.972842i	$0.425647\pi$
$884$	0.694240	−	4.82855i	0.0233498	−	0.162402i
$885$	−2.11051	+	3.62964i	−0.0709440	+	0.122009i
$886$	8.11374	−	17.7666i	0.272586	−	0.596881i
$887$	41.5040	+	5.96737i	1.39357	+	0.200365i	0.797863	−	0.602839i	$-0.205964\pi$
$887$	41.5040	+	5.96737i	1.39357	+	0.200365i	0.595705	+	0.803204i	$0.296873\pi$
$888$	7.24674	+	14.1637i	0.243185	+	0.475301i
$889$	−7.75603	+	26.4146i	−0.260129	+	0.885917i
$890$	10.8163	−	1.55514i	0.362562	−	0.0521285i
$891$	6.89927	+	20.7582i	0.231134	+	0.695426i
$892$	−23.3203	−	14.9871i	−0.780822	−	0.501804i
$893$	−14.6887	+	16.9516i	−0.491538	+	0.567265i
$894$	3.80870	−	0.721906i	0.127382	−	0.0241441i
$895$	−26.7419	+	12.2126i	−0.893882	+	0.408222i
$896$	1.50627			0.0503209
$897$	−3.83274	+	9.31509i	−0.127971	+	0.311022i
$898$	−24.4655			−0.816426
$899$	13.3776	−	6.10935i	0.446169	−	0.203758i
$900$	9.64282	−	0.860862i	0.321427	−	0.0286954i
$901$	19.7981	−	22.8482i	0.659571	−	0.761185i
$902$	−23.9141	−	15.3687i	−0.796254	−	0.511721i
$903$	5.04961	−	3.57242i	0.168040	−	0.118883i
$904$	13.7228	−	1.97304i	0.456414	−	0.0656225i
$905$	1.06479	−	3.62633i	0.0353947	−	0.120543i
$906$	18.6330	−	9.53344i	0.619040	−	0.316727i
$907$	0.903134	+	0.129851i	0.0299881	+	0.00431164i	0.157293	−	0.987552i	$-0.449723\pi$
$907$	0.903134	+	0.129851i	0.0299881	+	0.00431164i	−0.127304	+	0.991864i	$0.540633\pi$
$908$	−3.14808	+	6.89332i	−0.104473	+	0.228763i
$909$	3.53669	+	2.55145i	0.117305	+	0.0846263i
$910$	0.346119	−	2.40731i	0.0114737	−	0.0798015i
$911$	−47.3025	+	30.3995i	−1.56720	+	1.00718i	−0.586905	+	0.809656i	$0.699654\pi$
$911$	−47.3025	+	30.3995i	−1.56720	+	1.00718i	−0.980298	+	0.197524i	$0.936710\pi$
$912$	9.27249	+	3.74533i	0.307043	+	0.124020i
$913$	−2.51003	−	17.4577i	−0.0830699	−	0.577764i
$914$	−19.1717	−	22.1253i	−0.634144	−	0.731841i
$915$	−3.37239	−	2.66893i	−0.111488	−	0.0882322i
$916$	−15.0065	−	13.0032i	−0.495829	−	0.429639i
$917$	29.2151	−	8.57832i	0.964766	−	0.283281i
$918$	−2.78353	−	20.7172i	−0.0918702	−	0.683771i
$919$		−	24.9442i		−	0.822834i	−0.911447	−	0.411417i	$-0.865034\pi$
$919$		−	24.9442i		−	0.822834i	0.911447	−	0.411417i	$-0.134966\pi$
$920$	1.75944	+	6.13857i	0.0580070	+	0.202383i
$921$	1.54821	−	15.7023i	0.0510153	−	0.517407i
$922$	6.46577	+	14.1581i	0.212939	+	0.466271i
$923$	1.02400	+	3.48743i	0.0337055	+	0.114790i
$924$	−4.60271	+	4.36169i	−0.151418	+	0.143489i
$925$	−16.0259	+	24.9367i	−0.526927	+	0.819915i
$926$	−18.3472	+	15.8979i	−0.602926	+	0.522439i
$927$	37.5746	+	2.02199i	1.23411	+	0.0664107i
$928$	2.46549	+	0.723933i	0.0809337	+	0.0237643i
$929$	−12.5312	−	19.4990i	−0.411137	−	0.639742i	0.572500	−	0.819905i	$-0.305974\pi$
$929$	−12.5312	−	19.4990i	−0.411137	−	0.639742i	−0.983637	+	0.180163i	$0.942337\pi$
$930$	3.15142	−	12.8178i	0.103339	−	0.420314i
$931$	−24.8477	−	11.3476i	−0.814351	−	0.371901i
$932$	14.4767	+	6.61130i	0.474201	+	0.216560i
$933$	4.86300	−	19.7794i	0.159207	−	0.647549i
$934$	−0.0183016	−	0.0284778i	−0.000598845	−	0.000931821i
$935$	12.4918	+	3.66791i	0.408525	+	0.119954i
$936$	3.63260	+	0.195480i	0.118735	+	0.00638946i
$937$	8.48804	−	7.35493i	0.277292	−	0.240275i	−0.505100	−	0.863061i	$-0.668545\pi$
$937$	8.48804	−	7.35493i	0.277292	−	0.240275i	0.782393	+	0.622786i	$0.213999\pi$
$938$	−7.99687	+	12.4434i	−0.261107	+	0.406291i
$939$	5.36342	−	5.08256i	0.175029	−	0.165863i
$940$	1.45735	+	4.96328i	0.0475336	+	0.161885i
$941$	18.1293	+	39.6976i	0.590998	+	1.29411i	0.934837	+	0.355077i	$0.115545\pi$
$941$	18.1293	+	39.6976i	0.590998	+	1.29411i	−0.343839	+	0.939029i	$0.611727\pi$
$942$	1.66201	−	16.8564i	0.0541511	−	0.549211i
$943$	−30.0194	−	47.3816i	−0.977567	−	1.54296i
$944$		−	1.82054i		−	0.0592536i
$945$	−1.38775	−	10.3287i	−0.0451435	−	0.335994i
$946$	−5.52911	+	1.62349i	−0.179767	+	0.0527843i
$947$	−12.7432	−	11.0420i	−0.414097	−	0.358817i	0.422757	−	0.906243i	$-0.361062\pi$
$947$	−12.7432	−	11.0420i	−0.414097	−	0.358817i	−0.836854	+	0.547426i	$0.815608\pi$
$948$	−10.1867	−	8.06180i	−0.330848	−	0.261835i
$949$	−10.5632	−	12.1905i	−0.342895	−	0.395721i
$950$	2.65161	+	18.4424i	0.0860297	+	0.598350i
$951$	−8.51720	−	3.44025i	−0.276189	−	0.111558i
$952$	5.09758	−	3.27602i	0.165214	−	0.106176i
$953$	−5.98608	+	41.6341i	−0.193908	+	1.34866i	0.627632	+	0.778510i	$0.284024\pi$
$953$	−5.98608	+	41.6341i	−0.193908	+	1.34866i	−0.821540	+	0.570151i	$0.806885\pi$
$954$	18.2842	+	13.1906i	0.591972	+	0.427062i
$955$	−10.8134	+	23.6780i	−0.349913	+	0.766204i
$956$	0.447667	+	0.0643648i	0.0144786	+	0.00208171i
$957$	−9.63009	+	4.92717i	−0.311297	+	0.159273i
$958$	0.593397	−	2.02093i	0.0191718	−	0.0652932i
$959$	−2.55995	+	0.368066i	−0.0826652	+	0.0118855i
$960$	1.88274	−	1.33197i	0.0607650	−	0.0429891i
$961$	1.47802	+	0.949868i	0.0476782	+	0.0306409i
$962$	−7.29424	+	8.41800i	−0.235176	+	0.271407i
$963$	19.7288	−	1.76129i	0.635752	−	0.0567567i
$964$	0.138748	−	0.0633640i	0.00446877	−	0.00204082i
$965$	−3.13313			−0.100859
$966$	−11.8624	+	3.97926i	−0.381666	+	0.128031i
$967$	2.83746			0.0912467			0.0456233	−	0.998959i	$-0.485473\pi$
$967$	2.83746			0.0912467			0.0456233	+	0.998959i	$0.485473\pi$
$968$	−4.63235	+	2.11552i	−0.148889	+	0.0679955i
$969$	39.5262	−	7.49184i	1.26976	−	0.240673i
$970$	−14.7563	+	17.0297i	−0.473796	+	0.546790i
$971$	−19.9812	−	12.8411i	−0.641227	−	0.412091i	0.179224	−	0.983808i	$-0.442641\pi$
$971$	−19.9812	−	12.8411i	−0.641227	−	0.412091i	−0.820451	+	0.571717i	$0.806278\pi$
$972$	15.2038	−	3.44136i	0.487664	−	0.110382i
$973$	13.7779	−	1.98096i	0.441699	−	0.0635067i
$974$	−9.30813	+	31.7006i	−0.298252	+	1.01575i
$975$	3.08722	+	6.03393i	0.0988701	+	0.193240i
$976$	1.84582	+	0.265389i	0.0590834	+	0.00849491i
$977$	15.9516	−	34.9292i	0.510338	−	1.11748i	−0.462631	−	0.886551i	$-0.653095\pi$
$977$	15.9516	−	34.9292i	0.510338	−	1.11748i	0.972969	−	0.230934i	$-0.0741781\pi$
$978$	−14.8313	+	25.5069i	−0.474254	+	0.815620i
$979$	2.83872	−	19.7437i	0.0907259	−	0.631013i
$980$	−5.29958	+	3.40583i	−0.169289	+	0.108795i
$981$	25.8116	−	49.3192i	0.824102	−	1.57464i
$982$	3.69468	+	25.6970i	0.117902	+	0.820025i
$983$	35.9135	+	41.4464i	1.14546	+	1.32193i	0.939174	+	0.343442i	$0.111593\pi$
$983$	35.9135	+	41.4464i	1.14546	+	1.32193i	0.206288	+	0.978491i	$0.433862\pi$
$984$	−12.5714	+	15.8849i	−0.400763	+	0.506393i
$985$	9.30938	+	8.06662i	0.296622	+	0.257024i
$986$	9.91832	−	2.91228i	0.315864	−	0.0927459i
$987$	−9.58818	+	3.28546i	−0.305195	+	0.104577i
$988$			7.00129i			0.222741i
$989$	−11.2440	−	1.69088i	−0.357539	−	0.0537669i
$990$	−1.89611	+	9.52191i	−0.0602625	+	0.302626i
$991$	0.417874	+	0.915016i	0.0132742	+	0.0290664i	0.916153	−	0.400829i	$-0.131278\pi$
$991$	0.417874	+	0.915016i	0.0132742	+	0.0290664i	−0.902879	+	0.429895i	$0.858551\pi$
$992$	1.61246	+	5.49153i	0.0511956	+	0.174356i
$993$	14.7107	+	15.5237i	0.466831	+	0.492628i
$994$	−2.44091	+	3.79812i	−0.0774208	+	0.120469i
$995$	−13.3726	+	11.5874i	−0.423939	+	0.367345i
$996$	−12.5562	+	0.559367i	−0.397860	+	0.0177242i
$997$	44.4382	+	13.0482i	1.40737	+	0.413242i	0.895209	−	0.445647i	$-0.147026\pi$
$997$	44.4382	+	13.0482i	1.40737	+	0.413242i	0.512163	+	0.858888i	$0.328844\pi$
$998$	−15.2910	−	23.7932i	−0.484027	−	0.753161i
$999$	−20.2280	+	43.2313i	−0.639985	+	1.36778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.65.3	yes	80
3.2	odd	2	inner	138.2.f.a.65.6	yes	80
23.17	odd	22	inner	138.2.f.a.17.6	yes	80
69.17	even	22	inner	138.2.f.a.17.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.3	✓	80	69.17	even	22	inner
138.2.f.a.17.6	yes	80	23.17	odd	22	inner
138.2.f.a.65.3	yes	80	1.1	even	1	trivial
138.2.f.a.65.6	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.322552 + 1.70175i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.12015 + 0.719874i) q^{5} +(-1.00034 - 1.41398i) q^{6} +(1.49094 - 0.214365i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.79192 + 1.09781i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.322552 + 1.70175i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.12015 + 0.719874i) q^{5} +(-1.00034 - 1.41398i) q^{6} +(1.49094 - 0.214365i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.79192 + 1.09781i) q^{9} +(-1.31797 - 0.189495i) q^{10} +(-1.00968 + 2.21088i) q^{11} +(1.49733 + 0.870642i) q^{12} +(-0.172574 + 1.20028i) q^{13} +(-1.26715 + 0.814351i) q^{14} +(-0.863741 + 2.13841i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-2.63441 - 3.04027i) q^{17} +(2.08357 - 2.15841i) q^{18} +(4.36347 + 3.78096i) q^{19} +(1.27758 - 0.375132i) q^{20} +(0.845700 + 2.46806i) q^{21} -2.43052i q^{22} +(2.02041 - 4.34948i) q^{23} +(-1.72369 - 0.169952i) q^{24} +(-1.34057 - 2.93543i) q^{25} +(-0.341634 - 1.16350i) q^{26} +(-2.76874 - 4.39706i) q^{27} +(0.814351 - 1.26715i) q^{28} +(1.94196 - 1.68271i) q^{29} +(-0.102640 - 2.30397i) q^{30} +(5.49153 + 1.61246i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-4.08805 - 1.00509i) q^{33} +(3.65932 + 1.67116i) q^{34} +(1.82438 + 0.833168i) q^{35} +(-0.998651 + 2.82890i) q^{36} +(-4.96610 - 7.72740i) q^{37} +(-5.53982 - 1.62664i) q^{38} +(-2.09824 + 0.0934742i) q^{39} +(-1.00630 + 0.871960i) q^{40} +(6.32320 - 9.83909i) q^{41} +(-1.79455 - 1.89371i) q^{42} +(-0.667960 - 2.27486i) q^{43} +(1.00968 + 2.21088i) q^{44} +(-3.91764 - 0.780126i) q^{45} +(-0.0309926 + 4.79573i) q^{46} +3.88490i q^{47} +(1.63853 - 0.561454i) q^{48} +(-4.53951 + 1.33292i) q^{49} +(2.43885 + 2.11327i) q^{50} +(4.32406 - 5.46376i) q^{51} +(0.794097 + 0.916437i) q^{52} +(1.06952 + 7.43870i) q^{53} +(4.34513 + 2.84953i) q^{54} +(-2.72254 + 1.74967i) q^{55} +(-0.214365 + 1.49094i) q^{56} +(-5.02682 + 8.64509i) q^{57} +(-1.06744 + 2.33737i) q^{58} +(1.80201 + 0.259090i) q^{59} +(1.05047 + 2.05313i) q^{60} +(-0.525376 + 1.78927i) q^{61} +(-5.66511 + 0.814520i) q^{62} +(-3.92725 + 2.23525i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-1.05736 + 1.22025i) q^{65} +(4.13615 - 0.783971i) q^{66} +(8.93253 - 4.07935i) q^{67} -4.02286 q^{68} +(8.05342 + 2.03531i) q^{69} -2.00563 q^{70} +(2.72650 - 1.24515i) q^{71} +(-0.266764 - 2.98812i) q^{72} +(-8.71102 + 10.0531i) q^{73} +(7.72740 + 4.96610i) q^{74} +(4.56298 - 3.22814i) q^{75} +(5.71492 - 0.821682i) q^{76} +(-1.03143 + 3.51273i) q^{77} +(1.86979 - 0.956667i) q^{78} +(-7.42390 - 1.06740i) q^{79} +(0.553133 - 1.21119i) q^{80} +(6.58964 - 6.12998i) q^{81} +(-1.66448 + 11.5767i) q^{82} +(-6.10459 + 3.92318i) q^{83} +(2.41905 + 0.977100i) q^{84} +(-0.762312 - 5.30199i) q^{85} +(1.55261 + 1.79181i) q^{86} +(3.48994 + 2.76196i) q^{87} +(-1.83687 - 1.59165i) q^{88} +(-7.87435 + 2.31212i) q^{89} +(3.88769 - 0.917819i) q^{90} +1.82653i q^{91} +(-1.96403 - 4.37523i) q^{92} +(-0.972700 + 9.86533i) q^{93} +(-1.61385 - 3.53383i) q^{94} +(2.16590 + 7.37638i) q^{95} +(-1.25722 + 1.19138i) q^{96} +(9.14934 - 14.2367i) q^{97} +(3.57557 - 3.09825i) q^{98} +(0.391811 - 7.28103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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