LMFDB - Embedded newform 189.2.ba.a.101.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02575 - 1.22245i) q^{2} +(0.732884 + 1.56936i) q^{3} +(-0.0949069 - 0.538244i) q^{4} +(1.45366 - 1.21977i) q^{5} +(2.67021 + 0.713863i) q^{6} +(-2.50057 - 0.864386i) q^{7} +(2.00866 + 1.15970i) q^{8} +(-1.92576 + 2.30031i) q^{9} +O(q^{10})$	\(q+(1.02575 - 1.22245i) q^{2} +(0.732884 + 1.56936i) q^{3} +(-0.0949069 - 0.538244i) q^{4} +(1.45366 - 1.21977i) q^{5} +(2.67021 + 0.713863i) q^{6} +(-2.50057 - 0.864386i) q^{7} +(2.00866 + 1.15970i) q^{8} +(-1.92576 + 2.30031i) q^{9} -3.02821i q^{10} +(0.811915 - 0.967602i) q^{11} +(0.775141 - 0.543413i) q^{12} +(-0.326917 + 0.898197i) q^{13} +(-3.62163 + 2.17016i) q^{14} +(2.97962 + 1.38737i) q^{15} +(4.50524 - 1.63977i) q^{16} -4.01374 q^{17} +(0.836650 + 4.71370i) q^{18} -7.67461i q^{19} +(-0.794495 - 0.666660i) q^{20} +(-0.476096 - 4.55778i) q^{21} +(-0.350017 - 1.98504i) q^{22} +(-1.95808 + 5.37979i) q^{23} +(-0.347870 + 4.00224i) q^{24} +(-0.242940 + 1.37778i) q^{25} +(0.762661 + 1.32097i) q^{26} +(-5.02137 - 1.33635i) q^{27} +(-0.227929 + 1.42795i) q^{28} +(-1.22870 - 3.37583i) q^{29} +(4.75234 - 2.21932i) q^{30} +(-8.76565 + 1.54562i) q^{31} +(1.03017 - 2.83037i) q^{32} +(2.11355 + 0.565044i) q^{33} +(-4.11711 + 4.90658i) q^{34} +(-4.68933 + 1.79359i) q^{35} +(1.42090 + 0.818214i) q^{36} +(3.99935 - 6.92708i) q^{37} +(-9.38179 - 7.87226i) q^{38} +(-1.64918 + 0.145225i) q^{39} +(4.33449 - 0.764287i) q^{40} +(3.01647 + 1.09790i) q^{41} +(-6.06000 - 4.09316i) q^{42} +(0.111496 - 0.632326i) q^{43} +(-0.597862 - 0.345176i) q^{44} +(0.00643857 + 5.69286i) q^{45} +(4.56799 + 7.91199i) q^{46} +(-1.48485 + 8.42098i) q^{47} +(5.87521 + 5.86857i) q^{48} +(5.50567 + 4.32291i) q^{49} +(1.43506 + 1.71024i) q^{50} +(-2.94160 - 6.29898i) q^{51} +(0.514475 + 0.0907159i) q^{52} +(11.3329 + 6.54305i) q^{53} +(-6.78431 + 4.76759i) q^{54} -2.39691i q^{55} +(-4.02037 - 4.63618i) q^{56} +(12.0442 - 5.62459i) q^{57} +(-5.38712 - 1.96075i) q^{58} +(-2.02915 - 0.738551i) q^{59} +(0.463955 - 1.73543i) q^{60} +(-3.03575 - 0.535284i) q^{61} +(-7.10196 + 12.3010i) q^{62} +(6.80386 - 4.08749i) q^{63} +(2.39111 + 4.14152i) q^{64} +(0.620364 + 1.70444i) q^{65} +(2.85872 - 2.00411i) q^{66} +(1.63854 - 1.37490i) q^{67} +(0.380931 + 2.16037i) q^{68} +(-9.87786 + 0.869829i) q^{69} +(-2.61754 + 7.57223i) q^{70} +(-0.154696 + 0.0893139i) q^{71} +(-6.53589 + 2.38724i) q^{72} +(9.96274 - 5.75199i) q^{73} +(-4.36563 - 11.9945i) q^{74} +(-2.34027 + 0.628493i) q^{75} +(-4.13081 + 0.728373i) q^{76} +(-2.86663 + 1.71775i) q^{77} +(-1.51413 + 2.16500i) q^{78} +(-0.935206 - 0.784731i) q^{79} +(4.54896 - 7.87903i) q^{80} +(-1.58288 - 8.85971i) q^{81} +(4.43628 - 2.56129i) q^{82} +(5.11532 - 1.86183i) q^{83} +(-2.40801 + 0.688820i) q^{84} +(-5.83462 + 4.89582i) q^{85} +(-0.658617 - 0.784910i) q^{86} +(4.39739 - 4.40236i) q^{87} +(2.75300 - 1.00201i) q^{88} +5.63916 q^{89} +(6.96582 + 5.83160i) q^{90} +(1.59387 - 1.96342i) q^{91} +(3.08147 + 0.543347i) q^{92} +(-8.84983 - 12.6237i) q^{93} +(8.77111 + 10.4530i) q^{94} +(-9.36123 - 11.1563i) q^{95} +(5.19685 - 0.457627i) q^{96} +(-5.97585 - 1.05370i) q^{97} +(10.9320 - 2.29615i) q^{98} +(0.662233 + 3.73103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.02575	−	1.22245i	0.725318	−	0.864400i	−0.269818	−	0.962911i	$-0.586964\pi$
$2$	1.02575	−	1.22245i	0.725318	−	0.864400i	0.995136	+	0.0985112i	$0.0314080\pi$
$3$	0.732884	+	1.56936i	0.423131	+	0.906069i
$3$	0.732884	+	1.56936i	0.423131	+	0.906069i
$4$	−0.0949069	−	0.538244i	−0.0474534	−	0.269122i
$5$	1.45366	−	1.21977i	0.650097	−	0.545497i	−0.257003	−	0.966411i	$-0.582735\pi$
$5$	1.45366	−	1.21977i	0.650097	−	0.545497i	0.907101	+	0.420914i	$0.138291\pi$
$6$	2.67021	+	0.713863i	1.09011	+	0.291434i
$7$	−2.50057	−	0.864386i	−0.945126	−	0.326707i
$7$	−2.50057	−	0.864386i	−0.945126	−	0.326707i
$8$	2.00866	+	1.15970i	0.710170	+	0.410017i
$9$	−1.92576	+	2.30031i	−0.641921	+	0.766771i
$10$		−	3.02821i		−	0.957603i
$11$	0.811915	−	0.967602i	0.244802	−	0.291743i	−0.629627	−	0.776898i	$-0.716792\pi$
$11$	0.811915	−	0.967602i	0.244802	−	0.291743i	0.874428	+	0.485155i	$0.161237\pi$
$12$	0.775141	−	0.543413i	0.223764	−	0.156870i
$13$	−0.326917	+	0.898197i	−0.0906704	+	0.249115i	−0.976736	−	0.214445i	$-0.931206\pi$
$13$	−0.326917	+	0.898197i	−0.0906704	+	0.249115i	0.886066	+	0.463560i	$0.153428\pi$
$14$	−3.62163	+	2.17016i	−0.967922	+	0.580000i
$15$	2.97962	+	1.38737i	0.769334	+	0.358217i
$16$	4.50524	−	1.63977i	1.12631	−	0.409944i
$17$	−4.01374			−0.973474			−0.486737	−	0.873549i	$-0.661813\pi$
$17$	−4.01374			−0.973474			−0.486737	+	0.873549i	$0.661813\pi$
$18$	0.836650	+	4.71370i	0.197200	+	1.11103i
$19$		−	7.67461i		−	1.76068i	−0.474348	−	0.880338i	$-0.657316\pi$
$19$		−	7.67461i		−	1.76068i	0.474348	−	0.880338i	$-0.342684\pi$
$20$	−0.794495	−	0.666660i	−0.177654	−	0.149070i
$21$	−0.476096	−	4.55778i	−0.103893	−	0.994589i
$22$	−0.350017	−	1.98504i	−0.0746239	−	0.423213i
$23$	−1.95808	+	5.37979i	−0.408288	+	1.12176i	0.549801	+	0.835295i	$0.314703\pi$
$23$	−1.95808	+	5.37979i	−0.408288	+	1.12176i	−0.958090	+	0.286468i	$0.907519\pi$
$24$	−0.347870	+	4.00224i	−0.0710087	+	0.816954i
$25$	−0.242940	+	1.37778i	−0.0485879	+	0.275556i
$26$	0.762661	+	1.32097i	0.149570	+	0.259063i
$27$	−5.02137	−	1.33635i	−0.966364	−	0.257180i
$28$	−0.227929	+	1.42795i	−0.0430745	+	0.269857i
$29$	−1.22870	−	3.37583i	−0.228164	−	0.626876i	0.771795	−	0.635871i	$-0.219359\pi$
$29$	−1.22870	−	3.37583i	−0.228164	−	0.626876i	−0.999960	+	0.00899503i	$0.997137\pi$
$30$	4.75234	−	2.21932i	0.867654	−	0.405191i
$31$	−8.76565	+	1.54562i	−1.57436	+	0.277602i	−0.891524	−	0.452973i	$-0.850363\pi$
$31$	−8.76565	+	1.54562i	−1.57436	+	0.277602i	−0.682833	+	0.730575i	$0.739252\pi$
$32$	1.03017	−	2.83037i	0.182110	−	0.500343i
$33$	2.11355	+	0.565044i	0.367922	+	0.0983615i
$34$	−4.11711	+	4.90658i	−0.706078	+	0.841471i
$35$	−4.68933	+	1.79359i	−0.792641	+	0.303171i
$36$	1.42090	+	0.818214i	0.236816	+	0.136369i
$37$	3.99935	−	6.92708i	0.657489	−	1.13880i	−0.323774	−	0.946134i	$-0.604952\pi$
$37$	3.99935	−	6.92708i	0.657489	−	1.13880i	0.981264	−	0.192670i	$-0.0617148\pi$
$38$	−9.38179	−	7.87226i	−1.52193	−	1.27705i
$39$	−1.64918	+	0.145225i	−0.264081	+	0.0232546i
$40$	4.33449	−	0.764287i	0.685343	−	0.120844i
$41$	3.01647	+	1.09790i	0.471093	+	0.171464i	0.566647	−	0.823960i	$-0.308240\pi$
$41$	3.01647	+	1.09790i	0.471093	+	0.171464i	−0.0955544	+	0.995424i	$0.530462\pi$
$42$	−6.06000	−	4.09316i	−0.935078	−	0.631588i
$43$	0.111496	−	0.632326i	0.0170030	−	0.0964289i	−0.975125	−	0.221654i	$-0.928854\pi$
$43$	0.111496	−	0.632326i	0.0170030	−	0.0964289i	0.992128	+	0.125226i	$0.0399654\pi$
$44$	−0.597862	−	0.345176i	−0.0901311	−	0.0520372i
$45$	0.00643857	+	5.69286i	0.000959805	+	0.848641i
$46$	4.56799	+	7.91199i	0.673513	+	1.16656i
$47$	−1.48485	+	8.42098i	−0.216587	+	1.22833i	0.661544	+	0.749906i	$0.269901\pi$
$47$	−1.48485	+	8.42098i	−0.216587	+	1.22833i	−0.878131	+	0.478420i	$0.841210\pi$
$48$	5.87521	+	5.86857i	0.848014	+	0.847055i
$49$	5.50567	+	4.32291i	0.786525	+	0.617558i
$50$	1.43506	+	1.71024i	0.202949	+	0.241865i
$51$	−2.94160	−	6.29898i	−0.411907	−	0.882034i
$52$	0.514475	+	0.0907159i	0.0713449	+	0.0125800i
$53$	11.3329	+	6.54305i	1.55669	+	0.898757i	0.997570	+	0.0696726i	$0.0221955\pi$
$53$	11.3329	+	6.54305i	1.55669	+	0.898757i	0.559123	+	0.829085i	$0.311138\pi$
$54$	−6.78431	+	4.76759i	−0.923227	+	0.648787i
$55$		−	2.39691i		−	0.323200i
$56$	−4.02037	−	4.63618i	−0.537245	−	0.619535i
$57$	12.0442	−	5.62459i	1.59529	−	0.744996i
$58$	−5.38712	−	1.96075i	−0.707363	−	0.257459i
$59$	−2.02915	−	0.738551i	−0.264173	−	0.0961512i	0.206538	−	0.978439i	$-0.433780\pi$
$59$	−2.02915	−	0.738551i	−0.264173	−	0.0961512i	−0.470711	+	0.882287i	$0.656003\pi$
$60$	0.463955	−	1.73543i	0.0598964	−	0.224043i
$61$	−3.03575	−	0.535284i	−0.388688	−	0.0685361i	−0.0241106	−	0.999709i	$-0.507675\pi$
$61$	−3.03575	−	0.535284i	−0.388688	−	0.0685361i	−0.364577	+	0.931173i	$0.618786\pi$
$62$	−7.10196	+	12.3010i	−0.901950	+	1.56222i
$63$	6.80386	−	4.08749i	0.857205	−	0.514975i
$64$	2.39111	+	4.14152i	0.298889	+	0.517690i
$65$	0.620364	+	1.70444i	0.0769467	+	0.211409i
$66$	2.85872	−	2.00411i	0.351884	−	0.246689i
$67$	1.63854	−	1.37490i	0.200180	−	0.167971i	−0.537187	−	0.843463i	$-0.680513\pi$
$67$	1.63854	−	1.37490i	0.200180	−	0.167971i	0.737367	+	0.675492i	$0.236069\pi$
$68$	0.380931	+	2.16037i	0.0461947	+	0.261983i
$69$	−9.87786	+	0.869829i	−1.18915	+	0.104715i
$70$	−2.61754	+	7.57223i	−0.312856	+	0.905055i
$71$	−0.154696	+	0.0893139i	−0.0183591	+	0.0105996i	−0.509151	−	0.860677i	$-0.670041\pi$
$71$	−0.154696	+	0.0893139i	−0.0183591	+	0.0105996i	0.490792	+	0.871277i	$0.336707\pi$
$72$	−6.53589	+	2.38724i	−0.770262	+	0.281339i
$73$	9.96274	−	5.75199i	1.16605	−	0.673220i	0.213304	−	0.976986i	$-0.431578\pi$
$73$	9.96274	−	5.75199i	1.16605	−	0.673220i	0.952747	+	0.303766i	$0.0982442\pi$
$74$	−4.36563	−	11.9945i	−0.507494	−	1.39433i
$75$	−2.34027	+	0.628493i	−0.270232	+	0.0725721i
$76$	−4.13081	+	0.728373i	−0.473836	+	0.0835501i
$77$	−2.86663	+	1.71775i	−0.326683	+	0.195756i
$78$	−1.51413	+	2.16500i	−0.171441	+	0.245138i
$79$	−0.935206	−	0.784731i	−0.105219	−	0.0882891i	0.588661	−	0.808380i	$-0.299655\pi$
$79$	−0.935206	−	0.784731i	−0.105219	−	0.0882891i	−0.693879	+	0.720091i	$0.744100\pi$
$80$	4.54896	−	7.87903i	0.508589	−	0.880902i
$81$	−1.58288	−	8.85971i	−0.175875	−	0.984412i
$82$	4.43628	−	2.56129i	0.489906	−	0.282847i
$83$	5.11532	−	1.86183i	0.561480	−	0.204362i	−0.0456599	−	0.998957i	$-0.514539\pi$
$83$	5.11532	−	1.86183i	0.561480	−	0.204362i	0.607140	+	0.794595i	$0.292317\pi$
$84$	−2.40801	+	0.688820i	−0.262735	+	0.0751564i
$85$	−5.83462	+	4.89582i	−0.632853	+	0.531027i
$86$	−0.658617	−	0.784910i	−0.0710205	−	0.0846390i
$87$	4.39739	−	4.40236i	0.471449	−	0.471983i
$88$	2.75300	−	1.00201i	0.293470	−	0.106814i
$89$	5.63916			0.597750			0.298875	−	0.954292i	$-0.403389\pi$
$89$	5.63916			0.597750			0.298875	+	0.954292i	$0.403389\pi$
$90$	6.96582	+	5.83160i	0.734262	+	0.614705i
$91$	1.59387	−	1.96342i	0.167083	−	0.205822i
$92$	3.08147	+	0.543347i	0.321266	+	0.0566478i
$93$	−8.84983	−	12.6237i	−0.917685	−	1.30901i
$94$	8.77111	+	10.4530i	0.904671	+	1.07814i
$95$	−9.36123	−	11.1563i	−0.960442	−	1.14461i
$96$	5.19685	−	0.457627i	0.530401	−	0.0467063i
$97$	−5.97585	−	1.05370i	−0.606755	−	0.106987i	−0.138174	−	0.990408i	$-0.544123\pi$
$97$	−5.97585	−	1.05370i	−0.606755	−	0.106987i	−0.468581	+	0.883421i	$0.655235\pi$
$98$	10.9320	−	2.29615i	1.10430	−	0.231946i
$99$	0.662233	+	3.73103i	0.0665569	+	0.374983i
$100$	0.764638			0.0764638
$101$	6.52215	−	2.37387i	0.648978	−	0.236209i	0.00350738	−	0.999994i	$-0.498884\pi$
$101$	6.52215	−	2.37387i	0.648978	−	0.236209i	0.645470	+	0.763785i	$0.276661\pi$
$102$	−10.7175	−	2.86526i	−1.06119	−	0.283703i
$103$	−8.28238	−	9.87055i	−0.816087	−	0.972574i	0.183859	−	0.982953i	$-0.441141\pi$
$103$	−8.28238	−	9.87055i	−0.816087	−	0.972574i	−0.999946	+	0.0103782i	$0.996696\pi$
$104$	−1.69831	+	1.42505i	−0.166533	+	0.139738i
$105$	−6.25151	−	6.04474i	−0.610085	−	0.589906i
$106$	19.6233	−	7.14230i	1.90598	−	0.693721i
$107$	1.24002	−	0.715923i	0.119877	−	0.0692109i	−0.438863	−	0.898554i	$-0.644619\pi$
$107$	1.24002	−	0.715923i	0.119877	−	0.0692109i	0.558739	+	0.829343i	$0.311285\pi$
$108$	−0.242717	+	2.82955i	−0.0233555	+	0.272274i
$109$	−0.946256	+	1.63896i	−0.0906349	+	0.156984i	−0.907778	−	0.419450i	$-0.862223\pi$
$109$	−0.946256	+	1.63896i	−0.0906349	+	0.156984i	0.817144	+	0.576434i	$0.195556\pi$
$110$	−2.93010	−	2.45865i	−0.279374	−	0.234423i
$111$	13.8021	+	1.19966i	1.31004	+	0.113867i
$112$	−12.6831	+	0.206099i	−1.19844	+	0.0194745i
$113$	0.855475	−	0.150843i	0.0804763	−	0.0141901i	−0.133265	−	0.991080i	$-0.542546\pi$
$113$	0.855475	−	0.150843i	0.0804763	−	0.0141901i	0.213741	+	0.976890i	$0.431435\pi$
$114$	5.47862	−	20.4928i	0.513120	−	1.91933i
$115$	3.71570	+	10.2088i	0.346491	+	0.951976i
$116$	−1.70041	+	0.981731i	−0.157879	+	0.0911514i
$117$	−1.43657	−	2.48172i	−0.132811	−	0.229436i
$118$	−2.98425	+	1.72296i	−0.274723	+	0.158611i
$119$	10.0366	+	3.46942i	0.920055	+	0.318041i
$120$	4.37612	+	6.24223i	0.399483	+	0.569835i
$121$	1.63308	+	9.26166i	0.148462	+	0.841969i
$122$	−3.76829	+	3.16197i	−0.341165	+	0.286271i
$123$	0.487717	+	5.53855i	0.0439759	+	0.499394i
$124$	1.66384	+	4.57136i	0.149417	+	0.410521i
$125$	6.07147	+	10.5161i	0.543049	+	0.940588i
$126$	1.98235	−	12.5101i	0.176602	−	1.11449i
$127$	−6.79273	+	11.7654i	−0.602757	+	1.04401i	0.389644	+	0.920965i	$0.372598\pi$
$127$	−6.79273	+	11.7654i	−0.602757	+	1.04401i	−0.992402	+	0.123041i	$0.960735\pi$
$128$	13.4480	+	2.37124i	1.18865	+	0.209590i
$129$	1.07406	−	0.288444i	0.0945657	−	0.0253961i
$130$	2.71992	+	0.989972i	0.238553	+	0.0868263i
$131$	8.52376	+	3.10240i	0.744725	+	0.271058i	0.686384	−	0.727239i	$-0.259197\pi$
$131$	8.52376	+	3.10240i	0.744725	+	0.271058i	0.0583404	+	0.998297i	$0.481419\pi$
$132$	0.103541	−	1.19123i	0.00901205	−	0.103684i
$133$	−6.63382	+	19.1909i	−0.575225	+	1.66406i
$134$		−	3.41334i		−	0.294867i
$135$	−8.92941	+	4.18231i	−0.768521	+	0.359956i
$136$	−8.06225	−	4.65474i	−0.691332	−	0.399141i
$137$	19.7829	+	3.48826i	1.69017	+	0.298022i	0.934243	−	0.356638i	$-0.116077\pi$
$137$	19.7829	+	3.48826i	1.69017	+	0.298022i	0.755923	+	0.654660i	$0.227188\pi$
$138$	−9.06893	+	12.9674i	−0.771999	+	1.10386i
$139$	−4.91571	−	5.85831i	−0.416945	−	0.496895i	0.516164	−	0.856490i	$-0.327360\pi$
$139$	−4.91571	−	5.85831i	−0.416945	−	0.496895i	−0.933109	+	0.359594i	$0.882915\pi$
$140$	1.41044	+	2.35378i	0.119204	+	0.198931i
$141$	−14.3037	+	3.84135i	−1.20459	+	0.323500i
$142$	−0.0494988	+	0.280722i	−0.00415385	+	0.0235577i
$143$	0.603669	+	1.04558i	0.0504813	+	0.0874362i
$144$	−4.90403	+	13.5213i	−0.408670	+	1.12677i
$145$	−5.90385	−	3.40859i	−0.490288	−	0.283068i
$146$	3.18782	−	18.0790i	0.263826	−	1.49623i
$147$	−2.74917	+	11.8086i	−0.226747	+	0.973954i
$148$	−4.10802	−	1.49520i	−0.337677	−	0.122904i
$149$	−7.28668	+	1.28484i	−0.596948	+	0.105258i	−0.463955	−	0.885859i	$-0.653570\pi$
$149$	−7.28668	+	1.28484i	−0.596948	+	0.105258i	−0.132993	+	0.991117i	$0.542459\pi$
$150$	−1.63225	+	3.50554i	−0.133272	+	0.286226i
$151$	−4.72726	−	3.96664i	−0.384699	−	0.322801i	0.429845	−	0.902903i	$-0.358568\pi$
$151$	−4.72726	−	3.96664i	−0.384699	−	0.322801i	−0.814544	+	0.580102i	$0.803013\pi$
$152$	8.90026	−	15.4157i	0.721907	−	1.25038i
$153$	7.72950	−	9.23285i	0.624893	−	0.746432i
$154$	−0.840603	+	5.26629i	−0.0677377	+	0.424370i
$155$	−10.8570	+	12.9389i	−0.872055	+	1.03927i
$156$	0.234685	+	0.873880i	0.0187898	+	0.0699664i
$157$	6.49586	−	17.8472i	0.518426	−	1.42436i	−0.353828	−	0.935311i	$-0.615120\pi$
$157$	6.49586	−	17.8472i	0.518426	−	1.42436i	0.872254	−	0.489053i	$-0.162658\pi$
$158$	−1.91858	+	0.338298i	−0.152634	+	0.0269135i
$159$	−1.96269	+	22.5807i	−0.155651	+	1.79076i
$160$	−1.95487	−	5.37096i	−0.154546	−	0.424612i
$161$	9.54653	−	11.7600i	0.752372	−	0.926817i
$162$	−12.4542	−	7.15290i	−0.978492	−	0.561985i
$163$	−0.709039	−	1.22809i	−0.0555362	−	0.0961915i	0.836921	−	0.547324i	$-0.184353\pi$
$163$	−0.709039	−	1.22809i	−0.0555362	−	0.0961915i	−0.892457	+	0.451133i	$0.851020\pi$
$164$	0.304657	−	1.72779i	0.0237897	−	0.134918i
$165$	3.76161	−	1.75666i	0.292841	−	0.136756i
$166$	2.97108	−	8.16299i	0.230601	−	0.633571i
$167$	2.73878	+	15.5324i	0.211933	+	1.20193i	0.886150	+	0.463398i	$0.153370\pi$
$167$	2.73878	+	15.5324i	0.211933	+	1.20193i	−0.674217	+	0.738533i	$0.735519\pi$
$168$	4.32935	−	9.70718i	0.334017	−	0.748925i
$169$	9.25869	+	7.76897i	0.712207	+	0.597613i
$170$			12.1544i			0.932201i
$171$	17.6540	+	14.7795i	1.35003	+	1.13021i
$172$	−0.350927			−0.0267580
$173$	−10.2513	+	3.73118i	−0.779394	+	0.283676i	−0.700920	−	0.713240i	$-0.747227\pi$
$173$	−10.2513	+	3.73118i	−0.779394	+	0.283676i	−0.0784741	+	0.996916i	$0.525005\pi$
$174$	−0.871014	−	9.89131i	−0.0660314	−	0.749859i
$175$	1.79842	−	3.23524i	0.135948	−	0.244561i
$176$	2.07122	−	5.69064i	0.156124	−	0.428948i
$177$	−0.328083	−	3.72574i	−0.0246602	−	0.280043i
$178$	5.78440	−	6.89357i	0.433559	−	0.516695i
$179$		−	23.6413i		−	1.76703i	−0.468403	−	0.883515i	$-0.655170\pi$
$179$		−	23.6413i		−	1.76703i	0.468403	−	0.883515i	$-0.344830\pi$
$180$	3.06353	−	0.543757i	0.228342	−	0.0405293i
$181$	−18.7421	−	10.8208i	−1.39309	−	0.804301i	−0.399434	−	0.916762i	$-0.630793\pi$
$181$	−18.7421	−	10.8208i	−1.39309	−	0.804301i	−0.993656	+	0.112461i	$0.964127\pi$
$182$	−0.765260	−	3.96240i	−0.0567248	−	0.293713i
$183$	−1.38480	−	5.15647i	−0.102367	−	0.381178i
$184$	−10.1721	+	8.53540i	−0.749896	+	0.629238i
$185$	−2.63572	−	14.9479i	−0.193782	−	1.09899i
$186$	−24.5095	−	2.13034i	−1.79712	−	0.156204i
$187$	−3.25881	+	3.88370i	−0.238308	+	0.284004i
$188$	4.67346			0.340847
$189$	11.4012	+	7.68203i	0.829312	+	0.558785i
$190$	−23.2403			−1.68603
$191$	−14.0821	+	16.7824i	−1.01894	+	1.21433i	−0.0423797	+	0.999102i	$0.513494\pi$
$191$	−14.0821	+	16.7824i	−1.01894	+	1.21433i	−0.976564	+	0.215228i	$0.930951\pi$
$192$	−4.74712	+	6.78776i	−0.342594	+	0.489864i
$193$	2.52946	+	14.3453i	0.182074	+	1.03259i	0.929657	+	0.368426i	$0.120103\pi$
$193$	2.52946	+	14.3453i	0.182074	+	1.03259i	−0.747583	+	0.664169i	$0.768786\pi$
$194$	−7.41785	+	6.22431i	−0.532570	+	0.446880i
$195$	−2.22022	+	2.22273i	−0.158993	+	0.159173i
$196$	1.80425	−	3.37367i	0.128875	−	0.240976i
$197$	−2.06396	−	1.19163i	−0.147051	−	0.0849001i	0.424669	−	0.905349i	$-0.360390\pi$
$197$	−2.06396	−	1.19163i	−0.147051	−	0.0849001i	−0.571720	+	0.820449i	$0.693724\pi$
$198$	5.24027	+	3.01758i	0.372410	+	0.214450i
$199$			10.2598i			0.727298i	0.931536	+	0.363649i	$0.118469\pi$
$199$			10.2598i			0.727298i	−0.931536	+	0.363649i	$0.881531\pi$
$200$	−2.08580	+	2.48576i	−0.147488	+	0.175770i
$201$	3.35857	+	1.56381i	0.236895	+	0.110303i
$202$	3.78819	−	10.4080i	0.266536	−	0.732303i
$203$	0.154432	+	9.50356i	0.0108390	+	0.667019i
$204$	−3.11121	+	2.18112i	−0.217828	+	0.152709i
$205$	5.72411	−	2.08341i	0.399789	−	0.145511i
$206$	−20.5619			−1.43262
$207$	−8.60439	−	14.8644i	−0.598047	−	1.03315i
$208$			4.58267i			0.317751i
$209$	−7.42597	−	6.23113i	−0.513665	−	0.431016i
$210$	−13.8019	+	1.44172i	−0.952421	+	0.0994879i
$211$	−1.98228	−	11.2421i	−0.136466	−	0.773938i	−0.973828	−	0.227288i	$-0.927014\pi$
$211$	−1.98228	−	11.2421i	−0.136466	−	0.773938i	0.837361	−	0.546650i	$-0.184097\pi$
$212$	2.44619	−	6.72084i	0.168005	−	0.461589i
$213$	−0.253540	−	0.177317i	−0.0173723	−	0.0121495i
$214$	0.396774	−	2.25021i	0.0271229	−	0.153821i
$215$	−0.609213	−	1.05519i	−0.0415480	−	0.0719632i
$216$	−8.53649	−	8.50757i	−0.580834	−	0.578867i
$217$	23.2551	+	3.71197i	1.57866	+	0.251985i
$218$	1.03292	+	2.83792i	0.0699581	+	0.192208i
$219$	16.3285	+	11.4196i	1.10338	+	0.771662i
$220$	−1.29012	+	0.227484i	−0.0869801	+	0.0153369i
$221$	1.31216	−	3.60512i	0.0882653	−	0.242507i
$222$	15.6241	−	15.6418i	1.04862	−	1.04981i
$223$	−7.05545	+	8.40836i	−0.472468	+	0.563065i	−0.948669	−	0.316271i	$-0.897569\pi$
$223$	−7.05545	+	8.40836i	−0.472468	+	0.563065i	0.476201	+	0.879336i	$0.342013\pi$
$224$	−5.02254	+	6.18706i	−0.335582	+	0.413390i
$225$	−2.70148	−	3.21211i	−0.180099	−	0.214141i
$226$	0.693109	−	1.20050i	0.0461049	−	0.0798561i
$227$	11.5294	+	9.67429i	0.765231	+	0.642105i	0.939483	−	0.342596i	$-0.111306\pi$
$227$	11.5294	+	9.67429i	0.765231	+	0.642105i	−0.174252	+	0.984701i	$0.555751\pi$
$228$	−4.17048	−	5.94890i	−0.276197	−	0.393975i
$229$	−22.1302	+	3.90215i	−1.46240	+	0.257861i	−0.847523	−	0.530758i	$-0.821907\pi$
$229$	−22.1302	+	3.90215i	−1.46240	+	0.257861i	−0.614881	+	0.788620i	$0.710796\pi$
$230$	16.2911	+	5.92948i	1.07420	+	0.390978i
$231$	−4.79667	−	3.23986i	−0.315597	−	0.213167i
$232$	1.44691	−	8.20584i	0.0949944	−	0.538740i
$233$	−25.4109	−	14.6710i	−1.66472	−	0.961128i	−0.970413	−	0.241452i	$-0.922376\pi$
$233$	−25.4109	−	14.6710i	−1.66472	−	0.961128i	−0.694310	−	0.719676i	$-0.744290\pi$
$234$	−4.50734	−	0.789511i	−0.294654	−	0.0516119i
$235$	8.11317	+	14.0524i	0.529245	+	0.916679i
$236$	−0.204940	+	1.16227i	−0.0133405	+	0.0756575i
$237$	0.546126	−	2.04279i	0.0354747	−	0.132693i
$238$	14.5363	−	8.71046i	0.942247	−	0.564615i
$239$	−17.8608	−	21.2856i	−1.15532	−	1.37685i	−0.913655	−	0.406491i	$-0.866752\pi$
$239$	−17.8608	−	21.2856i	−1.15532	−	1.37685i	−0.241661	−	0.970361i	$-0.577692\pi$
$240$	15.6989	+	1.36453i	1.01336	+	0.0880799i
$241$	0.0739095	+	0.0130322i	0.00476093	+	0.000839480i	0.176028	−	0.984385i	$-0.443675\pi$
$241$	0.0739095	+	0.0130322i	0.00476093	+	0.000839480i	−0.171267	+	0.985225i	$0.554786\pi$
$242$	12.9970	+	7.50384i	0.835481	+	0.482365i
$243$	12.7440	−	8.97724i	0.817527	−	0.575890i
$244$			1.68477i			0.107857i
$245$	13.2763	−	0.431593i	0.848194	−	0.0275735i
$246$	7.27086	+	5.08498i	0.463573	+	0.324207i
$247$	6.89331	+	2.50896i	0.438611	+	0.159641i
$248$	−19.3997	−	7.06092i	−1.23188	−	0.448369i
$249$	6.67081	+	6.66327i	0.422745	+	0.422267i
$250$	19.0832	+	3.36488i	1.20693	+	0.212814i
$251$	−9.64254	+	16.7014i	−0.608632	+	1.05418i	0.382834	+	0.923817i	$0.374948\pi$
$251$	−9.64254	+	16.7014i	−0.608632	+	1.05418i	−0.991466	+	0.130364i	$0.958385\pi$
$252$	−2.84580	−	3.27420i	−0.179268	−	0.206255i
$253$	3.61570	+	6.26258i	0.227317	+	0.393725i
$254$	7.41484	+	20.3721i	0.465248	+	1.27826i
$255$	−11.9594	−	5.56852i	−0.748926	−	0.348715i
$256$	9.36627	−	7.85923i	0.585392	−	0.491202i
$257$	−0.541867	−	3.07308i	−0.0338008	−	0.191694i	0.963232	−	0.268671i	$-0.0865843\pi$
$257$	−0.541867	−	3.07308i	−0.0338008	−	0.191694i	−0.997033	+	0.0769770i	$0.975473\pi$
$258$	0.749113	−	1.60885i	0.0466378	−	0.100163i
$259$	−15.9883	+	13.8646i	−0.993465	+	0.861507i
$260$	0.858526	−	0.495670i	0.0532435	−	0.0307402i
$261$	10.1317	+	3.67465i	0.627134	+	0.227455i
$262$	12.5358	−	7.23755i	0.774464	−	0.447137i
$263$	1.49413	+	4.10510i	0.0921322	+	0.253131i	0.977196	−	0.212338i	$-0.0681078\pi$
$263$	1.49413	+	4.10510i	0.0921322	+	0.253131i	−0.885064	+	0.465469i	$0.845886\pi$
$264$	3.59014	+	3.58608i	0.220958	+	0.220708i
$265$	24.4552	−	4.31211i	1.50227	−	0.264891i
$266$	16.6551	+	27.7946i	1.02119	+	1.70420i
$267$	4.13285	+	8.84986i	0.252926	+	0.541603i
$268$	−0.895540	−	0.751447i	−0.0547038	−	0.0459019i
$269$	0.429514	−	0.743940i	0.0261879	−	0.0453588i	−0.852634	−	0.522508i	$-0.824997\pi$
$269$	0.429514	−	0.743940i	0.0261879	−	0.0453588i	0.878822	+	0.477149i	$0.158330\pi$
$270$	−4.04673	+	15.2057i	−0.246276	+	0.925392i
$271$	4.73193	−	2.73198i	0.287444	−	0.165956i	−0.349344	−	0.936994i	$-0.613596\pi$
$271$	4.73193	−	2.73198i	0.287444	−	0.165956i	0.636789	+	0.771038i	$0.280262\pi$
$272$	−18.0829	+	6.58162i	−1.09643	+	0.399069i
$273$	4.24942	+	1.06239i	0.257187	+	0.0642986i
$274$	24.5566	−	20.6054i	1.48352	−	1.24482i
$275$	1.13590	+	1.35371i	0.0684971	+	0.0816317i
$276$	1.40566	+	5.23414i	0.0846106	+	0.315058i
$277$	18.3788	−	6.68933i	1.10427	−	0.401923i	0.275383	−	0.961334i	$-0.411195\pi$
$277$	18.3788	−	6.68933i	1.10427	−	0.401923i	0.828890	+	0.559412i	$0.188973\pi$
$278$	−12.2038			−0.731934
$279$	13.3251	−	23.1402i	0.797756	−	1.38537i
$280$	−11.4993	−	1.83552i	−0.687216	−	0.109693i
$281$	−13.1907	−	2.32587i	−0.786890	−	0.138750i	−0.234257	−	0.972175i	$-0.575266\pi$
$281$	−13.1907	−	2.32587i	−0.786890	−	0.138750i	−0.552633	+	0.833425i	$0.686377\pi$
$282$	−9.97629	+	21.4258i	−0.594079	+	1.27589i
$283$	6.91516	+	8.24117i	0.411064	+	0.489886i	0.931360	−	0.364099i	$-0.118623\pi$
$283$	6.91516	+	8.24117i	0.411064	+	0.489886i	−0.520297	+	0.853986i	$0.674179\pi$
$284$	0.0627544	+	0.0747877i	0.00372379	+	0.00443784i
$285$	10.6475	−	22.8674i	0.630703	−	1.35455i
$286$	1.89739	+	0.334561i	0.112195	+	0.0197830i
$287$	−6.59387	−	5.35278i	−0.389224	−	0.315964i
$288$	4.52687	+	7.82033i	0.266748	+	0.460817i
$289$	−0.889923			−0.0523484
$290$	−10.2227	+	3.72076i	−0.600298	+	0.218491i
$291$	−2.72597	−	10.1505i	−0.159799	−	0.595032i
$292$	−4.04151	−	4.81648i	−0.236511	−	0.281863i
$293$	6.87623	−	5.76984i	0.401714	−	0.337078i	−0.419442	−	0.907782i	$-0.637774\pi$
$293$	6.87623	−	5.76984i	0.401714	−	0.337078i	0.821156	+	0.570704i	$0.193330\pi$
$294$	11.6154	+	15.4734i	0.677422	+	0.902426i
$295$	−3.85056	+	1.40149i	−0.224188	+	0.0815979i
$296$	16.0667	−	9.27612i	0.933858	−	0.539163i
$297$	−5.36998	+	3.77369i	−0.311598	+	0.218972i
$298$	−5.90370	+	10.2255i	−0.341992	+	0.592348i
$299$	−4.19198	−	3.51749i	−0.242428	−	0.203422i
$300$	0.560391	+	1.19999i	0.0323542	+	0.0692814i
$301$	−0.825378	+	1.48480i	−0.0475740	+	0.0855824i
$302$	−9.69802	+	1.71002i	−0.558058	+	0.0984007i
$303$	8.50542	+	8.49581i	0.488624	+	0.488071i
$304$	−12.5846	−	34.5760i	−0.721778	−	1.98307i
$305$	−5.06588	+	2.92478i	−0.290071	+	0.167473i
$306$	−3.35809	−	18.9195i	−0.191969	−	1.08156i
$307$	17.4494	−	10.0744i	0.995890	−	0.574977i	0.0888603	−	0.996044i	$-0.471678\pi$
$307$	17.4494	−	10.0744i	0.995890	−	0.574977i	0.907030	+	0.421067i	$0.138344\pi$
$308$	1.19663	+	1.37992i	0.0681843	+	0.0786282i
$309$	9.42040	−	20.2320i	0.535908	−	1.15096i
$310$	4.68046	+	26.5442i	0.265832	+	1.50761i
$311$	−2.17551	+	1.82547i	−0.123362	+	0.103513i	−0.702382	−	0.711801i	$-0.747880\pi$
$311$	−2.17551	+	1.82547i	−0.123362	+	0.103513i	0.579020	+	0.815314i	$0.303435\pi$
$312$	−3.48107	−	1.62086i	−0.197077	−	0.0917629i
$313$	−3.18984	−	8.76400i	−0.180300	−	0.495371i	0.816312	−	0.577611i	$-0.196015\pi$
$313$	−3.18984	−	8.76400i	−0.180300	−	0.495371i	−0.996613	+	0.0822401i	$0.973793\pi$
$314$	−15.1541	−	26.2477i	−0.855197	−	1.48124i
$315$	4.90473	−	14.2409i	0.276350	−	0.802386i
$316$	−0.333619	+	0.577845i	−0.0187675	+	0.0325063i
$317$	17.3656	+	3.06203i	0.975352	+	0.171981i	0.638538	−	0.769590i	$-0.279540\pi$
$317$	17.3656	+	3.06203i	0.975352	+	0.171981i	0.336814	+	0.941571i	$0.390651\pi$
$318$	25.5904	+	25.5615i	1.43504	+	1.43342i
$319$	−4.26406	−	1.55199i	−0.238742	−	0.0868949i
$320$	8.52756	+	3.10378i	0.476705	+	0.173506i
$321$	2.03233	+	1.42134i	0.113433	+	0.0793314i
$322$	−4.58356	−	23.7330i	−0.255432	−	1.32259i
$323$			30.8038i			1.71397i
$324$	−4.61846	+	1.69282i	−0.256581	+	0.0940457i
$325$	−1.15810	−	0.668627i	−0.0642396	−	0.0370887i
$326$	−2.22858	−	0.392958i	−0.123429	−	0.0217639i
$327$	−3.26561	−	0.283843i	−0.180589	−	0.0156966i
$328$	4.78583	+	5.70353i	0.264253	+	0.314925i
$329$	10.9919	−	19.7738i	0.606005	−	1.09016i
$330$	1.71107	−	6.40027i	0.0941913	−	0.352323i
$331$	4.75223	−	26.9513i	0.261206	−	1.48138i	−0.518418	−	0.855128i	$-0.673479\pi$
$331$	4.75223	−	26.9513i	0.261206	−	1.48138i	0.779624	−	0.626248i	$-0.215410\pi$
$332$	−1.48760	−	2.57659i	−0.0816424	−	0.141409i
$333$	8.23265	+	22.5397i	0.451146	+	1.23517i
$334$	21.7968	+	12.5844i	1.19267	+	0.688588i
$335$	0.704828	−	3.99728i	0.0385089	−	0.218395i
$336$	−9.61866	−	19.7532i	−0.524741	−	1.07763i
$337$	−14.1672	−	5.15645i	−0.771738	−	0.280889i	−0.0740145	−	0.997257i	$-0.523581\pi$
$337$	−14.1672	−	5.15645i	−0.771738	−	0.280889i	−0.697723	+	0.716368i	$0.745803\pi$
$338$	18.9943	−	3.34921i	1.03315	−	0.182173i
$339$	0.863690	+	1.23199i	0.0469092	+	0.0669128i
$340$	3.18889	+	2.67580i	0.172942	+	0.145116i
$341$	−5.62141	+	9.73657i	−0.304417	+	0.527265i
$342$	36.1758	−	6.42096i	1.95616	−	0.347206i
$343$	−10.0307	−	15.5688i	−0.541604	−	0.840634i
$344$	0.957269	−	1.14083i	0.0516125	−	0.0615094i
$345$	−13.2981	+	13.3131i	−0.715944	+	0.716755i
$346$	−5.95418	+	16.3590i	−0.320099	+	0.879464i
$347$	−23.8521	+	4.20577i	−1.28045	+	0.225777i	−0.772170	−	0.635416i	$-0.780829\pi$
$347$	−23.8521	+	4.20577i	−1.28045	+	0.225777i	−0.508278	+	0.861193i	$0.669718\pi$
$348$	−2.78689	−	1.94905i	−0.149393	−	0.104480i
$349$	1.92048	+	5.27647i	0.102801	+	0.282443i	0.980421	−	0.196914i	$-0.0630921\pi$
$349$	1.92048	+	5.27647i	0.102801	+	0.282443i	−0.877620	+	0.479357i	$0.840870\pi$
$350$	−2.11017	−	5.51703i	−0.112793	−	0.294898i
$351$	2.84187	−	4.07331i	0.151688	−	0.217417i
$352$	−1.90226	−	3.29481i	−0.101391	−	0.175614i
$353$	−3.76585	+	21.3572i	−0.200436	+	1.13673i	0.704026	+	0.710174i	$0.251384\pi$
$353$	−3.76585	+	21.3572i	−0.200436	+	1.13673i	−0.904462	+	0.426555i	$0.859727\pi$
$354$	−4.89105	−	3.42063i	−0.259956	−	0.181804i
$355$	−0.115934	+	0.318526i	−0.00615313	+	0.0169056i
$356$	−0.535195	−	3.03524i	−0.0283653	−	0.160868i
$357$	1.91092	+	18.2937i	0.101137	+	0.968206i
$358$	−28.9002	−	24.2501i	−1.52742	−	1.28166i
$359$		−	21.9401i		−	1.15795i	−0.815344	−	0.578976i	$-0.803452\pi$
$359$		−	21.9401i		−	1.15795i	0.815344	−	0.578976i	$-0.196548\pi$
$360$	−6.58910	+	11.4425i	−0.347276	+	0.603073i
$361$	−39.8996			−2.09998
$362$	−32.4526	+	11.8118i	−1.70567	+	0.620813i
$363$	−13.3380	+	9.35061i	−0.700063	+	0.490780i
$364$	−1.20807	−	0.671546i	−0.0633199	−	0.0351986i
$365$	7.46637	−	20.5137i	0.390808	−	1.07374i
$366$	−7.72398	−	3.59643i	−0.403739	−	0.187989i
$367$	7.32658	−	8.73148i	0.382444	−	0.455780i	−0.540140	−	0.841575i	$-0.681629\pi$
$367$	7.32658	−	8.73148i	0.382444	−	0.455780i	0.922584	+	0.385796i	$0.126073\pi$
$368$			27.4481i			1.43083i
$369$	−8.33452	+	4.82452i	−0.433878	+	0.251154i
$370$	−20.9766	−	12.1109i	−1.09052	−	0.629613i
$371$	−22.6830	−	26.1573i	−1.17764	−	1.35802i
$372$	−5.95470	+	5.96144i	−0.308737	+	0.309086i
$373$	−28.7091	+	24.0898i	−1.48650	+	1.24732i	−0.587617	+	0.809139i	$0.699934\pi$
$373$	−28.7091	+	24.0898i	−1.48650	+	1.24732i	−0.898885	+	0.438184i	$0.855622\pi$
$374$	1.40488	+	7.96745i	0.0726444	+	0.411987i
$375$	−12.0538	+	17.2354i	−0.622457	+	0.890031i
$376$	−12.7484	+	15.1929i	−0.657448	+	0.783516i
$377$	3.43384			0.176852
$378$	21.0857	−	6.05744i	1.08453	−	0.311561i
$379$	4.71335			0.242108			0.121054	−	0.992646i	$-0.461373\pi$
$379$	4.71335			0.242108			0.121054	+	0.992646i	$0.461373\pi$
$380$	−5.11635	+	6.09743i	−0.262463	+	0.312792i
$381$	−23.4423	−	2.03758i	−1.20099	−	0.104388i
$382$	6.07079	+	34.4292i	0.310609	+	1.76155i
$383$	5.74641	−	4.82181i	0.293628	−	0.246383i	−0.484058	−	0.875036i	$-0.660838\pi$
$383$	5.74641	−	4.82181i	0.293628	−	0.246383i	0.777686	+	0.628653i	$0.216393\pi$
$384$	6.13449	+	22.8425i	0.313049	+	1.16568i
$385$	−2.07186	+	5.99365i	−0.105592	+	0.305464i
$386$	20.1309	+	11.6226i	1.02464	+	0.591574i
$387$	1.23983	+	1.47419i	0.0630243	+	0.0749371i
$388$			3.31647i			0.168368i
$389$	14.8316	−	17.6756i	0.751993	−	0.896190i	−0.245320	−	0.969442i	$-0.578893\pi$
$389$	14.8316	−	17.6756i	0.751993	−	0.896190i	0.997313	+	0.0732516i	$0.0233376\pi$
$390$	0.439770	+	4.99407i	0.0222686	+	0.252884i
$391$	7.85923	−	21.5931i	0.397458	−	1.09201i
$392$	6.04576	+	15.0682i	0.305357	+	0.761060i
$393$	1.37816	+	15.6505i	0.0695191	+	0.789464i
$394$	−3.57382	+	1.30076i	−0.180047	+	0.0655316i
$395$	−2.31666			−0.116564
$396$	1.94535	−	0.710543i	0.0977577	−	0.0357061i
$397$		−	17.4192i		−	0.874245i	−0.899402	−	0.437122i	$-0.855998\pi$
$397$		−	17.4192i		−	0.874245i	0.899402	−	0.437122i	$-0.144002\pi$
$398$	12.5421	+	10.5240i	0.628677	+	0.527522i
$399$	−34.9791	+	3.65385i	−1.75115	+	0.182921i
$400$	1.16475	+	6.60560i	0.0582373	+	0.330280i
$401$	7.35970	−	20.2206i	0.367526	−	1.00977i	−0.608773	−	0.793344i	$-0.708338\pi$
$401$	7.35970	−	20.2206i	0.367526	−	1.00977i	0.976299	−	0.216425i	$-0.0694398\pi$
$402$	5.35674	−	2.50158i	0.267170	−	0.124767i
$403$	1.47737	−	8.37857i	0.0735929	−	0.417366i
$404$	−1.89672	−	3.28521i	−0.0943651	−	0.163445i
$405$	−13.1078	−	10.9483i	−0.651330	−	0.544025i
$406$	11.7760	+	9.55954i	0.584433	+	0.474432i
$407$	−3.45553	−	9.49398i	−0.171284	−	0.470599i
$408$	1.39626	−	16.0639i	0.0691251	−	0.795283i
$409$	26.2126	−	4.62199i	1.29613	−	0.228543i	0.517314	−	0.855796i	$-0.326932\pi$
$409$	26.2126	−	4.62199i	1.29613	−	0.228543i	0.778815	+	0.627253i	$0.215821\pi$
$410$	3.32468	−	9.13448i	0.164194	−	0.451120i
$411$	9.02424	+	33.6029i	0.445133	+	1.65751i
$412$	−4.52671	+	5.39472i	−0.223015	+	0.265779i
$413$	4.43564	+	3.60077i	0.218264	+	0.177182i
$414$	−26.9969	−	4.72881i	−1.32683	−	0.232408i
$415$	5.16496	−	8.94597i	0.253538	−	0.439140i
$416$	2.20545	+	1.85059i	0.108131	+	0.0907326i
$417$	5.59114	−	12.0080i	0.273799	−	0.588032i
$418$	−15.2344	+	2.68624i	−0.745140	+	0.131388i
$419$	−5.47160	−	1.99150i	−0.267305	−	0.0972911i	0.204890	−	0.978785i	$-0.434316\pi$
$419$	−5.47160	−	1.99150i	−0.267305	−	0.0972911i	−0.472196	+	0.881494i	$0.656538\pi$
$420$	−2.66023	+	3.93852i	−0.129806	+	0.192180i
$421$	−0.858573	+	4.86921i	−0.0418443	+	0.237311i	−0.998556	−	0.0537277i	$-0.982890\pi$
$421$	−0.858573	+	4.86921i	−0.0418443	+	0.237311i	0.956711	+	0.291039i	$0.0940008\pi$
$422$	−15.7762	−	9.10839i	−0.767973	−	0.443389i
$423$	−16.5114	−	19.6324i	−0.802813	−	0.954561i
$424$	15.1760	+	26.2856i	0.737011	+	1.27654i
$425$	0.975096	−	5.53004i	0.0472991	−	0.268246i
$426$	−0.476830	+	0.128055i	−0.0231025	+	0.00620429i
$427$	7.12840	+	3.96257i	0.344968	+	0.191762i
$428$	−0.503027	−	0.599485i	−0.0243147	−	0.0289772i
$429$	−1.19848	+	1.71366i	−0.0578630	+	0.0827365i
$430$	−1.91481	−	0.337633i	−0.0923405	−	0.0162821i
$431$	−10.1898	−	5.88309i	−0.490826	−	0.283378i	0.234091	−	0.972215i	$-0.424789\pi$
$431$	−10.1898	−	5.88309i	−0.490826	−	0.283378i	−0.724917	+	0.688836i	$0.758122\pi$
$432$	−24.8138	+	2.21335i	−1.19386	+	0.106490i
$433$			28.6389i			1.37630i	0.725569	+	0.688150i	$0.241577\pi$
$433$			28.6389i			1.37630i	−0.725569	+	0.688150i	$0.758423\pi$
$434$	28.3917	−	24.6205i	1.36285	−	1.18182i
$435$	1.02246	−	11.7633i	0.0490230	−	0.564009i
$436$	0.971968	+	0.353767i	0.0465488	+	0.0169424i
$437$	41.2878	+	15.0275i	1.97506	+	0.718863i
$438$	30.7088	−	8.24701i	1.46732	−	0.394057i
$439$	10.5707	+	1.86390i	0.504513	+	0.0889593i	0.420111	−	0.907473i	$-0.361991\pi$
$439$	10.5707	+	1.86390i	0.504513	+	0.0889593i	0.0844017	+	0.996432i	$0.473102\pi$
$440$	2.77971	−	4.81460i	0.132517	−	0.229527i
$441$	−20.5467	+	4.33988i	−0.978413	+	0.206661i
$442$	−3.06112	−	5.30202i	−0.145603	−	0.252191i
$443$	5.48081	+	15.0584i	0.260401	+	0.715447i	0.999140	+	0.0414550i	$0.0131993\pi$
$443$	5.48081	+	15.0584i	0.260401	+	0.715447i	−0.738739	+	0.673991i	$0.764578\pi$
$444$	−0.664204	−	7.54276i	−0.0315217	−	0.357963i
$445$	8.19744	−	6.87847i	0.388596	−	0.326071i
$446$	3.04161	+	17.2498i	0.144024	+	0.816802i
$447$	−7.35666	−	10.4938i	−0.347958	−	0.496338i
$448$	−2.39926	−	12.4230i	−0.113354	−	0.586931i
$449$	−15.5368	+	8.97017i	−0.733226	+	0.423328i	−0.819601	−	0.572934i	$-0.805805\pi$
$449$	−15.5368	+	8.97017i	−0.733226	+	0.423328i	0.0863750	+	0.996263i	$0.472472\pi$
$450$	−6.69769	+	0.00757502i	−0.315732	+	0.000357090i
$451$	3.51145	−	2.02734i	0.165348	−	0.0954635i
$452$	−0.162381	−	0.446138i	−0.00763775	−	0.0209846i
$453$	2.76055	−	10.3258i	0.129702	−	0.485151i
$454$	23.6526	−	4.17059i	1.11007	−	0.195736i
$455$	−0.0779720	−	4.79829i	−0.00365538	−	0.224948i
$456$	30.7156	+	2.66977i	1.43839	+	0.125023i
$457$	−17.5604	−	14.7349i	−0.821441	−	0.689271i	0.131868	−	0.991267i	$-0.457902\pi$
$457$	−17.5604	−	14.7349i	−0.821441	−	0.689271i	−0.953309	+	0.301997i	$0.902347\pi$
$458$	−17.9300	+	31.0556i	−0.837813	+	1.45113i
$459$	20.1545	+	5.36374i	0.940730	+	0.250358i
$460$	5.14218	−	2.96884i	0.239755	−	0.138423i
$461$	−11.2905	+	4.10942i	−0.525852	+	0.191395i	−0.591285	−	0.806462i	$-0.701379\pi$
$461$	−11.2905	+	4.10942i	−0.525852	+	0.191395i	0.0654330	+	0.997857i	$0.479157\pi$
$462$	−8.88075	+	2.54037i	−0.413170	+	0.118189i
$463$	−0.859491	+	0.721198i	−0.0399439	+	0.0335169i	−0.662541	−	0.749026i	$-0.730522\pi$
$463$	−0.859491	+	0.721198i	−0.0399439	+	0.0335169i	0.622597	+	0.782543i	$0.286078\pi$
$464$	−11.0712	−	13.1941i	−0.513968	−	0.612523i
$465$	−28.2626	−	7.55581i	−1.31065	−	0.350393i
$466$	−43.9998	+	16.0146i	−2.03825	+	0.741863i
$467$	−13.1684			−0.609360			−0.304680	−	0.952455i	$-0.598550\pi$
$467$	−13.1684			−0.609360			−0.304680	+	0.952455i	$0.598550\pi$
$468$	−1.19943	+	1.00876i	−0.0554438	+	0.0466298i
$469$	−5.28573	+	2.02170i	−0.244072	+	0.0933533i
$470$	25.5005	+	4.49642i	1.17625	+	0.207404i
$471$	32.7694	−	2.88562i	1.50993	−	0.132963i
$472$	−3.21939	−	3.83672i	−0.148184	−	0.176599i
$473$	−0.521315	−	0.621279i	−0.0239701	−	0.0285664i
$474$	−1.93701	−	2.76301i	−0.0889698	−	0.126909i
$475$	10.5739	+	1.86447i	0.485164	+	0.0855476i
$476$	0.914847	−	5.73142i	0.0419319	−	0.262699i
$477$	−36.8755	+	13.4688i	−1.68841	+	0.616696i
$478$	−44.3413			−2.02812
$479$	21.0370	−	7.65686i	0.961207	−	0.349851i	0.186701	−	0.982417i	$-0.440221\pi$
$479$	21.0370	−	7.65686i	0.961207	−	0.349851i	0.774506	+	0.632566i	$0.217998\pi$
$480$	6.99627	−	7.00418i	0.319334	−	0.319696i
$481$	4.91442	+	5.85678i	0.224078	+	0.267046i
$482$	0.0917442	−	0.0769825i	0.00417883	−	0.00350646i
$483$	25.4521	+	6.36321i	1.15811	+	0.289536i
$484$	4.83004	−	1.75799i	0.219547	−	0.0799087i
$485$	−9.97214	+	5.75742i	−0.452811	+	0.261431i
$486$	2.09800	−	24.7873i	0.0951673	−	1.12437i
$487$	14.1370	−	24.4860i	0.640609	−	1.10957i	−0.344688	−	0.938717i	$-0.612015\pi$
$487$	14.1370	−	24.4860i	0.640609	−	1.10957i	0.985297	−	0.170850i	$-0.0546514\pi$
$488$	−5.47703	−	4.59577i	−0.247934	−	0.208041i
$489$	1.40767	−	2.01278i	0.0636571	−	0.0910212i
$490$	13.0907	−	16.6723i	0.591376	−	0.753178i
$491$	36.4384	−	6.42508i	1.64444	−	0.289960i	0.726647	−	0.687012i	$-0.241078\pi$
$491$	36.4384	−	6.42508i	1.64444	−	0.289960i	0.917796	+	0.397052i	$0.129967\pi$
$492$	2.93480	−	0.788157i	0.132311	−	0.0355329i
$493$	4.93168	+	13.5497i	0.222112	+	0.610247i
$494$	10.1379	−	5.85312i	0.456126	−	0.263344i
$495$	5.51365	+	4.61589i	0.247820	+	0.207469i
$496$	−36.9569	+	21.3371i	−1.65941	+	0.958063i
$497$	0.464030	−	0.0896182i	0.0208146	−	0.00401993i
$498$	14.9881	−	1.31983i	0.671633	−	0.0591430i
$499$	−2.84889	−	16.1568i	−0.127534	−	0.723279i	−0.979771	−	0.200123i	$-0.935866\pi$
$499$	−2.84889	−	16.1568i	−0.127534	−	0.723279i	0.852237	−	0.523156i	$-0.175245\pi$
$500$	5.08400	−	4.26598i	0.227363	−	0.190780i
$501$	−22.3686	+	15.6816i	−0.999357	+	0.700600i
$502$	10.5257	+	28.9190i	0.469783	+	1.29072i
$503$	4.98173	+	8.62860i	0.222124	+	0.384730i	0.955453	−	0.295144i	$-0.0953676\pi$
$503$	4.98173	+	8.62860i	0.222124	+	0.384730i	−0.733329	+	0.679874i	$0.762034\pi$
$504$	18.4069	−	0.319936i	0.819910	−	0.0142511i
$505$	6.58543	−	11.4063i	0.293048	−	0.507574i
$506$	11.3645	+	2.00386i	0.505213	+	0.0890827i
$507$	−5.40673	+	20.2239i	−0.240122	+	0.898177i
$508$	6.97730	+	2.53953i	0.309568	+	0.112673i
$509$	6.46284	+	2.35228i	0.286461	+	0.104263i	0.481254	−	0.876581i	$-0.340181\pi$
$509$	6.46284	+	2.35228i	0.286461	+	0.104263i	−0.194794	+	0.980844i	$0.562404\pi$
$510$	−19.0746	+	8.90778i	−0.844638	+	0.394443i
$511$	−29.8844	+	5.77159i	−1.32201	+	0.255320i
$512$			7.79950i			0.344692i
$513$	−10.2559	+	38.5370i	−0.452810	+	1.70145i
$514$	−4.31250	−	2.48982i	−0.190216	−	0.109821i
$515$	−24.0796	−	4.24588i	−1.06107	−	0.187096i
$516$	−0.257189	−	0.550730i	−0.0113221	−	0.0242446i
$517$	6.94259	+	8.27386i	0.305335	+	0.363884i
$518$	0.548705	+	33.7666i	0.0241087	+	1.48362i
$519$	−13.3686	−	13.3535i	−0.586816	−	0.586152i
$520$	−0.730537	+	4.14308i	−0.0320362	+	0.181686i
$521$	−6.74329	−	11.6797i	−0.295429	−	0.511698i	0.679656	−	0.733531i	$-0.262129\pi$
$521$	−6.74329	−	11.6797i	−0.295429	−	0.511698i	−0.975085	+	0.221833i	$0.928796\pi$
$522$	14.8846	−	8.61612i	0.651483	−	0.377117i
$523$	30.3095	+	17.4992i	1.32534	+	0.765188i	0.984576	−	0.174960i	$-0.0559796\pi$
$523$	30.3095	+	17.4992i	1.32534	+	0.765188i	0.340768	+	0.940147i	$0.389313\pi$
$524$	0.860881	−	4.88230i	0.0376078	−	0.213284i
$525$	6.39527	+	0.451310i	0.279113	+	0.0196968i
$526$	6.55088	+	2.38432i	0.285632	+	0.103961i
$527$	35.1830	−	6.20371i	1.53260	−	0.270238i
$528$	10.4486	−	0.920090i	0.454718	−	0.0400418i
$529$	−7.48901	−	6.28403i	−0.325609	−	0.273219i
$530$	19.8137	−	34.3183i	0.860652	−	1.49069i
$531$	5.60656	−	3.24541i	0.243304	−	0.140839i
$532$	10.9590	+	1.74927i	0.475131	+	0.0758403i
$533$	−1.97227	+	2.35046i	−0.0854284	+	0.101810i
$534$	15.0578	+	4.02559i	0.651613	+	0.174204i
$535$	0.929304	−	2.55324i	0.0401773	−	0.110386i
$536$	4.88576	−	0.861490i	0.211032	−	0.0372107i
$537$	37.1016	−	17.3263i	1.60105	−	0.747685i
$538$	−0.468851	−	1.28816i	−0.0202136	−	0.0555364i
$539$	8.65300	−	1.81747i	0.372711	−	0.0782840i
$540$	3.09856	+	4.40927i	0.133341	+	0.189745i
$541$	0.619421	+	1.07287i	0.0266310	+	0.0461262i	0.879034	−	0.476760i	$-0.158189\pi$
$541$	0.619421	+	1.07287i	0.0266310	+	0.0461262i	−0.852403	+	0.522886i	$0.824855\pi$
$542$	1.51410	−	8.58688i	0.0650361	−	0.368838i
$543$	3.24585	−	37.3434i	0.139293	−	1.60256i
$544$	−4.13483	+	11.3603i	−0.177279	+	0.487071i
$545$	0.623617	+	3.53671i	0.0267128	+	0.151496i
$546$	5.65758	−	4.10495i	0.242122	−	0.175675i
$547$	21.3784	+	17.9386i	0.914076	+	0.767000i	0.972890	−	0.231269i	$-0.0742876\pi$
$547$	21.3784	+	17.9386i	0.914076	+	0.767000i	−0.0588145	+	0.998269i	$0.518732\pi$
$548$		−	10.9791i		−	0.469003i
$549$	7.07745	−	5.95234i	0.302058	−	0.254040i
$550$	2.81999			0.120245
$551$	−25.9082	+	9.42980i	−1.10372	+	0.401723i
$552$	−20.8500	−	9.70819i	−0.887437	−	0.413208i
$553$	1.66024	+	2.77065i	0.0706004	+	0.117820i
$554$	10.6748	−	29.3287i	0.453527	−	1.24606i
$555$	21.5269	−	15.0915i	0.913767	−	0.640597i
$556$	−2.68666	+	3.20184i	−0.113940	+	0.135788i
$557$		−	3.08064i		−	0.130531i	−0.997868	−	0.0652654i	$-0.979211\pi$
$557$		−	3.08064i		−	0.130531i	0.997868	−	0.0652654i	$-0.0207894\pi$
$558$	−14.6194	−	40.0255i	−0.618887	−	1.69441i
$559$	0.531504	+	0.306864i	0.0224802	+	0.0129790i
$560$	−18.1855	+	15.7700i	−0.768478	+	0.666404i
$561$	−8.48324	−	2.26794i	−0.358163	−	0.0957524i
$562$	−16.3736	+	13.7391i	−0.690681	+	0.579550i
$563$	−0.842562	−	4.77841i	−0.0355098	−	0.201386i	0.961892	−	0.273431i	$-0.0881585\pi$
$563$	−0.842562	−	4.77841i	−0.0355098	−	0.201386i	−0.997401	+	0.0720452i	$0.977047\pi$
$564$	3.42510	+	7.33433i	0.144223	+	0.308831i
$565$	1.05958	−	1.26276i	0.0445768	−	0.0531245i
$566$	17.1676			0.721610
$567$	−3.70011	+	23.5225i	−0.155390	+	0.987853i
$568$	−0.414310			−0.0173841
$569$	5.87514	−	7.00171i	0.246298	−	0.293527i	−0.628705	−	0.777644i	$-0.716415\pi$
$569$	5.87514	−	7.00171i	0.246298	−	0.293527i	0.875003	+	0.484117i	$0.160859\pi$
$570$	−17.0324	−	36.4723i	−0.713410	−	1.52766i
$571$	−7.38382	−	41.8757i	−0.309003	−	1.75244i	−0.604036	−	0.796957i	$-0.706442\pi$
$571$	−7.38382	−	41.8757i	−0.309003	−	1.75244i	0.295033	−	0.955487i	$-0.404669\pi$
$572$	0.505487	−	0.424154i	0.0211355	−	0.0177348i
$573$	−36.6581	−	9.80028i	−1.53141	−	0.409413i
$574$	−13.3072	+	2.57002i	−0.555431	+	0.107270i
$575$	−6.93646	−	4.00477i	−0.289271	−	0.167010i
$576$	−14.1315	−	2.47529i	−0.588813	−	0.103137i
$577$			36.8985i			1.53611i	0.640386	+	0.768053i	$0.278774\pi$
$577$			36.8985i			1.53611i	−0.640386	+	0.768053i	$0.721226\pi$
$578$	−0.912842	+	1.08788i	−0.0379692	+	0.0452500i
$579$	−20.6590	+	14.4830i	−0.858561	+	0.601894i
$580$	−1.27433	+	3.50121i	−0.0529139	+	0.145380i
$581$	−14.4005	+	0.234008i	−0.597435	+	0.00970829i
$582$	−15.2046	−	7.07955i	−0.630251	−	0.293457i
$583$	15.5324	−	5.65334i	0.643287	−	0.234137i
$584$	26.6824			1.10413
$585$	−5.11541	−	1.85531i	−0.211496	−	0.0767076i
$586$		−	14.3243i		−	0.591730i
$587$	21.4793	+	18.0233i	0.886545	+	0.743900i	0.967514	−	0.252817i	$-0.0813570\pi$
$587$	21.4793	+	18.0233i	0.886545	+	0.743900i	−0.0809690	+	0.996717i	$0.525801\pi$
$588$	6.61680	+	0.359008i	0.272872	+	0.0148052i
$589$	11.8620	+	67.2729i	0.488766	+	2.77193i
$590$	−2.23648	+	6.14469i	−0.0920746	+	0.252973i
$591$	0.357447	−	4.11242i	0.0147034	−	0.169162i
$592$	6.65920	−	37.7662i	0.273691	−	1.55218i
$593$	−12.0746	−	20.9138i	−0.495845	−	0.858828i	0.504144	−	0.863620i	$-0.331808\pi$
$593$	−12.0746	−	20.9138i	−0.495845	−	0.858828i	−0.999989	+	0.00479135i	$0.998475\pi$
$594$	−0.895142	+	10.4354i	−0.0367281	+	0.428169i
$595$	18.8217	−	7.19898i	0.771616	−	0.295129i
$596$	1.38311	+	3.80007i	0.0566545	+	0.155657i
$597$	−16.1013	+	7.51924i	−0.658982	+	0.307742i
$598$	−8.59988	+	1.51639i	−0.351675	+	0.0620098i
$599$	−12.4973	+	34.3360i	−0.510625	+	1.40293i	0.369963	+	0.929046i	$0.379370\pi$
$599$	−12.4973	+	34.3360i	−0.510625	+	1.40293i	−0.880588	+	0.473883i	$0.842852\pi$
$600$	−5.42969	−	1.45159i	−0.221666	−	0.0592610i
$601$	7.41347	−	8.83503i	0.302402	−	0.360388i	−0.593349	−	0.804945i	$-0.702195\pi$
$601$	7.41347	−	8.83503i	0.302402	−	0.360388i	0.895750	+	0.444557i	$0.146639\pi$
$602$	0.968453	+	2.53202i	0.0394712	+	0.103197i
$603$	0.00725744	+	6.41689i	0.000295546	+	0.261316i
$604$	−1.68637	+	2.92088i	−0.0686175	+	0.118849i
$605$	13.6710	+	11.4714i	0.555806	+	0.466377i
$606$	19.1101	−	1.68281i	0.776296	−	0.0683595i
$607$	−23.6818	+	4.17574i	−0.961215	+	0.169488i	−0.632173	−	0.774827i	$-0.717837\pi$
$607$	−23.6818	+	4.17574i	−0.961215	+	0.169488i	−0.329042	+	0.944315i	$0.606726\pi$
$608$	−21.7219	−	7.90614i	−0.880941	−	0.320636i
$609$	−14.8013	+	7.20737i	−0.599779	+	0.292057i
$610$	−1.62095	+	9.19287i	−0.0656304	+	0.372208i
$611$	−7.07828	−	4.08664i	−0.286356	−	0.165328i
$612$	−5.70311	−	3.28409i	−0.230534	−	0.132752i
$613$	16.8432	+	29.1732i	0.680289	+	1.17830i	0.974893	+	0.222676i	$0.0714790\pi$
$613$	16.8432	+	29.1732i	0.680289	+	1.17830i	−0.294604	+	0.955620i	$0.595188\pi$
$614$	5.58336	−	31.6648i	0.225326	−	1.27789i
$615$	7.46472	+	7.45628i	0.301007	+	0.300666i
$616$	−7.75017	+	0.125940i	−0.312263	+	0.00507426i
$617$	5.69508	+	6.78713i	0.229275	+	0.273240i	0.868401	−	0.495863i	$-0.165148\pi$
$617$	5.69508	+	6.78713i	0.229275	+	0.273240i	−0.639126	+	0.769102i	$0.720704\pi$
$618$	−15.0695	−	32.2690i	−0.606184	−	1.29805i
$619$	−3.94848	−	0.696223i	−0.158703	−	0.0279836i	0.0937322	−	0.995597i	$-0.470120\pi$
$619$	−3.94848	−	0.696223i	−0.158703	−	0.0279836i	−0.252435	+	0.967614i	$0.581231\pi$
$620$	7.99466	+	4.61572i	0.321073	+	0.185372i
$621$	17.0215	−	24.3972i	0.683050	−	0.979028i
$622$			4.53193i			0.181714i
$623$	−14.1011	−	4.87441i	−0.564949	−	0.195289i
$624$	−7.19184	+	3.35856i	−0.287904	+	0.134450i
$625$	15.0798	+	5.48858i	0.603190	+	0.219543i
$626$	−13.9855	−	5.09031i	−0.558973	−	0.203450i
$627$	4.33649	−	16.2207i	0.173183	−	0.647792i
$628$	−10.2227	−	1.80253i	−0.407929	−	0.0719288i
$629$	−16.0523	+	27.8035i	−0.640049	+	1.10860i
$630$	−12.3777	−	20.6035i	−0.493141	−	0.820862i
$631$	−6.55511	−	11.3538i	−0.260955	−	0.451987i	0.705541	−	0.708669i	$-0.250704\pi$
$631$	−6.55511	−	11.3538i	−0.260955	−	0.451987i	−0.966496	+	0.256682i	$0.917371\pi$
$632$	−0.968460	−	2.66082i	−0.0385233	−	0.105842i
$633$	16.1901	−	11.3501i	0.643498	−	0.451124i
$634$	21.5561	−	18.0877i	0.856100	−	0.718354i
$635$	4.47666	+	25.3884i	0.177651	+	1.00751i
$636$	12.3402	−	1.08666i	0.489320	−	0.0430887i
$637$	−5.68272	+	3.53195i	−0.225158	+	0.139941i
$638$	−6.27111	+	3.62063i	−0.248276	+	0.143342i
$639$	0.0924582	−	0.527847i	0.00365759	−	0.0208813i
$640$	22.4412	−	12.9564i	0.887066	−	0.512148i
$641$	2.73177	+	7.50547i	0.107898	+	0.296448i	0.981878	−	0.189514i	$-0.0606913\pi$
$641$	2.73177	+	7.50547i	0.107898	+	0.296448i	−0.873980	+	0.485963i	$0.838469\pi$
$642$	3.82218	−	1.02647i	0.150849	−	0.0405114i
$643$	−38.0449	+	6.70834i	−1.50034	+	0.264551i	−0.862675	−	0.505759i	$-0.831213\pi$
$643$	−38.0449	+	6.70834i	−1.50034	+	0.264551i	−0.637669	+	0.770310i	$0.720101\pi$
$644$	−7.23577	−	4.02226i	−0.285129	−	0.158499i
$645$	1.20948	−	1.72940i	0.0476234	−	0.0680952i
$646$	37.6560	+	31.5972i	1.48156	+	1.24317i
$647$	19.9091	−	34.4836i	0.782707	−	1.35569i	−0.147652	−	0.989039i	$-0.547171\pi$
$647$	19.9091	−	34.4836i	0.782707	−	1.35569i	0.930359	−	0.366650i	$-0.119495\pi$
$648$	7.09516	−	19.6319i	0.278724	−	0.771212i
$649$	−2.36212	+	1.36377i	−0.0927214	+	0.0535327i
$650$	−2.00528	+	0.729863i	−0.0786536	+	0.0286276i
$651$	11.2179	+	39.2160i	0.439663	+	1.53700i
$652$	−0.593720	+	0.498190i	−0.0232519	+	0.0195106i
$653$	−18.7469	−	22.3417i	−0.733623	−	0.874298i	0.262255	−	0.964999i	$-0.415534\pi$
$653$	−18.7469	−	22.3417i	−0.733623	−	0.874298i	−0.995878	+	0.0907005i	$0.971089\pi$
$654$	−3.69670	+	3.70088i	−0.144552	+	0.144716i
$655$	16.1749	−	5.88717i	0.632005	−	0.230031i
$656$	15.3902			0.600888
$657$	−5.95449	+	33.9944i	−0.232307	+	1.32625i
$658$	−12.8973	−	33.7201i	−0.502790	−	1.31454i
$659$	20.9180	+	3.68841i	0.814851	+	0.143680i	0.565516	−	0.824737i	$-0.308677\pi$
$659$	20.9180	+	3.68841i	0.814851	+	0.143680i	0.249335	+	0.968417i	$0.419788\pi$
$660$	−1.30251	−	1.85795i	−0.0507003	−	0.0723204i
$661$	−14.2388	−	16.9691i	−0.553824	−	0.660021i	0.414404	−	0.910093i	$-0.363990\pi$
$661$	−14.2388	−	16.9691i	−0.553824	−	0.660021i	−0.968227	+	0.250072i	$0.919546\pi$
$662$	−28.0718	−	33.4547i	−1.09104	−	1.30025i
$663$	6.61939	−	0.582893i	0.257076	−	0.0226377i
$664$	12.4341	+	2.19247i	0.482538	+	0.0850845i
$665$	13.7651	+	35.9888i	0.533786	+	1.39558i
$666$	35.9982	+	13.0562i	1.39490	+	0.505917i
$667$	20.5672			0.796363
$668$	8.10028	−	2.94826i	0.313409	−	0.114072i
$669$	−18.3665	−	4.91017i	−0.710091	−	0.189838i
$670$	−4.16348	−	4.96184i	−0.160849	−	0.191693i
$671$	−2.98271	+	2.50279i	−0.115146	+	0.0966192i
$672$	−13.3906	−	3.34776i	−0.516555	−	0.129142i
$673$	15.9545	−	5.80696i	0.615000	−	0.223842i	−0.0156895	−	0.999877i	$-0.504994\pi$
$673$	15.9545	−	5.80696i	0.615000	−	0.223842i	0.630690	+	0.776035i	$0.282772\pi$
$674$	−20.8356	+	12.0294i	−0.802556	+	0.463356i
$675$	3.06108	−	6.59369i	0.117821	−	0.253791i
$676$	3.30288	−	5.72076i	0.127034	−	0.220029i
$677$	32.1184	+	26.9506i	1.23441	+	1.03579i	0.997940	+	0.0641557i	$0.0204354\pi$
$677$	32.1184	+	26.9506i	1.23441	+	1.03579i	0.236471	+	0.971638i	$0.424009\pi$
$678$	2.39198	+	0.207908i	0.0918635	+	0.00798467i
$679$	14.0322	+	7.80029i	0.538507	+	0.299348i
$680$	−17.3975	+	3.06765i	−0.667163	+	0.117639i
$681$	−6.73273	+	25.1838i	−0.257999	+	0.965046i
$682$	6.13625	+	16.8592i	0.234969	+	0.645572i
$683$	1.35935	−	0.784820i	0.0520140	−	0.0300303i	−0.473767	−	0.880650i	$-0.657106\pi$
$683$	1.35935	−	0.784820i	0.0520140	−	0.0300303i	0.525782	+	0.850620i	$0.323773\pi$
$684$	6.27947	−	10.9048i	0.240101	−	0.416956i
$685$	33.0125	−	19.0598i	1.26134	−	0.728236i
$686$	−29.3209	−	3.70778i	−1.11948	−	0.141564i
$687$	−22.3427	−	31.8704i	−0.852428	−	1.21593i
$688$	−0.534555	−	3.03161i	−0.0203797	−	0.115579i
$689$	−9.58186	+	8.04014i	−0.365040	+	0.306305i
$690$	2.63402	+	29.9122i	0.100276	+	1.13874i
$691$	12.6872	+	34.8577i	0.482643	+	1.32605i	0.907219	+	0.420658i	$0.138201\pi$
$691$	12.6872	+	34.8577i	0.482643	+	1.32605i	−0.424577	+	0.905392i	$0.639577\pi$
$692$	2.98121	+	5.16360i	0.113328	+	0.196291i
$693$	1.56909	−	9.90212i	0.0596048	−	0.376150i
$694$	−19.3251	+	33.4720i	−0.733569	+	1.27058i
$695$	−14.2916	−	2.51999i	−0.542109	−	0.0955885i
$696$	13.9383	−	3.74321i	0.528330	−	0.141886i
$697$	−12.1073	−	4.40670i	−0.458597	−	0.166916i
$698$	8.42014	+	3.06468i	0.318707	+	0.116000i
$699$	4.40078	−	50.6309i	0.166453	−	1.91504i
$700$	−1.91203	−	0.660942i	−0.0722679	−	0.0249813i
$701$		−	8.24161i		−	0.311281i	−0.987814	−	0.155641i	$-0.950256\pi$
$701$		−	8.24161i		−	0.311281i	0.987814	−	0.155641i	$-0.0497442\pi$
$702$	−2.06433	−	7.65225i	−0.0779133	−	0.288816i
$703$	−53.1626	−	30.6934i	−2.00506	−	1.15762i
$704$	5.94872	+	1.04892i	0.224201	+	0.0395327i
$705$	−16.1073	+	23.0313i	−0.606635	+	0.867408i
$706$	22.2452	+	26.5108i	0.837209	+	0.997747i
$707$	−18.3610	+	0.298365i	−0.690537	+	0.0112212i
$708$	−1.97422	+	0.530187i	−0.0741956	+	0.0199256i
$709$	2.29888	−	13.0376i	0.0863361	−	0.489636i	−0.910724	−	0.413015i	$-0.864476\pi$
$709$	2.29888	−	13.0376i	0.0863361	−	0.489636i	0.997060	−	0.0766212i	$-0.0244132\pi$
$710$	0.270461	+	0.468452i	0.0101502	+	0.0175807i
$711$	3.60611	−	0.640061i	0.135240	−	0.0240042i
$712$	11.3272	+	6.53976i	0.424504	+	0.245088i
$713$	8.84875	−	50.1838i	0.331388	−	1.87940i
$714$	24.3232	+	16.4289i	0.910274	+	0.614834i
$715$	2.15290	+	0.783592i	0.0805139	+	0.0293047i
$716$	−12.7248	+	2.24372i	−0.475546	+	0.0838517i
$717$	20.3149	−	43.6298i	0.758673	−	1.62938i
$718$	−26.8206	−	22.5051i	−1.00093	−	0.839884i
$719$	5.67371	−	9.82715i	0.211594	−	0.366491i	−0.740620	−	0.671924i	$-0.765468\pi$
$719$	5.67371	−	9.82715i	0.211594	−	0.366491i	0.952213	+	0.305433i	$0.0988013\pi$
$720$	9.36401	+	25.6372i	0.348976	+	0.955441i
$721$	12.1787	+	31.8411i	0.453558	+	1.18583i
$722$	−40.9271	+	48.7751i	−1.52315	+	1.81522i
$723$	0.0337148	+	0.125541i	0.00125387	+	0.00466894i
$724$	−4.04545	+	11.1148i	−0.150348	+	0.413078i
$725$	4.94965	−	0.872757i	0.183825	−	0.0324134i
$726$	−2.25089	+	25.8964i	−0.0835383	+	0.961106i
$727$	7.94102	+	21.8178i	0.294516	+	0.809176i	0.995392	+	0.0958928i	$0.0305706\pi$
$727$	7.94102	+	21.8178i	0.294516	+	0.809176i	−0.700876	+	0.713284i	$0.747207\pi$
$728$	5.47853	−	2.09544i	0.203048	−	0.0776622i
$729$	23.4284	+	13.4206i	0.867717	+	0.497059i
$730$	−17.4182	−	30.1692i	−0.644677	−	1.11661i
$731$	−0.447516	+	2.53799i	−0.0165520	+	0.0938710i
$732$	−2.64401	+	1.23474i	−0.0977255	+	0.0456375i
$733$	5.56879	−	15.3001i	0.205688	−	0.565123i	−0.793360	−	0.608753i	$-0.791670\pi$
$733$	5.56879	−	15.3001i	0.205688	−	0.565123i	0.999048	+	0.0436299i	$0.0138922\pi$
$734$	−3.15849	−	17.9127i	−0.116582	−	0.661170i
$735$	10.4073	+	20.5190i	0.383880	+	0.756855i
$736$	13.2096	+	11.0842i	0.486913	+	0.408568i
$737$		−	2.70176i		−	0.0995205i
$738$	−2.65146	+	15.1373i	−0.0976016	+	0.557211i
$739$	−10.8959			−0.400813			−0.200406	−	0.979713i	$-0.564226\pi$
$739$	−10.8959			−0.400813			−0.200406	+	0.979713i	$0.564226\pi$
$740$	−7.79547	+	2.83732i	−0.286567	+	0.104302i
$741$	1.11454	+	12.6568i	0.0409437	+	0.464960i
$742$	−55.2431	+	0.897697i	−2.02804	+	0.0329555i
$743$	−16.4197	+	45.1128i	−0.602381	+	1.65503i	0.144054	+	0.989570i	$0.453986\pi$
$743$	−16.4197	+	45.1128i	−0.602381	+	1.65503i	−0.746435	+	0.665458i	$0.768236\pi$
$744$	−3.13664	−	35.6199i	−0.114995	−	1.30589i
$745$	−9.02517	+	10.7558i	−0.330657	+	0.394061i
$746$			59.8056i			2.18964i
$747$	−5.56812	+	15.3523i	−0.203727	+	0.561711i
$748$	2.39966	+	1.38544i	0.0877403	+	0.0506569i
$749$	−3.71958	+	0.718363i	−0.135910	+	0.0262484i
$750$	8.70507	+	32.4144i	0.317864	+	1.18361i
$751$	16.0679	−	13.4826i	0.586328	−	0.491987i	−0.300690	−	0.953722i	$-0.597217\pi$
$751$	16.0679	−	13.4826i	0.586328	−	0.491987i	0.887018	+	0.461734i	$0.152773\pi$
$752$	7.11892	+	40.3734i	0.259600	+	1.47227i
$753$	−33.2773	−	2.89242i	−1.21269	−	0.105406i
$754$	3.52228	−	4.19769i	0.128274	−	0.152871i
$755$	−11.7102			−0.426179
$756$	3.05275	−	6.86568i	0.111028	−	0.249702i
$757$	−24.6333			−0.895314			−0.447657	−	0.894205i	$-0.647741\pi$
$757$	−24.6333			−0.895314			−0.447657	+	0.894205i	$0.647741\pi$
$758$	4.83473	−	5.76181i	0.175605	−	0.209278i
$759$	−7.17833	+	10.2641i	−0.260557	+	0.372562i
$760$	−5.86560	−	33.2655i	−0.212768	−	1.20667i
$761$	−7.15928	+	6.00735i	−0.259524	+	0.217766i	−0.763260	−	0.646091i	$-0.776403\pi$
$761$	−7.15928	+	6.00735i	−0.259524	+	0.217766i	0.503737	+	0.863857i	$0.331958\pi$
$762$	−26.5369	+	26.5669i	−0.961330	+	0.962418i
$763$	3.78287	−	3.28041i	0.136949	−	0.118759i
$764$	10.3695	+	5.98683i	0.375155	+	0.216596i
$765$	−0.0258427	−	22.8496i	−0.000934345	−	0.826130i
$766$		−	11.9707i		−	0.432518i
$767$	1.32673	−	1.58113i	0.0479054	−	0.0570914i
$768$	19.1983	+	8.93911i	0.692760	+	0.322562i
$769$	−3.02496	+	8.31100i	−0.109083	+	0.299702i	−0.982209	−	0.187792i	$-0.939867\pi$
$769$	−3.02496	+	8.31100i	−0.109083	+	0.299702i	0.873126	+	0.487494i	$0.162089\pi$
$770$	5.20169	+	8.68074i	0.187456	+	0.312832i
$771$	4.42564	−	3.10260i	0.159385	−	0.111737i
$772$	7.48119	−	2.72293i	0.269254	−	0.0980004i
$773$	14.1312			0.508263			0.254131	−	0.967170i	$-0.418210\pi$
$773$	14.1312			0.508263			0.254131	+	0.967170i	$0.418210\pi$
$774$	3.07388	−	0.00347653i	0.110488	−	0.000124961i
$775$		−	12.4526i		−	0.447311i
$776$	−10.7815	−	9.04675i	−0.387033	−	0.324759i
$777$	−33.4761	−	14.9302i	−1.20095	−	0.535618i
$778$	−6.39392	−	36.2617i	−0.229233	−	1.30005i
$779$	8.42598	−	23.1502i	0.301892	−	0.829442i
$780$	1.40708	+	0.984065i	0.0503817	+	0.0352352i
$781$	−0.0391798	+	0.222200i	−0.00140196	+	0.00795093i
$782$	−18.3347	−	31.7566i	−0.655648	−	1.13562i
$783$	1.65849	+	18.5933i	0.0592696	+	0.664469i
$784$	31.8930	+	10.4477i	1.13904	+	0.373132i
$785$	−12.3267	−	33.8673i	−0.439958	−	1.20878i
$786$	20.5456	+	14.3689i	0.732837	+	0.512520i
$787$	−27.1926	+	4.79479i	−0.969312	+	0.170916i	−0.635820	−	0.771837i	$-0.719338\pi$
$787$	−27.1926	+	4.79479i	−0.969312	+	0.170916i	−0.333492	+	0.942753i	$0.608227\pi$
$788$	−0.445503	+	1.22401i	−0.0158704	+	0.0436035i
$789$	−5.34734	+	5.35339i	−0.190370	+	0.190586i
$790$	−2.37633	+	2.83200i	−0.0845459	+	0.100758i
$791$	−2.26956	−	0.362266i	−0.0806962	−	0.0128807i
$792$	−2.99668	+	8.26238i	−0.106483	+	0.293591i
$793$	1.47323	−	2.55171i	0.0523159	−	0.0906137i
$794$	−21.2940	−	17.8678i	−0.755697	−	0.634105i
$795$	24.6901	+	35.2187i	0.875666	+	1.24908i
$796$	5.52227	−	0.973726i	0.195732	−	0.0345128i
$797$	−32.0647	−	11.6706i	−1.13579	−	0.413394i	−0.295399	−	0.955374i	$-0.595453\pi$
$797$	−32.0647	−	11.6706i	−1.13579	−	0.413394i	−0.840391	+	0.541980i	$0.817675\pi$
$798$	−31.4134	+	46.5081i	−1.11202	+	1.64637i
$799$	5.95978	−	33.7996i	0.210842	−	1.19574i
$800$	3.64935	+	2.10695i	0.129024	+	0.0744921i
$801$	−10.8597	+	12.9718i	−0.383708	+	0.458337i
$802$	−17.1694	−	29.7382i	−0.606272	−	1.05009i
$803$	2.52326	−	14.3101i	0.0890438	−	0.504992i
$804$	0.522962	−	1.95614i	0.0184434	−	0.0689879i
$805$	−0.467017	−	28.7396i	−0.0164602	−	1.01294i
$806$	−8.72693	−	10.4004i	−0.307393	−	0.366337i
$807$	1.48229	+	0.128839i	0.0521791	+	0.00453535i
$808$	15.8538	+	2.79545i	0.557734	+	0.0983436i
$809$	8.13629	+	4.69749i	0.286057	+	0.165155i	0.636162	−	0.771555i	$-0.280521\pi$
$809$	8.13629	+	4.69749i	0.286057	+	0.165155i	−0.350105	+	0.936710i	$0.613854\pi$
$810$	−26.8290	+	4.79328i	−0.942676	+	0.168419i
$811$			31.3300i			1.10014i	0.835117	+	0.550072i	$0.185400\pi$
$811$			31.3300i			1.10014i	−0.835117	+	0.550072i	$0.814600\pi$
$812$	5.10058	−	0.985076i	0.178995	−	0.0345694i
$813$	7.75541	+	5.42387i	0.271994	+	0.190223i
$814$	−15.1504	−	5.51429i	−0.531021	−	0.193276i
$815$	−2.52869	−	0.920367i	−0.0885761	−	0.0322391i
$816$	−23.5816	−	23.5549i	−0.825519	−	0.824586i
$817$	−4.85286	−	0.855689i	−0.169780	−	0.0299368i
$818$	21.2375	−	36.7845i	0.742554	−	1.28614i
$819$	1.44707	+	7.44747i	0.0505648	+	0.260236i
$820$	−1.66464	−	2.88324i	−0.0581317	−	0.100687i
$821$	2.24413	+	6.16570i	0.0783208	+	0.215185i	0.972673	−	0.232179i	$-0.0745854\pi$
$821$	2.24413	+	6.16570i	0.0783208	+	0.215185i	−0.894352	+	0.447363i	$0.852363\pi$
$822$	50.3344	+	23.4367i	1.75561	+	0.817448i
$823$	−17.8354	+	14.9657i	−0.621704	+	0.521672i	−0.898339	−	0.439303i	$-0.855225\pi$
$823$	−17.8354	+	14.9657i	−0.621704	+	0.521672i	0.276634	+	0.960975i	$0.410781\pi$
$824$	−5.18961	−	29.4317i	−0.180789	−	1.02530i
$825$	−1.29197	+	2.77474i	−0.0449807	+	0.0966040i
$826$	8.95162	−	1.72883i	0.311467	−	0.0601537i
$827$	33.9354	−	19.5926i	1.18005	−	0.681302i	0.224023	−	0.974584i	$-0.428081\pi$
$827$	33.9354	−	19.5926i	1.18005	−	0.681302i	0.956026	+	0.293282i	$0.0947476\pi$
$828$	−7.18405	+	6.04199i	−0.249663	+	0.209974i
$829$	−31.3173	+	18.0811i	−1.08770	+	0.627981i	−0.932962	−	0.359975i	$-0.882785\pi$
$829$	−31.3173	+	18.0811i	−1.08770	+	0.627981i	−0.154733	+	0.987956i	$0.549452\pi$
$830$	−5.63799	−	15.4903i	−0.195698	−	0.537675i
$831$	23.9674	+	23.9404i	0.831421	+	0.830482i
$832$	−4.50160	+	0.793753i	−0.156065	+	0.0275184i
$833$	−22.0983	−	17.3510i	−0.765662	−	0.601177i
$834$	−8.94395	−	19.1521i	−0.309704	−	0.663182i
$835$	22.9272	+	19.2382i	0.793427	+	0.665764i
$836$	−2.64909	+	4.58836i	−0.0916206	+	0.158692i
$837$	46.0811	+	3.95281i	1.59279	+	0.136629i
$838$	−8.04702	+	4.64595i	−0.277980	+	0.160492i
$839$	−35.7513	+	13.0124i	−1.23427	+	0.449238i	−0.875058	−	0.484018i	$-0.839177\pi$
$839$	−35.7513	+	13.0124i	−1.23427	+	0.449238i	−0.359212	+	0.933256i	$0.616955\pi$
$840$	−5.54708	−	19.3918i	−0.191393	−	0.669079i
$841$	12.3288	−	10.3451i	0.425130	−	0.356726i
$842$	5.07166	+	6.04417i	0.174781	+	0.208296i
$843$	−6.01711	−	22.4055i	−0.207240	−	0.771686i
$844$	−5.86285	+	2.13390i	−0.201808	+	0.0734520i
$845$	22.9353			0.789000
$846$	−40.9362	+	0.0462985i	−1.40742	+	0.00159178i
$847$	3.92202	−	24.5710i	0.134762	−	0.844270i
$848$	61.7866	+	10.8946i	2.12176	+	0.374124i
$849$	−7.86532	+	16.8922i	−0.269937	+	0.579738i
$850$	−5.75997	−	6.86447i	−0.197565	−	0.235449i
$851$	29.4352	+	35.0794i	1.00902	+	1.20251i
$852$	−0.0713770	+	0.153295i	−0.00244534	+	0.00525179i
$853$	−30.3259	−	5.34727i	−1.03834	−	0.183087i	−0.371611	−	0.928389i	$-0.621194\pi$
$853$	−30.3259	−	5.34727i	−1.03834	−	0.183087i	−0.666728	+	0.745301i	$0.732306\pi$
$854$	12.1560	−	4.64946i	0.415970	−	0.159101i
$855$	43.6905	−	0.0494135i	1.49418	−	0.00168991i
$856$	3.32104			0.113511
$857$	−19.0597	+	6.93716i	−0.651067	+	0.236969i	−0.646375	−	0.763020i	$-0.723716\pi$
$857$	−19.0597	+	6.93716i	−0.651067	+	0.236969i	−0.00469191	+	0.999989i	$0.501493\pi$
$858$	0.865520	+	3.22287i	0.0295483	+	0.110027i
$859$	−22.2737	−	26.5448i	−0.759969	−	0.905696i	0.237877	−	0.971295i	$-0.423549\pi$
$859$	−22.2737	−	26.5448i	−0.759969	−	0.905696i	−0.997846	+	0.0655991i	$0.979104\pi$
$860$	−0.510130	+	0.428050i	−0.0173953	+	0.0145964i
$861$	3.56788	−	14.2711i	0.121593	−	0.486358i
$862$	−17.6440	+	6.42189i	−0.600957	+	0.218731i
$863$	−32.8141	+	18.9452i	−1.11700	+	0.644902i	−0.940634	−	0.339422i	$-0.889769\pi$
$863$	−32.8141	+	18.9452i	−1.11700	+	0.644902i	−0.176369	+	0.984324i	$0.556435\pi$
$864$	−8.95521	+	12.8357i	−0.304663	+	0.436678i
$865$	−10.3508	+	17.9281i	−0.351938	+	0.609574i
$866$	35.0096	+	29.3765i	1.18967	+	0.998255i
$867$	−0.652210	−	1.39661i	−0.0221502	−	0.0474312i
$868$	−0.209124	−	12.8692i	−0.00709813	−	0.436809i
$869$	−1.51862	+	0.267773i	−0.0515155	+	0.00908357i
$870$	−13.3313	−	13.3162i	−0.451972	−	0.451461i
$871$	0.699263	+	1.92121i	0.0236936	+	0.0650977i
$872$	−3.80142	+	2.19475i	−0.128732	+	0.0743237i
$873$	13.9319	−	11.7171i	0.471524	−	0.396565i
$874$	60.7214	−	35.0575i	2.05393	−	1.18584i
$875$	−6.09216	−	31.5443i	−0.205953	−	1.06639i
$876$	4.59682	−	9.87248i	0.155312	−	0.333560i
$877$	−2.06483	−	11.7102i	−0.0697243	−	0.395426i	−0.999619	−	0.0276005i	$-0.991213\pi$
$877$	−2.06483	−	11.7102i	−0.0697243	−	0.395426i	0.929895	−	0.367826i	$-0.119898\pi$
$878$	13.1215	−	11.0102i	0.442829	−	0.371577i
$879$	14.0944	+	6.56263i	0.475393	+	0.221352i
$880$	−3.93040	−	10.7987i	−0.132494	−	0.364024i
$881$	19.8758	+	34.4258i	0.669631	+	1.15984i	0.978007	+	0.208571i	$0.0668813\pi$
$881$	19.8758	+	34.4258i	0.669631	+	1.15984i	−0.308376	+	0.951265i	$0.599785\pi$
$882$	−15.7706	+	29.5688i	−0.531022	+	0.995635i
$883$	25.4955	−	44.1595i	0.857992	−	1.48609i	−0.0158499	−	0.999874i	$-0.505045\pi$
$883$	25.4955	−	44.1595i	0.857992	−	1.48609i	0.873842	−	0.486211i	$-0.161621\pi$
$884$	−2.06497	−	0.364110i	−0.0694524	−	0.0122463i
$885$	−5.02145	−	5.01578i	−0.168794	−	0.168604i
$886$	24.0301	+	8.74623i	0.807306	+	0.293835i
$887$	25.2472	+	9.18922i	0.847717	+	0.308544i	0.729109	−	0.684398i	$-0.239935\pi$
$887$	25.2472	+	9.18922i	0.847717	+	0.308544i	0.118608	+	0.992941i	$0.462157\pi$
$888$	26.3326	+	18.4161i	0.883663	+	0.618003i
$889$	27.1555	−	23.5485i	0.910765	−	0.789792i
$890$		−	17.0765i		−	0.572407i
$891$	−9.85784	−	5.66173i	−0.330250	−	0.189675i
$892$	5.19536	+	2.99954i	0.173953	+	0.100432i
$893$	64.6277	+	11.3956i	2.16268	+	0.381339i
$894$	−20.3742	−	1.77090i	−0.681415	−	0.0592278i
$895$	−28.8368	−	34.3664i	−0.963909	−	1.14874i
$896$	−31.5779	−	17.5537i	−1.05494	−	0.586428i
$897$	2.44796	−	9.15662i	0.0817350	−	0.305731i
$898$	−4.97138	+	28.1941i	−0.165897	+	0.940849i
$899$	15.9881	+	27.6922i	0.533234	+	0.923588i
$900$	−1.47251	+	1.75891i	−0.0490837	+	0.0586302i
$901$	−45.4873	−	26.2621i	−1.51540	−	0.874917i
$902$	1.12357	−	6.37211i	0.0374109	−	0.212168i
$903$	−2.93509	−	0.207127i	−0.0976735	−	0.00689275i
$904$	1.89330	+	0.689103i	0.0629701	+	0.0229192i
$905$	−40.4435	+	7.13128i	−1.34439	+	0.237052i
$906$	−9.79116	−	13.9664i	−0.325289	−	0.464003i
$907$	−30.9893	−	26.0031i	−1.02898	−	0.863418i	−0.0382522	−	0.999268i	$-0.512179\pi$
$907$	−30.9893	−	26.0031i	−1.02898	−	0.863418i	−0.990729	+	0.135850i	$0.956623\pi$
$908$	4.11291	−	7.12377i	0.136492	−	0.236411i
$909$	−7.09947	+	19.5745i	−0.235474	+	0.649245i
$910$	−5.94564	−	4.82655i	−0.197096	−	0.159999i
$911$	12.3517	−	14.7202i	0.409231	−	0.487702i	−0.521581	−	0.853202i	$-0.674658\pi$
$911$	12.3517	−	14.7202i	0.409231	−	0.487702i	0.930811	+	0.365500i	$0.119102\pi$
$912$	45.0390	−	45.0899i	1.49139	−	1.49308i
$913$	2.35170	−	6.46124i	0.0778299	−	0.213836i
$914$	−36.0253	+	6.35223i	−1.19161	+	0.210113i
$915$	−8.30273	−	5.80664i	−0.274480	−	0.191962i
$916$	4.20062	+	11.5411i	0.138792	+	0.381329i
$917$	−18.6326	−	15.1256i	−0.615302	−	0.499490i
$918$	27.2304	−	19.1359i	0.898738	−	0.631578i
$919$	1.00540	+	1.74140i	0.0331650	+	0.0574435i	0.882132	−	0.471003i	$-0.156108\pi$
$919$	1.00540	+	1.74140i	0.0331650	+	0.0574435i	−0.848966	+	0.528447i	$0.822775\pi$
$920$	−4.37558	+	24.8152i	−0.144259	+	0.818132i
$921$	28.5987	+	20.0010i	0.942361	+	0.659054i
$922$	−6.55777	+	18.0173i	−0.215969	+	0.593369i
$923$	−0.0296486	−	0.168146i	−0.000975897	−	0.00553459i
$924$	−1.28860	+	2.88926i	−0.0423917	+	0.0950497i
$925$	8.57238	+	7.19308i	0.281858	+	0.236507i
$926$			1.79045i			0.0588380i
$927$	38.6552	−	0.0437187i	1.26960	−	0.00143591i
$928$	−10.8206			−0.355204
$929$	−3.28266	+	1.19479i	−0.107700	+	0.0391998i	−0.395308	−	0.918548i	$-0.629362\pi$
$929$	−3.28266	+	1.19479i	−0.107700	+	0.0391998i	0.287608	+	0.957748i	$0.407140\pi$
$930$	−38.2271	+	26.7991i	−1.25351	+	0.878777i
$931$	33.1766	−	42.2539i	1.08732	−	1.38482i
$932$	−5.48490	+	15.0696i	−0.179664	+	0.493622i
$933$	−4.45921	−	2.07630i	−0.145988	−	0.0679749i
$934$	−13.5075	+	16.0976i	−0.441980	+	0.526731i
$935$			9.62058i			0.314627i
$936$	−0.00752216	−	6.65095i	−0.000245869	−	0.217393i
$937$	29.0222	+	16.7560i	0.948114	+	0.547394i	0.892495	−	0.451058i	$-0.148953\pi$
$937$	29.0222	+	16.7560i	0.948114	+	0.547394i	0.0556194	+	0.998452i	$0.482287\pi$
$938$	−2.95044	+	8.53528i	−0.0963353	+	0.278687i
$939$	11.4161	−	11.4290i	0.372549	−	0.372971i
$940$	6.79363	−	5.70054i	0.221584	−	0.185931i
$941$	−5.86663	−	33.2713i	−0.191247	−	1.08461i	−0.917663	−	0.397359i	$-0.869927\pi$
$941$	−5.86663	−	33.2713i	−0.191247	−	1.08461i	0.726416	−	0.687255i	$-0.241184\pi$
$942$	30.0858	−	43.0188i	0.980249	−	1.40163i
$943$	−11.8130	+	14.0782i	−0.384684	+	0.458448i
$944$	−10.3529			−0.336958
$945$	25.9437	−	2.73969i	0.843949	−	0.0891222i
$946$	−1.29422			−0.0420788
$947$	1.00618	−	1.19912i	0.0326965	−	0.0389662i	−0.749448	−	0.662063i	$-0.769681\pi$
$947$	1.00618	−	1.19912i	0.0326965	−	0.0389662i	0.782145	+	0.623097i	$0.214126\pi$
$948$	−1.15135	−	0.100074i	−0.0373941	−	0.00325025i
$949$	1.90943	+	10.8289i	0.0619828	+	0.351522i
$950$	13.1254	−	11.0136i	0.425846	−	0.357327i
$951$	7.92158	+	29.4970i	0.256875	+	0.956506i
$952$	16.1367	+	18.6084i	0.522994	+	0.603101i
$953$	−13.8156	−	7.97645i	−0.447532	−	0.258383i	0.259255	−	0.965809i	$-0.416523\pi$
$953$	−13.8156	−	7.97645i	−0.447532	−	0.258383i	−0.706787	+	0.707426i	$0.749856\pi$
$954$	−21.3603	+	58.8941i	−0.691565	+	1.90677i
$955$			41.5728i			1.34526i
$956$	−9.76174	+	11.6336i	−0.315717	+	0.376257i
$957$	−0.689434	−	7.82927i	−0.0222862	−	0.253084i
$958$	12.2187	−	33.5707i	0.394770	−	1.08462i
$959$	−46.4532	−	25.8227i	−1.50005	−	0.833857i
$960$	1.37878	+	15.6575i	0.0444998	+	0.505343i
$961$	45.3172	−	16.4941i	1.46184	−	0.532068i
$962$	12.2006			0.393363
$963$	−0.741128	+	4.23112i	−0.0238825	+	0.136346i
$964$		−	0.0410182i		−	0.00132111i
$965$	21.1749	+	17.7678i	0.681643	+	0.571966i
$966$	33.8863	−	24.5868i	1.09027	−	0.791066i
$967$	0.704391	+	3.99480i	0.0226517	+	0.128464i	0.994037	−	0.109046i	$-0.0347797\pi$
$967$	0.704391	+	3.99480i	0.0226517	+	0.128464i	−0.971385	+	0.237510i	$0.923669\pi$
$968$	−7.46047	+	20.4975i	−0.239789	+	0.658814i
$969$	−48.3422	+	22.5756i	−1.55298	+	0.725234i
$970$	−3.19083	+	18.0961i	−0.102451	+	0.581031i
$971$	20.1944	+	34.9777i	0.648068	+	1.12249i	0.983584	+	0.180453i	$0.0577563\pi$
$971$	20.1944	+	34.9777i	0.648068	+	1.12249i	−0.335515	+	0.942035i	$0.608910\pi$
$972$	−6.04144	−	6.00737i	−0.193779	−	0.192686i
$973$	7.22821	+	18.8982i	0.231726	+	0.605847i
$974$	−15.4317	−	42.3984i	−0.494465	−	1.35853i
$975$	0.200565	−	2.30749i	0.00642321	−	0.0738989i
$976$	−14.5545	+	2.56636i	−0.465879	+	0.0821471i
$977$	−2.97539	+	8.17481i	−0.0951910	+	0.261535i	−0.978145	−	0.207925i	$-0.933329\pi$
$977$	−2.97539	+	8.17481i	−0.0951910	+	0.261535i	0.882954	+	0.469460i	$0.155551\pi$
$978$	−1.01660	−	3.78542i	−0.0325071	−	0.121044i
$979$	4.57852	−	5.45647i	0.146330	−	0.174389i
$980$	−1.49232	−	7.10494i	−0.0476703	−	0.226959i
$981$	−1.94786	−	5.33294i	−0.0621905	−	0.170268i
$982$	29.5226	−	51.1346i	0.942102	−	1.63177i
$983$	−25.8458	−	21.6872i	−0.824352	−	0.691714i	0.129635	−	0.991562i	$-0.458620\pi$
$983$	−25.8458	−	21.6872i	−0.824352	−	0.691714i	−0.953987	+	0.299848i	$0.903064\pi$
$984$	−5.44342	+	11.6907i	−0.173530	+	0.372686i
$985$	−4.45381	+	0.785328i	−0.141910	+	0.0250226i
$986$	21.6225	+	7.86994i	0.688600	+	0.250630i
$987$	39.0879	+	2.75840i	1.24418	+	0.0878009i
$988$	0.696209	−	3.94840i	0.0221493	−	0.125615i
$989$	3.18346	+	1.83797i	0.101228	+	0.0584442i
$990$	11.2983	−	2.00538i	0.359084	−	0.0637351i
$991$	12.7307	+	22.0503i	0.404405	+	0.700450i	0.994252	−	0.107065i	$-0.0341453\pi$
$991$	12.7307	+	22.0503i	0.404405	+	0.700450i	−0.589847	+	0.807515i	$0.700812\pi$
$992$	−4.65543	+	26.4022i	−0.147810	+	0.838272i
$993$	45.7790	−	12.2942i	1.45275	−	0.390144i
$994$	0.366427	−	0.659178i	0.0116224	−	0.0209079i
$995$	12.5146	+	14.9143i	0.396739	+	0.472815i
$996$	2.95336	−	4.22291i	0.0935807	−	0.133808i
$997$	8.61062	+	1.51829i	0.272701	+	0.0480846i	0.308326	−	0.951281i	$-0.400231\pi$
$997$	8.61062	+	1.51829i	0.272701	+	0.0480846i	−0.0356252	+	0.999365i	$0.511342\pi$
$998$	−22.6731	−	13.0903i	−0.717705	−	0.414367i
$999$	−29.3392	+	29.4389i	−0.928251	+	0.931406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.17	✓	132
3.2	odd	2		567.2.ba.a.143.6		132
7.5	odd	6		189.2.bd.a.47.6	yes	132
21.5	even	6		567.2.bd.a.467.17		132
27.4	even	9		567.2.bd.a.17.17		132
27.23	odd	18		189.2.bd.a.185.6	yes	132
189.131	even	18	inner	189.2.ba.a.131.17	yes	132
189.166	odd	18		567.2.ba.a.341.6		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.17	✓	132	1.1	even	1	trivial
189.2.ba.a.131.17	yes	132	189.131	even	18	inner
189.2.bd.a.47.6	yes	132	7.5	odd	6
189.2.bd.a.185.6	yes	132	27.23	odd	18
567.2.ba.a.143.6		132	3.2	odd	2
567.2.ba.a.341.6		132	189.166	odd	18
567.2.bd.a.17.17		132	27.4	even	9
567.2.bd.a.467.17		132	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02575 - 1.22245i) q^{2} +(0.732884 + 1.56936i) q^{3} +(-0.0949069 - 0.538244i) q^{4} +(1.45366 - 1.21977i) q^{5} +(2.67021 + 0.713863i) q^{6} +(-2.50057 - 0.864386i) q^{7} +(2.00866 + 1.15970i) q^{8} +(-1.92576 + 2.30031i) q^{9} +O(q^{10})\)	\(q+(1.02575 - 1.22245i) q^{2} +(0.732884 + 1.56936i) q^{3} +(-0.0949069 - 0.538244i) q^{4} +(1.45366 - 1.21977i) q^{5} +(2.67021 + 0.713863i) q^{6} +(-2.50057 - 0.864386i) q^{7} +(2.00866 + 1.15970i) q^{8} +(-1.92576 + 2.30031i) q^{9} -3.02821i q^{10} +(0.811915 - 0.967602i) q^{11} +(0.775141 - 0.543413i) q^{12} +(-0.326917 + 0.898197i) q^{13} +(-3.62163 + 2.17016i) q^{14} +(2.97962 + 1.38737i) q^{15} +(4.50524 - 1.63977i) q^{16} -4.01374 q^{17} +(0.836650 + 4.71370i) q^{18} -7.67461i q^{19} +(-0.794495 - 0.666660i) q^{20} +(-0.476096 - 4.55778i) q^{21} +(-0.350017 - 1.98504i) q^{22} +(-1.95808 + 5.37979i) q^{23} +(-0.347870 + 4.00224i) q^{24} +(-0.242940 + 1.37778i) q^{25} +(0.762661 + 1.32097i) q^{26} +(-5.02137 - 1.33635i) q^{27} +(-0.227929 + 1.42795i) q^{28} +(-1.22870 - 3.37583i) q^{29} +(4.75234 - 2.21932i) q^{30} +(-8.76565 + 1.54562i) q^{31} +(1.03017 - 2.83037i) q^{32} +(2.11355 + 0.565044i) q^{33} +(-4.11711 + 4.90658i) q^{34} +(-4.68933 + 1.79359i) q^{35} +(1.42090 + 0.818214i) q^{36} +(3.99935 - 6.92708i) q^{37} +(-9.38179 - 7.87226i) q^{38} +(-1.64918 + 0.145225i) q^{39} +(4.33449 - 0.764287i) q^{40} +(3.01647 + 1.09790i) q^{41} +(-6.06000 - 4.09316i) q^{42} +(0.111496 - 0.632326i) q^{43} +(-0.597862 - 0.345176i) q^{44} +(0.00643857 + 5.69286i) q^{45} +(4.56799 + 7.91199i) q^{46} +(-1.48485 + 8.42098i) q^{47} +(5.87521 + 5.86857i) q^{48} +(5.50567 + 4.32291i) q^{49} +(1.43506 + 1.71024i) q^{50} +(-2.94160 - 6.29898i) q^{51} +(0.514475 + 0.0907159i) q^{52} +(11.3329 + 6.54305i) q^{53} +(-6.78431 + 4.76759i) q^{54} -2.39691i q^{55} +(-4.02037 - 4.63618i) q^{56} +(12.0442 - 5.62459i) q^{57} +(-5.38712 - 1.96075i) q^{58} +(-2.02915 - 0.738551i) q^{59} +(0.463955 - 1.73543i) q^{60} +(-3.03575 - 0.535284i) q^{61} +(-7.10196 + 12.3010i) q^{62} +(6.80386 - 4.08749i) q^{63} +(2.39111 + 4.14152i) q^{64} +(0.620364 + 1.70444i) q^{65} +(2.85872 - 2.00411i) q^{66} +(1.63854 - 1.37490i) q^{67} +(0.380931 + 2.16037i) q^{68} +(-9.87786 + 0.869829i) q^{69} +(-2.61754 + 7.57223i) q^{70} +(-0.154696 + 0.0893139i) q^{71} +(-6.53589 + 2.38724i) q^{72} +(9.96274 - 5.75199i) q^{73} +(-4.36563 - 11.9945i) q^{74} +(-2.34027 + 0.628493i) q^{75} +(-4.13081 + 0.728373i) q^{76} +(-2.86663 + 1.71775i) q^{77} +(-1.51413 + 2.16500i) q^{78} +(-0.935206 - 0.784731i) q^{79} +(4.54896 - 7.87903i) q^{80} +(-1.58288 - 8.85971i) q^{81} +(4.43628 - 2.56129i) q^{82} +(5.11532 - 1.86183i) q^{83} +(-2.40801 + 0.688820i) q^{84} +(-5.83462 + 4.89582i) q^{85} +(-0.658617 - 0.784910i) q^{86} +(4.39739 - 4.40236i) q^{87} +(2.75300 - 1.00201i) q^{88} +5.63916 q^{89} +(6.96582 + 5.83160i) q^{90} +(1.59387 - 1.96342i) q^{91} +(3.08147 + 0.543347i) q^{92} +(-8.84983 - 12.6237i) q^{93} +(8.77111 + 10.4530i) q^{94} +(-9.36123 - 11.1563i) q^{95} +(5.19685 - 0.457627i) q^{96} +(-5.97585 - 1.05370i) q^{97} +(10.9320 - 2.29615i) q^{98} +(0.662233 + 3.73103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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