LMFDB - Embedded newform 135.2.q.a.122.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.12
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.865920 + 0.606324i) q^{2} +(-0.905161 - 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(2.13636 + 0.660292i) q^{5} +(0.111569 - 1.82754i) q^{6} +(-1.22161 - 2.61975i) q^{7} +(0.788655 - 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +O(q^{10})$	\(q+(0.865920 + 0.606324i) q^{2} +(-0.905161 - 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(2.13636 + 0.660292i) q^{5} +(0.111569 - 1.82754i) q^{6} +(-1.22161 - 2.61975i) q^{7} +(0.788655 - 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +(1.44956 + 1.86708i) q^{10} +(1.51740 + 1.80836i) q^{11} +(-0.951458 + 1.19642i) q^{12} +(3.11956 + 4.45519i) q^{13} +(0.530600 - 3.00918i) q^{14} +(-0.958684 - 3.75246i) q^{15} +(1.11535 - 0.935892i) q^{16} +(-0.716894 - 2.67549i) q^{17} +(-2.79974 + 1.48946i) q^{18} +(-5.35751 + 3.09316i) q^{19} +(-0.0972619 - 1.97105i) q^{20} +(-2.76286 + 4.17526i) q^{21} +(0.217491 + 2.48593i) q^{22} +(0.646627 + 0.301527i) q^{23} +(-5.06027 + 1.49954i) q^{24} +(4.12803 + 2.82124i) q^{25} +5.74930i q^{26} +(5.18000 - 0.409444i) q^{27} +(-1.80389 + 1.80389i) q^{28} +(0.623300 + 3.53491i) q^{29} +(1.44506 - 3.83060i) q^{30} +(-5.18043 + 1.88552i) q^{31} +(-4.53781 + 0.397007i) q^{32} +(1.29695 - 3.87762i) q^{33} +(1.00144 - 2.75143i) q^{34} +(-0.879991 - 6.40333i) q^{35} +(2.62800 + 0.322074i) q^{36} +(-4.26173 + 1.14193i) q^{37} +(-6.51463 - 0.569956i) q^{38} +(3.75534 - 8.63936i) q^{39} +(3.62828 - 5.76719i) q^{40} +(5.70140 + 1.00531i) q^{41} +(-4.92398 + 1.94025i) q^{42} +(0.126221 - 1.44271i) q^{43} +(1.04170 - 1.80428i) q^{44} +(-4.67354 + 4.81228i) q^{45} +(0.377104 + 0.653164i) q^{46} +(9.40770 - 4.38688i) q^{47} +(-2.39162 - 0.799924i) q^{48} +(-0.871236 + 1.03830i) q^{49} +(1.86396 + 4.94589i) q^{50} +(-3.30202 + 3.48039i) q^{51} +(2.75318 - 3.93195i) q^{52} +(-7.22940 - 7.22940i) q^{53} +(4.73372 + 2.78621i) q^{54} +(2.04765 + 4.86523i) q^{55} +(-8.67413 + 1.52948i) q^{56} +(9.41712 + 5.11170i) q^{57} +(-1.60357 + 3.43887i) q^{58} +(6.27320 + 5.26384i) q^{59} +(-2.82264 + 1.92775i) q^{60} +(2.64019 + 0.960952i) q^{61} +(-5.62907 - 1.50831i) q^{62} +(8.66650 + 0.300676i) q^{63} +(-6.69194 - 3.86359i) q^{64} +(3.72276 + 11.5777i) q^{65} +(3.47414 - 2.57134i) q^{66} +(6.11610 - 4.28254i) q^{67} +(-2.00246 + 1.40214i) q^{68} +(-0.140033 - 1.22781i) q^{69} +(3.12049 - 6.07833i) q^{70} +(-4.24004 - 2.44799i) q^{71} +(6.79476 + 6.11524i) q^{72} +(-6.73088 - 1.80353i) q^{73} +(-4.38269 - 1.59517i) q^{74} +(0.429628 - 8.64959i) q^{75} +(4.18242 + 3.50947i) q^{76} +(2.88379 - 6.18430i) q^{77} +(8.49007 - 5.20404i) q^{78} +(-12.8661 + 2.26863i) q^{79} +(3.00075 - 1.26294i) q^{80} +(-5.29336 - 7.27876i) q^{81} +(4.32741 + 4.32741i) q^{82} +(-2.73492 + 3.90587i) q^{83} +(4.29664 + 1.03102i) q^{84} +(0.235061 - 6.18915i) q^{85} +(0.984048 - 1.17274i) q^{86} +(4.65586 - 4.12010i) q^{87} +(6.51925 - 3.03998i) q^{88} +(3.33276 + 5.77251i) q^{89} +(-6.96471 + 1.33337i) q^{90} +(7.86060 - 13.6150i) q^{91} +(0.0548802 - 0.627283i) q^{92} +(7.47350 + 5.94331i) q^{93} +(10.8062 + 1.90542i) q^{94} +(-13.4879 + 3.07057i) q^{95} +(4.69371 + 6.34168i) q^{96} +(-18.2758 - 1.59893i) q^{97} +(-1.38397 + 0.370833i) q^{98} +(-6.90008 + 1.59465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.865920	+	0.606324i	0.612298	+	0.428736i	0.838161	−	0.545424i	$-0.183631\pi$
$2$	0.865920	+	0.606324i	0.612298	+	0.428736i	−0.225863	+	0.974159i	$0.572520\pi$
$3$	−0.905161	−	1.47671i	−0.522595	−	0.852581i
$3$	−0.905161	−	1.47671i	−0.522595	−	0.852581i
$4$	−0.301851	−	0.829330i	−0.150926	−	0.414665i
$5$	2.13636	+	0.660292i	0.955407	+	0.295292i
$5$	2.13636	+	0.660292i	0.955407	+	0.295292i
$6$	0.111569	−	1.82754i	0.0455480	−	0.746089i
$7$	−1.22161	−	2.61975i	−0.461725	−	0.990171i	−0.989996	−	0.141096i	$-0.954937\pi$
$7$	−1.22161	−	2.61975i	−0.461725	−	0.990171i	0.528271	−	0.849076i	$-0.322840\pi$
$8$	0.788655	−	2.94330i	0.278832	−	1.04061i
$9$	−1.36137	+	2.67333i	−0.453789	+	0.891109i
$10$	1.44956	+	1.86708i	0.458392	+	0.590424i
$11$	1.51740	+	1.80836i	0.457512	+	0.545242i	0.944648	−	0.328084i	$-0.106403\pi$
$11$	1.51740	+	1.80836i	0.457512	+	0.545242i	−0.487136	+	0.873326i	$0.661959\pi$
$12$	−0.951458	+	1.19642i	−0.274662	+	0.345378i
$13$	3.11956	+	4.45519i	0.865210	+	1.23565i	0.970475	+	0.241203i	$0.0775421\pi$
$13$	3.11956	+	4.45519i	0.865210	+	1.23565i	−0.105265	+	0.994444i	$0.533569\pi$
$14$	0.530600	−	3.00918i	0.141809	−	0.804238i
$15$	−0.958684	−	3.75246i	−0.247531	−	0.968880i
$16$	1.11535	−	0.935892i	0.278838	−	0.233973i
$17$	−0.716894	−	2.67549i	−0.173872	−	0.648901i	−0.996741	−	0.0806688i	$-0.974294\pi$
$17$	−0.716894	−	2.67549i	−0.173872	−	0.648901i	0.822869	−	0.568232i	$-0.192372\pi$
$18$	−2.79974	+	1.48946i	−0.659904	+	0.351069i
$19$	−5.35751	+	3.09316i	−1.22910	+	0.709619i	−0.966841	−	0.255379i	$-0.917800\pi$
$19$	−5.35751	+	3.09316i	−1.22910	+	0.709619i	−0.262256	+	0.964998i	$0.584466\pi$
$20$	−0.0972619	−	1.97105i	−0.0217484	−	0.440741i
$21$	−2.76286	+	4.17526i	−0.602906	+	0.911116i
$22$	0.217491	+	2.48593i	0.0463692	+	0.530002i
$23$	0.646627	+	0.301527i	0.134831	+	0.0628728i	0.488863	−	0.872361i	$-0.337412\pi$
$23$	0.646627	+	0.301527i	0.134831	+	0.0628728i	−0.354032	+	0.935233i	$0.615190\pi$
$24$	−5.06027	+	1.49954i	−1.03292	+	0.306093i
$25$	4.12803	+	2.82124i	0.825606	+	0.564247i
$26$			5.74930i			1.12753i
$27$	5.18000	−	0.409444i	0.996891	−	0.0787976i
$28$	−1.80389	+	1.80389i	−0.340903	+	0.340903i
$29$	0.623300	+	3.53491i	0.115744	+	0.656416i	0.986379	+	0.164487i	$0.0525969\pi$
$29$	0.623300	+	3.53491i	0.115744	+	0.656416i	−0.870635	+	0.491929i	$0.836292\pi$
$30$	1.44506	−	3.83060i	0.263831	−	0.699369i
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.762381	−	0.647129i	$-0.775970\pi$
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.168051	+	0.985778i	$0.553747\pi$
$32$	−4.53781	+	0.397007i	−0.802178	+	0.0701815i
$33$	1.29695	−	3.87762i	0.225769	−	0.675007i
$34$	1.00144	−	2.75143i	0.171745	−	0.471866i
$35$	−0.879991	−	6.40333i	−0.148746	−	1.08236i
$36$	2.62800	+	0.322074i	0.438000	+	0.0536790i
$37$	−4.26173	+	1.14193i	−0.700624	+	0.187732i	−0.591510	−	0.806298i	$-0.701468\pi$
$37$	−4.26173	+	1.14193i	−0.700624	+	0.187732i	−0.109114	+	0.994029i	$0.534801\pi$
$38$	−6.51463	−	0.569956i	−1.05681	−	0.0924591i
$39$	3.75534	−	8.63936i	0.601335	−	1.38340i
$40$	3.62828	−	5.76719i	0.573682	−	0.911873i
$41$	5.70140	+	1.00531i	0.890409	+	0.157003i	0.600095	−	0.799928i	$-0.295129\pi$
$41$	5.70140	+	1.00531i	0.890409	+	0.157003i	0.290314	+	0.956932i	$0.406240\pi$
$42$	−4.92398	+	1.94025i	−0.759786	+	0.299387i
$43$	0.126221	−	1.44271i	0.0192485	−	0.220012i	−0.980478	−	0.196629i	$-0.937001\pi$
$43$	0.126221	−	1.44271i	0.0192485	−	0.220012i	0.999727	−	0.0233831i	$-0.00744375\pi$
$44$	1.04170	−	1.80428i	0.157042	−	0.272005i
$45$	−4.67354	+	4.81228i	−0.696690	+	0.717372i
$46$	0.377104	+	0.653164i	0.0556010	+	0.0963037i
$47$	9.40770	−	4.38688i	1.37225	−	0.639893i	0.410010	−	0.912081i	$-0.365525\pi$
$47$	9.40770	−	4.38688i	1.37225	−	0.639893i	0.962244	+	0.272188i	$0.0877473\pi$
$48$	−2.39162	−	0.799924i	−0.345201	−	0.115459i
$49$	−0.871236	+	1.03830i	−0.124462	+	0.148328i
$50$	1.86396	+	4.94589i	0.263604	+	0.699454i
$51$	−3.30202	+	3.48039i	−0.462375	+	0.487353i
$52$	2.75318	−	3.93195i	0.381797	−	0.545263i
$53$	−7.22940	−	7.22940i	−0.993035	−	0.993035i	0.00694140	−	0.999976i	$-0.497790\pi$
$53$	−7.22940	−	7.22940i	−0.993035	−	0.993035i	−0.999976	+	0.00694140i	$0.997790\pi$
$54$	4.73372	+	2.78621i	0.644177	+	0.379155i
$55$	2.04765	+	4.86523i	0.276105	+	0.656027i
$56$	−8.67413	+	1.52948i	−1.15913	+	0.204386i
$57$	9.41712	+	5.11170i	1.24733	+	0.677061i
$58$	−1.60357	+	3.43887i	−0.210559	+	0.451546i
$59$	6.27320	+	5.26384i	0.816701	+	0.685293i	0.952197	−	0.305484i	$-0.0988184\pi$
$59$	6.27320	+	5.26384i	0.816701	+	0.685293i	−0.135496	+	0.990778i	$0.543263\pi$
$60$	−2.82264	+	1.92775i	−0.364402	+	0.248871i
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	0.505463	−	0.862848i	$-0.331322\pi$
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	−0.167421	+	0.985885i	$0.553544\pi$
$62$	−5.62907	−	1.50831i	−0.714893	−	0.191555i
$63$	8.66650	+	0.300676i	1.09188	+	0.0378817i
$64$	−6.69194	−	3.86359i	−0.836493	−	0.482949i
$65$	3.72276	+	11.5777i	0.461751	+	1.43604i
$66$	3.47414	−	2.57134i	0.427637	−	0.316510i
$67$	6.11610	−	4.28254i	0.747201	−	0.523196i	−0.136847	−	0.990592i	$-0.543697\pi$
$67$	6.11610	−	4.28254i	0.747201	−	0.523196i	0.884048	+	0.467396i	$0.154808\pi$
$68$	−2.00246	+	1.40214i	−0.242834	+	0.170034i
$69$	−0.140033	−	1.22781i	−0.0168579	−	0.147811i
$70$	3.12049	−	6.07833i	0.372970	−	0.726499i
$71$	−4.24004	−	2.44799i	−0.503200	−	0.290523i	0.226834	−	0.973933i	$-0.427162\pi$
$71$	−4.24004	−	2.44799i	−0.503200	−	0.290523i	−0.730034	+	0.683411i	$0.760496\pi$
$72$	6.79476	+	6.11524i	0.800770	+	0.720688i
$73$	−6.73088	−	1.80353i	−0.787790	−	0.211088i	−0.157574	−	0.987507i	$-0.550367\pi$
$73$	−6.73088	−	1.80353i	−0.787790	−	0.211088i	−0.630216	+	0.776420i	$0.717034\pi$
$74$	−4.38269	−	1.59517i	−0.509478	−	0.185435i
$75$	0.429628	−	8.64959i	0.0496091	−	0.998769i
$76$	4.18242	+	3.50947i	0.479756	+	0.402563i
$77$	2.88379	−	6.18430i	0.328638	−	0.704767i
$78$	8.49007	−	5.20404i	0.961311	−	0.589242i
$79$	−12.8661	+	2.26863i	−1.44754	+	0.255241i	−0.841529	−	0.540212i	$-0.818344\pi$
$79$	−12.8661	+	2.26863i	−1.44754	+	0.255241i	−0.606015	+	0.795453i	$0.707233\pi$
$80$	3.00075	−	1.26294i	0.335494	−	0.141201i
$81$	−5.29336	−	7.27876i	−0.588151	−	0.808751i
$82$	4.32741	+	4.32741i	0.477883	+	0.477883i
$83$	−2.73492	+	3.90587i	−0.300196	+	0.428724i	−0.940705	−	0.339227i	$-0.889835\pi$
$83$	−2.73492	+	3.90587i	−0.300196	+	0.428724i	0.640509	+	0.767951i	$0.278724\pi$
$84$	4.29664	+	1.03102i	0.468802	+	0.112493i
$85$	0.235061	−	6.18915i	0.0254960	−	0.671307i
$86$	0.984048	−	1.17274i	0.106113	−	0.126460i
$87$	4.65586	−	4.12010i	0.499161	−	0.441721i
$88$	6.51925	−	3.03998i	0.694955	−	0.324063i
$89$	3.33276	+	5.77251i	0.353272	+	0.611885i	0.986821	−	0.161818i	$-0.0517357\pi$
$89$	3.33276	+	5.77251i	0.353272	+	0.611885i	−0.633549	+	0.773703i	$0.718402\pi$
$90$	−6.96471	+	1.33337i	−0.734145	+	0.140550i
$91$	7.86060	−	13.6150i	0.824014	−	1.42723i
$92$	0.0548802	−	0.627283i	0.00572165	−	0.0653988i
$93$	7.47350	+	5.94331i	0.774966	+	0.616292i
$94$	10.8062	+	1.90542i	1.11457	+	0.196529i
$95$	−13.4879	+	3.07057i	−1.38383	+	0.315033i
$96$	4.69371	+	6.34168i	0.479050	+	0.647245i
$97$	−18.2758	−	1.59893i	−1.85563	−	0.162346i	−0.896079	−	0.443894i	$-0.853597\pi$
$97$	−18.2758	−	1.59893i	−1.85563	−	0.162346i	−0.959547	+	0.281548i	$0.909152\pi$
$98$	−1.38397	+	0.370833i	−0.139802	+	0.0374597i
$99$	−6.90008	+	1.59465i	−0.693484	+	0.160269i
$100$	1.09368	−	4.27509i	0.109368	−	0.427509i
$101$	−1.15191	+	3.16484i	−0.114619	+	0.314913i	−0.983716	−	0.179728i	$-0.942478\pi$
$101$	−1.15191	+	3.16484i	−0.114619	+	0.314913i	0.869097	+	0.494641i	$0.164701\pi$
$102$	−4.96953	+	1.01165i	−0.492057	+	0.100168i
$103$	−3.61346	+	0.316137i	−0.356045	+	0.0311499i	−0.263775	−	0.964584i	$-0.584968\pi$
$103$	−3.61346	+	0.316137i	−0.356045	+	0.0311499i	−0.0922694	+	0.995734i	$0.529412\pi$
$104$	15.5732	−	5.66819i	1.52708	−	0.555812i
$105$	−8.65935	+	7.09554i	−0.845066	+	0.692454i
$106$	−1.87673	−	10.6434i	−0.182284	−	1.03378i
$107$	−4.03460	+	4.03460i	−0.390039	+	0.390039i	−0.874701	−	0.484662i	$-0.838943\pi$
$107$	−4.03460	+	4.03460i	−0.390039	+	0.390039i	0.484662	+	0.874701i	$0.338943\pi$
$108$	−1.90315	−	4.17233i	−0.183131	−	0.401483i
$109$		−	15.8226i		−	1.51553i	−0.652527	−	0.757765i	$-0.726291\pi$
$109$		−	15.8226i		−	1.51553i	0.652527	−	0.757765i	$-0.273709\pi$
$110$	−1.17680	+	5.45444i	−0.112204	+	0.520060i
$111$	5.54385	+	5.25972i	0.526199	+	0.499231i
$112$	−3.81433	−	1.77865i	−0.360420	−	0.168067i
$113$	−0.232615	−	2.65880i	−0.0218825	−	0.250119i	−0.999255	−	0.0385931i	$-0.987712\pi$
$113$	−0.232615	−	2.65880i	−0.0218825	−	0.250119i	0.977372	−	0.211526i	$-0.0678432\pi$
$114$	5.05513	+	10.1361i	0.473456	+	0.949337i
$115$	1.18233	+	1.07113i	0.110253	+	0.0998836i
$116$	2.74346	−	1.58394i	0.254724	−	0.147065i
$117$	−16.1570	+	2.27446i	−1.49372	+	0.210273i
$118$	2.24050	+	8.36165i	0.206255	+	0.769753i
$119$	−6.13333	+	5.14648i	−0.562242	+	0.471777i
$120$	−11.8007	−	0.137699i	−1.07725	−	0.0125701i
$121$	0.942447	−	5.34488i	0.0856770	−	0.485898i
$122$	1.70355	+	2.43292i	0.154232	+	0.220266i
$123$	−3.67613	−	9.32930i	−0.331466	−	0.841195i
$124$	3.12744	+	3.72713i	0.280852	+	0.334707i
$125$	6.95610	+	8.75287i	0.622172	+	0.782880i
$126$	7.32219	+	5.51507i	0.652312	+	0.491321i
$127$	−0.846401	+	3.15881i	−0.0751059	+	0.280299i	−0.993257	−	0.115931i	$-0.963015\pi$
$127$	−0.846401	+	3.15881i	−0.0751059	+	0.280299i	0.918151	+	0.396230i	$0.129682\pi$
$128$	0.398073	+	0.853671i	0.0351850	+	0.0754546i
$129$	−2.24472	+	1.11950i	−0.197637	+	0.0985661i
$130$	−3.79622	+	12.2826i	−0.332950	+	1.07725i
$131$	0.497235	+	1.36614i	0.0434436	+	0.119360i	0.959517	−	0.281649i	$-0.0908815\pi$
$131$	0.497235	+	1.36614i	0.0434436	+	0.119360i	−0.916074	+	0.401010i	$0.868659\pi$
$132$	−3.60731	+	0.0948693i	−0.313976	+	0.00825731i
$133$	14.6481	+	10.2567i	1.27015	+	0.889368i
$134$	7.89266			0.681822
$135$	11.3367	+	2.54559i	0.975705	+	0.219090i
$136$	−8.44014			−0.723736
$137$	−13.0703	−	9.15193i	−1.11667	−	0.781902i	−0.138637	−	0.990343i	$-0.544272\pi$
$137$	−13.0703	−	9.15193i	−1.11667	−	0.781902i	−0.978035	+	0.208442i	$0.933161\pi$
$138$	0.623196	−	1.14809i	0.0530499	−	0.0977322i
$139$	−3.12149	−	8.57623i	−0.264762	−	0.727426i	−0.998830	−	0.0483514i	$-0.984603\pi$
$139$	−3.12149	−	8.57623i	−0.264762	−	0.727426i	0.734069	−	0.679075i	$-0.237619\pi$
$140$	−5.04484	+	2.66266i	−0.426367	+	0.225035i
$141$	−14.9937	−	9.92164i	−1.26269	−	0.835553i
$142$	−2.18726	−	4.69060i	−0.183551	−	0.393626i
$143$	−3.32299	+	12.4016i	−0.277883	+	1.03707i
$144$	0.983543	+	4.25580i	0.0819619	+	0.354650i
$145$	−1.00248	+	7.96338i	−0.0832517	+	0.661323i
$146$	−4.73488	−	5.64281i	−0.391861	−	0.467002i
$147$	2.32188	+	0.346738i	0.191505	+	0.0285985i
$148$	2.23344	+	3.18968i	0.183588	+	0.262190i
$149$	1.63395	−	9.26659i	0.133858	−	0.759149i	−0.841789	−	0.539806i	$-0.818498\pi$
$149$	1.63395	−	9.26659i	0.133858	−	0.759149i	0.975648	−	0.219343i	$-0.0703913\pi$
$150$	5.61648	−	7.22936i	0.458583	−	0.590275i
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	−0.675104	−	0.737723i	$-0.735901\pi$
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	0.609284	+	0.792952i	$0.291457\pi$
$152$	4.87887	+	18.2082i	0.395729	+	1.47688i
$153$	8.12841	+	1.72582i	0.657143	+	0.139525i
$154$	6.24682	−	3.60660i	0.503383	−	0.290628i
$155$	−12.3122	+	0.607549i	−0.988942	+	0.0487995i
$156$	−8.29843	−	0.506611i	−0.664406	−	0.0405613i
$157$	1.94520	+	22.2338i	0.155244	+	1.77445i	0.530652	+	0.847590i	$0.321947\pi$
$157$	1.94520	+	22.2338i	0.155244	+	1.77445i	−0.375408	+	0.926860i	$0.622497\pi$
$158$	−12.5165	−	5.83654i	−0.995759	−	0.464330i
$159$	−4.13198	+	17.2195i	−0.327687	+	1.36560i
$160$	−9.95651	−	2.14813i	−0.787131	−	0.169825i
$161$		−	2.06235i		−	0.162536i
$162$	−0.170346	−	9.51231i	−0.0133837	−	0.747358i
$163$	−1.74889	+	1.74889i	−0.136983	+	0.136983i	−0.772274	−	0.635290i	$-0.780881\pi$
$163$	−1.74889	+	1.74889i	−0.136983	+	0.136983i	0.635290	+	0.772274i	$0.280881\pi$
$164$	−0.887241	−	5.03179i	−0.0692819	−	0.392917i
$165$	5.33110	−	7.42761i	0.415025	−	0.578239i
$166$	−4.73644	+	1.72392i	−0.367619	+	0.133802i
$167$	7.25686	−	0.634893i	0.561553	−	0.0491295i	0.197154	−	0.980373i	$-0.436830\pi$
$167$	7.25686	−	0.634893i	0.561553	−	0.0491295i	0.364399	+	0.931243i	$0.381275\pi$
$168$	10.1101	+	11.4248i	0.780011	+	0.881441i
$169$	−5.67082	+	15.5805i	−0.436217	+	1.19850i
$170$	3.95617	−	5.21678i	0.303424	−	0.400109i
$171$	−0.975496	−	18.5333i	−0.0745981	−	1.41728i
$172$	−1.23458	+	0.330806i	−0.0941362	+	0.0252237i
$173$	20.4232	+	1.78680i	1.55275	+	0.135848i	0.830985	−	0.556295i	$-0.187778\pi$
$173$	20.4232	+	1.78680i	1.55275	+	0.135848i	0.721760	+	0.692143i	$0.243333\pi$
$174$	6.52972	−	0.744716i	0.495017	−	0.0564568i
$175$	2.34809	−	14.2608i	0.177499	−	1.07802i
$176$	3.38487	+	0.596843i	0.255144	+	0.0449887i
$177$	2.09493	−	14.0283i	0.157464	−	1.05443i
$178$	−0.614106	+	7.01926i	−0.0460292	+	0.526116i
$179$	7.17079	−	12.4202i	0.535970	−	0.928327i	−0.463146	−	0.886282i	$-0.653279\pi$
$179$	7.17079	−	12.4202i	0.535970	−	0.928327i	0.999116	−	0.0420450i	$-0.0133873\pi$
$180$	5.40168	+	2.42331i	0.402617	+	0.180623i
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	0.901916	−	0.431912i	$-0.142161\pi$
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	−0.825005	+	0.565126i	$0.808828\pi$
$182$	15.0617	−	7.02339i	1.11645	−	0.520609i
$183$	−0.970750	−	4.76862i	−0.0717599	−	0.352507i
$184$	1.39745	−	1.66542i	0.103021	−	0.122776i
$185$	−9.85857	−	0.374424i	−0.724816	−	0.0275282i
$186$	2.86788	+	9.67779i	0.210283	+	0.709610i
$187$	3.75043	−	5.35618i	0.274259	−	0.391682i
$188$	−6.47790	−	6.47790i	−0.472449	−	0.472449i
$189$	−7.40057	−	13.0701i	−0.538312	−	0.950710i
$190$	−13.5412	−	5.51919i	−0.982384	−	0.400404i
$191$	22.9618	−	4.04878i	1.66145	−	0.292959i	0.737467	−	0.675383i	$-0.236022\pi$
$191$	22.9618	−	4.04878i	1.66145	−	0.292959i	0.923987	+	0.382424i	$0.124911\pi$
$192$	0.351864	+	13.3793i	0.0253936	+	0.965564i
$193$	−0.131693	+	0.282417i	−0.00947948	+	0.0203288i	−0.910991	−	0.412427i	$-0.864681\pi$
$193$	−0.131693	+	0.282417i	−0.00947948	+	0.0203288i	0.901511	+	0.432756i	$0.142459\pi$
$194$	−14.8559	−	12.4656i	−1.06659	−	0.894977i
$195$	13.7272	−	15.9771i	0.983028	−	1.14415i
$196$	1.12408	+	0.409130i	0.0802911	+	0.0292236i
$197$	−3.13774	−	0.840756i	−0.223555	−	0.0599014i	0.145303	−	0.989387i	$-0.453584\pi$
$197$	−3.13774	−	0.840756i	−0.223555	−	0.0599014i	−0.368858	+	0.929486i	$0.620251\pi$
$198$	−6.94179	−	2.80284i	−0.493332	−	0.199189i
$199$	5.52277	+	3.18857i	0.391499	+	0.226032i	0.682809	−	0.730596i	$-0.260758\pi$
$199$	5.52277	+	3.18857i	0.391499	+	0.226032i	−0.291310	+	0.956629i	$0.594091\pi$
$200$	11.5593	−	9.92504i	0.817369	−	0.701807i
$201$	−11.8601	−	5.15534i	−0.836550	−	0.363630i
$202$	−2.91638	+	2.04207i	−0.205196	+	0.143679i
$203$	8.49914	−	5.95116i	0.596523	−	0.417690i
$204$	3.88311	+	1.68790i	0.271872	+	0.118177i
$205$	11.5164	+	5.91229i	0.804342	+	0.412932i
$206$	−3.32065	−	1.91718i	−0.231360	−	0.133576i
$207$	−1.68638	+	1.31816i	−0.117211	+	0.0916183i
$208$	7.64899	+	2.04954i	0.530362	+	0.142110i
$209$	−13.7230	−	4.99477i	−0.949241	−	0.345495i
$210$	−11.8005	+	0.893801i	−0.814312	+	0.0616781i
$211$	4.91430	+	4.12359i	0.338314	+	0.283879i	0.796077	−	0.605195i	$-0.206905\pi$
$211$	4.91430	+	4.12359i	0.338314	+	0.283879i	−0.457763	+	0.889074i	$0.651349\pi$
$212$	−3.81335	+	8.17776i	−0.261902	+	0.561651i
$213$	0.222942	+	8.47715i	0.0152757	+	0.580844i
$214$	−5.93991	+	1.04737i	−0.406044	+	0.0715965i
$215$	1.22226	−	2.99880i	0.0833578	−	0.204517i
$216$	2.88011	−	15.5692i	0.195967	−	1.05935i
$217$	11.2680	+	11.2680i	0.764925	+	0.764925i
$218$	9.59362	−	13.7011i	0.649762	−	0.927956i
$219$	3.42923	+	11.5721i	0.231726	+	0.781968i
$220$	3.41679	−	3.16675i	0.230360	−	0.213502i
$221$	9.68341	−	11.5402i	0.651376	−	0.776280i
$222$	1.61143	+	7.91587i	0.108152	+	0.531278i
$223$	−9.41489	+	4.39023i	−0.630467	+	0.293992i	−0.711464	−	0.702723i	$-0.751968\pi$
$223$	−9.41489	+	4.39023i	−0.630467	+	0.293992i	0.0809965	+	0.996714i	$0.474190\pi$
$224$	6.58348	+	11.4029i	0.439877	+	0.761889i
$225$	−13.1619	+	7.19484i	−0.877457	+	0.479656i
$226$	1.41067	−	2.44335i	0.0938361	−	0.162529i
$227$	0.272304	−	3.11245i	0.0180734	−	0.206580i	−0.981789	−	0.189976i	$-0.939159\pi$
$227$	0.272304	−	3.11245i	0.0180734	−	0.206580i	0.999862	−	0.0166042i	$-0.00528553\pi$
$228$	1.39671	−	9.35287i	0.0924996	−	0.619409i
$229$	23.1368	+	4.07964i	1.52892	+	0.269590i	0.873933	−	0.486047i	$-0.161562\pi$
$229$	23.1368	+	4.07964i	1.52892	+	0.269590i	0.654990	+	0.755638i	$0.272673\pi$
$230$	0.374350	+	1.64439i	0.0246839	+	0.108428i
$231$	−11.7427	+	1.33926i	−0.772616	+	0.0881170i
$232$	10.8959	+	0.953265i	0.715349	+	0.0625849i
$233$	−3.20411	+	0.858538i	−0.209908	+	0.0562447i	−0.362241	−	0.932085i	$-0.617988\pi$
$233$	−3.20411	+	0.858538i	−0.209908	+	0.0562447i	0.152333	+	0.988329i	$0.451321\pi$
$234$	−15.3698	−	7.82690i	−1.00475	−	0.511661i
$235$	22.9948	−	3.16011i	1.50002	−	0.206143i
$236$	2.47188	−	6.79145i	0.160906	−	0.442085i
$237$	14.9960	+	16.9460i	0.974093	+	1.10076i
$238$	−8.43141	+	0.737653i	−0.546527	+	0.0478149i
$239$	−15.9837	+	5.81759i	−1.03390	+	0.376309i	−0.802564	−	0.596566i	$-0.796532\pi$
$239$	−15.9837	+	5.81759i	−1.03390	+	0.376309i	−0.231335	+	0.972874i	$0.574309\pi$
$240$	−4.58117	−	3.28809i	−0.295713	−	0.212245i
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	0.893349	+	0.449364i	$0.148349\pi$
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	−0.685782	+	0.727807i	$0.740540\pi$
$242$	4.05681	−	4.05681i	0.260782	−	0.260782i
$243$	−5.95729	+	14.4052i	−0.382160	+	0.924096i
$244$		−	2.47965i		−	0.158744i
$245$	−2.54685	+	1.64290i	−0.162712	+	0.104961i
$246$	2.47334	−	10.3074i	0.157695	−	0.657173i
$247$	−30.4937	−	14.2194i	−1.94027	−	0.904761i
$248$	1.46409	+	16.7346i	0.0929695	+	1.06265i
$249$	8.24339	+	0.503250i	0.522403	+	0.0318922i
$250$	0.716350	+	11.7969i	0.0453060	+	0.746103i
$251$	−13.1493	+	7.59178i	−0.829979	+	0.479189i	−0.853846	−	0.520527i	$-0.825736\pi$
$251$	−13.1493	+	7.59178i	−0.829979	+	0.479189i	0.0238664	+	0.999715i	$0.492402\pi$
$252$	−2.36663	−	7.27814i	−0.149084	−	0.458480i
$253$	0.435919	+	1.62687i	0.0274060	+	0.102281i
$254$	−2.64818	+	2.22208i	−0.166161	+	0.139426i
$255$	−9.35237	+	5.25506i	−0.585668	+	0.329085i
$256$	−2.85653	+	16.2002i	−0.178533	+	1.01251i
$257$	4.98418	+	7.11815i	0.310905	+	0.444018i	0.943946	−	0.330100i	$-0.107083\pi$
$257$	4.98418	+	7.11815i	0.310905	+	0.444018i	−0.633041	+	0.774118i	$0.718194\pi$
$258$	−2.62253	−	0.391636i	−0.163271	−	0.0243822i
$259$	8.19772	+	9.76966i	0.509382	+	0.607057i
$260$	8.47800	−	6.58213i	0.525783	−	0.408207i
$261$	−10.2985	−	3.14602i	−0.637462	−	0.194734i
$262$	−0.397759	+	1.48446i	−0.0245736	+	0.0917099i
$263$	9.97382	+	21.3889i	0.615012	+	1.31890i	0.929214	+	0.369541i	$0.120485\pi$
$263$	9.97382	+	21.3889i	0.615012	+	1.31890i	−0.314203	+	0.949356i	$0.601737\pi$
$264$	−10.3902	−	6.87540i	−0.639470	−	0.423152i
$265$	−10.6711	−	20.2181i	−0.655518	−	1.24199i
$266$	6.46518	+	17.7629i	0.396406	+	1.08912i
$267$	5.50766	−	10.1466i	0.337063	−	0.620961i
$268$	−5.39779	−	3.77957i	−0.329723	−	0.230874i
$269$	10.2124			0.622659			0.311330	−	0.950302i	$-0.399226\pi$
$269$	10.2124			0.622659			0.311330	+	0.950302i	$0.399226\pi$
$270$	8.27319	+	9.07797i	0.503490	+	0.552467i
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	−3.30356	−	2.31318i	−0.200308	−	0.140257i
$273$	−27.2205	+	0.715877i	−1.64746	+	0.0433268i
$274$	−5.76881	−	15.8497i	−0.348506	−	0.957514i
$275$	1.16204	+	11.7459i	0.0700734	+	0.708305i
$276$	−0.975993	+	0.486750i	−0.0587479	+	0.0292989i
$277$	−5.71185	−	12.2491i	−0.343192	−	0.735978i	0.656642	−	0.754203i	$-0.271976\pi$
$277$	−5.71185	−	12.2491i	−0.343192	−	0.735978i	−0.999834	+	0.0182248i	$0.994199\pi$
$278$	2.49701	−	9.31897i	0.149761	−	0.558914i
$279$	2.01184	−	16.4159i	0.120446	−	0.982792i
$280$	−19.5409	−	2.45994i	−1.16779	−	0.147010i
$281$	−10.1156	−	12.0553i	−0.603445	−	0.719158i	0.374685	−	0.927152i	$-0.377751\pi$
$281$	−10.1156	−	12.0553i	−0.603445	−	0.719158i	−0.978130	+	0.207994i	$0.933306\pi$
$282$	−6.96758	−	17.6824i	−0.414913	−	1.05297i
$283$	−17.2952	−	24.7001i	−1.02809	−	1.46827i	−0.877443	−	0.479680i	$-0.840753\pi$
$283$	−17.2952	−	24.7001i	−1.02809	−	1.46827i	−0.150648	−	0.988587i	$-0.548136\pi$
$284$	−0.750327	+	4.25532i	−0.0445237	+	0.252507i
$285$	16.7431	+	17.1385i	0.991775	+	1.01519i
$286$	−10.3968	+	8.72397i	−0.614777	+	0.515859i
$287$	−4.33122	−	16.1643i	−0.255664	−	0.954150i
$288$	5.11629	−	12.6715i	0.301480	−	0.746676i
$289$	8.07815	−	4.66392i	0.475185	−	0.274348i
$290$	−5.69646	+	6.28782i	−0.334508	+	0.369234i
$291$	14.1814	+	28.4354i	0.831328	+	1.66691i
$292$	0.536001	+	6.12652i	0.0313671	+	0.358527i
$293$	−6.65512	−	3.10333i	−0.388796	−	0.181299i	0.218384	−	0.975863i	$-0.429922\pi$
$293$	−6.65512	−	3.10333i	−0.388796	−	0.181299i	−0.607180	+	0.794564i	$0.707699\pi$
$294$	1.80033	+	1.70806i	0.104997	+	0.0996160i
$295$	9.92611	+	15.3876i	0.577921	+	0.895899i
$296$			13.4441i			0.781424i
$297$	8.60053	+	8.74602i	0.499053	+	0.507496i
$298$	7.03343	−	7.03343i	0.407435	−	0.407435i
$299$	0.673830	+	3.82148i	0.0389686	+	0.221002i
$300$	−7.30304	+	2.25459i	−0.421641	+	0.130169i
$301$	−3.93374	+	1.43176i	−0.226737	+	0.0825254i
$302$	−1.11185	+	0.0972742i	−0.0639798	+	0.00559750i
$303$	5.71622	−	1.16365i	0.328388	−	0.0668501i
$304$	−3.08065	+	8.46402i	−0.176687	+	0.485445i
$305$	5.00588	+	3.79623i	0.286636	+	0.217372i
$306$	5.99214	+	6.42287i	0.342548	+	0.367171i
$307$	13.2129	−	3.54038i	0.754099	−	0.202060i	0.138764	−	0.990326i	$-0.455687\pi$
$307$	13.2129	−	3.54038i	0.754099	−	0.202060i	0.615336	+	0.788265i	$0.289020\pi$
$308$	−5.99930	−	0.524871i	−0.341842	−	0.0299073i
$309$	3.73760	+	5.04989i	0.212625	+	0.287278i
$310$	−11.0298	−	6.93911i	−0.626449	−	0.394115i
$311$	3.80231	+	0.670449i	0.215609	+	0.0380177i	0.280409	−	0.959881i	$-0.409530\pi$
$311$	3.80231	+	0.670449i	0.215609	+	0.0380177i	−0.0648001	+	0.997898i	$0.520641\pi$
$312$	−22.4666	−	17.8666i	−1.27192	−	1.01149i
$313$	2.14418	−	24.5081i	0.121196	−	1.38528i	−0.655401	−	0.755281i	$-0.727500\pi$
$313$	2.14418	−	24.5081i	0.121196	−	1.38528i	0.776597	−	0.629997i	$-0.216944\pi$
$314$	−11.7965	+	20.4321i	−0.665714	+	1.15305i
$315$	18.3162	+	6.36477i	1.03200	+	0.358614i
$316$	5.76508	+	9.98541i	0.324311	+	0.561723i
$317$	14.9555	−	6.97386i	0.839984	−	0.391691i	0.0454916	−	0.998965i	$-0.485515\pi$
$317$	14.9555	−	6.97386i	0.839984	−	0.391691i	0.794493	+	0.607274i	$0.207737\pi$
$318$	−14.0186	+	12.4054i	−0.786123	+	0.695661i
$319$	−5.44660	+	6.49101i	−0.304951	+	0.363427i
$320$	−11.7453	−	12.6726i	−0.656580	−	0.708422i
$321$	9.60991	+	2.30598i	0.536373	+	0.128707i
$322$	1.25045	−	1.78583i	0.0696849	−	0.0995203i
$323$	12.1165	+	12.1165i	0.674178	+	0.674178i
$324$	−4.43868	+	6.58704i	−0.246593	+	0.365947i
$325$	0.308476	+	27.1922i	0.0171112	+	1.50835i
$326$	−2.57479	+	0.454005i	−0.142604	+	0.0251450i
$327$	−23.3654	+	14.3220i	−1.29211	+	0.792009i
$328$	7.45537	−	15.9881i	0.411654	−	0.882794i
$329$	−22.9851	−	19.2867i	−1.26721	−	1.06331i
$330$	9.11984	−	3.19935i	0.502031	−	0.176118i
$331$	−19.3973	−	7.06005i	−1.06617	−	0.388056i	−0.251429	−	0.967876i	$-0.580901\pi$
$331$	−19.3973	−	7.06005i	−1.06617	−	0.388056i	−0.814744	+	0.579820i	$0.803123\pi$
$332$	4.06479	+	1.08916i	0.223084	+	0.0597752i
$333$	2.74903	−	12.9476i	0.150646	−	0.709523i
$334$	6.66881	+	3.85024i	0.364901	+	0.210676i
$335$	15.8939	−	5.11062i	0.868377	−	0.279223i
$336$	0.826024	+	7.24263i	0.0450633	+	0.395118i
$337$	−8.57053	+	6.00115i	−0.466867	+	0.326904i	−0.783227	−	0.621735i	$-0.786428\pi$
$337$	−8.57053	+	6.00115i	−0.466867	+	0.326904i	0.316361	+	0.948639i	$0.397539\pi$
$338$	−14.3573	+	10.0531i	−0.780933	+	0.546815i
$339$	−3.71573	+	2.75015i	−0.201811	+	0.149367i
$340$	−5.20380	+	1.67326i	−0.282215	+	0.0907452i
$341$	−11.2705	−	6.50701i	−0.610330	−	0.352374i
$342$	10.3925	−	16.6398i	0.561961	−	0.899778i
$343$	−15.7602	−	4.22292i	−0.850968	−	0.228016i
$344$	−4.14679	−	1.50931i	−0.223580	−	0.0813765i
$345$	0.511557	−	2.71551i	0.0275413	−	0.146198i
$346$	16.6015	+	13.9303i	0.892500	+	0.748896i
$347$	−4.85639	+	10.4146i	−0.260705	+	0.559083i	−0.992472	−	0.122472i	$-0.960918\pi$
$347$	−4.85639	+	10.4146i	−0.260705	+	0.559083i	0.731767	+	0.681554i	$0.238696\pi$
$348$	−4.82230	−	2.61759i	−0.258502	−	0.140317i
$349$	15.6377	−	2.75735i	0.837067	−	0.147597i	0.261347	−	0.965245i	$-0.415833\pi$
$349$	15.6377	−	2.75735i	0.837067	−	0.147597i	0.575719	+	0.817647i	$0.304722\pi$
$350$	10.6799	−	10.9250i	0.570867	−	0.583968i
$351$	17.9835	+	21.8006i	0.959886	+	1.16363i
$352$	−7.60358	−	7.60358i	−0.405272	−	0.405272i
$353$	4.97772	−	7.10893i	0.264938	−	0.378370i	−0.664538	−	0.747255i	$-0.731371\pi$
$353$	4.97772	−	7.10893i	0.264938	−	0.378370i	0.929475	+	0.368885i	$0.120260\pi$
$354$	10.3198	−	10.8772i	0.548489	−	0.578118i
$355$	−7.44184	−	8.02943i	−0.394972	−	0.426158i
$356$	3.78131	−	4.50640i	0.200409	−	0.238838i
$357$	13.1515	+	4.39878i	0.696053	+	0.232808i
$358$	13.7400	−	6.40706i	0.726180	−	0.338623i
$359$	10.2032	+	17.6725i	0.538505	+	0.932718i	0.998985	+	0.0450476i	$0.0143439\pi$
$359$	10.2032	+	17.6725i	0.538505	+	0.932718i	−0.460480	+	0.887670i	$0.652323\pi$
$360$	10.4782	+	17.5509i	0.552248	+	0.925011i
$361$	9.63526	−	16.6888i	0.507119	−	0.878356i
$362$	−0.190664	+	2.17930i	−0.0100211	+	0.114541i
$363$	−8.74593	+	3.44626i	−0.459042	+	0.180881i
$364$	−13.6640	−	2.40933i	−0.716189	−	0.126283i
$365$	−13.1887	−	8.29733i	−0.690328	−	0.434302i
$366$	2.05074	−	4.71784i	0.107194	−	0.246605i
$367$	25.8506	+	2.26163i	1.34939	+	0.118056i	0.738818	−	0.673906i	$-0.235385\pi$
$367$	25.8506	+	2.26163i	1.34939	+	0.118056i	0.610571	+	0.791962i	$0.290940\pi$
$368$	1.00341	−	0.268864i	0.0523066	−	0.0140155i
$369$	−10.4492	+	13.8731i	−0.543965	+	0.722206i
$370$	−8.30971	−	6.30171i	−0.432001	−	0.327610i
$371$	−10.1077	+	27.7707i	−0.524766	+	1.44178i
$372$	2.67308	−	7.99199i	0.138593	−	0.414365i
$373$	4.75950	−	0.416402i	0.246438	−	0.0215605i	0.0367323	−	0.999325i	$-0.488305\pi$
$373$	4.75950	−	0.416402i	0.246438	−	0.0215605i	0.209705	+	0.977765i	$0.432750\pi$
$374$	6.49515	−	2.36404i	0.335856	−	0.122242i
$375$	6.62909	−	18.1949i	0.342325	−	0.939582i
$376$	−5.49248	−	31.1494i	−0.283253	−	1.60641i
$377$	−13.8043	+	13.8043i	−0.710956	+	0.710956i
$378$	1.51641	−	15.8048i	0.0779958	−	0.812911i
$379$		−	25.3002i		−	1.29958i	−0.760112	−	0.649792i	$-0.774856\pi$
$379$		−	25.3002i		−	1.29958i	0.760112	−	0.649792i	$-0.225144\pi$
$380$	6.61786	+	10.2591i	0.339489	+	0.526280i
$381$	5.43079	−	1.60934i	0.278228	−	0.0824491i
$382$	22.3379	+	10.4163i	1.14291	+	0.532946i
$383$	−1.07406	−	12.2766i	−0.0548819	−	0.627303i	−0.972971	−	0.230929i	$-0.925824\pi$
$383$	−1.07406	−	12.2766i	−0.0548819	−	0.627303i	0.918089	−	0.396375i	$-0.129732\pi$
$384$	0.900307	−	1.36055i	0.0459436	−	0.0694303i
$385$	10.2442	−	11.3077i	0.522095	−	0.576295i
$386$	−0.285272	+	0.164702i	−0.0145200	+	0.00838310i
$387$	3.68501	+	2.30149i	0.187320	+	0.116991i
$388$	4.19054	+	15.6393i	0.212742	+	0.793965i
$389$	6.83430	−	5.73466i	0.346513	−	0.290759i	−0.452875	−	0.891574i	$-0.649602\pi$
$389$	6.83430	−	5.73466i	0.346513	−	0.290759i	0.799388	+	0.600815i	$0.205157\pi$
$390$	21.5740	−	5.51176i	1.09244	−	0.279099i
$391$	0.343168	−	1.94620i	0.0173548	−	0.0984238i
$392$	2.36892	+	3.38317i	0.119649	+	0.170876i
$393$	1.56732	−	1.97085i	0.0790610	−	0.0994164i
$394$	−2.20727	−	2.63052i	−0.111200	−	0.132524i
$395$	−28.9844	−	3.64875i	−1.45836	−	0.183588i
$396$	3.40529	+	5.24109i	0.171122	+	0.263375i
$397$	3.52782	−	13.1660i	0.177056	−	0.660782i	−0.819136	−	0.573599i	$-0.805547\pi$
$397$	3.52782	−	13.1660i	0.177056	−	0.660782i	0.996192	−	0.0871833i	$-0.0277866\pi$
$398$	2.84897	+	6.10964i	0.142806	+	0.306249i
$399$	1.88733	−	30.9150i	0.0944846	−	1.54768i
$400$	7.24458	−	0.716715i	0.362229	−	0.0358358i
$401$	−1.00354	−	2.75721i	−0.0501146	−	0.137689i	0.912110	−	0.409945i	$-0.134452\pi$
$401$	−1.00354	−	2.75721i	−0.0501146	−	0.137689i	−0.962225	+	0.272257i	$0.912230\pi$
$402$	−7.14413	−	11.6552i	−0.356317	−	0.581309i
$403$	−24.5610	−	17.1978i	−1.22347	−	0.856683i
$404$	2.97240			0.147882
$405$	−6.50240	−	19.0452i	−0.323107	−	0.946362i
$406$	10.9679			0.544328
$407$	−8.53175	−	5.97399i	−0.422903	−	0.296120i
$408$	7.63969	+	12.4637i	0.378221	+	0.617044i
$409$	9.80467	+	26.9381i	0.484810	+	1.33200i	0.905325	+	0.424719i	$0.139627\pi$
$409$	9.80467	+	26.9381i	0.484810	+	1.33200i	−0.420515	+	0.907285i	$0.638151\pi$
$410$	6.38754	+	12.1022i	0.315458	+	0.597687i
$411$	−1.68404	+	27.5851i	−0.0830676	+	1.36067i
$412$	1.35291	+	2.90132i	0.0666530	+	0.142938i
$413$	6.12654	−	22.8645i	0.301467	−	1.12509i
$414$	−2.25950	+	0.118928i	−0.111048	+	0.00584500i
$415$	−8.42177	+	6.53847i	−0.413408	+	0.320961i
$416$	−15.9247	−	18.9783i	−0.780772	−	0.930488i
$417$	−9.83918	+	12.3724i	−0.481827	+	0.605880i
$418$	−8.85459	−	12.6457i	−0.433092	−	0.618519i
$419$	−2.30839	+	13.0915i	−0.112772	+	0.639563i	0.875057	+	0.484020i	$0.160824\pi$
$419$	−2.30839	+	13.0915i	−0.112772	+	0.639563i	−0.987829	+	0.155543i	$0.950287\pi$
$420$	8.49838	+	5.03966i	0.414678	+	0.245910i
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	−0.457974	−	0.888966i	$-0.651425\pi$
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	0.795934	+	0.605383i	$0.206980\pi$
$422$	1.75516	+	6.55035i	0.0854399	+	0.318866i
$423$	−1.07975	+	31.1220i	−0.0524993	+	1.51320i
$424$	−26.9798	+	15.5768i	−1.31025	+	0.756476i
$425$	4.58882	−	13.0670i	0.222590	−	0.633843i
$426$	−4.94684	+	7.47571i	−0.239675	+	0.362199i
$427$	−0.707831	−	8.09054i	−0.0342543	−	0.391529i
$428$	4.56386	+	2.12816i	0.220602	+	0.102869i
$429$	21.3214	−	6.31832i	1.02941	−	0.305051i
$430$	2.87663	−	1.85564i	0.138723	−	0.0894868i
$431$			0.295969i			0.0142563i	0.999975	+	0.00712817i	$0.00226899\pi$
$431$			0.295969i			0.0142563i	−0.999975	+	0.00712817i	$0.997731\pi$
$432$	5.39433	−	5.30459i	0.259535	−	0.255217i
$433$	12.8171	−	12.8171i	0.615949	−	0.615949i	−0.328541	−	0.944490i	$-0.606557\pi$
$433$	12.8171	−	12.8171i	0.615949	−	0.615949i	0.944490	+	0.328541i	$0.106557\pi$
$434$	2.92514	+	16.5893i	0.140411	+	0.796312i
$435$	12.6670	−	5.72777i	0.607338	−	0.274625i
$436$	−13.1221	+	4.77607i	−0.628437	+	0.228732i
$437$	−4.39698	+	0.384686i	−0.210336	+	0.0184020i
$438$	−4.04698	+	12.0997i	−0.193372	+	0.578146i
$439$	−9.75841	+	26.8110i	−0.465743	+	1.27962i	0.455362	+	0.890306i	$0.349510\pi$
$439$	−9.75841	+	26.8110i	−0.465743	+	1.27962i	−0.921105	+	0.389313i	$0.872712\pi$
$440$	15.9347	−	2.18986i	0.759658	−	0.104398i
$441$	−1.58964	−	3.74260i	−0.0756972	−	0.178219i
$442$	15.3822	−	4.12164i	0.731655	−	0.196046i
$443$	−40.1651	−	3.51399i	−1.90830	−	0.166955i	−0.929098	−	0.369833i	$-0.879415\pi$
$443$	−40.1651	−	3.51399i	−1.90830	−	0.166955i	−0.979204	+	0.202878i	$0.934970\pi$
$444$	2.68863	−	6.18533i	0.127597	−	0.293543i
$445$	3.30842	+	14.5327i	0.156834	+	0.688917i
$446$	−10.8144	−	1.90688i	−0.512079	−	0.0902933i
$447$	−15.1631	+	5.97488i	−0.717190	+	0.282602i
$448$	−1.94671	+	22.2510i	−0.0919734	+	1.05126i
$449$	−3.91232	+	6.77634i	−0.184634	+	0.319795i	−0.943453	−	0.331506i	$-0.892443\pi$
$449$	−3.91232	+	6.77634i	−0.184634	+	0.319795i	0.758819	+	0.651301i	$0.225777\pi$
$450$	−15.7595	−	1.75019i	−0.742910	−	0.0825047i
$451$	6.83332	+	11.8357i	0.321768	+	0.557319i
$452$	−2.13480	+	0.995476i	−0.100413	+	0.0468232i
$453$	1.73429	+	0.580068i	0.0814841	+	0.0272540i
$454$	2.12294	−	2.53003i	0.0996347	−	0.118740i
$455$	25.7829	−	23.8961i	1.20872	−	1.12027i
$456$	22.4721	−	23.6860i	1.05235	−	1.10920i
$457$	−3.14363	+	4.48957i	−0.147053	+	0.210013i	−0.885920	−	0.463838i	$-0.846472\pi$
$457$	−3.14363	+	4.48957i	−0.147053	+	0.210013i	0.738867	+	0.673851i	$0.235361\pi$
$458$	17.5610	+	17.5610i	0.820573	+	0.820573i
$459$	−4.80897	−	13.5655i	−0.224464	−	0.633182i
$460$	0.531434	−	1.30386i	0.0247782	−	0.0607929i
$461$	29.6880	−	5.23480i	1.38271	−	0.243809i	0.567689	−	0.823243i	$-0.307837\pi$
$461$	29.6880	−	5.23480i	1.38271	−	0.243809i	0.815019	+	0.579434i	$0.196726\pi$
$462$	−10.9803	−	5.96021i	−0.510850	−	0.277294i
$463$	0.0761934	−	0.163397i	0.00354101	−	0.00759371i	−0.904529	−	0.426411i	$-0.859778\pi$
$463$	0.0761934	−	0.163397i	0.00354101	−	0.00759371i	0.908070	+	0.418818i	$0.137555\pi$
$464$	4.00350	+	3.35933i	0.185858	+	0.155953i
$465$	12.0417	+	17.6317i	0.558422	+	0.817651i
$466$	−3.29505	−	1.19930i	−0.152640	−	0.0555566i
$467$	−12.1916	−	3.26672i	−0.564158	−	0.151166i	−0.0345422	−	0.999403i	$-0.510997\pi$
$467$	−12.1916	−	3.26672i	−0.564158	−	0.151166i	−0.529616	+	0.848238i	$0.677664\pi$
$468$	6.76330	+	12.7130i	0.312634	+	0.587657i
$469$	−18.6907	−	10.7911i	−0.863055	−	0.498285i
$470$	21.8277	+	11.2059i	1.00684	+	0.516890i
$471$	31.0722	−	22.9977i	1.43173	−	1.05968i
$472$	20.4404	−	14.3126i	0.940848	−	0.658789i
$473$	2.80048	−	1.96091i	0.128766	−	0.0901629i
$474$	2.71055	+	23.7663i	0.124500	+	1.09162i
$475$	−30.8425	−	2.34615i	−1.41515	−	0.107649i
$476$	6.11948	+	3.53308i	0.280486	+	0.161939i
$477$	29.1684	−	9.48470i	1.33553	−	0.434274i
$478$	−17.3679	−	4.65373i	−0.794391	−	0.212857i
$479$	−33.4923	−	12.1902i	−1.53030	−	0.556985i	−0.566607	−	0.823988i	$-0.691744\pi$
$479$	−33.4923	−	12.1902i	−1.53030	−	0.556985i	−0.963696	+	0.267003i	$0.913966\pi$
$480$	5.84007	+	16.6473i	0.266561	+	0.759842i
$481$	−18.3822	−	15.4245i	−0.838157	−	0.703297i
$482$	−8.29007	+	17.7781i	−0.377602	+	0.809771i
$483$	−3.04550	+	1.86676i	−0.138575	+	0.0849404i
$484$	−4.71715	+	0.831760i	−0.214416	+	0.0378073i
$485$	−37.9878	−	15.4832i	−1.72494	−	0.703058i
$486$	−13.8928	+	8.86173i	−0.630189	+	0.401976i
$487$	4.88907	+	4.88907i	0.221545	+	0.221545i	0.809149	−	0.587604i	$-0.199929\pi$
$487$	4.88907	+	4.88907i	0.221545	+	0.221545i	−0.587604	+	0.809149i	$0.699929\pi$
$488$	4.91057	−	7.01302i	0.222291	−	0.317464i
$489$	4.16563	+	0.999581i	0.188376	+	0.0452026i
$490$	−3.20150	−	0.121592i	−0.144629	−	0.00549295i
$491$	−16.6934	+	19.8944i	−0.753361	+	0.897821i	−0.997409	−	0.0719426i	$-0.977080\pi$
$491$	−16.6934	+	19.8944i	−0.753361	+	0.897821i	0.244048	+	0.969763i	$0.421525\pi$
$492$	−6.62742	+	5.86479i	−0.298787	+	0.264405i
$493$	9.01076	−	4.20179i	0.405824	−	0.189239i
$494$	−17.7835	−	30.8019i	−0.800117	−	1.38584i
$495$	−15.7940	−	1.14932i	−0.709885	−	0.0516581i
$496$	−4.01336	+	6.95135i	−0.180205	+	0.312125i
$497$	−1.23344	+	14.0983i	−0.0553275	+	0.632396i
$498$	6.83298	+	5.43393i	0.306193	+	0.243500i
$499$	11.0477	+	1.94801i	0.494564	+	0.0872050i	0.415367	−	0.909654i	$-0.363653\pi$
$499$	11.0477	+	1.94801i	0.494564	+	0.0872050i	0.0791972	+	0.996859i	$0.474764\pi$
$500$	5.15931	−	8.41096i	0.230731	−	0.376150i
$501$	−7.50619	−	10.1416i	−0.335352	−	0.453095i
$502$	−15.9894	−	1.39889i	−0.713640	−	0.0624354i
$503$	29.1890	−	7.82118i	1.30147	−	0.348729i	0.459467	−	0.888195i	$-0.348040\pi$
$503$	29.1890	−	7.82118i	1.30147	−	0.348729i	0.842008	+	0.539466i	$0.181374\pi$
$504$	7.71986	−	25.2710i	0.343870	−	1.12566i
$505$	−4.55060	+	6.00063i	−0.202499	+	0.267024i
$506$	−0.608940	+	1.67305i	−0.0270707	+	0.0743761i
$507$	28.1409	−	5.72864i	1.24978	−	0.254418i
$508$	2.87518	−	0.251546i	0.127566	−	0.0111605i
$509$	22.0511	−	8.02596i	0.977399	−	0.355744i	0.196571	−	0.980490i	$-0.437019\pi$
$509$	22.0511	−	8.02596i	0.977399	−	0.355744i	0.780829	+	0.624745i	$0.214797\pi$
$510$	−11.2847	−	1.12010i	−0.499694	−	0.0495989i
$511$	3.49769	+	19.8364i	0.154729	+	0.877511i
$512$	−10.9640	+	10.9640i	−0.484544	+	0.484544i
$513$	−26.4854	+	18.2162i	−1.16936	+	0.804263i
$514$			9.18578i			0.405167i
$515$	−7.92837	−	1.71056i	−0.349366	−	0.0753762i
$516$	1.60600	+	1.52370i	0.0707004	+	0.0670769i
$517$	22.2083	+	10.3559i	0.976719	+	0.455452i
$518$	1.17499	+	13.4302i	0.0516262	+	0.590090i
$519$	−15.8477	−	31.7765i	−0.695636	−	1.39483i
$520$	37.0126	−	1.82639i	1.62311	−	0.0800925i
$521$	−14.2319	+	8.21681i	−0.623512	+	0.359985i	−0.778235	−	0.627973i	$-0.783885\pi$
$521$	−14.2319	+	8.21681i	−0.623512	+	0.359985i	0.154723	+	0.987958i	$0.450551\pi$
$522$	−7.01018	−	8.96844i	−0.306827	−	0.392538i
$523$	3.78176	+	14.1137i	0.165365	+	0.617150i	0.997993	+	0.0633182i	$0.0201683\pi$
$523$	3.78176	+	14.1137i	0.165365	+	0.617150i	−0.832629	+	0.553832i	$0.813165\pi$
$524$	0.982891	−	0.824743i	0.0429378	−	0.0360291i
$525$	−23.1846	+	9.44090i	−1.01186	+	0.412034i
$526$	−4.33208	+	24.5685i	−0.188888	+	1.07124i
$527$	8.75850	+	12.5084i	0.381526	+	0.544876i
$528$	−2.18248	−	5.53872i	−0.0949804	−	0.241042i
$529$	−14.4569	−	17.2291i	−0.628561	−	0.749090i
$530$	3.01843	−	23.9774i	0.131112	−	1.04151i
$531$	−22.6121	+	9.60430i	−0.981281	+	0.416791i
$532$	4.08464	−	15.2441i	0.177091	−	0.660914i
$533$	13.3070	+	28.5370i	0.576390	+	1.23607i
$534$	10.9213	−	5.44671i	0.472611	−	0.235702i
$535$	−11.2833	+	5.95532i	−0.487822	+	0.257471i
$536$	−7.78131	−	21.3790i	−0.336101	−	0.923431i
$537$	−24.8318	+	0.653055i	−1.07157	+	0.0281814i
$538$	8.84309	+	6.19200i	0.381253	+	0.266956i
$539$	−3.19963			−0.137818
$540$	−1.31085	−	10.1702i	−0.0564101	−	0.437657i
$541$	−28.4337			−1.22246			−0.611230	−	0.791453i	$-0.709325\pi$
$541$	−28.4337			−1.22246			−0.611230	+	0.791453i	$0.709325\pi$
$542$	4.19460	+	2.93709i	0.180173	+	0.126159i
$543$	1.70998	−	3.15025i	0.0733824	−	0.135190i
$544$	4.31531	+	11.8562i	0.185017	+	0.508331i
$545$	10.4475	−	33.8027i	0.447523	−	1.44795i
$546$	−24.0048	−	15.8845i	−1.02731	−	0.679795i
$547$	4.44356	+	9.52924i	0.189993	+	0.407441i	0.978111	−	0.208083i	$-0.0667224\pi$
$547$	4.44356	+	9.52924i	0.189993	+	0.407441i	−0.788118	+	0.615524i	$0.788945\pi$
$548$	−3.64467	+	13.6021i	−0.155693	+	0.581053i
$549$	−6.16321	+	5.74989i	−0.263039	+	0.245399i
$550$	−6.11559	+	10.8756i	−0.260770	+	0.463737i
$551$	−14.2734	−	17.0103i	−0.608066	−	0.724665i
$552$	−3.72426	−	0.556164i	−0.158515	−	0.0236719i
$553$	21.6605	+	30.9344i	0.921099	+	1.31547i
$554$	2.48092	−	14.0700i	0.105404	−	0.597776i
$555$	8.37068	+	14.8972i	0.355315	+	0.632351i
$556$	−6.17030	+	5.17749i	−0.261679	+	0.219575i
$557$	−4.48926	−	16.7541i	−0.190216	−	0.709896i	−0.993454	−	0.114237i	$-0.963558\pi$
$557$	−4.48926	−	16.7541i	−0.190216	−	0.709896i	0.803238	−	0.595659i	$-0.203109\pi$
$558$	11.6954	−	12.9950i	0.495107	−	0.550122i
$559$	6.82132	−	3.93829i	0.288511	−	0.166572i
$560$	−6.97433	−	6.31840i	−0.294719	−	0.267001i
$561$	−11.3043	−	0.690115i	−0.477267	−	0.0291367i
$562$	−1.44988	−	16.5722i	−0.0611596	−	0.699057i
$563$	21.2542	+	9.91099i	0.895758	+	0.417699i	0.815286	−	0.579058i	$-0.196580\pi$
$563$	21.2542	+	9.91099i	0.895758	+	0.417699i	0.0804714	+	0.996757i	$0.474357\pi$
$564$	−3.70246	+	15.4295i	−0.155902	+	0.649701i
$565$	1.25864	−	5.83373i	0.0529512	−	0.245427i
$566$		−	31.8748i		−	1.33980i
$567$	−12.6021	+	22.7591i	−0.529238	+	0.955791i
$568$	−10.5491	+	10.5491i	−0.442630	+	0.442630i
$569$	6.84027	+	38.7931i	0.286759	+	1.62629i	0.698934	+	0.715186i	$0.253658\pi$
$569$	6.84027	+	38.7931i	0.286759	+	1.62629i	−0.412175	+	0.911105i	$0.635231\pi$
$570$	4.10673	+	24.9923i	0.172012	+	1.04681i
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.415285	−	0.909691i	$-0.363682\pi$
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.902865	+	0.429924i	$0.141460\pi$
$572$	11.2880	−	0.987576i	0.471977	−	0.0412926i
$573$	−26.7630	−	30.2431i	−1.11804	−	1.26343i
$574$	6.05032	−	16.6231i	0.252536	−	0.693836i
$575$	1.81862	+	3.06900i	0.0758415	+	0.127986i
$576$	19.4388	−	12.6300i	0.809951	−	0.526249i
$577$	−21.0819	+	5.64888i	−0.877651	+	0.235166i	−0.669393	−	0.742908i	$-0.733446\pi$
$577$	−21.0819	+	5.64888i	−0.877651	+	0.235166i	−0.208257	+	0.978074i	$0.566779\pi$
$578$	9.82287	+	0.859390i	0.408578	+	0.0357459i
$579$	0.536252	−	0.0611597i	0.0222859	−	0.00254171i
$580$	6.90687	−	1.57237i	0.286792	−	0.0652891i
$581$	13.5734	+	2.39335i	0.563119	+	0.0992930i
$582$	−4.96111	+	33.2213i	−0.205645	+	1.37707i
$583$	2.10351	−	24.0432i	0.0871185	−	0.995769i
$584$	−10.6167	+	18.3886i	−0.439321	+	0.760927i
$585$	−36.0190	−	5.80933i	−1.48920	−	0.240186i
$586$	−3.88117	−	6.72239i	−0.160330	−	0.277699i
$587$	−22.1244	+	10.3168i	−0.913173	+	0.425819i	−0.821656	−	0.569984i	$-0.806949\pi$
$587$	−22.1244	+	10.3168i	−0.913173	+	0.425819i	−0.0915170	+	0.995804i	$0.529172\pi$
$588$	−0.413302	−	2.03027i	−0.0170443	−	0.0837268i
$589$	21.9220	−	26.1256i	0.903279	−	1.07649i
$590$	−0.734633	+	19.3428i	−0.0302444	+	0.796332i
$591$	1.59861	+	5.39457i	0.0657580	+	0.221903i
$592$	−3.68461	+	5.26217i	−0.151437	+	0.216274i
$593$	−4.09490	−	4.09490i	−0.168157	−	0.168157i	0.618012	−	0.786169i	$-0.287938\pi$
$593$	−4.09490	−	4.09490i	−0.168157	−	0.168157i	−0.786169	+	0.618012i	$0.787938\pi$
$594$	2.14445	+	12.7881i	0.0879879	+	0.524700i
$595$	−16.5012	+	6.94491i	−0.676481	+	0.284714i
$596$	−8.17827	+	1.44205i	−0.334995	+	0.0590687i
$597$	−0.290389	−	11.0417i	−0.0118848	−	0.451908i
$598$	−1.73357	+	3.71765i	−0.0708910	+	0.152026i
$599$	30.3866	+	25.4974i	1.24156	+	1.04180i	0.997400	+	0.0720615i	$0.0229578\pi$
$599$	30.3866	+	25.4974i	1.24156	+	1.04180i	0.244163	+	0.969734i	$0.421487\pi$
$600$	−25.1195	−	8.08606i	−1.02550	−	0.330112i
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.159969	−	0.987122i	$-0.551139\pi$
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.757053	+	0.653353i	$0.773362\pi$
$602$	−4.27441	−	1.14533i	−0.174212	−	0.0466800i
$603$	3.12238	+	22.1805i	0.127153	+	0.903258i
$604$	0.806976	+	0.465908i	0.0328354	+	0.0189575i
$605$	5.54258	−	10.7963i	0.225338	−	0.438931i
$606$	5.65534	+	2.45825i	0.229733	+	0.0998596i
$607$	−26.5308	+	18.5771i	−1.07685	+	0.754020i	−0.970691	−	0.240329i	$-0.922745\pi$
$607$	−26.5308	+	18.5771i	−1.07685	+	0.754020i	−0.106160	+	0.994349i	$0.533856\pi$
$608$	23.0833	−	16.1631i	0.936152	−	0.655501i
$609$	−16.4813	−	7.16404i	−0.667854	−	0.290301i
$610$	2.03295	+	6.32242i	0.0823116	+	0.255987i
$611$	48.8923	+	28.2280i	1.97797	+	1.14198i
$612$	−1.02229	−	7.26207i	−0.0413238	−	0.293552i
$613$	14.7737	+	3.95860i	0.596704	+	0.159886i	0.544515	−	0.838751i	$-0.316714\pi$
$613$	14.7737	+	3.95860i	0.596704	+	0.159886i	0.0521885	+	0.998637i	$0.483380\pi$
$614$	13.5879	+	4.94560i	0.548364	+	0.199588i
$615$	−1.69346	−	22.3580i	−0.0682867	−	0.901563i
$616$	−15.9279	−	13.3651i	−0.641755	−	0.538497i
$617$	11.3221	−	24.2804i	0.455812	−	0.977492i	−0.535325	−	0.844646i	$-0.679811\pi$
$617$	11.3221	−	24.2804i	0.455812	−	0.977492i	0.991137	−	0.132845i	$-0.0424114\pi$
$618$	0.174600	+	6.63900i	0.00702345	+	0.267060i
$619$	18.6300	−	3.28497i	0.748802	−	0.132034i	0.213792	−	0.976879i	$-0.431419\pi$
$619$	18.6300	−	3.28497i	0.748802	−	0.132034i	0.535011	+	0.844845i	$0.320308\pi$
$620$	4.22032	+	10.0275i	0.169492	+	0.402714i
$621$	3.47298	+	1.29715i	0.139366	+	0.0520529i
$622$	2.88598	+	2.88598i	0.115717	+	0.115717i
$623$	11.0512	−	15.7827i	0.442757	−	0.632322i
$624$	−3.89698	−	13.1505i	−0.156004	−	0.526443i
$625$	9.08124	+	23.2923i	0.363250	+	0.931692i
$626$	16.7165	−	19.9220i	0.668126	−	0.796242i
$627$	5.04570	+	24.7860i	0.201506	+	0.989859i
$628$	17.8520	−	8.32451i	0.712371	−	0.332184i
$629$	6.11042	+	10.5836i	0.243638	+	0.421994i
$630$	12.0012	+	16.6169i	0.478141	+	0.662034i
$631$	0.0126965	−	0.0219910i	0.000505440	−	0.000875448i	−0.865773	−	0.500438i	$-0.833172\pi$
$631$	0.0126965	−	0.0219910i	0.000505440	−	0.000875448i	0.866278	+	0.499562i	$0.166506\pi$
$632$	−3.46961	+	39.6578i	−0.138014	+	1.57750i
$633$	1.64112	−	10.9895i	0.0652288	−	0.436794i
$634$	17.1787	+	3.02907i	0.682253	+	0.120300i
$635$	−3.89395	+	6.18947i	−0.154527	+	0.245622i
$636$	15.5279	−	1.77096i	0.615722	−	0.0702232i
$637$	−7.34369	−	0.642490i	−0.290968	−	0.0254564i
$638$	−8.65198	+	2.31829i	−0.342535	+	0.0917820i
$639$	12.3165	−	8.00241i	0.487234	−	0.316570i
$640$	0.286754	+	2.08659i	0.0113349	+	0.0824797i
$641$	9.97230	−	27.3987i	0.393882	−	1.08218i	−0.571331	−	0.820720i	$-0.693573\pi$
$641$	9.97230	−	27.3987i	0.393882	−	1.08218i	0.965214	−	0.261463i	$-0.0842049\pi$
$642$	6.92324	+	7.82351i	0.273238	+	0.308769i
$643$	−1.74781	+	0.152914i	−0.0689270	+	0.00603033i	−0.121567	−	0.992583i	$-0.538792\pi$
$643$	−1.74781	+	0.152914i	−0.0689270	+	0.00603033i	0.0526401	+	0.998614i	$0.483236\pi$
$644$	−1.71037	+	0.622522i	−0.0673979	+	0.0245308i
$645$	−5.53472	+	0.909467i	−0.217930	+	0.0358102i
$646$	3.14539	+	17.8384i	0.123754	+	0.701842i
$647$	14.7341	−	14.7341i	0.579259	−	0.579259i	−0.355440	−	0.934699i	$-0.615669\pi$
$647$	14.7341	−	14.7341i	0.579259	−	0.579259i	0.934699	+	0.355440i	$0.115669\pi$
$648$	−25.5982	+	9.83953i	−1.00559	+	0.386533i
$649$			19.3315i			0.758830i
$650$	−16.2201	+	23.7333i	−0.636206	+	0.930896i
$651$	6.44028	−	26.8391i	0.252414	−	1.05191i
$652$	1.97831	+	0.922501i	0.0774766	+	0.0361279i
$653$	0.812604	+	9.28810i	0.0317996	+	0.363471i	0.995377	+	0.0960426i	$0.0306185\pi$
$653$	0.812604	+	9.28810i	0.0317996	+	0.363471i	−0.963578	+	0.267429i	$0.913826\pi$
$654$	−28.9164	−	1.76532i	−1.13072	−	0.0690293i
$655$	0.160218	+	3.24688i	0.00626023	+	0.126866i
$656$	7.29994	−	4.21462i	0.285015	−	0.164553i
$657$	13.9846	−	15.5386i	0.545592	−	0.606218i
$658$	−8.20920	−	30.6372i	−0.320028	−	1.19436i
$659$	−14.0775	+	11.8125i	−0.548383	+	0.460148i	−0.874393	−	0.485218i	$-0.838740\pi$
$659$	−14.0775	+	11.8125i	−0.548383	+	0.460148i	0.326010	+	0.945366i	$0.394296\pi$
$660$	−7.76913	−	2.17920i	−0.302413	−	0.0848253i
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	−0.768647	−	0.639674i	$-0.779070\pi$
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	0.941073	−	0.338204i	$-0.109819\pi$
$662$	−12.5159	−	17.8745i	−0.486443	−	0.694712i
$663$	−25.8067	−	3.85385i	−1.00225	−	0.149671i
$664$	9.33923	+	11.1301i	0.362432	+	0.431930i
$665$	24.5211	+	31.5839i	0.950886	+	1.22477i
$666$	10.2309	−	9.54476i	0.396438	−	0.369852i
$667$	−0.662829	+	2.47371i	−0.0256648	+	0.0957825i
$668$	−2.71703	−	5.82669i	−0.105125	−	0.225441i
$669$	15.0051	+	9.92922i	0.580131	+	0.383886i
$670$	16.8615	+	5.21146i	0.651418	+	0.201336i
$671$	2.26847	+	6.23257i	0.0875733	+	0.240606i
$672$	10.8797	−	20.0434i	0.419695	−	0.773191i
$673$	3.83098	+	2.68248i	0.147673	+	0.103402i	0.645078	−	0.764117i	$-0.276825\pi$
$673$	3.83098	+	2.68248i	0.147673	+	0.103402i	−0.497405	+	0.867518i	$0.665714\pi$
$674$	−11.0600			−0.426017
$675$	22.5383	+	12.9238i	0.867500	+	0.497437i
$676$	14.6331			0.562810
$677$	−32.1483	−	22.5105i	−1.23556	−	0.865147i	−0.241123	−	0.970495i	$-0.577516\pi$
$677$	−32.1483	−	22.5105i	−1.23556	−	0.865147i	−0.994436	+	0.105347i	$0.966405\pi$
$678$	−4.88500	+	0.128472i	−0.187607	+	0.00493392i
$679$	18.1371	+	49.8312i	0.696038	+	1.91235i
$680$	−18.0311	−	5.57296i	−0.691462	−	0.213713i
$681$	−4.84267	+	2.41515i	−0.185572	+	0.0925488i
$682$	−5.81397	−	12.4681i	−0.222628	−	0.477428i
$683$	9.77386	−	36.4765i	0.373986	−	1.39574i	−0.480834	−	0.876812i	$-0.659666\pi$
$683$	9.77386	−	36.4765i	0.373986	−	1.39574i	0.854820	−	0.518924i	$-0.173667\pi$
$684$	−15.0758	+	6.40331i	−0.576436	+	0.244837i
$685$	−21.8799	−	28.1820i	−0.835987	−	1.07678i
$686$	−11.0866	−	13.2125i	−0.423287	−	0.504454i
$687$	−14.9181	−	37.8592i	−0.569160	−	1.44442i
$688$	−1.20944	−	1.72726i	−0.0461096	−	0.0658513i
$689$	9.65582	−	54.7609i	0.367858	−	2.08622i
$690$	2.08944	−	2.04124i	0.0795438	−	0.0777089i
$691$	10.1478	−	8.51501i	0.386040	−	0.323926i	−0.429028	−	0.903291i	$-0.641144\pi$
$691$	10.1478	−	8.51501i	0.386040	−	0.323926i	0.815068	+	0.579365i	$0.196699\pi$
$692$	−4.68292	−	17.4769i	−0.178018	−	0.664372i
$693$	12.6068	+	16.1284i	0.478892	+	0.612668i
$694$	−10.5198	+	6.07363i	−0.399327	+	0.230552i
$695$	−1.00580	−	20.3830i	−0.0381522	−	0.773170i
$696$	−8.45482	−	16.9529i	−0.320479	−	0.642599i
$697$	−1.39761	−	15.9747i	−0.0529381	−	0.605086i
$698$	15.2128	+	7.09386i	0.575814	+	0.268507i
$699$	4.16805	+	3.95443i	0.157650	+	0.149570i
$700$	−12.5357	+	2.35731i	−0.473805	+	0.0890979i
$701$			1.42181i			0.0537011i	0.999639	+	0.0268505i	$0.00854782\pi$
$701$			1.42181i			0.0537011i	−0.999639	+	0.0268505i	$0.991452\pi$
$702$	2.35402	+	29.7814i	0.0888467	+	1.12402i
$703$	19.3001	−	19.3001i	0.727916	−	0.727916i
$704$	−3.16755	−	17.9641i	−0.119381	−	0.677046i
$705$	−25.4806	−	31.0964i	−0.959655	−	1.17116i
$706$	8.62062	−	3.13765i	0.324441	−	0.118087i
$707$	9.69826	−	0.848488i	0.364741	−	0.0319107i
$708$	−12.2665	+	2.49709i	−0.461002	+	0.0938463i
$709$	12.4901	−	34.3163i	0.469077	−	1.28878i	−0.449410	−	0.893325i	$-0.648366\pi$
$709$	12.4901	−	34.3163i	0.469077	−	1.28878i	0.918487	−	0.395452i	$-0.129412\pi$
$710$	−1.57560	−	11.4650i	−0.0591313	−	0.430274i
$711$	11.4506	−	37.4836i	0.429432	−	1.40575i
$712$	19.6186	−	5.25679i	0.735239	−	0.197007i
$713$	−3.91834	−	0.342810i	−0.146743	−	0.0128384i
$714$	8.72108	+	11.7831i	0.326378	+	0.440971i
$715$	−15.2878	+	24.3000i	−0.571730	+	0.908770i
$716$	−12.4649	−	2.19790i	−0.465836	−	0.0821395i
$717$	23.0587	+	18.3375i	0.861144	+	0.684826i
$718$	−1.88008	+	21.4894i	−0.0701639	+	0.801977i
$719$	12.9014	−	22.3459i	0.481142	−	0.833363i	−0.518624	−	0.855003i	$-0.673555\pi$
$719$	12.9014	−	22.3459i	0.481142	−	0.833363i	0.999766	+	0.0216398i	$0.00688871\pi$
$720$	−0.708872	+	9.74132i	−0.0264181	+	0.363038i
$721$	5.24243	+	9.08015i	0.195238	+	0.338162i
$722$	18.4622	−	8.60904i	0.687090	−	0.320395i
$723$	24.0697	−	21.2999i	0.895160	−	0.792152i
$724$	1.17400	−	1.39912i	0.0436314	−	0.0519978i
$725$	−7.39982	+	16.3507i	−0.274822	+	0.607249i
$726$	−9.66282	−	2.31868i	−0.358621	−	0.0860543i
$727$	−0.926059	+	1.32255i	−0.0343456	+	0.0490507i	−0.835958	−	0.548794i	$-0.815087\pi$
$727$	−0.926059	+	1.32255i	−0.0343456	+	0.0490507i	0.801612	+	0.597845i	$0.203976\pi$
$728$	−33.8736	−	33.8736i	−1.25544	−	1.25544i
$729$	26.6647	−	4.24184i	0.987582	−	0.157105i
$730$	−6.38948	−	15.1814i	−0.236485	−	0.561890i
$731$	−3.95045	+	0.696570i	−0.146112	+	0.0257636i
$732$	−3.66174	+	2.24449i	−0.135342	+	0.0829586i
$733$	−5.62244	+	12.0574i	−0.207669	+	0.445349i	−0.982362	−	0.186990i	$-0.940127\pi$
$733$	−5.62244	+	12.0574i	−0.207669	+	0.445349i	0.774692	+	0.632338i	$0.217905\pi$
$734$	21.0132	+	17.6322i	0.775613	+	0.650816i
$735$	4.73141	+	2.27388i	0.174521	+	0.0838731i
$736$	−3.05398	−	1.11156i	−0.112571	−	0.0409725i
$737$	17.0249	+	4.56182i	0.627122	+	0.168037i
$738$	−17.4598	+	5.67740i	−0.642704	+	0.208988i
$739$	30.9063	+	17.8437i	1.13691	+	0.656393i	0.945663	−	0.325150i	$-0.105415\pi$
$739$	30.9063	+	17.8437i	1.13691	+	0.656393i	0.191243	+	0.981543i	$0.438748\pi$
$740$	2.66530	+	8.28902i	0.0979784	+	0.304711i
$741$	6.60366	+	57.9013i	0.242591	+	2.12706i
$742$	−25.5905	+	17.9187i	−0.939457	+	0.657815i
$743$	−28.8465	+	20.1985i	−1.05828	+	0.741012i	−0.966990	−	0.254813i	$-0.917986\pi$
$743$	−28.8465	+	20.1985i	−1.05828	+	0.741012i	−0.0912848	+	0.995825i	$0.529097\pi$
$744$	23.3869	−	17.3095i	0.857407	−	0.634598i
$745$	9.60936	−	18.7179i	0.352060	−	0.685769i
$746$	4.37382	+	2.52523i	0.160137	+	0.0924551i
$747$	−6.71844	−	12.6286i	−0.245815	−	0.462058i
$748$	−5.57411	−	1.49358i	−0.203810	−	0.0546106i
$749$	15.4983	+	5.64093i	0.566296	+	0.206115i
$750$	16.7723	−	11.7360i	0.612437	−	0.428537i
$751$	19.0262	+	15.9649i	0.694275	+	0.582566i	0.920138	−	0.391593i	$-0.128076\pi$
$751$	19.0262	+	15.9649i	0.694275	+	0.582566i	−0.225864	+	0.974159i	$0.572520\pi$
$752$	6.38726	−	13.6975i	0.232919	−	0.499497i
$753$	23.1132	+	12.5460i	0.842290	+	0.457203i
$754$	−20.3233	+	3.58354i	−0.740130	+	0.130505i
$755$	−2.17601	+	0.915826i	−0.0791930	+	0.0333303i
$756$	−8.60555	+	10.0827i	−0.312981	+	0.366706i
$757$	17.8009	+	17.8009i	0.646986	+	0.646986i	0.952263	−	0.305278i	$-0.0987493\pi$
$757$	17.8009	+	17.8009i	0.646986	+	0.646986i	−0.305278	+	0.952263i	$0.598749\pi$
$758$	15.3401	−	21.9080i	0.557178	−	0.795733i
$759$	2.00785	−	2.11631i	0.0728802	−	0.0768172i
$760$	−1.59972	+	42.1206i	−0.0580281	+	1.52788i
$761$	−31.3105	+	37.3144i	−1.13500	+	1.35265i	−0.207765	+	0.978179i	$0.566619\pi$
$761$	−31.3105	+	37.3144i	−1.13500	+	1.35265i	−0.927240	+	0.374467i	$0.877826\pi$
$762$	5.67841	+	1.89925i	0.205707	+	0.0688027i
$763$	−41.4512	+	19.3290i	−1.50063	+	0.699757i
$764$	−10.2888	−	17.8207i	−0.372236	−	0.644731i
$765$	16.2256	+	9.05409i	0.586638	+	0.327351i
$766$	6.51352	−	11.2818i	0.235343	−	0.407626i
$767$	−3.88180	+	44.3691i	−0.140164	+	1.60208i
$768$	26.5086	−	10.4455i	0.956547	−	0.376919i
$769$	−43.1365	−	7.60612i	−1.55554	−	0.274284i	−0.671254	−	0.741227i	$-0.734244\pi$
$769$	−43.1365	−	7.60612i	−1.55554	−	0.274284i	−0.884287	+	0.466944i	$0.845355\pi$
$770$	15.7268	−	3.58026i	0.566756	−	0.129024i
$771$	5.99998	−	13.8033i	0.216084	−	0.497113i
$772$	0.273968	+	0.0239691i	0.00986034	+	0.000862668i
$773$	−22.0592	+	5.91076i	−0.793416	+	0.212595i	−0.632691	−	0.774404i	$-0.718050\pi$
$773$	−22.0592	+	5.91076i	−0.793416	+	0.212595i	−0.160725	+	0.986999i	$0.551383\pi$
$774$	1.79548	+	4.22722i	0.0645371	+	0.151944i
$775$	−26.7045	−	6.83173i	−0.959252	−	0.245403i
$776$	−19.1194	+	52.5302i	−0.686347	+	1.88572i
$777$	7.00674	−	20.9488i	0.251365	−	0.751534i
$778$	9.39502	−	0.821958i	0.336828	−	0.0294686i
$779$	−33.6549	+	12.2494i	−1.20581	+	0.438879i
$780$	−17.3939	−	6.56169i	−0.622801	−	0.234946i
$781$	−2.00697	−	11.3821i	−0.0718150	−	0.407283i
$782$	1.47719	−	1.47719i	0.0528241	−	0.0528241i
$783$	4.67604	+	18.0556i	0.167108	+	0.645255i
$784$			1.97345i			0.0704805i
$785$	−10.5251	+	48.7837i	−0.375659	+	1.74116i
$786$	2.55215	−	0.756296i	0.0910322	−	0.0269762i
$787$	−15.6093	−	7.27876i	−0.556413	−	0.259460i	0.124008	−	0.992281i	$-0.460425\pi$
$787$	−15.6093	−	7.27876i	−0.556413	−	0.259460i	−0.680421	+	0.732822i	$0.738203\pi$
$788$	0.249868	+	2.85601i	0.00890119	+	0.101741i
$789$	22.5574	−	34.0889i	0.803064	−	1.21360i
$790$	−22.8859	−	20.7335i	−0.814243	−	0.737664i
$791$	−6.68122	+	3.85740i	−0.237557	+	0.137153i
$792$	−0.748235	+	21.5666i	−0.0265874	+	0.766337i
$793$	3.95501	+	14.7603i	0.140447	+	0.524154i
$794$	11.0377	−	9.26170i	0.391712	−	0.328685i
$795$	−20.1973	+	34.0587i	−0.716324	+	1.20794i
$796$	0.977323	−	5.54267i	0.0346403	−	0.196455i
$797$	18.8617	+	26.9373i	0.668115	+	0.954166i	0.999941	+	0.0108262i	$0.00344614\pi$
$797$	18.8617	+	26.9373i	0.668115	+	0.954166i	−0.331827	+	0.943340i	$0.607665\pi$
$798$	20.3787	−	25.6256i	0.721400	−	0.907135i
$799$	−18.4814	−	22.0252i	−0.653824	−	0.779197i
$800$	−19.8522	−	11.1634i	−0.701883	−	0.394685i
$801$	−19.9689	+	1.05106i	−0.705567	+	0.0371374i
$802$	0.802775	−	2.99600i	0.0283470	−	0.105792i
$803$	−6.95197	−	14.9085i	−0.245330	−	0.526111i
$804$	−0.695477	+	11.3921i	−0.0245276	+	0.401769i
$805$	1.36175	−	4.40591i	0.0479954	−	0.155288i
$806$	−10.8404	−	29.7838i	−0.381838	−	1.04909i
$807$	−9.24384	−	15.0807i	−0.325399	−	0.530867i
$808$	8.40661	+	5.88637i	0.295744	+	0.207082i
$809$	−0.589848			−0.0207379			−0.0103690	−	0.999946i	$-0.503301\pi$
$809$	−0.589848			−0.0207379			−0.0103690	+	0.999946i	$0.503301\pi$
$810$	5.91698	−	20.4342i	0.207902	−	0.717983i
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	−7.50095	−	5.25222i	−0.263232	−	0.184317i
$813$	−4.38469	−	7.15334i	−0.153778	−	0.250879i
$814$	−3.76564	−	10.3460i	−0.131985	−	0.362627i
$815$	−4.89102	+	2.58147i	−0.171325	+	0.0904249i
$816$	−0.425646	+	6.97221i	−0.0149006	+	0.244076i
$817$	3.78631	+	8.11977i	0.132466	+	0.284075i
$818$	−7.84316	+	29.2711i	−0.274230	+	1.02344i
$819$	25.6961	+	39.5489i	0.897894	+	1.38195i
$820$	1.42699	−	11.3355i	0.0498327	−	0.395854i
$821$	12.3182	+	14.6802i	0.429907	+	0.512343i	0.936895	−	0.349610i	$-0.113686\pi$
$821$	12.3182	+	14.6802i	0.429907	+	0.512343i	−0.506989	+	0.861953i	$0.669241\pi$
$822$	−18.1837	+	22.8654i	−0.634230	+	0.797522i
$823$	−0.358433	−	0.511895i	−0.0124942	−	0.0178435i	0.812856	−	0.582464i	$-0.197911\pi$
$823$	−0.358433	−	0.511895i	−0.0124942	−	0.0178435i	−0.825351	+	0.564621i	$0.809022\pi$
$824$	−1.91929	+	10.8848i	−0.0668615	+	0.379190i
$825$	16.2935	−	12.3479i	0.567267	−	0.429900i
$826$	19.1684	−	16.0842i	0.666954	−	0.559641i
$827$	3.05127	+	11.3875i	0.106103	+	0.395981i	0.998468	−	0.0553328i	$-0.0176220\pi$
$827$	3.05127	+	11.3875i	0.106103	+	0.395981i	−0.892365	+	0.451314i	$0.850955\pi$
$828$	1.60222	+	1.00068i	0.0556811	+	0.0347759i
$829$	−38.0844	+	21.9880i	−1.32272	+	0.763675i	−0.984163	−	0.177269i	$-0.943274\pi$
$829$	−38.0844	+	21.9880i	−1.32272	+	0.763675i	−0.338562	+	0.940944i	$0.609941\pi$
$830$	−11.2570	+	0.555479i	−0.390736	+	0.0192809i
$831$	−12.9183	+	19.5222i	−0.448130	+	0.677217i
$832$	−3.66285	−	41.8666i	−0.126986	−	1.45146i
$833$	3.40254	+	1.58663i	0.117891	+	0.0549735i
$834$	−16.0216	+	4.74780i	−0.554784	+	0.164403i
$835$	15.9225	+	3.43529i	0.551019	+	0.118883i
$836$			12.8886i			0.445761i
$837$	−26.0626	+	11.8881i	−0.900854	+	0.410913i
$838$	−9.93659	+	9.93659i	−0.343254	+	0.343254i
$839$	0.173429	+	0.983567i	0.00598745	+	0.0339565i	0.987655	−	0.156644i	$-0.0500676\pi$
$839$	0.173429	+	0.983567i	0.00598745	+	0.0339565i	−0.981668	+	0.190601i	$0.938956\pi$
$840$	14.0551	+	31.0830i	0.484946	+	1.07247i
$841$	15.1440	−	5.51197i	0.522207	−	0.190068i
$842$	9.53258	−	0.833993i	0.328514	−	0.0287413i
$843$	−8.64597	+	25.8498i	−0.297783	+	0.890314i
$844$	1.93642	−	5.32028i	0.0666545	−	0.183132i
$845$	−22.4025	+	29.5410i	−0.770671	+	1.01624i
$846$	−19.8050	+	26.2945i	−0.680910	+	0.904024i
$847$	−15.1535	+	4.06038i	−0.520682	+	0.139516i
$848$	−14.8293	−	1.29739i	−0.509239	−	0.0445527i
$849$	−20.8200	+	47.8976i	−0.714541	+	1.64384i
$850$	11.8964	−	8.53268i	0.408043	−	0.292668i
$851$	−3.10007	−	0.546626i	−0.106269	−	0.0187381i
$852$	6.96305	−	2.74373i	0.238550	−	0.0939986i
$853$	0.394403	−	4.50805i	0.0135041	−	0.154353i	−0.986449	−	0.164070i	$-0.947538\pi$
$853$	0.394403	−	4.50805i	0.0135041	−	0.154353i	0.999953	+	0.00971747i	$0.00309322\pi$
$854$	4.29256	−	7.43494i	0.146889	−	0.254418i
$855$	10.1534	−	40.2378i	0.347238	−	1.37610i
$856$	8.69313	+	15.0569i	0.297125	+	0.514635i
$857$	51.8892	−	24.1963i	1.77250	−	0.826531i	0.797831	−	0.602881i	$-0.205981\pi$
$857$	51.8892	−	24.1963i	1.77250	−	0.826531i	0.974670	−	0.223650i	$-0.0717973\pi$
$858$	22.2936	+	7.45653i	0.761091	+	0.254562i
$859$	20.9711	−	24.9924i	0.715526	−	0.852730i	−0.278662	−	0.960389i	$-0.589891\pi$
$859$	20.9711	−	24.9924i	0.715526	−	0.852730i	0.994188	+	0.107659i	$0.0343354\pi$
$860$	−2.85594	−	0.108467i	−0.0973867	−	0.00369871i
$861$	−19.9496	+	21.0273i	−0.679881	+	0.716608i
$862$	−0.179453	+	0.256286i	−0.00611220	+	0.00872913i
$863$	28.5706	+	28.5706i	0.972554	+	0.972554i	0.999633	−	0.0270792i	$-0.00862062\pi$
$863$	28.5706	+	28.5706i	0.972554	+	0.972554i	−0.0270792	+	0.999633i	$0.508621\pi$
$864$	−23.3433	+	3.91447i	−0.794154	+	0.133173i
$865$	42.4513	+	17.3025i	1.44339	+	0.588302i
$866$	18.8698	−	3.32726i	0.641223	−	0.113065i
$867$	−14.1993	−	7.70751i	−0.482233	−	0.261761i
$868$	5.94365	−	12.7462i	0.201741	−	0.432634i
$869$	−23.6254	−	19.8241i	−0.801437	−	0.672486i
$870$	14.4415	+	2.72054i	0.489614	+	0.0922350i
$871$	38.1591	+	13.8888i	1.29297	+	0.470603i
$872$	−46.5707	−	12.4786i	−1.57708	−	0.422578i
$873$	29.1545	−	46.6805i	0.986731	−	1.57989i
$874$	−4.04068	−	2.33289i	−0.136678	−	0.0789111i
$875$	14.4327	−	28.9158i	0.487914	−	0.977532i
$876$	8.56194	−	6.33700i	0.289281	−	0.214108i
$877$	−29.1215	+	20.3911i	−0.983364	+	0.688559i	−0.950443	−	0.310899i	$-0.899370\pi$
$877$	−29.1215	+	20.3911i	−0.983364	+	0.688559i	−0.0329214	+	0.999458i	$0.510481\pi$
$878$	−24.7062	+	17.2994i	−0.833792	+	0.583828i
$879$	1.44122	+	12.6367i	0.0486112	+	0.426226i
$880$	6.83718	+	3.51007i	0.230481	+	0.118324i
$881$	−30.9752	−	17.8836i	−1.04358	−	0.602512i	−0.122736	−	0.992439i	$-0.539167\pi$
$881$	−30.9752	−	17.8836i	−1.04358	−	0.602512i	−0.920846	+	0.389927i	$0.872500\pi$
$882$	0.892728	−	4.20463i	0.0300597	−	0.141577i
$883$	−3.38029	−	0.905746i	−0.113756	−	0.0304808i	0.201492	−	0.979490i	$-0.435421\pi$
$883$	−3.38029	−	0.905746i	−0.113756	−	0.0304808i	−0.315248	+	0.949009i	$0.602088\pi$
$884$	−12.4936	−	4.54730i	−0.420205	−	0.152942i
$885$	13.7383	−	28.5863i	0.461808	−	0.960917i
$886$	−32.6492	−	27.3959i	−1.09687	−	0.920383i
$887$	12.0260	−	25.7899i	0.403794	−	0.865939i	−0.594301	−	0.804243i	$-0.702571\pi$
$887$	12.0260	−	25.7899i	0.403794	−	0.865939i	0.998095	−	0.0616962i	$-0.0196510\pi$
$888$	19.8531	−	12.1691i	0.666227	−	0.408368i
$889$	9.30926	−	1.64147i	0.312222	−	0.0550532i
$890$	−5.94671	+	14.5902i	−0.199334	+	0.489063i
$891$	5.13050	−	20.6171i	0.171878	−	0.690698i
$892$	6.48285	+	6.48285i	0.217062	+	0.217062i
$893$	−36.8325	+	52.6023i	−1.23255	+	1.76027i
$894$	−16.7527	−	4.01997i	−0.560296	−	0.134448i
$895$	23.5203	−	21.7991i	0.786197	−	0.728663i
$896$	1.75011	−	2.08570i	0.0584672	−	0.0696785i
$897$	5.03331	−	4.45411i	0.168057	−	0.148718i
$898$	−7.49641	+	3.49564i	−0.250159	+	0.116651i
$899$	−9.89411	−	17.1371i	−0.329987	−	0.571554i
$900$	9.93981	+	8.74374i	0.331327	+	0.291458i
$901$	−14.1594	+	24.5249i	−0.471719	+	0.817042i
$902$	−1.25913	+	14.3919i	−0.0419245	+	0.479199i
$903$	5.67497	+	4.51303i	0.188851	+	0.150184i
$904$	−8.00909	−	1.41222i	−0.266378	−	0.0469697i
$905$	1.02718	+	4.51203i	0.0341445	+	0.149985i
$906$	1.15005	+	1.55383i	0.0382078	+	0.0516227i
$907$	32.6761	+	2.85879i	1.08499	+	0.0949246i	0.615596	−	0.788062i	$-0.288915\pi$
$907$	32.6761	+	2.85879i	1.08499	+	0.0949246i	0.469398	+	0.882987i	$0.344471\pi$
$908$	−2.66344	+	0.713667i	−0.0883894	+	0.0236839i
$909$	−6.89249	−	7.38793i	−0.228609	−	0.245042i
$910$	36.8147	−	5.05933i	1.22039	−	0.167715i
$911$	9.92857	−	27.2785i	0.328948	−	0.903778i	−0.659430	−	0.751766i	$-0.729202\pi$
$911$	9.92857	−	27.2785i	0.328948	−	0.903778i	0.988379	−	0.152012i	$-0.0485753\pi$
$912$	15.2874	−	3.11206i	0.506217	−	0.103051i
$913$	−11.2132	+	0.981025i	−0.371102	+	0.0324672i
$914$	−5.44427	+	1.98155i	−0.180080	+	0.0655439i
$915$	1.07482	−	10.8285i	0.0355324	−	0.357978i
$916$	−3.60050	−	20.4195i	−0.118964	−	0.674678i
$917$	2.97152	−	2.97152i	0.0981282	−	0.0981282i
$918$	4.06088	−	14.6624i	0.134029	−	0.483932i
$919$		−	28.2931i		−	0.933302i	−0.884442	−	0.466651i	$-0.845460\pi$
$919$		−	28.2931i		−	0.933302i	0.884442	−	0.466651i	$-0.154540\pi$
$920$	4.08511	−	2.63520i	0.134682	−	0.0868798i
$921$	−17.1879	−	16.3070i	−0.566361	−	0.537335i
$922$	28.8814	+	13.4676i	0.951159	+	0.443533i
$923$	−2.32080	−	26.5268i	−0.0763899	−	0.873141i
$924$	4.65525	+	9.33434i	0.153147	+	0.307077i
$925$	−20.8142	−	7.30944i	−0.684366	−	0.240333i
$926$	0.165049	−	0.0952911i	0.00542385	−	0.00313146i
$927$	4.07410	−	10.0903i	0.133811	−	0.331410i
$928$	−4.23180	−	15.7933i	−0.138916	−	0.518440i
$929$	25.1788	−	21.1275i	0.826089	−	0.693171i	−0.128300	−	0.991735i	$-0.540952\pi$
$929$	25.1788	−	21.1275i	0.826089	−	0.693171i	0.954390	+	0.298564i	$0.0965076\pi$
$930$	−0.263349	+	22.5688i	−0.00863557	+	0.740061i
$931$	1.45603	−	8.25757i	0.0477195	−	0.270631i
$932$	1.67917	+	2.39811i	0.0550032	+	0.0785527i
$933$	−2.45164	−	6.22178i	−0.0802630	−	0.203692i
$934$	−8.57623	−	10.2208i	−0.280623	−	0.334433i
$935$	11.5489	−	8.96631i	0.377690	−	0.293230i
$936$	−6.04793	+	49.3488i	−0.197683	+	1.61302i
$937$	−1.30584	+	4.87347i	−0.0426600	+	0.159209i	−0.983970	−	0.178334i	$-0.942929\pi$
$937$	−1.30584	+	4.87347i	−0.0426600	+	0.159209i	0.941310	+	0.337543i	$0.109596\pi$
$938$	−9.64174	−	20.6768i	−0.314814	−	0.675121i
$939$	−38.1322	+	19.0174i	−1.24440	+	0.620610i
$940$	−9.56179	−	18.1164i	−0.311871	−	0.590892i
$941$	19.6715	+	54.0471i	0.641274	+	1.76189i	0.647687	+	0.761906i	$0.275736\pi$
$941$	19.6715	+	54.0471i	0.641274	+	1.76189i	−0.00641343	+	0.999979i	$0.502041\pi$
$942$	40.8501	−	1.07432i	1.33097	−	0.0350034i
$943$	3.38355	+	2.36919i	0.110184	+	0.0771514i
$944$	11.9232			0.388068
$945$	−7.18016	−	32.8089i	−0.233571	−	1.06727i
$946$	3.61394			0.117499
$947$	−26.3740	−	18.4673i	−0.857041	−	0.600107i	0.0603125	−	0.998180i	$-0.480790\pi$
$947$	−26.3740	−	18.4673i	−0.857041	−	0.600107i	−0.917354	+	0.398073i	$0.869679\pi$
$948$	9.52727	−	17.5518i	0.309431	−	0.570055i
$949$	−12.9623	−	35.6136i	−0.420773	−	1.15607i
$950$	−25.2846	−	20.7321i	−0.820341	−	0.672638i
$951$	−23.8355	−	15.7725i	−0.772920	−	0.511459i
$952$	10.3105	+	22.1110i	0.334167	+	0.716623i
$953$	−5.59819	+	20.8927i	−0.181343	+	0.676782i	0.814041	+	0.580808i	$0.197263\pi$
$953$	−5.59819	+	20.8927i	−0.181343	+	0.676782i	−0.995384	+	0.0959743i	$0.969403\pi$
$954$	31.0083	+	9.47252i	1.00393	+	0.306684i
$955$	51.7278	+	6.51184i	1.67387	+	0.210718i
$956$	9.64940	+	11.4997i	0.312084	+	0.371927i
$957$	14.5154	+	2.16766i	0.469217	+	0.0700706i
$958$	−21.6105	−	30.8629i	−0.698202	−	0.997136i
$959$	−8.00894	+	45.4210i	−0.258622	+	1.46672i
$960$	−8.08251	+	28.8152i	−0.260862	+	0.930006i
$961$	−0.465741	+	0.390803i	−0.0150239	+	0.0126065i
$962$	−6.56528	−	24.5020i	−0.211673	−	0.789975i
$963$	−5.29324	−	16.2784i	−0.170572	−	0.524563i
$964$	14.1830	−	8.18857i	0.456804	−	0.263736i
$965$	−0.467821	+	0.516387i	−0.0150597	+	0.0166231i
$966$	−3.76902	−	0.230095i	−0.121266	−	0.00740317i
$967$	0.961701	+	10.9923i	0.0309262	+	0.353488i	0.995854	+	0.0909711i	$0.0289971\pi$
$967$	0.961701	+	10.9923i	0.0309262	+	0.353488i	−0.964927	+	0.262517i	$0.915447\pi$
$968$	−14.9883	−	6.98917i	−0.481743	−	0.224640i
$969$	6.92520	−	28.8599i	0.222469	−	0.927114i
$970$	−23.5066	−	36.4402i	−0.754751	−	1.17002i
$971$		−	21.9387i		−	0.704047i	−0.935991	−	0.352023i	$-0.885494\pi$
$971$		−	21.9387i		−	0.704047i	0.935991	−	0.352023i	$-0.114506\pi$
$972$	13.7449	+	0.592321i	0.440868	+	0.0189987i
$973$	−18.6543	+	18.6543i	−0.598030	+	0.598030i
$974$	1.26918	+	7.19790i	0.0406673	+	0.230635i
$975$	39.8758	−	25.0688i	1.27705	−	0.802845i
$976$	3.84410	−	1.39914i	0.123046	−	0.0447853i
$977$	−5.48124	+	0.479546i	−0.175360	+	0.0153420i	−0.174498	−	0.984658i	$-0.555830\pi$
$977$	−5.48124	+	0.479546i	−0.175360	+	0.0153420i	−0.000862648		1.00000i	$0.500275\pi$
$978$	3.00104	+	3.39128i	0.0959625	+	0.108441i
$979$	−5.38167	+	14.7860i	−0.171999	+	0.472563i
$980$	2.13128	+	1.61627i	0.0680812	+	0.0516297i
$981$	42.2990	+	21.5404i	1.35050	+	0.687731i
$982$	−26.5176	+	7.10536i	−0.846209	+	0.226741i
$983$	−27.3904	−	2.39635i	−0.873618	−	0.0764316i	−0.358478	−	0.933538i	$-0.616704\pi$
$983$	−27.3904	−	2.39635i	−0.873618	−	0.0764316i	−0.515139	+	0.857106i	$0.672260\pi$
$984$	−30.3581	+	3.46235i	−0.967782	+	0.110376i
$985$	−6.14819	−	3.86798i	−0.195898	−	0.123244i
$986$	10.3502	+	1.82503i	0.329619	+	0.0581207i
$987$	−7.67583	+	51.4000i	−0.244324	+	1.63608i
$988$	−2.58804	+	29.5815i	−0.0823366	+	0.941111i
$989$	0.516635	−	0.894838i	0.0164280	−	0.0284542i
$990$	−12.9794	−	10.5715i	−0.412514	−	0.335983i
$991$	7.95205	+	13.7734i	0.252605	+	0.437525i	0.964242	−	0.265022i	$-0.0853793\pi$
$991$	7.95205	+	13.7734i	0.252605	+	0.437525i	−0.711637	+	0.702547i	$0.752046\pi$
$992$	22.7592	−	10.6128i	0.722606	−	0.336956i
$993$	7.13204	+	35.0348i	0.226328	+	1.11180i
$994$	−9.61620	+	11.4601i	−0.305007	+	0.363494i
$995$	9.69322	+	10.4586i	0.307296	+	0.331559i
$996$	−2.07092	−	6.98839i	−0.0656195	−	0.221436i
$997$	−2.10376	+	3.00447i	−0.0666266	+	0.0951527i	−0.851083	−	0.525032i	$-0.824053\pi$
$997$	−2.10376	+	3.00447i	−0.0666266	+	0.0951527i	0.784456	+	0.620185i	$0.212942\pi$
$998$	8.38532	+	8.38532i	0.265433	+	0.265433i
$999$	−21.6082	+	7.66011i	−0.683652	+	0.242355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.12	yes	192
3.2	odd	2		405.2.r.a.152.5		192
5.2	odd	4		675.2.ba.b.68.5		192
5.3	odd	4	inner	135.2.q.a.68.12	yes	192
5.4	even	2		675.2.ba.b.257.5		192
15.8	even	4		405.2.r.a.233.5		192
27.2	odd	18	inner	135.2.q.a.2.12	✓	192
27.25	even	9		405.2.r.a.332.5		192
135.2	even	36		675.2.ba.b.218.5		192
135.29	odd	18		675.2.ba.b.407.5		192
135.83	even	36	inner	135.2.q.a.83.12	yes	192
135.133	odd	36		405.2.r.a.8.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	27.2	odd	18	inner
135.2.q.a.68.12	yes	192	5.3	odd	4	inner
135.2.q.a.83.12	yes	192	135.83	even	36	inner
135.2.q.a.122.12	yes	192	1.1	even	1	trivial
405.2.r.a.8.5		192	135.133	odd	36
405.2.r.a.152.5		192	3.2	odd	2
405.2.r.a.233.5		192	15.8	even	4
405.2.r.a.332.5		192	27.25	even	9
675.2.ba.b.68.5		192	5.2	odd	4
675.2.ba.b.218.5		192	135.2	even	36
675.2.ba.b.257.5		192	5.4	even	2
675.2.ba.b.407.5		192	135.29	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.865920 + 0.606324i) q^{2} +(-0.905161 - 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(2.13636 + 0.660292i) q^{5} +(0.111569 - 1.82754i) q^{6} +(-1.22161 - 2.61975i) q^{7} +(0.788655 - 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +O(q^{10})\)	\(q+(0.865920 + 0.606324i) q^{2} +(-0.905161 - 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(2.13636 + 0.660292i) q^{5} +(0.111569 - 1.82754i) q^{6} +(-1.22161 - 2.61975i) q^{7} +(0.788655 - 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +(1.44956 + 1.86708i) q^{10} +(1.51740 + 1.80836i) q^{11} +(-0.951458 + 1.19642i) q^{12} +(3.11956 + 4.45519i) q^{13} +(0.530600 - 3.00918i) q^{14} +(-0.958684 - 3.75246i) q^{15} +(1.11535 - 0.935892i) q^{16} +(-0.716894 - 2.67549i) q^{17} +(-2.79974 + 1.48946i) q^{18} +(-5.35751 + 3.09316i) q^{19} +(-0.0972619 - 1.97105i) q^{20} +(-2.76286 + 4.17526i) q^{21} +(0.217491 + 2.48593i) q^{22} +(0.646627 + 0.301527i) q^{23} +(-5.06027 + 1.49954i) q^{24} +(4.12803 + 2.82124i) q^{25} +5.74930i q^{26} +(5.18000 - 0.409444i) q^{27} +(-1.80389 + 1.80389i) q^{28} +(0.623300 + 3.53491i) q^{29} +(1.44506 - 3.83060i) q^{30} +(-5.18043 + 1.88552i) q^{31} +(-4.53781 + 0.397007i) q^{32} +(1.29695 - 3.87762i) q^{33} +(1.00144 - 2.75143i) q^{34} +(-0.879991 - 6.40333i) q^{35} +(2.62800 + 0.322074i) q^{36} +(-4.26173 + 1.14193i) q^{37} +(-6.51463 - 0.569956i) q^{38} +(3.75534 - 8.63936i) q^{39} +(3.62828 - 5.76719i) q^{40} +(5.70140 + 1.00531i) q^{41} +(-4.92398 + 1.94025i) q^{42} +(0.126221 - 1.44271i) q^{43} +(1.04170 - 1.80428i) q^{44} +(-4.67354 + 4.81228i) q^{45} +(0.377104 + 0.653164i) q^{46} +(9.40770 - 4.38688i) q^{47} +(-2.39162 - 0.799924i) q^{48} +(-0.871236 + 1.03830i) q^{49} +(1.86396 + 4.94589i) q^{50} +(-3.30202 + 3.48039i) q^{51} +(2.75318 - 3.93195i) q^{52} +(-7.22940 - 7.22940i) q^{53} +(4.73372 + 2.78621i) q^{54} +(2.04765 + 4.86523i) q^{55} +(-8.67413 + 1.52948i) q^{56} +(9.41712 + 5.11170i) q^{57} +(-1.60357 + 3.43887i) q^{58} +(6.27320 + 5.26384i) q^{59} +(-2.82264 + 1.92775i) q^{60} +(2.64019 + 0.960952i) q^{61} +(-5.62907 - 1.50831i) q^{62} +(8.66650 + 0.300676i) q^{63} +(-6.69194 - 3.86359i) q^{64} +(3.72276 + 11.5777i) q^{65} +(3.47414 - 2.57134i) q^{66} +(6.11610 - 4.28254i) q^{67} +(-2.00246 + 1.40214i) q^{68} +(-0.140033 - 1.22781i) q^{69} +(3.12049 - 6.07833i) q^{70} +(-4.24004 - 2.44799i) q^{71} +(6.79476 + 6.11524i) q^{72} +(-6.73088 - 1.80353i) q^{73} +(-4.38269 - 1.59517i) q^{74} +(0.429628 - 8.64959i) q^{75} +(4.18242 + 3.50947i) q^{76} +(2.88379 - 6.18430i) q^{77} +(8.49007 - 5.20404i) q^{78} +(-12.8661 + 2.26863i) q^{79} +(3.00075 - 1.26294i) q^{80} +(-5.29336 - 7.27876i) q^{81} +(4.32741 + 4.32741i) q^{82} +(-2.73492 + 3.90587i) q^{83} +(4.29664 + 1.03102i) q^{84} +(0.235061 - 6.18915i) q^{85} +(0.984048 - 1.17274i) q^{86} +(4.65586 - 4.12010i) q^{87} +(6.51925 - 3.03998i) q^{88} +(3.33276 + 5.77251i) q^{89} +(-6.96471 + 1.33337i) q^{90} +(7.86060 - 13.6150i) q^{91} +(0.0548802 - 0.627283i) q^{92} +(7.47350 + 5.94331i) q^{93} +(10.8062 + 1.90542i) q^{94} +(-13.4879 + 3.07057i) q^{95} +(4.69371 + 6.34168i) q^{96} +(-18.2758 - 1.59893i) q^{97} +(-1.38397 + 0.370833i) q^{98} +(-6.90008 + 1.59465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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