LMFDB - Embedded newform 135.2.q.a.83.12

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			83.12
Character	$\chi$	$=$	135.83
Dual form			135.2.q.a.122.12

$q$-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} +(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} - 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}+ \cdots + 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

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.225863	−	0.974159i	$-0.572520\pi$
$2$	0.865920	−	0.606324i	0.612298	−	0.428736i	0.838161	+	0.545424i	$0.183631\pi$
$3$	−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	0.528271	+	0.849076i	$0.322840\pi$
$7$	−1.22161	+	2.61975i	−0.461725	+	0.990171i	−0.989996	+	0.141096i	$0.954937\pi$
$8$	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	−0.487136	−	0.873326i	$-0.661959\pi$
$11$	1.51740	−	1.80836i	0.457512	−	0.545242i	0.944648	+	0.328084i	$0.106403\pi$
$12$	−0.951458	−	1.19642i	−0.274662	−	0.345378i
$13$	3.11956	−	4.45519i	0.865210	−	1.23565i	−0.105265	−	0.994444i	$-0.533569\pi$
$13$	3.11956	−	4.45519i	0.865210	−	1.23565i	0.970475	−	0.241203i	$-0.0775421\pi$
$14$	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	0.822869	+	0.568232i	$0.192372\pi$
$17$	−0.716894	+	2.67549i	−0.173872	+	0.648901i	−0.996741	+	0.0806688i	$0.974294\pi$
$18$	−2.79974	−	1.48946i	−0.659904	−	0.351069i
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.262256	−	0.964998i	$-0.584466\pi$
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.966841	+	0.255379i	$0.917800\pi$
$20$	−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	−0.354032	−	0.935233i	$-0.615190\pi$
$23$	0.646627	−	0.301527i	0.134831	−	0.0628728i	0.488863	+	0.872361i	$0.337412\pi$
$24$	−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	−0.870635	−	0.491929i	$-0.836292\pi$
$29$	0.623300	−	3.53491i	0.115744	−	0.656416i	0.986379	−	0.164487i	$-0.0525969\pi$
$30$	1.44506	+	3.83060i	0.263831	+	0.699369i
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.168051	−	0.985778i	$-0.553747\pi$
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.762381	+	0.647129i	$0.775970\pi$
$32$	−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	−0.109114	−	0.994029i	$-0.534801\pi$
$37$	−4.26173	−	1.14193i	−0.700624	−	0.187732i	−0.591510	+	0.806298i	$0.701468\pi$
$38$	−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	0.290314	−	0.956932i	$-0.406240\pi$
$41$	5.70140	−	1.00531i	0.890409	−	0.157003i	0.600095	+	0.799928i	$0.295129\pi$
$42$	−4.92398	−	1.94025i	−0.759786	−	0.299387i
$43$	0.126221	+	1.44271i	0.0192485	+	0.220012i	0.999727	+	0.0233831i	$0.00744375\pi$
$43$	0.126221	+	1.44271i	0.0192485	+	0.220012i	−0.980478	+	0.196629i	$0.937001\pi$
$44$	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	0.962244	−	0.272188i	$-0.0877473\pi$
$47$	9.40770	+	4.38688i	1.37225	+	0.639893i	0.410010	+	0.912081i	$0.365525\pi$
$48$	−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	−0.999976	−	0.00694140i	$-0.997790\pi$
$53$	−7.22940	+	7.22940i	−0.993035	+	0.993035i	0.00694140	+	0.999976i	$0.497790\pi$
$54$	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	−0.135496	−	0.990778i	$-0.543263\pi$
$59$	6.27320	−	5.26384i	0.816701	−	0.685293i	0.952197	+	0.305484i	$0.0988184\pi$
$60$	−2.82264	−	1.92775i	−0.364402	−	0.248871i
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	−0.167421	−	0.985885i	$-0.553544\pi$
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	0.505463	+	0.862848i	$0.331322\pi$
$62$	−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	0.884048	−	0.467396i	$-0.154808\pi$
$67$	6.11610	+	4.28254i	0.747201	+	0.523196i	−0.136847	+	0.990592i	$0.543697\pi$
$68$	−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	−0.730034	−	0.683411i	$-0.760496\pi$
$71$	−4.24004	+	2.44799i	−0.503200	+	0.290523i	0.226834	+	0.973933i	$0.427162\pi$
$72$	6.79476	−	6.11524i	0.800770	−	0.720688i
$73$	−6.73088	+	1.80353i	−0.787790	+	0.211088i	−0.630216	−	0.776420i	$-0.717034\pi$
$73$	−6.73088	+	1.80353i	−0.787790	+	0.211088i	−0.157574	+	0.987507i	$0.550367\pi$
$74$	−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	−0.606015	−	0.795453i	$-0.707233\pi$
$79$	−12.8661	−	2.26863i	−1.44754	−	0.255241i	−0.841529	+	0.540212i	$0.818344\pi$
$80$	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	0.640509	−	0.767951i	$-0.278724\pi$
$83$	−2.73492	−	3.90587i	−0.300196	−	0.428724i	−0.940705	+	0.339227i	$0.889835\pi$
$84$	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	−0.633549	−	0.773703i	$-0.718402\pi$
$89$	3.33276	−	5.77251i	0.353272	−	0.611885i	0.986821	+	0.161818i	$0.0517357\pi$
$90$	−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	−0.959547	−	0.281548i	$-0.909152\pi$
$97$	−18.2758	+	1.59893i	−1.85563	+	0.162346i	−0.896079	+	0.443894i	$0.853597\pi$
$98$	−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	0.869097	−	0.494641i	$-0.164701\pi$
$101$	−1.15191	−	3.16484i	−0.114619	−	0.314913i	−0.983716	+	0.179728i	$0.942478\pi$
$102$	−4.96953	−	1.01165i	−0.492057	−	0.100168i
$103$	−3.61346	−	0.316137i	−0.356045	−	0.0311499i	−0.0922694	−	0.995734i	$-0.529412\pi$
$103$	−3.61346	−	0.316137i	−0.356045	−	0.0311499i	−0.263775	+	0.964584i	$0.584968\pi$
$104$	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	0.484662	−	0.874701i	$-0.338943\pi$
$107$	−4.03460	−	4.03460i	−0.390039	−	0.390039i	−0.874701	+	0.484662i	$0.838943\pi$
$108$	−1.90315	+	4.17233i	−0.183131	+	0.401483i
$109$			15.8226i			1.51553i	0.652527	+	0.757765i	$0.273709\pi$
$109$			15.8226i			1.51553i	−0.652527	+	0.757765i	$0.726291\pi$
$110$	−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	0.977372	+	0.211526i	$0.0678432\pi$
$113$	−0.232615	+	2.65880i	−0.0218825	+	0.250119i	−0.999255	+	0.0385931i	$0.987712\pi$
$114$	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	0.918151	−	0.396230i	$-0.129682\pi$
$127$	−0.846401	−	3.15881i	−0.0751059	−	0.280299i	−0.993257	+	0.115931i	$0.963015\pi$
$128$	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	−0.916074	−	0.401010i	$-0.868659\pi$
$131$	0.497235	−	1.36614i	0.0434436	−	0.119360i	0.959517	+	0.281649i	$0.0908815\pi$
$132$	−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	−0.978035	−	0.208442i	$-0.933161\pi$
$137$	−13.0703	+	9.15193i	−1.11667	+	0.781902i	−0.138637	+	0.990343i	$0.544272\pi$
$138$	0.623196	+	1.14809i	0.0530499	+	0.0977322i
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	0.734069	+	0.679075i	$0.237619\pi$
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	−0.998830	+	0.0483514i	$0.984603\pi$
$140$	−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	0.975648	+	0.219343i	$0.0703913\pi$
$149$	1.63395	+	9.26659i	0.133858	+	0.759149i	−0.841789	+	0.539806i	$0.818498\pi$
$150$	5.61648	+	7.22936i	0.458583	+	0.590275i
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	0.609284	−	0.792952i	$-0.291457\pi$
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	−0.675104	+	0.737723i	$0.735901\pi$
$152$	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	−0.375408	−	0.926860i	$-0.622497\pi$
$157$	1.94520	−	22.2338i	0.155244	−	1.77445i	0.530652	−	0.847590i	$-0.321947\pi$
$158$	−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	0.635290	−	0.772274i	$-0.280881\pi$
$163$	−1.74889	−	1.74889i	−0.136983	−	0.136983i	−0.772274	+	0.635290i	$0.780881\pi$
$164$	−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	0.364399	−	0.931243i	$-0.381275\pi$
$167$	7.25686	+	0.634893i	0.561553	+	0.0491295i	0.197154	+	0.980373i	$0.436830\pi$
$168$	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	0.721760	−	0.692143i	$-0.243333\pi$
$173$	20.4232	−	1.78680i	1.55275	−	0.135848i	0.830985	+	0.556295i	$0.187778\pi$
$174$	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	0.999116	+	0.0420450i	$0.0133873\pi$
$179$	7.17079	+	12.4202i	0.535970	+	0.928327i	−0.463146	+	0.886282i	$0.653279\pi$
$180$	5.40168	−	2.42331i	0.402617	−	0.180623i
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	−0.825005	−	0.565126i	$-0.808828\pi$
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	0.901916	+	0.431912i	$0.142161\pi$
$182$	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	0.923987	−	0.382424i	$-0.124911\pi$
$191$	22.9618	+	4.04878i	1.66145	+	0.292959i	0.737467	+	0.675383i	$0.236022\pi$
$192$	0.351864	−	13.3793i	0.0253936	−	0.965564i
$193$	−0.131693	−	0.282417i	−0.00947948	−	0.0203288i	0.901511	−	0.432756i	$-0.142459\pi$
$193$	−0.131693	−	0.282417i	−0.00947948	−	0.0203288i	−0.910991	+	0.412427i	$0.864681\pi$
$194$	−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	−0.368858	−	0.929486i	$-0.620251\pi$
$197$	−3.13774	+	0.840756i	−0.223555	+	0.0599014i	0.145303	+	0.989387i	$0.453584\pi$
$198$	−6.94179	+	2.80284i	−0.493332	+	0.199189i
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	−0.291310	−	0.956629i	$-0.594091\pi$
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	0.682809	+	0.730596i	$0.260758\pi$
$200$	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	−0.457763	−	0.889074i	$-0.651349\pi$
$211$	4.91430	−	4.12359i	0.338314	−	0.283879i	0.796077	+	0.605195i	$0.206905\pi$
$212$	−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	0.0809965	−	0.996714i	$-0.474190\pi$
$223$	−9.41489	−	4.39023i	−0.630467	−	0.293992i	−0.711464	+	0.702723i	$0.751968\pi$
$224$	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	0.999862	+	0.0166042i	$0.00528553\pi$
$227$	0.272304	+	3.11245i	0.0180734	+	0.206580i	−0.981789	+	0.189976i	$0.939159\pi$
$228$	1.39671	+	9.35287i	0.0924996	+	0.619409i
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.654990	−	0.755638i	$-0.272673\pi$
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.873933	+	0.486047i	$0.161562\pi$
$230$	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	0.152333	−	0.988329i	$-0.451321\pi$
$233$	−3.20411	−	0.858538i	−0.209908	−	0.0562447i	−0.362241	+	0.932085i	$0.617988\pi$
$234$	−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	−0.231335	−	0.972874i	$-0.574309\pi$
$239$	−15.9837	−	5.81759i	−1.03390	−	0.376309i	−0.802564	+	0.596566i	$0.796532\pi$
$240$	−4.58117	+	3.28809i	−0.295713	+	0.212245i
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	−0.685782	−	0.727807i	$-0.740540\pi$
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	0.893349	−	0.449364i	$-0.148349\pi$
$242$	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	0.0238664	−	0.999715i	$-0.492402\pi$
$251$	−13.1493	−	7.59178i	−0.829979	−	0.479189i	−0.853846	+	0.520527i	$0.825736\pi$
$252$	−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	−0.633041	−	0.774118i	$-0.718194\pi$
$257$	4.98418	−	7.11815i	0.310905	−	0.444018i	0.943946	+	0.330100i	$0.107083\pi$
$258$	−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	−0.314203	−	0.949356i	$-0.601737\pi$
$263$	9.97382	−	21.3889i	0.615012	−	1.31890i	0.929214	−	0.369541i	$-0.120485\pi$
$264$	−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	−0.999834	−	0.0182248i	$-0.994199\pi$
$277$	−5.71185	+	12.2491i	−0.343192	+	0.735978i	0.656642	+	0.754203i	$0.271976\pi$
$278$	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	−0.978130	−	0.207994i	$-0.933306\pi$
$281$	−10.1156	+	12.0553i	−0.603445	+	0.719158i	0.374685	+	0.927152i	$0.377751\pi$
$282$	−6.96758	+	17.6824i	−0.414913	+	1.05297i
$283$	−17.2952	+	24.7001i	−1.02809	+	1.46827i	−0.150648	+	0.988587i	$0.548136\pi$
$283$	−17.2952	+	24.7001i	−1.02809	+	1.46827i	−0.877443	+	0.479680i	$0.840753\pi$
$284$	−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	−0.607180	−	0.794564i	$-0.707699\pi$
$293$	−6.65512	+	3.10333i	−0.388796	+	0.181299i	0.218384	+	0.975863i	$0.429922\pi$
$294$	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	0.615336	−	0.788265i	$-0.289020\pi$
$307$	13.2129	+	3.54038i	0.754099	+	0.202060i	0.138764	+	0.990326i	$0.455687\pi$
$308$	−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	−0.0648001	−	0.997898i	$-0.520641\pi$
$311$	3.80231	−	0.670449i	0.215609	−	0.0380177i	0.280409	+	0.959881i	$0.409530\pi$
$312$	−22.4666	+	17.8666i	−1.27192	+	1.01149i
$313$	2.14418	+	24.5081i	0.121196	+	1.38528i	0.776597	+	0.629997i	$0.216944\pi$
$313$	2.14418	+	24.5081i	0.121196	+	1.38528i	−0.655401	+	0.755281i	$0.727500\pi$
$314$	−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	0.794493	−	0.607274i	$-0.207737\pi$
$317$	14.9555	+	6.97386i	0.839984	+	0.391691i	0.0454916	+	0.998965i	$0.485515\pi$
$318$	−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	−0.814744	−	0.579820i	$-0.803123\pi$
$331$	−19.3973	+	7.06005i	−1.06617	+	0.388056i	−0.251429	+	0.967876i	$0.580901\pi$
$332$	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	0.316361	−	0.948639i	$-0.397539\pi$
$337$	−8.57053	−	6.00115i	−0.466867	−	0.326904i	−0.783227	+	0.621735i	$0.786428\pi$
$338$	−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	0.731767	−	0.681554i	$-0.238696\pi$
$347$	−4.85639	−	10.4146i	−0.260705	−	0.559083i	−0.992472	+	0.122472i	$0.960918\pi$
$348$	−4.82230	+	2.61759i	−0.258502	+	0.140317i
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.575719	−	0.817647i	$-0.304722\pi$
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.261347	+	0.965245i	$0.415833\pi$
$350$	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	0.929475	−	0.368885i	$-0.120260\pi$
$353$	4.97772	+	7.10893i	0.264938	+	0.378370i	−0.664538	+	0.747255i	$0.731371\pi$
$354$	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	−0.460480	−	0.887670i	$-0.652323\pi$
$359$	10.2032	−	17.6725i	0.538505	−	0.932718i	0.998985	−	0.0450476i	$-0.0143439\pi$
$360$	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	0.610571	−	0.791962i	$-0.290940\pi$
$367$	25.8506	−	2.26163i	1.34939	−	0.118056i	0.738818	+	0.673906i	$0.235385\pi$
$368$	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	0.209705	−	0.977765i	$-0.432750\pi$
$373$	4.75950	+	0.416402i	0.246438	+	0.0215605i	0.0367323	+	0.999325i	$0.488305\pi$
$374$	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	$0.225144\pi$
$379$			25.3002i			1.29958i	−0.760112	+	0.649792i	$0.774856\pi$
$380$	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	0.918089	+	0.396375i	$0.129732\pi$
$383$	−1.07406	+	12.2766i	−0.0548819	+	0.627303i	−0.972971	+	0.230929i	$0.925824\pi$
$384$	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	0.799388	−	0.600815i	$-0.205157\pi$
$389$	6.83430	+	5.73466i	0.346513	+	0.290759i	−0.452875	+	0.891574i	$0.649602\pi$
$390$	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	0.996192	+	0.0871833i	$0.0277866\pi$
$397$	3.52782	+	13.1660i	0.177056	+	0.660782i	−0.819136	+	0.573599i	$0.805547\pi$
$398$	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	−0.962225	−	0.272257i	$-0.912230\pi$
$401$	−1.00354	+	2.75721i	−0.0501146	+	0.137689i	0.912110	+	0.409945i	$0.134452\pi$
$402$	−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	−0.420515	−	0.907285i	$-0.638151\pi$
$409$	9.80467	−	26.9381i	0.484810	−	1.33200i	0.905325	−	0.424719i	$-0.139627\pi$
$410$	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	−0.987829	−	0.155543i	$-0.950287\pi$
$419$	−2.30839	−	13.0915i	−0.112772	−	0.639563i	0.875057	−	0.484020i	$-0.160824\pi$
$420$	8.49838	−	5.03966i	0.414678	−	0.245910i
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	0.795934	−	0.605383i	$-0.206980\pi$
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	−0.457974	+	0.888966i	$0.651425\pi$
$422$	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	$-0.997731\pi$
$431$		−	0.295969i		−	0.0142563i	0.999975	−	0.00712817i	$-0.00226899\pi$
$432$	5.39433	+	5.30459i	0.259535	+	0.255217i
$433$	12.8171	+	12.8171i	0.615949	+	0.615949i	0.944490	−	0.328541i	$-0.106557\pi$
$433$	12.8171	+	12.8171i	0.615949	+	0.615949i	−0.328541	+	0.944490i	$0.606557\pi$
$434$	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	−0.921105	−	0.389313i	$-0.872712\pi$
$439$	−9.75841	−	26.8110i	−0.465743	−	1.27962i	0.455362	−	0.890306i	$-0.349510\pi$
$440$	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	−0.979204	−	0.202878i	$-0.934970\pi$
$443$	−40.1651	+	3.51399i	−1.90830	+	0.166955i	−0.929098	+	0.369833i	$0.879415\pi$
$444$	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	0.758819	−	0.651301i	$-0.225777\pi$
$449$	−3.91232	−	6.77634i	−0.184634	−	0.319795i	−0.943453	+	0.331506i	$0.892443\pi$
$450$	−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	0.738867	−	0.673851i	$-0.235361\pi$
$457$	−3.14363	−	4.48957i	−0.147053	−	0.210013i	−0.885920	+	0.463838i	$0.846472\pi$
$458$	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	0.815019	−	0.579434i	$-0.196726\pi$
$461$	29.6880	+	5.23480i	1.38271	+	0.243809i	0.567689	+	0.823243i	$0.307837\pi$
$462$	−10.9803	+	5.96021i	−0.510850	+	0.277294i
$463$	0.0761934	+	0.163397i	0.00354101	+	0.00759371i	0.908070	−	0.418818i	$-0.137555\pi$
$463$	0.0761934	+	0.163397i	0.00354101	+	0.00759371i	−0.904529	+	0.426411i	$0.859778\pi$
$464$	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	−0.529616	−	0.848238i	$-0.677664\pi$
$467$	−12.1916	+	3.26672i	−0.564158	+	0.151166i	−0.0345422	+	0.999403i	$0.510997\pi$
$468$	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	−0.963696	−	0.267003i	$-0.913966\pi$
$479$	−33.4923	+	12.1902i	−1.53030	+	0.556985i	−0.566607	+	0.823988i	$0.691744\pi$
$480$	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	−0.587604	−	0.809149i	$-0.699929\pi$
$487$	4.88907	−	4.88907i	0.221545	−	0.221545i	0.809149	+	0.587604i	$0.199929\pi$
$488$	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	0.244048	−	0.969763i	$-0.421525\pi$
$491$	−16.6934	−	19.8944i	−0.753361	−	0.897821i	−0.997409	+	0.0719426i	$0.977080\pi$
$492$	−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	0.0791972	−	0.996859i	$-0.474764\pi$
$499$	11.0477	−	1.94801i	0.494564	−	0.0872050i	0.415367	+	0.909654i	$0.363653\pi$
$500$	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	0.842008	−	0.539466i	$-0.181374\pi$
$503$	29.1890	+	7.82118i	1.30147	+	0.348729i	0.459467	+	0.888195i	$0.348040\pi$
$504$	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	0.780829	−	0.624745i	$-0.214797\pi$
$509$	22.0511	+	8.02596i	0.977399	+	0.355744i	0.196571	+	0.980490i	$0.437019\pi$
$510$	−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	0.154723	−	0.987958i	$-0.450551\pi$
$521$	−14.2319	−	8.21681i	−0.623512	−	0.359985i	−0.778235	+	0.627973i	$0.783885\pi$
$522$	−7.01018	+	8.96844i	−0.306827	+	0.392538i
$523$	3.78176	−	14.1137i	0.165365	−	0.617150i	−0.832629	−	0.553832i	$-0.813165\pi$
$523$	3.78176	−	14.1137i	0.165365	−	0.617150i	0.997993	−	0.0633182i	$-0.0201683\pi$
$524$	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	−0.788118	−	0.615524i	$-0.788945\pi$
$547$	4.44356	−	9.52924i	0.189993	−	0.407441i	0.978111	+	0.208083i	$0.0667224\pi$
$548$	−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	0.803238	+	0.595659i	$0.203109\pi$
$557$	−4.48926	+	16.7541i	−0.190216	+	0.709896i	−0.993454	+	0.114237i	$0.963558\pi$
$558$	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	0.0804714	−	0.996757i	$-0.474357\pi$
$563$	21.2542	−	9.91099i	0.895758	−	0.417699i	0.815286	+	0.579058i	$0.196580\pi$
$564$	−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	−0.412175	−	0.911105i	$-0.635231\pi$
$569$	6.84027	−	38.7931i	0.286759	−	1.62629i	0.698934	−	0.715186i	$-0.253658\pi$
$570$	4.10673	−	24.9923i	0.172012	−	1.04681i
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.902865	−	0.429924i	$-0.141460\pi$
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.415285	+	0.909691i	$0.363682\pi$
$572$	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	−0.208257	−	0.978074i	$-0.566779\pi$
$577$	−21.0819	−	5.64888i	−0.877651	−	0.235166i	−0.669393	+	0.742908i	$0.733446\pi$
$578$	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	−0.0915170	−	0.995804i	$-0.529172\pi$
$587$	−22.1244	−	10.3168i	−0.913173	−	0.425819i	−0.821656	+	0.569984i	$0.806949\pi$
$588$	−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	−0.786169	−	0.618012i	$-0.787938\pi$
$593$	−4.09490	+	4.09490i	−0.168157	+	0.168157i	0.618012	+	0.786169i	$0.287938\pi$
$594$	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	0.244163	−	0.969734i	$-0.421487\pi$
$599$	30.3866	−	25.4974i	1.24156	−	1.04180i	0.997400	−	0.0720615i	$-0.0229578\pi$
$600$	−25.1195	+	8.08606i	−1.02550	+	0.330112i
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.757053	−	0.653353i	$-0.773362\pi$
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.159969	+	0.987122i	$0.551139\pi$
$602$	−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	−0.106160	−	0.994349i	$-0.533856\pi$
$607$	−26.5308	−	18.5771i	−1.07685	−	0.754020i	−0.970691	+	0.240329i	$0.922745\pi$
$608$	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	0.0521885	−	0.998637i	$-0.483380\pi$
$613$	14.7737	−	3.95860i	0.596704	−	0.159886i	0.544515	+	0.838751i	$0.316714\pi$
$614$	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	0.991137	+	0.132845i	$0.0424114\pi$
$617$	11.3221	+	24.2804i	0.455812	+	0.977492i	−0.535325	+	0.844646i	$0.679811\pi$
$618$	0.174600	−	6.63900i	0.00702345	−	0.267060i
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.535011	−	0.844845i	$-0.320308\pi$
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.213792	+	0.976879i	$0.431419\pi$
$620$	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	0.866278	−	0.499562i	$-0.166506\pi$
$631$	0.0126965	+	0.0219910i	0.000505440	+	0.000875448i	−0.865773	+	0.500438i	$0.833172\pi$
$632$	−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	0.965214	+	0.261463i	$0.0842049\pi$
$641$	9.97230	+	27.3987i	0.393882	+	1.08218i	−0.571331	+	0.820720i	$0.693573\pi$
$642$	6.92324	−	7.82351i	0.273238	−	0.308769i
$643$	−1.74781	−	0.152914i	−0.0689270	−	0.00603033i	0.0526401	−	0.998614i	$-0.483236\pi$
$643$	−1.74781	−	0.152914i	−0.0689270	−	0.00603033i	−0.121567	+	0.992583i	$0.538792\pi$
$644$	−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	0.934699	−	0.355440i	$-0.115669\pi$
$647$	14.7341	+	14.7341i	0.579259	+	0.579259i	−0.355440	+	0.934699i	$0.615669\pi$
$648$	−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	−0.963578	−	0.267429i	$-0.913826\pi$
$653$	0.812604	−	9.28810i	0.0317996	−	0.363471i	0.995377	−	0.0960426i	$-0.0306185\pi$
$654$	−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	0.326010	−	0.945366i	$-0.394296\pi$
$659$	−14.0775	−	11.8125i	−0.548383	−	0.460148i	−0.874393	+	0.485218i	$0.838740\pi$
$660$	−7.76913	+	2.17920i	−0.302413	+	0.0848253i
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	0.941073	+	0.338204i	$0.109819\pi$
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	−0.768647	+	0.639674i	$0.779070\pi$
$662$	−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	−0.497405	−	0.867518i	$-0.665714\pi$
$673$	3.83098	−	2.68248i	0.147673	−	0.103402i	0.645078	+	0.764117i	$0.276825\pi$
$674$	−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	−0.994436	−	0.105347i	$-0.966405\pi$
$677$	−32.1483	+	22.5105i	−1.23556	+	0.865147i	−0.241123	+	0.970495i	$0.577516\pi$
$678$	−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	0.854820	+	0.518924i	$0.173667\pi$
$683$	9.77386	+	36.4765i	0.373986	+	1.39574i	−0.480834	+	0.876812i	$0.659666\pi$
$684$	−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	0.815068	−	0.579365i	$-0.196699\pi$
$691$	10.1478	+	8.51501i	0.386040	+	0.323926i	−0.429028	+	0.903291i	$0.641144\pi$
$692$	−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	$-0.991452\pi$
$701$		−	1.42181i		−	0.0537011i	0.999639	−	0.0268505i	$-0.00854782\pi$
$702$	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	0.918487	+	0.395452i	$0.129412\pi$
$709$	12.4901	+	34.3163i	0.469077	+	1.28878i	−0.449410	+	0.893325i	$0.648366\pi$
$710$	−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	0.999766	−	0.0216398i	$-0.00688871\pi$
$719$	12.9014	+	22.3459i	0.481142	+	0.833363i	−0.518624	+	0.855003i	$0.673555\pi$
$720$	−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	0.801612	−	0.597845i	$-0.203976\pi$
$727$	−0.926059	−	1.32255i	−0.0343456	−	0.0490507i	−0.835958	+	0.548794i	$0.815087\pi$
$728$	−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	0.774692	−	0.632338i	$-0.217905\pi$
$733$	−5.62244	−	12.0574i	−0.207669	−	0.445349i	−0.982362	+	0.186990i	$0.940127\pi$
$734$	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	0.191243	−	0.981543i	$-0.438748\pi$
$739$	30.9063	−	17.8437i	1.13691	−	0.656393i	0.945663	+	0.325150i	$0.105415\pi$
$740$	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	−0.0912848	−	0.995825i	$-0.529097\pi$
$743$	−28.8465	−	20.1985i	−1.05828	−	0.741012i	−0.966990	+	0.254813i	$0.917986\pi$
$744$	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	−0.225864	−	0.974159i	$-0.572520\pi$
$751$	19.0262	−	15.9649i	0.694275	−	0.582566i	0.920138	+	0.391593i	$0.128076\pi$
$752$	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	−0.305278	−	0.952263i	$-0.598749\pi$
$757$	17.8009	−	17.8009i	0.646986	−	0.646986i	0.952263	+	0.305278i	$0.0987493\pi$
$758$	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	−0.927240	−	0.374467i	$-0.877826\pi$
$761$	−31.3105	−	37.3144i	−1.13500	−	1.35265i	−0.207765	−	0.978179i	$-0.566619\pi$
$762$	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	−0.884287	−	0.466944i	$-0.845355\pi$
$769$	−43.1365	+	7.60612i	−1.55554	+	0.274284i	−0.671254	+	0.741227i	$0.734244\pi$
$770$	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	−0.160725	−	0.986999i	$-0.551383\pi$
$773$	−22.0592	−	5.91076i	−0.793416	−	0.212595i	−0.632691	+	0.774404i	$0.718050\pi$
$774$	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	−0.680421	−	0.732822i	$-0.738203\pi$
$787$	−15.6093	+	7.27876i	−0.556413	+	0.259460i	0.124008	+	0.992281i	$0.460425\pi$
$788$	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	−0.331827	−	0.943340i	$-0.607665\pi$
$797$	18.8617	−	26.9373i	0.668115	−	0.954166i	0.999941	−	0.0108262i	$-0.00344614\pi$
$798$	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	−0.506989	−	0.861953i	$-0.669241\pi$
$821$	12.3182	−	14.6802i	0.429907	−	0.512343i	0.936895	+	0.349610i	$0.113686\pi$
$822$	−18.1837	−	22.8654i	−0.634230	−	0.797522i
$823$	−0.358433	+	0.511895i	−0.0124942	+	0.0178435i	−0.825351	−	0.564621i	$-0.809022\pi$
$823$	−0.358433	+	0.511895i	−0.0124942	+	0.0178435i	0.812856	+	0.582464i	$0.197911\pi$
$824$	−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	−0.892365	−	0.451314i	$-0.850955\pi$
$827$	3.05127	−	11.3875i	0.106103	−	0.395981i	0.998468	+	0.0553328i	$0.0176220\pi$
$828$	1.60222	−	1.00068i	0.0556811	−	0.0347759i
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.338562	−	0.940944i	$-0.609941\pi$
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.984163	+	0.177269i	$0.943274\pi$
$830$	−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	−0.981668	−	0.190601i	$-0.938956\pi$
$839$	0.173429	−	0.983567i	0.00598745	−	0.0339565i	0.987655	+	0.156644i	$0.0500676\pi$
$840$	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	0.999953	−	0.00971747i	$-0.00309322\pi$
$853$	0.394403	+	4.50805i	0.0135041	+	0.154353i	−0.986449	+	0.164070i	$0.947538\pi$
$854$	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	0.974670	+	0.223650i	$0.0717973\pi$
$857$	51.8892	+	24.1963i	1.77250	+	0.826531i	0.797831	+	0.602881i	$0.205981\pi$
$858$	22.2936	−	7.45653i	0.761091	−	0.254562i
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	0.994188	−	0.107659i	$-0.0343354\pi$
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	−0.278662	+	0.960389i	$0.589891\pi$
$860$	−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	−0.0270792	−	0.999633i	$-0.508621\pi$
$863$	28.5706	−	28.5706i	0.972554	−	0.972554i	0.999633	+	0.0270792i	$0.00862062\pi$
$864$	−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	−0.0329214	−	0.999458i	$-0.510481\pi$
$877$	−29.1215	−	20.3911i	−0.983364	−	0.688559i	−0.950443	+	0.310899i	$0.899370\pi$
$878$	−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	−0.920846	−	0.389927i	$-0.872500\pi$
$881$	−30.9752	+	17.8836i	−1.04358	+	0.602512i	−0.122736	+	0.992439i	$0.539167\pi$
$882$	0.892728	+	4.20463i	0.0300597	+	0.141577i
$883$	−3.38029	+	0.905746i	−0.113756	+	0.0304808i	−0.315248	−	0.949009i	$-0.602088\pi$
$883$	−3.38029	+	0.905746i	−0.113756	+	0.0304808i	0.201492	+	0.979490i	$0.435421\pi$
$884$	−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	0.998095	+	0.0616962i	$0.0196510\pi$
$887$	12.0260	+	25.7899i	0.403794	+	0.865939i	−0.594301	+	0.804243i	$0.702571\pi$
$888$	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	0.469398	−	0.882987i	$-0.344471\pi$
$907$	32.6761	−	2.85879i	1.08499	−	0.0949246i	0.615596	+	0.788062i	$0.288915\pi$
$908$	−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	0.988379	+	0.152012i	$0.0485753\pi$
$911$	9.92857	+	27.2785i	0.328948	+	0.903778i	−0.659430	+	0.751766i	$0.729202\pi$
$912$	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	$0.154540\pi$
$919$			28.2931i			0.933302i	−0.884442	+	0.466651i	$0.845460\pi$
$920$	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	0.954390	−	0.298564i	$-0.0965076\pi$
$929$	25.1788	+	21.1275i	0.826089	+	0.693171i	−0.128300	+	0.991735i	$0.540952\pi$
$930$	−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	0.941310	−	0.337543i	$-0.109596\pi$
$937$	−1.30584	−	4.87347i	−0.0426600	−	0.159209i	−0.983970	+	0.178334i	$0.942929\pi$
$938$	−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	−0.00641343	−	0.999979i	$-0.502041\pi$
$941$	19.6715	−	54.0471i	0.641274	−	1.76189i	0.647687	−	0.761906i	$-0.275736\pi$
$942$	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	−0.917354	−	0.398073i	$-0.869679\pi$
$947$	−26.3740	+	18.4673i	−0.857041	+	0.600107i	0.0603125	+	0.998180i	$0.480790\pi$
$948$	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	−0.995384	−	0.0959743i	$-0.969403\pi$
$953$	−5.59819	−	20.8927i	−0.181343	−	0.676782i	0.814041	−	0.580808i	$-0.197263\pi$
$954$	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	−0.964927	−	0.262517i	$-0.915447\pi$
$967$	0.961701	−	10.9923i	0.0309262	−	0.353488i	0.995854	−	0.0909711i	$-0.0289971\pi$
$968$	−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	$0.114506\pi$
$971$			21.9387i			0.704047i	−0.935991	+	0.352023i	$0.885494\pi$
$972$	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	−0.000862648	−	1.00000i	$-0.500275\pi$
$977$	−5.48124	−	0.479546i	−0.175360	−	0.0153420i	−0.174498	+	0.984658i	$0.555830\pi$
$978$	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	−0.515139	−	0.857106i	$-0.672260\pi$
$983$	−27.3904	+	2.39635i	−0.873618	+	0.0764316i	−0.358478	+	0.933538i	$0.616704\pi$
$984$	−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	−0.711637	−	0.702547i	$-0.752046\pi$
$991$	7.95205	−	13.7734i	0.252605	−	0.437525i	0.964242	+	0.265022i	$0.0853793\pi$
$992$	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	0.784456	−	0.620185i	$-0.212942\pi$
$997$	−2.10376	−	3.00447i	−0.0666266	−	0.0951527i	−0.851083	+	0.525032i	$0.824053\pi$
$998$	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.83.12	yes	192
3.2	odd	2		405.2.r.a.8.5		192
5.2	odd	4	inner	135.2.q.a.2.12	✓	192
5.3	odd	4		675.2.ba.b.407.5		192
5.4	even	2		675.2.ba.b.218.5		192
15.2	even	4		405.2.r.a.332.5		192
27.13	even	9		405.2.r.a.233.5		192
27.14	odd	18	inner	135.2.q.a.68.12	yes	192
135.14	odd	18		675.2.ba.b.68.5		192
135.67	odd	36		405.2.r.a.152.5		192
135.68	even	36		675.2.ba.b.257.5		192
135.122	even	36	inner	135.2.q.a.122.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	5.2	odd	4	inner
135.2.q.a.68.12	yes	192	27.14	odd	18	inner
135.2.q.a.83.12	yes	192	1.1	even	1	trivial
135.2.q.a.122.12	yes	192	135.122	even	36	inner
405.2.r.a.8.5		192	3.2	odd	2
405.2.r.a.152.5		192	135.67	odd	36
405.2.r.a.233.5		192	27.13	even	9
405.2.r.a.332.5		192	15.2	even	4
675.2.ba.b.68.5		192	135.14	odd	18
675.2.ba.b.218.5		192	5.4	even	2
675.2.ba.b.257.5		192	135.68	even	36
675.2.ba.b.407.5		192	5.3	odd	4

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 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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Representations

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Database

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