LMFDB - Embedded newform 135.2.q.a.2.12

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			2.12
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.606324 + 0.865920i) q^{2} +(1.47671 + 0.905161i) q^{3} +(0.301851 - 0.829330i) q^{4} +(-1.02123 + 1.98924i) q^{5} +(0.111569 + 1.82754i) q^{6} +(-2.61975 - 1.22161i) q^{7} +(2.94330 - 0.788655i) q^{8} +(1.36137 + 2.67333i) q^{9} +O(q^{10})$	\(q+(0.606324 + 0.865920i) q^{2} +(1.47671 + 0.905161i) q^{3} +(0.301851 - 0.829330i) q^{4} +(-1.02123 + 1.98924i) q^{5} +(0.111569 + 1.82754i) q^{6} +(-2.61975 - 1.22161i) q^{7} +(2.94330 - 0.788655i) q^{8} +(1.36137 + 2.67333i) q^{9} +(-2.34172 + 0.321816i) q^{10} +(1.51740 - 1.80836i) q^{11} +(1.19642 - 0.951458i) q^{12} +(-4.45519 - 3.11956i) q^{13} +(-0.530600 - 3.00918i) q^{14} +(-3.30866 + 2.01316i) q^{15} +(1.11535 + 0.935892i) q^{16} +(-2.67549 - 0.716894i) q^{17} +(-1.48946 + 2.79974i) q^{18} +(5.35751 + 3.09316i) q^{19} +(1.34148 + 1.44740i) q^{20} +(-2.76286 - 4.17526i) q^{21} +(2.48593 + 0.217491i) q^{22} +(-0.301527 - 0.646627i) q^{23} +(5.06027 + 1.49954i) q^{24} +(-2.91416 - 4.06296i) q^{25} -5.74930i q^{26} +(-0.409444 + 5.18000i) q^{27} +(-1.80389 + 1.80389i) q^{28} +(-0.623300 + 3.53491i) q^{29} +(-3.74935 - 1.64441i) q^{30} +(-5.18043 - 1.88552i) q^{31} +(0.397007 - 4.53781i) q^{32} +(3.87762 - 1.29695i) q^{33} +(-1.00144 - 2.75143i) q^{34} +(5.10545 - 3.96376i) q^{35} +(2.62800 - 0.322074i) q^{36} +(1.14193 - 4.26173i) q^{37} +(0.569956 + 6.51463i) q^{38} +(-3.75534 - 8.63936i) q^{39} +(-1.43698 + 6.66033i) q^{40} +(5.70140 - 1.00531i) q^{41} +(1.94025 - 4.92398i) q^{42} +(1.44271 - 0.126221i) q^{43} +(-1.04170 - 1.80428i) q^{44} +(-6.70817 - 0.0220104i) q^{45} +(0.377104 - 0.653164i) q^{46} +(-4.38688 + 9.40770i) q^{47} +(0.799924 + 2.39162i) q^{48} +(0.871236 + 1.03830i) q^{49} +(1.75128 - 4.98690i) q^{50} +(-3.30202 - 3.48039i) q^{51} +(-3.93195 + 2.75318i) 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} +(5.11170 + 9.41712i) q^{57} +(-3.43887 + 1.60357i) q^{58} +(-6.27320 + 5.26384i) q^{59} +(0.670849 + 3.35164i) q^{60} +(2.64019 - 0.960952i) q^{61} +(-1.50831 - 5.62907i) q^{62} +(-0.300676 - 8.66650i) q^{63} +(6.69194 - 3.86359i) q^{64} +(10.7553 - 5.67665i) q^{65} +(3.47414 + 2.57134i) q^{66} +(-4.28254 + 6.11610i) q^{67} +(-1.40214 + 2.00246i) q^{68} +(0.140033 - 1.22781i) q^{69} +(6.52785 + 2.01759i) q^{70} +(-4.24004 + 2.44799i) q^{71} +(6.11524 + 6.79476i) q^{72} +(1.80353 + 6.73088i) q^{73} +(4.38269 - 1.59517i) q^{74} +(-0.625739 - 8.63762i) q^{75} +(4.18242 - 3.50947i) q^{76} +(-6.18430 + 2.88379i) q^{77} +(5.20404 - 8.49007i) 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} +(-3.90587 + 2.73492i) q^{83} +(-4.29664 + 1.03102i) q^{84} +(4.15837 - 4.59007i) q^{85} +(0.984048 + 1.17274i) q^{86} +(-4.12010 + 4.65586i) q^{87} +(3.03998 - 6.51925i) q^{88} +(-3.33276 + 5.77251i) q^{89} +(-4.04826 - 5.82208i) q^{90} +(7.86060 + 13.6150i) q^{91} +(-0.627283 + 0.0548802i) q^{92} +(-5.94331 - 7.47350i) q^{93} +(-10.8062 + 1.90542i) q^{94} +(-11.6243 + 7.49853i) q^{95} +(4.69371 - 6.34168i) q^{96} +(-1.59893 - 18.2758i) q^{97} +(-0.370833 + 1.38397i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.606324	+	0.865920i	0.428736	+	0.612298i	0.974159	−	0.225863i	$-0.0725201\pi$
$2$	0.606324	+	0.865920i	0.428736	+	0.612298i	−0.545424	+	0.838161i	$0.683631\pi$
$3$	1.47671	+	0.905161i	0.852581	+	0.522595i
$3$	1.47671	+	0.905161i	0.852581	+	0.522595i
$4$	0.301851	−	0.829330i	0.150926	−	0.414665i
$5$	−1.02123	+	1.98924i	−0.456710	+	0.889616i
$5$	−1.02123	+	1.98924i	−0.456710	+	0.889616i
$6$	0.111569	+	1.82754i	0.0455480	+	0.746089i
$7$	−2.61975	−	1.22161i	−0.990171	−	0.461725i	−0.141096	−	0.989996i	$-0.545063\pi$
$7$	−2.61975	−	1.22161i	−0.990171	−	0.461725i	−0.849076	+	0.528271i	$0.822840\pi$
$8$	2.94330	−	0.788655i	1.04061	−	0.278832i
$9$	1.36137	+	2.67333i	0.453789	+	0.891109i
$10$	−2.34172	+	0.321816i	−0.740518	+	0.101767i
$11$	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	$0.106403\pi$
$12$	1.19642	−	0.951458i	0.345378	−	0.274662i
$13$	−4.45519	−	3.11956i	−1.23565	−	0.865210i	−0.241203	−	0.970475i	$-0.577542\pi$
$13$	−4.45519	−	3.11956i	−1.23565	−	0.865210i	−0.994444	+	0.105265i	$0.966431\pi$
$14$	−0.530600	−	3.00918i	−0.141809	−	0.804238i
$15$	−3.30866	+	2.01316i	−0.854291	+	0.519795i
$16$	1.11535	+	0.935892i	0.278838	+	0.233973i
$17$	−2.67549	−	0.716894i	−0.648901	−	0.173872i	−0.0806688	−	0.996741i	$-0.525706\pi$
$17$	−2.67549	−	0.716894i	−0.648901	−	0.173872i	−0.568232	+	0.822869i	$0.692372\pi$
$18$	−1.48946	+	2.79974i	−0.351069	+	0.659904i
$19$	5.35751	+	3.09316i	1.22910	+	0.709619i	0.966841	−	0.255379i	$-0.0822003\pi$
$19$	5.35751	+	3.09316i	1.22910	+	0.709619i	0.262256	+	0.964998i	$0.415534\pi$
$20$	1.34148	+	1.44740i	0.299963	+	0.323647i
$21$	−2.76286	−	4.17526i	−0.602906	−	0.911116i
$22$	2.48593	+	0.217491i	0.530002	+	0.0463692i
$23$	−0.301527	−	0.646627i	−0.0628728	−	0.134831i	0.872361	−	0.488863i	$-0.162588\pi$
$23$	−0.301527	−	0.646627i	−0.0628728	−	0.134831i	−0.935233	+	0.354032i	$0.884810\pi$
$24$	5.06027	+	1.49954i	1.03292	+	0.306093i
$25$	−2.91416	−	4.06296i	−0.582832	−	0.812593i
$26$		−	5.74930i		−	1.12753i
$27$	−0.409444	+	5.18000i	−0.0787976	+	0.996891i
$28$	−1.80389	+	1.80389i	−0.340903	+	0.340903i
$29$	−0.623300	+	3.53491i	−0.115744	+	0.656416i	0.870635	+	0.491929i	$0.163708\pi$
$29$	−0.623300	+	3.53491i	−0.115744	+	0.656416i	−0.986379	+	0.164487i	$0.947403\pi$
$30$	−3.74935	−	1.64441i	−0.684534	−	0.300226i
$31$	−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	$0.775970\pi$
$32$	0.397007	−	4.53781i	0.0701815	−	0.802178i
$33$	3.87762	−	1.29695i	0.675007	−	0.225769i
$34$	−1.00144	−	2.75143i	−0.171745	−	0.471866i
$35$	5.10545	−	3.96376i	0.862979	−	0.669998i
$36$	2.62800	−	0.322074i	0.438000	−	0.0536790i
$37$	1.14193	−	4.26173i	0.187732	−	0.700624i	−0.806298	−	0.591510i	$-0.798532\pi$
$37$	1.14193	−	4.26173i	0.187732	−	0.700624i	0.994029	−	0.109114i	$-0.0348013\pi$
$38$	0.569956	+	6.51463i	0.0924591	+	1.05681i
$39$	−3.75534	−	8.63936i	−0.601335	−	1.38340i
$40$	−1.43698	+	6.66033i	−0.227206	+	1.05309i
$41$	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	$0.295129\pi$
$42$	1.94025	−	4.92398i	0.299387	−	0.759786i
$43$	1.44271	−	0.126221i	0.220012	−	0.0192485i	0.0233831	−	0.999727i	$-0.492556\pi$
$43$	1.44271	−	0.126221i	0.220012	−	0.0192485i	0.196629	+	0.980478i	$0.437001\pi$
$44$	−1.04170	−	1.80428i	−0.157042	−	0.272005i
$45$	−6.70817	−	0.0220104i	−0.999995	−	0.00328112i
$46$	0.377104	−	0.653164i	0.0556010	−	0.0963037i
$47$	−4.38688	+	9.40770i	−0.639893	+	1.37225i	0.272188	+	0.962244i	$0.412253\pi$
$47$	−4.38688	+	9.40770i	−0.639893	+	1.37225i	−0.912081	+	0.410010i	$0.865525\pi$
$48$	0.799924	+	2.39162i	0.115459	+	0.345201i
$49$	0.871236	+	1.03830i	0.124462	+	0.148328i
$50$	1.75128	−	4.98690i	0.247668	−	0.705254i
$51$	−3.30202	−	3.48039i	−0.462375	−	0.487353i
$52$	−3.93195	+	2.75318i	−0.545263	+	0.381797i
$53$	7.22940	+	7.22940i	0.993035	+	0.993035i	0.999976	−	0.00694140i	$-0.00220953\pi$
$53$	7.22940	+	7.22940i	0.993035	+	0.993035i	−0.00694140	+	0.999976i	$0.502210\pi$
$54$	−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
$57$	5.11170	+	9.41712i	0.677061	+	1.24733i
$58$	−3.43887	+	1.60357i	−0.451546	+	0.210559i
$59$	−6.27320	+	5.26384i	−0.816701	+	0.685293i	−0.952197	−	0.305484i	$-0.901182\pi$
$59$	−6.27320	+	5.26384i	−0.816701	+	0.685293i	0.135496	+	0.990778i	$0.456737\pi$
$60$	0.670849	+	3.35164i	0.0866062	+	0.432695i
$61$	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	$0.331322\pi$
$62$	−1.50831	−	5.62907i	−0.191555	−	0.714893i
$63$	−0.300676	−	8.66650i	−0.0378817	−	1.09188i
$64$	6.69194	−	3.86359i	0.836493	−	0.482949i
$65$	10.7553	−	5.67665i	1.33404	−	0.704101i
$66$	3.47414	+	2.57134i	0.427637	+	0.316510i
$67$	−4.28254	+	6.11610i	−0.523196	+	0.747201i	−0.990592	−	0.136847i	$-0.956303\pi$
$67$	−4.28254	+	6.11610i	−0.523196	+	0.747201i	0.467396	+	0.884048i	$0.345192\pi$
$68$	−1.40214	+	2.00246i	−0.170034	+	0.242834i
$69$	0.140033	−	1.22781i	0.0168579	−	0.147811i
$70$	6.52785	+	2.01759i	0.780228	+	0.241148i
$71$	−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	$0.427162\pi$
$72$	6.11524	+	6.79476i	0.720688	+	0.800770i
$73$	1.80353	+	6.73088i	0.211088	+	0.787790i	0.987507	+	0.157574i	$0.0503671\pi$
$73$	1.80353	+	6.73088i	0.211088	+	0.787790i	−0.776420	+	0.630216i	$0.782966\pi$
$74$	4.38269	−	1.59517i	0.509478	−	0.185435i
$75$	−0.625739	−	8.63762i	−0.0722541	−	0.997386i
$76$	4.18242	−	3.50947i	0.479756	−	0.402563i
$77$	−6.18430	+	2.88379i	−0.704767	+	0.328638i
$78$	5.20404	−	8.49007i	0.589242	−	0.961311i
$79$	12.8661	+	2.26863i	1.44754	+	0.255241i	0.841529	−	0.540212i	$-0.181656\pi$
$79$	12.8661	+	2.26863i	1.44754	+	0.255241i	0.606015	+	0.795453i	$0.292767\pi$
$80$	−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
$83$	−3.90587	+	2.73492i	−0.428724	+	0.300196i	−0.767951	−	0.640509i	$-0.778724\pi$
$83$	−3.90587	+	2.73492i	−0.428724	+	0.300196i	0.339227	+	0.940705i	$0.389835\pi$
$84$	−4.29664	+	1.03102i	−0.468802	+	0.112493i
$85$	4.15837	−	4.59007i	0.451039	−	0.497863i
$86$	0.984048	+	1.17274i	0.106113	+	0.126460i
$87$	−4.12010	+	4.65586i	−0.441721	+	0.499161i
$88$	3.03998	−	6.51925i	0.324063	−	0.694955i
$89$	−3.33276	+	5.77251i	−0.353272	+	0.611885i	−0.986821	−	0.161818i	$-0.948264\pi$
$89$	−3.33276	+	5.77251i	−0.353272	+	0.611885i	0.633549	+	0.773703i	$0.281598\pi$
$90$	−4.04826	−	5.82208i	−0.426724	−	0.613701i
$91$	7.86060	+	13.6150i	0.824014	+	1.42723i
$92$	−0.627283	+	0.0548802i	−0.0653988	+	0.00572165i
$93$	−5.94331	−	7.47350i	−0.616292	−	0.774966i
$94$	−10.8062	+	1.90542i	−1.11457	+	0.196529i
$95$	−11.6243	+	7.49853i	−1.19263	+	0.769333i
$96$	4.69371	−	6.34168i	0.479050	−	0.647245i
$97$	−1.59893	−	18.2758i	−0.162346	−	1.85563i	−0.443894	−	0.896079i	$-0.646403\pi$
$97$	−1.59893	−	18.2758i	−0.162346	−	1.85563i	0.281548	−	0.959547i	$-0.409152\pi$
$98$	−0.370833	+	1.38397i	−0.0374597	+	0.139802i
$99$	6.90008	+	1.59465i	0.693484	+	0.160269i
$100$	−4.24918	+	1.19039i	−0.424918	+	0.119039i
$101$	−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	$0.942478\pi$
$102$	1.01165	−	4.96953i	0.100168	−	0.492057i
$103$	−0.316137	+	3.61346i	−0.0311499	+	0.356045i	0.964584	+	0.263775i	$0.0849677\pi$
$103$	−0.316137	+	3.61346i	−0.0311499	+	0.356045i	−0.995734	+	0.0922694i	$0.970588\pi$
$104$	−15.5732	−	5.66819i	−1.52708	−	0.555812i
$105$	11.1271	−	1.23208i	1.08590	−	0.120239i
$106$	−1.87673	+	10.6434i	−0.182284	+	1.03378i
$107$	4.03460	−	4.03460i	0.390039	−	0.390039i	−0.484662	−	0.874701i	$-0.661057\pi$
$107$	4.03460	−	4.03460i	0.390039	−	0.390039i	0.874701	+	0.484662i	$0.161057\pi$
$108$	4.17233	+	1.90315i	0.401483	+	0.183131i
$109$		−	15.8226i		−	1.51553i	−0.652527	−	0.757765i	$-0.726291\pi$
$109$		−	15.8226i		−	1.51553i	0.652527	−	0.757765i	$-0.273709\pi$
$110$	−2.97136	+	4.72301i	−0.283308	+	0.450321i
$111$	5.54385	−	5.25972i	0.526199	−	0.499231i
$112$	−1.77865	−	3.81433i	−0.168067	−	0.360420i
$113$	2.65880	+	0.232615i	0.250119	+	0.0218825i	0.211526	−	0.977372i	$-0.432157\pi$
$113$	2.65880	+	0.232615i	0.250119	+	0.0218825i	0.0385931	+	0.999255i	$0.487712\pi$
$114$	−5.05513	+	10.1361i	−0.473456	+	0.949337i
$115$	1.59423	+	0.0605481i	0.148662	+	0.00564614i
$116$	2.74346	+	1.58394i	0.254724	+	0.147065i
$117$	2.27446	−	16.1570i	0.210273	−	1.49372i
$118$	−8.36165	−	2.24050i	−0.769753	−	0.206255i
$119$	6.13333	+	5.14648i	0.562242	+	0.471777i
$120$	−8.15068	+	8.53471i	−0.744052	+	0.779109i
$121$	0.942447	+	5.34488i	0.0856770	+	0.485898i
$122$	2.43292	+	1.70355i	0.220266	+	0.154232i
$123$	9.32930	+	3.67613i	0.841195	+	0.331466i
$124$	−3.12744	+	3.72713i	−0.280852	+	0.334707i
$125$	11.0583	−	1.64772i	0.989080	−	0.147377i
$126$	7.32219	−	5.51507i	0.652312	−	0.491321i
$127$	3.15881	−	0.846401i	0.280299	−	0.0751059i	−0.115931	−	0.993257i	$-0.536985\pi$
$127$	3.15881	−	0.846401i	0.280299	−	0.0751059i	0.396230	+	0.918151i	$0.370318\pi$
$128$	−0.853671	−	0.398073i	−0.0754546	−	0.0351850i
$129$	2.24472	+	1.11950i	0.197637	+	0.0985661i
$130$	11.4367	+	5.87139i	1.00307	+	0.514955i
$131$	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	$0.0908815\pi$
$132$	0.0948693	−	3.60731i	0.00825731	−	0.313976i
$133$	−10.2567	−	14.6481i	−0.889368	−	1.27015i
$134$	−7.89266			−0.681822
$135$	−9.88612	−	6.10448i	−0.850862	−	0.525390i
$136$	−8.44014			−0.723736
$137$	−9.15193	−	13.0703i	−0.781902	−	1.11667i	−0.990343	−	0.138637i	$-0.955728\pi$
$137$	−9.15193	−	13.0703i	−0.781902	−	1.11667i	0.208442	−	0.978035i	$-0.433161\pi$
$138$	1.14809	−	0.623196i	0.0977322	−	0.0530499i
$139$	3.12149	−	8.57623i	0.264762	−	0.727426i	−0.734069	−	0.679075i	$-0.762381\pi$
$139$	3.12149	−	8.57623i	0.264762	−	0.727426i	0.998830	−	0.0483514i	$-0.0153967\pi$
$140$	−1.74618	−	5.43057i	−0.147579	−	0.458967i
$141$	−14.9937	+	9.92164i	−1.26269	+	0.835553i
$142$	−4.69060	−	2.18726i	−0.393626	−	0.183551i
$143$	−12.4016	+	3.32299i	−1.03707	+	0.277883i
$144$	−0.983543	+	4.25580i	−0.0819619	+	0.354650i
$145$	−6.39525	−	4.84987i	−0.531097	−	0.402760i
$146$	−4.73488	+	5.64281i	−0.391861	+	0.467002i
$147$	0.346738	+	2.32188i	0.0285985	+	0.191505i
$148$	−3.18968	−	2.23344i	−0.262190	−	0.183588i
$149$	−1.63395	−	9.26659i	−0.133858	−	0.759149i	−0.975648	−	0.219343i	$-0.929609\pi$
$149$	−1.63395	−	9.26659i	−0.133858	−	0.759149i	0.841789	−	0.539806i	$-0.181502\pi$
$150$	7.10009	−	5.77903i	0.579720	−	0.471856i
$151$	−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	$0.735901\pi$
$152$	18.2082	+	4.87887i	1.47688	+	0.395729i
$153$	−1.72582	−	8.12841i	−0.139525	−	0.657143i
$154$	−6.24682	−	3.60660i	−0.503383	−	0.290628i
$155$	9.04119	−	8.37956i	0.726206	−	0.673062i
$156$	−8.29843	+	0.506611i	−0.664406	+	0.0405613i
$157$	22.2338	+	1.94520i	1.77445	+	0.155244i	0.926860	−	0.375408i	$-0.122497\pi$
$157$	22.2338	+	1.94520i	1.77445	+	0.155244i	0.847590	+	0.530652i	$0.178053\pi$
$158$	5.83654	+	12.5165i	0.464330	+	0.995759i
$159$	4.13198	+	17.2195i	0.327687	+	1.36560i
$160$	8.62135	+	5.42391i	0.681578	+	0.428798i
$161$			2.06235i			0.162536i
$162$	−9.51231	−	0.170346i	−0.747358	−	0.0133837i
$163$	−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
$165$	−1.38002	+	9.03800i	−0.107435	+	0.703608i
$166$	−4.73644	−	1.72392i	−0.367619	−	0.133802i
$167$	−0.634893	+	7.25686i	−0.0491295	+	0.561553i	0.931243	+	0.364399i	$0.118725\pi$
$167$	−0.634893	+	7.25686i	−0.0491295	+	0.561553i	−0.980373	+	0.197154i	$0.936830\pi$
$168$	−11.4248	−	10.1101i	−0.881441	−	0.780011i
$169$	5.67082	+	15.5805i	0.436217	+	1.19850i
$170$	6.49595	+	0.817753i	0.498217	+	0.0627188i
$171$	−0.975496	+	18.5333i	−0.0745981	+	1.41728i
$172$	0.330806	−	1.23458i	0.0252237	−	0.0941362i
$173$	−1.78680	−	20.4232i	−0.135848	−	1.55275i	−0.692143	−	0.721760i	$-0.743333\pi$
$173$	−1.78680	−	20.4232i	−0.135848	−	1.55275i	0.556295	−	0.830985i	$-0.312222\pi$
$174$	−6.52972	−	0.744716i	−0.495017	−	0.0564568i
$175$	2.67101	+	14.2039i	0.201909	+	1.07371i
$176$	3.38487	−	0.596843i	0.255144	−	0.0449887i
$177$	−14.0283	+	2.09493i	−1.05443	+	0.157464i
$178$	−7.01926	+	0.614106i	−0.526116	+	0.0460292i
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	−0.999116	−	0.0420450i	$-0.986613\pi$
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	0.463146	−	0.886282i	$-0.346721\pi$
$180$	−2.04312	+	5.55664i	−0.152285	+	0.414167i
$181$	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	$0.142161\pi$
$182$	−7.02339	+	15.0617i	−0.520609	+	1.11645i
$183$	4.76862	+	0.970750i	0.352507	+	0.0717599i
$184$	−1.39745	−	1.66542i	−0.103021	−	0.122776i
$185$	7.31143	+	6.62379i	0.537547	+	0.486991i
$186$	2.86788	−	9.67779i	0.210283	−	0.709610i
$187$	−5.35618	+	3.75043i	−0.391682	+	0.274259i
$188$	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	$0.236022\pi$
$192$	13.3793	+	0.351864i	0.965564	+	0.0253936i
$193$	−0.282417	+	0.131693i	−0.0203288	+	0.00947948i	−0.432756	−	0.901511i	$-0.642459\pi$
$193$	−0.282417	+	0.131693i	−0.0203288	+	0.00947948i	0.412427	+	0.910991i	$0.364681\pi$
$194$	14.8559	−	12.4656i	1.06659	−	0.894977i
$195$	21.0209	+	1.35255i	1.50533	+	0.0968578i
$196$	1.12408	−	0.409130i	0.0802911	−	0.0292236i
$197$	−0.840756	−	3.13774i	−0.0599014	−	0.223555i	0.929486	−	0.368858i	$-0.120251\pi$
$197$	−0.840756	−	3.13774i	−0.0599014	−	0.223555i	−0.989387	+	0.145303i	$0.953584\pi$
$198$	2.80284	+	6.94179i	0.199189	+	0.493332i
$199$	−5.52277	+	3.18857i	−0.391499	+	0.226032i	−0.682809	−	0.730596i	$-0.739242\pi$
$199$	−5.52277	+	3.18857i	−0.391499	+	0.226032i	0.291310	+	0.956629i	$0.405909\pi$
$200$	−11.7815	−	9.66026i	−0.833079	−	0.683083i
$201$	−11.8601	+	5.15534i	−0.836550	+	0.363630i
$202$	2.04207	−	2.91638i	0.143679	−	0.205196i
$203$	5.95116	−	8.49914i	0.417690	−	0.596523i
$204$	−3.88311	+	1.68790i	−0.271872	+	0.118177i
$205$	−3.82266	+	12.3681i	−0.266986	+	0.863827i
$206$	−3.32065	+	1.91718i	−0.231360	+	0.133576i
$207$	1.31816	−	1.68638i	0.0916183	−	0.117211i
$208$	−2.04954	−	7.64899i	−0.142110	−	0.530362i
$209$	13.7230	−	4.99477i	0.949241	−	0.345495i
$210$	7.81353	+	8.88816i	0.539185	+	0.613342i
$211$	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	$0.206905\pi$
$212$	8.17776	−	3.81335i	0.561651	−	0.261902i
$213$	−8.47715	−	0.222942i	−0.580844	−	0.0152757i
$214$	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
$218$	13.7011	−	9.59362i	0.927956	−	0.649762i
$219$	−3.42923	+	11.5721i	−0.231726	+	0.781968i
$220$	4.65296	−	0.229601i	0.313703	−	0.0154797i
$221$	9.68341	+	11.5402i	0.651376	+	0.776280i
$222$	7.91587	+	1.61143i	0.531278	+	0.108152i
$223$	−4.39023	+	9.41489i	−0.293992	+	0.630467i	−0.996714	−	0.0809965i	$-0.974190\pi$
$223$	−4.39023	+	9.41489i	−0.293992	+	0.630467i	0.702723	+	0.711464i	$0.251968\pi$
$224$	−6.58348	+	11.4029i	−0.439877	+	0.761889i
$225$	6.89440	−	13.3217i	0.459627	−	0.888112i
$226$	1.41067	+	2.44335i	0.0938361	+	0.162529i
$227$	−3.11245	+	0.272304i	−0.206580	+	0.0180734i	−0.189976	−	0.981789i	$-0.560841\pi$
$227$	−3.11245	+	0.272304i	−0.206580	+	0.0180734i	−0.0166042	+	0.999862i	$0.505286\pi$
$228$	9.35287	−	1.39671i	0.619409	−	0.0924996i
$229$	−23.1368	+	4.07964i	−1.52892	+	0.269590i	−0.873933	−	0.486047i	$-0.838438\pi$
$229$	−23.1368	+	4.07964i	−1.52892	+	0.269590i	−0.654990	+	0.755638i	$0.727327\pi$
$230$	0.914188	+	1.41718i	0.0602798	+	0.0934464i
$231$	−11.7427	−	1.33926i	−0.772616	−	0.0881170i
$232$	0.953265	+	10.8959i	0.0625849	+	0.715349i
$233$	−0.858538	+	3.20411i	−0.0562447	+	0.209908i	−0.988329	−	0.152333i	$-0.951321\pi$
$233$	−0.858538	+	3.20411i	−0.0562447	+	0.209908i	0.932085	+	0.362241i	$0.117988\pi$
$234$	15.3698	−	7.82690i	1.00475	−	0.511661i
$235$	−14.2341	−	18.3340i	−0.928533	−	1.19598i
$236$	2.47188	+	6.79145i	0.160906	+	0.442085i
$237$	16.9460	+	14.9960i	1.10076	+	0.974093i
$238$	−0.737653	+	8.43141i	−0.0478149	+	0.546527i
$239$	15.9837	+	5.81759i	1.03390	+	0.376309i	0.802564	−	0.596566i	$-0.203468\pi$
$239$	15.9837	+	5.81759i	1.03390	+	0.376309i	0.231335	+	0.972874i	$0.425691\pi$
$240$	−5.57442	−	0.851165i	−0.359827	−	0.0549424i
$241$	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
$243$	−14.4052	+	5.95729i	−0.924096	+	0.382160i
$244$		−	2.47965i		−	0.158744i
$245$	−2.95516	+	0.672751i	−0.188798	+	0.0429805i
$246$	2.47334	+	10.3074i	0.157695	+	0.657173i
$247$	−14.2194	−	30.4937i	−0.904761	−	1.94027i
$248$	−16.7346	−	1.46409i	−1.06265	−	0.0929695i
$249$	−8.24339	+	0.503250i	−0.522403	+	0.0318922i
$250$	8.13168	+	8.57651i	0.514292	+	0.542426i
$251$	−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	$0.825736\pi$
$252$	−7.27814	−	2.36663i	−0.458480	−	0.149084i
$253$	−1.62687	−	0.435919i	−0.102281	−	0.0274060i
$254$	2.64818	+	2.22208i	0.166161	+	0.139426i
$255$	10.2955	−	3.01422i	0.644728	−	0.188758i
$256$	−2.85653	−	16.2002i	−0.178533	−	1.01251i
$257$	7.11815	+	4.98418i	0.444018	+	0.310905i	0.774118	−	0.633041i	$-0.218194\pi$
$257$	7.11815	+	4.98418i	0.444018	+	0.310905i	−0.330100	+	0.943946i	$0.607083\pi$
$258$	0.391636	+	2.62253i	0.0243822	+	0.163271i
$259$	−8.19772	+	9.76966i	−0.509382	+	0.607057i
$260$	−1.46129	−	10.6332i	−0.0906256	−	0.659445i
$261$	−10.2985	+	3.14602i	−0.637462	+	0.194734i
$262$	1.48446	−	0.397759i	0.0917099	−	0.0245736i
$263$	−21.3889	−	9.97382i	−1.31890	−	0.615012i	−0.369541	−	0.929214i	$-0.620485\pi$
$263$	−21.3889	−	9.97382i	−1.31890	−	0.615012i	−0.949356	+	0.314203i	$0.898263\pi$
$264$	10.3902	−	6.87540i	0.639470	−	0.423152i
$265$	−21.7639	+	6.99810i	−1.33695	+	0.429890i
$266$	6.46518	−	17.7629i	0.396406	−	1.08912i
$267$	−10.1466	+	5.50766i	−0.620961	+	0.337063i
$268$	3.77957	+	5.39779i	0.230874	+	0.329723i
$269$	−10.2124			−0.622659			−0.311330	−	0.950302i	$-0.600774\pi$
$269$	−10.2124			−0.622659			−0.311330	+	0.950302i	$0.600774\pi$
$270$	−0.708201	−	12.2619i	−0.0430997	−	0.746234i
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	−2.31318	−	3.30356i	−0.140257	−	0.200308i
$273$	−0.715877	+	27.2205i	−0.0433268	+	1.64746i
$274$	5.76881	−	15.8497i	0.348506	−	0.957514i
$275$	−11.7692	−	0.895273i	−0.709712	−	0.0539870i
$276$	−0.975993	−	0.486750i	−0.0587479	−	0.0292989i
$277$	−12.2491	−	5.71185i	−0.735978	−	0.343192i	0.0182248	−	0.999834i	$-0.494199\pi$
$277$	−12.2491	−	5.71185i	−0.735978	−	0.343192i	−0.754203	+	0.656642i	$0.771976\pi$
$278$	9.31897	−	2.49701i	0.558914	−	0.149761i
$279$	−2.01184	−	16.4159i	−0.120446	−	0.982792i
$280$	11.9008	−	15.6930i	0.711211	−	0.937834i
$281$	−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	$0.377751\pi$
$282$	−17.6824	−	6.96758i	−1.05297	−	0.414913i
$283$	24.7001	+	17.2952i	1.46827	+	1.02809i	0.988587	+	0.150648i	$0.0481361\pi$
$283$	24.7001	+	17.2952i	1.46827	+	1.02809i	0.479680	+	0.877443i	$0.340753\pi$
$284$	0.750327	+	4.25532i	0.0445237	+	0.252507i
$285$	−23.9532	+	0.551308i	−1.41886	+	0.0326566i
$286$	−10.3968	−	8.72397i	−0.614777	−	0.515859i
$287$	−16.1643	−	4.33122i	−0.954150	−	0.255664i
$288$	12.6715	−	5.11629i	0.746676	−	0.301480i
$289$	−8.07815	−	4.66392i	−0.475185	−	0.274348i
$290$	0.322005	−	8.47837i	0.0189088	−	0.497867i
$291$	14.1814	−	28.4354i	0.831328	−	1.66691i
$292$	6.12652	+	0.536001i	0.358527	+	0.0313671i
$293$	3.10333	+	6.65512i	0.181299	+	0.388796i	0.975863	−	0.218384i	$-0.0700785\pi$
$293$	3.10333	+	6.65512i	0.181299	+	0.388796i	−0.794564	+	0.607180i	$0.792301\pi$
$294$	−1.80033	+	1.70806i	−0.104997	+	0.0996160i
$295$	−4.06463	−	17.8545i	−0.236652	−	1.03953i
$296$		−	13.4441i		−	0.781424i
$297$	8.74602	+	8.60053i	0.507496	+	0.499053i
$298$	7.03343	−	7.03343i	0.407435	−	0.407435i
$299$	−0.673830	+	3.82148i	−0.0389686	+	0.221002i
$300$	−7.35231	−	2.08833i	−0.424486	−	0.120570i
$301$	−3.93374	−	1.43176i	−0.226737	−	0.0825254i
$302$	0.0972742	−	1.11185i	0.00559750	−	0.0639798i
$303$	1.16365	−	5.71622i	0.0668501	−	0.328388i
$304$	3.08065	+	8.46402i	0.176687	+	0.485445i
$305$	−0.784693	+	6.23334i	−0.0449314	+	0.356920i
$306$	5.99214	−	6.42287i	0.342548	−	0.367171i
$307$	−3.54038	+	13.2129i	−0.202060	+	0.754099i	0.788265	+	0.615336i	$0.210980\pi$
$307$	−3.54038	+	13.2129i	−0.202060	+	0.754099i	−0.990326	+	0.138764i	$0.955687\pi$
$308$	0.524871	+	5.99930i	0.0299073	+	0.341842i
$309$	−3.73760	+	5.04989i	−0.212625	+	0.287278i
$310$	12.7379	+	2.74822i	0.723465	+	0.156089i
$311$	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	$0.409530\pi$
$312$	−17.8666	−	22.4666i	−1.01149	−	1.27192i
$313$	24.5081	−	2.14418i	1.38528	−	0.121196i	0.629997	−	0.776597i	$-0.283056\pi$
$313$	24.5081	−	2.14418i	1.38528	−	0.121196i	0.755281	+	0.655401i	$0.227500\pi$
$314$	11.7965	+	20.4321i	0.665714	+	1.15305i
$315$	17.5468	+	8.25241i	0.988651	+	0.464971i
$316$	5.76508	−	9.98541i	0.324311	−	0.561723i
$317$	−6.97386	+	14.9555i	−0.391691	+	0.839984i	0.607274	+	0.794493i	$0.292263\pi$
$317$	−6.97386	+	14.9555i	−0.391691	+	0.839984i	−0.998965	+	0.0454916i	$0.985515\pi$
$318$	−12.4054	+	14.0186i	−0.695661	+	0.786123i
$319$	5.44660	+	6.49101i	0.304951	+	0.363427i
$320$	0.851574	+	17.2575i	0.0476045	+	0.964725i
$321$	9.60991	−	2.30598i	0.536373	−	0.128707i
$322$	−1.78583	+	1.25045i	−0.0995203	+	0.0696849i
$323$	−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
$327$	14.3220	−	23.3654i	0.792009	−	1.29211i
$328$	15.9881	−	7.45537i	0.882794	−	0.411654i
$329$	22.9851	−	19.2867i	1.26721	−	1.06331i
$330$	−8.66293	+	4.28497i	−0.476879	+	0.235880i
$331$	−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	$0.580901\pi$
$332$	1.08916	+	4.06479i	0.0597752	+	0.223084i
$333$	12.9476	−	2.74903i	0.709523	−	0.150646i
$334$	−6.66881	+	3.85024i	−0.364901	+	0.210676i
$335$	−7.79292	−	14.7650i	−0.425773	−	0.806697i
$336$	0.826024	−	7.24263i	0.0450633	−	0.395118i
$337$	6.00115	−	8.57053i	0.326904	−	0.466867i	−0.621735	−	0.783227i	$-0.713572\pi$
$337$	6.00115	−	8.57053i	0.326904	−	0.466867i	0.948639	+	0.316361i	$0.102461\pi$
$338$	−10.0531	+	14.3573i	−0.546815	+	0.780933i
$339$	3.71573	+	2.75015i	0.201811	+	0.149367i
$340$	−2.55147	−	4.83418i	−0.138373	−	0.262170i
$341$	−11.2705	+	6.50701i	−0.610330	+	0.352374i
$342$	−16.6398	+	10.3925i	−0.899778	+	0.561961i
$343$	4.22292	+	15.7602i	0.228016	+	0.850968i
$344$	4.14679	−	1.50931i	0.223580	−	0.0813765i
$345$	2.29941	+	1.53244i	0.123796	+	0.0825041i
$346$	16.6015	−	13.9303i	0.892500	−	0.748896i
$347$	10.4146	−	4.85639i	0.559083	−	0.260705i	−0.122472	−	0.992472i	$-0.539082\pi$
$347$	10.4146	−	4.85639i	0.559083	−	0.260705i	0.681554	+	0.731767i	$0.261304\pi$
$348$	2.61759	+	4.82230i	0.140317	+	0.258502i
$349$	−15.6377	−	2.75735i	−0.837067	−	0.147597i	−0.261347	−	0.965245i	$-0.584167\pi$
$349$	−15.6377	−	2.75735i	−0.837067	−	0.147597i	−0.575719	+	0.817647i	$0.695278\pi$
$350$	−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
$353$	7.10893	−	4.97772i	0.378370	−	0.264938i	−0.368885	−	0.929475i	$-0.620260\pi$
$353$	7.10893	−	4.97772i	0.378370	−	0.264938i	0.747255	+	0.664538i	$0.231371\pi$
$354$	−10.3198	−	10.8772i	−0.548489	−	0.578118i
$355$	−0.539561	−	10.9344i	−0.0286369	−	0.580339i
$356$	3.78131	+	4.50640i	0.200409	+	0.238838i
$357$	4.39878	+	13.1515i	0.232808	+	0.696053i
$358$	6.40706	−	13.7400i	0.338623	−	0.726180i
$359$	−10.2032	+	17.6725i	−0.538505	+	0.932718i	0.460480	+	0.887670i	$0.347677\pi$
$359$	−10.2032	+	17.6725i	−0.538505	+	0.932718i	−0.998985	+	0.0450476i	$0.985656\pi$
$360$	−19.7615	+	5.22565i	−1.04152	+	0.275416i
$361$	9.63526	+	16.6888i	0.507119	+	0.878356i
$362$	2.17930	−	0.190664i	0.114541	−	0.0100211i
$363$	−3.44626	+	8.74593i	−0.180881	+	0.459042i
$364$	13.6640	−	2.40933i	0.716189	−	0.126283i
$365$	−15.2312	−	3.28615i	−0.797236	−	0.172005i
$366$	2.05074	+	4.71784i	0.107194	+	0.246605i
$367$	2.26163	+	25.8506i	0.118056	+	1.34939i	0.791962	+	0.610571i	$0.209060\pi$
$367$	2.26163	+	25.8506i	0.118056	+	1.34939i	−0.673906	+	0.738818i	$0.735385\pi$
$368$	0.268864	−	1.00341i	0.0140155	−	0.0523066i
$369$	10.4492	+	13.8731i	0.543965	+	0.722206i
$370$	−1.30258	+	10.3473i	−0.0677180	+	0.537929i
$371$	−10.1077	−	27.7707i	−0.524766	−	1.44178i
$372$	−7.99199	+	2.67308i	−0.414365	+	0.138593i
$373$	0.416402	−	4.75950i	0.0215605	−	0.246438i	−0.977765	−	0.209705i	$-0.932750\pi$
$373$	0.416402	−	4.75950i	0.0215605	−	0.246438i	0.999325	−	0.0367323i	$-0.0116949\pi$
$374$	−6.49515	−	2.36404i	−0.335856	−	0.122242i
$375$	17.8213	+	7.57629i	0.920290	+	0.391238i
$376$	−5.49248	+	31.1494i	−0.283253	+	1.60641i
$377$	13.8043	−	13.8043i	0.710956	−	0.710956i
$378$	15.8048	−	1.51641i	0.812911	−	0.0779958i
$379$		−	25.3002i		−	1.29958i	−0.760112	−	0.649792i	$-0.774856\pi$
$379$		−	25.3002i		−	1.29958i	0.760112	−	0.649792i	$-0.225144\pi$
$380$	2.70994	+	11.9038i	0.139017	+	0.610653i
$381$	5.43079	+	1.60934i	0.278228	+	0.0824491i
$382$	10.4163	+	22.3379i	0.532946	+	1.14291i
$383$	12.2766	+	1.07406i	0.627303	+	0.0548819i	0.396375	−	0.918089i	$-0.370268\pi$
$383$	12.2766	+	1.07406i	0.627303	+	0.0548819i	0.230929	+	0.972971i	$0.425824\pi$
$384$	−0.900307	−	1.36055i	−0.0459436	−	0.0694303i
$385$	0.579078	−	15.2471i	0.0295126	−	0.777064i
$386$	−0.285272	−	0.164702i	−0.0145200	−	0.00838310i
$387$	2.30149	+	3.68501i	0.116991	+	0.187320i
$388$	−15.6393	−	4.19054i	−0.793965	−	0.212742i
$389$	−6.83430	−	5.73466i	−0.346513	−	0.290759i	0.452875	−	0.891574i	$-0.350398\pi$
$389$	−6.83430	−	5.73466i	−0.346513	−	0.290759i	−0.799388	+	0.600815i	$0.794843\pi$
$390$	11.5742	+	19.0225i	0.586085	+	0.963239i
$391$	0.343168	+	1.94620i	0.0173548	+	0.0984238i
$392$	3.38317	+	2.36892i	0.170876	+	0.119649i
$393$	1.97085	−	1.56732i	0.0994164	−	0.0790610i
$394$	2.20727	−	2.63052i	0.111200	−	0.132524i
$395$	−17.6521	+	23.2769i	−0.888175	+	1.17119i
$396$	3.40529	−	5.24109i	0.171122	−	0.263375i
$397$	−13.1660	+	3.52782i	−0.660782	+	0.177056i	−0.573599	−	0.819136i	$-0.694453\pi$
$397$	−13.1660	+	3.52782i	−0.660782	+	0.177056i	−0.0871833	+	0.996192i	$0.527787\pi$
$398$	−6.10964	−	2.84897i	−0.306249	−	0.142806i
$399$	−1.88733	−	30.9150i	−0.0944846	−	1.54768i
$400$	0.552182	−	7.25898i	0.0276091	−	0.362949i
$401$	−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	$0.134452\pi$
$402$	−11.6552	−	7.14413i	−0.581309	−	0.356317i
$403$	17.1978	+	24.5610i	0.856683	+	1.22347i
$404$	−2.97240			−0.147882
$405$	−9.07343	−	17.9631i	−0.450862	−	0.892593i
$406$	10.9679			0.544328
$407$	−5.97399	−	8.53175i	−0.296120	−	0.422903i
$408$	−12.4637	−	7.63969i	−0.617044	−	0.378221i
$409$	−9.80467	+	26.9381i	−0.484810	+	1.33200i	0.420515	+	0.907285i	$0.361849\pi$
$409$	−9.80467	+	26.9381i	−0.484810	+	1.33200i	−0.905325	+	0.424719i	$0.860373\pi$
$410$	−13.0276	+	4.18896i	−0.643386	+	0.206878i
$411$	−1.68404	−	27.5851i	−0.0830676	−	1.36067i
$412$	2.90132	+	1.35291i	0.142938	+	0.0666530i
$413$	22.8645	−	6.12654i	1.12509	−	0.301467i
$414$	2.25950	+	0.118928i	0.111048	+	0.00584500i
$415$	−1.45160	−	10.5627i	−0.0712563	−	0.518503i
$416$	−15.9247	+	18.9783i	−0.780772	+	0.930488i
$417$	12.3724	−	9.83918i	0.605880	−	0.481827i
$418$	12.6457	+	8.85459i	0.618519	+	0.433092i
$419$	2.30839	+	13.0915i	0.112772	+	0.639563i	0.987829	+	0.155543i	$0.0497127\pi$
$419$	2.30839	+	13.0915i	0.112772	+	0.639563i	−0.875057	+	0.484020i	$0.839176\pi$
$420$	2.33694	−	9.59996i	0.114031	−	0.468430i
$421$	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	$0.651425\pi$
$422$	6.55035	+	1.75516i	0.318866	+	0.0854399i
$423$	−31.1220	+	1.07975i	−1.51320	+	0.0524993i
$424$	26.9798	+	15.5768i	1.31025	+	0.756476i
$425$	4.88407	+	12.9595i	0.236912	+	0.628630i
$426$	−4.94684	−	7.47571i	−0.239675	−	0.362199i
$427$	−8.09054	−	0.707831i	−0.391529	−	0.0342543i
$428$	−2.12816	−	4.56386i	−0.102869	−	0.220602i
$429$	−21.3214	−	6.31832i	−1.02941	−	0.305051i
$430$	−3.33781	+	0.759863i	−0.160964	+	0.0366438i
$431$		−	0.295969i		−	0.0142563i	−0.999975	−	0.00712817i	$-0.997731\pi$
$431$		−	0.295969i		−	0.0142563i	0.999975	−	0.00712817i	$-0.00226899\pi$
$432$	−5.30459	+	5.39433i	−0.255217	+	0.259535i
$433$	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
$435$	−5.05404	−	12.9506i	−0.242323	−	0.620934i
$436$	−13.1221	−	4.77607i	−0.628437	−	0.228732i
$437$	0.384686	−	4.39698i	0.0184020	−	0.210336i
$438$	−12.0997	+	4.04698i	−0.578146	+	0.193372i
$439$	9.75841	+	26.8110i	0.465743	+	1.27962i	0.921105	+	0.389313i	$0.127288\pi$
$439$	9.75841	+	26.8110i	0.465743	+	1.27962i	−0.455362	+	0.890306i	$0.650490\pi$
$440$	9.86383	+	12.7049i	0.470240	+	0.605684i
$441$	−1.58964	+	3.74260i	−0.0756972	+	0.178219i
$442$	−4.12164	+	15.3822i	−0.196046	+	0.731655i
$443$	3.51399	+	40.1651i	0.166955	+	1.90830i	0.369833	+	0.929098i	$0.379415\pi$
$443$	3.51399	+	40.1651i	0.166955	+	1.90830i	−0.202878	+	0.979204i	$0.565030\pi$
$444$	−2.68863	−	6.18533i	−0.127597	−	0.293543i
$445$	−8.07938	−	12.5248i	−0.382999	−	0.593730i
$446$	−10.8144	+	1.90688i	−0.512079	+	0.0902933i
$447$	5.97488	−	15.1631i	0.282602	−	0.717190i
$448$	−22.2510	+	1.94671i	−1.05126	+	0.0919734i
$449$	3.91232	+	6.77634i	0.184634	+	0.319795i	0.943453	−	0.331506i	$-0.107557\pi$
$449$	3.91232	+	6.77634i	0.184634	+	0.319795i	−0.758819	+	0.651301i	$0.774223\pi$
$450$	15.7158	−	2.10725i	0.740848	−	0.0993369i
$451$	6.83332	−	11.8357i	0.321768	−	0.557319i
$452$	0.995476	−	2.13480i	0.0468232	−	0.100413i
$453$	−0.580068	−	1.73429i	−0.0272540	−	0.0814841i
$454$	−2.12294	−	2.53003i	−0.0996347	−	0.118740i
$455$	−35.1109	+	1.73255i	−1.64603	+	0.0812234i
$456$	22.4721	+	23.6860i	1.05235	+	1.10920i
$457$	4.48957	−	3.14363i	0.210013	−	0.147053i	−0.463838	−	0.885920i	$-0.653528\pi$
$457$	4.48957	−	3.14363i	0.210013	−	0.147053i	0.673851	+	0.738867i	$0.264639\pi$
$458$	−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	$0.307837\pi$
$462$	−5.96021	−	10.9803i	−0.277294	−	0.510850i
$463$	0.163397	−	0.0761934i	0.00759371	−	0.00354101i	−0.418818	−	0.908070i	$-0.637555\pi$
$463$	0.163397	−	0.0761934i	0.00759371	−	0.00354101i	0.426411	+	0.904529i	$0.359778\pi$
$464$	−4.00350	+	3.35933i	−0.185858	+	0.155953i
$465$	20.9361	−	4.19047i	0.970888	−	0.194328i
$466$	−3.29505	+	1.19930i	−0.152640	+	0.0555566i
$467$	−3.26672	−	12.1916i	−0.151166	−	0.564158i	−0.999403	−	0.0345422i	$-0.989003\pi$
$467$	−3.26672	−	12.1916i	−0.151166	−	0.564158i	0.848238	−	0.529616i	$-0.177664\pi$
$468$	−12.7130	−	6.76330i	−0.587657	−	0.312634i
$469$	18.6907	−	10.7911i	0.863055	−	0.498285i
$470$	7.24531	−	23.4420i	0.334201	−	1.08130i
$471$	31.0722	+	22.9977i	1.43173	+	1.05968i
$472$	−14.3126	+	20.4404i	−0.658789	+	0.940848i
$473$	1.96091	−	2.80048i	0.0901629	−	0.128766i
$474$	−2.71055	+	23.7663i	−0.124500	+	1.09162i
$475$	−3.04523	−	30.7813i	−0.139725	−	1.41234i
$476$	6.11948	−	3.53308i	0.280486	−	0.161939i
$477$	−9.48470	+	29.1684i	−0.434274	+	1.33553i
$478$	4.65373	+	17.3679i	0.212857	+	0.794391i
$479$	33.4923	−	12.1902i	1.53030	−	0.556985i	0.566607	−	0.823988i	$-0.308256\pi$
$479$	33.4923	−	12.1902i	1.53030	−	0.556985i	0.963696	+	0.267003i	$0.0860335\pi$
$480$	7.82176	+	15.8133i	0.357013	+	0.721774i
$481$	−18.3822	+	15.4245i	−0.838157	+	0.703297i
$482$	17.7781	−	8.29007i	0.809771	−	0.377602i
$483$	−1.86676	+	3.04550i	−0.0849404	+	0.138575i
$484$	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	$0.699929\pi$
$488$	7.01302	−	4.91057i	0.317464	−	0.222291i
$489$	−4.16563	+	0.999581i	−0.188376	+	0.0452026i
$490$	−2.37433	−	2.15103i	−0.107262	−	0.0971736i
$491$	−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	$0.977080\pi$
$492$	5.86479	−	6.62742i	0.264405	−	0.298787i
$493$	4.20179	−	9.01076i	0.189239	−	0.405824i
$494$	17.7835	−	30.8019i	0.800117	−	1.38584i
$495$	−10.2188	+	12.0974i	−0.459299	+	0.543738i
$496$	−4.01336	−	6.95135i	−0.180205	−	0.312125i
$497$	14.0983	−	1.23344i	0.632396	−	0.0553275i
$498$	−5.43393	−	6.83298i	−0.243500	−	0.306193i
$499$	−11.0477	+	1.94801i	−0.494564	+	0.0872050i	−0.415367	−	0.909654i	$-0.636347\pi$
$499$	−11.0477	+	1.94801i	−0.494564	+	0.0872050i	−0.0791972	+	0.996859i	$0.525236\pi$
$500$	1.97144	−	9.66830i	0.0881657	−	0.432380i
$501$	−7.50619	+	10.1416i	−0.335352	+	0.453095i
$502$	−1.39889	−	15.9894i	−0.0624354	−	0.713640i
$503$	7.82118	−	29.1890i	0.348729	−	1.30147i	−0.539466	−	0.842008i	$-0.681374\pi$
$503$	7.82118	−	29.1890i	0.348729	−	1.30147i	0.888195	−	0.459467i	$-0.151960\pi$
$504$	−7.71986	−	25.2710i	−0.343870	−	1.12566i
$505$	7.47200	+	0.940624i	0.332499	+	0.0418572i
$506$	−0.608940	−	1.67305i	−0.0270707	−	0.0743761i
$507$	−5.72864	+	28.1409i	−0.254418	+	1.24978i
$508$	0.251546	−	2.87518i	0.0111605	−	0.127566i
$509$	−22.0511	−	8.02596i	−0.977399	−	0.355744i	−0.196571	−	0.980490i	$-0.562981\pi$
$509$	−22.0511	−	8.02596i	−0.977399	−	0.355744i	−0.780829	+	0.624745i	$0.785203\pi$
$510$	8.85246	+	7.08747i	0.391994	+	0.313839i
$511$	3.49769	−	19.8364i	0.154729	−	0.877511i
$512$	10.9640	−	10.9640i	0.484544	−	0.484544i
$513$	−18.2162	+	26.4854i	−0.804263	+	1.16936i
$514$			9.18578i			0.405167i
$515$	−6.86519	−	4.31906i	−0.302516	−	0.190321i
$516$	1.60600	−	1.52370i	0.0707004	−	0.0670769i
$517$	10.3559	+	22.2083i	0.455452	+	0.976719i
$518$	−13.4302	−	1.17499i	−0.590090	−	0.0516262i
$519$	15.8477	−	31.7765i	0.695636	−	1.39483i
$520$	27.1793	−	25.1903i	1.19189	−	1.10467i
$521$	−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	$0.783885\pi$
$522$	−8.96844	−	7.01018i	−0.392538	−	0.306827i
$523$	−14.1137	−	3.78176i	−0.617150	−	0.165365i	−0.0633182	−	0.997993i	$-0.520168\pi$
$523$	−14.1137	−	3.78176i	−0.617150	−	0.165365i	−0.553832	+	0.832629i	$0.686835\pi$
$524$	−0.982891	−	0.824743i	−0.0429378	−	0.0360291i
$525$	−8.91251	+	23.3928i	−0.388974	+	1.02094i
$526$	−4.33208	−	24.5685i	−0.188888	−	1.07124i
$527$	12.5084	+	8.75850i	0.544876	+	0.381526i
$528$	5.53872	+	2.18248i	0.241042	+	0.0949804i
$529$	14.4569	−	17.2291i	0.628561	−	0.749090i
$530$	−19.2558	−	14.6027i	−0.836418	−	0.634301i
$531$	−22.6121	−	9.60430i	−0.981281	−	0.416791i
$532$	−15.2441	+	4.08464i	−0.660914	+	0.177091i
$533$	−28.5370	−	13.3070i	−1.23607	−	0.576390i
$534$	−10.9213	−	5.44671i	−0.472611	−	0.235702i
$535$	3.90551	+	12.1461i	0.168850	+	0.525120i
$536$	−7.78131	+	21.3790i	−0.336101	+	0.923431i
$537$	0.653055	−	24.8318i	0.0281814	−	1.07157i
$538$	−6.19200	−	8.84309i	−0.266956	−	0.381253i
$539$	3.19963			0.137818
$540$	−8.04676	+	6.35621i	−0.346277	+	0.273528i
$541$	−28.4337			−1.22246			−0.611230	−	0.791453i	$-0.709325\pi$
$541$	−28.4337			−1.22246			−0.611230	+	0.791453i	$0.709325\pi$
$542$	2.93709	+	4.19460i	0.126159	+	0.180173i
$543$	3.15025	−	1.70998i	0.135190	−	0.0733824i
$544$	−4.31531	+	11.8562i	−0.185017	+	0.508331i
$545$	31.4750	+	16.1586i	1.34824	+	0.692158i
$546$	−24.0048	+	15.8845i	−1.02731	+	0.679795i
$547$	9.52924	+	4.44356i	0.407441	+	0.189993i	0.615524	−	0.788118i	$-0.288945\pi$
$547$	9.52924	+	4.44356i	0.407441	+	0.189993i	−0.208083	+	0.978111i	$0.566722\pi$
$548$	−13.6021	+	3.64467i	−0.581053	+	0.155693i
$549$	6.16321	+	5.74989i	0.263039	+	0.245399i
$550$	−6.36074	−	10.7340i	−0.271223	−	0.457701i
$551$	−14.2734	+	17.0103i	−0.608066	+	0.724665i
$552$	−0.556164	−	3.72426i	−0.0236719	−	0.158515i
$553$	−30.9344	−	21.6605i	−1.31547	−	0.921099i
$554$	−2.48092	−	14.0700i	−0.105404	−	0.597776i
$555$	4.80128	+	16.3995i	0.203803	+	0.696118i
$556$	−6.17030	−	5.17749i	−0.261679	−	0.219575i
$557$	−16.7541	−	4.48926i	−0.709896	−	0.190216i	−0.114237	−	0.993454i	$-0.536442\pi$
$557$	−16.7541	−	4.48926i	−0.709896	−	0.190216i	−0.595659	+	0.803238i	$0.703109\pi$
$558$	12.9950	−	11.6954i	0.550122	−	0.495107i
$559$	−6.82132	−	3.93829i	−0.288511	−	0.166572i
$560$	9.40403	+	0.357161i	0.397393	+	0.0150928i
$561$	−11.3043	+	0.690115i	−0.477267	+	0.0291367i
$562$	−16.5722	−	1.44988i	−0.699057	−	0.0611596i
$563$	−9.91099	−	21.2542i	−0.417699	−	0.895758i	−0.996757	−	0.0804714i	$-0.974357\pi$
$563$	−9.91099	−	21.2542i	−0.417699	−	0.895758i	0.579058	−	0.815286i	$-0.303420\pi$
$564$	3.70246	+	15.4295i	0.155902	+	0.649701i
$565$	−3.17798	+	5.05144i	−0.133699	+	0.212515i
$566$			31.8748i			1.33980i
$567$	22.7591	−	12.6021i	0.955791	−	0.529238i
$568$	−10.5491	+	10.5491i	−0.442630	+	0.442630i
$569$	−6.84027	+	38.7931i	−0.286759	+	1.62629i	0.412175	+	0.911105i	$0.364769\pi$
$569$	−6.84027	+	38.7931i	−0.286759	+	1.62629i	−0.698934	+	0.715186i	$0.746342\pi$
$570$	−15.0008	−	20.4072i	−0.628313	−	0.854766i
$571$	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	$0.363682\pi$
$572$	−0.987576	+	11.2880i	−0.0412926	+	0.471977i
$573$	30.2431	+	26.7630i	1.26343	+	1.11804i
$574$	−6.05032	−	16.6231i	−0.252536	−	0.693836i
$575$	−1.74853	+	3.10947i	−0.0729185	+	0.129674i
$576$	19.4388	+	12.6300i	0.809951	+	0.526249i
$577$	5.64888	−	21.0819i	0.235166	−	0.877651i	−0.742908	−	0.669393i	$-0.766554\pi$
$577$	5.64888	−	21.0819i	0.235166	−	0.877651i	0.978074	−	0.208257i	$-0.0667792\pi$
$578$	−0.859390	−	9.82287i	−0.0357459	−	0.408578i
$579$	−0.536252	−	0.0611597i	−0.0222859	−	0.00254171i
$580$	−5.95255	+	3.83983i	−0.247166	+	0.159440i
$581$	13.5734	−	2.39335i	0.563119	−	0.0992930i
$582$	33.2213	−	4.96111i	1.37707	−	0.205645i
$583$	24.0432	−	2.10351i	0.995769	−	0.0871185i
$584$	10.6167	+	18.3886i	0.439321	+	0.760927i
$585$	29.8175	+	21.0246i	1.23280	+	0.869259i
$586$	−3.88117	+	6.72239i	−0.160330	+	0.277699i
$587$	10.3168	−	22.1244i	0.425819	−	0.913173i	−0.569984	−	0.821656i	$-0.693051\pi$
$587$	10.3168	−	22.1244i	0.425819	−	0.913173i	0.995804	−	0.0915170i	$-0.0291716\pi$
$588$	2.03027	+	0.413302i	0.0837268	+	0.0170443i
$589$	−21.9220	−	26.1256i	−0.903279	−	1.07649i
$590$	12.9961	−	14.3453i	0.535041	−	0.590585i
$591$	1.59861	−	5.39457i	0.0657580	−	0.221903i
$592$	5.26217	−	3.68461i	0.216274	−	0.151437i
$593$	4.09490	+	4.09490i	0.168157	+	0.168157i	0.786169	−	0.618012i	$-0.212062\pi$
$593$	4.09490	+	4.09490i	0.168157	+	0.168157i	−0.618012	+	0.786169i	$0.712062\pi$
$594$	−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
$597$	−11.0417	−	0.290389i	−0.451908	−	0.0118848i
$598$	−3.71765	+	1.73357i	−0.152026	+	0.0708910i
$599$	−30.3866	+	25.4974i	−1.24156	+	1.04180i	−0.244163	+	0.969734i	$0.578513\pi$
$599$	−30.3866	+	25.4974i	−1.24156	+	1.04180i	−0.997400	+	0.0720615i	$0.977042\pi$
$600$	−8.65384	−	24.9296i	−0.353291	−	1.01775i
$601$	−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	$0.551139\pi$
$602$	−1.14533	−	4.27441i	−0.0466800	−	0.174212i
$603$	−22.1805	−	3.12238i	−0.903258	−	0.127153i
$604$	−0.806976	+	0.465908i	−0.0328354	+	0.0189575i
$605$	−11.5947	−	3.58363i	−0.471392	−	0.145695i
$606$	5.65534	−	2.45825i	0.229733	−	0.0998596i
$607$	18.5771	−	26.5308i	0.754020	−	1.07685i	−0.240329	−	0.970691i	$-0.577255\pi$
$607$	18.5771	−	26.5308i	0.754020	−	1.07685i	0.994349	−	0.106160i	$-0.0338557\pi$
$608$	16.1631	−	23.0833i	0.655501	−	0.936152i
$609$	16.4813	−	7.16404i	0.667854	−	0.290301i
$610$	−5.87335	+	3.09994i	−0.237805	+	0.125513i
$611$	48.8923	−	28.2280i	1.97797	−	1.14198i
$612$	−7.26207	−	1.02229i	−0.293552	−	0.0413238i
$613$	−3.95860	−	14.7737i	−0.159886	−	0.596704i	−0.998637	−	0.0521885i	$-0.983380\pi$
$613$	−3.95860	−	14.7737i	−0.159886	−	0.596704i	0.838751	−	0.544515i	$-0.183286\pi$
$614$	−13.5879	+	4.94560i	−0.548364	+	0.199588i
$615$	−16.8401	+	14.8040i	−0.679059	+	0.596956i
$616$	−15.9279	+	13.3651i	−0.641755	+	0.538497i
$617$	−24.2804	+	11.3221i	−0.977492	+	0.455812i	−0.844646	−	0.535325i	$-0.820189\pi$
$617$	−24.2804	+	11.3221i	−0.977492	+	0.455812i	−0.132845	+	0.991137i	$0.542411\pi$
$618$	−6.63900	−	0.174600i	−0.267060	−	0.00702345i
$619$	−18.6300	−	3.28497i	−0.748802	−	0.132034i	−0.213792	−	0.976879i	$-0.568581\pi$
$619$	−18.6300	−	3.28497i	−0.748802	−	0.132034i	−0.535011	+	0.844845i	$0.679692\pi$
$620$	−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
$623$	15.7827	−	11.0512i	0.632322	−	0.442757i
$624$	3.89698	−	13.1505i	0.156004	−	0.526443i
$625$	−8.01536	+	23.6802i	−0.320615	+	0.947210i
$626$	16.7165	+	19.9220i	0.668126	+	0.796242i
$627$	24.7860	+	5.04570i	0.989859	+	0.201506i
$628$	8.32451	−	17.8520i	0.332184	−	0.712371i
$629$	−6.11042	+	10.5836i	−0.243638	+	0.421994i
$630$	3.49312	+	20.1978i	0.139169	+	0.804699i
$631$	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	$0.833172\pi$
$632$	39.6578	−	3.46961i	1.57750	−	0.138014i
$633$	10.9895	−	1.64112i	0.436794	−	0.0652288i
$634$	−17.1787	+	3.02907i	−0.682253	+	0.120300i
$635$	−1.54219	+	7.14801i	−0.0612001	+	0.283660i
$636$	15.5279	+	1.77096i	0.615722	+	0.0702232i
$637$	−0.642490	−	7.34369i	−0.0254564	−	0.290968i
$638$	−2.31829	+	8.65198i	−0.0917820	+	0.342535i
$639$	−12.3165	−	8.00241i	−0.487234	−	0.316570i
$640$	1.66366	−	1.29163i	0.0657620	−	0.0510562i
$641$	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	$0.693573\pi$
$642$	7.82351	+	6.92324i	0.308769	+	0.273238i
$643$	−0.152914	+	1.74781i	−0.00603033	+	0.0689270i	−0.998614	−	0.0526401i	$-0.983236\pi$
$643$	−0.152914	+	1.74781i	−0.00603033	+	0.0689270i	0.992583	+	0.121567i	$0.0387920\pi$
$644$	1.71037	+	0.622522i	0.0673979	+	0.0245308i
$645$	−4.51934	+	3.32203i	−0.177949	+	0.130805i
$646$	3.14539	−	17.8384i	0.123754	−	0.701842i
$647$	−14.7341	+	14.7341i	−0.579259	+	0.579259i	−0.934699	−	0.355440i	$-0.884331\pi$
$647$	−14.7341	+	14.7341i	−0.579259	+	0.579259i	0.355440	+	0.934699i	$0.384331\pi$
$648$	−9.83953	+	25.5982i	−0.386533	+	1.00559i
$649$			19.3315i			0.758830i
$650$	−23.3592	+	16.7544i	−0.916223	+	0.657161i
$651$	6.44028	+	26.8391i	0.252414	+	1.05191i
$652$	0.922501	+	1.97831i	0.0361279	+	0.0774766i
$653$	−9.28810	−	0.812604i	−0.363471	−	0.0317996i	−0.0960426	−	0.995377i	$-0.530618\pi$
$653$	−9.28810	−	0.812604i	−0.363471	−	0.0317996i	−0.267429	+	0.963578i	$0.586174\pi$
$654$	28.9164	−	1.76532i	1.13072	−	0.0690293i
$655$	2.20979	+	2.38427i	0.0863437	+	0.0931612i
$656$	7.29994	+	4.21462i	0.285015	+	0.164553i
$657$	−15.5386	+	13.9846i	−0.606218	+	0.545592i
$658$	30.6372	+	8.20920i	1.19436	+	0.320028i
$659$	14.0775	+	11.8125i	0.548383	+	0.460148i	0.874393	−	0.485218i	$-0.161260\pi$
$659$	14.0775	+	11.8125i	0.548383	+	0.460148i	−0.326010	+	0.945366i	$0.605704\pi$
$660$	7.07892	+	3.87263i	0.275547	+	0.150742i
$661$	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	$0.779070\pi$
$662$	−17.8745	−	12.5159i	−0.694712	−	0.486443i
$663$	3.85385	+	25.8067i	0.149671	+	1.00225i
$664$	−9.33923	+	11.1301i	−0.362432	+	0.431930i
$665$	39.6130	−	5.44390i	1.53613	−	0.211106i
$666$	10.2309	+	9.54476i	0.396438	+	0.369852i
$667$	2.47371	−	0.662829i	0.0957825	−	0.0256648i
$668$	5.82669	+	2.71703i	0.225441	+	0.105125i
$669$	−15.0051	+	9.92922i	−0.580131	+	0.383886i
$670$	8.06026	−	15.7004i	0.311395	−	0.606560i
$671$	2.26847	−	6.23257i	0.0875733	−	0.240606i
$672$	−20.0434	+	10.8797i	−0.773191	+	0.419695i
$673$	−2.68248	−	3.83098i	−0.103402	−	0.147673i	0.764117	−	0.645078i	$-0.223175\pi$
$673$	−2.68248	−	3.83098i	−0.103402	−	0.147673i	−0.867518	+	0.497405i	$0.834286\pi$
$674$	11.0600			0.426017
$675$	22.2393	−	13.4318i	0.855992	−	0.516989i
$676$	14.6331			0.562810
$677$	−22.5105	−	32.1483i	−0.865147	−	1.23556i	−0.970495	−	0.241123i	$-0.922484\pi$
$677$	−22.5105	−	32.1483i	−0.865147	−	1.23556i	0.105347	−	0.994436i	$-0.466405\pi$
$678$	−0.128472	+	4.88500i	−0.00493392	+	0.187607i
$679$	−18.1371	+	49.8312i	−0.696038	+	1.91235i
$680$	8.61936	−	16.7895i	0.330538	−	0.643847i
$681$	−4.84267	−	2.41515i	−0.185572	−	0.0925488i
$682$	−12.4681	−	5.81397i	−0.477428	−	0.222628i
$683$	36.4765	−	9.77386i	1.39574	−	0.373986i	0.518924	−	0.854820i	$-0.326333\pi$
$683$	36.4765	−	9.77386i	1.39574	−	0.373986i	0.876812	+	0.480834i	$0.159666\pi$
$684$	15.0758	+	6.40331i	0.576436	+	0.244837i
$685$	35.3462	−	4.85753i	1.35051	−	0.185597i
$686$	−11.0866	+	13.2125i	−0.423287	+	0.504454i
$687$	−37.8592	−	14.9181i	−1.44442	−	0.569160i
$688$	1.72726	+	1.20944i	0.0658513	+	0.0461096i
$689$	−9.65582	−	54.7609i	−0.367858	−	2.08622i
$690$	0.0672130	+	2.92026i	0.00255875	+	0.111173i
$691$	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	$0.641144\pi$
$692$	−17.4769	−	4.68292i	−0.664372	−	0.178018i
$693$	−16.1284	−	12.6068i	−0.612668	−	0.478892i
$694$	10.5198	+	6.07363i	0.399327	+	0.230552i
$695$	13.8724	+	14.9677i	0.526211	+	0.567759i
$696$	−8.45482	+	16.9529i	−0.320479	+	0.642599i
$697$	−15.9747	−	1.39761i	−0.605086	−	0.0529381i
$698$	−7.09386	−	15.2128i	−0.268507	−	0.575814i
$699$	−4.16805	+	3.95443i	−0.157650	+	0.149570i
$700$	12.5860	+	2.07232i	0.475705	+	0.0783263i
$701$		−	1.42181i		−	0.0537011i	−0.999639	−	0.0268505i	$-0.991452\pi$
$701$		−	1.42181i		−	0.0537011i	0.999639	−	0.0268505i	$-0.00854782\pi$
$702$	29.7814	+	2.35402i	1.12402	+	0.0888467i
$703$	19.3001	−	19.3001i	0.727916	−	0.727916i
$704$	3.16755	−	17.9641i	0.119381	−	0.677046i
$705$	−4.42449	−	39.9583i	−0.166636	−	1.50492i
$706$	8.62062	+	3.13765i	0.324441	+	0.118087i
$707$	−0.848488	+	9.69826i	−0.0319107	+	0.364741i
$708$	−2.49709	+	12.2665i	−0.0938463	+	0.461002i
$709$	−12.4901	−	34.3163i	−0.469077	−	1.28878i	−0.918487	−	0.395452i	$-0.870588\pi$
$709$	−12.4901	−	34.3163i	−0.469077	−	1.28878i	0.449410	−	0.893325i	$-0.351634\pi$
$710$	9.14119	−	7.09702i	0.343063	−	0.266346i
$711$	11.4506	+	37.4836i	0.429432	+	1.40575i
$712$	−5.25679	+	19.6186i	−0.197007	+	0.735239i
$713$	0.342810	+	3.91834i	0.0128384	+	0.146743i
$714$	−8.72108	+	11.7831i	−0.326378	+	0.440971i
$715$	6.05469	−	28.0633i	0.226433	−	1.04951i
$716$	−12.4649	+	2.19790i	−0.465836	+	0.0821395i
$717$	18.3375	+	23.0587i	0.684826	+	0.861144i
$718$	−21.4894	+	1.88008i	−0.801977	+	0.0701639i
$719$	−12.9014	−	22.3459i	−0.481142	−	0.833363i	0.518624	−	0.855003i	$-0.326445\pi$
$719$	−12.9014	−	22.3459i	−0.481142	−	0.833363i	−0.999766	+	0.0216398i	$0.993111\pi$
$720$	−7.46138	−	6.30267i	−0.278069	−	0.234887i
$721$	5.24243	−	9.08015i	0.195238	−	0.338162i
$722$	−8.60904	+	18.4622i	−0.320395	+	0.687090i
$723$	21.2999	−	24.0697i	0.792152	−	0.895160i
$724$	−1.17400	−	1.39912i	−0.0436314	−	0.0519978i
$725$	16.1786	−	7.76884i	0.600858	−	0.288528i
$726$	−9.66282	+	2.31868i	−0.358621	+	0.0860543i
$727$	1.32255	−	0.926059i	0.0490507	−	0.0343456i	−0.548794	−	0.835958i	$-0.684913\pi$
$727$	1.32255	−	0.926059i	0.0490507	−	0.0343456i	0.597845	+	0.801612i	$0.296024\pi$
$728$	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
$732$	2.24449	−	3.66174i	0.0829586	−	0.135342i
$733$	−12.0574	+	5.62244i	−0.445349	+	0.207669i	−0.632338	−	0.774692i	$-0.717905\pi$
$733$	−12.0574	+	5.62244i	−0.445349	+	0.207669i	0.186990	+	0.982362i	$0.440127\pi$
$734$	−21.0132	+	17.6322i	−0.775613	+	0.650816i
$735$	−4.97288	−	1.68144i	−0.183427	−	0.0620208i
$736$	−3.05398	+	1.11156i	−0.112571	+	0.0409725i
$737$	4.56182	+	17.0249i	0.168037	+	0.627122i
$738$	−5.67740	+	17.4598i	−0.208988	+	0.642704i
$739$	−30.9063	+	17.8437i	−1.13691	+	0.656393i	−0.945663	−	0.325150i	$-0.894585\pi$
$739$	−30.9063	+	17.8437i	−1.13691	+	0.656393i	−0.191243	+	0.981543i	$0.561252\pi$
$740$	7.70027	−	4.06418i	0.283068	−	0.149402i
$741$	6.60366	−	57.9013i	0.242591	−	2.12706i
$742$	17.9187	−	25.5905i	0.657815	−	0.939457i
$743$	−20.1985	+	28.8465i	−0.741012	+	1.05828i	0.254813	+	0.966990i	$0.417986\pi$
$743$	−20.1985	+	28.8465i	−0.741012	+	1.05828i	−0.995825	+	0.0912848i	$0.970903\pi$
$744$	−23.3869	−	17.3095i	−0.857407	−	0.634598i
$745$	20.1021	+	6.21305i	0.736485	+	0.227629i
$746$	4.37382	−	2.52523i	0.160137	−	0.0924551i
$747$	−12.6286	−	6.71844i	−0.462058	−	0.245815i
$748$	1.49358	+	5.57411i	0.0546106	+	0.203810i
$749$	−15.4983	+	5.64093i	−0.566296	+	0.206115i
$750$	4.24503	+	20.0255i	0.155007	+	0.731229i
$751$	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	$0.128076\pi$
$752$	−13.6975	+	6.38726i	−0.499497	+	0.232919i
$753$	−12.5460	−	23.1132i	−0.457203	−	0.842290i
$754$	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	$0.598749\pi$
$758$	21.9080	−	15.3401i	0.795733	−	0.557178i
$759$	−2.00785	−	2.11631i	−0.0728802	−	0.0768172i
$760$	−28.3001	+	31.2380i	−1.02655	+	1.13312i
$761$	−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	$-0.566619\pi$
$762$	1.89925	+	5.67841i	0.0688027	+	0.205707i
$763$	−19.3290	+	41.4512i	−0.699757	+	1.50063i
$764$	10.2888	−	17.8207i	0.372236	−	0.644731i
$765$	17.9318	+	4.86794i	0.648327	+	0.176001i
$766$	6.51352	+	11.2818i	0.235343	+	0.407626i
$767$	44.3691	−	3.88180i	1.60208	−	0.140164i
$768$	10.4455	−	26.5086i	0.376919	−	0.956547i
$769$	43.1365	−	7.60612i	1.55554	−	0.274284i	0.671254	−	0.741227i	$-0.265756\pi$
$769$	43.1365	−	7.60612i	1.55554	−	0.274284i	0.884287	+	0.466944i	$0.154645\pi$
$770$	13.5539	−	8.74324i	0.488448	−	0.315085i
$771$	5.99998	+	13.8033i	0.216084	+	0.497113i
$772$	0.0239691	+	0.273968i	0.000862668	+	0.00986034i
$773$	−5.91076	+	22.0592i	−0.212595	+	0.793416i	0.774404	+	0.632691i	$0.218050\pi$
$773$	−5.91076	+	22.0592i	−0.212595	+	0.793416i	−0.986999	+	0.160725i	$0.948617\pi$
$774$	−1.79548	+	4.22722i	−0.0645371	+	0.151944i
$775$	7.43578	+	26.5426i	0.267101	+	0.953438i
$776$	−19.1194	−	52.5302i	−0.686347	−	1.88572i
$777$	−20.9488	+	7.00674i	−0.751534	+	0.251365i
$778$	0.821958	−	9.39502i	0.0294686	−	0.336828i
$779$	33.6549	+	12.2494i	1.20581	+	0.438879i
$780$	7.46688	−	17.0249i	0.267357	−	0.609591i
$781$	−2.00697	+	11.3821i	−0.0718150	+	0.407283i
$782$	−1.47719	+	1.47719i	−0.0528241	+	0.0528241i
$783$	−18.0556	−	4.67604i	−0.645255	−	0.167108i
$784$			1.97345i			0.0704805i
$785$	−26.5754	+	42.2419i	−0.948517	+	1.50768i
$786$	2.55215	+	0.756296i	0.0910322	+	0.0269762i
$787$	−7.27876	−	15.6093i	−0.259460	−	0.556413i	0.732822	−	0.680421i	$-0.238203\pi$
$787$	−7.27876	−	15.6093i	−0.259460	−	0.556413i	−0.992281	+	0.124008i	$0.960425\pi$
$788$	−2.85601	−	0.249868i	−0.101741	−	0.00890119i
$789$	−22.5574	−	34.0889i	−0.803064	−	1.21360i
$790$	−30.8588	−	1.17200i	−1.09791	−	0.0416980i
$791$	−6.68122	−	3.85740i	−0.237557	−	0.137153i
$792$	21.5666	−	0.748235i	0.766337	−	0.0265874i
$793$	−14.7603	−	3.95501i	−0.524154	−	0.140447i
$794$	−11.0377	−	9.26170i	−0.391712	−	0.328685i
$795$	−38.4735	−	9.36568i	−1.36451	−	0.332166i
$796$	0.977323	+	5.54267i	0.0346403	+	0.196455i
$797$	26.9373	+	18.8617i	0.954166	+	0.668115i	0.943340	−	0.331827i	$-0.107665\pi$
$797$	26.9373	+	18.8617i	0.954166	+	0.668115i	0.0108262	+	0.999941i	$0.496554\pi$
$798$	25.6256	−	20.3787i	0.907135	−	0.721400i
$799$	18.4814	−	22.0252i	0.653824	−	0.779197i
$800$	−19.5939	+	11.6109i	−0.692748	+	0.410506i
$801$	−19.9689	−	1.05106i	−0.705567	−	0.0371374i
$802$	−2.99600	+	0.802775i	−0.105792	+	0.0283470i
$803$	14.9085	+	6.95197i	0.526111	+	0.245330i
$804$	0.695477	+	11.3921i	0.0245276	+	0.401769i
$805$	−4.10251	−	2.10614i	−0.144594	−	0.0742317i
$806$	−10.8404	+	29.7838i	−0.381838	+	1.04909i
$807$	−15.0807	−	9.24384i	−0.530867	−	0.325399i
$808$	−5.88637	−	8.40661i	−0.207082	−	0.295744i
$809$	0.589848			0.0207379			0.0103690	−	0.999946i	$-0.496699\pi$
$809$	0.589848			0.0207379			0.0103690	+	0.999946i	$0.496699\pi$
$810$	10.0532	−	18.7483i	0.353232	−	0.658749i
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	−5.25222	−	7.50095i	−0.184317	−	0.263232i
$813$	7.15334	+	4.38469i	0.250879	+	0.153778i
$814$	3.76564	−	10.3460i	0.131985	−	0.362627i
$815$	−1.69293	−	5.26499i	−0.0593009	−	0.184424i
$816$	−0.425646	−	6.97221i	−0.0149006	−	0.244076i
$817$	8.11977	+	3.78631i	0.284075	+	0.132466i
$818$	−29.2711	+	7.84316i	−1.02344	+	0.274230i
$819$	−25.6961	+	39.5489i	−0.897894	+	1.38195i
$820$	9.10337	+	6.90358i	0.317903	+	0.241083i
$821$	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	$0.113686\pi$
$822$	22.8654	−	18.1837i	0.797522	−	0.634230i
$823$	0.511895	+	0.358433i	0.0178435	+	0.0124942i	0.582464	−	0.812856i	$-0.302089\pi$
$823$	0.511895	+	0.358433i	0.0178435	+	0.0124942i	−0.564621	+	0.825351i	$0.690978\pi$
$824$	1.91929	+	10.8848i	0.0668615	+	0.379190i
$825$	−16.5694	−	11.9751i	−0.576874	−	0.416920i
$826$	19.1684	+	16.0842i	0.666954	+	0.559641i
$827$	11.3875	+	3.05127i	0.395981	+	0.106103i	0.451314	−	0.892365i	$-0.350955\pi$
$827$	11.3875	+	3.05127i	0.395981	+	0.106103i	−0.0553328	+	0.998468i	$0.517622\pi$
$828$	−1.00068	−	1.60222i	−0.0347759	−	0.0556811i
$829$	38.0844	+	21.9880i	1.32272	+	0.763675i	0.984163	−	0.177269i	$-0.0567261\pi$
$829$	38.0844	+	21.9880i	1.32272	+	0.763675i	0.338562	+	0.940944i	$0.390059\pi$
$830$	8.26631	−	7.66139i	0.286928	−	0.265931i
$831$	−12.9183	−	19.5222i	−0.448130	−	0.677217i
$832$	−41.8666	−	3.66285i	−1.45146	−	0.126986i
$833$	−1.58663	−	3.40254i	−0.0549735	−	0.117891i
$834$	16.0216	+	4.74780i	0.554784	+	0.164403i
$835$	−13.7873	−	8.67392i	−0.477128	−	0.300173i
$836$		−	12.8886i		−	0.445761i
$837$	11.8881	−	26.0626i	0.410913	−	0.900854i
$838$	−9.93659	+	9.93659i	−0.343254	+	0.343254i
$839$	−0.173429	+	0.983567i	−0.00598745	+	0.0339565i	−0.987655	−	0.156644i	$-0.949932\pi$
$839$	−0.173429	+	0.983567i	−0.00598745	+	0.0339565i	0.981668	+	0.190601i	$0.0610435\pi$
$840$	31.7788	−	12.4018i	1.09647	−	0.427904i
$841$	15.1440	+	5.51197i	0.522207	+	0.190068i
$842$	−0.833993	+	9.53258i	−0.0287413	+	0.328514i
$843$	−25.8498	+	8.64597i	−0.890314	+	0.297783i
$844$	−1.93642	−	5.32028i	−0.0666545	−	0.183132i
$845$	−36.7845	−	4.63067i	−1.26543	−	0.159300i
$846$	−19.8050	−	26.2945i	−0.680910	−	0.904024i
$847$	4.06038	−	15.1535i	0.139516	−	0.520682i
$848$	1.29739	+	14.8293i	0.0445527	+	0.509239i
$849$	20.8200	+	47.8976i	0.714541	+	1.64384i
$850$	−8.26060	+	12.0869i	−0.283336	+	0.414577i
$851$	−3.10007	+	0.546626i	−0.106269	+	0.0187381i
$852$	−2.74373	+	6.96305i	−0.0939986	+	0.238550i
$853$	4.50805	−	0.394403i	0.154353	−	0.0135041i	−0.00971747	−	0.999953i	$-0.503093\pi$
$853$	4.50805	−	0.394403i	0.154353	−	0.0135041i	0.164070	+	0.986449i	$0.447538\pi$
$854$	−4.29256	−	7.43494i	−0.146889	−	0.254418i
$855$	−35.8710	−	20.8673i	−1.22676	−	0.713648i
$856$	8.69313	−	15.0569i	0.297125	−	0.514635i
$857$	−24.1963	+	51.8892i	−0.826531	+	1.77250i	−0.223650	+	0.974670i	$0.571797\pi$
$857$	−24.1963	+	51.8892i	−0.826531	+	1.77250i	−0.602881	+	0.797831i	$0.705981\pi$
$858$	−7.45653	−	22.2936i	−0.254562	−	0.761091i
$859$	−20.9711	−	24.9924i	−0.715526	−	0.852730i	0.278662	−	0.960389i	$-0.410109\pi$
$859$	−20.9711	−	24.9924i	−0.715526	−	0.852730i	−0.994188	+	0.107659i	$0.965665\pi$
$860$	2.11806	+	1.91885i	0.0722251	+	0.0654324i
$861$	−19.9496	−	21.0273i	−0.679881	−	0.716608i
$862$	0.256286	−	0.179453i	0.00872913	−	0.00611220i
$863$	−28.5706	−	28.5706i	−0.972554	−	0.972554i	0.0270792	−	0.999633i	$-0.491379\pi$
$863$	−28.5706	−	28.5706i	−0.972554	−	0.972554i	−0.999633	+	0.0270792i	$0.991379\pi$
$864$	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
$867$	−7.70751	−	14.1993i	−0.261761	−	0.482233i
$868$	12.7462	−	5.94365i	0.432634	−	0.201741i
$869$	23.6254	−	19.8241i	0.801437	−	0.672486i
$870$	8.14980	−	12.2287i	0.276304	−	0.414590i
$871$	38.1591	−	13.8888i	1.29297	−	0.470603i
$872$	−12.4786	−	46.5707i	−0.422578	−	1.57708i
$873$	46.6805	−	29.1545i	1.57989	−	0.986731i
$874$	4.04068	−	2.33289i	0.136678	−	0.0789111i
$875$	−30.9827	−	9.19224i	−1.04741	−	0.310755i
$876$	8.56194	+	6.33700i	0.289281	+	0.214108i
$877$	20.3911	−	29.1215i	0.688559	−	0.983364i	−0.310899	−	0.950443i	$-0.600630\pi$
$877$	20.3911	−	29.1215i	0.688559	−	0.983364i	0.999458	−	0.0329214i	$-0.0104811\pi$
$878$	−17.2994	+	24.7062i	−0.583828	+	0.833792i
$879$	−1.44122	+	12.6367i	−0.0486112	+	0.426226i
$880$	−2.26948	+	7.34283i	−0.0765041	+	0.247527i
$881$	−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	$0.539167\pi$
$882$	−4.20463	+	0.892728i	−0.141577	+	0.0300597i
$883$	0.905746	+	3.38029i	0.0304808	+	0.113756i	0.979490	−	0.201492i	$-0.0645790\pi$
$883$	0.905746	+	3.38029i	0.0304808	+	0.113756i	−0.949009	+	0.315248i	$0.897912\pi$
$884$	12.4936	−	4.54730i	0.420205	−	0.152942i
$885$	10.1589	−	30.0452i	0.341488	−	1.00996i
$886$	−32.6492	+	27.3959i	−1.09687	+	0.920383i
$887$	−25.7899	+	12.0260i	−0.865939	+	0.403794i	−0.804243	−	0.594301i	$-0.797429\pi$
$887$	−25.7899	+	12.0260i	−0.865939	+	0.403794i	−0.0616962	+	0.998095i	$0.519651\pi$
$888$	12.1691	−	19.8531i	0.408368	−	0.666227i
$889$	−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
$893$	−52.6023	+	36.8325i	−1.76027	+	1.23255i
$894$	16.7527	−	4.01997i	0.560296	−	0.134448i
$895$	32.0298	−	1.58051i	1.07064	−	0.0528307i
$896$	1.75011	+	2.08570i	0.0584672	+	0.0696785i
$897$	−4.45411	+	5.03331i	−0.148718	+	0.168057i
$898$	−3.49564	+	7.49641i	−0.116651	+	0.250159i
$899$	9.89411	−	17.1371i	0.329987	−	0.571554i
$900$	−8.96698	−	9.73890i	−0.298899	−	0.324630i
$901$	−14.1594	−	24.5249i	−0.471719	−	0.817042i
$902$	14.3919	−	1.25913i	0.479199	−	0.0419245i
$903$	−4.51303	−	5.67497i	−0.150184	−	0.188851i
$904$	8.00909	−	1.41222i	0.266378	−	0.0469697i
$905$	2.50844	+	3.88861i	0.0833833	+	0.129262i
$906$	1.15005	−	1.55383i	0.0382078	−	0.0516227i
$907$	2.85879	+	32.6761i	0.0949246	+	1.08499i	0.882987	+	0.469398i	$0.155529\pi$
$907$	2.85879	+	32.6761i	0.0949246	+	1.08499i	−0.788062	+	0.615596i	$0.788915\pi$
$908$	−0.713667	+	2.66344i	−0.0236839	+	0.0883894i
$909$	6.89249	−	7.38793i	0.228609	−	0.245042i
$910$	−22.7888	−	29.3528i	−0.755443	−	0.973035i
$911$	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	$0.729202\pi$
$912$	−3.11206	+	15.2874i	−0.103051	+	0.506217i
$913$	−0.981025	+	11.2132i	−0.0324672	+	0.371102i
$914$	5.44427	+	1.98155i	0.180080	+	0.0655439i
$915$	−6.80094	+	8.49458i	−0.224832	+	0.280822i
$916$	−3.60050	+	20.4195i	−0.118964	+	0.674678i
$917$	−2.97152	+	2.97152i	−0.0981282	+	0.0981282i
$918$	14.6624	−	4.06088i	0.483932	−	0.134029i
$919$		−	28.2931i		−	0.933302i	−0.884442	−	0.466651i	$-0.845460\pi$
$919$		−	28.2931i		−	0.933302i	0.884442	−	0.466651i	$-0.154540\pi$
$920$	4.74004	−	1.07908i	0.156274	−	0.0355763i
$921$	−17.1879	+	16.3070i	−0.566361	+	0.537335i
$922$	13.4676	+	28.8814i	0.443533	+	0.951159i
$923$	26.5268	+	2.32080i	0.873141	+	0.0763899i
$924$	−4.65525	+	9.33434i	−0.153147	+	0.307077i
$925$	−20.6430	+	7.77974i	−0.678738	+	0.255796i
$926$	0.165049	+	0.0952911i	0.00542385	+	0.00313146i
$927$	−10.0903	+	4.07410i	−0.331410	+	0.133811i
$928$	15.7933	+	4.23180i	0.518440	+	0.138916i
$929$	−25.1788	−	21.1275i	−0.826089	−	0.693171i	0.128300	−	0.991735i	$-0.459048\pi$
$929$	−25.1788	−	21.1275i	−0.826089	−	0.693171i	−0.954390	+	0.298564i	$0.903492\pi$
$930$	16.3227	+	15.5882i	0.535241	+	0.511157i
$931$	1.45603	+	8.25757i	0.0477195	+	0.270631i
$932$	2.39811	+	1.67917i	0.0785527	+	0.0550032i
$933$	6.22178	+	2.45164i	0.203692	+	0.0802630i
$934$	8.57623	−	10.2208i	0.280623	−	0.334433i
$935$	−1.99060	−	14.4848i	−0.0650997	−	0.473704i
$936$	−6.04793	−	49.3488i	−0.197683	−	1.61302i
$937$	4.87347	−	1.30584i	0.159209	−	0.0426600i	−0.178334	−	0.983970i	$-0.557071\pi$
$937$	4.87347	−	1.30584i	0.159209	−	0.0426600i	0.337543	+	0.941310i	$0.390404\pi$
$938$	20.6768	+	9.64174i	0.675121	+	0.314814i
$939$	38.1322	+	19.0174i	1.24440	+	0.620610i
$940$	−19.5016	+	6.27064i	−0.636071	+	0.204526i
$941$	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	$-0.275736\pi$
$942$	−1.07432	+	40.8501i	−0.0350034	+	1.33097i
$943$	−2.36919	−	3.38355i	−0.0771514	−	0.110184i
$944$	−11.9232			−0.388068
$945$	18.4419	+	28.0692i	0.599914	+	0.913090i
$946$	3.61394			0.117499
$947$	−18.4673	−	26.3740i	−0.600107	−	0.857041i	0.398073	−	0.917354i	$-0.369679\pi$
$947$	−18.4673	−	26.3740i	−0.600107	−	0.857041i	−0.998180	+	0.0603125i	$0.980790\pi$
$948$	17.5518	−	9.52727i	0.570055	−	0.309431i
$949$	12.9623	−	35.6136i	0.420773	−	1.15607i
$950$	24.8078	−	21.3004i	0.804870	−	0.691075i
$951$	−23.8355	+	15.7725i	−0.772920	+	0.511459i
$952$	22.1110	+	10.3105i	0.716623	+	0.334167i
$953$	−20.8927	+	5.59819i	−0.676782	+	0.181343i	−0.580808	−	0.814041i	$-0.697263\pi$
$953$	−20.8927	+	5.59819i	−0.676782	+	0.181343i	−0.0959743	+	0.995384i	$0.530597\pi$
$954$	−31.0083	+	9.47252i	−1.00393	+	0.306684i
$955$	−31.5033	+	41.5417i	−1.01942	+	1.34426i
$956$	9.64940	−	11.4997i	0.312084	−	0.371927i
$957$	2.16766	+	14.5154i	0.0700706	+	0.469217i
$958$	30.8629	+	21.6105i	0.997136	+	0.698202i
$959$	8.00894	+	45.4210i	0.258622	+	1.46672i
$960$	−14.3633	+	26.2552i	−0.463574	+	0.847384i
$961$	−0.465741	−	0.390803i	−0.0150239	−	0.0126065i
$962$	−24.5020	−	6.56528i	−0.789975	−	0.211673i
$963$	16.2784	+	5.29324i	0.524563	+	0.170572i
$964$	−14.1830	−	8.18857i	−0.456804	−	0.263736i
$965$	0.0264446	−	0.696285i	0.000851282	−	0.0224142i
$966$	−3.76902	+	0.230095i	−0.121266	+	0.00740317i
$967$	10.9923	+	0.961701i	0.353488	+	0.0309262i	0.262517	−	0.964927i	$-0.415447\pi$
$967$	10.9923	+	0.961701i	0.353488	+	0.0309262i	0.0909711	+	0.995854i	$0.471003\pi$
$968$	6.98917	+	14.9883i	0.224640	+	0.481743i
$969$	−6.92520	−	28.8599i	−0.222469	−	0.927114i
$970$	9.62569	+	42.2823i	0.309062	+	1.35760i
$971$			21.9387i			0.704047i	0.935991	+	0.352023i	$0.114506\pi$
$971$			21.9387i			0.704047i	−0.935991	+	0.352023i	$0.885494\pi$
$972$	0.592321	+	13.7449i	0.0189987	+	0.440868i
$973$	−18.6543	+	18.6543i	−0.598030	+	0.598030i
$974$	−1.26918	+	7.19790i	−0.0406673	+	0.230635i
$975$	−24.1578	+	40.4343i	−0.773668	+	1.29493i
$976$	3.84410	+	1.39914i	0.123046	+	0.0447853i
$977$	0.479546	−	5.48124i	0.0153420	−	0.175360i	−0.984658	−	0.174498i	$-0.944170\pi$
$977$	0.479546	−	5.48124i	0.0153420	−	0.175360i	1.00000		0.000862648i	$-0.000274589\pi$
$978$	−3.39128	−	3.00104i	−0.108441	−	0.0959625i
$979$	5.38167	+	14.7860i	0.171999	+	0.472563i
$980$	−0.334087	+	2.65388i	−0.0106720	+	0.0847749i
$981$	42.2990	−	21.5404i	1.35050	−	0.687731i
$982$	7.10536	−	26.5176i	0.226741	−	0.846209i
$983$	2.39635	+	27.3904i	0.0764316	+	0.873618i	0.933538	+	0.358478i	$0.116704\pi$
$983$	2.39635	+	27.3904i	0.0764316	+	0.873618i	−0.857106	+	0.515139i	$0.827740\pi$
$984$	30.3581	+	3.46235i	0.967782	+	0.110376i
$985$	7.10034	+	1.53191i	0.226236	+	0.0488107i
$986$	10.3502	−	1.82503i	0.329619	−	0.0581207i
$987$	51.4000	−	7.67583i	1.63608	−	0.244324i
$988$	−29.5815	+	2.58804i	−0.941111	+	0.0823366i
$989$	−0.516635	−	0.894838i	−0.0164280	−	0.0284542i
$990$	−16.6713	−	1.51368i	−0.529847	−	0.0481079i
$991$	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	$0.0853793\pi$
$992$	−10.6128	+	22.7592i	−0.336956	+	0.722606i
$993$	−35.0348	−	7.13204i	−1.11180	−	0.226328i
$994$	9.61620	+	11.4601i	0.305007	+	0.363494i
$995$	−0.702794	−	14.2424i	−0.0222801	−	0.451515i
$996$	−2.07092	+	6.98839i	−0.0656195	+	0.221436i
$997$	3.00447	−	2.10376i	0.0951527	−	0.0666266i	−0.525032	−	0.851083i	$-0.675947\pi$
$997$	3.00447	−	2.10376i	0.0951527	−	0.0666266i	0.620185	+	0.784456i	$0.287058\pi$
$998$	−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.2.12	✓	192
3.2	odd	2		405.2.r.a.332.5		192
5.2	odd	4		675.2.ba.b.218.5		192
5.3	odd	4	inner	135.2.q.a.83.12	yes	192
5.4	even	2		675.2.ba.b.407.5		192
15.8	even	4		405.2.r.a.8.5		192
27.13	even	9		405.2.r.a.152.5		192
27.14	odd	18	inner	135.2.q.a.122.12	yes	192
135.13	odd	36		405.2.r.a.233.5		192
135.14	odd	18		675.2.ba.b.257.5		192
135.68	even	36	inner	135.2.q.a.68.12	yes	192
135.122	even	36		675.2.ba.b.68.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	1.1	even	1	trivial
135.2.q.a.68.12	yes	192	135.68	even	36	inner
135.2.q.a.83.12	yes	192	5.3	odd	4	inner
135.2.q.a.122.12	yes	192	27.14	odd	18	inner
405.2.r.a.8.5		192	15.8	even	4
405.2.r.a.152.5		192	27.13	even	9
405.2.r.a.233.5		192	135.13	odd	36
405.2.r.a.332.5		192	3.2	odd	2
675.2.ba.b.68.5		192	135.122	even	36
675.2.ba.b.218.5		192	5.2	odd	4
675.2.ba.b.257.5		192	135.14	odd	18
675.2.ba.b.407.5		192	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.606324 + 0.865920i) q^{2} +(1.47671 + 0.905161i) q^{3} +(0.301851 - 0.829330i) q^{4} +(-1.02123 + 1.98924i) q^{5} +(0.111569 + 1.82754i) q^{6} +(-2.61975 - 1.22161i) q^{7} +(2.94330 - 0.788655i) q^{8} +(1.36137 + 2.67333i) q^{9} +O(q^{10})\)	\(q+(0.606324 + 0.865920i) q^{2} +(1.47671 + 0.905161i) q^{3} +(0.301851 - 0.829330i) q^{4} +(-1.02123 + 1.98924i) q^{5} +(0.111569 + 1.82754i) q^{6} +(-2.61975 - 1.22161i) q^{7} +(2.94330 - 0.788655i) q^{8} +(1.36137 + 2.67333i) q^{9} +(-2.34172 + 0.321816i) q^{10} +(1.51740 - 1.80836i) q^{11} +(1.19642 - 0.951458i) q^{12} +(-4.45519 - 3.11956i) q^{13} +(-0.530600 - 3.00918i) q^{14} +(-3.30866 + 2.01316i) q^{15} +(1.11535 + 0.935892i) q^{16} +(-2.67549 - 0.716894i) q^{17} +(-1.48946 + 2.79974i) q^{18} +(5.35751 + 3.09316i) q^{19} +(1.34148 + 1.44740i) q^{20} +(-2.76286 - 4.17526i) q^{21} +(2.48593 + 0.217491i) q^{22} +(-0.301527 - 0.646627i) q^{23} +(5.06027 + 1.49954i) q^{24} +(-2.91416 - 4.06296i) q^{25} -5.74930i q^{26} +(-0.409444 + 5.18000i) q^{27} +(-1.80389 + 1.80389i) q^{28} +(-0.623300 + 3.53491i) q^{29} +(-3.74935 - 1.64441i) q^{30} +(-5.18043 - 1.88552i) q^{31} +(0.397007 - 4.53781i) q^{32} +(3.87762 - 1.29695i) q^{33} +(-1.00144 - 2.75143i) q^{34} +(5.10545 - 3.96376i) q^{35} +(2.62800 - 0.322074i) q^{36} +(1.14193 - 4.26173i) q^{37} +(0.569956 + 6.51463i) q^{38} +(-3.75534 - 8.63936i) q^{39} +(-1.43698 + 6.66033i) q^{40} +(5.70140 - 1.00531i) q^{41} +(1.94025 - 4.92398i) q^{42} +(1.44271 - 0.126221i) q^{43} +(-1.04170 - 1.80428i) q^{44} +(-6.70817 - 0.0220104i) q^{45} +(0.377104 - 0.653164i) q^{46} +(-4.38688 + 9.40770i) q^{47} +(0.799924 + 2.39162i) q^{48} +(0.871236 + 1.03830i) q^{49} +(1.75128 - 4.98690i) q^{50} +(-3.30202 - 3.48039i) q^{51} +(-3.93195 + 2.75318i) 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} +(5.11170 + 9.41712i) q^{57} +(-3.43887 + 1.60357i) q^{58} +(-6.27320 + 5.26384i) q^{59} +(0.670849 + 3.35164i) q^{60} +(2.64019 - 0.960952i) q^{61} +(-1.50831 - 5.62907i) q^{62} +(-0.300676 - 8.66650i) q^{63} +(6.69194 - 3.86359i) q^{64} +(10.7553 - 5.67665i) q^{65} +(3.47414 + 2.57134i) q^{66} +(-4.28254 + 6.11610i) q^{67} +(-1.40214 + 2.00246i) q^{68} +(0.140033 - 1.22781i) q^{69} +(6.52785 + 2.01759i) q^{70} +(-4.24004 + 2.44799i) q^{71} +(6.11524 + 6.79476i) q^{72} +(1.80353 + 6.73088i) q^{73} +(4.38269 - 1.59517i) q^{74} +(-0.625739 - 8.63762i) q^{75} +(4.18242 - 3.50947i) q^{76} +(-6.18430 + 2.88379i) q^{77} +(5.20404 - 8.49007i) 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} +(-3.90587 + 2.73492i) q^{83} +(-4.29664 + 1.03102i) q^{84} +(4.15837 - 4.59007i) q^{85} +(0.984048 + 1.17274i) q^{86} +(-4.12010 + 4.65586i) q^{87} +(3.03998 - 6.51925i) q^{88} +(-3.33276 + 5.77251i) q^{89} +(-4.04826 - 5.82208i) q^{90} +(7.86060 + 13.6150i) q^{91} +(-0.627283 + 0.0548802i) q^{92} +(-5.94331 - 7.47350i) q^{93} +(-10.8062 + 1.90542i) q^{94} +(-11.6243 + 7.49853i) q^{95} +(4.69371 - 6.34168i) q^{96} +(-1.59893 - 18.2758i) q^{97} +(-0.370833 + 1.38397i) 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

Fields

Representations

Groups

Database

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