LMFDB - Embedded newform 162.2.g.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	162.13
Dual form			162.2.g.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893633 - 0.448799i) q^{2} +(0.674015 + 1.59553i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.195520 + 0.653084i) q^{5} +(0.113749 - 1.72831i) q^{6} +(0.386069 + 0.895009i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.09141 + 2.15082i) q^{9} +O(q^{10})$	\(q+(-0.893633 - 0.448799i) q^{2} +(0.674015 + 1.59553i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.195520 + 0.653084i) q^{5} +(0.113749 - 1.72831i) q^{6} +(0.386069 + 0.895009i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.09141 + 2.15082i) q^{9} +(0.118380 - 0.671366i) q^{10} +(-2.53703 + 0.601286i) q^{11} +(-0.877315 + 1.49343i) q^{12} +(4.17145 + 2.74361i) q^{13} +(0.0566753 - 0.973077i) q^{14} +(-0.910229 + 0.752146i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(0.260353 - 0.0947609i) q^{17} +(2.83424 - 0.983417i) q^{18} +(0.980818 + 0.356989i) q^{19} +(-0.407097 + 0.546826i) q^{20} +(-1.16779 + 1.21923i) q^{21} +(2.53703 + 0.601286i) q^{22} +(1.91135 - 4.43101i) q^{23} +(1.45425 - 0.940835i) q^{24} +(3.78915 - 2.49216i) q^{25} +(-2.49642 - 4.32392i) q^{26} +(-4.84132 - 1.88722i) q^{27} +(-0.487363 + 0.844138i) q^{28} +(0.0947041 + 1.62601i) q^{29} +(1.15097 - 0.263632i) q^{30} +(-0.00909867 + 0.00106348i) q^{31} +(0.686242 - 0.727374i) q^{32} +(-2.66936 - 3.64262i) q^{33} +(-0.275189 - 0.0321650i) q^{34} +(-0.509032 + 0.427128i) q^{35} +(-2.97412 - 0.393189i) q^{36} +(-4.52007 - 3.79279i) q^{37} +(-0.716275 - 0.759207i) q^{38} +(-1.56588 + 8.50489i) q^{39} +(0.609210 - 0.305957i) q^{40} +(7.48493 - 3.75907i) q^{41} +(1.59077 - 0.565441i) q^{42} +(-8.21135 - 8.70352i) q^{43} +(-1.99731 - 1.67594i) q^{44} +(-1.81358 - 0.945337i) q^{45} +(-3.69668 + 3.10188i) q^{46} +(-9.17545 - 1.07246i) q^{47} +(-1.72181 + 0.188097i) q^{48} +(4.15170 - 4.40054i) q^{49} +(-4.50459 + 0.526511i) q^{50} +(0.326676 + 0.351531i) q^{51} +(0.290307 + 4.98439i) q^{52} +(1.58100 - 2.73837i) q^{53} +(3.47938 + 3.85926i) q^{54} +(-0.888731 - 1.53933i) q^{55} +(0.814372 - 0.535621i) q^{56} +(0.0915010 + 1.80554i) q^{57} +(0.645120 - 1.49556i) q^{58} +(13.2141 + 3.13179i) q^{59} +(-1.14686 - 0.280965i) q^{60} +(3.46192 - 4.65017i) q^{61} +(0.00860816 + 0.00313311i) q^{62} +(-2.73243 - 1.04147i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.976201 + 3.26074i) q^{65} +(0.750624 + 4.45317i) q^{66} +(-0.747251 + 12.8298i) q^{67} +(0.231482 + 0.152248i) q^{68} +(8.35807 + 0.0630455i) q^{69} +(0.646582 - 0.153243i) q^{70} +(-0.445365 + 2.52579i) q^{71} +(2.48131 + 1.68615i) q^{72} +(0.289549 + 1.64211i) q^{73} +(2.33708 + 5.41796i) q^{74} +(6.53025 + 4.36593i) q^{75} +(0.299355 + 0.999916i) q^{76} +(-1.51762 - 2.03852i) q^{77} +(5.21631 - 6.89748i) q^{78} +(-4.63186 - 2.32621i) q^{79} -0.681723 q^{80} +(-0.252020 - 8.99647i) q^{81} -8.37585 q^{82} +(10.6058 + 5.32643i) q^{83} +(-1.67533 - 0.208640i) q^{84} +(0.112791 + 0.151505i) q^{85} +(3.43180 + 11.4630i) q^{86} +(-2.53050 + 1.24706i) q^{87} +(1.03270 + 2.39407i) q^{88} +(1.45217 + 8.23569i) q^{89} +(1.19640 + 1.65872i) q^{90} +(-0.845084 + 4.79271i) q^{91} +(4.69559 - 1.11288i) q^{92} +(-0.00782945 - 0.0138004i) q^{93} +(7.71817 + 5.07632i) q^{94} +(-0.0413735 + 0.710355i) q^{95} +(1.62308 + 0.604656i) q^{96} +(4.54640 - 15.1860i) q^{97} +(-5.68505 + 2.06919i) q^{98} +(4.01270 - 6.71421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$3$	0.674015	+	1.59553i	0.389143	+	0.921178i
$3$	0.674015	+	1.59553i	0.389143	+	0.921178i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	0.195520	+	0.653084i	0.0874394	+	0.292068i	0.990513	−	0.137417i	$-0.0438802\pi$
$5$	0.195520	+	0.653084i	0.0874394	+	0.292068i	−0.903074	+	0.429485i	$0.858695\pi$
$6$	0.113749	−	1.72831i	0.0464380	−	0.705580i
$7$	0.386069	+	0.895009i	0.145921	+	0.338282i	0.975464	−	0.220161i	$-0.0706583\pi$
$7$	0.386069	+	0.895009i	0.145921	+	0.338282i	−0.829543	+	0.558443i	$0.811399\pi$
$8$	−0.173648	−	0.984808i	−0.0613939	−	0.348182i
$9$	−2.09141	+	2.15082i	−0.697136	+	0.716939i
$10$	0.118380	−	0.671366i	0.0374350	−	0.212305i
$11$	−2.53703	+	0.601286i	−0.764942	+	0.181295i	−0.594525	−	0.804077i	$-0.702660\pi$
$11$	−2.53703	+	0.601286i	−0.764942	+	0.181295i	−0.170417	+	0.985372i	$0.554512\pi$
$12$	−0.877315	+	1.49343i	−0.253259	+	0.431115i
$13$	4.17145	+	2.74361i	1.15695	+	0.760940i	0.974964	−	0.222361i	$-0.0713764\pi$
$13$	4.17145	+	2.74361i	1.15695	+	0.760940i	0.181988	+	0.983301i	$0.441747\pi$
$14$	0.0566753	−	0.973077i	0.0151471	−	0.260066i
$15$	−0.910229	+	0.752146i	−0.235020	+	0.194203i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	0.260353	−	0.0947609i	0.0631450	−	0.0229829i	−0.310255	−	0.950654i	$-0.600414\pi$
$17$	0.260353	−	0.0947609i	0.0631450	−	0.0229829i	0.373400	+	0.927671i	$0.378192\pi$
$18$	2.83424	−	0.983417i	0.668036	−	0.231794i
$19$	0.980818	+	0.356989i	0.225015	+	0.0818988i	0.452067	−	0.891984i	$-0.350687\pi$
$19$	0.980818	+	0.356989i	0.225015	+	0.0818988i	−0.227052	+	0.973883i	$0.572909\pi$
$20$	−0.407097	+	0.546826i	−0.0910296	+	0.122274i
$21$	−1.16779	+	1.21923i	−0.254834	+	0.266059i
$22$	2.53703	+	0.601286i	0.540896	+	0.128195i
$23$	1.91135	−	4.43101i	0.398544	−	0.923929i	−0.594271	−	0.804265i	$-0.702559\pi$
$23$	1.91135	−	4.43101i	0.398544	−	0.923929i	0.992815	−	0.119664i	$-0.0381816\pi$
$24$	1.45425	−	0.940835i	0.296847	−	0.192047i
$25$	3.78915	−	2.49216i	0.757830	−	0.498432i
$26$	−2.49642	−	4.32392i	−0.489588	−	0.847991i
$27$	−4.84132	−	1.88722i	−0.931713	−	0.363195i
$28$	−0.487363	+	0.844138i	−0.0921030	+	0.159527i
$29$	0.0947041	+	1.62601i	0.0175861	+	0.301942i	0.995620	+	0.0934948i	$0.0298038\pi$
$29$	0.0947041	+	1.62601i	0.0175861	+	0.301942i	−0.978034	+	0.208447i	$0.933159\pi$
$30$	1.15097	−	0.263632i	0.210138	−	0.0481325i
$31$	−0.00909867	+	0.00106348i	−0.00163417	+	0.000191007i	−0.116910	−	0.993143i	$-0.537299\pi$
$31$	−0.00909867	+	0.00106348i	−0.00163417	+	0.000191007i	0.115276	+	0.993334i	$0.463225\pi$
$32$	0.686242	−	0.727374i	0.121312	−	0.128583i
$33$	−2.66936	−	3.64262i	−0.464676	−	0.634098i
$34$	−0.275189	−	0.0321650i	−0.0471945	−	0.00551625i
$35$	−0.509032	+	0.427128i	−0.0860421	+	0.0721979i
$36$	−2.97412	−	0.393189i	−0.495687	−	0.0655315i
$37$	−4.52007	−	3.79279i	−0.743094	−	0.623530i	0.190573	−	0.981673i	$-0.438966\pi$
$37$	−4.52007	−	3.79279i	−0.743094	−	0.623530i	−0.933667	+	0.358143i	$0.883410\pi$
$38$	−0.716275	−	0.759207i	−0.116195	−	0.123160i
$39$	−1.56588	+	8.50489i	−0.250741	+	1.36187i
$40$	0.609210	−	0.305957i	0.0963246	−	0.0483760i
$41$	7.48493	−	3.75907i	1.16895	−	0.587069i	0.244978	−	0.969529i	$-0.421219\pi$
$41$	7.48493	−	3.75907i	1.16895	−	0.587069i	0.923972	+	0.382460i	$0.124923\pi$
$42$	1.59077	−	0.565441i	0.245461	−	0.0872495i
$43$	−8.21135	−	8.70352i	−1.25222	−	1.32727i	−0.923865	−	0.382720i	$-0.874988\pi$
$43$	−8.21135	−	8.70352i	−1.25222	−	1.32727i	−0.328354	−	0.944555i	$-0.606494\pi$
$44$	−1.99731	−	1.67594i	−0.301106	−	0.252658i
$45$	−1.81358	−	0.945337i	−0.270352	−	0.140922i
$46$	−3.69668	+	3.10188i	−0.545045	+	0.457347i
$47$	−9.17545	−	1.07246i	−1.33838	−	0.156434i	−0.583400	−	0.812185i	$-0.698278\pi$
$47$	−9.17545	−	1.07246i	−1.33838	−	0.156434i	−0.754977	+	0.655751i	$0.772352\pi$
$48$	−1.72181	+	0.188097i	−0.248521	+	0.0271494i
$49$	4.15170	−	4.40054i	0.593100	−	0.628649i
$50$	−4.50459	+	0.526511i	−0.637045	+	0.0744599i
$51$	0.326676	+	0.351531i	0.0457437	+	0.0492241i
$52$	0.290307	+	4.98439i	0.0402584	+	0.691210i
$53$	1.58100	−	2.73837i	0.217167	−	0.376144i	−0.736774	−	0.676139i	$-0.763652\pi$
$53$	1.58100	−	2.73837i	0.217167	−	0.376144i	0.953941	+	0.299995i	$0.0969850\pi$
$54$	3.47938	+	3.85926i	0.473484	+	0.525179i
$55$	−0.888731	−	1.53933i	−0.119836	−	0.207563i
$56$	0.814372	−	0.535621i	0.108825	−	0.0715753i
$57$	0.0915010	+	1.80554i	0.0121196	+	0.239149i
$58$	0.645120	−	1.49556i	0.0847084	−	0.196376i
$59$	13.2141	+	3.13179i	1.72032	+	0.407724i	0.967976	−	0.251042i	$-0.0807732\pi$
$59$	13.2141	+	3.13179i	1.72032	+	0.407724i	0.752348	+	0.658766i	$0.228921\pi$
$60$	−1.14686	−	0.280965i	−0.148060	−	0.0362724i
$61$	3.46192	−	4.65017i	0.443254	−	0.595393i	−0.523207	−	0.852205i	$-0.675265\pi$
$61$	3.46192	−	4.65017i	0.443254	−	0.595393i	0.966461	+	0.256812i	$0.0826721\pi$
$62$	0.00860816	+	0.00313311i	0.00109324	+	0.000397906i
$63$	−2.73243	−	1.04147i	−0.344254	−	0.131212i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	−0.976201	+	3.26074i	−0.121083	+	0.404445i
$66$	0.750624	+	4.45317i	0.0923955	+	0.548147i
$67$	−0.747251	+	12.8298i	−0.0912913	+	1.56741i	0.572760	+	0.819723i	$0.305873\pi$
$67$	−0.747251	+	12.8298i	−0.0912913	+	1.56741i	−0.664051	+	0.747687i	$0.731164\pi$
$68$	0.231482	+	0.152248i	0.0280713	+	0.0184628i
$69$	8.35807	+	0.0630455i	1.00619	+	0.00758978i
$70$	0.646582	−	0.153243i	0.0772813	−	0.0183160i
$71$	−0.445365	+	2.52579i	−0.0528552	+	0.299757i	−0.999764	−	0.0217471i	$-0.993077\pi$
$71$	−0.445365	+	2.52579i	−0.0528552	+	0.299757i	0.946908	+	0.321504i	$0.104188\pi$
$72$	2.48131	+	1.68615i	0.292425	+	0.198715i
$73$	0.289549	+	1.64211i	0.0338891	+	0.192195i	0.997053	−	0.0767220i	$-0.0244454\pi$
$73$	0.289549	+	1.64211i	0.0338891	+	0.192195i	−0.963163	+	0.268917i	$0.913334\pi$
$74$	2.33708	+	5.41796i	0.271680	+	0.629825i
$75$	6.53025	+	4.36593i	0.754049	+	0.504135i
$76$	0.299355	+	0.999916i	0.0343384	+	0.114698i
$77$	−1.51762	−	2.03852i	−0.172949	−	0.232311i
$78$	5.21631	−	6.89748i	0.590631	−	0.780986i
$79$	−4.63186	−	2.32621i	−0.521125	−	0.261719i	0.168735	−	0.985661i	$-0.446032\pi$
$79$	−4.63186	−	2.32621i	−0.521125	−	0.261719i	−0.689860	+	0.723943i	$0.742328\pi$
$80$	−0.681723			−0.0762190
$81$	−0.252020	−	8.99647i	−0.0280023	−	0.999608i
$82$	−8.37585			−0.924958
$83$	10.6058	+	5.32643i	1.16414	+	0.584651i	0.922607	−	0.385742i	$-0.126054\pi$
$83$	10.6058	+	5.32643i	1.16414	+	0.584651i	0.241530	+	0.970393i	$0.422351\pi$
$84$	−1.67533	−	0.208640i	−0.182794	−	0.0227644i
$85$	0.112791	+	0.151505i	0.0122339	+	0.0164330i
$86$	3.43180	+	11.4630i	0.370060	+	1.23609i
$87$	−2.53050	+	1.24706i	−0.271299	+	0.133698i
$88$	1.03270	+	2.39407i	0.110086	+	0.255209i
$89$	1.45217	+	8.23569i	0.153930	+	0.872981i	0.959757	+	0.280830i	$0.0906098\pi$
$89$	1.45217	+	8.23569i	0.153930	+	0.872981i	−0.805827	+	0.592151i	$0.798279\pi$
$90$	1.19640	+	1.65872i	0.126112	+	0.174844i
$91$	−0.845084	+	4.79271i	−0.0885889	+	0.502413i
$92$	4.69559	−	1.11288i	0.489549	−	0.116025i
$93$	−0.00782945	−	0.0138004i	−0.000811876	−	0.00143103i
$94$	7.71817	+	5.07632i	0.796068	+	0.523582i
$95$	−0.0413735	+	0.710355i	−0.00424483	+	0.0728809i
$96$	1.62308	+	0.604656i	0.165655	+	0.0617125i
$97$	4.54640	−	15.1860i	0.461617	−	1.54191i	−0.337852	−	0.941199i	$-0.609700\pi$
$97$	4.54640	−	15.1860i	0.461617	−	1.54191i	0.799469	−	0.600708i	$-0.205114\pi$
$98$	−5.68505	+	2.06919i	−0.574277	+	0.209020i
$99$	4.01270	−	6.71421i	0.403292	−	0.674803i
$100$	4.26174	+	1.55115i	0.426174	+	0.155115i
$101$	−8.68662	+	11.6682i	−0.864351	+	1.16103i	0.121364	+	0.992608i	$0.461273\pi$
$101$	−8.68662	+	11.6682i	−0.864351	+	1.16103i	−0.985716	+	0.168417i	$0.946134\pi$
$102$	−0.134161	−	0.460751i	−0.0132840	−	0.0456211i
$103$	−7.77307	−	1.84225i	−0.765903	−	0.181522i	−0.170947	−	0.985280i	$-0.554683\pi$
$103$	−7.77307	−	1.84225i	−0.765903	−	0.181522i	−0.594957	+	0.803758i	$0.702831\pi$
$104$	1.97756	−	4.58450i	0.193916	−	0.449547i
$105$	−1.02459	−	0.524283i	−0.0999897	−	0.0511648i
$106$	−2.64181	+	1.73755i	−0.256596	+	0.168766i
$107$	−4.72648	−	8.18650i	−0.456926	−	0.791419i	0.541871	−	0.840462i	$-0.317716\pi$
$107$	−4.72648	−	8.18650i	−0.456926	−	0.791419i	−0.998797	+	0.0490431i	$0.984383\pi$
$108$	−1.37726	−	5.01031i	−0.132527	−	0.482117i
$109$	−2.22505	+	3.85390i	−0.213121	+	0.369137i	−0.952690	−	0.303945i	$-0.901696\pi$
$109$	−2.22505	+	3.85390i	−0.213121	+	0.369137i	0.739569	+	0.673081i	$0.235030\pi$
$110$	0.103350	+	1.77445i	0.00985405	+	0.169188i
$111$	3.00490	−	9.76828i	0.285212	−	0.927164i
$112$	−0.968136	+	0.113159i	−0.0914802	+	0.0106925i
$113$	−0.476925	+	0.505511i	−0.0448653	+	0.0475545i	−0.749418	−	0.662098i	$-0.769666\pi$
$113$	−0.476925	+	0.505511i	−0.0448653	+	0.0475545i	0.704552	+	0.709652i	$0.251148\pi$
$114$	0.728555	−	1.65455i	0.0682354	−	0.154963i
$115$	3.26753	+	0.381919i	0.304698	+	0.0356141i
$116$	−1.24770	+	1.04695i	−0.115846	+	0.0972067i
$117$	−14.6252	+	3.23402i	−1.35210	+	0.298986i
$118$	−10.4030	−	8.72913i	−0.957671	−	0.803581i
$119$	0.185326	+	0.196435i	0.0169888	+	0.0180071i
$120$	0.898779	+	0.765792i	0.0820469	+	0.0699069i
$121$	−3.75501	+	1.88584i	−0.341364	+	0.171440i
$122$	−5.18068	+	2.60184i	−0.469037	+	0.235559i
$123$	11.0427	+	9.40873i	0.995683	+	0.848357i
$124$	−0.00628639	−	0.00666318i	−0.000564535	−	0.000598372i
$125$	4.97960	+	4.17838i	0.445389	+	0.373726i
$126$	1.97438	+	2.15700i	0.175892	+	0.192161i
$127$	−12.8393	+	10.7734i	−1.13930	+	0.955988i	−0.999416	−	0.0341795i	$-0.989118\pi$
$127$	−12.8393	+	10.7734i	−1.13930	+	0.955988i	−0.139886	+	0.990168i	$0.544674\pi$
$128$	0.993238	+	0.116093i	0.0877907	+	0.0102613i
$129$	8.35213	−	18.9677i	0.735364	−	1.67001i
$130$	2.33578	−	2.47578i	0.204862	−	0.217141i
$131$	−17.8557	+	2.08704i	−1.56006	+	0.182345i	−0.851900	−	0.523704i	$-0.824550\pi$
$131$	−17.8557	+	2.08704i	−1.56006	+	0.182345i	−0.708163	+	0.706049i	$0.750476\pi$
$132$	1.32779	−	4.31637i	0.115570	−	0.375692i
$133$	0.0591557	+	1.01566i	0.00512945	+	0.0880692i
$134$	6.42577	−	11.1298i	0.555102	−	0.961466i
$135$	0.285932	−	3.53078i	0.0246091	−	0.303881i
$136$	−0.138531	−	0.239943i	−0.0118790	−	0.0205749i
$137$	6.40237	−	4.21091i	0.546992	−	0.359762i	−0.245737	−	0.969336i	$-0.579030\pi$
$137$	6.40237	−	4.21091i	0.546992	−	0.359762i	0.792729	+	0.609574i	$0.208660\pi$
$138$	−7.44075	−	3.80743i	−0.633398	−	0.324110i
$139$	−2.97470	+	6.89612i	−0.252311	+	0.584922i	−0.996550	−	0.0829909i	$-0.973553\pi$
$139$	−2.97470	+	6.89612i	−0.252311	+	0.584922i	0.744240	+	0.667913i	$0.232812\pi$
$140$	−0.646582	−	0.153243i	−0.0546462	−	0.0129514i
$141$	−4.47326	−	15.3625i	−0.376716	−	1.29376i
$142$	1.53157	−	2.05725i	0.128526	−	0.172641i
$143$	−12.2328	−	4.45236i	−1.02296	−	0.372325i
$144$	−1.46064	−	2.62041i	−0.121720	−	0.218367i
$145$	−1.04340	+	0.379767i	−0.0866498	+	0.0315380i
$146$	0.478229	−	1.59740i	0.0395785	−	0.132201i
$147$	9.81949	+	3.65811i	0.809898	+	0.301716i
$148$	0.343085	−	5.89054i	0.0282014	−	0.484200i
$149$	11.6176	+	7.64102i	0.951752	+	0.625977i	0.927538	−	0.373730i	$-0.121921\pi$
$149$	11.6176	+	7.64102i	0.951752	+	0.625977i	0.0242141	+	0.999707i	$0.492292\pi$
$150$	−3.87622	−	6.83231i	−0.316492	−	0.557856i
$151$	−9.19351	+	2.17890i	−0.748158	+	0.177317i	−0.586972	−	0.809607i	$-0.699680\pi$
$151$	−9.19351	+	2.17890i	−0.748158	+	0.177317i	−0.161186	+	0.986924i	$0.551532\pi$
$152$	0.181248	−	1.02791i	0.0147011	−	0.0833743i
$153$	−0.340692	+	0.758156i	−0.0275433	+	0.0612933i
$154$	0.441311	+	2.50280i	0.0355619	+	0.201681i
$155$	−0.00247352	−	0.00573426i	−0.000198678	−	0.000460587i
$156$	−7.75705	+	3.82274i	−0.621061	+	0.306064i
$157$	−4.03874	−	13.4903i	−0.322327	−	1.07665i	−0.953598	−	0.301084i	$-0.902652\pi$
$157$	−4.03874	−	13.4903i	−0.322327	−	1.07665i	0.631271	−	0.775562i	$-0.282533\pi$
$158$	3.09518	+	4.15755i	0.246239	+	0.330757i
$159$	5.43476	+	0.676824i	0.431005	+	0.0536756i
$160$	0.609210	+	0.305957i	0.0481623	+	0.0241880i
$161$	4.70371			0.370704
$162$	−3.81240	+	8.15265i	−0.299530	+	0.640532i
$163$	22.6445			1.77366			0.886829	−	0.462098i	$-0.152903\pi$
$163$	22.6445			1.77366			0.886829	+	0.462098i	$0.152903\pi$
$164$	7.48493	+	3.75907i	0.584475	+	0.293534i
$165$	1.85702	−	2.45552i	0.144569	−	0.191162i
$166$	−7.08718	−	9.51974i	−0.550072	−	0.738875i
$167$	−2.40433	−	8.03101i	−0.186052	−	0.621458i	−0.999222	−	0.0394319i	$-0.987445\pi$
$167$	−2.40433	−	8.03101i	−0.186052	−	0.621458i	0.813170	−	0.582026i	$-0.197740\pi$
$168$	1.40350	+	0.938336i	0.108282	+	0.0723942i
$169$	4.72459	+	10.9528i	0.363430	+	0.842526i
$170$	−0.0327986	−	0.186010i	−0.00251554	−	0.0142663i
$171$	−2.81911	+	1.36295i	−0.215583	+	0.104227i
$172$	2.07782	−	11.7839i	0.158432	−	0.898513i
$173$	−19.3671	+	4.59010i	−1.47246	+	0.348979i	−0.887017	−	0.461737i	$-0.847226\pi$
$173$	−19.3671	+	4.59010i	−1.47246	+	0.348979i	−0.585440	+	0.810716i	$0.699078\pi$
$174$	2.82102	+	0.0212791i	0.213861	+	0.00161317i
$175$	3.69338	+	2.42918i	0.279194	+	0.183628i
$176$	0.151601	−	2.60289i	0.0114274	−	0.196201i
$177$	3.90962	+	23.1943i	0.293865	+	1.74339i
$178$	2.39846	−	8.01141i	0.179772	−	0.600481i
$179$	15.8770	−	5.77875i	1.18670	−	0.431924i	0.328137	−	0.944630i	$-0.393579\pi$
$179$	15.8770	−	5.77875i	1.18670	−	0.431924i	0.858564	+	0.512706i	$0.171357\pi$
$180$	−0.324716	−	2.01923i	−0.0242029	−	0.150504i
$181$	23.1653	+	8.43147i	1.72186	+	0.626707i	0.997999	−	0.0632366i	$-0.0201423\pi$
$181$	23.1653	+	8.43147i	1.72186	+	0.626707i	0.723864	+	0.689943i	$0.242365\pi$
$182$	2.90616	−	3.90365i	0.215419	−	0.289358i
$183$	9.75286	+	2.38931i	0.720952	+	0.176623i
$184$	−4.69559	−	1.11288i	−0.346164	−	0.0820423i
$185$	1.59324	−	3.69355i	0.117137	−	0.271555i
$186$	0.000803059		0.0158463i	5.88832e−5		0.00116191i
$187$	−0.603545	+	0.396958i	−0.0441356	+	0.0290284i
$188$	−4.61896	−	8.00027i	−0.336872	−	0.583480i
$189$	−0.180011	−	5.06163i	−0.0130939	−	0.368179i
$190$	0.355779	−	0.616228i	0.0258110	−	0.0447059i
$191$	−0.899470	−	15.4433i	−0.0650834	−	1.11744i	−0.859858	−	0.510533i	$-0.829448\pi$
$191$	−0.899470	−	15.4433i	−0.0650834	−	1.11744i	0.794775	−	0.606905i	$-0.207589\pi$
$192$	−1.17907	−	1.26878i	−0.0850920	−	0.0915661i
$193$	−13.6223	+	1.59222i	−0.980553	+	0.114610i	−0.591240	−	0.806495i	$-0.701362\pi$
$193$	−13.6223	+	1.59222i	−0.980553	+	0.114610i	−0.389313	+	0.921106i	$0.627287\pi$
$194$	−10.8783	+	11.5303i	−0.781015	+	0.827828i
$195$	−5.86057	+	0.640231i	−0.419684	+	0.0458479i
$196$	6.00900	+	0.702352i	0.429214	+	0.0501680i
$197$	−15.3766	+	12.9025i	−1.09554	+	0.919266i	−0.997117	−	0.0758785i	$-0.975824\pi$
$197$	−15.3766	+	12.9025i	−1.09554	+	0.919266i	−0.0984219	+	0.995145i	$0.531379\pi$
$198$	−6.59921	+	4.19914i	−0.468986	+	0.298420i
$199$	−6.75579	−	5.66878i	−0.478905	−	0.401849i	0.371125	−	0.928583i	$-0.378972\pi$
$199$	−6.75579	−	5.66878i	−0.478905	−	0.401849i	−0.850030	+	0.526734i	$0.823417\pi$
$200$	−3.11228	−	3.29882i	−0.220071	−	0.233262i
$201$	−20.9740	+	7.45522i	−1.47939	+	0.525851i
$202$	12.9993	−	6.52850i	0.914628	−	0.459344i
$203$	−1.41873	+	0.712512i	−0.0995752	+	0.0500086i
$204$	−0.0868937	+	0.471954i	−0.00608378	+	0.0330434i
$205$	3.91845	+	4.15331i	0.273676	+	0.290080i
$206$	6.11947	+	5.13484i	0.426363	+	0.357761i
$207$	5.53287	+	13.3780i	0.384561	+	0.929836i
$208$	−3.82473	+	3.20933i	−0.265197	+	0.222527i
$209$	−2.70301	−	0.315937i	−0.186971	−	0.0218538i
$210$	0.680309	+	0.928351i	0.0469458	+	0.0640623i
$211$	0.218012	−	0.231079i	0.0150086	−	0.0159082i	−0.719826	−	0.694155i	$-0.755778\pi$
$211$	0.218012	−	0.231079i	0.0150086	−	0.0159082i	0.734834	+	0.678247i	$0.237260\pi$
$212$	3.14062	−	0.367086i	0.215699	−	0.0252116i
$213$	−4.33015	+	0.991829i	−0.296697	+	0.0679590i
$214$	0.549640	+	9.43696i	0.0375726	+	0.645097i
$215$	4.07864	−	7.06441i	0.278161	−	0.481789i
$216$	−1.01786	+	5.09548i	−0.0692564	+	0.346704i
$217$	−0.00446454	−	0.00773281i	−0.000303073	−	0.000524938i
$218$	3.71800	−	2.44537i	0.251815	−	0.165621i
$219$	−2.42488	+	1.56879i	−0.163858	+	0.106009i
$220$	0.704016	−	1.63209i	0.0474648	−	0.110036i
$221$	1.34604	+	0.319017i	0.0905444	+	0.0214594i
$222$	−7.06927	+	7.38065i	−0.474458	+	0.495357i
$223$	−5.88880	+	7.91003i	−0.394343	+	0.529694i	−0.954309	−	0.298821i	$-0.903407\pi$
$223$	−5.88880	+	7.91003i	−0.394343	+	0.529694i	0.559966	+	0.828515i	$0.310814\pi$
$224$	0.915943	+	0.333376i	0.0611990	+	0.0222746i
$225$	−2.56448	+	13.3619i	−0.170965	+	0.890793i
$226$	0.653069	−	0.237698i	0.0434415	−	0.0158114i
$227$	4.67574	−	15.6181i	0.310340	−	1.03661i	−0.650501	−	0.759505i	$-0.725441\pi$
$227$	4.67574	−	15.6181i	0.310340	−	1.03661i	0.960841	−	0.277101i	$-0.0893737\pi$
$228$	−1.39362	+	1.15159i	−0.0922949	+	0.0762657i
$229$	−0.361341	+	6.20398i	−0.0238781	+	0.409971i	0.965097	+	0.261891i	$0.0843462\pi$
$229$	−0.361341	+	6.20398i	−0.0238781	+	0.409971i	−0.988975	+	0.148079i	$0.952691\pi$
$230$	−2.74856	−	1.80776i	−0.181235	−	0.119200i
$231$	2.22962	−	3.79540i	0.146698	−	0.249719i
$232$	1.58486	−	0.375618i	0.104051	−	0.0246606i
$233$	−1.22137	+	6.92674i	−0.0800146	+	0.453786i	0.918307	+	0.395869i	$0.129557\pi$
$233$	−1.22137	+	6.92674i	−0.0800146	+	0.453786i	−0.998321	+	0.0579161i	$0.981554\pi$
$234$	14.5210	+	3.67375i	0.949267	+	0.240161i
$235$	−1.09358	−	6.20203i	−0.0713376	−	0.404576i
$236$	5.37881	+	12.4695i	0.350131	+	0.811694i
$237$	0.589584	−	8.95815i	0.0382976	−	0.581894i
$238$	−0.0774541	−	0.258715i	−0.00502060	−	0.0167700i
$239$	−2.18145	−	2.93019i	−0.141106	−	0.189538i	0.725952	−	0.687745i	$-0.241399\pi$
$239$	−2.18145	−	2.93019i	−0.141106	−	0.189538i	−0.867058	+	0.498207i	$0.833992\pi$
$240$	−0.459491	−	1.08771i	−0.0296600	−	0.0702112i
$241$	−1.58703	−	0.797036i	−0.102230	−	0.0513416i	0.396950	−	0.917840i	$-0.370069\pi$
$241$	−1.58703	−	0.797036i	−0.102230	−	0.0513416i	−0.499179	+	0.866499i	$0.666365\pi$
$242$	4.20196			0.270112
$243$	14.1842	−	6.46586i	0.909919	−	0.414785i
$244$	5.79733			0.371136
$245$	3.68567	+	1.85101i	0.235469	+	0.118257i
$246$	−5.64544	−	13.3639i	−0.359940	−	0.852050i
$247$	3.11200	+	4.18014i	0.198012	+	0.265976i
$248$	0.00262729	+	0.00877577i	0.000166833	+	0.000557262i
$249$	−1.35000	+	20.5119i	−0.0855527	+	1.29989i
$250$	−2.57468	−	5.96878i	−0.162837	−	0.377499i
$251$	−2.28500	−	12.9589i	−0.144228	−	0.817957i	−0.967984	−	0.251013i	$-0.919236\pi$
$251$	−2.28500	−	12.9589i	−0.144228	−	0.817957i	0.823756	−	0.566945i	$-0.191875\pi$
$252$	−0.796310	−	2.81367i	−0.0501628	−	0.177244i
$253$	−2.18484	+	12.3908i	−0.137360	+	0.779006i
$254$	16.3087	−	3.86524i	1.02330	−	0.242526i
$255$	−0.165707	+	0.282078i	−0.0103770	+	0.0176644i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	1.35881	−	23.3300i	0.0847606	−	1.45528i	−0.641109	−	0.767450i	$-0.721525\pi$
$257$	1.35881	−	23.3300i	0.0847606	−	1.45528i	0.725869	−	0.687833i	$-0.241438\pi$
$258$	−15.9764	+	13.2017i	−0.994649	+	0.821905i
$259$	1.64952	−	5.50978i	0.102496	−	0.342361i
$260$	−3.19846	+	1.16414i	−0.198360	+	0.0721972i
$261$	−3.69531	−	3.19695i	−0.228734	−	0.197886i
$262$	16.8931	+	6.14860i	1.04366	+	0.379862i
$263$	3.51810	−	4.72563i	0.216935	−	0.291395i	−0.680312	−	0.732922i	$-0.738156\pi$
$263$	3.51810	−	4.72563i	0.216935	−	0.291395i	0.897248	+	0.441527i	$0.145563\pi$
$264$	−3.12375	+	3.26134i	−0.192253	+	0.200722i
$265$	2.09750	+	0.497118i	0.128849	+	0.0305377i
$266$	0.402966	−	0.934179i	0.0247074	−	0.0572782i
$267$	−12.1615	+	7.86795i	−0.744270	+	0.481511i
$268$	−10.7373	+	7.06204i	−0.655886	+	0.431383i
$269$	8.42808	+	14.5979i	0.513869	+	0.890048i	0.999871	+	0.0160897i	$0.00512174\pi$
$269$	8.42808	+	14.5979i	0.513869	+	0.890048i	−0.486001	+	0.873958i	$0.661545\pi$
$270$	−1.84013	+	3.02689i	−0.111987	+	0.184211i
$271$	11.1983	−	19.3960i	0.680248	−	1.17822i	−0.294657	−	0.955603i	$-0.595205\pi$
$271$	11.1983	−	19.3960i	0.680248	−	1.17822i	0.974905	−	0.222622i	$-0.0714614\pi$
$272$	0.0161097	+	0.276594i	0.000976797	+	0.0167710i
$273$	−8.21650	+	1.88200i	−0.497285	+	0.113904i
$274$	−7.61122	+	0.889624i	−0.459811	+	0.0537441i
$275$	−8.11466	+	8.60104i	−0.489333	+	0.518662i
$276$	4.94052	+	6.74185i	0.297384	+	0.405811i
$277$	30.6082	+	3.57759i	1.83907	+	0.214956i	0.963421	−	0.267993i	$-0.0863603\pi$
$277$	30.6082	+	3.57759i	1.83907	+	0.214956i	0.875648	+	0.482949i	$0.160434\pi$
$278$	5.75326	−	4.82756i	0.345058	−	0.289538i
$279$	0.0167417	−	0.0217937i	0.00100230	−	0.00130476i
$280$	0.509032	+	0.427128i	0.0304205	+	0.0255258i
$281$	−7.84237	−	8.31243i	−0.467837	−	0.495878i	0.449894	−	0.893082i	$-0.351462\pi$
$281$	−7.84237	−	8.31243i	−0.467837	−	0.495878i	−0.917730	+	0.397204i	$0.869980\pi$
$282$	−2.89724	+	15.7361i	−0.172528	+	0.937068i
$283$	−4.73586	+	2.37844i	−0.281518	+	0.141384i	−0.583956	−	0.811786i	$-0.698496\pi$
$283$	−4.73586	+	2.37844i	−0.281518	+	0.141384i	0.302438	+	0.953169i	$0.402200\pi$
$284$	−2.29195	+	1.15106i	−0.136002	+	0.0683029i
$285$	−1.16128	+	0.412777i	−0.0687881	+	0.0244508i
$286$	8.93339	+	9.46884i	0.528242	+	0.559904i
$287$	6.25411	+	5.24782i	0.369168	+	0.309769i
$288$	0.129235	+	2.99722i	0.00761527	+	0.176613i
$289$	−12.9640	+	10.8780i	−0.762585	+	0.639885i
$290$	1.10286	+	0.128906i	0.0647620	+	0.00756959i
$291$	27.2940	−	2.98171i	1.60000	−	0.174791i
$292$	−1.14427	+	1.21286i	−0.0669634	+	0.0709770i
$293$	−31.3742	+	3.66712i	−1.83290	+	0.214235i	−0.961210	−	0.275818i	$-0.911051\pi$
$293$	−31.3742	+	3.66712i	−1.83290	+	0.214235i	−0.871692	+	0.490054i	$0.836977\pi$
$294$	−7.13326	−	7.67599i	−0.416020	−	0.447673i
$295$	0.538298	+	9.24222i	0.0313409	+	0.538103i
$296$	−2.95026	+	5.11001i	−0.171481	+	0.297013i
$297$	13.4173	+	1.87689i	0.778552	+	0.108908i
$298$	−6.95259	−	12.0422i	−0.402753	−	0.697588i
$299$	20.1300	−	13.2397i	1.16415	−	0.765674i
$300$	0.397580	+	7.84522i	0.0229543	+	0.452944i
$301$	4.61958	−	10.7094i	0.266268	−	0.617279i
$302$	9.19351	+	2.17890i	0.529027	+	0.125382i
$303$	−24.4718	−	5.99523i	−1.40587	−	0.344417i
$304$	−0.623293	+	0.837228i	−0.0357483	+	0.0480183i
$305$	3.71383	+	1.35172i	0.212653	+	0.0773994i
$306$	0.644714	−	0.524611i	0.0368558	−	0.0299900i
$307$	13.3693	−	4.86604i	0.763028	−	0.277720i	0.0689510	−	0.997620i	$-0.478035\pi$
$307$	13.3693	−	4.86604i	0.763028	−	0.277720i	0.694077	+	0.719900i	$0.255813\pi$
$308$	0.728884	−	2.43464i	0.0415320	−	0.138727i
$309$	−2.29980	−	13.6438i	−0.130831	−	0.776171i
$310$	−0.000363114		0.00623443i	−2.06235e−5		0.000354092i
$311$	−0.716561	−	0.471289i	−0.0406324	−	0.0267244i	0.529030	−	0.848603i	$-0.322556\pi$
$311$	−0.716561	−	0.471289i	−0.0406324	−	0.0267244i	−0.569663	+	0.821879i	$0.692926\pi$
$312$	8.64760	+	0.0652294i	0.489574	+	0.00369289i
$313$	−15.3577	+	3.63984i	−0.868069	+	0.205736i	−0.640437	−	0.768011i	$-0.721247\pi$
$313$	−15.3577	+	3.63984i	−0.868069	+	0.205736i	−0.227632	+	0.973747i	$0.573098\pi$
$314$	−2.44530	+	13.8680i	−0.137996	+	0.782616i
$315$	0.145919	−	1.98813i	0.00822159	−	0.112019i
$316$	−0.900049	−	5.10443i	−0.0506317	−	0.287147i
$317$	−7.60463	−	17.6295i	−0.427119	−	0.990172i	−0.986871	−	0.161512i	$-0.948363\pi$
$317$	−7.60463	−	17.6295i	−0.427119	−	0.990172i	0.559752	−	0.828660i	$-0.310896\pi$
$318$	−4.55292	−	3.04395i	−0.255315	−	0.170696i
$319$	−1.21796	−	4.06828i	−0.0681928	−	0.227780i
$320$	−0.407097	−	0.546826i	−0.0227574	−	0.0305685i
$321$	9.87606	−	13.0590i	0.551228	−	0.728884i
$322$	−4.20339	−	2.11102i	−0.234245	−	0.117643i
$323$	0.289188			0.0160908
$324$	7.06578	−	5.57447i	0.392543	−	0.309693i
$325$	22.6438			1.25605
$326$	−20.2359	−	10.1629i	−1.12076	−	0.562868i
$327$	−7.64871	−	0.952541i	−0.422975	−	0.0526756i
$328$	−5.00171	−	6.71846i	−0.276173	−	0.370965i
$329$	−2.58250	−	8.62616i	−0.142378	−	0.475576i
$330$	−2.76153	+	1.36091i	−0.152017	+	0.0749154i
$331$	5.27278	+	12.2237i	0.289818	+	0.671874i	0.999466	−	0.0326828i	$-0.0104051\pi$
$331$	5.27278	+	12.2237i	0.289818	+	0.671874i	−0.709648	+	0.704557i	$0.751146\pi$
$332$	2.06089	+	11.6879i	0.113106	+	0.641455i
$333$	17.6109	−	1.78957i	0.965071	−	0.0980676i
$334$	−1.45573	+	8.25583i	−0.0796538	+	0.451739i
$335$	−8.52504	+	2.02047i	−0.465773	+	0.110390i
$336$	−0.833085	−	1.46842i	−0.0454485	−	0.0801086i
$337$	−11.5600	−	7.60315i	−0.629715	−	0.414170i	0.194138	−	0.980974i	$-0.437809\pi$
$337$	−11.5600	−	7.60315i	−0.629715	−	0.414170i	−0.823852	+	0.566804i	$0.808180\pi$
$338$	0.693574	−	11.9082i	0.0377255	−	0.647721i
$339$	−1.12801	−	0.420225i	−0.0612651	−	0.0228235i
$340$	−0.0541714	+	0.180945i	−0.00293785	+	0.00981312i
$341$	0.0224441	−	0.00816898i	0.00121542	−	0.000442375i
$342$	3.13094	+	0.0472365i	0.169302	+	0.00255426i
$343$	11.9530	+	4.35053i	0.645400	+	0.234906i
$344$	−7.14541	+	9.59795i	−0.385255	+	0.517487i
$345$	1.59300	+	5.47084i	0.0857642	+	0.294540i
$346$	19.3671	+	4.59010i	1.04118	+	0.246765i
$347$	0.690508	−	1.60078i	0.0370684	−	0.0859343i	−0.898676	−	0.438613i	$-0.855470\pi$
$347$	0.690508	−	1.60078i	0.0370684	−	0.0859343i	0.935744	+	0.352679i	$0.114729\pi$
$348$	−2.51140	−	1.28509i	−0.134625	−	0.0688879i
$349$	−8.01784	+	5.27342i	−0.429185	+	0.282280i	−0.745667	−	0.666319i	$-0.767869\pi$
$349$	−8.01784	+	5.27342i	−0.429185	+	0.282280i	0.316481	+	0.948599i	$0.397499\pi$
$350$	−2.21032	−	3.82838i	−0.118146	−	0.204635i
$351$	−15.0176	−	21.1551i	−0.801579	−	1.12918i
$352$	−1.30365	+	2.25799i	−0.0694849	+	0.120351i
$353$	0.637958	+	10.9533i	0.0339551	+	0.582986i	0.971782	+	0.235882i	$0.0757979\pi$
$353$	0.637958	+	10.9533i	0.0339551	+	0.582986i	−0.937827	+	0.347104i	$0.887165\pi$
$354$	6.91580	−	22.4818i	0.367571	−	1.19489i
$355$	−1.73663	+	0.202983i	−0.0921709	+	0.0107732i
$356$	−5.73886	+	6.08283i	−0.304159	+	0.322389i
$357$	−0.188504	+	0.428093i	−0.00997668	+	0.0226571i
$358$	−16.7817	−	1.96150i	−0.886940	−	0.103668i
$359$	−8.44791	+	7.08864i	−0.445864	+	0.374124i	−0.837898	−	0.545827i	$-0.816216\pi$
$359$	−8.44791	+	7.08864i	−0.445864	+	0.374124i	0.392035	+	0.919950i	$0.371771\pi$
$360$	−0.616050	+	1.95018i	−0.0324687	+	0.102784i
$361$	−13.7203	−	11.5127i	−0.722120	−	0.605931i
$362$	−16.9172	−	17.9312i	−0.889149	−	0.942443i
$363$	−5.53983	−	4.72013i	−0.290766	−	0.247743i
$364$	−4.34899	+	2.18415i	−0.227949	+	0.114480i
$365$	−1.01583	+	0.510167i	−0.0531707	+	0.0267033i
$366$	−7.64315	−	6.51224i	−0.399514	−	0.340400i
$367$	−11.6508	−	12.3492i	−0.608169	−	0.644621i	0.347980	−	0.937502i	$-0.386868\pi$
$367$	−11.6508	−	12.3492i	−0.608169	−	0.644621i	−0.956149	+	0.292881i	$0.905386\pi$
$368$	3.69668	+	3.10188i	0.192703	+	0.161697i
$369$	−7.56897	+	23.9605i	−0.394025	+	1.24733i
$370$	−3.08143	+	2.58563i	−0.160196	+	0.134421i
$371$	3.06124	+	0.357808i	0.158932	+	0.0185765i
$372$	0.00639417	−	0.0145212i	0.000331522	−	0.000752888i
$373$	11.9333	−	12.6486i	0.617885	−	0.654919i	−0.340552	−	0.940226i	$-0.610614\pi$
$373$	11.9333	−	12.6486i	0.617885	−	0.654919i	0.958436	+	0.285306i	$0.0920953\pi$
$374$	0.717502	−	0.0838639i	0.0371011	−	0.00433650i
$375$	−3.31039	+	10.7614i	−0.170948	+	0.555715i
$376$	0.537137	+	9.22229i	0.0277007	+	0.475603i
$377$	−4.06607	+	7.04264i	−0.209413	+	0.362714i
$378$	−2.11079	+	4.60402i	−0.108567	+	0.236805i
$379$	−6.65132	−	11.5204i	−0.341655	−	0.591764i	0.643085	−	0.765795i	$-0.277654\pi$
$379$	−6.65132	−	11.5204i	−0.341655	−	0.591764i	−0.984740	+	0.174030i	$0.944321\pi$
$380$	−0.594499	+	0.391008i	−0.0304971	+	0.0200583i
$381$	−25.8432	−	13.2240i	−1.32399	−	0.677484i
$382$	−6.12715	+	14.2043i	−0.313492	+	0.726756i
$383$	−11.0324	−	2.61472i	−0.563727	−	0.133606i	−0.0611349	−	0.998130i	$-0.519472\pi$
$383$	−11.0324	−	2.61472i	−0.563727	−	0.133606i	−0.502592	+	0.864524i	$0.667620\pi$
$384$	0.484228	+	1.66299i	0.0247107	+	0.0848639i
$385$	1.03460	−	1.38971i	0.0527281	−	0.0708261i
$386$	12.8879	+	4.69081i	0.655977	+	0.238756i
$387$	35.8930	+	0.541517i	1.82454	+	0.0275269i
$388$	14.8960	−	5.42169i	0.756229	−	0.275245i
$389$	3.15997	−	10.5550i	0.160217	−	0.535162i	−0.839753	−	0.542969i	$-0.817300\pi$
$389$	3.15997	−	10.5550i	0.160217	−	0.535162i	0.999970	+	0.00780729i	$0.00248516\pi$
$390$	5.52453	+	2.05809i	0.279745	+	0.104215i
$391$	0.0777403	−	1.33475i	0.00393150	−	0.0675012i
$392$	−5.05462	−	3.32448i	−0.255297	−	0.167912i
$393$	−15.3650	−	27.0826i	−0.775059	−	1.36614i
$394$	19.5317	−	4.62910i	0.983992	−	0.233210i
$395$	0.613585	−	3.47981i	0.0308728	−	0.175088i
$396$	7.78184	−	0.790768i	0.391052	−	0.0397376i
$397$	−6.90621	−	39.1671i	−0.346613	−	1.96574i	−0.235066	−	0.971980i	$-0.575531\pi$
$397$	−6.90621	−	39.1671i	−0.346613	−	1.96574i	−0.111547	−	0.993759i	$-0.535581\pi$
$398$	3.49305	+	8.09780i	0.175091	+	0.405906i
$399$	−1.58065	+	0.778957i	−0.0791313	+	0.0389966i
$400$	1.30073	+	4.34473i	0.0650363	+	0.217236i
$401$	5.35717	+	7.19593i	0.267524	+	0.359348i	0.915503	−	0.402311i	$-0.131793\pi$
$401$	5.35717	+	7.19593i	0.267524	+	0.359348i	−0.647979	+	0.761658i	$0.724385\pi$
$402$	22.0889	+	2.75087i	1.10169	+	0.137201i
$403$	−0.0408724	−	0.0205269i	−0.00203600	−	0.00102252i
$404$	−14.5466			−0.723720
$405$	5.82617	−	1.92358i	0.289505	−	0.0955837i
$406$	1.58760			0.0787911
$407$	13.7481	+	6.90454i	0.681467	+	0.342245i
$408$	0.289463	−	0.382755i	0.0143306	−	0.0189492i
$409$	2.31810	+	3.11375i	0.114623	+	0.153965i	0.855732	−	0.517419i	$-0.173107\pi$
$409$	2.31810	+	3.11375i	0.114623	+	0.153965i	−0.741109	+	0.671385i	$0.765700\pi$
$410$	−1.63765	−	5.47013i	−0.0808777	−	0.270150i
$411$	11.0339	+	7.37694i	0.544262	+	0.363878i
$412$	−3.16404	−	7.33508i	−0.155881	−	0.361373i
$413$	2.29856	+	13.0358i	0.113105	+	0.641450i
$414$	1.05969	−	14.4382i	0.0520808	−	0.709597i
$415$	−1.40496	+	7.96790i	−0.0689665	+	0.391129i
$416$	4.85825	−	1.15143i	0.238195	−	0.0564533i
$417$	−13.0079	−	0.0981198i	−0.637001	−	0.00480495i
$418$	2.27371	+	1.49544i	0.111211	+	0.0731444i
$419$	−0.356253	+	6.11664i	−0.0174041	+	0.298817i	0.978362	+	0.206899i	$0.0663370\pi$
$419$	−0.356253	+	6.11664i	−0.0174041	+	0.298817i	−0.995767	+	0.0919186i	$0.970700\pi$
$420$	−0.191303	−	1.13493i	−0.00933463	−	0.0553788i
$421$	−9.41492	+	31.4480i	−0.458855	+	1.53268i	0.345433	+	0.938443i	$0.387732\pi$
$421$	−9.41492	+	31.4480i	−0.458855	+	1.53268i	−0.804288	+	0.594239i	$0.797453\pi$
$422$	−0.298531	+	0.108656i	−0.0145323	+	0.00528931i
$423$	21.4963	−	17.4918i	1.04518	−	0.850479i
$424$	−2.97131	−	1.08147i	−0.144299	−	0.0525207i
$425$	0.750358	−	1.00791i	0.0363977	−	0.0488906i
$426$	4.31470	+	1.05704i	0.209048	+	0.0512137i
$427$	5.49849	+	1.30317i	0.266091	+	0.0630646i
$428$	3.74412	−	8.67985i	0.180979	−	0.419557i
$429$	−1.14120	−	22.5187i	−0.0550977	−	1.08721i
$430$	−6.81531	+	4.48250i	−0.328663	+	0.216165i
$431$	14.0661	+	24.3632i	0.677539	+	1.17353i	0.975720	+	0.219023i	$0.0702869\pi$
$431$	14.0661	+	24.3632i	0.677539	+	1.17353i	−0.298181	+	0.954509i	$0.596380\pi$
$432$	3.19644	−	4.09668i	0.153789	−	0.197102i
$433$	0.0327624	−	0.0567461i	0.00157446	−	0.00272704i	−0.865237	−	0.501363i	$-0.832832\pi$
$433$	0.0327624	−	0.0567461i	0.00157446	−	0.00272704i	0.866812	+	0.498636i	$0.166166\pi$
$434$	0.000519180		0.00891398i	2.49214e−5		0.000427885i
$435$	−1.30920	−	1.40881i	−0.0627712	−	0.0675471i
$436$	−4.42001	+	0.516625i	−0.211680	+	0.0247419i
$437$	3.45651	−	3.66368i	0.165347	−	0.175258i
$438$	2.87102	−	0.313641i	0.137183	−	0.0149864i
$439$	−26.2057	−	3.06301i	−1.25073	−	0.146190i	−0.535173	−	0.844742i	$-0.679754\pi$
$439$	−26.2057	−	3.06301i	−1.25073	−	0.146190i	−0.715558	+	0.698553i	$0.753828\pi$
$440$	−1.36161	+	1.14253i	−0.0649124	+	0.0544680i
$441$	0.781862	+	18.1329i	0.0372315	+	0.863470i
$442$	−1.05969	−	0.889185i	−0.0504043	−	0.0422942i
$443$	20.9284	+	22.1828i	0.994340	+	1.05394i	0.998544	+	0.0539475i	$0.0171804\pi$
$443$	20.9284	+	22.1828i	0.994340	+	1.05394i	−0.00420393	+	0.999991i	$0.501338\pi$
$444$	9.62976	−	3.42291i	0.457008	−	0.162444i
$445$	−5.09466	+	2.55864i	−0.241510	+	0.121291i
$446$	8.81243	−	4.42577i	0.417281	−	0.209566i
$447$	−4.36101	+	23.6864i	−0.206269	+	1.12033i
$448$	−0.668898	−	0.708990i	−0.0316024	−	0.0334966i
$449$	22.6326	+	18.9910i	1.06810	+	0.896241i	0.994879	−	0.101074i	$-0.0322280\pi$
$449$	22.6326	+	18.9910i	1.06810	+	0.896241i	0.0732200	+	0.997316i	$0.476672\pi$
$450$	8.28851	−	10.7897i	0.390724	−	0.508631i
$451$	−16.7292	+	14.0374i	−0.787746	+	0.660998i
$452$	−0.690282	−	0.0806824i	−0.0324681	−	0.00379498i
$453$	−9.67306	−	13.1999i	−0.454480	−	0.620185i
$454$	−11.1878	+	11.8583i	−0.525068	+	0.556539i
$455$	−3.29527	+	0.385162i	−0.154485	+	0.0180567i
$456$	1.76222	−	0.403639i	0.0825234	−	0.0189021i
$457$	−0.0172113	−	0.295507i	−0.000805111	−	0.0138232i	0.997882	−	0.0650550i	$-0.0207223\pi$
$457$	−0.0172113	−	0.295507i	−0.000805111	−	0.0138232i	−0.998687	+	0.0512318i	$0.983685\pi$
$458$	3.10725	−	5.38191i	0.145192	−	0.251480i
$459$	−1.43929	−	0.0325749i	−0.0671803	−	0.00152047i
$460$	1.64489	+	2.84903i	0.0766932	+	0.132836i
$461$	−23.5098	+	15.4627i	−1.09496	+	0.720168i	−0.962571	−	0.271030i	$-0.912636\pi$
$461$	−23.5098	+	15.4627i	−1.09496	+	0.720168i	−0.132391	+	0.991198i	$0.542265\pi$
$462$	−3.69583	+	2.39105i	−0.171946	+	0.111242i
$463$	−11.5483	+	26.7720i	−0.536696	+	1.24420i	0.407012	+	0.913423i	$0.366571\pi$
$463$	−11.5483	+	26.7720i	−0.536696	+	1.24420i	−0.943708	+	0.330779i	$0.892689\pi$
$464$	−1.58486	−	0.375618i	−0.0735752	−	0.0174376i
$465$	0.00748198	−	0.00781154i	0.000346968	−	0.000362251i
$466$	4.20017	−	5.64181i	0.194569	−	0.261352i
$467$	−24.2175	−	8.81443i	−1.12065	−	0.407883i	−0.285761	−	0.958301i	$-0.592246\pi$
$467$	−24.2175	−	8.81443i	−1.12065	−	0.407883i	−0.834889	+	0.550418i	$0.814469\pi$
$468$	−11.3277	−	9.79999i	−0.523621	−	0.453005i
$469$	−11.7713	+	4.28440i	−0.543548	+	0.197835i
$470$	−1.80620	+	6.03313i	−0.0833139	+	0.278288i
$471$	18.8020	−	15.5366i	0.866351	−	0.715889i
$472$	0.789613	−	13.5571i	0.0363449	−	0.624018i
$473$	26.0657	+	17.1437i	1.19850	+	0.788267i
$474$	−4.54728	+	7.74069i	−0.208864	+	0.355542i
$475$	4.60614	−	1.09168i	0.211344	−	0.0500895i
$476$	−0.0468954	+	0.265957i	−0.00214945	+	0.0121901i
$477$	2.58322	+	9.12750i	0.118277	+	0.417919i
$478$	0.634345	+	3.59755i	0.0290143	+	0.164548i
$479$	5.15165	+	11.9429i	0.235385	+	0.545683i	0.994435	−	0.105348i	$-0.0335958\pi$
$479$	5.15165	+	11.9429i	0.235385	+	0.545683i	−0.759051	+	0.651032i	$0.774337\pi$
$480$	−0.0775456	+	1.17823i	−0.00353946	+	0.0537786i
$481$	−8.44932	−	28.2227i	−0.385256	−	1.28684i
$482$	1.06051	+	1.42452i	0.0483050	+	0.0648849i
$483$	3.17037	+	7.50489i	0.144257	+	0.341484i
$484$	−3.75501	−	1.88584i	−0.170682	−	0.0857198i
$485$	10.8067			0.490705
$486$	−15.5774	−	0.587774i	−0.706604	−	0.0266620i
$487$	16.2711			0.737314			0.368657	−	0.929566i	$-0.379818\pi$
$487$	16.2711			0.737314			0.368657	+	0.929566i	$0.379818\pi$
$488$	−5.18068	−	2.60184i	−0.234518	−	0.117780i
$489$	15.2628	+	36.1300i	0.690206	+	1.63385i
$490$	−2.46290	−	3.30825i	−0.111262	−	0.149451i
$491$	8.17641	+	27.3111i	0.368996	+	1.23253i	0.917955	+	0.396684i	$0.129839\pi$
$491$	8.17641	+	27.3111i	0.368996	+	1.23253i	−0.548959	+	0.835849i	$0.684976\pi$
$492$	−0.952748	+	14.4761i	−0.0429532	+	0.652632i
$493$	0.178738	+	0.414362i	0.00804997	+	0.0186619i
$494$	−0.904940	−	5.13217i	−0.0407152	−	0.230907i
$495$	5.16951	+	1.30786i	0.232352	+	0.0587841i
$496$	0.00159072	−	0.00902144i	7.14256e−5	−	0.000405075i
$497$	−2.43255	+	0.576525i	−0.109115	+	0.0258607i
$498$	10.4121	−	17.7242i	0.466579	−	0.794242i
$499$	−2.61866	−	1.72232i	−0.117227	−	0.0771017i	0.489541	−	0.871980i	$-0.337164\pi$
$499$	−2.61866	−	1.72232i	−0.117227	−	0.0771017i	−0.606769	+	0.794878i	$0.707535\pi$
$500$	−0.377965	+	6.48941i	−0.0169031	+	0.290215i
$501$	11.1931	−	9.24919i	0.500073	−	0.413223i
$502$	−3.77398	+	12.6060i	−0.168441	+	0.562633i
$503$	13.0619	−	4.75415i	0.582403	−	0.211977i	−0.0339819	−	0.999422i	$-0.510819\pi$
$503$	13.0619	−	4.75415i	0.582403	−	0.211977i	0.616385	+	0.787445i	$0.288597\pi$
$504$	−0.551162	+	2.87177i	−0.0245507	+	0.127919i
$505$	−9.31870	−	3.39173i	−0.414677	−	0.150930i
$506$	7.51345	−	10.0923i	0.334013	−	0.448658i
$507$	−14.2911	+	14.9206i	−0.634690	+	0.662646i
$508$	−16.3087	−	3.86524i	−0.723582	−	0.171492i
$509$	−0.811521	+	1.88132i	−0.0359700	+	0.0833879i	−0.935254	−	0.353977i	$-0.884829\pi$
$509$	−0.811521	+	1.88132i	−0.0359700	+	0.0833879i	0.899284	+	0.437365i	$0.144088\pi$
$510$	0.274678	−	0.177705i	0.0121629	−	0.00786890i
$511$	−1.35792	+	0.893119i	−0.0600709	+	0.0395093i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−4.07474	−	3.57931i	−0.179904	−	0.158031i
$514$	−11.6847	+	20.2386i	−0.515392	+	0.892685i
$515$	−0.316650	−	5.43666i	−0.0139532	−	0.239568i
$516$	20.2020	−	4.62730i	0.889343	−	0.203706i
$517$	23.9232	−	2.79622i	1.05214	−	0.122978i
$518$	−3.94685	+	4.18342i	−0.173415	+	0.183809i
$519$	−20.3774	−	27.8070i	−0.894467	−	1.22059i
$520$	3.38072	+	0.395149i	0.148254	+	0.0173284i
$521$	16.3308	−	13.7032i	0.715467	−	0.600348i	−0.210660	−	0.977559i	$-0.567561\pi$
$521$	16.3308	−	13.7032i	0.715467	−	0.600348i	0.926127	+	0.377211i	$0.123117\pi$
$522$	1.86746	+	4.51535i	0.0817363	+	0.197632i
$523$	4.87547	+	4.09101i	0.213190	+	0.178887i	0.743129	−	0.669148i	$-0.233341\pi$
$523$	4.87547	+	4.09101i	0.213190	+	0.178887i	−0.529939	+	0.848036i	$0.677785\pi$
$524$	−12.3368	−	13.0762i	−0.538934	−	0.571237i
$525$	−1.38642	+	7.53019i	−0.0605083	+	0.328644i
$526$	−5.26475	+	2.64406i	−0.229554	+	0.115286i
$527$	−0.00226809	+	0.00113908i	−9.87997e−5	+	4.96191e-5i
$528$	4.25517	−	1.51251i	0.185182	−	0.0658233i
$529$	−0.197004	−	0.208812i	−0.00856540	−	0.00907879i
$530$	−1.65129	−	1.38560i	−0.0717276	−	0.0601866i
$531$	−34.3719	+	21.8712i	−1.49161	+	0.949128i
$532$	−0.779362	+	0.653962i	−0.0337896	+	0.0283529i
$533$	41.5364	+	4.85491i	1.79914	+	0.210290i
$534$	14.3990	−	1.57300i	0.623106	−	0.0680705i
$535$	4.42235	−	4.68741i	0.191195	−	0.202655i
$536$	12.7647	−	1.49197i	0.551349	−	0.0644435i
$537$	19.9215	+	21.4372i	0.859675	+	0.925083i
$538$	−0.980099	−	16.8277i	−0.0422551	−	0.725492i
$539$	−7.88698	+	13.6607i	−0.339716	+	0.588406i
$540$	3.00287	−	1.87908i	0.129223	−	0.0808628i
$541$	2.99347	+	5.18483i	0.128699	+	0.222913i	0.923173	−	0.384385i	$-0.125587\pi$
$541$	2.99347	+	5.18483i	0.128699	+	0.222913i	−0.794474	+	0.607299i	$0.792253\pi$
$542$	−18.7121	+	12.3071i	−0.803753	+	0.528637i
$543$	2.16110	+	42.6438i	0.0927418	+	1.83002i
$544$	0.109739	−	0.254403i	0.00470501	−	0.0109074i
$545$	−2.95196	−	0.699628i	−0.126448	−	0.0299688i
$546$	8.18717	+	2.00574i	0.350379	+	0.0858376i
$547$	3.01067	−	4.04404i	0.128727	−	0.172911i	−0.733087	−	0.680135i	$-0.761921\pi$
$547$	3.01067	−	4.04404i	0.128727	−	0.172911i	0.861814	+	0.507225i	$0.169329\pi$
$548$	7.20090	+	2.62091i	0.307607	+	0.111960i
$549$	2.76137	+	17.1714i	0.117852	+	0.732856i
$550$	11.1117	−	4.04432i	0.473803	−	0.172450i
$551$	−0.487578	+	1.62862i	−0.0207715	+	0.0693818i
$552$	−1.38928	−	8.24204i	−0.0591315	−	0.350804i
$553$	0.293758	−	5.04363i	0.0124919	−	0.214477i
$554$	−25.7469	−	16.9340i	−1.09388	−	0.719456i
$555$	6.96702	+	0.0525527i	0.295734	+	0.00223074i
$556$	−7.30791	+	1.73201i	−0.309924	+	0.0734534i
$557$	4.92319	−	27.9208i	0.208602	−	1.18304i	−0.683067	−	0.730355i	$-0.739354\pi$
$557$	4.92319	−	27.9208i	0.208602	−	1.18304i	0.891670	−	0.452687i	$-0.149534\pi$
$558$	−0.0247419	+	0.0119619i	−0.00104741	+	0.000506389i
$559$	−10.3742	−	58.8350i	−0.438782	−	2.48846i
$560$	−0.263192	−	0.610149i	−0.0111219	−	0.0257835i
$561$	−1.04015	−	0.695417i	−0.0439154	−	0.0293605i
$562$	3.27759	+	10.9479i	0.138257	+	0.461809i
$563$	22.8192	+	30.6514i	0.961713	+	1.29180i	0.956474	+	0.291818i	$0.0942603\pi$
$563$	22.8192	+	30.6514i	0.961713	+	1.29180i	0.00523909	+	0.999986i	$0.498332\pi$
$564$	9.65140	−	12.7620i	0.406397	−	0.537376i
$565$	−0.423390	−	0.212634i	−0.0178121	−	0.00894559i
$566$	5.29956			0.222757
$567$	7.95463	−	3.69882i	0.334063	−	0.155336i
$568$	2.56476			0.107615
$569$	3.30279	+	1.65872i	0.138460	+	0.0695373i	0.516680	−	0.856178i	$-0.327168\pi$
$569$	3.30279	+	1.65872i	0.138460	+	0.0695373i	−0.378220	+	0.925716i	$0.623464\pi$
$570$	1.22301	+	0.152309i	0.0512262	+	0.00637951i
$571$	−11.9989	−	16.1173i	−0.502137	−	0.674487i	0.476715	−	0.879058i	$-0.341827\pi$
$571$	−11.9989	−	16.1173i	−0.502137	−	0.674487i	−0.978852	+	0.204571i	$0.934420\pi$
$572$	−3.73356	−	12.4710i	−0.156108	−	0.521437i
$573$	24.0339	−	11.8441i	1.00403	−	0.494796i
$574$	−3.23366	−	7.49646i	−0.134970	−	0.312896i
$575$	−3.80040	−	21.5531i	−0.158488	−	0.898828i
$576$	1.22966	−	2.73641i	0.0512358	−	0.114017i
$577$	−4.54140	+	25.7556i	−0.189061	+	1.07222i	0.731565	+	0.681772i	$0.238790\pi$
$577$	−4.54140	+	25.7556i	−0.189061	+	1.07222i	−0.920626	+	0.390446i	$0.872321\pi$
$578$	16.4671	−	3.90277i	0.684940	−	0.162334i
$579$	−11.7220	−	20.6615i	−0.487151	−	0.858664i
$580$	−0.927697	−	0.610156i	−0.0385205	−	0.0253353i
$581$	−0.672632	+	11.5487i	−0.0279055	+	0.479119i
$582$	−25.7290	−	9.58499i	−1.06650	−	0.397311i
$583$	−2.36449	+	7.89795i	−0.0979273	+	0.327100i
$584$	1.56689	−	0.570300i	0.0648382	−	0.0235992i
$585$	−4.97161	−	8.91917i	−0.205551	−	0.368762i
$586$	29.6828	+	10.8037i	1.22619	+	0.446295i
$587$	−10.4529	+	14.0407i	−0.431439	+	0.579523i	−0.963677	−	0.267072i	$-0.913944\pi$
$587$	−10.4529	+	14.0407i	−0.431439	+	0.579523i	0.532238	+	0.846595i	$0.321351\pi$
$588$	2.92953	+	10.0609i	0.120812	+	0.414905i
$589$	−0.00930379	−	0.00220504i	−0.000383356	−	9.08570e-5i
$590$	3.66686	−	8.50073i	0.150962	−	0.349970i
$591$	−30.9504	−	15.8373i	−1.27313	−	0.651460i
$592$	4.92982	−	3.24239i	0.202614	−	0.133262i
$593$	−13.7463	−	23.8092i	−0.564491	−	0.977728i	−0.997097	−	0.0761445i	$-0.975739\pi$
$593$	−13.7463	−	23.8092i	−0.564491	−	0.977728i	0.432605	−	0.901583i	$-0.357594\pi$
$594$	−11.1478	−	7.69894i	−0.457400	−	0.315891i
$595$	−0.0920531	+	0.159441i	−0.00377381	+	0.00653643i
$596$	0.808514	+	13.8817i	0.0331180	+	0.568615i
$597$	4.49119	−	14.5999i	0.183812	−	0.597534i
$598$	−23.9308	+	2.79711i	−0.978605	+	0.114383i
$599$	0.159947	−	0.169534i	0.00653525	−	0.00692696i	−0.724098	−	0.689697i	$-0.757744\pi$
$599$	0.159947	−	0.169534i	0.00653525	−	0.00692696i	0.730633	+	0.682770i	$0.239225\pi$
$600$	3.16564	−	7.18918i	0.129237	−	0.293497i
$601$	12.0045	+	1.40313i	0.489675	+	0.0572348i	0.357348	−	0.933971i	$-0.383681\pi$
$601$	12.0045	+	1.40313i	0.489675	+	0.0572348i	0.132327	+	0.991206i	$0.457755\pi$
$602$	−8.93458	+	7.49700i	−0.364146	+	0.305555i
$603$	−26.0317	−	28.4396i	−1.06009	−	1.15815i
$604$	−7.23773	−	6.07318i	−0.294499	−	0.247114i
$605$	−1.96579	−	2.08361i	−0.0799207	−	0.0847110i
$606$	19.1781	+	16.3404i	0.779058	+	0.663785i
$607$	23.4296	−	11.7668i	0.950978	−	0.477599i	0.0954949	−	0.995430i	$-0.469557\pi$
$607$	23.4296	−	11.7668i	0.950978	−	0.477599i	0.855483	+	0.517831i	$0.173260\pi$
$608$	0.932742	−	0.468441i	0.0378277	−	0.0189978i
$609$	−2.09308	−	1.78338i	−0.0848157	−	0.0722660i
$610$	−2.71215	−	2.87471i	−0.109812	−	0.116393i
$611$	−35.3326	−	29.6475i	−1.42940	−	1.19941i
$612$	−0.811582	+	0.179462i	−0.0328063	+	0.00725434i
$613$	−29.4042	+	24.6730i	−1.18762	+	0.996535i	−0.187726	+	0.982221i	$0.560112\pi$
$613$	−29.4042	+	24.6730i	−1.18762	+	0.996535i	−0.999898	+	0.0143131i	$0.995444\pi$
$614$	−14.1312	−	1.65169i	−0.570287	−	0.0666570i
$615$	−3.98563	+	9.05138i	−0.160716	+	0.364987i
$616$	−1.74402	+	1.84855i	−0.0702686	+	0.0744804i
$617$	−2.77897	+	0.324815i	−0.111877	+	0.0130765i	−0.171847	−	0.985124i	$-0.554974\pi$
$617$	−2.77897	+	0.324815i	−0.111877	+	0.0130765i	0.0599702	+	0.998200i	$0.480899\pi$
$618$	−4.06817	+	13.2247i	−0.163646	+	0.531977i
$619$	−1.63200	−	28.0204i	−0.0655957	−	1.12624i	−0.857127	−	0.515106i	$-0.827753\pi$
$619$	−1.63200	−	28.0204i	−0.0655957	−	1.12624i	0.791531	−	0.611129i	$-0.209284\pi$
$620$	0.00312250	−	0.00540833i	0.000125403	−	0.000217204i
$621$	−17.6157	+	17.8448i	−0.706895	+	0.716087i
$622$	0.428828	+	0.742751i	0.0171944	+	0.0297816i
$623$	−6.81038	+	4.47925i	−0.272852	+	0.179458i
$624$	−7.69850	−	3.93932i	−0.308187	−	0.157699i
$625$	7.22639	−	16.7527i	0.289056	−	0.670106i
$626$	15.3577	+	3.63984i	0.613818	+	0.145477i
$627$	−1.31778	−	4.52567i	−0.0526272	−	0.180738i
$628$	8.40914	−	11.2954i	0.335561	−	0.450737i
$629$	−1.53622	−	0.559139i	−0.0612532	−	0.0222943i
$630$	−1.02267	+	1.71117i	−0.0407442	+	0.0681747i
$631$	11.4241	−	4.15805i	0.454788	−	0.165529i	−0.104461	−	0.994529i	$-0.533312\pi$
$631$	11.4241	−	4.15805i	0.454788	−	0.165529i	0.559249	+	0.829000i	$0.311090\pi$
$632$	−1.48655	+	4.96543i	−0.0591319	+	0.197514i
$633$	0.515637	+	0.192093i	0.0204947	+	0.00763502i
$634$	−1.11637	+	19.1673i	−0.0443366	+	0.761229i
$635$	−9.54630	−	6.27870i	−0.378833	−	0.249163i
$636$	2.70252	+	4.76352i	0.107162	+	0.188886i
$637$	29.3920	−	6.96603i	1.16455	−	0.276004i
$638$	−0.737428	+	4.18216i	−0.0291951	+	0.165573i
$639$	−4.50108	−	6.24036i	−0.178060	−	0.246865i
$640$	0.118380	+	0.671366i	0.00467938	+	0.0265381i
$641$	−16.2590	−	37.6927i	−0.642194	−	1.48877i	−0.858693	−	0.512490i	$-0.828723\pi$
$641$	−16.2590	−	37.6927i	−0.642194	−	1.48877i	0.216500	−	0.976283i	$-0.430536\pi$
$642$	−14.6865	+	7.23762i	−0.579628	+	0.285646i
$643$	9.89673	+	33.0574i	0.390289	+	1.30366i	0.897187	+	0.441650i	$0.145607\pi$
$643$	9.89673	+	33.0574i	0.390289	+	1.30366i	−0.506898	+	0.862006i	$0.669208\pi$
$644$	2.80886	+	3.77295i	0.110685	+	0.148675i
$645$	14.0205	+	1.74606i	0.552058	+	0.0687511i
$646$	−0.258428	−	0.129787i	−0.0101677	−	0.00510641i
$647$	−37.4511			−1.47236			−0.736178	−	0.676788i	$-0.763371\pi$
$647$	−37.4511			−1.47236			−0.736178	+	0.676788i	$0.763371\pi$
$648$	−8.81603	+	1.81041i	−0.346326	+	0.0711197i
$649$	−35.4075			−1.38987
$650$	−20.2352	−	10.1625i	−0.793690	−	0.398606i
$651$	0.00932874	−	0.0123353i	0.000365622	−	0.000483460i
$652$	13.5224	+	18.1637i	0.529578	+	0.711346i
$653$	−12.3198	−	41.1511i	−0.482112	−	1.61037i	−0.760116	−	0.649787i	$-0.774858\pi$
$653$	−12.3198	−	41.1511i	−0.482112	−	1.61037i	0.278004	−	0.960580i	$-0.410327\pi$
$654$	6.40764	+	4.28396i	0.250559	+	0.167516i
$655$	−4.85417	−	11.2532i	−0.189668	−	0.439700i
$656$	1.45445	+	8.24860i	0.0567868	+	0.322054i
$657$	−4.13745	−	2.81156i	−0.161417	−	0.109690i
$658$	−1.56360	+	8.86764i	−0.0609557	+	0.345697i
$659$	18.1944	−	4.31214i	0.708752	−	0.167977i	0.139598	−	0.990208i	$-0.455419\pi$
$659$	18.1944	−	4.31214i	0.708752	−	0.167977i	0.569154	+	0.822231i	$0.307271\pi$
$660$	3.07857	+	0.0232218i	0.119833	+	0.000903909i
$661$	−16.6117	−	10.9257i	−0.646121	−	0.424961i	0.183706	−	0.982981i	$-0.441191\pi$
$661$	−16.6117	−	10.9257i	−0.646121	−	0.424961i	−0.829827	+	0.558021i	$0.811561\pi$
$662$	0.774048	−	13.2899i	0.0300842	−	0.516526i
$663$	0.398250	+	2.36266i	0.0154667	+	0.0917582i
$664$	3.40383	−	11.3696i	0.132094	−	0.441226i
$665$	−0.651747	+	0.237217i	−0.0252737	+	0.00919887i
$666$	−16.5408	−	6.30454i	−0.640944	−	0.244296i
$667$	7.38586	+	2.68823i	0.285982	+	0.104089i
$668$	5.00610	−	6.72435i	0.193692	−	0.260173i
$669$	−16.5898	−	4.06426i	−0.641398	−	0.157133i
$670$	8.52504	+	2.02047i	0.329351	+	0.0780576i
$671$	−5.98691	+	13.8792i	−0.231122	+	0.535801i
$672$	0.0854488	+	1.68611i	0.00329626	+	0.0650432i
$673$	16.3598	−	10.7600i	0.630622	−	0.414767i	−0.193562	−	0.981088i	$-0.562004\pi$
$673$	16.3598	−	10.7600i	0.630622	−	0.414767i	0.824185	+	0.566321i	$0.191634\pi$
$674$	6.91813	+	11.9826i	0.266477	+	0.461551i
$675$	−23.0477	+	4.91442i	−0.887108	+	0.189156i
$676$	−5.96419	+	10.3303i	−0.229392	+	0.397319i
$677$	1.11217	+	19.0953i	0.0427443	+	0.733891i	0.949796	+	0.312871i	$0.101291\pi$
$677$	1.11217	+	19.0953i	0.0427443	+	0.733891i	−0.907051	+	0.421020i	$0.861672\pi$
$678$	0.819431	+	0.881777i	0.0314700	+	0.0338644i
$679$	15.3469	−	1.79379i	0.588958	−	0.0688394i
$680$	0.129617	−	0.137386i	0.00497059	−	0.00526852i
$681$	28.0705	−	3.06653i	1.07567	−	0.117510i
$682$	−0.0237230	−	0.00277282i	−0.000908401	−	0.000106177i
$683$	15.2990	−	12.8374i	0.585399	−	0.491208i	−0.301316	−	0.953524i	$-0.597426\pi$
$683$	15.2990	−	12.8374i	0.585399	−	0.491208i	0.886715	+	0.462316i	$0.152981\pi$
$684$	−2.77671	−	1.44737i	−0.106170	−	0.0553417i
$685$	4.00187	+	3.35797i	0.152904	+	0.128301i
$686$	−8.72905	−	9.25226i	−0.333277	−	0.353253i
$687$	−10.1422	+	3.60505i	−0.386948	+	0.137541i
$688$	10.6929	−	5.37019i	0.407664	−	0.204736i
$689$	14.1081	−	7.08535i	0.537475	−	0.269930i
$690$	1.03175	−	5.60386i	0.0392782	−	0.213335i
$691$	4.83484	+	5.12463i	0.183926	+	0.194950i	0.812776	−	0.582577i	$-0.197955\pi$
$691$	4.83484	+	5.12463i	0.183926	+	0.194950i	−0.628850	+	0.777527i	$0.716474\pi$
$692$	−15.2471	−	12.7938i	−0.579607	−	0.486348i
$693$	7.55846	+	0.999254i	0.287122	+	0.0379585i
$694$	−1.33549	+	1.12061i	−0.0506945	+	0.0425377i
$695$	−5.08536	−	0.594394i	−0.192899	−	0.0225466i
$696$	1.66753	+	2.27551i	0.0632074	+	0.0862530i
$697$	1.59251	−	1.68797i	0.0603208	−	0.0639363i
$698$	9.53171	−	1.11410i	0.360781	−	0.0421692i
$699$	−11.8750	+	2.71999i	−0.449154	+	0.102880i
$700$	0.257037	+	4.41315i	0.00971508	+	0.166801i
$701$	−9.39432	+	16.2714i	−0.354818	+	0.614563i	−0.987087	−	0.160186i	$-0.948791\pi$
$701$	−9.39432	+	16.2714i	−0.354818	+	0.614563i	0.632268	+	0.774749i	$0.282124\pi$
$702$	3.92579	+	25.6448i	0.148169	+	0.967900i
$703$	−3.07938	−	5.33364i	−0.116141	−	0.201162i
$704$	2.17837	−	1.43274i	0.0821005	−	0.0539983i
$705$	9.15841	−	5.92510i	0.344926	−	0.223152i
$706$	4.34574	−	10.0746i	0.163554	−	0.379161i
$707$	−13.7968	−	3.26989i	−0.518880	−	0.122977i
$708$	−16.2700	+	16.9866i	−0.611463	+	0.638397i
$709$	15.6720	−	21.0512i	0.588574	−	0.790593i	−0.403669	−	0.914905i	$-0.632265\pi$
$709$	15.6720	−	21.0512i	0.588574	−	0.790593i	0.992243	+	0.124313i	$0.0396726\pi$
$710$	1.64301	+	0.598007i	0.0616611	+	0.0224428i
$711$	14.6903	−	5.09723i	0.550931	−	0.191161i
$712$	7.85840	−	2.86022i	0.294506	−	0.107191i
$713$	−0.0126784	+	0.0423489i	−0.000474811	+	0.00158598i
$714$	0.360581	−	0.297957i	0.0134944	−	0.0111508i
$715$	0.516010	−	8.85955i	0.0192977	−	0.331329i
$716$	14.1163	+	9.28447i	0.527553	+	0.346977i
$717$	3.20487	−	5.45555i	0.119688	−	0.203741i
$718$	10.7307	−	2.54322i	0.400466	−	0.0949122i
$719$	4.61192	−	26.1555i	0.171996	−	0.975436i	−0.769559	−	0.638576i	$-0.779524\pi$
$719$	4.61192	−	26.1555i	0.171996	−	0.975436i	0.941555	−	0.336860i	$-0.109365\pi$
$720$	1.42576	−	1.46626i	0.0531350	−	0.0546443i
$721$	−1.35211	−	7.66821i	−0.0503553	−	0.285579i
$722$	7.09401	+	16.4458i	0.264012	+	0.612048i
$723$	0.202011	−	3.06936i	0.00751288	−	0.114151i
$724$	7.07027	+	23.6163i	0.262764	+	0.877694i
$725$	4.41112	+	5.92516i	0.163825	+	0.220055i
$726$	2.83218	+	6.70433i	0.105112	+	0.248821i
$727$	33.4417	+	16.7951i	1.24028	+	0.622894i	0.943285	−	0.331983i	$-0.107718\pi$
$727$	33.4417	+	16.7951i	1.24028	+	0.622894i	0.296999	+	0.954878i	$0.404014\pi$
$728$	4.86665			0.180370
$729$	19.8768	+	18.2732i	0.736179	+	0.676787i
$730$	1.13674			0.0420725
$731$	−2.96261	−	1.48788i	−0.109576	−	0.0550311i
$732$	3.90748	+	9.24979i	0.144425	+	0.341882i
$733$	28.2887	+	37.9983i	1.04487	+	1.40350i	0.910954	+	0.412507i	$0.135347\pi$
$733$	28.2887	+	37.9983i	1.04487	+	1.40350i	0.133913	+	0.990993i	$0.457246\pi$
$734$	4.86927	+	16.2645i	0.179728	+	0.600334i
$735$	−0.469144	+	7.12819i	−0.0173046	+	0.262927i
$736$	−1.91135	−	4.43101i	−0.0704533	−	0.163329i
$737$	−5.81859	−	32.9989i	−0.214330	−	1.21553i
$738$	17.5173	−	18.0149i	0.644821	−	0.663138i
$739$	−7.64685	+	43.3675i	−0.281294	+	1.59530i	0.436936	+	0.899492i	$0.356063\pi$
$739$	−7.64685	+	43.3675i	−0.281294	+	1.59530i	−0.718230	+	0.695805i	$0.755048\pi$
$740$	3.91410	−	0.927658i	0.143885	−	0.0341014i
$741$	−4.57199	+	7.78275i	−0.167956	+	0.285907i
$742$	−2.57504	−	1.69363i	−0.0945328	−	0.0621752i
$743$	−0.933379	+	16.0255i	−0.0342423	+	0.587918i	0.936927	+	0.349526i	$0.113657\pi$
$743$	−0.933379	+	16.0255i	−0.0342423	+	0.587918i	−0.971169	+	0.238392i	$0.923380\pi$
$744$	−0.0122311	+	0.0101069i	−0.000448415	+	0.000370537i
$745$	−2.71875	+	9.08125i	−0.0996072	+	0.332711i
$746$	−16.3407	+	5.94753i	−0.598275	+	0.217754i
$747$	−33.6372	+	11.6714i	−1.23072	+	0.427033i
$748$	−0.678821	−	0.247071i	−0.0248202	−	0.00903380i
$749$	5.50224	−	7.39080i	0.201048	−	0.270054i
$750$	7.78797	−	8.13101i	0.284376	−	0.296903i
$751$	34.4012	+	8.15324i	1.25532	+	0.297516i	0.803883	−	0.594787i	$-0.202764\pi$
$751$	34.4012	+	8.15324i	1.25532	+	0.297516i	0.451436	+	0.892304i	$0.350912\pi$
$752$	3.65895	−	8.48240i	0.133428	−	0.309321i
$753$	19.1361	−	12.3803i	0.697359	−	0.451162i
$754$	6.79430	−	4.46868i	0.247434	−	0.162740i
$755$	−3.22053	−	5.57811i	−0.117207	−	0.203008i
$756$	3.95255	−	3.16698i	0.143753	−	0.115182i
$757$	−25.8210	+	44.7233i	−0.938480	+	1.62549i	−0.170171	+	0.985414i	$0.554432\pi$
$757$	−25.8210	+	44.7233i	−0.938480	+	1.62549i	−0.768308	+	0.640080i	$0.778901\pi$
$758$	0.773480	+	13.2801i	0.0280941	+	0.482356i
$759$	−21.2425	+	4.86564i	−0.771055	+	0.176612i
$760$	0.706748	−	0.0826069i	0.0256364	−	0.00299647i
$761$	21.8017	−	23.1085i	0.790311	−	0.837681i	−0.199525	−	0.979893i	$-0.563940\pi$
$761$	21.8017	−	23.1085i	0.790311	−	0.837681i	0.989836	+	0.142212i	$0.0454214\pi$
$762$	17.1594	+	23.4158i	0.621619	+	0.848263i
$763$	−4.30830	−	0.503568i	−0.155971	−	0.0182304i
$764$	11.8503	−	9.94359i	0.428729	−	0.359746i
$765$	−0.561752	−	0.0742655i	−0.0203102	−	0.00268507i
$766$	8.68539	+	7.28790i	0.313816	+	0.263323i
$767$	46.5294	+	49.3183i	1.68008	+	1.78078i
$768$	0.313625	−	1.70342i	0.0113170	−	0.0614669i
$769$	−26.0622	+	13.0889i	−0.939827	+	0.471999i	−0.851653	−	0.524106i	$-0.824399\pi$
$769$	−26.0622	+	13.0889i	−0.939827	+	0.471999i	−0.0881740	+	0.996105i	$0.528103\pi$
$770$	−1.54825	+	0.777562i	−0.0557951	+	0.0280214i
$771$	38.1394	−	13.5567i	1.37356	−	0.488233i
$772$	−9.41181	−	9.97594i	−0.338739	−	0.359042i
$773$	−25.1297	−	21.0863i	−0.903851	−	0.758421i	0.0670881	−	0.997747i	$-0.478629\pi$
$773$	−25.1297	−	21.0863i	−0.903851	−	0.758421i	−0.970939	+	0.239326i	$0.923074\pi$
$774$	−31.8321	−	16.5926i	−1.14418	−	0.596410i
$775$	−0.0318258	+	0.0267050i	−0.00114322	+	0.000959274i
$776$	−15.7448	−	1.84030i	−0.565205	−	0.0660630i
$777$	9.90280	−	1.08182i	0.355261	−	0.0388101i
$778$	−7.56095	+	8.01414i	−0.271073	+	0.287321i
$779$	8.68330	−	1.01493i	0.311112	−	0.0363637i
$780$	−4.01323	−	4.31858i	−0.143697	−	0.154630i
$781$	−0.388821	−	6.67579i	−0.0139131	−	0.238879i
$782$	−0.668506	+	1.15789i	−0.0239057	+	0.0414059i
$783$	2.61013	−	8.05075i	0.0932785	−	0.287710i
$784$	3.02495	+	5.23937i	0.108034	+	0.187121i
$785$	8.02066	−	5.27527i	0.286270	−	0.188283i
$786$	1.57597	+	31.0977i	0.0562130	+	1.10922i
$787$	9.80264	−	22.7251i	0.349426	−	0.810061i	−0.649345	−	0.760494i	$-0.724957\pi$
$787$	9.80264	−	22.7251i	0.349426	−	0.810061i	0.998771	−	0.0495668i	$-0.0157841\pi$
$788$	−19.5317	−	4.62910i	−0.695788	−	0.164905i
$789$	9.91112	+	2.42808i	0.352845	+	0.0864419i
$790$	−2.11006	+	2.83430i	−0.0750724	+	0.100840i
$791$	−0.636563	−	0.231690i	−0.0226336	−	0.00823795i
$792$	−7.30900	−	2.78583i	−0.259714	−	0.0989901i
$793$	27.1995	−	9.89981i	0.965882	−	0.351552i
$794$	−11.4065	+	38.1005i	−0.404803	+	1.35214i
$795$	0.620584	+	3.68169i	0.0220099	+	0.130576i
$796$	0.512783	−	8.80414i	0.0181751	−	0.312054i
$797$	−22.0421	−	14.4973i	−0.780771	−	0.513521i	0.0954478	−	0.995434i	$-0.469572\pi$
$797$	−22.0421	−	14.4973i	−0.780771	−	0.513521i	−0.876219	+	0.481913i	$0.839942\pi$
$798$	1.76211	+	0.0132917i	0.0623781	+	0.000470522i
$799$	−2.49049	+	0.590257i	−0.0881071	+	0.0208818i
$800$	0.787538	−	4.46635i	0.0278437	−	0.157909i
$801$	−20.7505	−	14.1008i	−0.733184	−	0.498228i
$802$	−1.55782	−	8.83481i	−0.0550084	−	0.311968i
$803$	−1.72197	−	3.99198i	−0.0607671	−	0.140874i
$804$	−18.5048	−	12.3717i	−0.652613	−	0.436318i
$805$	0.919671	+	3.07191i	0.0324141	+	0.108271i
$806$	0.0273125	+	0.0366870i	0.000962041	+	0.00129225i
$807$	−17.6106	+	23.2864i	−0.619924	+	0.819720i
$808$	12.9993	+	6.52850i	0.457314	+	0.229672i
$809$	10.8987			0.383176			0.191588	−	0.981475i	$-0.438636\pi$
$809$	10.8987			0.383176			0.191588	+	0.981475i	$0.438636\pi$
$810$	−6.06976	−	0.895804i	−0.213270	−	0.0314754i
$811$	−17.2405			−0.605397			−0.302699	−	0.953086i	$-0.597888\pi$
$811$	−17.2405			−0.605397			−0.302699	+	0.953086i	$0.597888\pi$
$812$	−1.41873	−	0.712512i	−0.0497876	−	0.0250043i
$813$	38.4947	+	4.79398i	1.35007	+	0.168132i
$814$	−9.18697	−	12.3402i	−0.322003	−	0.432525i
$815$	4.42747	+	14.7888i	0.155088	+	0.518029i
$816$	−0.430454	+	0.212132i	−0.0150689	+	0.00742609i
$817$	−4.94678	−	11.4679i	−0.173066	−	0.401212i
$818$	−0.674083	−	3.82292i	−0.0235688	−	0.133665i
$819$	−8.54082	−	11.8411i	−0.298441	−	0.413763i
$820$	−0.991533	+	5.62326i	−0.0346258	+	0.196373i
$821$	−47.3916	+	11.2320i	−1.65398	+	0.392000i	−0.948512	−	0.316742i	$-0.897411\pi$
$821$	−47.3916	+	11.2320i	−1.65398	+	0.392000i	−0.705468	+	0.708742i	$0.749263\pi$
$822$	−6.54949	−	11.5443i	−0.228440	−	0.402653i
$823$	26.3696	+	17.3436i	0.919186	+	0.604558i	0.918491	−	0.395441i	$-0.129408\pi$
$823$	26.3696	+	17.3436i	0.919186	+	0.604558i	0.000695173		1.00000i	$0.499779\pi$
$824$	−0.464484	+	7.97488i	−0.0161811	+	0.277818i
$825$	−19.1926	−	7.14993i	−0.668200	−	0.248929i
$826$	3.79638	−	12.6808i	0.132093	−	0.441222i
$827$	−10.8079	+	3.93377i	−0.375829	+	0.136791i	−0.523026	−	0.852317i	$-0.675197\pi$
$827$	−10.8079	+	3.93377i	−0.375829	+	0.136791i	0.147197	+	0.989107i	$0.452975\pi$
$828$	−7.42681	+	12.4268i	−0.258099	+	0.431862i
$829$	14.8843	+	5.41744i	0.516953	+	0.188155i	0.587303	−	0.809367i	$-0.300190\pi$
$829$	14.8843	+	5.41744i	0.516953	+	0.188155i	−0.0703505	+	0.997522i	$0.522412\pi$
$830$	4.83150	−	6.48983i	0.167704	−	0.225265i
$831$	14.9222	+	51.2476i	0.517647	+	1.77776i
$832$	−4.85825	−	1.15143i	−0.168430	−	0.0399185i
$833$	0.663910	−	1.53912i	0.0230031	−	0.0533272i
$834$	11.5803	+	5.92563i	0.400992	+	0.205188i
$835$	4.77483	−	3.14045i	0.165240	−	0.108680i
$836$	−1.36071	−	2.35681i	−0.0470610	−	0.0815121i
$837$	0.0460566	+	0.0120225i	0.00159195	+	0.000415558i
$838$	3.06350	−	5.30614i	0.105827	−	0.183298i
$839$	−1.17284	−	20.1368i	−0.0404908	−	0.695201i	−0.956084	−	0.293094i	$-0.905315\pi$
$839$	−1.17284	−	20.1368i	−0.0404908	−	0.695201i	0.915593	−	0.402107i	$-0.131722\pi$
$840$	−0.338400	+	1.10006i	−0.0116759	+	0.0379558i
$841$	26.1690	−	3.05872i	0.902379	−	0.105473i
$842$	22.5273	−	23.8776i	0.776343	−	0.822875i
$843$	7.97682	−	18.1154i	0.274736	−	0.623928i
$844$	0.315542	+	0.0368816i	0.0108614	+	0.00126952i
$845$	−6.22937	+	5.22706i	−0.214297	+	0.179816i
$846$	−27.0601	+	5.98370i	−0.930344	+	0.205724i
$847$	−3.13753	−	2.63270i	−0.107807	−	0.0904607i
$848$	2.16990	+	2.29996i	0.0745145	+	0.0789808i
$849$	−6.98690	−	5.95309i	−0.239790	−	0.204310i
$850$	−1.12289	+	0.563938i	−0.0385149	+	0.0193429i
$851$	−25.4453	+	12.7791i	−0.872253	+	0.438062i
$852$	−3.38136	−	2.88104i	−0.115843	−	0.0987027i
$853$	22.4383	+	23.7833i	0.768274	+	0.814323i	0.986874	−	0.161492i	$-0.0516305\pi$
$853$	22.4383	+	23.7833i	0.768274	+	0.814323i	−0.218600	+	0.975815i	$0.570149\pi$
$854$	−4.32877	−	3.63227i	−0.148127	−	0.124294i
$855$	−1.44131	−	1.57463i	−0.0492919	−	0.0538512i
$856$	−7.24138	+	6.07624i	−0.247505	+	0.207682i
$857$	−0.168627	−	0.0197097i	−0.00576019	−	0.000673270i	0.113212	−	0.993571i	$-0.463886\pi$
$857$	−0.168627	−	0.0197097i	−0.00576019	−	0.000673270i	−0.118973	+	0.992898i	$0.537960\pi$
$858$	−9.08654	+	20.6356i	−0.310210	+	0.704487i
$859$	−21.1604	+	22.4287i	−0.721983	+	0.765257i	−0.979593	−	0.200992i	$-0.935584\pi$
$859$	−21.1604	+	22.4287i	−0.721983	+	0.765257i	0.257610	+	0.966249i	$0.417065\pi$
$860$	8.10213	−	0.947003i	0.276280	−	0.0322925i
$861$	−4.15767	+	13.5157i	−0.141693	+	0.460614i
$862$	−1.63574	−	28.0846i	−0.0557135	−	0.956564i
$863$	−3.21440	+	5.56751i	−0.109419	+	0.189520i	−0.915535	−	0.402238i	$-0.868233\pi$
$863$	−3.21440	+	5.56751i	−0.109419	+	0.189520i	0.806116	+	0.591758i	$0.201566\pi$
$864$	−4.69503	+	2.22637i	−0.159728	+	0.0757425i
$865$	−6.78439	−	11.7509i	−0.230676	−	0.399543i
$866$	−0.0547451	+	0.0360064i	−0.00186032	+	0.00122355i
$867$	−26.0941	−	13.3524i	−0.886202	−	0.453470i
$868$	0.00353663	−	0.00819883i	0.000120041	−	0.000278286i
$869$	13.1499	+	3.11657i	0.446078	+	0.105722i
$870$	0.537670	+	1.84652i	0.0182287	+	0.0626030i
$871$	−38.3171	+	51.4688i	−1.29832	+	1.74395i
$872$	4.18173	+	1.52202i	0.141611	+	0.0515422i
$873$	23.1540	+	41.5386i	0.783643	+	1.40587i
$874$	−4.73310	+	1.72271i	−0.160100	+	0.0582715i
$875$	−1.81722	+	6.06993i	−0.0614332	+	0.205201i
$876$	−2.70640	−	1.00823i	−0.0914408	−	0.0340650i
$877$	0.562610	−	9.65963i	0.0189980	−	0.326183i	−0.975397	−	0.220455i	$-0.929246\pi$
$877$	0.562610	−	9.65963i	0.0189980	−	0.326183i	0.994395	−	0.105728i	$-0.0337172\pi$
$878$	22.0436	+	14.4983i	0.743936	+	0.489295i
$879$	−26.9977	−	47.5867i	−0.910609	−	1.60506i
$880$	1.72955	−	0.409911i	0.0583031	−	0.0138181i
$881$	−0.142708	+	0.809340i	−0.00480797	+	0.0272674i	−0.987117	−	0.159998i	$-0.948851\pi$
$881$	−0.142708	+	0.809340i	−0.00480797	+	0.0272674i	0.982309	+	0.187265i	$0.0599624\pi$
$882$	7.43932	−	16.5550i	0.250495	−	0.557437i
$883$	−3.50111	−	19.8558i	−0.117822	−	0.668200i	−0.985314	−	0.170750i	$-0.945381\pi$
$883$	−3.50111	−	19.8558i	−0.117822	−	0.668200i	0.867493	−	0.497450i	$-0.165730\pi$
$884$	0.547908	+	1.27019i	0.0184281	+	0.0427212i
$885$	−14.3834	+	7.08826i	−0.483492	+	0.238269i
$886$	−8.74669	−	29.2160i	−0.293851	−	0.981530i
$887$	−11.3035	−	15.1832i	−0.379533	−	0.509801i	0.570778	−	0.821105i	$-0.306642\pi$
$887$	−11.3035	−	15.1832i	−0.379533	−	0.509801i	−0.950311	+	0.311303i	$0.899234\pi$
$888$	−10.1417	−	1.26300i	−0.340332	−	0.0423836i
$889$	−14.5992	−	7.33198i	−0.489641	−	0.245907i
$890$	5.70107			0.191100
$891$	6.04883	+	22.6727i	0.202644	+	0.759565i
$892$	−9.86136			−0.330183
$893$	−8.61660	−	4.32742i	−0.288343	−	0.144811i
$894$	14.5276	−	19.2097i	0.485874	−	0.642468i
$895$	6.87828	+	9.23914i	0.229916	+	0.308830i
$896$	0.279555	+	0.933778i	0.00933927	+	0.0311953i
$897$	34.6923	+	23.1942i	1.15834	+	0.774433i
$898$	−11.7021	−	27.1285i	−0.390504	−	0.905289i
$899$	−0.00259091	−	0.0146938i	−8.64117e−5	−	0.000490065i
$900$	−12.2493	+	5.92214i	−0.408309	+	0.197405i
$901$	0.152128	−	0.862762i	0.00506812	−	0.0287428i
$902$	21.2497	−	5.03628i	0.707539	−	0.167690i
$903$	20.2008	+	0.152376i	0.672240	+	0.00507076i
$904$	0.580648	+	0.381898i	0.0193121	+	0.0127018i
$905$	−0.977172	+	16.7774i	−0.0324823	+	0.557700i
$906$	2.72007	+	16.1371i	0.0903681	+	0.536119i
$907$	7.55127	−	25.2230i	0.250736	−	0.837516i	−0.736250	−	0.676710i	$-0.763405\pi$
$907$	7.55127	−	25.2230i	0.250736	−	0.837516i	0.986986	−	0.160807i	$-0.0514095\pi$
$908$	15.3198	−	5.57594i	0.508404	−	0.185044i
$909$	−6.92879	−	43.0862i	−0.229813	−	1.42908i
$910$	3.11762	+	1.13472i	0.103348	+	0.0376157i
$911$	−1.56795	+	2.10612i	−0.0519486	+	0.0697790i	−0.827338	−	0.561704i	$-0.810146\pi$
$911$	−1.56795	+	2.10612i	−0.0519486	+	0.0697790i	0.775390	+	0.631483i	$0.217553\pi$
$912$	−1.75593	−	0.430177i	−0.0581446	−	0.0142446i
$913$	−30.1099	−	7.13617i	−0.996491	−	0.236173i
$914$	−0.117243	+	0.271799i	−0.00387804	+	0.00899031i
$915$	0.346465	+	6.83659i	0.0114538	+	0.226011i
$916$	−5.19214	+	3.41492i	−0.171553	+	0.112832i
$917$	−8.76147	−	15.1753i	−0.289329	−	0.501133i
$918$	1.27158	+	0.675062i	0.0419683	+	0.0222804i
$919$	−2.52799	+	4.37860i	−0.0833906	+	0.144437i	−0.904704	−	0.426040i	$-0.859908\pi$
$919$	−2.52799	+	4.37860i	−0.0833906	+	0.144437i	0.821314	+	0.570477i	$0.193242\pi$
$920$	−0.191283	−	3.28421i	−0.00630642	−	0.108277i
$921$	16.7750	+	18.0513i	0.552756	+	0.594812i
$922$	27.9488	−	3.26674i	0.920444	−	0.107584i
$923$	−8.78760	+	9.31432i	−0.289248	+	0.306584i
$924$	4.37582	−	0.478031i	0.143954	−	0.0157261i
$925$	−26.5794	−	3.10669i	−0.873927	−	0.102147i
$926$	22.3352	−	18.7415i	0.733981	−	0.615883i
$927$	20.2190	−	12.8655i	0.664079	−	0.422560i
$928$	1.24770	+	1.04695i	0.0409579	+	0.0343678i
$929$	20.5881	+	21.8221i	0.675473	+	0.715959i	0.970921	−	0.239399i	$-0.0769505\pi$
$929$	20.5881	+	21.8221i	0.675473	+	0.715959i	−0.295448	+	0.955359i	$0.595469\pi$
$930$	−0.0101919	+	0.00362274i	−0.000334207	+	0.000118794i
$931$	5.64301	−	2.83402i	0.184942	−	0.0928814i
$932$	−6.28545	+	3.15667i	−0.205887	+	0.103400i
$933$	0.268982	−	1.46095i	0.00880608	−	0.0478293i
$934$	17.6856	+	18.7456i	0.578690	+	0.613376i
$935$	−0.377252	−	0.316552i	−0.0123375	−	0.0103524i
$936$	5.72453	+	13.8414i	0.187112	+	0.452421i
$937$	−13.2012	+	11.0771i	−0.431264	+	0.361874i	−0.832429	−	0.554132i	$-0.813050\pi$
$937$	−13.2012	+	11.0771i	−0.431264	+	0.361874i	0.401164	+	0.916006i	$0.368606\pi$
$938$	12.4420	+	1.45427i	0.406247	+	0.0474835i
$939$	−16.1588	−	22.0503i	−0.527322	−	0.719585i
$940$	4.32175	−	4.58078i	0.140960	−	0.149409i
$941$	54.8351	−	6.40930i	1.78757	−	0.208937i	0.843152	−	0.537676i	$-0.180698\pi$
$941$	54.8351	−	6.40930i	1.78757	−	0.208937i	0.944421	+	0.328739i	$0.106624\pi$
$942$	−23.7749	+	5.44568i	−0.774628	+	0.177430i
$943$	−2.35016	−	40.3507i	−0.0765317	−	1.31400i
$944$	−6.79006	+	11.7607i	−0.220998	+	0.382779i
$945$	3.27047	−	1.10721i	0.106388	−	0.0360177i
$946$	−15.5991	−	27.0184i	−0.507170	−	0.878445i
$947$	−13.3009	+	8.74814i	−0.432221	+	0.284276i	−0.746918	−	0.664916i	$-0.768467\pi$
$947$	−13.3009	+	8.74814i	−0.432221	+	0.284276i	0.314697	+	0.949192i	$0.398097\pi$
$948$	7.53761	−	4.87652i	0.244810	−	0.158382i
$949$	−3.29748	+	7.64441i	−0.107041	+	0.248148i
$950$	−4.60614	−	1.09168i	−0.149443	−	0.0354186i
$951$	23.0027	−	24.0159i	0.745914	−	0.778770i
$952$	0.161269	−	0.216621i	0.00522675	−	0.00702074i
$953$	38.2836	+	13.9341i	1.24013	+	0.451369i	0.877054	−	0.480391i	$-0.159505\pi$
$953$	38.2836	+	13.9341i	1.24013	+	0.451369i	0.363073	+	0.931761i	$0.381728\pi$
$954$	1.78796	−	9.31597i	0.0578875	−	0.301616i
$955$	9.90991	−	3.60691i	0.320677	−	0.116717i
$956$	1.04771	−	3.49958i	0.0338852	−	0.113185i
$957$	5.67012	−	4.68537i	0.183289	−	0.151456i
$958$	0.756266	−	12.9846i	0.0244338	−	0.419513i
$959$	6.24056	+	4.10448i	0.201518	+	0.132541i
$960$	0.598086	−	1.01810i	0.0193031	−	0.0328591i
$961$	−30.1643	+	7.14907i	−0.973042	+	0.230615i
$962$	−5.11574	+	29.0128i	−0.164938	+	0.935410i
$963$	27.4926	+	6.95553i	0.885938	+	0.224139i
$964$	−0.308387	−	1.74895i	−0.00993248	−	0.0563299i
$965$	−3.70328	−	8.58518i	−0.119213	−	0.276367i
$966$	0.535044	−	8.12947i	0.0172148	−	0.261561i
$967$	14.8294	+	49.5335i	0.476880	+	1.59289i	0.770812	+	0.637063i	$0.219851\pi$
$967$	14.8294	+	49.5335i	0.476880	+	1.59289i	−0.293932	+	0.955826i	$0.594964\pi$
$968$	2.50923	+	3.37049i	0.0806499	+	0.108332i
$969$	0.194917	+	0.461407i	0.00626163	+	0.0148225i
$970$	−9.65718	−	4.85002i	−0.310073	−	0.155725i
$971$	11.1071			0.356443			0.178222	−	0.983990i	$-0.442966\pi$
$971$	11.1071			0.356443			0.178222	+	0.983990i	$0.442966\pi$
$972$	13.6567	+	7.51637i	0.438037	+	0.241088i
$973$	−7.32054			−0.234686
$974$	−14.5404	−	7.30245i	−0.465904	−	0.233986i
$975$	15.2622	+	36.1287i	0.488783	+	1.15705i
$976$	3.46192	+	4.65017i	0.110813	+	0.148848i
$977$	−14.6515	−	48.9395i	−0.468744	−	1.56571i	−0.786530	−	0.617552i	$-0.788125\pi$
$977$	−14.6515	−	48.9395i	−0.468744	−	1.56571i	0.317786	−	0.948162i	$-0.397061\pi$
$978$	2.57580	−	39.1368i	0.0823652	−	1.25146i
$979$	−8.63620	−	20.0210i	−0.276014	−	0.639873i
$980$	0.716188	+	4.06171i	0.0228778	+	0.129746i
$981$	−3.63554	−	12.8458i	−0.116074	−	0.410133i
$982$	4.95050	−	28.0757i	0.157977	−	0.895931i
$983$	−30.5571	+	7.24217i	−0.974621	+	0.230989i	−0.686922	−	0.726731i	$-0.741038\pi$
$983$	−30.5571	+	7.24217i	−0.974621	+	0.230989i	−0.287699	+	0.957721i	$0.592890\pi$
$984$	7.34826	−	12.5087i	0.234254	−	0.398763i
$985$	−11.4329	−	7.51952i	−0.364282	−	0.239592i
$986$	0.0262389	−	0.450505i	0.000835618	−	0.0143470i
$987$	12.0226	−	9.93461i	0.382684	−	0.316222i
$988$	−1.49463	+	4.99241i	−0.0475505	+	0.158830i
$989$	−54.2601	+	19.7491i	−1.72537	+	0.627984i
$990$	−4.03267	−	3.48882i	−0.128167	−	0.110882i
$991$	2.60338	+	0.947553i	0.0826991	+	0.0301000i	0.383038	−	0.923732i	$-0.374878\pi$
$991$	2.60338	+	0.947553i	0.0826991	+	0.0301000i	−0.300339	+	0.953832i	$0.597100\pi$
$992$	−0.00547034	+	0.00734794i	−0.000173683	+	0.000233297i
$993$	−15.9493	+	16.6518i	−0.506135	+	0.528429i
$994$	2.43255	+	0.576525i	0.0771558	+	0.0182863i
$995$	2.38129	−	5.52046i	0.0754921	−	0.175010i
$996$	−17.2592	+	11.1660i	−0.546880	+	0.353808i
$997$	14.8300	−	9.75383i	0.469670	−	0.308907i	−0.292521	−	0.956259i	$-0.594494\pi$
$997$	14.8300	−	9.75383i	0.469670	−	0.308907i	0.762191	+	0.647352i	$0.224124\pi$
$998$	1.56715	+	2.71438i	0.0496072	+	0.0859221i
$999$	14.7253	+	26.8924i	0.465888	+	0.850839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.13.4	✓	72
3.2	odd	2		486.2.g.a.253.2		72
81.25	even	27	inner	162.2.g.a.25.4	yes	72
81.56	odd	54		486.2.g.a.73.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.4	✓	72	1.1	even	1	trivial
162.2.g.a.25.4	yes	72	81.25	even	27	inner
486.2.g.a.73.2		72	81.56	odd	54
486.2.g.a.253.2		72	3.2	odd	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 - 0.448799i) q^{2} +(0.674015 + 1.59553i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.195520 + 0.653084i) q^{5} +(0.113749 - 1.72831i) q^{6} +(0.386069 + 0.895009i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.09141 + 2.15082i) q^{9} +O(q^{10})\)	\(q+(-0.893633 - 0.448799i) q^{2} +(0.674015 + 1.59553i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.195520 + 0.653084i) q^{5} +(0.113749 - 1.72831i) q^{6} +(0.386069 + 0.895009i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.09141 + 2.15082i) q^{9} +(0.118380 - 0.671366i) q^{10} +(-2.53703 + 0.601286i) q^{11} +(-0.877315 + 1.49343i) q^{12} +(4.17145 + 2.74361i) q^{13} +(0.0566753 - 0.973077i) q^{14} +(-0.910229 + 0.752146i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(0.260353 - 0.0947609i) q^{17} +(2.83424 - 0.983417i) q^{18} +(0.980818 + 0.356989i) q^{19} +(-0.407097 + 0.546826i) q^{20} +(-1.16779 + 1.21923i) q^{21} +(2.53703 + 0.601286i) q^{22} +(1.91135 - 4.43101i) q^{23} +(1.45425 - 0.940835i) q^{24} +(3.78915 - 2.49216i) q^{25} +(-2.49642 - 4.32392i) q^{26} +(-4.84132 - 1.88722i) q^{27} +(-0.487363 + 0.844138i) q^{28} +(0.0947041 + 1.62601i) q^{29} +(1.15097 - 0.263632i) q^{30} +(-0.00909867 + 0.00106348i) q^{31} +(0.686242 - 0.727374i) q^{32} +(-2.66936 - 3.64262i) q^{33} +(-0.275189 - 0.0321650i) q^{34} +(-0.509032 + 0.427128i) q^{35} +(-2.97412 - 0.393189i) q^{36} +(-4.52007 - 3.79279i) q^{37} +(-0.716275 - 0.759207i) q^{38} +(-1.56588 + 8.50489i) q^{39} +(0.609210 - 0.305957i) q^{40} +(7.48493 - 3.75907i) q^{41} +(1.59077 - 0.565441i) q^{42} +(-8.21135 - 8.70352i) q^{43} +(-1.99731 - 1.67594i) q^{44} +(-1.81358 - 0.945337i) q^{45} +(-3.69668 + 3.10188i) q^{46} +(-9.17545 - 1.07246i) q^{47} +(-1.72181 + 0.188097i) q^{48} +(4.15170 - 4.40054i) q^{49} +(-4.50459 + 0.526511i) q^{50} +(0.326676 + 0.351531i) q^{51} +(0.290307 + 4.98439i) q^{52} +(1.58100 - 2.73837i) q^{53} +(3.47938 + 3.85926i) q^{54} +(-0.888731 - 1.53933i) q^{55} +(0.814372 - 0.535621i) q^{56} +(0.0915010 + 1.80554i) q^{57} +(0.645120 - 1.49556i) q^{58} +(13.2141 + 3.13179i) q^{59} +(-1.14686 - 0.280965i) q^{60} +(3.46192 - 4.65017i) q^{61} +(0.00860816 + 0.00313311i) q^{62} +(-2.73243 - 1.04147i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.976201 + 3.26074i) q^{65} +(0.750624 + 4.45317i) q^{66} +(-0.747251 + 12.8298i) q^{67} +(0.231482 + 0.152248i) q^{68} +(8.35807 + 0.0630455i) q^{69} +(0.646582 - 0.153243i) q^{70} +(-0.445365 + 2.52579i) q^{71} +(2.48131 + 1.68615i) q^{72} +(0.289549 + 1.64211i) q^{73} +(2.33708 + 5.41796i) q^{74} +(6.53025 + 4.36593i) q^{75} +(0.299355 + 0.999916i) q^{76} +(-1.51762 - 2.03852i) q^{77} +(5.21631 - 6.89748i) q^{78} +(-4.63186 - 2.32621i) q^{79} -0.681723 q^{80} +(-0.252020 - 8.99647i) q^{81} -8.37585 q^{82} +(10.6058 + 5.32643i) q^{83} +(-1.67533 - 0.208640i) q^{84} +(0.112791 + 0.151505i) q^{85} +(3.43180 + 11.4630i) q^{86} +(-2.53050 + 1.24706i) q^{87} +(1.03270 + 2.39407i) q^{88} +(1.45217 + 8.23569i) q^{89} +(1.19640 + 1.65872i) q^{90} +(-0.845084 + 4.79271i) q^{91} +(4.69559 - 1.11288i) q^{92} +(-0.00782945 - 0.0138004i) q^{93} +(7.71817 + 5.07632i) q^{94} +(-0.0413735 + 0.710355i) q^{95} +(1.62308 + 0.604656i) q^{96} +(4.54640 - 15.1860i) q^{97} +(-5.68505 + 2.06919i) q^{98} +(4.01270 - 6.71421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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