LMFDB - Embedded newform 162.2.g.a.25.4

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			25.4
Character	$\chi$	$=$	162.25
Dual form			162.2.g.a.13.4

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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	−0.903074	−	0.429485i	$-0.858695\pi$
$5$	0.195520	−	0.653084i	0.0874394	−	0.292068i	0.990513	+	0.137417i	$0.0438802\pi$
$6$	0.113749	+	1.72831i	0.0464380	+	0.705580i
$7$	0.386069	−	0.895009i	0.145921	−	0.338282i	−0.829543	−	0.558443i	$-0.811399\pi$
$7$	0.386069	−	0.895009i	0.145921	−	0.338282i	0.975464	+	0.220161i	$0.0706583\pi$
$8$	−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	−0.170417	−	0.985372i	$-0.554512\pi$
$11$	−2.53703	−	0.601286i	−0.764942	−	0.181295i	−0.594525	+	0.804077i	$0.702660\pi$
$12$	−0.877315	−	1.49343i	−0.253259	−	0.431115i
$13$	4.17145	−	2.74361i	1.15695	−	0.760940i	0.181988	−	0.983301i	$-0.441747\pi$
$13$	4.17145	−	2.74361i	1.15695	−	0.760940i	0.974964	+	0.222361i	$0.0713764\pi$
$14$	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	0.373400	−	0.927671i	$-0.378192\pi$
$17$	0.260353	+	0.0947609i	0.0631450	+	0.0229829i	−0.310255	+	0.950654i	$0.600414\pi$
$18$	2.83424	+	0.983417i	0.668036	+	0.231794i
$19$	0.980818	−	0.356989i	0.225015	−	0.0818988i	−0.227052	−	0.973883i	$-0.572909\pi$
$19$	0.980818	−	0.356989i	0.225015	−	0.0818988i	0.452067	+	0.891984i	$0.350687\pi$
$20$	−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	0.992815	+	0.119664i	$0.0381816\pi$
$23$	1.91135	+	4.43101i	0.398544	+	0.923929i	−0.594271	+	0.804265i	$0.702559\pi$
$24$	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	−0.978034	−	0.208447i	$-0.933159\pi$
$29$	0.0947041	−	1.62601i	0.0175861	−	0.301942i	0.995620	−	0.0934948i	$-0.0298038\pi$
$30$	1.15097	+	0.263632i	0.210138	+	0.0481325i
$31$	−0.00909867	−	0.00106348i	−0.00163417	−	0.000191007i	0.115276	−	0.993334i	$-0.463225\pi$
$31$	−0.00909867	−	0.00106348i	−0.00163417	−	0.000191007i	−0.116910	+	0.993143i	$0.537299\pi$
$32$	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	−0.933667	−	0.358143i	$-0.883410\pi$
$37$	−4.52007	+	3.79279i	−0.743094	+	0.623530i	0.190573	+	0.981673i	$0.438966\pi$
$38$	−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	0.923972	−	0.382460i	$-0.124923\pi$
$41$	7.48493	+	3.75907i	1.16895	+	0.587069i	0.244978	+	0.969529i	$0.421219\pi$
$42$	1.59077	+	0.565441i	0.245461	+	0.0872495i
$43$	−8.21135	+	8.70352i	−1.25222	+	1.32727i	−0.328354	+	0.944555i	$0.606494\pi$
$43$	−8.21135	+	8.70352i	−1.25222	+	1.32727i	−0.923865	+	0.382720i	$0.874988\pi$
$44$	−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	−0.754977	−	0.655751i	$-0.772352\pi$
$47$	−9.17545	+	1.07246i	−1.33838	+	0.156434i	−0.583400	+	0.812185i	$0.698278\pi$
$48$	−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	0.953941	−	0.299995i	$-0.0969850\pi$
$53$	1.58100	+	2.73837i	0.217167	+	0.376144i	−0.736774	+	0.676139i	$0.763652\pi$
$54$	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	0.752348	−	0.658766i	$-0.228921\pi$
$59$	13.2141	−	3.13179i	1.72032	−	0.407724i	0.967976	+	0.251042i	$0.0807732\pi$
$60$	−1.14686	+	0.280965i	−0.148060	+	0.0362724i
$61$	3.46192	+	4.65017i	0.443254	+	0.595393i	0.966461	−	0.256812i	$-0.0826721\pi$
$61$	3.46192	+	4.65017i	0.443254	+	0.595393i	−0.523207	+	0.852205i	$0.675265\pi$
$62$	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	−0.664051	−	0.747687i	$-0.731164\pi$
$67$	−0.747251	−	12.8298i	−0.0912913	−	1.56741i	0.572760	−	0.819723i	$-0.305873\pi$
$68$	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	0.946908	−	0.321504i	$-0.104188\pi$
$71$	−0.445365	−	2.52579i	−0.0528552	−	0.299757i	−0.999764	+	0.0217471i	$0.993077\pi$
$72$	2.48131	−	1.68615i	0.292425	−	0.198715i
$73$	0.289549	−	1.64211i	0.0338891	−	0.192195i	−0.963163	−	0.268917i	$-0.913334\pi$
$73$	0.289549	−	1.64211i	0.0338891	−	0.192195i	0.997053	+	0.0767220i	$0.0244454\pi$
$74$	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	−0.689860	−	0.723943i	$-0.742328\pi$
$79$	−4.63186	+	2.32621i	−0.521125	+	0.261719i	0.168735	+	0.985661i	$0.446032\pi$
$80$	−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	0.241530	−	0.970393i	$-0.422351\pi$
$83$	10.6058	−	5.32643i	1.16414	−	0.584651i	0.922607	+	0.385742i	$0.126054\pi$
$84$	−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	−0.805827	−	0.592151i	$-0.798279\pi$
$89$	1.45217	−	8.23569i	0.153930	−	0.872981i	0.959757	−	0.280830i	$-0.0906098\pi$
$90$	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	0.799469	+	0.600708i	$0.205114\pi$
$97$	4.54640	+	15.1860i	0.461617	+	1.54191i	−0.337852	+	0.941199i	$0.609700\pi$
$98$	−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	−0.985716	−	0.168417i	$-0.946134\pi$
$101$	−8.68662	−	11.6682i	−0.864351	−	1.16103i	0.121364	−	0.992608i	$-0.461273\pi$
$102$	−0.134161	+	0.460751i	−0.0132840	+	0.0456211i
$103$	−7.77307	+	1.84225i	−0.765903	+	0.181522i	−0.594957	−	0.803758i	$-0.702831\pi$
$103$	−7.77307	+	1.84225i	−0.765903	+	0.181522i	−0.170947	+	0.985280i	$0.554683\pi$
$104$	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	−0.998797	−	0.0490431i	$-0.984383\pi$
$107$	−4.72648	+	8.18650i	−0.456926	+	0.791419i	0.541871	+	0.840462i	$0.317716\pi$
$108$	−1.37726	+	5.01031i	−0.132527	+	0.482117i
$109$	−2.22505	−	3.85390i	−0.213121	−	0.369137i	0.739569	−	0.673081i	$-0.235030\pi$
$109$	−2.22505	−	3.85390i	−0.213121	−	0.369137i	−0.952690	+	0.303945i	$0.901696\pi$
$110$	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	0.704552	−	0.709652i	$-0.251148\pi$
$113$	−0.476925	−	0.505511i	−0.0448653	−	0.0475545i	−0.749418	+	0.662098i	$0.769666\pi$
$114$	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	−0.139886	−	0.990168i	$-0.544674\pi$
$127$	−12.8393	−	10.7734i	−1.13930	−	0.955988i	−0.999416	+	0.0341795i	$0.989118\pi$
$128$	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	−0.708163	−	0.706049i	$-0.750476\pi$
$131$	−17.8557	−	2.08704i	−1.56006	−	0.182345i	−0.851900	+	0.523704i	$0.824550\pi$
$132$	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	0.792729	−	0.609574i	$-0.208660\pi$
$137$	6.40237	+	4.21091i	0.546992	+	0.359762i	−0.245737	+	0.969336i	$0.579030\pi$
$138$	−7.44075	+	3.80743i	−0.633398	+	0.324110i
$139$	−2.97470	−	6.89612i	−0.252311	−	0.584922i	0.744240	−	0.667913i	$-0.232812\pi$
$139$	−2.97470	−	6.89612i	−0.252311	−	0.584922i	−0.996550	+	0.0829909i	$0.973553\pi$
$140$	−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	0.0242141	−	0.999707i	$-0.492292\pi$
$149$	11.6176	−	7.64102i	0.951752	−	0.625977i	0.927538	+	0.373730i	$0.121921\pi$
$150$	−3.87622	+	6.83231i	−0.316492	+	0.557856i
$151$	−9.19351	−	2.17890i	−0.748158	−	0.177317i	−0.161186	−	0.986924i	$-0.551532\pi$
$151$	−9.19351	−	2.17890i	−0.748158	−	0.177317i	−0.586972	+	0.809607i	$0.699680\pi$
$152$	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	0.631271	+	0.775562i	$0.282533\pi$
$157$	−4.03874	+	13.4903i	−0.322327	+	1.07665i	−0.953598	+	0.301084i	$0.902652\pi$
$158$	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	0.813170	+	0.582026i	$0.197740\pi$
$167$	−2.40433	+	8.03101i	−0.186052	+	0.621458i	−0.999222	+	0.0394319i	$0.987445\pi$
$168$	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	−0.585440	−	0.810716i	$-0.699078\pi$
$173$	−19.3671	−	4.59010i	−1.47246	−	0.348979i	−0.887017	+	0.461737i	$0.847226\pi$
$174$	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	0.858564	−	0.512706i	$-0.171357\pi$
$179$	15.8770	+	5.77875i	1.18670	+	0.431924i	0.328137	+	0.944630i	$0.393579\pi$
$180$	−0.324716	+	2.01923i	−0.0242029	+	0.150504i
$181$	23.1653	−	8.43147i	1.72186	−	0.626707i	0.723864	−	0.689943i	$-0.242365\pi$
$181$	23.1653	−	8.43147i	1.72186	−	0.626707i	0.997999	+	0.0632366i	$0.0201423\pi$
$182$	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	0.794775	+	0.606905i	$0.207589\pi$
$191$	−0.899470	+	15.4433i	−0.0650834	+	1.11744i	−0.859858	+	0.510533i	$0.829448\pi$
$192$	−1.17907	+	1.26878i	−0.0850920	+	0.0915661i
$193$	−13.6223	−	1.59222i	−0.980553	−	0.114610i	−0.389313	−	0.921106i	$-0.627287\pi$
$193$	−13.6223	−	1.59222i	−0.980553	−	0.114610i	−0.591240	+	0.806495i	$0.701362\pi$
$194$	−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	−0.0984219	−	0.995145i	$-0.531379\pi$
$197$	−15.3766	−	12.9025i	−1.09554	−	0.919266i	−0.997117	+	0.0758785i	$0.975824\pi$
$198$	−6.59921	−	4.19914i	−0.468986	−	0.298420i
$199$	−6.75579	+	5.66878i	−0.478905	+	0.401849i	−0.850030	−	0.526734i	$-0.823417\pi$
$199$	−6.75579	+	5.66878i	−0.478905	+	0.401849i	0.371125	+	0.928583i	$0.378972\pi$
$200$	−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	0.734834	−	0.678247i	$-0.237260\pi$
$211$	0.218012	+	0.231079i	0.0150086	+	0.0159082i	−0.719826	+	0.694155i	$0.755778\pi$
$212$	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	0.559966	−	0.828515i	$-0.310814\pi$
$223$	−5.88880	−	7.91003i	−0.394343	−	0.529694i	−0.954309	+	0.298821i	$0.903407\pi$
$224$	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	0.960841	+	0.277101i	$0.0893737\pi$
$227$	4.67574	+	15.6181i	0.310340	+	1.03661i	−0.650501	+	0.759505i	$0.725441\pi$
$228$	−1.39362	−	1.15159i	−0.0922949	−	0.0762657i
$229$	−0.361341	−	6.20398i	−0.0238781	−	0.409971i	−0.988975	−	0.148079i	$-0.952691\pi$
$229$	−0.361341	−	6.20398i	−0.0238781	−	0.409971i	0.965097	−	0.261891i	$-0.0843462\pi$
$230$	−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	−0.998321	−	0.0579161i	$-0.981554\pi$
$233$	−1.22137	−	6.92674i	−0.0800146	−	0.453786i	0.918307	−	0.395869i	$-0.129557\pi$
$234$	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	−0.867058	−	0.498207i	$-0.833992\pi$
$239$	−2.18145	+	2.93019i	−0.141106	+	0.189538i	0.725952	+	0.687745i	$0.241399\pi$
$240$	−0.459491	+	1.08771i	−0.0296600	+	0.0702112i
$241$	−1.58703	+	0.797036i	−0.102230	+	0.0513416i	−0.499179	−	0.866499i	$-0.666365\pi$
$241$	−1.58703	+	0.797036i	−0.102230	+	0.0513416i	0.396950	+	0.917840i	$0.370069\pi$
$242$	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	0.823756	+	0.566945i	$0.191875\pi$
$251$	−2.28500	+	12.9589i	−0.144228	+	0.817957i	−0.967984	+	0.251013i	$0.919236\pi$
$252$	−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	0.725869	+	0.687833i	$0.241438\pi$
$257$	1.35881	+	23.3300i	0.0847606	+	1.45528i	−0.641109	+	0.767450i	$0.721525\pi$
$258$	−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	0.897248	−	0.441527i	$-0.145563\pi$
$263$	3.51810	+	4.72563i	0.216935	+	0.291395i	−0.680312	+	0.732922i	$0.738156\pi$
$264$	−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	−0.486001	−	0.873958i	$-0.661545\pi$
$269$	8.42808	−	14.5979i	0.513869	−	0.890048i	0.999871	−	0.0160897i	$-0.00512174\pi$
$270$	−1.84013	−	3.02689i	−0.111987	−	0.184211i
$271$	11.1983	+	19.3960i	0.680248	+	1.17822i	0.974905	+	0.222622i	$0.0714614\pi$
$271$	11.1983	+	19.3960i	0.680248	+	1.17822i	−0.294657	+	0.955603i	$0.595205\pi$
$272$	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	0.875648	−	0.482949i	$-0.160434\pi$
$277$	30.6082	−	3.57759i	1.83907	−	0.214956i	0.963421	+	0.267993i	$0.0863603\pi$
$278$	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	−0.917730	−	0.397204i	$-0.869980\pi$
$281$	−7.84237	+	8.31243i	−0.467837	+	0.495878i	0.449894	+	0.893082i	$0.351462\pi$
$282$	−2.89724	−	15.7361i	−0.172528	−	0.937068i
$283$	−4.73586	−	2.37844i	−0.281518	−	0.141384i	0.302438	−	0.953169i	$-0.402200\pi$
$283$	−4.73586	−	2.37844i	−0.281518	−	0.141384i	−0.583956	+	0.811786i	$0.698496\pi$
$284$	−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	−0.871692	−	0.490054i	$-0.836977\pi$
$293$	−31.3742	−	3.66712i	−1.83290	−	0.214235i	−0.961210	+	0.275818i	$0.911051\pi$
$294$	−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	0.694077	−	0.719900i	$-0.255813\pi$
$307$	13.3693	+	4.86604i	0.763028	+	0.277720i	0.0689510	+	0.997620i	$0.478035\pi$
$308$	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	−0.569663	−	0.821879i	$-0.692926\pi$
$311$	−0.716561	+	0.471289i	−0.0406324	+	0.0267244i	0.529030	+	0.848603i	$0.322556\pi$
$312$	8.64760	−	0.0652294i	0.489574	−	0.00369289i
$313$	−15.3577	−	3.63984i	−0.868069	−	0.205736i	−0.227632	−	0.973747i	$-0.573098\pi$
$313$	−15.3577	−	3.63984i	−0.868069	−	0.205736i	−0.640437	+	0.768011i	$0.721247\pi$
$314$	−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	0.559752	+	0.828660i	$0.310896\pi$
$317$	−7.60463	+	17.6295i	−0.427119	+	0.990172i	−0.986871	+	0.161512i	$0.948363\pi$
$318$	−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	−0.709648	−	0.704557i	$-0.751146\pi$
$331$	5.27278	−	12.2237i	0.289818	−	0.671874i	0.999466	+	0.0326828i	$0.0104051\pi$
$332$	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	−0.823852	−	0.566804i	$-0.808180\pi$
$337$	−11.5600	+	7.60315i	−0.629715	+	0.414170i	0.194138	+	0.980974i	$0.437809\pi$
$338$	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	0.935744	−	0.352679i	$-0.114729\pi$
$347$	0.690508	+	1.60078i	0.0370684	+	0.0859343i	−0.898676	+	0.438613i	$0.855470\pi$
$348$	−2.51140	+	1.28509i	−0.134625	+	0.0688879i
$349$	−8.01784	−	5.27342i	−0.429185	−	0.282280i	0.316481	−	0.948599i	$-0.397499\pi$
$349$	−8.01784	−	5.27342i	−0.429185	−	0.282280i	−0.745667	+	0.666319i	$0.767869\pi$
$350$	−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	−0.937827	−	0.347104i	$-0.887165\pi$
$353$	0.637958	−	10.9533i	0.0339551	−	0.582986i	0.971782	−	0.235882i	$-0.0757979\pi$
$354$	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	0.392035	−	0.919950i	$-0.371771\pi$
$359$	−8.44791	−	7.08864i	−0.445864	−	0.374124i	−0.837898	+	0.545827i	$0.816216\pi$
$360$	−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	−0.956149	−	0.292881i	$-0.905386\pi$
$367$	−11.6508	+	12.3492i	−0.608169	+	0.644621i	0.347980	+	0.937502i	$0.386868\pi$
$368$	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	0.958436	−	0.285306i	$-0.0920953\pi$
$373$	11.9333	+	12.6486i	0.617885	+	0.654919i	−0.340552	+	0.940226i	$0.610614\pi$
$374$	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	−0.984740	−	0.174030i	$-0.944321\pi$
$379$	−6.65132	+	11.5204i	−0.341655	+	0.591764i	0.643085	+	0.765795i	$0.277654\pi$
$380$	−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	−0.502592	−	0.864524i	$-0.667620\pi$
$383$	−11.0324	+	2.61472i	−0.563727	+	0.133606i	−0.0611349	+	0.998130i	$0.519472\pi$
$384$	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	0.999970	−	0.00780729i	$-0.00248516\pi$
$389$	3.15997	+	10.5550i	0.160217	+	0.535162i	−0.839753	+	0.542969i	$0.817300\pi$
$390$	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	−0.111547	+	0.993759i	$0.535581\pi$
$397$	−6.90621	+	39.1671i	−0.346613	+	1.96574i	−0.235066	+	0.971980i	$0.575531\pi$
$398$	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	−0.647979	−	0.761658i	$-0.724385\pi$
$401$	5.35717	−	7.19593i	0.267524	−	0.359348i	0.915503	+	0.402311i	$0.131793\pi$
$402$	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	−0.741109	−	0.671385i	$-0.765700\pi$
$409$	2.31810	−	3.11375i	0.114623	−	0.153965i	0.855732	+	0.517419i	$0.173107\pi$
$410$	−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	−0.995767	−	0.0919186i	$-0.970700\pi$
$419$	−0.356253	−	6.11664i	−0.0174041	−	0.298817i	0.978362	−	0.206899i	$-0.0663370\pi$
$420$	−0.191303	+	1.13493i	−0.00933463	+	0.0553788i
$421$	−9.41492	−	31.4480i	−0.458855	−	1.53268i	−0.804288	−	0.594239i	$-0.797453\pi$
$421$	−9.41492	−	31.4480i	−0.458855	−	1.53268i	0.345433	−	0.938443i	$-0.387732\pi$
$422$	−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	−0.298181	−	0.954509i	$-0.596380\pi$
$431$	14.0661	−	24.3632i	0.677539	−	1.17353i	0.975720	−	0.219023i	$-0.0702869\pi$
$432$	3.19644	+	4.09668i	0.153789	+	0.197102i
$433$	0.0327624	+	0.0567461i	0.00157446	+	0.00272704i	0.866812	−	0.498636i	$-0.166166\pi$
$433$	0.0327624	+	0.0567461i	0.00157446	+	0.00272704i	−0.865237	+	0.501363i	$0.832832\pi$
$434$	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	−0.715558	−	0.698553i	$-0.753828\pi$
$439$	−26.2057	+	3.06301i	−1.25073	+	0.146190i	−0.535173	+	0.844742i	$0.679754\pi$
$440$	−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	−0.00420393	−	0.999991i	$-0.501338\pi$
$443$	20.9284	−	22.1828i	0.994340	−	1.05394i	0.998544	−	0.0539475i	$-0.0171804\pi$
$444$	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	0.0732200	−	0.997316i	$-0.476672\pi$
$449$	22.6326	−	18.9910i	1.06810	−	0.896241i	0.994879	+	0.101074i	$0.0322280\pi$
$450$	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	−0.998687	−	0.0512318i	$-0.983685\pi$
$457$	−0.0172113	+	0.295507i	−0.000805111	+	0.0138232i	0.997882	+	0.0650550i	$0.0207223\pi$
$458$	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	−0.132391	−	0.991198i	$-0.542265\pi$
$461$	−23.5098	−	15.4627i	−1.09496	−	0.720168i	−0.962571	+	0.271030i	$0.912636\pi$
$462$	−3.69583	−	2.39105i	−0.171946	−	0.111242i
$463$	−11.5483	−	26.7720i	−0.536696	−	1.24420i	−0.943708	−	0.330779i	$-0.892689\pi$
$463$	−11.5483	−	26.7720i	−0.536696	−	1.24420i	0.407012	−	0.913423i	$-0.366571\pi$
$464$	−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	−0.834889	−	0.550418i	$-0.814469\pi$
$467$	−24.2175	+	8.81443i	−1.12065	+	0.407883i	−0.285761	+	0.958301i	$0.592246\pi$
$468$	−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	−0.759051	−	0.651032i	$-0.774337\pi$
$479$	5.15165	−	11.9429i	0.235385	−	0.545683i	0.994435	+	0.105348i	$0.0335958\pi$
$480$	−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	−0.548959	−	0.835849i	$-0.684976\pi$
$491$	8.17641	−	27.3111i	0.368996	−	1.23253i	0.917955	−	0.396684i	$-0.129839\pi$
$492$	−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	−0.606769	−	0.794878i	$-0.707535\pi$
$499$	−2.61866	+	1.72232i	−0.117227	+	0.0771017i	0.489541	+	0.871980i	$0.337164\pi$
$500$	−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	0.616385	−	0.787445i	$-0.288597\pi$
$503$	13.0619	+	4.75415i	0.582403	+	0.211977i	−0.0339819	+	0.999422i	$0.510819\pi$
$504$	−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	0.899284	−	0.437365i	$-0.144088\pi$
$509$	−0.811521	−	1.88132i	−0.0359700	−	0.0833879i	−0.935254	+	0.353977i	$0.884829\pi$
$510$	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	0.926127	−	0.377211i	$-0.123117\pi$
$521$	16.3308	+	13.7032i	0.715467	+	0.600348i	−0.210660	+	0.977559i	$0.567561\pi$
$522$	1.86746	−	4.51535i	0.0817363	−	0.197632i
$523$	4.87547	−	4.09101i	0.213190	−	0.178887i	−0.529939	−	0.848036i	$-0.677785\pi$
$523$	4.87547	−	4.09101i	0.213190	−	0.178887i	0.743129	+	0.669148i	$0.233341\pi$
$524$	−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	−0.794474	−	0.607299i	$-0.792253\pi$
$541$	2.99347	−	5.18483i	0.128699	−	0.222913i	0.923173	+	0.384385i	$0.125587\pi$
$542$	−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	0.861814	−	0.507225i	$-0.169329\pi$
$547$	3.01067	+	4.04404i	0.128727	+	0.172911i	−0.733087	+	0.680135i	$0.761921\pi$
$548$	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	0.891670	+	0.452687i	$0.149534\pi$
$557$	4.92319	+	27.9208i	0.208602	+	1.18304i	−0.683067	+	0.730355i	$0.739354\pi$
$558$	−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	0.00523909	−	0.999986i	$-0.498332\pi$
$563$	22.8192	−	30.6514i	0.961713	−	1.29180i	0.956474	−	0.291818i	$-0.0942603\pi$
$564$	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	−0.378220	−	0.925716i	$-0.623464\pi$
$569$	3.30279	−	1.65872i	0.138460	−	0.0695373i	0.516680	+	0.856178i	$0.327168\pi$
$570$	1.22301	−	0.152309i	0.0512262	−	0.00637951i
$571$	−11.9989	+	16.1173i	−0.502137	+	0.674487i	−0.978852	−	0.204571i	$-0.934420\pi$
$571$	−11.9989	+	16.1173i	−0.502137	+	0.674487i	0.476715	+	0.879058i	$0.341827\pi$
$572$	−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	−0.920626	−	0.390446i	$-0.872321\pi$
$577$	−4.54140	−	25.7556i	−0.189061	−	1.07222i	0.731565	−	0.681772i	$-0.238790\pi$
$578$	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	0.532238	−	0.846595i	$-0.321351\pi$
$587$	−10.4529	−	14.0407i	−0.431439	−	0.579523i	−0.963677	+	0.267072i	$0.913944\pi$
$588$	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	0.432605	+	0.901583i	$0.357594\pi$
$593$	−13.7463	+	23.8092i	−0.564491	+	0.977728i	−0.997097	+	0.0761445i	$0.975739\pi$
$594$	−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	0.730633	−	0.682770i	$-0.239225\pi$
$599$	0.159947	+	0.169534i	0.00653525	+	0.00692696i	−0.724098	+	0.689697i	$0.757744\pi$
$600$	3.16564	+	7.18918i	0.129237	+	0.293497i
$601$	12.0045	−	1.40313i	0.489675	−	0.0572348i	0.132327	−	0.991206i	$-0.457755\pi$
$601$	12.0045	−	1.40313i	0.489675	−	0.0572348i	0.357348	+	0.933971i	$0.383681\pi$
$602$	−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	0.855483	−	0.517831i	$-0.173260\pi$
$607$	23.4296	+	11.7668i	0.950978	+	0.477599i	0.0954949	+	0.995430i	$0.469557\pi$
$608$	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	−0.999898	−	0.0143131i	$-0.995444\pi$
$613$	−29.4042	−	24.6730i	−1.18762	−	0.996535i	−0.187726	−	0.982221i	$-0.560112\pi$
$614$	−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	0.0599702	−	0.998200i	$-0.480899\pi$
$617$	−2.77897	−	0.324815i	−0.111877	−	0.0130765i	−0.171847	+	0.985124i	$0.554974\pi$
$618$	−4.06817	−	13.2247i	−0.163646	−	0.531977i
$619$	−1.63200	+	28.0204i	−0.0655957	+	1.12624i	0.791531	+	0.611129i	$0.209284\pi$
$619$	−1.63200	+	28.0204i	−0.0655957	+	1.12624i	−0.857127	+	0.515106i	$0.827753\pi$
$620$	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	0.559249	−	0.829000i	$-0.311090\pi$
$631$	11.4241	+	4.15805i	0.454788	+	0.165529i	−0.104461	+	0.994529i	$0.533312\pi$
$632$	−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	0.216500	+	0.976283i	$0.430536\pi$
$641$	−16.2590	+	37.6927i	−0.642194	+	1.48877i	−0.858693	+	0.512490i	$0.828723\pi$
$642$	−14.6865	−	7.23762i	−0.579628	−	0.285646i
$643$	9.89673	−	33.0574i	0.390289	−	1.30366i	−0.506898	−	0.862006i	$-0.669208\pi$
$643$	9.89673	−	33.0574i	0.390289	−	1.30366i	0.897187	−	0.441650i	$-0.145607\pi$
$644$	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	0.278004	+	0.960580i	$0.410327\pi$
$653$	−12.3198	+	41.1511i	−0.482112	+	1.61037i	−0.760116	+	0.649787i	$0.774858\pi$
$654$	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	0.569154	−	0.822231i	$-0.307271\pi$
$659$	18.1944	+	4.31214i	0.708752	+	0.167977i	0.139598	+	0.990208i	$0.455419\pi$
$660$	3.07857	−	0.0232218i	0.119833	−	0.000903909i
$661$	−16.6117	+	10.9257i	−0.646121	+	0.424961i	−0.829827	−	0.558021i	$-0.811561\pi$
$661$	−16.6117	+	10.9257i	−0.646121	+	0.424961i	0.183706	+	0.982981i	$0.441191\pi$
$662$	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	0.824185	−	0.566321i	$-0.191634\pi$
$673$	16.3598	+	10.7600i	0.630622	+	0.414767i	−0.193562	+	0.981088i	$0.562004\pi$
$674$	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	−0.907051	−	0.421020i	$-0.861672\pi$
$677$	1.11217	−	19.0953i	0.0427443	−	0.733891i	0.949796	−	0.312871i	$-0.101291\pi$
$678$	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	0.886715	−	0.462316i	$-0.152981\pi$
$683$	15.2990	+	12.8374i	0.585399	+	0.491208i	−0.301316	+	0.953524i	$0.597426\pi$
$684$	−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	−0.628850	−	0.777527i	$-0.716474\pi$
$691$	4.83484	−	5.12463i	0.183926	−	0.194950i	0.812776	+	0.582577i	$0.197955\pi$
$692$	−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	0.632268	−	0.774749i	$-0.282124\pi$
$701$	−9.39432	−	16.2714i	−0.354818	−	0.614563i	−0.987087	+	0.160186i	$0.948791\pi$
$702$	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	0.992243	−	0.124313i	$-0.0396726\pi$
$709$	15.6720	+	21.0512i	0.588574	+	0.790593i	−0.403669	+	0.914905i	$0.632265\pi$
$710$	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	0.941555	+	0.336860i	$0.109365\pi$
$719$	4.61192	+	26.1555i	0.171996	+	0.975436i	−0.769559	+	0.638576i	$0.779524\pi$
$720$	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	0.296999	−	0.954878i	$-0.404014\pi$
$727$	33.4417	−	16.7951i	1.24028	−	0.622894i	0.943285	+	0.331983i	$0.107718\pi$
$728$	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	0.133913	−	0.990993i	$-0.457246\pi$
$733$	28.2887	−	37.9983i	1.04487	−	1.40350i	0.910954	−	0.412507i	$-0.135347\pi$
$734$	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	−0.718230	−	0.695805i	$-0.755048\pi$
$739$	−7.64685	−	43.3675i	−0.281294	−	1.59530i	0.436936	−	0.899492i	$-0.356063\pi$
$740$	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	−0.971169	−	0.238392i	$-0.923380\pi$
$743$	−0.933379	−	16.0255i	−0.0342423	−	0.587918i	0.936927	−	0.349526i	$-0.113657\pi$
$744$	−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	0.451436	−	0.892304i	$-0.350912\pi$
$751$	34.4012	−	8.15324i	1.25532	−	0.297516i	0.803883	+	0.594787i	$0.202764\pi$
$752$	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	−0.768308	−	0.640080i	$-0.778901\pi$
$757$	−25.8210	−	44.7233i	−0.938480	−	1.62549i	−0.170171	−	0.985414i	$-0.554432\pi$
$758$	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	0.989836	−	0.142212i	$-0.0454214\pi$
$761$	21.8017	+	23.1085i	0.790311	+	0.837681i	−0.199525	+	0.979893i	$0.563940\pi$
$762$	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	−0.0881740	−	0.996105i	$-0.528103\pi$
$769$	−26.0622	−	13.0889i	−0.939827	−	0.471999i	−0.851653	+	0.524106i	$0.824399\pi$
$770$	−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	−0.970939	−	0.239326i	$-0.923074\pi$
$773$	−25.1297	+	21.0863i	−0.903851	+	0.758421i	0.0670881	+	0.997747i	$0.478629\pi$
$774$	−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	0.998771	+	0.0495668i	$0.0157841\pi$
$787$	9.80264	+	22.7251i	0.349426	+	0.810061i	−0.649345	+	0.760494i	$0.724957\pi$
$788$	−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	−0.876219	−	0.481913i	$-0.839942\pi$
$797$	−22.0421	+	14.4973i	−0.780771	+	0.513521i	0.0954478	+	0.995434i	$0.469572\pi$
$798$	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	−0.705468	−	0.708742i	$-0.749263\pi$
$821$	−47.3916	−	11.2320i	−1.65398	−	0.392000i	−0.948512	+	0.316742i	$0.897411\pi$
$822$	−6.54949	+	11.5443i	−0.228440	+	0.402653i
$823$	26.3696	−	17.3436i	0.919186	−	0.604558i	0.000695173	−	1.00000i	$-0.499779\pi$
$823$	26.3696	−	17.3436i	0.919186	−	0.604558i	0.918491	+	0.395441i	$0.129408\pi$
$824$	−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	0.147197	−	0.989107i	$-0.452975\pi$
$827$	−10.8079	−	3.93377i	−0.375829	−	0.136791i	−0.523026	+	0.852317i	$0.675197\pi$
$828$	−7.42681	−	12.4268i	−0.258099	−	0.431862i
$829$	14.8843	−	5.41744i	0.516953	−	0.188155i	−0.0703505	−	0.997522i	$-0.522412\pi$
$829$	14.8843	−	5.41744i	0.516953	−	0.188155i	0.587303	+	0.809367i	$0.300190\pi$
$830$	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	0.915593	+	0.402107i	$0.131722\pi$
$839$	−1.17284	+	20.1368i	−0.0404908	+	0.695201i	−0.956084	+	0.293094i	$0.905315\pi$
$840$	−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	−0.218600	−	0.975815i	$-0.570149\pi$
$853$	22.4383	−	23.7833i	0.768274	−	0.814323i	0.986874	+	0.161492i	$0.0516305\pi$
$854$	−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	−0.118973	−	0.992898i	$-0.537960\pi$
$857$	−0.168627	+	0.0197097i	−0.00576019	+	0.000673270i	0.113212	+	0.993571i	$0.463886\pi$
$858$	−9.08654	−	20.6356i	−0.310210	−	0.704487i
$859$	−21.1604	−	22.4287i	−0.721983	−	0.765257i	0.257610	−	0.966249i	$-0.417065\pi$
$859$	−21.1604	−	22.4287i	−0.721983	−	0.765257i	−0.979593	+	0.200992i	$0.935584\pi$
$860$	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	0.806116	−	0.591758i	$-0.201566\pi$
$863$	−3.21440	−	5.56751i	−0.109419	−	0.189520i	−0.915535	+	0.402238i	$0.868233\pi$
$864$	−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	0.994395	+	0.105728i	$0.0337172\pi$
$877$	0.562610	+	9.65963i	0.0189980	+	0.326183i	−0.975397	+	0.220455i	$0.929246\pi$
$878$	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	0.982309	−	0.187265i	$-0.0599624\pi$
$881$	−0.142708	−	0.809340i	−0.00480797	−	0.0272674i	−0.987117	+	0.159998i	$0.948851\pi$
$882$	7.43932	+	16.5550i	0.250495	+	0.557437i
$883$	−3.50111	+	19.8558i	−0.117822	+	0.668200i	0.867493	+	0.497450i	$0.165730\pi$
$883$	−3.50111	+	19.8558i	−0.117822	+	0.668200i	−0.985314	+	0.170750i	$0.945381\pi$
$884$	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	−0.950311	−	0.311303i	$-0.899234\pi$
$887$	−11.3035	+	15.1832i	−0.379533	+	0.509801i	0.570778	+	0.821105i	$0.306642\pi$
$888$	−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	0.986986	+	0.160807i	$0.0514095\pi$
$907$	7.55127	+	25.2230i	0.250736	+	0.837516i	−0.736250	+	0.676710i	$0.763405\pi$
$908$	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	0.775390	−	0.631483i	$-0.217553\pi$
$911$	−1.56795	−	2.10612i	−0.0519486	−	0.0697790i	−0.827338	+	0.561704i	$0.810146\pi$
$912$	−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	0.821314	−	0.570477i	$-0.193242\pi$
$919$	−2.52799	−	4.37860i	−0.0833906	−	0.144437i	−0.904704	+	0.426040i	$0.859908\pi$
$920$	−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	−0.295448	−	0.955359i	$-0.595469\pi$
$929$	20.5881	−	21.8221i	0.675473	−	0.715959i	0.970921	+	0.239399i	$0.0769505\pi$
$930$	−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	0.401164	−	0.916006i	$-0.368606\pi$
$937$	−13.2012	−	11.0771i	−0.431264	−	0.361874i	−0.832429	+	0.554132i	$0.813050\pi$
$938$	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	0.944421	−	0.328739i	$-0.106624\pi$
$941$	54.8351	+	6.40930i	1.78757	+	0.208937i	0.843152	+	0.537676i	$0.180698\pi$
$942$	−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	0.314697	−	0.949192i	$-0.398097\pi$
$947$	−13.3009	−	8.74814i	−0.432221	−	0.284276i	−0.746918	+	0.664916i	$0.768467\pi$
$948$	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	0.363073	−	0.931761i	$-0.381728\pi$
$953$	38.2836	−	13.9341i	1.24013	−	0.451369i	0.877054	+	0.480391i	$0.159505\pi$
$954$	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	−0.293932	−	0.955826i	$-0.594964\pi$
$967$	14.8294	−	49.5335i	0.476880	−	1.59289i	0.770812	−	0.637063i	$-0.219851\pi$
$968$	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	0.317786	+	0.948162i	$0.397061\pi$
$977$	−14.6515	+	48.9395i	−0.468744	+	1.56571i	−0.786530	+	0.617552i	$0.788125\pi$
$978$	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	−0.287699	−	0.957721i	$-0.592890\pi$
$983$	−30.5571	−	7.24217i	−0.974621	−	0.230989i	−0.686922	+	0.726731i	$0.741038\pi$
$984$	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	−0.300339	−	0.953832i	$-0.597100\pi$
$991$	2.60338	−	0.947553i	0.0826991	−	0.0301000i	0.383038	+	0.923732i	$0.374878\pi$
$992$	−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	0.762191	−	0.647352i	$-0.224124\pi$
$997$	14.8300	+	9.75383i	0.469670	+	0.308907i	−0.292521	+	0.956259i	$0.594494\pi$
$998$	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.25.4	yes	72
3.2	odd	2		486.2.g.a.73.2		72
81.13	even	27	inner	162.2.g.a.13.4	✓	72
81.68	odd	54		486.2.g.a.253.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.4	✓	72	81.13	even	27	inner
162.2.g.a.25.4	yes	72	1.1	even	1	trivial
486.2.g.a.73.2		72	3.2	odd	2
486.2.g.a.253.2		72	81.68	odd	54

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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