LMFDB - Embedded newform 110.2.k.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	110.17
Dual form			110.2.k.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-1.23025 + 0.194853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.87069 + 1.22496i) q^{5} +(1.18463 + 0.384908i) q^{6} +(-0.466963 + 2.94829i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.37761 + 0.447613i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.23025 + 0.194853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.87069 + 1.22496i) q^{5} +(1.18463 + 0.384908i) q^{6} +(-0.466963 + 2.94829i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.37761 + 0.447613i) q^{9} +(2.22292 - 0.242173i) q^{10} +(3.28440 + 0.461210i) q^{11} +(-0.880765 - 0.880765i) q^{12} +(-2.73193 + 5.36172i) q^{13} +(1.75456 - 2.41495i) q^{14} +(2.06273 - 1.87152i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.00301 - 5.89374i) q^{17} +(1.43067 + 0.226596i) q^{18} +(1.55596 + 1.13047i) q^{19} +(-2.09058 - 0.793405i) q^{20} -3.71813i q^{21} +(-2.71704 - 1.90203i) q^{22} +(0.606759 - 0.606759i) q^{23} +(0.384908 + 1.18463i) q^{24} +(1.99894 - 4.58304i) q^{25} +(4.86834 - 3.53706i) q^{26} +(4.93708 - 2.51557i) q^{27} +(-2.65969 + 1.35518i) q^{28} +(-3.56404 + 2.58943i) q^{29} +(-2.68756 + 0.731076i) q^{30} +(-0.337483 - 1.03867i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.13052 + 0.0725706i) q^{33} +6.61470i q^{34} +(-2.73799 - 6.08734i) q^{35} +(-1.17187 - 0.851411i) q^{36} +(7.26743 + 1.15105i) q^{37} +(-0.873149 - 1.71365i) q^{38} +(2.31622 - 7.12861i) q^{39} +(1.50252 + 1.65603i) q^{40} +(-4.84236 + 6.66494i) q^{41} +(-1.68800 + 3.31288i) q^{42} +(3.90436 + 3.90436i) q^{43} +(1.55740 + 2.92823i) q^{44} +(2.02877 - 2.52486i) q^{45} +(-0.816089 + 0.265163i) q^{46} +(1.14432 + 7.22493i) q^{47} +(0.194853 - 1.23025i) q^{48} +(-1.81695 - 0.590364i) q^{49} +(-3.86173 + 3.17601i) q^{50} +(4.84288 + 6.66565i) q^{51} +(-5.94352 + 0.941360i) q^{52} +(4.55740 + 2.32211i) q^{53} -5.54101 q^{54} +(-6.70905 + 3.16048i) q^{55} +2.98504 q^{56} +(-2.13451 - 1.08759i) q^{57} +(4.35116 - 0.689156i) q^{58} +(4.39097 + 6.04365i) q^{59} +(2.72654 + 0.568734i) q^{60} +(-4.11435 - 1.33683i) q^{61} +(-0.170845 + 1.07867i) q^{62} +(-0.676399 - 4.27062i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.45730 - 13.3766i) q^{65} +(3.71326 + 1.81055i) q^{66} +(-1.06709 - 1.06709i) q^{67} +(3.00301 - 5.89374i) q^{68} +(-0.628239 + 0.864697i) q^{69} +(-0.324023 + 6.66688i) q^{70} +(1.18906 - 3.65955i) q^{71} +(0.657608 + 1.29063i) q^{72} +(0.684302 + 0.108383i) q^{73} +(-5.95276 - 4.32493i) q^{74} +(-1.56619 + 6.02780i) q^{75} +1.92328i q^{76} +(-2.89347 + 9.46799i) q^{77} +(-5.30009 + 5.30009i) q^{78} +(1.26384 + 3.88969i) q^{79} +(-0.586932 - 2.15766i) q^{80} +(-2.06810 + 1.50256i) q^{81} +(7.34040 - 3.74012i) q^{82} +(-0.881701 + 0.449249i) q^{83} +(3.00803 - 2.18546i) q^{84} +(12.8373 + 7.34678i) q^{85} +(-1.70627 - 5.25135i) q^{86} +(3.88012 - 3.88012i) q^{87} +(-0.0582620 - 3.31611i) q^{88} -12.5362i q^{89} +(-2.95391 + 1.32863i) q^{90} +(-14.5322 - 10.5583i) q^{91} +(0.847523 + 0.134234i) q^{92} +(0.617578 + 1.21207i) q^{93} +(2.26046 - 6.95697i) q^{94} +(-4.29551 - 0.208770i) q^{95} +(-0.732139 + 1.00770i) q^{96} +(-2.26820 + 4.45160i) q^{97} +(1.35090 + 1.35090i) q^{98} +(-4.73107 + 0.834773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	−1.23025	+	0.194853i	−0.710288	+	0.112498i	−0.501116	−	0.865380i	$-0.667077\pi$
$3$	−1.23025	+	0.194853i	−0.710288	+	0.112498i	−0.209172	+	0.977879i	$0.567077\pi$
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	−1.87069	+	1.22496i	−0.836597	+	0.547819i
$5$	−1.87069	+	1.22496i	−0.836597	+	0.547819i
$6$	1.18463	+	0.384908i	0.483622	+	0.157138i
$7$	−0.466963	+	2.94829i	−0.176495	+	1.11435i	0.727280	+	0.686341i	$0.240784\pi$
$7$	−0.466963	+	2.94829i	−0.176495	+	1.11435i	−0.903775	+	0.428007i	$0.859216\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−1.37761	+	0.447613i	−0.459204	+	0.149204i
$10$	2.22292	−	0.242173i	0.702948	−	0.0765819i
$11$	3.28440	+	0.461210i	0.990284	+	0.139060i
$11$	3.28440	+	0.461210i	0.990284	+	0.139060i
$12$	−0.880765	−	0.880765i	−0.254255	−	0.254255i
$13$	−2.73193	+	5.36172i	−0.757702	+	1.48707i	0.112112	+	0.993696i	$0.464238\pi$
$13$	−2.73193	+	5.36172i	−0.757702	+	1.48707i	−0.869815	+	0.493379i	$0.835762\pi$
$14$	1.75456	−	2.41495i	0.468926	−	0.645422i
$15$	2.06273	−	1.87152i	0.532596	−	0.483225i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−3.00301	−	5.89374i	−0.728337	−	1.42944i	−0.896209	−	0.443632i	$-0.853690\pi$
$17$	−3.00301	−	5.89374i	−0.728337	−	1.42944i	0.167872	−	0.985809i	$-0.446310\pi$
$18$	1.43067	+	0.226596i	0.337213	+	0.0534093i
$19$	1.55596	+	1.13047i	0.356962	+	0.259348i	0.751784	−	0.659409i	$-0.229194\pi$
$19$	1.55596	+	1.13047i	0.356962	+	0.259348i	−0.394822	+	0.918758i	$0.629194\pi$
$20$	−2.09058	−	0.793405i	−0.467467	−	0.177411i
$21$		−	3.71813i		−	0.811363i
$22$	−2.71704	−	1.90203i	−0.579274	−	0.405514i
$23$	0.606759	−	0.606759i	0.126518	−	0.126518i	−0.641012	−	0.767530i	$-0.721485\pi$
$23$	0.606759	−	0.606759i	0.126518	−	0.126518i	0.767530	+	0.641012i	$0.221485\pi$
$24$	0.384908	+	1.18463i	0.0785691	+	0.241811i
$25$	1.99894	−	4.58304i	0.399789	−	0.916607i
$26$	4.86834	−	3.53706i	0.954760	−	0.693674i
$27$	4.93708	−	2.51557i	0.950141	−	0.484121i
$28$	−2.65969	+	1.35518i	−0.502634	+	0.256105i
$29$	−3.56404	+	2.58943i	−0.661826	+	0.480844i	−0.867279	−	0.497823i	$-0.834133\pi$
$29$	−3.56404	+	2.58943i	−0.661826	+	0.480844i	0.205453	+	0.978667i	$0.434133\pi$
$30$	−2.68756	+	0.731076i	−0.490680	+	0.133476i
$31$	−0.337483	−	1.03867i	−0.0606138	−	0.186550i	0.916165	−	0.400802i	$-0.131269\pi$
$31$	−0.337483	−	1.03867i	−0.0606138	−	0.186550i	−0.976778	+	0.214252i	$0.931269\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.13052	+	0.0725706i	−0.719030	+	0.0126329i
$34$			6.61470i			1.13441i
$35$	−2.73799	−	6.08734i	−0.462805	−	1.02895i
$36$	−1.17187	−	0.851411i	−0.195311	−	0.141902i
$37$	7.26743	+	1.15105i	1.19476	+	0.189231i	0.721957	−	0.691938i	$-0.243243\pi$
$37$	7.26743	+	1.15105i	1.19476	+	0.189231i	0.472801	+	0.881169i	$0.343243\pi$
$38$	−0.873149	−	1.71365i	−0.141643	−	0.277991i
$39$	2.31622	−	7.12861i	0.370893	−	1.14149i
$40$	1.50252	+	1.65603i	0.237569	+	0.261841i
$41$	−4.84236	+	6.66494i	−0.756250	+	1.04089i	0.241267	+	0.970459i	$0.422437\pi$
$41$	−4.84236	+	6.66494i	−0.756250	+	1.04089i	−0.997517	+	0.0704302i	$0.977563\pi$
$42$	−1.68800	+	3.31288i	−0.260464	+	0.511189i
$43$	3.90436	+	3.90436i	0.595409	+	0.595409i	0.939087	−	0.343679i	$-0.111673\pi$
$43$	3.90436	+	3.90436i	0.595409	+	0.595409i	−0.343679	+	0.939087i	$0.611673\pi$
$44$	1.55740	+	2.92823i	0.234786	+	0.441447i
$45$	2.02877	−	2.52486i	0.302432	−	0.376385i
$46$	−0.816089	+	0.265163i	−0.120326	+	0.0390962i
$47$	1.14432	+	7.22493i	0.166916	+	1.05386i	0.918845	+	0.394620i	$0.129124\pi$
$47$	1.14432	+	7.22493i	0.166916	+	1.05386i	−0.751929	+	0.659244i	$0.770876\pi$
$48$	0.194853	−	1.23025i	0.0281246	−	0.177572i
$49$	−1.81695	−	0.590364i	−0.259565	−	0.0843378i
$50$	−3.86173	+	3.17601i	−0.546131	+	0.449156i
$51$	4.84288	+	6.66565i	0.678138	+	0.933378i
$52$	−5.94352	+	0.941360i	−0.824217	+	0.130543i
$53$	4.55740	+	2.32211i	0.626008	+	0.318967i	0.738060	−	0.674736i	$-0.235742\pi$
$53$	4.55740	+	2.32211i	0.626008	+	0.318967i	−0.112052	+	0.993702i	$0.535742\pi$
$54$	−5.54101			−0.754036
$55$	−6.70905	+	3.16048i	−0.904648	+	0.426159i
$56$	2.98504			0.398893
$57$	−2.13451	−	1.08759i	−0.282722	−	0.144054i
$58$	4.35116	−	0.689156i	0.571335	−	0.0904906i
$59$	4.39097	+	6.04365i	0.571656	+	0.786817i	0.992750	−	0.120200i	$-0.0383537\pi$
$59$	4.39097	+	6.04365i	0.571656	+	0.786817i	−0.421094	+	0.907017i	$0.638354\pi$
$60$	2.72654	+	0.568734i	0.351994	+	0.0734232i
$61$	−4.11435	−	1.33683i	−0.526788	−	0.171164i	0.0335354	−	0.999438i	$-0.489323\pi$
$61$	−4.11435	−	1.33683i	−0.526788	−	0.171164i	−0.560324	+	0.828274i	$0.689323\pi$
$62$	−0.170845	+	1.07867i	−0.0216974	+	0.136992i
$63$	−0.676399	−	4.27062i	−0.0852183	−	0.538047i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−1.45730	−	13.3766i	−0.180756	−	1.65917i
$66$	3.71326	+	1.81055i	0.457071	+	0.222864i
$67$	−1.06709	−	1.06709i	−0.130366	−	0.130366i	0.638913	−	0.769279i	$-0.279384\pi$
$67$	−1.06709	−	1.06709i	−0.130366	−	0.130366i	−0.769279	+	0.638913i	$0.779384\pi$
$68$	3.00301	−	5.89374i	0.364168	−	0.714721i
$69$	−0.628239	+	0.864697i	−0.0756311	+	0.104097i
$70$	−0.324023	+	6.66688i	−0.0387282	+	0.796845i
$71$	1.18906	−	3.65955i	0.141115	−	0.434308i	−0.855376	−	0.518008i	$-0.826674\pi$
$71$	1.18906	−	3.65955i	0.141115	−	0.434308i	0.996491	+	0.0836998i	$0.0266737\pi$
$72$	0.657608	+	1.29063i	0.0774999	+	0.152102i
$73$	0.684302	+	0.108383i	0.0800915	+	0.0126852i	0.196352	−	0.980534i	$-0.437091\pi$
$73$	0.684302	+	0.108383i	0.0800915	+	0.0126852i	−0.116260	+	0.993219i	$0.537091\pi$
$74$	−5.95276	−	4.32493i	−0.691994	−	0.502763i
$75$	−1.56619	+	6.02780i	−0.180848	+	0.696030i
$76$			1.92328i			0.220615i
$77$	−2.89347	+	9.46799i	−0.329742	+	1.07898i
$78$	−5.30009	+	5.30009i	−0.600117	+	0.600117i
$79$	1.26384	+	3.88969i	0.142193	+	0.437624i	0.996639	−	0.0819149i	$-0.0261036\pi$
$79$	1.26384	+	3.88969i	0.142193	+	0.437624i	−0.854447	+	0.519539i	$0.826104\pi$
$80$	−0.586932	−	2.15766i	−0.0656210	−	0.241234i
$81$	−2.06810	+	1.50256i	−0.229788	+	0.166951i
$82$	7.34040	−	3.74012i	0.810611	−	0.413027i
$83$	−0.881701	+	0.449249i	−0.0967792	+	0.0493115i	−0.501710	−	0.865036i	$-0.667296\pi$
$83$	−0.881701	+	0.449249i	−0.0967792	+	0.0493115i	0.404931	+	0.914347i	$0.367296\pi$
$84$	3.00803	−	2.18546i	0.328203	−	0.238454i
$85$	12.8373	+	7.34678i	1.39240	+	0.796870i
$86$	−1.70627	−	5.25135i	−0.183991	−	0.566267i
$87$	3.88012	−	3.88012i	0.415992	−	0.415992i
$88$	−0.0582620	−	3.31611i	−0.00621075	−	0.353499i
$89$		−	12.5362i		−	1.32883i	−0.747362	−	0.664417i	$-0.768680\pi$
$89$		−	12.5362i		−	1.32883i	0.747362	−	0.664417i	$-0.231320\pi$
$90$	−2.95391	+	1.32863i	−0.311370	+	0.140050i
$91$	−14.5322	−	10.5583i	−1.52339	−	1.10681i
$92$	0.847523	+	0.134234i	0.0883603	+	0.0139949i
$93$	0.617578	+	1.21207i	0.0640399	+	0.125685i
$94$	2.26046	−	6.95697i	0.233148	−	0.717556i
$95$	−4.29551	−	0.208770i	−0.440710	−	0.0214193i
$96$	−0.732139	+	1.00770i	−0.0747236	+	0.102848i
$97$	−2.26820	+	4.45160i	−0.230301	+	0.451991i	−0.977020	−	0.213149i	$-0.931628\pi$
$97$	−2.26820	+	4.45160i	−0.230301	+	0.451991i	0.746719	+	0.665140i	$0.231628\pi$
$98$	1.35090	+	1.35090i	0.136461	+	0.136461i
$99$	−4.73107	+	0.834773i	−0.475491	+	0.0838979i
$100$	4.88270	−	1.07666i	0.488270	−	0.107666i
$101$	−1.43174	+	0.465200i	−0.142463	+	0.0462891i	−0.379381	−	0.925241i	$-0.623863\pi$
$101$	−1.43174	+	0.465200i	−0.142463	+	0.0462891i	0.236917	+	0.971530i	$0.423863\pi$
$102$	−1.28889	−	8.13776i	−0.127620	−	0.805758i
$103$	2.88546	−	18.2181i	0.284313	−	1.79508i	−0.270094	−	0.962834i	$-0.587055\pi$
$103$	2.88546	−	18.2181i	0.284313	−	1.79508i	0.554407	−	0.832246i	$-0.312945\pi$
$104$	5.72308	+	1.85954i	0.561194	+	0.182343i
$105$	4.55457	+	6.95547i	0.444480	+	0.678784i
$106$	−3.00646	−	4.13804i	−0.292013	−	0.401922i
$107$	3.84509	−	0.609002i	0.371719	−	0.0588744i	0.0322195	−	0.999481i	$-0.489742\pi$
$107$	3.84509	−	0.609002i	0.371719	−	0.0588744i	0.339499	+	0.940606i	$0.389742\pi$
$108$	4.93708	+	2.51557i	0.475071	+	0.242061i
$109$	−0.603873			−0.0578405			−0.0289203	−	0.999582i	$-0.509207\pi$
$109$	−0.603873			−0.0578405			−0.0289203	+	0.999582i	$0.509207\pi$
$110$	7.41264	+	0.229836i	0.706767	+	0.0219140i
$111$	−9.16507			−0.869909
$112$	−2.65969	−	1.35518i	−0.251317	−	0.128052i
$113$	−1.87248	+	0.296572i	−0.176149	+	0.0278992i	−0.243886	−	0.969804i	$-0.578422\pi$
$113$	−1.87248	+	0.296572i	−0.176149	+	0.0278992i	0.0677370	+	0.997703i	$0.478422\pi$
$114$	1.40811	+	1.93809i	0.131881	+	0.181519i
$115$	−0.391801	+	1.87831i	−0.0365356	+	0.175154i
$116$	−4.18978	−	1.36134i	−0.389011	−	0.126397i
$117$	1.36357	−	8.60922i	0.126062	−	0.795923i
$118$	−1.16862	−	7.37839i	−0.107580	−	0.679236i
$119$	18.7787	−	6.10158i	1.72144	−	0.559331i
$120$	−2.17116	−	1.74457i	−0.198199	−	0.159257i
$121$	10.5746	+	3.02959i	0.961325	+	0.275418i
$122$	3.05900	+	3.05900i	0.276949	+	0.276949i
$123$	4.65865	−	9.14312i	0.420057	−	0.824408i
$124$	0.641932	−	0.883543i	0.0576472	−	0.0793445i
$125$	1.87464	+	11.0221i	0.167672	+	0.985843i
$126$	−1.33614	+	4.11223i	−0.119033	+	0.366346i
$127$	−0.932788	−	1.83070i	−0.0827715	−	0.162448i	0.845911	−	0.533324i	$-0.179057\pi$
$127$	−0.932788	−	1.83070i	−0.0827715	−	0.162448i	−0.928682	+	0.370876i	$0.879057\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−5.56413	−	4.04257i	−0.489894	−	0.355929i
$130$	−4.77439	+	12.5803i	−0.418742	+	1.10336i
$131$			19.3469i			1.69035i	0.534490	+	0.845175i	$0.320504\pi$
$131$			19.3469i			1.69035i	−0.534490	+	0.845175i	$0.679496\pi$
$132$	−2.48657	−	3.29900i	−0.216428	−	0.287141i
$133$	−4.05954	+	4.05954i	−0.352007	+	0.352007i
$134$	0.466336	+	1.43523i	0.0402853	+	0.123985i
$135$	−6.15426	+	10.7536i	−0.529675	+	0.925520i
$136$	−5.35140	+	3.88802i	−0.458879	+	0.333395i
$137$	−5.46818	+	2.78618i	−0.467178	+	0.238039i	−0.671701	−	0.740823i	$-0.734436\pi$
$137$	−5.46818	+	2.78618i	−0.467178	+	0.238039i	0.204522	+	0.978862i	$0.434436\pi$
$138$	0.952329	−	0.485236i	0.0810677	−	0.0413060i
$139$	−16.2922	+	11.8369i	−1.38188	+	1.00400i	−0.385181	+	0.922841i	$0.625861\pi$
$139$	−16.2922	+	11.8369i	−1.38188	+	1.00400i	−0.996701	+	0.0811552i	$0.974139\pi$
$140$	3.31541	−	5.79313i	0.280203	−	0.489609i
$141$	−2.81560	−	8.66552i	−0.237116	−	0.729769i
$142$	−2.72086	+	2.72086i	−0.228329	+	0.228329i
$143$	−11.4456	+	16.3500i	−0.957133	+	1.36726i
$144$		−	1.44851i		−	0.120709i
$145$	3.49526	−	9.20981i	0.290266	−	0.764833i
$146$	−0.560513	−	0.407236i	−0.0463884	−	0.0337031i
$147$	2.35035	+	0.372259i	0.193854	+	0.0307034i
$148$	3.34047	+	6.55604i	0.274585	+	0.538903i
$149$	−0.660141	+	2.03170i	−0.0540808	+	0.166444i	−0.974449	−	0.224610i	$-0.927889\pi$
$149$	−0.660141	+	2.03170i	−0.0540808	+	0.166444i	0.920368	+	0.391053i	$0.127889\pi$
$150$	4.13205	−	4.65977i	0.337381	−	0.380469i
$151$	4.91322	−	6.76246i	0.399832	−	0.550321i	−0.560870	−	0.827904i	$-0.689533\pi$
$151$	4.91322	−	6.76246i	0.399832	−	0.550321i	0.960702	+	0.277583i	$0.0895332\pi$
$152$	0.873149	−	1.71365i	0.0708217	−	0.138995i
$153$	6.77510	+	6.77510i	0.547734	+	0.547734i
$154$	6.87648	−	7.12243i	0.554123	−	0.573942i
$155$	1.90365	+	1.52962i	0.152905	+	0.122862i
$156$	7.12861	−	2.31622i	0.570745	−	0.185446i
$157$	2.04916	+	12.9379i	0.163541	+	1.03256i	0.923783	+	0.382917i	$0.125080\pi$
$157$	2.04916	+	12.9379i	0.163541	+	1.03256i	−0.760242	+	0.649640i	$0.774920\pi$
$158$	0.639796	−	4.03951i	0.0508994	−	0.321366i
$159$	−6.05924	−	1.96877i	−0.480529	−	0.156133i
$160$	−0.456598	+	2.18895i	−0.0360973	+	0.173052i
$161$	1.50557	+	2.07224i	0.118655	+	0.163315i
$162$	2.52483	−	0.399894i	0.198370	−	0.0314187i
$163$	−6.96278	−	3.54771i	−0.545367	−	0.277878i	0.159524	−	0.987194i	$-0.449004\pi$
$163$	−6.96278	−	3.54771i	−0.545367	−	0.277878i	−0.704891	+	0.709316i	$0.749004\pi$
$164$	−8.23832			−0.643305
$165$	7.63801	−	5.19547i	0.594618	−	0.404467i
$166$	0.989556			0.0768044
$167$	10.7468	+	5.47577i	0.831613	+	0.423728i	0.817330	−	0.576170i	$-0.195453\pi$
$167$	10.7468	+	5.47577i	0.831613	+	0.423728i	0.0142828	+	0.999898i	$0.495453\pi$
$168$	−3.67236	+	0.581644i	−0.283328	+	0.0448748i
$169$	−13.6434	−	18.7785i	−1.04949	−	1.44450i
$170$	−8.10274	−	12.3740i	−0.621452	−	0.949045i
$171$	−2.64953	−	0.860884i	−0.202614	−	0.0658334i
$172$	−0.863768	+	5.45361i	−0.0658617	+	0.415834i
$173$	−0.326443	−	2.06108i	−0.0248190	−	0.156701i	0.972166	−	0.234292i	$-0.0752772\pi$
$173$	−0.326443	−	2.06108i	−0.0248190	−	0.156701i	−0.996985	+	0.0775909i	$0.975277\pi$
$174$	−5.21875	+	1.69567i	−0.395632	+	0.128549i
$175$	12.5787	+	8.03357i	0.950859	+	0.607281i
$176$	−1.45357	+	2.98113i	−0.109567	+	0.224711i
$177$	−6.57964	−	6.57964i	−0.494556	−	0.494556i
$178$	−5.69132	+	11.1698i	−0.426582	+	0.837215i
$179$	11.2024	−	15.4187i	0.837303	−	1.15245i	−0.149216	−	0.988805i	$-0.547675\pi$
$179$	11.2024	−	15.4187i	0.837303	−	1.15245i	0.986519	−	0.163645i	$-0.0523251\pi$
$180$	3.23514	+	0.157234i	0.241133	+	0.0117195i
$181$	0.553354	−	1.70305i	0.0411305	−	0.126587i	−0.928383	−	0.371625i	$-0.878801\pi$
$181$	0.553354	−	1.70305i	0.0411305	−	0.126587i	0.969513	+	0.245039i	$0.0788007\pi$
$182$	8.15493	+	16.0050i	0.604484	+	1.18637i
$183$	5.32218	+	0.842951i	0.393427	+	0.0623127i
$184$	−0.694207	−	0.504371i	−0.0511776	−	0.0371827i
$185$	−15.0051	+	6.74906i	−1.10319	+	0.496201i
$186$		−	1.36033i		−	0.0997444i
$187$	−7.14484	−	20.7424i	−0.522482	−	1.51684i
$188$	−5.17248	+	5.17248i	−0.377242	+	0.377242i
$189$	5.11118	+	15.7306i	0.371784	+	1.14423i
$190$	3.73254	+	2.13613i	0.270787	+	0.154971i
$191$	−21.7457	+	15.7992i	−1.57346	+	1.14319i	−0.649718	+	0.760175i	$0.725113\pi$
$191$	−21.7457	+	15.7992i	−1.57346	+	1.14319i	−0.923743	+	0.383012i	$0.874887\pi$
$192$	1.10983	−	0.565486i	0.0800950	−	0.0408104i
$193$	20.7217	−	10.5582i	1.49158	−	0.759998i	0.497379	−	0.867534i	$-0.334296\pi$
$193$	20.7217	−	10.5582i	1.49158	−	0.759998i	0.994201	+	0.107536i	$0.0342960\pi$
$194$	4.04197	−	2.93666i	0.290196	−	0.210840i
$195$	4.39933	+	16.1727i	0.315042	+	1.15815i
$196$	−0.590364	−	1.81695i	−0.0421689	−	0.129782i
$197$	−5.14362	+	5.14362i	−0.366468	+	0.366468i	−0.866187	−	0.499720i	$-0.833436\pi$
$197$	−5.14362	+	5.14362i	−0.366468	+	0.366468i	0.499720	+	0.866187i	$0.333436\pi$
$198$	4.59440	+	1.40407i	0.326510	+	0.0997832i
$199$			5.52773i			0.391851i	0.980619	+	0.195925i	$0.0627710\pi$
$199$			5.52773i			0.391851i	−0.980619	+	0.195925i	$0.937229\pi$
$200$	−4.83932	−	1.25739i	−0.342191	−	0.0889109i
$201$	1.52072	+	1.10487i	0.107263	+	0.0779313i
$202$	1.48688	+	0.235499i	0.104617	+	0.0165697i
$203$	−5.97010	−	11.7170i	−0.419019	−	0.822371i
$204$	−2.54605	+	7.83594i	−0.178259	+	0.548626i
$205$	0.894261	−	18.3997i	0.0624579	−	1.28509i
$206$	−10.8418	+	14.9224i	−0.755384	+	1.03970i
$207$	−0.564285	+	1.10747i	−0.0392205	+	0.0769746i
$208$	−4.25509	−	4.25509i	−0.295037	−	0.295037i
$209$	4.58902	+	4.43055i	0.317429	+	0.306468i
$210$	−0.900432	−	8.26510i	−0.0621357	−	0.570346i
$211$	13.6787	−	4.44447i	0.941679	−	0.305970i	0.202349	−	0.979313i	$-0.435142\pi$
$211$	13.6787	−	4.44447i	0.941679	−	0.305970i	0.739330	+	0.673343i	$0.235142\pi$
$212$	0.800146	+	5.05192i	0.0549542	+	0.346967i
$213$	−0.749771	+	4.73387i	−0.0513734	+	0.324359i
$214$	−3.70248	−	1.20301i	−0.253096	−	0.0822360i
$215$	−12.0865	−	2.52115i	−0.824293	−	0.171941i
$216$	−3.25693	−	4.48277i	−0.221606	−	0.305014i
$217$	3.21988	−	0.509979i	0.218580	−	0.0346197i
$218$	0.538055	+	0.274153i	0.0364417	+	0.0185680i
$219$	−0.862984			−0.0583151
$220$	−6.50036	−	3.57005i	−0.438254	−	0.240693i
$221$	39.8046			2.67755
$222$	8.16613	+	4.16085i	0.548075	+	0.279258i
$223$	10.7587	−	1.70401i	0.720455	−	0.114109i	0.214569	−	0.976709i	$-0.431165\pi$
$223$	10.7587	−	1.70401i	0.720455	−	0.114109i	0.505886	+	0.862600i	$0.331165\pi$
$224$	1.75456	+	2.41495i	0.117232	+	0.161355i
$225$	−0.702343	+	7.20840i	−0.0468228	+	0.480560i
$226$	1.80304	+	0.585842i	0.119936	+	0.0389696i
$227$	3.03548	−	19.1653i	0.201472	−	1.27204i	−0.654913	−	0.755705i	$-0.727295\pi$
$227$	3.03548	−	19.1653i	0.201472	−	1.27204i	0.856384	−	0.516339i	$-0.172705\pi$
$228$	−0.374756	−	2.36612i	−0.0248188	−	0.156700i
$229$	22.6436	−	7.35735i	1.49633	−	0.486188i	0.557386	−	0.830253i	$-0.311804\pi$
$229$	22.6436	−	7.35735i	1.49633	−	0.486188i	0.938946	+	0.344066i	$0.111804\pi$
$230$	1.20183	−	1.49572i	0.0792466	−	0.0986245i
$231$	1.71484	−	12.2118i	0.112828	−	0.803480i
$232$	3.11508	+	3.11508i	0.204515	+	0.204515i
$233$	−4.15559	+	8.15580i	−0.272241	+	0.534304i	−0.986134	−	0.165951i	$-0.946931\pi$
$233$	−4.15559	+	8.15580i	−0.272241	+	0.534304i	0.713892	+	0.700255i	$0.246931\pi$
$234$	−5.12345	+	7.05183i	−0.334931	+	0.460992i
$235$	−10.9909	−	12.1138i	−0.716968	−	0.790220i
$236$	−2.30847	+	7.10474i	−0.150269	+	0.462479i
$237$	−2.31276	−	4.53905i	−0.150230	−	0.294843i
$238$	−19.5020	−	3.08882i	−1.26413	−	0.200218i
$239$	10.2431	+	7.44206i	0.662572	+	0.481387i	0.867531	−	0.497384i	$-0.165706\pi$
$239$	10.2431	+	7.44206i	0.662572	+	0.481387i	−0.204958	+	0.978771i	$0.565706\pi$
$240$	1.14250	+	2.54011i	0.0737483	+	0.163963i
$241$		−	21.3861i		−	1.37760i	−0.724952	−	0.688799i	$-0.758138\pi$
$241$		−	21.3861i		−	1.37760i	0.724952	−	0.688799i	$-0.241862\pi$
$242$	−8.04661	−	7.50014i	−0.517255	−	0.482127i
$243$	−9.50276	+	9.50276i	−0.609602	+	0.609602i
$244$	−1.33683	−	4.11435i	−0.0855820	−	0.263394i
$245$	4.12213	−	1.12131i	0.263353	−	0.0716379i
$246$	−8.30178	+	6.03160i	−0.529302	+	0.384561i
$247$	−10.3121	+	5.25426i	−0.656141	+	0.334321i
$248$	−0.973086	+	0.495812i	−0.0617910	+	0.0314841i
$249$	0.997179	−	0.724493i	0.0631936	−	0.0459129i
$250$	3.33360	−	10.6718i	0.210835	−	0.674943i
$251$	−7.07662	−	21.7796i	−0.446672	−	1.37472i	−0.880639	−	0.473787i	$-0.842887\pi$
$251$	−7.07662	−	21.7796i	−0.446672	−	1.37472i	0.433967	−	0.900929i	$-0.357113\pi$
$252$	3.05742	−	3.05742i	0.192600	−	0.192600i
$253$	2.27268	−	1.71300i	0.142882	−	0.107695i
$254$			2.05464i			0.128920i
$255$	−17.2247	−	6.53702i	−1.07865	−	0.409364i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−10.0983	−	1.59941i	−0.629912	−	0.0997682i	−0.166688	−	0.986010i	$-0.553307\pi$
$257$	−10.0983	−	1.59941i	−0.629912	−	0.0997682i	−0.463224	+	0.886241i	$0.653307\pi$
$258$	3.12238	+	6.12802i	0.194391	+	0.381514i
$259$	−6.78724	+	20.8890i	−0.421738	+	1.29798i
$260$	9.96533	−	9.04156i	0.618024	−	0.560734i
$261$	3.75080	−	5.16254i	0.232169	−	0.319553i
$262$	8.78333	−	17.2383i	0.542636	−	1.06498i
$263$	−14.5957	−	14.5957i	−0.900008	−	0.900008i	0.0954281	−	0.995436i	$-0.469578\pi$
$263$	−14.5957	−	14.5957i	−0.900008	−	0.900008i	−0.995436	+	0.0954281i	$0.969578\pi$
$264$	0.717832	+	4.06831i	0.0441795	+	0.250387i
$265$	−11.3700	+	1.23869i	−0.698452	+	0.0760921i
$266$	5.46007	−	1.77408i	0.334778	−	0.108776i
$267$	2.44272	+	15.4227i	0.149492	+	0.943855i
$268$	0.236074	−	1.49052i	0.0144205	−	0.0910477i
$269$	0.345400	+	0.112227i	0.0210594	+	0.00684263i	0.319528	−	0.947577i	$-0.396476\pi$
$269$	0.345400	+	0.112227i	0.0210594	+	0.00684263i	−0.298468	+	0.954420i	$0.596476\pi$
$270$	10.3655	−	6.78752i	0.630825	−	0.413075i
$271$	10.0890	+	13.8863i	0.612864	+	0.843534i	0.996809	−	0.0798214i	$-0.0254350\pi$
$271$	10.0890	+	13.8863i	0.612864	+	0.843534i	−0.383946	+	0.923356i	$0.625435\pi$
$272$	6.53326	−	1.03477i	0.396137	−	0.0627419i
$273$	19.9356	+	10.1577i	1.20656	+	0.614772i
$274$	6.13709			0.370755
$275$	8.67908	−	14.1306i	0.523368	−	0.852107i
$276$	−1.06882			−0.0643357
$277$	−10.4575	−	5.32834i	−0.628328	−	0.320149i	0.110669	−	0.993857i	$-0.464701\pi$
$277$	−10.4575	−	5.32834i	−0.628328	−	0.320149i	−0.738998	+	0.673708i	$0.764701\pi$
$278$	19.8903	−	3.15031i	1.19294	−	0.188943i
$279$	0.929843	+	1.27982i	0.0556682	+	0.0766207i
$280$	−5.58408	+	3.65655i	−0.333712	+	0.218521i
$281$	7.58400	+	2.46419i	0.452424	+	0.147001i	0.526360	−	0.850262i	$-0.323556\pi$
$281$	7.58400	+	2.46419i	0.452424	+	0.147001i	−0.0739367	+	0.997263i	$0.523556\pi$
$282$	−1.42535	+	8.99929i	−0.0848782	+	0.535900i
$283$	−0.761344	−	4.80693i	−0.0452572	−	0.285743i	0.954672	−	0.297660i	$-0.0962063\pi$
$283$	−0.761344	−	4.80693i	−0.0452572	−	0.285743i	−0.999929	+	0.0119179i	$0.996206\pi$
$284$	3.65955	−	1.18906i	0.217154	−	0.0705577i
$285$	5.32524	−	0.580153i	0.315440	−	0.0343653i
$286$	17.6209	−	9.37179i	1.04195	−	0.554165i
$287$	−17.3890	−	17.3890i	−1.02644	−	1.02644i
$288$	−0.657608	+	1.29063i	−0.0387499	+	0.0760511i
$289$	−15.7257	+	21.6446i	−0.925043	+	1.27321i
$290$	−7.29547	+	6.61919i	−0.428405	+	0.388692i
$291$	1.92306	−	5.91856i	0.112732	−	0.346952i
$292$	0.314539	+	0.617318i	0.0184070	+	0.0361258i
$293$	−11.1251	−	1.76204i	−0.649935	−	0.102940i	−0.177243	−	0.984167i	$-0.556718\pi$
$293$	−11.1251	−	1.76204i	−0.649935	−	0.102940i	−0.472692	+	0.881228i	$0.656718\pi$
$294$	−1.92518	−	1.39872i	−0.112279	−	0.0815751i
$295$	−15.6174	−	5.92702i	−0.909279	−	0.345085i
$296$		−	7.35801i		−	0.427676i
$297$	17.3755	−	5.98510i	1.00823	−	0.347291i
$298$	1.51056	−	1.51056i	0.0875046	−	0.0875046i
$299$	1.59565	+	4.91090i	0.0922787	+	0.284005i
$300$	−5.79718	+	2.27598i	−0.334700	+	0.131404i
$301$	−13.3344	+	9.68798i	−0.768580	+	0.558406i
$302$	−7.44780	+	3.79484i	−0.428573	+	0.218369i
$303$	1.67076	−	0.851292i	0.0959824	−	0.0489055i
$304$	−1.55596	+	1.13047i	−0.0892406	+	0.0648371i
$305$	9.33423	−	2.53912i	0.534476	−	0.145389i
$306$	−2.96083	−	9.11249i	−0.169259	−	0.520926i
$307$	−12.9419	+	12.9419i	−0.738636	+	0.738636i	−0.972314	−	0.233678i	$-0.924924\pi$
$307$	−12.9419	+	12.9419i	−0.738636	+	0.738636i	0.233678	+	0.972314i	$0.424924\pi$
$308$	−9.36051	+	3.22428i	−0.533364	+	0.183720i
$309$			22.9751i			1.30701i
$310$	−1.00173	−	2.22714i	−0.0568947	−	0.126493i
$311$	23.9368	+	17.3911i	1.35733	+	0.986160i	0.998610	+	0.0527163i	$0.0167879\pi$
$311$	23.9368	+	17.3911i	1.35733	+	0.986160i	0.358723	+	0.933444i	$0.383212\pi$
$312$	−7.40318	−	1.17255i	−0.419123	−	0.0663825i
$313$	5.89179	+	11.5633i	0.333024	+	0.653595i	0.995424	−	0.0955543i	$-0.0304623\pi$
$313$	5.89179	+	11.5633i	0.333024	+	0.653595i	−0.662401	+	0.749150i	$0.730462\pi$
$314$	4.04787	−	12.4581i	0.228434	−	0.703049i
$315$	6.49667	+	7.16043i	0.366046	+	0.403444i
$316$	−2.40396	+	3.30877i	−0.135233	+	0.186133i
$317$	−12.6147	+	24.7577i	−0.708512	+	1.39053i	0.202967	+	0.979186i	$0.434942\pi$
$317$	−12.6147	+	24.7577i	−0.708512	+	1.39053i	−0.911479	+	0.411347i	$0.865058\pi$
$318$	4.50502	+	4.50502i	0.252629	+	0.252629i
$319$	−12.9000	+	6.86094i	−0.722261	+	0.384139i
$320$	1.40060	−	1.74308i	0.0782957	−	0.0974412i
$321$	−4.61177	+	1.49845i	−0.257404	+	0.0836356i
$322$	−0.400695	−	2.52989i	−0.0223299	−	0.140985i
$323$	1.99014	−	12.5653i	0.110734	−	0.699150i
$324$	−2.43119	−	0.789942i	−0.135066	−	0.0438857i
$325$	19.1120	+	23.2383i	1.06014	+	1.28903i
$326$	4.59325	+	6.32207i	0.254397	+	0.350147i
$327$	0.742917	−	0.117667i	0.0410834	−	0.00650697i
$328$	7.34040	+	3.74012i	0.405306	+	0.206514i
$329$	−21.8355			−1.20383
$330$	−9.16421	+	1.16162i	−0.504473	+	0.0639450i
$331$	11.9037			0.654287			0.327144	−	0.944975i	$-0.393914\pi$
$331$	11.9037			0.654287			0.327144	+	0.944975i	$0.393914\pi$
$332$	−0.881701	−	0.449249i	−0.0483896	−	0.0246557i
$333$	−10.5269	+	1.66730i	−0.576871	+	0.0913675i
$334$	−7.08952	−	9.75789i	−0.387921	−	0.533928i
$335$	3.30334	+	0.689050i	0.180481	+	0.0376468i
$336$	3.53615	+	1.14897i	0.192913	+	0.0626813i
$337$	1.55178	−	9.79753i	0.0845306	−	0.533705i	−0.908691	−	0.417469i	$-0.862917\pi$
$337$	1.55178	−	9.79753i	0.0845306	−	0.533705i	0.993222	−	0.116236i	$-0.0370829\pi$
$338$	3.63108	+	22.9258i	0.197505	+	1.24700i
$339$	2.24584	−	0.729719i	0.121978	−	0.0396329i
$340$	1.60190	+	14.7039i	0.0868753	+	0.797431i
$341$	−0.629388	−	3.56705i	−0.0340832	−	0.193167i
$342$	1.96991	+	1.96991i	0.106521	+	0.106521i
$343$	−6.89724	+	13.5366i	−0.372416	+	0.730908i
$344$	3.24551	−	4.46706i	0.174986	−	0.240848i
$345$	0.116020	−	2.38715i	0.00624630	−	0.128520i
$346$	−0.644848	+	1.98464i	−0.0346673	+	0.106695i
$347$	6.97122	+	13.6818i	0.374235	+	0.734477i	0.998923	−	0.0463971i	$-0.0147739\pi$
$347$	6.97122	+	13.6818i	0.374235	+	0.734477i	−0.624688	+	0.780874i	$0.714774\pi$
$348$	5.41976	+	0.858405i	0.290529	+	0.0460153i
$349$	−13.5530	−	9.84686i	−0.725478	−	0.527090i	0.162652	−	0.986684i	$-0.447995\pi$
$349$	−13.5530	−	9.84686i	−0.725478	−	0.527090i	−0.888130	+	0.459593i	$0.847995\pi$
$350$	−7.56052	−	12.8686i	−0.404127	−	0.687854i
$351$			33.3436i			1.77975i
$352$	2.64855	−	1.99630i	0.141168	−	0.106403i
$353$	1.15786	−	1.15786i	0.0616269	−	0.0616269i	−0.675622	−	0.737249i	$-0.736125\pi$
$353$	1.15786	−	1.15786i	0.0616269	−	0.0616269i	0.737249	+	0.675622i	$0.236125\pi$
$354$	2.87541	+	8.84959i	0.152826	+	0.470350i
$355$	2.25844	+	8.30242i	0.119866	+	0.440647i
$356$	10.1420	−	7.36859i	0.537525	−	0.390535i
$357$	−21.9137	+	11.1656i	−1.15980	+	0.590946i
$358$	−16.9813	+	8.65242i	−0.897491	+	0.457295i
$359$	18.7571	−	13.6278i	0.989962	−	0.719249i	0.0300489	−	0.999548i	$-0.490434\pi$
$359$	18.7571	−	13.6278i	0.989962	−	0.719249i	0.959913	+	0.280299i	$0.0904337\pi$
$360$	−2.81115	−	1.60882i	−0.148161	−	0.0847923i
$361$	−4.72827	−	14.5521i	−0.248856	−	0.765901i
$362$	−1.26621	+	1.26621i	−0.0665505	+	0.0665505i
$363$	−13.5997	−	1.66668i	−0.713801	−	0.0874782i
$364$		−	17.9628i		−	0.941505i
$365$	−1.41288	+	0.635492i	−0.0739535	+	0.0332632i
$366$	−4.35941	−	3.16729i	−0.227870	−	0.165557i
$367$	22.8016	+	3.61142i	1.19023	+	0.188514i	0.719966	−	0.694010i	$-0.244158\pi$
$367$	22.8016	+	3.61142i	1.19023	+	0.188514i	0.470267	+	0.882524i	$0.344158\pi$
$368$	0.389563	+	0.764561i	0.0203074	+	0.0398555i
$369$	3.68758	−	11.3492i	0.191968	−	0.590816i
$370$	16.4336	+	0.798705i	0.854343	+	0.0415227i
$371$	−8.97440	+	12.3522i	−0.465928	+	0.641294i
$372$	−0.617578	+	1.21207i	−0.0320199	+	0.0628427i
$373$	1.62215	+	1.62215i	0.0839919	+	0.0839919i	0.747855	−	0.663863i	$-0.231084\pi$
$373$	1.62215	+	1.62215i	0.0839919	+	0.0839919i	−0.663863	+	0.747855i	$0.731084\pi$
$374$	−3.05076	+	21.7253i	−0.157751	+	1.12339i
$375$	−4.45396	−	13.1947i	−0.230002	−	0.681369i
$376$	6.95697	−	2.26046i	0.358778	−	0.116574i
$377$	−4.14706	−	26.1835i	−0.213585	−	1.34852i
$378$	2.58745	−	16.3365i	0.133084	−	0.840259i
$379$	34.7072	+	11.2771i	1.78279	+	0.579263i	0.999121	−	0.0419163i	$-0.0133463\pi$
$379$	34.7072	+	11.2771i	1.78279	+	0.579263i	0.783668	+	0.621180i	$0.213346\pi$
$380$	−2.35594	−	3.59785i	−0.120857	−	0.184566i
$381$	1.50428	+	2.07047i	0.0770668	+	0.106073i
$382$	26.5482	−	4.20482i	1.35832	−	0.215137i
$383$	−6.24242	−	3.18067i	−0.318973	−	0.162525i	0.287172	−	0.957879i	$-0.407285\pi$
$383$	−6.24242	−	3.18067i	−0.318973	−	0.162525i	−0.606145	+	0.795354i	$0.707285\pi$
$384$	−1.24559			−0.0635637
$385$	−6.18513	−	21.2560i	−0.315223	−	1.08331i
$386$	−23.2565			−1.18372
$387$	−7.12633	−	3.63105i	−0.362252	−	0.184576i
$388$	−4.93463	+	0.781569i	−0.250518	+	0.0396782i
$389$	1.01424	+	1.39598i	0.0514240	+	0.0707791i	0.833955	−	0.551833i	$-0.186071\pi$
$389$	1.01424	+	1.39598i	0.0514240	+	0.0707791i	−0.782531	+	0.622612i	$0.786071\pi$
$390$	3.42241	−	16.4072i	0.173301	−	0.830812i
$391$	−5.39818	−	1.75398i	−0.272998	−	0.0887024i
$392$	−0.298862	+	1.88694i	−0.0150948	+	0.0953048i
$393$	−3.76981	−	23.8017i	−0.190162	−	1.20063i
$394$	6.91815	−	2.24784i	0.348531	−	0.113245i
$395$	−7.12896	−	5.72825i	−0.358697	−	0.288219i
$396$	−3.45620	−	3.33685i	−0.173681	−	0.167683i
$397$	2.25110	+	2.25110i	0.112979	+	0.112979i	0.761336	−	0.648357i	$-0.224544\pi$
$397$	2.25110	+	2.25110i	0.112979	+	0.112979i	−0.648357	+	0.761336i	$0.724544\pi$
$398$	2.50954	−	4.92525i	0.125792	−	0.246880i
$399$	4.20325	−	5.78528i	0.210426	−	0.289626i
$400$	3.74102	+	3.31735i	0.187051	+	0.165867i
$401$	0.900663	−	2.77195i	0.0449769	−	0.138425i	−0.926046	−	0.377410i	$-0.876815\pi$
$401$	0.900663	−	2.77195i	0.0449769	−	0.138425i	0.971023	+	0.238985i	$0.0768147\pi$
$402$	−0.853372	−	1.67484i	−0.0425623	−	0.0835332i
$403$	6.49103	+	1.02808i	0.323341	+	0.0512122i
$404$	−1.21791	−	0.884862i	−0.0605932	−	0.0440235i
$405$	2.02819	−	5.34415i	0.100781	−	0.265553i
$406$			13.1503i			0.652637i
$407$	23.3383	+	7.13231i	1.15683	+	0.353535i
$408$	5.82599	−	5.82599i	0.288430	−	0.288430i
$409$	−4.87809	−	15.0132i	−0.241206	−	0.742356i	−0.996237	−	0.0866672i	$-0.972378\pi$
$409$	−4.87809	−	15.0132i	−0.241206	−	0.742356i	0.755031	−	0.655689i	$-0.227622\pi$
$410$	−9.15009	+	15.9883i	−0.451891	+	0.789605i
$411$	6.18436	−	4.49320i	0.305052	−	0.221633i
$412$	16.4348	−	8.37393i	0.809682	−	0.412554i
$413$	−19.8689	+	10.1237i	−0.977683	+	0.498154i
$414$	1.00556	−	0.730585i	0.0494208	−	0.0359063i
$415$	1.09907	−	1.92045i	0.0539515	−	0.0942713i
$416$	1.85954	+	5.72308i	0.0911715	+	0.280597i
$417$	17.7370	−	17.7370i	0.868586	−	0.868586i
$418$	−2.07742	−	6.03102i	−0.101610	−	0.294987i
$419$		−	3.20703i		−	0.156674i	−0.996927	−	0.0783368i	$-0.975039\pi$
$419$		−	3.20703i		−	0.156674i	0.996927	−	0.0783368i	$-0.0249609\pi$
$420$	−2.94998	+	7.77304i	−0.143944	+	0.379286i
$421$	−30.3692	−	22.0645i	−1.48011	−	1.07536i	−0.977522	−	0.210832i	$-0.932383\pi$
$421$	−30.3692	−	22.0645i	−1.48011	−	1.07536i	−0.502584	−	0.864528i	$-0.667617\pi$
$422$	−14.2055	−	2.24994i	−0.691515	−	0.109525i
$423$	−4.81040	−	9.44094i	−0.233890	−	0.459034i
$424$	1.58059	−	4.86455i	0.0767602	−	0.236244i
$425$	−33.0141	+	1.98164i	−1.60142	+	0.0961238i
$426$	2.81718	−	3.87752i	0.136493	−	0.187866i
$427$	5.86262	−	11.5060i	0.283712	−	0.556816i
$428$	2.75278	+	2.75278i	0.133061	+	0.133061i
$429$	10.8952	−	22.3449i	0.526025	−	1.07882i
$430$	9.62458	+	7.73352i	0.464139	+	0.372944i
$431$	24.7647	−	8.04654i	1.19287	−	0.387588i	0.355740	−	0.934585i	$-0.384229\pi$
$431$	24.7647	−	8.04654i	1.19287	−	0.387588i	0.837135	+	0.546997i	$0.184229\pi$
$432$	0.866805	+	5.47279i	0.0417042	+	0.263310i
$433$	−5.94173	+	37.5146i	−0.285541	+	1.80284i	0.260929	+	0.965358i	$0.415971\pi$
$433$	−5.94173	+	37.5146i	−0.285541	+	1.80284i	−0.546470	+	0.837478i	$0.684029\pi$
$434$	−3.10046	−	1.00740i	−0.148827	−	0.0483568i
$435$	−2.50550	+	12.0115i	−0.120129	+	0.575906i
$436$	−0.354948	−	0.488544i	−0.0169989	−	0.0233970i
$437$	1.63002	−	0.258170i	0.0779744	−	0.0123499i
$438$	0.768924	+	0.391787i	0.0367406	+	0.0187203i
$439$	1.90085			0.0907227			0.0453614	−	0.998971i	$-0.485556\pi$
$439$	1.90085			0.0907227			0.0453614	+	0.998971i	$0.485556\pi$
$440$	4.17110	+	6.13204i	0.198849	+	0.292334i
$441$	2.76731			0.131777
$442$	−35.4662	−	18.0709i	−1.68695	−	0.859546i
$443$	34.5198	−	5.46740i	1.64009	−	0.259764i	0.732851	−	0.680389i	$-0.238189\pi$
$443$	34.5198	−	5.46740i	1.64009	−	0.259764i	0.907235	+	0.420625i	$0.138189\pi$
$444$	−5.38709	−	7.41469i	−0.255660	−	0.351886i
$445$	15.3563	+	23.4513i	0.727961	+	1.11170i
$446$	−10.3597	−	3.36606i	−0.490544	−	0.159388i
$447$	0.416257	−	2.62814i	0.0196883	−	0.124307i
$448$	−0.466963	−	2.94829i	−0.0220619	−	0.139294i
$449$	−1.14828	+	0.373099i	−0.0541908	+	0.0176076i	−0.335987	−	0.941867i	$-0.609070\pi$
$449$	−1.14828	+	0.373099i	−0.0541908	+	0.0176076i	0.281796	+	0.959474i	$0.409070\pi$
$450$	3.89834	−	6.10387i	0.183769	−	0.287739i
$451$	−18.9782	+	19.6570i	−0.893648	+	0.925612i
$452$	−1.34055	−	1.34055i	−0.0630542	−	0.0630542i
$453$	−4.72682	+	9.27690i	−0.222085	+	0.435867i
$454$	−11.4055	+	15.6983i	−0.535286	+	0.736758i
$455$	40.1186	+	1.94984i	1.88079	+	0.0914100i
$456$	−0.740285	+	2.27836i	−0.0346670	+	0.106694i
$457$	0.887977	+	1.74275i	0.0415378	+	0.0815225i	0.910843	−	0.412754i	$-0.135433\pi$
$457$	0.887977	+	1.74275i	0.0415378	+	0.0815225i	−0.869305	+	0.494276i	$0.835433\pi$
$458$	−23.5158	−	3.72453i	−1.09882	−	0.174036i
$459$	−29.6522	−	21.5436i	−1.38405	−	1.00557i
$460$	−1.74988	+	0.787071i	−0.0815887	+	0.0366974i
$461$		−	22.2043i		−	1.03416i	−0.855938	−	0.517078i	$-0.827020\pi$
$461$		−	22.2043i		−	1.03416i	0.855938	−	0.517078i	$-0.172980\pi$
$462$	−7.07199	+	10.1023i	−0.329019	+	0.470002i
$463$	2.15186	−	2.15186i	0.100006	−	0.100006i	−0.655334	−	0.755339i	$-0.727472\pi$
$463$	2.15186	−	2.15186i	0.100006	−	0.100006i	0.755339	+	0.655334i	$0.227472\pi$
$464$	−1.36134	−	4.18978i	−0.0631987	−	0.194506i
$465$	−2.64003	−	1.51089i	−0.122428	−	0.0700657i
$466$	7.40531	−	5.38027i	0.343044	−	0.249236i
$467$	3.13488	−	1.59730i	0.145065	−	0.0739142i	−0.379951	−	0.925006i	$-0.624059\pi$
$467$	3.13488	−	1.59730i	0.145065	−	0.0739142i	0.525016	+	0.851092i	$0.324059\pi$
$468$	7.76649	−	3.95723i	0.359006	−	0.182923i
$469$	3.64439	−	2.64780i	0.168282	−	0.122264i
$470$	4.29340	+	15.7833i	0.198040	+	0.728028i
$471$	−5.04198	−	15.5176i	−0.232322	−	0.715014i
$472$	5.28235	−	5.28235i	0.243140	−	0.243140i
$473$	11.0227	+	14.6242i	0.506826	+	0.672421i
$474$			5.09429i			0.233989i
$475$	8.29128	−	4.87128i	0.380430	−	0.223510i
$476$	15.9741	+	11.6059i	0.732174	+	0.531955i
$477$	−7.31774	−	1.15902i	−0.335056	−	0.0530677i
$478$	−5.74806	−	11.2812i	−0.262910	−	0.515990i
$479$	1.84581	−	5.68081i	0.0843370	−	0.259563i	−0.899991	−	0.435908i	$-0.856427\pi$
$479$	1.84581	−	5.68081i	0.0843370	−	0.259563i	0.984328	+	0.176345i	$0.0564274\pi$
$480$	0.135207	−	2.78194i	0.00617135	−	0.126978i
$481$	−26.0257	+	35.8213i	−1.18667	+	1.63331i
$482$	−9.70908	+	19.0551i	−0.442236	+	0.867938i
$483$	−2.25601	−	2.25601i	−0.102652	−	0.102652i
$484$	3.76458	+	10.3358i	0.171117	+	0.469807i
$485$	−1.20993	−	11.1060i	−0.0549402	−	0.504298i
$486$	12.7812	−	4.15286i	0.579766	−	0.188377i
$487$	−1.93979	−	12.2474i	−0.0879003	−	0.554981i	−0.991857	−	0.127357i	$-0.959351\pi$
$487$	−1.93979	−	12.2474i	−0.0879003	−	0.554981i	0.903957	−	0.427624i	$-0.140649\pi$
$488$	−0.676748	+	4.27282i	−0.0306350	+	0.193422i
$489$	9.25727	+	3.00787i	0.418628	+	0.136020i
$490$	−4.18191	−	0.872312i	−0.188919	−	0.0394071i
$491$	−5.35143	−	7.36561i	−0.241507	−	0.332405i	0.671008	−	0.741451i	$-0.265862\pi$
$491$	−5.35143	−	7.36561i	−0.241507	−	0.332405i	−0.912514	+	0.409045i	$0.865862\pi$
$492$	10.1352	−	1.60526i	0.456931	−	0.0723708i
$493$	25.9642	+	13.2294i	1.16937	+	0.595824i
$494$	11.5735			0.520717
$495$	7.82780	−	7.35698i	0.351833	−	0.330671i
$496$	1.09212			0.0490376
$497$	10.2342	+	5.21456i	0.459065	+	0.233905i
$498$	−1.21741	+	0.192818i	−0.0545532	+	0.00864038i
$499$	−13.7888	−	18.9787i	−0.617272	−	0.849601i	0.379879	−	0.925036i	$-0.375966\pi$
$499$	−13.7888	−	18.9787i	−0.617272	−	0.849601i	−0.997151	+	0.0754347i	$0.975966\pi$
$500$	−7.81515	+	7.99521i	−0.349504	+	0.357557i
$501$	−14.2883	−	4.64254i	−0.638353	−	0.207413i
$502$	−3.58242	+	22.6185i	−0.159891	+	1.00951i
$503$	−0.668113	−	4.21830i	−0.0297897	−	0.188085i	0.968306	−	0.249766i	$-0.0803537\pi$
$503$	−0.668113	−	4.21830i	−0.0297897	−	0.188085i	−0.998096	+	0.0616815i	$0.980354\pi$
$504$	−4.11223	+	1.33614i	−0.183173	+	0.0595166i
$505$	2.10848	−	2.62406i	0.0938262	−	0.116769i
$506$	−2.80266	+	0.494515i	−0.124593	+	0.0219839i
$507$	20.4439	+	20.4439i	0.907945	+	0.907945i
$508$	0.932788	−	1.83070i	0.0413858	−	0.0812241i
$509$	12.0220	−	16.5468i	0.532865	−	0.733425i	−0.454699	−	0.890645i	$-0.650253\pi$
$509$	12.0220	−	16.5468i	0.532865	−	0.733425i	0.987564	+	0.157220i	$0.0502531\pi$
$510$	12.3795	+	13.6444i	0.548176	+	0.604182i
$511$	−0.639087	+	1.96691i	−0.0282716	+	0.0870109i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	10.5257	+	1.66711i	0.464721	+	0.0736045i
$514$	8.27149	+	6.00959i	0.364840	+	0.265072i
$515$	16.9186	+	37.6149i	0.745523	+	1.65751i
$516$		−	6.87764i		−	0.302771i
$517$	0.426186	+	24.2573i	0.0187436	+	1.06684i
$518$	15.5309	−	15.5309i	0.682387	−	0.682387i
$519$	0.803216	+	2.47205i	0.0352573	+	0.108511i
$520$	−12.9840	+	3.53192i	−0.569384	+	0.154885i
$521$	−12.5171	+	9.09421i	−0.548384	+	0.398425i	−0.827189	−	0.561923i	$-0.810062\pi$
$521$	−12.5171	+	9.09421i	−0.548384	+	0.398425i	0.278805	+	0.960348i	$0.410062\pi$
$522$	−5.68573	+	2.89702i	−0.248858	+	0.126799i
$523$	26.2662	−	13.3833i	1.14854	−	0.585210i	0.227154	−	0.973859i	$-0.427058\pi$
$523$	26.2662	−	13.3833i	1.14854	−	0.585210i	0.921386	+	0.388649i	$0.127058\pi$
$524$	−15.6520	+	11.3718i	−0.683761	+	0.496781i
$525$	−17.0403	−	7.43234i	−0.743701	−	0.324374i
$526$	6.37855	+	19.6311i	0.278118	+	0.855959i
$527$	−5.10817	+	5.10817i	−0.222515	+	0.222515i
$528$	1.20738	−	3.95078i	0.0525445	−	0.171936i
$529$			22.2637i			0.967986i
$530$	10.6931	+	4.05818i	0.464478	+	0.176276i
$531$	−8.75428	−	6.36035i	−0.379903	−	0.276016i
$532$	−5.67037	−	0.898099i	−0.245842	−	0.0389375i
$533$	−22.5066	−	44.1716i	−0.974867	−	1.91328i
$534$	4.82529	−	14.8507i	0.208811	−	0.642653i
$535$	−6.44695	+	5.84933i	−0.278726	+	0.252889i
$536$	−0.887024	+	1.22088i	−0.0383136	+	0.0527341i
$537$	−10.7774	+	21.1518i	−0.465077	+	0.912766i
$538$	−0.256804	−	0.256804i	−0.0110716	−	0.0110716i
$539$	−5.69533	−	2.77699i	−0.245315	−	0.119613i
$540$	−12.3172	+	1.34188i	−0.530048	+	0.0577455i
$541$	−9.60606	+	3.12120i	−0.412997	+	0.134191i	−0.508143	−	0.861273i	$-0.669668\pi$
$541$	−9.60606	+	3.12120i	−0.412997	+	0.134191i	0.0951467	+	0.995463i	$0.469668\pi$
$542$	−2.68511	−	16.9531i	−0.115335	−	0.728199i
$543$	−0.348922	+	2.20300i	−0.0149737	+	0.0945400i
$544$	−6.29095	−	2.04405i	−0.269722	−	0.0876381i
$545$	1.12966	−	0.739720i	0.0483892	−	0.0316861i
$546$	−13.1513	−	18.1011i	−0.562822	−	0.774657i
$547$	−19.8531	+	3.14442i	−0.848858	+	0.134446i	−0.565683	−	0.824623i	$-0.691388\pi$
$547$	−19.8531	+	3.14442i	−0.848858	+	0.134446i	−0.283174	+	0.959068i	$0.591388\pi$
$548$	−5.46818	−	2.78618i	−0.233589	−	0.119020i
$549$	6.26636			0.267442
$550$	−14.1483	+	8.65023i	−0.603284	+	0.368847i
$551$	−8.47279			−0.360953
$552$	0.952329	+	0.485236i	0.0405338	+	0.0206530i
$553$	−12.0581	+	1.90981i	−0.512762	+	0.0812136i
$554$	6.89865	+	9.49518i	0.293096	+	0.403411i
$555$	17.1450	−	11.2268i	0.727764	−	0.476553i
$556$	−19.1526	−	6.22305i	−0.812250	−	0.263916i
$557$	−0.0786778	+	0.496752i	−0.00333369	+	0.0210481i	−0.989299	−	0.145902i	$-0.953392\pi$
$557$	−0.0786778	+	0.496752i	−0.00333369	+	0.0210481i	0.985965	+	0.166950i	$0.0533917\pi$
$558$	−0.247470	−	1.56247i	−0.0104763	−	0.0661445i
$559$	−31.6005	+	10.2676i	−1.33656	+	0.434275i
$560$	6.63549	−	0.722896i	0.280401	−	0.0305479i
$561$	12.8317	+	24.1262i	0.541754	+	1.01861i
$562$	−5.63868	−	5.63868i	−0.237853	−	0.237853i
$563$	−4.02970	+	7.90873i	−0.169832	+	0.333313i	−0.960198	−	0.279322i	$-0.909890\pi$
$563$	−4.02970	+	7.90873i	−0.169832	+	0.333313i	0.790366	+	0.612635i	$0.209890\pi$
$564$	5.35559	−	7.37134i	0.225511	−	0.310389i
$565$	3.13954	−	2.84851i	0.132082	−	0.119838i
$566$	−1.50394	+	4.62865i	−0.0632153	+	0.194557i
$567$	−3.46425	−	6.79898i	−0.145485	−	0.285530i
$568$	−3.80050	−	0.601940i	−0.159466	−	0.0252569i
$569$	17.8490	+	12.9680i	0.748267	+	0.543648i	0.895289	−	0.445485i	$-0.146969\pi$
$569$	17.8490	+	12.9680i	0.748267	+	0.543648i	−0.147022	+	0.989133i	$0.546969\pi$
$570$	−5.00821	−	1.90069i	−0.209771	−	0.0796111i
$571$			2.16814i			0.0907340i	0.998970	+	0.0453670i	$0.0144457\pi$
$571$			2.16814i			0.0907340i	−0.998970	+	0.0453670i	$0.985554\pi$
$572$	−19.9550	+	0.350598i	−0.834362	+	0.0146592i
$573$	23.6742	−	23.6742i	0.989004	−	0.989004i
$574$	7.59926	+	23.3881i	0.317187	+	0.976201i
$575$	−1.56792	−	3.99368i	−0.0653868	−	0.166548i
$576$	1.17187	−	0.851411i	0.0488278	−	0.0354755i
$577$	28.7003	−	14.6235i	1.19481	−	0.608786i	0.260579	−	0.965453i	$-0.416087\pi$
$577$	28.7003	−	14.6235i	1.19481	−	0.608786i	0.934232	+	0.356666i	$0.116087\pi$
$578$	23.8382	−	12.1462i	0.991537	−	0.505213i
$579$	−23.4356	+	17.0270i	−0.973952	+	0.707617i
$580$	9.50536	−	2.58567i	0.394689	−	0.107364i
$581$	−0.912794	−	2.80929i	−0.0378691	−	0.116549i
$582$	−4.40043	+	4.40043i	−0.182404	+	0.182404i
$583$	13.8974	+	9.72867i	0.575570	+	0.402920i
$584$		−	0.692832i		−	0.0286696i
$585$	7.99515	+	17.7755i	0.330559	+	0.734926i
$586$	9.11258	+	6.62068i	0.376437	+	0.273498i
$587$	30.0954	+	4.76664i	1.24217	+	0.196740i	0.742719	−	0.669603i	$-0.233536\pi$
$587$	30.0954	+	4.76664i	1.24217	+	0.196740i	0.499449	+	0.866343i	$0.333536\pi$
$588$	1.08034	+	2.12028i	0.0445524	+	0.0874390i
$589$	0.649074	−	1.99764i	0.0267446	−	0.0823115i
$590$	11.2244	+	12.3712i	0.462100	+	0.509312i
$591$	5.32571	−	7.33021i	0.219070	−	0.301524i
$592$	−3.34047	+	6.55604i	−0.137292	+	0.269452i
$593$	−31.2314	−	31.2314i	−1.28252	−	1.28252i	−0.939230	−	0.343289i	$-0.888459\pi$
$593$	−31.2314	−	31.2314i	−1.28252	−	1.28252i	−0.343289	−	0.939230i	$-0.611541\pi$
$594$	−18.1989	−	2.55557i	−0.746710	−	0.104856i
$595$	−27.6550	+	34.4174i	−1.13374	+	1.41097i
$596$	−2.03170	+	0.660141i	−0.0832218	+	0.0270404i
$597$	−1.07710	−	6.80052i	−0.0440826	−	0.278327i
$598$	0.807769	−	5.10005i	0.0330321	−	0.208557i
$599$	−31.8408	−	10.3457i	−1.30098	−	0.422714i	−0.425058	−	0.905166i	$-0.639746\pi$
$599$	−31.8408	−	10.3457i	−1.30098	−	0.422714i	−0.875923	+	0.482451i	$0.839746\pi$
$600$	6.19859	+	0.603953i	0.253057	+	0.0246563i
$601$	14.8093	+	20.3833i	0.604086	+	0.831453i	0.996075	−	0.0885173i	$-0.0282129\pi$
$601$	14.8093	+	20.3833i	0.604086	+	0.831453i	−0.391989	+	0.919970i	$0.628213\pi$
$602$	16.2793	−	2.57838i	0.663493	−	0.105087i
$603$	1.94768	+	0.992394i	0.0793157	+	0.0404134i
$604$	8.35886			0.340117
$605$	−23.4929	+	7.28600i	−0.955120	+	0.296218i
$606$	−1.87513			−0.0761720
$607$	21.6399	+	11.0261i	0.878337	+	0.447535i	0.834182	−	0.551490i	$-0.185940\pi$
$607$	21.6399	+	11.0261i	0.878337	+	0.447535i	0.0441550	+	0.999025i	$0.485940\pi$
$608$	1.89960	−	0.300867i	0.0770388	−	0.0122018i
$609$	9.62783	+	13.2516i	0.390139	+	0.536981i
$610$	−9.46960	−	1.97528i	−0.383413	−	0.0799768i
$611$	−41.8643	−	13.6025i	−1.69365	−	0.550299i
$612$	−1.49887	+	9.46347i	−0.0605881	+	0.382538i
$613$	−3.67031	−	23.1734i	−0.148242	−	0.935965i	−0.943903	−	0.330222i	$-0.892876\pi$
$613$	−3.67031	−	23.1734i	−0.148242	−	0.935965i	0.795661	−	0.605742i	$-0.207124\pi$
$614$	17.4069	−	5.65584i	0.702484	−	0.228251i
$615$	2.48508	+	22.8106i	0.100208	+	0.919812i
$616$	9.80406	+	1.37673i	0.395017	+	0.0554700i
$617$	15.5463	+	15.5463i	0.625871	+	0.625871i	0.947027	−	0.321155i	$-0.104071\pi$
$617$	15.5463	+	15.5463i	0.625871	+	0.625871i	−0.321155	+	0.947027i	$0.604071\pi$
$618$	10.4305	−	20.4710i	0.419575	−	0.823463i
$619$	13.7116	−	18.8724i	0.551115	−	0.758545i	−0.439048	−	0.898464i	$-0.644684\pi$
$619$	13.7116	−	18.8724i	0.551115	−	0.758545i	0.990163	+	0.139919i	$0.0446841\pi$
$620$	−0.118548	+	2.43917i	−0.00476102	+	0.0979596i
$621$	1.46927	−	4.52196i	0.0589600	−	0.181460i
$622$	−13.4325	−	26.3627i	−0.538593	−	1.05705i
$623$	36.9603	+	5.85394i	1.48078	+	0.234533i
$624$	6.06396	+	4.40572i	0.242752	+	0.176370i
$625$	−17.0084	−	18.3225i	−0.680338	−	0.732899i
$626$		−	12.9778i		−	0.518696i
$627$	−6.50897	−	4.55652i	−0.259943	−	0.181970i
$628$	−9.26252	+	9.26252i	−0.369615	+	0.369615i
$629$	−15.0402	−	46.2889i	−0.599691	−	1.84566i
$630$	−2.53781	−	9.32941i	−0.101109	−	0.371693i
$631$	18.3812	−	13.3547i	0.731744	−	0.531643i	−0.158371	−	0.987380i	$-0.550624\pi$
$631$	18.3812	−	13.3547i	0.731744	−	0.531643i	0.890115	+	0.455737i	$0.150624\pi$
$632$	3.64410	−	1.85676i	0.144954	−	0.0738579i
$633$	−15.9622	+	8.13316i	−0.634442	+	0.323264i
$634$	22.4795	−	16.3323i	0.892777	−	0.648640i
$635$	3.98749	+	2.28204i	0.158239	+	0.0905599i
$636$	−1.96877	−	6.05924i	−0.0780666	−	0.240264i
$637$	8.12917	−	8.12917i	0.322089	−	0.322089i
$638$	14.6088	−	0.256667i	0.578367	−	0.0101616i
$639$			5.57368i			0.220491i
$640$	−2.03928	+	0.917239i	−0.0806097	+	0.0362571i
$641$	−1.78774	−	1.29887i	−0.0706114	−	0.0513022i	0.551920	−	0.833897i	$-0.313896\pi$
$641$	−1.78774	−	1.29887i	−0.0706114	−	0.0513022i	−0.622531	+	0.782595i	$0.713896\pi$
$642$	4.78940	+	0.758566i	0.189023	+	0.0299382i
$643$	16.0452	+	31.4906i	0.632763	+	1.24187i	0.955392	+	0.295341i	$0.0954333\pi$
$643$	16.0452	+	31.4906i	0.632763	+	1.24187i	−0.322629	+	0.946525i	$0.604567\pi$
$644$	−0.791523	+	2.43606i	−0.0311904	+	0.0959942i
$645$	15.3607	+	0.746561i	0.604828	+	0.0293958i
$646$	−7.47774	+	10.2922i	−0.294208	+	0.404942i
$647$	−3.70438	+	7.27025i	−0.145634	+	0.285823i	−0.952288	−	0.305201i	$-0.901276\pi$
$647$	−3.70438	+	7.27025i	−0.145634	+	0.285823i	0.806654	+	0.591024i	$0.201276\pi$
$648$	1.80758	+	1.80758i	0.0710085	+	0.0710085i
$649$	11.6343	+	21.8749i	0.456687	+	0.858666i
$650$	−6.47891	−	29.3822i	−0.254124	−	1.15246i
$651$	−3.86190	+	1.25481i	−0.151360	+	0.0491798i
$652$	−1.22246	−	7.71830i	−0.0478751	−	0.302272i
$653$	−3.68690	+	23.2782i	−0.144279	+	0.910945i	0.804258	+	0.594280i	$0.202563\pi$
$653$	−3.68690	+	23.2782i	−0.144279	+	0.910945i	−0.948538	+	0.316665i	$0.897437\pi$
$654$	−0.715364	−	0.232436i	−0.0279729	−	0.00908896i
$655$	−23.6992	−	36.1921i	−0.926006	−	1.41414i
$656$	−4.84236	−	6.66494i	−0.189063	−	0.260222i
$657$	−0.991216	+	0.156993i	−0.0386710	+	0.00612489i
$658$	19.4556	+	9.91312i	0.758458	+	0.386454i
$659$	36.8038			1.43367			0.716836	−	0.697242i	$-0.245590\pi$
$659$	36.8038			1.43367			0.716836	+	0.697242i	$0.245590\pi$
$660$	8.69274	+	3.12546i	0.338364	+	0.121658i
$661$	−29.0538			−1.13006			−0.565032	−	0.825069i	$-0.691136\pi$
$661$	−29.0538			−1.13006			−0.565032	+	0.825069i	$0.691136\pi$
$662$	−10.6063	−	5.40417i	−0.412225	−	0.210039i
$663$	−48.9698	+	7.75605i	−1.90183	+	0.301220i
$664$	0.581646	+	0.800568i	0.0225723	+	0.0310680i
$665$	2.62136	−	12.5669i	0.101652	−	0.487324i
$666$	10.1365	+	3.29355i	0.392781	+	0.127622i
$667$	−0.591356	+	3.73367i	−0.0228974	+	0.144568i
$668$	1.88682	+	11.9129i	0.0730033	+	0.460925i
$669$	−12.9039	+	4.19273i	−0.498893	+	0.162100i
$670$	−2.63047	−	2.11363i	−0.101624	−	0.0816568i
$671$	−12.8966	−	6.28827i	−0.497868	−	0.242756i
$672$	−2.62912	−	2.62912i	−0.101420	−	0.101420i
$673$	5.71300	−	11.2124i	0.220220	−	0.432206i	−0.754293	−	0.656538i	$-0.772020\pi$
$673$	5.71300	−	11.2124i	0.220220	−	0.432206i	0.974513	+	0.224332i	$0.0720201\pi$
$674$	−5.83063	+	8.02517i	−0.224587	+	0.309118i
$675$	−1.65999	−	27.6553i	−0.0638929	−	1.06445i
$676$	7.17276	−	22.0755i	0.275875	−	0.849057i
$677$	−0.317369	−	0.622871i	−0.0121975	−	0.0239389i	0.884827	−	0.465919i	$-0.154276\pi$
$677$	−0.317369	−	0.622871i	−0.0121975	−	0.0239389i	−0.897025	+	0.441980i	$0.854276\pi$
$678$	−2.33235	−	0.369407i	−0.0895733	−	0.0141870i
$679$	−12.0654	−	8.76605i	−0.463029	−	0.336410i
$680$	5.24813	−	13.8285i	0.201257	−	0.530300i
$681$			24.1696i			0.926182i
$682$	−1.05862	+	3.46400i	−0.0405366	+	0.132643i
$683$	−27.3975	+	27.3975i	−1.04834	+	1.04834i	−0.0495661	+	0.998771i	$0.515784\pi$
$683$	−27.3975	+	27.3975i	−1.04834	+	1.04834i	−0.998771	+	0.0495661i	$0.984216\pi$
$684$	−0.860884	−	2.64953i	−0.0329167	−	0.101307i
$685$	6.81631	−	11.9104i	0.260438	−	0.455072i
$686$	12.2910	−	8.92991i	0.469272	−	0.340946i
$687$	−26.4238	+	13.4636i	−1.00813	+	0.513668i
$688$	−4.91978	+	2.50675i	−0.187565	+	0.0955690i
$689$	−24.9011	+	18.0917i	−0.948655	+	0.689238i
$690$	−1.18712	+	2.07429i	−0.0451927	+	0.0789669i
$691$	9.94862	+	30.6187i	0.378463	+	1.16479i	0.941112	+	0.338094i	$0.109782\pi$
$691$	9.94862	+	30.6187i	0.378463	+	1.16479i	−0.562649	+	0.826696i	$0.690218\pi$
$692$	1.47557	−	1.47557i	0.0560928	−	0.0560928i
$693$	−0.251916	−	14.3384i	−0.00956951	−	0.544670i
$694$		−	15.3554i		−	0.582884i
$695$	15.9777	−	42.1005i	0.606070	−	1.59696i
$696$	−4.43933	−	3.22536i	−0.168272	−	0.122257i
$697$	53.8231	+	8.52474i	2.03869	+	0.322898i
$698$	7.60547	+	14.9266i	0.287871	+	0.564979i
$699$	3.52324	−	10.8434i	0.133261	−	0.410136i
$700$	0.894264	+	14.8984i	0.0338000	+	0.563106i
$701$	15.0390	−	20.6993i	0.568013	−	0.781803i	−0.424304	−	0.905520i	$-0.639481\pi$
$701$	15.0390	−	20.6993i	0.568013	−	0.781803i	0.992318	+	0.123716i	$0.0394813\pi$
$702$	15.1377	−	29.7094i	0.571335	−	1.12131i
$703$	10.0066	+	10.0066i	0.377407	+	0.377407i
$704$	−3.26617	+	0.576299i	−0.123098	+	0.0217201i
$705$	15.8820	+	12.7615i	0.598152	+	0.480626i
$706$	−1.55732	+	0.506005i	−0.0586107	+	0.0190438i
$707$	−0.702974	−	4.43841i	−0.0264381	−	0.166923i
$708$	1.45562	−	9.19045i	0.0547057	−	0.345398i
$709$	−3.93545	−	1.27871i	−0.147799	−	0.0480228i	0.234183	−	0.972192i	$-0.424758\pi$
$709$	−3.93545	−	1.27871i	−0.147799	−	0.0480228i	−0.381982	+	0.924170i	$0.624758\pi$
$710$	1.75693	−	8.42282i	0.0659365	−	0.316103i
$711$	−3.48215	−	4.79278i	−0.130591	−	0.179743i
$712$	−12.3819	+	1.96109i	−0.464030	+	0.0734951i
$713$	−0.834992	−	0.425450i	−0.0312707	−	0.0159332i
$714$	24.5943			0.920419
$715$	1.38306	−	44.6063i	0.0517237	−	1.66818i
$716$	19.0586			0.712253
$717$	−14.0517	−	7.15972i	−0.524772	−	0.267385i
$718$	−22.8996	+	3.62694i	−0.854605	+	0.135356i
$719$	11.8781	+	16.3488i	0.442979	+	0.609708i	0.970871	−	0.239603i	$-0.0770174\pi$
$719$	11.8781	+	16.3488i	0.442979	+	0.609708i	−0.527892	+	0.849312i	$0.677017\pi$
$720$	1.77436	+	2.70970i	0.0661266	+	0.100985i
$721$	52.3647	+	17.0143i	1.95016	+	0.633647i
$722$	−2.39361	+	15.1126i	−0.0890808	+	0.562434i
$723$	4.16714	+	26.3103i	0.154978	+	0.978491i
$724$	1.70305	−	0.553354i	0.0632933	−	0.0205652i
$725$	4.74312	+	21.5102i	0.176155	+	0.798870i
$726$	11.3608	+	7.65918i	0.421639	+	0.284259i
$727$	−22.5814	−	22.5814i	−0.837496	−	0.837496i	0.151033	−	0.988529i	$-0.451740\pi$
$727$	−22.5814	−	22.5814i	−0.837496	−	0.837496i	−0.988529	+	0.151033i	$0.951740\pi$
$728$	−8.15493	+	16.0050i	−0.302242	+	0.593183i
$729$	14.3468	−	19.7467i	0.531365	−	0.731361i
$730$	1.54739	+	0.0752062i	0.0572716	+	0.00278351i
$731$	11.2864	−	34.7361i	0.417444	−	1.28476i
$732$	2.44634	+	4.80121i	0.0904193	+	0.177458i
$733$	−40.8776	−	6.47437i	−1.50985	−	0.239136i	−0.654052	−	0.756450i	$-0.726932\pi$
$733$	−40.8776	−	6.47437i	−1.50985	−	0.239136i	−0.855796	+	0.517313i	$0.826932\pi$
$734$	−18.6768	−	13.5695i	−0.689374	−	0.500859i
$735$	−4.85277	+	2.18271i	−0.178997	+	0.0805103i
$736$		−	0.858087i		−	0.0316295i
$737$	−3.01260	−	3.99691i	−0.110971	−	0.147228i
$738$	−8.43809	+	8.43809i	−0.310611	+	0.310611i
$739$	7.84400	+	24.1413i	0.288546	+	0.888054i	0.985313	+	0.170756i	$0.0546211\pi$
$739$	7.84400	+	24.1413i	0.288546	+	0.888054i	−0.696767	+	0.717297i	$0.745379\pi$
$740$	−14.2799	−	8.17236i	−0.524938	−	0.300422i
$741$	11.6627	−	8.47342i	0.428438	−	0.311279i
$742$	13.6040	−	6.93160i	0.499420	−	0.254467i
$743$	−4.18773	+	2.13376i	−0.153633	+	0.0782799i	−0.529117	−	0.848549i	$-0.677477\pi$
$743$	−4.18773	+	2.13376i	−0.153633	+	0.0782799i	0.375484	+	0.926829i	$0.377477\pi$
$744$	1.10053	−	0.799583i	0.0403475	−	0.0293141i
$745$	−1.25384	−	4.60933i	−0.0459371	−	0.168873i
$746$	−0.708906	−	2.18179i	−0.0259549	−	0.0798810i
$747$	1.01355	−	1.01355i	0.0370839	−	0.0370839i
$748$	12.5813	−	17.9724i	0.460019	−	0.657135i
$749$			11.6208i			0.424615i
$750$	−2.02174	+	13.7786i	−0.0738235	+	0.503123i
$751$	−8.70104	−	6.32168i	−0.317506	−	0.230681i	0.417605	−	0.908629i	$-0.362870\pi$
$751$	−8.70104	−	6.32168i	−0.317506	−	0.230681i	−0.735110	+	0.677947i	$0.762870\pi$
$752$	−7.22493	−	1.14432i	−0.263466	−	0.0417289i
$753$	12.9499	+	25.4155i	0.471919	+	0.926194i
$754$	−8.19201	+	25.2124i	−0.298336	+	0.918182i
$755$	−0.907346	+	18.6689i	−0.0330217	+	0.679433i
$756$	−9.72205	+	13.3813i	−0.353588	+	0.486672i
$757$	−5.59212	+	10.9752i	−0.203249	+	0.398899i	−0.970021	−	0.243021i	$-0.921862\pi$
$757$	−5.59212	+	10.9752i	−0.203249	+	0.398899i	0.766772	+	0.641920i	$0.221862\pi$
$758$	−25.8047	−	25.8047i	−0.937268	−	0.937268i
$759$	−2.46220	+	2.55026i	−0.0893720	+	0.0925686i
$760$	0.465766	+	4.27528i	0.0168951	+	0.155081i
$761$	−36.4442	+	11.8414i	−1.32110	+	0.429252i	−0.882873	−	0.469612i	$-0.844394\pi$
$761$	−36.4442	+	11.8414i	−1.32110	+	0.429252i	−0.438228	+	0.898864i	$0.644394\pi$
$762$	−0.400353	−	2.52773i	−0.0145033	−	0.0915700i
$763$	0.281986	−	1.78039i	0.0102086	−	0.0644545i
$764$	−25.5636	−	8.30611i	−0.924858	−	0.300504i
$765$	−20.9733	−	4.37487i	−0.758292	−	0.158174i
$766$	4.11804	+	5.66800i	0.148791	+	0.204793i
$767$	−44.4002	+	7.03231i	−1.60320	+	0.253922i
$768$	1.10983	+	0.565486i	0.0400475	+	0.0204052i
$769$	−8.00094			−0.288521			−0.144261	−	0.989540i	$-0.546080\pi$
$769$	−8.00094			−0.288521			−0.144261	+	0.989540i	$0.546080\pi$
$770$	−4.13905	+	21.7473i	−0.149161	+	0.783717i
$771$	12.7351			0.458642
$772$	20.7217	+	10.5582i	0.745790	+	0.379999i
$773$	44.3526	−	7.02476i	1.59525	−	0.252663i	0.705365	−	0.708844i	$-0.250783\pi$
$773$	44.3526	−	7.02476i	1.59525	−	0.252663i	0.889887	+	0.456181i	$0.150783\pi$
$774$	4.70115	+	6.47057i	0.168979	+	0.232580i
$775$	−5.43486	−	0.529540i	−0.195226	−	0.0190216i
$776$	4.75162	+	1.54389i	0.170573	+	0.0554226i
$777$	4.27975	−	27.0213i	0.153535	−	0.969382i
$778$	−0.269932	−	1.70428i	−0.00967754	−	0.0611016i
$779$	−15.0691	+	4.89624i	−0.539906	+	0.175426i
$780$	−10.4981	+	13.0652i	−0.375893	+	0.467809i
$781$	5.59316	−	11.4710i	0.200139	−	0.410465i
$782$	4.01353	+	4.01353i	0.143523	+	0.143523i
$783$	−11.0821	+	21.7498i	−0.396041	+	0.777274i
$784$	1.12294	−	1.54559i	0.0401050	−	0.0551998i
$785$	−19.6818	−	21.6926i	−0.702472	−	0.774243i
$786$	−7.44680	+	22.9189i	−0.265618	+	0.817490i
$787$	1.80178	+	3.53620i	0.0642266	+	0.126052i	0.920888	−	0.389827i	$-0.127465\pi$
$787$	1.80178	+	3.53620i	0.0642266	+	0.126052i	−0.856661	+	0.515879i	$0.827465\pi$
$788$	−7.18462	−	1.13793i	−0.255941	−	0.0405371i
$789$	20.8004	+	15.1124i	0.740514	+	0.538015i
$790$	3.75138	+	8.34039i	0.133468	+	0.296738i
$791$		−	5.65911i		−	0.201215i
$792$	1.56460	+	4.54224i	0.0555956	+	0.161401i
$793$	18.4079	−	18.4079i	0.653682	−	0.653682i
$794$	−0.983765	−	3.02772i	−0.0349125	−	0.107450i
$795$	13.7466	−	3.73938i	0.487542	−	0.132622i
$796$	−4.47203	+	3.24912i	−0.158507	+	0.115162i
$797$	18.2820	−	9.31514i	0.647582	−	0.329959i	−0.0991621	−	0.995071i	$-0.531616\pi$
$797$	18.2820	−	9.31514i	0.647582	−	0.329959i	0.746744	+	0.665112i	$0.231616\pi$
$798$	−6.37158	+	3.24648i	−0.225552	+	0.114924i
$799$	39.1454	−	28.4408i	1.38487	−	1.00616i
$800$	−1.82723	−	4.65416i	−0.0646023	−	0.164550i
$801$	5.61137	+	17.2700i	0.198268	+	0.610206i
$802$	−2.06094	+	2.06094i	−0.0727742	+	0.0727742i
$803$	2.19753	+	0.671579i	0.0775493	+	0.0236995i
$804$			1.87971i			0.0662924i
$805$	−5.35485	−	2.03225i	−0.188734	−	0.0716272i
$806$	−5.31681	−	3.86289i	−0.187277	−	0.136064i
$807$	−0.446798	−	0.0707659i	−0.0157280	−	0.00249108i
$808$	0.683445	+	1.34134i	0.0240435	+	0.0471881i
$809$	−4.52189	+	13.9169i	−0.158981	+	0.489294i	−0.998542	−	0.0539713i	$-0.982812\pi$
$809$	−4.52189	+	13.9169i	−0.158981	+	0.489294i	0.839561	+	0.543265i	$0.182812\pi$
$810$	−4.23332	+	3.84090i	−0.148744	+	0.134955i
$811$	17.2191	−	23.7001i	0.604644	−	0.832222i	−0.391479	−	0.920187i	$-0.628036\pi$
$811$	17.2191	−	23.7001i	0.604644	−	0.832222i	0.996124	+	0.0879653i	$0.0280365\pi$
$812$	5.97010	−	11.7170i	0.209509	−	0.411185i
$813$	−15.1178	−	15.1178i	−0.530206	−	0.530206i
$814$	−17.5565	−	16.9503i	−0.615357	−	0.594107i
$815$	17.3710	−	1.89246i	0.608479	−	0.0662901i
$816$	−7.83594	+	2.54605i	−0.274313	+	0.0891296i
$817$	1.66126	+	10.4888i	0.0581203	+	0.366957i
$818$	−2.46945	+	15.5915i	−0.0863423	+	0.545144i
$819$	24.7457	+	8.04038i	0.864686	+	0.280954i
$820$	15.4113	−	10.0916i	0.538187	−	0.352415i
$821$	29.5782	+	40.7109i	1.03229	+	1.42082i	0.903216	+	0.429185i	$0.141199\pi$
$821$	29.5782	+	40.7109i	1.03229	+	1.42082i	0.129070	+	0.991635i	$0.458801\pi$
$822$	−7.55018	+	1.19583i	−0.263343	+	0.0417094i
$823$	−41.8957	−	21.3469i	−1.46039	−	0.744106i	−0.470034	−	0.882648i	$-0.655758\pi$
$823$	−41.8957	−	21.3469i	−1.46039	−	0.744106i	−0.990357	+	0.138542i	$0.955758\pi$
$824$	−18.4452			−0.642568
$825$	−7.92408	+	19.0754i	−0.275881	+	0.664119i
$826$	22.2993			0.775893
$827$	−30.0724	−	15.3227i	−1.04572	−	0.532821i	−0.155257	−	0.987874i	$-0.549620\pi$
$827$	−30.0724	−	15.3227i	−1.04572	−	0.532821i	−0.890465	+	0.455053i	$0.849620\pi$
$828$	−1.22764	+	0.194439i	−0.0426635	+	0.00675724i
$829$	−17.2790	−	23.7825i	−0.600124	−	0.825999i	0.395596	−	0.918425i	$-0.370538\pi$
$829$	−17.2790	−	23.7825i	−0.600124	−	0.825999i	−0.995720	+	0.0924253i	$0.970538\pi$
$830$	−1.85115	+	1.21217i	−0.0642544	+	0.0420749i
$831$	13.9036	+	4.51755i	0.482310	+	0.156712i
$832$	0.941360	−	5.94352i	0.0326358	−	0.206054i
$833$	1.97688	+	12.4815i	0.0684948	+	0.432459i
$834$	−23.8562	+	7.75136i	−0.826074	+	0.268408i
$835$	−26.8115	+	2.92095i	−0.927851	+	0.101084i
$836$	−0.887033	+	6.31681i	−0.0306787	+	0.218471i
$837$	−4.27902	−	4.27902i	−0.147905	−	0.147905i
$838$	−1.45596	+	2.85748i	−0.0502953	+	0.0987101i
$839$	−20.4278	+	28.1165i	−0.705246	+	0.970688i	0.294640	+	0.955608i	$0.404800\pi$
$839$	−20.4278	+	28.1165i	−0.705246	+	0.970688i	−0.999886	+	0.0150799i	$0.995200\pi$
$840$	6.15734	−	5.58657i	0.212448	−	0.192755i
$841$	−2.96424	+	9.12300i	−0.102215	+	0.314586i
$842$	17.0421	+	33.4470i	0.587310	+	1.15266i
$843$	−9.81041	−	1.55382i	−0.337888	−	0.0535163i
$844$	11.6358	+	8.45389i	0.400520	+	0.290995i
$845$	48.5255	+	18.4161i	1.66933	+	0.633534i
$846$			10.5958i			0.364291i
$847$	−13.8701	+	29.7622i	−0.476581	+	1.02264i
$848$	−3.61678	+	3.61678i	−0.124201	+	0.124201i
$849$	1.87329	+	5.76540i	0.0642912	+	0.197868i
$850$	30.3154	+	13.2224i	1.03981	+	0.453525i
$851$	5.10799	−	3.71117i	0.175099	−	0.127217i
$852$	−4.27048	+	2.17592i	−0.146304	+	0.0745458i
$853$	13.0696	−	6.65927i	0.447493	−	0.228009i	−0.215697	−	0.976460i	$-0.569202\pi$
$853$	13.0696	−	6.65927i	0.447493	−	0.228009i	0.663190	+	0.748451i	$0.269202\pi$
$854$	−10.4473	+	7.59038i	−0.357498	+	0.259737i
$855$	6.01099	−	1.63512i	0.205571	−	0.0559200i
$856$	−1.20301	−	3.70248i	−0.0411180	−	0.126548i
$857$	9.19555	−	9.19555i	0.314114	−	0.314114i	−0.532387	−	0.846501i	$-0.678705\pi$
$857$	9.19555	−	9.19555i	0.314114	−	0.314114i	0.846501	+	0.532387i	$0.178705\pi$
$858$	−19.8521	+	14.9632i	−0.677739	+	0.510834i
$859$		−	17.4249i		−	0.594531i	−0.954795	−	0.297265i	$-0.903925\pi$
$859$		−	17.4249i		−	0.594531i	0.954795	−	0.297265i	$-0.0960746\pi$
$860$	−5.06462	−	11.2601i	−0.172702	−	0.383966i
$861$	24.7811	+	18.0046i	0.844539	+	0.613594i
$862$	−25.7186	−	4.07342i	−0.875978	−	0.138741i
$863$	16.0397	+	31.4796i	0.545996	+	1.07158i	0.984913	+	0.173050i	$0.0553623\pi$
$863$	16.0397	+	31.4796i	0.545996	+	1.07158i	−0.438917	+	0.898528i	$0.644638\pi$
$864$	1.71227	−	5.26982i	0.0582525	−	0.179283i
$865$	3.13542	+	3.45576i	0.106607	+	0.117499i
$866$	22.3254	−	30.7283i	0.758648	−	1.04419i
$867$	15.1291	−	29.6926i	0.513812	−	1.00841i
$868$	2.30518	+	2.30518i	0.0782430	+	0.0782430i
$869$	2.35698	+	13.3582i	0.0799552	+	0.453146i
$870$	7.68551	−	9.56483i	0.260563	−	0.324278i
$871$	8.63667	−	2.80622i	0.292642	−	0.0950853i
$872$	0.0944666	+	0.596438i	0.00319904	+	0.0201980i
$873$	1.13211	−	7.14785i	0.0383161	−	0.241918i
$874$	−1.56956	−	0.509983i	−0.0530913	−	0.0172504i
$875$	−33.3716	+	0.380073i	−1.12817	+	0.0128488i
$876$	−0.507249	−	0.698169i	−0.0171384	−	0.0235889i
$877$	−34.3545	+	5.44121i	−1.16007	+	0.183737i	−0.706651	−	0.707562i	$-0.749795\pi$
$877$	−34.3545	+	5.44121i	−1.16007	+	0.183737i	−0.453417	+	0.891299i	$0.649795\pi$
$878$	−1.69367	−	0.862969i	−0.0571586	−	0.0291238i
$879$	14.0300			0.473221
$880$	−0.932585	−	7.35733i	−0.0314374	−	0.248015i
$881$	4.04983			0.136442			0.0682211	−	0.997670i	$-0.478268\pi$
$881$	4.04983			0.136442			0.0682211	+	0.997670i	$0.478268\pi$
$882$	−2.46569	−	1.25633i	−0.0830243	−	0.0423030i
$883$	−25.8940	+	4.10121i	−0.871404	+	0.138017i	−0.576093	−	0.817384i	$-0.695423\pi$
$883$	−25.8940	+	4.10121i	−0.871404	+	0.138017i	−0.295311	+	0.955401i	$0.595423\pi$
$884$	23.3966	+	32.2026i	0.786911	+	1.08309i
$885$	20.3682	+	4.24865i	0.684671	+	0.142817i
$886$	−33.2395	−	10.8002i	−1.11670	−	0.362839i
$887$	7.16884	−	45.2623i	0.240706	−	1.51976i	−0.510608	−	0.859814i	$-0.670580\pi$
$887$	7.16884	−	45.2623i	0.240706	−	1.51976i	0.751314	−	0.659945i	$-0.229420\pi$
$888$	1.43373	+	9.05223i	0.0481129	+	0.303773i
$889$	5.83301	−	1.89526i	0.195633	−	0.0635649i
$890$	−3.03593	−	27.8669i	−0.101765	−	0.934101i
$891$	−7.48545	+	3.98118i	−0.250772	+	0.133375i
$892$	7.70237	+	7.70237i	0.257894	+	0.257894i
$893$	−6.38707	+	12.5353i	−0.213735	+	0.419479i
$894$	−1.56404	+	2.15272i	−0.0523093	+	0.0719976i
$895$	−2.06879	+	42.5661i	−0.0691520	+	1.42283i
$896$	−0.922428	+	2.83894i	−0.0308162	+	0.0948424i
$897$	−2.91996	−	5.73074i	−0.0974945	−	0.191344i
$898$	1.19251	+	0.188875i	0.0397946	+	0.00630284i
$899$	3.89236	+	2.82796i	0.129817	+	0.0943178i
$900$	−6.24454	+	3.66878i	−0.208151	+	0.122293i
$901$		−	33.8335i		−	1.12716i
$902$	25.8338	−	8.89859i	0.860171	−	0.296291i
$903$	14.5169	−	14.5169i	0.483093	−	0.483093i
$904$	0.585842	+	1.80304i	0.0194848	+	0.0599681i
$905$	1.05101	+	3.86371i	0.0349369	+	0.128434i
$906$	8.42325	−	6.11985i	0.279844	−	0.203318i
$907$	−49.2679	+	25.1033i	−1.63591	+	0.833540i	−0.637929	+	0.770095i	$0.720209\pi$
$907$	−49.2679	+	25.1033i	−1.63591	+	0.833540i	−0.997985	+	0.0634452i	$0.979791\pi$
$908$	17.2892	−	8.80931i	0.573763	−	0.292347i
$909$	1.76415	−	1.28173i	0.0585131	−	0.0425123i
$910$	−34.8608	−	19.9508i	−1.15562	−	0.661363i
$911$	1.84128	+	5.66688i	0.0610044	+	0.187752i	0.976914	−	0.213632i	$-0.0685293\pi$
$911$	1.84128	+	5.66688i	0.0610044	+	0.187752i	−0.915910	+	0.401384i	$0.868529\pi$
$912$	1.69395	−	1.69395i	0.0560924	−	0.0560924i
$913$	−3.10306	+	1.06886i	−0.102696	+	0.0353743i
$914$		−	1.95594i		−	0.0646966i
$915$	−10.9887	+	4.94256i	−0.363276	+	0.163396i
$916$	19.2618	+	13.9945i	0.636428	+	0.462392i
$917$	−57.0404	−	9.03431i	−1.88364	−	0.298339i
$918$	16.6397	+	32.6573i	0.549192	+	1.07785i
$919$	−11.5408	+	35.5189i	−0.380695	+	1.17166i	0.558860	+	0.829262i	$0.311239\pi$
$919$	−11.5408	+	35.5189i	−0.380695	+	1.17166i	−0.939555	+	0.342397i	$0.888761\pi$
$920$	1.91648	+	0.0931445i	0.0631844	+	0.00307088i
$921$	13.4001	−	18.4437i	0.441548	−	0.607739i
$922$	−10.0805	+	19.7842i	−0.331985	+	0.651557i
$923$	16.3730	+	16.3730i	0.538925	+	0.538925i
$924$	10.8875	−	5.79060i	0.358174	−	0.190497i
$925$	19.8025	−	31.0060i	0.651101	−	1.01947i
$926$	−2.89425	+	0.940399i	−0.0951109	+	0.0309034i
$927$	4.17961	+	26.3890i	0.137276	+	0.866729i
$928$	−0.689156	+	4.35116i	−0.0226226	+	0.142834i
$929$	20.1125	+	6.53494i	0.659869	+	0.214404i	0.619761	−	0.784791i	$-0.287230\pi$
$929$	20.1125	+	6.53494i	0.659869	+	0.214404i	0.0401085	+	0.999195i	$0.487230\pi$
$930$	1.66635	+	2.54476i	0.0546419	+	0.0834459i
$931$	−2.15972	−	2.97260i	−0.0707821	−	0.0974232i
$932$	−9.04077	+	1.43192i	−0.296140	+	0.0469040i
$933$	−32.8371	−	16.7313i	−1.07504	−	0.547759i
$934$	−3.51836			−0.115124
$935$	38.7744	+	30.0504i	1.26806	+	0.982754i
$936$	−8.71654			−0.284909
$937$	−1.00242	−	0.510760i	−0.0327477	−	0.0166858i	0.437540	−	0.899199i	$-0.355850\pi$
$937$	−1.00242	−	0.510760i	−0.0327477	−	0.0166858i	−0.470288	+	0.882513i	$0.655850\pi$
$938$	−4.44925	+	0.704692i	−0.145273	+	0.0230090i
$939$	−9.50154	−	13.0777i	−0.310071	−	0.426776i
$940$	3.34001	−	16.0122i	0.108939	−	0.522259i
$941$	20.4465	+	6.64347i	0.666537	+	0.216571i	0.622692	−	0.782467i	$-0.286039\pi$
$941$	20.4465	+	6.64347i	0.666537	+	0.216571i	0.0438452	+	0.999038i	$0.486039\pi$
$942$	−2.55242	+	16.1153i	−0.0831622	+	0.525065i
$943$	1.10587	+	6.98216i	0.0360120	+	0.227371i
$944$	−7.10474	+	2.30847i	−0.231240	+	0.0751343i
$945$	−28.8308	−	23.1661i	−0.937866	−	0.753592i
$946$	−3.18209	−	18.0345i	−0.103459	−	0.586351i
$947$	−11.3068	−	11.3068i	−0.367421	−	0.367421i	0.499115	−	0.866536i	$-0.333658\pi$
$947$	−11.3068	−	11.3068i	−0.367421	−	0.367421i	−0.866536	+	0.499115i	$0.833658\pi$
$948$	2.31276	−	4.53905i	0.0751149	−	0.147421i
$949$	−2.45059	+	3.37294i	−0.0795494	+	0.109490i
$950$	−9.59910	+	0.576179i	−0.311436	+	0.0186937i
$951$	10.6952	−	32.9163i	0.346814	−	1.06738i
$952$	−8.96410	−	17.5930i	−0.290528	−	0.570194i
$953$	28.3068	+	4.48336i	0.916947	+	0.145230i	0.597033	−	0.802216i	$-0.296346\pi$
$953$	28.3068	+	4.48336i	0.916947	+	0.145230i	0.319914	+	0.947447i	$0.396346\pi$
$954$	5.99397	+	4.35488i	0.194062	+	0.140994i
$955$	21.3260	−	56.1929i	0.690094	−	1.81836i
$956$			12.6612i			0.409492i
$957$	14.5334	−	10.9543i	0.469798	−	0.354103i
$958$	−4.22366	+	4.22366i	−0.136460	+	0.136460i
$959$	−5.66102	−	17.4228i	−0.182804	−	0.562612i
$960$	−1.38344	+	2.41734i	−0.0446505	+	0.0780194i
$961$	24.1146	−	17.5203i	0.777890	−	0.565170i
$962$	39.4516	−	20.1016i	1.27197	−	0.648102i
$963$	−5.02444	+	2.56008i	−0.161910	+	0.0824974i
$964$	17.3017	−	12.5704i	0.557250	−	0.404866i
$965$	−25.8304	+	45.1344i	−0.831510	+	1.45293i
$966$	0.985913	+	3.03433i	0.0317212	+	0.0976279i
$967$	29.6097	−	29.6097i	0.952185	−	0.952185i	−0.0467233	−	0.998908i	$-0.514878\pi$
$967$	29.6097	−	29.6097i	0.952185	−	0.952185i	0.998908	+	0.0467233i	$0.0148779\pi$
$968$	1.33807	−	10.9183i	0.0430071	−	0.350928i
$969$			15.8462i			0.509055i
$970$	−3.96396	+	10.4448i	−0.127275	+	0.335363i
$971$	15.4852	+	11.2507i	0.496945	+	0.361052i	0.807849	−	0.589390i	$-0.200632\pi$
$971$	15.4852	+	11.2507i	0.496945	+	0.361052i	−0.310904	+	0.950441i	$0.600632\pi$
$972$	−13.2735	−	2.10231i	−0.425747	−	0.0674317i
$973$	−27.2909	−	53.5614i	−0.874906	−	1.71710i
$974$	−3.83182	+	11.7931i	−0.122779	+	0.377876i
$975$	−28.0407	−	24.8650i	−0.898020	−	0.796318i
$976$	2.54281	−	3.49987i	0.0813933	−	0.112028i
$977$	20.7901	−	40.8029i	0.665136	−	1.30540i	−0.273958	−	0.961742i	$-0.588333\pi$
$977$	20.7901	−	40.8029i	0.665136	−	1.30540i	0.939094	−	0.343660i	$-0.111667\pi$
$978$	−6.88274	−	6.88274i	−0.220086	−	0.220086i
$979$	5.78182	−	41.1739i	0.184788	−	1.31592i
$980$	3.33008	+	2.67578i	0.106376	+	0.0854747i
$981$	0.831903	−	0.270302i	0.0265606	−	0.00863007i
$982$	1.42424	+	8.99230i	0.0454494	+	0.286956i
$983$	0.219782	−	1.38765i	0.00700995	−	0.0442591i	−0.983935	−	0.178525i	$-0.942868\pi$
$983$	0.219782	−	1.38765i	0.00700995	−	0.0442591i	0.990945	+	0.134266i	$0.0428675\pi$
$984$	−9.75933	−	3.17100i	−0.311116	−	0.101088i
$985$	3.32138	−	15.9228i	0.105828	−	0.507344i
$986$	−17.1283	−	23.5750i	−0.545475	−	0.750782i
$987$	26.8632	−	4.25472i	0.855067	−	0.135429i
$988$	−10.3121	−	5.25426i	−0.328071	−	0.167160i
$989$	4.73801			0.150660
$990$	−10.3146	+	3.00137i	−0.327820	+	0.0953898i
$991$	−40.1839			−1.27648			−0.638241	−	0.769836i	$-0.720338\pi$
$991$	−40.1839			−1.27648			−0.638241	+	0.769836i	$0.720338\pi$
$992$	−0.973086	−	0.495812i	−0.0308955	−	0.0157420i
$993$	−14.6446	+	2.31948i	−0.464732	+	0.0736063i
$994$	−6.75134	−	9.29242i	−0.214139	−	0.294738i
$995$	−6.77125	−	10.3407i	−0.214663	−	0.327821i
$996$	1.17225	+	0.380888i	0.0371443	+	0.0120689i
$997$	−2.70973	+	17.1086i	−0.0858181	+	0.541834i	0.906897	+	0.421352i	$0.138444\pi$
$997$	−2.70973	+	17.1086i	−0.0858181	+	0.541834i	−0.992715	+	0.120483i	$0.961556\pi$
$998$	3.66978	+	23.1701i	0.116165	+	0.733436i
$999$	38.7754	−	12.5989i	1.22680	−	0.398611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.17.2	yes	48
3.2	odd	2		990.2.bh.c.127.6		48
4.3	odd	2		880.2.cm.c.17.4		48
5.2	odd	4		550.2.bh.b.193.5		48
5.3	odd	4	inner	110.2.k.a.83.2	yes	48
5.4	even	2		550.2.bh.b.457.5		48
11.2	odd	10	inner	110.2.k.a.57.2	yes	48
15.8	even	4		990.2.bh.c.523.4		48
20.3	even	4		880.2.cm.c.193.4		48
33.2	even	10		990.2.bh.c.937.4		48
44.35	even	10		880.2.cm.c.497.4		48
55.2	even	20		550.2.bh.b.343.5		48
55.13	even	20	inner	110.2.k.a.13.2	✓	48
55.24	odd	10		550.2.bh.b.57.5		48
165.68	odd	20		990.2.bh.c.343.6		48
220.123	odd	20		880.2.cm.c.673.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.2	✓	48	55.13	even	20	inner
110.2.k.a.17.2	yes	48	1.1	even	1	trivial
110.2.k.a.57.2	yes	48	11.2	odd	10	inner
110.2.k.a.83.2	yes	48	5.3	odd	4	inner
550.2.bh.b.57.5		48	55.24	odd	10
550.2.bh.b.193.5		48	5.2	odd	4
550.2.bh.b.343.5		48	55.2	even	20
550.2.bh.b.457.5		48	5.4	even	2
880.2.cm.c.17.4		48	4.3	odd	2
880.2.cm.c.193.4		48	20.3	even	4
880.2.cm.c.497.4		48	44.35	even	10
880.2.cm.c.673.4		48	220.123	odd	20
990.2.bh.c.127.6		48	3.2	odd	2
990.2.bh.c.343.6		48	165.68	odd	20
990.2.bh.c.523.4		48	15.8	even	4
990.2.bh.c.937.4		48	33.2	even	10

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.23025 + 0.194853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.87069 + 1.22496i) q^{5} +(1.18463 + 0.384908i) q^{6} +(-0.466963 + 2.94829i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.37761 + 0.447613i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.23025 + 0.194853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.87069 + 1.22496i) q^{5} +(1.18463 + 0.384908i) q^{6} +(-0.466963 + 2.94829i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.37761 + 0.447613i) q^{9} +(2.22292 - 0.242173i) q^{10} +(3.28440 + 0.461210i) q^{11} +(-0.880765 - 0.880765i) q^{12} +(-2.73193 + 5.36172i) q^{13} +(1.75456 - 2.41495i) q^{14} +(2.06273 - 1.87152i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.00301 - 5.89374i) q^{17} +(1.43067 + 0.226596i) q^{18} +(1.55596 + 1.13047i) q^{19} +(-2.09058 - 0.793405i) q^{20} -3.71813i q^{21} +(-2.71704 - 1.90203i) q^{22} +(0.606759 - 0.606759i) q^{23} +(0.384908 + 1.18463i) q^{24} +(1.99894 - 4.58304i) q^{25} +(4.86834 - 3.53706i) q^{26} +(4.93708 - 2.51557i) q^{27} +(-2.65969 + 1.35518i) q^{28} +(-3.56404 + 2.58943i) q^{29} +(-2.68756 + 0.731076i) q^{30} +(-0.337483 - 1.03867i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.13052 + 0.0725706i) q^{33} +6.61470i q^{34} +(-2.73799 - 6.08734i) q^{35} +(-1.17187 - 0.851411i) q^{36} +(7.26743 + 1.15105i) q^{37} +(-0.873149 - 1.71365i) q^{38} +(2.31622 - 7.12861i) q^{39} +(1.50252 + 1.65603i) q^{40} +(-4.84236 + 6.66494i) q^{41} +(-1.68800 + 3.31288i) q^{42} +(3.90436 + 3.90436i) q^{43} +(1.55740 + 2.92823i) q^{44} +(2.02877 - 2.52486i) q^{45} +(-0.816089 + 0.265163i) q^{46} +(1.14432 + 7.22493i) q^{47} +(0.194853 - 1.23025i) q^{48} +(-1.81695 - 0.590364i) q^{49} +(-3.86173 + 3.17601i) q^{50} +(4.84288 + 6.66565i) q^{51} +(-5.94352 + 0.941360i) q^{52} +(4.55740 + 2.32211i) q^{53} -5.54101 q^{54} +(-6.70905 + 3.16048i) q^{55} +2.98504 q^{56} +(-2.13451 - 1.08759i) q^{57} +(4.35116 - 0.689156i) q^{58} +(4.39097 + 6.04365i) q^{59} +(2.72654 + 0.568734i) q^{60} +(-4.11435 - 1.33683i) q^{61} +(-0.170845 + 1.07867i) q^{62} +(-0.676399 - 4.27062i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.45730 - 13.3766i) q^{65} +(3.71326 + 1.81055i) q^{66} +(-1.06709 - 1.06709i) q^{67} +(3.00301 - 5.89374i) q^{68} +(-0.628239 + 0.864697i) q^{69} +(-0.324023 + 6.66688i) q^{70} +(1.18906 - 3.65955i) q^{71} +(0.657608 + 1.29063i) q^{72} +(0.684302 + 0.108383i) q^{73} +(-5.95276 - 4.32493i) q^{74} +(-1.56619 + 6.02780i) q^{75} +1.92328i q^{76} +(-2.89347 + 9.46799i) q^{77} +(-5.30009 + 5.30009i) q^{78} +(1.26384 + 3.88969i) q^{79} +(-0.586932 - 2.15766i) q^{80} +(-2.06810 + 1.50256i) q^{81} +(7.34040 - 3.74012i) q^{82} +(-0.881701 + 0.449249i) q^{83} +(3.00803 - 2.18546i) q^{84} +(12.8373 + 7.34678i) q^{85} +(-1.70627 - 5.25135i) q^{86} +(3.88012 - 3.88012i) q^{87} +(-0.0582620 - 3.31611i) q^{88} -12.5362i q^{89} +(-2.95391 + 1.32863i) q^{90} +(-14.5322 - 10.5583i) q^{91} +(0.847523 + 0.134234i) q^{92} +(0.617578 + 1.21207i) q^{93} +(2.26046 - 6.95697i) q^{94} +(-4.29551 - 0.208770i) q^{95} +(-0.732139 + 1.00770i) q^{96} +(-2.26820 + 4.45160i) q^{97} +(1.35090 + 1.35090i) q^{98} +(-4.73107 + 0.834773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

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