LMFDB - Embedded newform 603.2.u.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			91.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	603.91
Dual form			603.2.u.b.550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0366213 + 0.0801894i) q^{2} +(1.30463 + 1.50563i) q^{4} +(-0.260554 + 1.81219i) q^{5} +(-0.253098 + 0.554206i) q^{7} +(-0.337683 + 0.0991526i) q^{8} +O(q^{10})$	\(q+(-0.0366213 + 0.0801894i) q^{2} +(1.30463 + 1.50563i) q^{4} +(-0.260554 + 1.81219i) q^{5} +(-0.253098 + 0.554206i) q^{7} +(-0.337683 + 0.0991526i) q^{8} +(-0.135777 - 0.0872586i) q^{10} +(-0.769529 + 5.35219i) q^{11} +(-5.48325 - 1.61003i) q^{13} +(-0.0351727 - 0.0405915i) q^{14} +(-0.562632 + 3.91319i) q^{16} +(3.76413 - 4.34403i) q^{17} +(-0.821251 - 1.79829i) q^{19} +(-3.06841 + 1.97195i) q^{20} +(-0.401008 - 0.257712i) q^{22} +(-2.95918 + 1.90175i) q^{23} +(1.58130 + 0.464313i) q^{25} +(0.329911 - 0.380738i) q^{26} +(-1.16463 + 0.341965i) q^{28} -4.50909 q^{29} +(3.92487 - 1.15244i) q^{31} +(-0.885331 - 0.568968i) q^{32} +(0.210498 + 0.460927i) q^{34} +(-0.938384 - 0.603063i) q^{35} +3.02889 q^{37} +0.174279 q^{38} +(-0.0916991 - 0.637781i) q^{40} +(1.80542 - 2.08357i) q^{41} +(-4.28868 + 4.94940i) q^{43} +(-9.06235 + 5.82402i) q^{44} +(-0.0441312 - 0.306939i) q^{46} +(1.86582 - 1.19909i) q^{47} +(4.34094 + 5.00971i) q^{49} +(-0.0951423 + 0.109800i) q^{50} +(-4.72953 - 10.3562i) q^{52} +(5.19664 + 5.99724i) q^{53} +(-9.49871 - 2.78907i) q^{55} +(0.0305157 - 0.212241i) q^{56} +(0.165129 - 0.361582i) q^{58} +(-0.733886 + 0.215488i) q^{59} +(1.49662 + 10.4092i) q^{61} +(-0.0513198 + 0.356937i) q^{62} +(-6.57363 + 4.22462i) q^{64} +(4.34637 - 9.51722i) q^{65} +(8.14151 + 0.846014i) q^{67} +11.4513 q^{68} +(0.0827241 - 0.0531636i) q^{70} +(8.46440 + 9.76844i) q^{71} +(-1.52925 - 10.6362i) q^{73} +(-0.110922 + 0.242885i) q^{74} +(1.63612 - 3.58260i) q^{76} +(-2.77145 - 1.78111i) q^{77} +(11.3848 + 3.34289i) q^{79} +(-6.94487 - 2.03920i) q^{80} +(0.100963 + 0.221079i) q^{82} +(-0.467569 + 3.25201i) q^{83} +(6.89147 + 7.95318i) q^{85} +(-0.239833 - 0.525160i) q^{86} +(-0.270827 - 1.88364i) q^{88} +(-4.42253 - 2.84219i) q^{89} +(2.28009 - 2.63136i) q^{91} +(-6.72396 - 1.97433i) q^{92} +(0.0278255 + 0.193531i) q^{94} +(3.47283 - 1.01971i) q^{95} -9.24945 q^{97} +(-0.560697 + 0.164635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−0.0366213	+	0.0801894i	−0.0258952	+	0.0567025i	−0.922138	−	0.386862i	$-0.873559\pi$
$2$	−0.0366213	+	0.0801894i	−0.0258952	+	0.0567025i	0.896242	+	0.443564i	$0.146286\pi$
$3$		0			0
$3$		0			0
$4$	1.30463	+	1.50563i	0.652316	+	0.752813i
$5$	−0.260554	+	1.81219i	−0.116523	+	0.810438i	0.844813	+	0.535062i	$0.179712\pi$
$5$	−0.260554	+	1.81219i	−0.116523	+	0.810438i	−0.961336	+	0.275377i	$0.911197\pi$
$6$		0			0
$7$	−0.253098	+	0.554206i	−0.0956619	+	0.209470i	−0.951413	−	0.307917i	$-0.900368\pi$
$7$	−0.253098	+	0.554206i	−0.0956619	+	0.209470i	0.855751	+	0.517387i	$0.173095\pi$
$8$	−0.337683	+	0.0991526i	−0.119389	+	0.0350557i
$9$		0			0
$10$	−0.135777	−	0.0872586i	−0.0429365	−	0.0275936i
$11$	−0.769529	+	5.35219i	−0.232022	+	1.61375i	0.457314	+	0.889305i	$0.348812\pi$
$11$	−0.769529	+	5.35219i	−0.232022	+	1.61375i	−0.689336	+	0.724442i	$0.742098\pi$
$12$		0			0
$13$	−5.48325	−	1.61003i	−1.52078	−	0.446542i	−0.588567	−	0.808449i	$-0.700308\pi$
$13$	−5.48325	−	1.61003i	−1.52078	−	0.446542i	−0.932214	+	0.361907i	$0.882126\pi$
$14$	−0.0351727	−	0.0405915i	−0.00940031	−	0.0108485i
$15$		0			0
$16$	−0.562632	+	3.91319i	−0.140658	+	0.978298i
$17$	3.76413	−	4.34403i	0.912934	−	1.05358i	−0.0854261	−	0.996345i	$-0.527225\pi$
$17$	3.76413	−	4.34403i	0.912934	−	1.05358i	0.998361	−	0.0572380i	$-0.0182294\pi$
$18$		0			0
$19$	−0.821251	−	1.79829i	−0.188408	−	0.412556i	0.791730	−	0.610871i	$-0.209180\pi$
$19$	−0.821251	−	1.79829i	−0.188408	−	0.412556i	−0.980138	+	0.198315i	$0.936453\pi$
$20$	−3.06841	+	1.97195i	−0.686118	+	0.440942i
$21$		0			0
$22$	−0.401008	−	0.257712i	−0.0854953	−	0.0549445i
$23$	−2.95918	+	1.90175i	−0.617031	+	0.396542i	−0.811488	−	0.584369i	$-0.801342\pi$
$23$	−2.95918	+	1.90175i	−0.617031	+	0.396542i	0.194457	+	0.980911i	$0.437706\pi$
$24$		0			0
$25$	1.58130	+	0.464313i	0.316261	+	0.0928625i
$26$	0.329911	−	0.380738i	0.0647009	−	0.0746688i
$27$		0			0
$28$	−1.16463	+	0.341965i	−0.220094	+	0.0646254i
$29$	−4.50909			−0.837317			−0.418659	−	0.908144i	$-0.637500\pi$
$29$	−4.50909			−0.837317			−0.418659	+	0.908144i	$0.637500\pi$
$30$		0			0
$31$	3.92487	−	1.15244i	0.704927	−	0.206985i	0.0904281	−	0.995903i	$-0.471176\pi$
$31$	3.92487	−	1.15244i	0.704927	−	0.206985i	0.614499	+	0.788918i	$0.289358\pi$
$32$	−0.885331	−	0.568968i	−0.156506	−	0.100580i
$33$		0			0
$34$	0.210498	+	0.460927i	0.0361002	+	0.0790484i
$35$	−0.938384	−	0.603063i	−0.158616	−	0.101936i
$36$		0			0
$37$	3.02889			0.497946			0.248973	−	0.968510i	$-0.419907\pi$
$37$	3.02889			0.497946			0.248973	+	0.968510i	$0.419907\pi$
$38$	0.174279			0.0282718
$39$		0			0
$40$	−0.0916991	−	0.637781i	−0.0144989	−	0.100842i
$41$	1.80542	−	2.08357i	0.281960	−	0.325399i	−0.597049	−	0.802205i	$-0.703660\pi$
$41$	1.80542	−	2.08357i	0.281960	−	0.325399i	0.879009	+	0.476806i	$0.158206\pi$
$42$		0			0
$43$	−4.28868	+	4.94940i	−0.654017	+	0.754776i	−0.981788	−	0.189981i	$-0.939157\pi$
$43$	−4.28868	+	4.94940i	−0.654017	+	0.754776i	0.327771	+	0.944757i	$0.393703\pi$
$44$	−9.06235	+	5.82402i	−1.36620	+	0.878004i
$45$		0			0
$46$	−0.0441312	−	0.306939i	−0.00650679	−	0.0452557i
$47$	1.86582	−	1.19909i	0.272157	−	0.174905i	−0.397442	−	0.917627i	$-0.630102\pi$
$47$	1.86582	−	1.19909i	0.272157	−	0.174905i	0.669600	+	0.742722i	$0.266466\pi$
$48$		0			0
$49$	4.34094	+	5.00971i	0.620134	+	0.715673i
$50$	−0.0951423	+	0.109800i	−0.0134552	+	0.0155281i
$51$		0			0
$52$	−4.72953	−	10.3562i	−0.655868	−	1.43615i
$53$	5.19664	+	5.99724i	0.713813	+	0.823784i	0.990549	−	0.137162i	$-0.0437982\pi$
$53$	5.19664	+	5.99724i	0.713813	+	0.823784i	−0.276736	+	0.960946i	$0.589253\pi$
$54$		0			0
$55$	−9.49871	−	2.78907i	−1.28081	−	0.376079i
$56$	0.0305157	−	0.212241i	0.00407783	−	0.0283619i
$57$		0			0
$58$	0.165129	−	0.361582i	0.0216825	−	0.0474780i
$59$	−0.733886	+	0.215488i	−0.0955439	+	0.0280542i	−0.329155	−	0.944276i	$-0.606764\pi$
$59$	−0.733886	+	0.215488i	−0.0955439	+	0.0280542i	0.233611	+	0.972330i	$0.424946\pi$
$60$		0			0
$61$	1.49662	+	10.4092i	0.191622	+	1.33276i	0.827715	+	0.561148i	$0.189640\pi$
$61$	1.49662	+	10.4092i	0.191622	+	1.33276i	−0.636093	+	0.771612i	$0.719451\pi$
$62$	−0.0513198	+	0.356937i	−0.00651762	+	0.0453310i
$63$		0			0
$64$	−6.57363	+	4.22462i	−0.821704	+	0.528077i
$65$	4.34637	−	9.51722i	0.539101	−	1.18047i
$66$		0			0
$67$	8.14151	+	0.846014i	0.994644	+	0.103357i
$67$	8.14151	+	0.846014i	0.994644	+	0.103357i
$68$	11.4513			1.38867
$69$		0			0
$70$	0.0827241	−	0.0531636i	0.00988743	−	0.00635426i
$71$	8.46440	+	9.76844i	1.00454	+	1.15930i	0.987206	+	0.159451i	$0.0509723\pi$
$71$	8.46440	+	9.76844i	1.00454	+	1.15930i	0.0173337	+	0.999850i	$0.494482\pi$
$72$		0			0
$73$	−1.52925	−	10.6362i	−0.178986	−	1.24487i	−0.859116	−	0.511781i	$-0.828986\pi$
$73$	−1.52925	−	10.6362i	−0.178986	−	1.24487i	0.680130	−	0.733091i	$-0.261923\pi$
$74$	−0.110922	+	0.242885i	−0.0128944	+	0.0282348i
$75$		0			0
$76$	1.63612	−	3.58260i	0.187676	−	0.410953i
$77$	−2.77145	−	1.78111i	−0.315837	−	0.202976i
$78$		0			0
$79$	11.3848	+	3.34289i	1.28089	+	0.376104i	0.850232	−	0.526409i	$-0.176462\pi$
$79$	11.3848	+	3.34289i	1.28089	+	0.376104i	0.430662	+	0.902513i	$0.358280\pi$
$80$	−6.94487	−	2.03920i	−0.776460	−	0.227989i
$81$		0			0
$82$	0.100963	+	0.221079i	0.0111495	+	0.0244141i
$83$	−0.467569	+	3.25201i	−0.0513224	+	0.356955i	0.947936	+	0.318460i	$0.103166\pi$
$83$	−0.467569	+	3.25201i	−0.0513224	+	0.356955i	−0.999259	+	0.0384952i	$0.987744\pi$
$84$		0			0
$85$	6.89147	+	7.95318i	0.747485	+	0.862644i
$86$	−0.239833	−	0.525160i	−0.0258618	−	0.0566295i
$87$		0			0
$88$	−0.270827	−	1.88364i	−0.0288703	−	0.200797i
$89$	−4.42253	−	2.84219i	−0.468787	−	0.301271i	0.284838	−	0.958576i	$-0.408060\pi$
$89$	−4.42253	−	2.84219i	−0.468787	−	0.301271i	−0.753625	+	0.657304i	$0.771697\pi$
$90$		0			0
$91$	2.28009	−	2.63136i	0.239018	−	0.275841i
$92$	−6.72396	−	1.97433i	−0.701021	−	0.205838i
$93$		0			0
$94$	0.0278255	+	0.193531i	0.00286998	+	0.0199612i
$95$	3.47283	−	1.01971i	0.356305	−	0.104621i
$96$		0			0
$97$	−9.24945			−0.939139			−0.469570	−	0.882895i	$-0.655591\pi$
$97$	−9.24945			−0.939139			−0.469570	+	0.882895i	$0.655591\pi$
$98$	−0.560697	+	0.164635i	−0.0566389	+	0.0166307i
$99$		0			0
$100$	1.36394	+	2.98661i	0.136394	+	0.298661i
$101$	2.15093	+	4.70988i	0.214026	+	0.468651i	0.985945	−	0.167070i	$-0.0534305\pi$
$101$	2.15093	+	4.70988i	0.214026	+	0.468651i	−0.771919	+	0.635720i	$0.780703\pi$
$102$		0			0
$103$	9.60270	−	2.81961i	0.946182	−	0.277824i	0.227985	−	0.973665i	$-0.426786\pi$
$103$	9.60270	−	2.81961i	0.946182	−	0.277824i	0.718196	+	0.695840i	$0.244968\pi$
$104$	2.01124			0.197218
$105$		0			0
$106$	−0.671223	+	0.197089i	−0.0651949	+	0.0191430i
$107$	−1.21428	−	8.44550i	−0.117389	−	0.816457i	−0.960413	−	0.278581i	$-0.910136\pi$
$107$	−1.21428	−	8.44550i	−0.117389	−	0.816457i	0.843024	−	0.537876i	$-0.180773\pi$
$108$		0			0
$109$	−5.34446	−	1.56927i	−0.511906	−	0.150309i	0.0155705	−	0.999879i	$-0.495044\pi$
$109$	−5.34446	−	1.56927i	−0.511906	−	0.150309i	−0.527477	+	0.849570i	$0.676862\pi$
$110$	0.571509	−	0.659557i	0.0544913	−	0.0628863i
$111$		0			0
$112$	−2.02632	−	1.30223i	−0.191469	−	0.123050i
$113$	−1.48006	−	10.2941i	−0.139232	−	0.968383i	−0.932927	−	0.360066i	$-0.882754\pi$
$113$	−1.48006	−	10.2941i	−0.139232	−	0.968383i	0.793694	−	0.608317i	$-0.208155\pi$
$114$		0			0
$115$	−2.67531	−	5.85812i	−0.249474	−	0.546272i
$116$	−5.88271	−	6.78901i	−0.546196	−	0.630343i
$117$		0			0
$118$	0.00959596	−	0.0667414i	0.000883380	−	0.00614404i
$119$	1.45480	+	3.18557i	0.133361	+	0.292020i
$120$		0			0
$121$	−17.4994	−	5.13828i	−1.59085	−	0.467116i
$122$	−0.889516	−	0.261185i	−0.0805330	−	0.0236466i
$123$		0			0
$124$	6.85566	+	4.40586i	0.615656	+	0.395658i
$125$	−5.05621	+	11.0716i	−0.452241	+	0.990270i
$126$		0			0
$127$	5.32196	−	11.6535i	0.472247	−	1.03408i	−0.512276	−	0.858821i	$-0.671197\pi$
$127$	5.32196	−	11.6535i	0.472247	−	1.03408i	0.984523	−	0.175256i	$-0.0560754\pi$
$128$	−0.397578	−	2.76521i	−0.0351412	−	0.244413i
$129$		0			0
$130$	0.604011	+	0.697066i	0.0529753	+	0.0611367i
$131$	13.9362	−	8.95624i	1.21761	−	0.782510i	0.235694	−	0.971827i	$-0.424264\pi$
$131$	13.9362	−	8.95624i	1.21761	−	0.782510i	0.981916	+	0.189317i	$0.0606275\pi$
$132$		0			0
$133$	1.20448			0.104442
$134$	−0.365994	+	0.621881i	−0.0316171	+	0.0537224i
$135$		0			0
$136$	−0.840358	+	1.84013i	−0.0720601	+	0.157790i
$137$	14.1127	−	9.06967i	1.20573	−	0.774874i	0.225789	−	0.974176i	$-0.427504\pi$
$137$	14.1127	−	9.06967i	1.20573	−	0.774874i	0.979938	+	0.199302i	$0.0638675\pi$
$138$		0			0
$139$	1.70167	−	11.8353i	0.144333	−	1.00386i	−0.780953	−	0.624590i	$-0.785266\pi$
$139$	1.70167	−	11.8353i	0.144333	−	1.00386i	0.925286	−	0.379270i	$-0.123825\pi$
$140$	−0.316259	−	2.19963i	−0.0267288	−	0.185903i
$141$		0			0
$142$	−1.09330	+	0.321023i	−0.0917480	+	0.0269396i
$143$	12.8367	−	28.1085i	1.07346	−	2.35055i
$144$		0			0
$145$	1.17486	−	8.17135i	0.0975671	−	0.678594i
$146$	0.908914	+	0.266881i	0.0752223	+	0.0220872i
$147$		0			0
$148$	3.95158	+	4.56037i	0.324818	+	0.374860i
$149$	−3.05447	−	6.68836i	−0.250232	−	0.547932i	0.742278	−	0.670092i	$-0.233745\pi$
$149$	−3.05447	−	6.68836i	−0.250232	−	0.547932i	−0.992510	+	0.122160i	$0.961018\pi$
$150$		0			0
$151$	−3.02720	+	3.49357i	−0.246350	+	0.284303i	−0.865435	−	0.501021i	$-0.832958\pi$
$151$	−3.02720	+	3.49357i	−0.246350	+	0.284303i	0.619085	+	0.785324i	$0.287503\pi$
$152$	0.455627	+	0.525822i	0.0369562	+	0.0426498i
$153$		0			0
$154$	0.244320	−	0.157015i	0.0196879	−	0.0126526i
$155$	1.06581	+	7.41290i	0.0856082	+	0.595418i
$156$		0			0
$157$	1.91636	−	1.23157i	0.152942	−	0.0982898i	−0.461932	−	0.886916i	$-0.652843\pi$
$157$	1.91636	−	1.23157i	0.152942	−	0.0982898i	0.614873	+	0.788626i	$0.289207\pi$
$158$	−0.684992	+	0.790523i	−0.0544950	+	0.0628906i
$159$		0			0
$160$	1.26176	−	1.45615i	0.0997507	−	0.115118i
$161$	−0.305000	−	2.12132i	−0.0240374	−	0.167184i
$162$		0			0
$163$	−11.9173			−0.933433			−0.466717	−	0.884407i	$-0.654563\pi$
$163$	−11.9173			−0.933433			−0.466717	+	0.884407i	$0.654563\pi$
$164$	5.49249			0.428891
$165$		0			0
$166$	−0.243654	−	0.156587i	−0.0189112	−	0.0121535i
$167$	7.73872	+	16.9454i	0.598840	+	1.31128i	0.929950	+	0.367685i	$0.119849\pi$
$167$	7.73872	+	16.9454i	0.598840	+	1.31128i	−0.331110	+	0.943592i	$0.607423\pi$
$168$		0			0
$169$	16.5376	+	10.6281i	1.27212	+	0.817543i
$170$	−0.890136	+	0.261368i	−0.0682703	+	0.0200460i
$171$		0			0
$172$	−13.0471			−0.994831
$173$	−8.82447	+	2.59110i	−0.670912	+	0.196998i	−0.599409	−	0.800443i	$-0.704598\pi$
$173$	−8.82447	+	2.59110i	−0.670912	+	0.196998i	−0.0715029	+	0.997440i	$0.522780\pi$
$174$		0			0
$175$	−0.657549	+	0.758852i	−0.0497060	+	0.0573638i
$176$	−20.5112	−	6.02263i	−1.54609	−	0.453973i
$177$		0			0
$178$	0.389872	−	0.250556i	0.0292222	−	0.0187799i
$179$	14.7436	+	9.47515i	1.10199	+	0.708206i	0.959533	−	0.281595i	$-0.0908634\pi$
$179$	14.7436	+	9.47515i	1.10199	+	0.708206i	0.142457	+	0.989801i	$0.454500\pi$
$180$		0			0
$181$	16.3259	−	10.4920i	1.21349	−	0.779864i	0.232253	−	0.972655i	$-0.425390\pi$
$181$	16.3259	−	10.4920i	1.21349	−	0.779864i	0.981240	+	0.192791i	$0.0617540\pi$
$182$	0.127508	+	0.279203i	0.00945149	+	0.0206959i
$183$		0			0
$184$	0.810700	−	0.935597i	0.0597656	−	0.0689732i
$185$	−0.789189	+	5.48893i	−0.0580223	+	0.403554i
$186$		0			0
$187$	20.3535	+	23.4892i	1.48839	+	1.71770i
$188$	4.23958	+	1.24485i	0.309203	+	0.0907902i
$189$		0			0
$190$	−0.0454092	+	0.315828i	−0.00329433	+	0.0229125i
$191$	−12.4377	−	7.99323i	−0.899960	−	0.578369i	0.00681804	−	0.999977i	$-0.497830\pi$
$191$	−12.4377	−	7.99323i	−0.899960	−	0.578369i	−0.906779	+	0.421607i	$0.861466\pi$
$192$		0			0
$193$	−8.21738	+	2.41284i	−0.591500	+	0.173680i	−0.563765	−	0.825935i	$-0.690648\pi$
$193$	−8.21738	+	2.41284i	−0.591500	+	0.173680i	−0.0277350	+	0.999615i	$0.508829\pi$
$194$	0.338727	−	0.741708i	0.0243192	−	0.0532515i
$195$		0			0
$196$	−1.87942	+	13.0717i	−0.134244	+	0.933690i
$197$	−0.886535	−	1.02312i	−0.0631630	−	0.0728940i	0.723289	−	0.690546i	$-0.242630\pi$
$197$	−0.886535	−	1.02312i	−0.0631630	−	0.0728940i	−0.786452	+	0.617652i	$0.788084\pi$
$198$		0			0
$199$	0.637120	−	1.39510i	0.0451642	−	0.0988958i	−0.885705	−	0.464249i	$-0.846324\pi$
$199$	0.637120	−	1.39510i	0.0451642	−	0.0988958i	0.930869	+	0.365353i	$0.119052\pi$
$200$	−0.580016			−0.0410134
$201$		0			0
$202$	−0.456453			−0.0321159
$203$	1.14124	−	2.49897i	0.0800994	−	0.175393i
$204$		0			0
$205$	3.30542	+	3.81466i	0.230861	+	0.266428i
$206$	−0.125561	+	0.873293i	−0.00874822	+	0.0608452i
$207$		0			0
$208$	9.38540	−	20.5512i	0.650761	−	1.42497i
$209$	10.2568	−	3.01166i	0.709475	−	0.208321i
$210$		0			0
$211$	−15.4357	−	9.91993i	−1.06264	−	0.682916i	−0.112155	−	0.993691i	$-0.535775\pi$
$211$	−15.4357	−	9.91993i	−1.06264	−	0.682916i	−0.950484	+	0.310775i	$0.899412\pi$
$212$	−2.24990	+	15.6484i	−0.154524	+	1.07473i
$213$		0			0
$214$	0.721708	+	0.211913i	0.0493350	+	0.0144861i
$215$	−7.85184	−	9.06150i	−0.535491	−	0.617990i
$216$		0			0
$217$	−0.354682	+	2.46687i	−0.0240774	+	0.167462i
$218$	0.321560	−	0.371100i	0.0217788	−	0.0251341i
$219$		0			0
$220$	−8.19303	−	17.9402i	−0.552374	−	1.20953i
$221$	−27.6337	+	17.7591i	−1.85884	+	1.19461i
$222$		0			0
$223$	23.8768	+	15.3447i	1.59891	+	1.02756i	0.967752	+	0.251906i	$0.0810573\pi$
$223$	23.8768	+	15.3447i	1.59891	+	1.02756i	0.631160	+	0.775653i	$0.282579\pi$
$224$	0.539401	−	0.346652i	0.0360402	−	0.0231617i
$225$		0			0
$226$	0.879676	+	0.258296i	0.0585152	+	0.0171816i
$227$	12.8108	−	14.7845i	0.850284	−	0.981280i	−0.149689	−	0.988733i	$-0.547827\pi$
$227$	12.8108	−	14.7845i	0.850284	−	0.981280i	0.999972	+	0.00745367i	$0.00237260\pi$
$228$		0			0
$229$	−17.6410	+	5.17987i	−1.16575	+	0.342295i	−0.806665	−	0.591009i	$-0.798730\pi$
$229$	−17.6410	+	5.17987i	−1.16575	+	0.342295i	−0.359086	+	0.933305i	$0.616911\pi$
$230$	0.567732			0.0374352
$231$		0			0
$232$	1.52264	−	0.447088i	0.0999663	−	0.0293528i
$233$	8.52122	+	5.47626i	0.558244	+	0.358762i	0.789137	−	0.614218i	$-0.210528\pi$
$233$	8.52122	+	5.47626i	0.558244	+	0.358762i	−0.230893	+	0.972979i	$0.574165\pi$
$234$		0			0
$235$	1.68683	+	3.69365i	0.110037	+	0.240947i
$236$	−1.28190	−	0.823825i	−0.0834444	−	0.0536264i
$237$		0			0
$238$	−0.308725			−0.0200117
$239$	11.7728			0.761516			0.380758	−	0.924675i	$-0.375663\pi$
$239$	11.7728			0.761516			0.380758	+	0.924675i	$0.375663\pi$
$240$		0			0
$241$	−2.33109	−	16.2131i	−0.150159	−	1.04438i	−0.915951	−	0.401290i	$-0.868562\pi$
$241$	−2.33109	−	16.2131i	−0.150159	−	1.04438i	0.765792	−	0.643088i	$-0.222347\pi$
$242$	1.05289	−	1.21509i	0.0676821	−	0.0781093i
$243$		0			0
$244$	−13.7198	+	15.8335i	−0.878321	+	1.01364i
$245$	−10.2096	+	6.56133i	−0.652269	+	0.419188i
$246$		0			0
$247$	1.60783	+	11.1827i	0.102304	+	0.711539i
$248$	−1.21109	+	0.778321i	−0.0769044	+	0.0494234i
$249$		0			0
$250$	−0.702657	−	0.810910i	−0.0444399	−	0.0512864i
$251$	−9.08000	+	10.4789i	−0.573125	+	0.661421i	−0.966112	−	0.258123i	$-0.916896\pi$
$251$	−9.08000	+	10.4789i	−0.573125	+	0.661421i	0.392988	+	0.919544i	$0.371442\pi$
$252$		0			0
$253$	−7.90135	−	17.3015i	−0.496754	−	1.08774i
$254$	0.739588	+	0.853530i	0.0464059	+	0.0535552i
$255$		0			0
$256$	−14.7588	−	4.33358i	−0.922427	−	0.270849i
$257$	0.366322	−	2.54783i	0.0228506	−	0.158929i	−0.975201	−	0.221320i	$-0.928963\pi$
$257$	0.366322	−	2.54783i	0.0228506	−	0.158929i	0.998052	+	0.0623909i	$0.0198726\pi$
$258$		0			0
$259$	−0.766604	+	1.67863i	−0.0476344	+	0.104305i
$260$	19.9998	−	5.87247i	1.24033	−	0.364195i
$261$		0			0
$262$	0.207835	+	1.44552i	0.0128401	+	0.0893047i
$263$	−2.11259	+	14.6934i	−0.130268	+	0.906033i	0.814936	+	0.579551i	$0.196772\pi$
$263$	−2.11259	+	14.6934i	−0.130268	+	0.906033i	−0.945204	+	0.326481i	$0.894137\pi$
$264$		0			0
$265$	−12.2222	+	7.85471i	−0.750802	+	0.482511i
$266$	−0.0441096	+	0.0965866i	−0.00270453	+	0.00592210i
$267$		0			0
$268$	9.34790	+	13.3618i	0.571014	+	0.816203i
$269$	−1.38543			−0.0844712			−0.0422356	−	0.999108i	$-0.513448\pi$
$269$	−1.38543			−0.0844712			−0.0422356	+	0.999108i	$0.513448\pi$
$270$		0			0
$271$	−18.1863	+	11.6876i	−1.10474	+	0.709973i	−0.960141	−	0.279517i	$-0.909826\pi$
$271$	−18.1863	+	11.6876i	−1.10474	+	0.709973i	−0.144599	+	0.989490i	$0.546189\pi$
$272$	14.8812	+	17.1738i	0.902306	+	1.04132i
$273$		0			0
$274$	0.210467	+	1.46383i	0.0127148	+	0.0884332i
$275$	−3.70195	+	8.10614i	−0.223236	+	0.488819i
$276$		0			0
$277$	−1.14858	+	2.51504i	−0.0690115	+	0.151114i	−0.940994	−	0.338422i	$-0.890107\pi$
$277$	−1.14858	+	2.51504i	−0.0690115	+	0.151114i	0.871983	+	0.489537i	$0.162834\pi$
$278$	0.886752	+	0.569881i	0.0531839	+	0.0341792i
$279$		0			0
$280$	0.376671	+	0.110601i	0.0225104	+	0.00660965i
$281$	−18.2435	−	5.35677i	−1.08831	−	0.319558i	−0.312114	−	0.950045i	$-0.601037\pi$
$281$	−18.2435	−	5.35677i	−1.08831	−	0.319558i	−0.776200	+	0.630487i	$0.782855\pi$
$282$		0			0
$283$	7.95612	+	17.4215i	0.472942	+	1.03560i	0.984344	+	0.176257i	$0.0563991\pi$
$283$	7.95612	+	17.4215i	0.472942	+	1.03560i	−0.511402	+	0.859342i	$0.670874\pi$
$284$	−3.66468	+	25.4884i	−0.217459	+	1.51246i
$285$		0			0
$286$	1.78391	+	2.05874i	0.105485	+	0.121736i
$287$	0.697779	+	1.52792i	0.0411886	+	0.0901905i
$288$		0			0
$289$	−2.28262	−	15.8760i	−0.134272	−	0.933882i
$290$	0.612231	+	0.393457i	0.0359515	+	0.0231046i
$291$		0			0
$292$	14.0190	−	16.1788i	0.820401	−	0.946793i
$293$	−12.4636	−	3.65963i	−0.728129	−	0.213798i	−0.103401	−	0.994640i	$-0.532972\pi$
$293$	−12.4636	−	3.65963i	−0.728129	−	0.213798i	−0.624729	+	0.780842i	$0.714791\pi$
$294$		0			0
$295$	−0.199290	−	1.38609i	−0.0116031	−	0.0807014i
$296$	−1.02280	+	0.300322i	−0.0594492	+	0.0174559i
$297$		0			0
$298$	0.648195			0.0375489
$299$	19.2878	−	5.66341i	1.11544	−	0.327523i
$300$		0			0
$301$	−1.65753	−	3.62949i	−0.0955387	−	0.209201i
$302$	−0.169288	−	0.370688i	−0.00974141	−	0.0213307i
$303$		0			0
$304$	7.49911	−	2.20194i	0.430103	−	0.126290i
$305$	−19.2534			−1.10245
$306$		0			0
$307$	−6.51335	+	1.91249i	−0.371737	+	0.109152i	−0.462264	−	0.886742i	$-0.652963\pi$
$307$	−6.51335	+	1.91249i	−0.371737	+	0.109152i	0.0905276	+	0.995894i	$0.471145\pi$
$308$	−0.934050	−	6.49646i	−0.0532224	−	0.370170i
$309$		0			0
$310$	−0.633468	−	0.186003i	−0.0359785	−	0.0105643i
$311$	−1.77969	+	2.05387i	−0.100917	+	0.116464i	−0.803961	−	0.594682i	$-0.797278\pi$
$311$	−1.77969	+	2.05387i	−0.100917	+	0.116464i	0.703044	+	0.711146i	$0.251824\pi$
$312$		0			0
$313$	10.5780	+	6.79806i	0.597903	+	0.384249i	0.804304	−	0.594219i	$-0.202539\pi$
$313$	10.5780	+	6.79806i	0.597903	+	0.384249i	−0.206401	+	0.978468i	$0.566175\pi$
$314$	0.0285793	+	0.198773i	0.00161282	+	0.0112174i
$315$		0			0
$316$	9.81988	+	21.5025i	0.552412	+	1.20961i
$317$	−13.9644	−	16.1158i	−0.784321	−	0.905155i	0.213092	−	0.977032i	$-0.431646\pi$
$317$	−13.9644	−	16.1158i	−0.784321	−	0.905155i	−0.997413	+	0.0718773i	$0.977101\pi$
$318$		0			0
$319$	3.46988	−	24.1335i	0.194276	−	1.35122i
$320$	−5.94304	−	13.0134i	−0.332226	−	0.727473i
$321$		0			0
$322$	0.181277	+	0.0532278i	0.0101022	+	0.00296627i
$323$	−10.9031	−	3.20144i	−0.606666	−	0.178133i
$324$		0			0
$325$	−7.92313	−	5.09189i	−0.439496	−	0.282447i
$326$	0.436426	−	0.955640i	0.0241714	−	0.0529280i
$327$		0			0
$328$	−0.403069	+	0.882598i	−0.0222558	+	0.0487333i
$329$	0.192308	+	1.33753i	0.0106023	+	0.0737406i
$330$		0			0
$331$	0.0106833	+	0.0123292i	0.000587207	+	0.000677673i	0.756043	−	0.654522i	$-0.227130\pi$
$331$	0.0106833	+	0.0123292i	0.000587207	+	0.000677673i	−0.755456	+	0.655200i	$0.772585\pi$
$332$	−5.50632	+	3.53870i	−0.302199	+	0.194211i
$333$		0			0
$334$	−1.64225			−0.0898597
$335$	−3.65445	+	14.5336i	−0.199664	+	0.794054i
$336$		0			0
$337$	1.41867	−	3.10645i	0.0772797	−	0.169219i	−0.867049	−	0.498224i	$-0.833986\pi$
$337$	1.41867	−	3.10645i	0.0772797	−	0.169219i	0.944328	+	0.329005i	$0.106713\pi$
$338$	−1.45789	+	0.936926i	−0.0792985	+	0.0509621i
$339$		0			0
$340$	−2.98368	+	20.7520i	−0.161813	+	1.12543i
$341$	3.14781	+	21.8935i	0.170463	+	1.18560i
$342$		0			0
$343$	−7.96719	+	2.33938i	−0.430188	+	0.126315i
$344$	0.957466	−	2.09656i	0.0516231	−	0.113039i
$345$		0			0
$346$	0.115385	−	0.802519i	0.00620312	−	0.0431437i
$347$	−31.1374	−	9.14275i	−1.67154	−	0.490809i	−0.697387	−	0.716694i	$-0.745654\pi$
$347$	−31.1374	−	9.14275i	−1.67154	−	0.490809i	−0.974154	+	0.225886i	$0.927472\pi$
$348$		0			0
$349$	−13.0668	−	15.0799i	−0.699451	−	0.807210i	0.289227	−	0.957260i	$-0.406602\pi$
$349$	−13.0668	−	15.0799i	−0.699451	−	0.807210i	−0.988678	+	0.150051i	$0.952056\pi$
$350$	−0.0367716	−	0.0805186i	−0.00196553	−	0.00430390i
$351$		0			0
$352$	3.72652	−	4.30063i	0.198624	−	0.229224i
$353$	−17.0378	−	19.6627i	−0.906832	−	1.04654i	−0.998710	−	0.0507694i	$-0.983833\pi$
$353$	−17.0378	−	19.6627i	−0.906832	−	1.04654i	0.0918787	−	0.995770i	$-0.470713\pi$
$354$		0			0
$355$	−19.9078	+	12.7939i	−1.05659	+	0.679032i
$356$	−1.49050	−	10.3667i	−0.0789966	−	0.549433i
$357$		0			0
$358$	−1.29974	+	0.835291i	−0.0686933	+	0.0441465i
$359$	1.65826	−	1.91374i	0.0875198	−	0.101003i	−0.710300	−	0.703899i	$-0.751441\pi$
$359$	1.65826	−	1.91374i	0.0875198	−	0.101003i	0.797820	+	0.602895i	$0.205986\pi$
$360$		0			0
$361$	9.88296	−	11.4055i	0.520156	−	0.600292i
$362$	0.243473	+	1.69339i	0.0127967	+	0.0890028i
$363$		0			0
$364$	6.93652			0.363572
$365$	19.6733			1.02975
$366$		0			0
$367$	19.1827	+	12.3279i	1.00133	+	0.643513i	0.935134	−	0.354294i	$-0.115279\pi$
$367$	19.1827	+	12.3279i	1.00133	+	0.643513i	0.0661920	+	0.997807i	$0.478915\pi$
$368$	−5.77698	−	12.6498i	−0.301146	−	0.659417i
$369$		0			0
$370$	−0.411253	−	0.264296i	−0.0213800	−	0.0137401i
$371$	−4.63896	+	1.36212i	−0.240843	+	0.0707179i
$372$		0			0
$373$	19.9389			1.03240			0.516198	−	0.856469i	$-0.327347\pi$
$373$	19.9389			1.03240			0.516198	+	0.856469i	$0.327347\pi$
$374$	−2.62896	+	0.771931i	−0.135940	+	0.0399156i
$375$		0			0
$376$	−0.511161	+	0.589911i	−0.0263611	+	0.0304223i
$377$	24.7245	+	7.25977i	1.27338	+	0.373897i
$378$		0			0
$379$	2.79789	−	1.79809i	0.143718	−	0.0923618i	−0.466806	−	0.884360i	$-0.654595\pi$
$379$	2.79789	−	1.79809i	0.143718	−	0.0923618i	0.610524	+	0.791998i	$0.290959\pi$
$380$	6.06608	+	3.89843i	0.311183	+	0.199985i
$381$		0			0
$382$	1.09646	−	0.704650i	0.0560996	−	0.0360530i
$383$	14.5032	+	31.7575i	0.741077	+	1.62273i	0.781776	+	0.623560i	$0.214314\pi$
$383$	14.5032	+	31.7575i	0.741077	+	1.62273i	−0.0406989	+	0.999171i	$0.512958\pi$
$384$		0			0
$385$	3.94982	−	4.55834i	0.201302	−	0.232315i
$386$	0.107447	−	0.747309i	0.00546890	−	0.0380370i
$387$		0			0
$388$	−12.0671	−	13.9262i	−0.612616	−	0.706996i
$389$	19.9764	+	5.86559i	1.01284	+	0.297397i	0.745716	−	0.666264i	$-0.232108\pi$
$389$	19.9764	+	5.86559i	1.01284	+	0.297397i	0.267127	+	0.963661i	$0.413926\pi$
$390$		0			0
$391$	−2.87746	+	20.0132i	−0.145519	+	1.01211i
$392$	−1.96259	−	1.26128i	−0.0991255	−	0.0637041i
$393$		0			0
$394$	0.114509	−	0.0336229i	0.00576889	−	0.00169390i
$395$	−9.02433	+	19.7605i	−0.454064	+	0.994260i
$396$		0			0
$397$	1.61108	−	11.2053i	0.0808576	−	0.562377i	−0.908613	−	0.417640i	$-0.862857\pi$
$397$	1.61108	−	11.2053i	0.0808576	−	0.562377i	0.989470	−	0.144737i	$-0.0462336\pi$
$398$	0.0885399	+	0.102181i	0.00443811	+	0.00512185i
$399$		0			0
$400$	−2.70664	+	5.92671i	−0.135332	+	0.296335i
$401$	28.6373			1.43008			0.715040	−	0.699084i	$-0.246408\pi$
$401$	28.6373			1.43008			0.715040	+	0.699084i	$0.246408\pi$
$402$		0			0
$403$	−23.3765			−1.16447
$404$	−4.28515	+	9.38316i	−0.213194	+	0.466830i
$405$		0			0
$406$	0.158597	+	0.183031i	0.00787105	+	0.00908367i
$407$	−2.33082	+	16.2112i	−0.115534	+	0.803559i
$408$		0			0
$409$	−13.5827	+	29.7420i	−0.671622	+	1.47065i	0.199660	+	0.979865i	$0.436016\pi$
$409$	−13.5827	+	29.7420i	−0.671622	+	1.47065i	−0.871282	+	0.490783i	$0.836711\pi$
$410$	−0.426945	+	0.125362i	−0.0210853	+	0.00619120i
$411$		0			0
$412$	16.7733	+	10.7795i	0.826359	+	0.531069i
$413$	0.0663198	−	0.461264i	0.00326338	−	0.0226973i
$414$		0			0
$415$	−5.77145	−	1.69465i	−0.283310	−	0.0831872i
$416$	3.93844	+	4.54520i	0.193098	+	0.222847i
$417$		0			0
$418$	−0.134113	+	0.932775i	−0.00655967	+	0.0456235i
$419$	13.7478	−	15.8658i	0.671623	−	0.775095i	−0.313006	−	0.949751i	$-0.601336\pi$
$419$	13.7478	−	15.8658i	0.671623	−	0.775095i	0.984629	+	0.174656i	$0.0558815\pi$
$420$		0			0
$421$	3.57395	+	7.82586i	0.174184	+	0.381409i	0.976509	−	0.215478i	$-0.0691311\pi$
$421$	3.57395	+	7.82586i	0.174184	+	0.381409i	−0.802325	+	0.596888i	$0.796404\pi$
$422$	1.36075	−	0.874501i	0.0662402	−	0.0425700i
$423$		0			0
$424$	−2.34945	−	1.50990i	−0.114100	−	0.0733274i
$425$	7.96921	−	5.12150i	0.386564	−	0.248429i
$426$		0			0
$427$	−6.14763	−	1.80511i	−0.297505	−	0.0873553i
$428$	11.1316	−	12.8465i	0.538065	−	0.620960i
$429$		0			0
$430$	1.01418	−	0.297791i	0.0489082	−	0.0143607i
$431$	−12.6021			−0.607023			−0.303512	−	0.952828i	$-0.598159\pi$
$431$	−12.6021			−0.607023			−0.303512	+	0.952828i	$0.598159\pi$
$432$		0			0
$433$	16.9210	−	4.96844i	0.813169	−	0.238768i	0.151397	−	0.988473i	$-0.451623\pi$
$433$	16.9210	−	4.96844i	0.813169	−	0.238768i	0.661772	+	0.749705i	$0.269805\pi$
$434$	−0.184828	−	0.118782i	−0.00887202	−	0.00570170i
$435$		0			0
$436$	−4.60981	−	10.0941i	−0.220770	−	0.483419i
$437$	5.85012	+	3.75964i	0.279849	+	0.179848i
$438$		0			0
$439$	−14.6293			−0.698218			−0.349109	−	0.937082i	$-0.613516\pi$
$439$	−14.6293			−0.698218			−0.349109	+	0.937082i	$0.613516\pi$
$440$	3.48409			0.166098
$441$		0			0
$442$	−0.412110	−	2.86629i	−0.0196021	−	0.136335i
$443$	−16.1101	+	18.5920i	−0.765413	+	0.883334i	−0.995967	−	0.0897255i	$-0.971401\pi$
$443$	−16.1101	+	18.5920i	−0.765413	+	0.883334i	0.230553	+	0.973060i	$0.425946\pi$
$444$		0			0
$445$	6.30291	−	7.27394i	0.298786	−	0.344818i
$446$	−2.10489	+	1.35273i	−0.0996692	+	0.0640535i
$447$		0			0
$448$	−0.677539	−	4.71239i	−0.0320107	−	0.222639i
$449$	−6.96526	+	4.47630i	−0.328711	+	0.211250i	−0.694578	−	0.719417i	$-0.744409\pi$
$449$	−6.96526	+	4.47630i	−0.328711	+	0.211250i	0.365867	+	0.930667i	$0.380772\pi$
$450$		0			0
$451$	9.76234	+	11.2663i	0.459691	+	0.530511i
$452$	13.5681	−	15.6584i	0.638188	−	0.736508i
$453$		0			0
$454$	0.716410	+	1.56872i	0.0336228	+	0.0736236i
$455$	4.17445	+	4.81757i	0.195701	+	0.225851i
$456$		0			0
$457$	17.1852	+	5.04602i	0.803888	+	0.236043i	0.657764	−	0.753224i	$-0.271502\pi$
$457$	17.1852	+	5.04602i	0.803888	+	0.236043i	0.146123	+	0.989266i	$0.453320\pi$
$458$	0.230666	−	1.60432i	0.0107783	−	0.0749647i
$459$		0			0
$460$	5.32983	−	11.6707i	0.248505	−	0.544149i
$461$	−29.9290	+	8.78795i	−1.39393	+	0.409295i	−0.890596	−	0.454795i	$-0.849712\pi$
$461$	−29.9290	+	8.78795i	−1.39393	+	0.409295i	−0.503336	+	0.864091i	$0.667894\pi$
$462$		0			0
$463$	−1.52541	−	10.6095i	−0.0708919	−	0.493064i	−0.994074	−	0.108702i	$-0.965331\pi$
$463$	−1.52541	−	10.6095i	−0.0708919	−	0.493064i	0.923182	−	0.384362i	$-0.125579\pi$
$464$	2.53696	−	17.6449i	0.117775	−	0.819146i
$465$		0			0
$466$	−0.751196	+	0.482765i	−0.0347985	+	0.0223636i
$467$	6.39935	−	14.0126i	0.296126	−	0.648427i	−0.701829	−	0.712346i	$-0.747633\pi$
$467$	6.39935	−	14.0126i	0.296126	−	0.648427i	0.997955	+	0.0639193i	$0.0203600\pi$
$468$		0			0
$469$	−2.52946	+	4.29796i	−0.116800	+	0.198461i
$470$	−0.357966			−0.0165117
$471$		0			0
$472$	0.226454	−	0.145533i	0.0104234	−	0.00669872i
$473$	−23.1899	−	26.7625i	−1.06627	−	1.23054i
$474$		0			0
$475$	−0.463679	−	3.22496i	−0.0212750	−	0.147971i
$476$	−2.89829	+	6.34638i	−0.132843	+	0.290886i
$477$		0			0
$478$	−0.431133	+	0.944050i	−0.0197196	+	0.0431799i
$479$	−4.08518	−	2.62539i	−0.186657	−	0.119957i	0.443975	−	0.896039i	$-0.353568\pi$
$479$	−4.08518	−	2.62539i	−0.186657	−	0.119957i	−0.630632	+	0.776082i	$0.717204\pi$
$480$		0			0
$481$	−16.6082	−	4.87659i	−0.757266	−	0.222354i
$482$	1.38549	+	0.406816i	0.0631073	+	0.0185300i
$483$		0			0
$484$	−15.0939	−	33.0511i	−0.686087	−	1.50232i
$485$	2.40998	−	16.7618i	0.109432	−	0.761114i
$486$		0			0
$487$	−20.0466	−	23.1350i	−0.908397	−	1.04835i	−0.998625	−	0.0524251i	$-0.983305\pi$
$487$	−20.0466	−	23.1350i	−0.908397	−	1.04835i	0.0902277	−	0.995921i	$-0.471241\pi$
$488$	−1.53748	−	3.36661i	−0.0695984	−	0.152399i
$489$		0			0
$490$	−0.152260	−	1.05899i	−0.00687838	−	0.0478402i
$491$	34.8002	+	22.3647i	1.57051	+	1.00931i	0.979209	+	0.202855i	$0.0650219\pi$
$491$	34.8002	+	22.3647i	1.57051	+	1.00931i	0.591301	+	0.806451i	$0.298615\pi$
$492$		0			0
$493$	−16.9728	+	19.5876i	−0.764416	+	0.882183i
$494$	−0.955616	−	0.280594i	−0.0429952	−	0.0126245i
$495$		0			0
$496$	2.30148	+	16.0072i	0.103340	+	0.718742i
$497$	−7.55605	+	2.21866i	−0.338935	+	0.0995204i
$498$		0			0
$499$	19.2162			0.860234			0.430117	−	0.902773i	$-0.358472\pi$
$499$	19.2162			0.860234			0.430117	+	0.902773i	$0.358472\pi$
$500$	−23.2661	+	6.83155i	−1.04049	+	0.305516i
$501$		0			0
$502$	−0.507774	−	1.11187i	−0.0226631	−	0.0496252i
$503$	−13.2513	−	29.0164i	−0.590848	−	1.29378i	−0.934928	−	0.354836i	$-0.884537\pi$
$503$	−13.2513	−	29.0164i	−0.590848	−	1.29378i	0.344080	−	0.938940i	$-0.388191\pi$
$504$		0			0
$505$	−9.09566	+	2.67073i	−0.404751	+	0.118846i
$506$	1.67676			0.0745410
$507$		0			0
$508$	24.4889	−	7.19060i	1.08652	−	0.319031i
$509$	−5.05555	−	35.1621i	−0.224083	−	1.55853i	−0.722361	−	0.691516i	$-0.756943\pi$
$509$	−5.05555	−	35.1621i	−0.224083	−	1.55853i	0.498277	−	0.867018i	$-0.333966\pi$
$510$		0			0
$511$	6.28170	+	1.84447i	0.277886	+	0.0815947i
$512$	4.54690	−	5.24740i	0.200946	−	0.231904i
$513$		0			0
$514$	0.190894	+	0.122680i	0.00841996	+	0.00541118i
$515$	2.60765	+	18.1366i	0.114907	+	0.799195i
$516$		0			0
$517$	4.98195	+	10.9089i	0.219106	+	0.479775i
$518$	−0.106534	−	0.122947i	−0.00468085	−	0.00540198i
$519$		0			0
$520$	−0.524037	+	3.64475i	−0.0229805	+	0.159833i
$521$	−0.968264	−	2.12020i	−0.0424204	−	0.0928878i	0.887235	−	0.461317i	$-0.152623\pi$
$521$	−0.968264	−	2.12020i	−0.0424204	−	0.0928878i	−0.929656	+	0.368429i	$0.879896\pi$
$522$		0			0
$523$	15.9480	+	4.68275i	0.697357	+	0.204762i	0.611150	−	0.791515i	$-0.290707\pi$
$523$	15.9480	+	4.68275i	0.697357	+	0.204762i	0.0862069	+	0.996277i	$0.472525\pi$
$524$	31.6663	+	9.29807i	1.38335	+	0.406188i
$525$		0			0
$526$	−1.10089	−	0.707498i	−0.0480010	−	0.0308484i
$527$	9.76743	−	21.3877i	0.425476	−	0.931662i
$528$		0			0
$529$	−4.41446	+	9.66631i	−0.191933	+	0.420274i
$530$	−0.182273	−	1.26774i	−0.00791745	−	0.0550670i
$531$		0			0
$532$	1.57140	+	1.81350i	0.0681290	+	0.0786250i
$533$	−13.2542	+	8.51796i	−0.574103	+	0.368954i
$534$		0			0
$535$	15.6213			0.675367
$536$	−2.83313	+	0.521568i	−0.122373	+	0.0225283i
$537$		0			0
$538$	0.0507363	−	0.111097i	0.00218740	−	0.00478973i
$539$	−30.1534	+	19.3784i	−1.29880	+	0.834688i
$540$		0			0
$541$	0.587839	−	4.08851i	0.0252732	−	0.175779i	−0.973275	−	0.229642i	$-0.926244\pi$
$541$	0.587839	−	4.08851i	0.0252732	−	0.175779i	0.998548	+	0.0538633i	$0.0171535\pi$
$542$	−0.271219	−	1.88637i	−0.0116498	−	0.0810264i
$543$		0			0
$544$	−5.80411	+	1.70424i	−0.248849	+	0.0730688i
$545$	4.23635	−	9.27632i	0.181465	−	0.397354i
$546$		0			0
$547$	5.22380	−	36.3323i	0.223354	−	1.55346i	−0.501869	−	0.864944i	$-0.667354\pi$
$547$	5.22380	−	36.3323i	0.223354	−	1.55346i	0.725222	−	0.688515i	$-0.241737\pi$
$548$	32.0674	+	9.41583i	1.36985	+	0.402224i
$549$		0			0
$550$	−0.514457	−	0.593715i	−0.0219365	−	0.0253161i
$551$	3.70310	+	8.10865i	0.157757	+	0.345440i
$552$		0			0
$553$	−4.73413	+	5.46347i	−0.201316	+	0.232330i
$554$	−0.159617	−	0.184208i	−0.00678149	−	0.00782625i
$555$		0			0
$556$	20.0396	−	12.8787i	0.849870	−	0.546178i
$557$	−2.08976	−	14.5346i	−0.0885460	−	0.615851i	−0.984979	−	0.172672i	$-0.944760\pi$
$557$	−2.08976	−	14.5346i	−0.0885460	−	0.615851i	0.896433	−	0.443178i	$-0.146149\pi$
$558$		0			0
$559$	31.4846	−	20.2339i	1.33166	−	0.855803i
$560$	2.88787	−	3.33278i	0.122035	−	0.140835i
$561$		0			0
$562$	1.09766	−	1.26676i	0.0463018	−	0.0534351i
$563$	1.57990	+	10.9884i	0.0665847	+	0.463107i	0.995649	+	0.0931876i	$0.0297056\pi$
$563$	1.57990	+	10.9884i	0.0665847	+	0.463107i	−0.929064	+	0.369919i	$0.879385\pi$
$564$		0			0
$565$	19.0405			0.801039
$566$	−1.68838			−0.0709680
$567$		0			0
$568$	−3.82685	−	2.45937i	−0.160571	−	0.103193i
$569$	−5.08937	−	11.1442i	−0.213357	−	0.467187i	0.772448	−	0.635078i	$-0.219032\pi$
$569$	−5.08937	−	11.1442i	−0.213357	−	0.467187i	−0.985806	+	0.167890i	$0.946305\pi$
$570$		0			0
$571$	−1.45466	−	0.934851i	−0.0608754	−	0.0391223i	0.509849	−	0.860264i	$-0.329701\pi$
$571$	−1.45466	−	0.934851i	−0.0608754	−	0.0391223i	−0.570725	+	0.821142i	$0.693338\pi$
$572$	59.0680	−	17.3439i	2.46976	−	0.725186i
$573$		0			0
$574$	−0.148077			−0.00618061
$575$	−5.56236	+	1.63326i	−0.231967	+	0.0681115i
$576$		0			0
$577$	−11.1528	+	12.8710i	−0.464297	+	0.535827i	−0.938817	−	0.344418i	$-0.888076\pi$
$577$	−11.1528	+	12.8710i	−0.464297	+	0.535827i	0.474520	+	0.880245i	$0.342622\pi$
$578$	1.35668	+	0.398357i	0.0564304	+	0.0165695i
$579$		0			0
$580$	13.8358	−	8.89171i	0.574499	−	0.369208i
$581$	−1.68395	−	1.08221i	−0.0698619	−	0.0448975i
$582$		0			0
$583$	−36.0973	+	23.1983i	−1.49500	+	0.960777i
$584$	1.57101	+	3.44003i	0.0650088	+	0.142349i
$585$		0			0
$586$	0.749896	−	0.865426i	0.0309779	−	0.0357504i
$587$	6.82036	−	47.4367i	0.281507	−	1.95792i	−0.00547471	−	0.999985i	$-0.501743\pi$
$587$	6.82036	−	47.4367i	0.281507	−	1.95792i	0.286981	−	0.957936i	$-0.407348\pi$
$588$		0			0
$589$	−5.29573	−	6.11160i	−0.218207	−	0.251824i
$590$	0.118448	+	0.0347795i	0.00487643	+	0.00143185i
$591$		0			0
$592$	−1.70415	+	11.8526i	−0.0700401	+	0.487139i
$593$	9.45013	+	6.07323i	0.388070	+	0.249398i	0.720099	−	0.693872i	$-0.244097\pi$
$593$	9.45013	+	6.07323i	0.388070	+	0.249398i	−0.332028	+	0.943269i	$0.607733\pi$
$594$		0			0
$595$	−6.15192	+	1.80637i	−0.252204	+	0.0740538i
$596$	6.08520	−	13.3247i	0.249260	−	0.545803i
$597$		0			0
$598$	−0.252198	+	1.75408i	−0.0103132	+	0.0717296i
$599$	10.9098	+	12.5906i	0.445762	+	0.514436i	0.933512	−	0.358547i	$-0.116728\pi$
$599$	10.9098	+	12.5906i	0.445762	+	0.514436i	−0.487750	+	0.872983i	$0.662182\pi$
$600$		0			0
$601$	2.76753	−	6.06004i	0.112890	−	0.247194i	−0.844751	−	0.535160i	$-0.820251\pi$
$601$	2.76753	−	6.06004i	0.112890	−	0.247194i	0.957641	+	0.287965i	$0.0929788\pi$
$602$	0.351748			0.0143362
$603$		0			0
$604$	−9.20939			−0.374725
$605$	13.8711	−	30.3735i	0.563941	−	1.23486i
$606$		0			0
$607$	1.23245	+	1.42233i	0.0500238	+	0.0577305i	0.780210	−	0.625518i	$-0.215112\pi$
$607$	1.23245	+	1.42233i	0.0500238	+	0.0577305i	−0.730186	+	0.683248i	$0.760567\pi$
$608$	−0.296089	+	2.05935i	−0.0120080	+	0.0835176i
$609$		0			0
$610$	0.705086	−	1.54392i	0.0285481	−	0.0625116i
$611$	−12.1613	+	3.57088i	−0.491994	+	0.144462i
$612$		0			0
$613$	−12.6595	−	8.13578i	−0.511313	−	0.328601i	0.259414	−	0.965766i	$-0.416471\pi$
$613$	−12.6595	−	8.13578i	−0.511313	−	0.328601i	−0.770727	+	0.637165i	$0.780107\pi$
$614$	0.0851656	−	0.592340i	0.00343701	−	0.0239049i
$615$		0			0
$616$	1.11247	+	0.326652i	0.0448228	+	0.0131612i
$617$	−17.5223	−	20.2218i	−0.705422	−	0.814100i	0.284053	−	0.958809i	$-0.408321\pi$
$617$	−17.5223	−	20.2218i	−0.705422	−	0.814100i	−0.989474	+	0.144709i	$0.953775\pi$
$618$		0			0
$619$	−1.17040	+	8.14034i	−0.0470425	+	0.327188i	0.952687	+	0.303952i	$0.0983061\pi$
$619$	−1.17040	+	8.14034i	−0.0470425	+	0.327188i	−0.999730	+	0.0232363i	$0.992603\pi$
$620$	−9.77055	+	11.2758i	−0.392395	+	0.452848i
$621$		0			0
$622$	−0.0995242	−	0.217928i	−0.00399056	−	0.00873810i
$623$	2.69449	−	1.73164i	0.107952	−	0.0693768i
$624$		0			0
$625$	−11.8142	−	7.59254i	−0.472569	−	0.303701i
$626$	−0.932512	+	0.599289i	−0.0372707	+	0.0239524i
$627$		0			0
$628$	4.35442	+	1.27857i	0.173760	+	0.0510206i
$629$	11.4011	−	13.1576i	0.454592	−	0.524627i
$630$		0			0
$631$	6.08050	−	1.78540i	0.242061	−	0.0710755i	−0.158452	−	0.987367i	$-0.550650\pi$
$631$	6.08050	−	1.78540i	0.242061	−	0.0710755i	0.400513	+	0.916291i	$0.368832\pi$
$632$	−4.17592			−0.166109
$633$		0			0
$634$	1.80371	−	0.529618i	0.0716347	−	0.0210338i
$635$	19.7317	+	12.6808i	0.783028	+	0.503222i
$636$		0			0
$637$	−15.7367	−	34.4585i	−0.623510	−	1.36530i
$638$	1.80818	+	1.16205i	0.0715867	+	0.0460060i
$639$		0			0
$640$	5.11470			0.202176
$641$	−31.3903			−1.23984			−0.619920	−	0.784665i	$-0.712835\pi$
$641$	−31.3903			−1.23984			−0.619920	+	0.784665i	$0.712835\pi$
$642$		0			0
$643$	−1.53429	−	10.6712i	−0.0605064	−	0.420832i	−0.997451	−	0.0713537i	$-0.977268\pi$
$643$	−1.53429	−	10.6712i	−0.0605064	−	0.420832i	0.936945	−	0.349478i	$-0.113641\pi$
$644$	2.79601	−	3.22676i	0.110178	−	0.127152i
$645$		0			0
$646$	0.656008	−	0.757074i	0.0258103	−	0.0297867i
$647$	17.5914	−	11.3053i	0.691590	−	0.444458i	−0.147060	−	0.989128i	$-0.546981\pi$
$647$	17.5914	−	11.3053i	0.691590	−	0.444458i	0.838651	+	0.544669i	$0.183345\pi$
$648$		0			0
$649$	−0.588589	−	4.09373i	−0.0231041	−	0.160693i
$650$	0.698471	−	0.448880i	0.0273963	−	0.0176065i
$651$		0			0
$652$	−15.5477	−	17.9430i	−0.608893	−	0.702701i
$653$	7.64947	−	8.82796i	0.299347	−	0.345465i	−0.586072	−	0.810259i	$-0.699326\pi$
$653$	7.64947	−	8.82796i	0.299347	−	0.345465i	0.885419	+	0.464794i	$0.153872\pi$
$654$		0			0
$655$	12.5993	+	27.5887i	0.492296	+	1.07798i
$656$	7.13762	+	8.23725i	0.278677	+	0.321611i
$657$		0			0
$658$	−0.114299	−	0.0335611i	−0.00445582	−	0.00130835i
$659$	−1.85448	+	12.8982i	−0.0722403	+	0.502442i	0.921290	+	0.388876i	$0.127137\pi$
$659$	−1.85448	+	12.8982i	−0.0722403	+	0.502442i	−0.993530	+	0.113566i	$0.963773\pi$
$660$		0			0
$661$	−2.67480	+	5.85700i	−0.104038	+	0.227811i	−0.954491	−	0.298240i	$-0.903601\pi$
$661$	−2.67480	+	5.85700i	−0.104038	+	0.227811i	0.850453	+	0.526051i	$0.176328\pi$
$662$	−0.00137991		0.000405177i	−5.36316e−5		1.57477e-5i
$663$		0			0
$664$	−0.164556	−	1.14451i	−0.00638599	−	0.0444156i
$665$	−0.313832	+	2.18275i	−0.0121699	+	0.0846435i
$666$		0			0
$667$	13.3432	−	8.57516i	0.516651	−	0.332031i
$668$	−15.4173	+	33.7592i	−0.596513	+	1.30618i
$669$		0			0
$670$	−1.03161	−	0.825287i	−0.0398545	−	0.0318836i
$671$	−56.8637			−2.19520
$672$		0			0
$673$	24.8760	−	15.9868i	0.958898	−	0.616247i	0.0352054	−	0.999380i	$-0.488791\pi$
$673$	24.8760	−	15.9868i	0.958898	−	0.616247i	0.923693	+	0.383134i	$0.125155\pi$
$674$	0.197151	+	0.227524i	0.00759397	+	0.00876390i
$675$		0			0
$676$	5.57358	+	38.7651i	0.214369	+	1.49097i
$677$	0.770116	−	1.68632i	0.0295980	−	0.0648105i	−0.894256	−	0.447557i	$-0.852294\pi$
$677$	0.770116	−	1.68632i	0.0295980	−	0.0648105i	0.923854	+	0.382746i	$0.125022\pi$
$678$		0			0
$679$	2.34101	−	5.12610i	0.0898398	−	0.196722i
$680$	−3.11571	−	2.00234i	−0.119482	−	0.0767864i
$681$		0			0
$682$	−1.87090	−	0.549347i	−0.0716406	−	0.0210356i
$683$	20.1696	+	5.92233i	0.771768	+	0.226612i	0.643828	−	0.765170i	$-0.277345\pi$
$683$	20.1696	+	5.92233i	0.771768	+	0.226612i	0.127940	+	0.991782i	$0.459163\pi$
$684$		0			0
$685$	12.7589	+	27.9381i	0.487492	+	1.06746i
$686$	0.104175	−	0.724556i	0.00397743	−	0.0276637i
$687$		0			0
$688$	−16.9550	−	19.5671i	−0.646403	−	0.745989i
$689$	−18.8387	−	41.2511i	−0.717699	−	1.57154i
$690$		0			0
$691$	0.260219	+	1.80986i	0.00989918	+	0.0688503i	0.994172	−	0.107804i	$-0.0343818\pi$
$691$	0.260219	+	1.80986i	0.00989918	+	0.0688503i	−0.984273	+	0.176654i	$0.943473\pi$
$692$	−15.4139	−	9.90592i	−0.585949	−	0.376567i
$693$		0			0
$694$	1.87344	−	2.16207i	0.0711149	−	0.0820710i
$695$	21.0046	+	6.16750i	0.796749	+	0.233947i
$696$		0			0
$697$	−2.25525	−	15.6856i	−0.0854238	−	0.594136i
$698$	1.68777	−	0.495575i	0.0638832	−	0.0187578i
$699$		0			0
$700$	−2.00041			−0.0756083
$701$	37.4058	−	10.9833i	1.41280	−	0.414835i	0.515739	−	0.856746i	$-0.327517\pi$
$701$	37.4058	−	10.9833i	1.41280	−	0.414835i	0.897059	+	0.441911i	$0.145699\pi$
$702$		0			0
$703$	−2.48748	−	5.44681i	−0.0938169	−	0.205430i
$704$	−17.5524	−	38.4343i	−0.661529	−	1.44855i
$705$		0			0
$706$	2.20069	−	0.646180i	0.0828240	−	0.0243193i
$707$	−3.15464			−0.118643
$708$		0			0
$709$	−11.9961	+	3.52237i	−0.450523	+	0.132286i	−0.499120	−	0.866533i	$-0.666343\pi$
$709$	−11.9961	+	3.52237i	−0.450523	+	0.132286i	0.0485967	+	0.998818i	$0.484525\pi$
$710$	−0.296891	−	2.06492i	−0.0111421	−	0.0774951i
$711$		0			0
$712$	1.77522	+	0.521252i	0.0665292	+	0.0195347i
$713$	−9.42272	+	10.8744i	−0.352884	+	0.407249i
$714$		0			0
$715$	47.5934	+	30.5864i	1.77989	+	1.14387i
$716$	4.96897	+	34.5600i	0.185699	+	1.29157i
$717$		0			0
$718$	0.0927339	+	0.203059i	0.00346080	+	0.00757809i
$719$	−2.50283	−	2.88841i	−0.0933396	−	0.107720i	0.707158	−	0.707055i	$-0.249977\pi$
$719$	−2.50283	−	2.88841i	−0.0933396	−	0.107720i	−0.800498	+	0.599336i	$0.795431\pi$
$720$		0			0
$721$	−0.867776	+	6.03551i	−0.0323177	+	0.224774i
$722$	0.552678	+	1.21020i	0.0205685	+	0.0450388i
$723$		0			0
$724$	37.0963	+	10.8925i	1.37867	+	0.404815i
$725$	−7.13024	−	2.09363i	−0.264811	−	0.0777554i
$726$		0			0
$727$	−40.4373	−	25.9874i	−1.49973	−	0.963821i	−0.994928	−	0.100589i	$-0.967927\pi$
$727$	−40.4373	−	25.9874i	−1.49973	−	0.963821i	−0.504807	−	0.863232i	$-0.668436\pi$
$728$	−0.509039	+	1.11464i	−0.0188663	+	0.0413113i
$729$		0			0
$730$	−0.720462	+	1.57759i	−0.0266655	+	0.0583893i
$731$	5.35722	+	37.2603i	0.198144	+	1.37812i
$732$		0			0
$733$	4.59960	+	5.30822i	0.169890	+	0.196064i	0.834310	−	0.551296i	$-0.185867\pi$
$733$	4.59960	+	5.30822i	0.169890	+	0.196064i	−0.664420	+	0.747360i	$0.731321\pi$
$734$	−1.69106	+	1.08678i	−0.0624183	+	0.0401138i
$735$		0			0
$736$	3.70189			0.136453
$737$	−10.7932	+	42.9239i	−0.397571	+	1.58112i
$738$		0			0
$739$	9.72934	−	21.3043i	0.357899	−	0.783691i	−0.641957	−	0.766741i	$-0.721877\pi$
$739$	9.72934	−	21.3043i	0.357899	−	0.783691i	0.999856	−	0.0169498i	$-0.00539555\pi$
$740$	−9.29388	+	5.97281i	−0.341650	+	0.219565i
$741$		0			0
$742$	0.0606570	−	0.421879i	0.00222679	−	0.0154877i
$743$	5.34442	+	37.1713i	0.196068	+	1.36368i	0.815557	+	0.578677i	$0.196431\pi$
$743$	5.34442	+	37.1713i	0.196068	+	1.36368i	−0.619489	+	0.785005i	$0.712660\pi$
$744$		0			0
$745$	12.9165	−	3.79262i	0.473223	−	0.138951i
$746$	−0.730187	+	1.59889i	−0.0267341	+	0.0585394i
$747$		0			0
$748$	−8.81210	+	61.2895i	−0.322202	+	2.24097i
$749$	4.98788	+	1.46457i	0.182253	+	0.0535144i
$750$		0			0
$751$	−13.8434	−	15.9762i	−0.505153	−	0.582978i	0.444698	−	0.895681i	$-0.353311\pi$
$751$	−13.8434	−	15.9762i	−0.505153	−	0.582978i	−0.949851	+	0.312703i	$0.898766\pi$
$752$	3.64249	+	7.97594i	0.132828	+	0.290853i
$753$		0			0
$754$	−1.48760	+	1.71678i	−0.0541752	+	0.0625215i
$755$	−5.54228	−	6.39614i	−0.201704	−	0.232779i
$756$		0			0
$757$	−36.7982	+	23.6488i	−1.33745	+	0.859529i	−0.996743	−	0.0806401i	$-0.974304\pi$
$757$	−36.7982	+	23.6488i	−1.33745	+	0.859529i	−0.340709	+	0.940169i	$0.610667\pi$
$758$	0.0417258	+	0.290210i	0.00151555	+	0.0105409i
$759$		0			0
$760$	−1.07161	+	0.688680i	−0.0388713	+	0.0249810i
$761$	−25.9898	+	29.9938i	−0.942129	+	1.08727i	0.0539270	+	0.998545i	$0.482826\pi$
$761$	−25.9898	+	29.9938i	−0.942129	+	1.08727i	−0.996056	+	0.0887296i	$0.971719\pi$
$762$		0			0
$763$	2.22237	−	2.56475i	0.0804552	−	0.0928503i
$764$	−4.19182	−	29.1547i	−0.151655	−	1.05478i
$765$		0			0
$766$	−3.07774			−0.111203
$767$	4.37103			0.157829
$768$		0			0
$769$	4.07970	+	2.62187i	0.147118	+	0.0945469i	0.612129	−	0.790758i	$-0.290313\pi$
$769$	4.07970	+	2.62187i	0.147118	+	0.0945469i	−0.465011	+	0.885305i	$0.653950\pi$
$770$	0.220883	+	0.483667i	0.00796007	+	0.0174301i
$771$		0			0
$772$	−14.3535	−	9.22443i	−0.516594	−	0.331995i
$773$	−18.6381	+	5.47263i	−0.670365	+	0.196837i	−0.599166	−	0.800625i	$-0.704501\pi$
$773$	−18.6381	+	5.47263i	−0.670365	+	0.196837i	−0.0711995	+	0.997462i	$0.522683\pi$
$774$		0			0
$775$	6.74150			0.242162
$776$	3.12338	−	0.917106i	0.112123	−	0.0329222i
$777$		0			0
$778$	−1.20192	+	1.38709i	−0.0430909	+	0.0497296i
$779$	−5.22957	−	1.53554i	−0.187369	−	0.0550164i
$780$		0			0
$781$	−58.7962	+	37.7860i	−2.10389	+	1.35209i
$782$	−1.49947	−	0.963651i	−0.0536209	−	0.0344601i
$783$		0			0
$784$	−22.0463	+	14.1683i	−0.787368	+	0.506011i
$785$	1.73253	+	3.79370i	0.0618365	+	0.135403i
$786$		0			0
$787$	5.58375	−	6.44399i	0.199039	−	0.229703i	−0.647452	−	0.762106i	$-0.724165\pi$
$787$	5.58375	−	6.44399i	0.199039	−	0.229703i	0.846491	+	0.532403i	$0.178711\pi$
$788$	0.383828	−	2.66958i	0.0136733	−	0.0950999i
$789$		0			0
$790$	−1.25410	−	1.44731i	−0.0446190	−	0.0514931i
$791$	6.07963	+	1.78514i	0.216167	+	0.0634723i
$792$		0			0
$793$	8.55277	−	59.4858i	0.303718	−	2.11240i
$794$	0.839546	+	0.539543i	0.0297944	+	0.0191477i
$795$		0			0
$796$	2.93170	−	0.860825i	0.103911	−	0.0305111i
$797$	−8.92659	+	19.5465i	−0.316196	+	0.692373i	−0.999279	−	0.0379681i	$-0.987911\pi$
$797$	−8.92659	+	19.5465i	−0.316196	+	0.692373i	0.683083	+	0.730341i	$0.260639\pi$
$798$		0			0
$799$	1.81429	−	12.6187i	0.0641850	−	0.446417i
$800$	−1.13580	−	1.31078i	−0.0401565	−	0.0463431i
$801$		0			0
$802$	−1.04874	+	2.29641i	−0.0370322	+	0.0810891i
$803$	58.1038			2.05044
$804$		0			0
$805$	3.92372			0.138293
$806$	0.856078	−	1.87455i	0.0301541	−	0.0660282i
$807$		0			0
$808$	−1.19333	−	1.37717i	−0.0419812	−	0.0484488i
$809$	2.98856	−	20.7859i	0.105072	−	0.730793i	−0.867373	−	0.497659i	$-0.834193\pi$
$809$	2.98856	−	20.7859i	0.105072	−	0.730793i	0.972445	−	0.233133i	$-0.0748979\pi$
$810$		0			0
$811$	−13.0404	+	28.5545i	−0.457910	+	1.00268i	0.530049	+	0.847967i	$0.322174\pi$
$811$	−13.0404	+	28.5545i	−0.457910	+	1.00268i	−0.987959	+	0.154716i	$0.950554\pi$
$812$	5.25141	−	1.54195i	0.184288	−	0.0541119i
$813$		0			0
$814$	−1.21461	−	0.780581i	−0.0425720	−	0.0273594i
$815$	3.10510	−	21.5964i	0.108767	−	0.756490i
$816$		0			0
$817$	12.4225	+	3.64758i	0.434609	+	0.127613i
$818$	−1.88758	−	2.17838i	−0.0659976	−	0.0761653i
$819$		0			0
$820$	−1.43109	+	9.95346i	−0.0499759	+	0.347590i
$821$	−10.6982	+	12.3464i	−0.373370	+	0.430892i	−0.911075	−	0.412241i	$-0.864746\pi$
$821$	−10.6982	+	12.3464i	−0.373370	+	0.430892i	0.537704	+	0.843133i	$0.319292\pi$
$822$		0			0
$823$	14.5611	+	31.8845i	0.507570	+	1.11142i	0.973934	+	0.226830i	$0.0728362\pi$
$823$	14.5611	+	31.8845i	0.507570	+	1.11142i	−0.466365	+	0.884593i	$0.654437\pi$
$824$	−2.96309	+	1.90426i	−0.103224	+	0.0663382i
$825$		0			0
$826$	0.0345598	+	0.0222102i	0.00120249	+	0.000772793i
$827$	45.1650	−	29.0258i	1.57054	−	1.00933i	0.591345	−	0.806419i	$-0.298597\pi$
$827$	45.1650	−	29.0258i	1.57054	−	1.00933i	0.979198	−	0.202908i	$-0.0650391\pi$
$828$		0			0
$829$	−15.7651	−	4.62906i	−0.547546	−	0.160774i	−0.00375207	−	0.999993i	$-0.501194\pi$
$829$	−15.7651	−	4.62906i	−0.547546	−	0.160774i	−0.543793	+	0.839219i	$0.683013\pi$
$830$	0.347251	−	0.400749i	0.0120533	−	0.0139102i
$831$		0			0
$832$	42.8466	−	12.5809i	1.48544	−	0.436164i
$833$	38.1022			1.32016
$834$		0			0
$835$	−32.7248	+	9.60886i	−1.13249	+	0.332528i
$836$	17.9157	+	11.5137i	0.619629	+	0.398211i
$837$		0			0
$838$	0.768807	+	1.68345i	0.0265580	+	0.0581539i
$839$	19.1274	+	12.2924i	0.660350	+	0.424381i	0.827435	−	0.561561i	$-0.189799\pi$
$839$	19.1274	+	12.2924i	0.660350	+	0.424381i	−0.167085	+	0.985943i	$0.553435\pi$
$840$		0			0
$841$	−8.66809			−0.298900
$842$	−0.758434			−0.0261374
$843$		0			0
$844$	−5.20223	−	36.1823i	−0.179068	−	1.24545i
$845$	−23.5691	+	27.2001i	−0.810800	+	0.935713i
$846$		0			0
$847$	7.27672	−	8.39778i	0.250031	−	0.288551i
$848$	−26.3921	+	16.9612i	−0.906309	+	0.582450i
$849$		0			0
$850$	0.118848	+	0.826603i	0.00407644	+	0.0283522i
$851$	−8.96301	+	5.76018i	−0.307248	+	0.197456i
$852$		0			0
$853$	−28.5348	−	32.9309i	−0.977012	−	1.12753i	−0.991820	−	0.127642i	$-0.959259\pi$
$853$	−28.5348	−	32.9309i	−0.977012	−	1.12753i	0.0148083	−	0.999890i	$-0.495286\pi$
$854$	0.369885	−	0.426870i	0.0126572	−	0.0146072i
$855$		0			0
$856$	1.24743	+	2.73150i	0.0426364	+	0.0933607i
$857$	−10.2674	−	11.8492i	−0.350727	−	0.404761i	0.552784	−	0.833324i	$-0.313565\pi$
$857$	−10.2674	−	11.8492i	−0.350727	−	0.404761i	−0.903512	+	0.428563i	$0.859020\pi$
$858$		0			0
$859$	53.1792	+	15.6148i	1.81445	+	0.532771i	0.998943	−	0.0459724i	$-0.0146386\pi$
$859$	53.1792	+	15.6148i	1.81445	+	0.532771i	0.815510	+	0.578744i	$0.196457\pi$
$860$	3.39947	−	23.6439i	0.115921	−	0.806249i
$861$		0			0
$862$	0.461506	−	1.01056i	0.0157190	−	0.0344197i
$863$	−6.85007	+	2.01136i	−0.233179	+	0.0684676i	−0.396235	−	0.918149i	$-0.629683\pi$
$863$	−6.85007	+	2.01136i	−0.233179	+	0.0684676i	0.163055	+	0.986617i	$0.447865\pi$
$864$		0			0
$865$	−2.39632	−	16.6668i	−0.0814774	−	0.566687i
$866$	−0.221251	+	1.53883i	−0.00751841	+	0.0522917i
$867$		0			0
$868$	−4.17691	+	2.68434i	−0.141774	+	0.0911123i
$869$	−26.6528	+	58.3614i	−0.904133	+	1.97977i
$870$		0			0
$871$	−43.2799	−	17.7470i	−1.46648	−	0.601333i
$872$	1.96033			0.0663851
$873$		0			0
$874$	−0.515723	+	0.331435i	−0.0174446	+	0.0112110i
$875$	−4.85621	−	5.60437i	−0.164170	−	0.189462i
$876$		0			0
$877$	7.02816	+	48.8819i	0.237324	+	1.65062i	0.665111	+	0.746745i	$0.268384\pi$
$877$	7.02816	+	48.8819i	0.237324	+	1.65062i	−0.427787	+	0.903880i	$0.640707\pi$
$878$	0.535744	−	1.17312i	0.0180805	−	0.0395907i
$879$		0			0
$880$	16.2585	−	35.6011i	0.548073	−	1.20011i
$881$	−30.4594	−	19.5751i	−1.02620	−	0.659501i	−0.0846666	−	0.996409i	$-0.526983\pi$
$881$	−30.4594	−	19.5751i	−1.02620	−	0.659501i	−0.941538	+	0.336908i	$0.890619\pi$
$882$		0			0
$883$	−8.13126	−	2.38755i	−0.273639	−	0.0803475i	0.142034	−	0.989862i	$-0.454636\pi$
$883$	−8.13126	−	2.38755i	−0.273639	−	0.0803475i	−0.415673	+	0.909514i	$0.636454\pi$
$884$	−62.7903	−	18.4369i	−2.11187	−	0.620100i
$885$		0			0
$886$	−0.900913	−	1.97272i	−0.0302668	−	0.0662749i
$887$	−2.31772	+	16.1201i	−0.0778214	+	0.541260i	0.913195	+	0.407522i	$0.133607\pi$
$887$	−2.31772	+	16.1201i	−0.0778214	+	0.541260i	−0.991017	+	0.133738i	$0.957302\pi$
$888$		0			0
$889$	5.11145	+	5.89893i	0.171432	+	0.197844i
$890$	0.352473	+	0.771808i	0.0118149	+	0.0258710i
$891$		0			0
$892$	8.04710	+	55.9688i	0.269437	+	1.87397i
$893$	−3.68861	−	2.37052i	−0.123435	−	0.0793266i
$894$		0			0
$895$	−21.0123	+	24.2495i	−0.702365	+	0.810572i
$896$	1.63313	+	0.479529i	0.0545589	+	0.0160199i
$897$		0			0
$898$	−0.103875	−	0.722468i	−0.00346636	−	0.0241091i
$899$	−17.6976	+	5.19648i	−0.590247	+	0.173312i
$900$		0			0
$901$	45.6130			1.51959
$902$	−1.26095	+	0.370249i	−0.0419851	+	0.0123279i
$903$		0			0
$904$	1.52047	+	3.32937i	0.0505702	+	0.110733i
$905$	14.7598	+	32.3194i	0.490631	+	1.07433i
$906$		0			0
$907$	22.8509	−	6.70964i	0.758753	−	0.222790i	0.120602	−	0.992701i	$-0.461518\pi$
$907$	22.8509	−	6.70964i	0.758753	−	0.222790i	0.638151	+	0.769911i	$0.279699\pi$
$908$	38.9733			1.29337
$909$		0			0
$910$	−0.539192	+	0.158321i	−0.0178741	+	0.00524830i
$911$	−3.93263	−	27.3520i	−0.130294	−	0.906214i	−0.945170	−	0.326579i	$-0.894104\pi$
$911$	−3.93263	−	27.3520i	−0.130294	−	0.906214i	0.814876	−	0.579635i	$-0.196805\pi$
$912$		0			0
$913$	−17.0456	−	5.00504i	−0.564127	−	0.165643i
$914$	−1.03398	+	1.19328i	−0.0342010	+	0.0394701i
$915$		0			0
$916$	−30.8140	−	19.8029i	−1.01812	−	0.654307i
$917$	1.43639	+	9.99032i	0.0474338	+	0.329910i
$918$		0			0
$919$	9.95976	+	21.8088i	0.328542	+	0.719407i	0.999761	−	0.0218519i	$-0.00695622\pi$
$919$	9.95976	+	21.8088i	0.328542	+	0.719407i	−0.671219	+	0.741259i	$0.734229\pi$
$920$	1.48425	+	1.71292i	0.0489344	+	0.0564733i
$921$		0			0
$922$	0.391338	−	2.72182i	0.0128880	−	0.0896382i
$923$	−30.6850	−	67.1908i	−1.01001	−	2.21161i
$924$		0			0
$925$	4.78959	+	1.40635i	0.157481	+	0.0462405i
$926$	0.906631	+	0.266211i	0.0297937	+	0.00874823i
$927$		0			0
$928$	3.99204	+	2.56553i	0.131045	+	0.0842176i
$929$	5.99449	−	13.1261i	0.196673	−	0.430653i	−0.785442	−	0.618935i	$-0.787564\pi$
$929$	5.99449	−	13.1261i	0.196673	−	0.430653i	0.982115	+	0.188282i	$0.0602917\pi$
$930$		0			0
$931$	5.44391	−	11.9205i	0.178417	−	0.390678i
$932$	2.87187	+	19.9743i	0.0940711	+	0.654279i
$933$		0			0
$934$	0.889312	+	1.02632i	0.0290992	+	0.0335822i
$935$	−47.8702	+	30.7643i	−1.56552	+	1.00610i
$936$		0			0
$937$	46.5263			1.51995			0.759974	−	0.649954i	$-0.225212\pi$
$937$	46.5263			1.51995			0.759974	+	0.649954i	$0.225212\pi$
$938$	−0.252018	−	0.360233i	−0.00822869	−	0.0117620i
$939$		0			0
$940$	−3.36056	+	7.35859i	−0.109609	+	0.240011i
$941$	−18.2882	+	11.7531i	−0.596178	+	0.383140i	−0.803651	−	0.595100i	$-0.797112\pi$
$941$	−18.2882	+	11.7531i	−0.596178	+	0.383140i	0.207474	+	0.978241i	$0.433476\pi$
$942$		0			0
$943$	−1.38014	+	9.59912i	−0.0449437	+	0.312590i
$944$	−0.430340	−	2.99308i	−0.0140064	−	0.0974164i
$945$		0			0
$946$	2.99532	−	0.879504i	0.0973861	−	0.0285951i
$947$	−11.0735	+	24.2476i	−0.359840	+	0.787941i	0.639969	+	0.768401i	$0.278947\pi$
$947$	−11.0735	+	24.2476i	−0.359840	+	0.787941i	−0.999809	+	0.0195397i	$0.993780\pi$
$948$		0			0
$949$	−8.73929	+	60.7831i	−0.283689	+	1.97310i
$950$	0.275588	+	0.0809200i	0.00894126	+	0.00262539i
$951$		0			0
$952$	−0.807118	−	0.931463i	−0.0261588	−	0.0301889i
$953$	19.2026	+	42.0478i	0.622032	+	1.36206i	0.914032	+	0.405643i	$0.132952\pi$
$953$	19.2026	+	42.0478i	0.622032	+	1.36206i	−0.291999	+	0.956419i	$0.594320\pi$
$954$		0			0
$955$	17.7260	−	20.4569i	0.573599	−	0.661969i
$956$	15.3591	+	17.7254i	0.496749	+	0.573279i
$957$		0			0
$958$	0.360133	−	0.231443i	0.0116354	−	0.00747760i
$959$	1.45458	+	10.1168i	0.0469709	+	0.326690i
$960$		0			0
$961$	−12.0024	+	7.71348i	−0.387175	+	0.248822i
$962$	0.999263	−	1.15321i	0.0322175	−	0.0371810i
$963$		0			0
$964$	21.3697	−	24.6619i	0.688271	−	0.794307i
$965$	−2.23146	−	15.5202i	−0.0718334	−	0.499612i
$966$		0			0
$967$	−15.5543			−0.500191			−0.250096	−	0.968221i	$-0.580462\pi$
$967$	−15.5543			−0.500191			−0.250096	+	0.968221i	$0.580462\pi$
$968$	6.41871			0.206305
$969$		0			0
$970$	1.25586	+	0.807094i	0.0403233	+	0.0259142i
$971$	−10.9719	−	24.0251i	−0.352104	−	0.771001i	−0.999957	−	0.00923549i	$-0.997060\pi$
$971$	−10.9719	−	24.0251i	−0.352104	−	0.771001i	0.647853	−	0.761765i	$-0.275667\pi$
$972$		0			0
$973$	6.12854	+	3.93857i	0.196472	+	0.126265i
$974$	2.58931	−	0.760291i	0.0829669	−	0.0243613i
$975$		0			0
$976$	−41.5752			−1.33079
$977$	−23.9357	+	7.02816i	−0.765771	+	0.224851i	−0.641215	−	0.767362i	$-0.721569\pi$
$977$	−23.9357	+	7.02816i	−0.765771	+	0.224851i	−0.124557	+	0.992212i	$0.539751\pi$
$978$		0			0
$979$	18.6152	−	21.4831i	0.594944	−	0.686602i
$980$	−23.1987	−	6.81175i	−0.741055	−	0.217593i
$981$		0			0
$982$	−3.06784	+	1.97158i	−0.0978988	+	0.0629157i
$983$	15.8752	+	10.2024i	0.506340	+	0.325405i	0.768748	−	0.639552i	$-0.220880\pi$
$983$	15.8752	+	10.2024i	0.506340	+	0.325405i	−0.262407	+	0.964957i	$0.584516\pi$
$984$		0			0
$985$	2.08508	−	1.34000i	0.0664360	−	0.0426959i
$986$	−0.949157	−	2.07836i	−0.0302273	−	0.0661886i
$987$		0			0
$988$	−14.7394	+	17.0101i	−0.468921	+	0.541164i
$989$	3.27845	−	22.8021i	0.104249	−	0.725066i
$990$		0			0
$991$	12.0999	+	13.9641i	0.384367	+	0.443584i	0.914656	−	0.404234i	$-0.132462\pi$
$991$	12.0999	+	13.9641i	0.384367	+	0.443584i	−0.530288	+	0.847817i	$0.677916\pi$
$992$	−4.13051	−	1.21283i	−0.131144	−	0.0385073i
$993$		0			0
$994$	0.0987995	−	0.687166i	0.00313373	−	0.0217956i
$995$	2.36218	+	1.51808i	0.0748863	+	0.0481265i
$996$		0			0
$997$	−2.80076	+	0.822378i	−0.0887011	+	0.0260450i	−0.325782	−	0.945445i	$-0.605628\pi$
$997$	−2.80076	+	0.822378i	−0.0887011	+	0.0260450i	0.237081	+	0.971490i	$0.423809\pi$
$998$	−0.703721	+	1.54094i	−0.0222759	+	0.0487774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.b.91.1		10
3.2	odd	2		67.2.e.a.24.1	yes	10
67.14	even	11	inner	603.2.u.b.550.1		10
201.14	odd	22		67.2.e.a.14.1	✓	10
201.125	even	22		4489.2.a.k.1.2		5
201.143	odd	22		4489.2.a.f.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.a.14.1	✓	10	201.14	odd	22
67.2.e.a.24.1	yes	10	3.2	odd	2
603.2.u.b.91.1		10	1.1	even	1	trivial
603.2.u.b.550.1		10	67.14	even	11	inner
4489.2.a.f.1.4		5	201.143	odd	22
4489.2.a.k.1.2		5	201.125	even	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0366213 + 0.0801894i) q^{2} +(1.30463 + 1.50563i) q^{4} +(-0.260554 + 1.81219i) q^{5} +(-0.253098 + 0.554206i) q^{7} +(-0.337683 + 0.0991526i) q^{8} +O(q^{10})\)	\(q+(-0.0366213 + 0.0801894i) q^{2} +(1.30463 + 1.50563i) q^{4} +(-0.260554 + 1.81219i) q^{5} +(-0.253098 + 0.554206i) q^{7} +(-0.337683 + 0.0991526i) q^{8} +(-0.135777 - 0.0872586i) q^{10} +(-0.769529 + 5.35219i) q^{11} +(-5.48325 - 1.61003i) q^{13} +(-0.0351727 - 0.0405915i) q^{14} +(-0.562632 + 3.91319i) q^{16} +(3.76413 - 4.34403i) q^{17} +(-0.821251 - 1.79829i) q^{19} +(-3.06841 + 1.97195i) q^{20} +(-0.401008 - 0.257712i) q^{22} +(-2.95918 + 1.90175i) q^{23} +(1.58130 + 0.464313i) q^{25} +(0.329911 - 0.380738i) q^{26} +(-1.16463 + 0.341965i) q^{28} -4.50909 q^{29} +(3.92487 - 1.15244i) q^{31} +(-0.885331 - 0.568968i) q^{32} +(0.210498 + 0.460927i) q^{34} +(-0.938384 - 0.603063i) q^{35} +3.02889 q^{37} +0.174279 q^{38} +(-0.0916991 - 0.637781i) q^{40} +(1.80542 - 2.08357i) q^{41} +(-4.28868 + 4.94940i) q^{43} +(-9.06235 + 5.82402i) q^{44} +(-0.0441312 - 0.306939i) q^{46} +(1.86582 - 1.19909i) q^{47} +(4.34094 + 5.00971i) q^{49} +(-0.0951423 + 0.109800i) q^{50} +(-4.72953 - 10.3562i) q^{52} +(5.19664 + 5.99724i) q^{53} +(-9.49871 - 2.78907i) q^{55} +(0.0305157 - 0.212241i) q^{56} +(0.165129 - 0.361582i) q^{58} +(-0.733886 + 0.215488i) q^{59} +(1.49662 + 10.4092i) q^{61} +(-0.0513198 + 0.356937i) q^{62} +(-6.57363 + 4.22462i) q^{64} +(4.34637 - 9.51722i) q^{65} +(8.14151 + 0.846014i) q^{67} +11.4513 q^{68} +(0.0827241 - 0.0531636i) q^{70} +(8.46440 + 9.76844i) q^{71} +(-1.52925 - 10.6362i) q^{73} +(-0.110922 + 0.242885i) q^{74} +(1.63612 - 3.58260i) q^{76} +(-2.77145 - 1.78111i) q^{77} +(11.3848 + 3.34289i) q^{79} +(-6.94487 - 2.03920i) q^{80} +(0.100963 + 0.221079i) q^{82} +(-0.467569 + 3.25201i) q^{83} +(6.89147 + 7.95318i) q^{85} +(-0.239833 - 0.525160i) q^{86} +(-0.270827 - 1.88364i) q^{88} +(-4.42253 - 2.84219i) q^{89} +(2.28009 - 2.63136i) q^{91} +(-6.72396 - 1.97433i) q^{92} +(0.0278255 + 0.193531i) q^{94} +(3.47283 - 1.01971i) q^{95} -9.24945 q^{97} +(-0.560697 + 0.164635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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