LMFDB - Embedded newform 504.2.p.g.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(307,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("504.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.p (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.2
Root			$-0.474920 - 1.33209i$ of defining polynomial
Character	$\chi$	$=$	504.307
Dual form			504.2.p.g.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33209 - 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(2.37995 - 1.15578i) q^{7} +(-1.46237 - 2.42105i) q^{8} +O(q^{10})$	\(q+(-1.33209 - 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(2.37995 - 1.15578i) q^{7} +(-1.46237 - 2.42105i) q^{8} +(-2.10562 - 0.750703i) q^{10} +2.26057 q^{11} -0.548664 q^{13} +(-3.71920 + 0.409313i) q^{14} +(0.798200 + 3.91955i) q^{16} -0.433635i q^{17} -6.02255i q^{19} +(2.44834 + 2.00000i) q^{20} +(-3.01127 - 1.07359i) q^{22} +8.24028i q^{23} -2.50141 q^{25} +(0.730867 + 0.260571i) q^{26} +(5.14869 + 1.22108i) q^{28} -0.548664i q^{29} +7.50941 q^{31} +(0.798200 - 5.60026i) q^{32} +(-0.205942 + 0.577639i) q^{34} +(3.76198 - 1.82694i) q^{35} +4.21124i q^{37} +(-2.86023 + 8.02255i) q^{38} +(-2.31156 - 3.82694i) q^{40} -7.09032i q^{41} -1.82694 q^{43} +(3.50141 + 2.86023i) q^{44} +(3.91347 - 10.9768i) q^{46} +11.5839 q^{47} +(4.32834 - 5.50141i) q^{49} +(3.33209 + 1.18797i) q^{50} +(-0.849827 - 0.694206i) q^{52} -3.71005i q^{53} +3.57327 q^{55} +(-6.27857 - 4.07180i) q^{56} +(-0.260571 + 0.730867i) q^{58} -11.5240i q^{59} -12.1325 q^{61} +(-10.0032 - 3.56636i) q^{62} +(-3.72294 + 7.08094i) q^{64} -0.867270 q^{65} +9.35089 q^{67} +(0.548664 - 0.671659i) q^{68} +(-5.87892 + 0.646999i) q^{70} +1.27953i q^{71} +0.867270i q^{73} +(2.00000 - 5.60973i) q^{74} +(7.62013 - 9.32834i) q^{76} +(5.38005 - 2.61272i) q^{77} +10.3696i q^{79} +(1.26171 + 6.19561i) q^{80} +(-3.36733 + 9.44491i) q^{82} +6.13554i q^{83} -0.685444i q^{85} +(2.43364 + 0.867648i) q^{86} +(-3.30579 - 5.47295i) q^{88} +7.95759i q^{89} +(-1.30579 + 0.634135i) q^{91} +(-10.4261 + 12.7634i) q^{92} +(-15.4307 - 5.50141i) q^{94} -9.51981i q^{95} +19.1778i q^{97} +(-8.37845 + 5.27273i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.33209	−	0.474920i	−0.941927	−	0.335819i
$2$	−1.33209	−	0.474920i	−0.941927	−	0.335819i
$3$		0			0
$3$		0			0
$4$	1.54890	+	1.26527i	0.774451	+	0.632633i
$5$	1.58069			0.706908			0.353454	−	0.935452i	$-0.385007\pi$
$5$	1.58069			0.706908			0.353454	+	0.935452i	$0.385007\pi$
$6$		0			0
$7$	2.37995	−	1.15578i	0.899537	−	0.436844i
$7$	2.37995	−	1.15578i	0.899537	−	0.436844i
$8$	−1.46237	−	2.42105i	−0.517026	−	0.855970i
$9$		0			0
$10$	−2.10562	−	0.750703i	−0.665855	−	0.237393i
$11$	2.26057			0.681588			0.340794	−	0.940138i	$-0.389304\pi$
$11$	2.26057			0.681588			0.340794	+	0.940138i	$0.389304\pi$
$12$		0			0
$13$	−0.548664			−0.152172			−0.0760860	−	0.997101i	$-0.524242\pi$
$13$	−0.548664			−0.152172			−0.0760860	+	0.997101i	$0.524242\pi$
$14$	−3.71920	+	0.409313i	−0.993999	+	0.109394i
$15$		0			0
$16$	0.798200	+	3.91955i	0.199550	+	0.979888i
$17$		−	0.433635i		−	0.105172i	−0.998616	−	0.0525860i	$-0.983254\pi$
$17$		−	0.433635i		−	0.105172i	0.998616	−	0.0525860i	$-0.0167464\pi$
$18$		0			0
$19$		−	6.02255i		−	1.38167i	−0.723014	−	0.690834i	$-0.757244\pi$
$19$		−	6.02255i		−	1.38167i	0.723014	−	0.690834i	$-0.242756\pi$
$20$	2.44834	+	2.00000i	0.547466	+	0.447214i
$21$		0			0
$22$	−3.01127	−	1.07359i	−0.642006	−	0.228890i
$23$			8.24028i			1.71822i	0.511794	+	0.859108i	$0.328981\pi$
$23$			8.24028i			1.71822i	−0.511794	+	0.859108i	$0.671019\pi$
$24$		0			0
$25$	−2.50141			−0.500281
$26$	0.730867	+	0.260571i	0.143335	+	0.0511022i
$27$		0			0
$28$	5.14869	+	1.22108i	0.973010	+	0.230763i
$29$		−	0.548664i		−	0.101884i	−0.998702	−	0.0509422i	$-0.983778\pi$
$29$		−	0.548664i		−	0.101884i	0.998702	−	0.0509422i	$-0.0162224\pi$
$30$		0			0
$31$	7.50941			1.34873			0.674365	−	0.738398i	$-0.264418\pi$
$31$	7.50941			1.34873			0.674365	+	0.738398i	$0.264418\pi$
$32$	0.798200	−	5.60026i	0.141103	−	0.989995i
$33$		0			0
$34$	−0.205942	+	0.577639i	−0.0353187	+	0.0990642i
$35$	3.76198	−	1.82694i	0.635890	−	0.308809i
$36$		0			0
$37$			4.21124i			0.692324i	0.938175	+	0.346162i	$0.112515\pi$
$37$			4.21124i			0.692324i	−0.938175	+	0.346162i	$0.887485\pi$
$38$	−2.86023	+	8.02255i	−0.463990	+	1.30143i
$39$		0			0
$40$	−2.31156	−	3.82694i	−0.365490	−	0.605092i
$41$		−	7.09032i		−	1.10732i	−0.832742	−	0.553661i	$-0.813230\pi$
$41$		−	7.09032i		−	1.10732i	0.832742	−	0.553661i	$-0.186770\pi$
$42$		0			0
$43$	−1.82694			−0.278605			−0.139303	−	0.990250i	$-0.544486\pi$
$43$	−1.82694			−0.278605			−0.139303	+	0.990250i	$0.544486\pi$
$44$	3.50141	+	2.86023i	0.527857	+	0.431195i
$45$		0			0
$46$	3.91347	−	10.9768i	0.577009	−	1.61843i
$47$	11.5839			1.68968			0.844840	−	0.535018i	$-0.179695\pi$
$47$	11.5839			1.68968			0.844840	+	0.535018i	$0.179695\pi$
$48$		0			0
$49$	4.32834	−	5.50141i	0.618334	−	0.785915i
$50$	3.33209	+	1.18797i	0.471228	+	0.168004i
$51$		0			0
$52$	−0.849827	−	0.694206i	−0.117850	−	0.0962691i
$53$		−	3.71005i		−	0.509615i	−0.966992	−	0.254807i	$-0.917988\pi$
$53$		−	3.71005i		−	0.509615i	0.966992	−	0.254807i	$-0.0820121\pi$
$54$		0			0
$55$	3.57327			0.481820
$56$	−6.27857	−	4.07180i	−0.839010	−	0.544117i
$57$		0			0
$58$	−0.260571	+	0.730867i	−0.0342147	+	0.0959676i
$59$		−	11.5240i		−	1.50029i	−0.661273	−	0.750145i	$-0.729983\pi$
$59$		−	11.5240i		−	1.50029i	0.661273	−	0.750145i	$-0.270017\pi$
$60$		0			0
$61$	−12.1325			−1.55341			−0.776706	−	0.629864i	$-0.783111\pi$
$61$	−12.1325			−1.55341			−0.776706	+	0.629864i	$0.783111\pi$
$62$	−10.0032	−	3.56636i	−1.27040	−	0.452929i
$63$		0			0
$64$	−3.72294	+	7.08094i	−0.465368	+	0.885117i
$65$	−0.867270			−0.107572
$66$		0			0
$67$	9.35089			1.14239			0.571196	−	0.820813i	$-0.306479\pi$
$67$	9.35089			1.14239			0.571196	+	0.820813i	$0.306479\pi$
$68$	0.548664	−	0.671659i	0.0665353	−	0.0814506i
$69$		0			0
$70$	−5.87892	+	0.646999i	−0.702666	+	0.0773312i
$71$			1.27953i			0.151852i	0.997113	+	0.0759262i	$0.0241913\pi$
$71$			1.27953i			0.151852i	−0.997113	+	0.0759262i	$0.975809\pi$
$72$		0			0
$73$			0.867270i			0.101506i	0.998711	+	0.0507531i	$0.0161622\pi$
$73$			0.867270i			0.101506i	−0.998711	+	0.0507531i	$0.983838\pi$
$74$	2.00000	−	5.60973i	0.232495	−	0.652118i
$75$		0			0
$76$	7.62013	−	9.32834i	0.874089	−	1.07003i
$77$	5.38005	−	2.61272i	0.613114	−	0.297748i
$78$		0			0
$79$			10.3696i			1.16668i	0.812230	+	0.583338i	$0.198253\pi$
$79$			10.3696i			1.16668i	−0.812230	+	0.583338i	$0.801747\pi$
$80$	1.26171	+	6.19561i	0.141064	+	0.692690i
$81$		0			0
$82$	−3.36733	+	9.44491i	−0.371859	+	1.04302i
$83$			6.13554i			0.673463i	0.941601	+	0.336732i	$0.109321\pi$
$83$			6.13554i			0.673463i	−0.941601	+	0.336732i	$0.890679\pi$
$84$		0			0
$85$		−	0.685444i		−	0.0743469i
$86$	2.43364	+	0.867648i	0.262426	+	0.0935609i
$87$		0			0
$88$	−3.30579	−	5.47295i	−0.352399	−	0.583418i
$89$			7.95759i			0.843503i	0.906712	+	0.421751i	$0.138584\pi$
$89$			7.95759i			0.843503i	−0.906712	+	0.421751i	$0.861416\pi$
$90$		0			0
$91$	−1.30579	+	0.634135i	−0.136884	+	0.0664754i
$92$	−10.4261	+	12.7634i	−1.08700	+	1.33068i
$93$		0			0
$94$	−15.4307	−	5.50141i	−1.59156	−	0.567427i
$95$		−	9.51981i		−	0.976712i
$96$		0			0
$97$			19.1778i			1.94721i	0.228233	+	0.973607i	$0.426705\pi$
$97$			19.1778i			1.94721i	−0.228233	+	0.973607i	$0.573295\pi$
$98$	−8.37845	+	5.27273i	−0.846351	+	0.532626i
$99$		0			0
$100$	−3.87443	−	3.16494i	−0.387443	−	0.316494i
$101$	−4.74208			−0.471855			−0.235927	−	0.971771i	$-0.575813\pi$
$101$	−4.74208			−0.471855			−0.235927	+	0.971771i	$0.575813\pi$
$102$		0			0
$103$	2.01040			0.198090			0.0990452	−	0.995083i	$-0.468421\pi$
$103$	2.01040			0.198090			0.0990452	+	0.995083i	$0.468421\pi$
$104$	0.802350	+	1.32834i	0.0786769	+	0.130255i
$105$		0			0
$106$	−1.76198	+	4.94211i	−0.171138	+	0.480020i
$107$	−17.7845			−1.71929			−0.859647	−	0.510888i	$-0.829317\pi$
$107$	−17.7845			−1.71929			−0.859647	+	0.510888i	$0.829317\pi$
$108$		0			0
$109$		−	12.0432i		−	1.15353i	−0.816909	−	0.576766i	$-0.804314\pi$
$109$		−	12.0432i		−	1.15353i	0.816909	−	0.576766i	$-0.195686\pi$
$110$	−4.75990	−	1.69702i	−0.453839	−	0.161804i
$111$		0			0
$112$	6.42982	+	8.40580i	0.607561	+	0.794273i
$113$	2.86727			0.269730			0.134865	−	0.990864i	$-0.456940\pi$
$113$	2.86727			0.269730			0.134865	+	0.990864i	$0.456940\pi$
$114$		0			0
$115$			13.0254i			1.21462i
$116$	0.694206	−	0.849827i	0.0644554	−	0.0789045i
$117$		0			0
$118$	−5.47295	+	15.3509i	−0.503826	+	1.41316i
$119$	−0.501187	−	1.03203i	−0.0459437	−	0.0946061i
$120$		0			0
$121$	−5.88982			−0.535438
$122$	16.1616	+	5.76198i	1.46320	+	0.521665i
$123$		0			0
$124$	11.6313	+	9.50141i	1.04453	+	0.853251i
$125$	−11.8574			−1.06056
$126$		0			0
$127$			14.9928i			1.33039i	0.746669	+	0.665196i	$0.231652\pi$
$127$			14.9928i			1.33039i	−0.746669	+	0.665196i	$0.768348\pi$
$128$	8.32215	−	7.66432i	0.735581	−	0.677436i
$129$		0			0
$130$	1.15528	+	0.411883i	0.101325	+	0.0361246i
$131$			8.52114i			0.744496i	0.928133	+	0.372248i	$0.121413\pi$
$131$			8.52114i			0.744496i	−0.928133	+	0.372248i	$0.878587\pi$
$132$		0			0
$133$	−6.96075	−	14.3334i	−0.603573	−	1.24286i
$134$	−12.4562	−	4.44092i	−1.07605	−	0.383637i
$135$		0			0
$136$	−1.04985	+	0.634135i	−0.0900240	+	0.0543766i
$137$	−5.00281			−0.427419			−0.213709	−	0.976897i	$-0.568555\pi$
$137$	−5.00281			−0.427419			−0.213709	+	0.976897i	$0.568555\pi$
$138$		0			0
$139$		−	14.3106i		−	1.21381i	−0.794776	−	0.606903i	$-0.792412\pi$
$139$		−	14.3106i		−	1.21381i	0.794776	−	0.606903i	$-0.207588\pi$
$140$	8.13850	+	1.93016i	0.687829	+	0.163128i
$141$		0			0
$142$	0.607674	−	1.70444i	0.0509949	−	0.143034i
$143$	−1.24029			−0.103719
$144$		0			0
$145$		−	0.867270i		−	0.0720229i
$146$	0.411883	−	1.15528i	0.0340877	−	0.0956115i
$147$		0			0
$148$	−5.32834	+	6.52280i	−0.437987	+	0.536171i
$149$			18.4553i			1.51192i	0.654619	+	0.755959i	$0.272829\pi$
$149$			18.4553i			1.51192i	−0.654619	+	0.755959i	$0.727171\pi$
$150$		0			0
$151$		−	14.5334i		−	1.18271i	−0.806411	−	0.591356i	$-0.798593\pi$
$151$		−	14.5334i		−	1.18271i	0.806411	−	0.591356i	$-0.201407\pi$
$152$	−14.5809	+	8.80720i	−1.18267	+	0.714358i
$153$		0			0
$154$	−8.40752	+	0.925281i	−0.677497	+	0.0745613i
$155$	11.8701			0.953428
$156$		0			0
$157$	−5.80975			−0.463669			−0.231834	−	0.972755i	$-0.574473\pi$
$157$	−5.80975			−0.463669			−0.231834	+	0.972755i	$0.574473\pi$
$158$	4.92474	−	13.8132i	0.391791	−	1.09892i
$159$		0			0
$160$	1.26171	−	8.85229i	0.0997470	−	0.699835i
$161$	9.52395	+	19.6115i	0.750593	+	1.54560i
$162$		0			0
$163$	−17.3509			−1.35903			−0.679513	−	0.733663i	$-0.737809\pi$
$163$	−17.3509			−1.35903			−0.679513	+	0.733663i	$0.737809\pi$
$164$	8.97114	−	10.9822i	0.700529	−	0.857567i
$165$		0			0
$166$	2.91389	−	8.17306i	0.226162	−	0.634353i
$167$	−0.823767			−0.0637450			−0.0318725	−	0.999492i	$-0.510147\pi$
$167$	−0.823767			−0.0637450			−0.0318725	+	0.999492i	$0.510147\pi$
$168$		0			0
$169$	−12.6990			−0.976844
$170$	−0.325531	+	0.913070i	−0.0249671	+	0.0700293i
$171$		0			0
$172$	−2.82975	−	2.31156i	−0.215766	−	0.176255i
$173$	−19.5230			−1.48430			−0.742152	−	0.670231i	$-0.766195\pi$
$173$	−19.5230			−1.48430			−0.742152	+	0.670231i	$0.766195\pi$
$174$		0			0
$175$	−5.95322	+	2.89108i	−0.450021	+	0.218545i
$176$	1.80439	+	8.86042i	0.136011	+	0.667880i
$177$		0			0
$178$	3.77921	−	10.6002i	0.283264	−	0.794518i
$179$	4.39611			0.328581			0.164290	−	0.986412i	$-0.447467\pi$
$179$	4.39611			0.328581			0.164290	+	0.986412i	$0.447467\pi$
$180$		0			0
$181$	8.14738			0.605590			0.302795	−	0.953056i	$-0.402080\pi$
$181$	8.14738			0.605590			0.302795	+	0.953056i	$0.402080\pi$
$182$	2.04059	−	0.224575i	0.151259	−	0.0166466i
$183$		0			0
$184$	19.9501	−	12.0503i	1.47074	−	0.888363i
$185$			6.65668i			0.489409i
$186$		0			0
$187$		−	0.980263i		−	0.0716839i
$188$	17.9423	+	14.6567i	1.30858	+	1.06895i
$189$		0			0
$190$	−4.52114	+	12.6812i	−0.327998	+	0.919991i
$191$			0.420123i			0.0303990i	0.999884	+	0.0151995i	$0.00483834\pi$
$191$			0.420123i			0.0303990i	−0.999884	+	0.0151995i	$0.995162\pi$
$192$		0			0
$193$	−11.1553			−0.802974			−0.401487	−	0.915865i	$-0.631507\pi$
$193$	−11.1553			−0.802974			−0.401487	+	0.915865i	$0.631507\pi$
$194$	9.10792	−	25.5465i	0.653911	−	1.83413i
$195$		0			0
$196$	13.6649	−	3.04464i	0.976066	−	0.217474i
$197$		−	4.95035i		−	0.352698i	−0.984328	−	0.176349i	$-0.943571\pi$
$197$		−	4.95035i		−	0.352698i	0.984328	−	0.176349i	$-0.0564287\pi$
$198$		0			0
$199$	12.0851			0.856687			0.428343	−	0.903616i	$-0.359097\pi$
$199$	12.0851			0.856687			0.428343	+	0.903616i	$0.359097\pi$
$200$	3.65798	+	6.05602i	0.258658	+	0.428225i
$201$		0			0
$202$	6.31686	+	2.25211i	0.444453	+	0.158458i
$203$	−0.634135	−	1.30579i	−0.0445076	−	0.0916488i
$204$		0			0
$205$		−	11.2076i		−	0.782775i
$206$	−2.67802	−	0.954777i	−0.186587	−	0.0665225i
$207$		0			0
$208$	−0.437944	−	2.15052i	−0.0303659	−	0.149111i
$209$		−	13.6144i		−	0.941728i
$210$		0			0
$211$	6.17306			0.424971			0.212486	−	0.977164i	$-0.431844\pi$
$211$	6.17306			0.424971			0.212486	+	0.977164i	$0.431844\pi$
$212$	4.69421	−	5.74651i	0.322399	−	0.394672i
$213$		0			0
$214$	23.6905	+	8.44622i	1.61945	+	0.577372i
$215$	−2.88783			−0.196948
$216$		0			0
$217$	17.8720	−	8.67923i	1.21323	−	0.589185i
$218$	−5.71956	+	16.0426i	−0.387378	+	1.08654i
$219$		0			0
$220$	5.53465	+	4.52114i	0.373146	+	0.304815i
$221$			0.237920i			0.0160042i
$222$		0			0
$223$	−18.4078			−1.23268			−0.616340	−	0.787480i	$-0.711385\pi$
$223$	−18.4078			−1.23268			−0.616340	+	0.787480i	$0.711385\pi$
$224$	−4.57299	−	14.2509i	−0.305546	−	0.952177i
$225$		0			0
$226$	−3.81945	−	1.36172i	−0.254066	−	0.0905804i
$227$		−	10.6567i		−	0.707309i	−0.935376	−	0.353654i	$-0.884939\pi$
$227$		−	10.6567i		−	0.707309i	0.935376	−	0.353654i	$-0.115061\pi$
$228$		0			0
$229$	8.97114			0.592830			0.296415	−	0.955059i	$-0.404209\pi$
$229$	8.97114			0.592830			0.296415	+	0.955059i	$0.404209\pi$
$230$	6.18600	−	17.3509i	0.407893	−	1.14408i
$231$		0			0
$232$	−1.32834	+	0.802350i	−0.0872099	+	0.0526769i
$233$	−14.9124			−0.976942			−0.488471	−	0.872580i	$-0.662445\pi$
$233$	−14.9124			−0.976942			−0.488471	+	0.872580i	$0.662445\pi$
$234$		0			0
$235$	18.3106			1.19445
$236$	14.5809	−	17.8495i	0.949134	−	1.16190i
$237$		0			0
$238$	0.177492	+	1.61278i	0.0115051	+	0.104541i
$239$		−	13.1370i		−	0.849759i	−0.905250	−	0.424880i	$-0.860316\pi$
$239$		−	13.1370i		−	0.849759i	0.905250	−	0.424880i	$-0.139684\pi$
$240$		0			0
$241$		−	10.1355i		−	0.652888i	−0.945217	−	0.326444i	$-0.894150\pi$
$241$		−	10.1355i		−	0.652888i	0.945217	−	0.326444i	$-0.105850\pi$
$242$	7.84574	+	2.79719i	0.504343	+	0.179810i
$243$		0			0
$244$	−18.7921	−	15.3509i	−1.20304	−	0.982740i
$245$	6.84179	−	8.69604i	0.437106	−	0.555570i
$246$		0			0
$247$			3.30435i			0.210251i
$248$	−10.9815	−	18.1806i	−0.697329	−	1.15447i
$249$		0			0
$250$	15.7951	+	5.63132i	0.998970	+	0.356156i
$251$			22.7018i			1.43292i	0.697626	+	0.716462i	$0.254240\pi$
$251$			22.7018i			1.43292i	−0.697626	+	0.716462i	$0.745760\pi$
$252$		0			0
$253$			18.6277i			1.17112i
$254$	7.12035	−	19.9716i	0.446771	−	1.25313i
$255$		0			0
$256$	−14.7258	+	6.25717i	−0.920360	+	0.391073i
$257$		−	16.1326i		−	1.00632i	−0.864192	−	0.503162i	$-0.832170\pi$
$257$		−	16.1326i		−	1.00632i	0.864192	−	0.503162i	$-0.167830\pi$
$258$		0			0
$259$	4.86727	+	10.0225i	0.302437	+	0.622771i
$260$	−1.34332	−	1.09733i	−0.0833090	−	0.0680534i
$261$		0			0
$262$	4.04686	−	11.3509i	0.250016	−	0.701260i
$263$			15.0581i			0.928519i	0.885699	+	0.464260i	$0.153680\pi$
$263$			15.0581i			0.928519i	−0.885699	+	0.464260i	$0.846320\pi$
$264$		0			0
$265$		−	5.86446i		−	0.360251i
$266$	2.46511	+	22.3991i	0.151145	+	1.37338i
$267$		0			0
$268$	14.4836	+	11.8314i	0.884728	+	0.722716i
$269$	−8.76288			−0.534282			−0.267141	−	0.963657i	$-0.586079\pi$
$269$	−8.76288			−0.534282			−0.267141	+	0.963657i	$0.586079\pi$
$270$		0			0
$271$	4.31238			0.261958			0.130979	−	0.991385i	$-0.458188\pi$
$271$	4.31238			0.261958			0.130979	+	0.991385i	$0.458188\pi$
$272$	1.69965	−	0.346128i	0.103057	−	0.0209871i
$273$		0			0
$274$	6.66417	+	2.37593i	0.402597	+	0.143535i
$275$	−5.65460			−0.340985
$276$		0			0
$277$			25.5528i			1.53532i	0.640857	+	0.767661i	$0.278579\pi$
$277$			25.5528i			1.53532i	−0.640857	+	0.767661i	$0.721421\pi$
$278$	−6.79636	+	19.0629i	−0.407619	+	1.14332i
$279$		0			0
$280$	−9.92450	−	6.43627i	−0.593103	−	0.384640i
$281$	−2.17501			−0.129751			−0.0648753	−	0.997893i	$-0.520665\pi$
$281$	−2.17501			−0.129751			−0.0648753	+	0.997893i	$0.520665\pi$
$282$		0			0
$283$			12.2880i			0.730446i	0.930920	+	0.365223i	$0.119007\pi$
$283$			12.2880i			0.730446i	−0.930920	+	0.365223i	$0.880993\pi$
$284$	−1.61895	+	1.98187i	−0.0960669	+	0.117602i
$285$		0			0
$286$	1.65218	+	0.589040i	0.0976953	+	0.0348307i
$287$	−8.19485	−	16.8746i	−0.483727	−	0.996077i
$288$		0			0
$289$	16.8120			0.988939
$290$	−0.411883	+	1.15528i	−0.0241866	+	0.0678402i
$291$		0			0
$292$	−1.09733	+	1.34332i	−0.0642163	+	0.0786117i
$293$	24.8790			1.45345			0.726724	−	0.686929i	$-0.241042\pi$
$293$	24.8790			1.45345			0.726724	+	0.686929i	$0.241042\pi$
$294$		0			0
$295$		−	18.2158i		−	1.06057i
$296$	10.1956	−	6.15839i	0.592608	−	0.357949i
$297$		0			0
$298$	8.76479	−	24.5840i	0.507730	−	1.42412i
$299$		−	4.52114i		−	0.261464i
$300$		0			0
$301$	−4.34802	+	2.11154i	−0.250616	+	0.121707i
$302$	−6.90219	+	19.3597i	−0.397177	+	1.11403i
$303$		0			0
$304$	23.6057	−	4.80720i	1.35388	−	0.275712i
$305$	−19.1778			−1.09812
$306$		0			0
$307$		−	17.0254i		−	0.971689i	−0.874045	−	0.485844i	$-0.838512\pi$
$307$		−	17.0254i		−	0.971689i	0.874045	−	0.485844i	$-0.161488\pi$
$308$	11.6390	+	2.76034i	0.663192	+	0.157285i
$309$		0			0
$310$	−15.8120	−	5.63733i	−0.898059	−	0.320179i
$311$	−23.2983			−1.32113			−0.660564	−	0.750770i	$-0.729683\pi$
$311$	−23.2983			−1.32113			−0.660564	+	0.750770i	$0.729683\pi$
$312$		0			0
$313$			15.0479i			0.850558i	0.905062	+	0.425279i	$0.139824\pi$
$313$			15.0479i			0.850558i	−0.905062	+	0.425279i	$0.860176\pi$
$314$	7.73909	+	2.75917i	0.436742	+	0.155709i
$315$		0			0
$316$	−13.1204	+	16.0616i	−0.738078	+	0.903533i
$317$		−	22.4761i		−	1.26238i	−0.775627	−	0.631192i	$-0.782566\pi$
$317$		−	22.4761i		−	1.26238i	0.775627	−	0.631192i	$-0.217434\pi$
$318$		0			0
$319$		−	1.24029i		−	0.0694431i
$320$	−5.88483	+	11.1928i	−0.328972	+	0.625697i
$321$		0			0
$322$	−3.37285	−	30.6473i	−0.187962	−	1.70790i
$323$	−2.61159			−0.145313
$324$		0			0
$325$	1.37243			0.0761288
$326$	23.1129	+	8.24028i	1.28010	+	0.456387i
$327$		0			0
$328$	−17.1660	+	10.3687i	−0.947834	+	0.572514i
$329$	27.5690	−	13.3884i	1.51993	−	0.738127i
$330$		0			0
$331$	−23.5315			−1.29341			−0.646705	−	0.762740i	$-0.723853\pi$
$331$	−23.5315			−1.29341			−0.646705	+	0.762740i	$0.723853\pi$
$332$	−7.76310	+	9.50336i	−0.426055	+	0.521564i
$333$		0			0
$334$	1.09733	+	0.391223i	0.0600431	+	0.0214068i
$335$	14.7809			0.807567
$336$		0			0
$337$	8.77682			0.478104			0.239052	−	0.971007i	$-0.423163\pi$
$337$	8.77682			0.478104			0.239052	+	0.971007i	$0.423163\pi$
$338$	16.9161	+	6.03099i	0.920115	+	0.328042i
$339$		0			0
$340$	0.867270	−	1.06169i	0.0470343	−	0.0575781i
$341$	16.9756			0.919278
$342$		0			0
$343$	3.94283	−	18.0957i	0.212893	−	0.977076i
$344$	2.67166	+	4.42310i	0.144046	+	0.238478i
$345$		0			0
$346$	26.0063	+	9.27185i	1.39811	+	0.498457i
$347$	4.00489			0.214994			0.107497	−	0.994205i	$-0.465716\pi$
$347$	4.00489			0.214994			0.107497	+	0.994205i	$0.465716\pi$
$348$		0			0
$349$	−3.43649			−0.183951			−0.0919756	−	0.995761i	$-0.529318\pi$
$349$	−3.43649			−0.183951			−0.0919756	+	0.995761i	$0.529318\pi$
$350$	9.30323	−	1.02386i	0.497279	−	0.0547275i
$351$		0			0
$352$	1.80439	−	12.6598i	0.0961742	−	0.674769i
$353$			23.0903i			1.22897i	0.788927	+	0.614487i	$0.210637\pi$
$353$			23.0903i			1.22897i	−0.788927	+	0.614487i	$0.789363\pi$
$354$		0			0
$355$			2.02255i			0.107346i
$356$	−10.0685	+	12.3255i	−0.533628	+	0.653252i
$357$		0			0
$358$	−5.85600	−	2.08780i	−0.309499	−	0.110344i
$359$			21.8882i			1.15522i	0.816315	+	0.577608i	$0.196014\pi$
$359$			21.8882i			1.15522i	−0.816315	+	0.577608i	$0.803986\pi$
$360$		0			0
$361$	−17.2711			−0.909004
$362$	−10.8530	−	3.86935i	−0.570421	−	0.203368i
$363$		0			0
$364$	−2.82490	−	0.669963i	−0.148065	−	0.0351156i
$365$			1.37089i			0.0717556i
$366$		0			0
$367$	−27.9276			−1.45781			−0.728905	−	0.684614i	$-0.759971\pi$
$367$	−27.9276			−1.45781			−0.728905	+	0.684614i	$0.759971\pi$
$368$	−32.2982	+	6.57739i	−1.68366	+	0.342870i
$369$		0			0
$370$	3.16139	−	8.86727i	0.164353	−	0.460987i
$371$	−4.28801	−	8.82975i	−0.222622	−	0.458418i
$372$		0			0
$373$			15.2403i			0.789111i	0.918872	+	0.394555i	$0.129101\pi$
$373$			15.2403i			0.789111i	−0.918872	+	0.394555i	$0.870899\pi$
$374$	−0.465546	+	1.30579i	−0.0240728	+	0.0675210i
$375$		0			0
$376$	−16.9399	−	28.0451i	−0.873609	−	1.44632i
$377$			0.301032i			0.0155039i
$378$		0			0
$379$	11.4864			0.590018			0.295009	−	0.955494i	$-0.404677\pi$
$379$	11.4864			0.590018			0.295009	+	0.955494i	$0.404677\pi$
$380$	12.0451	−	14.7453i	0.617900	−	0.756416i
$381$		0			0
$382$	0.199525	−	0.559640i	0.0102086	−	0.0286337i
$383$	−22.4746			−1.14840			−0.574198	−	0.818716i	$-0.694686\pi$
$383$	−22.4746			−1.14840			−0.574198	+	0.818716i	$0.694686\pi$
$384$		0			0
$385$	8.50422	−	4.12992i	0.433415	−	0.210480i
$386$	14.8598	+	5.29786i	0.756343	+	0.269654i
$387$		0			0
$388$	−24.2651	+	29.7046i	−1.23187	+	1.50802i
$389$			20.5907i			1.04399i	0.852949	+	0.521994i	$0.174812\pi$
$389$			20.5907i			1.04399i	−0.852949	+	0.521994i	$0.825188\pi$
$390$		0			0
$391$	3.57327			0.180708
$392$	−19.6488	−	2.43402i	−0.992414	−	0.122937i
$393$		0			0
$394$	−2.35102	+	6.59428i	−0.118442	+	0.332215i
$395$			16.3912i			0.824732i
$396$		0			0
$397$	26.8778			1.34896			0.674479	−	0.738294i	$-0.264368\pi$
$397$	26.8778			1.34896			0.674479	+	0.738294i	$0.264368\pi$
$398$	−16.0983	−	5.73943i	−0.806936	−	0.287692i
$399$		0			0
$400$	−1.99662	−	9.80438i	−0.0998311	−	0.490219i
$401$	−9.00281			−0.449579			−0.224789	−	0.974407i	$-0.572169\pi$
$401$	−9.00281			−0.449579			−0.224789	+	0.974407i	$0.572169\pi$
$402$		0			0
$403$	−4.12014			−0.205239
$404$	−7.34503	−	6.00000i	−0.365429	−	0.298511i
$405$		0			0
$406$	0.224575	+	2.04059i	0.0111455	+	0.101273i
$407$			9.51981i			0.471879i
$408$		0			0
$409$		−	4.91237i		−	0.242901i	−0.992597	−	0.121450i	$-0.961245\pi$
$409$		−	4.91237i		−	0.242901i	0.992597	−	0.121450i	$-0.0387545\pi$
$410$	−5.32272	+	14.9295i	−0.262870	+	0.737316i
$411$		0			0
$412$	3.11391	+	2.54369i	0.153411	+	0.125319i
$413$	−13.3192	−	27.4265i	−0.655393	−	1.34957i
$414$		0			0
$415$			9.69841i			0.476076i
$416$	−0.437944	+	3.07266i	−0.0214720	+	0.150650i
$417$		0			0
$418$	−6.46574	+	18.1355i	−0.316250	+	0.887038i
$419$			4.17501i			0.203963i	0.994786	+	0.101981i	$0.0325182\pi$
$419$			4.17501i			0.203963i	−0.994786	+	0.101981i	$0.967482\pi$
$420$		0			0
$421$		−	3.11391i		−	0.151763i	−0.997117	−	0.0758814i	$-0.975823\pi$
$421$		−	3.11391i		−	0.151763i	0.997117	−	0.0758814i	$-0.0241770\pi$
$422$	−8.22305	−	2.93171i	−0.400292	−	0.142713i
$423$		0			0
$424$	−8.98221	+	5.42547i	−0.436215	+	0.263484i
$425$			1.08470i			0.0526155i
$426$		0			0
$427$	−28.8748	+	14.0225i	−1.39735	+	0.678599i
$428$	−27.5465	−	22.5022i	−1.33151	−	1.08768i
$429$		0			0
$430$	3.84683	+	1.37149i	0.185511	+	0.0661389i
$431$			0.641564i			0.0309030i	0.999881	+	0.0154515i	$0.00491857\pi$
$431$			0.641564i			0.0309030i	−0.999881	+	0.0154515i	$0.995081\pi$
$432$		0			0
$433$			6.95772i			0.334366i	0.985926	+	0.167183i	$0.0534671\pi$
$433$			6.95772i			0.334366i	−0.985926	+	0.167183i	$0.946533\pi$
$434$	−27.9290	+	3.07370i	−1.34064	+	0.147542i
$435$		0			0
$436$	15.2379	−	18.6538i	0.729763	−	0.893355i
$437$	49.6275			2.37400
$438$		0			0
$439$	−17.4055			−0.830717			−0.415359	−	0.909658i	$-0.636344\pi$
$439$	−17.4055			−0.830717			−0.415359	+	0.909658i	$0.636344\pi$
$440$	−5.22545	−	8.65106i	−0.249114	−	0.412423i
$441$		0			0
$442$	0.112993	−	0.316930i	0.00537452	−	0.0150748i
$443$	−18.0856			−0.859271			−0.429635	−	0.903002i	$-0.641358\pi$
$443$	−18.0856			−0.859271			−0.429635	+	0.903002i	$0.641358\pi$
$444$		0			0
$445$			12.5785i			0.596279i
$446$	24.5208	+	8.74224i	1.16109	+	0.413957i
$447$		0			0
$448$	−0.676409	+	21.1552i	−0.0319573	+	0.999489i
$449$	21.2229			1.00157			0.500786	−	0.865571i	$-0.333044\pi$
$449$	21.2229			1.00157			0.500786	+	0.865571i	$0.333044\pi$
$450$		0			0
$451$		−	16.0282i		−	0.754737i
$452$	4.44112	+	3.62786i	0.208893	+	0.170640i
$453$		0			0
$454$	−5.06107	+	14.1956i	−0.237528	+	0.666233i
$455$	−2.06406	+	1.00237i	−0.0967647	+	0.0469920i
$456$		0			0
$457$	27.7046			1.29597			0.647983	−	0.761655i	$-0.275613\pi$
$457$	27.7046			1.29597			0.647983	+	0.761655i	$0.275613\pi$
$458$	−11.9503	−	4.26057i	−0.558402	−	0.199083i
$459$		0			0
$460$	−16.4806	+	20.1750i	−0.768410	+	0.940665i
$461$	−23.5438			−1.09654			−0.548272	−	0.836300i	$-0.684714\pi$
$461$	−23.5438			−1.09654			−0.548272	+	0.836300i	$0.684714\pi$
$462$		0			0
$463$		−	26.8145i		−	1.24618i	−0.782151	−	0.623089i	$-0.785878\pi$
$463$		−	26.8145i		−	1.24618i	0.782151	−	0.623089i	$-0.214122\pi$
$464$	2.15052	−	0.437944i	0.0998352	−	0.0203310i
$465$		0			0
$466$	19.8645	+	7.08217i	0.920207	+	0.328075i
$467$		−	17.3884i		−	0.804640i	−0.915499	−	0.402320i	$-0.868204\pi$
$467$		−	17.3884i		−	0.804640i	0.915499	−	0.402320i	$-0.131796\pi$
$468$		0			0
$469$	22.2547	−	10.8076i	1.02762	−	0.499048i
$470$	−24.3912	−	8.69604i	−1.12508	−	0.401118i
$471$		0			0
$472$	−27.9000	+	16.8523i	−1.28420	+	0.775690i
$473$	−4.12992			−0.189894
$474$		0			0
$475$			15.0648i			0.691222i
$476$	0.529504	−	2.23265i	0.0242698	−	0.102333i
$477$		0			0
$478$	−6.23900	+	17.4996i	−0.285365	+	0.800411i
$479$	25.6003			1.16971			0.584854	−	0.811139i	$-0.301152\pi$
$479$	25.6003			1.16971			0.584854	+	0.811139i	$0.301152\pi$
$480$		0			0
$481$		−	2.31056i		−	0.105352i
$482$	−4.81357	+	13.5014i	−0.219252	+	0.614972i
$483$		0			0
$484$	−9.12276	−	7.45219i	−0.414671	−	0.338736i
$485$			30.3143i			1.37650i
$486$		0			0
$487$			0.940673i			0.0426260i	0.999773	+	0.0213130i	$0.00678464\pi$
$487$			0.940673i			0.0426260i	−0.999773	+	0.0213130i	$0.993215\pi$
$488$	17.7423	+	29.3734i	0.803155	+	1.32967i
$489$		0			0
$490$	−13.2438	+	8.33457i	−0.598292	+	0.376518i
$491$	24.0500			1.08536			0.542680	−	0.839939i	$-0.317410\pi$
$491$	24.0500			1.08536			0.542680	+	0.839939i	$0.317410\pi$
$492$		0			0
$493$	−0.237920			−0.0107154
$494$	1.56930	−	4.40168i	0.0706063	−	0.198041i
$495$		0			0
$496$	5.99401	+	29.4335i	0.269139	+	1.32160i
$497$	1.47886	+	3.04522i	0.0663358	+	0.136597i
$498$		0			0
$499$	−26.8354			−1.20132			−0.600658	−	0.799506i	$-0.705095\pi$
$499$	−26.8354			−1.20132			−0.600658	+	0.799506i	$0.705095\pi$
$500$	−18.3660	−	15.0028i	−0.821353	−	0.670946i
$501$		0			0
$502$	10.7815	−	30.2407i	0.481203	−	1.34971i
$503$	−1.13297			−0.0505166			−0.0252583	−	0.999681i	$-0.508041\pi$
$503$	−1.13297			−0.0505166			−0.0252583	+	0.999681i	$0.508041\pi$
$504$		0			0
$505$	−7.49578			−0.333558
$506$	8.84667	−	24.8137i	0.393283	−	1.10310i
$507$		0			0
$508$	−18.9698	+	23.2223i	−0.841650	+	1.03032i
$509$	11.7937			0.522745			0.261373	−	0.965238i	$-0.415825\pi$
$509$	11.7937			0.522745			0.261373	+	0.965238i	$0.415825\pi$
$510$		0			0
$511$	1.00237	+	2.06406i	0.0443424	+	0.0913087i
$512$	22.5876	−	1.34154i	0.998241	−	0.0592883i
$513$		0			0
$514$	−7.66169	+	21.4900i	−0.337943	+	0.947883i
$515$	3.17783			0.140032
$516$		0			0
$517$	26.1862			1.15167
$518$	−1.72372	−	15.6625i	−0.0757357	−	0.688169i
$519$		0			0
$520$	1.26827	+	2.09970i	0.0556173	+	0.0920780i
$521$		−	14.6991i		−	0.643979i	−0.946743	−	0.321990i	$-0.895648\pi$
$521$		−	14.6991i		−	0.643979i	0.946743	−	0.321990i	$-0.104352\pi$
$522$		0			0
$523$			7.69507i			0.336482i	0.985746	+	0.168241i	$0.0538086\pi$
$523$			7.69507i			0.336482i	−0.985746	+	0.168241i	$0.946191\pi$
$524$	−10.7815	+	13.1984i	−0.470993	+	0.576576i
$525$		0			0
$526$	7.15136	−	20.0586i	0.311814	−	0.874597i
$527$		−	3.25634i		−	0.141849i
$528$		0			0
$529$	−44.9022			−1.95227
$530$	−2.78515	+	7.81196i	−0.120979	+	0.339330i
$531$		0			0
$532$	7.35402	−	31.0082i	0.318837	−	1.34438i
$533$			3.89020i			0.168503i
$534$		0			0
$535$	−28.1119			−1.21538
$536$	−13.6745	−	22.6389i	−0.590647	−	0.977854i
$537$		0			0
$538$	11.6729	+	4.16166i	0.503255	+	0.179422i
$539$	9.78452	−	12.4363i	0.421449	−	0.535670i
$540$		0			0
$541$			11.6313i			0.500071i	0.968237	+	0.250035i	$0.0804422\pi$
$541$			11.6313i			0.500071i	−0.968237	+	0.250035i	$0.919558\pi$
$542$	−5.74446	−	2.04803i	−0.246746	−	0.0879706i
$543$		0			0
$544$	−2.42847	−	0.346128i	−0.104120	−	0.0148401i
$545$		−	19.0367i		−	0.815441i
$546$		0			0
$547$	21.0048			0.898099			0.449049	−	0.893507i	$-0.351763\pi$
$547$	21.0048			0.898099			0.449049	+	0.893507i	$0.351763\pi$
$548$	−7.74887	−	6.32989i	−0.331015	−	0.270399i
$549$		0			0
$550$	7.53242	+	2.68548i	0.321183	+	0.114509i
$551$	−3.30435			−0.140770
$552$		0			0
$553$	11.9850	+	24.6792i	0.509655	+	1.04947i
$554$	12.1355	−	34.0386i	0.515590	−	1.44616i
$555$		0			0
$556$	18.1067	−	22.1657i	0.767894	−	0.940033i
$557$			34.7501i			1.47241i	0.676760	+	0.736204i	$0.263383\pi$
$557$			34.7501i			1.47241i	−0.676760	+	0.736204i	$0.736617\pi$
$558$		0			0
$559$	1.00237			0.0423959
$560$	10.1636	+	13.2870i	0.429490	+	0.561478i
$561$		0			0
$562$	2.89731	+	1.03296i	0.122215	+	0.0435727i
$563$			16.9124i			0.712771i	0.934339	+	0.356386i	$0.115991\pi$
$563$			16.9124i			0.712771i	−0.934339	+	0.356386i	$0.884009\pi$
$564$		0			0
$565$	4.53228			0.190674
$566$	5.83581	−	16.3687i	0.245298	−	0.688027i
$567$		0			0
$568$	3.09781	−	1.87115i	0.129981	−	0.0785117i
$569$	20.4856			0.858800			0.429400	−	0.903114i	$-0.358725\pi$
$569$	20.4856			0.858800			0.429400	+	0.903114i	$0.358725\pi$
$570$		0			0
$571$	46.0132			1.92559			0.962796	−	0.270229i	$-0.0870994\pi$
$571$	46.0132			1.92559			0.962796	+	0.270229i	$0.0870994\pi$
$572$	−1.92109	−	1.56930i	−0.0803250	−	0.0656158i
$573$		0			0
$574$	2.90216	+	26.3703i	0.121134	+	1.10068i
$575$		−	20.6123i		−	0.859591i
$576$		0			0
$577$		−	35.8191i		−	1.49117i	−0.666411	−	0.745585i	$-0.732170\pi$
$577$		−	35.8191i		−	1.49117i	0.666411	−	0.745585i	$-0.267830\pi$
$578$	−22.3950	−	7.98433i	−0.931508	−	0.332104i
$579$		0			0
$580$	1.09733	−	1.34332i	0.0455641	−	0.0557782i
$581$	7.09134	+	14.6023i	0.294198	+	0.605805i
$582$		0			0
$583$		−	8.38684i		−	0.347347i
$584$	2.09970	−	1.26827i	0.0868863	−	0.0524814i
$585$		0			0
$586$	−33.1410	−	11.8155i	−1.36904	−	0.488095i
$587$		−	30.4007i		−	1.25477i	−0.778708	−	0.627387i	$-0.784125\pi$
$587$		−	30.4007i		−	1.25477i	0.778708	−	0.627387i	$-0.215875\pi$
$588$		0			0
$589$		−	45.2258i		−	1.86350i
$590$	−8.65106	+	24.2651i	−0.356159	+	0.998977i
$591$		0			0
$592$	−16.5062	+	3.36141i	−0.678399	+	0.138153i
$593$		−	23.3065i		−	0.957084i	−0.878065	−	0.478542i	$-0.841165\pi$
$593$		−	23.3065i		−	0.957084i	0.878065	−	0.478542i	$-0.158835\pi$
$594$		0			0
$595$	−0.792224	−	1.63132i	−0.0324780	−	0.0668778i
$596$	−23.3509	+	28.5855i	−0.956490	+	1.17091i
$597$		0			0
$598$	−2.14718	+	6.02255i	−0.0878047	+	0.246280i
$599$		−	19.9547i		−	0.815329i	−0.913132	−	0.407664i	$-0.866343\pi$
$599$		−	19.9547i		−	0.815329i	0.913132	−	0.407664i	$-0.133657\pi$
$600$		0			0
$601$		−	27.0028i		−	1.10147i	−0.834681	−	0.550734i	$-0.814348\pi$
$601$		−	27.0028i		−	1.10147i	0.834681	−	0.550734i	$-0.185652\pi$
$602$	6.79474	−	0.747789i	0.276933	−	0.0304776i
$603$		0			0
$604$	18.3886	−	22.5108i	0.748222	−	0.915952i
$605$	−9.31000			−0.378505
$606$		0			0
$607$	−1.63416			−0.0663283			−0.0331642	−	0.999450i	$-0.510558\pi$
$607$	−1.63416			−0.0663283			−0.0331642	+	0.999450i	$0.510558\pi$
$608$	−33.7278	−	4.80720i	−1.36784	−	0.194958i
$609$		0			0
$610$	25.5465	+	9.10792i	1.03435	+	0.368769i
$611$	−6.35565			−0.257122
$612$		0			0
$613$			16.3500i			0.660369i	0.943916	+	0.330184i	$0.107111\pi$
$613$			16.3500i			0.660369i	−0.943916	+	0.330184i	$0.892889\pi$
$614$	−8.08568	+	22.6792i	−0.326311	+	0.915259i
$615$		0			0
$616$	−14.1932	−	9.20459i	−0.571859	−	0.370863i
$617$	−0.220365			−0.00887154			−0.00443577	−	0.999990i	$-0.501412\pi$
$617$	−0.220365			−0.00887154			−0.00443577	+	0.999990i	$0.501412\pi$
$618$		0			0
$619$		−	16.9972i		−	0.683175i	−0.939850	−	0.341587i	$-0.889035\pi$
$619$		−	16.9972i		−	0.683175i	0.939850	−	0.341587i	$-0.110965\pi$
$620$	18.3856	+	15.0188i	0.738384	+	0.603170i
$621$		0			0
$622$	31.0354	+	11.0648i	1.24440	+	0.443659i
$623$	9.19723	+	18.9387i	0.368479	+	0.758762i
$624$		0			0
$625$	−6.23595			−0.249438
$626$	7.14654	−	20.0451i	0.285633	−	0.801163i
$627$		0			0
$628$	−8.99875	−	7.35089i	−0.359089	−	0.293332i
$629$	1.82614			0.0728130
$630$		0			0
$631$			13.8402i			0.550971i	0.961305	+	0.275485i	$0.0888386\pi$
$631$			13.8402i			0.550971i	−0.961305	+	0.275485i	$0.911161\pi$
$632$	25.1054	−	15.1643i	0.998638	−	0.603202i
$633$		0			0
$634$	−10.6743	+	29.9401i	−0.423932	+	1.18907i
$635$			23.6990i			0.940465i
$636$		0			0
$637$	−2.37480	+	3.01842i	−0.0940932	+	0.119594i
$638$	−0.589040	+	1.65218i	−0.0233203	+	0.0654103i
$639$		0			0
$640$	13.1548	−	12.1149i	0.519988	−	0.478885i
$641$	−13.0479			−0.515361			−0.257681	−	0.966230i	$-0.582958\pi$
$641$	−13.0479			−0.515361			−0.257681	+	0.966230i	$0.582958\pi$
$642$		0			0
$643$			12.2880i			0.484592i	0.970202	+	0.242296i	$0.0779005\pi$
$643$			12.2880i			0.484592i	−0.970202	+	0.242296i	$0.922100\pi$
$644$	−10.0621	+	42.4266i	−0.396500	+	1.67184i
$645$		0			0
$646$	3.47886	+	1.24029i	0.136874	+	0.0487987i
$647$	31.8638			1.25269			0.626347	−	0.779544i	$-0.284549\pi$
$647$	31.8638			1.25269			0.626347	+	0.779544i	$0.284549\pi$
$648$		0			0
$649$		−	26.0507i		−	1.02258i
$650$	−1.82820	−	0.651794i	−0.0717077	−	0.0255655i
$651$		0			0
$652$	−26.8748	−	21.9535i	−1.05250	−	0.859766i
$653$			14.6007i			0.571371i	0.958323	+	0.285686i	$0.0922213\pi$
$653$			14.6007i			0.571371i	−0.958323	+	0.285686i	$0.907779\pi$
$654$		0			0
$655$			13.4693i			0.526290i
$656$	27.7909	−	5.65949i	1.08505	−	0.220966i
$657$		0			0
$658$	−43.0827	+	4.74143i	−1.67954	+	0.184840i
$659$	−7.25776			−0.282722			−0.141361	−	0.989958i	$-0.545148\pi$
$659$	−7.25776			−0.282722			−0.141361	+	0.989958i	$0.545148\pi$
$660$		0			0
$661$	15.6031			0.606891			0.303446	−	0.952849i	$-0.401863\pi$
$661$	15.6031			0.606891			0.303446	+	0.952849i	$0.401863\pi$
$662$	31.3460	+	11.1756i	1.21830	+	0.434351i
$663$		0			0
$664$	14.8544	−	8.97244i	0.576464	−	0.348198i
$665$	−11.0028	−	22.6567i	−0.426671	−	0.878588i
$666$		0			0
$667$	4.52114			0.175059
$668$	−1.27593	−	1.04228i	−0.0493674	−	0.0403272i
$669$		0			0
$670$	−19.6894	−	7.01974i	−0.760669	−	0.271196i
$671$	−27.4265			−1.05879
$672$		0			0
$673$	9.19475			0.354432			0.177216	−	0.984172i	$-0.443291\pi$
$673$	9.19475			0.354432			0.177216	+	0.984172i	$0.443291\pi$
$674$	−11.6915	−	4.16829i	−0.450339	−	0.160556i
$675$		0			0
$676$	−19.6695	−	16.0676i	−0.756518	−	0.617984i
$677$	14.1669			0.544480			0.272240	−	0.962229i	$-0.412236\pi$
$677$	14.1669			0.544480			0.272240	+	0.962229i	$0.412236\pi$
$678$		0			0
$679$	22.1654	+	45.6423i	0.850629	+	1.75159i
$680$	−1.65949	+	1.00237i	−0.0636387	+	0.0384393i
$681$		0			0
$682$	−22.6129	−	8.06202i	−0.865892	−	0.308711i
$683$	35.9201			1.37444			0.687222	−	0.726448i	$-0.258830\pi$
$683$	35.9201			1.37444			0.687222	+	0.726448i	$0.258830\pi$
$684$		0			0
$685$	−7.90791			−0.302146
$686$	−13.8462	+	22.2325i	−0.528650	+	0.848840i
$687$		0			0
$688$	−1.45826	−	7.16077i	−0.0555957	−	0.273002i
$689$			2.03557i			0.0775491i
$690$		0			0
$691$			24.0451i			0.914719i	0.889282	+	0.457359i	$0.151205\pi$
$691$			24.0451i			0.914719i	−0.889282	+	0.457359i	$0.848795\pi$
$692$	−30.2392	−	24.7018i	−1.14952	−	0.939021i
$693$		0			0
$694$	−5.33485	−	1.90200i	−0.202508	−	0.0721989i
$695$		−	22.6206i		−	0.858049i
$696$		0			0
$697$	−3.07461			−0.116459
$698$	4.57770	+	1.63206i	0.173269	+	0.0617743i
$699$		0			0
$700$	−12.8789	−	3.05442i	−0.486778	−	0.115446i
$701$		−	39.3211i		−	1.48514i	−0.669771	−	0.742568i	$-0.733608\pi$
$701$		−	39.3211i		−	1.48514i	0.669771	−	0.742568i	$-0.266392\pi$
$702$		0			0
$703$	25.3624			0.956561
$704$	−8.41598	+	16.0070i	−0.317189	+	0.603285i
$705$		0			0
$706$	10.9660	−	30.7583i	0.412712	−	1.15760i
$707$	−11.2859	+	5.48081i	−0.424451	+	0.206127i
$708$		0			0
$709$		−	37.8578i		−	1.42178i	−0.703304	−	0.710890i	$-0.748293\pi$
$709$		−	37.8578i		−	1.42178i	0.703304	−	0.710890i	$-0.251707\pi$
$710$	0.960547	−	2.69421i	0.0360487	−	0.101112i
$711$		0			0
$712$	19.2657	−	11.6369i	0.722013	−	0.436113i
$713$			61.8796i			2.31741i
$714$		0			0
$715$	−1.96053			−0.0733195
$716$	6.80915	+	5.56225i	0.254470	+	0.207871i
$717$		0			0
$718$	10.3951	−	29.1570i	0.387943	−	1.08813i
$719$	25.6003			0.954731			0.477365	−	0.878705i	$-0.341592\pi$
$719$	25.6003			0.954731			0.477365	+	0.878705i	$0.341592\pi$
$720$		0			0
$721$	4.78465	−	2.32358i	0.178190	−	0.0865346i
$722$	23.0066	+	8.20237i	0.856215	+	0.305261i
$723$		0			0
$724$	12.6195	+	10.3086i	0.469000	+	0.383116i
$725$			1.37243i			0.0509708i
$726$		0			0
$727$	2.11772			0.0785420			0.0392710	−	0.999229i	$-0.487496\pi$
$727$	2.11772			0.0785420			0.0392710	+	0.999229i	$0.487496\pi$
$728$	3.44483	+	2.23405i	0.127674	+	0.0827993i
$729$		0			0
$730$	0.651062	−	1.82614i	0.0240969	−	0.0675885i
$731$			0.792224i			0.0293014i
$732$		0			0
$733$	−20.4120			−0.753936			−0.376968	−	0.926226i	$-0.623033\pi$
$733$	−20.4120			−0.753936			−0.376968	+	0.926226i	$0.623033\pi$
$734$	37.2020	+	13.2634i	1.37315	+	0.489560i
$735$		0			0
$736$	46.1477	+	6.57739i	1.70103	+	0.242446i
$737$	21.1384			0.778641
$738$		0			0
$739$	18.3932			0.676604			0.338302	−	0.941038i	$-0.390147\pi$
$739$	18.3932			0.676604			0.338302	+	0.941038i	$0.390147\pi$
$740$	−8.42248	+	10.3106i	−0.309617	+	0.379024i
$741$		0			0
$742$	1.51857	+	13.7984i	0.0557486	+	0.506556i
$743$		−	33.3812i		−	1.22464i	−0.790611	−	0.612319i	$-0.790237\pi$
$743$		−	33.3812i		−	1.22464i	0.790611	−	0.612319i	$-0.209763\pi$
$744$		0			0
$745$			29.1722i			1.06879i
$746$	7.23790	−	20.3013i	0.264998	−	0.743284i
$747$		0			0
$748$	1.24029	−	1.51833i	0.0453496	−	0.0555157i
$749$	−42.3263	+	20.5550i	−1.54657	+	0.751064i
$750$		0			0
$751$			9.83899i			0.359030i	0.983755	+	0.179515i	$0.0574528\pi$
$751$			9.83899i			0.359030i	−0.983755	+	0.179515i	$0.942547\pi$
$752$	9.24625	+	45.4036i	0.337176	+	1.65570i
$753$		0			0
$754$	0.142966	−	0.401000i	0.00520652	−	0.0146036i
$755$		−	22.9729i		−	0.836068i
$756$		0			0
$757$			23.9363i			0.869980i	0.900435	+	0.434990i	$0.143248\pi$
$757$			23.9363i			0.869980i	−0.900435	+	0.434990i	$0.856752\pi$
$758$	−15.3009	−	5.45513i	−0.555754	−	0.198139i
$759$		0			0
$760$	−23.0479	+	13.9215i	−0.836035	+	0.504986i
$761$			14.6991i			0.532842i	0.963857	+	0.266421i	$0.0858411\pi$
$761$			14.6991i			0.532842i	−0.963857	+	0.266421i	$0.914159\pi$
$762$		0			0
$763$	−13.9193	−	28.6623i	−0.503914	−	1.03765i
$764$	−0.531568	+	0.650730i	−0.0192315	+	0.0235426i
$765$		0			0
$766$	29.9380	+	10.6736i	1.08171	+	0.385653i
$767$			6.32278i			0.228302i
$768$		0			0
$769$			22.7317i			0.819727i	0.912147	+	0.409864i	$0.134424\pi$
$769$			22.7317i			0.819727i	−0.912147	+	0.409864i	$0.865576\pi$
$770$	−13.2897	+	1.46259i	−0.478928	+	0.0527080i
$771$		0			0
$772$	−17.2784	−	14.1144i	−0.621865	−	0.507988i
$773$	8.21267			0.295389			0.147695	−	0.989033i	$-0.452815\pi$
$773$	8.21267			0.295389			0.147695	+	0.989033i	$0.452815\pi$
$774$		0			0
$775$	−18.7841			−0.674744
$776$	46.4304	−	28.0451i	1.66676	−	1.00676i
$777$		0			0
$778$	9.77890	−	27.4285i	0.350591	−	0.983360i
$779$	−42.7018			−1.52995
$780$		0			0
$781$			2.89247i			0.103501i
$782$	−4.75990	−	1.69702i	−0.170214	−	0.0606852i
$783$		0			0
$784$	25.0179	+	12.5739i	0.893497	+	0.449069i
$785$	−9.18345			−0.327771
$786$		0			0
$787$		−	25.3134i		−	0.902324i	−0.892442	−	0.451162i	$-0.851010\pi$
$787$		−	25.3134i		−	0.902324i	0.892442	−	0.451162i	$-0.148990\pi$
$788$	6.26351	−	7.66761i	0.223128	−	0.273147i
$789$		0			0
$790$	7.78451	−	21.8345i	0.276961	−	0.776837i
$791$	6.82396	−	3.31394i	0.242632	−	0.117830i
$792$		0			0
$793$	6.65668			0.236386
$794$	−35.8035	−	12.7648i	−1.27062	−	0.453005i
$795$		0			0
$796$	18.7186	+	15.2908i	0.663462	+	0.541969i
$797$	10.2767			0.364021			0.182010	−	0.983297i	$-0.441740\pi$
$797$	10.2767			0.364021			0.182010	+	0.983297i	$0.441740\pi$
$798$		0			0
$799$		−	5.02317i		−	0.177707i
$800$	−1.99662	+	14.0085i	−0.0705913	+	0.495276i
$801$		0			0
$802$	11.9925	+	4.27561i	0.423470	+	0.150977i
$803$			1.96053i			0.0691854i
$804$		0			0
$805$	15.0545	+	30.9997i	0.530600	+	1.09260i
$806$	5.48838	+	1.95674i	0.193320	+	0.0689231i
$807$		0			0
$808$	6.93468	+	11.4808i	0.243961	+	0.403893i
$809$	−28.4968			−1.00189			−0.500947	−	0.865478i	$-0.667015\pi$
$809$	−28.4968			−1.00189			−0.500947	+	0.865478i	$0.667015\pi$
$810$		0			0
$811$			13.2683i			0.465912i	0.972487	+	0.232956i	$0.0748398\pi$
$811$			13.2683i			0.465912i	−0.972487	+	0.232956i	$0.925160\pi$
$812$	0.669963	−	2.82490i	0.0235111	−	0.0991345i
$813$		0			0
$814$	4.52114	−	12.6812i	0.158466	−	0.444476i
$815$	−27.4265			−0.960707
$816$		0			0
$817$			11.0028i			0.384940i
$818$	−2.33298	+	6.54369i	−0.0815707	+	0.228795i
$819$		0			0
$820$	14.1806	−	17.3595i	0.495209	−	0.606221i
$821$		−	50.5926i		−	1.76570i	−0.469659	−	0.882848i	$-0.655623\pi$
$821$		−	50.5926i		−	1.76570i	0.469659	−	0.882848i	$-0.344377\pi$
$822$		0			0
$823$		−	19.5730i		−	0.682274i	−0.940014	−	0.341137i	$-0.889188\pi$
$823$		−	19.5730i		−	0.682274i	0.940014	−	0.341137i	$-0.110812\pi$
$824$	−2.93995	−	4.86727i	−0.102418	−	0.169559i
$825$		0			0
$826$	4.71690	+	42.8599i	0.164122	+	1.49129i
$827$	4.64617			0.161563			0.0807816	−	0.996732i	$-0.474258\pi$
$827$	4.64617			0.161563			0.0807816	+	0.996732i	$0.474258\pi$
$828$		0			0
$829$	−22.2382			−0.772364			−0.386182	−	0.922423i	$-0.626206\pi$
$829$	−22.2382			−0.772364			−0.386182	+	0.922423i	$0.626206\pi$
$830$	4.60597	−	12.9191i	0.159875	−	0.448429i
$831$		0			0
$832$	2.04264	−	3.88506i	0.0708159	−	0.134690i
$833$	−2.38560	−	1.87692i	−0.0826562	−	0.0650314i
$834$		0			0
$835$	−1.30212			−0.0450619
$836$	17.2258	−	21.0874i	0.595768	−	0.729322i
$837$		0			0
$838$	1.98280	−	5.56148i	0.0684946	−	0.192118i
$839$	36.5297			1.26115			0.630573	−	0.776130i	$-0.282820\pi$
$839$	36.5297			1.26115			0.630573	+	0.776130i	$0.282820\pi$
$840$		0			0
$841$	28.6990			0.989620
$842$	−1.47886	+	4.14800i	−0.0509648	+	0.142949i
$843$		0			0
$844$	9.56148	+	7.81057i	0.329120	+	0.268851i
$845$	−20.0732			−0.690539
$846$		0			0
$847$	−14.0175	+	6.80734i	−0.481646	+	0.233903i
$848$	14.5417	−	2.96136i	0.499365	−	0.101694i
$849$		0			0
$850$	0.515144	−	1.44491i	0.0176693	−	0.0495600i
$851$	−34.7018			−1.18956
$852$		0			0
$853$	−42.1702			−1.44388			−0.721940	−	0.691956i	$-0.756749\pi$
$853$	−42.1702			−1.44388			−0.721940	+	0.691956i	$0.756749\pi$
$854$	45.1233	−	4.96600i	1.54409	−	0.169933i
$855$		0			0
$856$	26.0076	+	43.0572i	0.888921	+	1.47166i
$857$		−	37.5720i		−	1.28343i	−0.766941	−	0.641717i	$-0.778222\pi$
$857$		−	37.5720i		−	1.28343i	0.766941	−	0.641717i	$-0.221778\pi$
$858$		0			0
$859$		−	12.7543i		−	0.435170i	−0.976041	−	0.217585i	$-0.930182\pi$
$859$		−	12.7543i		−	0.435170i	0.976041	−	0.217585i	$-0.0698180\pi$
$860$	−4.47296	−	3.65387i	−0.152527	−	0.124596i
$861$		0			0
$862$	0.304691	−	0.854618i	0.0103778	−	0.0291084i
$863$			51.1449i			1.74099i	0.492175	+	0.870496i	$0.336202\pi$
$863$			51.1449i			1.74099i	−0.492175	+	0.870496i	$0.663798\pi$
$864$		0			0
$865$	−30.8599			−1.04927
$866$	3.30435	−	9.26827i	0.112287	−	0.314949i
$867$		0			0
$868$	38.6636	+	9.16960i	1.31233	+	0.311237i
$869$			23.4413i			0.795192i
$870$		0			0
$871$	−5.13050			−0.173840
$872$	−29.1572	+	17.6117i	−0.987388	+	0.596406i
$873$		0			0
$874$	−66.1080	−	23.5690i	−2.23614	−	0.797235i
$875$	−28.2201	+	13.7046i	−0.954014	+	0.463300i
$876$		0			0
$877$		−	13.8694i		−	0.468335i	−0.972196	−	0.234168i	$-0.924764\pi$
$877$		−	13.8694i		−	0.468335i	0.972196	−	0.234168i	$-0.0752365\pi$
$878$	23.1856	+	8.26619i	0.782475	+	0.278970i
$879$		0			0
$880$	2.85219	+	14.0056i	0.0961472	+	0.472129i
$881$			5.92202i			0.199518i	0.995012	+	0.0997589i	$0.0318071\pi$
$881$			5.92202i			0.199518i	−0.995012	+	0.0997589i	$0.968193\pi$
$882$		0			0
$883$	−3.17025			−0.106688			−0.0533438	−	0.998576i	$-0.516988\pi$
$883$	−3.17025			−0.106688			−0.0533438	+	0.998576i	$0.516988\pi$
$884$	−0.301032	+	0.368515i	−0.0101248	+	0.0123945i
$885$		0			0
$886$	24.0915	+	8.58918i	0.809370	+	0.288559i
$887$	−49.9010			−1.67551			−0.837756	−	0.546045i	$-0.816133\pi$
$887$	−49.9010			−1.67551			−0.837756	+	0.546045i	$0.816133\pi$
$888$		0			0
$889$	17.3283	+	35.6820i	0.581174	+	1.19674i
$890$	5.97378	−	16.7557i	0.200242	−	0.561651i
$891$		0			0
$892$	−28.5119	−	23.2908i	−0.954651	−	0.779834i
$893$		−	69.7644i		−	2.33458i
$894$		0			0
$895$	6.94891			0.232276
$896$	10.9481	−	27.8593i	0.365749	−	0.930714i
$897$		0			0
$898$	−28.2707	−	10.0792i	−0.943407	−	0.336347i
$899$		−	4.12014i		−	0.137414i
$900$		0			0
$901$	−1.60881			−0.0535972
$902$	−7.61209	+	21.3509i	−0.253455	+	0.710907i
$903$		0			0
$904$	−4.19301	−	6.94180i	−0.139458	−	0.230881i
$905$	12.8785			0.428096
$906$		0			0
$907$	−2.60938			−0.0866431			−0.0433216	−	0.999061i	$-0.513794\pi$
$907$	−2.60938			−0.0866431			−0.0433216	+	0.999061i	$0.513794\pi$
$908$	13.4835	−	16.5062i	0.447467	−	0.547776i
$909$		0			0
$910$	3.22555	−	0.354985i	0.106926	−	0.0117676i
$911$			42.9082i			1.42161i	0.703388	+	0.710807i	$0.251670\pi$
$911$			42.9082i			1.42161i	−0.703388	+	0.710807i	$0.748330\pi$
$912$		0			0
$913$			13.8698i			0.459024i
$914$	−36.9049	−	13.1575i	−1.22070	−	0.435210i
$915$		0			0
$916$	13.8954	+	11.3509i	0.459118	+	0.375044i
$917$	9.84857	+	20.2799i	0.325229	+	0.669702i
$918$		0			0
$919$			24.4217i			0.805598i	0.915288	+	0.402799i	$0.131963\pi$
$919$			24.4217i			0.805598i	−0.915288	+	0.402799i	$0.868037\pi$
$920$	31.5350	−	19.0479i	1.03968	−	0.627991i
$921$		0			0
$922$	31.3623	+	11.1814i	1.03286	+	0.368240i
$923$		−	0.702033i		−	0.0231077i
$924$		0			0
$925$		−	10.5340i		−	0.346356i
$926$	−12.7348	+	35.7193i	−0.418490	+	1.17381i
$927$		0			0
$928$	−3.07266	−	0.437944i	−0.100865	−	0.0143762i
$929$			32.9150i			1.07991i	0.841695	+	0.539954i	$0.181558\pi$
$929$			32.9150i			1.07991i	−0.841695	+	0.539954i	$0.818442\pi$
$930$		0			0
$931$	−33.1325	−	26.0676i	−1.08587	−	0.854332i
$932$	−23.0978	−	18.8681i	−0.756594	−	0.618046i
$933$		0			0
$934$	−8.25810	+	23.1628i	−0.270213	+	0.757912i
$935$		−	1.54950i		−	0.0506739i
$936$		0			0
$937$		−	41.2683i		−	1.34818i	−0.738651	−	0.674088i	$-0.764537\pi$
$937$		−	41.2683i		−	1.34818i	0.738651	−	0.674088i	$-0.235463\pi$
$938$	−34.7778	+	3.82744i	−1.13554	+	0.124970i
$939$		0			0
$940$	28.3613	+	23.1677i	0.925043	+	0.755648i
$941$	−53.4508			−1.74245			−0.871223	−	0.490887i	$-0.836673\pi$
$941$	−53.4508			−1.74245			−0.871223	+	0.490887i	$0.836673\pi$
$942$		0			0
$943$	58.4262			1.90262
$944$	45.1687	−	9.19842i	1.47012	−	0.299383i
$945$		0			0
$946$	5.50141	+	1.96138i	0.178866	+	0.0637699i
$947$	55.2631			1.79581			0.897905	−	0.440189i	$-0.145089\pi$
$947$	55.2631			1.79581			0.897905	+	0.440189i	$0.145089\pi$
$948$		0			0
$949$		−	0.475840i		−	0.0154464i
$950$	7.15458	−	20.0676i	0.232125	−	0.651080i
$951$		0			0
$952$	−1.76567	+	2.72261i	−0.0572258	+	0.0882403i
$953$	22.5760			0.731309			0.365654	−	0.930751i	$-0.380845\pi$
$953$	22.5760			0.731309			0.365654	+	0.930751i	$0.380845\pi$
$954$		0			0
$955$			0.664086i			0.0214893i
$956$	16.6218	−	20.3479i	0.537586	−	0.658097i
$957$		0			0
$958$	−34.1018	−	12.1581i	−1.10178	−	0.392810i
$959$	−11.9064	+	5.78215i	−0.384479	+	0.186715i
$960$		0			0
$961$	25.3912			0.819072
$962$	−1.09733	+	3.07786i	−0.0353793	+	0.0992341i
$963$		0			0
$964$	12.8242	−	15.6990i	0.413038	−	0.505630i
$965$	−17.6331			−0.567629
$966$		0			0
$967$		−	24.2911i		−	0.781150i	−0.920571	−	0.390575i	$-0.872276\pi$
$967$		−	24.2911i		−	0.781150i	0.920571	−	0.390575i	$-0.127724\pi$
$968$	8.61310	+	14.2595i	0.276835	+	0.458319i
$969$		0			0
$970$	14.3968	−	40.3812i	0.462255	−	1.29656i
$971$		−	24.9221i		−	0.799790i	−0.916561	−	0.399895i	$-0.869047\pi$
$971$		−	24.9221i		−	0.799790i	0.916561	−	0.399895i	$-0.130953\pi$
$972$		0			0
$973$	−16.5399	−	34.0584i	−0.530244	−	1.09186i
$974$	0.446744	−	1.25306i	0.0143146	−	0.0401505i
$975$		0			0
$976$	−9.68419	−	47.5541i	−0.309983	−	1.52217i
$977$	−1.13273			−0.0362392			−0.0181196	−	0.999836i	$-0.505768\pi$
$977$	−1.13273			−0.0362392			−0.0181196	+	0.999836i	$0.505768\pi$
$978$		0			0
$979$			17.9887i			0.574921i
$980$	21.6001	−	4.81264i	0.689989	−	0.153734i
$981$		0			0
$982$	−32.0366	−	11.4218i	−1.02233	−	0.364485i
$983$	−11.8218			−0.377056			−0.188528	−	0.982068i	$-0.560372\pi$
$983$	−11.8218			−0.377056			−0.188528	+	0.982068i	$0.560372\pi$
$984$		0			0
$985$		−	7.82499i		−	0.249325i
$986$	0.316930	+	0.112993i	0.0100931	+	0.00359842i
$987$		0			0
$988$	−4.18089	+	5.11812i	−0.133012	+	0.162829i
$989$		−	15.0545i		−	0.478704i
$990$		0			0
$991$		−	52.1176i		−	1.65557i	−0.561045	−	0.827785i	$-0.689600\pi$
$991$		−	52.1176i		−	1.65557i	0.561045	−	0.827785i	$-0.310400\pi$
$992$	5.99401	−	42.0546i	0.190310	−	1.33524i
$993$		0			0
$994$	−0.523729	−	4.75883i	−0.0166117	−	0.150941i
$995$	19.1028			0.605599
$996$		0			0
$997$	26.2326			0.830796			0.415398	−	0.909640i	$-0.363642\pi$
$997$	26.2326			0.830796			0.415398	+	0.909640i	$0.363642\pi$
$998$	35.7470	+	12.7446i	1.13155	+	0.403425i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.p.g.307.2		16
3.2	odd	2		168.2.p.a.139.16	yes	16
4.3	odd	2		2016.2.p.g.559.12		16
7.6	odd	2	inner	504.2.p.g.307.1		16
8.3	odd	2	inner	504.2.p.g.307.3		16
8.5	even	2		2016.2.p.g.559.5		16
12.11	even	2		672.2.p.a.559.3		16
21.20	even	2		168.2.p.a.139.15	yes	16
24.5	odd	2		672.2.p.a.559.6		16
24.11	even	2		168.2.p.a.139.14	yes	16
28.27	even	2		2016.2.p.g.559.6		16
56.13	odd	2		2016.2.p.g.559.11		16
56.27	even	2	inner	504.2.p.g.307.4		16
84.83	odd	2		672.2.p.a.559.14		16
168.83	odd	2		168.2.p.a.139.13	✓	16
168.125	even	2		672.2.p.a.559.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.13	✓	16	168.83	odd	2
168.2.p.a.139.14	yes	16	24.11	even	2
168.2.p.a.139.15	yes	16	21.20	even	2
168.2.p.a.139.16	yes	16	3.2	odd	2
504.2.p.g.307.1		16	7.6	odd	2	inner
504.2.p.g.307.2		16	1.1	even	1	trivial
504.2.p.g.307.3		16	8.3	odd	2	inner
504.2.p.g.307.4		16	56.27	even	2	inner
672.2.p.a.559.3		16	12.11	even	2
672.2.p.a.559.6		16	24.5	odd	2
672.2.p.a.559.11		16	168.125	even	2
672.2.p.a.559.14		16	84.83	odd	2
2016.2.p.g.559.5		16	8.5	even	2
2016.2.p.g.559.6		16	28.27	even	2
2016.2.p.g.559.11		16	56.13	odd	2
2016.2.p.g.559.12		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33209 - 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(2.37995 - 1.15578i) q^{7} +(-1.46237 - 2.42105i) q^{8} +O(q^{10})\)	\(q+(-1.33209 - 0.474920i) q^{2} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(2.37995 - 1.15578i) q^{7} +(-1.46237 - 2.42105i) q^{8} +(-2.10562 - 0.750703i) q^{10} +2.26057 q^{11} -0.548664 q^{13} +(-3.71920 + 0.409313i) q^{14} +(0.798200 + 3.91955i) q^{16} -0.433635i q^{17} -6.02255i q^{19} +(2.44834 + 2.00000i) q^{20} +(-3.01127 - 1.07359i) q^{22} +8.24028i q^{23} -2.50141 q^{25} +(0.730867 + 0.260571i) q^{26} +(5.14869 + 1.22108i) q^{28} -0.548664i q^{29} +7.50941 q^{31} +(0.798200 - 5.60026i) q^{32} +(-0.205942 + 0.577639i) q^{34} +(3.76198 - 1.82694i) q^{35} +4.21124i q^{37} +(-2.86023 + 8.02255i) q^{38} +(-2.31156 - 3.82694i) q^{40} -7.09032i q^{41} -1.82694 q^{43} +(3.50141 + 2.86023i) q^{44} +(3.91347 - 10.9768i) q^{46} +11.5839 q^{47} +(4.32834 - 5.50141i) q^{49} +(3.33209 + 1.18797i) q^{50} +(-0.849827 - 0.694206i) q^{52} -3.71005i q^{53} +3.57327 q^{55} +(-6.27857 - 4.07180i) q^{56} +(-0.260571 + 0.730867i) q^{58} -11.5240i q^{59} -12.1325 q^{61} +(-10.0032 - 3.56636i) q^{62} +(-3.72294 + 7.08094i) q^{64} -0.867270 q^{65} +9.35089 q^{67} +(0.548664 - 0.671659i) q^{68} +(-5.87892 + 0.646999i) q^{70} +1.27953i q^{71} +0.867270i q^{73} +(2.00000 - 5.60973i) q^{74} +(7.62013 - 9.32834i) q^{76} +(5.38005 - 2.61272i) q^{77} +10.3696i q^{79} +(1.26171 + 6.19561i) q^{80} +(-3.36733 + 9.44491i) q^{82} +6.13554i q^{83} -0.685444i q^{85} +(2.43364 + 0.867648i) q^{86} +(-3.30579 - 5.47295i) q^{88} +7.95759i q^{89} +(-1.30579 + 0.634135i) q^{91} +(-10.4261 + 12.7634i) q^{92} +(-15.4307 - 5.50141i) q^{94} -9.51981i q^{95} +19.1778i q^{97} +(-8.37845 + 5.27273i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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