LMFDB - Embedded newform 864.2.v.a.109.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.15
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.114947 + 1.40953i) q^{2} +(-1.97357 - 0.324044i) q^{4} +(-2.86147 + 1.18526i) q^{5} +(-2.81522 + 2.81522i) q^{7} +(0.683608 - 2.74457i) q^{8} +O(q^{10})$	\(q+(-0.114947 + 1.40953i) q^{2} +(-1.97357 - 0.324044i) q^{4} +(-2.86147 + 1.18526i) q^{5} +(-2.81522 + 2.81522i) q^{7} +(0.683608 - 2.74457i) q^{8} +(-1.34175 - 4.16959i) q^{10} +(-1.61200 - 3.89171i) q^{11} +(0.251988 + 0.104377i) q^{13} +(-3.64455 - 4.29176i) q^{14} +(3.78999 + 1.27905i) q^{16} -4.45400i q^{17} +(6.24427 + 2.58646i) q^{19} +(6.03140 - 1.41196i) q^{20} +(5.67079 - 1.82483i) q^{22} +(1.13166 + 1.13166i) q^{23} +(3.24764 - 3.24764i) q^{25} +(-0.176088 + 0.343189i) q^{26} +(6.46831 - 4.64380i) q^{28} +(-1.24837 + 3.01383i) q^{29} -6.19011 q^{31} +(-2.23851 + 5.19510i) q^{32} +(6.27807 + 0.511975i) q^{34} +(4.71891 - 11.3925i) q^{35} +(3.63120 - 1.50409i) q^{37} +(-4.36347 + 8.50420i) q^{38} +(1.29691 + 8.66377i) q^{40} +(2.17515 + 2.17515i) q^{41} +(2.48476 + 5.99874i) q^{43} +(1.92031 + 8.20293i) q^{44} +(-1.72519 + 1.46503i) q^{46} -5.97132i q^{47} -8.85098i q^{49} +(4.20436 + 4.95097i) q^{50} +(-0.463495 - 0.287651i) q^{52} +(-4.91142 - 11.8572i) q^{53} +(9.22538 + 9.22538i) q^{55} +(5.80208 + 9.65110i) q^{56} +(-4.10459 - 2.10605i) q^{58} +(8.72352 - 3.61340i) q^{59} +(4.24159 - 10.2401i) q^{61} +(0.711536 - 8.72517i) q^{62} +(-7.06536 - 3.75243i) q^{64} -0.844772 q^{65} +(5.46508 - 13.1939i) q^{67} +(-1.44329 + 8.79031i) q^{68} +(15.5156 + 7.96100i) q^{70} +(-4.47445 + 4.47445i) q^{71} +(-7.25497 - 7.25497i) q^{73} +(1.70267 + 5.29119i) q^{74} +(-11.4854 - 7.12799i) q^{76} +(15.4942 + 6.41790i) q^{77} -6.73384i q^{79} +(-12.3610 + 0.832159i) q^{80} +(-3.31598 + 2.81593i) q^{82} +(-11.1232 - 4.60738i) q^{83} +(5.27915 + 12.7450i) q^{85} +(-8.74105 + 2.81282i) q^{86} +(-11.7831 + 1.76384i) q^{88} +(0.420332 - 0.420332i) q^{89} +(-1.00325 + 0.415559i) q^{91} +(-1.86670 - 2.60011i) q^{92} +(8.41678 + 0.686387i) q^{94} -20.9334 q^{95} +0.576440 q^{97} +(12.4758 + 1.01740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−0.114947	+	1.40953i	−0.0812800	+	0.996691i
$2$	−0.114947	+	1.40953i	−0.0812800	+	0.996691i
$3$		0			0
$3$		0			0
$4$	−1.97357	−	0.324044i	−0.986787	−	0.162022i
$5$	−2.86147	+	1.18526i	−1.27969	+	0.530065i	−0.915896	−	0.401415i	$-0.868518\pi$
$5$	−2.86147	+	1.18526i	−1.27969	+	0.530065i	−0.363793	+	0.931480i	$0.618518\pi$
$6$		0			0
$7$	−2.81522	+	2.81522i	−1.06405	+	1.06405i	−0.0662521	+	0.997803i	$0.521104\pi$
$7$	−2.81522	+	2.81522i	−1.06405	+	1.06405i	−0.997803	+	0.0662521i	$0.978896\pi$
$8$	0.683608	−	2.74457i	0.241692	−	0.970353i
$9$		0			0
$10$	−1.34175	−	4.16959i	−0.424298	−	1.31854i
$11$	−1.61200	−	3.89171i	−0.486036	−	1.17339i	−0.956698	−	0.291081i	$-0.905985\pi$
$11$	−1.61200	−	3.89171i	−0.486036	−	1.17339i	0.470663	−	0.882313i	$-0.344015\pi$
$12$		0			0
$13$	0.251988	+	0.104377i	0.0698890	+	0.0289490i	0.417354	−	0.908744i	$-0.362957\pi$
$13$	0.251988	+	0.104377i	0.0698890	+	0.0289490i	−0.347465	+	0.937693i	$0.612957\pi$
$14$	−3.64455	−	4.29176i	−0.974048	−	1.14702i
$15$		0			0
$16$	3.78999	+	1.27905i	0.947498	+	0.319763i
$17$		−	4.45400i		−	1.08025i	−0.841583	−	0.540127i	$-0.818376\pi$
$17$		−	4.45400i		−	1.08025i	0.841583	−	0.540127i	$-0.181624\pi$
$18$		0			0
$19$	6.24427	+	2.58646i	1.43253	+	0.593375i	0.957976	−	0.286850i	$-0.0926080\pi$
$19$	6.24427	+	2.58646i	1.43253	+	0.593375i	0.474558	+	0.880224i	$0.342608\pi$
$20$	6.03140	−	1.41196i	1.34866	−	0.315723i
$21$		0			0
$22$	5.67079	−	1.82483i	1.20902	−	0.389054i
$23$	1.13166	+	1.13166i	0.235967	+	0.235967i	0.815178	−	0.579211i	$-0.196639\pi$
$23$	1.13166	+	1.13166i	0.235967	+	0.235967i	−0.579211	+	0.815178i	$0.696639\pi$
$24$		0			0
$25$	3.24764	−	3.24764i	0.649529	−	0.649529i
$26$	−0.176088	+	0.343189i	−0.0345338	+	0.0673048i
$27$		0			0
$28$	6.46831	−	4.64380i	1.22240	−	0.877595i
$29$	−1.24837	+	3.01383i	−0.231816	+	0.559653i	−0.996391	−	0.0848813i	$-0.972949\pi$
$29$	−1.24837	+	3.01383i	−0.231816	+	0.559653i	0.764575	+	0.644535i	$0.222949\pi$
$30$		0			0
$31$	−6.19011			−1.11178			−0.555888	−	0.831257i	$-0.687622\pi$
$31$	−6.19011			−1.11178			−0.555888	+	0.831257i	$0.687622\pi$
$32$	−2.23851	+	5.19510i	−0.395717	+	0.918372i
$33$		0			0
$34$	6.27807	+	0.511975i	1.07668	+	0.0878031i
$35$	4.71891	−	11.3925i	0.797642	−	1.92568i
$36$		0			0
$37$	3.63120	−	1.50409i	0.596966	−	0.247271i	−0.0636785	−	0.997970i	$-0.520283\pi$
$37$	3.63120	−	1.50409i	0.596966	−	0.247271i	0.660644	+	0.750699i	$0.270283\pi$
$38$	−4.36347	+	8.50420i	−0.707848	+	1.37956i
$39$		0			0
$40$	1.29691	+	8.66377i	0.205059	+	1.36986i
$41$	2.17515	+	2.17515i	0.339702	+	0.339702i	0.856255	−	0.516553i	$-0.172785\pi$
$41$	2.17515	+	2.17515i	0.339702	+	0.339702i	−0.516553	+	0.856255i	$0.672785\pi$
$42$		0			0
$43$	2.48476	+	5.99874i	0.378922	+	0.914799i	0.992168	+	0.124907i	$0.0398634\pi$
$43$	2.48476	+	5.99874i	0.378922	+	0.914799i	−0.613246	+	0.789892i	$0.710137\pi$
$44$	1.92031	+	8.20293i	0.289498	+	1.23664i
$45$		0			0
$46$	−1.72519	+	1.46503i	−0.254365	+	0.216006i
$47$		−	5.97132i		−	0.871007i	−0.900187	−	0.435503i	$-0.856570\pi$
$47$		−	5.97132i		−	0.871007i	0.900187	−	0.435503i	$-0.143430\pi$
$48$		0			0
$49$		−	8.85098i		−	1.26443i
$50$	4.20436	+	4.95097i	0.594586	+	0.700173i
$51$		0			0
$52$	−0.463495	−	0.287651i	−0.0642752	−	0.0398901i
$53$	−4.91142	−	11.8572i	−0.674635	−	1.62871i	−0.773640	−	0.633626i	$-0.781566\pi$
$53$	−4.91142	−	11.8572i	−0.674635	−	1.62871i	0.0990049	−	0.995087i	$-0.468434\pi$
$54$		0			0
$55$	9.22538	+	9.22538i	1.24395	+	1.24395i
$56$	5.80208	+	9.65110i	0.775335	+	1.28968i
$57$		0			0
$58$	−4.10459	−	2.10605i	−0.538960	−	0.276538i
$59$	8.72352	−	3.61340i	1.13571	−	0.470425i	0.265989	−	0.963976i	$-0.414301\pi$
$59$	8.72352	−	3.61340i	1.13571	−	0.470425i	0.869717	+	0.493551i	$0.164301\pi$
$60$		0			0
$61$	4.24159	−	10.2401i	0.543080	−	1.31111i	−0.379460	−	0.925208i	$-0.623890\pi$
$61$	4.24159	−	10.2401i	0.543080	−	1.31111i	0.922540	−	0.385902i	$-0.126110\pi$
$62$	0.711536	−	8.72517i	0.0903651	−	1.10810i
$63$		0			0
$64$	−7.06536	−	3.75243i	−0.883170	−	0.469053i
$65$	−0.844772			−0.104781
$66$		0			0
$67$	5.46508	−	13.1939i	0.667666	−	1.61189i	−0.117840	−	0.993033i	$-0.537597\pi$
$67$	5.46508	−	13.1939i	0.667666	−	1.61189i	0.785505	−	0.618855i	$-0.212403\pi$
$68$	−1.44329	+	8.79031i	−0.175025	+	1.06598i
$69$		0			0
$70$	15.5156	+	7.96100i	1.85447	+	0.951522i
$71$	−4.47445	+	4.47445i	−0.531019	+	0.531019i	−0.920876	−	0.389856i	$-0.872525\pi$
$71$	−4.47445	+	4.47445i	−0.531019	+	0.531019i	0.389856	+	0.920876i	$0.372525\pi$
$72$		0			0
$73$	−7.25497	−	7.25497i	−0.849130	−	0.849130i	0.140895	−	0.990025i	$-0.455002\pi$
$73$	−7.25497	−	7.25497i	−0.849130	−	0.849130i	−0.990025	+	0.140895i	$0.955002\pi$
$74$	1.70267	+	5.29119i	0.197932	+	0.615089i
$75$		0			0
$76$	−11.4854	−	7.12799i	−1.31747	−	0.817637i
$77$	15.4942	+	6.41790i	1.76572	+	0.731387i
$78$		0			0
$79$		−	6.73384i		−	0.757616i	−0.925475	−	0.378808i	$-0.876334\pi$
$79$		−	6.73384i		−	0.757616i	0.925475	−	0.378808i	$-0.123666\pi$
$80$	−12.3610	+	0.832159i	−1.38200	+	0.0930382i
$81$		0			0
$82$	−3.31598	+	2.81593i	−0.366189	+	0.310967i
$83$	−11.1232	−	4.60738i	−1.22093	−	0.505726i	−0.323225	−	0.946322i	$-0.604767\pi$
$83$	−11.1232	−	4.60738i	−1.22093	−	0.505726i	−0.897706	+	0.440596i	$0.854767\pi$
$84$		0			0
$85$	5.27915	+	12.7450i	0.572605	+	1.38239i
$86$	−8.74105	+	2.81282i	−0.942571	+	0.303314i
$87$		0			0
$88$	−11.7831	+	1.76384i	−1.25608	+	0.188026i
$89$	0.420332	−	0.420332i	0.0445552	−	0.0445552i	−0.684478	−	0.729033i	$-0.739970\pi$
$89$	0.420332	−	0.420332i	0.0445552	−	0.0445552i	0.729033	+	0.684478i	$0.239970\pi$
$90$		0			0
$91$	−1.00325	+	0.415559i	−0.105169	+	0.0435625i
$92$	−1.86670	−	2.60011i	−0.194617	−	0.271081i
$93$		0			0
$94$	8.41678	+	0.686387i	0.868125	+	0.0707954i
$95$	−20.9334			−2.14772
$96$		0			0
$97$	0.576440			0.0585286			0.0292643	−	0.999572i	$-0.490684\pi$
$97$	0.576440			0.0585286			0.0292643	+	0.999572i	$0.490684\pi$
$98$	12.4758	+	1.01740i	1.26024	+	0.102773i
$99$		0			0
$100$	−7.46185	+	5.35709i	−0.746185	+	0.535709i
$101$	−2.99242	+	1.23950i	−0.297757	+	0.123335i	−0.526560	−	0.850138i	$-0.676519\pi$
$101$	−2.99242	+	1.23950i	−0.297757	+	0.123335i	0.228804	+	0.973473i	$0.426519\pi$
$102$		0			0
$103$	−9.58310	+	9.58310i	−0.944251	+	0.944251i	−0.998526	−	0.0542747i	$-0.982715\pi$
$103$	−9.58310	+	9.58310i	−0.944251	+	0.944251i	0.0542747	+	0.998526i	$0.482715\pi$
$104$	0.458732	−	0.620248i	0.0449824	−	0.0608203i
$105$		0			0
$106$	17.2777	−	5.55986i	1.67816	−	0.540021i
$107$	2.17600	+	5.25333i	0.210362	+	0.507859i	0.993479	−	0.114016i	$-0.0363714\pi$
$107$	2.17600	+	5.25333i	0.210362	+	0.507859i	−0.783117	+	0.621874i	$0.786371\pi$
$108$		0			0
$109$	−3.58121	−	1.48338i	−0.343017	−	0.142082i	0.204523	−	0.978862i	$-0.434436\pi$
$109$	−3.58121	−	1.48338i	−0.343017	−	0.142082i	−0.547540	+	0.836779i	$0.684436\pi$
$110$	−14.0639	+	11.9431i	−1.34094	+	1.13873i
$111$		0			0
$112$	−14.2705	+	7.06886i	−1.34843	+	0.667945i
$113$		−	15.5734i		−	1.46502i	−0.680754	−	0.732512i	$-0.738348\pi$
$113$		−	15.5734i		−	1.46502i	0.680754	−	0.732512i	$-0.261652\pi$
$114$		0			0
$115$	−4.57951	−	1.89689i	−0.427041	−	0.176886i
$116$	3.44036	−	5.54348i	0.319429	−	0.514699i
$117$		0			0
$118$	4.09047	+	12.7115i	0.376558	+	1.17018i
$119$	12.5390	+	12.5390i	1.14945	+	1.14945i
$120$		0			0
$121$	−4.76868	+	4.76868i	−0.433516	+	0.433516i
$122$	13.9462	+	7.15573i	1.26263	+	0.647850i
$123$		0			0
$124$	12.2166	+	2.00587i	1.09709	+	0.180132i
$125$	0.482564	−	1.16501i	0.0431618	−	0.104202i
$126$		0			0
$127$	10.7319			0.952301			0.476150	−	0.879364i	$-0.342032\pi$
$127$	10.7319			0.952301			0.476150	+	0.879364i	$0.342032\pi$
$128$	6.10132	−	9.52754i	0.539285	−	0.842123i
$129$		0			0
$130$	0.0971042	−	1.19074i	0.00851660	−	0.104434i
$131$	−2.80094	+	6.76206i	−0.244719	+	0.590804i	−0.997740	−	0.0671924i	$-0.978596\pi$
$131$	−2.80094	+	6.76206i	−0.244719	+	0.590804i	0.753021	+	0.657997i	$0.228596\pi$
$132$		0			0
$133$	−24.8605	+	10.2976i	−2.15568	+	0.892911i
$134$	17.9690	+	9.21981i	1.55229	+	0.796471i
$135$		0			0
$136$	−12.2243	−	3.04479i	−1.04823	−	0.261089i
$137$	−13.7474	−	13.7474i	−1.17452	−	1.17452i	−0.981120	−	0.193400i	$-0.938048\pi$
$137$	−13.7474	−	13.7474i	−1.17452	−	1.17452i	−0.193400	−	0.981120i	$-0.561952\pi$
$138$		0			0
$139$	7.23175	+	17.4590i	0.613389	+	1.48085i	0.859255	+	0.511547i	$0.170928\pi$
$139$	7.23175	+	17.4590i	0.613389	+	1.48085i	−0.245866	+	0.969304i	$0.579072\pi$
$140$	−13.0048	+	20.9547i	−1.09910	+	1.77100i
$141$		0			0
$142$	−5.79256	−	6.82122i	−0.486101	−	0.572424i
$143$		−	1.14892i		−	0.0960776i
$144$		0			0
$145$		−	10.1036i		−	0.839060i
$146$	11.0601	−	9.39219i	0.915337	−	0.777303i
$147$		0			0
$148$	−7.65384	+	1.79177i	−0.629142	+	0.147282i
$149$	3.05995	+	7.38738i	0.250681	+	0.605198i	0.998259	−	0.0589759i	$-0.0187835\pi$
$149$	3.05995	+	7.38738i	0.250681	+	0.605198i	−0.747578	+	0.664174i	$0.768784\pi$
$150$		0			0
$151$	−4.24713	−	4.24713i	−0.345626	−	0.345626i	0.512851	−	0.858478i	$-0.328589\pi$
$151$	−4.24713	−	4.24713i	−0.345626	−	0.345626i	−0.858478	+	0.512851i	$0.828589\pi$
$152$	11.3674	−	15.3697i	0.922015	−	1.24665i
$153$		0			0
$154$	−10.8273	+	21.1018i	−0.872485	+	1.70044i
$155$	17.7128	−	7.33689i	1.42273	−	0.589313i
$156$		0			0
$157$	8.93871	−	21.5799i	0.713386	−	1.72227i	0.0220259	−	0.999757i	$-0.492988\pi$
$157$	8.93871	−	21.5799i	0.713386	−	1.72227i	0.691361	−	0.722510i	$-0.257012\pi$
$158$	9.49158	+	0.774036i	0.755109	+	0.0615790i
$159$		0			0
$160$	0.247901	−	17.5189i	0.0195983	−	1.38499i
$161$	−6.37173			−0.502163
$162$		0			0
$163$	−7.00310	+	16.9070i	−0.548525	+	1.32426i	0.370050	+	0.929012i	$0.379341\pi$
$163$	−7.00310	+	16.9070i	−0.548525	+	1.32426i	−0.918575	+	0.395246i	$0.870659\pi$
$164$	−3.58798	−	4.99768i	−0.280174	−	0.390253i
$165$		0			0
$166$	7.77285	−	15.1489i	0.603290	−	1.17579i
$167$	−12.5851	+	12.5851i	−0.973866	+	0.973866i	−0.999667	−	0.0258009i	$-0.991786\pi$
$167$	−12.5851	+	12.5851i	−0.973866	+	0.973866i	0.0258009	+	0.999667i	$0.491786\pi$
$168$		0			0
$169$	−9.13978	−	9.13978i	−0.703060	−	0.703060i
$170$	−18.5713	+	5.97615i	−1.42436	+	0.458349i
$171$		0			0
$172$	−2.96000	−	12.6441i	−0.225698	−	0.964106i
$173$	4.99979	+	2.07098i	0.380127	+	0.157454i	0.564561	−	0.825391i	$-0.309045\pi$
$173$	4.99979	+	2.07098i	0.380127	+	0.157454i	−0.184435	+	0.982845i	$0.559045\pi$
$174$		0			0
$175$			18.2857i			1.38227i
$176$	−1.13177	−	16.8114i	−0.0853102	−	1.26720i
$177$		0			0
$178$	0.544157	+	0.640789i	0.0407863	+	0.0480292i
$179$	13.5562	+	5.61514i	1.01323	+	0.419695i	0.826634	−	0.562740i	$-0.190253\pi$
$179$	13.5562	+	5.61514i	1.01323	+	0.419695i	0.186601	+	0.982436i	$0.440253\pi$
$180$		0			0
$181$	2.66845	+	6.44220i	0.198344	+	0.478845i	0.991489	−	0.130188i	$-0.0415580\pi$
$181$	2.66845	+	6.44220i	0.198344	+	0.478845i	−0.793145	+	0.609032i	$0.791558\pi$
$182$	−0.470425	−	1.46188i	−0.0348702	−	0.108362i
$183$		0			0
$184$	3.87952	−	2.33230i	0.286002	−	0.171940i
$185$	−8.60784	+	8.60784i	−0.632861	+	0.632861i
$186$		0			0
$187$	−17.3337	+	7.17985i	−1.26756	+	0.525042i
$188$	−1.93497	+	11.7848i	−0.141122	+	0.859498i
$189$		0			0
$190$	2.40624	−	29.5064i	0.174567	−	2.14062i
$191$	13.8714			1.00370			0.501849	−	0.864955i	$-0.332653\pi$
$191$	13.8714			1.00370			0.501849	+	0.864955i	$0.332653\pi$
$192$		0			0
$193$	−13.9970			−1.00753			−0.503764	−	0.863841i	$-0.668052\pi$
$193$	−13.9970			−1.00753			−0.503764	+	0.863841i	$0.668052\pi$
$194$	−0.0662602	+	0.812512i	−0.00475720	+	0.0583350i
$195$		0			0
$196$	−2.86811	+	17.4681i	−0.204865	+	1.24772i
$197$	19.9449	−	8.26146i	1.42102	−	0.588605i	0.465902	−	0.884837i	$-0.345730\pi$
$197$	19.9449	−	8.26146i	1.42102	−	0.588605i	0.955116	+	0.296232i	$0.0957301\pi$
$198$		0			0
$199$	−2.37495	+	2.37495i	−0.168356	+	0.168356i	−0.786256	−	0.617900i	$-0.787983\pi$
$199$	−2.37495	+	2.37495i	−0.168356	+	0.168356i	0.617900	+	0.786256i	$0.287983\pi$
$200$	−6.69328	−	11.1335i	−0.473286	−	0.787258i
$201$		0			0
$202$	−1.40315	−	4.36039i	−0.0987251	−	0.306796i
$203$	−4.97016	−	11.9990i	−0.348837	−	0.842167i
$204$		0			0
$205$	−8.80227	−	3.64602i	−0.614777	−	0.254649i
$206$	−12.4062	−	14.6093i	−0.864378	−	1.01788i
$207$		0			0
$208$	0.821530	+	0.717894i	0.0569629	+	0.0497770i
$209$		−	28.4702i		−	1.96933i
$210$		0			0
$211$	−15.0316	−	6.22631i	−1.03482	−	0.428637i	−0.200371	−	0.979720i	$-0.564215\pi$
$211$	−15.0316	−	6.22631i	−1.03482	−	0.428637i	−0.834450	+	0.551083i	$0.814215\pi$
$212$	5.85079	+	24.9926i	0.401834	+	1.71650i
$213$		0			0
$214$	−7.65487	+	2.46329i	−0.523276	+	0.168387i
$215$	−14.2201	−	14.2201i	−0.969805	−	0.969805i
$216$		0			0
$217$	17.4265	−	17.4265i	1.18299	−	1.18299i
$218$	2.50253	−	4.87732i	0.169493	−	0.330334i
$219$		0			0
$220$	−15.2175	−	21.1964i	−1.02597	−	1.42906i
$221$	0.464896	−	1.12236i	0.0312723	−	0.0754979i
$222$		0			0
$223$	5.85578			0.392132			0.196066	−	0.980591i	$-0.437183\pi$
$223$	5.85578			0.392132			0.196066	+	0.980591i	$0.437183\pi$
$224$	−8.32345	−	20.9273i	−0.556134	−	1.39826i
$225$		0			0
$226$	21.9513	+	1.79012i	1.46018	+	0.119077i
$227$	−8.60174	+	20.7664i	−0.570918	+	1.37832i	0.329857	+	0.944031i	$0.392999\pi$
$227$	−8.60174	+	20.7664i	−0.570918	+	1.37832i	−0.900775	+	0.434286i	$0.857001\pi$
$228$		0			0
$229$	16.8856	−	6.99425i	1.11583	−	0.462193i	0.252890	−	0.967495i	$-0.418619\pi$
$229$	16.8856	−	6.99425i	1.11583	−	0.462193i	0.862943	+	0.505302i	$0.168619\pi$
$230$	3.20014	−	6.23693i	0.211011	−	0.411251i
$231$		0			0
$232$	7.41827	+	5.48651i	0.487033	+	0.360207i
$233$	−16.2575	−	16.2575i	−1.06507	−	1.06507i	−0.997730	−	0.0673364i	$-0.978550\pi$
$233$	−16.2575	−	16.2575i	−1.06507	−	1.06507i	−0.0673364	−	0.997730i	$-0.521450\pi$
$234$		0			0
$235$	7.07757	+	17.0868i	0.461690	+	1.11462i
$236$	−18.3874	+	4.30451i	−1.19692	+	0.280200i
$237$		0			0
$238$	−19.1155	+	16.2329i	−1.23907	+	1.05222i
$239$		−	11.9315i		−	0.771783i	−0.922544	−	0.385891i	$-0.873894\pi$
$239$		−	11.9315i		−	0.771783i	0.922544	−	0.385891i	$-0.126106\pi$
$240$		0			0
$241$			17.7781i			1.14519i	0.819839	+	0.572594i	$0.194063\pi$
$241$			17.7781i			1.14519i	−0.819839	+	0.572594i	$0.805937\pi$
$242$	−6.17347	−	7.26976i	−0.396846	−	0.467318i
$243$		0			0
$244$	−11.6893	+	18.8351i	−0.748333	+	1.20580i
$245$	10.4907	+	25.3268i	0.670227	+	1.61807i
$246$		0			0
$247$	1.30352	+	1.30352i	0.0829408	+	0.0829408i
$248$	−4.23161	+	16.9892i	−0.268707	+	1.07882i
$249$		0			0
$250$	1.58666	+	0.814105i	0.100349	+	0.0514885i
$251$	12.1441	−	5.03027i	0.766532	−	0.317508i	0.0350650	−	0.999385i	$-0.488836\pi$
$251$	12.1441	−	5.03027i	0.766532	−	0.317508i	0.731467	+	0.681877i	$0.238836\pi$
$252$		0			0
$253$	2.57985	−	6.22830i	0.162194	−	0.391570i
$254$	−1.23360	+	15.1270i	−0.0774030	+	0.949150i
$255$		0			0
$256$	12.7281	+	9.69518i	0.795504	+	0.605949i
$257$	0.552731			0.0344784			0.0172392	−	0.999851i	$-0.494512\pi$
$257$	0.552731			0.0344784			0.0172392	+	0.999851i	$0.494512\pi$
$258$		0			0
$259$	−5.98829	+	14.4570i	−0.372094	+	0.898315i
$260$	1.66722	+	0.273743i	0.103397	+	0.0169768i
$261$		0			0
$262$	−9.20940	−	4.72530i	−0.568959	−	0.291930i
$263$	−0.913776	+	0.913776i	−0.0563459	+	0.0563459i	−0.734718	−	0.678372i	$-0.762686\pi$
$263$	−0.913776	+	0.913776i	−0.0563459	+	0.0563459i	0.678372	+	0.734718i	$0.262686\pi$
$264$		0			0
$265$	28.1078	+	28.1078i	1.72665	+	1.72665i
$266$	−11.6571	−	36.2254i	−0.714743	−	2.22112i
$267$		0			0
$268$	−15.0611	+	24.2681i	−0.920005	+	1.48241i
$269$	8.24770	+	3.41631i	0.502871	+	0.208296i	0.619674	−	0.784859i	$-0.287265\pi$
$269$	8.24770	+	3.41631i	0.502871	+	0.208296i	−0.116803	+	0.993155i	$0.537265\pi$
$270$		0			0
$271$		−	16.9938i		−	1.03230i	−0.856498	−	0.516151i	$-0.827364\pi$
$271$		−	16.9938i		−	1.03230i	0.856498	−	0.516151i	$-0.172636\pi$
$272$	5.69690	−	16.8806i	0.345425	−	1.02354i
$273$		0			0
$274$	20.9577	−	17.7972i	1.26610	−	1.07517i
$275$	−17.8741	−	7.40369i	−1.07785	−	0.446459i
$276$		0			0
$277$	−10.9387	−	26.4085i	−0.657246	−	1.58673i	−0.802041	−	0.597270i	$-0.796252\pi$
$277$	−10.9387	−	26.4085i	−0.657246	−	1.58673i	0.144795	−	0.989462i	$-0.453748\pi$
$278$	−25.4403	+	8.18653i	−1.52581	+	0.490996i
$279$		0			0
$280$	−28.0416	−	20.7394i	−1.67580	−	1.23941i
$281$	−11.4003	+	11.4003i	−0.680085	+	0.680085i	−0.960019	−	0.279934i	$-0.909687\pi$
$281$	−11.4003	+	11.4003i	−0.680085	+	0.680085i	0.279934	+	0.960019i	$0.409687\pi$
$282$		0			0
$283$	20.8562	−	8.63890i	1.23977	−	0.513529i	0.336127	−	0.941817i	$-0.390883\pi$
$283$	20.8562	−	8.63890i	1.23977	−	0.513529i	0.903643	+	0.428287i	$0.140883\pi$
$284$	10.2806	−	7.38074i	0.610040	−	0.437966i
$285$		0			0
$286$	1.61944	+	0.132065i	0.0957597	+	0.00780919i
$287$	−12.2471			−0.722923
$288$		0			0
$289$	−2.83814			−0.166950
$290$	14.2414	+	1.16138i	0.836284	+	0.0681988i
$291$		0			0
$292$	11.9673	+	16.6691i	0.700333	+	0.975488i
$293$	−0.812112	+	0.336388i	−0.0474441	+	0.0196520i	−0.406279	−	0.913749i	$-0.633174\pi$
$293$	−0.812112	+	0.336388i	−0.0474441	+	0.0196520i	0.358835	+	0.933401i	$0.383174\pi$
$294$		0			0
$295$	−20.6793	+	20.6793i	−1.20400	+	1.20400i
$296$	−1.64577	−	10.9943i	−0.0956586	−	0.639031i
$297$		0			0
$298$	−10.7645	+	3.46395i	−0.623571	+	0.200661i
$299$	0.167045	+	0.403283i	0.00966048	+	0.0233225i
$300$		0			0
$301$	−23.8830	−	9.89265i	−1.37659	−	0.570203i
$302$	6.47467	−	5.49828i	0.372575	−	0.316390i
$303$		0			0
$304$	20.3575	+	17.7894i	1.16758	+	1.02029i
$305$			34.3291i			1.96568i
$306$		0			0
$307$	−17.9175	−	7.42166i	−1.02260	−	0.423577i	−0.192567	−	0.981284i	$-0.561681\pi$
$307$	−17.9175	−	7.42166i	−1.02260	−	0.423577i	−0.830038	+	0.557707i	$0.811681\pi$
$308$	−28.4992	−	17.6870i	−1.62389	−	1.00781i
$309$		0			0
$310$	8.30556	+	25.8102i	0.471724	+	1.46592i
$311$	0.967724	+	0.967724i	0.0548746	+	0.0548746i	0.734012	−	0.679137i	$-0.237646\pi$
$311$	0.967724	+	0.967724i	0.0548746	+	0.0548746i	−0.679137	+	0.734012i	$0.737646\pi$
$312$		0			0
$313$	9.38067	−	9.38067i	0.530227	−	0.530227i	−0.390413	−	0.920640i	$-0.627668\pi$
$313$	9.38067	−	9.38067i	0.530227	−	0.530227i	0.920640	+	0.390413i	$0.127668\pi$
$314$	29.3902	+	15.0800i	1.65858	+	0.851012i
$315$		0			0
$316$	−2.18206	+	13.2897i	−0.122751	+	0.747606i
$317$	−0.114200	+	0.275703i	−0.00641412	+	0.0154850i	−0.927054	−	0.374927i	$-0.877668\pi$
$317$	−0.114200	+	0.275703i	−0.00641412	+	0.0154850i	0.920640	+	0.390413i	$0.127668\pi$
$318$		0			0
$319$	13.7413			0.769365
$320$	24.6649	+	2.36317i	1.37881	+	0.132105i
$321$		0			0
$322$	0.732413	−	8.98117i	0.0408158	−	0.500501i
$323$	11.5201	−	27.8120i	0.640996	−	1.54750i
$324$		0			0
$325$	1.15735	−	0.479389i	0.0641981	−	0.0265917i
$326$	−23.0260	−	11.8145i	−1.27529	−	0.654346i
$327$		0			0
$328$	7.45683	−	4.48292i	0.411734	−	0.247528i
$329$	16.8106	+	16.8106i	0.926799	+	0.926799i
$330$		0			0
$331$	−7.41330	−	17.8973i	−0.407472	−	0.983724i	−0.985801	−	0.167921i	$-0.946295\pi$
$331$	−7.41330	−	17.8973i	−0.407472	−	0.983724i	0.578329	−	0.815804i	$-0.303705\pi$
$332$	20.4595	+	12.6974i	1.12286	+	0.696862i
$333$		0			0
$334$	−16.2925	−	19.1858i	−0.891488	−	1.04980i
$335$			44.2314i			2.41662i
$336$		0			0
$337$		−	14.3807i		−	0.783369i	−0.920100	−	0.391685i	$-0.871892\pi$
$337$		−	14.3807i		−	0.783369i	0.920100	−	0.391685i	$-0.128108\pi$
$338$	13.9334	−	11.8322i	0.757879	−	0.643589i
$339$		0			0
$340$	−6.28886	−	26.8639i	−0.341061	−	1.45690i
$341$	9.97844	+	24.0901i	0.540363	+	1.30455i
$342$		0			0
$343$	5.21093	+	5.21093i	0.281364	+	0.281364i
$344$	18.1626	−	2.71881i	0.979261	−	0.146589i
$345$		0			0
$346$	−3.49383	+	6.80932i	−0.187829	+	0.366071i
$347$	0.654863	−	0.271253i	0.0351549	−	0.0145616i	−0.365037	−	0.930993i	$-0.618944\pi$
$347$	0.654863	−	0.271253i	0.0351549	−	0.0145616i	0.400192	+	0.916431i	$0.368944\pi$
$348$		0			0
$349$	4.71961	−	11.3942i	0.252635	−	0.609915i	−0.745780	−	0.666192i	$-0.767923\pi$
$349$	4.71961	−	11.3942i	0.252635	−	0.609915i	0.998415	+	0.0562771i	$0.0179230\pi$
$350$	−25.7743	−	2.10189i	−1.37770	−	0.112351i
$351$		0			0
$352$	23.8263	+	0.337155i	1.26995	+	0.0179704i
$353$	−12.3077			−0.655074			−0.327537	−	0.944838i	$-0.606219\pi$
$353$	−12.3077			−0.655074			−0.327537	+	0.944838i	$0.606219\pi$
$354$		0			0
$355$	7.50012	−	18.1069i	0.398065	−	0.961014i
$356$	−0.965764	+	0.693351i	−0.0511854	+	0.0367475i
$357$		0			0
$358$	−9.47298	+	18.4624i	−0.500662	+	0.975769i
$359$	−12.3853	+	12.3853i	−0.653670	+	0.653670i	−0.953875	−	0.300205i	$-0.902945\pi$
$359$	−12.3853	+	12.3853i	−0.653670	+	0.653670i	0.300205	+	0.953875i	$0.402945\pi$
$360$		0			0
$361$	18.8661	+	18.8661i	0.992952	+	0.992952i
$362$	−9.38723	+	3.02075i	−0.493382	+	0.158767i
$363$		0			0
$364$	2.11465	−	0.495040i	0.110838	−	0.0259472i
$365$	29.3589	+	12.1609i	1.53672	+	0.636528i
$366$		0			0
$367$		−	11.0077i		−	0.574597i	−0.957841	−	0.287298i	$-0.907243\pi$
$367$		−	11.0077i		−	0.574597i	0.957841	−	0.287298i	$-0.0927571\pi$
$368$	2.84152	+	5.73641i	0.148124	+	0.299031i
$369$		0			0
$370$	−11.1436	−	13.1225i	−0.579328	−	0.682206i
$371$	47.2074	+	19.5540i	2.45089	+	1.01519i
$372$		0			0
$373$	−9.58424	−	23.1384i	−0.496253	−	1.19806i	−0.951487	−	0.307689i	$-0.900444\pi$
$373$	−9.58424	−	23.1384i	−0.496253	−	1.19806i	0.455234	−	0.890372i	$-0.349556\pi$
$374$	−8.12778	−	25.2577i	−0.420278	−	1.30605i
$375$		0			0
$376$	−16.3887	−	4.08205i	−0.845184	−	0.210515i
$377$	−0.629148	+	0.629148i	−0.0324028	+	0.0324028i
$378$		0			0
$379$	−6.56938	+	2.72113i	−0.337446	+	0.139775i	−0.544971	−	0.838455i	$-0.683459\pi$
$379$	−6.56938	+	2.72113i	−0.337446	+	0.139775i	0.207525	+	0.978230i	$0.433459\pi$
$380$	41.3137	+	6.78336i	2.11935	+	0.347979i
$381$		0			0
$382$	−1.59448	+	19.5522i	−0.0815806	+	1.00038i
$383$	−10.4037			−0.531607			−0.265803	−	0.964027i	$-0.585637\pi$
$383$	−10.4037			−0.531607			−0.265803	+	0.964027i	$0.585637\pi$
$384$		0			0
$385$	−51.9430			−2.64726
$386$	1.60892	−	19.7293i	0.0818919	−	1.00419i
$387$		0			0
$388$	−1.13765	−	0.186792i	−0.0577553	−	0.00948293i
$389$	−26.8731	+	11.1312i	−1.36252	+	0.564374i	−0.939750	−	0.341863i	$-0.888942\pi$
$389$	−26.8731	+	11.1312i	−1.36252	+	0.564374i	−0.422770	+	0.906237i	$0.638942\pi$
$390$		0			0
$391$	5.04040	−	5.04040i	0.254904	−	0.254904i
$392$	−24.2922	−	6.05061i	−1.22694	−	0.305602i
$393$		0			0
$394$	9.35220	+	29.0627i	0.471157	+	1.46416i
$395$	7.98135	+	19.2687i	0.401585	+	0.969513i
$396$		0			0
$397$	23.0069	+	9.52976i	1.15468	+	0.478285i	0.876101	−	0.482127i	$-0.160136\pi$
$397$	23.0069	+	9.52976i	1.15468	+	0.478285i	0.278581	+	0.960413i	$0.410136\pi$
$398$	−3.07458	−	3.62057i	−0.154115	−	0.181483i
$399$		0			0
$400$	16.4624	−	8.15464i	0.823122	−	0.407732i
$401$			15.3915i			0.768613i	0.923205	+	0.384307i	$0.125559\pi$
$401$			15.3915i			0.768613i	−0.923205	+	0.384307i	$0.874441\pi$
$402$		0			0
$403$	−1.55984	−	0.646105i	−0.0777010	−	0.0321848i
$404$	6.30741	−	1.47657i	0.313805	−	0.0734621i
$405$		0			0
$406$	17.4844	−	5.62636i	0.867734	−	0.279231i
$407$	−11.7070	−	11.7070i	−0.580293	−	0.580293i
$408$		0			0
$409$	−2.62138	+	2.62138i	−0.129619	+	0.129619i	−0.768940	−	0.639321i	$-0.779216\pi$
$409$	−2.62138	+	2.62138i	−0.129619	+	0.129619i	0.639321	+	0.768940i	$0.279216\pi$
$410$	6.15099	−	11.9880i	0.303776	−	0.592045i
$411$		0			0
$412$	22.0183	−	15.8076i	1.08476	−	0.778785i
$413$	−14.3861	+	34.7312i	−0.707896	+	1.70901i
$414$		0			0
$415$	37.2897			1.83048
$416$	−1.10633	+	1.07546i	−0.0542422	+	0.0527285i
$417$		0			0
$418$	40.1298	+	3.27258i	1.96281	+	0.160067i
$419$	4.70335	−	11.3549i	0.229774	−	0.554723i	−0.766376	−	0.642392i	$-0.777942\pi$
$419$	4.70335	−	11.3549i	0.229774	−	0.554723i	0.996150	+	0.0876695i	$0.0279420\pi$
$420$		0			0
$421$	10.0268	−	4.15326i	0.488679	−	0.202417i	−0.124718	−	0.992192i	$-0.539803\pi$
$421$	10.0268	−	4.15326i	0.488679	−	0.202417i	0.613397	+	0.789775i	$0.289803\pi$
$422$	10.5040	−	20.4719i	0.511329	−	0.996557i
$423$		0			0
$424$	−35.9005	+	5.37405i	−1.74348	+	0.260987i
$425$	−14.4650	−	14.4650i	−0.701656	−	0.701656i
$426$		0			0
$427$	16.8872	+	40.7692i	0.817227	+	1.97296i
$428$	−2.59219	−	11.0730i	−0.125298	−	0.535232i
$429$		0			0
$430$	21.6783	−	18.4092i	1.04542	−	0.887771i
$431$			23.9686i			1.15453i	0.816559	+	0.577263i	$0.195879\pi$
$431$			23.9686i			1.15453i	−0.816559	+	0.577263i	$0.804121\pi$
$432$		0			0
$433$			17.3851i			0.835475i	0.908568	+	0.417737i	$0.137177\pi$
$433$			17.3851i			0.835475i	−0.908568	+	0.417737i	$0.862823\pi$
$434$	22.5602	+	26.5664i	1.08292	+	1.27523i
$435$		0			0
$436$	6.58710	+	4.08804i	0.315465	+	0.195782i
$437$	4.13938	+	9.99335i	0.198013	+	0.478047i
$438$		0			0
$439$	−12.9137	−	12.9137i	−0.616338	−	0.616338i	0.328252	−	0.944590i	$-0.393541\pi$
$439$	−12.9137	−	12.9137i	−0.616338	−	0.616338i	−0.944590	+	0.328252i	$0.893541\pi$
$440$	31.6263	−	19.0132i	1.50772	−	0.906417i
$441$		0			0
$442$	1.52856	+	0.784298i	0.0727063	+	0.0373053i
$443$	7.88818	−	3.26739i	0.374779	−	0.155238i	−0.187340	−	0.982295i	$-0.559987\pi$
$443$	7.88818	−	3.26739i	0.374779	−	0.155238i	0.562118	+	0.827057i	$0.309987\pi$
$444$		0			0
$445$	−0.704566	+	1.70097i	−0.0333996	+	0.0806338i
$446$	−0.673106	+	8.25392i	−0.0318725	+	0.390834i
$447$		0			0
$448$	30.4545	−	9.32665i	1.43884	−	0.440643i
$449$	−9.89758			−0.467096			−0.233548	−	0.972345i	$-0.575034\pi$
$449$	−9.89758			−0.467096			−0.233548	+	0.972345i	$0.575034\pi$
$450$		0			0
$451$	4.95872	−	11.9714i	0.233497	−	0.563712i
$452$	−5.04648	+	30.7353i	−0.237366	+	1.44567i
$453$		0			0
$454$	−28.2823	−	14.5115i	−1.32735	−	0.681058i
$455$	2.37822	−	2.37822i	0.111493	−	0.111493i
$456$		0			0
$457$	26.7445	+	26.7445i	1.25105	+	1.25105i	0.955248	+	0.295805i	$0.0955878\pi$
$457$	26.7445	+	26.7445i	1.25105	+	1.25105i	0.295805	+	0.955248i	$0.404412\pi$
$458$	7.91768	+	24.6048i	0.369969	+	1.14971i
$459$		0			0
$460$	8.42332	+	5.22763i	0.392739	+	0.243739i
$461$	−20.0912	−	8.32206i	−0.935742	−	0.387597i	−0.137888	−	0.990448i	$-0.544031\pi$
$461$	−20.0912	−	8.32206i	−0.935742	−	0.387597i	−0.797854	+	0.602851i	$0.794031\pi$
$462$		0			0
$463$		−	8.95585i		−	0.416214i	−0.978106	−	0.208107i	$-0.933270\pi$
$463$		−	8.95585i		−	0.416214i	0.978106	−	0.208107i	$-0.0667302\pi$
$464$	−8.58614	+	9.82565i	−0.398601	+	0.456144i
$465$		0			0
$466$	24.7843	−	21.0468i	1.14811	−	0.974974i
$467$	−3.41884	−	1.41613i	−0.158205	−	0.0655306i	0.302176	−	0.953252i	$-0.402287\pi$
$467$	−3.41884	−	1.41613i	−0.158205	−	0.0655306i	−0.460381	+	0.887722i	$0.652287\pi$
$468$		0			0
$469$	21.7583	+	52.5291i	1.00470	+	2.42557i
$470$	−24.8979	+	8.01200i	−1.14846	+	0.369566i
$471$		0			0
$472$	−3.95377	−	26.4125i	−0.181987	−	1.21573i
$473$	19.3399	−	19.3399i	0.889250	−	0.889250i
$474$		0			0
$475$	28.6791	−	11.8793i	1.31589	−	0.545058i
$476$	−20.6835	−	28.8099i	−0.948026	−	1.32050i
$477$		0			0
$478$	16.8178	+	1.37149i	0.769229	+	0.0627305i
$479$	20.1997			0.922949			0.461475	−	0.887153i	$-0.347321\pi$
$479$	20.1997			0.922949			0.461475	+	0.887153i	$0.347321\pi$
$480$		0			0
$481$	1.07201			0.0488796
$482$	−25.0588	−	2.04354i	−1.14140	−	0.0930808i
$483$		0			0
$484$	10.9566	−	7.86608i	0.498028	−	0.357549i
$485$	−1.64947	+	0.683232i	−0.0748984	+	0.0310239i
$486$		0			0
$487$	16.3401	−	16.3401i	0.740441	−	0.740441i	−0.232222	−	0.972663i	$-0.574600\pi$
$487$	16.3401	−	16.3401i	0.740441	−	0.740441i	0.972663	+	0.232222i	$0.0745996\pi$
$488$	−25.2051	−	18.6416i	−1.14098	−	0.843864i
$489$		0			0
$490$	−36.9049	+	11.8758i	−1.66719	+	0.536493i
$491$	−9.97577	−	24.0836i	−0.450200	−	1.08688i	−0.972246	−	0.233962i	$-0.924831\pi$
$491$	−9.97577	−	24.0836i	−0.450200	−	1.08688i	0.522045	−	0.852918i	$-0.325169\pi$
$492$		0			0
$493$	13.4236	+	5.56023i	0.604568	+	0.250420i
$494$	−1.98719	+	1.68752i	−0.0894078	+	0.0759249i
$495$		0			0
$496$	−23.4604	−	7.91746i	−1.05341	−	0.355504i
$497$		−	25.1932i		−	1.13007i
$498$		0			0
$499$	−9.83066	−	4.07199i	−0.440081	−	0.182287i	0.151631	−	0.988437i	$-0.451548\pi$
$499$	−9.83066	−	4.07199i	−0.440081	−	0.182287i	−0.591711	+	0.806150i	$0.701548\pi$
$500$	−1.32989	+	2.14287i	−0.0594745	+	0.0958319i
$501$		0			0
$502$	5.69440	+	17.6958i	0.254154	+	0.789802i
$503$	19.9292	+	19.9292i	0.888599	+	0.888599i	0.994389	−	0.105790i	$-0.0337370\pi$
$503$	19.9292	+	19.9292i	0.888599	+	0.888599i	−0.105790	+	0.994389i	$0.533737\pi$
$504$		0			0
$505$	7.09359	−	7.09359i	0.315661	−	0.315661i
$506$	8.48246	+	4.35231i	0.377091	+	0.193484i
$507$		0			0
$508$	−21.1802	−	3.47761i	−0.939718	−	0.154294i
$509$	−0.830808	+	2.00575i	−0.0368249	+	0.0889032i	−0.941222	−	0.337789i	$-0.890321\pi$
$509$	−0.830808	+	2.00575i	−0.0368249	+	0.0889032i	0.904397	+	0.426692i	$0.140321\pi$
$510$		0			0
$511$	40.8487			1.80704
$512$	−15.1287	+	16.8262i	−0.668602	+	0.743620i
$513$		0			0
$514$	−0.0635349	+	0.779094i	−0.00280241	+	0.0343643i
$515$	16.0633	−	38.7803i	0.707834	−	1.70886i
$516$		0			0
$517$	−23.2386	+	9.62576i	−1.02203	+	0.423341i
$518$	−19.6893	−	10.1025i	−0.865099	−	0.443878i
$519$		0			0
$520$	−0.577493	+	2.31854i	−0.0253247	+	0.101675i
$521$	8.36495	+	8.36495i	0.366475	+	0.366475i	0.866190	−	0.499715i	$-0.166562\pi$
$521$	8.36495	+	8.36495i	0.366475	+	0.366475i	−0.499715	+	0.866190i	$0.666562\pi$
$522$		0			0
$523$	−5.63567	−	13.6057i	−0.246430	−	0.594936i	0.751465	−	0.659773i	$-0.229347\pi$
$523$	−5.63567	−	13.6057i	−0.246430	−	0.594936i	−0.997896	+	0.0648367i	$0.979347\pi$
$524$	7.71907	−	12.4378i	0.337209	−	0.543348i
$525$		0			0
$526$	−1.18296	−	1.39303i	−0.0515796	−	0.0607392i
$527$			27.5708i			1.20100i
$528$		0			0
$529$		−	20.4387i		−	0.888640i
$530$	−42.8498	+	36.3879i	−1.86127	+	1.58059i
$531$		0			0
$532$	52.4009	−	12.2671i	2.27187	−	0.531846i
$533$	0.321078	+	0.775150i	0.0139074	+	0.0335755i
$534$		0			0
$535$	−12.4531	−	12.4531i	−0.538396	−	0.538396i
$536$	−32.4756	−	24.0187i	−1.40273	−	1.03745i
$537$		0			0
$538$	−5.76346	+	11.2327i	−0.248480	+	0.484277i
$539$	−34.4454	+	14.2678i	−1.48367	+	0.614556i
$540$		0			0
$541$	−7.64853	+	18.4652i	−0.328836	+	0.793880i	0.669843	+	0.742502i	$0.266361\pi$
$541$	−7.64853	+	18.4652i	−0.328836	+	0.793880i	−0.998679	+	0.0513776i	$0.983639\pi$
$542$	23.9534	+	1.95339i	1.02889	+	0.0839054i
$543$		0			0
$544$	23.1390	+	9.97035i	0.992076	+	0.427475i
$545$	12.0057			0.514269
$546$		0			0
$547$	8.26506	−	19.9536i	0.353389	−	0.853155i	−0.642809	−	0.766027i	$-0.722231\pi$
$547$	8.26506	−	19.9536i	0.353389	−	0.853155i	0.996197	−	0.0871286i	$-0.0277691\pi$
$548$	22.6768	+	31.5863i	0.968703	+	1.34930i
$549$		0			0
$550$	12.4903	−	24.3431i	0.532589	−	1.03799i
$551$	−15.5903	+	15.5903i	−0.664168	+	0.664168i
$552$		0			0
$553$	18.9573	+	18.9573i	0.806145	+	0.806145i
$554$	38.4810	−	12.3830i	1.63490	−	0.526102i
$555$		0			0
$556$	−8.61491	−	36.8000i	−0.365353	−	1.56067i
$557$	−27.4067	−	11.3522i	−1.16126	−	0.481009i	−0.282964	−	0.959130i	$-0.591318\pi$
$557$	−27.4067	−	11.3522i	−1.16126	−	0.481009i	−0.878294	+	0.478122i	$0.841318\pi$
$558$		0			0
$559$			1.77097i			0.0749039i
$560$	32.4562	−	37.1416i	1.37152	−	1.56952i
$561$		0			0
$562$	−14.7587	−	17.3795i	−0.622557	−	0.733112i
$563$	8.63043	+	3.57484i	0.363729	+	0.150662i	0.557060	−	0.830472i	$-0.311929\pi$
$563$	8.63043	+	3.57484i	0.363729	+	0.150662i	−0.193331	+	0.981134i	$0.561929\pi$
$564$		0			0
$565$	18.4586	+	44.5629i	0.776558	+	1.87478i
$566$	9.77947	+	30.3905i	0.411062	+	1.27741i
$567$		0			0
$568$	9.22168	+	15.3392i	0.386933	+	0.643620i
$569$	−2.60675	+	2.60675i	−0.109281	+	0.109281i	−0.759633	−	0.650352i	$-0.774621\pi$
$569$	−2.60675	+	2.60675i	−0.109281	+	0.109281i	0.650352	+	0.759633i	$0.274621\pi$
$570$		0			0
$571$	30.9581	−	12.8233i	1.29556	−	0.536637i	0.374920	−	0.927057i	$-0.377670\pi$
$571$	30.9581	−	12.8233i	1.29556	−	0.536637i	0.920637	+	0.390420i	$0.127670\pi$
$572$	−0.372301	+	2.26748i	−0.0155667	+	0.0948082i
$573$		0			0
$574$	1.40777	−	17.2627i	0.0587592	−	0.720532i
$575$	7.35043			0.306534
$576$		0			0
$577$	−46.1666			−1.92194			−0.960970	−	0.276651i	$-0.910775\pi$
$577$	−46.1666			−1.92194			−0.960970	+	0.276651i	$0.910775\pi$
$578$	0.326237	−	4.00046i	0.0135697	−	0.166397i
$579$		0			0
$580$	−3.27402	+	19.9402i	−0.135946	+	0.827973i
$581$	44.2852	−	18.3435i	1.83726	−	0.761017i
$582$		0			0
$583$	−38.2276	+	38.2276i	−1.58323	+	1.58323i
$584$	−24.8713	+	14.9522i	−1.02918	+	0.618728i
$585$		0			0
$586$	−0.380800	−	1.18337i	−0.0157307	−	0.0488844i
$587$	−3.34399	−	8.07311i	−0.138021	−	0.333213i	0.839722	−	0.543016i	$-0.182718\pi$
$587$	−3.34399	−	8.07311i	−0.138021	−	0.333213i	−0.977744	+	0.209803i	$0.932718\pi$
$588$		0			0
$589$	−38.6527	−	16.0105i	−1.59266	−	0.659700i
$590$	−26.7712	−	31.5252i	−1.10215	−	1.29787i
$591$		0			0
$592$	15.6860	−	1.05601i	0.644692	−	0.0434017i
$593$			1.23628i			0.0507679i	0.999678	+	0.0253840i	$0.00808084\pi$
$593$			1.23628i			0.0507679i	−0.999678	+	0.0253840i	$0.991919\pi$
$594$		0			0
$595$	−50.7421	−	21.0180i	−2.08022	−	0.861656i
$596$	−3.64521	−	15.5711i	−0.149314	−	0.637817i
$597$		0			0
$598$	−0.587643	+	0.189100i	−0.0240305	+	0.00773287i
$599$	1.52393	+	1.52393i	0.0622659	+	0.0622659i	0.737554	−	0.675288i	$-0.235981\pi$
$599$	1.52393	+	1.52393i	0.0622659	+	0.0622659i	−0.675288	+	0.737554i	$0.735981\pi$
$600$		0			0
$601$	18.3980	−	18.3980i	0.750470	−	0.750470i	−0.224097	−	0.974567i	$-0.571943\pi$
$601$	18.3980	−	18.3980i	0.750470	−	0.750470i	0.974567	+	0.224097i	$0.0719433\pi$
$602$	16.6893	−	32.5267i	0.680205	−	1.32569i
$603$		0			0
$604$	7.00576	+	9.75828i	0.285060	+	0.397059i
$605$	7.99331	−	19.2976i	0.324974	−	0.784558i
$606$		0			0
$607$	−37.2373			−1.51141			−0.755707	−	0.654910i	$-0.772707\pi$
$607$	−37.2373			−1.51141			−0.755707	+	0.654910i	$0.772707\pi$
$608$	−27.4148	+	26.6498i	−1.11182	+	1.08079i
$609$		0			0
$610$	−48.3881	−	3.94604i	−1.95918	−	0.159770i
$611$	0.623269	−	1.50470i	0.0252148	−	0.0608738i
$612$		0			0
$613$	−18.3188	+	7.58791i	−0.739891	+	0.306473i	−0.720609	−	0.693341i	$-0.756138\pi$
$613$	−18.3188	+	7.58791i	−0.739891	+	0.306473i	−0.0192813	+	0.999814i	$0.506138\pi$
$614$	12.5207	−	24.4022i	0.505293	−	0.984793i
$615$		0			0
$616$	28.2063	−	38.1376i	1.13647	−	1.53661i
$617$	−1.91212	−	1.91212i	−0.0769789	−	0.0769789i	0.667569	−	0.744548i	$-0.267335\pi$
$617$	−1.91212	−	1.91212i	−0.0769789	−	0.0769789i	−0.744548	+	0.667569i	$0.767335\pi$
$618$		0			0
$619$	3.60872	+	8.71222i	0.145047	+	0.350174i	0.979661	−	0.200662i	$-0.0643092\pi$
$619$	3.60872	+	8.71222i	0.145047	+	0.350174i	−0.834614	+	0.550835i	$0.814309\pi$
$620$	−37.3350	+	8.74016i	−1.49941	+	0.351013i
$621$		0			0
$622$	−1.47528	+	1.25280i	−0.0591532	+	0.0502328i
$623$			2.36666i			0.0948183i
$624$		0			0
$625$			26.8699i			1.07480i
$626$	12.1441	+	14.3007i	0.485376	+	0.571569i
$627$		0			0
$628$	−24.6341	+	39.6931i	−0.983006	+	1.58393i
$629$	−6.69923	−	16.1734i	−0.267116	−	0.644875i
$630$		0			0
$631$	−32.2728	−	32.2728i	−1.28476	−	1.28476i	−0.937928	−	0.346831i	$-0.887258\pi$
$631$	−32.2728	−	32.2728i	−1.28476	−	1.28476i	−0.346831	−	0.937928i	$-0.612742\pi$
$632$	−18.4815	−	4.60331i	−0.735155	−	0.183110i
$633$		0			0
$634$	−0.375486	−	0.192660i	−0.0149125	−	0.00765152i
$635$	−30.7090	+	12.7201i	−1.21865	+	0.504781i
$636$		0			0
$637$	0.923839	−	2.23035i	0.0366038	−	0.0883695i
$638$	−1.57952	+	19.3688i	−0.0625340	+	0.766819i
$639$		0			0
$640$	−6.16613	+	34.4944i	−0.243738	+	1.36351i
$641$	8.20747			0.324176			0.162088	−	0.986776i	$-0.448177\pi$
$641$	8.20747			0.324176			0.162088	+	0.986776i	$0.448177\pi$
$642$		0			0
$643$	−7.78566	+	18.7963i	−0.307037	+	0.741252i	0.692762	+	0.721167i	$0.256394\pi$
$643$	−7.78566	+	18.7963i	−0.307037	+	0.741252i	−0.999798	+	0.0200853i	$0.993606\pi$
$644$	12.5751	+	2.06472i	0.495528	+	0.0813615i
$645$		0			0
$646$	37.8778	+	19.4349i	1.49028	+	0.764656i
$647$	6.36993	−	6.36993i	0.250428	−	0.250428i	−0.570718	−	0.821146i	$-0.693335\pi$
$647$	6.36993	−	6.36993i	0.250428	−	0.250428i	0.821146	+	0.570718i	$0.193335\pi$
$648$		0			0
$649$	−28.1246	−	28.1246i	−1.10399	−	1.10399i
$650$	0.542682	+	1.68643i	0.0212857	+	0.0661471i
$651$		0			0
$652$	19.2998	−	31.0979i	0.755837	−	1.21789i
$653$	−12.8025	−	5.30296i	−0.501000	−	0.207521i	0.117848	−	0.993032i	$-0.462400\pi$
$653$	−12.8025	−	5.30296i	−0.501000	−	0.207521i	−0.618848	+	0.785511i	$0.712400\pi$
$654$		0			0
$655$		−	22.6693i		−	0.885763i
$656$	5.46168	+	11.0260i	0.213243	+	0.430491i
$657$		0			0
$658$	−25.6275	+	21.7628i	−0.999063	+	0.848402i
$659$	−14.9178	−	6.17917i	−0.581116	−	0.240706i	0.0727073	−	0.997353i	$-0.476836\pi$
$659$	−14.9178	−	6.17917i	−0.581116	−	0.240706i	−0.653823	+	0.756647i	$0.726836\pi$
$660$		0			0
$661$	9.32053	+	22.5017i	0.362526	+	0.875216i	0.994929	+	0.100577i	$0.0320687\pi$
$661$	9.32053	+	22.5017i	0.362526	+	0.875216i	−0.632403	+	0.774640i	$0.717931\pi$
$662$	26.0790	−	8.39206i	1.01359	−	0.326167i
$663$		0			0
$664$	−20.2492	+	27.3788i	−0.785822	+	1.06250i
$665$	58.9323	−	58.9323i	2.28530	−	2.28530i
$666$		0			0
$667$	−4.82334	+	1.99789i	−0.186760	+	0.0773587i
$668$	28.9158	−	20.7595i	1.11879	−	0.803211i
$669$		0			0
$670$	−62.3457	−	5.08428i	−2.40862	−	0.196423i
$671$	−46.6889			−1.80241
$672$		0			0
$673$	8.62566			0.332495			0.166247	−	0.986084i	$-0.446835\pi$
$673$	8.62566			0.332495			0.166247	+	0.986084i	$0.446835\pi$
$674$	20.2702	+	1.65303i	0.780777	+	0.0636722i
$675$		0			0
$676$	15.0763	+	20.9997i	0.579860	+	0.807682i
$677$	17.4562	−	7.23059i	0.670895	−	0.277894i	−0.0211197	−	0.999777i	$-0.506723\pi$
$677$	17.4562	−	7.23059i	0.670895	−	0.277894i	0.692015	+	0.721883i	$0.256723\pi$
$678$		0			0
$679$	−1.62281	+	1.62281i	−0.0622777	+	0.0622777i
$680$	38.5885	−	5.77643i	1.47980	−	0.221516i
$681$		0			0
$682$	−35.1028	+	11.2959i	−1.34416	+	0.432541i
$683$	−0.0848120	−	0.204754i	−0.00324524	−	0.00783471i	0.922249	−	0.386597i	$-0.126350\pi$
$683$	−0.0848120	−	0.204754i	−0.00324524	−	0.00783471i	−0.925494	+	0.378763i	$0.876350\pi$
$684$		0			0
$685$	55.6321	+	23.0436i	2.12559	+	0.880449i
$686$	−7.94397	+	6.74600i	−0.303302	+	0.257564i
$687$		0			0
$688$	1.74452	+	25.9133i	0.0665093	+	0.987935i
$689$		−	3.50052i		−	0.133359i
$690$		0			0
$691$	10.3264	+	4.27735i	0.392836	+	0.162718i	0.570353	−	0.821400i	$-0.306806\pi$
$691$	10.3264	+	4.27735i	0.392836	+	0.162718i	−0.177517	+	0.984118i	$0.556806\pi$
$692$	−9.19636	−	5.70738i	−0.349593	−	0.216962i
$693$		0			0
$694$	0.307066	+	0.954232i	0.0116561	+	0.0362221i
$695$	−41.3869	−	41.3869i	−1.56989	−	1.56989i
$696$		0			0
$697$	9.68815	−	9.68815i	0.366965	−	0.366965i
$698$	15.5179	+	7.96218i	0.587363	+	0.301373i
$699$		0			0
$700$	5.92537	−	36.0882i	0.223958	−	1.36401i
$701$	−6.75326	+	16.3038i	−0.255067	+	0.615786i	−0.998599	−	0.0529141i	$-0.983149\pi$
$701$	−6.75326	+	16.3038i	−0.255067	+	0.615786i	0.743532	+	0.668700i	$0.233149\pi$
$702$		0			0
$703$	26.5645			1.00190
$704$	−3.21400	+	33.5452i	−0.121132	+	1.26428i
$705$		0			0
$706$	1.41474	−	17.3481i	0.0532444	−	0.652906i
$707$	4.93486	−	11.9138i	0.185594	−	0.448065i
$708$		0			0
$709$	−24.8973	+	10.3128i	−0.935038	+	0.387305i	−0.797587	−	0.603203i	$-0.793891\pi$
$709$	−24.8973	+	10.3128i	−0.935038	+	0.387305i	−0.137450	+	0.990509i	$0.543891\pi$
$710$	24.6602	+	12.6530i	0.925480	+	0.474859i
$711$		0			0
$712$	−0.866290	−	1.44098i	−0.0324656	−	0.0540029i
$713$	−7.00507	−	7.00507i	−0.262342	−	0.262342i
$714$		0			0
$715$	1.36177	+	3.28761i	0.0509273	+	0.122949i
$716$	−24.9345	−	15.4747i	−0.931847	−	0.578316i
$717$		0			0
$718$	−16.0338	−	18.8811i	−0.598377	−	0.704638i
$719$			11.2496i			0.419538i	0.977751	+	0.209769i	$0.0672711\pi$
$719$			11.2496i			0.419538i	−0.977751	+	0.209769i	$0.932729\pi$
$720$		0			0
$721$		−	53.9572i		−	2.00947i
$722$	−28.7610	+	24.4238i	−1.07037	+	0.908959i
$723$		0			0
$724$	−3.17882	−	13.5788i	−0.118140	−	0.504654i
$725$	5.73358	+	13.8421i	0.212940	+	0.514082i
$726$		0			0
$727$	8.72990	+	8.72990i	0.323774	+	0.323774i	0.850213	−	0.526439i	$-0.176473\pi$
$727$	8.72990	+	8.72990i	0.323774	+	0.323774i	−0.526439	+	0.850213i	$0.676473\pi$
$728$	0.454704	+	3.03757i	0.0168524	+	0.112580i
$729$		0			0
$730$	−20.5159	+	39.9845i	−0.759327	+	1.47989i
$731$	26.7184	−	11.0671i	0.988216	−	0.409332i
$732$		0			0
$733$	3.44755	−	8.32313i	0.127338	−	0.307422i	−0.847334	−	0.531061i	$-0.821794\pi$
$733$	3.44755	−	8.32313i	0.127338	−	0.307422i	0.974672	+	0.223639i	$0.0717936\pi$
$734$	15.5157	+	1.26530i	0.572695	+	0.0467032i
$735$		0			0
$736$	−8.41229	+	3.34584i	−0.310081	+	0.123329i
$737$	−60.1564			−2.21589
$738$		0			0
$739$	3.96749	−	9.57838i	0.145947	−	0.352346i	−0.833954	−	0.551835i	$-0.813928\pi$
$739$	3.96749	−	9.57838i	0.145947	−	0.352346i	0.979900	+	0.199488i	$0.0639280\pi$
$740$	19.7775	−	14.1989i	0.727036	−	0.521961i
$741$		0			0
$742$	−32.9883	+	64.2928i	−1.21104	+	2.36026i
$743$	16.5554	−	16.5554i	0.607360	−	0.607360i	−0.334895	−	0.942255i	$-0.608701\pi$
$743$	16.5554	−	16.5554i	0.607360	−	0.607360i	0.942255	+	0.334895i	$0.108701\pi$
$744$		0			0
$745$	−17.5119	−	17.5119i	−0.641588	−	0.641588i
$746$	33.7161	−	10.8496i	1.23443	−	0.397233i
$747$		0			0
$748$	36.5359	−	8.55308i	1.33588	−	0.312732i
$749$	−20.9152	−	8.66337i	−0.764226	−	0.316553i
$750$		0			0
$751$		−	14.5467i		−	0.530816i	−0.964136	−	0.265408i	$-0.914493\pi$
$751$		−	14.5467i		−	0.530816i	0.964136	−	0.265408i	$-0.0855066\pi$
$752$	7.63762	−	22.6313i	0.278515	−	0.825277i
$753$		0			0
$754$	−0.814488	−	0.959125i	−0.0296619	−	0.0349293i
$755$	17.1870	+	7.11908i	0.625498	+	0.259090i
$756$		0			0
$757$	−1.09093	−	2.63375i	−0.0396507	−	0.0957252i	0.902814	−	0.430032i	$-0.141498\pi$
$757$	−1.09093	−	2.63375i	−0.0396507	−	0.0957252i	−0.942464	+	0.334307i	$0.891498\pi$
$758$	−3.08039	−	9.57255i	−0.111885	−	0.347691i
$759$		0			0
$760$	−14.3103	+	57.4533i	−0.519088	+	2.08405i
$761$	18.5594	−	18.5594i	0.672779	−	0.672779i	−0.285577	−	0.958356i	$-0.592185\pi$
$761$	18.5594	−	18.5594i	0.672779	−	0.672779i	0.958356	+	0.285577i	$0.0921851\pi$
$762$		0			0
$763$	14.2580	−	5.90584i	0.516173	−	0.213806i
$764$	−27.3762	−	4.49494i	−0.990436	−	0.162621i
$765$		0			0
$766$	1.19588	−	14.6644i	0.0432090	−	0.529848i
$767$	2.57538			0.0929917
$768$		0			0
$769$	6.33271			0.228363			0.114182	−	0.993460i	$-0.463575\pi$
$769$	6.33271			0.228363			0.114182	+	0.993460i	$0.463575\pi$
$770$	5.97071	−	73.2155i	0.215169	−	2.63850i
$771$		0			0
$772$	27.6242	+	4.53566i	0.994216	+	0.163242i
$773$	5.08175	−	2.10493i	0.182778	−	0.0757091i	−0.289418	−	0.957203i	$-0.593462\pi$
$773$	5.08175	−	2.10493i	0.182778	−	0.0757091i	0.472196	+	0.881494i	$0.343462\pi$
$774$		0			0
$775$	−20.1033	+	20.1033i	−0.722131	+	0.722131i
$776$	0.394059	−	1.58208i	0.0141459	−	0.0567934i
$777$		0			0
$778$	−12.6008	−	39.1581i	−0.451761	−	1.40388i
$779$	7.95630	+	19.2082i	0.285064	+	0.688205i
$780$		0			0
$781$	24.6261	+	10.2004i	0.881190	+	0.365001i
$782$	6.52524	+	7.68400i	0.233342	+	0.274779i
$783$		0			0
$784$	11.3209	−	33.5451i	0.404316	−	1.19804i
$785$			72.3451i			2.58211i
$786$		0			0
$787$	−7.83533	−	3.24550i	−0.279299	−	0.115690i	0.238637	−	0.971109i	$-0.423300\pi$
$787$	−7.83533	−	3.24550i	−0.279299	−	0.115690i	−0.517936	+	0.855419i	$0.673300\pi$
$788$	−42.0399	+	9.84157i	−1.49761	+	0.350591i
$789$		0			0
$790$	−28.0773	+	9.03511i	−0.998946	+	0.321455i
$791$	43.8427	+	43.8427i	1.55887	+	1.55887i
$792$		0			0
$793$	2.13766	−	2.13766i	0.0759106	−	0.0759106i
$794$	−16.0771	+	31.3336i	−0.570555	+	1.11199i
$795$		0			0
$796$	5.45674	−	3.91756i	0.193409	−	0.138854i
$797$	11.8149	−	28.5237i	0.418505	−	1.01036i	−0.564276	−	0.825586i	$-0.690845\pi$
$797$	11.8149	−	28.5237i	0.418505	−	1.01036i	0.982781	−	0.184774i	$-0.0591552\pi$
$798$		0			0
$799$	−26.5963			−0.940909
$800$	9.60193	+	24.1417i	0.339480	+	0.853539i
$801$		0			0
$802$	−21.6948	−	1.76921i	−0.766070	−	0.0624729i
$803$	−16.5392	+	39.9292i	−0.583656	+	1.40907i
$804$		0			0
$805$	18.2325	−	7.55216i	0.642612	−	0.266179i
$806$	1.09001	−	2.12437i	0.0383938	−	0.0748279i
$807$		0			0
$808$	1.35626	+	9.06024i	0.0477129	+	0.318738i
$809$	−11.1239	−	11.1239i	−0.391097	−	0.391097i	0.483981	−	0.875078i	$-0.339190\pi$
$809$	−11.1239	−	11.1239i	−0.391097	−	0.391097i	−0.875078	+	0.483981i	$0.839190\pi$
$810$		0			0
$811$	3.02057	+	7.29231i	0.106067	+	0.256068i	0.967998	−	0.250957i	$-0.0807453\pi$
$811$	3.02057	+	7.29231i	0.106067	+	0.256068i	−0.861932	+	0.507025i	$0.830745\pi$
$812$	5.92077	+	25.2915i	0.207778	+	0.887559i
$813$		0			0
$814$	17.8471	−	15.1557i	0.625540	−	0.531207i
$815$		−	56.6794i		−	1.98539i
$816$		0			0
$817$			43.8845i			1.53532i
$818$	−3.39361	−	3.99625i	−0.118655	−	0.139726i
$819$		0			0
$820$	16.1905	+	10.0480i	0.565395	+	0.350892i
$821$	−4.69123	−	11.3256i	−0.163725	−	0.395267i	0.820631	−	0.571459i	$-0.193622\pi$
$821$	−4.69123	−	11.3256i	−0.163725	−	0.395267i	−0.984356	+	0.176191i	$0.943622\pi$
$822$		0			0
$823$	−13.3252	−	13.3252i	−0.464488	−	0.464488i	0.435635	−	0.900123i	$-0.356524\pi$
$823$	−13.3252	−	13.3252i	−0.464488	−	0.464488i	−0.900123	+	0.435635i	$0.856524\pi$
$824$	19.7504	+	32.8526i	0.688039	+	1.14448i
$825$		0			0
$826$	−47.3012	−	24.2700i	−1.64582	−	0.844462i
$827$	−24.7877	+	10.2674i	−0.861953	+	0.357032i	−0.769471	−	0.638682i	$-0.779480\pi$
$827$	−24.7877	+	10.2674i	−0.861953	+	0.357032i	−0.0924817	+	0.995714i	$0.529480\pi$
$828$		0			0
$829$	12.6756	−	30.6015i	0.440241	−	1.06284i	−0.535623	−	0.844457i	$-0.679923\pi$
$829$	12.6756	−	30.6015i	0.440241	−	1.06284i	0.975864	−	0.218378i	$-0.0700766\pi$
$830$	−4.28635	+	52.5611i	−0.148781	+	1.82442i
$831$		0			0
$832$	−1.38872	−	1.68303i	−0.0481453	−	0.0583485i
$833$	−39.4223			−1.36590
$834$		0			0
$835$	21.0953	−	50.9286i	0.730034	−	1.76246i
$836$	−9.22562	+	56.1881i	−0.319075	+	1.94331i
$837$		0			0
$838$	15.4645	+	7.93475i	0.534211	+	0.274101i
$839$	14.0565	−	14.0565i	0.485284	−	0.485284i	−0.421530	−	0.906814i	$-0.638507\pi$
$839$	14.0565	−	14.0565i	0.485284	−	0.485284i	0.906814	+	0.421530i	$0.138507\pi$
$840$		0			0
$841$	12.9814	+	12.9814i	0.447634	+	0.447634i
$842$	4.70160	+	14.6106i	0.162028	+	0.503514i
$843$		0			0
$844$	27.6485	+	17.1590i	0.951699	+	0.590637i
$845$	36.9863	+	15.3202i	1.27237	+	0.527031i
$846$		0			0
$847$		−	26.8498i		−	0.922570i
$848$	−3.44825	−	51.2207i	−0.118414	−	1.75892i
$849$		0			0
$850$	22.0517	−	18.7262i	0.756366	−	0.642304i
$851$	5.81138	+	2.40715i	0.199212	+	0.0825162i
$852$		0			0
$853$	21.7957	+	52.6194i	0.746270	+	1.80166i	0.578227	+	0.815876i	$0.303745\pi$
$853$	21.7957	+	52.6194i	0.746270	+	1.80166i	0.168043	+	0.985780i	$0.446255\pi$
$854$	−59.4067	+	19.1167i	−2.03286	+	0.654161i
$855$		0			0
$856$	15.9057	−	2.38097i	0.543645	−	0.0813799i
$857$	−31.4630	+	31.4630i	−1.07476	+	1.07476i	−0.0777868	+	0.996970i	$0.524785\pi$
$857$	−31.4630	+	31.4630i	−1.07476	+	1.07476i	−0.996970	+	0.0777868i	$0.975215\pi$
$858$		0			0
$859$	1.24841	−	0.517110i	0.0425954	−	0.0176436i	−0.361284	−	0.932456i	$-0.617662\pi$
$859$	1.24841	−	0.517110i	0.0425954	−	0.0176436i	0.403879	+	0.914812i	$0.367662\pi$
$860$	23.4565	+	32.6725i	0.799862	+	1.11412i
$861$		0			0
$862$	−33.7845	−	2.75512i	−1.15071	−	0.0938398i
$863$	−46.5335			−1.58402			−0.792009	−	0.610509i	$-0.790965\pi$
$863$	−46.5335			−1.58402			−0.792009	+	0.610509i	$0.790965\pi$
$864$		0			0
$865$	−16.7614			−0.569905
$866$	−24.5049	−	1.99837i	−0.832710	−	0.0679074i
$867$		0			0
$868$	−40.0395	+	28.7456i	−1.35903	+	0.975690i
$869$	−26.2061	+	10.8549i	−0.888982	+	0.368228i
$870$		0			0
$871$	2.75427	−	2.75427i	0.0933250	−	0.0933250i
$872$	−6.51940	+	8.81483i	−0.220775	+	0.298508i
$873$		0			0
$874$	−14.5618	+	4.68589i	−0.492559	+	0.158503i
$875$	1.92125	+	4.63830i	0.0649499	+	0.156803i
$876$		0			0
$877$	−35.7696	−	14.8162i	−1.20785	−	0.500309i	−0.314324	−	0.949316i	$-0.601778\pi$
$877$	−35.7696	−	14.8162i	−1.20785	−	0.500309i	−0.893528	+	0.449007i	$0.851778\pi$
$878$	19.6867	−	16.7179i	0.664395	−	0.564203i
$879$		0			0
$880$	23.1644	+	46.7638i	0.780871	+	1.57641i
$881$		−	32.5531i		−	1.09674i	−0.836235	−	0.548371i	$-0.815248\pi$
$881$		−	32.5531i		−	1.09674i	0.836235	−	0.548371i	$-0.184752\pi$
$882$		0			0
$883$	−15.2577	−	6.31994i	−0.513462	−	0.212683i	0.110880	−	0.993834i	$-0.464633\pi$
$883$	−15.2577	−	6.31994i	−0.513462	−	0.212683i	−0.624342	+	0.781151i	$0.714633\pi$
$884$	−1.28120	+	2.06441i	−0.0430914	+	0.0694336i
$885$		0			0
$886$	3.69878	+	11.4942i	0.124263	+	0.386156i
$887$	−38.7891	−	38.7891i	−1.30241	−	1.30241i	−0.926763	−	0.375646i	$-0.877421\pi$
$887$	−38.7891	−	38.7891i	−1.30241	−	1.30241i	−0.375646	−	0.926763i	$-0.622579\pi$
$888$		0			0
$889$	−30.2127	+	30.2127i	−1.01330	+	1.01330i
$890$	−2.31659	−	1.18863i	−0.0776523	−	0.0398430i
$891$		0			0
$892$	−11.5568	−	1.89753i	−0.386951	−	0.0635340i
$893$	15.4446	−	37.2865i	0.516834	−	1.24775i
$894$		0			0
$895$	−45.4460			−1.51909
$896$	9.64558	+	43.9987i	0.322236	+	1.46989i
$897$		0			0
$898$	1.13770	−	13.9510i	0.0379655	−	0.465550i
$899$	7.72753	−	18.6559i	0.257728	−	0.622209i
$900$		0			0
$901$	−52.8120	+	21.8755i	−1.75942	+	0.728777i
$902$	16.3041	+	8.36557i	0.542868	+	0.278543i
$903$		0			0
$904$	−42.7424	−	10.6461i	−1.42159	−	0.354085i
$905$	−15.2714	−	15.2714i	−0.507637	−	0.507637i
$906$		0			0
$907$	−0.647948	−	1.56428i	−0.0215148	−	0.0519412i	0.912757	−	0.408503i	$-0.133949\pi$
$907$	−0.647948	−	1.56428i	−0.0215148	−	0.0519412i	−0.934272	+	0.356562i	$0.883949\pi$
$908$	23.7054	−	38.1968i	0.786692	−	1.26760i
$909$		0			0
$910$	3.07882	+	3.62556i	0.102062	+	0.120186i
$911$		−	15.2416i		−	0.504976i	−0.967600	−	0.252488i	$-0.918751\pi$
$911$		−	15.2416i		−	0.504976i	0.967600	−	0.252488i	$-0.0812489\pi$
$912$		0			0
$913$			50.7154i			1.67843i
$914$	−40.7714	+	34.6230i	−1.34860	+	1.14523i
$915$		0			0
$916$	−35.5915	+	8.33199i	−1.17597	+	0.275297i
$917$	−11.1515	−	26.9220i	−0.368254	−	0.889043i
$918$		0			0
$919$	18.1881	+	18.1881i	0.599969	+	0.599969i	0.940304	−	0.340336i	$-0.110541\pi$
$919$	18.1881	+	18.1881i	0.599969	+	0.599969i	−0.340336	+	0.940304i	$0.610541\pi$
$920$	−8.33675	+	11.2721i	−0.274855	+	0.371629i
$921$		0			0
$922$	14.0397	−	27.3627i	0.462371	−	0.901142i
$923$	−1.59454	+	0.660480i	−0.0524849	+	0.0217400i
$924$		0			0
$925$	6.90809	−	16.6776i	0.227137	−	0.548356i
$926$	12.6236	+	1.02945i	0.414836	+	0.0338298i
$927$		0			0
$928$	−12.8626	−	13.2319i	−0.422237	−	0.434358i
$929$	47.5709			1.56075			0.780375	−	0.625312i	$-0.215028\pi$
$929$	47.5709			1.56075			0.780375	+	0.625312i	$0.215028\pi$
$930$		0			0
$931$	22.8927	−	55.2679i	0.750279	−	1.81133i
$932$	26.8173	+	37.3536i	0.878430	+	1.22356i
$933$		0			0
$934$	2.38907	−	4.65619i	0.0781727	−	0.152355i
$935$	41.0899	−	41.0899i	1.34378	−	1.34378i
$936$		0			0
$937$	16.5877	+	16.5877i	0.541898	+	0.541898i	0.924085	−	0.382187i	$-0.124829\pi$
$937$	16.5877	+	16.5877i	0.541898	+	0.541898i	−0.382187	+	0.924085i	$0.624829\pi$
$938$	−76.5427	+	24.6310i	−2.49921	+	0.804229i
$939$		0			0
$940$	−8.43125	−	36.0155i	−0.274997	−	1.17469i
$941$	−0.0773893	−	0.0320557i	−0.00252282	−	0.00104499i	0.381422	−	0.924401i	$-0.375435\pi$
$941$	−0.0773893	−	0.0320557i	−0.00252282	−	0.00104499i	−0.383944	+	0.923356i	$0.625435\pi$
$942$		0			0
$943$			4.92305i			0.160317i
$944$	37.6838	−	2.53693i	1.22650	−	0.0825701i
$945$		0			0
$946$	25.0372	+	29.4833i	0.814030	+	0.958586i
$947$	7.87201	+	3.26069i	0.255806	+	0.105958i	0.506901	−	0.862004i	$-0.330791\pi$
$947$	7.87201	+	3.26069i	0.255806	+	0.105958i	−0.251095	+	0.967962i	$0.580791\pi$
$948$		0			0
$949$	−1.07092	−	2.58542i	−0.0347634	−	0.0839263i
$950$	13.4476	+	41.7896i	0.436299	+	1.35583i
$951$		0			0
$952$	42.9860	−	25.8425i	1.39319	−	0.837559i
$953$	−25.0680	+	25.0680i	−0.812033	+	0.812033i	−0.984938	−	0.172906i	$-0.944684\pi$
$953$	−25.0680	+	25.0680i	−0.812033	+	0.812033i	0.172906	+	0.984938i	$0.444684\pi$
$954$		0			0
$955$	−39.6926	+	16.4412i	−1.28442	+	0.532025i
$956$	−3.86632	+	23.5476i	−0.125046	+	0.761585i
$957$		0			0
$958$	−2.32190	+	28.4722i	−0.0750173	+	0.919895i
$959$	77.4041			2.49951
$960$		0			0
$961$	7.31743			0.236046
$962$	−0.123225	+	1.51104i	−0.00397293	+	0.0487179i
$963$		0			0
$964$	5.76089	−	35.0864i	0.185546	−	1.13006i
$965$	40.0521	−	16.5901i	1.28932	−	0.534055i
$966$		0			0
$967$	−23.5221	+	23.5221i	−0.756418	+	0.756418i	−0.975669	−	0.219250i	$-0.929639\pi$
$967$	−23.5221	+	23.5221i	−0.756418	+	0.756418i	0.219250	+	0.975669i	$0.429639\pi$
$968$	9.82808	+	16.3479i	0.315886	+	0.525441i
$969$		0			0
$970$	−0.773437	−	2.40352i	−0.0248336	−	0.0771722i
$971$	1.36013	+	3.28364i	0.0436485	+	0.105377i	0.944200	−	0.329372i	$-0.106837\pi$
$971$	1.36013	+	3.28364i	0.0436485	+	0.105377i	−0.900552	+	0.434749i	$0.856837\pi$
$972$		0			0
$973$	−69.5099	−	28.7920i	−2.22839	−	0.923028i
$974$	21.1537	+	24.9102i	0.677808	+	0.798174i
$975$		0			0
$976$	29.1732	−	33.3847i	0.933811	−	1.06862i
$977$		−	0.224119i		−	0.00717021i	−0.999994	−	0.00358510i	$-0.998859\pi$
$977$		−	0.224119i		−	0.00717021i	0.999994	−	0.00358510i	$-0.00114118\pi$
$978$		0			0
$979$	−2.31339	−	0.958236i	−0.0739362	−	0.0306254i
$980$	−12.4972	−	53.3838i	−0.399208	−	1.70528i
$981$		0			0
$982$	35.0934	−	11.2928i	1.11988	−	0.360369i
$983$	1.11496	+	1.11496i	0.0355616	+	0.0355616i	0.724664	−	0.689102i	$-0.241995\pi$
$983$	1.11496	+	1.11496i	0.0355616	+	0.0355616i	−0.689102	+	0.724664i	$0.741995\pi$
$984$		0			0
$985$	−47.2799	+	47.2799i	−1.50646	+	1.50646i
$986$	−9.38034	+	18.2819i	−0.298731	+	0.582214i
$987$		0			0
$988$	−2.15019	−	2.99498i	−0.0684067	−	0.0952831i
$989$	−3.97662	+	9.60040i	−0.126449	+	0.305275i
$990$		0			0
$991$	6.56184			0.208444			0.104222	−	0.994554i	$-0.466765\pi$
$991$	6.56184			0.208444			0.104222	+	0.994554i	$0.466765\pi$
$992$	13.8566	−	32.1582i	0.439949	−	1.02102i
$993$		0			0
$994$	35.5106	+	2.89588i	1.12633	+	0.0918519i
$995$	3.98092	−	9.61080i	0.126204	−	0.304683i
$996$		0			0
$997$	33.2328	−	13.7655i	1.05249	−	0.435958i	0.211713	−	0.977332i	$-0.432096\pi$
$997$	33.2328	−	13.7655i	1.05249	−	0.435958i	0.840782	+	0.541374i	$0.182096\pi$
$998$	6.86962	−	13.3886i	0.217454	−	0.423808i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.15	✓	128
3.2	odd	2	inner	864.2.v.a.109.18	yes	128
32.5	even	8	inner	864.2.v.a.325.15	yes	128
96.5	odd	8	inner	864.2.v.a.325.18	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.15	✓	128	1.1	even	1	trivial
864.2.v.a.109.18	yes	128	3.2	odd	2	inner
864.2.v.a.325.15	yes	128	32.5	even	8	inner
864.2.v.a.325.18	yes	128	96.5	odd	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.114947 + 1.40953i) q^{2} +(-1.97357 - 0.324044i) q^{4} +(-2.86147 + 1.18526i) q^{5} +(-2.81522 + 2.81522i) q^{7} +(0.683608 - 2.74457i) q^{8} +O(q^{10})\)	\(q+(-0.114947 + 1.40953i) q^{2} +(-1.97357 - 0.324044i) q^{4} +(-2.86147 + 1.18526i) q^{5} +(-2.81522 + 2.81522i) q^{7} +(0.683608 - 2.74457i) q^{8} +(-1.34175 - 4.16959i) q^{10} +(-1.61200 - 3.89171i) q^{11} +(0.251988 + 0.104377i) q^{13} +(-3.64455 - 4.29176i) q^{14} +(3.78999 + 1.27905i) q^{16} -4.45400i q^{17} +(6.24427 + 2.58646i) q^{19} +(6.03140 - 1.41196i) q^{20} +(5.67079 - 1.82483i) q^{22} +(1.13166 + 1.13166i) q^{23} +(3.24764 - 3.24764i) q^{25} +(-0.176088 + 0.343189i) q^{26} +(6.46831 - 4.64380i) q^{28} +(-1.24837 + 3.01383i) q^{29} -6.19011 q^{31} +(-2.23851 + 5.19510i) q^{32} +(6.27807 + 0.511975i) q^{34} +(4.71891 - 11.3925i) q^{35} +(3.63120 - 1.50409i) q^{37} +(-4.36347 + 8.50420i) q^{38} +(1.29691 + 8.66377i) q^{40} +(2.17515 + 2.17515i) q^{41} +(2.48476 + 5.99874i) q^{43} +(1.92031 + 8.20293i) q^{44} +(-1.72519 + 1.46503i) q^{46} -5.97132i q^{47} -8.85098i q^{49} +(4.20436 + 4.95097i) q^{50} +(-0.463495 - 0.287651i) q^{52} +(-4.91142 - 11.8572i) q^{53} +(9.22538 + 9.22538i) q^{55} +(5.80208 + 9.65110i) q^{56} +(-4.10459 - 2.10605i) q^{58} +(8.72352 - 3.61340i) q^{59} +(4.24159 - 10.2401i) q^{61} +(0.711536 - 8.72517i) q^{62} +(-7.06536 - 3.75243i) q^{64} -0.844772 q^{65} +(5.46508 - 13.1939i) q^{67} +(-1.44329 + 8.79031i) q^{68} +(15.5156 + 7.96100i) q^{70} +(-4.47445 + 4.47445i) q^{71} +(-7.25497 - 7.25497i) q^{73} +(1.70267 + 5.29119i) q^{74} +(-11.4854 - 7.12799i) q^{76} +(15.4942 + 6.41790i) q^{77} -6.73384i q^{79} +(-12.3610 + 0.832159i) q^{80} +(-3.31598 + 2.81593i) q^{82} +(-11.1232 - 4.60738i) q^{83} +(5.27915 + 12.7450i) q^{85} +(-8.74105 + 2.81282i) q^{86} +(-11.7831 + 1.76384i) q^{88} +(0.420332 - 0.420332i) q^{89} +(-1.00325 + 0.415559i) q^{91} +(-1.86670 - 2.60011i) q^{92} +(8.41678 + 0.686387i) q^{94} -20.9334 q^{95} +0.576440 q^{97} +(12.4758 + 1.01740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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