LMFDB - Embedded newform 684.2.r.a.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(487,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("684.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.r (of order $6$, degree $2$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 3 x^{15} + 6 x^{14} - 9 x^{13} + 12 x^{12} - 9 x^{11} + 3 x^{10} + 6 x^{9} - 10 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 6x^14 - 9x^13 + 12x^12 - 9x^11 + 3x^10 + 6x^9 - 10x^8 + 12x^7 + 12x^6 - 72x^5 + 192x^4 - 288x^3 + 384x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			487.5
Root			$0.570443 - 1.29406i$ of defining polynomial
Character	$\chi$	$=$	684.487
Dual form			684.2.r.a.559.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.570443 + 1.29406i) q^{2} +(-1.34919 + 1.47638i) q^{4} +(1.60333 + 2.77705i) q^{5} +1.25044i q^{7} +(-2.68016 - 0.903746i) q^{8} +(-2.67906 + 3.65895i) q^{10} +2.11093i q^{11} +(2.12978 + 1.22963i) q^{13} +(-1.61815 + 0.713305i) q^{14} +(-0.359374 - 3.98382i) q^{16} +(-0.765026 - 1.32506i) q^{17} +(3.76307 - 2.19984i) q^{19} +(-6.26316 - 1.37965i) q^{20} +(-2.73167 + 1.20416i) q^{22} +(-7.61951 - 4.39913i) q^{23} +(-2.64132 + 4.57491i) q^{25} +(-0.376297 + 3.45750i) q^{26} +(-1.84612 - 1.68708i) q^{28} +(5.20937 + 3.00763i) q^{29} -7.78947 q^{31} +(4.95031 - 2.73760i) q^{32} +(1.27831 - 1.74586i) q^{34} +(-3.47253 + 2.00487i) q^{35} +9.97599i q^{37} +(4.99335 + 3.61476i) q^{38} +(-1.78743 - 8.89192i) q^{40} +(-1.09450 + 0.631908i) q^{41} +(5.04619 - 2.91342i) q^{43} +(-3.11653 - 2.84804i) q^{44} +(1.34624 - 12.3696i) q^{46} +(6.12910 + 3.53864i) q^{47} +5.43640 q^{49} +(-7.42693 - 0.808311i) q^{50} +(-4.68887 + 1.48535i) q^{52} +(-6.18988 - 3.57373i) q^{53} +(-5.86215 + 3.38451i) q^{55} +(1.13008 - 3.35138i) q^{56} +(-0.920411 + 8.45692i) q^{58} +(-2.83541 - 4.91107i) q^{59} +(2.80998 - 4.86704i) q^{61} +(-4.44345 - 10.0801i) q^{62} +(6.36649 + 4.84436i) q^{64} +7.88599i q^{65} +(0.0235835 - 0.0408478i) q^{67} +(2.98846 + 0.658296i) q^{68} +(-4.57530 - 3.35000i) q^{70} +(-3.12595 - 5.41430i) q^{71} +(0.658098 + 1.13986i) q^{73} +(-12.9095 + 5.69073i) q^{74} +(-1.82930 + 8.52371i) q^{76} -2.63959 q^{77} +(3.77194 + 6.53320i) q^{79} +(10.4871 - 7.38538i) q^{80} +(-1.44208 - 1.05588i) q^{82} +7.84164i q^{83} +(2.45317 - 4.24902i) q^{85} +(6.64871 + 4.86814i) q^{86} +(1.90774 - 5.65762i) q^{88} +(6.02458 + 3.47830i) q^{89} +(-1.53758 + 2.66316i) q^{91} +(16.7749 - 5.31401i) q^{92} +(-1.08291 + 9.95003i) q^{94} +(12.1425 + 6.92315i) q^{95} +(8.51935 - 4.91865i) q^{97} +(3.10116 + 7.03503i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 3 q^{4} + 2 q^{5} - 6 q^{10} - 18 q^{13} + 6 q^{14} - 3 q^{16} - 2 q^{17} - 4 q^{20} + 3 q^{22} - 2 q^{25} + 24 q^{26} - 4 q^{28} + 6 q^{29} - 27 q^{32} + 36 q^{34} + 24 q^{38} + 48 q^{40}+ \cdots - 51 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 3 * q^4 + 2 * q^5 - 6 * q^10 - 18 * q^13 + 6 * q^14 - 3 * q^16 - 2 * q^17 - 4 * q^20 + 3 * q^22 - 2 * q^25 + 24 * q^26 - 4 * q^28 + 6 * q^29 - 27 * q^32 + 36 * q^34 + 24 * q^38 + 48 * q^40 + 48 * q^41 + 25 * q^44 + 16 * q^49 + 6 * q^52 - 6 * q^53 - 40 * q^58 - 26 * q^61 - 32 * q^62 - 18 * q^64 + 36 * q^68 - 54 * q^70 + 16 * q^73 + 2 * q^74 + 43 * q^76 - 80 * q^77 + 30 * q^80 + 11 * q^82 + 14 * q^85 + 48 * q^86 - 18 * q^89 + 52 * q^92 - 12 * q^97 - 51 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.570443	+	1.29406i	0.403364	+	0.915040i
$2$	0.570443	+	1.29406i	0.403364	+	0.915040i
$3$		0			0
$3$		0			0
$4$	−1.34919	+	1.47638i	−0.674595	+	0.738188i
$5$	1.60333	+	2.77705i	0.717030	+	1.24193i	0.962171	+	0.272445i	$0.0878324\pi$
$5$	1.60333	+	2.77705i	0.717030	+	1.24193i	−0.245141	+	0.969487i	$0.578834\pi$
$6$		0			0
$7$			1.25044i			0.472622i	0.971677	+	0.236311i	$0.0759384\pi$
$7$			1.25044i			0.472622i	−0.971677	+	0.236311i	$0.924062\pi$
$8$	−2.68016	−	0.903746i	−0.947579	−	0.319522i
$9$		0			0
$10$	−2.67906	+	3.65895i	−0.847193	+	1.15706i
$11$			2.11093i			0.636469i	0.948012	+	0.318234i	$0.103090\pi$
$11$			2.11093i			0.636469i	−0.948012	+	0.318234i	$0.896910\pi$
$12$		0			0
$13$	2.12978	+	1.22963i	0.590695	+	0.341038i	0.765372	−	0.643588i	$-0.222555\pi$
$13$	2.12978	+	1.22963i	0.590695	+	0.341038i	−0.174678	+	0.984626i	$0.555888\pi$
$14$	−1.61815	+	0.713305i	−0.432468	+	0.190639i
$15$		0			0
$16$	−0.359374	−	3.98382i	−0.0898436	−	0.995956i
$17$	−0.765026	−	1.32506i	−0.185546	−	0.321375i	0.758214	−	0.652005i	$-0.226072\pi$
$17$	−0.765026	−	1.32506i	−0.185546	−	0.321375i	−0.943760	+	0.330630i	$0.892739\pi$
$18$		0			0
$19$	3.76307	−	2.19984i	0.863308	−	0.504678i
$19$	3.76307	−	2.19984i	0.863308	−	0.504678i
$20$	−6.26316	−	1.37965i	−1.40048	−	0.308498i
$21$		0			0
$22$	−2.73167	+	1.20416i	−0.582394	+	0.256729i
$23$	−7.61951	−	4.39913i	−1.58878	−	0.917282i	−0.993509	−	0.113756i	$-0.963712\pi$
$23$	−7.61951	−	4.39913i	−1.58878	−	0.917282i	−0.595270	−	0.803526i	$-0.702955\pi$
$24$		0			0
$25$	−2.64132	+	4.57491i	−0.528265	+	0.914981i
$26$	−0.376297	+	3.45750i	−0.0737980	+	0.678071i
$27$		0			0
$28$	−1.84612	−	1.68708i	−0.348884	−	0.318828i
$29$	5.20937	+	3.00763i	0.967356	+	0.558503i	0.898429	−	0.439119i	$-0.144709\pi$
$29$	5.20937	+	3.00763i	0.967356	+	0.558503i	0.0689265	+	0.997622i	$0.478043\pi$
$30$		0			0
$31$	−7.78947			−1.39903			−0.699515	−	0.714618i	$-0.746601\pi$
$31$	−7.78947			−1.39903			−0.699515	+	0.714618i	$0.746601\pi$
$32$	4.95031	−	2.73760i	0.875099	−	0.483943i
$33$		0			0
$34$	1.27831	−	1.74586i	0.219228	−	0.299413i
$35$	−3.47253	+	2.00487i	−0.586965	+	0.338884i
$36$		0			0
$37$			9.97599i			1.64004i	0.572334	+	0.820021i	$0.306038\pi$
$37$			9.97599i			1.64004i	−0.572334	+	0.820021i	$0.693962\pi$
$38$	4.99335	+	3.61476i	0.810028	+	0.586391i
$39$		0			0
$40$	−1.78743	−	8.89192i	−0.282617	−	1.40594i
$41$	−1.09450	+	0.631908i	−0.170932	+	0.0986875i	−0.583025	−	0.812454i	$-0.698131\pi$
$41$	−1.09450	+	0.631908i	−0.170932	+	0.0986875i	0.412093	+	0.911142i	$0.364798\pi$
$42$		0			0
$43$	5.04619	−	2.91342i	0.769537	−	0.444292i	−0.0631725	−	0.998003i	$-0.520122\pi$
$43$	5.04619	−	2.91342i	0.769537	−	0.444292i	0.832709	+	0.553710i	$0.186789\pi$
$44$	−3.11653	−	2.84804i	−0.469834	−	0.429359i
$45$		0			0
$46$	1.34624	−	12.3696i	0.198493	−	1.82379i
$47$	6.12910	+	3.53864i	0.894022	+	0.516164i	0.875256	−	0.483660i	$-0.160693\pi$
$47$	6.12910	+	3.53864i	0.894022	+	0.516164i	0.0187658	+	0.999824i	$0.494026\pi$
$48$		0			0
$49$	5.43640			0.776629
$50$	−7.42693	−	0.808311i	−1.05033	−	0.114312i
$51$		0			0
$52$	−4.68887	+	1.48535i	−0.650230	+	0.205982i
$53$	−6.18988	−	3.57373i	−0.850246	−	0.490890i	0.0104881	−	0.999945i	$-0.496661\pi$
$53$	−6.18988	−	3.57373i	−0.850246	−	0.490890i	−0.860734	+	0.509055i	$0.829995\pi$
$54$		0			0
$55$	−5.86215	+	3.38451i	−0.790452	+	0.456367i
$56$	1.13008	−	3.35138i	0.151013	−	0.447846i
$57$		0			0
$58$	−0.920411	+	8.45692i	−0.120856	+	1.11045i
$59$	−2.83541	−	4.91107i	−0.369138	−	0.639367i	0.620293	−	0.784371i	$-0.287014\pi$
$59$	−2.83541	−	4.91107i	−0.369138	−	0.639367i	−0.989431	+	0.145004i	$0.953681\pi$
$60$		0			0
$61$	2.80998	−	4.86704i	0.359782	−	0.623160i	−0.628142	−	0.778098i	$-0.716185\pi$
$61$	2.80998	−	4.86704i	0.359782	−	0.623160i	0.987924	+	0.154938i	$0.0495178\pi$
$62$	−4.44345	−	10.0801i	−0.564319	−	1.28017i
$63$		0			0
$64$	6.36649	+	4.84436i	0.795811	+	0.605545i
$65$			7.88599i			0.978137i
$66$		0			0
$67$	0.0235835	−	0.0408478i	0.00288118	−	0.00499036i	−0.864581	−	0.502493i	$-0.832416\pi$
$67$	0.0235835	−	0.0408478i	0.00288118	−	0.00499036i	0.867462	+	0.497503i	$0.165750\pi$
$68$	2.98846	+	0.658296i	0.362404	+	0.0798301i
$69$		0			0
$70$	−4.57530	−	3.35000i	−0.546853	−	0.400402i
$71$	−3.12595	−	5.41430i	−0.370982	−	0.642559i	0.618735	−	0.785600i	$-0.287645\pi$
$71$	−3.12595	−	5.41430i	−0.370982	−	0.642559i	−0.989717	+	0.143041i	$0.954312\pi$
$72$		0			0
$73$	0.658098	+	1.13986i	0.0770245	+	0.133410i	0.901965	−	0.431809i	$-0.142125\pi$
$73$	0.658098	+	1.13986i	0.0770245	+	0.133410i	−0.824940	+	0.565220i	$0.808791\pi$
$74$	−12.9095	+	5.69073i	−1.50070	+	0.661534i
$75$		0			0
$76$	−1.82930	+	8.52371i	−0.209835	+	0.977737i
$77$	−2.63959			−0.300809
$78$		0			0
$79$	3.77194	+	6.53320i	0.424377	+	0.735042i	0.996362	−	0.0852216i	$-0.0271598\pi$
$79$	3.77194	+	6.53320i	0.424377	+	0.735042i	−0.571985	+	0.820264i	$0.693826\pi$
$80$	10.4871	−	7.38538i	1.17249	−	0.825710i
$81$		0			0
$82$	−1.44208	−	1.05588i	−0.159251	−	0.116602i
$83$			7.84164i			0.860732i	0.902655	+	0.430366i	$0.141615\pi$
$83$			7.84164i			0.860732i	−0.902655	+	0.430366i	$0.858385\pi$
$84$		0			0
$85$	2.45317	−	4.24902i	0.266084	−	0.460871i
$86$	6.64871	+	4.86814i	0.716949	+	0.524945i
$87$		0			0
$88$	1.90774	−	5.65762i	0.203366	−	0.603104i
$89$	6.02458	+	3.47830i	0.638605	+	0.368699i	0.784077	−	0.620664i	$-0.213137\pi$
$89$	6.02458	+	3.47830i	0.638605	+	0.368699i	−0.145472	+	0.989362i	$0.546470\pi$
$90$		0			0
$91$	−1.53758	+	2.66316i	−0.161182	+	0.279175i
$92$	16.7749	−	5.31401i	1.74891	−	0.554024i
$93$		0			0
$94$	−1.08291	+	9.95003i	−0.111694	+	1.02627i
$95$	12.1425	+	6.92315i	1.24579	+	0.710300i
$96$		0			0
$97$	8.51935	−	4.91865i	0.865009	−	0.499413i	−0.000677265	−	1.00000i	$-0.500216\pi$
$97$	8.51935	−	4.91865i	0.865009	−	0.499413i	0.865687	+	0.500586i	$0.166882\pi$
$98$	3.10116	+	7.03503i	0.313264	+	0.710646i
$99$		0			0
$100$	−3.19064	−	10.0720i	−0.319064	−	1.00720i
$101$	3.13338	−	5.42717i	0.311783	−	0.540024i	−0.666965	−	0.745089i	$-0.732407\pi$
$101$	3.13338	−	5.42717i	0.311783	−	0.540024i	0.978748	+	0.205065i	$0.0657405\pi$
$102$		0			0
$103$	−0.526662			−0.0518936			−0.0259468	−	0.999663i	$-0.508260\pi$
$103$	−0.526662			−0.0518936			−0.0259468	+	0.999663i	$0.508260\pi$
$104$	−4.59687	−	5.22038i	−0.450760	−	0.511900i
$105$		0			0
$106$	1.09365	−	10.0487i	0.106225	−	0.976016i
$107$	6.91564			0.668560			0.334280	−	0.942474i	$-0.391507\pi$
$107$	6.91564			0.668560			0.334280	+	0.942474i	$0.391507\pi$
$108$		0			0
$109$	−10.4902	+	6.05651i	−1.00478	+	0.580109i	−0.909658	−	0.415357i	$-0.863657\pi$
$109$	−10.4902	+	6.05651i	−1.00478	+	0.580109i	−0.0951195	+	0.995466i	$0.530323\pi$
$110$	−7.72379	−	5.65531i	−0.736434	−	0.539212i
$111$		0			0
$112$	4.98153	−	0.449376i	0.470711	−	0.0424621i
$113$			4.95424i			0.466056i	0.972470	+	0.233028i	$0.0748633\pi$
$113$			4.95424i			0.466056i	−0.972470	+	0.233028i	$0.925137\pi$
$114$		0			0
$115$		−	28.2130i		−	2.63087i
$116$	−11.4688	+	3.63313i	−1.06485	+	0.337327i
$117$		0			0
$118$	4.73779	−	6.47067i	0.436149	−	0.595674i
$119$	1.65691	−	0.956619i	0.151889	−	0.0876931i
$120$		0			0
$121$	6.54398			0.594907
$122$	7.90118	+	0.859926i	0.715339	+	0.0778541i
$123$		0			0
$124$	10.5095	−	11.5002i	0.943779	−	1.03275i
$125$	−0.906349			−0.0810663
$126$		0			0
$127$	−2.86262	+	4.95820i	−0.254016	+	0.439969i	−0.964628	−	0.263616i	$-0.915085\pi$
$127$	−2.86262	+	4.95820i	−0.254016	+	0.439969i	0.710612	+	0.703584i	$0.248418\pi$
$128$	−2.63718	+	11.0021i	−0.233096	+	0.972454i
$129$		0			0
$130$	−10.2050	+	4.49851i	−0.895034	+	0.394545i
$131$	16.1689	−	9.33512i	1.41268	−	0.815613i	0.417043	−	0.908887i	$-0.363067\pi$
$131$	16.1689	−	9.33512i	1.41268	−	0.815613i	0.995640	+	0.0932738i	$0.0297332\pi$
$132$		0			0
$133$	2.75077	+	4.70549i	0.238522	+	0.408018i
$134$	0.0663126	+	0.00721715i	0.00572854	+	0.000623466i
$135$		0			0
$136$	0.852869	+	4.24277i	0.0731329	+	0.363814i
$137$	9.96622	−	17.2620i	0.851471	−	1.47479i	−0.0284092	−	0.999596i	$-0.509044\pi$
$137$	9.96622	−	17.2620i	0.851471	−	1.47479i	0.879880	−	0.475195i	$-0.157623\pi$
$138$		0			0
$139$	9.04013	+	5.21932i	0.766774	+	0.442697i	0.831723	−	0.555191i	$-0.187355\pi$
$139$	9.04013	+	5.21932i	0.766774	+	0.442697i	−0.0649485	+	0.997889i	$0.520688\pi$
$140$	1.72516	−	7.83170i	0.145803	−	0.661900i
$141$		0			0
$142$	5.22326	−	7.13372i	0.438326	−	0.598648i
$143$	−2.59566	+	4.49581i	−0.217060	+	0.375959i
$144$		0			0
$145$			19.2889i			1.60185i
$146$	−1.09964	+	1.50184i	−0.0910068	+	0.124293i
$147$		0			0
$148$	−14.7283	−	13.4595i	−1.21066	−	1.10636i
$149$	4.83307	+	8.37113i	0.395941	+	0.685789i	0.993221	−	0.116243i	$-0.0370853\pi$
$149$	4.83307	+	8.37113i	0.395941	+	0.685789i	−0.597280	+	0.802033i	$0.703752\pi$
$150$		0			0
$151$	11.1033			0.903573			0.451787	−	0.892126i	$-0.350787\pi$
$151$	11.1033			0.903573			0.451787	+	0.892126i	$0.350787\pi$
$152$	−12.0737	+	2.49506i	−0.979308	+	0.202376i
$153$		0			0
$154$	−1.50574	−	3.41579i	−0.121336	−	0.275252i
$155$	−12.4891	−	21.6317i	−1.00315	−	1.73750i
$156$		0			0
$157$	−5.65983	−	9.80311i	−0.451704	−	0.782374i	0.546788	−	0.837271i	$-0.315850\pi$
$157$	−5.65983	−	9.80311i	−0.451704	−	0.782374i	−0.998492	+	0.0548972i	$0.982517\pi$
$158$	−6.30268	+	8.60795i	−0.501414	+	0.684811i
$159$		0			0
$160$	15.5394	+	9.35797i	1.22850	+	0.739813i
$161$	5.50085	−	9.52774i	0.433527	−	0.750891i
$162$		0			0
$163$			15.6778i			1.22798i	0.789312	+	0.613992i	$0.210437\pi$
$163$			15.6778i			1.22798i	−0.789312	+	0.613992i	$0.789563\pi$
$164$	0.543750	−	2.46845i	0.0424597	−	0.192754i
$165$		0			0
$166$	−10.1476	+	4.47321i	−0.787603	+	0.347188i
$167$	−1.80453	+	3.12555i	−0.139639	+	0.241862i	−0.927360	−	0.374170i	$-0.877928\pi$
$167$	−1.80453	+	3.12555i	−0.139639	+	0.241862i	0.787721	+	0.616032i	$0.211261\pi$
$168$		0			0
$169$	−3.47603	−	6.02065i	−0.267387	−	0.463127i
$170$	6.89789	+	0.750733i	0.529044	+	0.0575786i
$171$		0			0
$172$	−2.50696	+	11.3808i	−0.191154	+	0.867780i
$173$	4.46906	−	2.58021i	0.339776	−	0.196170i	−0.320397	−	0.947283i	$-0.603816\pi$
$173$	4.46906	−	2.58021i	0.339776	−	0.196170i	0.660173	+	0.751113i	$0.270483\pi$
$174$		0			0
$175$	−5.72065	−	3.30282i	−0.432440	−	0.249669i
$176$	8.40957	−	0.758614i	0.633895	−	0.0571827i
$177$		0			0
$178$	−1.06445	+	9.78035i	−0.0797836	+	0.733068i
$179$	2.76216			0.206454			0.103227	−	0.994658i	$-0.467083\pi$
$179$	2.76216			0.206454			0.103227	+	0.994658i	$0.467083\pi$
$180$		0			0
$181$	2.07870	+	1.20014i	0.154509	+	0.0892056i	0.575261	−	0.817970i	$-0.304901\pi$
$181$	2.07870	+	1.20014i	0.154509	+	0.0892056i	−0.420752	+	0.907176i	$0.638234\pi$
$182$	−4.32339	−	0.470537i	−0.320471	−	0.0348785i
$183$		0			0
$184$	16.4458	+	18.6765i	1.21240	+	1.37685i
$185$	−27.7038	+	15.9948i	−2.03682	+	1.17596i
$186$		0			0
$187$	2.79711	−	1.61491i	0.204545	−	0.118094i
$188$	−13.4937	+	4.27457i	−0.984128	+	0.311755i
$189$		0			0
$190$	−2.03238	+	19.6624i	−0.147444	+	1.42646i
$191$			4.38525i			0.317305i	0.987334	+	0.158653i	$0.0507150\pi$
$191$			4.38525i			0.317305i	−0.987334	+	0.158653i	$0.949285\pi$
$192$		0			0
$193$	−7.76503	+	4.48314i	−0.558939	+	0.322703i	−0.752719	−	0.658341i	$-0.771258\pi$
$193$	−7.76503	+	4.48314i	−0.558939	+	0.322703i	0.193781	+	0.981045i	$0.437925\pi$
$194$	11.2248	+	8.21876i	0.805897	+	0.590072i
$195$		0			0
$196$	−7.33473	+	8.02617i	−0.523910	+	0.573298i
$197$	−1.39218			−0.0991890			−0.0495945	−	0.998769i	$-0.515793\pi$
$197$	−1.39218			−0.0991890			−0.0495945	+	0.998769i	$0.515793\pi$
$198$		0			0
$199$	0.241956	+	0.139694i	0.0171518	+	0.00990261i	0.508551	−	0.861032i	$-0.330181\pi$
$199$	0.241956	+	0.139694i	0.0171518	+	0.00990261i	−0.491400	+	0.870934i	$0.663515\pi$
$200$	11.2137	−	9.87438i	0.792929	−	0.698224i
$201$		0			0
$202$	8.81051	+	0.958893i	0.619905	+	0.0674675i
$203$	−3.76086	+	6.51400i	−0.263961	+	0.457193i
$204$		0			0
$205$	−3.50968	−	2.02631i	−0.245126	−	0.141524i
$206$	−0.300431	−	0.681533i	−0.0209320	−	0.0474847i
$207$		0			0
$208$	4.13324	−	8.92656i	0.286588	−	0.618946i
$209$	4.64371	+	7.94357i	0.321212	+	0.549468i
$210$		0			0
$211$	−0.0832510	−	0.144195i	−0.00573123	−	0.00992679i	0.863146	−	0.504955i	$-0.168491\pi$
$211$	−0.0832510	−	0.144195i	−0.00573123	−	0.00992679i	−0.868877	+	0.495028i	$0.835158\pi$
$212$	13.6275	−	4.31696i	0.935940	−	0.296490i
$213$		0			0
$214$	3.94498	+	8.94926i	0.269673	+	0.611759i
$215$	16.1814	+	9.34234i	1.10356	+	0.637142i
$216$		0			0
$217$		−	9.74027i		−	0.661212i
$218$	−13.8216	−	10.1201i	−0.936114	−	0.685417i
$219$		0			0
$220$	2.91233	−	13.2211i	0.196350	−	0.891365i
$221$		−	3.76279i		−	0.253113i
$222$		0			0
$223$	−5.86577	−	10.1598i	−0.392801	−	0.680352i	0.600017	−	0.799987i	$-0.295161\pi$
$223$	−5.86577	−	10.1598i	−0.392801	−	0.680352i	−0.992818	+	0.119636i	$0.961827\pi$
$224$	3.42320	+	6.19007i	0.228722	+	0.413591i
$225$		0			0
$226$	−6.41109	+	2.82611i	−0.426459	+	0.187990i
$227$	8.78264			0.582924			0.291462	−	0.956582i	$-0.405858\pi$
$227$	8.78264			0.582924			0.291462	+	0.956582i	$0.405858\pi$
$228$		0			0
$229$	−6.53352			−0.431747			−0.215874	−	0.976421i	$-0.569260\pi$
$229$	−6.53352			−0.431747			−0.215874	+	0.976421i	$0.569260\pi$
$230$	36.5093	−	16.0939i	2.40735	−	1.06120i
$231$		0			0
$232$	−11.2438	−	12.7689i	−0.738191	−	0.838317i
$233$	−13.1315	−	22.7444i	−0.860274	−	1.49004i	−0.871664	−	0.490103i	$-0.836959\pi$
$233$	−13.1315	−	22.7444i	−0.860274	−	1.49004i	0.0113904	−	0.999935i	$-0.496374\pi$
$234$		0			0
$235$			22.6944i			1.48042i
$236$	11.0761	+	2.43984i	0.720992	+	0.158820i
$237$		0			0
$238$	2.18310	+	1.59845i	0.141509	+	0.103612i
$239$			23.5704i			1.52464i	0.647198	+	0.762322i	$0.275941\pi$
$239$			23.5704i			1.52464i	−0.647198	+	0.762322i	$0.724059\pi$
$240$		0			0
$241$	−13.5642	−	7.83128i	−0.873746	−	0.504457i	−0.00515448	−	0.999987i	$-0.501641\pi$
$241$	−13.5642	−	7.83128i	−0.873746	−	0.504457i	−0.868591	+	0.495529i	$0.834974\pi$
$242$	3.73297	+	8.46831i	0.239964	+	0.544364i
$243$		0			0
$244$	3.39438	+	10.7152i	0.217303	+	0.685967i
$245$	8.71633	+	15.0971i	0.556866	+	0.964520i
$246$		0			0
$247$	10.7195	−	0.0579979i	0.682065	−	0.00369032i
$248$	20.8770	+	7.03970i	1.32569	+	0.447022i
$249$		0			0
$250$	−0.517020	−	1.17287i	−0.0326992	−	0.0741789i
$251$	−22.1575	−	12.7926i	−1.39857	−	0.807463i	−0.404324	−	0.914616i	$-0.632493\pi$
$251$	−22.1575	−	12.7926i	−1.39857	−	0.807463i	−0.994243	+	0.107153i	$0.965827\pi$
$252$		0			0
$253$	9.28625	−	16.0842i	0.583821	−	1.01121i
$254$	−8.04917	−	0.876033i	−0.505050	−	0.0549672i
$255$		0			0
$256$	−15.7417	+	2.86337i	−0.983856	+	0.178961i
$257$	−17.4440	−	10.0713i	−1.08813	−	0.628229i	−0.155049	−	0.987907i	$-0.549553\pi$
$257$	−17.4440	−	10.0713i	−1.08813	−	0.628229i	−0.933077	+	0.359677i	$0.882887\pi$
$258$		0			0
$259$	−12.4744			−0.775120
$260$	−11.6427	−	10.6397i	−0.722049	−	0.659846i
$261$		0			0
$262$	21.3037	+	15.5984i	1.31614	+	0.963672i
$263$	−3.14828	+	1.81766i	−0.194131	+	0.112082i	−0.593915	−	0.804528i	$-0.702419\pi$
$263$	−3.14828	+	1.81766i	−0.194131	+	0.112082i	0.399784	+	0.916609i	$0.369085\pi$
$264$		0			0
$265$		−	22.9194i		−	1.40793i
$266$	−4.52004	+	6.24388i	−0.277141	+	0.382837i
$267$		0			0
$268$	0.0284881	+	0.0899296i	0.00174019	+	0.00549332i
$269$	−15.9194	+	9.19106i	−0.970622	+	0.560389i	−0.899426	−	0.437073i	$-0.856015\pi$
$269$	−15.9194	+	9.19106i	−0.970622	+	0.560389i	−0.0711964	+	0.997462i	$0.522682\pi$
$270$		0			0
$271$	16.7304	−	9.65930i	1.01630	−	0.586761i	0.103269	−	0.994653i	$-0.467070\pi$
$271$	16.7304	−	9.65930i	1.01630	−	0.586761i	0.913030	+	0.407893i	$0.133736\pi$
$272$	−5.00389	+	3.52392i	−0.303405	+	0.213669i
$273$		0			0
$274$	28.0232	+	3.04991i	1.69295	+	0.184252i
$275$	−9.65730	−	5.57564i	−0.582357	−	0.336224i
$276$		0			0
$277$	−16.5581			−0.994879			−0.497440	−	0.867499i	$-0.665726\pi$
$277$	−16.5581			−0.994879			−0.497440	+	0.867499i	$0.665726\pi$
$278$	−1.59724	+	14.6758i	−0.0957964	+	0.880197i
$279$		0			0
$280$	11.1188	−	2.23507i	0.664476	−	0.133571i
$281$	−3.45491	−	1.99469i	−0.206103	−	0.118993i	0.393396	−	0.919369i	$-0.371300\pi$
$281$	−3.45491	−	1.99469i	−0.206103	−	0.118993i	−0.599499	+	0.800376i	$0.704633\pi$
$282$		0			0
$283$	−12.8457	+	7.41645i	−0.763596	+	0.440862i	−0.830585	−	0.556892i	$-0.811994\pi$
$283$	−12.8457	+	7.41645i	−0.763596	+	0.440862i	0.0669896	+	0.997754i	$0.478661\pi$
$284$	12.2110	+	2.68984i	0.724592	+	0.159613i
$285$		0			0
$286$	−7.29853	−	0.794337i	−0.431571	−	0.0469701i
$287$	−0.790163	−	1.36860i	−0.0466419	−	0.0807861i
$288$		0			0
$289$	7.32947	−	12.6950i	0.431145	−	0.746766i
$290$	−24.9610	+	11.0032i	−1.46576	+	0.646130i
$291$		0			0
$292$	−2.57076	−	0.566285i	−0.150442	−	0.0331394i
$293$		−	22.9900i		−	1.34309i	−0.740963	−	0.671546i	$-0.765631\pi$
$293$		−	22.9900i		−	1.34309i	0.740963	−	0.671546i	$-0.234369\pi$
$294$		0			0
$295$	9.09217	−	15.7481i	0.529367	−	0.916890i
$296$	9.01575	−	26.7372i	0.524030	−	1.55407i
$297$		0			0
$298$	−8.07576	+	11.0295i	−0.467816	+	0.638924i
$299$	−10.8186	−	18.7383i	−0.625655	−	1.08367i
$300$		0			0
$301$	3.64306	+	6.30996i	0.209982	+	0.363700i
$302$	6.33380	+	14.3683i	0.364469	+	0.826805i
$303$		0			0
$304$	−10.1161	−	14.2008i	−0.580200	−	0.814474i
$305$	18.0213			1.03190
$306$		0			0
$307$	−10.3144	−	17.8650i	−0.588673	−	1.01961i	−0.994407	−	0.105620i	$-0.966317\pi$
$307$	−10.3144	−	17.8650i	−0.588673	−	1.01961i	0.405734	−	0.913991i	$-0.367016\pi$
$308$	3.56131	−	3.89703i	0.202924	−	0.222054i
$309$		0			0
$310$	20.8685	−	28.5013i	1.18525	−	1.61876i
$311$			3.16368i			0.179396i	0.995969	+	0.0896978i	$0.0285901\pi$
$311$			3.16368i			0.179396i	−0.995969	+	0.0896978i	$0.971410\pi$
$312$		0			0
$313$	−7.67203	+	13.2883i	−0.433649	+	0.751101i	−0.997184	−	0.0749904i	$-0.976107\pi$
$313$	−7.67203	+	13.2883i	−0.433649	+	0.751101i	0.563536	+	0.826092i	$0.309441\pi$
$314$	9.45722	−	12.9163i	0.533702	−	0.728908i
$315$		0			0
$316$	−14.7345	−	3.24572i	−0.828882	−	0.182586i
$317$	2.28007	+	1.31640i	0.128061	+	0.0739362i	0.562662	−	0.826687i	$-0.309777\pi$
$317$	2.28007	+	1.31640i	0.128061	+	0.0739362i	−0.434601	+	0.900623i	$0.643111\pi$
$318$		0			0
$319$	−6.34889	+	10.9966i	−0.355470	+	0.615692i
$320$	−3.24545	+	25.4471i	−0.181426	+	1.42254i
$321$		0			0
$322$	15.4674	+	1.68340i	0.861965	+	0.0938121i
$323$	−5.79377	−	3.30337i	−0.322374	−	0.183804i
$324$		0			0
$325$	−11.2509	+	6.49569i	−0.624086	+	0.360316i
$326$	−20.2881	+	8.94332i	−1.12365	+	0.495324i
$327$		0			0
$328$	3.50451	−	0.704466i	0.193504	−	0.0388977i
$329$	−4.42486	+	7.66408i	−0.243950	+	0.422534i
$330$		0			0
$331$	−9.30930			−0.511685			−0.255843	−	0.966718i	$-0.582353\pi$
$331$	−9.30930			−0.511685			−0.255843	+	0.966718i	$0.582353\pi$
$332$	−11.5772	−	10.5799i	−0.635382	−	0.580645i
$333$		0			0
$334$	−5.07403	−	0.552233i	−0.277639	−	0.0302168i
$335$	0.151248			0.00826358
$336$		0			0
$337$	−3.28961	+	1.89926i	−0.179196	+	0.103459i	−0.586915	−	0.809648i	$-0.699658\pi$
$337$	−3.28961	+	1.89926i	−0.179196	+	0.103459i	0.407719	+	0.913108i	$0.366324\pi$
$338$	5.80822	−	7.93263i	0.315926	−	0.431478i
$339$		0			0
$340$	2.96336	+	9.35455i	0.160711	+	0.507321i
$341$		−	16.4430i		−	0.890439i
$342$		0			0
$343$			15.5510i			0.839674i
$344$	−16.1576	+	3.24795i	−0.871158	+	0.175118i
$345$		0			0
$346$	5.88830	+	4.31137i	0.316557	+	0.231781i
$347$	−3.07657	+	1.77626i	−0.165159	+	0.0953546i	−0.580301	−	0.814402i	$-0.697065\pi$
$347$	−3.07657	+	1.77626i	−0.165159	+	0.0953546i	0.415142	+	0.909757i	$0.363732\pi$
$348$		0			0
$349$	−1.91850			−0.102695			−0.0513475	−	0.998681i	$-0.516352\pi$
$349$	−1.91850			−0.102695			−0.0513475	+	0.998681i	$0.516352\pi$
$350$	1.01074	−	9.28693i	0.0540266	−	0.496407i
$351$		0			0
$352$	5.77887	+	10.4498i	0.308015	+	0.556974i
$353$	7.11843			0.378876			0.189438	−	0.981893i	$-0.439333\pi$
$353$	7.11843			0.378876			0.189438	+	0.981893i	$0.439333\pi$
$354$		0			0
$355$	10.0238	−	17.3618i	0.532010	−	0.921469i
$356$	−13.2636	+	4.20167i	−0.702968	+	0.222688i
$357$		0			0
$358$	1.57566	+	3.57441i	0.0832760	+	0.188913i
$359$	−7.25210	+	4.18700i	−0.382751	+	0.220982i	−0.679015	−	0.734125i	$-0.737593\pi$
$359$	−7.25210	+	4.18700i	−0.382751	+	0.220982i	0.296263	+	0.955106i	$0.404259\pi$
$360$		0			0
$361$	9.32139	−	16.5563i	0.490600	−	0.871385i
$362$	−0.367273	+	3.37458i	−0.0193034	+	0.177364i
$363$		0			0
$364$	−1.85735	−	5.86315i	−0.0973514	−	0.307313i
$365$	−2.11029	+	3.65513i	−0.110458	+	0.191318i
$366$		0			0
$367$	19.7381	+	11.3958i	1.03032	+	0.594857i	0.917077	−	0.398710i	$-0.130542\pi$
$367$	19.7381	+	11.3958i	1.03032	+	0.594857i	0.113246	+	0.993567i	$0.463875\pi$
$368$	−14.7871	+	31.9357i	−0.770830	+	1.66477i
$369$		0			0
$370$	−36.5016	−	26.7263i	−1.89763	−	1.38943i
$371$	4.46874	−	7.74008i	0.232005	−	0.401845i
$372$		0			0
$373$		−	23.5670i		−	1.22025i	−0.792305	−	0.610125i	$-0.791119\pi$
$373$		−	23.5670i		−	1.22025i	0.792305	−	0.610125i	$-0.208881\pi$
$374$	3.68539	+	2.69842i	0.190567	+	0.139532i
$375$		0			0
$376$	−13.2289	−	15.0233i	−0.682230	−	0.774766i
$377$	7.39654	+	12.8112i	0.380941	+	0.659809i
$378$		0			0
$379$	−38.1884			−1.96161			−0.980804	−	0.194995i	$-0.937531\pi$
$379$	−38.1884			−1.96161			−0.980804	+	0.194995i	$0.937531\pi$
$380$	−26.6037	+	8.58625i	−1.36474	+	0.440465i
$381$		0			0
$382$	−5.67478	+	2.50153i	−0.290347	+	0.127990i
$383$	10.8906	+	18.8631i	0.556483	+	0.963857i	0.997786	+	0.0664990i	$0.0211829\pi$
$383$	10.8906	+	18.8631i	0.556483	+	0.963857i	−0.441303	+	0.897358i	$0.645484\pi$
$384$		0			0
$385$	−4.23213	−	7.33026i	−0.215689	−	0.373585i
$386$	−10.2310	−	7.49104i	−0.520742	−	0.381284i
$387$		0			0
$388$	−4.23244	+	19.2140i	−0.214870	+	0.975441i
$389$	13.4725	−	23.3351i	0.683084	−	1.18314i	−0.290950	−	0.956738i	$-0.593971\pi$
$389$	13.4725	−	23.3351i	0.683084	−	1.18314i	0.974035	−	0.226399i	$-0.0726952\pi$
$390$		0			0
$391$			13.4618i			0.680792i
$392$	−14.5704	−	4.91312i	−0.735917	−	0.248150i
$393$		0			0
$394$	−0.794162	−	1.80157i	−0.0400093	−	0.0907619i
$395$	−12.0953	+	20.9497i	−0.608582	+	1.05410i
$396$		0			0
$397$	2.35770	+	4.08365i	0.118329	+	0.204953i	0.919106	−	0.394011i	$-0.128913\pi$
$397$	2.35770	+	4.08365i	0.118329	+	0.204953i	−0.800776	+	0.598964i	$0.795579\pi$
$398$	−0.0427497	+	0.392794i	−0.00214285	+	0.0196890i
$399$		0			0
$400$	19.1748	+	8.87846i	0.958742	+	0.443923i
$401$	−4.16941	+	2.40721i	−0.208210	+	0.120210i	−0.600479	−	0.799640i	$-0.705024\pi$
$401$	−4.16941	+	2.40721i	−0.208210	+	0.120210i	0.392269	+	0.919850i	$0.371690\pi$
$402$		0			0
$403$	−16.5899	−	9.57816i	−0.826400	−	0.477122i
$404$	3.78503	+	11.9483i	0.188312	+	0.594452i
$405$		0			0
$406$	−10.5749	−	1.15092i	−0.524822	−	0.0571191i
$407$	−21.0586			−1.04384
$408$		0			0
$409$	12.2147	+	7.05216i	0.603978	+	0.348707i	0.770605	−	0.637313i	$-0.219954\pi$
$409$	12.2147	+	7.05216i	0.603978	+	0.348707i	−0.166627	+	0.986020i	$0.553288\pi$
$410$	0.620103	−	5.69763i	0.0306247	−	0.281386i
$411$		0			0
$412$	0.710568	−	0.777552i	0.0350071	−	0.0383072i
$413$	6.14100	−	3.54551i	0.302179	−	0.174463i
$414$		0			0
$415$	−21.7766	+	12.5727i	−1.06897	+	0.617171i
$416$	13.9093	+	0.256566i	0.681959	+	0.0125792i
$417$		0			0
$418$	−7.63050	+	10.5406i	−0.373220	+	0.515558i
$419$		−	31.5299i		−	1.54034i	−0.637840	−	0.770169i	$-0.720172\pi$
$419$		−	31.5299i		−	1.54034i	0.637840	−	0.770169i	$-0.279828\pi$
$420$		0			0
$421$	23.2374	−	13.4161i	1.13252	−	0.653862i	0.187954	−	0.982178i	$-0.439814\pi$
$421$	23.2374	−	13.4161i	1.13252	−	0.653862i	0.944568	+	0.328316i	$0.106481\pi$
$422$	0.139107	−	0.189987i	0.00677163	−	0.00924841i
$423$		0			0
$424$	13.3601	+	15.1722i	0.648825	+	0.736829i
$425$	8.08272			0.392069
$426$		0			0
$427$	6.08594	+	3.51372i	0.294519	+	0.170041i
$428$	−9.33051	+	10.2101i	−0.451007	+	0.493523i
$429$		0			0
$430$	−2.85899	+	26.2690i	−0.137873	+	1.26680i
$431$	3.89128	−	6.73989i	0.187436	−	0.324649i	−0.756958	−	0.653463i	$-0.773316\pi$
$431$	3.89128	−	6.73989i	0.187436	−	0.324649i	0.944395	+	0.328814i	$0.106649\pi$
$432$		0			0
$433$	−13.2846	−	7.66988i	−0.638418	−	0.368591i	0.145587	−	0.989345i	$-0.453493\pi$
$433$	−13.2846	−	7.66988i	−0.638418	−	0.368591i	−0.784005	+	0.620755i	$0.786826\pi$
$434$	12.6045	−	5.55627i	0.605036	−	0.266709i
$435$		0			0
$436$	5.21156	−	23.6589i	0.249589	−	1.13305i
$437$	−38.3501	+	0.207494i	−1.83454	+	0.00992577i
$438$		0			0
$439$	−12.6149	−	21.8497i	−0.602077	−	1.04283i	−0.992506	−	0.122195i	$-0.961007\pi$
$439$	−12.6149	−	21.8497i	−0.602077	−	1.04283i	0.390429	−	0.920633i	$-0.372327\pi$
$440$	18.7702	−	3.77313i	0.894835	−	0.179877i
$441$		0			0
$442$	4.86928	−	2.14646i	0.231608	−	0.102097i
$443$	2.05095	+	1.18412i	0.0974435	+	0.0562590i	0.547930	−	0.836524i	$-0.315416\pi$
$443$	2.05095	+	1.18412i	0.0974435	+	0.0562590i	−0.450486	+	0.892783i	$0.648749\pi$
$444$		0			0
$445$			22.3074i			1.05747i
$446$	9.80134	−	13.3863i	0.464107	−	0.633858i
$447$		0			0
$448$	−6.05758	+	7.96091i	−0.286194	+	0.376118i
$449$			11.6774i			0.551093i	0.961288	+	0.275546i	$0.0888587\pi$
$449$			11.6774i			0.551093i	−0.961288	+	0.275546i	$0.911141\pi$
$450$		0			0
$451$	−1.33391	−	2.31041i	−0.0628115	−	0.108793i
$452$	−7.31432	−	6.68421i	−0.344037	−	0.314399i
$453$		0			0
$454$	5.00999	+	11.3653i	0.235131	+	0.533399i
$455$	−9.86096			−0.462289
$456$		0			0
$457$	−8.71735			−0.407781			−0.203890	−	0.978994i	$-0.565359\pi$
$457$	−8.71735			−0.407781			−0.203890	+	0.978994i	$0.565359\pi$
$458$	−3.72700	−	8.45477i	−0.174151	−	0.395066i
$459$		0			0
$460$	41.6530	+	38.0647i	1.94208	+	1.77477i
$461$	10.5590	+	18.2887i	0.491781	+	0.851789i	0.999955	−	0.00946495i	$-0.00301283\pi$
$461$	10.5590	+	18.2887i	0.491781	+	0.851789i	−0.508174	+	0.861254i	$0.669679\pi$
$462$		0			0
$463$			0.355651i			0.0165285i	0.999966	+	0.00826426i	$0.00263062\pi$
$463$			0.355651i			0.0165285i	−0.999966	+	0.00826426i	$0.997369\pi$
$464$	10.1098	−	21.8341i	0.469334	−	1.01362i
$465$		0			0
$466$	21.9419	−	29.9674i	1.01644	−	1.38821i
$467$		−	4.47951i		−	0.207287i	−0.994615	−	0.103643i	$-0.966950\pi$
$467$		−	4.47951i		−	0.207287i	0.994615	−	0.103643i	$-0.0330501\pi$
$468$		0			0
$469$	0.0510778	+	0.0294898i	0.00235855	+	0.00136171i
$470$	−29.3679	+	12.9459i	−1.35464	+	0.597148i
$471$		0			0
$472$	3.16098	+	15.7249i	0.145496	+	0.723798i
$473$	6.15002	+	10.6521i	0.282778	+	0.489786i
$474$		0			0
$475$	0.124583	+	23.0262i	0.00571627	+	1.05651i
$476$	−0.823159	+	3.73689i	−0.0377295	+	0.171280i
$477$		0			0
$478$	−30.5016	+	13.4456i	−1.39511	+	0.614987i
$479$	21.4965	+	12.4110i	0.982199	+	0.567073i	0.902933	−	0.429781i	$-0.141409\pi$
$479$	21.4965	+	12.4110i	0.982199	+	0.567073i	0.0792655	+	0.996854i	$0.474743\pi$
$480$		0			0
$481$	−12.2668	+	21.2466i	−0.559316	+	0.968764i
$482$	2.39657	−	22.0202i	0.109161	−	1.00299i
$483$		0			0
$484$	−8.82907	+	9.66138i	−0.401321	+	0.439154i
$485$	27.3186	+	15.7724i	1.24048	+	0.716189i
$486$		0			0
$487$	36.2102			1.64084			0.820420	−	0.571761i	$-0.193739\pi$
$487$	36.2102			1.64084			0.820420	+	0.571761i	$0.193739\pi$
$488$	−11.9298	+	10.5049i	−0.540035	+	0.475535i
$489$		0			0
$490$	−14.5644	+	19.8915i	−0.657955	+	0.898607i
$491$	5.16077	−	2.97957i	0.232902	−	0.134466i	−0.379008	−	0.925393i	$-0.623735\pi$
$491$	5.16077	−	2.97957i	0.232902	−	0.134466i	0.611910	+	0.790927i	$0.290401\pi$
$492$		0			0
$493$		−	9.20366i		−	0.414512i
$494$	6.18992	+	13.8386i	0.278497	+	0.622628i
$495$		0			0
$496$	2.79934	+	31.0319i	0.125694	+	1.39337i
$497$	6.77026	−	3.90881i	0.303688	−	0.175334i
$498$		0			0
$499$	20.1581	−	11.6383i	0.902402	−	0.521002i	0.0244234	−	0.999702i	$-0.492225\pi$
$499$	20.1581	−	11.6383i	0.902402	−	0.521002i	0.877979	+	0.478700i	$0.158892\pi$
$500$	1.22284	−	1.33811i	0.0546869	−	0.0598422i
$501$		0			0
$502$	3.91486	−	35.9706i	0.174729	−	1.60545i
$503$	16.4493	+	9.49702i	0.733439	+	0.423451i	0.819679	−	0.572823i	$-0.194152\pi$
$503$	16.4493	+	9.49702i	0.733439	+	0.423451i	−0.0862401	+	0.996274i	$0.527485\pi$
$504$		0			0
$505$	20.0953			0.894231
$506$	26.1113	+	2.84183i	1.16079	+	0.126335i
$507$		0			0
$508$	−3.45795	−	10.9158i	−0.153422	−	0.484312i
$509$	−11.3577	−	6.55740i	−0.503423	−	0.290652i	0.226703	−	0.973964i	$-0.427205\pi$
$509$	−11.3577	−	6.55740i	−0.503423	−	0.290652i	−0.730126	+	0.683312i	$0.760539\pi$
$510$		0			0
$511$	−1.42532	+	0.822911i	−0.0630526	+	0.0364035i
$512$	−12.6851	−	18.7373i	−0.560608	−	0.828081i
$513$		0			0
$514$	3.08207	−	28.3187i	0.135944	−	1.24908i
$515$	−0.844413	−	1.46257i	−0.0372093	−	0.0644483i
$516$		0			0
$517$	−7.46982	+	12.9381i	−0.328522	+	0.569017i
$518$	−7.11592	−	16.1426i	−0.312655	−	0.709265i
$519$		0			0
$520$	7.12693	−	21.1357i	0.312537	−	0.926862i
$521$			24.9294i			1.09218i	0.837727	+	0.546089i	$0.183884\pi$
$521$			24.9294i			1.09218i	−0.837727	+	0.546089i	$0.816116\pi$
$522$		0			0
$523$	−15.1705	+	26.2761i	−0.663359	+	1.14897i	0.316368	+	0.948636i	$0.397536\pi$
$523$	−15.1705	+	26.2761i	−0.663359	+	1.14897i	−0.979727	+	0.200335i	$0.935797\pi$
$524$	−8.03276	+	36.4662i	−0.350913	+	1.59303i
$525$		0			0
$526$	−4.14808	−	3.03720i	−0.180865	−	0.132428i
$527$	5.95915	+	10.3215i	0.259584	+	0.449613i
$528$		0			0
$529$	27.2047	+	47.1198i	1.18281	+	2.04869i
$530$	29.6592	−	13.0742i	1.28831	−	0.567909i
$531$		0			0
$532$	−10.6584	−	2.28743i	−0.462100	−	0.0991727i
$533$	−3.10805			−0.134625
$534$		0			0
$535$	11.0880	+	19.2051i	0.479378	+	0.830307i
$536$	−0.100124	+	0.0881651i	−0.00432468	+	0.00380815i
$537$		0			0
$538$	−20.9749	−	15.3577i	−0.904292	−	0.662117i
$539$			11.4759i			0.494300i
$540$		0			0
$541$	12.1933	−	21.1195i	0.524233	−	0.907998i	−0.475369	−	0.879787i	$-0.657685\pi$
$541$	12.1933	−	21.1195i	0.524233	−	0.907998i	0.999602	−	0.0282117i	$-0.00898124\pi$
$542$	22.0435	+	16.1401i	0.946848	+	0.693276i
$543$		0			0
$544$	−7.41460	−	4.46514i	−0.317898	−	0.191441i
$545$	−33.6384	−	19.4212i	−1.44091	−	0.831911i
$546$		0			0
$547$	18.7226	−	32.4286i	0.800522	−	1.38655i	−0.118751	−	0.992924i	$-0.537889\pi$
$547$	18.7226	−	32.4286i	0.800522	−	1.38655i	0.919273	−	0.393621i	$-0.128778\pi$
$548$	12.0389	+	38.0036i	0.514276	+	1.62343i
$549$		0			0
$550$	1.70629	−	15.6777i	0.0727564	−	0.668500i
$551$	26.2195	−	0.141861i	1.11699	−	0.00604348i
$552$		0			0
$553$	−8.16937	+	4.71659i	−0.347397	+	0.200570i
$554$	−9.44545	−	21.4272i	−0.401299	−	0.910354i
$555$		0			0
$556$	−19.9025	+	6.30478i	−0.844056	+	0.267382i
$557$	7.69507	−	13.3283i	0.326051	−	0.564736i	−0.655674	−	0.755044i	$-0.727615\pi$
$557$	7.69507	−	13.3283i	0.326051	−	0.564736i	0.981724	+	0.190308i	$0.0609487\pi$
$558$		0			0
$559$	14.3297			0.606082
$560$	9.23497	+	13.1134i	0.390249	+	0.554144i
$561$		0			0
$562$	0.610426	−	5.60872i	0.0257493	−	0.236590i
$563$	−25.2567			−1.06444			−0.532222	−	0.846605i	$-0.678643\pi$
$563$	−25.2567			−1.06444			−0.532222	+	0.846605i	$0.678643\pi$
$564$		0			0
$565$	−13.7582	+	7.94327i	−0.578810	+	0.334176i
$566$	−16.9251	−	12.3924i	−0.711413	−	0.520892i
$567$		0			0
$568$	3.48488	+	17.3362i	0.146222	+	0.727412i
$569$		−	46.3413i		−	1.94273i	−0.237599	−	0.971363i	$-0.576361\pi$
$569$		−	46.3413i		−	1.94273i	0.237599	−	0.971363i	$-0.423639\pi$
$570$		0			0
$571$		−	32.1609i		−	1.34589i	−0.739692	−	0.672946i	$-0.765029\pi$
$571$		−	32.1609i		−	1.34589i	0.739692	−	0.672946i	$-0.234971\pi$
$572$	−3.13548	−	9.89787i	−0.131101	−	0.413851i
$573$		0			0
$574$	1.32031	−	1.80323i	0.0551088	−	0.0752654i
$575$	40.2512	−	23.2390i	1.67859	−	0.969135i
$576$		0			0
$577$	−39.2983			−1.63601			−0.818004	−	0.575212i	$-0.804919\pi$
$577$	−39.2983			−1.63601			−0.818004	+	0.575212i	$0.804919\pi$
$578$	20.6092	+	2.24300i	0.857229	+	0.0932966i
$579$		0			0
$580$	−28.4776	−	26.0244i	−1.18247	−	1.08060i
$581$	−9.80550			−0.406801
$582$		0			0
$583$	7.54389	−	13.0664i	0.312436	−	0.541155i
$584$	−0.733663	−	3.64975i	−0.0303592	−	0.151028i
$585$		0			0
$586$	29.7505	−	13.1145i	1.22898	−	0.541755i
$587$	−15.4560	+	8.92352i	−0.637937	+	0.368313i	−0.783819	−	0.620989i	$-0.786731\pi$
$587$	−15.4560	+	8.92352i	−0.637937	+	0.368313i	0.145883	+	0.989302i	$0.453398\pi$
$588$		0			0
$589$	−29.3123	+	17.1356i	−1.20779	+	0.706060i
$590$	25.5656	+	2.78243i	1.05252	+	0.114551i
$591$		0			0
$592$	39.7426	−	3.58511i	1.63341	−	0.147347i
$593$	−11.7249	+	20.3082i	−0.481485	+	0.833957i	−0.999774	−	0.0212488i	$-0.993236\pi$
$593$	−11.7249	+	20.3082i	−0.481485	+	0.833957i	0.518289	+	0.855205i	$0.326569\pi$
$594$		0			0
$595$	5.31315	+	3.06755i	0.217818	+	0.125757i
$596$	−18.8797	−	4.15880i	−0.773341	−	0.170351i
$597$		0			0
$598$	18.0772	−	24.6891i	0.739231	−	1.00961i
$599$	7.40584	−	12.8273i	0.302595	−	0.524109i	−0.674128	−	0.738614i	$-0.735481\pi$
$599$	7.40584	−	12.8273i	0.302595	−	0.524109i	0.976723	+	0.214505i	$0.0688138\pi$
$600$		0			0
$601$			4.30046i			0.175419i	0.996146	+	0.0877097i	$0.0279548\pi$
$601$			4.30046i			0.175419i	−0.996146	+	0.0877097i	$0.972045\pi$
$602$	−6.08732	+	8.31381i	−0.248101	+	0.338846i
$603$		0			0
$604$	−14.9805	+	16.3926i	−0.609546	+	0.667007i
$605$	10.4921	+	18.1729i	0.426566	+	0.738835i
$606$		0			0
$607$	−20.1844			−0.819260			−0.409630	−	0.912252i	$-0.634342\pi$
$607$	−20.1844			−0.819260			−0.409630	+	0.912252i	$0.634342\pi$
$608$	12.6061	−	21.1917i	0.511244	−	0.859435i
$609$		0			0
$610$	10.2801	+	23.3207i	0.416230	+	0.944227i
$611$	8.70243	+	15.0730i	0.352062	+	0.609790i
$612$		0			0
$613$	0.467103	+	0.809046i	0.0188661	+	0.0326771i	0.875304	−	0.483572i	$-0.160661\pi$
$613$	0.467103	+	0.809046i	0.0188661	+	0.0326771i	−0.856438	+	0.516250i	$0.827328\pi$
$614$	17.2347	−	23.5384i	0.695535	−	0.949933i
$615$		0			0
$616$	7.07452	+	2.38552i	0.285040	+	0.0961153i
$617$	4.11324	−	7.12434i	0.165593	−	0.286815i	−0.771273	−	0.636505i	$-0.780380\pi$
$617$	4.11324	−	7.12434i	0.165593	−	0.286815i	0.936866	+	0.349690i	$0.113713\pi$
$618$		0			0
$619$			7.04730i			0.283255i	0.989920	+	0.141627i	$0.0452335\pi$
$619$			7.04730i			0.283255i	−0.989920	+	0.141627i	$0.954766\pi$
$620$	48.7867	+	10.7467i	1.95932	+	0.431598i
$621$		0			0
$622$	−4.09399	+	1.80470i	−0.164154	+	0.0723618i
$623$	−4.34940	+	7.53338i	−0.174255	+	0.301819i
$624$		0			0
$625$	11.7534	+	20.3576i	0.470138	+	0.814302i
$626$	−21.5724	−	2.34783i	−0.862206	−	0.0938383i
$627$		0			0
$628$	22.1093	+	4.87022i	0.882256	+	0.194343i
$629$	13.2188	−	7.63188i	0.527068	−	0.304303i
$630$		0			0
$631$	−17.5204	−	10.1154i	−0.697476	−	0.402688i	0.108931	−	0.994049i	$-0.465257\pi$
$631$	−17.5204	−	10.1154i	−0.697476	−	0.402688i	−0.806407	+	0.591362i	$0.798591\pi$
$632$	−4.20505	−	20.9189i	−0.167268	−	0.832108i
$633$		0			0
$634$	−0.402851	+	3.70148i	−0.0159992	+	0.147004i
$635$	−18.3589			−0.728549
$636$		0			0
$637$	11.5783	+	6.68475i	0.458750	+	0.264860i
$638$	−17.8520	−	1.94292i	−0.706766	−	0.0769210i
$639$		0			0
$640$	−34.7815	+	10.3163i	−1.37486	+	0.407789i
$641$	6.91570	−	3.99278i	0.273154	−	0.157705i	−0.357166	−	0.934041i	$-0.616257\pi$
$641$	6.91570	−	3.99278i	0.273154	−	0.157705i	0.630320	+	0.776335i	$0.282924\pi$
$642$		0			0
$643$	9.89926	−	5.71534i	0.390389	−	0.225391i	−0.291940	−	0.956437i	$-0.594301\pi$
$643$	9.89926	−	5.71534i	0.390389	−	0.225391i	0.682328	+	0.731046i	$0.260967\pi$
$644$	6.64485	+	20.9761i	0.261844	+	0.826572i
$645$		0			0
$646$	0.969747	−	9.38188i	0.0381542	−	0.369125i
$647$		−	48.3776i		−	1.90192i	−0.309312	−	0.950961i	$-0.600099\pi$
$647$		−	48.3776i		−	1.90192i	0.309312	−	0.950961i	$-0.399901\pi$
$648$		0			0
$649$	10.3669	−	5.98534i	0.406937	−	0.234945i
$650$	−14.8238	−	10.8539i	−0.581438	−	0.425725i
$651$		0			0
$652$	−23.1464	−	21.1524i	−0.906483	−	0.828391i
$653$	−32.2260			−1.26110			−0.630551	−	0.776148i	$-0.717171\pi$
$653$	−32.2260			−1.26110			−0.630551	+	0.776148i	$0.717171\pi$
$654$		0			0
$655$	51.8481	+	29.9345i	2.02587	+	1.16964i
$656$	2.91075	+	4.13319i	0.113646	+	0.161374i
$657$		0			0
$658$	−12.4419	−	1.35412i	−0.485036	−	0.0527890i
$659$	13.5111	−	23.4019i	0.526317	−	0.911608i	−0.473213	−	0.880948i	$-0.656906\pi$
$659$	13.5111	−	23.4019i	0.526317	−	0.911608i	0.999530	−	0.0306595i	$-0.00976076\pi$
$660$		0			0
$661$	23.1686	+	13.3764i	0.901155	+	0.520282i	0.877575	−	0.479440i	$-0.159160\pi$
$661$	23.1686	+	13.3764i	0.901155	+	0.520282i	0.0235802	+	0.999722i	$0.492493\pi$
$662$	−5.31042	−	12.0468i	−0.206396	−	0.468212i
$663$		0			0
$664$	7.08685	−	21.0168i	0.275023	−	0.815611i
$665$	−8.65699	+	15.1835i	−0.335703	+	0.588790i
$666$		0			0
$667$	−26.4619	−	45.8334i	−1.02461	−	1.77467i
$668$	−2.17982	−	6.88113i	−0.0843398	−	0.266239i
$669$		0			0
$670$	0.0862786	+	0.195725i	0.00333323	+	0.00756150i
$671$	10.2740	+	5.93168i	0.396622	+	0.228990i
$672$		0			0
$673$		−	29.5414i		−	1.13874i	−0.822083	−	0.569368i	$-0.807188\pi$
$673$		−	29.5414i		−	1.13874i	0.822083	−	0.569368i	$-0.192812\pi$
$674$	−4.33429	−	3.17354i	−0.166951	−	0.122240i
$675$		0			0
$676$	13.5786	+	2.99108i	0.522253	+	0.115042i
$677$			15.6682i			0.602176i	0.953596	+	0.301088i	$0.0973498\pi$
$677$			15.6682i			0.602176i	−0.953596	+	0.301088i	$0.902650\pi$
$678$		0			0
$679$	6.15048	+	10.6529i	0.236034	+	0.408822i
$680$	−10.4149	+	9.17100i	−0.399394	+	0.351692i
$681$		0			0
$682$	21.2783	−	9.37980i	0.814787	−	0.359171i
$683$	−29.7127			−1.13693			−0.568463	−	0.822709i	$-0.692462\pi$
$683$	−29.7127			−1.13693			−0.568463	+	0.822709i	$0.692462\pi$
$684$		0			0
$685$	63.9165			2.44212
$686$	−20.1239	+	8.87094i	−0.768335	+	0.338694i
$687$		0			0
$688$	−13.4200	−	19.0561i	−0.511634	−	0.726508i
$689$	−8.78872	−	15.2225i	−0.334824	−	0.579932i
$690$		0			0
$691$			32.8555i			1.24988i	0.780671	+	0.624942i	$0.214877\pi$
$691$			32.8555i			1.24988i	−0.780671	+	0.624942i	$0.785123\pi$
$692$	−2.22024	+	10.0792i	−0.0844010	+	0.383154i
$693$		0			0
$694$	−4.05360	−	2.96802i	−0.153872	−	0.112664i
$695$			33.4732i			1.26971i
$696$		0			0
$697$	1.67464	+	0.966852i	0.0634314	+	0.0366221i
$698$	−1.09440	−	2.48266i	−0.0414235	−	0.0939701i
$699$		0			0
$700$	12.5944	−	3.98970i	0.476025	−	0.150796i
$701$	8.96916	+	15.5350i	0.338761	+	0.586751i	0.984200	−	0.177061i	$-0.0566590\pi$
$701$	8.96916	+	15.5350i	0.338761	+	0.586751i	−0.645439	+	0.763812i	$0.723326\pi$
$702$		0			0
$703$	21.9456	+	37.5403i	0.827693	+	1.41586i
$704$	−10.2261	+	13.4392i	−0.385411	+	0.506509i
$705$		0			0
$706$	4.06066	+	9.21169i	0.152825	+	0.346686i
$707$	6.78635	+	3.91810i	0.255227	+	0.147355i
$708$		0			0
$709$	3.51145	−	6.08201i	0.131875	−	0.228415i	−0.792524	−	0.609841i	$-0.791233\pi$
$709$	3.51145	−	6.08201i	0.131875	−	0.228415i	0.924399	+	0.381426i	$0.124567\pi$
$710$	28.1853	+	3.06755i	1.05777	+	0.115123i
$711$		0			0
$712$	−13.0033	−	14.7671i	−0.487321	−	0.553419i
$713$	59.3520	+	34.2669i	2.22275	+	1.28330i
$714$		0			0
$715$	−16.6468			−0.622554
$716$	−3.72668	+	4.07799i	−0.139273	+	0.152402i
$717$		0			0
$718$	−9.55515	−	6.99622i	−0.356595	−	0.261097i
$719$	23.4325	−	13.5288i	0.873886	−	0.504538i	0.00524853	−	0.999986i	$-0.498329\pi$
$719$	23.4325	−	13.5288i	0.873886	−	0.504538i	0.868638	+	0.495448i	$0.164996\pi$
$720$		0			0
$721$		−	0.658560i		−	0.0245260i
$722$	26.7422	+	2.61802i	0.995242	+	0.0974327i
$723$		0			0
$724$	−4.57642	+	1.44973i	−0.170081	+	0.0538788i
$725$	−27.5193	+	15.8882i	−1.02204	+	0.590075i
$726$		0			0
$727$	−23.9684	+	13.8381i	−0.888938	+	0.513229i	−0.873595	−	0.486654i	$-0.838217\pi$
$727$	−23.9684	+	13.8381i	−0.888938	+	0.513229i	−0.0153429	+	0.999882i	$0.504884\pi$
$728$	6.52777	−	5.74811i	0.241935	−	0.213039i
$729$		0			0
$730$	−5.93377	−	0.645803i	−0.219619	−	0.0239022i
$731$	−7.72093	−	4.45768i	−0.285569	−	0.164873i
$732$		0			0
$733$	−2.82689			−0.104414			−0.0522068	−	0.998636i	$-0.516626\pi$
$733$	−2.82689			−0.104414			−0.0522068	+	0.998636i	$0.516626\pi$
$734$	−3.48741	+	32.0430i	−0.128723	+	1.18273i
$735$		0			0
$736$	−49.7620	−	0.917891i	−1.83425	−	0.0338339i
$737$	0.0862268	+	0.0497831i	0.00317621	+	0.00183378i
$738$		0			0
$739$	21.3233	−	12.3110i	0.784392	−	0.452869i	−0.0535927	−	0.998563i	$-0.517067\pi$
$739$	21.3233	−	12.3110i	0.784392	−	0.452869i	0.837984	+	0.545694i	$0.183734\pi$
$740$	13.7633	−	62.4812i	0.505950	−	2.29685i
$741$		0			0
$742$	12.5653	+	1.36755i	0.461286	+	0.0502042i
$743$	3.96328	+	6.86460i	0.145399	+	0.251838i	0.929522	−	0.368768i	$-0.120220\pi$
$743$	3.96328	+	6.86460i	0.145399	+	0.251838i	−0.784123	+	0.620605i	$0.786887\pi$
$744$		0			0
$745$	−15.4980	+	26.8433i	−0.567803	+	0.983463i
$746$	30.4971	−	13.4436i	1.11658	−	0.492205i
$747$		0			0
$748$	−1.38962	+	6.30842i	−0.0508094	+	0.230659i
$749$			8.64759i			0.315976i
$750$		0			0
$751$	−7.13985	+	12.3666i	−0.260537	+	0.451263i	−0.966385	−	0.257101i	$-0.917233\pi$
$751$	−7.13985	+	12.3666i	−0.260537	+	0.451263i	0.705848	+	0.708363i	$0.250566\pi$
$752$	11.8947	−	25.6890i	0.433754	−	0.936780i
$753$		0			0
$754$	−12.3592	+	16.8796i	−0.450094	+	0.614720i
$755$	17.8022	+	30.8344i	0.647889	+	1.12218i
$756$		0			0
$757$	−17.1966	−	29.7854i	−0.625021	−	1.08257i	−0.988537	−	0.150981i	$-0.951757\pi$
$757$	−17.1966	−	29.7854i	−0.625021	−	1.08257i	0.363515	−	0.931588i	$-0.381576\pi$
$758$	−21.7843	−	49.4182i	−0.791242	−	1.79495i
$759$		0			0
$760$	−26.2870	−	29.5289i	−0.953531	−	1.07112i
$761$	31.6267			1.14647			0.573233	−	0.819392i	$-0.305689\pi$
$761$	31.6267			1.14647			0.573233	+	0.819392i	$0.305689\pi$
$762$		0			0
$763$	−7.57331	−	13.1174i	−0.274172	−	0.474880i
$764$	−6.47428	−	5.91653i	−0.234231	−	0.214053i
$765$		0			0
$766$	−18.1975	+	24.8534i	−0.657502	+	0.897989i
$767$		−	13.9460i		−	0.503561i
$768$		0			0
$769$	11.7685	−	20.3836i	0.424383	−	0.735052i	−0.571980	−	0.820268i	$-0.693824\pi$
$769$	11.7685	−	20.3836i	0.424383	−	0.735052i	0.996363	+	0.0852153i	$0.0271578\pi$
$770$	7.07162	−	9.65813i	0.254844	−	0.348055i
$771$		0			0
$772$	3.85769	−	17.5127i	0.138841	−	0.630296i
$773$	10.5693	+	6.10219i	0.380152	+	0.219481i	0.677884	−	0.735169i	$-0.262897\pi$
$773$	10.5693	+	6.10219i	0.380152	+	0.219481i	−0.297733	+	0.954649i	$0.596230\pi$
$774$		0			0
$775$	20.5745	−	35.6361i	0.739058	−	1.28009i
$776$	−27.2784	+	5.48343i	−0.979238	+	0.196844i
$777$		0			0
$778$	37.8824	+	4.12293i	1.35815	+	0.147814i
$779$	−2.72857	+	4.78564i	−0.0977612	+	0.171463i
$780$		0			0
$781$	11.4292	−	6.59865i	0.408969	−	0.236118i
$782$	−17.4204	+	7.67918i	−0.622951	+	0.274607i
$783$		0			0
$784$	−1.95370	−	21.6577i	−0.0697751	−	0.773488i
$785$	18.1491	−	31.4352i	0.647770	−	1.12197i
$786$		0			0
$787$	−36.6534			−1.30655			−0.653276	−	0.757120i	$-0.726606\pi$
$787$	−36.6534			−1.30655			−0.653276	+	0.757120i	$0.726606\pi$
$788$	1.87832	−	2.05539i	0.0669124	−	0.0732202i
$789$		0			0
$790$	−34.0099	−	3.70148i	−1.21002	−	0.131693i
$791$	−6.19498			−0.220268
$792$		0			0
$793$	11.9693	−	6.91048i	0.425042	−	0.245398i
$794$	−3.93956	+	5.38050i	−0.139810	+	0.190947i
$795$		0			0
$796$	−0.532685	+	0.168746i	−0.0188805	+	0.00598103i
$797$			14.7351i			0.521944i	0.965346	+	0.260972i	$0.0840430\pi$
$797$			14.7351i			0.521944i	−0.965346	+	0.260972i	$0.915957\pi$
$798$		0			0
$799$		−	10.8286i		−	0.383088i
$800$	−0.551120	+	29.8781i	−0.0194850	+	1.05635i
$801$		0			0
$802$	−5.49348	−	4.02229i	−0.193982	−	0.142032i
$803$	−2.40616	+	1.38920i	−0.0849115	+	0.0490237i
$804$		0			0
$805$	35.2786			1.24341
$806$	2.93116	−	26.9321i	0.103246	−	0.948642i
$807$		0			0
$808$	−13.3027	+	11.7139i	−0.467989	+	0.412093i
$809$	−14.1872			−0.498796			−0.249398	−	0.968401i	$-0.580233\pi$
$809$	−14.1872			−0.498796			−0.249398	+	0.968401i	$0.580233\pi$
$810$		0			0
$811$	21.0255	−	36.4173i	0.738307	−	1.27879i	−0.214950	−	0.976625i	$-0.568959\pi$
$811$	21.0255	−	36.4173i	0.738307	−	1.27879i	0.953257	−	0.302160i	$-0.0977077\pi$
$812$	−4.54301	−	14.3411i	−0.159428	−	0.503273i
$813$		0			0
$814$	−12.0127	−	27.2511i	−0.421046	−	0.955151i
$815$	−43.5381	+	25.1367i	−1.52507	+	0.880501i
$816$		0			0
$817$	12.5801	−	22.0642i	0.440122	−	0.771929i
$818$	−2.15814	+	19.8294i	−0.0754576	+	0.693320i
$819$		0			0
$820$	7.72682	−	2.44772i	0.269832	−	0.0854782i
$821$	22.3593	−	38.7274i	0.780343	−	1.35159i	−0.151398	−	0.988473i	$-0.548378\pi$
$821$	22.3593	−	38.7274i	0.780343	−	1.35159i	0.931742	−	0.363122i	$-0.118289\pi$
$822$		0			0
$823$	−34.6560	−	20.0087i	−1.20803	−	0.697458i	−0.245703	−	0.969345i	$-0.579019\pi$
$823$	−34.6560	−	20.0087i	−1.20803	−	0.697458i	−0.962329	+	0.271887i	$0.912352\pi$
$824$	1.41154	+	0.475969i	0.0491733	+	0.0165812i
$825$		0			0
$826$	8.09119	+	5.92432i	0.281529	+	0.206133i
$827$	−13.1881	+	22.8424i	−0.458594	+	0.794309i	−0.998887	−	0.0471684i	$-0.984980\pi$
$827$	−13.1881	+	22.8424i	−0.458594	+	0.794309i	0.540293	+	0.841477i	$0.318314\pi$
$828$		0			0
$829$			39.6736i			1.37792i	0.724798	+	0.688961i	$0.241933\pi$
$829$			39.6736i			1.37792i	−0.724798	+	0.688961i	$0.758067\pi$
$830$	−28.6922	−	21.0082i	−0.995920	−	0.729206i
$831$		0			0
$832$	7.60245	+	18.1458i	0.263567	+	0.629094i
$833$	−4.15898	−	7.20357i	−0.144100	−	0.249589i
$834$		0			0
$835$	−11.5730			−0.400502
$836$	−17.9929	−	3.86152i	−0.622299	−	0.133554i
$837$		0			0
$838$	40.8017	−	17.9860i	1.40947	−	0.621317i
$839$	7.96193	+	13.7905i	0.274876	+	0.476100i	0.970104	−	0.242690i	$-0.0780298\pi$
$839$	7.96193	+	13.7905i	0.274876	+	0.476100i	−0.695228	+	0.718790i	$0.744696\pi$
$840$		0			0
$841$	3.59168	+	6.22098i	0.123851	+	0.214516i
$842$	30.6169	+	22.4175i	1.05513	+	0.772558i
$843$		0			0
$844$	0.325207	+	0.0716365i	0.0111941	+	0.00246583i
$845$	11.1464	−	19.3062i	0.383449	−	0.664152i
$846$		0			0
$847$			8.18285i			0.281166i
$848$	−12.0126	+	25.9437i	−0.412515	+	0.890910i
$849$		0			0
$850$	4.61073	+	10.4595i	0.158147	+	0.358759i
$851$	43.8856	−	76.0122i	1.50438	−	2.60566i
$852$		0			0
$853$	19.4390	+	33.6693i	0.665578	+	1.15281i	0.979128	+	0.203243i	$0.0651482\pi$
$853$	19.4390	+	33.6693i	0.665578	+	1.15281i	−0.313550	+	0.949572i	$0.601518\pi$
$854$	−1.07529	+	9.87995i	−0.0367955	+	0.338085i
$855$		0			0
$856$	−18.5350	−	6.24998i	−0.633513	−	0.213620i
$857$	−28.7983	+	16.6267i	−0.983730	+	0.567957i	−0.903394	−	0.428811i	$-0.858933\pi$
$857$	−28.7983	+	16.6267i	−0.983730	+	0.567957i	−0.0803358	+	0.996768i	$0.525599\pi$
$858$		0			0
$859$	28.1710	+	16.2645i	0.961183	+	0.554939i	0.896537	−	0.442969i	$-0.146075\pi$
$859$	28.1710	+	16.2645i	0.961183	+	0.554939i	0.0646461	+	0.997908i	$0.479408\pi$
$860$	−35.6246	+	11.2853i	−1.21479	+	0.384824i
$861$		0			0
$862$	10.9416	+	1.19083i	0.372672	+	0.0405598i
$863$	20.4964			0.697707			0.348853	−	0.937177i	$-0.386571\pi$
$863$	20.4964			0.697707			0.348853	+	0.937177i	$0.386571\pi$
$864$		0			0
$865$	14.3307	+	8.27386i	0.487260	+	0.281320i
$866$	2.34718	−	21.5663i	0.0797603	−	0.732854i
$867$		0			0
$868$	14.3803	+	13.1415i	0.488099	+	0.446050i
$869$	−13.7911	+	7.96231i	−0.467832	+	0.270103i
$870$		0			0
$871$	0.100455	−	0.0579979i	0.00340380	−	0.00196518i
$872$	33.5889	−	6.75195i	1.13746	−	0.228650i
$873$		0			0
$874$	−22.1451	−	49.5091i	−0.749069	−	1.67467i
$875$		−	1.13333i		−	0.0383137i
$876$		0			0
$877$	−29.2384	+	16.8808i	−0.987312	+	0.570025i	−0.904470	−	0.426538i	$-0.859733\pi$
$877$	−29.2384	+	16.8808i	−0.987312	+	0.570025i	−0.0828424	+	0.996563i	$0.526400\pi$
$878$	21.0787	−	28.7885i	0.711372	−	0.971563i
$879$		0			0
$880$	15.5900	+	22.1374i	0.525539	+	0.746253i
$881$	37.8371			1.27476			0.637382	−	0.770548i	$-0.280017\pi$
$881$	37.8371			1.27476			0.637382	+	0.770548i	$0.280017\pi$
$882$		0			0
$883$	23.2555	+	13.4265i	0.782609	+	0.451839i	0.837354	−	0.546661i	$-0.184101\pi$
$883$	23.2555	+	13.4265i	0.782609	+	0.451839i	−0.0547454	+	0.998500i	$0.517435\pi$
$884$	5.55529	+	5.07672i	0.186845	+	0.170748i
$885$		0			0
$886$	−0.362369	+	3.32952i	−0.0121740	+	0.111858i
$887$	−4.11911	+	7.13451i	−0.138306	+	0.239554i	−0.926856	−	0.375418i	$-0.877499\pi$
$887$	−4.11911	+	7.13451i	−0.138306	+	0.239554i	0.788549	+	0.614972i	$0.210832\pi$
$888$		0			0
$889$	−6.19993	−	3.57953i	−0.207939	−	0.120054i
$890$	−28.8671	+	12.7251i	−0.967629	+	0.426546i
$891$		0			0
$892$	22.9138	+	5.04743i	0.767209	+	0.169000i
$893$	30.8487	−	0.166907i	1.03231	−	0.00558533i
$894$		0			0
$895$	4.42865	+	7.67065i	0.148033	+	0.256401i
$896$	−13.7574	−	3.29764i	−0.459603	−	0.110166i
$897$		0			0
$898$	−15.1113	+	6.66132i	−0.504272	+	0.222291i
$899$	−40.5782	−	23.4279i	−1.35336	−	0.781363i
$900$		0			0
$901$			10.9360i			0.364330i
$902$	2.22889	−	3.04412i	0.0742138	−	0.101358i
$903$		0			0
$904$	4.47737	−	13.2781i	0.148915	−	0.441624i
$905$			7.69687i			0.255853i
$906$		0			0
$907$	12.9847	+	22.4902i	0.431150	+	0.746774i	0.996973	−	0.0777533i	$-0.0247747\pi$
$907$	12.9847	+	22.4902i	0.431150	+	0.746774i	−0.565823	+	0.824527i	$0.691441\pi$
$908$	−11.8494	+	12.9665i	−0.393238	+	0.430308i
$909$		0			0
$910$	−5.62512	−	12.7607i	−0.186471	−	0.423013i
$911$	−35.0480			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$911$	−35.0480			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$912$		0			0
$913$	−16.5531			−0.547829
$914$	−4.97275	−	11.2808i	−0.164484	−	0.373135i
$915$		0			0
$916$	8.81495	−	9.64593i	0.291254	−	0.318711i
$917$	11.6730	+	20.2182i	0.385477	+	0.667665i
$918$		0			0
$919$			6.29627i			0.207695i	0.994593	+	0.103847i	$0.0331153\pi$
$919$			6.29627i			0.207695i	−0.994593	+	0.103847i	$0.966885\pi$
$920$	−25.4974	+	75.6152i	−0.840623	+	2.49296i
$921$		0			0
$922$	−17.6434	+	24.0966i	−0.581054	+	0.793580i
$923$		−	15.3750i		−	0.506075i
$924$		0			0
$925$	−45.6392	−	26.3498i	−1.50061	−	0.866376i
$926$	−0.460234	+	0.202879i	−0.0151242	+	0.00666701i
$927$		0			0
$928$	34.0217	+	0.627551i	1.11682	+	0.0206004i
$929$	1.85864	+	3.21925i	0.0609799	+	0.105620i	0.894904	−	0.446259i	$-0.147244\pi$
$929$	1.85864	+	3.21925i	0.0609799	+	0.105620i	−0.833924	+	0.551880i	$0.813911\pi$
$930$		0			0
$931$	20.4576	−	11.9592i	0.670469	−	0.391948i
$932$	51.2963	+	11.2995i	1.68027	+	0.370128i
$933$		0			0
$934$	5.79675	−	2.55530i	0.189676	−	0.0836120i
$935$	8.96938	+	5.17848i	0.293330	+	0.169354i
$936$		0			0
$937$	−21.7674	+	37.7022i	−0.711109	+	1.23168i	0.253332	+	0.967379i	$0.418473\pi$
$937$	−21.7674	+	37.7022i	−0.711109	+	1.23168i	−0.964441	+	0.264298i	$0.914860\pi$
$938$	−0.00902461	+	0.0829200i	−0.000294664	+	0.00270743i
$939$		0			0
$940$	−33.5055	−	30.6191i	−1.09283	−	0.998683i
$941$	−34.9810	−	20.1963i	−1.14035	−	0.658380i	−0.193831	−	0.981035i	$-0.562091\pi$
$941$	−34.9810	−	20.1963i	−1.14035	−	0.658380i	−0.946517	+	0.322655i	$0.895425\pi$
$942$		0			0
$943$	11.1194			0.362097
$944$	−18.5459	+	13.0607i	−0.603616	+	0.425089i
$945$		0			0
$946$	−10.2763	+	14.0349i	−0.334111	+	0.456315i
$947$	21.1885	−	12.2332i	0.688533	−	0.397525i	−0.114529	−	0.993420i	$-0.536536\pi$
$947$	21.1885	−	12.2332i	0.688533	−	0.397525i	0.803062	+	0.595895i	$0.203203\pi$
$948$		0			0
$949$			3.23686i			0.105073i
$950$	−29.7262	+	13.2963i	−0.964446	+	0.431390i
$951$		0			0
$952$	−5.30533	+	1.06646i	−0.171947	+	0.0345642i
$953$	43.7145	−	25.2386i	1.41605	−	0.817557i	0.420101	−	0.907477i	$-0.361994\pi$
$953$	43.7145	−	25.2386i	1.41605	−	0.817557i	0.995949	+	0.0899200i	$0.0286611\pi$
$954$		0			0
$955$	−12.1780	+	7.03099i	−0.394072	+	0.227518i
$956$	−34.7988	−	31.8010i	−1.12547	−	1.02852i
$957$		0			0
$958$	−3.79808	+	34.8975i	−0.122710	+	1.12749i
$959$	21.5851	+	12.4622i	0.697019	+	0.402424i
$960$		0			0
$961$	29.6759			0.957286
$962$	−34.4920	−	3.75394i	−1.11207	−	0.121032i
$963$		0			0
$964$	29.8626	−	9.45995i	0.961809	−	0.304684i
$965$	−24.8998	−	14.3759i	−0.801552	−	0.462776i
$966$		0			0
$967$	−43.6786	+	25.2179i	−1.40461	+	0.810952i	−0.994861	−	0.101246i	$-0.967717\pi$
$967$	−43.6786	+	25.2179i	−1.40461	+	0.810952i	−0.409749	+	0.912198i	$0.634384\pi$
$968$	−17.5389	−	5.91409i	−0.563721	−	0.190086i
$969$		0			0
$970$	−4.82676	+	44.3493i	−0.154978	+	1.42397i
$971$	−5.26456	−	9.11849i	−0.168948	−	0.292626i	0.769102	−	0.639126i	$-0.220704\pi$
$971$	−5.26456	−	9.11849i	−0.168948	−	0.292626i	−0.938050	+	0.346499i	$0.887370\pi$
$972$		0			0
$973$	−6.52645	+	11.3041i	−0.209228	+	0.362394i
$974$	20.6559	+	46.8582i	0.661856	+	1.50143i
$975$		0			0
$976$	−20.3993	−	9.44539i	−0.652964	−	0.302340i
$977$		−	6.92660i		−	0.221602i	−0.993843	−	0.110801i	$-0.964658\pi$
$977$		−	6.92660i		−	0.221602i	0.993843	−	0.110801i	$-0.0353415\pi$
$978$		0			0
$979$	−7.34243	+	12.7175i	−0.234665	+	0.406452i
$980$	−34.0490	−	7.50031i	−1.08766	−	0.239588i
$981$		0			0
$982$	6.79967	+	4.97868i	0.216986	+	0.158876i
$983$	17.5996	+	30.4835i	0.561341	+	0.972272i	0.997380	+	0.0723437i	$0.0230479\pi$
$983$	17.5996	+	30.4835i	0.561341	+	0.972272i	−0.436038	+	0.899928i	$0.643619\pi$
$984$		0			0
$985$	−2.23213	−	3.86616i	−0.0711215	−	0.123186i
$986$	11.9101	−	5.25016i	0.379295	−	0.167199i
$987$		0			0
$988$	−14.3770	+	15.9043i	−0.457394	+	0.505982i
$989$	−51.2660			−1.63016
$990$		0			0
$991$	−24.9524	−	43.2188i	−0.792638	−	1.37289i	−0.924328	−	0.381599i	$-0.875374\pi$
$991$	−24.9524	−	43.2188i	−0.792638	−	1.37289i	0.131690	−	0.991291i	$-0.457960\pi$
$992$	−38.5603	+	21.3244i	−1.22429	+	0.677051i
$993$		0			0
$994$	8.92028	+	6.53137i	0.282934	+	0.207163i
$995$			0.895899i			0.0284019i
$996$		0			0
$997$	−2.63314	+	4.56074i	−0.0833925	+	0.144440i	−0.904705	−	0.426038i	$-0.859909\pi$
$997$	−2.63314	+	4.56074i	−0.0833925	+	0.144440i	0.821313	+	0.570478i	$0.193242\pi$
$998$	26.5598	+	19.4469i	0.840734	+	0.615580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.r.a.487.5		16
3.2	odd	2		76.2.f.a.31.4	yes	16
4.3	odd	2	inner	684.2.r.a.487.2		16
12.11	even	2		76.2.f.a.31.7	yes	16
19.8	odd	6	inner	684.2.r.a.559.2		16
24.5	odd	2		1216.2.n.f.639.6		16
24.11	even	2		1216.2.n.f.639.3		16
57.8	even	6		76.2.f.a.27.7	yes	16
76.27	even	6	inner	684.2.r.a.559.5		16
228.179	odd	6		76.2.f.a.27.4	✓	16
456.179	odd	6		1216.2.n.f.255.6		16
456.293	even	6		1216.2.n.f.255.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.f.a.27.4	✓	16	228.179	odd	6
76.2.f.a.27.7	yes	16	57.8	even	6
76.2.f.a.31.4	yes	16	3.2	odd	2
76.2.f.a.31.7	yes	16	12.11	even	2
684.2.r.a.487.2		16	4.3	odd	2	inner
684.2.r.a.487.5		16	1.1	even	1	trivial
684.2.r.a.559.2		16	19.8	odd	6	inner
684.2.r.a.559.5		16	76.27	even	6	inner
1216.2.n.f.255.3		16	456.293	even	6
1216.2.n.f.255.6		16	456.179	odd	6
1216.2.n.f.639.3		16	24.11	even	2
1216.2.n.f.639.6		16	24.5	odd	2

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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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.570443 + 1.29406i) q^{2} +(-1.34919 + 1.47638i) q^{4} +(1.60333 + 2.77705i) q^{5} +1.25044i q^{7} +(-2.68016 - 0.903746i) q^{8} +(-2.67906 + 3.65895i) q^{10} +2.11093i q^{11} +(2.12978 + 1.22963i) q^{13} +(-1.61815 + 0.713305i) q^{14} +(-0.359374 - 3.98382i) q^{16} +(-0.765026 - 1.32506i) q^{17} +(3.76307 - 2.19984i) q^{19} +(-6.26316 - 1.37965i) q^{20} +(-2.73167 + 1.20416i) q^{22} +(-7.61951 - 4.39913i) q^{23} +(-2.64132 + 4.57491i) q^{25} +(-0.376297 + 3.45750i) q^{26} +(-1.84612 - 1.68708i) q^{28} +(5.20937 + 3.00763i) q^{29} -7.78947 q^{31} +(4.95031 - 2.73760i) q^{32} +(1.27831 - 1.74586i) q^{34} +(-3.47253 + 2.00487i) q^{35} +9.97599i q^{37} +(4.99335 + 3.61476i) q^{38} +(-1.78743 - 8.89192i) q^{40} +(-1.09450 + 0.631908i) q^{41} +(5.04619 - 2.91342i) q^{43} +(-3.11653 - 2.84804i) q^{44} +(1.34624 - 12.3696i) q^{46} +(6.12910 + 3.53864i) q^{47} +5.43640 q^{49} +(-7.42693 - 0.808311i) q^{50} +(-4.68887 + 1.48535i) q^{52} +(-6.18988 - 3.57373i) q^{53} +(-5.86215 + 3.38451i) q^{55} +(1.13008 - 3.35138i) q^{56} +(-0.920411 + 8.45692i) q^{58} +(-2.83541 - 4.91107i) q^{59} +(2.80998 - 4.86704i) q^{61} +(-4.44345 - 10.0801i) q^{62} +(6.36649 + 4.84436i) q^{64} +7.88599i q^{65} +(0.0235835 - 0.0408478i) q^{67} +(2.98846 + 0.658296i) q^{68} +(-4.57530 - 3.35000i) q^{70} +(-3.12595 - 5.41430i) q^{71} +(0.658098 + 1.13986i) q^{73} +(-12.9095 + 5.69073i) q^{74} +(-1.82930 + 8.52371i) q^{76} -2.63959 q^{77} +(3.77194 + 6.53320i) q^{79} +(10.4871 - 7.38538i) q^{80} +(-1.44208 - 1.05588i) q^{82} +7.84164i q^{83} +(2.45317 - 4.24902i) q^{85} +(6.64871 + 4.86814i) q^{86} +(1.90774 - 5.65762i) q^{88} +(6.02458 + 3.47830i) q^{89} +(-1.53758 + 2.66316i) q^{91} +(16.7749 - 5.31401i) q^{92} +(-1.08291 + 9.95003i) q^{94} +(12.1425 + 6.92315i) q^{95} +(8.51935 - 4.91865i) q^{97} +(3.10116 + 7.03503i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 3 q^{4} + 2 q^{5} - 6 q^{10} - 18 q^{13} + 6 q^{14} - 3 q^{16} - 2 q^{17} - 4 q^{20} + 3 q^{22} - 2 q^{25} + 24 q^{26} - 4 q^{28} + 6 q^{29} - 27 q^{32} + 36 q^{34} + 24 q^{38} + 48 q^{40}+ \cdots - 51 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 3 * q^4 + 2 * q^5 - 6 * q^10 - 18 * q^13 + 6 * q^14 - 3 * q^16 - 2 * q^17 - 4 * q^20 + 3 * q^22 - 2 * q^25 + 24 * q^26 - 4 * q^28 + 6 * q^29 - 27 * q^32 + 36 * q^34 + 24 * q^38 + 48 * q^40 + 48 * q^41 + 25 * q^44 + 16 * q^49 + 6 * q^52 - 6 * q^53 - 40 * q^58 - 26 * q^61 - 32 * q^62 - 18 * q^64 + 36 * q^68 - 54 * q^70 + 16 * q^73 + 2 * q^74 + 43 * q^76 - 80 * q^77 + 30 * q^80 + 11 * q^82 + 14 * q^85 + 48 * q^86 - 18 * q^89 + 52 * q^92 - 12 * q^97 - 51 * q^98

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