LMFDB - Embedded newform 1216.2.n.f.255.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(255,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1216.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.n (of order $6$, degree $2$, not 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:	$9.70980888579$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.6
Root			$0.570443 - 1.29406i$ of defining polynomial
Character	$\chi$	$=$	1216.255
Dual form			1216.2.n.f.639.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.637123 - 1.10353i) q^{3} +(1.60333 - 2.77705i) q^{5} -1.25044i q^{7} +(0.688149 + 1.19191i) q^{9} -2.11093i q^{11} +(-2.12978 + 1.22963i) q^{13} +(-2.04303 - 3.53864i) q^{15} +(0.765026 - 1.32506i) q^{17} +(-3.76307 - 2.19984i) q^{19} +(-1.37990 - 0.796684i) q^{21} +(7.61951 - 4.39913i) q^{23} +(-2.64132 - 4.57491i) q^{25} +5.57648 q^{27} +(5.20937 - 3.00763i) q^{29} -7.78947 q^{31} +(-2.32947 - 1.34492i) q^{33} +(-3.47253 - 2.00487i) q^{35} +9.97599i q^{37} +3.13370i q^{39} +(1.09450 + 0.631908i) q^{41} +(-5.04619 - 2.91342i) q^{43} +4.41331 q^{45} +(-6.12910 + 3.53864i) q^{47} +5.43640 q^{49} +(-0.974831 - 1.68846i) q^{51} +(-6.18988 + 3.57373i) q^{53} +(-5.86215 - 3.38451i) q^{55} +(-4.82513 + 2.75109i) q^{57} +(-2.83541 + 4.91107i) q^{59} +(-2.80998 - 4.86704i) q^{61} +(1.49041 - 0.860489i) q^{63} +7.88599i q^{65} +(-0.0235835 - 0.0408478i) q^{67} -11.2111i q^{69} +(3.12595 - 5.41430i) q^{71} +(0.658098 - 1.13986i) q^{73} -6.73139 q^{75} -2.63959 q^{77} +(3.77194 - 6.53320i) q^{79} +(1.48846 - 2.57808i) q^{81} -7.84164i q^{83} +(-2.45317 - 4.24902i) q^{85} -7.66492i q^{87} +(-6.02458 + 3.47830i) q^{89} +(1.53758 + 2.66316i) q^{91} +(-4.96285 + 8.59591i) q^{93} +(-12.1425 + 6.92315i) q^{95} +(8.51935 + 4.91865i) q^{97} +(2.51603 - 1.45263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} - 4 q^{9} + 18 q^{13} + 2 q^{17} - 2 q^{25} + 6 q^{29} + 18 q^{33} - 48 q^{41} - 24 q^{45} + 16 q^{49} - 6 q^{53} - 26 q^{57} + 26 q^{61} + 16 q^{73} - 80 q^{77} + 12 q^{81} - 14 q^{85} + 18 q^{89}+ \cdots - 12 q^{97}+O(q^{100}) $ 16 * q + 2 * q^5 - 4 * q^9 + 18 * q^13 + 2 * q^17 - 2 * q^25 + 6 * q^29 + 18 * q^33 - 48 * q^41 - 24 * q^45 + 16 * q^49 - 6 * q^53 - 26 * q^57 + 26 * q^61 + 16 * q^73 - 80 * q^77 + 12 * q^81 - 14 * q^85 + 18 * q^89 + 20 * q^93 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.637123	−	1.10353i	0.367843	−	0.637123i	−0.621385	−	0.783505i	$-0.713430\pi$
$3$	0.637123	−	1.10353i	0.367843	−	0.637123i	0.989228	+	0.146382i	$0.0467630\pi$
$4$		0			0
$5$	1.60333	−	2.77705i	0.717030	−	1.24193i	−0.245141	−	0.969487i	$-0.578834\pi$
$5$	1.60333	−	2.77705i	0.717030	−	1.24193i	0.962171	−	0.272445i	$-0.0878324\pi$
$6$		0			0
$7$		−	1.25044i		−	0.472622i	−0.971677	−	0.236311i	$-0.924062\pi$
$7$		−	1.25044i		−	0.472622i	0.971677	−	0.236311i	$-0.0759384\pi$
$8$		0			0
$9$	0.688149	+	1.19191i	0.229383	+	0.397303i
$10$		0			0
$11$		−	2.11093i		−	0.636469i	−0.948012	−	0.318234i	$-0.896910\pi$
$11$		−	2.11093i		−	0.636469i	0.948012	−	0.318234i	$-0.103090\pi$
$12$		0			0
$13$	−2.12978	+	1.22963i	−0.590695	+	0.341038i	−0.765372	−	0.643588i	$-0.777445\pi$
$13$	−2.12978	+	1.22963i	−0.590695	+	0.341038i	0.174678	+	0.984626i	$0.444112\pi$
$14$		0			0
$15$	−2.04303	−	3.53864i	−0.527509	−	0.913673i
$16$		0			0
$17$	0.765026	−	1.32506i	0.185546	−	0.321375i	−0.758214	−	0.652005i	$-0.773928\pi$
$17$	0.765026	−	1.32506i	0.185546	−	0.321375i	0.943760	+	0.330630i	$0.107261\pi$
$18$		0			0
$19$	−3.76307	−	2.19984i	−0.863308	−	0.504678i
$19$	−3.76307	−	2.19984i	−0.863308	−	0.504678i
$20$		0			0
$21$	−1.37990	−	0.796684i	−0.301118	−	0.173851i
$22$		0			0
$23$	7.61951	−	4.39913i	1.58878	−	0.917282i	0.595270	−	0.803526i	$-0.297045\pi$
$23$	7.61951	−	4.39913i	1.58878	−	0.917282i	0.993509	−	0.113756i	$-0.0362881\pi$
$24$		0			0
$25$	−2.64132	−	4.57491i	−0.528265	−	0.914981i
$26$		0			0
$27$	5.57648			1.07319
$28$		0			0
$29$	5.20937	−	3.00763i	0.967356	−	0.558503i	0.0689265	−	0.997622i	$-0.478043\pi$
$29$	5.20937	−	3.00763i	0.967356	−	0.558503i	0.898429	+	0.439119i	$0.144709\pi$
$30$		0			0
$31$	−7.78947			−1.39903			−0.699515	−	0.714618i	$-0.746601\pi$
$31$	−7.78947			−1.39903			−0.699515	+	0.714618i	$0.746601\pi$
$32$		0			0
$33$	−2.32947	−	1.34492i	−0.405509	−	0.234121i
$34$		0			0
$35$	−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	$0.693962\pi$
$38$		0			0
$39$			3.13370i			0.501793i
$40$		0			0
$41$	1.09450	+	0.631908i	0.170932	+	0.0986875i	0.583025	−	0.812454i	$-0.301869\pi$
$41$	1.09450	+	0.631908i	0.170932	+	0.0986875i	−0.412093	+	0.911142i	$0.635202\pi$
$42$		0			0
$43$	−5.04619	−	2.91342i	−0.769537	−	0.444292i	0.0631725	−	0.998003i	$-0.479878\pi$
$43$	−5.04619	−	2.91342i	−0.769537	−	0.444292i	−0.832709	+	0.553710i	$0.813211\pi$
$44$		0			0
$45$	4.41331			0.657898
$46$		0			0
$47$	−6.12910	+	3.53864i	−0.894022	+	0.516164i	−0.875256	−	0.483660i	$-0.839307\pi$
$47$	−6.12910	+	3.53864i	−0.894022	+	0.516164i	−0.0187658	+	0.999824i	$0.505974\pi$
$48$		0			0
$49$	5.43640			0.776629
$50$		0			0
$51$	−0.974831	−	1.68846i	−0.136504	−	0.236431i
$52$		0			0
$53$	−6.18988	+	3.57373i	−0.850246	+	0.490890i	−0.860734	−	0.509055i	$-0.829995\pi$
$53$	−6.18988	+	3.57373i	−0.850246	+	0.490890i	0.0104881	+	0.999945i	$0.496661\pi$
$54$		0			0
$55$	−5.86215	−	3.38451i	−0.790452	−	0.456367i
$56$		0			0
$57$	−4.82513	+	2.75109i	−0.639104	+	0.364391i
$58$		0			0
$59$	−2.83541	+	4.91107i	−0.369138	+	0.639367i	−0.989431	−	0.145004i	$-0.953681\pi$
$59$	−2.83541	+	4.91107i	−0.369138	+	0.639367i	0.620293	+	0.784371i	$0.287014\pi$
$60$		0			0
$61$	−2.80998	−	4.86704i	−0.359782	−	0.623160i	0.628142	−	0.778098i	$-0.283815\pi$
$61$	−2.80998	−	4.86704i	−0.359782	−	0.623160i	−0.987924	+	0.154938i	$0.950482\pi$
$62$		0			0
$63$	1.49041	−	0.860489i	0.187774	−	0.108411i
$64$		0			0
$65$			7.88599i			0.978137i
$66$		0			0
$67$	−0.0235835	−	0.0408478i	−0.00288118	−	0.00499036i	0.864581	−	0.502493i	$-0.167584\pi$
$67$	−0.0235835	−	0.0408478i	−0.00288118	−	0.00499036i	−0.867462	+	0.497503i	$0.834250\pi$
$68$		0			0
$69$		−	11.2111i		−	1.34966i
$70$		0			0
$71$	3.12595	−	5.41430i	0.370982	−	0.642559i	−0.618735	−	0.785600i	$-0.712355\pi$
$71$	3.12595	−	5.41430i	0.370982	−	0.642559i	0.989717	+	0.143041i	$0.0456879\pi$
$72$		0			0
$73$	0.658098	−	1.13986i	0.0770245	−	0.133410i	−0.824940	−	0.565220i	$-0.808791\pi$
$73$	0.658098	−	1.13986i	0.0770245	−	0.133410i	0.901965	+	0.431809i	$0.142125\pi$
$74$		0			0
$75$	−6.73139			−0.777274
$76$		0			0
$77$	−2.63959			−0.300809
$78$		0			0
$79$	3.77194	−	6.53320i	0.424377	−	0.735042i	−0.571985	−	0.820264i	$-0.693826\pi$
$79$	3.77194	−	6.53320i	0.424377	−	0.735042i	0.996362	+	0.0852216i	$0.0271598\pi$
$80$		0			0
$81$	1.48846	−	2.57808i	0.165384	−	0.286454i
$82$		0			0
$83$		−	7.84164i		−	0.860732i	−0.902655	−	0.430366i	$-0.858385\pi$
$83$		−	7.84164i		−	0.860732i	0.902655	−	0.430366i	$-0.141615\pi$
$84$		0			0
$85$	−2.45317	−	4.24902i	−0.266084	−	0.460871i
$86$		0			0
$87$		−	7.66492i		−	0.821766i
$88$		0			0
$89$	−6.02458	+	3.47830i	−0.638605	+	0.368699i	−0.784077	−	0.620664i	$-0.786863\pi$
$89$	−6.02458	+	3.47830i	−0.638605	+	0.368699i	0.145472	+	0.989362i	$0.453530\pi$
$90$		0			0
$91$	1.53758	+	2.66316i	0.161182	+	0.279175i
$92$		0			0
$93$	−4.96285	+	8.59591i	−0.514624	+	0.891354i
$94$		0			0
$95$	−12.1425	+	6.92315i	−1.24579	+	0.710300i
$96$		0			0
$97$	8.51935	+	4.91865i	0.865009	+	0.499413i	0.865687	−	0.500586i	$-0.166882\pi$
$97$	8.51935	+	4.91865i	0.865009	+	0.499413i	−0.000677265		1.00000i	$0.500216\pi$
$98$		0			0
$99$	2.51603	−	1.45263i	0.252871	−	0.145995i
$100$		0			0
$101$	3.13338	+	5.42717i	0.311783	+	0.540024i	0.978748	−	0.205065i	$-0.0657405\pi$
$101$	3.13338	+	5.42717i	0.311783	+	0.540024i	−0.666965	+	0.745089i	$0.732407\pi$
$102$		0			0
$103$	−0.526662			−0.0518936			−0.0259468	−	0.999663i	$-0.508260\pi$
$103$	−0.526662			−0.0518936			−0.0259468	+	0.999663i	$0.508260\pi$
$104$		0			0
$105$	−4.42486	+	2.55469i	−0.431822	+	0.249312i
$106$		0			0
$107$	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	$-0.136343\pi$
$109$	10.4902	+	6.05651i	1.00478	+	0.580109i	0.0951195	+	0.995466i	$0.469677\pi$
$110$		0			0
$111$	11.0088	+	6.35593i	1.04491	+	0.603278i
$112$		0			0
$113$			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
$116$		0			0
$117$	−2.93121	−	1.69233i	−0.270990	−	0.156456i
$118$		0			0
$119$	−1.65691	−	0.956619i	−0.151889	−	0.0876931i
$120$		0			0
$121$	6.54398			0.594907
$122$		0			0
$123$	1.39466	−	0.805207i	0.125752	−	0.0726030i
$124$		0			0
$125$	−0.906349			−0.0810663
$126$		0			0
$127$	−2.86262	−	4.95820i	−0.254016	−	0.439969i	0.710612	−	0.703584i	$-0.248418\pi$
$127$	−2.86262	−	4.95820i	−0.254016	−	0.439969i	−0.964628	+	0.263616i	$0.915085\pi$
$128$		0			0
$129$	−6.43009	+	3.71241i	−0.566138	+	0.326860i
$130$		0			0
$131$	16.1689	+	9.33512i	1.41268	+	0.815613i	0.995640	−	0.0932738i	$-0.0297332\pi$
$131$	16.1689	+	9.33512i	1.41268	+	0.815613i	0.417043	+	0.908887i	$0.363067\pi$
$132$		0			0
$133$	−2.75077	+	4.70549i	−0.238522	+	0.408018i
$134$		0			0
$135$	8.94093	−	15.4861i	0.769512	−	1.33283i
$136$		0			0
$137$	−9.96622	−	17.2620i	−0.851471	−	1.47479i	−0.879880	−	0.475195i	$-0.842377\pi$
$137$	−9.96622	−	17.2620i	−0.851471	−	1.47479i	0.0284092	−	0.999596i	$-0.490956\pi$
$138$		0			0
$139$	−9.04013	+	5.21932i	−0.766774	+	0.442697i	−0.831723	−	0.555191i	$-0.812645\pi$
$139$	−9.04013	+	5.21932i	−0.766774	+	0.442697i	0.0649485	+	0.997889i	$0.479312\pi$
$140$		0			0
$141$			9.01819i			0.759469i
$142$		0			0
$143$	2.59566	+	4.49581i	0.217060	+	0.375959i
$144$		0			0
$145$		−	19.2889i		−	1.60185i
$146$		0			0
$147$	3.46366	−	5.99923i	0.285677	−	0.494808i
$148$		0			0
$149$	4.83307	−	8.37113i	0.395941	−	0.685789i	−0.597280	−	0.802033i	$-0.703752\pi$
$149$	4.83307	−	8.37113i	0.395941	−	0.685789i	0.993221	+	0.116243i	$0.0370853\pi$
$150$		0			0
$151$	11.1033			0.903573			0.451787	−	0.892126i	$-0.350787\pi$
$151$	11.1033			0.903573			0.451787	+	0.892126i	$0.350787\pi$
$152$		0			0
$153$	2.10581			0.170244
$154$		0			0
$155$	−12.4891	+	21.6317i	−1.00315	+	1.73750i
$156$		0			0
$157$	5.65983	−	9.80311i	0.451704	−	0.782374i	−0.546788	−	0.837271i	$-0.684150\pi$
$157$	5.65983	−	9.80311i	0.451704	−	0.782374i	0.998492	+	0.0548972i	$0.0174831\pi$
$158$		0			0
$159$			9.10762i			0.722281i
$160$		0			0
$161$	−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			0
$165$	−7.46982	+	4.31270i	−0.581524	+	0.335743i
$166$		0			0
$167$	1.80453	+	3.12555i	0.139639	+	0.241862i	0.927360	−	0.374170i	$-0.122072\pi$
$167$	1.80453	+	3.12555i	0.139639	+	0.241862i	−0.787721	+	0.616032i	$0.788739\pi$
$168$		0			0
$169$	−3.47603	+	6.02065i	−0.267387	+	0.463127i
$170$		0			0
$171$	0.0324579	−	5.99905i	0.00248212	−	0.458759i
$172$		0			0
$173$	4.46906	+	2.58021i	0.339776	+	0.196170i	0.660173	−	0.751113i	$-0.270483\pi$
$173$	4.46906	+	2.58021i	0.339776	+	0.196170i	−0.320397	+	0.947283i	$0.603816\pi$
$174$		0			0
$175$	−5.72065	+	3.30282i	−0.432440	+	0.249669i
$176$		0			0
$177$	3.61301	+	6.25791i	0.271570	+	0.470373i
$178$		0			0
$179$	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	$-0.695099\pi$
$181$	−2.07870	+	1.20014i	−0.154509	+	0.0892056i	0.420752	+	0.907176i	$0.361766\pi$
$182$		0			0
$183$	−7.16122			−0.529373
$184$		0			0
$185$	27.7038	+	15.9948i	2.03682	+	1.17596i
$186$		0			0
$187$	−2.79711	−	1.61491i	−0.204545	−	0.118094i
$188$		0			0
$189$		−	6.97305i		−	0.507215i
$190$		0			0
$191$			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	0.193781	−	0.981045i	$-0.437925\pi$
$193$	−7.76503	−	4.48314i	−0.558939	−	0.322703i	−0.752719	+	0.658341i	$0.771258\pi$
$194$		0			0
$195$	8.70243	+	5.02435i	0.623194	+	0.359801i
$196$		0			0
$197$	−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	−0.491400	−	0.870934i	$-0.663515\pi$
$199$	0.241956	−	0.139694i	0.0171518	−	0.00990261i	0.508551	+	0.861032i	$0.330181\pi$
$200$		0			0
$201$	−0.0601024			−0.00423929
$202$		0			0
$203$	−3.76086	−	6.51400i	−0.263961	−	0.457193i
$204$		0			0
$205$	3.50968	−	2.02631i	0.245126	−	0.141524i
$206$		0			0
$207$	10.4867	+	6.05451i	0.728877	+	0.420817i
$208$		0			0
$209$	−4.64371	+	7.94357i	−0.321212	+	0.549468i
$210$		0			0
$211$	0.0832510	−	0.144195i	0.00573123	−	0.00992679i	−0.863146	−	0.504955i	$-0.831509\pi$
$211$	0.0832510	−	0.144195i	0.00573123	−	0.00992679i	0.868877	+	0.495028i	$0.164842\pi$
$212$		0			0
$213$	−3.98323	−	6.89915i	−0.272926	−	0.472722i
$214$		0			0
$215$	−16.1814	+	9.34234i	−1.10356	+	0.637142i
$216$		0			0
$217$			9.74027i			0.661212i
$218$		0			0
$219$	−0.838578	−	1.45246i	−0.0566659	−	0.0981481i
$220$		0			0
$221$			3.76279i			0.253113i
$222$		0			0
$223$	−5.86577	+	10.1598i	−0.392801	+	0.680352i	−0.992818	−	0.119636i	$-0.961827\pi$
$223$	−5.86577	+	10.1598i	−0.392801	+	0.680352i	0.600017	+	0.799987i	$0.295161\pi$
$224$		0			0
$225$	3.63525	−	6.29643i	0.242350	−	0.419762i
$226$		0			0
$227$	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	$-0.430740\pi$
$229$	6.53352			0.431747			0.215874	+	0.976421i	$0.430740\pi$
$230$		0			0
$231$	−1.68174	+	2.91286i	−0.110651	+	0.191652i
$232$		0			0
$233$	13.1315	−	22.7444i	0.860274	−	1.49004i	−0.0113904	−	0.999935i	$-0.503626\pi$
$233$	13.1315	−	22.7444i	0.860274	−	1.49004i	0.871664	−	0.490103i	$-0.163041\pi$
$234$		0			0
$235$			22.6944i			1.48042i
$236$		0			0
$237$	−4.80638	−	8.32490i	−0.312208	−	0.540761i
$238$		0			0
$239$			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	−0.868591	−	0.495529i	$-0.834974\pi$
$241$	−13.5642	+	7.83128i	−0.873746	+	0.504457i	−0.00515448	+	0.999987i	$0.501641\pi$
$242$		0			0
$243$	6.46806	+	11.2030i	0.414926	+	0.718673i
$244$		0			0
$245$	8.71633	−	15.0971i	0.556866	−	0.964520i
$246$		0			0
$247$	10.7195	+	0.0579979i	0.682065	+	0.00369032i
$248$		0			0
$249$	−8.65348	−	4.99609i	−0.548392	−	0.316614i
$250$		0			0
$251$	−22.1575	+	12.7926i	−1.39857	+	0.807463i	−0.994243	−	0.107153i	$-0.965827\pi$
$251$	−22.1575	+	12.7926i	−1.39857	+	0.807463i	−0.404324	+	0.914616i	$0.632493\pi$
$252$		0			0
$253$	−9.28625	−	16.0842i	−0.583821	−	1.01121i
$254$		0			0
$255$	−6.25189			−0.391509
$256$		0			0
$257$	17.4440	−	10.0713i	1.08813	−	0.628229i	0.155049	−	0.987907i	$-0.450447\pi$
$257$	17.4440	−	10.0713i	1.08813	−	0.628229i	0.933077	+	0.359677i	$0.117113\pi$
$258$		0			0
$259$	12.4744			0.775120
$260$		0			0
$261$	7.16964	+	4.13939i	0.443790	+	0.256222i
$262$		0			0
$263$	3.14828	+	1.81766i	0.194131	+	0.112082i	0.593915	−	0.804528i	$-0.297581\pi$
$263$	3.14828	+	1.81766i	0.194131	+	0.112082i	−0.399784	+	0.916609i	$0.630915\pi$
$264$		0			0
$265$			22.9194i			1.40793i
$266$		0			0
$267$			8.86441i			0.542493i
$268$		0			0
$269$	−15.9194	−	9.19106i	−0.970622	−	0.560389i	−0.0711964	−	0.997462i	$-0.522682\pi$
$269$	−15.9194	−	9.19106i	−0.970622	−	0.560389i	−0.899426	+	0.437073i	$0.856015\pi$
$270$		0			0
$271$	16.7304	+	9.65930i	1.01630	+	0.586761i	0.913030	−	0.407893i	$-0.133736\pi$
$271$	16.7304	+	9.65930i	1.01630	+	0.586761i	0.103269	+	0.994653i	$0.467070\pi$
$272$		0			0
$273$	3.91850			0.237159
$274$		0			0
$275$	−9.65730	+	5.57564i	−0.582357	+	0.336224i
$276$		0			0
$277$	16.5581			0.994879			0.497440	−	0.867499i	$-0.334274\pi$
$277$	16.5581			0.994879			0.497440	+	0.867499i	$0.334274\pi$
$278$		0			0
$279$	−5.36031	−	9.28434i	−0.320914	−	0.555839i
$280$		0			0
$281$	3.45491	−	1.99469i	0.206103	−	0.118993i	−0.393396	−	0.919369i	$-0.628700\pi$
$281$	3.45491	−	1.99469i	0.206103	−	0.118993i	0.599499	+	0.800376i	$0.295367\pi$
$282$		0			0
$283$	12.8457	+	7.41645i	0.763596	+	0.440862i	0.830585	−	0.556892i	$-0.188006\pi$
$283$	12.8457	+	7.41645i	0.763596	+	0.440862i	−0.0669896	+	0.997754i	$0.521339\pi$
$284$		0			0
$285$	−0.0963638	+	17.8105i	−0.00570810	+	1.05500i
$286$		0			0
$287$	0.790163	−	1.36860i	0.0466419	−	0.0807861i
$288$		0			0
$289$	7.32947	+	12.6950i	0.431145	+	0.746766i
$290$		0			0
$291$	10.8558	−	6.26757i	0.636375	−	0.367412i
$292$		0			0
$293$			22.9900i			1.34309i	0.740963	+	0.671546i	$0.234369\pi$
$293$			22.9900i			1.34309i	−0.740963	+	0.671546i	$0.765631\pi$
$294$		0			0
$295$	9.09217	+	15.7481i	0.529367	+	0.916890i
$296$		0			0
$297$		−	11.7715i		−	0.683055i
$298$		0			0
$299$	−10.8186	+	18.7383i	−0.625655	+	1.08367i
$300$		0			0
$301$	−3.64306	+	6.30996i	−0.209982	+	0.363700i
$302$		0			0
$303$	7.98539			0.458749
$304$		0			0
$305$	−18.0213			−1.03190
$306$		0			0
$307$	10.3144	−	17.8650i	0.588673	−	1.01961i	−0.405734	−	0.913991i	$-0.632984\pi$
$307$	10.3144	−	17.8650i	0.588673	−	1.01961i	0.994407	−	0.105620i	$-0.0336827\pi$
$308$		0			0
$309$	−0.335549	+	0.581187i	−0.0190887	+	0.0330626i
$310$		0			0
$311$			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	0.563536	−	0.826092i	$-0.309441\pi$
$313$	−7.67203	−	13.2883i	−0.433649	−	0.751101i	−0.997184	+	0.0749904i	$0.976107\pi$
$314$		0			0
$315$		−	5.51858i		−	0.310937i
$316$		0			0
$317$	2.28007	−	1.31640i	0.128061	−	0.0739362i	−0.434601	−	0.900623i	$-0.643111\pi$
$317$	2.28007	−	1.31640i	0.128061	−	0.0739362i	0.562662	+	0.826687i	$0.309777\pi$
$318$		0			0
$319$	−6.34889	−	10.9966i	−0.355470	−	0.615692i
$320$		0			0
$321$	4.40611	−	7.63161i	0.245925	−	0.425955i
$322$		0			0
$323$	−5.79377	+	3.30337i	−0.322374	+	0.183804i
$324$		0			0
$325$	11.2509	+	6.49569i	0.624086	+	0.360316i
$326$		0			0
$327$	13.3671	−	7.71749i	0.739201	−	0.426778i
$328$		0			0
$329$	4.42486	+	7.66408i	0.243950	+	0.422534i
$330$		0			0
$331$	9.30930			0.511685			0.255843	−	0.966718i	$-0.417647\pi$
$331$	9.30930			0.511685			0.255843	+	0.966718i	$0.417647\pi$
$332$		0			0
$333$	−11.8905	+	6.86496i	−0.651593	+	0.376198i
$334$		0			0
$335$	−0.151248			−0.00826358
$336$		0			0
$337$	−3.28961	−	1.89926i	−0.179196	−	0.103459i	0.407719	−	0.913108i	$-0.366324\pi$
$337$	−3.28961	−	1.89926i	−0.179196	−	0.103459i	−0.586915	+	0.809648i	$0.699658\pi$
$338$		0			0
$339$	5.46715	+	3.15646i	0.296935	+	0.171435i
$340$		0			0
$341$			16.4430i			0.890439i
$342$		0			0
$343$		−	15.5510i		−	0.839674i
$344$		0			0
$345$	−31.1339	−	17.9751i	−1.67619	−	0.967749i
$346$		0			0
$347$	−3.07657	−	1.77626i	−0.165159	−	0.0953546i	0.415142	−	0.909757i	$-0.363732\pi$
$347$	−3.07657	−	1.77626i	−0.165159	−	0.0953546i	−0.580301	+	0.814402i	$0.697065\pi$
$348$		0			0
$349$	1.91850			0.102695			0.0513475	−	0.998681i	$-0.483648\pi$
$349$	1.91850			0.102695			0.0513475	+	0.998681i	$0.483648\pi$
$350$		0			0
$351$	−11.8767	+	6.85700i	−0.633930	+	0.366000i
$352$		0			0
$353$	−7.11843			−0.378876			−0.189438	−	0.981893i	$-0.560667\pi$
$353$	−7.11843			−0.378876			−0.189438	+	0.981893i	$0.560667\pi$
$354$		0			0
$355$	−10.0238	−	17.3618i	−0.532010	−	0.921469i
$356$		0			0
$357$	−2.11131	+	1.21897i	−0.111743	+	0.0645146i
$358$		0			0
$359$	7.25210	+	4.18700i	0.382751	+	0.220982i	0.679015	−	0.734125i	$-0.262407\pi$
$359$	7.25210	+	4.18700i	0.382751	+	0.220982i	−0.296263	+	0.955106i	$0.595741\pi$
$360$		0			0
$361$	9.32139	+	16.5563i	0.490600	+	0.871385i
$362$		0			0
$363$	4.16932	−	7.22147i	0.218833	−	0.379029i
$364$		0			0
$365$	−2.11029	−	3.65513i	−0.110458	−	0.191318i
$366$		0			0
$367$	19.7381	−	11.3958i	1.03032	−	0.594857i	0.113246	−	0.993567i	$-0.463875\pi$
$367$	19.7381	−	11.3958i	1.03032	−	0.594857i	0.917077	+	0.398710i	$0.130542\pi$
$368$		0			0
$369$			1.73939i			0.0905489i
$370$		0			0
$371$	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	$-0.208881\pi$
$374$		0			0
$375$	−0.577455	+	1.00018i	−0.0298197	+	0.0516492i
$376$		0			0
$377$	−7.39654	+	12.8112i	−0.380941	+	0.659809i
$378$		0			0
$379$	38.1884			1.96161			0.980804	−	0.194995i	$-0.0624689\pi$
$379$	38.1884			1.96161			0.980804	+	0.194995i	$0.0624689\pi$
$380$		0			0
$381$	−7.29535			−0.373752
$382$		0			0
$383$	−10.8906	+	18.8631i	−0.556483	+	0.963857i	0.441303	+	0.897358i	$0.354516\pi$
$383$	−10.8906	+	18.8631i	−0.556483	+	0.963857i	−0.997786	+	0.0664990i	$0.978817\pi$
$384$		0			0
$385$	−4.23213	+	7.33026i	−0.215689	+	0.373585i
$386$		0			0
$387$		−	8.01946i		−	0.407652i
$388$		0			0
$389$	13.4725	+	23.3351i	0.683084	+	1.18314i	0.974035	+	0.226399i	$0.0726952\pi$
$389$	13.4725	+	23.3351i	0.683084	+	1.18314i	−0.290950	+	0.956738i	$0.593971\pi$
$390$		0			0
$391$		−	13.4618i		−	0.680792i
$392$		0			0
$393$	20.6032	−	11.8952i	1.03929	−	0.600035i
$394$		0			0
$395$	−12.0953	−	20.9497i	−0.608582	−	1.05410i
$396$		0			0
$397$	−2.35770	+	4.08365i	−0.118329	+	0.204953i	−0.919106	−	0.394011i	$-0.871087\pi$
$397$	−2.35770	+	4.08365i	−0.118329	+	0.204953i	0.800776	+	0.598964i	$0.204421\pi$
$398$		0			0
$399$	3.44007	+	6.03353i	0.172219	+	0.302054i
$400$		0			0
$401$	4.16941	+	2.40721i	0.208210	+	0.120210i	0.600479	−	0.799640i	$-0.294976\pi$
$401$	4.16941	+	2.40721i	0.208210	+	0.120210i	−0.392269	+	0.919850i	$0.628310\pi$
$402$		0			0
$403$	16.5899	−	9.57816i	0.826400	−	0.477122i
$404$		0			0
$405$	−4.77297	−	8.26703i	−0.237171	−	0.410792i
$406$		0			0
$407$	21.0586			1.04384
$408$		0			0
$409$	12.2147	−	7.05216i	0.603978	−	0.348707i	−0.166627	−	0.986020i	$-0.553288\pi$
$409$	12.2147	−	7.05216i	0.603978	−	0.348707i	0.770605	+	0.637313i	$0.219954\pi$
$410$		0			0
$411$	−25.3988			−1.25283
$412$		0			0
$413$	6.14100	+	3.54551i	0.302179	+	0.174463i
$414$		0			0
$415$	−21.7766	−	12.5727i	−1.06897	−	0.617171i
$416$		0			0
$417$			13.3014i			0.651373i
$418$		0			0
$419$			31.5299i			1.54034i	0.637840	+	0.770169i	$0.279828\pi$
$419$			31.5299i			1.54034i	−0.637840	+	0.770169i	$0.720172\pi$
$420$		0			0
$421$	−23.2374	−	13.4161i	−1.13252	−	0.653862i	−0.187954	−	0.982178i	$-0.560186\pi$
$421$	−23.2374	−	13.4161i	−1.13252	−	0.653862i	−0.944568	+	0.328316i	$0.893519\pi$
$422$		0			0
$423$	−8.43547	−	4.87022i	−0.410147	−	0.236798i
$424$		0			0
$425$	−8.08272			−0.392069
$426$		0			0
$427$	−6.08594	+	3.51372i	−0.294519	+	0.170041i
$428$		0			0
$429$	6.61502			0.319376
$430$		0			0
$431$	−3.89128	−	6.73989i	−0.187436	−	0.324649i	0.756958	−	0.653463i	$-0.226684\pi$
$431$	−3.89128	−	6.73989i	−0.187436	−	0.324649i	−0.944395	+	0.328814i	$0.893351\pi$
$432$		0			0
$433$	−13.2846	+	7.66988i	−0.638418	+	0.368591i	−0.784005	−	0.620755i	$-0.786826\pi$
$433$	−13.2846	+	7.66988i	−0.638418	+	0.368591i	0.145587	+	0.989345i	$0.453493\pi$
$434$		0			0
$435$	−21.2858	−	12.2894i	−1.02058	−	0.589231i
$436$		0			0
$437$	−38.3501	−	0.207494i	−1.83454	−	0.00992577i
$438$		0			0
$439$	−12.6149	+	21.8497i	−0.602077	+	1.04283i	0.390429	+	0.920633i	$0.372327\pi$
$439$	−12.6149	+	21.8497i	−0.602077	+	1.04283i	−0.992506	+	0.122195i	$0.961007\pi$
$440$		0			0
$441$	3.74105	+	6.47969i	0.178145	+	0.308557i
$442$		0			0
$443$	2.05095	−	1.18412i	0.0974435	−	0.0562590i	−0.450486	−	0.892783i	$-0.648749\pi$
$443$	2.05095	−	1.18412i	0.0974435	−	0.0562590i	0.547930	+	0.836524i	$0.315416\pi$
$444$		0			0
$445$			22.3074i			1.05747i
$446$		0			0
$447$	−6.15852	−	10.6669i	−0.291288	−	0.504526i
$448$		0			0
$449$			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
$452$		0			0
$453$	7.07416	−	12.2528i	0.332373	−	0.575687i
$454$		0			0
$455$	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	$0.565359\pi$
$458$		0			0
$459$	4.26615	−	7.38919i	0.199127	−	0.344898i
$460$		0			0
$461$	10.5590	−	18.2887i	0.491781	−	0.851789i	−0.508174	−	0.861254i	$-0.669679\pi$
$461$	10.5590	−	18.2887i	0.491781	−	0.851789i	0.999955	+	0.00946495i	$0.00301283\pi$
$462$		0			0
$463$		−	0.355651i		−	0.0165285i	−0.999966	−	0.00826426i	$-0.997369\pi$
$463$		−	0.355651i		−	0.0165285i	0.999966	−	0.00826426i	$-0.00263062\pi$
$464$		0			0
$465$	15.9142	+	27.5641i	0.738001	+	1.27826i
$466$		0			0
$467$			4.47951i			0.207287i	0.994615	+	0.103643i	$0.0330501\pi$
$467$			4.47951i			0.207287i	−0.994615	+	0.103643i	$0.966950\pi$
$468$		0			0
$469$	−0.0510778	+	0.0294898i	−0.00235855	+	0.00136171i
$470$		0			0
$471$	−7.21202	−	12.4916i	−0.332312	−	0.575582i
$472$		0			0
$473$	−6.15002	+	10.6521i	−0.282778	+	0.489786i
$474$		0			0
$475$	−0.124583	+	23.0262i	−0.00571627	+	1.05651i
$476$		0			0
$477$	−8.51912	−	4.91852i	−0.390064	−	0.225203i
$478$		0			0
$479$	−21.4965	+	12.4110i	−0.982199	+	0.567073i	−0.902933	−	0.429781i	$-0.858591\pi$
$479$	−21.4965	+	12.4110i	−0.982199	+	0.567073i	−0.0792655	+	0.996854i	$0.525257\pi$
$480$		0			0
$481$	−12.2668	−	21.2466i	−0.559316	−	0.968764i
$482$		0			0
$483$	−14.0189			−0.637880
$484$		0			0
$485$	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	$0.193739\pi$
$488$		0			0
$489$	17.3010	+	9.98871i	0.782376	+	0.451705i
$490$		0			0
$491$	5.16077	+	2.97957i	0.232902	+	0.134466i	0.611910	−	0.790927i	$-0.290401\pi$
$491$	5.16077	+	2.97957i	0.232902	+	0.134466i	−0.379008	+	0.925393i	$0.623735\pi$
$492$		0			0
$493$		−	9.20366i		−	0.414512i
$494$		0			0
$495$		−	9.31619i		−	0.418732i
$496$		0			0
$497$	−6.77026	−	3.90881i	−0.303688	−	0.175334i
$498$		0			0
$499$	−20.1581	−	11.6383i	−0.902402	−	0.521002i	−0.0244234	−	0.999702i	$-0.507775\pi$
$499$	−20.1581	−	11.6383i	−0.902402	−	0.521002i	−0.877979	+	0.478700i	$0.841108\pi$
$500$		0			0
$501$	4.59884			0.205461
$502$		0			0
$503$	−16.4493	+	9.49702i	−0.733439	+	0.423451i	−0.819679	−	0.572823i	$-0.805848\pi$
$503$	−16.4493	+	9.49702i	−0.733439	+	0.423451i	0.0862401	+	0.996274i	$0.472515\pi$
$504$		0			0
$505$	20.0953			0.894231
$506$		0			0
$507$	4.42931	+	7.67179i	0.196713	+	0.340716i
$508$		0			0
$509$	−11.3577	+	6.55740i	−0.503423	+	0.290652i	−0.730126	−	0.683312i	$-0.760539\pi$
$509$	−11.3577	+	6.55740i	−0.503423	+	0.290652i	0.226703	+	0.973964i	$0.427205\pi$
$510$		0			0
$511$	−1.42532	−	0.822911i	−0.0630526	−	0.0364035i
$512$		0			0
$513$	−20.9847	−	12.2674i	−0.926496	−	0.541618i
$514$		0			0
$515$	−0.844413	+	1.46257i	−0.0372093	+	0.0644483i
$516$		0			0
$517$	7.46982	+	12.9381i	0.328522	+	0.569017i
$518$		0			0
$519$	5.69468	−	3.28783i	0.249969	−	0.144320i
$520$		0			0
$521$			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	0.979727	+	0.200335i	$0.0642031\pi$
$523$	15.1705	+	26.2761i	0.663359	+	1.14897i	−0.316368	+	0.948636i	$0.602464\pi$
$524$		0			0
$525$			8.41720i			0.367357i
$526$		0			0
$527$	−5.95915	+	10.3215i	−0.259584	+	0.449613i
$528$		0			0
$529$	27.2047	−	47.1198i	1.18281	−	2.04869i
$530$		0			0
$531$	−7.80473			−0.338696
$532$		0			0
$533$	−3.10805			−0.134625
$534$		0			0
$535$	11.0880	−	19.2051i	0.479378	−	0.830307i
$536$		0			0
$537$	1.75984	−	3.04813i	0.0759425	−	0.131536i
$538$		0			0
$539$		−	11.4759i		−	0.494300i
$540$		0			0
$541$	−12.1933	−	21.1195i	−0.524233	−	0.907998i	−0.999602	−	0.0282117i	$-0.991019\pi$
$541$	−12.1933	−	21.1195i	−0.524233	−	0.907998i	0.475369	−	0.879787i	$-0.342315\pi$
$542$		0			0
$543$			3.05854i			0.131255i
$544$		0			0
$545$	33.6384	−	19.4212i	1.44091	−	0.831911i
$546$		0			0
$547$	−18.7226	−	32.4286i	−0.800522	−	1.38655i	−0.919273	−	0.393621i	$-0.871222\pi$
$547$	−18.7226	−	32.4286i	−0.800522	−	1.38655i	0.118751	−	0.992924i	$-0.462111\pi$
$548$		0			0
$549$	3.86737	−	6.69849i	0.165056	−	0.285885i
$550$		0			0
$551$	−26.2195	−	0.141861i	−1.11699	−	0.00604348i
$552$		0			0
$553$	−8.16937	−	4.71659i	−0.347397	−	0.200570i
$554$		0			0
$555$	35.3014	−	20.3813i	1.49846	−	0.865137i
$556$		0			0
$557$	7.69507	+	13.3283i	0.326051	+	0.564736i	0.981724	−	0.190308i	$-0.0609487\pi$
$557$	7.69507	+	13.3283i	0.326051	+	0.564736i	−0.655674	+	0.755044i	$0.727615\pi$
$558$		0			0
$559$	14.3297			0.606082
$560$		0			0
$561$	−3.56421	+	2.05780i	−0.150481	+	0.0868803i
$562$		0			0
$563$	−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
$566$		0			0
$567$	−3.22374	−	1.86123i	−0.135384	−	0.0781641i
$568$		0			0
$569$		−	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	$-0.234971\pi$
$572$		0			0
$573$	4.83925	+	2.79394i	0.202163	+	0.116719i
$574$		0			0
$575$	−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	$0.804919\pi$
$578$		0			0
$579$	−9.89455	+	5.71262i	−0.411204	+	0.237408i
$580$		0			0
$581$	−9.80550			−0.406801
$582$		0			0
$583$	7.54389	+	13.0664i	0.312436	+	0.541155i
$584$		0			0
$585$	−9.39938	+	5.42674i	−0.388617	+	0.224368i
$586$		0			0
$587$	−15.4560	−	8.92352i	−0.637937	−	0.368313i	0.145883	−	0.989302i	$-0.453398\pi$
$587$	−15.4560	−	8.92352i	−0.637937	−	0.368313i	−0.783819	+	0.620989i	$0.786731\pi$
$588$		0			0
$589$	29.3123	+	17.1356i	1.20779	+	0.706060i
$590$		0			0
$591$	−0.886993	+	1.53632i	−0.0364860	+	0.0631956i
$592$		0			0
$593$	11.7249	+	20.3082i	0.481485	+	0.833957i	0.999774	−	0.0212488i	$-0.00676420\pi$
$593$	11.7249	+	20.3082i	0.481485	+	0.833957i	−0.518289	+	0.855205i	$0.673431\pi$
$594$		0			0
$595$	−5.31315	+	3.06755i	−0.217818	+	0.125757i
$596$		0			0
$597$		−	0.356008i		−	0.0145704i
$598$		0			0
$599$	−7.40584	−	12.8273i	−0.302595	−	0.524109i	0.674128	−	0.738614i	$-0.264519\pi$
$599$	−7.40584	−	12.8273i	−0.302595	−	0.524109i	−0.976723	+	0.214505i	$0.931186\pi$
$600$		0			0
$601$		−	4.30046i		−	0.175419i	−0.996146	−	0.0877097i	$-0.972045\pi$
$601$		−	4.30046i		−	0.175419i	0.996146	−	0.0877097i	$-0.0279548\pi$
$602$		0			0
$603$	0.0324579	−	0.0562188i	0.00132179	−	0.00228940i
$604$		0			0
$605$	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	$0.634342\pi$
$608$		0			0
$609$	−9.58452			−0.388385
$610$		0			0
$611$	8.70243	−	15.0730i	0.352062	−	0.609790i
$612$		0			0
$613$	−0.467103	+	0.809046i	−0.0188661	+	0.0326771i	−0.875304	−	0.483572i	$-0.839339\pi$
$613$	−0.467103	+	0.809046i	−0.0188661	+	0.0326771i	0.856438	+	0.516250i	$0.172672\pi$
$614$		0			0
$615$		−	5.16404i		−	0.208234i
$616$		0			0
$617$	−4.11324	−	7.12434i	−0.165593	−	0.286815i	0.771273	−	0.636505i	$-0.219620\pi$
$617$	−4.11324	−	7.12434i	−0.165593	−	0.286815i	−0.936866	+	0.349690i	$0.886287\pi$
$618$		0			0
$619$			7.04730i			0.283255i	0.989920	+	0.141627i	$0.0452335\pi$
$619$			7.04730i			0.283255i	−0.989920	+	0.141627i	$0.954766\pi$
$620$		0			0
$621$	42.4901	−	24.5316i	1.70507	−	0.984421i
$622$		0			0
$623$	4.34940	+	7.53338i	0.174255	+	0.301819i
$624$		0			0
$625$	11.7534	−	20.3576i	0.470138	−	0.814302i
$626$		0			0
$627$	5.80735	+	10.1855i	0.231923	+	0.406770i
$628$		0			0
$629$	13.2188	+	7.63188i	0.527068	+	0.304303i
$630$		0			0
$631$	−17.5204	+	10.1154i	−0.697476	+	0.402688i	−0.806407	−	0.591362i	$-0.798591\pi$
$631$	−17.5204	+	10.1154i	−0.697476	+	0.402688i	0.108931	+	0.994049i	$0.465257\pi$
$632$		0			0
$633$	−0.106082	−	0.183740i	−0.00421639	−	0.00730300i
$634$		0			0
$635$	−18.3589			−0.728549
$636$		0			0
$637$	−11.5783	+	6.68475i	−0.458750	+	0.264860i
$638$		0			0
$639$	8.60447			0.340387
$640$		0			0
$641$	−6.91570	−	3.99278i	−0.273154	−	0.157705i	0.357166	−	0.934041i	$-0.383743\pi$
$641$	−6.91570	−	3.99278i	−0.273154	−	0.157705i	−0.630320	+	0.776335i	$0.717076\pi$
$642$		0			0
$643$	−9.89926	−	5.71534i	−0.390389	−	0.225391i	0.291940	−	0.956437i	$-0.405699\pi$
$643$	−9.89926	−	5.71534i	−0.390389	−	0.225391i	−0.682328	+	0.731046i	$0.739033\pi$
$644$		0			0
$645$			23.8089i			0.937473i
$646$		0			0
$647$		−	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
$650$		0			0
$651$	10.7487	+	6.20575i	0.421274	+	0.243222i
$652$		0			0
$653$	−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
$656$		0			0
$657$	1.81148			0.0706724
$658$		0			0
$659$	13.5111	+	23.4019i	0.526317	+	0.911608i	0.999530	+	0.0306595i	$0.00976076\pi$
$659$	13.5111	+	23.4019i	0.526317	+	0.911608i	−0.473213	+	0.880948i	$0.656906\pi$
$660$		0			0
$661$	−23.1686	+	13.3764i	−0.901155	+	0.520282i	−0.877575	−	0.479440i	$-0.840840\pi$
$661$	−23.1686	+	13.3764i	−0.901155	+	0.520282i	−0.0235802	+	0.999722i	$0.507507\pi$
$662$		0			0
$663$	4.15235	+	2.39736i	0.161264	+	0.0931057i
$664$		0			0
$665$	8.65699	+	15.1835i	0.335703	+	0.588790i
$666$		0			0
$667$	26.4619	−	45.8334i	1.02461	−	1.77467i
$668$		0			0
$669$	7.47444	+	12.9461i	0.288978	+	0.500525i
$670$		0			0
$671$	−10.2740	+	5.93168i	−0.396622	+	0.228990i
$672$		0			0
$673$			29.5414i			1.13874i	0.822083	+	0.569368i	$0.192812\pi$
$673$			29.5414i			1.13874i	−0.822083	+	0.569368i	$0.807188\pi$
$674$		0			0
$675$	−14.7293	−	25.5119i	−0.566930	−	0.981952i
$676$		0			0
$677$		−	15.6682i		−	0.602176i	−0.953596	−	0.301088i	$-0.902650\pi$
$677$		−	15.6682i		−	0.602176i	0.953596	−	0.301088i	$-0.0973498\pi$
$678$		0			0
$679$	6.15048	−	10.6529i	0.236034	−	0.408822i
$680$		0			0
$681$	5.59562	−	9.69190i	0.214425	−	0.371394i
$682$		0			0
$683$	−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
$686$		0			0
$687$	4.16265	−	7.20993i	0.158815	−	0.275076i
$688$		0			0
$689$	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	$0.785123\pi$
$692$		0			0
$693$	−1.81643	−	3.14615i	−0.0690005	−	0.119512i
$694$		0			0
$695$			33.4732i			1.26971i
$696$		0			0
$697$	1.67464	−	0.966852i	0.0634314	−	0.0366221i
$698$		0			0
$699$	−16.7328	−	28.9820i	−0.632892	−	1.09620i
$700$		0			0
$701$	8.96916	−	15.5350i	0.338761	−	0.586751i	−0.645439	−	0.763812i	$-0.723326\pi$
$701$	8.96916	−	15.5350i	0.338761	−	0.586751i	0.984200	+	0.177061i	$0.0566590\pi$
$702$		0			0
$703$	21.9456	−	37.5403i	0.827693	−	1.41586i
$704$		0			0
$705$	25.0439	+	14.4591i	0.943209	+	0.544562i
$706$		0			0
$707$	6.78635	−	3.91810i	0.255227	−	0.147355i
$708$		0			0
$709$	−3.51145	−	6.08201i	−0.131875	−	0.228415i	0.792524	−	0.609841i	$-0.208767\pi$
$709$	−3.51145	−	6.08201i	−0.131875	−	0.228415i	−0.924399	+	0.381426i	$0.875433\pi$
$710$		0			0
$711$	10.3826			0.389379
$712$		0			0
$713$	−59.3520	+	34.2669i	−2.22275	+	1.28330i
$714$		0			0
$715$	16.6468			0.622554
$716$		0			0
$717$	26.0107	+	15.0173i	0.971386	+	0.560830i
$718$		0			0
$719$	−23.4325	−	13.5288i	−0.873886	−	0.504538i	−0.00524853	−	0.999986i	$-0.501671\pi$
$719$	−23.4325	−	13.5288i	−0.873886	−	0.504538i	−0.868638	+	0.495448i	$0.835004\pi$
$720$		0			0
$721$			0.658560i			0.0245260i
$722$		0			0
$723$			19.9580i			0.742245i
$724$		0			0
$725$	−27.5193	−	15.8882i	−1.02204	−	0.590075i
$726$		0			0
$727$	−23.9684	−	13.8381i	−0.888938	−	0.513229i	−0.0153429	−	0.999882i	$-0.504884\pi$
$727$	−23.9684	−	13.8381i	−0.888938	−	0.513229i	−0.873595	+	0.486654i	$0.838217\pi$
$728$		0			0
$729$	25.4145			0.941279
$730$		0			0
$731$	−7.72093	+	4.45768i	−0.285569	+	0.164873i
$732$		0			0
$733$	2.82689			0.104414			0.0522068	−	0.998636i	$-0.483374\pi$
$733$	2.82689			0.104414			0.0522068	+	0.998636i	$0.483374\pi$
$734$		0			0
$735$	−11.1068	−	19.2375i	−0.409679	−	0.709584i
$736$		0			0
$737$	−0.0862268	+	0.0497831i	−0.00317621	+	0.00183378i
$738$		0			0
$739$	−21.3233	−	12.3110i	−0.784392	−	0.452869i	0.0535927	−	0.998563i	$-0.482933\pi$
$739$	−21.3233	−	12.3110i	−0.784392	−	0.452869i	−0.837984	+	0.545694i	$0.816266\pi$
$740$		0			0
$741$	6.89364	−	11.7923i	0.253244	−	0.433202i
$742$		0			0
$743$	−3.96328	+	6.86460i	−0.145399	+	0.251838i	−0.929522	−	0.368768i	$-0.879780\pi$
$743$	−3.96328	+	6.86460i	−0.145399	+	0.251838i	0.784123	+	0.620605i	$0.213113\pi$
$744$		0			0
$745$	−15.4980	−	26.8433i	−0.567803	−	0.983463i
$746$		0			0
$747$	9.34651	−	5.39621i	0.341971	−	0.197437i
$748$		0			0
$749$		−	8.64759i		−	0.315976i
$750$		0			0
$751$	−7.13985	−	12.3666i	−0.260537	−	0.451263i	0.705848	−	0.708363i	$-0.250566\pi$
$751$	−7.13985	−	12.3666i	−0.260537	−	0.451263i	−0.966385	+	0.257101i	$0.917233\pi$
$752$		0			0
$753$			32.6019i			1.18808i
$754$		0			0
$755$	17.8022	−	30.8344i	0.647889	−	1.12218i
$756$		0			0
$757$	17.1966	−	29.7854i	0.625021	−	1.08257i	−0.363515	−	0.931588i	$-0.618424\pi$
$757$	17.1966	−	29.7854i	0.625021	−	1.08257i	0.988537	−	0.150981i	$-0.0482431\pi$
$758$		0			0
$759$	−23.6659			−0.859019
$760$		0			0
$761$	−31.6267			−1.14647			−0.573233	−	0.819392i	$-0.694311\pi$
$761$	−31.6267			−1.14647			−0.573233	+	0.819392i	$0.694311\pi$
$762$		0			0
$763$	7.57331	−	13.1174i	0.274172	−	0.474880i
$764$		0			0
$765$	3.37630	−	5.84792i	0.122070	−	0.211432i
$766$		0			0
$767$		−	13.9460i		−	0.503561i
$768$		0			0
$769$	11.7685	+	20.3836i	0.424383	+	0.735052i	0.996363	−	0.0852153i	$-0.0271578\pi$
$769$	11.7685	+	20.3836i	0.424383	+	0.735052i	−0.571980	+	0.820268i	$0.693824\pi$
$770$		0			0
$771$		−	25.6666i		−	0.924359i
$772$		0			0
$773$	10.5693	−	6.10219i	0.380152	−	0.219481i	−0.297733	−	0.954649i	$-0.596230\pi$
$773$	10.5693	−	6.10219i	0.380152	−	0.219481i	0.677884	+	0.735169i	$0.262897\pi$
$774$		0			0
$775$	20.5745	+	35.6361i	0.739058	+	1.28009i
$776$		0			0
$777$	7.94771	−	13.7658i	0.285122	−	0.493847i
$778$		0			0
$779$	−2.72857	−	4.78564i	−0.0977612	−	0.171463i
$780$		0			0
$781$	−11.4292	−	6.59865i	−0.408969	−	0.236118i
$782$		0			0
$783$	29.0499	−	16.7720i	1.03816	−	0.599382i
$784$		0			0
$785$	−18.1491	−	31.4352i	−0.647770	−	1.12197i
$786$		0			0
$787$	36.6534			1.30655			0.653276	−	0.757120i	$-0.273394\pi$
$787$	36.6534			1.30655			0.653276	+	0.757120i	$0.273394\pi$
$788$		0			0
$789$	4.01169	−	2.31615i	0.142820	−	0.0824571i
$790$		0			0
$791$	6.19498			0.220268
$792$		0			0
$793$	11.9693	+	6.91048i	0.425042	+	0.245398i
$794$		0			0
$795$	25.2923	+	14.6025i	0.897025	+	0.517898i
$796$		0			0
$797$		−	14.7351i		−	0.521944i	−0.965346	−	0.260972i	$-0.915957\pi$
$797$		−	14.7351i		−	0.521944i	0.965346	−	0.260972i	$-0.0840430\pi$
$798$		0			0
$799$			10.8286i			0.383088i
$800$		0			0
$801$	−8.29162	−	4.78717i	−0.292970	−	0.169146i
$802$		0			0
$803$	−2.40616	−	1.38920i	−0.0849115	−	0.0490237i
$804$		0			0
$805$	−35.2786			−1.24341
$806$		0			0
$807$	−20.2852	+	11.7117i	−0.714073	+	0.412271i
$808$		0			0
$809$	14.1872			0.498796			0.249398	−	0.968401i	$-0.419767\pi$
$809$	14.1872			0.498796			0.249398	+	0.968401i	$0.419767\pi$
$810$		0			0
$811$	−21.0255	−	36.4173i	−0.738307	−	1.27879i	−0.953257	−	0.302160i	$-0.902292\pi$
$811$	−21.0255	−	36.4173i	−0.738307	−	1.27879i	0.214950	−	0.976625i	$-0.431041\pi$
$812$		0			0
$813$	21.3186	−	12.3083i	0.747677	−	0.431672i
$814$		0			0
$815$	43.5381	+	25.1367i	1.52507	+	0.880501i
$816$		0			0
$817$	12.5801	+	22.0642i	0.440122	+	0.771929i
$818$		0			0
$819$	−2.11616	+	3.66530i	−0.0739447	+	0.128076i
$820$		0			0
$821$	22.3593	+	38.7274i	0.780343	+	1.35159i	0.931742	+	0.363122i	$0.118289\pi$
$821$	22.3593	+	38.7274i	0.780343	+	1.35159i	−0.151398	+	0.988473i	$0.548378\pi$
$822$		0			0
$823$	−34.6560	+	20.0087i	−1.20803	+	0.697458i	−0.962329	−	0.271887i	$-0.912352\pi$
$823$	−34.6560	+	20.0087i	−1.20803	+	0.697458i	−0.245703	+	0.969345i	$0.579019\pi$
$824$		0			0
$825$			14.2095i			0.494711i
$826$		0			0
$827$	−13.1881	−	22.8424i	−0.458594	−	0.794309i	0.540293	−	0.841477i	$-0.318314\pi$
$827$	−13.1881	−	22.8424i	−0.458594	−	0.794309i	−0.998887	+	0.0471684i	$0.984980\pi$
$828$		0			0
$829$			39.6736i			1.37792i	0.724798	+	0.688961i	$0.241933\pi$
$829$			39.6736i			1.37792i	−0.724798	+	0.688961i	$0.758067\pi$
$830$		0			0
$831$	10.5495	−	18.2723i	0.365960	−	0.633860i
$832$		0			0
$833$	4.15898	−	7.20357i	0.144100	−	0.249589i
$834$		0			0
$835$	11.5730			0.400502
$836$		0			0
$837$	−43.4378			−1.50143
$838$		0			0
$839$	−7.96193	+	13.7905i	−0.274876	+	0.476100i	−0.970104	−	0.242690i	$-0.921970\pi$
$839$	−7.96193	+	13.7905i	−0.274876	+	0.476100i	0.695228	+	0.718790i	$0.255304\pi$
$840$		0			0
$841$	3.59168	−	6.22098i	0.123851	−	0.214516i
$842$		0			0
$843$		−	5.08346i		−	0.175084i
$844$		0			0
$845$	11.1464	+	19.3062i	0.383449	+	0.664152i
$846$		0			0
$847$		−	8.18285i		−	0.281166i
$848$		0			0
$849$	16.3685	−	9.45038i	0.561767	−	0.324336i
$850$		0			0
$851$	43.8856	+	76.0122i	1.50438	+	2.60566i
$852$		0			0
$853$	−19.4390	+	33.6693i	−0.665578	+	1.15281i	0.313550	+	0.949572i	$0.398482\pi$
$853$	−19.4390	+	33.6693i	−0.665578	+	1.15281i	−0.979128	+	0.203243i	$0.934852\pi$
$854$		0			0
$855$	−16.6076	−	9.70859i	−0.567968	−	0.332027i
$856$		0			0
$857$	28.7983	+	16.6267i	0.983730	+	0.567957i	0.903394	−	0.428811i	$-0.141067\pi$
$857$	28.7983	+	16.6267i	0.983730	+	0.567957i	0.0803358	+	0.996768i	$0.474401\pi$
$858$		0			0
$859$	−28.1710	+	16.2645i	−0.961183	+	0.554939i	−0.896537	−	0.442969i	$-0.853925\pi$
$859$	−28.1710	+	16.2645i	−0.961183	+	0.554939i	−0.0646461	+	0.997908i	$0.520592\pi$
$860$		0			0
$861$	−1.00686	−	1.74394i	−0.0343138	−	0.0594332i
$862$		0			0
$863$	−20.4964			−0.697707			−0.348853	−	0.937177i	$-0.613429\pi$
$863$	−20.4964			−0.697707			−0.348853	+	0.937177i	$0.613429\pi$
$864$		0			0
$865$	14.3307	−	8.27386i	0.487260	−	0.281320i
$866$		0			0
$867$	18.6791			0.634375
$868$		0			0
$869$	−13.7911	−	7.96231i	−0.467832	−	0.270103i
$870$		0			0
$871$	0.100455	+	0.0579979i	0.00340380	+	0.00196518i
$872$		0			0
$873$			13.5391i			0.458228i
$874$		0			0
$875$			1.13333i			0.0383137i
$876$		0			0
$877$	29.2384	+	16.8808i	0.987312	+	0.570025i	0.904470	−	0.426538i	$-0.140267\pi$
$877$	29.2384	+	16.8808i	0.987312	+	0.570025i	0.0828424	+	0.996563i	$0.473600\pi$
$878$		0			0
$879$	25.3702	+	14.6475i	0.855715	+	0.494047i
$880$		0			0
$881$	−37.8371			−1.27476			−0.637382	−	0.770548i	$-0.719983\pi$
$881$	−37.8371			−1.27476			−0.637382	+	0.770548i	$0.719983\pi$
$882$		0			0
$883$	−23.2555	+	13.4265i	−0.782609	+	0.451839i	−0.837354	−	0.546661i	$-0.815899\pi$
$883$	−23.2555	+	13.4265i	−0.782609	+	0.451839i	0.0547454	+	0.998500i	$0.482565\pi$
$884$		0			0
$885$	23.1713			0.778896
$886$		0			0
$887$	4.11911	+	7.13451i	0.138306	+	0.239554i	0.926856	−	0.375418i	$-0.122501\pi$
$887$	4.11911	+	7.13451i	0.138306	+	0.239554i	−0.788549	+	0.614972i	$0.789168\pi$
$888$		0			0
$889$	−6.19993	+	3.57953i	−0.207939	+	0.120054i
$890$		0			0
$891$	−5.44215	−	3.14203i	−0.182319	−	0.105262i
$892$		0			0
$893$	30.8487	+	0.166907i	1.03231	+	0.00558533i
$894$		0			0
$895$	4.42865	−	7.67065i	0.148033	−	0.256401i
$896$		0			0
$897$	13.7855	+	23.8773i	0.460286	+	0.797239i
$898$		0			0
$899$	−40.5782	+	23.4279i	−1.35336	+	0.781363i
$900$		0			0
$901$			10.9360i			0.364330i
$902$		0			0
$903$	4.64215	+	8.04044i	0.154481	+	0.267569i
$904$		0			0
$905$			7.69687i			0.255853i
$906$		0			0
$907$	−12.9847	+	22.4902i	−0.431150	+	0.746774i	−0.996973	−	0.0777533i	$-0.975225\pi$
$907$	−12.9847	+	22.4902i	−0.431150	+	0.746774i	0.565823	+	0.824527i	$0.308559\pi$
$908$		0			0
$909$	−4.31246	+	7.46940i	−0.143035	+	0.247744i
$910$		0			0
$911$	35.0480			1.16119			0.580597	−	0.814191i	$-0.302819\pi$
$911$	35.0480			1.16119			0.580597	+	0.814191i	$0.302819\pi$
$912$		0			0
$913$	−16.5531			−0.547829
$914$		0			0
$915$	−11.4818	+	19.8870i	−0.379576	+	0.657445i
$916$		0			0
$917$	11.6730	−	20.2182i	0.385477	−	0.667665i
$918$		0			0
$919$		−	6.29627i		−	0.207695i	−0.994593	−	0.103847i	$-0.966885\pi$
$919$		−	6.29627i		−	0.207695i	0.994593	−	0.103847i	$-0.0331153\pi$
$920$		0			0
$921$	−13.1431	−	22.7644i	−0.433078	−	0.750114i
$922$		0			0
$923$			15.3750i			0.506075i
$924$		0			0
$925$	45.6392	−	26.3498i	1.50061	−	0.866376i
$926$		0			0
$927$	−0.362422	−	0.627733i	−0.0119035	−	0.0206175i
$928$		0			0
$929$	−1.85864	+	3.21925i	−0.0609799	+	0.105620i	−0.894904	−	0.446259i	$-0.852756\pi$
$929$	−1.85864	+	3.21925i	−0.0609799	+	0.105620i	0.833924	+	0.551880i	$0.186089\pi$
$930$		0			0
$931$	−20.4576	−	11.9592i	−0.670469	−	0.391948i
$932$		0			0
$933$	3.49121	+	2.01565i	0.114297	+	0.0659895i
$934$		0			0
$935$	−8.96938	+	5.17848i	−0.293330	+	0.169354i
$936$		0			0
$937$	−21.7674	−	37.7022i	−0.711109	−	1.23168i	−0.964441	−	0.264298i	$-0.914860\pi$
$937$	−21.7674	−	37.7022i	−0.711109	−	1.23168i	0.253332	−	0.967379i	$-0.418473\pi$
$938$		0			0
$939$	−19.5521			−0.638059
$940$		0			0
$941$	−34.9810	+	20.1963i	−1.14035	+	0.658380i	−0.946517	−	0.322655i	$-0.895425\pi$
$941$	−34.9810	+	20.1963i	−1.14035	+	0.658380i	−0.193831	+	0.981035i	$0.562091\pi$
$942$		0			0
$943$	11.1194			0.362097
$944$		0			0
$945$	−19.3645	−	11.1801i	−0.629927	−	0.363688i
$946$		0			0
$947$	21.1885	+	12.2332i	0.688533	+	0.397525i	0.803062	−	0.595895i	$-0.203203\pi$
$947$	21.1885	+	12.2332i	0.688533	+	0.397525i	−0.114529	+	0.993420i	$0.536536\pi$
$948$		0			0
$949$			3.23686i			0.105073i
$950$		0			0
$951$		−	3.35483i		−	0.108788i
$952$		0			0
$953$	−43.7145	−	25.2386i	−1.41605	−	0.817557i	−0.420101	−	0.907477i	$-0.638006\pi$
$953$	−43.7145	−	25.2386i	−1.41605	−	0.817557i	−0.995949	+	0.0899200i	$0.971339\pi$
$954$		0			0
$955$	12.1780	+	7.03099i	0.394072	+	0.227518i
$956$		0			0
$957$	−16.1801			−0.523028
$958$		0			0
$959$	−21.5851	+	12.4622i	−0.697019	+	0.402424i
$960$		0			0
$961$	29.6759			0.957286
$962$		0			0
$963$	4.75899	+	8.24281i	0.153356	+	0.265621i
$964$		0			0
$965$	−24.8998	+	14.3759i	−0.801552	+	0.462776i
$966$		0			0
$967$	−43.6786	−	25.2179i	−1.40461	−	0.810952i	−0.409749	−	0.912198i	$-0.634384\pi$
$967$	−43.6786	−	25.2179i	−1.40461	−	0.810952i	−0.994861	+	0.101246i	$0.967717\pi$
$968$		0			0
$969$	−0.0459798	+	8.49825i	−0.00147709	+	0.273003i
$970$		0			0
$971$	−5.26456	+	9.11849i	−0.168948	+	0.292626i	−0.938050	−	0.346499i	$-0.887370\pi$
$971$	−5.26456	+	9.11849i	−0.168948	+	0.292626i	0.769102	+	0.639126i	$0.220704\pi$
$972$		0			0
$973$	6.52645	+	11.3041i	0.209228	+	0.362394i
$974$		0			0
$975$	14.3364	−	8.27711i	0.459132	−	0.265080i
$976$		0			0
$977$		−	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
$980$		0			0
$981$			16.6711i			0.532268i
$982$		0			0
$983$	−17.5996	+	30.4835i	−0.561341	+	0.972272i	0.436038	+	0.899928i	$0.356381\pi$
$983$	−17.5996	+	30.4835i	−0.561341	+	0.972272i	−0.997380	+	0.0723437i	$0.976952\pi$
$984$		0			0
$985$	−2.23213	+	3.86616i	−0.0711215	+	0.123186i
$986$		0			0
$987$	11.2767			0.358942
$988$		0			0
$989$	−51.2660			−1.63016
$990$		0			0
$991$	−24.9524	+	43.2188i	−0.792638	+	1.37289i	0.131690	+	0.991291i	$0.457960\pi$
$991$	−24.9524	+	43.2188i	−0.792638	+	1.37289i	−0.924328	+	0.381599i	$0.875374\pi$
$992$		0			0
$993$	5.93117	−	10.2731i	0.188220	−	0.326007i
$994$		0			0
$995$		−	0.895899i		−	0.0284019i
$996$		0			0
$997$	2.63314	+	4.56074i	0.0833925	+	0.144440i	0.904705	−	0.426038i	$-0.140091\pi$
$997$	2.63314	+	4.56074i	0.0833925	+	0.144440i	−0.821313	+	0.570478i	$0.806758\pi$
$998$		0			0
$999$			55.6309i			1.76008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.n.f.255.6		16
4.3	odd	2	inner	1216.2.n.f.255.3		16
8.3	odd	2		76.2.f.a.27.7	yes	16
8.5	even	2		76.2.f.a.27.4	✓	16
19.12	odd	6	inner	1216.2.n.f.639.3		16
24.5	odd	2		684.2.r.a.559.5		16
24.11	even	2		684.2.r.a.559.2		16
76.31	even	6	inner	1216.2.n.f.639.6		16
152.69	odd	6		76.2.f.a.31.7	yes	16
152.107	even	6		76.2.f.a.31.4	yes	16
456.107	odd	6		684.2.r.a.487.5		16
456.221	even	6		684.2.r.a.487.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.f.a.27.4	✓	16	8.5	even	2
76.2.f.a.27.7	yes	16	8.3	odd	2
76.2.f.a.31.4	yes	16	152.107	even	6
76.2.f.a.31.7	yes	16	152.69	odd	6
684.2.r.a.487.2		16	456.221	even	6
684.2.r.a.487.5		16	456.107	odd	6
684.2.r.a.559.2		16	24.11	even	2
684.2.r.a.559.5		16	24.5	odd	2
1216.2.n.f.255.3		16	4.3	odd	2	inner
1216.2.n.f.255.6		16	1.1	even	1	trivial
1216.2.n.f.639.3		16	19.12	odd	6	inner
1216.2.n.f.639.6		16	76.31	even	6	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.637123 - 1.10353i) q^{3} +(1.60333 - 2.77705i) q^{5} -1.25044i q^{7} +(0.688149 + 1.19191i) q^{9} -2.11093i q^{11} +(-2.12978 + 1.22963i) q^{13} +(-2.04303 - 3.53864i) q^{15} +(0.765026 - 1.32506i) q^{17} +(-3.76307 - 2.19984i) q^{19} +(-1.37990 - 0.796684i) q^{21} +(7.61951 - 4.39913i) q^{23} +(-2.64132 - 4.57491i) q^{25} +5.57648 q^{27} +(5.20937 - 3.00763i) q^{29} -7.78947 q^{31} +(-2.32947 - 1.34492i) q^{33} +(-3.47253 - 2.00487i) q^{35} +9.97599i q^{37} +3.13370i q^{39} +(1.09450 + 0.631908i) q^{41} +(-5.04619 - 2.91342i) q^{43} +4.41331 q^{45} +(-6.12910 + 3.53864i) q^{47} +5.43640 q^{49} +(-0.974831 - 1.68846i) q^{51} +(-6.18988 + 3.57373i) q^{53} +(-5.86215 - 3.38451i) q^{55} +(-4.82513 + 2.75109i) q^{57} +(-2.83541 + 4.91107i) q^{59} +(-2.80998 - 4.86704i) q^{61} +(1.49041 - 0.860489i) q^{63} +7.88599i q^{65} +(-0.0235835 - 0.0408478i) q^{67} -11.2111i q^{69} +(3.12595 - 5.41430i) q^{71} +(0.658098 - 1.13986i) q^{73} -6.73139 q^{75} -2.63959 q^{77} +(3.77194 - 6.53320i) q^{79} +(1.48846 - 2.57808i) q^{81} -7.84164i q^{83} +(-2.45317 - 4.24902i) q^{85} -7.66492i q^{87} +(-6.02458 + 3.47830i) q^{89} +(1.53758 + 2.66316i) q^{91} +(-4.96285 + 8.59591i) q^{93} +(-12.1425 + 6.92315i) q^{95} +(8.51935 + 4.91865i) q^{97} +(2.51603 - 1.45263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} - 4 q^{9} + 18 q^{13} + 2 q^{17} - 2 q^{25} + 6 q^{29} + 18 q^{33} - 48 q^{41} - 24 q^{45} + 16 q^{49} - 6 q^{53} - 26 q^{57} + 26 q^{61} + 16 q^{73} - 80 q^{77} + 12 q^{81} - 14 q^{85} + 18 q^{89}+ \cdots - 12 q^{97}+O(q^{100}) \) 16 * q + 2 * q^5 - 4 * q^9 + 18 * q^13 + 2 * q^17 - 2 * q^25 + 6 * q^29 + 18 * q^33 - 48 * q^41 - 24 * q^45 + 16 * q^49 - 6 * q^53 - 26 * q^57 + 26 * q^61 + 16 * q^73 - 80 * q^77 + 12 * q^81 - 14 * q^85 + 18 * q^89 + 20 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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