LMFDB - Embedded newform 440.2.y.b.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(81,440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("440.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1,0,3,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.3
Root			$-1.51700 - 1.10216i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.b.401.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.45455 - 1.78334i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-0.700550 - 0.508979i) q^{7} +(1.91748 - 5.90141i) q^{9} +(-1.21410 - 3.08642i) q^{11} +(-1.37052 + 4.21802i) q^{13} +(-2.45455 - 1.78334i) q^{15} +(-0.169969 - 0.523110i) q^{17} +(0.209505 - 0.152214i) q^{19} -2.62722 q^{21} +7.92701 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-3.00497 - 9.24833i) q^{27} +(7.57410 + 5.50291i) q^{29} +(-1.64270 + 5.05570i) q^{31} +(-8.48418 - 5.41063i) q^{33} +(-0.267586 + 0.823546i) q^{35} +(-5.16751 - 3.75441i) q^{37} +(4.15814 + 12.7974i) q^{39} +(-7.07258 + 5.13853i) q^{41} +6.38622 q^{43} -6.20511 q^{45} +(-0.665989 + 0.483870i) q^{47} +(-1.93141 - 5.94426i) q^{49} +(-1.35008 - 0.980890i) q^{51} +(0.741981 - 2.28358i) q^{53} +(-2.56018 + 2.10843i) q^{55} +(0.242791 - 0.747235i) q^{57} +(10.9337 + 7.94382i) q^{59} +(-2.04186 - 6.28421i) q^{61} +(-4.34699 + 3.15827i) q^{63} +4.43509 q^{65} +7.17725 q^{67} +(19.4573 - 14.1365i) q^{69} +(0.864970 + 2.66210i) q^{71} +(2.33866 + 1.69913i) q^{73} +(-0.937555 + 2.88550i) q^{75} +(-0.720387 + 2.78014i) q^{77} +(-1.82769 + 5.62505i) q^{79} +(-8.80862 - 6.39983i) q^{81} +(-2.19347 - 6.75080i) q^{83} +(-0.444984 + 0.323300i) q^{85} +28.4046 q^{87} -16.6470 q^{89} +(3.10700 - 2.25737i) q^{91} +(4.98393 + 15.3390i) q^{93} +(-0.209505 - 0.152214i) q^{95} +(-2.42082 + 7.45053i) q^{97} +(-20.5422 + 1.24672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.45455	−	1.78334i	1.41714	−	1.02961i	0.424900	−	0.905240i	$-0.360309\pi$
$3$	2.45455	−	1.78334i	1.41714	−	1.02961i	0.992236	−	0.124369i	$-0.0396907\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−0.700550	−	0.508979i	−0.264783	−	0.192376i	0.447470	−	0.894299i	$-0.352325\pi$
$7$	−0.700550	−	0.508979i	−0.264783	−	0.192376i	−0.712253	+	0.701923i	$0.752325\pi$
$8$		0			0
$9$	1.91748	−	5.90141i	0.639161	−	1.96714i
$10$		0			0
$11$	−1.21410	−	3.08642i	−0.366064	−	0.930590i
$11$	−1.21410	−	3.08642i	−0.366064	−	0.930590i
$12$		0			0
$13$	−1.37052	+	4.21802i	−0.380114	+	1.16987i	0.559850	+	0.828594i	$0.310859\pi$
$13$	−1.37052	+	4.21802i	−0.380114	+	1.16987i	−0.939963	+	0.341275i	$0.889141\pi$
$14$		0			0
$15$	−2.45455	−	1.78334i	−0.633762	−	0.460455i
$16$		0			0
$17$	−0.169969	−	0.523110i	−0.0412235	−	0.126873i	0.928327	−	0.371765i	$-0.121247\pi$
$17$	−0.169969	−	0.523110i	−0.0412235	−	0.126873i	−0.969550	+	0.244892i	$0.921247\pi$
$18$		0			0
$19$	0.209505	−	0.152214i	0.0480637	−	0.0349203i	−0.563494	−	0.826120i	$-0.690543\pi$
$19$	0.209505	−	0.152214i	0.0480637	−	0.0349203i	0.611558	+	0.791200i	$0.290543\pi$
$20$		0			0
$21$	−2.62722			−0.573306
$22$		0			0
$23$	7.92701			1.65290			0.826448	−	0.563013i	$-0.190358\pi$
$23$	7.92701			1.65290			0.826448	+	0.563013i	$0.190358\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−3.00497	−	9.24833i	−0.578306	−	1.77984i
$28$		0			0
$29$	7.57410	+	5.50291i	1.40648	+	1.02186i	0.993823	+	0.110976i	$0.0353975\pi$
$29$	7.57410	+	5.50291i	1.40648	+	1.02186i	0.412652	+	0.910889i	$0.364602\pi$
$30$		0			0
$31$	−1.64270	+	5.05570i	−0.295037	+	0.908031i	0.688172	+	0.725548i	$0.258413\pi$
$31$	−1.64270	+	5.05570i	−0.295037	+	0.908031i	−0.983209	+	0.182483i	$0.941587\pi$
$32$		0			0
$33$	−8.48418	−	5.41063i	−1.47691	−	0.941869i
$34$		0			0
$35$	−0.267586	+	0.823546i	−0.0452303	+	0.139205i
$36$		0			0
$37$	−5.16751	−	3.75441i	−0.849533	−	0.617222i	0.0754844	−	0.997147i	$-0.475950\pi$
$37$	−5.16751	−	3.75441i	−0.849533	−	0.617222i	−0.925017	+	0.379925i	$0.875950\pi$
$38$		0			0
$39$	4.15814	+	12.7974i	0.665836	+	2.04923i
$40$		0			0
$41$	−7.07258	+	5.13853i	−1.10455	+	0.802503i	−0.981797	−	0.189934i	$-0.939173\pi$
$41$	−7.07258	+	5.13853i	−1.10455	+	0.802503i	−0.122754	+	0.992437i	$0.539173\pi$
$42$		0			0
$43$	6.38622			0.973890			0.486945	−	0.873433i	$-0.338111\pi$
$43$	6.38622			0.973890			0.486945	+	0.873433i	$0.338111\pi$
$44$		0			0
$45$	−6.20511			−0.925003
$46$		0			0
$47$	−0.665989	+	0.483870i	−0.0971445	+	0.0705796i	−0.635297	−	0.772268i	$-0.719122\pi$
$47$	−0.665989	+	0.483870i	−0.0971445	+	0.0705796i	0.538153	+	0.842847i	$0.319122\pi$
$48$		0			0
$49$	−1.93141	−	5.94426i	−0.275916	−	0.849181i
$50$		0			0
$51$	−1.35008	−	0.980890i	−0.189049	−	0.137352i
$52$		0			0
$53$	0.741981	−	2.28358i	0.101919	−	0.313674i	−0.887076	−	0.461623i	$-0.847267\pi$
$53$	0.741981	−	2.28358i	0.101919	−	0.313674i	0.988995	+	0.147949i	$0.0472672\pi$
$54$		0			0
$55$	−2.56018	+	2.10843i	−0.345215	+	0.284301i
$56$		0			0
$57$	0.242791	−	0.747235i	0.0321585	−	0.0989737i
$58$		0			0
$59$	10.9337	+	7.94382i	1.42345	+	1.03420i	0.991190	+	0.132449i	$0.0422840\pi$
$59$	10.9337	+	7.94382i	1.42345	+	1.03420i	0.432261	+	0.901749i	$0.357716\pi$
$60$		0			0
$61$	−2.04186	−	6.28421i	−0.261434	−	0.804611i	−0.992494	−	0.122297i	$-0.960974\pi$
$61$	−2.04186	−	6.28421i	−0.261434	−	0.804611i	0.731060	−	0.682313i	$-0.239026\pi$
$62$		0			0
$63$	−4.34699	+	3.15827i	−0.547669	+	0.397905i
$64$		0			0
$65$	4.43509			0.550105
$66$		0			0
$67$	7.17725			0.876840			0.438420	−	0.898770i	$-0.355538\pi$
$67$	7.17725			0.876840			0.438420	+	0.898770i	$0.355538\pi$
$68$		0			0
$69$	19.4573	−	14.1365i	2.34238	−	1.70184i
$70$		0			0
$71$	0.864970	+	2.66210i	0.102653	+	0.315934i	0.989172	−	0.146758i	$-0.0468838\pi$
$71$	0.864970	+	2.66210i	0.102653	+	0.315934i	−0.886519	+	0.462691i	$0.846884\pi$
$72$		0			0
$73$	2.33866	+	1.69913i	0.273719	+	0.198868i	0.716173	−	0.697923i	$-0.245892\pi$
$73$	2.33866	+	1.69913i	0.273719	+	0.198868i	−0.442454	+	0.896791i	$0.645892\pi$
$74$		0			0
$75$	−0.937555	+	2.88550i	−0.108260	+	0.333189i
$76$		0			0
$77$	−0.720387	+	2.78014i	−0.0820958	+	0.316826i
$78$		0			0
$79$	−1.82769	+	5.62505i	−0.205631	+	0.632867i	0.794056	+	0.607845i	$0.207966\pi$
$79$	−1.82769	+	5.62505i	−0.205631	+	0.632867i	−0.999687	+	0.0250225i	$0.992034\pi$
$80$		0			0
$81$	−8.80862	−	6.39983i	−0.978735	−	0.711093i
$82$		0			0
$83$	−2.19347	−	6.75080i	−0.240764	−	0.740996i	−0.996304	−	0.0858936i	$-0.972625\pi$
$83$	−2.19347	−	6.75080i	−0.240764	−	0.740996i	0.755540	−	0.655102i	$-0.227375\pi$
$84$		0			0
$85$	−0.444984	+	0.323300i	−0.0482653	+	0.0350668i
$86$		0			0
$87$	28.4046			3.04529
$88$		0			0
$89$	−16.6470			−1.76458			−0.882291	−	0.470704i	$-0.844000\pi$
$89$	−16.6470			−1.76458			−0.882291	+	0.470704i	$0.844000\pi$
$90$		0			0
$91$	3.10700	−	2.25737i	0.325702	−	0.236637i
$92$		0			0
$93$	4.98393	+	15.3390i	0.516809	+	1.59058i
$94$		0			0
$95$	−0.209505	−	0.152214i	−0.0214948	−	0.0156169i
$96$		0			0
$97$	−2.42082	+	7.45053i	−0.245797	+	0.756486i	0.749707	+	0.661770i	$0.230194\pi$
$97$	−2.42082	+	7.45053i	−0.245797	+	0.756486i	−0.995504	+	0.0947164i	$0.969806\pi$
$98$		0			0
$99$	−20.5422	+	1.24672i	−2.06457	+	0.125300i
$100$		0			0
$101$	−5.62378	+	17.3082i	−0.559587	+	1.72223i	0.123923	+	0.992292i	$0.460452\pi$
$101$	−5.62378	+	17.3082i	−0.559587	+	1.72223i	−0.683511	+	0.729941i	$0.739548\pi$
$102$		0			0
$103$	−9.54845	−	6.93735i	−0.940837	−	0.683558i	0.00778529	−	0.999970i	$-0.497522\pi$
$103$	−9.54845	−	6.93735i	−0.940837	−	0.683558i	−0.948622	+	0.316412i	$0.897522\pi$
$104$		0			0
$105$	0.811855	+	2.49863i	0.0792289	+	0.243841i
$106$		0			0
$107$	0.421469	−	0.306215i	0.0407450	−	0.0296030i	−0.567226	−	0.823562i	$-0.691984\pi$
$107$	0.421469	−	0.306215i	0.0407450	−	0.0296030i	0.607971	+	0.793959i	$0.291984\pi$
$108$		0			0
$109$	−6.22545			−0.596290			−0.298145	−	0.954521i	$-0.596368\pi$
$109$	−6.22545			−0.596290			−0.298145	+	0.954521i	$0.596368\pi$
$110$		0			0
$111$	−19.3793			−1.83940
$112$		0			0
$113$	7.98968	−	5.80484i	0.751605	−	0.546073i	−0.144719	−	0.989473i	$-0.546228\pi$
$113$	7.98968	−	5.80484i	0.751605	−	0.546073i	0.896324	+	0.443400i	$0.146228\pi$
$114$		0			0
$115$	−2.44958	−	7.53904i	−0.228425	−	0.703019i
$116$		0			0
$117$	22.2643	+	16.1760i	2.05834	+	1.49547i
$118$		0			0
$119$	−0.147181	+	0.452976i	−0.0134920	+	0.0415242i
$120$		0			0
$121$	−8.05194	+	7.49442i	−0.731995	+	0.681310i
$122$		0			0
$123$	−8.19628	+	25.2256i	−0.739034	+	2.27451i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	1.14934	+	3.53730i	0.101987	+	0.313885i	0.989012	−	0.147838i	$-0.0472315\pi$
$127$	1.14934	+	3.53730i	0.101987	+	0.313885i	−0.887024	+	0.461723i	$0.847231\pi$
$128$		0			0
$129$	15.6753	−	11.3888i	1.38013	−	1.00273i
$130$		0			0
$131$	20.4259			1.78462			0.892308	−	0.451426i	$-0.149085\pi$
$131$	20.4259			1.78462			0.892308	+	0.451426i	$0.149085\pi$
$132$		0			0
$133$	−0.224243			−0.0194443
$134$		0			0
$135$	−7.86710	+	5.71579i	−0.677092	+	0.491936i
$136$		0			0
$137$	4.14751	+	12.7647i	0.354346	+	1.09056i	0.956388	+	0.292100i	$0.0943540\pi$
$137$	4.14751	+	12.7647i	0.354346	+	1.09056i	−0.602042	+	0.798465i	$0.705646\pi$
$138$		0			0
$139$	−11.3955	−	8.27933i	−0.966555	−	0.702243i	−0.0118911	−	0.999929i	$-0.503785\pi$
$139$	−11.3955	−	8.27933i	−0.966555	−	0.702243i	−0.954664	+	0.297686i	$0.903785\pi$
$140$		0			0
$141$	−0.771803	+	2.37537i	−0.0649975	+	0.200042i
$142$		0			0
$143$	14.6825	−	0.891094i	1.22781	−	0.0745170i
$144$		0			0
$145$	2.89305	−	8.90389i	0.240255	−	0.739428i
$146$		0			0
$147$	−15.3414	−	11.1462i	−1.26533	−	0.919319i
$148$		0			0
$149$	0.553674	+	1.70403i	0.0453588	+	0.139600i	0.971171	−	0.238384i	$-0.0766176\pi$
$149$	0.553674	+	1.70403i	0.0453588	+	0.139600i	−0.925812	+	0.377984i	$0.876618\pi$
$150$		0			0
$151$	−15.4418	+	11.2191i	−1.25663	+	0.912996i	−0.998587	−	0.0531366i	$-0.983078\pi$
$151$	−15.4418	+	11.2191i	−1.25663	+	0.912996i	−0.258045	+	0.966133i	$0.583078\pi$
$152$		0			0
$153$	−3.41300			−0.275925
$154$		0			0
$155$	5.31588			0.426982
$156$		0			0
$157$	−7.91828	+	5.75296i	−0.631947	+	0.459137i	−0.857074	−	0.515193i	$-0.827720\pi$
$157$	−7.91828	+	5.75296i	−0.631947	+	0.459137i	0.225127	+	0.974329i	$0.427720\pi$
$158$		0			0
$159$	−2.25116	−	6.92837i	−0.178529	−	0.549455i
$160$		0			0
$161$	−5.55327	−	4.03469i	−0.437659	−	0.317978i
$162$		0			0
$163$	0.122631	−	0.377420i	0.00960522	−	0.0295618i	−0.946139	−	0.323761i	$-0.895053\pi$
$163$	0.122631	−	0.377420i	0.00960522	−	0.0295618i	0.955744	+	0.294199i	$0.0950528\pi$
$164$		0			0
$165$	−2.52406	+	9.74091i	−0.196498	+	0.758329i
$166$		0			0
$167$	4.29967	−	13.2330i	0.332718	−	1.02400i	−0.635117	−	0.772416i	$-0.719048\pi$
$167$	4.29967	−	13.2330i	0.332718	−	1.02400i	0.967835	−	0.251585i	$-0.0809518\pi$
$168$		0			0
$169$	−5.39618	−	3.92055i	−0.415091	−	0.301581i
$170$		0			0
$171$	−0.496556	−	1.52824i	−0.0379726	−	0.116868i
$172$		0			0
$173$	−4.31522	+	3.13519i	−0.328080	+	0.238364i	−0.739615	−	0.673030i	$-0.764993\pi$
$173$	−4.31522	+	3.13519i	−0.328080	+	0.238364i	0.411535	+	0.911394i	$0.364993\pi$
$174$		0			0
$175$	0.865927			0.0654580
$176$		0			0
$177$	41.0039			3.08204
$178$		0			0
$179$	−6.17667	+	4.48761i	−0.461666	+	0.335420i	−0.794184	−	0.607677i	$-0.792102\pi$
$179$	−6.17667	+	4.48761i	−0.461666	+	0.335420i	0.332519	+	0.943097i	$0.392102\pi$
$180$		0			0
$181$	0.403121	+	1.24068i	0.0299638	+	0.0922189i	0.964920	−	0.262544i	$-0.0845615\pi$
$181$	0.403121	+	1.24068i	0.0299638	+	0.0922189i	−0.934956	+	0.354763i	$0.884562\pi$
$182$		0			0
$183$	−16.2187	−	11.7836i	−1.19892	−	0.871068i
$184$		0			0
$185$	−1.97381	+	6.07477i	−0.145118	+	0.446626i
$186$		0			0
$187$	−1.40818	+	1.15970i	−0.102976	+	0.0848058i
$188$		0			0
$189$	−2.60208	+	8.00839i	−0.189274	+	0.582524i
$190$		0			0
$191$	−20.2928	−	14.7436i	−1.46834	−	1.06681i	−0.981091	−	0.193547i	$-0.938001\pi$
$191$	−20.2928	−	14.7436i	−1.46834	−	1.06681i	−0.487248	−	0.873264i	$-0.661999\pi$
$192$		0			0
$193$	−6.16676	−	18.9793i	−0.443893	−	1.36616i	−0.883693	−	0.468067i	$-0.844950\pi$
$193$	−6.16676	−	18.9793i	−0.443893	−	1.36616i	0.439799	−	0.898096i	$-0.355050\pi$
$194$		0			0
$195$	10.8862	−	7.90926i	0.779574	−	0.566394i
$196$		0			0
$197$	−1.31088			−0.0933960			−0.0466980	−	0.998909i	$-0.514870\pi$
$197$	−1.31088			−0.0933960			−0.0466980	+	0.998909i	$0.514870\pi$
$198$		0			0
$199$	−4.99115			−0.353813			−0.176907	−	0.984228i	$-0.556609\pi$
$199$	−4.99115			−0.353813			−0.176907	+	0.984228i	$0.556609\pi$
$200$		0			0
$201$	17.6169	−	12.7994i	1.24260	−	0.902803i
$202$		0			0
$203$	−2.50517	−	7.71012i	−0.175829	−	0.541145i
$204$		0			0
$205$	7.07258	+	5.13853i	0.493970	+	0.358890i
$206$		0			0
$207$	15.1999	−	46.7805i	1.05647	−	3.25147i
$208$		0			0
$209$	−0.724156	−	0.461817i	−0.0500909	−	0.0319445i
$210$		0			0
$211$	−1.98113	+	6.09730i	−0.136387	+	0.419755i	−0.995803	−	0.0915210i	$-0.970827\pi$
$211$	−1.98113	+	6.09730i	−0.136387	+	0.419755i	0.859416	+	0.511276i	$0.170827\pi$
$212$		0			0
$213$	6.87054	+	4.99174i	0.470762	+	0.342028i
$214$		0			0
$215$	−1.97345	−	6.07366i	−0.134588	−	0.414220i
$216$		0			0
$217$	3.72404	−	2.70567i	0.252804	−	0.183673i
$218$		0			0
$219$	8.77047			0.592654
$220$		0			0
$221$	2.43944			0.164094
$222$		0			0
$223$	12.0126	−	8.72766i	0.804423	−	0.584447i	−0.107786	−	0.994174i	$-0.534376\pi$
$223$	12.0126	−	8.72766i	0.804423	−	0.584447i	0.912208	+	0.409727i	$0.134376\pi$
$224$		0			0
$225$	1.91748	+	5.90141i	0.127832	+	0.393427i
$226$		0			0
$227$	18.9925	+	13.7989i	1.26058	+	0.915865i	0.998786	−	0.0492591i	$-0.0156860\pi$
$227$	18.9925	+	13.7989i	1.26058	+	0.915865i	0.261794	+	0.965124i	$0.415686\pi$
$228$		0			0
$229$	6.06694	−	18.6721i	0.400914	−	1.23389i	−0.523344	−	0.852121i	$-0.675316\pi$
$229$	6.06694	−	18.6721i	0.400914	−	1.23389i	0.924259	−	0.381766i	$-0.124684\pi$
$230$		0			0
$231$	3.18969	+	8.10869i	0.209866	+	0.533512i
$232$		0			0
$233$	6.48770	−	19.9671i	0.425024	−	1.30809i	−0.477948	−	0.878388i	$-0.658619\pi$
$233$	6.48770	−	19.9671i	0.425024	−	1.30809i	0.902972	−	0.429700i	$-0.141381\pi$
$234$		0			0
$235$	0.665989	+	0.483870i	0.0434444	+	0.0315642i
$236$		0			0
$237$	5.54519	+	17.0664i	0.360199	+	1.10858i
$238$		0			0
$239$	15.2527	−	11.0817i	0.986614	−	0.716817i	0.0274367	−	0.999624i	$-0.491266\pi$
$239$	15.2527	−	11.0817i	0.986614	−	0.716817i	0.959177	+	0.282807i	$0.0912655\pi$
$240$		0			0
$241$	−13.8318			−0.890987			−0.445494	−	0.895285i	$-0.646972\pi$
$241$	−13.8318			−0.890987			−0.445494	+	0.895285i	$0.646972\pi$
$242$		0			0
$243$	−3.86143			−0.247711
$244$		0			0
$245$	−5.05649	+	3.67376i	−0.323048	+	0.234708i
$246$		0			0
$247$	0.354913	+	1.09231i	0.0225826	+	0.0695020i
$248$		0			0
$249$	−17.4229	−	12.6585i	−1.10413	−	0.802199i
$250$		0			0
$251$	4.71929	−	14.5245i	0.297879	−	0.916777i	−0.684360	−	0.729144i	$-0.739919\pi$
$251$	4.71929	−	14.5245i	0.297879	−	0.916777i	0.982239	−	0.187633i	$-0.0600815\pi$
$252$		0			0
$253$	−9.62416	−	24.4661i	−0.605066	−	1.53817i
$254$		0			0
$255$	−0.515684	+	1.58711i	−0.0322934	+	0.0993889i
$256$		0			0
$257$	−23.2900	−	16.9212i	−1.45279	−	1.05551i	−0.985170	−	0.171584i	$-0.945112\pi$
$257$	−23.2900	−	16.9212i	−1.45279	−	1.05551i	−0.467620	−	0.883930i	$-0.654888\pi$
$258$		0			0
$259$	1.70918	+	5.26031i	0.106203	+	0.326860i
$260$		0			0
$261$	46.9981	−	34.1461i	2.90911	−	2.11359i
$262$		0			0
$263$	−9.23218			−0.569281			−0.284640	−	0.958634i	$-0.591874\pi$
$263$	−9.23218			−0.569281			−0.284640	+	0.958634i	$0.591874\pi$
$264$		0			0
$265$	−2.40110			−0.147498
$266$		0			0
$267$	−40.8610	+	29.6873i	−2.50065	+	1.81683i
$268$		0			0
$269$	8.29165	+	25.5191i	0.505551	+	1.55593i	0.799842	+	0.600210i	$0.204916\pi$
$269$	8.29165	+	25.5191i	0.505551	+	1.55593i	−0.294291	+	0.955716i	$0.595084\pi$
$270$		0			0
$271$	−19.0614	−	13.8489i	−1.15790	−	0.841261i	−0.168386	−	0.985721i	$-0.553856\pi$
$271$	−19.0614	−	13.8489i	−1.15790	−	0.841261i	−0.989511	+	0.144460i	$0.953856\pi$
$272$		0			0
$273$	3.60065	−	11.0817i	0.217921	−	0.670693i
$274$		0			0
$275$	2.79638	+	1.78334i	0.168628	+	0.107539i
$276$		0			0
$277$	3.08782	−	9.50334i	0.185529	−	0.571001i	−0.814428	−	0.580265i	$-0.802949\pi$
$277$	3.08782	−	9.50334i	0.185529	−	0.571001i	0.999957	+	0.00926435i	$0.00294898\pi$
$278$		0			0
$279$	26.6859	+	19.3884i	1.59764	+	1.16076i
$280$		0			0
$281$	1.26401	+	3.89022i	0.0754044	+	0.232071i	0.981654	−	0.190673i	$-0.0610670\pi$
$281$	1.26401	+	3.89022i	0.0754044	+	0.232071i	−0.906249	+	0.422744i	$0.861067\pi$
$282$		0			0
$283$	−3.86118	+	2.80531i	−0.229523	+	0.166758i	−0.696603	−	0.717457i	$-0.745306\pi$
$283$	−3.86118	+	2.80531i	−0.229523	+	0.166758i	0.467080	+	0.884215i	$0.345306\pi$
$284$		0			0
$285$	−0.785690			−0.0465402
$286$		0			0
$287$	7.57010			0.446849
$288$		0			0
$289$	13.5085	−	9.81452i	0.794620	−	0.577325i
$290$		0			0
$291$	7.34476	+	22.6048i	0.430557	+	1.32512i
$292$		0			0
$293$	−0.116508	−	0.0846481i	−0.00680648	−	0.00494520i	0.584377	−	0.811482i	$-0.301339\pi$
$293$	−0.116508	−	0.0846481i	−0.00680648	−	0.00494520i	−0.591183	+	0.806537i	$0.701339\pi$
$294$		0			0
$295$	4.17631	−	12.8534i	0.243154	−	0.748352i
$296$		0			0
$297$	−24.8959	+	20.5029i	−1.44461	+	1.18970i
$298$		0			0
$299$	−10.8641	+	33.4363i	−0.628288	+	1.93367i
$300$		0			0
$301$	−4.47387	−	3.25046i	−0.257869	−	0.187353i
$302$		0			0
$303$	17.0625	+	52.5130i	0.980216	+	3.01679i
$304$		0			0
$305$	−5.34567	+	3.88385i	−0.306092	+	0.222389i
$306$		0			0
$307$	−25.7576			−1.47006			−0.735031	−	0.678034i	$-0.762832\pi$
$307$	−25.7576			−1.47006			−0.735031	+	0.678034i	$0.762832\pi$
$308$		0			0
$309$	−35.8088			−2.03709
$310$		0			0
$311$	−13.2610	+	9.63467i	−0.751961	+	0.546332i	−0.896434	−	0.443177i	$-0.853851\pi$
$311$	−13.2610	+	9.63467i	−0.751961	+	0.546332i	0.144473	+	0.989509i	$0.453851\pi$
$312$		0			0
$313$	8.19629	+	25.2256i	0.463282	+	1.42583i	0.861131	+	0.508384i	$0.169757\pi$
$313$	8.19629	+	25.2256i	0.463282	+	1.42583i	−0.397849	+	0.917451i	$0.630243\pi$
$314$		0			0
$315$	4.34699	+	3.15827i	0.244925	+	0.177948i
$316$		0			0
$317$	5.16546	−	15.8977i	0.290121	−	0.892902i	−0.694695	−	0.719304i	$-0.744461\pi$
$317$	5.16546	−	15.8977i	0.290121	−	0.892902i	0.984817	−	0.173598i	$-0.0555392\pi$
$318$		0			0
$319$	7.78858	−	30.0579i	0.436077	−	1.68292i
$320$		0			0
$321$	0.488433	−	1.50324i	0.0272617	−	0.0839028i
$322$		0			0
$323$	−0.115234	−	0.0837225i	−0.00641180	−	0.00465845i
$324$		0			0
$325$	−1.37052	−	4.21802i	−0.0760227	−	0.233974i
$326$		0			0
$327$	−15.2807	+	11.1021i	−0.845025	+	0.613946i
$328$		0			0
$329$	0.712839			0.0393001
$330$		0			0
$331$	4.39584			0.241617			0.120809	−	0.992676i	$-0.461451\pi$
$331$	4.39584			0.241617			0.120809	+	0.992676i	$0.461451\pi$
$332$		0			0
$333$	−32.0649	+	23.2965i	−1.75715	+	1.27664i
$334$		0			0
$335$	−2.21789	−	6.82597i	−0.121176	−	0.372942i
$336$		0			0
$337$	−10.1965	−	7.40817i	−0.555437	−	0.403549i	0.274349	−	0.961630i	$-0.411538\pi$
$337$	−10.1965	−	7.40817i	−0.555437	−	0.403549i	−0.829786	+	0.558082i	$0.811538\pi$
$338$		0			0
$339$	9.25909	−	28.4966i	0.502885	−	1.54772i
$340$		0			0
$341$	17.5984	−	1.06806i	0.953006	−	0.0578387i
$342$		0			0
$343$	−3.54556	+	10.9121i	−0.191442	+	0.589199i
$344$		0			0
$345$	−19.4573	−	14.1365i	−1.04754	−	0.761085i
$346$		0			0
$347$	−7.41108	−	22.8089i	−0.397847	−	1.22445i	−0.926722	−	0.375748i	$-0.877386\pi$
$347$	−7.41108	−	22.8089i	−0.397847	−	1.22445i	0.528874	−	0.848700i	$-0.322614\pi$
$348$		0			0
$349$	−19.0848	+	13.8659i	−1.02159	+	0.742227i	−0.966608	−	0.256261i	$-0.917509\pi$
$349$	−19.0848	+	13.8659i	−1.02159	+	0.742227i	−0.0549798	+	0.998487i	$0.517509\pi$
$350$		0			0
$351$	43.1281			2.30201
$352$		0			0
$353$	6.46751			0.344231			0.172115	−	0.985077i	$-0.444940\pi$
$353$	6.46751			0.344231			0.172115	+	0.985077i	$0.444940\pi$
$354$		0			0
$355$	2.26452	−	1.64527i	0.120188	−	0.0873219i
$356$		0			0
$357$	0.446545	+	1.37432i	0.0236337	+	0.0727370i
$358$		0			0
$359$	−9.56591	−	6.95004i	−0.504869	−	0.366809i	0.306005	−	0.952030i	$-0.401008\pi$
$359$	−9.56591	−	6.95004i	−0.504869	−	0.366809i	−0.810874	+	0.585221i	$0.801008\pi$
$360$		0			0
$361$	−5.85060	+	18.0063i	−0.307926	+	0.947700i
$362$		0			0
$363$	−6.39884	+	32.7547i	−0.335852	+	1.71918i
$364$		0			0
$365$	0.893287	−	2.74925i	0.0467568	−	0.143903i
$366$		0			0
$367$	−6.78533	−	4.92983i	−0.354191	−	0.257335i	0.396434	−	0.918063i	$-0.370248\pi$
$367$	−6.78533	−	4.92983i	−0.354191	−	0.257335i	−0.750625	+	0.660728i	$0.770248\pi$
$368$		0			0
$369$	16.7630	+	51.5912i	0.872647	+	2.68573i
$370$		0			0
$371$	−1.68209	+	1.22211i	−0.0873298	+	0.0634488i
$372$		0			0
$373$	34.6263			1.79288			0.896441	−	0.443163i	$-0.146144\pi$
$373$	34.6263			1.79288			0.896441	+	0.443163i	$0.146144\pi$
$374$		0			0
$375$	3.03399			0.156675
$376$		0			0
$377$	−33.5918	+	24.4059i	−1.73007	+	1.25697i
$378$		0			0
$379$	4.96669	+	15.2859i	0.255122	+	0.785185i	0.993806	+	0.111132i	$0.0354478\pi$
$379$	4.96669	+	15.2859i	0.255122	+	0.785185i	−0.738684	+	0.674052i	$0.764552\pi$
$380$		0			0
$381$	9.12931	+	6.63283i	0.467709	+	0.339810i
$382$		0			0
$383$	2.60059	−	8.00380i	0.132884	−	0.408975i	−0.862371	−	0.506277i	$-0.831021\pi$
$383$	2.60059	−	8.00380i	0.132884	−	0.408975i	0.995255	+	0.0973020i	$0.0310213\pi$
$384$		0			0
$385$	2.86668	−	0.173981i	0.146100	−	0.00886690i
$386$		0			0
$387$	12.2455	−	37.6877i	0.622473	−	1.91577i
$388$		0			0
$389$	−15.0410	−	10.9279i	−0.762608	−	0.554067i	0.137101	−	0.990557i	$-0.456222\pi$
$389$	−15.0410	−	10.9279i	−0.762608	−	0.554067i	−0.899709	+	0.436490i	$0.856222\pi$
$390$		0			0
$391$	−1.34735	−	4.14670i	−0.0681382	−	0.209708i
$392$		0			0
$393$	50.1364	−	36.4262i	2.52904	−	1.83746i
$394$		0			0
$395$	5.91452			0.297592
$396$		0			0
$397$	−11.9897			−0.601743			−0.300872	−	0.953665i	$-0.597278\pi$
$397$	−11.9897			−0.601743			−0.300872	+	0.953665i	$0.597278\pi$
$398$		0			0
$399$	−0.550415	+	0.399900i	−0.0275552	+	0.0200200i
$400$		0			0
$401$	5.80924	+	17.8790i	0.290099	+	0.892834i	0.984824	+	0.173558i	$0.0555264\pi$
$401$	5.80924	+	17.8790i	0.290099	+	0.892834i	−0.694724	+	0.719276i	$0.744474\pi$
$402$		0			0
$403$	−19.0737	−	13.8579i	−0.950129	−	0.690309i
$404$		0			0
$405$	−3.36459	+	10.3551i	−0.167188	+	0.514551i
$406$		0			0
$407$	−5.31383	+	20.5073i	−0.263397	+	1.01651i
$408$		0			0
$409$	−2.93699	+	9.03912i	−0.145225	+	0.446956i	−0.997040	−	0.0768869i	$-0.975502\pi$
$409$	−2.93699	+	9.03912i	−0.145225	+	0.446956i	0.851815	+	0.523842i	$0.175502\pi$
$410$		0			0
$411$	32.9441	+	23.9353i	1.62501	+	1.18064i
$412$		0			0
$413$	−3.61638	−	11.1301i	−0.177951	−	0.547676i
$414$		0			0
$415$	−5.74257	+	4.17222i	−0.281892	+	0.204806i
$416$		0			0
$417$	−42.7357			−2.09278
$418$		0			0
$419$	32.9152			1.60801			0.804007	−	0.594620i	$-0.202698\pi$
$419$	32.9152			1.60801			0.804007	+	0.594620i	$0.202698\pi$
$420$		0			0
$421$	0.837812	−	0.608706i	0.0408325	−	0.0296665i	−0.567182	−	0.823593i	$-0.691966\pi$
$421$	0.837812	−	0.608706i	0.0408325	−	0.0296665i	0.608014	+	0.793926i	$0.291966\pi$
$422$		0			0
$423$	1.57849	+	4.85809i	0.0767487	+	0.236208i
$424$		0			0
$425$	0.444984	+	0.323300i	0.0215849	+	0.0156824i
$426$		0			0
$427$	−1.76811	+	5.44167i	−0.0855646	+	0.263341i
$428$		0			0
$429$	34.4499	−	28.3711i	1.66326	−	1.36977i
$430$		0			0
$431$	7.96068	−	24.5005i	0.383452	−	1.18015i	−0.554144	−	0.832421i	$-0.686954\pi$
$431$	7.96068	−	24.5005i	0.383452	−	1.18015i	0.937597	−	0.347725i	$-0.113046\pi$
$432$		0			0
$433$	14.9188	+	10.8391i	0.716951	+	0.520896i	0.885409	−	0.464813i	$-0.153879\pi$
$433$	14.9188	+	10.8391i	0.716951	+	0.520896i	−0.168457	+	0.985709i	$0.553879\pi$
$434$		0			0
$435$	−8.77749	−	27.0143i	−0.420848	−	1.29524i
$436$		0			0
$437$	1.66075	−	1.20660i	0.0794444	−	0.0577197i
$438$		0			0
$439$	−4.44724			−0.212255			−0.106128	−	0.994353i	$-0.533845\pi$
$439$	−4.44724			−0.212255			−0.106128	+	0.994353i	$0.533845\pi$
$440$		0			0
$441$	−38.7830			−1.84681
$442$		0			0
$443$	20.2851	−	14.7380i	0.963775	−	0.700224i	0.00975065	−	0.999952i	$-0.496896\pi$
$443$	20.2851	−	14.7380i	0.963775	−	0.700224i	0.954024	+	0.299729i	$0.0968962\pi$
$444$		0			0
$445$	5.14422	+	15.8323i	0.243859	+	0.750522i
$446$		0			0
$447$	4.39789	+	3.19525i	0.208013	+	0.151130i
$448$		0			0
$449$	−5.77075	+	17.7605i	−0.272338	+	0.838172i	0.717573	+	0.696483i	$0.245253\pi$
$449$	−5.77075	+	17.7605i	−0.272338	+	0.838172i	−0.989911	+	0.141688i	$0.954747\pi$
$450$		0			0
$451$	24.4464	+	15.5903i	1.15114	+	0.734116i
$452$		0			0
$453$	−17.8952	+	55.0757i	−0.840788	+	2.58768i
$454$		0			0
$455$	−3.10700	−	2.25737i	−0.145659	−	0.105827i
$456$		0			0
$457$	−4.49832	−	13.8444i	−0.210422	−	0.647614i	−0.999447	−	0.0332521i	$-0.989414\pi$
$457$	−4.49832	−	13.8444i	−0.210422	−	0.647614i	0.789025	−	0.614362i	$-0.210586\pi$
$458$		0			0
$459$	−4.32715	+	3.14386i	−0.201974	+	0.146743i
$460$		0			0
$461$	20.6525			0.961884			0.480942	−	0.876752i	$-0.340295\pi$
$461$	20.6525			0.961884			0.480942	+	0.876752i	$0.340295\pi$
$462$		0			0
$463$	−21.8605			−1.01594			−0.507971	−	0.861374i	$-0.669604\pi$
$463$	−21.8605			−1.01594			−0.507971	+	0.861374i	$0.669604\pi$
$464$		0			0
$465$	13.0481	−	9.48000i	0.605091	−	0.439624i
$466$		0			0
$467$	6.27254	+	19.3049i	0.290258	+	0.893324i	0.984773	+	0.173845i	$0.0556192\pi$
$467$	6.27254	+	19.3049i	0.290258	+	0.893324i	−0.694515	+	0.719479i	$0.744381\pi$
$468$		0			0
$469$	−5.02802	−	3.65307i	−0.232172	−	0.168683i
$470$		0			0
$471$	−9.17635	+	28.2419i	−0.422824	+	1.30132i
$472$		0			0
$473$	−7.75349	−	19.7105i	−0.356506	−	0.906292i
$474$		0			0
$475$	−0.0800238	+	0.246288i	−0.00367174	+	0.0113005i
$476$		0			0
$477$	−12.0536	−	8.75746i	−0.551897	−	0.400977i
$478$		0			0
$479$	−3.05665	−	9.40740i	−0.139662	−	0.429835i	0.856624	−	0.515941i	$-0.172558\pi$
$479$	−3.05665	−	9.40740i	−0.139662	−	0.429835i	−0.996286	+	0.0861060i	$0.972558\pi$
$480$		0			0
$481$	22.9184	−	16.6512i	1.04499	−	0.759228i
$482$		0			0
$483$	−20.8260			−0.947615
$484$		0			0
$485$	7.83395			0.355721
$486$		0			0
$487$	−4.80458	+	3.49073i	−0.217716	+	0.158180i	−0.691298	−	0.722570i	$-0.742961\pi$
$487$	−4.80458	+	3.49073i	−0.217716	+	0.158180i	0.473582	+	0.880750i	$0.342961\pi$
$488$		0			0
$489$	−0.372062	−	1.14509i	−0.0168252	−	0.0517828i
$490$		0			0
$491$	−22.1143	−	16.0670i	−0.998005	−	0.725093i	−0.0363455	−	0.999339i	$-0.511572\pi$
$491$	−22.1143	−	16.0670i	−0.998005	−	0.725093i	−0.961660	+	0.274246i	$0.911572\pi$
$492$		0			0
$493$	1.59127	−	4.89741i	0.0716670	−	0.220568i
$494$		0			0
$495$	7.53360	+	19.1516i	0.338610	+	0.860798i
$496$		0			0
$497$	0.749001	−	2.30519i	0.0335973	−	0.103402i
$498$		0			0
$499$	9.84395	+	7.15205i	0.440676	+	0.320170i	0.785903	−	0.618349i	$-0.212198\pi$
$499$	9.84395	+	7.15205i	0.440676	+	0.320170i	−0.345228	+	0.938519i	$0.612198\pi$
$500$		0			0
$501$	−13.0452	−	40.1488i	−0.582814	−	1.79372i
$502$		0			0
$503$	7.67903	−	5.57914i	0.342391	−	0.248762i	−0.403279	−	0.915077i	$-0.632130\pi$
$503$	7.67903	−	5.57914i	0.342391	−	0.248762i	0.745670	+	0.666315i	$0.232130\pi$
$504$		0			0
$505$	18.1989			0.809842
$506$		0			0
$507$	−20.2369			−0.898750
$508$		0			0
$509$	0.774792	−	0.562919i	0.0343421	−	0.0249510i	−0.570482	−	0.821310i	$-0.693244\pi$
$509$	0.774792	−	0.562919i	0.0343421	−	0.0249510i	0.604824	+	0.796359i	$0.293244\pi$
$510$		0			0
$511$	−0.773521	−	2.38065i	−0.0342186	−	0.105314i
$512$		0			0
$513$	−2.03728	−	1.48017i	−0.0899483	−	0.0653512i
$514$		0			0
$515$	−3.64718	+	11.2249i	−0.160714	+	0.494627i
$516$		0			0
$517$	2.30200	+	1.46806i	0.101242	+	0.0645651i
$518$		0			0
$519$	−5.00083	+	15.3910i	−0.219512	+	0.675589i
$520$		0			0
$521$	14.7577	+	10.7221i	0.646547	+	0.469744i	0.862093	−	0.506750i	$-0.169153\pi$
$521$	14.7577	+	10.7221i	0.646547	+	0.469744i	−0.215546	+	0.976494i	$0.569153\pi$
$522$		0			0
$523$	8.75364	+	26.9409i	0.382770	+	1.17804i	0.938085	+	0.346405i	$0.112598\pi$
$523$	8.75364	+	26.9409i	0.382770	+	1.17804i	−0.555315	+	0.831640i	$0.687402\pi$
$524$		0			0
$525$	2.12546	−	1.54424i	0.0927628	−	0.0673961i
$526$		0			0
$527$	2.92390			0.127367
$528$		0			0
$529$	39.8375			1.73207
$530$		0			0
$531$	67.8450	−	49.2923i	2.94422	−	2.13910i
$532$		0			0
$533$	−11.9813	−	36.8747i	−0.518969	−	1.59722i
$534$		0			0
$535$	−0.421469	−	0.306215i	−0.0182217	−	0.0132388i
$536$		0			0
$537$	−7.15803	+	22.0301i	−0.308892	+	0.950671i
$538$		0			0
$539$	−16.0016	+	13.1780i	−0.689236	+	0.567618i
$540$		0			0
$541$	−9.81343	+	30.2026i	−0.421912	+	1.29851i	0.484008	+	0.875064i	$0.339181\pi$
$541$	−9.81343	+	30.2026i	−0.421912	+	1.29851i	−0.905920	+	0.423448i	$0.860819\pi$
$542$		0			0
$543$	3.20203	+	2.32641i	0.137412	+	0.0998358i
$544$		0			0
$545$	1.92377	+	5.92076i	0.0824053	+	0.253617i
$546$		0			0
$547$	−2.89975	+	2.10679i	−0.123984	+	0.0900798i	−0.648049	−	0.761598i	$-0.724415\pi$
$547$	−2.89975	+	2.10679i	−0.123984	+	0.0900798i	0.524065	+	0.851678i	$0.324415\pi$
$548$		0			0
$549$	−41.0009			−1.74988
$550$		0			0
$551$	2.42443			0.103284
$552$		0			0
$553$	4.14342	−	3.01037i	0.176196	−	0.128014i
$554$		0			0
$555$	5.98853	+	18.4308i	0.254199	+	0.782344i
$556$		0			0
$557$	13.4746	+	9.78990i	0.570939	+	0.414811i	0.835446	−	0.549572i	$-0.185209\pi$
$557$	13.4746	+	9.78990i	0.570939	+	0.414811i	−0.264507	+	0.964384i	$0.585209\pi$
$558$		0			0
$559$	−8.75244	+	26.9372i	−0.370189	+	1.13932i
$560$		0			0
$561$	−1.38831	+	5.35780i	−0.0586144	+	0.226207i
$562$		0			0
$563$	12.3291	−	37.9450i	0.519609	−	1.59919i	−0.255127	−	0.966907i	$-0.582117\pi$
$563$	12.3291	−	37.9450i	0.519609	−	1.59919i	0.774736	−	0.632285i	$-0.217883\pi$
$564$		0			0
$565$	−7.98968	−	5.80484i	−0.336128	−	0.244211i
$566$		0			0
$567$	2.91349	+	8.96681i	0.122355	+	0.376570i
$568$		0			0
$569$	−36.7814	+	26.7233i	−1.54196	+	1.12030i	−0.592866	+	0.805301i	$0.702004\pi$
$569$	−36.7814	+	26.7233i	−1.54196	+	1.12030i	−0.949093	+	0.314997i	$0.897996\pi$
$570$		0			0
$571$	−15.8877			−0.664880			−0.332440	−	0.943124i	$-0.607872\pi$
$571$	−15.8877			−0.664880			−0.332440	+	0.943124i	$0.607872\pi$
$572$		0			0
$573$	−76.1027			−3.17923
$574$		0			0
$575$	−6.41309	+	4.65938i	−0.267444	+	0.194310i
$576$		0			0
$577$	−4.06088	−	12.4981i	−0.169057	−	0.520302i	0.830256	−	0.557383i	$-0.188194\pi$
$577$	−4.06088	−	12.4981i	−0.169057	−	0.520302i	−0.999312	+	0.0370801i	$0.988194\pi$
$578$		0			0
$579$	−48.9832	−	35.5884i	−2.03567	−	1.47900i
$580$		0			0
$581$	−1.89938	+	5.84570i	−0.0787997	+	0.242520i
$582$		0			0
$583$	−7.94892	+	0.482427i	−0.329211	+	0.0199801i
$584$		0			0
$585$	8.50422	−	26.1733i	0.351606	−	1.08213i
$586$		0			0
$587$	−12.1061	−	8.79560i	−0.499672	−	0.363033i	0.309220	−	0.950991i	$-0.399932\pi$
$587$	−12.1061	−	8.79560i	−0.499672	−	0.363033i	−0.808892	+	0.587958i	$0.799932\pi$
$588$		0			0
$589$	0.425397	+	1.30924i	0.0175282	+	0.0539461i
$590$		0			0
$591$	−3.21761	+	2.33773i	−0.132355	+	0.0961615i
$592$		0			0
$593$	−13.7967			−0.566564			−0.283282	−	0.959037i	$-0.591423\pi$
$593$	−13.7967			−0.566564			−0.283282	+	0.959037i	$0.591423\pi$
$594$		0			0
$595$	0.476287			0.0195259
$596$		0			0
$597$	−12.2510	+	8.90090i	−0.501401	+	0.364289i
$598$		0			0
$599$	9.69984	+	29.8530i	0.396325	+	1.21976i	0.927925	+	0.372767i	$0.121591\pi$
$599$	9.69984	+	29.8530i	0.396325	+	1.21976i	−0.531600	+	0.846995i	$0.678409\pi$
$600$		0			0
$601$	2.06813	+	1.50259i	0.0843608	+	0.0612917i	0.629166	−	0.777271i	$-0.283396\pi$
$601$	2.06813	+	1.50259i	0.0843608	+	0.0612917i	−0.544805	+	0.838563i	$0.683396\pi$
$602$		0			0
$603$	13.7623	−	42.3559i	0.560442	−	1.72486i
$604$		0			0
$605$	9.61580	+	5.34195i	0.390938	+	0.217181i
$606$		0			0
$607$	−11.6898	+	35.9774i	−0.474473	+	1.46028i	0.372194	+	0.928155i	$0.378605\pi$
$607$	−11.6898	+	35.9774i	−0.474473	+	1.46028i	−0.846667	+	0.532123i	$0.821395\pi$
$608$		0			0
$609$	−19.8988	−	14.4573i	−0.806340	−	0.585841i
$610$		0			0
$611$	−1.12822	−	3.47231i	−0.0456430	−	0.140475i
$612$		0			0
$613$	−9.43309	+	6.85354i	−0.380999	+	0.276812i	−0.761757	−	0.647863i	$-0.775663\pi$
$613$	−9.43309	+	6.85354i	−0.380999	+	0.276812i	0.380758	+	0.924675i	$0.375663\pi$
$614$		0			0
$615$	26.5237			1.06954
$616$		0			0
$617$	38.5910			1.55361			0.776807	−	0.629739i	$-0.216838\pi$
$617$	38.5910			1.55361			0.776807	+	0.629739i	$0.216838\pi$
$618$		0			0
$619$	6.60453	−	4.79847i	0.265458	−	0.192867i	−0.447092	−	0.894488i	$-0.647540\pi$
$619$	6.60453	−	4.79847i	0.265458	−	0.192867i	0.712550	+	0.701621i	$0.247540\pi$
$620$		0			0
$621$	−23.8204	−	73.3117i	−0.955880	−	2.94190i
$622$		0			0
$623$	11.6621	+	8.47300i	0.467231	+	0.339463i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−2.60105	+	0.157860i	−0.103876	+	0.00630432i
$628$		0			0
$629$	−1.08566	+	3.34131i	−0.0432880	+	0.133227i
$630$		0			0
$631$	10.5830	+	7.68900i	0.421303	+	0.306094i	0.778162	−	0.628064i	$-0.216152\pi$
$631$	10.5830	+	7.68900i	0.421303	+	0.306094i	−0.356859	+	0.934158i	$0.616152\pi$
$632$		0			0
$633$	6.01074	+	18.4992i	0.238906	+	0.735276i
$634$		0			0
$635$	3.00901	−	2.18617i	0.119409	−	0.0867556i
$636$		0			0
$637$	27.7201			1.09831
$638$		0			0
$639$	17.3687			0.687096
$640$		0			0
$641$	−28.8414	+	20.9545i	−1.13917	+	0.827654i	−0.987003	−	0.160702i	$-0.948624\pi$
$641$	−28.8414	+	20.9545i	−1.13917	+	0.827654i	−0.152164	+	0.988355i	$0.548624\pi$
$642$		0			0
$643$	−2.36588	−	7.28142i	−0.0933011	−	0.287151i	0.893506	−	0.449051i	$-0.148238\pi$
$643$	−2.36588	−	7.28142i	−0.0933011	−	0.287151i	−0.986807	+	0.161900i	$0.948238\pi$
$644$		0			0
$645$	−15.6753	−	11.3888i	−0.617215	−	0.448433i
$646$		0			0
$647$	2.83754	−	8.73304i	0.111555	−	0.343331i	−0.879658	−	0.475607i	$-0.842228\pi$
$647$	2.83754	−	8.73304i	0.111555	−	0.343331i	0.991213	+	0.132276i	$0.0422285\pi$
$648$		0			0
$649$	11.2433	−	43.3906i	0.441340	−	1.70323i
$650$		0			0
$651$	4.31572	−	13.2824i	0.169146	−	0.520579i
$652$		0			0
$653$	4.73503	+	3.44020i	0.185296	+	0.134626i	0.676566	−	0.736382i	$-0.263467\pi$
$653$	4.73503	+	3.44020i	0.185296	+	0.134626i	−0.491270	+	0.871007i	$0.663467\pi$
$654$		0			0
$655$	−6.31194	−	19.4262i	−0.246628	−	0.759043i
$656$		0			0
$657$	14.5116	−	10.5433i	0.566152	−	0.411333i
$658$		0			0
$659$	−22.6530			−0.882434			−0.441217	−	0.897400i	$-0.645453\pi$
$659$	−22.6530			−0.882434			−0.441217	+	0.897400i	$0.645453\pi$
$660$		0			0
$661$	1.68482			0.0655320			0.0327660	−	0.999463i	$-0.489568\pi$
$661$	1.68482			0.0655320			0.0327660	+	0.999463i	$0.489568\pi$
$662$		0			0
$663$	5.98772	−	4.35034i	0.232544	−	0.168953i
$664$		0			0
$665$	0.0692948	+	0.213267i	0.00268714	+	0.00827015i
$666$		0			0
$667$	60.0400	+	43.6216i	2.32476	+	1.68904i
$668$		0			0
$669$	13.9212	−	42.8450i	0.538224	−	1.65648i
$670$		0			0
$671$	−16.9167	+	13.9317i	−0.653061	+	0.537826i
$672$		0			0
$673$	−2.93100	+	9.02070i	−0.112982	+	0.347722i	−0.991521	−	0.129948i	$-0.958519\pi$
$673$	−2.93100	+	9.02070i	−0.112982	+	0.347722i	0.878539	+	0.477671i	$0.158519\pi$
$674$		0			0
$675$	7.86710	+	5.71579i	0.302805	+	0.220001i
$676$		0			0
$677$	−1.27300	−	3.91790i	−0.0489255	−	0.150577i	0.923609	−	0.383336i	$-0.125225\pi$
$677$	−1.27300	−	3.91790i	−0.0489255	−	0.150577i	−0.972535	+	0.232759i	$0.925225\pi$
$678$		0			0
$679$	5.48807	−	3.98732i	0.210613	−	0.153019i
$680$		0			0
$681$	71.2262			2.72940
$682$		0			0
$683$	29.0594			1.11193			0.555963	−	0.831207i	$-0.312349\pi$
$683$	29.0594			1.11193			0.555963	+	0.831207i	$0.312349\pi$
$684$		0			0
$685$	10.8583	−	7.88904i	0.414875	−	0.301425i
$686$		0			0
$687$	−18.4070	−	56.6510i	−0.702272	−	2.16137i
$688$		0			0
$689$	8.61530	+	6.25938i	0.328217	+	0.238464i
$690$		0			0
$691$	6.01448	−	18.5107i	0.228802	−	0.704179i	−0.769082	−	0.639150i	$-0.779286\pi$
$691$	6.01448	−	18.5107i	0.228802	−	0.704179i	0.997883	−	0.0650287i	$-0.0207139\pi$
$692$		0			0
$693$	15.0254	+	9.58217i	0.570768	+	0.363997i
$694$		0			0
$695$	−4.35270	+	13.3962i	−0.165107	+	0.508148i
$696$		0			0
$697$	3.89013	+	2.82635i	0.147349	+	0.107056i
$698$		0			0
$699$	−19.6836	−	60.5800i	−0.744504	−	2.29135i
$700$		0			0
$701$	12.2452	−	8.89666i	0.462495	−	0.336022i	−0.332014	−	0.943274i	$-0.607728\pi$
$701$	12.2452	−	8.89666i	0.462495	−	0.336022i	0.794509	+	0.607252i	$0.207728\pi$
$702$		0			0
$703$	−1.65409			−0.0623853
$704$		0			0
$705$	2.49761			0.0940653
$706$		0			0
$707$	12.7493	−	9.26288i	0.479486	−	0.348367i
$708$		0			0
$709$	−8.35512	−	25.7144i	−0.313783	−	0.965725i	−0.976252	−	0.216636i	$-0.930492\pi$
$709$	−8.35512	−	25.7144i	−0.313783	−	0.965725i	0.662469	−	0.749089i	$-0.269508\pi$
$710$		0			0
$711$	29.6911	+	21.5719i	1.11350	+	0.809009i
$712$		0			0
$713$	−13.0217	+	40.0766i	−0.487666	+	1.50088i
$714$		0			0
$715$	−5.38463	−	13.6885i	−0.201374	−	0.511923i
$716$		0			0
$717$	17.6760	−	54.4013i	0.660124	−	2.03165i
$718$		0			0
$719$	−3.03354	−	2.20400i	−0.113132	−	0.0821953i	0.529781	−	0.848135i	$-0.322274\pi$
$719$	−3.03354	−	2.20400i	−0.113132	−	0.0821953i	−0.642913	+	0.765939i	$0.722274\pi$
$720$		0			0
$721$	3.15820	+	9.71993i	0.117617	+	0.361989i
$722$		0			0
$723$	−33.9510	+	24.6668i	−1.26265	+	0.917369i
$724$		0			0
$725$	−9.36210			−0.347700
$726$		0			0
$727$	45.5685			1.69004			0.845022	−	0.534732i	$-0.179587\pi$
$727$	45.5685			1.69004			0.845022	+	0.534732i	$0.179587\pi$
$728$		0			0
$729$	16.9478	−	12.3133i	0.627695	−	0.456047i
$730$		0			0
$731$	−1.08546	−	3.34070i	−0.0401472	−	0.123560i
$732$		0			0
$733$	30.0787	+	21.8535i	1.11098	+	0.807176i	0.982818	−	0.184577i	$-0.0590915\pi$
$733$	30.0787	+	21.8535i	1.11098	+	0.807176i	0.128164	+	0.991753i	$0.459091\pi$
$734$		0			0
$735$	−5.85988	+	18.0349i	−0.216145	+	0.665226i
$736$		0			0
$737$	−8.71387	−	22.1520i	−0.320980	−	0.815979i
$738$		0			0
$739$	−1.19398	+	3.67469i	−0.0439213	+	0.135176i	−0.970613	−	0.240648i	$-0.922640\pi$
$739$	−1.19398	+	3.67469i	−0.0439213	+	0.135176i	0.926691	+	0.375824i	$0.122640\pi$
$740$		0			0
$741$	2.81911	+	2.04820i	0.103562	+	0.0752425i
$742$		0			0
$743$	−2.39028	−	7.35652i	−0.0876908	−	0.269885i	0.897589	−	0.440833i	$-0.145317\pi$
$743$	−2.39028	−	7.35652i	−0.0876908	−	0.269885i	−0.985280	+	0.170948i	$0.945317\pi$
$744$		0			0
$745$	1.44954	−	1.05315i	0.0531070	−	0.0385845i
$746$		0			0
$747$	−44.0451			−1.61153
$748$		0			0
$749$	−0.451118			−0.0164835
$750$		0			0
$751$	15.9688	−	11.6020i	0.582711	−	0.423364i	−0.256989	−	0.966414i	$-0.582731\pi$
$751$	15.9688	−	11.6020i	0.582711	−	0.423364i	0.839700	+	0.543050i	$0.182731\pi$
$752$		0			0
$753$	−14.3183	−	44.0671i	−0.521787	−	1.60590i
$754$		0			0
$755$	15.4418	+	11.2191i	0.561983	+	0.408304i
$756$		0			0
$757$	3.27026	−	10.0648i	0.118859	−	0.365812i	−0.873873	−	0.486154i	$-0.838399\pi$
$757$	3.27026	−	10.0648i	0.118859	−	0.365812i	0.992732	+	0.120343i	$0.0383993\pi$
$758$		0			0
$759$	−67.2542	−	42.8901i	−2.44117	−	1.55681i
$760$		0			0
$761$	15.6578	−	48.1899i	0.567596	−	1.74688i	−0.0925129	−	0.995711i	$-0.529490\pi$
$761$	15.6578	−	48.1899i	0.567596	−	1.74688i	0.660109	−	0.751170i	$-0.270510\pi$
$762$		0			0
$763$	4.36124	+	3.16863i	0.157888	+	0.114712i
$764$		0			0
$765$	1.05468	+	3.24596i	0.0381319	+	0.117358i
$766$		0			0
$767$	−48.4921	+	35.2316i	−1.75095	+	1.27214i
$768$		0			0
$769$	−16.2588			−0.586306			−0.293153	−	0.956066i	$-0.594705\pi$
$769$	−16.2588			−0.586306			−0.293153	+	0.956066i	$0.594705\pi$
$770$		0			0
$771$	−87.3426			−3.14557
$772$		0			0
$773$	−13.3405	+	9.69243i	−0.479824	+	0.348612i	−0.801257	−	0.598320i	$-0.795835\pi$
$773$	−13.3405	+	9.69243i	−0.479824	+	0.348612i	0.321434	+	0.946932i	$0.395835\pi$
$774$		0			0
$775$	−1.64270	−	5.05570i	−0.0590074	−	0.181606i
$776$		0			0
$777$	13.5762	+	9.86366i	0.487042	+	0.353857i
$778$		0			0
$779$	−0.699582	+	2.15309i	−0.0250651	+	0.0771426i
$780$		0			0
$781$	7.16621	−	5.90171i	0.256427	−	0.211180i
$782$		0			0
$783$	28.1328	−	86.5839i	1.00538	−	3.09426i
$784$		0			0
$785$	7.91828	+	5.75296i	0.282615	+	0.205332i
$786$		0			0
$787$	7.94742	+	24.4597i	0.283295	+	0.871892i	0.986905	+	0.161306i	$0.0515705\pi$
$787$	7.94742	+	24.4597i	0.283295	+	0.871892i	−0.703610	+	0.710587i	$0.748430\pi$
$788$		0			0
$789$	−22.6609	+	16.4641i	−0.806748	+	0.586137i
$790$		0			0
$791$	−8.55171			−0.304064
$792$		0			0
$793$	29.3054			1.04066
$794$		0			0
$795$	−5.89362	+	4.28197i	−0.209025	+	0.151866i
$796$		0			0
$797$	1.72973	+	5.32356i	0.0612701	+	0.188570i	0.977006	−	0.213210i	$-0.0683917\pi$
$797$	1.72973	+	5.32356i	0.0612701	+	0.188570i	−0.915736	+	0.401780i	$0.868392\pi$
$798$		0			0
$799$	0.366315	+	0.266143i	0.0129593	+	0.00941547i
$800$		0			0
$801$	−31.9204	+	98.2410i	−1.12785	+	3.47117i
$802$		0			0
$803$	2.40488	−	9.28098i	0.0848663	−	0.327519i
$804$		0			0
$805$	−2.12116	+	6.52826i	−0.0747611	+	0.230091i
$806$		0			0
$807$	65.8614	+	47.8511i	2.31843	+	1.68444i
$808$		0			0
$809$	6.08110	+	18.7157i	0.213800	+	0.658009i	0.999237	+	0.0390667i	$0.0124385\pi$
$809$	6.08110	+	18.7157i	0.213800	+	0.658009i	−0.785437	+	0.618942i	$0.787562\pi$
$810$		0			0
$811$	5.99885	−	4.35842i	0.210648	−	0.153045i	−0.477459	−	0.878654i	$-0.658442\pi$
$811$	5.99885	−	4.35842i	0.210648	−	0.153045i	0.688107	+	0.725609i	$0.258442\pi$
$812$		0			0
$813$	−71.4844			−2.50707
$814$		0			0
$815$	−0.396843			−0.0139008
$816$		0			0
$817$	1.33795	−	0.972074i	0.0468088	−	0.0340086i
$818$		0			0
$819$	−7.36404	−	22.6642i	−0.257320	−	0.791950i
$820$		0			0
$821$	4.29404	+	3.11981i	0.149863	+	0.108882i	0.660190	−	0.751098i	$-0.270476\pi$
$821$	4.29404	+	3.11981i	0.149863	+	0.108882i	−0.510327	+	0.859980i	$0.670476\pi$
$822$		0			0
$823$	−5.00458	+	15.4025i	−0.174449	+	0.536898i	−0.999608	−	0.0280024i	$-0.991085\pi$
$823$	−5.00458	+	15.4025i	−0.174449	+	0.536898i	0.825159	+	0.564900i	$0.191085\pi$
$824$		0			0
$825$	10.0441	−	0.609587i	0.349692	−	0.0212231i
$826$		0			0
$827$	−3.08205	+	9.48557i	−0.107173	+	0.329846i	−0.990234	−	0.139412i	$-0.955479\pi$
$827$	−3.08205	+	9.48557i	−0.107173	+	0.329846i	0.883061	+	0.469258i	$0.155479\pi$
$828$		0			0
$829$	21.4275	+	15.5680i	0.744209	+	0.540700i	0.894027	−	0.448014i	$-0.147869\pi$
$829$	21.4275	+	15.5680i	0.744209	+	0.540700i	−0.149817	+	0.988714i	$0.547869\pi$
$830$		0			0
$831$	−9.36843	−	28.8331i	−0.324987	−	1.00021i
$832$		0			0
$833$	−2.78123	+	2.02068i	−0.0963638	+	0.0700124i
$834$		0			0
$835$	−13.9140			−0.481514
$836$		0			0
$837$	51.6931			1.78677
$838$		0			0
$839$	−19.4642	+	14.1416i	−0.671980	+	0.488222i	−0.870687	−	0.491837i	$-0.836326\pi$
$839$	−19.4642	+	14.1416i	−0.671980	+	0.488222i	0.198707	+	0.980059i	$0.436326\pi$
$840$		0			0
$841$	18.1235	+	55.7785i	0.624950	+	1.92340i
$842$		0			0
$843$	10.0401	+	7.29458i	0.345801	+	0.251239i
$844$		0			0
$845$	−2.06116	+	6.34359i	−0.0709059	+	0.218226i
$846$		0			0
$847$	9.45529	−	1.15194i	0.324888	−	0.0395812i
$848$		0			0
$849$	−4.47465	+	13.7716i	−0.153570	+	0.472639i
$850$		0			0
$851$	−40.9629	−	29.7613i	−1.40419	−	1.02020i
$852$		0			0
$853$	6.96743	+	21.4436i	0.238560	+	0.734213i	0.996629	+	0.0820386i	$0.0261431\pi$
$853$	6.96743	+	21.4436i	0.238560	+	0.734213i	−0.758069	+	0.652175i	$0.773857\pi$
$854$		0			0
$855$	−1.30000	+	0.944506i	−0.0444591	+	0.0323014i
$856$		0			0
$857$	10.0453			0.343143			0.171571	−	0.985172i	$-0.445116\pi$
$857$	10.0453			0.343143			0.171571	+	0.985172i	$0.445116\pi$
$858$		0			0
$859$	15.7921			0.538819			0.269409	−	0.963026i	$-0.413172\pi$
$859$	15.7921			0.538819			0.269409	+	0.963026i	$0.413172\pi$
$860$		0			0
$861$	18.5812	−	13.5000i	0.633245	−	0.460080i
$862$		0			0
$863$	−6.99653	−	21.5331i	−0.238165	−	0.732995i	−0.996686	−	0.0813469i	$-0.974078\pi$
$863$	−6.99653	−	21.5331i	−0.238165	−	0.732995i	0.758521	−	0.651648i	$-0.225922\pi$
$864$		0			0
$865$	4.31522	+	3.13519i	0.146722	+	0.106600i
$866$		0			0
$867$	15.6548	−	48.1805i	0.531665	−	1.63630i
$868$		0			0
$869$	19.5802	−	1.18834i	0.664214	−	0.0403117i
$870$		0			0
$871$	−9.83655	+	30.2738i	−0.333299	+	1.02579i
$872$		0			0
$873$	39.3267	+	28.5725i	1.33101	+	0.967034i
$874$		0			0
$875$	−0.267586	−	0.823546i	−0.00904607	−	0.0278409i
$876$		0			0
$877$	−19.2215	+	13.9652i	−0.649064	+	0.471573i	−0.862952	−	0.505285i	$-0.831387\pi$
$877$	−19.2215	+	13.9652i	−0.649064	+	0.471573i	0.213888	+	0.976858i	$0.431387\pi$
$878$		0			0
$879$	−0.436931			−0.0147373
$880$		0			0
$881$	−21.6772			−0.730323			−0.365161	−	0.930944i	$-0.618986\pi$
$881$	−21.6772			−0.730323			−0.365161	+	0.930944i	$0.618986\pi$
$882$		0			0
$883$	32.8621	−	23.8757i	1.10590	−	0.803482i	0.123885	−	0.992297i	$-0.460465\pi$
$883$	32.8621	−	23.8757i	1.10590	−	0.803482i	0.982013	+	0.188815i	$0.0604645\pi$
$884$		0			0
$885$	−12.6709	−	38.9970i	−0.425928	−	1.31087i
$886$		0			0
$887$	−27.6287	−	20.0734i	−0.927680	−	0.673999i	0.0177436	−	0.999843i	$-0.494352\pi$
$887$	−27.6287	−	20.0734i	−0.927680	−	0.673999i	−0.945424	+	0.325843i	$0.894352\pi$
$888$		0			0
$889$	0.995244	−	3.06305i	0.0333794	−	0.102731i
$890$		0			0
$891$	−9.05805	+	34.9571i	−0.303456	+	1.17111i
$892$		0			0
$893$	−0.0658762	+	0.202746i	−0.00220446	+	0.00678464i
$894$		0			0
$895$	6.17667	+	4.48761i	0.206463	+	0.150004i
$896$		0			0
$897$	32.9617	+	101.446i	1.10056	+	3.38717i
$898$		0			0
$899$	−40.2630	+	29.2528i	−1.34285	+	0.975635i
$900$		0			0
$901$	−1.32068			−0.0439982
$902$		0			0
$903$	−16.7780			−0.558337
$904$		0			0
$905$	1.05538	−	0.766782i	0.0350822	−	0.0254887i
$906$		0			0
$907$	3.57041	+	10.9886i	0.118554	+	0.364870i	0.992672	−	0.120843i	$-0.0385598\pi$
$907$	3.57041	+	10.9886i	0.118554	+	0.364870i	−0.874118	+	0.485714i	$0.838560\pi$
$908$		0			0
$909$	91.3594	+	66.3765i	3.03020	+	2.20157i
$910$		0			0
$911$	−4.45162	+	13.7007i	−0.147489	+	0.453924i	−0.997323	−	0.0731269i	$-0.976702\pi$
$911$	−4.45162	+	13.7007i	−0.147489	+	0.453924i	0.849834	+	0.527051i	$0.176702\pi$
$912$		0			0
$913$	−18.1727	+	14.9661i	−0.601428	+	0.495305i
$914$		0			0
$915$	−6.19500	+	19.0662i	−0.204800	+	0.630310i
$916$		0			0
$917$	−14.3093	−	10.3963i	−0.472536	−	0.343318i
$918$		0			0
$919$	−15.1775	−	46.7116i	−0.500660	−	1.54087i	−0.807946	−	0.589256i	$-0.799421\pi$
$919$	−15.1775	−	46.7116i	−0.500660	−	1.54087i	0.307286	−	0.951617i	$-0.400579\pi$
$920$		0			0
$921$	−63.2232	+	45.9344i	−2.08328	+	1.51359i
$922$		0			0
$923$	−12.4143			−0.408621
$924$		0			0
$925$	6.38739			0.210016
$926$		0			0
$927$	−59.2492	+	43.0470i	−1.94600	+	1.41385i
$928$		0			0
$929$	7.41296	+	22.8147i	0.243211	+	0.748527i	0.995925	+	0.0901799i	$0.0287442\pi$
$929$	7.41296	+	22.8147i	0.243211	+	0.748527i	−0.752714	+	0.658347i	$0.771256\pi$
$930$		0			0
$931$	−1.30944	−	0.951365i	−0.0429152	−	0.0311797i
$932$		0			0
$933$	−15.3679	+	47.2976i	−0.503123	+	1.54845i
$934$		0			0
$935$	1.53809	+	0.980890i	0.0503010	+	0.0320785i
$936$		0			0
$937$	4.04879	−	12.4609i	0.132268	−	0.407079i	−0.862887	−	0.505397i	$-0.831346\pi$
$937$	4.04879	−	12.4609i	0.132268	−	0.407079i	0.995155	+	0.0983175i	$0.0313461\pi$
$938$		0			0
$939$	65.1039	+	47.3008i	2.12459	+	1.54360i
$940$		0			0
$941$	−11.3355	−	34.8872i	−0.369528	−	1.13729i	−0.947097	−	0.320948i	$-0.895998\pi$
$941$	−11.3355	−	34.8872i	−0.369528	−	1.13729i	0.577569	−	0.816342i	$-0.304002\pi$
$942$		0			0
$943$	−56.0644	+	40.7332i	−1.82571	+	1.32645i
$944$		0			0
$945$	8.42052			0.273919
$946$		0			0
$947$	20.6112			0.669774			0.334887	−	0.942258i	$-0.391302\pi$
$947$	20.6112			0.669774			0.334887	+	0.942258i	$0.391302\pi$
$948$		0			0
$949$	−10.3722	+	7.53581i	−0.336694	+	0.244623i
$950$		0			0
$951$	−15.6720	−	48.2334i	−0.508199	−	1.56407i
$952$		0			0
$953$	−14.3964	−	10.4596i	−0.466344	−	0.338819i	0.329671	−	0.944096i	$-0.393062\pi$
$953$	−14.3964	−	10.4596i	−0.466344	−	0.338819i	−0.796015	+	0.605277i	$0.793062\pi$
$954$		0			0
$955$	−7.75118	+	23.8557i	−0.250822	+	0.771951i
$956$		0			0
$957$	−34.4859	−	87.6683i	−1.11477	−	2.83391i
$958$		0			0
$959$	3.59144	−	11.0533i	0.115974	−	0.356931i
$960$		0			0
$961$	2.21787	+	1.61138i	0.0715443	+	0.0519800i
$962$		0			0
$963$	−0.998941	−	3.07443i	−0.0321904	−	0.0990720i
$964$		0			0
$965$	−16.1448	+	11.7299i	−0.519719	+	0.377598i
$966$		0			0
$967$	−0.828077			−0.0266292			−0.0133146	−	0.999911i	$-0.504238\pi$
$967$	−0.828077			−0.0266292			−0.0133146	+	0.999911i	$0.504238\pi$
$968$		0			0
$969$	−0.432154			−0.0138828
$970$		0			0
$971$	0.100751	−	0.0732001i	0.00323326	−	0.00234910i	−0.586167	−	0.810190i	$-0.699364\pi$
$971$	0.100751	−	0.0732001i	0.00323326	−	0.00234910i	0.589401	+	0.807841i	$0.299364\pi$
$972$		0			0
$973$	3.76912	+	11.6002i	0.120832	+	0.371884i
$974$		0			0
$975$	−10.8862	−	7.90926i	−0.348636	−	0.253299i
$976$		0			0
$977$	−6.63347	+	20.4157i	−0.212223	+	0.653157i	0.787116	+	0.616805i	$0.211573\pi$
$977$	−6.63347	+	20.4157i	−0.212223	+	0.653157i	−0.999339	+	0.0363512i	$0.988427\pi$
$978$		0			0
$979$	20.2111	+	51.3797i	0.645950	+	1.64210i
$980$		0			0
$981$	−11.9372	+	36.7390i	−0.381126	+	1.17298i
$982$		0			0
$983$	−25.6917	−	18.6661i	−0.819436	−	0.595355i	0.0971146	−	0.995273i	$-0.469039\pi$
$983$	−25.6917	−	18.6661i	−0.819436	−	0.595355i	−0.916551	+	0.399918i	$0.869039\pi$
$984$		0			0
$985$	0.405083	+	1.24672i	0.0129070	+	0.0397237i
$986$		0			0
$987$	1.74970	−	1.27123i	0.0556935	−	0.0404637i
$988$		0			0
$989$	50.6237			1.60974
$990$		0			0
$991$	46.7101			1.48379			0.741897	−	0.670514i	$-0.233926\pi$
$991$	46.7101			1.48379			0.741897	+	0.670514i	$0.233926\pi$
$992$		0			0
$993$	10.7898	−	7.83927i	0.342405	−	0.248772i
$994$		0			0
$995$	1.54235	+	4.74686i	0.0488958	+	0.150486i
$996$		0			0
$997$	−41.7896	−	30.3619i	−1.32349	−	0.961572i	−0.999882	−	0.0153805i	$-0.995104\pi$
$997$	−41.7896	−	30.3619i	−1.32349	−	0.961572i	−0.323608	−	0.946191i	$-0.604896\pi$
$998$		0			0
$999$	−19.1939	+	59.0727i	−0.607268	+	1.86898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.b.361.3	✓	12
4.3	odd	2		880.2.bo.j.801.1		12
11.4	even	5		4840.2.a.bf.1.1		6
11.5	even	5	inner	440.2.y.b.401.3	yes	12
11.7	odd	10		4840.2.a.be.1.1		6
44.7	even	10		9680.2.a.cy.1.6		6
44.15	odd	10		9680.2.a.cx.1.6		6
44.27	odd	10		880.2.bo.j.401.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.361.3	✓	12	1.1	even	1	trivial
440.2.y.b.401.3	yes	12	11.5	even	5	inner
880.2.bo.j.401.1		12	44.27	odd	10
880.2.bo.j.801.1		12	4.3	odd	2
4840.2.a.be.1.1		6	11.7	odd	10
4840.2.a.bf.1.1		6	11.4	even	5
9680.2.a.cx.1.6		6	44.15	odd	10
9680.2.a.cy.1.6		6	44.7	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.45455 - 1.78334i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-0.700550 - 0.508979i) q^{7} +(1.91748 - 5.90141i) q^{9} +(-1.21410 - 3.08642i) q^{11} +(-1.37052 + 4.21802i) q^{13} +(-2.45455 - 1.78334i) q^{15} +(-0.169969 - 0.523110i) q^{17} +(0.209505 - 0.152214i) q^{19} -2.62722 q^{21} +7.92701 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-3.00497 - 9.24833i) q^{27} +(7.57410 + 5.50291i) q^{29} +(-1.64270 + 5.05570i) q^{31} +(-8.48418 - 5.41063i) q^{33} +(-0.267586 + 0.823546i) q^{35} +(-5.16751 - 3.75441i) q^{37} +(4.15814 + 12.7974i) q^{39} +(-7.07258 + 5.13853i) q^{41} +6.38622 q^{43} -6.20511 q^{45} +(-0.665989 + 0.483870i) q^{47} +(-1.93141 - 5.94426i) q^{49} +(-1.35008 - 0.980890i) q^{51} +(0.741981 - 2.28358i) q^{53} +(-2.56018 + 2.10843i) q^{55} +(0.242791 - 0.747235i) q^{57} +(10.9337 + 7.94382i) q^{59} +(-2.04186 - 6.28421i) q^{61} +(-4.34699 + 3.15827i) q^{63} +4.43509 q^{65} +7.17725 q^{67} +(19.4573 - 14.1365i) q^{69} +(0.864970 + 2.66210i) q^{71} +(2.33866 + 1.69913i) q^{73} +(-0.937555 + 2.88550i) q^{75} +(-0.720387 + 2.78014i) q^{77} +(-1.82769 + 5.62505i) q^{79} +(-8.80862 - 6.39983i) q^{81} +(-2.19347 - 6.75080i) q^{83} +(-0.444984 + 0.323300i) q^{85} +28.4046 q^{87} -16.6470 q^{89} +(3.10700 - 2.25737i) q^{91} +(4.98393 + 15.3390i) q^{93} +(-0.209505 - 0.152214i) q^{95} +(-2.42082 + 7.45053i) q^{97} +(-20.5422 + 1.24672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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