LMFDB - Embedded newform 1716.2.z.f.625.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8, 0]))

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.7023289869$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 41 x^{18} - 146 x^{17} + 650 x^{16} - 1400 x^{15} + 5756 x^{14} - 2122 x^{13} + \cdots + 4096 $ x^20 - 6x^19 + 41x^18 - 146x^17 + 650x^16 - 1400x^15 + 5756x^14 - 2122x^13 + 27469x^12 + 11286x^11 + 72308x^10 + 48512x^9 + 142448x^8 - 37952x^7 + 295552x^6 + 300160x^5 + 272128x^4 + 194048x^3 + 236544x^2 + 49152*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			625.4
Root			$-0.694526 + 0.504603i$ of defining polynomial
Character	$\chi$	$=$	1716.625
Dual form			1716.2.z.f.313.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +(-0.343051 - 1.05580i) q^{5} +(4.04943 + 2.94208i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} +(-0.343051 - 1.05580i) q^{5} +(4.04943 + 2.94208i) q^{7} +(0.309017 - 0.951057i) q^{9} +(2.74104 + 1.86727i) q^{11} +(0.309017 - 0.951057i) q^{13} +(-0.898118 - 0.652521i) q^{15} +(1.38285 + 4.25598i) q^{17} +(-5.62475 + 4.08662i) q^{19} +5.00536 q^{21} -1.21043 q^{23} +(3.04805 - 2.21454i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(7.07776 + 5.14230i) q^{29} +(-2.75136 + 8.46781i) q^{31} +(3.31510 - 0.100492i) q^{33} +(1.71709 - 5.28467i) q^{35} +(-6.70307 - 4.87006i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(1.30422 - 0.947573i) q^{41} -9.39145 q^{43} -1.11014 q^{45} +(6.32725 - 4.59702i) q^{47} +(5.57889 + 17.1701i) q^{49} +(3.62035 + 2.63034i) q^{51} +(2.44788 - 7.53379i) q^{53} +(1.03115 - 3.53456i) q^{55} +(-2.14846 + 6.61229i) q^{57} +(-8.40880 - 6.10935i) q^{59} +(0.911737 + 2.80604i) q^{61} +(4.04943 - 2.94208i) q^{63} -1.11014 q^{65} -0.550966 q^{67} +(-0.979261 + 0.711475i) q^{69} +(-3.71511 - 11.4339i) q^{71} +(-1.81542 - 1.31898i) q^{73} +(1.16425 - 3.58320i) q^{75} +(5.60599 + 15.6257i) q^{77} +(-3.00854 + 9.25932i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.20016 + 12.9268i) q^{83} +(4.01908 - 2.92003i) q^{85} +8.74860 q^{87} +11.6003 q^{89} +(4.04943 - 2.94208i) q^{91} +(2.75136 + 8.46781i) q^{93} +(6.24424 + 4.53670i) q^{95} +(5.00076 - 15.3908i) q^{97} +(2.62291 - 2.02987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$		0			0
$5$	−0.343051	−	1.05580i	−0.153417	−	0.472169i	0.844580	−	0.535429i	$-0.179850\pi$
$5$	−0.343051	−	1.05580i	−0.153417	−	0.472169i	−0.997997	+	0.0632604i	$0.979850\pi$
$6$		0			0
$7$	4.04943	+	2.94208i	1.53054	+	1.11200i	0.955938	+	0.293567i	$0.0948425\pi$
$7$	4.04943	+	2.94208i	1.53054	+	1.11200i	0.574600	+	0.818434i	$0.305157\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	2.74104	+	1.86727i	0.826455	+	0.563002i
$11$	2.74104	+	1.86727i	0.826455	+	0.563002i
$12$		0			0
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$		0			0
$15$	−0.898118	−	0.652521i	−0.231893	−	0.168480i
$16$		0			0
$17$	1.38285	+	4.25598i	0.335390	+	1.03223i	0.966529	+	0.256556i	$0.0825878\pi$
$17$	1.38285	+	4.25598i	0.335390	+	1.03223i	−0.631139	+	0.775670i	$0.717412\pi$
$18$		0			0
$19$	−5.62475	+	4.08662i	−1.29041	+	0.937535i	−0.999814	−	0.0193113i	$-0.993853\pi$
$19$	−5.62475	+	4.08662i	−1.29041	+	0.937535i	−0.290593	+	0.956847i	$0.593853\pi$
$20$		0			0
$21$	5.00536			1.09226
$22$		0			0
$23$	−1.21043			−0.252393			−0.126196	−	0.992005i	$-0.540277\pi$
$23$	−1.21043			−0.252393			−0.126196	+	0.992005i	$0.540277\pi$
$24$		0			0
$25$	3.04805	−	2.21454i	0.609610	−	0.442908i
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	7.07776	+	5.14230i	1.31431	+	0.954900i	0.999984	+	0.00558451i	$0.00177761\pi$
$29$	7.07776	+	5.14230i	1.31431	+	0.954900i	0.314323	+	0.949316i	$0.398222\pi$
$30$		0			0
$31$	−2.75136	+	8.46781i	−0.494159	+	1.52086i	0.324105	+	0.946021i	$0.394937\pi$
$31$	−2.75136	+	8.46781i	−0.494159	+	1.52086i	−0.818264	+	0.574843i	$0.805063\pi$
$32$		0			0
$33$	3.31510	−	0.100492i	0.577085	−	0.0174935i
$34$		0			0
$35$	1.71709	−	5.28467i	0.290242	−	0.893273i
$36$		0			0
$37$	−6.70307	−	4.87006i	−1.10198	−	0.800633i	−0.120596	−	0.992702i	$-0.538480\pi$
$37$	−6.70307	−	4.87006i	−1.10198	−	0.800633i	−0.981382	+	0.192068i	$0.938480\pi$
$38$		0			0
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$		0			0
$41$	1.30422	−	0.947573i	0.203685	−	0.147986i	−0.481267	−	0.876574i	$-0.659823\pi$
$41$	1.30422	−	0.947573i	0.203685	−	0.147986i	0.684952	+	0.728588i	$0.259823\pi$
$42$		0			0
$43$	−9.39145			−1.43218			−0.716091	−	0.698007i	$-0.754071\pi$
$43$	−9.39145			−1.43218			−0.716091	+	0.698007i	$0.754071\pi$
$44$		0			0
$45$	−1.11014			−0.165489
$46$		0			0
$47$	6.32725	−	4.59702i	0.922924	−	0.670544i	−0.0213258	−	0.999773i	$-0.506789\pi$
$47$	6.32725	−	4.59702i	0.922924	−	0.670544i	0.944250	+	0.329229i	$0.106789\pi$
$48$		0			0
$49$	5.57889	+	17.1701i	0.796985	+	2.45287i
$50$		0			0
$51$	3.62035	+	2.63034i	0.506950	+	0.368321i
$52$		0			0
$53$	2.44788	−	7.53379i	0.336242	−	1.03485i	−0.629865	−	0.776704i	$-0.716890\pi$
$53$	2.44788	−	7.53379i	0.336242	−	1.03485i	0.966107	−	0.258141i	$-0.0831100\pi$
$54$		0			0
$55$	1.03115	−	3.53456i	0.139040	−	0.476600i
$56$		0			0
$57$	−2.14846	+	6.61229i	−0.284571	+	0.875820i
$58$		0			0
$59$	−8.40880	−	6.10935i	−1.09473	−	0.795370i	−0.114540	−	0.993419i	$-0.536539\pi$
$59$	−8.40880	−	6.10935i	−1.09473	−	0.795370i	−0.980192	+	0.198049i	$0.936539\pi$
$60$		0			0
$61$	0.911737	+	2.80604i	0.116736	+	0.359276i	0.992305	−	0.123816i	$-0.0395134\pi$
$61$	0.911737	+	2.80604i	0.116736	+	0.359276i	−0.875569	+	0.483093i	$0.839513\pi$
$62$		0			0
$63$	4.04943	−	2.94208i	0.510180	−	0.370667i
$64$		0			0
$65$	−1.11014			−0.137695
$66$		0			0
$67$	−0.550966			−0.0673112			−0.0336556	−	0.999433i	$-0.510715\pi$
$67$	−0.550966			−0.0673112			−0.0336556	+	0.999433i	$0.510715\pi$
$68$		0			0
$69$	−0.979261	+	0.711475i	−0.117889	+	0.0856515i
$70$		0			0
$71$	−3.71511	−	11.4339i	−0.440902	−	1.35696i	−0.886916	−	0.461932i	$-0.847157\pi$
$71$	−3.71511	−	11.4339i	−0.440902	−	1.35696i	0.446013	−	0.895026i	$-0.352843\pi$
$72$		0			0
$73$	−1.81542	−	1.31898i	−0.212478	−	0.154375i	0.476456	−	0.879198i	$-0.341921\pi$
$73$	−1.81542	−	1.31898i	−0.212478	−	0.154375i	−0.688934	+	0.724824i	$0.741921\pi$
$74$		0			0
$75$	1.16425	−	3.58320i	0.134436	−	0.413752i
$76$		0			0
$77$	5.60599	+	15.6257i	0.638862	+	1.78072i
$78$		0			0
$79$	−3.00854	+	9.25932i	−0.338487	+	1.04176i	0.626492	+	0.779428i	$0.284490\pi$
$79$	−3.00854	+	9.25932i	−0.338487	+	1.04176i	−0.964979	+	0.262327i	$0.915510\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	4.20016	+	12.9268i	0.461027	+	1.41890i	0.863911	+	0.503645i	$0.168008\pi$
$83$	4.20016	+	12.9268i	0.461027	+	1.41890i	−0.402883	+	0.915251i	$0.631992\pi$
$84$		0			0
$85$	4.01908	−	2.92003i	0.435930	−	0.316722i
$86$		0			0
$87$	8.74860			0.937948
$88$		0			0
$89$	11.6003			1.22962			0.614812	−	0.788673i	$-0.289232\pi$
$89$	11.6003			1.22962			0.614812	+	0.788673i	$0.289232\pi$
$90$		0			0
$91$	4.04943	−	2.94208i	0.424495	−	0.308414i
$92$		0			0
$93$	2.75136	+	8.46781i	0.285303	+	0.878071i
$94$		0			0
$95$	6.24424	+	4.53670i	0.640645	+	0.465456i
$96$		0			0
$97$	5.00076	−	15.3908i	0.507750	−	1.56269i	−0.288347	−	0.957526i	$-0.593106\pi$
$97$	5.00076	−	15.3908i	0.507750	−	1.56269i	0.796098	−	0.605168i	$-0.206894\pi$
$98$		0			0
$99$	2.62291	−	2.02987i	0.263612	−	0.204009i
$100$		0			0
$101$	3.18191	−	9.79290i	0.316611	−	0.974430i	−0.658475	−	0.752603i	$-0.728798\pi$
$101$	3.18191	−	9.79290i	0.316611	−	0.974430i	0.975086	−	0.221827i	$-0.0712020\pi$
$102$		0			0
$103$	1.26089	+	0.916092i	0.124239	+	0.0902653i	0.648170	−	0.761496i	$-0.275535\pi$
$103$	1.26089	+	0.916092i	0.124239	+	0.0902653i	−0.523930	+	0.851761i	$0.675535\pi$
$104$		0			0
$105$	−1.71709	−	5.28467i	−0.167571	−	0.515731i
$106$		0			0
$107$	10.5102	−	7.63608i	1.01606	−	0.738208i	0.0505855	−	0.998720i	$-0.483891\pi$
$107$	10.5102	−	7.63608i	1.01606	−	0.738208i	0.965471	+	0.260512i	$0.0838913\pi$
$108$		0			0
$109$	8.01889			0.768071			0.384035	−	0.923318i	$-0.374534\pi$
$109$	8.01889			0.768071			0.384035	+	0.923318i	$0.374534\pi$
$110$		0			0
$111$	−8.28544			−0.786420
$112$		0			0
$113$	7.26075	−	5.27525i	0.683034	−	0.496253i	−0.191329	−	0.981526i	$-0.561280\pi$
$113$	7.26075	−	5.27525i	0.683034	−	0.496253i	0.874363	+	0.485273i	$0.161280\pi$
$114$		0			0
$115$	0.415240	+	1.27798i	0.0387213	+	0.119172i
$116$		0			0
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$		0			0
$119$	−6.92167	+	21.3027i	−0.634508	+	1.95282i
$120$		0			0
$121$	4.02662	+	10.2365i	0.366056	+	0.930593i
$122$		0			0
$123$	0.498168	−	1.53320i	0.0449183	−	0.138244i
$124$		0			0
$125$	−7.87434	−	5.72104i	−0.704303	−	0.511706i
$126$		0			0
$127$	1.88804	+	5.81079i	0.167536	+	0.515624i	0.999214	−	0.0396344i	$-0.0126193\pi$
$127$	1.88804	+	5.81079i	0.167536	+	0.515624i	−0.831678	+	0.555258i	$0.812619\pi$
$128$		0			0
$129$	−7.59784	+	5.52015i	−0.668953	+	0.486023i
$130$		0			0
$131$	14.0141			1.22442			0.612208	−	0.790697i	$-0.290281\pi$
$131$	14.0141			1.22442			0.612208	+	0.790697i	$0.290281\pi$
$132$		0			0
$133$	−34.8002			−3.01756
$134$		0			0
$135$	−0.898118	+	0.652521i	−0.0772977	+	0.0561601i
$136$		0			0
$137$	−4.75975	−	14.6490i	−0.406653	−	1.25155i	−0.919507	−	0.393073i	$-0.871412\pi$
$137$	−4.75975	−	14.6490i	−0.406653	−	1.25155i	0.512855	−	0.858475i	$-0.328588\pi$
$138$		0			0
$139$	−7.76415	−	5.64098i	−0.658546	−	0.478462i	0.207625	−	0.978208i	$-0.433427\pi$
$139$	−7.76415	−	5.64098i	−0.658546	−	0.478462i	−0.866172	+	0.499746i	$0.833427\pi$
$140$		0			0
$141$	2.41679	−	7.43813i	0.203531	−	0.626403i
$142$		0			0
$143$	2.62291	−	2.02987i	0.219338	−	0.169746i
$144$		0			0
$145$	3.00121	−	9.23678i	0.249237	−	0.767073i
$146$		0			0
$147$	14.6057	+	10.6117i	1.20466	+	0.875237i
$148$		0			0
$149$	0.312112	+	0.960582i	0.0255692	+	0.0786939i	0.963027	−	0.269405i	$-0.0868272\pi$
$149$	0.312112	+	0.960582i	0.0255692	+	0.0786939i	−0.937458	+	0.348099i	$0.886827\pi$
$150$		0			0
$151$	11.1267	−	8.08405i	0.905482	−	0.657871i	−0.0343865	−	0.999409i	$-0.510948\pi$
$151$	11.1267	−	8.08405i	0.905482	−	0.657871i	0.939868	+	0.341538i	$0.110948\pi$
$152$		0			0
$153$	4.47500			0.361782
$154$		0			0
$155$	9.88418			0.793917
$156$		0			0
$157$	3.65273	−	2.65387i	0.291520	−	0.211802i	−0.432407	−	0.901679i	$-0.642335\pi$
$157$	3.65273	−	2.65387i	0.291520	−	0.211802i	0.723926	+	0.689877i	$0.242335\pi$
$158$		0			0
$159$	−2.44788	−	7.53379i	−0.194129	−	0.597468i
$160$		0			0
$161$	−4.90156	−	3.56119i	−0.386297	−	0.280661i
$162$		0			0
$163$	1.81030	−	5.57154i	0.141794	−	0.436397i	−0.854791	−	0.518973i	$-0.826315\pi$
$163$	1.81030	−	5.57154i	0.141794	−	0.436397i	0.996585	+	0.0825758i	$0.0263147\pi$
$164$		0			0
$165$	−1.24335	−	3.46562i	−0.0967945	−	0.269798i
$166$		0			0
$167$	−0.690950	+	2.12652i	−0.0534673	+	0.164555i	−0.974224	−	0.225581i	$-0.927572\pi$
$167$	−0.690950	+	2.12652i	−0.0534673	+	0.164555i	0.920757	+	0.390136i	$0.127572\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	2.14846	+	6.61229i	0.164297	+	0.505655i
$172$		0			0
$173$	−11.4712	+	8.33429i	−0.872137	+	0.633644i	−0.931159	−	0.364612i	$-0.881202\pi$
$173$	−11.4712	+	8.33429i	−0.872137	+	0.633644i	0.0590228	+	0.998257i	$0.481202\pi$
$174$		0			0
$175$	18.8582			1.42555
$176$		0			0
$177$	−10.3938			−0.781249
$178$		0			0
$179$	−8.70851	+	6.32710i	−0.650905	+	0.472910i	−0.863579	−	0.504213i	$-0.831783\pi$
$179$	−8.70851	+	6.32710i	−0.650905	+	0.472910i	0.212675	+	0.977123i	$0.431783\pi$
$180$		0			0
$181$	−4.81202	−	14.8099i	−0.357674	−	1.10081i	−0.954443	−	0.298395i	$-0.903549\pi$
$181$	−4.81202	−	14.8099i	−0.357674	−	1.10081i	0.596768	−	0.802414i	$-0.296451\pi$
$182$		0			0
$183$	2.38696	+	1.73423i	0.176449	+	0.128198i
$184$		0			0
$185$	−2.84233	+	8.74778i	−0.208972	+	0.643150i
$186$		0			0
$187$	−4.15660	+	14.2480i	−0.303960	+	1.04191i
$188$		0			0
$189$	1.54674	−	4.76038i	0.112509	−	0.346267i
$190$		0			0
$191$	−2.61877	−	1.90265i	−0.189488	−	0.137671i	0.488997	−	0.872286i	$-0.337363\pi$
$191$	−2.61877	−	1.90265i	−0.189488	−	0.137671i	−0.678485	+	0.734615i	$0.737363\pi$
$192$		0			0
$193$	−2.99417	−	9.21510i	−0.215525	−	0.663318i	−0.999116	−	0.0420405i	$-0.986614\pi$
$193$	−2.99417	−	9.21510i	−0.215525	−	0.663318i	0.783591	−	0.621277i	$-0.213386\pi$
$194$		0			0
$195$	−0.898118	+	0.652521i	−0.0643156	+	0.0467280i
$196$		0			0
$197$	−4.95293			−0.352882			−0.176441	−	0.984311i	$-0.556458\pi$
$197$	−4.95293			−0.352882			−0.176441	+	0.984311i	$0.556458\pi$
$198$		0			0
$199$	7.30766			0.518026			0.259013	−	0.965874i	$-0.416603\pi$
$199$	7.30766			0.518026			0.259013	+	0.965874i	$0.416603\pi$
$200$		0			0
$201$	−0.445741	+	0.323850i	−0.0314401	+	0.0228426i
$202$		0			0
$203$	13.5318	+	41.6467i	0.949748	+	2.92302i
$204$		0			0
$205$	−1.44786	−	1.05193i	−0.101123	−	0.0734703i
$206$		0			0
$207$	−0.374045	+	1.15119i	−0.0259979	+	0.0800133i
$208$		0			0
$209$	−23.0485	+	0.698681i	−1.59430	+	0.0483288i
$210$		0			0
$211$	6.96288	−	21.4295i	0.479345	−	1.47527i	−0.360663	−	0.932696i	$-0.617450\pi$
$211$	6.96288	−	21.4295i	0.479345	−	1.47527i	0.840008	−	0.542575i	$-0.182550\pi$
$212$		0			0
$213$	−9.72628	−	7.06656i	−0.666434	−	0.484193i
$214$		0			0
$215$	3.22174	+	9.91550i	0.219721	+	0.676232i
$216$		0			0
$217$	−36.0544	+	26.1950i	−2.44753	+	1.77824i
$218$		0			0
$219$	−2.24398			−0.151634
$220$		0			0
$221$	4.47500			0.301021
$222$		0			0
$223$	−15.4593	+	11.2318i	−1.03523	+	0.752138i	−0.969349	−	0.245689i	$-0.920986\pi$
$223$	−15.4593	+	11.2318i	−1.03523	+	0.752138i	−0.0658810	+	0.997827i	$0.520986\pi$
$224$		0			0
$225$	−1.16425	−	3.58320i	−0.0776168	−	0.238880i
$226$		0			0
$227$	−19.9209	−	14.4733i	−1.32219	−	0.960630i	−0.999902	−	0.0139891i	$-0.995547\pi$
$227$	−19.9209	−	14.4733i	−1.32219	−	0.960630i	−0.322291	−	0.946641i	$-0.604453\pi$
$228$		0			0
$229$	−4.95636	+	15.2541i	−0.327526	+	1.00802i	0.642762	+	0.766066i	$0.277788\pi$
$229$	−4.95636	+	15.2541i	−0.327526	+	1.00802i	−0.970288	+	0.241954i	$0.922212\pi$
$230$		0			0
$231$	13.7199	+	9.34636i	0.902704	+	0.614945i
$232$		0			0
$233$	3.23640	−	9.96060i	0.212023	−	0.652541i	−0.787328	−	0.616534i	$-0.788536\pi$
$233$	3.23640	−	9.96060i	0.212023	−	0.652541i	0.999352	−	0.0360066i	$-0.0114637\pi$
$234$		0			0
$235$	−7.02410	−	5.10331i	−0.458202	−	0.332903i
$236$		0			0
$237$	3.00854	+	9.25932i	0.195425	+	0.601458i
$238$		0			0
$239$	−8.40475	+	6.10641i	−0.543658	+	0.394991i	−0.825442	−	0.564487i	$-0.809074\pi$
$239$	−8.40475	+	6.10641i	−0.543658	+	0.394991i	0.281784	+	0.959478i	$0.409074\pi$
$240$		0			0
$241$	−8.59352			−0.553557			−0.276779	−	0.960934i	$-0.589267\pi$
$241$	−8.59352			−0.553557			−0.276779	+	0.960934i	$0.589267\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	16.2143	−	11.7804i	1.03590	−	0.752623i
$246$		0			0
$247$	2.14846	+	6.61229i	0.136704	+	0.420730i
$248$		0			0
$249$	10.9962	+	7.98918i	0.696853	+	0.506294i
$250$		0			0
$251$	−1.52022	+	4.67875i	−0.0959552	+	0.295320i	−0.987501	−	0.157610i	$-0.949621\pi$
$251$	−1.52022	+	4.67875i	−0.0959552	+	0.295320i	0.891546	+	0.452930i	$0.149621\pi$
$252$		0			0
$253$	−3.31785	−	2.26020i	−0.208591	−	0.142098i
$254$		0			0
$255$	1.53515	−	4.72471i	0.0961349	−	0.295873i
$256$		0			0
$257$	15.8487	+	11.5148i	0.988617	+	0.718273i	0.959618	−	0.281307i	$-0.0907679\pi$
$257$	15.8487	+	11.5148i	0.988617	+	0.718273i	0.0289996	+	0.999579i	$0.490768\pi$
$258$		0			0
$259$	−12.8155	−	39.4419i	−0.796313	−	2.45080i
$260$		0			0
$261$	7.07776	−	5.14230i	0.438103	−	0.318300i
$262$		0			0
$263$	−3.01064			−0.185644			−0.0928220	−	0.995683i	$-0.529589\pi$
$263$	−3.01064			−0.185644			−0.0928220	+	0.995683i	$0.529589\pi$
$264$		0			0
$265$	−8.79393			−0.540207
$266$		0			0
$267$	9.38480	−	6.81846i	0.574341	−	0.417283i
$268$		0			0
$269$	−3.54069	−	10.8971i	−0.215880	−	0.664409i	−0.999090	−	0.0426524i	$-0.986419\pi$
$269$	−3.54069	−	10.8971i	−0.215880	−	0.664409i	0.783210	−	0.621757i	$-0.213581\pi$
$270$		0			0
$271$	11.1331	+	8.08865i	0.676286	+	0.491351i	0.872124	−	0.489286i	$-0.162742\pi$
$271$	11.1331	+	8.08865i	0.676286	+	0.491351i	−0.195837	+	0.980636i	$0.562742\pi$
$272$		0			0
$273$	1.54674	−	4.76038i	0.0936131	−	0.288112i
$274$		0			0
$275$	12.4900	−	0.378615i	0.753174	−	0.0228313i
$276$		0			0
$277$	3.25288	−	10.0113i	0.195446	−	0.601522i	−0.804525	−	0.593919i	$-0.797580\pi$
$277$	3.25288	−	10.0113i	0.195446	−	0.601522i	0.999971	−	0.00760299i	$-0.00242013\pi$
$278$		0			0
$279$	7.20315	+	5.23339i	0.431241	+	0.313315i
$280$		0			0
$281$	−5.78853	−	17.8153i	−0.345315	−	1.06277i	−0.961415	−	0.275101i	$-0.911289\pi$
$281$	−5.78853	−	17.8153i	−0.345315	−	1.06277i	0.616101	−	0.787667i	$-0.288711\pi$
$282$		0			0
$283$	−14.1881	+	10.3083i	−0.843396	+	0.612763i	−0.923317	−	0.384038i	$-0.874533\pi$
$283$	−14.1881	+	10.3083i	−0.843396	+	0.612763i	0.0799210	+	0.996801i	$0.474533\pi$
$284$		0			0
$285$	7.71830			0.457193
$286$		0			0
$287$	8.06918			0.476309
$288$		0			0
$289$	−2.44777	+	1.77841i	−0.143986	+	0.104612i
$290$		0			0
$291$	−5.00076	−	15.3908i	−0.293150	−	0.902222i
$292$		0			0
$293$	−21.0315	−	15.2802i	−1.22867	−	0.892682i	−0.231881	−	0.972744i	$-0.574488\pi$
$293$	−21.0315	−	15.2802i	−1.22867	−	0.892682i	−0.996790	+	0.0800626i	$0.974488\pi$
$294$		0			0
$295$	−3.56562	+	10.9738i	−0.207598	+	0.638922i
$296$		0			0
$297$	0.928849	−	3.18390i	0.0538973	−	0.184749i
$298$		0			0
$299$	−0.374045	+	1.15119i	−0.0216316	+	0.0665751i
$300$		0			0
$301$	−38.0300	−	27.6304i	−2.19201	−	1.59259i
$302$		0			0
$303$	−3.18191	−	9.79290i	−0.182796	−	0.562587i
$304$		0			0
$305$	2.64985	−	1.92523i	0.151730	−	0.110238i
$306$		0			0
$307$	−6.24021			−0.356148			−0.178074	−	0.984017i	$-0.556987\pi$
$307$	−6.24021			−0.356148			−0.178074	+	0.984017i	$0.556987\pi$
$308$		0			0
$309$	1.55855			0.0886628
$310$		0			0
$311$	20.7653	−	15.0868i	1.17749	−	0.855496i	0.185604	−	0.982625i	$-0.440576\pi$
$311$	20.7653	−	15.0868i	1.17749	−	0.855496i	0.991886	+	0.127128i	$0.0405760\pi$
$312$		0			0
$313$	9.17580	+	28.2402i	0.518647	+	1.59623i	0.776547	+	0.630060i	$0.216970\pi$
$313$	9.17580	+	28.2402i	0.518647	+	1.59623i	−0.257900	+	0.966172i	$0.583030\pi$
$314$		0			0
$315$	−4.49541	−	3.26611i	−0.253288	−	0.184024i
$316$		0			0
$317$	−8.44598	+	25.9941i	−0.474374	+	1.45997i	0.372427	+	0.928062i	$0.378526\pi$
$317$	−8.44598	+	25.9941i	−0.474374	+	1.45997i	−0.846801	+	0.531911i	$0.821474\pi$
$318$		0			0
$319$	9.79840	+	27.3113i	0.548605	+	1.52914i
$320$		0			0
$321$	4.01453	−	12.3554i	0.224069	−	0.689614i
$322$		0			0
$323$	−25.1708	−	18.2876i	−1.40054	−	1.01755i
$324$		0			0
$325$	−1.16425	−	3.58320i	−0.0645811	−	0.198760i
$326$		0			0
$327$	6.48742	−	4.71339i	0.358755	−	0.260651i
$328$		0			0
$329$	39.1465			2.15822
$330$		0			0
$331$	−18.3029			−1.00602			−0.503010	−	0.864280i	$-0.667774\pi$
$331$	−18.3029			−1.00602			−0.503010	+	0.864280i	$0.667774\pi$
$332$		0			0
$333$	−6.70307	+	4.87006i	−0.367326	+	0.266878i
$334$		0			0
$335$	0.189009	+	0.581711i	0.0103267	+	0.0317823i
$336$		0			0
$337$	−9.50714	−	6.90735i	−0.517887	−	0.376267i	0.297920	−	0.954591i	$-0.403707\pi$
$337$	−9.50714	−	6.90735i	−0.517887	−	0.376267i	−0.815807	+	0.578324i	$0.803707\pi$
$338$		0			0
$339$	2.77336	−	8.53553i	0.150628	−	0.463586i
$340$		0			0
$341$	−23.3533	+	18.0731i	−1.26465	+	0.978713i
$342$		0			0
$343$	−17.0972	+	52.6197i	−0.923162	+	2.84120i
$344$		0			0
$345$	1.08711	+	0.789834i	0.0585282	+	0.0425232i
$346$		0			0
$347$	6.30006	+	19.3896i	0.338205	+	1.04089i	0.965122	+	0.261802i	$0.0843166\pi$
$347$	6.30006	+	19.3896i	0.338205	+	1.04089i	−0.626917	+	0.779086i	$0.715683\pi$
$348$		0			0
$349$	1.12851	−	0.819912i	0.0604079	−	0.0438889i	−0.557172	−	0.830397i	$-0.688113\pi$
$349$	1.12851	−	0.819912i	0.0604079	−	0.0438889i	0.617579	+	0.786509i	$0.288113\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	15.3308			0.815977			0.407988	−	0.912987i	$-0.366230\pi$
$353$	15.3308			0.815977			0.407988	+	0.912987i	$0.366230\pi$
$354$		0			0
$355$	−10.7975	+	7.84484i	−0.573071	+	0.416361i
$356$		0			0
$357$	6.92167	+	21.3027i	0.366334	+	1.12746i
$358$		0			0
$359$	−17.3997	−	12.6416i	−0.918319	−	0.667198i	0.0247860	−	0.999693i	$-0.492110\pi$
$359$	−17.3997	−	12.6416i	−0.918319	−	0.667198i	−0.943105	+	0.332495i	$0.892110\pi$
$360$		0			0
$361$	9.06604	−	27.9024i	0.477160	−	1.46855i
$362$		0			0
$363$	9.27448	+	5.91473i	0.486784	+	0.310443i
$364$		0			0
$365$	−0.769798	+	2.36919i	−0.0402931	+	0.124009i
$366$		0			0
$367$	8.91463	+	6.47686i	0.465340	+	0.338089i	0.795622	−	0.605793i	$-0.207144\pi$
$367$	8.91463	+	6.47686i	0.465340	+	0.338089i	−0.330283	+	0.943882i	$0.607144\pi$
$368$		0			0
$369$	−0.498168	−	1.53320i	−0.0259336	−	0.0798155i
$370$		0			0
$371$	32.0775	−	23.3057i	1.66538	−	1.20997i
$372$		0			0
$373$	11.2816			0.584141			0.292070	−	0.956397i	$-0.405656\pi$
$373$	11.2816			0.584141			0.292070	+	0.956397i	$0.405656\pi$
$374$		0			0
$375$	−9.73322			−0.502621
$376$		0			0
$377$	7.07776	−	5.14230i	0.364523	−	0.264842i
$378$		0			0
$379$	−3.77922	−	11.6312i	−0.194125	−	0.597456i	−0.999986	−	0.00535071i	$-0.998297\pi$
$379$	−3.77922	−	11.6312i	−0.194125	−	0.597456i	0.805860	−	0.592106i	$-0.201703\pi$
$380$		0			0
$381$	4.94295	+	3.59126i	0.253235	+	0.183986i
$382$		0			0
$383$	2.32579	−	7.15805i	0.118842	−	0.365759i	−0.873887	−	0.486130i	$-0.838408\pi$
$383$	2.32579	−	7.15805i	0.118842	−	0.365759i	0.992729	+	0.120371i	$0.0384083\pi$
$384$		0			0
$385$	14.5745	−	11.2792i	0.742787	−	0.574843i
$386$		0			0
$387$	−2.90212	+	8.93180i	−0.147523	+	0.454029i
$388$		0			0
$389$	−15.9241	−	11.5696i	−0.807386	−	0.586600i	0.105686	−	0.994400i	$-0.466296\pi$
$389$	−15.9241	−	11.5696i	−0.807386	−	0.586600i	−0.913072	+	0.407799i	$0.866296\pi$
$390$		0			0
$391$	−1.67385	−	5.15158i	−0.0846502	−	0.260526i
$392$		0			0
$393$	11.3376	−	8.23727i	0.571908	−	0.415516i
$394$		0			0
$395$	10.8081			0.543814
$396$		0			0
$397$	−16.3599			−0.821079			−0.410540	−	0.911843i	$-0.634660\pi$
$397$	−16.3599			−0.821079			−0.410540	+	0.911843i	$0.634660\pi$
$398$		0			0
$399$	−28.1539	+	20.4550i	−1.40946	+	1.02403i
$400$		0			0
$401$	−0.891601	−	2.74406i	−0.0445244	−	0.137032i	0.926323	−	0.376730i	$-0.122952\pi$
$401$	−0.891601	−	2.74406i	−0.0445244	−	0.137032i	−0.970847	+	0.239698i	$0.922952\pi$
$402$		0			0
$403$	7.20315	+	5.23339i	0.358814	+	0.260694i
$404$		0			0
$405$	−0.343051	+	1.05580i	−0.0170463	+	0.0524632i
$406$		0			0
$407$	−9.27967	−	25.8655i	−0.459976	−	1.28210i
$408$		0			0
$409$	−3.16685	+	9.74656i	−0.156591	+	0.481936i	−0.998319	−	0.0579655i	$-0.981539\pi$
$409$	−3.16685	+	9.74656i	−0.156591	+	0.481936i	0.841728	+	0.539902i	$0.181539\pi$
$410$		0			0
$411$	−12.4612	−	9.05358i	−0.614665	−	0.446580i
$412$		0			0
$413$	−16.0766	−	49.4787i	−0.791078	−	2.43469i
$414$		0			0
$415$	12.2072	−	8.86907i	0.599229	−	0.435365i
$416$		0			0
$417$	−9.59701			−0.469968
$418$		0			0
$419$	15.1937			0.742261			0.371131	−	0.928581i	$-0.378970\pi$
$419$	15.1937			0.742261			0.371131	+	0.928581i	$0.378970\pi$
$420$		0			0
$421$	−9.19935	+	6.68372i	−0.448349	+	0.325745i	−0.788944	−	0.614466i	$-0.789372\pi$
$421$	−9.19935	+	6.68372i	−0.448349	+	0.325745i	0.340595	+	0.940210i	$0.389372\pi$
$422$		0			0
$423$	−2.41679	−	7.43813i	−0.117509	−	0.361654i
$424$		0			0
$425$	13.6400	+	9.91006i	0.661638	+	0.480708i
$426$		0			0
$427$	−4.56358	+	14.0452i	−0.220847	+	0.679697i
$428$		0			0
$429$	0.928849	−	3.18390i	0.0448452	−	0.153720i
$430$		0			0
$431$	−11.6938	+	35.9898i	−0.563271	+	1.73357i	0.109763	+	0.993958i	$0.464991\pi$
$431$	−11.6938	+	35.9898i	−0.563271	+	1.73357i	−0.673034	+	0.739612i	$0.735009\pi$
$432$		0			0
$433$	−13.5200	−	9.82283i	−0.649728	−	0.472055i	0.213451	−	0.976954i	$-0.431530\pi$
$433$	−13.5200	−	9.82283i	−0.649728	−	0.472055i	−0.863179	+	0.504899i	$0.831530\pi$
$434$		0			0
$435$	−3.00121	−	9.23678i	−0.143897	−	0.442870i
$436$		0			0
$437$	6.80839	−	4.94659i	0.325689	−	0.236627i
$438$		0			0
$439$	−24.0385			−1.14729			−0.573647	−	0.819102i	$-0.694472\pi$
$439$	−24.0385			−1.14729			−0.573647	+	0.819102i	$0.694472\pi$
$440$		0			0
$441$	18.0537			0.859699
$442$		0			0
$443$	18.1460	−	13.1838i	0.862140	−	0.626381i	−0.0663262	−	0.997798i	$-0.521128\pi$
$443$	18.1460	−	13.1838i	0.862140	−	0.626381i	0.928466	+	0.371417i	$0.121128\pi$
$444$		0			0
$445$	−3.97948	−	12.2476i	−0.188645	−	0.580590i
$446$		0			0
$447$	0.817120	+	0.593672i	0.0386484	+	0.0280797i
$448$		0			0
$449$	−11.8671	+	36.5231i	−0.560042	+	1.72363i	0.122198	+	0.992506i	$0.461006\pi$
$449$	−11.8671	+	36.5231i	−0.560042	+	1.72363i	−0.682241	+	0.731128i	$0.738994\pi$
$450$		0			0
$451$	5.34430	−	0.162004i	0.251653	−	0.00762849i
$452$		0			0
$453$	4.25004	−	13.0803i	0.199684	−	0.614565i
$454$		0			0
$455$	−4.49541	−	3.26611i	−0.210748	−	0.153117i
$456$		0			0
$457$	−8.76600	−	26.9790i	−0.410056	−	1.26202i	−0.916599	−	0.399808i	$-0.869077\pi$
$457$	−8.76600	−	26.9790i	−0.410056	−	1.26202i	0.506543	−	0.862215i	$-0.330923\pi$
$458$		0			0
$459$	3.62035	−	2.63034i	0.168983	−	0.122774i
$460$		0			0
$461$	19.5651			0.911237			0.455619	−	0.890175i	$-0.349418\pi$
$461$	19.5651			0.911237			0.455619	+	0.890175i	$0.349418\pi$
$462$		0			0
$463$	14.8479			0.690038			0.345019	−	0.938596i	$-0.387872\pi$
$463$	14.8479			0.690038			0.345019	+	0.938596i	$0.387872\pi$
$464$		0			0
$465$	7.99647	−	5.80978i	0.370827	−	0.269422i
$466$		0			0
$467$	−5.68183	−	17.4869i	−0.262924	−	0.809196i	−0.992164	−	0.124939i	$-0.960127\pi$
$467$	−5.68183	−	17.4869i	−0.262924	−	0.809196i	0.729241	−	0.684257i	$-0.239873\pi$
$468$		0			0
$469$	−2.23110	−	1.62099i	−0.103022	−	0.0748502i
$470$		0			0
$471$	1.39522	−	4.29405i	0.0642883	−	0.197859i
$472$		0			0
$473$	−25.7424	−	17.5364i	−1.18363	−	0.806322i
$474$		0			0
$475$	−8.09455	+	24.9125i	−0.371404	+	1.14306i
$476$		0			0
$477$	−6.40862	−	4.65614i	−0.293431	−	0.213190i
$478$		0			0
$479$	2.99683	+	9.22330i	0.136929	+	0.421423i	0.995885	−	0.0906256i	$-0.0288867\pi$
$479$	2.99683	+	9.22330i	0.136929	+	0.421423i	−0.858956	+	0.512049i	$0.828887\pi$
$480$		0			0
$481$	−6.70307	+	4.87006i	−0.305633	+	0.222056i
$482$		0			0
$483$	−6.05866			−0.275679
$484$		0			0
$485$	−17.9651			−0.815753
$486$		0			0
$487$	−12.0758	+	8.77360i	−0.547208	+	0.397570i	−0.826755	−	0.562562i	$-0.809816\pi$
$487$	−12.0758	+	8.77360i	−0.547208	+	0.397570i	0.279547	+	0.960132i	$0.409816\pi$
$488$		0			0
$489$	−1.81030	−	5.57154i	−0.0818648	−	0.251954i
$490$		0			0
$491$	−16.4216	−	11.9310i	−0.741097	−	0.538438i	0.151958	−	0.988387i	$-0.451442\pi$
$491$	−16.4216	−	11.9310i	−0.741097	−	0.538438i	−0.893054	+	0.449949i	$0.851442\pi$
$492$		0			0
$493$	−12.0980	+	37.2338i	−0.544867	+	1.67693i
$494$		0			0
$495$	−3.04293	−	2.07292i	−0.136769	−	0.0931708i
$496$		0			0
$497$	18.5955	−	57.2310i	0.834121	−	2.56716i
$498$		0			0
$499$	21.4634	+	15.5940i	0.960832	+	0.698085i	0.953344	−	0.301887i	$-0.0976165\pi$
$499$	21.4634	+	15.5940i	0.960832	+	0.698085i	0.00748799	+	0.999972i	$0.497616\pi$
$500$		0			0
$501$	0.690950	+	2.12652i	0.0308694	+	0.0950061i
$502$		0			0
$503$	−13.6812	+	9.93994i	−0.610012	+	0.443200i	−0.849419	−	0.527719i	$-0.823047\pi$
$503$	−13.6812	+	9.93994i	−0.610012	+	0.443200i	0.239406	+	0.970919i	$0.423047\pi$
$504$		0			0
$505$	−11.4309			−0.508669
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	−22.0750	+	16.0385i	−0.978459	+	0.710892i	−0.957364	−	0.288885i	$-0.906715\pi$
$509$	−22.0750	+	16.0385i	−0.978459	+	0.710892i	−0.0210954	+	0.999777i	$0.506715\pi$
$510$		0			0
$511$	−3.47085	−	10.6822i	−0.153542	−	0.472552i
$512$		0			0
$513$	5.62475	+	4.08662i	0.248339	+	0.180429i
$514$		0			0
$515$	0.534661	−	1.64552i	0.0235600	−	0.0725102i
$516$		0			0
$517$	25.9271	−	0.785942i	1.14027	−	0.0345657i
$518$		0			0
$519$	−4.38160	+	13.4852i	−0.192331	+	0.591933i
$520$		0			0
$521$	19.4928	+	14.1623i	0.853993	+	0.620462i	0.926244	−	0.376924i	$-0.123018\pi$
$521$	19.4928	+	14.1623i	0.853993	+	0.620462i	−0.0722510	+	0.997386i	$0.523018\pi$
$522$		0			0
$523$	−2.41757	−	7.44052i	−0.105713	−	0.325351i	0.884184	−	0.467138i	$-0.154715\pi$
$523$	−2.41757	−	7.44052i	−0.105713	−	0.325351i	−0.989897	+	0.141787i	$0.954715\pi$
$524$		0			0
$525$	15.2566	−	11.0846i	0.665853	−	0.483771i
$526$		0			0
$527$	−39.8435			−1.73561
$528$		0			0
$529$	−21.5349			−0.936298
$530$		0			0
$531$	−8.40880	+	6.10935i	−0.364911	+	0.265123i
$532$		0			0
$533$	−0.498168	−	1.53320i	−0.0215781	−	0.0664105i
$534$		0			0
$535$	−11.6677	−	8.47709i	−0.504439	−	0.366496i
$536$		0			0
$537$	−3.32636	+	10.2375i	−0.143543	+	0.441779i
$538$		0			0
$539$	−16.7691	+	57.4812i	−0.722298	+	2.47589i
$540$		0			0
$541$	−7.70091	+	23.7010i	−0.331088	+	1.01898i	0.637529	+	0.770426i	$0.279957\pi$
$541$	−7.70091	+	23.7010i	−0.331088	+	1.01898i	−0.968617	+	0.248558i	$0.920043\pi$
$542$		0			0
$543$	−12.5980	−	9.15300i	−0.540633	−	0.392793i
$544$		0			0
$545$	−2.75089	−	8.46636i	−0.117835	−	0.362659i
$546$		0			0
$547$	22.0798	−	16.0419i	0.944065	−	0.685904i	−0.00533048	−	0.999986i	$-0.501697\pi$
$547$	22.0798	−	16.0419i	0.944065	−	0.685904i	0.949396	+	0.314082i	$0.101697\pi$
$548$		0			0
$549$	2.95044			0.125922
$550$		0			0
$551$	−60.8253			−2.59124
$552$		0			0
$553$	−39.4245	+	28.6436i	−1.67650	+	1.21805i
$554$		0			0
$555$	2.84233	+	8.74778i	0.120650	+	0.371323i
$556$		0			0
$557$	2.59321	+	1.88408i	0.109878	+	0.0798309i	0.641367	−	0.767234i	$-0.278367\pi$
$557$	2.59321	+	1.88408i	0.109878	+	0.0798309i	−0.531489	+	0.847065i	$0.678367\pi$
$558$		0			0
$559$	−2.90212	+	8.93180i	−0.122746	+	0.377775i
$560$		0			0
$561$	5.01198	+	13.9700i	0.211606	+	0.589815i
$562$		0			0
$563$	9.85711	−	30.3371i	0.415428	−	1.27855i	−0.496440	−	0.868071i	$-0.665360\pi$
$563$	9.85711	−	30.3371i	0.415428	−	1.27855i	0.911868	−	0.410484i	$-0.134640\pi$
$564$		0			0
$565$	−8.06042	−	5.85624i	−0.339104	−	0.246374i
$566$		0			0
$567$	−1.54674	−	4.76038i	−0.0649571	−	0.199917i
$568$		0			0
$569$	33.8219	−	24.5730i	1.41789	−	1.03016i	0.425772	−	0.904831i	$-0.360003\pi$
$569$	33.8219	−	24.5730i	1.41789	−	1.03016i	0.992116	−	0.125325i	$-0.0399973\pi$
$570$		0			0
$571$	0.597791			0.0250168			0.0125084	−	0.999922i	$-0.496018\pi$
$571$	0.597791			0.0250168			0.0125084	+	0.999922i	$0.496018\pi$
$572$		0			0
$573$	−3.23698			−0.135227
$574$		0			0
$575$	−3.68946	+	2.68055i	−0.153861	+	0.111787i
$576$		0			0
$577$	−11.0381	−	33.9719i	−0.459524	−	1.41427i	−0.865741	−	0.500493i	$-0.833152\pi$
$577$	−11.0381	−	33.9719i	−0.459524	−	1.41427i	0.406217	−	0.913777i	$-0.366848\pi$
$578$		0			0
$579$	−7.83883	−	5.69525i	−0.325771	−	0.236686i
$580$		0			0
$581$	−21.0233	+	64.7032i	−0.872195	+	2.68434i
$582$		0			0
$583$	20.7773	−	16.0796i	0.860509	−	0.665949i
$584$		0			0
$585$	−0.343051	+	1.05580i	−0.0141834	+	0.0436520i
$586$		0			0
$587$	24.4127	+	17.7368i	1.00762	+	0.732078i	0.963708	−	0.266958i	$-0.0860184\pi$
$587$	24.4127	+	17.7368i	1.00762	+	0.732078i	0.0439103	+	0.999035i	$0.486018\pi$
$588$		0			0
$589$	−19.1290	−	58.8731i	−0.788198	−	2.42582i
$590$		0			0
$591$	−4.00700	+	2.91126i	−0.164826	+	0.119753i
$592$		0			0
$593$	37.4004			1.53585			0.767925	−	0.640540i	$-0.221290\pi$
$593$	37.4004			1.53585			0.767925	+	0.640540i	$0.221290\pi$
$594$		0			0
$595$	24.8659			1.01940
$596$		0			0
$597$	5.91202	−	4.29533i	0.241963	−	0.175796i
$598$		0			0
$599$	−7.18752	−	22.1209i	−0.293674	−	0.903836i	−0.983664	−	0.180016i	$-0.942385\pi$
$599$	−7.18752	−	22.1209i	−0.293674	−	0.903836i	0.689990	−	0.723819i	$-0.257615\pi$
$600$		0			0
$601$	−3.30190	−	2.39897i	−0.134687	−	0.0978562i	0.518402	−	0.855137i	$-0.326527\pi$
$601$	−3.30190	−	2.39897i	−0.134687	−	0.0978562i	−0.653089	+	0.757281i	$0.726527\pi$
$602$		0			0
$603$	−0.170258	+	0.524000i	−0.00693344	+	0.0213389i
$604$		0			0
$605$	9.42640	−	7.76296i	0.383238	−	0.315609i
$606$		0			0
$607$	−1.79422	+	5.52205i	−0.0728253	+	0.224133i	−0.980843	−	0.194798i	$-0.937595\pi$
$607$	−1.79422	+	5.52205i	−0.0728253	+	0.224133i	0.908018	+	0.418931i	$0.137595\pi$
$608$		0			0
$609$	35.4268	+	25.7391i	1.43557	+	1.04300i
$610$		0			0
$611$	−2.41679	−	7.43813i	−0.0977730	−	0.300915i
$612$		0			0
$613$	−13.1332	+	9.54185i	−0.530446	+	0.385392i	−0.820525	−	0.571611i	$-0.806319\pi$
$613$	−13.1332	+	9.54185i	−0.530446	+	0.385392i	0.290079	+	0.957003i	$0.406319\pi$
$614$		0			0
$615$	−1.78966			−0.0721659
$616$		0			0
$617$	−42.4507			−1.70900			−0.854499	−	0.519452i	$-0.826136\pi$
$617$	−42.4507			−1.70900			−0.854499	+	0.519452i	$0.826136\pi$
$618$		0			0
$619$	11.0912	−	8.05826i	0.445795	−	0.323889i	−0.342138	−	0.939650i	$-0.611151\pi$
$619$	11.0912	−	8.05826i	0.445795	−	0.323889i	0.787933	+	0.615761i	$0.211151\pi$
$620$		0			0
$621$	0.374045	+	1.15119i	0.0150099	+	0.0461957i
$622$		0			0
$623$	46.9744	+	34.1289i	1.88199	+	1.36734i
$624$		0			0
$625$	2.48227	−	7.63965i	0.0992909	−	0.305586i
$626$		0			0
$627$	−18.2360	+	14.1128i	−0.728274	+	0.563611i
$628$		0			0
$629$	11.4575	−	35.2627i	0.456842	−	1.40601i
$630$		0			0
$631$	28.7440	+	20.8837i	1.14428	+	0.831368i	0.987710	−	0.156298i	$-0.0499561\pi$
$631$	28.7440	+	20.8837i	1.14428	+	0.831368i	0.156571	+	0.987667i	$0.449956\pi$
$632$		0			0
$633$	−6.96288	−	21.4295i	−0.276750	−	0.851748i
$634$		0			0
$635$	5.48735	−	3.98679i	0.217759	−	0.158211i
$636$		0			0
$637$	18.0537			0.715313
$638$		0			0
$639$	−12.0223			−0.475597
$640$		0			0
$641$	−8.77724	+	6.37704i	−0.346680	+	0.251878i	−0.747475	−	0.664290i	$-0.768734\pi$
$641$	−8.77724	+	6.37704i	−0.346680	+	0.251878i	0.400795	+	0.916168i	$0.368734\pi$
$642$		0			0
$643$	−3.82840	−	11.7826i	−0.150977	−	0.464660i	0.846754	−	0.531985i	$-0.178554\pi$
$643$	−3.82840	−	11.7826i	−0.150977	−	0.464660i	−0.997731	+	0.0673247i	$0.978554\pi$
$644$		0			0
$645$	8.43463	+	6.12812i	0.332113	+	0.241294i
$646$		0			0
$647$	−9.04358	+	27.8333i	−0.355540	+	1.09424i	0.600156	+	0.799883i	$0.295105\pi$
$647$	−9.04358	+	27.8333i	−0.355540	+	1.09424i	−0.955696	+	0.294356i	$0.904895\pi$
$648$		0			0
$649$	−11.6411	−	32.4475i	−0.456952	−	1.27367i
$650$		0			0
$651$	−13.7716	+	42.3845i	−0.539750	+	1.66118i
$652$		0			0
$653$	26.4813	+	19.2398i	1.03629	+	0.752911i	0.969558	−	0.244860i	$-0.0787420\pi$
$653$	26.4813	+	19.2398i	1.03629	+	0.752911i	0.0667343	+	0.997771i	$0.478742\pi$
$654$		0			0
$655$	−4.80754	−	14.7961i	−0.187846	−	0.578131i
$656$		0			0
$657$	−1.81542	+	1.31898i	−0.0708261	+	0.0514582i
$658$		0			0
$659$	−29.0966			−1.13344			−0.566722	−	0.823909i	$-0.691789\pi$
$659$	−29.0966			−1.13344			−0.566722	+	0.823909i	$0.691789\pi$
$660$		0			0
$661$	−2.51813			−0.0979438			−0.0489719	−	0.998800i	$-0.515594\pi$
$661$	−2.51813			−0.0979438			−0.0489719	+	0.998800i	$0.515594\pi$
$662$		0			0
$663$	3.62035	−	2.63034i	0.140603	−	0.102154i
$664$		0			0
$665$	11.9382	+	36.7421i	0.462945	+	1.42480i
$666$		0			0
$667$	−8.56716	−	6.22441i	−0.331722	−	0.241010i
$668$		0			0
$669$	−5.90492	+	18.1735i	−0.228297	+	0.702627i
$670$		0			0
$671$	−2.74052	+	9.39393i	−0.105796	+	0.362648i
$672$		0			0
$673$	2.32892	−	7.16768i	0.0897732	−	0.276294i	−0.896083	−	0.443886i	$-0.853599\pi$
$673$	2.32892	−	7.16768i	0.0897732	−	0.276294i	0.985856	+	0.167593i	$0.0535994\pi$
$674$		0			0
$675$	−3.04805	−	2.21454i	−0.117320	−	0.0852377i
$676$		0			0
$677$	−7.67923	−	23.6342i	−0.295137	−	0.908338i	−0.983175	−	0.182664i	$-0.941528\pi$
$677$	−7.67923	−	23.6342i	−0.295137	−	0.908338i	0.688039	−	0.725674i	$-0.258472\pi$
$678$		0			0
$679$	65.5310	−	47.6111i	2.51485	−	1.82715i
$680$		0			0
$681$	−24.6235			−0.943576
$682$		0			0
$683$	−25.5504			−0.977658			−0.488829	−	0.872380i	$-0.662576\pi$
$683$	−25.5504			−0.977658			−0.488829	+	0.872380i	$0.662576\pi$
$684$		0			0
$685$	−13.8336	+	10.0507i	−0.528555	+	0.384017i
$686$		0			0
$687$	4.95636	+	15.2541i	0.189097	+	0.581981i
$688$		0			0
$689$	−6.40862	−	4.65614i	−0.244149	−	0.177385i
$690$		0			0
$691$	0.465483	−	1.43261i	0.0177078	−	0.0544990i	−0.941812	−	0.336140i	$-0.890879\pi$
$691$	0.465483	−	1.43261i	0.0177078	−	0.0544990i	0.959520	+	0.281641i	$0.0908786\pi$
$692$		0			0
$693$	16.5933	−	0.503001i	0.630327	−	0.0191074i
$694$		0			0
$695$	−3.29226	+	10.1325i	−0.124883	+	0.384349i
$696$		0			0
$697$	5.83639	+	4.24039i	0.221069	+	0.160616i
$698$		0			0
$699$	−3.23640	−	9.96060i	−0.122412	−	0.376745i
$700$		0			0
$701$	−1.71472	+	1.24582i	−0.0647640	+	0.0470538i	−0.619696	−	0.784842i	$-0.712744\pi$
$701$	−1.71472	+	1.24582i	−0.0647640	+	0.0470538i	0.554932	+	0.831896i	$0.312744\pi$
$702$		0			0
$703$	57.6052			2.17262
$704$		0			0
$705$	−8.68227			−0.326993
$706$		0			0
$707$	41.6964	−	30.2942i	1.56815	−	1.13933i
$708$		0			0
$709$	10.5373	+	32.4305i	0.395737	+	1.21795i	0.928386	+	0.371617i	$0.121197\pi$
$709$	10.5373	+	32.4305i	0.395737	+	1.21795i	−0.532649	+	0.846336i	$0.678803\pi$
$710$		0			0
$711$	7.87645	+	5.72258i	0.295390	+	0.214613i
$712$		0			0
$713$	3.33034	−	10.2497i	0.124722	−	0.383855i
$714$		0			0
$715$	−3.04293	−	2.07292i	−0.113799	−	0.0775228i
$716$		0			0
$717$	−3.21033	+	9.88037i	−0.119892	+	0.368989i
$718$		0			0
$719$	−5.59797	−	4.06717i	−0.208769	−	0.151680i	0.478487	−	0.878094i	$-0.341185\pi$
$719$	−5.59797	−	4.06717i	−0.208769	−	0.151680i	−0.687257	+	0.726415i	$0.741185\pi$
$720$		0			0
$721$	2.41068	+	7.41930i	0.0897782	+	0.276309i
$722$		0			0
$723$	−6.95230	+	5.05114i	−0.258559	+	0.187854i
$724$		0			0
$725$	32.9612			1.22415
$726$		0			0
$727$	43.3345			1.60719			0.803594	−	0.595178i	$-0.202919\pi$
$727$	43.3345			1.60719			0.803594	+	0.595178i	$0.202919\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−12.9870	−	39.9698i	−0.480340	−	1.47834i
$732$		0			0
$733$	18.4855	+	13.4305i	0.682776	+	0.496066i	0.874277	−	0.485427i	$-0.161336\pi$
$733$	18.4855	+	13.4305i	0.682776	+	0.496066i	−0.191502	+	0.981492i	$0.561336\pi$
$734$		0			0
$735$	6.19333	−	19.0611i	0.228444	−	0.703079i
$736$		0			0
$737$	−1.51022	−	1.02880i	−0.0556297	−	0.0378964i
$738$		0			0
$739$	7.87001	−	24.2214i	0.289503	−	0.890998i	−0.695510	−	0.718516i	$-0.744821\pi$
$739$	7.87001	−	24.2214i	0.289503	−	0.890998i	0.985013	−	0.172482i	$-0.0551785\pi$
$740$		0			0
$741$	5.62475	+	4.08662i	0.206630	+	0.150126i
$742$		0			0
$743$	−6.16809	−	18.9834i	−0.226285	−	0.696434i	−0.998159	−	0.0606579i	$-0.980680\pi$
$743$	−6.16809	−	18.9834i	−0.226285	−	0.696434i	0.771873	−	0.635776i	$-0.219320\pi$
$744$		0			0
$745$	0.907113	−	0.659056i	0.0332341	−	0.0241460i
$746$		0			0
$747$	13.5920			0.497305
$748$		0			0
$749$	65.0261			2.37600
$750$		0			0
$751$	17.3755	−	12.6241i	0.634043	−	0.460659i	−0.223756	−	0.974645i	$-0.571832\pi$
$751$	17.3755	−	12.6241i	0.634043	−	0.460659i	0.857798	+	0.513986i	$0.171832\pi$
$752$		0			0
$753$	1.52022	+	4.67875i	0.0553998	+	0.170503i
$754$		0			0
$755$	−12.3522	−	8.97439i	−0.449542	−	0.326612i
$756$		0			0
$757$	8.49976	−	26.1596i	0.308929	−	0.950786i	−0.669253	−	0.743035i	$-0.733386\pi$
$757$	8.49976	−	26.1596i	0.308929	−	0.950786i	0.978182	−	0.207751i	$-0.0666143\pi$
$758$		0			0
$759$	−4.01271	+	0.121639i	−0.145652	+	0.00441523i
$760$		0			0
$761$	−11.0483	+	34.0030i	−0.400499	+	1.23261i	0.524097	+	0.851659i	$0.324403\pi$
$761$	−11.0483	+	34.0030i	−0.400499	+	1.23261i	−0.924596	+	0.380950i	$0.875597\pi$
$762$		0			0
$763$	32.4719	+	23.5922i	1.17556	+	0.854096i
$764$		0			0
$765$	−1.53515	−	4.72471i	−0.0555035	−	0.170822i
$766$		0			0
$767$	−8.40880	+	6.10935i	−0.303624	+	0.220596i
$768$		0			0
$769$	48.9611			1.76558			0.882790	−	0.469767i	$-0.155662\pi$
$769$	48.9611			1.76558			0.882790	+	0.469767i	$0.155662\pi$
$770$		0			0
$771$	19.5901			0.705521
$772$		0			0
$773$	19.9349	−	14.4836i	0.717010	−	0.520938i	−0.168417	−	0.985716i	$-0.553866\pi$
$773$	19.9349	−	14.4836i	0.717010	−	0.520938i	0.885428	+	0.464777i	$0.153866\pi$
$774$		0			0
$775$	10.3660	+	31.9033i	0.372358	+	1.14600i
$776$		0			0
$777$	−33.5513	−	24.3764i	−1.20365	−	0.874500i
$778$		0			0
$779$	−3.46355	+	10.6597i	−0.124095	+	0.381924i
$780$		0			0
$781$	11.1669	−	38.2780i	0.399585	−	1.36969i
$782$		0			0
$783$	2.70347	−	8.32041i	0.0966140	−	0.297347i
$784$		0			0
$785$	−4.05503	−	2.94615i	−0.144730	−	0.105153i
$786$		0			0
$787$	6.15145	+	18.9322i	0.219275	+	0.674860i	0.998822	+	0.0485166i	$0.0154494\pi$
$787$	6.15145	+	18.9322i	0.219275	+	0.674860i	−0.779547	+	0.626344i	$0.784551\pi$
$788$		0			0
$789$	−2.43566	+	1.76961i	−0.0867118	+	0.0629998i
$790$		0			0
$791$	44.9221			1.59725
$792$		0			0
$793$	2.95044			0.104773
$794$		0			0
$795$	−7.11444	+	5.16894i	−0.252323	+	0.183324i
$796$		0			0
$797$	8.89517	+	27.3765i	0.315083	+	0.969726i	0.975720	+	0.219021i	$0.0702862\pi$
$797$	8.89517	+	27.3765i	0.315083	+	0.969726i	−0.660637	+	0.750705i	$0.729714\pi$
$798$		0			0
$799$	28.3144	+	20.5716i	1.00169	+	0.727772i
$800$		0			0
$801$	3.58468	−	11.0325i	0.126658	−	0.389814i
$802$		0			0
$803$	−2.51325	−	7.00524i	−0.0886905	−	0.247209i
$804$		0			0
$805$	−2.07843	+	6.39674i	−0.0732550	+	0.225456i
$806$		0			0
$807$	−9.26964	−	6.73479i	−0.326307	−	0.237076i
$808$		0			0
$809$	−2.80203	−	8.62376i	−0.0985141	−	0.303195i	0.889639	−	0.456664i	$-0.150956\pi$
$809$	−2.80203	−	8.62376i	−0.0985141	−	0.303195i	−0.988154	+	0.153468i	$0.950956\pi$
$810$		0			0
$811$	17.9992	−	13.0772i	0.632038	−	0.459203i	−0.225068	−	0.974343i	$-0.572260\pi$
$811$	17.9992	−	13.0772i	0.632038	−	0.459203i	0.857106	+	0.515141i	$0.172260\pi$
$812$		0			0
$813$	13.7612			0.482628
$814$		0			0
$815$	−6.50347			−0.227807
$816$		0			0
$817$	52.8246	−	38.3793i	1.84810	−	1.34272i
$818$		0			0
$819$	−1.54674	−	4.76038i	−0.0540476	−	0.166341i
$820$		0			0
$821$	−9.62694	−	6.99438i	−0.335983	−	0.244106i	0.406982	−	0.913436i	$-0.366581\pi$
$821$	−9.62694	−	6.99438i	−0.335983	−	0.244106i	−0.742965	+	0.669330i	$0.766581\pi$
$822$		0			0
$823$	−7.61959	+	23.4507i	−0.265602	+	0.817440i	0.725952	+	0.687746i	$0.241400\pi$
$823$	−7.61959	+	23.4507i	−0.265602	+	0.817440i	−0.991554	+	0.129694i	$0.958600\pi$
$824$		0			0
$825$	9.88206	−	7.64773i	0.344049	−	0.266260i
$826$		0			0
$827$	−10.8027	+	33.2474i	−0.375648	+	1.15612i	0.567393	+	0.823447i	$0.307952\pi$
$827$	−10.8027	+	33.2474i	−0.375648	+	1.15612i	−0.943041	+	0.332678i	$0.892048\pi$
$828$		0			0
$829$	−5.94789	−	4.32140i	−0.206579	−	0.150088i	0.479686	−	0.877440i	$-0.340751\pi$
$829$	−5.94789	−	4.32140i	−0.206579	−	0.150088i	−0.686264	+	0.727352i	$0.740751\pi$
$830$		0			0
$831$	−3.25288	−	10.0113i	−0.112841	−	0.347289i
$832$		0			0
$833$	−65.3606	+	47.4873i	−2.26461	+	1.64534i
$834$		0			0
$835$	2.48222			0.0859007
$836$		0			0
$837$	8.90358			0.307753
$838$		0			0
$839$	16.5750	−	12.0425i	0.572233	−	0.415752i	−0.263682	−	0.964610i	$-0.584937\pi$
$839$	16.5750	−	12.0425i	0.572233	−	0.415752i	0.835916	+	0.548858i	$0.184937\pi$
$840$		0			0
$841$	14.6900	+	45.2113i	0.506553	+	1.55901i
$842$		0			0
$843$	−15.1546	−	11.0104i	−0.521951	−	0.379219i
$844$		0			0
$845$	−0.343051	+	1.05580i	−0.0118013	+	0.0363207i
$846$		0			0
$847$	−13.8112	+	53.2987i	−0.474557	+	1.83136i
$848$		0			0
$849$	−5.41938	+	16.6791i	−0.185993	+	0.572427i
$850$		0			0
$851$	8.11362	+	5.89489i	0.278131	+	0.202074i
$852$		0			0
$853$	4.46335	+	13.7368i	0.152822	+	0.470338i	0.997934	−	0.0642517i	$-0.0204660\pi$
$853$	4.46335	+	13.7368i	0.152822	+	0.470338i	−0.845112	+	0.534590i	$0.820466\pi$
$854$		0			0
$855$	6.24424	−	4.53670i	0.213548	−	0.155152i
$856$		0			0
$857$	11.3981			0.389353			0.194676	−	0.980868i	$-0.437634\pi$
$857$	11.3981			0.389353			0.194676	+	0.980868i	$0.437634\pi$
$858$		0			0
$859$	7.56889			0.258247			0.129124	−	0.991629i	$-0.458784\pi$
$859$	7.56889			0.258247			0.129124	+	0.991629i	$0.458784\pi$
$860$		0			0
$861$	6.52811	−	4.74295i	0.222477	−	0.161639i
$862$		0			0
$863$	2.54302	+	7.82661i	0.0865653	+	0.266421i	0.984964	−	0.172760i	$-0.0552686\pi$
$863$	2.54302	+	7.82661i	0.0865653	+	0.266421i	−0.898399	+	0.439181i	$0.855269\pi$
$864$		0			0
$865$	12.7345	+	9.25219i	0.432988	+	0.314584i
$866$		0			0
$867$	−0.934964	+	2.87752i	−0.0317530	+	0.0977258i
$868$		0			0
$869$	−25.5362	+	19.7624i	−0.866255	+	0.670395i
$870$		0			0
$871$	−0.170258	+	0.524000i	−0.00576897	+	0.0177551i
$872$		0			0
$873$	−13.0922	−	9.51201i	−0.443102	−	0.321933i
$874$		0			0
$875$	−15.0548	−	46.3339i	−0.508945	−	1.56637i
$876$		0			0
$877$	38.5872	−	28.0353i	1.30300	−	0.946684i	0.303018	−	0.952985i	$-0.402006\pi$
$877$	38.5872	−	28.0353i	1.30300	−	0.946684i	0.999980	+	0.00630082i	$0.00200563\pi$
$878$		0			0
$879$	−25.9963			−0.876834
$880$		0			0
$881$	−9.69559			−0.326653			−0.163326	−	0.986572i	$-0.552222\pi$
$881$	−9.69559			−0.326653			−0.163326	+	0.986572i	$0.552222\pi$
$882$		0			0
$883$	19.9907	−	14.5241i	0.672740	−	0.488774i	−0.198201	−	0.980161i	$-0.563510\pi$
$883$	19.9907	−	14.5241i	0.672740	−	0.488774i	0.870941	+	0.491387i	$0.163510\pi$
$884$		0			0
$885$	3.56562	+	10.9738i	0.119857	+	0.368882i
$886$		0			0
$887$	27.6235	+	20.0697i	0.927508	+	0.673874i	0.945381	−	0.325966i	$-0.105690\pi$
$887$	27.6235	+	20.0697i	0.927508	+	0.673874i	−0.0178735	+	0.999840i	$0.505690\pi$
$888$		0			0
$889$	−9.45033	+	29.0851i	−0.316954	+	0.975483i
$890$		0			0
$891$	−1.12000	−	3.12180i	−0.0375213	−	0.104584i
$892$		0			0
$893$	−16.8030	+	51.7142i	−0.562289	+	1.73055i
$894$		0			0
$895$	9.66763	+	7.02394i	0.323153	+	0.234784i
$896$		0			0
$897$	0.374045	+	1.15119i	0.0124890	+	0.0384371i
$898$		0			0
$899$	−63.0175	+	45.7849i	−2.10175	+	1.52701i
$900$		0			0
$901$	35.4487			1.18097
$902$		0			0
$903$	−47.0076			−1.56432
$904$		0			0
$905$	−13.9855	+	10.1611i	−0.464894	+	0.337765i
$906$		0			0
$907$	3.48187	+	10.7161i	0.115614	+	0.355822i	0.992075	−	0.125651i	$-0.0401020\pi$
$907$	3.48187	+	10.7161i	0.115614	+	0.355822i	−0.876461	+	0.481473i	$0.840102\pi$
$908$		0			0
$909$	−8.33034	−	6.05234i	−0.276300	−	0.200744i
$910$		0			0
$911$	−16.9472	+	52.1582i	−0.561487	+	1.72808i	0.116678	+	0.993170i	$0.462776\pi$
$911$	−16.9472	+	52.1582i	−0.561487	+	1.72808i	−0.678165	+	0.734910i	$0.737224\pi$
$912$		0			0
$913$	−12.6249	+	43.2756i	−0.417824	+	1.43221i
$914$		0			0
$915$	1.01215	−	3.11508i	0.0334607	−	0.102981i
$916$		0			0
$917$	56.7490	+	41.2306i	1.87402	+	1.36155i
$918$		0			0
$919$	4.21284	+	12.9658i	0.138969	+	0.427702i	0.996186	−	0.0872525i	$-0.0278087\pi$
$919$	4.21284	+	12.9658i	0.138969	+	0.427702i	−0.857217	+	0.514955i	$0.827809\pi$
$920$		0			0
$921$	−5.04844	+	3.66791i	−0.166352	+	0.120862i
$922$		0			0
$923$	−12.0223			−0.395720
$924$		0			0
$925$	−31.2162			−1.02638
$926$		0			0
$927$	1.26089	−	0.916092i	0.0414132	−	0.0300884i
$928$		0			0
$929$	−7.82605	−	24.0861i	−0.256764	−	0.790239i	−0.993477	−	0.114033i	$-0.963623\pi$
$929$	−7.82605	−	24.0861i	−0.256764	−	0.790239i	0.736713	−	0.676206i	$-0.236377\pi$
$930$		0			0
$931$	−101.547	−	73.7785i	−3.32808	−	2.41799i
$932$		0			0
$933$	7.93162	−	24.4110i	0.259670	−	0.799181i
$934$		0			0
$935$	16.4689	−	0.499231i	0.538592	−	0.0163266i
$936$		0			0
$937$	9.14744	−	28.1529i	0.298834	−	0.919716i	−0.683073	−	0.730350i	$-0.739357\pi$
$937$	9.14744	−	28.1529i	0.298834	−	0.919716i	0.981907	−	0.189366i	$-0.0606431\pi$
$938$		0			0
$939$	24.0226	+	17.4534i	0.783947	+	0.569571i
$940$		0			0
$941$	11.9638	+	36.8209i	0.390009	+	1.20033i	0.932781	+	0.360445i	$0.117375\pi$
$941$	11.9638	+	36.8209i	0.390009	+	1.20033i	−0.542771	+	0.839881i	$0.682625\pi$
$942$		0			0
$943$	−1.57867	+	1.14697i	−0.0514087	+	0.0373506i
$944$		0			0
$945$	−5.55663			−0.180757
$946$		0			0
$947$	3.99443			0.129801			0.0649007	−	0.997892i	$-0.479327\pi$
$947$	3.99443			0.129801			0.0649007	+	0.997892i	$0.479327\pi$
$948$		0			0
$949$	−1.81542	+	1.31898i	−0.0589309	+	0.0428158i
$950$		0			0
$951$	8.44598	+	25.9941i	0.273880	+	0.842915i
$952$		0			0
$953$	4.83865	+	3.51549i	0.156739	+	0.113878i	0.663391	−	0.748273i	$-0.269117\pi$
$953$	4.83865	+	3.51549i	0.156739	+	0.113878i	−0.506651	+	0.862151i	$0.669117\pi$
$954$		0			0
$955$	−1.11045	+	3.41761i	−0.0359333	+	0.110591i
$956$		0			0
$957$	23.9803	+	16.3360i	0.775172	+	0.528067i
$958$		0			0
$959$	23.8243	−	73.3236i	0.769326	−	2.36774i
$960$		0			0
$961$	−39.0543	−	28.3746i	−1.25982	−	0.915310i
$962$		0			0
$963$	−4.01453	−	12.3554i	−0.129366	−	0.398149i
$964$		0			0
$965$	−8.70217	+	6.32249i	−0.280133	+	0.203528i
$966$		0			0
$967$	−21.8862			−0.703814			−0.351907	−	0.936035i	$-0.614467\pi$
$967$	−21.8862			−0.703814			−0.351907	+	0.936035i	$0.614467\pi$
$968$		0			0
$969$	−31.1128			−0.999486
$970$		0			0
$971$	21.4911	−	15.6142i	0.689683	−	0.501084i	−0.186873	−	0.982384i	$-0.559835\pi$
$971$	21.4911	−	15.6142i	0.689683	−	0.501084i	0.876556	+	0.481300i	$0.159835\pi$
$972$		0			0
$973$	−14.8441	−	45.6855i	−0.475880	−	1.46461i
$974$		0			0
$975$	−3.04805	−	2.21454i	−0.0976158	−	0.0709220i
$976$		0			0
$977$	4.61239	−	14.1955i	0.147563	−	0.454153i	−0.849768	−	0.527156i	$-0.823258\pi$
$977$	4.61239	−	14.1955i	0.147563	−	0.454153i	0.997332	+	0.0730029i	$0.0232582\pi$
$978$		0			0
$979$	31.7968	+	21.6608i	1.01623	+	0.692282i
$980$		0			0
$981$	2.47797	−	7.62642i	0.0791156	−	0.243493i
$982$		0			0
$983$	−8.90036	−	6.46649i	−0.283877	−	0.206249i	0.436729	−	0.899593i	$-0.356137\pi$
$983$	−8.90036	−	6.46649i	−0.283877	−	0.206249i	−0.720607	+	0.693344i	$0.756137\pi$
$984$		0			0
$985$	1.69911	+	5.22931i	0.0541380	+	0.166620i
$986$		0			0
$987$	31.6702	−	23.0097i	1.00807	−	0.732408i
$988$		0			0
$989$	11.3677			0.361473
$990$		0			0
$991$	−50.6153			−1.60785			−0.803925	−	0.594731i	$-0.797258\pi$
$991$	−50.6153			−1.60785			−0.803925	+	0.594731i	$0.797258\pi$
$992$		0			0
$993$	−14.8074	+	10.7582i	−0.469898	+	0.341401i
$994$		0			0
$995$	−2.50690	−	7.71544i	−0.0794740	−	0.244596i
$996$		0			0
$997$	−11.7538	−	8.53963i	−0.372246	−	0.270453i	0.385895	−	0.922543i	$-0.373893\pi$
$997$	−11.7538	−	8.53963i	−0.372246	−	0.270453i	−0.758142	+	0.652090i	$0.773893\pi$
$998$		0			0
$999$	−2.56034	+	7.87993i	−0.0810057	+	0.249310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.625.4	yes	20
11.5	even	5	inner	1716.2.z.f.313.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.313.4	✓	20	11.5	even	5	inner
1716.2.z.f.625.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.343051 - 1.05580i) q^{5} +(4.04943 + 2.94208i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.343051 - 1.05580i) q^{5} +(4.04943 + 2.94208i) q^{7} +(0.309017 - 0.951057i) q^{9} +(2.74104 + 1.86727i) q^{11} +(0.309017 - 0.951057i) q^{13} +(-0.898118 - 0.652521i) q^{15} +(1.38285 + 4.25598i) q^{17} +(-5.62475 + 4.08662i) q^{19} +5.00536 q^{21} -1.21043 q^{23} +(3.04805 - 2.21454i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(7.07776 + 5.14230i) q^{29} +(-2.75136 + 8.46781i) q^{31} +(3.31510 - 0.100492i) q^{33} +(1.71709 - 5.28467i) q^{35} +(-6.70307 - 4.87006i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(1.30422 - 0.947573i) q^{41} -9.39145 q^{43} -1.11014 q^{45} +(6.32725 - 4.59702i) q^{47} +(5.57889 + 17.1701i) q^{49} +(3.62035 + 2.63034i) q^{51} +(2.44788 - 7.53379i) q^{53} +(1.03115 - 3.53456i) q^{55} +(-2.14846 + 6.61229i) q^{57} +(-8.40880 - 6.10935i) q^{59} +(0.911737 + 2.80604i) q^{61} +(4.04943 - 2.94208i) q^{63} -1.11014 q^{65} -0.550966 q^{67} +(-0.979261 + 0.711475i) q^{69} +(-3.71511 - 11.4339i) q^{71} +(-1.81542 - 1.31898i) q^{73} +(1.16425 - 3.58320i) q^{75} +(5.60599 + 15.6257i) q^{77} +(-3.00854 + 9.25932i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.20016 + 12.9268i) q^{83} +(4.01908 - 2.92003i) q^{85} +8.74860 q^{87} +11.6003 q^{89} +(4.04943 - 2.94208i) q^{91} +(2.75136 + 8.46781i) q^{93} +(6.24424 + 4.53670i) q^{95} +(5.00076 - 15.3908i) q^{97} +(2.62291 - 2.02987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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