LMFDB - Embedded newform 1386.2.bu.a.701.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.3
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.14907 + 1.58155i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.14907 + 1.58155i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} -1.95491i q^{10} +(-3.11122 + 1.14906i) q^{11} +(-3.07823 - 4.23682i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.56776 + 4.04522i) q^{17} +(-3.10464 + 1.00876i) q^{19} +(1.14907 + 1.58155i) q^{20} +(1.84163 - 2.75834i) q^{22} -4.67171i q^{23} +(0.364124 + 1.12066i) q^{25} +(4.98068 + 1.61832i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(1.03594 - 3.18831i) q^{29} +(6.95040 - 5.04976i) q^{31} +1.00000 q^{32} -6.88213 q^{34} +(1.58155 - 1.14907i) q^{35} +(2.00445 - 6.16906i) q^{37} +(1.91877 - 2.64096i) q^{38} +(-1.85923 - 0.604100i) q^{40} +(-0.0804575 - 0.247623i) q^{41} -0.320624i q^{43} +(0.131402 + 3.31402i) q^{44} +(2.74596 + 3.77949i) q^{46} +(-2.31798 + 0.753158i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-0.953290 - 0.692606i) q^{50} +(-4.98068 + 1.61832i) q^{52} +(2.65509 + 3.65441i) q^{53} +(1.75769 - 6.24090i) q^{55} -1.00000i q^{56} +(1.03594 + 3.18831i) q^{58} +(1.57908 + 0.513075i) q^{59} +(3.29887 - 4.54051i) q^{61} +(-2.65482 + 8.17068i) q^{62} +(-0.809017 + 0.587785i) q^{64} +10.2378 q^{65} +1.70439 q^{67} +(5.56776 - 4.04522i) q^{68} +(-0.604100 + 1.85923i) q^{70} +(0.800779 - 1.10218i) q^{71} +(2.13456 + 0.693562i) q^{73} +(2.00445 + 6.16906i) q^{74} +3.26441i q^{76} +(3.31402 - 0.131402i) q^{77} +(-7.06493 - 9.72405i) q^{79} +(1.85923 - 0.604100i) q^{80} +(0.210640 + 0.153039i) q^{82} +(1.89373 + 1.37587i) q^{83} +(-12.7955 + 4.15750i) q^{85} +(0.188458 + 0.259390i) q^{86} +(-2.05424 - 2.60386i) q^{88} -8.82988i q^{89} +(1.61832 + 4.98068i) q^{91} +(-4.44306 - 1.44364i) q^{92} +(1.43259 - 1.97179i) q^{94} +(1.97203 - 6.06929i) q^{95} +(11.6907 - 8.49376i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.14907	+	1.58155i	−0.513878	+	0.707293i	−0.984567	−	0.175006i	$-0.944005\pi$
$5$	−1.14907	+	1.58155i	−0.513878	+	0.707293i	0.470689	+	0.882299i	$0.344005\pi$
$6$		0			0
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$		−	1.95491i		−	0.618196i
$11$	−3.11122	+	1.14906i	−0.938067	+	0.346455i
$11$	−3.11122	+	1.14906i	−0.938067	+	0.346455i
$12$		0			0
$13$	−3.07823	−	4.23682i	−0.853747	−	1.17508i	−0.983025	−	0.183474i	$-0.941266\pi$
$13$	−3.07823	−	4.23682i	−0.853747	−	1.17508i	0.129277	−	0.991608i	$-0.458734\pi$
$14$	0.951057	−	0.309017i	0.254181	−	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.56776	+	4.04522i	1.35038	+	0.981109i	0.998992	+	0.0448797i	$0.0142904\pi$
$17$	5.56776	+	4.04522i	1.35038	+	0.981109i	0.351389	+	0.936230i	$0.385710\pi$
$18$		0			0
$19$	−3.10464	+	1.00876i	−0.712253	+	0.231425i	−0.642661	−	0.766150i	$-0.722170\pi$
$19$	−3.10464	+	1.00876i	−0.712253	+	0.231425i	−0.0695919	+	0.997576i	$0.522170\pi$
$20$	1.14907	+	1.58155i	0.256939	+	0.353646i
$21$		0			0
$22$	1.84163	−	2.75834i	0.392636	−	0.588079i
$23$		−	4.67171i		−	0.974119i	−0.873369	−	0.487059i	$-0.838070\pi$
$23$		−	4.67171i		−	0.974119i	0.873369	−	0.487059i	$-0.161930\pi$
$24$		0			0
$25$	0.364124	+	1.12066i	0.0728249	+	0.224132i
$26$	4.98068	+	1.61832i	0.976792	+	0.317379i
$27$		0			0
$28$	−0.587785	+	0.809017i	−0.111081	+	0.152890i
$29$	1.03594	−	3.18831i	0.192370	−	0.592054i	−0.807627	−	0.589694i	$-0.799249\pi$
$29$	1.03594	−	3.18831i	0.192370	−	0.592054i	0.999997	−	0.00236079i	$-0.000751464\pi$
$30$		0			0
$31$	6.95040	−	5.04976i	1.24833	−	0.906964i	0.250205	−	0.968193i	$-0.419502\pi$
$31$	6.95040	−	5.04976i	1.24833	−	0.906964i	0.998124	+	0.0612294i	$0.0195021\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.88213			−1.18028
$35$	1.58155	−	1.14907i	0.267331	−	0.194228i
$36$		0			0
$37$	2.00445	−	6.16906i	0.329530	−	1.01419i	−0.639825	−	0.768521i	$-0.720993\pi$
$37$	2.00445	−	6.16906i	0.329530	−	1.01419i	0.969354	−	0.245667i	$-0.0790069\pi$
$38$	1.91877	−	2.64096i	0.311266	−	0.428421i
$39$		0			0
$40$	−1.85923	−	0.604100i	−0.293970	−	0.0955166i
$41$	−0.0804575	−	0.247623i	−0.0125653	−	0.0386722i	0.944577	−	0.328289i	$-0.106472\pi$
$41$	−0.0804575	−	0.247623i	−0.0125653	−	0.0386722i	−0.957143	+	0.289617i	$0.906472\pi$
$42$		0			0
$43$		−	0.320624i		−	0.0488947i	−0.999701	−	0.0244473i	$-0.992217\pi$
$43$		−	0.320624i		−	0.0488947i	0.999701	−	0.0244473i	$-0.00778260\pi$
$44$	0.131402	+	3.31402i	0.0198097	+	0.499607i
$45$		0			0
$46$	2.74596	+	3.77949i	0.404870	+	0.557256i
$47$	−2.31798	+	0.753158i	−0.338112	+	0.109859i	−0.473152	−	0.880981i	$-0.656884\pi$
$47$	−2.31798	+	0.753158i	−0.338112	+	0.109859i	0.135040	+	0.990840i	$0.456884\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−0.953290	−	0.692606i	−0.134816	−	0.0979493i
$51$		0			0
$52$	−4.98068	+	1.61832i	−0.690696	+	0.224421i
$53$	2.65509	+	3.65441i	0.364704	+	0.501972i	0.951452	−	0.307797i	$-0.0995919\pi$
$53$	2.65509	+	3.65441i	0.364704	+	0.501972i	−0.586748	+	0.809770i	$0.699592\pi$
$54$		0			0
$55$	1.75769	−	6.24090i	0.237007	−	0.841523i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	1.03594	+	3.18831i	0.136026	+	0.418646i
$59$	1.57908	+	0.513075i	0.205579	+	0.0667967i	0.409996	−	0.912087i	$-0.365530\pi$
$59$	1.57908	+	0.513075i	0.205579	+	0.0667967i	−0.204417	+	0.978884i	$0.565530\pi$
$60$		0			0
$61$	3.29887	−	4.54051i	0.422377	−	0.581353i	−0.543805	−	0.839211i	$-0.683017\pi$
$61$	3.29887	−	4.54051i	0.422377	−	0.581353i	0.966183	+	0.257859i	$0.0830170\pi$
$62$	−2.65482	+	8.17068i	−0.337162	+	1.03768i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	10.2378			1.26985
$66$		0			0
$67$	1.70439			0.208224			0.104112	−	0.994566i	$-0.466800\pi$
$67$	1.70439			0.208224			0.104112	+	0.994566i	$0.466800\pi$
$68$	5.56776	−	4.04522i	0.675191	−	0.490555i
$69$		0			0
$70$	−0.604100	+	1.85923i	−0.0722038	+	0.222220i
$71$	0.800779	−	1.10218i	0.0950350	−	0.130805i	−0.758852	−	0.651264i	$-0.774239\pi$
$71$	0.800779	−	1.10218i	0.0950350	−	0.130805i	0.853887	+	0.520459i	$0.174239\pi$
$72$		0			0
$73$	2.13456	+	0.693562i	0.249832	+	0.0811753i	0.431256	−	0.902230i	$-0.358071\pi$
$73$	2.13456	+	0.693562i	0.249832	+	0.0811753i	−0.181424	+	0.983405i	$0.558071\pi$
$74$	2.00445	+	6.16906i	0.233013	+	0.717139i
$75$		0			0
$76$			3.26441i			0.374454i
$77$	3.31402	−	0.131402i	0.377668	−	0.0149747i
$78$		0			0
$79$	−7.06493	−	9.72405i	−0.794867	−	1.09404i	−0.993485	−	0.113964i	$-0.963645\pi$
$79$	−7.06493	−	9.72405i	−0.794867	−	1.09404i	0.198618	−	0.980077i	$-0.436355\pi$
$80$	1.85923	−	0.604100i	0.207868	−	0.0675404i
$81$		0			0
$82$	0.210640	+	0.153039i	0.0232613	+	0.0169004i
$83$	1.89373	+	1.37587i	0.207864	+	0.151022i	0.686847	−	0.726802i	$-0.258994\pi$
$83$	1.89373	+	1.37587i	0.207864	+	0.151022i	−0.478983	+	0.877824i	$0.658994\pi$
$84$		0			0
$85$	−12.7955	+	4.15750i	−1.38786	+	0.450944i
$86$	0.188458	+	0.259390i	0.0203219	+	0.0279707i
$87$		0			0
$88$	−2.05424	−	2.60386i	−0.218983	−	0.277573i
$89$		−	8.82988i		−	0.935965i	−0.883738	−	0.467983i	$-0.844981\pi$
$89$		−	8.82988i		−	0.935965i	0.883738	−	0.467983i	$-0.155019\pi$
$90$		0			0
$91$	1.61832	+	4.98068i	0.169646	+	0.522117i
$92$	−4.44306	−	1.44364i	−0.463221	−	0.150510i
$93$		0			0
$94$	1.43259	−	1.97179i	0.147761	−	0.203375i
$95$	1.97203	−	6.06929i	0.202326	−	0.622696i
$96$		0			0
$97$	11.6907	−	8.49376i	1.18701	−	0.862411i	0.194062	−	0.980989i	$-0.437834\pi$
$97$	11.6907	−	8.49376i	1.18701	−	0.862411i	0.992945	+	0.118579i	$0.0378338\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	1.17833			0.117833
$101$	11.1395	−	8.09333i	1.10842	−	0.805317i	0.126009	−	0.992029i	$-0.459783\pi$
$101$	11.1395	−	8.09333i	1.10842	−	0.805317i	0.982415	+	0.186713i	$0.0597833\pi$
$102$		0			0
$103$	3.73892	−	11.5072i	0.368407	−	1.13384i	−0.579414	−	0.815034i	$-0.696718\pi$
$103$	3.73892	−	11.5072i	0.368407	−	1.13384i	0.947820	−	0.318805i	$-0.103282\pi$
$104$	3.07823	−	4.23682i	0.301845	−	0.415454i
$105$		0			0
$106$	−4.29602	−	1.39586i	−0.417266	−	0.135578i
$107$	0.560019	+	1.72356i	0.0541391	+	0.166623i	0.974470	−	0.224518i	$-0.0720806\pi$
$107$	0.560019	+	1.72356i	0.0541391	+	0.166623i	−0.920331	+	0.391141i	$0.872081\pi$
$108$		0			0
$109$			19.2419i			1.84304i	0.388327	+	0.921522i	$0.373053\pi$
$109$			19.2419i			1.84304i	−0.388327	+	0.921522i	$0.626947\pi$
$110$	2.24631	+	6.08214i	0.214177	+	0.579910i
$111$		0			0
$112$	0.587785	+	0.809017i	0.0555405	+	0.0764449i
$113$	−6.10633	+	1.98407i	−0.574435	+	0.186645i	−0.581806	−	0.813328i	$-0.697654\pi$
$113$	−6.10633	+	1.98407i	−0.574435	+	0.186645i	0.00737115	+	0.999973i	$0.497654\pi$
$114$		0			0
$115$	7.38856	+	5.36811i	0.688987	+	0.500578i
$116$	−2.71214	−	1.97048i	−0.251816	−	0.182955i
$117$		0			0
$118$	−1.57908	+	0.513075i	−0.145366	+	0.0472324i
$119$	−4.04522	−	5.56776i	−0.370824	−	0.510396i
$120$		0			0
$121$	8.35932	−	7.14995i	0.759938	−	0.649995i
$122$			5.61238i			0.508121i
$123$		0			0
$124$	−2.65482	−	8.17068i	−0.238409	−	0.733749i
$125$	−11.4869	−	3.73233i	−1.02742	−	0.333830i
$126$		0			0
$127$	7.11660	−	9.79516i	0.631496	−	0.869180i	−0.366630	−	0.930367i	$-0.619489\pi$
$127$	7.11660	−	9.79516i	0.631496	−	0.869180i	0.998126	+	0.0611868i	$0.0194885\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	−8.28259	+	6.01766i	−0.726432	+	0.527783i
$131$	−5.58096			−0.487611			−0.243805	−	0.969824i	$-0.578396\pi$
$131$	−5.58096			−0.487611			−0.243805	+	0.969824i	$0.578396\pi$
$132$		0			0
$133$	3.26441			0.283060
$134$	−1.37888	+	1.00181i	−0.119117	+	0.0865436i
$135$		0			0
$136$	−2.12670	+	6.54530i	−0.182363	+	0.561255i
$137$	12.4698	−	17.1631i	1.06536	−	1.46635i	0.190679	−	0.981653i	$-0.438931\pi$
$137$	12.4698	−	17.1631i	1.06536	−	1.46635i	0.874684	−	0.484693i	$-0.161069\pi$
$138$		0			0
$139$	8.60931	+	2.79733i	0.730232	+	0.237267i	0.650454	−	0.759546i	$-0.274579\pi$
$139$	8.60931	+	2.79733i	0.730232	+	0.237267i	0.0797783	+	0.996813i	$0.474579\pi$
$140$	−0.604100	−	1.85923i	−0.0510558	−	0.157134i
$141$		0			0
$142$			1.36237i			0.114327i
$143$	14.4454	+	9.64459i	1.20798	+	0.806521i
$144$		0			0
$145$	3.85212	+	5.30198i	0.319901	+	0.440306i
$146$	−2.13456	+	0.693562i	−0.176658	+	0.0573996i
$147$		0			0
$148$	−5.24772	−	3.81269i	−0.431360	−	0.313401i
$149$	−6.42716	−	4.66960i	−0.526533	−	0.382549i	0.292526	−	0.956258i	$-0.405504\pi$
$149$	−6.42716	−	4.66960i	−0.526533	−	0.382549i	−0.819059	+	0.573709i	$0.805504\pi$
$150$		0			0
$151$	8.37006	−	2.71960i	0.681146	−	0.221318i	0.0520487	−	0.998645i	$-0.483425\pi$
$151$	8.37006	−	2.71960i	0.681146	−	0.221318i	0.629097	+	0.777327i	$0.283425\pi$
$152$	−1.91877	−	2.64096i	−0.155633	−	0.214210i
$153$		0			0
$154$	−2.60386	+	2.05424i	−0.209825	+	0.165535i
$155$			16.7949i			1.34900i
$156$		0			0
$157$	−3.33097	−	10.2517i	−0.265841	−	0.818173i	−0.991499	−	0.130118i	$-0.958465\pi$
$157$	−3.33097	−	10.2517i	−0.265841	−	0.818173i	0.725658	−	0.688056i	$-0.241535\pi$
$158$	11.4313	+	3.71426i	0.909426	+	0.295490i
$159$		0			0
$160$	−1.14907	+	1.58155i	−0.0908417	+	0.125033i
$161$	−1.44364	+	4.44306i	−0.113775	+	0.350162i
$162$		0			0
$163$	−5.06912	+	3.68293i	−0.397044	+	0.288469i	−0.768336	−	0.640047i	$-0.778915\pi$
$163$	−5.06912	+	3.68293i	−0.397044	+	0.288469i	0.371292	+	0.928516i	$0.378915\pi$
$164$	−0.260366			−0.0203312
$165$		0			0
$166$	−2.34078			−0.181680
$167$	−11.7727	+	8.55336i	−0.910998	+	0.661879i	−0.941267	−	0.337663i	$-0.890364\pi$
$167$	−11.7727	+	8.55336i	−0.910998	+	0.661879i	0.0302691	+	0.999542i	$0.490364\pi$
$168$		0			0
$169$	−4.45792	+	13.7201i	−0.342917	+	1.05539i
$170$	7.90803	−	10.8845i	0.606518	−	0.834801i
$171$		0			0
$172$	−0.304931	−	0.0990782i	−0.0232508	−	0.00755464i
$173$	0.462448	+	1.42327i	0.0351593	+	0.108209i	0.967096	−	0.254412i	$-0.0818819\pi$
$173$	0.462448	+	1.42327i	0.0351593	+	0.108209i	−0.931937	+	0.362621i	$0.881882\pi$
$174$		0			0
$175$		−	1.17833i		−	0.0890735i
$176$	3.19243	+	0.899118i	0.240638	+	0.0677735i
$177$		0			0
$178$	5.19007	+	7.14352i	0.389012	+	0.535429i
$179$	−18.5406	+	6.02420i	−1.38579	+	0.450270i	−0.904568	−	0.426330i	$-0.859806\pi$
$179$	−18.5406	+	6.02420i	−1.38579	+	0.450270i	−0.481220	+	0.876600i	$0.659806\pi$
$180$		0			0
$181$	13.5248	+	9.82635i	1.00529	+	0.730387i	0.963216	−	0.268727i	$-0.0866031\pi$
$181$	13.5248	+	9.82635i	1.00529	+	0.730387i	0.0420753	+	0.999114i	$0.486603\pi$
$182$	−4.23682	−	3.07823i	−0.314054	−	0.228174i
$183$		0			0
$184$	4.44306	−	1.44364i	0.327547	−	0.106426i
$185$	7.45346	+	10.2588i	0.547989	+	0.754243i
$186$		0			0
$187$	−21.9707	−	6.18785i	−1.60666	−	0.452500i
$188$			2.43727i			0.177756i
$189$		0			0
$190$	1.97203	+	6.06929i	0.143066	+	0.440312i
$191$	12.4400	+	4.04200i	0.900127	+	0.292469i	0.722289	−	0.691591i	$-0.243090\pi$
$191$	12.4400	+	4.04200i	0.900127	+	0.292469i	0.177837	+	0.984060i	$0.443090\pi$
$192$		0			0
$193$	0.344321	−	0.473918i	0.0247848	−	0.0341133i	−0.796445	−	0.604711i	$-0.793289\pi$
$193$	0.344321	−	0.473918i	0.0247848	−	0.0341133i	0.821230	+	0.570598i	$0.193289\pi$
$194$	−4.46543	+	13.7432i	−0.320599	+	0.986704i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	−13.1723			−0.938485			−0.469243	−	0.883069i	$-0.655473\pi$
$197$	−13.1723			−0.938485			−0.469243	+	0.883069i	$0.655473\pi$
$198$		0			0
$199$	18.0436			1.27908			0.639540	−	0.768758i	$-0.279125\pi$
$199$	18.0436			1.27908			0.639540	+	0.768758i	$0.279125\pi$
$200$	−0.953290	+	0.692606i	−0.0674078	+	0.0489746i
$201$		0			0
$202$	−4.25492	+	13.0953i	−0.299375	+	0.921381i
$203$	−1.97048	+	2.71214i	−0.138301	+	0.190355i
$204$		0			0
$205$	0.484080	+	0.157287i	0.0338096	+	0.0109854i
$206$	3.73892	+	11.5072i	0.260503	+	0.801745i
$207$		0			0
$208$			5.23700i			0.363120i
$209$	8.50008	−	6.70588i	0.587963	−	0.463856i
$210$		0			0
$211$	−14.5077	−	19.9681i	−0.998751	−	1.37466i	−0.926088	−	0.377306i	$-0.876850\pi$
$211$	−14.5077	−	19.9681i	−0.998751	−	1.37466i	−0.0726627	−	0.997357i	$-0.523150\pi$
$212$	4.29602	−	1.39586i	0.295052	−	0.0958682i
$213$		0			0
$214$	−1.46615	−	1.06522i	−0.100224	−	0.0728169i
$215$	0.507084	+	0.368418i	0.0345828	+	0.0251259i
$216$		0			0
$217$	−8.17068	+	2.65482i	−0.554662	+	0.180221i
$218$	−11.3101	−	15.5671i	−0.766018	−	1.05433i
$219$		0			0
$220$	−5.39229	−	3.60021i	−0.363548	−	0.242726i
$221$		−	36.0417i		−	2.42443i
$222$		0			0
$223$	5.28842	+	16.2761i	0.354139	+	1.08993i	0.956507	+	0.291709i	$0.0942240\pi$
$223$	5.28842	+	16.2761i	0.354139	+	1.08993i	−0.602368	+	0.798219i	$0.705776\pi$
$224$	−0.951057	−	0.309017i	−0.0635451	−	0.0206471i
$225$		0			0
$226$	3.77392	−	5.19435i	0.251037	−	0.345523i
$227$	−0.728652	+	2.24256i	−0.0483623	+	0.148844i	−0.972321	−	0.233647i	$-0.924934\pi$
$227$	−0.728652	+	2.24256i	−0.0483623	+	0.148844i	0.923959	+	0.382491i	$0.124934\pi$
$228$		0			0
$229$	2.84743	−	2.06878i	0.188163	−	0.136709i	−0.489715	−	0.871882i	$-0.662899\pi$
$229$	2.84743	−	2.06878i	0.188163	−	0.136709i	0.677879	+	0.735174i	$0.262899\pi$
$230$	−9.13277			−0.602197
$231$		0			0
$232$	3.35239			0.220095
$233$	−12.4768	+	9.06495i	−0.817384	+	0.593864i	−0.915962	−	0.401265i	$-0.868571\pi$
$233$	−12.4768	+	9.06495i	−0.817384	+	0.593864i	0.0985777	+	0.995129i	$0.468571\pi$
$234$		0			0
$235$	1.47236	−	4.53144i	0.0960459	−	0.295599i
$236$	0.975927	−	1.34325i	0.0635275	−	0.0874381i
$237$		0			0
$238$	6.54530	+	2.12670i	0.424269	+	0.137853i
$239$	−7.27591	−	22.3929i	−0.470639	−	1.44848i	−0.851750	−	0.523949i	$-0.824458\pi$
$239$	−7.27591	−	22.3929i	−0.470639	−	1.44848i	0.381110	−	0.924530i	$-0.375542\pi$
$240$		0			0
$241$		−	8.11384i		−	0.522658i	−0.965250	−	0.261329i	$-0.915839\pi$
$241$		−	8.11384i		−	0.522658i	0.965250	−	0.261329i	$-0.0841608\pi$
$242$	−2.56020	+	10.6979i	−0.164576	+	0.687688i
$243$		0			0
$244$	−3.29887	−	4.54051i	−0.211189	−	0.290676i
$245$	−1.85923	+	0.604100i	−0.118782	+	0.0385945i
$246$		0			0
$247$	13.8307	+	10.0486i	0.880028	+	0.639377i
$248$	6.95040	+	5.04976i	0.441351	+	0.320660i
$249$		0			0
$250$	11.4869	−	3.73233i	0.726497	−	0.236053i
$251$	−10.5149	−	14.4725i	−0.663694	−	0.913496i	0.335903	−	0.941897i	$-0.390959\pi$
$251$	−10.5149	−	14.4725i	−0.663694	−	0.913496i	−0.999597	+	0.0284003i	$0.990959\pi$
$252$		0			0
$253$	5.36807	+	14.5347i	0.337488	+	0.913788i
$254$			12.1075i			0.759691i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	19.4257	+	6.31180i	1.21174	+	0.393719i	0.844069	−	0.536235i	$-0.180154\pi$
$257$	19.4257	+	6.31180i	1.21174	+	0.393719i	0.367675	+	0.929954i	$0.380154\pi$
$258$		0			0
$259$	−3.81269	+	5.24772i	−0.236909	+	0.326077i
$260$	3.16367	−	9.73677i	0.196202	−	0.603849i
$261$		0			0
$262$	4.51509	−	3.28041i	0.278943	−	0.202664i
$263$	−22.0512			−1.35973			−0.679866	−	0.733336i	$-0.737962\pi$
$263$	−22.0512			−1.35973			−0.679866	+	0.733336i	$0.737962\pi$
$264$		0			0
$265$	−8.83053			−0.542455
$266$	−2.64096	+	1.91877i	−0.161928	+	0.117648i
$267$		0			0
$268$	0.526685	−	1.62097i	0.0321724	−	0.0990165i
$269$	17.8555	−	24.5760i	1.08867	−	1.49842i	0.239063	−	0.971004i	$-0.423160\pi$
$269$	17.8555	−	24.5760i	1.08867	−	1.49842i	0.849605	−	0.527419i	$-0.176840\pi$
$270$		0			0
$271$	−16.2268	−	5.27241i	−0.985709	−	0.320276i	−0.228568	−	0.973528i	$-0.573404\pi$
$271$	−16.2268	−	5.27241i	−0.985709	−	0.320276i	−0.757141	+	0.653252i	$0.773404\pi$
$272$	−2.12670	−	6.54530i	−0.128950	−	0.396867i
$273$		0			0
$274$			21.2148i			1.28163i
$275$	−2.42057	−	3.06821i	−0.145966	−	0.185020i
$276$		0			0
$277$	15.7626	+	21.6953i	0.947081	+	1.30354i	0.952812	+	0.303561i	$0.0981757\pi$
$277$	15.7626	+	21.6953i	0.947081	+	1.30354i	−0.00573112	+	0.999984i	$0.501824\pi$
$278$	−8.60931	+	2.79733i	−0.516352	+	0.167773i
$279$		0			0
$280$	1.58155	+	1.14907i	0.0945160	+	0.0686699i
$281$	−23.4861	−	17.0636i	−1.40106	−	1.01793i	−0.994547	−	0.104288i	$-0.966744\pi$
$281$	−23.4861	−	17.0636i	−1.40106	−	1.01793i	−0.406516	−	0.913644i	$-0.633256\pi$
$282$		0			0
$283$	−4.15948	+	1.35150i	−0.247255	+	0.0803381i	−0.430023	−	0.902818i	$-0.641494\pi$
$283$	−4.15948	+	1.35150i	−0.247255	+	0.0803381i	0.182767	+	0.983156i	$0.441494\pi$
$284$	−0.800779	−	1.10218i	−0.0475175	−	0.0654023i
$285$		0			0
$286$	−17.3555	+	0.688154i	−1.02625	+	0.0406914i
$287$			0.260366i			0.0153689i
$288$		0			0
$289$	9.38292	+	28.8777i	0.551937	+	1.69869i
$290$	−6.23286	−	2.02518i	−0.366006	−	0.118923i
$291$		0			0
$292$	1.31923	−	1.81577i	0.0772023	−	0.106260i
$293$	−3.17574	+	9.77392i	−0.185529	+	0.570999i	−0.999957	−	0.00926552i	$-0.997051\pi$
$293$	−3.17574	+	9.77392i	−0.185529	+	0.570999i	0.814428	+	0.580264i	$0.197051\pi$
$294$		0			0
$295$	−2.62593	+	1.90785i	−0.152888	+	0.111079i
$296$	6.48654			0.377022
$297$		0			0
$298$	7.94441			0.460207
$299$	−19.7932	+	14.3806i	−1.14467	+	0.831651i
$300$		0			0
$301$	−0.0990782	+	0.304931i	−0.00571077	+	0.0175759i
$302$	−5.17298	+	7.12000i	−0.297672	+	0.409710i
$303$		0			0
$304$	3.10464	+	1.00876i	0.178063	+	0.0578563i
$305$	3.39044	+	10.4347i	0.194136	+	0.597489i
$306$		0			0
$307$			5.94602i			0.339357i	0.985499	+	0.169679i	$0.0542729\pi$
$307$			5.94602i			0.339357i	−0.985499	+	0.169679i	$0.945727\pi$
$308$	0.899118	−	3.19243i	0.0512320	−	0.181905i
$309$		0			0
$310$	−9.87182	−	13.5874i	−0.560682	−	0.771712i
$311$	−11.5815	+	3.76307i	−0.656729	+	0.213384i	−0.618379	−	0.785880i	$-0.712210\pi$
$311$	−11.5815	+	3.76307i	−0.656729	+	0.213384i	−0.0383503	+	0.999264i	$0.512210\pi$
$312$		0			0
$313$	−6.48792	−	4.71375i	−0.366719	−	0.266437i	0.389130	−	0.921183i	$-0.372776\pi$
$313$	−6.48792	−	4.71375i	−0.366719	−	0.266437i	−0.755849	+	0.654746i	$0.772776\pi$
$314$	8.72060	+	6.33589i	0.492132	+	0.357555i
$315$		0			0
$316$	−11.4313	+	3.71426i	−0.643061	+	0.208943i
$317$	17.9866	+	24.7564i	1.01023	+	1.39046i	0.918835	+	0.394643i	$0.129132\pi$
$317$	17.9866	+	24.7564i	1.01023	+	1.39046i	0.0913923	+	0.995815i	$0.470868\pi$
$318$		0			0
$319$	0.440512	+	11.1099i	0.0246639	+	0.622034i
$320$		−	1.95491i		−	0.109283i
$321$		0			0
$322$	−1.44364	−	4.44306i	−0.0804508	−	0.247602i
$323$	−21.3665	−	6.94241i	−1.18887	−	0.386286i
$324$		0			0
$325$	3.62717	−	4.99238i	0.201199	−	0.276927i
$326$	1.93623	−	5.95911i	0.107238	−	0.330044i
$327$		0			0
$328$	0.210640	−	0.153039i	0.0116307	−	0.00845018i
$329$	2.43727			0.134371
$330$		0			0
$331$	−31.9390			−1.75553			−0.877763	−	0.479096i	$-0.840965\pi$
$331$	−31.9390			−1.75553			−0.877763	+	0.479096i	$0.840965\pi$
$332$	1.89373	−	1.37587i	0.103932	−	0.0755109i
$333$		0			0
$334$	4.49677	−	13.8396i	0.246052	−	0.757271i
$335$	−1.95846	+	2.69558i	−0.107002	+	0.147275i
$336$		0			0
$337$	−9.39201	−	3.05165i	−0.511615	−	0.166234i	0.0418214	−	0.999125i	$-0.486684\pi$
$337$	−9.39201	−	3.05165i	−0.511615	−	0.166234i	−0.553437	+	0.832891i	$0.686684\pi$
$338$	−4.45792	−	13.7201i	−0.242479	−	0.746273i
$339$		0			0
$340$			13.4539i			0.729643i
$341$	−15.8217	+	23.6973i	−0.856794	+	1.28328i
$342$		0			0
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	0.304931	−	0.0990782i	0.0164408	−	0.00534194i
$345$		0			0
$346$	−1.21071	−	0.879629i	−0.0650879	−	0.0472892i
$347$	−16.7859	−	12.1957i	−0.901116	−	0.654699i	0.0376362	−	0.999292i	$-0.488017\pi$
$347$	−16.7859	−	12.1957i	−0.901116	−	0.654699i	−0.938752	+	0.344592i	$0.888017\pi$
$348$		0			0
$349$	−26.4949	+	8.60871i	−1.41824	+	0.460814i	−0.915042	−	0.403358i	$-0.867843\pi$
$349$	−26.4949	+	8.60871i	−1.41824	+	0.460814i	−0.503197	+	0.864172i	$0.667843\pi$
$350$	0.692606	+	0.953290i	0.0370213	+	0.0509555i
$351$		0			0
$352$	−3.11122	+	1.14906i	−0.165828	+	0.0612451i
$353$			15.8540i			0.843826i	0.906636	+	0.421913i	$0.138641\pi$
$353$			15.8540i			0.843826i	−0.906636	+	0.421913i	$0.861359\pi$
$354$		0			0
$355$	0.823006	+	2.53295i	0.0436806	+	0.134435i
$356$	−8.39771	−	2.72858i	−0.445078	−	0.144615i
$357$		0			0
$358$	11.4587	−	15.7716i	0.605612	−	0.833553i
$359$	1.13824	−	3.50315i	0.0600742	−	0.184889i	−0.916516	−	0.399998i	$-0.869011\pi$
$359$	1.13824	−	3.50315i	0.0600742	−	0.184889i	0.976590	+	0.215109i	$0.0690107\pi$
$360$		0			0
$361$	−6.75013	+	4.90426i	−0.355270	+	0.258119i
$362$	−16.7176			−0.878657
$363$		0			0
$364$	5.23700			0.274493
$365$	−3.54966	+	2.57898i	−0.185798	+	0.134990i
$366$		0			0
$367$	8.49646	−	26.1494i	0.443512	−	1.36499i	−0.440596	−	0.897705i	$-0.645233\pi$
$367$	8.49646	−	26.1494i	0.443512	−	1.36499i	0.884108	−	0.467283i	$-0.154767\pi$
$368$	−2.74596	+	3.77949i	−0.143143	+	0.197020i
$369$		0			0
$370$	−12.0600	−	3.91852i	−0.626967	−	0.203714i
$371$	−1.39586	−	4.29602i	−0.0724695	−	0.223038i
$372$		0			0
$373$			30.7864i			1.59406i	0.603940	+	0.797030i	$0.293597\pi$
$373$			30.7864i			1.59406i	−0.603940	+	0.797030i	$0.706403\pi$
$374$	21.4118	−	7.90799i	1.10718	−	0.408912i
$375$		0			0
$376$	−1.43259	−	1.97179i	−0.0738803	−	0.101687i
$377$	−16.6972	+	5.42524i	−0.859948	+	0.279414i
$378$		0			0
$379$	18.2132	+	13.2326i	0.935547	+	0.679715i	0.947345	−	0.320216i	$-0.103755\pi$
$379$	18.2132	+	13.2326i	0.935547	+	0.679715i	−0.0117977	+	0.999930i	$0.503755\pi$
$380$	−5.16284	−	3.75103i	−0.264848	−	0.192424i
$381$		0			0
$382$	−12.4400	+	4.04200i	−0.636486	+	0.206807i
$383$	−2.75854	−	3.79681i	−0.140955	−	0.194008i	0.732703	−	0.680549i	$-0.238258\pi$
$383$	−2.75854	−	3.79681i	−0.140955	−	0.194008i	−0.873658	+	0.486541i	$0.838258\pi$
$384$		0			0
$385$	−3.60021	+	5.39229i	−0.183484	+	0.274817i
$386$			0.585794i			0.0298162i
$387$		0			0
$388$	−4.46543	−	13.7432i	−0.226698	−	0.697705i
$389$	−33.1759	−	10.7795i	−1.68208	−	0.546543i	−0.696771	−	0.717294i	$-0.745381\pi$
$389$	−33.1759	−	10.7795i	−1.68208	−	0.546543i	−0.985314	+	0.170751i	$0.945381\pi$
$390$		0			0
$391$	18.8981	−	26.0110i	0.955717	−	1.31543i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	10.6566	−	7.74246i	0.536871	−	0.390060i
$395$	23.4972			1.18227
$396$		0			0
$397$	11.1675			0.560479			0.280239	−	0.959930i	$-0.409586\pi$
$397$	11.1675			0.560479			0.280239	+	0.959930i	$0.409586\pi$
$398$	−14.5976	+	10.6058i	−0.731712	+	0.531620i
$399$		0			0
$400$	0.364124	−	1.12066i	0.0182062	−	0.0560330i
$401$	5.17312	−	7.12019i	0.258333	−	0.355565i	−0.660075	−	0.751200i	$-0.729475\pi$
$401$	5.17312	−	7.12019i	0.258333	−	0.355565i	0.918408	+	0.395635i	$0.129475\pi$
$402$		0			0
$403$	−42.7898	−	13.9033i	−2.13151	−	0.692571i
$404$	−4.25492	−	13.0953i	−0.211690	−	0.651515i
$405$		0			0
$406$		−	3.35239i		−	0.166376i
$407$	0.852347	+	21.4965i	0.0422493	+	1.06554i
$408$		0			0
$409$	−17.4107	−	23.9638i	−0.860905	−	1.18493i	−0.981353	−	0.192214i	$-0.938433\pi$
$409$	−17.4107	−	23.9638i	−0.860905	−	1.18493i	0.120448	−	0.992720i	$-0.461567\pi$
$410$	−0.484080	+	0.157287i	−0.0239070	+	0.00776785i
$411$		0			0
$412$	−9.78861	−	7.11184i	−0.482250	−	0.350375i
$413$	−1.34325	−	0.975927i	−0.0660970	−	0.0480223i
$414$		0			0
$415$	−4.35204	+	1.41406i	−0.213633	+	0.0694136i
$416$	−3.07823	−	4.23682i	−0.150923	−	0.207727i
$417$		0			0
$418$	−2.93509	+	10.4214i	−0.143560	+	0.509727i
$419$		−	35.5244i		−	1.73548i	−0.497016	−	0.867741i	$-0.665571\pi$
$419$		−	35.5244i		−	1.73548i	0.497016	−	0.867741i	$-0.334429\pi$
$420$		0			0
$421$	−5.63824	−	17.3527i	−0.274791	−	0.845720i	−0.989275	−	0.146068i	$-0.953338\pi$
$421$	−5.63824	−	17.3527i	−0.274791	−	0.845720i	0.714483	−	0.699652i	$-0.246662\pi$
$422$	23.4739	+	7.62715i	1.14269	+	0.371284i
$423$		0			0
$424$	−2.65509	+	3.65441i	−0.128942	+	0.177474i
$425$	−2.50595	+	7.71253i	−0.121557	+	0.374113i
$426$		0			0
$427$	−4.54051	+	3.29887i	−0.219731	+	0.159644i
$428$	1.81226			0.0875989
$429$		0			0
$430$	−0.626790			−0.0302265
$431$	−27.3723	+	19.8871i	−1.31848	+	0.957930i	−0.318528	+	0.947913i	$0.603188\pi$
$431$	−27.3723	+	19.8871i	−1.31848	+	0.957930i	−0.999950	+	0.0100167i	$0.996812\pi$
$432$		0			0
$433$	−2.25019	+	6.92536i	−0.108137	+	0.332812i	−0.990454	−	0.137844i	$-0.955983\pi$
$433$	−2.25019	+	6.92536i	−0.108137	+	0.332812i	0.882317	+	0.470656i	$0.155983\pi$
$434$	5.04976	−	6.95040i	0.242396	−	0.333630i
$435$		0			0
$436$	18.3002	+	5.94609i	0.876419	+	0.284766i
$437$	4.71263	+	14.5040i	0.225436	+	0.693819i
$438$		0			0
$439$		−	28.9329i		−	1.38089i	−0.723385	−	0.690445i	$-0.757415\pi$
$439$		−	28.9329i		−	1.38089i	0.723385	−	0.690445i	$-0.242585\pi$
$440$	6.47861	−	0.256880i	0.308856	−	0.0122463i
$441$		0			0
$442$	21.1848	+	29.1584i	1.00766	+	1.38692i
$443$	12.5921	−	4.09143i	0.598270	−	0.194390i	0.00580119	−	0.999983i	$-0.498153\pi$
$443$	12.5921	−	4.09143i	0.598270	−	0.194390i	0.592469	+	0.805594i	$0.298153\pi$
$444$		0			0
$445$	13.9649	+	10.1461i	0.662001	+	0.480972i
$446$	−13.8453	−	10.0592i	−0.655593	−	0.476316i
$447$		0			0
$448$	0.951057	−	0.309017i	0.0449332	−	0.0145997i
$449$	17.6543	+	24.2991i	0.833159	+	1.14674i	0.987327	+	0.158700i	$0.0507302\pi$
$449$	17.6543	+	24.2991i	0.833159	+	1.14674i	−0.154168	+	0.988045i	$0.549270\pi$
$450$		0			0
$451$	0.534854	+	0.677957i	0.0251853	+	0.0319237i
$452$			6.42057i			0.301998i
$453$		0			0
$454$	−0.728652	−	2.24256i	−0.0341973	−	0.105249i
$455$	−9.73677	−	3.16367i	−0.456467	−	0.148315i
$456$		0			0
$457$	6.32507	−	8.70571i	0.295874	−	0.407236i	−0.635037	−	0.772482i	$-0.719015\pi$
$457$	6.32507	−	8.70571i	0.295874	−	0.407236i	0.930911	+	0.365246i	$0.119015\pi$
$458$	−1.08762	+	3.34735i	−0.0508212	+	0.156412i
$459$		0			0
$460$	7.38856	−	5.36811i	0.344494	−	0.250289i
$461$	34.3208			1.59848			0.799240	−	0.601012i	$-0.205236\pi$
$461$	34.3208			1.59848			0.799240	+	0.601012i	$0.205236\pi$
$462$		0			0
$463$	−9.62362			−0.447248			−0.223624	−	0.974676i	$-0.571789\pi$
$463$	−9.62362			−0.447248			−0.223624	+	0.974676i	$0.571789\pi$
$464$	−2.71214	+	1.97048i	−0.125908	+	0.0914774i
$465$		0			0
$466$	4.76573	−	14.6674i	0.220768	−	0.679454i
$467$	12.9233	−	17.7874i	0.598018	−	0.823102i	−0.397507	−	0.917599i	$-0.630124\pi$
$467$	12.9233	−	17.7874i	0.598018	−	0.823102i	0.995525	+	0.0944977i	$0.0301245\pi$
$468$		0			0
$469$	−1.62097	−	0.526685i	−0.0748495	−	0.0243201i
$470$	1.47236	+	4.53144i	0.0679147	+	0.209020i
$471$		0			0
$472$			1.66035i			0.0764237i
$473$	0.368416	+	0.997529i	0.0169398	+	0.0458664i
$474$		0			0
$475$	−2.26095	−	3.11193i	−0.103740	−	0.142785i
$476$	−6.54530	+	2.12670i	−0.300003	+	0.0974770i
$477$		0			0
$478$	19.0486	+	13.8396i	0.871261	+	0.633008i
$479$	22.1314	+	16.0794i	1.01121	+	0.734688i	0.964463	−	0.264219i	$-0.0851142\pi$
$479$	22.1314	+	16.0794i	1.01121	+	0.734688i	0.0467482	+	0.998907i	$0.485114\pi$
$480$		0			0
$481$	−32.3074	+	10.4973i	−1.47309	+	0.478635i
$482$	4.76919	+	6.56423i	0.217231	+	0.298993i
$483$		0			0
$484$	−4.21683	−	10.1596i	−0.191674	−	0.461802i
$485$			28.2493i			1.28273i
$486$		0			0
$487$	10.9951	+	33.8393i	0.498233	+	1.53340i	0.811856	+	0.583857i	$0.198457\pi$
$487$	10.9951	+	33.8393i	0.498233	+	1.53340i	−0.313623	+	0.949548i	$0.601543\pi$
$488$	5.33769	+	1.73432i	0.241626	+	0.0785090i
$489$		0			0
$490$	1.14907	−	1.58155i	0.0519095	−	0.0714473i
$491$	0.355412	−	1.09384i	0.0160395	−	0.0493645i	−0.942716	−	0.333595i	$-0.891738\pi$
$491$	0.355412	−	1.09384i	0.0160395	−	0.0493645i	0.958756	+	0.284231i	$0.0917381\pi$
$492$		0			0
$493$	18.6653	−	13.5611i	0.840643	−	0.610763i
$494$	−17.0957			−0.769172
$495$		0			0
$496$	−8.59116			−0.385755
$497$	−1.10218	+	0.800779i	−0.0494395	+	0.0359199i
$498$		0			0
$499$	8.61195	−	26.5048i	0.385524	−	1.18652i	−0.550576	−	0.834785i	$-0.685592\pi$
$499$	8.61195	−	26.5048i	0.385524	−	1.18652i	0.936100	−	0.351735i	$-0.114408\pi$
$500$	−7.09931	+	9.77137i	−0.317491	+	0.436989i
$501$		0			0
$502$	17.0135	+	5.52801i	0.759347	+	0.246727i
$503$	−9.15395	−	28.1730i	−0.408154	−	1.25617i	−0.918232	−	0.396042i	$-0.870384\pi$
$503$	−9.15395	−	28.1730i	−0.408154	−	1.25617i	0.510078	−	0.860128i	$-0.329616\pi$
$504$		0			0
$505$			26.9175i			1.19781i
$506$	−12.8861	−	8.60354i	−0.572859	−	0.382474i
$507$		0			0
$508$	−7.11660	−	9.79516i	−0.315748	−	0.434590i
$509$	8.06771	−	2.62136i	0.357595	−	0.116190i	−0.124710	−	0.992193i	$-0.539800\pi$
$509$	8.06771	−	2.62136i	0.357595	−	0.116190i	0.482304	+	0.876004i	$0.339800\pi$
$510$		0			0
$511$	−1.81577	−	1.31923i	−0.0803249	−	0.0583595i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	−19.4257	+	6.31180i	−0.856832	+	0.278402i
$515$	13.9030	+	19.1358i	0.612640	+	0.843226i
$516$		0			0
$517$	6.34632	−	5.00674i	0.279111	−	0.220196i
$518$		−	6.48654i		−	0.285002i
$519$		0			0
$520$	3.16367	+	9.73677i	0.138736	+	0.426986i
$521$	−18.8924	−	6.13851i	−0.827691	−	0.268933i	−0.135618	−	0.990761i	$-0.543302\pi$
$521$	−18.8924	−	6.13851i	−0.827691	−	0.268933i	−0.692072	+	0.721828i	$0.743302\pi$
$522$		0			0
$523$	6.99315	−	9.62524i	0.305789	−	0.420882i	−0.628273	−	0.777993i	$-0.716238\pi$
$523$	6.99315	−	9.62524i	0.305789	−	0.420882i	0.934062	+	0.357110i	$0.116238\pi$
$524$	−1.72461	+	5.30781i	−0.0753400	+	0.231873i
$525$		0			0
$526$	17.8398	−	12.9613i	0.777851	−	0.565141i
$527$	59.1255			2.57555
$528$		0			0
$529$	1.17513			0.0510925
$530$	7.14405	−	5.19045i	0.310318	−	0.225459i
$531$		0			0
$532$	1.00876	−	3.10464i	0.0437352	−	0.134603i
$533$	−0.801466	+	1.10312i	−0.0347153	+	0.0477816i
$534$		0			0
$535$	−3.36941	−	1.09479i	−0.145672	−	0.0473318i
$536$	0.526685	+	1.62097i	0.0227493	+	0.0700152i
$537$		0			0
$538$			30.3776i			1.30967i
$539$	−3.19243	−	0.899118i	−0.137508	−	0.0387277i
$540$		0			0
$541$	8.25934	+	11.3680i	0.355097	+	0.488749i	0.948774	−	0.315954i	$-0.102325\pi$
$541$	8.25934	+	11.3680i	0.355097	+	0.488749i	−0.593678	+	0.804703i	$0.702325\pi$
$542$	16.2268	−	5.27241i	0.697001	−	0.226469i
$543$		0			0
$544$	5.56776	+	4.04522i	0.238716	+	0.173437i
$545$	−30.4322	−	22.1103i	−1.30357	−	0.947100i
$546$		0			0
$547$	−24.7835	+	8.05264i	−1.05966	+	0.344306i	−0.786454	−	0.617648i	$-0.788085\pi$
$547$	−24.7835	+	8.05264i	−1.05966	+	0.344306i	−0.273210	+	0.961954i	$0.588085\pi$
$548$	−12.4698	−	17.1631i	−0.532681	−	0.733173i
$549$		0			0
$550$	3.76174	+	1.05946i	0.160401	+	0.0451755i
$551$			10.9436i			0.466212i
$552$		0			0
$553$	3.71426	+	11.4313i	0.157946	+	0.486108i
$554$	−25.5044	−	8.28687i	−1.08358	−	0.352075i
$555$		0			0
$556$	5.32085	−	7.32352i	0.225654	−	0.310586i
$557$	−1.38688	+	4.26838i	−0.0587641	+	0.180857i	−0.976130	−	0.217188i	$-0.930311\pi$
$557$	−1.38688	+	4.26838i	−0.0587641	+	0.180857i	0.917366	+	0.398046i	$0.130311\pi$
$558$		0			0
$559$	−1.35842	+	0.986953i	−0.0574552	+	0.0417437i
$560$	−1.95491			−0.0826100
$561$		0			0
$562$	29.0304			1.22457
$563$	1.73678	−	1.26184i	0.0731963	−	0.0531803i	−0.550585	−	0.834779i	$-0.685595\pi$
$563$	1.73678	−	1.26184i	0.0731963	−	0.0531803i	0.623782	+	0.781599i	$0.285595\pi$
$564$		0			0
$565$	3.87867	−	11.9373i	0.163177	−	0.502206i
$566$	2.57070	−	3.53826i	0.108055	−	0.148724i
$567$		0			0
$568$	1.29569	+	0.420995i	0.0543659	+	0.0176645i
$569$	1.71658	+	5.28308i	0.0719626	+	0.221478i	0.980569	−	0.196176i	$-0.0628524\pi$
$569$	1.71658	+	5.28308i	0.0719626	+	0.221478i	−0.908606	+	0.417654i	$0.862852\pi$
$570$		0			0
$571$		−	31.2300i		−	1.30693i	−0.756955	−	0.653467i	$-0.773314\pi$
$571$		−	31.2300i		−	1.30693i	0.756955	−	0.653467i	$-0.226686\pi$
$572$	13.6364	−	10.7580i	0.570167	−	0.449816i
$573$		0			0
$574$	−0.153039	−	0.210640i	−0.00638773	−	0.00879196i
$575$	5.23540	−	1.70108i	0.218331	−	0.0709401i
$576$		0			0
$577$	16.0220	+	11.6407i	0.667005	+	0.484608i	0.869021	−	0.494775i	$-0.164749\pi$
$577$	16.0220	+	11.6407i	0.667005	+	0.484608i	−0.202016	+	0.979382i	$0.564749\pi$
$578$	−24.5648	−	17.8474i	−1.02176	−	0.742353i
$579$		0			0
$580$	6.23286	−	2.02518i	0.258805	−	0.0840909i
$581$	−1.37587	−	1.89373i	−0.0570809	−	0.0785651i
$582$		0			0
$583$	−12.4597	−	8.31882i	−0.516028	−	0.344530i
$584$			2.24441i			0.0928745i
$585$		0			0
$586$	−3.17574	−	9.77392i	−0.131189	−	0.403757i
$587$	8.96778	+	2.91381i	0.370140	+	0.120266i	0.488180	−	0.872743i	$-0.337661\pi$
$587$	8.96778	+	2.91381i	0.370140	+	0.120266i	−0.118040	+	0.993009i	$0.537661\pi$
$588$		0			0
$589$	−16.4845	+	22.6890i	−0.679232	+	0.934882i
$590$	1.00302	−	3.08696i	0.0412935	−	0.127088i
$591$		0			0
$592$	−5.24772	+	3.81269i	−0.215680	+	0.156701i
$593$	39.8227			1.63532			0.817662	−	0.575699i	$-0.195270\pi$
$593$	39.8227			1.63532			0.817662	+	0.575699i	$0.195270\pi$
$594$		0			0
$595$	13.4539			0.551558
$596$	−6.42716	+	4.66960i	−0.263267	+	0.191274i
$597$		0			0
$598$	7.56033	−	23.2683i	0.309165	−	0.951511i
$599$	17.7566	−	24.4398i	0.725514	−	0.998584i	−0.273809	−	0.961784i	$-0.588284\pi$
$599$	17.7566	−	24.4398i	0.725514	−	0.998584i	0.999323	−	0.0367999i	$-0.0117164\pi$
$600$		0			0
$601$	18.6733	+	6.06731i	0.761699	+	0.247491i	0.664007	−	0.747726i	$-0.268854\pi$
$601$	18.6733	+	6.06731i	0.761699	+	0.247491i	0.0976911	+	0.995217i	$0.468854\pi$
$602$	−0.0990782	−	0.304931i	−0.00403812	−	0.0124281i
$603$		0			0
$604$		−	8.80080i		−	0.358099i
$605$	1.70261	+	21.4365i	0.0692210	+	0.871517i
$606$		0			0
$607$	28.7589	+	39.5832i	1.16729	+	1.60663i	0.679513	+	0.733664i	$0.262191\pi$
$607$	28.7589	+	39.5832i	1.16729	+	1.60663i	0.487775	+	0.872970i	$0.337809\pi$
$608$	−3.10464	+	1.00876i	−0.125910	+	0.0409106i
$609$		0			0
$610$	−8.87628	−	6.44900i	−0.359390	−	0.261112i
$611$	10.3263	+	7.50248i	0.417756	+	0.303518i
$612$		0			0
$613$	−12.4850	+	4.05662i	−0.504265	+	0.163845i	−0.550092	−	0.835104i	$-0.685407\pi$
$613$	−12.4850	+	4.05662i	−0.504265	+	0.163845i	0.0458277	+	0.998949i	$0.485407\pi$
$614$	−3.49498	−	4.81043i	−0.141046	−	0.194133i
$615$		0			0
$616$	1.14906	+	3.11122i	0.0462969	+	0.125354i
$617$			24.8535i			1.00056i	0.865862	+	0.500282i	$0.166770\pi$
$617$			24.8535i			1.00056i	−0.865862	+	0.500282i	$0.833230\pi$
$618$		0			0
$619$	−4.40031	−	13.5428i	−0.176864	−	0.544330i	0.822850	−	0.568258i	$-0.192383\pi$
$619$	−4.40031	−	13.5428i	−0.176864	−	0.544330i	−0.999714	+	0.0239285i	$0.992383\pi$
$620$	15.9729	+	5.18992i	0.641489	+	0.208432i
$621$		0			0
$622$	7.15779	−	9.85185i	0.287001	−	0.395023i
$623$	−2.72858	+	8.39771i	−0.109318	+	0.336447i
$624$		0			0
$625$	14.3357	−	10.4155i	0.573427	−	0.416619i
$626$	8.01951			0.320524
$627$		0			0
$628$	−10.7793			−0.430139
$629$	36.1155	−	26.2394i	1.44002	−	1.04624i
$630$		0			0
$631$	−6.56247	+	20.1972i	−0.261248	+	0.804038i	0.731286	+	0.682071i	$0.238920\pi$
$631$	−6.56247	+	20.1972i	−0.261248	+	0.804038i	−0.992534	+	0.121968i	$0.961080\pi$
$632$	7.06493	−	9.72405i	0.281028	−	0.386802i
$633$		0			0
$634$	−29.1029	−	9.45610i	−1.15582	−	0.375550i
$635$	7.31413	+	22.5106i	0.290252	+	0.893305i
$636$		0			0
$637$		−	5.23700i		−	0.207497i
$638$	−6.88661	−	8.72916i	−0.272643	−	0.345591i
$639$		0			0
$640$	1.14907	+	1.58155i	0.0454208	+	0.0625164i
$641$	42.1737	−	13.7031i	1.66576	−	0.541238i	0.683693	−	0.729770i	$-0.260373\pi$
$641$	42.1737	−	13.7031i	1.66576	−	0.541238i	0.982067	+	0.188532i	$0.0603728\pi$
$642$		0			0
$643$	−26.4090	−	19.1873i	−1.04147	−	0.756672i	−0.0708974	−	0.997484i	$-0.522586\pi$
$643$	−26.4090	−	19.1873i	−1.04147	−	0.756672i	−0.970572	+	0.240812i	$0.922586\pi$
$644$	3.77949	+	2.74596i	0.148933	+	0.108206i
$645$		0			0
$646$	21.3665	−	6.94241i	0.840656	−	0.273146i
$647$	15.2586	+	21.0017i	0.599878	+	0.825662i	0.995697	−	0.0926669i	$-0.0295392\pi$
$647$	15.2586	+	21.0017i	0.599878	+	0.825662i	−0.395819	+	0.918329i	$0.629539\pi$
$648$		0			0
$649$	−5.50242	+	0.218174i	−0.215989	+	0.00856407i
$650$			6.17092i			0.242043i
$651$		0			0
$652$	1.93623	+	5.95911i	0.0758287	+	0.233377i
$653$	3.70498	+	1.20382i	0.144987	+	0.0471092i	0.380612	−	0.924735i	$-0.375714\pi$
$653$	3.70498	+	1.20382i	0.144987	+	0.0471092i	−0.235624	+	0.971844i	$0.575714\pi$
$654$		0			0
$655$	6.41289	−	8.82659i	0.250572	−	0.344883i
$656$	−0.0804575	+	0.247623i	−0.00314134	+	0.00966804i
$657$		0			0
$658$	−1.97179	+	1.43259i	−0.0768685	+	0.0558482i
$659$	34.6565			1.35002			0.675012	−	0.737807i	$-0.264138\pi$
$659$	34.6565			1.35002			0.675012	+	0.737807i	$0.264138\pi$
$660$		0			0
$661$	12.3673			0.481032			0.240516	−	0.970645i	$-0.422683\pi$
$661$	12.3673			0.481032			0.240516	+	0.970645i	$0.422683\pi$
$662$	25.8392	−	18.7733i	1.00427	−	0.729644i
$663$		0			0
$664$	−0.723340	+	2.22621i	−0.0280710	+	0.0863937i
$665$	−3.75103	+	5.16284i	−0.145459	+	0.200207i
$666$		0			0
$667$	−14.8949	−	4.83963i	−0.576731	−	0.187391i
$668$	4.49677	+	13.8396i	0.173985	+	0.535471i
$669$		0			0
$670$		−	3.33193i		−	0.128723i
$671$	−5.04619	+	17.9171i	−0.194806	+	0.691682i
$672$		0			0
$673$	13.8476	+	19.0595i	0.533785	+	0.734691i	0.987701	−	0.156353i	$-0.0499736\pi$
$673$	13.8476	+	19.0595i	0.533785	+	0.734691i	−0.453917	+	0.891044i	$0.649974\pi$
$674$	9.39201	−	3.05165i	0.361767	−	0.117545i
$675$		0			0
$676$	11.6710	+	8.47947i	0.448884	+	0.326133i
$677$	21.5716	+	15.6727i	0.829064	+	0.602350i	0.919294	−	0.393571i	$-0.128760\pi$
$677$	21.5716	+	15.6727i	0.829064	+	0.602350i	−0.0902303	+	0.995921i	$0.528760\pi$
$678$		0			0
$679$	−13.7432	+	4.46543i	−0.527415	+	0.171368i
$680$	−7.90803	−	10.8845i	−0.303259	−	0.417400i
$681$		0			0
$682$	−1.12890	−	28.4713i	−0.0432278	−	1.09022i
$683$			0.199835i			0.00764649i	0.999993	+	0.00382324i	$0.00121698\pi$
$683$			0.199835i			0.00764649i	−0.999993	+	0.00382324i	$0.998783\pi$
$684$		0			0
$685$	12.8159	+	39.4432i	0.489669	+	1.50705i
$686$	0.951057	+	0.309017i	0.0363115	+	0.0117983i
$687$		0			0
$688$	−0.188458	+	0.259390i	−0.00718489	+	0.00988915i
$689$	7.31012	−	22.4982i	0.278494	−	0.857115i
$690$		0			0
$691$	20.4257	−	14.8402i	0.777031	−	0.564546i	−0.127055	−	0.991896i	$-0.540553\pi$
$691$	20.4257	−	14.8402i	0.777031	−	0.564546i	0.904086	+	0.427350i	$0.140553\pi$
$692$	1.49651			0.0568889
$693$		0			0
$694$	20.7486			0.787605
$695$	−14.3168	+	10.4018i	−0.543067	+	0.394562i
$696$		0			0
$697$	0.553719	−	1.70417i	0.0209736	−	0.0645501i
$698$	16.3747	−	22.5379i	0.619793	−	0.853072i
$699$		0			0
$700$	−1.12066	−	0.364124i	−0.0423570	−	0.0137626i
$701$	−4.33098	−	13.3294i	−0.163579	−	0.503443i	0.835350	−	0.549718i	$-0.185265\pi$
$701$	−4.33098	−	13.3294i	−0.163579	−	0.503443i	−0.998929	+	0.0462749i	$0.985265\pi$
$702$		0			0
$703$			21.1747i			0.798620i
$704$	1.84163	−	2.75834i	0.0694089	−	0.103959i
$705$		0			0
$706$	−9.31878	−	12.8262i	−0.350717	−	0.482720i
$707$	−13.0953	+	4.25492i	−0.492499	+	0.160023i
$708$		0			0
$709$	−17.3146	−	12.5798i	−0.650264	−	0.472444i	0.213097	−	0.977031i	$-0.431645\pi$
$709$	−17.3146	−	12.5798i	−0.650264	−	0.472444i	−0.863361	+	0.504587i	$0.831645\pi$
$710$	−2.15466	−	1.56545i	−0.0808629	−	0.0587503i
$711$		0			0
$712$	8.39771	−	2.72858i	0.314718	−	0.102258i
$713$	−23.5910	−	32.4702i	−0.883490	−	1.21602i
$714$		0			0
$715$	−31.8522	+	11.7639i	−1.19120	+	0.439945i
$716$			19.4947i			0.728552i
$717$		0			0
$718$	1.13824	+	3.50315i	0.0424788	+	0.130736i
$719$	3.29837	+	1.07170i	0.123008	+	0.0399678i	0.369874	−	0.929082i	$-0.379401\pi$
$719$	3.29837	+	1.07170i	0.123008	+	0.0399678i	−0.246866	+	0.969050i	$0.579401\pi$
$720$		0			0
$721$	−7.11184	+	9.78861i	−0.264859	+	0.364547i
$722$	2.57832	−	7.93525i	0.0959551	−	0.295320i
$723$		0			0
$724$	13.5248	−	9.82635i	0.502646	−	0.365194i
$725$	3.95022			0.146708
$726$		0			0
$727$	9.75693			0.361864			0.180932	−	0.983496i	$-0.442089\pi$
$727$	9.75693			0.361864			0.180932	+	0.983496i	$0.442089\pi$
$728$	−4.23682	+	3.07823i	−0.157027	+	0.114087i
$729$		0			0
$730$	1.35585	−	4.17288i	0.0501823	−	0.154445i
$731$	1.29699	−	1.78516i	0.0479710	−	0.0660264i
$732$		0			0
$733$	−10.2235	−	3.32180i	−0.377612	−	0.122693i	0.114061	−	0.993474i	$-0.463614\pi$
$733$	−10.2235	−	3.32180i	−0.377612	−	0.122693i	−0.491672	+	0.870780i	$0.663614\pi$
$734$	8.49646	+	26.1494i	0.313610	+	0.965193i
$735$		0			0
$736$		−	4.67171i		−	0.172202i
$737$	−5.30272	+	1.95845i	−0.195328	+	0.0721403i
$738$		0			0
$739$	−21.9294	−	30.1832i	−0.806686	−	1.11031i	−0.991826	−	0.127596i	$-0.959274\pi$
$739$	−21.9294	−	30.1832i	−0.806686	−	1.11031i	0.185140	−	0.982712i	$-0.440726\pi$
$740$	12.0600	−	3.91852i	0.443333	−	0.144048i
$741$		0			0
$742$	3.65441	+	2.65509i	0.134158	+	0.0974713i
$743$	−39.3318	−	28.5762i	−1.44294	−	1.04836i	−0.987417	−	0.158136i	$-0.949452\pi$
$743$	−39.3318	−	28.5762i	−1.44294	−	1.04836i	−0.455525	−	0.890223i	$-0.650548\pi$
$744$		0			0
$745$	14.7705	−	4.79922i	0.541148	−	0.175830i
$746$	−18.0958	−	24.9067i	−0.662534	−	0.911900i
$747$		0			0
$748$	−12.6743	+	18.9832i	−0.463419	+	0.694096i
$749$		−	1.81226i		−	0.0662186i
$750$		0			0
$751$	−12.4818	−	38.4149i	−0.455466	−	1.40178i	−0.870588	−	0.492013i	$-0.836261\pi$
$751$	−12.4818	−	38.4149i	−0.455466	−	1.40178i	0.415122	−	0.909766i	$-0.363739\pi$
$752$	2.31798	+	0.753158i	0.0845281	+	0.0274648i
$753$		0			0
$754$	10.3194	−	14.2035i	0.375811	−	0.517259i
$755$	−5.31656	+	16.3627i	−0.193490	+	0.595500i
$756$		0			0
$757$	6.59766	−	4.79348i	0.239796	−	0.174222i	−0.461396	−	0.887194i	$-0.652651\pi$
$757$	6.59766	−	4.79348i	0.239796	−	0.174222i	0.701192	+	0.712972i	$0.252651\pi$
$758$	−22.5127			−0.817698
$759$		0			0
$760$	6.38163			0.231486
$761$	21.2873	−	15.4661i	0.771664	−	0.560647i	−0.130802	−	0.991409i	$-0.541755\pi$
$761$	21.2873	−	15.4661i	0.771664	−	0.560647i	0.902466	+	0.430762i	$0.141755\pi$
$762$		0			0
$763$	5.94609	−	18.3002i	0.215263	−	0.662511i
$764$	7.68834	−	10.5821i	0.278154	−	0.382847i
$765$		0			0
$766$	4.46341	+	1.45025i	0.161270	+	0.0523997i
$767$	−2.68697	−	8.26966i	−0.0970210	−	0.298600i
$768$		0			0
$769$			44.4548i			1.60308i	0.597941	+	0.801540i	$0.295986\pi$
$769$			44.4548i			1.60308i	−0.597941	+	0.801540i	$0.704014\pi$
$770$	−0.256880	−	6.47861i	−0.00925731	−	0.233473i
$771$		0			0
$772$	−0.344321	−	0.473918i	−0.0123924	−	0.0170567i
$773$	31.1828	−	10.1319i	1.12157	−	0.364419i	0.311201	−	0.950344i	$-0.399269\pi$
$773$	31.1828	−	10.1319i	1.12157	−	0.364419i	0.810365	+	0.585925i	$0.199269\pi$
$774$		0			0
$775$	8.18987	+	5.95029i	0.294189	+	0.213741i
$776$	11.6907	+	8.49376i	0.419670	+	0.304908i
$777$		0			0
$778$	33.1759	−	10.7795i	1.18941	−	0.386464i
$779$	0.499583	+	0.687617i	0.0178994	+	0.0246364i
$780$		0			0
$781$	−1.22493	+	4.34926i	−0.0438314	+	0.155629i
$782$			32.1513i			1.14973i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	20.0411	+	6.51175i	0.715297	+	0.232414i
$786$		0			0
$787$	−16.6696	+	22.9437i	−0.594205	+	0.817854i	−0.995162	−	0.0982433i	$-0.968678\pi$
$787$	−16.6696	+	22.9437i	−0.594205	+	0.817854i	0.400957	+	0.916097i	$0.368678\pi$
$788$	−4.07045	+	12.5276i	−0.145004	+	0.446276i
$789$		0			0
$790$	−19.0096	+	13.8113i	−0.676332	+	0.491384i
$791$	6.42057			0.228289
$792$		0			0
$793$	−29.3920			−1.04374
$794$	−9.03467	+	6.56407i	−0.320628	+	0.232950i
$795$		0			0
$796$	5.57579	−	17.1605i	0.197629	−	0.608239i
$797$	5.47760	−	7.53927i	0.194027	−	0.267055i	−0.700908	−	0.713251i	$-0.747222\pi$
$797$	5.47760	−	7.53927i	0.194027	−	0.267055i	0.894935	+	0.446197i	$0.147222\pi$
$798$		0			0
$799$	−15.9527	−	5.18334i	−0.564365	−	0.183373i
$800$	0.364124	+	1.12066i	0.0128737	+	0.0396213i
$801$		0			0
$802$			8.80104i			0.310775i
$803$	−7.43804	+	0.294922i	−0.262483	+	0.0104076i
$804$		0			0
$805$	−5.36811	−	7.38856i	−0.189201	−	0.260413i
$806$	42.7898	−	13.9033i	1.50721	−	0.489721i
$807$		0			0
$808$	11.1395	+	8.09333i	0.391887	+	0.284722i
$809$	15.0031	+	10.9004i	0.527481	+	0.383237i	0.819415	−	0.573201i	$-0.194299\pi$
$809$	15.0031	+	10.9004i	0.527481	+	0.383237i	−0.291934	+	0.956439i	$0.594299\pi$
$810$		0			0
$811$	29.3103	−	9.52350i	1.02923	−	0.334415i	0.254741	−	0.967009i	$-0.418010\pi$
$811$	29.3103	−	9.52350i	1.02923	−	0.334415i	0.774484	+	0.632594i	$0.218010\pi$
$812$	1.97048	+	2.71214i	0.0691504	+	0.0951774i
$813$		0			0
$814$	−13.3249	−	16.8900i	−0.467037	−	0.591996i
$815$		−	12.2490i		−	0.429064i
$816$		0			0
$817$	0.323432	+	0.995421i	0.0113154	+	0.0348254i
$818$	28.1711	+	9.15336i	0.984981	+	0.320040i
$819$		0			0
$820$	0.299178	−	0.411783i	0.0104477	−	0.0143801i
$821$	−1.04887	+	3.22810i	−0.0366059	+	0.112661i	−0.967690	−	0.252144i	$-0.918864\pi$
$821$	−1.04887	+	3.22810i	−0.0366059	+	0.112661i	0.931084	+	0.364805i	$0.118864\pi$
$822$		0			0
$823$	38.6862	−	28.1072i	1.34852	−	0.979755i	0.349433	−	0.936961i	$-0.386374\pi$
$823$	38.6862	−	28.1072i	1.34852	−	0.979755i	0.999084	−	0.0427932i	$-0.0136257\pi$
$824$	12.0994			0.421502
$825$		0			0
$826$	1.66035			0.0577709
$827$	−33.0924	+	24.0430i	−1.15074	+	0.836058i	−0.988579	−	0.150706i	$-0.951845\pi$
$827$	−33.0924	+	24.0430i	−1.15074	+	0.836058i	−0.162157	+	0.986765i	$0.551845\pi$
$828$		0			0
$829$	16.1015	−	49.5554i	0.559229	−	1.72113i	−0.125277	−	0.992122i	$-0.539982\pi$
$829$	16.1015	−	49.5554i	0.559229	−	1.72113i	0.684506	−	0.729008i	$-0.260018\pi$
$830$	2.68971	−	3.70207i	0.0933611	−	0.128501i
$831$		0			0
$832$	4.98068	+	1.61832i	0.172674	+	0.0561052i
$833$	2.12670	+	6.54530i	0.0736857	+	0.226781i
$834$		0			0
$835$		−	28.4475i		−	0.984467i
$836$	−3.75100	−	10.1563i	−0.129731	−	0.351263i
$837$		0			0
$838$	20.8807	+	28.7399i	0.721313	+	0.992803i
$839$	−31.2659	+	10.1589i	−1.07942	+	0.350725i	−0.794149	−	0.607722i	$-0.792083\pi$
$839$	−31.2659	+	10.1589i	−1.07942	+	0.350725i	−0.285270	+	0.958447i	$0.592083\pi$
$840$		0			0
$841$	14.3694	+	10.4399i	0.495495	+	0.359998i
$842$	14.7611	+	10.7246i	0.508702	+	0.369593i
$843$		0			0
$844$	−23.4739	+	7.62715i	−0.808007	+	0.262537i
$845$	−16.5766	−	22.8157i	−0.570252	−	0.784884i
$846$		0			0
$847$	−10.1596	+	4.21683i	−0.349089	+	0.144892i
$848$		−	4.51710i		−	0.155118i
$849$		0			0
$850$	−2.50595	−	7.71253i	−0.0859535	−	0.264538i
$851$	−28.8201	−	9.36421i	−0.987939	−	0.321001i
$852$		0			0
$853$	12.8614	−	17.7022i	0.440367	−	0.606113i	−0.529927	−	0.848044i	$-0.677781\pi$
$853$	12.8614	−	17.7022i	0.440367	−	0.606113i	0.970294	+	0.241930i	$0.0777805\pi$
$854$	1.73432	−	5.33769i	0.0593472	−	0.182652i
$855$		0			0
$856$	−1.46615	+	1.06522i	−0.0501120	+	0.0364085i
$857$	10.2880			0.351430			0.175715	−	0.984441i	$-0.443776\pi$
$857$	10.2880			0.351430			0.175715	+	0.984441i	$0.443776\pi$
$858$		0			0
$859$	−36.8976			−1.25893			−0.629465	−	0.777029i	$-0.716726\pi$
$859$	−36.8976			−1.25893			−0.629465	+	0.777029i	$0.716726\pi$
$860$	0.507084	−	0.368418i	0.0172914	−	0.0125629i
$861$		0			0
$862$	10.4553	−	32.1781i	0.356109	−	1.09599i
$863$	5.53805	−	7.62248i	0.188518	−	0.259472i	−0.704288	−	0.709914i	$-0.748734\pi$
$863$	5.53805	−	7.62248i	0.188518	−	0.259472i	0.892806	+	0.450442i	$0.148734\pi$
$864$		0			0
$865$	−2.78236	−	0.904045i	−0.0946032	−	0.0307384i
$866$	−2.25019	−	6.92536i	−0.0764645	−	0.235333i
$867$		0			0
$868$			8.59116i			0.291603i
$869$	33.1540	+	22.1356i	1.12467	+	0.750898i
$870$		0			0
$871$	−5.24650	−	7.22119i	−0.177771	−	0.244681i
$872$	−18.3002	+	5.94609i	−0.619722	+	0.201360i
$873$		0			0
$874$	−12.3378	−	8.96395i	−0.417333	−	0.303210i
$875$	9.77137	+	7.09931i	0.330333	+	0.240001i
$876$		0			0
$877$	−48.8966	+	15.8875i	−1.65112	+	0.536482i	−0.978983	−	0.203943i	$-0.934624\pi$
$877$	−48.8966	+	15.8875i	−1.65112	+	0.536482i	−0.672139	+	0.740425i	$0.734624\pi$
$878$	17.0063	+	23.4072i	0.573935	+	0.789954i
$879$		0			0
$880$	−5.09031	+	4.01585i	−0.171594	+	0.135374i
$881$		−	4.41624i		−	0.148787i	−0.997229	−	0.0743934i	$-0.976298\pi$
$881$		−	4.41624i		−	0.148787i	0.997229	−	0.0743934i	$-0.0237021\pi$
$882$		0			0
$883$	−14.9797	−	46.1029i	−0.504108	−	1.55149i	−0.802265	−	0.596968i	$-0.796372\pi$
$883$	−14.9797	−	46.1029i	−0.504108	−	1.55149i	0.298157	−	0.954517i	$-0.403628\pi$
$884$	−34.2777	−	11.1375i	−1.15288	−	0.374595i
$885$		0			0
$886$	−7.78236	+	10.7115i	−0.261453	+	0.359860i
$887$	−9.44911	+	29.0814i	−0.317270	+	0.976456i	0.657540	+	0.753420i	$0.271597\pi$
$887$	−9.44911	+	29.0814i	−0.317270	+	0.976456i	−0.974810	+	0.223037i	$0.928403\pi$
$888$		0			0
$889$	−9.79516	+	7.11660i	−0.328519	+	0.238683i
$890$	−17.2616			−0.578610
$891$		0			0
$892$	17.1137			0.573009
$893$	6.43674	−	4.67657i	0.215397	−	0.156495i
$894$		0			0
$895$	11.7768	−	36.2451i	0.393654	−	1.21154i
$896$	−0.587785	+	0.809017i	−0.0196365	+	0.0270274i
$897$		0			0
$898$	−28.5653	−	9.28142i	−0.953236	−	0.309725i
$899$	−8.89997	−	27.3913i	−0.296831	−	0.913551i
$900$		0			0
$901$			31.0873i			1.03567i
$902$	−0.831199	−	0.234100i	−0.0276759	−	0.00779466i
$903$		0			0
$904$	−3.77392	−	5.19435i	−0.125519	−	0.172762i
$905$	−31.0818	+	10.0991i	−1.03319	+	0.335705i
$906$		0			0
$907$	40.2931	+	29.2747i	1.33791	+	0.972050i	0.999518	+	0.0310454i	$0.00988363\pi$
$907$	40.2931	+	29.2747i	1.33791	+	0.972050i	0.338394	+	0.941005i	$0.390116\pi$
$908$	1.90764	+	1.38598i	0.0633071	+	0.0459953i
$909$		0			0
$910$	9.73677	−	3.16367i	0.322771	−	0.104875i
$911$	−18.6304	−	25.6425i	−0.617252	−	0.849575i	0.379897	−	0.925029i	$-0.375959\pi$
$911$	−18.6304	−	25.6425i	−0.617252	−	0.849575i	−0.997149	+	0.0754537i	$0.975959\pi$
$912$		0			0
$913$	−7.47276	−	2.10463i	−0.247312	−	0.0696532i
$914$			10.7608i			0.355937i
$915$		0			0
$916$	−1.08762	−	3.34735i	−0.0359360	−	0.110600i
$917$	5.30781	+	1.72461i	0.175279	+	0.0569517i
$918$		0			0
$919$	8.65665	−	11.9149i	0.285557	−	0.393035i	−0.642008	−	0.766698i	$-0.721898\pi$
$919$	8.65665	−	11.9149i	0.285557	−	0.393035i	0.927564	+	0.373663i	$0.121898\pi$
$920$	−2.82218	+	8.68578i	−0.0930445	+	0.286362i
$921$		0			0
$922$	−27.7661	+	20.1733i	−0.914429	+	0.664371i
$923$	−7.13471			−0.234842
$924$		0			0
$925$	7.64329			0.251310
$926$	7.78567	−	5.65662i	0.255853	−	0.185888i
$927$		0			0
$928$	1.03594	−	3.18831i	0.0340066	−	0.104661i
$929$	−0.890210	+	1.22527i	−0.0292068	+	0.0401998i	−0.823371	−	0.567504i	$-0.807909\pi$
$929$	−0.890210	+	1.22527i	−0.0292068	+	0.0401998i	0.794164	+	0.607704i	$0.207909\pi$
$930$		0			0
$931$	−3.10464	−	1.00876i	−0.101750	−	0.0330607i
$932$	4.76573	+	14.6674i	0.156107	+	0.480446i
$933$		0			0
$934$			21.9864i			0.719417i
$935$	35.0322	−	27.6376i	1.14568	−	0.903847i
$936$		0			0
$937$	−12.1998	−	16.7917i	−0.398552	−	0.548559i	0.561828	−	0.827254i	$-0.310098\pi$
$937$	−12.1998	−	16.7917i	−0.398552	−	0.548559i	−0.960380	+	0.278695i	$0.910098\pi$
$938$	1.62097	−	0.526685i	0.0529266	−	0.0171969i
$939$		0			0
$940$	−3.85468	−	2.80059i	−0.125726	−	0.0913451i
$941$	−4.11590	−	2.99038i	−0.134174	−	0.0974835i	0.518674	−	0.854972i	$-0.326426\pi$
$941$	−4.11590	−	2.99038i	−0.134174	−	0.0974835i	−0.652848	+	0.757489i	$0.726426\pi$
$942$		0			0
$943$	−1.15682	+	0.375874i	−0.0376713	+	0.0122401i
$944$	−0.975927	−	1.34325i	−0.0317637	−	0.0437190i
$945$		0			0
$946$	−0.884388	−	0.590469i	−0.0287539	−	0.0191978i
$947$			32.3323i			1.05066i	0.850899	+	0.525330i	$0.176058\pi$
$947$			32.3323i			1.05066i	−0.850899	+	0.525330i	$0.823942\pi$
$948$		0			0
$949$	−3.63218	−	11.1787i	−0.117906	−	0.362876i
$950$	3.65829	+	1.18865i	0.118691	+	0.0385650i
$951$		0			0
$952$	4.04522	−	5.56776i	0.131106	−	0.180452i
$953$	6.73463	−	20.7270i	0.218156	−	0.671415i	−0.780759	−	0.624833i	$-0.785167\pi$
$953$	6.73463	−	20.7270i	0.218156	−	0.671415i	0.998914	−	0.0465820i	$-0.0148329\pi$
$954$		0			0
$955$	−20.6870	+	15.0300i	−0.669417	+	0.486360i
$956$	−23.5453			−0.761510
$957$		0			0
$958$	−27.3560			−0.883831
$959$	−17.1631	+	12.4698i	−0.554227	+	0.402669i
$960$		0			0
$961$	13.2284	−	40.7129i	0.426724	−	1.31332i
$962$	19.9670	−	27.4823i	0.643763	−	0.886064i
$963$		0			0
$964$	−7.71672	−	2.50731i	−0.248539	−	0.0807551i
$965$	0.353878	+	1.08913i	0.0113918	+	0.0350602i
$966$		0			0
$967$			10.4215i			0.335133i	0.985861	+	0.167566i	$0.0535908\pi$
$967$			10.4215i			0.335133i	−0.985861	+	0.167566i	$0.946409\pi$
$968$	9.38318	+	5.74073i	0.301587	+	0.184514i
$969$		0			0
$970$	−16.6045	−	22.8542i	−0.533139	−	0.733803i
$971$	−21.2679	+	6.91035i	−0.682519	+	0.221764i	−0.629698	−	0.776840i	$-0.716821\pi$
$971$	−21.2679	+	6.91035i	−0.682519	+	0.221764i	−0.0528209	+	0.998604i	$0.516821\pi$
$972$		0			0
$973$	−7.32352	−	5.32085i	−0.234781	−	0.170578i
$974$	−28.7854	−	20.9138i	−0.922345	−	0.670123i
$975$		0			0
$976$	−5.33769	+	1.73432i	−0.170855	+	0.0555142i
$977$	22.5272	+	31.0060i	0.720709	+	0.991971i	0.999500	+	0.0316193i	$0.0100664\pi$
$977$	22.5272	+	31.0060i	0.720709	+	0.991971i	−0.278791	+	0.960352i	$0.589934\pi$
$978$		0			0
$979$	10.1461	+	27.4716i	0.324269	+	0.877998i
$980$			1.95491i			0.0624473i
$981$		0			0
$982$	0.355412	+	1.09384i	0.0113416	+	0.0349060i
$983$	38.2646	+	12.4329i	1.22045	+	0.396549i	0.847247	−	0.531200i	$-0.178259\pi$
$983$	38.2646	+	12.4329i	1.22045	+	0.396549i	0.373205	+	0.927749i	$0.378259\pi$
$984$		0			0
$985$	15.1358	−	20.8327i	0.482267	−	0.663784i
$986$	−7.12951	+	21.9424i	−0.227050	+	0.698788i
$987$		0			0
$988$	13.8307	−	10.0486i	0.440014	−	0.319689i
$989$	−1.49786			−0.0476292
$990$		0			0
$991$	−2.06259			−0.0655205			−0.0327602	−	0.999463i	$-0.510430\pi$
$991$	−2.06259			−0.0655205			−0.0327602	+	0.999463i	$0.510430\pi$
$992$	6.95040	−	5.04976i	0.220675	−	0.160330i
$993$		0			0
$994$	0.420995	−	1.29569i	0.0133531	−	0.0410967i
$995$	−20.7333	+	28.5370i	−0.657291	+	0.904684i
$996$		0			0
$997$	−38.1981	−	12.4113i	−1.20975	−	0.393070i	−0.366408	−	0.930454i	$-0.619413\pi$
$997$	−38.1981	−	12.4113i	−1.20975	−	0.393070i	−0.843338	+	0.537384i	$0.819413\pi$
$998$	8.61195	+	26.5048i	0.272606	+	0.838996i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.3	✓	48
3.2	odd	2		1386.2.bu.b.701.10	yes	48
11.7	odd	10		1386.2.bu.b.953.10	yes	48
33.29	even	10	inner	1386.2.bu.a.953.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.3	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.3	yes	48	33.29	even	10	inner
1386.2.bu.b.701.10	yes	48	3.2	odd	2
1386.2.bu.b.953.10	yes	48	11.7	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.14907 + 1.58155i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.14907 + 1.58155i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} -1.95491i q^{10} +(-3.11122 + 1.14906i) q^{11} +(-3.07823 - 4.23682i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.56776 + 4.04522i) q^{17} +(-3.10464 + 1.00876i) q^{19} +(1.14907 + 1.58155i) q^{20} +(1.84163 - 2.75834i) q^{22} -4.67171i q^{23} +(0.364124 + 1.12066i) q^{25} +(4.98068 + 1.61832i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(1.03594 - 3.18831i) q^{29} +(6.95040 - 5.04976i) q^{31} +1.00000 q^{32} -6.88213 q^{34} +(1.58155 - 1.14907i) q^{35} +(2.00445 - 6.16906i) q^{37} +(1.91877 - 2.64096i) q^{38} +(-1.85923 - 0.604100i) q^{40} +(-0.0804575 - 0.247623i) q^{41} -0.320624i q^{43} +(0.131402 + 3.31402i) q^{44} +(2.74596 + 3.77949i) q^{46} +(-2.31798 + 0.753158i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-0.953290 - 0.692606i) q^{50} +(-4.98068 + 1.61832i) q^{52} +(2.65509 + 3.65441i) q^{53} +(1.75769 - 6.24090i) q^{55} -1.00000i q^{56} +(1.03594 + 3.18831i) q^{58} +(1.57908 + 0.513075i) q^{59} +(3.29887 - 4.54051i) q^{61} +(-2.65482 + 8.17068i) q^{62} +(-0.809017 + 0.587785i) q^{64} +10.2378 q^{65} +1.70439 q^{67} +(5.56776 - 4.04522i) q^{68} +(-0.604100 + 1.85923i) q^{70} +(0.800779 - 1.10218i) q^{71} +(2.13456 + 0.693562i) q^{73} +(2.00445 + 6.16906i) q^{74} +3.26441i q^{76} +(3.31402 - 0.131402i) q^{77} +(-7.06493 - 9.72405i) q^{79} +(1.85923 - 0.604100i) q^{80} +(0.210640 + 0.153039i) q^{82} +(1.89373 + 1.37587i) q^{83} +(-12.7955 + 4.15750i) q^{85} +(0.188458 + 0.259390i) q^{86} +(-2.05424 - 2.60386i) q^{88} -8.82988i q^{89} +(1.61832 + 4.98068i) q^{91} +(-4.44306 - 1.44364i) q^{92} +(1.43259 - 1.97179i) q^{94} +(1.97203 - 6.06929i) q^{95} +(11.6907 - 8.49376i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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