LMFDB - Embedded newform 1386.2.bu.b.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.b.953.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.24209 + 1.70960i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.24209 + 1.70960i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +2.11318i q^{10} +(0.422357 + 3.28962i) q^{11} +(-0.352783 - 0.485565i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.694714 - 0.504739i) q^{17} +(2.22130 - 0.721743i) q^{19} +(1.24209 + 1.70960i) q^{20} +(2.27529 + 2.41311i) q^{22} +2.92626i q^{23} +(0.165166 + 0.508328i) q^{25} +(-0.570816 - 0.185469i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-1.88832 + 5.81166i) q^{29} +(0.894583 - 0.649953i) q^{31} -1.00000 q^{32} -0.858714 q^{34} +(-1.70960 + 1.24209i) q^{35} +(-2.37600 + 7.31259i) q^{37} +(1.37284 - 1.88955i) q^{38} +(2.00975 + 0.653007i) q^{40} +(3.44823 + 10.6126i) q^{41} +2.69544i q^{43} +(3.25913 + 0.614864i) q^{44} +(1.72001 + 2.36740i) q^{46} +(5.90450 - 1.91849i) q^{47} +(0.809017 + 0.587785i) q^{49} +(0.432410 + 0.314164i) q^{50} +(-0.570816 + 0.185469i) q^{52} +(1.49336 + 2.05544i) q^{53} +(-6.14853 - 3.36396i) q^{55} -1.00000i q^{56} +(1.88832 + 5.81166i) q^{58} +(-0.201105 - 0.0653429i) q^{59} +(7.31298 - 10.0654i) q^{61} +(0.341700 - 1.05165i) q^{62} +(-0.809017 + 0.587785i) q^{64} +1.26831 q^{65} -2.58944 q^{67} +(-0.694714 + 0.504739i) q^{68} +(-0.653007 + 2.00975i) q^{70} +(-2.88156 + 3.96613i) q^{71} +(1.80178 + 0.585433i) q^{73} +(2.37600 + 7.31259i) q^{74} -2.33561i q^{76} +(-0.614864 + 3.25913i) q^{77} +(-5.03313 - 6.92752i) q^{79} +(2.00975 - 0.653007i) q^{80} +(9.02758 + 6.55892i) q^{82} +(6.58339 + 4.78311i) q^{83} +(1.72580 - 0.560746i) q^{85} +(1.58434 + 2.18065i) q^{86} +(2.99810 - 1.41823i) q^{88} -11.4083i q^{89} +(-0.185469 - 0.570816i) q^{91} +(2.78304 + 0.904265i) q^{92} +(3.64918 - 5.02267i) q^{94} +(-1.52517 + 4.69399i) q^{95} +(5.61470 - 4.07932i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.24209	+	1.70960i	−0.555481	+	0.764554i	−0.990743	−	0.135750i	$-0.956656\pi$
$5$	−1.24209	+	1.70960i	−0.555481	+	0.764554i	0.435262	+	0.900304i	$0.356656\pi$
$6$		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
$10$			2.11318i			0.668245i
$11$	0.422357	+	3.28962i	0.127345	+	0.991858i
$11$	0.422357	+	3.28962i	0.127345	+	0.991858i
$12$		0			0
$13$	−0.352783	−	0.485565i	−0.0978445	−	0.134671i	0.757288	−	0.653081i	$-0.226524\pi$
$13$	−0.352783	−	0.485565i	−0.0978445	−	0.134671i	−0.855132	+	0.518410i	$0.826524\pi$
$14$	0.951057	−	0.309017i	0.254181	−	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.694714	−	0.504739i	−0.168493	−	0.122417i	0.500343	−	0.865827i	$-0.333207\pi$
$17$	−0.694714	−	0.504739i	−0.168493	−	0.122417i	−0.668836	+	0.743410i	$0.733207\pi$
$18$		0			0
$19$	2.22130	−	0.721743i	0.509600	−	0.165579i	−0.0429202	−	0.999079i	$-0.513666\pi$
$19$	2.22130	−	0.721743i	0.509600	−	0.165579i	0.552520	+	0.833499i	$0.313666\pi$
$20$	1.24209	+	1.70960i	0.277741	+	0.382277i
$21$		0			0
$22$	2.27529	+	2.41311i	0.485092	+	0.514476i
$23$			2.92626i			0.610168i	0.952325	+	0.305084i	$0.0986845\pi$
$23$			2.92626i			0.610168i	−0.952325	+	0.305084i	$0.901315\pi$
$24$		0			0
$25$	0.165166	+	0.508328i	0.0330332	+	0.101666i
$26$	−0.570816	−	0.185469i	−0.111946	−	0.0363735i
$27$		0			0
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−1.88832	+	5.81166i	−0.350653	+	1.07920i	0.607835	+	0.794063i	$0.292038\pi$
$29$	−1.88832	+	5.81166i	−0.350653	+	1.07920i	−0.958488	+	0.285134i	$0.907962\pi$
$30$		0			0
$31$	0.894583	−	0.649953i	0.160672	−	0.116735i	−0.504544	−	0.863386i	$-0.668339\pi$
$31$	0.894583	−	0.649953i	0.160672	−	0.116735i	0.665216	+	0.746651i	$0.268339\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−0.858714			−0.147268
$35$	−1.70960	+	1.24209i	−0.288974	+	0.209952i
$36$		0			0
$37$	−2.37600	+	7.31259i	−0.390613	+	1.20218i	0.541713	+	0.840563i	$0.317776\pi$
$37$	−2.37600	+	7.31259i	−0.390613	+	1.20218i	−0.932326	+	0.361619i	$0.882224\pi$
$38$	1.37284	−	1.88955i	0.222703	−	0.306525i
$39$		0			0
$40$	2.00975	+	0.653007i	0.317769	+	0.103250i
$41$	3.44823	+	10.6126i	0.538523	+	1.65740i	0.735912	+	0.677078i	$0.236754\pi$
$41$	3.44823	+	10.6126i	0.538523	+	1.65740i	−0.197389	+	0.980325i	$0.563246\pi$
$42$		0			0
$43$			2.69544i			0.411050i	0.978652	+	0.205525i	$0.0658902\pi$
$43$			2.69544i			0.411050i	−0.978652	+	0.205525i	$0.934110\pi$
$44$	3.25913	+	0.614864i	0.491333	+	0.0926943i
$45$		0			0
$46$	1.72001	+	2.36740i	0.253602	+	0.349054i
$47$	5.90450	−	1.91849i	0.861261	−	0.279841i	0.155106	−	0.987898i	$-0.450428\pi$
$47$	5.90450	−	1.91849i	0.861261	−	0.279841i	0.706155	+	0.708057i	$0.250428\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	0.432410	+	0.314164i	0.0611520	+	0.0444295i
$51$		0			0
$52$	−0.570816	+	0.185469i	−0.0791579	+	0.0257200i
$53$	1.49336	+	2.05544i	0.205129	+	0.282336i	0.899170	−	0.437600i	$-0.144171\pi$
$53$	1.49336	+	2.05544i	0.205129	+	0.282336i	−0.694041	+	0.719936i	$0.744171\pi$
$54$		0			0
$55$	−6.14853	−	3.36396i	−0.829067	−	0.453596i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	1.88832	+	5.81166i	0.247949	+	0.763108i
$59$	−0.201105	−	0.0653429i	−0.0261816	−	0.00850692i	0.295897	−	0.955220i	$-0.404382\pi$
$59$	−0.201105	−	0.0653429i	−0.0261816	−	0.00850692i	−0.322079	+	0.946713i	$0.604382\pi$
$60$		0			0
$61$	7.31298	−	10.0654i	0.936331	−	1.28875i	−0.0210075	−	0.999779i	$-0.506687\pi$
$61$	7.31298	−	10.0654i	0.936331	−	1.28875i	0.957338	−	0.288969i	$-0.0933126\pi$
$62$	0.341700	−	1.05165i	0.0433960	−	0.133559i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.26831			0.157314
$66$		0			0
$67$	−2.58944			−0.316351			−0.158176	−	0.987411i	$-0.550561\pi$
$67$	−2.58944			−0.316351			−0.158176	+	0.987411i	$0.550561\pi$
$68$	−0.694714	+	0.504739i	−0.0842464	+	0.0612086i
$69$		0			0
$70$	−0.653007	+	2.00975i	−0.0780493	+	0.240211i
$71$	−2.88156	+	3.96613i	−0.341979	+	0.470693i	−0.945018	−	0.327018i	$-0.893956\pi$
$71$	−2.88156	+	3.96613i	−0.341979	+	0.470693i	0.603039	+	0.797711i	$0.293956\pi$
$72$		0			0
$73$	1.80178	+	0.585433i	0.210882	+	0.0685197i	0.412553	−	0.910934i	$-0.364637\pi$
$73$	1.80178	+	0.585433i	0.210882	+	0.0685197i	−0.201671	+	0.979453i	$0.564637\pi$
$74$	2.37600	+	7.31259i	0.276205	+	0.850071i
$75$		0			0
$76$		−	2.33561i		−	0.267913i
$77$	−0.614864	+	3.25913i	−0.0700703	+	0.371413i
$78$		0			0
$79$	−5.03313	−	6.92752i	−0.566272	−	0.779406i	0.425835	−	0.904801i	$-0.359980\pi$
$79$	−5.03313	−	6.92752i	−0.566272	−	0.779406i	−0.992107	+	0.125394i	$0.959980\pi$
$80$	2.00975	−	0.653007i	0.224697	−	0.0730084i
$81$		0			0
$82$	9.02758	+	6.55892i	0.996929	+	0.724312i
$83$	6.58339	+	4.78311i	0.722621	+	0.525015i	0.887220	−	0.461346i	$-0.152633\pi$
$83$	6.58339	+	4.78311i	0.722621	+	0.525015i	−0.164600	+	0.986360i	$0.552633\pi$
$84$		0			0
$85$	1.72580	−	0.560746i	0.187189	−	0.0608215i
$86$	1.58434	+	2.18065i	0.170844	+	0.235146i
$87$		0			0
$88$	2.99810	−	1.41823i	0.319599	−	0.151184i
$89$		−	11.4083i		−	1.20927i	−0.796501	−	0.604637i	$-0.793318\pi$
$89$		−	11.4083i		−	1.20927i	0.796501	−	0.604637i	$-0.206682\pi$
$90$		0			0
$91$	−0.185469	−	0.570816i	−0.0194425	−	0.0598377i
$92$	2.78304	+	0.904265i	0.290152	+	0.0942761i
$93$		0			0
$94$	3.64918	−	5.02267i	0.376385	−	0.518049i
$95$	−1.52517	+	4.69399i	−0.156479	+	0.481593i
$96$		0			0
$97$	5.61470	−	4.07932i	0.570087	−	0.414192i	−0.265050	−	0.964235i	$-0.585388\pi$
$97$	5.61470	−	4.07932i	0.570087	−	0.414192i	0.835137	+	0.550042i	$0.185388\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	0.534488			0.0534488
$101$	3.62269	−	2.63204i	0.360471	−	0.261897i	−0.392778	−	0.919633i	$-0.628486\pi$
$101$	3.62269	−	2.63204i	0.360471	−	0.261897i	0.753248	+	0.657736i	$0.228486\pi$
$102$		0			0
$103$	0.998572	−	3.07329i	0.0983922	−	0.302820i	−0.889731	−	0.456486i	$-0.849108\pi$
$103$	0.998572	−	3.07329i	0.0983922	−	0.302820i	0.988123	+	0.153666i	$0.0491079\pi$
$104$	−0.352783	+	0.485565i	−0.0345933	+	0.0476135i
$105$		0			0
$106$	2.41631	+	0.785108i	0.234693	+	0.0762564i
$107$	5.30493	+	16.3269i	0.512847	+	1.57838i	0.787166	+	0.616741i	$0.211547\pi$
$107$	5.30493	+	16.3269i	0.512847	+	1.57838i	−0.274320	+	0.961639i	$0.588453\pi$
$108$		0			0
$109$		−	0.0237558i		−	0.00227539i	−0.999999	−	0.00113770i	$-0.999638\pi$
$109$		−	0.0237558i		−	0.00227539i	0.999999	−	0.00113770i	$-0.000362140\pi$
$110$	−6.95155	+	0.892514i	−0.662804	+	0.0850979i
$111$		0			0
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	−13.8713	+	4.50705i	−1.30490	+	0.423988i	−0.877283	−	0.479973i	$-0.840646\pi$
$113$	−13.8713	+	4.50705i	−1.30490	+	0.423988i	−0.427616	+	0.903960i	$0.640646\pi$
$114$		0			0
$115$	−5.00272	−	3.63469i	−0.466506	−	0.338937i
$116$	4.94369	+	3.59180i	0.459010	+	0.333490i
$117$		0			0
$118$	−0.201105	+	0.0653429i	−0.0185132	+	0.00601530i
$119$	−0.504739	−	0.694714i	−0.0462694	−	0.0636843i
$120$		0			0
$121$	−10.6432	+	2.77879i	−0.967566	+	0.252617i
$122$		−	12.4416i		−	1.12641i
$123$		0			0
$124$	−0.341700	−	1.05165i	−0.0306856	−	0.0944405i
$125$	−11.1229	−	3.61406i	−0.994866	−	0.323251i
$126$		0			0
$127$	7.07185	−	9.73356i	0.627525	−	0.863714i	−0.370349	−	0.928893i	$-0.620762\pi$
$127$	7.07185	−	9.73356i	0.627525	−	0.863714i	0.997874	+	0.0651787i	$0.0207617\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	1.02608	−	0.745493i	0.0899935	−	0.0653841i
$131$	−14.8391			−1.29649			−0.648247	−	0.761430i	$-0.724498\pi$
$131$	−14.8391			−1.29649			−0.648247	+	0.761430i	$0.724498\pi$
$132$		0			0
$133$	2.33561			0.202523
$134$	−2.09490	+	1.52204i	−0.180972	+	0.131484i
$135$		0			0
$136$	−0.265357	+	0.816685i	−0.0227542	+	0.0700302i
$137$	2.90157	−	3.99366i	0.247898	−	0.341202i	−0.666876	−	0.745169i	$-0.732369\pi$
$137$	2.90157	−	3.99366i	0.247898	−	0.341202i	0.914774	+	0.403967i	$0.132369\pi$
$138$		0			0
$139$	11.3492	+	3.68758i	0.962626	+	0.312776i	0.747836	−	0.663884i	$-0.231093\pi$
$139$	11.3492	+	3.68758i	0.962626	+	0.312776i	0.214791	+	0.976660i	$0.431093\pi$
$140$	0.653007	+	2.00975i	0.0551892	+	0.169855i
$141$		0			0
$142$			4.90241i			0.411401i
$143$	1.44832	−	1.36561i	0.121115	−	0.114198i
$144$		0			0
$145$	−7.59011	−	10.4469i	−0.630324	−	0.867567i
$146$	1.80178	−	0.585433i	0.149116	−	0.0484508i
$147$		0			0
$148$	6.22046	+	4.51943i	0.511319	+	0.371495i
$149$	−18.2519	−	13.2608i	−1.49526	−	1.08637i	−0.972223	−	0.234055i	$-0.924800\pi$
$149$	−18.2519	−	13.2608i	−1.49526	−	1.08637i	−0.523033	−	0.852312i	$-0.675200\pi$
$150$		0			0
$151$	3.55555	−	1.15527i	0.289346	−	0.0940143i	−0.160748	−	0.986996i	$-0.551391\pi$
$151$	3.55555	−	1.15527i	0.289346	−	0.0940143i	0.450094	+	0.892981i	$0.351391\pi$
$152$	−1.37284	−	1.88955i	−0.111352	−	0.153263i
$153$		0			0
$154$	1.41823	+	2.99810i	0.114285	+	0.241594i
$155$			2.33668i			0.187686i
$156$		0			0
$157$	−0.462859	−	1.42453i	−0.0369402	−	0.113690i	0.930886	−	0.365310i	$-0.119037\pi$
$157$	−0.462859	−	1.42453i	−0.0369402	−	0.113690i	−0.967826	+	0.251619i	$0.919037\pi$
$158$	−8.14378	−	2.64608i	−0.647885	−	0.210510i
$159$		0			0
$160$	1.24209	−	1.70960i	0.0981961	−	0.135155i
$161$	−0.904265	+	2.78304i	−0.0712661	+	0.219334i
$162$		0			0
$163$	−6.03237	+	4.38277i	−0.472491	+	0.343285i	−0.798411	−	0.602112i	$-0.794326\pi$
$163$	−6.03237	+	4.38277i	−0.472491	+	0.343285i	0.325920	+	0.945397i	$0.394326\pi$
$164$	11.1587			0.871348
$165$		0			0
$166$	8.13751			0.631594
$167$	4.68976	−	3.40731i	0.362905	−	0.263666i	−0.391358	−	0.920239i	$-0.627995\pi$
$167$	4.68976	−	3.40731i	0.362905	−	0.263666i	0.754263	+	0.656573i	$0.227995\pi$
$168$		0			0
$169$	3.90590	−	12.0211i	0.300454	−	0.924703i
$170$	1.06660	−	1.46805i	0.0818047	−	0.112594i
$171$		0			0
$172$	2.56351	+	0.832936i	0.195466	+	0.0635107i
$173$	−2.79107	−	8.59003i	−0.212201	−	0.653088i	−0.999340	−	0.0363127i	$-0.988439\pi$
$173$	−2.79107	−	8.59003i	−0.212201	−	0.653088i	0.787139	−	0.616775i	$-0.211561\pi$
$174$		0			0
$175$			0.534488i			0.0404035i
$176$	1.59190	−	2.90962i	0.119994	−	0.219321i
$177$		0			0
$178$	−6.70561	−	9.22948i	−0.502607	−	0.691779i
$179$	3.73969	−	1.21510i	0.279517	−	0.0908206i	−0.165904	−	0.986142i	$-0.553054\pi$
$179$	3.73969	−	1.21510i	0.279517	−	0.0908206i	0.445421	+	0.895321i	$0.353054\pi$
$180$		0			0
$181$	15.5473	+	11.2958i	1.15562	+	0.839610i	0.989218	−	0.146447i	$-0.0467839\pi$
$181$	15.5473	+	11.2958i	1.15562	+	0.839610i	0.166406	+	0.986057i	$0.446784\pi$
$182$	−0.485565	−	0.352783i	−0.0359925	−	0.0261501i
$183$		0			0
$184$	2.78304	−	0.904265i	0.205169	−	0.0666633i
$185$	−9.55035	−	13.1449i	−0.702156	−	0.966434i
$186$		0			0
$187$	1.36698	−	2.49853i	0.0999638	−	0.182710i
$188$		−	6.20836i		−	0.452791i
$189$		0			0
$190$	1.52517	+	4.69399i	0.110647	+	0.340538i
$191$	1.25293	+	0.407103i	0.0906592	+	0.0294569i	0.353995	−	0.935247i	$-0.384823\pi$
$191$	1.25293	+	0.407103i	0.0906592	+	0.0294569i	−0.263336	+	0.964704i	$0.584823\pi$
$192$		0			0
$193$	4.44167	−	6.11344i	0.319719	−	0.440055i	−0.618663	−	0.785657i	$-0.712325\pi$
$193$	4.44167	−	6.11344i	0.319719	−	0.440055i	0.938381	+	0.345602i	$0.112325\pi$
$194$	2.14463	−	6.60048i	0.153975	−	0.473887i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	0.889707			0.0633890			0.0316945	−	0.999498i	$-0.489910\pi$
$197$	0.889707			0.0633890			0.0316945	+	0.999498i	$0.489910\pi$
$198$		0			0
$199$	−21.7988			−1.54528			−0.772638	−	0.634847i	$-0.781063\pi$
$199$	−21.7988			−1.54528			−0.772638	+	0.634847i	$0.781063\pi$
$200$	0.432410	−	0.314164i	0.0305760	−	0.0222148i
$201$		0			0
$202$	1.38374	−	4.25872i	0.0973598	−	0.299643i
$203$	−3.59180	+	4.94369i	−0.252095	+	0.346979i
$204$		0			0
$205$	−22.4262	−	7.28671i	−1.56631	−	0.508926i
$206$	−0.998572	−	3.07329i	−0.0695738	−	0.214126i
$207$		0			0
$208$			0.600191i			0.0416158i
$209$	3.31244	+	7.00239i	0.229126	+	0.484366i
$210$		0			0
$211$	−1.84528	−	2.53981i	−0.127035	−	0.174848i	0.740762	−	0.671767i	$-0.234465\pi$
$211$	−1.84528	−	2.53981i	−0.127035	−	0.174848i	−0.867797	+	0.496919i	$0.834465\pi$
$212$	2.41631	−	0.785108i	0.165953	−	0.0539214i
$213$		0			0
$214$	13.8885	+	10.0906i	0.949397	+	0.689777i
$215$	−4.60810	−	3.34798i	−0.314270	−	0.228331i
$216$		0			0
$217$	1.05165	−	0.341700i	0.0713903	−	0.0231961i
$218$	−0.0139633	−	0.0192188i	−0.000945714	−	0.00130166i
$219$		0			0
$220$	−5.09932	+	4.80808i	−0.343796	+	0.324161i
$221$			0.515392i			0.0346690i
$222$		0			0
$223$	−0.980901	−	3.01890i	−0.0656860	−	0.202161i	0.912827	−	0.408347i	$-0.133895\pi$
$223$	−0.980901	−	3.01890i	−0.0656860	−	0.202161i	−0.978513	+	0.206186i	$0.933895\pi$
$224$	−0.951057	−	0.309017i	−0.0635451	−	0.0206471i
$225$		0			0
$226$	−8.57292	+	11.7996i	−0.570262	+	0.784898i
$227$	2.06754	−	6.36324i	0.137228	−	0.422343i	−0.858702	−	0.512475i	$-0.828729\pi$
$227$	2.06754	−	6.36324i	0.137228	−	0.422343i	0.995930	+	0.0901317i	$0.0287288\pi$
$228$		0			0
$229$	2.63213	−	1.91236i	0.173936	−	0.126372i	−0.497411	−	0.867515i	$-0.665716\pi$
$229$	2.63213	−	1.91236i	0.173936	−	0.126372i	0.671347	+	0.741143i	$0.265716\pi$
$230$	−6.18371			−0.407742
$231$		0			0
$232$	6.11074			0.401190
$233$	11.6680	−	8.47730i	0.764396	−	0.555366i	−0.135859	−	0.990728i	$-0.543380\pi$
$233$	11.6680	−	8.47730i	0.764396	−	0.555366i	0.900256	+	0.435362i	$0.143380\pi$
$234$		0			0
$235$	−4.05411	+	12.4773i	−0.264461	+	0.813926i
$236$	−0.124290	+	0.171070i	−0.00809056	+	0.0111357i
$237$		0			0
$238$	−0.816685	−	0.265357i	−0.0529378	−	0.0172005i
$239$	5.75478	+	17.7114i	0.372246	+	1.14566i	0.945318	+	0.326150i	$0.105752\pi$
$239$	5.75478	+	17.7114i	0.372246	+	1.14566i	−0.573072	+	0.819505i	$0.694248\pi$
$240$		0			0
$241$			1.34299i			0.0865099i	0.999064	+	0.0432549i	$0.0137728\pi$
$241$			1.34299i			0.0865099i	−0.999064	+	0.0432549i	$0.986227\pi$
$242$	−6.97722	+	8.50402i	−0.448513	+	0.546659i
$243$		0			0
$244$	−7.31298	−	10.0654i	−0.468165	−	0.644374i
$245$	−2.00975	+	0.653007i	−0.128398	+	0.0417191i
$246$		0			0
$247$	−1.13409	−	0.823964i	−0.0721604	−	0.0524276i
$248$	−0.894583	−	0.649953i	−0.0568061	−	0.0412720i
$249$		0			0
$250$	−11.1229	+	3.61406i	−0.703476	+	0.228573i
$251$	−3.85918	−	5.31170i	−0.243589	−	0.335272i	0.669664	−	0.742664i	$-0.266438\pi$
$251$	−3.85918	−	5.31170i	−0.243589	−	0.335272i	−0.913253	+	0.407392i	$0.866438\pi$
$252$		0			0
$253$	−9.62630	+	1.23593i	−0.605200	+	0.0777020i
$254$		−	12.0313i		−	0.754914i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−13.1614	−	4.27641i	−0.820987	−	0.266755i	−0.131743	−	0.991284i	$-0.542057\pi$
$257$	−13.1614	−	4.27641i	−0.820987	−	0.266755i	−0.689244	+	0.724529i	$0.742057\pi$
$258$		0			0
$259$	−4.51943	+	6.22046i	−0.280824	+	0.386521i
$260$	0.391929	−	1.20623i	0.0243064	−	0.0748074i
$261$		0			0
$262$	−12.0050	+	8.72218i	−0.741674	+	0.538858i
$263$	10.0488			0.619636			0.309818	−	0.950796i	$-0.399732\pi$
$263$	10.0488			0.619636			0.309818	+	0.950796i	$0.399732\pi$
$264$		0			0
$265$	−5.36886			−0.329807
$266$	1.88955	−	1.37284i	0.115856	−	0.0841740i
$267$		0			0
$268$	−0.800182	+	2.46271i	−0.0488789	+	0.150434i
$269$	11.8314	−	16.2846i	0.721374	−	0.992887i	−0.278103	−	0.960551i	$-0.589706\pi$
$269$	11.8314	−	16.2846i	0.721374	−	0.992887i	0.999477	−	0.0323353i	$-0.0102945\pi$
$270$		0			0
$271$	−27.7908	−	9.02976i	−1.68817	−	0.548519i	−0.701700	−	0.712472i	$-0.747575\pi$
$271$	−27.7908	−	9.02976i	−1.68817	−	0.548519i	−0.986468	+	0.163953i	$0.947575\pi$
$272$	0.265357	+	0.816685i	0.0160896	+	0.0495188i
$273$		0			0
$274$		−	4.93644i		−	0.298221i
$275$	−1.60245	+	0.758029i	−0.0966313	+	0.0457109i
$276$		0			0
$277$	6.99377	+	9.62610i	0.420215	+	0.578376i	0.965673	−	0.259762i	$-0.0836441\pi$
$277$	6.99377	+	9.62610i	0.420215	+	0.578376i	−0.545458	+	0.838138i	$0.683644\pi$
$278$	11.3492	−	3.68758i	0.680680	−	0.221166i
$279$		0			0
$280$	1.70960	+	1.24209i	0.102168	+	0.0742293i
$281$	3.88186	+	2.82033i	0.231572	+	0.168247i	0.697520	−	0.716565i	$-0.254287\pi$
$281$	3.88186	+	2.82033i	0.231572	+	0.168247i	−0.465948	+	0.884812i	$0.654287\pi$
$282$		0			0
$283$	−22.4415	+	7.29170i	−1.33401	+	0.433446i	−0.887284	−	0.461224i	$-0.847410\pi$
$283$	−22.4415	+	7.29170i	−1.33401	+	0.433446i	−0.446727	+	0.894670i	$0.647410\pi$
$284$	2.88156	+	3.96613i	0.170989	+	0.235347i
$285$		0			0
$286$	0.369036	−	1.95610i	0.0218216	−	0.115667i
$287$			11.1587i			0.658677i
$288$		0			0
$289$	−5.02542	−	15.4667i	−0.295613	−	0.909804i
$290$	−12.2811	−	3.99036i	−0.721168	−	0.234322i
$291$		0			0
$292$	1.11356	−	1.53268i	0.0651661	−	0.0896935i
$293$	1.45061	−	4.46451i	0.0847454	−	0.260819i	−0.899700	−	0.436508i	$-0.856215\pi$
$293$	1.45061	−	4.46451i	0.0847454	−	0.260819i	0.984446	+	0.175688i	$0.0562151\pi$
$294$		0			0
$295$	0.361501	−	0.262646i	0.0210474	−	0.0152918i
$296$	7.68891			0.446909
$297$		0			0
$298$	−22.5606			−1.30690
$299$	1.42089	−	1.03234i	0.0821722	−	0.0597016i
$300$		0			0
$301$	−0.832936	+	2.56351i	−0.0480096	+	0.147758i
$302$	2.19745	−	3.02453i	0.126449	−	0.174042i
$303$		0			0
$304$	−2.22130	−	0.721743i	−0.127400	−	0.0413948i
$305$	8.12444	+	25.0045i	0.465204	+	1.43175i
$306$		0			0
$307$			34.1087i			1.94669i	0.229352	+	0.973343i	$0.426339\pi$
$307$			34.1087i			1.94669i	−0.229352	+	0.973343i	$0.573661\pi$
$308$	2.90962	+	1.59190i	0.165791	+	0.0907068i
$309$		0			0
$310$	1.37346	+	1.89041i	0.0780075	+	0.107368i
$311$	12.5737	−	4.08545i	0.712990	−	0.231664i	0.0700084	−	0.997546i	$-0.477697\pi$
$311$	12.5737	−	4.08545i	0.712990	−	0.231664i	0.642981	+	0.765882i	$0.277697\pi$
$312$		0			0
$313$	15.3604	+	11.1599i	0.868218	+	0.630798i	0.930108	−	0.367285i	$-0.119713\pi$
$313$	15.3604	+	11.1599i	0.868218	+	0.630798i	−0.0618899	+	0.998083i	$0.519713\pi$
$314$	−1.21178	−	0.880411i	−0.0683848	−	0.0496844i
$315$		0			0
$316$	−8.14378	+	2.64608i	−0.458124	+	0.148853i
$317$	−16.0993	−	22.1588i	−0.904229	−	1.24456i	−0.969099	−	0.246671i	$-0.920663\pi$
$317$	−16.0993	−	22.1588i	−0.904229	−	1.24456i	0.0648706	−	0.997894i	$-0.479337\pi$
$318$		0			0
$319$	−19.9157	−	3.75727i	−1.11507	−	0.210367i
$320$		−	2.11318i		−	0.118130i
$321$		0			0
$322$	0.904265	+	2.78304i	0.0503927	+	0.155093i
$323$	−1.90746	−	0.619770i	−0.106134	−	0.0344849i
$324$		0			0
$325$	0.188559	−	0.259529i	0.0104593	−	0.0143961i
$326$	−2.30416	+	7.09147i	−0.127616	+	0.392760i
$327$		0			0
$328$	9.02758	−	6.55892i	0.498465	−	0.362156i
$329$	6.20836			0.342278
$330$		0			0
$331$	6.57734			0.361523			0.180762	−	0.983527i	$-0.442144\pi$
$331$	6.57734			0.361523			0.180762	+	0.983527i	$0.442144\pi$
$332$	6.58339	−	4.78311i	0.361310	−	0.262507i
$333$		0			0
$334$	1.79133	−	5.51315i	0.0980172	−	0.301666i
$335$	3.21633	−	4.42690i	0.175727	−	0.241867i
$336$		0			0
$337$	31.3987	+	10.2020i	1.71039	+	0.555741i	0.990399	−	0.138238i	$-0.0441439\pi$
$337$	31.3987	+	10.2020i	1.71039	+	0.555741i	0.719995	+	0.693979i	$0.244144\pi$
$338$	−3.90590	−	12.0211i	−0.212453	−	0.653864i
$339$		0			0
$340$		−	1.81461i		−	0.0984112i
$341$	2.51593	+	2.66833i	0.136245	+	0.144498i
$342$		0			0
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	2.56351	−	0.832936i	0.138215	−	0.0449089i
$345$		0			0
$346$	−7.30712	−	5.30893i	−0.392833	−	0.285410i
$347$	−12.1343	−	8.81608i	−0.651403	−	0.473272i	0.212346	−	0.977195i	$-0.431890\pi$
$347$	−12.1343	−	8.81608i	−0.651403	−	0.473272i	−0.863749	+	0.503922i	$0.831890\pi$
$348$		0			0
$349$	20.8579	−	6.77715i	1.11650	−	0.362772i	0.308068	−	0.951364i	$-0.400318\pi$
$349$	20.8579	−	6.77715i	1.11650	−	0.362772i	0.808430	+	0.588592i	$0.200318\pi$
$350$	0.314164	+	0.432410i	0.0167928	+	0.0231133i
$351$		0			0
$352$	−0.422357	−	3.28962i	−0.0225117	−	0.175337i
$353$		−	25.7581i		−	1.37096i	−0.728090	−	0.685482i	$-0.759592\pi$
$353$		−	25.7581i		−	1.37096i	0.728090	−	0.685482i	$-0.240408\pi$
$354$		0			0
$355$	−3.20131	−	9.85261i	−0.169908	−	0.522922i
$356$	−10.8499	−	3.52535i	−0.575044	−	0.186843i
$357$		0			0
$358$	2.31125	−	3.18117i	0.122153	−	0.168130i
$359$	2.72080	−	8.37377i	0.143598	−	0.441950i	−0.853230	−	0.521535i	$-0.825359\pi$
$359$	2.72080	−	8.37377i	0.143598	−	0.441950i	0.996828	+	0.0795849i	$0.0253595\pi$
$360$		0			0
$361$	−10.9581	+	7.96151i	−0.576741	+	0.419027i
$362$	19.2176			1.01005
$363$		0			0
$364$	−0.600191			−0.0314586
$365$	−3.23883	+	2.35315i	−0.169528	+	0.123169i
$366$		0			0
$367$	−5.20597	+	16.0223i	−0.271749	+	0.836358i	0.718312	+	0.695721i	$0.244915\pi$
$367$	−5.20597	+	16.0223i	−0.271749	+	0.836358i	−0.990061	+	0.140637i	$0.955085\pi$
$368$	1.72001	−	2.36740i	0.0896619	−	0.123409i
$369$		0			0
$370$	−15.4528	−	5.02091i	−0.803352	−	0.261025i
$371$	0.785108	+	2.41631i	0.0407608	+	0.125449i
$372$		0			0
$373$			2.73568i			0.141648i	0.997489	+	0.0708240i	$0.0225629\pi$
$373$			2.73568i			0.141648i	−0.997489	+	0.0708240i	$0.977437\pi$
$374$	−0.362683	−	2.82484i	−0.0187539	−	0.146069i
$375$		0			0
$376$	−3.64918	−	5.02267i	−0.188192	−	0.259025i
$377$	3.48811	−	1.13335i	0.179647	−	0.0583707i
$378$		0			0
$379$	21.6825	+	15.7532i	1.11375	+	0.809189i	0.983251	−	0.182258i	$-0.0583407\pi$
$379$	21.6825	+	15.7532i	1.11375	+	0.809189i	0.130503	+	0.991448i	$0.458341\pi$
$380$	3.99295	+	2.90104i	0.204834	+	0.148820i
$381$		0			0
$382$	1.25293	−	0.407103i	0.0641057	−	0.0208292i
$383$	−8.54533	−	11.7616i	−0.436646	−	0.600991i	0.532817	−	0.846231i	$-0.321134\pi$
$383$	−8.54533	−	11.7616i	−0.436646	−	0.600991i	−0.969463	+	0.245239i	$0.921134\pi$
$384$		0			0
$385$	−4.80808	−	5.09932i	−0.245042	−	0.259885i
$386$		−	7.55663i		−	0.384622i
$387$		0			0
$388$	−2.14463	−	6.60048i	−0.108877	−	0.335089i
$389$	13.6859	+	4.44683i	0.693905	+	0.225463i	0.634673	−	0.772781i	$-0.281135\pi$
$389$	13.6859	+	4.44683i	0.693905	+	0.225463i	0.0592321	+	0.998244i	$0.481135\pi$
$390$		0			0
$391$	1.47700	−	2.03292i	0.0746951	−	0.102809i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$		0			0
$394$	0.719788	−	0.522957i	0.0362624	−	0.0263462i
$395$	18.0949			0.910452
$396$		0			0
$397$	0.407954			0.0204746			0.0102373	−	0.999948i	$-0.496741\pi$
$397$	0.407954			0.0204746			0.0102373	+	0.999948i	$0.496741\pi$
$398$	−17.6356	+	12.8130i	−0.883992	+	0.642258i
$399$		0			0
$400$	0.165166	−	0.508328i	0.00825830	−	0.0254164i
$401$	11.9982	−	16.5141i	0.599162	−	0.824675i	−0.396470	−	0.918048i	$-0.629765\pi$
$401$	11.9982	−	16.5141i	0.599162	−	0.824675i	0.995631	+	0.0933725i	$0.0297648\pi$
$402$		0			0
$403$	−0.631188	−	0.205085i	−0.0314417	−	0.0102160i
$404$	−1.38374	−	4.25872i	−0.0688438	−	0.211879i
$405$		0			0
$406$			6.11074i			0.303271i
$407$	−25.0592	−	4.72764i	−1.24214	−	0.234340i
$408$		0			0
$409$	−13.3683	−	18.3998i	−0.661019	−	0.909814i	0.338496	−	0.940968i	$-0.390082\pi$
$409$	−13.3683	−	18.3998i	−0.661019	−	0.909814i	−0.999515	+	0.0311538i	$0.990082\pi$
$410$	−22.4262	+	7.28671i	−1.10755	+	0.359865i
$411$		0			0
$412$	−2.61429	−	1.89940i	−0.128797	−	0.0935765i
$413$	−0.171070	−	0.124290i	−0.00841780	−	0.00611589i
$414$		0			0
$415$	−16.3544	+	5.31386i	−0.802804	+	0.260847i
$416$	0.352783	+	0.485565i	0.0172966	+	0.0238068i
$417$		0			0
$418$	6.79572	+	3.71805i	0.332390	+	0.181856i
$419$			9.58055i			0.468041i	0.972232	+	0.234020i	$0.0751882\pi$
$419$			9.58055i			0.468041i	−0.972232	+	0.234020i	$0.924812\pi$
$420$		0			0
$421$	−6.61485	−	20.3584i	−0.322388	−	0.992208i	−0.972606	−	0.232460i	$-0.925322\pi$
$421$	−6.61485	−	20.3584i	−0.322388	−	0.992208i	0.650218	−	0.759748i	$-0.274678\pi$
$422$	−2.98573	−	0.970123i	−0.145343	−	0.0472248i
$423$		0			0
$424$	1.49336	−	2.05544i	0.0725241	−	0.0998209i
$425$	0.141830	−	0.436509i	0.00687978	−	0.0211738i
$426$		0			0
$427$	10.0654	−	7.31298i	0.487101	−	0.353900i
$428$	17.1671			0.829803
$429$		0			0
$430$	−5.69593			−0.274682
$431$	10.1216	−	7.35380i	0.487542	−	0.354220i	−0.316696	−	0.948527i	$-0.602574\pi$
$431$	10.1216	−	7.35380i	0.487542	−	0.354220i	0.804238	+	0.594307i	$0.202574\pi$
$432$		0			0
$433$	−2.24129	+	6.89797i	−0.107709	+	0.331495i	−0.990357	−	0.138540i	$-0.955759\pi$
$433$	−2.24129	+	6.89797i	−0.107709	+	0.331495i	0.882647	+	0.470036i	$0.155759\pi$
$434$	0.649953	−	0.894583i	0.0311987	−	0.0429414i
$435$		0			0
$436$	−0.0225931	−	0.00734095i	−0.00108201	−	0.000351568i
$437$	2.11201	+	6.50010i	0.101031	+	0.310942i
$438$		0			0
$439$			12.6026i			0.601491i	0.953704	+	0.300745i	$0.0972354\pi$
$439$			12.6026i			0.601491i	−0.953704	+	0.300745i	$0.902765\pi$
$440$	−1.29932	+	6.88712i	−0.0619425	+	0.328331i
$441$		0			0
$442$	0.302940	+	0.416961i	0.0144094	+	0.0198328i
$443$	26.2306	−	8.52285i	1.24626	−	0.404933i	0.389678	−	0.920951i	$-0.372586\pi$
$443$	26.2306	−	8.52285i	1.24626	−	0.404933i	0.856577	+	0.516018i	$0.172586\pi$
$444$		0			0
$445$	19.5035	+	14.1701i	0.924555	+	0.671729i
$446$	−2.56803	−	1.86578i	−0.121600	−	0.0883475i
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−19.9800	−	27.5001i	−0.942914	−	1.29781i	−0.954604	−	0.297878i	$-0.903721\pi$
$449$	−19.9800	−	27.5001i	−0.942914	−	1.29781i	0.0116901	−	0.999932i	$-0.496279\pi$
$450$		0			0
$451$	−33.4549	+	15.8257i	−1.57533	+	0.745201i
$452$			14.5851i			0.686026i
$453$		0			0
$454$	−2.06754	−	6.36324i	−0.0970346	−	0.298642i
$455$	1.20623	+	0.391929i	0.0565491	+	0.0183739i
$456$		0			0
$457$	20.8571	−	28.7073i	0.975654	−	1.34287i	0.0365163	−	0.999333i	$-0.488374\pi$
$457$	20.8571	−	28.7073i	0.975654	−	1.34287i	0.939138	−	0.343540i	$-0.111626\pi$
$458$	1.00538	−	3.09426i	0.0469785	−	0.144585i
$459$		0			0
$460$	−5.00272	+	3.63469i	−0.233253	+	0.169468i
$461$	−7.83195			−0.364771			−0.182385	−	0.983227i	$-0.558382\pi$
$461$	−7.83195			−0.364771			−0.182385	+	0.983227i	$0.558382\pi$
$462$		0			0
$463$	6.35723			0.295445			0.147723	−	0.989029i	$-0.452806\pi$
$463$	6.35723			0.295445			0.147723	+	0.989029i	$0.452806\pi$
$464$	4.94369	−	3.59180i	0.229505	−	0.166745i
$465$		0			0
$466$	4.45678	−	13.7166i	0.206456	−	0.635407i
$467$	5.79854	−	7.98101i	0.268325	−	0.369317i	−0.653499	−	0.756928i	$-0.726699\pi$
$467$	5.79854	−	7.98101i	0.268325	−	0.369317i	0.921823	+	0.387611i	$0.126699\pi$
$468$		0			0
$469$	−2.46271	−	0.800182i	−0.113717	−	0.0369490i
$470$	4.05411	+	12.4773i	0.187002	+	0.575533i
$471$		0			0
$472$			0.211454i			0.00973296i
$473$	−8.86697	+	1.13844i	−0.407704	+	0.0523453i
$474$		0			0
$475$	0.733765	+	1.00994i	0.0336674	+	0.0463393i
$476$	−0.816685	+	0.265357i	−0.0374327	+	0.0121626i
$477$		0			0
$478$	15.0662	+	10.9463i	0.689113	+	0.500670i
$479$	−29.4919	−	21.4271i	−1.34752	−	0.979031i	−0.999131	−	0.0416811i	$-0.986729\pi$
$479$	−29.4919	−	21.4271i	−1.34752	−	0.979031i	−0.348390	−	0.937350i	$-0.613271\pi$
$480$		0			0
$481$	4.38895	−	1.42606i	0.200119	−	0.0650226i
$482$	0.789392	+	1.08650i	0.0359558	+	0.0494889i
$483$		0			0
$484$	−0.646155	+	10.9810i	−0.0293707	+	0.499137i
$485$			14.6658i			0.665938i
$486$		0			0
$487$	7.76895	+	23.9104i	0.352045	+	1.08348i	0.957703	+	0.287758i	$0.0929098\pi$
$487$	7.76895	+	23.9104i	0.352045	+	1.08348i	−0.605659	+	0.795725i	$0.707090\pi$
$488$	−11.8326	−	3.84466i	−0.535639	−	0.174040i
$489$		0			0
$490$	−1.24209	+	1.70960i	−0.0561121	+	0.0772316i
$491$	−12.8737	+	39.6212i	−0.580983	+	1.78808i	0.0338536	+	0.999427i	$0.489222\pi$
$491$	−12.8737	+	39.6212i	−0.580983	+	1.78808i	−0.614836	+	0.788655i	$0.710778\pi$
$492$		0			0
$493$	4.24521	−	3.08433i	0.191195	−	0.138911i
$494$	−1.40181			−0.0630705
$495$		0			0
$496$	−1.10577			−0.0496503
$497$	−3.96613	+	2.88156i	−0.177905	+	0.129256i
$498$		0			0
$499$	6.68502	−	20.5744i	0.299263	−	0.921036i	−0.682494	−	0.730892i	$-0.739104\pi$
$499$	6.68502	−	20.5744i	0.299263	−	0.921036i	0.981756	−	0.190144i	$-0.0608955\pi$
$500$	−6.87435	+	9.46173i	−0.307430	+	0.423142i
$501$		0			0
$502$	−6.24428	−	2.02889i	−0.278696	−	0.0905538i
$503$	3.23601	+	9.95943i	0.144287	+	0.444069i	0.996919	−	0.0784432i	$-0.0249949\pi$
$503$	3.23601	+	9.95943i	0.144287	+	0.444069i	−0.852632	+	0.522512i	$0.824995\pi$
$504$		0			0
$505$			9.46256i			0.421078i
$506$	−7.06138	+	6.65808i	−0.313917	+	0.295988i
$507$		0			0
$508$	−7.07185	−	9.73356i	−0.313763	−	0.431857i
$509$	31.4815	−	10.2290i	1.39539	−	0.453391i	0.487695	−	0.873014i	$-0.337838\pi$
$509$	31.4815	−	10.2290i	1.39539	−	0.453391i	0.907698	+	0.419624i	$0.137838\pi$
$510$		0			0
$511$	1.53268	+	1.11356i	0.0678019	+	0.0492610i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−13.1614	+	4.27641i	−0.580525	+	0.188624i
$515$	4.01376	+	5.52446i	0.176867	+	0.243437i
$516$		0			0
$517$	8.80491	+	18.6133i	0.387240	+	0.818612i
$518$			7.68891i			0.337831i
$519$		0			0
$520$	−0.391929	−	1.20623i	−0.0171872	−	0.0528969i
$521$	23.8373	+	7.74520i	1.04433	+	0.339324i	0.780441	−	0.625229i	$-0.214995\pi$
$521$	23.8373	+	7.74520i	1.04433	+	0.339324i	0.263889	+	0.964553i	$0.414995\pi$
$522$		0			0
$523$	−14.2514	+	19.6154i	−0.623170	+	0.857720i	−0.997579	−	0.0695438i	$-0.977846\pi$
$523$	−14.2514	+	19.6154i	−0.623170	+	0.857720i	0.374409	+	0.927264i	$0.377846\pi$
$524$	−4.58552	+	14.1128i	−0.200319	+	0.616520i
$525$		0			0
$526$	8.12965	−	5.90654i	0.354470	−	0.257537i
$527$	−0.949536			−0.0413624
$528$		0			0
$529$	14.4370			0.627695
$530$	−4.34350	+	3.15574i	−0.188670	+	0.137077i
$531$		0			0
$532$	0.721743	−	2.22130i	0.0312915	−	0.0963054i
$533$	3.93661	−	5.41827i	0.170513	−	0.234691i
$534$		0			0
$535$	−34.5016	−	11.2102i	−1.49163	−	0.484661i
$536$	0.800182	+	2.46271i	0.0345626	+	0.106373i
$537$		0			0
$538$		−	20.1288i		−	0.867815i
$539$	−1.59190	+	2.90962i	−0.0685679	+	0.125326i
$540$		0			0
$541$	15.2824	+	21.0344i	0.657042	+	0.904340i	0.999379	−	0.0352367i	$-0.0112185\pi$
$541$	15.2824	+	21.0344i	0.657042	+	0.904340i	−0.342337	+	0.939577i	$0.611219\pi$
$542$	−27.7908	+	9.02976i	−1.19372	+	0.387862i
$543$		0			0
$544$	0.694714	+	0.504739i	0.0297856	+	0.0216405i
$545$	0.0406128	+	0.0295069i	0.00173966	+	0.00126394i
$546$		0			0
$547$	−8.11283	+	2.63602i	−0.346880	+	0.112708i	−0.477275	−	0.878754i	$-0.658375\pi$
$547$	−8.11283	+	2.63602i	−0.346880	+	0.112708i	0.130395	+	0.991462i	$0.458375\pi$
$548$	−2.90157	−	3.99366i	−0.123949	−	0.170601i
$549$		0			0
$550$	−0.850850	+	1.55515i	−0.0362804	+	0.0663120i
$551$			14.2723i			0.608020i
$552$		0			0
$553$	−2.64608	−	8.14378i	−0.112523	−	0.346309i
$554$	11.3162	+	3.67684i	0.480778	+	0.156214i
$555$		0			0
$556$	7.01419	−	9.65420i	0.297468	−	0.409429i
$557$	−11.5341	+	35.4983i	−0.488715	+	1.50411i	0.337812	+	0.941214i	$0.390313\pi$
$557$	−11.5341	+	35.4983i	−0.488715	+	1.50411i	−0.826527	+	0.562897i	$0.809687\pi$
$558$		0			0
$559$	1.30881	−	0.950905i	0.0553567	−	0.0402190i
$560$	2.11318			0.0892980
$561$		0			0
$562$	4.79824			0.202402
$563$	14.9350	−	10.8509i	0.629434	−	0.457311i	−0.226770	−	0.973948i	$-0.572817\pi$
$563$	14.9350	−	10.8509i	0.629434	−	0.457311i	0.856204	+	0.516638i	$0.172817\pi$
$564$		0			0
$565$	9.52419	−	29.3124i	0.400686	−	1.23318i
$566$	−13.8696	+	19.0899i	−0.582984	+	0.802409i
$567$		0			0
$568$	4.66247	+	1.51493i	0.195633	+	0.0635649i
$569$	−9.35357	−	28.7873i	−0.392122	−	1.20683i	−0.931180	−	0.364559i	$-0.881220\pi$
$569$	−9.35357	−	28.7873i	−0.392122	−	1.20683i	0.539058	−	0.842269i	$-0.318780\pi$
$570$		0			0
$571$			29.3456i			1.22808i	0.789276	+	0.614038i	$0.210456\pi$
$571$			29.3456i			1.22808i	−0.789276	+	0.614038i	$0.789544\pi$
$572$	−0.851212	−	1.79943i	−0.0355909	−	0.0752381i
$573$		0			0
$574$	6.55892	+	9.02758i	0.273764	+	0.376804i
$575$	−1.48750	+	0.483319i	−0.0620331	+	0.0201558i
$576$		0			0
$577$	8.53498	+	6.20102i	0.355316	+	0.258152i	0.751096	−	0.660193i	$-0.229526\pi$
$577$	8.53498	+	6.20102i	0.355316	+	0.258152i	−0.395780	+	0.918345i	$0.629526\pi$
$578$	−13.1567	−	9.55892i	−0.547248	−	0.397599i
$579$		0			0
$580$	−12.2811	+	3.99036i	−0.509943	+	0.165691i
$581$	4.78311	+	6.58339i	0.198437	+	0.273125i
$582$		0			0
$583$	−6.13088	+	5.78073i	−0.253915	+	0.239413i
$584$		−	1.89450i		−	0.0783950i
$585$		0			0
$586$	−1.45061	−	4.46451i	−0.0599240	−	0.184427i
$587$	−20.9946	−	6.82155i	−0.866538	−	0.281555i	−0.158182	−	0.987410i	$-0.550563\pi$
$587$	−20.9946	−	6.82155i	−0.866538	−	0.281555i	−0.708357	+	0.705855i	$0.750563\pi$
$588$		0			0
$589$	1.51804	−	2.08940i	0.0625496	−	0.0860921i
$590$	0.138081	−	0.424970i	0.00568470	−	0.0174957i
$591$		0			0
$592$	6.22046	−	4.51943i	0.255659	−	0.185747i
$593$	17.1090			0.702581			0.351291	−	0.936266i	$-0.385743\pi$
$593$	17.1090			0.702581			0.351291	+	0.936266i	$0.385743\pi$
$594$		0			0
$595$	1.81461			0.0743919
$596$	−18.2519	+	13.2608i	−0.747628	+	0.543184i
$597$		0			0
$598$	0.542732	−	1.67036i	0.0221940	−	0.0683060i
$599$	−5.66432	+	7.79626i	−0.231438	+	0.318547i	−0.908903	−	0.417008i	$-0.863079\pi$
$599$	−5.66432	+	7.79626i	−0.231438	+	0.318547i	0.677465	+	0.735555i	$0.263079\pi$
$600$		0			0
$601$	12.8074	+	4.16139i	0.522427	+	0.169747i	0.558346	−	0.829608i	$-0.311436\pi$
$601$	12.8074	+	4.16139i	0.522427	+	0.169747i	−0.0359196	+	0.999355i	$0.511436\pi$
$602$	0.832936	+	2.56351i	0.0339479	+	0.104481i
$603$		0			0
$604$		−	3.73852i		−	0.152118i
$605$	8.46928	−	21.6471i	0.344325	−	0.880081i
$606$		0			0
$607$	−4.56626	−	6.28491i	−0.185339	−	0.255097i	0.706230	−	0.707983i	$-0.250395\pi$
$607$	−4.56626	−	6.28491i	−0.185339	−	0.255097i	−0.891569	+	0.452886i	$0.850395\pi$
$608$	−2.22130	+	0.721743i	−0.0900855	+	0.0292705i
$609$		0			0
$610$	21.2701	+	15.4536i	0.861200	+	0.625698i
$611$	−3.01456	−	2.19021i	−0.121956	−	0.0886063i
$612$		0			0
$613$	28.5134	−	9.26455i	1.15164	−	0.374192i	0.329881	−	0.944022i	$-0.392991\pi$
$613$	28.5134	−	9.26455i	1.15164	−	0.374192i	0.821762	+	0.569831i	$0.192991\pi$
$614$	20.0486	+	27.5945i	0.809096	+	1.11362i
$615$		0			0
$616$	3.28962	−	0.422357i	0.132543	−	0.0170172i
$617$			34.2483i			1.37878i	0.724389	+	0.689391i	$0.242122\pi$
$617$			34.2483i			1.37878i	−0.724389	+	0.689391i	$0.757878\pi$
$618$		0			0
$619$	7.30246	+	22.4747i	0.293511	+	0.903333i	0.983718	+	0.179721i	$0.0575194\pi$
$619$	7.30246	+	22.4747i	0.293511	+	0.903333i	−0.690207	+	0.723612i	$0.742481\pi$
$620$	2.22231	+	0.722073i	0.0892502	+	0.0289991i
$621$		0			0
$622$	7.77098	−	10.6958i	0.311588	−	0.428864i
$623$	3.52535	−	10.8499i	0.141240	−	0.434692i
$624$		0			0
$625$	17.8323	−	12.9559i	0.713290	−	0.518236i
$626$	18.9864			0.758851
$627$		0			0
$628$	−1.49784			−0.0597705
$629$	5.34159	−	3.88089i	0.212983	−	0.154741i
$630$		0			0
$631$	14.4681	−	44.5283i	0.575967	−	1.77265i	−0.0568936	−	0.998380i	$-0.518120\pi$
$631$	14.4681	−	44.5283i	0.575967	−	1.77265i	0.632861	−	0.774265i	$-0.281880\pi$
$632$	−5.03313	+	6.92752i	−0.200207	+	0.275562i
$633$		0			0
$634$	−26.0493	−	8.46392i	−1.03455	−	0.336145i
$635$	7.85656	+	24.1800i	0.311778	+	0.959554i
$636$		0			0
$637$		−	0.600191i		−	0.0237804i
$638$	−18.3206	+	8.66646i	−0.725320	+	0.343108i
$639$		0			0
$640$	−1.24209	−	1.70960i	−0.0490981	−	0.0675777i
$641$	−9.38727	+	3.05011i	−0.370775	+	0.120472i	−0.488477	−	0.872577i	$-0.662447\pi$
$641$	−9.38727	+	3.05011i	−0.370775	+	0.120472i	0.117702	+	0.993049i	$0.462447\pi$
$642$		0			0
$643$	18.1775	+	13.2067i	0.716850	+	0.520822i	0.885376	−	0.464875i	$-0.153901\pi$
$643$	18.1775	+	13.2067i	0.716850	+	0.520822i	−0.168527	+	0.985697i	$0.553901\pi$
$644$	2.36740	+	1.72001i	0.0932885	+	0.0677781i
$645$		0			0
$646$	−1.90746	+	0.619770i	−0.0750479	+	0.0243845i
$647$	−20.2137	−	27.8218i	−0.794683	−	1.09379i	−0.993509	−	0.113752i	$-0.963713\pi$
$647$	−20.2137	−	27.8218i	−0.794683	−	1.09379i	0.198826	−	0.980035i	$-0.436287\pi$
$648$		0			0
$649$	0.130015	−	0.689156i	0.00510355	−	0.0270518i
$650$		−	0.320795i		−	0.0125826i
$651$		0			0
$652$	2.30416	+	7.09147i	0.0902378	+	0.277723i
$653$	−6.92872	−	2.25128i	−0.271142	−	0.0880993i	0.170290	−	0.985394i	$-0.445529\pi$
$653$	−6.92872	−	2.25128i	−0.271142	−	0.0880993i	−0.441432	+	0.897295i	$0.645529\pi$
$654$		0			0
$655$	18.4315	−	25.3688i	0.720178	−	0.991240i
$656$	3.44823	−	10.6126i	0.134631	−	0.414351i
$657$		0			0
$658$	5.02267	−	3.64918i	0.195804	−	0.142260i
$659$	48.5116			1.88974			0.944871	−	0.327442i	$-0.106186\pi$
$659$	48.5116			1.88974			0.944871	+	0.327442i	$0.106186\pi$
$660$		0			0
$661$	26.7975			1.04230			0.521151	−	0.853465i	$-0.325503\pi$
$661$	26.7975			1.04230			0.521151	+	0.853465i	$0.325503\pi$
$662$	5.32118	−	3.86606i	0.206814	−	0.150259i
$663$		0			0
$664$	2.51463	−	7.73924i	0.0975866	−	0.300341i
$665$	−2.90104	+	3.99295i	−0.112498	+	0.154840i
$666$		0			0
$667$	−17.0064	−	5.52573i	−0.658492	−	0.213957i
$668$	−1.79133	−	5.51315i	−0.0693086	−	0.213310i
$669$		0			0
$670$		−	5.47195i		−	0.211400i
$671$	36.2002	+	19.8057i	1.39749	+	0.764591i
$672$		0			0
$673$	−4.37393	−	6.02020i	−0.168603	−	0.232062i	0.716352	−	0.697739i	$-0.245811\pi$
$673$	−4.37393	−	6.02020i	−0.168603	−	0.232062i	−0.884954	+	0.465678i	$0.845811\pi$
$674$	31.3987	−	10.2020i	1.20943	−	0.392968i
$675$		0			0
$676$	−10.2258	−	7.42947i	−0.393300	−	0.285749i
$677$	−11.8906	−	8.63903i	−0.456993	−	0.332025i	0.335357	−	0.942091i	$-0.391143\pi$
$677$	−11.8906	−	8.63903i	−0.456993	−	0.332025i	−0.792351	+	0.610066i	$0.791143\pi$
$678$		0			0
$679$	6.60048	−	2.14463i	0.253303	−	0.0823032i
$680$	−1.06660	−	1.46805i	−0.0409023	−	0.0562972i
$681$		0			0
$682$	3.60384	+	0.679896i	0.137998	+	0.0260345i
$683$			19.7565i			0.755963i	0.925813	+	0.377982i	$0.123382\pi$
$683$			19.7565i			0.755963i	−0.925813	+	0.377982i	$0.876618\pi$
$684$		0			0
$685$	3.22353	+	9.92101i	0.123165	+	0.379062i
$686$	0.951057	+	0.309017i	0.0363115	+	0.0117983i
$687$		0			0
$688$	1.58434	−	2.18065i	0.0604023	−	0.0831366i
$689$	0.471215	−	1.45025i	0.0179518	−	0.0552501i
$690$		0			0
$691$	−14.7322	+	10.7036i	−0.560439	+	0.407182i	−0.831619	−	0.555346i	$-0.812586\pi$
$691$	−14.7322	+	10.7036i	−0.560439	+	0.407182i	0.271181	+	0.962528i	$0.412586\pi$
$692$	−9.03209			−0.343349
$693$		0			0
$694$	−14.9988			−0.569347
$695$	−20.4010	+	14.8222i	−0.773855	+	0.562239i
$696$		0			0
$697$	2.96104	−	9.11315i	0.112157	−	0.345185i
$698$	12.8909	−	17.7428i	0.487928	−	0.671575i
$699$		0			0
$700$	0.508328	+	0.165166i	0.0192130	+	0.00624268i
$701$	2.39846	+	7.38171i	0.0905886	+	0.278803i	0.986079	−	0.166278i	$-0.0531749\pi$
$701$	2.39846	+	7.38171i	0.0905886	+	0.278803i	−0.895490	+	0.445081i	$0.853175\pi$
$702$		0			0
$703$			17.9583i			0.677310i
$704$	−2.27529	−	2.41311i	−0.0857530	−	0.0909473i
$705$		0			0
$706$	−15.1402	−	20.8387i	−0.569809	−	0.784275i
$707$	4.25872	−	1.38374i	0.160166	−	0.0520410i
$708$		0			0
$709$	3.02506	+	2.19784i	0.113609	+	0.0825415i	0.643139	−	0.765750i	$-0.277632\pi$
$709$	3.02506	+	2.19784i	0.113609	+	0.0825415i	−0.529530	+	0.848291i	$0.677632\pi$
$710$	−8.38113	−	6.08925i	−0.314538	−	0.228525i
$711$		0			0
$712$	−10.8499	+	3.52535i	−0.406617	+	0.132118i
$713$	1.90193	+	2.61779i	0.0712279	+	0.0980368i
$714$		0			0
$715$	0.535679	+	4.17226i	0.0200333	+	0.156034i
$716$		−	3.93214i		−	0.146951i
$717$		0			0
$718$	−2.72080	−	8.37377i	−0.101539	−	0.312506i
$719$	−18.6439	−	6.05777i	−0.695300	−	0.225917i	−0.0600185	−	0.998197i	$-0.519116\pi$
$719$	−18.6439	−	6.05777i	−0.695300	−	0.225917i	−0.635282	+	0.772281i	$0.719116\pi$
$720$		0			0
$721$	1.89940	−	2.61429i	0.0707372	−	0.0973614i
$722$	−4.18561	+	12.8820i	−0.155772	+	0.479418i
$723$		0			0
$724$	15.5473	−	11.2958i	0.577812	−	0.419805i
$725$	−3.26612			−0.121301
$726$		0			0
$727$	48.5356			1.80009			0.900043	−	0.435801i	$-0.143535\pi$
$727$	48.5356			1.80009			0.900043	+	0.435801i	$0.143535\pi$
$728$	−0.485565	+	0.352783i	−0.0179962	+	0.0130750i
$729$		0			0
$730$	−1.23712	+	3.80747i	−0.0457880	+	0.140921i
$731$	1.36049	−	1.87256i	0.0503196	−	0.0692590i
$732$		0			0
$733$	−3.40954	−	1.10783i	−0.125934	−	0.0409186i	0.245372	−	0.969429i	$-0.421090\pi$
$733$	−3.40954	−	1.10783i	−0.125934	−	0.0409186i	−0.371306	+	0.928510i	$0.621090\pi$
$734$	5.20597	+	16.0223i	0.192156	+	0.591394i
$735$		0			0
$736$		−	2.92626i		−	0.107863i
$737$	−1.09367	−	8.51830i	−0.0402858	−	0.313775i
$738$		0			0
$739$	21.8544	+	30.0800i	0.803927	+	1.10651i	0.992232	+	0.124400i	$0.0397004\pi$
$739$	21.8544	+	30.0800i	0.803927	+	1.10651i	−0.188306	+	0.982110i	$0.560300\pi$
$740$	−15.4528	+	5.02091i	−0.568056	+	0.184572i
$741$		0			0
$742$	2.05544	+	1.49336i	0.0754575	+	0.0548231i
$743$	15.0100	+	10.9054i	0.550662	+	0.400079i	0.828029	−	0.560685i	$-0.189462\pi$
$743$	15.0100	+	10.9054i	0.550662	+	0.400079i	−0.277368	+	0.960764i	$0.589462\pi$
$744$		0			0
$745$	45.3412	−	14.7323i	1.66117	−	0.539748i
$746$	1.60799	+	2.21321i	0.0588727	+	0.0810314i
$747$		0			0
$748$	−1.95382	−	2.07217i	−0.0714387	−	0.0757659i
$749$			17.1671i			0.627272i
$750$		0			0
$751$	−14.2380	−	43.8199i	−0.519550	−	1.59901i	−0.774847	−	0.632149i	$-0.782173\pi$
$751$	−14.2380	−	43.8199i	−0.519550	−	1.59901i	0.255296	−	0.966863i	$-0.417827\pi$
$752$	−5.90450	−	1.91849i	−0.215315	−	0.0699601i
$753$		0			0
$754$	2.15577	−	2.96716i	0.0785084	−	0.108058i
$755$	−2.44128	+	7.51349i	−0.0888473	+	0.273444i
$756$		0			0
$757$	−11.4405	+	8.31203i	−0.415813	+	0.302106i	−0.775951	−	0.630793i	$-0.782730\pi$
$757$	−11.4405	+	8.31203i	−0.415813	+	0.302106i	0.360138	+	0.932899i	$0.382730\pi$
$758$	26.8010			0.973457
$759$		0			0
$760$	4.93555			0.179031
$761$	−40.0387	+	29.0898i	−1.45140	+	1.05451i	−0.465901	+	0.884837i	$0.654270\pi$
$761$	−40.0387	+	29.0898i	−1.45140	+	1.05451i	−0.985501	+	0.169668i	$0.945730\pi$
$762$		0			0
$763$	0.00734095	−	0.0225931i	0.000265760	−	0.000817925i
$764$	0.774356	−	1.06581i	0.0280152	−	0.0385596i
$765$		0			0
$766$	−13.8266	−	4.49254i	−0.499576	−	0.162322i
$767$	0.0392182	+	0.120701i	0.00141609	+	0.00435827i
$768$		0			0
$769$			47.8573i			1.72578i	0.505393	+	0.862889i	$0.331348\pi$
$769$			47.8573i			1.72578i	−0.505393	+	0.862889i	$0.668652\pi$
$770$	−6.88712	−	1.29932i	−0.248195	−	0.0468241i
$771$		0			0
$772$	−4.44167	−	6.11344i	−0.159859	−	0.220027i
$773$	15.0070	−	4.87608i	0.539765	−	0.175380i	−0.0264312	−	0.999651i	$-0.508414\pi$
$773$	15.0070	−	4.87608i	0.539765	−	0.175380i	0.566197	+	0.824270i	$0.308414\pi$
$774$		0			0
$775$	0.478144	+	0.347392i	0.0171754	+	0.0124787i
$776$	−5.61470	−	4.07932i	−0.201556	−	0.146439i
$777$		0			0
$778$	13.6859	−	4.44683i	0.490665	−	0.159427i
$779$	15.3191	+	21.0849i	0.548863	+	0.755445i
$780$		0			0
$781$	−14.2641	−	7.80413i	−0.510410	−	0.279254i
$782$		−	2.51282i		−	0.0898583i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	3.01029	+	0.978103i	0.107442	+	0.0349100i
$786$		0			0
$787$	13.5966	−	18.7141i	0.484667	−	0.667087i	−0.494726	−	0.869049i	$-0.664732\pi$
$787$	13.5966	−	18.7141i	0.484667	−	0.667087i	0.979393	+	0.201962i	$0.0647316\pi$
$788$	0.274935	−	0.846162i	0.00979414	−	0.0301433i
$789$		0			0
$790$	14.6391	−	10.6359i	0.520834	−	0.378408i
$791$	−14.5851			−0.518587
$792$		0			0
$793$	−7.46733			−0.265173
$794$	0.330042	−	0.239789i	0.0117127	−	0.00850981i
$795$		0			0
$796$	−6.73620	+	20.7319i	−0.238758	+	0.734822i
$797$	10.9782	−	15.1102i	0.388869	−	0.535232i	−0.569038	−	0.822311i	$-0.692684\pi$
$797$	10.9782	−	15.1102i	0.388869	−	0.535232i	0.957907	+	0.287079i	$0.0926843\pi$
$798$		0			0
$799$	−5.07028	−	1.64743i	−0.179374	−	0.0582820i
$800$	−0.165166	−	0.508328i	−0.00583950	−	0.0179721i
$801$		0			0
$802$		−	20.4126i		−	0.720793i
$803$	−1.16486	+	6.17443i	−0.0411070	+	0.217891i
$804$		0			0
$805$	−3.63469	−	5.00272i	−0.128106	−	0.176323i
$806$	−0.631188	+	0.205085i	−0.0222327	+	0.00722383i
$807$		0			0
$808$	−3.62269	−	2.63204i	−0.127446	−	0.0925947i
$809$	13.8157	+	10.0377i	0.485736	+	0.352908i	0.803542	−	0.595248i	$-0.202946\pi$
$809$	13.8157	+	10.0377i	0.485736	+	0.352908i	−0.317806	+	0.948156i	$0.602946\pi$
$810$		0			0
$811$	−41.8880	+	13.6102i	−1.47089	+	0.477920i	−0.931376	−	0.364059i	$-0.881391\pi$
$811$	−41.8880	+	13.6102i	−1.47089	+	0.477920i	−0.539510	+	0.841979i	$0.681391\pi$
$812$	3.59180	+	4.94369i	0.126048	+	0.173490i
$813$		0			0
$814$	−23.0521	+	10.9047i	−0.807977	+	0.382209i
$815$		−	15.7567i		−	0.551934i
$816$		0			0
$817$	1.94541	+	5.98736i	0.0680613	+	0.209471i
$818$	−21.6303	−	7.02812i	−0.756286	−	0.245732i
$819$		0			0
$820$	−13.8602	+	19.0769i	−0.484018	+	0.666193i
$821$	2.89084	−	8.89709i	0.100891	−	0.310511i	−0.887853	−	0.460127i	$-0.847804\pi$
$821$	2.89084	−	8.89709i	0.100891	−	0.310511i	0.988744	+	0.149616i	$0.0478039\pi$
$822$		0			0
$823$	29.6911	−	21.5718i	1.03497	−	0.751946i	0.0656690	−	0.997841i	$-0.479082\pi$
$823$	29.6911	−	21.5718i	1.03497	−	0.751946i	0.969296	+	0.245895i	$0.0790819\pi$
$824$	−3.23145			−0.112573
$825$		0			0
$826$	−0.211454			−0.00735742
$827$	−38.8499	+	28.2261i	−1.35094	+	0.981518i	−0.351980	+	0.936007i	$0.614492\pi$
$827$	−38.8499	+	28.2261i	−1.35094	+	0.981518i	−0.998964	+	0.0455108i	$0.985508\pi$
$828$		0			0
$829$	10.7867	−	33.1982i	0.374639	−	1.15302i	−0.569083	−	0.822280i	$-0.692702\pi$
$829$	10.7867	−	33.1982i	0.374639	−	1.15302i	0.943722	−	0.330740i	$-0.107298\pi$
$830$	−10.1076	+	13.9119i	−0.350838	+	0.482888i
$831$		0			0
$832$	0.570816	+	0.185469i	0.0197895	+	0.00642999i
$833$	−0.265357	−	0.816685i	−0.00919408	−	0.0282965i
$834$		0			0
$835$			12.2498i			0.423922i
$836$	7.68327	−	0.986460i	0.265731	−	0.0341174i
$837$		0			0
$838$	5.63131	+	7.75083i	0.194530	+	0.267748i
$839$	34.7671	−	11.2965i	1.20029	−	0.389999i	0.360424	−	0.932788i	$-0.382632\pi$
$839$	34.7671	−	11.2965i	1.20029	−	0.389999i	0.839869	+	0.542790i	$0.182632\pi$
$840$		0			0
$841$	−6.74811	−	4.90279i	−0.232694	−	0.169062i
$842$	−17.3179	−	12.5822i	−0.596814	−	0.433611i
$843$		0			0
$844$	−2.98573	+	0.970123i	−0.102773	+	0.0333930i
$845$	15.6998	+	21.6089i	0.540089	+	0.743368i
$846$		0			0
$847$	−10.9810	−	0.646155i	−0.377312	−	0.0222021i
$848$		−	2.54066i		−	0.0872467i
$849$		0			0
$850$	−0.141830	−	0.436509i	−0.00486474	−	0.0149721i
$851$	−21.3986	−	6.95281i	−0.733533	−	0.238339i
$852$		0			0
$853$	9.86968	−	13.5845i	0.337931	−	0.465123i	−0.605904	−	0.795537i	$-0.707189\pi$
$853$	9.86968	−	13.5845i	0.337931	−	0.465123i	0.943836	+	0.330415i	$0.107189\pi$
$854$	3.84466	−	11.8326i	0.131562	−	0.404905i
$855$		0			0
$856$	13.8885	−	10.0906i	0.474698	−	0.344889i
$857$	−8.11019			−0.277039			−0.138519	−	0.990360i	$-0.544234\pi$
$857$	−8.11019			−0.277039			−0.138519	+	0.990360i	$0.544234\pi$
$858$		0			0
$859$	42.0535			1.43485			0.717424	−	0.696637i	$-0.245321\pi$
$859$	42.0535			1.43485			0.717424	+	0.696637i	$0.245321\pi$
$860$	−4.60810	+	3.34798i	−0.157135	+	0.114165i
$861$		0			0
$862$	3.86612	−	11.8987i	0.131681	−	0.405271i
$863$	−7.90347	+	10.8782i	−0.269037	+	0.370298i	−0.922064	−	0.387037i	$-0.873499\pi$
$863$	−7.90347	+	10.8782i	−0.269037	+	0.370298i	0.653027	+	0.757334i	$0.273499\pi$
$864$		0			0
$865$	18.1522	+	5.89802i	0.617195	+	0.200539i
$866$	2.24129	+	6.89797i	0.0761620	+	0.234403i
$867$		0			0
$868$		−	1.10577i		−	0.0375321i
$869$	20.6631	−	19.4830i	0.700949	−	0.660915i
$870$		0			0
$871$	0.913513	+	1.25734i	0.0309532	+	0.0426034i
$872$	−0.0225931	+	0.00734095i	−0.000765099	+	0.000248596i
$873$		0			0
$874$	5.52931	+	4.01728i	0.187032	+	0.135887i
$875$	−9.46173	−	6.87435i	−0.319865	−	0.232396i
$876$		0			0
$877$	−4.91927	+	1.59837i	−0.166112	+	0.0539731i	−0.390892	−	0.920436i	$-0.627834\pi$
$877$	−4.91927	+	1.59837i	−0.166112	+	0.0539731i	0.224780	+	0.974409i	$0.427834\pi$
$878$	7.40764	+	10.1957i	0.249996	+	0.344090i
$879$		0			0
$880$	2.99698	+	6.33552i	0.101028	+	0.213570i
$881$		−	22.3708i		−	0.753692i	−0.926276	−	0.376846i	$-0.877009\pi$
$881$		−	22.3708i		−	0.753692i	0.926276	−	0.376846i	$-0.122991\pi$
$882$		0			0
$883$	2.76973	+	8.52434i	0.0932087	+	0.286867i	0.986783	−	0.162049i	$-0.0518103\pi$
$883$	2.76973	+	8.52434i	0.0932087	+	0.286867i	−0.893574	+	0.448916i	$0.851810\pi$
$884$	0.490167	+	0.159265i	0.0164861	+	0.00535666i
$885$		0			0
$886$	16.2114	−	22.3131i	0.544633	−	0.749624i
$887$	−3.07113	+	9.45197i	−0.103119	+	0.317366i	−0.989284	−	0.146002i	$-0.953359\pi$
$887$	−3.07113	+	9.45197i	−0.103119	+	0.317366i	0.886166	+	0.463368i	$0.153359\pi$
$888$		0			0
$889$	9.73356	−	7.07185i	0.326453	−	0.237182i
$890$	24.1077			0.808091
$891$		0			0
$892$	−3.17426			−0.106282
$893$	11.7310	−	8.52307i	0.392563	−	0.285214i
$894$		0			0
$895$	−2.56771	+	7.90261i	−0.0858292	+	0.264155i
$896$	−0.587785	+	0.809017i	−0.0196365	+	0.0270274i
$897$		0			0
$898$	−32.3283	−	10.5041i	−1.07881	−	0.350526i
$899$	2.08804	+	6.42633i	0.0696401	+	0.214330i
$900$		0			0
$901$		−	2.18170i		−	0.0726830i
$902$	−17.7635	+	32.4675i	−0.591460	+	1.08105i
$903$		0			0
$904$	8.57292	+	11.7996i	0.285131	+	0.392449i
$905$	−38.6225	+	12.5492i	−1.28385	+	0.417150i
$906$		0			0
$907$	40.0310	+	29.0842i	1.32921	+	0.965726i	0.999768	+	0.0215493i	$0.00685988\pi$
$907$	40.0310	+	29.0842i	1.32921	+	0.965726i	0.329440	+	0.944177i	$0.393140\pi$
$908$	−5.41290	−	3.93270i	−0.179633	−	0.130511i
$909$		0			0
$910$	1.20623	−	0.391929i	0.0399863	−	0.0129923i
$911$	7.02717	+	9.67206i	0.232820	+	0.320450i	0.909402	−	0.415918i	$-0.136540\pi$
$911$	7.02717	+	9.67206i	0.232820	+	0.320450i	−0.676582	+	0.736367i	$0.736540\pi$
$912$		0			0
$913$	−12.9541	+	23.6770i	−0.428718	+	0.783596i
$914$		−	35.4842i		−	1.17371i
$915$		0			0
$916$	−1.00538	−	3.09426i	−0.0332189	−	0.102237i
$917$	−14.1128	−	4.58552i	−0.466045	−	0.151427i
$918$		0			0
$919$	3.92433	−	5.40138i	0.129452	−	0.178175i	−0.739371	−	0.673298i	$-0.764877\pi$
$919$	3.92433	−	5.40138i	0.129452	−	0.178175i	0.868823	+	0.495123i	$0.164877\pi$
$920$	−1.91087	+	5.88106i	−0.0629995	+	0.193893i
$921$		0			0
$922$	−6.33618	+	4.60351i	−0.208671	+	0.151608i
$923$	2.94238			0.0968497
$924$		0			0
$925$	−4.10963			−0.135124
$926$	5.14311	−	3.73669i	0.169013	−	0.122795i
$927$		0			0
$928$	1.88832	−	5.81166i	0.0619872	−	0.190777i
$929$	22.0163	−	30.3028i	0.722330	−	0.994202i	−0.277113	−	0.960837i	$-0.589378\pi$
$929$	22.0163	−	30.3028i	0.722330	−	0.994202i	0.999443	−	0.0333649i	$-0.0106224\pi$
$930$		0			0
$931$	2.22130	+	0.721743i	0.0728000	+	0.0236542i
$932$	−4.45678	−	13.7166i	−0.145987	−	0.449301i
$933$		0			0
$934$		−	9.86507i		−	0.322795i
$935$	2.57355	+	5.44039i	0.0841640	+	0.177920i
$936$		0			0
$937$	−1.11690	−	1.53729i	−0.0364877	−	0.0502210i	0.790383	−	0.612613i	$-0.209881\pi$
$937$	−1.11690	−	1.53729i	−0.0364877	−	0.0502210i	−0.826871	+	0.562392i	$0.809881\pi$
$938$	−2.46271	+	0.800182i	−0.0804103	+	0.0261269i
$939$		0			0
$940$	10.6138	+	7.71137i	0.346184	+	0.251517i
$941$	−5.71909	−	4.15516i	−0.186437	−	0.135454i	0.490652	−	0.871356i	$-0.336759\pi$
$941$	−5.71909	−	4.15516i	−0.186437	−	0.135454i	−0.677089	+	0.735901i	$0.736759\pi$
$942$		0			0
$943$	−31.0551	+	10.0904i	−1.01129	+	0.328589i
$944$	0.124290	+	0.171070i	0.00404528	+	0.00556785i
$945$		0			0
$946$	−6.50437	+	6.13289i	−0.211475	+	0.199397i
$947$			42.6131i			1.38474i	0.721542	+	0.692371i	$0.243434\pi$
$947$			42.6131i			1.38474i	−0.721542	+	0.692371i	$0.756566\pi$
$948$		0			0
$949$	−0.351372	−	1.08141i	−0.0114060	−	0.0351041i
$950$	1.18726	+	0.385763i	0.0385197	+	0.0125158i
$951$		0			0
$952$	−0.504739	+	0.694714i	−0.0163587	+	0.0225158i
$953$	−15.3115	+	47.1239i	−0.495988	+	1.52649i	0.319424	+	0.947612i	$0.396511\pi$
$953$	−15.3115	+	47.1239i	−0.495988	+	1.52649i	−0.815412	+	0.578881i	$0.803489\pi$
$954$		0			0
$955$	−2.25224	+	1.63635i	−0.0728809	+	0.0529511i
$956$	18.6229			0.602307
$957$		0			0
$958$	−36.4540			−1.17778
$959$	3.99366	−	2.90157i	0.128962	−	0.0936965i
$960$		0			0
$961$	−9.20169	+	28.3199i	−0.296829	+	0.913544i
$962$	2.71252	−	3.73346i	0.0874552	−	0.120372i
$963$		0			0
$964$	1.27726	+	0.415008i	0.0411379	+	0.0133665i
$965$	4.93453	+	15.1869i	0.158848	+	0.488884i
$966$		0			0
$967$		−	9.85304i		−	0.316852i	−0.987371	−	0.158426i	$-0.949358\pi$
$967$		−	9.85304i		−	0.316852i	0.987371	−	0.158426i	$-0.0506420\pi$
$968$	5.93172	+	9.26362i	0.190653	+	0.297744i
$969$		0			0
$970$	8.62032	+	11.8649i	0.276782	+	0.380958i
$971$	41.8625	−	13.6020i	1.34343	−	0.436508i	0.452954	−	0.891534i	$-0.350370\pi$
$971$	41.8625	−	13.6020i	1.34343	−	0.436508i	0.890478	+	0.455026i	$0.150370\pi$
$972$		0			0
$973$	9.65420	+	7.01419i	0.309500	+	0.224865i
$974$	20.3394	+	14.7774i	0.651716	+	0.473499i
$975$		0			0
$976$	−11.8326	+	3.84466i	−0.378754	+	0.123065i
$977$	−21.2185	−	29.2047i	−0.678838	−	0.934341i	0.321081	−	0.947052i	$-0.395954\pi$
$977$	−21.2185	−	29.2047i	−0.678838	−	0.934341i	−0.999919	+	0.0127108i	$0.995954\pi$
$978$		0			0
$979$	37.5289	−	4.81836i	1.19943	−	0.153995i
$980$			2.11318i			0.0675029i
$981$		0			0
$982$	12.8737	+	39.6212i	0.410817	+	1.26436i
$983$	16.5325	+	5.37174i	0.527305	+	0.171332i	0.560558	−	0.828115i	$-0.310587\pi$
$983$	16.5325	+	5.37174i	0.527305	+	0.171332i	−0.0332529	+	0.999447i	$0.510587\pi$
$984$		0			0
$985$	−1.10510	+	1.52104i	−0.0352114	+	0.0484643i
$986$	1.62153	−	4.99055i	0.0516400	−	0.158931i
$987$		0			0
$988$	−1.13409	+	0.823964i	−0.0360802	+	0.0262138i
$989$	−7.88756			−0.250810
$990$		0			0
$991$	−17.1515			−0.544835			−0.272418	−	0.962179i	$-0.587823\pi$
$991$	−17.1515			−0.544835			−0.272418	+	0.962179i	$0.587823\pi$
$992$	−0.894583	+	0.649953i	−0.0284030	+	0.0206360i
$993$		0			0
$994$	−1.51493	+	4.66247i	−0.0480506	+	0.147884i
$995$	27.0761	−	37.2671i	0.858371	−	1.18145i
$996$		0			0
$997$	6.29490	+	2.04534i	0.199362	+	0.0647765i	0.406996	−	0.913430i	$-0.366576\pi$
$997$	6.29490	+	2.04534i	0.199362	+	0.0647765i	−0.207634	+	0.978207i	$0.566576\pi$
$998$	−6.68502	−	20.5744i	−0.211611	−	0.651271i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.24209 + 1.70960i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.24209 + 1.70960i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +2.11318i q^{10} +(0.422357 + 3.28962i) q^{11} +(-0.352783 - 0.485565i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.694714 - 0.504739i) q^{17} +(2.22130 - 0.721743i) q^{19} +(1.24209 + 1.70960i) q^{20} +(2.27529 + 2.41311i) q^{22} +2.92626i q^{23} +(0.165166 + 0.508328i) q^{25} +(-0.570816 - 0.185469i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-1.88832 + 5.81166i) q^{29} +(0.894583 - 0.649953i) q^{31} -1.00000 q^{32} -0.858714 q^{34} +(-1.70960 + 1.24209i) q^{35} +(-2.37600 + 7.31259i) q^{37} +(1.37284 - 1.88955i) q^{38} +(2.00975 + 0.653007i) q^{40} +(3.44823 + 10.6126i) q^{41} +2.69544i q^{43} +(3.25913 + 0.614864i) q^{44} +(1.72001 + 2.36740i) q^{46} +(5.90450 - 1.91849i) q^{47} +(0.809017 + 0.587785i) q^{49} +(0.432410 + 0.314164i) q^{50} +(-0.570816 + 0.185469i) q^{52} +(1.49336 + 2.05544i) q^{53} +(-6.14853 - 3.36396i) q^{55} -1.00000i q^{56} +(1.88832 + 5.81166i) q^{58} +(-0.201105 - 0.0653429i) q^{59} +(7.31298 - 10.0654i) q^{61} +(0.341700 - 1.05165i) q^{62} +(-0.809017 + 0.587785i) q^{64} +1.26831 q^{65} -2.58944 q^{67} +(-0.694714 + 0.504739i) q^{68} +(-0.653007 + 2.00975i) q^{70} +(-2.88156 + 3.96613i) q^{71} +(1.80178 + 0.585433i) q^{73} +(2.37600 + 7.31259i) q^{74} -2.33561i q^{76} +(-0.614864 + 3.25913i) q^{77} +(-5.03313 - 6.92752i) q^{79} +(2.00975 - 0.653007i) q^{80} +(9.02758 + 6.55892i) q^{82} +(6.58339 + 4.78311i) q^{83} +(1.72580 - 0.560746i) q^{85} +(1.58434 + 2.18065i) q^{86} +(2.99810 - 1.41823i) q^{88} -11.4083i q^{89} +(-0.185469 - 0.570816i) q^{91} +(2.78304 + 0.904265i) q^{92} +(3.64918 - 5.02267i) q^{94} +(-1.52517 + 4.69399i) q^{95} +(5.61470 - 4.07932i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 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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