LMFDB - Embedded newform 832.2.bu.n.319.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(63,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("832.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.bu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.4
Root			$1.31256 - 0.526485i$ of defining polynomial
Character	$\chi$	$=$	832.319
Dual form			832.2.bu.n.639.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16981 + 1.25274i) q^{3} +(2.19962 + 2.19962i) q^{5} +(0.152604 - 0.569525i) q^{7} +(1.63871 + 2.83834i) q^{9} +O(q^{10})$	\(q+(2.16981 + 1.25274i) q^{3} +(2.19962 + 2.19962i) q^{5} +(0.152604 - 0.569525i) q^{7} +(1.63871 + 2.83834i) q^{9} +(-2.85302 + 0.764465i) q^{11} +(-2.37076 + 2.71652i) q^{13} +(2.01721 + 7.52831i) q^{15} +(-2.30986 + 1.33360i) q^{17} +(3.11932 + 0.835818i) q^{19} +(1.04459 - 1.04459i) q^{21} +(1.03076 - 1.78533i) q^{23} +4.67667i q^{25} +0.695088i q^{27} +(0.621816 - 1.07702i) q^{29} +(6.34495 - 6.34495i) q^{31} +(-7.14819 - 1.91535i) q^{33} +(1.58841 - 0.917069i) q^{35} +(0.133975 + 0.500000i) q^{37} +(-8.54720 + 2.92438i) q^{39} +(5.59808 - 1.50000i) q^{41} +(-3.60759 - 6.24853i) q^{43} +(-2.63871 + 9.84781i) q^{45} +(-3.16813 - 3.16813i) q^{47} +(5.76111 + 3.32618i) q^{49} -6.68260 q^{51} -3.67667 q^{53} +(-7.95711 - 4.59404i) q^{55} +(5.72126 + 5.72126i) q^{57} +(1.82424 - 6.80816i) q^{59} +(3.97705 + 6.88845i) q^{61} +(1.86658 - 0.500148i) q^{63} +(-11.1901 + 0.760530i) q^{65} +(1.92408 + 7.18077i) q^{67} +(4.47310 - 2.58254i) q^{69} +(-1.98027 - 0.530611i) q^{71} +(0.0440105 - 0.0440105i) q^{73} +(-5.85865 + 10.1475i) q^{75} +1.74153i q^{77} -2.73286i q^{79} +(4.04538 - 7.00680i) q^{81} +(10.1844 - 10.1844i) q^{83} +(-8.01422 - 2.14740i) q^{85} +(2.69844 - 1.55795i) q^{87} +(2.14761 + 8.01501i) q^{89} +(1.18534 + 1.76476i) q^{91} +(21.7159 - 5.81876i) q^{93} +(5.02283 + 8.69980i) q^{95} +(-1.22731 + 4.58039i) q^{97} +(-6.84510 - 6.84510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 4 q^{9}+O(q^{10}) $ 16 * q + 12 * q^5 + 4 * q^9	$ 16 q + 12 q^{5} + 4 q^{9} + 12 q^{13} + 12 q^{17} + 28 q^{21} + 8 q^{29} - 20 q^{33} + 16 q^{37} + 48 q^{41} - 20 q^{45} + 60 q^{49} + 32 q^{53} + 12 q^{57} - 4 q^{61} - 8 q^{65} + 12 q^{69} + 20 q^{73} + 48 q^{81} - 20 q^{85} - 52 q^{89} + 92 q^{93} - 28 q^{97}+O(q^{100}) $ 16 * q + 12 * q^5 + 4 * q^9 + 12 * q^13 + 12 * q^17 + 28 * q^21 + 8 * q^29 - 20 * q^33 + 16 * q^37 + 48 * q^41 - 20 * q^45 + 60 * q^49 + 32 * q^53 + 12 * q^57 - 4 * q^61 - 8 * q^65 + 12 * q^69 + 20 * q^73 + 48 * q^81 - 20 * q^85 - 52 * q^89 + 92 * q^93 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.16981	+	1.25274i	1.25274	+	0.723270i	0.971653	−	0.236413i	$-0.0759717\pi$
$3$	2.16981	+	1.25274i	1.25274	+	0.723270i	0.281087	+	0.959682i	$0.409305\pi$
$4$		0			0
$5$	2.19962	+	2.19962i	0.983701	+	0.983701i	0.999869	−	0.0161686i	$-0.00514685\pi$
$5$	2.19962	+	2.19962i	0.983701	+	0.983701i	−0.0161686	+	0.999869i	$0.505147\pi$
$6$		0			0
$7$	0.152604	−	0.569525i	0.0576788	−	0.215260i	−0.931071	−	0.364837i	$-0.881125\pi$
$7$	0.152604	−	0.569525i	0.0576788	−	0.215260i	0.988750	+	0.149577i	$0.0477912\pi$
$8$		0			0
$9$	1.63871	+	2.83834i	0.546238	+	0.946112i
$10$		0			0
$11$	−2.85302	+	0.764465i	−0.860219	+	0.230495i	−0.661854	−	0.749633i	$-0.730230\pi$
$11$	−2.85302	+	0.764465i	−0.860219	+	0.230495i	−0.198365	+	0.980128i	$0.563563\pi$
$12$		0			0
$13$	−2.37076	+	2.71652i	−0.657532	+	0.753427i
$13$	−2.37076	+	2.71652i	−0.657532	+	0.753427i
$14$		0			0
$15$	2.01721	+	7.52831i	0.520840	+	1.94380i
$16$		0			0
$17$	−2.30986	+	1.33360i	−0.560222	+	0.323445i	−0.753235	−	0.657752i	$-0.771508\pi$
$17$	−2.30986	+	1.33360i	−0.560222	+	0.323445i	0.193012	+	0.981196i	$0.438174\pi$
$18$		0			0
$19$	3.11932	+	0.835818i	0.715620	+	0.191750i	0.598217	−	0.801334i	$-0.295876\pi$
$19$	3.11932	+	0.835818i	0.715620	+	0.191750i	0.117404	+	0.993084i	$0.462543\pi$
$20$		0			0
$21$	1.04459	−	1.04459i	0.227948	−	0.227948i
$22$		0			0
$23$	1.03076	−	1.78533i	0.214928	−	0.372266i	−0.738322	−	0.674448i	$-0.764382\pi$
$23$	1.03076	−	1.78533i	0.214928	−	0.372266i	0.953250	+	0.302182i	$0.0977150\pi$
$24$		0			0
$25$			4.67667i			0.935334i
$26$		0			0
$27$			0.695088i			0.133770i
$28$		0			0
$29$	0.621816	−	1.07702i	0.115468	−	0.199997i	−0.802499	−	0.596654i	$-0.796496\pi$
$29$	0.621816	−	1.07702i	0.115468	−	0.199997i	0.917967	+	0.396657i	$0.129830\pi$
$30$		0			0
$31$	6.34495	−	6.34495i	1.13959	−	1.13959i	0.151062	−	0.988524i	$-0.451731\pi$
$31$	6.34495	−	6.34495i	1.13959	−	1.13959i	0.988524	−	0.151062i	$-0.0482694\pi$
$32$		0			0
$33$	−7.14819	−	1.91535i	−1.24434	−	0.333420i
$34$		0			0
$35$	1.58841	−	0.917069i	0.268490	−	0.155013i
$36$		0			0
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	0.976064	−	0.217485i	$-0.0697853\pi$
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	−0.954038	+	0.299684i	$0.903119\pi$
$38$		0			0
$39$	−8.54720	+	2.92438i	−1.36865	+	0.468275i
$40$		0			0
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.206338	−	0.978481i	$-0.433845\pi$
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.667934	+	0.744220i	$0.267179\pi$
$42$		0			0
$43$	−3.60759	−	6.24853i	−0.550152	−	0.952892i	−0.998263	−	0.0589139i	$-0.981236\pi$
$43$	−3.60759	−	6.24853i	−0.550152	−	0.952892i	0.448111	−	0.893978i	$-0.352097\pi$
$44$		0			0
$45$	−2.63871	+	9.84781i	−0.393356	+	1.46803i
$46$		0			0
$47$	−3.16813	−	3.16813i	−0.462119	−	0.462119i	0.437230	−	0.899350i	$-0.355959\pi$
$47$	−3.16813	−	3.16813i	−0.462119	−	0.462119i	−0.899350	+	0.437230i	$0.855959\pi$
$48$		0			0
$49$	5.76111	+	3.32618i	0.823015	+	0.475168i
$50$		0			0
$51$	−6.68260			−0.935751
$52$		0			0
$53$	−3.67667			−0.505030			−0.252515	−	0.967593i	$-0.581258\pi$
$53$	−3.67667			−0.505030			−0.252515	+	0.967593i	$0.581258\pi$
$54$		0			0
$55$	−7.95711	−	4.59404i	−1.07294	−	0.619460i
$56$		0			0
$57$	5.72126	+	5.72126i	0.757799	+	0.757799i
$58$		0			0
$59$	1.82424	−	6.80816i	0.237496	−	0.886347i	−0.739512	−	0.673143i	$-0.764944\pi$
$59$	1.82424	−	6.80816i	0.237496	−	0.886347i	0.977008	−	0.213203i	$-0.0683897\pi$
$60$		0			0
$61$	3.97705	+	6.88845i	0.509209	+	0.881976i	0.999943	+	0.0106664i	$0.00339528\pi$
$61$	3.97705	+	6.88845i	0.509209	+	0.881976i	−0.490734	+	0.871309i	$0.663271\pi$
$62$		0			0
$63$	1.86658	−	0.500148i	0.235167	−	0.0630127i
$64$		0			0
$65$	−11.1901	+	0.760530i	−1.38796	+	0.0943321i
$66$		0			0
$67$	1.92408	+	7.18077i	0.235064	+	0.877270i	0.978120	+	0.208041i	$0.0667088\pi$
$67$	1.92408	+	7.18077i	0.235064	+	0.877270i	−0.743056	+	0.669229i	$0.766624\pi$
$68$		0			0
$69$	4.47310	−	2.58254i	0.538498	−	0.310902i
$70$		0			0
$71$	−1.98027	−	0.530611i	−0.235014	−	0.0629719i	0.139390	−	0.990238i	$-0.455486\pi$
$71$	−1.98027	−	0.530611i	−0.235014	−	0.0629719i	−0.374404	+	0.927266i	$0.622153\pi$
$72$		0			0
$73$	0.0440105	−	0.0440105i	0.00515104	−	0.00515104i	−0.704527	−	0.709678i	$-0.748841\pi$
$73$	0.0440105	−	0.0440105i	0.00515104	−	0.00515104i	0.709678	+	0.704527i	$0.248841\pi$
$74$		0			0
$75$	−5.85865	+	10.1475i	−0.676499	+	1.17173i
$76$		0			0
$77$			1.74153i			0.198466i
$78$		0			0
$79$		−	2.73286i		−	0.307471i	−0.988112	−	0.153735i	$-0.950870\pi$
$79$		−	2.73286i		−	0.307471i	0.988112	−	0.153735i	$-0.0491303\pi$
$80$		0			0
$81$	4.04538	−	7.00680i	0.449486	−	0.778533i
$82$		0			0
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.125834	−	0.992051i	$-0.459839\pi$
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.992051	−	0.125834i	$-0.0401606\pi$
$84$		0			0
$85$	−8.01422	−	2.14740i	−0.869264	−	0.232919i
$86$		0			0
$87$	2.69844	−	1.55795i	0.289304	−	0.167029i
$88$		0			0
$89$	2.14761	+	8.01501i	0.227647	+	0.849589i	0.981327	+	0.192348i	$0.0616101\pi$
$89$	2.14761	+	8.01501i	0.227647	+	0.849589i	−0.753680	+	0.657241i	$0.771723\pi$
$90$		0			0
$91$	1.18534	+	1.76476i	0.124257	+	0.184997i
$92$		0			0
$93$	21.7159	−	5.81876i	2.25183	−	0.603377i
$94$		0			0
$95$	5.02283	+	8.69980i	0.515332	+	0.892581i
$96$		0			0
$97$	−1.22731	+	4.58039i	−0.124615	+	0.465068i	−0.999826	−	0.0186732i	$-0.994056\pi$
$97$	−1.22731	+	4.58039i	−0.124615	+	0.465068i	0.875211	+	0.483741i	$0.160722\pi$
$98$		0			0
$99$	−6.84510	−	6.84510i	−0.687958	−	0.687958i
$100$		0			0
$101$	−7.77554	−	4.48921i	−0.773695	−	0.446693i	0.0604964	−	0.998168i	$-0.480732\pi$
$101$	−7.77554	−	4.48921i	−0.773695	−	0.446693i	−0.834191	+	0.551476i	$0.814065\pi$
$102$		0			0
$103$	9.60170			0.946084			0.473042	−	0.881040i	$-0.343156\pi$
$103$	9.60170			0.946084			0.473042	+	0.881040i	$0.343156\pi$
$104$		0			0
$105$	4.59540			0.448465
$106$		0			0
$107$	−16.3364	−	9.43183i	−1.57930	−	0.911809i	−0.994957	−	0.100302i	$-0.968019\pi$
$107$	−16.3364	−	9.43183i	−1.57930	−	0.911809i	−0.584343	−	0.811507i	$-0.698648\pi$
$108$		0			0
$109$	2.95252	+	2.95252i	0.282800	+	0.282800i	0.834225	−	0.551425i	$-0.185916\pi$
$109$	2.95252	+	2.95252i	0.282800	+	0.282800i	−0.551425	+	0.834225i	$0.685916\pi$
$110$		0			0
$111$	−0.335671	+	1.25274i	−0.0318604	+	0.118905i
$112$		0			0
$113$	−2.82144	−	4.88687i	−0.265419	−	0.459718i	0.702255	−	0.711926i	$-0.252177\pi$
$113$	−2.82144	−	4.88687i	−0.265419	−	0.459718i	−0.967673	+	0.252207i	$0.918843\pi$
$114$		0			0
$115$	6.19432	−	1.65976i	0.577623	−	0.154774i
$116$		0			0
$117$	−11.5954	−	2.27743i	−1.07199	−	0.210548i
$118$		0			0
$119$	0.407024	+	1.51903i	0.0373118	+	0.139250i
$120$		0			0
$121$	−1.97094	+	1.13792i	−0.179177	+	0.103448i
$122$		0			0
$123$	14.0259	+	3.75822i	1.26467	+	0.338867i
$124$		0			0
$125$	0.711203	−	0.711203i	0.0636119	−	0.0636119i
$126$		0			0
$127$	−6.04172	+	10.4646i	−0.536116	+	0.928580i	0.462993	+	0.886362i	$0.346776\pi$
$127$	−6.04172	+	10.4646i	−0.536116	+	0.928580i	−0.999108	+	0.0422176i	$0.986558\pi$
$128$		0			0
$129$		−	18.0775i		−	1.59163i
$130$		0			0
$131$			19.1689i			1.67479i	0.546597	+	0.837396i	$0.315923\pi$
$131$			19.1689i			1.67479i	−0.546597	+	0.837396i	$0.684077\pi$
$132$		0			0
$133$	0.952039	−	1.64898i	0.0825523	−	0.142985i
$134$		0			0
$135$	−1.52893	+	1.52893i	−0.131589	+	0.131589i
$136$		0			0
$137$	−7.01027	−	1.87840i	−0.598927	−	0.160482i	−0.0533974	−	0.998573i	$-0.517005\pi$
$137$	−7.01027	−	1.87840i	−0.598927	−	0.160482i	−0.545530	+	0.838091i	$0.683672\pi$
$138$		0			0
$139$	−9.61885	+	5.55344i	−0.815860	+	0.471037i	−0.848987	−	0.528414i	$-0.822787\pi$
$139$	−9.61885	+	5.55344i	−0.815860	+	0.471037i	0.0331268	+	0.999451i	$0.489453\pi$
$140$		0			0
$141$	−2.90539	−	10.8431i	−0.244678	−	0.913152i
$142$		0			0
$143$	4.68716	−	9.56266i	0.391960	−	0.799670i
$144$		0			0
$145$	3.73679	−	1.00127i	0.310324	−	0.0831509i
$146$		0			0
$147$	8.33367	+	14.4343i	0.687349	+	1.19052i
$148$		0			0
$149$	−1.34497	+	5.01948i	−0.110184	+	0.411212i	−0.998882	−	0.0472817i	$-0.984944\pi$
$149$	−1.34497	+	5.01948i	−0.110184	+	0.411212i	0.888698	+	0.458494i	$0.151611\pi$
$150$		0			0
$151$	3.67697	+	3.67697i	0.299227	+	0.299227i	0.840711	−	0.541484i	$-0.182137\pi$
$151$	3.67697	+	3.67697i	0.299227	+	0.299227i	−0.541484	+	0.840711i	$0.682137\pi$
$152$		0			0
$153$	−7.57039	−	4.37076i	−0.612029	−	0.353355i
$154$		0			0
$155$	27.9130			2.24202
$156$		0			0
$157$	10.7605			0.858780			0.429390	−	0.903119i	$-0.358729\pi$
$157$	10.7605			0.858780			0.429390	+	0.903119i	$0.358729\pi$
$158$		0			0
$159$	−7.97767	−	4.60591i	−0.632671	−	0.365272i
$160$		0			0
$161$	−0.859490	−	0.859490i	−0.0677373	−	0.0677373i
$162$		0			0
$163$	3.67817	−	13.7271i	0.288097	−	1.07519i	−0.658450	−	0.752625i	$-0.728787\pi$
$163$	3.67817	−	13.7271i	0.288097	−	1.07519i	0.946547	−	0.322567i	$-0.104546\pi$
$164$		0			0
$165$	−11.5103	−	19.9364i	−0.896073	−	1.55204i
$166$		0			0
$167$	9.00303	−	2.41236i	0.696676	−	0.186674i	0.106935	−	0.994266i	$-0.465896\pi$
$167$	9.00303	−	2.41236i	0.696676	−	0.186674i	0.589741	+	0.807592i	$0.299230\pi$
$168$		0			0
$169$	−1.75895	−	12.8805i	−0.135304	−	0.990804i
$170$		0			0
$171$	2.73933	+	10.2233i	0.209482	+	0.781798i
$172$		0			0
$173$	−19.8249	+	11.4459i	−1.50726	+	0.870215i	−0.507292	+	0.861774i	$0.669353\pi$
$173$	−19.8249	+	11.4459i	−1.50726	+	0.870215i	−0.999964	+	0.00844060i	$0.997313\pi$
$174$		0			0
$175$	2.66348	+	0.713678i	0.201340	+	0.0539490i
$176$		0			0
$177$	12.4871	−	12.4871i	0.938588	−	0.938588i
$178$		0			0
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	−0.999976	−	0.00691464i	$-0.997799\pi$
$179$	−6.60927	+	11.4476i	−0.494000	+	0.855633i	0.505976	+	0.862547i	$0.331132\pi$
$180$		0			0
$181$		−	26.1208i		−	1.94154i	−0.240009	−	0.970771i	$-0.577151\pi$
$181$		−	26.1208i		−	1.94154i	0.240009	−	0.970771i	$-0.422849\pi$
$182$		0			0
$183$			19.9288i			1.47318i
$184$		0			0
$185$	−0.805117	+	1.39450i	−0.0591934	+	0.102526i
$186$		0			0
$187$	5.57059	−	5.57059i	0.407362	−	0.407362i
$188$		0			0
$189$	0.395870	+	0.106073i	0.0287953	+	0.00771568i
$190$		0			0
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.872613	−	0.488412i	$-0.837576\pi$
$191$	−12.2440	+	7.06905i	−0.885942	+	0.511499i	−0.0133290	+	0.999911i	$0.504243\pi$
$192$		0			0
$193$	−6.00426	−	22.4082i	−0.432196	−	1.61298i	−0.747689	−	0.664049i	$-0.768837\pi$
$193$	−6.00426	−	22.4082i	−0.432196	−	1.61298i	0.315493	−	0.948928i	$-0.397830\pi$
$194$		0			0
$195$	−25.2331	−	12.3681i	−1.80698	−	0.885696i
$196$		0			0
$197$	−5.99473	+	1.60628i	−0.427107	+	0.114443i	−0.465968	−	0.884802i	$-0.654294\pi$
$197$	−5.99473	+	1.60628i	−0.427107	+	0.114443i	0.0388607	+	0.999245i	$0.487627\pi$
$198$		0			0
$199$	−1.50716	−	2.61048i	−0.106840	−	0.185052i	0.807649	−	0.589664i	$-0.200740\pi$
$199$	−1.50716	−	2.61048i	−0.106840	−	0.185052i	−0.914488	+	0.404612i	$0.867407\pi$
$200$		0			0
$201$	−4.82075	+	17.9913i	−0.340029	+	1.26901i
$202$		0			0
$203$	−0.518497	−	0.518497i	−0.0363913	−	0.0363913i
$204$		0			0
$205$	15.6131	+	9.01422i	1.09046	+	0.629580i
$206$		0			0
$207$	6.75647			0.469607
$208$		0			0
$209$	−9.53844			−0.659788
$210$		0			0
$211$	−15.7735	−	9.10682i	−1.08589	−	0.626940i	−0.153412	−	0.988162i	$-0.549026\pi$
$211$	−15.7735	−	9.10682i	−1.08589	−	0.626940i	−0.932480	+	0.361223i	$0.882359\pi$
$212$		0			0
$213$	−3.63208	−	3.63208i	−0.248866	−	0.248866i
$214$		0			0
$215$	5.80907	−	21.6797i	0.396175	−	1.47855i
$216$		0			0
$217$	−2.64534	−	4.58187i	−0.179578	−	0.311038i
$218$		0			0
$219$	0.150628	−	0.0403607i	0.0101785	−	0.00272732i
$220$		0			0
$221$	1.85339	−	9.43641i	0.124672	−	0.634762i
$222$		0			0
$223$	−0.919045	−	3.42992i	−0.0615438	−	0.229685i	0.928303	−	0.371826i	$-0.121268\pi$
$223$	−0.919045	−	3.42992i	−0.0615438	−	0.229685i	−0.989846	+	0.142141i	$0.954601\pi$
$224$		0			0
$225$	−13.2740	+	7.66372i	−0.884931	+	0.510915i
$226$		0			0
$227$	−16.8419	−	4.51279i	−1.11784	−	0.299524i	−0.347831	−	0.937557i	$-0.613082\pi$
$227$	−16.8419	−	4.51279i	−1.11784	−	0.299524i	−0.770009	+	0.638033i	$0.779748\pi$
$228$		0			0
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	−0.0544132	−	0.998519i	$-0.517329\pi$
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	0.998519	+	0.0544132i	$0.0173288\pi$
$230$		0			0
$231$	−2.18168	+	3.77878i	−0.143544	+	0.248626i
$232$		0			0
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$		−	13.9374i		−	0.909174i
$236$		0			0
$237$	3.42356	−	5.92978i	0.222384	−	0.385181i
$238$		0			0
$239$	10.2493	−	10.2493i	0.662972	−	0.662972i	−0.293108	−	0.956079i	$-0.594689\pi$
$239$	10.2493	−	10.2493i	0.662972	−	0.662972i	0.956079	+	0.293108i	$0.0946894\pi$
$240$		0			0
$241$	13.3784	+	3.58474i	0.861781	+	0.230914i	0.662531	−	0.749035i	$-0.269482\pi$
$241$	13.3784	+	3.58474i	0.861781	+	0.230914i	0.199251	+	0.979949i	$0.436149\pi$
$242$		0			0
$243$	19.3613	−	11.1782i	1.24203	−	0.717084i
$244$		0			0
$245$	5.35593	+	19.9886i	0.342178	+	1.27702i
$246$		0			0
$247$	−9.66568	+	6.49216i	−0.615013	+	0.413086i
$248$		0			0
$249$	34.8567	−	9.33982i	2.20895	−	0.591887i
$250$		0			0
$251$	1.25814	+	2.17916i	0.0794129	+	0.137547i	0.902997	−	0.429647i	$-0.141362\pi$
$251$	1.25814	+	2.17916i	0.0794129	+	0.137547i	−0.823584	+	0.567195i	$0.808029\pi$
$252$		0			0
$253$	−1.57596	+	5.88156i	−0.0990797	+	0.369770i
$254$		0			0
$255$	−14.6992	−	14.6992i	−0.920498	−	0.920498i
$256$		0			0
$257$	5.55423	+	3.20673i	0.346463	+	0.200031i	0.663126	−	0.748507i	$-0.269229\pi$
$257$	5.55423	+	3.20673i	0.346463	+	0.200031i	−0.316663	+	0.948538i	$0.602563\pi$
$258$		0			0
$259$	0.305208			0.0189647
$260$		0			0
$261$	4.07591			0.252293
$262$		0			0
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	0.351524	−	0.936179i	$-0.385664\pi$
$263$	−4.59709	−	2.65413i	−0.283469	−	0.163661i	−0.634993	+	0.772518i	$0.718997\pi$
$264$		0			0
$265$	−8.08728	−	8.08728i	−0.496798	−	0.496798i
$266$		0			0
$267$	−5.38080	+	20.0814i	−0.329300	+	1.22896i
$268$		0			0
$269$	−5.00048	−	8.66109i	−0.304885	−	0.528076i	0.672351	−	0.740233i	$-0.265285\pi$
$269$	−5.00048	−	8.66109i	−0.304885	−	0.528076i	−0.977236	+	0.212157i	$0.931951\pi$
$270$		0			0
$271$	−24.6484	+	6.60453i	−1.49729	+	0.401196i	−0.912190	−	0.409768i	$-0.865610\pi$
$271$	−24.6484	+	6.60453i	−1.49729	+	0.401196i	−0.585096	+	0.810964i	$0.698943\pi$
$272$		0			0
$273$	0.361171	+	5.31411i	0.0218591	+	0.321625i
$274$		0			0
$275$	−3.57515	−	13.3427i	−0.215590	−	0.804592i
$276$		0			0
$277$	−0.462736	+	0.267161i	−0.0278031	+	0.0160521i	−0.513837	−	0.857888i	$-0.671776\pi$
$277$	−0.462736	+	0.267161i	−0.0278031	+	0.0160521i	0.486034	+	0.873940i	$0.338443\pi$
$278$		0			0
$279$	28.4066	+	7.61154i	1.70066	+	0.455691i
$280$		0			0
$281$	−0.275535	+	0.275535i	−0.0164370	+	0.0164370i	−0.715278	−	0.698840i	$-0.753700\pi$
$281$	−0.275535	+	0.275535i	−0.0164370	+	0.0164370i	0.698840	+	0.715278i	$0.253700\pi$
$282$		0			0
$283$	8.03188	−	13.9116i	0.477446	−	0.826960i	−0.522220	−	0.852811i	$-0.674896\pi$
$283$	8.03188	−	13.9116i	0.477446	−	0.826960i	0.999666	+	0.0258504i	$0.00822935\pi$
$284$		0			0
$285$			25.1692i			1.49090i
$286$		0			0
$287$		−	3.41715i		−	0.201708i
$288$		0			0
$289$	−4.94304	+	8.56160i	−0.290767	+	0.503624i
$290$		0			0
$291$	−8.40107	+	8.40107i	−0.492479	+	0.492479i
$292$		0			0
$293$	−1.97920	−	0.530326i	−0.115626	−	0.0309820i	0.200542	−	0.979685i	$-0.435730\pi$
$293$	−1.97920	−	0.530326i	−0.115626	−	0.0309820i	−0.316168	+	0.948703i	$0.602396\pi$
$294$		0			0
$295$	18.9880	−	10.9627i	1.10552	−	0.638275i
$296$		0			0
$297$	−0.531371	−	1.98310i	−0.0308333	−	0.115071i
$298$		0			0
$299$	2.40619	+	7.03266i	0.139153	+	0.406709i
$300$		0			0
$301$	−4.10923	+	1.10106i	−0.236852	+	0.0634643i
$302$		0			0
$303$	−11.2476	−	19.4814i	−0.646159	−	1.11918i
$304$		0			0
$305$	−6.40398	+	23.9000i	−0.366691	+	1.36851i
$306$		0			0
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	0.953608	−	0.301050i	$-0.0973372\pi$
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	−0.301050	+	0.953608i	$0.597337\pi$
$308$		0			0
$309$	20.8339	+	12.0284i	1.18520	+	0.684274i
$310$		0			0
$311$	−24.0242			−1.36229			−0.681143	−	0.732151i	$-0.738517\pi$
$311$	−24.0242			−1.36229			−0.681143	+	0.732151i	$0.738517\pi$
$312$		0			0
$313$	28.9008			1.63357			0.816786	−	0.576941i	$-0.195754\pi$
$313$	28.9008			1.63357			0.816786	+	0.576941i	$0.195754\pi$
$314$		0			0
$315$	5.20590	+	3.00563i	0.293319	+	0.169348i
$316$		0			0
$317$	−0.0141017	−	0.0141017i	−0.000792031	−	0.000792031i	0.706711	−	0.707503i	$-0.250178\pi$
$317$	−0.0141017	−	0.0141017i	−0.000792031	−	0.000792031i	−0.707503	+	0.706711i	$0.750178\pi$
$318$		0			0
$319$	−0.950714	+	3.54811i	−0.0532297	+	0.198656i
$320$		0			0
$321$	−23.6312	−	40.9305i	−1.31897	−	2.28452i
$322$		0			0
$323$	−8.31982	+	2.22929i	−0.462927	+	0.124041i
$324$		0			0
$325$	−12.7043	−	11.0873i	−0.704706	−	0.615012i
$326$		0			0
$327$	2.70767	+	10.1051i	0.149734	+	0.558816i
$328$		0			0
$329$	−2.28780	+	1.32086i	−0.126130	+	0.0728214i
$330$		0			0
$331$	−4.08070	−	1.09342i	−0.224295	−	0.0600998i	0.144921	−	0.989443i	$-0.453707\pi$
$331$	−4.08070	−	1.09342i	−0.224295	−	0.0600998i	−0.369216	+	0.929343i	$0.620374\pi$
$332$		0			0
$333$	−1.19962	+	1.19962i	−0.0657389	+	0.0657389i
$334$		0			0
$335$	−11.5627	+	20.0272i	−0.631739	+	1.09420i
$336$		0			0
$337$		−	9.58550i		−	0.522155i	−0.965318	−	0.261078i	$-0.915922\pi$
$337$		−	9.58550i		−	0.522155i	0.965318	−	0.261078i	$-0.0840778\pi$
$338$		0			0
$339$		−	14.1381i		−	0.767877i
$340$		0			0
$341$	−13.2518	+	22.9528i	−0.717625	+	1.24296i
$342$		0			0
$343$	5.69196	−	5.69196i	0.307337	−	0.307337i
$344$		0			0
$345$	15.5197	+	4.15850i	0.835555	+	0.223886i
$346$		0			0
$347$	−3.56473	+	2.05810i	−0.191364	+	0.110484i	−0.592621	−	0.805481i	$-0.701907\pi$
$347$	−3.56473	+	2.05810i	−0.191364	+	0.110484i	0.401257	+	0.915966i	$0.368574\pi$
$348$		0			0
$349$	−7.51958	−	28.0634i	−0.402514	−	1.50220i	−0.808595	−	0.588365i	$-0.799772\pi$
$349$	−7.51958	−	28.0634i	−0.402514	−	1.50220i	0.406082	−	0.913837i	$-0.366895\pi$
$350$		0			0
$351$	−1.88822	−	1.64789i	−0.100786	−	0.0879579i
$352$		0			0
$353$	−25.4328	+	6.81469i	−1.35365	+	0.362709i	−0.861481	−	0.507790i	$-0.830463\pi$
$353$	−25.4328	+	6.81469i	−1.35365	+	0.362709i	−0.492169	+	0.870500i	$0.663796\pi$
$354$		0			0
$355$	−3.18869	−	5.52298i	−0.169238	−	0.293129i
$356$		0			0
$357$	−1.01979	+	3.80591i	−0.0539730	+	0.201430i
$358$		0			0
$359$	7.69873	+	7.69873i	0.406324	+	0.406324i	0.880454	−	0.474131i	$-0.157238\pi$
$359$	7.69873	+	7.69873i	0.406324	+	0.406324i	−0.474131	+	0.880454i	$0.657238\pi$
$360$		0			0
$361$	−7.42294	−	4.28564i	−0.390681	−	0.225560i
$362$		0			0
$363$	−5.70210			−0.299282
$364$		0			0
$365$	0.193613			0.0101342
$366$		0			0
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	0.451824	−	0.892107i	$-0.350774\pi$
$367$	−1.81711	−	1.04911i	−0.0948522	−	0.0547630i	−0.546676	+	0.837344i	$0.684107\pi$
$368$		0			0
$369$	13.4311	+	13.4311i	0.699198	+	0.699198i
$370$		0			0
$371$	−0.561074	+	2.09396i	−0.0291295	+	0.108713i
$372$		0			0
$373$	−14.1524	−	24.5126i	−0.732781	−	1.26921i	−0.955690	−	0.294375i	$-0.904889\pi$
$373$	−14.1524	−	24.5126i	−0.732781	−	1.26921i	0.222909	−	0.974839i	$-0.428445\pi$
$374$		0			0
$375$	2.43413	−	0.652222i	0.125698	−	0.0336806i
$376$		0			0
$377$	1.45156	+	4.24253i	0.0747590	+	0.218501i
$378$		0			0
$379$	7.48268	+	27.9257i	0.384360	+	1.43445i	0.839174	+	0.543863i	$0.183039\pi$
$379$	7.48268	+	27.9257i	0.384360	+	1.43445i	−0.454814	+	0.890586i	$0.650294\pi$
$380$		0			0
$381$	−26.2187	+	15.1374i	−1.34323	+	0.775512i
$382$		0			0
$383$	14.6205	+	3.91754i	0.747070	+	0.200177i	0.612218	−	0.790689i	$-0.290277\pi$
$383$	14.6205	+	3.91754i	0.747070	+	0.200177i	0.134852	+	0.990866i	$0.456944\pi$
$384$		0			0
$385$	−3.83070	+	3.83070i	−0.195231	+	0.195231i
$386$		0			0
$387$	11.8236	−	20.4791i	0.601028	−	1.04101i
$388$		0			0
$389$			30.3695i			1.53979i	0.638168	+	0.769897i	$0.279692\pi$
$389$			30.3695i			1.53979i	−0.638168	+	0.769897i	$0.720308\pi$
$390$		0			0
$391$			5.49846i			0.278069i
$392$		0			0
$393$	−24.0136	+	41.5928i	−1.21133	+	2.09808i
$394$		0			0
$395$	6.01125	−	6.01125i	0.302459	−	0.302459i
$396$		0			0
$397$	15.4588	+	4.14218i	0.775857	+	0.207890i	0.624957	−	0.780659i	$-0.285116\pi$
$397$	15.4588	+	4.14218i	0.775857	+	0.207890i	0.150899	+	0.988549i	$0.451783\pi$
$398$		0			0
$399$	4.13149	−	2.38531i	0.206833	−	0.119415i
$400$		0			0
$401$	3.56354	+	13.2993i	0.177955	+	0.664137i	0.996029	+	0.0890245i	$0.0283749\pi$
$401$	3.56354	+	13.2993i	0.177955	+	0.664137i	−0.818075	+	0.575112i	$0.804958\pi$
$402$		0			0
$403$	2.19380	+	32.2786i	0.109281	+	1.60791i
$404$		0			0
$405$	24.3106	−	6.51401i	1.20800	−	0.323684i
$406$		0			0
$407$	−0.764465	−	1.32409i	−0.0378931	−	0.0656328i
$408$		0			0
$409$	0.151353	−	0.564858i	0.00748394	−	0.0279305i	−0.962083	−	0.272757i	$-0.912064\pi$
$409$	0.151353	−	0.564858i	0.00748394	−	0.0279305i	0.969567	+	0.244827i	$0.0787311\pi$
$410$		0			0
$411$	−12.8578	−	12.8578i	−0.634228	−	0.634228i
$412$		0			0
$413$	−3.59903	−	2.07790i	−0.177097	−	0.102247i
$414$		0			0
$415$	44.8037			2.19933
$416$		0			0
$417$	−27.8281			−1.36275
$418$		0			0
$419$	31.9541	+	18.4487i	1.56106	+	0.901278i	0.997150	+	0.0754420i	$0.0240368\pi$
$419$	31.9541	+	18.4487i	1.56106	+	0.901278i	0.563910	+	0.825836i	$0.309297\pi$
$420$		0			0
$421$	22.1875	+	22.1875i	1.08135	+	1.08135i	0.996384	+	0.0849697i	$0.0270794\pi$
$421$	22.1875	+	22.1875i	1.08135	+	1.08135i	0.0849697	+	0.996384i	$0.472921\pi$
$422$		0			0
$423$	3.80056	−	14.1839i	0.184789	−	0.689643i
$424$		0			0
$425$	−6.23679	−	10.8024i	−0.302529	−	0.523995i
$426$		0			0
$427$	4.53006	−	1.21383i	0.219225	−	0.0587411i
$428$		0			0
$429$	22.1498	−	14.8774i	1.06940	−	0.718285i
$430$		0			0
$431$	8.05023	+	30.0439i	0.387766	+	1.44716i	0.833760	+	0.552127i	$0.186183\pi$
$431$	8.05023	+	30.0439i	0.387766	+	1.44716i	−0.445994	+	0.895036i	$0.647150\pi$
$432$		0			0
$433$	9.34712	−	5.39656i	0.449194	−	0.259342i	−0.258296	−	0.966066i	$-0.583161\pi$
$433$	9.34712	−	5.39656i	0.449194	−	0.259342i	0.707490	+	0.706724i	$0.249828\pi$
$434$		0			0
$435$	9.36245	+	2.50866i	0.448895	+	0.120281i
$436$		0			0
$437$	4.70747	−	4.70747i	0.225189	−	0.225189i
$438$		0			0
$439$	−6.48316	+	11.2292i	−0.309424	+	0.535938i	−0.978237	−	0.207493i	$-0.933470\pi$
$439$	−6.48316	+	11.2292i	−0.309424	+	0.535938i	0.668812	+	0.743431i	$0.266803\pi$
$440$		0			0
$441$			21.8026i			1.03822i
$442$		0			0
$443$		−	15.6512i		−	0.743611i	−0.928311	−	0.371805i	$-0.878739\pi$
$443$		−	15.6512i		−	0.743611i	0.928311	−	0.371805i	$-0.121261\pi$
$444$		0			0
$445$	−12.9060	+	22.3539i	−0.611805	+	1.05968i
$446$		0			0
$447$	−9.20642	+	9.20642i	−0.435449	+	0.435449i
$448$		0			0
$449$	10.8227	+	2.89994i	0.510755	+	0.136856i	0.504987	−	0.863127i	$-0.331497\pi$
$449$	10.8227	+	2.89994i	0.510755	+	0.136856i	0.00576812	+	0.999983i	$0.498164\pi$
$450$		0			0
$451$	−14.8247	+	8.55907i	−0.698070	+	0.403031i
$452$		0			0
$453$	3.37203	+	12.5846i	0.158432	+	0.591276i
$454$		0			0
$455$	−1.27451	+	6.48910i	−0.0597500	+	0.304214i
$456$		0			0
$457$	18.5601	−	4.97316i	0.868204	−	0.232634i	0.202893	−	0.979201i	$-0.434966\pi$
$457$	18.5601	−	4.97316i	0.868204	−	0.232634i	0.665311	+	0.746566i	$0.268299\pi$
$458$		0			0
$459$	−0.926967	−	1.60555i	−0.0432671	−	0.0749408i
$460$		0			0
$461$	−6.34751	+	23.6892i	−0.295633	+	1.10332i	0.645081	+	0.764114i	$0.276824\pi$
$461$	−6.34751	+	23.6892i	−0.295633	+	1.10332i	−0.940713	+	0.339202i	$0.889843\pi$
$462$		0			0
$463$	13.2027	+	13.2027i	0.613581	+	0.613581i	0.943877	−	0.330296i	$-0.107149\pi$
$463$	13.2027	+	13.2027i	0.613581	+	0.613581i	−0.330296	+	0.943877i	$0.607149\pi$
$464$		0			0
$465$	60.5658	+	34.9677i	2.80867	+	1.62159i
$466$		0			0
$467$	−22.6548			−1.04834			−0.524171	−	0.851613i	$-0.675625\pi$
$467$	−22.6548			−1.04834			−0.524171	+	0.851613i	$0.675625\pi$
$468$		0			0
$469$	4.38325			0.202400
$470$		0			0
$471$	23.3482	+	13.4801i	1.07583	+	0.621130i
$472$		0			0
$473$	15.0693	+	15.0693i	0.692888	+	0.692888i
$474$		0			0
$475$	−3.90885	+	14.5880i	−0.179350	+	0.669344i
$476$		0			0
$477$	−6.02501	−	10.4356i	−0.275866	−	0.477814i
$478$		0			0
$479$	−3.13701	+	0.840559i	−0.143334	+	0.0384061i	−0.329772	−	0.944060i	$-0.606972\pi$
$479$	−3.13701	+	0.840559i	−0.143334	+	0.0384061i	0.186439	+	0.982467i	$0.440305\pi$
$480$		0			0
$481$	−1.67588	−	0.821438i	−0.0764136	−	0.0374543i
$482$		0			0
$483$	−0.788212	−	2.94165i	−0.0358649	−	0.133850i
$484$		0			0
$485$	−12.7747	+	7.37550i	−0.580071	+	0.334904i
$486$		0			0
$487$	−41.4268	−	11.1003i	−1.87723	−	0.503002i	−0.999725	−	0.0234304i	$-0.992541\pi$
$487$	−41.4268	−	11.1003i	−1.87723	−	0.503002i	−0.877503	−	0.479571i	$-0.840792\pi$
$488$		0			0
$489$	25.1775	−	25.1775i	1.13856	−	1.13856i
$490$		0			0
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	−0.883447	−	0.468531i	$-0.844783\pi$
$491$	−0.796904	+	1.38028i	−0.0359638	+	0.0622911i	0.847483	+	0.530822i	$0.178117\pi$
$492$		0			0
$493$			3.31701i			0.149390i
$494$		0			0
$495$		−	30.1132i		−	1.35349i
$496$		0			0
$497$	−0.604392	+	1.04684i	−0.0271107	+	0.0469571i
$498$		0			0
$499$	−2.89721	+	2.89721i	−0.129697	+	0.129697i	−0.768975	−	0.639278i	$-0.779233\pi$
$499$	−2.89721	+	2.89721i	−0.129697	+	0.129697i	0.639278	+	0.768975i	$0.279233\pi$
$500$		0			0
$501$	22.5569	+	6.04411i	1.00777	+	0.270031i
$502$		0			0
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	−0.762744	−	0.646701i	$-0.776148\pi$
$503$	−13.0990	+	7.56273i	−0.584057	+	0.337205i	0.178687	+	0.983906i	$0.442815\pi$
$504$		0			0
$505$	−7.22868	−	26.9778i	−0.321672	−	1.20050i
$506$		0			0
$507$	12.3193	−	30.1516i	0.547118	−	1.33908i
$508$		0			0
$509$	24.1589	−	6.47337i	1.07083	−	0.286927i	0.319994	−	0.947420i	$-0.396319\pi$
$509$	24.1589	−	6.47337i	1.07083	−	0.286927i	0.750832	+	0.660493i	$0.229653\pi$
$510$		0			0
$511$	−0.0183489	−	0.0317812i	−0.000811708	−	0.00140592i
$512$		0			0
$513$	−0.580967	+	2.16820i	−0.0256503	+	0.0957284i
$514$		0			0
$515$	21.1201	+	21.1201i	0.930663	+	0.930663i
$516$		0			0
$517$	11.4607	+	6.61682i	0.504040	+	0.291007i
$518$		0			0
$519$	−57.3549			−2.51760
$520$		0			0
$521$	−41.1166			−1.80135			−0.900675	−	0.434494i	$-0.856927\pi$
$521$	−41.1166			−1.80135			−0.900675	+	0.434494i	$0.856927\pi$
$522$		0			0
$523$	−2.27834	−	1.31540i	−0.0996249	−	0.0575185i	0.449360	−	0.893351i	$-0.351652\pi$
$523$	−2.27834	−	1.31540i	−0.0996249	−	0.0575185i	−0.548985	+	0.835832i	$0.684985\pi$
$524$		0			0
$525$	4.88519	+	4.88519i	0.213207	+	0.213207i
$526$		0			0
$527$	−6.19432	+	23.1175i	−0.269829	+	1.00702i
$528$		0			0
$529$	9.37507	+	16.2381i	0.407612	+	0.706004i
$530$		0			0
$531$	22.3132	−	5.97882i	0.968312	−	0.259459i
$532$		0			0
$533$	−9.19694	+	18.7634i	−0.398364	+	0.812734i
$534$		0			0
$535$	−15.1875	−	56.6804i	−0.656611	−	2.45051i
$536$		0			0
$537$	−28.6817	+	16.5594i	−1.23771	+	0.714590i
$538$		0			0
$539$	−18.9793	−	5.08549i	−0.817497	−	0.219048i
$540$		0			0
$541$	−14.2591	+	14.2591i	−0.613047	+	0.613047i	−0.943739	−	0.330692i	$-0.892718\pi$
$541$	−14.2591	+	14.2591i	−0.613047	+	0.613047i	0.330692	+	0.943739i	$0.392718\pi$
$542$		0			0
$543$	32.7225	−	56.6771i	1.40426	−	2.43225i
$544$		0			0
$545$			12.9889i			0.556381i
$546$		0			0
$547$			40.9532i			1.75103i	0.483190	+	0.875515i	$0.339478\pi$
$547$			40.9532i			1.75103i	−0.483190	+	0.875515i	$0.660522\pi$
$548$		0			0
$549$	−13.0345	+	22.5764i	−0.556298	+	0.963537i
$550$		0			0
$551$	2.83983	−	2.83983i	0.120981	−	0.120981i
$552$		0			0
$553$	−1.55643	−	0.417045i	−0.0661862	−	0.0177345i
$554$		0			0
$555$	−3.49390	+	2.01721i	−0.148308	+	0.0856256i
$556$		0			0
$557$	−7.78980	−	29.0719i	−0.330064	−	1.23182i	−0.909122	−	0.416530i	$-0.863246\pi$
$557$	−7.78980	−	29.0719i	−0.330064	−	1.23182i	0.579058	−	0.815287i	$-0.303421\pi$
$558$		0			0
$559$	25.5270	+	5.01370i	1.07968	+	0.212057i
$560$		0			0
$561$	19.0656	−	5.10861i	0.804950	−	0.215686i
$562$		0			0
$563$	−7.94721	−	13.7650i	−0.334935	−	0.580124i	0.648537	−	0.761183i	$-0.275381\pi$
$563$	−7.94721	−	13.7650i	−0.334935	−	0.580124i	−0.983472	+	0.181058i	$0.942048\pi$
$564$		0			0
$565$	4.54318	−	16.9554i	0.191133	−	0.713318i
$566$		0			0
$567$	−3.37321	−	3.37321i	−0.141661	−	0.141661i
$568$		0			0
$569$	−19.5646	−	11.2956i	−0.820192	−	0.473538i	0.0302909	−	0.999541i	$-0.490357\pi$
$569$	−19.5646	−	11.2956i	−0.820192	−	0.473538i	−0.850483	+	0.526003i	$0.823690\pi$
$570$		0			0
$571$	−2.17784			−0.0911398			−0.0455699	−	0.998961i	$-0.514510\pi$
$571$	−2.17784			−0.0911398			−0.0455699	+	0.998961i	$0.514510\pi$
$572$		0			0
$573$	−35.4227			−1.47981
$574$		0			0
$575$	8.34938	+	4.82052i	0.348193	+	0.201030i
$576$		0			0
$577$	15.8624	+	15.8624i	0.660361	+	0.660361i	0.955465	−	0.295104i	$-0.0953543\pi$
$577$	15.8624	+	15.8624i	0.660361	+	0.660361i	−0.295104	+	0.955465i	$0.595354\pi$
$578$		0			0
$579$	15.0435	−	56.1433i	0.625188	−	2.33323i
$580$		0			0
$581$	−4.24610	−	7.35446i	−0.176158	−	0.305115i
$582$		0			0
$583$	10.4896	−	2.81069i	0.434436	−	0.116407i
$584$		0			0
$585$	−20.4960	−	30.5150i	−0.847406	−	1.26164i
$586$		0			0
$587$	−5.61437	−	20.9531i	−0.231730	−	0.864827i	−0.979596	−	0.200978i	$-0.935588\pi$
$587$	−5.61437	−	20.9531i	−0.231730	−	0.864827i	0.747866	−	0.663850i	$-0.231079\pi$
$588$		0			0
$589$	25.0951	−	14.4887i	1.03403	−	0.596996i
$590$		0			0
$591$	−15.0197	−	4.02451i	−0.617827	−	0.165546i
$592$		0			0
$593$	0.858298	−	0.858298i	0.0352461	−	0.0352461i	−0.689264	−	0.724510i	$-0.742066\pi$
$593$	0.858298	−	0.858298i	0.0352461	−	0.0352461i	0.724510	+	0.689264i	$0.242066\pi$
$594$		0			0
$595$	−2.44600	+	4.23660i	−0.100276	+	0.173683i
$596$		0			0
$597$		−	7.55231i		−	0.309096i
$598$		0			0
$599$			7.16374i			0.292702i	0.989233	+	0.146351i	$0.0467529\pi$
$599$			7.16374i			0.292702i	−0.989233	+	0.146351i	$0.953247\pi$
$600$		0			0
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	−0.981988	−	0.188941i	$-0.939495\pi$
$601$	−8.02549	+	13.9006i	−0.327367	+	0.567016i	0.654622	+	0.755956i	$0.272828\pi$
$602$		0			0
$603$	−17.2284	+	17.2284i	−0.701595	+	0.701595i
$604$		0			0
$605$	−6.83834	−	1.83233i	−0.278018	−	0.0744947i
$606$		0			0
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.967098	−	0.254404i	$-0.918121\pi$
$607$	−30.3120	+	17.5006i	−1.23033	+	0.710329i	−0.263229	+	0.964734i	$0.584787\pi$
$608$		0			0
$609$	−0.475497	−	1.77458i	−0.0192681	−	0.0719096i
$610$		0			0
$611$	16.1172	−	1.09540i	0.652031	−	0.0443150i
$612$		0			0
$613$	−19.8339	+	5.31448i	−0.801084	+	0.214650i	−0.636060	−	0.771640i	$-0.719437\pi$
$613$	−19.8339	+	5.31448i	−0.801084	+	0.214650i	−0.165024	+	0.986290i	$0.552770\pi$
$614$		0			0
$615$	22.5849	+	39.1183i	0.910712	+	1.57740i
$616$		0			0
$617$	4.87361	−	18.1886i	0.196204	−	0.732244i	−0.795748	−	0.605628i	$-0.792922\pi$
$617$	4.87361	−	18.1886i	0.196204	−	0.732244i	0.991952	−	0.126616i	$-0.0404115\pi$
$618$		0			0
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.989798	−	0.142478i	$-0.954493\pi$
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.142478	−	0.989798i	$-0.545507\pi$
$620$		0			0
$621$	1.24096	+	0.716468i	0.0497980	+	0.0287509i
$622$		0			0
$623$	4.89248			0.196013
$624$		0			0
$625$	26.5121			1.06048
$626$		0			0
$627$	−20.6966	−	11.9492i	−0.826542	−	0.477204i
$628$		0			0
$629$	−0.976260	−	0.976260i	−0.0389260	−	0.0389260i
$630$		0			0
$631$	−3.23895	+	12.0879i	−0.128941	+	0.481213i	−0.999949	−	0.0100543i	$-0.996800\pi$
$631$	−3.23895	+	12.0879i	−0.128941	+	0.481213i	0.871009	+	0.491267i	$0.163466\pi$
$632$		0			0
$633$	−22.8170	−	39.5201i	−0.906893	−	1.57078i
$634$		0			0
$635$	−36.3076	+	9.72858i	−1.44082	+	0.386067i
$636$		0			0
$637$	−22.6938	+	7.76458i	−0.899163	+	0.307644i
$638$		0			0
$639$	−1.73904	−	6.49018i	−0.0687953	−	0.256748i
$640$		0			0
$641$	−22.6933	+	13.1020i	−0.896331	+	0.517497i	−0.876008	−	0.482296i	$-0.839803\pi$
$641$	−22.6933	+	13.1020i	−0.896331	+	0.517497i	−0.0203232	+	0.999793i	$0.506470\pi$
$642$		0			0
$643$	0.362291	+	0.0970757i	0.0142874	+	0.00382829i	0.265956	−	0.963985i	$-0.414313\pi$
$643$	0.362291	+	0.0970757i	0.0142874	+	0.00382829i	−0.251668	+	0.967814i	$0.580979\pi$
$644$		0			0
$645$	39.7636	−	39.7636i	1.56569	−	1.56569i
$646$		0			0
$647$	17.6527	−	30.5754i	0.693999	−	1.20204i	−0.276517	−	0.961009i	$-0.589180\pi$
$647$	17.6527	−	30.5754i	0.693999	−	1.20204i	0.970517	−	0.241033i	$-0.0774863\pi$
$648$		0			0
$649$			20.8184i			0.817194i
$650$		0			0
$651$		−	13.2557i		−	0.519532i
$652$		0			0
$653$	16.0606	−	27.8178i	0.628500	−	1.08859i	−0.359353	−	0.933202i	$-0.617003\pi$
$653$	16.0606	−	27.8178i	0.628500	−	1.08859i	0.987853	−	0.155392i	$-0.0496639\pi$
$654$		0			0
$655$	−42.1642	+	42.1642i	−1.64749	+	1.64749i
$656$		0			0
$657$	0.197037	+	0.0527959i	0.00768715	+	0.00205977i
$658$		0			0
$659$	9.20996	−	5.31737i	0.358769	−	0.207135i	−0.309772	−	0.950811i	$-0.600253\pi$
$659$	9.20996	−	5.31737i	0.358769	−	0.207135i	0.668541	+	0.743676i	$0.266919\pi$
$660$		0			0
$661$	−2.08438	−	7.77900i	−0.0810729	−	0.302568i	0.913469	−	0.406909i	$-0.133393\pi$
$661$	−2.08438	−	7.77900i	−0.0810729	−	0.302568i	−0.994542	+	0.104341i	$0.966727\pi$
$662$		0			0
$663$	15.8429	−	18.1534i	0.615286	−	0.705020i
$664$		0			0
$665$	5.72126	−	1.53301i	0.221861	−	0.0594474i
$666$		0			0
$667$	−1.28188	−	2.22029i	−0.0496348	−	0.0859699i
$668$		0			0
$669$	2.30265	−	8.59360i	0.0890255	−	0.332248i
$670$		0			0
$671$	−16.6126	−	16.6126i	−0.641322	−	0.641322i
$672$		0			0
$673$	1.15151	+	0.664827i	0.0443876	+	0.0256272i	0.522030	−	0.852927i	$-0.325175\pi$
$673$	1.15151	+	0.664827i	0.0443876	+	0.0256272i	−0.477642	+	0.878555i	$0.658508\pi$
$674$		0			0
$675$	−3.25070			−0.125119
$676$		0			0
$677$	−33.7816			−1.29833			−0.649167	−	0.760646i	$-0.724882\pi$
$677$	−33.7816			−1.29833			−0.649167	+	0.760646i	$0.724882\pi$
$678$		0			0
$679$	2.42135	+	1.39797i	0.0929231	+	0.0536492i
$680$		0			0
$681$	−30.8905	−	30.8905i	−1.18373	−	1.18373i
$682$		0			0
$683$	−11.4324	+	42.6664i	−0.437449	+	1.63258i	0.297687	+	0.954664i	$0.403785\pi$
$683$	−11.4324	+	42.6664i	−0.437449	+	1.63258i	−0.735136	+	0.677920i	$0.762882\pi$
$684$		0			0
$685$	−11.2882	−	19.5517i	−0.431299	−	0.747032i
$686$		0			0
$687$	48.8976	−	13.1021i	1.86556	−	0.499876i
$688$		0			0
$689$	8.71652	−	9.98775i	0.332073	−	0.380503i
$690$		0			0
$691$	−10.7564	−	40.1436i	−0.409195	−	1.52714i	−0.796186	−	0.605052i	$-0.793152\pi$
$691$	−10.7564	−	40.1436i	−0.409195	−	1.52714i	0.386991	−	0.922083i	$-0.373514\pi$
$692$		0			0
$693$	−4.94304	+	2.85387i	−0.187771	+	0.108409i
$694$		0			0
$695$	−33.3733	−	8.94235i	−1.26592	−	0.339203i
$696$		0			0
$697$	−10.9304	+	10.9304i	−0.414017	+	0.414017i
$698$		0			0
$699$	−16.6871	+	28.9030i	−0.631165	+	1.09321i
$700$		0			0
$701$		−	17.2912i		−	0.653080i	−0.945183	−	0.326540i	$-0.894117\pi$
$701$		−	17.2912i		−	0.653080i	0.945183	−	0.326540i	$-0.105883\pi$
$702$		0			0
$703$			1.67164i			0.0630470i
$704$		0			0
$705$	17.4599	−	30.2414i	0.657578	−	1.13896i
$706$		0			0
$707$	−3.74329	+	3.74329i	−0.140781	+	0.140781i
$708$		0			0
$709$	40.4498	+	10.8385i	1.51913	+	0.407048i	0.919454	−	0.393198i	$-0.128631\pi$
$709$	40.4498	+	10.8385i	1.51913	+	0.407048i	0.599672	+	0.800246i	$0.295298\pi$
$710$		0			0
$711$	7.75677	−	4.47837i	0.290902	−	0.167952i
$712$		0			0
$713$	−4.78769	−	17.8679i	−0.179301	−	0.669159i
$714$		0			0
$715$	31.3442	−	10.7243i	1.17221	−	0.401064i
$716$		0			0
$717$	35.0787	−	9.39931i	1.31004	−	0.351024i
$718$		0			0
$719$	−17.2567	−	29.8894i	−0.643565	−	1.11469i	−0.984631	−	0.174647i	$-0.944121\pi$
$719$	−17.2567	−	29.8894i	−0.643565	−	1.11469i	0.341066	−	0.940039i	$-0.389212\pi$
$720$		0			0
$721$	1.46526	−	5.46841i	0.0545690	−	0.203654i
$722$		0			0
$723$	24.5379	+	24.5379i	0.912575	+	0.912575i
$724$		0			0
$725$	5.03685	+	2.90803i	0.187064	+	0.108001i
$726$		0			0
$727$	−3.77644			−0.140060			−0.0700302	−	0.997545i	$-0.522310\pi$
$727$	−3.77644			−0.140060			−0.0700302	+	0.997545i	$0.522310\pi$
$728$		0			0
$729$	31.7414			1.17561
$730$		0			0
$731$	16.6660	+	9.62214i	0.616416	+	0.355888i
$732$		0			0
$733$	−4.25026	−	4.25026i	−0.156987	−	0.156987i	0.624243	−	0.781230i	$-0.285407\pi$
$733$	−4.25026	−	4.25026i	−0.156987	−	0.156987i	−0.781230	+	0.624243i	$0.785407\pi$
$734$		0			0
$735$	−13.4192	+	50.0810i	−0.494973	+	1.84727i
$736$		0			0
$737$	−10.9789	−	19.0160i	−0.404413	−	0.700464i
$738$		0			0
$739$	17.4311	−	4.67066i	0.641215	−	0.171813i	0.0764613	−	0.997073i	$-0.475638\pi$
$739$	17.4311	−	4.67066i	0.641215	−	0.171813i	0.564754	+	0.825260i	$0.308971\pi$
$740$		0			0
$741$	−29.1057	+	1.97815i	−1.06922	+	0.0726692i
$742$		0			0
$743$	−3.46818	−	12.9434i	−0.127235	−	0.474848i	0.872674	−	0.488303i	$-0.162384\pi$
$743$	−3.46818	−	12.9434i	−0.127235	−	0.474848i	−0.999909	+	0.0134546i	$0.995717\pi$
$744$		0			0
$745$	−13.9994	+	8.08254i	−0.512898	+	0.296122i
$746$		0			0
$747$	45.5961	+	12.2174i	1.66828	+	0.447013i
$748$		0			0
$749$	−7.86466	+	7.86466i	−0.287368	+	0.287368i
$750$		0			0
$751$	12.5103	−	21.6684i	0.456506	−	0.790691i	−0.542268	−	0.840206i	$-0.682434\pi$
$751$	12.5103	−	21.6684i	0.456506	−	0.790691i	0.998773	+	0.0495148i	$0.0157675\pi$
$752$		0			0
$753$			6.30448i			0.229748i
$754$		0			0
$755$			16.1759i			0.588700i
$756$		0			0
$757$	−19.6123	+	33.9695i	−0.712821	+	1.23464i	0.250973	+	0.967994i	$0.419249\pi$
$757$	−19.6123	+	33.9695i	−0.712821	+	1.23464i	−0.963794	+	0.266648i	$0.914084\pi$
$758$		0			0
$759$	−10.7876	+	10.7876i	−0.391565	+	0.391565i
$760$		0			0
$761$	13.7578	+	3.68640i	0.498722	+	0.133632i	0.499407	−	0.866368i	$-0.333551\pi$
$761$	13.7578	+	3.68640i	0.498722	+	0.133632i	−0.000685009		1.00000i	$0.500218\pi$
$762$		0			0
$763$	2.13210	−	1.23097i	0.0771872	−	0.0445641i
$764$		0			0
$765$	−7.03796	−	26.2660i	−0.254458	−	0.949650i
$766$		0			0
$767$	14.1696	+	21.0961i	0.511636	+	0.761737i
$768$		0			0
$769$	19.3143	−	5.17525i	0.696491	−	0.186624i	0.106833	−	0.994277i	$-0.465929\pi$
$769$	19.3143	−	5.17525i	0.696491	−	0.186624i	0.589658	+	0.807653i	$0.299262\pi$
$770$		0			0
$771$	8.03441	+	13.9160i	0.289352	+	0.501172i
$772$		0			0
$773$	−7.82826	+	29.2155i	−0.281563	+	1.05081i	0.669751	+	0.742585i	$0.266401\pi$
$773$	−7.82826	+	29.2155i	−0.281563	+	1.05081i	−0.951314	+	0.308222i	$0.900266\pi$
$774$		0			0
$775$	29.6732	+	29.6732i	1.06589	+	1.06589i
$776$		0			0
$777$	0.662242	+	0.382346i	0.0237578	+	0.0137166i
$778$		0			0
$779$	18.7159			0.670567
$780$		0			0
$781$	6.05538			0.216679
$782$		0			0
$783$	0.748622	+	0.432217i	0.0267536	+	0.0154462i
$784$		0			0
$785$	23.6690	+	23.6690i	0.844783	+	0.844783i
$786$		0			0
$787$	−2.42897	+	9.06504i	−0.0865834	+	0.323134i	−0.995609	−	0.0936059i	$-0.970161\pi$
$787$	−2.42897	+	9.06504i	−0.0865834	+	0.323134i	0.909026	+	0.416740i	$0.136827\pi$
$788$		0			0
$789$	−6.64987	−	11.5179i	−0.236742	−	0.410049i
$790$		0			0
$791$	−3.21376	+	0.861124i	−0.114268	+	0.0306181i
$792$		0			0
$793$	−28.1413	−	5.52716i	−0.999325	−	0.196275i
$794$		0			0
$795$	−7.41660	−	27.6791i	−0.263040	−	0.981677i
$796$		0			0
$797$	10.0960	−	5.82891i	0.357617	−	0.206471i	−0.310418	−	0.950600i	$-0.600469\pi$
$797$	10.0960	−	5.82891i	0.357617	−	0.206471i	0.668035	+	0.744130i	$0.267136\pi$
$798$		0			0
$799$	11.5429	+	3.09292i	0.408359	+	0.109420i
$800$		0			0
$801$	−19.2299	+	19.2299i	−0.679457	+	0.679457i
$802$		0			0
$803$	−0.0919184	+	0.159207i	−0.00324373	+	0.00561831i
$804$		0			0
$805$		−	3.78111i		−	0.133267i
$806$		0			0
$807$		−	25.0572i		−	0.882055i
$808$		0			0
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	−0.452052	−	0.891992i	$-0.649308\pi$
$809$	15.5430	−	26.9212i	0.546461	−	0.946499i	0.998513	−	0.0545072i	$-0.0173588\pi$
$810$		0			0
$811$	0.110267	−	0.110267i	0.00387201	−	0.00387201i	−0.705168	−	0.709040i	$-0.749128\pi$
$811$	0.110267	−	0.110267i	0.00387201	−	0.00387201i	0.709040	+	0.705168i	$0.249128\pi$
$812$		0			0
$813$	−61.7561	−	16.5475i	−2.16588	−	0.580346i
$814$		0			0
$815$	38.2851	−	22.1039i	1.34107	−	0.774266i
$816$		0			0
$817$	−6.03058	−	22.5064i	−0.210983	−	0.787401i
$818$		0			0
$819$	−3.06655	+	6.25632i	−0.107154	+	0.218614i
$820$		0			0
$821$	17.4699	−	4.68104i	0.609703	−	0.163370i	0.0592608	−	0.998243i	$-0.481126\pi$
$821$	17.4699	−	4.68104i	0.609703	−	0.163370i	0.550443	+	0.834873i	$0.314459\pi$
$822$		0			0
$823$	13.0969	+	22.6845i	0.456530	+	0.790733i	0.998775	−	0.0494874i	$-0.0157588\pi$
$823$	13.0969	+	22.6845i	0.456530	+	0.790733i	−0.542245	+	0.840221i	$0.682425\pi$
$824$		0			0
$825$	8.95747	−	33.4297i	0.311859	−	1.16387i
$826$		0			0
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	0.471930	−	0.881636i	$-0.343558\pi$
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	−0.881636	+	0.471930i	$0.843558\pi$
$828$		0			0
$829$	11.3492	+	6.55249i	0.394176	+	0.227577i	0.683968	−	0.729512i	$-0.260253\pi$
$829$	11.3492	+	6.55249i	0.394176	+	0.227577i	−0.289792	+	0.957090i	$0.593586\pi$
$830$		0			0
$831$	−1.33873			−0.0464401
$832$		0			0
$833$	−17.7431			−0.614762
$834$		0			0
$835$	25.1095	+	14.4970i	0.868951	+	0.501689i
$836$		0			0
$837$	4.41030	+	4.41030i	0.152442	+	0.152442i
$838$		0			0
$839$	−6.19456	+	23.1184i	−0.213860	+	0.798136i	0.772705	+	0.634766i	$0.218903\pi$
$839$	−6.19456	+	23.1184i	−0.213860	+	0.798136i	−0.986565	+	0.163371i	$0.947763\pi$
$840$		0			0
$841$	13.7267	+	23.7753i	0.473334	+	0.819839i
$842$		0			0
$843$	−0.943032	+	0.252685i	−0.0324798	+	0.00870293i
$844$		0			0
$845$	24.4631	−	32.2012i	0.841556	−	1.10775i
$846$		0			0
$847$	0.347303	+	1.29615i	0.0119335	+	0.0445364i
$848$		0			0
$849$	34.8553	−	20.1237i	1.19623	−	0.690644i
$850$		0			0
$851$	1.03076	+	0.276191i	0.0353340	+	0.00946770i
$852$		0			0
$853$	12.1913	−	12.1913i	0.417422	−	0.417422i	−0.466892	−	0.884314i	$-0.654626\pi$
$853$	12.1913	−	12.1913i	0.417422	−	0.417422i	0.884314	+	0.466892i	$0.154626\pi$
$854$		0			0
$855$	−16.4620	+	28.5130i	−0.562987	+	0.975123i
$856$		0			0
$857$		−	20.1694i		−	0.688974i	−0.938791	−	0.344487i	$-0.888053\pi$
$857$		−	20.1694i		−	0.688974i	0.938791	−	0.344487i	$-0.111947\pi$
$858$		0			0
$859$			10.5286i			0.359231i	0.983737	+	0.179616i	$0.0574854\pi$
$859$			10.5286i			0.359231i	−0.983737	+	0.179616i	$0.942515\pi$
$860$		0			0
$861$	4.28080	−	7.41456i	0.145889	−	0.252688i
$862$		0			0
$863$	−0.357134	+	0.357134i	−0.0121570	+	0.0121570i	−0.713159	−	0.701002i	$-0.752736\pi$
$863$	−0.357134	+	0.357134i	−0.0121570	+	0.0121570i	0.701002	+	0.713159i	$0.252736\pi$
$864$		0			0
$865$	−68.7838	−	18.4306i	−2.33872	−	0.626658i
$866$		0			0
$867$	−21.4509	+	12.3847i	−0.728511	+	0.420606i
$868$		0			0
$869$	2.08918	+	7.79691i	0.0708704	+	0.264492i
$870$		0			0
$871$	−24.0682	−	11.7971i	−0.815521	−	0.399730i
$872$		0			0
$873$	−15.0119	+	4.02243i	−0.508076	+	0.136138i
$874$		0			0
$875$	−0.296516	−	0.513580i	−0.0100241	−	0.0173622i
$876$		0			0
$877$	−8.27012	+	30.8645i	−0.279262	+	1.04222i	0.673669	+	0.739033i	$0.264717\pi$
$877$	−8.27012	+	30.8645i	−0.279262	+	1.04222i	−0.952931	+	0.303187i	$0.901949\pi$
$878$		0			0
$879$	−3.63013	−	3.63013i	−0.122441	−	0.122441i
$880$		0			0
$881$	26.4430	+	15.2668i	0.890886	+	0.514353i	0.874232	−	0.485508i	$-0.161365\pi$
$881$	26.4430	+	15.2668i	0.890886	+	0.514353i	0.0166536	+	0.999861i	$0.494699\pi$
$882$		0			0
$883$	−49.7844			−1.67538			−0.837689	−	0.546148i	$-0.816094\pi$
$883$	−49.7844			−1.67538			−0.837689	+	0.546148i	$0.816094\pi$
$884$		0			0
$885$	54.9338			1.84658
$886$		0			0
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	0.817917	−	0.575336i	$-0.195129\pi$
$887$	21.7002	+	12.5286i	0.728621	+	0.420669i	−0.0892967	+	0.996005i	$0.528462\pi$
$888$		0			0
$889$	5.03784	+	5.03784i	0.168964	+	0.168964i
$890$		0			0
$891$	−6.18510	+	23.0831i	−0.207209	+	0.773313i
$892$		0			0
$893$	−7.23442	−	12.5304i	−0.242091	−	0.419313i
$894$		0			0
$895$	−39.7182	+	10.6425i	−1.32763	+	0.355739i
$896$		0			0
$897$	−3.58913	+	18.2739i	−0.119838	+	0.610146i
$898$		0			0
$899$	−2.88823	−	10.7790i	−0.0963278	−	0.359500i
$900$		0			0
$901$	8.49258	−	4.90319i	0.282929	−	0.163349i
$902$		0			0
$903$	−10.2956	−	2.75869i	−0.342616	−	0.0918036i
$904$		0			0
$905$	57.4558	−	57.4558i	1.90990	−	1.90990i
$906$		0			0
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	−0.0560094	−	0.998430i	$-0.517838\pi$
$907$	25.1973	−	43.6429i	0.836661	−	1.44914i	0.892671	−	0.450710i	$-0.148829\pi$
$908$		0			0
$909$		−	29.4261i		−	0.976002i
$910$		0			0
$911$			7.50959i			0.248804i	0.992232	+	0.124402i	$0.0397012\pi$
$911$			7.50959i			0.248804i	−0.992232	+	0.124402i	$0.960299\pi$
$912$		0			0
$913$	−21.2708	+	36.8420i	−0.703959	+	1.21929i
$914$		0			0
$915$	−43.8359	+	43.8359i	−1.44917	+	1.44917i
$916$		0			0
$917$	10.9171	+	2.92524i	0.360516	+	0.0966000i
$918$		0			0
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	−0.0413499	−	0.999145i	$-0.513166\pi$
$919$	24.3508	−	14.0590i	0.803260	−	0.463762i	0.844610	+	0.535382i	$0.179832\pi$
$920$		0			0
$921$	10.4855	+	39.1325i	0.345510	+	1.28946i
$922$		0			0
$923$	6.13616	−	4.12148i	0.201974	−	0.135660i
$924$		0			0
$925$	−2.33834	+	0.626555i	−0.0768840	+	0.0206010i
$926$		0			0
$927$	15.7344	+	27.2528i	0.516787	+	0.895101i
$928$		0			0
$929$	−11.1025	+	41.4351i	−0.364261	+	1.35944i	0.504159	+	0.863611i	$0.331802\pi$
$929$	−11.1025	+	41.4351i	−0.364261	+	1.35944i	−0.868420	+	0.495829i	$0.834864\pi$
$930$		0			0
$931$	15.1906	+	15.1906i	0.497853	+	0.497853i
$932$		0			0
$933$	−52.1278	−	30.0960i	−1.70659	−	0.985300i
$934$		0			0
$935$	24.5064			0.801444
$936$		0			0
$937$	−0.397858			−0.0129975			−0.00649873	−	0.999979i	$-0.502069\pi$
$937$	−0.397858			−0.0129975			−0.00649873	+	0.999979i	$0.502069\pi$
$938$		0			0
$939$	62.7093	+	36.2052i	2.04644	+	1.18151i
$940$		0			0
$941$	4.33123	+	4.33123i	0.141194	+	0.141194i	0.774171	−	0.632977i	$-0.218167\pi$
$941$	4.33123	+	4.33123i	0.141194	+	0.141194i	−0.632977	+	0.774171i	$0.718167\pi$
$942$		0			0
$943$	3.09228	−	11.5405i	0.100698	−	0.375811i
$944$		0			0
$945$	0.637444	+	1.10409i	0.0207360	+	0.0359159i
$946$		0			0
$947$	−7.47663	+	2.00336i	−0.242958	+	0.0651003i	−0.378243	−	0.925706i	$-0.623472\pi$
$947$	−7.47663	+	2.00336i	−0.242958	+	0.0651003i	0.135285	+	0.990807i	$0.456805\pi$
$948$		0			0
$949$	0.0152168	+	0.223894i	0.000493959	+	0.00726790i
$950$		0			0
$951$	−0.0129322	−	0.0482638i	−0.000419357	−	0.00156506i
$952$		0			0
$953$	−12.6528	+	7.30512i	−0.409866	+	0.236636i	−0.690732	−	0.723111i	$-0.742712\pi$
$953$	−12.6528	+	7.30512i	−0.409866	+	0.236636i	0.280866	+	0.959747i	$0.409378\pi$
$954$		0			0
$955$	−42.4813	−	11.3828i	−1.37466	−	0.368340i
$956$		0			0
$957$	−6.50773	+	6.50773i	−0.210365	+	0.210365i
$958$		0			0
$959$	−2.13959	+	3.70587i	−0.0690909	+	0.119669i
$960$		0			0
$961$		−	49.5168i		−	1.59731i
$962$		0			0
$963$		−	61.8243i		−	1.99226i
$964$		0			0
$965$	36.0825	−	62.4966i	1.16154	−	2.01184i
$966$		0			0
$967$	6.52725	−	6.52725i	0.209902	−	0.209902i	−0.594324	−	0.804226i	$-0.702580\pi$
$967$	6.52725	−	6.52725i	0.209902	−	0.209902i	0.804226	+	0.594324i	$0.202580\pi$
$968$		0			0
$969$	−20.8451	−	5.58544i	−0.669642	−	0.179430i
$970$		0			0
$971$	33.9607	−	19.6072i	1.08985	−	0.629226i	0.156315	−	0.987707i	$-0.450038\pi$
$971$	33.9607	−	19.6072i	1.08985	−	0.629226i	0.933537	+	0.358481i	$0.116705\pi$
$972$		0			0
$973$	1.69495	+	6.32565i	0.0543377	+	0.202791i
$974$		0			0
$975$	−13.6763	−	39.9724i	−0.437994	−	1.28014i
$976$		0			0
$977$	11.3491	−	3.04098i	0.363089	−	0.0972895i	−0.0726619	−	0.997357i	$-0.523149\pi$
$977$	11.3491	−	3.04098i	0.363089	−	0.0972895i	0.435751	+	0.900067i	$0.356483\pi$
$978$		0			0
$979$	−12.2544	−	21.2252i	−0.391652	−	0.678361i
$980$		0			0
$981$	−3.54191	+	13.2186i	−0.113084	+	0.422037i
$982$		0			0
$983$	17.0818	+	17.0818i	0.544823	+	0.544823i	0.924939	−	0.380116i	$-0.124116\pi$
$983$	17.0818	+	17.0818i	0.544823	+	0.544823i	−0.380116	+	0.924939i	$0.624116\pi$
$984$		0			0
$985$	−16.7194	−	9.65293i	−0.532723	−	0.307568i
$986$		0			0
$987$	−6.61878			−0.210678
$988$		0			0
$989$	−14.8742			−0.472973
$990$		0			0
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	0.840796	−	0.541353i	$-0.182088\pi$
$991$	24.9439	+	14.4013i	0.792368	+	0.457474i	−0.0484275	+	0.998827i	$0.515421\pi$
$992$		0			0
$993$	−7.48456	−	7.48456i	−0.237515	−	0.237515i
$994$		0			0
$995$	2.42688	−	9.05724i	0.0769373	−	0.287134i
$996$		0			0
$997$	26.9659	+	46.7063i	0.854019	+	1.47920i	0.877552	+	0.479481i	$0.159175\pi$
$997$	26.9659	+	46.7063i	0.854019	+	1.47920i	−0.0235336	+	0.999723i	$0.507492\pi$
$998$		0			0
$999$	−0.347544	+	0.0931241i	−0.0109958	+	0.00294632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.bu.n.319.4		16
4.3	odd	2	inner	832.2.bu.n.319.1		16
8.3	odd	2		52.2.l.b.7.2	yes	16
8.5	even	2		52.2.l.b.7.1	✓	16
13.2	odd	12	inner	832.2.bu.n.639.1		16
24.5	odd	2		468.2.cb.f.163.4		16
24.11	even	2		468.2.cb.f.163.3		16
52.15	even	12	inner	832.2.bu.n.639.4		16
104.3	odd	6		676.2.l.m.427.2		16
104.5	odd	4		676.2.l.m.19.2		16
104.11	even	12		676.2.l.k.587.4		16
104.19	even	12		676.2.f.h.239.5		16
104.21	odd	4		676.2.l.i.19.3		16
104.29	even	6		676.2.l.m.427.4		16
104.35	odd	6		676.2.f.h.99.8		16
104.37	odd	12		676.2.l.k.587.3		16
104.43	odd	6		676.2.f.i.99.1		16
104.45	odd	12		676.2.f.h.239.8		16
104.51	odd	2		676.2.l.k.319.3		16
104.59	even	12		676.2.f.i.239.4		16
104.61	even	6		676.2.f.h.99.5		16
104.67	even	12		52.2.l.b.15.1	yes	16
104.69	even	6		676.2.f.i.99.4		16
104.75	odd	6		676.2.l.i.427.3		16
104.77	even	2		676.2.l.k.319.4		16
104.83	even	4		676.2.l.m.19.4		16
104.85	odd	12		676.2.f.i.239.1		16
104.93	odd	12		52.2.l.b.15.2	yes	16
104.99	even	4		676.2.l.i.19.1		16
104.101	even	6		676.2.l.i.427.1		16
312.197	even	12		468.2.cb.f.379.3		16
312.275	odd	12		468.2.cb.f.379.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	8.5	even	2
52.2.l.b.7.2	yes	16	8.3	odd	2
52.2.l.b.15.1	yes	16	104.67	even	12
52.2.l.b.15.2	yes	16	104.93	odd	12
468.2.cb.f.163.3		16	24.11	even	2
468.2.cb.f.163.4		16	24.5	odd	2
468.2.cb.f.379.3		16	312.197	even	12
468.2.cb.f.379.4		16	312.275	odd	12
676.2.f.h.99.5		16	104.61	even	6
676.2.f.h.99.8		16	104.35	odd	6
676.2.f.h.239.5		16	104.19	even	12
676.2.f.h.239.8		16	104.45	odd	12
676.2.f.i.99.1		16	104.43	odd	6
676.2.f.i.99.4		16	104.69	even	6
676.2.f.i.239.1		16	104.85	odd	12
676.2.f.i.239.4		16	104.59	even	12
676.2.l.i.19.1		16	104.99	even	4
676.2.l.i.19.3		16	104.21	odd	4
676.2.l.i.427.1		16	104.101	even	6
676.2.l.i.427.3		16	104.75	odd	6
676.2.l.k.319.3		16	104.51	odd	2
676.2.l.k.319.4		16	104.77	even	2
676.2.l.k.587.3		16	104.37	odd	12
676.2.l.k.587.4		16	104.11	even	12
676.2.l.m.19.2		16	104.5	odd	4
676.2.l.m.19.4		16	104.83	even	4
676.2.l.m.427.2		16	104.3	odd	6
676.2.l.m.427.4		16	104.29	even	6
832.2.bu.n.319.1		16	4.3	odd	2	inner
832.2.bu.n.319.4		16	1.1	even	1	trivial
832.2.bu.n.639.1		16	13.2	odd	12	inner
832.2.bu.n.639.4		16	52.15	even	12	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:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.bu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.16981 + 1.25274i) q^{3} +(2.19962 + 2.19962i) q^{5} +(0.152604 - 0.569525i) q^{7} +(1.63871 + 2.83834i) q^{9} +O(q^{10})\)	\(q+(2.16981 + 1.25274i) q^{3} +(2.19962 + 2.19962i) q^{5} +(0.152604 - 0.569525i) q^{7} +(1.63871 + 2.83834i) q^{9} +(-2.85302 + 0.764465i) q^{11} +(-2.37076 + 2.71652i) q^{13} +(2.01721 + 7.52831i) q^{15} +(-2.30986 + 1.33360i) q^{17} +(3.11932 + 0.835818i) q^{19} +(1.04459 - 1.04459i) q^{21} +(1.03076 - 1.78533i) q^{23} +4.67667i q^{25} +0.695088i q^{27} +(0.621816 - 1.07702i) q^{29} +(6.34495 - 6.34495i) q^{31} +(-7.14819 - 1.91535i) q^{33} +(1.58841 - 0.917069i) q^{35} +(0.133975 + 0.500000i) q^{37} +(-8.54720 + 2.92438i) q^{39} +(5.59808 - 1.50000i) q^{41} +(-3.60759 - 6.24853i) q^{43} +(-2.63871 + 9.84781i) q^{45} +(-3.16813 - 3.16813i) q^{47} +(5.76111 + 3.32618i) q^{49} -6.68260 q^{51} -3.67667 q^{53} +(-7.95711 - 4.59404i) q^{55} +(5.72126 + 5.72126i) q^{57} +(1.82424 - 6.80816i) q^{59} +(3.97705 + 6.88845i) q^{61} +(1.86658 - 0.500148i) q^{63} +(-11.1901 + 0.760530i) q^{65} +(1.92408 + 7.18077i) q^{67} +(4.47310 - 2.58254i) q^{69} +(-1.98027 - 0.530611i) q^{71} +(0.0440105 - 0.0440105i) q^{73} +(-5.85865 + 10.1475i) q^{75} +1.74153i q^{77} -2.73286i q^{79} +(4.04538 - 7.00680i) q^{81} +(10.1844 - 10.1844i) q^{83} +(-8.01422 - 2.14740i) q^{85} +(2.69844 - 1.55795i) q^{87} +(2.14761 + 8.01501i) q^{89} +(1.18534 + 1.76476i) q^{91} +(21.7159 - 5.81876i) q^{93} +(5.02283 + 8.69980i) q^{95} +(-1.22731 + 4.58039i) q^{97} +(-6.84510 - 6.84510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 4 q^{9}+O(q^{10}) \) 16 * q + 12 * q^5 + 4 * q^9	\( 16 q + 12 q^{5} + 4 q^{9} + 12 q^{13} + 12 q^{17} + 28 q^{21} + 8 q^{29} - 20 q^{33} + 16 q^{37} + 48 q^{41} - 20 q^{45} + 60 q^{49} + 32 q^{53} + 12 q^{57} - 4 q^{61} - 8 q^{65} + 12 q^{69} + 20 q^{73} + 48 q^{81} - 20 q^{85} - 52 q^{89} + 92 q^{93} - 28 q^{97}+O(q^{100}) \) 16 * q + 12 * q^5 + 4 * q^9 + 12 * q^13 + 12 * q^17 + 28 * q^21 + 8 * q^29 - 20 * q^33 + 16 * q^37 + 48 * q^41 - 20 * q^45 + 60 * q^49 + 32 * q^53 + 12 * q^57 - 4 * q^61 - 8 * q^65 + 12 * q^69 + 20 * q^73 + 48 * q^81 - 20 * q^85 - 52 * q^89 + 92 * q^93 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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