LMFDB - Embedded newform 1024.2.g.f.385.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([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("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, 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:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			385.4
Root			$0.991445 + 0.130526i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.f.641.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40211 - 0.580775i) q^{3} +(1.36603 - 3.29788i) q^{5} +(1.02642 + 1.02642i) q^{7} +(-0.492694 + 0.492694i) q^{9} +O(q^{10})$	\(q+(1.40211 - 0.580775i) q^{3} +(1.36603 - 3.29788i) q^{5} +(1.02642 + 1.02642i) q^{7} +(-0.492694 + 0.492694i) q^{9} +(-4.97171 - 2.05935i) q^{11} +(-1.56583 - 3.78024i) q^{13} -5.41736i q^{15} -2.35311i q^{17} +(-1.15885 - 2.79772i) q^{19} +(2.03528 + 0.843039i) q^{21} +(-1.06460 + 1.06460i) q^{23} +(-5.47443 - 5.47443i) q^{25} +(-2.14699 + 5.18330i) q^{27} +(3.86540 - 1.60110i) q^{29} +10.5829 q^{31} -8.16693 q^{33} +(4.78712 - 1.98289i) q^{35} +(1.75201 - 4.22973i) q^{37} +(-4.39094 - 4.39094i) q^{39} +(-6.27792 + 6.27792i) q^{41} +(8.60205 + 3.56308i) q^{43} +(0.951812 + 2.29788i) q^{45} +3.06910i q^{47} -4.89293i q^{49} +(-1.36663 - 3.29934i) q^{51} +(-0.384286 - 0.159176i) q^{53} +(-13.5830 + 13.5830i) q^{55} +(-3.24969 - 3.24969i) q^{57} +(-3.22287 + 7.78071i) q^{59} +(2.58044 - 1.06885i) q^{61} -1.01142 q^{63} -14.6057 q^{65} +(4.79363 - 1.98559i) q^{67} +(-0.874400 + 2.11099i) q^{69} +(2.84718 + 2.84718i) q^{71} +(8.43123 - 8.43123i) q^{73} +(-10.8552 - 4.49637i) q^{75} +(-2.98930 - 7.21682i) q^{77} -4.59983i q^{79} +6.42418i q^{81} +(3.14911 + 7.60263i) q^{83} +(-7.76028 - 3.21441i) q^{85} +(4.48986 - 4.48986i) q^{87} +(-0.967128 - 0.967128i) q^{89} +(2.27292 - 5.48730i) q^{91} +(14.8384 - 6.14626i) q^{93} -10.8096 q^{95} +11.2672 q^{97} +(3.46416 - 1.43490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^5 - 16 * q^9	$ 16 q + 8 q^{5} - 16 q^{9} - 8 q^{13} + 16 q^{21} - 32 q^{25} - 24 q^{29} - 80 q^{33} + 40 q^{37} - 16 q^{41} + 24 q^{45} - 56 q^{53} - 16 q^{57} + 8 q^{61} - 32 q^{65} - 64 q^{69} + 32 q^{73} + 64 q^{77} - 48 q^{85} + 32 q^{89} + 80 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 - 16 * q^9 - 8 * q^13 + 16 * q^21 - 32 * q^25 - 24 * q^29 - 80 * q^33 + 40 * q^37 - 16 * q^41 + 24 * q^45 - 56 * q^53 - 16 * q^57 + 8 * q^61 - 32 * q^65 - 64 * q^69 + 32 * q^73 + 64 * q^77 - 48 * q^85 + 32 * q^89 + 80 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.40211	−	0.580775i	0.809511	−	0.335311i	0.0607523	−	0.998153i	$-0.480650\pi$
$3$	1.40211	−	0.580775i	0.809511	−	0.335311i	0.748759	+	0.662842i	$0.230650\pi$
$4$		0			0
$5$	1.36603	−	3.29788i	0.610905	−	1.47486i	−0.251103	−	0.967960i	$-0.580793\pi$
$5$	1.36603	−	3.29788i	0.610905	−	1.47486i	0.862008	−	0.506895i	$-0.169207\pi$
$6$		0			0
$7$	1.02642	+	1.02642i	0.387950	+	0.387950i	0.873956	−	0.486006i	$-0.161547\pi$
$7$	1.02642	+	1.02642i	0.387950	+	0.387950i	−0.486006	+	0.873956i	$0.661547\pi$
$8$		0			0
$9$	−0.492694	+	0.492694i	−0.164231	+	0.164231i
$10$		0			0
$11$	−4.97171	−	2.05935i	−1.49903	−	0.620917i	−0.525768	−	0.850628i	$-0.676222\pi$
$11$	−4.97171	−	2.05935i	−1.49903	−	0.620917i	−0.973259	+	0.229710i	$0.926222\pi$
$12$		0			0
$13$	−1.56583	−	3.78024i	−0.434282	−	1.04845i	−0.977892	−	0.209112i	$-0.932943\pi$
$13$	−1.56583	−	3.78024i	−0.434282	−	1.04845i	0.543610	−	0.839338i	$-0.317057\pi$
$14$		0			0
$15$		−	5.41736i		−	1.39876i
$16$		0			0
$17$		−	2.35311i		−	0.570714i	−0.958421	−	0.285357i	$-0.907888\pi$
$17$		−	2.35311i		−	0.570714i	0.958421	−	0.285357i	$-0.0921121\pi$
$18$		0			0
$19$	−1.15885	−	2.79772i	−0.265859	−	0.641840i	0.733421	−	0.679774i	$-0.237922\pi$
$19$	−1.15885	−	2.79772i	−0.265859	−	0.641840i	−0.999280	+	0.0379340i	$0.987922\pi$
$20$		0			0
$21$	2.03528	+	0.843039i	0.444134	+	0.183966i
$22$		0			0
$23$	−1.06460	+	1.06460i	−0.221985	+	0.221985i	−0.809334	−	0.587349i	$-0.800172\pi$
$23$	−1.06460	+	1.06460i	−0.221985	+	0.221985i	0.587349	+	0.809334i	$0.300172\pi$
$24$		0			0
$25$	−5.47443	−	5.47443i	−1.09489	−	1.09489i
$26$		0			0
$27$	−2.14699	+	5.18330i	−0.413189	+	0.997527i
$28$		0			0
$29$	3.86540	−	1.60110i	0.717787	−	0.297317i	0.00626466	−	0.999980i	$-0.498006\pi$
$29$	3.86540	−	1.60110i	0.717787	−	0.297317i	0.711523	+	0.702663i	$0.248006\pi$
$30$		0			0
$31$	10.5829			1.90074			0.950370	−	0.311123i	$-0.100705\pi$
$31$	10.5829			1.90074			0.950370	+	0.311123i	$0.100705\pi$
$32$		0			0
$33$	−8.16693			−1.42168
$34$		0			0
$35$	4.78712	−	1.98289i	0.809171	−	0.335170i
$36$		0			0
$37$	1.75201	−	4.22973i	0.288029	−	0.695363i	−0.711948	−	0.702233i	$-0.752187\pi$
$37$	1.75201	−	4.22973i	0.288029	−	0.695363i	0.999976	+	0.00686951i	$0.00218665\pi$
$38$		0			0
$39$	−4.39094	−	4.39094i	−0.703113	−	0.703113i
$40$		0			0
$41$	−6.27792	+	6.27792i	−0.980446	+	0.980446i	−0.999812	−	0.0193666i	$-0.993835\pi$
$41$	−6.27792	+	6.27792i	−0.980446	+	0.980446i	0.0193666	+	0.999812i	$0.493835\pi$
$42$		0			0
$43$	8.60205	+	3.56308i	1.31180	+	0.543365i	0.925409	−	0.378970i	$-0.123722\pi$
$43$	8.60205	+	3.56308i	1.31180	+	0.543365i	0.386391	+	0.922335i	$0.373722\pi$
$44$		0			0
$45$	0.951812	+	2.29788i	0.141888	+	0.342547i
$46$		0			0
$47$			3.06910i			0.447674i	0.974627	+	0.223837i	$0.0718583\pi$
$47$			3.06910i			0.447674i	−0.974627	+	0.223837i	$0.928142\pi$
$48$		0			0
$49$		−	4.89293i		−	0.698990i
$50$		0			0
$51$	−1.36663	−	3.29934i	−0.191366	−	0.461999i
$52$		0			0
$53$	−0.384286	−	0.159176i	−0.0527857	−	0.0218646i	0.356134	−	0.934435i	$-0.384095\pi$
$53$	−0.384286	−	0.159176i	−0.0527857	−	0.0218646i	−0.408920	+	0.912570i	$0.634095\pi$
$54$		0			0
$55$	−13.5830	+	13.5830i	−1.83153	+	1.83153i
$56$		0			0
$57$	−3.24969	−	3.24969i	−0.430432	−	0.430432i
$58$		0			0
$59$	−3.22287	+	7.78071i	−0.419583	+	1.01296i	0.562886	+	0.826534i	$0.309691\pi$
$59$	−3.22287	+	7.78071i	−0.419583	+	1.01296i	−0.982469	+	0.186427i	$0.940309\pi$
$60$		0			0
$61$	2.58044	−	1.06885i	0.330391	−	0.136853i	−0.211321	−	0.977417i	$-0.567776\pi$
$61$	2.58044	−	1.06885i	0.330391	−	0.136853i	0.541712	+	0.840564i	$0.317776\pi$
$62$		0			0
$63$	−1.01142			−0.127427
$64$		0			0
$65$	−14.6057			−1.81162
$66$		0			0
$67$	4.79363	−	1.98559i	0.585635	−	0.242578i	−0.0701364	−	0.997537i	$-0.522343\pi$
$67$	4.79363	−	1.98559i	0.585635	−	0.242578i	0.655772	+	0.754959i	$0.272343\pi$
$68$		0			0
$69$	−0.874400	+	2.11099i	−0.105265	+	0.254133i
$70$		0			0
$71$	2.84718	+	2.84718i	0.337898	+	0.337898i	0.855576	−	0.517678i	$-0.173203\pi$
$71$	2.84718	+	2.84718i	0.337898	+	0.337898i	−0.517678	+	0.855576i	$0.673203\pi$
$72$		0			0
$73$	8.43123	−	8.43123i	0.986801	−	0.986801i	−0.0131133	−	0.999914i	$-0.504174\pi$
$73$	8.43123	−	8.43123i	0.986801	−	0.986801i	0.999914	+	0.0131133i	$0.00417420\pi$
$74$		0			0
$75$	−10.8552	−	4.49637i	−1.25345	−	0.519196i
$76$		0			0
$77$	−2.98930	−	7.21682i	−0.340663	−	0.822433i
$78$		0			0
$79$		−	4.59983i		−	0.517521i	−0.965941	−	0.258761i	$-0.916686\pi$
$79$		−	4.59983i		−	0.517521i	0.965941	−	0.258761i	$-0.0833141\pi$
$80$		0			0
$81$			6.42418i			0.713798i
$82$		0			0
$83$	3.14911	+	7.60263i	0.345660	+	0.834497i	0.997122	+	0.0758155i	$0.0241560\pi$
$83$	3.14911	+	7.60263i	0.345660	+	0.834497i	−0.651462	+	0.758681i	$0.725844\pi$
$84$		0			0
$85$	−7.76028	−	3.21441i	−0.841720	−	0.348652i
$86$		0			0
$87$	4.48986	−	4.48986i	0.481363	−	0.481363i
$88$		0			0
$89$	−0.967128	−	0.967128i	−0.102515	−	0.102515i	0.653989	−	0.756504i	$-0.273094\pi$
$89$	−0.967128	−	0.967128i	−0.102515	−	0.102515i	−0.756504	+	0.653989i	$0.773094\pi$
$90$		0			0
$91$	2.27292	−	5.48730i	0.238266	−	0.575226i
$92$		0			0
$93$	14.8384	−	6.14626i	1.53867	−	0.637338i
$94$		0			0
$95$	−10.8096			−1.10904
$96$		0			0
$97$	11.2672			1.14401			0.572006	−	0.820249i	$-0.306165\pi$
$97$	11.2672			1.14401			0.572006	+	0.820249i	$0.306165\pi$
$98$		0			0
$99$	3.46416	−	1.43490i	0.348161	−	0.144213i
$100$		0			0
$101$	3.58649	−	8.65855i	0.356869	−	0.861558i	−0.638868	−	0.769317i	$-0.720597\pi$
$101$	3.58649	−	8.65855i	0.356869	−	0.861558i	0.995737	−	0.0922416i	$-0.0294032\pi$
$102$		0			0
$103$	−1.20450	−	1.20450i	−0.118683	−	0.118683i	0.645271	−	0.763954i	$-0.276744\pi$
$103$	−1.20450	−	1.20450i	−0.118683	−	0.118683i	−0.763954	+	0.645271i	$0.776744\pi$
$104$		0			0
$105$	5.56048	−	5.56048i	0.542647	−	0.542647i
$106$		0			0
$107$	2.68959	+	1.11406i	0.260012	+	0.107701i	0.508882	−	0.860836i	$-0.330059\pi$
$107$	2.68959	+	1.11406i	0.260012	+	0.107701i	−0.248870	+	0.968537i	$0.580059\pi$
$108$		0			0
$109$	−1.46240	−	3.53055i	−0.140073	−	0.338165i	0.838239	−	0.545303i	$-0.183585\pi$
$109$	−1.46240	−	3.53055i	−0.140073	−	0.338165i	−0.978312	+	0.207137i	$0.933585\pi$
$110$		0			0
$111$		−	6.94809i		−	0.659483i
$112$		0			0
$113$			2.13630i			0.200966i	0.994939	+	0.100483i	$0.0320388\pi$
$113$			2.13630i			0.200966i	−0.994939	+	0.100483i	$0.967961\pi$
$114$		0			0
$115$	2.05665	+	4.96520i	0.191784	+	0.463007i
$116$		0			0
$117$	2.63397	+	1.09103i	0.243511	+	0.100866i
$118$		0			0
$119$	2.41528	−	2.41528i	0.221408	−	0.221408i
$120$		0			0
$121$	12.6988	+	12.6988i	1.15444	+	1.15444i
$122$		0			0
$123$	−5.15630	+	12.4484i	−0.464928	+	1.12244i
$124$		0			0
$125$	−9.04284	+	3.74567i	−0.808816	+	0.335023i
$126$		0			0
$127$	1.09821			0.0974502			0.0487251	−	0.998812i	$-0.484484\pi$
$127$	1.09821			0.0974502			0.0487251	+	0.998812i	$0.484484\pi$
$128$		0			0
$129$	14.1304			1.24411
$130$		0			0
$131$	−0.655166	+	0.271379i	−0.0572421	+	0.0237105i	−0.411121	−	0.911581i	$-0.634863\pi$
$131$	−0.655166	+	0.271379i	−0.0572421	+	0.0237105i	0.353879	+	0.935291i	$0.384863\pi$
$132$		0			0
$133$	1.68216	−	4.06110i	0.145862	−	0.352142i
$134$		0			0
$135$	14.1610	+	14.1610i	1.21879	+	1.21879i
$136$		0			0
$137$	−11.4887	+	11.4887i	−0.981544	+	0.981544i	−0.999833	−	0.0182885i	$-0.994178\pi$
$137$	−11.4887	+	11.4887i	−0.981544	+	0.981544i	0.0182885	+	0.999833i	$0.494178\pi$
$138$		0			0
$139$	0.781087	+	0.323537i	0.0662510	+	0.0274421i	0.415563	−	0.909564i	$-0.363585\pi$
$139$	0.781087	+	0.323537i	0.0662510	+	0.0274421i	−0.349312	+	0.937007i	$0.613585\pi$
$140$		0			0
$141$	1.78245	+	4.30323i	0.150110	+	0.362397i
$142$		0			0
$143$			22.0188i			1.84131i
$144$		0			0
$145$		−	14.9348i		−	1.24027i
$146$		0			0
$147$	−2.84169	−	6.86045i	−0.234379	−	0.565840i
$148$		0			0
$149$	6.52350	+	2.70212i	0.534426	+	0.221367i	0.633541	−	0.773710i	$-0.281601\pi$
$149$	6.52350	+	2.70212i	0.534426	+	0.221367i	−0.0991144	+	0.995076i	$0.531601\pi$
$150$		0			0
$151$	9.87443	−	9.87443i	0.803569	−	0.803569i	−0.180082	−	0.983652i	$-0.557636\pi$
$151$	9.87443	−	9.87443i	0.803569	−	0.803569i	0.983652	+	0.180082i	$0.0576364\pi$
$152$		0			0
$153$	1.15937	+	1.15937i	0.0937291	+	0.0937291i
$154$		0			0
$155$	14.4565	−	34.9010i	1.16117	−	2.80332i
$156$		0			0
$157$	−22.3677	+	9.26500i	−1.78514	+	0.739428i	−0.793785	+	0.608199i	$0.791892\pi$
$157$	−22.3677	+	9.26500i	−1.78514	+	0.739428i	−0.991352	+	0.131229i	$0.958108\pi$
$158$		0			0
$159$	−0.631258			−0.0500620
$160$		0			0
$161$	−2.18546			−0.172238
$162$		0			0
$163$	−16.1774	+	6.70092i	−1.26712	+	0.524856i	−0.912086	−	0.409999i	$-0.865529\pi$
$163$	−16.1774	+	6.70092i	−1.26712	+	0.524856i	−0.355029	+	0.934855i	$0.615529\pi$
$164$		0			0
$165$	−11.1562	+	26.9335i	−0.868511	+	2.09677i
$166$		0			0
$167$	−15.9204	−	15.9204i	−1.23196	−	1.23196i	−0.963210	−	0.268751i	$-0.913389\pi$
$167$	−15.9204	−	15.9204i	−1.23196	−	1.23196i	−0.268751	−	0.963210i	$-0.586611\pi$
$168$		0			0
$169$	−2.64601	+	2.64601i	−0.203539	+	0.203539i
$170$		0			0
$171$	1.94938	+	0.807459i	0.149073	+	0.0617479i
$172$		0			0
$173$	3.46532	+	8.36603i	0.263463	+	0.636057i	0.999148	−	0.0412671i	$-0.0131394\pi$
$173$	3.46532	+	8.36603i	0.263463	+	0.636057i	−0.735685	+	0.677324i	$0.763139\pi$
$174$		0			0
$175$		−	11.2381i		−	0.849523i
$176$		0			0
$177$			12.7812i			0.960695i
$178$		0			0
$179$	−0.0548557	−	0.132433i	−0.00410011	−	0.00989854i	0.921816	−	0.387627i	$-0.126705\pi$
$179$	−0.0548557	−	0.132433i	−0.00410011	−	0.00989854i	−0.925916	+	0.377729i	$0.876705\pi$
$180$		0			0
$181$	2.37724	+	0.984684i	0.176699	+	0.0731910i	0.469279	−	0.883050i	$-0.344514\pi$
$181$	2.37724	+	0.984684i	0.176699	+	0.0731910i	−0.292580	+	0.956241i	$0.594514\pi$
$182$		0			0
$183$	2.99731	−	2.99731i	0.221567	−	0.221567i
$184$		0			0
$185$	−11.5558	−	11.5558i	−0.849602	−	0.849602i
$186$		0			0
$187$	−4.84588	+	11.6990i	−0.354366	+	0.855516i
$188$		0			0
$189$	−7.52396	+	3.11653i	−0.547287	+	0.226694i
$190$		0			0
$191$	16.4603			1.19103			0.595514	−	0.803345i	$-0.296948\pi$
$191$	16.4603			1.19103			0.595514	+	0.803345i	$0.296948\pi$
$192$		0			0
$193$	9.84445			0.708619			0.354309	−	0.935128i	$-0.384716\pi$
$193$	9.84445			0.708619			0.354309	+	0.935128i	$0.384716\pi$
$194$		0			0
$195$	−20.4789	+	8.48264i	−1.46652	+	0.607454i
$196$		0			0
$197$	−3.91048	+	9.44074i	−0.278610	+	0.672625i	−0.999798	−	0.0201152i	$-0.993597\pi$
$197$	−3.91048	+	9.44074i	−0.278610	+	0.672625i	0.721187	+	0.692740i	$0.243597\pi$
$198$		0			0
$199$	−2.41726	−	2.41726i	−0.171355	−	0.171355i	0.616220	−	0.787574i	$-0.288663\pi$
$199$	−2.41726	−	2.41726i	−0.171355	−	0.171355i	−0.787574	+	0.616220i	$0.788663\pi$
$200$		0			0
$201$	5.56804	−	5.56804i	0.392739	−	0.392739i
$202$		0			0
$203$	5.61093	+	2.32412i	0.393810	+	0.163121i
$204$		0			0
$205$	12.1280	+	29.2796i	0.847057	+	2.04498i
$206$		0			0
$207$		−	1.04905i		−	0.0729137i
$208$		0			0
$209$			16.2959i			1.12721i
$210$		0			0
$211$	−6.06529	−	14.6429i	−0.417552	−	1.00806i	−0.983055	−	0.183312i	$-0.941318\pi$
$211$	−6.06529	−	14.6429i	−0.417552	−	1.00806i	0.565503	−	0.824746i	$-0.308682\pi$
$212$		0			0
$213$	5.64564	+	2.33850i	0.386833	+	0.160231i
$214$		0			0
$215$	23.5012	−	23.5012i	1.60277	−	1.60277i
$216$		0			0
$217$	10.8625	+	10.8625i	0.737392	+	0.737392i
$218$		0			0
$219$	6.92490	−	16.7182i	0.467942	−	1.12971i
$220$		0			0
$221$	−8.89533	+	3.68457i	−0.598365	+	0.247851i
$222$		0			0
$223$	−20.9031			−1.39978			−0.699888	−	0.714253i	$-0.746767\pi$
$223$	−20.9031			−1.39978			−0.699888	+	0.714253i	$0.746767\pi$
$224$		0			0
$225$	5.39444			0.359629
$226$		0			0
$227$	−12.5201	+	5.18600i	−0.830989	+	0.344207i	−0.757294	−	0.653074i	$-0.773479\pi$
$227$	−12.5201	+	5.18600i	−0.830989	+	0.344207i	−0.0736948	+	0.997281i	$0.523479\pi$
$228$		0			0
$229$	−2.21925	+	5.35773i	−0.146652	+	0.354049i	−0.980087	−	0.198568i	$-0.936371\pi$
$229$	−2.21925	+	5.35773i	−0.146652	+	0.354049i	0.833435	+	0.552617i	$0.186371\pi$
$230$		0			0
$231$	−8.38269	−	8.38269i	−0.551541	−	0.551541i
$232$		0			0
$233$	−0.0268197	+	0.0268197i	−0.00175702	+	0.00175702i	−0.707985	−	0.706228i	$-0.750395\pi$
$233$	−0.0268197	+	0.0268197i	−0.00175702	+	0.00175702i	0.706228	+	0.707985i	$0.250395\pi$
$234$		0			0
$235$	10.1215	+	4.19246i	0.660254	+	0.273486i
$236$		0			0
$237$	−2.67147	−	6.44949i	−0.173530	−	0.418939i
$238$		0			0
$239$			25.6128i			1.65676i	0.560169	+	0.828378i	$0.310736\pi$
$239$			25.6128i			1.65676i	−0.560169	+	0.828378i	$0.689264\pi$
$240$		0			0
$241$			1.28132i			0.0825369i	0.999148	+	0.0412684i	$0.0131399\pi$
$241$			1.28132i			0.0825369i	−0.999148	+	0.0412684i	$0.986860\pi$
$242$		0			0
$243$	−2.70998	−	6.54247i	−0.173845	−	0.419699i
$244$		0			0
$245$	−16.1363	−	6.68386i	−1.03091	−	0.427016i
$246$		0			0
$247$	−8.76148	+	8.76148i	−0.557480	+	0.557480i
$248$		0			0
$249$	8.83083	+	8.83083i	0.559631	+	0.559631i
$250$		0			0
$251$	4.01245	−	9.68691i	0.253263	−	0.611432i	−0.745200	−	0.666841i	$-0.767646\pi$
$251$	4.01245	−	9.68691i	0.253263	−	0.611432i	0.998464	+	0.0554086i	$0.0176461\pi$
$252$		0			0
$253$	7.48528	−	3.10051i	0.470596	−	0.194927i
$254$		0			0
$255$	−12.7477			−0.798289
$256$		0			0
$257$	8.01513			0.499970			0.249985	−	0.968250i	$-0.419574\pi$
$257$	8.01513			0.499970			0.249985	+	0.968250i	$0.419574\pi$
$258$		0			0
$259$	6.13977	−	2.54318i	0.381507	−	0.158025i
$260$		0			0
$261$	−1.11561	+	2.69331i	−0.0690544	+	0.166712i
$262$		0			0
$263$	13.8663	+	13.8663i	0.855030	+	0.855030i	0.990748	−	0.135718i	$-0.0433340\pi$
$263$	13.8663	+	13.8663i	0.855030	+	0.855030i	−0.135718	+	0.990748i	$0.543334\pi$
$264$		0			0
$265$	−1.04989	+	1.04989i	−0.0644941	+	0.0644941i
$266$		0			0
$267$	−1.91771	−	0.794341i	−0.117362	−	0.0486129i
$268$		0			0
$269$	−6.54616	−	15.8038i	−0.399126	−	0.963576i	−0.987874	−	0.155259i	$-0.950379\pi$
$269$	−6.54616	−	15.8038i	−0.399126	−	0.963576i	0.588748	−	0.808317i	$-0.299621\pi$
$270$		0			0
$271$			15.6152i			0.948557i	0.880375	+	0.474279i	$0.157291\pi$
$271$			15.6152i			0.948557i	−0.880375	+	0.474279i	$0.842709\pi$
$272$		0			0
$273$		−	9.01388i		−	0.545545i
$274$		0			0
$275$	15.9435	+	38.4911i	0.961431	+	2.32110i
$276$		0			0
$277$	12.8489	+	5.32219i	0.772016	+	0.319779i	0.733689	−	0.679486i	$-0.237797\pi$
$277$	12.8489	+	5.32219i	0.772016	+	0.319779i	0.0383271	+	0.999265i	$0.487797\pi$
$278$		0			0
$279$	−5.21412	+	5.21412i	−0.312161	+	0.312161i
$280$		0			0
$281$	18.7289	+	18.7289i	1.11727	+	1.11727i	0.992140	+	0.125134i	$0.0399360\pi$
$281$	18.7289	+	18.7289i	1.11727	+	1.11727i	0.125134	+	0.992140i	$0.460064\pi$
$282$		0			0
$283$	−0.410064	+	0.989981i	−0.0243758	+	0.0588483i	−0.935599	−	0.353065i	$-0.885139\pi$
$283$	−0.410064	+	0.989981i	−0.0243758	+	0.0588483i	0.911223	+	0.411913i	$0.135139\pi$
$284$		0			0
$285$	−15.1562	+	6.27792i	−0.897778	+	0.371872i
$286$		0			0
$287$	−12.8875			−0.760728
$288$		0			0
$289$	11.4629			0.674286
$290$		0			0
$291$	15.7979	−	6.54372i	0.926091	−	0.383600i
$292$		0			0
$293$	6.81087	−	16.4429i	0.397895	−	0.960604i	−0.590269	−	0.807206i	$-0.700978\pi$
$293$	6.81087	−	16.4429i	0.397895	−	0.960604i	0.988165	−	0.153398i	$-0.0490216\pi$
$294$		0			0
$295$	21.2573	+	21.2573i	1.23765	+	1.23765i
$296$		0			0
$297$	21.3485	−	21.3485i	1.23876	−	1.23876i
$298$		0			0
$299$	5.69143	+	2.35747i	0.329144	+	0.136336i
$300$		0			0
$301$	5.17209	+	12.4865i	0.298114	+	0.719711i
$302$		0			0
$303$		−	14.2232i		−	0.817103i
$304$		0			0
$305$		−	9.97005i		−	0.570883i
$306$		0			0
$307$	7.89068	+	19.0498i	0.450345	+	1.08723i	0.972191	+	0.234189i	$0.0752435\pi$
$307$	7.89068	+	19.0498i	0.450345	+	1.08723i	−0.521846	+	0.853040i	$0.674757\pi$
$308$		0			0
$309$	−2.38839	−	0.989303i	−0.135871	−	0.0562795i
$310$		0			0
$311$	1.42704	−	1.42704i	0.0809203	−	0.0809203i	−0.665488	−	0.746408i	$-0.731777\pi$
$311$	1.42704	−	1.42704i	0.0809203	−	0.0809203i	0.746408	+	0.665488i	$0.231777\pi$
$312$		0			0
$313$	−1.27186	−	1.27186i	−0.0718900	−	0.0718900i	0.670248	−	0.742138i	$-0.266188\pi$
$313$	−1.27186	−	1.27186i	−0.0718900	−	0.0718900i	−0.742138	+	0.670248i	$0.766188\pi$
$314$		0			0
$315$	−1.38163	+	3.33554i	−0.0778459	+	0.187937i
$316$		0			0
$317$	22.9106	−	9.48990i	1.28679	−	0.533006i	0.368763	−	0.929523i	$-0.379781\pi$
$317$	22.9106	−	9.48990i	1.28679	−	0.533006i	0.918027	+	0.396518i	$0.129781\pi$
$318$		0			0
$319$	−22.5149			−1.26059
$320$		0			0
$321$	4.41813			0.246596
$322$		0			0
$323$	−6.58335	+	2.72691i	−0.366307	+	0.151729i
$324$		0			0
$325$	−12.1227	+	29.2667i	−0.672444	+	1.62342i
$326$		0			0
$327$	−4.10091	−	4.10091i	−0.226781	−	0.226781i
$328$		0			0
$329$	−3.15018	+	3.15018i	−0.173675	+	0.173675i
$330$		0			0
$331$	−21.1789	−	8.77257i	−1.16410	−	0.482184i	−0.284859	−	0.958570i	$-0.591947\pi$
$331$	−21.1789	−	8.77257i	−1.16410	−	0.482184i	−0.879236	+	0.476386i	$0.841947\pi$
$332$		0			0
$333$	1.22076	+	2.94717i	0.0668971	+	0.161504i
$334$		0			0
$335$		−	18.5212i		−	1.01192i
$336$		0			0
$337$			27.4961i			1.49781i	0.662677	+	0.748905i	$0.269420\pi$
$337$			27.4961i			1.49781i	−0.662677	+	0.748905i	$0.730580\pi$
$338$		0			0
$339$	1.24071	+	2.99533i	0.0673860	+	0.162684i
$340$		0			0
$341$	−52.6150	−	21.7938i	−2.84926	−	1.18020i
$342$		0			0
$343$	12.2071	−	12.2071i	0.659123	−	0.659123i
$344$		0			0
$345$	5.76733	+	5.76733i	0.310502	+	0.310502i
$346$		0			0
$347$	−1.87785	+	4.53353i	−0.100808	+	0.243373i	−0.966235	−	0.257663i	$-0.917048\pi$
$347$	−1.87785	+	4.53353i	−0.100808	+	0.243373i	0.865427	+	0.501036i	$0.167048\pi$
$348$		0			0
$349$	19.9976	−	8.28327i	1.07045	−	0.443393i	0.223298	−	0.974750i	$-0.428318\pi$
$349$	19.9976	−	8.28327i	1.07045	−	0.443393i	0.847148	+	0.531357i	$0.178318\pi$
$350$		0			0
$351$	22.9559			1.22530
$352$		0			0
$353$	−11.5498			−0.614733			−0.307366	−	0.951591i	$-0.599448\pi$
$353$	−11.5498			−0.614733			−0.307366	+	0.951591i	$0.599448\pi$
$354$		0			0
$355$	13.2790	−	5.50033i	0.704774	−	0.291927i
$356$		0			0
$357$	1.98377	−	4.78924i	0.104992	−	0.253473i
$358$		0			0
$359$	−19.0741	−	19.0741i	−1.00669	−	1.00669i	−0.999977	−	0.00671431i	$-0.997863\pi$
$359$	−19.0741	−	19.0741i	−1.00669	−	1.00669i	−0.00671431	−	0.999977i	$-0.502137\pi$
$360$		0			0
$361$	6.95074	−	6.95074i	0.365829	−	0.365829i
$362$		0			0
$363$	25.1803	+	10.4300i	1.32163	+	0.547435i
$364$		0			0
$365$	−16.2879	−	39.3224i	−0.852547	−	2.05823i
$366$		0			0
$367$			12.4379i			0.649251i	0.945843	+	0.324626i	$0.105238\pi$
$367$			12.4379i			0.649251i	−0.945843	+	0.324626i	$0.894762\pi$
$368$		0			0
$369$		−	6.18618i		−	0.322040i
$370$		0			0
$371$	−0.231057	−	0.557820i	−0.0119959	−	0.0289606i
$372$		0			0
$373$	31.1238	+	12.8919i	1.61153	+	0.667518i	0.992986	−	0.118232i	$-0.0377228\pi$
$373$	31.1238	+	12.8919i	1.61153	+	0.667518i	0.618544	+	0.785750i	$0.287723\pi$
$374$		0			0
$375$	−10.5037	+	10.5037i	−0.542409	+	0.542409i
$376$		0			0
$377$	−12.1051	−	12.1051i	−0.623444	−	0.623444i
$378$		0			0
$379$	−5.42584	+	13.0991i	−0.278707	+	0.672858i	−0.999800	−	0.0199800i	$-0.993640\pi$
$379$	−5.42584	+	13.0991i	−0.278707	+	0.672858i	0.721094	+	0.692838i	$0.243640\pi$
$380$		0			0
$381$	1.53981	−	0.637812i	0.0788870	−	0.0326761i
$382$		0			0
$383$	−7.14287			−0.364984			−0.182492	−	0.983207i	$-0.558416\pi$
$383$	−7.14287			−0.364984			−0.182492	+	0.983207i	$0.558416\pi$
$384$		0			0
$385$	−27.8836			−1.42108
$386$		0			0
$387$	−5.99369	+	2.48267i	−0.304676	+	0.126201i
$388$		0			0
$389$	10.8578	−	26.2131i	0.550514	−	1.32906i	−0.366579	−	0.930387i	$-0.619471\pi$
$389$	10.8578	−	26.2131i	0.550514	−	1.32906i	0.917093	−	0.398672i	$-0.130529\pi$
$390$		0			0
$391$	2.50513	+	2.50513i	0.126690	+	0.126690i
$392$		0			0
$393$	−0.761008	+	0.761008i	−0.0383878	+	0.0383878i
$394$		0			0
$395$	−15.1697	−	6.28348i	−0.763269	−	0.316156i
$396$		0			0
$397$	3.55362	+	8.57919i	0.178351	+	0.430577i	0.987621	−	0.156860i	$-0.0501370\pi$
$397$	3.55362	+	8.57919i	0.178351	+	0.430577i	−0.809270	+	0.587437i	$0.800137\pi$
$398$		0			0
$399$		−	6.67109i		−	0.333972i
$400$		0			0
$401$			9.43274i			0.471049i	0.971868	+	0.235524i	$0.0756807\pi$
$401$			9.43274i			0.471049i	−0.971868	+	0.235524i	$0.924319\pi$
$402$		0			0
$403$	−16.5709	−	40.0058i	−0.825457	−	1.99283i
$404$		0			0
$405$	21.1862	+	8.77559i	1.05275	+	0.436063i
$406$		0			0
$407$	−17.4210	+	17.4210i	−0.863526	+	0.863526i
$408$		0			0
$409$	−15.4495	−	15.4495i	−0.763928	−	0.763928i	0.213102	−	0.977030i	$-0.431643\pi$
$409$	−15.4495	−	15.4495i	−0.763928	−	0.763928i	−0.977030	+	0.213102i	$0.931643\pi$
$410$		0			0
$411$	−9.43611	+	22.7808i	−0.465449	+	1.12369i
$412$		0			0
$413$	−11.2943	+	4.67825i	−0.555756	+	0.230202i
$414$		0			0
$415$	29.3743			1.44193
$416$		0			0
$417$	1.28308			0.0628325
$418$		0			0
$419$	−19.7592	+	8.18452i	−0.965299	+	0.399840i	−0.808960	−	0.587864i	$-0.799969\pi$
$419$	−19.7592	+	8.18452i	−0.965299	+	0.399840i	−0.156339	+	0.987703i	$0.549969\pi$
$420$		0			0
$421$	−10.1504	+	24.5052i	−0.494700	+	1.19431i	0.457602	+	0.889157i	$0.348708\pi$
$421$	−10.1504	+	24.5052i	−0.494700	+	1.19431i	−0.952303	+	0.305155i	$0.901292\pi$
$422$		0			0
$423$	−1.51213	−	1.51213i	−0.0735221	−	0.0735221i
$424$		0			0
$425$	−12.8820	+	12.8820i	−0.624867	+	0.624867i
$426$		0			0
$427$	3.74570	+	1.55152i	0.181267	+	0.0750833i
$428$		0			0
$429$	12.7880	+	30.8729i	0.617410	+	1.49056i
$430$		0			0
$431$			24.7162i			1.19054i	0.803528	+	0.595268i	$0.202954\pi$
$431$			24.7162i			1.19054i	−0.803528	+	0.595268i	$0.797046\pi$
$432$		0			0
$433$		−	9.69501i		−	0.465913i	−0.972487	−	0.232956i	$-0.925160\pi$
$433$		−	9.69501i		−	0.465913i	0.972487	−	0.232956i	$-0.0748399\pi$
$434$		0			0
$435$	−8.67374	−	20.9403i	−0.415874	−	1.00401i
$436$		0			0
$437$	4.21217	+	1.74474i	0.201496	+	0.0834622i
$438$		0			0
$439$	−8.45429	+	8.45429i	−0.403501	+	0.403501i	−0.879465	−	0.475964i	$-0.842099\pi$
$439$	−8.45429	+	8.45429i	−0.403501	+	0.403501i	0.475964	+	0.879465i	$0.342099\pi$
$440$		0			0
$441$	2.41072	+	2.41072i	0.114796	+	0.114796i
$442$		0			0
$443$	14.5182	−	35.0500i	0.689780	−	1.66528i	−0.0554440	−	0.998462i	$-0.517657\pi$
$443$	14.5182	−	35.0500i	0.689780	−	1.66528i	0.745224	−	0.666814i	$-0.232343\pi$
$444$		0			0
$445$	−4.51059	+	1.86835i	−0.213822	+	0.0885682i
$446$		0			0
$447$	10.7160			0.506851
$448$		0			0
$449$	−22.3365			−1.05413			−0.527063	−	0.849826i	$-0.676707\pi$
$449$	−22.3365			−1.05413			−0.527063	+	0.849826i	$0.676707\pi$
$450$		0			0
$451$	44.1404	−	18.2836i	2.07849	−	0.860939i
$452$		0			0
$453$	8.11026	−	19.5799i	0.381053	−	0.919944i
$454$		0			0
$455$	−14.9916	−	14.9916i	−0.702817	−	0.702817i
$456$		0			0
$457$	−22.4049	+	22.4049i	−1.04806	+	1.04806i	−0.0492728	+	0.998785i	$0.515690\pi$
$457$	−22.4049	+	22.4049i	−1.04806	+	1.04806i	−0.998785	+	0.0492728i	$0.984310\pi$
$458$		0			0
$459$	12.1969	+	5.05212i	0.569302	+	0.235813i
$460$		0			0
$461$	1.20979	+	2.92070i	0.0563457	+	0.136031i	0.949545	−	0.313630i	$-0.101545\pi$
$461$	1.20979	+	2.92070i	0.0563457	+	0.136031i	−0.893200	+	0.449660i	$0.851545\pi$
$462$		0			0
$463$		−	26.3825i		−	1.22610i	−0.790045	−	0.613048i	$-0.789943\pi$
$463$		−	26.3825i		−	1.22610i	0.790045	−	0.613048i	$-0.210057\pi$
$464$		0			0
$465$		−	57.3312i		−	2.65867i
$466$		0			0
$467$	3.92750	+	9.48183i	0.181743	+	0.438767i	0.988326	−	0.152354i	$-0.0486855\pi$
$467$	3.92750	+	9.48183i	0.181743	+	0.438767i	−0.806583	+	0.591121i	$0.798686\pi$
$468$		0			0
$469$	6.95832	+	2.88223i	0.321305	+	0.133089i
$470$		0			0
$471$	−25.9812	+	25.9812i	−1.19715	+	1.19715i
$472$		0			0
$473$	−35.4293	−	35.4293i	−1.62904	−	1.62904i
$474$		0			0
$475$	−8.97186	+	21.6600i	−0.411657	+	0.993828i
$476$		0			0
$477$	0.267761	−	0.110910i	0.0122599	−	0.00507822i
$478$		0			0
$479$	26.4855			1.21015			0.605077	−	0.796167i	$-0.293142\pi$
$479$	26.4855			1.21015			0.605077	+	0.796167i	$0.293142\pi$
$480$		0			0
$481$	−18.7327			−0.854139
$482$		0			0
$483$	−3.06426	+	1.26926i	−0.139429	+	0.0577532i
$484$		0			0
$485$	15.3913	−	37.1579i	0.698883	−	1.68725i
$486$		0			0
$487$	5.38394	+	5.38394i	0.243970	+	0.243970i	0.818490	−	0.574521i	$-0.194811\pi$
$487$	5.38394	+	5.38394i	0.243970	+	0.243970i	−0.574521	+	0.818490i	$0.694811\pi$
$488$		0			0
$489$	−18.7909	+	18.7909i	−0.849754	+	0.849754i
$490$		0			0
$491$	−15.9889	−	6.62284i	−0.721571	−	0.298884i	−0.00848784	−	0.999964i	$-0.502702\pi$
$491$	−15.9889	−	6.62284i	−0.721571	−	0.298884i	−0.713083	+	0.701080i	$0.752702\pi$
$492$		0			0
$493$	−3.76758	−	9.09573i	−0.169683	−	0.409651i
$494$		0			0
$495$		−	13.3845i		−	0.601588i
$496$		0			0
$497$			5.84480i			0.262175i
$498$		0			0
$499$	−1.68675	−	4.07217i	−0.0755091	−	0.182295i	0.881618	−	0.471964i	$-0.156455\pi$
$499$	−1.68675	−	4.07217i	−0.0755091	−	0.182295i	−0.957127	+	0.289669i	$0.906455\pi$
$500$		0			0
$501$	−31.5685	−	13.0761i	−1.41038	−	0.584197i
$502$		0			0
$503$	22.1132	−	22.1132i	0.985978	−	0.985978i	−0.0139248	−	0.999903i	$-0.504433\pi$
$503$	22.1132	−	22.1132i	0.985978	−	0.985978i	0.999903	+	0.0139248i	$0.00443254\pi$
$504$		0			0
$505$	−23.6556	−	23.6556i	−1.05266	−	1.05266i
$506$		0			0
$507$	−2.17327	+	5.24674i	−0.0965183	+	0.233016i
$508$		0			0
$509$	−12.6528	+	5.24094i	−0.560823	+	0.232301i	−0.645043	−	0.764147i	$-0.723160\pi$
$509$	−12.6528	+	5.24094i	−0.560823	+	0.232301i	0.0842193	+	0.996447i	$0.473160\pi$
$510$		0			0
$511$	17.3080			0.765659
$512$		0			0
$513$	16.9895			0.750103
$514$		0			0
$515$	−5.61767	+	2.32691i	−0.247544	+	0.102536i
$516$		0			0
$517$	6.32034	−	15.2587i	0.277968	−	0.671075i
$518$		0			0
$519$	9.71756	+	9.71756i	0.426553	+	0.426553i
$520$		0			0
$521$	7.89757	−	7.89757i	0.345999	−	0.345999i	−0.512618	−	0.858617i	$-0.671324\pi$
$521$	7.89757	−	7.89757i	0.345999	−	0.345999i	0.858617	+	0.512618i	$0.171324\pi$
$522$		0			0
$523$	−11.2606	−	4.66429i	−0.492391	−	0.203955i	0.122650	−	0.992450i	$-0.460861\pi$
$523$	−11.2606	−	4.66429i	−0.492391	−	0.203955i	−0.615041	+	0.788495i	$0.710861\pi$
$524$		0			0
$525$	−6.52682	−	15.7571i	−0.284854	−	0.687698i
$526$		0			0
$527$		−	24.9027i		−	1.08478i
$528$		0			0
$529$			20.7332i			0.901445i
$530$		0			0
$531$	−2.24562	−	5.42140i	−0.0974515	−	0.235269i
$532$		0			0
$533$	33.5622	+	13.9019i	1.45374	+	0.602158i
$534$		0			0
$535$	7.34809	−	7.34809i	0.317685	−	0.317685i
$536$		0			0
$537$	−0.153828	−	0.153828i	−0.00663817	−	0.00663817i
$538$		0			0
$539$	−10.0763	+	24.3262i	−0.434015	+	1.04780i
$540$		0			0
$541$	11.7860	−	4.88194i	0.506722	−	0.209891i	−0.114652	−	0.993406i	$-0.536575\pi$
$541$	11.7860	−	4.88194i	0.506722	−	0.209891i	0.621373	+	0.783515i	$0.286575\pi$
$542$		0			0
$543$	3.90504			0.167581
$544$		0			0
$545$	−13.6410			−0.584316
$546$		0			0
$547$	26.1348	−	10.8254i	1.11745	−	0.462861i	0.253950	−	0.967217i	$-0.418270\pi$
$547$	26.1348	−	10.8254i	1.11745	−	0.462861i	0.863496	+	0.504356i	$0.168270\pi$
$548$		0			0
$549$	−0.744749	+	1.79798i	−0.0317851	+	0.0767361i
$550$		0			0
$551$	−8.95887	−	8.95887i	−0.381661	−	0.381661i
$552$		0			0
$553$	4.72135	−	4.72135i	0.200772	−	0.200772i
$554$		0			0
$555$	−22.9139	−	9.49127i	−0.972643	−	0.402882i
$556$		0			0
$557$	−13.5899	−	32.8089i	−0.575822	−	1.39016i	−0.896532	−	0.442980i	$-0.853921\pi$
$557$	−13.5899	−	32.8089i	−0.575822	−	1.39016i	0.320709	−	0.947178i	$-0.396079\pi$
$558$		0			0
$559$		−	38.0970i		−	1.61133i
$560$		0			0
$561$			19.2177i			0.811372i
$562$		0			0
$563$	−4.48742	−	10.8336i	−0.189122	−	0.456582i	0.800669	−	0.599107i	$-0.204478\pi$
$563$	−4.48742	−	10.8336i	−0.189122	−	0.456582i	−0.989791	+	0.142526i	$0.954478\pi$
$564$		0			0
$565$	7.04524	+	2.91824i	0.296396	+	0.122771i
$566$		0			0
$567$	−6.59390	+	6.59390i	−0.276918	+	0.276918i
$568$		0			0
$569$	18.7673	+	18.7673i	0.786767	+	0.786767i	0.980963	−	0.194196i	$-0.0622096\pi$
$569$	18.7673	+	18.7673i	0.786767	+	0.786767i	−0.194196	+	0.980963i	$0.562210\pi$
$570$		0			0
$571$	−5.03334	+	12.1516i	−0.210639	+	0.508527i	−0.993522	−	0.113642i	$-0.963748\pi$
$571$	−5.03334	+	12.1516i	−0.210639	+	0.508527i	0.782883	+	0.622169i	$0.213748\pi$
$572$		0			0
$573$	23.0793	−	9.55975i	0.964151	−	0.399364i
$574$		0			0
$575$	11.6562			0.486097
$576$		0			0
$577$	25.2275			1.05024			0.525118	−	0.851029i	$-0.324021\pi$
$577$	25.2275			1.05024			0.525118	+	0.851029i	$0.324021\pi$
$578$		0			0
$579$	13.8030	−	5.71741i	0.573635	−	0.237607i
$580$		0			0
$581$	−4.57117	+	11.0358i	−0.189644	+	0.457842i
$582$		0			0
$583$	1.58276	+	1.58276i	0.0655511	+	0.0655511i
$584$		0			0
$585$	7.19615	−	7.19615i	0.297524	−	0.297524i
$586$		0			0
$587$	−16.4971	−	6.83331i	−0.680907	−	0.282041i	0.0152989	−	0.999883i	$-0.495130\pi$
$587$	−16.4971	−	6.83331i	−0.680907	−	0.282041i	−0.696206	+	0.717842i	$0.745130\pi$
$588$		0			0
$589$	−12.2640	−	29.6079i	−0.505329	−	1.21997i
$590$		0			0
$591$			15.5081i			0.637919i
$592$		0			0
$593$		−	41.3009i		−	1.69602i	−0.529976	−	0.848012i	$-0.677799\pi$
$593$		−	41.3009i		−	1.69602i	0.529976	−	0.848012i	$-0.322201\pi$
$594$		0			0
$595$	−4.66596	−	11.2646i	−0.191286	−	0.461805i
$596$		0			0
$597$	−4.79315	−	1.98539i	−0.196171	−	0.0812565i
$598$		0			0
$599$	−6.73920	+	6.73920i	−0.275356	+	0.275356i	−0.831252	−	0.555896i	$-0.812375\pi$
$599$	−6.73920	+	6.73920i	−0.275356	+	0.275356i	0.555896	+	0.831252i	$0.312375\pi$
$600$		0			0
$601$	23.2456	+	23.2456i	0.948206	+	0.948206i	0.998723	−	0.0505170i	$-0.0160869\pi$
$601$	23.2456	+	23.2456i	0.948206	+	0.948206i	−0.0505170	+	0.998723i	$0.516087\pi$
$602$		0			0
$603$	−1.38351	+	3.34008i	−0.0563407	+	0.136019i
$604$		0			0
$605$	59.2260	−	24.5322i	2.40788	−	0.997377i
$606$		0			0
$607$	−18.7402			−0.760642			−0.380321	−	0.924855i	$-0.624187\pi$
$607$	−18.7402			−0.760642			−0.380321	+	0.924855i	$0.624187\pi$
$608$		0			0
$609$	9.21695			0.373490
$610$		0			0
$611$	11.6019	−	4.80567i	0.469363	−	0.194417i
$612$		0			0
$613$	14.2609	−	34.4288i	0.575991	−	1.39057i	−0.320391	−	0.947285i	$-0.603814\pi$
$613$	14.2609	−	34.4288i	0.575991	−	1.39057i	0.896383	−	0.443281i	$-0.146186\pi$
$614$		0			0
$615$	34.0097	+	34.0097i	1.37140	+	1.37140i
$616$		0			0
$617$	−11.5470	+	11.5470i	−0.464866	+	0.464866i	−0.900246	−	0.435381i	$-0.856614\pi$
$617$	−11.5470	+	11.5470i	−0.464866	+	0.464866i	0.435381	+	0.900246i	$0.356614\pi$
$618$		0			0
$619$	−39.8529	−	16.5076i	−1.60182	−	0.663498i	−0.610153	−	0.792284i	$-0.708892\pi$
$619$	−39.8529	−	16.5076i	−1.60182	−	0.663498i	−0.991672	+	0.128786i	$0.958892\pi$
$620$		0			0
$621$	−3.23246	−	7.80385i	−0.129714	−	0.313158i
$622$		0			0
$623$		−	1.98536i		−	0.0795417i
$624$		0			0
$625$		−	3.77124i		−	0.150850i
$626$		0			0
$627$	9.46427	+	22.8488i	0.377966	+	0.912492i
$628$		0			0
$629$	−9.95303	−	4.12268i	−0.396853	−	0.164382i
$630$		0			0
$631$	−4.48591	+	4.48591i	−0.178581	+	0.178581i	−0.790737	−	0.612156i	$-0.790302\pi$
$631$	−4.48591	+	4.48591i	−0.178581	+	0.178581i	0.612156	+	0.790737i	$0.290302\pi$
$632$		0			0
$633$	−17.0085	−	17.0085i	−0.676025	−	0.676025i
$634$		0			0
$635$	1.50018	−	3.62175i	0.0595328	−	0.143725i
$636$		0			0
$637$	−18.4964	+	7.66147i	−0.732855	+	0.303559i
$638$		0			0
$639$	−2.80558			−0.110987
$640$		0			0
$641$	−39.5996			−1.56409			−0.782045	−	0.623221i	$-0.785824\pi$
$641$	−39.5996			−1.56409			−0.782045	+	0.623221i	$0.785824\pi$
$642$		0			0
$643$	−22.6057	+	9.36360i	−0.891483	+	0.369264i	−0.780939	−	0.624607i	$-0.785259\pi$
$643$	−22.6057	+	9.36360i	−0.891483	+	0.369264i	−0.110544	+	0.993871i	$0.535259\pi$
$644$		0			0
$645$	19.3025	−	46.6003i	0.760035	−	1.83489i
$646$		0			0
$647$	−25.4317	−	25.4317i	−0.999823	−	0.999823i	0.000176614	−	1.00000i	$-0.499944\pi$
$647$	−25.4317	−	25.4317i	−0.999823	−	0.999823i	−1.00000		0.000176614i	$0.999944\pi$
$648$		0			0
$649$	32.0464	−	32.0464i	1.25793	−	1.25793i
$650$		0			0
$651$	21.5391	+	8.92177i	0.844182	+	0.349672i
$652$		0			0
$653$	−9.37458	−	22.6322i	−0.366856	−	0.885668i	−0.994262	−	0.106976i	$-0.965883\pi$
$653$	−9.37458	−	22.6322i	−0.366856	−	0.885668i	0.627406	−	0.778692i	$-0.284117\pi$
$654$		0			0
$655$			2.53137i			0.0989087i
$656$		0			0
$657$			8.30803i			0.324127i
$658$		0			0
$659$	10.3595	+	25.0100i	0.403547	+	0.974250i	0.986798	+	0.161957i	$0.0517807\pi$
$659$	10.3595	+	25.0100i	0.403547	+	0.974250i	−0.583250	+	0.812292i	$0.698219\pi$
$660$		0			0
$661$	−11.6719	−	4.83467i	−0.453985	−	0.188047i	0.143961	−	0.989583i	$-0.454016\pi$
$661$	−11.6719	−	4.83467i	−0.453985	−	0.188047i	−0.597946	+	0.801537i	$0.704016\pi$
$662$		0			0
$663$	−10.3324	+	10.3324i	−0.401276	+	0.401276i
$664$		0			0
$665$	−11.0951	−	11.0951i	−0.430251	−	0.430251i
$666$		0			0
$667$	−2.41058	+	5.81965i	−0.0933380	+	0.225338i
$668$		0			0
$669$	−29.3085	+	12.1400i	−1.13313	+	0.469359i
$670$		0			0
$671$	−15.0303			−0.580240
$672$		0			0
$673$	9.29926			0.358460			0.179230	−	0.983807i	$-0.442639\pi$
$673$	9.29926			0.358460			0.179230	+	0.983807i	$0.442639\pi$
$674$		0			0
$675$	40.1292	−	16.6221i	1.54457	−	0.639784i
$676$		0			0
$677$	−8.59697	+	20.7549i	−0.330409	+	0.797677i	0.668151	+	0.744026i	$0.267086\pi$
$677$	−8.59697	+	20.7549i	−0.330409	+	0.797677i	−0.998560	+	0.0536513i	$0.982914\pi$
$678$		0			0
$679$	11.5649	+	11.5649i	0.443820	+	0.443820i
$680$		0			0
$681$	−14.5427	+	14.5427i	−0.557279	+	0.557279i
$682$		0			0
$683$	5.15512	+	2.13532i	0.197255	+	0.0817058i	0.479124	−	0.877747i	$-0.340954\pi$
$683$	5.15512	+	2.13532i	0.197255	+	0.0817058i	−0.281869	+	0.959453i	$0.590954\pi$
$684$		0			0
$685$	22.1944	+	53.5821i	0.848005	+	2.04727i
$686$		0			0
$687$			8.80104i			0.335781i
$688$		0			0
$689$			1.70193i			0.0648385i
$690$		0			0
$691$	9.50357	+	22.9436i	0.361533	+	0.872817i	0.995076	+	0.0991103i	$0.0315997\pi$
$691$	9.50357	+	22.9436i	0.361533	+	0.872817i	−0.633544	+	0.773707i	$0.718400\pi$
$692$		0			0
$693$	5.02849	+	2.08287i	0.191017	+	0.0791217i
$694$		0			0
$695$	2.13397	−	2.13397i	0.0809461	−	0.0809461i
$696$		0			0
$697$	14.7727	+	14.7727i	0.559554	+	0.559554i
$698$		0			0
$699$	−0.0220281	+	0.0531806i	−0.000833180	+	0.00201147i
$700$		0			0
$701$	−18.3625	+	7.60601i	−0.693544	+	0.287275i	−0.701476	−	0.712693i	$-0.747475\pi$
$701$	−18.3625	+	7.60601i	−0.693544	+	0.287275i	0.00793210	+	0.999969i	$0.497475\pi$
$702$		0			0
$703$	−13.8639			−0.522887
$704$		0			0
$705$	16.6264			0.626186
$706$		0			0
$707$	12.5685	−	5.20606i	0.472689	−	0.195794i
$708$		0			0
$709$	−10.0866	+	24.3512i	−0.378810	+	0.914529i	0.613379	+	0.789788i	$0.289810\pi$
$709$	−10.0866	+	24.3512i	−0.378810	+	0.914529i	−0.992189	+	0.124740i	$0.960190\pi$
$710$		0			0
$711$	2.26631	+	2.26631i	0.0849932	+	0.0849932i
$712$		0			0
$713$	−11.2665	+	11.2665i	−0.421935	+	0.421935i
$714$		0			0
$715$	72.6154	+	30.0783i	2.71566	+	1.12486i
$716$		0			0
$717$	14.8753	+	35.9121i	0.555528	+	1.34116i
$718$		0			0
$719$			34.6091i			1.29070i	0.763887	+	0.645350i	$0.223289\pi$
$719$			34.6091i			1.29070i	−0.763887	+	0.645350i	$0.776711\pi$
$720$		0			0
$721$		−	2.47264i		−	0.0920860i
$722$		0			0
$723$	0.744157	+	1.79655i	0.0276755	+	0.0668145i
$724$		0			0
$725$	−29.9260	−	12.3958i	−1.11142	−	0.460367i
$726$		0			0
$727$	−30.7749	+	30.7749i	−1.14138	+	1.14138i	−0.153181	+	0.988198i	$0.548952\pi$
$727$	−30.7749	+	30.7749i	−1.14138	+	1.14138i	−0.988198	+	0.153181i	$0.951048\pi$
$728$		0			0
$729$	−21.2271	−	21.2271i	−0.786191	−	0.786191i
$730$		0			0
$731$	8.38434	−	20.2416i	0.310106	−	0.748662i
$732$		0			0
$733$	42.0588	−	17.4213i	1.55348	−	0.643472i	0.569537	−	0.821965i	$-0.307122\pi$
$733$	42.0588	−	17.4213i	1.55348	−	0.643472i	0.983941	+	0.178494i	$0.0571224\pi$
$734$		0			0
$735$	−26.5067			−0.977715
$736$		0			0
$737$	−27.9216			−1.02850
$738$		0			0
$739$	−25.8560	+	10.7099i	−0.951128	+	0.393970i	−0.803655	−	0.595096i	$-0.797114\pi$
$739$	−25.8560	+	10.7099i	−0.951128	+	0.393970i	−0.147474	+	0.989066i	$0.547114\pi$
$740$		0			0
$741$	−7.19615	+	17.3730i	−0.264357	+	0.638215i
$742$		0			0
$743$	26.2978	+	26.2978i	0.964774	+	0.964774i	0.999400	−	0.0346265i	$-0.0110242\pi$
$743$	26.2978	+	26.2978i	0.964774	+	0.964774i	−0.0346265	+	0.999400i	$0.511024\pi$
$744$		0			0
$745$	17.8225	−	17.8225i	0.652967	−	0.652967i
$746$		0			0
$747$	−5.29732	−	2.19422i	−0.193819	−	0.0802823i
$748$		0			0
$749$	1.61715	+	3.90414i	0.0590893	+	0.142654i
$750$		0			0
$751$		−	37.4098i		−	1.36510i	−0.730837	−	0.682552i	$-0.760870\pi$
$751$		−	37.4098i		−	1.36510i	0.730837	−	0.682552i	$-0.239130\pi$
$752$		0			0
$753$		−	15.9125i		−	0.579883i
$754$		0			0
$755$	−19.0759	−	46.0534i	−0.694244	−	1.67605i
$756$		0			0
$757$	−7.53295	−	3.12025i	−0.273790	−	0.113407i	0.241564	−	0.970385i	$-0.422340\pi$
$757$	−7.53295	−	3.12025i	−0.273790	−	0.113407i	−0.515354	+	0.856977i	$0.672340\pi$
$758$		0			0
$759$	8.69453	−	8.69453i	0.315591	−	0.315591i
$760$		0			0
$761$	8.08516	+	8.08516i	0.293087	+	0.293087i	0.838299	−	0.545212i	$-0.183551\pi$
$761$	8.08516	+	8.08516i	0.293087	+	0.293087i	−0.545212	+	0.838299i	$0.683551\pi$
$762$		0			0
$763$	2.12279	−	5.12486i	0.0768501	−	0.185532i
$764$		0			0
$765$	5.40717	−	2.23972i	0.195496	−	0.0809773i
$766$		0			0
$767$	34.4594			1.24426
$768$		0			0
$769$	−30.6572			−1.10553			−0.552764	−	0.833338i	$-0.686427\pi$
$769$	−30.6572			−1.10553			−0.552764	+	0.833338i	$0.686427\pi$
$770$		0			0
$771$	11.2381	−	4.65499i	0.404731	−	0.167645i
$772$		0			0
$773$	−12.1942	+	29.4394i	−0.438595	+	1.05886i	0.537839	+	0.843047i	$0.319241\pi$
$773$	−12.1942	+	29.4394i	−0.438595	+	1.05886i	−0.976434	+	0.215815i	$0.930759\pi$
$774$		0			0
$775$	−57.9352	−	57.9352i	−2.08109	−	2.08109i
$776$		0			0
$777$	7.13165	−	7.13165i	0.255847	−	0.255847i
$778$		0			0
$779$	24.8390	+	10.2887i	0.889950	+	0.368629i
$780$		0			0
$781$	−8.29201	−	20.0187i	−0.296712	−	0.716325i
$782$		0			0
$783$			23.4731i			0.838861i
$784$		0			0
$785$			86.4222i			3.08454i
$786$		0			0
$787$	−0.209491	−	0.505757i	−0.00746756	−	0.0180283i	0.920102	−	0.391679i	$-0.128106\pi$
$787$	−0.209491	−	0.505757i	−0.00746756	−	0.0180283i	−0.927569	+	0.373651i	$0.878106\pi$
$788$		0			0
$789$	27.4952	+	11.3889i	0.978857	+	0.405456i
$790$		0			0
$791$	−2.19274	+	2.19274i	−0.0779647	+	0.0779647i
$792$		0			0
$793$	−8.08104	−	8.08104i	−0.286966	−	0.286966i
$794$		0			0
$795$	−0.862315	+	2.08181i	−0.0305832	+	0.0738343i
$796$		0			0
$797$	−28.9652	+	11.9978i	−1.02600	+	0.424983i	−0.831267	−	0.555873i	$-0.812384\pi$
$797$	−28.9652	+	11.9978i	−1.02600	+	0.424983i	−0.194733	+	0.980856i	$0.562384\pi$
$798$		0			0
$799$	7.22193			0.255494
$800$		0			0
$801$	0.952996			0.0336725
$802$		0			0
$803$	−59.2805	+	24.5548i	−2.09196	+	0.866519i
$804$		0			0
$805$	−2.98539	+	7.20736i	−0.105221	+	0.254026i
$806$		0			0
$807$	−18.3569	−	18.3569i	−0.646194	−	0.646194i
$808$		0			0
$809$	5.60821	−	5.60821i	0.197174	−	0.197174i	−0.601613	−	0.798787i	$-0.705475\pi$
$809$	5.60821	−	5.60821i	0.197174	−	0.197174i	0.798787	+	0.601613i	$0.205475\pi$
$810$		0			0
$811$	−38.0138	−	15.7458i	−1.33484	−	0.552910i	−0.402811	−	0.915283i	$-0.631967\pi$
$811$	−38.0138	−	15.7458i	−1.33484	−	0.552910i	−0.932033	+	0.362373i	$0.881967\pi$
$812$		0			0
$813$	9.06893	+	21.8943i	0.318061	+	0.767868i
$814$		0			0
$815$			62.5049i			2.18945i
$816$		0			0
$817$		−	28.1952i		−	0.986425i
$818$		0			0
$819$	1.58371	+	3.82341i	0.0553393	+	0.133601i
$820$		0			0
$821$	24.6328	+	10.2032i	0.859689	+	0.356095i	0.768586	−	0.639746i	$-0.220961\pi$
$821$	24.6328	+	10.2032i	0.859689	+	0.356095i	0.0911034	+	0.995841i	$0.470961\pi$
$822$		0			0
$823$	26.4269	−	26.4269i	0.921185	−	0.921185i	−0.0759281	−	0.997113i	$-0.524192\pi$
$823$	26.4269	−	26.4269i	0.921185	−	0.921185i	0.997113	+	0.0759281i	$0.0241919\pi$
$824$		0			0
$825$	44.7093	+	44.7093i	1.55658	+	1.55658i
$826$		0			0
$827$	−1.90206	+	4.59197i	−0.0661410	+	0.159678i	−0.953494	−	0.301413i	$-0.902542\pi$
$827$	−1.90206	+	4.59197i	−0.0661410	+	0.159678i	0.887353	+	0.461091i	$0.152542\pi$
$828$		0			0
$829$	0.0370609	−	0.0153511i	0.00128718	−	0.000533166i	−0.382040	−	0.924146i	$-0.624778\pi$
$829$	0.0370609	−	0.0153511i	0.00128718	−	0.000533166i	0.383327	+	0.923613i	$0.374778\pi$
$830$		0			0
$831$	21.1066			0.732181
$832$		0			0
$833$	−11.5136			−0.398923
$834$		0			0
$835$	−74.2514	+	30.7559i	−2.56957	+	1.06435i
$836$		0			0
$837$	−22.7214	+	54.8542i	−0.785365	+	1.89604i
$838$		0			0
$839$	3.78014	+	3.78014i	0.130505	+	0.130505i	0.769342	−	0.638837i	$-0.220584\pi$
$839$	3.78014	+	3.78014i	0.130505	+	0.130505i	−0.638837	+	0.769342i	$0.720584\pi$
$840$		0			0
$841$	−8.12828	+	8.12828i	−0.280286	+	0.280286i
$842$		0			0
$843$	37.1374	+	15.3828i	1.27908	+	0.529812i
$844$		0			0
$845$	5.11169	+	12.3407i	0.175848	+	0.424534i
$846$		0			0
$847$			26.0686i			0.895728i
$848$		0			0
$849$			1.62622i			0.0558118i
$850$		0			0
$851$	2.63778	+	6.36817i	0.0904220	+	0.218298i
$852$		0			0
$853$	−42.7872	−	17.7231i	−1.46501	−	0.606826i	−0.499293	−	0.866433i	$-0.666407\pi$
$853$	−42.7872	−	17.7231i	−1.46501	−	0.606826i	−0.965714	+	0.259607i	$0.916407\pi$
$854$		0			0
$855$	5.32580	−	5.32580i	0.182139	−	0.182139i
$856$		0			0
$857$	−1.25991	−	1.25991i	−0.0430375	−	0.0430375i	0.685261	−	0.728298i	$-0.259688\pi$
$857$	−1.25991	−	1.25991i	−0.0430375	−	0.0430375i	−0.728298	+	0.685261i	$0.759688\pi$
$858$		0			0
$859$	−4.66511	+	11.2626i	−0.159171	+	0.384274i	−0.983265	−	0.182179i	$-0.941685\pi$
$859$	−4.66511	+	11.2626i	−0.159171	+	0.384274i	0.824094	+	0.566453i	$0.191685\pi$
$860$		0			0
$861$	−18.0698	+	7.48477i	−0.615818	+	0.255080i
$862$		0			0
$863$	−55.7303			−1.89708			−0.948541	−	0.316653i	$-0.897441\pi$
$863$	−55.7303			−1.89708			−0.948541	+	0.316653i	$0.897441\pi$
$864$		0			0
$865$	32.3238			1.09904
$866$		0			0
$867$	16.0722	−	6.65734i	0.545842	−	0.226095i
$868$		0			0
$869$	−9.47266	+	22.8690i	−0.321338	+	0.775779i
$870$		0			0
$871$	−15.0120	−	15.0120i	−0.508662	−	0.508662i
$872$		0			0
$873$	−5.55129	+	5.55129i	−0.187883	+	0.187883i
$874$		0			0
$875$	−13.1264	−	5.43712i	−0.443752	−	0.183808i
$876$		0			0
$877$	−4.27570	−	10.3225i	−0.144380	−	0.348565i	0.835102	−	0.550095i	$-0.185409\pi$
$877$	−4.27570	−	10.3225i	−0.144380	−	0.348565i	−0.979482	+	0.201530i	$0.935409\pi$
$878$		0			0
$879$		−	27.0104i		−	0.911039i
$880$		0			0
$881$			13.1185i			0.441972i	0.975277	+	0.220986i	$0.0709276\pi$
$881$			13.1185i			0.441972i	−0.975277	+	0.220986i	$0.929072\pi$
$882$		0			0
$883$	4.36561	+	10.5395i	0.146915	+	0.354683i	0.980156	−	0.198226i	$-0.0635178\pi$
$883$	4.36561	+	10.5395i	0.146915	+	0.354683i	−0.833242	+	0.552909i	$0.813518\pi$
$884$		0			0
$885$	42.1509	+	17.4595i	1.41689	+	0.586893i
$886$		0			0
$887$	32.1505	−	32.1505i	1.07951	−	1.07951i	0.0829550	−	0.996553i	$-0.473564\pi$
$887$	32.1505	−	32.1505i	1.07951	−	1.07951i	0.996553	−	0.0829550i	$-0.0264358\pi$
$888$		0			0
$889$	1.12722	+	1.12722i	0.0378058	+	0.0378058i
$890$		0			0
$891$	13.2296	−	31.9392i	0.443210	−	1.07000i
$892$		0			0
$893$	8.58647	−	3.55663i	0.287335	−	0.119018i
$894$		0			0
$895$	−0.511683			−0.0171037
$896$		0			0
$897$	9.34920			0.312161
$898$		0			0
$899$	40.9070	−	16.9443i	1.36433	−	0.565123i
$900$		0			0
$901$	−0.374560	+	0.904268i	−0.0124784	+	0.0301255i
$902$		0			0
$903$	14.5037	+	14.5037i	0.482654	+	0.482654i
$904$		0			0
$905$	6.49473	−	6.49473i	0.215892	−	0.215892i
$906$		0			0
$907$	29.2431	+	12.1129i	0.971000	+	0.402202i	0.811084	−	0.584929i	$-0.198878\pi$
$907$	29.2431	+	12.1129i	0.971000	+	0.402202i	0.159916	+	0.987131i	$0.448878\pi$
$908$		0			0
$909$	2.49898	+	6.03306i	0.0828858	+	0.200104i
$910$		0			0
$911$		−	41.1501i		−	1.36336i	−0.731649	−	0.681681i	$-0.761249\pi$
$911$		−	41.1501i		−	1.36336i	0.731649	−	0.681681i	$-0.238751\pi$
$912$		0			0
$913$		−	44.2832i		−	1.46556i
$914$		0			0
$915$	−5.79035	−	13.9792i	−0.191423	−	0.462136i
$916$		0			0
$917$	−0.951023	−	0.393927i	−0.0314055	−	0.0130086i
$918$		0			0
$919$	−1.00540	+	1.00540i	−0.0331651	+	0.0331651i	−0.723495	−	0.690330i	$-0.757465\pi$
$919$	−1.00540	+	1.00540i	−0.0331651	+	0.0331651i	0.690330	+	0.723495i	$0.257465\pi$
$920$		0			0
$921$	22.1273	+	22.1273i	0.729119	+	0.729119i
$922$		0			0
$923$	6.30483	−	15.2212i	0.207526	−	0.501012i
$924$		0			0
$925$	−32.7466	+	13.5641i	−1.07670	+	0.445985i
$926$		0			0
$927$	1.18690			0.0389829
$928$		0			0
$929$	52.8710			1.73464			0.867320	−	0.497751i	$-0.165841\pi$
$929$	52.8710			1.73464			0.867320	+	0.497751i	$0.165841\pi$
$930$		0			0
$931$	−13.6890	+	5.67018i	−0.448640	+	0.185833i
$932$		0			0
$933$	1.17209	−	2.82967i	0.0383724	−	0.0926393i
$934$		0			0
$935$	31.9623	+	31.9623i	1.04528	+	1.04528i
$936$		0			0
$937$	3.85201	−	3.85201i	0.125840	−	0.125840i	−0.641382	−	0.767222i	$-0.721639\pi$
$937$	3.85201	−	3.85201i	0.125840	−	0.125840i	0.767222	+	0.641382i	$0.221639\pi$
$938$		0			0
$939$	−2.52197	−	1.04463i	−0.0823013	−	0.0340903i
$940$		0			0
$941$	16.2416	+	39.2107i	0.529462	+	1.27823i	0.931876	+	0.362776i	$0.118171\pi$
$941$	16.2416	+	39.2107i	0.529462	+	1.27823i	−0.402415	+	0.915458i	$0.631829\pi$
$942$		0			0
$943$		−	13.3670i		−	0.435288i
$944$		0			0
$945$			29.0703i			0.945658i
$946$		0			0
$947$	13.4056	+	32.3640i	0.435624	+	1.05169i	0.977444	+	0.211194i	$0.0677353\pi$
$947$	13.4056	+	32.3640i	0.435624	+	1.05169i	−0.541820	+	0.840494i	$0.682265\pi$
$948$		0			0
$949$	−45.0739	−	18.6702i	−1.46316	−	0.606061i
$950$		0			0
$951$	26.6119	−	26.6119i	0.862949	−	0.862949i
$952$		0			0
$953$	−13.8976	−	13.8976i	−0.450186	−	0.450186i	0.445230	−	0.895416i	$-0.353122\pi$
$953$	−13.8976	−	13.8976i	−0.450186	−	0.450186i	−0.895416	+	0.445230i	$0.853122\pi$
$954$		0			0
$955$	22.4852	−	54.2842i	0.727605	−	1.75659i
$956$		0			0
$957$	−31.5685	+	13.0761i	−1.02046	+	0.422690i
$958$		0			0
$959$	−23.5844			−0.761580
$960$		0			0
$961$	80.9971			2.61281
$962$		0			0
$963$	−1.87404	+	0.776251i	−0.0603900	+	0.0250143i
$964$		0			0
$965$	13.4478	−	32.4658i	0.432899	−	1.04511i
$966$		0			0
$967$	36.8527	+	36.8527i	1.18510	+	1.18510i	0.978404	+	0.206700i	$0.0662724\pi$
$967$	36.8527	+	36.8527i	1.18510	+	1.18510i	0.206700	+	0.978404i	$0.433728\pi$
$968$		0			0
$969$	−7.64689	+	7.64689i	−0.245653	+	0.245653i
$970$		0			0
$971$	−37.5712	−	15.5625i	−1.20572	−	0.499425i	−0.312875	−	0.949794i	$-0.601292\pi$
$971$	−37.5712	−	15.5625i	−1.20572	−	0.499425i	−0.892842	+	0.450370i	$0.851292\pi$
$972$		0			0
$973$	0.469639	+	1.13381i	0.0150559	+	0.0363482i
$974$		0			0
$975$			48.0758i			1.53966i
$976$		0			0
$977$		−	2.89004i		−	0.0924607i	−0.998931	−	0.0462303i	$-0.985279\pi$
$977$		−	2.89004i		−	0.0924607i	0.998931	−	0.0462303i	$-0.0147208\pi$
$978$		0			0
$979$	2.81663	+	6.79994i	0.0900197	+	0.217327i
$980$		0			0
$981$	2.46000	+	1.01896i	0.0785417	+	0.0325330i
$982$		0			0
$983$	10.1625	−	10.1625i	0.324135	−	0.324135i	−0.526216	−	0.850351i	$-0.676390\pi$
$983$	10.1625	−	10.1625i	0.324135	−	0.324135i	0.850351	+	0.526216i	$0.176390\pi$
$984$		0			0
$985$	25.7926	+	25.7926i	0.821820	+	0.821820i
$986$		0			0
$987$	−2.58737	+	6.24646i	−0.0823568	+	0.198827i
$988$		0			0
$989$	−12.9510	+	5.36449i	−0.411819	+	0.170581i
$990$		0			0
$991$	51.7294			1.64324			0.821619	−	0.570038i	$-0.193071\pi$
$991$	51.7294			1.64324			0.821619	+	0.570038i	$0.193071\pi$
$992$		0			0
$993$	−34.7901			−1.10403
$994$		0			0
$995$	−11.2738	+	4.66978i	−0.357405	+	0.148042i
$996$		0			0
$997$	7.46746	−	18.0280i	0.236497	−	0.570954i	−0.760419	−	0.649433i	$-0.775006\pi$
$997$	7.46746	−	18.0280i	0.236497	−	0.570954i	0.996916	+	0.0784791i	$0.0250064\pi$
$998$		0			0
$999$	18.1624	+	18.1624i	0.574633	+	0.574633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.f.385.4	yes	16
4.3	odd	2	inner	1024.2.g.f.385.1	yes	16
8.3	odd	2		1024.2.g.a.385.4	yes	16
8.5	even	2		1024.2.g.a.385.1	✓	16
16.3	odd	4		1024.2.g.d.897.1	yes	16
16.5	even	4		1024.2.g.g.897.1	yes	16
16.11	odd	4		1024.2.g.g.897.4	yes	16
16.13	even	4		1024.2.g.d.897.4	yes	16
32.3	odd	8	inner	1024.2.g.f.641.1	yes	16
32.5	even	8		1024.2.g.g.129.1	yes	16
32.11	odd	8		1024.2.g.d.129.1	yes	16
32.13	even	8		1024.2.g.a.641.1	yes	16
32.19	odd	8		1024.2.g.a.641.4	yes	16
32.21	even	8		1024.2.g.d.129.4	yes	16
32.27	odd	8		1024.2.g.g.129.4	yes	16
32.29	even	8	inner	1024.2.g.f.641.4	yes	16
64.3	odd	16		4096.2.a.s.1.6		8
64.29	even	16		4096.2.a.s.1.5		8
64.35	odd	16		4096.2.a.i.1.3		8
64.61	even	16		4096.2.a.i.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.385.1	✓	16	8.5	even	2
1024.2.g.a.385.4	yes	16	8.3	odd	2
1024.2.g.a.641.1	yes	16	32.13	even	8
1024.2.g.a.641.4	yes	16	32.19	odd	8
1024.2.g.d.129.1	yes	16	32.11	odd	8
1024.2.g.d.129.4	yes	16	32.21	even	8
1024.2.g.d.897.1	yes	16	16.3	odd	4
1024.2.g.d.897.4	yes	16	16.13	even	4
1024.2.g.f.385.1	yes	16	4.3	odd	2	inner
1024.2.g.f.385.4	yes	16	1.1	even	1	trivial
1024.2.g.f.641.1	yes	16	32.3	odd	8	inner
1024.2.g.f.641.4	yes	16	32.29	even	8	inner
1024.2.g.g.129.1	yes	16	32.5	even	8
1024.2.g.g.129.4	yes	16	32.27	odd	8
1024.2.g.g.897.1	yes	16	16.5	even	4
1024.2.g.g.897.4	yes	16	16.11	odd	4
4096.2.a.i.1.3		8	64.35	odd	16
4096.2.a.i.1.4		8	64.61	even	16
4096.2.a.s.1.5		8	64.29	even	16
4096.2.a.s.1.6		8	64.3	odd	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40211 - 0.580775i) q^{3} +(1.36603 - 3.29788i) q^{5} +(1.02642 + 1.02642i) q^{7} +(-0.492694 + 0.492694i) q^{9} +O(q^{10})\)	\(q+(1.40211 - 0.580775i) q^{3} +(1.36603 - 3.29788i) q^{5} +(1.02642 + 1.02642i) q^{7} +(-0.492694 + 0.492694i) q^{9} +(-4.97171 - 2.05935i) q^{11} +(-1.56583 - 3.78024i) q^{13} -5.41736i q^{15} -2.35311i q^{17} +(-1.15885 - 2.79772i) q^{19} +(2.03528 + 0.843039i) q^{21} +(-1.06460 + 1.06460i) q^{23} +(-5.47443 - 5.47443i) q^{25} +(-2.14699 + 5.18330i) q^{27} +(3.86540 - 1.60110i) q^{29} +10.5829 q^{31} -8.16693 q^{33} +(4.78712 - 1.98289i) q^{35} +(1.75201 - 4.22973i) q^{37} +(-4.39094 - 4.39094i) q^{39} +(-6.27792 + 6.27792i) q^{41} +(8.60205 + 3.56308i) q^{43} +(0.951812 + 2.29788i) q^{45} +3.06910i q^{47} -4.89293i q^{49} +(-1.36663 - 3.29934i) q^{51} +(-0.384286 - 0.159176i) q^{53} +(-13.5830 + 13.5830i) q^{55} +(-3.24969 - 3.24969i) q^{57} +(-3.22287 + 7.78071i) q^{59} +(2.58044 - 1.06885i) q^{61} -1.01142 q^{63} -14.6057 q^{65} +(4.79363 - 1.98559i) q^{67} +(-0.874400 + 2.11099i) q^{69} +(2.84718 + 2.84718i) q^{71} +(8.43123 - 8.43123i) q^{73} +(-10.8552 - 4.49637i) q^{75} +(-2.98930 - 7.21682i) q^{77} -4.59983i q^{79} +6.42418i q^{81} +(3.14911 + 7.60263i) q^{83} +(-7.76028 - 3.21441i) q^{85} +(4.48986 - 4.48986i) q^{87} +(-0.967128 - 0.967128i) q^{89} +(2.27292 - 5.48730i) q^{91} +(14.8384 - 6.14626i) q^{93} -10.8096 q^{95} +11.2672 q^{97} +(3.46416 - 1.43490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^5 - 16 * q^9	\( 16 q + 8 q^{5} - 16 q^{9} - 8 q^{13} + 16 q^{21} - 32 q^{25} - 24 q^{29} - 80 q^{33} + 40 q^{37} - 16 q^{41} + 24 q^{45} - 56 q^{53} - 16 q^{57} + 8 q^{61} - 32 q^{65} - 64 q^{69} + 32 q^{73} + 64 q^{77} - 48 q^{85} + 32 q^{89} + 80 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 16 * q^9 - 8 * q^13 + 16 * q^21 - 32 * q^25 - 24 * q^29 - 80 * q^33 + 40 * q^37 - 16 * q^41 + 24 * q^45 - 56 * q^53 - 16 * q^57 + 8 * q^61 - 32 * q^65 - 64 * q^69 + 32 * q^73 + 64 * q^77 - 48 * q^85 + 32 * q^89 + 80 * q^93 - 16 * q^97

Introduction

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