LMFDB - Embedded newform 1024.2.g.g.129.4

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			129.4
Root			$0.991445 - 0.130526i$ of defining polynomial
Character	$\chi$	$=$	1024.129
Dual form			1024.2.g.g.897.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	0.580775	−	1.40211i	0.335311	−	0.809511i	−0.662842	−	0.748759i	$-0.730650\pi$
$3$	0.580775	−	1.40211i	0.335311	−	0.809511i	0.998153	−	0.0607523i	$-0.0193500\pi$
$4$		0			0
$5$	3.29788	−	1.36603i	1.47486	−	0.610905i	0.506895	−	0.862008i	$-0.330793\pi$
$5$	3.29788	−	1.36603i	1.47486	−	0.610905i	0.967960	+	0.251103i	$0.0807932\pi$
$6$		0			0
$7$	1.02642	−	1.02642i	0.387950	−	0.387950i	−0.486006	−	0.873956i	$-0.661547\pi$
$7$	1.02642	−	1.02642i	0.387950	−	0.387950i	0.873956	+	0.486006i	$0.161547\pi$
$8$		0			0
$9$	0.492694	+	0.492694i	0.164231	+	0.164231i
$10$		0			0
$11$	−2.05935	−	4.97171i	−0.620917	−	1.49903i	−0.850628	−	0.525768i	$-0.823778\pi$
$11$	−2.05935	−	4.97171i	−0.620917	−	1.49903i	0.229710	−	0.973259i	$-0.426222\pi$
$12$		0			0
$13$	−3.78024	−	1.56583i	−1.04845	−	0.434282i	−0.209112	−	0.977892i	$-0.567057\pi$
$13$	−3.78024	−	1.56583i	−1.04845	−	0.434282i	−0.839338	+	0.543610i	$0.817057\pi$
$14$		0			0
$15$		−	5.41736i		−	1.39876i
$16$		0			0
$17$			2.35311i			0.570714i	0.958421	+	0.285357i	$0.0921121\pi$
$17$			2.35311i			0.570714i	−0.958421	+	0.285357i	$0.907888\pi$
$18$		0			0
$19$	2.79772	+	1.15885i	0.641840	+	0.265859i	0.679774	−	0.733421i	$-0.262078\pi$
$19$	2.79772	+	1.15885i	0.641840	+	0.265859i	−0.0379340	+	0.999280i	$0.512078\pi$
$20$		0			0
$21$	−0.843039	−	2.03528i	−0.183966	−	0.444134i
$22$		0			0
$23$	−1.06460	−	1.06460i	−0.221985	−	0.221985i	0.587349	−	0.809334i	$-0.300172\pi$
$23$	−1.06460	−	1.06460i	−0.221985	−	0.221985i	−0.809334	+	0.587349i	$0.800172\pi$
$24$		0			0
$25$	5.47443	−	5.47443i	1.09489	−	1.09489i
$26$		0			0
$27$	5.18330	−	2.14699i	0.997527	−	0.413189i
$28$		0			0
$29$	−1.60110	+	3.86540i	−0.297317	+	0.717787i	0.702663	+	0.711523i	$0.251994\pi$
$29$	−1.60110	+	3.86540i	−0.297317	+	0.717787i	−0.999980	+	0.00626466i	$0.998006\pi$
$30$		0			0
$31$	−10.5829			−1.90074			−0.950370	−	0.311123i	$-0.899295\pi$
$31$	−10.5829			−1.90074			−0.950370	+	0.311123i	$0.899295\pi$
$32$		0			0
$33$	−8.16693			−1.42168
$34$		0			0
$35$	1.98289	−	4.78712i	0.335170	−	0.809171i
$36$		0			0
$37$	4.22973	−	1.75201i	0.695363	−	0.288029i	−0.00686951	−	0.999976i	$-0.502187\pi$
$37$	4.22973	−	1.75201i	0.695363	−	0.288029i	0.702233	+	0.711948i	$0.252187\pi$
$38$		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	$-0.00616495\pi$
$41$	6.27792	+	6.27792i	0.980446	+	0.980446i	−0.0193666	+	0.999812i	$0.506165\pi$
$42$		0			0
$43$	3.56308	+	8.60205i	0.543365	+	1.31180i	0.922335	+	0.386391i	$0.126278\pi$
$43$	3.56308	+	8.60205i	0.543365	+	1.31180i	−0.378970	+	0.925409i	$0.623722\pi$
$44$		0			0
$45$	2.29788	+	0.951812i	0.342547	+	0.141888i
$46$		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
$51$	3.29934	+	1.36663i	0.461999	+	0.191366i
$52$		0			0
$53$	0.159176	+	0.384286i	0.0218646	+	0.0527857i	0.934435	−	0.356134i	$-0.115905\pi$
$53$	0.159176	+	0.384286i	0.0218646	+	0.0527857i	−0.912570	+	0.408920i	$0.865905\pi$
$54$		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
$59$	7.78071	−	3.22287i	1.01296	−	0.419583i	0.186427	−	0.982469i	$-0.440309\pi$
$59$	7.78071	−	3.22287i	1.01296	−	0.419583i	0.826534	+	0.562886i	$0.190309\pi$
$60$		0			0
$61$	−1.06885	+	2.58044i	−0.136853	+	0.330391i	−0.977417	−	0.211321i	$-0.932224\pi$
$61$	−1.06885	+	2.58044i	−0.136853	+	0.330391i	0.840564	+	0.541712i	$0.182224\pi$
$62$		0			0
$63$	1.01142			0.127427
$64$		0			0
$65$	−14.6057			−1.81162
$66$		0			0
$67$	1.98559	−	4.79363i	0.242578	−	0.585635i	−0.754959	−	0.655772i	$-0.772343\pi$
$67$	1.98559	−	4.79363i	0.242578	−	0.585635i	0.997537	+	0.0701364i	$0.0223434\pi$
$68$		0			0
$69$	−2.11099	+	0.874400i	−0.254133	+	0.105265i
$70$		0			0
$71$	2.84718	−	2.84718i	0.337898	−	0.337898i	−0.517678	−	0.855576i	$-0.673203\pi$
$71$	2.84718	−	2.84718i	0.337898	−	0.337898i	0.855576	+	0.517678i	$0.173203\pi$
$72$		0			0
$73$	−8.43123	−	8.43123i	−0.986801	−	0.986801i	0.0131133	−	0.999914i	$-0.495826\pi$
$73$	−8.43123	−	8.43123i	−0.986801	−	0.986801i	−0.999914	+	0.0131133i	$0.995826\pi$
$74$		0			0
$75$	−4.49637	−	10.8552i	−0.519196	−	1.25345i
$76$		0			0
$77$	−7.21682	−	2.98930i	−0.822433	−	0.340663i
$78$		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
$83$	−7.60263	−	3.14911i	−0.834497	−	0.345660i	−0.0758155	−	0.997122i	$-0.524156\pi$
$83$	−7.60263	−	3.14911i	−0.834497	−	0.345660i	−0.758681	+	0.651462i	$0.774156\pi$
$84$		0			0
$85$	3.21441	+	7.76028i	0.348652	+	0.841720i
$86$		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	$-0.726906\pi$
$89$	0.967128	−	0.967128i	0.102515	−	0.102515i	0.756504	+	0.653989i	$0.226906\pi$
$90$		0			0
$91$	−5.48730	+	2.27292i	−0.575226	+	0.238266i
$92$		0			0
$93$	−6.14626	+	14.8384i	−0.637338	+	1.53867i
$94$		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
$99$	1.43490	−	3.46416i	0.144213	−	0.348161i
$100$		0			0
$101$	8.65855	−	3.58649i	0.861558	−	0.356869i	0.0922416	−	0.995737i	$-0.470597\pi$
$101$	8.65855	−	3.58649i	0.861558	−	0.356869i	0.769317	+	0.638868i	$0.220597\pi$
$102$		0			0
$103$	−1.20450	+	1.20450i	−0.118683	+	0.118683i	−0.763954	−	0.645271i	$-0.776744\pi$
$103$	−1.20450	+	1.20450i	−0.118683	+	0.118683i	0.645271	+	0.763954i	$0.276744\pi$
$104$		0			0
$105$	−5.56048	−	5.56048i	−0.542647	−	0.542647i
$106$		0			0
$107$	1.11406	+	2.68959i	0.107701	+	0.260012i	0.968537	−	0.248870i	$-0.0800591\pi$
$107$	1.11406	+	2.68959i	0.107701	+	0.260012i	−0.860836	+	0.508882i	$0.830059\pi$
$108$		0			0
$109$	−3.53055	−	1.46240i	−0.338165	−	0.140073i	0.207137	−	0.978312i	$-0.433585\pi$
$109$	−3.53055	−	1.46240i	−0.338165	−	0.140073i	−0.545303	+	0.838239i	$0.683585\pi$
$110$		0			0
$111$		−	6.94809i		−	0.659483i
$112$		0			0
$113$		−	2.13630i		−	0.200966i	−0.994939	−	0.100483i	$-0.967961\pi$
$113$		−	2.13630i		−	0.200966i	0.994939	−	0.100483i	$-0.0320388\pi$
$114$		0			0
$115$	−4.96520	−	2.05665i	−0.463007	−	0.191784i
$116$		0			0
$117$	−1.09103	−	2.63397i	−0.100866	−	0.243511i
$118$		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
$123$	12.4484	−	5.15630i	1.12244	−	0.464928i
$124$		0			0
$125$	3.74567	−	9.04284i	0.335023	−	0.808816i
$126$		0			0
$127$	−1.09821			−0.0974502			−0.0487251	−	0.998812i	$-0.515516\pi$
$127$	−1.09821			−0.0974502			−0.0487251	+	0.998812i	$0.515516\pi$
$128$		0			0
$129$	14.1304			1.24411
$130$		0			0
$131$	−0.271379	+	0.655166i	−0.0237105	+	0.0572421i	−0.935291	−	0.353879i	$-0.884863\pi$
$131$	−0.271379	+	0.655166i	−0.0237105	+	0.0572421i	0.911581	+	0.411121i	$0.134863\pi$
$132$		0			0
$133$	4.06110	−	1.68216i	0.352142	−	0.145862i
$134$		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	$-0.00582173\pi$
$137$	11.4887	+	11.4887i	0.981544	+	0.981544i	−0.0182885	+	0.999833i	$0.505822\pi$
$138$		0			0
$139$	0.323537	+	0.781087i	0.0274421	+	0.0662510i	0.937007	−	0.349312i	$-0.113585\pi$
$139$	0.323537	+	0.781087i	0.0274421	+	0.0662510i	−0.909564	+	0.415563i	$0.863585\pi$
$140$		0			0
$141$	4.30323	+	1.78245i	0.362397	+	0.150110i
$142$		0			0
$143$			22.0188i			1.84131i
$144$		0			0
$145$			14.9348i			1.24027i
$146$		0			0
$147$	6.86045	+	2.84169i	0.565840	+	0.234379i
$148$		0			0
$149$	−2.70212	−	6.52350i	−0.221367	−	0.534426i	0.773710	−	0.633541i	$-0.218399\pi$
$149$	−2.70212	−	6.52350i	−0.221367	−	0.534426i	−0.995076	+	0.0991144i	$0.968399\pi$
$150$		0			0
$151$	9.87443	+	9.87443i	0.803569	+	0.803569i	0.983652	−	0.180082i	$-0.0576364\pi$
$151$	9.87443	+	9.87443i	0.803569	+	0.803569i	−0.180082	+	0.983652i	$0.557636\pi$
$152$		0			0
$153$	−1.15937	+	1.15937i	−0.0937291	+	0.0937291i
$154$		0			0
$155$	−34.9010	+	14.4565i	−2.80332	+	1.16117i
$156$		0			0
$157$	9.26500	−	22.3677i	0.739428	−	1.78514i	0.131229	−	0.991352i	$-0.458108\pi$
$157$	9.26500	−	22.3677i	0.739428	−	1.78514i	0.608199	−	0.793785i	$-0.291892\pi$
$158$		0			0
$159$	0.631258			0.0500620
$160$		0			0
$161$	−2.18546			−0.172238
$162$		0			0
$163$	−6.70092	+	16.1774i	−0.524856	+	1.26712i	0.409999	+	0.912086i	$0.365529\pi$
$163$	−6.70092	+	16.1774i	−0.524856	+	1.26712i	−0.934855	+	0.355029i	$0.884471\pi$
$164$		0			0
$165$	−26.9335	+	11.1562i	−2.09677	+	0.868511i
$166$		0			0
$167$	−15.9204	+	15.9204i	−1.23196	+	1.23196i	−0.268751	+	0.963210i	$0.586611\pi$
$167$	−15.9204	+	15.9204i	−1.23196	+	1.23196i	−0.963210	+	0.268751i	$0.913389\pi$
$168$		0			0
$169$	2.64601	+	2.64601i	0.203539	+	0.203539i
$170$		0			0
$171$	0.807459	+	1.94938i	0.0617479	+	0.149073i
$172$		0			0
$173$	8.36603	+	3.46532i	0.636057	+	0.263463i	0.677324	−	0.735685i	$-0.263139\pi$
$173$	8.36603	+	3.46532i	0.636057	+	0.263463i	−0.0412671	+	0.999148i	$0.513139\pi$
$174$		0			0
$175$		−	11.2381i		−	0.849523i
$176$		0			0
$177$		−	12.7812i		−	0.960695i
$178$		0			0
$179$	0.132433	+	0.0548557i	0.00989854	+	0.00410011i	0.387627	−	0.921816i	$-0.373295\pi$
$179$	0.132433	+	0.0548557i	0.00989854	+	0.00410011i	−0.377729	+	0.925916i	$0.623295\pi$
$180$		0			0
$181$	−0.984684	−	2.37724i	−0.0731910	−	0.176699i	0.883050	−	0.469279i	$-0.155486\pi$
$181$	−0.984684	−	2.37724i	−0.0731910	−	0.176699i	−0.956241	+	0.292580i	$0.905486\pi$
$182$		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
$187$	11.6990	−	4.84588i	0.855516	−	0.354366i
$188$		0			0
$189$	3.11653	−	7.52396i	0.226694	−	0.547287i
$190$		0			0
$191$	−16.4603			−1.19103			−0.595514	−	0.803345i	$-0.703052\pi$
$191$	−16.4603			−1.19103			−0.595514	+	0.803345i	$0.703052\pi$
$192$		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
$195$	−8.48264	+	20.4789i	−0.607454	+	1.46652i
$196$		0			0
$197$	−9.44074	+	3.91048i	−0.672625	+	0.278610i	−0.692740	−	0.721187i	$-0.743597\pi$
$197$	−9.44074	+	3.91048i	−0.672625	+	0.278610i	0.0201152	+	0.999798i	$0.493597\pi$
$198$		0			0
$199$	−2.41726	+	2.41726i	−0.171355	+	0.171355i	−0.787574	−	0.616220i	$-0.788663\pi$
$199$	−2.41726	+	2.41726i	−0.171355	+	0.171355i	0.616220	+	0.787574i	$0.288663\pi$
$200$		0			0
$201$	−5.56804	−	5.56804i	−0.392739	−	0.392739i
$202$		0			0
$203$	2.32412	+	5.61093i	0.163121	+	0.393810i
$204$		0			0
$205$	29.2796	+	12.1280i	2.04498	+	0.847057i
$206$		0			0
$207$		−	1.04905i		−	0.0729137i
$208$		0			0
$209$		−	16.2959i		−	1.12721i
$210$		0			0
$211$	14.6429	+	6.06529i	1.00806	+	0.417552i	0.824746	−	0.565503i	$-0.191318\pi$
$211$	14.6429	+	6.06529i	1.00806	+	0.417552i	0.183312	+	0.983055i	$0.441318\pi$
$212$		0			0
$213$	−2.33850	−	5.64564i	−0.160231	−	0.386833i
$214$		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
$219$	−16.7182	+	6.92490i	−1.12971	+	0.467942i
$220$		0			0
$221$	3.68457	−	8.89533i	0.247851	−	0.598365i
$222$		0			0
$223$	20.9031			1.39978			0.699888	−	0.714253i	$-0.253233\pi$
$223$	20.9031			1.39978			0.699888	+	0.714253i	$0.253233\pi$
$224$		0			0
$225$	5.39444			0.359629
$226$		0			0
$227$	−5.18600	+	12.5201i	−0.344207	+	0.830989i	0.653074	+	0.757294i	$0.273479\pi$
$227$	−5.18600	+	12.5201i	−0.344207	+	0.830989i	−0.997281	+	0.0736948i	$0.976521\pi$
$228$		0			0
$229$	−5.35773	+	2.21925i	−0.354049	+	0.146652i	−0.552617	−	0.833435i	$-0.686371\pi$
$229$	−5.35773	+	2.21925i	−0.354049	+	0.146652i	0.198568	+	0.980087i	$0.436371\pi$
$230$		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	$-0.249605\pi$
$233$	0.0268197	+	0.0268197i	0.00175702	+	0.00175702i	−0.706228	+	0.707985i	$0.749605\pi$
$234$		0			0
$235$	4.19246	+	10.1215i	0.273486	+	0.660254i
$236$		0			0
$237$	−6.44949	−	2.67147i	−0.418939	−	0.173530i
$238$		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	$-0.986860\pi$
$241$		−	1.28132i		−	0.0825369i	0.999148	−	0.0412684i	$-0.0131399\pi$
$242$		0			0
$243$	6.54247	+	2.70998i	0.419699	+	0.173845i
$244$		0			0
$245$	6.68386	+	16.1363i	0.427016	+	1.03091i
$246$		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
$251$	−9.68691	+	4.01245i	−0.611432	+	0.253263i	−0.666841	−	0.745200i	$-0.732354\pi$
$251$	−9.68691	+	4.01245i	−0.611432	+	0.253263i	0.0554086	+	0.998464i	$0.482354\pi$
$252$		0			0
$253$	−3.10051	+	7.48528i	−0.194927	+	0.470596i
$254$		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
$259$	2.54318	−	6.13977i	0.158025	−	0.381507i
$260$		0			0
$261$	−2.69331	+	1.11561i	−0.166712	+	0.0690544i
$262$		0			0
$263$	13.8663	−	13.8663i	0.855030	−	0.855030i	−0.135718	−	0.990748i	$-0.543334\pi$
$263$	13.8663	−	13.8663i	0.855030	−	0.855030i	0.990748	+	0.135718i	$0.0433340\pi$
$264$		0			0
$265$	1.04989	+	1.04989i	0.0644941	+	0.0644941i
$266$		0			0
$267$	−0.794341	−	1.91771i	−0.0486129	−	0.117362i
$268$		0			0
$269$	−15.8038	−	6.54616i	−0.963576	−	0.399126i	−0.155259	−	0.987874i	$-0.549621\pi$
$269$	−15.8038	−	6.54616i	−0.963576	−	0.399126i	−0.808317	+	0.588748i	$0.799621\pi$
$270$		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
$275$	−38.4911	−	15.9435i	−2.32110	−	0.961431i
$276$		0			0
$277$	−5.32219	−	12.8489i	−0.319779	−	0.772016i	−0.999265	−	0.0383271i	$-0.987797\pi$
$277$	−5.32219	−	12.8489i	−0.319779	−	0.772016i	0.679486	−	0.733689i	$-0.262203\pi$
$278$		0			0
$279$	−5.21412	−	5.21412i	−0.312161	−	0.312161i
$280$		0			0
$281$	−18.7289	+	18.7289i	−1.11727	+	1.11727i	−0.125134	+	0.992140i	$0.539936\pi$
$281$	−18.7289	+	18.7289i	−1.11727	+	1.11727i	−0.992140	+	0.125134i	$0.960064\pi$
$282$		0			0
$283$	0.989981	−	0.410064i	0.0588483	−	0.0243758i	−0.353065	−	0.935599i	$-0.614861\pi$
$283$	0.989981	−	0.410064i	0.0588483	−	0.0243758i	0.411913	+	0.911223i	$0.364861\pi$
$284$		0			0
$285$	6.27792	−	15.1562i	0.371872	−	0.897778i
$286$		0			0
$287$	12.8875			0.760728
$288$		0			0
$289$	11.4629			0.674286
$290$		0			0
$291$	6.54372	−	15.7979i	0.383600	−	0.926091i
$292$		0			0
$293$	16.4429	−	6.81087i	0.960604	−	0.397895i	0.153398	−	0.988165i	$-0.450978\pi$
$293$	16.4429	−	6.81087i	0.960604	−	0.397895i	0.807206	+	0.590269i	$0.200978\pi$
$294$		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
$299$	2.35747	+	5.69143i	0.136336	+	0.329144i
$300$		0			0
$301$	12.4865	+	5.17209i	0.719711	+	0.298114i
$302$		0			0
$303$		−	14.2232i		−	0.817103i
$304$		0			0
$305$			9.97005i			0.570883i
$306$		0			0
$307$	−19.0498	−	7.89068i	−1.08723	−	0.450345i	−0.234189	−	0.972191i	$-0.575243\pi$
$307$	−19.0498	−	7.89068i	−1.08723	−	0.450345i	−0.853040	+	0.521846i	$0.825243\pi$
$308$		0			0
$309$	0.989303	+	2.38839i	0.0562795	+	0.135871i
$310$		0			0
$311$	1.42704	+	1.42704i	0.0809203	+	0.0809203i	0.746408	−	0.665488i	$-0.231777\pi$
$311$	1.42704	+	1.42704i	0.0809203	+	0.0809203i	−0.665488	+	0.746408i	$0.731777\pi$
$312$		0			0
$313$	1.27186	−	1.27186i	0.0718900	−	0.0718900i	−0.670248	−	0.742138i	$-0.733812\pi$
$313$	1.27186	−	1.27186i	0.0718900	−	0.0718900i	0.742138	+	0.670248i	$0.233812\pi$
$314$		0			0
$315$	3.33554	−	1.38163i	0.187937	−	0.0778459i
$316$		0			0
$317$	−9.48990	+	22.9106i	−0.533006	+	1.28679i	0.396518	+	0.918027i	$0.370219\pi$
$317$	−9.48990	+	22.9106i	−0.533006	+	1.28679i	−0.929523	+	0.368763i	$0.879781\pi$
$318$		0			0
$319$	22.5149			1.26059
$320$		0			0
$321$	4.41813			0.246596
$322$		0			0
$323$	−2.72691	+	6.58335i	−0.151729	+	0.366307i
$324$		0			0
$325$	−29.2667	+	12.1227i	−1.62342	+	0.672444i
$326$		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
$331$	−8.77257	−	21.1789i	−0.482184	−	1.16410i	−0.958570	−	0.284859i	$-0.908053\pi$
$331$	−8.77257	−	21.1789i	−0.482184	−	1.16410i	0.476386	−	0.879236i	$-0.341947\pi$
$332$		0			0
$333$	2.94717	+	1.22076i	0.161504	+	0.0668971i
$334$		0			0
$335$		−	18.5212i		−	1.01192i
$336$		0			0
$337$		−	27.4961i		−	1.49781i	−0.662677	−	0.748905i	$-0.730580\pi$
$337$		−	27.4961i		−	1.49781i	0.662677	−	0.748905i	$-0.269420\pi$
$338$		0			0
$339$	−2.99533	−	1.24071i	−0.162684	−	0.0673860i
$340$		0			0
$341$	21.7938	+	52.6150i	1.18020	+	2.84926i
$342$		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
$347$	4.53353	−	1.87785i	0.243373	−	0.100808i	−0.257663	−	0.966235i	$-0.582952\pi$
$347$	4.53353	−	1.87785i	0.243373	−	0.100808i	0.501036	+	0.865427i	$0.332952\pi$
$348$		0			0
$349$	−8.28327	+	19.9976i	−0.443393	+	1.07045i	0.531357	+	0.847148i	$0.321682\pi$
$349$	−8.28327	+	19.9976i	−0.443393	+	1.07045i	−0.974750	+	0.223298i	$0.928318\pi$
$350$		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
$355$	5.50033	−	13.2790i	0.291927	−	0.704774i
$356$		0			0
$357$	4.78924	−	1.98377i	0.253473	−	0.104992i
$358$		0			0
$359$	−19.0741	+	19.0741i	−1.00669	+	1.00669i	−0.00671431	+	0.999977i	$0.502137\pi$
$359$	−19.0741	+	19.0741i	−1.00669	+	1.00669i	−0.999977	+	0.00671431i	$0.997863\pi$
$360$		0			0
$361$	−6.95074	−	6.95074i	−0.365829	−	0.365829i
$362$		0			0
$363$	10.4300	+	25.1803i	0.547435	+	1.32163i
$364$		0			0
$365$	−39.3224	−	16.2879i	−2.05823	−	0.852547i
$366$		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
$371$	0.557820	+	0.231057i	0.0289606	+	0.0119959i
$372$		0			0
$373$	−12.8919	−	31.1238i	−0.667518	−	1.61153i	−0.785750	−	0.618544i	$-0.787723\pi$
$373$	−12.8919	−	31.1238i	−0.667518	−	1.61153i	0.118232	−	0.992986i	$-0.462277\pi$
$374$		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
$379$	13.0991	−	5.42584i	0.672858	−	0.278707i	−0.0199800	−	0.999800i	$-0.506360\pi$
$379$	13.0991	−	5.42584i	0.672858	−	0.278707i	0.692838	+	0.721094i	$0.256360\pi$
$380$		0			0
$381$	−0.637812	+	1.53981i	−0.0326761	+	0.0788870i
$382$		0			0
$383$	7.14287			0.364984			0.182492	−	0.983207i	$-0.441584\pi$
$383$	7.14287			0.364984			0.182492	+	0.983207i	$0.441584\pi$
$384$		0			0
$385$	−27.8836			−1.42108
$386$		0			0
$387$	−2.48267	+	5.99369i	−0.126201	+	0.304676i
$388$		0			0
$389$	26.2131	−	10.8578i	1.32906	−	0.550514i	0.398672	−	0.917093i	$-0.369471\pi$
$389$	26.2131	−	10.8578i	1.32906	−	0.550514i	0.930387	+	0.366579i	$0.119471\pi$
$390$		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
$395$	−6.28348	−	15.1697i	−0.316156	−	0.763269i
$396$		0			0
$397$	8.57919	+	3.55362i	0.430577	+	0.178351i	0.587437	−	0.809270i	$-0.300137\pi$
$397$	8.57919	+	3.55362i	0.430577	+	0.178351i	−0.156860	+	0.987621i	$0.550137\pi$
$398$		0			0
$399$		−	6.67109i		−	0.333972i
$400$		0			0
$401$		−	9.43274i		−	0.471049i	−0.971868	−	0.235524i	$-0.924319\pi$
$401$		−	9.43274i		−	0.471049i	0.971868	−	0.235524i	$-0.0756807\pi$
$402$		0			0
$403$	40.0058	+	16.5709i	1.99283	+	0.825457i
$404$		0			0
$405$	−8.77559	−	21.1862i	−0.436063	−	1.05275i
$406$		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	$-0.568357\pi$
$409$	15.4495	−	15.4495i	0.763928	−	0.763928i	0.977030	+	0.213102i	$0.0683566\pi$
$410$		0			0
$411$	22.7808	−	9.43611i	1.12369	−	0.465449i
$412$		0			0
$413$	4.67825	−	11.2943i	0.230202	−	0.555756i
$414$		0			0
$415$	−29.3743			−1.44193
$416$		0			0
$417$	1.28308			0.0628325
$418$		0			0
$419$	−8.18452	+	19.7592i	−0.399840	+	0.965299i	0.587864	+	0.808960i	$0.299969\pi$
$419$	−8.18452	+	19.7592i	−0.399840	+	0.965299i	−0.987703	+	0.156339i	$0.950031\pi$
$420$		0			0
$421$	−24.5052	+	10.1504i	−1.19431	+	0.494700i	−0.889157	−	0.457602i	$-0.848708\pi$
$421$	−24.5052	+	10.1504i	−1.19431	+	0.494700i	−0.305155	+	0.952303i	$0.598708\pi$
$422$		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
$427$	1.55152	+	3.74570i	0.0750833	+	0.181267i
$428$		0			0
$429$	30.8729	+	12.7880i	1.49056	+	0.617410i
$430$		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	$0.0748399\pi$
$433$			9.69501i			0.465913i	−0.972487	+	0.232956i	$0.925160\pi$
$434$		0			0
$435$	20.9403	+	8.67374i	1.00401	+	0.415874i
$436$		0			0
$437$	−1.74474	−	4.21217i	−0.0834622	−	0.201496i
$438$		0			0
$439$	−8.45429	−	8.45429i	−0.403501	−	0.403501i	0.475964	−	0.879465i	$-0.342099\pi$
$439$	−8.45429	−	8.45429i	−0.403501	−	0.403501i	−0.879465	+	0.475964i	$0.842099\pi$
$440$		0			0
$441$	−2.41072	+	2.41072i	−0.114796	+	0.114796i
$442$		0			0
$443$	−35.0500	+	14.5182i	−1.66528	+	0.689780i	−0.998462	−	0.0554440i	$-0.982343\pi$
$443$	−35.0500	+	14.5182i	−1.66528	+	0.689780i	−0.666814	+	0.745224i	$0.732343\pi$
$444$		0			0
$445$	1.86835	−	4.51059i	0.0885682	−	0.213822i
$446$		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
$451$	18.2836	−	44.1404i	0.860939	−	2.07849i
$452$		0			0
$453$	19.5799	−	8.11026i	0.919944	−	0.381053i
$454$		0			0
$455$	−14.9916	+	14.9916i	−0.702817	+	0.702817i
$456$		0			0
$457$	22.4049	+	22.4049i	1.04806	+	1.04806i	0.998785	+	0.0492728i	$0.0156904\pi$
$457$	22.4049	+	22.4049i	1.04806	+	1.04806i	0.0492728	+	0.998785i	$0.484310\pi$
$458$		0			0
$459$	5.05212	+	12.1969i	0.235813	+	0.569302i
$460$		0			0
$461$	2.92070	+	1.20979i	0.136031	+	0.0563457i	0.449660	−	0.893200i	$-0.351545\pi$
$461$	2.92070	+	1.20979i	0.136031	+	0.0563457i	−0.313630	+	0.949545i	$0.601545\pi$
$462$		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
$467$	−9.48183	−	3.92750i	−0.438767	−	0.181743i	0.152354	−	0.988326i	$-0.451314\pi$
$467$	−9.48183	−	3.92750i	−0.438767	−	0.181743i	−0.591121	+	0.806583i	$0.701314\pi$
$468$		0			0
$469$	−2.88223	−	6.95832i	−0.133089	−	0.321305i
$470$		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
$475$	21.6600	−	8.97186i	0.993828	−	0.411657i
$476$		0			0
$477$	−0.110910	+	0.267761i	−0.00507822	+	0.0122599i
$478$		0			0
$479$	−26.4855			−1.21015			−0.605077	−	0.796167i	$-0.706858\pi$
$479$	−26.4855			−1.21015			−0.605077	+	0.796167i	$0.706858\pi$
$480$		0			0
$481$	−18.7327			−0.854139
$482$		0			0
$483$	−1.26926	+	3.06426i	−0.0577532	+	0.139429i
$484$		0			0
$485$	37.1579	−	15.3913i	1.68725	−	0.698883i
$486$		0			0
$487$	5.38394	−	5.38394i	0.243970	−	0.243970i	−0.574521	−	0.818490i	$-0.694811\pi$
$487$	5.38394	−	5.38394i	0.243970	−	0.243970i	0.818490	+	0.574521i	$0.194811\pi$
$488$		0			0
$489$	18.7909	+	18.7909i	0.849754	+	0.849754i
$490$		0			0
$491$	−6.62284	−	15.9889i	−0.298884	−	0.721571i	−0.999964	−	0.00848784i	$-0.997298\pi$
$491$	−6.62284	−	15.9889i	−0.298884	−	0.721571i	0.701080	−	0.713083i	$-0.252702\pi$
$492$		0			0
$493$	−9.09573	−	3.76758i	−0.409651	−	0.169683i
$494$		0			0
$495$		−	13.3845i		−	0.601588i
$496$		0			0
$497$		−	5.84480i		−	0.262175i
$498$		0			0
$499$	4.07217	+	1.68675i	0.182295	+	0.0755091i	0.471964	−	0.881618i	$-0.343545\pi$
$499$	4.07217	+	1.68675i	0.182295	+	0.0755091i	−0.289669	+	0.957127i	$0.593545\pi$
$500$		0			0
$501$	13.0761	+	31.5685i	0.584197	+	1.41038i
$502$		0			0
$503$	22.1132	+	22.1132i	0.985978	+	0.985978i	0.999903	−	0.0139248i	$-0.00443254\pi$
$503$	22.1132	+	22.1132i	0.985978	+	0.985978i	−0.0139248	+	0.999903i	$0.504433\pi$
$504$		0			0
$505$	23.6556	−	23.6556i	1.05266	−	1.05266i
$506$		0			0
$507$	5.24674	−	2.17327i	0.233016	−	0.0965183i
$508$		0			0
$509$	5.24094	−	12.6528i	0.232301	−	0.560823i	−0.764147	−	0.645043i	$-0.776840\pi$
$509$	5.24094	−	12.6528i	0.232301	−	0.560823i	0.996447	+	0.0842193i	$0.0268396\pi$
$510$		0			0
$511$	−17.3080			−0.765659
$512$		0			0
$513$	16.9895			0.750103
$514$		0			0
$515$	−2.32691	+	5.61767i	−0.102536	+	0.247544i
$516$		0			0
$517$	15.2587	−	6.32034i	0.671075	−	0.277968i
$518$		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	$-0.328676\pi$
$521$	−7.89757	−	7.89757i	−0.345999	−	0.345999i	−0.858617	+	0.512618i	$0.828676\pi$
$522$		0			0
$523$	−4.66429	−	11.2606i	−0.203955	−	0.492391i	0.788495	−	0.615041i	$-0.210861\pi$
$523$	−4.66429	−	11.2606i	−0.203955	−	0.492391i	−0.992450	+	0.122650i	$0.960861\pi$
$524$		0			0
$525$	−15.7571	−	6.52682i	−0.687698	−	0.284854i
$526$		0			0
$527$		−	24.9027i		−	1.08478i
$528$		0			0
$529$		−	20.7332i		−	0.901445i
$530$		0			0
$531$	5.42140	+	2.24562i	0.235269	+	0.0974515i
$532$		0			0
$533$	−13.9019	−	33.5622i	−0.602158	−	1.45374i
$534$		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
$539$	24.3262	−	10.0763i	1.04780	−	0.434015i
$540$		0			0
$541$	−4.88194	+	11.7860i	−0.209891	+	0.506722i	−0.993406	−	0.114652i	$-0.963425\pi$
$541$	−4.88194	+	11.7860i	−0.209891	+	0.506722i	0.783515	+	0.621373i	$0.213425\pi$
$542$		0			0
$543$	−3.90504			−0.167581
$544$		0			0
$545$	−13.6410			−0.584316
$546$		0			0
$547$	10.8254	−	26.1348i	0.462861	−	1.11745i	−0.504356	−	0.863496i	$-0.668270\pi$
$547$	10.8254	−	26.1348i	0.462861	−	1.11745i	0.967217	−	0.253950i	$-0.0817298\pi$
$548$		0			0
$549$	−1.79798	+	0.744749i	−0.0767361	+	0.0317851i
$550$		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
$555$	−9.49127	−	22.9139i	−0.402882	−	0.972643i
$556$		0			0
$557$	−32.8089	−	13.5899i	−1.39016	−	0.575822i	−0.442980	−	0.896532i	$-0.646079\pi$
$557$	−32.8089	−	13.5899i	−1.39016	−	0.575822i	−0.947178	+	0.320709i	$0.896079\pi$
$558$		0			0
$559$		−	38.0970i		−	1.61133i
$560$		0			0
$561$		−	19.2177i		−	0.811372i
$562$		0			0
$563$	10.8336	+	4.48742i	0.456582	+	0.189122i	0.599107	−	0.800669i	$-0.295522\pi$
$563$	10.8336	+	4.48742i	0.456582	+	0.189122i	−0.142526	+	0.989791i	$0.545522\pi$
$564$		0			0
$565$	−2.91824	−	7.04524i	−0.122771	−	0.296396i
$566$		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	$-0.937790\pi$
$569$	−18.7673	+	18.7673i	−0.786767	+	0.786767i	0.194196	+	0.980963i	$0.437790\pi$
$570$		0			0
$571$	12.1516	−	5.03334i	0.508527	−	0.210639i	−0.113642	−	0.993522i	$-0.536252\pi$
$571$	12.1516	−	5.03334i	0.508527	−	0.210639i	0.622169	+	0.782883i	$0.286252\pi$
$572$		0			0
$573$	−9.55975	+	23.0793i	−0.399364	+	0.964151i
$574$		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
$579$	5.71741	−	13.8030i	0.237607	−	0.573635i
$580$		0			0
$581$	−11.0358	+	4.57117i	−0.457842	+	0.189644i
$582$		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
$587$	−6.83331	−	16.4971i	−0.282041	−	0.680907i	0.717842	−	0.696206i	$-0.245130\pi$
$587$	−6.83331	−	16.4971i	−0.282041	−	0.680907i	−0.999883	+	0.0152989i	$0.995130\pi$
$588$		0			0
$589$	−29.6079	−	12.2640i	−1.21997	−	0.505329i
$590$		0			0
$591$			15.5081i			0.637919i
$592$		0			0
$593$			41.3009i			1.69602i	0.529976	+	0.848012i	$0.322201\pi$
$593$			41.3009i			1.69602i	−0.529976	+	0.848012i	$0.677799\pi$
$594$		0			0
$595$	11.2646	+	4.66596i	0.461805	+	0.191286i
$596$		0			0
$597$	1.98539	+	4.79315i	0.0812565	+	0.196171i
$598$		0			0
$599$	−6.73920	−	6.73920i	−0.275356	−	0.275356i	0.555896	−	0.831252i	$-0.312375\pi$
$599$	−6.73920	−	6.73920i	−0.275356	−	0.275356i	−0.831252	+	0.555896i	$0.812375\pi$
$600$		0			0
$601$	−23.2456	+	23.2456i	−0.948206	+	0.948206i	−0.998723	−	0.0505170i	$-0.983913\pi$
$601$	−23.2456	+	23.2456i	−0.948206	+	0.948206i	0.0505170	+	0.998723i	$0.483913\pi$
$602$		0			0
$603$	3.34008	−	1.38351i	0.136019	−	0.0563407i
$604$		0			0
$605$	−24.5322	+	59.2260i	−0.997377	+	2.40788i
$606$		0			0
$607$	18.7402			0.760642			0.380321	−	0.924855i	$-0.375813\pi$
$607$	18.7402			0.760642			0.380321	+	0.924855i	$0.375813\pi$
$608$		0			0
$609$	9.21695			0.373490
$610$		0			0
$611$	4.80567	−	11.6019i	0.194417	−	0.469363i
$612$		0			0
$613$	34.4288	−	14.2609i	1.39057	−	0.575991i	0.443281	−	0.896383i	$-0.353814\pi$
$613$	34.4288	−	14.2609i	1.39057	−	0.575991i	0.947285	+	0.320391i	$0.103814\pi$
$614$		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	$-0.143386\pi$
$617$	11.5470	+	11.5470i	0.464866	+	0.464866i	−0.435381	+	0.900246i	$0.643386\pi$
$618$		0			0
$619$	−16.5076	−	39.8529i	−0.663498	−	1.60182i	−0.792284	−	0.610153i	$-0.791108\pi$
$619$	−16.5076	−	39.8529i	−0.663498	−	1.60182i	0.128786	−	0.991672i	$-0.458892\pi$
$620$		0			0
$621$	−7.80385	−	3.23246i	−0.313158	−	0.129714i
$622$		0			0
$623$		−	1.98536i		−	0.0795417i
$624$		0			0
$625$			3.77124i			0.150850i
$626$		0			0
$627$	−22.8488	−	9.46427i	−0.912492	−	0.377966i
$628$		0			0
$629$	4.12268	+	9.95303i	0.164382	+	0.396853i
$630$		0			0
$631$	−4.48591	−	4.48591i	−0.178581	−	0.178581i	0.612156	−	0.790737i	$-0.290302\pi$
$631$	−4.48591	−	4.48591i	−0.178581	−	0.178581i	−0.790737	+	0.612156i	$0.790302\pi$
$632$		0			0
$633$	17.0085	−	17.0085i	0.676025	−	0.676025i
$634$		0			0
$635$	−3.62175	+	1.50018i	−0.143725	+	0.0595328i
$636$		0			0
$637$	7.66147	−	18.4964i	0.303559	−	0.732855i
$638$		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
$643$	−9.36360	+	22.6057i	−0.369264	+	0.891483i	0.624607	+	0.780939i	$0.285259\pi$
$643$	−9.36360	+	22.6057i	−0.369264	+	0.891483i	−0.993871	+	0.110544i	$0.964741\pi$
$644$		0			0
$645$	46.6003	−	19.3025i	1.83489	−	0.760035i
$646$		0			0
$647$	−25.4317	+	25.4317i	−0.999823	+	0.999823i	−1.00000		0.000176614i	$-0.999944\pi$
$647$	−25.4317	+	25.4317i	−0.999823	+	0.999823i	0.000176614		1.00000i	$0.499944\pi$
$648$		0			0
$649$	−32.0464	−	32.0464i	−1.25793	−	1.25793i
$650$		0			0
$651$	8.92177	+	21.5391i	0.349672	+	0.844182i
$652$		0			0
$653$	−22.6322	−	9.37458i	−0.885668	−	0.366856i	−0.106976	−	0.994262i	$-0.534117\pi$
$653$	−22.6322	−	9.37458i	−0.885668	−	0.366856i	−0.778692	+	0.627406i	$0.784117\pi$
$654$		0			0
$655$			2.53137i			0.0989087i
$656$		0			0
$657$		−	8.30803i		−	0.324127i
$658$		0			0
$659$	−25.0100	−	10.3595i	−0.974250	−	0.403547i	−0.161957	−	0.986798i	$-0.551781\pi$
$659$	−25.0100	−	10.3595i	−0.974250	−	0.403547i	−0.812292	+	0.583250i	$0.801781\pi$
$660$		0			0
$661$	4.83467	+	11.6719i	0.188047	+	0.453985i	0.989583	−	0.143961i	$-0.0459838\pi$
$661$	4.83467	+	11.6719i	0.188047	+	0.453985i	−0.801537	+	0.597946i	$0.795984\pi$
$662$		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
$667$	5.81965	−	2.41058i	0.225338	−	0.0933380i
$668$		0			0
$669$	12.1400	−	29.3085i	0.469359	−	1.13313i
$670$		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
$675$	16.6221	−	40.1292i	0.639784	−	1.54457i
$676$		0			0
$677$	−20.7549	+	8.59697i	−0.797677	+	0.330409i	−0.744026	−	0.668151i	$-0.767086\pi$
$677$	−20.7549	+	8.59697i	−0.797677	+	0.330409i	−0.0536513	+	0.998560i	$0.517086\pi$
$678$		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
$683$	2.13532	+	5.15512i	0.0817058	+	0.197255i	0.959453	−	0.281869i	$-0.0909543\pi$
$683$	2.13532	+	5.15512i	0.0817058	+	0.197255i	−0.877747	+	0.479124i	$0.840954\pi$
$684$		0			0
$685$	53.5821	+	22.1944i	2.04727	+	0.848005i
$686$		0			0
$687$			8.80104i			0.335781i
$688$		0			0
$689$		−	1.70193i		−	0.0648385i
$690$		0			0
$691$	−22.9436	−	9.50357i	−0.872817	−	0.361533i	−0.0991103	−	0.995076i	$-0.531600\pi$
$691$	−22.9436	−	9.50357i	−0.872817	−	0.361533i	−0.773707	+	0.633544i	$0.781600\pi$
$692$		0			0
$693$	−2.08287	−	5.02849i	−0.0791217	−	0.191017i
$694$		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
$699$	0.0531806	−	0.0220281i	0.00201147	−	0.000833180i
$700$		0			0
$701$	7.60601	−	18.3625i	0.287275	−	0.693544i	−0.712693	−	0.701476i	$-0.752525\pi$
$701$	7.60601	−	18.3625i	0.287275	−	0.693544i	0.999969	+	0.00793210i	$0.00252489\pi$
$702$		0			0
$703$	13.8639			0.522887
$704$		0			0
$705$	16.6264			0.626186
$706$		0			0
$707$	5.20606	−	12.5685i	0.195794	−	0.472689i
$708$		0			0
$709$	−24.3512	+	10.0866i	−0.914529	+	0.378810i	−0.789788	−	0.613379i	$-0.789810\pi$
$709$	−24.3512	+	10.0866i	−0.914529	+	0.378810i	−0.124740	+	0.992189i	$0.539810\pi$
$710$		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
$715$	30.0783	+	72.6154i	1.12486	+	2.71566i
$716$		0			0
$717$	35.9121	+	14.8753i	1.34116	+	0.555528i
$718$		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
$723$	−1.79655	−	0.744157i	−0.0668145	−	0.0276755i
$724$		0			0
$725$	12.3958	+	29.9260i	0.460367	+	1.11142i
$726$		0			0
$727$	−30.7749	−	30.7749i	−1.14138	−	1.14138i	−0.988198	−	0.153181i	$-0.951048\pi$
$727$	−30.7749	−	30.7749i	−1.14138	−	1.14138i	−0.153181	−	0.988198i	$-0.548952\pi$
$728$		0			0
$729$	21.2271	−	21.2271i	0.786191	−	0.786191i
$730$		0			0
$731$	−20.2416	+	8.38434i	−0.748662	+	0.310106i
$732$		0			0
$733$	−17.4213	+	42.0588i	−0.643472	+	1.55348i	0.178494	+	0.983941i	$0.442878\pi$
$733$	−17.4213	+	42.0588i	−0.643472	+	1.55348i	−0.821965	+	0.569537i	$0.807122\pi$
$734$		0			0
$735$	26.5067			0.977715
$736$		0			0
$737$	−27.9216			−1.02850
$738$		0			0
$739$	−10.7099	+	25.8560i	−0.393970	+	0.951128i	0.595096	+	0.803655i	$0.297114\pi$
$739$	−10.7099	+	25.8560i	−0.393970	+	0.951128i	−0.989066	+	0.147474i	$0.952886\pi$
$740$		0			0
$741$	−17.3730	+	7.19615i	−0.638215	+	0.264357i
$742$		0			0
$743$	26.2978	−	26.2978i	0.964774	−	0.964774i	−0.0346265	−	0.999400i	$-0.511024\pi$
$743$	26.2978	−	26.2978i	0.964774	−	0.964774i	0.999400	+	0.0346265i	$0.0110242\pi$
$744$		0			0
$745$	−17.8225	−	17.8225i	−0.652967	−	0.652967i
$746$		0			0
$747$	−2.19422	−	5.29732i	−0.0802823	−	0.193819i
$748$		0			0
$749$	3.90414	+	1.61715i	0.142654	+	0.0590893i
$750$		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
$755$	46.0534	+	19.0759i	1.67605	+	0.694244i
$756$		0			0
$757$	3.12025	+	7.53295i	0.113407	+	0.273790i	0.970385	−	0.241564i	$-0.0776604\pi$
$757$	3.12025	+	7.53295i	0.113407	+	0.273790i	−0.856977	+	0.515354i	$0.827660\pi$
$758$		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	$-0.816449\pi$
$761$	−8.08516	+	8.08516i	−0.293087	+	0.293087i	0.545212	+	0.838299i	$0.316449\pi$
$762$		0			0
$763$	−5.12486	+	2.12279i	−0.185532	+	0.0768501i
$764$		0			0
$765$	−2.23972	+	5.40717i	−0.0809773	+	0.195496i
$766$		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
$771$	4.65499	−	11.2381i	0.167645	−	0.404731i
$772$		0			0
$773$	−29.4394	+	12.1942i	−1.05886	+	0.438595i	−0.843047	−	0.537839i	$-0.819241\pi$
$773$	−29.4394	+	12.1942i	−1.05886	+	0.438595i	−0.215815	+	0.976434i	$0.569241\pi$
$774$		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
$779$	10.2887	+	24.8390i	0.368629	+	0.889950i
$780$		0			0
$781$	−20.0187	−	8.29201i	−0.716325	−	0.296712i
$782$		0			0
$783$			23.4731i			0.838861i
$784$		0			0
$785$		−	86.4222i		−	3.08454i
$786$		0			0
$787$	0.505757	+	0.209491i	0.0180283	+	0.00746756i	0.391679	−	0.920102i	$-0.371894\pi$
$787$	0.505757	+	0.209491i	0.0180283	+	0.00746756i	−0.373651	+	0.927569i	$0.621894\pi$
$788$		0			0
$789$	−11.3889	−	27.4952i	−0.405456	−	0.978857i
$790$		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
$795$	2.08181	−	0.862315i	0.0738343	−	0.0305832i
$796$		0			0
$797$	11.9978	−	28.9652i	0.424983	−	1.02600i	−0.555873	−	0.831267i	$-0.687616\pi$
$797$	11.9978	−	28.9652i	0.424983	−	1.02600i	0.980856	−	0.194733i	$-0.0623841\pi$
$798$		0			0
$799$	−7.22193			−0.255494
$800$		0			0
$801$	0.952996			0.0336725
$802$		0			0
$803$	−24.5548	+	59.2805i	−0.866519	+	2.09196i
$804$		0			0
$805$	−7.20736	+	2.98539i	−0.254026	+	0.105221i
$806$		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	$-0.294525\pi$
$809$	−5.60821	−	5.60821i	−0.197174	−	0.197174i	−0.798787	+	0.601613i	$0.794525\pi$
$810$		0			0
$811$	−15.7458	−	38.0138i	−0.552910	−	1.33484i	−0.915283	−	0.402811i	$-0.868033\pi$
$811$	−15.7458	−	38.0138i	−0.552910	−	1.33484i	0.362373	−	0.932033i	$-0.381967\pi$
$812$		0			0
$813$	21.8943	+	9.06893i	0.767868	+	0.318061i
$814$		0			0
$815$			62.5049i			2.18945i
$816$		0			0
$817$			28.1952i			0.986425i
$818$		0			0
$819$	−3.82341	−	1.58371i	−0.133601	−	0.0553393i
$820$		0			0
$821$	−10.2032	−	24.6328i	−0.356095	−	0.859689i	−0.995841	−	0.0911034i	$-0.970961\pi$
$821$	−10.2032	−	24.6328i	−0.356095	−	0.859689i	0.639746	−	0.768586i	$-0.279039\pi$
$822$		0			0
$823$	26.4269	+	26.4269i	0.921185	+	0.921185i	0.997113	−	0.0759281i	$-0.0241919\pi$
$823$	26.4269	+	26.4269i	0.921185	+	0.921185i	−0.0759281	+	0.997113i	$0.524192\pi$
$824$		0			0
$825$	−44.7093	+	44.7093i	−1.55658	+	1.55658i
$826$		0			0
$827$	4.59197	−	1.90206i	0.159678	−	0.0661410i	−0.301413	−	0.953494i	$-0.597458\pi$
$827$	4.59197	−	1.90206i	0.159678	−	0.0661410i	0.461091	+	0.887353i	$0.347458\pi$
$828$		0			0
$829$	−0.0153511	+	0.0370609i	−0.000533166	+	0.00128718i	−0.924146	−	0.382040i	$-0.875222\pi$
$829$	−0.0153511	+	0.0370609i	−0.000533166	+	0.00128718i	0.923613	+	0.383327i	$0.125222\pi$
$830$		0			0
$831$	−21.1066			−0.732181
$832$		0			0
$833$	−11.5136			−0.398923
$834$		0			0
$835$	−30.7559	+	74.2514i	−1.06435	+	2.56957i
$836$		0			0
$837$	−54.8542	+	22.7214i	−1.89604	+	0.785365i
$838$		0			0
$839$	3.78014	−	3.78014i	0.130505	−	0.130505i	−0.638837	−	0.769342i	$-0.720584\pi$
$839$	3.78014	−	3.78014i	0.130505	−	0.130505i	0.769342	+	0.638837i	$0.220584\pi$
$840$		0			0
$841$	8.12828	+	8.12828i	0.280286	+	0.280286i
$842$		0			0
$843$	15.3828	+	37.1374i	0.529812	+	1.27908i
$844$		0			0
$845$	12.3407	+	5.11169i	0.424534	+	0.175848i
$846$		0			0
$847$			26.0686i			0.895728i
$848$		0			0
$849$		−	1.62622i		−	0.0558118i
$850$		0			0
$851$	−6.36817	−	2.63778i	−0.218298	−	0.0904220i
$852$		0			0
$853$	17.7231	+	42.7872i	0.606826	+	1.46501i	0.866433	+	0.499293i	$0.166407\pi$
$853$	17.7231	+	42.7872i	0.606826	+	1.46501i	−0.259607	+	0.965714i	$0.583593\pi$
$854$		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	$-0.740312\pi$
$857$	1.25991	−	1.25991i	0.0430375	−	0.0430375i	0.728298	+	0.685261i	$0.240312\pi$
$858$		0			0
$859$	11.2626	−	4.66511i	0.384274	−	0.159171i	−0.182179	−	0.983265i	$-0.558315\pi$
$859$	11.2626	−	4.66511i	0.384274	−	0.159171i	0.566453	+	0.824094i	$0.308315\pi$
$860$		0			0
$861$	7.48477	−	18.0698i	0.255080	−	0.615818i
$862$		0			0
$863$	55.7303			1.89708			0.948541	−	0.316653i	$-0.102559\pi$
$863$	55.7303			1.89708			0.948541	+	0.316653i	$0.102559\pi$
$864$		0			0
$865$	32.3238			1.09904
$866$		0			0
$867$	6.65734	−	16.0722i	0.226095	−	0.545842i
$868$		0			0
$869$	−22.8690	+	9.47266i	−0.775779	+	0.321338i
$870$		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
$875$	−5.43712	−	13.1264i	−0.183808	−	0.443752i
$876$		0			0
$877$	−10.3225	−	4.27570i	−0.348565	−	0.144380i	0.201530	−	0.979482i	$-0.435409\pi$
$877$	−10.3225	−	4.27570i	−0.348565	−	0.144380i	−0.550095	+	0.835102i	$0.685409\pi$
$878$		0			0
$879$		−	27.0104i		−	0.911039i
$880$		0			0
$881$		−	13.1185i		−	0.441972i	−0.975277	−	0.220986i	$-0.929072\pi$
$881$		−	13.1185i		−	0.441972i	0.975277	−	0.220986i	$-0.0709276\pi$
$882$		0			0
$883$	−10.5395	−	4.36561i	−0.354683	−	0.146915i	0.198226	−	0.980156i	$-0.436482\pi$
$883$	−10.5395	−	4.36561i	−0.354683	−	0.146915i	−0.552909	+	0.833242i	$0.686482\pi$
$884$		0			0
$885$	−17.4595	−	42.1509i	−0.586893	−	1.41689i
$886$		0			0
$887$	32.1505	+	32.1505i	1.07951	+	1.07951i	0.996553	+	0.0829550i	$0.0264358\pi$
$887$	32.1505	+	32.1505i	1.07951	+	1.07951i	0.0829550	+	0.996553i	$0.473564\pi$
$888$		0			0
$889$	−1.12722	+	1.12722i	−0.0378058	+	0.0378058i
$890$		0			0
$891$	−31.9392	+	13.2296i	−1.07000	+	0.443210i
$892$		0			0
$893$	−3.55663	+	8.58647i	−0.119018	+	0.287335i
$894$		0			0
$895$	0.511683			0.0171037
$896$		0			0
$897$	9.34920			0.312161
$898$		0			0
$899$	16.9443	−	40.9070i	0.565123	−	1.36433i
$900$		0			0
$901$	−0.904268	+	0.374560i	−0.0301255	+	0.0124784i
$902$		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
$907$	12.1129	+	29.2431i	0.402202	+	0.971000i	0.987131	+	0.159916i	$0.0511223\pi$
$907$	12.1129	+	29.2431i	0.402202	+	0.971000i	−0.584929	+	0.811084i	$0.698878\pi$
$908$		0			0
$909$	6.03306	+	2.49898i	0.200104	+	0.0828858i
$910$		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
$915$	13.9792	+	5.79035i	0.462136	+	0.191423i
$916$		0			0
$917$	0.393927	+	0.951023i	0.0130086	+	0.0314055i
$918$		0			0
$919$	−1.00540	−	1.00540i	−0.0331651	−	0.0331651i	0.690330	−	0.723495i	$-0.257465\pi$
$919$	−1.00540	−	1.00540i	−0.0331651	−	0.0331651i	−0.723495	+	0.690330i	$0.757465\pi$
$920$		0			0
$921$	−22.1273	+	22.1273i	−0.729119	+	0.729119i
$922$		0			0
$923$	−15.2212	+	6.30483i	−0.501012	+	0.207526i
$924$		0			0
$925$	13.5641	−	32.7466i	0.445985	−	1.07670i
$926$		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
$931$	−5.67018	+	13.6890i	−0.185833	+	0.448640i
$932$		0			0
$933$	2.82967	−	1.17209i	0.0926393	−	0.0383724i
$934$		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	$-0.278361\pi$
$937$	−3.85201	−	3.85201i	−0.125840	−	0.125840i	−0.767222	+	0.641382i	$0.778361\pi$
$938$		0			0
$939$	−1.04463	−	2.52197i	−0.0340903	−	0.0823013i
$940$		0			0
$941$	39.2107	+	16.2416i	1.27823	+	0.529462i	0.915458	−	0.402415i	$-0.131829\pi$
$941$	39.2107	+	16.2416i	1.27823	+	0.529462i	0.362776	+	0.931876i	$0.381829\pi$
$942$		0			0
$943$		−	13.3670i		−	0.435288i
$944$		0			0
$945$		−	29.0703i		−	0.945658i
$946$		0			0
$947$	−32.3640	−	13.4056i	−1.05169	−	0.435624i	−0.211194	−	0.977444i	$-0.567735\pi$
$947$	−32.3640	−	13.4056i	−1.05169	−	0.435624i	−0.840494	+	0.541820i	$0.817735\pi$
$948$		0			0
$949$	18.6702	+	45.0739i	0.606061	+	1.46316i
$950$		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	$-0.646878\pi$
$953$	13.8976	−	13.8976i	0.450186	−	0.450186i	0.895416	+	0.445230i	$0.146878\pi$
$954$		0			0
$955$	−54.2842	+	22.4852i	−1.75659	+	0.727605i
$956$		0			0
$957$	13.0761	−	31.5685i	0.422690	−	1.02046i
$958$		0			0
$959$	23.5844			0.761580
$960$		0			0
$961$	80.9971			2.61281
$962$		0			0
$963$	−0.776251	+	1.87404i	−0.0250143	+	0.0603900i
$964$		0			0
$965$	32.4658	−	13.4478i	1.04511	−	0.432899i
$966$		0			0
$967$	36.8527	−	36.8527i	1.18510	−	1.18510i	0.206700	−	0.978404i	$-0.433728\pi$
$967$	36.8527	−	36.8527i	1.18510	−	1.18510i	0.978404	−	0.206700i	$-0.0662724\pi$
$968$		0			0
$969$	7.64689	+	7.64689i	0.245653	+	0.245653i
$970$		0			0
$971$	−15.5625	−	37.5712i	−0.499425	−	1.20572i	−0.949794	−	0.312875i	$-0.898708\pi$
$971$	−15.5625	−	37.5712i	−0.499425	−	1.20572i	0.450370	−	0.892842i	$-0.351292\pi$
$972$		0			0
$973$	1.13381	+	0.469639i	0.0363482	+	0.0150559i
$974$		0			0
$975$			48.0758i			1.53966i
$976$		0			0
$977$			2.89004i			0.0924607i	0.998931	+	0.0462303i	$0.0147208\pi$
$977$			2.89004i			0.0924607i	−0.998931	+	0.0462303i	$0.985279\pi$
$978$		0			0
$979$	−6.79994	−	2.81663i	−0.217327	−	0.0900197i
$980$		0			0
$981$	−1.01896	−	2.46000i	−0.0325330	−	0.0785417i
$982$		0			0
$983$	10.1625	+	10.1625i	0.324135	+	0.324135i	0.850351	−	0.526216i	$-0.176390\pi$
$983$	10.1625	+	10.1625i	0.324135	+	0.324135i	−0.526216	+	0.850351i	$0.676390\pi$
$984$		0			0
$985$	−25.7926	+	25.7926i	−0.821820	+	0.821820i
$986$		0			0
$987$	6.24646	−	2.58737i	0.198827	−	0.0823568i
$988$		0			0
$989$	5.36449	−	12.9510i	0.170581	−	0.411819i
$990$		0			0
$991$	−51.7294			−1.64324			−0.821619	−	0.570038i	$-0.806929\pi$
$991$	−51.7294			−1.64324			−0.821619	+	0.570038i	$0.806929\pi$
$992$		0			0
$993$	−34.7901			−1.10403
$994$		0			0
$995$	−4.66978	+	11.2738i	−0.148042	+	0.357405i
$996$		0			0
$997$	18.0280	−	7.46746i	0.570954	−	0.236497i	−0.0784791	−	0.996916i	$-0.525006\pi$
$997$	18.0280	−	7.46746i	0.570954	−	0.236497i	0.649433	+	0.760419i	$0.275006\pi$
$998$		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.g.129.4	yes	16
4.3	odd	2	inner	1024.2.g.g.129.1	yes	16
8.3	odd	2		1024.2.g.d.129.4	yes	16
8.5	even	2		1024.2.g.d.129.1	yes	16
16.3	odd	4		1024.2.g.a.641.1	yes	16
16.5	even	4		1024.2.g.f.641.1	yes	16
16.11	odd	4		1024.2.g.f.641.4	yes	16
16.13	even	4		1024.2.g.a.641.4	yes	16
32.3	odd	8		1024.2.g.a.385.1	✓	16
32.5	even	8	inner	1024.2.g.g.897.4	yes	16
32.11	odd	8		1024.2.g.d.897.4	yes	16
32.13	even	8		1024.2.g.f.385.1	yes	16
32.19	odd	8		1024.2.g.f.385.4	yes	16
32.21	even	8		1024.2.g.d.897.1	yes	16
32.27	odd	8	inner	1024.2.g.g.897.1	yes	16
32.29	even	8		1024.2.g.a.385.4	yes	16
64.5	even	16		4096.2.a.s.1.6		8
64.27	odd	16		4096.2.a.s.1.5		8
64.37	even	16		4096.2.a.i.1.3		8
64.59	odd	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	32.3	odd	8
1024.2.g.a.385.4	yes	16	32.29	even	8
1024.2.g.a.641.1	yes	16	16.3	odd	4
1024.2.g.a.641.4	yes	16	16.13	even	4
1024.2.g.d.129.1	yes	16	8.5	even	2
1024.2.g.d.129.4	yes	16	8.3	odd	2
1024.2.g.d.897.1	yes	16	32.21	even	8
1024.2.g.d.897.4	yes	16	32.11	odd	8
1024.2.g.f.385.1	yes	16	32.13	even	8
1024.2.g.f.385.4	yes	16	32.19	odd	8
1024.2.g.f.641.1	yes	16	16.5	even	4
1024.2.g.f.641.4	yes	16	16.11	odd	4
1024.2.g.g.129.1	yes	16	4.3	odd	2	inner
1024.2.g.g.129.4	yes	16	1.1	even	1	trivial
1024.2.g.g.897.1	yes	16	32.27	odd	8	inner
1024.2.g.g.897.4	yes	16	32.5	even	8	inner
4096.2.a.i.1.3		8	64.37	even	16
4096.2.a.i.1.4		8	64.59	odd	16
4096.2.a.s.1.5		8	64.27	odd	16
4096.2.a.s.1.6		8	64.5	even	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)

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

Introduction

L-functions

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Database

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