LMFDB - Embedded newform 1024.2.g.e.385.1

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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 $ x^16 - 8x^14 + 32x^12 - 64x^10 + 127x^8 - 576x^6 + 2592x^4 - 5832*x^2 + 6561
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			385.1
Root			$1.59056 - 0.685641i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.e.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27621 + 0.942835i) q^{3} +(1.03503 - 2.49877i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(2.17085 - 2.17085i) q^{9} +O(q^{10})$	\(q+(-2.27621 + 0.942835i) q^{3} +(1.03503 - 2.49877i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(2.17085 - 2.17085i) q^{9} +(-4.12396 - 1.70820i) q^{11} +(-2.01451 - 4.86345i) q^{13} +6.66358i q^{15} +6.31269i q^{17} +(1.95918 + 4.72988i) q^{19} +(4.41421 + 1.82843i) q^{21} +(0.288890 - 0.288890i) q^{23} +(-1.63706 - 1.63706i) q^{25} +(-0.0660470 + 0.159452i) q^{27} +(1.03503 - 0.428722i) q^{29} +3.69552 q^{31} +10.9975 q^{33} +(-4.84584 + 2.00721i) q^{35} +(-4.32720 + 10.4468i) q^{37} +(9.17087 + 9.17087i) q^{39} +(-1.68485 + 1.68485i) q^{41} +(-4.03244 - 1.67029i) q^{43} +(-3.17758 - 7.67136i) q^{45} +4.83153i q^{47} -3.23917i q^{49} +(-5.95183 - 14.3690i) q^{51} +(0.501227 + 0.207615i) q^{53} +(-8.53682 + 8.53682i) q^{55} +(-8.91900 - 8.91900i) q^{57} +(-3.00366 + 7.25148i) q^{59} +(-3.39971 + 1.40820i) q^{61} -5.95371 q^{63} -14.2377 q^{65} +(0.299008 - 0.123853i) q^{67} +(-0.385197 + 0.929949i) q^{69} +(6.54392 + 6.54392i) q^{71} +(-5.53380 + 5.53380i) q^{73} +(5.26975 + 2.18280i) q^{75} +(3.31269 + 7.99755i) q^{77} +0.877131i q^{79} +8.78494i q^{81} +(1.41931 + 3.42652i) q^{83} +(15.7740 + 6.53380i) q^{85} +(-1.95172 + 1.95172i) q^{87} +(-6.46129 - 6.46129i) q^{89} +(-3.90671 + 9.43162i) q^{91} +(-8.41176 + 3.48427i) q^{93} +13.8467 q^{95} -3.58333 q^{97} +(-12.6608 + 5.24427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 q^{85} + 32 q^{89} - 16 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 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * q^85 + 32 * q^89 - 16 * 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
$3$	−2.27621	+	0.942835i	−1.31417	+	0.544346i	−0.926098	−	0.377284i	$-0.876858\pi$
$3$	−2.27621	+	0.942835i	−1.31417	+	0.544346i	−0.388070	+	0.921630i	$0.626858\pi$
$4$		0			0
$5$	1.03503	−	2.49877i	0.462878	−	1.11749i	−0.504333	−	0.863509i	$-0.668262\pi$
$5$	1.03503	−	2.49877i	0.462878	−	1.11749i	0.967211	−	0.253976i	$-0.0817384\pi$
$6$		0			0
$7$	−1.37128	−	1.37128i	−0.518296	−	0.518296i	0.398760	−	0.917056i	$-0.369441\pi$
$7$	−1.37128	−	1.37128i	−0.518296	−	0.518296i	−0.917056	+	0.398760i	$0.869441\pi$
$8$		0			0
$9$	2.17085	−	2.17085i	0.723618	−	0.723618i
$10$		0			0
$11$	−4.12396	−	1.70820i	−1.24342	−	0.515042i	−0.338640	−	0.940916i	$-0.609967\pi$
$11$	−4.12396	−	1.70820i	−1.24342	−	0.515042i	−0.904783	+	0.425874i	$0.859967\pi$
$12$		0			0
$13$	−2.01451	−	4.86345i	−0.558724	−	1.34888i	−0.910777	−	0.412899i	$-0.864516\pi$
$13$	−2.01451	−	4.86345i	−0.558724	−	1.34888i	0.352053	−	0.935980i	$-0.385484\pi$
$14$		0			0
$15$			6.66358i			1.72053i
$16$		0			0
$17$			6.31269i			1.53105i	0.643405	+	0.765526i	$0.277521\pi$
$17$			6.31269i			1.53105i	−0.643405	+	0.765526i	$0.722479\pi$
$18$		0			0
$19$	1.95918	+	4.72988i	0.449467	+	1.08511i	0.972522	+	0.232810i	$0.0747921\pi$
$19$	1.95918	+	4.72988i	0.449467	+	1.08511i	−0.523055	+	0.852299i	$0.675208\pi$
$20$		0			0
$21$	4.41421	+	1.82843i	0.963260	+	0.398996i
$22$		0			0
$23$	0.288890	−	0.288890i	0.0602377	−	0.0602377i	−0.676346	−	0.736584i	$-0.736438\pi$
$23$	0.288890	−	0.288890i	0.0602377	−	0.0602377i	0.736584	+	0.676346i	$0.236438\pi$
$24$		0			0
$25$	−1.63706	−	1.63706i	−0.327411	−	0.327411i
$26$		0			0
$27$	−0.0660470	+	0.159452i	−0.0127108	+	0.0306865i
$28$		0			0
$29$	1.03503	−	0.428722i	0.192199	−	0.0796116i	−0.284508	−	0.958674i	$-0.591830\pi$
$29$	1.03503	−	0.428722i	0.192199	−	0.0796116i	0.476707	+	0.879062i	$0.341830\pi$
$30$		0			0
$31$	3.69552			0.663735			0.331867	−	0.943326i	$-0.392321\pi$
$31$	3.69552			0.663735			0.331867	+	0.943326i	$0.392321\pi$
$32$		0			0
$33$	10.9975			1.91443
$34$		0			0
$35$	−4.84584	+	2.00721i	−0.819096	+	0.339281i
$36$		0			0
$37$	−4.32720	+	10.4468i	−0.711387	+	1.71744i	−0.0148821	+	0.999889i	$0.504737\pi$
$37$	−4.32720	+	10.4468i	−0.711387	+	1.71744i	−0.696505	+	0.717552i	$0.745263\pi$
$38$		0			0
$39$	9.17087	+	9.17087i	1.46851	+	1.46851i
$40$		0			0
$41$	−1.68485	+	1.68485i	−0.263130	+	0.263130i	−0.826324	−	0.563194i	$-0.809572\pi$
$41$	−1.68485	+	1.68485i	−0.263130	+	0.263130i	0.563194	+	0.826324i	$0.309572\pi$
$42$		0			0
$43$	−4.03244	−	1.67029i	−0.614941	−	0.254717i	0.0533985	−	0.998573i	$-0.482995\pi$
$43$	−4.03244	−	1.67029i	−0.614941	−	0.254717i	−0.668340	+	0.743856i	$0.732995\pi$
$44$		0			0
$45$	−3.17758	−	7.67136i	−0.473686	−	1.14358i
$46$		0			0
$47$			4.83153i			0.704750i	0.935859	+	0.352375i	$0.114626\pi$
$47$			4.83153i			0.704750i	−0.935859	+	0.352375i	$0.885374\pi$
$48$		0			0
$49$		−	3.23917i		−	0.462739i
$50$		0			0
$51$	−5.95183	−	14.3690i	−0.833423	−	2.01206i
$52$		0			0
$53$	0.501227	+	0.207615i	0.0688488	+	0.0285181i	0.416842	−	0.908979i	$-0.363137\pi$
$53$	0.501227	+	0.207615i	0.0688488	+	0.0285181i	−0.347993	+	0.937497i	$0.613137\pi$
$54$		0			0
$55$	−8.53682	+	8.53682i	−1.15110	+	1.15110i
$56$		0			0
$57$	−8.91900	−	8.91900i	−1.18135	−	1.18135i
$58$		0			0
$59$	−3.00366	+	7.25148i	−0.391043	+	0.944062i	0.598670	+	0.800996i	$0.295696\pi$
$59$	−3.00366	+	7.25148i	−0.391043	+	0.944062i	−0.989713	+	0.143066i	$0.954304\pi$
$60$		0			0
$61$	−3.39971	+	1.40820i	−0.435288	+	0.180302i	−0.589557	−	0.807727i	$-0.700698\pi$
$61$	−3.39971	+	1.40820i	−0.435288	+	0.180302i	0.154269	+	0.988029i	$0.450698\pi$
$62$		0			0
$63$	−5.95371			−0.750097
$64$		0			0
$65$	−14.2377			−1.76597
$66$		0			0
$67$	0.299008	−	0.123853i	0.0365297	−	0.0151311i	−0.364344	−	0.931265i	$-0.618707\pi$
$67$	0.299008	−	0.123853i	0.0365297	−	0.0151311i	0.400873	+	0.916133i	$0.368707\pi$
$68$		0			0
$69$	−0.385197	+	0.929949i	−0.0463723	+	0.111953i
$70$		0			0
$71$	6.54392	+	6.54392i	0.776620	+	0.776620i	0.979255	−	0.202634i	$-0.0649502\pi$
$71$	6.54392	+	6.54392i	0.776620	+	0.776620i	−0.202634	+	0.979255i	$0.564950\pi$
$72$		0			0
$73$	−5.53380	+	5.53380i	−0.647682	+	0.647682i	−0.952432	−	0.304750i	$-0.901427\pi$
$73$	−5.53380	+	5.53380i	−0.647682	+	0.647682i	0.304750	+	0.952432i	$0.401427\pi$
$74$		0			0
$75$	5.26975	+	2.18280i	0.608498	+	0.252048i
$76$		0			0
$77$	3.31269	+	7.99755i	0.377516	+	0.911405i
$78$		0			0
$79$			0.877131i			0.0986849i	0.998782	+	0.0493425i	$0.0157126\pi$
$79$			0.877131i			0.0986849i	−0.998782	+	0.0493425i	$0.984287\pi$
$80$		0			0
$81$			8.78494i			0.976104i
$82$		0			0
$83$	1.41931	+	3.42652i	0.155790	+	0.376110i	0.982433	−	0.186617i	$-0.0597523\pi$
$83$	1.41931	+	3.42652i	0.155790	+	0.376110i	−0.826643	+	0.562727i	$0.809752\pi$
$84$		0			0
$85$	15.7740	+	6.53380i	1.71093	+	0.708690i
$86$		0			0
$87$	−1.95172	+	1.95172i	−0.209246	+	0.209246i
$88$		0			0
$89$	−6.46129	−	6.46129i	−0.684896	−	0.684896i	0.276203	−	0.961099i	$-0.410924\pi$
$89$	−6.46129	−	6.46129i	−0.684896	−	0.684896i	−0.961099	+	0.276203i	$0.910924\pi$
$90$		0			0
$91$	−3.90671	+	9.43162i	−0.409534	+	0.988703i
$92$		0			0
$93$	−8.41176	+	3.48427i	−0.872259	+	0.361301i
$94$		0			0
$95$	13.8467			1.42064
$96$		0			0
$97$	−3.58333			−0.363832			−0.181916	−	0.983314i	$-0.558230\pi$
$97$	−3.58333			−0.363832			−0.181916	+	0.983314i	$0.558230\pi$
$98$		0			0
$99$	−12.6608	+	5.24427i	−1.27246	+	0.527069i
$100$		0			0
$101$	−2.57128	+	6.20761i	−0.255852	+	0.617681i	−0.998656	−	0.0518279i	$-0.983495\pi$
$101$	−2.57128	+	6.20761i	−0.255852	+	0.617681i	0.742804	+	0.669509i	$0.233495\pi$
$102$		0			0
$103$	−10.9244	−	10.9244i	−1.07642	−	1.07642i	−0.996828	−	0.0795901i	$-0.974639\pi$
$103$	−10.9244	−	10.9244i	−1.07642	−	1.07642i	−0.0795901	−	0.996828i	$-0.525361\pi$
$104$		0			0
$105$	9.13765	−	9.13765i	0.891743	−	0.891743i
$106$		0			0
$107$	−4.70174	−	1.94753i	−0.454535	−	0.188274i	0.143657	−	0.989628i	$-0.454114\pi$
$107$	−4.70174	−	1.94753i	−0.454535	−	0.188274i	−0.598192	+	0.801353i	$0.704114\pi$
$108$		0			0
$109$	2.20660	+	5.32720i	0.211354	+	0.510253i	0.993632	−	0.112676i	$-0.0359423\pi$
$109$	2.20660	+	5.32720i	0.211354	+	0.510253i	−0.782278	+	0.622930i	$0.785942\pi$
$110$		0			0
$111$		−	27.8589i		−	2.64425i
$112$		0			0
$113$			1.06760i			0.100431i	0.998738	+	0.0502156i	$0.0159908\pi$
$113$			1.06760i			0.100431i	−0.998738	+	0.0502156i	$0.984009\pi$
$114$		0			0
$115$	−0.422862	−	1.02088i	−0.0394321	−	0.0951974i
$116$		0			0
$117$	−14.9311	−	6.18464i	−1.38038	−	0.571771i
$118$		0			0
$119$	8.65648	−	8.65648i	0.793538	−	0.793538i
$120$		0			0
$121$	6.31096	+	6.31096i	0.573723	+	0.573723i
$122$		0			0
$123$	2.24653	−	5.42362i	0.202563	−	0.489031i
$124$		0			0
$125$	6.70884	−	2.77889i	0.600057	−	0.248552i
$126$		0			0
$127$	−21.7979			−1.93425			−0.967127	−	0.254294i	$-0.918157\pi$
$127$	−21.7979			−1.93425			−0.967127	+	0.254294i	$0.918157\pi$
$128$		0			0
$129$	10.7535			0.946790
$130$		0			0
$131$	15.7883	−	6.53973i	1.37943	−	0.571379i	0.435101	−	0.900382i	$-0.356713\pi$
$131$	15.7883	−	6.53973i	1.37943	−	0.571379i	0.944329	+	0.329003i	$0.106713\pi$
$132$		0			0
$133$	3.79941	−	9.17259i	0.329451	−	0.795364i
$134$		0			0
$135$	0.330073	+	0.330073i	0.0284082	+	0.0284082i
$136$		0			0
$137$	3.85744	−	3.85744i	0.329564	−	0.329564i	−0.522857	−	0.852420i	$-0.675134\pi$
$137$	3.85744	−	3.85744i	0.329564	−	0.329564i	0.852420	+	0.522857i	$0.175134\pi$
$138$		0			0
$139$	−2.81420	−	1.16568i	−0.238697	−	0.0988715i	0.260128	−	0.965574i	$-0.416235\pi$
$139$	−2.81420	−	1.16568i	−0.238697	−	0.0988715i	−0.498825	+	0.866703i	$0.666235\pi$
$140$		0			0
$141$	−4.55533	−	10.9975i	−0.383628	−	0.926160i
$142$		0			0
$143$			23.4979i			1.96499i
$144$		0			0
$145$		−	3.03003i		−	0.251631i
$146$		0			0
$147$	3.05400	+	7.37302i	0.251890	+	0.608116i
$148$		0			0
$149$	−13.4503	−	5.57128i	−1.10189	−	0.456417i	−0.243751	−	0.969838i	$-0.578378\pi$
$149$	−13.4503	−	5.57128i	−1.10189	−	0.456417i	−0.858137	+	0.513421i	$0.828378\pi$
$150$		0			0
$151$	3.87718	−	3.87718i	0.315520	−	0.315520i	−0.531523	−	0.847044i	$-0.678380\pi$
$151$	3.87718	−	3.87718i	0.315520	−	0.315520i	0.847044	+	0.531523i	$0.178380\pi$
$152$		0			0
$153$	13.7039	+	13.7039i	1.10790	+	1.10790i
$154$		0			0
$155$	3.82496	−	9.23426i	0.307228	−	0.741714i
$156$		0			0
$157$	4.39725	−	1.82140i	0.350939	−	0.145364i	−0.200248	−	0.979745i	$-0.564175\pi$
$157$	4.39725	−	1.82140i	0.350939	−	0.145364i	0.551187	+	0.834381i	$0.314175\pi$
$158$		0			0
$159$	−1.33664			−0.106003
$160$		0			0
$161$	−0.792299			−0.0624419
$162$		0			0
$163$	−1.19381	+	0.494494i	−0.0935067	+	0.0387317i	−0.428946	−	0.903330i	$-0.641115\pi$
$163$	−1.19381	+	0.494494i	−0.0935067	+	0.0387317i	0.335440	+	0.942062i	$0.391115\pi$
$164$		0			0
$165$	11.3827	−	27.4804i	0.886145	−	2.13934i
$166$		0			0
$167$	−3.53607	−	3.53607i	−0.273629	−	0.273629i	0.556930	−	0.830559i	$-0.311979\pi$
$167$	−3.53607	−	3.53607i	−0.273629	−	0.273629i	−0.830559	+	0.556930i	$0.811979\pi$
$168$		0			0
$169$	−10.4025	+	10.4025i	−0.800196	+	0.800196i
$170$		0			0
$171$	14.5210	+	6.01479i	1.11045	+	0.459962i
$172$		0			0
$173$	4.19912	+	10.1376i	0.319253	+	0.770745i	0.999294	+	0.0375707i	$0.0119619\pi$
$173$	4.19912	+	10.1376i	0.319253	+	0.770745i	−0.680041	+	0.733174i	$0.738038\pi$
$174$		0			0
$175$			4.48973i			0.339392i
$176$		0			0
$177$		−	19.3378i		−	1.45352i
$178$		0			0
$179$	5.48359	+	13.2386i	0.409863	+	0.989497i	0.985173	+	0.171562i	$0.0548813\pi$
$179$	5.48359	+	13.2386i	0.409863	+	0.989497i	−0.575310	+	0.817935i	$0.695119\pi$
$180$		0			0
$181$	10.1761	+	4.21510i	0.756387	+	0.313306i	0.727345	−	0.686272i	$-0.240754\pi$
$181$	10.1761	+	4.21510i	0.756387	+	0.313306i	0.0290424	+	0.999578i	$0.490754\pi$
$182$		0			0
$183$	6.41072	−	6.41072i	0.473894	−	0.473894i
$184$		0			0
$185$	21.6254	+	21.6254i	1.58993	+	1.58993i
$186$		0			0
$187$	10.7834	−	26.0333i	0.788557	−	1.90374i
$188$		0			0
$189$	0.309222	−	0.128084i	0.0224926	−	0.00931674i
$190$		0			0
$191$	23.0607			1.66862			0.834308	−	0.551299i	$-0.185868\pi$
$191$	23.0607			1.66862			0.834308	+	0.551299i	$0.185868\pi$
$192$		0			0
$193$	9.24019			0.665123			0.332562	−	0.943082i	$-0.392087\pi$
$193$	9.24019			0.665123			0.332562	+	0.943082i	$0.392087\pi$
$194$		0			0
$195$	32.4080	−	13.4238i	2.32079	−	0.961301i
$196$		0			0
$197$	−4.50727	+	10.8815i	−0.321130	+	0.775276i	0.678059	+	0.735007i	$0.262821\pi$
$197$	−4.50727	+	10.8815i	−0.321130	+	0.775276i	−0.999189	+	0.0402686i	$0.987179\pi$
$198$		0			0
$199$	−14.5468	−	14.5468i	−1.03120	−	1.03120i	−0.999498	−	0.0316976i	$-0.989909\pi$
$199$	−14.5468	−	14.5468i	−1.03120	−	1.03120i	−0.0316976	−	0.999498i	$-0.510091\pi$
$200$		0			0
$201$	−0.563832	+	0.563832i	−0.0397696	+	0.0397696i
$202$		0			0
$203$	−2.00721	−	0.831414i	−0.140879	−	0.0583538i
$204$		0			0
$205$	2.46620	+	5.95394i	0.172247	+	0.415841i
$206$		0			0
$207$		−	1.25428i		−	0.0871782i
$208$		0			0
$209$		−	22.8525i		−	1.58074i
$210$		0			0
$211$	4.01023	+	9.68155i	0.276076	+	0.666506i	0.999720	−	0.0236676i	$-0.00753435\pi$
$211$	4.01023	+	9.68155i	0.276076	+	0.666506i	−0.723644	+	0.690173i	$0.757534\pi$
$212$		0			0
$213$	−21.0651	−	8.72547i	−1.44336	−	0.597859i
$214$		0			0
$215$	−8.34735	+	8.34735i	−0.569285	+	0.569285i
$216$		0			0
$217$	−5.06760	−	5.06760i	−0.344011	−	0.344011i
$218$		0			0
$219$	7.37860	−	17.8135i	0.498600	−	1.20373i
$220$		0			0
$221$	30.7015	−	12.7170i	2.06521	−	0.855436i
$222$		0			0
$223$	13.6174			0.911892			0.455946	−	0.890008i	$-0.349301\pi$
$223$	13.6174			0.911892			0.455946	+	0.890008i	$0.349301\pi$
$224$		0			0
$225$	−7.10762			−0.473841
$226$		0			0
$227$	−17.3172	+	7.17300i	−1.14938	+	0.476089i	−0.874326	−	0.485340i	$-0.838696\pi$
$227$	−17.3172	+	7.17300i	−1.14938	+	0.476089i	−0.275054	+	0.961429i	$0.588696\pi$
$228$		0			0
$229$	0.691880	−	1.67035i	0.0457207	−	0.110380i	−0.899369	−	0.437190i	$-0.855974\pi$
$229$	0.691880	−	1.67035i	0.0457207	−	0.110380i	0.945090	+	0.326810i	$0.105974\pi$
$230$		0			0
$231$	−15.0807	−	15.0807i	−0.992240	−	0.992240i
$232$		0			0
$233$	−0.606304	+	0.606304i	−0.0397203	+	0.0397203i	−0.726688	−	0.686968i	$-0.758941\pi$
$233$	−0.606304	+	0.606304i	−0.0397203	+	0.0397203i	0.686968	+	0.726688i	$0.258941\pi$
$234$		0			0
$235$	12.0729	+	5.00075i	0.787548	+	0.326213i
$236$		0			0
$237$	−0.826990	−	1.99653i	−0.0537188	−	0.129689i
$238$		0			0
$239$		−	23.5680i		−	1.52449i	−0.647291	−	0.762243i	$-0.724098\pi$
$239$		−	23.5680i		−	1.52449i	0.647291	−	0.762243i	$-0.275902\pi$
$240$		0			0
$241$			25.6775i			1.65403i	0.562178	+	0.827016i	$0.309964\pi$
$241$			25.6775i			1.65403i	−0.562178	+	0.827016i	$0.690036\pi$
$242$		0			0
$243$	−8.48089	−	20.4747i	−0.544049	−	1.31345i
$244$		0			0
$245$	−8.09395	−	3.35263i	−0.517104	−	0.214191i
$246$		0			0
$247$	19.0568	−	19.0568i	1.21255	−	1.21255i
$248$		0			0
$249$	−6.46129	−	6.46129i	−0.409468	−	0.409468i
$250$		0			0
$251$	−11.4208	+	27.5723i	−0.720876	+	1.74035i	−0.0500337	+	0.998748i	$0.515933\pi$
$251$	−11.4208	+	27.5723i	−0.720876	+	1.74035i	−0.670842	+	0.741600i	$0.734067\pi$
$252$		0			0
$253$	−1.68485	+	0.697889i	−0.105926	+	0.0438759i
$254$		0			0
$255$	−42.0651			−2.63422
$256$		0			0
$257$	−17.5578			−1.09522			−0.547612	−	0.836732i	$-0.684463\pi$
$257$	−17.5578			−1.09522			−0.547612	+	0.836732i	$0.684463\pi$
$258$		0			0
$259$	20.2593	−	8.39168i	1.25885	−	0.521433i
$260$		0			0
$261$	1.31620	−	3.17758i	0.0814706	−	0.196687i
$262$		0			0
$263$	8.89551	+	8.89551i	0.548521	+	0.548521i	0.926013	−	0.377492i	$-0.123213\pi$
$263$	8.89551	+	8.89551i	0.548521	+	0.548521i	−0.377492	+	0.926013i	$0.623213\pi$
$264$		0			0
$265$	1.03757	−	1.03757i	0.0637371	−	0.0637371i
$266$		0			0
$267$	20.7992	+	8.61530i	1.27289	+	0.527248i
$268$		0			0
$269$	6.57732	+	15.8791i	0.401026	+	0.968164i	0.987417	+	0.158135i	$0.0505482\pi$
$269$	6.57732	+	15.8791i	0.401026	+	0.968164i	−0.586391	+	0.810028i	$0.699452\pi$
$270$		0			0
$271$		−	23.9379i		−	1.45412i	−0.686573	−	0.727061i	$-0.740886\pi$
$271$		−	23.9379i		−	1.45412i	0.686573	−	0.727061i	$-0.259114\pi$
$272$		0			0
$273$		−	25.1517i		−	1.52225i
$274$		0			0
$275$	3.95474	+	9.54758i	0.238480	+	0.575741i
$276$		0			0
$277$	−12.0506	−	4.99154i	−0.724053	−	0.299912i	−0.00994710	−	0.999951i	$-0.503166\pi$
$277$	−12.0506	−	4.99154i	−0.724053	−	0.299912i	−0.714105	+	0.700038i	$0.753166\pi$
$278$		0			0
$279$	8.02243	−	8.02243i	0.480290	−	0.480290i
$280$		0			0
$281$	15.0761	+	15.0761i	0.899365	+	0.899365i	0.995380	−	0.0960153i	$-0.0306098\pi$
$281$	15.0761	+	15.0761i	0.899365	+	0.899365i	−0.0960153	+	0.995380i	$0.530610\pi$
$282$		0			0
$283$	−0.984018	+	2.37563i	−0.0584938	+	0.141217i	−0.950424	−	0.310956i	$-0.899351\pi$
$283$	−0.984018	+	2.37563i	−0.0584938	+	0.141217i	0.891931	+	0.452172i	$0.149351\pi$
$284$		0			0
$285$	−31.5179	+	13.0552i	−1.86696	+	0.773321i
$286$		0			0
$287$	4.62082			0.272758
$288$		0			0
$289$	−22.8501			−1.34412
$290$		0			0
$291$	8.15640	−	3.37849i	0.478137	−	0.198051i
$292$		0			0
$293$	5.50973	−	13.3017i	0.321882	−	0.777091i	−0.677263	−	0.735741i	$-0.736834\pi$
$293$	5.50973	−	13.3017i	0.321882	−	0.777091i	0.999145	−	0.0413500i	$-0.0131659\pi$
$294$		0			0
$295$	15.0109	+	15.0109i	0.873970	+	0.873970i
$296$		0			0
$297$	0.544751	−	0.544751i	0.0316097	−	0.0316097i
$298$		0			0
$299$	−1.98697	−	0.823031i	−0.114910	−	0.0475971i
$300$		0			0
$301$	3.23917	+	7.82005i	0.186703	+	0.450740i
$302$		0			0
$303$		−	16.5541i		−	0.951008i
$304$		0			0
$305$			9.95262i			0.569885i
$306$		0			0
$307$	−7.12343	−	17.1975i	−0.406556	−	0.981513i	−0.986037	−	0.166527i	$-0.946745\pi$
$307$	−7.12343	−	17.1975i	−0.406556	−	0.981513i	0.579481	−	0.814986i	$-0.303255\pi$
$308$		0			0
$309$	35.1662	+	14.5663i	2.00054	+	0.828650i
$310$		0			0
$311$	−19.1862	+	19.1862i	−1.08795	+	1.08795i	−0.0922102	+	0.995740i	$0.529393\pi$
$311$	−19.1862	+	19.1862i	−1.08795	+	1.08795i	−0.995740	+	0.0922102i	$0.970607\pi$
$312$		0			0
$313$	−14.7525	−	14.7525i	−0.833858	−	0.833858i	0.154184	−	0.988042i	$-0.450725\pi$
$313$	−14.7525	−	14.7525i	−0.833858	−	0.833858i	−0.988042	+	0.154184i	$0.950725\pi$
$314$		0			0
$315$	−6.16224	+	14.8770i	−0.347203	+	0.838222i
$316$		0			0
$317$	−25.2679	+	10.4663i	−1.41918	+	0.587845i	−0.954655	−	0.297713i	$-0.903776\pi$
$317$	−25.2679	+	10.4663i	−1.41918	+	0.587845i	−0.464529	+	0.885558i	$0.653776\pi$
$318$		0			0
$319$	−5.00075			−0.279988
$320$		0			0
$321$	12.5383			0.699822
$322$		0			0
$323$	−29.8583	+	12.3677i	−1.66136	+	0.688157i
$324$		0			0
$325$	−4.66388	+	11.2596i	−0.258706	+	0.624570i
$326$		0			0
$327$	−10.0453	−	10.0453i	−0.555509	−	0.555509i
$328$		0			0
$329$	6.62538	−	6.62538i	0.365269	−	0.365269i
$330$		0			0
$331$	−5.64829	−	2.33960i	−0.310458	−	0.128596i	0.222014	−	0.975043i	$-0.428737\pi$
$331$	−5.64829	−	2.33960i	−0.310458	−	0.128596i	−0.532472	+	0.846448i	$0.678737\pi$
$332$		0			0
$333$	13.2847	+	32.0722i	0.727999	+	1.75754i
$334$		0			0
$335$		−	0.875346i		−	0.0478253i
$336$		0			0
$337$		−	2.82843i		−	0.154074i	−0.997028	−	0.0770371i	$-0.975454\pi$
$337$		−	2.82843i		−	0.154074i	0.997028	−	0.0770371i	$-0.0245460\pi$
$338$		0			0
$339$	−1.00657	−	2.43007i	−0.0546693	−	0.131983i
$340$		0			0
$341$	−15.2402	−	6.31269i	−0.825302	−	0.341851i
$342$		0			0
$343$	−14.0408	+	14.0408i	−0.758131	+	0.758131i
$344$		0			0
$345$	1.92504	+	1.92504i	0.103641	+	0.103641i
$346$		0			0
$347$	−6.25084	+	15.0909i	−0.335563	+	0.810120i	0.662568	+	0.749002i	$0.269467\pi$
$347$	−6.25084	+	15.0909i	−0.335563	+	0.810120i	−0.998131	+	0.0611179i	$0.980533\pi$
$348$		0			0
$349$	−15.1737	+	6.28515i	−0.812229	+	0.336436i	−0.749843	−	0.661616i	$-0.769871\pi$
$349$	−15.1737	+	6.28515i	−0.812229	+	0.336436i	−0.0623861	+	0.998052i	$0.519871\pi$
$350$		0			0
$351$	0.908538			0.0484942
$352$		0			0
$353$	−32.5234			−1.73105			−0.865524	−	0.500867i	$-0.833014\pi$
$353$	−32.5234			−1.73105			−0.865524	+	0.500867i	$0.833014\pi$
$354$		0			0
$355$	23.1249	−	9.57864i	1.22734	−	0.508382i
$356$		0			0
$357$	−11.5423	+	27.8656i	−0.610883	+	1.47480i
$358$		0			0
$359$	4.30331	+	4.30331i	0.227120	+	0.227120i	0.811488	−	0.584368i	$-0.198658\pi$
$359$	4.30331	+	4.30331i	0.227120	+	0.227120i	−0.584368	+	0.811488i	$0.698658\pi$
$360$		0			0
$361$	−5.09835	+	5.09835i	−0.268334	+	0.268334i
$362$		0			0
$363$	−20.3152	−	8.41484i	−1.06627	−	0.441665i
$364$		0			0
$365$	8.10008	+	19.5553i	0.423978	+	1.02357i
$366$		0			0
$367$		−	3.45619i		−	0.180412i	−0.995923	−	0.0902059i	$-0.971247\pi$
$367$		−	3.45619i		−	0.180412i	0.995923	−	0.0902059i	$-0.0287525\pi$
$368$		0			0
$369$			7.31515i			0.380811i
$370$		0			0
$371$	−0.402625	−	0.972022i	−0.0209032	−	0.0504649i
$372$		0			0
$373$	−4.84294	−	2.00601i	−0.250758	−	0.103867i	0.253764	−	0.967266i	$-0.418331\pi$
$373$	−4.84294	−	2.00601i	−0.250758	−	0.103867i	−0.504522	+	0.863399i	$0.668331\pi$
$374$		0			0
$375$	−12.6507	+	12.6507i	−0.653278	+	0.653278i
$376$		0			0
$377$	−4.17014	−	4.17014i	−0.214773	−	0.214773i
$378$		0			0
$379$	10.3208	−	24.9167i	0.530146	−	1.27989i	−0.401280	−	0.915956i	$-0.631435\pi$
$379$	10.3208	−	24.9167i	0.530146	−	1.27989i	0.931426	−	0.363931i	$-0.118565\pi$
$380$		0			0
$381$	49.6166	−	20.5519i	2.54193	−	1.05290i
$382$		0			0
$383$	−3.16870			−0.161913			−0.0809564	−	0.996718i	$-0.525797\pi$
$383$	−3.16870			−0.161913			−0.0809564	+	0.996718i	$0.525797\pi$
$384$		0			0
$385$	23.4128			1.19323
$386$		0			0
$387$	−12.3798	+	5.12788i	−0.629300	+	0.260665i
$388$		0			0
$389$	−5.94099	+	14.3428i	−0.301220	+	0.727209i	0.698710	+	0.715405i	$0.253758\pi$
$389$	−5.94099	+	14.3428i	−0.301220	+	0.727209i	−0.999930	+	0.0118047i	$0.996242\pi$
$390$		0			0
$391$	1.82367	+	1.82367i	0.0922271	+	0.0922271i
$392$		0			0
$393$	−29.7715	+	29.7715i	−1.50178	+	1.50178i
$394$		0			0
$395$	2.19175	+	0.907853i	0.110279	+	0.0456790i
$396$		0			0
$397$	−14.9345	−	36.0551i	−0.749542	−	1.80955i	−0.561670	−	0.827361i	$-0.689841\pi$
$397$	−14.9345	−	36.0551i	−0.749542	−	1.80955i	−0.187872	−	0.982194i	$-0.560159\pi$
$398$		0			0
$399$			24.4609i			1.22458i
$400$		0			0
$401$			9.14806i			0.456832i	0.973564	+	0.228416i	$0.0733547\pi$
$401$			9.14806i			0.456832i	−0.973564	+	0.228416i	$0.926645\pi$
$402$		0			0
$403$	−7.44465	−	17.9730i	−0.370844	−	0.895298i
$404$		0			0
$405$	21.9516	+	9.09264i	1.09078	+	0.451817i
$406$		0			0
$407$	35.6904	−	35.6904i	1.76911	−	1.76911i
$408$		0			0
$409$	−22.4503	−	22.4503i	−1.11010	−	1.11010i	−0.993136	−	0.116961i	$-0.962685\pi$
$409$	−22.4503	−	22.4503i	−1.11010	−	1.11010i	−0.116961	−	0.993136i	$-0.537315\pi$
$410$		0			0
$411$	−5.14340	+	12.4173i	−0.253705	+	0.612499i
$412$		0			0
$413$	14.0627	−	5.82496i	0.691980	−	0.286627i
$414$		0			0
$415$	10.0311			0.492409
$416$		0			0
$417$	7.50473			0.367508
$418$		0			0
$419$	−18.0491	+	7.47620i	−0.881758	+	0.365236i	−0.777178	−	0.629280i	$-0.783350\pi$
$419$	−18.0491	+	7.47620i	−0.881758	+	0.365236i	−0.104580	+	0.994516i	$0.533350\pi$
$420$		0			0
$421$	12.3332	−	29.7751i	0.601086	−	1.45115i	−0.271379	−	0.962472i	$-0.587480\pi$
$421$	12.3332	−	29.7751i	0.601086	−	1.45115i	0.872465	−	0.488677i	$-0.162520\pi$
$422$		0			0
$423$	10.4885	+	10.4885i	0.509970	+	0.509970i
$424$		0			0
$425$	10.3342	−	10.3342i	0.501284	−	0.501284i
$426$		0			0
$427$	6.59300	+	2.73091i	0.319058	+	0.132158i
$428$		0			0
$429$	−22.1546	−	53.4860i	−1.06964	−	2.58233i
$430$		0			0
$431$			20.3993i			0.982599i	0.870991	+	0.491300i	$0.163478\pi$
$431$			20.3993i			0.982599i	−0.870991	+	0.491300i	$0.836522\pi$
$432$		0			0
$433$		−	10.8560i		−	0.521706i	−0.965378	−	0.260853i	$-0.915996\pi$
$433$		−	10.8560i		−	0.521706i	0.965378	−	0.260853i	$-0.0840038\pi$
$434$		0			0
$435$	2.85682	+	6.89698i	0.136974	+	0.330685i
$436$		0			0
$437$	1.93240	+	0.800427i	0.0924393	+	0.0382896i
$438$		0			0
$439$	−8.44342	+	8.44342i	−0.402982	+	0.402982i	−0.879283	−	0.476300i	$-0.841977\pi$
$439$	−8.44342	+	8.44342i	−0.402982	+	0.402982i	0.476300	+	0.879283i	$0.341977\pi$
$440$		0			0
$441$	−7.03177	−	7.03177i	−0.334846	−	0.334846i
$442$		0			0
$443$	−2.37877	+	5.74286i	−0.113019	+	0.272852i	−0.970261	−	0.242062i	$-0.922176\pi$
$443$	−2.37877	+	5.74286i	−0.113019	+	0.272852i	0.857242	+	0.514914i	$0.172176\pi$
$444$		0			0
$445$	−22.8329	+	9.45770i	−1.08238	+	0.448338i
$446$		0			0
$447$	35.8683			1.69651
$448$		0			0
$449$	7.69940			0.363357			0.181679	−	0.983358i	$-0.441847\pi$
$449$	7.69940			0.363357			0.181679	+	0.983358i	$0.441847\pi$
$450$		0			0
$451$	9.82635	−	4.07021i	0.462705	−	0.191659i
$452$		0			0
$453$	−5.16971	+	12.4808i	−0.242894	+	0.586399i
$454$		0			0
$455$	19.5239	+	19.5239i	0.915297	+	0.915297i
$456$		0			0
$457$	21.0976	−	21.0976i	0.986906	−	0.986906i	−0.0130098	−	0.999915i	$-0.504141\pi$
$457$	21.0976	−	21.0976i	0.986906	−	0.986906i	0.999915	+	0.0130098i	$0.00414128\pi$
$458$		0			0
$459$	−1.00657	−	0.416935i	−0.0469826	−	0.0194608i
$460$		0			0
$461$	−15.4023	−	37.1844i	−0.717356	−	1.73185i	−0.680745	−	0.732520i	$-0.738344\pi$
$461$	−15.4023	−	37.1844i	−0.717356	−	1.73185i	−0.0366105	−	0.999330i	$-0.511656\pi$
$462$		0			0
$463$			23.4608i			1.09031i	0.838334	+	0.545157i	$0.183530\pi$
$463$			23.4608i			1.09031i	−0.838334	+	0.545157i	$0.816470\pi$
$464$		0			0
$465$			24.6254i			1.14197i
$466$		0			0
$467$	13.7752	+	33.2562i	0.637438	+	1.53891i	0.830081	+	0.557643i	$0.188294\pi$
$467$	13.7752	+	33.2562i	0.637438	+	1.53891i	−0.192642	+	0.981269i	$0.561706\pi$
$468$		0			0
$469$	−0.579863	−	0.240187i	−0.0267756	−	0.0110908i
$470$		0			0
$471$	−8.29177	+	8.29177i	−0.382065	+	0.382065i
$472$		0			0
$473$	13.7764	+	13.7764i	0.633441	+	0.633441i
$474$		0			0
$475$	4.53579	−	10.9504i	0.208116	−	0.502437i
$476$		0			0
$477$	1.53879	−	0.637389i	0.0704565	−	0.0291840i
$478$		0			0
$479$	−9.55206			−0.436445			−0.218222	−	0.975899i	$-0.570026\pi$
$479$	−9.55206			−0.436445			−0.218222	+	0.975899i	$0.570026\pi$
$480$		0			0
$481$	59.5246			2.71409
$482$		0			0
$483$	1.80344	−	0.747008i	0.0820592	−	0.0339900i
$484$		0			0
$485$	−3.70884	+	8.95394i	−0.168410	+	0.406577i
$486$		0			0
$487$	3.14134	+	3.14134i	0.142348	+	0.142348i	0.774690	−	0.632342i	$-0.217906\pi$
$487$	3.14134	+	3.14134i	0.142348	+	0.142348i	−0.632342	+	0.774690i	$0.717906\pi$
$488$		0			0
$489$	2.25114	−	2.25114i	0.101800	−	0.101800i
$490$		0			0
$491$	14.9157	+	6.17829i	0.673136	+	0.278822i	0.692954	−	0.720981i	$-0.256309\pi$
$491$	14.9157	+	6.17829i	0.673136	+	0.278822i	−0.0198181	+	0.999804i	$0.506309\pi$
$492$		0			0
$493$	2.70639	+	6.53380i	0.121890	+	0.294268i
$494$		0			0
$495$			37.0644i			1.66592i
$496$		0			0
$497$		−	17.9471i		−	0.805038i
$498$		0			0
$499$	−3.70515	−	8.94503i	−0.165865	−	0.400435i	0.818991	−	0.573806i	$-0.194534\pi$
$499$	−3.70515	−	8.94503i	−0.165865	−	0.400435i	−0.984856	+	0.173372i	$0.944534\pi$
$500$		0			0
$501$	11.3827	+	4.71489i	0.508543	+	0.210646i
$502$		0			0
$503$	−15.3899	+	15.3899i	−0.686200	+	0.686200i	−0.961390	−	0.275190i	$-0.911259\pi$
$503$	−15.3899	+	15.3899i	−0.686200	+	0.686200i	0.275190	+	0.961390i	$0.411259\pi$
$504$		0			0
$505$	12.8501	+	12.8501i	0.571821	+	0.571821i
$506$		0			0
$507$	13.8704	−	33.4862i	0.616008	−	1.48717i
$508$		0			0
$509$	23.1591	−	9.59281i	1.02651	−	0.425194i	0.195058	−	0.980792i	$-0.437511\pi$
$509$	23.1591	−	9.59281i	1.02651	−	0.425194i	0.831451	+	0.555598i	$0.187511\pi$
$510$		0			0
$511$	15.1768			0.671382
$512$		0			0
$513$	−0.883585			−0.0390112
$514$		0			0
$515$	−38.6048	+	15.9906i	−1.70113	+	0.704631i
$516$		0			0
$517$	8.25322	−	19.9250i	0.362976	−	0.876302i
$518$		0			0
$519$	−19.1161	−	19.1161i	−0.839104	−	0.839104i
$520$		0			0
$521$	23.9005	−	23.9005i	1.04710	−	1.04710i	0.0482659	−	0.998835i	$-0.484631\pi$
$521$	23.9005	−	23.9005i	1.04710	−	1.04710i	0.998835	−	0.0482659i	$-0.0153695\pi$
$522$		0			0
$523$	−37.5104	−	15.5373i	−1.64022	−	0.679400i	−0.643896	−	0.765113i	$-0.722683\pi$
$523$	−37.5104	−	15.5373i	−1.64022	−	0.679400i	−0.996320	+	0.0857135i	$0.972683\pi$
$524$		0			0
$525$	−4.23308	−	10.2195i	−0.184747	−	0.446018i
$526$		0			0
$527$			23.3287i			1.01621i
$528$		0			0
$529$			22.8331i			0.992743i
$530$		0			0
$531$	9.22139	+	22.2624i	0.400174	+	0.966107i
$532$		0			0
$533$	11.5884	+	4.80006i	0.501948	+	0.207914i
$534$		0			0
$535$	−9.73285	+	9.73285i	−0.420788	+	0.420788i
$536$		0			0
$537$	−24.9636	−	24.9636i	−1.07726	−	1.07726i
$538$		0			0
$539$	−5.53316	+	13.3582i	−0.238330	+	0.575380i
$540$		0			0
$541$	9.81494	−	4.06548i	0.421977	−	0.174789i	−0.161582	−	0.986859i	$-0.551660\pi$
$541$	9.81494	−	4.06548i	0.421977	−	0.174789i	0.583559	+	0.812071i	$0.301660\pi$
$542$		0			0
$543$	−27.1371			−1.16457
$544$		0			0
$545$	15.5954			0.668031
$546$		0			0
$547$	−21.1552	+	8.76275i	−0.904529	+	0.374668i	−0.785960	−	0.618277i	$-0.787831\pi$
$547$	−21.1552	+	8.76275i	−0.904529	+	0.374668i	−0.118569	+	0.992946i	$0.537831\pi$
$548$		0			0
$549$	−4.32326	+	10.4373i	−0.184512	+	0.445452i
$550$		0			0
$551$	4.05560	+	4.05560i	0.172775	+	0.172775i
$552$		0			0
$553$	1.20279	−	1.20279i	0.0511480	−	0.0511480i
$554$		0			0
$555$	−69.6130	−	28.8346i	−2.95491	−	1.22396i
$556$		0			0
$557$	−3.15850	−	7.62530i	−0.133830	−	0.323094i	0.842731	−	0.538335i	$-0.180946\pi$
$557$	−3.15850	−	7.62530i	−0.133830	−	0.323094i	−0.976561	+	0.215241i	$0.930946\pi$
$558$		0			0
$559$			22.9764i			0.971798i
$560$		0			0
$561$			69.4241i			2.93109i
$562$		0			0
$563$	−2.81983	−	6.80767i	−0.118842	−	0.286909i	0.853253	−	0.521497i	$-0.174626\pi$
$563$	−2.81983	−	6.80767i	−0.118842	−	0.286909i	−0.972095	+	0.234587i	$0.924626\pi$
$564$		0			0
$565$	2.66768	+	1.10499i	0.112230	+	0.0464873i
$566$		0			0
$567$	12.0466	−	12.0466i	0.505911	−	0.505911i
$568$		0			0
$569$	14.9201	+	14.9201i	0.625485	+	0.625485i	0.946929	−	0.321444i	$-0.104168\pi$
$569$	14.9201	+	14.9201i	0.625485	+	0.625485i	−0.321444	+	0.946929i	$0.604168\pi$
$570$		0			0
$571$	−9.19481	+	22.1982i	−0.384791	+	0.928968i	0.606233	+	0.795287i	$0.292680\pi$
$571$	−9.19481	+	22.1982i	−0.384791	+	0.928968i	−0.991024	+	0.133681i	$0.957320\pi$
$572$		0			0
$573$	−52.4910	+	21.7425i	−2.19284	+	0.908305i
$574$		0			0
$575$	−0.945857			−0.0394450
$576$		0			0
$577$	−4.71236			−0.196178			−0.0980891	−	0.995178i	$-0.531273\pi$
$577$	−4.71236			−0.196178			−0.0980891	+	0.995178i	$0.531273\pi$
$578$		0			0
$579$	−21.0326	+	8.71197i	−0.874084	+	0.362057i
$580$		0			0
$581$	2.75245	−	6.64501i	0.114191	−	0.275681i
$582$		0			0
$583$	−1.71239	−	1.71239i	−0.0709201	−	0.0709201i
$584$		0			0
$585$	−30.9080	+	30.9080i	−1.27789	+	1.27789i
$586$		0			0
$587$	−27.8409	−	11.5321i	−1.14912	−	0.475981i	−0.274881	−	0.961478i	$-0.588638\pi$
$587$	−27.8409	−	11.5321i	−1.14912	−	0.475981i	−0.874238	+	0.485498i	$0.838638\pi$
$588$		0			0
$589$	7.24019	+	17.4794i	0.298327	+	0.720224i
$590$		0			0
$591$		−	29.0182i		−	1.19365i
$592$		0			0
$593$		−	10.4902i		−	0.430780i	−0.976528	−	0.215390i	$-0.930898\pi$
$593$		−	10.4902i		−	0.430780i	0.976528	−	0.215390i	$-0.0691023\pi$
$594$		0			0
$595$	−12.6709	−	30.5903i	−0.519456	−	1.25408i
$596$		0			0
$597$	46.8267	+	19.3963i	1.91649	+	0.793837i
$598$		0			0
$599$	17.7913	−	17.7913i	0.726934	−	0.726934i	−0.243074	−	0.970008i	$-0.578156\pi$
$599$	17.7913	−	17.7913i	0.726934	−	0.726934i	0.970008	+	0.243074i	$0.0781558\pi$
$600$		0			0
$601$	−8.81138	−	8.81138i	−0.359424	−	0.359424i	0.504177	−	0.863600i	$-0.331796\pi$
$601$	−8.81138	−	8.81138i	−0.359424	−	0.359424i	−0.863600	+	0.504177i	$0.831796\pi$
$602$		0			0
$603$	0.380236	−	0.917971i	0.0154844	−	0.0373827i
$604$		0			0
$605$	22.3017	−	9.23765i	0.906691	−	0.375564i
$606$		0			0
$607$	−18.9547			−0.769347			−0.384673	−	0.923053i	$-0.625686\pi$
$607$	−18.9547			−0.769347			−0.384673	+	0.923053i	$0.625686\pi$
$608$		0			0
$609$	5.35271			0.216903
$610$		0			0
$611$	23.4979	−	9.73315i	0.950623	−	0.393761i
$612$		0			0
$613$	−1.21963	+	2.94446i	−0.0492605	+	0.118925i	−0.946594	−	0.322427i	$-0.895501\pi$
$613$	−1.21963	+	2.94446i	−0.0492605	+	0.118925i	0.897334	+	0.441353i	$0.145501\pi$
$614$		0			0
$615$	−11.2272	−	11.2272i	−0.452723	−	0.452723i
$616$		0			0
$617$	−7.36121	+	7.36121i	−0.296351	+	0.296351i	−0.839583	−	0.543232i	$-0.817201\pi$
$617$	−7.36121	+	7.36121i	−0.296351	+	0.296351i	0.543232	+	0.839583i	$0.317201\pi$
$618$		0			0
$619$	10.6490	+	4.41098i	0.428021	+	0.177292i	0.586285	−	0.810105i	$-0.300590\pi$
$619$	10.6490	+	4.41098i	0.428021	+	0.177292i	−0.158264	+	0.987397i	$0.550590\pi$
$620$		0			0
$621$	0.0269836	+	0.0651443i	0.00108282	+	0.00261415i
$622$		0			0
$623$			17.7205i			0.709957i
$624$		0			0
$625$		−	31.2158i		−	1.24863i
$626$		0			0
$627$	21.5462	+	52.0171i	0.860471	+	2.07736i
$628$		0			0
$629$	−65.9473	−	27.3163i	−2.62949	−	1.08917i
$630$		0			0
$631$	22.1664	−	22.1664i	0.882431	−	0.882431i	−0.111351	−	0.993781i	$-0.535518\pi$
$631$	22.1664	−	22.1664i	0.882431	−	0.882431i	0.993781	+	0.111351i	$0.0355177\pi$
$632$		0			0
$633$	−18.2562	−	18.2562i	−0.725620	−	0.725620i
$634$		0			0
$635$	−22.5614	+	54.4681i	−0.895323	+	2.16150i
$636$		0			0
$637$	−15.7536	+	6.52534i	−0.624179	+	0.258543i
$638$		0			0
$639$	28.4118			1.12395
$640$		0			0
$641$	−24.2598			−0.958205			−0.479102	−	0.877759i	$-0.659038\pi$
$641$	−24.2598			−0.958205			−0.479102	+	0.877759i	$0.659038\pi$
$642$		0			0
$643$	−25.8323	+	10.7001i	−1.01872	+	0.421970i	−0.828630	−	0.559796i	$-0.810879\pi$
$643$	−25.8323	+	10.7001i	−1.01872	+	0.421970i	−0.190094	+	0.981766i	$0.560879\pi$
$644$		0			0
$645$	11.1301	−	26.8705i	0.438248	−	1.05802i
$646$		0			0
$647$	25.2804	+	25.2804i	0.993875	+	0.993875i	0.999981	−	0.00610682i	$-0.00194387\pi$
$647$	25.2804	+	25.2804i	0.993875	+	0.993875i	−0.00610682	+	0.999981i	$0.501944\pi$
$648$		0			0
$649$	24.7740	−	24.7740i	0.972464	−	0.972464i
$650$		0			0
$651$	16.3128	+	6.75699i	0.639349	+	0.264827i
$652$		0			0
$653$	−8.64737	−	20.8766i	−0.338398	−	0.816965i	−0.997870	−	0.0652357i	$-0.979220\pi$
$653$	−8.64737	−	20.8766i	−0.338398	−	0.816965i	0.659472	−	0.751729i	$-0.270780\pi$
$654$		0			0
$655$		−	46.2202i		−	1.80597i
$656$		0			0
$657$			24.0261i			0.937349i
$658$		0			0
$659$	−18.1343	−	43.7800i	−0.706410	−	1.70543i	−0.708781	−	0.705428i	$-0.750755\pi$
$659$	−18.1343	−	43.7800i	−0.706410	−	1.70543i	0.00237069	−	0.999997i	$-0.499245\pi$
$660$		0			0
$661$	28.3694	+	11.7510i	1.10344	+	0.457060i	0.858674	−	0.512522i	$-0.171289\pi$
$661$	28.3694	+	11.7510i	1.10344	+	0.457060i	0.244767	+	0.969582i	$0.421289\pi$
$662$		0			0
$663$	−57.8929	+	57.8929i	−2.24837	+	2.24837i
$664$		0			0
$665$	−18.9877	−	18.9877i	−0.736313	−	0.736313i
$666$		0			0
$667$	0.175155	−	0.422862i	0.00678203	−	0.0163733i
$668$		0			0
$669$	−30.9961	+	12.8390i	−1.19838	+	0.496385i
$670$		0			0
$671$	16.4258			0.634110
$672$		0			0
$673$	5.36607			0.206847			0.103423	−	0.994637i	$-0.467020\pi$
$673$	5.36607			0.206847			0.103423	+	0.994637i	$0.467020\pi$
$674$		0			0
$675$	0.369154	−	0.152908i	0.0142087	−	0.00588545i
$676$		0			0
$677$	−7.48178	+	18.0626i	−0.287548	+	0.694202i	−0.999972	−	0.00754748i	$-0.997598\pi$
$677$	−7.48178	+	18.0626i	−0.287548	+	0.694202i	0.712424	+	0.701750i	$0.247598\pi$
$678$		0			0
$679$	4.91376	+	4.91376i	0.188573	+	0.188573i
$680$		0			0
$681$	32.6545	−	32.6545i	1.25132	−	1.25132i
$682$		0			0
$683$	34.9686	+	14.4845i	1.33804	+	0.554232i	0.932937	−	0.360041i	$-0.117237\pi$
$683$	34.9686	+	14.4845i	1.33804	+	0.554232i	0.405099	+	0.914273i	$0.367237\pi$
$684$		0			0
$685$	−5.64632	−	13.6314i	−0.215735	−	0.520830i
$686$		0			0
$687$			4.45438i			0.169945i
$688$		0			0
$689$		−	2.85593i		−	0.108802i
$690$		0			0
$691$	8.75408	+	21.1342i	0.333021	+	0.803983i	0.998349	+	0.0574327i	$0.0182915\pi$
$691$	8.75408	+	21.1342i	0.333021	+	0.803983i	−0.665329	+	0.746551i	$0.731709\pi$
$692$		0			0
$693$	24.5529	+	10.1701i	0.932687	+	0.386332i
$694$		0			0
$695$	−5.82553	+	5.82553i	−0.220975	+	0.220975i
$696$		0			0
$697$	−10.6360	−	10.6360i	−0.402866	−	0.402866i
$698$		0			0
$699$	0.808428	−	1.95172i	0.0305776	−	0.0738207i
$700$		0			0
$701$	12.7610	−	5.28579i	0.481978	−	0.199642i	−0.128446	−	0.991716i	$-0.540999\pi$
$701$	12.7610	−	5.28579i	0.481978	−	0.199642i	0.610424	+	0.792075i	$0.290999\pi$
$702$		0			0
$703$	−57.8898			−2.18336
$704$		0			0
$705$	−32.1953			−1.21254
$706$		0			0
$707$	12.0383	−	4.98644i	0.452748	−	0.187535i
$708$		0			0
$709$	−14.3378	+	34.6145i	−0.538467	+	1.29997i	0.387326	+	0.921943i	$0.373399\pi$
$709$	−14.3378	+	34.6145i	−0.538467	+	1.29997i	−0.925793	+	0.378031i	$0.876601\pi$
$710$		0			0
$711$	1.90412	+	1.90412i	0.0714102	+	0.0714102i
$712$		0			0
$713$	1.06760	−	1.06760i	0.0399819	−	0.0399819i
$714$		0			0
$715$	58.7159	+	24.3209i	2.19585	+	0.909551i
$716$		0			0
$717$	22.2207	+	53.6456i	0.829849	+	2.00343i
$718$		0			0
$719$		−	17.6095i		−	0.656725i	−0.944552	−	0.328362i	$-0.893503\pi$
$719$		−	17.6095i		−	0.656725i	0.944552	−	0.328362i	$-0.106497\pi$
$720$		0			0
$721$			29.9610i			1.11581i
$722$		0			0
$723$	−24.2096	−	58.4473i	−0.900366	−	2.17368i
$724$		0			0
$725$	−2.39624	−	0.992553i	−0.0889940	−	0.0368625i
$726$		0			0
$727$	−0.0431541	+	0.0431541i	−0.00160050	+	0.00160050i	−0.707907	−	0.706306i	$-0.750360\pi$
$727$	−0.0431541	+	0.0431541i	−0.00160050	+	0.00160050i	0.706306	+	0.707907i	$0.250360\pi$
$728$		0			0
$729$	19.9728	+	19.9728i	0.739735	+	0.739735i
$730$		0			0
$731$	10.5440	−	25.4555i	0.389985	−	0.941507i
$732$		0			0
$733$	0.128170	−	0.0530897i	0.00473407	−	0.00196091i	−0.380315	−	0.924857i	$-0.624184\pi$
$733$	0.128170	−	0.0530897i	0.00473407	−	0.00196091i	0.385049	+	0.922896i	$0.374184\pi$
$734$		0			0
$735$	21.5845			0.796155
$736$		0			0
$737$	−1.44467			−0.0532150
$738$		0			0
$739$	−6.61892	+	2.74164i	−0.243481	+	0.100853i	−0.501087	−	0.865397i	$-0.667066\pi$
$739$	−6.61892	+	2.74164i	−0.243481	+	0.100853i	0.257606	+	0.966250i	$0.417066\pi$
$740$		0			0
$741$	−25.4097	+	61.3445i	−0.933450	+	2.25355i
$742$		0			0
$743$	28.5981	+	28.5981i	1.04916	+	1.04916i	0.998727	+	0.0504342i	$0.0160605\pi$
$743$	28.5981	+	28.5981i	1.04916	+	1.04916i	0.0504342	+	0.998727i	$0.483939\pi$
$744$		0			0
$745$	−27.8427	+	27.8427i	−1.02008	+	1.02008i
$746$		0			0
$747$	10.5196	+	4.35736i	0.384892	+	0.159428i
$748$		0			0
$749$	3.77681	+	9.11803i	0.138002	+	0.333165i
$750$		0			0
$751$		−	26.5222i		−	0.967810i	−0.875121	−	0.483905i	$-0.839218\pi$
$751$		−	26.5222i		−	0.967810i	0.875121	−	0.483905i	$-0.160782\pi$
$752$		0			0
$753$		−	73.5282i		−	2.67952i
$754$		0			0
$755$	−5.67521	−	13.7012i	−0.206542	−	0.498637i
$756$		0			0
$757$	−9.35610	−	3.87542i	−0.340053	−	0.140855i	0.206121	−	0.978527i	$-0.433916\pi$
$757$	−9.35610	−	3.87542i	−0.340053	−	0.140855i	−0.546174	+	0.837672i	$0.683916\pi$
$758$		0			0
$759$	3.17708	−	3.17708i	0.115321	−	0.115321i
$760$		0			0
$761$	−10.5904	−	10.5904i	−0.383903	−	0.383903i	0.488603	−	0.872506i	$-0.337507\pi$
$761$	−10.5904	−	10.5904i	−0.383903	−	0.383903i	−0.872506	+	0.488603i	$0.837507\pi$
$762$		0			0
$763$	4.27923	−	10.3310i	0.154918	−	0.374006i
$764$		0			0
$765$	48.4269	−	20.0591i	1.75088	−	0.725238i
$766$		0			0
$767$	41.3181			1.49191
$768$		0			0
$769$	−31.3754			−1.13143			−0.565713	−	0.824602i	$-0.691399\pi$
$769$	−31.3754			−1.13143			−0.565713	+	0.824602i	$0.691399\pi$
$770$		0			0
$771$	39.9651	−	16.5541i	1.43931	−	0.596181i
$772$		0			0
$773$	17.3962	−	41.9982i	0.625699	−	1.51057i	−0.219219	−	0.975676i	$-0.570351\pi$
$773$	17.3962	−	41.9982i	0.625699	−	1.51057i	0.844918	−	0.534896i	$-0.179649\pi$
$774$		0			0
$775$	−6.04977	−	6.04977i	−0.217314	−	0.217314i
$776$		0			0
$777$	−38.2024	+	38.2024i	−1.37050	+	1.37050i
$778$		0			0
$779$	−11.2701	−	4.66822i	−0.403793	−	0.167257i
$780$		0			0
$781$	−15.8086	−	38.1652i	−0.565675	−	1.36566i
$782$		0			0
$783$			0.193352i			0.00690985i
$784$		0			0
$785$		−	12.8729i		−	0.459455i
$786$		0			0
$787$	−5.75461	−	13.8929i	−0.205130	−	0.495227i	0.787514	−	0.616296i	$-0.211368\pi$
$787$	−5.75461	−	13.8929i	−0.205130	−	0.495227i	−0.992644	+	0.121070i	$0.961368\pi$
$788$		0			0
$789$	−28.6350	−	11.8610i	−1.01943	−	0.422263i
$790$		0			0
$791$	1.46398	−	1.46398i	0.0520531	−	0.0520531i
$792$		0			0
$793$	13.6975	+	13.6975i	0.486411	+	0.486411i
$794$		0			0
$795$	−1.38346	+	3.33997i	−0.0490662	+	0.118456i
$796$		0			0
$797$	−23.6665	+	9.80297i	−0.838309	+	0.347239i	−0.760187	−	0.649705i	$-0.774892\pi$
$797$	−23.6665	+	9.80297i	−0.838309	+	0.347239i	−0.0781223	+	0.996944i	$0.524892\pi$
$798$		0			0
$799$	−30.4999			−1.07901
$800$		0			0
$801$	−28.0531			−0.991206
$802$		0			0
$803$	32.2740	−	13.3683i	1.13893	−	0.471759i
$804$		0			0
$805$	−0.820050	+	1.97978i	−0.0289030	+	0.0697779i
$806$		0			0
$807$	−29.9427	−	29.9427i	−1.05403	−	1.05403i
$808$		0			0
$809$	−24.9526	+	24.9526i	−0.877287	+	0.877287i	−0.993253	−	0.115966i	$-0.963004\pi$
$809$	−24.9526	+	24.9526i	−0.877287	+	0.877287i	0.115966	+	0.993253i	$0.463004\pi$
$810$		0			0
$811$	8.36388	+	3.46443i	0.293696	+	0.121653i	0.524666	−	0.851308i	$-0.324190\pi$
$811$	8.36388	+	3.46443i	0.293696	+	0.121653i	−0.230971	+	0.972961i	$0.574190\pi$
$812$		0			0
$813$	22.5695	+	54.4875i	0.791545	+	1.91096i
$814$		0			0
$815$			3.49488i			0.122420i
$816$		0			0
$817$		−	22.3454i		−	0.781765i
$818$		0			0
$819$	11.9938	+	28.9556i	0.419097	+	1.01179i
$820$		0			0
$821$	4.95402	+	2.05202i	0.172897	+	0.0716161i	0.467453	−	0.884018i	$-0.345172\pi$
$821$	4.95402	+	2.05202i	0.172897	+	0.0716161i	−0.294556	+	0.955634i	$0.595172\pi$
$822$		0			0
$823$	10.6645	−	10.6645i	0.371740	−	0.371740i	−0.496371	−	0.868111i	$-0.665334\pi$
$823$	10.6645	−	10.6645i	0.371740	−	0.371740i	0.868111	+	0.496371i	$0.165334\pi$
$824$		0			0
$825$	−18.0036	−	18.0036i	−0.626805	−	0.626805i
$826$		0			0
$827$	−2.88993	+	6.97690i	−0.100493	+	0.242611i	−0.966128	−	0.258065i	$-0.916915\pi$
$827$	−2.88993	+	6.97690i	−0.100493	+	0.242611i	0.865635	+	0.500676i	$0.166915\pi$
$828$		0			0
$829$	13.9875	−	5.79382i	0.485807	−	0.201228i	−0.126317	−	0.991990i	$-0.540316\pi$
$829$	13.9875	−	5.79382i	0.485807	−	0.201228i	0.612123	+	0.790762i	$0.290316\pi$
$830$		0			0
$831$	32.1359			1.11478
$832$		0			0
$833$	20.4479			0.708477
$834$		0			0
$835$	−12.4957	+	5.17591i	−0.432433	+	0.179120i
$836$		0			0
$837$	−0.244078	+	0.589256i	−0.00843657	+	0.0203677i
$838$		0			0
$839$	22.3549	+	22.3549i	0.771777	+	0.771777i	0.978417	−	0.206640i	$-0.0662529\pi$
$839$	22.3549	+	22.3549i	0.771777	+	0.771777i	−0.206640	+	0.978417i	$0.566253\pi$
$840$		0			0
$841$	−19.6186	+	19.6186i	−0.676504	+	0.676504i
$842$		0			0
$843$	−48.5306	−	20.1020i	−1.67148	−	0.692350i
$844$		0			0
$845$	15.2267	+	36.7605i	0.523814	+	1.26460i
$846$		0			0
$847$		−	17.3082i		−	0.594717i
$848$		0			0
$849$		−	6.33519i		−	0.217423i
$850$		0			0
$851$	1.76789	+	4.26806i	0.0606024	+	0.146307i
$852$		0			0
$853$	−4.33211	−	1.79442i	−0.148329	−	0.0614397i	0.307284	−	0.951618i	$-0.400580\pi$
$853$	−4.33211	−	1.79442i	−0.148329	−	0.0614397i	−0.455613	+	0.890178i	$0.650580\pi$
$854$		0			0
$855$	30.0592	−	30.0592i	1.02800	−	1.02800i
$856$		0			0
$857$	14.4779	+	14.4779i	0.494556	+	0.494556i	0.909738	−	0.415182i	$-0.136282\pi$
$857$	14.4779	+	14.4779i	0.494556	+	0.494556i	−0.415182	+	0.909738i	$0.636282\pi$
$858$		0			0
$859$	−12.0744	+	29.1502i	−0.411974	+	0.994593i	0.572633	+	0.819812i	$0.305922\pi$
$859$	−12.0744	+	29.1502i	−0.411974	+	0.994593i	−0.984607	+	0.174781i	$0.944078\pi$
$860$		0			0
$861$	−10.5179	+	4.35667i	−0.358450	+	0.148475i
$862$		0			0
$863$	−49.2601			−1.67683			−0.838417	−	0.545030i	$-0.816518\pi$
$863$	−49.2601			−1.67683			−0.838417	+	0.545030i	$0.816518\pi$
$864$		0			0
$865$	29.6777			1.00907
$866$		0			0
$867$	52.0115	−	21.5439i	1.76640	−	0.731668i
$868$		0			0
$869$	1.49832	−	3.61726i	0.0508269	−	0.122707i
$870$		0			0
$871$	−1.20471	−	1.20471i	−0.0408200	−	0.0408200i
$872$		0			0
$873$	−7.77889	+	7.77889i	−0.263276	+	0.263276i
$874$		0			0
$875$	−13.0104	−	5.38907i	−0.439830	−	0.182184i
$876$		0			0
$877$	−1.83156	−	4.42178i	−0.0618475	−	0.149313i	0.889934	−	0.456088i	$-0.150750\pi$
$877$	−1.83156	−	4.42178i	−0.0618475	−	0.149313i	−0.951782	+	0.306775i	$0.900750\pi$
$878$		0			0
$879$			35.4721i			1.19644i
$880$		0			0
$881$		−	9.99509i		−	0.336743i	−0.985724	−	0.168372i	$-0.946149\pi$
$881$		−	9.99509i		−	0.336743i	0.985724	−	0.168372i	$-0.0538509\pi$
$882$		0			0
$883$	11.4420	+	27.6233i	0.385053	+	0.929600i	0.990971	+	0.134073i	$0.0428057\pi$
$883$	11.4420	+	27.6233i	0.385053	+	0.929600i	−0.605919	+	0.795527i	$0.707194\pi$
$884$		0			0
$885$	−48.3208	−	20.0151i	−1.62429	−	0.672802i
$886$		0			0
$887$	−19.4541	+	19.4541i	−0.653206	+	0.653206i	−0.953764	−	0.300557i	$-0.902827\pi$
$887$	−19.4541	+	19.4541i	−0.653206	+	0.653206i	0.300557	+	0.953764i	$0.402827\pi$
$888$		0			0
$889$	29.8911	+	29.8911i	1.00252	+	1.00252i
$890$		0			0
$891$	15.0065	−	36.2288i	0.502735	−	1.21371i
$892$		0			0
$893$	−22.8525	+	9.46583i	−0.764731	+	0.316762i
$894$		0			0
$895$	38.7558			1.29546
$896$		0			0
$897$	5.29874			0.176920
$898$		0			0
$899$	3.82496	−	1.58435i	0.127569	−	0.0528410i
$900$		0			0
$901$	−1.31061	+	3.16409i	−0.0436627	+	0.105411i
$902$		0			0
$903$	−14.7460	−	14.7460i	−0.490717	−	0.490717i
$904$		0			0
$905$	21.0651	−	21.0651i	0.700229	−	0.700229i
$906$		0			0
$907$	52.7454	+	21.8478i	1.75138	+	0.725446i	0.997669	+	0.0682409i	$0.0217386\pi$
$907$	52.7454	+	21.8478i	1.75138	+	0.725446i	0.753712	+	0.657205i	$0.228261\pi$
$908$		0			0
$909$	7.89396	+	19.0577i	0.261826	+	0.632104i
$910$		0			0
$911$		−	49.1777i		−	1.62933i	−0.579931	−	0.814666i	$-0.696920\pi$
$911$		−	49.1777i		−	1.62933i	0.579931	−	0.814666i	$-0.303080\pi$
$912$		0			0
$913$		−	16.5553i		−	0.547902i
$914$		0			0
$915$	−9.38368	−	22.6542i	−0.310215	−	0.748925i
$916$		0			0
$917$	−30.6180	−	12.6824i	−1.01110	−	0.418810i
$918$		0			0
$919$	−23.6738	+	23.6738i	−0.780928	+	0.780928i	−0.979987	−	0.199060i	$-0.936211\pi$
$919$	−23.6738	+	23.6738i	−0.780928	+	0.780928i	0.199060	+	0.979987i	$0.436211\pi$
$920$		0			0
$921$	32.4288	+	32.4288i	1.06857	+	1.06857i
$922$		0			0
$923$	18.6433	−	45.0088i	0.613650	−	1.48148i
$924$		0			0
$925$	24.1858	−	10.0181i	0.795225	−	0.329393i
$926$		0			0
$927$	−47.4308			−1.55783
$928$		0			0
$929$	−14.4698			−0.474738			−0.237369	−	0.971419i	$-0.576285\pi$
$929$	−14.4698			−0.474738			−0.237369	+	0.971419i	$0.576285\pi$
$930$		0			0
$931$	15.3209	−	6.34612i	0.502122	−	0.207986i
$932$		0			0
$933$	25.5823	−	61.7612i	0.837527	−	2.02197i
$934$		0			0
$935$	−53.8903	−	53.8903i	−1.76240	−	1.76240i
$936$		0			0
$937$	36.4154	−	36.4154i	1.18964	−	1.18964i	0.212470	−	0.977168i	$-0.431849\pi$
$937$	36.4154	−	36.4154i	1.18964	−	1.18964i	0.977168	−	0.212470i	$-0.0681508\pi$
$938$		0			0
$939$	47.4888	+	19.6705i	1.54974	+	0.641922i
$940$		0			0
$941$	−7.00804	−	16.9189i	−0.228456	−	0.551541i	0.767534	−	0.641008i	$-0.221484\pi$
$941$	−7.00804	−	16.9189i	−0.228456	−	0.551541i	−0.995990	+	0.0894674i	$0.971484\pi$
$942$		0			0
$943$			0.973475i			0.0317007i
$944$		0			0
$945$		−	0.905247i		−	0.0294477i
$946$		0			0
$947$	9.96206	+	24.0505i	0.323723	+	0.781537i	0.999031	+	0.0440017i	$0.0140107\pi$
$947$	9.96206	+	24.0505i	0.323723	+	0.781537i	−0.675308	+	0.737536i	$0.735989\pi$
$948$		0			0
$949$	38.0613	+	15.7655i	1.23552	+	0.511769i
$950$		0			0
$951$	47.6468	−	47.6468i	1.54505	−	1.54505i
$952$		0			0
$953$	40.0406	+	40.0406i	1.29704	+	1.29704i	0.930337	+	0.366706i	$0.119514\pi$
$953$	40.0406	+	40.0406i	1.29704	+	1.29704i	0.366706	+	0.930337i	$0.380486\pi$
$954$		0			0
$955$	23.8684	−	57.6235i	0.772365	−	1.86465i
$956$		0			0
$957$	11.3827	−	4.71489i	0.367952	−	0.152411i
$958$		0			0
$959$	−10.5793			−0.341623
$960$		0			0
$961$	−17.3431			−0.559456
$962$		0			0
$963$	−14.4346	+	5.97901i	−0.465148	+	0.192671i
$964$		0			0
$965$	9.56383	−	23.0891i	0.307871	−	0.743265i
$966$		0			0
$967$	−3.12949	−	3.12949i	−0.100637	−	0.100637i	0.654995	−	0.755633i	$-0.272671\pi$
$967$	−3.12949	−	3.12949i	−0.100637	−	0.100637i	−0.755633	+	0.654995i	$0.772671\pi$
$968$		0			0
$969$	56.3029	−	56.3029i	1.80871	−	1.80871i
$970$		0			0
$971$	15.7328	+	6.51674i	0.504890	+	0.209132i	0.620565	−	0.784155i	$-0.286903\pi$
$971$	15.7328	+	6.51674i	0.504890	+	0.209132i	−0.115675	+	0.993287i	$0.536903\pi$
$972$		0			0
$973$	2.26058	+	5.45753i	0.0724710	+	0.174960i
$974$		0			0
$975$		−	30.0264i		−	0.961616i
$976$		0			0
$977$			29.3535i			0.939101i	0.882906	+	0.469550i	$0.155584\pi$
$977$			29.3535i			0.939101i	−0.882906	+	0.469550i	$0.844416\pi$
$978$		0			0
$979$	15.6090	+	37.6833i	0.498864	+	1.20436i
$980$		0			0
$981$	16.3548	+	6.77437i	0.522168	+	0.216289i
$982$		0			0
$983$	24.2452	−	24.2452i	0.773302	−	0.773302i	−0.205380	−	0.978682i	$-0.565843\pi$
$983$	24.2452	−	24.2452i	0.773302	−	0.773302i	0.978682	+	0.205380i	$0.0658432\pi$
$984$		0			0
$985$	22.5253	+	22.5253i	0.717716	+	0.717716i
$986$		0			0
$987$	−8.83409	+	21.3274i	−0.281192	+	0.678858i
$988$		0			0
$989$	−1.64746	+	0.682401i	−0.0523862	+	0.0216991i
$990$		0			0
$991$	−32.7200			−1.03939			−0.519693	−	0.854353i	$-0.673954\pi$
$991$	−32.7200			−1.03939			−0.519693	+	0.854353i	$0.673954\pi$
$992$		0			0
$993$	15.0625			0.477995
$994$		0			0
$995$	−51.4055	+	21.2928i	−1.62966	+	0.675028i
$996$		0			0
$997$	1.15216	−	2.78155i	0.0364892	−	0.0880927i	−0.904584	−	0.426295i	$-0.859819\pi$
$997$	1.15216	−	2.78155i	0.0364892	−	0.0880927i	0.941074	+	0.338202i	$0.109819\pi$
$998$		0			0
$999$	−1.37996	−	1.37996i	−0.0436599	−	0.0436599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.e.385.1	yes	16
4.3	odd	2	inner	1024.2.g.e.385.4	yes	16
8.3	odd	2		1024.2.g.b.385.1	✓	16
8.5	even	2		1024.2.g.b.385.4	yes	16
16.3	odd	4		1024.2.g.h.897.4	yes	16
16.5	even	4		1024.2.g.c.897.4	yes	16
16.11	odd	4		1024.2.g.c.897.1	yes	16
16.13	even	4		1024.2.g.h.897.1	yes	16
32.3	odd	8	inner	1024.2.g.e.641.4	yes	16
32.5	even	8		1024.2.g.c.129.4	yes	16
32.11	odd	8		1024.2.g.h.129.4	yes	16
32.13	even	8		1024.2.g.b.641.4	yes	16
32.19	odd	8		1024.2.g.b.641.1	yes	16
32.21	even	8		1024.2.g.h.129.1	yes	16
32.27	odd	8		1024.2.g.c.129.1	yes	16
32.29	even	8	inner	1024.2.g.e.641.1	yes	16
64.3	odd	16		4096.2.a.o.1.2		8
64.29	even	16		4096.2.a.o.1.1		8
64.35	odd	16		4096.2.a.n.1.7		8
64.61	even	16		4096.2.a.n.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.385.1	✓	16	8.3	odd	2
1024.2.g.b.385.4	yes	16	8.5	even	2
1024.2.g.b.641.1	yes	16	32.19	odd	8
1024.2.g.b.641.4	yes	16	32.13	even	8
1024.2.g.c.129.1	yes	16	32.27	odd	8
1024.2.g.c.129.4	yes	16	32.5	even	8
1024.2.g.c.897.1	yes	16	16.11	odd	4
1024.2.g.c.897.4	yes	16	16.5	even	4
1024.2.g.e.385.1	yes	16	1.1	even	1	trivial
1024.2.g.e.385.4	yes	16	4.3	odd	2	inner
1024.2.g.e.641.1	yes	16	32.29	even	8	inner
1024.2.g.e.641.4	yes	16	32.3	odd	8	inner
1024.2.g.h.129.1	yes	16	32.21	even	8
1024.2.g.h.129.4	yes	16	32.11	odd	8
1024.2.g.h.897.1	yes	16	16.13	even	4
1024.2.g.h.897.4	yes	16	16.3	odd	4
4096.2.a.n.1.7		8	64.35	odd	16
4096.2.a.n.1.8		8	64.61	even	16
4096.2.a.o.1.1		8	64.29	even	16
4096.2.a.o.1.2		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)

\(f(q)\)	\(=\)	\(q+(-2.27621 + 0.942835i) q^{3} +(1.03503 - 2.49877i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(2.17085 - 2.17085i) q^{9} +O(q^{10})\)	\(q+(-2.27621 + 0.942835i) q^{3} +(1.03503 - 2.49877i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(2.17085 - 2.17085i) q^{9} +(-4.12396 - 1.70820i) q^{11} +(-2.01451 - 4.86345i) q^{13} +6.66358i q^{15} +6.31269i q^{17} +(1.95918 + 4.72988i) q^{19} +(4.41421 + 1.82843i) q^{21} +(0.288890 - 0.288890i) q^{23} +(-1.63706 - 1.63706i) q^{25} +(-0.0660470 + 0.159452i) q^{27} +(1.03503 - 0.428722i) q^{29} +3.69552 q^{31} +10.9975 q^{33} +(-4.84584 + 2.00721i) q^{35} +(-4.32720 + 10.4468i) q^{37} +(9.17087 + 9.17087i) q^{39} +(-1.68485 + 1.68485i) q^{41} +(-4.03244 - 1.67029i) q^{43} +(-3.17758 - 7.67136i) q^{45} +4.83153i q^{47} -3.23917i q^{49} +(-5.95183 - 14.3690i) q^{51} +(0.501227 + 0.207615i) q^{53} +(-8.53682 + 8.53682i) q^{55} +(-8.91900 - 8.91900i) q^{57} +(-3.00366 + 7.25148i) q^{59} +(-3.39971 + 1.40820i) q^{61} -5.95371 q^{63} -14.2377 q^{65} +(0.299008 - 0.123853i) q^{67} +(-0.385197 + 0.929949i) q^{69} +(6.54392 + 6.54392i) q^{71} +(-5.53380 + 5.53380i) q^{73} +(5.26975 + 2.18280i) q^{75} +(3.31269 + 7.99755i) q^{77} +0.877131i q^{79} +8.78494i q^{81} +(1.41931 + 3.42652i) q^{83} +(15.7740 + 6.53380i) q^{85} +(-1.95172 + 1.95172i) q^{87} +(-6.46129 - 6.46129i) q^{89} +(-3.90671 + 9.43162i) q^{91} +(-8.41176 + 3.48427i) q^{93} +13.8467 q^{95} -3.58333 q^{97} +(-12.6608 + 5.24427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^5 - 16 * q^9	\( 16 q + 8 q^{5} - 16 q^{9} - 24 q^{13} + 48 q^{21} - 32 q^{25} + 8 q^{29} + 80 q^{33} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 q^{85} + 32 q^{89} - 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 16 * q^9 - 24 * q^13 + 48 * q^21 - 32 * q^25 + 8 * q^29 + 80 * q^33 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * q^85 + 32 * q^89 - 16 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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