LMFDB - Embedded newform 1024.2.g.h.897.4

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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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			897.4
Root			$-1.59056 + 0.685641i$ of defining polynomial
Character	$\chi$	$=$	1024.897
Dual form			1024.2.g.h.129.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.942835 + 2.27621i) q^{3} +(-2.49877 - 1.03503i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(-2.17085 + 2.17085i) q^{9} +O(q^{10})$	\(q+(0.942835 + 2.27621i) q^{3} +(-2.49877 - 1.03503i) q^{5} +(-1.37128 - 1.37128i) q^{7} +(-2.17085 + 2.17085i) q^{9} +(1.70820 - 4.12396i) q^{11} +(4.86345 - 2.01451i) q^{13} -6.66358i q^{15} +6.31269i q^{17} +(4.72988 - 1.95918i) q^{19} +(1.82843 - 4.41421i) q^{21} +(0.288890 - 0.288890i) q^{23} +(1.63706 + 1.63706i) q^{25} +(-0.159452 - 0.0660470i) q^{27} +(0.428722 + 1.03503i) q^{29} -3.69552 q^{31} +10.9975 q^{33} +(2.00721 + 4.84584i) q^{35} +(10.4468 + 4.32720i) q^{37} +(9.17087 + 9.17087i) q^{39} +(1.68485 - 1.68485i) q^{41} +(1.67029 - 4.03244i) q^{43} +(7.67136 - 3.17758i) q^{45} -4.83153i q^{47} -3.23917i q^{49} +(-14.3690 + 5.95183i) q^{51} +(0.207615 - 0.501227i) q^{53} +(-8.53682 + 8.53682i) q^{55} +(8.91900 + 8.91900i) q^{57} +(-7.25148 - 3.00366i) q^{59} +(-1.40820 - 3.39971i) q^{61} +5.95371 q^{63} -14.2377 q^{65} +(-0.123853 - 0.299008i) q^{67} +(0.929949 + 0.385197i) q^{69} +(6.54392 + 6.54392i) q^{71} +(5.53380 - 5.53380i) q^{73} +(-2.18280 + 5.26975i) q^{75} +(-7.99755 + 3.31269i) q^{77} -0.877131i q^{79} +8.78494i q^{81} +(3.42652 - 1.41931i) q^{83} +(6.53380 - 15.7740i) q^{85} +(-1.95172 + 1.95172i) q^{87} +(6.46129 + 6.46129i) q^{89} +(-9.43162 - 3.90671i) q^{91} +(-3.48427 - 8.41176i) q^{93} -13.8467 q^{95} -3.58333 q^{97} +(5.24427 + 12.6608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 16 q^{21} + 32 q^{25} - 24 q^{29} + 80 q^{33} + 40 q^{37} + 16 q^{41} + 24 q^{45} - 56 q^{53} + 80 q^{57} + 8 q^{61} + 32 q^{65} + 32 q^{69} + 32 q^{73} - 32 q^{77} + 48 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 - 16 * q^21 + 32 * q^25 - 24 * q^29 + 80 * q^33 + 40 * q^37 + 16 * q^41 + 24 * q^45 - 56 * q^53 + 80 * q^57 + 8 * q^61 + 32 * q^65 + 32 * q^69 + 32 * q^73 - 32 * q^77 + 48 * 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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

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

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
$3$	0.942835	+	2.27621i	0.544346	+	1.31417i	0.921630	+	0.388070i	$0.126858\pi$
$3$	0.942835	+	2.27621i	0.544346	+	1.31417i	−0.377284	+	0.926098i	$0.623142\pi$
$4$		0			0
$5$	−2.49877	−	1.03503i	−1.11749	−	0.462878i	−0.253976	−	0.967211i	$-0.581738\pi$
$5$	−2.49877	−	1.03503i	−1.11749	−	0.462878i	−0.863509	+	0.504333i	$0.831738\pi$
$6$		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
$11$	1.70820	−	4.12396i	0.515042	−	1.24342i	−0.425874	−	0.904783i	$-0.640033\pi$
$11$	1.70820	−	4.12396i	0.515042	−	1.24342i	0.940916	−	0.338640i	$-0.109967\pi$
$12$		0			0
$13$	4.86345	−	2.01451i	1.34888	−	0.558724i	0.412899	−	0.910777i	$-0.364516\pi$
$13$	4.86345	−	2.01451i	1.34888	−	0.558724i	0.935980	+	0.352053i	$0.114516\pi$
$14$		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
$19$	4.72988	−	1.95918i	1.08511	−	0.449467i	0.232810	−	0.972522i	$-0.425208\pi$
$19$	4.72988	−	1.95918i	1.08511	−	0.449467i	0.852299	+	0.523055i	$0.175208\pi$
$20$		0			0
$21$	1.82843	−	4.41421i	0.398996	−	0.963260i
$22$		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
$27$	−0.159452	−	0.0660470i	−0.0306865	−	0.0127108i
$28$		0			0
$29$	0.428722	+	1.03503i	0.0796116	+	0.192199i	0.958674	−	0.284508i	$-0.0918302\pi$
$29$	0.428722	+	1.03503i	0.0796116	+	0.192199i	−0.879062	+	0.476707i	$0.841830\pi$
$30$		0			0
$31$	−3.69552			−0.663735			−0.331867	−	0.943326i	$-0.607679\pi$
$31$	−3.69552			−0.663735			−0.331867	+	0.943326i	$0.607679\pi$
$32$		0			0
$33$	10.9975			1.91443
$34$		0			0
$35$	2.00721	+	4.84584i	0.339281	+	0.819096i
$36$		0			0
$37$	10.4468	+	4.32720i	1.71744	+	0.711387i	0.999889	+	0.0148821i	$0.00473731\pi$
$37$	10.4468	+	4.32720i	1.71744	+	0.711387i	0.717552	+	0.696505i	$0.245263\pi$
$38$		0			0
$39$	9.17087	+	9.17087i	1.46851	+	1.46851i
$40$		0			0
$41$	1.68485	−	1.68485i	0.263130	−	0.263130i	−0.563194	−	0.826324i	$-0.690428\pi$
$41$	1.68485	−	1.68485i	0.263130	−	0.263130i	0.826324	+	0.563194i	$0.190428\pi$
$42$		0			0
$43$	1.67029	−	4.03244i	0.254717	−	0.614941i	−0.743856	−	0.668340i	$-0.767005\pi$
$43$	1.67029	−	4.03244i	0.254717	−	0.614941i	0.998573	+	0.0533985i	$0.0170053\pi$
$44$		0			0
$45$	7.67136	−	3.17758i	1.14358	−	0.473686i
$46$		0			0
$47$		−	4.83153i		−	0.704750i	−0.935859	−	0.352375i	$-0.885374\pi$
$47$		−	4.83153i		−	0.704750i	0.935859	−	0.352375i	$-0.114626\pi$
$48$		0			0
$49$		−	3.23917i		−	0.462739i
$50$		0			0
$51$	−14.3690	+	5.95183i	−2.01206	+	0.833423i
$52$		0			0
$53$	0.207615	−	0.501227i	0.0285181	−	0.0688488i	−0.908979	−	0.416842i	$-0.863137\pi$
$53$	0.207615	−	0.501227i	0.0285181	−	0.0688488i	0.937497	+	0.347993i	$0.113137\pi$
$54$		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
$59$	−7.25148	−	3.00366i	−0.944062	−	0.391043i	−0.143066	−	0.989713i	$-0.545696\pi$
$59$	−7.25148	−	3.00366i	−0.944062	−	0.391043i	−0.800996	+	0.598670i	$0.795696\pi$
$60$		0			0
$61$	−1.40820	−	3.39971i	−0.180302	−	0.435288i	0.807727	−	0.589557i	$-0.200698\pi$
$61$	−1.40820	−	3.39971i	−0.180302	−	0.435288i	−0.988029	+	0.154269i	$0.950698\pi$
$62$		0			0
$63$	5.95371			0.750097
$64$		0			0
$65$	−14.2377			−1.76597
$66$		0			0
$67$	−0.123853	−	0.299008i	−0.0151311	−	0.0365297i	0.916133	−	0.400873i	$-0.131293\pi$
$67$	−0.123853	−	0.299008i	−0.0151311	−	0.0365297i	−0.931265	+	0.364344i	$0.881293\pi$
$68$		0			0
$69$	0.929949	+	0.385197i	0.111953	+	0.0463723i
$70$		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	−0.304750	−	0.952432i	$-0.598573\pi$
$73$	5.53380	−	5.53380i	0.647682	−	0.647682i	0.952432	+	0.304750i	$0.0985730\pi$
$74$		0			0
$75$	−2.18280	+	5.26975i	−0.252048	+	0.608498i
$76$		0			0
$77$	−7.99755	+	3.31269i	−0.911405	+	0.377516i
$78$		0			0
$79$		−	0.877131i		−	0.0986849i	−0.998782	−	0.0493425i	$-0.984287\pi$
$79$		−	0.877131i		−	0.0986849i	0.998782	−	0.0493425i	$-0.0157126\pi$
$80$		0			0
$81$			8.78494i			0.976104i
$82$		0			0
$83$	3.42652	−	1.41931i	0.376110	−	0.155790i	−0.186617	−	0.982433i	$-0.559752\pi$
$83$	3.42652	−	1.41931i	0.376110	−	0.155790i	0.562727	+	0.826643i	$0.309752\pi$
$84$		0			0
$85$	6.53380	−	15.7740i	0.708690	−	1.71093i
$86$		0			0
$87$	−1.95172	+	1.95172i	−0.209246	+	0.209246i
$88$		0			0
$89$	6.46129	+	6.46129i	0.684896	+	0.684896i	0.961099	−	0.276203i	$-0.0890764\pi$
$89$	6.46129	+	6.46129i	0.684896	+	0.684896i	−0.276203	+	0.961099i	$0.589076\pi$
$90$		0			0
$91$	−9.43162	−	3.90671i	−0.988703	−	0.409534i
$92$		0			0
$93$	−3.48427	−	8.41176i	−0.361301	−	0.872259i
$94$		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
$99$	5.24427	+	12.6608i	0.527069	+	1.27246i
$100$		0			0
$101$	6.20761	+	2.57128i	0.617681	+	0.255852i	0.669509	−	0.742804i	$-0.266505\pi$
$101$	6.20761	+	2.57128i	0.617681	+	0.255852i	−0.0518279	+	0.998656i	$0.516505\pi$
$102$		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
$107$	1.94753	−	4.70174i	0.188274	−	0.454535i	−0.801353	−	0.598192i	$-0.795886\pi$
$107$	1.94753	−	4.70174i	0.188274	−	0.454535i	0.989628	+	0.143657i	$0.0458861\pi$
$108$		0			0
$109$	−5.32720	+	2.20660i	−0.510253	+	0.211354i	−0.622930	−	0.782278i	$-0.714058\pi$
$109$	−5.32720	+	2.20660i	−0.510253	+	0.211354i	0.112676	+	0.993632i	$0.464058\pi$
$110$		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
$115$	−1.02088	+	0.422862i	−0.0951974	+	0.0394321i
$116$		0			0
$117$	−6.18464	+	14.9311i	−0.571771	+	1.38038i
$118$		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
$123$	5.42362	+	2.24653i	0.489031	+	0.202563i
$124$		0			0
$125$	2.77889	+	6.70884i	0.248552	+	0.600057i
$126$		0			0
$127$	21.7979			1.93425			0.967127	−	0.254294i	$-0.0818431\pi$
$127$	21.7979			1.93425			0.967127	+	0.254294i	$0.0818431\pi$
$128$		0			0
$129$	10.7535			0.946790
$130$		0			0
$131$	−6.53973	−	15.7883i	−0.571379	−	1.37943i	−0.900382	−	0.435101i	$-0.856713\pi$
$131$	−6.53973	−	15.7883i	−0.571379	−	1.37943i	0.329003	−	0.944329i	$-0.393287\pi$
$132$		0			0
$133$	−9.17259	−	3.79941i	−0.795364	−	0.329451i
$134$		0			0
$135$	0.330073	+	0.330073i	0.0284082	+	0.0284082i
$136$		0			0
$137$	−3.85744	+	3.85744i	−0.329564	+	0.329564i	−0.852420	−	0.522857i	$-0.824866\pi$
$137$	−3.85744	+	3.85744i	−0.329564	+	0.329564i	0.522857	+	0.852420i	$0.324866\pi$
$138$		0			0
$139$	1.16568	−	2.81420i	0.0988715	−	0.238697i	−0.866703	−	0.498825i	$-0.833765\pi$
$139$	1.16568	−	2.81420i	0.0988715	−	0.238697i	0.965574	+	0.260128i	$0.0837649\pi$
$140$		0			0
$141$	10.9975	−	4.55533i	0.926160	−	0.383628i
$142$		0			0
$143$		−	23.4979i		−	1.96499i
$144$		0			0
$145$		−	3.03003i		−	0.251631i
$146$		0			0
$147$	7.37302	−	3.05400i	0.608116	−	0.251890i
$148$		0			0
$149$	−5.57128	+	13.4503i	−0.456417	+	1.10189i	0.513421	+	0.858137i	$0.328378\pi$
$149$	−5.57128	+	13.4503i	−0.456417	+	1.10189i	−0.969838	+	0.243751i	$0.921622\pi$
$150$		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
$155$	9.23426	+	3.82496i	0.741714	+	0.307228i
$156$		0			0
$157$	1.82140	+	4.39725i	0.145364	+	0.350939i	0.979745	−	0.200248i	$-0.0641749\pi$
$157$	1.82140	+	4.39725i	0.145364	+	0.350939i	−0.834381	+	0.551187i	$0.814175\pi$
$158$		0			0
$159$	1.33664			0.106003
$160$		0			0
$161$	−0.792299			−0.0624419
$162$		0			0
$163$	0.494494	+	1.19381i	0.0387317	+	0.0935067i	0.942062	−	0.335440i	$-0.108885\pi$
$163$	0.494494	+	1.19381i	0.0387317	+	0.0935067i	−0.903330	+	0.428946i	$0.858885\pi$
$164$		0			0
$165$	−27.4804	−	11.3827i	−2.13934	−	0.886145i
$166$		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
$171$	−6.01479	+	14.5210i	−0.459962	+	1.11045i
$172$		0			0
$173$	−10.1376	+	4.19912i	−0.770745	+	0.319253i	−0.733174	−	0.680041i	$-0.761962\pi$
$173$	−10.1376	+	4.19912i	−0.770745	+	0.319253i	−0.0375707	+	0.999294i	$0.511962\pi$
$174$		0			0
$175$		−	4.48973i		−	0.339392i
$176$		0			0
$177$		−	19.3378i		−	1.45352i
$178$		0			0
$179$	13.2386	−	5.48359i	0.989497	−	0.409863i	0.171562	−	0.985173i	$-0.445119\pi$
$179$	13.2386	−	5.48359i	0.989497	−	0.409863i	0.817935	+	0.575310i	$0.195119\pi$
$180$		0			0
$181$	4.21510	−	10.1761i	0.313306	−	0.756387i	−0.686272	−	0.727345i	$-0.740754\pi$
$181$	4.21510	−	10.1761i	0.313306	−	0.756387i	0.999578	−	0.0290424i	$-0.00924577\pi$
$182$		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
$187$	26.0333	+	10.7834i	1.90374	+	0.788557i
$188$		0			0
$189$	0.128084	+	0.309222i	0.00931674	+	0.0224926i
$190$		0			0
$191$	−23.0607			−1.66862			−0.834308	−	0.551299i	$-0.814132\pi$
$191$	−23.0607			−1.66862			−0.834308	+	0.551299i	$0.814132\pi$
$192$		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
$195$	−13.4238	−	32.4080i	−0.961301	−	2.32079i
$196$		0			0
$197$	10.8815	+	4.50727i	0.775276	+	0.321130i	0.735007	−	0.678059i	$-0.237179\pi$
$197$	10.8815	+	4.50727i	0.775276	+	0.321130i	0.0402686	+	0.999189i	$0.487179\pi$
$198$		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
$203$	0.831414	−	2.00721i	0.0583538	−	0.140879i
$204$		0			0
$205$	−5.95394	+	2.46620i	−0.415841	+	0.172247i
$206$		0			0
$207$			1.25428i			0.0871782i
$208$		0			0
$209$		−	22.8525i		−	1.58074i
$210$		0			0
$211$	9.68155	−	4.01023i	0.666506	−	0.276076i	−0.0236676	−	0.999720i	$-0.507534\pi$
$211$	9.68155	−	4.01023i	0.666506	−	0.276076i	0.690173	+	0.723644i	$0.257534\pi$
$212$		0			0
$213$	−8.72547	+	21.0651i	−0.597859	+	1.44336i
$214$		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
$219$	17.8135	+	7.37860i	1.20373	+	0.498600i
$220$		0			0
$221$	12.7170	+	30.7015i	0.855436	+	2.06521i
$222$		0			0
$223$	−13.6174			−0.911892			−0.455946	−	0.890008i	$-0.650699\pi$
$223$	−13.6174			−0.911892			−0.455946	+	0.890008i	$0.650699\pi$
$224$		0			0
$225$	−7.10762			−0.473841
$226$		0			0
$227$	7.17300	+	17.3172i	0.476089	+	1.14938i	0.961429	+	0.275054i	$0.0886959\pi$
$227$	7.17300	+	17.3172i	0.476089	+	1.14938i	−0.485340	+	0.874326i	$0.661304\pi$
$228$		0			0
$229$	−1.67035	−	0.691880i	−0.110380	−	0.0457207i	0.326810	−	0.945090i	$-0.394026\pi$
$229$	−1.67035	−	0.691880i	−0.110380	−	0.0457207i	−0.437190	+	0.899369i	$0.644026\pi$
$230$		0			0
$231$	−15.0807	−	15.0807i	−0.992240	−	0.992240i
$232$		0			0
$233$	0.606304	−	0.606304i	0.0397203	−	0.0397203i	−0.686968	−	0.726688i	$-0.741059\pi$
$233$	0.606304	−	0.606304i	0.0397203	−	0.0397203i	0.726688	+	0.686968i	$0.241059\pi$
$234$		0			0
$235$	−5.00075	+	12.0729i	−0.326213	+	0.787548i
$236$		0			0
$237$	1.99653	−	0.826990i	0.129689	−	0.0537188i
$238$		0			0
$239$			23.5680i			1.52449i	0.647291	+	0.762243i	$0.275902\pi$
$239$			23.5680i			1.52449i	−0.647291	+	0.762243i	$0.724098\pi$
$240$		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
$243$	−20.4747	+	8.48089i	−1.31345	+	0.544049i
$244$		0			0
$245$	−3.35263	+	8.09395i	−0.214191	+	0.517104i
$246$		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
$251$	−27.5723	−	11.4208i	−1.74035	−	0.720876i	−0.998748	−	0.0500337i	$-0.984067\pi$
$251$	−27.5723	−	11.4208i	−1.74035	−	0.720876i	−0.741600	−	0.670842i	$-0.765933\pi$
$252$		0			0
$253$	−0.697889	−	1.68485i	−0.0438759	−	0.105926i
$254$		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
$259$	−8.39168	−	20.2593i	−0.521433	−	1.25885i
$260$		0			0
$261$	−3.17758	−	1.31620i	−0.196687	−	0.0814706i
$262$		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
$267$	−8.61530	+	20.7992i	−0.527248	+	1.27289i
$268$		0			0
$269$	−15.8791	+	6.57732i	−0.968164	+	0.401026i	−0.810028	−	0.586391i	$-0.800548\pi$
$269$	−15.8791	+	6.57732i	−0.968164	+	0.401026i	−0.158135	+	0.987417i	$0.550548\pi$
$270$		0			0
$271$			23.9379i			1.45412i	0.686573	+	0.727061i	$0.259114\pi$
$271$			23.9379i			1.45412i	−0.686573	+	0.727061i	$0.740886\pi$
$272$		0			0
$273$		−	25.1517i		−	1.52225i
$274$		0			0
$275$	9.54758	−	3.95474i	0.575741	−	0.238480i
$276$		0			0
$277$	−4.99154	+	12.0506i	−0.299912	+	0.724053i	0.700038	+	0.714105i	$0.253166\pi$
$277$	−4.99154	+	12.0506i	−0.299912	+	0.724053i	−0.999951	+	0.00994710i	$0.996834\pi$
$278$		0			0
$279$	8.02243	−	8.02243i	0.480290	−	0.480290i
$280$		0			0
$281$	−15.0761	−	15.0761i	−0.899365	−	0.899365i	0.0960153	−	0.995380i	$-0.469390\pi$
$281$	−15.0761	−	15.0761i	−0.899365	−	0.899365i	−0.995380	+	0.0960153i	$0.969390\pi$
$282$		0			0
$283$	−2.37563	−	0.984018i	−0.141217	−	0.0584938i	0.310956	−	0.950424i	$-0.399351\pi$
$283$	−2.37563	−	0.984018i	−0.141217	−	0.0584938i	−0.452172	+	0.891931i	$0.649351\pi$
$284$		0			0
$285$	−13.0552	−	31.5179i	−0.773321	−	1.86696i
$286$		0			0
$287$	−4.62082			−0.272758
$288$		0			0
$289$	−22.8501			−1.34412
$290$		0			0
$291$	−3.37849	−	8.15640i	−0.198051	−	0.478137i
$292$		0			0
$293$	−13.3017	−	5.50973i	−0.777091	−	0.321882i	−0.0413500	−	0.999145i	$-0.513166\pi$
$293$	−13.3017	−	5.50973i	−0.777091	−	0.321882i	−0.735741	+	0.677263i	$0.763166\pi$
$294$		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
$299$	0.823031	−	1.98697i	0.0475971	−	0.114910i
$300$		0			0
$301$	−7.82005	+	3.23917i	−0.450740	+	0.186703i
$302$		0			0
$303$			16.5541i			0.951008i
$304$		0			0
$305$			9.95262i			0.569885i
$306$		0			0
$307$	−17.1975	+	7.12343i	−0.981513	+	0.406556i	−0.814986	−	0.579481i	$-0.803255\pi$
$307$	−17.1975	+	7.12343i	−0.981513	+	0.406556i	−0.166527	+	0.986037i	$0.553255\pi$
$308$		0			0
$309$	14.5663	−	35.1662i	0.828650	−	2.00054i
$310$		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	0.988042	−	0.154184i	$-0.0492749\pi$
$313$	14.7525	+	14.7525i	0.833858	+	0.833858i	−0.154184	+	0.988042i	$0.549275\pi$
$314$		0			0
$315$	−14.8770	−	6.16224i	−0.838222	−	0.347203i
$316$		0			0
$317$	−10.4663	−	25.2679i	−0.587845	−	1.41918i	−0.885558	−	0.464529i	$-0.846224\pi$
$317$	−10.4663	−	25.2679i	−0.587845	−	1.41918i	0.297713	−	0.954655i	$-0.403776\pi$
$318$		0			0
$319$	5.00075			0.279988
$320$		0			0
$321$	12.5383			0.699822
$322$		0			0
$323$	12.3677	+	29.8583i	0.688157	+	1.66136i
$324$		0			0
$325$	11.2596	+	4.66388i	0.624570	+	0.258706i
$326$		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
$331$	2.33960	−	5.64829i	0.128596	−	0.310458i	−0.846448	−	0.532472i	$-0.821263\pi$
$331$	2.33960	−	5.64829i	0.128596	−	0.310458i	0.975043	+	0.222014i	$0.0712631\pi$
$332$		0			0
$333$	−32.0722	+	13.2847i	−1.75754	+	0.727999i
$334$		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
$339$	−2.43007	+	1.00657i	−0.131983	+	0.0546693i
$340$		0			0
$341$	−6.31269	+	15.2402i	−0.341851	+	0.825302i
$342$		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
$347$	−15.0909	−	6.25084i	−0.810120	−	0.335563i	−0.0611179	−	0.998131i	$-0.519467\pi$
$347$	−15.0909	−	6.25084i	−0.810120	−	0.335563i	−0.749002	+	0.662568i	$0.769467\pi$
$348$		0			0
$349$	−6.28515	−	15.1737i	−0.336436	−	0.812229i	−0.998052	−	0.0623861i	$-0.980129\pi$
$349$	−6.28515	−	15.1737i	−0.336436	−	0.812229i	0.661616	−	0.749843i	$-0.269871\pi$
$350$		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
$355$	−9.57864	−	23.1249i	−0.508382	−	1.22734i
$356$		0			0
$357$	27.8656	+	11.5423i	1.47480	+	0.610883i
$358$		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
$363$	8.41484	−	20.3152i	0.441665	−	1.06627i
$364$		0			0
$365$	−19.5553	+	8.10008i	−1.02357	+	0.423978i
$366$		0			0
$367$			3.45619i			0.180412i	0.995923	+	0.0902059i	$0.0287525\pi$
$367$			3.45619i			0.180412i	−0.995923	+	0.0902059i	$0.971247\pi$
$368$		0			0
$369$			7.31515i			0.380811i
$370$		0			0
$371$	−0.972022	+	0.402625i	−0.0504649	+	0.0209032i
$372$		0			0
$373$	−2.00601	+	4.84294i	−0.103867	+	0.250758i	−0.967266	−	0.253764i	$-0.918331\pi$
$373$	−2.00601	+	4.84294i	−0.103867	+	0.250758i	0.863399	+	0.504522i	$0.168331\pi$
$374$		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
$379$	24.9167	+	10.3208i	1.27989	+	0.530146i	0.915956	−	0.401280i	$-0.131435\pi$
$379$	24.9167	+	10.3208i	1.27989	+	0.530146i	0.363931	+	0.931426i	$0.381435\pi$
$380$		0			0
$381$	20.5519	+	49.6166i	1.05290	+	2.54193i
$382$		0			0
$383$	3.16870			0.161913			0.0809564	−	0.996718i	$-0.474203\pi$
$383$	3.16870			0.161913			0.0809564	+	0.996718i	$0.474203\pi$
$384$		0			0
$385$	23.4128			1.19323
$386$		0			0
$387$	5.12788	+	12.3798i	0.260665	+	0.629300i
$388$		0			0
$389$	14.3428	+	5.94099i	0.727209	+	0.301220i	0.715405	−	0.698710i	$-0.246242\pi$
$389$	14.3428	+	5.94099i	0.727209	+	0.301220i	0.0118047	+	0.999930i	$0.496242\pi$
$390$		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
$395$	−0.907853	+	2.19175i	−0.0456790	+	0.110279i
$396$		0			0
$397$	36.0551	−	14.9345i	1.80955	−	0.749542i	0.827361	−	0.561670i	$-0.189841\pi$
$397$	36.0551	−	14.9345i	1.80955	−	0.749542i	0.982194	−	0.187872i	$-0.0601590\pi$
$398$		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
$403$	−17.9730	+	7.44465i	−0.895298	+	0.370844i
$404$		0			0
$405$	9.09264	−	21.9516i	0.451817	−	1.09078i
$406$		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	$0.0373154\pi$
$409$	22.4503	+	22.4503i	1.11010	+	1.11010i	0.116961	+	0.993136i	$0.462685\pi$
$410$		0			0
$411$	−12.4173	−	5.14340i	−0.612499	−	0.253705i
$412$		0			0
$413$	5.82496	+	14.0627i	0.286627	+	0.691980i
$414$		0			0
$415$	−10.0311			−0.492409
$416$		0			0
$417$	7.50473			0.367508
$418$		0			0
$419$	7.47620	+	18.0491i	0.365236	+	0.881758i	0.994516	+	0.104580i	$0.0333498\pi$
$419$	7.47620	+	18.0491i	0.365236	+	0.881758i	−0.629280	+	0.777178i	$0.716650\pi$
$420$		0			0
$421$	−29.7751	−	12.3332i	−1.45115	−	0.601086i	−0.488677	−	0.872465i	$-0.662520\pi$
$421$	−29.7751	−	12.3332i	−1.45115	−	0.601086i	−0.962472	+	0.271379i	$0.912520\pi$
$422$		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
$427$	−2.73091	+	6.59300i	−0.132158	+	0.319058i
$428$		0			0
$429$	53.4860	−	22.1546i	2.58233	−	1.06964i
$430$		0			0
$431$		−	20.3993i		−	0.982599i	−0.870991	−	0.491300i	$-0.836522\pi$
$431$		−	20.3993i		−	0.982599i	0.870991	−	0.491300i	$-0.163478\pi$
$432$		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
$435$	6.89698	−	2.85682i	0.330685	−	0.136974i
$436$		0			0
$437$	0.800427	−	1.93240i	0.0382896	−	0.0924393i
$438$		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
$443$	−5.74286	−	2.37877i	−0.272852	−	0.113019i	0.242062	−	0.970261i	$-0.422176\pi$
$443$	−5.74286	−	2.37877i	−0.272852	−	0.113019i	−0.514914	+	0.857242i	$0.672176\pi$
$444$		0			0
$445$	−9.45770	−	22.8329i	−0.448338	−	1.08238i
$446$		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
$451$	−4.07021	−	9.82635i	−0.191659	−	0.462705i
$452$		0			0
$453$	12.4808	+	5.16971i	0.586399	+	0.242894i
$454$		0			0
$455$	19.5239	+	19.5239i	0.915297	+	0.915297i
$456$		0			0
$457$	−21.0976	+	21.0976i	−0.986906	+	0.986906i	−0.999915	−	0.0130098i	$-0.995859\pi$
$457$	−21.0976	+	21.0976i	−0.986906	+	0.986906i	0.0130098	+	0.999915i	$0.495859\pi$
$458$		0			0
$459$	0.416935	−	1.00657i	0.0194608	−	0.0469826i
$460$		0			0
$461$	37.1844	−	15.4023i	1.73185	−	0.717356i	0.732520	−	0.680745i	$-0.238344\pi$
$461$	37.1844	−	15.4023i	1.73185	−	0.717356i	0.999330	−	0.0366105i	$-0.0116561\pi$
$462$		0			0
$463$		−	23.4608i		−	1.09031i	−0.838334	−	0.545157i	$-0.816470\pi$
$463$		−	23.4608i		−	1.09031i	0.838334	−	0.545157i	$-0.183530\pi$
$464$		0			0
$465$			24.6254i			1.14197i
$466$		0			0
$467$	33.2562	−	13.7752i	1.53891	−	0.637438i	0.557643	−	0.830081i	$-0.311706\pi$
$467$	33.2562	−	13.7752i	1.53891	−	0.637438i	0.981269	+	0.192642i	$0.0617057\pi$
$468$		0			0
$469$	−0.240187	+	0.579863i	−0.0110908	+	0.0267756i
$470$		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
$475$	10.9504	+	4.53579i	0.502437	+	0.208116i
$476$		0			0
$477$	0.637389	+	1.53879i	0.0291840	+	0.0704565i
$478$		0			0
$479$	9.55206			0.436445			0.218222	−	0.975899i	$-0.429974\pi$
$479$	9.55206			0.436445			0.218222	+	0.975899i	$0.429974\pi$
$480$		0			0
$481$	59.5246			2.71409
$482$		0			0
$483$	−0.747008	−	1.80344i	−0.0339900	−	0.0820592i
$484$		0			0
$485$	8.95394	+	3.70884i	0.406577	+	0.168410i
$486$		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
$491$	−6.17829	+	14.9157i	−0.278822	+	0.673136i	−0.999804	−	0.0198181i	$-0.993691\pi$
$491$	−6.17829	+	14.9157i	−0.278822	+	0.673136i	0.720981	+	0.692954i	$0.243691\pi$
$492$		0			0
$493$	−6.53380	+	2.70639i	−0.294268	+	0.121890i
$494$		0			0
$495$		−	37.0644i		−	1.66592i
$496$		0			0
$497$		−	17.9471i		−	0.805038i
$498$		0			0
$499$	−8.94503	+	3.70515i	−0.400435	+	0.165865i	−0.573806	−	0.818991i	$-0.694534\pi$
$499$	−8.94503	+	3.70515i	−0.400435	+	0.165865i	0.173372	+	0.984856i	$0.444534\pi$
$500$		0			0
$501$	4.71489	−	11.3827i	0.210646	−	0.508543i
$502$		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
$507$	33.4862	+	13.8704i	1.48717	+	0.616008i
$508$		0			0
$509$	9.59281	+	23.1591i	0.425194	+	1.02651i	0.980792	+	0.195058i	$0.0624894\pi$
$509$	9.59281	+	23.1591i	0.425194	+	1.02651i	−0.555598	+	0.831451i	$0.687511\pi$
$510$		0			0
$511$	−15.1768			−0.671382
$512$		0			0
$513$	−0.883585			−0.0390112
$514$		0			0
$515$	15.9906	+	38.6048i	0.704631	+	1.70113i
$516$		0			0
$517$	−19.9250	−	8.25322i	−0.876302	−	0.362976i
$518$		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	$0.515369\pi$
$521$	−23.9005	+	23.9005i	−1.04710	+	1.04710i	−0.998835	+	0.0482659i	$0.984631\pi$
$522$		0			0
$523$	15.5373	−	37.5104i	0.679400	−	1.64022i	−0.0857135	−	0.996320i	$-0.527317\pi$
$523$	15.5373	−	37.5104i	0.679400	−	1.64022i	0.765113	−	0.643896i	$-0.222683\pi$
$524$		0			0
$525$	10.2195	−	4.23308i	0.446018	−	0.184747i
$526$		0			0
$527$		−	23.3287i		−	1.01621i
$528$		0			0
$529$			22.8331i			0.992743i
$530$		0			0
$531$	22.2624	−	9.22139i	0.966107	−	0.400174i
$532$		0			0
$533$	4.80006	−	11.5884i	0.207914	−	0.501948i
$534$		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
$539$	−13.3582	−	5.53316i	−0.575380	−	0.238330i
$540$		0			0
$541$	4.06548	+	9.81494i	0.174789	+	0.421977i	0.986859	−	0.161582i	$-0.0516597\pi$
$541$	4.06548	+	9.81494i	0.174789	+	0.421977i	−0.812071	+	0.583559i	$0.801660\pi$
$542$		0			0
$543$	27.1371			1.16457
$544$		0			0
$545$	15.5954			0.668031
$546$		0			0
$547$	8.76275	+	21.1552i	0.374668	+	0.904529i	0.992946	+	0.118569i	$0.0378308\pi$
$547$	8.76275	+	21.1552i	0.374668	+	0.904529i	−0.618277	+	0.785960i	$0.712169\pi$
$548$		0			0
$549$	10.4373	+	4.32326i	0.445452	+	0.184512i
$550$		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
$555$	28.8346	−	69.6130i	1.22396	−	2.95491i
$556$		0			0
$557$	7.62530	−	3.15850i	0.323094	−	0.133830i	−0.215241	−	0.976561i	$-0.569054\pi$
$557$	7.62530	−	3.15850i	0.323094	−	0.133830i	0.538335	+	0.842731i	$0.319054\pi$
$558$		0			0
$559$		−	22.9764i		−	0.971798i
$560$		0			0
$561$			69.4241i			2.93109i
$562$		0			0
$563$	−6.80767	+	2.81983i	−0.286909	+	0.118842i	−0.521497	−	0.853253i	$-0.674626\pi$
$563$	−6.80767	+	2.81983i	−0.286909	+	0.118842i	0.234587	+	0.972095i	$0.424626\pi$
$564$		0			0
$565$	1.10499	−	2.66768i	0.0464873	−	0.112230i
$566$		0			0
$567$	12.0466	−	12.0466i	0.505911	−	0.505911i
$568$		0			0
$569$	−14.9201	−	14.9201i	−0.625485	−	0.625485i	0.321444	−	0.946929i	$-0.395832\pi$
$569$	−14.9201	−	14.9201i	−0.625485	−	0.625485i	−0.946929	+	0.321444i	$0.895832\pi$
$570$		0			0
$571$	−22.1982	−	9.19481i	−0.928968	−	0.384791i	−0.133681	−	0.991024i	$-0.542680\pi$
$571$	−22.1982	−	9.19481i	−0.928968	−	0.384791i	−0.795287	+	0.606233i	$0.792680\pi$
$572$		0			0
$573$	−21.7425	−	52.4910i	−0.908305	−	2.19284i
$574$		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
$579$	8.71197	+	21.0326i	0.362057	+	0.874084i
$580$		0			0
$581$	−6.64501	−	2.75245i	−0.275681	−	0.114191i
$582$		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
$587$	11.5321	−	27.8409i	0.475981	−	1.14912i	−0.485498	−	0.874238i	$-0.661362\pi$
$587$	11.5321	−	27.8409i	0.475981	−	1.14912i	0.961478	−	0.274881i	$-0.0886384\pi$
$588$		0			0
$589$	−17.4794	+	7.24019i	−0.720224	+	0.298327i
$590$		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
$595$	−30.5903	+	12.6709i	−1.25408	+	0.519456i
$596$		0			0
$597$	19.3963	−	46.8267i	0.793837	−	1.91649i
$598$		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	0.863600	−	0.504177i	$-0.168204\pi$
$601$	8.81138	+	8.81138i	0.359424	+	0.359424i	−0.504177	+	0.863600i	$0.668204\pi$
$602$		0			0
$603$	0.917971	+	0.380236i	0.0373827	+	0.0154844i
$604$		0			0
$605$	9.23765	+	22.3017i	0.375564	+	0.906691i
$606$		0			0
$607$	18.9547			0.769347			0.384673	−	0.923053i	$-0.374314\pi$
$607$	18.9547			0.769347			0.384673	+	0.923053i	$0.374314\pi$
$608$		0			0
$609$	5.35271			0.216903
$610$		0			0
$611$	−9.73315	−	23.4979i	−0.393761	−	0.950623i
$612$		0			0
$613$	2.94446	+	1.21963i	0.118925	+	0.0492605i	0.441353	−	0.897334i	$-0.354499\pi$
$613$	2.94446	+	1.21963i	0.118925	+	0.0492605i	−0.322427	+	0.946594i	$0.604499\pi$
$614$		0			0
$615$	−11.2272	−	11.2272i	−0.452723	−	0.452723i
$616$		0			0
$617$	7.36121	−	7.36121i	0.296351	−	0.296351i	−0.543232	−	0.839583i	$-0.682799\pi$
$617$	7.36121	−	7.36121i	0.296351	−	0.296351i	0.839583	+	0.543232i	$0.182799\pi$
$618$		0			0
$619$	−4.41098	+	10.6490i	−0.177292	+	0.428021i	−0.987397	−	0.158264i	$-0.949410\pi$
$619$	−4.41098	+	10.6490i	−0.177292	+	0.428021i	0.810105	+	0.586285i	$0.199410\pi$
$620$		0			0
$621$	−0.0651443	+	0.0269836i	−0.00261415	+	0.00108282i
$622$		0			0
$623$		−	17.7205i		−	0.709957i
$624$		0			0
$625$		−	31.2158i		−	1.24863i
$626$		0			0
$627$	52.0171	−	21.5462i	2.07736	−	0.860471i
$628$		0			0
$629$	−27.3163	+	65.9473i	−1.08917	+	2.62949i
$630$		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
$635$	−54.4681	−	22.5614i	−2.16150	−	0.895323i
$636$		0			0
$637$	−6.52534	−	15.7536i	−0.258543	−	0.624179i
$638$		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
$643$	10.7001	+	25.8323i	0.421970	+	1.01872i	0.981766	+	0.190094i	$0.0608794\pi$
$643$	10.7001	+	25.8323i	0.421970	+	1.01872i	−0.559796	+	0.828630i	$0.689121\pi$
$644$		0			0
$645$	−26.8705	−	11.1301i	−1.05802	−	0.438248i
$646$		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
$651$	−6.75699	+	16.3128i	−0.264827	+	0.639349i
$652$		0			0
$653$	20.8766	−	8.64737i	0.816965	−	0.338398i	0.0652357	−	0.997870i	$-0.479220\pi$
$653$	20.8766	−	8.64737i	0.816965	−	0.338398i	0.751729	+	0.659472i	$0.229220\pi$
$654$		0			0
$655$			46.2202i			1.80597i
$656$		0			0
$657$			24.0261i			0.937349i
$658$		0			0
$659$	−43.7800	+	18.1343i	−1.70543	+	0.706410i	−0.999997	−	0.00237069i	$-0.999245\pi$
$659$	−43.7800	+	18.1343i	−1.70543	+	0.706410i	−0.705428	+	0.708781i	$0.749245\pi$
$660$		0			0
$661$	11.7510	−	28.3694i	0.457060	−	1.10344i	−0.512522	−	0.858674i	$-0.671289\pi$
$661$	11.7510	−	28.3694i	0.457060	−	1.10344i	0.969582	−	0.244767i	$-0.0787113\pi$
$662$		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
$667$	0.422862	+	0.175155i	0.0163733	+	0.00678203i
$668$		0			0
$669$	−12.8390	−	30.9961i	−0.496385	−	1.19838i
$670$		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
$675$	−0.152908	−	0.369154i	−0.00588545	−	0.0142087i
$676$		0			0
$677$	18.0626	+	7.48178i	0.694202	+	0.287548i	0.701750	−	0.712424i	$-0.252402\pi$
$677$	18.0626	+	7.48178i	0.694202	+	0.287548i	−0.00754748	+	0.999972i	$0.502402\pi$
$678$		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
$683$	−14.4845	+	34.9686i	−0.554232	+	1.33804i	0.360041	+	0.932937i	$0.382763\pi$
$683$	−14.4845	+	34.9686i	−0.554232	+	1.33804i	−0.914273	+	0.405099i	$0.867237\pi$
$684$		0			0
$685$	13.6314	−	5.64632i	0.520830	−	0.215735i
$686$		0			0
$687$		−	4.45438i		−	0.169945i
$688$		0			0
$689$		−	2.85593i		−	0.108802i
$690$		0			0
$691$	21.1342	−	8.75408i	0.803983	−	0.333021i	0.0574327	−	0.998349i	$-0.481709\pi$
$691$	21.1342	−	8.75408i	0.803983	−	0.333021i	0.746551	+	0.665329i	$0.231709\pi$
$692$		0			0
$693$	10.1701	−	24.5529i	0.386332	−	0.932687i
$694$		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
$699$	1.95172	+	0.808428i	0.0738207	+	0.0305776i
$700$		0			0
$701$	5.28579	+	12.7610i	0.199642	+	0.481978i	0.991716	−	0.128446i	$-0.0409990\pi$
$701$	5.28579	+	12.7610i	0.199642	+	0.481978i	−0.792075	+	0.610424i	$0.790999\pi$
$702$		0			0
$703$	57.8898			2.18336
$704$		0			0
$705$	−32.1953			−1.21254
$706$		0			0
$707$	−4.98644	−	12.0383i	−0.187535	−	0.452748i
$708$		0			0
$709$	34.6145	+	14.3378i	1.29997	+	0.538467i	0.921943	−	0.387326i	$-0.126601\pi$
$709$	34.6145	+	14.3378i	1.29997	+	0.538467i	0.378031	+	0.925793i	$0.376601\pi$
$710$		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
$715$	−24.3209	+	58.7159i	−0.909551	+	2.19585i
$716$		0			0
$717$	−53.6456	+	22.2207i	−2.00343	+	0.829849i
$718$		0			0
$719$			17.6095i			0.656725i	0.944552	+	0.328362i	$0.106497\pi$
$719$			17.6095i			0.656725i	−0.944552	+	0.328362i	$0.893503\pi$
$720$		0			0
$721$			29.9610i			1.11581i
$722$		0			0
$723$	−58.4473	+	24.2096i	−2.17368	+	0.900366i
$724$		0			0
$725$	−0.992553	+	2.39624i	−0.0368625	+	0.0889940i
$726$		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
$731$	25.4555	+	10.5440i	0.941507	+	0.389985i
$732$		0			0
$733$	0.0530897	+	0.128170i	0.00196091	+	0.00473407i	0.924857	−	0.380315i	$-0.124184\pi$
$733$	0.0530897	+	0.128170i	0.00196091	+	0.00473407i	−0.922896	+	0.385049i	$0.874184\pi$
$734$		0			0
$735$	−21.5845			−0.796155
$736$		0			0
$737$	−1.44467			−0.0532150
$738$		0			0
$739$	2.74164	+	6.61892i	0.100853	+	0.243481i	0.966250	−	0.257606i	$-0.0829337\pi$
$739$	2.74164	+	6.61892i	0.100853	+	0.243481i	−0.865397	+	0.501087i	$0.832934\pi$
$740$		0			0
$741$	61.3445	+	25.4097i	2.25355	+	0.933450i
$742$		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
$747$	−4.35736	+	10.5196i	−0.159428	+	0.384892i
$748$		0			0
$749$	−9.11803	+	3.77681i	−0.333165	+	0.138002i
$750$		0			0
$751$			26.5222i			0.967810i	0.875121	+	0.483905i	$0.160782\pi$
$751$			26.5222i			0.967810i	−0.875121	+	0.483905i	$0.839218\pi$
$752$		0			0
$753$		−	73.5282i		−	2.67952i
$754$		0			0
$755$	−13.7012	+	5.67521i	−0.498637	+	0.206542i
$756$		0			0
$757$	−3.87542	+	9.35610i	−0.140855	+	0.340053i	−0.978527	−	0.206121i	$-0.933916\pi$
$757$	−3.87542	+	9.35610i	−0.140855	+	0.340053i	0.837672	+	0.546174i	$0.183916\pi$
$758$		0			0
$759$	3.17708	−	3.17708i	0.115321	−	0.115321i
$760$		0			0
$761$	10.5904	+	10.5904i	0.383903	+	0.383903i	0.872506	−	0.488603i	$-0.162493\pi$
$761$	10.5904	+	10.5904i	0.383903	+	0.383903i	−0.488603	+	0.872506i	$0.662493\pi$
$762$		0			0
$763$	10.3310	+	4.27923i	0.374006	+	0.154918i
$764$		0			0
$765$	20.0591	+	48.4269i	0.725238	+	1.75088i
$766$		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
$771$	−16.5541	−	39.9651i	−0.596181	−	1.43931i
$772$		0			0
$773$	−41.9982	−	17.3962i	−1.51057	−	0.625699i	−0.534896	−	0.844918i	$-0.679649\pi$
$773$	−41.9982	−	17.3962i	−1.51057	−	0.625699i	−0.975676	+	0.219219i	$0.929649\pi$
$774$		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
$779$	4.66822	−	11.2701i	0.167257	−	0.403793i
$780$		0			0
$781$	38.1652	−	15.8086i	1.36566	−	0.565675i
$782$		0			0
$783$		−	0.193352i		−	0.00690985i
$784$		0			0
$785$		−	12.8729i		−	0.459455i
$786$		0			0
$787$	−13.8929	+	5.75461i	−0.495227	+	0.205130i	−0.616296	−	0.787514i	$-0.711368\pi$
$787$	−13.8929	+	5.75461i	−0.495227	+	0.205130i	0.121070	+	0.992644i	$0.461368\pi$
$788$		0			0
$789$	−11.8610	+	28.6350i	−0.422263	+	1.01943i
$790$		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
$795$	−3.33997	−	1.38346i	−0.118456	−	0.0490662i
$796$		0			0
$797$	−9.80297	−	23.6665i	−0.347239	−	0.838309i	−0.996944	−	0.0781223i	$-0.975108\pi$
$797$	−9.80297	−	23.6665i	−0.347239	−	0.838309i	0.649705	−	0.760187i	$-0.274892\pi$
$798$		0			0
$799$	30.4999			1.07901
$800$		0			0
$801$	−28.0531			−0.991206
$802$		0			0
$803$	−13.3683	−	32.2740i	−0.471759	−	1.13893i
$804$		0			0
$805$	1.97978	+	0.820050i	0.0697779	+	0.0289030i
$806$		0			0
$807$	−29.9427	−	29.9427i	−1.05403	−	1.05403i
$808$		0			0
$809$	24.9526	−	24.9526i	0.877287	−	0.877287i	−0.115966	−	0.993253i	$-0.536996\pi$
$809$	24.9526	−	24.9526i	0.877287	−	0.877287i	0.993253	+	0.115966i	$0.0369963\pi$
$810$		0			0
$811$	−3.46443	+	8.36388i	−0.121653	+	0.293696i	−0.972961	−	0.230971i	$-0.925810\pi$
$811$	−3.46443	+	8.36388i	−0.121653	+	0.293696i	0.851308	+	0.524666i	$0.175810\pi$
$812$		0			0
$813$	−54.4875	+	22.5695i	−1.91096	+	0.791545i
$814$		0			0
$815$		−	3.49488i		−	0.122420i
$816$		0			0
$817$		−	22.3454i		−	0.781765i
$818$		0			0
$819$	28.9556	−	11.9938i	1.01179	−	0.419097i
$820$		0			0
$821$	2.05202	−	4.95402i	0.0716161	−	0.172897i	−0.884018	−	0.467453i	$-0.845172\pi$
$821$	2.05202	−	4.95402i	0.0716161	−	0.172897i	0.955634	+	0.294556i	$0.0951718\pi$
$822$		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
$827$	−6.97690	−	2.88993i	−0.242611	−	0.100493i	0.258065	−	0.966128i	$-0.416915\pi$
$827$	−6.97690	−	2.88993i	−0.242611	−	0.100493i	−0.500676	+	0.865635i	$0.666915\pi$
$828$		0			0
$829$	5.79382	+	13.9875i	0.201228	+	0.485807i	0.991990	−	0.126317i	$-0.0403155\pi$
$829$	5.79382	+	13.9875i	0.201228	+	0.485807i	−0.790762	+	0.612123i	$0.790316\pi$
$830$		0			0
$831$	−32.1359			−1.11478
$832$		0			0
$833$	20.4479			0.708477
$834$		0			0
$835$	5.17591	+	12.4957i	0.179120	+	0.432433i
$836$		0			0
$837$	0.589256	+	0.244078i	0.0203677	+	0.00843657i
$838$		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
$843$	20.1020	−	48.5306i	0.692350	−	1.67148i
$844$		0			0
$845$	−36.7605	+	15.2267i	−1.26460	+	0.523814i
$846$		0			0
$847$			17.3082i			0.594717i
$848$		0			0
$849$		−	6.33519i		−	0.217423i
$850$		0			0
$851$	4.26806	−	1.76789i	0.146307	−	0.0606024i
$852$		0			0
$853$	−1.79442	+	4.33211i	−0.0614397	+	0.148329i	−0.951618	−	0.307284i	$-0.900580\pi$
$853$	−1.79442	+	4.33211i	−0.0614397	+	0.148329i	0.890178	+	0.455613i	$0.150580\pi$
$854$		0			0
$855$	30.0592	−	30.0592i	1.02800	−	1.02800i
$856$		0			0
$857$	−14.4779	−	14.4779i	−0.494556	−	0.494556i	0.415182	−	0.909738i	$-0.363718\pi$
$857$	−14.4779	−	14.4779i	−0.494556	−	0.494556i	−0.909738	+	0.415182i	$0.863718\pi$
$858$		0			0
$859$	−29.1502	−	12.0744i	−0.994593	−	0.411974i	−0.174781	−	0.984607i	$-0.555922\pi$
$859$	−29.1502	−	12.0744i	−0.994593	−	0.411974i	−0.819812	+	0.572633i	$0.805922\pi$
$860$		0			0
$861$	−4.35667	−	10.5179i	−0.148475	−	0.358450i
$862$		0			0
$863$	49.2601			1.67683			0.838417	−	0.545030i	$-0.183482\pi$
$863$	49.2601			1.67683			0.838417	+	0.545030i	$0.183482\pi$
$864$		0			0
$865$	29.6777			1.00907
$866$		0			0
$867$	−21.5439	−	52.0115i	−0.731668	−	1.76640i
$868$		0			0
$869$	−3.61726	−	1.49832i	−0.122707	−	0.0508269i
$870$		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
$875$	5.38907	−	13.0104i	0.182184	−	0.439830i
$876$		0			0
$877$	4.42178	−	1.83156i	0.149313	−	0.0618475i	−0.306775	−	0.951782i	$-0.599250\pi$
$877$	4.42178	−	1.83156i	0.149313	−	0.0618475i	0.456088	+	0.889934i	$0.349250\pi$
$878$		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
$883$	27.6233	−	11.4420i	0.929600	−	0.385053i	0.134073	−	0.990971i	$-0.457194\pi$
$883$	27.6233	−	11.4420i	0.929600	−	0.385053i	0.795527	+	0.605919i	$0.207194\pi$
$884$		0			0
$885$	−20.0151	+	48.3208i	−0.672802	+	1.62429i
$886$		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
$891$	36.2288	+	15.0065i	1.21371	+	0.502735i
$892$		0			0
$893$	−9.46583	−	22.8525i	−0.316762	−	0.764731i
$894$		0			0
$895$	−38.7558			−1.29546
$896$		0			0
$897$	5.29874			0.176920
$898$		0			0
$899$	−1.58435	−	3.82496i	−0.0528410	−	0.127569i
$900$		0			0
$901$	3.16409	+	1.31061i	0.105411	+	0.0436627i
$902$		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
$907$	−21.8478	+	52.7454i	−0.725446	+	1.75138i	−0.0682409	+	0.997669i	$0.521739\pi$
$907$	−21.8478	+	52.7454i	−0.725446	+	1.75138i	−0.657205	+	0.753712i	$0.728261\pi$
$908$		0			0
$909$	−19.0577	+	7.89396i	−0.632104	+	0.261826i
$910$		0			0
$911$			49.1777i			1.62933i	0.579931	+	0.814666i	$0.303080\pi$
$911$			49.1777i			1.62933i	−0.579931	+	0.814666i	$0.696920\pi$
$912$		0			0
$913$		−	16.5553i		−	0.547902i
$914$		0			0
$915$	−22.6542	+	9.38368i	−0.748925	+	0.310215i
$916$		0			0
$917$	−12.6824	+	30.6180i	−0.418810	+	1.01110i
$918$		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
$923$	45.0088	+	18.6433i	1.48148	+	0.613650i
$924$		0			0
$925$	10.0181	+	24.1858i	0.329393	+	0.795225i
$926$		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
$931$	−6.34612	−	15.3209i	−0.207986	−	0.502122i
$932$		0			0
$933$	−61.7612	−	25.5823i	−2.02197	−	0.837527i
$934$		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	$0.568151\pi$
$937$	−36.4154	+	36.4154i	−1.18964	+	1.18964i	−0.977168	+	0.212470i	$0.931849\pi$
$938$		0			0
$939$	−19.6705	+	47.4888i	−0.641922	+	1.54974i
$940$		0			0
$941$	16.9189	−	7.00804i	0.551541	−	0.228456i	−0.0894674	−	0.995990i	$-0.528516\pi$
$941$	16.9189	−	7.00804i	0.551541	−	0.228456i	0.641008	+	0.767534i	$0.278516\pi$
$942$		0			0
$943$		−	0.973475i		−	0.0317007i
$944$		0			0
$945$		−	0.905247i		−	0.0294477i
$946$		0			0
$947$	24.0505	−	9.96206i	0.781537	−	0.323723i	0.0440017	−	0.999031i	$-0.485989\pi$
$947$	24.0505	−	9.96206i	0.781537	−	0.323723i	0.737536	+	0.675308i	$0.235989\pi$
$948$		0			0
$949$	15.7655	−	38.0613i	0.511769	−	1.23552i
$950$		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	$-0.880486\pi$
$953$	−40.0406	−	40.0406i	−1.29704	−	1.29704i	−0.366706	−	0.930337i	$-0.619514\pi$
$954$		0			0
$955$	57.6235	+	23.8684i	1.86465	+	0.772365i
$956$		0			0
$957$	4.71489	+	11.3827i	0.152411	+	0.367952i
$958$		0			0
$959$	10.5793			0.341623
$960$		0			0
$961$	−17.3431			−0.559456
$962$		0			0
$963$	5.97901	+	14.4346i	0.192671	+	0.465148i
$964$		0			0
$965$	−23.0891	−	9.56383i	−0.743265	−	0.307871i
$966$		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
$971$	−6.51674	+	15.7328i	−0.209132	+	0.504890i	−0.993287	−	0.115675i	$-0.963097\pi$
$971$	−6.51674	+	15.7328i	−0.209132	+	0.504890i	0.784155	+	0.620565i	$0.213097\pi$
$972$		0			0
$973$	−5.45753	+	2.26058i	−0.174960	+	0.0724710i
$974$		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
$979$	37.6833	−	15.6090i	1.20436	−	0.498864i
$980$		0			0
$981$	6.77437	−	16.3548i	0.216289	−	0.522168i
$982$		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
$987$	−21.3274	−	8.83409i	−0.678858	−	0.281192i
$988$		0			0
$989$	−0.682401	−	1.64746i	−0.0216991	−	0.0523862i
$990$		0			0
$991$	32.7200			1.03939			0.519693	−	0.854353i	$-0.326046\pi$
$991$	32.7200			1.03939			0.519693	+	0.854353i	$0.326046\pi$
$992$		0			0
$993$	15.0625			0.477995
$994$		0			0
$995$	21.2928	+	51.4055i	0.675028	+	1.62966i
$996$		0			0
$997$	−2.78155	−	1.15216i	−0.0880927	−	0.0364892i	0.338202	−	0.941074i	$-0.390181\pi$
$997$	−2.78155	−	1.15216i	−0.0880927	−	0.0364892i	−0.426295	+	0.904584i	$0.640181\pi$
$998$		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.h.897.4	yes	16
4.3	odd	2	inner	1024.2.g.h.897.1	yes	16
8.3	odd	2		1024.2.g.c.897.4	yes	16
8.5	even	2		1024.2.g.c.897.1	yes	16
16.3	odd	4		1024.2.g.b.385.4	yes	16
16.5	even	4		1024.2.g.e.385.4	yes	16
16.11	odd	4		1024.2.g.e.385.1	yes	16
16.13	even	4		1024.2.g.b.385.1	✓	16
32.3	odd	8		1024.2.g.c.129.4	yes	16
32.5	even	8		1024.2.g.b.641.1	yes	16
32.11	odd	8		1024.2.g.e.641.1	yes	16
32.13	even	8	inner	1024.2.g.h.129.4	yes	16
32.19	odd	8	inner	1024.2.g.h.129.1	yes	16
32.21	even	8		1024.2.g.e.641.4	yes	16
32.27	odd	8		1024.2.g.b.641.4	yes	16
32.29	even	8		1024.2.g.c.129.1	yes	16
64.13	even	16		4096.2.a.n.1.7		8
64.19	odd	16		4096.2.a.n.1.8		8
64.45	even	16		4096.2.a.o.1.2		8
64.51	odd	16		4096.2.a.o.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.385.1	✓	16	16.13	even	4
1024.2.g.b.385.4	yes	16	16.3	odd	4
1024.2.g.b.641.1	yes	16	32.5	even	8
1024.2.g.b.641.4	yes	16	32.27	odd	8
1024.2.g.c.129.1	yes	16	32.29	even	8
1024.2.g.c.129.4	yes	16	32.3	odd	8
1024.2.g.c.897.1	yes	16	8.5	even	2
1024.2.g.c.897.4	yes	16	8.3	odd	2
1024.2.g.e.385.1	yes	16	16.11	odd	4
1024.2.g.e.385.4	yes	16	16.5	even	4
1024.2.g.e.641.1	yes	16	32.11	odd	8
1024.2.g.e.641.4	yes	16	32.21	even	8
1024.2.g.h.129.1	yes	16	32.19	odd	8	inner
1024.2.g.h.129.4	yes	16	32.13	even	8	inner
1024.2.g.h.897.1	yes	16	4.3	odd	2	inner
1024.2.g.h.897.4	yes	16	1.1	even	1	trivial
4096.2.a.n.1.7		8	64.13	even	16
4096.2.a.n.1.8		8	64.19	odd	16
4096.2.a.o.1.1		8	64.51	odd	16
4096.2.a.o.1.2		8	64.45	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)

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

Introduction

L-functions

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Database

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