LMFDB - Embedded newform 128.2.g.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			17.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	128.17
Dual form			128.2.g.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.70711i) q^{3} +(-3.12132 + 1.29289i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-0.292893 - 0.292893i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.70711i) q^{3} +(-3.12132 + 1.29289i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-0.292893 - 0.292893i) q^{9} +(-0.121320 - 0.292893i) q^{11} +(1.70711 + 0.707107i) q^{13} -6.24264i q^{15} +2.82843i q^{17} +(5.53553 + 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(-0.171573 - 0.171573i) q^{23} +(4.53553 - 4.53553i) q^{25} +(-4.41421 + 1.82843i) q^{27} +(1.12132 - 2.70711i) q^{29} +4.00000 q^{31} +0.585786 q^{33} +(1.82843 - 4.41421i) q^{35} +(1.70711 - 0.707107i) q^{37} +(-2.41421 + 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(-3.29289 - 7.94975i) q^{43} +(1.29289 + 0.535534i) q^{45} +11.6569i q^{47} +5.00000i q^{49} +(-4.82843 - 2.00000i) q^{51} +(3.12132 + 7.53553i) q^{53} +(0.757359 + 0.757359i) q^{55} +(-7.82843 + 7.82843i) q^{57} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +0.585786 q^{63} -6.24264 q^{65} +(-1.53553 + 3.70711i) q^{67} +(0.414214 - 0.171573i) q^{69} +(0.171573 - 0.171573i) q^{71} +(7.00000 + 7.00000i) q^{73} +(4.53553 + 10.9497i) q^{75} +(0.414214 + 0.171573i) q^{77} -6.00000i q^{79} -10.0711i q^{81} +(-6.12132 - 2.53553i) q^{83} +(-3.65685 - 8.82843i) q^{85} +(3.82843 + 3.82843i) q^{87} +(-2.65685 + 2.65685i) q^{89} +(-2.41421 + 1.00000i) q^{91} +(-2.82843 + 6.82843i) q^{93} -20.2426 q^{95} -1.51472 q^{97} +(-0.0502525 + 0.121320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9	$ 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9} + 8 q^{11} + 4 q^{13} + 8 q^{19} - 4 q^{21} - 12 q^{23} + 4 q^{25} - 12 q^{27} - 4 q^{29} + 16 q^{31} + 8 q^{33} - 4 q^{35} + 4 q^{37} - 4 q^{39} - 12 q^{41} - 16 q^{43} + 8 q^{45} - 8 q^{51} + 4 q^{53} + 20 q^{55} - 20 q^{57} + 16 q^{59} + 4 q^{61} + 8 q^{63} - 8 q^{65} + 8 q^{67} - 4 q^{69} + 12 q^{71} + 28 q^{73} + 4 q^{75} - 4 q^{77} - 16 q^{83} + 8 q^{85} + 4 q^{87} + 12 q^{89} - 4 q^{91} - 64 q^{95} - 40 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9 + 8 * q^11 + 4 * q^13 + 8 * q^19 - 4 * q^21 - 12 * q^23 + 4 * q^25 - 12 * q^27 - 4 * q^29 + 16 * q^31 + 8 * q^33 - 4 * q^35 + 4 * q^37 - 4 * q^39 - 12 * q^41 - 16 * q^43 + 8 * q^45 - 8 * q^51 + 4 * q^53 + 20 * q^55 - 20 * q^57 + 16 * q^59 + 4 * q^61 + 8 * q^63 - 8 * q^65 + 8 * q^67 - 4 * q^69 + 12 * q^71 + 28 * q^73 + 4 * q^75 - 4 * q^77 - 16 * q^83 + 8 * q^85 + 4 * q^87 + 12 * q^89 - 4 * q^91 - 64 * q^95 - 40 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	1.70711i	−0.408248	+	0.985599i	0.577350	+	0.816497i	$0.304087\pi$
$3$	−0.707107	+	1.70711i	−0.408248	+	0.985599i	−0.985599	+	0.169102i	$0.945913\pi$
$4$		0			0
$5$	−3.12132	+	1.29289i	−1.39590	+	0.578199i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$	−3.12132	+	1.29289i	−1.39590	+	0.578199i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$		0			0
$9$	−0.292893	−	0.292893i	−0.0976311	−	0.0976311i
$10$		0			0
$11$	−0.121320	−	0.292893i	−0.0365795	−	0.0883106i	0.904534	−	0.426401i	$-0.140219\pi$
$11$	−0.121320	−	0.292893i	−0.0365795	−	0.0883106i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$	1.70711	+	0.707107i	0.473466	+	0.196116i	0.606640	−	0.794977i	$-0.292517\pi$
$13$	1.70711	+	0.707107i	0.473466	+	0.196116i	−0.133174	+	0.991093i	$0.542517\pi$
$14$		0			0
$15$		−	6.24264i		−	1.61184i
$16$		0			0
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$		0			0
$19$	5.53553	+	2.29289i	1.26994	+	0.526026i	0.912946	−	0.408081i	$-0.133802\pi$
$19$	5.53553	+	2.29289i	1.26994	+	0.526026i	0.356993	+	0.934107i	$0.383802\pi$
$20$		0			0
$21$	−1.00000	−	2.41421i	−0.218218	−	0.526825i
$22$		0			0
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	0.688993	−	0.724768i	$-0.258053\pi$
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	−0.724768	+	0.688993i	$0.758053\pi$
$24$		0			0
$25$	4.53553	−	4.53553i	0.907107	−	0.907107i
$26$		0			0
$27$	−4.41421	+	1.82843i	−0.849516	+	0.351881i
$28$		0			0
$29$	1.12132	−	2.70711i	0.208224	−	0.502697i	−0.784920	−	0.619598i	$-0.787296\pi$
$29$	1.12132	−	2.70711i	0.208224	−	0.502697i	0.993144	+	0.116900i	$0.0372958\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	0.585786			0.101972
$34$		0			0
$35$	1.82843	−	4.41421i	0.309061	−	0.746138i
$36$		0			0
$37$	1.70711	−	0.707107i	0.280647	−	0.116248i	−0.237920	−	0.971285i	$-0.576466\pi$
$37$	1.70711	−	0.707107i	0.280647	−	0.116248i	0.518567	+	0.855037i	$0.326466\pi$
$38$		0			0
$39$	−2.41421	+	2.41421i	−0.386584	+	0.386584i
$40$		0			0
$41$	−5.82843	−	5.82843i	−0.910247	−	0.910247i	0.0860440	−	0.996291i	$-0.472577\pi$
$41$	−5.82843	−	5.82843i	−0.910247	−	0.910247i	−0.996291	+	0.0860440i	$0.972577\pi$
$42$		0			0
$43$	−3.29289	−	7.94975i	−0.502162	−	1.21233i	−0.948304	−	0.317363i	$-0.897203\pi$
$43$	−3.29289	−	7.94975i	−0.502162	−	1.21233i	0.446143	−	0.894962i	$-0.352797\pi$
$44$		0			0
$45$	1.29289	+	0.535534i	0.192733	+	0.0798327i
$46$		0			0
$47$			11.6569i			1.70033i	0.526519	+	0.850163i	$0.323497\pi$
$47$			11.6569i			1.70033i	−0.526519	+	0.850163i	$0.676503\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$		0			0
$51$	−4.82843	−	2.00000i	−0.676115	−	0.280056i
$52$		0			0
$53$	3.12132	+	7.53553i	0.428746	+	1.03509i	0.979686	+	0.200540i	$0.0642696\pi$
$53$	3.12132	+	7.53553i	0.428746	+	1.03509i	−0.550939	+	0.834545i	$0.685730\pi$
$54$		0			0
$55$	0.757359	+	0.757359i	0.102122	+	0.102122i
$56$		0			0
$57$	−7.82843	+	7.82843i	−1.03690	+	1.03690i
$58$		0			0
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.0532027	−	0.998584i	$-0.483057\pi$
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.743725	+	0.668485i	$0.233057\pi$
$60$		0			0
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	−0.904019	−	0.427492i	$-0.859397\pi$
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	0.941520	+	0.336956i	$0.109397\pi$
$62$		0			0
$63$	0.585786			0.0738022
$64$		0			0
$65$	−6.24264			−0.774304
$66$		0			0
$67$	−1.53553	+	3.70711i	−0.187595	+	0.452895i	−0.989496	−	0.144563i	$-0.953822\pi$
$67$	−1.53553	+	3.70711i	−0.187595	+	0.452895i	0.801900	+	0.597458i	$0.203822\pi$
$68$		0			0
$69$	0.414214	−	0.171573i	0.0498655	−	0.0206549i
$70$		0			0
$71$	0.171573	−	0.171573i	0.0203620	−	0.0203620i	−0.696853	−	0.717214i	$-0.745417\pi$
$71$	0.171573	−	0.171573i	0.0203620	−	0.0203620i	0.717214	+	0.696853i	$0.245417\pi$
$72$		0			0
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	0.986005	−	0.166717i	$-0.0533166\pi$
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	−0.166717	+	0.986005i	$0.553317\pi$
$74$		0			0
$75$	4.53553	+	10.9497i	0.523718	+	1.26437i
$76$		0			0
$77$	0.414214	+	0.171573i	0.0472040	+	0.0195525i
$78$		0			0
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$		0			0
$81$		−	10.0711i		−	1.11901i
$82$		0			0
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	0.0205350	−	0.999789i	$-0.493463\pi$
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	−0.692437	+	0.721478i	$0.743463\pi$
$84$		0			0
$85$	−3.65685	−	8.82843i	−0.396642	−	0.957577i
$86$		0			0
$87$	3.82843	+	3.82843i	0.410450	+	0.410450i
$88$		0			0
$89$	−2.65685	+	2.65685i	−0.281626	+	0.281626i	−0.833757	−	0.552131i	$-0.813815\pi$
$89$	−2.65685	+	2.65685i	−0.281626	+	0.281626i	0.552131	+	0.833757i	$0.313815\pi$
$90$		0			0
$91$	−2.41421	+	1.00000i	−0.253078	+	0.104828i
$92$		0			0
$93$	−2.82843	+	6.82843i	−0.293294	+	0.708075i
$94$		0			0
$95$	−20.2426			−2.07685
$96$		0			0
$97$	−1.51472			−0.153796			−0.0768982	−	0.997039i	$-0.524502\pi$
$97$	−1.51472			−0.153796			−0.0768982	+	0.997039i	$0.524502\pi$
$98$		0			0
$99$	−0.0502525	+	0.121320i	−0.00505057	+	0.0121932i
$100$		0			0
$101$	11.3640	−	4.70711i	1.13076	−	0.468375i	0.262718	−	0.964873i	$-0.415381\pi$
$101$	11.3640	−	4.70711i	1.13076	−	0.468375i	0.868038	+	0.496498i	$0.165381\pi$
$102$		0			0
$103$	7.48528	−	7.48528i	0.737547	−	0.737547i	−0.234556	−	0.972103i	$-0.575364\pi$
$103$	7.48528	−	7.48528i	0.737547	−	0.737547i	0.972103	+	0.234556i	$0.0753636\pi$
$104$		0			0
$105$	6.24264	+	6.24264i	0.609219	+	0.609219i
$106$		0			0
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	0.917907	−	0.396796i	$-0.129878\pi$
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	−0.929635	+	0.368481i	$0.879878\pi$
$108$		0			0
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	0.167496	−	0.985873i	$-0.446432\pi$
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	−0.578680	+	0.815555i	$0.696432\pi$
$110$		0			0
$111$			3.41421i			0.324063i
$112$		0			0
$113$		−	17.6569i		−	1.66102i	−0.557006	−	0.830509i	$-0.688050\pi$
$113$		−	17.6569i		−	1.66102i	0.557006	−	0.830509i	$-0.311950\pi$
$114$		0			0
$115$	0.757359	+	0.313708i	0.0706241	+	0.0292535i
$116$		0			0
$117$	−0.292893	−	0.707107i	−0.0270780	−	0.0653720i
$118$		0			0
$119$	−2.82843	−	2.82843i	−0.259281	−	0.259281i
$120$		0			0
$121$	7.70711	−	7.70711i	0.700646	−	0.700646i
$122$		0			0
$123$	14.0711	−	5.82843i	1.26875	−	0.525532i
$124$		0			0
$125$	−1.82843	+	4.41421i	−0.163539	+	0.394819i
$126$		0			0
$127$	20.9706			1.86084			0.930418	−	0.366499i	$-0.119444\pi$
$127$	20.9706			1.86084			0.930418	+	0.366499i	$0.119444\pi$
$128$		0			0
$129$	15.8995			1.39987
$130$		0			0
$131$	3.63604	−	8.77817i	0.317682	−	0.766953i	−0.681694	−	0.731637i	$-0.738756\pi$
$131$	3.63604	−	8.77817i	0.317682	−	0.766953i	0.999376	−	0.0353153i	$-0.0112435\pi$
$132$		0			0
$133$	−7.82843	+	3.24264i	−0.678811	+	0.281173i
$134$		0			0
$135$	11.4142	−	11.4142i	0.982379	−	0.982379i
$136$		0			0
$137$	2.65685	+	2.65685i	0.226990	+	0.226990i	0.811434	−	0.584444i	$-0.198687\pi$
$137$	2.65685	+	2.65685i	0.226990	+	0.226990i	−0.584444	+	0.811434i	$0.698687\pi$
$138$		0			0
$139$	5.19239	+	12.5355i	0.440413	+	1.06325i	0.975804	+	0.218646i	$0.0701640\pi$
$139$	5.19239	+	12.5355i	0.440413	+	1.06325i	−0.535392	+	0.844604i	$0.679836\pi$
$140$		0			0
$141$	−19.8995	−	8.24264i	−1.67584	−	0.694156i
$142$		0			0
$143$		−	0.585786i		−	0.0489859i
$144$		0			0
$145$			9.89949i			0.822108i
$146$		0			0
$147$	−8.53553	−	3.53553i	−0.703999	−	0.291606i
$148$		0			0
$149$	5.60660	+	13.5355i	0.459311	+	1.10887i	0.968677	+	0.248324i	$0.0798799\pi$
$149$	5.60660	+	13.5355i	0.459311	+	1.10887i	−0.509366	+	0.860550i	$0.670120\pi$
$150$		0			0
$151$	−15.4853	−	15.4853i	−1.26017	−	1.26017i	−0.951008	−	0.309166i	$-0.899950\pi$
$151$	−15.4853	−	15.4853i	−1.26017	−	1.26017i	−0.309166	−	0.951008i	$-0.600050\pi$
$152$		0			0
$153$	0.828427	−	0.828427i	0.0669744	−	0.0669744i
$154$		0			0
$155$	−12.4853	+	5.17157i	−1.00284	+	0.415391i
$156$		0			0
$157$	0.292893	−	0.707107i	0.0233754	−	0.0564333i	−0.911761	−	0.410722i	$-0.865277\pi$
$157$	0.292893	−	0.707107i	0.0233754	−	0.0564333i	0.935136	+	0.354288i	$0.115277\pi$
$158$		0			0
$159$	−15.0711			−1.19521
$160$		0			0
$161$	0.343146			0.0270437
$162$		0			0
$163$	−7.53553	+	18.1924i	−0.590229	+	1.42494i	0.293054	+	0.956096i	$0.405329\pi$
$163$	−7.53553	+	18.1924i	−0.590229	+	1.42494i	−0.883282	+	0.468842i	$0.844671\pi$
$164$		0			0
$165$	−1.82843	+	0.757359i	−0.142343	+	0.0589603i
$166$		0			0
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	−0.824525	−	0.565825i	$-0.808558\pi$
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	0.565825	+	0.824525i	$0.308558\pi$
$168$		0			0
$169$	−6.77817	−	6.77817i	−0.521398	−	0.521398i
$170$		0			0
$171$	−0.949747	−	2.29289i	−0.0726290	−	0.175342i
$172$		0			0
$173$	−1.12132	−	0.464466i	−0.0852524	−	0.0353127i	0.339650	−	0.940552i	$-0.389691\pi$
$173$	−1.12132	−	0.464466i	−0.0852524	−	0.0353127i	−0.424902	+	0.905239i	$0.639691\pi$
$174$		0			0
$175$			9.07107i			0.685708i
$176$		0			0
$177$			12.2426i			0.920213i
$178$		0			0
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.848264	−	0.529573i	$-0.177648\pi$
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.225349	+	0.974278i	$0.427648\pi$
$180$		0			0
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	0.821216	−	0.570618i	$-0.193296\pi$
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	−0.984175	+	0.177200i	$0.943296\pi$
$182$		0			0
$183$	1.00000	+	1.00000i	0.0739221	+	0.0739221i
$184$		0			0
$185$	−4.41421	+	4.41421i	−0.324539	+	0.324539i
$186$		0			0
$187$	0.828427	−	0.343146i	0.0605806	−	0.0250933i
$188$		0			0
$189$	2.58579	−	6.24264i	0.188088	−	0.454085i
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	−18.4853			−1.33060			−0.665300	−	0.746576i	$-0.731696\pi$
$193$	−18.4853			−1.33060			−0.665300	+	0.746576i	$0.731696\pi$
$194$		0			0
$195$	4.41421	−	10.6569i	0.316108	−	0.763153i
$196$		0			0
$197$	17.3640	−	7.19239i	1.23713	−	0.512436i	0.334314	−	0.942462i	$-0.391495\pi$
$197$	17.3640	−	7.19239i	1.23713	−	0.512436i	0.902817	+	0.430025i	$0.141495\pi$
$198$		0			0
$199$	−17.9706	+	17.9706i	−1.27390	+	1.27390i	−0.329875	+	0.944025i	$0.607006\pi$
$199$	−17.9706	+	17.9706i	−1.27390	+	1.27390i	−0.944025	+	0.329875i	$0.892994\pi$
$200$		0			0
$201$	−5.24264	−	5.24264i	−0.369787	−	0.369787i
$202$		0			0
$203$	1.58579	+	3.82843i	0.111300	+	0.268703i
$204$		0			0
$205$	25.7279	+	10.6569i	1.79692	+	0.744307i
$206$		0			0
$207$			0.100505i			0.00698558i
$208$		0			0
$209$		−	1.89949i		−	0.131391i
$210$		0			0
$211$	−0.464466	−	0.192388i	−0.0319752	−	0.0132445i	0.366639	−	0.930363i	$-0.380509\pi$
$211$	−0.464466	−	0.192388i	−0.0319752	−	0.0132445i	−0.398614	+	0.917119i	$0.630509\pi$
$212$		0			0
$213$	0.171573	+	0.414214i	0.0117560	+	0.0283814i
$214$		0			0
$215$	20.5563	+	20.5563i	1.40193	+	1.40193i
$216$		0			0
$217$	−4.00000	+	4.00000i	−0.271538	+	0.271538i
$218$		0			0
$219$	−16.8995	+	7.00000i	−1.14196	+	0.473016i
$220$		0			0
$221$	−2.00000	+	4.82843i	−0.134535	+	0.324795i
$222$		0			0
$223$	−12.9706			−0.868573			−0.434287	−	0.900775i	$-0.642999\pi$
$223$	−12.9706			−0.868573			−0.434287	+	0.900775i	$0.642999\pi$
$224$		0			0
$225$	−2.65685			−0.177124
$226$		0			0
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	−0.813464	−	0.581616i	$-0.802421\pi$
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	0.986470	+	0.163942i	$0.0524208\pi$
$228$		0			0
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.996030	−	0.0890139i	$-0.971628\pi$
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.641357	+	0.767242i	$0.721628\pi$
$230$		0			0
$231$	−0.585786	+	0.585786i	−0.0385419	+	0.0385419i
$232$		0			0
$233$	8.65685	+	8.65685i	0.567129	+	0.567129i	0.931323	−	0.364194i	$-0.118655\pi$
$233$	8.65685	+	8.65685i	0.567129	+	0.567129i	−0.364194	+	0.931323i	$0.618655\pi$
$234$		0			0
$235$	−15.0711	−	36.3848i	−0.983128	−	2.37348i
$236$		0			0
$237$	10.2426	+	4.24264i	0.665331	+	0.275589i
$238$		0			0
$239$		−	17.3137i		−	1.11993i	−0.828516	−	0.559965i	$-0.810814\pi$
$239$		−	17.3137i		−	1.11993i	0.828516	−	0.559965i	$-0.189186\pi$
$240$		0			0
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$		0			0
$243$	3.94975	+	1.63604i	0.253376	+	0.104952i
$244$		0			0
$245$	−6.46447	−	15.6066i	−0.413000	−	0.997069i
$246$		0			0
$247$	7.82843	+	7.82843i	0.498111	+	0.498111i
$248$		0			0
$249$	8.65685	−	8.65685i	0.548606	−	0.548606i
$250$		0			0
$251$	14.6066	−	6.05025i	0.921961	−	0.381889i	0.129338	−	0.991601i	$-0.458715\pi$
$251$	14.6066	−	6.05025i	0.921961	−	0.381889i	0.792623	+	0.609712i	$0.208715\pi$
$252$		0			0
$253$	−0.0294373	+	0.0710678i	−0.00185070	+	0.00446800i
$254$		0			0
$255$	17.6569			1.10572
$256$		0			0
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	−1.00000	+	2.41421i	−0.0621370	+	0.150012i
$260$		0			0
$261$	−1.12132	+	0.464466i	−0.0694080	+	0.0287497i
$262$		0			0
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	−0.701797	−	0.712377i	$-0.747619\pi$
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	0.712377	+	0.701797i	$0.247619\pi$
$264$		0			0
$265$	−19.4853	−	19.4853i	−1.19697	−	1.19697i
$266$		0			0
$267$	−2.65685	−	6.41421i	−0.162597	−	0.392543i
$268$		0			0
$269$	4.87868	+	2.02082i	0.297458	+	0.123211i	0.526421	−	0.850224i	$-0.323533\pi$
$269$	4.87868	+	2.02082i	0.297458	+	0.123211i	−0.228963	+	0.973435i	$0.573533\pi$
$270$		0			0
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$		0			0
$273$		−	4.82843i		−	0.292230i
$274$		0			0
$275$	−1.87868	−	0.778175i	−0.113289	−	0.0469257i
$276$		0			0
$277$	0.292893	+	0.707107i	0.0175982	+	0.0424859i	0.932434	−	0.361339i	$-0.117680\pi$
$277$	0.292893	+	0.707107i	0.0175982	+	0.0424859i	−0.914836	+	0.403825i	$0.867680\pi$
$278$		0			0
$279$	−1.17157	−	1.17157i	−0.0701402	−	0.0701402i
$280$		0			0
$281$	−6.17157	+	6.17157i	−0.368165	+	0.368165i	−0.866808	−	0.498643i	$-0.833832\pi$
$281$	−6.17157	+	6.17157i	−0.368165	+	0.368165i	0.498643	+	0.866808i	$0.333832\pi$
$282$		0			0
$283$	9.77817	−	4.05025i	0.581252	−	0.240763i	−0.0726300	−	0.997359i	$-0.523139\pi$
$283$	9.77817	−	4.05025i	0.581252	−	0.240763i	0.653882	+	0.756596i	$0.273139\pi$
$284$		0			0
$285$	14.3137	−	34.5563i	0.847871	−	2.04694i
$286$		0			0
$287$	11.6569			0.688082
$288$		0			0
$289$	9.00000			0.529412
$290$		0			0
$291$	1.07107	−	2.58579i	0.0627871	−	0.151581i
$292$		0			0
$293$	−11.6066	+	4.80761i	−0.678065	+	0.280864i	−0.695018	−	0.718993i	$-0.744603\pi$
$293$	−11.6066	+	4.80761i	−0.678065	+	0.280864i	0.0169528	+	0.999856i	$0.494603\pi$
$294$		0			0
$295$	−15.8284	+	15.8284i	−0.921567	+	0.921567i
$296$		0			0
$297$	1.07107	+	1.07107i	0.0621497	+	0.0621497i
$298$		0			0
$299$	−0.171573	−	0.414214i	−0.00992232	−	0.0239546i
$300$		0			0
$301$	11.2426	+	4.65685i	0.648015	+	0.268417i
$302$		0			0
$303$			22.7279i			1.30569i
$304$		0			0
$305$			2.58579i			0.148062i
$306$		0			0
$307$	−2.94975	−	1.22183i	−0.168351	−	0.0697333i	0.296916	−	0.954904i	$-0.404042\pi$
$307$	−2.94975	−	1.22183i	−0.168351	−	0.0697333i	−0.465267	+	0.885170i	$0.654042\pi$
$308$		0			0
$309$	7.48528	+	18.0711i	0.425823	+	1.02803i
$310$		0			0
$311$	−8.65685	−	8.65685i	−0.490885	−	0.490885i	0.417700	−	0.908585i	$-0.362836\pi$
$311$	−8.65685	−	8.65685i	−0.490885	−	0.490885i	−0.908585	+	0.417700i	$0.862836\pi$
$312$		0			0
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	−0.386253	−	0.922393i	$-0.626231\pi$
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	0.922393	+	0.386253i	$0.126231\pi$
$314$		0			0
$315$	−1.82843	+	0.757359i	−0.103020	+	0.0426724i
$316$		0			0
$317$	4.63604	−	11.1924i	0.260386	−	0.628627i	−0.738577	−	0.674170i	$-0.764502\pi$
$317$	4.63604	−	11.1924i	0.260386	−	0.628627i	0.998962	+	0.0455425i	$0.0145016\pi$
$318$		0			0
$319$	−0.928932			−0.0520102
$320$		0			0
$321$	0.585786			0.0326954
$322$		0			0
$323$	−6.48528	+	15.6569i	−0.360851	+	0.871171i
$324$		0			0
$325$	10.9497	−	4.53553i	0.607383	−	0.251586i
$326$		0			0
$327$	6.07107	−	6.07107i	0.335731	−	0.335731i
$328$		0			0
$329$	−11.6569	−	11.6569i	−0.642663	−	0.642663i
$330$		0			0
$331$	2.70711	+	6.53553i	0.148796	+	0.359225i	0.980650	−	0.195769i	$-0.0627203\pi$
$331$	2.70711	+	6.53553i	0.148796	+	0.359225i	−0.831854	+	0.554995i	$0.812720\pi$
$332$		0			0
$333$	−0.707107	−	0.292893i	−0.0387492	−	0.0160504i
$334$		0			0
$335$		−	13.5563i		−	0.740662i
$336$		0			0
$337$			16.9706i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$337$			16.9706i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$338$		0			0
$339$	30.1421	+	12.4853i	1.63710	+	0.678107i
$340$		0			0
$341$	−0.485281	−	1.17157i	−0.0262795	−	0.0634442i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$	−1.07107	+	1.07107i	−0.0576644	+	0.0576644i
$346$		0			0
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.733317	−	0.679887i	$-0.762029\pi$
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.0377808	+	0.999286i	$0.512029\pi$
$348$		0			0
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	0.328662	+	0.944448i	$0.393402\pi$
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	−0.900224	+	0.435426i	$0.856598\pi$
$350$		0			0
$351$	−8.82843			−0.471227
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$	−0.313708	+	0.757359i	−0.0166499	+	0.0401965i
$356$		0			0
$357$	6.82843	−	2.82843i	0.361399	−	0.149696i
$358$		0			0
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	−0.308752	−	0.951143i	$-0.599911\pi$
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	0.951143	+	0.308752i	$0.0999112\pi$
$360$		0			0
$361$	11.9497	+	11.9497i	0.628934	+	0.628934i
$362$		0			0
$363$	7.70711	+	18.6066i	0.404518	+	0.976593i
$364$		0			0
$365$	−30.8995	−	12.7990i	−1.61735	−	0.669930i
$366$		0			0
$367$			6.00000i			0.313197i	0.987662	+	0.156599i	$0.0500529\pi$
$367$			6.00000i			0.313197i	−0.987662	+	0.156599i	$0.949947\pi$
$368$		0			0
$369$			3.41421i			0.177737i
$370$		0			0
$371$	−10.6569	−	4.41421i	−0.553276	−	0.229175i
$372$		0			0
$373$	−11.7071	−	28.2635i	−0.606171	−	1.46343i	−0.867133	−	0.498077i	$-0.834040\pi$
$373$	−11.7071	−	28.2635i	−0.606171	−	1.46343i	0.260962	−	0.965349i	$-0.415960\pi$
$374$		0			0
$375$	−6.24264	−	6.24264i	−0.322369	−	0.322369i
$376$		0			0
$377$	3.82843	−	3.82843i	0.197174	−	0.197174i
$378$		0			0
$379$	−21.6777	+	8.97918i	−1.11351	+	0.461230i	−0.862144	−	0.506663i	$-0.830879\pi$
$379$	−21.6777	+	8.97918i	−1.11351	+	0.461230i	−0.251363	+	0.967893i	$0.580879\pi$
$380$		0			0
$381$	−14.8284	+	35.7990i	−0.759683	+	1.83404i
$382$		0			0
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$		0			0
$385$	−1.51472			−0.0771972
$386$		0			0
$387$	−1.36396	+	3.29289i	−0.0693340	+	0.167387i
$388$		0			0
$389$	−29.6066	+	12.2635i	−1.50111	+	0.621782i	−0.973702	−	0.227827i	$-0.926838\pi$
$389$	−29.6066	+	12.2635i	−1.50111	+	0.621782i	−0.527413	+	0.849609i	$0.676838\pi$
$390$		0			0
$391$	0.485281	−	0.485281i	0.0245417	−	0.0245417i
$392$		0			0
$393$	12.4142	+	12.4142i	0.626214	+	0.626214i
$394$		0			0
$395$	7.75736	+	18.7279i	0.390315	+	0.942304i
$396$		0			0
$397$	−24.7782	−	10.2635i	−1.24358	−	0.515108i	−0.338749	−	0.940877i	$-0.610004\pi$
$397$	−24.7782	−	10.2635i	−1.24358	−	0.515108i	−0.904832	+	0.425769i	$0.860004\pi$
$398$		0			0
$399$		−	15.6569i		−	0.783823i
$400$		0			0
$401$			2.82843i			0.141245i	0.997503	+	0.0706225i	$0.0224986\pi$
$401$			2.82843i			0.141245i	−0.997503	+	0.0706225i	$0.977501\pi$
$402$		0			0
$403$	6.82843	+	2.82843i	0.340148	+	0.140894i
$404$		0			0
$405$	13.0208	+	31.4350i	0.647010	+	1.56202i
$406$		0			0
$407$	−0.414214	−	0.414214i	−0.0205318	−	0.0205318i
$408$		0			0
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	−0.586622	−	0.809861i	$-0.699543\pi$
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	0.809861	+	0.586622i	$0.199543\pi$
$410$		0			0
$411$	−6.41421	+	2.65685i	−0.316390	+	0.131053i
$412$		0			0
$413$	−3.58579	+	8.65685i	−0.176445	+	0.425976i
$414$		0			0
$415$	22.3848			1.09883
$416$		0			0
$417$	−25.0711			−1.22774
$418$		0			0
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	−0.561752	−	0.827306i	$-0.689873\pi$
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	0.982212	−	0.187775i	$-0.0601275\pi$
$420$		0			0
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	−0.186882	−	0.982382i	$-0.559838\pi$
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	0.562504	+	0.826795i	$0.309838\pi$
$422$		0			0
$423$	3.41421	−	3.41421i	0.166005	−	0.166005i
$424$		0			0
$425$	12.8284	+	12.8284i	0.622270	+	0.622270i
$426$		0			0
$427$	0.414214	+	1.00000i	0.0200452	+	0.0483934i
$428$		0			0
$429$	1.00000	+	0.414214i	0.0482805	+	0.0199984i
$430$		0			0
$431$			23.6569i			1.13951i	0.821814	+	0.569755i	$0.192962\pi$
$431$			23.6569i			1.13951i	−0.821814	+	0.569755i	$0.807038\pi$
$432$		0			0
$433$		−	32.4853i		−	1.56114i	−0.625067	−	0.780571i	$-0.714928\pi$
$433$		−	32.4853i		−	1.56114i	0.625067	−	0.780571i	$-0.285072\pi$
$434$		0			0
$435$	−16.8995	−	7.00000i	−0.810269	−	0.335624i
$436$		0			0
$437$	−0.556349	−	1.34315i	−0.0266138	−	0.0642514i
$438$		0			0
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	0.984839	−	0.173473i	$-0.0554989\pi$
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	−0.173473	+	0.984839i	$0.555499\pi$
$440$		0			0
$441$	1.46447	−	1.46447i	0.0697365	−	0.0697365i
$442$		0			0
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.164976	−	0.986298i	$-0.447245\pi$
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.814073	+	0.580762i	$0.197245\pi$
$444$		0			0
$445$	4.85786	−	11.7279i	0.230285	−	0.555957i
$446$		0			0
$447$	−27.0711			−1.28042
$448$		0			0
$449$	31.4558			1.48449			0.742247	−	0.670127i	$-0.233760\pi$
$449$	31.4558			1.48449			0.742247	+	0.670127i	$0.233760\pi$
$450$		0			0
$451$	−1.00000	+	2.41421i	−0.0470882	+	0.113681i
$452$		0			0
$453$	37.3848	−	15.4853i	1.75649	−	0.727562i
$454$		0			0
$455$	6.24264	−	6.24264i	0.292660	−	0.292660i
$456$		0			0
$457$	9.48528	+	9.48528i	0.443703	+	0.443703i	0.893254	−	0.449552i	$-0.148416\pi$
$457$	9.48528	+	9.48528i	0.443703	+	0.443703i	−0.449552	+	0.893254i	$0.648416\pi$
$458$		0			0
$459$	−5.17157	−	12.4853i	−0.241388	−	0.582763i
$460$		0			0
$461$	13.3640	+	5.53553i	0.622422	+	0.257816i	0.671529	−	0.740978i	$-0.265638\pi$
$461$	13.3640	+	5.53553i	0.622422	+	0.257816i	−0.0491076	+	0.998793i	$0.515638\pi$
$462$		0			0
$463$			10.9706i			0.509845i	0.966961	+	0.254923i	$0.0820500\pi$
$463$			10.9706i			0.509845i	−0.966961	+	0.254923i	$0.917950\pi$
$464$		0			0
$465$		−	24.9706i		−	1.15798i
$466$		0			0
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.410977	−	0.911646i	$-0.634812\pi$
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.935235	+	0.354027i	$0.884812\pi$
$468$		0			0
$469$	−2.17157	−	5.24264i	−0.100274	−	0.242083i
$470$		0			0
$471$	1.00000	+	1.00000i	0.0460776	+	0.0460776i
$472$		0			0
$473$	−1.92893	+	1.92893i	−0.0886924	+	0.0886924i
$474$		0			0
$475$	35.5061	−	14.7071i	1.62913	−	0.674808i
$476$		0			0
$477$	1.29289	−	3.12132i	0.0591975	−	0.142915i
$478$		0			0
$479$	4.97056			0.227111			0.113555	−	0.993532i	$-0.463776\pi$
$479$	4.97056			0.227111			0.113555	+	0.993532i	$0.463776\pi$
$480$		0			0
$481$	3.41421			0.155675
$482$		0			0
$483$	−0.242641	+	0.585786i	−0.0110405	+	0.0266542i
$484$		0			0
$485$	4.72792	−	1.95837i	0.214684	−	0.0889250i
$486$		0			0
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	−0.412500	−	0.910958i	$-0.635344\pi$
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	0.910958	+	0.412500i	$0.135344\pi$
$488$		0			0
$489$	−25.7279	−	25.7279i	−1.16346	−	1.16346i
$490$		0			0
$491$	7.33452	+	17.7071i	0.331002	+	0.799111i	0.998513	+	0.0545104i	$0.0173598\pi$
$491$	7.33452	+	17.7071i	0.331002	+	0.799111i	−0.667511	+	0.744600i	$0.732640\pi$
$492$		0			0
$493$	7.65685	+	3.17157i	0.344847	+	0.142840i
$494$		0			0
$495$		−	0.443651i		−	0.0199406i
$496$		0			0
$497$			0.343146i			0.0153922i
$498$		0			0
$499$	−8.94975	−	3.70711i	−0.400646	−	0.165953i	0.173256	−	0.984877i	$-0.444571\pi$
$499$	−8.94975	−	3.70711i	−0.400646	−	0.165953i	−0.573902	+	0.818924i	$0.694571\pi$
$500$		0			0
$501$	−3.34315	−	8.07107i	−0.149361	−	0.360589i
$502$		0			0
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	0.212772	−	0.977102i	$-0.431751\pi$
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	−0.977102	+	0.212772i	$0.931751\pi$
$504$		0			0
$505$	−29.3848	+	29.3848i	−1.30761	+	1.30761i
$506$		0			0
$507$	16.3640	−	6.77817i	0.726749	−	0.301029i
$508$		0			0
$509$	12.0919	−	29.1924i	0.535963	−	1.29393i	−0.391556	−	0.920154i	$-0.628063\pi$
$509$	12.0919	−	29.1924i	0.535963	−	1.29393i	0.927519	−	0.373776i	$-0.121937\pi$
$510$		0			0
$511$	−14.0000			−0.619324
$512$		0			0
$513$	−28.6274			−1.26393
$514$		0			0
$515$	−13.6863	+	33.0416i	−0.603090	+	1.45599i
$516$		0			0
$517$	3.41421	−	1.41421i	0.150157	−	0.0621970i
$518$		0			0
$519$	1.58579	−	1.58579i	0.0696083	−	0.0696083i
$520$		0			0
$521$	14.6569	+	14.6569i	0.642128	+	0.642128i	0.951078	−	0.308950i	$-0.0999775\pi$
$521$	14.6569	+	14.6569i	0.642128	+	0.642128i	−0.308950	+	0.951078i	$0.599978\pi$
$522$		0			0
$523$	−0.807612	−	1.94975i	−0.0353144	−	0.0852565i	0.905238	−	0.424904i	$-0.139692\pi$
$523$	−0.807612	−	1.94975i	−0.0353144	−	0.0852565i	−0.940553	+	0.339648i	$0.889692\pi$
$524$		0			0
$525$	−15.4853	−	6.41421i	−0.675833	−	0.279939i
$526$		0			0
$527$			11.3137i			0.492833i
$528$		0			0
$529$		−	22.9411i		−	0.997440i
$530$		0			0
$531$	−2.53553	−	1.05025i	−0.110033	−	0.0455771i
$532$		0			0
$533$	−5.82843	−	14.0711i	−0.252457	−	0.609486i
$534$		0			0
$535$	0.757359	+	0.757359i	0.0327435	+	0.0327435i
$536$		0			0
$537$	−20.3137	+	20.3137i	−0.876601	+	0.876601i
$538$		0			0
$539$	1.46447	−	0.606602i	0.0630790	−	0.0261282i
$540$		0			0
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	−0.769427	−	0.638735i	$-0.779458\pi$
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	0.995721	+	0.0924135i	$0.0294582\pi$
$542$		0			0
$543$	10.5858			0.454280
$544$		0			0
$545$	15.6985			0.672449
$546$		0			0
$547$	10.4645	−	25.2635i	0.447428	−	1.08019i	−0.525854	−	0.850575i	$-0.676254\pi$
$547$	10.4645	−	25.2635i	0.447428	−	1.08019i	0.973282	−	0.229612i	$-0.0737459\pi$
$548$		0			0
$549$	−0.292893	+	0.121320i	−0.0125004	+	0.00517783i
$550$		0			0
$551$	12.4142	−	12.4142i	0.528863	−	0.528863i
$552$		0			0
$553$	6.00000	+	6.00000i	0.255146	+	0.255146i
$554$		0			0
$555$	−4.41421	−	10.6569i	−0.187373	−	0.452358i
$556$		0			0
$557$	10.8787	+	4.50610i	0.460944	+	0.190929i	0.601057	−	0.799206i	$-0.294746\pi$
$557$	10.8787	+	4.50610i	0.460944	+	0.190929i	−0.140113	+	0.990136i	$0.544746\pi$
$558$		0			0
$559$		−	15.8995i		−	0.672477i
$560$		0			0
$561$			1.65685i			0.0699524i
$562$		0			0
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	0.112341	−	0.993670i	$-0.464165\pi$
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	−0.623194	+	0.782068i	$0.714165\pi$
$564$		0			0
$565$	22.8284	+	55.1127i	0.960399	+	2.31861i
$566$		0			0
$567$	10.0711	+	10.0711i	0.422945	+	0.422945i
$568$		0			0
$569$	3.34315	−	3.34315i	0.140152	−	0.140152i	−0.633550	−	0.773702i	$-0.718403\pi$
$569$	3.34315	−	3.34315i	0.140152	−	0.140152i	0.773702	+	0.633550i	$0.218403\pi$
$570$		0			0
$571$	1.29289	−	0.535534i	0.0541059	−	0.0224114i	−0.355466	−	0.934689i	$-0.615678\pi$
$571$	1.29289	−	0.535534i	0.0541059	−	0.0224114i	0.409572	+	0.912278i	$0.365678\pi$
$572$		0			0
$573$	−8.48528	+	20.4853i	−0.354478	+	0.855785i
$574$		0			0
$575$	−1.55635			−0.0649042
$576$		0			0
$577$	−14.9706			−0.623233			−0.311616	−	0.950208i	$-0.600870\pi$
$577$	−14.9706			−0.623233			−0.311616	+	0.950208i	$0.600870\pi$
$578$		0			0
$579$	13.0711	−	31.5563i	0.543215	−	1.31144i
$580$		0			0
$581$	8.65685	−	3.58579i	0.359147	−	0.148763i
$582$		0			0
$583$	1.82843	−	1.82843i	0.0757257	−	0.0757257i
$584$		0			0
$585$	1.82843	+	1.82843i	0.0755962	+	0.0755962i
$586$		0			0
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	−0.995957	−	0.0898359i	$-0.971366\pi$
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	0.640724	−	0.767771i	$-0.278634\pi$
$588$		0			0
$589$	22.1421	+	9.17157i	0.912351	+	0.377908i
$590$		0			0
$591$			34.7279i			1.42852i
$592$		0			0
$593$			28.2843i			1.16150i	0.814083	+	0.580748i	$0.197240\pi$
$593$			28.2843i			1.16150i	−0.814083	+	0.580748i	$0.802760\pi$
$594$		0			0
$595$	12.4853	+	5.17157i	0.511847	+	0.212014i
$596$		0			0
$597$	−17.9706	−	43.3848i	−0.735486	−	1.77562i
$598$		0			0
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	0.947288	−	0.320384i	$-0.103812\pi$
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	−0.320384	+	0.947288i	$0.603812\pi$
$600$		0			0
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	−0.419477	−	0.907766i	$-0.637786\pi$
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	0.907766	+	0.419477i	$0.137786\pi$
$602$		0			0
$603$	1.53553	−	0.636039i	0.0625318	−	0.0259015i
$604$		0			0
$605$	−14.0919	+	34.0208i	−0.572917	+	1.38314i
$606$		0			0
$607$	−0.970563			−0.0393939			−0.0196970	−	0.999806i	$-0.506270\pi$
$607$	−0.970563			−0.0393939			−0.0196970	+	0.999806i	$0.506270\pi$
$608$		0			0
$609$	−7.65685			−0.310271
$610$		0			0
$611$	−8.24264	+	19.8995i	−0.333462	+	0.805047i
$612$		0			0
$613$	36.6777	−	15.1924i	1.48140	−	0.613615i	0.511972	−	0.859002i	$-0.328915\pi$
$613$	36.6777	−	15.1924i	1.48140	−	0.613615i	0.969425	+	0.245387i	$0.0789151\pi$
$614$		0			0
$615$	−36.3848	+	36.3848i	−1.46718	+	1.46718i
$616$		0			0
$617$	−16.7990	−	16.7990i	−0.676302	−	0.676302i	0.282859	−	0.959161i	$-0.408717\pi$
$617$	−16.7990	−	16.7990i	−0.676302	−	0.676302i	−0.959161	+	0.282859i	$0.908717\pi$
$618$		0			0
$619$	6.22183	+	15.0208i	0.250076	+	0.603738i	0.998210	−	0.0598107i	$-0.0190497\pi$
$619$	6.22183	+	15.0208i	0.250076	+	0.603738i	−0.748133	+	0.663548i	$0.769050\pi$
$620$		0			0
$621$	1.07107	+	0.443651i	0.0429805	+	0.0178031i
$622$		0			0
$623$		−	5.31371i		−	0.212889i
$624$		0			0
$625$			15.9289i			0.637157i
$626$		0			0
$627$	3.24264	+	1.34315i	0.129499	+	0.0536401i
$628$		0			0
$629$	2.00000	+	4.82843i	0.0797452	+	0.192522i
$630$		0			0
$631$	18.4558	+	18.4558i	0.734716	+	0.734716i	0.971550	−	0.236834i	$-0.0761099\pi$
$631$	18.4558	+	18.4558i	0.734716	+	0.734716i	−0.236834	+	0.971550i	$0.576110\pi$
$632$		0			0
$633$	0.656854	−	0.656854i	0.0261076	−	0.0261076i
$634$		0			0
$635$	−65.4558	+	27.1127i	−2.59754	+	1.07593i
$636$		0			0
$637$	−3.53553	+	8.53553i	−0.140083	+	0.338190i
$638$		0			0
$639$	−0.100505			−0.00397592
$640$		0			0
$641$	−43.4558			−1.71640			−0.858201	−	0.513313i	$-0.828418\pi$
$641$	−43.4558			−1.71640			−0.858201	+	0.513313i	$0.828418\pi$
$642$		0			0
$643$	15.4350	−	37.2635i	0.608698	−	1.46953i	−0.255719	−	0.966751i	$-0.582312\pi$
$643$	15.4350	−	37.2635i	0.608698	−	1.46953i	0.864417	−	0.502776i	$-0.167688\pi$
$644$		0			0
$645$	−49.6274	+	20.5563i	−1.95408	+	0.809405i
$646$		0			0
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	−0.900298	−	0.435274i	$-0.856651\pi$
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	0.435274	+	0.900298i	$0.356651\pi$
$648$		0			0
$649$	−1.48528	−	1.48528i	−0.0583024	−	0.0583024i
$650$		0			0
$651$	−4.00000	−	9.65685i	−0.156772	−	0.378482i
$652$		0			0
$653$	−36.0919	−	14.9497i	−1.41238	−	0.585029i	−0.459450	−	0.888204i	$-0.651953\pi$
$653$	−36.0919	−	14.9497i	−1.41238	−	0.585029i	−0.952935	+	0.303175i	$0.901953\pi$
$654$		0			0
$655$			32.1005i			1.25427i
$656$		0			0
$657$		−	4.10051i		−	0.159976i
$658$		0			0
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	0.494234	−	0.869329i	$-0.335449\pi$
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	−0.265233	+	0.964184i	$0.585449\pi$
$660$		0			0
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	0.999927	+	0.0120477i	$0.00383499\pi$
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	−0.698536	+	0.715574i	$0.746165\pi$
$662$		0			0
$663$	−6.82843	−	6.82843i	−0.265194	−	0.265194i
$664$		0			0
$665$	20.2426	−	20.2426i	0.784976	−	0.784976i
$666$		0			0
$667$	−0.656854	+	0.272078i	−0.0254335	+	0.0105349i
$668$		0			0
$669$	9.17157	−	22.1421i	0.354593	−	0.856064i
$670$		0			0
$671$	−0.242641			−0.00936704
$672$		0			0
$673$	5.51472			0.212577			0.106288	−	0.994335i	$-0.466103\pi$
$673$	5.51472			0.212577			0.106288	+	0.994335i	$0.466103\pi$
$674$		0			0
$675$	−11.7279	+	28.3137i	−0.451408	+	1.08980i
$676$		0			0
$677$	−5.60660	+	2.32233i	−0.215479	+	0.0892544i	−0.487812	−	0.872949i	$-0.662205\pi$
$677$	−5.60660	+	2.32233i	−0.215479	+	0.0892544i	0.272333	+	0.962203i	$0.412205\pi$
$678$		0			0
$679$	1.51472	−	1.51472i	0.0581296	−	0.0581296i
$680$		0			0
$681$	8.89949	+	8.89949i	0.341029	+	0.341029i
$682$		0			0
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	0.995548	−	0.0942543i	$-0.0300467\pi$
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	−0.770607	+	0.637311i	$0.780047\pi$
$684$		0			0
$685$	−11.7279	−	4.85786i	−0.448101	−	0.185609i
$686$		0			0
$687$		−	49.5563i		−	1.89069i
$688$		0			0
$689$			15.0711i			0.574162i
$690$		0			0
$691$	28.5061	+	11.8076i	1.08442	+	0.449183i	0.852059	−	0.523446i	$-0.175354\pi$
$691$	28.5061	+	11.8076i	1.08442	+	0.449183i	0.232364	+	0.972629i	$0.425354\pi$
$692$		0			0
$693$	−0.0710678	−	0.171573i	−0.00269964	−	0.00651751i
$694$		0			0
$695$	−32.4142	−	32.4142i	−1.22954	−	1.22954i
$696$		0			0
$697$	16.4853	−	16.4853i	0.624425	−	0.624425i
$698$		0			0
$699$	−20.8995	+	8.65685i	−0.790491	+	0.327432i
$700$		0			0
$701$	7.12132	−	17.1924i	0.268969	−	0.649348i	−0.730467	−	0.682948i	$-0.760697\pi$
$701$	7.12132	−	17.1924i	0.268969	−	0.649348i	0.999435	+	0.0336007i	$0.0106974\pi$
$702$		0			0
$703$	11.0711			0.417553
$704$		0			0
$705$	72.7696			2.74066
$706$		0			0
$707$	−6.65685	+	16.0711i	−0.250357	+	0.604415i
$708$		0			0
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	−0.506314	−	0.862349i	$-0.668992\pi$
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	0.251755	+	0.967791i	$0.418992\pi$
$710$		0			0
$711$	−1.75736	+	1.75736i	−0.0659061	+	0.0659061i
$712$		0			0
$713$	−0.686292	−	0.686292i	−0.0257018	−	0.0257018i
$714$		0			0
$715$	0.757359	+	1.82843i	0.0283236	+	0.0683793i
$716$		0			0
$717$	29.5563	+	12.2426i	1.10380	+	0.457210i
$718$		0			0
$719$		−	24.3431i		−	0.907846i	−0.891041	−	0.453923i	$-0.850024\pi$
$719$		−	24.3431i		−	0.907846i	0.891041	−	0.453923i	$-0.149976\pi$
$720$		0			0
$721$			14.9706i			0.557533i
$722$		0			0
$723$	−14.4853	−	6.00000i	−0.538713	−	0.223142i
$724$		0			0
$725$	−7.19239	−	17.3640i	−0.267119	−	0.644881i
$726$		0			0
$727$	−23.9706	−	23.9706i	−0.889019	−	0.889019i	0.105410	−	0.994429i	$-0.466385\pi$
$727$	−23.9706	−	23.9706i	−0.889019	−	0.889019i	−0.994429	+	0.105410i	$0.966385\pi$
$728$		0			0
$729$	15.7782	−	15.7782i	0.584377	−	0.584377i
$730$		0			0
$731$	22.4853	−	9.31371i	0.831648	−	0.344480i
$732$		0			0
$733$	−0.736544	+	1.77817i	−0.0272049	+	0.0656784i	−0.936898	−	0.349602i	$-0.886317\pi$
$733$	−0.736544	+	1.77817i	−0.0272049	+	0.0656784i	0.909693	+	0.415281i	$0.136317\pi$
$734$		0			0
$735$	31.2132			1.15132
$736$		0			0
$737$	1.27208			0.0468576
$738$		0			0
$739$	−7.53553	+	18.1924i	−0.277199	+	0.669218i	−0.999756	−	0.0220937i	$-0.992967\pi$
$739$	−7.53553	+	18.1924i	−0.277199	+	0.669218i	0.722557	+	0.691312i	$0.242967\pi$
$740$		0			0
$741$	−18.8995	+	7.82843i	−0.694290	+	0.287584i
$742$		0			0
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	−0.411478	−	0.911420i	$-0.634987\pi$
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	0.911420	+	0.411478i	$0.134987\pi$
$744$		0			0
$745$	−35.0000	−	35.0000i	−1.28230	−	1.28230i
$746$		0			0
$747$	1.05025	+	2.53553i	0.0384267	+	0.0927703i
$748$		0			0
$749$	0.414214	+	0.171573i	0.0151350	+	0.00626914i
$750$		0			0
$751$		−	22.9706i		−	0.838208i	−0.907938	−	0.419104i	$-0.862344\pi$
$751$		−	22.9706i		−	0.838208i	0.907938	−	0.419104i	$-0.137656\pi$
$752$		0			0
$753$			29.2132i			1.06459i
$754$		0			0
$755$	68.3553	+	28.3137i	2.48771	+	1.03044i
$756$		0			0
$757$	−0.736544	−	1.77817i	−0.0267701	−	0.0646289i	0.909929	−	0.414764i	$-0.136136\pi$
$757$	−0.736544	−	1.77817i	−0.0267701	−	0.0646289i	−0.936699	+	0.350135i	$0.886136\pi$
$758$		0			0
$759$	−0.100505	−	0.100505i	−0.00364810	−	0.00364810i
$760$		0			0
$761$	−24.1716	+	24.1716i	−0.876219	+	0.876219i	−0.993141	−	0.116922i	$-0.962697\pi$
$761$	−24.1716	+	24.1716i	−0.876219	+	0.876219i	0.116922	+	0.993141i	$0.462697\pi$
$762$		0			0
$763$	6.07107	−	2.51472i	0.219787	−	0.0910389i
$764$		0			0
$765$	−1.51472	+	3.65685i	−0.0547648	+	0.132214i
$766$		0			0
$767$	12.2426			0.442056
$768$		0			0
$769$	22.4853			0.810840			0.405420	−	0.914131i	$-0.367125\pi$
$769$	22.4853			0.810840			0.405420	+	0.914131i	$0.367125\pi$
$770$		0			0
$771$	−4.24264	+	10.2426i	−0.152795	+	0.368880i
$772$		0			0
$773$	−26.0919	+	10.8076i	−0.938460	+	0.388723i	−0.798882	−	0.601488i	$-0.794575\pi$
$773$	−26.0919	+	10.8076i	−0.938460	+	0.388723i	−0.139578	+	0.990211i	$0.544575\pi$
$774$		0			0
$775$	18.1421	−	18.1421i	0.651685	−	0.651685i
$776$		0			0
$777$	−3.41421	−	3.41421i	−0.122484	−	0.122484i
$778$		0			0
$779$	−18.8995	−	45.6274i	−0.677145	−	1.63477i
$780$		0			0
$781$	−0.0710678	−	0.0294373i	−0.00254301	−	0.00105335i
$782$		0			0
$783$			14.0000i			0.500319i
$784$		0			0
$785$			2.58579i			0.0922907i
$786$		0			0
$787$	−8.94975	−	3.70711i	−0.319024	−	0.132144i	0.217424	−	0.976077i	$-0.430234\pi$
$787$	−8.94975	−	3.70711i	−0.319024	−	0.132144i	−0.536448	+	0.843933i	$0.680234\pi$
$788$		0			0
$789$	0.171573	+	0.414214i	0.00610816	+	0.0147464i
$790$		0			0
$791$	17.6569	+	17.6569i	0.627805	+	0.627805i
$792$		0			0
$793$	1.00000	−	1.00000i	0.0355110	−	0.0355110i
$794$		0			0
$795$	47.0416	−	19.4853i	1.66839	−	0.691072i
$796$		0			0
$797$	12.0919	−	29.1924i	0.428316	−	1.03405i	−0.551505	−	0.834172i	$-0.685946\pi$
$797$	12.0919	−	29.1924i	0.428316	−	1.03405i	0.979821	−	0.199876i	$-0.0640538\pi$
$798$		0			0
$799$	−32.9706			−1.16641
$800$		0			0
$801$	1.55635			0.0549909
$802$		0			0
$803$	1.20101	−	2.89949i	0.0423827	−	0.102321i
$804$		0			0
$805$	−1.07107	+	0.443651i	−0.0377502	+	0.0156366i
$806$		0			0
$807$	−6.89949	+	6.89949i	−0.242874	+	0.242874i
$808$		0			0
$809$	−0.857864	−	0.857864i	−0.0301609	−	0.0301609i	0.691865	−	0.722026i	$-0.256789\pi$
$809$	−0.857864	−	0.857864i	−0.0301609	−	0.0301609i	−0.722026	+	0.691865i	$0.756789\pi$
$810$		0			0
$811$	9.73654	+	23.5061i	0.341896	+	0.825411i	0.997524	+	0.0703264i	$0.0224041\pi$
$811$	9.73654	+	23.5061i	0.341896	+	0.825411i	−0.655628	+	0.755084i	$0.727596\pi$
$812$		0			0
$813$	30.7279	+	12.7279i	1.07768	+	0.446388i
$814$		0			0
$815$		−	66.5269i		−	2.33034i
$816$		0			0
$817$		−	51.5563i		−	1.80373i
$818$		0			0
$819$	1.00000	+	0.414214i	0.0349428	+	0.0144738i
$820$		0			0
$821$	−0.393398	−	0.949747i	−0.0137297	−	0.0331464i	0.916866	−	0.399195i	$-0.130710\pi$
$821$	−0.393398	−	0.949747i	−0.0137297	−	0.0331464i	−0.930596	+	0.366049i	$0.880710\pi$
$822$		0			0
$823$	−2.02944	−	2.02944i	−0.0707417	−	0.0707417i	0.670851	−	0.741592i	$-0.265929\pi$
$823$	−2.02944	−	2.02944i	−0.0707417	−	0.0707417i	−0.741592	+	0.670851i	$0.765929\pi$
$824$		0			0
$825$	2.65685	−	2.65685i	0.0924998	−	0.0924998i
$826$		0			0
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	−0.579530	−	0.814951i	$-0.696764\pi$
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	0.166468	+	0.986047i	$0.446764\pi$
$828$		0			0
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	−0.369187	−	0.929355i	$-0.620364\pi$
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	0.918208	−	0.396099i	$-0.129636\pi$
$830$		0			0
$831$	−1.41421			−0.0490585
$832$		0			0
$833$	−14.1421			−0.489996
$834$		0			0
$835$	6.11270	−	14.7574i	0.211539	−	0.510699i
$836$		0			0
$837$	−17.6569	+	7.31371i	−0.610310	+	0.252799i
$838$		0			0
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.123213	+	0.992380i	$0.539320\pi$
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.992380	+	0.123213i	$0.960680\pi$
$840$		0			0
$841$	14.4350	+	14.4350i	0.497760	+	0.497760i
$842$		0			0
$843$	−6.17157	−	14.8995i	−0.212560	−	0.513166i
$844$		0			0
$845$	29.9203	+	12.3934i	1.02929	+	0.426346i
$846$		0			0
$847$			15.4142i			0.529639i
$848$		0			0
$849$			19.5563i			0.671172i
$850$		0			0
$851$	−0.414214	−	0.171573i	−0.0141991	−	0.00588144i
$852$		0			0
$853$	−1.16295	−	2.80761i	−0.0398187	−	0.0961308i	0.902719	−	0.430231i	$-0.141568\pi$
$853$	−1.16295	−	2.80761i	−0.0398187	−	0.0961308i	−0.942538	+	0.334100i	$0.891568\pi$
$854$		0			0
$855$	5.92893	+	5.92893i	0.202765	+	0.202765i
$856$		0			0
$857$	32.3137	−	32.3137i	1.10382	−	1.10382i	0.109869	−	0.993946i	$-0.464957\pi$
$857$	32.3137	−	32.3137i	1.10382	−	1.10382i	0.993946	−	0.109869i	$-0.0350432\pi$
$858$		0			0
$859$	−33.6777	+	13.9497i	−1.14907	+	0.475959i	−0.874221	−	0.485529i	$-0.838627\pi$
$859$	−33.6777	+	13.9497i	−1.14907	+	0.475959i	−0.274847	+	0.961488i	$0.588627\pi$
$860$		0			0
$861$	−8.24264	+	19.8995i	−0.280908	+	0.678173i
$862$		0			0
$863$	45.9411			1.56385			0.781927	−	0.623370i	$-0.214237\pi$
$863$	45.9411			1.56385			0.781927	+	0.623370i	$0.214237\pi$
$864$		0			0
$865$	4.10051			0.139421
$866$		0			0
$867$	−6.36396	+	15.3640i	−0.216131	+	0.521787i
$868$		0			0
$869$	−1.75736	+	0.727922i	−0.0596143	+	0.0246931i
$870$		0			0
$871$	−5.24264	+	5.24264i	−0.177640	+	0.177640i
$872$		0			0
$873$	0.443651	+	0.443651i	0.0150153	+	0.0150153i
$874$		0			0
$875$	−2.58579	−	6.24264i	−0.0874155	−	0.211040i
$876$		0			0
$877$	−33.2635	−	13.7782i	−1.12323	−	0.465256i	−0.257754	−	0.966211i	$-0.582982\pi$
$877$	−33.2635	−	13.7782i	−1.12323	−	0.465256i	−0.865473	+	0.500955i	$0.832982\pi$
$878$		0			0
$879$		−	23.2132i		−	0.782962i
$880$		0			0
$881$		−	22.6274i		−	0.762337i	−0.924506	−	0.381169i	$-0.875522\pi$
$881$		−	22.6274i		−	0.762337i	0.924506	−	0.381169i	$-0.124478\pi$
$882$		0			0
$883$	−47.4350	−	19.6482i	−1.59632	−	0.661216i	−0.605427	−	0.795901i	$-0.706998\pi$
$883$	−47.4350	−	19.6482i	−1.59632	−	0.661216i	−0.990888	+	0.134685i	$0.956998\pi$
$884$		0			0
$885$	−15.8284	−	38.2132i	−0.532067	−	1.28452i
$886$		0			0
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	0.960466	−	0.278398i	$-0.0898035\pi$
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	−0.278398	+	0.960466i	$0.589803\pi$
$888$		0			0
$889$	−20.9706	+	20.9706i	−0.703330	+	0.703330i
$890$		0			0
$891$	−2.94975	+	1.22183i	−0.0988203	+	0.0409327i
$892$		0			0
$893$	−26.7279	+	64.5269i	−0.894416	+	2.15931i
$894$		0			0
$895$	−52.5269			−1.75578
$896$		0			0
$897$	0.828427			0.0276604
$898$		0			0
$899$	4.48528	−	10.8284i	0.149593	−	0.361148i
$900$		0			0
$901$	−21.3137	+	8.82843i	−0.710063	+	0.294118i
$902$		0			0
$903$	−15.8995	+	15.8995i	−0.529102	+	0.529102i
$904$		0			0
$905$	13.6863	+	13.6863i	0.454948	+	0.454948i
$906$		0			0
$907$	0.221825	+	0.535534i	0.00736559	+	0.0177821i	0.927520	−	0.373775i	$-0.121937\pi$
$907$	0.221825	+	0.535534i	0.00736559	+	0.0177821i	−0.920154	+	0.391557i	$0.871937\pi$
$908$		0			0
$909$	−4.70711	−	1.94975i	−0.156125	−	0.0646690i
$910$		0			0
$911$			45.5980i			1.51073i	0.655305	+	0.755364i	$0.272540\pi$
$911$			45.5980i			1.51073i	−0.655305	+	0.755364i	$0.727460\pi$
$912$		0			0
$913$			2.10051i			0.0695166i
$914$		0			0
$915$	−4.41421	−	1.82843i	−0.145929	−	0.0604459i
$916$		0			0
$917$	5.14214	+	12.4142i	0.169808	+	0.409953i
$918$		0			0
$919$	25.4853	+	25.4853i	0.840682	+	0.840682i	0.988948	−	0.148266i	$-0.0473691\pi$
$919$	25.4853	+	25.4853i	0.840682	+	0.840682i	−0.148266	+	0.988948i	$0.547369\pi$
$920$		0			0
$921$	4.17157	−	4.17157i	0.137458	−	0.137458i
$922$		0			0
$923$	0.414214	−	0.171573i	0.0136340	−	0.00564739i
$924$		0			0
$925$	4.53553	−	10.9497i	0.149127	−	0.360025i
$926$		0			0
$927$	−4.38478			−0.144015
$928$		0			0
$929$	−26.4853			−0.868954			−0.434477	−	0.900683i	$-0.643067\pi$
$929$	−26.4853			−0.868954			−0.434477	+	0.900683i	$0.643067\pi$
$930$		0			0
$931$	−11.4645	+	27.6777i	−0.375733	+	0.907099i
$932$		0			0
$933$	20.8995	−	8.65685i	0.684219	−	0.283413i
$934$		0			0
$935$	−2.14214	+	2.14214i	−0.0700553	+	0.0700553i
$936$		0			0
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	0.945711	−	0.325008i	$-0.105367\pi$
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	−0.325008	+	0.945711i	$0.605367\pi$
$938$		0			0
$939$	9.48528	+	22.8995i	0.309540	+	0.747297i
$940$		0			0
$941$	13.3640	+	5.53553i	0.435653	+	0.180453i	0.589721	−	0.807607i	$-0.299238\pi$
$941$	13.3640	+	5.53553i	0.435653	+	0.180453i	−0.154068	+	0.988060i	$0.549238\pi$
$942$		0			0
$943$			2.00000i			0.0651290i
$944$		0			0
$945$			22.8284i			0.742609i
$946$		0			0
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.895245	−	0.445575i	$-0.147001\pi$
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.317964	+	0.948103i	$0.397001\pi$
$948$		0			0
$949$	7.00000	+	16.8995i	0.227230	+	0.548581i
$950$		0			0
$951$	15.8284	+	15.8284i	0.513272	+	0.513272i
$952$		0			0
$953$	3.34315	−	3.34315i	0.108295	−	0.108295i	−0.650883	−	0.759178i	$-0.725601\pi$
$953$	3.34315	−	3.34315i	0.108295	−	0.108295i	0.759178	+	0.650883i	$0.225601\pi$
$954$		0			0
$955$	−37.4558	+	15.5147i	−1.21204	+	0.502045i
$956$		0			0
$957$	0.656854	−	1.58579i	0.0212331	−	0.0512612i
$958$		0			0
$959$	−5.31371			−0.171589
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−0.0502525	+	0.121320i	−0.00161937	+	0.00390949i
$964$		0			0
$965$	57.6985	−	23.8995i	1.85738	−	0.769352i
$966$		0			0
$967$	39.9706	−	39.9706i	1.28537	−	1.28537i	0.347797	−	0.937570i	$-0.386930\pi$
$967$	39.9706	−	39.9706i	1.28537	−	1.28537i	0.937570	−	0.347797i	$-0.113070\pi$
$968$		0			0
$969$	−22.1421	−	22.1421i	−0.711308	−	0.711308i
$970$		0			0
$971$	−9.63604	−	23.2635i	−0.309235	−	0.746560i	−0.999730	−	0.0232228i	$-0.992607\pi$
$971$	−9.63604	−	23.2635i	−0.309235	−	0.746560i	0.690495	−	0.723337i	$-0.257393\pi$
$972$		0			0
$973$	−17.7279	−	7.34315i	−0.568331	−	0.235410i
$974$		0			0
$975$			21.8995i			0.701345i
$976$		0			0
$977$		−	14.1421i		−	0.452447i	−0.974075	−	0.226224i	$-0.927362\pi$
$977$		−	14.1421i		−	0.452447i	0.974075	−	0.226224i	$-0.0726380\pi$
$978$		0			0
$979$	1.10051	+	0.455844i	0.0351723	+	0.0145688i
$980$		0			0
$981$	0.736544	+	1.77817i	0.0235160	+	0.0567727i
$982$		0			0
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	0.168341	−	0.985729i	$-0.446159\pi$
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	−0.985729	+	0.168341i	$0.946159\pi$
$984$		0			0
$985$	−44.8995	+	44.8995i	−1.43062	+	1.43062i
$986$		0			0
$987$	28.1421	−	11.6569i	0.895774	−	0.371042i
$988$		0			0
$989$	−0.798990	+	1.92893i	−0.0254064	+	0.0613365i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	−13.0711			−0.414798
$994$		0			0
$995$	32.8579	−	79.3259i	1.04166	−	2.51480i
$996$		0			0
$997$	−1.80761	+	0.748737i	−0.0572476	+	0.0237127i	−0.411124	−	0.911580i	$-0.634864\pi$
$997$	−1.80761	+	0.748737i	−0.0572476	+	0.0237127i	0.353876	+	0.935292i	$0.384864\pi$
$998$		0			0
$999$	−6.24264	+	6.24264i	−0.197508	+	0.197508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.g.a.17.1		4
3.2	odd	2		1152.2.v.a.145.1		4
4.3	odd	2		32.2.g.a.13.1	yes	4
8.3	odd	2		256.2.g.b.33.1		4
8.5	even	2		256.2.g.a.33.1		4
12.11	even	2		288.2.v.a.109.1		4
16.3	odd	4		512.2.g.d.321.1		4
16.5	even	4		512.2.g.c.321.1		4
16.11	odd	4		512.2.g.a.321.1		4
16.13	even	4		512.2.g.b.321.1		4
20.3	even	4		800.2.ba.b.749.1		4
20.7	even	4		800.2.ba.a.749.1		4
20.19	odd	2		800.2.y.a.301.1		4
32.3	odd	8		512.2.g.d.193.1		4
32.5	even	8	inner	128.2.g.a.113.1		4
32.11	odd	8		256.2.g.b.225.1		4
32.13	even	8		512.2.g.c.193.1		4
32.19	odd	8		512.2.g.a.193.1		4
32.21	even	8		256.2.g.a.225.1		4
32.27	odd	8		32.2.g.a.5.1	✓	4
32.29	even	8		512.2.g.b.193.1		4
64.5	even	16		4096.2.a.f.1.1		4
64.27	odd	16		4096.2.a.e.1.1		4
64.37	even	16		4096.2.a.f.1.4		4
64.59	odd	16		4096.2.a.e.1.4		4
96.5	odd	8		1152.2.v.a.1009.1		4
96.59	even	8		288.2.v.a.37.1		4
160.27	even	8		800.2.ba.b.549.1		4
160.59	odd	8		800.2.y.a.101.1		4
160.123	even	8		800.2.ba.a.549.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	32.27	odd	8
32.2.g.a.13.1	yes	4	4.3	odd	2
128.2.g.a.17.1		4	1.1	even	1	trivial
128.2.g.a.113.1		4	32.5	even	8	inner
256.2.g.a.33.1		4	8.5	even	2
256.2.g.a.225.1		4	32.21	even	8
256.2.g.b.33.1		4	8.3	odd	2
256.2.g.b.225.1		4	32.11	odd	8
288.2.v.a.37.1		4	96.59	even	8
288.2.v.a.109.1		4	12.11	even	2
512.2.g.a.193.1		4	32.19	odd	8
512.2.g.a.321.1		4	16.11	odd	4
512.2.g.b.193.1		4	32.29	even	8
512.2.g.b.321.1		4	16.13	even	4
512.2.g.c.193.1		4	32.13	even	8
512.2.g.c.321.1		4	16.5	even	4
512.2.g.d.193.1		4	32.3	odd	8
512.2.g.d.321.1		4	16.3	odd	4
800.2.y.a.101.1		4	160.59	odd	8
800.2.y.a.301.1		4	20.19	odd	2
800.2.ba.a.549.1		4	160.123	even	8
800.2.ba.a.749.1		4	20.7	even	4
800.2.ba.b.549.1		4	160.27	even	8
800.2.ba.b.749.1		4	20.3	even	4
1152.2.v.a.145.1		4	3.2	odd	2
1152.2.v.a.1009.1		4	96.5	odd	8
4096.2.a.e.1.1		4	64.27	odd	16
4096.2.a.e.1.4		4	64.59	odd	16
4096.2.a.f.1.1		4	64.5	even	16
4096.2.a.f.1.4		4	64.37	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.70711i) q^{3} +(-3.12132 + 1.29289i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-0.292893 - 0.292893i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.70711i) q^{3} +(-3.12132 + 1.29289i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-0.292893 - 0.292893i) q^{9} +(-0.121320 - 0.292893i) q^{11} +(1.70711 + 0.707107i) q^{13} -6.24264i q^{15} +2.82843i q^{17} +(5.53553 + 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(-0.171573 - 0.171573i) q^{23} +(4.53553 - 4.53553i) q^{25} +(-4.41421 + 1.82843i) q^{27} +(1.12132 - 2.70711i) q^{29} +4.00000 q^{31} +0.585786 q^{33} +(1.82843 - 4.41421i) q^{35} +(1.70711 - 0.707107i) q^{37} +(-2.41421 + 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(-3.29289 - 7.94975i) q^{43} +(1.29289 + 0.535534i) q^{45} +11.6569i q^{47} +5.00000i q^{49} +(-4.82843 - 2.00000i) q^{51} +(3.12132 + 7.53553i) q^{53} +(0.757359 + 0.757359i) q^{55} +(-7.82843 + 7.82843i) q^{57} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +0.585786 q^{63} -6.24264 q^{65} +(-1.53553 + 3.70711i) q^{67} +(0.414214 - 0.171573i) q^{69} +(0.171573 - 0.171573i) q^{71} +(7.00000 + 7.00000i) q^{73} +(4.53553 + 10.9497i) q^{75} +(0.414214 + 0.171573i) q^{77} -6.00000i q^{79} -10.0711i q^{81} +(-6.12132 - 2.53553i) q^{83} +(-3.65685 - 8.82843i) q^{85} +(3.82843 + 3.82843i) q^{87} +(-2.65685 + 2.65685i) q^{89} +(-2.41421 + 1.00000i) q^{91} +(-2.82843 + 6.82843i) q^{93} -20.2426 q^{95} -1.51472 q^{97} +(-0.0502525 + 0.121320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9	\( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9} + 8 q^{11} + 4 q^{13} + 8 q^{19} - 4 q^{21} - 12 q^{23} + 4 q^{25} - 12 q^{27} - 4 q^{29} + 16 q^{31} + 8 q^{33} - 4 q^{35} + 4 q^{37} - 4 q^{39} - 12 q^{41} - 16 q^{43} + 8 q^{45} - 8 q^{51} + 4 q^{53} + 20 q^{55} - 20 q^{57} + 16 q^{59} + 4 q^{61} + 8 q^{63} - 8 q^{65} + 8 q^{67} - 4 q^{69} + 12 q^{71} + 28 q^{73} + 4 q^{75} - 4 q^{77} - 16 q^{83} + 8 q^{85} + 4 q^{87} + 12 q^{89} - 4 q^{91} - 64 q^{95} - 40 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9 + 8 * q^11 + 4 * q^13 + 8 * q^19 - 4 * q^21 - 12 * q^23 + 4 * q^25 - 12 * q^27 - 4 * q^29 + 16 * q^31 + 8 * q^33 - 4 * q^35 + 4 * q^37 - 4 * q^39 - 12 * q^41 - 16 * q^43 + 8 * q^45 - 8 * q^51 + 4 * q^53 + 20 * q^55 - 20 * q^57 + 16 * q^59 + 4 * q^61 + 8 * q^63 - 8 * q^65 + 8 * q^67 - 4 * q^69 + 12 * q^71 + 28 * q^73 + 4 * q^75 - 4 * q^77 - 16 * q^83 + 8 * q^85 + 4 * q^87 + 12 * q^89 - 4 * q^91 - 64 * q^95 - 40 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more