LMFDB - Embedded newform 1040.2.da.e.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Root			$-1.30089 - 0.554694i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.e.641.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.170066 - 0.294562i) q^{3} -1.00000i q^{5} +(4.07999 + 2.35558i) q^{7} +(1.44216 - 2.49789i) q^{9} +O(q^{10})$	\(q+(-0.170066 - 0.294562i) q^{3} -1.00000i q^{5} +(4.07999 + 2.35558i) q^{7} +(1.44216 - 2.49789i) q^{9} +(3.59230 - 2.07402i) q^{11} +(-2.36575 + 2.72089i) q^{13} +(-0.294562 + 0.170066i) q^{15} +(-2.86858 + 4.96852i) q^{17} +(5.05704 + 2.91968i) q^{19} -1.60242i q^{21} +(-2.15298 - 3.72907i) q^{23} -1.00000 q^{25} -2.00144 q^{27} +(-4.09019 - 7.08441i) q^{29} +4.89530i q^{31} +(-1.22185 - 0.705438i) q^{33} +(2.35558 - 4.07999i) q^{35} +(5.87574 - 3.39236i) q^{37} +(1.20380 + 0.234130i) q^{39} +(6.13847 - 3.54404i) q^{41} +(2.26093 - 3.91604i) q^{43} +(-2.49789 - 1.44216i) q^{45} +13.0234i q^{47} +(7.59755 + 13.1593i) q^{49} +1.95139 q^{51} -3.11569 q^{53} +(-2.07402 - 3.59230i) q^{55} -1.98615i q^{57} +(-1.36905 - 0.790422i) q^{59} +(2.06863 - 3.58297i) q^{61} +(11.7680 - 6.79424i) q^{63} +(2.72089 + 2.36575i) q^{65} +(7.27646 - 4.20107i) q^{67} +(-0.732295 + 1.26837i) q^{69} +(0.708161 + 0.408857i) q^{71} +1.75355i q^{73} +(0.170066 + 0.294562i) q^{75} +19.5421 q^{77} +4.83956 q^{79} +(-3.98609 - 6.90411i) q^{81} -3.72439i q^{83} +(4.96852 + 2.86858i) q^{85} +(-1.39120 + 2.40963i) q^{87} +(5.73910 - 3.31347i) q^{89} +(-16.0615 + 5.52850i) q^{91} +(1.44197 - 0.832522i) q^{93} +(2.91968 - 5.05704i) q^{95} +(-13.2416 - 7.64505i) q^{97} -11.9642i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 + 2 * q^9	$ 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) $ 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.170066	−	0.294562i	−0.0981874	−	0.170066i	0.812747	−	0.582617i	$-0.197971\pi$
$3$	−0.170066	−	0.294562i	−0.0981874	−	0.170066i	−0.910934	+	0.412551i	$0.864638\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	4.07999	+	2.35558i	1.54209	+	0.890327i	0.998707	+	0.0508435i	$0.0161910\pi$
$7$	4.07999	+	2.35558i	1.54209	+	0.890327i	0.543385	+	0.839484i	$0.317142\pi$
$8$		0			0
$9$	1.44216	−	2.49789i	0.480718	−	0.832629i
$10$		0			0
$11$	3.59230	−	2.07402i	1.08312	−	0.625339i	0.151383	−	0.988475i	$-0.451627\pi$
$11$	3.59230	−	2.07402i	1.08312	−	0.625339i	0.931736	+	0.363136i	$0.118294\pi$
$12$		0			0
$13$	−2.36575	+	2.72089i	−0.656140	+	0.754639i
$13$	−2.36575	+	2.72089i	−0.656140	+	0.754639i
$14$		0			0
$15$	−0.294562	+	0.170066i	−0.0760557	+	0.0439108i
$16$		0			0
$17$	−2.86858	+	4.96852i	−0.695733	+	1.20504i	0.274201	+	0.961673i	$0.411587\pi$
$17$	−2.86858	+	4.96852i	−0.695733	+	1.20504i	−0.969933	+	0.243372i	$0.921747\pi$
$18$		0			0
$19$	5.05704	+	2.91968i	1.16016	+	0.669821i	0.951343	−	0.308133i	$-0.0997041\pi$
$19$	5.05704	+	2.91968i	1.16016	+	0.669821i	0.208821	+	0.977954i	$0.433037\pi$
$20$		0			0
$21$		−	1.60242i		−	0.349676i
$22$		0			0
$23$	−2.15298	−	3.72907i	−0.448927	−	0.777565i	0.549389	−	0.835566i	$-0.314860\pi$
$23$	−2.15298	−	3.72907i	−0.448927	−	0.777565i	−0.998316	+	0.0580019i	$0.981527\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−2.00144			−0.385177
$28$		0			0
$29$	−4.09019	−	7.08441i	−0.759529	−	1.31554i	−0.943091	−	0.332534i	$-0.892096\pi$
$29$	−4.09019	−	7.08441i	−0.759529	−	1.31554i	0.183562	−	0.983008i	$-0.441237\pi$
$30$		0			0
$31$			4.89530i			0.879222i	0.898188	+	0.439611i	$0.144884\pi$
$31$			4.89530i			0.879222i	−0.898188	+	0.439611i	$0.855116\pi$
$32$		0			0
$33$	−1.22185	−	0.705438i	−0.212697	−	0.122801i
$34$		0			0
$35$	2.35558	−	4.07999i	0.398166	−	0.689644i
$36$		0			0
$37$	5.87574	−	3.39236i	0.965965	−	0.557700i	0.0679616	−	0.997688i	$-0.478350\pi$
$37$	5.87574	−	3.39236i	0.965965	−	0.557700i	0.898004	+	0.439988i	$0.145017\pi$
$38$		0			0
$39$	1.20380	+	0.234130i	0.192763	+	0.0374907i
$40$		0			0
$41$	6.13847	−	3.54404i	0.958667	−	0.553487i	0.0629046	−	0.998020i	$-0.479964\pi$
$41$	6.13847	−	3.54404i	0.958667	−	0.553487i	0.895763	+	0.444533i	$0.146630\pi$
$42$		0			0
$43$	2.26093	−	3.91604i	0.344789	−	0.597191i	−0.640527	−	0.767936i	$-0.721284\pi$
$43$	2.26093	−	3.91604i	0.344789	−	0.597191i	0.985315	+	0.170745i	$0.0546173\pi$
$44$		0			0
$45$	−2.49789	−	1.44216i	−0.372363	−	0.214984i
$46$		0			0
$47$			13.0234i			1.89966i	0.312767	+	0.949830i	$0.398744\pi$
$47$			13.0234i			1.89966i	−0.312767	+	0.949830i	$0.601256\pi$
$48$		0			0
$49$	7.59755	+	13.1593i	1.08536	+	1.87991i
$50$		0			0
$51$	1.95139			0.273249
$52$		0			0
$53$	−3.11569			−0.427973			−0.213986	−	0.976837i	$-0.568645\pi$
$53$	−3.11569			−0.427973			−0.213986	+	0.976837i	$0.568645\pi$
$54$		0			0
$55$	−2.07402	−	3.59230i	−0.279660	−	0.484386i
$56$		0			0
$57$		−	1.98615i		−	0.263072i
$58$		0			0
$59$	−1.36905	−	0.790422i	−0.178235	−	0.102904i	0.408228	−	0.912880i	$-0.366147\pi$
$59$	−1.36905	−	0.790422i	−0.178235	−	0.102904i	−0.586463	+	0.809976i	$0.699480\pi$
$60$		0			0
$61$	2.06863	−	3.58297i	0.264861	−	0.458753i	−0.702666	−	0.711520i	$-0.748007\pi$
$61$	2.06863	−	3.58297i	0.264861	−	0.458753i	0.967527	+	0.252767i	$0.0813406\pi$
$62$		0			0
$63$	11.7680	−	6.79424i	1.48262	−	0.855993i
$64$		0			0
$65$	2.72089	+	2.36575i	0.337485	+	0.293435i
$66$		0			0
$67$	7.27646	−	4.20107i	0.888961	−	0.513242i	0.0153586	−	0.999882i	$-0.495111\pi$
$67$	7.27646	−	4.20107i	0.888961	−	0.513242i	0.873603	+	0.486640i	$0.161778\pi$
$68$		0			0
$69$	−0.732295	+	1.26837i	−0.0881580	+	0.152694i
$70$		0			0
$71$	0.708161	+	0.408857i	0.0840432	+	0.0485224i	0.541433	−	0.840744i	$-0.317882\pi$
$71$	0.708161	+	0.408857i	0.0840432	+	0.0485224i	−0.457389	+	0.889266i	$0.651215\pi$
$72$		0			0
$73$			1.75355i			0.205238i	0.994721	+	0.102619i	$0.0327222\pi$
$73$			1.75355i			0.205238i	−0.994721	+	0.102619i	$0.967278\pi$
$74$		0			0
$75$	0.170066	+	0.294562i	0.0196375	+	0.0340131i
$76$		0			0
$77$	19.5421			2.22703
$78$		0			0
$79$	4.83956			0.544493			0.272246	−	0.962228i	$-0.412233\pi$
$79$	4.83956			0.544493			0.272246	+	0.962228i	$0.412233\pi$
$80$		0			0
$81$	−3.98609	−	6.90411i	−0.442899	−	0.767123i
$82$		0			0
$83$		−	3.72439i		−	0.408805i	−0.978887	−	0.204402i	$-0.934475\pi$
$83$		−	3.72439i		−	0.408805i	0.978887	−	0.204402i	$-0.0655251\pi$
$84$		0			0
$85$	4.96852	+	2.86858i	0.538912	+	0.311141i
$86$		0			0
$87$	−1.39120	+	2.40963i	−0.149152	+	0.258339i
$88$		0			0
$89$	5.73910	−	3.31347i	0.608343	−	0.351227i	−0.163973	−	0.986465i	$-0.552431\pi$
$89$	5.73910	−	3.31347i	0.608343	−	0.351227i	0.772317	+	0.635237i	$0.219098\pi$
$90$		0			0
$91$	−16.0615	+	5.52850i	−1.68370	+	0.579544i
$92$		0			0
$93$	1.44197	−	0.832522i	0.149525	−	0.0863286i
$94$		0			0
$95$	2.91968	−	5.05704i	0.299553	−	0.518841i
$96$		0			0
$97$	−13.2416	−	7.64505i	−1.34448	−	0.776237i	−0.357020	−	0.934097i	$-0.616207\pi$
$97$	−13.2416	−	7.64505i	−1.34448	−	0.776237i	−0.987462	+	0.157860i	$0.949541\pi$
$98$		0			0
$99$		−	11.9642i		−	1.20245i
$100$		0			0
$101$	−3.81512	−	6.60798i	−0.379619	−	0.657519i	0.611388	−	0.791331i	$-0.290612\pi$
$101$	−3.81512	−	6.60798i	−0.379619	−	0.657519i	−0.991007	+	0.133812i	$0.957278\pi$
$102$		0			0
$103$	−5.98056			−0.589282			−0.294641	−	0.955608i	$-0.595200\pi$
$103$	−5.98056			−0.589282			−0.294641	+	0.955608i	$0.595200\pi$
$104$		0			0
$105$	−1.60242			−0.156380
$106$		0			0
$107$	−6.00943	−	10.4086i	−0.580954	−	1.00624i	−0.995367	−	0.0961523i	$-0.969346\pi$
$107$	−6.00943	−	10.4086i	−0.580954	−	1.00624i	0.414413	−	0.910089i	$-0.363987\pi$
$108$		0			0
$109$			16.1391i			1.54585i	0.634500	+	0.772923i	$0.281206\pi$
$109$			16.1391i			1.54585i	−0.634500	+	0.772923i	$0.718794\pi$
$110$		0			0
$111$	−1.99852	−	1.15385i	−0.189691	−	0.109518i
$112$		0			0
$113$	1.36540	−	2.36494i	0.128446	−	0.222475i	−0.794629	−	0.607096i	$-0.792334\pi$
$113$	1.36540	−	2.36494i	0.128446	−	0.222475i	0.923075	+	0.384621i	$0.125668\pi$
$114$		0			0
$115$	−3.72907	+	2.15298i	−0.347737	+	0.200766i
$116$		0			0
$117$	3.38470	+	9.83331i	0.312916	+	0.909090i
$118$		0			0
$119$	−23.4076	+	13.5144i	−2.14577	+	1.23886i
$120$		0			0
$121$	3.10309	−	5.37471i	0.282099	−	0.488610i
$122$		0			0
$123$	−2.08788	−	1.20544i	−0.188258	−	0.108691i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	6.01983	+	10.4266i	0.534173	+	0.925215i	0.999203	+	0.0399203i	$0.0127104\pi$
$127$	6.01983	+	10.4266i	0.534173	+	0.925215i	−0.465029	+	0.885295i	$0.653956\pi$
$128$		0			0
$129$	−1.53803			−0.135416
$130$		0			0
$131$	−5.73785			−0.501318			−0.250659	−	0.968075i	$-0.580647\pi$
$131$	−5.73785			−0.501318			−0.250659	+	0.968075i	$0.580647\pi$
$132$		0			0
$133$	13.7551	+	23.8246i	1.19272	+	2.06585i
$134$		0			0
$135$			2.00144i			0.172256i
$136$		0			0
$137$	11.0449	+	6.37677i	0.943628	+	0.544804i	0.891096	−	0.453815i	$-0.149937\pi$
$137$	11.0449	+	6.37677i	0.943628	+	0.544804i	0.0525324	+	0.998619i	$0.483271\pi$
$138$		0			0
$139$	−1.89379	+	3.28014i	−0.160629	+	0.278218i	−0.935094	−	0.354399i	$-0.884686\pi$
$139$	−1.89379	+	3.28014i	−0.160629	+	0.278218i	0.774465	+	0.632616i	$0.218019\pi$
$140$		0			0
$141$	3.83621	−	2.21483i	0.323067	−	0.186523i
$142$		0			0
$143$	−2.85530	+	14.6809i	−0.238772	+	1.22767i
$144$		0			0
$145$	−7.08441	+	4.09019i	−0.588329	+	0.339672i
$146$		0			0
$147$	2.58416	−	4.47590i	0.213138	−	0.369166i
$148$		0			0
$149$	−16.3779	−	9.45578i	−1.34173	−	0.774648i	−0.354668	−	0.934992i	$-0.615406\pi$
$149$	−16.3779	−	9.45578i	−1.34173	−	0.774648i	−0.987061	+	0.160344i	$0.948740\pi$
$150$		0			0
$151$		−	18.7385i		−	1.52492i	−0.647038	−	0.762458i	$-0.723993\pi$
$151$		−	18.7385i		−	1.52492i	0.647038	−	0.762458i	$-0.276007\pi$
$152$		0			0
$153$	8.27387	+	14.3308i	0.668903	+	1.15857i
$154$		0			0
$155$	4.89530			0.393200
$156$		0			0
$157$	−18.5213			−1.47816			−0.739079	−	0.673618i	$-0.764739\pi$
$157$	−18.5213			−1.47816			−0.739079	+	0.673618i	$0.764739\pi$
$158$		0			0
$159$	0.529872	+	0.917765i	0.0420216	+	0.0727835i
$160$		0			0
$161$		−	20.2861i		−	1.59877i
$162$		0			0
$163$	8.66383	+	5.00206i	0.678603	+	0.391792i	0.799329	−	0.600894i	$-0.205189\pi$
$163$	8.66383	+	5.00206i	0.678603	+	0.391792i	−0.120725	+	0.992686i	$0.538522\pi$
$164$		0			0
$165$	−0.705438	+	1.22185i	−0.0549183	+	0.0951212i
$166$		0			0
$167$	−11.0845	+	6.39963i	−0.857744	+	0.495219i	−0.863256	−	0.504766i	$-0.831579\pi$
$167$	−11.0845	+	6.39963i	−0.857744	+	0.495219i	0.00551239	+	0.999985i	$0.498245\pi$
$168$		0			0
$169$	−1.80649	−	12.8739i	−0.138961	−	0.990298i
$170$		0			0
$171$	14.5861	−	8.42127i	1.11542	−	0.643991i
$172$		0			0
$173$	−4.07551	+	7.05898i	−0.309855	+	0.536685i	−0.978330	−	0.207050i	$-0.933614\pi$
$173$	−4.07551	+	7.05898i	−0.309855	+	0.536685i	0.668475	+	0.743734i	$0.266947\pi$
$174$		0			0
$175$	−4.07999	−	2.35558i	−0.308418	−	0.178065i
$176$		0			0
$177$			0.537694i			0.0404156i
$178$		0			0
$179$	3.11999	+	5.40398i	0.233199	+	0.403912i	0.958748	−	0.284258i	$-0.0917474\pi$
$179$	3.11999	+	5.40398i	0.233199	+	0.403912i	−0.725549	+	0.688171i	$0.758414\pi$
$180$		0			0
$181$	−1.51583			−0.112670			−0.0563352	−	0.998412i	$-0.517942\pi$
$181$	−1.51583			−0.112670			−0.0563352	+	0.998412i	$0.517942\pi$
$182$		0			0
$183$	−1.40721			−0.104024
$184$		0			0
$185$	−3.39236	−	5.87574i	−0.249411	−	0.431993i
$186$		0			0
$187$			23.7979i			1.74028i
$188$		0			0
$189$	−8.16585	−	4.71455i	−0.593978	−	0.342933i
$190$		0			0
$191$	−10.0136	+	17.3440i	−0.724557	+	1.25497i	0.234599	+	0.972092i	$0.424622\pi$
$191$	−10.0136	+	17.3440i	−0.724557	+	1.25497i	−0.959156	+	0.282877i	$0.908711\pi$
$192$		0			0
$193$	−15.8771	+	9.16663i	−1.14286	+	0.659829i	−0.947136	−	0.320831i	$-0.896038\pi$
$193$	−15.8771	+	9.16663i	−1.14286	+	0.659829i	−0.195720	+	0.980660i	$0.562704\pi$
$194$		0			0
$195$	0.234130	−	1.20380i	0.0167664	−	0.0862062i
$196$		0			0
$197$	6.62369	−	3.82419i	0.471918	−	0.272462i	−0.245124	−	0.969492i	$-0.578829\pi$
$197$	6.62369	−	3.82419i	0.471918	−	0.272462i	0.717042	+	0.697030i	$0.245495\pi$
$198$		0			0
$199$	−6.63174	+	11.4865i	−0.470111	+	0.814257i	−0.999416	−	0.0341753i	$-0.989120\pi$
$199$	−6.63174	+	11.4865i	−0.470111	+	0.814257i	0.529305	+	0.848432i	$0.322453\pi$
$200$		0			0
$201$	−2.47495	−	1.42891i	−0.174570	−	0.100788i
$202$		0			0
$203$		−	38.5391i		−	2.70492i
$204$		0			0
$205$	−3.54404	−	6.13847i	−0.247527	−	0.428729i
$206$		0			0
$207$	−12.4197			−0.863230
$208$		0			0
$209$	24.2219			1.67546
$210$		0			0
$211$	−13.2773	−	22.9969i	−0.914044	−	1.58317i	−0.808295	−	0.588777i	$-0.799609\pi$
$211$	−13.2773	−	22.9969i	−0.914044	−	1.58317i	−0.105749	−	0.994393i	$-0.533724\pi$
$212$		0			0
$213$		−	0.278130i		−	0.0190571i
$214$		0			0
$215$	−3.91604	−	2.26093i	−0.267072	−	0.154194i
$216$		0			0
$217$	−11.5313	+	19.9728i	−0.782795	+	1.35584i
$218$		0			0
$219$	0.516531	−	0.298219i	0.0349039	−	0.0201518i
$220$		0			0
$221$	−6.73248	−	19.5594i	−0.452876	−	1.31570i
$222$		0			0
$223$	13.0774	−	7.55023i	0.875726	−	0.505601i	0.00647909	−	0.999979i	$-0.497938\pi$
$223$	13.0774	−	7.55023i	0.875726	−	0.505601i	0.869247	+	0.494378i	$0.164604\pi$
$224$		0			0
$225$	−1.44216	+	2.49789i	−0.0961437	+	0.166526i
$226$		0			0
$227$	2.78202	+	1.60620i	0.184649	+	0.106607i	0.589475	−	0.807787i	$-0.299335\pi$
$227$	2.78202	+	1.60620i	0.184649	+	0.106607i	−0.404826	+	0.914394i	$0.632668\pi$
$228$		0			0
$229$			20.4062i			1.34848i	0.738512	+	0.674241i	$0.235529\pi$
$229$			20.4062i			1.34848i	−0.738512	+	0.674241i	$0.764471\pi$
$230$		0			0
$231$	−3.32344	−	5.75636i	−0.218666	−	0.378741i
$232$		0			0
$233$	−2.96528			−0.194262			−0.0971311	−	0.995272i	$-0.530967\pi$
$233$	−2.96528			−0.194262			−0.0971311	+	0.995272i	$0.530967\pi$
$234$		0			0
$235$	13.0234			0.849554
$236$		0			0
$237$	−0.823042	−	1.42555i	−0.0534623	−	0.0925995i
$238$		0			0
$239$			2.70183i			0.174767i	0.996175	+	0.0873836i	$0.0278506\pi$
$239$			2.70183i			0.174767i	−0.996175	+	0.0873836i	$0.972149\pi$
$240$		0			0
$241$	−18.5216	−	10.6934i	−1.19308	−	0.688824i	−0.234075	−	0.972219i	$-0.575206\pi$
$241$	−18.5216	−	10.6934i	−1.19308	−	0.688824i	−0.959003	+	0.283394i	$0.908539\pi$
$242$		0			0
$243$	−4.35795	+	7.54819i	−0.279563	+	0.484217i
$244$		0			0
$245$	13.1593	−	7.59755i	0.840720	−	0.485390i
$246$		0			0
$247$	−19.9078	+	6.85242i	−1.26670	+	0.436009i
$248$		0			0
$249$	−1.09706	+	0.633391i	−0.0695236	+	0.0401395i
$250$		0			0
$251$	3.32148	−	5.75297i	0.209650	−	0.363124i	−0.741954	−	0.670450i	$-0.766101\pi$
$251$	3.32148	−	5.75297i	0.209650	−	0.363124i	0.951604	+	0.307326i	$0.0994343\pi$
$252$		0			0
$253$	−15.4683	−	8.93063i	−0.972484	−	0.561464i
$254$		0			0
$255$		−	1.95139i		−	0.122201i
$256$		0			0
$257$	−2.26604	−	3.92489i	−0.141351	−	0.244828i	0.786654	−	0.617394i	$-0.211811\pi$
$257$	−2.26604	−	3.92489i	−0.141351	−	0.244828i	−0.928006	+	0.372566i	$0.878478\pi$
$258$		0			0
$259$	31.9639			1.98614
$260$		0			0
$261$	−23.5947			−1.46048
$262$		0			0
$263$	11.3740	+	19.7003i	0.701350	+	1.21477i	0.967993	+	0.250978i	$0.0807522\pi$
$263$	11.3740	+	19.7003i	0.701350	+	1.21477i	−0.266643	+	0.963795i	$0.585914\pi$
$264$		0			0
$265$			3.11569i			0.191395i
$266$		0			0
$267$	−1.95205	−	1.12702i	−0.119463	−	0.0689722i
$268$		0			0
$269$	2.59679	−	4.49777i	0.158329	−	0.274234i	−0.775937	−	0.630810i	$-0.782723\pi$
$269$	2.59679	−	4.49777i	0.158329	−	0.274234i	0.934266	+	0.356576i	$0.116056\pi$
$270$		0			0
$271$	−12.3538	+	7.13246i	−0.750439	+	0.433266i	−0.825853	−	0.563886i	$-0.809306\pi$
$271$	−12.3538	+	7.13246i	−0.750439	+	0.433266i	0.0754133	+	0.997152i	$0.475972\pi$
$272$		0			0
$273$	4.36000	+	3.79091i	0.263879	+	0.229436i
$274$		0			0
$275$	−3.59230	+	2.07402i	−0.216624	+	0.125068i
$276$		0			0
$277$	−5.12854	+	8.88290i	−0.308144	+	0.533721i	−0.977956	−	0.208809i	$-0.933041\pi$
$277$	−5.12854	+	8.88290i	−0.308144	+	0.533721i	0.669812	+	0.742531i	$0.266375\pi$
$278$		0			0
$279$	12.2279	+	7.05978i	0.732066	+	0.422658i
$280$		0			0
$281$			2.97284i			0.177345i	0.996061	+	0.0886725i	$0.0282625\pi$
$281$			2.97284i			0.177345i	−0.996061	+	0.0886725i	$0.971738\pi$
$282$		0			0
$283$	−6.46006	−	11.1892i	−0.384011	−	0.665126i	0.607621	−	0.794227i	$-0.292124\pi$
$283$	−6.46006	−	11.1892i	−0.384011	−	0.665126i	−0.991631	+	0.129101i	$0.958791\pi$
$284$		0			0
$285$	−1.98615			−0.117649
$286$		0			0
$287$	33.3932			1.97114
$288$		0			0
$289$	−7.95749	−	13.7828i	−0.468087	−	0.810751i
$290$		0			0
$291$			5.20064i			0.304867i
$292$		0			0
$293$	−17.5847	−	10.1526i	−1.02731	−	0.593118i	−0.111098	−	0.993809i	$-0.535437\pi$
$293$	−17.5847	−	10.1526i	−1.02731	−	0.593118i	−0.916213	+	0.400691i	$0.868770\pi$
$294$		0			0
$295$	−0.790422	+	1.36905i	−0.0460201	+	0.0797092i
$296$		0			0
$297$	−7.18977	+	4.15101i	−0.417193	+	0.240866i
$298$		0			0
$299$	15.2398	+	2.96401i	0.881340	+	0.171413i
$300$		0			0
$301$	18.4491	−	10.6516i	1.06339	−	0.613949i
$302$		0			0
$303$	−1.29764	+	2.24758i	−0.0745476	+	0.129120i
$304$		0			0
$305$	−3.58297	−	2.06863i	−0.205160	−	0.118449i
$306$		0			0
$307$			16.7838i			0.957902i	0.877842	+	0.478951i	$0.158983\pi$
$307$			16.7838i			0.957902i	−0.877842	+	0.478951i	$0.841017\pi$
$308$		0			0
$309$	1.01709	+	1.76165i	0.0578600	+	0.100217i
$310$		0			0
$311$	12.5772			0.713188			0.356594	−	0.934260i	$-0.383938\pi$
$311$	12.5772			0.713188			0.356594	+	0.934260i	$0.383938\pi$
$312$		0			0
$313$	−12.1369			−0.686017			−0.343009	−	0.939332i	$-0.611446\pi$
$313$	−12.1369			−0.686017			−0.343009	+	0.939332i	$0.611446\pi$
$314$		0			0
$315$	−6.79424	−	11.7680i	−0.382812	−	0.663050i
$316$		0			0
$317$			17.6109i			0.989125i	0.869142	+	0.494563i	$0.164672\pi$
$317$			17.6109i			0.989125i	−0.869142	+	0.494563i	$0.835328\pi$
$318$		0			0
$319$	−29.3864	−	16.9662i	−1.64532	−	0.949927i
$320$		0			0
$321$	−2.04400	+	3.54030i	−0.114085	+	0.197600i
$322$		0			0
$323$	−29.0130	+	16.7507i	−1.61433	+	0.932033i
$324$		0			0
$325$	2.36575	−	2.72089i	0.131228	−	0.150928i
$326$		0			0
$327$	4.75397	−	2.74471i	0.262895	−	0.151783i
$328$		0			0
$329$	−30.6777	+	53.1354i	−1.69132	+	2.92945i
$330$		0			0
$331$	9.44444	+	5.45275i	0.519113	+	0.299710i	0.736572	−	0.676359i	$-0.236443\pi$
$331$	9.44444	+	5.45275i	0.519113	+	0.299710i	−0.217458	+	0.976070i	$0.569777\pi$
$332$		0			0
$333$		−	19.5692i		−	1.07239i
$334$		0			0
$335$	−4.20107	−	7.27646i	−0.229529	−	0.397555i
$336$		0			0
$337$	−2.66438			−0.145138			−0.0725689	−	0.997363i	$-0.523120\pi$
$337$	−2.66438			−0.145138			−0.0725689	+	0.997363i	$0.523120\pi$
$338$		0			0
$339$	−0.928831			−0.0504472
$340$		0			0
$341$	10.1529	+	17.5854i	0.549812	+	0.952303i
$342$		0			0
$343$			38.6085i			2.08466i
$344$		0			0
$345$	1.26837	+	0.732295i	0.0682869	+	0.0394255i
$346$		0			0
$347$	−7.42526	+	12.8609i	−0.398609	+	0.690410i	−0.993555	−	0.113355i	$-0.963840\pi$
$347$	−7.42526	+	12.8609i	−0.398609	+	0.690410i	0.594946	+	0.803766i	$0.297173\pi$
$348$		0			0
$349$	−6.91023	+	3.98962i	−0.369896	+	0.213560i	−0.673413	−	0.739266i	$-0.735172\pi$
$349$	−6.91023	+	3.98962i	−0.369896	+	0.213560i	0.303517	+	0.952826i	$0.401839\pi$
$350$		0			0
$351$	4.73489	−	5.44569i	0.252730	−	0.290670i
$352$		0			0
$353$	21.2750	−	12.2831i	1.13236	−	0.653766i	0.187829	−	0.982202i	$-0.439855\pi$
$353$	21.2750	−	12.2831i	1.13236	−	0.653766i	0.944526	+	0.328436i	$0.106522\pi$
$354$		0			0
$355$	0.408857	−	0.708161i	0.0216999	−	0.0375853i
$356$		0			0
$357$	7.96164	+	4.59665i	0.421375	+	0.243281i
$358$		0			0
$359$		−	7.85104i		−	0.414362i	−0.978303	−	0.207181i	$-0.933571\pi$
$359$		−	7.85104i		−	0.414362i	0.978303	−	0.207181i	$-0.0664289\pi$
$360$		0			0
$361$	7.54910	+	13.0754i	0.397321	+	0.688180i
$362$		0			0
$363$	−2.11091			−0.110794
$364$		0			0
$365$	1.75355			0.0917852
$366$		0			0
$367$	2.13958	+	3.70585i	0.111685	+	0.193444i	0.916450	−	0.400150i	$-0.131042\pi$
$367$	2.13958	+	3.70585i	0.111685	+	0.193444i	−0.804765	+	0.593594i	$0.797709\pi$
$368$		0			0
$369$		−	20.4443i		−	1.06429i
$370$		0			0
$371$	−12.7120	−	7.33927i	−0.659973	−	0.381036i
$372$		0			0
$373$	11.4135	−	19.7688i	0.590969	−	1.02359i	−0.403134	−	0.915141i	$-0.632079\pi$
$373$	11.4135	−	19.7688i	0.590969	−	1.02359i	0.994102	−	0.108447i	$-0.0345877\pi$
$374$		0			0
$375$	0.294562	−	0.170066i	0.0152111	−	0.00878215i
$376$		0			0
$377$	28.9523	+	5.63097i	1.49112	+	0.290010i
$378$		0			0
$379$	−15.9503	+	9.20890i	−0.819311	+	0.473030i	−0.850179	−	0.526494i	$-0.823506\pi$
$379$	−15.9503	+	9.20890i	−0.819311	+	0.473030i	0.0308675	+	0.999523i	$0.490173\pi$
$380$		0			0
$381$	2.04753	−	3.54643i	0.104898	−	0.181689i
$382$		0			0
$383$	−14.3090	−	8.26130i	−0.731155	−	0.422133i	0.0876895	−	0.996148i	$-0.472052\pi$
$383$	−14.3090	−	8.26130i	−0.731155	−	0.422133i	−0.818845	+	0.574015i	$0.805385\pi$
$384$		0			0
$385$		−	19.5421i		−	0.995957i
$386$		0			0
$387$	−6.52122	−	11.2951i	−0.331492	−	0.574162i
$388$		0			0
$389$	30.7528			1.55923			0.779614	−	0.626260i	$-0.215415\pi$
$389$	30.7528			1.55923			0.779614	+	0.626260i	$0.215415\pi$
$390$		0			0
$391$	24.7040			1.24933
$392$		0			0
$393$	0.975810	+	1.69015i	0.0492231	+	0.0852569i
$394$		0			0
$395$		−	4.83956i		−	0.243504i
$396$		0			0
$397$	−20.5476	−	11.8632i	−1.03125	−	0.595395i	−0.113911	−	0.993491i	$-0.536338\pi$
$397$	−20.5476	−	11.8632i	−1.03125	−	0.595395i	−0.917344	+	0.398096i	$0.869671\pi$
$398$		0			0
$399$	4.67854	−	8.10348i	0.234220	−	0.405681i
$400$		0			0
$401$	−20.1497	+	11.6335i	−1.00623	+	0.580947i	−0.910086	−	0.414421i	$-0.863984\pi$
$401$	−20.1497	+	11.6335i	−1.00623	+	0.580947i	−0.0961440	+	0.995367i	$0.530651\pi$
$402$		0			0
$403$	−13.3196	−	11.5810i	−0.663495	−	0.576893i
$404$		0			0
$405$	−6.90411	+	3.98609i	−0.343068	+	0.198070i
$406$		0			0
$407$	14.0716	−	24.3728i	0.697504	−	1.20811i
$408$		0			0
$409$	14.0038	+	8.08512i	0.692446	+	0.399784i	0.804528	−	0.593915i	$-0.202419\pi$
$409$	14.0038	+	8.08512i	0.692446	+	0.399784i	−0.112082	+	0.993699i	$0.535752\pi$
$410$		0			0
$411$		−	4.33788i		−	0.213972i
$412$		0			0
$413$	−3.72381	−	6.44983i	−0.183237	−	0.317375i
$414$		0			0
$415$	−3.72439			−0.182823
$416$		0			0
$417$	1.28827			0.0630870
$418$		0			0
$419$	−5.87492	−	10.1757i	−0.287009	−	0.497114i	0.686086	−	0.727521i	$-0.259328\pi$
$419$	−5.87492	−	10.1757i	−0.287009	−	0.497114i	−0.973094	+	0.230407i	$0.925994\pi$
$420$		0			0
$421$			12.6849i			0.618226i	0.951025	+	0.309113i	$0.100032\pi$
$421$			12.6849i			0.618226i	−0.951025	+	0.309113i	$0.899968\pi$
$422$		0			0
$423$	32.5310	+	18.7818i	1.58171	+	0.913201i
$424$		0			0
$425$	2.86858	−	4.96852i	0.139147	−	0.241009i
$426$		0			0
$427$	16.8800	−	9.74567i	0.816880	−	0.471626i
$428$		0			0
$429$	4.81002	−	1.65564i	0.232230	−	0.0799353i
$430$		0			0
$431$	−0.195428	+	0.112830i	−0.00941344	+	0.00543485i	−0.504699	−	0.863295i	$-0.668397\pi$
$431$	−0.195428	+	0.112830i	−0.00941344	+	0.00543485i	0.495286	+	0.868730i	$0.335063\pi$
$432$		0			0
$433$	0.979419	−	1.69640i	0.0470679	−	0.0815240i	−0.841532	−	0.540208i	$-0.818346\pi$
$433$	0.979419	−	1.69640i	0.0470679	−	0.0815240i	0.888600	+	0.458684i	$0.151679\pi$
$434$		0			0
$435$	2.40963	+	1.39120i	0.115533	+	0.0667030i
$436$		0			0
$437$		−	25.1441i		−	1.20280i
$438$		0			0
$439$	−4.66053	−	8.07227i	−0.222435	−	0.385269i	0.733112	−	0.680108i	$-0.238067\pi$
$439$	−4.66053	−	8.07227i	−0.222435	−	0.385269i	−0.955547	+	0.294840i	$0.904734\pi$
$440$		0			0
$441$	43.8274			2.08702
$442$		0			0
$443$	−3.33358			−0.158383			−0.0791915	−	0.996859i	$-0.525234\pi$
$443$	−3.33358			−0.158383			−0.0791915	+	0.996859i	$0.525234\pi$
$444$		0			0
$445$	−3.31347	−	5.73910i	−0.157074	−	0.272059i
$446$		0			0
$447$			6.43241i			0.304243i
$448$		0			0
$449$	−10.9209	−	6.30521i	−0.515391	−	0.297561i	0.219656	−	0.975577i	$-0.429507\pi$
$449$	−10.9209	−	6.30521i	−0.515391	−	0.297561i	−0.735047	+	0.678016i	$0.762840\pi$
$450$		0			0
$451$	14.7008	−	25.4626i	0.692234	−	1.19898i
$452$		0			0
$453$	−5.51965	+	3.18677i	−0.259336	+	0.149728i
$454$		0			0
$455$	5.52850	+	16.0615i	0.259180	+	0.752975i
$456$		0			0
$457$	16.1997	−	9.35289i	0.757789	−	0.437510i	−0.0707120	−	0.997497i	$-0.522527\pi$
$457$	16.1997	−	9.35289i	0.757789	−	0.437510i	0.828502	+	0.559987i	$0.189194\pi$
$458$		0			0
$459$	5.74128	−	9.94419i	0.267980	−	0.464155i
$460$		0			0
$461$	−15.2066	−	8.77953i	−0.708242	−	0.408904i	0.102168	−	0.994767i	$-0.467422\pi$
$461$	−15.2066	−	8.77953i	−0.708242	−	0.408904i	−0.810410	+	0.585864i	$0.800755\pi$
$462$		0			0
$463$		−	32.2687i		−	1.49965i	−0.661635	−	0.749826i	$-0.730137\pi$
$463$		−	32.2687i		−	1.49965i	0.661635	−	0.749826i	$-0.269863\pi$
$464$		0			0
$465$	−0.832522	−	1.44197i	−0.0386073	−	0.0668698i
$466$		0			0
$467$	15.4454			0.714729			0.357365	−	0.933965i	$-0.383675\pi$
$467$	15.4454			0.714729			0.357365	+	0.933965i	$0.383675\pi$
$468$		0			0
$469$	39.5839			1.82781
$470$		0			0
$471$	3.14983	+	5.45567i	0.145137	+	0.251384i
$472$		0			0
$473$		−	18.7568i		−	0.862439i
$474$		0			0
$475$	−5.05704	−	2.91968i	−0.232033	−	0.133964i
$476$		0			0
$477$	−4.49331	+	7.78264i	−0.205734	+	0.356343i
$478$		0			0
$479$	−20.0493	+	11.5755i	−0.916078	+	0.528898i	−0.882382	−	0.470534i	$-0.844061\pi$
$479$	−20.0493	+	11.5755i	−0.916078	+	0.528898i	−0.0336962	+	0.999432i	$0.510728\pi$
$480$		0			0
$481$	−4.67027	+	24.0127i	−0.212946	+	1.09488i
$482$		0			0
$483$	−5.97552	+	3.44997i	−0.271895	+	0.156979i
$484$		0			0
$485$	−7.64505	+	13.2416i	−0.347144	+	0.601271i
$486$		0			0
$487$	1.88202	+	1.08658i	0.0852823	+	0.0492377i	0.542035	−	0.840356i	$-0.317654\pi$
$487$	1.88202	+	1.08658i	0.0852823	+	0.0492377i	−0.456752	+	0.889594i	$0.650987\pi$
$488$		0			0
$489$		−	3.40271i		−	0.153876i
$490$		0			0
$491$	−0.335153	−	0.580502i	−0.0151252	−	0.0261977i	0.858364	−	0.513042i	$-0.171481\pi$
$491$	−0.335153	−	0.580502i	−0.0151252	−	0.0261977i	−0.873489	+	0.486844i	$0.838148\pi$
$492$		0			0
$493$	46.9321			2.11372
$494$		0			0
$495$	−11.9642			−0.537751
$496$		0			0
$497$	1.92619	+	3.33626i	0.0864016	+	0.149652i
$498$		0			0
$499$			7.03926i			0.315120i	0.987509	+	0.157560i	$0.0503628\pi$
$499$			7.03926i			0.315120i	−0.987509	+	0.157560i	$0.949637\pi$
$500$		0			0
$501$	3.77018	+	2.17672i	0.168439	+	0.0972485i
$502$		0			0
$503$	2.43422	−	4.21618i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$503$	2.43422	−	4.21618i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$504$		0			0
$505$	−6.60798	+	3.81512i	−0.294051	+	0.169771i
$506$		0			0
$507$	−3.48494	+	2.72153i	−0.154771	+	0.120867i
$508$		0			0
$509$	12.8064	−	7.39378i	0.567634	−	0.327724i	−0.188570	−	0.982060i	$-0.560385\pi$
$509$	12.8064	−	7.39378i	0.567634	−	0.327724i	0.756204	+	0.654336i	$0.227052\pi$
$510$		0			0
$511$	−4.13064	+	7.15448i	−0.182729	+	0.316496i
$512$		0			0
$513$	−10.1213	−	5.84356i	−0.446868	−	0.258000i
$514$		0			0
$515$			5.98056i			0.263535i
$516$		0			0
$517$	27.0108	+	46.7840i	1.18793	+	2.05756i
$518$		0			0
$519$	2.77241			0.121695
$520$		0			0
$521$	23.3120			1.02132			0.510659	−	0.859784i	$-0.329402\pi$
$521$	23.3120			1.02132			0.510659	+	0.859784i	$0.329402\pi$
$522$		0			0
$523$	2.85690	+	4.94830i	0.124924	+	0.216374i	0.921703	−	0.387896i	$-0.126798\pi$
$523$	2.85690	+	4.94830i	0.124924	+	0.216374i	−0.796779	+	0.604270i	$0.793465\pi$
$524$		0			0
$525$			1.60242i			0.0699351i
$526$		0			0
$527$	−24.3224	−	14.0426i	−1.05950	−	0.611703i
$528$		0			0
$529$	2.22936	−	3.86137i	0.0969289	−	0.167886i
$530$		0			0
$531$	−3.94877	+	2.27982i	−0.171362	+	0.0989358i
$532$		0			0
$533$	−4.87909	+	25.0864i	−0.211337	+	1.08661i
$534$		0			0
$535$	−10.4086	+	6.00943i	−0.450005	+	0.259810i
$536$		0			0
$537$	1.06121	−	1.83806i	0.0457944	−	0.0793182i
$538$		0			0
$539$	54.5854	+	31.5149i	2.35116	+	1.35744i
$540$		0			0
$541$			30.4300i			1.30829i	0.756370	+	0.654144i	$0.226971\pi$
$541$			30.4300i			1.30829i	−0.756370	+	0.654144i	$0.773029\pi$
$542$		0			0
$543$	0.257790	+	0.446505i	0.0110628	+	0.0191614i
$544$		0			0
$545$	16.1391			0.691323
$546$		0			0
$547$	−3.75894			−0.160721			−0.0803604	−	0.996766i	$-0.525607\pi$
$547$	−3.75894			−0.160721			−0.0803604	+	0.996766i	$0.525607\pi$
$548$		0			0
$549$	−5.96657	−	10.3344i	−0.254647	−	0.441062i
$550$		0			0
$551$		−	47.7682i		−	2.03499i
$552$		0			0
$553$	19.7453	+	11.4000i	0.839657	+	0.484776i
$554$		0			0
$555$	−1.15385	+	1.99852i	−0.0489781	+	0.0848325i
$556$		0			0
$557$	−1.39979	+	0.808167i	−0.0593109	+	0.0342431i	−0.529362	−	0.848396i	$-0.677569\pi$
$557$	−1.39979	+	0.808167i	−0.0593109	+	0.0342431i	0.470051	+	0.882639i	$0.344235\pi$
$558$		0			0
$559$	5.30634	+	15.4161i	0.224434	+	0.652032i
$560$		0			0
$561$	7.00997	−	4.04721i	0.295961	−	0.170873i
$562$		0			0
$563$	−21.5284	+	37.2882i	−0.907312	+	1.57151i	−0.0895290	+	0.995984i	$0.528536\pi$
$563$	−21.5284	+	37.2882i	−0.907312	+	1.57151i	−0.817783	+	0.575526i	$0.804797\pi$
$564$		0			0
$565$	−2.36494	−	1.36540i	−0.0994940	−	0.0574429i
$566$		0			0
$567$		−	37.5583i		−	1.57730i
$568$		0			0
$569$	−19.0513	−	32.9977i	−0.798670	−	1.38334i	−0.920482	−	0.390784i	$-0.872204\pi$
$569$	−19.0513	−	32.9977i	−0.798670	−	1.38334i	0.121812	−	0.992553i	$-0.461129\pi$
$570$		0			0
$571$	−24.7149			−1.03429			−0.517143	−	0.855899i	$-0.673004\pi$
$571$	−24.7149			−1.03429			−0.517143	+	0.855899i	$0.673004\pi$
$572$		0			0
$573$	6.81186			0.284569
$574$		0			0
$575$	2.15298	+	3.72907i	0.0897854	+	0.155513i
$576$		0			0
$577$		−	10.8009i		−	0.449647i	−0.974400	−	0.224823i	$-0.927819\pi$
$577$		−	10.8009i		−	0.449647i	0.974400	−	0.224823i	$-0.0721805\pi$
$578$		0			0
$579$	5.40029	+	3.11786i	0.224428	+	0.129574i
$580$		0			0
$581$	8.77311	−	15.1955i	0.363970	−	0.630415i
$582$		0			0
$583$	−11.1925	+	6.46199i	−0.463546	+	0.267628i
$584$		0			0
$585$	9.83331	−	3.38470i	0.406557	−	0.139940i
$586$		0			0
$587$	−0.923705	+	0.533302i	−0.0381254	+	0.0220117i	−0.518942	−	0.854810i	$-0.673674\pi$
$587$	−0.923705	+	0.533302i	−0.0381254	+	0.0220117i	0.480816	+	0.876821i	$0.340340\pi$
$588$		0			0
$589$	−14.2927	+	24.7557i	−0.588922	+	1.02004i
$590$		0			0
$591$	−2.25292	−	1.30073i	−0.0926728	−	0.0535047i
$592$		0			0
$593$		−	44.1309i		−	1.81224i	−0.423022	−	0.906119i	$-0.639031\pi$
$593$		−	44.1309i		−	1.81224i	0.423022	−	0.906119i	$-0.360969\pi$
$594$		0			0
$595$	13.5144	+	23.4076i	0.554035	+	0.959616i
$596$		0			0
$597$	4.51132			0.184636
$598$		0			0
$599$	−3.81629			−0.155929			−0.0779647	−	0.996956i	$-0.524842\pi$
$599$	−3.81629			−0.155929			−0.0779647	+	0.996956i	$0.524842\pi$
$600$		0			0
$601$	−11.1959	−	19.3919i	−0.456691	−	0.791012i	0.542093	−	0.840319i	$-0.317632\pi$
$601$	−11.1959	−	19.3919i	−0.456691	−	0.791012i	−0.998784	+	0.0493069i	$0.984299\pi$
$602$		0			0
$603$		−	24.2344i		−	0.986899i
$604$		0			0
$605$	−5.37471	−	3.10309i	−0.218513	−	0.126158i
$606$		0			0
$607$	−3.84247	+	6.65536i	−0.155961	+	0.270133i	−0.933409	−	0.358815i	$-0.883181\pi$
$607$	−3.84247	+	6.65536i	−0.155961	+	0.270133i	0.777447	+	0.628948i	$0.216514\pi$
$608$		0			0
$609$	−11.3522	+	6.55418i	−0.460013	+	0.265589i
$610$		0			0
$611$	−35.4353	−	30.8101i	−1.43356	−	1.24644i
$612$		0			0
$613$	−2.32840	+	1.34430i	−0.0940433	+	0.0542959i	−0.546284	−	0.837600i	$-0.683958\pi$
$613$	−2.32840	+	1.34430i	−0.0940433	+	0.0542959i	0.452241	+	0.891896i	$0.350625\pi$
$614$		0			0
$615$	−1.20544	+	2.08788i	−0.0486080	+	0.0841916i
$616$		0			0
$617$	1.77047	+	1.02218i	0.0712764	+	0.0411515i	0.535215	−	0.844716i	$-0.320231\pi$
$617$	1.77047	+	1.02218i	0.0712764	+	0.0411515i	−0.463938	+	0.885868i	$0.653564\pi$
$618$		0			0
$619$			23.4468i			0.942405i	0.882025	+	0.471202i	$0.156180\pi$
$619$			23.4468i			0.942405i	−0.882025	+	0.471202i	$0.843820\pi$
$620$		0			0
$621$	4.30905	+	7.46350i	0.172916	+	0.299500i
$622$		0			0
$623$	31.2206			1.25083
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−4.11931	−	7.13485i	−0.164509	−	0.284939i
$628$		0			0
$629$			38.9250i			1.55204i
$630$		0			0
$631$	36.4191	+	21.0266i	1.44982	+	0.837055i	0.998470	−	0.0552915i	$-0.0176088\pi$
$631$	36.4191	+	21.0266i	1.44982	+	0.837055i	0.451351	+	0.892346i	$0.350942\pi$
$632$		0			0
$633$	−4.51601	+	7.82196i	−0.179495	+	0.310895i
$634$		0			0
$635$	10.4266	−	6.01983i	0.413769	−	0.238890i
$636$		0			0
$637$	−53.7790	−	10.4596i	−2.13080	−	0.414423i
$638$		0			0
$639$	2.04256	−	1.17927i	0.0808023	−	0.0466512i
$640$		0			0
$641$	−9.78059	+	16.9405i	−0.386310	+	0.669109i	−0.991950	−	0.126630i	$-0.959584\pi$
$641$	−9.78059	+	16.9405i	−0.386310	+	0.669109i	0.605640	+	0.795739i	$0.292917\pi$
$642$		0			0
$643$	12.6016	+	7.27553i	0.496958	+	0.286919i	0.727456	−	0.686154i	$-0.240702\pi$
$643$	12.6016	+	7.27553i	0.496958	+	0.286919i	−0.230499	+	0.973073i	$0.574036\pi$
$644$		0			0
$645$			1.53803i			0.0605597i
$646$		0			0
$647$	19.1084	+	33.0968i	0.751230	+	1.30117i	0.947227	+	0.320564i	$0.103873\pi$
$647$	19.1084	+	33.0968i	0.751230	+	1.30117i	−0.195996	+	0.980605i	$0.562794\pi$
$648$		0			0
$649$	−6.55739			−0.257400
$650$		0			0
$651$	7.84431			0.307443
$652$		0			0
$653$	3.74138	+	6.48025i	0.146411	+	0.253592i	0.929899	−	0.367816i	$-0.119894\pi$
$653$	3.74138	+	6.48025i	0.146411	+	0.253592i	−0.783487	+	0.621408i	$0.786561\pi$
$654$		0			0
$655$			5.73785i			0.224196i
$656$		0			0
$657$	4.38018	+	2.52890i	0.170887	+	0.0986616i
$658$		0			0
$659$	4.47997	−	7.75953i	0.174515	−	0.302269i	−0.765478	−	0.643462i	$-0.777498\pi$
$659$	4.47997	−	7.75953i	0.174515	−	0.302269i	0.939993	+	0.341193i	$0.110831\pi$
$660$		0			0
$661$	−27.4261	+	15.8345i	−1.06675	+	0.615890i	−0.927293	−	0.374337i	$-0.877870\pi$
$661$	−27.4261	+	15.8345i	−1.06675	+	0.615890i	−0.139461	+	0.990228i	$0.544537\pi$
$662$		0			0
$663$	−4.61648	+	5.30951i	−0.179289	+	0.206204i
$664$		0			0
$665$	23.8246	−	13.7551i	0.923877	−	0.533401i
$666$		0			0
$667$	−17.6122	+	30.5052i	−0.681946	+	1.18117i
$668$		0			0
$669$	−4.44802	−	2.56807i	−0.171971	−	0.0992872i
$670$		0			0
$671$		−	17.1615i		−	0.662512i
$672$		0			0
$673$	19.0777	+	33.0435i	0.735391	+	1.27373i	0.954552	+	0.298045i	$0.0963347\pi$
$673$	19.0777	+	33.0435i	0.735391	+	1.27373i	−0.219161	+	0.975689i	$0.570332\pi$
$674$		0			0
$675$	2.00144			0.0770354
$676$		0			0
$677$	−7.06001			−0.271338			−0.135669	−	0.990754i	$-0.543318\pi$
$677$	−7.06001			−0.271338			−0.135669	+	0.990754i	$0.543318\pi$
$678$		0			0
$679$	−36.0171	−	62.3835i	−1.38221	−	2.39406i
$680$		0			0
$681$		−	1.09264i		−	0.0418699i
$682$		0			0
$683$	16.5608	+	9.56136i	0.633680	+	0.365855i	0.782176	−	0.623058i	$-0.214110\pi$
$683$	16.5608	+	9.56136i	0.633680	+	0.365855i	−0.148496	+	0.988913i	$0.547443\pi$
$684$		0			0
$685$	6.37677	−	11.0449i	0.243644	−	0.422003i
$686$		0			0
$687$	6.01090	−	3.47040i	0.229330	−	0.132404i
$688$		0			0
$689$	7.37093	−	8.47745i	0.280810	−	0.322965i
$690$		0			0
$691$	28.8223	−	16.6406i	1.09645	−	0.633037i	0.161165	−	0.986927i	$-0.448475\pi$
$691$	28.8223	−	16.6406i	1.09645	−	0.633037i	0.935287	+	0.353890i	$0.115141\pi$
$692$		0			0
$693$	28.1827	−	48.8139i	1.07057	−	1.85429i
$694$		0			0
$695$	3.28014	+	1.89379i	0.124423	+	0.0718355i
$696$		0			0
$697$			40.6655i			1.54031i
$698$		0			0
$699$	0.504293	+	0.873461i	0.0190741	+	0.0330373i
$700$		0			0
$701$	−9.92771			−0.374964			−0.187482	−	0.982268i	$-0.560033\pi$
$701$	−9.92771			−0.374964			−0.187482	+	0.982268i	$0.560033\pi$
$702$		0			0
$703$	39.6185			1.49424
$704$		0			0
$705$	−2.21483	−	3.83621i	−0.0834155	−	0.144480i
$706$		0			0
$707$		−	35.9474i		−	1.35194i
$708$		0			0
$709$	22.1139	+	12.7674i	0.830503	+	0.479491i	0.854025	−	0.520232i	$-0.174155\pi$
$709$	22.1139	+	12.7674i	0.830503	+	0.479491i	−0.0235216	+	0.999723i	$0.507488\pi$
$710$		0			0
$711$	6.97939	−	12.0887i	0.261748	−	0.453360i
$712$		0			0
$713$	18.2549	−	10.5395i	0.683652	−	0.394707i
$714$		0			0
$715$	14.6809	+	2.85530i	0.549033	+	0.106782i
$716$		0			0
$717$	0.795859	−	0.459489i	0.0297219	−	0.0171599i
$718$		0			0
$719$	19.9278	−	34.5159i	0.743181	−	1.28723i	−0.207859	−	0.978159i	$-0.566649\pi$
$719$	19.9278	−	34.5159i	0.743181	−	1.28723i	0.951040	−	0.309068i	$-0.100017\pi$
$720$		0			0
$721$	−24.4006	−	14.0877i	−0.908726	−	0.524653i
$722$		0			0
$723$			7.27434i			0.270535i
$724$		0			0
$725$	4.09019	+	7.08441i	0.151906	+	0.263109i
$726$		0			0
$727$	4.31689			0.160105			0.0800523	−	0.996791i	$-0.474491\pi$
$727$	4.31689			0.160105			0.0800523	+	0.996791i	$0.474491\pi$
$728$		0			0
$729$	−20.9520			−0.776000
$730$		0			0
$731$	12.9713	+	22.4670i	0.479761	+	0.830971i
$732$		0			0
$733$		−	49.3743i		−	1.82368i	−0.410544	−	0.911841i	$-0.634661\pi$
$733$		−	49.3743i		−	1.82368i	0.410544	−	0.911841i	$-0.365339\pi$
$734$		0			0
$735$	−4.47590	−	2.58416i	−0.165096	−	0.0953184i
$736$		0			0
$737$	17.4262	−	30.1830i	0.641901	−	1.11180i
$738$		0			0
$739$	−5.25658	+	3.03489i	−0.193366	+	0.111640i	−0.593557	−	0.804792i	$-0.702277\pi$
$739$	−5.25658	+	3.03489i	−0.193366	+	0.111640i	0.400191	+	0.916432i	$0.368944\pi$
$740$		0			0
$741$	5.40410	+	4.69873i	0.198525	+	0.172612i
$742$		0			0
$743$	8.28494	−	4.78331i	0.303945	−	0.175483i	−0.340269	−	0.940328i	$-0.610518\pi$
$743$	8.28494	−	4.78331i	0.303945	−	0.175483i	0.644214	+	0.764845i	$0.277185\pi$
$744$		0			0
$745$	−9.45578	+	16.3779i	−0.346433	+	0.600040i
$746$		0			0
$747$	−9.30310	−	5.37115i	−0.340383	−	0.196520i
$748$		0			0
$749$		−	56.6229i		−	2.06896i
$750$		0			0
$751$	12.7732	+	22.1238i	0.466100	+	0.807309i	0.999250	−	0.0387113i	$-0.0123253\pi$
$751$	12.7732	+	22.1238i	0.466100	+	0.807309i	−0.533150	+	0.846021i	$0.678992\pi$
$752$		0			0
$753$	−2.25948			−0.0823399
$754$		0			0
$755$	−18.7385			−0.681963
$756$		0			0
$757$	−7.30875	−	12.6591i	−0.265641	−	0.460104i	0.702090	−	0.712088i	$-0.252250\pi$
$757$	−7.30875	−	12.6591i	−0.265641	−	0.460104i	−0.967731	+	0.251984i	$0.918917\pi$
$758$		0			0
$759$			6.07517i			0.220515i
$760$		0			0
$761$	−14.7643	−	8.52418i	−0.535206	−	0.309001i	0.207928	−	0.978144i	$-0.433328\pi$
$761$	−14.7643	−	8.52418i	−0.535206	−	0.309001i	−0.743134	+	0.669143i	$0.766661\pi$
$762$		0			0
$763$	−38.0170	+	65.8474i	−1.37631	+	2.38384i
$764$		0			0
$765$	14.3308	−	8.27387i	0.518130	−	0.299142i
$766$		0			0
$767$	5.38948	−	1.85510i	0.194603	−	0.0669838i
$768$		0			0
$769$	−16.8396	+	9.72234i	−0.607251	+	0.350596i	−0.771889	−	0.635758i	$-0.780688\pi$
$769$	−16.8396	+	9.72234i	−0.607251	+	0.350596i	0.164638	+	0.986354i	$0.447354\pi$
$770$		0			0
$771$	−0.770750	+	1.33498i	−0.0277579	+	0.0480780i
$772$		0			0
$773$	5.30085	+	3.06045i	0.190658	+	0.110077i	0.592291	−	0.805724i	$-0.298224\pi$
$773$	5.30085	+	3.06045i	0.190658	+	0.110077i	−0.401632	+	0.915801i	$0.631557\pi$
$774$		0			0
$775$		−	4.89530i		−	0.175844i
$776$		0			0
$777$	−5.43597	−	9.41537i	−0.195014	−	0.337775i
$778$		0			0
$779$	41.3899			1.48295
$780$		0			0
$781$	3.39190			0.121372
$782$		0			0
$783$	8.18626	+	14.1790i	0.292553	+	0.506717i
$784$		0			0
$785$			18.5213i			0.661053i
$786$		0			0
$787$	12.5059	+	7.22029i	0.445787	+	0.257375i	0.706049	−	0.708163i	$-0.250476\pi$
$787$	12.5059	+	7.22029i	0.445787	+	0.257375i	−0.260262	+	0.965538i	$0.583809\pi$
$788$		0			0
$789$	3.86865	−	6.70069i	0.137727	−	0.238551i
$790$		0			0
$791$	11.1417	−	6.43264i	0.396152	−	0.228718i
$792$		0			0
$793$	4.85502	+	14.1049i	0.172407	+	0.500880i
$794$		0			0
$795$	0.917765	−	0.529872i	0.0325498	−	0.0187926i
$796$		0			0
$797$	−0.658591	+	1.14071i	−0.0233285	+	0.0404061i	−0.877454	−	0.479661i	$-0.840760\pi$
$797$	−0.658591	+	1.14071i	−0.0233285	+	0.0404061i	0.854125	+	0.520067i	$0.174093\pi$
$798$		0			0
$799$	−64.7071	−	37.3587i	−2.28917	−	1.32165i
$800$		0			0
$801$		−	19.1142i		−	0.675366i
$802$		0			0
$803$	3.63690	+	6.29929i	0.128343	+	0.222297i
$804$		0			0
$805$	−20.2861			−0.714991
$806$		0			0
$807$	−1.76650			−0.0621837
$808$		0			0
$809$	10.4930	+	18.1745i	0.368915	+	0.638980i	0.989396	−	0.145242i	$-0.0463960\pi$
$809$	10.4930	+	18.1745i	0.368915	+	0.638980i	−0.620481	+	0.784221i	$0.713063\pi$
$810$		0			0
$811$			27.8175i			0.976805i	0.872618	+	0.488403i	$0.162420\pi$
$811$			27.8175i			0.976805i	−0.872618	+	0.488403i	$0.837580\pi$
$812$		0			0
$813$	4.20191	+	2.42597i	0.147367	+	0.0850826i
$814$		0			0
$815$	5.00206	−	8.66383i	0.175215	−	0.303481i
$816$		0			0
$817$	22.8672	−	13.2024i	0.800023	−	0.461893i
$818$		0			0
$819$	−9.35364	+	48.0928i	−0.326843	+	1.68050i
$820$		0			0
$821$	−14.5119	+	8.37845i	−0.506469	+	0.292410i	−0.731381	−	0.681969i	$-0.761124\pi$
$821$	−14.5119	+	8.37845i	−0.506469	+	0.292410i	0.224912	+	0.974379i	$0.427791\pi$
$822$		0			0
$823$	−8.00556	+	13.8660i	−0.279056	+	0.483340i	−0.971150	−	0.238467i	$-0.923355\pi$
$823$	−8.00556	+	13.8660i	−0.279056	+	0.483340i	0.692094	+	0.721807i	$0.256688\pi$
$824$		0			0
$825$	1.22185	+	0.705438i	0.0425395	+	0.0245602i
$826$		0			0
$827$		−	53.9122i		−	1.87471i	−0.348373	−	0.937356i	$-0.613266\pi$
$827$		−	53.9122i		−	1.87471i	0.348373	−	0.937356i	$-0.386734\pi$
$828$		0			0
$829$	−18.6023	−	32.2202i	−0.646085	−	1.11905i	−0.984050	−	0.177894i	$-0.943072\pi$
$829$	−18.6023	−	32.2202i	−0.646085	−	1.11905i	0.337964	−	0.941159i	$-0.390262\pi$
$830$		0			0
$831$	3.48875			0.121024
$832$		0			0
$833$	−87.1767			−3.02049
$834$		0			0
$835$	6.39963	+	11.0845i	0.221468	+	0.383595i
$836$		0			0
$837$		−	9.79764i		−	0.338656i
$838$		0			0
$839$	−34.9606	−	20.1845i	−1.20697	−	0.696847i	−0.244877	−	0.969554i	$-0.578748\pi$
$839$	−34.9606	−	20.1845i	−1.20697	−	0.696847i	−0.962097	+	0.272707i	$0.912081\pi$
$840$		0			0
$841$	−18.9593	+	32.8384i	−0.653768	+	1.13236i
$842$		0			0
$843$	0.875688	−	0.505579i	0.0301603	−	0.0174131i
$844$		0			0
$845$	−12.8739	+	1.80649i	−0.442875	+	0.0621452i
$846$		0			0
$847$	25.3211	−	14.6192i	0.870045	−	0.502321i
$848$		0			0
$849$	−2.19727	+	3.80578i	−0.0754101	+	0.130614i
$850$		0			0
$851$	−25.3007	−	14.6074i	−0.867296	−	0.500734i
$852$		0			0
$853$			5.08258i			0.174024i	0.996207	+	0.0870120i	$0.0277319\pi$
$853$			5.08258i			0.174024i	−0.996207	+	0.0870120i	$0.972268\pi$
$854$		0			0
$855$	−8.42127	−	14.5861i	−0.288001	−	0.498833i
$856$		0			0
$857$	−41.4739			−1.41672			−0.708360	−	0.705851i	$-0.750565\pi$
$857$	−41.4739			−1.41672			−0.708360	+	0.705851i	$0.750565\pi$
$858$		0			0
$859$	−4.72012			−0.161049			−0.0805243	−	0.996753i	$-0.525659\pi$
$859$	−4.72012			−0.161049			−0.0805243	+	0.996753i	$0.525659\pi$
$860$		0			0
$861$	−5.67903	−	9.83637i	−0.193541	−	0.335223i
$862$		0			0
$863$			11.0511i			0.376183i	0.982151	+	0.188092i	$0.0602302\pi$
$863$			11.0511i			0.376183i	−0.982151	+	0.188092i	$0.939770\pi$
$864$		0			0
$865$	7.05898	+	4.07551i	0.240013	+	0.138571i
$866$		0			0
$867$	−2.70659	+	4.68795i	−0.0919206	+	0.159211i
$868$		0			0
$869$	17.3851	−	10.0373i	0.589751	−	0.340493i
$870$		0			0
$871$	−5.78362	+	29.7371i	−0.195970	+	1.00760i
$872$		0			0
$873$	−38.1929	+	22.0507i	−1.29263	+	0.746303i
$874$		0			0
$875$	−2.35558	+	4.07999i	−0.0796333	+	0.137929i
$876$		0			0
$877$	−37.0049	−	21.3648i	−1.24957	−	0.721437i	−0.278543	−	0.960424i	$-0.589851\pi$
$877$	−37.0049	−	21.3648i	−1.24957	−	0.721437i	−0.971023	+	0.238987i	$0.923185\pi$
$878$		0			0
$879$			6.90640i			0.232947i
$880$		0			0
$881$	21.4629	+	37.1748i	0.723102	+	1.25245i	0.959750	+	0.280854i	$0.0906178\pi$
$881$	21.4629	+	37.1748i	0.723102	+	1.25245i	−0.236648	+	0.971595i	$0.576049\pi$
$882$		0			0
$883$	−16.8041			−0.565501			−0.282751	−	0.959193i	$-0.591247\pi$
$883$	−16.8041			−0.565501			−0.282751	+	0.959193i	$0.591247\pi$
$884$		0			0
$885$	0.537694			0.0180744
$886$		0			0
$887$	−19.0451	−	32.9870i	−0.639471	−	1.10760i	−0.985549	−	0.169390i	$-0.945820\pi$
$887$	−19.0451	−	32.9870i	−0.639471	−	1.10760i	0.346078	−	0.938206i	$-0.387513\pi$
$888$		0			0
$889$			56.7208i			1.90236i
$890$		0			0
$891$	−28.6385	−	16.5344i	−0.959425	−	0.553924i
$892$		0			0
$893$	−38.0242	+	65.8599i	−1.27243	+	2.20392i
$894$		0			0
$895$	5.40398	−	3.11999i	0.180635	−	0.104290i
$896$		0			0
$897$	−1.71868	−	4.99314i	−0.0573850	−	0.166716i
$898$		0			0
$899$	34.6803	−	20.0227i	1.15665	−	0.667795i
$900$		0			0
$901$	8.93760	−	15.4804i	0.297755	−	0.515726i
$902$		0			0
$903$	−6.27513	−	3.62295i	−0.208823	−	0.120564i
$904$		0			0
$905$			1.51583i			0.0503877i
$906$		0			0
$907$	3.33093	+	5.76933i	0.110602	+	0.191568i	0.916013	−	0.401149i	$-0.131389\pi$
$907$	3.33093	+	5.76933i	0.110602	+	0.191568i	−0.805411	+	0.592716i	$0.798056\pi$
$908$		0			0
$909$	−22.0080			−0.729959
$910$		0			0
$911$	8.36233			0.277056			0.138528	−	0.990358i	$-0.455763\pi$
$911$	8.36233			0.277056			0.138528	+	0.990358i	$0.455763\pi$
$912$		0			0
$913$	−7.72444	−	13.3791i	−0.255642	−	0.442785i
$914$		0			0
$915$			1.40721i			0.0465210i
$916$		0			0
$917$	−23.4104	−	13.5160i	−0.773078	−	0.446337i
$918$		0			0
$919$	15.8879	−	27.5186i	0.524093	−	0.907755i	−0.475514	−	0.879708i	$-0.657738\pi$
$919$	15.8879	−	27.5186i	0.524093	−	0.907755i	0.999607	−	0.0280470i	$-0.00892880\pi$
$920$		0			0
$921$	4.94388	−	2.85435i	0.162906	−	0.0940540i
$922$		0			0
$923$	−2.78778	+	0.959577i	−0.0917610	+	0.0315848i
$924$		0			0
$925$	−5.87574	+	3.39236i	−0.193193	+	0.111540i
$926$		0			0
$927$	−8.62489	+	14.9387i	−0.283279	+	0.490653i
$928$		0			0
$929$	18.8951	+	10.9091i	0.619929	+	0.357916i	0.776841	−	0.629696i	$-0.216821\pi$
$929$	18.8951	+	10.9091i	0.619929	+	0.357916i	−0.156912	+	0.987613i	$0.550154\pi$
$930$		0			0
$931$			88.7298i			2.90800i
$932$		0			0
$933$	−2.13895	−	3.70477i	−0.0700261	−	0.121289i
$934$		0			0
$935$	23.7979			0.778275
$936$		0			0
$937$	56.2499			1.83761			0.918803	−	0.394717i	$-0.129157\pi$
$937$	56.2499			1.83761			0.918803	+	0.394717i	$0.129157\pi$
$938$		0			0
$939$	2.06407	+	3.57507i	0.0673583	+	0.116668i
$940$		0			0
$941$		−	22.4583i		−	0.732119i	−0.930591	−	0.366059i	$-0.880707\pi$
$941$		−	22.4583i		−	0.732119i	0.930591	−	0.366059i	$-0.119293\pi$
$942$		0			0
$943$	−26.4320	−	15.2605i	−0.860743	−	0.496950i
$944$		0			0
$945$	−4.71455	+	8.16585i	−0.153364	+	0.265635i
$946$		0			0
$947$	−5.22523	+	3.01679i	−0.169797	+	0.0980325i	−0.582490	−	0.812838i	$-0.697922\pi$
$947$	−5.22523	+	3.01679i	−0.169797	+	0.0980325i	0.412693	+	0.910870i	$0.364588\pi$
$948$		0			0
$949$	−4.77123	−	4.14846i	−0.154881	−	0.134665i
$950$		0			0
$951$	5.18750	−	2.99500i	0.168216	−	0.0971197i
$952$		0			0
$953$	14.2938	−	24.7576i	0.463021	−	0.801976i	−0.536089	−	0.844162i	$-0.680099\pi$
$953$	14.2938	−	24.7576i	0.463021	−	0.801976i	0.999110	+	0.0421856i	$0.0134321\pi$
$954$		0			0
$955$	17.3440	+	10.0136i	0.561239	+	0.324032i
$956$		0			0
$957$			11.5415i			0.373083i
$958$		0			0
$959$	30.0420	+	52.0343i	0.970107	+	1.68028i
$960$		0			0
$961$	7.03603			0.226969
$962$		0			0
$963$	−34.6661			−1.11710
$964$		0			0
$965$	9.16663	+	15.8771i	0.295084	+	0.511101i
$966$		0			0
$967$			14.0033i			0.450317i	0.974322	+	0.225158i	$0.0722900\pi$
$967$			14.0033i			0.450317i	−0.974322	+	0.225158i	$0.927710\pi$
$968$		0			0
$969$	9.86824	+	5.69743i	0.317013	+	0.183028i
$970$		0			0
$971$	−27.2084	+	47.1264i	−0.873160	+	1.51236i	−0.0144502	+	0.999896i	$0.504600\pi$
$971$	−27.2084	+	47.1264i	−0.873160	+	1.51236i	−0.858710	+	0.512462i	$0.828734\pi$
$972$		0			0
$973$	−15.4533	+	8.92196i	−0.495409	+	0.286025i
$974$		0			0
$975$	−1.20380	−	0.234130i	−0.0385526	−	0.00749815i
$976$		0			0
$977$	−25.7152	+	14.8467i	−0.822701	+	0.474987i	−0.851347	−	0.524603i	$-0.824214\pi$
$977$	−25.7152	+	14.8467i	−0.822701	+	0.474987i	0.0286457	+	0.999590i	$0.490881\pi$
$978$		0			0
$979$	13.7444	−	23.8060i	0.439273	−	0.760842i
$980$		0			0
$981$	40.3136	+	23.2751i	1.28712	+	0.743116i
$982$		0			0
$983$		−	35.3176i		−	1.12646i	−0.826302	−	0.563228i	$-0.809559\pi$
$983$		−	35.3176i		−	1.12646i	0.826302	−	0.563228i	$-0.190441\pi$
$984$		0			0
$985$	−3.82419	−	6.62369i	−0.121849	−	0.211048i
$986$		0			0
$987$	20.8689			0.664265
$988$		0			0
$989$	−19.4709			−0.619140
$990$		0			0
$991$	−13.1452	−	22.7682i	−0.417572	−	0.723256i	0.578123	−	0.815950i	$-0.303785\pi$
$991$	−13.1452	−	22.7682i	−0.417572	−	0.723256i	−0.995695	+	0.0926941i	$0.970452\pi$
$992$		0			0
$993$		−	3.70930i		−	0.117711i
$994$		0			0
$995$	11.4865	+	6.63174i	0.364147	+	0.210240i
$996$		0			0
$997$	11.2663	−	19.5138i	0.356807	−	0.618007i	−0.630619	−	0.776093i	$-0.717199\pi$
$997$	11.2663	−	19.5138i	0.356807	−	0.618007i	0.987425	+	0.158086i	$0.0505322\pi$
$998$		0			0
$999$	−11.7599	+	6.78960i	−0.372068	+	0.214813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.e.881.3		12
4.3	odd	2		520.2.bu.a.361.4	yes	12
13.4	even	6	inner	1040.2.da.e.641.3		12
52.11	even	12		6760.2.a.bj.1.3		6
52.15	even	12		6760.2.a.bg.1.3		6
52.43	odd	6		520.2.bu.a.121.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.a.121.4	✓	12	52.43	odd	6
520.2.bu.a.361.4	yes	12	4.3	odd	2
1040.2.da.e.641.3		12	13.4	even	6	inner
1040.2.da.e.881.3		12	1.1	even	1	trivial
6760.2.a.bg.1.3		6	52.15	even	12
6760.2.a.bj.1.3		6	52.11	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.170066 - 0.294562i) q^{3} -1.00000i q^{5} +(4.07999 + 2.35558i) q^{7} +(1.44216 - 2.49789i) q^{9} +O(q^{10})\)	\(q+(-0.170066 - 0.294562i) q^{3} -1.00000i q^{5} +(4.07999 + 2.35558i) q^{7} +(1.44216 - 2.49789i) q^{9} +(3.59230 - 2.07402i) q^{11} +(-2.36575 + 2.72089i) q^{13} +(-0.294562 + 0.170066i) q^{15} +(-2.86858 + 4.96852i) q^{17} +(5.05704 + 2.91968i) q^{19} -1.60242i q^{21} +(-2.15298 - 3.72907i) q^{23} -1.00000 q^{25} -2.00144 q^{27} +(-4.09019 - 7.08441i) q^{29} +4.89530i q^{31} +(-1.22185 - 0.705438i) q^{33} +(2.35558 - 4.07999i) q^{35} +(5.87574 - 3.39236i) q^{37} +(1.20380 + 0.234130i) q^{39} +(6.13847 - 3.54404i) q^{41} +(2.26093 - 3.91604i) q^{43} +(-2.49789 - 1.44216i) q^{45} +13.0234i q^{47} +(7.59755 + 13.1593i) q^{49} +1.95139 q^{51} -3.11569 q^{53} +(-2.07402 - 3.59230i) q^{55} -1.98615i q^{57} +(-1.36905 - 0.790422i) q^{59} +(2.06863 - 3.58297i) q^{61} +(11.7680 - 6.79424i) q^{63} +(2.72089 + 2.36575i) q^{65} +(7.27646 - 4.20107i) q^{67} +(-0.732295 + 1.26837i) q^{69} +(0.708161 + 0.408857i) q^{71} +1.75355i q^{73} +(0.170066 + 0.294562i) q^{75} +19.5421 q^{77} +4.83956 q^{79} +(-3.98609 - 6.90411i) q^{81} -3.72439i q^{83} +(4.96852 + 2.86858i) q^{85} +(-1.39120 + 2.40963i) q^{87} +(5.73910 - 3.31347i) q^{89} +(-16.0615 + 5.52850i) q^{91} +(1.44197 - 0.832522i) q^{93} +(2.91968 - 5.05704i) q^{95} +(-13.2416 - 7.64505i) q^{97} -11.9642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 + 2 * q^9	\( 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) \) 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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