LMFDB - Embedded newform 1040.2.da.e.641.5

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			641.5
Root			$1.40744 + 0.138282i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.e.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.823474 - 1.42630i) q^{3} +1.00000i q^{5} +(-1.33221 + 0.769155i) q^{7} +(0.143781 + 0.249036i) q^{9} +O(q^{10})$	\(q+(0.823474 - 1.42630i) q^{3} +1.00000i q^{5} +(-1.33221 + 0.769155i) q^{7} +(0.143781 + 0.249036i) q^{9} +(-2.55167 - 1.47321i) q^{11} +(1.44325 - 3.30409i) q^{13} +(1.42630 + 0.823474i) q^{15} +(2.39951 + 4.15607i) q^{17} +(5.26082 - 3.03733i) q^{19} +2.53352i q^{21} +(4.15171 - 7.19097i) q^{23} -1.00000 q^{25} +5.41444 q^{27} +(4.30264 - 7.45239i) q^{29} -6.96851i q^{31} +(-4.20247 + 2.42630i) q^{33} +(-0.769155 - 1.33221i) q^{35} +(-3.70226 - 2.13750i) q^{37} +(-3.52414 - 4.77934i) q^{39} +(10.2038 + 5.89117i) q^{41} +(2.53930 + 4.39819i) q^{43} +(-0.249036 + 0.143781i) q^{45} +6.64723i q^{47} +(-2.31680 + 4.01282i) q^{49} +7.90373 q^{51} -5.71244 q^{53} +(1.47321 - 2.55167i) q^{55} -10.0047i q^{57} +(1.08358 - 0.625605i) q^{59} +(5.24858 + 9.09081i) q^{61} +(-0.383094 - 0.221179i) q^{63} +(3.30409 + 1.44325i) q^{65} +(-9.25187 - 5.34157i) q^{67} +(-6.83765 - 11.8432i) q^{69} +(-8.09222 + 4.67205i) q^{71} -10.1094i q^{73} +(-0.823474 + 1.42630i) q^{75} +4.53250 q^{77} -7.47269 q^{79} +(4.02731 - 6.97551i) q^{81} +6.44046i q^{83} +(-4.15607 + 2.39951i) q^{85} +(-7.08622 - 12.2737i) q^{87} +(2.70494 + 1.56170i) q^{89} +(0.618638 + 5.51184i) q^{91} +(-9.93918 - 5.73839i) q^{93} +(3.03733 + 5.26082i) q^{95} +(-3.91324 + 2.25931i) q^{97} -0.847277i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

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

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
$3$	0.823474	−	1.42630i	0.475433	−	0.823474i	−0.524171	−	0.851613i	$-0.675625\pi$
$3$	0.823474	−	1.42630i	0.475433	−	0.823474i	0.999604	+	0.0281389i	$0.00895808\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−1.33221	+	0.769155i	−0.503530	+	0.290713i	−0.730170	−	0.683265i	$-0.760559\pi$
$7$	−1.33221	+	0.769155i	−0.503530	+	0.290713i	0.226640	+	0.973979i	$0.427226\pi$
$8$		0			0
$9$	0.143781	+	0.249036i	0.0479269	+	0.0830119i
$10$		0			0
$11$	−2.55167	−	1.47321i	−0.769358	−	0.444189i	0.0632873	−	0.997995i	$-0.479842\pi$
$11$	−2.55167	−	1.47321i	−0.769358	−	0.444189i	−0.832646	+	0.553806i	$0.813175\pi$
$12$		0			0
$13$	1.44325	−	3.30409i	0.400286	−	0.916390i
$13$	1.44325	−	3.30409i	0.400286	−	0.916390i
$14$		0			0
$15$	1.42630	+	0.823474i	0.368269	+	0.212620i
$16$		0			0
$17$	2.39951	+	4.15607i	0.581966	+	1.00799i	0.995246	+	0.0973910i	$0.0310497\pi$
$17$	2.39951	+	4.15607i	0.581966	+	1.00799i	−0.413280	+	0.910604i	$0.635617\pi$
$18$		0			0
$19$	5.26082	−	3.03733i	1.20691	−	0.696812i	0.244830	−	0.969566i	$-0.421268\pi$
$19$	5.26082	−	3.03733i	1.20691	−	0.696812i	0.962084	+	0.272754i	$0.0879344\pi$
$20$		0			0
$21$			2.53352i			0.552858i
$22$		0			0
$23$	4.15171	−	7.19097i	0.865692	−	1.49942i	−0.000667212	−	1.00000i	$-0.500212\pi$
$23$	4.15171	−	7.19097i	0.865692	−	1.49942i	0.866359	−	0.499422i	$-0.166454\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.41444			1.04201
$28$		0			0
$29$	4.30264	−	7.45239i	0.798980	−	1.38387i	−0.121301	−	0.992616i	$-0.538707\pi$
$29$	4.30264	−	7.45239i	0.798980	−	1.38387i	0.920281	−	0.391258i	$-0.127960\pi$
$30$		0			0
$31$		−	6.96851i		−	1.25158i	−0.779991	−	0.625790i	$-0.784777\pi$
$31$		−	6.96851i		−	1.25158i	0.779991	−	0.625790i	$-0.215223\pi$
$32$		0			0
$33$	−4.20247	+	2.42630i	−0.731557	+	0.422364i
$34$		0			0
$35$	−0.769155	−	1.33221i	−0.130011	−	0.225185i
$36$		0			0
$37$	−3.70226	−	2.13750i	−0.608647	−	0.351403i	0.163789	−	0.986495i	$-0.447629\pi$
$37$	−3.70226	−	2.13750i	−0.608647	−	0.351403i	−0.772436	+	0.635093i	$0.780962\pi$
$38$		0			0
$39$	−3.52414	−	4.77934i	−0.564315	−	0.765307i
$40$		0			0
$41$	10.2038	+	5.89117i	1.59357	+	0.920046i	0.992688	+	0.120706i	$0.0385159\pi$
$41$	10.2038	+	5.89117i	1.59357	+	0.920046i	0.600879	+	0.799340i	$0.294817\pi$
$42$		0			0
$43$	2.53930	+	4.39819i	0.387239	+	0.670718i	0.992077	−	0.125631i	$-0.0400955\pi$
$43$	2.53930	+	4.39819i	0.387239	+	0.670718i	−0.604838	+	0.796349i	$0.706762\pi$
$44$		0			0
$45$	−0.249036	+	0.143781i	−0.0371240	+	0.0214336i
$46$		0			0
$47$			6.64723i			0.969598i	0.874626	+	0.484799i	$0.161107\pi$
$47$			6.64723i			0.969598i	−0.874626	+	0.484799i	$0.838893\pi$
$48$		0			0
$49$	−2.31680	+	4.01282i	−0.330972	+	0.573260i
$50$		0			0
$51$	7.90373			1.10674
$52$		0			0
$53$	−5.71244			−0.784664			−0.392332	−	0.919824i	$-0.628332\pi$
$53$	−5.71244			−0.784664			−0.392332	+	0.919824i	$0.628332\pi$
$54$		0			0
$55$	1.47321	−	2.55167i	0.198647	−	0.344068i
$56$		0			0
$57$		−	10.0047i		−	1.32515i
$58$		0			0
$59$	1.08358	−	0.625605i	0.141070	−	0.0814468i	−0.427804	−	0.903872i	$-0.640713\pi$
$59$	1.08358	−	0.625605i	0.141070	−	0.0814468i	0.568874	+	0.822425i	$0.307379\pi$
$60$		0			0
$61$	5.24858	+	9.09081i	0.672012	+	1.16396i	0.977333	+	0.211709i	$0.0679030\pi$
$61$	5.24858	+	9.09081i	0.672012	+	1.16396i	−0.305321	+	0.952250i	$0.598764\pi$
$62$		0			0
$63$	−0.383094	−	0.221179i	−0.0482653	−	0.0278660i
$64$		0			0
$65$	3.30409	+	1.44325i	0.409822	+	0.179013i
$66$		0			0
$67$	−9.25187	−	5.34157i	−1.13030	−	0.652576i	−0.186286	−	0.982496i	$-0.559645\pi$
$67$	−9.25187	−	5.34157i	−1.13030	−	0.652576i	−0.944009	+	0.329919i	$0.892978\pi$
$68$		0			0
$69$	−6.83765	−	11.8432i	−0.823157	−	1.42575i
$70$		0			0
$71$	−8.09222	+	4.67205i	−0.960370	+	0.554470i	−0.896287	−	0.443475i	$-0.853746\pi$
$71$	−8.09222	+	4.67205i	−0.960370	+	0.554470i	−0.0640832	+	0.997945i	$0.520412\pi$
$72$		0			0
$73$		−	10.1094i		−	1.18322i	−0.806225	−	0.591610i	$-0.798493\pi$
$73$		−	10.1094i		−	1.18322i	0.806225	−	0.591610i	$-0.201507\pi$
$74$		0			0
$75$	−0.823474	+	1.42630i	−0.0950866	+	0.164695i
$76$		0			0
$77$	4.53250			0.516527
$78$		0			0
$79$	−7.47269			−0.840743			−0.420372	−	0.907352i	$-0.638100\pi$
$79$	−7.47269			−0.840743			−0.420372	+	0.907352i	$0.638100\pi$
$80$		0			0
$81$	4.02731	−	6.97551i	0.447479	−	0.775057i
$82$		0			0
$83$			6.44046i			0.706932i	0.935447	+	0.353466i	$0.114997\pi$
$83$			6.44046i			0.706932i	−0.935447	+	0.353466i	$0.885003\pi$
$84$		0			0
$85$	−4.15607	+	2.39951i	−0.450789	+	0.260263i
$86$		0			0
$87$	−7.08622	−	12.2737i	−0.759723	−	1.31588i
$88$		0			0
$89$	2.70494	+	1.56170i	0.286723	+	0.165539i	0.636463	−	0.771307i	$-0.280397\pi$
$89$	2.70494	+	1.56170i	0.286723	+	0.165539i	−0.349740	+	0.936847i	$0.613730\pi$
$90$		0			0
$91$	0.618638	+	5.51184i	0.0648509	+	0.577798i
$92$		0			0
$93$	−9.93918	−	5.73839i	−1.03064	−	0.595043i
$94$		0			0
$95$	3.03733	+	5.26082i	0.311624	+	0.539749i
$96$		0			0
$97$	−3.91324	+	2.25931i	−0.397329	+	0.229398i	−0.685331	−	0.728232i	$-0.740342\pi$
$97$	−3.91324	+	2.25931i	−0.397329	+	0.229398i	0.288002	+	0.957630i	$0.407009\pi$
$98$		0			0
$99$		−	0.847277i		−	0.0851545i
$100$		0			0
$101$	9.57957	−	16.5923i	0.953203	−	1.65100i	0.214775	−	0.976663i	$-0.431098\pi$
$101$	9.57957	−	16.5923i	0.953203	−	1.65100i	0.738428	−	0.674333i	$-0.235569\pi$
$102$		0			0
$103$	7.68480			0.757206			0.378603	−	0.925559i	$-0.376405\pi$
$103$	7.68480			0.757206			0.378603	+	0.925559i	$0.376405\pi$
$104$		0			0
$105$	−2.53352			−0.247246
$106$		0			0
$107$	−5.25120	+	9.09534i	−0.507652	+	0.879279i	0.492309	+	0.870421i	$0.336153\pi$
$107$	−5.25120	+	9.09534i	−0.507652	+	0.879279i	−0.999961	+	0.00885866i	$0.997180\pi$
$108$		0			0
$109$			0.934790i			0.0895366i	0.998997	+	0.0447683i	$0.0142550\pi$
$109$			0.934790i			0.0895366i	−0.998997	+	0.0447683i	$0.985745\pi$
$110$		0			0
$111$	−6.09742	+	3.52035i	−0.578742	+	0.334137i
$112$		0			0
$113$	−1.20043	−	2.07921i	−0.112927	−	0.195596i	0.804022	−	0.594599i	$-0.202689\pi$
$113$	−1.20043	−	2.07921i	−0.112927	−	0.195596i	−0.916949	+	0.399004i	$0.869356\pi$
$114$		0			0
$115$	7.19097	+	4.15171i	0.670562	+	0.387149i
$116$		0			0
$117$	1.03035	−	0.115644i	0.0952557	−	0.0106913i
$118$		0			0
$119$	−6.39332	−	3.69119i	−0.586075	−	0.338370i
$120$		0			0
$121$	−1.15931	−	2.00798i	−0.105392	−	0.182544i
$122$		0			0
$123$	16.8051	−	9.70245i	1.51527	−	0.874841i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−5.72798	+	9.92116i	−0.508276	+	0.880360i	0.491678	+	0.870777i	$0.336384\pi$
$127$	−5.72798	+	9.92116i	−0.508276	+	0.880360i	−0.999954	+	0.00958307i	$0.996950\pi$
$128$		0			0
$129$	8.36418			0.736425
$130$		0			0
$131$	7.28465			0.636463			0.318231	−	0.948013i	$-0.396911\pi$
$131$	7.28465			0.636463			0.318231	+	0.948013i	$0.396911\pi$
$132$		0			0
$133$	−4.67236	+	8.09277i	−0.405145	+	0.701732i
$134$		0			0
$135$			5.41444i			0.466001i
$136$		0			0
$137$	−10.1428	+	5.85597i	−0.866561	+	0.500309i	−0.866204	−	0.499691i	$-0.833447\pi$
$137$	−10.1428	+	5.85597i	−0.866561	+	0.500309i	−0.000357108		1.00000i	$0.500114\pi$
$138$		0			0
$139$	−0.0243610	−	0.0421945i	−0.00206628	−	0.00357889i	0.864990	−	0.501788i	$-0.167324\pi$
$139$	−0.0243610	−	0.0421945i	−0.00206628	−	0.00357889i	−0.867057	+	0.498209i	$0.833991\pi$
$140$		0			0
$141$	9.48094	+	5.47382i	0.798439	+	0.460979i
$142$		0			0
$143$	−8.55032	+	6.30475i	−0.715014	+	0.527230i
$144$		0			0
$145$	7.45239	+	4.30264i	0.618887	+	0.357315i
$146$		0			0
$147$	3.81565	+	6.60891i	0.314710	+	0.545093i
$148$		0			0
$149$	4.32392	−	2.49642i	0.354229	−	0.204514i	−0.312317	−	0.949978i	$-0.601105\pi$
$149$	4.32392	−	2.49642i	0.354229	−	0.204514i	0.666547	+	0.745463i	$0.267772\pi$
$150$		0			0
$151$			8.74125i			0.711353i	0.934609	+	0.355676i	$0.115749\pi$
$151$			8.74125i			0.711353i	−0.934609	+	0.355676i	$0.884251\pi$
$152$		0			0
$153$	−0.690006	+	1.19513i	−0.0557837	+	0.0966202i
$154$		0			0
$155$	6.96851			0.559724
$156$		0			0
$157$	−3.89618			−0.310949			−0.155475	−	0.987840i	$-0.549691\pi$
$157$	−3.89618			−0.310949			−0.155475	+	0.987840i	$0.549691\pi$
$158$		0			0
$159$	−4.70405	+	8.14765i	−0.373055	+	0.646150i
$160$		0			0
$161$			12.7732i			1.00667i
$162$		0			0
$163$	0.263298	−	0.152015i	0.0206231	−	0.0119067i	−0.489653	−	0.871917i	$-0.662877\pi$
$163$	0.263298	−	0.152015i	0.0206231	−	0.0119067i	0.510276	+	0.860011i	$0.329543\pi$
$164$		0			0
$165$	−2.42630	−	4.20247i	−0.188887	−	0.327162i
$166$		0			0
$167$	−19.4602	−	11.2354i	−1.50588	−	0.869418i	−0.999977	−	0.00682636i	$-0.997827\pi$
$167$	−19.4602	−	11.2354i	−1.50588	−	0.869418i	−0.505900	−	0.862592i	$-0.668840\pi$
$168$		0			0
$169$	−8.83406	−	9.53727i	−0.679543	−	0.733636i
$170$		0			0
$171$	1.51281	+	0.873421i	0.115687	+	0.0667921i
$172$		0			0
$173$	−0.211297	−	0.365977i	−0.0160646	−	0.0278247i	0.857881	−	0.513848i	$-0.171780\pi$
$173$	−0.211297	−	0.365977i	−0.0160646	−	0.0278247i	−0.873946	+	0.486023i	$0.838447\pi$
$174$		0			0
$175$	1.33221	−	0.769155i	0.100706	−	0.0581426i
$176$		0			0
$177$		−	2.06068i		−	0.154890i
$178$		0			0
$179$	6.71472	−	11.6302i	0.501882	−	0.869285i	−0.498116	−	0.867111i	$-0.665974\pi$
$179$	6.71472	−	11.6302i	0.501882	−	0.869285i	0.999998	−	0.00217450i	$-0.000692167\pi$
$180$		0			0
$181$	15.1748			1.12793			0.563967	−	0.825797i	$-0.309274\pi$
$181$	15.1748			1.12793			0.563967	+	0.825797i	$0.309274\pi$
$182$		0			0
$183$	17.2883			1.27799
$184$		0			0
$185$	2.13750	−	3.70226i	0.157152	−	0.272195i
$186$		0			0
$187$		−	14.1399i		−	1.03401i
$188$		0			0
$189$	−7.21320	+	4.16454i	−0.524683	+	0.302926i
$190$		0			0
$191$	3.67825	+	6.37092i	0.266149	+	0.460984i	0.967864	−	0.251474i	$-0.0809153\pi$
$191$	3.67825	+	6.37092i	0.266149	+	0.460984i	−0.701715	+	0.712458i	$0.747582\pi$
$192$		0			0
$193$	−10.6382	−	6.14197i	−0.765755	−	0.442109i	0.0656032	−	0.997846i	$-0.479103\pi$
$193$	−10.6382	−	6.14197i	−0.765755	−	0.442109i	−0.831358	+	0.555737i	$0.812436\pi$
$194$		0			0
$195$	4.77934	−	3.52414i	0.342256	−	0.252369i
$196$		0			0
$197$	5.87651	+	3.39281i	0.418684	+	0.241727i	0.694514	−	0.719479i	$-0.255619\pi$
$197$	5.87651	+	3.39281i	0.418684	+	0.241727i	−0.275830	+	0.961206i	$0.588953\pi$
$198$		0			0
$199$	8.92063	+	15.4510i	0.632366	+	1.09529i	0.987067	+	0.160311i	$0.0512496\pi$
$199$	8.92063	+	15.4510i	0.632366	+	1.09529i	−0.354700	+	0.934980i	$0.615417\pi$
$200$		0			0
$201$	−15.2373	+	8.79728i	−1.07476	+	0.620513i
$202$		0			0
$203$			13.2376i			0.929096i
$204$		0			0
$205$	−5.89117	+	10.2038i	−0.411457	+	0.712665i
$206$		0			0
$207$	2.38774			0.165960
$208$		0			0
$209$	−17.8985			−1.23807
$210$		0			0
$211$	−4.39950	+	7.62016i	−0.302874	+	0.524594i	−0.976786	−	0.214218i	$-0.931280\pi$
$211$	−4.39950	+	7.62016i	−0.302874	+	0.524594i	0.673912	+	0.738812i	$0.264613\pi$
$212$		0			0
$213$			15.3892i			1.05445i
$214$		0			0
$215$	−4.39819	+	2.53930i	−0.299954	+	0.173179i
$216$		0			0
$217$	5.35986	+	9.28355i	0.363851	+	0.630208i
$218$		0			0
$219$	−14.4191	−	8.32485i	−0.974350	−	0.562541i
$220$		0			0
$221$	17.1951	−	1.92995i	1.15667	−	0.129822i
$222$		0			0
$223$	−21.0373	−	12.1459i	−1.40876	−	0.813350i	−0.413494	−	0.910507i	$-0.635692\pi$
$223$	−21.0373	−	12.1459i	−1.40876	−	0.813350i	−0.995269	+	0.0971571i	$0.969025\pi$
$224$		0			0
$225$	−0.143781	−	0.249036i	−0.00958538	−	0.0166024i
$226$		0			0
$227$	−0.530513	+	0.306292i	−0.0352114	+	0.0203293i	−0.517502	−	0.855682i	$-0.673138\pi$
$227$	−0.530513	+	0.306292i	−0.0352114	+	0.0203293i	0.482291	+	0.876011i	$0.339805\pi$
$228$		0			0
$229$			16.8618i			1.11426i	0.830425	+	0.557131i	$0.188098\pi$
$229$			16.8618i			1.11426i	−0.830425	+	0.557131i	$0.811902\pi$
$230$		0			0
$231$	3.73240	−	6.46470i	0.245574	−	0.425346i
$232$		0			0
$233$	29.3058			1.91989			0.959945	−	0.280189i	$-0.0903972\pi$
$233$	29.3058			1.91989			0.959945	+	0.280189i	$0.0903972\pi$
$234$		0			0
$235$	−6.64723			−0.433617
$236$		0			0
$237$	−6.15357	+	10.6583i	−0.399717	+	0.692330i
$238$		0			0
$239$		−	2.49083i		−	0.161118i	−0.996750	−	0.0805592i	$-0.974329\pi$
$239$		−	2.49083i		−	0.161118i	0.996750	−	0.0805592i	$-0.0256706\pi$
$240$		0			0
$241$	−18.0434	+	10.4173i	−1.16227	+	0.671040i	−0.951848	−	0.306570i	$-0.900819\pi$
$241$	−18.0434	+	10.4173i	−1.16227	+	0.671040i	−0.210427	+	0.977610i	$0.567485\pi$
$242$		0			0
$243$	1.48889	+	2.57884i	0.0955124	+	0.165432i
$244$		0			0
$245$	−4.01282	−	2.31680i	−0.256370	−	0.148015i
$246$		0			0
$247$	−2.44296	−	21.7659i	−0.155442	−	1.38493i
$248$		0			0
$249$	9.18602	+	5.30355i	0.582140	+	0.336099i
$250$		0			0
$251$	12.0093	+	20.8007i	0.758018	+	1.31293i	0.943860	+	0.330346i	$0.107165\pi$
$251$	12.0093	+	20.8007i	0.758018	+	1.31293i	−0.185842	+	0.982580i	$0.559501\pi$
$252$		0			0
$253$	−21.1876	+	12.2327i	−1.33205	+	0.769062i
$254$		0			0
$255$			7.90373i			0.494951i
$256$		0			0
$257$	7.99177	−	13.8422i	0.498513	−	0.863450i	−0.501486	−	0.865166i	$-0.667213\pi$
$257$	7.99177	−	13.8422i	0.498513	−	0.863450i	0.999999	+	0.00171627i	$0.000546306\pi$
$258$		0			0
$259$	6.57627			0.408629
$260$		0			0
$261$	2.47455			0.153171
$262$		0			0
$263$	−7.15900	+	12.3997i	−0.441443	+	0.764601i	−0.997797	−	0.0663442i	$-0.978866\pi$
$263$	−7.15900	+	12.3997i	−0.441443	+	0.764601i	0.556354	+	0.830945i	$0.312200\pi$
$264$		0			0
$265$		−	5.71244i		−	0.350912i
$266$		0			0
$267$	4.45489	−	2.57203i	0.272635	−	0.157406i
$268$		0			0
$269$	9.76305	+	16.9101i	0.595264	+	1.03103i	0.993510	+	0.113748i	$0.0362857\pi$
$269$	9.76305	+	16.9101i	0.595264	+	1.03103i	−0.398246	+	0.917279i	$0.630381\pi$
$270$		0			0
$271$	−7.41809	−	4.28284i	−0.450617	−	0.260164i	0.257474	−	0.966285i	$-0.417110\pi$
$271$	−7.41809	−	4.28284i	−0.450617	−	0.260164i	−0.708091	+	0.706121i	$0.750443\pi$
$272$		0			0
$273$	8.37097	+	3.65650i	0.506634	+	0.221301i
$274$		0			0
$275$	2.55167	+	1.47321i	0.153872	+	0.0888378i
$276$		0			0
$277$	−10.3702	−	17.9616i	−0.623083	−	1.07921i	−0.988908	−	0.148527i	$-0.952547\pi$
$277$	−10.3702	−	17.9616i	−0.623083	−	1.07921i	0.365826	−	0.930683i	$-0.380787\pi$
$278$		0			0
$279$	1.73541	−	1.00194i	0.103896	−	0.0599844i
$280$		0			0
$281$		−	0.640036i		−	0.0381814i	−0.999818	−	0.0190907i	$-0.993923\pi$
$281$		−	0.640036i		−	0.0381814i	0.999818	−	0.0190907i	$-0.00607712\pi$
$282$		0			0
$283$	−6.10446	+	10.5732i	−0.362873	+	0.628514i	−0.988432	−	0.151663i	$-0.951537\pi$
$283$	−6.10446	+	10.5732i	−0.362873	+	0.628514i	0.625560	+	0.780176i	$0.284871\pi$
$284$		0			0
$285$	10.0047			0.592625
$286$		0			0
$287$	−18.1249			−1.06988
$288$		0			0
$289$	−3.01528	+	5.22261i	−0.177369	+	0.307213i
$290$		0			0
$291$			7.44193i			0.436254i
$292$		0			0
$293$	−10.2223	+	5.90183i	−0.597191	+	0.344789i	−0.767936	−	0.640527i	$-0.778716\pi$
$293$	−10.2223	+	5.90183i	−0.597191	+	0.344789i	0.170745	+	0.985315i	$0.445383\pi$
$294$		0			0
$295$	0.625605	+	1.08358i	0.0364241	+	0.0630884i
$296$		0			0
$297$	−13.8159	−	7.97661i	−0.801679	−	0.462850i
$298$		0			0
$299$	−17.7677	−	24.0960i	−1.02753	−	1.39351i
$300$		0			0
$301$	−6.76578	−	3.90622i	−0.389973	−	0.225151i
$302$		0			0
$303$	−15.7771	−	27.3267i	−0.906368	−	1.56988i
$304$		0			0
$305$	−9.09081	+	5.24858i	−0.520538	+	0.300533i
$306$		0			0
$307$		−	12.2753i		−	0.700586i	−0.936640	−	0.350293i	$-0.886082\pi$
$307$		−	12.2753i		−	0.700586i	0.936640	−	0.350293i	$-0.113918\pi$
$308$		0			0
$309$	6.32824	−	10.9608i	0.360001	−	0.623540i
$310$		0			0
$311$	−11.4367			−0.648514			−0.324257	−	0.945969i	$-0.605114\pi$
$311$	−11.4367			−0.648514			−0.324257	+	0.945969i	$0.605114\pi$
$312$		0			0
$313$	−23.5888			−1.33332			−0.666658	−	0.745364i	$-0.732276\pi$
$313$	−23.5888			−1.33332			−0.666658	+	0.745364i	$0.732276\pi$
$314$		0			0
$315$	0.221179	−	0.383094i	0.0124620	−	0.0215849i
$316$		0			0
$317$			16.2099i			0.910439i	0.890379	+	0.455220i	$0.150439\pi$
$317$			16.2099i			0.910439i	−0.890379	+	0.455220i	$0.849561\pi$
$318$		0			0
$319$	−21.9578	+	12.6774i	−1.22940	+	0.709796i
$320$		0			0
$321$	8.64845	+	14.9795i	0.482709	+	0.836077i
$322$		0			0
$323$	25.2467	+	14.5762i	1.40477	+	0.811042i
$324$		0			0
$325$	−1.44325	+	3.30409i	−0.0800571	+	0.183278i
$326$		0			0
$327$	1.33329	+	0.769775i	0.0737311	+	0.0425687i
$328$		0			0
$329$	−5.11275	−	8.85554i	−0.281875	−	0.488222i
$330$		0			0
$331$	5.14176	−	2.96859i	0.282617	−	0.163169i	−0.351991	−	0.936003i	$-0.614495\pi$
$331$	5.14176	−	2.96859i	0.282617	−	0.163169i	0.634607	+	0.772835i	$0.281162\pi$
$332$		0			0
$333$		−	1.22932i		−	0.0673666i
$334$		0			0
$335$	5.34157	−	9.25187i	0.291841	−	0.505483i
$336$		0			0
$337$	−1.08607			−0.0591623			−0.0295811	−	0.999562i	$-0.509417\pi$
$337$	−1.08607			−0.0591623			−0.0295811	+	0.999562i	$0.509417\pi$
$338$		0			0
$339$	−3.95410			−0.214757
$340$		0			0
$341$	−10.2661	+	17.7814i	−0.555939	+	0.962914i
$342$		0			0
$343$		−	17.8961i		−	0.966298i
$344$		0			0
$345$	11.8432	−	6.83765i	0.637614	−	0.368127i
$346$		0			0
$347$	5.79115	+	10.0306i	0.310885	+	0.538469i	0.978554	−	0.205989i	$-0.0660412\pi$
$347$	5.79115	+	10.0306i	0.310885	+	0.538469i	−0.667669	+	0.744458i	$0.732708\pi$
$348$		0			0
$349$	−14.6211	−	8.44148i	−0.782648	−	0.451862i	0.0547199	−	0.998502i	$-0.482573\pi$
$349$	−14.6211	−	8.44148i	−0.782648	−	0.451862i	−0.837368	+	0.546640i	$0.815907\pi$
$350$		0			0
$351$	7.81440	−	17.8898i	0.417102	−	0.954888i
$352$		0			0
$353$	23.2572	+	13.4275i	1.23785	+	0.714675i	0.968655	−	0.248410i	$-0.0799080\pi$
$353$	23.2572	+	13.4275i	1.23785	+	0.714675i	0.269198	+	0.963085i	$0.413241\pi$
$354$		0			0
$355$	−4.67205	−	8.09222i	−0.247966	−	0.429491i
$356$		0			0
$357$	−10.5295	+	6.07919i	−0.557279	+	0.321745i
$358$		0			0
$359$			12.4195i			0.655474i	0.944769	+	0.327737i	$0.106286\pi$
$359$			12.4195i			0.655474i	−0.944769	+	0.327737i	$0.893714\pi$
$360$		0			0
$361$	8.95080	−	15.5032i	0.471095	−	0.815960i
$362$		0			0
$363$	−3.81865			−0.200427
$364$		0			0
$365$	10.1094			0.529152
$366$		0			0
$367$	2.73937	−	4.74473i	0.142994	−	0.247673i	−0.785629	−	0.618698i	$-0.787660\pi$
$367$	2.73937	−	4.74473i	0.142994	−	0.247673i	0.928623	+	0.371025i	$0.120994\pi$
$368$		0			0
$369$			3.38815i			0.176380i
$370$		0			0
$371$	7.61020	−	4.39375i	0.395102	−	0.228112i
$372$		0			0
$373$	−16.8792	−	29.2357i	−0.873973	−	1.51377i	−0.857852	−	0.513896i	$-0.828202\pi$
$373$	−16.8792	−	29.2357i	−0.873973	−	1.51377i	−0.0161211	−	0.999870i	$-0.505132\pi$
$374$		0			0
$375$	−1.42630	−	0.823474i	−0.0736538	−	0.0425240i
$376$		0			0
$377$	−18.4136	−	24.9720i	−0.948348	−	1.28612i
$378$		0			0
$379$	20.2105	+	11.6686i	1.03815	+	0.599373i	0.919307	−	0.393540i	$-0.128750\pi$
$379$	20.2105	+	11.6686i	1.03815	+	0.599373i	0.118838	+	0.992914i	$0.462083\pi$
$380$		0			0
$381$	9.43369	+	16.3396i	0.483303	+	0.837105i
$382$		0			0
$383$	−0.799423	+	0.461547i	−0.0408486	+	0.0235840i	−0.520285	−	0.853993i	$-0.674174\pi$
$383$	−0.799423	+	0.461547i	−0.0408486	+	0.0235840i	0.479437	+	0.877577i	$0.340841\pi$
$384$		0			0
$385$			4.53250i			0.230998i
$386$		0			0
$387$	−0.730204	+	1.26475i	−0.0371184	+	0.0642909i
$388$		0			0
$389$	−10.9357			−0.554464			−0.277232	−	0.960803i	$-0.589417\pi$
$389$	−10.9357			−0.554464			−0.277232	+	0.960803i	$0.589417\pi$
$390$		0			0
$391$	39.8483			2.01521
$392$		0			0
$393$	5.99872	−	10.3901i	0.302595	−	0.524111i
$394$		0			0
$395$		−	7.47269i		−	0.375992i
$396$		0			0
$397$	10.8340	−	6.25503i	0.543745	−	0.313931i	−0.202851	−	0.979210i	$-0.565021\pi$
$397$	10.8340	−	6.25503i	0.543745	−	0.313931i	0.746595	+	0.665279i	$0.231687\pi$
$398$		0			0
$399$	7.69514	+	13.3284i	0.385239	+	0.667253i
$400$		0			0
$401$	13.0351	+	7.52579i	0.650940	+	0.375820i	0.788816	−	0.614629i	$-0.210694\pi$
$401$	13.0351	+	7.52579i	0.650940	+	0.375820i	−0.137877	+	0.990449i	$0.544028\pi$
$402$		0			0
$403$	−23.0246	−	10.0573i	−1.14694	−	0.500990i
$404$		0			0
$405$	6.97551	+	4.02731i	0.346616	+	0.200119i
$406$		0			0
$407$	6.29797	+	10.9084i	0.312179	+	0.540709i
$408$		0			0
$409$	−28.1153	+	16.2324i	−1.39021	+	0.802640i	−0.993339	−	0.115232i	$-0.963239\pi$
$409$	−28.1153	+	16.2324i	−1.39021	+	0.802640i	−0.396875	+	0.917873i	$0.629905\pi$
$410$		0			0
$411$			19.2890i			0.951454i
$412$		0			0
$413$	−0.962374	+	1.66688i	−0.0473553	+	0.0820218i
$414$		0			0
$415$	−6.44046			−0.316150
$416$		0			0
$417$	−0.0802427			−0.00392950
$418$		0			0
$419$	9.33626	−	16.1709i	0.456106	−	0.789999i	−0.542645	−	0.839962i	$-0.682577\pi$
$419$	9.33626	−	16.1709i	0.456106	−	0.789999i	0.998751	+	0.0499630i	$0.0159103\pi$
$420$		0			0
$421$		−	16.9365i		−	0.825434i	−0.910859	−	0.412717i	$-0.864580\pi$
$421$		−	16.9365i		−	0.825434i	0.910859	−	0.412717i	$-0.135420\pi$
$422$		0			0
$423$	−1.65540	+	0.955744i	−0.0804881	+	0.0464698i
$424$		0			0
$425$	−2.39951	−	4.15607i	−0.116393	−	0.201599i
$426$		0			0
$427$	−13.9845	−	8.07394i	−0.676756	−	0.390725i
$428$		0			0
$429$	1.95149	+	17.3871i	0.0942190	+	0.839458i
$430$		0			0
$431$	25.8927	+	14.9492i	1.24721	+	0.720077i	0.970552	−	0.240892i	$-0.0774400\pi$
$431$	25.8927	+	14.9492i	1.24721	+	0.720077i	0.276657	+	0.960969i	$0.410773\pi$
$432$		0			0
$433$	2.79856	+	4.84724i	0.134490	+	0.232944i	0.925403	−	0.378986i	$-0.123727\pi$
$433$	2.79856	+	4.84724i	0.134490	+	0.232944i	−0.790912	+	0.611929i	$0.790394\pi$
$434$		0			0
$435$	12.2737	−	7.08622i	0.588479	−	0.339758i
$436$		0			0
$437$		−	50.4405i		−	2.41290i
$438$		0			0
$439$	−12.0710	+	20.9076i	−0.576117	+	0.997863i	0.419803	+	0.907615i	$0.362099\pi$
$439$	−12.0710	+	20.9076i	−0.576117	+	0.997863i	−0.995919	+	0.0902479i	$0.971234\pi$
$440$		0			0
$441$	−1.33245			−0.0634498
$442$		0			0
$443$	−18.3797			−0.873245			−0.436622	−	0.899645i	$-0.643825\pi$
$443$	−18.3797			−0.873245			−0.436622	+	0.899645i	$0.643825\pi$
$444$		0			0
$445$	−1.56170	+	2.70494i	−0.0740315	+	0.128226i
$446$		0			0
$447$		−	8.22294i		−	0.388932i
$448$		0			0
$449$	29.4267	−	16.9895i	1.38873	−	0.801785i	0.395560	−	0.918440i	$-0.370550\pi$
$449$	29.4267	−	16.9895i	1.38873	−	0.801785i	0.993173	+	0.116655i	$0.0372172\pi$
$450$		0			0
$451$	−17.3579	−	30.0647i	−0.817349	−	1.41569i
$452$		0			0
$453$	12.4676	+	7.19819i	0.585781	+	0.338201i
$454$		0			0
$455$	−5.51184	+	0.618638i	−0.258399	+	0.0290022i
$456$		0			0
$457$	−10.9914	−	6.34586i	−0.514154	−	0.296847i	0.220386	−	0.975413i	$-0.429268\pi$
$457$	−10.9914	−	6.34586i	−0.514154	−	0.296847i	−0.734540	+	0.678566i	$0.762602\pi$
$458$		0			0
$459$	12.9920	+	22.5028i	0.606415	+	1.05034i
$460$		0			0
$461$	15.0963	−	8.71587i	0.703106	−	0.405938i	−0.105397	−	0.994430i	$-0.533611\pi$
$461$	15.0963	−	8.71587i	0.703106	−	0.405938i	0.808503	+	0.588492i	$0.200278\pi$
$462$		0			0
$463$			32.8872i			1.52840i	0.644980	+	0.764199i	$0.276866\pi$
$463$			32.8872i			1.52840i	−0.644980	+	0.764199i	$0.723134\pi$
$464$		0			0
$465$	5.73839	−	9.93918i	0.266111	−	0.460918i
$466$		0			0
$467$	27.5224			1.27358			0.636792	−	0.771036i	$-0.280261\pi$
$467$	27.5224			1.27358			0.636792	+	0.771036i	$0.280261\pi$
$468$		0			0
$469$	16.4340			0.758850
$470$		0			0
$471$	−3.20840	+	5.55712i	−0.147835	+	0.256058i
$472$		0			0
$473$		−	14.9637i		−	0.688030i
$474$		0			0
$475$	−5.26082	+	3.03733i	−0.241383	+	0.139362i
$476$		0			0
$477$	−0.821339	−	1.42260i	−0.0376065	−	0.0651364i
$478$		0			0
$479$	−6.80586	−	3.92937i	−0.310968	−	0.179537i	0.336392	−	0.941722i	$-0.390793\pi$
$479$	−6.80586	−	3.92937i	−0.310968	−	0.179537i	−0.647359	+	0.762185i	$0.724127\pi$
$480$		0			0
$481$	−12.4058	+	9.14765i	−0.565655	+	0.417097i
$482$		0			0
$483$	18.2184	+	10.5184i	0.828968	+	0.478605i
$484$		0			0
$485$	−2.25931	−	3.91324i	−0.102590	−	0.177691i
$486$		0			0
$487$	5.87277	−	3.39065i	0.266121	−	0.153645i	−0.361003	−	0.932565i	$-0.617566\pi$
$487$	5.87277	−	3.39065i	0.266121	−	0.153645i	0.627123	+	0.778920i	$0.284232\pi$
$488$		0			0
$489$		−	0.500721i		−	0.0226434i
$490$		0			0
$491$	−11.4087	+	19.7604i	−0.514867	+	0.891775i	0.484984	+	0.874523i	$0.338825\pi$
$491$	−11.4087	+	19.7604i	−0.514867	+	0.891775i	−0.999851	+	0.0172526i	$0.994508\pi$
$492$		0			0
$493$	41.2969			1.85992
$494$		0			0
$495$	0.847277			0.0380822
$496$		0			0
$497$	7.18705	−	12.4483i	0.322383	−	0.558384i
$498$		0			0
$499$			0.438454i			0.0196279i	0.999952	+	0.00981395i	$0.00312393\pi$
$499$			0.438454i			0.0196279i	−0.999952	+	0.00981395i	$0.996876\pi$
$500$		0			0
$501$	−32.0500	+	18.5041i	−1.43189	+	0.826700i
$502$		0			0
$503$	−14.3559	−	24.8651i	−0.640097	−	1.10868i	−0.985411	−	0.170193i	$-0.945561\pi$
$503$	−14.3559	−	24.8651i	−0.640097	−	1.10868i	0.345314	−	0.938487i	$-0.387773\pi$
$504$		0			0
$505$	16.5923	+	9.57957i	0.738348	+	0.426285i
$506$		0			0
$507$	−20.8776	+	4.74631i	−0.927207	+	0.210791i
$508$		0			0
$509$	21.7195	+	12.5398i	0.962701	+	0.555815i	0.897003	−	0.442024i	$-0.145739\pi$
$509$	21.7195	+	12.5398i	0.962701	+	0.555815i	0.0656975	+	0.997840i	$0.479073\pi$
$510$		0			0
$511$	7.77571	+	13.4679i	0.343977	+	0.595786i
$512$		0			0
$513$	28.4844	−	16.4455i	1.25762	−	0.726086i
$514$		0			0
$515$			7.68480i			0.338633i
$516$		0			0
$517$	9.79276	−	16.9616i	0.430685	−	0.745968i
$518$		0			0
$519$	−0.695990			−0.0305506
$520$		0			0
$521$	4.87849			0.213730			0.106865	−	0.994274i	$-0.465919\pi$
$521$	4.87849			0.213730			0.106865	+	0.994274i	$0.465919\pi$
$522$		0			0
$523$	−18.7578	+	32.4894i	−0.820219	+	1.42066i	0.0852996	+	0.996355i	$0.472815\pi$
$523$	−18.7578	+	32.4894i	−0.820219	+	1.42066i	−0.905519	+	0.424306i	$0.860518\pi$
$524$		0			0
$525$		−	2.53352i		−	0.110572i
$526$		0			0
$527$	28.9616	−	16.7210i	1.26159	−	0.728378i
$528$		0			0
$529$	−22.9734	−	39.7911i	−0.998844	−	1.73005i
$530$		0			0
$531$	0.311596	+	0.179900i	0.0135221	+	0.00780699i
$532$		0			0
$533$	34.1916	−	25.2119i	1.48100	−	1.09205i
$534$		0			0
$535$	−9.09534	−	5.25120i	−0.393226	−	0.227029i
$536$		0			0
$537$	−11.0588	−	19.1544i	−0.477223	−	0.826574i
$538$		0			0
$539$	11.8234	−	6.82627i	0.509272	−	0.294028i
$540$		0			0
$541$			19.0832i			0.820451i	0.911984	+	0.410226i	$0.134550\pi$
$541$			19.0832i			0.820451i	−0.911984	+	0.410226i	$0.865450\pi$
$542$		0			0
$543$	12.4961	−	21.6438i	0.536257	−	0.928825i
$544$		0			0
$545$	−0.934790			−0.0400420
$546$		0			0
$547$	7.99779			0.341961			0.170980	−	0.985274i	$-0.445307\pi$
$547$	7.99779			0.341961			0.170980	+	0.985274i	$0.445307\pi$
$548$		0			0
$549$	−1.50929	+	2.61417i	−0.0644149	+	0.111570i
$550$		0			0
$551$		−	52.2742i		−	2.22696i
$552$		0			0
$553$	9.95523	−	5.74766i	0.423339	−	0.244415i
$554$		0			0
$555$	−3.52035	−	6.09742i	−0.149431	−	0.258821i
$556$		0			0
$557$	−8.61308	−	4.97276i	−0.364948	−	0.210703i	0.306301	−	0.951935i	$-0.400909\pi$
$557$	−8.61308	−	4.97276i	−0.364948	−	0.210703i	−0.671249	+	0.741232i	$0.734242\pi$
$558$		0			0
$559$	18.1969	−	2.04238i	0.769646	−	0.0863835i
$560$		0			0
$561$	−20.1677	−	11.6438i	−0.851482	−	0.491604i
$562$		0			0
$563$	−19.3855	−	33.5766i	−0.817001	−	1.41509i	−0.907882	−	0.419225i	$-0.862302\pi$
$563$	−19.3855	−	33.5766i	−0.817001	−	1.41509i	0.0908815	−	0.995862i	$-0.471032\pi$
$564$		0			0
$565$	2.07921	−	1.20043i	0.0874731	−	0.0505026i
$566$		0			0
$567$			12.3905i			0.520352i
$568$		0			0
$569$	7.36051	−	12.7488i	0.308569	−	0.534457i	−0.669481	−	0.742829i	$-0.733483\pi$
$569$	7.36051	−	12.7488i	0.308569	−	0.534457i	0.978049	+	0.208373i	$0.0668167\pi$
$570$		0			0
$571$	20.8384			0.872058			0.436029	−	0.899933i	$-0.356385\pi$
$571$	20.8384			0.872058			0.436029	+	0.899933i	$0.356385\pi$
$572$		0			0
$573$	12.1158			0.506144
$574$		0			0
$575$	−4.15171	+	7.19097i	−0.173138	+	0.299884i
$576$		0			0
$577$			45.7696i			1.90541i	0.303894	+	0.952706i	$0.401713\pi$
$577$			45.7696i			1.90541i	−0.303894	+	0.952706i	$0.598287\pi$
$578$		0			0
$579$	−17.5206	+	10.1155i	−0.728130	+	0.420386i
$580$		0			0
$581$	−4.95371	−	8.58007i	−0.205514	−	0.355961i
$582$		0			0
$583$	14.5763	+	8.41562i	0.603688	+	0.348539i
$584$		0			0
$585$	0.115644	+	1.03035i	0.00478130	+	0.0425997i
$586$		0			0
$587$	21.4321	+	12.3738i	0.884597	+	0.510722i	0.872171	−	0.489201i	$-0.162711\pi$
$587$	21.4321	+	12.3738i	0.884597	+	0.510722i	0.0124256	+	0.999923i	$0.496045\pi$
$588$		0			0
$589$	−21.1657	−	36.6601i	−0.872117	−	1.51055i
$590$		0			0
$591$	9.67831	−	5.58778i	0.398113	−	0.229850i
$592$		0			0
$593$			48.3680i			1.98624i	0.117121	+	0.993118i	$0.462634\pi$
$593$			48.3680i			1.98624i	−0.117121	+	0.993118i	$0.537366\pi$
$594$		0			0
$595$	3.69119	−	6.39332i	0.151324	−	0.262101i
$596$		0			0
$597$	29.3836			1.20259
$598$		0			0
$599$	21.0823			0.861398			0.430699	−	0.902496i	$-0.358267\pi$
$599$	21.0823			0.861398			0.430699	+	0.902496i	$0.358267\pi$
$600$		0			0
$601$	17.5398	−	30.3798i	0.715462	−	1.23922i	−0.247319	−	0.968934i	$-0.579550\pi$
$601$	17.5398	−	30.3798i	0.715462	−	1.23922i	0.962781	−	0.270282i	$-0.0871171\pi$
$602$		0			0
$603$		−	3.07206i		−	0.125104i
$604$		0			0
$605$	2.00798	−	1.15931i	0.0816362	−	0.0471327i
$606$		0			0
$607$	11.8144	+	20.4632i	0.479532	+	0.830574i	0.999724	−	0.0234752i	$-0.00747306\pi$
$607$	11.8144	+	20.4632i	0.479532	+	0.830574i	−0.520192	+	0.854049i	$0.674140\pi$
$608$		0			0
$609$	18.8807	+	10.9008i	0.765086	+	0.441723i
$610$		0			0
$611$	21.9631	+	9.59362i	0.888530	+	0.388116i
$612$		0			0
$613$	−16.2549	−	9.38478i	−0.656530	−	0.379048i	0.134423	−	0.990924i	$-0.457082\pi$
$613$	−16.2549	−	9.38478i	−0.656530	−	0.379048i	−0.790954	+	0.611876i	$0.790415\pi$
$614$		0			0
$615$	9.70245	+	16.8051i	0.391241	+	0.677649i
$616$		0			0
$617$	−13.8300	+	7.98476i	−0.556775	+	0.321454i	−0.751850	−	0.659334i	$-0.770838\pi$
$617$	−13.8300	+	7.98476i	−0.556775	+	0.321454i	0.195075	+	0.980788i	$0.437505\pi$
$618$		0			0
$619$		−	21.1129i		−	0.848601i	−0.905521	−	0.424300i	$-0.860520\pi$
$619$		−	21.1129i		−	0.848601i	0.905521	−	0.424300i	$-0.139480\pi$
$620$		0			0
$621$	22.4792	−	38.9351i	0.902059	−	1.56241i
$622$		0			0
$623$	−4.80474			−0.192498
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−14.7390	+	25.5286i	−0.588618	+	1.01952i
$628$		0			0
$629$		−	20.5158i		−	0.818018i
$630$		0			0
$631$	−19.1719	+	11.0689i	−0.763221	+	0.440646i	−0.830451	−	0.557091i	$-0.811917\pi$
$631$	−19.1719	+	11.0689i	−0.763221	+	0.440646i	0.0672298	+	0.997738i	$0.478584\pi$
$632$		0			0
$633$	7.24575	+	12.5500i	0.287993	+	0.498818i
$634$		0			0
$635$	−9.92116	−	5.72798i	−0.393709	−	0.227308i
$636$		0			0
$637$	9.91500	+	13.4464i	0.392847	+	0.532767i
$638$		0			0
$639$	−2.32701	−	1.34350i	−0.0920552	−	0.0531481i
$640$		0			0
$641$	−3.56430	−	6.17355i	−0.140781	−	0.243841i	0.787010	−	0.616941i	$-0.211628\pi$
$641$	−3.56430	−	6.17355i	−0.140781	−	0.243841i	−0.927791	+	0.373100i	$0.878295\pi$
$642$		0			0
$643$	−4.38891	+	2.53394i	−0.173082	+	0.0999287i	−0.584038	−	0.811726i	$-0.698528\pi$
$643$	−4.38891	+	2.53394i	−0.173082	+	0.0999287i	0.410957	+	0.911655i	$0.365195\pi$
$644$		0			0
$645$			8.36418i			0.329339i
$646$		0			0
$647$	6.35433	−	11.0060i	0.249814	−	0.432691i	−0.713660	−	0.700493i	$-0.752964\pi$
$647$	6.35433	−	11.0060i	0.249814	−	0.432691i	0.963474	+	0.267801i	$0.0862970\pi$
$648$		0			0
$649$	−3.68659			−0.144711
$650$		0			0
$651$	17.6548			0.691947
$652$		0			0
$653$	−19.4644	+	33.7134i	−0.761703	+	1.31931i	0.180270	+	0.983617i	$0.442303\pi$
$653$	−19.4644	+	33.7134i	−0.761703	+	1.31931i	−0.941972	+	0.335690i	$0.891030\pi$
$654$		0			0
$655$			7.28465i			0.284635i
$656$		0			0
$657$	2.51761	−	1.45354i	0.0982212	−	0.0567081i
$658$		0			0
$659$	−21.5224	−	37.2780i	−0.838395	−	1.45214i	−0.891236	−	0.453540i	$-0.850161\pi$
$659$	−21.5224	−	37.2780i	−0.838395	−	1.45214i	0.0528408	−	0.998603i	$-0.483172\pi$
$660$		0			0
$661$	−21.1999	−	12.2398i	−0.824580	−	0.476071i	0.0274133	−	0.999624i	$-0.491273\pi$
$661$	−21.1999	−	12.2398i	−0.824580	−	0.476071i	−0.851993	+	0.523553i	$0.824606\pi$
$662$		0			0
$663$	11.4071	−	26.1147i	0.443014	−	1.01421i
$664$		0			0
$665$	−8.09277	−	4.67236i	−0.313824	−	0.181186i
$666$		0			0
$667$	−35.7266	−	61.8803i	−1.38334	−	2.39602i
$668$		0			0
$669$	−34.6474	+	20.0037i	−1.33954	+	0.773387i
$670$		0			0
$671$		−	30.9290i		−	1.19400i
$672$		0			0
$673$	−0.895617	+	1.55125i	−0.0345235	+	0.0597964i	−0.882771	−	0.469804i	$-0.844325\pi$
$673$	−0.895617	+	1.55125i	−0.0345235	+	0.0597964i	0.848247	+	0.529600i	$0.177658\pi$
$674$		0			0
$675$	−5.41444			−0.208402
$676$		0			0
$677$	−11.3544			−0.436384			−0.218192	−	0.975906i	$-0.570016\pi$
$677$	−11.3544			−0.436384			−0.218192	+	0.975906i	$0.570016\pi$
$678$		0			0
$679$	3.47552	−	6.01977i	0.133378	−	0.231018i
$680$		0			0
$681$			1.00889i			0.0386609i
$682$		0			0
$683$	−15.0699	+	8.70058i	−0.576632	+	0.332919i	−0.759794	−	0.650164i	$-0.774700\pi$
$683$	−15.0699	+	8.70058i	−0.576632	+	0.332919i	0.183162	+	0.983083i	$0.441367\pi$
$684$		0			0
$685$	−5.85597	−	10.1428i	−0.223745	−	0.387538i
$686$		0			0
$687$	24.0500	+	13.8853i	0.917566	+	0.529757i
$688$		0			0
$689$	−8.24448	+	18.8744i	−0.314090	+	0.719058i
$690$		0			0
$691$	4.30102	+	2.48319i	0.163618	+	0.0944651i	0.579573	−	0.814920i	$-0.303219\pi$
$691$	4.30102	+	2.48319i	0.163618	+	0.0944651i	−0.415955	+	0.909385i	$0.636553\pi$
$692$		0			0
$693$	0.651687	+	1.12875i	0.0247555	+	0.0428778i
$694$		0			0
$695$	0.0421945	−	0.0243610i	0.00160053	−	0.000924066i
$696$		0			0
$697$			56.5437i			2.14174i
$698$		0			0
$699$	24.1326	−	41.7989i	0.912779	−	1.58098i
$700$		0			0
$701$	−41.4041			−1.56381			−0.781906	−	0.623397i	$-0.785752\pi$
$701$	−41.4041			−1.56381			−0.781906	+	0.623397i	$0.785752\pi$
$702$		0			0
$703$	−25.9692			−0.979447
$704$		0			0
$705$	−5.47382	+	9.48094i	−0.206156	+	0.357073i
$706$		0			0
$707$			29.4727i			1.10843i
$708$		0			0
$709$	14.1811	−	8.18745i	0.532582	−	0.307486i	−0.209485	−	0.977812i	$-0.567179\pi$
$709$	14.1811	−	8.18745i	0.532582	−	0.307486i	0.742067	+	0.670326i	$0.233846\pi$
$710$		0			0
$711$	−1.07443	−	1.86097i	−0.0402942	−	0.0697917i
$712$		0			0
$713$	−50.1104	−	28.9312i	−1.87665	−	1.08348i
$714$		0			0
$715$	−6.30475	−	8.55032i	−0.235784	−	0.319764i
$716$		0			0
$717$	−3.55267	−	2.05113i	−0.132677	−	0.0766010i
$718$		0			0
$719$	4.21735	+	7.30467i	0.157281	+	0.272418i	0.933887	−	0.357568i	$-0.116394\pi$
$719$	4.21735	+	7.30467i	0.157281	+	0.272418i	−0.776606	+	0.629986i	$0.783061\pi$
$720$		0			0
$721$	−10.2378	+	5.91080i	−0.381276	+	0.220130i
$722$		0			0
$723$			34.3136i			1.27614i
$724$		0			0
$725$	−4.30264	+	7.45239i	−0.159796	+	0.276775i
$726$		0			0
$727$	−1.17930			−0.0437379			−0.0218689	−	0.999761i	$-0.506962\pi$
$727$	−1.17930			−0.0437379			−0.0218689	+	0.999761i	$0.506962\pi$
$728$		0			0
$729$	29.0681			1.07660
$730$		0			0
$731$	−12.1861	+	21.1070i	−0.450720	+	0.780670i
$732$		0			0
$733$			7.65380i			0.282700i	0.989960	+	0.141350i	$0.0451442\pi$
$733$			7.65380i			0.282700i	−0.989960	+	0.141350i	$0.954856\pi$
$734$		0			0
$735$	−6.60891	+	3.81565i	−0.243773	+	0.140742i
$736$		0			0
$737$	15.7385	+	27.2599i	0.579735	+	1.00413i
$738$		0			0
$739$	−38.3105	−	22.1186i	−1.40927	−	0.813645i	−0.413956	−	0.910297i	$-0.635853\pi$
$739$	−38.3105	−	22.1186i	−1.40927	−	0.813645i	−0.995318	+	0.0966526i	$0.969186\pi$
$740$		0			0
$741$	−33.0563	−	14.4392i	−1.21436	−	0.530439i
$742$		0			0
$743$	5.02990	+	2.90402i	0.184529	+	0.106538i	0.589419	−	0.807828i	$-0.299357\pi$
$743$	5.02990	+	2.90402i	0.184529	+	0.106538i	−0.404890	+	0.914366i	$0.632690\pi$
$744$		0			0
$745$	2.49642	+	4.32392i	0.0914617	+	0.158416i
$746$		0			0
$747$	−1.60390	+	0.926014i	−0.0586837	+	0.0338811i
$748$		0			0
$749$		−	16.1559i		−	0.590325i
$750$		0			0
$751$	−5.24012	+	9.07615i	−0.191215	+	0.331193i	−0.945653	−	0.325177i	$-0.894576\pi$
$751$	−5.24012	+	9.07615i	−0.191215	+	0.331193i	0.754438	+	0.656371i	$0.227909\pi$
$752$		0			0
$753$	39.5573			1.44155
$754$		0			0
$755$	−8.74125			−0.318127
$756$		0			0
$757$	−15.8761	+	27.4982i	−0.577027	+	0.999440i	0.418791	+	0.908083i	$0.362454\pi$
$757$	−15.8761	+	27.4982i	−0.577027	+	0.999440i	−0.995818	+	0.0913575i	$0.970879\pi$
$758$		0			0
$759$			40.2932i			1.46255i
$760$		0			0
$761$	−35.5387	+	20.5183i	−1.28828	+	0.743786i	−0.978346	−	0.206974i	$-0.933639\pi$
$761$	−35.5387	+	20.5183i	−1.28828	+	0.743786i	−0.309929	+	0.950760i	$0.600305\pi$
$762$		0			0
$763$	−0.718998	−	1.24534i	−0.0260295	−	0.0450844i
$764$		0			0
$765$	−1.19513	−	0.690006i	−0.0432099	−	0.0249472i
$766$		0			0
$767$	−0.503180	−	4.48315i	−0.0181688	−	0.161877i
$768$		0			0
$769$	25.7638	+	14.8747i	0.929067	+	0.536397i	0.886516	−	0.462698i	$-0.153118\pi$
$769$	25.7638	+	14.8747i	0.929067	+	0.536397i	0.0425503	+	0.999094i	$0.486452\pi$
$770$		0			0
$771$	−13.1620	−	22.7973i	−0.474019	−	0.821025i
$772$		0			0
$773$	−6.03551	+	3.48461i	−0.217082	+	0.125333i	−0.604599	−	0.796530i	$-0.706666\pi$
$773$	−6.03551	+	3.48461i	−0.217082	+	0.125333i	0.387516	+	0.921863i	$0.373333\pi$
$774$		0			0
$775$			6.96851i			0.250316i
$776$		0			0
$777$	5.41539	−	9.37973i	0.194276	−	0.336496i
$778$		0			0
$779$	71.5738			2.56440
$780$		0			0
$781$	27.5316			0.985158
$782$		0			0
$783$	23.2964	−	40.3505i	0.832545	−	1.44201i
$784$		0			0
$785$		−	3.89618i		−	0.139061i
$786$		0			0
$787$	−6.21965	+	3.59092i	−0.221707	+	0.128002i	−0.606740	−	0.794900i	$-0.707523\pi$
$787$	−6.21965	+	3.59092i	−0.221707	+	0.128002i	0.385034	+	0.922903i	$0.374190\pi$
$788$		0			0
$789$	11.7905	+	20.4217i	0.419753	+	0.727033i
$790$		0			0
$791$	3.19847	+	1.84664i	0.113725	+	0.0656589i
$792$		0			0
$793$	37.6119	−	4.22148i	1.33564	−	0.149909i
$794$		0			0
$795$	−8.14765	−	4.70405i	−0.288967	−	0.166835i
$796$		0			0
$797$	1.26438	+	2.18997i	0.0447867	+	0.0775729i	0.887550	−	0.460712i	$-0.152406\pi$
$797$	1.26438	+	2.18997i	0.0447867	+	0.0775729i	−0.842763	+	0.538285i	$0.819073\pi$
$798$		0			0
$799$	−27.6263	+	15.9501i	−0.977350	+	0.564273i
$800$		0			0
$801$			0.898167i			0.0317352i
$802$		0			0
$803$	−14.8933	+	25.7960i	−0.525573	+	0.910319i
$804$		0			0
$805$	−12.7732			−0.450197
$806$		0			0
$807$	32.1585			1.13203
$808$		0			0
$809$	−15.2300	+	26.3792i	−0.535460	+	0.927443i	0.463681	+	0.886002i	$0.346528\pi$
$809$	−15.2300	+	26.3792i	−0.535460	+	0.927443i	−0.999141	+	0.0414411i	$0.986805\pi$
$810$		0			0
$811$		−	52.3924i		−	1.83975i	−0.392216	−	0.919873i	$-0.628291\pi$
$811$		−	52.3924i		−	1.83975i	0.392216	−	0.919873i	$-0.371709\pi$
$812$		0			0
$813$	−12.2172	+	7.05361i	−0.428476	+	0.247381i
$814$		0			0
$815$	0.152015	+	0.263298i	0.00532485	+	0.00922291i
$816$		0			0
$817$	26.7176	+	15.4254i	0.934729	+	0.539666i
$818$		0			0
$819$	−1.28370	+	0.946560i	−0.0448560	+	0.0330755i
$820$		0			0
$821$	23.7857	+	13.7327i	0.830126	+	0.479273i	0.853896	−	0.520444i	$-0.174234\pi$
$821$	23.7857	+	13.7327i	0.830126	+	0.479273i	−0.0237699	+	0.999717i	$0.507567\pi$
$822$		0			0
$823$	−14.3157	−	24.7955i	−0.499013	−	0.864316i	0.500986	−	0.865455i	$-0.332971\pi$
$823$	−14.3157	−	24.7955i	−0.499013	−	0.864316i	−0.999999	+	0.00113913i	$0.999637\pi$
$824$		0			0
$825$	4.20247	−	2.42630i	0.146311	−	0.0844729i
$826$		0			0
$827$		−	16.5867i		−	0.576776i	−0.957514	−	0.288388i	$-0.906881\pi$
$827$		−	16.5867i		−	0.576776i	0.957514	−	0.288388i	$-0.0931193\pi$
$828$		0			0
$829$	−17.6553	+	30.5799i	−0.613194	+	1.06208i	0.377504	+	0.926008i	$0.376782\pi$
$829$	−17.6553	+	30.5799i	−0.613194	+	1.06208i	−0.990698	+	0.136076i	$0.956551\pi$
$830$		0			0
$831$	−34.1582			−1.18494
$832$		0			0
$833$	−22.2367			−0.770457
$834$		0			0
$835$	11.2354	−	19.4602i	0.388816	−	0.673449i
$836$		0			0
$837$		−	37.7306i		−	1.30416i
$838$		0			0
$839$	15.7188	−	9.07528i	0.542675	−	0.313314i	−0.203487	−	0.979078i	$-0.565228\pi$
$839$	15.7188	−	9.07528i	0.542675	−	0.313314i	0.746162	+	0.665764i	$0.231894\pi$
$840$		0			0
$841$	−22.5254	−	39.0151i	−0.776737	−	1.34535i
$842$		0			0
$843$	−0.912883	−	0.527053i	−0.0314414	−	0.0181527i
$844$		0			0
$845$	9.53727	−	8.83406i	0.328092	−	0.303901i
$846$		0			0
$847$	3.08890	+	1.78338i	0.106136	+	0.0612776i
$848$		0			0
$849$	10.0537	+	17.4136i	0.345043	+	0.597632i
$850$		0			0
$851$	−30.7414	+	17.7486i	−1.05380	+	0.608413i
$852$		0			0
$853$		−	25.0441i		−	0.857492i	−0.903425	−	0.428746i	$-0.858956\pi$
$853$		−	25.0441i		−	0.857492i	0.903425	−	0.428746i	$-0.141044\pi$
$854$		0			0
$855$	−0.873421	+	1.51281i	−0.0298704	+	0.0517370i
$856$		0			0
$857$	9.46634			0.323364			0.161682	−	0.986843i	$-0.448308\pi$
$857$	9.46634			0.323364			0.161682	+	0.986843i	$0.448308\pi$
$858$		0			0
$859$	−22.7817			−0.777300			−0.388650	−	0.921385i	$-0.627058\pi$
$859$	−22.7817			−0.777300			−0.388650	+	0.921385i	$0.627058\pi$
$860$		0			0
$861$	−14.9254	+	25.8515i	−0.508655	+	0.881017i
$862$		0			0
$863$		−	14.4067i		−	0.490409i	−0.969471	−	0.245205i	$-0.921145\pi$
$863$		−	14.4067i		−	0.490409i	0.969471	−	0.245205i	$-0.0788551\pi$
$864$		0			0
$865$	0.365977	−	0.211297i	0.0124436	−	0.00718431i
$866$		0			0
$867$	4.96601	+	8.60137i	0.168654	+	0.292118i
$868$		0			0
$869$	19.0679	+	11.0088i	0.646833	+	0.373449i
$870$		0			0
$871$	−31.0018	+	22.8598i	−1.05046	+	0.774575i
$872$		0			0
$873$	−1.12530	−	0.649691i	−0.0380855	−	0.0219887i
$874$		0			0
$875$	0.769155	+	1.33221i	0.0260022	+	0.0450371i
$876$		0			0
$877$	18.9775	−	10.9566i	0.640823	−	0.369980i	−0.144108	−	0.989562i	$-0.546031\pi$
$877$	18.9775	−	10.9566i	0.640823	−	0.369980i	0.784932	+	0.619582i	$0.212698\pi$
$878$		0			0
$879$			19.4400i			0.655695i
$880$		0			0
$881$	−10.6781	+	18.4950i	−0.359754	+	0.623112i	−0.987920	−	0.154967i	$-0.950473\pi$
$881$	−10.6781	+	18.4950i	−0.359754	+	0.623112i	0.628166	+	0.778080i	$0.283806\pi$
$882$		0			0
$883$	−25.2150			−0.848553			−0.424277	−	0.905533i	$-0.639472\pi$
$883$	−25.2150			−0.848553			−0.424277	+	0.905533i	$0.639472\pi$
$884$		0			0
$885$	2.06068			0.0692689
$886$		0			0
$887$	−7.94012	+	13.7527i	−0.266603	+	0.461770i	−0.967982	−	0.251018i	$-0.919235\pi$
$887$	−7.94012	+	13.7527i	−0.266603	+	0.461770i	0.701379	+	0.712788i	$0.252568\pi$
$888$		0			0
$889$		−	17.6228i		−	0.591050i
$890$		0			0
$891$	−20.5528	+	11.8661i	−0.688544	+	0.397531i
$892$		0			0
$893$	20.1899	+	34.9699i	0.675628	+	1.17022i
$894$		0			0
$895$	11.6302	+	6.71472i	0.388756	+	0.224448i
$896$		0			0
$897$	−48.9994	+	5.49959i	−1.63604	+	0.183626i
$898$		0			0
$899$	−51.9320	−	29.9830i	−1.73203	−	0.999988i
$900$		0			0
$901$	−13.7070	−	23.7413i	−0.456648	−	0.790937i
$902$		0			0
$903$	−11.1429	+	6.43335i	−0.370812	+	0.214088i
$904$		0			0
$905$			15.1748i			0.504428i
$906$		0			0
$907$	2.87308	−	4.97632i	0.0953990	−	0.165236i	−0.814376	−	0.580338i	$-0.802921\pi$
$907$	2.87308	−	4.97632i	0.0953990	−	0.165236i	0.909775	+	0.415102i	$0.136254\pi$
$908$		0			0
$909$	5.50943			0.182736
$910$		0			0
$911$	48.7290			1.61446			0.807232	−	0.590235i	$-0.200965\pi$
$911$	48.7290			1.61446			0.807232	+	0.590235i	$0.200965\pi$
$912$		0			0
$913$	9.48814	−	16.4339i	0.314012	−	0.543884i
$914$		0			0
$915$			17.2883i			0.571533i
$916$		0			0
$917$	−9.70472	+	5.60302i	−0.320478	+	0.185028i
$918$		0			0
$919$	23.4600	+	40.6340i	0.773875	+	1.34039i	0.935425	+	0.353526i	$0.115017\pi$
$919$	23.4600	+	40.6340i	0.773875	+	1.34039i	−0.161550	+	0.986865i	$0.551649\pi$
$920$		0			0
$921$	−17.5082	−	10.1084i	−0.576914	−	0.333082i
$922$		0			0
$923$	3.75777	+	33.4804i	0.123689	+	1.10202i
$924$		0			0
$925$	3.70226	+	2.13750i	0.121729	+	0.0702805i
$926$		0			0
$927$	1.10493	+	1.91379i	0.0362906	+	0.0628571i
$928$		0			0
$929$	−28.0051	+	16.1687i	−0.918816	+	0.530479i	−0.883257	−	0.468889i	$-0.844655\pi$
$929$	−28.0051	+	16.1687i	−0.918816	+	0.530479i	−0.0355591	+	0.999368i	$0.511321\pi$
$930$		0			0
$931$			28.1476i			0.922501i
$932$		0			0
$933$	−9.41780	+	16.3121i	−0.308325	+	0.534035i
$934$		0			0
$935$	14.1399			0.462424
$936$		0			0
$937$	3.30275			0.107896			0.0539481	−	0.998544i	$-0.482819\pi$
$937$	3.30275			0.107896			0.0539481	+	0.998544i	$0.482819\pi$
$938$		0			0
$939$	−19.4247	+	33.6446i	−0.633902	+	1.09795i
$940$		0			0
$941$		−	34.7436i		−	1.13261i	−0.824196	−	0.566305i	$-0.808372\pi$
$941$		−	34.7436i		−	1.13261i	0.824196	−	0.566305i	$-0.191628\pi$
$942$		0			0
$943$	84.7265	−	48.9169i	2.75908	−	1.59295i
$944$		0			0
$945$	−4.16454	−	7.21320i	−0.135473	−	0.234646i
$946$		0			0
$947$	8.44603	+	4.87631i	0.274459	+	0.158459i	0.630912	−	0.775854i	$-0.282681\pi$
$947$	8.44603	+	4.87631i	0.274459	+	0.158459i	−0.356453	+	0.934313i	$0.616014\pi$
$948$		0			0
$949$	−33.4025	−	14.5904i	−1.08429	−	0.473626i
$950$		0			0
$951$	23.1202	+	13.3484i	0.749723	+	0.432853i
$952$		0			0
$953$	6.95249	+	12.0421i	0.225213	+	0.390081i	0.956383	−	0.292114i	$-0.0943588\pi$
$953$	6.95249	+	12.0421i	0.225213	+	0.390081i	−0.731170	+	0.682195i	$0.761025\pi$
$954$		0			0
$955$	−6.37092	+	3.67825i	−0.206158	+	0.119025i
$956$		0			0
$957$			41.7579i			1.34984i
$958$		0			0
$959$	9.00829	−	15.6028i	0.290893	−	0.503841i
$960$		0			0
$961$	−17.5601			−0.566455
$962$		0			0
$963$	−3.02008			−0.0973208
$964$		0			0
$965$	6.14197	−	10.6382i	0.197717	−	0.342456i
$966$		0			0
$967$		−	5.96794i		−	0.191916i	−0.995385	−	0.0959579i	$-0.969409\pi$
$967$		−	5.96794i		−	0.191916i	0.995385	−	0.0959579i	$-0.0305914\pi$
$968$		0			0
$969$	41.5801	−	24.0063i	1.33574	−	0.771193i
$970$		0			0
$971$	−11.3059	−	19.5823i	−0.362823	−	0.628427i	0.625602	−	0.780143i	$-0.284854\pi$
$971$	−11.3059	−	19.5823i	−0.362823	−	0.628427i	−0.988424	+	0.151716i	$0.951520\pi$
$972$		0			0
$973$	0.0649082	+	0.0374748i	0.00208086	+	0.00120139i
$974$		0			0
$975$	3.52414	+	4.77934i	0.112863	+	0.153061i
$976$		0			0
$977$	37.2445	+	21.5031i	1.19156	+	0.687946i	0.958660	−	0.284555i	$-0.0918457\pi$
$977$	37.2445	+	21.5031i	1.19156	+	0.687946i	0.232898	+	0.972501i	$0.425179\pi$
$978$		0			0
$979$	−4.60141	−	7.96987i	−0.147062	−	0.254718i
$980$		0			0
$981$	−0.232796	+	0.134405i	−0.00743260	+	0.00429122i
$982$		0			0
$983$			34.0663i			1.08654i	0.839557	+	0.543272i	$0.182815\pi$
$983$			34.0663i			1.08654i	−0.839557	+	0.543272i	$0.817185\pi$
$984$		0			0
$985$	−3.39281	+	5.87651i	−0.108104	+	0.187241i
$986$		0			0
$987$	−16.8409			−0.536050
$988$		0			0
$989$	42.1697			1.34092
$990$		0			0
$991$	11.1972	−	19.3941i	0.355690	−	0.616073i	−0.631546	−	0.775338i	$-0.717579\pi$
$991$	11.1972	−	19.3941i	0.355690	−	0.616073i	0.987236	+	0.159266i	$0.0509126\pi$
$992$		0			0
$993$		−	9.77824i		−	0.310303i
$994$		0			0
$995$	−15.4510	+	8.92063i	−0.489829	+	0.282803i
$996$		0			0
$997$	30.8372	+	53.4115i	0.976623	+	1.69156i	0.674473	+	0.738299i	$0.264371\pi$
$997$	30.8372	+	53.4115i	0.976623	+	1.69156i	0.302149	+	0.953261i	$0.402296\pi$
$998$		0			0
$999$	−20.0457	−	11.5734i	−0.634217	−	0.366165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.e.641.5		12
4.3	odd	2		520.2.bu.a.121.2	✓	12
13.10	even	6	inner	1040.2.da.e.881.5		12
52.7	even	12		6760.2.a.bg.1.5		6
52.19	even	12		6760.2.a.bj.1.5		6
52.23	odd	6		520.2.bu.a.361.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.a.121.2	✓	12	4.3	odd	2
520.2.bu.a.361.2	yes	12	52.23	odd	6
1040.2.da.e.641.5		12	1.1	even	1	trivial
1040.2.da.e.881.5		12	13.10	even	6	inner
6760.2.a.bg.1.5		6	52.7	even	12
6760.2.a.bj.1.5		6	52.19	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)

\(f(q)\)	\(=\)	\(q+(0.823474 - 1.42630i) q^{3} +1.00000i q^{5} +(-1.33221 + 0.769155i) q^{7} +(0.143781 + 0.249036i) q^{9} +O(q^{10})\)	\(q+(0.823474 - 1.42630i) q^{3} +1.00000i q^{5} +(-1.33221 + 0.769155i) q^{7} +(0.143781 + 0.249036i) q^{9} +(-2.55167 - 1.47321i) q^{11} +(1.44325 - 3.30409i) q^{13} +(1.42630 + 0.823474i) q^{15} +(2.39951 + 4.15607i) q^{17} +(5.26082 - 3.03733i) q^{19} +2.53352i q^{21} +(4.15171 - 7.19097i) q^{23} -1.00000 q^{25} +5.41444 q^{27} +(4.30264 - 7.45239i) q^{29} -6.96851i q^{31} +(-4.20247 + 2.42630i) q^{33} +(-0.769155 - 1.33221i) q^{35} +(-3.70226 - 2.13750i) q^{37} +(-3.52414 - 4.77934i) q^{39} +(10.2038 + 5.89117i) q^{41} +(2.53930 + 4.39819i) q^{43} +(-0.249036 + 0.143781i) q^{45} +6.64723i q^{47} +(-2.31680 + 4.01282i) q^{49} +7.90373 q^{51} -5.71244 q^{53} +(1.47321 - 2.55167i) q^{55} -10.0047i q^{57} +(1.08358 - 0.625605i) q^{59} +(5.24858 + 9.09081i) q^{61} +(-0.383094 - 0.221179i) q^{63} +(3.30409 + 1.44325i) q^{65} +(-9.25187 - 5.34157i) q^{67} +(-6.83765 - 11.8432i) q^{69} +(-8.09222 + 4.67205i) q^{71} -10.1094i q^{73} +(-0.823474 + 1.42630i) q^{75} +4.53250 q^{77} -7.47269 q^{79} +(4.02731 - 6.97551i) q^{81} +6.44046i q^{83} +(-4.15607 + 2.39951i) q^{85} +(-7.08622 - 12.2737i) q^{87} +(2.70494 + 1.56170i) q^{89} +(0.618638 + 5.51184i) q^{91} +(-9.93918 - 5.73839i) q^{93} +(3.03733 + 5.26082i) q^{95} +(-3.91324 + 2.25931i) q^{97} -0.847277i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 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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