LMFDB - Embedded newform 912.3.be.d.673.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.3
Root			$-1.13654 + 1.96854i$ of defining polynomial
Character	$\chi$	$=$	912.673
Dual form			912.3.be.d.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(2.27307 - 3.93708i) q^{5} -9.87987 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(2.27307 - 3.93708i) q^{5} -9.87987 q^{7} +(1.50000 + 2.59808i) q^{9} +15.6384 q^{11} +(13.3053 - 7.68182i) q^{13} +(-6.81922 + 3.93708i) q^{15} +(-12.4260 + 21.5225i) q^{17} +(18.4260 - 4.63488i) q^{19} +(14.8198 + 8.55622i) q^{21} +(-4.15294 - 7.19310i) q^{23} +(2.16628 + 3.75211i) q^{25} -5.19615i q^{27} +(27.3059 - 15.7651i) q^{29} -30.9353i q^{31} +(-23.4577 - 13.5433i) q^{33} +(-22.4577 + 38.8978i) q^{35} -17.3225i q^{37} -26.6106 q^{39} +(-44.2502 - 25.5479i) q^{41} +(0.773073 - 1.33900i) q^{43} +13.6384 q^{45} +(-5.09113 - 8.81810i) q^{47} +48.6118 q^{49} +(37.2780 - 21.5225i) q^{51} +(4.54002 - 2.62118i) q^{53} +(35.5473 - 61.5697i) q^{55} +(-31.6529 - 9.00508i) q^{57} +(-68.4321 - 39.5093i) q^{59} +(-53.9426 - 93.4313i) q^{61} +(-14.8198 - 25.6686i) q^{63} -69.8453i q^{65} +(16.9843 - 9.80591i) q^{67} +14.3862i q^{69} +(45.3604 + 26.1888i) q^{71} +(-36.6301 + 63.4451i) q^{73} -7.50421i q^{75} -154.506 q^{77} +(27.1512 + 15.6758i) q^{79} +(-4.50000 + 7.79423i) q^{81} +42.6674 q^{83} +(56.4905 + 97.8443i) q^{85} -54.6118 q^{87} +(114.819 - 66.2909i) q^{89} +(-131.455 + 75.8953i) q^{91} +(-26.7908 + 46.4030i) q^{93} +(23.6358 - 83.0801i) q^{95} +(-70.2270 - 40.5456i) q^{97} +(23.4577 + 40.6299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	2.27307	−	3.93708i	0.454615	−	0.787416i	−0.544051	−	0.839052i	$-0.683110\pi$
$5$	2.27307	−	3.93708i	0.454615	−	0.787416i	0.998666	+	0.0516364i	$0.0164437\pi$
$6$		0			0
$7$	−9.87987			−1.41141			−0.705705	−	0.708506i	$-0.749369\pi$
$7$	−9.87987			−1.41141			−0.705705	+	0.708506i	$0.749369\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	15.6384			1.42168			0.710838	−	0.703356i	$-0.248316\pi$
$11$	15.6384			1.42168			0.710838	+	0.703356i	$0.248316\pi$
$12$		0			0
$13$	13.3053	−	7.68182i	1.02348	−	0.590909i	0.108373	−	0.994110i	$-0.465436\pi$
$13$	13.3053	−	7.68182i	1.02348	−	0.590909i	0.915111	+	0.403201i	$0.132103\pi$
$14$		0			0
$15$	−6.81922	+	3.93708i	−0.454615	+	0.262472i
$16$		0			0
$17$	−12.4260	+	21.5225i	−0.730942	+	1.26603i	0.225539	+	0.974234i	$0.427586\pi$
$17$	−12.4260	+	21.5225i	−0.730942	+	1.26603i	−0.956481	+	0.291794i	$0.905748\pi$
$18$		0			0
$19$	18.4260	−	4.63488i	0.969790	−	0.243941i
$19$	18.4260	−	4.63488i	0.969790	−	0.243941i
$20$		0			0
$21$	14.8198	+	8.55622i	0.705705	+	0.407439i
$22$		0			0
$23$	−4.15294	−	7.19310i	−0.180563	−	0.312744i	0.761510	−	0.648154i	$-0.224458\pi$
$23$	−4.15294	−	7.19310i	−0.180563	−	0.312744i	−0.942072	+	0.335410i	$0.891125\pi$
$24$		0			0
$25$	2.16628	+	3.75211i	0.0866512	+	0.150084i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	27.3059	−	15.7651i	0.941582	−	0.543623i	0.0511261	−	0.998692i	$-0.483719\pi$
$29$	27.3059	−	15.7651i	0.941582	−	0.543623i	0.890456	+	0.455070i	$0.150386\pi$
$30$		0			0
$31$		−	30.9353i		−	0.997914i	−0.866627	−	0.498957i	$-0.833716\pi$
$31$		−	30.9353i		−	0.997914i	0.866627	−	0.498957i	$-0.166284\pi$
$32$		0			0
$33$	−23.4577	−	13.5433i	−0.710838	−	0.410403i
$34$		0			0
$35$	−22.4577	+	38.8978i	−0.641647	+	1.11137i
$36$		0			0
$37$		−	17.3225i		−	0.468176i	−0.972215	−	0.234088i	$-0.924790\pi$
$37$		−	17.3225i		−	0.468176i	0.972215	−	0.234088i	$-0.0752104\pi$
$38$		0			0
$39$	−26.6106			−0.682323
$40$		0			0
$41$	−44.2502	−	25.5479i	−1.07927	−	0.623119i	−0.148573	−	0.988901i	$-0.547468\pi$
$41$	−44.2502	−	25.5479i	−1.07927	−	0.623119i	−0.930700	+	0.365783i	$0.880801\pi$
$42$		0			0
$43$	0.773073	−	1.33900i	0.0179784	−	0.0311396i	−0.856896	−	0.515489i	$-0.827610\pi$
$43$	0.773073	−	1.33900i	0.0179784	−	0.0311396i	0.874875	+	0.484349i	$0.160944\pi$
$44$		0			0
$45$	13.6384			0.303076
$46$		0			0
$47$	−5.09113	−	8.81810i	−0.108322	−	0.187619i	0.806769	−	0.590867i	$-0.201214\pi$
$47$	−5.09113	−	8.81810i	−0.108322	−	0.187619i	−0.915091	+	0.403248i	$0.867881\pi$
$48$		0			0
$49$	48.6118			0.992077
$50$		0			0
$51$	37.2780	−	21.5225i	0.730942	−	0.422009i
$52$		0			0
$53$	4.54002	−	2.62118i	0.0856608	−	0.0494563i	−0.456558	−	0.889694i	$-0.650918\pi$
$53$	4.54002	−	2.62118i	0.0856608	−	0.0494563i	0.542219	+	0.840238i	$0.317584\pi$
$54$		0			0
$55$	35.5473	−	61.5697i	0.646315	−	1.11945i
$56$		0			0
$57$	−31.6529	−	9.00508i	−0.555315	−	0.157984i
$58$		0			0
$59$	−68.4321	−	39.5093i	−1.15987	−	0.669649i	−0.208595	−	0.978002i	$-0.566889\pi$
$59$	−68.4321	−	39.5093i	−1.15987	−	0.669649i	−0.951272	+	0.308353i	$0.900222\pi$
$60$		0			0
$61$	−53.9426	−	93.4313i	−0.884304	−	1.53166i	−0.846509	−	0.532375i	$-0.821300\pi$
$61$	−53.9426	−	93.4313i	−0.884304	−	1.53166i	−0.0377957	−	0.999285i	$-0.512034\pi$
$62$		0			0
$63$	−14.8198	−	25.6686i	−0.235235	−	0.407439i
$64$		0			0
$65$		−	69.8453i		−	1.07454i
$66$		0			0
$67$	16.9843	−	9.80591i	0.253498	−	0.146357i	−0.367867	−	0.929878i	$-0.619912\pi$
$67$	16.9843	−	9.80591i	0.253498	−	0.146357i	0.621365	+	0.783521i	$0.286579\pi$
$68$		0			0
$69$			14.3862i			0.208496i
$70$		0			0
$71$	45.3604	+	26.1888i	0.638879	+	0.368857i	0.784183	−	0.620530i	$-0.213083\pi$
$71$	45.3604	+	26.1888i	0.638879	+	0.368857i	−0.145304	+	0.989387i	$0.546416\pi$
$72$		0			0
$73$	−36.6301	+	63.4451i	−0.501782	+	0.869111i	0.498216	+	0.867053i	$0.333989\pi$
$73$	−36.6301	+	63.4451i	−0.501782	+	0.869111i	−0.999998	+	0.00205848i	$0.999345\pi$
$74$		0			0
$75$		−	7.50421i		−	0.100056i
$76$		0			0
$77$	−154.506			−2.00657
$78$		0			0
$79$	27.1512	+	15.6758i	0.343686	+	0.198427i	0.661901	−	0.749591i	$-0.269750\pi$
$79$	27.1512	+	15.6758i	0.343686	+	0.198427i	−0.318215	+	0.948019i	$0.603083\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	42.6674			0.514066			0.257033	−	0.966403i	$-0.417255\pi$
$83$	42.6674			0.514066			0.257033	+	0.966403i	$0.417255\pi$
$84$		0			0
$85$	56.4905	+	97.8443i	0.664594	+	1.15111i
$86$		0			0
$87$	−54.6118			−0.627721
$88$		0			0
$89$	114.819	−	66.2909i	1.29010	−	0.744842i	0.311431	−	0.950269i	$-0.399192\pi$
$89$	114.819	−	66.2909i	1.29010	−	0.744842i	0.978672	+	0.205427i	$0.0658583\pi$
$90$		0			0
$91$	−131.455	+	75.8953i	−1.44456	+	0.834015i
$92$		0			0
$93$	−26.7908	+	46.4030i	−0.288073	+	0.498957i
$94$		0			0
$95$	23.6358	−	83.0801i	0.248798	−	0.874527i
$96$		0			0
$97$	−70.2270	−	40.5456i	−0.723990	−	0.417996i	0.0922297	−	0.995738i	$-0.470601\pi$
$97$	−70.2270	−	40.5456i	−0.723990	−	0.417996i	−0.816219	+	0.577742i	$0.803934\pi$
$98$		0			0
$99$	23.4577	+	40.6299i	0.236946	+	0.410403i
$100$		0			0
$101$	−44.8242	−	77.6378i	−0.443804	−	0.768691i	0.554164	−	0.832407i	$-0.313038\pi$
$101$	−44.8242	−	77.6378i	−0.443804	−	0.768691i	−0.997968	+	0.0637166i	$0.979705\pi$
$102$		0			0
$103$			59.2876i			0.575608i	0.957689	+	0.287804i	$0.0929251\pi$
$103$			59.2876i			0.575608i	−0.957689	+	0.287804i	$0.907075\pi$
$104$		0			0
$105$	67.3730	−	38.8978i	0.641647	−	0.370455i
$106$		0			0
$107$		−	45.0373i		−	0.420910i	−0.977604	−	0.210455i	$-0.932505\pi$
$107$		−	45.0373i		−	0.420910i	0.977604	−	0.210455i	$-0.0674945\pi$
$108$		0			0
$109$	4.30356	+	2.48466i	0.0394822	+	0.0227950i	0.519611	−	0.854403i	$-0.326077\pi$
$109$	4.30356	+	2.48466i	0.0394822	+	0.0227950i	−0.480129	+	0.877198i	$0.659410\pi$
$110$		0			0
$111$	−15.0017	+	25.9838i	−0.135151	+	0.234088i
$112$		0			0
$113$		−	124.048i		−	1.09777i	−0.835898	−	0.548885i	$-0.815053\pi$
$113$		−	124.048i		−	1.09777i	0.835898	−	0.548885i	$-0.184947\pi$
$114$		0			0
$115$	−37.7597			−0.328345
$116$		0			0
$117$	39.9159	+	23.0455i	0.341161	+	0.196970i
$118$		0			0
$119$	122.767	−	212.639i	1.03166	−	1.78688i
$120$		0			0
$121$	123.561			1.02116
$122$		0			0
$123$	44.2502	+	76.6436i	0.359758	+	0.623119i
$124$		0			0
$125$	133.350			1.06680
$126$		0			0
$127$	−99.9211	+	57.6895i	−0.786780	+	0.454248i	−0.838828	−	0.544397i	$-0.816759\pi$
$127$	−99.9211	+	57.6895i	−0.786780	+	0.454248i	0.0520474	+	0.998645i	$0.483425\pi$
$128$		0			0
$129$	−2.31922	+	1.33900i	−0.0179784	+	0.0103799i
$130$		0			0
$131$	53.1834	−	92.1164i	0.405980	−	0.703179i	−0.588455	−	0.808530i	$-0.700263\pi$
$131$	53.1834	−	92.1164i	0.405980	−	0.703179i	0.994435	+	0.105352i	$0.0335968\pi$
$132$		0			0
$133$	−182.047	+	45.7920i	−1.36877	+	0.344300i
$134$		0			0
$135$	−20.4577	−	11.8112i	−0.151538	−	0.0874906i
$136$		0			0
$137$	−58.9455	−	102.097i	−0.430259	−	0.745230i	0.566636	−	0.823968i	$-0.308244\pi$
$137$	−58.9455	−	102.097i	−0.430259	−	0.745230i	−0.996895	+	0.0787376i	$0.974911\pi$
$138$		0			0
$139$	−88.9275	−	154.027i	−0.639766	−	1.10811i	−0.985484	−	0.169769i	$-0.945698\pi$
$139$	−88.9275	−	154.027i	−0.639766	−	1.10811i	0.345718	−	0.938339i	$-0.387635\pi$
$140$		0			0
$141$			17.6362i			0.125079i
$142$		0			0
$143$	208.074	−	120.132i	1.45506	−	0.840081i
$144$		0			0
$145$		−	143.340i		−	0.988555i
$146$		0			0
$147$	−72.9176	−	42.0990i	−0.496038	−	0.286388i
$148$		0			0
$149$	89.8593	−	155.641i	0.603083	−	1.04457i	−0.389269	−	0.921124i	$-0.627272\pi$
$149$	89.8593	−	155.641i	0.603083	−	1.04457i	0.992351	−	0.123445i	$-0.0393944\pi$
$150$		0			0
$151$		−	225.138i		−	1.49098i	−0.666517	−	0.745490i	$-0.732215\pi$
$151$		−	225.138i		−	1.49098i	0.666517	−	0.745490i	$-0.267785\pi$
$152$		0			0
$153$	−74.5561			−0.487295
$154$		0			0
$155$	−121.795	−	70.3183i	−0.785773	−	0.453666i
$156$		0			0
$157$	−13.5101	+	23.4002i	−0.0860517	+	0.149046i	−0.905839	−	0.423622i	$-0.860758\pi$
$157$	−13.5101	+	23.4002i	−0.0860517	+	0.149046i	0.819787	+	0.572668i	$0.194092\pi$
$158$		0			0
$159$	−9.08004			−0.0571072
$160$		0			0
$161$	41.0305	+	71.0669i	0.254848	+	0.441409i
$162$		0			0
$163$	151.210			0.927667			0.463833	−	0.885922i	$-0.346474\pi$
$163$	151.210			0.927667			0.463833	+	0.885922i	$0.346474\pi$
$164$		0			0
$165$	−106.642	+	61.5697i	−0.646315	+	0.373150i
$166$		0			0
$167$	−123.259	+	71.1638i	−0.738079	+	0.426130i	−0.821371	−	0.570395i	$-0.806790\pi$
$167$	−123.259	+	71.1638i	−0.738079	+	0.426130i	0.0832911	+	0.996525i	$0.473457\pi$
$168$		0			0
$169$	33.5206	−	58.0594i	0.198347	−	0.343547i
$170$		0			0
$171$	39.6808	+	40.9199i	0.232051	+	0.239297i
$172$		0			0
$173$	205.442	+	118.612i	1.18753	+	0.685620i	0.957744	−	0.287622i	$-0.0928646\pi$
$173$	205.442	+	118.612i	1.18753	+	0.685620i	0.229784	+	0.973242i	$0.426198\pi$
$174$		0			0
$175$	−21.4026	−	37.0703i	−0.122300	−	0.211830i
$176$		0			0
$177$	68.4321	+	118.528i	0.386622	+	0.669649i
$178$		0			0
$179$		−	1.84122i		−	0.0102862i	−0.999987	−	0.00514308i	$-0.998363\pi$
$179$		−	1.84122i		−	0.0102862i	0.999987	−	0.00514308i	$-0.00163710\pi$
$180$		0			0
$181$	−30.9176	+	17.8503i	−0.170816	+	0.0986205i	−0.582970	−	0.812493i	$-0.698110\pi$
$181$	−30.9176	+	17.8503i	−0.170816	+	0.0986205i	0.412155	+	0.911114i	$0.364776\pi$
$182$		0			0
$183$			186.863i			1.02111i
$184$		0			0
$185$	−68.2001	−	39.3753i	−0.368649	−	0.212840i
$186$		0			0
$187$	−194.323	+	336.578i	−1.03916	+	1.79988i
$188$		0			0
$189$			51.3373i			0.271626i
$190$		0			0
$191$	−166.346			−0.870919			−0.435460	−	0.900208i	$-0.643414\pi$
$191$	−166.346			−0.870919			−0.435460	+	0.900208i	$0.643414\pi$
$192$		0			0
$193$	150.645	+	86.9747i	0.780542	+	0.450646i	0.836622	−	0.547780i	$-0.184527\pi$
$193$	150.645	+	86.9747i	0.780542	+	0.450646i	−0.0560803	+	0.998426i	$0.517860\pi$
$194$		0			0
$195$	−60.4878	+	104.768i	−0.310194	+	0.537272i
$196$		0			0
$197$	−86.5637			−0.439410			−0.219705	−	0.975566i	$-0.570509\pi$
$197$	−86.5637			−0.439410			−0.219705	+	0.975566i	$0.570509\pi$
$198$		0			0
$199$	125.922	+	218.103i	0.632774	+	1.09600i	0.986982	+	0.160830i	$0.0514171\pi$
$199$	125.922	+	218.103i	0.632774	+	1.09600i	−0.354208	+	0.935167i	$0.615250\pi$
$200$		0			0
$201$	−33.9687			−0.168998
$202$		0			0
$203$	−269.778	+	155.757i	−1.32896	+	0.767274i
$204$		0			0
$205$	−201.168	+	116.144i	−0.981306	+	0.566558i
$206$		0			0
$207$	12.4588	−	21.5793i	0.0601875	−	0.104248i
$208$		0			0
$209$	288.154	−	72.4822i	1.37873	−	0.346805i
$210$		0			0
$211$	143.105	+	82.6215i	0.678221	+	0.391571i	0.799184	−	0.601086i	$-0.205265\pi$
$211$	143.105	+	82.6215i	0.678221	+	0.391571i	−0.120963	+	0.992657i	$0.538598\pi$
$212$		0			0
$213$	−45.3604	−	78.5665i	−0.212960	−	0.368857i
$214$		0			0
$215$	−3.51450	−	6.08730i	−0.0163465	−	0.0283130i
$216$		0			0
$217$			305.637i			1.40847i
$218$		0			0
$219$	109.890	−	63.4451i	0.501782	−	0.289704i
$220$		0			0
$221$			381.817i			1.72768i
$222$		0			0
$223$	178.604	+	103.117i	0.800915	+	0.462408i	0.843791	−	0.536672i	$-0.180319\pi$
$223$	178.604	+	103.117i	0.800915	+	0.462408i	−0.0428761	+	0.999080i	$0.513652\pi$
$224$		0			0
$225$	−6.49884	+	11.2563i	−0.0288837	+	0.0500281i
$226$		0			0
$227$			329.381i			1.45102i	0.688213	+	0.725509i	$0.258395\pi$
$227$			329.381i			1.45102i	−0.688213	+	0.725509i	$0.741605\pi$
$228$		0			0
$229$	109.771			0.479351			0.239676	−	0.970853i	$-0.422959\pi$
$229$	109.771			0.479351			0.239676	+	0.970853i	$0.422959\pi$
$230$		0			0
$231$	231.759	+	133.806i	1.00328	+	0.579246i
$232$		0			0
$233$	−107.428	+	186.071i	−0.461066	+	0.798589i	−0.999014	−	0.0443883i	$-0.985866\pi$
$233$	−107.428	+	186.071i	−0.461066	+	0.798589i	0.537949	+	0.842978i	$0.319199\pi$
$234$		0			0
$235$	−46.2900			−0.196979
$236$		0			0
$237$	−27.1512	−	47.0273i	−0.114562	−	0.198427i
$238$		0			0
$239$	332.860			1.39272			0.696359	−	0.717694i	$-0.254802\pi$
$239$	332.860			1.39272			0.696359	+	0.717694i	$0.254802\pi$
$240$		0			0
$241$	−243.721	+	140.712i	−1.01129	+	0.583869i	−0.911569	−	0.411146i	$-0.865129\pi$
$241$	−243.721	+	140.712i	−1.01129	+	0.583869i	−0.0997218	+	0.995015i	$0.531795\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	110.498	−	191.388i	0.451013	−	0.781177i
$246$		0			0
$247$	209.559	−	203.214i	0.848418	−	0.822727i
$248$		0			0
$249$	−64.0012	−	36.9511i	−0.257033	−	0.148398i
$250$		0			0
$251$	−203.986	−	353.314i	−0.812694	−	1.40763i	−0.910972	−	0.412468i	$-0.864667\pi$
$251$	−203.986	−	353.314i	−0.812694	−	1.40763i	0.0982779	−	0.995159i	$-0.468667\pi$
$252$		0			0
$253$	−64.9455	−	112.489i	−0.256701	−	0.444620i
$254$		0			0
$255$		−	195.689i		−	0.767407i
$256$		0			0
$257$	37.5180	−	21.6610i	0.145984	−	0.0842841i	−0.425229	−	0.905086i	$-0.639806\pi$
$257$	37.5180	−	21.6610i	0.145984	−	0.0842841i	0.571213	+	0.820802i	$0.306473\pi$
$258$		0			0
$259$			171.144i			0.660788i
$260$		0			0
$261$	81.9176	+	47.2952i	0.313861	+	0.181208i
$262$		0			0
$263$	242.738	−	420.434i	0.922958	−	1.59861i	0.128145	−	0.991755i	$-0.459098\pi$
$263$	242.738	−	420.434i	0.922958	−	1.59861i	0.794813	−	0.606855i	$-0.207569\pi$
$264$		0			0
$265$		−	23.8326i		−	0.0899342i
$266$		0			0
$267$	−229.638			−0.860069
$268$		0			0
$269$	335.484	+	193.692i	1.24715	+	0.720044i	0.970540	−	0.240938i	$-0.0774551\pi$
$269$	335.484	+	193.692i	1.24715	+	0.720044i	0.276612	+	0.960982i	$0.410788\pi$
$270$		0			0
$271$	−173.258	+	300.091i	−0.639328	+	1.10735i	0.346253	+	0.938141i	$0.387454\pi$
$271$	−173.258	+	300.091i	−0.639328	+	1.10735i	−0.985581	+	0.169207i	$0.945879\pi$
$272$		0			0
$273$	262.909			0.963037
$274$		0			0
$275$	33.8772	+	58.6771i	0.123190	+	0.213371i
$276$		0			0
$277$	−115.366			−0.416484			−0.208242	−	0.978077i	$-0.566774\pi$
$277$	−115.366			−0.416484			−0.208242	+	0.978077i	$0.566774\pi$
$278$		0			0
$279$	80.3724	−	46.4030i	0.288073	−	0.166319i
$280$		0			0
$281$	−377.987	+	218.231i	−1.34515	+	0.776622i	−0.987558	−	0.157257i	$-0.949735\pi$
$281$	−377.987	+	218.231i	−1.34515	+	0.776622i	−0.357591	+	0.933878i	$0.616402\pi$
$282$		0			0
$283$	−217.321	+	376.411i	−0.767919	+	1.33007i	0.170770	+	0.985311i	$0.445374\pi$
$283$	−217.321	+	376.411i	−0.767919	+	1.33007i	−0.938689	+	0.344764i	$0.887959\pi$
$284$		0			0
$285$	−107.403	+	104.151i	−0.376853	+	0.365442i
$286$		0			0
$287$	437.186	+	252.409i	1.52330	+	0.879475i
$288$		0			0
$289$	−164.312	−	284.596i	−0.568552	−	0.984761i
$290$		0			0
$291$	70.2270	+	121.637i	0.241330	+	0.417996i
$292$		0			0
$293$		−	297.624i		−	1.01578i	−0.861421	−	0.507891i	$-0.830425\pi$
$293$		−	297.624i		−	1.01578i	0.861421	−	0.507891i	$-0.169575\pi$
$294$		0			0
$295$	−311.102	+	179.615i	−1.05458	+	0.608865i
$296$		0			0
$297$		−	81.2597i		−	0.273602i
$298$		0			0
$299$	−110.512	−	63.8042i	−0.369606	−	0.213392i
$300$		0			0
$301$	−7.63786	+	13.2292i	−0.0253749	+	0.0439507i
$302$		0			0
$303$			155.276i			0.512460i
$304$		0			0
$305$	−490.462			−1.60807
$306$		0			0
$307$	−69.6945	−	40.2381i	−0.227018	−	0.131069i	0.382178	−	0.924089i	$-0.375174\pi$
$307$	−69.6945	−	40.2381i	−0.227018	−	0.131069i	−0.609196	+	0.793020i	$0.708508\pi$
$308$		0			0
$309$	51.3445	−	88.9314i	0.166164	−	0.287804i
$310$		0			0
$311$	120.522			0.387529			0.193765	−	0.981048i	$-0.437930\pi$
$311$	120.522			0.387529			0.193765	+	0.981048i	$0.437930\pi$
$312$		0			0
$313$	189.243	+	327.778i	0.604610	+	1.04721i	0.992113	+	0.125346i	$0.0400042\pi$
$313$	189.243	+	327.778i	0.604610	+	1.04721i	−0.387503	+	0.921868i	$0.626662\pi$
$314$		0			0
$315$	−134.746			−0.427765
$316$		0			0
$317$	197.232	−	113.872i	0.622182	−	0.359217i	−0.155536	−	0.987830i	$-0.549710\pi$
$317$	197.232	−	113.872i	0.622182	−	0.359217i	0.777718	+	0.628613i	$0.216377\pi$
$318$		0			0
$319$	427.021	−	246.541i	1.33862	−	0.772855i
$320$		0			0
$321$	−39.0035	+	67.5560i	−0.121506	+	0.210455i
$322$		0			0
$323$	−129.208	+	454.167i	−0.400024	+	1.40609i
$324$		0			0
$325$	57.6460	+	33.2819i	0.177372	+	0.102406i
$326$		0			0
$327$	−4.30356	−	7.45398i	−0.0131607	−	0.0227950i
$328$		0			0
$329$	50.2997	+	87.1216i	0.152887	+	0.264807i
$330$		0			0
$331$		−	398.204i		−	1.20303i	−0.798861	−	0.601516i	$-0.794564\pi$
$331$		−	398.204i		−	1.20303i	0.798861	−	0.601516i	$-0.205436\pi$
$332$		0			0
$333$	45.0052	−	25.9838i	0.135151	−	0.0780294i
$334$		0			0
$335$		−	89.1582i		−	0.266144i
$336$		0			0
$337$	556.961	+	321.561i	1.65270	+	0.954188i	0.975955	+	0.217972i	$0.0699442\pi$
$337$	556.961	+	321.561i	1.65270	+	0.954188i	0.676747	+	0.736216i	$0.263389\pi$
$338$		0			0
$339$	−107.429	+	186.072i	−0.316899	+	0.548885i
$340$		0			0
$341$		−	483.780i		−	1.41871i
$342$		0			0
$343$	3.83580			0.0111831
$344$		0			0
$345$	56.6396	+	32.7009i	0.164173	+	0.0947852i
$346$		0			0
$347$	64.6475	−	111.973i	0.186304	−	0.322688i	−0.757711	−	0.652590i	$-0.773682\pi$
$347$	64.6475	−	111.973i	0.186304	−	0.322688i	0.944015	+	0.329902i	$0.107016\pi$
$348$		0			0
$349$	−10.4853			−0.0300438			−0.0150219	−	0.999887i	$-0.504782\pi$
$349$	−10.4853			−0.0300438			−0.0150219	+	0.999887i	$0.504782\pi$
$350$		0			0
$351$	−39.9159	−	69.1364i	−0.113720	−	0.196970i
$352$		0			0
$353$	−388.861			−1.10159			−0.550794	−	0.834641i	$-0.685675\pi$
$353$	−388.861			−1.10159			−0.550794	+	0.834641i	$0.685675\pi$
$354$		0			0
$355$	206.215	−	119.058i	0.580887	−	0.335375i
$356$		0			0
$357$	−368.302	+	212.639i	−1.03166	+	0.595628i
$358$		0			0
$359$	142.019	−	245.985i	0.395597	−	0.685194i	−0.597580	−	0.801809i	$-0.703871\pi$
$359$	142.019	−	245.985i	0.395597	−	0.685194i	0.993177	+	0.116615i	$0.0372045\pi$
$360$		0			0
$361$	318.036	−	170.805i	0.880986	−	0.473143i
$362$		0			0
$363$	−185.341	−	107.007i	−0.510581	−	0.294784i
$364$		0			0
$365$	166.526	+	288.431i	0.456234	+	0.790221i
$366$		0			0
$367$	−81.5487	−	141.247i	−0.222204	−	0.384868i	0.733273	−	0.679934i	$-0.237992\pi$
$367$	−81.5487	−	141.247i	−0.222204	−	0.384868i	−0.955477	+	0.295066i	$0.904658\pi$
$368$		0			0
$369$		−	153.287i		−	0.415412i
$370$		0			0
$371$	−44.8548	+	25.8969i	−0.120902	+	0.0698031i
$372$		0			0
$373$		−	329.361i		−	0.883004i	−0.897260	−	0.441502i	$-0.854446\pi$
$373$		−	329.361i		−	0.883004i	0.897260	−	0.441502i	$-0.145554\pi$
$374$		0			0
$375$	−200.025	−	115.485i	−0.533400	−	0.307959i
$376$		0			0
$377$	242.209	−	419.518i	0.642463	−	1.11278i
$378$		0			0
$379$			590.484i			1.55801i	0.627021	+	0.779003i	$0.284274\pi$
$379$			590.484i			1.55801i	−0.627021	+	0.779003i	$0.715726\pi$
$380$		0			0
$381$	199.842			0.524520
$382$		0			0
$383$	−417.346	−	240.955i	−1.08968	−	0.629125i	−0.156187	−	0.987728i	$-0.549920\pi$
$383$	−417.346	−	240.955i	−1.08968	−	0.629125i	−0.933490	+	0.358602i	$0.883253\pi$
$384$		0			0
$385$	−351.203	+	608.301i	−0.912215	+	1.58000i
$386$		0			0
$387$	4.63844			0.0119856
$388$		0			0
$389$	−86.5071	−	149.835i	−0.222383	−	0.385179i	0.733148	−	0.680069i	$-0.238050\pi$
$389$	−86.5071	−	149.835i	−0.222383	−	0.385179i	−0.955531	+	0.294890i	$0.904717\pi$
$390$		0			0
$391$	206.418			0.527923
$392$		0			0
$393$	−159.550	+	92.1164i	−0.405980	+	0.234393i
$394$		0			0
$395$	123.433	−	71.2642i	0.312489	−	0.180416i
$396$		0			0
$397$	−80.0448	+	138.642i	−0.201624	+	0.349223i	−0.949052	−	0.315120i	$-0.897955\pi$
$397$	−80.0448	+	138.642i	−0.201624	+	0.349223i	0.747428	+	0.664343i	$0.231289\pi$
$398$		0			0
$399$	312.727	+	88.9690i	0.783776	+	0.222980i
$400$		0			0
$401$	83.3196	+	48.1046i	0.207780	+	0.119962i	0.600279	−	0.799791i	$-0.295056\pi$
$401$	83.3196	+	48.1046i	0.207780	+	0.119962i	−0.392499	+	0.919752i	$0.628390\pi$
$402$		0			0
$403$	−237.640	−	411.604i	−0.589677	−	1.02135i
$404$		0			0
$405$	20.4577	+	35.4337i	0.0505127	+	0.0874906i
$406$		0			0
$407$		−	270.897i		−	0.665595i
$408$		0			0
$409$	−472.302	+	272.684i	−1.15477	+	0.666709i	−0.950046	−	0.312110i	$-0.898964\pi$
$409$	−472.302	+	272.684i	−1.15477	+	0.666709i	−0.204728	+	0.978819i	$0.565631\pi$
$410$		0			0
$411$			204.193i			0.496820i
$412$		0			0
$413$	676.100	+	390.347i	1.63705	+	0.945149i
$414$		0			0
$415$	96.9862	−	167.985i	0.233702	−	0.404783i
$416$		0			0
$417$			308.054i			0.738738i
$418$		0			0
$419$	−81.4631			−0.194423			−0.0972114	−	0.995264i	$-0.530992\pi$
$419$	−81.4631			−0.194423			−0.0972114	+	0.995264i	$0.530992\pi$
$420$		0			0
$421$	326.092	+	188.269i	0.774565	+	0.447196i	0.834501	−	0.551007i	$-0.185756\pi$
$421$	326.092	+	188.269i	0.774565	+	0.447196i	−0.0599354	+	0.998202i	$0.519089\pi$
$422$		0			0
$423$	15.2734	−	26.4543i	0.0361073	−	0.0625397i
$424$		0			0
$425$	−107.673			−0.253348
$426$		0			0
$427$	532.945	+	923.089i	1.24812	+	2.16180i
$428$		0			0
$429$	−416.148			−0.970042
$430$		0			0
$431$	−504.983	+	291.552i	−1.17165	+	0.676454i	−0.954069	−	0.299587i	$-0.903151\pi$
$431$	−504.983	+	291.552i	−1.17165	+	0.676454i	−0.217584	+	0.976042i	$0.569818\pi$
$432$		0			0
$433$	552.877	−	319.204i	1.27685	−	0.737191i	0.300585	−	0.953755i	$-0.402818\pi$
$433$	552.877	−	319.204i	1.27685	−	0.737191i	0.976268	+	0.216564i	$0.0694849\pi$
$434$		0			0
$435$	−124.137	+	215.011i	−0.285371	+	0.494278i
$436$		0			0
$437$	−109.861	−	113.292i	−0.251399	−	0.259249i
$438$		0			0
$439$	−267.855	−	154.646i	−0.610148	−	0.352269i	0.162875	−	0.986647i	$-0.447923\pi$
$439$	−267.855	−	154.646i	−0.610148	−	0.352269i	−0.773023	+	0.634378i	$0.781256\pi$
$440$		0			0
$441$	72.9176	+	126.297i	0.165346	+	0.286388i
$442$		0			0
$443$	76.4634	+	132.438i	0.172604	+	0.298958i	0.939329	−	0.343017i	$-0.111449\pi$
$443$	76.4634	+	132.438i	0.172604	+	0.298958i	−0.766726	+	0.641975i	$0.778115\pi$
$444$		0			0
$445$		−	602.736i		−	1.35446i
$446$		0			0
$447$	−269.578	+	155.641i	−0.603083	+	0.348190i
$448$		0			0
$449$		−	128.150i		−	0.285413i	−0.989765	−	0.142706i	$-0.954420\pi$
$449$		−	128.150i		−	0.285413i	0.989765	−	0.142706i	$-0.0455805\pi$
$450$		0			0
$451$	−692.004	−	399.529i	−1.53438	−	0.885873i
$452$		0			0
$453$	−194.975	+	337.707i	−0.430409	+	0.745490i
$454$		0			0
$455$			690.062i			1.51662i
$456$		0			0
$457$	338.690			0.741117			0.370558	−	0.928809i	$-0.379166\pi$
$457$	338.690			0.741117			0.370558	+	0.928809i	$0.379166\pi$
$458$		0			0
$459$	111.834	+	64.5675i	0.243647	+	0.140670i
$460$		0			0
$461$	262.476	−	454.623i	0.569363	−	0.986166i	−0.427266	−	0.904126i	$-0.640523\pi$
$461$	262.476	−	454.623i	0.569363	−	0.986166i	0.996629	−	0.0820401i	$-0.0261436\pi$
$462$		0			0
$463$	−107.360			−0.231879			−0.115940	−	0.993256i	$-0.536988\pi$
$463$	−107.360			−0.231879			−0.115940	+	0.993256i	$0.536988\pi$
$464$		0			0
$465$	121.795	+	210.955i	0.261924	+	0.453666i
$466$		0			0
$467$	−60.2392			−0.128992			−0.0644959	−	0.997918i	$-0.520544\pi$
$467$	−60.2392			−0.128992			−0.0644959	+	0.997918i	$0.520544\pi$
$468$		0			0
$469$	−167.803	+	96.8811i	−0.357789	+	0.206569i
$470$		0			0
$471$	40.5304	−	23.4002i	0.0860517	−	0.0496820i
$472$		0			0
$473$	12.0897	−	20.9399i	0.0255595	−	0.0442704i
$474$		0			0
$475$	57.3064	+	59.0959i	0.120645	+	0.124412i
$476$		0			0
$477$	13.6201	+	7.86355i	0.0285536	+	0.0164854i
$478$		0			0
$479$	−38.8318	−	67.2586i	−0.0810684	−	0.140415i	0.822641	−	0.568562i	$-0.192500\pi$
$479$	−38.8318	−	67.2586i	−0.0810684	−	0.140415i	−0.903709	+	0.428147i	$0.859167\pi$
$480$		0			0
$481$	−133.068	−	230.481i	−0.276650	−	0.479171i
$482$		0			0
$483$		−	142.134i		−	0.294273i
$484$		0			0
$485$	−319.262	+	184.326i	−0.658272	+	0.380054i
$486$		0			0
$487$			248.267i			0.509789i	0.966969	+	0.254895i	$0.0820408\pi$
$487$			248.267i			0.509789i	−0.966969	+	0.254895i	$0.917959\pi$
$488$		0			0
$489$	−226.815	−	130.951i	−0.463833	−	0.267794i
$490$		0			0
$491$	176.358	−	305.461i	0.359182	−	0.622121i	−0.628643	−	0.777694i	$-0.716389\pi$
$491$	176.358	−	305.461i	0.359182	−	0.622121i	0.987824	+	0.155573i	$0.0497225\pi$
$492$		0			0
$493$			783.587i			1.58943i
$494$		0			0
$495$	213.284			0.430876
$496$		0			0
$497$	−448.155	−	258.742i	−0.901720	−	0.520608i
$498$		0			0
$499$	−103.370	+	179.043i	−0.207155	+	0.358803i	−0.950817	−	0.309753i	$-0.899754\pi$
$499$	−103.370	+	179.043i	−0.207155	+	0.358803i	0.743662	+	0.668555i	$0.233087\pi$
$500$		0			0
$501$	246.519			0.492053
$502$		0			0
$503$	−292.748	−	507.055i	−0.582005	−	1.00806i	−0.995242	−	0.0974382i	$-0.968935\pi$
$503$	−292.748	−	507.055i	−0.582005	−	1.00806i	0.413237	−	0.910624i	$-0.364398\pi$
$504$		0			0
$505$	−407.555			−0.807039
$506$		0			0
$507$	−100.562	+	58.0594i	−0.198347	+	0.114516i
$508$		0			0
$509$	436.147	−	251.810i	0.856870	−	0.494714i	−0.00609272	−	0.999981i	$-0.501939\pi$
$509$	436.147	−	251.810i	0.856870	−	0.494714i	0.862963	+	0.505267i	$0.168606\pi$
$510$		0			0
$511$	361.900	−	626.829i	0.708219	−	1.22667i
$512$		0			0
$513$	−24.0835	−	95.7444i	−0.0469464	−	0.186636i
$514$		0			0
$515$	233.420	+	134.765i	0.453242	+	0.261680i
$516$		0			0
$517$	−79.6173	−	137.901i	−0.153999	−	0.266734i
$518$		0			0
$519$	−205.442	−	355.837i	−0.395843	−	0.685620i
$520$		0			0
$521$			622.860i			1.19551i	0.801679	+	0.597754i	$0.203940\pi$
$521$			622.860i			1.19551i	−0.801679	+	0.597754i	$0.796060\pi$
$522$		0			0
$523$	−197.688	+	114.136i	−0.377989	+	0.218232i	−0.676943	−	0.736035i	$-0.736696\pi$
$523$	−197.688	+	114.136i	−0.377989	+	0.218232i	0.298954	+	0.954268i	$0.403362\pi$
$524$		0			0
$525$			74.1406i			0.141220i
$526$		0			0
$527$	665.805	+	384.403i	1.26339	+	0.729417i
$528$		0			0
$529$	230.006	−	398.382i	0.434794	−	0.753086i
$530$		0			0
$531$		−	237.056i		−	0.446433i
$532$		0			0
$533$	−785.016			−1.47283
$534$		0			0
$535$	−177.316	−	102.373i	−0.331431	−	0.191352i
$536$		0			0
$537$	−1.59454	+	2.76183i	−0.00296936	+	0.00514308i
$538$		0			0
$539$	760.212			1.41041
$540$		0			0
$541$	156.080	+	270.338i	0.288502	+	0.499701i	0.973452	−	0.228889i	$-0.0735094\pi$
$541$	156.080	+	270.338i	0.288502	+	0.499701i	−0.684950	+	0.728590i	$0.740176\pi$
$542$		0			0
$543$	61.8353			0.113877
$544$		0			0
$545$	19.5646	−	11.2956i	0.0358983	−	0.0207259i
$546$		0			0
$547$	588.922	−	340.015i	1.07664	−	0.621599i	0.146652	−	0.989188i	$-0.453150\pi$
$547$	588.922	−	340.015i	1.07664	−	0.621599i	0.929988	+	0.367589i	$0.119817\pi$
$548$		0			0
$549$	161.828	−	280.294i	0.294768	−	0.510553i
$550$		0			0
$551$	430.069	−	417.046i	0.780525	−	0.756890i
$552$		0			0
$553$	−268.250	−	154.874i	−0.485082	−	0.280062i
$554$		0			0
$555$	68.2001	+	118.126i	0.122883	+	0.212840i
$556$		0			0
$557$	−452.880	−	784.411i	−0.813070	−	1.40828i	−0.910706	−	0.413056i	$-0.864462\pi$
$557$	−452.880	−	784.411i	−0.813070	−	1.40828i	0.0976363	−	0.995222i	$-0.468872\pi$
$558$		0			0
$559$		−	23.7544i		−	0.0424945i
$560$		0			0
$561$	582.970	−	336.578i	1.03916	−	0.599961i
$562$		0			0
$563$		−	190.842i		−	0.338974i	−0.985532	−	0.169487i	$-0.945789\pi$
$563$		−	190.842i		−	0.338974i	0.985532	−	0.169487i	$-0.0542110\pi$
$564$		0			0
$565$	−488.386	−	281.970i	−0.864401	−	0.499062i
$566$		0			0
$567$	44.4594	−	77.0059i	0.0784116	−	0.135813i
$568$		0			0
$569$			283.587i			0.498396i	0.968453	+	0.249198i	$0.0801669\pi$
$569$			283.587i			0.498396i	−0.968453	+	0.249198i	$0.919833\pi$
$570$		0			0
$571$	147.076			0.257576			0.128788	−	0.991672i	$-0.458891\pi$
$571$	147.076			0.257576			0.128788	+	0.991672i	$0.458891\pi$
$572$		0			0
$573$	249.518	+	144.059i	0.435460	+	0.251413i
$574$		0			0
$575$	17.9929	−	31.1645i	0.0312919	−	0.0541992i
$576$		0			0
$577$	270.982			0.469639			0.234819	−	0.972039i	$-0.424550\pi$
$577$	270.982			0.469639			0.234819	+	0.972039i	$0.424550\pi$
$578$		0			0
$579$	−150.645	−	260.924i	−0.260181	−	0.450646i
$580$		0			0
$581$	−421.549			−0.725557
$582$		0			0
$583$	70.9988	−	40.9912i	0.121782	−	0.0703108i
$584$		0			0
$585$	181.463	−	104.768i	0.310194	−	0.179091i
$586$		0			0
$587$	−83.4124	+	144.475i	−0.142100	+	0.246124i	−0.928287	−	0.371864i	$-0.878719\pi$
$587$	−83.4124	+	144.475i	−0.142100	+	0.246124i	0.786188	+	0.617988i	$0.212052\pi$
$588$		0			0
$589$	−143.382	−	570.015i	−0.243432	−	0.967767i
$590$		0			0
$591$	129.846	+	74.9663i	0.219705	+	0.126847i
$592$		0			0
$593$	−153.105	−	265.186i	−0.258188	−	0.447194i	0.707569	−	0.706644i	$-0.249792\pi$
$593$	−153.105	−	265.186i	−0.258188	−	0.447194i	−0.965756	+	0.259450i	$0.916459\pi$
$594$		0			0
$595$	−558.118	−	966.689i	−0.938014	−	1.62469i
$596$		0			0
$597$		−	436.207i		−	0.730664i
$598$		0			0
$599$	40.3854	−	23.3165i	0.0674213	−	0.0389257i	−0.465910	−	0.884832i	$-0.654273\pi$
$599$	40.3854	−	23.3165i	0.0674213	−	0.0389257i	0.533332	+	0.845906i	$0.320940\pi$
$600$		0			0
$601$			47.7571i			0.0794627i	0.999210	+	0.0397314i	$0.0126502\pi$
$601$			47.7571i			0.0794627i	−0.999210	+	0.0397314i	$0.987350\pi$
$602$		0			0
$603$	50.9530	+	29.4177i	0.0844992	+	0.0487856i
$604$		0			0
$605$	280.863	−	486.468i	0.464236	−	0.804080i
$606$		0			0
$607$		−	304.461i		−	0.501583i	−0.968041	−	0.250792i	$-0.919309\pi$
$607$		−	304.461i		−	0.501583i	0.968041	−	0.250792i	$-0.0806909\pi$
$608$		0			0
$609$	539.557			0.885972
$610$		0			0
$611$	−135.478	−	78.2183i	−0.221732	−	0.128017i
$612$		0			0
$613$	−411.325	+	712.436i	−0.671004	+	1.16221i	0.306616	+	0.951833i	$0.400803\pi$
$613$	−411.325	+	712.436i	−0.671004	+	1.16221i	−0.977620	+	0.210379i	$0.932530\pi$
$614$		0			0
$615$	402.336			0.654204
$616$		0			0
$617$	−279.527	−	484.154i	−0.453042	−	0.784691i	0.545532	−	0.838090i	$-0.316328\pi$
$617$	−279.527	−	484.154i	−0.453042	−	0.784691i	−0.998573	+	0.0533993i	$0.982994\pi$
$618$		0			0
$619$	−582.672			−0.941311			−0.470656	−	0.882317i	$-0.655983\pi$
$619$	−582.672			−0.941311			−0.470656	+	0.882317i	$0.655983\pi$
$620$		0			0
$621$	−37.3765	+	21.5793i	−0.0601875	+	0.0347493i
$622$		0			0
$623$	−1134.40	+	654.945i	−1.82086	+	1.05128i
$624$		0			0
$625$	248.957	−	431.207i	0.398332	−	0.689931i
$626$		0			0
$627$	−495.002	−	140.825i	−0.789478	−	0.224602i
$628$		0			0
$629$	372.824	+	215.250i	0.592724	+	0.342210i
$630$		0			0
$631$	421.987	+	730.904i	0.668760	+	1.15833i	0.978251	+	0.207424i	$0.0665078\pi$
$631$	421.987	+	730.904i	0.668760	+	1.15833i	−0.309492	+	0.950902i	$0.600159\pi$
$632$		0			0
$633$	−143.105	−	247.864i	−0.226074	−	0.391571i
$634$		0			0
$635$			524.530i			0.826031i
$636$		0			0
$637$	646.794	−	373.427i	1.01538	−	0.586227i
$638$		0			0
$639$			157.133i			0.245905i
$640$		0			0
$641$	386.782	+	223.309i	0.603404	+	0.348375i	0.770380	−	0.637586i	$-0.220067\pi$
$641$	386.782	+	223.309i	0.603404	+	0.348375i	−0.166976	+	0.985961i	$0.553400\pi$
$642$		0			0
$643$	−502.768	+	870.820i	−0.781910	+	1.35431i	0.148918	+	0.988850i	$0.452421\pi$
$643$	−502.768	+	870.820i	−0.781910	+	1.35431i	−0.930828	+	0.365458i	$0.880912\pi$
$644$		0			0
$645$			12.1746i			0.0188753i
$646$		0			0
$647$	189.919			0.293538			0.146769	−	0.989171i	$-0.453113\pi$
$647$	189.919			0.293538			0.146769	+	0.989171i	$0.453113\pi$
$648$		0			0
$649$	−1070.17	−	617.864i	−1.64895	−	0.952024i
$650$		0			0
$651$	264.689	−	458.456i	0.406589	−	0.704233i
$652$		0			0
$653$	1018.29			1.55940			0.779700	−	0.626153i	$-0.215371\pi$
$653$	1018.29			1.55940			0.779700	+	0.626153i	$0.215371\pi$
$654$		0			0
$655$	−241.780	−	418.775i	−0.369129	−	0.639350i
$656$		0			0
$657$	−219.780			−0.334521
$658$		0			0
$659$	979.725	−	565.644i	1.48668	−	0.858338i	0.486799	−	0.873514i	$-0.338164\pi$
$659$	979.725	−	565.644i	1.48668	−	0.858338i	0.999885	+	0.0151763i	$0.00483095\pi$
$660$		0			0
$661$	105.628	−	60.9841i	0.159800	−	0.0922604i	−0.417968	−	0.908462i	$-0.637257\pi$
$661$	105.628	−	60.9841i	0.159800	−	0.0922604i	0.577767	+	0.816202i	$0.303924\pi$
$662$		0			0
$663$	330.664	−	572.726i	0.498738	−	0.863840i
$664$		0			0
$665$	−233.519	+	820.820i	−0.351156	+	1.23432i
$666$		0			0
$667$	−226.799	−	130.943i	−0.340029	−	0.196316i
$668$		0			0
$669$	−178.604	−	309.351i	−0.266972	−	0.462408i
$670$		0			0
$671$	−843.578	−	1461.12i	−1.25719	−	2.17752i
$672$		0			0
$673$			353.592i			0.525397i	0.964878	+	0.262699i	$0.0846125\pi$
$673$			353.592i			0.525397i	−0.964878	+	0.262699i	$0.915387\pi$
$674$		0			0
$675$	19.4965	−	11.2563i	0.0288837	−	0.0166760i
$676$		0			0
$677$			333.896i			0.493199i	0.969118	+	0.246599i	$0.0793132\pi$
$677$			333.896i			0.493199i	−0.969118	+	0.246599i	$0.920687\pi$
$678$		0			0
$679$	693.833	+	400.585i	1.02185	+	0.589963i
$680$		0			0
$681$	285.252	−	494.071i	0.418873	−	0.725509i
$682$		0			0
$683$			160.520i			0.235022i	0.993072	+	0.117511i	$0.0374915\pi$
$683$			160.520i			0.235022i	−0.993072	+	0.117511i	$0.962509\pi$
$684$		0			0
$685$	−535.949			−0.782408
$686$		0			0
$687$	−164.657	−	95.0649i	−0.239676	−	0.138377i
$688$		0			0
$689$	40.2709	−	69.7512i	0.0584483	−	0.101235i
$690$		0			0
$691$	417.343			0.603969			0.301985	−	0.953313i	$-0.402351\pi$
$691$	417.343			0.603969			0.301985	+	0.953313i	$0.402351\pi$
$692$		0			0
$693$	−231.759	−	401.417i	−0.334428	−	0.579246i
$694$		0			0
$695$	−808.555			−1.16339
$696$		0			0
$697$	1099.71	−	634.916i	1.57777	−	0.910927i
$698$		0			0
$699$	322.285	−	186.071i	0.461066	−	0.266196i
$700$		0			0
$701$	−546.106	+	945.883i	−0.779039	+	1.34933i	0.153458	+	0.988155i	$0.450959\pi$
$701$	−546.106	+	945.883i	−0.779039	+	1.34933i	−0.932496	+	0.361179i	$0.882374\pi$
$702$		0			0
$703$	−80.2877	−	319.185i	−0.114207	−	0.454033i
$704$		0			0
$705$	69.4351	+	40.0883i	0.0984894	+	0.0568629i
$706$		0			0
$707$	442.857	+	767.051i	0.626389	+	1.08494i
$708$		0			0
$709$	255.378	+	442.327i	0.360194	+	0.623875i	0.987993	−	0.154501i	$-0.0493771\pi$
$709$	255.378	+	442.327i	0.360194	+	0.623875i	−0.627798	+	0.778376i	$0.716044\pi$
$710$		0			0
$711$			94.0545i			0.132285i
$712$		0			0
$713$	−222.521	+	128.473i	−0.312091	+	0.180186i
$714$		0			0
$715$		−	1092.27i		−	1.52765i
$716$		0			0
$717$	−499.289	−	288.265i	−0.696359	−	0.402043i
$718$		0			0
$719$	−143.484	+	248.522i	−0.199561	+	0.345649i	−0.948386	−	0.317118i	$-0.897285\pi$
$719$	−143.484	+	248.522i	−0.199561	+	0.345649i	0.748825	+	0.662767i	$0.230618\pi$
$720$		0			0
$721$		−	585.753i		−	0.812418i
$722$		0			0
$723$	487.442			0.674194
$724$		0			0
$725$	118.304	+	68.3030i	0.163178	+	0.0942111i
$726$		0			0
$727$	358.442	−	620.840i	0.493043	−	0.853975i	−0.506925	−	0.861990i	$-0.669218\pi$
$727$	358.442	−	620.840i	0.493043	−	0.853975i	0.999968	+	0.00801511i	$0.00255132\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	19.2124	+	33.2769i	0.0262824	+	0.0455224i
$732$		0			0
$733$	−534.712			−0.729484			−0.364742	−	0.931109i	$-0.618843\pi$
$733$	−534.712			−0.729484			−0.364742	+	0.931109i	$0.618843\pi$
$734$		0			0
$735$	−331.494	+	191.388i	−0.451013	+	0.260392i
$736$		0			0
$737$	265.608	−	153.349i	0.360391	−	0.208072i
$738$		0			0
$739$	−337.022	+	583.739i	−0.456051	+	0.789904i	−0.998748	−	0.0500248i	$-0.984070\pi$
$739$	−337.022	+	583.739i	−0.456051	+	0.789904i	0.542697	+	0.839929i	$0.317403\pi$
$740$		0			0
$741$	−490.327	+	123.337i	−0.661710	+	0.166446i
$742$		0			0
$743$	794.193	+	458.527i	1.06890	+	0.617130i	0.927881	−	0.372877i	$-0.121629\pi$
$743$	794.193	+	458.527i	1.06890	+	0.617130i	0.141019	+	0.990007i	$0.454962\pi$
$744$		0			0
$745$	−408.514	−	707.566i	−0.548340	−	0.949753i
$746$		0			0
$747$	64.0012	+	110.853i	0.0856776	+	0.148398i
$748$		0			0
$749$			444.963i			0.594076i
$750$		0			0
$751$	387.655	−	223.813i	0.516185	−	0.298019i	−0.219188	−	0.975683i	$-0.570341\pi$
$751$	387.655	−	223.813i	0.516185	−	0.298019i	0.735372	+	0.677663i	$0.237007\pi$
$752$		0			0
$753$			706.629i			0.938418i
$754$		0			0
$755$	−886.386	−	511.755i	−1.17402	−	0.677821i
$756$		0			0
$757$	−118.319	+	204.934i	−0.156299	+	0.270718i	−0.933531	−	0.358496i	$-0.883290\pi$
$757$	−118.319	+	204.934i	−0.156299	+	0.270718i	0.777232	+	0.629214i	$0.216623\pi$
$758$		0			0
$759$			224.978i			0.296413i
$760$		0			0
$761$	−213.593			−0.280674			−0.140337	−	0.990104i	$-0.544819\pi$
$761$	−213.593			−0.280674			−0.140337	+	0.990104i	$0.544819\pi$
$762$		0			0
$763$	−42.5186	−	24.5481i	−0.0557255	−	0.0321731i
$764$		0			0
$765$	−169.471	+	293.533i	−0.221531	+	0.383703i
$766$		0			0
$767$	−1214.01			−1.58281
$768$		0			0
$769$	442.292	+	766.072i	0.575152	+	0.996192i	0.996025	+	0.0890727i	$0.0283903\pi$
$769$	442.292	+	766.072i	0.575152	+	0.996192i	−0.420873	+	0.907119i	$0.638276\pi$
$770$		0			0
$771$	−75.0360			−0.0973229
$772$		0			0
$773$	1110.22	−	640.988i	1.43625	−	0.829222i	0.438667	−	0.898650i	$-0.355451\pi$
$773$	1110.22	−	640.988i	1.43625	−	0.829222i	0.997587	+	0.0694281i	$0.0221174\pi$
$774$		0			0
$775$	116.073	−	67.0146i	0.149771	−	0.0864705i
$776$		0			0
$777$	148.215	−	256.716i	0.190753	−	0.330394i
$778$		0			0
$779$	−933.766	−	265.651i	−1.19867	−	0.341015i
$780$		0			0
$781$	709.366	+	409.553i	0.908279	+	0.524395i
$782$		0			0
$783$	−81.9176	−	141.886i	−0.104620	−	0.181208i
$784$		0			0
$785$	61.4190	+	106.381i	0.0782407	+	0.135517i
$786$		0			0
$787$		−	282.196i		−	0.358572i	−0.983797	−	0.179286i	$-0.942621\pi$
$787$		−	282.196i		−	0.358572i	0.983797	−	0.179286i	$-0.0573787\pi$
$788$		0			0
$789$	−728.214	+	420.434i	−0.922958	+	0.532870i
$790$		0			0
$791$			1225.58i			1.54940i
$792$		0			0
$793$	−1435.44	−	828.754i	−1.81014	−	1.04509i
$794$		0			0
$795$	−20.6396	+	35.7488i	−0.0259618	+	0.0449671i
$796$		0			0
$797$			1021.78i			1.28203i	0.767527	+	0.641016i	$0.221487\pi$
$797$			1021.78i			1.28203i	−0.767527	+	0.641016i	$0.778513\pi$
$798$		0			0
$799$	253.050			0.316708
$800$		0			0
$801$	344.458	+	198.873i	0.430035	+	0.248281i
$802$		0			0
$803$	−572.837	+	992.183i	−0.713371	+	1.23559i
$804$		0			0
$805$	373.061			0.463430
$806$		0			0
$807$	−335.484	−	581.075i	−0.415717	−	0.720044i
$808$		0			0
$809$	−6.57043			−0.00812167			−0.00406083	−	0.999992i	$-0.501293\pi$
$809$	−6.57043			−0.00812167			−0.00406083	+	0.999992i	$0.501293\pi$
$810$		0			0
$811$	−127.276	+	73.4831i	−0.156938	+	0.0906080i	−0.576412	−	0.817159i	$-0.695548\pi$
$811$	−127.276	+	73.4831i	−0.156938	+	0.0906080i	0.419474	+	0.907767i	$0.362214\pi$
$812$		0			0
$813$	519.773	−	300.091i	0.639328	−	0.369116i
$814$		0			0
$815$	343.711	−	595.324i	0.421731	−	0.730459i
$816$		0			0
$817$	8.03854	−	28.2556i	0.00983910	−	0.0345845i
$818$		0			0
$819$	−394.364	−	227.686i	−0.481519	−	0.278005i
$820$		0			0
$821$	−120.857	−	209.330i	−0.147206	−	0.254969i	0.782987	−	0.622037i	$-0.213695\pi$
$821$	−120.857	−	209.330i	−0.147206	−	0.254969i	−0.930194	+	0.367068i	$0.880362\pi$
$822$		0			0
$823$	148.726	+	257.601i	0.180712	+	0.313003i	0.942123	−	0.335267i	$-0.108826\pi$
$823$	148.726	+	257.601i	0.180712	+	0.313003i	−0.761411	+	0.648269i	$0.775493\pi$
$824$		0			0
$825$		−	117.354i		−	0.142247i
$826$		0			0
$827$	587.474	−	339.179i	0.710368	−	0.410131i	−0.100829	−	0.994904i	$-0.532150\pi$
$827$	587.474	−	339.179i	0.710368	−	0.410131i	0.811197	+	0.584773i	$0.198816\pi$
$828$		0			0
$829$		−	924.892i		−	1.11567i	−0.829951	−	0.557836i	$-0.811632\pi$
$829$		−	924.892i		−	1.11567i	0.829951	−	0.557836i	$-0.188368\pi$
$830$		0			0
$831$	173.049	+	99.9099i	0.208242	+	0.120229i
$832$		0			0
$833$	−604.050	+	1046.25i	−0.725150	+	1.25600i
$834$		0			0
$835$			647.042i			0.774900i
$836$		0			0
$837$	−160.745			−0.192049
$838$		0			0
$839$	−294.467	−	170.011i	−0.350974	−	0.202635i	0.314140	−	0.949377i	$-0.398284\pi$
$839$	−294.467	−	170.011i	−0.350974	−	0.202635i	−0.665114	+	0.746742i	$0.731617\pi$
$840$		0			0
$841$	76.5740	−	132.630i	0.0910511	−	0.157705i
$842$		0			0
$843$	755.973			0.896766
$844$		0			0
$845$	−152.390	−	263.947i	−0.180343	−	0.312363i
$846$		0			0
$847$	−1220.76			−1.44128
$848$		0			0
$849$	651.963	−	376.411i	0.767919	−	0.443358i
$850$		0			0
$851$	−124.603	+	71.9394i	−0.146419	+	0.0845351i
$852$		0			0
$853$	−436.122	+	755.386i	−0.511280	+	0.885564i	0.488634	+	0.872489i	$0.337495\pi$
$853$	−436.122	+	755.386i	−0.511280	+	0.885564i	−0.999915	+	0.0130749i	$0.995838\pi$
$854$		0			0
$855$	251.302	−	63.2125i	0.293920	−	0.0739327i
$856$		0			0
$857$	−429.491	−	247.967i	−0.501156	−	0.289343i	0.228035	−	0.973653i	$-0.426770\pi$
$857$	−429.491	−	247.967i	−0.501156	−	0.289343i	−0.729191	+	0.684310i	$0.760103\pi$
$858$		0			0
$859$	−707.860	−	1226.05i	−0.824051	−	1.42730i	−0.902643	−	0.430391i	$-0.858376\pi$
$859$	−707.860	−	1226.05i	−0.824051	−	1.42730i	0.0785919	−	0.996907i	$-0.474958\pi$
$860$		0			0
$861$	−437.186	−	757.228i	−0.507765	−	0.879475i
$862$		0			0
$863$			1132.56i			1.31236i	0.754605	+	0.656179i	$0.227828\pi$
$863$			1132.56i			1.31236i	−0.754605	+	0.656179i	$0.772172\pi$
$864$		0			0
$865$	933.971	−	539.228i	1.07974	−	0.623385i
$866$		0			0
$867$			569.192i			0.656507i
$868$		0			0
$869$	424.602	+	245.144i	0.488610	+	0.282099i
$870$		0			0
$871$	150.654	−	260.941i	0.172967	−	0.299588i
$872$		0			0
$873$		−	243.273i		−	0.278664i
$874$		0			0
$875$	−1317.48			−1.50569
$876$		0			0
$877$	−879.491	−	507.775i	−1.00284	−	0.578990i	−0.0937531	−	0.995595i	$-0.529886\pi$
$877$	−879.491	−	507.775i	−1.00284	−	0.578990i	−0.909088	+	0.416605i	$0.863220\pi$
$878$		0			0
$879$	−257.750	+	446.436i	−0.293231	+	0.507891i
$880$		0			0
$881$	356.912			0.405121			0.202561	−	0.979270i	$-0.435074\pi$
$881$	356.912			0.405121			0.202561	+	0.979270i	$0.435074\pi$
$882$		0			0
$883$	−466.592	−	808.161i	−0.528416	−	0.915244i	−0.999451	−	0.0331294i	$-0.989453\pi$
$883$	−466.592	−	808.161i	−0.528416	−	0.915244i	0.471035	−	0.882115i	$-0.343881\pi$
$884$		0			0
$885$	622.205			0.703056
$886$		0			0
$887$	610.275	−	352.343i	0.688022	−	0.397229i	−0.114849	−	0.993383i	$-0.536638\pi$
$887$	610.275	−	352.343i	0.688022	−	0.397229i	0.802870	+	0.596154i	$0.203305\pi$
$888$		0			0
$889$	987.207	−	569.964i	1.11047	−	0.641130i
$890$		0			0
$891$	−70.3730	+	121.890i	−0.0789820	+	0.136801i
$892$		0			0
$893$	−134.680	−	138.886i	−0.150817	−	0.155527i
$894$		0			0
$895$	−7.24903	−	4.18523i	−0.00809948	−	0.00467624i
$896$		0			0
$897$	110.512	+	191.413i	0.123202	+	0.213392i
$898$		0			0
$899$	−487.697	−	844.717i	−0.542489	−	0.939618i
$900$		0			0
$901$			130.283i			0.144599i
$902$		0			0
$903$	22.9136	−	13.2292i	0.0253749	−	0.0146502i
$904$		0			0
$905$			162.300i			0.179337i
$906$		0			0
$907$	1101.29	+	635.829i	1.21421	+	0.701024i	0.963673	−	0.267084i	$-0.0860600\pi$
$907$	1101.29	+	635.829i	1.21421	+	0.701024i	0.250535	+	0.968107i	$0.419393\pi$
$908$		0			0
$909$	134.473	−	232.913i	0.147935	−	0.256230i
$910$		0			0
$911$		−	340.787i		−	0.374080i	−0.982352	−	0.187040i	$-0.940111\pi$
$911$		−	340.787i		−	0.374080i	0.982352	−	0.187040i	$-0.0598894\pi$
$912$		0			0
$913$	667.252			0.730835
$914$		0			0
$915$	735.692	+	424.752i	0.804035	+	0.464210i
$916$		0			0
$917$	−525.445	+	910.098i	−0.573004	+	0.992473i
$918$		0			0
$919$	−204.788			−0.222837			−0.111419	−	0.993774i	$-0.535539\pi$
$919$	−204.788			−0.222837			−0.111419	+	0.993774i	$0.535539\pi$
$920$		0			0
$921$	69.6945	+	120.714i	0.0756726	+	0.131069i
$922$		0			0
$923$	804.712			0.871843
$924$		0			0
$925$	64.9959	−	37.5254i	0.0702659	−	0.0405680i
$926$		0			0
$927$	−154.034	+	88.9314i	−0.166164	+	0.0959346i
$928$		0			0
$929$	−807.733	+	1399.03i	−0.869465	+	1.50596i	−0.00692012	+	0.999976i	$0.502203\pi$
$929$	−807.733	+	1399.03i	−0.869465	+	1.50596i	−0.862545	+	0.505981i	$0.831131\pi$
$930$		0			0
$931$	895.721	−	225.310i	0.962106	−	0.242008i
$932$		0			0
$933$	−180.782	−	104.375i	−0.193765	−	0.111870i
$934$		0			0
$935$	883.423	+	1530.13i	0.944837	+	1.63651i
$936$		0			0
$937$	−269.027	−	465.968i	−0.287115	−	0.497298i	0.686005	−	0.727597i	$-0.259363\pi$
$937$	−269.027	−	465.968i	−0.287115	−	0.497298i	−0.973120	+	0.230299i	$0.926030\pi$
$938$		0			0
$939$		−	655.556i		−	0.698143i
$940$		0			0
$941$	389.138	−	224.669i	0.413537	−	0.238756i	−0.278771	−	0.960358i	$-0.589927\pi$
$941$	389.138	−	224.669i	0.413537	−	0.238756i	0.692308	+	0.721602i	$0.256594\pi$
$942$		0			0
$943$			424.395i			0.450048i
$944$		0			0
$945$	202.119	+	116.693i	0.213882	+	0.123485i
$946$		0			0
$947$	767.818	−	1329.90i	0.810789	−	1.40433i	−0.101523	−	0.994833i	$-0.532371\pi$
$947$	767.818	−	1329.90i	0.810789	−	1.40433i	0.912312	−	0.409495i	$-0.134295\pi$
$948$		0			0
$949$			1125.54i			1.18603i
$950$		0			0
$951$	−394.464			−0.414788
$952$		0			0
$953$	−1343.91	−	775.904i	−1.41018	−	0.814170i	−0.414779	−	0.909922i	$-0.636141\pi$
$953$	−1343.91	−	775.904i	−1.41018	−	0.814170i	−0.995405	+	0.0957525i	$0.969474\pi$
$954$		0			0
$955$	−378.116	+	654.915i	−0.395933	+	0.685775i
$956$		0			0
$957$	−854.043			−0.892416
$958$		0			0
$959$	582.373	+	1008.70i	0.607272	+	1.05183i
$960$		0			0
$961$	4.00437			0.00416687
$962$		0			0
$963$	117.010	−	67.5560i	0.121506	−	0.0701516i
$964$		0			0
$965$	684.852	−	395.400i	0.709692	−	0.409741i
$966$		0			0
$967$	−379.617	+	657.515i	−0.392571	+	0.679954i	−0.992788	−	0.119884i	$-0.961748\pi$
$967$	−379.617	+	657.515i	−0.392571	+	0.679954i	0.600217	+	0.799838i	$0.295081\pi$
$968$		0			0
$969$	587.131	−	569.353i	0.605915	−	0.587567i
$970$		0			0
$971$	−691.147	−	399.034i	−0.711788	−	0.410951i	0.0999344	−	0.994994i	$-0.468137\pi$
$971$	−691.147	−	399.034i	−0.711788	−	0.410951i	−0.811723	+	0.584043i	$0.801470\pi$
$972$		0			0
$973$	878.592	+	1521.77i	0.902972	+	1.56399i
$974$		0			0
$975$	−57.6460	−	99.8458i	−0.0591241	−	0.102406i
$976$		0			0
$977$			1031.50i			1.05578i	0.849313	+	0.527889i	$0.177016\pi$
$977$			1031.50i			1.05578i	−0.849313	+	0.527889i	$0.822984\pi$
$978$		0			0
$979$	1795.59	−	1036.69i	1.83411	−	1.05892i
$980$		0			0
$981$			14.9080i			0.0151967i
$982$		0			0
$983$	630.248	+	363.874i	0.641148	+	0.370167i	0.785056	−	0.619424i	$-0.212634\pi$
$983$	630.248	+	363.874i	0.641148	+	0.370167i	−0.143909	+	0.989591i	$0.545967\pi$
$984$		0			0
$985$	−196.766	+	340.808i	−0.199762	+	0.345998i
$986$		0			0
$987$		−	174.243i		−	0.176538i
$988$		0			0
$989$	−12.8421			−0.0129849
$990$		0			0
$991$	122.900	+	70.9565i	0.124016	+	0.0716009i	0.560725	−	0.828002i	$-0.310523\pi$
$991$	122.900	+	70.9565i	0.124016	+	0.0716009i	−0.436708	+	0.899603i	$0.643856\pi$
$992$		0			0
$993$	−344.854	+	597.305i	−0.347285	+	0.601516i
$994$		0			0
$995$	1144.92			1.15067
$996$		0			0
$997$	−908.384	−	1573.37i	−0.911118	−	1.57810i	−0.812488	−	0.582978i	$-0.801887\pi$
$997$	−908.384	−	1573.37i	−0.911118	−	1.57810i	−0.0986299	−	0.995124i	$-0.531446\pi$
$998$		0			0
$999$	−90.0105			−0.0901006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.d.673.3		6
4.3	odd	2		57.3.g.a.46.2	yes	6
12.11	even	2		171.3.p.e.46.2		6
19.12	odd	6	inner	912.3.be.d.145.3		6
76.31	even	6		57.3.g.a.31.2	✓	6
228.107	odd	6		171.3.p.e.145.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.a.31.2	✓	6	76.31	even	6
57.3.g.a.46.2	yes	6	4.3	odd	2
171.3.p.e.46.2		6	12.11	even	2
171.3.p.e.145.2		6	228.107	odd	6
912.3.be.d.145.3		6	19.12	odd	6	inner
912.3.be.d.673.3		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(2.27307 - 3.93708i) q^{5} -9.87987 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(2.27307 - 3.93708i) q^{5} -9.87987 q^{7} +(1.50000 + 2.59808i) q^{9} +15.6384 q^{11} +(13.3053 - 7.68182i) q^{13} +(-6.81922 + 3.93708i) q^{15} +(-12.4260 + 21.5225i) q^{17} +(18.4260 - 4.63488i) q^{19} +(14.8198 + 8.55622i) q^{21} +(-4.15294 - 7.19310i) q^{23} +(2.16628 + 3.75211i) q^{25} -5.19615i q^{27} +(27.3059 - 15.7651i) q^{29} -30.9353i q^{31} +(-23.4577 - 13.5433i) q^{33} +(-22.4577 + 38.8978i) q^{35} -17.3225i q^{37} -26.6106 q^{39} +(-44.2502 - 25.5479i) q^{41} +(0.773073 - 1.33900i) q^{43} +13.6384 q^{45} +(-5.09113 - 8.81810i) q^{47} +48.6118 q^{49} +(37.2780 - 21.5225i) q^{51} +(4.54002 - 2.62118i) q^{53} +(35.5473 - 61.5697i) q^{55} +(-31.6529 - 9.00508i) q^{57} +(-68.4321 - 39.5093i) q^{59} +(-53.9426 - 93.4313i) q^{61} +(-14.8198 - 25.6686i) q^{63} -69.8453i q^{65} +(16.9843 - 9.80591i) q^{67} +14.3862i q^{69} +(45.3604 + 26.1888i) q^{71} +(-36.6301 + 63.4451i) q^{73} -7.50421i q^{75} -154.506 q^{77} +(27.1512 + 15.6758i) q^{79} +(-4.50000 + 7.79423i) q^{81} +42.6674 q^{83} +(56.4905 + 97.8443i) q^{85} -54.6118 q^{87} +(114.819 - 66.2909i) q^{89} +(-131.455 + 75.8953i) q^{91} +(-26.7908 + 46.4030i) q^{93} +(23.6358 - 83.0801i) q^{95} +(-70.2270 - 40.5456i) q^{97} +(23.4577 + 40.6299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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