LMFDB - Embedded newform 405.3.h.j.134.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.1
Root			$1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	405.134
Dual form			405.3.h.j.269.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32288 - 2.29129i) q^{2} +(-1.50000 + 2.59808i) q^{4} +(-2.35136 - 4.41261i) q^{5} +(-9.72111 + 5.61249i) q^{7} -2.64575 q^{8} +(-7.00000 + 11.2250i) q^{10} +(3.67423 - 2.12132i) q^{11} +(-9.72111 - 5.61249i) q^{13} +(25.7196 + 14.8492i) q^{14} +(9.50000 + 16.4545i) q^{16} +10.5830 q^{17} +20.0000 q^{19} +(14.9913 + 0.509903i) q^{20} +(-9.72111 - 5.61249i) q^{22} +(2.64575 - 4.58258i) q^{23} +(-13.9422 + 20.7513i) q^{25} +29.6985i q^{26} -33.6749i q^{28} +(-7.34847 + 4.24264i) q^{29} +(-13.0000 + 22.5167i) q^{31} +(19.8431 - 34.3693i) q^{32} +(-14.0000 - 24.2487i) q^{34} +(47.6235 + 29.6985i) q^{35} +33.6749i q^{37} +(-26.4575 - 45.8258i) q^{38} +(6.22111 + 11.6747i) q^{40} +(47.7650 + 27.5772i) q^{41} +(19.4422 - 11.2250i) q^{43} +12.7279i q^{44} -14.0000 q^{46} +(10.5830 + 18.3303i) q^{47} +(38.5000 - 66.6840i) q^{49} +(65.9909 + 4.49432i) q^{50} +(29.1633 - 16.8375i) q^{52} -84.6640 q^{53} +(-18.0000 - 11.2250i) q^{55} +(25.7196 - 14.8492i) q^{56} +(19.4422 + 11.2250i) q^{58} +(-40.4166 - 23.3345i) q^{59} +(11.0000 + 19.0526i) q^{61} +68.7895 q^{62} -29.0000 q^{64} +(-1.90788 + 56.0924i) q^{65} +(77.7689 + 44.8999i) q^{67} +(-15.8745 + 27.4955i) q^{68} +(5.04778 - 148.407i) q^{70} -50.9117i q^{71} +67.3498i q^{73} +(77.1589 - 44.5477i) q^{74} +(-30.0000 + 51.9615i) q^{76} +(-23.8118 + 41.2432i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(50.2693 - 80.6102i) q^{80} -145.925i q^{82} +(-37.0405 - 64.1561i) q^{83} +(-24.8844 - 46.6987i) q^{85} +(-51.4393 - 29.6985i) q^{86} +(-9.72111 + 5.61249i) q^{88} +89.0955i q^{89} +126.000 q^{91} +(7.93725 + 13.7477i) q^{92} +(28.0000 - 48.4974i) q^{94} +(-47.0272 - 88.2522i) q^{95} +(19.4422 - 11.2250i) q^{97} -203.723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} - 56 q^{10} + 76 q^{16} + 160 q^{19} + 44 q^{25} - 104 q^{31} - 112 q^{34} - 28 q^{40} - 112 q^{46} + 308 q^{49} - 144 q^{55} + 88 q^{61} - 232 q^{64} - 504 q^{70} - 240 q^{76} - 56 q^{79}+ \cdots + 224 q^{94}+O(q^{100}) $ 8 * q - 12 * q^4 - 56 * q^10 + 76 * q^16 + 160 * q^19 + 44 * q^25 - 104 * q^31 - 112 * q^34 - 28 * q^40 - 112 * q^46 + 308 * q^49 - 144 * q^55 + 88 * q^61 - 232 * q^64 - 504 * q^70 - 240 * q^76 - 56 * q^79 + 112 * q^85 + 1008 * q^91 + 224 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.32288	−	2.29129i	−0.661438	−	1.14564i	−0.980238	−	0.197822i	$-0.936613\pi$
$2$	−1.32288	−	2.29129i	−0.661438	−	1.14564i	0.318800	−	0.947822i	$-0.396720\pi$
$3$		0			0
$3$		0			0
$4$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$5$	−2.35136	−	4.41261i	−0.470272	−	0.882522i
$5$	−2.35136	−	4.41261i	−0.470272	−	0.882522i
$6$		0			0
$7$	−9.72111	+	5.61249i	−1.38873	+	0.801784i	−0.993172	−	0.116657i	$-0.962782\pi$
$7$	−9.72111	+	5.61249i	−1.38873	+	0.801784i	−0.395558	+	0.918441i	$0.629449\pi$
$8$	−2.64575			−0.330719
$9$		0			0
$10$	−7.00000	+	11.2250i	−0.700000	+	1.12250i
$11$	3.67423	−	2.12132i	0.334021	−	0.192847i	−0.323604	−	0.946193i	$-0.604894\pi$
$11$	3.67423	−	2.12132i	0.334021	−	0.192847i	0.657625	+	0.753345i	$0.271561\pi$
$12$		0			0
$13$	−9.72111	−	5.61249i	−0.747778	−	0.431730i	0.0771126	−	0.997022i	$-0.475430\pi$
$13$	−9.72111	−	5.61249i	−0.747778	−	0.431730i	−0.824890	+	0.565293i	$0.808763\pi$
$14$	25.7196	+	14.8492i	1.83712	+	1.06066i
$15$		0			0
$16$	9.50000	+	16.4545i	0.593750	+	1.02841i
$17$	10.5830			0.622530			0.311265	−	0.950323i	$-0.399247\pi$
$17$	10.5830			0.622530			0.311265	+	0.950323i	$0.399247\pi$
$18$		0			0
$19$	20.0000			1.05263			0.526316	−	0.850289i	$-0.323573\pi$
$19$	20.0000			1.05263			0.526316	+	0.850289i	$0.323573\pi$
$20$	14.9913	+	0.509903i	0.749567	+	0.0254951i
$21$		0			0
$22$	−9.72111	−	5.61249i	−0.441869	−	0.255113i
$23$	2.64575	−	4.58258i	0.115033	−	0.199242i	−0.802760	−	0.596302i	$-0.796636\pi$
$23$	2.64575	−	4.58258i	0.115033	−	0.199242i	0.917793	+	0.397060i	$0.129969\pi$
$24$		0			0
$25$	−13.9422	+	20.7513i	−0.557689	+	0.830050i
$26$			29.6985i			1.14225i
$27$		0			0
$28$		−	33.6749i		−	1.20268i
$29$	−7.34847	+	4.24264i	−0.253395	+	0.146298i	−0.621318	−	0.783558i	$-0.713402\pi$
$29$	−7.34847	+	4.24264i	−0.253395	+	0.146298i	0.367923	+	0.929856i	$0.380069\pi$
$30$		0			0
$31$	−13.0000	+	22.5167i	−0.419355	+	0.726344i	−0.995875	−	0.0907393i	$-0.971077\pi$
$31$	−13.0000	+	22.5167i	−0.419355	+	0.726344i	0.576520	+	0.817083i	$0.304410\pi$
$32$	19.8431	−	34.3693i	0.620098	−	1.07404i
$33$		0			0
$34$	−14.0000	−	24.2487i	−0.411765	−	0.713197i
$35$	47.6235	+	29.6985i	1.36067	+	0.848528i
$36$		0			0
$37$			33.6749i			0.910133i	0.890457	+	0.455066i	$0.150384\pi$
$37$			33.6749i			0.910133i	−0.890457	+	0.455066i	$0.849616\pi$
$38$	−26.4575	−	45.8258i	−0.696250	−	1.20594i
$39$		0			0
$40$	6.22111	+	11.6747i	0.155528	+	0.291867i
$41$	47.7650	+	27.5772i	1.16500	+	0.672614i	0.952497	−	0.304546i	$-0.0985049\pi$
$41$	47.7650	+	27.5772i	1.16500	+	0.672614i	0.212504	+	0.977160i	$0.431838\pi$
$42$		0			0
$43$	19.4422	−	11.2250i	0.452145	−	0.261046i	−0.256591	−	0.966520i	$-0.582599\pi$
$43$	19.4422	−	11.2250i	0.452145	−	0.261046i	0.708736	+	0.705474i	$0.249266\pi$
$44$			12.7279i			0.289271i
$45$		0			0
$46$	−14.0000			−0.304348
$47$	10.5830	+	18.3303i	0.225170	+	0.390006i	0.956371	−	0.292156i	$-0.0943728\pi$
$47$	10.5830	+	18.3303i	0.225170	+	0.390006i	−0.731200	+	0.682163i	$0.761039\pi$
$48$		0			0
$49$	38.5000	−	66.6840i	0.785714	−	1.36090i
$50$	65.9909	+	4.49432i	1.31982	+	0.0898864i
$51$		0			0
$52$	29.1633	−	16.8375i	0.560833	−	0.323797i
$53$	−84.6640			−1.59743			−0.798717	−	0.601706i	$-0.794488\pi$
$53$	−84.6640			−1.59743			−0.798717	+	0.601706i	$0.794488\pi$
$54$		0			0
$55$	−18.0000	−	11.2250i	−0.327273	−	0.204090i
$56$	25.7196	−	14.8492i	0.459279	−	0.265165i
$57$		0			0
$58$	19.4422	+	11.2250i	0.335211	+	0.193534i
$59$	−40.4166	−	23.3345i	−0.685027	−	0.395500i	0.116720	−	0.993165i	$-0.462762\pi$
$59$	−40.4166	−	23.3345i	−0.685027	−	0.395500i	−0.801746	+	0.597665i	$0.796095\pi$
$60$		0			0
$61$	11.0000	+	19.0526i	0.180328	+	0.312337i	0.941992	−	0.335635i	$-0.108951\pi$
$61$	11.0000	+	19.0526i	0.180328	+	0.312337i	−0.761664	+	0.647972i	$0.775617\pi$
$62$	68.7895			1.10951
$63$		0			0
$64$	−29.0000			−0.453125
$65$	−1.90788	+	56.0924i	−0.0293520	+	0.862960i
$66$		0			0
$67$	77.7689	+	44.8999i	1.16073	+	0.670148i	0.951479	−	0.307714i	$-0.0995641\pi$
$67$	77.7689	+	44.8999i	1.16073	+	0.670148i	0.209251	+	0.977862i	$0.432897\pi$
$68$	−15.8745	+	27.4955i	−0.233449	+	0.404345i
$69$		0			0
$70$	5.04778	−	148.407i	0.0721111	−	2.12009i
$71$		−	50.9117i		−	0.717066i	−0.933517	−	0.358533i	$-0.883277\pi$
$71$		−	50.9117i		−	0.717066i	0.933517	−	0.358533i	$-0.116723\pi$
$72$		0			0
$73$			67.3498i			0.922600i	0.887244	+	0.461300i	$0.152617\pi$
$73$			67.3498i			0.922600i	−0.887244	+	0.461300i	$0.847383\pi$
$74$	77.1589	−	44.5477i	1.04269	−	0.601996i
$75$		0			0
$76$	−30.0000	+	51.9615i	−0.394737	+	0.683704i
$77$	−23.8118	+	41.2432i	−0.309244	+	0.535626i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.0886076	−	0.153473i	0.818315	−	0.574770i	$-0.194908\pi$
$79$	−7.00000	−	12.1244i	−0.0886076	−	0.153473i	−0.906923	+	0.421297i	$0.861575\pi$
$80$	50.2693	−	80.6102i	0.628366	−	1.00763i
$81$		0			0
$82$		−	145.925i		−	1.77957i
$83$	−37.0405	−	64.1561i	−0.446271	−	0.772965i	0.551869	−	0.833931i	$-0.313915\pi$
$83$	−37.0405	−	64.1561i	−0.446271	−	0.772965i	−0.998140	+	0.0609666i	$0.980582\pi$
$84$		0			0
$85$	−24.8844	−	46.6987i	−0.292758	−	0.549396i
$86$	−51.4393	−	29.6985i	−0.598131	−	0.345331i
$87$		0			0
$88$	−9.72111	+	5.61249i	−0.110467	+	0.0637783i
$89$			89.0955i			1.00107i	0.865716	+	0.500536i	$0.166864\pi$
$89$			89.0955i			1.00107i	−0.865716	+	0.500536i	$0.833136\pi$
$90$		0			0
$91$	126.000			1.38462
$92$	7.93725	+	13.7477i	0.0862745	+	0.149432i
$93$		0			0
$94$	28.0000	−	48.4974i	0.297872	−	0.515930i
$95$	−47.0272	−	88.2522i	−0.495023	−	0.928970i
$96$		0			0
$97$	19.4422	−	11.2250i	0.200435	−	0.115721i	−0.396423	−	0.918068i	$-0.629749\pi$
$97$	19.4422	−	11.2250i	0.200435	−	0.115721i	0.596858	+	0.802347i	$0.296415\pi$
$98$	−203.723			−2.07880
$99$		0			0
$100$	−33.0000	−	67.3498i	−0.330000	−	0.673498i
$101$	−117.576	+	67.8823i	−1.16411	+	0.672101i	−0.952286	−	0.305206i	$-0.901275\pi$
$101$	−117.576	+	67.8823i	−1.16411	+	0.672101i	−0.211827	+	0.977307i	$0.567941\pi$
$102$		0			0
$103$	48.6056	+	28.0624i	0.471899	+	0.272451i	0.717034	−	0.697038i	$-0.245499\pi$
$103$	48.6056	+	28.0624i	0.471899	+	0.272451i	−0.245136	+	0.969489i	$0.578832\pi$
$104$	25.7196	+	14.8492i	0.247304	+	0.142781i
$105$		0			0
$106$	112.000	+	193.990i	1.05660	+	1.83009i
$107$	10.5830			0.0989066			0.0494533	−	0.998776i	$-0.484252\pi$
$107$	10.5830			0.0989066			0.0494533	+	0.998776i	$0.484252\pi$
$108$		0			0
$109$	−70.0000			−0.642202			−0.321101	−	0.947045i	$-0.604053\pi$
$109$	−70.0000			−0.642202			−0.321101	+	0.947045i	$0.604053\pi$
$110$	−1.90788	+	56.0924i	−0.0173444	+	0.509931i
$111$		0			0
$112$	−184.701	−	106.637i	−1.64912	−	0.952118i
$113$	−68.7895	+	119.147i	−0.608757	+	1.05440i	0.382689	+	0.923877i	$0.374998\pi$
$113$	−68.7895	+	119.147i	−0.608757	+	1.05440i	−0.991446	+	0.130521i	$0.958335\pi$
$114$		0			0
$115$	−26.4422	−	0.899383i	−0.229932	−	0.00782073i
$116$		−	25.4558i		−	0.219447i
$117$		0			0
$118$			123.475i			1.04640i
$119$	−102.879	+	59.3970i	−0.864526	+	0.499134i
$120$		0			0
$121$	−51.5000	+	89.2006i	−0.425620	+	0.737195i
$122$	29.1033	−	50.4083i	0.238551	−	0.413183i
$123$		0			0
$124$	−39.0000	−	67.5500i	−0.314516	−	0.544758i
$125$	124.350	+	12.7279i	0.994802	+	0.101823i
$126$		0			0
$127$			168.375i			1.32578i	0.748715	+	0.662892i	$0.230671\pi$
$127$			168.375i			1.32578i	−0.748715	+	0.662892i	$0.769329\pi$
$128$	−41.0091	−	71.0299i	−0.320384	−	0.554921i
$129$		0			0
$130$	131.048	−	69.8318i	1.00806	−	0.537168i
$131$	−128.598	−	74.2462i	−0.981666	−	0.566765i	−0.0788931	−	0.996883i	$-0.525139\pi$
$131$	−128.598	−	74.2462i	−0.981666	−	0.566765i	−0.902773	+	0.430118i	$0.858472\pi$
$132$		0			0
$133$	−194.422	+	112.250i	−1.46182	+	0.843983i
$134$		−	237.588i		−	1.77304i
$135$		0			0
$136$	−28.0000			−0.205882
$137$	105.830	+	183.303i	0.772482	+	1.33798i	0.936199	+	0.351471i	$0.114318\pi$
$137$	105.830	+	183.303i	0.772482	+	1.33798i	−0.163717	+	0.986507i	$0.552348\pi$
$138$		0			0
$139$	−103.000	+	178.401i	−0.741007	+	1.28346i	0.211030	+	0.977480i	$0.432318\pi$
$139$	−103.000	+	178.401i	−0.741007	+	1.28346i	−0.952037	+	0.305983i	$0.901015\pi$
$140$	−148.594	+	79.1818i	−1.06139	+	0.565584i
$141$		0			0
$142$	−116.653	+	67.3498i	−0.821502	+	0.474295i
$143$	−47.6235			−0.333032
$144$		0			0
$145$	36.0000	+	22.4499i	0.248276	+	0.154827i
$146$	154.318	−	89.0955i	1.05697	−	0.610243i
$147$		0			0
$148$	−87.4900	−	50.5124i	−0.591149	−	0.341300i
$149$	−117.576	−	67.8823i	−0.789097	−	0.455586i	0.0505473	−	0.998722i	$-0.483903\pi$
$149$	−117.576	−	67.8823i	−0.789097	−	0.455586i	−0.839645	+	0.543136i	$0.817237\pi$
$150$		0			0
$151$	101.000	+	174.937i	0.668874	+	1.15852i	0.978219	+	0.207574i	$0.0665568\pi$
$151$	101.000	+	174.937i	0.668874	+	1.15852i	−0.309345	+	0.950950i	$0.600110\pi$
$152$	−52.9150			−0.348125
$153$		0			0
$154$	126.000			0.818182
$155$	129.925	+	4.41916i	0.838225	+	0.0285107i
$156$		0			0
$157$	48.6056	+	28.0624i	0.309590	+	0.178742i	0.646743	−	0.762708i	$-0.276131\pi$
$157$	48.6056	+	28.0624i	0.309590	+	0.178742i	−0.337153	+	0.941450i	$0.609464\pi$
$158$	−18.5203	+	32.0780i	−0.117217	+	0.203026i
$159$		0			0
$160$	−198.317	−	6.74538i	−1.23948	−	0.0421586i
$161$			59.3970i			0.368925i
$162$		0			0
$163$		−	202.049i		−	1.23957i	−0.784773	−	0.619784i	$-0.787220\pi$
$163$		−	202.049i		−	1.23957i	0.784773	−	0.619784i	$-0.212780\pi$
$164$	−143.295	+	82.7315i	−0.873751	+	0.504460i
$165$		0			0
$166$	−98.0000	+	169.741i	−0.590361	+	1.02254i
$167$	−92.6013	+	160.390i	−0.554499	+	0.960420i	0.443444	+	0.896302i	$0.353757\pi$
$167$	−92.6013	+	160.390i	−0.554499	+	0.960420i	−0.997942	+	0.0641178i	$0.979577\pi$
$168$		0			0
$169$	−21.5000	−	37.2391i	−0.127219	−	0.220350i
$170$	−74.0810	+	118.794i	−0.435771	+	0.698788i
$171$		0			0
$172$			67.3498i			0.391569i
$173$	10.5830	+	18.3303i	0.0611734	+	0.105956i	0.894990	−	0.446086i	$-0.147182\pi$
$173$	10.5830	+	18.3303i	0.0611734	+	0.105956i	−0.833817	+	0.552041i	$0.813849\pi$
$174$		0			0
$175$	19.0678	−	279.976i	0.108959	−	1.59986i
$176$	69.8105	+	40.3051i	0.396650	+	0.229006i
$177$		0			0
$178$	204.143	−	117.862i	1.14687	−	0.662147i
$179$		−	241.831i		−	1.35101i	−0.737356	−	0.675504i	$-0.763926\pi$
$179$		−	241.831i		−	1.35101i	0.737356	−	0.675504i	$-0.236074\pi$
$180$		0			0
$181$	74.0000			0.408840			0.204420	−	0.978883i	$-0.434469\pi$
$181$	74.0000			0.408840			0.204420	+	0.978883i	$0.434469\pi$
$182$	−166.682	−	288.702i	−0.915837	−	1.58628i
$183$		0			0
$184$	−7.00000	+	12.1244i	−0.0380435	+	0.0658932i
$185$	148.594	−	79.1818i	0.803212	−	0.428010i
$186$		0			0
$187$	38.8844	−	22.4499i	0.207938	−	0.120053i
$188$	−63.4980			−0.337755
$189$		0			0
$190$	−140.000	+	224.499i	−0.736842	+	1.18158i
$191$	−139.621	+	80.6102i	−0.731000	+	0.422043i	−0.818788	−	0.574096i	$-0.805353\pi$
$191$	−139.621	+	80.6102i	−0.731000	+	0.422043i	0.0877882	+	0.996139i	$0.472020\pi$
$192$		0			0
$193$	−155.538	−	89.7998i	−0.805895	−	0.465284i	0.0396332	−	0.999214i	$-0.487381\pi$
$193$	−155.538	−	89.7998i	−0.805895	−	0.465284i	−0.845528	+	0.533930i	$0.820714\pi$
$194$	−51.4393	−	29.6985i	−0.265151	−	0.153085i
$195$		0			0
$196$	115.500	+	200.052i	0.589286	+	1.02067i
$197$	−37.0405			−0.188023			−0.0940115	−	0.995571i	$-0.529969\pi$
$197$	−37.0405			−0.188023			−0.0940115	+	0.995571i	$0.529969\pi$
$198$		0			0
$199$	−250.000			−1.25628			−0.628141	−	0.778100i	$-0.716184\pi$
$199$	−250.000			−1.25628			−0.628141	+	0.778100i	$0.716184\pi$
$200$	36.8877	−	54.9027i	0.184438	−	0.274513i
$201$		0			0
$202$	311.076	+	179.600i	1.53998	+	0.889107i
$203$	47.6235	−	82.4864i	0.234599	−	0.406337i
$204$		0			0
$205$	9.37444	−	275.612i	0.0457290	−	1.34445i
$206$		−	148.492i		−	0.720837i
$207$		0			0
$208$		−	213.274i		−	1.02536i
$209$	73.4847	−	42.4264i	0.351601	−	0.202997i
$210$		0			0
$211$	77.0000	−	133.368i	0.364929	−	0.632075i	−0.623836	−	0.781555i	$-0.714427\pi$
$211$	77.0000	−	133.368i	0.364929	−	0.632075i	0.988765	+	0.149480i	$0.0477600\pi$
$212$	126.996	−	219.964i	0.599038	−	1.03756i
$213$		0			0
$214$	−14.0000	−	24.2487i	−0.0654206	−	0.113312i
$215$	−95.2470	−	59.3970i	−0.443010	−	0.276265i
$216$		0			0
$217$		−	291.849i		−	1.34493i
$218$	92.6013	+	160.390i	0.424777	+	0.735735i
$219$		0			0
$220$	56.1633	−	29.9279i	0.255288	−	0.136036i
$221$	−102.879	−	59.3970i	−0.465514	−	0.268765i
$222$		0			0
$223$	340.239	−	196.437i	1.52573	−	0.880883i	0.526201	−	0.850360i	$-0.323616\pi$
$223$	340.239	−	196.437i	1.52573	−	0.880883i	0.999534	−	0.0305232i	$-0.00971733\pi$
$224$			445.477i			1.98874i
$225$		0			0
$226$	364.000			1.61062
$227$	10.5830	+	18.3303i	0.0466212	+	0.0807502i	0.888394	−	0.459081i	$-0.151821\pi$
$227$	10.5830	+	18.3303i	0.0466212	+	0.0807502i	−0.841773	+	0.539831i	$0.818488\pi$
$228$		0			0
$229$	59.0000	−	102.191i	0.257642	−	0.446249i	−0.707968	−	0.706245i	$-0.750388\pi$
$229$	59.0000	−	102.191i	0.257642	−	0.446249i	0.965610	+	0.259996i	$0.0837212\pi$
$230$	32.9190	+	61.7765i	0.143126	+	0.268594i
$231$		0			0
$232$	19.4422	−	11.2250i	0.0838027	−	0.0483835i
$233$	391.571			1.68056			0.840282	−	0.542150i	$-0.182390\pi$
$233$	391.571			1.68056			0.840282	+	0.542150i	$0.182390\pi$
$234$		0			0
$235$	56.0000	−	89.7998i	0.238298	−	0.382127i
$236$	121.250	−	70.0036i	0.513770	−	0.296625i
$237$		0			0
$238$	272.191	+	157.150i	1.14366	+	0.660292i
$239$	301.287	+	173.948i	1.26062	+	0.727817i	0.973194	−	0.229987i	$-0.0738683\pi$
$239$	301.287	+	173.948i	1.26062	+	0.727817i	0.287422	+	0.957804i	$0.407202\pi$
$240$		0			0
$241$	20.0000	+	34.6410i	0.0829876	+	0.143739i	0.904532	−	0.426406i	$-0.140220\pi$
$241$	20.0000	+	34.6410i	0.0829876	+	0.143739i	−0.821544	+	0.570145i	$0.806887\pi$
$242$	272.512			1.12608
$243$		0			0
$244$	−66.0000			−0.270492
$245$	−384.777	−	13.0875i	−1.57052	−	0.0534184i
$246$		0			0
$247$	−194.422	−	112.250i	−0.787134	−	0.454452i
$248$	34.3948	−	59.5735i	0.138689	−	0.240216i
$249$		0			0
$250$	−135.337	−	301.760i	−0.541347	−	1.20704i
$251$			241.831i			0.963468i	0.876317	+	0.481734i	$0.159993\pi$
$251$			241.831i			0.963468i	−0.876317	+	0.481734i	$0.840007\pi$
$252$		0			0
$253$		−	22.4499i		−	0.0887350i
$254$	385.795	−	222.739i	1.51888	−	0.876924i
$255$		0			0
$256$	−166.500	+	288.386i	−0.650391	+	1.12651i
$257$	−116.413	+	201.633i	−0.452969	+	0.784565i	−0.998569	−	0.0534804i	$-0.982969\pi$
$257$	−116.413	+	201.633i	−0.452969	+	0.784565i	0.545600	+	0.838046i	$0.316302\pi$
$258$		0			0
$259$	−189.000	−	327.358i	−0.729730	−	1.26393i
$260$	−142.871	−	89.0955i	−0.549502	−	0.342675i
$261$		0			0
$262$			392.874i			1.49952i
$263$	82.0183	+	142.060i	0.311857	+	0.540152i	0.978764	−	0.204989i	$-0.0657158\pi$
$263$	82.0183	+	142.060i	0.311857	+	0.540152i	−0.666908	+	0.745140i	$0.732382\pi$
$264$		0			0
$265$	199.076	+	373.589i	0.751229	+	1.40977i
$266$	514.393	+	296.985i	1.93381	+	1.11648i
$267$		0			0
$268$	−233.307	+	134.700i	−0.870547	+	0.502611i
$269$			534.573i			1.98726i	0.112695	+	0.993630i	$0.464052\pi$
$269$			534.573i			1.98726i	−0.112695	+	0.993630i	$0.535948\pi$
$270$		0			0
$271$	−286.000			−1.05535			−0.527675	−	0.849446i	$-0.676936\pi$
$271$	−286.000			−1.05535			−0.527675	+	0.849446i	$0.676936\pi$
$272$	100.539	+	174.138i	0.369627	+	0.640213i
$273$		0			0
$274$	280.000	−	484.974i	1.02190	−	1.76998i
$275$	−7.20694	+	105.821i	−0.0262071	+	0.384803i
$276$		0			0
$277$	165.259	−	95.4123i	0.596602	−	0.344449i	−0.171101	−	0.985253i	$-0.554733\pi$
$277$	165.259	−	95.4123i	0.596602	−	0.344449i	0.767704	+	0.640805i	$0.221399\pi$
$278$	545.025			1.96052
$279$		0			0
$280$	−126.000	−	78.5748i	−0.450000	−	0.280624i
$281$	69.8105	−	40.3051i	0.248436	−	0.143434i	−0.370612	−	0.928788i	$-0.620852\pi$
$281$	69.8105	−	40.3051i	0.248436	−	0.143434i	0.619048	+	0.785353i	$0.287519\pi$
$282$		0			0
$283$	77.7689	+	44.8999i	0.274802	+	0.158657i	0.631068	−	0.775728i	$-0.282617\pi$
$283$	77.7689	+	44.8999i	0.274802	+	0.158657i	−0.356266	+	0.934385i	$0.615950\pi$
$284$	132.272	+	76.3675i	0.465748	+	0.268900i
$285$		0			0
$286$	63.0000	+	109.119i	0.220280	+	0.381536i
$287$	−619.106			−2.15716
$288$		0			0
$289$	−177.000			−0.612457
$290$	3.81576	−	112.185i	0.0131578	−	0.386844i
$291$		0			0
$292$	−174.980	−	101.025i	−0.599247	−	0.345975i
$293$	288.387	−	499.501i	0.984256	−	1.70478i	0.339057	−	0.940766i	$-0.389892\pi$
$293$	288.387	−	499.501i	0.984256	−	1.70478i	0.645199	−	0.764015i	$-0.276775\pi$
$294$		0			0
$295$	−7.93222	+	233.210i	−0.0268889	+	0.790544i
$296$		−	89.0955i		−	0.300998i
$297$		0			0
$298$			359.199i			1.20537i
$299$	−51.4393	+	29.6985i	−0.172038	+	0.0993260i
$300$		0			0
$301$	−126.000	+	218.238i	−0.418605	+	0.725045i
$302$	267.221	−	462.840i	0.884837	−	1.53258i
$303$		0			0
$304$	190.000	+	329.090i	0.625000	+	1.08253i
$305$	58.2065	−	93.3381i	0.190841	−	0.306027i
$306$		0			0
$307$		−	269.399i		−	0.877522i	−0.898604	−	0.438761i	$-0.855417\pi$
$307$		−	269.399i		−	0.877522i	0.898604	−	0.438761i	$-0.144583\pi$
$308$	−71.4353	−	123.730i	−0.231933	−	0.401719i
$309$		0			0
$310$	−161.749	−	303.541i	−0.521771	−	0.979165i
$311$	−51.4393	−	29.6985i	−0.165400	−	0.0954935i	0.415015	−	0.909814i	$-0.363776\pi$
$311$	−51.4393	−	29.6985i	−0.165400	−	0.0954935i	−0.580415	+	0.814321i	$0.697110\pi$
$312$		0			0
$313$	−155.538	+	89.7998i	−0.496926	+	0.286900i	−0.727443	−	0.686168i	$-0.759291\pi$
$313$	−155.538	+	89.7998i	−0.496926	+	0.286900i	0.230517	+	0.973068i	$0.425958\pi$
$314$		−	148.492i		−	0.472906i
$315$		0			0
$316$	42.0000			0.132911
$317$	−156.099	−	270.372i	−0.492427	−	0.852908i	0.507535	−	0.861631i	$-0.330557\pi$
$317$	−156.099	−	270.372i	−0.492427	−	0.852908i	−0.999962	+	0.00872270i	$0.997223\pi$
$318$		0			0
$319$	−18.0000	+	31.1769i	−0.0564263	+	0.0977333i
$320$	68.1894	+	127.966i	0.213092	+	0.399893i
$321$		0			0
$322$	136.096	−	78.5748i	0.422657	−	0.244021i
$323$	211.660			0.655294
$324$		0			0
$325$	252.000	−	123.475i	0.775385	−	0.379922i
$326$	−462.954	+	267.286i	−1.42010	+	0.819897i
$327$		0			0
$328$	−126.374	−	72.9623i	−0.385288	−	0.222446i
$329$	−205.757	−	118.794i	−0.625402	−	0.361076i
$330$		0			0
$331$	56.0000	+	96.9948i	0.169184	+	0.293036i	0.938133	−	0.346274i	$-0.112553\pi$
$331$	56.0000	+	96.9948i	0.169184	+	0.293036i	−0.768949	+	0.639310i	$0.779220\pi$
$332$	222.243			0.669407
$333$		0			0
$334$	490.000			1.46707
$335$	15.2630	−	448.739i	0.0455613	−	1.33952i
$336$		0			0
$337$	−97.2111	−	56.1249i	−0.288460	−	0.166543i	0.348787	−	0.937202i	$-0.386594\pi$
$337$	−97.2111	−	56.1249i	−0.288460	−	0.166543i	−0.637247	+	0.770659i	$0.719927\pi$
$338$	−56.8837	+	98.5254i	−0.168295	+	0.291495i
$339$		0			0
$340$	158.653	+	5.39630i	0.466627	+	0.0158715i
$341$			110.309i			0.323486i
$342$		0			0
$343$			314.299i			0.916324i
$344$	−51.4393	+	29.6985i	−0.149533	+	0.0863328i
$345$		0			0
$346$	28.0000	−	48.4974i	0.0809249	−	0.140166i
$347$	−259.284	+	449.092i	−0.747215	+	1.29421i	0.201938	+	0.979398i	$0.435276\pi$
$347$	−259.284	+	449.092i	−0.747215	+	1.29421i	−0.949153	+	0.314816i	$0.898057\pi$
$348$		0			0
$349$	−61.0000	−	105.655i	−0.174785	−	0.302737i	0.765302	−	0.643672i	$-0.222590\pi$
$349$	−61.0000	−	105.655i	−0.174785	−	0.302737i	−0.940087	+	0.340935i	$0.889256\pi$
$350$	−666.729	+	326.683i	−1.90494	+	0.933381i
$351$		0			0
$352$		−	168.375i		−	0.478337i
$353$	201.077	+	348.276i	0.569624	+	0.986617i	0.996603	+	0.0823556i	$0.0262443\pi$
$353$	201.077	+	348.276i	0.569624	+	0.986617i	−0.426979	+	0.904261i	$0.640422\pi$
$354$		0			0
$355$	−224.653	+	119.712i	−0.632826	+	0.337216i
$356$	−231.477	−	133.643i	−0.650216	−	0.375402i
$357$		0			0
$358$	−554.103	+	319.912i	−1.54777	+	0.893608i
$359$		−	636.396i		−	1.77269i	−0.463024	−	0.886346i	$-0.653236\pi$
$359$		−	636.396i		−	1.77269i	0.463024	−	0.886346i	$-0.346764\pi$
$360$		0			0
$361$	39.0000			0.108033
$362$	−97.8928	−	169.555i	−0.270422	−	0.468385i
$363$		0			0
$364$	−189.000	+	327.358i	−0.519231	+	0.899334i
$365$	297.188	−	158.364i	0.814215	−	0.433873i
$366$		0			0
$367$	−592.988	+	342.362i	−1.61577	+	0.932866i	−0.627773	+	0.778397i	$0.716033\pi$
$367$	−592.988	+	342.362i	−1.61577	+	0.932866i	−0.987998	+	0.154469i	$0.950633\pi$
$368$	100.539			0.273203
$369$		0			0
$370$	−378.000	−	235.724i	−1.02162	−	0.637093i
$371$	823.029	−	475.176i	2.21841	−	1.28080i
$372$		0			0
$373$	−126.374	−	72.9623i	−0.338805	−	0.195609i	0.320938	−	0.947100i	$-0.396002\pi$
$373$	−126.374	−	72.9623i	−0.338805	−	0.195609i	−0.659744	+	0.751491i	$0.729335\pi$
$374$	−102.879	−	59.3970i	−0.275076	−	0.158815i
$375$		0			0
$376$	−28.0000	−	48.4974i	−0.0744681	−	0.128983i
$377$	95.2470			0.252645
$378$		0			0
$379$	362.000			0.955145			0.477573	−	0.878592i	$-0.341517\pi$
$379$	362.000			0.955145			0.477573	+	0.878592i	$0.341517\pi$
$380$	299.827	+	10.1981i	0.789017	+	0.0268370i
$381$		0			0
$382$	369.402	+	213.274i	0.967022	+	0.558310i
$383$	−21.1660	+	36.6606i	−0.0552637	+	0.0957196i	−0.892334	−	0.451376i	$-0.850933\pi$
$383$	−21.1660	+	36.6606i	−0.0552637	+	0.0957196i	0.837070	+	0.547096i	$0.184267\pi$
$384$		0			0
$385$	237.980	+	8.09445i	0.618130	+	0.0210245i
$386$			475.176i			1.23103i
$387$		0			0
$388$			67.3498i			0.173582i
$389$	−227.803	+	131.522i	−0.585611	+	0.338102i	−0.763360	−	0.645973i	$-0.776452\pi$
$389$	−227.803	+	131.522i	−0.585611	+	0.338102i	0.177749	+	0.984076i	$0.443118\pi$
$390$		0			0
$391$	28.0000	−	48.4974i	0.0716113	−	0.124034i
$392$	−101.861	+	176.429i	−0.259851	+	0.450074i
$393$		0			0
$394$	49.0000	+	84.8705i	0.124365	+	0.215407i
$395$	−37.0405	+	59.3970i	−0.0937735	+	0.150372i
$396$		0			0
$397$		−	33.6749i		−	0.0848235i	−0.999100	−	0.0424117i	$-0.986496\pi$
$397$		−	33.6749i		−	0.0848235i	0.999100	−	0.0424117i	$-0.0135041\pi$
$398$	330.719	+	572.822i	0.830952	+	1.43925i
$399$		0			0
$400$	−473.902	−	32.2752i	−1.18476	−	0.0806879i
$401$	400.492	+	231.224i	0.998732	+	0.576618i	0.907873	−	0.419246i	$-0.137705\pi$
$401$	400.492	+	231.224i	0.998732	+	0.576618i	0.0908592	+	0.995864i	$0.471039\pi$
$402$		0			0
$403$	252.749	−	145.925i	0.627168	−	0.362096i
$404$		−	407.294i		−	1.00815i
$405$		0			0
$406$	−252.000			−0.620690
$407$	71.4353	+	123.730i	0.175517	+	0.304004i
$408$		0			0
$409$	41.0000	−	71.0141i	0.100244	−	0.173629i	−0.811541	−	0.584296i	$-0.801371\pi$
$409$	41.0000	−	71.0141i	0.100244	−	0.173629i	0.911785	+	0.410667i	$0.134704\pi$
$410$	−643.908	+	343.121i	−1.57051	+	0.836881i
$411$		0			0
$412$	−145.817	+	84.1873i	−0.353924	+	0.204338i
$413$	523.859			1.26842
$414$		0			0
$415$	−196.000	+	314.299i	−0.472289	+	0.757348i
$416$	−385.795	+	222.739i	−0.927391	+	0.535429i
$417$		0			0
$418$	−194.422	−	112.250i	−0.465125	−	0.268540i
$419$	180.037	+	103.945i	0.429684	+	0.248078i	0.699212	−	0.714914i	$-0.253534\pi$
$419$	180.037	+	103.945i	0.429684	+	0.248078i	−0.269528	+	0.962993i	$0.586868\pi$
$420$		0			0
$421$	245.000	+	424.352i	0.581948	+	1.00796i	0.995248	+	0.0973684i	$0.0310425\pi$
$421$	245.000	+	424.352i	0.581948	+	1.00796i	−0.413301	+	0.910595i	$0.635624\pi$
$422$	−407.446			−0.965511
$423$		0			0
$424$	224.000			0.528302
$425$	−147.551	+	219.611i	−0.347178	+	0.516731i
$426$		0			0
$427$	−213.864	−	123.475i	−0.500853	−	0.289168i
$428$	−15.8745	+	27.4955i	−0.0370900	+	0.0642417i
$429$		0			0
$430$	−10.0956	+	296.813i	−0.0234780	+	0.690263i
$431$		−	687.308i		−	1.59468i	−0.603529	−	0.797341i	$-0.706239\pi$
$431$		−	687.308i		−	1.59468i	0.603529	−	0.797341i	$-0.293761\pi$
$432$		0			0
$433$			202.049i			0.466627i	0.972402	+	0.233314i	$0.0749568\pi$
$433$			202.049i			0.466627i	−0.972402	+	0.233314i	$0.925043\pi$
$434$	−668.711	+	386.080i	−1.54081	+	0.889586i
$435$		0			0
$436$	105.000	−	181.865i	0.240826	−	0.417122i
$437$	52.9150	−	91.6515i	0.121087	−	0.209729i
$438$		0			0
$439$	−151.000	−	261.540i	−0.343964	−	0.595762i	0.641201	−	0.767373i	$-0.278436\pi$
$439$	−151.000	−	261.540i	−0.343964	−	0.595762i	−0.985165	+	0.171610i	$0.945103\pi$
$440$	47.6235	+	29.6985i	0.108235	+	0.0674966i
$441$		0			0
$442$			314.299i			0.711084i
$443$	−132.288	−	229.129i	−0.298618	−	0.517221i	0.677202	−	0.735797i	$-0.263192\pi$
$443$	−132.288	−	229.129i	−0.298618	−	0.517221i	−0.975820	+	0.218576i	$0.929859\pi$
$444$		0			0
$445$	393.143	−	209.495i	0.883468	−	0.470776i
$446$	−900.187	−	519.723i	−2.01836	−	1.16530i
$447$		0			0
$448$	281.912	−	162.762i	0.629268	−	0.363308i
$449$			216.375i			0.481904i	0.970537	+	0.240952i	$0.0774596\pi$
$449$			216.375i			0.481904i	−0.970537	+	0.240952i	$0.922540\pi$
$450$		0			0
$451$	234.000			0.518847
$452$	−206.369	−	357.441i	−0.456568	−	0.790798i
$453$		0			0
$454$	28.0000	−	48.4974i	0.0616740	−	0.106823i
$455$	−296.271	−	555.989i	−0.651146	−	1.22195i
$456$		0			0
$457$	486.056	−	280.624i	1.06358	−	0.614058i	0.137159	−	0.990549i	$-0.456203\pi$
$457$	486.056	−	280.624i	1.06358	−	0.614058i	0.926420	+	0.376492i	$0.122870\pi$
$458$	−312.199			−0.681656
$459$		0			0
$460$	42.0000	−	67.3498i	0.0913043	−	0.146413i
$461$	−205.757	+	118.794i	−0.446328	+	0.257688i	−0.706278	−	0.707935i	$-0.749627\pi$
$461$	−205.757	+	118.794i	−0.446328	+	0.257688i	0.259950	+	0.965622i	$0.416294\pi$
$462$		0			0
$463$	631.872	+	364.812i	1.36473	+	0.787930i	0.990250	−	0.139303i	$-0.0444862\pi$
$463$	631.872	+	364.812i	1.36473	+	0.787930i	0.374485	+	0.927233i	$0.377820\pi$
$464$	−139.621	−	80.6102i	−0.300907	−	0.173729i
$465$		0			0
$466$	−518.000	−	897.202i	−1.11159	−	1.92533i
$467$	−465.652			−0.997114			−0.498557	−	0.866857i	$-0.666137\pi$
$467$	−465.652			−0.997114			−0.498557	+	0.866857i	$0.666137\pi$
$468$		0			0
$469$	−1008.00			−2.14925
$470$	−279.838	−	9.51818i	−0.595400	−	0.0202514i
$471$		0			0
$472$	106.932	+	61.7373i	0.226551	+	0.130799i
$473$	47.6235	−	82.4864i	0.100684	−	0.174390i
$474$		0			0
$475$	−278.844	+	415.025i	−0.587041	+	0.873737i
$476$		−	356.382i		−	0.748701i
$477$		0			0
$478$		−	920.448i		−	1.92562i
$479$	411.514	−	237.588i	0.859111	−	0.496008i	−0.00460334	−	0.999989i	$-0.501465\pi$
$479$	411.514	−	237.588i	0.859111	−	0.496008i	0.863715	+	0.503981i	$0.168132\pi$
$480$		0			0
$481$	189.000	−	327.358i	0.392931	−	0.680577i
$482$	52.9150	−	91.6515i	0.109782	−	0.190148i
$483$		0			0
$484$	−154.500	−	267.602i	−0.319215	−	0.552896i
$485$	−95.2470	−	59.3970i	−0.196386	−	0.122468i
$486$		0			0
$487$			505.124i			1.03722i	0.855012	+	0.518608i	$0.173549\pi$
$487$			505.124i			1.03722i	−0.855012	+	0.518608i	$0.826451\pi$
$488$	−29.1033	−	50.4083i	−0.0596378	−	0.103296i
$489$		0			0
$490$	479.026	+	898.949i	0.977603	+	1.83459i
$491$	−238.825	−	137.886i	−0.486406	−	0.280827i	0.236676	−	0.971589i	$-0.423942\pi$
$491$	−238.825	−	137.886i	−0.486406	−	0.280827i	−0.723082	+	0.690762i	$0.757275\pi$
$492$		0			0
$493$	−77.7689	+	44.8999i	−0.157746	+	0.0910748i
$494$			593.970i			1.20237i
$495$		0			0
$496$	−494.000			−0.995968
$497$	285.741	+	494.918i	0.574932	+	0.995811i
$498$		0			0
$499$	−184.000	+	318.697i	−0.368737	+	0.638672i	−0.989368	−	0.145431i	$-0.953543\pi$
$499$	−184.000	+	318.697i	−0.368737	+	0.638672i	0.620631	+	0.784103i	$0.286877\pi$
$500$	−219.594	+	303.980i	−0.439187	+	0.607959i
$501$		0			0
$502$	554.103	−	319.912i	1.10379	−	0.637274i
$503$	−275.158			−0.547034			−0.273517	−	0.961867i	$-0.588187\pi$
$503$	−275.158			−0.547034			−0.273517	+	0.961867i	$0.588187\pi$
$504$		0			0
$505$	576.000	+	359.199i	1.14059	+	0.711285i
$506$	−51.4393	+	29.6985i	−0.101659	+	0.0586927i
$507$		0			0
$508$	−437.450	−	252.562i	−0.861122	−	0.497169i
$509$	102.879	+	59.3970i	0.202119	+	0.116693i	0.597643	−	0.801762i	$-0.296104\pi$
$509$	102.879	+	59.3970i	0.202119	+	0.116693i	−0.395524	+	0.918455i	$0.629437\pi$
$510$		0			0
$511$	−378.000	−	654.715i	−0.739726	−	1.28124i
$512$	552.962			1.08000
$513$		0			0
$514$	616.000			1.19844
$515$	9.53940	−	280.462i	0.0185231	−	0.544587i
$516$		0			0
$517$	77.7689	+	44.8999i	0.150423	+	0.0868470i
$518$	−500.047	+	866.107i	−0.965342	+	1.67202i
$519$		0			0
$520$	5.04778	−	148.407i	0.00970726	−	0.285397i
$521$			89.0955i			0.171009i	0.996338	+	0.0855043i	$0.0272501\pi$
$521$			89.0955i			0.171009i	−0.996338	+	0.0855043i	$0.972750\pi$
$522$		0			0
$523$		−	875.548i		−	1.67409i	−0.547136	−	0.837044i	$-0.684282\pi$
$523$		−	875.548i		−	1.67409i	0.547136	−	0.837044i	$-0.315718\pi$
$524$	385.795	−	222.739i	0.736249	−	0.425074i
$525$		0			0
$526$	217.000	−	375.855i	0.412548	−	0.714553i
$527$	−137.579	+	238.294i	−0.261061	+	0.452171i
$528$		0			0
$529$	250.500	+	433.879i	0.473535	+	0.820187i
$530$	592.648	−	950.352i	1.11820	−	1.79312i
$531$		0			0
$532$		−	673.498i		−	1.26597i
$533$	−309.553	−	536.161i	−0.580775	−	1.00593i
$534$		0			0
$535$	−24.8844	−	46.6987i	−0.0465130	−	0.0872872i
$536$	−205.757	−	118.794i	−0.383875	−	0.221630i
$537$		0			0
$538$	1224.86	−	707.173i	2.27669	−	1.31445i
$539$		−	326.683i		−	0.606092i
$540$		0			0
$541$	434.000			0.802218			0.401109	−	0.916030i	$-0.368625\pi$
$541$	434.000			0.802218			0.401109	+	0.916030i	$0.368625\pi$
$542$	378.342	+	655.308i	0.698049	+	1.20906i
$543$		0			0
$544$	210.000	−	363.731i	0.386029	−	0.668623i
$545$	164.595	+	308.883i	0.302009	+	0.566757i
$546$		0			0
$547$	−97.2111	+	56.1249i	−0.177717	+	0.102605i	−0.586220	−	0.810152i	$-0.699384\pi$
$547$	−97.2111	+	56.1249i	−0.177717	+	0.102605i	0.408503	+	0.912757i	$0.366051\pi$
$548$	−634.980			−1.15872
$549$		0			0
$550$	252.000	−	123.475i	0.458182	−	0.224499i
$551$	−146.969	+	84.8528i	−0.266732	+	0.153998i
$552$		0			0
$553$	136.096	+	78.5748i	0.246104	+	0.142088i
$554$	−437.234	−	252.437i	−0.789231	−	0.455663i
$555$		0			0
$556$	−309.000	−	535.204i	−0.555755	−	0.962597i
$557$	−465.652			−0.836000			−0.418000	−	0.908447i	$-0.637269\pi$
$557$	−465.652			−0.836000			−0.418000	+	0.908447i	$0.637269\pi$
$558$		0			0
$559$	−252.000			−0.450805
$560$	−36.2497	+	1065.76i	−0.0647317	+	1.90314i
$561$		0			0
$562$	−184.701	−	106.637i	−0.328650	−	0.189746i
$563$	26.4575	−	45.8258i	0.0469938	−	0.0813957i	−0.841572	−	0.540145i	$-0.818369\pi$
$563$	26.4575	−	45.8258i	0.0469938	−	0.0813957i	0.888566	+	0.458750i	$0.151703\pi$
$564$		0			0
$565$	687.498	+	23.3840i	1.21681	+	0.0413876i
$566$		−	237.588i		−	0.419767i
$567$		0			0
$568$			134.700i			0.237147i
$569$	554.809	−	320.319i	0.975061	−	0.562951i	0.0742853	−	0.997237i	$-0.476332\pi$
$569$	554.809	−	320.319i	0.975061	−	0.562951i	0.900775	+	0.434286i	$0.142999\pi$
$570$		0			0
$571$	284.000	−	491.902i	0.497373	−	0.861475i	−0.502622	−	0.864506i	$-0.667631\pi$
$571$	284.000	−	491.902i	0.497373	−	0.861475i	0.999995	+	0.00303071i	$0.000964707\pi$
$572$	71.4353	−	123.730i	0.124887	−	0.216310i
$573$		0			0
$574$	819.000	+	1418.55i	1.42683	+	2.47134i
$575$	58.2065	+	118.794i	0.101229	+	0.206598i
$576$		0			0
$577$		−	67.3498i		−	0.116724i	−0.998295	−	0.0583621i	$-0.981412\pi$
$577$		−	67.3498i		−	0.116724i	0.998295	−	0.0583621i	$-0.0185878\pi$
$578$	234.149	+	405.558i	0.405102	+	0.701657i
$579$		0			0
$580$	−112.327	+	59.8558i	−0.193667	+	0.103200i
$581$	720.150	+	415.779i	1.23950	+	0.715626i
$582$		0			0
$583$	−311.076	+	179.600i	−0.533577	+	0.308061i
$584$		−	178.191i		−	0.305121i
$585$		0			0
$586$	−1526.00			−2.60410
$587$	−513.276	−	889.020i	−0.874405	−	1.51451i	−0.857395	−	0.514659i	$-0.827919\pi$
$587$	−513.276	−	889.020i	−0.874405	−	1.51451i	−0.0170098	−	0.999855i	$-0.505415\pi$
$588$		0			0
$589$	−260.000	+	450.333i	−0.441426	+	0.764573i
$590$	544.845	−	290.333i	0.923467	−	0.492090i
$591$		0			0
$592$	−554.103	+	319.912i	−0.935985	+	0.540391i
$593$	−656.146			−1.10649			−0.553243	−	0.833020i	$-0.686610\pi$
$593$	−656.146			−1.10649			−0.553243	+	0.833020i	$0.686610\pi$
$594$		0			0
$595$	504.000	+	314.299i	0.847059	+	0.528234i
$596$	352.727	−	203.647i	0.591823	−	0.341689i
$597$		0			0
$598$	136.096	+	78.5748i	0.227585	+	0.131396i
$599$	−800.983	−	462.448i	−1.33720	−	0.772033i	−0.350809	−	0.936447i	$-0.614093\pi$
$599$	−800.983	−	462.448i	−1.33720	−	0.772033i	−0.986391	+	0.164414i	$0.947427\pi$
$600$		0			0
$601$	−394.000	−	682.428i	−0.655574	−	1.13549i	−0.981750	−	0.190178i	$-0.939093\pi$
$601$	−394.000	−	682.428i	−0.655574	−	1.13549i	0.326176	−	0.945309i	$-0.394240\pi$
$602$	666.729			1.10752
$603$		0			0
$604$	−606.000			−1.00331
$605$	514.702	+	17.5067i	0.850748	+	0.0289366i
$606$		0			0
$607$	−9.72111	−	5.61249i	−0.0160150	−	0.00924627i	0.491971	−	0.870612i	$-0.336277\pi$
$607$	−9.72111	−	5.61249i	−0.0160150	−	0.00924627i	−0.507986	+	0.861365i	$0.669610\pi$
$608$	396.863	−	687.386i	0.652735	−	1.13057i
$609$		0			0
$610$	−290.864	−	9.89322i	−0.476827	−	0.0162184i
$611$		−	237.588i		−	0.388851i
$612$		0			0
$613$			572.474i			0.933888i	0.884287	+	0.466944i	$0.154645\pi$
$613$			572.474i			0.933888i	−0.884287	+	0.466944i	$0.845355\pi$
$614$	−617.271	+	356.382i	−1.00533	+	0.580426i
$615$		0			0
$616$	63.0000	−	109.119i	0.102273	−	0.177142i
$617$	−211.660	+	366.606i	−0.343047	+	0.594175i	−0.984997	−	0.172572i	$-0.944792\pi$
$617$	−211.660	+	366.606i	−0.343047	+	0.594175i	0.641950	+	0.766747i	$0.278126\pi$
$618$		0			0
$619$	−97.0000	−	168.009i	−0.156704	−	0.271420i	0.776974	−	0.629533i	$-0.216754\pi$
$619$	−97.0000	−	168.009i	−0.156704	−	0.271420i	−0.933678	+	0.358113i	$0.883420\pi$
$620$	−206.369	+	330.926i	−0.332853	+	0.533752i
$621$		0			0
$622$			157.150i			0.252652i
$623$	−500.047	−	866.107i	−0.802644	−	1.39022i
$624$		0			0
$625$	−236.229	−	578.637i	−0.377966	−	0.925819i
$626$	411.514	+	237.588i	0.657371	+	0.379533i
$627$		0			0
$628$	−145.817	+	84.1873i	−0.232192	+	0.134056i
$629$			356.382i			0.566585i
$630$		0			0
$631$	1190.00			1.88590			0.942948	−	0.332941i	$-0.108041\pi$
$631$	1190.00			1.88590			0.942948	+	0.332941i	$0.108041\pi$
$632$	18.5203	+	32.0780i	0.0293042	+	0.0507564i
$633$		0			0
$634$	−413.000	+	715.337i	−0.651420	+	1.12829i
$635$	742.971	−	395.909i	1.17003	−	0.623479i
$636$		0			0
$637$	−748.526	+	432.161i	−1.17508	+	0.678432i
$638$	95.2470			0.149290
$639$		0			0
$640$	−217.000	+	347.974i	−0.339062	+	0.543710i
$641$	−613.597	+	354.260i	−0.957250	+	0.552668i	−0.895326	−	0.445412i	$-0.853057\pi$
$641$	−613.597	+	354.260i	−0.957250	+	0.552668i	−0.0619243	+	0.998081i	$0.519724\pi$
$642$		0			0
$643$	−563.824	−	325.524i	−0.876865	−	0.506258i	−0.00724179	−	0.999974i	$-0.502305\pi$
$643$	−563.824	−	325.524i	−0.876865	−	0.506258i	−0.869624	+	0.493715i	$0.835638\pi$
$644$	−154.318	−	89.0955i	−0.239624	−	0.138347i
$645$		0			0
$646$	−280.000	−	484.974i	−0.433437	−	0.750734i
$647$	1058.30			1.63570			0.817852	−	0.575429i	$-0.195165\pi$
$647$	1058.30			1.63570			0.817852	+	0.575429i	$0.195165\pi$
$648$		0			0
$649$	−198.000			−0.305085
$650$	−616.281	−	414.063i	−0.948124	−	0.637020i
$651$		0			0
$652$	524.940	+	303.074i	0.805123	+	0.464838i
$653$	−235.472	+	407.849i	−0.360600	+	0.624578i	−0.988060	−	0.154071i	$-0.950761\pi$
$653$	−235.472	+	407.849i	−0.360600	+	0.624578i	0.627460	+	0.778649i	$0.284095\pi$
$654$		0			0
$655$	−25.2389	+	742.033i	−0.0385327	+	1.13287i
$656$			1047.93i			1.59746i
$657$		0			0
$658$			628.598i			0.955317i
$659$	69.8105	−	40.3051i	0.105934	−	0.0611610i	−0.446097	−	0.894985i	$-0.647186\pi$
$659$	69.8105	−	40.3051i	0.105934	−	0.0611610i	0.552031	+	0.833824i	$0.313853\pi$
$660$		0			0
$661$	−85.0000	+	147.224i	−0.128593	+	0.222730i	−0.923132	−	0.384484i	$-0.874379\pi$
$661$	−85.0000	+	147.224i	−0.128593	+	0.222730i	0.794539	+	0.607214i	$0.207713\pi$
$662$	148.162	−	256.624i	0.223810	−	0.387650i
$663$		0			0
$664$	98.0000	+	169.741i	0.147590	+	0.255634i
$665$	952.470	+	593.970i	1.43229	+	0.893188i
$666$		0			0
$667$			44.8999i			0.0673162i
$668$	−277.804	−	481.170i	−0.415874	−	0.720315i
$669$		0			0
$670$	−1048.38	+	558.654i	−1.56475	+	0.833813i
$671$	80.8332	+	46.6690i	0.120467	+	0.0695515i
$672$		0			0
$673$	−913.784	+	527.574i	−1.35778	+	0.783913i	−0.989324	−	0.145733i	$-0.953446\pi$
$673$	−913.784	+	527.574i	−1.35778	+	0.783913i	−0.368454	+	0.929646i	$0.620113\pi$
$674$			296.985i			0.440630i
$675$		0			0
$676$	129.000			0.190828
$677$	415.383	+	719.464i	0.613564	+	1.06272i	0.990635	+	0.136540i	$0.0435981\pi$
$677$	415.383	+	719.464i	0.613564	+	1.06272i	−0.377070	+	0.926185i	$0.623069\pi$
$678$		0			0
$679$	−126.000	+	218.238i	−0.185567	+	0.321411i
$680$	65.8381	+	123.553i	0.0968207	+	0.181696i
$681$		0			0
$682$	252.749	−	145.925i	0.370600	−	0.213966i
$683$	−1037.13			−1.51850			−0.759249	−	0.650800i	$-0.774434\pi$
$683$	−1037.13			−1.51850			−0.759249	+	0.650800i	$0.774434\pi$
$684$		0			0
$685$	560.000	−	897.998i	0.817518	−	1.31095i
$686$	720.150	−	415.779i	1.04978	−	0.606092i
$687$		0			0
$688$	369.402	+	213.274i	0.536922	+	0.309992i
$689$	823.029	+	475.176i	1.19453	+	0.689660i
$690$		0			0
$691$	326.000	+	564.649i	0.471780	+	0.817147i	0.999479	−	0.0322847i	$-0.0102783\pi$
$691$	326.000	+	564.649i	0.471780	+	0.817147i	−0.527699	+	0.849432i	$0.676945\pi$
$692$	−63.4980			−0.0917602
$693$		0			0
$694$	1372.00			1.97695
$695$	1029.40	+	35.0133i	1.48116	+	0.0503789i
$696$		0			0
$697$	505.498	+	291.849i	0.725248	+	0.418722i
$698$	−161.391	+	279.537i	−0.231219	+	0.400483i
$699$		0			0
$700$	698.797	+	469.503i	0.998281	+	0.670719i
$701$			763.675i			1.08941i	0.838628	+	0.544704i	$0.183358\pi$
$701$			763.675i			1.08941i	−0.838628	+	0.544704i	$0.816642\pi$
$702$		0			0
$703$			673.498i			0.958035i
$704$	−106.553	+	61.5183i	−0.151353	+	0.0873839i
$705$		0			0
$706$	532.000	−	921.451i	0.753541	−	1.30517i
$707$	761.976	−	1319.78i	1.07776	−	1.86674i
$708$		0			0
$709$	−79.0000	−	136.832i	−0.111425	−	0.192993i	0.804920	−	0.593383i	$-0.202208\pi$
$709$	−79.0000	−	136.832i	−0.111425	−	0.192993i	−0.916345	+	0.400390i	$0.868875\pi$
$710$	571.482	+	356.382i	0.804905	+	0.501946i
$711$		0			0
$712$		−	235.724i		−	0.331074i
$713$	68.7895	+	119.147i	0.0964790	+	0.167107i
$714$		0			0
$715$	111.980	+	210.144i	0.156615	+	0.293908i
$716$	628.294	+	362.746i	0.877506	+	0.506628i
$717$		0			0
$718$	−1458.17	+	841.873i	−2.03087	+	1.17252i
$719$		−	127.279i		−	0.177023i	−0.996075	−	0.0885113i	$-0.971789\pi$
$719$		−	127.279i		−	0.177023i	0.996075	−	0.0885113i	$-0.0282109\pi$
$720$		0			0
$721$	−630.000			−0.873786
$722$	−51.5922	−	89.3602i	−0.0714573	−	0.123768i
$723$		0			0
$724$	−111.000	+	192.258i	−0.153315	+	0.265549i
$725$	14.4139	−	211.642i	0.0198812	−	0.291920i
$726$		0			0
$727$	573.546	−	331.137i	0.788921	−	0.455484i	−0.0506616	−	0.998716i	$-0.516133\pi$
$727$	573.546	−	331.137i	0.788921	−	0.455484i	0.839583	+	0.543232i	$0.182800\pi$
$728$	−333.365			−0.457918
$729$		0			0
$730$	−756.000	−	471.449i	−1.03562	−	0.645820i
$731$	205.757	−	118.794i	0.281474	−	0.162509i
$732$		0			0
$733$	−592.988	−	342.362i	−0.808987	−	0.467069i	0.0376167	−	0.999292i	$-0.488023\pi$
$733$	−592.988	−	342.362i	−0.808987	−	0.467069i	−0.846604	+	0.532223i	$0.821357\pi$
$734$	1568.90	+	905.804i	2.13746	+	1.23407i
$735$		0			0
$736$	−105.000	−	181.865i	−0.142663	−	0.247100i
$737$	380.988			0.516945
$738$		0			0
$739$	−1240.00			−1.67794			−0.838972	−	0.544175i	$-0.816843\pi$
$739$	−1240.00			−1.67794			−0.838972	+	0.544175i	$0.816843\pi$
$740$	−17.1709	+	504.832i	−0.0232040	+	0.682205i
$741$		0			0
$742$	−2177.53	−	1257.20i	−2.93468	−	1.69434i
$743$	−21.1660	+	36.6606i	−0.0284872	+	0.0493413i	−0.879918	−	0.475126i	$-0.842402\pi$
$743$	−21.1660	+	36.6606i	−0.0284872	+	0.0493413i	0.851430	+	0.524468i	$0.175736\pi$
$744$		0			0
$745$	−23.0756	+	678.430i	−0.0309739	+	0.910645i
$746$			386.080i			0.517534i
$747$		0			0
$748$			134.700i			0.180080i
$749$	−102.879	+	59.3970i	−0.137355	+	0.0793017i
$750$		0			0
$751$	77.0000	−	133.368i	0.102530	−	0.177587i	−0.810196	−	0.586159i	$-0.800640\pi$
$751$	77.0000	−	133.368i	0.102530	−	0.177587i	0.912726	+	0.408571i	$0.133973\pi$
$752$	−201.077	+	348.276i	−0.267390	+	0.463133i
$753$		0			0
$754$	−126.000	−	218.238i	−0.167109	−	0.289441i
$755$	534.442	−	857.013i	0.707870	−	1.13512i
$756$		0			0
$757$			1313.32i			1.73490i	0.497522	+	0.867452i	$0.334244\pi$
$757$			1313.32i			1.73490i	−0.497522	+	0.867452i	$0.665756\pi$
$758$	−478.881	−	829.446i	−0.631769	−	1.09426i
$759$		0			0
$760$	124.422	+	233.493i	0.163713	+	0.307228i
$761$	−437.234	−	252.437i	−0.574552	−	0.331718i	0.184413	−	0.982849i	$-0.440961\pi$
$761$	−437.234	−	252.437i	−0.574552	−	0.331718i	−0.758965	+	0.651131i	$0.774295\pi$
$762$		0			0
$763$	680.478	−	392.874i	0.891845	−	0.514907i
$764$		−	483.661i		−	0.633064i
$765$		0			0
$766$	112.000			0.146214
$767$	261.929	+	453.675i	0.341499	+	0.591493i
$768$		0			0
$769$	−184.000	+	318.697i	−0.239272	+	0.414431i	−0.960506	−	0.278261i	$-0.910242\pi$
$769$	−184.000	+	318.697i	−0.239272	+	0.414431i	0.721234	+	0.692692i	$0.243575\pi$
$770$	−296.271	−	555.989i	−0.384768	−	0.722063i
$771$		0			0
$772$	466.613	−	269.399i	0.604421	−	0.348963i
$773$	153.454			0.198517			0.0992585	−	0.995062i	$-0.468353\pi$
$773$	153.454			0.198517			0.0992585	+	0.995062i	$0.468353\pi$
$774$		0			0
$775$	−286.000	−	583.699i	−0.369032	−	0.753159i
$776$	−51.4393	+	29.6985i	−0.0662877	+	0.0382712i
$777$		0			0
$778$	602.709	+	347.974i	0.774690	+	0.447268i
$779$	955.301	+	551.543i	1.22632	+	0.708014i
$780$		0			0
$781$	−108.000	−	187.061i	−0.138284	−	0.239515i
$782$	−148.162			−0.189466
$783$		0			0
$784$	1463.00			1.86607
$785$	9.53940	−	280.462i	0.0121521	−	0.357277i
$786$		0			0
$787$	369.402	+	213.274i	0.469380	+	0.270997i	0.715980	−	0.698121i	$-0.245980\pi$
$787$	369.402	+	213.274i	0.469380	+	0.270997i	−0.246600	+	0.969117i	$0.579313\pi$
$788$	55.5608	−	96.2341i	0.0705086	−	0.122124i
$789$		0			0
$790$	185.096	+	6.29568i	0.234298	+	0.00796922i
$791$		−	1544.32i		−	1.95237i
$792$		0			0
$793$		−	246.949i		−	0.311412i
$794$	−77.1589	+	44.5477i	−0.0971775	+	0.0561054i
$795$		0			0
$796$	375.000	−	649.519i	0.471106	−	0.815979i
$797$	−116.413	+	201.633i	−0.146064	+	0.252990i	−0.929769	−	0.368142i	$-0.879994\pi$
$797$	−116.413	+	201.633i	−0.146064	+	0.252990i	0.783705	+	0.621133i	$0.213327\pi$
$798$		0			0
$799$	112.000	+	193.990i	0.140175	+	0.242791i
$800$	436.549	+	890.955i	0.545686	+	1.11369i
$801$		0			0
$802$		−	1223.52i		−	1.52559i
$803$	142.871	+	247.459i	0.177921	+	0.308168i
$804$		0			0
$805$	262.096	−	139.664i	0.325585	−	0.173495i
$806$	−668.711	−	386.080i	−0.829666	−	0.479008i
$807$		0			0
$808$	311.076	−	179.600i	0.384994	−	0.222277i
$809$			420.021i			0.519186i	0.965718	+	0.259593i	$0.0835884\pi$
$809$			420.021i			0.519186i	−0.965718	+	0.259593i	$0.916412\pi$
$810$		0			0
$811$	−970.000			−1.19605			−0.598027	−	0.801476i	$-0.704049\pi$
$811$	−970.000			−1.19605			−0.598027	+	0.801476i	$0.704049\pi$
$812$	142.871	+	247.459i	0.175949	+	0.304753i
$813$		0			0
$814$	189.000	−	327.358i	0.232187	−	0.402159i
$815$	−891.565	+	475.091i	−1.09395	+	0.582934i
$816$		0			0
$817$	388.844	−	224.499i	0.475942	−	0.274785i
$818$	−216.952			−0.265222
$819$		0			0
$820$	702.000	+	437.774i	0.856098	+	0.533871i
$821$	36.7423	−	21.2132i	0.0447532	−	0.0258383i	−0.477456	−	0.878655i	$-0.658441\pi$
$821$	36.7423	−	21.2132i	0.0447532	−	0.0258383i	0.522210	+	0.852817i	$0.325108\pi$
$822$		0			0
$823$	340.239	+	196.437i	0.413413	+	0.238684i	0.692255	−	0.721653i	$-0.256617\pi$
$823$	340.239	+	196.437i	0.413413	+	0.238684i	−0.278842	+	0.960337i	$0.589951\pi$
$824$	−128.598	−	74.2462i	−0.156066	−	0.0901046i
$825$		0			0
$826$	−693.000	−	1200.31i	−0.838983	−	1.45316i
$827$	−560.899			−0.678234			−0.339117	−	0.940744i	$-0.610128\pi$
$827$	−560.899			−0.678234			−0.339117	+	0.940744i	$0.610128\pi$
$828$		0			0
$829$	1010.00			1.21834			0.609168	−	0.793041i	$-0.291504\pi$
$829$	1010.00			1.21834			0.609168	+	0.793041i	$0.291504\pi$
$830$	979.434	+	33.3136i	1.18004	+	0.0401369i
$831$		0			0
$832$	281.912	+	162.762i	0.338837	+	0.195628i
$833$	407.446	−	705.717i	0.489130	−	0.847199i
$834$		0			0
$835$	925.478	+	31.4784i	1.10836	+	0.0376987i
$836$			254.558i			0.304496i
$837$		0			0
$838$		−	550.024i		−	0.656353i
$839$	389.469	−	224.860i	0.464206	−	0.268009i	−0.249605	−	0.968348i	$-0.580301\pi$
$839$	389.469	−	224.860i	0.464206	−	0.268009i	0.713811	+	0.700338i	$0.246967\pi$
$840$		0			0
$841$	−384.500	+	665.974i	−0.457194	+	0.791883i
$842$	648.209	−	1122.73i	0.769845	−	1.33341i
$843$		0			0
$844$	231.000	+	400.104i	0.273697	+	0.474057i
$845$	−113.767	+	182.434i	−0.134636	+	0.215898i
$846$		0			0
$847$		−	1156.17i		−	1.36502i
$848$	−804.308	−	1393.10i	−0.948477	−	1.64281i
$849$		0			0
$850$	698.382	+	47.5634i	0.821626	+	0.0559569i
$851$	154.318	+	89.0955i	0.181337	+	0.104695i
$852$		0			0
$853$	806.852	−	465.836i	0.945899	−	0.546115i	0.0540947	−	0.998536i	$-0.482773\pi$
$853$	806.852	−	465.836i	0.945899	−	0.546115i	0.891805	+	0.452421i	$0.149439\pi$
$854$			653.367i			0.765066i
$855$		0			0
$856$	−28.0000			−0.0327103
$857$	−656.146	−	1136.48i	−0.765632	−	1.32611i	−0.939912	−	0.341417i	$-0.889093\pi$
$857$	−656.146	−	1136.48i	−0.765632	−	1.32611i	0.174280	−	0.984696i	$-0.444240\pi$
$858$		0			0
$859$	347.000	−	601.022i	0.403958	−	0.699676i	−0.590242	−	0.807227i	$-0.700967\pi$
$859$	347.000	−	601.022i	0.403958	−	0.699676i	0.994200	+	0.107551i	$0.0343008\pi$
$860$	297.188	−	158.364i	0.345568	−	0.184144i
$861$		0			0
$862$	−1574.82	+	909.223i	−1.82694	+	1.05478i
$863$	−799.017			−0.925860			−0.462930	−	0.886395i	$-0.653202\pi$
$863$	−799.017			−0.925860			−0.462930	+	0.886395i	$0.653202\pi$
$864$		0			0
$865$	56.0000	−	89.7998i	0.0647399	−	0.103815i
$866$	462.954	−	267.286i	0.534588	−	0.308645i
$867$		0			0
$868$	758.247	+	437.774i	0.873556	+	0.504348i
$869$	−51.4393	−	29.6985i	−0.0591937	−	0.0341755i
$870$		0			0
$871$	−504.000	−	872.954i	−0.578645	−	1.00224i
$872$	185.203			0.212388
$873$		0			0
$874$	−280.000			−0.320366
$875$	−1280.26	+	574.185i	−1.46315	+	0.656211i
$876$		0			0
$877$	690.199	+	398.487i	0.787000	+	0.454375i	0.838905	−	0.544277i	$-0.183196\pi$
$877$	690.199	+	398.487i	0.787000	+	0.454375i	−0.0519054	+	0.998652i	$0.516529\pi$
$878$	−399.508	+	691.969i	−0.455021	+	0.788120i
$879$		0			0
$880$	13.7011	−	402.818i	0.0155694	−	0.457748i
$881$			827.315i			0.939063i	0.882916	+	0.469532i	$0.155577\pi$
$881$			827.315i			0.939063i	−0.882916	+	0.469532i	$0.844423\pi$
$882$		0			0
$883$			471.449i			0.533917i	0.963708	+	0.266959i	$0.0860187\pi$
$883$			471.449i			0.533917i	−0.963708	+	0.266959i	$0.913981\pi$
$884$	308.636	−	178.191i	0.349135	−	0.201573i
$885$		0			0
$886$	−350.000	+	606.218i	−0.395034	+	0.684219i
$887$	−568.837	+	985.254i	−0.641304	+	1.11077i	0.343838	+	0.939029i	$0.388273\pi$
$887$	−568.837	+	985.254i	−0.641304	+	1.11077i	−0.985142	+	0.171742i	$0.945060\pi$
$888$		0			0
$889$	−945.000	−	1636.79i	−1.06299	−	1.84116i
$890$	−1000.09	−	623.668i	−1.12370	−	0.700751i
$891$		0			0
$892$			1178.62i			1.32133i
$893$	211.660	+	366.606i	0.237021	+	0.410533i
$894$		0			0
$895$	−1067.10	+	568.630i	−1.19229	+	0.635341i
$896$	797.309	+	460.327i	0.889854	+	0.513757i
$897$		0			0
$898$	495.777	−	286.237i	0.552090	−	0.318749i
$899$		−	220.617i		−	0.245403i
$900$		0			0
$901$	−896.000			−0.994451
$902$	−309.553	−	536.161i	−0.343185	−	0.594414i
$903$		0			0
$904$	182.000	−	315.233i	0.201327	−	0.348709i
$905$	−174.001	−	326.533i	−0.192266	−	0.360810i
$906$		0			0
$907$	1069.32	−	617.373i	1.17897	−	0.680676i	0.223191	−	0.974775i	$-0.428353\pi$
$907$	1069.32	−	617.373i	1.17897	−	0.680676i	0.955775	+	0.294098i	$0.0950193\pi$
$908$	−63.4980			−0.0699318
$909$		0			0
$910$	−882.000	+	1414.35i	−0.969231	+	1.55423i
$911$	−249.848	+	144.250i	−0.274257	+	0.158342i	−0.630821	−	0.775929i	$-0.717282\pi$
$911$	−249.848	+	144.250i	−0.274257	+	0.158342i	0.356564	+	0.934271i	$0.383948\pi$
$912$		0			0
$913$	−272.191	−	157.150i	−0.298128	−	0.172124i
$914$	−1285.98	−	742.462i	−1.40698	−	0.812322i
$915$		0			0
$916$	177.000	+	306.573i	0.193231	+	0.334687i
$917$	1666.82			1.81769
$918$		0			0
$919$	−1078.00			−1.17301			−0.586507	−	0.809944i	$-0.699497\pi$
$919$	−1078.00			−1.17301			−0.586507	+	0.809944i	$0.699497\pi$
$920$	69.9595	+	2.37955i	0.0760430	+	0.00258646i
$921$		0			0
$922$	544.382	+	314.299i	0.590436	+	0.340889i
$923$	−285.741	+	494.918i	−0.309579	+	0.536206i
$924$		0			0
$925$	−698.797	−	469.503i	−0.755456	−	0.507571i
$926$		−	1930.40i		−	2.08467i
$927$		0			0
$928$			336.749i			0.362876i
$929$	−1517.46	+	876.105i	−1.63343	+	0.943063i	−0.650409	+	0.759584i	$0.725402\pi$
$929$	−1517.46	+	876.105i	−1.63343	+	0.943063i	−0.983024	+	0.183478i	$0.941264\pi$
$930$		0			0
$931$	770.000	−	1333.68i	0.827068	−	1.43252i
$932$	−587.357	+	1017.33i	−0.630211	+	1.09156i
$933$		0			0
$934$	616.000	+	1066.94i	0.659529	+	1.14234i
$935$	−190.494	−	118.794i	−0.203737	−	0.127052i
$936$		0			0
$937$		−	942.898i		−	1.00629i	−0.864201	−	0.503147i	$-0.832175\pi$
$937$		−	942.898i		−	1.00629i	0.864201	−	0.503147i	$-0.167825\pi$
$938$	1333.46	+	2309.62i	1.42160	+	2.46228i
$939$		0			0
$940$	149.307	+	280.192i	0.158837	+	0.298077i
$941$	−889.165	−	513.360i	−0.944915	−	0.545547i	−0.0534172	−	0.998572i	$-0.517011\pi$
$941$	−889.165	−	513.360i	−0.944915	−	0.545547i	−0.891498	+	0.453025i	$0.850345\pi$
$942$		0			0
$943$	252.749	−	145.925i	0.268026	−	0.154745i
$944$		−	886.712i		−	0.939313i
$945$		0			0
$946$	−252.000			−0.266385
$947$	248.701	+	430.762i	0.262619	+	0.454870i	0.966937	−	0.255015i	$-0.0820803\pi$
$947$	248.701	+	430.762i	0.262619	+	0.454870i	−0.704318	+	0.709885i	$0.748747\pi$
$948$		0			0
$949$	378.000	−	654.715i	0.398314	−	0.689900i
$950$	1319.82	+	89.8864i	1.38928	+	0.0946172i
$951$		0			0
$952$	272.191	−	157.150i	0.285915	−	0.165073i
$953$	486.818			0.510827			0.255414	−	0.966832i	$-0.417788\pi$
$953$	486.818			0.510827			0.255414	+	0.966832i	$0.417788\pi$
$954$		0			0
$955$	684.000	+	426.549i	0.716230	+	0.446648i
$956$	−903.862	+	521.845i	−0.945462	+	0.545863i
$957$		0			0
$958$	−1088.76	−	628.598i	−1.13650	−	0.656157i
$959$	−2057.57	−	1187.94i	−2.14554	−	1.23873i
$960$		0			0
$961$	142.500	+	246.817i	0.148283	+	0.256834i
$962$	−1000.09			−1.03960
$963$		0			0
$964$	−120.000			−0.124481
$965$	−30.5261	+	897.479i	−0.0316333	+	0.930030i
$966$		0			0
$967$	573.546	+	331.137i	0.593118	+	0.342437i	0.766330	−	0.642448i	$-0.222081\pi$
$967$	573.546	+	331.137i	0.593118	+	0.342437i	−0.173211	+	0.984885i	$0.555414\pi$
$968$	136.256	−	236.003i	0.140761	−	0.243804i
$969$		0			0
$970$	−10.0956	+	296.813i	−0.0104078	+	0.305993i
$971$			1641.90i			1.69094i	0.534024	+	0.845470i	$0.320679\pi$
$971$			1641.90i			1.69094i	−0.534024	+	0.845470i	$0.679321\pi$
$972$		0			0
$973$		−	2312.34i		−	2.37651i
$974$	1157.38	−	668.216i	1.18828	−	0.686053i
$975$		0			0
$976$	−209.000	+	361.999i	−0.214139	+	0.370900i
$977$	645.563	−	1118.15i	0.660761	−	1.14447i	−0.319655	−	0.947534i	$-0.603567\pi$
$977$	645.563	−	1118.15i	0.660761	−	1.14447i	0.980416	−	0.196937i	$-0.0630996\pi$
$978$		0			0
$979$	189.000	+	327.358i	0.193054	+	0.334380i
$980$	611.169	−	980.050i	0.623641	−	1.00005i
$981$		0			0
$982$			729.623i			0.742997i
$983$	296.324	+	513.248i	0.301449	+	0.522125i	0.976464	−	0.215679i	$-0.0691964\pi$
$983$	296.324	+	513.248i	0.301449	+	0.522125i	−0.675016	+	0.737803i	$0.735863\pi$
$984$		0			0
$985$	87.0956	+	163.445i	0.0884219	+	0.165934i
$986$	205.757	+	118.794i	0.208679	+	0.120481i
$987$		0			0
$988$	583.267	−	336.749i	0.590351	−	0.340839i
$989$		−	118.794i		−	0.120115i
$990$		0			0
$991$	1694.00			1.70938			0.854692	−	0.519135i	$-0.173746\pi$
$991$	1694.00			1.70938			0.854692	+	0.519135i	$0.173746\pi$
$992$	515.922	+	893.602i	0.520082	+	0.900809i
$993$		0			0
$994$	756.000	−	1309.43i	0.760563	−	1.31733i
$995$	587.840	+	1103.15i	0.590794	+	1.10870i
$996$		0			0
$997$	−826.294	+	477.061i	−0.828781	+	0.478497i	−0.853435	−	0.521199i	$-0.825485\pi$
$997$	−826.294	+	477.061i	−0.828781	+	0.478497i	0.0246543	+	0.999696i	$0.492152\pi$
$998$	973.636			0.975588
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.j.134.1		8
3.2	odd	2	inner	405.3.h.j.134.4		8
5.4	even	2	inner	405.3.h.j.134.3		8
9.2	odd	6	inner	405.3.h.j.269.3		8
9.4	even	3		45.3.d.a.44.4	yes	4
9.5	odd	6		45.3.d.a.44.1	✓	4
9.7	even	3	inner	405.3.h.j.269.2		8
15.14	odd	2	inner	405.3.h.j.134.2		8
36.23	even	6		720.3.c.a.449.3		4
36.31	odd	6		720.3.c.a.449.2		4
45.4	even	6		45.3.d.a.44.2	yes	4
45.13	odd	12		225.3.c.d.26.1		4
45.14	odd	6		45.3.d.a.44.3	yes	4
45.22	odd	12		225.3.c.d.26.4		4
45.23	even	12		225.3.c.d.26.3		4
45.29	odd	6	inner	405.3.h.j.269.1		8
45.32	even	12		225.3.c.d.26.2		4
45.34	even	6	inner	405.3.h.j.269.4		8
72.5	odd	6		2880.3.c.b.449.2		4
72.13	even	6		2880.3.c.b.449.3		4
72.59	even	6		2880.3.c.g.449.2		4
72.67	odd	6		2880.3.c.g.449.3		4
180.23	odd	12		3600.3.l.s.1601.4		4
180.59	even	6		720.3.c.a.449.1		4
180.67	even	12		3600.3.l.s.1601.1		4
180.103	even	12		3600.3.l.s.1601.3		4
180.139	odd	6		720.3.c.a.449.4		4
180.167	odd	12		3600.3.l.s.1601.2		4
360.59	even	6		2880.3.c.g.449.4		4
360.139	odd	6		2880.3.c.g.449.1		4
360.149	odd	6		2880.3.c.b.449.4		4
360.229	even	6		2880.3.c.b.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.d.a.44.1	✓	4	9.5	odd	6
45.3.d.a.44.2	yes	4	45.4	even	6
45.3.d.a.44.3	yes	4	45.14	odd	6
45.3.d.a.44.4	yes	4	9.4	even	3
225.3.c.d.26.1		4	45.13	odd	12
225.3.c.d.26.2		4	45.32	even	12
225.3.c.d.26.3		4	45.23	even	12
225.3.c.d.26.4		4	45.22	odd	12
405.3.h.j.134.1		8	1.1	even	1	trivial
405.3.h.j.134.2		8	15.14	odd	2	inner
405.3.h.j.134.3		8	5.4	even	2	inner
405.3.h.j.134.4		8	3.2	odd	2	inner
405.3.h.j.269.1		8	45.29	odd	6	inner
405.3.h.j.269.2		8	9.7	even	3	inner
405.3.h.j.269.3		8	9.2	odd	6	inner
405.3.h.j.269.4		8	45.34	even	6	inner
720.3.c.a.449.1		4	180.59	even	6
720.3.c.a.449.2		4	36.31	odd	6
720.3.c.a.449.3		4	36.23	even	6
720.3.c.a.449.4		4	180.139	odd	6
2880.3.c.b.449.1		4	360.229	even	6
2880.3.c.b.449.2		4	72.5	odd	6
2880.3.c.b.449.3		4	72.13	even	6
2880.3.c.b.449.4		4	360.149	odd	6
2880.3.c.g.449.1		4	360.139	odd	6
2880.3.c.g.449.2		4	72.59	even	6
2880.3.c.g.449.3		4	72.67	odd	6
2880.3.c.g.449.4		4	360.59	even	6
3600.3.l.s.1601.1		4	180.67	even	12
3600.3.l.s.1601.2		4	180.167	odd	12
3600.3.l.s.1601.3		4	180.103	even	12
3600.3.l.s.1601.4		4	180.23	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 - 2.29129i) q^{2} +(-1.50000 + 2.59808i) q^{4} +(-2.35136 - 4.41261i) q^{5} +(-9.72111 + 5.61249i) q^{7} -2.64575 q^{8} +(-7.00000 + 11.2250i) q^{10} +(3.67423 - 2.12132i) q^{11} +(-9.72111 - 5.61249i) q^{13} +(25.7196 + 14.8492i) q^{14} +(9.50000 + 16.4545i) q^{16} +10.5830 q^{17} +20.0000 q^{19} +(14.9913 + 0.509903i) q^{20} +(-9.72111 - 5.61249i) q^{22} +(2.64575 - 4.58258i) q^{23} +(-13.9422 + 20.7513i) q^{25} +29.6985i q^{26} -33.6749i q^{28} +(-7.34847 + 4.24264i) q^{29} +(-13.0000 + 22.5167i) q^{31} +(19.8431 - 34.3693i) q^{32} +(-14.0000 - 24.2487i) q^{34} +(47.6235 + 29.6985i) q^{35} +33.6749i q^{37} +(-26.4575 - 45.8258i) q^{38} +(6.22111 + 11.6747i) q^{40} +(47.7650 + 27.5772i) q^{41} +(19.4422 - 11.2250i) q^{43} +12.7279i q^{44} -14.0000 q^{46} +(10.5830 + 18.3303i) q^{47} +(38.5000 - 66.6840i) q^{49} +(65.9909 + 4.49432i) q^{50} +(29.1633 - 16.8375i) q^{52} -84.6640 q^{53} +(-18.0000 - 11.2250i) q^{55} +(25.7196 - 14.8492i) q^{56} +(19.4422 + 11.2250i) q^{58} +(-40.4166 - 23.3345i) q^{59} +(11.0000 + 19.0526i) q^{61} +68.7895 q^{62} -29.0000 q^{64} +(-1.90788 + 56.0924i) q^{65} +(77.7689 + 44.8999i) q^{67} +(-15.8745 + 27.4955i) q^{68} +(5.04778 - 148.407i) q^{70} -50.9117i q^{71} +67.3498i q^{73} +(77.1589 - 44.5477i) q^{74} +(-30.0000 + 51.9615i) q^{76} +(-23.8118 + 41.2432i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(50.2693 - 80.6102i) q^{80} -145.925i q^{82} +(-37.0405 - 64.1561i) q^{83} +(-24.8844 - 46.6987i) q^{85} +(-51.4393 - 29.6985i) q^{86} +(-9.72111 + 5.61249i) q^{88} +89.0955i q^{89} +126.000 q^{91} +(7.93725 + 13.7477i) q^{92} +(28.0000 - 48.4974i) q^{94} +(-47.0272 - 88.2522i) q^{95} +(19.4422 - 11.2250i) q^{97} -203.723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} - 56 q^{10} + 76 q^{16} + 160 q^{19} + 44 q^{25} - 104 q^{31} - 112 q^{34} - 28 q^{40} - 112 q^{46} + 308 q^{49} - 144 q^{55} + 88 q^{61} - 232 q^{64} - 504 q^{70} - 240 q^{76} - 56 q^{79}+ \cdots + 224 q^{94}+O(q^{100}) \) 8 * q - 12 * q^4 - 56 * q^10 + 76 * q^16 + 160 * q^19 + 44 * q^25 - 104 * q^31 - 112 * q^34 - 28 * q^40 - 112 * q^46 + 308 * q^49 - 144 * q^55 + 88 * q^61 - 232 * q^64 - 504 * q^70 - 240 * q^76 - 56 * q^79 + 112 * q^85 + 1008 * q^91 + 224 * q^94

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