LMFDB - Embedded newform 1512.2.j.b.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.1
Root			$0.500000 + 2.19293i$ of defining polynomial
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.b.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -2.38587 q^{5} -1.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -2.38587 q^{5} -1.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +(0.873288 + 3.25916i) q^{10} +1.65382i q^{11} -0.253423i q^{13} +(-1.36603 + 0.366025i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.00000i q^{17} +7.03969 q^{19} +(4.13244 - 2.38587i) q^{20} +(2.25916 - 0.605339i) q^{22} -2.82481 q^{23} +0.692366 q^{25} +(-0.346183 + 0.0927594i) q^{26} +(1.00000 + 1.73205i) q^{28} +1.26795 q^{29} -0.746577i q^{31} +(-5.46410 - 1.46410i) q^{32} +(2.73205 - 0.732051i) q^{34} +2.38587i q^{35} -6.94273i q^{37} +(-2.57670 - 9.61639i) q^{38} +(-4.77174 - 4.77174i) q^{40} -5.55686i q^{41} +8.67478 q^{43} +(-1.65382 - 2.86450i) q^{44} +(1.03395 + 3.85876i) q^{46} -10.9679 q^{47} -1.00000 q^{49} +(-0.253423 - 0.945789i) q^{50} +(0.253423 + 0.438942i) q^{52} +3.30763 q^{53} -3.94579i q^{55} +(2.00000 - 2.00000i) q^{56} +(-0.464102 - 1.73205i) q^{58} -10.0397i q^{59} -4.53590i q^{61} +(-1.01984 + 0.273266i) q^{62} +8.00000i q^{64} +0.604635i q^{65} +0.253423 q^{67} +(-2.00000 - 3.46410i) q^{68} +(3.25916 - 0.873288i) q^{70} -3.17519 q^{71} -3.05421 q^{73} +(-9.48394 + 2.54122i) q^{74} +(-12.1931 + 7.03969i) q^{76} +1.65382 q^{77} -14.5183i q^{79} +(-4.77174 + 8.26489i) q^{80} +(-7.59081 + 2.03395i) q^{82} -1.77480i q^{83} -4.77174i q^{85} +(-3.17519 - 11.8500i) q^{86} +(-3.30763 + 3.30763i) q^{88} +3.13550i q^{89} -0.253423 q^{91} +(4.89271 - 2.82481i) q^{92} +(4.01453 + 14.9824i) q^{94} -16.7958 q^{95} -5.49315 q^{97} +(0.366025 + 1.36603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8	$ 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8} + 4 q^{10} - 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} - 16 q^{23} + 32 q^{25} - 16 q^{26} + 8 q^{28} + 24 q^{29} - 16 q^{32} + 8 q^{34} + 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} + 8 q^{47} - 8 q^{49} - 8 q^{50} + 8 q^{52} + 16 q^{56} + 24 q^{58} + 12 q^{62} + 8 q^{67} - 16 q^{68} - 4 q^{70} - 32 q^{71} + 8 q^{73} - 28 q^{74} + 24 q^{76} + 16 q^{80} - 36 q^{82} - 32 q^{86} - 8 q^{91} + 24 q^{92} + 40 q^{94} - 112 q^{95} - 32 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8 + 4 * q^10 - 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 - 16 * q^23 + 32 * q^25 - 16 * q^26 + 8 * q^28 + 24 * q^29 - 16 * q^32 + 8 * q^34 + 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 + 8 * q^47 - 8 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^56 + 24 * q^58 + 12 * q^62 + 8 * q^67 - 16 * q^68 - 4 * q^70 - 32 * q^71 + 8 * q^73 - 28 * q^74 + 24 * q^76 + 16 * q^80 - 36 * q^82 - 32 * q^86 - 8 * q^91 + 24 * q^92 + 40 * q^94 - 112 * q^95 - 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−2.38587			−1.06699			−0.533496	−	0.845802i	$-0.679122\pi$
$5$	−2.38587			−1.06699			−0.533496	+	0.845802i	$0.679122\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		0			0
$10$	0.873288	+	3.25916i	0.276158	+	1.03064i
$11$			1.65382i			0.498645i	0.968421	+	0.249322i	$0.0802079\pi$
$11$			1.65382i			0.498645i	−0.968421	+	0.249322i	$0.919792\pi$
$12$		0			0
$13$		−	0.253423i		−	0.0702870i	−0.999382	−	0.0351435i	$-0.988811\pi$
$13$		−	0.253423i		−	0.0702870i	0.999382	−	0.0351435i	$-0.0111888\pi$
$14$	−1.36603	+	0.366025i	−0.365086	+	0.0978244i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	7.03969			1.61501			0.807507	−	0.589858i	$-0.200816\pi$
$19$	7.03969			1.61501			0.807507	+	0.589858i	$0.200816\pi$
$20$	4.13244	−	2.38587i	0.924043	−	0.533496i
$21$		0			0
$22$	2.25916	−	0.605339i	0.481654	−	0.129059i
$23$	−2.82481			−0.589014			−0.294507	−	0.955649i	$-0.595155\pi$
$23$	−2.82481			−0.589014			−0.294507	+	0.955649i	$0.595155\pi$
$24$		0			0
$25$	0.692366			0.138473
$26$	−0.346183	+	0.0927594i	−0.0678920	+	0.0181916i
$27$		0			0
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	1.26795			0.235452			0.117726	−	0.993046i	$-0.462440\pi$
$29$	1.26795			0.235452			0.117726	+	0.993046i	$0.462440\pi$
$30$		0			0
$31$		−	0.746577i		−	0.134089i	−0.997750	−	0.0670446i	$-0.978643\pi$
$31$		−	0.746577i		−	0.134089i	0.997750	−	0.0670446i	$-0.0213570\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$	2.73205	−	0.732051i	0.468543	−	0.125546i
$35$			2.38587i			0.403285i
$36$		0			0
$37$		−	6.94273i		−	1.14138i	−0.821166	−	0.570689i	$-0.806676\pi$
$37$		−	6.94273i		−	1.14138i	0.821166	−	0.570689i	$-0.193324\pi$
$38$	−2.57670	−	9.61639i	−0.417997	−	1.55998i
$39$		0			0
$40$	−4.77174	−	4.77174i	−0.754478	−	0.754478i
$41$		−	5.55686i		−	0.867836i	−0.900952	−	0.433918i	$-0.857131\pi$
$41$		−	5.55686i		−	0.867836i	0.900952	−	0.433918i	$-0.142869\pi$
$42$		0			0
$43$	8.67478			1.32289			0.661446	−	0.749993i	$-0.269943\pi$
$43$	8.67478			1.32289			0.661446	+	0.749993i	$0.269943\pi$
$44$	−1.65382	−	2.86450i	−0.249322	−	0.431839i
$45$		0			0
$46$	1.03395	+	3.85876i	0.152448	+	0.568943i
$47$	−10.9679			−1.59983			−0.799915	−	0.600113i	$-0.795122\pi$
$47$	−10.9679			−1.59983			−0.799915	+	0.600113i	$0.795122\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.253423	−	0.945789i	−0.0358395	−	0.133755i
$51$		0			0
$52$	0.253423	+	0.438942i	0.0351435	+	0.0608703i
$53$	3.30763			0.454339			0.227169	−	0.973855i	$-0.427053\pi$
$53$	3.30763			0.454339			0.227169	+	0.973855i	$0.427053\pi$
$54$		0			0
$55$		−	3.94579i		−	0.532050i
$56$	2.00000	−	2.00000i	0.267261	−	0.267261i
$57$		0			0
$58$	−0.464102	−	1.73205i	−0.0609395	−	0.227429i
$59$		−	10.0397i		−	1.30706i	−0.756902	−	0.653528i	$-0.773288\pi$
$59$		−	10.0397i		−	1.30706i	0.756902	−	0.653528i	$-0.226712\pi$
$60$		0			0
$61$		−	4.53590i		−	0.580762i	−0.956911	−	0.290381i	$-0.906218\pi$
$61$		−	4.53590i		−	0.580762i	0.956911	−	0.290381i	$-0.0937821\pi$
$62$	−1.01984	+	0.273266i	−0.129520	+	0.0347048i
$63$		0			0
$64$			8.00000i			1.00000i
$65$			0.604635i			0.0749957i
$66$		0			0
$67$	0.253423			0.0309606			0.0154803	−	0.999880i	$-0.495072\pi$
$67$	0.253423			0.0309606			0.0154803	+	0.999880i	$0.495072\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	3.25916	−	0.873288i	0.389544	−	0.104378i
$71$	−3.17519			−0.376826			−0.188413	−	0.982090i	$-0.560334\pi$
$71$	−3.17519			−0.376826			−0.188413	+	0.982090i	$0.560334\pi$
$72$		0			0
$73$	−3.05421			−0.357468			−0.178734	−	0.983897i	$-0.557200\pi$
$73$	−3.05421			−0.357468			−0.178734	+	0.983897i	$0.557200\pi$
$74$	−9.48394	+	2.54122i	−1.10249	+	0.295410i
$75$		0			0
$76$	−12.1931	+	7.03969i	−1.39864	+	0.807507i
$77$	1.65382			0.188470
$78$		0			0
$79$		−	14.5183i		−	1.63344i	−0.577036	−	0.816719i	$-0.695791\pi$
$79$		−	14.5183i		−	1.63344i	0.577036	−	0.816719i	$-0.304209\pi$
$80$	−4.77174	+	8.26489i	−0.533496	+	0.924043i
$81$		0			0
$82$	−7.59081	+	2.03395i	−0.838265	+	0.224612i
$83$		−	1.77480i		−	0.194809i	−0.995245	−	0.0974046i	$-0.968946\pi$
$83$		−	1.77480i		−	0.194809i	0.995245	−	0.0974046i	$-0.0310541\pi$
$84$		0			0
$85$		−	4.77174i		−	0.517567i
$86$	−3.17519	−	11.8500i	−0.342390	−	1.27782i
$87$		0			0
$88$	−3.30763	+	3.30763i	−0.352595	+	0.352595i
$89$			3.13550i			0.332363i	0.986095	+	0.166181i	$0.0531437\pi$
$89$			3.13550i			0.332363i	−0.986095	+	0.166181i	$0.946856\pi$
$90$		0			0
$91$	−0.253423			−0.0265660
$92$	4.89271	−	2.82481i	0.510101	−	0.294507i
$93$		0			0
$94$	4.01453	+	14.9824i	0.414067	+	1.54532i
$95$	−16.7958			−1.72321
$96$		0			0
$97$	−5.49315			−0.557745			−0.278873	−	0.960328i	$-0.589961\pi$
$97$	−5.49315			−0.557745			−0.278873	+	0.960328i	$0.589961\pi$
$98$	0.366025	+	1.36603i	0.0369741	+	0.137989i
$99$		0			0
$100$	−1.19921	+	0.692366i	−0.119921	+	0.0692366i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$		−	3.28247i		−	0.323432i	−0.986837	−	0.161716i	$-0.948297\pi$
$103$		−	3.28247i		−	0.323432i	0.986837	−	0.161716i	$-0.0517028\pi$
$104$	0.506847	−	0.506847i	0.0497004	−	0.0497004i
$105$		0			0
$106$	−1.21068	−	4.51831i	−0.117591	−	0.438857i
$107$		−	13.1931i		−	1.27542i	−0.770275	−	0.637712i	$-0.779881\pi$
$107$		−	13.1931i		−	1.27542i	0.770275	−	0.637712i	$-0.220119\pi$
$108$		0			0
$109$		−	7.29311i		−	0.698553i	−0.937020	−	0.349277i	$-0.886427\pi$
$109$		−	7.29311i		−	0.698553i	0.937020	−	0.349277i	$-0.113573\pi$
$110$	−5.39005	+	1.44426i	−0.513921	+	0.137705i
$111$		0			0
$112$	−3.46410	−	2.00000i	−0.327327	−	0.188982i
$113$		−	19.0076i		−	1.78808i	−0.447985	−	0.894041i	$-0.647858\pi$
$113$		−	19.0076i		−	1.78808i	0.447985	−	0.894041i	$-0.352142\pi$
$114$		0			0
$115$	6.73962			0.628473
$116$	−2.19615	+	1.26795i	−0.203908	+	0.117726i
$117$		0			0
$118$	−13.7145	+	3.67478i	−1.26252	+	0.338291i
$119$	2.00000			0.183340
$120$		0			0
$121$	8.26489			0.751354
$122$	−6.19615	+	1.66025i	−0.560973	+	0.150312i
$123$		0			0
$124$	0.746577	+	1.29311i	0.0670446	+	0.116125i
$125$	10.2774			0.919243
$126$		0			0
$127$			5.05421i			0.448489i	0.974533	+	0.224244i	$0.0719914\pi$
$127$			5.05421i			0.448489i	−0.974533	+	0.224244i	$0.928009\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	0.825947	−	0.221312i	0.0724403	−	0.0194103i
$131$		−	11.6893i		−	1.02130i	−0.859789	−	0.510650i	$-0.829405\pi$
$131$		−	11.6893i		−	1.02130i	0.859789	−	0.510650i	$-0.170595\pi$
$132$		0			0
$133$		−	7.03969i		−	0.610418i
$134$	−0.0927594	−	0.346183i	−0.00801319	−	0.0299056i
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$			1.03211i			0.0881793i	0.999028	+	0.0440896i	$0.0140387\pi$
$137$			1.03211i			0.0881793i	−0.999028	+	0.0440896i	$0.985961\pi$
$138$		0			0
$139$	−12.0794			−1.02456			−0.512279	−	0.858819i	$-0.671199\pi$
$139$	−12.0794			−1.02456			−0.512279	+	0.858819i	$0.671199\pi$
$140$	−2.38587	−	4.13244i	−0.201643	−	0.349255i
$141$		0			0
$142$	1.16220	+	4.33739i	0.0975297	+	0.363986i
$143$	0.419116			0.0350482
$144$		0			0
$145$	−3.02516			−0.251226
$146$	1.11792	+	4.17213i	0.0925196	+	0.345288i
$147$		0			0
$148$	6.94273	+	12.0252i	0.570689	+	0.988462i
$149$	18.1213			1.48455			0.742277	−	0.670093i	$-0.233746\pi$
$149$	18.1213			1.48455			0.742277	+	0.670093i	$0.233746\pi$
$150$		0			0
$151$			19.4289i			1.58110i	0.612395	+	0.790552i	$0.290206\pi$
$151$			19.4289i			1.58110i	−0.612395	+	0.790552i	$0.709794\pi$
$152$	14.0794	+	14.0794i	1.14199	+	1.14199i
$153$		0			0
$154$	−0.605339	−	2.25916i	−0.0487796	−	0.182048i
$155$			1.78123i			0.143072i
$156$		0			0
$157$			18.2183i			1.45397i	0.686651	+	0.726987i	$0.259080\pi$
$157$			18.2183i			1.45397i	−0.686651	+	0.726987i	$0.740920\pi$
$158$	−19.8324	+	5.31407i	−1.57778	+	0.422765i
$159$		0			0
$160$	13.0366	+	3.49315i	1.03064	+	0.276158i
$161$			2.82481i			0.222626i
$162$		0			0
$163$	3.71753			0.291179			0.145590	−	0.989345i	$-0.453492\pi$
$163$	3.71753			0.291179			0.145590	+	0.989345i	$0.453492\pi$
$164$	5.55686	+	9.62477i	0.433918	+	0.751568i
$165$		0			0
$166$	−2.42442	+	0.649620i	−0.188171	+	0.0504203i
$167$	−5.97095			−0.462046			−0.231023	−	0.972948i	$-0.574207\pi$
$167$	−5.97095			−0.462046			−0.231023	+	0.972948i	$0.574207\pi$
$168$		0			0
$169$	12.9358			0.995060
$170$	−6.51831	+	1.74658i	−0.499932	+	0.133956i
$171$		0			0
$172$	−15.0252	+	8.67478i	−1.14566	+	0.661446i
$173$	−16.0858			−1.22298			−0.611491	−	0.791252i	$-0.709430\pi$
$173$	−16.0858			−1.22298			−0.611491	+	0.791252i	$0.709430\pi$
$174$		0			0
$175$		−	0.692366i		−	0.0523379i
$176$	5.72899	+	3.30763i	0.431839	+	0.249322i
$177$		0			0
$178$	4.28318	−	1.14767i	0.321038	−	0.0860218i
$179$			13.3786i			0.999964i	0.866036	+	0.499982i	$0.166660\pi$
$179$			13.3786i			0.999964i	−0.866036	+	0.499982i	$0.833340\pi$
$180$		0			0
$181$		−	20.4214i		−	1.51791i	−0.651145	−	0.758954i	$-0.725711\pi$
$181$		−	20.4214i		−	1.51791i	0.651145	−	0.758954i	$-0.274289\pi$
$182$	0.0927594	+	0.346183i	0.00687579	+	0.0256608i
$183$		0			0
$184$	−5.64962	−	5.64962i	−0.416496	−	0.416496i
$185$			16.5644i			1.21784i
$186$		0			0
$187$	−3.30763			−0.241878
$188$	18.9969	−	10.9679i	1.38549	−	0.799915i
$189$		0			0
$190$	6.14767	+	22.9434i	0.445999	+	1.66449i
$191$	19.9889			1.44634			0.723171	−	0.690669i	$-0.242684\pi$
$191$	19.9889			1.44634			0.723171	+	0.690669i	$0.242684\pi$
$192$		0			0
$193$	19.0076			1.36820			0.684098	−	0.729391i	$-0.260196\pi$
$193$	19.0076			1.36820			0.684098	+	0.729391i	$0.260196\pi$
$194$	2.01063	+	7.50379i	0.144355	+	0.538740i
$195$		0			0
$196$	1.73205	−	1.00000i	0.123718	−	0.0714286i
$197$	16.9573			1.20815			0.604077	−	0.796926i	$-0.293542\pi$
$197$	16.9573			1.20815			0.604077	+	0.796926i	$0.293542\pi$
$198$		0			0
$199$		−	25.4541i		−	1.80439i	−0.431326	−	0.902196i	$-0.641954\pi$
$199$		−	25.4541i		−	1.80439i	0.431326	−	0.902196i	$-0.358046\pi$
$200$	1.38473	+	1.38473i	0.0979153	+	0.0979153i
$201$		0			0
$202$	−0.732051	−	2.73205i	−0.0515069	−	0.192226i
$203$		−	1.26795i		−	0.0889926i
$204$		0			0
$205$			13.2579i			0.925974i
$206$	−4.48394	+	1.20147i	−0.312411	+	0.0837103i
$207$		0			0
$208$	−0.877885	−	0.506847i	−0.0608703	−	0.0351435i
$209$			11.6424i			0.805318i
$210$		0			0
$211$	−19.5435			−1.34543			−0.672714	−	0.739903i	$-0.734872\pi$
$211$	−19.5435			−1.34543			−0.672714	+	0.739903i	$0.734872\pi$
$212$	−5.72899	+	3.30763i	−0.393469	+	0.227169i
$213$		0			0
$214$	−18.0221	+	4.82901i	−1.23197	+	0.330104i
$215$	−20.6969			−1.41152
$216$		0			0
$217$	−0.746577			−0.0506809
$218$	−9.96257	+	2.66946i	−0.674750	+	0.180799i
$219$		0			0
$220$	3.94579	+	6.83431i	0.266025	+	0.460769i
$221$	0.506847			0.0340942
$222$		0			0
$223$		−	3.09696i		−	0.207388i	−0.994609	−	0.103694i	$-0.966934\pi$
$223$		−	3.09696i		−	0.207388i	0.994609	−	0.103694i	$-0.0330662\pi$
$224$	−1.46410	+	5.46410i	−0.0978244	+	0.365086i
$225$		0			0
$226$	−25.9648	+	6.95725i	−1.72715	+	0.462790i
$227$			23.5854i			1.56542i	0.622388	+	0.782709i	$0.286163\pi$
$227$			23.5854i			1.56542i	−0.622388	+	0.782709i	$0.713837\pi$
$228$		0			0
$229$		−	6.53590i		−	0.431904i	−0.976404	−	0.215952i	$-0.930714\pi$
$229$		−	6.53590i		−	0.431904i	0.976404	−	0.215952i	$-0.0692855\pi$
$230$	−2.46687	−	9.20650i	−0.162661	−	0.607058i
$231$		0			0
$232$	2.53590	+	2.53590i	0.166490	+	0.166490i
$233$			10.5359i			0.690230i	0.938560	+	0.345115i	$0.112160\pi$
$233$			10.5359i			0.690230i	−0.938560	+	0.345115i	$0.887840\pi$
$234$		0			0
$235$	26.1679			1.70701
$236$	10.0397	+	17.3892i	0.653528	+	1.13194i
$237$		0			0
$238$	−0.732051	−	2.73205i	−0.0474518	−	0.177093i
$239$	−22.5298			−1.45733			−0.728665	−	0.684870i	$-0.759859\pi$
$239$	−22.5298			−1.45733			−0.728665	+	0.684870i	$0.759859\pi$
$240$		0			0
$241$	−9.53201			−0.614010			−0.307005	−	0.951708i	$-0.599327\pi$
$241$	−9.53201			−0.614010			−0.307005	+	0.951708i	$0.599327\pi$
$242$	−3.02516	−	11.2900i	−0.194465	−	0.725752i
$243$		0			0
$244$	4.53590	+	7.85641i	0.290381	+	0.502955i
$245$	2.38587			0.152428
$246$		0			0
$247$		−	1.78402i		−	0.113515i
$248$	1.49315	−	1.49315i	0.0948153	−	0.0948153i
$249$		0			0
$250$	−3.76181	−	14.0393i	−0.237918	−	0.887920i
$251$		−	27.1931i		−	1.71641i	−0.513305	−	0.858206i	$-0.671579\pi$
$251$		−	27.1931i		−	1.71641i	0.513305	−	0.858206i	$-0.328421\pi$
$252$		0			0
$253$		−	4.67172i		−	0.293708i
$254$	6.90418	−	1.84997i	0.433207	−	0.116077i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$			19.2568i			1.20121i	0.799547	+	0.600603i	$0.205073\pi$
$257$			19.2568i			1.20121i	−0.799547	+	0.600603i	$0.794927\pi$
$258$		0			0
$259$	−6.94273			−0.431400
$260$	−0.604635	−	1.04726i	−0.0374979	−	0.0649482i
$261$		0			0
$262$	−15.9679	+	4.27858i	−0.986499	+	0.264332i
$263$	12.1828			0.751221			0.375611	−	0.926778i	$-0.377433\pi$
$263$	12.1828			0.751221			0.375611	+	0.926778i	$0.377433\pi$
$264$		0			0
$265$	−7.89158			−0.484776
$266$	−9.61639	+	2.57670i	−0.589619	+	0.157988i
$267$		0			0
$268$	−0.438942	+	0.253423i	−0.0268127	+	0.0154803i
$269$	26.1149			1.59225			0.796126	−	0.605132i	$-0.206879\pi$
$269$	26.1149			1.59225			0.796126	+	0.605132i	$0.206879\pi$
$270$		0			0
$271$		−	31.3999i		−	1.90741i	−0.300749	−	0.953703i	$-0.597237\pi$
$271$		−	31.3999i		−	1.90741i	0.300749	−	0.953703i	$-0.402763\pi$
$272$	6.92820	+	4.00000i	0.420084	+	0.242536i
$273$		0			0
$274$	1.40989	−	0.377779i	0.0851746	−	0.0228225i
$275$			1.14505i			0.0690489i
$276$		0			0
$277$			12.8846i			0.774162i	0.922046	+	0.387081i	$0.126517\pi$
$277$			12.8846i			0.774162i	−0.922046	+	0.387081i	$0.873483\pi$
$278$	4.42136	+	16.5007i	0.265175	+	0.989648i
$279$		0			0
$280$	−4.77174	+	4.77174i	−0.285166	+	0.285166i
$281$		−	8.35262i		−	0.498276i	−0.968468	−	0.249138i	$-0.919853\pi$
$281$		−	8.35262i		−	0.498276i	0.968468	−	0.249138i	$-0.0801472\pi$
$282$		0			0
$283$	−4.45041			−0.264549			−0.132275	−	0.991213i	$-0.542228\pi$
$283$	−4.45041			−0.264549			−0.132275	+	0.991213i	$0.542228\pi$
$284$	5.49959	−	3.17519i	0.326341	−	0.188413i
$285$		0			0
$286$	−0.153407	−	0.572523i	−0.00907115	−	0.0338540i
$287$	−5.55686			−0.328011
$288$		0			0
$289$	13.0000			0.764706
$290$	1.10729	+	4.13244i	0.0650220	+	0.242665i
$291$		0			0
$292$	5.29005	−	3.05421i	0.309577	−	0.178734i
$293$	23.0495			1.34657			0.673283	−	0.739385i	$-0.264884\pi$
$293$	23.0495			1.34657			0.673283	+	0.739385i	$0.264884\pi$
$294$		0			0
$295$			23.9534i			1.39462i
$296$	13.8855	−	13.8855i	0.807076	−	0.807076i
$297$		0			0
$298$	−6.63285	−	24.7541i	−0.384231	−	1.43397i
$299$			0.715873i			0.0414000i
$300$		0			0
$301$		−	8.67478i		−	0.500006i
$302$	26.5404	−	7.11148i	1.52723	−	0.409220i
$303$		0			0
$304$	14.0794	−	24.3862i	0.807507	−	1.39864i
$305$			10.8221i			0.619669i
$306$		0			0
$307$	−13.4610			−0.768262			−0.384131	−	0.923279i	$-0.625499\pi$
$307$	−13.4610			−0.768262			−0.384131	+	0.923279i	$0.625499\pi$
$308$	−2.86450	+	1.65382i	−0.163220	+	0.0942350i
$309$		0			0
$310$	2.43321	−	0.651977i	0.138197	−	0.0370298i
$311$	−33.5038			−1.89983			−0.949913	−	0.312515i	$-0.898828\pi$
$311$	−33.5038			−1.89983			−0.949913	+	0.312515i	$0.898828\pi$
$312$		0			0
$313$	4.94579			0.279553			0.139776	−	0.990183i	$-0.455362\pi$
$313$	4.94579			0.279553			0.139776	+	0.990183i	$0.455362\pi$
$314$	24.8866	−	6.66834i	1.40443	−	0.376316i
$315$		0			0
$316$	14.5183	+	25.1465i	0.816719	+	1.41460i
$317$	24.4029			1.37061			0.685303	−	0.728258i	$-0.259670\pi$
$317$	24.4029			1.37061			0.685303	+	0.728258i	$0.259670\pi$
$318$		0			0
$319$			2.09696i			0.117407i
$320$		−	19.0869i		−	1.06699i
$321$		0			0
$322$	3.85876	−	1.03395i	0.215040	−	0.0576199i
$323$			14.0794i			0.783397i
$324$		0			0
$325$		−	0.175462i		−	0.00973287i
$326$	−1.36071	−	5.07823i	−0.0753627	−	0.281257i
$327$		0			0
$328$	11.1137	−	11.1137i	0.613653	−	0.613653i
$329$			10.9679i			0.604679i
$330$		0			0
$331$	−17.9648			−0.987436			−0.493718	−	0.869622i	$-0.664363\pi$
$331$	−17.9648			−0.987436			−0.493718	+	0.869622i	$0.664363\pi$
$332$	1.77480	+	3.07404i	0.0974046	+	0.168710i
$333$		0			0
$334$	2.18552	+	8.15647i	0.119586	+	0.446302i
$335$	−0.604635			−0.0330347
$336$		0			0
$337$	−7.02905			−0.382897			−0.191448	−	0.981503i	$-0.561318\pi$
$337$	−7.02905			−0.382897			−0.191448	+	0.981503i	$0.561318\pi$
$338$	−4.73482	−	17.6706i	−0.257540	−	0.961154i
$339$		0			0
$340$	4.77174	+	8.26489i	0.258784	+	0.448227i
$341$	1.23470			0.0668628
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	17.3496	+	17.3496i	0.935426	+	0.935426i
$345$		0			0
$346$	5.88781	+	21.9736i	0.316531	+	1.18131i
$347$			0.473599i			0.0254241i	0.999919	+	0.0127121i	$0.00404648\pi$
$347$			0.473599i			0.0254241i	−0.999919	+	0.0127121i	$0.995954\pi$
$348$		0			0
$349$		−	10.5007i		−	0.562091i	−0.959694	−	0.281045i	$-0.909319\pi$
$349$		−	10.5007i		−	0.562091i	0.959694	−	0.281045i	$-0.0906812\pi$
$350$	−0.945789	+	0.253423i	−0.0505546	+	0.0135461i
$351$		0			0
$352$	2.42136	−	9.03662i	0.129059	−	0.481654i
$353$		−	4.48506i		−	0.238716i	−0.992851	−	0.119358i	$-0.961916\pi$
$353$		−	4.48506i		−	0.238716i	0.992851	−	0.119358i	$-0.0380836\pi$
$354$		0			0
$355$	7.57558			0.402070
$356$	−3.13550	−	5.43085i	−0.166181	−	0.287835i
$357$		0			0
$358$	18.2755	−	4.89691i	0.965891	−	0.258810i
$359$	−1.60770			−0.0848509			−0.0424255	−	0.999100i	$-0.513508\pi$
$359$	−1.60770			−0.0848509			−0.0424255	+	0.999100i	$0.513508\pi$
$360$		0			0
$361$	30.5572			1.60827
$362$	−27.8961	+	7.47474i	−1.46619	+	0.392863i
$363$		0			0
$364$	0.438942	−	0.253423i	0.0230068	−	0.0132830i
$365$	7.28694			0.381416
$366$		0			0
$367$		−	18.4968i		−	0.965527i	−0.875751	−	0.482763i	$-0.839633\pi$
$367$		−	18.4968i		−	0.965527i	0.875751	−	0.482763i	$-0.160367\pi$
$368$	−5.64962	+	9.78543i	−0.294507	+	0.510101i
$369$		0			0
$370$	22.6274	−	6.06300i	1.17634	−	0.315201i
$371$		−	3.30763i		−	0.171724i
$372$		0			0
$373$			26.1358i			1.35326i	0.736322	+	0.676631i	$0.236561\pi$
$373$			26.1358i			1.35326i	−0.736322	+	0.676631i	$0.763439\pi$
$374$	1.21068	+	4.51831i	0.0626027	+	0.233636i
$375$		0			0
$376$	−21.9358	−	21.9358i	−1.13125	−	1.13125i
$377$		−	0.321328i		−	0.0165492i
$378$		0			0
$379$	15.1816			0.779828			0.389914	−	0.920851i	$-0.372505\pi$
$379$	15.1816			0.779828			0.389914	+	0.920851i	$0.372505\pi$
$380$	29.0911	−	16.7958i	1.49234	−	0.861604i
$381$		0			0
$382$	−7.31643	−	27.3053i	−0.374341	−	1.39706i
$383$	−2.47780			−0.126609			−0.0633047	−	0.997994i	$-0.520164\pi$
$383$	−2.47780			−0.126609			−0.0633047	+	0.997994i	$0.520164\pi$
$384$		0			0
$385$	−3.94579			−0.201096
$386$	−6.95725	−	25.9648i	−0.354115	−	1.32157i
$387$		0			0
$388$	9.51442	−	5.49315i	0.483022	−	0.278873i
$389$	11.4932			0.582726			0.291363	−	0.956613i	$-0.405891\pi$
$389$	11.4932			0.582726			0.291363	+	0.956613i	$0.405891\pi$
$390$		0			0
$391$		−	5.64962i		−	0.285714i
$392$	−2.00000	−	2.00000i	−0.101015	−	0.101015i
$393$		0			0
$394$	−6.20679	−	23.1640i	−0.312693	−	1.16699i
$395$			34.6388i			1.74287i
$396$		0			0
$397$			5.57252i			0.279677i	0.990174	+	0.139838i	$0.0446583\pi$
$397$			5.57252i			0.279677i	−0.990174	+	0.139838i	$0.955342\pi$
$398$	−34.7709	+	9.31684i	−1.74291	+	0.467011i
$399$		0			0
$400$	1.38473	−	2.39843i	0.0692366	−	0.119921i
$401$		−	24.0045i		−	1.19873i	−0.800477	−	0.599364i	$-0.795420\pi$
$401$		−	24.0045i		−	1.19873i	0.800477	−	0.599364i	$-0.204580\pi$
$402$		0			0
$403$	−0.189200			−0.00942472
$404$	−3.46410	+	2.00000i	−0.172345	+	0.0995037i
$405$		0			0
$406$	−1.73205	+	0.464102i	−0.0859602	+	0.0230330i
$407$	11.4820			0.569142
$408$		0			0
$409$	6.24503			0.308797			0.154398	−	0.988009i	$-0.450656\pi$
$409$	6.24503			0.308797			0.154398	+	0.988009i	$0.450656\pi$
$410$	18.1107	−	4.85274i	0.894423	−	0.239660i
$411$		0			0
$412$	3.28247	+	5.68541i	0.161716	+	0.280100i
$413$	−10.0397			−0.494021
$414$		0			0
$415$			4.23443i			0.207860i
$416$	−0.371038	+	1.38473i	−0.0181916	+	0.0678920i
$417$		0			0
$418$	15.9037	−	4.26140i	0.777878	−	0.208432i
$419$			2.80079i			0.136827i	0.997657	+	0.0684137i	$0.0217938\pi$
$419$			2.80079i			0.136827i	−0.997657	+	0.0684137i	$0.978206\pi$
$420$		0			0
$421$			10.8634i			0.529448i	0.964324	+	0.264724i	$0.0852808\pi$
$421$			10.8634i			0.529448i	−0.964324	+	0.264724i	$0.914719\pi$
$422$	7.15341	+	26.6969i	0.348222	+	1.29958i
$423$		0			0
$424$	6.61527	+	6.61527i	0.321266	+	0.321266i
$425$			1.38473i			0.0671693i
$426$		0			0
$427$	−4.53590			−0.219508
$428$	13.1931	+	22.8511i	0.637712	+	1.10455i
$429$		0			0
$430$	7.57558	+	28.2725i	0.365327	+	1.36342i
$431$	−8.87513			−0.427500			−0.213750	−	0.976888i	$-0.568568\pi$
$431$	−8.87513			−0.427500			−0.213750	+	0.976888i	$0.568568\pi$
$432$		0			0
$433$	10.0115			0.481120			0.240560	−	0.970634i	$-0.422669\pi$
$433$	10.0115			0.481120			0.240560	+	0.970634i	$0.422669\pi$
$434$	0.273266	+	1.01984i	0.0131172	+	0.0489540i
$435$		0			0
$436$	7.29311	+	12.6320i	0.349277	+	0.604965i
$437$	−19.8858			−0.951266
$438$		0			0
$439$			31.3999i			1.49863i	0.662211	+	0.749317i	$0.269618\pi$
$439$			31.3999i			1.49863i	−0.662211	+	0.749317i	$0.730382\pi$
$440$	7.89158	−	7.89158i	0.376216	−	0.376216i
$441$		0			0
$442$	−0.185519	−	0.692366i	−0.00882423	−	0.0329325i
$443$		−	35.7751i		−	1.69973i	−0.527003	−	0.849863i	$-0.676684\pi$
$443$		−	35.7751i		−	1.69973i	0.527003	−	0.849863i	$-0.323316\pi$
$444$		0			0
$445$		−	7.48090i		−	0.354629i
$446$	−4.23052	+	1.13356i	−0.200321	+	0.0536758i
$447$		0			0
$448$	8.00000			0.377964
$449$			20.3443i			0.960105i	0.877240	+	0.480052i	$0.159382\pi$
$449$			20.3443i			0.960105i	−0.877240	+	0.480052i	$0.840618\pi$
$450$		0			0
$451$	9.19003			0.432742
$452$	19.0076	+	32.9221i	0.894041	+	1.54852i
$453$		0			0
$454$	32.2183	−	8.63285i	1.51208	−	0.405160i
$455$	0.604635			0.0283457
$456$		0			0
$457$	−24.3205			−1.13767			−0.568833	−	0.822453i	$-0.692605\pi$
$457$	−24.3205			−1.13767			−0.568833	+	0.822453i	$0.692605\pi$
$458$	−8.92820	+	2.39230i	−0.417188	+	0.111785i
$459$		0			0
$460$	−11.6734	+	6.73962i	−0.544274	+	0.314237i
$461$	−30.5423			−1.42250			−0.711249	−	0.702940i	$-0.751870\pi$
$461$	−30.5423			−1.42250			−0.711249	+	0.702940i	$0.751870\pi$
$462$		0			0
$463$			1.71612i			0.0797547i	0.999205	+	0.0398774i	$0.0126967\pi$
$463$			1.71612i			0.0797547i	−0.999205	+	0.0398774i	$0.987303\pi$
$464$	2.53590	−	4.39230i	0.117726	−	0.203908i
$465$		0			0
$466$	14.3923	−	3.85641i	0.666711	−	0.178645i
$467$			3.60994i			0.167048i	0.996506	+	0.0835239i	$0.0266175\pi$
$467$			3.60994i			0.167048i	−0.996506	+	0.0835239i	$0.973382\pi$
$468$		0			0
$469$		−	0.253423i		−	0.0117020i
$470$	−9.57813	−	35.7461i	−0.441806	−	1.64884i
$471$		0			0
$472$	20.0794	−	20.0794i	0.924228	−	0.924228i
$473$			14.3465i			0.659653i
$474$		0			0
$475$	4.87404			0.223636
$476$	−3.46410	+	2.00000i	−0.158777	+	0.0916698i
$477$		0			0
$478$	8.24647	+	30.7762i	0.377185	+	1.40767i
$479$	3.62057			0.165428			0.0827140	−	0.996573i	$-0.473641\pi$
$479$	3.62057			0.165428			0.0827140	+	0.996573i	$0.473641\pi$
$480$		0			0
$481$	−1.75945			−0.0802240
$482$	3.48896	+	13.0210i	0.158918	+	0.593089i
$483$		0			0
$484$	−14.3152	+	8.26489i	−0.650691	+	0.375677i
$485$	13.1059			0.595110
$486$		0			0
$487$			10.3808i			0.470401i	0.971947	+	0.235200i	$0.0755746\pi$
$487$			10.3808i			0.470401i	−0.971947	+	0.235200i	$0.924425\pi$
$488$	9.07180	−	9.07180i	0.410661	−	0.410661i
$489$		0			0
$490$	−0.873288	−	3.25916i	−0.0394511	−	0.147234i
$491$		−	2.66139i		−	0.120107i	−0.998195	−	0.0600534i	$-0.980873\pi$
$491$		−	2.66139i		−	0.120107i	0.998195	−	0.0600534i	$-0.0191271\pi$
$492$		0			0
$493$			2.53590i			0.114211i
$494$	−2.43702	+	0.652997i	−0.109647	+	0.0293797i
$495$		0			0
$496$	−2.58622	−	1.49315i	−0.116125	−	0.0670446i
$497$			3.17519i			0.142427i
$498$		0			0
$499$	33.1755			1.48514			0.742570	−	0.669769i	$-0.233607\pi$
$499$	33.1755			1.48514			0.742570	+	0.669769i	$0.233607\pi$
$500$	−17.8011	+	10.2774i	−0.796088	+	0.459621i
$501$		0			0
$502$	−37.1465	+	9.95336i	−1.65793	+	0.444240i
$503$	11.2679			0.502413			0.251207	−	0.967934i	$-0.419173\pi$
$503$	11.2679			0.502413			0.251207	+	0.967934i	$0.419173\pi$
$504$		0			0
$505$	−4.77174			−0.212339
$506$	−6.38169	+	1.70997i	−0.283701	+	0.0760174i
$507$		0			0
$508$	−5.05421	−	8.75415i	−0.224244	−	0.388403i
$509$	38.9221			1.72519			0.862595	−	0.505894i	$-0.168837\pi$
$509$	38.9221			1.72519			0.862595	+	0.505894i	$0.168837\pi$
$510$		0			0
$511$			3.05421i			0.135110i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	26.3053	−	7.04848i	1.16028	−	0.310895i
$515$			7.83155i			0.345099i
$516$		0			0
$517$		−	18.1389i		−	0.797747i
$518$	2.54122	+	9.48394i	0.111655	+	0.416701i
$519$		0			0
$520$	−1.20927	+	1.20927i	−0.0530300	+	0.0530300i
$521$		−	37.1797i		−	1.62887i	−0.580253	−	0.814436i	$-0.697046\pi$
$521$		−	37.1797i		−	1.62887i	0.580253	−	0.814436i	$-0.302954\pi$
$522$		0			0
$523$	−5.58846			−0.244366			−0.122183	−	0.992508i	$-0.538990\pi$
$523$	−5.58846			−0.244366			−0.122183	+	0.992508i	$0.538990\pi$
$524$	11.6893	+	20.2465i	0.510650	+	0.884471i
$525$		0			0
$526$	−4.45920	−	16.6420i	−0.194430	−	0.725624i
$527$	1.49315			0.0650428
$528$		0			0
$529$	−15.0204			−0.653063
$530$	2.88852	+	10.7801i	0.125469	+	0.468257i
$531$		0			0
$532$	7.03969	+	12.1931i	0.305209	+	0.528638i
$533$	−1.40824			−0.0609976
$534$		0			0
$535$			31.4770i			1.36087i
$536$	0.506847	+	0.506847i	0.0218925	+	0.0218925i
$537$		0			0
$538$	−9.55870	−	35.6736i	−0.412105	−	1.53800i
$539$		−	1.65382i		−	0.0712349i
$540$		0			0
$541$		−	31.8358i		−	1.36873i	−0.729141	−	0.684363i	$-0.760080\pi$
$541$		−	31.8358i		−	1.36873i	0.729141	−	0.684363i	$-0.239920\pi$
$542$	−42.8930	+	11.4932i	−1.84241	+	0.493673i
$543$		0			0
$544$	2.92820	−	10.9282i	0.125546	−	0.468543i
$545$			17.4004i			0.745351i
$546$		0			0
$547$	−29.9648			−1.28120			−0.640602	−	0.767873i	$-0.721315\pi$
$547$	−29.9648			−1.28120			−0.640602	+	0.767873i	$0.721315\pi$
$548$	−1.03211	−	1.78767i	−0.0440896	−	0.0763655i
$549$		0			0
$550$	1.56416	−	0.419116i	0.0666961	−	0.0178712i
$551$	8.92596			0.380259
$552$		0			0
$553$	−14.5183			−0.617381
$554$	17.6007	−	4.71610i	0.747783	−	0.200368i
$555$		0			0
$556$	20.9221	−	12.0794i	0.887294	−	0.512279i
$557$	20.9573			0.887987			0.443994	−	0.896030i	$-0.353561\pi$
$557$	20.9573			0.887987			0.443994	+	0.896030i	$0.353561\pi$
$558$		0			0
$559$		−	2.19839i		−	0.0929821i
$560$	8.26489	+	4.77174i	0.349255	+	0.201643i
$561$		0			0
$562$	−11.4099	+	3.05727i	−0.481297	+	0.128963i
$563$			5.56801i			0.234664i	0.993093	+	0.117332i	$0.0374341\pi$
$563$			5.56801i			0.234664i	−0.993093	+	0.117332i	$0.962566\pi$
$564$		0			0
$565$			45.3496i			1.90787i
$566$	1.62896	+	6.07937i	0.0684704	+	0.255535i
$567$		0			0
$568$	−6.35038	−	6.35038i	−0.266456	−	0.266456i
$569$		−	24.3571i		−	1.02110i	−0.859847	−	0.510552i	$-0.829441\pi$
$569$		−	24.3571i		−	1.02110i	0.859847	−	0.510552i	$-0.170559\pi$
$570$		0			0
$571$	29.3496			1.22824			0.614120	−	0.789212i	$-0.289511\pi$
$571$	29.3496			1.22824			0.614120	+	0.789212i	$0.289511\pi$
$572$	−0.725930	+	0.419116i	−0.0303527	+	0.0175241i
$573$		0			0
$574$	2.03395	+	7.59081i	0.0848955	+	0.316834i
$575$	−1.95580			−0.0815626
$576$		0			0
$577$	−32.8992			−1.36961			−0.684805	−	0.728727i	$-0.740113\pi$
$577$	−32.8992			−1.36961			−0.684805	+	0.728727i	$0.740113\pi$
$578$	−4.75833	−	17.7583i	−0.197920	−	0.738649i
$579$		0			0
$580$	5.23973	−	3.02516i	0.217568	−	0.125613i
$581$	−1.77480			−0.0736309
$582$		0			0
$583$			5.47022i			0.226553i
$584$	−6.10842	−	6.10842i	−0.252768	−	0.252768i
$585$		0			0
$586$	−8.43670	−	31.4862i	−0.348517	−	1.30068i
$587$		−	17.9939i		−	0.742687i	−0.928496	−	0.371343i	$-0.878897\pi$
$587$		−	17.9939i		−	0.742687i	0.928496	−	0.371343i	$-0.121103\pi$
$588$		0			0
$589$		−	5.25566i		−	0.216556i
$590$	32.7209	−	8.76754i	1.34710	−	0.360954i
$591$		0			0
$592$	−24.0503	−	13.8855i	−0.988462	−	0.570689i
$593$			6.72702i			0.276246i	0.990415	+	0.138123i	$0.0441069\pi$
$593$			6.72702i			0.276246i	−0.990415	+	0.138123i	$0.955893\pi$
$594$		0			0
$595$	−4.77174			−0.195622
$596$	−31.3870	+	18.1213i	−1.28566	+	0.742277i
$597$		0			0
$598$	0.977901	−	0.262028i	0.0399893	−	0.0107151i
$599$	−10.9752			−0.448433			−0.224216	−	0.974539i	$-0.571982\pi$
$599$	−10.9752			−0.448433			−0.224216	+	0.974539i	$0.571982\pi$
$600$		0			0
$601$	−13.0542			−0.532492			−0.266246	−	0.963905i	$-0.585783\pi$
$601$	−13.0542			−0.532492			−0.266246	+	0.963905i	$0.585783\pi$
$602$	−11.8500	+	3.17519i	−0.482969	+	0.129411i
$603$		0			0
$604$	−19.4289	−	33.6519i	−0.790552	−	1.36928i
$605$	−19.7189			−0.801689
$606$		0			0
$607$			23.2350i			0.943080i	0.881845	+	0.471540i	$0.156302\pi$
$607$			23.2350i			0.943080i	−0.881845	+	0.471540i	$0.843698\pi$
$608$	−38.4656	−	10.3068i	−1.55998	−	0.417997i
$609$		0			0
$610$	14.7832	−	3.96115i	0.598554	−	0.160382i
$611$			2.77952i			0.112447i
$612$		0			0
$613$			31.6854i			1.27976i	0.768474	+	0.639881i	$0.221016\pi$
$613$			31.6854i			1.27976i	−0.768474	+	0.639881i	$0.778984\pi$
$614$	4.92708	+	18.3881i	0.198841	+	0.742084i
$615$		0			0
$616$	3.30763	+	3.30763i	0.133268	+	0.133268i
$617$		−	31.7312i		−	1.27745i	−0.769435	−	0.638726i	$-0.779462\pi$
$617$		−	31.7312i		−	1.27745i	0.769435	−	0.638726i	$-0.220538\pi$
$618$		0			0
$619$	−48.4602			−1.94778			−0.973890	−	0.227019i	$-0.927102\pi$
$619$	−48.4602			−1.94778			−0.973890	+	0.227019i	$0.927102\pi$
$620$	−1.78123	−	3.08519i	−0.0715360	−	0.123904i
$621$		0			0
$622$	12.2632	+	45.7670i	0.491711	+	1.83509i
$623$	3.13550			0.125621
$624$		0			0
$625$	−27.9825			−1.11930
$626$	−1.81028	−	6.75607i	−0.0723535	−	0.270027i
$627$		0			0
$628$	−18.2183	−	31.5549i	−0.726987	−	1.25918i
$629$	13.8855			0.553649
$630$		0			0
$631$			23.9472i			0.953325i	0.879086	+	0.476662i	$0.158154\pi$
$631$			23.9472i			0.953325i	−0.879086	+	0.476662i	$0.841846\pi$
$632$	29.0366	−	29.0366i	1.15501	−	1.15501i
$633$		0			0
$634$	−8.93210	−	33.3350i	−0.354739	−	1.32390i
$635$		−	12.0587i		−	0.478534i
$636$		0			0
$637$			0.253423i			0.0100410i
$638$	2.86450	−	0.767539i	0.113406	−	0.0303872i
$639$		0			0
$640$	−26.0732	+	6.98631i	−1.03064	+	0.276158i
$641$		−	3.24953i		−	0.128349i	−0.997939	−	0.0641744i	$-0.979559\pi$
$641$		−	3.24953i		−	0.128349i	0.997939	−	0.0641744i	$-0.0204414\pi$
$642$		0			0
$643$	−24.2808			−0.957542			−0.478771	−	0.877940i	$-0.658918\pi$
$643$	−24.2808			−0.957542			−0.478771	+	0.877940i	$0.658918\pi$
$644$	−2.82481	−	4.89271i	−0.111313	−	0.192800i
$645$		0			0
$646$	19.2328	−	5.15341i	0.756703	−	0.202758i
$647$	−36.6388			−1.44042			−0.720209	−	0.693757i	$-0.755954\pi$
$647$	−36.6388			−1.44042			−0.720209	+	0.693757i	$0.755954\pi$
$648$		0			0
$649$	16.6038			0.651756
$650$	−0.239685	+	0.0642234i	−0.00940123	+	0.00251905i
$651$		0			0
$652$	−6.43894	+	3.71753i	−0.252168	+	0.145590i
$653$	15.8748			0.621230			0.310615	−	0.950536i	$-0.399465\pi$
$653$	15.8748			0.621230			0.310615	+	0.950536i	$0.399465\pi$
$654$		0			0
$655$			27.8891i			1.08972i
$656$	−19.2495	−	11.1137i	−0.751568	−	0.433918i
$657$		0			0
$658$	14.9824	−	4.01453i	0.584075	−	0.156503i
$659$			23.4538i			0.913630i	0.889562	+	0.456815i	$0.151010\pi$
$659$			23.4538i			0.913630i	−0.889562	+	0.456815i	$0.848990\pi$
$660$		0			0
$661$			25.0090i			0.972737i	0.873754	+	0.486368i	$0.161679\pi$
$661$			25.0090i			0.972737i	−0.873754	+	0.486368i	$0.838321\pi$
$662$	6.57558	+	24.5404i	0.255567	+	0.953790i
$663$		0			0
$664$	3.54959	−	3.54959i	0.137751	−	0.137751i
$665$			16.7958i			0.651312i
$666$		0			0
$667$	−3.58172			−0.138685
$668$	10.3420	−	5.97095i	0.400143	−	0.231023i
$669$		0			0
$670$	0.221312	+	0.825947i	0.00855002	+	0.0319091i
$671$	7.50155			0.289594
$672$		0			0
$673$	−22.8137			−0.879402			−0.439701	−	0.898144i	$-0.644916\pi$
$673$	−22.8137			−0.879402			−0.439701	+	0.898144i	$0.644916\pi$
$674$	2.57281	+	9.60186i	0.0991010	+	0.369850i
$675$		0			0
$676$	−22.4054	+	12.9358i	−0.861747	+	0.497530i
$677$	−29.6851			−1.14089			−0.570446	−	0.821335i	$-0.693230\pi$
$677$	−29.6851			−1.14089			−0.570446	+	0.821335i	$0.693230\pi$
$678$		0			0
$679$			5.49315i			0.210808i
$680$	9.54347	−	9.54347i	0.365975	−	0.365975i
$681$		0			0
$682$	−0.451932	−	1.68663i	−0.0173054	−	0.0645845i
$683$		−	36.8469i		−	1.40991i	−0.709253	−	0.704954i	$-0.750968\pi$
$683$		−	36.8469i		−	1.40991i	0.709253	−	0.704954i	$-0.249032\pi$
$684$		0			0
$685$		−	2.46248i		−	0.0940866i
$686$	1.36603	−	0.366025i	0.0521551	−	0.0139749i
$687$		0			0
$688$	17.3496	−	30.0503i	0.661446	−	1.14566i
$689$		−	0.838232i		−	0.0319341i
$690$		0			0
$691$	30.7556			1.17000			0.584998	−	0.811035i	$-0.301095\pi$
$691$	30.7556			1.17000			0.584998	+	0.811035i	$0.301095\pi$
$692$	27.8614	−	16.0858i	1.05913	−	0.611491i
$693$		0			0
$694$	0.646948	−	0.173349i	0.0245578	−	0.00658025i
$695$	28.8198			1.09320
$696$		0			0
$697$	11.1137			0.420962
$698$	−14.3443	+	3.84353i	−0.542938	+	0.145480i
$699$		0			0
$700$	0.692366	+	1.19921i	0.0261690	+	0.0453260i
$701$	−4.88852			−0.184637			−0.0923184	−	0.995730i	$-0.529428\pi$
$701$	−4.88852			−0.184637			−0.0923184	+	0.995730i	$0.529428\pi$
$702$		0			0
$703$		−	48.8746i		−	1.84334i
$704$	−13.2305			−0.498645
$705$		0			0
$706$	−6.12671	+	1.64165i	−0.230582	+	0.0617842i
$707$		−	2.00000i		−	0.0752177i
$708$		0			0
$709$			27.1221i			1.01859i	0.860591	+	0.509296i	$0.170094\pi$
$709$			27.1221i			1.01859i	−0.860591	+	0.509296i	$0.829906\pi$
$710$	−2.77286	−	10.3484i	−0.104063	−	0.388370i
$711$		0			0
$712$	−6.27101	+	6.27101i	−0.235016	+	0.235016i
$713$			2.10894i			0.0789803i
$714$		0			0
$715$	−0.999956			−0.0373962
$716$	−13.3786	−	23.1724i	−0.499982	−	0.865995i
$717$		0			0
$718$	0.588457	+	2.19615i	0.0219610	+	0.0819597i
$719$	2.95501			0.110203			0.0551017	−	0.998481i	$-0.482452\pi$
$719$	2.95501			0.110203			0.0551017	+	0.998481i	$0.482452\pi$
$720$		0			0
$721$	−3.28247			−0.122246
$722$	−11.1847	−	41.7419i	−0.416251	−	1.55347i
$723$		0			0
$724$	20.4214	+	35.3708i	0.758954	+	1.31455i
$725$	0.877885			0.0326038
$726$		0			0
$727$			18.3923i			0.682133i	0.940039	+	0.341066i	$0.110788\pi$
$727$			18.3923i			0.682133i	−0.940039	+	0.341066i	$0.889212\pi$
$728$	−0.506847	−	0.506847i	−0.0187850	−	0.0187850i
$729$		0			0
$730$	−2.66721	−	9.95415i	−0.0987177	−	0.368420i
$731$			17.3496i			0.641697i
$732$		0			0
$733$			19.6885i			0.727210i	0.931553	+	0.363605i	$0.118454\pi$
$733$			19.6885i			0.727210i	−0.931553	+	0.363605i	$0.881546\pi$
$734$	−25.2671	+	6.77031i	−0.932627	+	0.249897i
$735$		0			0
$736$	15.4351	+	4.13581i	0.568943	+	0.152448i
$737$			0.419116i			0.0154383i
$738$		0			0
$739$	8.03517			0.295579			0.147789	−	0.989019i	$-0.452784\pi$
$739$	8.03517			0.295579			0.147789	+	0.989019i	$0.452784\pi$
$740$	−16.5644	−	28.6904i	−0.608921	−	1.05468i
$741$		0			0
$742$	−4.51831	+	1.21068i	−0.165872	+	0.0444454i
$743$	−29.4820			−1.08159			−0.540795	−	0.841154i	$-0.681876\pi$
$743$	−29.4820			−1.08159			−0.540795	+	0.841154i	$0.681876\pi$
$744$		0			0
$745$	−43.2350			−1.58401
$746$	35.7022	−	9.56637i	1.30715	−	0.350250i
$747$		0			0
$748$	5.72899	−	3.30763i	0.209473	−	0.120939i
$749$	−13.1931			−0.482065
$750$		0			0
$751$			0.103077i			0.00376132i	0.999998	+	0.00188066i	$0.000598633\pi$
$751$			0.103077i			0.00376132i	−0.999998	+	0.00188066i	$0.999401\pi$
$752$	−21.9358	+	37.9939i	−0.799915	+	1.38549i
$753$		0			0
$754$	−0.438942	+	0.117614i	−0.0159853	+	0.00428326i
$755$		−	46.3549i		−	1.68703i
$756$		0			0
$757$		−	32.1006i		−	1.16672i	−0.812215	−	0.583359i	$-0.801738\pi$
$757$		−	32.1006i		−	1.16672i	0.812215	−	0.583359i	$-0.198262\pi$
$758$	−5.55686	−	20.7385i	−0.201834	−	0.753256i
$759$		0			0
$760$	−33.5915	−	33.5915i	−1.21849	−	1.21849i
$761$			39.3228i			1.42545i	0.701444	+	0.712725i	$0.252539\pi$
$761$			39.3228i			1.42545i	−0.701444	+	0.712725i	$0.747461\pi$
$762$		0			0
$763$	−7.29311			−0.264028
$764$	−34.6217	+	19.9889i	−1.25257	+	0.723171i
$765$		0			0
$766$	0.906936	+	3.38473i	0.0327689	+	0.122295i
$767$	−2.54429			−0.0918690
$768$		0			0
$769$	−38.1199			−1.37464			−0.687319	−	0.726356i	$-0.741213\pi$
$769$	−38.1199			−1.37464			−0.687319	+	0.726356i	$0.741213\pi$
$770$	1.44426	+	5.39005i	0.0520475	+	0.194244i
$771$		0			0
$772$	−32.9221	+	19.0076i	−1.18489	+	0.684098i
$773$	−25.6583			−0.922866			−0.461433	−	0.887175i	$-0.652665\pi$
$773$	−25.6583			−0.922866			−0.461433	+	0.887175i	$0.652665\pi$
$774$		0			0
$775$		−	0.516904i		−	0.0185677i
$776$	−10.9863	−	10.9863i	−0.394385	−	0.394385i
$777$		0			0
$778$	−4.20679	−	15.6999i	−0.150821	−	0.562870i
$779$		−	39.1186i		−	1.40157i
$780$		0			0
$781$		−	5.25118i		−	0.187902i
$782$	−7.71753	+	2.06790i	−0.275978	+	0.0739481i
$783$		0			0
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$		−	43.4663i		−	1.55138i
$786$		0			0
$787$	22.7785			0.811965			0.405983	−	0.913881i	$-0.366929\pi$
$787$	22.7785			0.811965			0.405983	+	0.913881i	$0.366929\pi$
$788$	−29.3708	+	16.9573i	−1.04629	+	0.604077i
$789$		0			0
$790$	47.3174	−	12.6787i	1.68348	−	0.451087i
$791$	−19.0076			−0.675832
$792$		0			0
$793$	−1.14950			−0.0408201
$794$	7.61221	−	2.03969i	0.270147	−	0.0723857i
$795$		0			0
$796$	25.4541	+	44.0878i	0.902196	+	1.56265i
$797$	7.04306			0.249478			0.124739	−	0.992190i	$-0.460191\pi$
$797$	7.04306			0.249478			0.124739	+	0.992190i	$0.460191\pi$
$798$		0			0
$799$		−	21.9358i		−	0.776032i
$800$	−3.78316	−	1.01369i	−0.133755	−	0.0358395i
$801$		0			0
$802$	−32.7908	+	8.78626i	−1.15788	+	0.310254i
$803$		−	5.05111i		−	0.178250i
$804$		0			0
$805$		−	6.73962i		−	0.237541i
$806$	0.0692520	+	0.258452i	0.00243930	+	0.00910358i
$807$		0			0
$808$	4.00000	+	4.00000i	0.140720	+	0.140720i
$809$		−	36.1772i		−	1.27192i	−0.771722	−	0.635961i	$-0.780604\pi$
$809$		−	36.1772i		−	1.27192i	0.771722	−	0.635961i	$-0.219396\pi$
$810$		0			0
$811$	−7.84047			−0.275316			−0.137658	−	0.990480i	$-0.543958\pi$
$811$	−7.84047			−0.275316			−0.137658	+	0.990480i	$0.543958\pi$
$812$	1.26795	+	2.19615i	0.0444963	+	0.0770698i
$813$		0			0
$814$	−4.20271	−	15.6847i	−0.147305	−	0.549749i
$815$	−8.86952			−0.310686
$816$		0			0
$817$	61.0677			2.13649
$818$	−2.28584	−	8.53087i	−0.0799225	−	0.298275i
$819$		0			0
$820$	−13.2579	−	22.9634i	−0.462987	−	0.801917i
$821$	−52.1342			−1.81950			−0.909748	−	0.415161i	$-0.863725\pi$
$821$	−52.1342			−1.81950			−0.909748	+	0.415161i	$0.863725\pi$
$822$		0			0
$823$			48.1923i			1.67988i	0.542682	+	0.839939i	$0.317409\pi$
$823$			48.1923i			1.67988i	−0.542682	+	0.839939i	$0.682591\pi$
$824$	6.56495	−	6.56495i	0.228701	−	0.228701i
$825$		0			0
$826$	3.67478	+	13.7145i	0.127862	+	0.477187i
$827$			34.6966i			1.20652i	0.797545	+	0.603259i	$0.206131\pi$
$827$			34.6966i			1.20652i	−0.797545	+	0.603259i	$0.793869\pi$
$828$		0			0
$829$			12.5848i			0.437088i	0.975827	+	0.218544i	$0.0701308\pi$
$829$			12.5848i			0.437088i	−0.975827	+	0.218544i	$0.929869\pi$
$830$	5.78434	−	1.54991i	0.200777	−	0.0537981i
$831$		0			0
$832$	2.02739			0.0702870
$833$		−	2.00000i		−	0.0692959i
$834$		0			0
$835$	14.2459			0.493000
$836$	−11.6424	−	20.1651i	−0.402659	−	0.697426i
$837$		0			0
$838$	3.82595	−	1.02516i	0.132165	−	0.0354135i
$839$	9.30987			0.321413			0.160706	−	0.987002i	$-0.448623\pi$
$839$	9.30987			0.321413			0.160706	+	0.987002i	$0.448623\pi$
$840$		0			0
$841$	−27.3923			−0.944562
$842$	14.8396	−	3.97627i	0.511407	−	0.137031i
$843$		0			0
$844$	33.8503	−	19.5435i	1.16517	−	0.672714i
$845$	−30.8631			−1.06172
$846$		0			0
$847$		−	8.26489i		−	0.283985i
$848$	6.61527	−	11.4580i	0.227169	−	0.393469i
$849$		0			0
$850$	1.89158	−	0.506847i	0.0648806	−	0.0173847i
$851$			19.6119i			0.672287i
$852$		0			0
$853$			31.3099i			1.07203i	0.844208	+	0.536015i	$0.180071\pi$
$853$			31.3099i			1.07203i	−0.844208	+	0.536015i	$0.819929\pi$
$854$	1.66025	+	6.19615i	0.0568127	+	0.212028i
$855$		0			0
$856$	26.3862	−	26.3862i	0.901861	−	0.901861i
$857$		−	7.14838i		−	0.244184i	−0.992519	−	0.122092i	$-0.961040\pi$
$857$		−	7.14838i		−	0.244184i	0.992519	−	0.122092i	$-0.0389603\pi$
$858$		0			0
$859$	−14.7022			−0.501632			−0.250816	−	0.968035i	$-0.580699\pi$
$859$	−14.7022			−0.501632			−0.250816	+	0.968035i	$0.580699\pi$
$860$	35.8480	−	20.6969i	1.22241	−	0.705758i
$861$		0			0
$862$	3.24852	+	12.1237i	0.110645	+	0.412933i
$863$	−30.8640			−1.05062			−0.525311	−	0.850910i	$-0.676051\pi$
$863$	−30.8640			−1.05062			−0.525311	+	0.850910i	$0.676051\pi$
$864$		0			0
$865$	38.3786			1.30491
$866$	−3.66445	−	13.6759i	−0.124523	−	0.464727i
$867$		0			0
$868$	1.29311	−	0.746577i	0.0438910	−	0.0253405i
$869$	24.0106			0.814505
$870$		0			0
$871$		−	0.0642234i		−	0.00217613i
$872$	14.5862	−	14.5862i	0.493952	−	0.493952i
$873$		0			0
$874$	7.27870	+	27.1645i	0.246206	+	0.918852i
$875$		−	10.2774i		−	0.347441i
$876$		0			0
$877$			43.9570i			1.48432i	0.670221	+	0.742162i	$0.266199\pi$
$877$			43.9570i			1.48432i	−0.670221	+	0.742162i	$0.733801\pi$
$878$	42.8930	−	11.4932i	1.44757	−	0.387875i
$879$		0			0
$880$	−13.6686	−	7.89158i	−0.460769	−	0.266025i
$881$		−	10.7432i		−	0.361948i	−0.983488	−	0.180974i	$-0.942075\pi$
$881$		−	10.7432i		−	0.361948i	0.983488	−	0.180974i	$-0.0579249\pi$
$882$		0			0
$883$	−36.8640			−1.24057			−0.620286	−	0.784376i	$-0.712983\pi$
$883$	−36.8640			−1.24057			−0.620286	+	0.784376i	$0.712983\pi$
$884$	−0.877885	+	0.506847i	−0.0295265	+	0.0170471i
$885$		0			0
$886$	−48.8697	+	13.0946i	−1.64181	+	0.439922i
$887$	32.0710			1.07684			0.538420	−	0.842677i	$-0.319022\pi$
$887$	32.0710			1.07684			0.538420	+	0.842677i	$0.319022\pi$
$888$		0			0
$889$	5.05421			0.169513
$890$	−10.2191	+	2.73820i	−0.342545	+	0.0917847i
$891$		0			0
$892$	3.09696	+	5.36409i	0.103694	+	0.179603i
$893$	−77.2105			−2.58375
$894$		0			0
$895$		−	31.9196i		−	1.06695i
$896$	−2.92820	−	10.9282i	−0.0978244	−	0.365086i
$897$		0			0
$898$	27.7908	−	7.44652i	0.927390	−	0.248493i
$899$		−	0.946621i		−	0.0315716i
$900$		0			0
$901$			6.61527i			0.220387i
$902$	−3.36379	−	12.5538i	−0.112002	−	0.417996i
$903$		0			0
$904$	38.0151	−	38.0151i	1.26436	−	1.26436i
$905$			48.7227i			1.61960i
$906$		0			0
$907$	12.2733			0.407528			0.203764	−	0.979020i	$-0.434683\pi$
$907$	12.2733			0.407528			0.203764	+	0.979020i	$0.434683\pi$
$908$	−23.5854	−	40.8511i	−0.782709	−	1.35569i
$909$		0			0
$910$	−0.221312	−	0.825947i	−0.00733641	−	0.0273799i
$911$	39.9487			1.32356			0.661779	−	0.749699i	$-0.269802\pi$
$911$	39.9487			1.32356			0.661779	+	0.749699i	$0.269802\pi$
$912$		0			0
$913$	2.93519			0.0971406
$914$	8.90192	+	33.2224i	0.294449	+	1.09890i
$915$		0			0
$916$	6.53590	+	11.3205i	0.215952	+	0.374040i
$917$	−11.6893			−0.386015
$918$		0			0
$919$			27.5374i			0.908373i	0.890907	+	0.454187i	$0.150070\pi$
$919$			27.5374i			0.908373i	−0.890907	+	0.454187i	$0.849930\pi$
$920$	13.4792	+	13.4792i	0.444398	+	0.444398i
$921$		0			0
$922$	11.1793	+	41.7216i	0.368170	+	1.37403i
$923$			0.804668i			0.0264860i
$924$		0			0
$925$		−	4.80691i		−	0.158050i
$926$	2.34426	−	0.628142i	0.0770371	−	0.0206420i
$927$		0			0
$928$	−6.92820	−	1.85641i	−0.227429	−	0.0609395i
$929$			43.6938i			1.43355i	0.697306	+	0.716774i	$0.254382\pi$
$929$			43.6938i			1.43355i	−0.697306	+	0.716774i	$0.745618\pi$
$930$		0			0
$931$	−7.03969			−0.230716
$932$	−10.5359	−	18.2487i	−0.345115	−	0.597756i
$933$		0			0
$934$	4.93126	−	1.32133i	0.161356	−	0.0432352i
$935$	7.89158			0.258082
$936$		0			0
$937$	−32.3923			−1.05821			−0.529105	−	0.848556i	$-0.677472\pi$
$937$	−32.3923			−1.05821			−0.529105	+	0.848556i	$0.677472\pi$
$938$	−0.346183	+	0.0927594i	−0.0113033	+	0.00302870i
$939$		0			0
$940$	−45.3242	+	26.1679i	−1.47831	+	0.853504i
$941$	23.4806			0.765446			0.382723	−	0.923863i	$-0.374986\pi$
$941$	23.4806			0.765446			0.382723	+	0.923863i	$0.374986\pi$
$942$		0			0
$943$			15.6971i			0.511167i
$944$	−34.7785	−	20.0794i	−1.13194	−	0.653528i
$945$		0			0
$946$	19.5977	−	5.25118i	0.637176	−	0.170731i
$947$		−	8.76079i		−	0.284687i	−0.989817	−	0.142344i	$-0.954536\pi$
$947$		−	8.76079i		−	0.284687i	0.989817	−	0.142344i	$-0.0454638\pi$
$948$		0			0
$949$			0.774009i			0.0251254i
$950$	−1.78402	−	6.65806i	−0.0578813	−	0.216016i
$951$		0			0
$952$	4.00000	+	4.00000i	0.129641	+	0.129641i
$953$		−	42.8617i		−	1.38843i	−0.719769	−	0.694214i	$-0.755752\pi$
$953$		−	42.8617i		−	1.38843i	0.719769	−	0.694214i	$-0.244248\pi$
$954$		0			0
$955$	−47.6908			−1.54324
$956$	39.0227	−	22.5298i	1.26208	−	0.728665i
$957$		0			0
$958$	−1.32522	−	4.94579i	−0.0428159	−	0.159791i
$959$	1.03211			0.0333286
$960$		0			0
$961$	30.4426			0.982020
$962$	0.644004	+	2.40345i	0.0207635	+	0.0774905i
$963$		0			0
$964$	16.5099	−	9.53201i	0.531749	−	0.307005i
$965$	−45.3496			−1.45985
$966$		0			0
$967$		−	31.8855i		−	1.02537i	−0.858578	−	0.512684i	$-0.828651\pi$
$967$		−	31.8855i		−	1.02537i	0.858578	−	0.512684i	$-0.171349\pi$
$968$	16.5298	+	16.5298i	0.531287	+	0.531287i
$969$		0			0
$970$	−4.79711	−	17.9030i	−0.154026	−	0.574832i
$971$		−	19.2518i		−	0.617819i	−0.951091	−	0.308909i	$-0.900036\pi$
$971$		−	19.2518i		−	0.617819i	0.951091	−	0.308909i	$-0.0999640\pi$
$972$		0			0
$973$			12.0794i			0.387247i
$974$	14.1805	−	3.79965i	0.454372	−	0.121749i
$975$		0			0
$976$	−15.7128	−	9.07180i	−0.502955	−	0.290381i
$977$		−	54.2449i		−	1.73545i	−0.497047	−	0.867723i	$-0.665582\pi$
$977$		−	54.2449i		−	1.73545i	0.497047	−	0.867723i	$-0.334418\pi$
$978$		0			0
$979$	−5.18555			−0.165731
$980$	−4.13244	+	2.38587i	−0.132006	+	0.0762138i
$981$		0			0
$982$	−3.63553	+	0.974137i	−0.116014	+	0.0310859i
$983$	17.3764			0.554220			0.277110	−	0.960838i	$-0.410623\pi$
$983$	17.3764			0.554220			0.277110	+	0.960838i	$0.410623\pi$
$984$		0			0
$985$	−40.4578			−1.28909
$986$	3.46410	−	0.928203i	0.110319	−	0.0295600i
$987$		0			0
$988$	1.78402	+	3.09002i	0.0567573	+	0.0983065i
$989$	−24.5046			−0.779201
$990$		0			0
$991$			13.3107i			0.422829i	0.977397	+	0.211414i	$0.0678069\pi$
$991$			13.3107i			0.422829i	−0.977397	+	0.211414i	$0.932193\pi$
$992$	−1.09306	+	4.07937i	−0.0347048	+	0.129520i
$993$		0			0
$994$	4.33739	−	1.16220i	0.137574	−	0.0368627i
$995$			60.7301i			1.92527i
$996$		0			0
$997$		−	49.6564i		−	1.57263i	−0.617824	−	0.786317i	$-0.711986\pi$
$997$		−	49.6564i		−	1.57263i	0.617824	−	0.786317i	$-0.288014\pi$
$998$	−12.1431	−	45.3186i	−0.384382	−	1.43453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.b.323.1	yes	8
3.2	odd	2		1512.2.j.a.323.8	yes	8
4.3	odd	2		6048.2.j.b.5615.2		8
8.3	odd	2		1512.2.j.a.323.6	✓	8
8.5	even	2		6048.2.j.a.5615.7		8
12.11	even	2		6048.2.j.a.5615.8		8
24.5	odd	2		6048.2.j.b.5615.1		8
24.11	even	2	inner	1512.2.j.b.323.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.a.323.6	✓	8	8.3	odd	2
1512.2.j.a.323.8	yes	8	3.2	odd	2
1512.2.j.b.323.1	yes	8	1.1	even	1	trivial
1512.2.j.b.323.3	yes	8	24.11	even	2	inner
6048.2.j.a.5615.7		8	8.5	even	2
6048.2.j.a.5615.8		8	12.11	even	2
6048.2.j.b.5615.1		8	24.5	odd	2
6048.2.j.b.5615.2		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -2.38587 q^{5} -1.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} -2.38587 q^{5} -1.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +(0.873288 + 3.25916i) q^{10} +1.65382i q^{11} -0.253423i q^{13} +(-1.36603 + 0.366025i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.00000i q^{17} +7.03969 q^{19} +(4.13244 - 2.38587i) q^{20} +(2.25916 - 0.605339i) q^{22} -2.82481 q^{23} +0.692366 q^{25} +(-0.346183 + 0.0927594i) q^{26} +(1.00000 + 1.73205i) q^{28} +1.26795 q^{29} -0.746577i q^{31} +(-5.46410 - 1.46410i) q^{32} +(2.73205 - 0.732051i) q^{34} +2.38587i q^{35} -6.94273i q^{37} +(-2.57670 - 9.61639i) q^{38} +(-4.77174 - 4.77174i) q^{40} -5.55686i q^{41} +8.67478 q^{43} +(-1.65382 - 2.86450i) q^{44} +(1.03395 + 3.85876i) q^{46} -10.9679 q^{47} -1.00000 q^{49} +(-0.253423 - 0.945789i) q^{50} +(0.253423 + 0.438942i) q^{52} +3.30763 q^{53} -3.94579i q^{55} +(2.00000 - 2.00000i) q^{56} +(-0.464102 - 1.73205i) q^{58} -10.0397i q^{59} -4.53590i q^{61} +(-1.01984 + 0.273266i) q^{62} +8.00000i q^{64} +0.604635i q^{65} +0.253423 q^{67} +(-2.00000 - 3.46410i) q^{68} +(3.25916 - 0.873288i) q^{70} -3.17519 q^{71} -3.05421 q^{73} +(-9.48394 + 2.54122i) q^{74} +(-12.1931 + 7.03969i) q^{76} +1.65382 q^{77} -14.5183i q^{79} +(-4.77174 + 8.26489i) q^{80} +(-7.59081 + 2.03395i) q^{82} -1.77480i q^{83} -4.77174i q^{85} +(-3.17519 - 11.8500i) q^{86} +(-3.30763 + 3.30763i) q^{88} +3.13550i q^{89} -0.253423 q^{91} +(4.89271 - 2.82481i) q^{92} +(4.01453 + 14.9824i) q^{94} -16.7958 q^{95} -5.49315 q^{97} +(0.366025 + 1.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8	\( 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8} + 4 q^{10} - 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} - 16 q^{23} + 32 q^{25} - 16 q^{26} + 8 q^{28} + 24 q^{29} - 16 q^{32} + 8 q^{34} + 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} + 8 q^{47} - 8 q^{49} - 8 q^{50} + 8 q^{52} + 16 q^{56} + 24 q^{58} + 12 q^{62} + 8 q^{67} - 16 q^{68} - 4 q^{70} - 32 q^{71} + 8 q^{73} - 28 q^{74} + 24 q^{76} + 16 q^{80} - 36 q^{82} - 32 q^{86} - 8 q^{91} + 24 q^{92} + 40 q^{94} - 112 q^{95} - 32 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8 + 4 * q^10 - 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 - 16 * q^23 + 32 * q^25 - 16 * q^26 + 8 * q^28 + 24 * q^29 - 16 * q^32 + 8 * q^34 + 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 + 8 * q^47 - 8 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^56 + 24 * q^58 + 12 * q^62 + 8 * q^67 - 16 * q^68 - 4 * q^70 - 32 * q^71 + 8 * q^73 - 28 * q^74 + 24 * q^76 + 16 * q^80 - 36 * q^82 - 32 * q^86 - 8 * q^91 + 24 * q^92 + 40 * q^94 - 112 * q^95 - 32 * q^97 - 4 * q^98

Introduction

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