LMFDB - Embedded newform 784.2.bg.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(65,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 20]))

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

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

chi := DirichletCharacter("784.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bg (of order $21$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	784.193
Dual form			784.2.bg.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0519131 + 0.692733i) q^{3} +(1.52046 + 1.03663i) q^{5} +(-2.03934 - 1.68555i) q^{7} +(2.48931 + 0.375203i) q^{9} +O(q^{10})$	\(q+(-0.0519131 + 0.692733i) q^{3} +(1.52046 + 1.03663i) q^{5} +(-2.03934 - 1.68555i) q^{7} +(2.48931 + 0.375203i) q^{9} +(3.95404 - 0.595976i) q^{11} +(-3.60921 - 4.52581i) q^{13} +(-0.797043 + 0.999460i) q^{15} +(3.30352 + 1.01900i) q^{17} +(1.51977 + 2.63232i) q^{19} +(1.27351 - 1.32522i) q^{21} +(7.69889 - 2.37479i) q^{23} +(-0.589506 - 1.50204i) q^{25} +(-0.852883 + 3.73672i) q^{27} +(0.392906 + 1.72143i) q^{29} +(-2.70101 + 4.67829i) q^{31} +(0.207585 + 2.77003i) q^{33} +(-1.35344 - 4.67687i) q^{35} +(-4.51246 + 4.18695i) q^{37} +(3.32254 - 2.26527i) q^{39} +(2.82949 - 1.36261i) q^{41} +(3.50635 + 1.68857i) q^{43} +(3.39596 + 3.15099i) q^{45} +(2.66104 - 6.78022i) q^{47} +(1.31782 + 6.87483i) q^{49} +(-0.877392 + 2.23556i) q^{51} +(6.56061 + 6.08735i) q^{53} +(6.62979 + 3.19274i) q^{55} +(-1.90239 + 0.916142i) q^{57} +(-5.93817 + 4.04858i) q^{59} +(2.83727 - 2.63260i) q^{61} +(-4.44412 - 4.96103i) q^{63} +(-0.796066 - 10.6228i) q^{65} +(0.927324 - 1.60617i) q^{67} +(1.24542 + 5.45656i) q^{69} +(-1.61191 + 7.06223i) q^{71} +(-4.28338 - 10.9139i) q^{73} +(1.07111 - 0.330395i) q^{75} +(-9.06819 - 5.44935i) q^{77} +(-2.23103 - 3.86426i) q^{79} +(4.67248 + 1.44127i) q^{81} +(3.42482 - 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(-1.21289 + 0.182814i) q^{87} +(-11.3049 - 1.70393i) q^{89} +(-0.268082 + 15.3132i) q^{91} +(-3.10059 - 2.11395i) q^{93} +(-0.417998 + 5.57779i) q^{95} +9.72695 q^{97} +10.0664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 7 q^{3} - 33 q^{9}+O(q^{10}) $ 24 * q - 7 * q^3 - 33 * q^9	$ 24 q - 7 q^{3} - 33 q^{9} + 7 q^{11} + 14 q^{13} + 7 q^{15} - 7 q^{17} + 7 q^{21} + 21 q^{23} + 4 q^{25} + 35 q^{27} - 11 q^{29} - 28 q^{31} + 14 q^{33} - 21 q^{35} - 24 q^{37} + 40 q^{39} + 28 q^{41} - 10 q^{43} + 7 q^{45} + 70 q^{47} + 84 q^{49} - 60 q^{51} + 26 q^{53} - 56 q^{55} - 33 q^{57} + 7 q^{59} + 14 q^{61} + 14 q^{63} + 36 q^{67} - 35 q^{69} - 7 q^{73} + 28 q^{75} - 91 q^{77} + 26 q^{79} + 55 q^{81} + 7 q^{83} + 49 q^{85} - 35 q^{87} - 56 q^{89} - 7 q^{91} + 72 q^{93} + 14 q^{95} - 126 q^{97} + 14 q^{99}+O(q^{100}) $ 24 * q - 7 * q^3 - 33 * q^9 + 7 * q^11 + 14 * q^13 + 7 * q^15 - 7 * q^17 + 7 * q^21 + 21 * q^23 + 4 * q^25 + 35 * q^27 - 11 * q^29 - 28 * q^31 + 14 * q^33 - 21 * q^35 - 24 * q^37 + 40 * q^39 + 28 * q^41 - 10 * q^43 + 7 * q^45 + 70 * q^47 + 84 * q^49 - 60 * q^51 + 26 * q^53 - 56 * q^55 - 33 * q^57 + 7 * q^59 + 14 * q^61 + 14 * q^63 + 36 * q^67 - 35 * q^69 - 7 * q^73 + 28 * q^75 - 91 * q^77 + 26 * q^79 + 55 * q^81 + 7 * q^83 + 49 * q^85 - 35 * q^87 - 56 * q^89 - 7 * q^91 + 72 * q^93 + 14 * q^95 - 126 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{21}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0519131	+	0.692733i	−0.0299721	+	0.399949i	0.961961	+	0.273187i	$0.0880777\pi$
$3$	−0.0519131	+	0.692733i	−0.0299721	+	0.399949i	−0.991933	+	0.126763i	$0.959541\pi$
$4$		0			0
$5$	1.52046	+	1.03663i	0.679972	+	0.463597i	0.853405	−	0.521249i	$-0.174534\pi$
$5$	1.52046	+	1.03663i	0.679972	+	0.463597i	−0.173433	+	0.984846i	$0.555486\pi$
$6$		0			0
$7$	−2.03934	−	1.68555i	−0.770798	−	0.637079i
$7$	−2.03934	−	1.68555i	−0.770798	−	0.637079i
$8$		0			0
$9$	2.48931	+	0.375203i	0.829770	+	0.125068i
$10$		0			0
$11$	3.95404	−	0.595976i	1.19219	−	0.179694i	0.477178	−	0.878807i	$-0.341660\pi$
$11$	3.95404	−	0.595976i	1.19219	−	0.179694i	0.715011	+	0.699113i	$0.246422\pi$
$12$		0			0
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.966724	−	0.255821i	$-0.917654\pi$
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.0342904	−	0.999412i	$-0.510917\pi$
$14$		0			0
$15$	−0.797043	+	0.999460i	−0.205796	+	0.258060i
$16$		0			0
$17$	3.30352	+	1.01900i	0.801222	+	0.247144i	0.668212	−	0.743970i	$-0.267060\pi$
$17$	3.30352	+	1.01900i	0.801222	+	0.247144i	0.133010	+	0.991115i	$0.457536\pi$
$18$		0			0
$19$	1.51977	+	2.63232i	0.348659	+	0.603895i	0.986012	−	0.166677i	$-0.0533038\pi$
$19$	1.51977	+	2.63232i	0.348659	+	0.603895i	−0.637352	+	0.770572i	$0.719970\pi$
$20$		0			0
$21$	1.27351	−	1.32522i	0.277902	−	0.289186i
$22$		0			0
$23$	7.69889	−	2.37479i	1.60533	−	0.495179i	0.642727	−	0.766095i	$-0.277803\pi$
$23$	7.69889	−	2.37479i	1.60533	−	0.495179i	0.962603	+	0.270916i	$0.0873266\pi$
$24$		0			0
$25$	−0.589506	−	1.50204i	−0.117901	−	0.300407i
$26$		0			0
$27$	−0.852883	+	3.73672i	−0.164137	+	0.719133i
$28$		0			0
$29$	0.392906	+	1.72143i	0.0729607	+	0.319662i	0.998218	−	0.0596793i	$-0.0190078\pi$
$29$	0.392906	+	1.72143i	0.0729607	+	0.319662i	−0.925257	+	0.379341i	$0.876151\pi$
$30$		0			0
$31$	−2.70101	+	4.67829i	−0.485116	+	0.840246i	−0.999854	−	0.0171017i	$-0.994556\pi$
$31$	−2.70101	+	4.67829i	−0.485116	+	0.840246i	0.514737	+	0.857348i	$0.327889\pi$
$32$		0			0
$33$	0.207585	+	2.77003i	0.0361360	+	0.482201i
$34$		0			0
$35$	−1.35344	−	4.67687i	−0.228773	−	0.790536i
$36$		0			0
$37$	−4.51246	+	4.18695i	−0.741844	+	0.688331i	−0.957595	−	0.288118i	$-0.906971\pi$
$37$	−4.51246	+	4.18695i	−0.741844	+	0.688331i	0.215751	+	0.976448i	$0.430780\pi$
$38$		0			0
$39$	3.32254	−	2.26527i	0.532032	−	0.362733i
$40$		0			0
$41$	2.82949	−	1.36261i	0.441893	−	0.212804i	−0.199689	−	0.979859i	$-0.563993\pi$
$41$	2.82949	−	1.36261i	0.441893	−	0.212804i	0.641581	+	0.767055i	$0.278279\pi$
$42$		0			0
$43$	3.50635	+	1.68857i	0.534714	+	0.257505i	0.681697	−	0.731634i	$-0.261242\pi$
$43$	3.50635	+	1.68857i	0.534714	+	0.257505i	−0.146983	+	0.989139i	$0.546956\pi$
$44$		0			0
$45$	3.39596	+	3.15099i	0.506239	+	0.469721i
$46$		0			0
$47$	2.66104	−	6.78022i	0.388153	−	0.988997i	−0.594592	−	0.804028i	$-0.702686\pi$
$47$	2.66104	−	6.78022i	0.388153	−	0.988997i	0.982744	−	0.184969i	$-0.0592185\pi$
$48$		0			0
$49$	1.31782	+	6.87483i	0.188260	+	0.982119i
$50$		0			0
$51$	−0.877392	+	2.23556i	−0.122859	+	0.313041i
$52$		0			0
$53$	6.56061	+	6.08735i	0.901169	+	0.836162i	0.987094	−	0.160139i	$-0.0511944\pi$
$53$	6.56061	+	6.08735i	0.901169	+	0.836162i	−0.0859259	+	0.996302i	$0.527385\pi$
$54$		0			0
$55$	6.62979	+	3.19274i	0.893961	+	0.430509i
$56$		0			0
$57$	−1.90239	+	0.916142i	−0.251978	+	0.121346i
$58$		0			0
$59$	−5.93817	+	4.04858i	−0.773084	+	0.527080i	−0.884414	−	0.466703i	$-0.845442\pi$
$59$	−5.93817	+	4.04858i	−0.773084	+	0.527080i	0.111329	+	0.993784i	$0.464489\pi$
$60$		0			0
$61$	2.83727	−	2.63260i	0.363276	−	0.337071i	−0.477324	−	0.878727i	$-0.658393\pi$
$61$	2.83727	−	2.63260i	0.363276	−	0.337071i	0.840600	+	0.541657i	$0.182203\pi$
$62$		0			0
$63$	−4.44412	−	4.96103i	−0.559907	−	0.625031i
$64$		0			0
$65$	−0.796066	−	10.6228i	−0.0987398	−	1.31759i
$66$		0			0
$67$	0.927324	−	1.60617i	0.113291	−	0.196225i	−0.803804	−	0.594894i	$-0.797194\pi$
$67$	0.927324	−	1.60617i	0.113291	−	0.196225i	0.917095	+	0.398668i	$0.130528\pi$
$68$		0			0
$69$	1.24542	+	5.45656i	0.149931	+	0.656892i
$70$		0			0
$71$	−1.61191	+	7.06223i	−0.191298	+	0.838133i	0.784616	+	0.619981i	$0.212860\pi$
$71$	−1.61191	+	7.06223i	−0.191298	+	0.838133i	−0.975915	+	0.218152i	$0.929997\pi$
$72$		0			0
$73$	−4.28338	−	10.9139i	−0.501332	−	1.27737i	−0.927870	−	0.372904i	$-0.878362\pi$
$73$	−4.28338	−	10.9139i	−0.501332	−	1.27737i	0.426538	−	0.904470i	$-0.359733\pi$
$74$		0			0
$75$	1.07111	−	0.330395i	0.123681	−	0.0381507i
$76$		0			0
$77$	−9.06819	−	5.44935i	−1.03342	−	0.621012i
$78$		0			0
$79$	−2.23103	−	3.86426i	−0.251011	−	0.434763i	0.712794	−	0.701374i	$-0.247430\pi$
$79$	−2.23103	−	3.86426i	−0.251011	−	0.434763i	−0.963804	+	0.266611i	$0.914096\pi$
$80$		0			0
$81$	4.67248	+	1.44127i	0.519164	+	0.160141i
$82$		0			0
$83$	3.42482	−	4.29459i	0.375923	−	0.471393i	−0.557497	−	0.830179i	$-0.688238\pi$
$83$	3.42482	−	4.29459i	0.375923	−	0.471393i	0.933420	+	0.358787i	$0.116809\pi$
$84$		0			0
$85$	3.96656	+	4.97390i	0.430233	+	0.539496i
$86$		0			0
$87$	−1.21289	+	0.182814i	−0.130035	+	0.0195997i
$88$		0			0
$89$	−11.3049	−	1.70393i	−1.19831	−	0.180617i	−0.480590	−	0.876945i	$-0.659578\pi$
$89$	−11.3049	−	1.70393i	−1.19831	−	0.180617i	−0.717723	+	0.696328i	$0.754816\pi$
$90$		0			0
$91$	−0.268082	+	15.3132i	−0.0281026	+	1.60526i
$92$		0			0
$93$	−3.10059	−	2.11395i	−0.321516	−	0.219206i
$94$		0			0
$95$	−0.417998	+	5.57779i	−0.0428857	+	0.572269i
$96$		0			0
$97$	9.72695			0.987622			0.493811	−	0.869569i	$-0.335603\pi$
$97$	9.72695			0.987622			0.493811	+	0.869569i	$0.335603\pi$
$98$		0			0
$99$	10.0664			1.01172
$100$		0			0
$101$	−0.595353	+	7.94443i	−0.0592398	+	0.790500i	0.885909	+	0.463859i	$0.153536\pi$
$101$	−0.595353	+	7.94443i	−0.0592398	+	0.790500i	−0.945149	+	0.326641i	$0.894083\pi$
$102$		0			0
$103$	−14.6593	−	9.99453i	−1.44442	−	0.984790i	−0.995847	−	0.0910448i	$-0.970979\pi$
$103$	−14.6593	−	9.99453i	−1.44442	−	0.984790i	−0.448575	−	0.893745i	$-0.648068\pi$
$104$		0			0
$105$	3.31009	−	0.694781i	0.323031	−	0.0678037i
$106$		0			0
$107$	3.03234	+	0.457052i	0.293147	+	0.0441849i	0.293969	−	0.955815i	$-0.405024\pi$
$107$	3.03234	+	0.457052i	0.293147	+	0.0441849i	−0.000822121		1.00000i	$0.500262\pi$
$108$		0			0
$109$	13.0815	−	1.97171i	1.25298	−	0.188856i	0.511176	−	0.859476i	$-0.329210\pi$
$109$	13.0815	−	1.97171i	1.25298	−	0.188856i	0.741801	+	0.670620i	$0.233972\pi$
$110$		0			0
$111$	−2.66618	−	3.34329i	−0.253063	−	0.317331i
$112$		0			0
$113$	−6.47458	+	8.11886i	−0.609077	+	0.763758i	−0.986762	−	0.162176i	$-0.948149\pi$
$113$	−6.47458	+	8.11886i	−0.609077	+	0.763758i	0.377685	+	0.925934i	$0.376720\pi$
$114$		0			0
$115$	14.1677	+	4.37015i	1.32114	+	0.407519i
$116$		0			0
$117$	−7.28634	−	12.6203i	−0.673623	−	1.16675i
$118$		0			0
$119$	−5.01943	−	7.64636i	−0.460130	−	0.700940i
$120$		0			0
$121$	4.76797	−	1.47072i	0.433452	−	0.133702i
$122$		0			0
$123$	0.797038	+	2.03082i	0.0718665	+	0.183113i
$124$		0			0
$125$	2.70818	−	11.8653i	0.242227	−	1.06127i
$126$		0			0
$127$	−2.76490	−	12.1138i	−0.245346	−	1.07493i	−0.936071	−	0.351812i	$-0.885566\pi$
$127$	−2.76490	−	12.1138i	−0.245346	−	1.07493i	0.690725	−	0.723117i	$-0.257291\pi$
$128$		0			0
$129$	−1.35175	+	2.34131i	−0.119015	+	0.206141i
$130$		0			0
$131$	0.551935	+	7.36506i	0.0482228	+	0.643488i	0.967984	+	0.251011i	$0.0807629\pi$
$131$	0.551935	+	7.36506i	0.0482228	+	0.643488i	−0.919762	+	0.392478i	$0.871618\pi$
$132$		0			0
$133$	1.33759	−	7.92985i	0.115983	−	0.687605i
$134$		0			0
$135$	−5.17039	+	4.79742i	−0.444997	+	0.412897i
$136$		0			0
$137$	−10.1511	+	6.92090i	−0.867266	+	0.591292i	−0.913136	−	0.407655i	$-0.866346\pi$
$137$	−10.1511	+	6.92090i	−0.867266	+	0.591292i	0.0458697	+	0.998947i	$0.485394\pi$
$138$		0			0
$139$	−1.06666	+	0.513677i	−0.0904730	+	0.0435695i	−0.478573	−	0.878048i	$-0.658846\pi$
$139$	−1.06666	+	0.513677i	−0.0904730	+	0.0435695i	0.388100	+	0.921617i	$0.373132\pi$
$140$		0			0
$141$	4.55874	+	2.19537i	0.383915	+	0.184884i
$142$		0			0
$143$	−16.9682	−	15.7442i	−1.41896	−	1.31660i
$144$		0			0
$145$	−1.18710	+	3.02467i	−0.0985831	+	0.251186i
$146$		0			0
$147$	−4.83084	+	0.556001i	−0.398441	+	0.0458582i
$148$		0			0
$149$	5.82474	−	14.8412i	0.477181	−	1.21584i	−0.466364	−	0.884593i	$-0.654436\pi$
$149$	5.82474	−	14.8412i	0.477181	−	1.21584i	0.943545	−	0.331245i	$-0.107469\pi$
$150$		0			0
$151$	−9.02056	−	8.36986i	−0.734083	−	0.681129i	0.221729	−	0.975108i	$-0.428830\pi$
$151$	−9.02056	−	8.36986i	−0.734083	−	0.681129i	−0.955812	+	0.293979i	$0.905020\pi$
$152$		0			0
$153$	7.84116	+	3.77610i	0.633920	+	0.305280i
$154$		0			0
$155$	−8.95647	+	4.31321i	−0.719401	+	0.346445i
$156$		0			0
$157$	−18.0040	+	12.2749i	−1.43688	+	0.979647i	−0.440227	+	0.897887i	$0.645102\pi$
$157$	−18.0040	+	12.2749i	−1.43688	+	0.979647i	−0.996652	+	0.0817605i	$0.973946\pi$
$158$		0			0
$159$	−4.55749	+	4.22873i	−0.361432	+	0.335360i
$160$		0			0
$161$	−19.7035	−	8.13388i	−1.55285	−	0.641040i
$162$		0			0
$163$	−0.641955	−	8.56630i	−0.0502818	−	0.670964i	−0.964219	−	0.265108i	$-0.914592\pi$
$163$	−0.641955	−	8.56630i	−0.0502818	−	0.670964i	0.913937	−	0.405856i	$-0.133027\pi$
$164$		0			0
$165$	−2.55589	+	4.42693i	−0.198976	+	0.344636i
$166$		0			0
$167$	0.890473	+	3.90142i	0.0689069	+	0.301901i	0.997624	−	0.0688871i	$-0.0219448\pi$
$167$	0.890473	+	3.90142i	0.0689069	+	0.301901i	−0.928718	+	0.370788i	$0.879088\pi$
$168$		0			0
$169$	−4.56375	+	19.9951i	−0.351058	+	1.53808i
$170$		0			0
$171$	2.79552	+	7.12288i	0.213779	+	0.544700i
$172$		0			0
$173$	−17.6452	+	5.44282i	−1.34154	+	0.413810i	−0.880701	−	0.473673i	$-0.842928\pi$
$173$	−17.6452	+	5.44282i	−1.34154	+	0.413810i	−0.460839	+	0.887484i	$0.652452\pi$
$174$		0			0
$175$	−1.32956	+	4.05681i	−0.100505	+	0.306666i
$176$		0			0
$177$	−2.49631	−	4.32374i	−0.187634	−	0.324992i
$178$		0			0
$179$	−13.6180	−	4.20059i	−1.01785	−	0.313966i	−0.259454	−	0.965755i	$-0.583543\pi$
$179$	−13.6180	−	4.20059i	−1.01785	−	0.313966i	−0.758400	+	0.651789i	$0.774019\pi$
$180$		0			0
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	0.119211	+	0.992869i	$0.461963\pi$
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	−0.994503	+	0.104712i	$0.966608\pi$
$182$		0			0
$183$	1.67640	+	2.10214i	0.123923	+	0.155395i
$184$		0			0
$185$	−11.2014	+	1.68834i	−0.823541	+	0.124129i
$186$		0			0
$187$	13.6696	+	2.06036i	0.999618	+	0.150668i
$188$		0			0
$189$	8.03776	−	6.18287i	0.584661	−	0.449738i
$190$		0			0
$191$	−13.7270	−	9.35892i	−0.993252	−	0.677188i	−0.0464221	−	0.998922i	$-0.514782\pi$
$191$	−13.7270	−	9.35892i	−0.993252	−	0.677188i	−0.946830	+	0.321734i	$0.895734\pi$
$192$		0			0
$193$	1.99942	−	26.6805i	0.143922	−	1.92050i	−0.196989	−	0.980406i	$-0.563116\pi$
$193$	1.99942	−	26.6805i	0.143922	−	1.92050i	0.340910	−	0.940096i	$-0.389265\pi$
$194$		0			0
$195$	7.40006			0.529929
$196$		0			0
$197$	−7.32209			−0.521677			−0.260839	−	0.965382i	$-0.583999\pi$
$197$	−7.32209			−0.521677			−0.260839	+	0.965382i	$0.583999\pi$
$198$		0			0
$199$	0.284299	−	3.79370i	0.0201534	−	0.268928i	−0.978020	−	0.208512i	$-0.933138\pi$
$199$	0.284299	−	3.79370i	0.0201534	−	0.268928i	0.998173	−	0.0604166i	$-0.0192429\pi$
$200$		0			0
$201$	1.06451	+	0.725769i	0.0750846	+	0.0511918i
$202$		0			0
$203$	2.10030	−	4.17285i	0.147412	−	0.292877i
$204$		0			0
$205$	5.71467	+	0.861349i	0.399130	+	0.0601592i
$206$		0			0
$207$	20.0560	−	3.02295i	1.39399	−	0.210109i
$208$		0			0
$209$	7.57803	+	9.50255i	0.524184	+	0.657305i
$210$		0			0
$211$	−13.3917	+	16.7927i	−0.921923	+	1.15605i	0.0654839	+	0.997854i	$0.479141\pi$
$211$	−13.3917	+	16.7927i	−0.921923	+	1.15605i	−0.987407	+	0.158201i	$0.949431\pi$
$212$		0			0
$213$	−4.80856	−	1.48324i	−0.329477	−	0.101630i
$214$		0			0
$215$	3.58085	+	6.20222i	0.244212	+	0.422988i
$216$		0			0
$217$	13.3938	−	4.98793i	0.909230	−	0.338603i
$218$		0			0
$219$	7.78277	−	2.40067i	0.525911	−	0.162222i
$220$		0			0
$221$	−7.31130	−	18.6289i	−0.491811	−	1.25312i
$222$		0			0
$223$	1.33464	−	5.84744i	0.0893741	−	0.391573i	−0.910379	−	0.413774i	$-0.864210\pi$
$223$	1.33464	−	5.84744i	0.0893741	−	0.391573i	0.999754	+	0.0222010i	$0.00706738\pi$
$224$		0			0
$225$	−0.903894	−	3.96022i	−0.0602596	−	0.264014i
$226$		0			0
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	−0.986308	−	0.164913i	$-0.947266\pi$
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	0.635973	+	0.771711i	$0.280599\pi$
$228$		0			0
$229$	0.666120	+	8.88875i	0.0440184	+	0.587385i	0.974984	+	0.222277i	$0.0713489\pi$
$229$	0.666120	+	8.88875i	0.0440184	+	0.587385i	−0.930965	+	0.365108i	$0.881032\pi$
$230$		0			0
$231$	4.24570	−	5.99894i	0.279347	−	0.394701i
$232$		0			0
$233$	1.15069	−	1.06768i	0.0753841	−	0.0699462i	−0.641581	−	0.767055i	$-0.721721\pi$
$233$	1.15069	−	1.06768i	0.0753841	−	0.0699462i	0.716965	+	0.697109i	$0.245531\pi$
$234$		0			0
$235$	11.0746	−	7.55055i	0.722429	−	0.492544i
$236$		0			0
$237$	2.79272	−	1.34490i	0.181407	−	0.0873608i
$238$		0			0
$239$	20.8411	+	10.0366i	1.34810	+	0.649211i	0.961950	−	0.273225i	$-0.0880903\pi$
$239$	20.8411	+	10.0366i	1.34810	+	0.649211i	0.386150	+	0.922436i	$0.373805\pi$
$240$		0			0
$241$	−3.76369	−	3.49219i	−0.242441	−	0.224952i	0.549588	−	0.835436i	$-0.314785\pi$
$241$	−3.76369	−	3.49219i	−0.242441	−	0.224952i	−0.792029	+	0.610484i	$0.790975\pi$
$242$		0			0
$243$	−5.44184	+	13.8656i	−0.349094	+	0.889477i
$244$		0			0
$245$	−5.12300	+	11.8190i	−0.327296	+	0.755090i
$246$		0			0
$247$	6.42819	−	16.3788i	0.409016	−	1.04216i
$248$		0			0
$249$	2.79721	+	2.59543i	0.177266	+	0.164479i
$250$		0			0
$251$	−4.60431	−	2.21732i	−0.290622	−	0.139956i	0.282893	−	0.959152i	$-0.408706\pi$
$251$	−4.60431	−	2.21732i	−0.290622	−	0.139956i	−0.573514	+	0.819196i	$0.694420\pi$
$252$		0			0
$253$	29.0264	−	13.9784i	1.82488	−	0.878814i
$254$		0			0
$255$	−3.65150	+	2.48955i	−0.228666	+	0.155902i
$256$		0			0
$257$	11.5498	−	10.7166i	0.720455	−	0.668484i	−0.232155	−	0.972679i	$-0.574578\pi$
$257$	11.5498	−	10.7166i	0.720455	−	0.668484i	0.952610	+	0.304195i	$0.0983873\pi$
$258$		0			0
$259$	16.2598	−	0.932625i	1.01033	−	0.0579505i
$260$		0			0
$261$	0.332177	+	4.43259i	0.0205612	+	0.274371i
$262$		0			0
$263$	−0.926808	+	1.60528i	−0.0571494	+	0.0989857i	−0.893185	−	0.449690i	$-0.851534\pi$
$263$	−0.926808	+	1.60528i	−0.0571494	+	0.0989857i	0.836035	+	0.548676i	$0.184868\pi$
$264$		0			0
$265$	3.66480	+	16.0566i	0.225127	+	0.986346i
$266$		0			0
$267$	1.76724	−	7.74280i	0.108153	−	0.473851i
$268$		0			0
$269$	0.548519	+	1.39760i	0.0334438	+	0.0852134i	0.946620	−	0.322351i	$-0.104473\pi$
$269$	0.548519	+	1.39760i	0.0334438	+	0.0852134i	−0.913176	+	0.407565i	$0.866378\pi$
$270$		0			0
$271$	−15.7625	+	4.86208i	−0.957502	+	0.295350i	−0.733845	−	0.679317i	$-0.762276\pi$
$271$	−15.7625	+	4.86208i	−0.957502	+	0.295350i	−0.223658	+	0.974668i	$0.571800\pi$
$272$		0			0
$273$	−10.5940	−	0.980664i	−0.641179	−	0.0593525i
$274$		0			0
$275$	−3.22611	−	5.58779i	−0.194542	−	0.336956i
$276$		0			0
$277$	14.8945	+	4.59433i	0.894921	+	0.276047i	0.707903	−	0.706310i	$-0.249641\pi$
$277$	14.8945	+	4.59433i	0.894921	+	0.276047i	0.187018	+	0.982356i	$0.440118\pi$
$278$		0			0
$279$	−8.47897	+	10.6323i	−0.507622	+	0.636538i
$280$		0			0
$281$	−0.198061	−	0.248361i	−0.0118153	−	0.0148160i	0.775889	−	0.630870i	$-0.217302\pi$
$281$	−0.198061	−	0.248361i	−0.0118153	−	0.0148160i	−0.787704	+	0.616054i	$0.788730\pi$
$282$		0			0
$283$	−21.1609	+	3.18950i	−1.25789	+	0.189596i	−0.743952	−	0.668233i	$-0.767051\pi$
$283$	−21.1609	+	3.18950i	−1.25789	+	0.189596i	−0.513935	+	0.857829i	$0.671813\pi$
$284$		0			0
$285$	−3.84222	−	0.579121i	−0.227593	−	0.0343042i
$286$		0			0
$287$	−8.06706	−	1.99043i	−0.476183	−	0.117492i
$288$		0			0
$289$	−4.17116	−	2.84385i	−0.245362	−	0.167285i
$290$		0			0
$291$	−0.504957	+	6.73818i	−0.0296011	+	0.394999i
$292$		0			0
$293$	−9.40795			−0.549618			−0.274809	−	0.961499i	$-0.588615\pi$
$293$	−9.40795			−0.549618			−0.274809	+	0.961499i	$0.588615\pi$
$294$		0			0
$295$	−13.2257			−0.770029
$296$		0			0
$297$	−1.14534	+	15.2835i	−0.0664592	+	0.886836i
$298$		0			0
$299$	−38.5348	−	26.2726i	−2.22852	−	1.51938i
$300$		0			0
$301$	−4.30447	−	9.35372i	−0.248106	−	0.539139i
$302$		0			0
$303$	−5.47246	−	0.824840i	−0.314385	−	0.0473858i
$304$		0			0
$305$	7.04302	−	1.06156i	0.403282	−	0.0607850i
$306$		0			0
$307$	16.7984	+	21.0645i	0.958736	+	1.20222i	0.979297	+	0.202429i	$0.0648834\pi$
$307$	16.7984	+	21.0645i	0.958736	+	1.20222i	−0.0205607	+	0.999789i	$0.506545\pi$
$308$		0			0
$309$	7.68455	−	9.63612i	0.437159	−	0.548179i
$310$		0			0
$311$	11.1908	+	3.45192i	0.634574	+	0.195740i	0.595320	−	0.803489i	$-0.297025\pi$
$311$	11.1908	+	3.45192i	0.634574	+	0.195740i	0.0392546	+	0.999229i	$0.487502\pi$
$312$		0			0
$313$	9.35940	+	16.2110i	0.529025	+	0.916297i	0.999427	+	0.0338455i	$0.0107754\pi$
$313$	9.35940	+	16.2110i	0.529025	+	0.916297i	−0.470402	+	0.882452i	$0.655891\pi$
$314$		0			0
$315$	−1.61435	−	12.1500i	−0.0909585	−	0.684575i
$316$		0			0
$317$	19.6159	−	6.05070i	1.10174	−	0.339841i	0.310021	−	0.950730i	$-0.399664\pi$
$317$	19.6159	−	6.05070i	1.10174	−	0.339841i	0.791717	+	0.610889i	$0.209188\pi$
$318$		0			0
$319$	2.57950	+	6.57245i	0.144424	+	0.367987i
$320$		0			0
$321$	−0.474033	+	2.07687i	−0.0264579	+	0.115920i
$322$		0			0
$323$	2.33826	+	10.2446i	0.130104	+	0.570023i
$324$		0			0
$325$	−4.67028	+	8.08915i	−0.259060	+	0.448706i
$326$		0			0
$327$	0.686770	+	9.16431i	0.0379785	+	0.506788i
$328$		0			0
$329$	−16.8552	+	9.34185i	−0.929257	+	0.515033i
$330$		0			0
$331$	12.7258	−	11.8078i	0.699473	−	0.649016i	−0.248034	−	0.968751i	$-0.579784\pi$
$331$	12.7258	−	11.8078i	0.699473	−	0.649016i	0.947507	+	0.319735i	$0.103594\pi$
$332$		0			0
$333$	−12.8039	+	8.72953i	−0.701647	+	0.478375i
$334$		0			0
$335$	3.07498	−	1.48083i	0.168004	−	0.0809065i
$336$		0			0
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	0.168894	−	0.985634i	$-0.445981\pi$
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	−0.665296	+	0.746579i	$0.731695\pi$
$338$		0			0
$339$	−5.28809	−	4.90663i	−0.287209	−	0.266491i
$340$		0			0
$341$	−7.89177	+	20.1079i	−0.427363	+	1.08890i
$342$		0			0
$343$	8.90042	−	16.2414i	0.480578	−	0.876952i
$344$		0			0
$345$	−3.76284	+	9.58755i	−0.202584	+	0.516176i
$346$		0			0
$347$	10.6803	+	9.90990i	0.573350	+	0.531991i	0.912679	−	0.408677i	$-0.134010\pi$
$347$	10.6803	+	9.90990i	0.573350	+	0.531991i	−0.339329	+	0.940668i	$0.610200\pi$
$348$		0			0
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	0.580359	−	0.814361i	$-0.302912\pi$
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	−0.274845	+	0.961489i	$0.588627\pi$
$350$		0			0
$351$	19.9899	−	9.62663i	1.06698	−	0.513832i
$352$		0			0
$353$	28.7868	−	19.6265i	1.53217	−	1.04461i	0.555073	−	0.831801i	$-0.312690\pi$
$353$	28.7868	−	19.6265i	1.53217	−	1.04461i	0.977093	−	0.212812i	$-0.0682622\pi$
$354$		0			0
$355$	−9.77181	+	9.06691i	−0.518634	+	0.481222i
$356$		0			0
$357$	5.55746	−	3.08017i	0.294132	−	0.163020i
$358$		0			0
$359$	1.28072	+	17.0900i	0.0675938	+	0.901977i	0.923193	+	0.384337i	$0.125570\pi$
$359$	1.28072	+	17.0900i	0.0675938	+	0.901977i	−0.855599	+	0.517639i	$0.826811\pi$
$360$		0			0
$361$	4.88060	−	8.45345i	0.256874	−	0.444918i
$362$		0			0
$363$	0.771298	+	3.37928i	0.0404827	+	0.177366i
$364$		0			0
$365$	4.80098	−	21.0345i	0.251295	−	1.10099i
$366$		0			0
$367$	12.1106	+	30.8572i	0.632166	+	1.61073i	0.782893	+	0.622157i	$0.213743\pi$
$367$	12.1106	+	30.8572i	0.632166	+	1.61073i	−0.150727	+	0.988575i	$0.548161\pi$
$368$		0			0
$369$	7.55474	−	2.33033i	0.393284	−	0.121312i
$370$		0			0
$371$	−3.11875	−	23.4724i	−0.161917	−	1.21863i
$372$		0			0
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	0.833638	−	0.552311i	$-0.186254\pi$
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	−0.895135	+	0.445796i	$0.852921\pi$
$374$		0			0
$375$	8.07891	+	2.49201i	0.417193	+	0.128687i
$376$		0			0
$377$	6.37279	−	7.99122i	0.328215	−	0.411569i
$378$		0			0
$379$	9.78749	+	12.2731i	0.502749	+	0.630428i	0.966847	−	0.255356i	$-0.0821927\pi$
$379$	9.78749	+	12.2731i	0.502749	+	0.630428i	−0.464098	+	0.885784i	$0.653621\pi$
$380$		0			0
$381$	8.53519	−	1.28647i	0.437271	−	0.0659080i
$382$		0			0
$383$	−16.4926	−	2.48586i	−0.842733	−	0.127022i	−0.286533	−	0.958070i	$-0.592503\pi$
$383$	−16.4926	−	2.48586i	−0.842733	−	0.127022i	−0.556200	+	0.831049i	$0.687741\pi$
$384$		0			0
$385$	−8.13887	−	17.6859i	−0.414795	−	0.901359i
$386$		0			0
$387$	8.09484	+	5.51897i	0.411484	+	0.280545i
$388$		0			0
$389$	−1.15309	+	15.3869i	−0.0584640	+	0.780148i	0.888514	+	0.458850i	$0.151738\pi$
$389$	−1.15309	+	15.3869i	−0.0584640	+	0.780148i	−0.946978	+	0.321299i	$0.895881\pi$
$390$		0			0
$391$	27.8534			1.40861
$392$		0			0
$393$	−5.13067			−0.258808
$394$		0			0
$395$	0.613623	−	8.18823i	0.0308747	−	0.411995i
$396$		0			0
$397$	−21.4778	−	14.6433i	−1.07794	−	0.734926i	−0.112002	−	0.993708i	$-0.535726\pi$
$397$	−21.4778	−	14.6433i	−1.07794	−	0.734926i	−0.965936	+	0.258782i	$0.916679\pi$
$398$		0			0
$399$	5.42383	+	1.33825i	0.271531	+	0.0669965i
$400$		0			0
$401$	−20.8981	−	3.14988i	−1.04360	−	0.157298i	−0.395199	−	0.918595i	$-0.629325\pi$
$401$	−20.8981	−	3.14988i	−1.04360	−	0.157298i	−0.648403	+	0.761298i	$0.724563\pi$
$402$		0			0
$403$	30.9216	−	4.66068i	1.54031	−	0.232165i
$404$		0			0
$405$	5.61027	+	7.03505i	0.278776	+	0.349574i
$406$		0			0
$407$	−15.3471	+	19.2447i	−0.760730	+	0.953925i
$408$		0			0
$409$	−2.81007	−	0.866793i	−0.138949	−	0.0428601i	0.224501	−	0.974474i	$-0.427925\pi$
$409$	−2.81007	−	0.866793i	−0.138949	−	0.0428601i	−0.363450	+	0.931614i	$0.618401\pi$
$410$		0			0
$411$	−4.26736	−	7.39128i	−0.210493	−	0.364585i
$412$		0			0
$413$	18.9341	+	1.75268i	0.931684	+	0.0862438i
$414$		0			0
$415$	9.65924	−	2.97948i	0.474153	−	0.146257i
$416$		0			0
$417$	−0.300467	−	0.765578i	−0.0147139	−	0.0374905i
$418$		0			0
$419$	2.46363	−	10.7939i	0.120356	−	0.527315i	−0.878422	−	0.477887i	$-0.841403\pi$
$419$	2.46363	−	10.7939i	0.120356	−	0.527315i	0.998778	−	0.0494281i	$-0.0157399\pi$
$420$		0			0
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	0.965090	+	0.261919i	$0.0843554\pi$
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	−0.755873	+	0.654718i	$0.772787\pi$
$422$		0			0
$423$	9.16811	−	15.8796i	0.445769	−	0.772094i
$424$		0			0
$425$	−0.416868	−	5.56272i	−0.0202211	−	0.269832i
$426$		0			0
$427$	−10.2236	+	0.586401i	−0.494753	+	0.0283779i
$428$		0			0
$429$	11.7874	−	10.9371i	0.569102	−	0.528049i
$430$		0			0
$431$	8.51664	−	5.80655i	0.410232	−	0.279692i	−0.340569	−	0.940219i	$-0.610620\pi$
$431$	8.51664	−	5.80655i	0.410232	−	0.279692i	0.750802	+	0.660528i	$0.229667\pi$
$432$		0			0
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	−0.362447	−	0.932004i	$-0.618059\pi$
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	0.502688	+	0.864468i	$0.332344\pi$
$434$		0			0
$435$	−2.03367	−	0.979361i	−0.0975068	−	0.0469568i
$436$		0			0
$437$	17.9518	+	16.6568i	0.858749	+	0.796803i
$438$		0			0
$439$	13.2114	−	33.6621i	0.630547	−	1.60661i	−0.155077	−	0.987902i	$-0.549563\pi$
$439$	13.2114	−	33.6621i	0.630547	−	1.60661i	0.785624	−	0.618704i	$-0.212342\pi$
$440$		0			0
$441$	0.700997	+	17.6080i	0.0333808	+	0.838478i
$442$		0			0
$443$	3.58165	−	9.12590i	0.170169	−	0.433584i	−0.820193	−	0.572087i	$-0.806134\pi$
$443$	3.58165	−	9.12590i	0.170169	−	0.433584i	0.990362	+	0.138503i	$0.0442291\pi$
$444$		0			0
$445$	−15.4223	−	14.3098i	−0.731087	−	0.678349i
$446$		0			0
$447$	9.97860	+	4.80544i	0.471972	+	0.227290i
$448$		0			0
$449$	−6.60499	+	3.18080i	−0.311709	+	0.150111i	−0.583197	−	0.812331i	$-0.698198\pi$
$449$	−6.60499	+	3.18080i	−0.311709	+	0.150111i	0.271488	+	0.962442i	$0.412484\pi$
$450$		0			0
$451$	10.3759	−	7.07414i	0.488580	−	0.333108i
$452$		0			0
$453$	6.26636	−	5.81433i	0.294419	−	0.273181i
$454$		0			0
$455$	−16.2818	+	23.0052i	−0.763302	+	1.07850i
$456$		0			0
$457$	2.19345	+	29.2696i	0.102605	+	1.36917i	0.776394	+	0.630248i	$0.217047\pi$
$457$	2.19345	+	29.2696i	0.102605	+	1.36917i	−0.673789	+	0.738924i	$0.735334\pi$
$458$		0			0
$459$	−6.62524	+	11.4753i	−0.309240	+	0.535619i
$460$		0			0
$461$	0.0546636	+	0.239497i	0.00254594	+	0.0111545i	0.976185	−	0.216940i	$-0.0696076\pi$
$461$	0.0546636	+	0.239497i	0.00254594	+	0.0111545i	−0.973639	+	0.228095i	$0.926750\pi$
$462$		0			0
$463$	−2.07391	+	9.08638i	−0.0963826	+	0.422280i	−0.999981	−	0.00610002i	$-0.998058\pi$
$463$	−2.07391	+	9.08638i	−0.0963826	+	0.422280i	0.903599	+	0.428380i	$0.140915\pi$
$464$		0			0
$465$	−2.52294	−	6.42836i	−0.116999	−	0.298108i
$466$		0			0
$467$	10.1934	−	3.14424i	0.471693	−	0.145498i	−0.0497897	−	0.998760i	$-0.515855\pi$
$467$	10.1934	−	3.14424i	0.471693	−	0.145498i	0.521483	+	0.853262i	$0.325379\pi$
$468$		0			0
$469$	−4.59842	+	1.71248i	−0.212335	+	0.0790749i
$470$		0			0
$471$	−7.56861	−	13.1092i	−0.348743	−	0.604041i
$472$		0			0
$473$	14.8706	+	4.58698i	0.683752	+	0.210910i
$474$		0			0
$475$	3.05793	−	3.83452i	0.140307	−	0.175940i
$476$		0			0
$477$	14.0474	+	17.6149i	0.643185	+	0.806529i
$478$		0			0
$479$	12.9253	−	1.94818i	0.590574	−	0.0890147i	0.153045	−	0.988219i	$-0.451092\pi$
$479$	12.9253	−	1.94818i	0.590574	−	0.0890147i	0.437529	+	0.899204i	$0.355854\pi$
$480$		0			0
$481$	35.2357	+	5.31093i	1.60661	+	0.242158i
$482$		0			0
$483$	6.65748	−	13.2270i	0.302926	−	0.601850i
$484$		0			0
$485$	14.7895	+	10.0833i	0.671556	+	0.457859i
$486$		0			0
$487$	−0.223941	+	2.98828i	−0.0101477	+	0.135412i	−0.999977	−	0.00685174i	$-0.997819\pi$
$487$	−0.223941	+	2.98828i	−0.0101477	+	0.135412i	0.989829	+	0.142264i	$0.0454381\pi$
$488$		0			0
$489$	5.96748			0.269859
$490$		0			0
$491$	−5.19765			−0.234567			−0.117283	−	0.993098i	$-0.537419\pi$
$491$	−5.19765			−0.234567			−0.117283	+	0.993098i	$0.537419\pi$
$492$		0			0
$493$	−0.456170	+	6.08716i	−0.0205448	+	0.274152i
$494$		0			0
$495$	15.3057	+	10.4352i	0.687939	+	0.469029i
$496$		0			0
$497$	15.1910	−	11.6853i	0.681410	−	0.524159i
$498$		0			0
$499$	−7.32099	−	1.10346i	−0.327733	−	0.0493978i	−0.0168848	−	0.999857i	$-0.505375\pi$
$499$	−7.32099	−	1.10346i	−0.327733	−	0.0493978i	−0.310848	+	0.950460i	$0.600613\pi$
$500$		0			0
$501$	−2.74887	+	0.414325i	−0.122810	+	0.0185107i
$502$		0			0
$503$	6.13267	+	7.69012i	0.273442	+	0.342886i	0.899524	−	0.436872i	$-0.143914\pi$
$503$	6.13267	+	7.69012i	0.273442	+	0.342886i	−0.626081	+	0.779758i	$0.715342\pi$
$504$		0			0
$505$	−9.14068	+	11.4621i	−0.406755	+	0.510055i
$506$		0			0
$507$	−13.6143	−	4.19947i	−0.604634	−	0.186505i
$508$		0			0
$509$	−15.8336	−	27.4246i	−0.701812	−	1.21557i	−0.967830	−	0.251606i	$-0.919041\pi$
$509$	−15.8336	−	27.4246i	−0.701812	−	1.21557i	0.266018	−	0.963968i	$-0.414292\pi$
$510$		0			0
$511$	−9.66066	+	29.4770i	−0.427362	+	1.30399i
$512$		0			0
$513$	−11.1324	+	3.43390i	−0.491509	+	0.151610i
$514$		0			0
$515$	−11.9282	−	30.3926i	−0.525621	−	1.33926i
$516$		0			0
$517$	6.48102	−	28.3952i	0.285035	−	1.24882i
$518$		0			0
$519$	−2.85441	−	12.5060i	−0.125294	−	0.548951i
$520$		0			0
$521$	−7.33441	+	12.7036i	−0.321326	+	0.556553i	−0.980762	−	0.195208i	$-0.937462\pi$
$521$	−7.33441	+	12.7036i	−0.321326	+	0.556553i	0.659436	+	0.751761i	$0.270795\pi$
$522$		0			0
$523$	1.22630	+	16.3639i	0.0536226	+	0.715543i	0.957625	+	0.288017i	$0.0929959\pi$
$523$	1.22630	+	16.3639i	0.0536226	+	0.715543i	−0.904003	+	0.427527i	$0.859385\pi$
$524$		0			0
$525$	−2.74126	−	1.13163i	−0.119638	−	0.0493884i
$526$		0			0
$527$	−13.6900	+	12.7025i	−0.596348	+	0.553330i
$528$		0			0
$529$	34.6298	−	23.6102i	1.50564	−	1.02653i
$530$		0			0
$531$	−16.3010	+	7.85014i	−0.707403	+	0.340667i
$532$		0			0
$533$	−16.3792	−	7.88778i	−0.709460	−	0.341658i
$534$		0			0
$535$	4.13677	+	3.83836i	0.178848	+	0.165947i
$536$		0			0
$537$	3.61683	−	9.21554i	0.156078	−	0.397680i
$538$		0			0
$539$	9.30795	+	26.3980i	0.400922	+	1.13704i
$540$		0			0
$541$	−3.54489	+	9.03222i	−0.152407	+	0.388326i	−0.986603	−	0.163143i	$-0.947837\pi$
$541$	−3.54489	+	9.03222i	−0.152407	+	0.388326i	0.834196	+	0.551468i	$0.185932\pi$
$542$		0			0
$543$	−9.61787	−	8.92408i	−0.412742	−	0.382969i
$544$		0			0
$545$	21.9338	+	10.5628i	0.939542	+	0.452460i
$546$		0			0
$547$	−20.1772	+	9.71681i	−0.862713	+	0.415461i	−0.812281	−	0.583267i	$-0.801774\pi$
$547$	−20.1772	+	9.71681i	−0.862713	+	0.415461i	−0.0504324	+	0.998727i	$0.516060\pi$
$548$		0			0
$549$	8.05061	−	5.48881i	0.343592	−	0.234257i
$550$		0			0
$551$	−3.93423	+	3.65043i	−0.167604	+	0.155514i
$552$		0			0
$553$	−1.96358	+	11.6411i	−0.0835001	+	0.495028i
$554$		0			0
$555$	−0.588067	−	7.84721i	−0.0249620	−	0.333095i
$556$		0			0
$557$	−21.4133	+	37.0889i	−0.907309	+	1.57151i	−0.0895221	+	0.995985i	$0.528534\pi$
$557$	−21.4133	+	37.0889i	−0.907309	+	1.57151i	−0.817787	+	0.575521i	$0.804799\pi$
$558$		0			0
$559$	−5.01302	−	21.9635i	−0.212028	−	0.928957i
$560$		0			0
$561$	−2.13691	+	9.36240i	−0.0902203	+	0.395281i
$562$		0			0
$563$	4.11282	+	10.4793i	0.173335	+	0.441649i	0.990969	−	0.134088i	$-0.0428104\pi$
$563$	4.11282	+	10.4793i	0.173335	+	0.441649i	−0.817635	+	0.575737i	$0.804715\pi$
$564$		0			0
$565$	−18.2607	+	5.63267i	−0.768232	+	0.236968i
$566$		0			0
$567$	−7.09944	−	10.8149i	−0.298148	−	0.454185i
$568$		0			0
$569$	−17.0173	−	29.4748i	−0.713402	−	1.23565i	−0.963573	−	0.267446i	$-0.913820\pi$
$569$	−17.0173	−	29.4748i	−0.713402	−	1.23565i	0.250171	−	0.968202i	$-0.419513\pi$
$570$		0			0
$571$	9.91625	+	3.05876i	0.414982	+	0.128005i	0.495214	−	0.868771i	$-0.335090\pi$
$571$	9.91625	+	3.05876i	0.414982	+	0.128005i	−0.0802314	+	0.996776i	$0.525566\pi$
$572$		0			0
$573$	7.19585	−	9.02330i	0.300611	−	0.376954i
$574$		0			0
$575$	−8.10557	−	10.1641i	−0.338026	−	0.423871i
$576$		0			0
$577$	−41.1444	+	6.20152i	−1.71286	+	0.258173i	−0.930933	−	0.365191i	$-0.881004\pi$
$577$	−41.1444	+	6.20152i	−1.71286	+	0.258173i	−0.781932	+	0.623364i	$0.785766\pi$
$578$		0			0
$579$	18.3786	+	2.77013i	0.763790	+	0.115123i
$580$		0			0
$581$	−14.2231	+	2.98541i	−0.590075	+	0.123856i
$582$		0			0
$583$	29.5688	+	20.1597i	1.22462	+	0.834929i
$584$		0			0
$585$	2.00404	−	26.7420i	0.0828567	−	1.10565i
$586$		0			0
$587$	−1.39293			−0.0574923			−0.0287461	−	0.999587i	$-0.509151\pi$
$587$	−1.39293			−0.0574923			−0.0287461	+	0.999587i	$0.509151\pi$
$588$		0			0
$589$	−16.4197			−0.676561
$590$		0			0
$591$	0.380113	−	5.07225i	0.0156357	−	0.208645i
$592$		0			0
$593$	−21.4199	−	14.6038i	−0.879610	−	0.599708i	0.0370779	−	0.999312i	$-0.488195\pi$
$593$	−21.4199	−	14.6038i	−0.879610	−	0.599708i	−0.916688	+	0.399605i	$0.869147\pi$
$594$		0			0
$595$	0.294624	−	16.8293i	0.0120784	−	0.689935i
$596$		0			0
$597$	2.61326	+	0.393886i	0.106954	+	0.0161207i
$598$		0			0
$599$	−37.2838	+	5.61963i	−1.52338	+	0.229612i	−0.856731	−	0.515764i	$-0.827508\pi$
$599$	−37.2838	+	5.61963i	−1.52338	+	0.229612i	−0.666645	+	0.745376i	$0.732270\pi$
$600$		0			0
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	0.658253	−	0.752797i	$-0.271296\pi$
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	−0.880398	+	0.474236i	$0.842724\pi$
$602$		0			0
$603$	2.91104	−	3.65032i	0.118547	−	0.148653i
$604$		0			0
$605$	8.77413	+	2.70646i	0.356719	+	0.110033i
$606$		0			0
$607$	8.77440	+	15.1977i	0.356142	+	0.616856i	0.987313	−	0.158788i	$-0.0507586\pi$
$607$	8.77440	+	15.1977i	0.356142	+	0.616856i	−0.631171	+	0.775644i	$0.717425\pi$
$608$		0			0
$609$	2.78164	+	1.67157i	0.112718	+	0.0677354i
$610$		0			0
$611$	−40.2902	+	12.4279i	−1.62997	+	0.502778i
$612$		0			0
$613$	0.961474	+	2.44979i	0.0388336	+	0.0989463i	0.948975	−	0.315352i	$-0.102122\pi$
$613$	0.961474	+	2.44979i	0.0388336	+	0.0989463i	−0.910141	+	0.414298i	$0.864027\pi$
$614$		0			0
$615$	−0.893351	+	3.91403i	−0.0360234	+	0.157829i
$616$		0			0
$617$	6.31918	+	27.6861i	0.254401	+	1.11460i	0.927138	+	0.374720i	$0.122261\pi$
$617$	6.31918	+	27.6861i	0.254401	+	1.11460i	−0.672737	+	0.739881i	$0.734882\pi$
$618$		0			0
$619$	−12.7296	+	22.0482i	−0.511644	+	0.886194i	0.488265	+	0.872696i	$0.337630\pi$
$619$	−12.7296	+	22.0482i	−0.511644	+	0.886194i	−0.999909	+	0.0134982i	$0.995703\pi$
$620$		0			0
$621$	2.30769	+	30.7940i	0.0926046	+	1.23572i
$622$		0			0
$623$	20.1824	+	22.5299i	0.808591	+	0.902640i
$624$		0			0
$625$	10.5035	−	9.74584i	0.420141	−	0.389834i
$626$		0			0
$627$	−6.97613	+	4.75625i	−0.278600	+	0.189946i
$628$		0			0
$629$	−19.1735	+	9.23348i	−0.764499	+	0.368163i
$630$		0			0
$631$	6.67445	+	3.21424i	0.265706	+	0.127957i	0.561994	−	0.827142i	$-0.310035\pi$
$631$	6.67445	+	3.21424i	0.265706	+	0.127957i	−0.296288	+	0.955099i	$0.595749\pi$
$632$		0			0
$633$	−10.9376	−	10.1486i	−0.434732	−	0.403372i
$634$		0			0
$635$	8.35369	−	21.2848i	0.331506	−	0.844663i
$636$		0			0
$637$	26.3579	−	30.7769i	1.04434	−	1.21943i
$638$		0			0
$639$	−6.66231	+	16.9753i	−0.263557	+	0.671532i
$640$		0			0
$641$	10.2302	+	9.49228i	0.404070	+	0.374922i	0.855865	−	0.517200i	$-0.173025\pi$
$641$	10.2302	+	9.49228i	0.404070	+	0.374922i	−0.451794	+	0.892122i	$0.649216\pi$
$642$		0			0
$643$	−39.4273	−	18.9872i	−1.55486	−	0.748782i	−0.558144	−	0.829744i	$-0.688486\pi$
$643$	−39.4273	−	18.9872i	−1.55486	−	0.748782i	−0.996717	+	0.0809624i	$0.974201\pi$
$644$		0			0
$645$	−4.48238	+	2.15860i	−0.176493	+	0.0849947i
$646$		0			0
$647$	−12.5605	+	8.56364i	−0.493806	+	0.336671i	−0.784483	−	0.620150i	$-0.787072\pi$
$647$	−12.5605	+	8.56364i	−0.493806	+	0.336671i	0.290677	+	0.956821i	$0.406119\pi$
$648$		0			0
$649$	−21.0669	+	19.5473i	−0.826950	+	0.767297i
$650$		0			0
$651$	2.75999	+	9.53726i	0.108172	+	0.373795i
$652$		0			0
$653$	−0.857998	−	11.4492i	−0.0335760	−	0.448041i	−0.988503	−	0.151201i	$-0.951686\pi$
$653$	−0.857998	−	11.4492i	−0.0335760	−	0.448041i	0.954927	−	0.296841i	$-0.0959330\pi$
$654$		0			0
$655$	−6.79568	+	11.7705i	−0.265529	+	0.459910i
$656$		0			0
$657$	−6.56774	−	28.7752i	−0.256232	−	1.12263i
$658$		0			0
$659$	5.36325	−	23.4979i	0.208923	−	0.915350i	−0.756363	−	0.654152i	$-0.773025\pi$
$659$	5.36325	−	23.4979i	0.208923	−	0.915350i	0.965285	−	0.261197i	$-0.0841174\pi$
$660$		0			0
$661$	11.1968	+	28.5290i	0.435506	+	1.10965i	0.965212	+	0.261470i	$0.0842072\pi$
$661$	11.1968	+	28.5290i	0.435506	+	1.10965i	−0.529706	+	0.848182i	$0.677698\pi$
$662$		0			0
$663$	13.2844	−	4.09769i	0.515923	−	0.159141i
$664$		0			0
$665$	10.2541	−	10.6705i	0.397637	−	0.413783i
$666$		0			0
$667$	7.11298	+	12.3200i	0.275416	+	0.477034i
$668$		0			0
$669$	3.98143	+	1.22811i	0.153931	+	0.0474814i
$670$		0			0
$671$	9.64973	−	12.1004i	0.372524	−	0.467130i
$672$		0			0
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	0.699966	−	0.714176i	$-0.253198\pi$
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	−0.852027	+	0.523498i	$0.824627\pi$
$674$		0			0
$675$	6.11547	−	0.921759i	0.235385	−	0.0354785i
$676$		0			0
$677$	−10.6386	−	1.60352i	−0.408876	−	0.0616282i	−0.0586160	−	0.998281i	$-0.518669\pi$
$677$	−10.6386	−	1.60352i	−0.408876	−	0.0616282i	−0.350260	+	0.936652i	$0.613907\pi$
$678$		0			0
$679$	−19.8366	−	16.3953i	−0.761257	−	0.629194i
$680$		0			0
$681$	−6.05918	−	4.13108i	−0.232188	−	0.158303i
$682$		0			0
$683$	3.18207	−	42.4618i	0.121759	−	1.62476i	−0.517443	−	0.855718i	$-0.673116\pi$
$683$	3.18207	−	42.4618i	0.121759	−	1.62476i	0.639202	−	0.769039i	$-0.279265\pi$
$684$		0			0
$685$	−22.6088			−0.863838
$686$		0			0
$687$	−6.19211			−0.236244
$688$		0			0
$689$	3.87157	−	51.6626i	0.147495	−	1.96819i
$690$		0			0
$691$	15.2523	+	10.3989i	0.580227	+	0.395592i	0.817566	−	0.575835i	$-0.195323\pi$
$691$	15.2523	+	10.3989i	0.580227	+	0.395592i	−0.237339	+	0.971427i	$0.576275\pi$
$692$		0			0
$693$	−20.5289	−	16.9675i	−0.779829	−	0.644543i
$694$		0			0
$695$	−2.15432	−	0.324711i	−0.0817179	−	0.0123170i
$696$		0			0
$697$	10.7358	−	1.61816i	0.406647	−	0.0612922i
$698$		0			0
$699$	0.679883	+	0.852547i	0.0257155	+	0.0322463i
$700$		0			0
$701$	5.44005	−	6.82161i	0.205468	−	0.257649i	−0.668411	−	0.743792i	$-0.733025\pi$
$701$	5.44005	−	6.82161i	0.205468	−	0.257649i	0.873879	+	0.486143i	$0.161597\pi$
$702$		0			0
$703$	−17.8793	−	5.51503i	−0.674330	−	0.208003i
$704$		0			0
$705$	4.65560	+	8.06373i	0.175340	+	0.303698i
$706$		0			0
$707$	14.6049	−	15.1979i	0.549273	−	0.571576i
$708$		0			0
$709$	5.85484	−	1.80598i	0.219883	−	0.0678249i	−0.182856	−	0.983140i	$-0.558534\pi$
$709$	5.85484	−	1.80598i	0.219883	−	0.0678249i	0.402739	+	0.915315i	$0.368058\pi$
$710$		0			0
$711$	−4.10384	−	10.4564i	−0.153906	−	0.392147i
$712$		0			0
$713$	−9.68483	+	42.4320i	−0.362700	+	1.58909i
$714$		0			0
$715$	−9.47859	−	41.5284i	−0.354479	−	1.55307i
$716$		0			0
$717$	−8.03458	+	13.9163i	−0.300057	+	0.519714i
$718$		0			0
$719$	1.03637	+	13.8294i	0.0386501	+	0.515750i	0.982609	+	0.185687i	$0.0594509\pi$
$719$	1.03637	+	13.8294i	0.0386501	+	0.515750i	−0.943959	+	0.330063i	$0.892930\pi$
$720$		0			0
$721$	13.0489	+	45.0912i	0.485968	+	1.67929i
$722$		0			0
$723$	2.61454	−	2.42594i	0.0972359	−	0.0902217i
$724$		0			0
$725$	2.35403	−	1.60495i	0.0874266	−	0.0596064i
$726$		0			0
$727$	−43.4455	+	20.9222i	−1.61130	+	0.775963i	−0.999882	−	0.0153432i	$-0.995116\pi$
$727$	−43.4455	+	20.9222i	−1.61130	+	0.775963i	−0.611421	+	0.791306i	$0.709402\pi$
$728$		0			0
$729$	3.89381	+	1.87516i	0.144215	+	0.0694504i
$730$		0			0
$731$	9.86267	+	9.15122i	0.364784	+	0.338470i
$732$		0			0
$733$	15.9382	−	40.6099i	0.588691	−	1.49996i	−0.257066	−	0.966394i	$-0.582756\pi$
$733$	15.9382	−	40.6099i	0.588691	−	1.49996i	0.845757	−	0.533568i	$-0.179149\pi$
$734$		0			0
$735$	−7.92148	−	4.16243i	−0.292188	−	0.153534i
$736$		0			0
$737$	2.70944	−	6.90354i	0.0998035	−	0.254295i
$738$		0			0
$739$	−23.4656	−	21.7729i	−0.863198	−	0.800930i	0.118185	−	0.992992i	$-0.462292\pi$
$739$	−23.4656	−	21.7729i	−0.863198	−	0.800930i	−0.981383	+	0.192061i	$0.938483\pi$
$740$		0			0
$741$	11.0124	+	5.30329i	0.404551	+	0.194821i
$742$		0			0
$743$	35.8504	−	17.2646i	1.31522	−	0.633378i	0.361025	−	0.932556i	$-0.382427\pi$
$743$	35.8504	−	17.2646i	1.31522	−	0.633378i	0.954197	+	0.299179i	$0.0967126\pi$
$744$		0			0
$745$	24.2412	−	16.5274i	0.888129	−	0.605516i
$746$		0			0
$747$	10.1368	−	9.40556i	0.370885	−	0.344131i
$748$		0			0
$749$	−5.41359	−	6.04326i	−0.197808	−	0.220816i
$750$		0			0
$751$	1.41074	+	18.8250i	0.0514787	+	0.686936i	0.961926	+	0.273310i	$0.0881186\pi$
$751$	1.41074	+	18.8250i	0.0514787	+	0.686936i	−0.910447	+	0.413625i	$0.864262\pi$
$752$		0			0
$753$	1.77504	−	3.07445i	0.0646859	−	0.112039i
$754$		0			0
$755$	−5.03895	−	22.0771i	−0.183386	−	0.803468i
$756$		0			0
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	−0.999899	−	0.0141791i	$-0.995487\pi$
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	0.907030	+	0.421065i	$0.138344\pi$
$758$		0			0
$759$	8.17644	+	20.8332i	0.296786	+	0.756198i
$760$		0			0
$761$	26.0094	−	8.02283i	0.942840	−	0.290828i	0.215031	−	0.976607i	$-0.431015\pi$
$761$	26.0094	−	8.02283i	0.942840	−	0.290828i	0.727809	+	0.685780i	$0.240539\pi$
$762$		0			0
$763$	−30.0010	−	18.0285i	−1.08611	−	0.652676i
$764$		0			0
$765$	8.00776	+	13.8698i	0.289521	+	0.501465i
$766$		0			0
$767$	39.7552	+	12.2629i	1.43548	+	0.442786i
$768$		0			0
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	−0.999999	−	0.00129128i	$-0.999589\pi$
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	0.223780	+	0.974640i	$0.428160\pi$
$770$		0			0
$771$	6.82417	+	8.55724i	0.245766	+	0.308181i
$772$		0			0
$773$	−3.38417	+	0.510082i	−0.121720	+	0.0183464i	−0.209620	−	0.977783i	$-0.567223\pi$
$773$	−3.38417	+	0.510082i	−0.121720	+	0.0183464i	0.0878996	+	0.996129i	$0.471985\pi$
$774$		0			0
$775$	8.61923	+	1.29914i	0.309612	+	0.0466665i
$776$		0			0
$777$	−0.198036	+	11.3121i	−0.00710451	+	0.405819i
$778$		0			0
$779$	7.88701	+	5.37727i	0.282581	+	0.192661i
$780$		0			0
$781$	−2.16463	+	28.8850i	−0.0774567	+	1.03359i
$782$		0			0
$783$	−6.76761			−0.241855
$784$		0			0
$785$	−40.0991			−1.43120
$786$		0			0
$787$	3.04589	−	40.6446i	0.108574	−	1.44882i	−0.631019	−	0.775767i	$-0.717363\pi$
$787$	3.04589	−	40.6446i	0.108574	−	1.44882i	0.739593	−	0.673054i	$-0.235018\pi$
$788$		0			0
$789$	−1.06392	−	0.725365i	−0.0378764	−	0.0258237i
$790$		0			0
$791$	26.8886	−	5.64388i	0.956050	−	0.200673i
$792$		0			0
$793$	−22.1550	−	3.33932i	−0.786746	−	0.118583i
$794$		0			0
$795$	−11.3132	+	1.70518i	−0.401236	+	0.0604766i
$796$		0			0
$797$	−24.6176	−	30.8695i	−0.872000	−	1.09345i	−0.994883	−	0.101033i	$-0.967785\pi$
$797$	−24.6176	−	30.8695i	−0.872000	−	1.09345i	0.122883	−	0.992421i	$-0.460786\pi$
$798$		0			0
$799$	15.6999	−	19.6870i	0.555421	−	0.696476i
$800$		0			0
$801$	−27.5020	−	8.48324i	−0.971735	−	0.299741i
$802$		0			0
$803$	−23.4411	−	40.6012i	−0.827219	−	1.43278i
$804$		0			0
$805$	−21.5266	−	32.7926i	−0.758713	−	1.15579i
$806$		0			0
$807$	−0.996641	+	0.307423i	−0.0350834	+	0.0108218i
$808$		0			0
$809$	0.611202	+	1.55732i	0.0214887	+	0.0547523i	0.941215	−	0.337807i	$-0.109685\pi$
$809$	0.611202	+	1.55732i	0.0214887	+	0.0547523i	−0.919727	+	0.392559i	$0.871590\pi$
$810$		0			0
$811$	−5.23122	+	22.9195i	−0.183693	+	0.804812i	0.796159	+	0.605087i	$0.206862\pi$
$811$	−5.23122	+	22.9195i	−0.183693	+	0.804812i	−0.979852	+	0.199724i	$0.935995\pi$
$812$		0			0
$813$	−2.54984	−	11.1716i	−0.0894269	−	0.391805i
$814$		0			0
$815$	7.90405	−	13.6902i	0.276867	−	0.479548i
$816$		0			0
$817$	0.883994	+	11.7961i	0.0309270	+	0.412693i
$818$		0			0
$819$	−6.41289	+	38.0186i	−0.224084	+	1.32848i
$820$		0			0
$821$	−17.2928	+	16.0454i	−0.603522	+	0.559987i	−0.921631	−	0.388067i	$-0.873143\pi$
$821$	−17.2928	+	16.0454i	−0.603522	+	0.559987i	0.318109	+	0.948054i	$0.396952\pi$
$822$		0			0
$823$	−28.7697	+	19.6148i	−1.00285	+	0.683730i	−0.949149	−	0.314827i	$-0.898053\pi$
$823$	−28.7697	+	19.6148i	−1.00285	+	0.683730i	−0.0536984	+	0.998557i	$0.517101\pi$
$824$		0			0
$825$	4.03832	−	1.94475i	0.140596	−	0.0677076i
$826$		0			0
$827$	−29.7539	−	14.3287i	−1.03464	−	0.498258i	−0.162089	−	0.986776i	$-0.551823\pi$
$827$	−29.7539	−	14.3287i	−1.03464	−	0.498258i	−0.872554	+	0.488518i	$0.837538\pi$
$828$		0			0
$829$	−5.57507	−	5.17291i	−0.193630	−	0.179663i	0.577399	−	0.816462i	$-0.304068\pi$
$829$	−5.57507	−	5.17291i	−0.193630	−	0.179663i	−0.771030	+	0.636799i	$0.780258\pi$
$830$		0			0
$831$	−3.95586	+	10.0794i	−0.137227	+	0.349650i
$832$		0			0
$833$	−2.65203	+	24.0540i	−0.0918873	+	0.833423i
$834$		0			0
$835$	−2.69041	+	6.85506i	−0.0931056	+	0.237229i
$836$		0			0
$837$	−15.1778	−	14.0830i	−0.524623	−	0.486779i
$838$		0			0
$839$	27.2423	+	13.1192i	0.940510	+	0.452926i	0.840349	−	0.542046i	$-0.182350\pi$
$839$	27.2423	+	13.1192i	0.940510	+	0.452926i	0.100161	+	0.994971i	$0.468064\pi$
$840$		0			0
$841$	23.3191	−	11.2299i	0.804108	−	0.387238i
$842$		0			0
$843$	0.182330	−	0.124310i	0.00627976	−	0.00428147i
$844$		0			0
$845$	−27.6666	+	25.6709i	−0.951761	+	0.883105i
$846$		0			0
$847$	−12.2025	−	5.03736i	−0.419283	−	0.173086i
$848$		0			0
$849$	−1.11094	−	14.8245i	−0.0381273	−	0.508774i
$850$		0			0
$851$	−24.7978	+	42.9511i	−0.850058	+	1.47234i
$852$		0			0
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	−0.654345	−	0.756197i	$-0.727055\pi$
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	0.261443	−	0.965219i	$-0.415802\pi$
$854$		0			0
$855$	−3.13333	+	13.7280i	−0.107158	+	0.469488i
$856$		0			0
$857$	6.74701	+	17.1911i	0.230473	+	0.587236i	0.998591	−	0.0530727i	$-0.0169015\pi$
$857$	6.74701	+	17.1911i	0.230473	+	0.587236i	−0.768117	+	0.640309i	$0.778806\pi$
$858$		0			0
$859$	−14.2380	+	4.39183i	−0.485793	+	0.149847i	−0.527970	−	0.849263i	$-0.677047\pi$
$859$	−14.2380	+	4.39183i	−0.485793	+	0.149847i	0.0421773	+	0.999110i	$0.486571\pi$
$860$		0			0
$861$	1.79762	−	5.48498i	0.0612629	−	0.186928i
$862$		0			0
$863$	2.10510	+	3.64613i	0.0716583	+	0.124116i	0.899628	−	0.436657i	$-0.143838\pi$
$863$	2.10510	+	3.64613i	0.0716583	+	0.124116i	−0.827970	+	0.560773i	$0.810504\pi$
$864$		0			0
$865$	−32.4711	−	10.0160i	−1.10405	−	0.340555i
$866$		0			0
$867$	2.18657	−	2.74187i	0.0742597	−	0.0931187i
$868$		0			0
$869$	−11.1246	−	13.9498i	−0.377376	−	0.473215i
$870$		0			0
$871$	−10.6161	+	1.60012i	−0.359714	+	0.0542182i
$872$		0			0
$873$	24.2134	+	3.64958i	0.819499	+	0.123520i
$874$		0			0
$875$	−25.5225	+	19.6326i	−0.862819	+	0.663704i
$876$		0			0
$877$	20.4536	+	13.9451i	0.690670	+	0.470891i	0.857092	−	0.515164i	$-0.172269\pi$
$877$	20.4536	+	13.9451i	0.690670	+	0.470891i	−0.166422	+	0.986055i	$0.553221\pi$
$878$		0			0
$879$	0.488396	−	6.51720i	0.0164732	−	0.219820i
$880$		0			0
$881$	−7.51988			−0.253351			−0.126676	−	0.991944i	$-0.540431\pi$
$881$	−7.51988			−0.253351			−0.126676	+	0.991944i	$0.540431\pi$
$882$		0			0
$883$	27.5069			0.925681			0.462840	−	0.886442i	$-0.346830\pi$
$883$	27.5069			0.925681			0.462840	+	0.886442i	$0.346830\pi$
$884$		0			0
$885$	0.686587	−	9.16186i	0.0230794	−	0.307973i
$886$		0			0
$887$	12.3971	+	8.45222i	0.416255	+	0.283798i	0.753283	−	0.657697i	$-0.228469\pi$
$887$	12.3971	+	8.45222i	0.416255	+	0.283798i	−0.337028	+	0.941495i	$0.609422\pi$
$888$		0			0
$889$	−14.7799	+	29.3646i	−0.495703	+	0.984858i
$890$		0			0
$891$	19.3341	+	2.91415i	0.647718	+	0.0976278i
$892$		0			0
$893$	21.8919	−	3.29967i	0.732583	−	0.110419i
$894$		0			0
$895$	−16.3511	−	20.5037i	−0.546559	−	0.685363i
$896$		0			0
$897$	20.2003	−	25.3304i	0.674469	−	0.845758i
$898$		0			0
$899$	−9.11460	−	2.81148i	−0.303989	−	0.0937682i
$900$		0			0
$901$	15.4701	+	26.7950i	0.515383	+	0.892670i
$902$		0			0
$903$	6.70309	−	2.49627i	0.223065	−	0.0830706i
$904$		0			0
$905$	−33.2121	+	10.2446i	−1.10401	+	0.340542i
$906$		0			0
$907$	1.92231	+	4.89796i	0.0638292	+	0.162634i	0.959230	−	0.282627i	$-0.0912060\pi$
$907$	1.92231	+	4.89796i	0.0638292	+	0.162634i	−0.895401	+	0.445262i	$0.853111\pi$
$908$		0			0
$909$	−4.46279	+	19.5528i	−0.148021	+	0.648524i
$910$		0			0
$911$	11.1707	+	48.9420i	0.370102	+	1.62152i	0.726486	+	0.687182i	$0.241152\pi$
$911$	11.1707	+	48.9420i	0.370102	+	1.62152i	−0.356384	+	0.934340i	$0.615991\pi$
$912$		0			0
$913$	10.9824	−	19.0221i	0.363465	−	0.629540i
$914$		0			0
$915$	0.369755	+	4.93404i	0.0122237	+	0.163114i
$916$		0			0
$917$	11.2886	−	15.9502i	0.372783	−	0.526721i
$918$		0			0
$919$	12.4506	−	11.5525i	0.410708	−	0.381081i	−0.447585	−	0.894241i	$-0.647716\pi$
$919$	12.4506	−	11.5525i	0.410708	−	0.381081i	0.858293	+	0.513160i	$0.171525\pi$
$920$		0			0
$921$	−15.4642	+	10.5433i	−0.509561	+	0.347413i
$922$		0			0
$923$	37.7800	−	18.1939i	1.24354	−	0.598859i
$924$		0			0
$925$	8.94908	+	4.30965i	0.294244	+	0.141700i
$926$		0			0
$927$	−32.7415	−	30.3797i	−1.07537	−	0.997799i
$928$		0			0
$929$	20.6196	−	52.5378i	0.676506	−	1.72371i	−0.0135021	−	0.999909i	$-0.504298\pi$
$929$	20.6196	−	52.5378i	0.676506	−	1.72371i	0.690008	−	0.723801i	$-0.257607\pi$
$930$		0			0
$931$	−16.0940	+	13.9171i	−0.527459	+	0.456114i
$932$		0			0
$933$	−2.97221	+	7.57306i	−0.0973057	+	0.247931i
$934$		0			0
$935$	18.6483	+	17.3031i	0.609863	+	0.565870i
$936$		0			0
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	0.340210	−	0.940350i	$-0.389502\pi$
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	−0.523077	+	0.852285i	$0.675216\pi$
$938$		0			0
$939$	−11.7157	+	5.64200i	−0.382329	+	0.184120i
$940$		0			0
$941$	43.0772	−	29.3696i	1.40428	−	0.957420i	0.405211	−	0.914223i	$-0.367198\pi$
$941$	43.0772	−	29.3696i	1.40428	−	0.957420i	0.999067	−	0.0431974i	$-0.0137544\pi$
$942$		0			0
$943$	18.5480	−	17.2101i	0.604007	−	0.560437i
$944$		0			0
$945$	18.6305	−	1.06860i	0.606051	−	0.0347617i
$946$		0			0
$947$	−3.43458	−	45.8312i	−0.111609	−	1.48931i	−0.719055	−	0.694954i	$-0.755425\pi$
$947$	−3.43458	−	45.8312i	−0.111609	−	1.48931i	0.607446	−	0.794361i	$-0.292194\pi$
$948$		0			0
$949$	−33.9345	+	58.7763i	−1.10156	+	1.90796i
$950$		0			0
$951$	3.17320	+	13.9027i	0.102898	+	0.450825i
$952$		0			0
$953$	5.15402	−	22.5812i	0.166955	−	0.731478i	−0.820248	−	0.572008i	$-0.806164\pi$
$953$	5.15402	−	22.5812i	0.166955	−	0.731478i	0.987203	−	0.159470i	$-0.0509784\pi$
$954$		0			0
$955$	−11.1697	−	28.4598i	−0.361441	−	0.920938i
$956$		0			0
$957$	−4.68686	+	1.44571i	−0.151505	+	0.0467330i
$958$		0			0
$959$	32.3671	+	2.99614i	1.04519	+	0.0967506i
$960$		0			0
$961$	0.909053	+	1.57453i	0.0293243	+	0.0507912i
$962$		0			0
$963$	7.37694	+	2.27549i	0.237719	+	0.0733265i
$964$		0			0
$965$	30.6979	−	38.4940i	0.988202	−	1.23917i
$966$		0			0
$967$	−6.29969	−	7.89956i	−0.202584	−	0.254033i	0.670153	−	0.742223i	$-0.266229\pi$
$967$	−6.29969	−	7.89956i	−0.202584	−	0.254033i	−0.872737	+	0.488190i	$0.837657\pi$
$968$		0			0
$969$	−7.21814	+	1.08796i	−0.231880	+	0.0349503i
$970$		0			0
$971$	28.7761	+	4.33729i	0.923468	+	0.139190i	0.593529	−	0.804812i	$-0.297734\pi$
$971$	28.7761	+	4.33729i	0.923468	+	0.139190i	0.329938	+	0.944003i	$0.392972\pi$
$972$		0			0
$973$	3.04112	+	0.750353i	0.0974937	+	0.0240552i
$974$		0			0
$975$	−5.36117	−	3.65519i	−0.171695	−	0.117060i
$976$		0			0
$977$	−2.33543	+	31.1641i	−0.0747170	+	0.997029i	0.826296	+	0.563236i	$0.190444\pi$
$977$	−2.33543	+	31.1641i	−0.0747170	+	0.997029i	−0.901013	+	0.433792i	$0.857175\pi$
$978$		0			0
$979$	−45.7154			−1.46107
$980$		0			0
$981$	33.3036			1.06330
$982$		0			0
$983$	−2.21235	+	29.5217i	−0.0705629	+	0.941596i	0.843789	+	0.536675i	$0.180320\pi$
$983$	−2.21235	+	29.5217i	−0.0705629	+	0.941596i	−0.914352	+	0.404921i	$0.867299\pi$
$984$		0			0
$985$	−11.1330	−	7.59033i	−0.354726	−	0.241848i
$986$		0			0
$987$	−5.59640	−	12.1611i	−0.178135	−	0.387092i
$988$		0			0
$989$	31.0051	+	4.67326i	0.985904	+	0.148601i
$990$		0			0
$991$	39.1017	−	5.89363i	1.24211	−	0.187217i	0.505074	−	0.863076i	$-0.331465\pi$
$991$	39.1017	−	5.89363i	1.24211	−	0.187217i	0.737031	+	0.675859i	$0.236227\pi$
$992$		0			0
$993$	7.51903	+	9.42856i	0.238609	+	0.299206i
$994$		0			0
$995$	4.36495	−	5.47347i	0.138378	−	0.173521i
$996$		0			0
$997$	47.6032	+	14.6836i	1.50761	+	0.465035i	0.934956	−	0.354764i	$-0.115439\pi$
$997$	47.6032	+	14.6836i	1.50761	+	0.465035i	0.572652	+	0.819799i	$0.305915\pi$
$998$		0			0
$999$	−11.7969	−	20.4328i	−0.373237	−	0.646465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bg.a.193.1		24
4.3	odd	2		98.2.g.a.95.2	yes	24
12.11	even	2		882.2.z.d.487.1		24
28.3	even	6		686.2.e.e.393.4		24
28.11	odd	6		686.2.e.f.393.1		24
28.19	even	6		686.2.g.c.79.1		24
28.23	odd	6		686.2.g.a.79.2		24
28.27	even	2		686.2.g.b.557.1		24
49.16	even	21	inner	784.2.bg.a.65.1		24
196.39	odd	42		686.2.e.f.295.1		24
196.43	odd	14		686.2.g.a.165.2		24
196.55	even	14		686.2.g.c.165.1		24
196.59	even	42		686.2.e.e.295.4		24
196.131	even	42		686.2.g.b.569.1		24
196.143	even	42		4802.2.a.k.1.3		12
196.151	odd	42		4802.2.a.i.1.10		12
196.163	odd	42		98.2.g.a.65.2	✓	24
588.359	even	42		882.2.z.d.163.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.2	✓	24	196.163	odd	42
98.2.g.a.95.2	yes	24	4.3	odd	2
686.2.e.e.295.4		24	196.59	even	42
686.2.e.e.393.4		24	28.3	even	6
686.2.e.f.295.1		24	196.39	odd	42
686.2.e.f.393.1		24	28.11	odd	6
686.2.g.a.79.2		24	28.23	odd	6
686.2.g.a.165.2		24	196.43	odd	14
686.2.g.b.557.1		24	28.27	even	2
686.2.g.b.569.1		24	196.131	even	42
686.2.g.c.79.1		24	28.19	even	6
686.2.g.c.165.1		24	196.55	even	14
784.2.bg.a.65.1		24	49.16	even	21	inner
784.2.bg.a.193.1		24	1.1	even	1	trivial
882.2.z.d.163.1		24	588.359	even	42
882.2.z.d.487.1		24	12.11	even	2
4802.2.a.i.1.10		12	196.151	odd	42
4802.2.a.k.1.3		12	196.143	even	42

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0519131 + 0.692733i) q^{3} +(1.52046 + 1.03663i) q^{5} +(-2.03934 - 1.68555i) q^{7} +(2.48931 + 0.375203i) q^{9} +O(q^{10})\)	\(q+(-0.0519131 + 0.692733i) q^{3} +(1.52046 + 1.03663i) q^{5} +(-2.03934 - 1.68555i) q^{7} +(2.48931 + 0.375203i) q^{9} +(3.95404 - 0.595976i) q^{11} +(-3.60921 - 4.52581i) q^{13} +(-0.797043 + 0.999460i) q^{15} +(3.30352 + 1.01900i) q^{17} +(1.51977 + 2.63232i) q^{19} +(1.27351 - 1.32522i) q^{21} +(7.69889 - 2.37479i) q^{23} +(-0.589506 - 1.50204i) q^{25} +(-0.852883 + 3.73672i) q^{27} +(0.392906 + 1.72143i) q^{29} +(-2.70101 + 4.67829i) q^{31} +(0.207585 + 2.77003i) q^{33} +(-1.35344 - 4.67687i) q^{35} +(-4.51246 + 4.18695i) q^{37} +(3.32254 - 2.26527i) q^{39} +(2.82949 - 1.36261i) q^{41} +(3.50635 + 1.68857i) q^{43} +(3.39596 + 3.15099i) q^{45} +(2.66104 - 6.78022i) q^{47} +(1.31782 + 6.87483i) q^{49} +(-0.877392 + 2.23556i) q^{51} +(6.56061 + 6.08735i) q^{53} +(6.62979 + 3.19274i) q^{55} +(-1.90239 + 0.916142i) q^{57} +(-5.93817 + 4.04858i) q^{59} +(2.83727 - 2.63260i) q^{61} +(-4.44412 - 4.96103i) q^{63} +(-0.796066 - 10.6228i) q^{65} +(0.927324 - 1.60617i) q^{67} +(1.24542 + 5.45656i) q^{69} +(-1.61191 + 7.06223i) q^{71} +(-4.28338 - 10.9139i) q^{73} +(1.07111 - 0.330395i) q^{75} +(-9.06819 - 5.44935i) q^{77} +(-2.23103 - 3.86426i) q^{79} +(4.67248 + 1.44127i) q^{81} +(3.42482 - 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(-1.21289 + 0.182814i) q^{87} +(-11.3049 - 1.70393i) q^{89} +(-0.268082 + 15.3132i) q^{91} +(-3.10059 - 2.11395i) q^{93} +(-0.417998 + 5.57779i) q^{95} +9.72695 q^{97} +10.0664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 7 q^{3} - 33 q^{9}+O(q^{10}) \) 24 * q - 7 * q^3 - 33 * q^9	\( 24 q - 7 q^{3} - 33 q^{9} + 7 q^{11} + 14 q^{13} + 7 q^{15} - 7 q^{17} + 7 q^{21} + 21 q^{23} + 4 q^{25} + 35 q^{27} - 11 q^{29} - 28 q^{31} + 14 q^{33} - 21 q^{35} - 24 q^{37} + 40 q^{39} + 28 q^{41} - 10 q^{43} + 7 q^{45} + 70 q^{47} + 84 q^{49} - 60 q^{51} + 26 q^{53} - 56 q^{55} - 33 q^{57} + 7 q^{59} + 14 q^{61} + 14 q^{63} + 36 q^{67} - 35 q^{69} - 7 q^{73} + 28 q^{75} - 91 q^{77} + 26 q^{79} + 55 q^{81} + 7 q^{83} + 49 q^{85} - 35 q^{87} - 56 q^{89} - 7 q^{91} + 72 q^{93} + 14 q^{95} - 126 q^{97} + 14 q^{99}+O(q^{100}) \) 24 * q - 7 * q^3 - 33 * q^9 + 7 * q^11 + 14 * q^13 + 7 * q^15 - 7 * q^17 + 7 * q^21 + 21 * q^23 + 4 * q^25 + 35 * q^27 - 11 * q^29 - 28 * q^31 + 14 * q^33 - 21 * q^35 - 24 * q^37 + 40 * q^39 + 28 * q^41 - 10 * q^43 + 7 * q^45 + 70 * q^47 + 84 * q^49 - 60 * q^51 + 26 * q^53 - 56 * q^55 - 33 * q^57 + 7 * q^59 + 14 * q^61 + 14 * q^63 + 36 * q^67 - 35 * q^69 - 7 * q^73 + 28 * q^75 - 91 * q^77 + 26 * q^79 + 55 * q^81 + 7 * q^83 + 49 * q^85 - 35 * q^87 - 56 * q^89 - 7 * q^91 + 72 * q^93 + 14 * q^95 - 126 * q^97 + 14 * q^99

Introduction

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Database

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