LMFDB - Embedded newform 819.2.dx.a.503.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(503,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dx (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.8
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} +3.88703 q^{5} +(2.55113 - 0.701238i) q^{7} +1.45513i q^{8} +O(q^{10})$	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} +3.88703 q^{5} +(2.55113 - 0.701238i) q^{7} +1.45513i q^{8} +(-6.00725 - 3.46829i) q^{10} +(-4.08611 - 2.35911i) q^{11} +(3.16085 - 1.73466i) q^{13} +(-4.56836 - 1.19257i) q^{14} +(2.48296 - 4.30062i) q^{16} +(-1.32706 - 2.29853i) q^{17} +(0.696729 - 0.402257i) q^{19} +(2.30227 + 3.98766i) q^{20} +(4.20994 + 7.29183i) q^{22} +(-6.08975 - 3.51592i) q^{23} +10.1090 q^{25} +(-6.43275 - 0.139494i) q^{26} +(2.23042 + 2.20183i) q^{28} +(7.82728 + 4.51908i) q^{29} +2.23409i q^{31} +(-5.15428 + 2.97582i) q^{32} +4.73637i q^{34} +(9.91632 - 2.72573i) q^{35} +(0.166787 - 0.288883i) q^{37} -1.43569 q^{38} +5.65613i q^{40} +(-3.12853 + 5.41877i) q^{41} +(-0.936635 - 1.62230i) q^{43} -5.58918i q^{44} +(6.27431 + 10.8674i) q^{46} +6.09646 q^{47} +(6.01653 - 3.57790i) q^{49} +(-15.6231 - 9.01998i) q^{50} +(3.65172 + 2.21525i) q^{52} +1.76104i q^{53} +(-15.8828 - 9.16995i) q^{55} +(1.02039 + 3.71222i) q^{56} +(-8.06450 - 13.9681i) q^{58} +(-5.01546 - 8.68704i) q^{59} +(3.87813 - 2.23904i) q^{61} +(1.99341 - 3.45269i) q^{62} +0.689124 q^{64} +(12.2863 - 6.74266i) q^{65} +(0.558805 - 0.967879i) q^{67} +(1.57202 - 2.72282i) q^{68} +(-17.7574 - 4.63554i) q^{70} +(10.0923 - 5.82681i) q^{71} -3.68800i q^{73} +(-0.515524 + 0.297638i) q^{74} +(0.825340 + 0.476510i) q^{76} +(-12.0785 - 3.15307i) q^{77} -5.71025 q^{79} +(9.65135 - 16.7166i) q^{80} +(9.67002 - 5.58299i) q^{82} -0.490867 q^{83} +(-5.15830 - 8.93444i) q^{85} +3.34293i q^{86} +(3.43281 - 5.94581i) q^{88} +(-6.95536 + 12.0470i) q^{89} +(6.84733 - 6.64184i) q^{91} -8.32987i q^{92} +(-9.42183 - 5.43969i) q^{94} +(2.70821 - 1.56358i) q^{95} +(-1.72166 + 0.994004i) q^{97} +(-12.4908 + 0.161123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.54546	−	0.892271i	−1.09280	−	0.630931i	−0.158483	−	0.987362i	$-0.550660\pi$
$2$	−1.54546	−	0.892271i	−1.09280	−	0.630931i	−0.934322	+	0.356431i	$0.883994\pi$
$3$		0			0
$3$		0			0
$4$	0.592297	+	1.02589i	0.296148	+	0.512944i
$5$	3.88703			1.73833			0.869166	−	0.494520i	$-0.164656\pi$
$5$	3.88703			1.73833			0.869166	+	0.494520i	$0.164656\pi$
$6$		0			0
$7$	2.55113	−	0.701238i	0.964237	−	0.265043i
$7$	2.55113	−	0.701238i	0.964237	−	0.265043i
$8$			1.45513i			0.514466i
$9$		0			0
$10$	−6.00725	−	3.46829i	−1.89966	−	1.09677i
$11$	−4.08611	−	2.35911i	−1.23201	−	0.711300i	−0.264559	−	0.964369i	$-0.585226\pi$
$11$	−4.08611	−	2.35911i	−1.23201	−	0.711300i	−0.967448	+	0.253070i	$0.918560\pi$
$12$		0			0
$13$	3.16085	−	1.73466i	0.876662	−	0.481107i
$13$	3.16085	−	1.73466i	0.876662	−	0.481107i
$14$	−4.56836	−	1.19257i	−1.22095	−	0.318726i
$15$		0			0
$16$	2.48296	−	4.30062i	0.620741	−	1.07515i
$17$	−1.32706	−	2.29853i	−0.321858	−	0.557475i	0.659013	−	0.752131i	$-0.270974\pi$
$17$	−1.32706	−	2.29853i	−0.321858	−	0.557475i	−0.980871	+	0.194657i	$0.937641\pi$
$18$		0			0
$19$	0.696729	−	0.402257i	0.159841	−	0.0922840i	−0.417946	−	0.908472i	$-0.637250\pi$
$19$	0.696729	−	0.402257i	0.159841	−	0.0922840i	0.577787	+	0.816188i	$0.303917\pi$
$20$	2.30227	+	3.98766i	0.514804	+	0.891667i
$21$		0			0
$22$	4.20994	+	7.29183i	0.897562	+	1.55462i
$23$	−6.08975	−	3.51592i	−1.26980	−	0.733120i	−0.294851	−	0.955543i	$-0.595270\pi$
$23$	−6.08975	−	3.51592i	−1.26980	−	0.733120i	−0.974950	+	0.222423i	$0.928603\pi$
$24$		0			0
$25$	10.1090			2.02180
$26$	−6.43275	−	0.139494i	−1.26157	−	0.0273570i
$27$		0			0
$28$	2.23042	+	2.20183i	0.421509	+	0.416107i
$29$	7.82728	+	4.51908i	1.45349	+	0.839173i	0.998677	−	0.0514146i	$-0.0163730\pi$
$29$	7.82728	+	4.51908i	1.45349	+	0.839173i	0.454812	+	0.890587i	$0.349706\pi$
$30$		0			0
$31$			2.23409i			0.401254i	0.979668	+	0.200627i	$0.0642979\pi$
$31$			2.23409i			0.401254i	−0.979668	+	0.200627i	$0.935702\pi$
$32$	−5.15428	+	2.97582i	−0.911157	+	0.526056i
$33$		0			0
$34$			4.73637i			0.812281i
$35$	9.91632	−	2.72573i	1.67616	−	0.460733i
$36$		0			0
$37$	0.166787	−	0.288883i	0.0274196	−	0.0474921i	−0.851990	−	0.523558i	$-0.824604\pi$
$37$	0.166787	−	0.288883i	0.0274196	−	0.0474921i	0.879410	+	0.476066i	$0.157938\pi$
$38$	−1.43569			−0.232899
$39$		0			0
$40$			5.65613i			0.894312i
$41$	−3.12853	+	5.41877i	−0.488594	+	0.846269i	−0.999914	−	0.0131210i	$-0.995823\pi$
$41$	−3.12853	+	5.41877i	−0.488594	+	0.846269i	0.511320	+	0.859390i	$0.329157\pi$
$42$		0			0
$43$	−0.936635	−	1.62230i	−0.142835	−	0.247398i	0.785728	−	0.618572i	$-0.212289\pi$
$43$	−0.936635	−	1.62230i	−0.142835	−	0.247398i	−0.928563	+	0.371174i	$0.878955\pi$
$44$		−	5.58918i		−	0.842601i
$45$		0			0
$46$	6.27431	+	10.8674i	0.925097	+	1.60231i
$47$	6.09646			0.889260			0.444630	−	0.895714i	$-0.353335\pi$
$47$	6.09646			0.889260			0.444630	+	0.895714i	$0.353335\pi$
$48$		0			0
$49$	6.01653	−	3.57790i	0.859504	−	0.511129i
$50$	−15.6231	−	9.01998i	−2.20943	−	1.27562i
$51$		0			0
$52$	3.65172	+	2.21525i	0.506403	+	0.307199i
$53$			1.76104i			0.241898i	0.992659	+	0.120949i	$0.0385937\pi$
$53$			1.76104i			0.241898i	−0.992659	+	0.120949i	$0.961406\pi$
$54$		0			0
$55$	−15.8828	−	9.16995i	−2.14164	−	1.23648i
$56$	1.02039	+	3.71222i	0.136356	+	0.496067i
$57$		0			0
$58$	−8.06450	−	13.9681i	−1.05892	−	1.83410i
$59$	−5.01546	−	8.68704i	−0.652958	−	1.13096i	−0.982402	−	0.186781i	$-0.940195\pi$
$59$	−5.01546	−	8.68704i	−0.652958	−	1.13096i	0.329444	−	0.944175i	$-0.393139\pi$
$60$		0			0
$61$	3.87813	−	2.23904i	0.496544	−	0.286680i	−0.230741	−	0.973015i	$-0.574115\pi$
$61$	3.87813	−	2.23904i	0.496544	−	0.286680i	0.727285	+	0.686335i	$0.240782\pi$
$62$	1.99341	−	3.45269i	0.253163	−	0.438492i
$63$		0			0
$64$	0.689124			0.0861404
$65$	12.2863	−	6.74266i	1.52393	−	0.836324i
$66$		0			0
$67$	0.558805	−	0.967879i	0.0682689	−	0.118245i	−0.829870	−	0.557956i	$-0.811586\pi$
$67$	0.558805	−	0.967879i	0.0682689	−	0.118245i	0.898139	+	0.439711i	$0.144919\pi$
$68$	1.57202	−	2.72282i	0.190635	−	0.330190i
$69$		0			0
$70$	−17.7574	−	4.63554i	−2.12241	−	0.554053i
$71$	10.0923	−	5.82681i	1.19774	−	0.691516i	0.237689	−	0.971341i	$-0.423610\pi$
$71$	10.0923	−	5.82681i	1.19774	−	0.691516i	0.960051	+	0.279826i	$0.0902767\pi$
$72$		0			0
$73$		−	3.68800i		−	0.431648i	−0.976432	−	0.215824i	$-0.930756\pi$
$73$		−	3.68800i		−	0.431648i	0.976432	−	0.215824i	$-0.0692437\pi$
$74$	−0.515524	+	0.297638i	−0.0599285	+	0.0345997i
$75$		0			0
$76$	0.825340	+	0.476510i	0.0946730	+	0.0546595i
$77$	−12.0785	−	3.15307i	−1.37647	−	0.359326i
$78$		0			0
$79$	−5.71025			−0.642453			−0.321227	−	0.947002i	$-0.604095\pi$
$79$	−5.71025			−0.642453			−0.321227	+	0.947002i	$0.604095\pi$
$80$	9.65135	−	16.7166i	1.07905	−	1.86898i
$81$		0			0
$82$	9.67002	−	5.58299i	1.06788	−	0.616538i
$83$	−0.490867			−0.0538796			−0.0269398	−	0.999637i	$-0.508576\pi$
$83$	−0.490867			−0.0538796			−0.0269398	+	0.999637i	$0.508576\pi$
$84$		0			0
$85$	−5.15830	−	8.93444i	−0.559497	−	0.969076i
$86$			3.34293i			0.360477i
$87$		0			0
$88$	3.43281	−	5.94581i	0.365939	−	0.633825i
$89$	−6.95536	+	12.0470i	−0.737266	+	1.27698i	0.216456	+	0.976292i	$0.430550\pi$
$89$	−6.95536	+	12.0470i	−0.737266	+	1.27698i	−0.953722	+	0.300690i	$0.902783\pi$
$90$		0			0
$91$	6.84733	−	6.64184i	0.717795	−	0.696254i
$92$		−	8.32987i		−	0.868449i
$93$		0			0
$94$	−9.42183	−	5.43969i	−0.971787	−	0.561062i
$95$	2.70821	−	1.56358i	0.277856	−	0.160420i
$96$		0			0
$97$	−1.72166	+	0.994004i	−0.174809	+	0.100926i	−0.584851	−	0.811141i	$-0.698847\pi$
$97$	−1.72166	+	0.994004i	−0.174809	+	0.100926i	0.410043	+	0.912066i	$0.365514\pi$
$98$	−12.4908	+	0.161123i	−1.26176	+	0.0162759i
$99$		0			0
$100$	5.98753	+	10.3707i	0.598753	+	1.03707i
$101$	5.62467	−	9.74222i	0.559676	−	0.969387i	−0.437847	−	0.899049i	$-0.644259\pi$
$101$	5.62467	−	9.74222i	0.559676	−	0.969387i	0.997523	−	0.0703378i	$-0.0224077\pi$
$102$		0			0
$103$			15.4344i			1.52079i	0.649459	+	0.760396i	$0.274995\pi$
$103$			15.4344i			1.52079i	−0.649459	+	0.760396i	$0.725005\pi$
$104$	2.52415	+	4.59944i	0.247513	+	0.451012i
$105$		0			0
$106$	1.57133	−	2.72162i	0.152621	−	0.264347i
$107$	7.62329	+	4.40131i	0.736971	+	0.425490i	0.820967	−	0.570976i	$-0.193435\pi$
$107$	7.62329	+	4.40131i	0.736971	+	0.425490i	−0.0839959	+	0.996466i	$0.526768\pi$
$108$		0			0
$109$	−13.4210			−1.28550			−0.642748	−	0.766078i	$-0.722206\pi$
$109$	−13.4210			−1.28550			−0.642748	+	0.766078i	$0.722206\pi$
$110$	16.3642	+	28.3436i	1.56026	+	2.70245i
$111$		0			0
$112$	3.31860	−	12.7126i	0.313578	−	1.20123i
$113$	−11.7676	+	6.79404i	−1.10700	+	0.639129i	−0.938052	−	0.346495i	$-0.887372\pi$
$113$	−11.7676	+	6.79404i	−1.10700	+	0.639129i	−0.168952	+	0.985624i	$0.554038\pi$
$114$		0			0
$115$	−23.6711	−	13.6665i	−2.20734	−	1.27441i
$116$			10.7066i			0.994078i
$117$		0			0
$118$			17.9006i			1.64789i
$119$	−4.99731	−	4.93326i	−0.458102	−	0.452231i
$120$		0			0
$121$	5.63084	+	9.75290i	0.511894	+	0.886627i
$122$	−7.99133			−0.723501
$123$		0			0
$124$	−2.29192	+	1.32324i	−0.205821	+	0.118831i
$125$	19.8589			1.77623
$126$		0			0
$127$	0.996604	−	1.72617i	0.0884343	−	0.153173i	−0.818415	−	0.574627i	$-0.805147\pi$
$127$	0.996604	−	1.72617i	0.0884343	−	0.153173i	0.906849	+	0.421455i	$0.138480\pi$
$128$	9.24355	+	5.33676i	0.817022	+	0.471708i
$129$		0			0
$130$	−25.0043	−	0.542216i	−2.19302	−	0.0475555i
$131$	−2.29765			−0.200747			−0.100373	−	0.994950i	$-0.532004\pi$
$131$	−2.29765			−0.200747			−0.100373	+	0.994950i	$0.532004\pi$
$132$		0			0
$133$	1.49537	−	1.51478i	0.129665	−	0.131348i
$134$	−1.72722	+	0.997212i	−0.149209	+	0.0861460i
$135$		0			0
$136$	3.34465	−	1.93104i	0.286802	−	0.165585i
$137$	12.2337	−	7.06316i	1.04520	−	0.603446i	0.123898	−	0.992295i	$-0.460461\pi$
$137$	12.2337	−	7.06316i	1.04520	−	0.603446i	0.921302	+	0.388849i	$0.127127\pi$
$138$		0			0
$139$	−11.4186	+	6.59251i	−0.968510	+	0.559169i	−0.898782	−	0.438397i	$-0.855547\pi$
$139$	−11.4186	+	6.59251i	−0.968510	+	0.559169i	−0.0697283	+	0.997566i	$0.522213\pi$
$140$	8.66970	+	8.55859i	0.732723	+	0.723333i
$141$		0			0
$142$	−20.7964			−1.74519
$143$	−17.0078	−	0.368813i	−1.42226	−	0.0308417i
$144$		0			0
$145$	30.4249	+	17.5658i	2.52665	+	1.45876i
$146$	−3.29070	+	5.69966i	−0.272340	+	0.471707i
$147$		0			0
$148$	0.395149			0.0324810
$149$	5.16680	−	2.98306i	0.423281	−	0.244381i	−0.273199	−	0.961958i	$-0.588082\pi$
$149$	5.16680	−	2.98306i	0.423281	−	0.244381i	0.696480	+	0.717576i	$0.254748\pi$
$150$		0			0
$151$	13.7080			1.11554			0.557772	−	0.829994i	$-0.311656\pi$
$151$	13.7080			1.11554			0.557772	+	0.829994i	$0.311656\pi$
$152$	0.585335	+	1.01383i	0.0474769	+	0.0822325i
$153$		0			0
$154$	15.8534	+	15.6502i	1.27750	+	1.26113i
$155$			8.68396i			0.697512i
$156$		0			0
$157$			10.3038i			0.822329i	0.911561	+	0.411165i	$0.134878\pi$
$157$			10.3038i			0.822329i	−0.911561	+	0.411165i	$0.865122\pi$
$158$	8.82496	+	5.09509i	0.702076	+	0.405344i
$159$		0			0
$160$	−20.0348	+	11.5671i	−1.58389	+	0.914461i
$161$	−18.0013	−	4.69920i	−1.41870	−	0.370349i
$162$		0			0
$163$	7.71649	+	13.3654i	0.604402	+	1.04686i	0.992146	+	0.125088i	$0.0399213\pi$
$163$	7.71649	+	13.3654i	0.604402	+	1.04686i	−0.387743	+	0.921767i	$0.626745\pi$
$164$	−7.41206			−0.578785
$165$		0			0
$166$	0.758615	+	0.437986i	0.0588799	+	0.0339943i
$167$	11.7152	−	20.2913i	0.906549	−	1.57019i	0.0877238	−	0.996145i	$-0.472041\pi$
$167$	11.7152	−	20.2913i	0.906549	−	1.57019i	0.818825	−	0.574043i	$-0.194626\pi$
$168$		0			0
$169$	6.98193	−	10.9660i	0.537072	−	0.843537i
$170$			18.4104i			1.41202i
$171$		0			0
$172$	1.10953	−	1.92176i	0.0846009	−	0.146533i
$173$	−8.25591	−	14.2997i	−0.627685	−	1.08718i	−0.988015	−	0.154358i	$-0.950669\pi$
$173$	−8.25591	−	14.2997i	−0.627685	−	1.08718i	0.360330	−	0.932825i	$-0.382664\pi$
$174$		0			0
$175$	25.7894	−	7.08882i	1.94949	−	0.535865i
$176$	−20.2913	+	11.7152i	−1.52951	+	0.883065i
$177$		0			0
$178$	21.4984	−	12.4121i	1.61138	−	0.930329i
$179$	−4.61081	−	2.66205i	−0.344628	−	0.198971i	0.317688	−	0.948195i	$-0.397093\pi$
$179$	−4.61081	−	2.66205i	−0.344628	−	0.198971i	−0.662317	+	0.749224i	$0.730427\pi$
$180$		0			0
$181$		−	18.2531i		−	1.35674i	−0.734719	−	0.678372i	$-0.762686\pi$
$181$		−	18.2531i		−	1.35674i	0.734719	−	0.678372i	$-0.237314\pi$
$182$	−16.5086	+	4.15502i	−1.22370	+	0.307991i
$183$		0			0
$184$	5.11612	−	8.86137i	0.377165	−	0.653269i
$185$	0.648305	−	1.12290i	0.0476643	−	0.0825570i
$186$		0			0
$187$			12.5227i			0.915750i
$188$	3.61091	+	6.25428i	0.263353	+	0.456140i
$189$		0			0
$190$	−5.58056			−0.404857
$191$	−17.0813	+	9.86191i	−1.23596	+	0.713583i	−0.968266	−	0.249921i	$-0.919595\pi$
$191$	−17.0813	+	9.86191i	−1.23596	+	0.713583i	−0.267695	+	0.963504i	$0.586262\pi$
$192$		0			0
$193$	−11.4922	+	19.9051i	−0.827227	+	1.43280i	0.0729782	+	0.997334i	$0.476750\pi$
$193$	−11.4922	+	19.9051i	−0.827227	+	1.43280i	−0.900205	+	0.435466i	$0.856584\pi$
$194$	3.54768			0.254709
$195$		0			0
$196$	7.23409	+	4.05311i	0.516721	+	0.289508i
$197$	23.1670	+	13.3755i	1.65058	+	0.952963i	0.976834	+	0.213999i	$0.0686490\pi$
$197$	23.1670	+	13.3755i	1.65058	+	0.952963i	0.673746	+	0.738963i	$0.264684\pi$
$198$		0			0
$199$	−11.1651	+	6.44615i	−0.791470	+	0.456956i	−0.840480	−	0.541843i	$-0.817727\pi$
$199$	−11.1651	+	6.44615i	−0.791470	+	0.456956i	0.0490095	+	0.998798i	$0.484394\pi$
$200$			14.7099i			1.04015i
$201$		0			0
$202$	−17.3854	+	10.0375i	−1.22323	+	0.706234i
$203$	23.1374	+	6.03998i	1.62392	+	0.423923i
$204$		0			0
$205$	−12.1607	+	21.0629i	−0.849339	+	1.47110i
$206$	13.7716	−	23.8532i	0.959516	−	1.66193i
$207$		0			0
$208$	0.388175	−	17.9007i	0.0269151	−	1.24119i
$209$	−3.79588			−0.262566
$210$		0			0
$211$	−9.40738	+	16.2941i	−0.647630	+	1.12173i	0.336057	+	0.941842i	$0.390907\pi$
$211$	−9.40738	+	16.2941i	−0.647630	+	1.12173i	−0.983687	+	0.179887i	$0.942427\pi$
$212$	−1.80663	+	1.04306i	−0.124080	+	0.0716376i
$213$		0			0
$214$	−7.85432	−	13.6041i	−0.536910	−	0.929956i
$215$	−3.64073	−	6.30592i	−0.248296	−	0.430060i
$216$		0			0
$217$	1.56663	+	5.69944i	0.106350	+	0.386904i
$218$	20.7416	+	11.9751i	1.40480	+	0.811059i
$219$		0			0
$220$		−	21.7253i		−	1.46472i
$221$	−8.18178	−	4.96331i	−0.550366	−	0.333868i
$222$		0			0
$223$	9.36607	+	5.40750i	0.627198	+	0.362113i	0.779666	−	0.626195i	$-0.215389\pi$
$223$	9.36607	+	5.40750i	0.627198	+	0.362113i	−0.152468	+	0.988308i	$0.548722\pi$
$224$	−11.0625	+	11.2061i	−0.739143	+	0.748739i
$225$		0			0
$226$	24.2485			1.61299
$227$	4.90894	+	8.50254i	0.325818	+	0.564334i	0.981678	−	0.190549i	$-0.0610270\pi$
$227$	4.90894	+	8.50254i	0.325818	+	0.564334i	−0.655859	+	0.754883i	$0.727694\pi$
$228$		0			0
$229$		−	18.9204i		−	1.25029i	−0.780507	−	0.625147i	$-0.785039\pi$
$229$		−	18.9204i		−	1.25029i	0.780507	−	0.625147i	$-0.214961\pi$
$230$	24.3884	+	42.2420i	1.60813	+	2.78536i
$231$		0			0
$232$	−6.57585	+	11.3897i	−0.431725	+	0.747770i
$233$			15.7788i			1.03370i	0.856075	+	0.516851i	$0.172896\pi$
$233$			15.7788i			1.03370i	−0.856075	+	0.516851i	$0.827104\pi$
$234$		0			0
$235$	23.6971			1.54583
$236$	5.94128	−	10.2906i	0.386745	−	0.669861i
$237$		0			0
$238$	3.32133	+	12.0831i	0.215290	+	0.783231i
$239$		−	14.5950i		−	0.944075i	−0.881579	−	0.472037i	$-0.843519\pi$
$239$		−	14.5950i		−	0.944075i	0.881579	−	0.472037i	$-0.156481\pi$
$240$		0			0
$241$	−3.56523	+	2.05838i	−0.229656	+	0.132592i	−0.610414	−	0.792083i	$-0.708997\pi$
$241$	−3.56523	+	2.05838i	−0.229656	+	0.132592i	0.380757	+	0.924675i	$0.375663\pi$
$242$		−	20.0969i		−	1.29188i
$243$		0			0
$244$	4.59401	+	2.65235i	0.294101	+	0.169799i
$245$	23.3864	−	13.9074i	1.49410	−	0.888512i
$246$		0			0
$247$	1.50448	−	2.48006i	0.0957276	−	0.157802i
$248$	−3.25088			−0.206431
$249$		0			0
$250$	−30.6910	−	17.7195i	−1.94107	−	1.12068i
$251$	15.6579	+	27.1203i	0.988320	+	1.71182i	0.626135	+	0.779715i	$0.284636\pi$
$251$	15.6579	+	27.1203i	0.988320	+	1.71182i	0.362186	+	0.932106i	$0.382031\pi$
$252$		0			0
$253$	16.5889	+	28.7328i	1.04294	+	1.80642i
$254$	−3.08042	+	1.77848i	−0.193283	+	0.111592i
$255$		0			0
$256$	−10.2128	−	17.6891i	−0.638301	−	1.10557i
$257$	−11.6283	+	20.1408i	−0.725354	+	1.25635i	0.233475	+	0.972363i	$0.424990\pi$
$257$	−11.6283	+	20.1408i	−0.725354	+	1.25635i	−0.958828	+	0.283987i	$0.908343\pi$
$258$		0			0
$259$	0.222919	−	0.853936i	0.0138515	−	0.0530610i
$260$	14.1944	+	8.61072i	0.880297	+	0.534014i
$261$		0			0
$262$	3.55093	+	2.05013i	0.219377	+	0.126657i
$263$	−1.36516	−	0.788174i	−0.0841792	−	0.0486009i	0.457320	−	0.889302i	$-0.348810\pi$
$263$	−1.36516	−	0.788174i	−0.0841792	−	0.0486009i	−0.541499	+	0.840702i	$0.682143\pi$
$264$		0			0
$265$			6.84522i			0.420499i
$266$	−3.66263	+	1.00676i	−0.224570	+	0.0617284i
$267$		0			0
$268$	1.32391			0.0808709
$269$	11.0232	+	19.0928i	0.672098	+	1.16411i	0.977308	+	0.211823i	$0.0679399\pi$
$269$	11.0232	+	19.0928i	0.672098	+	1.16411i	−0.305210	+	0.952285i	$0.598727\pi$
$270$		0			0
$271$	−12.8469	−	7.41717i	−0.780395	−	0.450561i	0.0561755	−	0.998421i	$-0.482109\pi$
$271$	−12.8469	−	7.41717i	−0.780395	−	0.450561i	−0.836570	+	0.547860i	$0.815443\pi$
$272$	−13.1801			−0.799162
$273$		0			0
$274$	−25.2090			−1.52293
$275$	−41.3065	−	23.8483i	−2.49087	−	1.43811i
$276$		0			0
$277$	−5.00875	−	8.67541i	−0.300947	−	0.521255i	0.675404	−	0.737448i	$-0.263969\pi$
$277$	−5.00875	−	8.67541i	−0.300947	−	0.521255i	−0.976351	+	0.216193i	$0.930636\pi$
$278$	23.5292			1.41119
$279$		0			0
$280$	3.96629	+	14.4295i	0.237031	+	0.862329i
$281$		−	10.6025i		−	0.632489i	−0.948678	−	0.316245i	$-0.897578\pi$
$281$		−	10.6025i		−	0.632489i	0.948678	−	0.316245i	$-0.102422\pi$
$282$		0			0
$283$	−13.3265	−	7.69404i	−0.792176	−	0.457363i	0.0485521	−	0.998821i	$-0.484539\pi$
$283$	−13.3265	−	7.69404i	−0.792176	−	0.457363i	−0.840728	+	0.541458i	$0.817873\pi$
$284$	11.9553	+	6.90240i	0.709417	+	0.409582i
$285$		0			0
$286$	25.9558	+	15.7456i	1.53480	+	0.931055i
$287$	−4.18143	+	16.0178i	−0.246822	+	0.945502i
$288$		0			0
$289$	4.97785	−	8.62189i	0.292815	−	0.507170i
$290$	−31.3469	−	54.2945i	−1.84076	−	3.18828i
$291$		0			0
$292$	3.78347	−	2.18439i	0.221411	−	0.127832i
$293$	0.146581	+	0.253886i	0.00856335	+	0.0148322i	0.870275	−	0.492566i	$-0.163941\pi$
$293$	0.146581	+	0.253886i	0.00856335	+	0.0148322i	−0.861712	+	0.507398i	$0.830608\pi$
$294$		0			0
$295$	−19.4953	−	33.7668i	−1.13506	−	1.96598i
$296$	0.420362	+	0.242696i	0.0244330	+	0.0141064i
$297$		0			0
$298$	−10.6468			−0.616751
$299$	−25.3477	−	0.549663i	−1.46590	−	0.0317879i
$300$		0			0
$301$	−3.52709	−	3.48189i	−0.203298	−	0.200693i
$302$	−21.1852	−	12.2313i	−1.21907	−	0.703832i
$303$		0			0
$304$		−	3.99515i		−	0.229138i
$305$	15.0744	−	8.70322i	0.863158	−	0.498345i
$306$		0			0
$307$		−	2.60896i		−	0.148901i	−0.997225	−	0.0744505i	$-0.976280\pi$
$307$		−	2.60896i		−	0.148901i	0.997225	−	0.0744505i	$-0.0237203\pi$
$308$	−3.91935	−	14.2587i	−0.223326	−	0.812466i
$309$		0			0
$310$	7.74845	−	13.4207i	0.440082	−	0.762245i
$311$	−14.0619			−0.797380			−0.398690	−	0.917086i	$-0.630535\pi$
$311$	−14.0619			−0.797380			−0.398690	+	0.917086i	$0.630535\pi$
$312$		0			0
$313$			26.3541i			1.48962i	0.667275	+	0.744812i	$0.267461\pi$
$313$			26.3541i			1.48962i	−0.667275	+	0.744812i	$0.732539\pi$
$314$	9.19374	−	15.9240i	0.518833	−	0.898645i
$315$		0			0
$316$	−3.38216	−	5.85807i	−0.190261	−	0.329542i
$317$			6.51310i			0.365812i	0.983130	+	0.182906i	$0.0585504\pi$
$317$			6.51310i			0.365812i	−0.983130	+	0.182906i	$0.941450\pi$
$318$		0			0
$319$	−21.3221	−	36.9309i	−1.19381	−	2.06773i
$320$	2.67864			0.149741
$321$		0			0
$322$	23.6272	+	23.3244i	1.31669	+	1.29982i
$323$	−1.84919	−	1.06763i	−0.102892	−	0.0594047i
$324$		0			0
$325$	31.9530	−	17.5357i	1.77244	−	0.972703i
$326$		−	27.5408i		−	1.52534i
$327$		0			0
$328$	−7.88500	−	4.55241i	−0.435376	−	0.251365i
$329$	15.5529	−	4.27507i	0.857457	−	0.235692i
$330$		0			0
$331$	0.796900	+	1.38027i	0.0438016	+	0.0758666i	0.887095	−	0.461587i	$-0.152720\pi$
$331$	0.796900	+	1.38027i	0.0438016	+	0.0758666i	−0.843293	+	0.537453i	$0.819386\pi$
$332$	−0.290739	−	0.503574i	−0.0159564	−	0.0276372i
$333$		0			0
$334$	−36.2107	+	20.9063i	−1.98136	+	1.14394i
$335$	2.17209	−	3.76217i	0.118674	−	0.205550i
$336$		0			0
$337$	17.4419			0.950123			0.475061	−	0.879953i	$-0.342426\pi$
$337$	17.4419			0.950123			0.475061	+	0.879953i	$0.342426\pi$
$338$	−20.5749	+	10.7177i	−1.11913	+	0.582966i
$339$		0			0
$340$	6.11049	−	10.5837i	0.331388	−	0.573981i
$341$	5.27046	−	9.12871i	0.285412	−	0.494347i
$342$		0			0
$343$	12.8400	−	13.3467i	0.693294	−	0.720655i
$344$	2.36065	−	1.36292i	0.127278	−	0.0734839i
$345$		0			0
$346$			29.4660i			1.58410i
$347$	−1.96288	+	1.13327i	−0.105373	+	0.0608372i	−0.551760	−	0.834003i	$-0.686044\pi$
$347$	−1.96288	+	1.13327i	−0.105373	+	0.0608372i	0.446387	+	0.894840i	$0.352710\pi$
$348$		0			0
$349$	−0.448257	−	0.258801i	−0.0239947	−	0.0138533i	0.487955	−	0.872869i	$-0.337743\pi$
$349$	−0.448257	−	0.258801i	−0.0239947	−	0.0138533i	−0.511949	+	0.859016i	$0.671076\pi$
$350$	−46.1816	−	12.0556i	−2.46851	−	0.644401i
$351$		0			0
$352$	28.0812			1.49674
$353$	−5.01559	+	8.68726i	−0.266953	+	0.462376i	−0.968073	−	0.250667i	$-0.919350\pi$
$353$	−5.01559	+	8.68726i	−0.266953	+	0.462376i	0.701121	+	0.713043i	$0.252683\pi$
$354$		0			0
$355$	39.2292	−	22.6490i	2.08207	−	1.20208i
$356$	−16.4785			−0.873361
$357$		0			0
$358$	4.75055	+	8.22820i	0.251074	+	0.434874i
$359$		−	34.4131i		−	1.81625i	−0.418695	−	0.908127i	$-0.637513\pi$
$359$		−	34.4131i		−	1.81625i	0.418695	−	0.908127i	$-0.362487\pi$
$360$		0			0
$361$	−9.17638	+	15.8940i	−0.482967	+	0.836524i
$362$	−16.2867	+	28.2095i	−0.856012	+	1.48266i
$363$		0			0
$364$	10.8694	+	3.09065i	0.569713	+	0.161994i
$365$		−	14.3354i		−	0.750348i
$366$		0			0
$367$	5.43012	+	3.13508i	0.283450	+	0.163650i	0.634984	−	0.772525i	$-0.281007\pi$
$367$	5.43012	+	3.13508i	0.283450	+	0.163650i	−0.351534	+	0.936175i	$0.614340\pi$
$368$	−30.2413	+	17.4598i	−1.57643	+	0.910155i
$369$		0			0
$370$	−2.00386	+	1.15693i	−0.104176	+	0.0601458i
$371$	1.23491	+	4.49265i	0.0641133	+	0.233247i
$372$		0			0
$373$	6.58135	+	11.3992i	0.340770	+	0.590230i	0.984576	−	0.174958i	$-0.0559791\pi$
$373$	6.58135	+	11.3992i	0.340770	+	0.590230i	−0.643806	+	0.765188i	$0.722646\pi$
$374$	11.1736	−	19.3533i	0.577775	−	1.00074i
$375$		0			0
$376$			8.87113i			0.457494i
$377$	32.5799	+	0.706493i	1.67795	+	0.0363863i
$378$		0			0
$379$	−7.37553	+	12.7748i	−0.378856	+	0.656197i	−0.990896	−	0.134629i	$-0.957016\pi$
$379$	−7.37553	+	12.7748i	−0.378856	+	0.656197i	0.612040	+	0.790827i	$0.290349\pi$
$380$	3.20812	+	1.85221i	0.164573	+	0.0950164i
$381$		0			0
$382$	35.1980			1.80089
$383$	17.1261	+	29.6632i	0.875101	+	1.51572i	0.856655	+	0.515890i	$0.172539\pi$
$383$	17.1261	+	29.6632i	0.875101	+	1.51572i	0.0184462	+	0.999830i	$0.494128\pi$
$384$		0			0
$385$	−46.9494	−	12.2561i	−2.39277	−	0.624628i
$386$	35.5215	−	20.5083i	1.80800	−	1.04385i
$387$		0			0
$388$	−2.03947	−	1.17749i	−0.103539	−	0.0597780i
$389$		−	9.80077i		−	0.496919i	−0.968642	−	0.248459i	$-0.920076\pi$
$389$		−	9.80077i		−	0.496919i	0.968642	−	0.248459i	$-0.0799242\pi$
$390$		0			0
$391$			18.6633i			0.943843i
$392$	5.20630	+	8.75482i	0.262958	+	0.442185i
$393$		0			0
$394$	−23.8691	−	41.3425i	−1.20251	−	2.08280i
$395$	−22.1959			−1.11680
$396$		0			0
$397$	−27.9778	+	16.1530i	−1.40416	+	0.810694i	−0.994817	−	0.101685i	$-0.967577\pi$
$397$	−27.9778	+	16.1530i	−1.40416	+	0.810694i	−0.409347	+	0.912379i	$0.634243\pi$
$398$	23.0069			1.15323
$399$		0			0
$400$	25.1003	−	43.4750i	1.25501	−	2.17375i
$401$	0.762545	+	0.440255i	0.0380797	+	0.0219853i	0.518919	−	0.854823i	$-0.326335\pi$
$401$	0.762545	+	0.440255i	0.0380797	+	0.0219853i	−0.480839	+	0.876809i	$0.659668\pi$
$402$		0			0
$403$	3.87537	+	7.06161i	0.193046	+	0.351764i
$404$	13.3259			0.662988
$405$		0			0
$406$	−30.3686	−	29.9794i	−1.50717	−	1.48785i
$407$	−1.36302	+	0.786938i	−0.0675622	+	0.0390071i
$408$		0			0
$409$	−8.95661	+	5.17110i	−0.442876	+	0.255694i	−0.704817	−	0.709389i	$-0.748971\pi$
$409$	−8.95661	+	5.17110i	−0.442876	+	0.255694i	0.261941	+	0.965084i	$0.415637\pi$
$410$	37.5877	−	21.7013i	1.85632	−	1.07175i
$411$		0			0
$412$	−15.8339	+	9.14172i	−0.780081	+	0.450380i
$413$	−18.8868	−	18.6447i	−0.929358	−	0.917447i
$414$		0			0
$415$	−1.90801			−0.0936607
$416$	−11.1299	+	18.3470i	−0.545687	+	0.899538i
$417$		0			0
$418$	5.86637	+	3.38695i	0.286934	+	0.165661i
$419$	−13.9563	+	24.1730i	−0.681811	+	1.18093i	0.292617	+	0.956230i	$0.405474\pi$
$419$	−13.9563	+	24.1730i	−0.681811	+	1.18093i	−0.974428	+	0.224701i	$0.927859\pi$
$420$		0			0
$421$	7.16310			0.349108			0.174554	−	0.984648i	$-0.444152\pi$
$421$	7.16310			0.349108			0.174554	+	0.984648i	$0.444152\pi$
$422$	29.0774	−	16.7879i	1.41547	−	0.817220i
$423$		0			0
$424$	−2.56254			−0.124448
$425$	−13.4152	−	23.2358i	−0.650733	−	1.12710i
$426$		0			0
$427$	8.32352	−	8.43158i	0.402803	−	0.408033i
$428$			10.4275i			0.504033i
$429$		0			0
$430$			12.9941i			0.626629i
$431$	−5.83105	−	3.36656i	−0.280872	−	0.162161i	0.352946	−	0.935644i	$-0.385180\pi$
$431$	−5.83105	−	3.36656i	−0.280872	−	0.162161i	−0.633818	+	0.773482i	$0.718513\pi$
$432$		0			0
$433$	−18.1857	+	10.4995i	−0.873947	+	0.504573i	−0.868658	−	0.495413i	$-0.835017\pi$
$433$	−18.1857	+	10.4995i	−0.873947	+	0.504573i	−0.00528907	+	0.999986i	$0.501684\pi$
$434$	2.66429	−	10.2061i	0.127890	−	0.489909i
$435$		0			0
$436$	−7.94920	−	13.7684i	−0.380697	−	0.659387i
$437$	−5.65721			−0.270621
$438$		0			0
$439$	3.55392	+	2.05186i	0.169619	+	0.0979297i	0.582406	−	0.812898i	$-0.302111\pi$
$439$	3.55392	+	2.05186i	0.169619	+	0.0979297i	−0.412787	+	0.910828i	$0.635445\pi$
$440$	13.3435	−	23.1115i	0.636124	−	1.10180i
$441$		0			0
$442$	8.21598	+	14.9710i	0.390794	+	0.712096i
$443$			16.4373i			0.780960i	0.920611	+	0.390480i	$0.127691\pi$
$443$			16.4373i			0.780960i	−0.920611	+	0.390480i	$0.872309\pi$
$444$		0			0
$445$	−27.0357	+	46.8272i	−1.28161	+	2.21982i
$446$	−9.64992	−	16.7141i	−0.456937	−	0.791438i
$447$		0			0
$448$	1.75804	−	0.483240i	0.0830598	−	0.0228309i
$449$	10.5009	−	6.06269i	0.495568	−	0.286116i	−0.231314	−	0.972879i	$-0.574302\pi$
$449$	10.5009	−	6.06269i	0.495568	−	0.286116i	0.726881	+	0.686763i	$0.240969\pi$
$450$		0			0
$451$	25.5670	−	14.7611i	1.20390	−	0.695073i
$452$	−13.9398	−	8.04817i	−0.655675	−	0.378554i
$453$		0			0
$454$		−	17.5204i		−	0.822275i
$455$	26.6158	−	25.8170i	1.24777	−	1.21032i
$456$		0			0
$457$	−4.04728	+	7.01009i	−0.189324	+	0.327918i	−0.945025	−	0.326998i	$-0.893963\pi$
$457$	−4.04728	+	7.01009i	−0.189324	+	0.327918i	0.755701	+	0.654916i	$0.227296\pi$
$458$	−16.8821	+	29.2407i	−0.788849	+	1.36633i
$459$		0			0
$460$		−	32.3785i		−	1.50965i
$461$	12.8067	+	22.1819i	0.596470	+	1.03312i	0.993338	+	0.115240i	$0.0367638\pi$
$461$	12.8067	+	22.1819i	0.596470	+	1.03312i	−0.396868	+	0.917876i	$0.629903\pi$
$462$		0			0
$463$	10.9213			0.507556			0.253778	−	0.967262i	$-0.418327\pi$
$463$	10.9213			0.507556			0.253778	+	0.967262i	$0.418327\pi$
$464$	38.8697	−	22.4414i	1.80448	−	1.04182i
$465$		0			0
$466$	14.0790	−	24.3855i	0.652195	−	1.12964i
$467$	−27.5925			−1.27683			−0.638414	−	0.769694i	$-0.720409\pi$
$467$	−27.5925			−1.27683			−0.638414	+	0.769694i	$0.720409\pi$
$468$		0			0
$469$	0.746871	−	2.86104i	0.0344873	−	0.132111i
$470$	−36.6229	−	21.1443i	−1.68929	−	0.975312i
$471$		0			0
$472$	12.6408	−	7.29814i	0.581838	−	0.335924i
$473$			8.83851i			0.406395i
$474$		0			0
$475$	7.04323	−	4.06641i	0.323166	−	0.186580i
$476$	2.10108	−	8.04863i	0.0963030	−	0.368908i
$477$		0			0
$478$	−13.0227	+	22.5560i	−0.595646	+	1.03169i
$479$	1.75566	−	3.04089i	0.0802181	−	0.138942i	−0.823125	−	0.567860i	$-0.807772\pi$
$479$	1.75566	−	3.04089i	0.0802181	−	0.138942i	0.903344	+	0.428918i	$0.141105\pi$
$480$		0			0
$481$	0.0260747	−	1.20243i	0.00118890	−	0.0548262i
$482$	7.34655			0.334626
$483$		0			0
$484$	−6.67025	+	11.5532i	−0.303193	+	0.525146i
$485$	−6.69216	+	3.86372i	−0.303875	+	0.175443i
$486$		0			0
$487$	−6.03766	−	10.4575i	−0.273592	−	0.473876i	0.696187	−	0.717861i	$-0.254879\pi$
$487$	−6.03766	−	10.4575i	−0.273592	−	0.473876i	−0.969779	+	0.243985i	$0.921545\pi$
$488$	3.25809	+	5.64318i	0.147487	+	0.255455i
$489$		0			0
$490$	−48.5520	+	0.626289i	−2.19335	+	0.0282929i
$491$	−33.3443	−	19.2513i	−1.50481	−	0.868800i	−0.999984	−	0.00557706i	$-0.998225\pi$
$491$	−33.3443	−	19.2513i	−1.50481	−	0.868800i	−0.504822	−	0.863223i	$-0.668442\pi$
$492$		0			0
$493$		−	23.9883i		−	1.08038i
$494$	−4.53799	+	2.49043i	−0.204174	+	0.112050i
$495$		0			0
$496$	9.60795	+	5.54715i	0.431410	+	0.249075i
$497$	21.6609	−	21.9421i	0.971623	−	0.984237i
$498$		0			0
$499$	−14.8740			−0.665851			−0.332926	−	0.942953i	$-0.608036\pi$
$499$	−14.8740			−0.665851			−0.332926	+	0.942953i	$0.608036\pi$
$500$	11.7623	+	20.3730i	0.526027	+	0.911106i
$501$		0			0
$502$		−	55.8845i		−	2.49425i
$503$	−1.27659	−	2.21112i	−0.0569203	−	0.0985888i	0.836161	−	0.548484i	$-0.184795\pi$
$503$	−1.27659	−	2.21112i	−0.0569203	−	0.0985888i	−0.893081	+	0.449895i	$0.851461\pi$
$504$		0			0
$505$	21.8633	−	37.8683i	0.972903	−	1.68512i
$506$		−	59.2073i		−	2.63208i
$507$		0			0
$508$	2.36114			0.104759
$509$	20.3850	−	35.3078i	0.903547	−	1.56499i	0.0806919	−	0.996739i	$-0.474287\pi$
$509$	20.3850	−	35.3078i	0.903547	−	1.56499i	0.822855	−	0.568251i	$-0.192380\pi$
$510$		0			0
$511$	−2.58617	−	9.40857i	−0.114405	−	0.416211i
$512$			15.1033i			0.667479i
$513$		0			0
$514$	35.9421	−	20.7512i	1.58534	−	0.915296i
$515$			59.9938i			2.64364i
$516$		0			0
$517$	−24.9108	−	14.3822i	−1.09557	−	0.632530i
$518$	−1.10645	+	1.12082i	−0.0486148	+	0.0492459i
$519$		0			0
$520$	9.81144	+	17.8782i	0.430260	+	0.784009i
$521$	−23.0735			−1.01087			−0.505433	−	0.862866i	$-0.668667\pi$
$521$	−23.0735			−1.01087			−0.505433	+	0.862866i	$0.668667\pi$
$522$		0			0
$523$	12.0355	+	6.94871i	0.526277	+	0.303846i	0.739499	−	0.673158i	$-0.235063\pi$
$523$	12.0355	+	6.94871i	0.526277	+	0.303846i	−0.213222	+	0.977004i	$0.568396\pi$
$524$	−1.36089	−	2.35713i	−0.0594508	−	0.102972i
$525$		0			0
$526$	1.40653	+	2.43618i	0.0613276	+	0.106223i
$527$	5.13511	−	2.96476i	0.223689	−	0.129147i
$528$		0			0
$529$	13.2234	+	22.9036i	0.574930	+	0.995809i
$530$	6.10779	−	10.5790i	0.265306	−	0.459523i
$531$		0			0
$532$	2.43970	+	0.636880i	0.105774	+	0.0276122i
$533$	−0.489100	+	22.5548i	−0.0211853	+	0.976958i
$534$		0			0
$535$	29.6319	+	17.1080i	1.28110	+	0.739644i
$536$	1.40839	+	0.813133i	0.0608331	+	0.0351220i
$537$		0			0
$538$		−	39.3428i		−	1.69619i
$539$	−33.0248	+	0.425999i	−1.42248	+	0.0183491i
$540$		0			0
$541$	−16.5310			−0.710724			−0.355362	−	0.934729i	$-0.615642\pi$
$541$	−16.5310			−0.710724			−0.355362	+	0.934729i	$0.615642\pi$
$542$	13.2363	+	22.9259i	0.568546	+	0.984751i
$543$		0			0
$544$	13.6800	+	7.89817i	0.586526	+	0.338631i
$545$	−52.1677			−2.23462
$546$		0			0
$547$	7.18339			0.307139			0.153570	−	0.988138i	$-0.450923\pi$
$547$	7.18339			0.307139			0.153570	+	0.988138i	$0.450923\pi$
$548$	14.4920	+	8.36697i	0.619068	+	0.357419i
$549$		0			0
$550$	42.5583	+	73.7131i	1.81469	+	3.14314i
$551$	7.27132			0.309769
$552$		0			0
$553$	−14.5676	+	4.00424i	−0.619477	+	0.170278i
$554$			17.8767i			0.759506i
$555$		0			0
$556$	−13.5264	−	7.80944i	−0.573645	−	0.331194i
$557$	−21.7071	−	12.5326i	−0.919757	−	0.531022i	−0.0361996	−	0.999345i	$-0.511525\pi$
$557$	−21.7071	−	12.5326i	−0.919757	−	0.531022i	−0.883558	+	0.468322i	$0.844859\pi$
$558$		0			0
$559$	−5.77469	−	3.50310i	−0.244243	−	0.148165i
$560$	12.8995	−	49.4142i	0.545104	−	2.08813i
$561$		0			0
$562$	−9.46027	+	16.3857i	−0.399057	+	0.691187i
$563$	9.78613	+	16.9501i	0.412436	+	0.714360i	0.995156	−	0.0983132i	$-0.0313447\pi$
$563$	9.78613	+	16.9501i	0.412436	+	0.714360i	−0.582719	+	0.812673i	$0.698011\pi$
$564$		0			0
$565$	−45.7411	+	26.4086i	−1.92434	+	1.11102i
$566$	13.7303	+	23.7816i	0.577129	+	0.999617i
$567$		0			0
$568$	8.47876	+	14.6856i	0.355761	+	0.616196i
$569$	13.2680	+	7.66027i	0.556223	+	0.321135i	0.751628	−	0.659587i	$-0.229269\pi$
$569$	13.2680	+	7.66027i	0.556223	+	0.321135i	−0.195405	+	0.980723i	$0.562602\pi$
$570$		0			0
$571$	39.3506			1.64677			0.823386	−	0.567482i	$-0.192082\pi$
$571$	39.3506			1.64677			0.823386	+	0.567482i	$0.192082\pi$
$572$	−9.69531	−	17.6666i	−0.405381	−	0.738676i
$573$		0			0
$574$	20.7545	−	21.0239i	0.866275	−	0.877522i
$575$	−61.5613	−	35.5425i	−2.56729	−	1.48222i
$576$		0			0
$577$			15.3698i			0.639853i	0.947442	+	0.319927i	$0.103658\pi$
$577$			15.3698i			0.639853i	−0.947442	+	0.319927i	$0.896342\pi$
$578$	−15.3861	+	8.88319i	−0.639979	+	0.369492i
$579$		0			0
$580$			41.6167i			1.72804i
$581$	−1.25227	+	0.344215i	−0.0519527	+	0.0142804i
$582$		0			0
$583$	4.15450	−	7.19580i	0.172062	−	0.298020i
$584$	5.36651			0.222068
$585$		0			0
$586$		−	0.523160i		−	0.0216115i
$587$	−4.48891	+	7.77502i	−0.185277	+	0.320910i	−0.943670	−	0.330888i	$-0.892652\pi$
$587$	−4.48891	+	7.77502i	−0.185277	+	0.320910i	0.758393	+	0.651798i	$0.225985\pi$
$588$		0			0
$589$	0.898676	+	1.55655i	0.0370293	+	0.0641366i
$590$			69.5802i			2.86457i
$591$		0			0
$592$	−0.828250	−	1.43457i	−0.0340409	−	0.0589605i
$593$	14.2760			0.586247			0.293123	−	0.956075i	$-0.405305\pi$
$593$	14.2760			0.586247			0.293123	+	0.956075i	$0.405305\pi$
$594$		0			0
$595$	−19.4247	−	19.1757i	−0.796334	−	0.786128i
$596$	6.12056	+	3.53371i	0.250708	+	0.144746i
$597$		0			0
$598$	38.6834	+	23.4665i	1.58188	+	0.959617i
$599$			0.992460i			0.0405508i	0.999794	+	0.0202754i	$0.00645431\pi$
$599$			0.992460i			0.0405508i	−0.999794	+	0.0202754i	$0.993546\pi$
$600$		0			0
$601$	15.2558	+	8.80796i	0.622298	+	0.359284i	0.777763	−	0.628557i	$-0.216354\pi$
$601$	15.2558	+	8.80796i	0.622298	+	0.359284i	−0.155465	+	0.987841i	$0.549688\pi$
$602$	2.34419	+	8.52825i	0.0955421	+	0.347585i
$603$		0			0
$604$	8.11923	+	14.0629i	0.330367	+	0.572212i
$605$	21.8872	+	37.9098i	0.889843	+	1.54125i
$606$		0			0
$607$	5.63702	−	3.25454i	0.228800	−	0.132098i	−0.381219	−	0.924485i	$-0.624495\pi$
$607$	5.63702	−	3.25454i	0.228800	−	0.132098i	0.610018	+	0.792387i	$0.291162\pi$
$608$	−2.39409	+	4.14669i	−0.0970932	+	0.168170i
$609$		0			0
$610$	−31.0625			−1.25768
$611$	19.2700	−	10.5753i	0.779580	−	0.427829i
$612$		0			0
$613$	14.2607	−	24.7002i	0.575984	−	0.997633i	−0.419950	−	0.907547i	$-0.637952\pi$
$613$	14.2607	−	24.7002i	0.575984	−	0.997633i	0.995934	−	0.0900860i	$-0.0287142\pi$
$614$	−2.32790	+	4.03204i	−0.0939463	+	0.162720i
$615$		0			0
$616$	4.58813	−	17.5757i	0.184861	−	0.708147i
$617$	−0.532720	+	0.307566i	−0.0214465	+	0.0123821i	−0.510685	−	0.859768i	$-0.670608\pi$
$617$	−0.532720	+	0.307566i	−0.0214465	+	0.0123821i	0.489238	+	0.872150i	$0.337275\pi$
$618$		0			0
$619$			47.7359i			1.91867i	0.282275	+	0.959334i	$0.408911\pi$
$619$			47.7359i			1.91867i	−0.282275	+	0.959334i	$0.591089\pi$
$620$	−8.90877	+	5.14348i	−0.357785	+	0.206567i
$621$		0			0
$622$	21.7322	+	12.5471i	0.871380	+	0.503092i
$623$	−9.29618	+	35.6109i	−0.372444	+	1.42672i
$624$		0			0
$625$	26.6469			1.06588
$626$	23.5150	−	40.7292i	0.939850	−	1.62787i
$627$		0			0
$628$	−10.5705	+	6.10288i	−0.421809	+	0.243531i
$629$	−0.885341			−0.0353008
$630$		0			0
$631$	7.04444	+	12.2013i	0.280435	+	0.485727i	0.971492	−	0.237073i	$-0.0761880\pi$
$631$	7.04444	+	12.2013i	0.280435	+	0.485727i	−0.691057	+	0.722800i	$0.742855\pi$
$632$		−	8.30914i		−	0.330520i
$633$		0			0
$634$	5.81145	−	10.0657i	0.230802	−	0.399761i
$635$	3.87383	−	6.70967i	0.153728	−	0.266265i
$636$		0			0
$637$	12.8109	−	21.7458i	0.507587	−	0.861601i
$638$			76.1003i			3.01284i
$639$		0			0
$640$	35.9299	+	20.7442i	1.42026	+	0.819985i
$641$	−21.4432	+	12.3802i	−0.846956	+	0.488990i	−0.859623	−	0.510930i	$-0.829301\pi$
$641$	−21.4432	+	12.3802i	−0.846956	+	0.488990i	0.0126667	+	0.999920i	$0.495968\pi$
$642$		0			0
$643$	−4.23619	+	2.44576i	−0.167059	+	0.0964515i	−0.581198	−	0.813762i	$-0.697416\pi$
$643$	−4.23619	+	2.44576i	−0.167059	+	0.0964515i	0.414139	+	0.910213i	$0.364083\pi$
$644$	−5.84123	−	21.2506i	−0.230177	−	0.837390i
$645$		0			0
$646$	1.90524	+	3.29997i	0.0749606	+	0.129835i
$647$	−18.5924	+	32.2029i	−0.730941	+	1.26603i	0.225540	+	0.974234i	$0.427585\pi$
$647$	−18.5924	+	32.2029i	−0.730941	+	1.26603i	−0.956481	+	0.291793i	$0.905748\pi$
$648$		0			0
$649$			47.3282i			1.85779i
$650$	−65.0287	−	1.41014i	−2.55063	−	0.0553103i
$651$		0			0
$652$	−9.14090	+	15.8325i	−0.357985	+	0.620049i
$653$	33.3158	+	19.2349i	1.30375	+	0.752718i	0.981045	−	0.193782i	$-0.0620755\pi$
$653$	33.3158	+	19.2349i	1.30375	+	0.752718i	0.322702	+	0.946501i	$0.395409\pi$
$654$		0			0
$655$	−8.93104			−0.348965
$656$	15.5360	+	26.9092i	0.606580	+	1.05063i
$657$		0			0
$658$	−27.8508	−	7.27042i	−1.08574	−	0.283431i
$659$	23.6197	−	13.6368i	0.920091	−	0.531215i	0.0364270	−	0.999336i	$-0.488402\pi$
$659$	23.6197	−	13.6368i	0.920091	−	0.531215i	0.883664	+	0.468121i	$0.155069\pi$
$660$		0			0
$661$	−34.5149	−	19.9272i	−1.34247	−	0.775078i	−0.355305	−	0.934750i	$-0.615623\pi$
$661$	−34.5149	−	19.9272i	−1.34247	−	0.775078i	−0.987170	+	0.159672i	$0.948956\pi$
$662$		−	2.84421i		−	0.110543i
$663$		0			0
$664$		−	0.714274i		−	0.0277192i
$665$	5.81254	−	5.88800i	0.225401	−	0.228327i
$666$		0			0
$667$	−31.7775	−	55.0402i	−1.23043	−	2.13117i
$668$	27.7555			1.07389
$669$		0			0
$670$	−6.71376	+	3.87619i	−0.259375	+	0.149750i
$671$	−21.1286			−0.815661
$672$		0			0
$673$	−7.12114	+	12.3342i	−0.274500	+	0.475448i	−0.970009	−	0.243070i	$-0.921846\pi$
$673$	−7.12114	+	12.3342i	−0.274500	+	0.475448i	0.695509	+	0.718517i	$0.255179\pi$
$674$	−26.9558	−	15.5629i	−1.03830	−	0.599462i
$675$		0			0
$676$	15.3852	+	0.667570i	0.591740	+	0.0256758i
$677$	39.2974			1.51032			0.755160	−	0.655540i	$-0.227559\pi$
$677$	39.2974			1.51032			0.755160	+	0.655540i	$0.227559\pi$
$678$		0			0
$679$	−3.69516	+	3.74313i	−0.141807	+	0.143648i
$680$	13.0008	−	7.50599i	0.498556	−	0.287842i
$681$		0			0
$682$	−16.2906	+	9.40537i	−0.623798	+	0.360150i
$683$	−7.80737	+	4.50759i	−0.298741	+	0.172478i	−0.641877	−	0.766808i	$-0.721844\pi$
$683$	−7.80737	+	4.50759i	−0.298741	+	0.172478i	0.343136	+	0.939286i	$0.388511\pi$
$684$		0			0
$685$	47.5529	−	27.4547i	1.81690	−	1.04899i
$686$	−31.7526	+	9.17005i	−1.21232	+	0.350114i
$687$		0			0
$688$	−9.30251			−0.354655
$689$	3.05480	+	5.56639i	0.116379	+	0.212062i
$690$		0			0
$691$	−10.0607	−	5.80857i	−0.382728	−	0.220968i	0.296276	−	0.955102i	$-0.404255\pi$
$691$	−10.0607	−	5.80857i	−0.382728	−	0.220968i	−0.679005	+	0.734134i	$0.737588\pi$
$692$	9.77989	−	16.9393i	0.371776	−	0.643935i
$693$		0			0
$694$	4.04474			0.153536
$695$	−44.3843	+	25.6253i	−1.68359	+	0.972023i
$696$		0			0
$697$	16.6069			0.629032
$698$	0.461842	+	0.799934i	0.0174810	+	0.0302780i
$699$		0			0
$700$	22.5473	+	22.2583i	0.852208	+	0.841286i
$701$			36.4342i			1.37610i	0.725663	+	0.688050i	$0.241533\pi$
$701$			36.4342i			1.37610i	−0.725663	+	0.688050i	$0.758467\pi$
$702$		0			0
$703$		−	0.268364i		−	0.0101215i
$704$	−2.81583	−	1.62572i	−0.106126	−	0.0612717i
$705$		0			0
$706$	15.5028	−	8.95053i	0.583455	−	0.336858i
$707$	7.51766	−	28.7979i	0.282731	−	1.08306i
$708$		0			0
$709$	1.69480	+	2.93548i	0.0636495	+	0.110244i	0.896094	−	0.443864i	$-0.146393\pi$
$709$	1.69480	+	2.93548i	0.0636495	+	0.110244i	−0.832445	+	0.554108i	$0.813059\pi$
$710$	−80.8362			−3.03373
$711$		0			0
$712$	−17.5300	−	10.1209i	−0.656964	−	0.379298i
$713$	7.85487	−	13.6050i	0.294167	−	0.509513i
$714$		0			0
$715$	−66.1099	−	1.43359i	−2.47237	−	0.0536132i
$716$		−	6.30690i		−	0.235700i
$717$		0			0
$718$	−30.7058	+	53.1840i	−1.14593	+	1.98481i
$719$	−10.3981	−	18.0101i	−0.387785	−	0.671663i	0.604366	−	0.796707i	$-0.293426\pi$
$719$	−10.3981	−	18.0101i	−0.387785	−	0.671663i	−0.992151	+	0.125043i	$0.960093\pi$
$720$		0			0
$721$	10.8232	+	39.3751i	0.403076	+	1.46640i
$722$	28.3634	−	16.3756i	1.05558	−	0.609438i
$723$		0			0
$724$	18.7256	−	10.8113i	0.695933	−	0.401797i
$725$	79.1260	+	45.6834i	2.93867	+	1.69664i
$726$		0			0
$727$		−	22.1844i		−	0.822773i	−0.911461	−	0.411387i	$-0.865045\pi$
$727$		−	22.1844i		−	0.822773i	0.911461	−	0.411387i	$-0.134955\pi$
$728$	9.66473	+	9.96374i	0.358199	+	0.369281i
$729$		0			0
$730$	−12.7910	+	22.1547i	−0.473418	+	0.819983i
$731$	−2.48593	+	4.30576i	−0.0919455	+	0.159254i
$732$		0			0
$733$			14.6577i			0.541394i	0.962665	+	0.270697i	$0.0872541\pi$
$733$			14.6577i			0.541394i	−0.962665	+	0.270697i	$0.912746\pi$
$734$	−5.59469	−	9.69029i	−0.206504	−	0.357675i
$735$		0			0
$736$	41.8511			1.54265
$737$	−4.56667	+	2.63657i	−0.168216	+	0.0971193i
$738$		0			0
$739$	4.33821	−	7.51399i	0.159583	−	0.276407i	−0.775135	−	0.631796i	$-0.782318\pi$
$739$	4.33821	−	7.51399i	0.159583	−	0.276407i	0.934719	+	0.355389i	$0.115652\pi$
$740$	1.53596			0.0564628
$741$		0			0
$742$	2.10016	−	8.04508i	0.0770992	−	0.295344i
$743$	21.5507	+	12.4423i	0.790618	+	0.456463i	0.840180	−	0.542308i	$-0.182449\pi$
$743$	21.5507	+	12.4423i	0.790618	+	0.456463i	−0.0495623	+	0.998771i	$0.515783\pi$
$744$		0			0
$745$	20.0835	−	11.5952i	0.735803	−	0.424816i
$746$		−	23.4894i		−	0.860008i
$747$		0			0
$748$	−12.8469	+	7.41715i	−0.469729	+	0.271198i
$749$	22.5344	+	5.88257i	0.823388	+	0.214944i
$750$		0			0
$751$	−9.04807	+	15.6717i	−0.330169	+	0.571869i	−0.982545	−	0.186026i	$-0.940439\pi$
$751$	−9.04807	+	15.6717i	−0.330169	+	0.571869i	0.652376	+	0.757896i	$0.273772\pi$
$752$	15.1373	−	26.2185i	0.552000	−	0.956091i
$753$		0			0
$754$	−49.7206	−	30.1620i	−1.81072	−	1.09843i
$755$	53.2836			1.93919
$756$		0			0
$757$	8.40877	−	14.5644i	0.305622	−	0.529353i	−0.671778	−	0.740753i	$-0.734469\pi$
$757$	8.40877	−	14.5644i	0.305622	−	0.529353i	0.977400	+	0.211400i	$0.0678023\pi$
$758$	22.7972	−	13.1620i	0.828031	−	0.478064i
$759$		0			0
$760$	2.27521	+	3.94079i	0.0825307	+	0.142947i
$761$	−9.86345	−	17.0840i	−0.357550	−	0.619294i	0.630001	−	0.776594i	$-0.283054\pi$
$761$	−9.86345	−	17.0840i	−0.357550	−	0.619294i	−0.987551	+	0.157300i	$0.949721\pi$
$762$		0			0
$763$	−34.2386	+	9.41130i	−1.23952	+	0.340712i
$764$	−20.2344	−	11.6823i	−0.732056	−	0.422653i
$765$		0			0
$766$		−	61.1244i		−	2.20851i
$767$	−30.9221	−	18.7583i	−1.11653	−	0.677323i
$768$		0			0
$769$	−36.1153	−	20.8512i	−1.30235	−	0.751913i	−0.321544	−	0.946895i	$-0.604202\pi$
$769$	−36.1153	−	20.8512i	−1.30235	−	0.751913i	−0.980807	+	0.194982i	$0.937535\pi$
$770$	61.6227	+	60.8329i	2.22073	+	2.19227i
$771$		0			0
$772$	−27.2272			−0.979928
$773$	−4.42516	−	7.66459i	−0.159162	−	0.275676i	0.775405	−	0.631464i	$-0.217546\pi$
$773$	−4.42516	−	7.66459i	−0.159162	−	0.275676i	−0.934567	+	0.355788i	$0.884212\pi$
$774$		0			0
$775$			22.5844i			0.811255i
$776$	−1.44640	−	2.50524i	−0.0519228	−	0.0899330i
$777$		0			0
$778$	−8.74495	+	15.1467i	−0.313521	+	0.543035i
$779$			5.03388i			0.180358i
$780$		0			0
$781$	−54.9845			−1.96750
$782$	16.6527	−	28.8433i	0.595500	−	1.03144i
$783$		0			0
$784$	−0.448364	−	34.7586i	−0.0160130	−	1.24138i
$785$			40.0510i			1.42948i
$786$		0			0
$787$	−14.9967	+	8.65836i	−0.534575	+	0.308637i	−0.742878	−	0.669427i	$-0.766540\pi$
$787$	−14.9967	+	8.65836i	−0.534575	+	0.308637i	0.208302	+	0.978064i	$0.433206\pi$
$788$			31.6890i			1.12887i
$789$		0			0
$790$	34.3029	+	19.8048i	1.22044	+	0.704622i
$791$	−25.2565	+	25.5844i	−0.898017	+	0.909676i
$792$		0			0
$793$	8.37422	−	13.8045i	0.297377	−	0.490212i
$794$	57.6513			2.04597
$795$		0			0
$796$	−13.2261	−	7.63607i	−0.468785	−	0.270653i
$797$	−13.5108	−	23.4015i	−0.478578	−	0.828922i	0.521120	−	0.853483i	$-0.325514\pi$
$797$	−13.5108	−	23.4015i	−0.478578	−	0.828922i	−0.999698	+	0.0245614i	$0.992181\pi$
$798$		0			0
$799$	−8.09033	−	14.0129i	−0.286215	−	0.495740i
$800$	−52.1046	+	30.0826i	−1.84218	+	1.06358i
$801$		0			0
$802$	−0.785655	−	1.36079i	−0.0277424	−	0.0480513i
$803$	−8.70041	+	15.0696i	−0.307031	+	0.531793i
$804$		0			0
$805$	−69.9714	−	18.2659i	−2.46617	−	0.643790i
$806$	0.311641	−	14.3713i	0.0109771	−	0.506208i
$807$		0			0
$808$	14.1762	+	8.18462i	0.498716	+	0.287934i
$809$	−11.1717	−	6.44996i	−0.392775	−	0.226769i	0.290587	−	0.956849i	$-0.406149\pi$
$809$	−11.1717	−	6.44996i	−0.392775	−	0.226769i	−0.683362	+	0.730080i	$0.739483\pi$
$810$		0			0
$811$			36.2612i			1.27330i	0.771152	+	0.636651i	$0.219681\pi$
$811$			36.2612i			1.27330i	−0.771152	+	0.636651i	$0.780319\pi$
$812$	7.50784	+	27.3138i	0.263474	+	0.958527i
$813$		0			0
$814$	2.80865			0.0984431
$815$	29.9942	+	51.9515i	1.05065	+	1.81978i
$816$		0			0
$817$	−1.30516	−	0.753535i	−0.0456618	−	0.0263628i
$818$	18.4561			0.645302
$819$		0			0
$820$	−28.8109			−1.00612
$821$	33.5827	+	19.3890i	1.17204	+	0.676679i	0.954160	−	0.299296i	$-0.0967516\pi$
$821$	33.5827	+	19.3890i	1.17204	+	0.676679i	0.217883	+	0.975975i	$0.430085\pi$
$822$		0			0
$823$	2.78193	+	4.81844i	0.0969719	+	0.167960i	0.910430	−	0.413663i	$-0.135751\pi$
$823$	2.78193	+	4.81844i	0.0969719	+	0.167960i	−0.813458	+	0.581624i	$0.802418\pi$
$824$	−22.4590			−0.782396
$825$		0			0
$826$	12.5526	+	45.6668i	0.436761	+	1.58895i
$827$		−	7.85776i		−	0.273241i	−0.990623	−	0.136621i	$-0.956376\pi$
$827$		−	7.85776i		−	0.273241i	0.990623	−	0.136621i	$-0.0436241\pi$
$828$		0			0
$829$	11.6520	+	6.72727i	0.404690	+	0.233648i	0.688505	−	0.725231i	$-0.258267\pi$
$829$	11.6520	+	6.72727i	0.404690	+	0.233648i	−0.283816	+	0.958879i	$0.591600\pi$
$830$	2.94876	+	1.70247i	0.102353	+	0.0590935i
$831$		0			0
$832$	2.17822	−	1.19539i	0.0755160	−	0.0414428i
$833$	−16.2082	−	9.08108i	−0.561580	−	0.314641i
$834$		0			0
$835$	45.5373	−	78.8729i	1.57588	−	2.72951i
$836$	−2.24828	−	3.89414i	−0.0777585	−	0.134682i
$837$		0			0
$838$	43.1378	−	24.9056i	1.49017	−	0.860351i
$839$	−2.20891	−	3.82595i	−0.0762601	−	0.132086i	0.825373	−	0.564587i	$-0.190965\pi$
$839$	−2.20891	−	3.82595i	−0.0762601	−	0.132086i	−0.901634	+	0.432501i	$0.857631\pi$
$840$		0			0
$841$	26.3442	+	45.6295i	0.908422	+	1.57343i
$842$	−11.0703	−	6.39143i	−0.381507	−	0.220263i
$843$		0			0
$844$	−22.2878			−0.767179
$845$	27.1390	−	42.6251i	0.933609	−	1.46635i
$846$		0			0
$847$	21.2041	+	20.9324i	0.728582	+	0.719244i
$848$	7.57357	+	4.37260i	0.260077	+	0.150156i
$849$		0			0
$850$			47.8800i			1.64227i
$851$	−2.03138	+	1.17282i	−0.0696348	+	0.0402037i
$852$		0			0
$853$			10.8155i			0.370317i	0.982709	+	0.185159i	$0.0592799\pi$
$853$			10.8155i			0.370317i	−0.982709	+	0.185159i	$0.940720\pi$
$854$	−20.3869	+	5.60382i	−0.697626	+	0.191759i
$855$		0			0
$856$	−6.40447	+	11.0929i	−0.218900	+	0.379146i
$857$	19.8061			0.676562			0.338281	−	0.941045i	$-0.390154\pi$
$857$	19.8061			0.676562			0.338281	+	0.941045i	$0.390154\pi$
$858$		0			0
$859$		−	29.8841i		−	1.01963i	−0.860284	−	0.509816i	$-0.829714\pi$
$859$		−	29.8841i		−	1.01963i	0.860284	−	0.509816i	$-0.170286\pi$
$860$	4.31278	−	7.46995i	0.147065	−	0.254723i
$861$		0			0
$862$	6.00777	+	10.4058i	0.204625	+	0.354422i
$863$		−	6.82228i		−	0.232233i	−0.993236	−	0.116117i	$-0.962955\pi$
$863$		−	6.82228i		−	0.232233i	0.993236	−	0.116117i	$-0.0370446\pi$
$864$		0			0
$865$	−32.0910	−	55.5832i	−1.09113	−	1.88989i
$866$	37.4736			1.27340
$867$		0			0
$868$	−4.91908	+	4.98295i	−0.166965	+	0.169132i
$869$	23.3327	+	13.4711i	0.791507	+	0.456977i
$870$		0			0
$871$	0.0873611	−	4.02865i	0.00296012	−	0.136506i
$872$		−	19.5292i		−	0.661343i
$873$		0			0
$874$	8.74299	+	5.04777i	0.295736	+	0.170743i
$875$	50.6625	−	13.9258i	1.71271	−	0.470778i
$876$		0			0
$877$	−13.3337	−	23.0947i	−0.450248	−	0.779853i	0.548153	−	0.836378i	$-0.315331\pi$
$877$	−13.3337	−	23.0947i	−0.450248	−	0.779853i	−0.998401	+	0.0565252i	$0.981998\pi$
$878$	−3.66162	−	6.34212i	−0.123574	−	0.214036i
$879$		0			0
$880$	−78.8729	+	45.5373i	−2.65880	+	1.53506i
$881$	6.30831	−	10.9263i	0.212532	−	0.368117i	−0.739974	−	0.672635i	$-0.765162\pi$
$881$	6.30831	−	10.9263i	0.212532	−	0.368117i	0.952506	+	0.304519i	$0.0984956\pi$
$882$		0			0
$883$	−30.5502			−1.02810			−0.514048	−	0.857761i	$-0.671855\pi$
$883$	−30.5502			−1.02810			−0.514048	+	0.857761i	$0.671855\pi$
$884$	0.245763	−	11.3333i	0.00826589	−	0.381181i
$885$		0			0
$886$	14.6665	−	25.4032i	0.492732	−	0.853437i
$887$	8.24847	−	14.2868i	0.276956	−	0.479702i	−0.693670	−	0.720292i	$-0.744008\pi$
$887$	8.24847	−	14.2868i	0.276956	−	0.479702i	0.970627	+	0.240590i	$0.0773409\pi$
$888$		0			0
$889$	1.33201	−	5.10254i	0.0446742	−	0.171134i
$890$	83.5651	−	48.2463i	2.80111	−	1.61722i
$891$		0			0
$892$			12.8114i			0.428957i
$893$	4.24758	−	2.45234i	0.142140	−	0.0820644i
$894$		0			0
$895$	−17.9224	−	10.3475i	−0.599079	−	0.345878i
$896$	27.3238	+	7.13285i	0.912825	+	0.238292i
$897$		0			0
$898$	−21.6383			−0.722078
$899$	−10.0960	+	17.4868i	−0.336721	+	0.583218i
$900$		0			0
$901$	4.04780	−	2.33700i	0.134852	−	0.0778567i
$902$	−52.6836			−1.75417
$903$		0			0
$904$	−9.88619	−	17.1234i	−0.328810	−	0.569515i
$905$		−	70.9504i		−	2.35847i
$906$		0			0
$907$	13.3346	−	23.0963i	0.442769	−	0.766899i	−0.555124	−	0.831767i	$-0.687329\pi$
$907$	13.3346	−	23.0963i	0.442769	−	0.766899i	0.997894	+	0.0648681i	$0.0206627\pi$
$908$	−5.81510	+	10.0721i	−0.192981	+	0.334253i
$909$		0			0
$910$	−64.1694	+	16.1507i	−2.12720	+	0.535391i
$911$		−	12.4400i		−	0.412156i	−0.978536	−	0.206078i	$-0.933930\pi$
$911$		−	12.4400i		−	0.412156i	0.978536	−	0.206078i	$-0.0660701\pi$
$912$		0			0
$913$	2.00573	+	1.15801i	0.0663801	+	0.0383246i
$914$	12.5098	−	7.22254i	0.413787	−	0.238900i
$915$		0			0
$916$	19.4102	−	11.2065i	0.641330	−	0.370272i
$917$	−5.86161	+	1.61120i	−0.193567	+	0.0532065i
$918$		0			0
$919$	−20.8215	−	36.0638i	−0.686837	−	1.18964i	−0.972856	−	0.231412i	$-0.925665\pi$
$919$	−20.8215	−	36.0638i	−0.686837	−	1.18964i	0.286019	−	0.958224i	$-0.407668\pi$
$920$	19.8865	−	34.4444i	0.655638	−	1.13560i
$921$		0			0
$922$		−	45.7084i		−	1.50533i
$923$	21.7928	−	35.9244i	0.717320	−	1.18247i
$924$		0			0
$925$	1.68605	−	2.92032i	0.0554369	−	0.0960195i
$926$	−16.8784	−	9.74477i	−0.554660	−	0.320233i
$927$		0			0
$928$	−53.7920			−1.76581
$929$	−27.7394	−	48.0460i	−0.910099	−	1.57634i	−0.813922	−	0.580974i	$-0.802672\pi$
$929$	−27.7394	−	48.0460i	−0.910099	−	1.57634i	−0.0961770	−	0.995364i	$-0.530661\pi$
$930$		0			0
$931$	2.75266	−	4.91301i	0.0902146	−	0.161018i
$932$	−16.1873	+	9.34572i	−0.530232	+	0.306129i
$933$		0			0
$934$	42.6430	+	24.6200i	1.39532	+	0.805590i
$935$			48.6761i			1.59188i
$936$		0			0
$937$		−	50.6718i		−	1.65538i	−0.561188	−	0.827688i	$-0.689656\pi$
$937$		−	50.6718i		−	1.65538i	0.561188	−	0.827688i	$-0.310344\pi$
$938$	−3.70708	+	3.75521i	−0.121041	+	0.122612i
$939$		0			0
$940$	14.0357	+	24.3106i	0.457795	+	0.792924i
$941$	−32.7877			−1.06885			−0.534424	−	0.845216i	$-0.679472\pi$
$941$	−32.7877			−1.06885			−0.534424	+	0.845216i	$0.679472\pi$
$942$		0			0
$943$	38.1039	−	21.9993i	1.24083	−	0.716396i
$944$	−49.8128			−1.62127
$945$		0			0
$946$	7.88635	−	13.6596i	0.256407	−	0.444111i
$947$	4.37815	+	2.52773i	0.142271	+	0.0821401i	0.569446	−	0.822029i	$-0.307158\pi$
$947$	4.37815	+	2.52773i	0.142271	+	0.0821401i	−0.427175	+	0.904169i	$0.640491\pi$
$948$		0			0
$949$	−6.39741	−	11.6572i	−0.207669	−	0.378409i
$950$	−14.5134			−0.470876
$951$		0			0
$952$	7.17853	−	7.27172i	0.232657	−	0.235678i
$953$	7.37256	−	4.25655i	0.238821	−	0.137883i	−0.375814	−	0.926695i	$-0.622637\pi$
$953$	7.37256	−	4.25655i	0.238821	−	0.137883i	0.614635	+	0.788812i	$0.289303\pi$
$954$		0			0
$955$	−66.3956	+	38.3335i	−2.14851	+	1.24044i
$956$	14.9729	−	8.64459i	0.484257	−	0.279586i
$957$		0			0
$958$	−5.42660	+	3.13305i	−0.175325	+	0.101224i
$959$	26.2569	−	26.5978i	0.847880	−	0.858888i
$960$		0			0
$961$	26.0089			0.838995
$962$	−1.11319	+	1.83505i	−0.0358908	+	0.0591643i
$963$		0			0
$964$	−4.22334	−	2.43835i	−0.136025	−	0.0785339i
$965$	−44.6706	+	77.3717i	−1.43800	+	2.49068i
$966$		0			0
$967$	−8.67683			−0.279028			−0.139514	−	0.990220i	$-0.544554\pi$
$967$	−8.67683			−0.279028			−0.139514	+	0.990220i	$0.544554\pi$
$968$	−14.1917	+	8.19359i	−0.456139	+	0.263352i
$969$		0			0
$970$	13.7900			0.442769
$971$	−3.00467	−	5.20424i	−0.0964243	−	0.167012i	0.813778	−	0.581176i	$-0.197407\pi$
$971$	−3.00467	−	5.20424i	−0.0964243	−	0.167012i	−0.910202	+	0.414164i	$0.864074\pi$
$972$		0			0
$973$	−24.5073	+	24.8255i	−0.785669	+	0.795869i
$974$			21.5489i			0.690472i
$975$		0			0
$976$		−	22.2378i		−	0.711815i
$977$	−14.2374	−	8.21998i	−0.455496	−	0.262981i	0.254653	−	0.967033i	$-0.418039\pi$
$977$	−14.2374	−	8.21998i	−0.455496	−	0.262981i	−0.710148	+	0.704052i	$0.751372\pi$
$978$		0			0
$979$	56.8406	−	32.8170i	1.81663	−	1.04883i
$980$	28.1191	+	15.7545i	0.898233	+	0.503260i
$981$		0			0
$982$	34.3548	+	59.5043i	1.09631	+	1.89886i
$983$	37.3863			1.19244			0.596218	−	0.802822i	$-0.296669\pi$
$983$	37.3863			1.19244			0.596218	+	0.802822i	$0.296669\pi$
$984$		0			0
$985$	90.0508	+	51.9908i	2.86926	+	1.65657i
$986$	−21.4041	+	37.0729i	−0.681644	+	1.18064i
$987$		0			0
$988$	3.43536	+	0.0744955i	0.109293	+	0.00237002i
$989$			13.1725i			0.418862i
$990$		0			0
$991$	−3.46091	+	5.99448i	−0.109940	+	0.190421i	−0.915746	−	0.401759i	$-0.868399\pi$
$991$	−3.46091	+	5.99448i	−0.109940	+	0.190421i	0.805806	+	0.592180i	$0.201732\pi$
$992$	−6.64825	−	11.5151i	−0.211082	−	0.365605i
$993$		0			0
$994$	−53.0543	+	14.5832i	−1.68278	+	0.462552i
$995$	−43.3989	+	25.0564i	−1.37584	+	0.794341i
$996$		0			0
$997$	0.117691	−	0.0679491i	0.00372732	−	0.00215197i	−0.498135	−	0.867099i	$-0.665982\pi$
$997$	0.117691	−	0.0679491i	0.00372732	−	0.00215197i	0.501863	+	0.864947i	$0.332648\pi$
$998$	22.9871	+	13.2716i	0.727645	+	0.420106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.8	yes	72
3.2	odd	2	inner	819.2.dx.a.503.29	yes	72
7.6	odd	2	inner	819.2.dx.a.503.7	✓	72
13.3	even	3	inner	819.2.dx.a.692.30	yes	72
21.20	even	2	inner	819.2.dx.a.503.30	yes	72
39.29	odd	6	inner	819.2.dx.a.692.7	yes	72
91.55	odd	6	inner	819.2.dx.a.692.29	yes	72
273.146	even	6	inner	819.2.dx.a.692.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.7	✓	72	7.6	odd	2	inner
819.2.dx.a.503.8	yes	72	1.1	even	1	trivial
819.2.dx.a.503.29	yes	72	3.2	odd	2	inner
819.2.dx.a.503.30	yes	72	21.20	even	2	inner
819.2.dx.a.692.7	yes	72	39.29	odd	6	inner
819.2.dx.a.692.8	yes	72	273.146	even	6	inner
819.2.dx.a.692.29	yes	72	91.55	odd	6	inner
819.2.dx.a.692.30	yes	72	13.3	even	3	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} +3.88703 q^{5} +(2.55113 - 0.701238i) q^{7} +1.45513i q^{8} +O(q^{10})\)	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} +3.88703 q^{5} +(2.55113 - 0.701238i) q^{7} +1.45513i q^{8} +(-6.00725 - 3.46829i) q^{10} +(-4.08611 - 2.35911i) q^{11} +(3.16085 - 1.73466i) q^{13} +(-4.56836 - 1.19257i) q^{14} +(2.48296 - 4.30062i) q^{16} +(-1.32706 - 2.29853i) q^{17} +(0.696729 - 0.402257i) q^{19} +(2.30227 + 3.98766i) q^{20} +(4.20994 + 7.29183i) q^{22} +(-6.08975 - 3.51592i) q^{23} +10.1090 q^{25} +(-6.43275 - 0.139494i) q^{26} +(2.23042 + 2.20183i) q^{28} +(7.82728 + 4.51908i) q^{29} +2.23409i q^{31} +(-5.15428 + 2.97582i) q^{32} +4.73637i q^{34} +(9.91632 - 2.72573i) q^{35} +(0.166787 - 0.288883i) q^{37} -1.43569 q^{38} +5.65613i q^{40} +(-3.12853 + 5.41877i) q^{41} +(-0.936635 - 1.62230i) q^{43} -5.58918i q^{44} +(6.27431 + 10.8674i) q^{46} +6.09646 q^{47} +(6.01653 - 3.57790i) q^{49} +(-15.6231 - 9.01998i) q^{50} +(3.65172 + 2.21525i) q^{52} +1.76104i q^{53} +(-15.8828 - 9.16995i) q^{55} +(1.02039 + 3.71222i) q^{56} +(-8.06450 - 13.9681i) q^{58} +(-5.01546 - 8.68704i) q^{59} +(3.87813 - 2.23904i) q^{61} +(1.99341 - 3.45269i) q^{62} +0.689124 q^{64} +(12.2863 - 6.74266i) q^{65} +(0.558805 - 0.967879i) q^{67} +(1.57202 - 2.72282i) q^{68} +(-17.7574 - 4.63554i) q^{70} +(10.0923 - 5.82681i) q^{71} -3.68800i q^{73} +(-0.515524 + 0.297638i) q^{74} +(0.825340 + 0.476510i) q^{76} +(-12.0785 - 3.15307i) q^{77} -5.71025 q^{79} +(9.65135 - 16.7166i) q^{80} +(9.67002 - 5.58299i) q^{82} -0.490867 q^{83} +(-5.15830 - 8.93444i) q^{85} +3.34293i q^{86} +(3.43281 - 5.94581i) q^{88} +(-6.95536 + 12.0470i) q^{89} +(6.84733 - 6.64184i) q^{91} -8.32987i q^{92} +(-9.42183 - 5.43969i) q^{94} +(2.70821 - 1.56358i) q^{95} +(-1.72166 + 0.994004i) q^{97} +(-12.4908 + 0.161123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

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