LMFDB - Embedded newform 819.2.dx.a.503.7

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			503.7
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} -3.88703 q^{5} +(-1.88286 + 1.85872i) q^{7} +1.45513i q^{8} +O(q^{10})$	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} -3.88703 q^{5} +(-1.88286 + 1.85872i) q^{7} +1.45513i q^{8} +(6.00725 + 3.46829i) q^{10} +(-4.08611 - 2.35911i) q^{11} +(-3.16085 + 1.73466i) q^{13} +(4.56836 - 1.19257i) q^{14} +(2.48296 - 4.30062i) q^{16} +(1.32706 + 2.29853i) q^{17} +(-0.696729 + 0.402257i) q^{19} +(-2.30227 - 3.98766i) q^{20} +(4.20994 + 7.29183i) q^{22} +(-6.08975 - 3.51592i) q^{23} +10.1090 q^{25} +(6.43275 + 0.139494i) q^{26} +(-3.02205 - 0.830682i) q^{28} +(7.82728 + 4.51908i) q^{29} -2.23409i q^{31} +(-5.15428 + 2.97582i) q^{32} -4.73637i q^{34} +(7.31872 - 7.22492i) q^{35} +(0.166787 - 0.288883i) q^{37} +1.43569 q^{38} -5.65613i q^{40} +(3.12853 - 5.41877i) q^{41} +(-0.936635 - 1.62230i) q^{43} -5.58918i q^{44} +(6.27431 + 10.8674i) q^{46} -6.09646 q^{47} +(0.0902880 - 6.99942i) q^{49} +(-15.6231 - 9.01998i) q^{50} +(-3.65172 - 2.21525i) q^{52} +1.76104i q^{53} +(15.8828 + 9.16995i) q^{55} +(-2.70468 - 2.73980i) q^{56} +(-8.06450 - 13.9681i) q^{58} +(5.01546 + 8.68704i) q^{59} +(-3.87813 + 2.23904i) q^{61} +(-1.99341 + 3.45269i) q^{62} +0.689124 q^{64} +(12.2863 - 6.74266i) q^{65} +(0.558805 - 0.967879i) q^{67} +(-1.57202 + 2.72282i) q^{68} +(-17.7574 + 4.63554i) q^{70} +(10.0923 - 5.82681i) q^{71} +3.68800i q^{73} +(-0.515524 + 0.297638i) q^{74} +(-0.825340 - 0.476510i) q^{76} +(12.0785 - 3.15307i) q^{77} -5.71025 q^{79} +(-9.65135 + 16.7166i) q^{80} +(-9.67002 + 5.58299i) q^{82} +0.490867 q^{83} +(-5.15830 - 8.93444i) q^{85} +3.34293i q^{86} +(3.43281 - 5.94581i) q^{88} +(6.95536 - 12.0470i) q^{89} +(2.72717 - 9.14125i) q^{91} -8.32987i q^{92} +(9.42183 + 5.43969i) q^{94} +(2.70821 - 1.56358i) q^{95} +(1.72166 - 0.994004i) q^{97} +(-6.38492 + 10.7368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.835344\pi$
$5$	−3.88703			−1.73833			−0.869166	+	0.494520i	$0.835344\pi$
$6$		0			0
$7$	−1.88286	+	1.85872i	−0.711652	+	0.702532i
$7$	−1.88286	+	1.85872i	−0.711652	+	0.702532i
$8$			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	0.980871	−	0.194657i	$-0.0623593\pi$
$17$	1.32706	+	2.29853i	0.321858	+	0.557475i	−0.659013	+	0.752131i	$0.729026\pi$
$18$		0			0
$19$	−0.696729	+	0.402257i	−0.159841	+	0.0922840i	−0.577787	−	0.816188i	$-0.696083\pi$
$19$	−0.696729	+	0.402257i	−0.159841	+	0.0922840i	0.417946	+	0.908472i	$0.362750\pi$
$20$	−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
$28$	−3.02205	−	0.830682i	−0.571114	−	0.156984i
$29$	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	$-0.935702\pi$
$31$		−	2.23409i		−	0.401254i	0.979668	−	0.200627i	$-0.0642979\pi$
$32$	−5.15428	+	2.97582i	−0.911157	+	0.526056i
$33$		0			0
$34$		−	4.73637i		−	0.812281i
$35$	7.31872	−	7.22492i	1.23709	−	1.22123i
$36$		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	−0.511320	−	0.859390i	$-0.670843\pi$
$41$	3.12853	−	5.41877i	0.488594	−	0.846269i	0.999914	+	0.0131210i	$0.00417666\pi$
$42$		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	$-0.646665\pi$
$47$	−6.09646			−0.889260			−0.444630	+	0.895714i	$0.646665\pi$
$48$		0			0
$49$	0.0902880	−	6.99942i	0.0128983	−	0.999917i
$50$	−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
$56$	−2.70468	−	2.73980i	−0.361428	−	0.366121i
$57$		0			0
$58$	−8.06450	−	13.9681i	−1.05892	−	1.83410i
$59$	5.01546	+	8.68704i	0.652958	+	1.13096i	0.982402	+	0.186781i	$0.0598054\pi$
$59$	5.01546	+	8.68704i	0.652958	+	1.13096i	−0.329444	+	0.944175i	$0.606861\pi$
$60$		0			0
$61$	−3.87813	+	2.23904i	−0.496544	+	0.286680i	−0.727285	−	0.686335i	$-0.759218\pi$
$61$	−3.87813	+	2.23904i	−0.496544	+	0.286680i	0.230741	+	0.973015i	$0.425885\pi$
$62$	−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	$0.0692437\pi$
$73$			3.68800i			0.431648i	−0.976432	+	0.215824i	$0.930756\pi$
$74$	−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	$-0.491424\pi$
$83$	0.490867			0.0538796			0.0269398	+	0.999637i	$0.491424\pi$
$84$		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	$-0.569450\pi$
$89$	6.95536	−	12.0470i	0.737266	−	1.27698i	0.953722	−	0.300690i	$-0.0972170\pi$
$90$		0			0
$91$	2.72717	−	9.14125i	0.285885	−	0.958264i
$92$		−	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	−0.410043	−	0.912066i	$-0.634486\pi$
$97$	1.72166	−	0.994004i	0.174809	−	0.100926i	0.584851	+	0.811141i	$0.301153\pi$
$98$	−6.38492	+	10.7368i	−0.644974	+	1.08458i
$99$		0			0
$100$	5.98753	+	10.3707i	0.598753	+	1.03707i
$101$	−5.62467	+	9.74222i	−0.559676	+	0.969387i	0.437847	+	0.899049i	$0.355741\pi$
$101$	−5.62467	+	9.74222i	−0.559676	+	0.969387i	−0.997523	+	0.0703378i	$0.977592\pi$
$102$		0			0
$103$		−	15.4344i		−	1.52079i	−0.649459	−	0.760396i	$-0.725005\pi$
$103$		−	15.4344i		−	1.52079i	0.649459	−	0.760396i	$-0.274995\pi$
$104$	−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
$119$	−6.77098	−	1.86116i	−0.620695	−	0.170613i
$120$		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	$-0.467996\pi$
$131$	2.29765			0.200747			0.100373	+	0.994950i	$0.467996\pi$
$132$		0			0
$133$	0.564155	−	2.05242i	0.0489185	−	0.177967i
$134$	−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	0.0697283	−	0.997566i	$-0.477787\pi$
$139$	11.4186	−	6.59251i	0.968510	−	0.559169i	0.898782	+	0.438397i	$0.144453\pi$
$140$	11.7468	+	3.22889i	0.992786	+	0.272891i
$141$		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
$154$	−21.4802	−	5.90434i	−1.73092	−	0.475786i
$155$			8.68396i			0.697512i
$156$		0			0
$157$		−	10.3038i		−	0.822329i	−0.911561	−	0.411165i	$-0.865122\pi$
$157$		−	10.3038i		−	0.822329i	0.911561	−	0.411165i	$-0.134878\pi$
$158$	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	$0.527959\pi$
$167$	−11.7152	+	20.2913i	−0.906549	+	1.57019i	−0.818825	+	0.574043i	$0.805374\pi$
$168$		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	$0.0493308\pi$
$173$	8.25591	+	14.2997i	0.627685	+	1.08718i	−0.360330	+	0.932825i	$0.617336\pi$
$174$		0			0
$175$	−19.0338	+	18.7899i	−1.43882	+	1.42038i
$176$	−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	$0.237314\pi$
$181$			18.2531i			1.35674i	−0.734719	+	0.678372i	$0.762686\pi$
$182$	−12.3712	+	11.6941i	−0.917015	+	0.866821i
$183$		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	−0.0490095	−	0.998798i	$-0.515606\pi$
$199$	11.1651	−	6.44615i	0.791470	−	0.456956i	0.840480	+	0.541843i	$0.182273\pi$
$200$			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
$217$	4.15255	+	4.20646i	0.281893	+	0.285553i
$218$	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	0.152468	−	0.988308i	$-0.451278\pi$
$223$	−9.36607	−	5.40750i	−0.627198	−	0.362113i	−0.779666	+	0.626195i	$0.784611\pi$
$224$	4.17353	−	15.1834i	0.278855	−	1.01449i
$225$		0			0
$226$	24.2485			1.61299
$227$	−4.90894	−	8.50254i	−0.325818	−	0.564334i	0.655859	−	0.754883i	$-0.272306\pi$
$227$	−4.90894	−	8.50254i	−0.325818	−	0.564334i	−0.981678	+	0.190549i	$0.938973\pi$
$228$		0			0
$229$			18.9204i			1.25029i	0.780507	+	0.625147i	$0.214961\pi$
$229$			18.9204i			1.25029i	−0.780507	+	0.625147i	$0.785039\pi$
$230$	−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
$238$	8.80361	+	8.91791i	0.570653	+	0.578062i
$239$		−	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	−0.380757	−	0.924675i	$-0.624337\pi$
$241$	3.56523	−	2.05838i	0.229656	−	0.132592i	0.610414	+	0.792083i	$0.291003\pi$
$242$		−	20.0969i		−	1.29188i
$243$		0			0
$244$	−4.59401	−	2.65235i	−0.294101	−	0.169799i
$245$	−0.350952	+	27.2069i	−0.0224215	+	1.73819i
$246$		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	$-0.715364\pi$
$251$	−15.6579	−	27.1203i	−0.988320	−	1.71182i	−0.362186	−	0.932106i	$-0.617969\pi$
$252$		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	$-0.575010\pi$
$257$	11.6283	−	20.1408i	0.725354	−	1.25635i	0.958828	−	0.283987i	$-0.0916571\pi$
$258$		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
$266$	−2.70319	+	2.66855i	−0.165743	+	0.163619i
$267$		0			0
$268$	1.32391			0.0808709
$269$	−11.0232	−	19.0928i	−0.672098	−	1.16411i	−0.977308	−	0.211823i	$-0.932060\pi$
$269$	−11.0232	−	19.0928i	−0.672098	−	1.16411i	0.305210	−	0.952285i	$-0.401273\pi$
$270$		0			0
$271$	12.8469	+	7.41717i	0.780395	+	0.450561i	0.836570	−	0.547860i	$-0.184557\pi$
$271$	12.8469	+	7.41717i	0.780395	+	0.450561i	−0.0561755	+	0.998421i	$0.517891\pi$
$272$	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
$280$	10.5132	+	10.6497i	0.628283	+	0.636440i
$281$		−	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	0.840728	−	0.541458i	$-0.182127\pi$
$283$	13.3265	+	7.69404i	0.792176	+	0.457363i	−0.0485521	+	0.998821i	$0.515461\pi$
$284$	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	0.861712	−	0.507398i	$-0.169392\pi$
$293$	−0.146581	−	0.253886i	−0.00856335	−	0.0148322i	−0.870275	+	0.492566i	$0.836059\pi$
$294$		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
$301$	4.77895	+	1.31361i	0.275454	+	0.0757151i
$302$	−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	$0.0237203\pi$
$307$			2.60896i			0.148901i	−0.997225	+	0.0744505i	$0.976280\pi$
$308$	10.3887	+	10.5236i	0.591954	+	0.599639i
$309$		0			0
$310$	7.74845	−	13.4207i	0.440082	−	0.762245i
$311$	14.0619			0.797380			0.398690	−	0.917086i	$-0.369465\pi$
$311$	14.0619			0.797380			0.398690	+	0.917086i	$0.369465\pi$
$312$		0			0
$313$		−	26.3541i		−	1.48962i	−0.667275	−	0.744812i	$-0.732539\pi$
$313$		−	26.3541i		−	1.48962i	0.667275	−	0.744812i	$-0.267461\pi$
$314$	−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
$322$	−32.0132	−	8.79958i	−1.78402	−	0.490381i
$323$	−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
$329$	11.4787	−	11.3316i	0.632844	−	0.624733i
$330$		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	0.511949	−	0.859016i	$-0.328924\pi$
$349$	0.448257	+	0.258801i	0.0239947	+	0.0138533i	−0.487955	+	0.872869i	$0.662257\pi$
$350$	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	−0.701121	−	0.713043i	$-0.747317\pi$
$353$	5.01559	−	8.68726i	0.266953	−	0.462376i	0.968073	+	0.250667i	$0.0806499\pi$
$354$		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
$364$	10.9932	−	2.61656i	0.576200	−	0.137145i
$365$		−	14.3354i		−	0.750348i
$366$		0			0
$367$	−5.43012	−	3.13508i	−0.283450	−	0.163650i	0.351534	−	0.936175i	$-0.385660\pi$
$367$	−5.43012	−	3.13508i	−0.283450	−	0.163650i	−0.634984	+	0.772525i	$0.718993\pi$
$368$	−30.2413	+	17.4598i	−1.57643	+	0.910155i
$369$		0			0
$370$	2.00386	−	1.15693i	0.104176	−	0.0601458i
$371$	−3.27329	−	3.31579i	−0.169941	−	0.172147i
$372$		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	$-0.827461\pi$
$383$	−17.1261	−	29.6632i	−0.875101	−	1.51572i	−0.0184462	−	0.999830i	$-0.505872\pi$
$384$		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
$392$	10.1851	+	0.131381i	0.514423	+	0.00663573i
$393$		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	0.409347	−	0.912379i	$-0.365757\pi$
$397$	27.9778	−	16.1530i	1.40416	−	0.810694i	0.994817	+	0.101685i	$0.0324233\pi$
$398$	−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
$406$	41.1472	+	11.3103i	2.04210	+	0.561319i
$407$	−1.36302	+	0.786938i	−0.0675622	+	0.0390071i
$408$		0			0
$409$	8.95661	−	5.17110i	0.442876	−	0.255694i	−0.261941	−	0.965084i	$-0.584363\pi$
$409$	8.95661	−	5.17110i	0.442876	−	0.255694i	0.704817	+	0.709389i	$0.251029\pi$
$410$	37.5877	−	21.7013i	1.85632	−	1.07175i
$411$		0			0
$412$	15.8339	−	9.14172i	0.780081	−	0.450380i
$413$	−25.5902	−	7.03407i	−1.25921	−	0.346124i
$414$		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	$-0.594526\pi$
$419$	13.9563	−	24.1730i	0.681811	−	1.18093i	0.974428	−	0.224701i	$-0.0721405\pi$
$420$		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
$427$	3.14020	−	11.4242i	0.151965	−	0.552854i
$428$			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	0.00528907	−	0.999986i	$-0.498316\pi$
$433$	18.1857	−	10.4995i	0.873947	−	0.504573i	0.868658	+	0.495413i	$0.164983\pi$
$434$	−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	0.412787	−	0.910828i	$-0.364555\pi$
$439$	−3.55392	−	2.05186i	−0.169619	−	0.0979297i	−0.582406	+	0.812898i	$0.697889\pi$
$440$	−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
$448$	−1.29752	+	1.28089i	−0.0613021	+	0.0605164i
$449$	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
$455$	−10.6006	+	35.5323i	−0.496964	+	1.66578i
$456$		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	$-0.963236\pi$
$461$	−12.8067	−	22.1819i	−0.596470	−	1.03312i	0.396868	−	0.917876i	$-0.370097\pi$
$462$		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	$-0.279591\pi$
$467$	27.5925			1.27683			0.638414	+	0.769694i	$0.279591\pi$
$468$		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	−0.903344	−	0.428918i	$-0.858895\pi$
$479$	−1.75566	+	3.04089i	−0.0802181	+	0.138942i	0.823125	+	0.567860i	$0.192228\pi$
$480$		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
$490$	24.8184	−	41.7341i	1.12118	−	1.88535i
$491$	−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
$497$	−8.17197	+	29.7299i	−0.366563	+	1.33357i
$498$		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	0.893081	−	0.449895i	$-0.148539\pi$
$503$	1.27659	+	2.21112i	0.0569203	+	0.0985888i	−0.836161	+	0.548484i	$0.815205\pi$
$504$		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	$0.525713\pi$
$509$	−20.3850	+	35.3078i	−0.903547	+	1.56499i	−0.822855	+	0.568251i	$0.807620\pi$
$510$		0			0
$511$	−6.85498	−	6.94397i	−0.303246	−	0.307183i
$512$			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
$518$	0.417430	−	1.51863i	0.0183408	−	0.0667246i
$519$		0			0
$520$	9.81144	+	17.8782i	0.430260	+	0.784009i
$521$	23.0735			1.01087			0.505433	−	0.862866i	$-0.331333\pi$
$521$	23.0735			1.01087			0.505433	+	0.862866i	$0.331333\pi$
$522$		0			0
$523$	−12.0355	−	6.94871i	−0.526277	−	0.303846i	0.213222	−	0.977004i	$-0.431604\pi$
$523$	−12.0355	−	6.94871i	−0.526277	−	0.303846i	−0.739499	+	0.673158i	$0.764937\pi$
$524$	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
$539$	−16.8814	+	28.3874i	−0.727131	+	1.22273i
$540$		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
$553$	10.7516	−	10.6138i	0.457203	−	0.451344i
$554$			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	0.582719	−	0.812673i	$-0.301989\pi$
$563$	−9.78613	−	16.9501i	−0.412436	−	0.714360i	−0.995156	+	0.0983132i	$0.968655\pi$
$564$		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
$574$	7.83001	−	28.4859i	0.326818	−	1.18898i
$575$	−61.5613	−	35.5425i	−2.56729	−	1.48222i
$576$		0			0
$577$		−	15.3698i		−	0.639853i	−0.947442	−	0.319927i	$-0.896342\pi$
$577$		−	15.3698i		−	0.639853i	0.947442	−	0.319927i	$-0.103658\pi$
$578$	−15.3861	+	8.88319i	−0.639979	+	0.369492i
$579$		0			0
$580$		−	41.6167i		−	1.72804i
$581$	−0.924231	+	0.912386i	−0.0383436	+	0.0378522i
$582$		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	−0.758393	−	0.651798i	$-0.774015\pi$
$587$	4.48891	−	7.77502i	0.185277	−	0.320910i	0.943670	+	0.330888i	$0.107348\pi$
$588$		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	$-0.594695\pi$
$593$	−14.2760			−0.586247			−0.293123	+	0.956075i	$0.594695\pi$
$594$		0			0
$595$	26.3190	+	7.23440i	1.07897	+	0.296581i
$596$	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	0.155465	−	0.987841i	$-0.450312\pi$
$601$	−15.2558	−	8.80796i	−0.622298	−	0.359284i	−0.777763	+	0.628557i	$0.783646\pi$
$602$	−6.21358	−	6.29425i	−0.253247	−	0.256535i
$603$		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	−0.610018	−	0.792387i	$-0.708838\pi$
$607$	−5.63702	+	3.25454i	−0.228800	+	0.132098i	0.381219	+	0.924485i	$0.375505\pi$
$608$	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	$-0.591089\pi$
$619$		−	47.7359i		−	1.91867i	0.282275	−	0.959334i	$-0.408911\pi$
$620$	−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
$637$	11.8562	+	22.2807i	0.469760	+	0.882794i
$638$			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	−0.414139	−	0.910213i	$-0.635917\pi$
$643$	4.23619	−	2.44576i	0.167059	−	0.0964515i	0.581198	+	0.813762i	$0.302584\pi$
$644$	15.4829	+	15.6839i	0.610113	+	0.618034i
$645$		0			0
$646$	1.90524	+	3.29997i	0.0749606	+	0.129835i
$647$	18.5924	−	32.2029i	0.730941	−	1.26603i	−0.225540	−	0.974234i	$-0.572415\pi$
$647$	18.5924	−	32.2029i	0.730941	−	1.26603i	0.956481	−	0.291793i	$-0.0942520\pi$
$648$		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	0.987170	−	0.159672i	$-0.0510437\pi$
$661$	34.5149	+	19.9272i	1.34247	+	0.775078i	0.355305	+	0.934750i	$0.384377\pi$
$662$		−	2.84421i		−	0.110543i
$663$		0			0
$664$			0.714274i			0.0277192i
$665$	−2.19289	+	7.97781i	−0.0850366	+	0.309366i
$666$		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	$-0.772441\pi$
$677$	−39.2974			−1.51032			−0.755160	+	0.655540i	$0.772441\pi$
$678$		0			0
$679$	−1.39407	+	5.07167i	−0.0534994	+	0.194633i
$680$	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
$686$	−7.93479	−	32.0836i	−0.302952	−	1.22496i
$687$		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	0.679005	−	0.734134i	$-0.262412\pi$
$691$	10.0607	+	5.80857i	0.382728	+	0.220968i	−0.296276	+	0.955102i	$0.595745\pi$
$692$	−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
$700$	−30.5499	−	8.39737i	−1.15468	−	0.317391i
$701$			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	0.992151	−	0.125043i	$-0.0399070\pi$
$719$	10.3981	+	18.0101i	0.387785	+	0.671663i	−0.604366	+	0.796707i	$0.706574\pi$
$720$		0			0
$721$	28.6882	+	29.0607i	1.06841	+	1.08228i
$722$	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	$0.134955\pi$
$727$			22.1844i			0.822773i	−0.911461	+	0.411387i	$0.865045\pi$
$728$	13.3017	+	3.96839i	0.492994	+	0.147078i
$729$		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	$-0.912746\pi$
$733$		−	14.6577i		−	0.541394i	0.962665	−	0.270697i	$-0.0872541\pi$
$734$	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	0.987551	−	0.157300i	$-0.0502789\pi$
$761$	9.86345	+	17.0840i	0.357550	+	0.619294i	−0.630001	+	0.776594i	$0.716946\pi$
$762$		0			0
$763$	25.2697	−	24.9459i	0.914826	−	0.903102i
$764$	−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	0.980807	−	0.194982i	$-0.0624648\pi$
$769$	36.1153	+	20.8512i	1.30235	+	0.751913i	0.321544	+	0.946895i	$0.395798\pi$
$770$	83.4942	+	22.9504i	3.00892	+	0.827074i
$771$		0			0
$772$	−27.2272			−0.979928
$773$	4.42516	+	7.66459i	0.159162	+	0.275676i	0.934567	−	0.355788i	$-0.115788\pi$
$773$	4.42516	+	7.66459i	0.159162	+	0.275676i	−0.775405	+	0.631464i	$0.782454\pi$
$774$		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
$784$	−29.8776	−	17.7676i	−1.06706	−	0.634557i
$785$			40.0510i			1.42948i
$786$		0			0
$787$	14.9967	−	8.65836i	0.534575	−	0.308637i	−0.208302	−	0.978064i	$-0.566794\pi$
$787$	14.9967	−	8.65836i	0.534575	−	0.308637i	0.742878	+	0.669427i	$0.233460\pi$
$788$			31.6890i			1.12887i
$789$		0			0
$790$	−34.3029	−	19.8048i	−1.22044	−	0.704622i
$791$	9.52848	−	34.6649i	0.338794	−	1.23254i
$792$		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	0.999698	−	0.0245614i	$-0.00781894\pi$
$797$	13.5108	+	23.4015i	0.478578	+	0.828922i	−0.521120	+	0.853483i	$0.674486\pi$
$798$		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	$-0.780319\pi$
$811$		−	36.2612i		−	1.27330i	0.771152	−	0.636651i	$-0.219681\pi$
$812$	−19.9005	−	20.1589i	−0.698372	−	0.707438i
$813$		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
$826$	33.2723	+	33.7043i	1.15769	+	1.17272i
$827$		−	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	0.283816	−	0.958879i	$-0.408400\pi$
$829$	−11.6520	−	6.72727i	−0.404690	−	0.233648i	−0.688505	+	0.725231i	$0.741733\pi$
$830$	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	0.901634	−	0.432501i	$-0.142369\pi$
$839$	2.20891	+	3.82595i	0.0762601	+	0.132086i	−0.825373	+	0.564587i	$0.809035\pi$
$840$		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
$847$	−28.7300	−	7.89712i	−0.987174	−	0.271348i
$848$	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	$-0.940720\pi$
$853$		−	10.8155i		−	0.370317i	0.982709	−	0.185159i	$-0.0592799\pi$
$854$	−15.0465	+	14.8537i	−0.514881	+	0.508282i
$855$		0			0
$856$	−6.40447	+	11.0929i	−0.218900	+	0.379146i
$857$	−19.8061			−0.676562			−0.338281	−	0.941045i	$-0.609846\pi$
$857$	−19.8061			−0.676562			−0.338281	+	0.941045i	$0.609846\pi$
$858$		0			0
$859$			29.8841i			1.01963i	0.860284	+	0.509816i	$0.170286\pi$
$859$			29.8841i			1.01963i	−0.860284	+	0.509816i	$0.829714\pi$
$860$	−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
$868$	−1.85582	+	6.75152i	−0.0629905	+	0.229162i
$869$	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
$875$	37.3913	−	36.9121i	1.26406	−	1.24786i
$876$		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	−0.952506	−	0.304519i	$-0.901504\pi$
$881$	−6.30831	+	10.9263i	−0.212532	+	0.368117i	0.739974	+	0.672635i	$0.234838\pi$
$882$		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	−0.970627	−	0.240590i	$-0.922659\pi$
$887$	−8.24847	+	14.2868i	−0.276956	+	0.479702i	0.693670	+	0.720292i	$0.255992\pi$
$888$		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
$910$	48.0873	−	45.4552i	1.59408	−	1.50682i
$911$		−	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
$917$	−4.32614	+	4.27070i	−0.142862	+	0.141031i
$918$		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	$0.197328\pi$
$929$	27.7394	+	48.0460i	0.910099	+	1.57634i	0.0961770	+	0.995364i	$0.469339\pi$
$930$		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	$0.310344\pi$
$937$			50.6718i			1.65538i	−0.561188	+	0.827688i	$0.689656\pi$
$938$	1.39857	−	5.08803i	0.0456648	−	0.166130i
$939$		0			0
$940$	14.0357	+	24.3106i	0.457795	+	0.792924i
$941$	32.7877			1.06885			0.534424	−	0.845216i	$-0.320528\pi$
$941$	32.7877			1.06885			0.534424	+	0.845216i	$0.320528\pi$
$942$		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
$952$	2.70823	−	9.85265i	0.0877743	−	0.319326i
$953$	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
$959$	−9.90591	+	36.0381i	−0.319879	+	1.16373i
$960$		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	0.910202	−	0.414164i	$-0.135926\pi$
$971$	3.00467	+	5.20424i	0.0964243	+	0.167012i	−0.813778	+	0.581176i	$0.802593\pi$
$972$		0			0
$973$	−9.24584	+	33.6367i	−0.296408	+	1.07834i
$974$			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	$-0.703331\pi$
$983$	−37.3863			−1.19244			−0.596218	+	0.802822i	$0.703331\pi$
$984$		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
$994$	39.1566	−	38.6548i	1.24197	−	1.22605i
$995$	−43.3989	+	25.0564i	−1.37584	+	0.794341i
$996$		0			0
$997$	−0.117691	+	0.0679491i	−0.00372732	+	0.00215197i	−0.501863	−	0.864947i	$-0.667352\pi$
$997$	−0.117691	+	0.0679491i	−0.00372732	+	0.00215197i	0.498135	+	0.867099i	$0.334018\pi$
$998$	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.503.7	✓	72
3.2	odd	2	inner	819.2.dx.a.503.30	yes	72
7.6	odd	2	inner	819.2.dx.a.503.8	yes	72
13.3	even	3	inner	819.2.dx.a.692.29	yes	72
21.20	even	2	inner	819.2.dx.a.503.29	yes	72
39.29	odd	6	inner	819.2.dx.a.692.8	yes	72
91.55	odd	6	inner	819.2.dx.a.692.30	yes	72
273.146	even	6	inner	819.2.dx.a.692.7	yes	72

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

\(f(q)\)	\(=\)	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} -3.88703 q^{5} +(-1.88286 + 1.85872i) q^{7} +1.45513i q^{8} +O(q^{10})\)	\(q+(-1.54546 - 0.892271i) q^{2} +(0.592297 + 1.02589i) q^{4} -3.88703 q^{5} +(-1.88286 + 1.85872i) q^{7} +1.45513i q^{8} +(6.00725 + 3.46829i) q^{10} +(-4.08611 - 2.35911i) q^{11} +(-3.16085 + 1.73466i) q^{13} +(4.56836 - 1.19257i) q^{14} +(2.48296 - 4.30062i) q^{16} +(1.32706 + 2.29853i) q^{17} +(-0.696729 + 0.402257i) q^{19} +(-2.30227 - 3.98766i) q^{20} +(4.20994 + 7.29183i) q^{22} +(-6.08975 - 3.51592i) q^{23} +10.1090 q^{25} +(6.43275 + 0.139494i) q^{26} +(-3.02205 - 0.830682i) q^{28} +(7.82728 + 4.51908i) q^{29} -2.23409i q^{31} +(-5.15428 + 2.97582i) q^{32} -4.73637i q^{34} +(7.31872 - 7.22492i) q^{35} +(0.166787 - 0.288883i) q^{37} +1.43569 q^{38} -5.65613i q^{40} +(3.12853 - 5.41877i) q^{41} +(-0.936635 - 1.62230i) q^{43} -5.58918i q^{44} +(6.27431 + 10.8674i) q^{46} -6.09646 q^{47} +(0.0902880 - 6.99942i) q^{49} +(-15.6231 - 9.01998i) q^{50} +(-3.65172 - 2.21525i) q^{52} +1.76104i q^{53} +(15.8828 + 9.16995i) q^{55} +(-2.70468 - 2.73980i) q^{56} +(-8.06450 - 13.9681i) q^{58} +(5.01546 + 8.68704i) q^{59} +(-3.87813 + 2.23904i) q^{61} +(-1.99341 + 3.45269i) q^{62} +0.689124 q^{64} +(12.2863 - 6.74266i) q^{65} +(0.558805 - 0.967879i) q^{67} +(-1.57202 + 2.72282i) q^{68} +(-17.7574 + 4.63554i) q^{70} +(10.0923 - 5.82681i) q^{71} +3.68800i q^{73} +(-0.515524 + 0.297638i) q^{74} +(-0.825340 - 0.476510i) q^{76} +(12.0785 - 3.15307i) q^{77} -5.71025 q^{79} +(-9.65135 + 16.7166i) q^{80} +(-9.67002 + 5.58299i) q^{82} +0.490867 q^{83} +(-5.15830 - 8.93444i) q^{85} +3.34293i q^{86} +(3.43281 - 5.94581i) q^{88} +(6.95536 - 12.0470i) q^{89} +(2.72717 - 9.14125i) q^{91} -8.32987i q^{92} +(9.42183 + 5.43969i) q^{94} +(2.70821 - 1.56358i) q^{95} +(1.72166 - 0.994004i) q^{97} +(-6.38492 + 10.7368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 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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