LMFDB - Embedded newform 819.2.dl.e.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(298,819)]

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([0, 4, 3]))

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

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

chi := DirichletCharacter("819.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dl (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			298.1
Root			$1.97871 + 1.14241i$ of defining polynomial
Character	$\chi$	$=$	819.298
Dual form			819.2.dl.e.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97871 + 1.14241i) q^{2} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} +(-2.62488 - 0.331665i) q^{7} +2.78832i q^{8} +O(q^{10})$	\(q+(-1.97871 + 1.14241i) q^{2} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} +(-2.62488 - 0.331665i) q^{7} +2.78832i q^{8} +(2.42760 - 4.20473i) q^{10} +(-0.267139 - 0.154233i) q^{11} +(-3.22037 - 1.62148i) q^{13} +(5.57276 - 2.34241i) q^{14} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(1.54266 - 0.890653i) q^{19} +6.84326i q^{20} +0.704786 q^{22} +(-0.575211 - 0.996294i) q^{23} +(-0.242207 + 0.419515i) q^{25} +(8.22456 - 0.470536i) q^{26} +(-5.15153 + 6.78655i) q^{28} -2.01052 q^{29} +(3.98791 + 2.30242i) q^{31} +(-4.96792 - 2.86823i) q^{32} +4.05494i q^{34} +(5.18295 - 2.17856i) q^{35} +(4.79901 - 2.77071i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(-2.96258 - 5.13134i) q^{40} +6.72984i q^{41} -1.52611 q^{43} +(-0.860286 + 0.496686i) q^{44} +(2.27635 + 1.31425i) q^{46} +(8.24297 - 4.75908i) q^{47} +(6.78000 + 1.74116i) q^{49} -1.10680i q^{50} +(-9.70759 + 6.37048i) q^{52} +(3.72037 - 6.44387i) q^{53} +0.655486 q^{55} +(0.924789 - 7.31901i) q^{56} +(3.97823 - 2.29683i) q^{58} +(7.03304 + 4.06053i) q^{59} +(1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +12.9669 q^{64} +(7.64926 - 0.437622i) q^{65} +(-10.9249 - 6.30747i) q^{67} +(-2.85765 - 4.94960i) q^{68} +(-7.76673 + 10.2318i) q^{70} +1.35070i q^{71} +(10.2894 + 5.94059i) q^{73} +(-6.33056 + 10.9648i) q^{74} -5.73646i q^{76} +(0.650054 + 0.493443i) q^{77} +(3.96258 + 6.86339i) q^{79} +(-0.128728 - 0.0743214i) q^{80} +(-7.68821 - 13.3164i) q^{82} +11.2290i q^{83} +3.77130i q^{85} +(3.01972 - 1.74344i) q^{86} +(0.430050 - 0.744869i) q^{88} +(-1.43688 + 0.829583i) q^{89} +(7.91530 + 5.32428i) q^{91} -3.70479 q^{92} +(-10.8736 + 18.8336i) q^{94} +(-1.89263 + 3.27813i) q^{95} -7.66641i q^{97} +(-15.4047 + 4.30026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4}+O(q^{10}) $ 16 * q + 6 * q^4	$ 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.97871	+	1.14241i	−1.39916	+	0.807803i	−0.994304	−	0.106579i	$-0.966010\pi$
$2$	−1.97871	+	1.14241i	−1.39916	+	0.807803i	−0.404852	+	0.914382i	$0.632677\pi$
$3$		0			0
$3$		0			0
$4$	1.61019	−	2.78892i	0.805093	−	1.39446i
$5$	−1.84030	+	1.06250i	−0.823005	+	0.475162i	−0.851452	−	0.524433i	$-0.824277\pi$
$5$	−1.84030	+	1.06250i	−0.823005	+	0.475162i	0.0284464	+	0.999595i	$0.490944\pi$
$6$		0			0
$7$	−2.62488	−	0.331665i	−0.992112	−	0.125358i
$7$	−2.62488	−	0.331665i	−0.992112	−	0.125358i
$8$			2.78832i			0.985820i
$9$		0			0
$10$	2.42760	−	4.20473i	0.767676	−	1.32965i
$11$	−0.267139	−	0.154233i	−0.0805454	−	0.0465029i	0.459186	−	0.888340i	$-0.348141\pi$
$11$	−0.267139	−	0.154233i	−0.0805454	−	0.0465029i	−0.539732	+	0.841837i	$0.681474\pi$
$12$		0			0
$13$	−3.22037	−	1.62148i	−0.893170	−	0.449718i
$13$	−3.22037	−	1.62148i	−0.893170	−	0.449718i
$14$	5.57276	−	2.34241i	1.48938	−	0.626036i
$15$		0			0
$16$	0.0349749	+	0.0605784i	0.00874373	+	0.0151446i
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	−0.738122	−	0.674667i	$-0.764287\pi$
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	0.953340	+	0.301898i	$0.0976204\pi$
$18$		0			0
$19$	1.54266	−	0.890653i	0.353909	−	0.204330i	−0.312496	−	0.949919i	$-0.601165\pi$
$19$	1.54266	−	0.890653i	0.353909	−	0.204330i	0.666406	+	0.745589i	$0.267832\pi$
$20$			6.84326i			1.53020i
$21$		0			0
$22$	0.704786			0.150261
$23$	−0.575211	−	0.996294i	−0.119940	−	0.207742i	0.799804	−	0.600261i	$-0.204937\pi$
$23$	−0.575211	−	0.996294i	−0.119940	−	0.207742i	−0.919744	+	0.392520i	$0.871603\pi$
$24$		0			0
$25$	−0.242207	+	0.419515i	−0.0484414	+	0.0839029i
$26$	8.22456	−	0.470536i	1.61297	−	0.0922796i
$27$		0			0
$28$	−5.15153	+	6.78655i	−0.973548	+	1.28254i
$29$	−2.01052			−0.373345			−0.186672	−	0.982422i	$-0.559770\pi$
$29$	−2.01052			−0.373345			−0.186672	+	0.982422i	$0.559770\pi$
$30$		0			0
$31$	3.98791	+	2.30242i	0.716251	+	0.413527i	0.813371	−	0.581745i	$-0.197630\pi$
$31$	3.98791	+	2.30242i	0.716251	+	0.413527i	−0.0971205	+	0.995273i	$0.530963\pi$
$32$	−4.96792	−	2.86823i	−0.878213	−	0.507037i
$33$		0			0
$34$			4.05494i			0.695416i
$35$	5.18295	−	2.17856i	0.876078	−	0.368244i
$36$		0			0
$37$	4.79901	−	2.77071i	0.788953	−	0.455502i	−0.0506410	−	0.998717i	$-0.516126\pi$
$37$	4.79901	−	2.77071i	0.788953	−	0.455502i	0.839594	+	0.543215i	$0.182793\pi$
$38$	−2.03497	+	3.52468i	−0.330117	+	0.571779i
$39$		0			0
$40$	−2.96258	−	5.13134i	−0.468425	−	0.811336i
$41$			6.72984i			1.05102i	0.850786	+	0.525512i	$0.176126\pi$
$41$			6.72984i			1.05102i	−0.850786	+	0.525512i	$0.823874\pi$
$42$		0			0
$43$	−1.52611			−0.232729			−0.116365	−	0.993207i	$-0.537124\pi$
$43$	−1.52611			−0.232729			−0.116365	+	0.993207i	$0.537124\pi$
$44$	−0.860286	+	0.496686i	−0.129693	+	0.0748783i
$45$		0			0
$46$	2.27635	+	1.31425i	0.335629	+	0.193776i
$47$	8.24297	−	4.75908i	1.20236	−	0.694183i	0.241281	−	0.970455i	$-0.422432\pi$
$47$	8.24297	−	4.75908i	1.20236	−	0.694183i	0.961079	+	0.276272i	$0.0890991\pi$
$48$		0			0
$49$	6.78000	+	1.74116i	0.968571	+	0.248738i
$50$		−	1.10680i		−	0.156524i
$51$		0			0
$52$	−9.70759	+	6.37048i	−1.34620	+	0.883427i
$53$	3.72037	−	6.44387i	0.511032	−	0.885134i	−0.488886	−	0.872348i	$-0.662597\pi$
$53$	3.72037	−	6.44387i	0.511032	−	0.885134i	0.999918	−	0.0127862i	$-0.00407010\pi$
$54$		0			0
$55$	0.655486			0.0883857
$56$	0.924789	−	7.31901i	0.123580	−	0.978044i
$57$		0			0
$58$	3.97823	−	2.29683i	0.522368	−	0.301589i
$59$	7.03304	+	4.06053i	0.915624	+	0.528636i	0.882236	−	0.470807i	$-0.156037\pi$
$59$	7.03304	+	4.06053i	0.915624	+	0.528636i	0.0333877	+	0.999442i	$0.489370\pi$
$60$		0			0
$61$	1.72037	+	2.97977i	0.220271	+	0.381521i	0.954890	−	0.296959i	$-0.0959725\pi$
$61$	1.72037	+	2.97977i	0.220271	+	0.381521i	−0.734619	+	0.678480i	$0.762639\pi$
$62$	−10.5212			−1.33620
$63$		0			0
$64$	12.9669			1.62086
$65$	7.64926	−	0.437622i	0.948773	−	0.0542803i
$66$		0			0
$67$	−10.9249	−	6.30747i	−1.33468	−	0.770580i	−0.348671	−	0.937245i	$-0.613367\pi$
$67$	−10.9249	−	6.30747i	−1.33468	−	0.770580i	−0.986014	+	0.166665i	$0.946700\pi$
$68$	−2.85765	−	4.94960i	−0.346541	−	0.600227i
$69$		0			0
$70$	−7.76673	+	10.2318i	−0.928302	+	1.22293i
$71$			1.35070i			0.160299i	0.996783	+	0.0801494i	$0.0255397\pi$
$71$			1.35070i			0.160299i	−0.996783	+	0.0801494i	$0.974460\pi$
$72$		0			0
$73$	10.2894	+	5.94059i	1.20428	+	0.695293i	0.961505	−	0.274789i	$-0.0886079\pi$
$73$	10.2894	+	5.94059i	1.20428	+	0.695293i	0.242778	+	0.970082i	$0.421941\pi$
$74$	−6.33056	+	10.9648i	−0.735912	+	1.27464i
$75$		0			0
$76$		−	5.73646i		−	0.658018i
$77$	0.650054	+	0.493443i	0.0740805	+	0.0562330i
$78$		0			0
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	0.998109	−	0.0614644i	$-0.0195771\pi$
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	−0.552284	+	0.833656i	$0.686244\pi$
$80$	−0.128728	−	0.0743214i	−0.0143923	−	0.00830939i
$81$		0			0
$82$	−7.68821	−	13.3164i	−0.849021	−	1.47055i
$83$			11.2290i			1.23255i	0.787533	+	0.616273i	$0.211358\pi$
$83$			11.2290i			1.23255i	−0.787533	+	0.616273i	$0.788642\pi$
$84$		0			0
$85$			3.77130i			0.409055i
$86$	3.01972	−	1.74344i	0.325625	−	0.188000i
$87$		0			0
$88$	0.430050	−	0.744869i	0.0458435	−	0.0794033i
$89$	−1.43688	+	0.829583i	−0.152309	+	0.0879357i	−0.574218	−	0.818703i	$-0.694694\pi$
$89$	−1.43688	+	0.829583i	−0.152309	+	0.0879357i	0.421909	+	0.906638i	$0.361360\pi$
$90$		0			0
$91$	7.91530	+	5.32428i	0.829749	+	0.558137i
$92$	−3.70479			−0.386251
$93$		0			0
$94$	−10.8736	+	18.8336i	−1.12153	+	1.94254i
$95$	−1.89263	+	3.27813i	−0.194180	+	0.336329i
$96$		0			0
$97$		−	7.66641i		−	0.778406i	−0.921152	−	0.389203i	$-0.872750\pi$
$97$		−	7.66641i		−	0.778406i	0.921152	−	0.389203i	$-0.127250\pi$
$98$	−15.4047	+	4.30026i	−1.55611	+	0.434392i
$99$		0			0
$100$	0.779996	+	1.35099i	0.0779996	+	0.135099i
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	−0.998607	−	0.0527721i	$-0.983194\pi$
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	0.545005	+	0.838433i	$0.316528\pi$
$102$		0			0
$103$	3.02085	+	5.23226i	0.297653	+	0.515550i	0.975599	−	0.219562i	$-0.0704629\pi$
$103$	3.02085	+	5.23226i	0.297653	+	0.515550i	−0.677946	+	0.735112i	$0.737130\pi$
$104$	4.52122	−	8.97943i	0.443342	−	0.880506i
$105$		0			0
$106$			17.0007i			1.65125i
$107$	6.04305	+	10.4669i	0.584204	+	1.01187i	0.994974	+	0.100132i	$0.0319264\pi$
$107$	6.04305	+	10.4669i	0.584204	+	1.01187i	−0.410770	+	0.911739i	$0.634740\pi$
$108$		0			0
$109$	−1.17942	−	0.680941i	−0.112968	−	0.0652223i	0.442451	−	0.896793i	$-0.354109\pi$
$109$	−1.17942	−	0.680941i	−0.112968	−	0.0652223i	−0.555420	+	0.831570i	$0.687442\pi$
$110$	−1.29701	+	0.748831i	−0.123665	+	0.0713983i
$111$		0			0
$112$	−0.0717133	−	0.170611i	−0.00677627	−	0.0161212i
$113$	9.42009			0.886168			0.443084	−	0.896480i	$-0.353884\pi$
$113$	9.42009			0.886168			0.443084	+	0.896480i	$0.353884\pi$
$114$		0			0
$115$	2.11712	+	1.22232i	0.197422	+	0.113982i
$116$	−3.23731	+	5.60719i	−0.300577	+	0.520615i
$117$		0			0
$118$	−18.5551			−1.70814
$119$	−2.83899	+	3.74004i	−0.260250	+	0.342849i
$120$		0			0
$121$	−5.45242	−	9.44388i	−0.495675	−	0.858534i
$122$	−6.80822	−	3.93073i	−0.616387	−	0.355871i
$123$		0			0
$124$	12.8426	−	7.41466i	1.15330	−	0.665856i
$125$		−	11.6543i		−	1.04239i
$126$		0			0
$127$	13.3998			1.18904			0.594519	−	0.804081i	$-0.297342\pi$
$127$	13.3998			1.18904			0.594519	+	0.804081i	$0.297342\pi$
$128$	−15.7217	+	9.07695i	−1.38962	+	0.802297i
$129$		0			0
$130$	−14.6357	+	9.60448i	−1.28363	+	0.842369i
$131$	6.69854	+	11.6022i	0.585254	+	1.01369i	0.994844	+	0.101420i	$0.0323385\pi$
$131$	6.69854	+	11.6022i	0.585254	+	1.01369i	−0.409590	+	0.912270i	$0.634328\pi$
$132$		0			0
$133$	−4.34469	+	1.82621i	−0.376732	+	0.158353i
$134$	28.8228			2.48991
$135$		0			0
$136$	4.28555	+	2.47427i	0.367483	+	0.212167i
$137$	−0.433917	−	0.250522i	−0.0370720	−	0.0214036i	0.481349	−	0.876529i	$-0.340147\pi$
$137$	−0.433917	−	0.250522i	−0.0370720	−	0.0214036i	−0.518421	+	0.855125i	$0.673480\pi$
$138$		0			0
$139$	1.41936			0.120388			0.0601941	−	0.998187i	$-0.480828\pi$
$139$	1.41936			0.120388			0.0601941	+	0.998187i	$0.480828\pi$
$140$	2.26967	−	17.9627i	0.191822	−	1.51813i
$141$		0			0
$142$	−1.54305	−	2.67264i	−0.129490	−	0.224283i
$143$	0.610200	+	0.929847i	0.0510275	+	0.0777577i
$144$		0			0
$145$	3.69996	−	2.13617i	0.307265	−	0.177399i
$146$	−27.1463			−2.24664
$147$		0			0
$148$		−	17.8454i		−	1.46689i
$149$	18.2652	−	10.5454i	1.49635	−	0.863916i	0.496355	−	0.868120i	$-0.334672\pi$
$149$	18.2652	−	10.5454i	1.49635	−	0.863916i	0.999991	+	0.00420426i	$0.00133826\pi$
$150$		0			0
$151$	−15.1591	−	8.75211i	−1.23363	−	0.712236i	−0.265845	−	0.964016i	$-0.585651\pi$
$151$	−15.1591	−	8.75211i	−1.23363	−	0.712236i	−0.967785	+	0.251779i	$0.918984\pi$
$152$	2.48343	+	4.30142i	0.201432	+	0.348891i
$153$		0			0
$154$	−1.84998	−	0.233753i	−0.149075	−	0.0188363i
$155$	−9.78526			−0.785971
$156$		0			0
$157$	−0.0377894	+	0.0654532i	−0.00301593	+	0.00522374i	−0.867529	−	0.497386i	$-0.834293\pi$
$157$	−0.0377894	+	0.0654532i	−0.00301593	+	0.00522374i	0.864514	+	0.502610i	$0.167627\pi$
$158$	−15.6816	−	9.05375i	−1.24756	−	0.720278i
$159$		0			0
$160$	12.1899			0.963699
$161$	1.17942	+	2.80593i	0.0929516	+	0.221138i
$162$		0			0
$163$	8.73102	−	5.04086i	0.683866	−	0.394830i	−0.117444	−	0.993080i	$-0.537470\pi$
$163$	8.73102	−	5.04086i	0.683866	−	0.394830i	0.801310	+	0.598249i	$0.204137\pi$
$164$	18.7690	+	10.8363i	1.46561	+	0.846172i
$165$		0			0
$166$	−12.8281	−	22.2189i	−0.995655	−	1.72452i
$167$		−	5.84989i		−	0.452678i	−0.974049	−	0.226339i	$-0.927324\pi$
$167$		−	5.84989i		−	0.452678i	0.974049	−	0.226339i	$-0.0726757\pi$
$168$		0			0
$169$	7.74159	+	10.4436i	0.595507	+	0.803350i
$170$	−4.30835	−	7.46229i	−0.330436	−	0.572331i
$171$		0			0
$172$	−2.45732	+	4.25620i	−0.187369	+	0.324532i
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	−0.984100	−	0.177617i	$-0.943161\pi$
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	0.338229	−	0.941064i	$-0.390172\pi$
$174$		0			0
$175$	0.774903	−	1.02084i	0.0585771	−	0.0771686i
$176$		−	0.0215771i		−	0.00162644i
$177$		0			0
$178$	1.89544	−	3.28300i	0.142069	−	0.246072i
$179$	7.65079	−	13.2516i	0.571847	−	0.990468i	−0.424529	−	0.905414i	$-0.639560\pi$
$179$	7.65079	−	13.2516i	0.571847	−	0.990468i	0.996376	−	0.0850537i	$-0.0271062\pi$
$180$		0			0
$181$	−5.84958			−0.434796			−0.217398	−	0.976083i	$-0.569757\pi$
$181$	−5.84958			−0.434796			−0.217398	+	0.976083i	$0.569757\pi$
$182$	−21.7446	−	1.49270i	−1.61181	−	0.110646i
$183$		0			0
$184$	2.77799	−	1.60387i	0.204796	−	0.118239i
$185$	−5.88774	+	10.1979i	−0.432875	+	0.749761i
$186$		0			0
$187$	−0.474101	+	0.273722i	−0.0346697	+	0.0200165i
$188$		−	30.6520i		−	2.23553i
$189$		0			0
$190$		−	8.64861i		−	0.627436i
$191$	−13.4090	−	23.2250i	−0.970238	−	1.68050i	−0.694831	−	0.719173i	$-0.744521\pi$
$191$	−13.4090	−	23.2250i	−0.970238	−	1.68050i	−0.275407	−	0.961328i	$-0.588812\pi$
$192$		0			0
$193$	−0.185315	−	0.106992i	−0.0133393	−	0.00770145i	0.493316	−	0.869850i	$-0.335785\pi$
$193$	−0.185315	−	0.106992i	−0.0133393	−	0.00770145i	−0.506655	+	0.862149i	$0.669118\pi$
$194$	8.75816	+	15.1696i	0.628799	+	1.08911i
$195$		0			0
$196$	15.7730	−	16.1053i	1.12664	−	1.15038i
$197$		−	11.2290i		−	0.800035i	−0.916508	−	0.400017i	$-0.869004\pi$
$197$		−	11.2290i		−	0.800035i	0.916508	−	0.400017i	$-0.130996\pi$
$198$		0			0
$199$	10.2100	−	17.6843i	0.723771	−	1.25361i	−0.235707	−	0.971824i	$-0.575741\pi$
$199$	10.2100	−	17.6843i	0.723771	−	1.25361i	0.959478	−	0.281784i	$-0.0909261\pi$
$200$	−1.16974	−	0.675351i	−0.0827132	−	0.0477545i
$201$		0			0
$202$		−	20.8313i		−	1.46568i
$203$	5.27738	+	0.666820i	0.370399	+	0.0468016i
$204$		0			0
$205$	−7.15042	−	12.3849i	−0.499407	−	0.864999i
$206$	−11.9547	−	6.90207i	−0.832926	−	0.480890i
$207$		0			0
$208$	−0.0144055	−	0.251796i	−0.000998842	−	0.0174589i
$209$	−0.549471			−0.0380077
$210$		0			0
$211$	8.41738			0.579476			0.289738	−	0.957106i	$-0.406432\pi$
$211$	8.41738			0.579476			0.289738	+	0.957106i	$0.406432\pi$
$212$	−11.9810	−	20.7517i	−0.822857	−	1.42523i
$213$		0			0
$214$	−23.9148	−	13.8072i	−1.63479	−	0.943844i
$215$	2.80849	−	1.62148i	0.191537	−	0.110584i
$216$		0			0
$217$	−9.70417	−	7.36624i	−0.658762	−	0.500053i
$218$	3.11164			0.210747
$219$		0			0
$220$	1.05545	−	1.82810i	0.0711587	−	0.123250i
$221$	−5.34982	+	3.51075i	−0.359868	+	0.236159i
$222$		0			0
$223$			13.6091i			0.911333i	0.890151	+	0.455666i	$0.150599\pi$
$223$			13.6091i			0.911333i	−0.890151	+	0.455666i	$0.849401\pi$
$224$	12.0889	+	9.17646i	0.807725	+	0.613128i
$225$		0			0
$226$	−18.6396	+	10.7616i	−1.23989	+	0.715849i
$227$	−3.12008	−	1.80138i	−0.207087	−	0.119562i	0.392870	−	0.919594i	$-0.371482\pi$
$227$	−3.12008	−	1.80138i	−0.207087	−	0.119562i	−0.599957	+	0.800032i	$0.704816\pi$
$228$		0			0
$229$	15.9212	−	9.19208i	1.05210	−	0.607430i	0.128863	−	0.991662i	$-0.458867\pi$
$229$	15.9212	−	9.19208i	1.05210	−	0.607430i	0.923236	+	0.384232i	$0.125534\pi$
$230$	−5.58554			−0.368299
$231$		0			0
$232$		−	5.60598i		−	0.368051i
$233$	−10.1348	−	17.5541i	−0.663955	−	1.15000i	−0.979567	−	0.201116i	$-0.935543\pi$
$233$	−10.1348	−	17.5541i	−0.663955	−	1.15000i	0.315612	−	0.948888i	$-0.397790\pi$
$234$		0			0
$235$	−10.1130	+	17.5162i	−0.659699	+	1.14263i
$236$	22.6490	−	13.0764i	1.47432	−	0.851202i
$237$		0			0
$238$	1.34488	−	10.6437i	0.0871758	−	0.689931i
$239$			20.8097i			1.34607i	0.739612	+	0.673033i	$0.235009\pi$
$239$			20.8097i			1.34607i	−0.739612	+	0.673033i	$0.764991\pi$
$240$		0			0
$241$	11.0113	+	6.35736i	0.709299	+	0.409514i	0.810801	−	0.585322i	$-0.199032\pi$
$241$	11.0113	+	6.35736i	0.709299	+	0.409514i	−0.101503	+	0.994835i	$0.532365\pi$
$242$	21.5775	+	12.4578i	1.38705	+	0.800816i
$243$		0			0
$244$	11.0805			0.709355
$245$	−14.3272	+	3.99946i	−0.915330	+	0.255516i
$246$		0			0
$247$	−6.41210	+	0.366843i	−0.407992	+	0.0233417i
$248$	−6.41990	+	11.1196i	−0.407664	+	0.706094i
$249$		0			0
$250$	13.3140	+	23.0605i	0.842050	+	1.45847i
$251$	13.7436			0.867486			0.433743	−	0.901037i	$-0.357193\pi$
$251$	13.7436			0.867486			0.433743	+	0.901037i	$0.357193\pi$
$252$		0			0
$253$			0.354865i			0.0223102i
$254$	−26.5142	+	15.3080i	−1.66365	+	0.960510i
$255$		0			0
$256$	7.77229	−	13.4620i	0.485768	−	0.841375i
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	0.957442	−	0.288626i	$-0.0931983\pi$
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	−0.728678	+	0.684856i	$0.759865\pi$
$258$		0			0
$259$	−13.5158	+	5.68112i	−0.839830	+	0.353008i
$260$	11.0962	−	22.0378i	0.688159	−	1.36673i
$261$		0			0
$262$	−26.5089	−	15.3049i	−1.63772	−	0.945540i
$263$	−3.33942	+	5.78405i	−0.205918	+	0.356660i	−0.950425	−	0.310955i	$-0.899351\pi$
$263$	−3.33942	+	5.78405i	−0.205918	+	0.356660i	0.744507	+	0.667615i	$0.232685\pi$
$264$		0			0
$265$			15.8115i			0.971293i
$266$	6.51058	−	8.57693i	0.399189	−	0.525886i
$267$		0			0
$268$	−35.1821	+	20.3124i	−2.14909	+	1.24078i
$269$	8.11263	−	14.0515i	0.494636	−	0.856735i	−0.505345	−	0.862917i	$-0.668635\pi$
$269$	8.11263	−	14.0515i	0.494636	−	0.856735i	0.999981	+	0.00618287i	$0.00196808\pi$
$270$		0			0
$271$	−16.2277	+	9.36904i	−0.985760	+	0.569129i	−0.904004	−	0.427524i	$-0.859386\pi$
$271$	−16.2277	+	9.36904i	−0.985760	+	0.569129i	−0.0817555	+	0.996652i	$0.526053\pi$
$272$	0.124143			0.00752725
$273$		0			0
$274$	1.14479			0.0691595
$275$	0.129406	−	0.0747124i	0.00780346	−	0.00450533i
$276$		0			0
$277$	15.0163	−	26.0090i	0.902243	−	1.56273i	0.0776679	−	0.996979i	$-0.475253\pi$
$277$	15.0163	−	26.0090i	0.902243	−	1.56273i	0.824575	−	0.565752i	$-0.191414\pi$
$278$	−2.80849	+	1.62148i	−0.168442	+	0.0972501i
$279$		0			0
$280$	6.07453	+	14.4517i	0.363023	+	0.863656i
$281$		−	2.23065i		−	0.133070i	−0.997784	−	0.0665348i	$-0.978806\pi$
$281$		−	2.23065i		−	0.133070i	0.997784	−	0.0665348i	$-0.0211943\pi$
$282$		0			0
$283$	6.88774	−	11.9299i	0.409433	−	0.709159i	−0.585393	−	0.810750i	$-0.699060\pi$
$283$	6.88774	−	11.9299i	0.409433	−	0.709159i	0.994826	+	0.101590i	$0.0323931\pi$
$284$	3.76700	+	2.17488i	0.223531	+	0.129055i
$285$		0			0
$286$	−2.26967	−	1.14280i	−0.134208	−	0.0675750i
$287$	2.23205	−	17.6650i	0.131754	−	1.04273i
$288$		0			0
$289$	6.92516	+	11.9947i	0.407362	+	0.705572i
$290$	−4.88075	+	8.45371i	−0.286608	+	0.496419i
$291$		0			0
$292$	33.1357	−	19.1309i	1.93912	−	1.11955i
$293$			1.01231i			0.0591400i	0.999563	+	0.0295700i	$0.00941380\pi$
$293$			1.01231i			0.0591400i	−0.999563	+	0.0295700i	$0.990586\pi$
$294$		0			0
$295$	−17.2572			−1.00475
$296$	7.72563	+	13.3812i	0.449043	+	0.777766i
$297$		0			0
$298$	−24.0943	+	41.7326i	−1.39575	+	2.41751i
$299$	0.236918	+	4.14113i	0.0137013	+	0.239488i
$300$		0			0
$301$	4.00585	+	0.506157i	0.230893	+	0.0291744i
$302$	39.9939			2.30139
$303$		0			0
$304$	0.107909	+	0.0623010i	0.00618898	+	0.00357321i
$305$	−6.33199	−	3.65577i	−0.362568	−	0.209329i
$306$		0			0
$307$			24.0527i			1.37276i	0.727244	+	0.686379i	$0.240801\pi$
$307$			24.0527i			1.37276i	−0.727244	+	0.686379i	$0.759199\pi$
$308$	2.42288	−	1.01842i	0.138057	−	0.0580296i
$309$		0			0
$310$	19.3622	−	11.1787i	1.09970	−	0.634910i
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	−0.709957	−	0.704245i	$-0.751286\pi$
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	0.964872	+	0.262719i	$0.0846192\pi$
$312$		0			0
$313$	7.61806	+	13.1949i	0.430598	+	0.745818i	0.996925	−	0.0783626i	$-0.0249692\pi$
$313$	7.61806	+	13.1949i	0.430598	+	0.745818i	−0.566326	+	0.824181i	$0.691636\pi$
$314$		−	0.172684i		−	0.00974510i
$315$		0			0
$316$	25.5220			1.43572
$317$	5.91972	−	3.41775i	0.332484	−	0.191960i	−0.324459	−	0.945900i	$-0.605182\pi$
$317$	5.91972	−	3.41775i	0.332484	−	0.191960i	0.656944	+	0.753940i	$0.271849\pi$
$318$		0			0
$319$	0.537088	+	0.310088i	0.0300712	+	0.0173616i
$320$	−23.8628	+	13.7772i	−1.33397	+	0.770170i
$321$		0			0
$322$	−5.53925	−	4.20473i	−0.308690	−	0.234321i
$323$		−	3.16135i		−	0.175902i
$324$		0			0
$325$	1.46023	−	0.958259i	0.0809991	−	0.0531546i
$326$	−11.5174	+	19.9487i	−0.637890	+	1.10486i
$327$		0			0
$328$	−18.7649			−1.03612
$329$	−23.2152	+	9.75811i	−1.27990	+	0.537982i
$330$		0			0
$331$	−11.9637	+	6.90727i	−0.657587	+	0.379658i	−0.791357	−	0.611354i	$-0.790625\pi$
$331$	−11.9637	+	6.90727i	−0.657587	+	0.379658i	0.133770	+	0.991012i	$0.457292\pi$
$332$	31.3169	+	18.0808i	1.71874	+	0.992314i
$333$		0			0
$334$	6.68295	+	11.5752i	0.365675	+	0.633367i
$335$	26.8066			1.46460
$336$		0			0
$337$	−27.0432			−1.47314			−0.736568	−	0.676364i	$-0.763555\pi$
$337$	−27.0432			−1.47314			−0.736568	+	0.676364i	$0.763555\pi$
$338$	−27.2491	−	11.8207i	−1.48216	−	0.642961i
$339$		0			0
$340$	10.5179	+	6.07249i	0.570411	+	0.329327i
$341$	−0.710218	−	1.23013i	−0.0384604	−	0.0666154i
$342$		0			0
$343$	−17.2192	−	6.81903i	−0.929749	−	0.368193i
$344$		−	4.25528i		−	0.229429i
$345$		0			0
$346$	33.6186	+	19.4097i	1.80735	+	1.04347i
$347$	−9.65568	+	16.7241i	−0.518344	+	0.897799i	0.481429	+	0.876485i	$0.340118\pi$
$347$	−9.65568	+	16.7241i	−0.518344	+	0.897799i	−0.999773	+	0.0213132i	$0.993215\pi$
$348$		0			0
$349$		−	14.1573i		−	0.757821i	−0.925433	−	0.378911i	$-0.876299\pi$
$349$		−	14.1573i		−	0.757821i	0.925433	−	0.378911i	$-0.123701\pi$
$350$	−0.367085	+	2.90521i	−0.0196215	+	0.155290i
$351$		0			0
$352$	0.884750	+	1.53243i	0.0471573	+	0.0816789i
$353$	14.6919	+	8.48235i	0.781969	+	0.451470i	0.837128	−	0.547008i	$-0.184233\pi$
$353$	14.6919	+	8.48235i	0.781969	+	0.451470i	−0.0551585	+	0.998478i	$0.517566\pi$
$354$		0			0
$355$	−1.43511	−	2.48569i	−0.0761680	−	0.131927i
$356$			5.34313i			0.283186i
$357$		0			0
$358$			34.9613i			1.84776i
$359$	−19.7136	+	11.3816i	−1.04044	+	0.600700i	−0.919959	−	0.392016i	$-0.871778\pi$
$359$	−19.7136	+	11.3816i	−1.04044	+	0.600700i	−0.120484	+	0.992715i	$0.538445\pi$
$360$		0			0
$361$	−7.91348	+	13.7065i	−0.416499	+	0.721397i
$362$	11.5746	−	6.68260i	0.608347	−	0.351229i
$363$		0			0
$364$	27.5941	−	13.5021i	1.44633	−	0.707702i
$365$	−25.2474			−1.32151
$366$		0			0
$367$	−8.29168	+	14.3616i	−0.432822	+	0.749670i	−0.997115	−	0.0759048i	$-0.975815\pi$
$367$	−8.29168	+	14.3616i	−0.432822	+	0.749670i	0.564293	+	0.825575i	$0.309149\pi$
$368$	0.0402359	−	0.0696907i	0.00209744	−	0.00363288i
$369$		0			0
$370$		−	26.9048i		−	1.39871i
$371$	−11.9027	+	15.6805i	−0.617959	+	0.814090i
$372$		0			0
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	−0.962677	−	0.270652i	$-0.912761\pi$
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	0.246947	−	0.969029i	$-0.420573\pi$
$374$	0.625404	−	1.08323i	0.0323389	−	0.0560126i
$375$		0			0
$376$	13.2698	+	22.9840i	0.684340	+	1.18531i
$377$	6.47463	+	3.26003i	0.333460	+	0.167900i
$378$		0			0
$379$		−	9.24228i		−	0.474744i	−0.971419	−	0.237372i	$-0.923714\pi$
$379$		−	9.24228i		−	0.474744i	0.971419	−	0.237372i	$-0.0762860\pi$
$380$	6.09497	+	10.5568i	0.312665	+	0.541552i
$381$		0			0
$382$	53.0648	+	30.6369i	2.71503	+	1.56752i
$383$	−6.62358	+	3.82413i	−0.338449	+	0.195404i	−0.659586	−	0.751629i	$-0.729268\pi$
$383$	−6.62358	+	3.82413i	−0.338449	+	0.195404i	0.321137	+	0.947033i	$0.395935\pi$
$384$		0			0
$385$	−1.72057	−	0.217402i	−0.0876885	−	0.0110798i
$386$	0.488913			0.0248850
$387$		0			0
$388$	−21.3810	−	12.3443i	−1.08546	−	0.626689i
$389$	−3.26868	+	5.66153i	−0.165729	+	0.287051i	−0.936914	−	0.349560i	$-0.886331\pi$
$389$	−3.26868	+	5.66153i	−0.165729	+	0.287051i	0.771185	+	0.636611i	$0.219664\pi$
$390$		0			0
$391$	−2.04169			−0.103253
$392$	−4.85492	+	18.9048i	−0.245211	+	0.954837i
$393$		0			0
$394$	12.8281	+	22.2189i	0.646271	+	1.11937i
$395$	−14.5846	−	8.42044i	−0.733833	−	0.423678i
$396$		0			0
$397$	−25.0548	+	14.4654i	−1.25746	+	0.725996i	−0.972581	−	0.232566i	$-0.925288\pi$
$397$	−25.0548	+	14.4654i	−1.25746	+	0.725996i	−0.284882	+	0.958563i	$0.591954\pi$
$398$			46.6561i			2.33866i
$399$		0			0
$400$	−0.0338847			−0.00169423
$401$	23.1603	−	13.3716i	1.15657	−	0.667747i	0.206092	−	0.978533i	$-0.433925\pi$
$401$	23.1603	−	13.3716i	1.15657	−	0.667747i	0.950480	+	0.310786i	$0.100592\pi$
$402$		0			0
$403$	−9.10923	−	13.8810i	−0.453763	−	0.691462i
$404$	14.6805	+	25.4274i	0.730382	+	1.26506i
$405$		0			0
$406$	−11.2042	+	4.70947i	−0.556053	+	0.233727i
$407$	−1.70934			−0.0847287
$408$		0			0
$409$	30.1138	+	17.3862i	1.48903	+	0.859694i	0.999922	−	0.0125273i	$-0.00398768\pi$
$409$	30.1138	+	17.3862i	1.48903	+	0.859694i	0.489112	+	0.872221i	$0.337321\pi$
$410$	28.2972	+	16.3374i	1.39750	+	0.806846i
$411$		0			0
$412$	19.4565			0.958553
$413$	−17.1142	−	12.9910i	−0.842133	−	0.639246i
$414$		0			0
$415$	−11.9308	−	20.6647i	−0.585659	−	1.01439i
$416$	11.3478	+	17.2922i	0.556370	+	0.847819i
$417$		0			0
$418$	1.08724	−	0.627719i	0.0531787	−	0.0307027i
$419$	4.19246			0.204815			0.102407	−	0.994743i	$-0.467345\pi$
$419$	4.19246			0.204815			0.102407	+	0.994743i	$0.467345\pi$
$420$		0			0
$421$		−	20.9526i		−	1.02117i	−0.859828	−	0.510584i	$-0.829429\pi$
$421$		−	20.9526i		−	1.02117i	0.859828	−	0.510584i	$-0.170571\pi$
$422$	−16.6555	+	9.61607i	−0.810778	+	0.468103i
$423$		0			0
$424$	17.9676	+	10.3736i	0.872583	+	0.503786i
$425$	0.429853	+	0.744528i	0.0208509	+	0.0361149i
$426$		0			0
$427$	−3.52748	−	8.39213i	−0.170707	−	0.406124i
$428$	38.9217			1.88135
$429$		0			0
$430$	−3.70479	+	6.41688i	−0.178661	+	0.309449i
$431$	14.6309	+	8.44713i	0.704744	+	0.406884i	0.809112	−	0.587655i	$-0.199949\pi$
$431$	14.6309	+	8.44713i	0.704744	+	0.406884i	−0.104368	+	0.994539i	$0.533282\pi$
$432$		0			0
$433$	3.42241			0.164471			0.0822353	−	0.996613i	$-0.473794\pi$
$433$	3.42241			0.164471			0.0822353	+	0.996613i	$0.473794\pi$
$434$	27.6169	+	3.48952i	1.32566	+	0.167502i
$435$		0			0
$436$	−3.79818	+	2.19288i	−0.181900	+	0.105020i
$437$	−1.77470	−	1.02463i	−0.0848956	−	0.0490145i
$438$		0			0
$439$	9.03253	+	15.6448i	0.431099	+	0.746685i	0.996968	−	0.0778096i	$-0.0247926\pi$
$439$	9.03253	+	15.6448i	0.431099	+	0.746685i	−0.565869	+	0.824495i	$0.691459\pi$
$440$			1.82771i			0.0871324i
$441$		0			0
$442$	6.57501	−	13.0584i	0.312742	−	0.621125i
$443$	3.22173	+	5.58020i	0.153069	+	0.265123i	0.932354	−	0.361546i	$-0.117751\pi$
$443$	3.22173	+	5.58020i	0.153069	+	0.265123i	−0.779285	+	0.626669i	$0.784418\pi$
$444$		0			0
$445$	1.76286	−	3.05336i	0.0835674	−	0.144743i
$446$	−15.5471	−	26.9284i	−0.736178	−	1.27510i
$447$		0			0
$448$	−34.0364	−	4.30065i	−1.60807	−	0.203187i
$449$			1.75306i			0.0827322i	0.999144	+	0.0413661i	$0.0131710\pi$
$449$			1.75306i			0.0827322i	−0.999144	+	0.0413661i	$0.986829\pi$
$450$		0			0
$451$	1.03796	−	1.79780i	0.0488757	−	0.0846551i
$452$	15.1681	−	26.2719i	0.713447	−	1.23573i
$453$		0			0
$454$	8.23163			0.386330
$455$	−20.2235	−	1.38829i	−0.948094	−	0.0650839i
$456$		0			0
$457$	28.3277	−	16.3550i	1.32511	−	0.765054i	0.340573	−	0.940218i	$-0.389379\pi$
$457$	28.3277	−	16.3550i	1.32511	−	0.765054i	0.984539	+	0.175164i	$0.0560455\pi$
$458$	−21.0022	+	36.3769i	−0.981368	+	1.69978i
$459$		0			0
$460$	6.81790	−	3.93632i	0.317886	−	0.183532i
$461$		−	7.66641i		−	0.357060i	−0.983934	−	0.178530i	$-0.942866\pi$
$461$		−	7.66641i		−	0.357060i	0.983934	−	0.178530i	$-0.0571342\pi$
$462$		0			0
$463$			14.4720i			0.672570i	0.941760	+	0.336285i	$0.109171\pi$
$463$			14.4720i			0.672570i	−0.941760	+	0.336285i	$0.890829\pi$
$464$	−0.0703179	−	0.121794i	−0.00326443	−	0.00565415i
$465$		0			0
$466$	40.1077	+	23.1562i	1.85795	+	1.07269i
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	0.902435	−	0.430825i	$-0.141777\pi$
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	−0.824323	+	0.566119i	$0.808444\pi$
$468$		0			0
$469$	26.5845	+	20.1798i	1.22756	+	0.931815i
$470$		−	46.2126i		−	2.13163i
$471$		0			0
$472$	−11.3221	+	19.6104i	−0.521140	+	0.902641i
$473$	0.407683	+	0.235376i	0.0187453	+	0.0108226i
$474$		0			0
$475$			0.862889i			0.0395921i
$476$	5.85939	+	13.9399i	0.268565	+	0.638934i
$477$		0			0
$478$	−23.7731	−	41.1763i	−1.08736	−	1.88336i
$479$	−0.125768	−	0.0726124i	−0.00574651	−	0.00331775i	0.497124	−	0.867680i	$-0.334389\pi$
$479$	−0.125768	−	0.0726124i	−0.00574651	−	0.00331775i	−0.502871	+	0.864362i	$0.667723\pi$
$480$		0			0
$481$	−19.9473	+	1.14120i	−0.909517	+	0.0520344i
$482$	−29.0508			−1.32323
$483$		0			0
$484$	−35.1177			−1.59626
$485$	8.14553	+	14.1085i	0.369869	+	0.640633i
$486$		0			0
$487$	14.2214	+	8.21073i	0.644433	+	0.372064i	0.786320	−	0.617819i	$-0.211984\pi$
$487$	14.2214	+	8.21073i	0.644433	+	0.372064i	−0.141887	+	0.989883i	$0.545317\pi$
$488$	−8.30856	+	4.79695i	−0.376111	+	0.217148i
$489$		0			0
$490$	23.7803	−	24.2812i	1.07428	−	1.09691i
$491$	18.2077			0.821701			0.410850	−	0.911703i	$-0.365232\pi$
$491$	18.2077			0.821701			0.410850	+	0.911703i	$0.365232\pi$
$492$		0			0
$493$	−1.78407	+	3.09010i	−0.0803506	+	0.139171i
$494$	12.2686	−	8.05110i	0.551990	−	0.362236i
$495$		0			0
$496$			0.322108i			0.0144631i
$497$	0.447981	−	3.54543i	0.0200947	−	0.159034i
$498$		0			0
$499$	32.5383	−	18.7860i	1.45661	−	0.840976i	0.457770	−	0.889070i	$-0.348648\pi$
$499$	32.5383	−	18.7860i	1.45661	−	0.840976i	0.998843	+	0.0480945i	$0.0153148\pi$
$500$	−32.5030	−	18.7656i	−1.45358	−	0.839225i
$501$		0			0
$502$	−27.1945	+	15.7007i	−1.21375	+	0.700758i
$503$	4.20535			0.187507			0.0937537	−	0.995595i	$-0.470113\pi$
$503$	4.20535			0.187507			0.0937537	+	0.995595i	$0.470113\pi$
$504$		0			0
$505$		−	19.3741i		−	0.862137i
$506$	−0.405400	−	0.702174i	−0.0180222	−	0.0312154i
$507$		0			0
$508$	21.5761	−	37.3710i	0.957287	−	1.65807i
$509$	7.30705	−	4.21873i	0.323879	−	0.186992i	−0.329241	−	0.944246i	$-0.606793\pi$
$509$	7.30705	−	4.21873i	0.323879	−	0.186992i	0.653120	+	0.757254i	$0.273460\pi$
$510$		0			0
$511$	−25.0382	−	19.0060i	−1.10762	−	0.840775i
$512$		−	0.791350i		−	0.0349731i
$513$		0			0
$514$	−14.5133	−	8.37924i	−0.640153	−	0.369593i
$515$	−11.1185	−	6.41927i	−0.489940	−	0.282867i
$516$		0			0
$517$	−2.93602			−0.129126
$518$	20.2536	−	26.6818i	0.889893	−	1.17233i
$519$		0			0
$520$	1.22023	+	21.3286i	0.0535106	+	0.935320i
$521$	12.9140	−	22.3677i	0.565773	−	0.979948i	−0.431204	−	0.902254i	$-0.641911\pi$
$521$	12.9140	−	22.3677i	0.565773	−	0.979948i	0.996977	−	0.0776936i	$-0.0247556\pi$
$522$		0			0
$523$	0.378202	+	0.655065i	0.0165376	+	0.0286440i	0.874176	−	0.485610i	$-0.161402\pi$
$523$	0.378202	+	0.655065i	0.0165376	+	0.0286440i	−0.857638	+	0.514254i	$0.828069\pi$
$524$	43.1436			1.88473
$525$		0			0
$526$		−	15.2599i		−	0.665364i
$527$	7.07749	−	4.08619i	0.308300	−	0.177997i
$528$		0			0
$529$	10.8383	−	18.7724i	0.471229	−	0.816192i
$530$	−18.0632	−	31.2863i	−0.784614	−	1.35899i
$531$		0			0
$532$	−1.90259	+	15.0575i	−0.0824876	+	0.652827i
$533$	10.9123	−	21.6726i	0.472665	−	0.938744i
$534$		0			0
$535$	−22.2420	−	12.8414i	−0.961606	−	0.555183i
$536$	17.5873	−	30.4620i	0.759654	−	1.31576i
$537$		0			0
$538$			37.0717i			1.59827i
$539$	−1.54266	−	1.51083i	−0.0664469	−	0.0650760i
$540$		0			0
$541$	−19.4099	+	11.2063i	−0.834496	+	0.481797i	−0.855390	−	0.517985i	$-0.826682\pi$
$541$	−19.4099	+	11.2063i	−0.834496	+	0.481797i	0.0208936	+	0.999782i	$0.493349\pi$
$542$	21.4065	−	37.0772i	0.919488	−	1.59260i
$543$		0			0
$544$	−8.81675	+	5.09035i	−0.378015	+	0.218247i
$545$	2.89398			0.123965
$546$		0			0
$547$	−11.8059			−0.504784			−0.252392	−	0.967625i	$-0.581217\pi$
$547$	−11.8059			−0.504784			−0.252392	+	0.967625i	$0.581217\pi$
$548$	−1.39737	+	0.806774i	−0.0596929	+	0.0344637i
$549$		0			0
$550$	−0.170704	+	0.295668i	−0.00727884	+	0.0126073i
$551$	−3.10154	+	1.79068i	−0.132130	+	0.0762854i
$552$		0			0
$553$	−8.12495	−	19.3298i	−0.345508	−	0.821988i
$554$			68.6190i			2.91534i
$555$		0			0
$556$	2.28543	−	3.95848i	0.0969238	−	0.167877i
$557$	−7.59273	−	4.38366i	−0.321714	−	0.185742i	0.330442	−	0.943826i	$-0.392802\pi$
$557$	−7.59273	−	4.38366i	−0.321714	−	0.185742i	−0.652156	+	0.758084i	$0.726135\pi$
$558$		0			0
$559$	4.91464	+	2.47456i	0.207867	+	0.104663i
$560$	0.313247	+	0.237780i	0.0132371	+	0.0100480i
$561$		0			0
$562$	2.54831	+	4.41380i	0.107494	+	0.186185i
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	0.159860	+	0.987140i	$0.448896\pi$
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	−0.934818	+	0.355127i	$0.884438\pi$
$564$		0			0
$565$	−17.3358	+	10.0088i	−0.729321	+	0.421074i
$566$			31.4744i			1.32297i
$567$		0			0
$568$	−3.76619			−0.158026
$569$	17.8918	+	30.9896i	0.750065	+	1.29915i	0.947791	+	0.318893i	$0.103311\pi$
$569$	17.8918	+	30.9896i	0.750065	+	1.29915i	−0.197726	+	0.980257i	$0.563356\pi$
$570$		0			0
$571$	7.46920	−	12.9370i	0.312576	−	0.541398i	−0.666343	−	0.745645i	$-0.732141\pi$
$571$	7.46920	−	12.9370i	0.312576	−	0.541398i	0.978919	+	0.204248i	$0.0654747\pi$
$572$	3.57581	−	0.204576i	0.149512	−	0.00855374i
$573$		0			0
$574$	15.7641	+	37.5038i	0.657979	+	1.56538i
$575$	0.557280			0.0232402
$576$		0			0
$577$	−14.5892	−	8.42309i	−0.607357	−	0.350658i	0.164573	−	0.986365i	$-0.447375\pi$
$577$	−14.5892	−	8.42309i	−0.607357	−	0.350658i	−0.771930	+	0.635707i	$0.780709\pi$
$578$	−27.4057	−	15.8227i	−1.13993	−	0.658137i
$579$		0			0
$580$		−	13.7585i		−	0.571292i
$581$	3.72428	−	29.4748i	0.154509	−	1.22282i
$582$		0			0
$583$	−1.98771	+	1.14761i	−0.0823226	+	0.0475290i
$584$	−16.5643	+	28.6901i	−0.685434	+	1.18721i
$585$		0			0
$586$	−1.15647	−	2.00307i	−0.0477735	−	0.0827461i
$587$			36.8833i			1.52234i	0.648555	+	0.761168i	$0.275374\pi$
$587$			36.8833i			1.52234i	−0.648555	+	0.761168i	$0.724626\pi$
$588$		0			0
$589$	8.20264			0.337984
$590$	34.1469	−	19.7147i	1.40580	−	0.811642i
$591$		0			0
$592$	0.335690	+	0.193811i	0.0137968	+	0.00796558i
$593$	−13.9894	+	8.07676i	−0.574474	+	0.331673i	−0.758934	−	0.651167i	$-0.774280\pi$
$593$	−13.9894	+	8.07676i	−0.574474	+	0.331673i	0.184460	+	0.982840i	$0.440946\pi$
$594$		0			0
$595$	1.25081	−	9.89920i	0.0512781	−	0.405828i
$596$		−	67.9204i		−	2.78213i
$597$		0			0
$598$	−5.19965	−	7.92343i	−0.212629	−	0.324013i
$599$	−1.24238	+	2.15186i	−0.0507622	+	0.0879227i	−0.890290	−	0.455394i	$-0.849498\pi$
$599$	−1.24238	+	2.15186i	−0.0507622	+	0.0879227i	0.839528	+	0.543317i	$0.182832\pi$
$600$		0			0
$601$	9.55999			0.389960			0.194980	−	0.980807i	$-0.437536\pi$
$601$	9.55999			0.389960			0.194980	+	0.980807i	$0.437536\pi$
$602$	−8.50464	+	3.57478i	−0.346623	+	0.145697i
$603$		0			0
$604$	−48.8179	+	28.1850i	−1.98637	+	1.14683i
$605$	20.0682	+	11.5864i	0.815886	+	0.471052i
$606$		0			0
$607$	9.74294	+	16.8753i	0.395454	+	0.684946i	0.993159	−	0.116770i	$-0.0372540\pi$
$607$	9.74294	+	16.8753i	0.395454	+	0.684946i	−0.597705	+	0.801716i	$0.703921\pi$
$608$	−10.2184			−0.414411
$609$		0			0
$610$	16.7055			0.676387
$611$	−34.2622	+	1.96017i	−1.38610	+	0.0793002i
$612$		0			0
$613$	−12.7896	−	7.38409i	−0.516568	−	0.298241i	0.218962	−	0.975733i	$-0.429733\pi$
$613$	−12.7896	−	7.38409i	−0.516568	−	0.298241i	−0.735529	+	0.677493i	$0.763066\pi$
$614$	−27.4779	−	47.5931i	−1.10892	−	1.92070i
$615$		0			0
$616$	−1.37588	+	1.81256i	−0.0554357	+	0.0730301i
$617$			30.9478i			1.24591i	0.782257	+	0.622955i	$0.214068\pi$
$617$			30.9478i			1.24591i	−0.782257	+	0.622955i	$0.785932\pi$
$618$		0			0
$619$	−11.3297	−	6.54123i	−0.455380	−	0.262914i	0.254719	−	0.967015i	$-0.418017\pi$
$619$	−11.3297	−	6.54123i	−0.455380	−	0.262914i	−0.710100	+	0.704101i	$0.751350\pi$
$620$	−15.7561	+	27.2903i	−0.632780	+	1.09601i
$621$		0			0
$622$			20.5426i			0.823685i
$623$	4.04678	−	1.70099i	0.162131	−	0.0681489i
$624$		0			0
$625$	11.1716	+	19.3498i	0.446865	+	0.773994i
$626$	−30.1478	−	17.4059i	−1.20495	−	0.695678i
$627$		0			0
$628$	0.121696	+	0.210784i	0.00485620	+	0.00841119i
$629$		−	9.83456i		−	0.392130i
$630$		0			0
$631$			35.3591i			1.40762i	0.710387	+	0.703812i	$0.248520\pi$
$631$			35.3591i			1.40762i	−0.710387	+	0.703812i	$0.751480\pi$
$632$	−19.1373	+	11.0489i	−0.761242	+	0.439503i
$633$		0			0
$634$	−7.80892	+	13.5254i	−0.310132	+	0.537164i
$635$	−24.6596	+	14.2372i	−0.978585	+	0.564986i
$636$		0			0
$637$	−19.0108	−	16.6008i	−0.753237	−	0.657749i
$638$	−1.41699			−0.0560990
$639$		0			0
$640$	19.2884	−	33.4086i	0.762443	−	1.32059i
$641$	10.6188	−	18.3923i	0.419417	−	0.726452i	−0.576464	−	0.817123i	$-0.695568\pi$
$641$	10.6188	−	18.3923i	0.419417	−	0.726452i	0.995881	+	0.0906706i	$0.0289010\pi$
$642$		0			0
$643$			25.4808i			1.00486i	0.864617	+	0.502432i	$0.167561\pi$
$643$			25.4808i			1.00486i	−0.864617	+	0.502432i	$0.832439\pi$
$644$	9.72462	+	1.22875i	0.383204	+	0.0484195i
$645$		0			0
$646$	3.61154	+	6.25537i	0.142094	+	0.246114i
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	−0.998249	−	0.0591522i	$-0.981160\pi$
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	0.550352	+	0.834933i	$0.314494\pi$
$648$		0			0
$649$	−1.25253	−	2.16945i	−0.0491662	−	0.0851583i
$650$	−1.79465	+	3.56429i	−0.0703919	+	0.139803i
$651$		0			0
$652$		−	32.4669i		−	1.27150i
$653$	8.13928	+	14.0976i	0.318515	+	0.551684i	0.980178	−	0.198117i	$-0.0634827\pi$
$653$	8.13928	+	14.0976i	0.318515	+	0.551684i	−0.661664	+	0.749801i	$0.730149\pi$
$654$		0			0
$655$	−24.6546	−	14.2343i	−0.963334	−	0.556181i
$656$	−0.407683	+	0.235376i	−0.0159173	+	0.00918988i
$657$		0			0
$658$	34.7884	−	45.8297i	1.35619	−	1.78663i
$659$	−20.5596			−0.800888			−0.400444	−	0.916321i	$-0.631144\pi$
$659$	−20.5596			−0.800888			−0.400444	+	0.916321i	$0.631144\pi$
$660$		0			0
$661$	−24.0518	−	13.8863i	−0.935507	−	0.540115i	−0.0469576	−	0.998897i	$-0.514953\pi$
$661$	−24.0518	−	13.8863i	−0.935507	−	0.540115i	−0.888549	+	0.458782i	$0.848286\pi$
$662$	15.7818	−	27.3349i	0.613378	−	1.06240i
$663$		0			0
$664$	−31.3101			−1.21507
$665$	6.05517	−	7.97698i	0.234809	−	0.309334i
$666$		0			0
$667$	1.15647	+	2.00307i	0.0447789	+	0.0775593i
$668$	−16.3149	−	9.41941i	−0.631242	−	0.364448i
$669$		0			0
$670$	−53.0425	+	30.6241i	−2.04921	+	1.18311i
$671$		−	1.06135i		−	0.0409730i
$672$		0			0
$673$	5.20337			0.200575			0.100288	−	0.994958i	$-0.468024\pi$
$673$	5.20337			0.200575			0.100288	+	0.994958i	$0.468024\pi$
$674$	53.5105	−	30.8943i	2.06115	−	1.19000i
$675$		0			0
$676$	41.5917	−	4.77463i	1.59968	−	0.183640i
$677$	22.4239	+	38.8394i	0.861821	+	1.49272i	0.870169	+	0.492753i	$0.164009\pi$
$677$	22.4239	+	38.8394i	0.861821	+	1.49272i	−0.00834820	+	0.999965i	$0.502657\pi$
$678$		0			0
$679$	−2.54268	+	20.1234i	−0.0975792	+	0.772266i
$680$	−10.5156			−0.403254
$681$		0			0
$682$	2.81062	+	1.62271i	0.107624	+	0.0621370i
$683$	−16.4318	−	9.48691i	−0.628745	−	0.363006i	0.151521	−	0.988454i	$-0.451583\pi$
$683$	−16.4318	−	9.48691i	−0.628745	−	0.363006i	−0.780266	+	0.625448i	$0.784916\pi$
$684$		0			0
$685$	1.06471			0.0406807
$686$	41.8618	−	6.17846i	1.59829	−	0.235895i
$687$		0			0
$688$	−0.0533755	−	0.0924491i	−0.00203492	−	0.00352459i
$689$	−22.4296	+	14.7191i	−0.854500	+	0.560755i
$690$		0			0
$691$	32.4085	−	18.7111i	1.23288	−	0.711803i	0.265250	−	0.964180i	$-0.414545\pi$
$691$	32.4085	−	18.7111i	1.23288	−	0.711803i	0.967629	+	0.252376i	$0.0812121\pi$
$692$	−54.7148			−2.07994
$693$		0			0
$694$		−	44.1229i		−	1.67488i
$695$	−2.61204	+	1.50806i	−0.0990802	+	0.0572040i
$696$		0			0
$697$	10.3435	+	5.97184i	0.391789	+	0.226200i
$698$	16.1734	+	28.0131i	0.612171	+	1.06031i
$699$		0			0
$700$	−1.59932	−	3.80489i	−0.0604486	−	0.143811i
$701$	−42.5513			−1.60714			−0.803570	−	0.595210i	$-0.797069\pi$
$701$	−42.5513			−1.60714			−0.803570	+	0.595210i	$0.797069\pi$
$702$		0			0
$703$	4.93548	−	8.54851i	0.186145	−	0.322413i
$704$	−3.46395	−	1.99991i	−0.130552	−	0.0753745i
$705$		0			0
$706$	−38.7612			−1.45880
$707$	14.5846	−	19.2136i	0.548512	−	0.722600i
$708$		0			0
$709$	43.5889	−	25.1661i	1.63702	−	0.945131i	0.655163	−	0.755488i	$-0.272600\pi$
$709$	43.5889	−	25.1661i	1.63702	−	0.945131i	0.981853	−	0.189644i	$-0.0607333\pi$
$710$	5.67934	+	3.27897i	0.213142	+	0.123057i
$711$		0			0
$712$	−2.31315	−	4.00648i	−0.0866888	−	0.150149i
$713$		−	5.29752i		−	0.198394i
$714$		0			0
$715$	−2.11091	−	1.06286i	−0.0789435	−	0.0397487i
$716$	−24.6384	−	42.6749i	−0.920780	−	1.59484i
$717$		0			0
$718$	26.0049	−	45.0418i	0.970495	−	1.68095i
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	−0.998940	−	0.0460219i	$-0.985346\pi$
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	0.459614	−	0.888119i	$-0.347988\pi$
$720$		0			0
$721$	−6.19400	−	14.7360i	−0.230677	−	0.548796i
$722$		−	36.1616i		−	1.34580i
$723$		0			0
$724$	−9.41891	+	16.3140i	−0.350051	+	0.606306i
$725$	0.486962	−	0.843444i	0.0180853	−	0.0313247i
$726$		0			0
$727$	19.8593			0.736539			0.368269	−	0.929719i	$-0.379950\pi$
$727$	19.8593			0.736539			0.368269	+	0.929719i	$0.379950\pi$
$728$	−14.8458	+	22.0704i	−0.550222	+	0.817984i
$729$		0			0
$730$	49.9572	−	28.8428i	1.84900	−	1.06752i
$731$	−1.35422	+	2.34558i	−0.0500876	+	0.0867543i
$732$		0			0
$733$	17.6237	−	10.1751i	0.650947	−	0.375824i	−0.137872	−	0.990450i	$-0.544026\pi$
$733$	17.6237	−	10.1751i	0.650947	−	0.375824i	0.788819	+	0.614626i	$0.210693\pi$
$734$		−	37.8899i		−	1.39854i
$735$		0			0
$736$			6.59935i			0.243255i
$737$	1.94564	+	3.36994i	0.0716684	+	0.124133i
$738$		0			0
$739$	16.4554	+	9.50055i	0.605323	+	0.349483i	0.771133	−	0.636674i	$-0.219690\pi$
$739$	16.4554	+	9.50055i	0.605323	+	0.349483i	−0.165810	+	0.986158i	$0.553024\pi$
$740$	18.9607	+	32.8409i	0.697009	+	1.20726i
$741$		0			0
$742$	5.63854	−	44.6248i	0.206997	−	1.63823i
$743$		−	8.15098i		−	0.299030i	−0.988759	−	0.149515i	$-0.952229\pi$
$743$		−	8.15098i		−	0.299030i	0.988759	−	0.149515i	$-0.0477713\pi$
$744$		0			0
$745$	−22.4090	+	38.8134i	−0.821000	+	1.42201i
$746$	54.7035	+	31.5831i	2.00284	+	1.15634i
$747$		0			0
$748$			1.76297i			0.0644607i
$749$	−12.3908	−	29.4786i	−0.452750	−	1.07712i
$750$		0			0
$751$	18.3713	+	31.8201i	0.670379	+	1.16113i	0.977797	+	0.209556i	$0.0672020\pi$
$751$	18.3713	+	31.8201i	0.670379	+	1.16113i	−0.307417	+	0.951575i	$0.599465\pi$
$752$	0.576595	+	0.332897i	0.0210262	+	0.0121395i
$753$		0			0
$754$	−16.5357	+	0.946022i	−0.602193	+	0.0344521i
$755$	37.1963			1.35371
$756$		0			0
$757$	38.3971			1.39557			0.697783	−	0.716310i	$-0.254170\pi$
$757$	38.3971			1.39557			0.697783	+	0.716310i	$0.254170\pi$
$758$	10.5584	+	18.2878i	0.383500	+	0.664241i
$759$		0			0
$760$	−9.14048	−	5.27726i	−0.331560	−	0.191426i
$761$	10.7922	−	6.23089i	0.391218	−	0.225870i	−0.291470	−	0.956580i	$-0.594144\pi$
$761$	10.7922	−	6.23089i	0.391218	−	0.225870i	0.682688	+	0.730710i	$0.260811\pi$
$762$		0			0
$763$	2.87000	+	2.17856i	0.103901	+	0.0788692i
$764$	−86.3636			−3.12453
$765$		0			0
$766$	8.73742	−	15.1336i	0.315696	−	0.546801i
$767$	−16.0649	−	24.4804i	−0.580071	−	0.883935i
$768$		0			0
$769$			4.81390i			0.173594i	0.996226	+	0.0867969i	$0.0276631\pi$
$769$			4.81390i			0.173594i	−0.996226	+	0.0867969i	$0.972337\pi$
$770$	3.65287	−	1.53542i	0.131640	−	0.0553326i
$771$		0			0
$772$	−0.596785	+	0.344554i	−0.0214787	+	0.0124008i
$773$	24.4863	+	14.1372i	0.880713	+	0.508480i	0.870893	−	0.491472i	$-0.163541\pi$
$773$	24.4863	+	14.1372i	0.880713	+	0.508480i	0.00981931	+	0.999952i	$0.496874\pi$
$774$		0			0
$775$	−1.93180	+	1.11533i	−0.0693923	+	0.0400637i
$776$	21.3764			0.767369
$777$		0			0
$778$		−	14.9367i		−	0.535505i
$779$	5.99395	+	10.3818i	0.214755	+	0.371967i
$780$		0			0
$781$	0.208322	−	0.360825i	0.00745436	−	0.0129113i
$782$	4.03991	−	2.33244i	0.144467	−	0.0834081i
$783$		0			0
$784$	0.131653	+	0.471618i	0.00470190	+	0.0168435i
$785$		−	0.160604i		−	0.00573222i
$786$		0			0
$787$	−43.0053	−	24.8291i	−1.53297	−	0.885062i	−0.999223	−	0.0394193i	$-0.987449\pi$
$787$	−43.0053	−	24.8291i	−1.53297	−	0.885062i	−0.533749	−	0.845643i	$-0.679217\pi$
$788$	−31.3169	−	18.0808i	−1.11562	−	0.644102i
$789$		0			0
$790$	38.4783			1.36900
$791$	−24.7266	−	3.12432i	−0.879177	−	0.111088i
$792$		0			0
$793$	−0.708588	−	12.3855i	−0.0251627	−	0.439823i
$794$	33.0507	−	57.2455i	1.17292	−	2.03157i
$795$		0			0
$796$	−32.8801	−	56.9501i	−1.16541	−	2.01854i
$797$	5.37263			0.190308			0.0951542	−	0.995463i	$-0.469666\pi$
$797$	5.37263			0.190308			0.0951542	+	0.995463i	$0.469666\pi$
$798$		0			0
$799$		−	16.8922i		−	0.597604i
$800$	2.40653	−	1.38941i	0.0850837	−	0.0491231i
$801$		0			0
$802$	−30.5517	+	52.9170i	−1.07882	+	1.86857i
$803$	−1.83246	−	3.17392i	−0.0646663	−	0.112005i
$804$		0			0
$805$	−5.15178	−	3.91061i	−0.181576	−	0.137831i
$806$	33.8822	+	17.0600i	1.19345	+	0.600912i
$807$		0			0
$808$	−22.0160	−	12.7109i	−0.774520	−	0.447169i
$809$	20.6184	−	35.7122i	0.724905	−	1.25557i	−0.234107	−	0.972211i	$-0.575217\pi$
$809$	20.6184	−	35.7122i	0.724905	−	1.25557i	0.959013	−	0.283362i	$-0.0914499\pi$
$810$		0			0
$811$			19.4366i			0.682512i	0.939970	+	0.341256i	$0.110852\pi$
$811$			19.4366i			0.682512i	−0.939970	+	0.341256i	$0.889148\pi$
$812$	10.3573	−	13.6445i	0.363469	−	0.478828i
$813$		0			0
$814$	3.38227	−	1.95276i	0.118549	−	0.0684441i
$815$	−10.7118	+	18.5533i	−0.375217	+	0.649895i
$816$		0			0
$817$	−2.35426	+	1.35923i	−0.0823651	+	0.0475535i
$818$	−79.4486			−2.77785
$819$		0			0
$820$	−46.0540			−1.60828
$821$	17.4856	−	10.0953i	0.610251	−	0.352329i	−0.162813	−	0.986657i	$-0.552057\pi$
$821$	17.4856	−	10.0953i	0.610251	−	0.352329i	0.773064	+	0.634328i	$0.218723\pi$
$822$		0			0
$823$	−21.4049	+	37.0743i	−0.746127	+	1.29233i	0.203539	+	0.979067i	$0.434756\pi$
$823$	−21.4049	+	37.0743i	−0.746127	+	1.29233i	−0.949666	+	0.313263i	$0.898578\pi$
$824$	−14.5892	+	8.42309i	−0.508240	+	0.293432i
$825$		0			0
$826$	48.7049	+	6.15408i	1.69466	+	0.214128i
$827$			33.5376i			1.16622i	0.812394	+	0.583109i	$0.198164\pi$
$827$			33.5376i			1.16622i	−0.812394	+	0.583109i	$0.801836\pi$
$828$		0			0
$829$	−19.8949	+	34.4590i	−0.690978	+	1.19681i	0.280540	+	0.959842i	$0.409487\pi$
$829$	−19.8949	+	34.4590i	−0.690978	+	1.19681i	−0.971518	+	0.236967i	$0.923847\pi$
$830$	47.2150	+	27.2596i	1.63886	+	0.946195i
$831$		0			0
$832$	−41.7581	−	21.0255i	−1.44770	−	0.728929i
$833$	8.69246	−	8.87557i	0.301176	−	0.307520i
$834$		0			0
$835$	6.21548	+	10.7655i	0.215096	+	0.372556i
$836$	−0.884750	+	1.53243i	−0.0305997	+	0.0530003i
$837$		0			0
$838$	−8.29564	+	4.78949i	−0.286568	+	0.165450i
$839$		−	36.7098i		−	1.26736i	−0.773594	−	0.633682i	$-0.781543\pi$
$839$		−	36.7098i		−	1.26736i	0.773594	−	0.633682i	$-0.218457\pi$
$840$		0			0
$841$	−24.9578			−0.860614
$842$	23.9364	+	41.4591i	0.824903	+	1.42877i
$843$		0			0
$844$	13.5535	−	23.4754i	0.466532	−	0.808058i
$845$	−25.3430	−	10.9938i	−0.871827	−	0.378199i
$846$		0			0
$847$	11.1798	+	26.5974i	0.384141	+	0.913898i
$848$	0.520479			0.0178733
$849$		0			0
$850$	−1.70111	−	0.982134i	−0.0583475	−	0.0336869i
$851$	−5.52089	−	3.18749i	−0.189254	−	0.109266i
$852$		0			0
$853$		−	11.7156i		−	0.401136i	−0.979680	−	0.200568i	$-0.935721\pi$
$853$		−	11.7156i		−	0.401136i	0.979680	−	0.200568i	$-0.0642788\pi$
$854$	16.5671	+	12.5757i	0.566914	+	0.430333i
$855$		0			0
$856$	−29.1850	+	16.8500i	−0.997523	+	0.575920i
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	−0.526576	−	0.850128i	$-0.676524\pi$
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	0.999521	+	0.0309639i	$0.00985769\pi$
$858$		0			0
$859$	19.2819	+	33.3972i	0.657890	+	1.13950i	0.981161	+	0.193192i	$0.0618840\pi$
$859$	19.2819	+	33.3972i	0.657890	+	1.13950i	−0.323271	+	0.946306i	$0.604783\pi$
$860$		−	10.4436i		−	0.356122i
$861$		0			0
$862$	−38.6002			−1.31473
$863$	15.4613	−	8.92660i	0.526310	−	0.303865i	−0.213203	−	0.977008i	$-0.568389\pi$
$863$	15.4613	−	8.92660i	0.526310	−	0.303865i	0.739512	+	0.673143i	$0.235056\pi$
$864$		0			0
$865$	31.2670	+	18.0520i	1.06311	+	0.613787i
$866$	−6.77195	+	3.90979i	−0.230120	+	0.132860i
$867$		0			0
$868$	−36.1694	+	15.2032i	−1.22767	+	0.516029i
$869$		−	2.44464i		−	0.0829286i
$870$		0			0
$871$	24.9547	+	38.0269i	0.845556	+	1.28849i
$872$	1.89868	−	3.28861i	0.0642975	−	0.111366i
$873$		0			0
$874$	4.68216			0.158376
$875$	−3.86534	+	30.5912i	−0.130672	+	1.03417i
$876$		0			0
$877$	7.72524	−	4.46017i	0.260863	−	0.150609i	−0.363865	−	0.931452i	$-0.618543\pi$
$877$	7.72524	−	4.46017i	0.260863	−	0.150609i	0.624728	+	0.780842i	$0.285210\pi$
$878$	−35.7454	−	20.6376i	−1.20635	−	0.696487i
$879$		0			0
$880$	0.0229256	+	0.0397083i	0.000772821	+	0.00133857i
$881$	−54.6144			−1.84001			−0.920003	−	0.391911i	$-0.871814\pi$
$881$	−54.6144			−1.84001			−0.920003	+	0.391911i	$0.871814\pi$
$882$		0			0
$883$	−7.51632			−0.252944			−0.126472	−	0.991970i	$-0.540365\pi$
$883$	−7.51632			−0.252944			−0.126472	+	0.991970i	$0.540365\pi$
$884$	1.17701	+	20.5732i	0.0395872	+	0.691951i
$885$		0			0
$886$	−12.7497	−	7.36105i	−0.428335	−	0.247299i
$887$	22.5391	+	39.0389i	0.756790	+	1.31080i	0.944479	+	0.328571i	$0.106567\pi$
$887$	22.5391	+	39.0389i	0.756790	+	1.31080i	−0.187689	+	0.982229i	$0.560100\pi$
$888$		0			0
$889$	−35.1728	−	4.44424i	−1.17966	−	0.149055i
$890$			8.05560i			0.270024i
$891$		0			0
$892$	37.9547	+	21.9132i	1.27082	+	0.733708i
$893$	8.47737	−	14.6832i	0.283684	−	0.491356i
$894$		0			0
$895$			32.5157i			1.08688i
$896$	44.2782	−	18.6116i	1.47923	−	0.621769i
$897$		0			0
$898$	−2.00271	−	3.46880i	−0.0668314	−	0.115755i
$899$	−8.01779	−	4.62907i	−0.267408	−	0.154388i
$900$		0			0
$901$	−6.60268	−	11.4362i	−0.219967	−	0.380994i
$902$			4.74309i			0.157928i
$903$		0			0
$904$			26.2662i			0.873602i
$905$	10.7650	−	6.21515i	0.357839	−	0.206599i
$906$		0			0
$907$	3.18295	−	5.51303i	0.105688	−	0.183057i	−0.808331	−	0.588728i	$-0.799629\pi$
$907$	3.18295	−	5.51303i	0.105688	−	0.183057i	0.914019	+	0.405671i	$0.132962\pi$
$908$	−10.0478	+	5.80111i	−0.333449	+	0.192517i
$909$		0			0
$910$	41.6024	−	20.3565i	1.37911	−	0.674811i
$911$	−20.9161			−0.692982			−0.346491	−	0.938053i	$-0.612627\pi$
$911$	−20.9161			−0.692982			−0.346491	+	0.938053i	$0.612627\pi$
$912$		0			0
$913$	1.73188	−	2.99971i	0.0573169	−	0.0992758i
$914$	−37.3681	+	64.7234i	−1.23603	+	2.14086i
$915$		0			0
$916$		−	59.2038i		−	1.95615i
$917$	−13.7348	−	32.6761i	−0.453563	−	1.07906i
$918$		0			0
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	0.822910	−	0.568171i	$-0.192349\pi$
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	−0.903506	+	0.428576i	$0.859016\pi$
$920$	−3.40821	+	5.90320i	−0.112366	+	0.194623i
$921$		0			0
$922$	8.75816	+	15.1696i	0.288435	+	0.499584i
$923$	2.19014	−	4.34976i	0.0720893	−	0.143174i
$924$		0			0
$925$			2.68434i			0.0882606i
$926$	−16.5329	−	28.6358i	−0.543305	−	0.941031i
$927$		0			0
$928$	9.98812	+	5.76664i	0.327876	+	0.189299i
$929$	44.6306	−	25.7675i	1.46428	−	0.845404i	0.465077	−	0.885270i	$-0.346027\pi$
$929$	44.6306	−	25.7675i	1.46428	−	0.845404i	0.999205	+	0.0398663i	$0.0126932\pi$
$930$		0			0
$931$	12.0100	−	3.35261i	0.393611	−	0.109877i
$932$	−65.2759			−2.13818
$933$		0			0
$934$	−6.68017	−	3.85680i	−0.218582	−	0.126198i
$935$	0.581657	−	1.00746i	0.0190222	−	0.0329474i
$936$		0			0
$937$	20.3565			0.665016			0.332508	−	0.943100i	$-0.392105\pi$
$937$	20.3565			0.665016			0.332508	+	0.943100i	$0.392105\pi$
$938$	−75.6564	−	9.55952i	−2.47027	−	0.312129i
$939$		0			0
$940$	32.5676	+	56.4088i	1.06224	+	1.83985i
$941$	−29.6730	−	17.1317i	−0.967314	−	0.558479i	−0.0688974	−	0.997624i	$-0.521948\pi$
$941$	−29.6730	−	17.1317i	−0.967314	−	0.558479i	−0.898416	+	0.439145i	$0.855281\pi$
$942$		0			0
$943$	6.70490	−	3.87108i	0.218342	−	0.126060i
$944$			0.568067i			0.0184890i
$945$		0			0
$946$	−1.07558			−0.0349701
$947$	−47.9046	+	27.6578i	−1.55669	+	0.898756i	−0.559122	+	0.829086i	$0.688862\pi$
$947$	−47.9046	+	27.6578i	−1.55669	+	0.898756i	−0.997570	+	0.0696707i	$0.977805\pi$
$948$		0			0
$949$	−23.5031	−	35.8150i	−0.762944	−	1.16260i
$950$	−0.985770	−	1.70740i	−0.0319826	−	0.0553955i
$951$		0			0
$952$	−10.4284	−	7.91602i	−0.337988	−	0.256560i
$953$	14.8378			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$953$	14.8378			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$954$		0			0
$955$	49.3529	+	28.4939i	1.59702	+	0.922041i
$956$	58.0366	+	33.5075i	1.87704	+	1.08371i
$957$		0			0
$958$	0.331812			0.0107203
$959$	1.05589	+	0.801506i	0.0340965	+	0.0258820i
$960$		0			0
$961$	−4.89769	−	8.48305i	−0.157990	−	0.273647i
$962$	38.1661	−	25.0460i	1.23052	−	0.807515i
$963$		0			0
$964$	35.4604	−	20.4731i	1.14210	−	0.659393i
$965$	0.454714			0.0146378
$966$		0			0
$967$		−	3.09473i		−	0.0995199i	−0.998761	−	0.0497600i	$-0.984154\pi$
$967$		−	3.09473i		−	0.0995199i	0.998761	−	0.0497600i	$-0.0158456\pi$
$968$	26.3326	−	15.2031i	0.846361	−	0.488647i
$969$		0			0
$970$	−32.2352	−	18.6110i	−1.03501	−	0.597564i
$971$	27.4506	+	47.5459i	0.880933	+	1.52582i	0.850305	+	0.526290i	$0.176417\pi$
$971$	27.4506	+	47.5459i	0.880933	+	1.52582i	0.0306280	+	0.999531i	$0.490249\pi$
$972$		0			0
$973$	−3.72564	−	0.470751i	−0.119439	−	0.0150916i
$974$	−37.5200			−1.20222
$975$		0			0
$976$	−0.120340	+	0.208435i	−0.00385198	+	0.00667183i
$977$	37.4196	+	21.6042i	1.19716	+	0.691181i	0.959921	−	0.280270i	$-0.0904242\pi$
$977$	37.4196	+	21.6042i	1.19716	+	0.691181i	0.237239	+	0.971451i	$0.423757\pi$
$978$		0			0
$979$	0.511795			0.0163570
$980$	−11.9152	+	46.3973i	−0.380618	+	1.48211i
$981$		0			0
$982$	−36.0276	+	20.8006i	−1.14969	+	0.663773i
$983$	21.5498	+	12.4418i	0.687332	+	0.396831i	0.802612	−	0.596502i	$-0.203443\pi$
$983$	21.5498	+	12.4418i	0.687332	+	0.396831i	−0.115280	+	0.993333i	$0.536776\pi$
$984$		0			0
$985$	11.9308	+	20.6647i	0.380146	+	0.658433i
$986$		−	8.15254i		−	0.259630i
$987$		0			0
$988$	−9.30158	+	18.4735i	−0.295923	+	0.587722i
$989$	0.877834	+	1.52045i	0.0279135	+	0.0483476i
$990$		0			0
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	−0.901509	−	0.432760i	$-0.857540\pi$
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	0.825536	+	0.564349i	$0.190873\pi$
$992$	−13.2078	−	22.8765i	−0.419347	−	0.726331i
$993$		0			0
$994$	3.16390	+	7.52714i	0.100353	+	0.238746i
$995$			43.3925i			1.37564i
$996$		0			0
$997$	−1.72037	+	2.97977i	−0.0544847	+	0.0943703i	−0.891981	−	0.452072i	$-0.850685\pi$
$997$	−1.72037	+	2.97977i	−0.0544847	+	0.0943703i	0.837497	+	0.546442i	$0.184018\pi$
$998$	−42.9225	+	74.3439i	−1.35869	+	2.35331i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dl.e.298.1		16
3.2	odd	2		91.2.r.a.25.8	yes	16
7.2	even	3	inner	819.2.dl.e.415.8		16
13.12	even	2	inner	819.2.dl.e.298.8		16
21.2	odd	6		91.2.r.a.51.1	yes	16
21.5	even	6		637.2.r.f.324.1		16
21.11	odd	6		637.2.c.f.246.8		8
21.17	even	6		637.2.c.e.246.8		8
21.20	even	2		637.2.r.f.116.8		16
39.5	even	4		1183.2.e.i.508.1		16
39.8	even	4		1183.2.e.i.508.8		16
39.38	odd	2		91.2.r.a.25.1	✓	16
91.51	even	6	inner	819.2.dl.e.415.1		16
273.38	even	6		637.2.c.e.246.1		8
273.44	even	12		1183.2.e.i.170.1		16
273.86	even	12		1183.2.e.i.170.8		16
273.116	odd	6		637.2.c.f.246.1		8
273.122	odd	12		8281.2.a.cj.1.8		8
273.164	odd	12		8281.2.a.cj.1.1		8
273.194	even	6		637.2.r.f.324.8		16
273.200	even	12		8281.2.a.ck.1.8		8
273.233	odd	6		91.2.r.a.51.8	yes	16
273.242	even	12		8281.2.a.ck.1.1		8
273.272	even	2		637.2.r.f.116.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.1	✓	16	39.38	odd	2
91.2.r.a.25.8	yes	16	3.2	odd	2
91.2.r.a.51.1	yes	16	21.2	odd	6
91.2.r.a.51.8	yes	16	273.233	odd	6
637.2.c.e.246.1		8	273.38	even	6
637.2.c.e.246.8		8	21.17	even	6
637.2.c.f.246.1		8	273.116	odd	6
637.2.c.f.246.8		8	21.11	odd	6
637.2.r.f.116.1		16	273.272	even	2
637.2.r.f.116.8		16	21.20	even	2
637.2.r.f.324.1		16	21.5	even	6
637.2.r.f.324.8		16	273.194	even	6
819.2.dl.e.298.1		16	1.1	even	1	trivial
819.2.dl.e.298.8		16	13.12	even	2	inner
819.2.dl.e.415.1		16	91.51	even	6	inner
819.2.dl.e.415.8		16	7.2	even	3	inner
1183.2.e.i.170.1		16	273.44	even	12
1183.2.e.i.170.8		16	273.86	even	12
1183.2.e.i.508.1		16	39.5	even	4
1183.2.e.i.508.8		16	39.8	even	4
8281.2.a.cj.1.1		8	273.164	odd	12
8281.2.a.cj.1.8		8	273.122	odd	12
8281.2.a.ck.1.1		8	273.242	even	12
8281.2.a.ck.1.8		8	273.200	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.97871 + 1.14241i) q^{2} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} +(-2.62488 - 0.331665i) q^{7} +2.78832i q^{8} +O(q^{10})\)	\(q+(-1.97871 + 1.14241i) q^{2} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} +(-2.62488 - 0.331665i) q^{7} +2.78832i q^{8} +(2.42760 - 4.20473i) q^{10} +(-0.267139 - 0.154233i) q^{11} +(-3.22037 - 1.62148i) q^{13} +(5.57276 - 2.34241i) q^{14} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(1.54266 - 0.890653i) q^{19} +6.84326i q^{20} +0.704786 q^{22} +(-0.575211 - 0.996294i) q^{23} +(-0.242207 + 0.419515i) q^{25} +(8.22456 - 0.470536i) q^{26} +(-5.15153 + 6.78655i) q^{28} -2.01052 q^{29} +(3.98791 + 2.30242i) q^{31} +(-4.96792 - 2.86823i) q^{32} +4.05494i q^{34} +(5.18295 - 2.17856i) q^{35} +(4.79901 - 2.77071i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(-2.96258 - 5.13134i) q^{40} +6.72984i q^{41} -1.52611 q^{43} +(-0.860286 + 0.496686i) q^{44} +(2.27635 + 1.31425i) q^{46} +(8.24297 - 4.75908i) q^{47} +(6.78000 + 1.74116i) q^{49} -1.10680i q^{50} +(-9.70759 + 6.37048i) q^{52} +(3.72037 - 6.44387i) q^{53} +0.655486 q^{55} +(0.924789 - 7.31901i) q^{56} +(3.97823 - 2.29683i) q^{58} +(7.03304 + 4.06053i) q^{59} +(1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +12.9669 q^{64} +(7.64926 - 0.437622i) q^{65} +(-10.9249 - 6.30747i) q^{67} +(-2.85765 - 4.94960i) q^{68} +(-7.76673 + 10.2318i) q^{70} +1.35070i q^{71} +(10.2894 + 5.94059i) q^{73} +(-6.33056 + 10.9648i) q^{74} -5.73646i q^{76} +(0.650054 + 0.493443i) q^{77} +(3.96258 + 6.86339i) q^{79} +(-0.128728 - 0.0743214i) q^{80} +(-7.68821 - 13.3164i) q^{82} +11.2290i q^{83} +3.77130i q^{85} +(3.01972 - 1.74344i) q^{86} +(0.430050 - 0.744869i) q^{88} +(-1.43688 + 0.829583i) q^{89} +(7.91530 + 5.32428i) q^{91} -3.70479 q^{92} +(-10.8736 + 18.8336i) q^{94} +(-1.89263 + 3.27813i) q^{95} -7.66641i q^{97} +(-15.4047 + 4.30026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4}+O(q^{10}) \) 16 * q + 6 * q^4	\( 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

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