LMFDB - Embedded newform 819.2.dl.e.298.4

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			298.4
Root			$0.287846 + 0.166188i$ of defining polynomial
Character	$\chi$	$=$	819.298
Dual form			819.2.dl.e.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.287846 + 0.166188i) q^{2} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} +(2.26391 + 1.36920i) q^{7} -1.29278i q^{8} +O(q^{10})$	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} +(2.26391 + 1.36920i) q^{7} -1.29278i q^{8} +(0.240245 - 0.416116i) q^{10} +(5.15732 + 2.97758i) q^{11} +(1.88953 - 3.07078i) q^{13} +(-0.879201 - 0.0178849i) q^{14} +(-1.67468 - 2.90063i) q^{16} +(-2.16436 + 3.74877i) q^{17} +(1.69527 - 0.978767i) q^{19} -2.73154i q^{20} -1.97935 q^{22} +(0.270081 + 0.467795i) q^{23} +(-1.45509 + 2.52029i) q^{25} +(-0.0335660 + 1.19793i) q^{26} +(-4.37939 + 2.41104i) q^{28} -7.15857 q^{29} +(5.28968 + 3.05400i) q^{31} +(3.20327 + 1.84941i) q^{32} -1.43876i q^{34} +(-3.82396 - 0.0777879i) q^{35} +(-6.95316 + 4.01441i) q^{37} +(-0.325318 + 0.563467i) q^{38} +(0.934437 + 1.61849i) q^{40} +7.55362i q^{41} -4.24839 q^{43} +(-9.74489 + 5.62622i) q^{44} +(-0.155483 - 0.0897684i) q^{46} +(5.42204 - 3.13042i) q^{47} +(3.25057 + 6.19950i) q^{49} -0.967272i q^{50} +(3.23980 + 5.99314i) q^{52} +(-1.38953 + 2.40673i) q^{53} -8.60891 q^{55} +(1.77008 - 2.92674i) q^{56} +(2.06056 - 1.18967i) q^{58} +(0.737119 + 0.425576i) q^{59} +(-3.38953 - 5.87083i) q^{61} -2.03015 q^{62} +5.46933 q^{64} +(-0.145991 + 5.21022i) q^{65} +(0.854859 + 0.493553i) q^{67} +(-4.08961 - 7.08341i) q^{68} +(1.11364 - 0.613105i) q^{70} -3.76223i q^{71} +(-7.91131 - 4.56760i) q^{73} +(1.33429 - 2.31106i) q^{74} +3.69881i q^{76} +(7.59879 + 13.8024i) q^{77} +(0.0655625 + 0.113558i) q^{79} +(4.19322 + 2.42096i) q^{80} +(-1.25532 - 2.17428i) q^{82} -2.66812i q^{83} -6.25768i q^{85} +(1.22288 - 0.706030i) q^{86} +(3.84936 - 6.66729i) q^{88} +(8.41550 - 4.85869i) q^{89} +(8.48224 - 4.36482i) q^{91} -1.02065 q^{92} +(-1.04047 + 1.80215i) q^{94} +(-1.41493 + 2.45072i) q^{95} +6.58319i q^{97} +(-1.96594 - 1.24429i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.287846	+	0.166188i	−0.203538	+	0.117512i	−0.598304	−	0.801269i	$-0.704159\pi$
$2$	−0.287846	+	0.166188i	−0.203538	+	0.117512i	0.394767	+	0.918781i	$0.370825\pi$
$3$		0			0
$3$		0			0
$4$	−0.944763	+	1.63638i	−0.472382	+	0.818189i
$5$	−1.25195	+	0.722811i	−0.559887	+	0.323251i	−0.753100	−	0.657906i	$-0.771442\pi$
$5$	−1.25195	+	0.722811i	−0.559887	+	0.323251i	0.193213	+	0.981157i	$0.438109\pi$
$6$		0			0
$7$	2.26391	+	1.36920i	0.855677	+	0.517510i
$7$	2.26391	+	1.36920i	0.855677	+	0.517510i
$8$		−	1.29278i		−	0.457068i
$9$		0			0
$10$	0.240245	−	0.416116i	0.0759720	−	0.131587i
$11$	5.15732	+	2.97758i	1.55499	+	0.897774i	0.997723	+	0.0674405i	$0.0214833\pi$
$11$	5.15732	+	2.97758i	1.55499	+	0.897774i	0.557267	+	0.830333i	$0.311850\pi$
$12$		0			0
$13$	1.88953	−	3.07078i	0.524060	−	0.851681i
$13$	1.88953	−	3.07078i	0.524060	−	0.851681i
$14$	−0.879201	−	0.0178849i	−0.234976	−	0.00477994i
$15$		0			0
$16$	−1.67468	−	2.90063i	−0.418670	−	0.725159i
$17$	−2.16436	+	3.74877i	−0.524933	+	0.909211i	0.474645	+	0.880177i	$0.342576\pi$
$17$	−2.16436	+	3.74877i	−0.524933	+	0.909211i	−0.999578	+	0.0290341i	$0.990757\pi$
$18$		0			0
$19$	1.69527	−	0.978767i	0.388923	−	0.224545i	−0.292771	−	0.956183i	$-0.594577\pi$
$19$	1.69527	−	0.978767i	0.388923	−	0.224545i	0.681693	+	0.731638i	$0.261244\pi$
$20$		−	2.73154i		−	0.610791i
$21$		0			0
$22$	−1.97935			−0.421998
$23$	0.270081	+	0.467795i	0.0563158	+	0.0975419i	0.892809	−	0.450436i	$-0.148731\pi$
$23$	0.270081	+	0.467795i	0.0563158	+	0.0975419i	−0.836493	+	0.547977i	$0.815398\pi$
$24$		0			0
$25$	−1.45509	+	2.52029i	−0.291018	+	0.504058i
$26$	−0.0335660	+	1.19793i	−0.00658282	+	0.234933i
$27$		0			0
$28$	−4.37939	+	2.41104i	−0.827627	+	0.455644i
$29$	−7.15857			−1.32931			−0.664656	−	0.747149i	$-0.731422\pi$
$29$	−7.15857			−1.32931			−0.664656	+	0.747149i	$0.731422\pi$
$30$		0			0
$31$	5.28968	+	3.05400i	0.950055	+	0.548514i	0.893098	−	0.449862i	$-0.148527\pi$
$31$	5.28968	+	3.05400i	0.950055	+	0.548514i	0.0569568	+	0.998377i	$0.481860\pi$
$32$	3.20327	+	1.84941i	0.566263	+	0.326932i
$33$		0			0
$34$		−	1.43876i		−	0.246745i
$35$	−3.82396	−	0.0777879i	−0.646368	−	0.0131486i
$36$		0			0
$37$	−6.95316	+	4.01441i	−1.14309	+	0.659964i	−0.947194	−	0.320660i	$-0.896095\pi$
$37$	−6.95316	+	4.01441i	−1.14309	+	0.659964i	−0.195897	+	0.980624i	$0.562762\pi$
$38$	−0.325318	+	0.563467i	−0.0527736	+	0.0914065i
$39$		0			0
$40$	0.934437	+	1.61849i	0.147748	+	0.255906i
$41$			7.55362i			1.17968i	0.807521	+	0.589839i	$0.200809\pi$
$41$			7.55362i			1.17968i	−0.807521	+	0.589839i	$0.799191\pi$
$42$		0			0
$43$	−4.24839			−0.647873			−0.323936	−	0.946079i	$-0.605006\pi$
$43$	−4.24839			−0.647873			−0.323936	+	0.946079i	$0.605006\pi$
$44$	−9.74489	+	5.62622i	−1.46910	+	0.848184i
$45$		0			0
$46$	−0.155483	−	0.0897684i	−0.0229248	−	0.0132356i
$47$	5.42204	−	3.13042i	0.790886	−	0.456618i	−0.0493882	−	0.998780i	$-0.515727\pi$
$47$	5.42204	−	3.13042i	0.790886	−	0.456618i	0.840274	+	0.542161i	$0.182394\pi$
$48$		0			0
$49$	3.25057	+	6.19950i	0.464367	+	0.885643i
$50$		−	0.967272i		−	0.136793i
$51$		0			0
$52$	3.23980	+	5.99314i	0.449280	+	0.831099i
$53$	−1.38953	+	2.40673i	−0.190866	+	0.330590i	−0.945538	−	0.325513i	$-0.894463\pi$
$53$	−1.38953	+	2.40673i	−0.190866	+	0.330590i	0.754671	+	0.656103i	$0.227796\pi$
$54$		0			0
$55$	−8.60891			−1.16082
$56$	1.77008	−	2.92674i	0.236537	−	0.391103i
$57$		0			0
$58$	2.06056	−	1.18967i	0.270565	−	0.156211i
$59$	0.737119	+	0.425576i	0.0959647	+	0.0554053i	0.547214	−	0.836993i	$-0.315688\pi$
$59$	0.737119	+	0.425576i	0.0959647	+	0.0554053i	−0.451250	+	0.892398i	$0.649022\pi$
$60$		0			0
$61$	−3.38953	−	5.87083i	−0.433984	−	0.751683i	0.563228	−	0.826302i	$-0.309559\pi$
$61$	−3.38953	−	5.87083i	−0.433984	−	0.751683i	−0.997212	+	0.0746187i	$0.976226\pi$
$62$	−2.03015			−0.257829
$63$		0			0
$64$	5.46933			0.683667
$65$	−0.145991	+	5.21022i	−0.0181079	+	0.646248i
$66$		0			0
$67$	0.854859	+	0.493553i	0.104438	+	0.0602971i	0.551309	−	0.834301i	$-0.314129\pi$
$67$	0.854859	+	0.493553i	0.104438	+	0.0602971i	−0.446871	+	0.894598i	$0.647462\pi$
$68$	−4.08961	−	7.08341i	−0.495938	−	0.858990i
$69$		0			0
$70$	1.11364	−	0.613105i	0.133105	−	0.0732801i
$71$		−	3.76223i		−	0.446494i	−0.974762	−	0.223247i	$-0.928334\pi$
$71$		−	3.76223i		−	0.446494i	0.974762	−	0.223247i	$-0.0716657\pi$
$72$		0			0
$73$	−7.91131	−	4.56760i	−0.925949	−	0.534597i	−0.0404208	−	0.999183i	$-0.512870\pi$
$73$	−7.91131	−	4.56760i	−0.925949	−	0.534597i	−0.885528	+	0.464586i	$0.846203\pi$
$74$	1.33429	−	2.31106i	0.155108	−	0.268655i
$75$		0			0
$76$			3.69881i			0.424283i
$77$	7.59879	+	13.8024i	0.865963	+	1.57293i
$78$		0			0
$79$	0.0655625	+	0.113558i	0.00737636	+	0.0127762i	0.869690	−	0.493598i	$-0.164319\pi$
$79$	0.0655625	+	0.113558i	0.00737636	+	0.0127762i	−0.862314	+	0.506375i	$0.830985\pi$
$80$	4.19322	+	2.42096i	0.468816	+	0.270671i
$81$		0			0
$82$	−1.25532	−	2.17428i	−0.138627	−	0.240109i
$83$		−	2.66812i		−	0.292865i	−0.989221	−	0.146432i	$-0.953221\pi$
$83$		−	2.66812i		−	0.292865i	0.989221	−	0.146432i	$-0.0467791\pi$
$84$		0			0
$85$		−	6.25768i		−	0.678741i
$86$	1.22288	−	0.706030i	0.131866	−	0.0761331i
$87$		0			0
$88$	3.84936	−	6.66729i	0.410344	−	0.710736i
$89$	8.41550	−	4.85869i	0.892042	−	0.515021i	0.0174319	−	0.999848i	$-0.494451\pi$
$89$	8.41550	−	4.85869i	0.892042	−	0.515021i	0.874610	+	0.484828i	$0.161118\pi$
$90$		0			0
$91$	8.48224	−	4.36482i	0.889180	−	0.457558i
$92$	−1.02065			−0.106410
$93$		0			0
$94$	−1.04047	+	1.80215i	−0.107317	+	0.185878i
$95$	−1.41493	+	2.45072i	−0.145168	+	0.251439i
$96$		0			0
$97$			6.58319i			0.668422i	0.942498	+	0.334211i	$0.108470\pi$
$97$			6.58319i			0.668422i	−0.942498	+	0.334211i	$0.891530\pi$
$98$	−1.96594	−	1.24429i	−0.198590	−	0.125693i
$99$		0			0
$100$	−2.74943	−	4.76215i	−0.274943	−	0.476215i
$101$	0.0354144	−	0.0613396i	0.00352387	−	0.00610352i	−0.864258	−	0.503049i	$-0.832212\pi$
$101$	0.0354144	−	0.0613396i	0.00352387	−	0.00610352i	0.867782	+	0.496945i	$0.165545\pi$
$102$		0			0
$103$	3.16910	+	5.48905i	0.312261	+	0.540852i	0.978852	−	0.204572i	$-0.0655803\pi$
$103$	3.16910	+	5.48905i	0.312261	+	0.540852i	−0.666590	+	0.745424i	$0.732247\pi$
$104$	−3.96985	−	2.44275i	−0.389276	−	0.239531i
$105$		0			0
$106$		−	0.923689i		−	0.0897166i
$107$	3.87476	+	6.71129i	0.374588	+	0.648805i	0.990265	−	0.139193i	$-0.0444510\pi$
$107$	3.87476	+	6.71129i	0.374588	+	0.648805i	−0.615678	+	0.787998i	$0.711118\pi$
$108$		0			0
$109$	0.0290658	+	0.0167811i	0.00278400	+	0.00160734i	0.501391	−	0.865221i	$-0.332822\pi$
$109$	0.0290658	+	0.0167811i	0.00278400	+	0.00160734i	−0.498607	+	0.866828i	$0.666155\pi$
$110$	2.47804	−	1.43069i	0.236271	−	0.136411i
$111$		0			0
$112$	0.180227	−	8.85975i	0.0170298	−	0.837168i
$113$	9.19987			0.865451			0.432725	−	0.901526i	$-0.357552\pi$
$113$	9.19987			0.865451			0.432725	+	0.901526i	$0.357552\pi$
$114$		0			0
$115$	−0.676254	−	0.390435i	−0.0630610	−	0.0364083i
$116$	6.76315	−	11.7141i	0.627943	−	1.08763i
$117$		0			0
$118$	−0.282902			−0.0260432
$119$	−10.0327	+	5.52344i	−0.919699	+	0.506333i
$120$		0			0
$121$	12.2320	+	21.1864i	1.11200	+	1.92603i
$122$	1.95132	+	1.12660i	0.176664	+	0.101997i
$123$		0			0
$124$	−9.99499	+	5.77061i	−0.897577	+	0.518216i
$125$		−	11.4351i		−	1.02279i
$126$		0			0
$127$	−14.3952			−1.27737			−0.638683	−	0.769470i	$-0.720520\pi$
$127$	−14.3952			−1.27737			−0.638683	+	0.769470i	$0.720520\pi$
$128$	−7.98085	+	4.60775i	−0.705414	+	0.407271i
$129$		0			0
$130$	−0.823851	−	1.52400i	−0.0722565	−	0.133664i
$131$	−4.73414	−	8.19978i	−0.413624	−	0.716418i	0.581659	−	0.813433i	$-0.302404\pi$
$131$	−4.73414	−	8.19978i	−0.413624	−	0.716418i	−0.995283	+	0.0970151i	$0.969070\pi$
$132$		0			0
$133$	5.17808	+	0.105334i	0.448996	+	0.00913357i
$134$	−0.328090			−0.0283426
$135$		0			0
$136$	4.84635	+	2.79804i	0.415571	+	0.239930i
$137$	−14.3814	−	8.30313i	−1.22869	−	0.709384i	−0.261934	−	0.965086i	$-0.584360\pi$
$137$	−14.3814	−	8.30313i	−1.22869	−	0.709384i	−0.966756	+	0.255702i	$0.917693\pi$
$138$		0			0
$139$	18.4778			1.56726			0.783632	−	0.621225i	$-0.213365\pi$
$139$	18.4778			1.56726			0.783632	+	0.621225i	$0.213365\pi$
$140$	3.74003	−	6.18396i	0.316090	−	0.522640i
$141$		0			0
$142$	0.625236	+	1.08294i	0.0524687	+	0.0908784i
$143$	18.8884	−	10.2108i	1.57953	−	0.853868i
$144$		0			0
$145$	8.96213	−	5.17429i	0.744264	−	0.429701i
$146$	3.03631			0.251287
$147$		0			0
$148$		−	15.1707i		−	1.24702i
$149$	2.66805	−	1.54040i	0.218575	−	0.126195i	−0.386715	−	0.922199i	$-0.626390\pi$
$149$	2.66805	−	1.54040i	0.218575	−	0.126195i	0.605290	+	0.796005i	$0.293057\pi$
$150$		0			0
$151$	2.20737	+	1.27442i	0.179633	+	0.103711i	0.587120	−	0.809500i	$-0.300262\pi$
$151$	2.20737	+	1.27442i	0.179633	+	0.103711i	−0.407487	+	0.913211i	$0.633595\pi$
$152$	−1.26533	−	2.19162i	−0.102632	−	0.177764i
$153$		0			0
$154$	−4.48106	−	2.71013i	−0.361095	−	0.218388i
$155$	−8.82985			−0.709231
$156$		0			0
$157$	4.70452	−	8.14847i	0.375461	−	0.650318i	−0.614935	−	0.788578i	$-0.710818\pi$
$157$	4.70452	−	8.14847i	0.375461	−	0.650318i	0.990396	+	0.138260i	$0.0441509\pi$
$158$	−0.0377438	−	0.0217914i	−0.00300273	−	0.00173363i
$159$		0			0
$160$	−5.34708			−0.422724
$161$	−0.0290658	+	1.42884i	−0.00229070	+	0.112608i
$162$		0			0
$163$	−0.602023	+	0.347578i	−0.0471541	+	0.0272244i	−0.523392	−	0.852092i	$-0.675334\pi$
$163$	−0.602023	+	0.347578i	−0.0471541	+	0.0272244i	0.476238	+	0.879317i	$0.342000\pi$
$164$	−12.3606	−	7.13638i	−0.965199	−	0.557258i
$165$		0			0
$166$	0.443409	+	0.768007i	0.0344152	+	0.0596089i
$167$			13.9840i			1.08211i	0.840986	+	0.541056i	$0.181975\pi$
$167$			13.9840i			1.08211i	−0.840986	+	0.541056i	$0.818025\pi$
$168$		0			0
$169$	−5.85938	−	11.6046i	−0.450721	−	0.892665i
$170$	1.03995	+	1.80125i	0.0797605	+	0.138149i
$171$		0			0
$172$	4.01372	−	6.95197i	0.306043	−	0.530083i
$173$	2.71824	+	4.70813i	0.206664	+	0.357952i	0.950662	−	0.310230i	$-0.100406\pi$
$173$	2.71824	+	4.70813i	0.206664	+	0.357952i	−0.743998	+	0.668182i	$0.767073\pi$
$174$		0			0
$175$	−6.74497	+	3.71339i	−0.509872	+	0.280706i
$176$		−	19.9460i		−	1.50349i
$177$		0			0
$178$	−1.61491	+	2.79711i	−0.121043	+	0.209652i
$179$	−2.67912	+	4.64037i	−0.200247	+	0.346838i	−0.948608	−	0.316454i	$-0.897508\pi$
$179$	−2.67912	+	4.64037i	−0.200247	+	0.346838i	0.748361	+	0.663292i	$0.230841\pi$
$180$		0			0
$181$	−7.54016			−0.560456			−0.280228	−	0.959933i	$-0.590410\pi$
$181$	−7.54016			−0.560456			−0.280228	+	0.959933i	$0.590410\pi$
$182$	−1.71619	+	2.66604i	−0.127213	+	0.197620i
$183$		0			0
$184$	0.604757	−	0.349157i	0.0445833	−	0.0257402i
$185$	5.80331	−	10.0516i	0.426668	−	0.739011i
$186$		0			0
$187$	−22.3245	+	12.8891i	−1.63253	+	0.942543i
$188$			11.8300i			0.862793i
$189$		0			0
$190$		−	0.940574i		−	0.0682364i
$191$	6.77316	+	11.7315i	0.490089	+	0.848859i	0.999935	−	0.0114067i	$-0.00363095\pi$
$191$	6.77316	+	11.7315i	0.490089	+	0.848859i	−0.509846	+	0.860266i	$0.670298\pi$
$192$		0			0
$193$	16.0702	+	9.27812i	1.15676	+	0.667853i	0.950524	−	0.310650i	$-0.100547\pi$
$193$	16.0702	+	9.27812i	1.15676	+	0.667853i	0.206232	+	0.978503i	$0.433880\pi$
$194$	−1.09405	−	1.89494i	−0.0785479	−	0.136049i
$195$		0			0
$196$	−13.2157	−	0.537898i	−0.943982	−	0.0384213i
$197$			2.66812i			0.190096i	0.995473	+	0.0950480i	$0.0303004\pi$
$197$			2.66812i			0.190096i	−0.995473	+	0.0950480i	$0.969700\pi$
$198$		0			0
$199$	10.0999	−	17.4936i	0.715965	−	1.24009i	−0.246621	−	0.969112i	$-0.579320\pi$
$199$	10.0999	−	17.4936i	0.715965	−	1.24009i	0.962586	−	0.270976i	$-0.0873465\pi$
$200$	3.25819	+	1.88111i	0.230389	+	0.133015i
$201$		0			0
$202$			0.0235418i			0.00165639i
$203$	−16.2063	−	9.80152i	−1.13746	−	0.687932i
$204$		0			0
$205$	−5.45984	−	9.45672i	−0.381332	−	0.660486i
$206$	−1.82443	−	1.05333i	−0.127114	−	0.0733891i
$207$		0			0
$208$	−12.0716	−	0.338246i	−0.837012	−	0.0234531i
$209$	11.6574			0.806361
$210$		0			0
$211$	13.1268			0.903683			0.451842	−	0.892098i	$-0.350767\pi$
$211$	13.1268			0.903683			0.451842	+	0.892098i	$0.350767\pi$
$212$	−2.62555	−	4.54758i	−0.180323	−	0.312329i
$213$		0			0
$214$	−2.23067	−	1.28788i	−0.152485	−	0.0880374i
$215$	5.31875	−	3.07078i	0.362736	−	0.209425i
$216$		0			0
$217$	7.79382	+	14.1566i	0.529079	+	0.961014i
$218$	−0.0111553			−0.000755530
$219$		0			0
$220$	8.13338	−	14.0874i	0.548352	−	0.949774i
$221$	7.42205	+	13.7297i	0.499261	+	0.923558i
$222$		0			0
$223$		−	2.22334i		−	0.148886i	−0.997225	−	0.0744428i	$-0.976282\pi$
$223$		−	2.22334i		−	0.148886i	0.997225	−	0.0744428i	$-0.0237178\pi$
$224$	4.71969	+	8.57281i	0.315348	+	0.572795i
$225$		0			0
$226$	−2.64814	+	1.52890i	−0.176152	+	0.101701i
$227$	23.4732	+	13.5523i	1.55797	+	0.899495i	0.997451	+	0.0713539i	$0.0227320\pi$
$227$	23.4732	+	13.5523i	1.55797	+	0.899495i	0.560520	+	0.828141i	$0.310601\pi$
$228$		0			0
$229$	16.4447	−	9.49437i	1.08670	−	0.627406i	0.154003	−	0.988070i	$-0.450783\pi$
$229$	16.4447	−	9.49437i	1.08670	−	0.627406i	0.932696	+	0.360665i	$0.117450\pi$
$230$	0.259542			0.0171137
$231$		0			0
$232$			9.25447i			0.607586i
$233$	−10.8700	−	18.8274i	−0.712118	−	1.23343i	−0.964060	−	0.265683i	$-0.914403\pi$
$233$	−10.8700	−	18.8274i	−0.712118	−	1.23343i	0.251942	−	0.967742i	$-0.418931\pi$
$234$		0			0
$235$	−4.52540	+	7.83822i	−0.295205	+	0.511309i
$236$	−1.39281	+	0.804137i	−0.0906639	+	0.0523449i
$237$		0			0
$238$	1.96995	−	3.25722i	0.127693	−	0.211134i
$239$		−	19.9695i		−	1.29172i	−0.763455	−	0.645861i	$-0.776499\pi$
$239$		−	19.9695i		−	1.29172i	0.763455	−	0.645861i	$-0.223501\pi$
$240$		0			0
$241$	2.79768	+	1.61524i	0.180214	+	0.104047i	0.587393	−	0.809302i	$-0.300154\pi$
$241$	2.79768	+	1.61524i	0.180214	+	0.104047i	−0.407179	+	0.913348i	$0.633487\pi$
$242$	−7.04183	−	4.06560i	−0.452666	−	0.261347i
$243$		0			0
$244$	12.8092			0.820025
$245$	−8.55060	−	5.41188i	−0.546278	−	0.345753i
$246$		0			0
$247$	0.197688	−	7.05522i	0.0125786	−	0.448913i
$248$	3.94816	−	6.83841i	0.250708	−	0.434239i
$249$		0			0
$250$	1.90038	+	3.29155i	0.120190	+	0.208176i
$251$	12.4916			0.788466			0.394233	−	0.919011i	$-0.371010\pi$
$251$	12.4916			0.788466			0.394233	+	0.919011i	$0.371010\pi$
$252$		0			0
$253$			3.21675i			0.202236i
$254$	4.14359	−	2.39230i	0.259992	−	0.150106i
$255$		0			0
$256$	−3.93783	+	6.82052i	−0.246114	+	0.426283i
$257$	−2.91379	−	5.04682i	−0.181757	−	0.314812i	0.760722	−	0.649078i	$-0.224845\pi$
$257$	−2.91379	−	5.04682i	−0.181757	−	0.314812i	−0.942479	+	0.334266i	$0.891512\pi$
$258$		0			0
$259$	−21.2378	−	0.432025i	−1.31966	−	0.0268447i
$260$	−8.38796	−	5.16132i	−0.520199	−	0.320091i
$261$		0			0
$262$	2.72540	+	1.57351i	0.168376	+	0.0972119i
$263$	8.75736	−	15.1682i	0.540002	−	0.935311i	−0.458901	−	0.888487i	$-0.651757\pi$
$263$	8.75736	−	15.1682i	0.540002	−	0.935311i	0.998903	−	0.0468234i	$-0.0149098\pi$
$264$		0			0
$265$		−	4.01746i		−	0.246791i
$266$	−1.50799	+	0.830213i	−0.0924609	+	0.0509036i
$267$		0			0
$268$	−1.61528	+	0.932581i	−0.0986688	+	0.0569665i
$269$	11.1644	−	19.3372i	0.680703	−	1.17901i	−0.294064	−	0.955786i	$-0.595008\pi$
$269$	11.1644	−	19.3372i	0.680703	−	1.17901i	0.974767	−	0.223226i	$-0.0716588\pi$
$270$		0			0
$271$	22.8366	−	13.1847i	1.38723	−	0.800916i	0.394225	−	0.919014i	$-0.371013\pi$
$271$	22.8366	−	13.1847i	1.38723	−	0.800916i	0.993002	+	0.118098i	$0.0376796\pi$
$272$	14.4984			0.879097
$273$		0			0
$274$	5.51951			0.333446
$275$	−15.0087	+	8.66529i	−0.905060	+	0.522536i
$276$		0			0
$277$	−4.68809	+	8.12001i	−0.281680	+	0.487884i	−0.971799	−	0.235812i	$-0.924225\pi$
$277$	−4.68809	+	8.12001i	−0.281680	+	0.487884i	0.690119	+	0.723696i	$0.257558\pi$
$278$	−5.31875	+	3.07078i	−0.318997	+	0.184173i
$279$		0			0
$280$	−0.100563	+	4.94356i	−0.00600978	+	0.295434i
$281$		−	17.7754i		−	1.06039i	−0.847876	−	0.530195i	$-0.822119\pi$
$281$		−	17.7754i		−	1.06039i	0.847876	−	0.530195i	$-0.177881\pi$
$282$		0			0
$283$	−4.80331	+	8.31958i	−0.285527	+	0.494548i	−0.972737	−	0.231911i	$-0.925502\pi$
$283$	−4.80331	+	8.31958i	−0.285527	+	0.494548i	0.687210	+	0.726459i	$0.258835\pi$
$284$	6.15643	+	3.55442i	0.365317	+	0.210916i
$285$		0			0
$286$	−3.74003	+	6.07814i	−0.221153	+	0.359408i
$287$	−10.3424	+	17.1007i	−0.610494	+	1.00942i
$288$		0			0
$289$	−0.868875	−	1.50494i	−0.0511103	−	0.0885256i
$290$	−1.71981	+	2.97879i	−0.100990	+	0.174921i
$291$		0			0
$292$	14.9486	−	8.63060i	0.874803	−	0.505067i
$293$		−	11.6338i		−	0.679654i	−0.940488	−	0.339827i	$-0.889631\pi$
$293$		−	11.6338i		−	0.679654i	0.940488	−	0.339827i	$-0.110369\pi$
$294$		0			0
$295$	−1.23044			−0.0716392
$296$	5.18976	+	8.98892i	0.301648	+	0.522470i
$297$		0			0
$298$	−0.511991	+	0.886795i	−0.0296588	+	0.0513706i
$299$	1.94682	+	0.0545500i	0.112588	+	0.00315471i
$300$		0			0
$301$	−9.61796	−	5.81690i	−0.554370	−	0.335281i
$302$	−0.847174			−0.0487494
$303$		0			0
$304$	−5.67809	−	3.27825i	−0.325661	−	0.188020i
$305$	8.48700	+	4.89997i	0.485964	+	0.280572i
$306$		0			0
$307$		−	13.8280i		−	0.789204i	−0.918852	−	0.394602i	$-0.870882\pi$
$307$		−	13.8280i		−	0.789204i	0.918852	−	0.394602i	$-0.129118\pi$
$308$	−29.7650	−	0.605485i	−1.69602	−	0.0345007i
$309$		0			0
$310$	2.54163	−	1.46741i	0.144355	−	0.0833435i
$311$	−15.3572	+	26.5994i	−0.870827	+	1.50832i	−0.00968369	+	0.999953i	$0.503082\pi$
$311$	−15.3572	+	26.5994i	−0.870827	+	1.50832i	−0.861143	+	0.508363i	$0.830251\pi$
$312$		0			0
$313$	−5.54334	−	9.60135i	−0.313328	−	0.542701i	0.665752	−	0.746173i	$-0.268111\pi$
$313$	−5.54334	−	9.60135i	−0.313328	−	0.542701i	−0.979081	+	0.203472i	$0.934777\pi$
$314$			3.12733i			0.176486i
$315$		0			0
$316$	−0.247764			−0.0139378
$317$	20.6836	−	11.9417i	1.16171	−	0.670712i	0.209994	−	0.977703i	$-0.432656\pi$
$317$	20.6836	−	11.9417i	1.16171	−	0.670712i	0.951712	+	0.306991i	$0.0993222\pi$
$318$		0			0
$319$	−36.9190	−	21.3152i	−2.06707	−	1.19342i
$320$	−6.84731	+	3.95329i	−0.382776	+	0.220996i
$321$		0			0
$322$	−0.229089	−	0.416116i	−0.0127666	−	0.0231892i
$323$			8.47360i			0.471484i
$324$		0			0
$325$	4.98982	+	9.23041i	0.276785	+	0.512011i
$326$	0.115526	−	0.200098i	0.00639842	−	0.0110824i
$327$		0			0
$328$	9.76519			0.539192
$329$	16.5612	+	0.336891i	0.913048	+	0.0185734i
$330$		0			0
$331$	−15.8690	+	9.16200i	−0.872241	+	0.503589i	−0.868092	−	0.496403i	$-0.834654\pi$
$331$	−15.8690	+	9.16200i	−0.872241	+	0.503589i	−0.00414903	+	0.999991i	$0.501321\pi$
$332$	4.36606	+	2.52075i	0.239619	+	0.138344i
$333$		0			0
$334$	−2.32396	−	4.02522i	−0.127162	−	0.220250i
$335$	−1.42698			−0.0779643
$336$		0			0
$337$	7.21762			0.393169			0.196584	−	0.980487i	$-0.437015\pi$
$337$	7.21762			0.393169			0.196584	+	0.980487i	$0.437015\pi$
$338$	3.61514	+	2.36659i	0.196638	+	0.128725i
$339$		0			0
$340$	10.2399	+	5.91203i	0.555338	+	0.320625i
$341$	18.1870	+	31.5009i	0.984884	+	1.70587i
$342$		0			0
$343$	−1.12937	+	18.4858i	−0.0609804	+	0.998139i
$344$			5.49224i			0.296122i
$345$		0			0
$346$	−1.56487	−	0.903476i	−0.0841277	−	0.0485712i
$347$	−10.5391	+	18.2543i	−0.565770	+	0.979942i	0.431208	+	0.902253i	$0.358088\pi$
$347$	−10.5391	+	18.2543i	−0.565770	+	0.979942i	−0.996978	+	0.0776892i	$0.975246\pi$
$348$		0			0
$349$			30.7629i			1.64670i	0.567534	+	0.823350i	$0.307898\pi$
$349$			30.7629i			1.64670i	−0.567534	+	0.823350i	$0.692102\pi$
$350$	1.32439	−	2.18982i	0.0707917	−	0.117051i
$351$		0			0
$352$	11.0135	+	19.0760i	0.587022	+	1.01675i
$353$	5.30157	+	3.06086i	0.282174	+	0.162913i	0.634407	−	0.772999i	$-0.281244\pi$
$353$	5.30157	+	3.06086i	0.282174	+	0.162913i	−0.352233	+	0.935912i	$0.614578\pi$
$354$		0			0
$355$	2.71938	+	4.71010i	0.144330	+	0.249986i
$356$			18.3613i			0.973145i
$357$		0			0
$358$		−	1.78095i		−	0.0941259i
$359$	−16.8257	+	9.71433i	−0.888028	+	0.512703i	−0.873297	−	0.487189i	$-0.838022\pi$
$359$	−16.8257	+	9.71433i	−0.888028	+	0.512703i	−0.0147308	+	0.999891i	$0.504689\pi$
$360$		0			0
$361$	−7.58403	+	13.1359i	−0.399160	+	0.691365i
$362$	2.17040	−	1.25308i	0.114074	−	0.0658605i
$363$		0			0
$364$	−0.871204	+	18.0039i	−0.0456635	+	0.943659i
$365$	13.2060			0.691235
$366$		0			0
$367$	2.70234	−	4.68058i	0.141061	−	0.244324i	−0.786836	−	0.617163i	$-0.788282\pi$
$367$	2.70234	−	4.68058i	0.141061	−	0.244324i	0.927896	+	0.372838i	$0.121615\pi$
$368$	0.904601	−	1.56681i	0.0471556	−	0.0816758i
$369$		0			0
$370$			3.85776i			0.200555i
$371$	−6.44106	+	3.54608i	−0.334403	+	0.184103i
$372$		0			0
$373$	−8.12533	−	14.0735i	−0.420714	−	0.728698i	0.575296	−	0.817946i	$-0.304887\pi$
$373$	−8.12533	−	14.0735i	−0.420714	−	0.728698i	−0.996009	+	0.0892478i	$0.971554\pi$
$374$	4.28401	−	7.42013i	0.221521	−	0.383686i
$375$		0			0
$376$	−4.04695	−	7.00952i	−0.208706	−	0.361489i
$377$	−13.5263	+	21.9824i	−0.696640	+	1.13215i
$378$		0			0
$379$			25.1730i			1.29305i	0.762893	+	0.646525i	$0.223778\pi$
$379$			25.1730i			1.29305i	−0.762893	+	0.646525i	$0.776222\pi$
$380$	−2.67354	−	4.63071i	−0.137150	−	0.237550i
$381$		0			0
$382$	−3.89925	−	2.25123i	−0.199503	−	0.115183i
$383$	−3.30335	+	1.90719i	−0.168793	+	0.0974529i	−0.582017	−	0.813177i	$-0.697736\pi$
$383$	−3.30335	+	1.90719i	−0.168793	+	0.0974529i	0.413223	+	0.910630i	$0.364403\pi$
$384$		0			0
$385$	−19.4898	−	11.7873i	−0.993291	−	0.600738i
$386$	−6.16764			−0.313924
$387$		0			0
$388$	−10.7726	−	6.21956i	−0.546895	−	0.315750i
$389$	1.43548	−	2.48632i	0.0727817	−	0.126062i	−0.827338	−	0.561705i	$-0.810146\pi$
$389$	1.43548	−	2.48632i	0.0727817	−	0.126062i	0.900119	+	0.435643i	$0.143479\pi$
$390$		0			0
$391$	−2.33821			−0.118248
$392$	8.01461	−	4.20228i	0.404799	−	0.212247i
$393$		0			0
$394$	−0.443409	−	0.768007i	−0.0223386	−	0.0386917i
$395$	−0.164161	−	0.0947786i	−0.00825986	−	0.00476883i
$396$		0			0
$397$	16.5570	−	9.55919i	0.830972	−	0.479762i	−0.0232131	−	0.999731i	$-0.507390\pi$
$397$	16.5570	−	9.55919i	0.830972	−	0.479762i	0.854185	+	0.519968i	$0.174056\pi$
$398$			6.71394i			0.336539i
$399$		0			0
$400$	9.74725			0.487362
$401$	2.59655	−	1.49912i	0.129666	−	0.0748625i	−0.433764	−	0.901026i	$-0.642815\pi$
$401$	2.59655	−	1.49912i	0.129666	−	0.0748625i	0.563430	+	0.826164i	$0.309482\pi$
$402$		0			0
$403$	19.3732	−	10.4728i	0.965045	−	0.521689i
$404$	0.0669165	+	0.115903i	0.00332922	+	0.00576638i
$405$		0			0
$406$	6.29382	+	0.128030i	0.312357	+	0.00635403i
$407$	−47.8129			−2.37000
$408$		0			0
$409$	29.5146	+	17.0403i	1.45940	+	0.842587i	0.998982	−	0.0451127i	$-0.0143647\pi$
$409$	29.5146	+	17.0403i	1.45940	+	0.842587i	0.460422	+	0.887700i	$0.347698\pi$
$410$	3.14318	+	1.81472i	0.155231	+	0.0896224i
$411$		0			0
$412$	−11.9762			−0.590026
$413$	1.08607	+	1.97273i	0.0534421	+	0.0970717i
$414$		0			0
$415$	1.92855	+	3.34034i	0.0946687	+	0.163971i
$416$	11.7318	−	6.34202i	0.575198	−	0.310943i
$417$		0			0
$418$	−3.35554	+	1.93732i	−0.164125	+	0.0947574i
$419$	−34.7759			−1.69891			−0.849457	−	0.527657i	$-0.823071\pi$
$419$	−34.7759			−1.69891			−0.849457	+	0.527657i	$0.823071\pi$
$420$		0			0
$421$		−	24.1400i		−	1.17651i	−0.808674	−	0.588257i	$-0.799814\pi$
$421$		−	24.1400i		−	1.17651i	0.808674	−	0.588257i	$-0.200186\pi$
$422$	−3.77848	+	2.18151i	−0.183933	+	0.106194i
$423$		0			0
$424$	3.11138	+	1.79636i	0.151102	+	0.0872388i
$425$	−6.29866	−	10.9096i	−0.305530	−	0.529193i
$426$		0			0
$427$	0.364776	−	17.9320i	0.0176528	−	0.867789i
$428$	−14.6429			−0.707793
$429$		0			0
$430$	−1.02065	+	1.76782i	−0.0492202	+	0.0852519i
$431$	−4.12641	−	2.38238i	−0.198762	−	0.114755i	0.397316	−	0.917682i	$-0.369942\pi$
$431$	−4.12641	−	2.38238i	−0.198762	−	0.114755i	−0.596078	+	0.802927i	$0.703275\pi$
$432$		0			0
$433$	−22.0231			−1.05836			−0.529181	−	0.848509i	$-0.677501\pi$
$433$	−22.0231			−1.05836			−0.529181	+	0.848509i	$0.677501\pi$
$434$	−4.59607	−	2.77968i	−0.220618	−	0.133429i
$435$		0			0
$436$	−0.0549206	+	0.0317084i	−0.00263022	+	0.00151856i
$437$	0.915724	+	0.528693i	0.0438050	+	0.0252908i
$438$		0			0
$439$	1.71620	+	2.97254i	0.0819097	+	0.141872i	0.904070	−	0.427384i	$-0.140565\pi$
$439$	1.71620	+	2.97254i	0.0819097	+	0.141872i	−0.822161	+	0.569256i	$0.807231\pi$
$440$			11.1294i			0.530576i
$441$		0			0
$442$	−4.41811	−	2.71857i	−0.210148	−	0.129309i
$443$	−4.35297	−	7.53957i	−0.206816	−	0.358216i	0.743894	−	0.668298i	$-0.232977\pi$
$443$	−4.35297	−	7.53957i	−0.206816	−	0.358216i	−0.950710	+	0.310082i	$0.899643\pi$
$444$		0			0
$445$	−7.02383	+	12.1656i	−0.332962	+	0.576706i
$446$	0.369491	+	0.639977i	0.0174959	+	0.0303038i
$447$		0			0
$448$	12.3821	+	7.48862i	0.584998	+	0.353804i
$449$		−	17.6120i		−	0.831159i	−0.909557	−	0.415580i	$-0.863579\pi$
$449$		−	17.6120i		−	0.831159i	0.909557	−	0.415580i	$-0.136421\pi$
$450$		0			0
$451$	−22.4915	+	38.9564i	−1.05908	+	1.83439i
$452$	−8.69170	+	15.0545i	−0.408823	+	0.708102i
$453$		0			0
$454$	−9.00887			−0.422807
$455$	−7.46435	+	11.5956i	−0.349934	+	0.543609i
$456$		0			0
$457$	7.85717	−	4.53634i	0.367543	−	0.212201i	−0.304842	−	0.952403i	$-0.598604\pi$
$457$	7.85717	−	4.53634i	0.367543	−	0.212201i	0.672384	+	0.740202i	$0.265270\pi$
$458$	−3.15570	+	5.46583i	−0.147456	+	0.255401i
$459$		0			0
$460$	1.27780	−	0.737738i	0.0595777	−	0.0343972i
$461$			6.58319i			0.306610i	0.988179	+	0.153305i	$0.0489917\pi$
$461$			6.58319i			0.306610i	−0.988179	+	0.153305i	$0.951008\pi$
$462$		0			0
$463$			3.47344i			0.161424i	0.996737	+	0.0807121i	$0.0257194\pi$
$463$			3.47344i			0.161424i	−0.996737	+	0.0807121i	$0.974281\pi$
$464$	11.9883	+	20.7644i	0.556544	+	0.963962i
$465$		0			0
$466$	6.25777	+	3.61293i	0.289886	+	0.167366i
$467$	−14.8927	−	25.7949i	−0.689152	−	1.19365i	−0.972112	−	0.234515i	$-0.924650\pi$
$467$	−14.8927	−	25.7949i	−0.689152	−	1.19365i	0.282960	−	0.959132i	$-0.408684\pi$
$468$		0			0
$469$	1.25955	+	2.28783i	0.0581606	+	0.105642i
$470$		−	3.00826i		−	0.138761i
$471$		0			0
$472$	0.550177	−	0.952935i	0.0253240	−	0.0438624i
$473$	−21.9103	−	12.6499i	−1.00744	−	0.581643i
$474$		0			0
$475$			5.69677i			0.261386i
$476$	0.440118	−	21.6357i	0.0201728	−	0.991671i
$477$		0			0
$478$	3.31869	+	5.74814i	0.151793	+	0.262914i
$479$	30.4715	+	17.5927i	1.39228	+	0.803833i	0.993567	−	0.113243i	$-0.0361240\pi$
$479$	30.4715	+	17.5927i	1.39228	+	0.803833i	0.398712	+	0.917076i	$0.369457\pi$
$480$		0			0
$481$	−0.810814	+	28.9369i	−0.0369700	+	1.31941i
$482$	−1.07373			−0.0489072
$483$		0			0
$484$	−46.2252			−2.10115
$485$	−4.75840	−	8.24179i	−0.216068	−	0.374241i
$486$		0			0
$487$	−1.56018	−	0.900769i	−0.0706984	−	0.0408178i	0.464234	−	0.885713i	$-0.346330\pi$
$487$	−1.56018	−	0.900769i	−0.0706984	−	0.0408178i	−0.534933	+	0.844895i	$0.679663\pi$
$488$	−7.58971	+	4.38192i	−0.343570	+	0.198360i
$489$		0			0
$490$	3.36064	+	0.136782i	0.151818	+	0.00617920i
$491$	−8.19322			−0.369755			−0.184877	−	0.982762i	$-0.559189\pi$
$491$	−8.19322			−0.369755			−0.184877	+	0.982762i	$0.559189\pi$
$492$		0			0
$493$	15.4937	−	26.8358i	0.697800	−	1.20863i
$494$	1.11559	+	2.06367i	0.0501926	+	0.0928487i
$495$		0			0
$496$		−	20.4579i		−	0.918587i
$497$	5.15125	−	8.51734i	0.231065	−	0.382055i
$498$		0			0
$499$	31.6242	−	18.2582i	1.41569	−	0.817350i	0.419775	−	0.907628i	$-0.362109\pi$
$499$	31.6242	−	18.2582i	1.41569	−	0.817350i	0.995917	+	0.0902781i	$0.0287756\pi$
$500$	18.7122	+	10.8035i	0.836834	+	0.483147i
$501$		0			0
$502$	−3.59566	+	2.07596i	−0.160482	+	0.0926545i
$503$	3.02972			0.135089			0.0675443	−	0.997716i	$-0.478484\pi$
$503$	3.02972			0.135089			0.0675443	+	0.997716i	$0.478484\pi$
$504$		0			0
$505$			0.102392i			0.00455637i
$506$	−0.534585	−	0.925928i	−0.0237652	−	0.0411625i
$507$		0			0
$508$	13.6000	−	23.5559i	0.603404	−	1.04513i
$509$	25.4133	−	14.6724i	1.12642	−	0.650341i	0.183391	−	0.983040i	$-0.441293\pi$
$509$	25.4133	−	14.6724i	1.12642	−	0.650341i	0.943033	+	0.332699i	$0.107959\pi$
$510$		0			0
$511$	−11.6565	−	21.1728i	−0.515654	−	0.936630i
$512$		−	21.0487i		−	0.930229i
$513$		0			0
$514$	1.67744	+	0.968471i	0.0739887	+	0.0427174i
$515$	−7.93509	−	4.58133i	−0.349662	−	0.201877i
$516$		0			0
$517$	37.2843			1.63976
$518$	6.18502	−	3.40511i	0.271754	−	0.149612i
$519$		0			0
$520$	6.73568	+	0.188734i	0.295379	+	0.00827654i
$521$	−14.8419	+	25.7069i	−0.650236	+	1.12624i	0.332830	+	0.942987i	$0.391997\pi$
$521$	−14.8419	+	25.7069i	−0.650236	+	1.12624i	−0.983066	+	0.183254i	$0.941337\pi$
$522$		0			0
$523$	−10.2864	−	17.8165i	−0.449791	−	0.779062i	0.548581	−	0.836098i	$-0.315168\pi$
$523$	−10.2864	−	17.8165i	−0.449791	−	0.779062i	−0.998372	+	0.0570361i	$0.981835\pi$
$524$	17.8906			0.781553
$525$		0			0
$526$			5.82146i			0.253828i
$527$	−22.8975	+	13.2199i	−0.997431	+	0.575867i
$528$		0			0
$529$	11.3541	−	19.6659i	0.493657	−	0.855039i
$530$	0.667652	+	1.15641i	0.0290010	+	0.0502311i
$531$		0			0
$532$	−5.06442	+	8.37377i	−0.219571	+	0.363049i
$533$	23.1955	+	14.2728i	1.00471	+	0.618222i
$534$		0			0
$535$	−9.70198	−	5.60144i	−0.419453	−	0.242171i
$536$	0.638057	−	1.10515i	0.0275599	−	0.0477351i
$537$		0			0
$538$			7.42151i			0.319964i
$539$	−1.69527	+	41.6516i	−0.0730206	+	1.79406i
$540$		0			0
$541$	−29.5027	+	17.0334i	−1.26842	+	0.732324i	−0.974689	−	0.223564i	$-0.928231\pi$
$541$	−29.5027	+	17.0334i	−1.26842	+	0.732324i	−0.293732	+	0.955888i	$0.594897\pi$
$542$	−4.38228	+	7.59034i	−0.188235	+	0.326033i
$543$		0			0
$544$	−13.8660	+	8.00555i	−0.594500	+	0.343235i
$545$	−0.0485183			−0.00207830
$546$		0			0
$547$	−0.850931			−0.0363832			−0.0181916	−	0.999835i	$-0.505791\pi$
$547$	−0.850931			−0.0363832			−0.0181916	+	0.999835i	$0.505791\pi$
$548$	27.1741	−	15.6890i	1.16082	−	0.670200i
$549$		0			0
$550$	2.88013	−	4.98853i	0.122809	−	0.212712i
$551$	−12.1357	+	7.00657i	−0.516999	+	0.298490i
$552$		0			0
$553$	−0.00705575	+	0.346853i	−0.000300041	+	0.0147497i
$554$		−	3.11641i		−	0.132404i
$555$		0			0
$556$	−17.4571	+	30.2366i	−0.740347	+	1.28232i
$557$	15.3530	+	8.86404i	0.650526	+	0.375581i	0.788658	−	0.614833i	$-0.210776\pi$
$557$	15.3530	+	8.86404i	0.650526	+	0.375581i	−0.138132	+	0.990414i	$0.544110\pi$
$558$		0			0
$559$	−8.02744	+	13.0459i	−0.339525	+	0.551781i
$560$	6.17829	+	11.2222i	0.261080	+	0.474224i
$561$		0			0
$562$	2.95405	+	5.11656i	0.124609	+	0.215829i
$563$	12.0903	−	20.9410i	0.509545	−	0.882558i	−0.490394	−	0.871501i	$-0.663147\pi$
$563$	12.0903	−	20.9410i	0.509545	−	0.882558i	0.999939	−	0.0110571i	$-0.00351966\pi$
$564$		0			0
$565$	−11.5177	+	6.64976i	−0.484555	+	0.279758i
$566$		−	3.19301i		−	0.134212i
$567$		0			0
$568$	−4.86375			−0.204078
$569$	21.3874	+	37.0441i	0.896608	+	1.55297i	0.831802	+	0.555073i	$0.187310\pi$
$569$	21.3874	+	37.0441i	0.896608	+	1.55297i	0.0648066	+	0.997898i	$0.479357\pi$
$570$		0			0
$571$	3.68140	−	6.37637i	0.154062	−	0.266843i	−0.778655	−	0.627452i	$-0.784098\pi$
$571$	3.68140	−	6.37637i	0.154062	−	0.266843i	0.932717	+	0.360609i	$0.117431\pi$
$572$	−1.13636	+	40.5553i	−0.0475137	+	1.69570i
$573$		0			0
$574$	0.135096	−	6.64115i	0.00563878	−	0.277196i
$575$	−1.57197			−0.0655557
$576$		0			0
$577$	7.09615	+	4.09696i	0.295417	+	0.170559i	0.640382	−	0.768057i	$-0.278776\pi$
$577$	7.09615	+	4.09696i	0.295417	+	0.170559i	−0.344965	+	0.938615i	$0.612109\pi$
$578$	0.500204	+	0.288793i	0.0208057	+	0.0120122i
$579$		0			0
$580$			19.5539i			0.811932i
$581$	3.65320	−	6.04039i	0.151560	−	0.250598i
$582$		0			0
$583$	−14.3325	+	8.27485i	−0.593590	+	0.342709i
$584$	−5.90491	+	10.2276i	−0.244347	+	0.423221i
$585$		0			0
$586$	1.93339	+	3.34874i	0.0798678	+	0.138335i
$587$		−	39.1141i		−	1.61441i	−0.590271	−	0.807205i	$-0.700979\pi$
$587$		−	39.1141i		−	1.61441i	0.590271	−	0.807205i	$-0.299021\pi$
$588$		0			0
$589$	11.9566			0.492664
$590$	0.354178	−	0.204485i	0.0145813	−	0.00841849i
$591$		0			0
$592$	23.2886	+	13.4457i	0.957158	+	0.552615i
$593$	−1.05082	+	0.606691i	−0.0431520	+	0.0249138i	−0.521421	−	0.853300i	$-0.674598\pi$
$593$	−1.05082	+	0.606691i	−0.0431520	+	0.0249138i	0.478269	+	0.878213i	$0.341264\pi$
$594$		0			0
$595$	8.56803	−	14.1668i	0.351255	−	0.580783i
$596$			5.82125i			0.238448i
$597$		0			0
$598$	−0.569449	+	0.307836i	−0.0232865	+	0.0125883i
$599$	16.3319	−	28.2877i	0.667303	−	1.15580i	−0.311352	−	0.950295i	$-0.600782\pi$
$599$	16.3319	−	28.2877i	0.667303	−	1.15580i	0.978655	−	0.205508i	$-0.0658847\pi$
$600$		0			0
$601$	2.50114			0.102024			0.0510118	−	0.998698i	$-0.483755\pi$
$601$	2.50114			0.102024			0.0510118	+	0.998698i	$0.483755\pi$
$602$	3.73519	+	0.0759819i	0.152235	+	0.00309679i
$603$		0			0
$604$	−4.17088	+	2.40806i	−0.169711	+	0.0979825i
$605$	−30.6275	−	17.6828i	−1.24518	−	0.718907i
$606$		0			0
$607$	−6.32282	−	10.9515i	−0.256635	−	0.444506i	0.708703	−	0.705507i	$-0.249281\pi$
$607$	−6.32282	−	10.9515i	−0.256635	−	0.444506i	−0.965338	+	0.261001i	$0.915947\pi$
$608$	7.24055			0.293643
$609$		0			0
$610$	−3.25726			−0.131883
$611$	0.632270	−	22.5649i	0.0255789	−	0.912879i
$612$		0			0
$613$	−17.3448	−	10.0140i	−0.700548	−	0.404462i	0.107003	−	0.994259i	$-0.465874\pi$
$613$	−17.3448	−	10.0140i	−0.700548	−	0.404462i	−0.807552	+	0.589797i	$0.799208\pi$
$614$	2.29804	+	3.98032i	0.0927413	+	0.160633i
$615$		0			0
$616$	17.8435	−	9.82359i	0.718934	−	0.395804i
$617$			45.2926i			1.82341i	0.410846	+	0.911705i	$0.365233\pi$
$617$			45.2926i			1.82341i	−0.410846	+	0.911705i	$0.634767\pi$
$618$		0			0
$619$	−3.83922	−	2.21658i	−0.154311	−	0.0890917i	0.420856	−	0.907127i	$-0.361730\pi$
$619$	−3.83922	−	2.21658i	−0.154311	−	0.0890917i	−0.575167	+	0.818036i	$0.695063\pi$
$620$	8.34212	−	14.4490i	0.335028	−	0.580285i
$621$		0			0
$622$		−	10.2087i		−	0.409332i
$623$	25.7045	+	0.522886i	1.02983	+	0.0209490i
$624$		0			0
$625$	0.989985	+	1.71471i	0.0395994	+	0.0685882i
$626$	3.19125	+	1.84247i	0.127548	+	0.0736400i
$627$		0			0
$628$	8.88931	+	15.3967i	0.354722	+	0.614397i
$629$		−	34.7544i		−	1.38575i
$630$		0			0
$631$		−	19.7358i		−	0.785672i	−0.919609	−	0.392836i	$-0.871494\pi$
$631$		−	19.7358i		−	0.785672i	0.919609	−	0.392836i	$-0.128506\pi$
$632$	0.146805	−	0.0847581i	0.00583961	−	0.00337150i
$633$		0			0
$634$	−3.96912	+	6.87472i	−0.157634	+	0.273030i
$635$	18.0220	−	10.4050i	0.715180	−	0.412909i
$636$		0			0
$637$	25.1793	+	1.73233i	0.997642	+	0.0686375i
$638$	14.1693			0.560968
$639$		0			0
$640$	6.66106	−	11.5373i	0.263302	−	0.456052i
$641$	−19.8213	+	34.3314i	−0.782893	+	1.35601i	0.147357	+	0.989083i	$0.452923\pi$
$641$	−19.8213	+	34.3314i	−0.782893	+	1.35601i	−0.930250	+	0.366926i	$0.880410\pi$
$642$		0			0
$643$		−	20.8300i		−	0.821453i	−0.911759	−	0.410727i	$-0.865275\pi$
$643$		−	20.8300i		−	0.821453i	0.911759	−	0.410727i	$-0.134725\pi$
$644$	−2.31066	−	1.39748i	−0.0910529	−	0.0550684i
$645$		0			0
$646$	−1.40821	−	2.43909i	−0.0554052	−	0.0959646i
$647$	7.87206	−	13.6348i	0.309482	−	0.536039i	−0.668767	−	0.743472i	$-0.733178\pi$
$647$	7.87206	−	13.6348i	0.309482	−	0.536039i	0.978249	+	0.207433i	$0.0665109\pi$
$648$		0			0
$649$	2.53437	+	4.38966i	0.0994828	+	0.172309i
$650$	−2.97028	−	1.82769i	−0.116504	−	0.0716877i
$651$		0			0
$652$		−	1.31352i		−	0.0514413i
$653$	−13.5132	−	23.4055i	−0.528812	−	0.915930i	−0.999436	−	0.0335954i	$-0.989304\pi$
$653$	−13.5132	−	23.4055i	−0.528812	−	0.915930i	0.470623	−	0.882334i	$-0.344029\pi$
$654$		0			0
$655$	11.8538	+	6.84378i	0.463165	+	0.267409i
$656$	21.9103	−	12.6499i	0.855453	−	0.493896i
$657$		0			0
$658$	−4.82305	+	2.65529i	−0.188022	+	0.103514i
$659$	6.79491			0.264692			0.132346	−	0.991204i	$-0.457749\pi$
$659$	6.79491			0.264692			0.132346	+	0.991204i	$0.457749\pi$
$660$		0			0
$661$	−6.23994	−	3.60263i	−0.242705	−	0.140126i	0.373714	−	0.927544i	$-0.378084\pi$
$661$	−6.23994	−	3.60263i	−0.242705	−	0.140126i	−0.616420	+	0.787418i	$0.711417\pi$
$662$	3.04522	−	5.27448i	0.118356	−	0.204998i
$663$		0			0
$664$	−3.44930			−0.133859
$665$	−6.55880	+	3.61090i	−0.254339	+	0.140025i
$666$		0			0
$667$	−1.93339	−	3.34874i	−0.0748613	−	0.129664i
$668$	−22.8831	−	13.2115i	−0.885372	−	0.511170i
$669$		0			0
$670$	0.410750	−	0.237147i	0.0158687	−	0.00916178i
$671$		−	40.3703i		−	1.55848i
$672$		0			0
$673$	−8.32130			−0.320763			−0.160381	−	0.987055i	$-0.551272\pi$
$673$	−8.32130			−0.320763			−0.160381	+	0.987055i	$0.551272\pi$
$674$	−2.07756	+	1.19948i	−0.0800246	+	0.0462022i
$675$		0			0
$676$	24.5253	+	1.37548i	0.943281	+	0.0529031i
$677$	−14.9978	−	25.9770i	−0.576413	−	0.998376i	−0.995887	−	0.0906086i	$-0.971119\pi$
$677$	−14.9978	−	25.9770i	−0.576413	−	0.998376i	0.419474	−	0.907767i	$-0.362215\pi$
$678$		0			0
$679$	−9.01372	+	14.9037i	−0.345915	+	0.571953i
$680$	−8.08982			−0.310231
$681$		0			0
$682$	−10.4701	−	6.04493i	−0.400922	−	0.231472i
$683$	−31.2496	−	18.0420i	−1.19573	−	0.690356i	−0.236132	−	0.971721i	$-0.575880\pi$
$683$	−31.2496	−	18.0420i	−1.19573	−	0.690356i	−0.959601	+	0.281365i	$0.909213\pi$
$684$		0			0
$685$	24.0064			0.917236
$686$	−2.74703	−	5.50874i	−0.104882	−	0.210325i
$687$		0			0
$688$	7.11470	+	12.3230i	0.271245	+	0.469811i
$689$	4.76499	+	8.81451i	0.181532	+	0.335806i
$690$		0			0
$691$	22.3155	−	12.8838i	0.848920	−	0.490124i	−0.0113665	−	0.999935i	$-0.503618\pi$
$691$	22.3155	−	12.8838i	0.848920	−	0.490124i	0.860286	+	0.509811i	$0.170285\pi$
$692$	−10.2724			−0.390497
$693$		0			0
$694$		−	7.00589i		−	0.265940i
$695$	−23.1332	+	13.3559i	−0.877491	+	0.506620i
$696$		0			0
$697$	−28.3168	−	16.3487i	−1.07258	−	0.619252i
$698$	−5.11242	−	8.85496i	−0.193508	−	0.335165i
$699$		0			0
$700$	0.295890	−	14.5456i	0.0111836	−	0.549772i
$701$	41.7872			1.57828			0.789141	−	0.614213i	$-0.210526\pi$
$701$	41.7872			1.57828			0.789141	+	0.614213i	$0.210526\pi$
$702$		0			0
$703$	−7.85834	+	13.6110i	−0.296383	+	0.513350i
$704$	28.2071	+	16.2854i	1.06310	+	0.613778i
$705$		0			0
$706$	−2.03471			−0.0765774
$707$	0.164161	−	0.0903778i	0.00617393	−	0.00339901i
$708$		0			0
$709$	0.297781	−	0.171924i	0.0111834	−	0.00645673i	−0.494398	−	0.869236i	$-0.664611\pi$
$709$	0.297781	−	0.171924i	0.0111834	−	0.00645673i	0.505581	+	0.862779i	$0.331278\pi$
$710$	−1.56552	−	0.903855i	−0.0587530	−	0.0339211i
$711$		0			0
$712$	−6.28124	−	10.8794i	−0.235399	−	0.407724i
$713$			3.29931i			0.123560i
$714$		0			0
$715$	−16.2668	+	26.4361i	−0.608342	+	0.988652i
$716$	−5.06227	−	8.76810i	−0.189186	−	0.327679i
$717$		0			0
$718$	3.22881	−	5.59246i	0.120498	−	0.208709i
$719$	−4.39005	−	7.60379i	−0.163721	−	0.283574i	0.772479	−	0.635040i	$-0.219016\pi$
$719$	−4.39005	−	7.60379i	−0.163721	−	0.283574i	−0.936200	+	0.351467i	$0.885683\pi$
$720$		0			0
$721$	−0.341055	+	16.7659i	−0.0127015	+	0.624393i
$722$		−	5.04149i		−	0.187625i
$723$		0			0
$724$	7.12367	−	12.3386i	0.264749	−	0.458559i
$725$	10.4164	−	18.0416i	0.386854	−	0.670050i
$726$		0			0
$727$	17.3658			0.644064			0.322032	−	0.946729i	$-0.395634\pi$
$727$	17.3658			0.644064			0.322032	+	0.946729i	$0.395634\pi$
$728$	−5.64277	−	10.9657i	−0.209135	−	0.406415i
$729$		0			0
$730$	−3.80130	+	2.19468i	−0.140692	+	0.0812288i
$731$	9.19502	−	15.9262i	0.340090	−	0.589053i
$732$		0			0
$733$	7.84528	−	4.52947i	0.289772	−	0.167300i	−0.348067	−	0.937470i	$-0.613162\pi$
$733$	7.84528	−	4.52947i	0.289772	−	0.167300i	0.637839	+	0.770170i	$0.279828\pi$
$734$			1.79638i			0.0663056i
$735$		0			0
$736$			1.99796i			0.0736458i
$737$	2.93919	+	5.09082i	0.108266	+	0.187523i
$738$		0			0
$739$	6.13010	+	3.53921i	0.225499	+	0.130192i	0.608494	−	0.793558i	$-0.291774\pi$
$739$	6.13010	+	3.53921i	0.225499	+	0.130192i	−0.382995	+	0.923751i	$0.625107\pi$
$740$	10.9655	+	18.9928i	0.403100	+	0.698190i
$741$		0			0
$742$	1.26472	−	2.09115i	0.0464292	−	0.0767685i
$743$		−	14.6779i		−	0.538479i	−0.963073	−	0.269240i	$-0.913228\pi$
$743$		−	14.6779i		−	0.538479i	0.963073	−	0.269240i	$-0.0867724\pi$
$744$		0			0
$745$	−2.22684	+	3.85699i	−0.0815849	+	0.141309i
$746$	4.67768	+	2.70066i	0.171262	+	0.0988782i
$747$		0			0
$748$		−	48.7085i		−	1.78096i
$749$	−0.416997	+	20.4991i	−0.0152367	+	0.749020i
$750$		0			0
$751$	−15.8556	−	27.4628i	−0.578580	−	1.00213i	−0.995643	−	0.0932523i	$-0.970274\pi$
$751$	−15.8556	−	27.4628i	−0.578580	−	1.00213i	0.417062	−	0.908878i	$-0.363060\pi$
$752$	−18.1604	−	10.4849i	−0.662241	−	0.382345i
$753$		0			0
$754$	0.240284	−	8.57543i	0.00875063	−	0.312299i
$755$	−3.68467			−0.134099
$756$		0			0
$757$	15.5317			0.564510			0.282255	−	0.959339i	$-0.408918\pi$
$757$	15.5317			0.564510			0.282255	+	0.959339i	$0.408918\pi$
$758$	−4.18344	−	7.24593i	−0.151949	−	0.263184i
$759$		0			0
$760$	3.16825	+	1.82919i	0.114925	+	0.0663518i
$761$	−0.216826	+	0.125185i	−0.00785993	+	0.00453794i	−0.503925	−	0.863748i	$-0.668111\pi$
$761$	−0.216826	+	0.125185i	−0.00785993	+	0.00453794i	0.496065	+	0.868285i	$0.334778\pi$
$762$		0			0
$763$	0.0428255	+	0.0777879i	0.00155039	+	0.00281611i
$764$	−25.5961			−0.926036
$765$		0			0
$766$	0.633903	−	1.09795i	0.0229039	−	0.0396706i
$767$	2.69966	−	1.45939i	0.0974789	−	0.0526956i
$768$		0			0
$769$			24.0146i			0.865988i	0.901397	+	0.432994i	$0.142543\pi$
$769$			24.0146i			0.865988i	−0.901397	+	0.432994i	$0.857457\pi$
$770$	7.56896	+	0.153969i	0.272766	+	0.00554867i
$771$		0			0
$772$	−30.3650	+	17.5312i	−1.09286	+	0.630963i
$773$	−26.4192	−	15.2531i	−0.950231	−	0.548616i	−0.0570784	−	0.998370i	$-0.518179\pi$
$773$	−26.4192	−	15.2531i	−0.950231	−	0.548616i	−0.893153	+	0.449753i	$0.851512\pi$
$774$		0			0
$775$	−15.3939	+	8.88768i	−0.552966	+	0.319255i
$776$	8.51064			0.305514
$777$		0			0
$778$			0.954237i			0.0342110i
$779$	7.39323	+	12.8055i	0.264890	+	0.458803i
$780$		0			0
$781$	11.2023	−	19.4030i	0.400851	−	0.694294i
$782$	0.673043	−	0.388582i	0.0240680	−	0.0138956i
$783$		0			0
$784$	12.5388	−	19.8109i	0.447815	−	0.707532i
$785$			13.6019i			0.485473i
$786$		0			0
$787$	−17.1899	−	9.92461i	−0.612755	−	0.353774i	0.161288	−	0.986907i	$-0.448435\pi$
$787$	−17.1899	−	9.92461i	−0.612755	−	0.353774i	−0.774043	+	0.633133i	$0.781769\pi$
$788$	−4.36606	−	2.52075i	−0.155534	−	0.0897978i
$789$		0			0
$790$	0.0630042			0.00224159
$791$	20.8277	+	12.5965i	0.740547	+	0.447879i
$792$		0			0
$793$	−24.4326	−	0.684604i	−0.867628	−	0.0243110i
$794$	−3.17724	+	5.50314i	−0.112756	+	0.195299i
$795$		0			0
$796$	19.0841	+	33.0546i	0.676418	+	1.17159i
$797$	52.2894			1.85219			0.926093	−	0.377296i	$-0.123146\pi$
$797$	52.2894			1.85219			0.926093	+	0.377296i	$0.123146\pi$
$798$		0			0
$799$			27.1014i			0.958777i
$800$	−9.32207	+	5.38210i	−0.329585	+	0.190286i
$801$		0			0
$802$	−0.498271	+	0.863031i	−0.0175946	+	0.0304747i
$803$	−27.2008	−	47.1131i	−0.959894	−	1.66259i
$804$		0			0
$805$	−0.996393	−	1.80984i	−0.0351182	−	0.0637884i
$806$	−3.83602	+	6.23414i	−0.135118	+	0.219588i
$807$		0			0
$808$	−0.0792988	−	0.0457832i	−0.00278972	−	0.00161065i
$809$	−1.18230	+	2.04780i	−0.0415674	+	0.0719969i	−0.886061	−	0.463569i	$-0.846568\pi$
$809$	−1.18230	+	2.04780i	−0.0415674	+	0.0719969i	0.844493	+	0.535566i	$0.179902\pi$
$810$		0			0
$811$		−	23.6646i		−	0.830978i	−0.909598	−	0.415489i	$-0.863610\pi$
$811$		−	23.6646i		−	0.830978i	0.909598	−	0.415489i	$-0.136390\pi$
$812$	31.3502	−	17.2596i	1.10017	−	0.605693i
$813$		0			0
$814$	13.7627	−	7.94591i	0.482383	−	0.278504i
$815$	0.502467	−	0.870298i	0.0176006	−	0.0304852i
$816$		0			0
$817$	−7.20218	+	4.15818i	−0.251972	+	0.145476i
$818$	−11.3275			−0.396058
$819$		0			0
$820$	20.6330			0.720536
$821$	−3.09823	+	1.78877i	−0.108129	+	0.0624284i	−0.553089	−	0.833122i	$-0.686551\pi$
$821$	−3.09823	+	1.78877i	−0.108129	+	0.0624284i	0.444960	+	0.895550i	$0.353218\pi$
$822$		0			0
$823$	−14.9711	+	25.9307i	−0.521859	+	0.903887i	0.477817	+	0.878459i	$0.341428\pi$
$823$	−14.9711	+	25.9307i	−0.521859	+	0.903887i	−0.999677	+	0.0254278i	$0.991905\pi$
$824$	7.09615	−	4.09696i	0.247206	−	0.142725i
$825$		0			0
$826$	−0.640464	−	0.387350i	−0.0222846	−	0.0134776i
$827$			9.32620i			0.324304i	0.986766	+	0.162152i	$0.0518435\pi$
$827$			9.32620i			0.324304i	−0.986766	+	0.162152i	$0.948157\pi$
$828$		0			0
$829$	19.1134	−	33.1054i	0.663836	−	1.14980i	−0.315763	−	0.948838i	$-0.602261\pi$
$829$	19.1134	−	33.1054i	0.663836	−	1.14980i	0.979599	−	0.200960i	$-0.0644062\pi$
$830$	−1.11025	−	0.641002i	−0.0385373	−	0.0222495i
$831$		0			0
$832$	10.3345	−	16.7951i	0.358283	−	0.582266i
$833$	−30.2759	−	1.23227i	−1.04900	−	0.0426956i
$834$		0			0
$835$	−10.1078	−	17.5072i	−0.349794	−	0.605860i
$836$	−11.0135	+	19.0760i	−0.380910	+	0.659756i
$837$		0			0
$838$	10.0101	−	5.77933i	0.345793	−	0.199644i
$839$			23.4981i			0.811244i	0.914041	+	0.405622i	$0.132945\pi$
$839$			23.4981i			0.811244i	−0.914041	+	0.405622i	$0.867055\pi$
$840$		0			0
$841$	22.2451			0.767071
$842$	4.01178	+	6.94860i	0.138255	+	0.239465i
$843$		0			0
$844$	−12.4017	+	21.4803i	−0.426883	+	0.739384i
$845$	15.7236	+	10.2931i	0.540908	+	0.354095i
$846$		0			0
$847$	−1.31639	+	64.7121i	−0.0452316	+	2.22353i
$848$	9.30806			0.319640
$849$		0			0
$850$	3.62608	+	2.09352i	0.124374	+	0.0718072i
$851$	−3.75584	−	2.16843i	−0.128748	−	0.0743329i
$852$		0			0
$853$		−	40.9295i		−	1.40140i	−0.713456	−	0.700700i	$-0.752871\pi$
$853$		−	40.9295i		−	1.40140i	0.713456	−	0.700700i	$-0.247129\pi$
$854$	2.87508	+	5.22226i	0.0983830	+	0.178702i
$855$		0			0
$856$	8.67624	−	5.00923i	0.296548	−	0.171212i
$857$	5.83099	−	10.0996i	0.199183	−	0.344995i	−0.749081	−	0.662479i	$-0.769505\pi$
$857$	5.83099	−	10.0996i	0.199183	−	0.344995i	0.948264	+	0.317484i	$0.102838\pi$
$858$		0			0
$859$	−14.1388	−	24.4891i	−0.482410	−	0.835559i	0.517386	−	0.855752i	$-0.326905\pi$
$859$	−14.1388	−	24.4891i	−0.482410	−	0.835559i	−0.999796	+	0.0201934i	$0.993572\pi$
$860$			11.6046i			0.395715i
$861$		0			0
$862$	1.58369			0.0539407
$863$	−9.91101	+	5.72212i	−0.337375	+	0.194783i	−0.659110	−	0.752046i	$-0.729067\pi$
$863$	−9.91101	+	5.72212i	−0.337375	+	0.194783i	0.321736	+	0.946829i	$0.395734\pi$
$864$		0			0
$865$	−6.80617	−	3.92954i	−0.231417	−	0.133609i
$866$	6.33924	−	3.65996i	0.215416	−	0.124371i
$867$		0			0
$868$	−30.5289	−	0.621025i	−1.03622	−	0.0210790i
$869$			0.780871i			0.0264892i
$870$		0			0
$871$	3.13087	−	1.69250i	0.106085	−	0.0573482i
$872$	0.0216944	−	0.0375757i	0.000734664	−	0.00127248i
$873$		0			0
$874$	−0.351449			−0.0118879
$875$	15.6570	−	25.8881i	0.529303	−	0.875177i
$876$		0			0
$877$	48.7993	−	28.1743i	1.64783	−	0.951378i	0.669904	−	0.742447i	$-0.266335\pi$
$877$	48.7993	−	28.1743i	1.64783	−	0.951378i	0.977930	−	0.208930i	$-0.0669982\pi$
$878$	−0.988000	−	0.570422i	−0.0333434	−	0.0192508i
$879$		0			0
$880$	14.4172	+	24.9713i	0.486003	+	0.841782i
$881$	−1.16418			−0.0392221			−0.0196111	−	0.999808i	$-0.506243\pi$
$881$	−1.16418			−0.0392221			−0.0196111	+	0.999808i	$0.506243\pi$
$882$		0			0
$883$	12.1881			0.410162			0.205081	−	0.978745i	$-0.434254\pi$
$883$	12.1881			0.410162			0.205081	+	0.978745i	$0.434254\pi$
$884$	−29.4790	−	0.826003i	−0.991487	−	0.0277815i
$885$		0			0
$886$	2.50597	+	1.44682i	0.0841896	+	0.0486069i
$887$	15.3320	+	26.5559i	0.514799	+	0.891659i	0.999853	+	0.0171740i	$0.00546693\pi$
$887$	15.3320	+	26.5559i	0.514799	+	0.891659i	−0.485053	+	0.874485i	$0.661200\pi$
$888$		0			0
$889$	−32.5894	−	19.7099i	−1.09301	−	0.661049i
$890$		−	4.66910i		−	0.156509i
$891$		0			0
$892$	3.63822	+	2.10053i	0.121817	+	0.0703308i
$893$	6.12790	−	10.6138i	0.205062	−	0.355178i
$894$		0			0
$895$		−	7.74598i		−	0.258920i
$896$	−24.3769	−	0.495879i	−0.814374	−	0.0165662i
$897$		0			0
$898$	2.92689	+	5.06952i	0.0976716	+	0.169172i
$899$	−37.8665	−	21.8622i	−1.26292	−	0.729147i
$900$		0			0
$901$	−6.01486	−	10.4180i	−0.200384	−	0.347075i
$902$		−	14.9512i		−	0.497822i
$903$		0			0
$904$		−	11.8934i		−	0.395570i
$905$	9.43987	−	5.45011i	0.313792	−	0.181168i
$906$		0			0
$907$	−5.82396	+	10.0874i	−0.193382	+	0.334947i	−0.946369	−	0.323088i	$-0.895279\pi$
$907$	−5.82396	+	10.0874i	−0.193382	+	0.334947i	0.752987	+	0.658035i	$0.228612\pi$
$908$	−44.3532	+	25.6074i	−1.47191	+	0.849810i
$909$		0			0
$910$	0.221539	−	4.57822i	0.00734395	−	0.151766i
$911$	26.5833			0.880743			0.440371	−	0.897816i	$-0.354847\pi$
$911$	26.5833			0.880743			0.440371	+	0.897816i	$0.354847\pi$
$912$		0			0
$913$	7.94455	−	13.7604i	0.262926	−	0.455402i
$914$	−1.50777	+	2.61153i	−0.0498725	+	0.0863817i
$915$		0			0
$916$			35.8797i			1.18550i
$917$	0.509482	−	25.0455i	0.0168246	−	0.827077i
$918$		0			0
$919$	22.8540	+	39.5842i	0.753883	+	1.30576i	0.945928	+	0.324377i	$0.105155\pi$
$919$	22.8540	+	39.5842i	0.753883	+	1.30576i	−0.192045	+	0.981386i	$0.561512\pi$
$920$	−0.504748	+	0.874250i	−0.0166411	+	0.0288232i
$921$		0			0
$922$	−1.09405	−	1.89494i	−0.0360305	−	0.0624066i
$923$	−11.5530	−	7.10883i	−0.380271	−	0.233990i
$924$		0			0
$925$		−	23.3653i		−	0.768246i
$926$	−0.577242	−	0.999813i	−0.0189694	−	0.0328559i
$927$		0			0
$928$	−22.9308	−	13.2391i	−0.752740	−	0.434595i
$929$	−9.58268	+	5.53257i	−0.314398	+	0.181518i	−0.648893	−	0.760880i	$-0.724768\pi$
$929$	−9.58268	+	5.53257i	−0.314398	+	0.181518i	0.334495	+	0.942398i	$0.391434\pi$
$930$		0			0
$931$	11.5785	+	7.32830i	0.379469	+	0.240175i
$932$	41.0784			1.34557
$933$		0			0
$934$	8.57360	+	4.94997i	0.280537	+	0.161968i
$935$	18.6327	−	32.2729i	0.609356	−	1.05544i
$936$		0			0
$937$	−57.6584			−1.88362			−0.941808	−	0.336150i	$-0.890875\pi$
$937$	−57.6584			−1.88362			−0.941808	+	0.336150i	$0.890875\pi$
$938$	−0.742765	−	0.449221i	−0.0242521	−	0.0146676i
$939$		0			0
$940$	−8.55086	−	14.8105i	−0.278898	−	0.483066i
$941$	14.7003	+	8.48723i	0.479216	+	0.276676i	0.720090	−	0.693881i	$-0.244101\pi$
$941$	14.7003	+	8.48723i	0.479216	+	0.276676i	−0.240874	+	0.970557i	$0.577434\pi$
$942$		0			0
$943$	−3.53354	+	2.04009i	−0.115068	+	0.0664345i
$944$		−	2.85082i		−	0.0927862i
$945$		0			0
$946$	8.40904			0.273401
$947$	14.4593	−	8.34808i	0.469864	−	0.271276i	−0.246319	−	0.969189i	$-0.579221\pi$
$947$	14.4593	−	8.34808i	0.469864	−	0.271276i	0.716183	+	0.697913i	$0.245888\pi$
$948$		0			0
$949$	−28.9747	+	15.6633i	−0.940559	+	0.508452i
$950$	−0.946733	−	1.63979i	−0.0307161	−	0.0532018i
$951$		0			0
$952$	7.14062	+	12.9702i	0.231429	+	0.420365i
$953$	−18.2473			−0.591089			−0.295545	−	0.955329i	$-0.595501\pi$
$953$	−18.2473			−0.591089			−0.295545	+	0.955329i	$0.595501\pi$
$954$		0			0
$955$	−16.9593	−	9.79143i	−0.548789	−	0.316843i
$956$	32.6777	+	18.8665i	1.05687	+	0.610186i
$957$		0			0
$958$	−11.6948			−0.377841
$959$	−21.1896	−	38.4886i	−0.684248	−	1.24286i
$960$		0			0
$961$	3.15382	+	5.46257i	0.101736	+	0.176212i
$962$	−4.57557	−	8.46412i	−0.147522	−	0.272894i
$963$		0			0
$964$	−5.28629	+	3.05204i	−0.170260	+	0.0982996i
$965$	−26.8253			−0.863537
$966$		0			0
$967$			29.5845i			0.951374i	0.879615	+	0.475687i	$0.157801\pi$
$967$			29.5845i			0.951374i	−0.879615	+	0.475687i	$0.842199\pi$
$968$	27.3894	−	15.8133i	0.880328	−	0.508258i
$969$		0			0
$970$	2.73937	+	1.58158i	0.0879558	+	0.0507813i
$971$	7.56504	+	13.1030i	0.242774	+	0.420497i	0.961503	−	0.274793i	$-0.0886094\pi$
$971$	7.56504	+	13.1030i	0.242774	+	0.420497i	−0.718730	+	0.695290i	$0.755276\pi$
$972$		0			0
$973$	41.8320	+	25.2998i	1.34107	+	0.811075i
$974$	0.598787			0.0191864
$975$		0			0
$976$	−11.3528	+	19.6636i	−0.363393	+	0.629415i
$977$	−28.1143	−	16.2318i	−0.899457	−	0.519301i	−0.0224327	−	0.999748i	$-0.507141\pi$
$977$	−28.1143	−	16.2318i	−0.899457	−	0.519301i	−0.877024	+	0.480447i	$0.840474\pi$
$978$		0			0
$979$	57.8686			1.84949
$980$	16.9342	−	8.87906i	0.540943	−	0.283631i
$981$		0			0
$982$	2.35838	−	1.36161i	0.0752590	−	0.0434508i
$983$	−38.3602	−	22.1473i	−1.22350	−	0.706388i	−0.257838	−	0.966188i	$-0.583010\pi$
$983$	−38.3602	−	22.1473i	−1.22350	−	0.706388i	−0.965662	+	0.259800i	$0.916343\pi$
$984$		0			0
$985$	−1.92855	−	3.34034i	−0.0614487	−	0.106432i
$986$			10.2994i			0.328001i
$987$		0			0
$988$	11.3582	+	6.98900i	0.361354	+	0.222350i
$989$	−1.14741	−	1.98737i	−0.0364855	−	0.0631948i
$990$		0			0
$991$	4.26058	−	7.37955i	0.135342	−	0.234419i	−0.790386	−	0.612609i	$-0.790120\pi$
$991$	4.26058	−	7.37955i	0.135342	−	0.234419i	0.925728	+	0.378190i	$0.123453\pi$
$992$	11.2962	+	19.5655i	0.358654	+	0.621206i
$993$		0			0
$994$	−0.0672870	+	3.30775i	−0.00213422	+	0.104916i
$995$			29.2014i			0.925746i
$996$		0			0
$997$	3.38953	−	5.87083i	0.107347	−	0.185931i	−0.807347	−	0.590076i	$-0.799098\pi$
$997$	3.38953	−	5.87083i	0.107347	−	0.185931i	0.914695	+	0.404145i	$0.132431\pi$
$998$	−6.06858	+	10.5111i	−0.192098	+	0.332723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dl.e.298.4		16
3.2	odd	2		91.2.r.a.25.5	yes	16
7.2	even	3	inner	819.2.dl.e.415.5		16
13.12	even	2	inner	819.2.dl.e.298.5		16
21.2	odd	6		91.2.r.a.51.4	yes	16
21.5	even	6		637.2.r.f.324.4		16
21.11	odd	6		637.2.c.f.246.5		8
21.17	even	6		637.2.c.e.246.5		8
21.20	even	2		637.2.r.f.116.5		16
39.5	even	4		1183.2.e.i.508.4		16
39.8	even	4		1183.2.e.i.508.5		16
39.38	odd	2		91.2.r.a.25.4	✓	16
91.51	even	6	inner	819.2.dl.e.415.4		16
273.38	even	6		637.2.c.e.246.4		8
273.44	even	12		1183.2.e.i.170.4		16
273.86	even	12		1183.2.e.i.170.5		16
273.116	odd	6		637.2.c.f.246.4		8
273.122	odd	12		8281.2.a.cj.1.5		8
273.164	odd	12		8281.2.a.cj.1.4		8
273.194	even	6		637.2.r.f.324.5		16
273.200	even	12		8281.2.a.ck.1.5		8
273.233	odd	6		91.2.r.a.51.5	yes	16
273.242	even	12		8281.2.a.ck.1.4		8
273.272	even	2		637.2.r.f.116.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.4	✓	16	39.38	odd	2
91.2.r.a.25.5	yes	16	3.2	odd	2
91.2.r.a.51.4	yes	16	21.2	odd	6
91.2.r.a.51.5	yes	16	273.233	odd	6
637.2.c.e.246.4		8	273.38	even	6
637.2.c.e.246.5		8	21.17	even	6
637.2.c.f.246.4		8	273.116	odd	6
637.2.c.f.246.5		8	21.11	odd	6
637.2.r.f.116.4		16	273.272	even	2
637.2.r.f.116.5		16	21.20	even	2
637.2.r.f.324.4		16	21.5	even	6
637.2.r.f.324.5		16	273.194	even	6
819.2.dl.e.298.4		16	1.1	even	1	trivial
819.2.dl.e.298.5		16	13.12	even	2	inner
819.2.dl.e.415.4		16	91.51	even	6	inner
819.2.dl.e.415.5		16	7.2	even	3	inner
1183.2.e.i.170.4		16	273.44	even	12
1183.2.e.i.170.5		16	273.86	even	12
1183.2.e.i.508.4		16	39.5	even	4
1183.2.e.i.508.5		16	39.8	even	4
8281.2.a.cj.1.4		8	273.164	odd	12
8281.2.a.cj.1.5		8	273.122	odd	12
8281.2.a.ck.1.4		8	273.242	even	12
8281.2.a.ck.1.5		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)

\(f(q)\)	\(=\)	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} +(2.26391 + 1.36920i) q^{7} -1.29278i q^{8} +O(q^{10})\)	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} +(2.26391 + 1.36920i) q^{7} -1.29278i q^{8} +(0.240245 - 0.416116i) q^{10} +(5.15732 + 2.97758i) q^{11} +(1.88953 - 3.07078i) q^{13} +(-0.879201 - 0.0178849i) q^{14} +(-1.67468 - 2.90063i) q^{16} +(-2.16436 + 3.74877i) q^{17} +(1.69527 - 0.978767i) q^{19} -2.73154i q^{20} -1.97935 q^{22} +(0.270081 + 0.467795i) q^{23} +(-1.45509 + 2.52029i) q^{25} +(-0.0335660 + 1.19793i) q^{26} +(-4.37939 + 2.41104i) q^{28} -7.15857 q^{29} +(5.28968 + 3.05400i) q^{31} +(3.20327 + 1.84941i) q^{32} -1.43876i q^{34} +(-3.82396 - 0.0777879i) q^{35} +(-6.95316 + 4.01441i) q^{37} +(-0.325318 + 0.563467i) q^{38} +(0.934437 + 1.61849i) q^{40} +7.55362i q^{41} -4.24839 q^{43} +(-9.74489 + 5.62622i) q^{44} +(-0.155483 - 0.0897684i) q^{46} +(5.42204 - 3.13042i) q^{47} +(3.25057 + 6.19950i) q^{49} -0.967272i q^{50} +(3.23980 + 5.99314i) q^{52} +(-1.38953 + 2.40673i) q^{53} -8.60891 q^{55} +(1.77008 - 2.92674i) q^{56} +(2.06056 - 1.18967i) q^{58} +(0.737119 + 0.425576i) q^{59} +(-3.38953 - 5.87083i) q^{61} -2.03015 q^{62} +5.46933 q^{64} +(-0.145991 + 5.21022i) q^{65} +(0.854859 + 0.493553i) q^{67} +(-4.08961 - 7.08341i) q^{68} +(1.11364 - 0.613105i) q^{70} -3.76223i q^{71} +(-7.91131 - 4.56760i) q^{73} +(1.33429 - 2.31106i) q^{74} +3.69881i q^{76} +(7.59879 + 13.8024i) q^{77} +(0.0655625 + 0.113558i) q^{79} +(4.19322 + 2.42096i) q^{80} +(-1.25532 - 2.17428i) q^{82} -2.66812i q^{83} -6.25768i q^{85} +(1.22288 - 0.706030i) q^{86} +(3.84936 - 6.66729i) q^{88} +(8.41550 - 4.85869i) q^{89} +(8.48224 - 4.36482i) q^{91} -1.02065 q^{92} +(-1.04047 + 1.80215i) q^{94} +(-1.41493 + 2.45072i) q^{95} +6.58319i q^{97} +(-1.96594 - 1.24429i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more