LMFDB - Embedded newform 819.2.dx.a.503.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.20
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.205179 + 0.118460i) q^{2} +(-0.971934 - 1.68344i) q^{4} +3.73403 q^{5} +(-1.71677 - 2.01313i) q^{7} -0.934382i q^{8} +O(q^{10})$	\(q+(0.205179 + 0.118460i) q^{2} +(-0.971934 - 1.68344i) q^{4} +3.73403 q^{5} +(-1.71677 - 2.01313i) q^{7} -0.934382i q^{8} +(0.766145 + 0.442334i) q^{10} +(4.60138 + 2.65661i) q^{11} +(2.35063 + 2.73396i) q^{13} +(-0.113769 - 0.616421i) q^{14} +(-1.83318 + 3.17516i) q^{16} +(-1.67409 - 2.89961i) q^{17} +(3.16091 - 1.82495i) q^{19} +(-3.62923 - 6.28602i) q^{20} +(0.629404 + 1.09016i) q^{22} +(-4.38915 - 2.53408i) q^{23} +8.94299 q^{25} +(0.158434 + 0.839407i) q^{26} +(-1.72040 + 4.84671i) q^{28} +(1.12617 + 0.650196i) q^{29} -7.57403i q^{31} +(-2.37066 + 1.36870i) q^{32} -0.793252i q^{34} +(-6.41047 - 7.51710i) q^{35} +(-1.79558 + 3.11003i) q^{37} +0.864737 q^{38} -3.48901i q^{40} +(5.91931 - 10.2526i) q^{41} +(-0.811226 - 1.40508i) q^{43} -10.3282i q^{44} +(-0.600374 - 1.03988i) q^{46} -4.90958 q^{47} +(-1.10540 + 6.91217i) q^{49} +(1.83491 + 1.05939i) q^{50} +(2.31781 - 6.61437i) q^{52} +6.27366i q^{53} +(17.1817 + 9.91985i) q^{55} +(-1.88104 + 1.60412i) q^{56} +(0.154045 + 0.266813i) q^{58} +(0.388312 + 0.672576i) q^{59} +(-8.73777 + 5.04475i) q^{61} +(0.897221 - 1.55403i) q^{62} +6.68418 q^{64} +(8.77732 + 10.2087i) q^{65} +(2.91276 - 5.04504i) q^{67} +(-3.25421 + 5.63646i) q^{68} +(-0.424818 - 2.30174i) q^{70} +(2.03610 - 1.17554i) q^{71} +12.6373i q^{73} +(-0.736830 + 0.425409i) q^{74} +(-6.14440 - 3.54747i) q^{76} +(-2.55141 - 13.8240i) q^{77} -6.71892 q^{79} +(-6.84516 + 11.8562i) q^{80} +(2.42904 - 1.40241i) q^{82} +10.2324 q^{83} +(-6.25110 - 10.8272i) q^{85} -0.384392i q^{86} +(2.48229 - 4.29945i) q^{88} +(3.58023 - 6.20113i) q^{89} +(1.46834 - 9.42571i) q^{91} +9.85183i q^{92} +(-1.00734 - 0.581589i) q^{94} +(11.8029 - 6.81443i) q^{95} +(4.99403 - 2.88330i) q^{97} +(-1.04562 + 1.28729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.205179	+	0.118460i	0.145083	+	0.0837640i	0.570785	−	0.821100i	$-0.306639\pi$
$2$	0.205179	+	0.118460i	0.145083	+	0.0837640i	−0.425701	+	0.904864i	$0.639972\pi$
$3$		0			0
$3$		0			0
$4$	−0.971934	−	1.68344i	−0.485967	−	0.841720i
$5$	3.73403			1.66991			0.834955	−	0.550319i	$-0.185494\pi$
$5$	3.73403			1.66991			0.834955	+	0.550319i	$0.185494\pi$
$6$		0			0
$7$	−1.71677	−	2.01313i	−0.648878	−	0.760892i
$7$	−1.71677	−	2.01313i	−0.648878	−	0.760892i
$8$		−	0.934382i		−	0.330354i
$9$		0			0
$10$	0.766145	+	0.442334i	0.242276	+	0.139878i
$11$	4.60138	+	2.65661i	1.38737	+	0.800997i	0.993018	−	0.117964i	$-0.0376367\pi$
$11$	4.60138	+	2.65661i	1.38737	+	0.800997i	0.394349	+	0.918961i	$0.370970\pi$
$12$		0			0
$13$	2.35063	+	2.73396i	0.651947	+	0.758265i
$13$	2.35063	+	2.73396i	0.651947	+	0.758265i
$14$	−0.113769	−	0.616421i	−0.0304061	−	0.164745i
$15$		0			0
$16$	−1.83318	+	3.17516i	−0.458295	+	0.793791i
$17$	−1.67409	−	2.89961i	−0.406026	−	0.703258i	0.588414	−	0.808560i	$-0.299753\pi$
$17$	−1.67409	−	2.89961i	−0.406026	−	0.703258i	−0.994440	+	0.105302i	$0.966419\pi$
$18$		0			0
$19$	3.16091	−	1.82495i	0.725163	−	0.418673i	−0.0914870	−	0.995806i	$-0.529162\pi$
$19$	3.16091	−	1.82495i	0.725163	−	0.418673i	0.816650	+	0.577133i	$0.195829\pi$
$20$	−3.62923	−	6.28602i	−0.811521	−	1.40560i
$21$		0			0
$22$	0.629404	+	1.09016i	0.134189	+	0.232423i
$23$	−4.38915	−	2.53408i	−0.915201	−	0.528392i	−0.0331003	−	0.999452i	$-0.510538\pi$
$23$	−4.38915	−	2.53408i	−0.915201	−	0.528392i	−0.882101	+	0.471060i	$0.843871\pi$
$24$		0			0
$25$	8.94299			1.78860
$26$	0.158434	+	0.839407i	0.0310714	+	0.164621i
$27$		0			0
$28$	−1.72040	+	4.84671i	−0.325125	+	0.915942i
$29$	1.12617	+	0.650196i	0.209125	+	0.120738i	0.600905	−	0.799321i	$-0.294807\pi$
$29$	1.12617	+	0.650196i	0.209125	+	0.120738i	−0.391780	+	0.920059i	$0.628140\pi$
$30$		0			0
$31$		−	7.57403i		−	1.36034i	−0.733056	−	0.680168i	$-0.761907\pi$
$31$		−	7.57403i		−	1.36034i	0.733056	−	0.680168i	$-0.238093\pi$
$32$	−2.37066	+	1.36870i	−0.419077	+	0.241954i
$33$		0			0
$34$		−	0.793252i		−	0.136042i
$35$	−6.41047	−	7.51710i	−1.08357	−	1.27062i
$36$		0			0
$37$	−1.79558	+	3.11003i	−0.295191	+	0.511286i	−0.975029	−	0.222076i	$-0.928717\pi$
$37$	−1.79558	+	3.11003i	−0.295191	+	0.511286i	0.679838	+	0.733362i	$0.262050\pi$
$38$	0.864737			0.140279
$39$		0			0
$40$		−	3.48901i		−	0.551661i
$41$	5.91931	−	10.2526i	0.924441	−	1.60118i	0.131984	−	0.991252i	$-0.457865\pi$
$41$	5.91931	−	10.2526i	0.924441	−	1.60118i	0.792457	−	0.609928i	$-0.208802\pi$
$42$		0			0
$43$	−0.811226	−	1.40508i	−0.123711	−	0.214273i	0.797517	−	0.603296i	$-0.206146\pi$
$43$	−0.811226	−	1.40508i	−0.123711	−	0.214273i	−0.921228	+	0.389022i	$0.872813\pi$
$44$		−	10.3282i		−	1.55703i
$45$		0			0
$46$	−0.600374	−	1.03988i	−0.0885204	−	0.153322i
$47$	−4.90958			−0.716136			−0.358068	−	0.933696i	$-0.616564\pi$
$47$	−4.90958			−0.716136			−0.358068	+	0.933696i	$0.616564\pi$
$48$		0			0
$49$	−1.10540	+	6.91217i	−0.157914	+	0.987453i
$50$	1.83491	+	1.05939i	0.259496	+	0.149820i
$51$		0			0
$52$	2.31781	−	6.61437i	0.321422	−	0.917248i
$53$			6.27366i			0.861753i	0.902411	+	0.430877i	$0.141796\pi$
$53$			6.27366i			0.861753i	−0.902411	+	0.430877i	$0.858204\pi$
$54$		0			0
$55$	17.1817	+	9.91985i	2.31678	+	1.33759i
$56$	−1.88104	+	1.60412i	−0.251364	+	0.214360i
$57$		0			0
$58$	0.154045	+	0.266813i	0.0202270	+	0.0350343i
$59$	0.388312	+	0.672576i	0.0505539	+	0.0875620i	0.890195	−	0.455580i	$-0.150568\pi$
$59$	0.388312	+	0.672576i	0.0505539	+	0.0875620i	−0.839641	+	0.543142i	$0.817235\pi$
$60$		0			0
$61$	−8.73777	+	5.04475i	−1.11876	+	0.645915i	−0.941083	−	0.338175i	$-0.890190\pi$
$61$	−8.73777	+	5.04475i	−1.11876	+	0.645915i	−0.177674	+	0.984089i	$0.556857\pi$
$62$	0.897221	−	1.55403i	0.113947	−	0.197362i
$63$		0			0
$64$	6.68418			0.835523
$65$	8.77732	+	10.2087i	1.08869	+	1.26623i
$66$		0			0
$67$	2.91276	−	5.04504i	0.355850	−	0.616350i	−0.631413	−	0.775446i	$-0.717525\pi$
$67$	2.91276	−	5.04504i	0.355850	−	0.616350i	0.987263	+	0.159097i	$0.0508582\pi$
$68$	−3.25421	+	5.63646i	−0.394631	+	0.683521i
$69$		0			0
$70$	−0.424818	−	2.30174i	−0.0507755	−	0.275110i
$71$	2.03610	−	1.17554i	0.241640	−	0.139511i	−0.374290	−	0.927312i	$-0.622114\pi$
$71$	2.03610	−	1.17554i	0.241640	−	0.139511i	0.615930	+	0.787801i	$0.288780\pi$
$72$		0			0
$73$			12.6373i			1.47908i	0.673112	+	0.739540i	$0.264957\pi$
$73$			12.6373i			1.47908i	−0.673112	+	0.739540i	$0.735043\pi$
$74$	−0.736830	+	0.425409i	−0.0856547	+	0.0494528i
$75$		0			0
$76$	−6.14440	−	3.54747i	−0.704811	−	0.406923i
$77$	−2.55141	−	13.8240i	−0.290760	−	1.57539i
$78$		0			0
$79$	−6.71892			−0.755938			−0.377969	−	0.925818i	$-0.623377\pi$
$79$	−6.71892			−0.755938			−0.377969	+	0.925818i	$0.623377\pi$
$80$	−6.84516	+	11.8562i	−0.765312	+	1.32556i
$81$		0			0
$82$	2.42904	−	1.40241i	0.268242	−	0.154870i
$83$	10.2324			1.12315			0.561577	−	0.827425i	$-0.310195\pi$
$83$	10.2324			1.12315			0.561577	+	0.827425i	$0.310195\pi$
$84$		0			0
$85$	−6.25110	−	10.8272i	−0.678027	−	1.17438i
$86$		−	0.384392i		−	0.0414500i
$87$		0			0
$88$	2.48229	−	4.29945i	0.264613	−	0.458322i
$89$	3.58023	−	6.20113i	0.379503	−	0.657319i	−0.611487	−	0.791255i	$-0.709428\pi$
$89$	3.58023	−	6.20113i	0.379503	−	0.657319i	0.990990	+	0.133936i	$0.0427616\pi$
$90$		0			0
$91$	1.46834	−	9.42571i	0.153924	−	0.988083i
$92$			9.85183i			1.02712i
$93$		0			0
$94$	−1.00734	−	0.581589i	−0.103899	−	0.0599864i
$95$	11.8029	−	6.81443i	1.21096	−	0.699146i
$96$		0			0
$97$	4.99403	−	2.88330i	0.507067	−	0.292755i	−0.224560	−	0.974460i	$-0.572095\pi$
$97$	4.99403	−	2.88330i	0.507067	−	0.292755i	0.731627	+	0.681705i	$0.238761\pi$
$98$	−1.04562	+	1.28729i	−0.105624	+	0.130036i
$99$		0			0
$100$	−8.69200	−	15.0550i	−0.869200	−	1.50550i
$101$	1.71815	−	2.97592i	0.170962	−	0.296115i	−0.767795	−	0.640696i	$-0.778646\pi$
$101$	1.71815	−	2.97592i	0.170962	−	0.296115i	0.938756	+	0.344581i	$0.111979\pi$
$102$		0			0
$103$			17.0038i			1.67543i	0.546104	+	0.837717i	$0.316110\pi$
$103$			17.0038i			1.67543i	−0.546104	+	0.837717i	$0.683890\pi$
$104$	2.55457	−	2.19638i	0.250496	−	0.215373i
$105$		0			0
$106$	−0.743178	+	1.28722i	−0.0721839	+	0.125026i
$107$	−8.43384	−	4.86928i	−0.815330	−	0.470731i	0.0334736	−	0.999440i	$-0.489343\pi$
$107$	−8.43384	−	4.86928i	−0.815330	−	0.470731i	−0.848803	+	0.528709i	$0.822676\pi$
$108$		0			0
$109$	7.82200			0.749212			0.374606	−	0.927184i	$-0.377778\pi$
$109$	7.82200			0.749212			0.374606	+	0.927184i	$0.377778\pi$
$110$	2.35021	+	4.07069i	0.224084	+	0.388125i
$111$		0			0
$112$	9.53918	−	1.76059i	0.901367	−	0.166360i
$113$	−6.01821	+	3.47461i	−0.566145	+	0.326864i	−0.755608	−	0.655024i	$-0.772659\pi$
$113$	−6.01821	+	3.47461i	−0.566145	+	0.326864i	0.189463	+	0.981888i	$0.439325\pi$
$114$		0			0
$115$	−16.3892	−	9.46232i	−1.52830	−	0.882366i
$116$		−	2.52779i		−	0.234699i
$117$		0			0
$118$			0.183998i			0.0169384i
$119$	−2.96327	+	8.34812i	−0.271642	+	0.765271i
$120$		0			0
$121$	8.61511	+	14.9218i	0.783192	+	1.35653i
$122$	−2.39041			−0.216417
$123$		0			0
$124$	−12.7504	+	7.36146i	−1.14502	+	0.661079i
$125$	14.7232			1.31689
$126$		0			0
$127$	−6.92686	+	11.9977i	−0.614660	+	1.06462i	0.375784	+	0.926707i	$0.377373\pi$
$127$	−6.92686	+	11.9977i	−0.614660	+	1.06462i	−0.990444	+	0.137915i	$0.955960\pi$
$128$	6.11277	+	3.52921i	0.540298	+	0.311941i
$129$		0			0
$130$	0.591596	+	3.13437i	0.0518864	+	0.274903i
$131$	0.828186			0.0723589			0.0361795	−	0.999345i	$-0.488481\pi$
$131$	0.828186			0.0723589			0.0361795	+	0.999345i	$0.488481\pi$
$132$		0			0
$133$	−9.10043	−	3.23031i	−0.789108	−	0.280103i
$134$	1.19527	−	0.690091i	0.103256	−	0.0596148i
$135$		0			0
$136$	−2.70934	+	1.56424i	−0.232324	+	0.134132i
$137$	−10.8846	+	6.28422i	−0.929933	+	0.536897i	−0.886790	−	0.462172i	$-0.847070\pi$
$137$	−10.8846	+	6.28422i	−0.929933	+	0.536897i	−0.0431428	+	0.999069i	$0.513737\pi$
$138$		0			0
$139$	5.54167	−	3.19948i	0.470038	−	0.271377i	−0.246218	−	0.969215i	$-0.579188\pi$
$139$	5.54167	−	3.19948i	0.470038	−	0.271377i	0.716256	+	0.697838i	$0.245854\pi$
$140$	−6.42402	+	18.0978i	−0.542929	+	1.52954i
$141$		0			0
$142$	0.557019			0.0467440
$143$	3.55306	+	18.8247i	0.297122	+	1.57420i
$144$		0			0
$145$	4.20516	+	2.42785i	0.349220	+	0.201622i
$146$	−1.49701	+	2.59290i	−0.123894	+	0.214590i
$147$		0			0
$148$	6.98073			0.573813
$149$	−15.8949	+	9.17691i	−1.30216	+	0.751802i	−0.980774	−	0.195147i	$-0.937482\pi$
$149$	−15.8949	+	9.17691i	−1.30216	+	0.751802i	−0.321385	+	0.946949i	$0.604148\pi$
$150$		0			0
$151$	−15.5911			−1.26879			−0.634393	−	0.773011i	$-0.718750\pi$
$151$	−15.5911			−1.26879			−0.634393	+	0.773011i	$0.718750\pi$
$152$	−1.70520	−	2.95350i	−0.138310	−	0.239561i
$153$		0			0
$154$	1.11409	−	3.13863i	0.0897762	−	0.252918i
$155$		−	28.2817i		−	2.27164i
$156$		0			0
$157$		−	0.113321i		−	0.00904402i	−0.999990	−	0.00452201i	$-0.998561\pi$
$157$		−	0.113321i		−	0.00904402i	0.999990	−	0.00452201i	$-0.00143941\pi$
$158$	−1.37858	−	0.795924i	−0.109674	−	0.0633203i
$159$		0			0
$160$	−8.85211	+	5.11077i	−0.699821	+	0.404042i
$161$	2.43373	+	13.1864i	0.191805	+	1.03923i
$162$		0			0
$163$	5.33698	+	9.24392i	0.418024	+	0.724039i	0.995741	−	0.0921982i	$-0.0293893\pi$
$163$	5.33698	+	9.24392i	0.418024	+	0.724039i	−0.577716	+	0.816238i	$0.696056\pi$
$164$	−23.0127			−1.79699
$165$		0			0
$166$	2.09948	+	1.21213i	0.162951	+	0.0940798i
$167$	5.21207	−	9.02758i	0.403322	−	0.698575i	−0.590802	−	0.806816i	$-0.701189\pi$
$167$	5.21207	−	9.02758i	0.403322	−	0.698575i	0.994125	+	0.108242i	$0.0345220\pi$
$168$		0			0
$169$	−1.94910	+	12.8531i	−0.149931	+	0.988696i
$170$		−	2.96203i		−	0.227177i
$171$		0			0
$172$	−1.57692	+	2.73130i	−0.120239	+	0.208260i
$173$	7.62485	+	13.2066i	0.579706	+	1.00408i	0.995513	+	0.0946277i	$0.0301661\pi$
$173$	7.62485	+	13.2066i	0.579706	+	1.00408i	−0.415806	+	0.909453i	$0.636501\pi$
$174$		0			0
$175$	−15.3531	−	18.0034i	−1.16058	−	1.36093i
$176$	−16.8703	+	9.74008i	−1.27165	+	0.734186i
$177$		0			0
$178$	1.46917	−	0.848228i	0.110119	−	0.0635774i
$179$	−3.52871	−	2.03730i	−0.263748	−	0.152275i	0.362295	−	0.932063i	$-0.381993\pi$
$179$	−3.52871	−	2.03730i	−0.263748	−	0.152275i	−0.626043	+	0.779788i	$0.715327\pi$
$180$		0			0
$181$			18.8759i			1.40303i	0.712653	+	0.701517i	$0.247493\pi$
$181$			18.8759i			1.40303i	−0.712653	+	0.701517i	$0.752507\pi$
$182$	1.41784	−	1.76002i	0.105098	−	0.130461i
$183$		0			0
$184$	−2.36780	+	4.10115i	−0.174556	+	0.302340i
$185$	−6.70474	+	11.6130i	−0.492942	+	0.853801i
$186$		0			0
$187$		−	17.7896i		−	1.30090i
$188$	4.77179	+	8.26498i	0.348018	+	0.602786i
$189$		0			0
$190$	3.22896			0.234253
$191$	−3.98609	+	2.30137i	−0.288423	+	0.166521i	−0.637231	−	0.770673i	$-0.719920\pi$
$191$	−3.98609	+	2.30137i	−0.288423	+	0.166521i	0.348807	+	0.937194i	$0.386587\pi$
$192$		0			0
$193$	−11.5926	+	20.0790i	−0.834455	+	1.44532i	0.0600175	+	0.998197i	$0.480884\pi$
$193$	−11.5926	+	20.0790i	−0.834455	+	1.44532i	−0.894473	+	0.447122i	$0.852449\pi$
$194$	1.36623			0.0980894
$195$		0			0
$196$	12.7106	−	4.85730i	0.907900	−	0.346950i
$197$	13.9401	+	8.04830i	0.993188	+	0.573418i	0.906226	−	0.422794i	$-0.138951\pi$
$197$	13.9401	+	8.04830i	0.993188	+	0.573418i	0.0869626	+	0.996212i	$0.472284\pi$
$198$		0			0
$199$	−5.45058	+	3.14689i	−0.386382	+	0.223077i	−0.680591	−	0.732663i	$-0.738277\pi$
$199$	−5.45058	+	3.14689i	−0.386382	+	0.223077i	0.294210	+	0.955741i	$0.404944\pi$
$200$		−	8.35617i		−	0.590871i
$201$		0			0
$202$	0.705055	−	0.407064i	0.0496075	−	0.0286409i
$203$	−0.624449	−	3.38337i	−0.0438277	−	0.237466i
$204$		0			0
$205$	22.1029	−	38.2833i	1.54373	−	2.67382i
$206$	−2.01427	+	3.48882i	−0.140341	+	0.243078i
$207$		0			0
$208$	−12.9899	+	2.45178i	−0.900688	+	0.170000i
$209$	19.3927			1.34142
$210$		0			0
$211$	5.70902	−	9.88831i	0.393025	−	0.680739i	−0.599822	−	0.800134i	$-0.704762\pi$
$211$	5.70902	−	9.88831i	0.393025	−	0.680739i	0.992847	+	0.119394i	$0.0380953\pi$
$212$	10.5613	−	6.09758i	0.725355	−	0.418784i
$213$		0			0
$214$	−1.15363	−	1.99815i	−0.0788606	−	0.136591i
$215$	−3.02914	−	5.24663i	−0.206586	−	0.357817i
$216$		0			0
$217$	−15.2475	+	13.0029i	−1.03507	+	0.882692i
$218$	1.60491	+	0.926595i	0.108698	+	0.0627569i
$219$		0			0
$220$		−	38.5658i		−	2.60010i
$221$	3.99226	−	11.3928i	0.268548	−	0.766362i
$222$		0			0
$223$	−15.4229	−	8.90441i	−1.03279	−	0.596283i	−0.115010	−	0.993364i	$-0.536690\pi$
$223$	−15.4229	−	8.90441i	−1.03279	−	0.596283i	−0.917784	+	0.397081i	$0.870023\pi$
$224$	6.82525	+	2.42270i	0.456031	+	0.161874i
$225$		0			0
$226$	−1.64641			−0.109518
$227$	−4.96898	−	8.60652i	−0.329803	−	0.571235i	0.652670	−	0.757642i	$-0.273649\pi$
$227$	−4.96898	−	8.60652i	−0.329803	−	0.571235i	−0.982473	+	0.186407i	$0.940316\pi$
$228$		0			0
$229$		−	10.4503i		−	0.690578i	−0.938496	−	0.345289i	$-0.887781\pi$
$229$		−	10.4503i		−	0.690578i	0.938496	−	0.345289i	$-0.112219\pi$
$230$	−2.24182	−	3.88294i	−0.147821	−	0.256033i
$231$		0			0
$232$	0.607532	−	1.05228i	0.0398864	−	0.0690853i
$233$			1.18410i			0.0775731i	0.999248	+	0.0387865i	$0.0123492\pi$
$233$			1.18410i			0.0775731i	−0.999248	+	0.0387865i	$0.987651\pi$
$234$		0			0
$235$	−18.3325			−1.19588
$236$	0.754828	−	1.30740i	0.0491351	−	0.0851045i
$237$		0			0
$238$	−1.59692	+	1.36183i	−0.103513	+	0.0882744i
$239$			14.1148i			0.913011i	0.889721	+	0.456506i	$0.150899\pi$
$239$			14.1148i			0.913011i	−0.889721	+	0.456506i	$0.849101\pi$
$240$		0			0
$241$	10.6575	−	6.15309i	0.686508	−	0.396355i	−0.115795	−	0.993273i	$-0.536941\pi$
$241$	10.6575	−	6.15309i	0.686508	−	0.396355i	0.802302	+	0.596918i	$0.203608\pi$
$242$			4.08219i			0.262413i
$243$		0			0
$244$	16.9851	+	9.80634i	1.08736	+	0.627787i
$245$	−4.12760	+	25.8103i	−0.263702	+	1.64896i
$246$		0			0
$247$	12.4195	+	4.35203i	0.790233	+	0.276913i
$248$	−7.07704			−0.449393
$249$		0			0
$250$	3.02090	+	1.74412i	0.191058	+	0.110308i
$251$	−7.53230	−	13.0463i	−0.475434	−	0.823476i	0.524170	−	0.851614i	$-0.324376\pi$
$251$	−7.53230	−	13.0463i	−0.475434	−	0.823476i	−0.999604	+	0.0281374i	$0.991042\pi$
$252$		0			0
$253$	−13.4641	−	23.3205i	−0.846480	−	1.46615i
$254$	−2.84249	+	1.64111i	−0.178354	+	0.102973i
$255$		0			0
$256$	−5.84804	−	10.1291i	−0.365502	−	0.633069i
$257$	1.66186	−	2.87842i	0.103664	−	0.179551i	−0.809528	−	0.587082i	$-0.800277\pi$
$257$	1.66186	−	2.87842i	0.103664	−	0.179551i	0.913192	+	0.407531i	$0.133610\pi$
$258$		0			0
$259$	9.34350	−	1.72448i	0.580577	−	0.107154i
$260$	8.65476	−	24.6983i	0.536745	−	1.53172i
$261$		0			0
$262$	0.169926	+	0.0981070i	0.0104981	+	0.00606107i
$263$	−13.5363	−	7.81516i	−0.834682	−	0.481904i	0.0207713	−	0.999784i	$-0.493388\pi$
$263$	−13.5363	−	7.81516i	−0.834682	−	0.481904i	−0.855453	+	0.517881i	$0.826721\pi$
$264$		0			0
$265$			23.4260i			1.43905i
$266$	−1.48455	−	1.74083i	−0.0910239	−	0.106737i
$267$		0			0
$268$	−11.3240			−0.691725
$269$	12.2279	+	21.1793i	0.745546	+	1.29132i	0.949939	+	0.312434i	$0.101144\pi$
$269$	12.2279	+	21.1793i	0.745546	+	1.29132i	−0.204394	+	0.978889i	$0.565522\pi$
$270$		0			0
$271$	25.7989	+	14.8950i	1.56717	+	0.904806i	0.996497	+	0.0836281i	$0.0266508\pi$
$271$	25.7989	+	14.8950i	1.56717	+	0.904806i	0.570673	+	0.821178i	$0.306683\pi$
$272$	12.2756			0.744320
$273$		0			0
$274$	−2.97772			−0.179891
$275$	41.1501	+	23.7580i	2.48144	+	1.43266i
$276$		0			0
$277$	5.15448	+	8.92782i	0.309703	+	0.536421i	0.978297	−	0.207206i	$-0.0664371\pi$
$277$	5.15448	+	8.92782i	0.309703	+	0.536421i	−0.668595	+	0.743627i	$0.733104\pi$
$278$	1.51605			0.0909263
$279$		0			0
$280$	−7.02384	+	5.98983i	−0.419755	+	0.357961i
$281$		−	21.2280i		−	1.26636i	−0.774005	−	0.633179i	$-0.781750\pi$
$281$		−	21.2280i		−	1.26636i	0.774005	−	0.633179i	$-0.218250\pi$
$282$		0			0
$283$	−27.1874	−	15.6967i	−1.61612	−	0.933070i	−0.987910	−	0.155030i	$-0.950453\pi$
$283$	−27.1874	−	15.6967i	−1.61612	−	0.933070i	−0.628215	−	0.778040i	$-0.716214\pi$
$284$	−3.95790	−	2.28510i	−0.234858	−	0.135595i
$285$		0			0
$286$	−1.50096	+	4.28332i	−0.0887537	+	0.253278i
$287$	−30.8018	+	5.68492i	−1.81818	+	0.335570i
$288$		0			0
$289$	2.89485	−	5.01402i	0.170285	−	0.294943i
$290$	0.575207	+	0.996288i	0.0337773	+	0.0585041i
$291$		0			0
$292$	21.2741	−	12.2826i	1.24497	−	0.718785i
$293$	12.2960	+	21.2973i	0.718340	+	1.24420i	0.961657	+	0.274255i	$0.0884312\pi$
$293$	12.2960	+	21.2973i	0.718340	+	1.24420i	−0.243317	+	0.969947i	$0.578236\pi$
$294$		0			0
$295$	1.44997	+	2.51142i	0.0844205	+	0.146221i
$296$	2.90596	+	1.67776i	0.168905	+	0.0975176i
$297$		0			0
$298$	−4.34839			−0.251896
$299$	−3.38918	−	17.9564i	−0.196002	−	1.03845i
$300$		0			0
$301$	−1.43593	+	4.04531i	−0.0827658	+	0.233168i
$302$	−3.19897	−	1.84692i	−0.184080	−	0.106279i
$303$		0			0
$304$			13.3819i			0.767504i
$305$	−32.6271	+	18.8373i	−1.86822	+	1.07862i
$306$		0			0
$307$			17.2681i			0.985542i	0.870159	+	0.492771i	$0.164016\pi$
$307$			17.2681i			0.985542i	−0.870159	+	0.492771i	$0.835984\pi$
$308$	−20.7920	+	17.7311i	−1.18473	+	1.01032i
$309$		0			0
$310$	3.35025	−	5.80280i	0.190281	−	0.329577i
$311$	13.6126			0.771900			0.385950	−	0.922520i	$-0.373874\pi$
$311$	13.6126			0.771900			0.385950	+	0.922520i	$0.373874\pi$
$312$		0			0
$313$		−	2.16017i		−	0.122100i	−0.998135	−	0.0610500i	$-0.980555\pi$
$313$		−	2.16017i		−	0.122100i	0.998135	−	0.0610500i	$-0.0194449\pi$
$314$	0.0134241	−	0.0232511i	0.000757563	−	0.00131214i
$315$		0			0
$316$	6.53035	+	11.3109i	0.367361	+	0.636288i
$317$		−	23.1518i		−	1.30033i	−0.759792	−	0.650167i	$-0.774699\pi$
$317$		−	23.1518i		−	1.30033i	0.759792	−	0.650167i	$-0.225301\pi$
$318$		0			0
$319$	3.45463	+	5.98359i	0.193422	+	0.335017i
$320$	24.9589			1.39525
$321$		0			0
$322$	−1.06271	+	2.99387i	−0.0592224	+	0.166842i
$323$	−10.5833	−	6.11027i	−0.588871	−	0.339985i
$324$		0			0
$325$	21.0216	+	24.4498i	1.16607	+	1.35623i
$326$			2.52888i			0.140062i
$327$		0			0
$328$	−9.57980	−	5.53090i	−0.528956	−	0.305393i
$329$	8.42862	+	9.88363i	0.464685	+	0.544902i
$330$		0			0
$331$	8.34471	+	14.4535i	0.458667	+	0.794434i	0.998891	−	0.0470870i	$-0.0149938\pi$
$331$	8.34471	+	14.4535i	0.458667	+	0.794434i	−0.540224	+	0.841521i	$0.681660\pi$
$332$	−9.94523	−	17.2256i	−0.545816	−	0.945380i
$333$		0			0
$334$	2.13882	−	1.23485i	0.117031	−	0.0675678i
$335$	10.8763	−	18.8383i	0.594237	−	1.02925i
$336$		0			0
$337$	0.713377			0.0388601			0.0194301	−	0.999811i	$-0.493815\pi$
$337$	0.713377			0.0388601			0.0194301	+	0.999811i	$0.493815\pi$
$338$	−1.92249	+	2.40629i	−0.104570	+	0.130885i
$339$		0			0
$340$	−12.1513	+	21.0467i	−0.658998	+	1.14142i
$341$	20.1212	−	34.8510i	1.08962	−	1.88729i
$342$		0			0
$343$	15.8128	−	9.64129i	0.853812	−	0.520581i
$344$	−1.31289	+	0.757996i	−0.0707861	+	0.0408684i
$345$		0			0
$346$			3.61296i			0.194234i
$347$	13.0611	−	7.54085i	0.701159	−	0.404814i	−0.106620	−	0.994300i	$-0.534003\pi$
$347$	13.0611	−	7.54085i	0.701159	−	0.404814i	0.807779	+	0.589486i	$0.200670\pi$
$348$		0			0
$349$	9.25253	+	5.34195i	0.495277	+	0.285948i	0.726761	−	0.686891i	$-0.241025\pi$
$349$	9.25253	+	5.34195i	0.495277	+	0.285948i	−0.231484	+	0.972839i	$0.574358\pi$
$350$	−1.01744	−	5.51265i	−0.0543843	−	0.294663i
$351$		0			0
$352$	−14.5444			−0.775219
$353$	3.05752	−	5.29579i	0.162736	−	0.281866i	−0.773113	−	0.634268i	$-0.781302\pi$
$353$	3.05752	−	5.29579i	0.162736	−	0.281866i	0.935849	+	0.352402i	$0.114635\pi$
$354$		0			0
$355$	7.60284	−	4.38950i	0.403517	−	0.232971i
$356$	−13.9190			−0.737704
$357$		0			0
$358$	−0.482678	−	0.836023i	−0.0255103	−	0.0441852i
$359$			25.7292i			1.35794i	0.734167	+	0.678968i	$0.237573\pi$
$359$			25.7292i			1.35794i	−0.734167	+	0.678968i	$0.762427\pi$
$360$		0			0
$361$	−2.83909	+	4.91744i	−0.149426	+	0.258813i
$362$	−2.23604	+	3.87294i	−0.117524	+	0.203557i
$363$		0			0
$364$	−17.2947	+	6.68931i	−0.906491	+	0.350615i
$365$			47.1880i			2.46993i
$366$		0			0
$367$	−1.35265	−	0.780955i	−0.0706080	−	0.0407655i	0.464280	−	0.885688i	$-0.346313\pi$
$367$	−1.35265	−	0.780955i	−0.0706080	−	0.0407655i	−0.534888	+	0.844923i	$0.679646\pi$
$368$	16.0922	−	9.29085i	0.838865	−	0.484319i
$369$		0			0
$370$	−2.75134	+	1.58849i	−0.143036	+	0.0825816i
$371$	12.6297	−	10.7704i	0.655701	−	0.559173i
$372$		0			0
$373$	−4.19480	−	7.26560i	−0.217198	−	0.376199i	0.736752	−	0.676163i	$-0.236359\pi$
$373$	−4.19480	−	7.26560i	−0.217198	−	0.376199i	−0.953950	+	0.299964i	$0.903025\pi$
$374$	2.10736	−	3.65005i	0.108969	−	0.188740i
$375$		0			0
$376$			4.58742i			0.236578i
$377$	0.869600	+	4.60728i	0.0447867	+	0.237287i
$378$		0			0
$379$	−9.68588	+	16.7764i	−0.497530	+	0.861748i	−0.999996	−	0.00284951i	$-0.999093\pi$
$379$	−9.68588	+	16.7764i	−0.497530	+	0.861748i	0.502466	+	0.864597i	$0.332426\pi$
$380$	−22.9434	−	13.2464i	−1.17697	−	0.679524i
$381$		0			0
$382$	−1.09048			−0.0557940
$383$	−8.23263	−	14.2593i	−0.420668	−	0.728618i	0.575337	−	0.817916i	$-0.304871\pi$
$383$	−8.23263	−	14.2593i	−0.420668	−	0.728618i	−0.996005	+	0.0892985i	$0.971537\pi$
$384$		0			0
$385$	−9.52704	−	51.6191i	−0.485543	−	2.63075i
$386$	−4.75713	+	2.74653i	−0.242131	+	0.139795i
$387$		0			0
$388$	−9.70774	−	5.60477i	−0.492836	−	0.284539i
$389$		−	27.8245i		−	1.41076i	−0.708831	−	0.705379i	$-0.750777\pi$
$389$		−	27.8245i		−	1.41076i	0.708831	−	0.705379i	$-0.249223\pi$
$390$		0			0
$391$			16.9691i			0.858164i
$392$	6.45861	+	1.03287i	0.326209	+	0.0521676i
$393$		0			0
$394$	1.90681	+	3.30268i	0.0960635	+	0.166387i
$395$	−25.0887			−1.26235
$396$		0			0
$397$	16.5711	−	9.56730i	0.831678	−	0.480169i	−0.0227491	−	0.999741i	$-0.507242\pi$
$397$	16.5711	−	9.56730i	0.831678	−	0.480169i	0.854427	+	0.519572i	$0.173909\pi$
$398$	−1.49113			−0.0747434
$399$		0			0
$400$	−16.3941	+	28.3955i	−0.819706	+	1.41977i
$401$	−17.6089	−	10.1665i	−0.879346	−	0.507691i	−0.00890358	−	0.999960i	$-0.502834\pi$
$401$	−17.6089	−	10.1665i	−0.879346	−	0.507691i	−0.870443	+	0.492269i	$0.836167\pi$
$402$		0			0
$403$	20.7071	−	17.8037i	1.03149	−	0.886867i
$404$	−6.67970			−0.332328
$405$		0			0
$406$	0.272671	−	0.768169i	0.0135324	−	0.0381236i
$407$	−16.5243	+	9.54028i	−0.819077	+	0.472894i
$408$		0			0
$409$	−16.5900	+	9.57826i	−0.820325	+	0.473615i	−0.850528	−	0.525929i	$-0.823718\pi$
$409$	−16.5900	+	9.57826i	−0.820325	+	0.473615i	0.0302039	+	0.999544i	$0.490384\pi$
$410$	9.07010	−	5.23663i	0.447940	−	0.258618i
$411$		0			0
$412$	28.6249	−	16.5266i	1.41025	−	0.814206i
$413$	0.687342	−	1.93638i	0.0338219	−	0.0952831i
$414$		0			0
$415$	38.2081			1.87556
$416$	−9.31451	−	3.26399i	−0.456681	−	0.160030i
$417$		0			0
$418$	3.97898	+	2.29727i	0.194618	+	0.112363i
$419$	13.1797	−	22.8279i	0.643870	−	1.11522i	−0.340691	−	0.940175i	$-0.610661\pi$
$419$	13.1797	−	22.8279i	0.643870	−	1.11522i	0.984561	−	0.175040i	$-0.0560055\pi$
$420$		0			0
$421$	−4.43205			−0.216005			−0.108002	−	0.994151i	$-0.534445\pi$
$421$	−4.43205			−0.216005			−0.108002	+	0.994151i	$0.534445\pi$
$422$	2.34274	−	1.35258i	0.114043	−	0.0658427i
$423$		0			0
$424$	5.86199			0.284684
$425$	−14.9714	−	25.9312i	−0.726218	−	1.25785i
$426$		0			0
$427$	25.1565	+	8.92960i	1.21741	+	0.432134i
$428$			18.9305i			0.915039i
$429$		0			0
$430$		−	1.43533i		−	0.0692178i
$431$	19.1618	+	11.0631i	0.922990	+	0.532889i	0.884588	−	0.466374i	$-0.154440\pi$
$431$	19.1618	+	11.0631i	0.922990	+	0.532889i	0.0384025	+	0.999262i	$0.487773\pi$
$432$		0			0
$433$	1.67755	−	0.968533i	0.0806179	−	0.0465447i	−0.459149	−	0.888359i	$-0.651846\pi$
$433$	1.67755	−	0.968533i	0.0806179	−	0.0465447i	0.539767	+	0.841814i	$0.318512\pi$
$434$	−4.66879	+	0.861692i	−0.224109	+	0.0413625i
$435$		0			0
$436$	−7.60247	−	13.1679i	−0.364092	−	0.630626i
$437$	−18.4983			−0.884894
$438$		0			0
$439$	14.5380	+	8.39351i	0.693861	+	0.400601i	0.805057	−	0.593198i	$-0.202135\pi$
$439$	14.5380	+	8.39351i	0.693861	+	0.400601i	−0.111196	+	0.993798i	$0.535468\pi$
$440$	9.26893	−	16.0543i	0.441879	−	0.765357i
$441$		0			0
$442$	2.16872	−	1.86464i	0.103155	−	0.0886918i
$443$		−	5.33141i		−	0.253303i	−0.991947	−	0.126651i	$-0.959577\pi$
$443$		−	5.33141i		−	0.253303i	0.991947	−	0.126651i	$-0.0404230\pi$
$444$		0			0
$445$	13.3687	−	23.1552i	0.633736	−	1.09766i
$446$	−2.10964	−	3.65400i	−0.0998941	−	0.173022i
$447$		0			0
$448$	−11.4752	−	13.4561i	−0.542152	−	0.635743i
$449$	33.3699	−	19.2661i	1.57482	−	0.909223i	0.579256	−	0.815145i	$-0.303343\pi$
$449$	33.3699	−	19.2661i	1.57482	−	0.909223i	0.995565	−	0.0940780i	$-0.0299903\pi$
$450$		0			0
$451$	54.4740	−	31.4506i	2.56508	−	1.48095i
$452$	11.6986	+	6.75419i	0.550256	+	0.317691i
$453$		0			0
$454$		−	2.35450i		−	0.110502i
$455$	5.48283	−	35.1959i	0.257039	−	1.65001i
$456$		0			0
$457$	−18.2510	+	31.6117i	−0.853747	+	1.47873i	0.0240549	+	0.999711i	$0.492342\pi$
$457$	−18.2510	+	31.6117i	−0.853747	+	1.47873i	−0.877802	+	0.479023i	$0.840991\pi$
$458$	1.23795	−	2.14419i	0.0578456	−	0.100191i
$459$		0			0
$460$			36.7870i			1.71520i
$461$	−14.8027	−	25.6391i	−0.689433	−	1.19413i	−0.972022	−	0.234891i	$-0.924527\pi$
$461$	−14.8027	−	25.6391i	−0.689433	−	1.19413i	0.282589	−	0.959241i	$-0.408807\pi$
$462$		0			0
$463$	13.3038			0.618278			0.309139	−	0.951017i	$-0.399959\pi$
$463$	13.3038			0.618278			0.309139	+	0.951017i	$0.399959\pi$
$464$	−4.12896	+	2.38385i	−0.191682	+	0.110668i
$465$		0			0
$466$	−0.140269	+	0.242953i	−0.00649783	+	0.0112546i
$467$	−37.2487			−1.72366			−0.861831	−	0.507195i	$-0.830682\pi$
$467$	−37.2487			−1.72366			−0.861831	+	0.507195i	$0.830682\pi$
$468$		0			0
$469$	−15.1569	+	2.79741i	−0.699879	+	0.129173i
$470$	−3.76145	−	2.17167i	−0.173503	−	0.100172i
$471$		0			0
$472$	0.628443	−	0.362832i	0.0289265	−	0.0167007i
$473$		−	8.62043i		−	0.396368i
$474$		0			0
$475$	28.2680	−	16.3205i	1.29703	−	0.748838i
$476$	16.9337	−	3.12535i	0.776153	−	0.143250i
$477$		0			0
$478$	−1.67204	+	2.89606i	−0.0764774	+	0.132463i
$479$	5.24074	−	9.07722i	0.239455	−	0.414749i	−0.721103	−	0.692828i	$-0.756364\pi$
$479$	5.24074	−	9.07722i	0.239455	−	0.414749i	0.960558	+	0.278079i	$0.0896978\pi$
$480$		0			0
$481$	−12.7234	+	2.40148i	−0.580139	+	0.109498i
$482$	2.91558			0.132801
$483$		0			0
$484$	16.7466	−	29.0060i	0.761211	−	1.31846i
$485$	18.6479	−	10.7663i	0.846756	−	0.488875i
$486$		0			0
$487$	−11.0239	−	19.0939i	−0.499540	−	0.865229i	0.500460	−	0.865760i	$-0.333164\pi$
$487$	−11.0239	−	19.0939i	−0.499540	−	0.865229i	−1.00000		0.000531083i	$0.999831\pi$
$488$	4.71373	+	8.16442i	0.213381	+	0.369586i
$489$		0			0
$490$	−3.90438	+	4.80677i	−0.176382	+	0.217148i
$491$	−4.94464	−	2.85479i	−0.223149	−	0.128835i	0.384259	−	0.923225i	$-0.374457\pi$
$491$	−4.94464	−	2.85479i	−0.223149	−	0.128835i	−0.607407	+	0.794391i	$0.707790\pi$
$492$		0			0
$493$		−	4.35394i		−	0.196092i
$494$	2.03267	+	2.36416i	0.0914544	+	0.106369i
$495$		0			0
$496$	24.0488	+	13.8846i	1.07982	+	0.623436i
$497$	−5.86202	−	2.08080i	−0.262948	−	0.0933364i
$498$		0			0
$499$	−39.3760			−1.76271			−0.881355	−	0.472455i	$-0.843368\pi$
$499$	−39.3760			−1.76271			−0.881355	+	0.472455i	$0.843368\pi$
$500$	−14.3100	−	24.7857i	−0.639964	−	1.10845i
$501$		0			0
$502$		−	3.56911i		−	0.159297i
$503$	15.3582	+	26.6012i	0.684789	+	1.18609i	0.973503	+	0.228675i	$0.0734392\pi$
$503$	15.3582	+	26.6012i	0.684789	+	1.18609i	−0.288713	+	0.957416i	$0.593227\pi$
$504$		0			0
$505$	6.41561	−	11.1122i	0.285491	−	0.494485i
$506$		−	6.37983i		−	0.283618i
$507$		0			0
$508$	26.9298			1.19482
$509$	−12.5768	+	21.7837i	−0.557458	+	0.965546i	0.440250	+	0.897875i	$0.354890\pi$
$509$	−12.5768	+	21.7837i	−0.557458	+	0.965546i	−0.997708	+	0.0676703i	$0.978443\pi$
$510$		0			0
$511$	25.4405	−	21.6953i	1.12542	−	0.959743i
$512$		−	16.8879i		−	0.746346i
$513$		0			0
$514$	0.681957	−	0.393728i	0.0300798	−	0.0173666i
$515$			63.4927i			2.79782i
$516$		0			0
$517$	−22.5908	−	13.0428i	−0.993543	−	0.573622i
$518$	2.12137	+	0.753006i	0.0932077	+	0.0330852i
$519$		0			0
$520$	9.53883	−	8.20137i	0.418305	−	0.359654i
$521$	−11.8201			−0.517847			−0.258924	−	0.965898i	$-0.583368\pi$
$521$	−11.8201			−0.517847			−0.258924	+	0.965898i	$0.583368\pi$
$522$		0			0
$523$	−36.5612	−	21.1086i	−1.59871	−	0.923016i	−0.991736	−	0.128294i	$-0.959050\pi$
$523$	−36.5612	−	21.1086i	−1.59871	−	0.923016i	−0.606974	−	0.794722i	$-0.707617\pi$
$524$	−0.804942	−	1.39420i	−0.0351641	−	0.0609060i
$525$		0			0
$526$	−1.85157	−	3.20701i	−0.0807323	−	0.139832i
$527$	−21.9617	+	12.6796i	−0.956668	+	0.552332i
$528$		0			0
$529$	1.34310	+	2.32631i	0.0583955	+	0.101144i
$530$	−2.77505	+	4.80653i	−0.120541	+	0.208782i
$531$		0			0
$532$	3.40700	+	18.4597i	0.147712	+	0.800329i
$533$	41.9442	−	7.91674i	1.81680	−	0.342912i
$534$		0			0
$535$	−31.4922	−	18.1820i	−1.36153	−	0.786078i
$536$	−4.71400	−	2.72163i	−0.203614	−	0.117556i
$537$		0			0
$538$			5.79406i			0.249799i
$539$	−23.4493	+	28.8689i	−1.01003	+	1.24347i
$540$		0			0
$541$	−32.7116			−1.40638			−0.703190	−	0.711002i	$-0.748242\pi$
$541$	−32.7116			−1.40638			−0.703190	+	0.711002i	$0.748242\pi$
$542$	3.52892	+	6.11227i	0.151580	+	0.262545i
$543$		0			0
$544$	7.93739	+	4.58265i	0.340313	+	0.196480i
$545$	29.2076			1.25112
$546$		0			0
$547$	5.56980			0.238148			0.119074	−	0.992885i	$-0.462007\pi$
$547$	5.56980			0.238148			0.119074	+	0.992885i	$0.462007\pi$
$548$	21.1582	+	12.2157i	0.903834	+	0.521829i
$549$		0			0
$550$	5.62875	+	9.74928i	0.240011	+	0.415711i
$551$	4.74631			0.202200
$552$		0			0
$553$	11.5348	+	13.5261i	0.490512	+	0.575187i
$554$			2.44240i			0.103768i
$555$		0			0
$556$	−10.7723	−	6.21938i	−0.456846	−	0.263760i
$557$	23.6321	+	13.6440i	1.00133	+	0.578115i	0.908640	−	0.417580i	$-0.137122\pi$
$557$	23.6321	+	13.6440i	1.00133	+	0.578115i	0.0926851	+	0.995695i	$0.470455\pi$
$558$		0			0
$559$	1.93456	−	5.52069i	0.0818231	−	0.233500i
$560$	35.6196	−	6.57410i	1.50520	−	0.277806i
$561$		0			0
$562$	2.51468	−	4.35555i	0.106075	−	0.183728i
$563$	−1.33723	−	2.31614i	−0.0563574	−	0.0976138i	0.836470	−	0.548012i	$-0.184615\pi$
$563$	−1.33723	−	2.31614i	−0.0563574	−	0.0976138i	−0.892828	+	0.450398i	$0.851282\pi$
$564$		0			0
$565$	−22.4722	+	12.9743i	−0.945412	+	0.545834i
$566$	−3.71886	−	6.44125i	−0.156315	−	0.270746i
$567$		0			0
$568$	−1.09840	−	1.90249i	−0.0460880	−	0.0798268i
$569$	−5.07309	−	2.92895i	−0.212675	−	0.122788i	0.389879	−	0.920866i	$-0.372517\pi$
$569$	−5.07309	−	2.92895i	−0.212675	−	0.122788i	−0.602554	+	0.798078i	$0.705850\pi$
$570$		0			0
$571$	34.9136			1.46109			0.730545	−	0.682865i	$-0.239266\pi$
$571$	34.9136			1.46109			0.730545	+	0.682865i	$0.239266\pi$
$572$	28.2369	−	24.2777i	1.18064	−	1.01510i
$573$		0			0
$574$	−6.99333	−	2.48236i	−0.291896	−	0.103612i
$575$	−39.2521	−	22.6622i	−1.63693	−	0.945080i
$576$		0			0
$577$			29.5000i			1.22810i	0.789266	+	0.614052i	$0.210461\pi$
$577$			29.5000i			1.22810i	−0.789266	+	0.614052i	$0.789539\pi$
$578$	1.18792	−	0.685848i	0.0494111	−	0.0285275i
$579$		0			0
$580$		−	9.43885i		−	0.391927i
$581$	−17.5667	−	20.5992i	−0.728790	−	0.854599i
$582$		0			0
$583$	−16.6666	+	28.8675i	−0.690261	+	1.19557i
$584$	11.8080			0.488620
$585$		0			0
$586$			5.82634i			0.240684i
$587$	2.65922	−	4.60591i	0.109758	−	0.190106i	−0.805914	−	0.592032i	$-0.798326\pi$
$587$	2.65922	−	4.60591i	0.109758	−	0.190106i	0.915672	+	0.401926i	$0.131659\pi$
$588$		0			0
$589$	−13.8223	−	23.9408i	−0.569536	−	0.986465i
$590$			0.687054i			0.0282856i
$591$		0			0
$592$	−6.58324	−	11.4025i	−0.270569	−	0.468640i
$593$	32.1571			1.32053			0.660266	−	0.751032i	$-0.270444\pi$
$593$	32.1571			1.32053			0.660266	+	0.751032i	$0.270444\pi$
$594$		0			0
$595$	−11.0649	+	31.1722i	−0.453618	+	1.27793i
$596$	30.8976	+	17.8387i	1.26561	+	0.730702i
$597$		0			0
$598$	1.43173	−	4.08577i	0.0585479	−	0.167080i
$599$		−	33.4659i		−	1.36738i	−0.729773	−	0.683689i	$-0.760374\pi$
$599$		−	33.4659i		−	1.36738i	0.729773	−	0.683689i	$-0.239626\pi$
$600$		0			0
$601$	−7.01358	−	4.04929i	−0.286090	−	0.165174i	0.350087	−	0.936717i	$-0.386152\pi$
$601$	−7.01358	−	4.04929i	−0.286090	−	0.165174i	−0.636177	+	0.771543i	$0.719485\pi$
$602$	−0.773832	+	0.659913i	−0.0315390	+	0.0268960i
$603$		0			0
$604$	15.1535	+	26.2467i	0.616589	+	1.06796i
$605$	32.1691	+	55.7185i	1.30786	+	2.26528i
$606$		0			0
$607$	−10.9603	+	6.32792i	−0.444864	+	0.256842i	−0.705659	−	0.708552i	$-0.749349\pi$
$607$	−10.9603	+	6.32792i	−0.444864	+	0.256842i	0.260795	+	0.965394i	$0.416015\pi$
$608$	−4.99563	+	8.65268i	−0.202600	+	0.350913i
$609$		0			0
$610$	−8.92586			−0.361398
$611$	−11.5406	−	13.4226i	−0.466882	−	0.543020i
$612$		0			0
$613$	−6.25250	+	10.8297i	−0.252536	+	0.437406i	−0.964223	−	0.265091i	$-0.914598\pi$
$613$	−6.25250	+	10.8297i	−0.252536	+	0.437406i	0.711687	+	0.702496i	$0.247931\pi$
$614$	−2.04558	+	3.54305i	−0.0825529	+	0.142986i
$615$		0			0
$616$	−12.9169	+	2.38399i	−0.520435	+	0.0960537i
$617$	−6.83245	+	3.94472i	−0.275064	+	0.158808i	−0.631187	−	0.775631i	$-0.717432\pi$
$617$	−6.83245	+	3.94472i	−0.275064	+	0.158808i	0.356123	+	0.934439i	$0.384099\pi$
$618$		0			0
$619$			44.1584i			1.77488i	0.460926	+	0.887439i	$0.347517\pi$
$619$			44.1584i			1.77488i	−0.460926	+	0.887439i	$0.652483\pi$
$620$	−47.6105	+	27.4879i	−1.91208	+	1.10394i
$621$		0			0
$622$	2.79302	+	1.61255i	0.111990	+	0.0646574i
$623$	−18.6301	+	3.43845i	−0.746400	+	0.137759i
$624$		0			0
$625$	10.2621			0.410484
$626$	0.255894	−	0.443222i	0.0102276	−	0.0177147i
$627$		0			0
$628$	−0.190769	+	0.110141i	−0.00761253	+	0.00439510i
$629$	12.0238			0.479422
$630$		0			0
$631$	11.9427	+	20.6853i	0.475430	+	0.823468i	0.999604	−	0.0281428i	$-0.00895931\pi$
$631$	11.9427	+	20.6853i	0.475430	+	0.823468i	−0.524174	+	0.851611i	$0.675626\pi$
$632$			6.27804i			0.249727i
$633$		0			0
$634$	2.74256	−	4.75026i	0.108921	−	0.188657i
$635$	−25.8651	+	44.7997i	−1.02643	+	1.77782i
$636$		0			0
$637$	−21.4960	+	13.2258i	−0.851702	+	0.524026i
$638$			1.63694i			0.0648072i
$639$		0			0
$640$	22.8253	+	13.1782i	0.902248	+	0.520913i
$641$	−9.89314	+	5.71181i	−0.390756	+	0.225603i	−0.682487	−	0.730897i	$-0.739102\pi$
$641$	−9.89314	+	5.71181i	−0.390756	+	0.225603i	0.291732	+	0.956500i	$0.405769\pi$
$642$		0			0
$643$	−11.8125	+	6.81995i	−0.465839	+	0.268952i	−0.714496	−	0.699639i	$-0.753344\pi$
$643$	−11.8125	+	6.81995i	−0.465839	+	0.268952i	0.248657	+	0.968592i	$0.420011\pi$
$644$	19.8330	−	16.9133i	0.781531	−	0.666478i
$645$		0			0
$646$	−1.44765	−	2.50740i	−0.0569569	−	0.0986523i
$647$	12.8335	−	22.2282i	0.504536	−	0.873883i	−0.495450	−	0.868636i	$-0.664997\pi$
$647$	12.8335	−	22.2282i	0.504536	−	0.873883i	0.999986	−	0.00524602i	$-0.00166987\pi$
$648$		0			0
$649$			4.12637i			0.161974i
$650$	1.41687	+	7.50681i	0.0555742	+	0.294441i
$651$		0			0
$652$	10.3744	−	17.9690i	0.406292	−	0.703719i
$653$	−39.7426	−	22.9454i	−1.55525	−	0.897923i	−0.997700	−	0.0677791i	$-0.978409\pi$
$653$	−39.7426	−	22.9454i	−1.55525	−	0.897923i	−0.557549	−	0.830144i	$-0.688258\pi$
$654$		0			0
$655$	3.09247			0.120833
$656$	21.7024	+	37.5896i	0.847335	+	1.46763i
$657$		0			0
$658$	0.558559	+	3.02637i	0.0217749	+	0.117980i
$659$	−17.0112	+	9.82140i	−0.662661	+	0.382587i	−0.793290	−	0.608844i	$-0.791634\pi$
$659$	−17.0112	+	9.82140i	−0.662661	+	0.382587i	0.130629	+	0.991431i	$0.458300\pi$
$660$		0			0
$661$	−28.4719	−	16.4382i	−1.10743	−	0.639373i	−0.169265	−	0.985571i	$-0.554139\pi$
$661$	−28.4719	−	16.4382i	−1.10743	−	0.639373i	−0.938162	+	0.346197i	$0.887473\pi$
$662$			3.95406i			0.153679i
$663$		0			0
$664$		−	9.56099i		−	0.371038i
$665$	−33.9813	−	12.0621i	−1.31774	−	0.467747i
$666$		0			0
$667$	−3.29529	−	5.70762i	−0.127594	−	0.221000i
$668$	−20.2632			−0.784006
$669$		0			0
$670$	4.46318	−	2.57682i	0.172428	−	0.0995513i
$671$	−53.6077			−2.06950
$672$		0			0
$673$	9.58017	−	16.5933i	0.369288	−	0.639626i	−0.620166	−	0.784470i	$-0.712935\pi$
$673$	9.58017	−	16.5933i	0.369288	−	0.639626i	0.989454	+	0.144844i	$0.0462682\pi$
$674$	0.146370	+	0.0845068i	0.00563796	+	0.00325508i
$675$		0			0
$676$	23.5317	−	9.21113i	0.905067	−	0.354274i
$677$	8.43326			0.324117			0.162058	−	0.986781i	$-0.448187\pi$
$677$	8.43326			0.324117			0.162058	+	0.986781i	$0.448187\pi$
$678$		0			0
$679$	−14.3781	−	5.10367i	−0.551780	−	0.195861i
$680$	−10.1168	+	5.84092i	−0.387960	+	0.223989i
$681$		0			0
$682$	8.25690	−	4.76712i	0.316173	−	0.182543i
$683$	−12.2459	+	7.07017i	−0.468576	+	0.270533i	−0.715643	−	0.698466i	$-0.753866\pi$
$683$	−12.2459	+	7.07017i	−0.468576	+	0.270533i	0.247067	+	0.968998i	$0.420533\pi$
$684$		0			0
$685$	−40.6434	+	23.4655i	−1.55290	+	0.896570i
$686$	4.38657	−	0.105001i	0.167480	−	0.00400896i
$687$		0			0
$688$	5.94850			0.226784
$689$	−17.1519	+	14.7470i	−0.653437	+	0.561817i
$690$		0			0
$691$	−7.18340	−	4.14734i	−0.273269	−	0.157772i	0.357103	−	0.934065i	$-0.383765\pi$
$691$	−7.18340	−	4.14734i	−0.273269	−	0.157772i	−0.630373	+	0.776293i	$0.717098\pi$
$692$	14.8217	−	25.6719i	0.563437	−	0.975901i
$693$		0			0
$694$	3.57316			0.135635
$695$	20.6928	−	11.9470i	0.784921	−	0.453174i
$696$		0			0
$697$	−39.6378			−1.50139
$698$	1.26562	+	2.19211i	0.0479043	+	0.0829727i
$699$		0			0
$700$	−15.3855	+	43.3441i	−0.581517	+	1.63825i
$701$		−	16.7368i		−	0.632139i	−0.948736	−	0.316070i	$-0.897637\pi$
$701$		−	16.7368i		−	0.632139i	0.948736	−	0.316070i	$-0.102363\pi$
$702$		0			0
$703$			13.1074i			0.494354i
$704$	30.7564	+	17.7572i	1.15918	+	0.669251i
$705$		0			0
$706$	1.25468	−	0.724390i	0.0472205	−	0.0272628i
$707$	−8.94057	+	1.65011i	−0.336245	+	0.0620588i
$708$		0			0
$709$	−14.8272	−	25.6814i	−0.556846	−	0.964486i	−0.997757	−	0.0669351i	$-0.978678\pi$
$709$	−14.8272	−	25.6814i	−0.556846	−	0.964486i	0.440911	−	0.897551i	$-0.354655\pi$
$710$	2.07992			0.0780582
$711$		0			0
$712$	−5.79423	−	3.34530i	−0.217148	−	0.125370i
$713$	−19.1932	+	33.2436i	−0.718790	+	1.24498i
$714$		0			0
$715$	13.2672	+	70.2919i	0.496166	+	2.62877i
$716$			7.92049i			0.296003i
$717$		0			0
$718$	−3.04789	+	5.27910i	−0.113746	+	0.197014i
$719$	12.7362	+	22.0598i	0.474981	+	0.822692i	0.999589	−	0.0286522i	$-0.00912151\pi$
$719$	12.7362	+	22.0598i	0.474981	+	0.822692i	−0.524608	+	0.851344i	$0.675788\pi$
$720$		0			0
$721$	34.2309	−	29.1916i	1.27483	−	1.08715i
$722$	−1.16504	+	0.672637i	−0.0433584	+	0.0250330i
$723$		0			0
$724$	31.7764	−	18.3461i	1.18096	−	0.681828i
$725$	10.0713	+	5.81469i	0.374040	+	0.215952i
$726$		0			0
$727$		−	44.9794i		−	1.66819i	−0.551618	−	0.834097i	$-0.685989\pi$
$727$		−	44.9794i		−	1.66819i	0.551618	−	0.834097i	$-0.314011\pi$
$728$	−8.80722	−	1.37199i	−0.326417	−	0.0508494i
$729$		0			0
$730$	−5.58989	+	9.68198i	−0.206891	+	0.358346i
$731$	−2.71613	+	4.70448i	−0.100460	+	0.174001i
$732$		0			0
$733$		−	43.3731i		−	1.60202i	−0.598650	−	0.801011i	$-0.704296\pi$
$733$		−	43.3731i		−	1.60202i	0.598650	−	0.801011i	$-0.295704\pi$
$734$	−0.185024	−	0.320471i	−0.00682937	−	0.0118288i
$735$		0			0
$736$	13.8736			0.511387
$737$	26.8054	−	15.4761i	0.987388	−	0.570069i
$738$		0			0
$739$	23.7272	−	41.0967i	0.872818	−	1.51176i	0.0137485	−	0.999905i	$-0.495624\pi$
$739$	23.7272	−	41.0967i	0.872818	−	1.51176i	0.859069	−	0.511859i	$-0.171043\pi$
$740$	26.0663			0.958215
$741$		0			0
$742$	3.86721	−	0.713750i	0.141970	−	0.0262026i
$743$	16.1095	+	9.30080i	0.590999	+	0.341213i	0.765492	−	0.643445i	$-0.222496\pi$
$743$	16.1095	+	9.30080i	0.590999	+	0.341213i	−0.174494	+	0.984658i	$0.555829\pi$
$744$		0			0
$745$	−59.3520	+	34.2669i	−2.17449	+	1.25544i
$746$		−	1.98766i		−	0.0727736i
$747$		0			0
$748$	−29.9477	+	17.2903i	−1.09500	+	0.632196i
$749$	4.67646	+	25.3379i	0.170874	+	0.925825i
$750$		0			0
$751$	1.37722	−	2.38541i	0.0502555	−	0.0870450i	−0.839803	−	0.542891i	$-0.817330\pi$
$751$	1.37722	−	2.38541i	0.0502555	−	0.0870450i	0.890059	+	0.455846i	$0.150663\pi$
$752$	9.00015	−	15.5887i	0.328202	−	0.568462i
$753$		0			0
$754$	−0.367356	+	1.04833i	−0.0133783	+	0.0381779i
$755$	−58.2177			−2.11876
$756$		0			0
$757$	16.4090	−	28.4213i	0.596396	−	1.03299i	−0.396952	−	0.917839i	$-0.629932\pi$
$757$	16.4090	−	28.4213i	0.596396	−	1.03299i	0.993348	−	0.115149i	$-0.0367346\pi$
$758$	−3.97468	+	2.29478i	−0.144367	+	0.0833502i
$759$		0			0
$760$	−6.36729	−	11.0285i	−0.230966	−	0.400045i
$761$	−11.2596	−	19.5022i	−0.408159	−	0.706953i	0.586524	−	0.809932i	$-0.300496\pi$
$761$	−11.2596	−	19.5022i	−0.408159	−	0.706953i	−0.994684	+	0.102979i	$0.967163\pi$
$762$		0			0
$763$	−13.4286	−	15.7467i	−0.486147	−	0.570069i
$764$	7.74844	+	4.47356i	0.280329	+	0.161848i
$765$		0			0
$766$		−	3.90095i		−	0.140947i
$767$	−0.926021	+	2.64261i	−0.0334367	+	0.0954190i
$768$		0			0
$769$	19.2783	+	11.1303i	0.695192	+	0.401369i	0.805554	−	0.592522i	$-0.201868\pi$
$769$	19.2783	+	11.1303i	0.695192	+	0.401369i	−0.110362	+	0.993891i	$0.535201\pi$
$770$	4.16006	−	11.7197i	0.149918	−	0.422350i
$771$		0			0
$772$	45.0691			1.62207
$773$	20.4660	+	35.4481i	0.736111	+	1.27498i	0.954234	+	0.299060i	$0.0966730\pi$
$773$	20.4660	+	35.4481i	0.736111	+	1.27498i	−0.218124	+	0.975921i	$0.569994\pi$
$774$		0			0
$775$		−	67.7345i		−	2.43309i
$776$	−2.69411	−	4.66633i	−0.0967129	−	0.167512i
$777$		0			0
$778$	3.29609	−	5.70900i	0.118171	−	0.204678i
$779$		−	43.2099i		−	1.54816i
$780$		0			0
$781$	12.4918			0.446991
$782$	−2.01016	+	3.48170i	−0.0718832	+	0.124505i
$783$		0			0
$784$	−19.9209	−	16.1811i	−0.711460	−	0.577896i
$785$		−	0.423145i		−	0.0151027i
$786$		0			0
$787$	−6.71141	+	3.87483i	−0.239236	+	0.138123i	−0.614825	−	0.788663i	$-0.710774\pi$
$787$	−6.71141	+	3.87483i	−0.239236	+	0.138123i	0.375590	+	0.926786i	$0.377440\pi$
$788$		−	31.2897i		−	1.11465i
$789$		0			0
$790$	−5.14767	−	2.97201i	−0.183146	−	0.105739i
$791$	17.3267	+	6.15033i	0.616068	+	0.218681i
$792$		0			0
$793$	−34.3314	−	12.0304i	−1.21914	−	0.427212i
$794$	4.53338			0.160884
$795$		0			0
$796$	10.5952	+	6.11715i	0.375537	+	0.216817i
$797$	14.2663	+	24.7100i	0.505339	+	0.875273i	0.999981	+	0.00617630i	$0.00196599\pi$
$797$	14.2663	+	24.7100i	0.505339	+	0.875273i	−0.494642	+	0.869097i	$0.664701\pi$
$798$		0			0
$799$	8.21907	+	14.2359i	0.290770	+	0.503628i
$800$	−21.2008	+	12.2403i	−0.749561	+	0.432759i
$801$		0			0
$802$	−2.40865	−	4.17191i	−0.0850524	−	0.147315i
$803$	−33.5722	+	58.1488i	−1.18474	+	2.05203i
$804$		0			0
$805$	9.08763	+	49.2383i	0.320297	+	1.73542i
$806$	6.35770	−	1.19998i	0.223940	−	0.0422675i
$807$		0			0
$808$	−2.78064	−	1.60541i	−0.0978227	−	0.0564780i
$809$	13.3827	+	7.72649i	0.470510	+	0.271649i	0.716453	−	0.697635i	$-0.245764\pi$
$809$	13.3827	+	7.72649i	0.470510	+	0.271649i	−0.245943	+	0.969284i	$0.579098\pi$
$810$		0			0
$811$		−	17.1358i		−	0.601718i	−0.953669	−	0.300859i	$-0.902727\pi$
$811$		−	17.1358i		−	0.601718i	0.953669	−	0.300859i	$-0.0972734\pi$
$812$	−5.08878	+	4.33964i	−0.178581	+	0.152291i
$813$		0			0
$814$	−4.52057			−0.158446
$815$	19.9284	+	34.5171i	0.698063	+	1.20908i
$816$		0			0
$817$	−5.12843	−	2.96090i	−0.179421	−	0.103589i
$818$	−4.53857			−0.158687
$819$		0			0
$820$	−85.9303			−3.00082
$821$	34.0233	+	19.6434i	1.18742	+	0.685558i	0.957720	−	0.287703i	$-0.0928916\pi$
$821$	34.0233	+	19.6434i	1.18742	+	0.685558i	0.229702	+	0.973261i	$0.426225\pi$
$822$		0			0
$823$	−9.69809	−	16.7976i	−0.338054	−	0.585527i	0.646013	−	0.763327i	$-0.276435\pi$
$823$	−9.69809	−	16.7976i	−0.338054	−	0.585527i	−0.984067	+	0.177800i	$0.943102\pi$
$824$	15.8881			0.553487
$825$		0			0
$826$	0.370412	−	0.315882i	0.0128883	−	0.0109910i
$827$		−	15.9406i		−	0.554309i	−0.960825	−	0.277154i	$-0.910609\pi$
$827$		−	15.9406i		−	0.554309i	0.960825	−	0.277154i	$-0.0893913\pi$
$828$		0			0
$829$	−20.2255	−	11.6772i	−0.702462	−	0.405567i	0.105802	−	0.994387i	$-0.466259\pi$
$829$	−20.2255	−	11.6772i	−0.702462	−	0.405567i	−0.808264	+	0.588821i	$0.799592\pi$
$830$	7.83951	+	4.52614i	0.272113	+	0.157105i
$831$		0			0
$832$	15.7120	+	18.2743i	0.544716	+	0.633547i
$833$	21.8931	−	8.36637i	0.758552	−	0.289877i
$834$		0			0
$835$	19.4620	−	33.7092i	0.673512	−	1.16656i
$836$	−18.8485	−	32.6465i	−0.651888	−	1.12910i
$837$		0			0
$838$	5.40839	−	3.12254i	0.186830	−	0.107866i
$839$	−14.2826	−	24.7382i	−0.493090	−	0.854057i	0.506878	−	0.862018i	$-0.330799\pi$
$839$	−14.2826	−	24.7382i	−0.493090	−	0.854057i	−0.999968	+	0.00796087i	$0.997466\pi$
$840$		0			0
$841$	−13.6545	−	23.6503i	−0.470845	−	0.815527i
$842$	−0.909364	−	0.525021i	−0.0313387	−	0.0180934i
$843$		0			0
$844$	−22.1952			−0.763989
$845$	−7.27801	+	47.9937i	−0.250371	+	1.65103i
$846$		0			0
$847$	15.2494	−	42.9607i	0.523976	−	1.47615i
$848$	−19.9199	−	11.5008i	−0.684052	−	0.394937i
$849$		0			0
$850$		−	7.09404i		−	0.243324i
$851$	15.7621	−	9.10027i	0.540319	−	0.311953i
$852$		0			0
$853$			14.0131i			0.479799i	0.970798	+	0.239900i	$0.0771145\pi$
$853$			14.0131i			0.479799i	−0.970798	+	0.239900i	$0.922886\pi$
$854$	4.10378	+	4.81221i	0.140429	+	0.164670i
$855$		0			0
$856$	−4.54977	+	7.88043i	−0.155508	+	0.269348i
$857$	26.5991			0.908608			0.454304	−	0.890847i	$-0.349888\pi$
$857$	26.5991			0.908608			0.454304	+	0.890847i	$0.349888\pi$
$858$		0			0
$859$		−	10.4389i		−	0.356172i	−0.984015	−	0.178086i	$-0.943009\pi$
$859$		−	10.4389i		−	0.356172i	0.984015	−	0.178086i	$-0.0569905\pi$
$860$	−5.88826	+	10.1988i	−0.200788	+	0.347775i
$861$		0			0
$862$	2.62106	+	4.53981i	0.0892737	+	0.154627i
$863$			4.95364i			0.168624i	0.996439	+	0.0843120i	$0.0268692\pi$
$863$			4.95364i			0.168624i	−0.996439	+	0.0843120i	$0.973131\pi$
$864$		0			0
$865$	28.4714	+	49.3139i	0.968057	+	1.67672i
$866$	0.458930			0.0155951
$867$		0			0
$868$	36.7091	+	13.0303i	1.24599	+	0.442279i
$869$	−30.9163	−	17.8495i	−1.04876	−	0.605504i
$870$		0			0
$871$	20.6398	−	3.89564i	0.699351	−	0.131999i
$872$		−	7.30874i		−	0.247505i
$873$		0			0
$874$	−3.79546	−	2.19131i	−0.128383	−	0.0741222i
$875$	−25.2764	−	29.6398i	−0.854499	−	1.00201i
$876$		0			0
$877$	−6.43389	−	11.1438i	−0.217257	−	0.376300i	0.736711	−	0.676207i	$-0.236378\pi$
$877$	−6.43389	−	11.1438i	−0.217257	−	0.376300i	−0.953968	+	0.299907i	$0.903044\pi$
$878$	1.98859	+	3.44435i	0.0671118	+	0.116241i
$879$		0			0
$880$	−62.9943	+	36.3698i	−2.12354	+	1.22602i
$881$	−1.03870	+	1.79908i	−0.0349947	+	0.0606125i	−0.882992	−	0.469387i	$-0.844475\pi$
$881$	−1.03870	+	1.79908i	−0.0349947	+	0.0606125i	0.847998	+	0.530000i	$0.177808\pi$
$882$		0			0
$883$	14.3460			0.482780			0.241390	−	0.970428i	$-0.422397\pi$
$883$	14.3460			0.482780			0.241390	+	0.970428i	$0.422397\pi$
$884$	−23.0593	+	4.35232i	−0.775568	+	0.146384i
$885$		0			0
$886$	0.631559	−	1.09389i	0.0212177	−	0.0367501i
$887$	−11.8707	+	20.5606i	−0.398578	+	0.690357i	−0.993551	−	0.113389i	$-0.963829\pi$
$887$	−11.8707	+	20.5606i	−0.398578	+	0.690357i	0.594973	+	0.803746i	$0.297163\pi$
$888$		0			0
$889$	36.0447	−	6.65257i	1.20890	−	0.223120i
$890$	5.48594	−	3.16731i	0.183889	−	0.106168i
$891$		0			0
$892$			34.6180i			1.15910i
$893$	−15.5187	+	8.95975i	−0.519315	+	0.299827i
$894$		0			0
$895$	−13.1763	−	7.60734i	−0.440435	−	0.254285i
$896$	−3.38946	−	18.3647i	−0.113234	−	0.613520i
$897$		0			0
$898$	9.12906			0.304641
$899$	4.92460	−	8.52966i	0.164245	−	0.284480i
$900$		0			0
$901$	18.1911	−	10.5027i	0.606035	−	0.349894i
$902$	14.9026			0.496201
$903$		0			0
$904$	3.24662	+	5.62331i	0.107981	+	0.187028i
$905$			70.4832i			2.34294i
$906$		0			0
$907$	3.80863	−	6.59674i	0.126463	−	0.219041i	−0.795841	−	0.605506i	$-0.792971\pi$
$907$	3.80863	−	6.59674i	0.126463	−	0.219041i	0.922304	+	0.386465i	$0.126304\pi$
$908$	−9.65904	+	16.7300i	−0.320547	+	0.555203i
$909$		0			0
$910$	5.29427	−	6.57196i	0.175503	−	0.217858i
$911$			55.7887i			1.84836i	0.381953	+	0.924182i	$0.375251\pi$
$911$			55.7887i			1.84836i	−0.381953	+	0.924182i	$0.624749\pi$
$912$		0			0
$913$	47.0832	+	27.1835i	1.55823	+	0.899642i
$914$	−7.48946	+	4.32404i	−0.247729	+	0.143027i
$915$		0			0
$916$	−17.5925	+	10.1571i	−0.581274	+	0.335598i
$917$	−1.42180	−	1.66725i	−0.0469521	−	0.0550574i
$918$		0			0
$919$	5.63161	+	9.75423i	0.185770	+	0.321762i	0.943836	−	0.330415i	$-0.107189\pi$
$919$	5.63161	+	9.75423i	0.185770	+	0.321762i	−0.758066	+	0.652178i	$0.773856\pi$
$920$	−8.84143	+	15.3138i	−0.291493	+	0.504881i
$921$		0			0
$922$		−	7.01414i		−	0.230998i
$923$	7.99998	+	2.80335i	0.263323	+	0.0922734i
$924$		0			0
$925$	−16.0578	+	27.8130i	−0.527978	+	0.914485i
$926$	2.72965	+	1.57597i	0.0897019	+	0.0517894i
$927$		0			0
$928$	−3.55969			−0.116853
$929$	−21.9642	−	38.0431i	−0.720622	−	1.24815i	−0.960751	−	0.277412i	$-0.910523\pi$
$929$	−21.9642	−	38.0431i	−0.720622	−	1.24815i	0.240129	−	0.970741i	$-0.422810\pi$
$930$		0			0
$931$	9.12032	+	23.8661i	0.298906	+	0.782179i
$932$	1.99336	−	1.15087i	0.0652948	−	0.0376980i
$933$		0			0
$934$	−7.64264	−	4.41248i	−0.250075	−	0.144381i
$935$		−	66.4269i		−	2.17239i
$936$		0			0
$937$		−	20.2349i		−	0.661046i	−0.943798	−	0.330523i	$-0.892775\pi$
$937$		−	20.2349i		−	0.661046i	0.943798	−	0.330523i	$-0.107225\pi$
$938$	−3.44125	−	1.22151i	−0.112361	−	0.0398838i
$939$		0			0
$940$	17.8180	+	30.8617i	0.581159	+	1.00660i
$941$	53.1364			1.73220			0.866098	−	0.499874i	$-0.166620\pi$
$941$	53.1364			1.73220			0.866098	+	0.499874i	$0.166620\pi$
$942$		0			0
$943$	−51.9615	+	30.0000i	−1.69210	+	0.976934i
$944$	−2.84739			−0.0926745
$945$		0			0
$946$	1.02118	−	1.76873i	0.0332014	−	0.0575064i
$947$	−18.6465	−	10.7656i	−0.605929	−	0.349834i	0.165441	−	0.986220i	$-0.447095\pi$
$947$	−18.6465	−	10.7656i	−0.605929	−	0.349834i	−0.771371	+	0.636386i	$0.780429\pi$
$948$		0			0
$949$	−34.5498	+	29.7055i	−1.12153	+	0.964282i
$950$	7.73333			0.250902
$951$		0			0
$952$	7.80034	+	2.76882i	0.252811	+	0.0897381i
$953$	−23.1239	+	13.3506i	−0.749056	+	0.432468i	−0.825353	−	0.564618i	$-0.809024\pi$
$953$	−23.1239	+	13.3506i	−0.749056	+	0.432468i	0.0762968	+	0.997085i	$0.475690\pi$
$954$		0			0
$955$	−14.8842	+	8.59339i	−0.481641	+	0.278076i
$956$	23.7614	−	13.7187i	0.768500	−	0.443693i
$957$		0			0
$958$	2.15058	−	1.24164i	0.0694820	−	0.0401155i
$959$	31.3373	+	11.1235i	1.01193	+	0.359198i
$960$		0			0
$961$	−26.3659			−0.850514
$962$	−2.89506	−	1.01449i	−0.0933406	−	0.0327084i
$963$		0			0
$964$	−20.7167	−	11.9608i	−0.667240	−	0.385231i
$965$	−43.2872	+	74.9757i	−1.39347	+	2.41355i
$966$		0			0
$967$	−19.7839			−0.636206			−0.318103	−	0.948056i	$-0.603046\pi$
$967$	−19.7839			−0.636206			−0.318103	+	0.948056i	$0.603046\pi$
$968$	13.9427	−	8.04981i	0.448135	−	0.258731i
$969$		0			0
$970$	5.10153			0.163800
$971$	−9.50019	−	16.4548i	−0.304876	−	0.528060i	0.672358	−	0.740226i	$-0.265282\pi$
$971$	−9.50019	−	16.4548i	−0.304876	−	0.528060i	−0.977234	+	0.212166i	$0.931948\pi$
$972$		0			0
$973$	−15.9548	−	5.66333i	−0.511486	−	0.181558i
$974$		−	5.22356i		−	0.167374i
$975$		0			0
$976$		−	36.9918i		−	1.18408i
$977$	−35.9002	−	20.7270i	−1.14855	−	0.663116i	−0.200017	−	0.979793i	$-0.564100\pi$
$977$	−35.9002	−	20.7270i	−1.14855	−	0.663116i	−0.948533	+	0.316677i	$0.897433\pi$
$978$		0			0
$979$	32.9479	−	19.0225i	1.05302	−	0.607962i
$980$	47.4618	−	18.1373i	1.51611	−	0.579375i
$981$		0			0
$982$	−0.676358	−	1.17149i	−0.0215834	−	0.0373836i
$983$	−37.6865			−1.20201			−0.601006	−	0.799245i	$-0.705233\pi$
$983$	−37.6865			−1.20201			−0.601006	+	0.799245i	$0.705233\pi$
$984$		0			0
$985$	52.0526	+	30.0526i	1.65853	+	0.957556i
$986$	0.515769	−	0.893338i	0.0164254	−	0.0284497i
$987$		0			0
$988$	−4.74454	−	25.1373i	−0.150944	−	0.799725i
$989$			8.22284i			0.261471i
$990$		0			0
$991$	−24.4002	+	42.2623i	−0.775097	+	1.34251i	0.159643	+	0.987175i	$0.448966\pi$
$991$	−24.4002	+	42.2623i	−0.775097	+	1.34251i	−0.934740	+	0.355332i	$0.884368\pi$
$992$	10.3666	+	17.9554i	0.329139	+	0.570086i
$993$		0			0
$994$	−0.956273	−	1.12135i	−0.0303311	−	0.0355671i
$995$	−20.3526	+	11.7506i	−0.645222	+	0.372519i
$996$		0			0
$997$	2.25551	−	1.30222i	0.0714326	−	0.0412416i	−0.463858	−	0.885909i	$-0.653535\pi$
$997$	2.25551	−	1.30222i	0.0714326	−	0.0412416i	0.535291	+	0.844668i	$0.320202\pi$
$998$	−8.07912	−	4.66448i	−0.255740	−	0.147652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.20	yes	72
3.2	odd	2	inner	819.2.dx.a.503.17	✓	72
7.6	odd	2	inner	819.2.dx.a.503.19	yes	72
13.3	even	3	inner	819.2.dx.a.692.18	yes	72
21.20	even	2	inner	819.2.dx.a.503.18	yes	72
39.29	odd	6	inner	819.2.dx.a.692.19	yes	72
91.55	odd	6	inner	819.2.dx.a.692.17	yes	72
273.146	even	6	inner	819.2.dx.a.692.20	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.17	✓	72	3.2	odd	2	inner
819.2.dx.a.503.18	yes	72	21.20	even	2	inner
819.2.dx.a.503.19	yes	72	7.6	odd	2	inner
819.2.dx.a.503.20	yes	72	1.1	even	1	trivial
819.2.dx.a.692.17	yes	72	91.55	odd	6	inner
819.2.dx.a.692.18	yes	72	13.3	even	3	inner
819.2.dx.a.692.19	yes	72	39.29	odd	6	inner
819.2.dx.a.692.20	yes	72	273.146	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.205179 + 0.118460i) q^{2} +(-0.971934 - 1.68344i) q^{4} +3.73403 q^{5} +(-1.71677 - 2.01313i) q^{7} -0.934382i q^{8} +O(q^{10})\)	\(q+(0.205179 + 0.118460i) q^{2} +(-0.971934 - 1.68344i) q^{4} +3.73403 q^{5} +(-1.71677 - 2.01313i) q^{7} -0.934382i q^{8} +(0.766145 + 0.442334i) q^{10} +(4.60138 + 2.65661i) q^{11} +(2.35063 + 2.73396i) q^{13} +(-0.113769 - 0.616421i) q^{14} +(-1.83318 + 3.17516i) q^{16} +(-1.67409 - 2.89961i) q^{17} +(3.16091 - 1.82495i) q^{19} +(-3.62923 - 6.28602i) q^{20} +(0.629404 + 1.09016i) q^{22} +(-4.38915 - 2.53408i) q^{23} +8.94299 q^{25} +(0.158434 + 0.839407i) q^{26} +(-1.72040 + 4.84671i) q^{28} +(1.12617 + 0.650196i) q^{29} -7.57403i q^{31} +(-2.37066 + 1.36870i) q^{32} -0.793252i q^{34} +(-6.41047 - 7.51710i) q^{35} +(-1.79558 + 3.11003i) q^{37} +0.864737 q^{38} -3.48901i q^{40} +(5.91931 - 10.2526i) q^{41} +(-0.811226 - 1.40508i) q^{43} -10.3282i q^{44} +(-0.600374 - 1.03988i) q^{46} -4.90958 q^{47} +(-1.10540 + 6.91217i) q^{49} +(1.83491 + 1.05939i) q^{50} +(2.31781 - 6.61437i) q^{52} +6.27366i q^{53} +(17.1817 + 9.91985i) q^{55} +(-1.88104 + 1.60412i) q^{56} +(0.154045 + 0.266813i) q^{58} +(0.388312 + 0.672576i) q^{59} +(-8.73777 + 5.04475i) q^{61} +(0.897221 - 1.55403i) q^{62} +6.68418 q^{64} +(8.77732 + 10.2087i) q^{65} +(2.91276 - 5.04504i) q^{67} +(-3.25421 + 5.63646i) q^{68} +(-0.424818 - 2.30174i) q^{70} +(2.03610 - 1.17554i) q^{71} +12.6373i q^{73} +(-0.736830 + 0.425409i) q^{74} +(-6.14440 - 3.54747i) q^{76} +(-2.55141 - 13.8240i) q^{77} -6.71892 q^{79} +(-6.84516 + 11.8562i) q^{80} +(2.42904 - 1.40241i) q^{82} +10.2324 q^{83} +(-6.25110 - 10.8272i) q^{85} -0.384392i q^{86} +(2.48229 - 4.29945i) q^{88} +(3.58023 - 6.20113i) q^{89} +(1.46834 - 9.42571i) q^{91} +9.85183i q^{92} +(-1.00734 - 0.581589i) q^{94} +(11.8029 - 6.81443i) q^{95} +(4.99403 - 2.88330i) q^{97} +(-1.04562 + 1.28729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

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