LMFDB - Embedded newform 855.2.k.i.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$0.823305 - 1.42601i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.i.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.823305 - 1.42601i) q^{2} +(-0.355663 + 0.616027i) q^{4} +(0.500000 + 0.866025i) q^{5} +4.47988 q^{7} -2.12194 q^{8} +(0.823305 - 1.42601i) q^{10} +3.44134 q^{11} +(-1.23994 + 2.14764i) q^{13} +(-3.68831 - 6.38834i) q^{14} +(2.45833 + 4.25796i) q^{16} +(3.81400 + 6.60604i) q^{17} +(-3.67522 + 2.34366i) q^{19} -0.711327 q^{20} +(-2.83327 - 4.90737i) q^{22} +(1.93528 - 3.35201i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.08340 q^{26} +(-1.59333 + 2.75973i) q^{28} +(-4.36728 + 7.56435i) q^{29} -0.422654 q^{31} +(1.92598 - 3.33589i) q^{32} +(6.28017 - 10.8776i) q^{34} +(2.23994 + 3.87969i) q^{35} +3.90253 q^{37} +(6.36790 + 3.31135i) q^{38} +(-1.06097 - 1.83766i) q^{40} +(2.64661 + 4.58406i) q^{41} +(-1.23994 - 2.14764i) q^{43} +(-1.22396 + 2.11996i) q^{44} -6.37332 q^{46} +(-0.338665 + 0.586585i) q^{47} +13.0693 q^{49} +1.64661 q^{50} +(-0.882003 - 1.52767i) q^{52} +(5.74928 - 9.95805i) q^{53} +(1.72067 + 2.98028i) q^{55} -9.50605 q^{56} +14.3824 q^{58} +(-4.26526 - 7.38765i) q^{59} +(-4.10117 + 7.10343i) q^{61} +(0.347973 + 0.602707i) q^{62} +3.49067 q^{64} -2.47988 q^{65} +(4.81729 - 8.34379i) q^{67} -5.42600 q^{68} +(3.68831 - 6.38834i) q^{70} +(-1.92594 - 3.33583i) q^{71} +(-8.39260 - 14.5364i) q^{73} +(-3.21298 - 5.56504i) q^{74} +(-0.136613 - 3.09759i) q^{76} +15.4168 q^{77} +(-6.06262 - 10.5008i) q^{79} +(-2.45833 + 4.25796i) q^{80} +(4.35794 - 7.54817i) q^{82} +2.03855 q^{83} +(-3.81400 + 6.60604i) q^{85} +(-2.04170 + 3.53633i) q^{86} -7.30232 q^{88} +(-1.57255 + 2.72374i) q^{89} +(-5.55478 + 9.62117i) q^{91} +(1.37662 + 2.38437i) q^{92} +1.11530 q^{94} +(-3.86728 - 2.01101i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(-10.7600 - 18.6370i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.823305	−	1.42601i	−0.582165	−	1.00834i	−0.995222	−	0.0976341i	$-0.968873\pi$
$2$	−0.823305	−	1.42601i	−0.582165	−	1.00834i	0.413058	−	0.910705i	$-0.364461\pi$
$3$		0			0
$3$		0			0
$4$	−0.355663	+	0.616027i	−0.177832	+	0.308014i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	4.47988			1.69324			0.846618	−	0.532201i	$-0.178635\pi$
$7$	4.47988			1.69324			0.846618	+	0.532201i	$0.178635\pi$
$8$	−2.12194			−0.750220
$9$		0			0
$10$	0.823305	−	1.42601i	0.260352	−	0.450943i
$11$	3.44134			1.03760			0.518801	−	0.854895i	$-0.326379\pi$
$11$	3.44134			1.03760			0.518801	+	0.854895i	$0.326379\pi$
$12$		0			0
$13$	−1.23994	+	2.14764i	−0.343898	+	0.595648i	−0.985153	−	0.171680i	$-0.945081\pi$
$13$	−1.23994	+	2.14764i	−0.343898	+	0.595648i	0.641255	+	0.767328i	$0.278414\pi$
$14$	−3.68831	−	6.38834i	−0.985742	−	1.70736i
$15$		0			0
$16$	2.45833	+	4.25796i	0.614583	+	1.06449i
$17$	3.81400	+	6.60604i	0.925030	+	1.60220i	0.791513	+	0.611153i	$0.209294\pi$
$17$	3.81400	+	6.60604i	0.925030	+	1.60220i	0.133518	+	0.991046i	$0.457373\pi$
$18$		0			0
$19$	−3.67522	+	2.34366i	−0.843154	+	0.537672i
$19$	−3.67522	+	2.34366i	−0.843154	+	0.537672i
$20$	−0.711327			−0.159058
$21$		0			0
$22$	−2.83327	−	4.90737i	−0.604055	−	1.04625i
$23$	1.93528	−	3.35201i	0.403535	−	0.698942i	−0.590615	−	0.806953i	$-0.701115\pi$
$23$	1.93528	−	3.35201i	0.403535	−	0.698942i	0.994150	+	0.108011i	$0.0344482\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.08340			0.800820
$27$		0			0
$28$	−1.59333	+	2.75973i	−0.301111	+	0.521540i
$29$	−4.36728	+	7.56435i	−0.810983	+	1.40466i	0.101193	+	0.994867i	$0.467734\pi$
$29$	−4.36728	+	7.56435i	−0.810983	+	1.40466i	−0.912177	+	0.409797i	$0.865599\pi$
$30$		0			0
$31$	−0.422654			−0.0759108			−0.0379554	−	0.999279i	$-0.512084\pi$
$31$	−0.422654			−0.0759108			−0.0379554	+	0.999279i	$0.512084\pi$
$32$	1.92598	−	3.33589i	0.340468	−	0.589707i
$33$		0			0
$34$	6.28017	−	10.8776i	1.07704	−	1.86549i
$35$	2.23994	+	3.87969i	0.378619	+	0.655787i
$36$		0			0
$37$	3.90253			0.641573			0.320786	−	0.947152i	$-0.396053\pi$
$37$	3.90253			0.641573			0.320786	+	0.947152i	$0.396053\pi$
$38$	6.36790	+	3.31135i	1.03301	+	0.537172i
$39$		0			0
$40$	−1.06097	−	1.83766i	−0.167754	−	0.290559i
$41$	2.64661	+	4.58406i	0.413331	+	0.715911i	0.995252	−	0.0973351i	$-0.0310319\pi$
$41$	2.64661	+	4.58406i	0.413331	+	0.715911i	−0.581921	+	0.813246i	$0.697699\pi$
$42$		0			0
$43$	−1.23994	−	2.14764i	−0.189089	−	0.327512i	0.755858	−	0.654736i	$-0.227220\pi$
$43$	−1.23994	−	2.14764i	−0.189089	−	0.327512i	−0.944947	+	0.327224i	$0.893887\pi$
$44$	−1.22396	+	2.11996i	−0.184518	+	0.319595i
$45$		0			0
$46$	−6.37332			−0.939695
$47$	−0.338665	+	0.586585i	−0.0493994	+	0.0855622i	−0.889668	−	0.456608i	$-0.849064\pi$
$47$	−0.338665	+	0.586585i	−0.0493994	+	0.0855622i	0.840268	+	0.542171i	$0.182397\pi$
$48$		0			0
$49$	13.0693			1.86705
$50$	1.64661			0.232866
$51$		0			0
$52$	−0.882003	−	1.52767i	−0.122312	−	0.211850i
$53$	5.74928	−	9.95805i	0.789725	−	1.36784i	−0.136411	−	0.990652i	$-0.543557\pi$
$53$	5.74928	−	9.95805i	0.789725	−	1.36784i	0.926136	−	0.377191i	$-0.123110\pi$
$54$		0			0
$55$	1.72067	+	2.98028i	0.232015	+	0.401861i
$56$	−9.50605			−1.27030
$57$		0			0
$58$	14.3824			1.88850
$59$	−4.26526	−	7.38765i	−0.555290	−	0.961791i	−0.997881	−	0.0650670i	$-0.979274\pi$
$59$	−4.26526	−	7.38765i	−0.555290	−	0.961791i	0.442591	−	0.896724i	$-0.354059\pi$
$60$		0			0
$61$	−4.10117	+	7.10343i	−0.525101	+	0.909501i	0.474472	+	0.880271i	$0.342639\pi$
$61$	−4.10117	+	7.10343i	−0.525101	+	0.909501i	−0.999573	+	0.0292304i	$0.990694\pi$
$62$	0.347973	+	0.602707i	0.0441926	+	0.0765439i
$63$		0			0
$64$	3.49067			0.436334
$65$	−2.47988			−0.307591
$66$		0			0
$67$	4.81729	−	8.34379i	0.588525	−	1.01936i	−0.405901	−	0.913917i	$-0.633042\pi$
$67$	4.81729	−	8.34379i	0.588525	−	1.01936i	0.994426	−	0.105438i	$-0.0336246\pi$
$68$	−5.42600			−0.657999
$69$		0			0
$70$	3.68831	−	6.38834i	0.440837	−	0.763553i
$71$	−1.92594	−	3.33583i	−0.228567	−	0.395890i	0.728816	−	0.684709i	$-0.240071\pi$
$71$	−1.92594	−	3.33583i	−0.228567	−	0.395890i	−0.957384	+	0.288819i	$0.906737\pi$
$72$		0			0
$73$	−8.39260	−	14.5364i	−0.982280	−	1.70136i	−0.653451	−	0.756969i	$-0.726679\pi$
$73$	−8.39260	−	14.5364i	−0.982280	−	1.70136i	−0.328829	−	0.944389i	$-0.606654\pi$
$74$	−3.21298	−	5.56504i	−0.373501	−	0.646923i
$75$		0			0
$76$	−0.136613	−	3.09759i	−0.0156706	−	0.355318i
$77$	15.4168			1.75690
$78$		0			0
$79$	−6.06262	−	10.5008i	−0.682098	−	1.18143i	−0.974339	−	0.225084i	$-0.927734\pi$
$79$	−6.06262	−	10.5008i	−0.682098	−	1.18143i	0.292241	−	0.956345i	$-0.405599\pi$
$80$	−2.45833	+	4.25796i	−0.274850	+	0.476054i
$81$		0			0
$82$	4.35794	−	7.54817i	0.481254	−	0.833556i
$83$	2.03855			0.223759			0.111880	−	0.993722i	$-0.464313\pi$
$83$	2.03855			0.223759			0.111880	+	0.993722i	$0.464313\pi$
$84$		0			0
$85$	−3.81400	+	6.60604i	−0.413686	+	0.716525i
$86$	−2.04170	+	3.53633i	−0.220162	+	0.381332i
$87$		0			0
$88$	−7.30232			−0.778430
$89$	−1.57255	+	2.72374i	−0.166690	+	0.288716i	−0.937254	−	0.348647i	$-0.886641\pi$
$89$	−1.57255	+	2.72374i	−0.166690	+	0.288716i	0.770564	+	0.637363i	$0.219975\pi$
$90$		0			0
$91$	−5.55478	+	9.62117i	−0.582300	+	1.00857i
$92$	1.37662	+	2.38437i	0.143522	+	0.248588i
$93$		0			0
$94$	1.11530			0.115034
$95$	−3.86728	−	2.01101i	−0.396774	−	0.206325i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−10.7600	−	18.6370i	−1.08693	−	1.88262i
$99$		0			0
$100$	−0.355663	−	0.616027i	−0.0355663	−	0.0616027i
$101$	−1.00934	+	1.74823i	−0.100433	+	0.173955i	−0.911863	−	0.410494i	$-0.865356\pi$
$101$	−1.00934	+	1.74823i	−0.100433	+	0.173955i	0.811430	+	0.584450i	$0.198690\pi$
$102$		0			0
$103$	6.48898			0.639378			0.319689	−	0.947523i	$-0.396422\pi$
$103$	6.48898			0.639378			0.319689	+	0.947523i	$0.396422\pi$
$104$	2.63108	−	4.55717i	0.257999	−	0.446867i
$105$		0			0
$106$	−18.9337			−1.83900
$107$	−3.96145			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$107$	−3.96145			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$108$		0			0
$109$	1.48402	+	2.57039i	0.142143	+	0.246199i	0.928303	−	0.371824i	$-0.121267\pi$
$109$	1.48402	+	2.57039i	0.142143	+	0.246199i	−0.786160	+	0.618023i	$0.787934\pi$
$110$	2.83327	−	4.90737i	0.270142	−	0.467899i
$111$		0			0
$112$	11.0130	+	19.0751i	1.04063	+	1.80243i
$113$	8.71719			0.820044			0.410022	−	0.912076i	$-0.365521\pi$
$113$	8.71719			0.820044			0.410022	+	0.912076i	$0.365521\pi$
$114$		0			0
$115$	3.87057			0.360932
$116$	−3.10656	−	5.38072i	−0.288437	−	0.499588i
$117$		0			0
$118$	−7.02323	+	12.1646i	−0.646541	+	1.11984i
$119$	17.0863	+	29.5943i	1.56629	+	2.71290i
$120$		0			0
$121$	0.842790			0.0766172
$122$	13.5061			1.22278
$123$		0			0
$124$	0.150322	−	0.260366i	0.0134994	−	0.0233816i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.28867	−	3.96410i	0.203087	−	0.351757i	−0.746435	−	0.665459i	$-0.768236\pi$
$127$	2.28867	−	3.96410i	0.203087	−	0.351757i	0.949522	+	0.313702i	$0.101569\pi$
$128$	−6.72584	−	11.6495i	−0.594486	−	1.02968i
$129$		0			0
$130$	2.04170	+	3.53633i	0.179069	+	0.310156i
$131$	−10.3364	−	17.9031i	−0.903094	−	1.56420i	−0.823456	−	0.567380i	$-0.807957\pi$
$131$	−10.3364	−	17.9031i	−0.903094	−	1.56420i	−0.0796380	−	0.996824i	$-0.525376\pi$
$132$		0			0
$133$	−16.4646	+	10.4993i	−1.42766	+	0.910405i
$134$	−15.8644			−1.37047
$135$		0			0
$136$	−8.09309	−	14.0176i	−0.693976	−	1.20200i
$137$	8.81400	−	15.2663i	0.753031	−	1.30429i	−0.193317	−	0.981136i	$-0.561925\pi$
$137$	8.81400	−	15.2663i	0.753031	−	1.30429i	0.946347	−	0.323151i	$-0.104742\pi$
$138$		0			0
$139$	−5.86728	+	10.1624i	−0.497656	+	0.861966i	−0.999996	−	0.00270444i	$-0.999139\pi$
$139$	−5.86728	+	10.1624i	−0.497656	+	0.861966i	0.502340	+	0.864670i	$0.332472\pi$
$140$	−3.18666			−0.269322
$141$		0			0
$142$	−3.17128	+	5.49282i	−0.266128	+	0.460947i
$143$	−4.26705	+	7.39075i	−0.356829	+	0.618045i
$144$		0			0
$145$	−8.73456			−0.725365
$146$	−13.8193	+	23.9358i	−1.14370	+	1.98094i
$147$		0			0
$148$	−1.38799	+	2.40407i	−0.114092	+	0.197613i
$149$	−10.7824	−	18.6757i	−0.883332	−	1.52998i	−0.847613	−	0.530614i	$-0.821961\pi$
$149$	−10.7824	−	18.6757i	−0.883332	−	1.52998i	−0.0357187	−	0.999362i	$-0.511372\pi$
$150$		0			0
$151$	18.3102			1.49006			0.745032	−	0.667029i	$-0.232434\pi$
$151$	18.3102			1.49006			0.745032	+	0.667029i	$0.232434\pi$
$152$	7.79862	−	4.97311i	0.632551	−	0.403372i
$153$		0			0
$154$	−12.6927	−	21.9844i	−1.02281	−	1.77156i
$155$	−0.211327	−	0.366029i	−0.0169742	−	0.0294001i
$156$		0			0
$157$	5.71527	+	9.89914i	0.456128	+	0.790038i	0.998752	−	0.0499382i	$-0.0159024\pi$
$157$	5.71527	+	9.89914i	0.456128	+	0.790038i	−0.542624	+	0.839976i	$0.682569\pi$
$158$	−9.98278	+	17.2907i	−0.794187	+	1.37557i
$159$		0			0
$160$	3.85195			0.304524
$161$	8.66984	−	15.0166i	0.683279	−	1.18347i
$162$		0			0
$163$	−8.19876			−0.642177			−0.321088	−	0.947049i	$-0.604049\pi$
$163$	−8.19876			−0.642177			−0.321088	+	0.947049i	$0.604049\pi$
$164$	−3.76521			−0.294014
$165$		0			0
$166$	−1.67835	−	2.90698i	−0.130265	−	0.225625i
$167$	−4.42206	+	7.65924i	−0.342189	+	0.592690i	−0.984839	−	0.173471i	$-0.944502\pi$
$167$	−4.42206	+	7.65924i	−0.342189	+	0.592690i	0.642650	+	0.766160i	$0.277835\pi$
$168$		0			0
$169$	3.42510	+	5.93244i	0.263469	+	0.456342i
$170$	12.5603			0.963334
$171$		0			0
$172$	1.76401			0.134504
$173$	8.77310	+	15.1955i	0.667007	+	1.15529i	0.978737	+	0.205119i	$0.0657581\pi$
$173$	8.77310	+	15.1955i	0.667007	+	1.15529i	−0.311731	+	0.950171i	$0.600909\pi$
$174$		0			0
$175$	−2.23994	+	3.87969i	−0.169324	+	0.293277i
$176$	8.45995	+	14.6531i	0.637693	+	1.10452i
$177$		0			0
$178$	5.17877			0.388165
$179$	−4.30890			−0.322062			−0.161031	−	0.986949i	$-0.551482\pi$
$179$	−4.30890			−0.322062			−0.161031	+	0.986949i	$0.551482\pi$
$180$		0			0
$181$	−3.17193	+	5.49395i	−0.235768	+	0.408362i	−0.959496	−	0.281724i	$-0.909094\pi$
$181$	−3.17193	+	5.49395i	−0.235768	+	0.408362i	0.723728	+	0.690086i	$0.242427\pi$
$182$	18.2931			1.35598
$183$		0			0
$184$	−4.10656	+	7.11277i	−0.302740	+	0.524361i
$185$	1.95127	+	3.37969i	0.143460	+	0.248480i
$186$		0			0
$187$	13.1252	+	22.7336i	0.959813	+	1.66244i
$188$	−0.240901	−	0.417254i	−0.0175695	−	0.0304313i
$189$		0			0
$190$	0.316239	+	7.17044i	0.0229424	+	0.520198i
$191$	−0.845796			−0.0611997			−0.0305998	−	0.999532i	$-0.509742\pi$
$191$	−0.845796			−0.0611997			−0.0305998	+	0.999532i	$0.509742\pi$
$192$		0			0
$193$	6.59039	+	11.4149i	0.474387	+	0.821662i	0.999570	−	0.0293275i	$-0.00933658\pi$
$193$	6.59039	+	11.4149i	0.474387	+	0.821662i	−0.525183	+	0.850989i	$0.676003\pi$
$194$	−1.64661	+	2.85201i	−0.118220	+	0.204763i
$195$		0			0
$196$	−4.64828	+	8.05106i	−0.332020	+	0.575076i
$197$	−6.91212			−0.492468			−0.246234	−	0.969210i	$-0.579193\pi$
$197$	−6.91212			−0.492468			−0.246234	+	0.969210i	$0.579193\pi$
$198$		0			0
$199$	6.69062	−	11.5885i	0.474285	−	0.821486i	−0.525281	−	0.850929i	$-0.676040\pi$
$199$	6.69062	−	11.5885i	0.474285	−	0.821486i	0.999566	+	0.0294426i	$0.00937321\pi$
$200$	1.06097	−	1.83766i	0.0750220	−	0.129942i
$201$		0			0
$202$	3.32398			0.233875
$203$	−19.5649	+	33.8874i	−1.37319	+	2.37843i
$204$		0			0
$205$	−2.64661	+	4.58406i	−0.184847	+	0.320165i
$206$	−5.34241	−	9.25332i	−0.372223	−	0.644710i
$207$		0			0
$208$	−12.1927			−0.845415
$209$	−12.6477	+	8.06531i	−0.874858	+	0.557889i
$210$		0			0
$211$	7.37512	+	12.7741i	0.507724	+	0.879404i	0.999960	+	0.00894190i	$0.00284633\pi$
$211$	7.37512	+	12.7741i	0.507724	+	0.879404i	−0.492236	+	0.870462i	$0.663820\pi$
$212$	4.08962	+	7.08343i	0.280876	+	0.486492i
$213$		0			0
$214$	3.26149	+	5.64906i	0.222951	+	0.386162i
$215$	1.23994	−	2.14764i	0.0845632	−	0.146468i
$216$		0			0
$217$	−1.89344			−0.128535
$218$	2.44360	−	4.23244i	0.165501	−	0.286657i
$219$		0			0
$220$	−2.44791			−0.165038
$221$	−18.9165			−1.27246
$222$		0			0
$223$	1.14417	+	1.98176i	0.0766192	+	0.132708i	0.901789	−	0.432176i	$-0.142254\pi$
$223$	1.14417	+	1.98176i	0.0766192	+	0.132708i	−0.825170	+	0.564884i	$0.808921\pi$
$224$	8.62814	−	14.9444i	0.576492	−	0.998513i
$225$		0			0
$226$	−7.17691	−	12.4308i	−0.477401	−	0.826882i
$227$	4.19493			0.278427			0.139214	−	0.990262i	$-0.455543\pi$
$227$	4.19493			0.278427			0.139214	+	0.990262i	$0.455543\pi$
$228$		0			0
$229$	−26.2742			−1.73625			−0.868123	−	0.496348i	$-0.834674\pi$
$229$	−26.2742			−1.73625			−0.868123	+	0.496348i	$0.834674\pi$
$230$	−3.18666	−	5.51946i	−0.210122	−	0.363942i
$231$		0			0
$232$	9.26712	−	16.0511i	0.608416	−	1.05381i
$233$	−2.78125	−	4.81726i	−0.182206	−	0.315589i	0.760426	−	0.649425i	$-0.224990\pi$
$233$	−2.78125	−	4.81726i	−0.182206	−	0.315589i	−0.942631	+	0.333836i	$0.891657\pi$
$234$		0			0
$235$	−0.677330			−0.0441841
$236$	6.06799			0.394993
$237$		0			0
$238$	28.1344	−	48.7302i	1.82368	−	3.15871i
$239$	6.84901			0.443026			0.221513	−	0.975157i	$-0.428901\pi$
$239$	6.84901			0.443026			0.221513	+	0.975157i	$0.428901\pi$
$240$		0			0
$241$	−7.42122	+	12.8539i	−0.478043	+	0.827994i	−0.999683	−	0.0251714i	$-0.991987\pi$
$241$	−7.42122	+	12.8539i	−0.478043	+	0.827994i	0.521641	+	0.853165i	$0.325320\pi$
$242$	−0.693873	−	1.20182i	−0.0446039	−	0.0772561i
$243$		0			0
$244$	−2.91727	−	5.05286i	−0.186759	−	0.323476i
$245$	6.53467	+	11.3184i	0.417484	+	0.723104i
$246$		0			0
$247$	−0.476272	−	10.7991i	−0.0303044	−	0.687127i
$248$	0.896847			0.0569498
$249$		0			0
$250$	0.823305	+	1.42601i	0.0520704	+	0.0901886i
$251$	−2.40128	+	4.15913i	−0.151567	+	0.262522i	−0.931804	−	0.362962i	$-0.881765\pi$
$251$	−2.40128	+	4.15913i	−0.151567	+	0.262522i	0.780237	+	0.625484i	$0.215099\pi$
$252$		0			0
$253$	6.65996	−	11.5354i	0.418708	−	0.725224i
$254$	−7.53711			−0.472920
$255$		0			0
$256$	−7.58417	+	13.1362i	−0.474011	+	0.821010i
$257$	1.74862	−	3.02871i	0.109076	−	0.188926i	−0.806320	−	0.591479i	$-0.798544\pi$
$257$	1.74862	−	3.02871i	0.109076	−	0.188926i	0.915396	+	0.402554i	$0.131877\pi$
$258$		0			0
$259$	17.4829			1.08633
$260$	0.882003	−	1.52767i	0.0546995	−	0.0947423i
$261$		0			0
$262$	−17.0200	+	29.4795i	−1.05150	+	1.82125i
$263$	−2.61621	−	4.53141i	−0.161322	−	0.279419i	0.774021	−	0.633160i	$-0.218243\pi$
$263$	−2.61621	−	4.53141i	−0.161322	−	0.279419i	−0.935343	+	0.353741i	$0.884909\pi$
$264$		0			0
$265$	11.4986			0.706351
$266$	28.5274	+	14.8344i	1.74913	+	0.909558i
$267$		0			0
$268$	3.42667	+	5.93516i	0.209317	+	0.362547i
$269$	−7.94917	−	13.7684i	−0.484670	−	0.839472i	0.515175	−	0.857085i	$-0.327727\pi$
$269$	−7.94917	−	13.7684i	−0.484670	−	0.839472i	−0.999845	+	0.0176124i	$0.994393\pi$
$270$		0			0
$271$	−4.99789	−	8.65661i	−0.303600	−	0.525851i	0.673348	−	0.739325i	$-0.264855\pi$
$271$	−4.99789	−	8.65661i	−0.303600	−	0.525851i	−0.976949	+	0.213474i	$0.931522\pi$
$272$	−18.7522	+	32.4797i	−1.13702	+	1.96937i
$273$		0			0
$274$	−29.0264			−1.75355
$275$	−1.72067	+	2.98028i	−0.103760	+	0.179718i
$276$		0			0
$277$	4.08619			0.245515			0.122758	−	0.992437i	$-0.460826\pi$
$277$	4.08619			0.245515			0.122758	+	0.992437i	$0.460826\pi$
$278$	19.3222			1.15887
$279$		0			0
$280$	−4.75303	−	8.23248i	−0.284048	−	0.491985i
$281$	−5.81920	+	10.0792i	−0.347144	+	0.601272i	−0.985741	−	0.168270i	$-0.946182\pi$
$281$	−5.81920	+	10.0792i	−0.347144	+	0.601272i	0.638596	+	0.769542i	$0.279515\pi$
$282$		0			0
$283$	−2.17910	−	3.77432i	−0.129534	−	0.224360i	0.793962	−	0.607967i	$-0.208015\pi$
$283$	−2.17910	−	3.77432i	−0.129534	−	0.224360i	−0.923496	+	0.383607i	$0.874682\pi$
$284$	2.73995			0.162586
$285$		0			0
$286$	14.0523			0.830932
$287$	11.8565	+	20.5361i	0.699867	+	1.21221i
$288$		0			0
$289$	−20.5932	+	35.6684i	−1.21136	+	2.09814i
$290$	7.19121	+	12.4555i	0.422282	+	0.731414i
$291$		0			0
$292$	11.9398			0.698722
$293$	7.20233			0.420765			0.210382	−	0.977619i	$-0.432529\pi$
$293$	7.20233			0.420765			0.210382	+	0.977619i	$0.432529\pi$
$294$		0			0
$295$	4.26526	−	7.38765i	0.248333	−	0.430126i
$296$	−8.28096			−0.481321
$297$		0			0
$298$	−17.7545	+	30.7517i	−1.02849	+	1.78140i
$299$	4.79927	+	8.31258i	0.277549	+	0.480729i
$300$		0			0
$301$	−5.55478	−	9.62117i	−0.320172	−	0.554555i
$302$	−15.0749	−	26.1105i	−0.867463	−	1.50249i
$303$		0			0
$304$	−19.0141	−	9.88746i	−1.09053	−	0.567085i
$305$	−8.20233			−0.469664
$306$		0			0
$307$	−8.14056	−	14.0999i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$307$	−8.14056	−	14.0999i	−0.464606	−	0.804722i	−0.999184	+	0.0403979i	$0.987137\pi$
$308$	−5.48318	+	9.49715i	−0.312433	+	0.541150i
$309$		0			0
$310$	−0.347973	+	0.602707i	−0.0197635	+	0.0342315i
$311$	4.07709			0.231191			0.115595	−	0.993296i	$-0.463122\pi$
$311$	4.07709			0.231191			0.115595	+	0.993296i	$0.463122\pi$
$312$		0			0
$313$	10.7777	−	18.6674i	0.609189	−	1.05515i	−0.382186	−	0.924086i	$-0.624828\pi$
$313$	10.7777	−	18.6674i	0.609189	−	1.05515i	0.991374	−	0.131060i	$-0.0418382\pi$
$314$	9.41083	−	16.3000i	0.531084	−	0.919864i
$315$		0			0
$316$	8.62501			0.485195
$317$	−7.13339	+	12.3554i	−0.400651	+	0.693948i	−0.993805	−	0.111141i	$-0.964549\pi$
$317$	−7.13339	+	12.3554i	−0.400651	+	0.693948i	0.593154	+	0.805089i	$0.297883\pi$
$318$		0			0
$319$	−15.0293	+	26.0315i	−0.841478	+	1.45748i
$320$	1.74534	+	3.02301i	0.0975672	+	0.168991i
$321$		0			0
$322$	−28.5517			−1.59112
$323$	−29.4996	−	15.3400i	−1.64140	−	0.853539i
$324$		0			0
$325$	−1.23994	−	2.14764i	−0.0687795	−	0.119130i
$326$	6.75008	+	11.6915i	0.373853	+	0.647532i
$327$		0			0
$328$	−5.61596	−	9.72712i	−0.310089	−	0.537091i
$329$	−1.51718	+	2.62783i	−0.0836448	+	0.144877i
$330$		0			0
$331$	23.9646			1.31722			0.658608	−	0.752486i	$-0.271146\pi$
$331$	23.9646			1.31722			0.658608	+	0.752486i	$0.271146\pi$
$332$	−0.725036	+	1.25580i	−0.0397915	+	0.0689209i
$333$		0			0
$334$	14.5628			0.796843
$335$	9.63457			0.526393
$336$		0			0
$337$	−16.3204	−	28.2678i	−0.889029	−	1.53984i	−0.841025	−	0.540996i	$-0.818048\pi$
$337$	−16.3204	−	28.2678i	−0.889029	−	1.53984i	−0.0480033	−	0.998847i	$-0.515286\pi$
$338$	5.63980	−	9.76842i	0.306765	−	0.531332i
$339$		0			0
$340$	−2.71300	−	4.69905i	−0.147133	−	0.254842i
$341$	−1.45449			−0.0787652
$342$		0			0
$343$	27.1899			1.46812
$344$	2.63108	+	4.55717i	0.141858	+	0.245706i
$345$		0			0
$346$	14.4459	−	25.0210i	0.776616	−	1.34514i
$347$	8.41457	+	14.5745i	0.451718	+	0.782398i	0.998493	−	0.0548811i	$-0.0174780\pi$
$347$	8.41457	+	14.5745i	0.451718	+	0.782398i	−0.546775	+	0.837280i	$0.684145\pi$
$348$		0			0
$349$	2.46947			0.132188			0.0660939	−	0.997813i	$-0.478946\pi$
$349$	2.46947			0.132188			0.0660939	+	0.997813i	$0.478946\pi$
$350$	7.37662			0.394297
$351$		0			0
$352$	6.62793	−	11.4799i	0.353270	−	0.611881i
$353$	−27.7653			−1.47780			−0.738900	−	0.673815i	$-0.764654\pi$
$353$	−27.7653			−1.47780			−0.738900	+	0.673815i	$0.764654\pi$
$354$		0			0
$355$	1.92594	−	3.33583i	0.102218	−	0.177048i
$356$	−1.11860	−	1.93747i	−0.0592857	−	0.102686i
$357$		0			0
$358$	3.54754	+	6.14452i	0.187493	+	0.324748i
$359$	−10.0245	−	17.3629i	−0.529072	−	0.916379i	−0.999425	−	0.0339009i	$-0.989207\pi$
$359$	−10.0245	−	17.3629i	−0.529072	−	0.916379i	0.470354	−	0.882478i	$-0.344126\pi$
$360$		0			0
$361$	8.01455	−	17.2269i	0.421818	−	0.906680i
$362$	10.4459			0.549023
$363$		0			0
$364$	−3.95127	−	6.84380i	−0.207103	−	0.358712i
$365$	8.39260	−	14.5364i	0.439289	−	0.760871i
$366$		0			0
$367$	3.33741	−	5.78056i	0.174211	−	0.301743i	−0.765677	−	0.643225i	$-0.777596\pi$
$367$	3.33741	−	5.78056i	0.174211	−	0.301743i	0.939888	+	0.341483i	$0.110929\pi$
$368$	19.0303			0.992023
$369$		0			0
$370$	3.21298	−	5.56504i	0.167035	−	0.289313i
$371$	25.7561	−	44.6109i	1.33719	−	2.31608i
$372$		0			0
$373$	−12.4380			−0.644014			−0.322007	−	0.946737i	$-0.604357\pi$
$373$	−12.4380			−0.644014			−0.322007	+	0.946737i	$0.604357\pi$
$374$	21.6122	−	37.4334i	1.11754	−	1.93563i
$375$		0			0
$376$	0.718628	−	1.24470i	0.0370604	−	0.0641905i
$377$	−10.8303	−	18.7587i	−0.557790	−	0.966121i
$378$		0			0
$379$	21.3994			1.09921			0.549607	−	0.835423i	$-0.314777\pi$
$379$	21.3994			1.09921			0.549607	+	0.835423i	$0.314777\pi$
$380$	2.61429	−	1.66711i	0.134110	−	0.0855207i
$381$		0			0
$382$	0.696349	+	1.20611i	0.0356283	+	0.0617100i
$383$	5.35405	+	9.27348i	0.273579	+	0.473853i	0.969776	−	0.243998i	$-0.0784592\pi$
$383$	5.35405	+	9.27348i	0.273579	+	0.473853i	−0.696197	+	0.717851i	$0.745126\pi$
$384$		0			0
$385$	7.70839	+	13.3513i	0.392856	+	0.680446i
$386$	10.8518	−	18.7959i	0.552342	−	0.956685i
$387$		0			0
$388$	1.42265			0.0722243
$389$	−1.75466	+	3.03917i	−0.0889650	+	0.154092i	−0.907074	−	0.420971i	$-0.861689\pi$
$389$	−1.75466	+	3.03917i	−0.0889650	+	0.154092i	0.818109	+	0.575063i	$0.195023\pi$
$390$		0			0
$391$	29.5247			1.49313
$392$	−27.7324			−1.40070
$393$		0			0
$394$	5.69079	+	9.85673i	0.286698	+	0.496575i
$395$	6.06262	−	10.5008i	0.305044	−	0.528351i
$396$		0			0
$397$	−15.5995	−	27.0191i	−0.782916	−	1.35605i	−0.930236	−	0.366961i	$-0.880398\pi$
$397$	−15.5995	−	27.0191i	−0.782916	−	1.35605i	0.147321	−	0.989089i	$-0.452935\pi$
$398$	−22.0337			−1.10445
$399$		0			0
$400$	−4.91667			−0.245833
$401$	−9.87661	−	17.1068i	−0.493214	−	0.854272i	0.506755	−	0.862090i	$-0.330845\pi$
$401$	−9.87661	−	17.1068i	−0.493214	−	0.854272i	−0.999969	+	0.00781786i	$0.997511\pi$
$402$		0			0
$403$	0.524065	−	0.907708i	0.0261055	−	0.0452161i
$404$	−0.717971	−	1.24356i	−0.0357204	−	0.0618696i
$405$		0			0
$406$	64.4315			3.19768
$407$	13.4299			0.665697
$408$		0			0
$409$	1.06951	−	1.85244i	0.0528838	−	0.0915974i	−0.838372	−	0.545099i	$-0.816492\pi$
$409$	1.06951	−	1.85244i	0.0528838	−	0.0915974i	0.891255	+	0.453502i	$0.149825\pi$
$410$	8.71588			0.430446
$411$		0			0
$412$	−2.30789	+	3.99739i	−0.113702	+	0.196937i
$413$	−19.1079	−	33.0958i	−0.940237	−	1.62854i
$414$		0			0
$415$	1.01927	+	1.76543i	0.0500341	+	0.0866616i
$416$	4.77619	+	8.27260i	0.234172	+	0.405598i
$417$		0			0
$418$	21.9141	+	11.3955i	1.07185	+	0.557370i
$419$	5.70341			0.278630			0.139315	−	0.990248i	$-0.455510\pi$
$419$	5.70341			0.278630			0.139315	+	0.990248i	$0.455510\pi$
$420$		0			0
$421$	−19.5265	−	33.8209i	−0.951664	−	1.64833i	−0.741823	−	0.670595i	$-0.766039\pi$
$421$	−19.5265	−	33.8209i	−0.951664	−	1.64833i	−0.209841	−	0.977736i	$-0.567295\pi$
$422$	12.1439	−	21.0339i	0.591158	−	1.02392i
$423$		0			0
$424$	−12.1996	+	21.1304i	−0.592467	+	1.02618i
$425$	−7.62799			−0.370012
$426$		0			0
$427$	−18.3727	+	31.8225i	−0.889119	+	1.54000i
$428$	1.40894	−	2.44036i	0.0681039	−	0.117959i
$429$		0			0
$430$	−4.08340			−0.196919
$431$	0.868782	−	1.50477i	0.0418477	−	0.0724824i	−0.844343	−	0.535803i	$-0.820009\pi$
$431$	0.868782	−	1.50477i	0.0418477	−	0.0724824i	0.886191	+	0.463321i	$0.153342\pi$
$432$		0			0
$433$	−11.8156	+	20.4652i	−0.567821	+	0.983495i	0.428960	+	0.903324i	$0.358880\pi$
$433$	−11.8156	+	20.4652i	−0.567821	+	0.983495i	−0.996781	+	0.0801716i	$0.974453\pi$
$434$	1.55888	+	2.70005i	0.0748285	+	0.129607i
$435$		0			0
$436$	−2.11124			−0.101110
$437$	0.743359	+	16.8550i	0.0355597	+	0.806285i
$438$		0			0
$439$	1.58465	+	2.74469i	0.0756310	+	0.130997i	0.901360	−	0.433070i	$-0.142570\pi$
$439$	1.58465	+	2.74469i	0.0756310	+	0.130997i	−0.825730	+	0.564066i	$0.809236\pi$
$440$	−3.65116	−	6.32399i	−0.174062	−	0.301485i
$441$		0			0
$442$	15.5741	+	26.9751i	0.740783	+	1.28307i
$443$	11.5916	−	20.0773i	0.550736	−	0.953902i	−0.447486	−	0.894291i	$-0.647681\pi$
$443$	11.5916	−	20.0773i	0.550736	−	0.953902i	0.998222	−	0.0596114i	$-0.0189861\pi$
$444$		0			0
$445$	−3.14511			−0.149092
$446$	1.88400	−	3.26318i	0.0892100	−	0.154516i
$447$		0			0
$448$	15.6378			0.738816
$449$	−13.2505			−0.625328			−0.312664	−	0.949864i	$-0.601221\pi$
$449$	−13.2505			−0.625328			−0.312664	+	0.949864i	$0.601221\pi$
$450$		0			0
$451$	9.10788	+	15.7753i	0.428873	+	0.742830i
$452$	−3.10038	+	5.37002i	−0.145830	+	0.252585i
$453$		0			0
$454$	−3.45371	−	5.98200i	−0.162091	−	0.280749i
$455$	−11.1096			−0.520825
$456$		0			0
$457$	4.13077			0.193229			0.0966146	−	0.995322i	$-0.469199\pi$
$457$	4.13077			0.193229			0.0966146	+	0.995322i	$0.469199\pi$
$458$	21.6317	+	37.4672i	1.01078	+	1.75073i
$459$		0			0
$460$	−1.37662	+	2.38437i	−0.0641852	+	0.111172i
$461$	10.9292	+	18.9300i	0.509026	+	0.881658i	0.999945	+	0.0104535i	$0.00332750\pi$
$461$	10.9292	+	18.9300i	0.509026	+	0.881658i	−0.490920	+	0.871205i	$0.663339\pi$
$462$		0			0
$463$	30.9461			1.43819			0.719094	−	0.694913i	$-0.244557\pi$
$463$	30.9461			1.43819			0.719094	+	0.694913i	$0.244557\pi$
$464$	−42.9449			−1.99367
$465$		0			0
$466$	−4.57963	+	7.93216i	−0.212147	+	0.367450i
$467$	−0.394259			−0.0182441			−0.00912207	−	0.999958i	$-0.502904\pi$
$467$	−0.394259			−0.0182441			−0.00912207	+	0.999958i	$0.502904\pi$
$468$		0			0
$469$	21.5809	−	37.3792i	0.996512	−	1.72601i
$470$	0.557649	+	0.965877i	0.0257224	+	0.0445526i
$471$		0			0
$472$	9.05065	+	15.6762i	0.416590	+	0.721555i
$473$	−4.26705	−	7.39075i	−0.196199	−	0.339827i
$474$		0			0
$475$	−0.192054	−	4.35467i	−0.00881205	−	0.199806i
$476$	−24.3078			−1.11415
$477$		0			0
$478$	−5.63883	−	9.76674i	−0.257914	−	0.446720i
$479$	−3.52119	+	6.09888i	−0.160887	+	0.278665i	−0.935187	−	0.354154i	$-0.884769\pi$
$479$	−3.52119	+	6.09888i	−0.160887	+	0.278665i	0.774300	+	0.632819i	$0.218102\pi$
$480$		0			0
$481$	−4.83891	+	8.38124i	−0.220635	+	0.382152i
$482$	24.4397			1.11320
$483$		0			0
$484$	−0.299749	+	0.519181i	−0.0136250	+	0.0235991i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	0.689174			0.0312295			0.0156147	−	0.999878i	$-0.495029\pi$
$487$	0.689174			0.0312295			0.0156147	+	0.999878i	$0.495029\pi$
$488$	8.70244	−	15.0731i	0.393941	−	0.682326i
$489$		0			0
$490$	10.7600	−	18.6370i	0.486089	−	0.841932i
$491$	4.54736	+	7.87626i	0.205219	+	0.355450i	0.950203	−	0.311633i	$-0.100876\pi$
$491$	4.54736	+	7.87626i	0.205219	+	0.355450i	−0.744983	+	0.667083i	$0.767543\pi$
$492$		0			0
$493$	−66.6272			−3.00074
$494$	−15.0074	+	9.57008i	−0.675215	+	0.430578i
$495$		0			0
$496$	−1.03902	−	1.79964i	−0.0466535	−	0.0808063i
$497$	−8.62799	−	14.9441i	−0.387018	−	0.670336i
$498$		0			0
$499$	11.5404	+	19.9886i	0.516619	+	0.894811i	0.999814	+	0.0192976i	$0.00614300\pi$
$499$	11.5404	+	19.9886i	0.516619	+	0.894811i	−0.483195	+	0.875513i	$0.660524\pi$
$500$	0.355663	−	0.616027i	0.0159058	−	0.0275496i
$501$		0			0
$502$	7.90793			0.352948
$503$	−10.5982	+	18.3567i	−0.472552	+	0.818483i	−0.999507	−	0.0314099i	$-0.990000\pi$
$503$	−10.5982	+	18.3567i	−0.472552	+	0.818483i	0.526955	+	0.849893i	$0.323334\pi$
$504$		0			0
$505$	−2.01868			−0.0898302
$506$	−21.9327			−0.975029
$507$		0			0
$508$	1.62799	+	2.81977i	0.0722306	+	0.125107i
$509$	9.12649	−	15.8075i	0.404525	−	0.700657i	−0.589741	−	0.807592i	$-0.700770\pi$
$509$	9.12649	−	15.8075i	0.404525	−	0.700657i	0.994266	+	0.106935i	$0.0341037\pi$
$510$		0			0
$511$	−37.5979	−	65.1214i	−1.66323	−	2.88080i
$512$	−1.92701			−0.0851627
$513$		0			0
$514$	−5.75861			−0.254001
$515$	3.24449	+	5.61962i	0.142969	+	0.247630i
$516$		0			0
$517$	−1.16546	+	2.01864i	−0.0512569	+	0.0887795i
$518$	−14.3938	−	24.9307i	−0.632425	−	1.09539i
$519$		0			0
$520$	5.26217			0.230761
$521$	34.4874			1.51092			0.755461	−	0.655194i	$-0.227413\pi$
$521$	34.4874			1.51092			0.755461	+	0.655194i	$0.227413\pi$
$522$		0			0
$523$	−8.06993	+	13.9775i	−0.352874	+	0.611195i	−0.986752	−	0.162238i	$-0.948129\pi$
$523$	−8.06993	+	13.9775i	−0.352874	+	0.611195i	0.633878	+	0.773433i	$0.281462\pi$
$524$	14.7051			0.642395
$525$		0			0
$526$	−4.30788	+	7.46147i	−0.187833	+	0.325336i
$527$	−1.61200	−	2.79207i	−0.0702198	−	0.121624i
$528$		0			0
$529$	4.00935	+	6.94440i	0.174320	+	0.301931i
$530$	−9.46683	−	16.3970i	−0.411213	−	0.712241i
$531$		0			0
$532$	−0.612011	−	13.8768i	−0.0265341	−	0.601637i
$533$	−13.1266			−0.568574
$534$		0			0
$535$	−1.98073	−	3.43072i	−0.0856343	−	0.148323i
$536$	−10.2220	+	17.7050i	−0.441523	+	0.764741i
$537$		0			0
$538$	−13.0892	+	22.6711i	−0.564315	+	0.977423i
$539$	44.9759			1.93725
$540$		0			0
$541$	−8.46634	+	14.6641i	−0.363996	+	0.630460i	−0.988615	−	0.150470i	$-0.951921\pi$
$541$	−8.46634	+	14.6641i	−0.363996	+	0.630460i	0.624618	+	0.780930i	$0.285255\pi$
$542$	−8.22959	+	14.2541i	−0.353491	+	0.612264i
$543$		0			0
$544$	29.3827			1.25977
$545$	−1.48402	+	2.57039i	−0.0635683	+	0.110104i
$546$		0			0
$547$	14.6871	−	25.4389i	0.627977	−	1.08769i	−0.359981	−	0.932960i	$-0.617217\pi$
$547$	14.6871	−	25.4389i	0.627977	−	1.08769i	0.987957	−	0.154728i	$-0.0494500\pi$
$548$	6.26963	+	10.8593i	0.267825	+	0.463887i
$549$		0			0
$550$	5.66654			0.241622
$551$	−1.67751	−	38.0361i	−0.0714643	−	1.62039i
$552$		0			0
$553$	−27.1598	−	47.0422i	−1.15495	−	2.00044i
$554$	−3.36418	−	5.82693i	−0.142930	−	0.247563i
$555$		0			0
$556$	−4.17355	−	7.22880i	−0.176998	−	0.306570i
$557$	4.29322	−	7.43608i	0.181910	−	0.315077i	−0.760621	−	0.649196i	$-0.775105\pi$
$557$	4.29322	−	7.43608i	0.181910	−	0.315077i	0.942531	+	0.334119i	$0.108439\pi$
$558$		0			0
$559$	6.14981			0.260109
$560$	−11.0130	+	19.0751i	−0.465386	+	0.806072i
$561$		0			0
$562$	19.1639			0.808381
$563$	−2.59685			−0.109444			−0.0547221	−	0.998502i	$-0.517427\pi$
$563$	−2.59685			−0.109444			−0.0547221	+	0.998502i	$0.517427\pi$
$564$		0			0
$565$	4.35859	+	7.54931i	0.183367	+	0.317602i
$566$	−3.58814	+	6.21483i	−0.150821	+	0.261229i
$567$		0			0
$568$	4.08674	+	7.07844i	0.171476	+	0.297005i
$569$	33.8768			1.42019			0.710094	−	0.704107i	$-0.248652\pi$
$569$	33.8768			1.42019			0.710094	+	0.704107i	$0.248652\pi$
$570$		0			0
$571$	−10.6731			−0.446657			−0.223329	−	0.974743i	$-0.571692\pi$
$571$	−10.6731			−0.446657			−0.223329	+	0.974743i	$0.571692\pi$
$572$	−3.03527	−	5.25724i	−0.126911	−	0.219816i
$573$		0			0
$574$	19.5230	−	33.8149i	0.814876	−	1.41141i
$575$	1.93528	+	3.35201i	0.0807069	+	0.139788i
$576$		0			0
$577$	−11.6607			−0.485440			−0.242720	−	0.970096i	$-0.578040\pi$
$577$	−11.6607			−0.485440			−0.242720	+	0.970096i	$0.578040\pi$
$578$	67.8178			2.82085
$579$		0			0
$580$	3.10656	−	5.38072i	0.128993	−	0.223422i
$581$	9.13244			0.378877
$582$		0			0
$583$	19.7852	−	34.2690i	0.819419	−	1.41928i
$584$	17.8086	+	30.8454i	0.736926	+	1.27639i
$585$		0			0
$586$	−5.92972	−	10.2706i	−0.244954	−	0.424274i
$587$	20.1362	+	34.8770i	0.831112	+	1.43953i	0.897157	+	0.441711i	$0.145628\pi$
$587$	20.1362	+	34.8770i	0.831112	+	1.43953i	−0.0660456	+	0.997817i	$0.521038\pi$
$588$		0			0
$589$	1.55335	−	0.990555i	0.0640045	−	0.0408151i
$590$	−14.0465			−0.578284
$591$		0			0
$592$	9.59373	+	16.6168i	0.394300	+	0.682948i
$593$	−7.05130	+	12.2132i	−0.289562	+	0.501537i	−0.973705	−	0.227811i	$-0.926843\pi$
$593$	−7.05130	+	12.2132i	−0.289562	+	0.501537i	0.684143	+	0.729348i	$0.260176\pi$
$594$		0			0
$595$	−17.0863	+	29.5943i	−0.700468	+	1.21325i
$596$	15.3397			0.628338
$597$		0			0
$598$	7.90253	−	13.6876i	0.323159	−	0.559727i
$599$	−5.24355	+	9.08209i	−0.214246	+	0.371084i	−0.953039	−	0.302848i	$-0.902063\pi$
$599$	−5.24355	+	9.08209i	−0.214246	+	0.371084i	0.738793	+	0.673932i	$0.235396\pi$
$600$		0			0
$601$	21.0718			0.859539			0.429769	−	0.902939i	$-0.358595\pi$
$601$	21.0718			0.859539			0.429769	+	0.902939i	$0.358595\pi$
$602$	−9.14657	+	15.8423i	−0.372786	+	0.645685i
$603$		0			0
$604$	−6.51227	+	11.2796i	−0.264981	+	0.458960i
$605$	0.421395	+	0.729877i	0.0171321	+	0.0296737i
$606$		0			0
$607$	−22.2759			−0.904149			−0.452074	−	0.891980i	$-0.649316\pi$
$607$	−22.2759			−0.904149			−0.452074	+	0.891980i	$0.649316\pi$
$608$	0.739784	+	16.7740i	0.0300022	+	0.680274i
$609$		0			0
$610$	6.75303	+	11.6966i	0.273422	+	0.473581i
$611$	−0.839849	−	1.45466i	−0.0339766	−	0.0588493i
$612$		0			0
$613$	8.94766	+	15.4978i	0.361393	+	0.625950i	0.988190	−	0.153232i	$-0.0489681\pi$
$613$	8.94766	+	15.4978i	0.361393	+	0.625950i	−0.626798	+	0.779182i	$0.715635\pi$
$614$	−13.4043	+	23.2170i	−0.540955	+	0.936961i
$615$		0			0
$616$	−32.7135			−1.31806
$617$	8.81560	−	15.2691i	0.354903	−	0.614710i	−0.632198	−	0.774806i	$-0.717847\pi$
$617$	8.81560	−	15.2691i	0.354903	−	0.614710i	0.987101	+	0.160097i	$0.0511806\pi$
$618$		0			0
$619$	−49.2003			−1.97753			−0.988763	−	0.149490i	$-0.952237\pi$
$619$	−49.2003			−1.97753			−0.988763	+	0.149490i	$0.952237\pi$
$620$	0.300645			0.0120742
$621$		0			0
$622$	−3.35669	−	5.81396i	−0.134591	−	0.233118i
$623$	−7.04485	+	12.2020i	−0.282246	+	0.488865i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−35.4932			−1.41859
$627$		0			0
$628$	−8.13085			−0.324456
$629$	14.8843	+	25.7803i	0.593474	+	1.02793i
$630$		0			0
$631$	16.6592	−	28.8547i	0.663194	−	1.14869i	−0.316578	−	0.948567i	$-0.602534\pi$
$631$	16.6592	−	28.8547i	0.663194	−	1.14869i	0.979772	−	0.200119i	$-0.0641329\pi$
$632$	12.8645	+	22.2820i	0.511724	+	0.886332i
$633$		0			0
$634$	23.4918			0.932980
$635$	4.57735			0.181646
$636$		0			0
$637$	−16.2052	+	28.0682i	−0.642073	+	1.11210i
$638$	49.4947			1.95951
$639$		0			0
$640$	6.72584	−	11.6495i	0.265862	−	0.460487i
$641$	6.61110	+	11.4508i	0.261123	+	0.452278i	0.966541	−	0.256514i	$-0.0825739\pi$
$641$	6.61110	+	11.4508i	0.261123	+	0.452278i	−0.705418	+	0.708792i	$0.749241\pi$
$642$		0			0
$643$	0.951267	+	1.64764i	0.0375143	+	0.0649767i	0.884173	−	0.467160i	$-0.154723\pi$
$643$	0.951267	+	1.64764i	0.0375143	+	0.0649767i	−0.846659	+	0.532136i	$0.821389\pi$
$644$	6.16709	+	10.6817i	0.243017	+	0.420918i
$645$		0			0
$646$	2.41227	+	54.6961i	0.0949093	+	2.15199i
$647$	−27.2141			−1.06989			−0.534947	−	0.844885i	$-0.679669\pi$
$647$	−27.2141			−1.06989			−0.534947	+	0.844885i	$0.679669\pi$
$648$		0			0
$649$	−14.6782	−	25.4234i	−0.576170	−	0.997956i
$650$	−2.04170	+	3.53633i	−0.0800820	+	0.138706i
$651$		0			0
$652$	2.91600	−	5.05066i	0.114199	−	0.197799i
$653$	43.6980			1.71004			0.855018	−	0.518599i	$-0.173546\pi$
$653$	43.6980			1.71004			0.855018	+	0.518599i	$0.173546\pi$
$654$		0			0
$655$	10.3364	−	17.9031i	0.403876	−	0.699533i
$656$	−13.0125	+	22.5383i	−0.508053	+	0.879974i
$657$		0			0
$658$	4.99640			0.194780
$659$	−3.43672	+	5.95258i	−0.133876	+	0.231879i	−0.925167	−	0.379559i	$-0.876076\pi$
$659$	−3.43672	+	5.95258i	−0.133876	+	0.231879i	0.791292	+	0.611439i	$0.209409\pi$
$660$		0			0
$661$	−18.6491	+	32.3012i	−0.725367	+	1.25637i	0.233456	+	0.972367i	$0.424996\pi$
$661$	−18.6491	+	32.3012i	−0.725367	+	1.25637i	−0.958823	+	0.284005i	$0.908337\pi$
$662$	−19.7302	−	34.1737i	−0.766837	−	1.32820i
$663$		0			0
$664$	−4.32568			−0.167869
$665$	−17.3249	−	9.00908i	−0.671833	−	0.349357i
$666$		0			0
$667$	16.9038	+	29.2783i	0.654520	+	1.13366i
$668$	−3.14553	−	5.44822i	−0.121704	−	0.210798i
$669$		0			0
$670$	−7.93220	−	13.7390i	−0.306447	−	0.530783i
$671$	−14.1135	+	24.4453i	−0.544845	+	0.943700i
$672$		0			0
$673$	50.6185			1.95120			0.975601	−	0.219553i	$-0.0704597\pi$
$673$	50.6185			1.95120			0.975601	+	0.219553i	$0.0704597\pi$
$674$	−26.8733	+	46.5460i	−1.03512	+	1.79288i
$675$		0			0
$676$	−4.87273			−0.187413
$677$	−33.8725			−1.30182			−0.650912	−	0.759153i	$-0.725613\pi$
$677$	−33.8725			−1.30182			−0.650912	+	0.759153i	$0.725613\pi$
$678$		0			0
$679$	−4.47988	−	7.75938i	−0.171922	−	0.297778i
$680$	8.09309	−	14.0176i	0.310356	−	0.537552i
$681$		0			0
$682$	1.19749	+	2.07412i	0.0458543	+	0.0794220i
$683$	−47.0846			−1.80164			−0.900822	−	0.434190i	$-0.857035\pi$
$683$	−47.0846			−1.80164			−0.900822	+	0.434190i	$0.857035\pi$
$684$		0			0
$685$	17.6280			0.673531
$686$	−22.3856	−	38.7729i	−0.854685	−	1.48036i
$687$		0			0
$688$	6.09637	−	10.5592i	0.232422	−	0.402567i
$689$	14.2575	+	24.6948i	0.543169	+	0.940796i
$690$		0			0
$691$	3.91269			0.148846			0.0744228	−	0.997227i	$-0.476289\pi$
$691$	3.91269			0.148846			0.0744228	+	0.997227i	$0.476289\pi$
$692$	−12.4811			−0.474460
$693$		0			0
$694$	13.8555	−	23.9985i	0.525949	−	0.910970i
$695$	−11.7346			−0.445117
$696$		0			0
$697$	−20.1883	+	34.9672i	−0.764688	+	1.32448i
$698$	−2.03313	−	3.52148i	−0.0769551	−	0.133290i
$699$		0			0
$700$	−1.59333	−	2.75973i	−0.0602222	−	0.104308i
$701$	6.60352	+	11.4376i	0.249411	+	0.431993i	0.963363	−	0.268202i	$-0.0864295\pi$
$701$	6.60352	+	11.4376i	0.249411	+	0.431993i	−0.713951	+	0.700195i	$0.753096\pi$
$702$		0			0
$703$	−14.3427	+	9.14620i	−0.540945	+	0.344955i
$704$	12.0126			0.452741
$705$		0			0
$706$	22.8594	+	39.5936i	0.860323	+	1.49012i
$707$	−4.52173	+	7.83186i	−0.170057	+	0.294547i
$708$		0			0
$709$	8.99856	−	15.5860i	0.337948	−	0.585343i	−0.646099	−	0.763254i	$-0.723600\pi$
$709$	8.99856	−	15.5860i	0.337948	−	0.585343i	0.984047	+	0.177911i	$0.0569338\pi$
$710$	−6.34256			−0.238032
$711$		0			0
$712$	3.33687	−	5.77963i	0.125054	−	0.216601i
$713$	−0.817955	+	1.41674i	−0.0306326	+	0.0530573i
$714$		0			0
$715$	−8.53410			−0.319157
$716$	1.53252	−	2.65440i	0.0572728	−	0.0991995i
$717$		0			0
$718$	−16.5064	+	28.5899i	−0.616014	+	1.06697i
$719$	−6.23909	−	10.8064i	−0.232679	−	0.403012i	0.725917	−	0.687783i	$-0.241416\pi$
$719$	−6.23909	−	10.8064i	−0.232679	−	0.403012i	−0.958596	+	0.284771i	$0.908082\pi$
$720$		0			0
$721$	29.0698			1.08262
$722$	−31.1641	+	2.75423i	−1.15981	+	0.102502i
$723$		0			0
$724$	−2.25628	−	3.90800i	−0.0838541	−	0.145240i
$725$	−4.36728	−	7.56435i	−0.162197	−	0.280933i
$726$		0			0
$727$	21.7065	+	37.5968i	0.805051	+	1.39439i	0.916257	+	0.400592i	$0.131195\pi$
$727$	21.7065	+	37.5968i	0.805051	+	1.39439i	−0.111206	+	0.993797i	$0.535471\pi$
$728$	11.7869	−	20.4156i	0.436853	−	0.756651i
$729$		0			0
$730$	−27.6387			−1.02295
$731$	9.45826	−	16.3822i	0.349826	−	0.605917i
$732$		0			0
$733$	−28.5740			−1.05540			−0.527702	−	0.849430i	$-0.676946\pi$
$733$	−28.5740			−1.05540			−0.527702	+	0.849430i	$0.676946\pi$
$734$	−10.9908			−0.405678
$735$		0			0
$736$	−7.45462	−	12.9118i	−0.274781	−	0.475935i
$737$	16.5779	−	28.7138i	0.610655	−	1.05769i
$738$		0			0
$739$	4.61769	+	7.99807i	0.169864	+	0.294214i	0.938372	−	0.345627i	$-0.112334\pi$
$739$	4.61769	+	7.99807i	0.169864	+	0.294214i	−0.768508	+	0.639841i	$0.779000\pi$
$740$	−2.77598			−0.102047
$741$		0			0
$742$	−84.8205			−3.11386
$743$	−2.51875	−	4.36259i	−0.0924038	−	0.160048i	0.816118	−	0.577885i	$-0.196122\pi$
$743$	−2.51875	−	4.36259i	−0.0924038	−	0.160048i	−0.908522	+	0.417837i	$0.862788\pi$
$744$		0			0
$745$	10.7824	−	18.6757i	0.395038	−	0.684226i
$746$	10.2402	+	17.7366i	0.374922	+	0.649384i
$747$		0			0
$748$	−18.6727			−0.682741
$749$	−17.7468			−0.648456
$750$		0			0
$751$	−6.41366	+	11.1088i	−0.234038	+	0.405365i	−0.958993	−	0.283431i	$-0.908527\pi$
$751$	−6.41366	+	11.1088i	−0.234038	+	0.405365i	0.724955	+	0.688796i	$0.241861\pi$
$752$	−3.33021			−0.121440
$753$		0			0
$754$	−17.8333	+	30.8882i	−0.649452	+	1.12488i
$755$	9.15510	+	15.8571i	0.333188	+	0.577099i
$756$		0			0
$757$	−12.9425	−	22.4171i	−0.470404	−	0.814764i	0.529023	−	0.848608i	$-0.322559\pi$
$757$	−12.9425	−	22.4171i	−0.470404	−	0.814764i	−0.999427	+	0.0338435i	$0.989225\pi$
$758$	−17.6183	−	30.5157i	−0.639924	−	1.10838i
$759$		0			0
$760$	8.20614	+	4.26725i	0.297668	+	0.154789i
$761$	28.9722			1.05024			0.525121	−	0.851028i	$-0.324020\pi$
$761$	28.9722			1.05024			0.525121	+	0.851028i	$0.324020\pi$
$762$		0			0
$763$	6.64822	+	11.5151i	0.240682	+	0.416873i
$764$	0.300819	−	0.521033i	0.0108832	−	0.0188503i
$765$		0			0
$766$	8.81603	−	15.2698i	0.318536	−	0.551721i
$767$	21.1547			0.763852
$768$		0			0
$769$	−2.72690	+	4.72313i	−0.0983345	+	0.170320i	−0.910995	−	0.412417i	$-0.864685\pi$
$769$	−2.72690	+	4.72313i	−0.0983345	+	0.170320i	0.812661	+	0.582737i	$0.198018\pi$
$770$	12.6927	−	21.9844i	0.457414	−	0.792263i
$771$		0			0
$772$	−9.37584			−0.337444
$773$	−23.5060	+	40.7135i	−0.845451	+	1.46436i	0.0397783	+	0.999209i	$0.487335\pi$
$773$	−23.5060	+	40.7135i	−0.845451	+	1.46436i	−0.885229	+	0.465155i	$0.845999\pi$
$774$		0			0
$775$	0.211327	−	0.366029i	0.00759108	−	0.0131481i
$776$	2.12194	+	3.67531i	0.0761733	+	0.131936i
$777$		0			0
$778$	5.77850			0.207169
$779$	−20.4704	−	10.6447i	−0.733427	−	0.381387i
$780$		0			0
$781$	−6.62782	−	11.4797i	−0.237162	−	0.410776i
$782$	−24.3078	−	42.1024i	−0.869246	−	1.50558i
$783$		0			0
$784$	32.1288	+	55.6487i	1.14746	+	1.98745i
$785$	−5.71527	+	9.89914i	−0.203987	+	0.353316i
$786$		0			0
$787$	3.86923			0.137923			0.0689616	−	0.997619i	$-0.478031\pi$
$787$	3.86923			0.137923			0.0689616	+	0.997619i	$0.478031\pi$
$788$	2.45839	−	4.25805i	0.0875764	−	0.151687i
$789$		0			0
$790$	−19.9656			−0.710343
$791$	39.0520			1.38853
$792$		0			0
$793$	−10.1704	−	17.6157i	−0.361162	−	0.625550i
$794$	−25.6863	+	44.4899i	−0.911572	+	1.57889i
$795$		0			0
$796$	4.75921	+	8.24320i	0.168686	+	0.292173i
$797$	12.6814			0.449198			0.224599	−	0.974451i	$-0.427893\pi$
$797$	12.6814			0.449198			0.224599	+	0.974451i	$0.427893\pi$
$798$		0			0
$799$	−5.16667			−0.182784
$800$	1.92598	+	3.33589i	0.0680935	+	0.117941i
$801$		0			0
$802$	−16.2629	+	28.1682i	−0.574264	+	0.994654i
$803$	−28.8818	−	50.0247i	−1.01922	−	1.76533i
$804$		0			0
$805$	17.3397			0.611143
$806$	−1.72586			−0.0607909
$807$		0			0
$808$	2.14176	−	3.70964i	0.0753470	−	0.130505i
$809$	−33.2439			−1.16879			−0.584397	−	0.811468i	$-0.698669\pi$
$809$	−33.2439			−1.16879			−0.584397	+	0.811468i	$0.698669\pi$
$810$		0			0
$811$	1.43265	−	2.48142i	0.0503072	−	0.0871346i	−0.839775	−	0.542934i	$-0.817313\pi$
$811$	1.43265	−	2.48142i	0.0503072	−	0.0871346i	0.890082	+	0.455800i	$0.150647\pi$
$812$	−13.9170	−	24.1050i	−0.488392	−	0.845920i
$813$		0			0
$814$	−11.0569	−	19.1512i	−0.387545	−	0.671248i
$815$	−4.09938	−	7.10034i	−0.143595	−	0.248714i
$816$		0			0
$817$	9.59039	+	4.98706i	0.335525	+	0.174475i
$818$	−3.52213			−0.123148
$819$		0			0
$820$	−1.88261	−	3.26077i	−0.0657434	−	0.113871i
$821$	−7.18851	+	12.4509i	−0.250881	+	0.434538i	−0.963769	−	0.266740i	$-0.914054\pi$
$821$	−7.18851	+	12.4509i	−0.250881	+	0.434538i	0.712888	+	0.701278i	$0.247387\pi$
$822$		0			0
$823$	−28.3639	+	49.1277i	−0.988702	+	1.71248i	−0.364540	+	0.931188i	$0.618774\pi$
$823$	−28.3639	+	49.1277i	−0.988702	+	1.71248i	−0.624163	+	0.781294i	$0.714560\pi$
$824$	−13.7692			−0.479674
$825$		0			0
$826$	−31.4632	+	54.4959i	−1.09475	+	1.89616i
$827$	10.0977	−	17.4897i	0.351131	−	0.608177i	−0.635317	−	0.772252i	$-0.719130\pi$
$827$	10.0977	−	17.4897i	0.351131	−	0.608177i	0.986448	+	0.164074i	$0.0524637\pi$
$828$		0			0
$829$	38.0954			1.32311			0.661554	−	0.749898i	$-0.269897\pi$
$829$	38.0954			1.32311			0.661554	+	0.749898i	$0.269897\pi$
$830$	1.67835	−	2.90698i	0.0582562	−	0.100903i
$831$		0			0
$832$	−4.32822	+	7.49670i	−0.150054	+	0.259901i
$833$	49.8464	+	86.3365i	1.72708	+	2.99138i
$834$		0			0
$835$	−8.84413			−0.306064
$836$	−0.470132	−	10.6598i	−0.0162599	−	0.368679i
$837$		0			0
$838$	−4.69565	−	8.13311i	−0.162209	−	0.280954i
$839$	19.1320	+	33.1376i	0.660511	+	1.14404i	0.980482	+	0.196611i	$0.0629934\pi$
$839$	19.1320	+	33.1376i	0.660511	+	1.14404i	−0.319971	+	0.947427i	$0.603673\pi$
$840$		0			0
$841$	−23.6462	−	40.9565i	−0.815388	−	1.41229i
$842$	−32.1526	+	55.6899i	−1.10805	+	1.91920i
$843$		0			0
$844$	−10.4922			−0.361158
$845$	−3.42510	+	5.93244i	−0.117827	+	0.204082i
$846$		0			0
$847$	3.77560			0.129731
$848$	56.5346			1.94141
$849$		0			0
$850$	6.28017	+	10.8776i	0.215408	+	0.373098i
$851$	7.55251	−	13.0813i	0.258897	−	0.448422i
$852$		0			0
$853$	−1.71697	−	2.97387i	−0.0587878	−	0.101823i	0.835134	−	0.550047i	$-0.185390\pi$
$853$	−1.71697	−	2.97387i	−0.0587878	−	0.101823i	−0.893922	+	0.448224i	$0.852057\pi$
$854$	60.5055			2.07046
$855$		0			0
$856$	8.40598			0.287311
$857$	−13.6630	−	23.6650i	−0.466719	−	0.808382i	0.532558	−	0.846394i	$-0.321231\pi$
$857$	−13.6630	−	23.6650i	−0.466719	−	0.808382i	−0.999277	+	0.0380118i	$0.987898\pi$
$858$		0			0
$859$	22.0603	−	38.2096i	0.752689	−	1.30370i	−0.193826	−	0.981036i	$-0.562090\pi$
$859$	22.0603	−	38.2096i	0.752689	−	1.30370i	0.946515	−	0.322660i	$-0.104577\pi$
$860$	0.882003	+	1.52767i	0.0300760	+	0.0520932i
$861$		0			0
$862$	−2.86109			−0.0974491
$863$	41.3721			1.40832			0.704161	−	0.710040i	$-0.251323\pi$
$863$	41.3721			1.40832			0.704161	+	0.710040i	$0.251323\pi$
$864$		0			0
$865$	−8.77310	+	15.1955i	−0.298294	+	0.516661i
$866$	38.9114			1.32226
$867$		0			0
$868$	0.673427	−	1.16641i	0.0228576	−	0.0395905i
$869$	−20.8635	−	36.1367i	−0.707746	−	1.22585i
$870$		0			0
$871$	11.9463	+	20.6916i	0.404785	+	0.701108i
$872$	−3.14900	−	5.45423i	−0.106639	−	0.184703i
$873$		0			0
$874$	23.4234	−	14.9369i	0.792307	−	0.505247i
$875$	−4.47988			−0.151448
$876$		0			0
$877$	−28.3151	−	49.0432i	−0.956134	−	1.65607i	−0.731751	−	0.681572i	$-0.761297\pi$
$877$	−28.3151	−	49.0432i	−0.956134	−	1.65607i	−0.224383	−	0.974501i	$-0.572037\pi$
$878$	2.60929	−	4.51943i	0.0880594	−	0.152523i
$879$		0			0
$880$	−8.45995	+	14.6531i	−0.285185	+	0.493955i
$881$	1.34253			0.0452311			0.0226156	−	0.999744i	$-0.492801\pi$
$881$	1.34253			0.0452311			0.0226156	+	0.999744i	$0.492801\pi$
$882$		0			0
$883$	−13.3420	+	23.1089i	−0.448993	+	0.777678i	−0.998321	−	0.0579288i	$-0.981550\pi$
$883$	−13.3420	+	23.1089i	−0.448993	+	0.777678i	0.549328	+	0.835607i	$0.314884\pi$
$884$	6.72791	−	11.6531i	0.226284	−	0.391936i
$885$		0			0
$886$	−38.1739			−1.28248
$887$	13.8879	−	24.0545i	0.466309	−	0.807671i	−0.532950	−	0.846147i	$-0.678917\pi$
$887$	13.8879	−	24.0545i	0.466309	−	0.807671i	0.999260	+	0.0384753i	$0.0122501\pi$
$888$		0			0
$889$	10.2530	−	17.7587i	0.343874	−	0.595607i
$890$	2.58938	+	4.48494i	0.0867963	+	0.150336i
$891$		0			0
$892$	−1.62776			−0.0545013
$893$	−0.130084	−	2.94955i	−0.00435310	−	0.0987028i
$894$		0			0
$895$	−2.15445	−	3.73161i	−0.0720153	−	0.124734i
$896$	−30.1310	−	52.1884i	−1.00660	−	1.74349i
$897$		0			0
$898$	10.9092	+	18.8953i	0.364044	+	0.630543i
$899$	1.84585	−	3.19710i	0.0615624	−	0.106629i
$900$		0			0
$901$	87.7110			2.92208
$902$	14.9971	−	25.9758i	0.499350	−	0.864899i
$903$		0			0
$904$	−18.4974			−0.615214
$905$	−6.34387			−0.210877
$906$		0			0
$907$	−3.69599	−	6.40164i	−0.122723	−	0.212563i	0.798117	−	0.602502i	$-0.205829\pi$
$907$	−3.69599	−	6.40164i	−0.122723	−	0.212563i	−0.920841	+	0.389939i	$0.872496\pi$
$908$	−1.49198	+	2.58419i	−0.0495132	+	0.0857594i
$909$		0			0
$910$	9.14657	+	15.8423i	0.303206	+	0.525168i
$911$	−13.3084			−0.440926			−0.220463	−	0.975395i	$-0.570757\pi$
$911$	−13.3084			−0.440926			−0.220463	+	0.975395i	$0.570757\pi$
$912$		0			0
$913$	7.01532			0.232173
$914$	−3.40088	−	5.89050i	−0.112491	−	0.194841i
$915$		0			0
$916$	9.34477	−	16.1856i	0.308760	−	0.534788i
$917$	−46.3058	−	80.2039i	−1.52915	−	2.64857i
$918$		0			0
$919$	−27.8298			−0.918022			−0.459011	−	0.888431i	$-0.651796\pi$
$919$	−27.8298			−0.918022			−0.459011	+	0.888431i	$0.651796\pi$
$920$	−8.21312			−0.270779
$921$		0			0
$922$	17.9962	−	31.1704i	0.592674	−	1.02654i
$923$	9.55222			0.314415
$924$		0			0
$925$	−1.95127	+	3.37969i	−0.0641573	+	0.111124i
$926$	−25.4781	−	44.1294i	−0.837262	−	1.45018i
$927$		0			0
$928$	16.8225	+	29.1375i	0.552227	+	0.956485i
$929$	3.17108	+	5.49247i	0.104040	+	0.180202i	0.913345	−	0.407186i	$-0.133490\pi$
$929$	3.17108	+	5.49247i	0.104040	+	0.180202i	−0.809306	+	0.587388i	$0.800156\pi$
$930$		0			0
$931$	−48.0327	+	30.6300i	−1.57421	+	1.00386i
$932$	3.95675			0.129608
$933$		0			0
$934$	0.324596	+	0.562216i	0.0106211	+	0.0183963i
$935$	−13.1252	+	22.7336i	−0.429241	+	0.743468i
$936$		0			0
$937$	21.9869	−	38.0825i	0.718282	−	1.24410i	−0.243398	−	0.969926i	$-0.578262\pi$
$937$	21.9869	−	38.0825i	0.718282	−	1.24410i	0.961680	−	0.274174i	$-0.0884045\pi$
$938$	−71.0706			−2.32054
$939$		0			0
$940$	0.240901	−	0.417254i	0.00785734	−	0.0136093i
$941$	7.97283	−	13.8093i	0.259907	−	0.450172i	−0.706310	−	0.707903i	$-0.749642\pi$
$941$	7.97283	−	13.8093i	0.259907	−	0.450172i	0.966217	+	0.257731i	$0.0829749\pi$
$942$		0			0
$943$	20.4878			0.667174
$944$	20.9709	−	36.3226i	0.682544	−	1.18220i
$945$		0			0
$946$	−7.02617	+	12.1697i	−0.228441	+	0.395671i
$947$	−1.55287	−	2.68965i	−0.0504615	−	0.0874018i	0.839691	−	0.543064i	$-0.182736\pi$
$947$	−1.55287	−	2.68965i	−0.0504615	−	0.0874018i	−0.890153	+	0.455662i	$0.849403\pi$
$948$		0			0
$949$	41.6253			1.35121
$950$	−6.05166	+	3.85909i	−0.196342	+	0.125205i
$951$		0			0
$952$	−36.2561	−	62.7973i	−1.17507	−	2.03527i
$953$	−10.2628	−	17.7757i	−0.332445	−	0.575812i	0.650545	−	0.759467i	$-0.274540\pi$
$953$	−10.2628	−	17.7757i	−0.332445	−	0.575812i	−0.982991	+	0.183655i	$0.941207\pi$
$954$		0			0
$955$	−0.422898	−	0.732481i	−0.0136847	−	0.0237025i
$956$	−2.43594	+	4.21918i	−0.0787840	+	0.136458i
$957$		0			0
$958$	11.5961			0.374651
$959$	39.4857	−	68.3912i	1.27506	−	2.20847i
$960$		0			0
$961$	−30.8214			−0.994238
$962$	15.9356			0.513784
$963$		0			0
$964$	−5.27891	−	9.14334i	−0.170022	−	0.294487i
$965$	−6.59039	+	11.4149i	−0.212152	+	0.367458i
$966$		0			0
$967$	−12.4113	−	21.4970i	−0.399120	−	0.691296i	0.594498	−	0.804097i	$-0.297351\pi$
$967$	−12.4113	−	21.4970i	−0.399120	−	0.691296i	−0.993618	+	0.112801i	$0.964018\pi$
$968$	−1.78835			−0.0574798
$969$		0			0
$970$	−3.29322			−0.105739
$971$	−18.2999	−	31.6963i	−0.587271	−	1.01718i	−0.994588	−	0.103896i	$-0.966869\pi$
$971$	−18.2999	−	31.6963i	−0.587271	−	1.01718i	0.407318	−	0.913287i	$-0.366464\pi$
$972$		0			0
$973$	−26.2847	+	45.5264i	−0.842649	+	1.45951i
$974$	−0.567401	−	0.982767i	−0.0181807	−	0.0314899i
$975$		0			0
$976$	−40.3282			−1.29087
$977$	−31.6228			−1.01170			−0.505851	−	0.862621i	$-0.668822\pi$
$977$	−31.6228			−1.01170			−0.505851	+	0.862621i	$0.668822\pi$
$978$		0			0
$979$	−5.41168	+	9.37331i	−0.172958	+	0.299572i
$980$	−9.29656			−0.296968
$981$		0			0
$982$	7.48773	−	12.9691i	0.238943	−	0.413862i
$983$	22.8804	+	39.6300i	0.729771	+	1.26400i	0.956980	+	0.290154i	$0.0937067\pi$
$983$	22.8804	+	39.6300i	0.729771	+	1.26400i	−0.227209	+	0.973846i	$0.572960\pi$
$984$		0			0
$985$	−3.45606	−	5.98607i	−0.110119	−	0.190732i
$986$	54.8545	+	95.0108i	1.74692	+	3.02576i
$987$		0			0
$988$	6.82190	+	3.54743i	0.217034	+	0.112859i
$989$	−9.59855			−0.305216
$990$		0			0
$991$	−13.2056	−	22.8728i	−0.419490	−	0.726579i	0.576398	−	0.817169i	$-0.304458\pi$
$991$	−13.2056	−	22.8728i	−0.419490	−	0.726579i	−0.995888	+	0.0905905i	$0.971125\pi$
$992$	−0.814021	+	1.40993i	−0.0258452	+	0.0447652i
$993$		0			0
$994$	−14.2069	+	24.6072i	−0.450617	+	0.780492i
$995$	13.3812			0.424214
$996$		0			0
$997$	20.5781	−	35.6423i	0.651714	−	1.12880i	−0.330992	−	0.943633i	$-0.607383\pi$
$997$	20.5781	−	35.6423i	0.651714	−	1.12880i	0.982707	−	0.185169i	$-0.0592832\pi$
$998$	19.0025	−	32.9134i	0.601515	−	1.04185i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.i.406.2		10
3.2	odd	2		285.2.i.f.121.4	yes	10
19.11	even	3	inner	855.2.k.i.676.2		10
57.11	odd	6		285.2.i.f.106.4	✓	10
57.26	odd	6		5415.2.a.y.1.2		5
57.50	even	6		5415.2.a.z.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.4	✓	10	57.11	odd	6
285.2.i.f.121.4	yes	10	3.2	odd	2
855.2.k.i.406.2		10	1.1	even	1	trivial
855.2.k.i.676.2		10	19.11	even	3	inner
5415.2.a.y.1.2		5	57.26	odd	6
5415.2.a.z.1.4		5	57.50	even	6

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.823305 - 1.42601i) q^{2} +(-0.355663 + 0.616027i) q^{4} +(0.500000 + 0.866025i) q^{5} +4.47988 q^{7} -2.12194 q^{8} +(0.823305 - 1.42601i) q^{10} +3.44134 q^{11} +(-1.23994 + 2.14764i) q^{13} +(-3.68831 - 6.38834i) q^{14} +(2.45833 + 4.25796i) q^{16} +(3.81400 + 6.60604i) q^{17} +(-3.67522 + 2.34366i) q^{19} -0.711327 q^{20} +(-2.83327 - 4.90737i) q^{22} +(1.93528 - 3.35201i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.08340 q^{26} +(-1.59333 + 2.75973i) q^{28} +(-4.36728 + 7.56435i) q^{29} -0.422654 q^{31} +(1.92598 - 3.33589i) q^{32} +(6.28017 - 10.8776i) q^{34} +(2.23994 + 3.87969i) q^{35} +3.90253 q^{37} +(6.36790 + 3.31135i) q^{38} +(-1.06097 - 1.83766i) q^{40} +(2.64661 + 4.58406i) q^{41} +(-1.23994 - 2.14764i) q^{43} +(-1.22396 + 2.11996i) q^{44} -6.37332 q^{46} +(-0.338665 + 0.586585i) q^{47} +13.0693 q^{49} +1.64661 q^{50} +(-0.882003 - 1.52767i) q^{52} +(5.74928 - 9.95805i) q^{53} +(1.72067 + 2.98028i) q^{55} -9.50605 q^{56} +14.3824 q^{58} +(-4.26526 - 7.38765i) q^{59} +(-4.10117 + 7.10343i) q^{61} +(0.347973 + 0.602707i) q^{62} +3.49067 q^{64} -2.47988 q^{65} +(4.81729 - 8.34379i) q^{67} -5.42600 q^{68} +(3.68831 - 6.38834i) q^{70} +(-1.92594 - 3.33583i) q^{71} +(-8.39260 - 14.5364i) q^{73} +(-3.21298 - 5.56504i) q^{74} +(-0.136613 - 3.09759i) q^{76} +15.4168 q^{77} +(-6.06262 - 10.5008i) q^{79} +(-2.45833 + 4.25796i) q^{80} +(4.35794 - 7.54817i) q^{82} +2.03855 q^{83} +(-3.81400 + 6.60604i) q^{85} +(-2.04170 + 3.53633i) q^{86} -7.30232 q^{88} +(-1.57255 + 2.72374i) q^{89} +(-5.55478 + 9.62117i) q^{91} +(1.37662 + 2.38437i) q^{92} +1.11530 q^{94} +(-3.86728 - 2.01101i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(-10.7600 - 18.6370i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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