LMFDB - Embedded newform 819.2.o.d.757.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.3
Root			$-0.688601 - 1.19269i$ of defining polynomial
Character	$\chi$	$=$	819.757
Dual form			819.2.o.d.568.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.825547 + 1.42989i) q^{2} +(-0.363055 + 0.628829i) q^{4} -2.92498 q^{5} +(0.500000 - 0.866025i) q^{7} +2.10331 q^{8} +O(q^{10})$	\(q+(0.825547 + 1.42989i) q^{2} +(-0.363055 + 0.628829i) q^{4} -2.92498 q^{5} +(0.500000 - 0.866025i) q^{7} +2.10331 q^{8} +(-2.41471 - 4.18240i) q^{10} +(-2.18860 - 3.79077i) q^{11} +(2.56580 - 2.53311i) q^{13} +1.65109 q^{14} +(2.46249 + 4.26516i) q^{16} +(1.82555 - 3.16194i) q^{17} +(2.87720 - 4.98346i) q^{19} +(1.06193 - 1.83932i) q^{20} +(3.61359 - 6.25891i) q^{22} +(3.51415 + 6.08668i) q^{23} +3.55553 q^{25} +(5.74026 + 1.57761i) q^{26} +(0.363055 + 0.628829i) q^{28} +(0.599437 + 1.03826i) q^{29} -6.47277 q^{31} +(-1.96249 + 3.39914i) q^{32} +6.02830 q^{34} +(-1.46249 + 2.53311i) q^{35} +(1.46249 + 2.53311i) q^{37} +9.50106 q^{38} -6.15215 q^{40} +(-4.30219 - 7.45161i) q^{41} +(2.86305 - 4.95896i) q^{43} +3.17833 q^{44} +(-5.80219 + 10.0497i) q^{46} +9.58383 q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.93526 + 5.08401i) q^{50} +(0.661367 + 2.53311i) q^{52} +0.302187 q^{53} +(6.40162 + 11.0879i) q^{55} +(1.05166 - 1.82152i) q^{56} +(-0.989727 + 1.71426i) q^{58} +(1.51415 - 2.62258i) q^{59} +(0.151093 - 0.261701i) q^{61} +(-5.34357 - 9.25533i) q^{62} +3.36945 q^{64} +(-7.50494 + 7.40931i) q^{65} +(4.35384 + 7.54108i) q^{67} +(1.32555 + 2.29591i) q^{68} -4.82942 q^{70} +(6.76855 - 11.7235i) q^{71} +0.932734 q^{73} +(-2.41471 + 4.18240i) q^{74} +(2.08916 + 3.61854i) q^{76} -4.37720 q^{77} -16.9426 q^{79} +(-7.20275 - 12.4755i) q^{80} +(7.10331 - 12.3033i) q^{82} +1.26614 q^{83} +(-5.33969 + 9.24862i) q^{85} +9.45434 q^{86} +(-4.60331 - 7.97317i) q^{88} +(-6.69887 - 11.6028i) q^{89} +(-0.910836 - 3.48861i) q^{91} -5.10331 q^{92} +(7.91190 + 13.7038i) q^{94} +(-8.41577 + 14.5765i) q^{95} +(-5.96249 + 10.3273i) q^{97} +(0.825547 - 1.42989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.825547	+	1.42989i	0.583750	+	1.01108i	0.995030	+	0.0995752i	$0.0317484\pi$
$2$	0.825547	+	1.42989i	0.583750	+	1.01108i	−0.411280	+	0.911509i	$0.634918\pi$
$3$		0			0
$3$		0			0
$4$	−0.363055	+	0.628829i	−0.181527	+	0.314415i
$5$	−2.92498			−1.30809			−0.654046	−	0.756455i	$-0.726930\pi$
$5$	−2.92498			−1.30809			−0.654046	+	0.756455i	$0.726930\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	2.10331			0.743633
$9$		0			0
$10$	−2.41471	−	4.18240i	−0.763599	−	1.32259i
$11$	−2.18860	−	3.79077i	−0.659888	−	1.14296i	−0.980644	−	0.195798i	$-0.937270\pi$
$11$	−2.18860	−	3.79077i	−0.659888	−	1.14296i	0.320756	−	0.947162i	$-0.396063\pi$
$12$		0			0
$13$	2.56580	−	2.53311i	0.711626	−	0.702558i
$13$	2.56580	−	2.53311i	0.711626	−	0.702558i
$14$	1.65109			0.441273
$15$		0			0
$16$	2.46249	+	4.26516i	0.615623	+	1.06629i
$17$	1.82555	−	3.16194i	0.442760	−	0.766883i	−0.555133	−	0.831762i	$-0.687333\pi$
$17$	1.82555	−	3.16194i	0.442760	−	0.766883i	0.997893	+	0.0648786i	$0.0206660\pi$
$18$		0			0
$19$	2.87720	−	4.98346i	0.660076	−	1.14328i	−0.320520	−	0.947242i	$-0.603858\pi$
$19$	2.87720	−	4.98346i	0.660076	−	1.14328i	0.980595	−	0.196043i	$-0.0628091\pi$
$20$	1.06193	−	1.83932i	0.237455	−	0.411283i
$21$		0			0
$22$	3.61359	−	6.25891i	0.770419	−	1.33440i
$23$	3.51415	+	6.08668i	0.732751	+	1.26916i	0.955703	+	0.294332i	$0.0950971\pi$
$23$	3.51415	+	6.08668i	0.732751	+	1.26916i	−0.222953	+	0.974829i	$0.571570\pi$
$24$		0			0
$25$	3.55553			0.711106
$26$	5.74026	+	1.57761i	1.12576	+	0.309396i
$27$		0			0
$28$	0.363055	+	0.628829i	0.0686109	+	0.118838i
$29$	0.599437	+	1.03826i	0.111313	+	0.192799i	0.916300	−	0.400493i	$-0.131161\pi$
$29$	0.599437	+	1.03826i	0.111313	+	0.192799i	−0.804987	+	0.593292i	$0.797828\pi$
$30$		0			0
$31$	−6.47277			−1.16254			−0.581271	−	0.813710i	$-0.697445\pi$
$31$	−6.47277			−1.16254			−0.581271	+	0.813710i	$0.697445\pi$
$32$	−1.96249	+	3.39914i	−0.346923	+	0.600888i
$33$		0			0
$34$	6.02830			1.03384
$35$	−1.46249	+	2.53311i	−0.247206	+	0.428174i
$36$		0			0
$37$	1.46249	+	2.53311i	0.240432	+	0.416441i	0.960837	−	0.277113i	$-0.0893775\pi$
$37$	1.46249	+	2.53311i	0.240432	+	0.416441i	−0.720405	+	0.693553i	$0.756044\pi$
$38$	9.50106			1.54128
$39$		0			0
$40$	−6.15215			−0.972741
$41$	−4.30219	−	7.45161i	−0.671889	−	1.16375i	−0.977368	−	0.211547i	$-0.932150\pi$
$41$	−4.30219	−	7.45161i	−0.671889	−	1.16375i	0.305479	−	0.952199i	$-0.401183\pi$
$42$		0			0
$43$	2.86305	−	4.95896i	0.436612	−	0.756234i	−0.560814	−	0.827942i	$-0.689512\pi$
$43$	2.86305	−	4.95896i	0.436612	−	0.756234i	0.997426	+	0.0717081i	$0.0228450\pi$
$44$	3.17833			0.479151
$45$		0			0
$46$	−5.80219	+	10.0497i	−0.855486	+	1.48174i
$47$	9.58383			1.39794			0.698972	−	0.715149i	$-0.253641\pi$
$47$	9.58383			1.39794			0.698972	+	0.715149i	$0.253641\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	2.93526	+	5.08401i	0.415108	+	0.718988i
$51$		0			0
$52$	0.661367	+	2.53311i	0.0917150	+	0.351279i
$53$	0.302187			0.0415086			0.0207543	−	0.999785i	$-0.493393\pi$
$53$	0.302187			0.0415086			0.0207543	+	0.999785i	$0.493393\pi$
$54$		0			0
$55$	6.40162	+	11.0879i	0.863195	+	1.49510i
$56$	1.05166	−	1.82152i	0.140533	−	0.243411i
$57$		0			0
$58$	−0.989727	+	1.71426i	−0.129958	+	0.225093i
$59$	1.51415	−	2.62258i	0.197125	−	0.341431i	−0.750470	−	0.660905i	$-0.770173\pi$
$59$	1.51415	−	2.62258i	0.197125	−	0.341431i	0.947595	+	0.319474i	$0.103506\pi$
$60$		0			0
$61$	0.151093	−	0.261701i	0.0193455	−	0.0335074i	−0.856191	−	0.516660i	$-0.827175\pi$
$61$	0.151093	−	0.261701i	0.0193455	−	0.0335074i	0.875536	+	0.483153i	$0.160508\pi$
$62$	−5.34357	−	9.25533i	−0.678634	−	1.17543i
$63$		0			0
$64$	3.36945			0.421182
$65$	−7.50494	+	7.40931i	−0.930873	+	0.919011i
$66$		0			0
$67$	4.35384	+	7.54108i	0.531907	+	0.921289i	0.999306	+	0.0372431i	$0.0118576\pi$
$67$	4.35384	+	7.54108i	0.531907	+	0.921289i	−0.467400	+	0.884046i	$0.654809\pi$
$68$	1.32555	+	2.29591i	0.160746	+	0.278420i
$69$		0			0
$70$	−4.82942			−0.577226
$71$	6.76855	−	11.7235i	0.803280	−	1.39132i	−0.114167	−	0.993462i	$-0.536420\pi$
$71$	6.76855	−	11.7235i	0.803280	−	1.39132i	0.917446	−	0.397859i	$-0.130247\pi$
$72$		0			0
$73$	0.932734			0.109168			0.0545841	−	0.998509i	$-0.482617\pi$
$73$	0.932734			0.109168			0.0545841	+	0.998509i	$0.482617\pi$
$74$	−2.41471	+	4.18240i	−0.280704	+	0.486194i
$75$		0			0
$76$	2.08916	+	3.61854i	0.239644	+	0.415075i
$77$	−4.37720			−0.498829
$78$		0			0
$79$	−16.9426			−1.90619			−0.953096	−	0.302668i	$-0.902123\pi$
$79$	−16.9426			−1.90619			−0.953096	+	0.302668i	$0.902123\pi$
$80$	−7.20275	−	12.4755i	−0.805292	−	1.39481i
$81$		0			0
$82$	7.10331	−	12.3033i	0.784430	−	1.35867i
$83$	1.26614			0.138977			0.0694885	−	0.997583i	$-0.477863\pi$
$83$	1.26614			0.138977			0.0694885	+	0.997583i	$0.477863\pi$
$84$		0			0
$85$	−5.33969	+	9.24862i	−0.579171	+	1.00315i
$86$	9.45434			1.01949
$87$		0			0
$88$	−4.60331	−	7.97317i	−0.490715	−	0.849943i
$89$	−6.69887	−	11.6028i	−0.710079	−	1.22989i	−0.964827	−	0.262886i	$-0.915326\pi$
$89$	−6.69887	−	11.6028i	−0.710079	−	1.22989i	0.254748	−	0.967008i	$-0.418008\pi$
$90$		0			0
$91$	−0.910836	−	3.48861i	−0.0954815	−	0.365705i
$92$	−5.10331			−0.532057
$93$		0			0
$94$	7.91190	+	13.7038i	0.816050	+	1.41344i
$95$	−8.41577	+	14.5765i	−0.863440	+	1.49552i
$96$		0			0
$97$	−5.96249	+	10.3273i	−0.605399	+	1.04858i	0.386589	+	0.922252i	$0.373653\pi$
$97$	−5.96249	+	10.3273i	−0.605399	+	1.04858i	−0.991988	+	0.126330i	$0.959680\pi$
$98$	0.825547	−	1.42989i	0.0833928	−	0.144441i
$99$		0			0
$100$	−1.29085	+	2.23582i	−0.129085	+	0.223582i
$101$	5.51415	+	9.55078i	0.548678	+	0.950339i	0.998365	+	0.0571525i	$0.0182021\pi$
$101$	5.51415	+	9.55078i	0.548678	+	0.950339i	−0.449687	+	0.893186i	$0.648465\pi$
$102$		0			0
$103$	−19.4543			−1.91689			−0.958447	−	0.285272i	$-0.907916\pi$
$103$	−19.4543			−1.91689			−0.958447	+	0.285272i	$0.907916\pi$
$104$	5.39669	−	5.32792i	0.529189	−	0.522446i
$105$		0			0
$106$	0.249469	+	0.432094i	0.0242306	+	0.0419686i
$107$	−0.711961	−	1.23315i	−0.0688279	−	0.119213i	0.829558	−	0.558421i	$-0.188593\pi$
$107$	−0.711961	−	1.23315i	−0.0688279	−	0.119213i	−0.898386	+	0.439208i	$0.855259\pi$
$108$		0			0
$109$	−0.0467198			−0.00447494			−0.00223747	−	0.999997i	$-0.500712\pi$
$109$	−0.0467198			−0.00447494			−0.00223747	+	0.999997i	$0.500712\pi$
$110$	−10.5697	+	18.3072i	−1.00778	+	1.74553i
$111$		0			0
$112$	4.92498			0.465367
$113$	−5.16912	+	8.95317i	−0.486270	+	0.842244i	−0.999875	−	0.0157826i	$-0.994976\pi$
$113$	−5.16912	+	8.95317i	−0.486270	+	0.842244i	0.513606	+	0.858026i	$0.328309\pi$
$114$		0			0
$115$	−10.2788	−	17.8035i	−0.958506	−	1.66018i
$116$	−0.870514			−0.0808252
$117$		0			0
$118$	5.00000			0.460287
$119$	−1.82555	−	3.16194i	−0.167348	−	0.289855i
$120$		0			0
$121$	−4.07995	+	7.06668i	−0.370905	+	0.642426i
$122$	0.498939			0.0451718
$123$		0			0
$124$	2.34997	−	4.07026i	0.211033	−	0.365520i
$125$	4.22505			0.377900
$126$		0			0
$127$	2.73638	+	4.73955i	0.242815	+	0.420567i	0.961515	−	0.274753i	$-0.0885960\pi$
$127$	2.73638	+	4.73955i	0.242815	+	0.420567i	−0.718700	+	0.695320i	$0.755263\pi$
$128$	6.70662	+	11.6162i	0.592787	+	1.02674i
$129$		0			0
$130$	−16.7902	−	4.61450i	−1.47259	−	0.404718i
$131$	−16.1706			−1.41283			−0.706415	−	0.707798i	$-0.749689\pi$
$131$	−16.1706			−1.41283			−0.706415	+	0.707798i	$0.749689\pi$
$132$		0			0
$133$	−2.87720	−	4.98346i	−0.249485	−	0.432121i
$134$	−7.18860	+	12.4510i	−0.621001	+	1.07560i
$135$		0			0
$136$	3.83969	−	6.65055i	0.329251	−	0.570280i
$137$	−6.00881	+	10.4076i	−0.513367	+	0.889178i	0.486512	+	0.873674i	$0.338269\pi$
$137$	−6.00881	+	10.4076i	−0.513367	+	0.889178i	−0.999880	+	0.0155048i	$0.995064\pi$
$138$		0			0
$139$	−0.674453	+	1.16819i	−0.0572064	+	0.0990844i	−0.893210	−	0.449639i	$-0.851553\pi$
$139$	−0.674453	+	1.16819i	−0.0572064	+	0.0990844i	0.836004	+	0.548723i	$0.184886\pi$
$140$	−1.06193	−	1.83932i	−0.0897494	−	0.155451i
$141$		0			0
$142$	22.3510			1.87566
$143$	−15.2180	−	4.18240i	−1.27259	−	0.349750i
$144$		0			0
$145$	−1.75334	−	3.03688i	−0.145607	−	0.252199i
$146$	0.770016	+	1.33371i	0.0637269	+	0.110378i
$147$		0			0
$148$	−2.12386			−0.174580
$149$	−1.53751	+	2.66304i	−0.125958	+	0.218165i	−0.922107	−	0.386935i	$-0.873534\pi$
$149$	−1.53751	+	2.66304i	−0.125958	+	0.218165i	0.796149	+	0.605100i	$0.206867\pi$
$150$		0			0
$151$	16.6610			1.35585			0.677925	−	0.735131i	$-0.262879\pi$
$151$	16.6610			1.35585			0.677925	+	0.735131i	$0.262879\pi$
$152$	6.05166	−	10.4818i	0.490854	−	0.850184i
$153$		0			0
$154$	−3.61359	−	6.25891i	−0.291191	−	0.504358i
$155$	18.9327			1.52071
$156$		0			0
$157$	12.8294			1.02390			0.511950	−	0.859015i	$-0.328923\pi$
$157$	12.8294			1.02390			0.511950	+	0.859015i	$0.328923\pi$
$158$	−13.9869	−	24.2260i	−1.11274	−	1.92732i
$159$		0			0
$160$	5.74026	−	9.94242i	0.453807	−	0.786017i
$161$	7.02830			0.553907
$162$		0			0
$163$	10.8022	−	18.7099i	0.846093	−	1.46548i	−0.0385764	−	0.999256i	$-0.512282\pi$
$163$	10.8022	−	18.7099i	0.846093	−	1.46548i	0.884669	−	0.466220i	$-0.154384\pi$
$164$	6.24772			0.487865
$165$		0			0
$166$	1.04526	+	1.81044i	0.0811278	+	0.140517i
$167$	10.6599	+	18.4635i	0.824888	+	1.42875i	0.902005	+	0.431726i	$0.142095\pi$
$167$	10.6599	+	18.4635i	0.824888	+	1.42875i	−0.0771165	+	0.997022i	$0.524571\pi$
$168$		0			0
$169$	0.166703	−	12.9989i	0.0128233	−	0.999918i
$170$	−17.6327			−1.35236
$171$		0			0
$172$	2.07889	+	3.60074i	0.158514	+	0.274554i
$173$	1.56087	−	2.70350i	0.118671	−	0.205543i	−0.800570	−	0.599239i	$-0.795470\pi$
$173$	1.56087	−	2.70350i	0.118671	−	0.205543i	0.919241	+	0.393695i	$0.128803\pi$
$174$		0			0
$175$	1.77777	−	3.07918i	0.134386	−	0.232764i
$176$	10.7788	−	18.6695i	0.812485	−	1.40726i
$177$		0			0
$178$	11.0605	−	19.1573i	0.829017	−	1.43590i
$179$	9.48545	+	16.4293i	0.708976	+	1.22798i	0.965237	+	0.261375i	$0.0841759\pi$
$179$	9.48545	+	16.4293i	0.708976	+	1.22798i	−0.256261	+	0.966608i	$0.582491\pi$
$180$		0			0
$181$	−1.93273			−0.143659			−0.0718295	−	0.997417i	$-0.522884\pi$
$181$	−1.93273			−0.143659			−0.0718295	+	0.997417i	$0.522884\pi$
$182$	4.23638	−	4.18240i	0.314022	−	0.310020i
$183$		0			0
$184$	7.39135	+	12.8022i	0.544898	+	0.943790i
$185$	−4.27777	−	7.40931i	−0.314508	−	0.544743i
$186$		0			0
$187$	−15.9816			−1.16869
$188$	−3.47945	+	6.02659i	−0.253765	+	0.439534i
$189$		0			0
$190$	−27.7905			−2.01613
$191$	−1.13695	+	1.96925i	−0.0822665	+	0.142490i	−0.904223	−	0.427060i	$-0.859549\pi$
$191$	−1.13695	+	1.96925i	−0.0822665	+	0.142490i	0.821957	+	0.569550i	$0.192883\pi$
$192$		0			0
$193$	2.19354	+	3.79932i	0.157894	+	0.273481i	0.934109	−	0.356988i	$-0.116196\pi$
$193$	2.19354	+	3.79932i	0.157894	+	0.273481i	−0.776215	+	0.630468i	$0.782863\pi$
$194$	−19.6893			−1.41361
$195$		0			0
$196$	0.726109			0.0518650
$197$	−2.62920	−	4.55390i	−0.187322	−	0.324452i	0.757034	−	0.653375i	$-0.226648\pi$
$197$	−2.62920	−	4.55390i	−0.187322	−	0.324452i	−0.944357	+	0.328923i	$0.893314\pi$
$198$		0			0
$199$	−6.59798	+	11.4280i	−0.467718	+	0.810111i	−0.999320	−	0.0368831i	$-0.988257\pi$
$199$	−6.59798	+	11.4280i	−0.467718	+	0.810111i	0.531601	+	0.846995i	$0.321590\pi$
$200$	7.47839			0.528802
$201$		0			0
$202$	−9.10437	+	15.7692i	−0.640581	+	1.10952i
$203$	1.19887			0.0841445
$204$		0			0
$205$	12.5838	+	21.7958i	0.878893	+	1.52229i
$206$	−16.0605	−	27.8175i	−1.11899	−	1.93814i
$207$		0			0
$208$	17.1224	+	4.70580i	1.18722	+	0.326289i
$209$	−25.1882			−1.74230
$210$		0			0
$211$	8.72077	+	15.1048i	0.600363	+	1.03986i	0.992766	+	0.120065i	$0.0383105\pi$
$211$	8.72077	+	15.1048i	0.600363	+	1.03986i	−0.392403	+	0.919793i	$0.628356\pi$
$212$	−0.109710	+	0.190024i	−0.00753494	+	0.0130509i
$213$		0			0
$214$	1.17551	−	2.03605i	0.0803565	−	0.139182i
$215$	−8.37439	+	14.5049i	−0.571129	+	0.989224i
$216$		0			0
$217$	−3.23638	+	5.60558i	−0.219700	+	0.380531i
$218$	−0.0385694	−	0.0668041i	−0.00261225	−	0.00452454i
$219$		0			0
$220$	−9.29656			−0.626774
$221$	−3.32555	−	12.7372i	−0.223700	−	0.856799i
$222$		0			0
$223$	−4.00106	−	6.93004i	−0.267931	−	0.464070i	0.700396	−	0.713754i	$-0.253007\pi$
$223$	−4.00106	−	6.93004i	−0.267931	−	0.464070i	−0.968327	+	0.249684i	$0.919673\pi$
$224$	1.96249	+	3.39914i	0.131125	+	0.227114i
$225$		0			0
$226$	−17.0694			−1.13544
$227$	−4.02976	+	6.97975i	−0.267464	+	0.463262i	−0.968206	−	0.250153i	$-0.919519\pi$
$227$	−4.02976	+	6.97975i	−0.267464	+	0.463262i	0.700742	+	0.713415i	$0.252852\pi$
$228$		0			0
$229$	−8.48052			−0.560408			−0.280204	−	0.959940i	$-0.590402\pi$
$229$	−8.48052			−0.560408			−0.280204	+	0.959940i	$0.590402\pi$
$230$	16.9713	−	29.3952i	1.11905	−	1.93826i
$231$		0			0
$232$	1.26080	+	2.18378i	0.0827758	+	0.143372i
$233$	10.2456			0.671211			0.335606	−	0.942003i	$-0.391059\pi$
$233$	10.2456			0.671211			0.335606	+	0.942003i	$0.391059\pi$
$234$		0			0
$235$	−28.0325			−1.82864
$236$	1.09944	+	1.90428i	0.0715673	+	0.123958i
$237$		0			0
$238$	3.01415	−	5.22066i	0.195378	−	0.338405i
$239$	11.3022			0.731078			0.365539	−	0.930796i	$-0.380885\pi$
$239$	11.3022			0.731078			0.365539	+	0.930796i	$0.380885\pi$
$240$		0			0
$241$	−0.518023	+	0.897242i	−0.0333688	+	0.0577965i	−0.882228	−	0.470823i	$-0.843957\pi$
$241$	−0.518023	+	0.897242i	−0.0333688	+	0.0577965i	0.848859	+	0.528620i	$0.177290\pi$
$242$	−13.4728			−0.866062
$243$		0			0
$244$	0.109710	+	0.190024i	0.00702349	+	0.0121650i
$245$	1.46249	+	2.53311i	0.0934352	+	0.161834i
$246$		0			0
$247$	−5.24132	−	20.0749i	−0.333497	−	1.27733i
$248$	−13.6142			−0.864506
$249$		0			0
$250$	3.48797	+	6.04135i	0.220599	+	0.382088i
$251$	6.64188	−	11.5041i	0.419232	−	0.726131i	−0.576631	−	0.817005i	$-0.695633\pi$
$251$	6.64188	−	11.5041i	0.419232	−	0.726131i	0.995862	+	0.0908742i	$0.0289661\pi$
$252$		0			0
$253$	15.3821	−	26.6426i	0.967067	−	1.67501i
$254$	−4.51802	+	7.82545i	−0.283486	+	0.491012i
$255$		0			0
$256$	−7.70381	+	13.3434i	−0.481488	+	0.833962i
$257$	6.22077	+	10.7747i	0.388041	+	0.672107i	0.992186	−	0.124768i	$-0.0398185\pi$
$257$	6.22077	+	10.7747i	0.388041	+	0.672107i	−0.604145	+	0.796875i	$0.706485\pi$
$258$		0			0
$259$	2.92498			0.181750
$260$	−1.93449	−	7.40931i	−0.119972	−	0.459506i
$261$		0			0
$262$	−13.3496	−	23.1221i	−0.824739	−	1.42849i
$263$	3.29579	+	5.70847i	0.203227	+	0.352000i	0.949566	−	0.313566i	$-0.101524\pi$
$263$	3.29579	+	5.70847i	0.203227	+	0.352000i	−0.746339	+	0.665566i	$0.768190\pi$
$264$		0			0
$265$	−0.883892			−0.0542970
$266$	4.75053	−	8.22816i	0.291274	−	0.504501i
$267$		0			0
$268$	−6.32273			−0.386222
$269$	−1.35812	+	2.35233i	−0.0828059	+	0.143424i	−0.904454	−	0.426571i	$-0.859721\pi$
$269$	−1.35812	+	2.35233i	−0.0828059	+	0.143424i	0.821648	+	0.569995i	$0.193055\pi$
$270$		0			0
$271$	15.3627	+	26.6089i	0.933215	+	1.61638i	0.777787	+	0.628528i	$0.216342\pi$
$271$	15.3627	+	26.6089i	0.933215	+	1.61638i	0.155428	+	0.987847i	$0.450324\pi$
$272$	17.9816			1.09029
$273$		0			0
$274$	−19.8422			−1.19871
$275$	−7.78164	−	13.4782i	−0.469251	−	0.812766i
$276$		0			0
$277$	10.7827	−	18.6762i	0.647870	−	1.12214i	−0.335761	−	0.941947i	$-0.608993\pi$
$277$	10.7827	−	18.6762i	0.647870	−	1.12214i	0.983631	−	0.180196i	$-0.0576732\pi$
$278$	−2.22717			−0.133577
$279$		0			0
$280$	−3.07608	+	5.32792i	−0.183831	+	0.318404i
$281$	−33.2058			−1.98089			−0.990447	−	0.137896i	$-0.955966\pi$
$281$	−33.2058			−1.98089			−0.990447	+	0.137896i	$0.955966\pi$
$282$		0			0
$283$	−0.741719	−	1.28470i	−0.0440906	−	0.0763672i	0.843138	−	0.537697i	$-0.180706\pi$
$283$	−0.741719	−	1.28470i	−0.0440906	−	0.0763672i	−0.887229	+	0.461330i	$0.847372\pi$
$284$	4.91471	+	8.51253i	0.291634	+	0.505126i
$285$		0			0
$286$	−6.58277	−	25.2128i	−0.389247	−	1.49086i
$287$	−8.60437			−0.507900
$288$		0			0
$289$	1.83476	+	3.17789i	0.107927	+	0.186935i
$290$	2.89494	−	5.01418i	0.169996	−	0.294442i
$291$		0			0
$292$	−0.338633	+	0.586530i	−0.0198170	+	0.0343241i
$293$	4.41577	−	7.64834i	0.257972	−	0.446821i	−0.707726	−	0.706487i	$-0.750279\pi$
$293$	4.41577	−	7.64834i	0.257972	−	0.446821i	0.965699	+	0.259666i	$0.0836124\pi$
$294$		0			0
$295$	−4.42886	+	7.67101i	−0.257858	+	0.446623i
$296$	3.07608	+	5.32792i	0.178793	+	0.309679i
$297$		0			0
$298$	−5.07714			−0.294111
$299$	24.4349	+	6.71551i	1.41310	+	0.388368i
$300$		0			0
$301$	−2.86305	−	4.95896i	−0.165024	−	0.285829i
$302$	13.7544	+	23.8233i	0.791477	+	1.37088i
$303$		0			0
$304$	28.3404			1.62543
$305$	−0.441946	+	0.765473i	−0.0253057	+	0.0438308i
$306$		0			0
$307$	11.6532			0.665084			0.332542	−	0.943088i	$-0.392094\pi$
$307$	11.6532			0.665084			0.332542	+	0.943088i	$0.392094\pi$
$308$	1.58916	−	2.75251i	0.0905510	−	0.156839i
$309$		0			0
$310$	15.6299	+	27.0717i	0.887716	+	1.53757i
$311$	25.0099			1.41818			0.709090	−	0.705118i	$-0.249106\pi$
$311$	25.0099			1.41818			0.709090	+	0.705118i	$0.249106\pi$
$312$		0			0
$313$	−0.186078			−0.0105178			−0.00525889	−	0.999986i	$-0.501674\pi$
$313$	−0.186078			−0.0105178			−0.00525889	+	0.999986i	$0.501674\pi$
$314$	10.5913	+	18.3446i	0.597701	+	1.03525i
$315$		0			0
$316$	6.15109	−	10.6540i	0.346026	−	0.599335i
$317$	0.540031			0.0303312			0.0151656	−	0.999885i	$-0.495172\pi$
$317$	0.540031			0.0303312			0.0151656	+	0.999885i	$0.495172\pi$
$318$		0			0
$319$	2.62386	−	4.54466i	0.146908	−	0.254452i
$320$	−9.85560			−0.550945
$321$		0			0
$322$	5.80219	+	10.0497i	0.323343	+	0.560047i
$323$	−10.5049	−	18.1951i	−0.584510	−	1.01240i
$324$		0			0
$325$	9.12280	−	9.00655i	0.506042	−	0.499594i
$326$	35.6708			1.97563
$327$		0			0
$328$	−9.04884	−	15.6731i	−0.499639	−	0.865400i
$329$	4.79191	−	8.29984i	0.264187	−	0.457585i
$330$		0			0
$331$	−0.770016	+	1.33371i	−0.0423239	+	0.0733071i	−0.886411	−	0.462898i	$-0.846809\pi$
$331$	−0.770016	+	1.33371i	−0.0423239	+	0.0733071i	0.844087	+	0.536206i	$0.180143\pi$
$332$	−0.459678	+	0.796186i	−0.0252281	+	0.0436964i
$333$		0			0
$334$	−17.6005	+	30.4850i	−0.963056	+	1.66806i
$335$	−12.7349	−	22.0575i	−0.695783	−	1.20513i
$336$		0			0
$337$	2.82942			0.154128			0.0770642	−	0.997026i	$-0.475445\pi$
$337$	2.82942			0.154128			0.0770642	+	0.997026i	$0.475445\pi$
$338$	18.7246	−	10.4929i	1.01849	−	0.570736i
$339$		0			0
$340$	−3.87720	−	6.71551i	−0.210271	−	0.364200i
$341$	14.1663	+	24.5368i	0.767148	+	1.32874i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	6.02190	−	10.4302i	0.324679	−	0.562361i
$345$		0			0
$346$	5.15428			0.277096
$347$	−12.6950	+	21.9884i	−0.681503	+	1.18040i	0.293019	+	0.956107i	$0.405340\pi$
$347$	−12.6950	+	21.9884i	−0.681503	+	1.18040i	−0.974522	+	0.224292i	$0.927993\pi$
$348$		0			0
$349$	0.542845	+	0.940235i	0.0290578	+	0.0503296i	0.880189	−	0.474624i	$-0.157416\pi$
$349$	0.542845	+	0.940235i	0.0290578	+	0.0503296i	−0.851131	+	0.524954i	$0.824083\pi$
$350$	5.87051			0.313792
$351$		0			0
$352$	17.1805			0.915721
$353$	5.26468	+	9.11869i	0.280211	+	0.485339i	0.971436	−	0.237300i	$-0.0762624\pi$
$353$	5.26468	+	9.11869i	0.280211	+	0.485339i	−0.691226	+	0.722639i	$0.742929\pi$
$354$		0			0
$355$	−19.7979	+	34.2910i	−1.05076	+	1.81998i
$356$	9.72823			0.515595
$357$		0			0
$358$	−15.6614	+	27.1263i	−0.827729	+	1.43367i
$359$	−27.2087			−1.43602			−0.718011	−	0.696031i	$-0.754947\pi$
$359$	−27.2087			−1.43602			−0.718011	+	0.696031i	$0.754947\pi$
$360$		0			0
$361$	−7.05659	−	12.2224i	−0.371400	−	0.643283i
$362$	−1.59556	−	2.76359i	−0.0838609	−	0.145251i
$363$		0			0
$364$	2.52442	+	0.693795i	0.132316	+	0.0363647i
$365$	−2.72823			−0.142802
$366$		0			0
$367$	3.12920	+	5.41993i	0.163343	+	0.282918i	0.936065	−	0.351826i	$-0.114439\pi$
$367$	3.12920	+	5.41993i	0.163343	+	0.282918i	−0.772723	+	0.634744i	$0.781106\pi$
$368$	−17.3071	+	29.9768i	−0.902196	+	1.56265i
$369$		0			0
$370$	7.06299	−	12.2335i	0.367187	−	0.635987i
$371$	0.151093	−	0.261701i	0.00784438	−	0.0135869i
$372$		0			0
$373$	0.589164	−	1.02046i	0.0305058	−	0.0528375i	−0.850369	−	0.526186i	$-0.823622\pi$
$373$	0.589164	−	1.02046i	0.0305058	−	0.0528375i	0.880875	+	0.473349i	$0.156955\pi$
$374$	−13.1935	−	22.8519i	−0.682222	−	1.18164i
$375$		0			0
$376$	20.1578			1.03956
$377$	4.16806	+	1.14552i	0.214666	+	0.0589973i
$378$		0			0
$379$	12.1033	+	20.9636i	0.621705	+	1.07683i	0.989168	+	0.146787i	$0.0468932\pi$
$379$	12.1033	+	20.9636i	0.621705	+	1.07683i	−0.367463	+	0.930038i	$0.619773\pi$
$380$	−6.11077	−	10.5842i	−0.313476	−	0.542956i
$381$		0			0
$382$	−3.75441			−0.192092
$383$	−1.24559	+	2.15743i	−0.0636469	+	0.110240i	−0.896093	−	0.443866i	$-0.853606\pi$
$383$	−1.24559	+	2.15743i	−0.0636469	+	0.110240i	0.832446	+	0.554106i	$0.186940\pi$
$384$		0			0
$385$	12.8032			0.652514
$386$	−3.62174	+	6.27303i	−0.184341	+	0.319289i
$387$		0			0
$388$	−4.32942	−	7.49878i	−0.219793	−	0.380693i
$389$	−23.6065			−1.19690			−0.598448	−	0.801161i	$-0.704216\pi$
$389$	−23.6065			−1.19690			−0.598448	+	0.801161i	$0.704216\pi$
$390$		0			0
$391$	25.6610			1.29773
$392$	−1.05166	−	1.82152i	−0.0531167	−	0.0920007i
$393$		0			0
$394$	4.34105	−	7.51891i	0.218699	−	0.378797i
$395$	49.5569			2.49348
$396$		0			0
$397$	4.42352	−	7.66177i	0.222010	−	0.384533i	−0.733408	−	0.679789i	$-0.762071\pi$
$397$	4.42352	−	7.66177i	0.222010	−	0.384533i	0.955418	+	0.295256i	$0.0954048\pi$
$398$	−21.7877			−1.09212
$399$		0			0
$400$	8.75547	+	15.1649i	0.437773	+	0.758246i
$401$	−9.45716	−	16.3803i	−0.472268	−	0.817992i	0.527229	−	0.849723i	$-0.323231\pi$
$401$	−9.45716	−	16.3803i	−0.472268	−	0.817992i	−0.999496	+	0.0317317i	$0.989898\pi$
$402$		0			0
$403$	−16.6078	+	16.3962i	−0.827296	+	0.816754i
$404$	−8.00775			−0.398400
$405$		0			0
$406$	0.989727	+	1.71426i	0.0491193	+	0.0850772i
$407$	6.40162	−	11.0879i	0.317317	−	0.549609i
$408$		0			0
$409$	−1.74947	+	3.03017i	−0.0865057	+	0.149832i	−0.906032	−	0.423210i	$-0.860903\pi$
$409$	−1.74947	+	3.03017i	−0.0865057	+	0.149832i	0.819526	+	0.573042i	$0.194237\pi$
$410$	−20.7771	+	35.9869i	−1.02611	+	1.77727i
$411$		0			0
$412$	7.06299	−	12.2335i	0.347969	−	0.602699i
$413$	−1.51415	−	2.62258i	−0.0745064	−	0.129049i
$414$		0			0
$415$	−3.70344			−0.181795
$416$	3.57502	+	13.6927i	0.175280	+	0.671341i
$417$		0			0
$418$	−20.7940	−	36.0163i	−1.01707	−	1.76162i
$419$	14.4158	+	24.9688i	0.704257	+	1.21981i	0.966959	+	0.254931i	$0.0820529\pi$
$419$	14.4158	+	24.9688i	0.704257	+	1.21981i	−0.262703	+	0.964877i	$0.584614\pi$
$420$		0			0
$421$	34.3227			1.67279			0.836394	−	0.548129i	$-0.184660\pi$
$421$	34.3227			1.67279			0.836394	+	0.548129i	$0.184660\pi$
$422$	−14.3988	+	24.9395i	−0.700923	+	1.21403i
$423$		0			0
$424$	0.635593			0.0308671
$425$	6.49079	−	11.2424i	0.314849	−	0.545335i
$426$		0			0
$427$	−0.151093	−	0.261701i	−0.00731192	−	0.0126646i
$428$	1.03392			0.0499766
$429$		0			0
$430$	−27.6538			−1.33358
$431$	14.6779	+	25.4229i	0.707011	+	1.22458i	0.965961	+	0.258688i	$0.0832902\pi$
$431$	14.6779	+	25.4229i	0.707011	+	1.22458i	−0.258950	+	0.965891i	$0.583376\pi$
$432$		0			0
$433$	−14.3032	+	24.7740i	−0.687370	+	1.19056i	0.285315	+	0.958434i	$0.407902\pi$
$433$	−14.3032	+	24.7740i	−0.687370	+	1.19056i	−0.972686	+	0.232126i	$0.925432\pi$
$434$	−10.6871			−0.512999
$435$		0			0
$436$	0.0169618	−	0.0293788i	0.000812325	−	0.00140699i
$437$	40.4437			1.93468
$438$		0			0
$439$	−17.2399	−	29.8603i	−0.822813	−	1.42515i	−0.903579	−	0.428422i	$-0.859070\pi$
$439$	−17.2399	−	29.8603i	−0.822813	−	1.42515i	0.0807654	−	0.996733i	$-0.474264\pi$
$440$	13.4646	+	23.3214i	0.641900	+	1.11180i
$441$		0			0
$442$	15.4674	−	15.2703i	0.735711	−	0.726336i
$443$	12.9066			0.613209			0.306605	−	0.951837i	$-0.400807\pi$
$443$	12.9066			0.613209			0.306605	+	0.951837i	$0.400807\pi$
$444$		0			0
$445$	19.5941	+	33.9380i	0.928849	+	1.60881i
$446$	6.60613	−	11.4421i	0.312809	−	0.541801i
$447$		0			0
$448$	1.68473	−	2.91803i	0.0795958	−	0.137864i
$449$	−2.81915	+	4.88291i	−0.133044	+	0.230439i	−0.924848	−	0.380336i	$-0.875808\pi$
$449$	−2.81915	+	4.88291i	−0.133044	+	0.230439i	0.791805	+	0.610774i	$0.209142\pi$
$450$		0			0
$451$	−18.8315	+	32.6172i	−0.886743	+	1.53588i
$452$	−3.75334	−	6.50098i	−0.176542	−	0.305781i
$453$		0			0
$454$	−13.3070			−0.624529
$455$	2.66418	+	10.2041i	0.124899	+	0.478376i
$456$		0			0
$457$	−18.9947	−	32.8997i	−0.888533	−	1.53898i	−0.841610	−	0.540086i	$-0.818392\pi$
$457$	−18.9947	−	32.8997i	−0.888533	−	1.53898i	−0.0469228	−	0.998899i	$-0.514941\pi$
$458$	−7.00106	−	12.1262i	−0.327138	−	0.566620i
$459$		0			0
$460$	14.9271			0.695980
$461$	−3.30365	+	5.72209i	−0.153866	+	0.266504i	−0.932646	−	0.360794i	$-0.882506\pi$
$461$	−3.30365	+	5.72209i	−0.153866	+	0.266504i	0.778779	+	0.627298i	$0.215839\pi$
$462$		0			0
$463$	9.98933			0.464243			0.232122	−	0.972687i	$-0.425433\pi$
$463$	9.98933			0.464243			0.232122	+	0.972687i	$0.425433\pi$
$464$	−2.95222	+	5.11339i	−0.137053	+	0.237383i
$465$		0			0
$466$	8.45822	+	14.6501i	0.391819	+	0.678651i
$467$	−3.42100			−0.158305			−0.0791525	−	0.996863i	$-0.525221\pi$
$467$	−3.42100			−0.158305			−0.0791525	+	0.996863i	$0.525221\pi$
$468$		0			0
$469$	8.70769			0.402084
$470$	−23.1422	−	40.0834i	−1.06747	−	1.84891i
$471$		0			0
$472$	3.18473	−	5.51611i	0.146589	−	0.253899i
$473$	−25.0643			−1.15246
$474$		0			0
$475$	10.2300	−	17.7189i	0.469384	−	0.812997i
$476$	2.65109			0.121513
$477$		0			0
$478$	9.33048	+	16.1609i	0.426766	+	0.739181i
$479$	9.92071	+	17.1832i	0.453289	+	0.785119i	0.998588	−	0.0531223i	$-0.0169173\pi$
$479$	9.92071	+	17.1832i	0.453289	+	0.785119i	−0.545299	+	0.838241i	$0.683584\pi$
$480$		0			0
$481$	10.1691	+	2.79481i	0.463672	+	0.127432i
$482$	−1.71061			−0.0779161
$483$		0			0
$484$	−2.96249	−	5.13119i	−0.134659	−	0.233236i
$485$	17.4402	−	30.2073i	0.791918	−	1.37164i
$486$		0			0
$487$	3.05166	−	5.28562i	0.138284	−	0.239514i	−0.788563	−	0.614954i	$-0.789175\pi$
$487$	3.05166	−	5.28562i	0.138284	−	0.239514i	0.926847	+	0.375439i	$0.122508\pi$
$488$	0.317797	−	0.550440i	0.0143860	−	0.0249172i
$489$		0			0
$490$	−2.41471	+	4.18240i	−0.109086	+	0.188942i
$491$	−1.18326	−	2.04947i	−0.0534000	−	0.0924915i	0.838090	−	0.545532i	$-0.183672\pi$
$491$	−1.18326	−	2.04947i	−0.0534000	−	0.0924915i	−0.891490	+	0.453041i	$0.850339\pi$
$492$		0			0
$493$	4.37720			0.197139
$494$	24.3779	−	24.0672i	1.09681	−	1.08284i
$495$		0			0
$496$	−15.9391	−	27.6074i	−0.715688	−	1.23961i
$497$	−6.76855	−	11.7235i	−0.303611	−	0.525870i
$498$		0			0
$499$	−4.29231			−0.192150			−0.0960752	−	0.995374i	$-0.530629\pi$
$499$	−4.29231			−0.192150			−0.0960752	+	0.995374i	$0.530629\pi$
$500$	−1.53392	+	2.65683i	−0.0685992	+	0.118817i
$501$		0			0
$502$	21.9327			0.978906
$503$	−1.05553	+	1.82823i	−0.0470638	+	0.0815169i	−0.888598	−	0.458687i	$-0.848320\pi$
$503$	−1.05553	+	1.82823i	−0.0470638	+	0.0815169i	0.841534	+	0.540204i	$0.181653\pi$
$504$		0			0
$505$	−16.1288	−	27.9359i	−0.717722	−	1.24313i
$506$	50.7947			2.25810
$507$		0			0
$508$	−3.97383			−0.176310
$509$	−12.1882	−	21.1106i	−0.540233	−	0.935710i	−0.998890	−	0.0470972i	$-0.985003\pi$
$509$	−12.1882	−	21.1106i	−0.540233	−	0.935710i	0.458658	−	0.888613i	$-0.348330\pi$
$510$		0			0
$511$	0.466367	−	0.807771i	0.0206309	−	0.0357337i
$512$	1.38708			0.0613007
$513$		0			0
$514$	−10.2711	+	17.7900i	−0.453038	+	0.784684i
$515$	56.9036			2.50747
$516$		0			0
$517$	−20.9752	−	36.3301i	−0.922487	−	1.59779i
$518$	2.41471	+	4.18240i	0.106096	+	0.183764i
$519$		0			0
$520$	−15.7852	+	15.5841i	−0.692228	+	0.683407i
$521$	17.8401			0.781589			0.390794	−	0.920478i	$-0.372200\pi$
$521$	17.8401			0.781589			0.390794	+	0.920478i	$0.372200\pi$
$522$		0			0
$523$	15.5279	+	26.8951i	0.678987	+	1.17604i	0.975286	+	0.220945i	$0.0709143\pi$
$523$	15.5279	+	26.8951i	0.678987	+	1.17604i	−0.296299	+	0.955095i	$0.595752\pi$
$524$	5.87080	−	10.1685i	0.256467	−	0.444214i
$525$		0			0
$526$	−5.44166	+	9.42522i	−0.237267	+	0.410959i
$527$	−11.8163	+	20.4665i	−0.514728	+	0.891534i
$528$		0			0
$529$	−13.1985	+	22.8604i	−0.573847	+	0.993932i
$530$	−0.729694	−	1.26387i	−0.0316959	−	0.0548989i
$531$		0			0
$532$	4.17833			0.181154
$533$	−29.9143	−	8.22145i	−1.29573	−	0.356110i
$534$		0			0
$535$	2.08248	+	3.60695i	0.0900333	+	0.155942i
$536$	9.15749	+	15.8612i	0.395543	+	0.685101i
$537$		0			0
$538$	−4.48476			−0.193352
$539$	−2.18860	+	3.79077i	−0.0942697	+	0.163280i
$540$		0			0
$541$	−33.3900			−1.43555			−0.717774	−	0.696276i	$-0.754839\pi$
$541$	−33.3900			−1.43555			−0.717774	+	0.696276i	$0.754839\pi$
$542$	−25.3652	+	43.9338i	−1.08953	+	1.88712i
$543$		0			0
$544$	7.16524	+	12.4106i	0.307207	+	0.532098i
$545$	0.136655			0.00585364
$546$		0			0
$547$	9.12306			0.390074			0.195037	−	0.980796i	$-0.437517\pi$
$547$	9.12306			0.390074			0.195037	+	0.980796i	$0.437517\pi$
$548$	−4.36305	−	7.55703i	−0.186380	−	0.322820i
$549$		0			0
$550$	12.8482	−	22.2538i	0.547850	−	0.948904i
$551$	6.89881			0.293899
$552$		0			0
$553$	−8.47130	+	14.6727i	−0.360236	+	0.623948i
$554$	35.6065			1.51278
$555$		0			0
$556$	−0.489727	−	0.848232i	−0.0207690	−	0.0359730i
$557$	−19.0148	−	32.9346i	−0.805683	−	1.39548i	−0.915829	−	0.401569i	$-0.868465\pi$
$557$	−19.0148	−	32.9346i	−0.805683	−	1.39548i	0.110145	−	0.993915i	$-0.464868\pi$
$558$		0			0
$559$	−5.21555	−	19.9761i	−0.220594	−	0.844901i
$560$	−14.4055			−0.608743
$561$		0			0
$562$	−27.4130	−	47.4806i	−1.15635	−	2.00285i
$563$	−1.68326	+	2.91550i	−0.0709411	+	0.122874i	−0.899314	−	0.437303i	$-0.855934\pi$
$563$	−1.68326	+	2.91550i	−0.0709411	+	0.122874i	0.828373	+	0.560177i	$0.189267\pi$
$564$		0			0
$565$	15.1196	−	26.1879i	0.636086	−	1.10173i
$566$	1.22465	−	2.12115i	0.0514758	−	0.0891587i
$567$		0			0
$568$	14.2364	−	24.6581i	0.597345	−	1.03463i
$569$	−8.96637	−	15.5302i	−0.375890	−	0.651060i	0.614570	−	0.788862i	$-0.289329\pi$
$569$	−8.96637	−	15.5302i	−0.375890	−	0.651060i	−0.990460	+	0.137802i	$0.955996\pi$
$570$		0			0
$571$	39.4274			1.64998			0.824992	−	0.565144i	$-0.191180\pi$
$571$	39.4274			1.64998			0.824992	+	0.565144i	$0.191180\pi$
$572$	8.15497	−	8.05106i	0.340976	−	0.336632i
$573$		0			0
$574$	−7.10331	−	12.3033i	−0.296487	−	0.513530i
$575$	12.4947	+	21.6414i	0.521063	+	0.902508i
$576$		0			0
$577$	16.4239			0.683737			0.341868	−	0.939748i	$-0.388940\pi$
$577$	16.4239			0.683737			0.341868	+	0.939748i	$0.388940\pi$
$578$	−3.02936	+	5.24700i	−0.126005	+	0.218246i
$579$		0			0
$580$	2.54624			0.105727
$581$	0.633070	−	1.09651i	0.0262642	−	0.0454909i
$582$		0			0
$583$	−0.661367	−	1.14552i	−0.0273910	−	0.0474426i
$584$	1.96183			0.0811811
$585$		0			0
$586$	14.5817			0.602365
$587$	−7.46355	−	12.9273i	−0.308054	−	0.533565i	0.669883	−	0.742467i	$-0.266344\pi$
$587$	−7.46355	−	12.9273i	−0.308054	−	0.533565i	−0.977937	+	0.208902i	$0.933011\pi$
$588$		0			0
$589$	−18.6235	+	32.2568i	−0.767366	+	1.32912i
$590$	−14.6249			−0.602098
$591$		0			0
$592$	−7.20275	+	12.4755i	−0.296031	+	0.512741i
$593$	−29.9164			−1.22852			−0.614260	−	0.789103i	$-0.710546\pi$
$593$	−29.9164			−1.22852			−0.614260	+	0.789103i	$0.710546\pi$
$594$		0			0
$595$	5.33969	+	9.24862i	0.218906	+	0.379157i
$596$	−1.11640	−	1.93366i	−0.0457295	−	0.0792058i
$597$		0			0
$598$	10.5697	+	40.4831i	0.432226	+	1.65548i
$599$	−35.1911			−1.43787			−0.718935	−	0.695077i	$-0.755370\pi$
$599$	−35.1911			−1.43787			−0.718935	+	0.695077i	$0.755370\pi$
$600$		0			0
$601$	−8.56580	−	14.8364i	−0.349406	−	0.605190i	0.636738	−	0.771080i	$-0.280283\pi$
$601$	−8.56580	−	14.8364i	−0.349406	−	0.605190i	−0.986144	+	0.165891i	$0.946950\pi$
$602$	4.72717	−	8.18770i	0.192665	−	0.333706i
$603$		0			0
$604$	−6.04884	+	10.4769i	−0.246124	+	0.426299i
$605$	11.9338	−	20.6699i	0.485178	−	0.840353i
$606$		0			0
$607$	−11.2233	+	19.4393i	−0.455540	+	0.789018i	−0.998719	−	0.0505990i	$-0.983887\pi$
$607$	−11.2233	+	19.4393i	−0.455540	+	0.789018i	0.543180	+	0.839617i	$0.317220\pi$
$608$	11.2930	+	19.5600i	0.457991	+	0.793263i
$609$		0			0
$610$	−1.45939			−0.0590889
$611$	24.5902	−	24.2769i	0.994814	−	0.982138i
$612$		0			0
$613$	10.1029	+	17.4988i	0.408053	+	0.706768i	0.994672	−	0.103095i	$-0.0328746\pi$
$613$	10.1029	+	17.4988i	0.408053	+	0.706768i	−0.586619	+	0.809863i	$0.699541\pi$
$614$	9.62027	+	16.6628i	0.388243	+	0.672456i
$615$		0			0
$616$	−9.20662			−0.370945
$617$	19.3408	−	33.4992i	0.778630	−	1.34863i	−0.154102	−	0.988055i	$-0.549249\pi$
$617$	19.3408	−	33.4992i	0.778630	−	1.34863i	0.932732	−	0.360571i	$-0.117418\pi$
$618$		0			0
$619$	32.5109			1.30672			0.653362	−	0.757045i	$-0.273358\pi$
$619$	32.5109			1.30672			0.653362	+	0.757045i	$0.273358\pi$
$620$	−6.87362	+	11.9055i	−0.276051	+	0.478135i
$621$		0			0
$622$	20.6468	+	35.7613i	0.827862	+	1.43390i
$623$	−13.3977			−0.536769
$624$		0			0
$625$	−30.1359			−1.20543
$626$	−0.153616	−	0.266071i	−0.00613975	−	0.0106344i
$627$		0			0
$628$	−4.65778	+	8.06752i	−0.185866	+	0.321929i
$629$	10.6794			0.425815
$630$		0			0
$631$	18.9310	−	32.7894i	0.753630	−	1.30533i	−0.192422	−	0.981312i	$-0.561634\pi$
$631$	18.9310	−	32.7894i	0.753630	−	1.30533i	0.946052	−	0.324014i	$-0.105032\pi$
$632$	−35.6356			−1.41751
$633$		0			0
$634$	0.445821	+	0.772184i	0.0177058	+	0.0306674i
$635$	−8.00388	−	13.8631i	−0.317624	−	0.550141i
$636$		0			0
$637$	−3.47664	−	0.955496i	−0.137749	−	0.0378581i
$638$	8.66447			0.343030
$639$		0			0
$640$	−19.6168	−	33.9772i	−0.775421	−	1.34307i
$641$	11.4314	−	19.7997i	0.451512	−	0.782042i	−0.546968	−	0.837154i	$-0.684218\pi$
$641$	11.4314	−	19.7997i	0.451512	−	0.782042i	0.998480	+	0.0551112i	$0.0175513\pi$
$642$		0			0
$643$	−21.7915	+	37.7440i	−0.859373	+	1.48848i	0.0131542	+	0.999913i	$0.495813\pi$
$643$	−21.7915	+	37.7440i	−0.859373	+	1.48848i	−0.872528	+	0.488565i	$0.837521\pi$
$644$	−2.55166	+	4.41960i	−0.100549	+	0.174157i
$645$		0			0
$646$	17.3446	−	30.0418i	0.682415	−	1.18198i
$647$	−1.50388	−	2.60479i	−0.0591234	−	0.102405i	0.834949	−	0.550328i	$-0.185497\pi$
$647$	−1.50388	−	2.60479i	−0.0591234	−	0.102405i	−0.894072	+	0.447923i	$0.852164\pi$
$648$		0			0
$649$	−13.2555			−0.520323
$650$	20.4097	+	5.60926i	0.800533	+	0.220013i
$651$		0			0
$652$	7.84357	+	13.5855i	0.307178	+	0.532048i
$653$	−16.9621	−	29.3792i	−0.663778	−	1.14970i	−0.979615	−	0.200884i	$-0.935619\pi$
$653$	−16.9621	−	29.3792i	−0.663778	−	1.14970i	0.315837	−	0.948813i	$-0.397715\pi$
$654$		0			0
$655$	47.2987			1.84811
$656$	21.1882	−	36.6990i	0.827260	−	1.43286i
$657$		0			0
$658$	15.8238			0.616876
$659$	−21.7297	+	37.6369i	−0.846469	+	1.46613i	0.0378709	+	0.999283i	$0.487942\pi$
$659$	−21.7297	+	37.6369i	−0.846469	+	1.46613i	−0.884340	+	0.466844i	$0.845391\pi$
$660$		0			0
$661$	−19.1429	−	33.1565i	−0.744574	−	1.28964i	−0.950393	−	0.311050i	$-0.899319\pi$
$661$	−19.1429	−	33.1565i	−0.744574	−	1.28964i	0.205819	−	0.978590i	$-0.434014\pi$
$662$	−2.54274			−0.0988262
$663$		0			0
$664$	2.66309			0.103348
$665$	8.41577	+	14.5765i	0.326350	+	0.565254i
$666$		0			0
$667$	−4.21302	+	7.29717i	−0.163129	+	0.282548i
$668$	−15.4805			−0.598959
$669$		0			0
$670$	21.0265	−	36.4190i	0.812326	−	1.40699i
$671$	−1.32273			−0.0510635
$672$		0			0
$673$	−14.0902	−	24.4050i	−0.543138	−	0.940743i	−0.998722	−	0.0505499i	$-0.983903\pi$
$673$	−14.0902	−	24.4050i	−0.543138	−	0.940743i	0.455583	−	0.890193i	$-0.349431\pi$
$674$	2.33582	+	4.04576i	0.0899724	+	0.155837i
$675$		0			0
$676$	8.11359	+	4.82415i	0.312061	+	0.185544i
$677$	31.7253			1.21930			0.609651	−	0.792670i	$-0.291309\pi$
$677$	31.7253			1.21930			0.609651	+	0.792670i	$0.291309\pi$
$678$		0			0
$679$	5.96249	+	10.3273i	0.228819	+	0.396327i
$680$	−11.2310	+	19.4527i	−0.430691	+	0.745979i
$681$		0			0
$682$	−23.3899	+	40.5125i	−0.895645	+	1.55130i
$683$	4.28698	−	7.42526i	0.164037	−	0.284120i	−0.772276	−	0.635287i	$-0.780882\pi$
$683$	4.28698	−	7.42526i	0.164037	−	0.284120i	0.936313	+	0.351167i	$0.114215\pi$
$684$		0			0
$685$	17.5757	−	30.4420i	0.671532	−	1.16313i
$686$	−0.825547	−	1.42989i	−0.0315195	−	0.0545934i
$687$		0			0
$688$	28.2010			1.07515
$689$	0.775352	−	0.765473i	0.0295386	−	0.0291622i
$690$		0			0
$691$	3.47518	+	6.01919i	0.132202	+	0.228981i	0.924525	−	0.381121i	$-0.124462\pi$
$691$	3.47518	+	6.01919i	0.132202	+	0.228981i	−0.792323	+	0.610102i	$0.791129\pi$
$692$	1.13336	+	1.96304i	0.0430839	+	0.0746235i
$693$		0			0
$694$	−41.9213			−1.59131
$695$	1.97277	−	3.41693i	0.0748312	−	0.129612i
$696$		0			0
$697$	−31.4154			−1.18994
$698$	−0.896287	+	1.55242i	−0.0339250	+	0.0587598i
$699$		0			0
$700$	1.29085	+	2.23582i	0.0487896	+	0.0845061i
$701$	21.8443			0.825049			0.412525	−	0.910946i	$-0.364647\pi$
$701$	21.8443			0.825049			0.412525	+	0.910946i	$0.364647\pi$
$702$		0			0
$703$	16.8315			0.634814
$704$	−7.37439	−	12.7728i	−0.277933	−	0.481394i
$705$		0			0
$706$	−8.69248	+	15.0558i	−0.327146	+	0.566633i
$707$	11.0283			0.414762
$708$		0			0
$709$	−4.87187	+	8.43832i	−0.182967	+	0.316908i	−0.942890	−	0.333106i	$-0.891903\pi$
$709$	−4.87187	+	8.43832i	−0.182967	+	0.316908i	0.759923	+	0.650013i	$0.225237\pi$
$710$	−65.3764			−2.45353
$711$		0			0
$712$	−14.0898	−	24.4043i	−0.528039	−	0.914590i
$713$	−22.7463	−	39.3977i	−0.851854	−	1.47545i
$714$		0			0
$715$	44.5123	+	12.2335i	1.66467	+	0.457505i
$716$	−13.7750			−0.514794
$717$		0			0
$718$	−22.4621	−	38.9055i	−0.838278	−	1.45194i
$719$	−2.52296	+	4.36989i	−0.0940905	+	0.162970i	−0.909229	−	0.416297i	$-0.863328\pi$
$719$	−2.52296	+	4.36989i	−0.0940905	+	0.162970i	0.815138	+	0.579267i	$0.196661\pi$
$720$		0			0
$721$	−9.72717	+	16.8480i	−0.362259	+	0.627451i
$722$	11.6511	−	20.1803i	0.433609	−	0.751032i
$723$		0			0
$724$	0.701688	−	1.21536i	0.0260780	−	0.0451685i
$725$	2.13132	+	3.69155i	0.0791552	+	0.137101i
$726$		0			0
$727$	6.66659			0.247250			0.123625	−	0.992329i	$-0.460548\pi$
$727$	6.66659			0.247250			0.123625	+	0.992329i	$0.460548\pi$
$728$	−1.91577	−	7.33763i	−0.0710032	−	0.271951i
$729$		0			0
$730$	−2.25228	−	3.90107i	−0.0833607	−	0.144385i
$731$	−10.4533	−	18.1056i	−0.386629	−	0.669660i
$732$		0			0
$733$	47.4076			1.75104			0.875520	−	0.483181i	$-0.160519\pi$
$733$	47.4076			1.75104			0.875520	+	0.483181i	$0.160519\pi$
$734$	−5.16659	+	8.94880i	−0.190702	+	0.330306i
$735$		0			0
$736$	−27.5860			−1.01683
$737$	19.0577	−	33.0088i	0.701998	−	1.21590i
$738$		0			0
$739$	−3.09023	−	5.35243i	−0.113676	−	0.196892i	0.803574	−	0.595205i	$-0.202929\pi$
$739$	−3.09023	−	5.35243i	−0.113676	−	0.196892i	−0.917250	+	0.398313i	$0.869596\pi$
$740$	6.21225			0.228367
$741$		0			0
$742$	0.498939			0.0183166
$743$	−11.6667	−	20.2073i	−0.428010	−	0.741335i	0.568686	−	0.822554i	$-0.307452\pi$
$743$	−11.6667	−	20.2073i	−0.428010	−	0.741335i	−0.996696	+	0.0812197i	$0.974118\pi$
$744$		0			0
$745$	4.49719	−	7.78936i	0.164764	−	0.285380i
$746$	1.94553			0.0712309
$747$		0			0
$748$	5.80219	−	10.0497i	0.212149	−	0.367453i
$749$	−1.42392			−0.0520290
$750$		0			0
$751$	0.488375	+	0.845890i	0.0178211	+	0.0308670i	0.874798	−	0.484487i	$-0.160994\pi$
$751$	0.488375	+	0.845890i	0.0178211	+	0.0308670i	−0.856977	+	0.515354i	$0.827660\pi$
$752$	23.6001	+	40.8766i	0.860607	+	1.49062i
$753$		0			0
$754$	1.80296	+	6.90554i	0.0656598	+	0.251485i
$755$	−48.7331			−1.77358
$756$		0			0
$757$	4.38254	+	7.59078i	0.159286	+	0.275892i	0.934611	−	0.355670i	$-0.115747\pi$
$757$	4.38254	+	7.59078i	0.159286	+	0.275892i	−0.775325	+	0.631562i	$0.782414\pi$
$758$	−19.9837	+	34.6128i	−0.725841	+	1.25719i
$759$		0			0
$760$	−17.7010	+	30.6590i	−0.642083	+	1.11212i
$761$	−10.7276	+	18.5807i	−0.388874	+	0.673550i	−0.992298	−	0.123871i	$-0.960469\pi$
$761$	−10.7276	+	18.5807i	−0.388874	+	0.673550i	0.603424	+	0.797420i	$0.293803\pi$
$762$		0			0
$763$	−0.0233599	+	0.0404605i	−0.000845685	+	0.00146477i
$764$	−0.825547	−	1.42989i	−0.0298672	−	0.0517316i
$765$		0			0
$766$	−4.11319			−0.148615
$767$	−2.75828	−	10.5645i	−0.0995957	−	0.381463i
$768$		0			0
$769$	−11.0750	−	19.1825i	−0.399375	−	0.691738i	0.594274	−	0.804263i	$-0.297440\pi$
$769$	−11.0750	−	19.1825i	−0.399375	−	0.691738i	−0.993649	+	0.112525i	$0.964106\pi$
$770$	10.5697	+	18.3072i	0.380905	+	0.659746i
$771$		0			0
$772$	−3.18550			−0.114649
$773$	−9.57995	+	16.5930i	−0.344567	+	0.596807i	−0.985275	−	0.170977i	$-0.945308\pi$
$773$	−9.57995	+	16.5930i	−0.344567	+	0.596807i	0.640708	+	0.767785i	$0.278641\pi$
$774$		0			0
$775$	−23.0141			−0.826692
$776$	−12.5410	+	21.7216i	−0.450195	+	0.779761i
$777$		0			0
$778$	−19.4883	−	33.7547i	−0.698688	−	1.21016i
$779$	−49.5131			−1.77399
$780$		0			0
$781$	−59.2547			−2.12030
$782$	21.1843	+	36.6923i	0.757550	+	1.31212i
$783$		0			0
$784$	2.46249	−	4.26516i	0.0879461	−	0.152327i
$785$	−37.5259			−1.33936
$786$		0			0
$787$	−22.0898	+	38.2607i	−0.787417	+	1.36385i	0.140127	+	0.990134i	$0.455249\pi$
$787$	−22.0898	+	38.2607i	−0.787417	+	1.36385i	−0.927544	+	0.373713i	$0.878084\pi$
$788$	3.81817			0.136017
$789$		0			0
$790$	40.9115	+	70.8608i	1.45557	+	2.52111i
$791$	5.16912	+	8.95317i	0.183793	+	0.318338i
$792$		0			0
$793$	−0.275243	−	1.05421i	−0.00977415	−	0.0374361i
$794$	14.6073			0.518394
$795$		0			0
$796$	−4.79085	−	8.29800i	−0.169807	−	0.294115i
$797$	6.82807	−	11.8266i	0.241863	−	0.418918i	−0.719382	−	0.694614i	$-0.755575\pi$
$797$	6.82807	−	11.8266i	0.241863	−	0.418918i	0.961245	+	0.275696i	$0.0889083\pi$
$798$		0			0
$799$	17.4957	−	30.3035i	0.618954	−	1.07206i
$800$	−6.97770	+	12.0857i	−0.246699	+	0.427295i
$801$		0			0
$802$	15.6146	−	27.0454i	0.551372	−	0.955005i
$803$	−2.04138	−	3.53578i	−0.0720388	−	0.124775i
$804$		0			0
$805$	−20.5577			−0.724562
$806$	−37.1553	−	10.2115i	−1.30874	−	0.359686i
$807$		0			0
$808$	11.5980	+	20.0883i	0.408015	+	0.706703i
$809$	17.0039	+	29.4516i	0.597824	+	1.03546i	0.993142	+	0.116918i	$0.0373013\pi$
$809$	17.0039	+	29.4516i	0.597824	+	1.03546i	−0.395317	+	0.918545i	$0.629365\pi$
$810$		0			0
$811$	−21.4084			−0.751751			−0.375876	−	0.926670i	$-0.622658\pi$
$811$	−21.4084			−0.751751			−0.375876	+	0.926670i	$0.622658\pi$
$812$	−0.435257	+	0.753887i	−0.0152745	+	0.0264563i
$813$		0			0
$814$	21.1394			0.740934
$815$	−31.5962	+	54.7263i	−1.10677	+	1.91698i
$816$		0			0
$817$	−16.4752	−	28.5358i	−0.576394	−	0.998343i
$818$	−5.77707			−0.201991
$819$		0			0
$820$	−18.2745			−0.638172
$821$	13.5683	+	23.5010i	0.473538	+	0.820192i	0.999541	−	0.0302909i	$-0.00964336\pi$
$821$	13.5683	+	23.5010i	0.473538	+	0.820192i	−0.526003	+	0.850483i	$0.676310\pi$
$822$		0			0
$823$	23.3209	−	40.3929i	0.812914	−	1.40801i	−0.0979013	−	0.995196i	$-0.531213\pi$
$823$	23.3209	−	40.3929i	0.812914	−	1.40801i	0.910816	−	0.412813i	$-0.135454\pi$
$824$	−40.9186			−1.42547
$825$		0			0
$826$	2.50000	−	4.33013i	0.0869861	−	0.150664i
$827$	27.2789			0.948582			0.474291	−	0.880368i	$-0.342705\pi$
$827$	27.2789			0.948582			0.474291	+	0.880368i	$0.342705\pi$
$828$		0			0
$829$	12.6610	+	21.9294i	0.439734	+	0.761641i	0.997669	−	0.0682437i	$-0.0217396\pi$
$829$	12.6610	+	21.9294i	0.439734	+	0.761641i	−0.557935	+	0.829885i	$0.688406\pi$
$830$	−3.05736	−	5.29551i	−0.106123	−	0.183810i
$831$		0			0
$832$	8.64536	−	8.53520i	0.299724	−	0.295905i
$833$	−3.65109			−0.126503
$834$		0			0
$835$	−31.1801	−	54.0054i	−1.07903	−	1.86894i
$836$	9.14470	−	15.8391i	0.316276	−	0.547806i
$837$		0			0
$838$	−23.8018	+	41.2259i	−0.822219	+	1.42413i
$839$	0.183265	−	0.317424i	0.00632700	−	0.0109587i	−0.862845	−	0.505469i	$-0.831319\pi$
$839$	0.183265	−	0.317424i	0.00632700	−	0.0109587i	0.869172	+	0.494511i	$0.164653\pi$
$840$		0			0
$841$	13.7813	−	23.8700i	0.475219	−	0.823103i
$842$	28.3350	+	49.0777i	0.976489	+	1.69133i
$843$		0			0
$844$	−12.6645			−0.435929
$845$	−0.487604	+	38.0217i	−0.0167741	+	1.30799i
$846$		0			0
$847$	4.07995	+	7.06668i	0.140189	+	0.242814i
$848$	0.744133	+	1.28888i	0.0255536	+	0.0442602i
$849$		0			0
$850$	21.4338			0.735173
$851$	−10.2788	+	17.8035i	−0.352354	+	0.610294i
$852$		0			0
$853$	−49.3134			−1.68846			−0.844229	−	0.535983i	$-0.819941\pi$
$853$	−49.3134			−1.68846			−0.844229	+	0.535983i	$0.819941\pi$
$854$	0.249469	−	0.432094i	0.00853666	−	0.0147859i
$855$		0			0
$856$	−1.49748	−	2.59371i	−0.0511827	−	0.0886511i
$857$	−26.0878			−0.891143			−0.445571	−	0.895246i	$-0.646999\pi$
$857$	−26.0878			−0.891143			−0.445571	+	0.895246i	$0.646999\pi$
$858$		0			0
$859$	29.6815			1.01272			0.506360	−	0.862322i	$-0.330991\pi$
$859$	29.6815			1.01272			0.506360	+	0.862322i	$0.330991\pi$
$860$	−6.08072	−	10.5321i	−0.207351	−	0.359142i
$861$		0			0
$862$	−24.2346	+	41.9756i	−0.825435	+	1.42969i
$863$	−17.8804			−0.608655			−0.304328	−	0.952567i	$-0.598432\pi$
$863$	−17.8804			−0.608655			−0.304328	+	0.952567i	$0.598432\pi$
$864$		0			0
$865$	−4.56551	+	7.90770i	−0.155232	+	0.268870i
$866$	−47.2320			−1.60501
$867$		0			0
$868$	−2.34997	−	4.07026i	−0.0797631	−	0.138154i
$869$	37.0806	+	64.2255i	1.25787	+	2.17870i
$870$		0			0
$871$	30.2735	+	8.32016i	1.02578	+	0.281918i
$872$	−0.0982663			−0.00332772
$873$		0			0
$874$	33.3881	+	57.8299i	1.12937	+	1.95613i
$875$	2.11252	−	3.65900i	0.0714163	−	0.123697i
$876$		0			0
$877$	−12.8061	+	22.1807i	−0.432430	+	0.748991i	−0.997082	−	0.0763384i	$-0.975677\pi$
$877$	−12.8061	+	22.1807i	−0.432430	+	0.748991i	0.564652	+	0.825329i	$0.309010\pi$
$878$	28.4646	−	49.3022i	0.960634	−	1.66387i
$879$		0			0
$880$	−31.5279	+	54.6079i	−1.06281	+	1.84083i
$881$	−21.0821	−	36.5152i	−0.710273	−	1.23023i	−0.964755	−	0.263152i	$-0.915238\pi$
$881$	−21.0821	−	36.5152i	−0.710273	−	1.23023i	0.254481	−	0.967078i	$-0.418095\pi$
$882$		0			0
$883$	−32.9992			−1.11051			−0.555256	−	0.831680i	$-0.687380\pi$
$883$	−32.9992			−1.11051			−0.555256	+	0.831680i	$0.687380\pi$
$884$	9.21690	+	2.53311i	0.309998	+	0.0851977i
$885$		0			0
$886$	10.6550	+	18.4549i	0.357961	+	0.620006i
$887$	4.64334	+	8.04251i	0.155908	+	0.270041i	0.933389	−	0.358865i	$-0.116836\pi$
$887$	4.64334	+	8.04251i	0.155908	+	0.270041i	−0.777481	+	0.628906i	$0.783503\pi$
$888$		0			0
$889$	5.47277			0.183551
$890$	−32.3517	+	56.0348i	−1.08443	+	1.87829i
$891$		0			0
$892$	5.81042			0.194547
$893$	27.5746	−	47.7606i	0.922749	−	1.59825i
$894$		0			0
$895$	−27.7448	−	48.0554i	−0.927406	−	1.60631i
$896$	13.4132			0.448105
$897$		0			0
$898$	−9.30936			−0.310657
$899$	−3.88002	−	6.72039i	−0.129406	−	0.224137i
$900$		0			0
$901$	0.551656	−	0.955496i	0.0183783	−	0.0318322i
$902$	−62.1853			−2.07054
$903$		0			0
$904$	−10.8723	+	18.8313i	−0.361606	+	0.626320i
$905$	5.65322			0.187919
$906$		0			0
$907$	−10.6224	−	18.3985i	−0.352711	−	0.610913i	0.634013	−	0.773323i	$-0.281407\pi$
$907$	−10.6224	−	18.3985i	−0.352711	−	0.610913i	−0.986723	+	0.162410i	$0.948073\pi$
$908$	−2.92605	−	5.06806i	−0.0971042	−	0.168189i
$909$		0			0
$910$	−12.3914	+	12.2335i	−0.410769	+	0.405535i
$911$	54.0785			1.79170			0.895850	−	0.444357i	$-0.146568\pi$
$911$	54.0785			1.79170			0.895850	+	0.444357i	$0.146568\pi$
$912$		0			0
$913$	−2.77108	−	4.79965i	−0.0917093	−	0.158845i
$914$	31.3620	−	54.3205i	1.03736	−	1.79676i
$915$		0			0
$916$	3.07889	−	5.33280i	0.101729	−	0.176201i
$917$	−8.08529	+	14.0041i	−0.267000	+	0.462457i
$918$		0			0
$919$	9.47130	−	16.4048i	0.312429	−	0.541144i	−0.666458	−	0.745542i	$-0.732191\pi$
$919$	9.47130	−	16.4048i	0.312429	−	0.541144i	0.978888	+	0.204399i	$0.0655239\pi$
$920$	−21.6196	−	37.4462i	−0.712777	−	1.23457i
$921$		0			0
$922$	−10.9093			−0.359277
$923$	−12.3301	−	47.2256i	−0.405850	−	1.55445i
$924$		0			0
$925$	5.19994	+	9.00655i	0.170973	+	0.296134i
$926$	8.24666	+	14.2836i	0.271002	+	0.469389i
$927$		0			0
$928$	−4.70556			−0.154468
$929$	−22.6674	+	39.2610i	−0.743692	+	1.28811i	0.207111	+	0.978317i	$0.433594\pi$
$929$	−22.6674	+	39.2610i	−0.743692	+	1.28811i	−0.950803	+	0.309795i	$0.899740\pi$
$930$		0			0
$931$	−5.75441			−0.188593
$932$	−3.71971	+	6.44273i	−0.121843	+	0.211039i
$933$		0			0
$934$	−2.82419	−	4.89165i	−0.0924105	−	0.160060i
$935$	46.7459			1.52875
$936$		0			0
$937$	3.71544			0.121378			0.0606890	−	0.998157i	$-0.480670\pi$
$937$	3.71544			0.121378			0.0606890	+	0.998157i	$0.480670\pi$
$938$	7.18860	+	12.4510i	0.234716	+	0.406540i
$939$		0			0
$940$	10.1773	−	17.6277i	0.331948	−	0.574952i
$941$	4.28376			0.139647			0.0698233	−	0.997559i	$-0.477756\pi$
$941$	4.28376			0.139647			0.0698233	+	0.997559i	$0.477756\pi$
$942$		0			0
$943$	30.2370	−	52.3721i	0.984654	−	1.70547i
$944$	14.9143			0.485419
$945$		0			0
$946$	−20.6918	−	35.8392i	−0.672748	−	1.16523i
$947$	−12.5103	−	21.6684i	−0.406529	−	0.704129i	0.587969	−	0.808884i	$-0.299928\pi$
$947$	−12.5103	−	21.6684i	−0.406529	−	0.704129i	−0.994498	+	0.104754i	$0.966594\pi$
$948$		0			0
$949$	2.39321	−	2.36272i	0.0776870	−	0.0766971i
$950$	33.7813			1.09601
$951$		0			0
$952$	−3.83969	−	6.65055i	−0.124445	−	0.215545i
$953$	−1.42217	+	2.46327i	−0.0460686	+	0.0797932i	−0.888140	−	0.459573i	$-0.848003\pi$
$953$	−1.42217	+	2.46327i	−0.0460686	+	0.0797932i	0.842072	+	0.539366i	$0.181336\pi$
$954$		0			0
$955$	3.32555	−	5.76002i	0.107612	−	0.186390i
$956$	−4.10331	+	7.10715i	−0.132711	+	0.229862i
$957$		0			0
$958$	−16.3800	+	28.3710i	−0.529214	+	0.916626i
$959$	6.00881	+	10.4076i	0.194035	+	0.336078i
$960$		0			0
$961$	10.8967			0.351506
$962$	4.39881	+	16.8480i	0.141823	+	0.543200i
$963$		0			0
$964$	−0.376142	−	0.651496i	−0.0121147	−	0.0209833i
$965$	−6.41606	−	11.1129i	−0.206540	−	0.357738i
$966$		0			0
$967$	−6.68444			−0.214957			−0.107478	−	0.994207i	$-0.534278\pi$
$967$	−6.68444			−0.214957			−0.107478	+	0.994207i	$0.534278\pi$
$968$	−8.58141	+	14.8634i	−0.275817	+	0.477729i
$969$		0			0
$970$	57.5908			1.84913
$971$	−13.3139	+	23.0604i	−0.427264	+	0.740043i	−0.996629	−	0.0820419i	$-0.973856\pi$
$971$	−13.3139	+	23.0604i	−0.427264	+	0.740043i	0.569365	+	0.822085i	$0.307189\pi$
$972$		0			0
$973$	0.674453	+	1.16819i	0.0216220	+	0.0374504i
$974$	10.0771			0.322892
$975$		0			0
$976$	1.48827			0.0476382
$977$	−13.9090	−	24.0910i	−0.444987	−	0.770741i	0.553064	−	0.833139i	$-0.313459\pi$
$977$	−13.9090	−	24.0910i	−0.444987	−	0.770741i	−0.998051	+	0.0623979i	$0.980125\pi$
$978$		0			0
$979$	−29.3223	+	50.7878i	−0.937146	+	1.62318i
$980$	−2.12386			−0.0678442
$981$		0			0
$982$	1.95368	−	3.38387i	0.0623445	−	0.107984i
$983$	−51.3454			−1.63766			−0.818832	−	0.574033i	$-0.805378\pi$
$983$	−51.3454			−1.63766			−0.818832	+	0.574033i	$0.805378\pi$
$984$		0			0
$985$	7.69035	+	13.3201i	0.245035	+	0.424413i
$986$	3.61359	+	6.25891i	0.115080	+	0.199324i
$987$		0			0
$988$	14.5265	+	3.99238i	0.462151	+	0.127014i
$989$	40.2448			1.27971
$990$		0			0
$991$	11.6872	+	20.2429i	0.371258	+	0.643037i	0.989759	−	0.142746i	$-0.0455933\pi$
$991$	11.6872	+	20.2429i	0.371258	+	0.643037i	−0.618502	+	0.785784i	$0.712260\pi$
$992$	12.7027	−	22.0018i	0.403313	−	0.698558i
$993$		0			0
$994$	11.1755	−	19.3566i	0.354466	−	0.613953i
$995$	19.2990	−	33.4268i	0.611819	−	1.05970i
$996$		0			0
$997$	14.3977	−	24.9376i	0.455981	−	0.789783i	−0.542763	−	0.839886i	$-0.682622\pi$
$997$	14.3977	−	24.9376i	0.455981	−	0.789783i	0.998744	+	0.0501033i	$0.0159551\pi$
$998$	−3.54351	−	6.13753i	−0.112168	−	0.194280i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.d.757.3		6
3.2	odd	2		273.2.k.d.211.1	yes	6
13.9	even	3	inner	819.2.o.d.568.3		6
39.23	odd	6		3549.2.a.s.1.1		3
39.29	odd	6		3549.2.a.h.1.3		3
39.35	odd	6		273.2.k.d.22.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.1	✓	6	39.35	odd	6
273.2.k.d.211.1	yes	6	3.2	odd	2
819.2.o.d.568.3		6	13.9	even	3	inner
819.2.o.d.757.3		6	1.1	even	1	trivial
3549.2.a.h.1.3		3	39.29	odd	6
3549.2.a.s.1.1		3	39.23	odd	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.825547 + 1.42989i) q^{2} +(-0.363055 + 0.628829i) q^{4} -2.92498 q^{5} +(0.500000 - 0.866025i) q^{7} +2.10331 q^{8} +O(q^{10})\)	\(q+(0.825547 + 1.42989i) q^{2} +(-0.363055 + 0.628829i) q^{4} -2.92498 q^{5} +(0.500000 - 0.866025i) q^{7} +2.10331 q^{8} +(-2.41471 - 4.18240i) q^{10} +(-2.18860 - 3.79077i) q^{11} +(2.56580 - 2.53311i) q^{13} +1.65109 q^{14} +(2.46249 + 4.26516i) q^{16} +(1.82555 - 3.16194i) q^{17} +(2.87720 - 4.98346i) q^{19} +(1.06193 - 1.83932i) q^{20} +(3.61359 - 6.25891i) q^{22} +(3.51415 + 6.08668i) q^{23} +3.55553 q^{25} +(5.74026 + 1.57761i) q^{26} +(0.363055 + 0.628829i) q^{28} +(0.599437 + 1.03826i) q^{29} -6.47277 q^{31} +(-1.96249 + 3.39914i) q^{32} +6.02830 q^{34} +(-1.46249 + 2.53311i) q^{35} +(1.46249 + 2.53311i) q^{37} +9.50106 q^{38} -6.15215 q^{40} +(-4.30219 - 7.45161i) q^{41} +(2.86305 - 4.95896i) q^{43} +3.17833 q^{44} +(-5.80219 + 10.0497i) q^{46} +9.58383 q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.93526 + 5.08401i) q^{50} +(0.661367 + 2.53311i) q^{52} +0.302187 q^{53} +(6.40162 + 11.0879i) q^{55} +(1.05166 - 1.82152i) q^{56} +(-0.989727 + 1.71426i) q^{58} +(1.51415 - 2.62258i) q^{59} +(0.151093 - 0.261701i) q^{61} +(-5.34357 - 9.25533i) q^{62} +3.36945 q^{64} +(-7.50494 + 7.40931i) q^{65} +(4.35384 + 7.54108i) q^{67} +(1.32555 + 2.29591i) q^{68} -4.82942 q^{70} +(6.76855 - 11.7235i) q^{71} +0.932734 q^{73} +(-2.41471 + 4.18240i) q^{74} +(2.08916 + 3.61854i) q^{76} -4.37720 q^{77} -16.9426 q^{79} +(-7.20275 - 12.4755i) q^{80} +(7.10331 - 12.3033i) q^{82} +1.26614 q^{83} +(-5.33969 + 9.24862i) q^{85} +9.45434 q^{86} +(-4.60331 - 7.97317i) q^{88} +(-6.69887 - 11.6028i) q^{89} +(-0.910836 - 3.48861i) q^{91} -5.10331 q^{92} +(7.91190 + 13.7038i) q^{94} +(-8.41577 + 14.5765i) q^{95} +(-5.96249 + 10.3273i) q^{97} +(0.825547 - 1.42989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

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