LMFDB - Embedded newform 819.2.dl.e.415.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("819.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.7
Root			$-1.84073 + 1.06275i$ of defining polynomial
Character	$\chi$	$=$	819.415
Dual form			819.2.dl.e.298.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84073 + 1.06275i) q^{2} +(1.25885 + 2.18040i) q^{4} +(-3.12291 - 1.80301i) q^{5} +(-1.20931 - 2.35320i) q^{7} +1.10038i q^{8} +O(q^{10})$	\(q+(1.84073 + 1.06275i) q^{2} +(1.25885 + 2.18040i) q^{4} +(-3.12291 - 1.80301i) q^{5} +(-1.20931 - 2.35320i) q^{7} +1.10038i q^{8} +(-3.83229 - 6.63772i) q^{10} +(-3.45748 + 1.99618i) q^{11} +(-2.51771 + 2.58092i) q^{13} +(0.274848 - 5.61680i) q^{14} +(1.34828 - 2.33529i) q^{16} +(-2.39458 - 4.14753i) q^{17} +(-2.72850 - 1.57530i) q^{19} -9.07892i q^{20} -8.48572 q^{22} +(1.08943 - 1.88694i) q^{23} +(4.00171 + 6.93117i) q^{25} +(-7.37728 + 2.07509i) q^{26} +(3.60858 - 5.59912i) q^{28} +6.57198 q^{29} +(-1.28753 + 0.743358i) q^{31} +(6.86956 - 3.96614i) q^{32} -10.1793i q^{34} +(-0.466298 + 9.52925i) q^{35} +(-4.29984 - 2.48252i) q^{37} +(-3.34828 - 5.79939i) q^{38} +(1.98401 - 3.43640i) q^{40} -2.11931i q^{41} -1.43145 q^{43} +(-8.70494 - 5.02580i) q^{44} +(4.01068 - 2.31557i) q^{46} +(0.882417 + 0.509464i) q^{47} +(-4.07515 + 5.69150i) q^{49} +17.0112i q^{50} +(-8.79686 - 2.24061i) q^{52} +(3.01771 + 5.22682i) q^{53} +14.3966 q^{55} +(2.58943 - 1.33070i) q^{56} +(12.0972 + 6.98434i) q^{58} +(4.24631 - 2.45161i) q^{59} +(1.01771 - 1.76272i) q^{61} -3.16000 q^{62} +11.4669 q^{64} +(12.5160 - 3.52052i) q^{65} +(-3.38694 + 1.95545i) q^{67} +(6.02885 - 10.4423i) q^{68} +(-10.9855 + 17.0452i) q^{70} -8.80684i q^{71} +(2.67497 - 1.54439i) q^{73} +(-5.27656 - 9.13927i) q^{74} -7.93228i q^{76} +(8.87858 + 5.72217i) q^{77} +(-0.984006 + 1.70435i) q^{79} +(-8.42112 + 4.86194i) q^{80} +(2.25229 - 3.90108i) q^{82} +7.66020i q^{83} +17.2698i q^{85} +(-2.63491 - 1.52126i) q^{86} +(-2.19656 - 3.80456i) q^{88} +(-11.0844 - 6.39960i) q^{89} +(9.11812 + 2.80355i) q^{91} +5.48572 q^{92} +(1.08286 + 1.87557i) q^{94} +(5.68057 + 9.83903i) q^{95} -1.35900i q^{97} +(-13.5499 + 6.14567i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4}+O(q^{10}) $ 16 * q + 6 * q^4	$ 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.84073	+	1.06275i	1.30159	+	0.751474i	0.980677	−	0.195634i	$-0.0626764\pi$
$2$	1.84073	+	1.06275i	1.30159	+	0.751474i	0.320915	+	0.947108i	$0.396010\pi$
$3$		0			0
$3$		0			0
$4$	1.25885	+	2.18040i	0.629427	+	1.09020i
$5$	−3.12291	−	1.80301i	−1.39661	−	0.806332i	−0.402572	−	0.915388i	$-0.631884\pi$
$5$	−3.12291	−	1.80301i	−1.39661	−	0.806332i	−0.994036	+	0.109056i	$0.965217\pi$
$6$		0			0
$7$	−1.20931	−	2.35320i	−0.457076	−	0.889428i
$7$	−1.20931	−	2.35320i	−0.457076	−	0.889428i
$8$			1.10038i			0.389044i
$9$		0			0
$10$	−3.83229	−	6.63772i	−1.21188	−	2.09903i
$11$	−3.45748	+	1.99618i	−1.04247	+	0.601871i	−0.920532	−	0.390667i	$-0.872244\pi$
$11$	−3.45748	+	1.99618i	−1.04247	+	0.601871i	−0.121939	+	0.992538i	$0.538911\pi$
$12$		0			0
$13$	−2.51771	+	2.58092i	−0.698287	+	0.715818i
$13$	−2.51771	+	2.58092i	−0.698287	+	0.715818i
$14$	0.274848	−	5.61680i	0.0734563	−	1.50115i
$15$		0			0
$16$	1.34828	−	2.33529i	0.337070	−	0.583823i
$17$	−2.39458	−	4.14753i	−0.580771	−	1.00592i	−0.995388	−	0.0959284i	$-0.969418\pi$
$17$	−2.39458	−	4.14753i	−0.580771	−	1.00592i	0.414618	−	0.909996i	$-0.363915\pi$
$18$		0			0
$19$	−2.72850	−	1.57530i	−0.625960	−	0.361398i	0.153226	−	0.988191i	$-0.451034\pi$
$19$	−2.72850	−	1.57530i	−0.625960	−	0.361398i	−0.779186	+	0.626793i	$0.784367\pi$
$20$		−	9.07892i		−	2.03011i
$21$		0			0
$22$	−8.48572			−1.80916
$23$	1.08943	−	1.88694i	0.227161	−	0.393455i	−0.729804	−	0.683656i	$-0.760389\pi$
$23$	1.08943	−	1.88694i	0.227161	−	0.393455i	0.956966	+	0.290201i	$0.0937222\pi$
$24$		0			0
$25$	4.00171	+	6.93117i	0.800343	+	1.38623i
$26$	−7.37728	+	2.07509i	−1.44680	+	0.406959i
$27$		0			0
$28$	3.60858	−	5.59912i	0.681958	−	1.05813i
$29$	6.57198			1.22039			0.610193	−	0.792253i	$-0.291092\pi$
$29$	6.57198			1.22039			0.610193	+	0.792253i	$0.291092\pi$
$30$		0			0
$31$	−1.28753	+	0.743358i	−0.231248	+	0.133511i	−0.611148	−	0.791517i	$-0.709292\pi$
$31$	−1.28753	+	0.743358i	−0.231248	+	0.133511i	0.379900	+	0.925028i	$0.375958\pi$
$32$	6.86956	−	3.96614i	1.21438	−	0.701121i
$33$		0			0
$34$		−	10.1793i		−	1.74574i
$35$	−0.466298	+	9.52925i	−0.0788187	+	1.61074i
$36$		0			0
$37$	−4.29984	−	2.48252i	−0.706890	−	0.408123i	0.103019	−	0.994679i	$-0.467150\pi$
$37$	−4.29984	−	2.48252i	−0.706890	−	0.408123i	−0.809908	+	0.586556i	$0.800483\pi$
$38$	−3.34828	−	5.79939i	−0.543163	−	0.940786i
$39$		0			0
$40$	1.98401	−	3.43640i	0.313699	−	0.543342i
$41$		−	2.11931i		−	0.330981i	−0.986211	−	0.165490i	$-0.947079\pi$
$41$		−	2.11931i		−	0.330981i	0.986211	−	0.165490i	$-0.0529207\pi$
$42$		0			0
$43$	−1.43145			−0.218294			−0.109147	−	0.994026i	$-0.534812\pi$
$43$	−1.43145			−0.218294			−0.109147	+	0.994026i	$0.534812\pi$
$44$	−8.70494	−	5.02580i	−1.31232	−	0.757667i
$45$		0			0
$46$	4.01068	−	2.31557i	0.591342	−	0.341412i
$47$	0.882417	+	0.509464i	0.128714	+	0.0743129i	0.562974	−	0.826474i	$-0.309657\pi$
$47$	0.882417	+	0.509464i	0.128714	+	0.0743129i	−0.434261	+	0.900787i	$0.642990\pi$
$48$		0			0
$49$	−4.07515	+	5.69150i	−0.582164	+	0.813072i
$50$			17.0112i			2.40575i
$51$		0			0
$52$	−8.79686	−	2.24061i	−1.21991	−	0.310716i
$53$	3.01771	+	5.22682i	0.414514	+	0.717959i	0.995377	−	0.0960417i	$-0.0306182\pi$
$53$	3.01771	+	5.22682i	0.414514	+	0.717959i	−0.580863	+	0.814001i	$0.697285\pi$
$54$		0			0
$55$	14.3966			1.94123
$56$	2.58943	−	1.33070i	0.346027	−	0.177823i
$57$		0			0
$58$	12.0972	+	6.98434i	1.58844	+	0.917089i
$59$	4.24631	−	2.45161i	0.552823	−	0.319172i	−0.197437	−	0.980316i	$-0.563262\pi$
$59$	4.24631	−	2.45161i	0.552823	−	0.319172i	0.750260	+	0.661143i	$0.229928\pi$
$60$		0			0
$61$	1.01771	−	1.76272i	0.130304	−	0.225693i	−0.793490	−	0.608584i	$-0.791738\pi$
$61$	1.01771	−	1.76272i	0.130304	−	0.225693i	0.923794	+	0.382890i	$0.125071\pi$
$62$	−3.16000			−0.401320
$63$		0			0
$64$	11.4669			1.43336
$65$	12.5160	−	3.52052i	1.55242	−	0.436667i
$66$		0			0
$67$	−3.38694	+	1.95545i	−0.413781	+	0.238896i	−0.692413	−	0.721501i	$-0.743452\pi$
$67$	−3.38694	+	1.95545i	−0.413781	+	0.238896i	0.278632	+	0.960398i	$0.410119\pi$
$68$	6.02885	−	10.4423i	0.731105	−	1.26631i
$69$		0			0
$70$	−10.9855	+	17.0452i	−1.31302	+	2.03729i
$71$		−	8.80684i		−	1.04518i	−0.852584	−	0.522590i	$-0.824966\pi$
$71$		−	8.80684i		−	1.04518i	0.852584	−	0.522590i	$-0.175034\pi$
$72$		0			0
$73$	2.67497	−	1.54439i	0.313081	−	0.180757i	−0.335223	−	0.942139i	$-0.608812\pi$
$73$	2.67497	−	1.54439i	0.313081	−	0.180757i	0.648304	+	0.761381i	$0.275478\pi$
$74$	−5.27656	−	9.13927i	−0.613388	−	1.06242i
$75$		0			0
$76$		−	7.93228i		−	0.909895i
$77$	8.87858	+	5.72217i	1.01181	+	0.652102i
$78$		0			0
$79$	−0.984006	+	1.70435i	−0.110709	+	0.191754i	−0.916056	−	0.401049i	$-0.868646\pi$
$79$	−0.984006	+	1.70435i	−0.110709	+	0.191754i	0.805347	+	0.592803i	$0.201979\pi$
$80$	−8.42112	+	4.86194i	−0.941510	+	0.543581i
$81$		0			0
$82$	2.25229	−	3.90108i	0.248724	−	0.430802i
$83$			7.66020i			0.840816i	0.907335	+	0.420408i	$0.138113\pi$
$83$			7.66020i			0.840816i	−0.907335	+	0.420408i	$0.861887\pi$
$84$		0			0
$85$			17.2698i			1.87318i
$86$	−2.63491	−	1.52126i	−0.284129	−	0.164042i
$87$		0			0
$88$	−2.19656	−	3.80456i	−0.234154	−	0.405567i
$89$	−11.0844	−	6.39960i	−1.17495	−	0.678356i	−0.220107	−	0.975476i	$-0.570641\pi$
$89$	−11.0844	−	6.39960i	−1.17495	−	0.678356i	−0.954840	+	0.297120i	$0.903974\pi$
$90$		0			0
$91$	9.11812	+	2.80355i	0.955839	+	0.293892i
$92$	5.48572			0.571926
$93$		0			0
$94$	1.08286	+	1.87557i	0.111689	+	0.193450i
$95$	5.68057	+	9.83903i	0.582814	+	1.00946i
$96$		0			0
$97$		−	1.35900i		−	0.137986i	−0.997617	−	0.0689930i	$-0.978021\pi$
$97$		−	1.35900i		−	0.137986i	0.997617	−	0.0689930i	$-0.0219786\pi$
$98$	−13.5499	+	6.14567i	−1.36874	+	0.620806i
$99$		0			0
$100$	−10.0751	+	17.4507i	−1.00751	+	1.74507i
$101$	−2.14400	−	3.71353i	−0.213336	−	0.369510i	0.739420	−	0.673244i	$-0.235100\pi$
$101$	−2.14400	−	3.71353i	−0.213336	−	0.369510i	−0.952757	+	0.303735i	$0.901766\pi$
$102$		0			0
$103$	7.21744	−	12.5010i	0.711155	−	1.23176i	−0.253269	−	0.967396i	$-0.581506\pi$
$103$	7.21744	−	12.5010i	0.711155	−	1.23176i	0.964424	−	0.264361i	$-0.0851610\pi$
$104$	−2.84000	−	2.77044i	−0.278485	−	0.271664i
$105$		0			0
$106$			12.8282i			1.24599i
$107$	−4.85942	+	8.41677i	−0.469778	+	0.813680i	−0.999403	−	0.0345525i	$-0.988999\pi$
$107$	−4.85942	+	8.41677i	−0.469778	+	0.813680i	0.529625	+	0.848232i	$0.322333\pi$
$108$		0			0
$109$	5.75782	−	3.32428i	0.551499	−	0.318408i	−0.198227	−	0.980156i	$-0.563518\pi$
$109$	5.75782	−	3.32428i	0.551499	−	0.318408i	0.749726	+	0.661748i	$0.230185\pi$
$110$	26.5001	+	15.2999i	2.52669	+	1.45878i
$111$		0			0
$112$	−7.12591	−	0.348694i	−0.673335	−	0.0329485i
$113$	−17.5434			−1.65035			−0.825173	−	0.564880i	$-0.808922\pi$
$113$	−17.5434			−1.65035			−0.825173	+	0.564880i	$0.808922\pi$
$114$		0			0
$115$	−6.80437	+	3.92850i	−0.634511	+	0.366335i
$116$	8.27316	+	14.3295i	0.768144	+	1.33046i
$117$		0			0
$118$	10.4217			0.959399
$119$	−6.86421	+	10.6506i	−0.629241	+	0.976337i
$120$		0			0
$121$	2.46946	−	4.27724i	0.224497	−	0.388840i
$122$	3.74665	−	2.16313i	0.339206	−	0.195840i
$123$		0			0
$124$	−3.24163	−	1.87156i	−0.291107	−	0.168071i
$125$		−	10.8304i		−	0.968704i
$126$		0			0
$127$	−19.5143			−1.73162			−0.865809	−	0.500375i	$-0.833195\pi$
$127$	−19.5143			−1.73162			−0.865809	+	0.500375i	$0.833195\pi$
$128$	7.36826	+	4.25407i	0.651269	+	0.376010i
$129$		0			0
$130$	26.7800	+	6.82100i	2.34876	+	0.598242i
$131$	9.53713	−	16.5188i	0.833263	−	1.44325i	−0.0621741	−	0.998065i	$-0.519803\pi$
$131$	9.53713	−	16.5188i	0.833263	−	1.44325i	0.895437	−	0.445188i	$-0.146863\pi$
$132$		0			0
$133$	−0.407406	+	8.32573i	−0.0353266	+	0.721933i
$134$	−8.31259			−0.718098
$135$		0			0
$136$	4.56387	−	2.63495i	0.391349	−	0.225945i
$137$	5.56759	−	3.21445i	0.475672	−	0.274629i	−0.242939	−	0.970042i	$-0.578112\pi$
$137$	5.56759	−	3.21445i	0.475672	−	0.274629i	0.718611	+	0.695412i	$0.244778\pi$
$138$		0			0
$139$	−2.42854			−0.205986			−0.102993	−	0.994682i	$-0.532842\pi$
$139$	−2.42854			−0.205986			−0.102993	+	0.994682i	$0.532842\pi$
$140$	−21.3646	+	10.9792i	−1.80564	+	0.927913i
$141$		0			0
$142$	9.35942	−	16.2110i	0.785425	−	1.36040i
$143$	3.55296	−	13.9493i	0.297113	−	1.16650i
$144$		0			0
$145$	−20.5237	−	11.8494i	−1.70440	−	0.984036i
$146$	6.56518			0.543338
$147$		0			0
$148$		−	12.5005i		−	1.02753i
$149$	0.0998984	+	0.0576764i	0.00818400	+	0.00472503i	0.504086	−	0.863653i	$-0.331829\pi$
$149$	0.0998984	+	0.0576764i	0.00818400	+	0.00472503i	−0.495902	+	0.868378i	$0.665163\pi$
$150$		0			0
$151$	10.2218	−	5.90155i	0.831838	−	0.480262i	−0.0226438	−	0.999744i	$-0.507208\pi$
$151$	10.2218	−	5.90155i	0.831838	−	0.480262i	0.854481	+	0.519482i	$0.173875\pi$
$152$	1.73343	−	3.00239i	0.140600	−	0.243526i
$153$		0			0
$154$	10.2619	+	19.9686i	0.826924	+	1.60912i
$155$	5.36114			0.430617
$156$		0			0
$157$	6.57343	+	11.3855i	0.524617	+	0.908663i	0.999589	+	0.0286625i	$0.00912481\pi$
$157$	6.57343	+	11.3855i	0.524617	+	0.908663i	−0.474972	+	0.880001i	$0.657542\pi$
$158$	−3.62257	+	2.09149i	−0.288197	+	0.166390i
$159$		0			0
$160$	−28.6040			−2.26135
$161$	−5.75782	−	0.281749i	−0.453780	−	0.0222049i
$162$		0			0
$163$	−16.1501	−	9.32424i	−1.26497	−	0.730331i	−0.290938	−	0.956742i	$-0.593967\pi$
$163$	−16.1501	−	9.32424i	−1.26497	−	0.730331i	−0.974032	+	0.226411i	$0.927301\pi$
$164$	4.62094	−	2.66790i	0.360835	−	0.208328i
$165$		0			0
$166$	−8.14084	+	14.1003i	−0.631852	+	1.09440i
$167$		−	0.972672i		−	0.0752676i	−0.999292	−	0.0376338i	$-0.988018\pi$
$167$		−	0.972672i		−	0.0752676i	0.999292	−	0.0376338i	$-0.0119820\pi$
$168$		0			0
$169$	−0.322293	−	12.9960i	−0.0247917	−	0.999693i
$170$	−18.3534	+	31.7891i	−1.40764	+	2.43811i
$171$		0			0
$172$	−1.80198	−	3.12113i	−0.137400	−	0.237984i
$173$	−1.22855	+	2.12791i	−0.0934050	+	0.161782i	−0.908942	−	0.416923i	$-0.863108\pi$
$173$	−1.22855	+	2.12791i	−0.0934050	+	0.161782i	0.815537	+	0.578705i	$0.196442\pi$
$174$		0			0
$175$	11.4712	−	17.7988i	0.867138	−	1.34546i
$176$			10.7656i			0.811491i
$177$		0			0
$178$	−13.6023	−	23.5598i	−1.01953	−	1.76588i
$179$	−7.23629	−	12.5336i	−0.540866	−	0.936807i	−0.998855	−	0.0478492i	$-0.984763\pi$
$179$	−7.23629	−	12.5336i	−0.540866	−	0.936807i	0.457989	−	0.888958i	$-0.348570\pi$
$180$		0			0
$181$	−9.17885			−0.682259			−0.341129	−	0.940016i	$-0.610809\pi$
$181$	−9.17885			−0.682259			−0.341129	+	0.940016i	$0.610809\pi$
$182$	13.8045	+	14.8508i	1.02326	+	1.10082i
$183$		0			0
$184$	2.07636	+	1.19879i	0.153071	+	0.0883758i
$185$	8.95202	+	15.5053i	0.658165	+	1.13998i
$186$		0			0
$187$	16.5584	+	9.56002i	1.21087	+	0.699098i
$188$			2.56536i			0.187098i
$189$		0			0
$190$			24.1480i			1.75188i
$191$	8.79202	−	15.2282i	0.636168	−	1.10188i	−0.350098	−	0.936713i	$-0.613852\pi$
$191$	8.79202	−	15.2282i	0.636168	−	1.10188i	0.986266	−	0.165162i	$-0.0528148\pi$
$192$		0			0
$193$	17.1090	−	9.87791i	1.23154	−	0.711028i	0.264186	−	0.964472i	$-0.414897\pi$
$193$	17.1090	−	9.87791i	1.23154	−	0.711028i	0.967350	+	0.253444i	$0.0815633\pi$
$194$	1.44428	−	2.50156i	0.103693	−	0.179601i
$195$		0			0
$196$	−17.5398	−	1.72068i	−1.25284	−	0.122905i
$197$		−	7.66020i		−	0.545767i	−0.962047	−	0.272883i	$-0.912023\pi$
$197$		−	7.66020i		−	0.545767i	0.962047	−	0.272883i	$-0.0879773\pi$
$198$		0			0
$199$	−3.27171	−	5.66677i	−0.231925	−	0.401706i	0.726449	−	0.687220i	$-0.241169\pi$
$199$	−3.27171	−	5.66677i	−0.231925	−	0.401706i	−0.958375	+	0.285514i	$0.907836\pi$
$200$	−7.62694	+	4.40342i	−0.539306	+	0.311369i
$201$		0			0
$202$		−	9.11412i		−	0.641267i
$203$	−7.94755	−	15.4652i	−0.557809	−	1.08545i
$204$		0			0
$205$	−3.82115	+	6.61842i	−0.266880	+	0.462250i
$206$	26.5707	−	15.3406i	1.85127	−	1.06883i
$207$		0			0
$208$	2.63262	+	9.35939i	0.182539	+	0.648957i
$209$	12.5783			0.870060
$210$		0			0
$211$	20.0452			1.37997			0.689983	−	0.723825i	$-0.257618\pi$
$211$	20.0452			1.37997			0.689983	+	0.723825i	$0.257618\pi$
$212$	−7.59771	+	13.1596i	−0.521813	+	0.903806i
$213$		0			0
$214$	−17.8898	+	10.3287i	−1.22292	+	0.706052i
$215$	4.47028	+	2.58092i	0.304871	+	0.176017i
$216$		0			0
$217$	3.30630	+	2.13088i	0.224446	+	0.144654i
$218$	14.1314			0.957102
$219$		0			0
$220$	18.1232	+	31.3902i	1.22186	+	2.11633i
$221$	16.7333	+	4.26206i	1.12560	+	0.286697i
$222$		0			0
$223$			27.7139i			1.85586i	0.372752	+	0.927931i	$0.378414\pi$
$223$			27.7139i			1.85586i	−0.372752	+	0.927931i	$0.621586\pi$
$224$	−17.6406	−	11.3692i	−1.17866	−	0.759636i
$225$		0			0
$226$	−32.2927	−	18.6442i	−2.14808	−	1.24019i
$227$	−9.84766	+	5.68555i	−0.653612	+	0.377363i	−0.789839	−	0.613315i	$-0.789836\pi$
$227$	−9.84766	+	5.68555i	−0.653612	+	0.377363i	0.136227	+	0.990678i	$0.456502\pi$
$228$		0			0
$229$	−7.54406	−	4.35556i	−0.498525	−	0.287824i	0.229579	−	0.973290i	$-0.426265\pi$
$229$	−7.54406	−	4.35556i	−0.498525	−	0.287824i	−0.728104	+	0.685466i	$0.759598\pi$
$230$	−16.7000			−1.10116
$231$		0			0
$232$			7.23170i			0.474784i
$233$	1.68228	−	2.91380i	0.110210	−	0.190889i	−0.805645	−	0.592399i	$-0.798181\pi$
$233$	1.68228	−	2.91380i	0.110210	−	0.190889i	0.915855	+	0.401510i	$0.131514\pi$
$234$		0			0
$235$	−1.83714	−	3.18202i	−0.119842	−	0.207572i
$236$	10.6910	+	6.17244i	0.695923	+	0.401791i
$237$		0			0
$238$	−23.9540	+	12.3099i	−1.55271	+	0.797934i
$239$			19.8798i			1.28592i	0.765902	+	0.642958i	$0.222293\pi$
$239$			19.8798i			1.28592i	−0.765902	+	0.642958i	$0.777707\pi$
$240$		0			0
$241$	16.3435	−	9.43595i	1.05278	−	0.607823i	0.129354	−	0.991599i	$-0.458710\pi$
$241$	16.3435	−	9.43595i	1.05278	−	0.607823i	0.923426	+	0.383776i	$0.125376\pi$
$242$	9.09123	−	5.24882i	0.584406	−	0.337407i
$243$		0			0
$244$	5.12458			0.328068
$245$	22.9882	−	10.4265i	1.46866	−	0.666125i
$246$		0			0
$247$	10.9353	−	3.07589i	0.695795	−	0.195714i
$248$	−0.817978	−	1.41678i	−0.0519417	−	0.0899656i
$249$		0			0
$250$	11.5100	−	19.9359i	0.727956	−	1.26086i
$251$	−9.79601			−0.618319			−0.309159	−	0.951010i	$-0.600048\pi$
$251$	−9.79601			−0.618319			−0.309159	+	0.951010i	$0.600048\pi$
$252$		0			0
$253$			8.69877i			0.546887i
$254$	−35.9206	−	20.7388i	−2.25386	−	1.30127i
$255$		0			0
$256$	−2.42488	−	4.20002i	−0.151555	−	0.262501i
$257$	−10.4697	+	18.1341i	−0.653083	+	1.13117i	0.329287	+	0.944230i	$0.393192\pi$
$257$	−10.4697	+	18.1341i	−0.653083	+	1.13117i	−0.982371	+	0.186944i	$0.940142\pi$
$258$		0			0
$259$	−0.642031	+	13.1205i	−0.0398939	+	0.815271i
$260$	23.4320	+	22.8581i	1.45319	+	1.41760i
$261$		0			0
$262$	35.1105	−	20.2711i	2.16914	−	1.25235i
$263$	−3.69340	−	6.39715i	−0.227745	−	0.394465i	0.729395	−	0.684093i	$-0.239802\pi$
$263$	−3.69340	−	6.39715i	−0.227745	−	0.394465i	−0.957139	+	0.289628i	$0.906468\pi$
$264$		0			0
$265$		−	21.7639i		−	1.33694i
$266$	−9.59806	+	14.8924i	−0.588495	+	0.913114i
$267$		0			0
$268$	−8.52733	−	4.92326i	−0.520890	−	0.300736i
$269$	11.3946	+	19.7360i	0.694740	+	1.20332i	0.970268	+	0.242032i	$0.0778138\pi$
$269$	11.3946	+	19.7360i	0.694740	+	1.20332i	−0.275529	+	0.961293i	$0.588853\pi$
$270$		0			0
$271$	−3.60814	−	2.08316i	−0.219179	−	0.126543i	0.386391	−	0.922335i	$-0.373722\pi$
$271$	−3.60814	−	2.08316i	−0.219179	−	0.126543i	−0.605570	+	0.795792i	$0.707055\pi$
$272$	−12.9143			−0.783042
$273$		0			0
$274$	13.6646			0.825507
$275$	−27.6717	−	15.9763i	−1.66867	−	0.963406i
$276$		0			0
$277$	0.388551	+	0.672989i	0.0233457	+	0.0404360i	0.877462	−	0.479646i	$-0.159235\pi$
$277$	0.388551	+	0.672989i	0.0233457	+	0.0404360i	−0.854116	+	0.520082i	$0.825901\pi$
$278$	−4.47028	−	2.58092i	−0.268110	−	0.154793i
$279$		0			0
$280$	−10.4858	−	0.513106i	−0.626648	−	0.0306639i
$281$			11.8988i			0.709824i	0.934900	+	0.354912i	$0.115489\pi$
$281$			11.8988i			0.709824i	−0.934900	+	0.354912i	$0.884511\pi$
$282$		0			0
$283$	−7.95202	−	13.7733i	−0.472698	−	0.818738i	0.526813	−	0.849981i	$-0.323387\pi$
$283$	−7.95202	−	13.7733i	−0.472698	−	0.818738i	−0.999512	+	0.0312434i	$0.990053\pi$
$284$	19.2024	−	11.0865i	1.13945	−	0.657864i
$285$		0			0
$286$	21.3646	−	21.9010i	1.26331	−	1.29503i
$287$	−4.98717	+	2.56290i	−0.294383	+	0.151283i
$288$		0			0
$289$	−2.96801	+	5.14075i	−0.174589	+	0.302397i
$290$	−25.1857	−	43.6229i	−1.47896	−	2.56163i
$291$		0			0
$292$	6.73478	+	3.88833i	0.394123	+	0.227547i
$293$			6.73698i			0.393579i	0.980446	+	0.196789i	$0.0630515\pi$
$293$			6.73698i			0.393579i	−0.980446	+	0.196789i	$0.936949\pi$
$294$		0			0
$295$	−17.6811			−1.02944
$296$	2.73172	−	4.73148i	0.158778	−	0.275011i
$297$		0			0
$298$	0.122591	+	0.212333i	0.00710148	+	0.0123001i
$299$	2.12719	+	7.56250i	0.123019	+	0.437350i
$300$		0			0
$301$	1.73106	+	3.36849i	0.0997768	+	0.194157i
$302$	25.0874			1.44362
$303$		0			0
$304$	−7.35756	+	4.24789i	−0.421985	+	0.243633i
$305$	−6.35642	+	3.66988i	−0.363968	+	0.210137i
$306$		0			0
$307$			14.7179i			0.839996i	0.907525	+	0.419998i	$0.137969\pi$
$307$			14.7179i			0.839996i	−0.907525	+	0.419998i	$0.862031\pi$
$308$	−1.29978	+	26.5622i	−0.0740617	+	1.51352i
$309$		0			0
$310$	9.86840	+	5.69752i	0.560487	+	0.323597i
$311$	−14.3289	−	24.8184i	−0.812517	−	1.40732i	−0.911097	−	0.412191i	$-0.864764\pi$
$311$	−14.3289	−	24.8184i	−0.812517	−	1.40732i	0.0985808	−	0.995129i	$-0.468570\pi$
$312$		0			0
$313$	16.4125	−	28.4274i	0.927692	−	1.60681i	0.140518	−	0.990078i	$-0.455123\pi$
$313$	16.4125	−	28.4274i	0.927692	−	1.60681i	0.787174	−	0.616732i	$-0.211544\pi$
$314$			27.9435i			1.57694i
$315$		0			0
$316$	−4.95488			−0.278734
$317$	9.01715	+	5.20605i	0.506453	+	0.292401i	0.731375	−	0.681976i	$-0.238879\pi$
$317$	9.01715	+	5.20605i	0.506453	+	0.292401i	−0.224921	+	0.974377i	$0.572212\pi$
$318$		0			0
$319$	−22.7225	+	13.1188i	−1.27222	+	0.734515i
$320$	−35.8100	−	20.6749i	−2.00184	−	1.15576i
$321$		0			0
$322$	−10.2992	−	6.63772i	−0.573949	−	0.369905i
$323$			15.0887i			0.839558i
$324$		0			0
$325$	−27.9639	−	7.12256i	−1.55116	−	0.395089i
$326$	−19.8186	−	34.3268i	−1.09765	−	1.90118i
$327$		0			0
$328$	2.33205			0.128766
$329$	0.131758	−	2.69261i	0.00726406	−	0.148448i
$330$		0			0
$331$	3.86260	+	2.23007i	0.212308	+	0.122576i	0.602383	−	0.798207i	$-0.294218\pi$
$331$	3.86260	+	2.23007i	0.212308	+	0.122576i	−0.390076	+	0.920783i	$0.627551\pi$
$332$	−16.7023	+	9.64307i	−0.916657	+	0.529232i
$333$		0			0
$334$	1.03370	−	1.79043i	0.0565617	−	0.0979677i
$335$	14.1028			0.770519
$336$		0			0
$337$	10.7949			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$337$	10.7949			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$338$	13.2182	−	24.2646i	0.718975	−	1.31982i
$339$		0			0
$340$	−37.6551	+	21.7402i	−2.04214	+	1.17903i
$341$	2.96775	−	5.14030i	0.160713	−	0.278363i
$342$		0			0
$343$	18.3214	+	2.70687i	0.989261	+	0.146157i
$344$		−	1.57514i		−	0.0849259i
$345$		0			0
$346$	−4.52286	+	2.61127i	−0.243150	+	0.140383i
$347$	−2.03516	−	3.52499i	−0.109253	−	0.189232i	0.806215	−	0.591623i	$-0.201513\pi$
$347$	−2.03516	−	3.52499i	−0.109253	−	0.189232i	−0.915468	+	0.402391i	$0.868179\pi$
$348$		0			0
$349$			23.8727i			1.27788i	0.769258	+	0.638938i	$0.220626\pi$
$349$			23.8727i			1.27788i	−0.769258	+	0.638938i	$0.779374\pi$
$350$	40.0309	−	20.5718i	2.13974	−	1.09961i
$351$		0			0
$352$	−15.8343	+	27.4257i	−0.843969	+	1.46180i
$353$	22.5894	−	13.0420i	1.20231	−	0.694154i	0.241242	−	0.970465i	$-0.422445\pi$
$353$	22.5894	−	13.0420i	1.20231	−	0.694154i	0.961068	+	0.276311i	$0.0891119\pi$
$354$		0			0
$355$	−15.8788	+	27.5030i	−0.842762	+	1.45971i
$356$		−	32.2246i		−	1.70790i
$357$		0			0
$358$		−	30.7613i		−	1.62579i
$359$	−19.8271	−	11.4472i	−1.04644	−	0.604160i	−0.124786	−	0.992184i	$-0.539824\pi$
$359$	−19.8271	−	11.4472i	−1.04644	−	0.604160i	−0.921649	+	0.388024i	$0.873158\pi$
$360$		0			0
$361$	−4.53687	−	7.85809i	−0.238783	−	0.413584i
$362$	−16.8958	−	9.75478i	−0.888022	−	0.512700i
$363$		0			0
$364$	5.36551	+	23.4104i	0.281229	+	1.22704i
$365$	−11.1382			−0.583002
$366$		0			0
$367$	9.08003	+	15.7271i	0.473974	+	0.820946i	0.999556	−	0.0297964i	$-0.00948589\pi$
$367$	9.08003	+	15.7271i	0.473974	+	0.820946i	−0.525582	+	0.850743i	$0.676153\pi$
$368$	−2.93771	−	5.08826i	−0.153139	−	0.265244i
$369$		0			0
$370$			38.0548i			1.97838i
$371$	8.65045	−	13.4221i	0.449109	−	0.696842i
$372$		0			0
$373$	7.93457	−	13.7431i	0.410836	−	0.711590i	−0.584145	−	0.811649i	$-0.698570\pi$
$373$	7.93457	−	13.7431i	0.410836	−	0.711590i	0.994981	+	0.100060i	$0.0319034\pi$
$374$	20.3197	+	35.1948i	1.05071	+	1.81988i
$375$		0			0
$376$	−0.560605	+	0.970997i	−0.0289110	+	0.0500754i
$377$	−16.5463	+	16.9618i	−0.852179	+	0.873575i
$378$		0			0
$379$		−	27.7634i		−	1.42611i	−0.701108	−	0.713055i	$-0.747311\pi$
$379$		−	27.7634i		−	1.42611i	0.701108	−	0.713055i	$-0.252689\pi$
$380$	−14.3020	+	24.7718i	−0.733678	+	1.27077i
$381$		0			0
$382$	32.3674	−	18.6873i	1.65606	−	0.956128i
$383$	22.7304	+	13.1234i	1.16147	+	0.670576i	0.951656	−	0.307165i	$-0.0993804\pi$
$383$	22.7304	+	13.1234i	1.16147	+	0.670576i	0.209815	+	0.977741i	$0.432714\pi$
$384$		0			0
$385$	−17.4099	−	33.8780i	−0.887289	−	1.72658i
$386$	41.9908			2.13728
$387$		0			0
$388$	2.96317	−	1.71079i	0.150432	−	0.0868521i
$389$	12.6277	+	21.8718i	0.640250	+	1.10895i	0.985377	+	0.170389i	$0.0545026\pi$
$389$	12.6277	+	21.8718i	0.640250	+	1.10895i	−0.345127	+	0.938556i	$0.612164\pi$
$390$		0			0
$391$	−10.4349			−0.527714
$392$	−6.26283	−	4.48422i	−0.316321	−	0.226487i
$393$		0			0
$394$	8.14084	−	14.1003i	0.410129	−	0.710365i
$395$	6.14592	−	3.54835i	0.309235	−	0.178537i
$396$		0			0
$397$	12.9701	+	7.48827i	0.650949	+	0.375826i	0.788820	−	0.614625i	$-0.210692\pi$
$397$	12.9701	+	7.48827i	0.650949	+	0.375826i	−0.137871	+	0.990450i	$0.544026\pi$
$398$		−	13.9080i		−	0.697143i
$399$		0			0
$400$	21.5817			1.07909
$401$	−4.62811	−	2.67204i	−0.231117	−	0.133435i	0.379970	−	0.924999i	$-0.375934\pi$
$401$	−4.62811	−	2.67204i	−0.231117	−	0.133435i	−0.611087	+	0.791563i	$0.709267\pi$
$402$		0			0
$403$	1.32309	−	5.19458i	0.0659076	−	0.258760i
$404$	5.39798	−	9.34957i	0.268559	−	0.465159i
$405$		0			0
$406$	1.80630	−	36.9135i	0.0896451	−	1.83199i
$407$	19.8222			0.982549
$408$		0			0
$409$	2.91433	−	1.68259i	0.144104	−	0.0831985i	−0.426214	−	0.904622i	$-0.640153\pi$
$409$	2.91433	−	1.68259i	0.144104	−	0.0831985i	0.570319	+	0.821424i	$0.306820\pi$
$410$	−14.0674	+	8.12181i	−0.694739	+	0.401107i
$411$		0			0
$412$	36.3428			1.79048
$413$	−10.9042	−	7.02769i	−0.536562	−	0.345810i
$414$		0			0
$415$	13.8114	−	23.9221i	0.677977	−	1.17429i
$416$	−7.05925	+	27.7154i	−0.346108	+	1.35886i
$417$		0			0
$418$	23.1533	+	13.3675i	1.13246	+	0.653828i
$419$	28.8639			1.41010			0.705048	−	0.709160i	$-0.250926\pi$
$419$	28.8639			1.41010			0.705048	+	0.709160i	$0.250926\pi$
$420$		0			0
$421$			16.6125i			0.809644i	0.914395	+	0.404822i	$0.132667\pi$
$421$			16.6125i			0.809644i	−0.914395	+	0.404822i	$0.867333\pi$
$422$	36.8977	+	21.3029i	1.79615	+	1.03701i
$423$		0			0
$424$	−5.75151	+	3.32064i	−0.279318	+	0.161264i
$425$	19.1648	−	33.1945i	0.929631	−	1.61017i
$426$		0			0
$427$	−5.37877	−	0.263201i	−0.260297	−	0.0127372i
$428$	−24.4692			−1.18276
$429$		0			0
$430$	5.48572	+	9.50154i	0.264545	+	0.458205i
$431$	17.8015	−	10.2777i	0.857469	−	0.495060i	−0.00569505	−	0.999984i	$-0.501813\pi$
$431$	17.8015	−	10.2777i	0.857469	−	0.495060i	0.863164	+	0.504924i	$0.168479\pi$
$432$		0			0
$433$	−19.4092			−0.932748			−0.466374	−	0.884588i	$-0.654440\pi$
$433$	−19.4092			−0.932748			−0.466374	+	0.884588i	$0.654440\pi$
$434$	3.82141	+	7.43613i	0.183434	+	0.356945i
$435$		0			0
$436$	14.4965	+	8.36956i	0.694257	+	0.400829i
$437$	−5.94500	+	3.43235i	−0.284388	+	0.164191i
$438$		0			0
$439$	6.71256	−	11.6265i	0.320373	−	0.554902i	−0.660192	−	0.751097i	$-0.729525\pi$
$439$	6.71256	−	11.6265i	0.320373	−	0.554902i	0.980565	+	0.196195i	$0.0628585\pi$
$440$			15.8417i			0.755225i
$441$		0			0
$442$	26.2720	+	25.6285i	1.24963	+	1.21902i
$443$	−16.7766	+	29.0579i	−0.797080	+	1.38058i	0.124430	+	0.992228i	$0.460290\pi$
$443$	−16.7766	+	29.0579i	−0.797080	+	1.38058i	−0.921510	+	0.388354i	$0.873044\pi$
$444$		0			0
$445$	23.0771	+	39.9707i	1.09396	+	1.89479i
$446$	−29.4528	+	51.0138i	−1.39463	+	2.41557i
$447$		0			0
$448$	−13.8670	−	26.9839i	−0.655153	−	1.27487i
$449$		−	34.4284i		−	1.62478i	−0.583117	−	0.812388i	$-0.698167\pi$
$449$		−	34.4284i		−	1.62478i	0.583117	−	0.812388i	$-0.301833\pi$
$450$		0			0
$451$	4.23052	+	7.32748i	0.199208	+	0.345038i
$452$	−22.0846	−	38.2517i	−1.03877	−	1.79921i
$453$		0			0
$454$	−24.1691			−1.13431
$455$	−23.4202	−	25.1953i	−1.09796	−	1.18118i
$456$		0			0
$457$	−11.6735	−	6.73967i	−0.546061	−	0.315269i	0.201471	−	0.979495i	$-0.435428\pi$
$457$	−11.6735	−	6.73967i	−0.546061	−	0.315269i	−0.747532	+	0.664226i	$0.768761\pi$
$458$	−9.25771	−	16.0348i	−0.432584	−	0.749258i
$459$		0			0
$460$	−17.1314	−	9.89082i	−0.798756	−	0.461162i
$461$		−	1.35900i		−	0.0632951i	−0.999499	−	0.0316476i	$-0.989925\pi$
$461$		−	1.35900i		−	0.0632951i	0.999499	−	0.0316476i	$-0.0100754\pi$
$462$		0			0
$463$			2.49836i			0.116109i	0.998313	+	0.0580543i	$0.0184897\pi$
$463$			2.49836i			0.116109i	−0.998313	+	0.0580543i	$0.981510\pi$
$464$	8.86088	−	15.3475i	0.411356	−	0.712489i
$465$		0			0
$466$	6.19325	−	3.57567i	0.286897	−	0.165640i
$467$	13.1091	−	22.7056i	0.606617	−	1.05069i	−0.385176	−	0.922843i	$-0.625859\pi$
$467$	13.1091	−	22.7056i	0.606617	−	1.05069i	0.991794	−	0.127849i	$-0.0408072\pi$
$468$		0			0
$469$	8.69744	+	5.60542i	0.401610	+	0.258834i
$470$		−	7.80965i		−	0.360232i
$471$		0			0
$472$	2.69771	+	4.67257i	0.124172	+	0.215072i
$473$	4.94921	−	2.85743i	0.227565	−	0.131385i
$474$		0			0
$475$		−	25.2156i		−	1.15697i
$476$	−31.8635	−	1.55919i	−1.46046	−	0.0714653i
$477$		0			0
$478$	−21.1271	+	36.5933i	−0.966332	+	1.67374i
$479$	−20.6513	+	11.9230i	−0.943583	+	0.544778i	−0.891082	−	0.453843i	$-0.850053\pi$
$479$	−20.6513	+	11.9230i	−0.943583	+	0.544778i	−0.0525011	+	0.998621i	$0.516719\pi$
$480$		0			0
$481$	17.2329	−	4.84730i	0.785754	−	0.221018i
$482$	40.1120			1.82705
$483$		0			0
$484$	12.4348			0.565217
$485$	−2.45030	+	4.24405i	−0.111263	+	0.192712i
$486$		0			0
$487$	−9.17524	+	5.29733i	−0.415770	+	0.240045i	−0.693266	−	0.720682i	$-0.743829\pi$
$487$	−9.17524	+	5.29733i	−0.415770	+	0.240045i	0.277496	+	0.960727i	$0.410496\pi$
$488$	1.93967	+	1.11987i	0.0878047	+	0.0506941i
$489$		0			0
$490$	53.3957	+	5.23820i	2.41217	+	0.236638i
$491$	−19.7704			−0.892224			−0.446112	−	0.894977i	$-0.647192\pi$
$491$	−19.7704			−0.892224			−0.446112	+	0.894977i	$0.647192\pi$
$492$		0			0
$493$	−15.7371	−	27.2575i	−0.708764	−	1.22762i
$494$	23.3978	+	5.95953i	1.05272	+	0.268132i
$495$		0			0
$496$			4.00902i			0.180010i
$497$	−20.7243	+	10.6502i	−0.929612	+	0.477726i
$498$		0			0
$499$	−11.4234	−	6.59530i	−0.511381	−	0.295246i	0.222020	−	0.975042i	$-0.428735\pi$
$499$	−11.4234	−	6.59530i	−0.511381	−	0.295246i	−0.733401	+	0.679796i	$0.762068\pi$
$500$	23.6147	−	13.6339i	1.05608	−	0.609728i
$501$		0			0
$502$	−18.0318	−	10.4107i	−0.804798	−	0.464651i
$503$	−37.9046			−1.69008			−0.845040	−	0.534703i	$-0.820424\pi$
$503$	−37.9046			−1.69008			−0.845040	+	0.534703i	$0.820424\pi$
$504$		0			0
$505$			15.4627i			0.688080i
$506$	−9.24457	+	16.0121i	−0.410971	+	0.711823i
$507$		0			0
$508$	−24.5657	−	42.5490i	−1.08993	−	1.88781i
$509$	23.9565	+	13.8313i	1.06185	+	0.613062i	0.925944	−	0.377660i	$-0.123271\pi$
$509$	23.9565	+	13.8313i	1.06185	+	0.613062i	0.135909	+	0.990721i	$0.456604\pi$
$510$		0			0
$511$	−6.86913	−	4.42710i	−0.303872	−	0.195843i
$512$		−	27.3244i		−	1.20758i
$513$		0			0
$514$	−38.5438	+	22.2533i	−1.70010	+	0.981551i
$515$	−45.0788	+	26.0263i	−1.98641	+	1.14685i
$516$		0			0
$517$	−4.06792			−0.178907
$518$	−15.1256	+	23.4690i	−0.664580	+	1.03117i
$519$		0			0
$520$	3.87392	+	13.7724i	0.169883	+	0.603960i
$521$	7.78339	+	13.4812i	0.340996	+	0.590623i	0.984618	−	0.174721i	$-0.0559022\pi$
$521$	7.78339	+	13.4812i	0.340996	+	0.590623i	−0.643622	+	0.765344i	$0.722569\pi$
$522$		0			0
$523$	−13.6169	+	23.5852i	−0.595425	+	1.03131i	0.398061	+	0.917359i	$0.369683\pi$
$523$	−13.6169	+	23.5852i	−0.595425	+	1.03131i	−0.993487	+	0.113948i	$0.963650\pi$
$524$	48.0234			2.09791
$525$		0			0
$526$		−	15.7005i		−	0.684577i
$527$	6.16620	+	3.56006i	0.268604	+	0.155079i
$528$		0			0
$529$	9.12630	+	15.8072i	0.396796	+	0.687270i
$530$	23.1294	−	40.0614i	1.00468	−	1.74015i
$531$		0			0
$532$	−18.6663	+	9.59258i	−0.809286	+	0.415891i
$533$	5.46977	+	5.33581i	0.236922	+	0.231119i
$534$		0			0
$535$	30.3511	−	17.5232i	1.31219	−	0.757594i
$536$	−2.15175	−	3.72693i	−0.0929413	−	0.160979i
$537$		0			0
$538$			48.4381i			2.08832i
$539$	2.72850	−	27.8130i	0.117525	−	1.19799i
$540$		0			0
$541$	20.9626	+	12.1027i	0.901251	+	0.520338i	0.877606	−	0.479383i	$-0.159139\pi$
$541$	20.9626	+	12.1027i	0.901251	+	0.520338i	0.0236453	+	0.999720i	$0.492473\pi$
$542$	−4.42774	−	7.66907i	−0.190188	−	0.329415i
$543$		0			0
$544$	−32.8994	−	18.9945i	−1.41055	−	0.814381i
$545$	−23.9749			−1.02697
$546$		0			0
$547$	−22.2177			−0.949960			−0.474980	−	0.879997i	$-0.657545\pi$
$547$	−22.2177			−0.949960			−0.474980	+	0.879997i	$0.657545\pi$
$548$	14.0176	+	8.09305i	0.598801	+	0.345718i
$549$		0			0
$550$	−33.9574	−	58.8160i	−1.44795	−	2.50792i
$551$	−17.9316	−	10.3528i	−0.763913	−	0.441045i
$552$		0			0
$553$	5.20065	+	0.254485i	0.221154	+	0.0108218i
$554$			1.65172i			0.0701749i
$555$		0			0
$556$	−3.05718	−	5.29519i	−0.129653	−	0.224566i
$557$	−19.3300	+	11.1602i	−0.819040	+	0.472873i	−0.850085	−	0.526645i	$-0.823450\pi$
$557$	−19.3300	+	11.1602i	−0.819040	+	0.472873i	0.0310455	+	0.999518i	$0.490116\pi$
$558$		0			0
$559$	3.60397	−	3.69445i	0.152432	−	0.156259i
$560$	21.6249	+	13.9370i	0.913818	+	0.588948i
$561$		0			0
$562$	−12.6454	+	21.9025i	−0.533415	+	0.923901i
$563$	−13.3519	−	23.1262i	−0.562717	−	0.974655i	−0.997258	−	0.0740027i	$-0.976423\pi$
$563$	−13.3519	−	23.1262i	−0.562717	−	0.974655i	0.434541	−	0.900652i	$-0.356911\pi$
$564$		0			0
$565$	54.7865	+	31.6310i	2.30489	+	1.33073i
$566$		−	33.8039i		−	1.42088i
$567$		0			0
$568$	9.69090			0.406621
$569$	−3.30510	+	5.72461i	−0.138557	+	0.239988i	−0.926951	−	0.375183i	$-0.877580\pi$
$569$	−3.30510	+	5.72461i	−0.138557	+	0.239988i	0.788393	+	0.615171i	$0.210913\pi$
$570$		0			0
$571$	−21.0643	−	36.4844i	−0.881513	−	1.52683i	−0.849659	−	0.527333i	$-0.823192\pi$
$571$	−21.0643	−	36.4844i	−0.881513	−	1.52683i	−0.0318546	−	0.999493i	$-0.510141\pi$
$572$	34.8877	−	9.81325i	1.45873	−	0.410313i
$573$		0			0
$574$	−11.9037	−	0.582489i	−0.496853	−	0.0243126i
$575$	17.4383			0.727227
$576$		0			0
$577$	13.7559	−	7.94195i	0.572664	−	0.330628i	−0.185549	−	0.982635i	$-0.559406\pi$
$577$	13.7559	−	7.94195i	0.572664	−	0.330628i	0.758213	+	0.652007i	$0.226073\pi$
$578$	−10.9266	+	6.30848i	−0.454487	+	0.262398i
$579$		0			0
$580$		−	59.6665i		−	2.47752i
$581$	18.0260	−	9.26354i	0.747845	−	0.384316i
$582$		0			0
$583$	−20.8674	−	12.0478i	−0.864238	−	0.498968i
$584$	1.69942	+	2.94349i	0.0703226	+	0.121802i
$585$		0			0
$586$	−7.15969	+	12.4010i	−0.295764	+	0.512279i
$587$		−	18.5676i		−	0.766366i	−0.923672	−	0.383183i	$-0.874828\pi$
$587$		−	18.5676i		−	0.766366i	0.923672	−	0.383183i	$-0.125172\pi$
$588$		0			0
$589$	4.68404			0.193003
$590$	−32.5462	−	18.7905i	−1.33990	−	0.773594i
$591$		0			0
$592$	−11.5948	+	6.69426i	−0.476543	+	0.275132i
$593$	17.8487	+	10.3050i	0.732960	+	0.423175i	0.819504	−	0.573073i	$-0.194249\pi$
$593$	17.8487	+	10.3050i	0.732960	+	0.423175i	−0.0865442	+	0.996248i	$0.527582\pi$
$594$		0			0
$595$	40.6394	−	20.8845i	1.66605	−	0.856183i
$596$			0.290425i			0.0118963i
$597$		0			0
$598$	−4.12143	+	16.1812i	−0.168538	+	0.661697i
$599$	−6.80224	−	11.7818i	−0.277932	−	0.481393i	0.692939	−	0.720997i	$-0.256316\pi$
$599$	−6.80224	−	11.7818i	−0.277932	−	0.481393i	−0.970871	+	0.239604i	$0.922982\pi$
$600$		0			0
$601$	−12.1503			−0.495621			−0.247810	−	0.968809i	$-0.579711\pi$
$601$	−12.1503			−0.495621			−0.247810	+	0.968809i	$0.579711\pi$
$602$	−0.393431	+	8.04015i	−0.0160351	+	0.327692i
$603$		0			0
$604$	25.7355	+	14.8584i	1.04716	+	0.604579i
$605$	−15.4238	+	8.90496i	−0.627068	+	0.362038i
$606$		0			0
$607$	−17.6166	+	30.5128i	−0.715035	+	1.23848i	0.247911	+	0.968783i	$0.420256\pi$
$607$	−17.6166	+	30.5128i	−0.715035	+	1.23848i	−0.962946	+	0.269695i	$0.913077\pi$
$608$	−24.9914			−1.01354
$609$		0			0
$610$	−15.6006			−0.631650
$611$	−3.53655	+	0.994767i	−0.143074	+	0.0402440i
$612$		0			0
$613$	26.0345	−	15.0310i	1.05152	−	0.607097i	0.128448	−	0.991716i	$-0.459000\pi$
$613$	26.0345	−	15.0310i	1.05152	−	0.607097i	0.923075	+	0.384619i	$0.125667\pi$
$614$	−15.6414	+	27.0917i	−0.631236	+	1.09333i
$615$		0			0
$616$	−6.29658	+	9.76984i	−0.253697	+	0.393638i
$617$			7.01712i			0.282499i	0.989974	+	0.141249i	$0.0451119\pi$
$617$			7.01712i			0.282499i	−0.989974	+	0.141249i	$0.954888\pi$
$618$		0			0
$619$	−37.9736	+	21.9241i	−1.52629	+	0.881203i	−0.526776	+	0.850004i	$0.676599\pi$
$619$	−37.9736	+	21.9241i	−1.52629	+	0.881203i	−0.999513	+	0.0311993i	$0.990067\pi$
$620$	6.74889	+	11.6894i	0.271042	+	0.469458i
$621$		0			0
$622$		−	60.9118i		−	2.44234i
$623$	−1.65507	+	33.8230i	−0.0663091	+	1.35509i
$624$		0			0
$625$	0.481145	−	0.833367i	0.0192458	−	0.0333347i
$626$	60.4221	−	34.8847i	2.41495	−	1.39427i
$627$		0			0
$628$	−16.5500	+	28.6654i	−0.660416	+	1.14387i
$629$			23.7783i			0.948103i
$630$		0			0
$631$		−	23.4936i		−	0.935267i	−0.883922	−	0.467634i	$-0.845107\pi$
$631$		−	23.4936i		−	0.935267i	0.883922	−	0.467634i	$-0.154893\pi$
$632$	−1.87544	−	1.08278i	−0.0746008	−	0.0430708i
$633$		0			0
$634$	11.0654	+	19.1659i	0.439464	+	0.761173i
$635$	60.9415	+	35.1846i	2.41839	+	1.39626i
$636$		0			0
$637$	−4.42928	−	24.8472i	−0.175494	−	0.984480i
$638$	−55.7680			−2.20788
$639$		0			0
$640$	−15.3403	−	26.5702i	−0.606378	−	1.05028i
$641$	−3.70233	−	6.41262i	−0.146233	−	0.253283i	0.783599	−	0.621267i	$-0.213382\pi$
$641$	−3.70233	−	6.41262i	−0.146233	−	0.253283i	−0.929832	+	0.367983i	$0.880048\pi$
$642$		0			0
$643$		−	39.9607i		−	1.57590i	−0.615742	−	0.787948i	$-0.711144\pi$
$643$		−	39.9607i		−	1.57590i	0.615742	−	0.787948i	$-0.288856\pi$
$644$	−6.63393	−	12.9090i	−0.261413	−	0.508687i
$645$		0			0
$646$	−16.0354	+	27.7742i	−0.630906	+	1.09276i
$647$	−13.6234	−	23.5964i	−0.535591	−	0.927670i	−0.999134	−	0.0415963i	$-0.986756\pi$
$647$	−13.6234	−	23.5964i	−0.535591	−	0.927670i	0.463544	−	0.886074i	$-0.346578\pi$
$648$		0			0
$649$	−9.78770	+	16.9528i	−0.384201	+	0.665456i
$650$	−43.9046	−	42.8292i	−1.72208	−	1.67990i
$651$		0			0
$652$		−	46.9514i		−	1.83876i
$653$	9.57255	−	16.5801i	0.374603	−	0.648831i	−0.615665	−	0.788008i	$-0.711112\pi$
$653$	9.57255	−	16.5801i	0.374603	−	0.648831i	0.990267	+	0.139177i	$0.0444458\pi$
$654$		0			0
$655$	−59.5672	+	34.3911i	−2.32748	+	1.34377i
$656$	−4.94921	−	2.85743i	−0.193234	−	0.111564i
$657$		0			0
$658$	3.10409	−	4.81633i	0.121010	−	0.187760i
$659$	−41.5725			−1.61943			−0.809717	−	0.586820i	$-0.800380\pi$
$659$	−41.5725			−1.61943			−0.809717	+	0.586820i	$0.800380\pi$
$660$		0			0
$661$	29.6221	−	17.1023i	1.15217	−	0.665203i	0.202752	−	0.979230i	$-0.435012\pi$
$661$	29.6221	−	17.1023i	1.15217	−	0.665203i	0.949414	+	0.314027i	$0.101678\pi$
$662$	4.74000	+	8.20992i	0.184225	+	0.319088i
$663$		0			0
$664$	−8.42915			−0.327115
$665$	16.2837	−	25.2660i	0.631455	−	0.979772i
$666$		0			0
$667$	7.15969	−	12.4010i	0.277224	−	0.480167i
$668$	2.12081	−	1.22445i	0.0820567	−	0.0473755i
$669$		0			0
$670$	25.9595	+	14.9877i	1.00290	+	0.579025i
$671$			8.12611i			0.313705i
$672$		0			0
$673$	−21.4308			−0.826098			−0.413049	−	0.910709i	$-0.635536\pi$
$673$	−21.4308			−0.826098			−0.413049	+	0.910709i	$0.635536\pi$
$674$	19.8704	+	11.4722i	0.765381	+	0.441893i
$675$		0			0
$676$	27.9308	−	17.0628i	1.07426	−	0.656261i
$677$	4.89083	−	8.47117i	0.187970	−	0.325573i	−0.756603	−	0.653874i	$-0.773143\pi$
$677$	4.89083	−	8.47117i	0.187970	−	0.325573i	0.944573	+	0.328301i	$0.106476\pi$
$678$		0			0
$679$	−3.19802	+	1.64346i	−0.122729	+	0.0630700i
$680$	−19.0034			−0.728748
$681$		0			0
$682$	10.9256	−	6.30793i	0.418365	−	0.241543i
$683$	−13.2297	+	7.63818i	−0.506221	+	0.292267i	−0.731279	−	0.682079i	$-0.761076\pi$
$683$	−13.2297	+	7.63818i	−0.506221	+	0.292267i	0.225058	+	0.974345i	$0.427743\pi$
$684$		0			0
$685$	−23.1828			−0.885769
$686$	30.8480	+	24.4536i	1.17778	+	0.933642i
$687$		0			0
$688$	−1.92999	+	3.34285i	−0.0735803	+	0.127445i
$689$	−21.0877	−	5.37115i	−0.803378	−	0.204625i
$690$		0			0
$691$	36.7690	+	21.2286i	1.39876	+	0.807573i	0.994263	−	0.106967i	$-0.0341138\pi$
$691$	36.7690	+	21.2286i	1.39876	+	0.807573i	0.404496	+	0.914540i	$0.367447\pi$
$692$	−6.18627			−0.235167
$693$		0			0
$694$		−	8.65141i		−	0.328403i
$695$	7.58412	+	4.37869i	0.287682	+	0.166093i
$696$		0			0
$697$	−8.78991	+	5.07486i	−0.332942	+	0.192224i
$698$	−25.3706	+	43.9432i	−0.960291	+	1.66327i
$699$		0			0
$700$	53.2489	+	2.60565i	2.01262	+	0.0984842i
$701$	−2.79985			−0.105749			−0.0528744	−	0.998601i	$-0.516838\pi$
$701$	−2.79985			−0.105749			−0.0528744	+	0.998601i	$0.516838\pi$
$702$		0			0
$703$	7.82141	+	13.5471i	0.294990	+	0.510937i
$704$	−39.6465	+	22.8899i	−1.49423	+	0.862696i
$705$		0			0
$706$	55.4412			2.08656
$707$	−6.14592	+	9.53608i	−0.231141	+	0.358641i
$708$		0			0
$709$	12.6149	+	7.28319i	0.473761	+	0.273526i	0.717813	−	0.696236i	$-0.245143\pi$
$709$	12.6149	+	7.28319i	0.473761	+	0.273526i	−0.244052	+	0.969762i	$0.578477\pi$
$710$	−58.4573	+	33.7503i	−2.19386	+	1.26663i
$711$		0			0
$712$	7.04201	−	12.1971i	0.263910	−	0.457106i
$713$			3.23934i			0.121314i
$714$		0			0
$715$	−36.2463	+	37.1563i	−1.35554	+	1.38957i
$716$	18.2189	−	31.5560i	0.680871	−	1.17930i
$717$		0			0
$718$	−24.3309	−	42.1423i	−0.908021	−	1.57274i
$719$	−17.2529	+	29.8828i	−0.643423	+	1.11444i	0.341240	+	0.939976i	$0.389153\pi$
$719$	−17.2529	+	29.8828i	−0.643423	+	1.11444i	−0.984663	+	0.174465i	$0.944180\pi$
$720$		0			0
$721$	−38.1454	−	1.86658i	−1.42061	−	0.0695152i
$722$		−	19.2861i		−	0.717756i
$723$		0			0
$724$	−11.5548	−	20.0136i	−0.429432	−	0.743798i
$725$	26.2992	+	45.5515i	0.976727	+	1.69174i
$726$		0			0
$727$	−35.7571			−1.32616			−0.663078	−	0.748550i	$-0.730750\pi$
$727$	−35.7571			−1.32616			−0.663078	+	0.748550i	$0.730750\pi$
$728$	−3.08498	+	10.0334i	−0.114337	+	0.371863i
$729$		0			0
$730$	−20.5025	−	11.8371i	−0.758830	−	0.438111i
$731$	3.42771	+	5.93698i	0.126779	+	0.219587i
$732$		0			0
$733$	−35.5504	−	20.5250i	−1.31308	−	0.758108i	−0.330477	−	0.943814i	$-0.607210\pi$
$733$	−35.5504	−	20.5250i	−1.31308	−	0.758108i	−0.982605	+	0.185706i	$0.940543\pi$
$734$			38.5990i			1.42472i
$735$		0			0
$736$		−	17.2833i		−	0.637071i
$737$	7.80686	−	13.5219i	0.287570	−	0.498085i
$738$		0			0
$739$	−0.629089	+	0.363205i	−0.0231414	+	0.0133607i	−0.511526	−	0.859268i	$-0.670920\pi$
$739$	−0.629089	+	0.363205i	−0.0231414	+	0.0133607i	0.488385	+	0.872628i	$0.337586\pi$
$740$	−22.5386	+	39.0379i	−0.828534	+	1.43506i
$741$		0			0
$742$	30.1874	−	15.5133i	1.10822	−	0.569510i
$743$			16.4547i			0.603664i	0.953361	+	0.301832i	$0.0975981\pi$
$743$			16.4547i			0.603664i	−0.953361	+	0.301832i	$0.902402\pi$
$744$		0			0
$745$	−0.207983	−	0.360236i	−0.00761989	−	0.0131980i
$746$	29.2108	−	16.8648i	1.06948	−	0.617466i
$747$		0			0
$748$			48.1387i			1.76012i
$749$	25.6829	+	1.25675i	0.938433	+	0.0459206i
$750$		0			0
$751$	12.5854	−	21.7985i	0.459247	−	0.795439i	−0.539675	−	0.841874i	$-0.681453\pi$
$751$	12.5854	−	21.7985i	0.459247	−	0.795439i	0.998921	+	0.0464350i	$0.0147860\pi$
$752$	2.37949	−	1.37380i	0.0867712	−	0.0500974i
$753$		0			0
$754$	−48.4833	+	13.6375i	−1.76566	+	0.496647i
$755$	−42.5623			−1.54900
$756$		0			0
$757$	44.0743			1.60191			0.800953	−	0.598727i	$-0.204327\pi$
$757$	44.0743			1.60191			0.800953	+	0.598727i	$0.204327\pi$
$758$	29.5054	−	51.1049i	1.07168	−	1.85621i
$759$		0			0
$760$	−10.8267	+	6.25080i	−0.392726	+	0.226740i
$761$	−33.5171	−	19.3511i	−1.21499	−	0.701477i	−0.251151	−	0.967948i	$-0.580809\pi$
$761$	−33.5171	−	19.3511i	−1.21499	−	0.701477i	−0.963843	+	0.266471i	$0.914142\pi$
$762$		0			0
$763$	−14.7857	−	9.52925i	−0.535278	−	0.344982i
$764$	44.2715			1.60169
$765$		0			0
$766$	27.8937	+	48.3133i	1.00784	+	1.74563i
$767$	−4.36357	+	17.1318i	−0.157559	+	0.618594i
$768$		0			0
$769$			36.1506i			1.30362i	0.758381	+	0.651811i	$0.225991\pi$
$769$			36.1506i			1.30362i	−0.758381	+	0.651811i	$0.774009\pi$
$770$	3.95687	−	80.8625i	0.142596	−	2.91408i
$771$		0			0
$772$	43.0756	+	24.8697i	1.55032	+	0.895080i
$773$	26.0441	−	15.0366i	0.936740	−	0.540827i	0.0478033	−	0.998857i	$-0.484778\pi$
$773$	26.0441	−	15.0366i	0.936740	−	0.540827i	0.888937	+	0.458030i	$0.151445\pi$
$774$		0			0
$775$	−10.3047	−	5.94941i	−0.370155	−	0.213709i
$776$	1.49543			0.0536827
$777$		0			0
$778$			53.6801i			1.92453i
$779$	−3.33855	+	5.78253i	−0.119616	+	0.207181i
$780$		0			0
$781$	17.5800	+	30.4495i	0.629063	+	1.08957i
$782$	−19.2078	−	11.0896i	−0.686868	−	0.396564i
$783$		0			0
$784$	7.79687	+	17.1904i	0.278460	+	0.613943i
$785$		−	47.4079i		−	1.69206i
$786$		0			0
$787$	−31.9106	+	18.4236i	−1.13749	+	0.656730i	−0.945808	−	0.324727i	$-0.894728\pi$
$787$	−31.9106	+	18.4236i	−1.13749	+	0.656730i	−0.191682	+	0.981457i	$0.561394\pi$
$788$	16.7023	−	9.64307i	0.594994	−	0.343520i
$789$		0			0
$790$	15.0840			0.536663
$791$	21.2154	+	41.2833i	0.754333	+	1.46786i
$792$		0			0
$793$	1.98715	+	7.06464i	0.0705658	+	0.250873i
$794$	15.9163	+	27.5678i	0.564847	+	0.978343i
$795$		0			0
$796$	8.23721	−	14.2673i	0.291960	−	0.505690i
$797$	27.5910			0.977323			0.488661	−	0.872474i	$-0.337485\pi$
$797$	27.5910			0.977323			0.488661	+	0.872474i	$0.337485\pi$
$798$		0			0
$799$		−	4.87980i		−	0.172635i
$800$	54.9800	+	31.7427i	1.94384	+	1.12227i
$801$		0			0
$802$	−5.67939	−	9.83700i	−0.200546	−	0.347356i
$803$	−6.16577	+	10.6794i	−0.217585	+	0.376869i
$804$		0			0
$805$	17.4732	+	11.2613i	0.615848	+	0.396909i
$806$	7.95596	−	8.15570i	0.280237	−	0.287272i
$807$		0			0
$808$	4.08630	−	2.35923i	0.143756	−	0.0829973i
$809$	17.8551	+	30.9260i	0.627752	+	1.08730i	0.988002	+	0.154443i	$0.0493582\pi$
$809$	17.8551	+	30.9260i	0.627752	+	1.08730i	−0.360250	+	0.932856i	$0.617308\pi$
$810$		0			0
$811$		−	2.22418i		−	0.0781015i	−0.999237	−	0.0390508i	$-0.987567\pi$
$811$		−	2.22418i		−	0.0781015i	0.999237	−	0.0390508i	$-0.0124334\pi$
$812$	23.7155	−	36.7973i	0.832252	−	1.29133i
$813$		0			0
$814$	36.4873	+	21.0659i	1.27888	+	0.738360i
$815$	33.6234	+	58.2375i	1.17778	+	2.03997i
$816$		0			0
$817$	3.90570	+	2.25496i	0.136643	+	0.0788910i
$818$	7.15264			0.250086
$819$		0			0
$820$	−19.2411			−0.671927
$821$	46.2192	+	26.6847i	1.61306	+	0.931302i	0.988655	+	0.150203i	$0.0479928\pi$
$821$	46.2192	+	26.6847i	1.61306	+	0.931302i	0.624407	+	0.781099i	$0.285341\pi$
$822$		0			0
$823$	25.6043	+	44.3479i	0.892509	+	1.54587i	0.836857	+	0.547421i	$0.184390\pi$
$823$	25.6043	+	44.3479i	0.892509	+	1.54587i	0.0556519	+	0.998450i	$0.482276\pi$
$824$	13.7559	+	7.94195i	0.479208	+	0.276671i
$825$		0			0
$826$	−12.6031	−	24.5245i	−0.438518	−	0.853316i
$827$		−	8.97196i		−	0.311986i	−0.987758	−	0.155993i	$-0.950142\pi$
$827$		−	8.97196i		−	0.311986i	0.987758	−	0.155993i	$-0.0498577\pi$
$828$		0			0
$829$	20.2858	+	35.1360i	0.704554	+	1.22032i	0.966852	+	0.255337i	$0.0821864\pi$
$829$	20.2858	+	35.1360i	0.704554	+	1.22032i	−0.262298	+	0.964987i	$0.584480\pi$
$830$	50.8462	−	29.3561i	1.76490	−	1.01896i
$831$		0			0
$832$	−28.8702	+	29.5951i	−1.00089	+	1.02602i
$833$	33.3639	+	3.27305i	1.15599	+	0.113405i
$834$		0			0
$835$	−1.75374	+	3.03757i	−0.0606907	+	0.105119i
$836$	15.8343	+	27.4257i	0.547639	+	0.948539i
$837$		0			0
$838$	53.1307	+	30.6750i	1.83537	+	1.05965i
$839$			32.3005i			1.11514i	0.830131	+	0.557568i	$0.188266\pi$
$839$			32.3005i			1.11514i	−0.830131	+	0.557568i	$0.811734\pi$
$840$		0			0
$841$	14.1909			0.489342
$842$	−17.6549	+	30.5791i	−0.608427	+	1.05383i
$843$		0			0
$844$	25.2340	+	43.7065i	0.868588	+	1.50444i
$845$	−22.4255	+	41.1665i	−0.771460	+	1.41617i
$846$		0			0
$847$	−13.0516	−	0.638656i	−0.448457	−	0.0219445i
$848$	16.2749			0.558882
$849$		0			0
$850$	70.5545	−	40.7347i	2.42000	−	1.39719i
$851$	−9.36873	+	5.40904i	−0.321156	+	0.185419i
$852$		0			0
$853$			35.5887i			1.21853i	0.792965	+	0.609267i	$0.208536\pi$
$853$			35.5887i			1.21853i	−0.792965	+	0.609267i	$0.791464\pi$
$854$	−9.62114	−	6.20074i	−0.329229	−	0.212185i
$855$		0			0
$856$	−9.26167	−	5.34723i	−0.316557	−	0.182764i
$857$	−23.0114	−	39.8570i	−0.786055	−	1.36149i	−0.928367	−	0.371666i	$-0.878787\pi$
$857$	−23.0114	−	39.8570i	−0.786055	−	1.36149i	0.142311	−	0.989822i	$-0.454547\pi$
$858$		0			0
$859$	−12.6229	+	21.8635i	−0.430689	+	0.745975i	−0.996933	−	0.0782630i	$-0.975063\pi$
$859$	−12.6229	+	21.8635i	−0.430689	+	0.745975i	0.566244	+	0.824238i	$0.308396\pi$
$860$			12.9960i			0.443160i
$861$		0			0
$862$	43.6903			1.48810
$863$	−11.9803	−	6.91684i	−0.407815	−	0.235452i	0.282036	−	0.959404i	$-0.408990\pi$
$863$	−11.9803	−	6.91684i	−0.407815	−	0.235452i	−0.689850	+	0.723952i	$0.742324\pi$
$864$		0			0
$865$	7.67331	−	4.43019i	0.260900	−	0.150631i
$866$	−35.7271	−	20.6271i	−1.21406	−	0.700936i
$867$		0			0
$868$	−0.484025	+	9.89152i	−0.0164289	+	0.335740i
$869$		−	7.85701i		−	0.266531i
$870$		0			0
$871$	3.48047	−	13.6647i	0.117931	−	0.463010i
$872$	3.65798	+	6.33581i	0.123875	+	0.214557i
$873$		0			0
$874$	−14.5908			−0.493542
$875$	−25.4862	+	13.0973i	−0.861592	+	0.442771i
$876$		0			0
$877$	−3.16459	−	1.82708i	−0.106861	−	0.0616961i	0.445617	−	0.895224i	$-0.352984\pi$
$877$	−3.16459	−	1.82708i	−0.106861	−	0.0616961i	−0.552478	+	0.833528i	$0.686318\pi$
$878$	24.7120	−	14.2675i	0.833989	−	0.481504i
$879$		0			0
$880$	19.4106	−	33.6201i	0.654331	−	1.13333i
$881$	36.6320			1.23416			0.617082	−	0.786899i	$-0.288315\pi$
$881$	36.6320			1.23416			0.617082	+	0.786899i	$0.288315\pi$
$882$		0			0
$883$	7.11145			0.239319			0.119660	−	0.992815i	$-0.461820\pi$
$883$	7.11145			0.239319			0.119660	+	0.992815i	$0.461820\pi$
$884$	11.7718	+	41.8506i	0.395928	+	1.40759i
$885$		0			0
$886$	−61.7623	+	35.6585i	−2.07494	+	1.19797i
$887$	−3.36773	+	5.83308i	−0.113077	+	0.195856i	−0.917010	−	0.398865i	$-0.869404\pi$
$887$	−3.36773	+	5.83308i	−0.113077	+	0.195856i	0.803932	+	0.594721i	$0.202737\pi$
$888$		0			0
$889$	23.5989	+	45.9212i	0.791480	+	1.54015i
$890$			98.1004i			3.28833i
$891$		0			0
$892$	−60.4274	+	34.8878i	−2.02326	+	1.16813i
$893$	−1.60512	−	2.78014i	−0.0537131	−	0.0930339i
$894$		0			0
$895$			52.1885i			1.74447i
$896$	1.10019	−	22.4835i	0.0367549	−	0.751122i
$897$		0			0
$898$	36.5886	−	63.3733i	1.22098	−	2.11479i
$899$	−8.46164	+	4.88533i	−0.282212	+	0.162935i
$900$		0			0
$901$	14.4523	−	25.0321i	0.481475	−	0.833939i
$902$			17.9839i			0.598798i
$903$		0			0
$904$		−	19.3045i		−	0.642058i
$905$	28.6647	+	16.5496i	0.952848	+	0.550127i
$906$		0			0
$907$	−2.46630	−	4.27175i	−0.0818921	−	0.141841i	0.822171	−	0.569241i	$-0.192763\pi$
$907$	−2.46630	−	4.27175i	−0.0818921	−	0.141841i	−0.904063	+	0.427400i	$0.859430\pi$
$908$	−24.7935	−	14.3145i	−0.822802	−	0.475045i
$909$		0			0
$910$	−16.3340	−	71.2675i	−0.541468	−	2.36249i
$911$	26.6258			0.882152			0.441076	−	0.897470i	$-0.354597\pi$
$911$	26.6258			0.882152			0.441076	+	0.897470i	$0.354597\pi$
$912$		0			0
$913$	−15.2911	−	26.4850i	−0.506063	−	0.876526i
$914$	−14.3251	−	24.8118i	−0.473833	−	0.820702i
$915$		0			0
$916$		−	21.9321i		−	0.724656i
$917$	−50.4054	−	2.46650i	−1.66453	−	0.0814512i
$918$		0			0
$919$	16.1918	−	28.0450i	0.534118	−	0.925119i	−0.465088	−	0.885265i	$-0.653977\pi$
$919$	16.1918	−	28.0450i	0.534118	−	0.925119i	0.999205	−	0.0398544i	$-0.0126894\pi$
$920$	−4.32286	−	7.48741i	−0.142520	−	0.246853i
$921$		0			0
$922$	1.44428	−	2.50156i	0.0475647	−	0.0823844i
$923$	22.7297	+	22.1730i	0.748158	+	0.729835i
$924$		0			0
$925$		−	39.7373i		−	1.30655i
$926$	−2.65512	+	4.59880i	−0.0872526	+	0.151126i
$927$		0			0
$928$	45.1466	−	26.0654i	1.48201	−	0.855639i
$929$	−24.2722	−	14.0135i	−0.796344	−	0.459769i	0.0458472	−	0.998948i	$-0.485401\pi$
$929$	−24.2722	−	14.0135i	−0.796344	−	0.459769i	−0.842191	+	0.539179i	$0.818735\pi$
$930$		0			0
$931$	20.0848	−	9.10967i	0.658254	−	0.298557i
$932$	8.47099			0.277476
$933$		0			0
$934$	48.2606	−	27.8633i	1.57914	−	0.911714i
$935$	−34.4737	−	59.7102i	−1.12741	−	1.95273i
$936$		0			0
$937$	14.1324			0.461686			0.230843	−	0.972991i	$-0.425852\pi$
$937$	14.1324			0.461686			0.230843	+	0.972991i	$0.425852\pi$
$938$	10.0525	+	19.5612i	0.328225	+	0.638696i
$939$		0			0
$940$	4.62538	−	8.01140i	0.150863	−	0.261303i
$941$	7.77080	−	4.48647i	0.253321	−	0.146255i	−0.367963	−	0.929840i	$-0.619945\pi$
$941$	7.77080	−	4.48647i	0.253321	−	0.146255i	0.621284	+	0.783586i	$0.286611\pi$
$942$		0			0
$943$	−3.99902	−	2.30883i	−0.130226	−	0.0751860i
$944$		−	13.2218i		−	0.430334i
$945$		0			0
$946$	12.1469			0.394929
$947$	−40.0933	−	23.1479i	−1.30286	−	0.752205i	−0.321964	−	0.946752i	$-0.604343\pi$
$947$	−40.0933	−	23.1479i	−1.30286	−	0.752205i	−0.980893	+	0.194546i	$0.937676\pi$
$948$		0			0
$949$	−2.74883	+	10.7922i	−0.0892308	+	0.350330i
$950$	26.7977	−	46.4150i	0.869433	−	1.50590i
$951$		0			0
$952$	−11.7197	−	7.55326i	−0.379838	−	0.244803i
$953$	19.1097			0.619023			0.309512	−	0.950896i	$-0.399834\pi$
$953$	19.1097			0.619023			0.309512	+	0.950896i	$0.399834\pi$
$954$		0			0
$955$	−54.9134	+	31.7042i	−1.77695	+	1.02593i
$956$	−43.3458	+	25.0257i	−1.40190	+	0.809390i
$957$		0			0
$958$	−50.6846			−1.63755
$959$	−14.2972	−	9.21443i	−0.461681	−	0.297549i
$960$		0			0
$961$	−14.3948	+	24.9326i	−0.464350	+	0.804277i
$962$	36.8726	+	9.39164i	1.18882	+	0.302799i
$963$		0			0
$964$	41.1483	+	23.7570i	1.32530	+	0.765160i
$965$	−71.2400			−2.29330
$966$		0			0
$967$		−	22.5432i		−	0.724942i	−0.931995	−	0.362471i	$-0.881933\pi$
$967$		−	22.5432i		−	0.724942i	0.931995	−	0.362471i	$-0.118067\pi$
$968$	4.70660	+	2.71736i	0.151276	+	0.0873392i
$969$		0			0
$970$	−9.02068	+	5.20809i	−0.289637	+	0.167222i
$971$	13.6429	−	23.6301i	0.437820	−	0.758327i	−0.559701	−	0.828695i	$-0.689084\pi$
$971$	13.6429	−	23.6301i	0.437820	−	0.758327i	0.997521	+	0.0703679i	$0.0224173\pi$
$972$		0			0
$973$	2.93685	+	5.71485i	0.0941512	+	0.183210i
$974$	−22.5188			−0.721550
$975$		0			0
$976$	−2.74431	−	4.75329i	−0.0878433	−	0.152149i
$977$	−48.6568	+	28.0920i	−1.55667	+	0.898744i	−0.559098	+	0.829101i	$0.688853\pi$
$977$	−48.6568	+	28.0920i	−1.55667	+	0.898744i	−0.997572	+	0.0696427i	$0.977814\pi$
$978$		0			0
$979$	51.0990			1.63313
$980$	51.6727	+	36.9979i	1.65062	+	1.18186i
$981$		0			0
$982$	−36.3919	−	21.0108i	−1.16131	−	0.670483i
$983$	−22.9402	+	13.2445i	−0.731678	+	0.422435i	−0.819036	−	0.573742i	$-0.805491\pi$
$983$	−22.9402	+	13.2445i	−0.731678	+	0.422435i	0.0873577	+	0.996177i	$0.472158\pi$
$984$		0			0
$985$	−13.8114	+	23.9221i	−0.440069	+	0.762222i
$986$		−	66.8982i		−	2.13047i
$987$		0			0
$988$	20.4726	+	19.9712i	0.651320	+	0.635368i
$989$	−1.55946	+	2.70106i	−0.0495879	+	0.0858887i
$990$		0			0
$991$	−2.55629	−	4.42763i	−0.0812033	−	0.140648i	0.822564	−	0.568673i	$-0.192543\pi$
$991$	−2.55629	−	4.42763i	−0.0812033	−	0.140648i	−0.903767	+	0.428025i	$0.859210\pi$
$992$	−5.89652	+	10.2131i	−0.187215	+	0.324266i
$993$		0			0
$994$	−49.4662	−	2.42055i	−1.56897	−	0.0767750i
$995$			23.5957i			0.748035i
$996$		0			0
$997$	−1.01771	−	1.76272i	−0.0322311	−	0.0558260i	0.849460	−	0.527653i	$-0.176928\pi$
$997$	−1.01771	−	1.76272i	−0.0322311	−	0.0558260i	−0.881691	+	0.471827i	$0.843595\pi$
$998$	−14.0182	−	24.2803i	−0.443740	−	0.768580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dl.e.415.7		16
3.2	odd	2		91.2.r.a.51.2	yes	16
7.4	even	3	inner	819.2.dl.e.298.2		16
13.12	even	2	inner	819.2.dl.e.415.2		16
21.2	odd	6		637.2.c.f.246.7		8
21.5	even	6		637.2.c.e.246.7		8
21.11	odd	6		91.2.r.a.25.7	yes	16
21.17	even	6		637.2.r.f.116.7		16
21.20	even	2		637.2.r.f.324.2		16
39.5	even	4		1183.2.e.i.170.2		16
39.8	even	4		1183.2.e.i.170.7		16
39.38	odd	2		91.2.r.a.51.7	yes	16
91.25	even	6	inner	819.2.dl.e.298.7		16
273.5	odd	12		8281.2.a.cj.1.7		8
273.38	even	6		637.2.r.f.116.2		16
273.44	even	12		8281.2.a.ck.1.7		8
273.47	odd	12		8281.2.a.cj.1.2		8
273.86	even	12		8281.2.a.ck.1.2		8
273.116	odd	6		91.2.r.a.25.2	✓	16
273.194	even	6		637.2.c.e.246.2		8
273.200	even	12		1183.2.e.i.508.2		16
273.233	odd	6		637.2.c.f.246.2		8
273.242	even	12		1183.2.e.i.508.7		16
273.272	even	2		637.2.r.f.324.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.2	✓	16	273.116	odd	6
91.2.r.a.25.7	yes	16	21.11	odd	6
91.2.r.a.51.2	yes	16	3.2	odd	2
91.2.r.a.51.7	yes	16	39.38	odd	2
637.2.c.e.246.2		8	273.194	even	6
637.2.c.e.246.7		8	21.5	even	6
637.2.c.f.246.2		8	273.233	odd	6
637.2.c.f.246.7		8	21.2	odd	6
637.2.r.f.116.2		16	273.38	even	6
637.2.r.f.116.7		16	21.17	even	6
637.2.r.f.324.2		16	21.20	even	2
637.2.r.f.324.7		16	273.272	even	2
819.2.dl.e.298.2		16	7.4	even	3	inner
819.2.dl.e.298.7		16	91.25	even	6	inner
819.2.dl.e.415.2		16	13.12	even	2	inner
819.2.dl.e.415.7		16	1.1	even	1	trivial
1183.2.e.i.170.2		16	39.5	even	4
1183.2.e.i.170.7		16	39.8	even	4
1183.2.e.i.508.2		16	273.200	even	12
1183.2.e.i.508.7		16	273.242	even	12
8281.2.a.cj.1.2		8	273.47	odd	12
8281.2.a.cj.1.7		8	273.5	odd	12
8281.2.a.ck.1.2		8	273.86	even	12
8281.2.a.ck.1.7		8	273.44	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.84073 + 1.06275i) q^{2} +(1.25885 + 2.18040i) q^{4} +(-3.12291 - 1.80301i) q^{5} +(-1.20931 - 2.35320i) q^{7} +1.10038i q^{8} +O(q^{10})\)	\(q+(1.84073 + 1.06275i) q^{2} +(1.25885 + 2.18040i) q^{4} +(-3.12291 - 1.80301i) q^{5} +(-1.20931 - 2.35320i) q^{7} +1.10038i q^{8} +(-3.83229 - 6.63772i) q^{10} +(-3.45748 + 1.99618i) q^{11} +(-2.51771 + 2.58092i) q^{13} +(0.274848 - 5.61680i) q^{14} +(1.34828 - 2.33529i) q^{16} +(-2.39458 - 4.14753i) q^{17} +(-2.72850 - 1.57530i) q^{19} -9.07892i q^{20} -8.48572 q^{22} +(1.08943 - 1.88694i) q^{23} +(4.00171 + 6.93117i) q^{25} +(-7.37728 + 2.07509i) q^{26} +(3.60858 - 5.59912i) q^{28} +6.57198 q^{29} +(-1.28753 + 0.743358i) q^{31} +(6.86956 - 3.96614i) q^{32} -10.1793i q^{34} +(-0.466298 + 9.52925i) q^{35} +(-4.29984 - 2.48252i) q^{37} +(-3.34828 - 5.79939i) q^{38} +(1.98401 - 3.43640i) q^{40} -2.11931i q^{41} -1.43145 q^{43} +(-8.70494 - 5.02580i) q^{44} +(4.01068 - 2.31557i) q^{46} +(0.882417 + 0.509464i) q^{47} +(-4.07515 + 5.69150i) q^{49} +17.0112i q^{50} +(-8.79686 - 2.24061i) q^{52} +(3.01771 + 5.22682i) q^{53} +14.3966 q^{55} +(2.58943 - 1.33070i) q^{56} +(12.0972 + 6.98434i) q^{58} +(4.24631 - 2.45161i) q^{59} +(1.01771 - 1.76272i) q^{61} -3.16000 q^{62} +11.4669 q^{64} +(12.5160 - 3.52052i) q^{65} +(-3.38694 + 1.95545i) q^{67} +(6.02885 - 10.4423i) q^{68} +(-10.9855 + 17.0452i) q^{70} -8.80684i q^{71} +(2.67497 - 1.54439i) q^{73} +(-5.27656 - 9.13927i) q^{74} -7.93228i q^{76} +(8.87858 + 5.72217i) q^{77} +(-0.984006 + 1.70435i) q^{79} +(-8.42112 + 4.86194i) q^{80} +(2.25229 - 3.90108i) q^{82} +7.66020i q^{83} +17.2698i q^{85} +(-2.63491 - 1.52126i) q^{86} +(-2.19656 - 3.80456i) q^{88} +(-11.0844 - 6.39960i) q^{89} +(9.11812 + 2.80355i) q^{91} +5.48572 q^{92} +(1.08286 + 1.87557i) q^{94} +(5.68057 + 9.83903i) q^{95} -1.35900i q^{97} +(-13.5499 + 6.14567i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4}+O(q^{10}) \) 16 * q + 6 * q^4	\( 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

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