LMFDB - Embedded newform 378.2.g.g.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(109,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("378.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.g (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	378.109
Dual form			378.2.g.g.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} +(-1.82288 + 3.15731i) q^{11} -4.64575 q^{13} +(1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.82288 + 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} -3.64575 q^{20} +3.64575 q^{22} +(0.645751 + 1.11847i) q^{23} +(-4.14575 + 7.18065i) q^{25} +(2.32288 + 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +2.35425 q^{29} +(2.32288 - 4.02334i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.64575 q^{34} +(-4.82288 - 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.82288 + 3.15731i) q^{40} +10.9373 q^{41} +5.00000 q^{43} +(-1.82288 - 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(-2.46863 - 4.27579i) q^{47} +7.00000 q^{49} +8.29150 q^{50} +(2.32288 - 4.02334i) q^{52} +(-3.00000 + 5.19615i) q^{53} -13.2915 q^{55} -2.64575 q^{56} +(-1.17712 - 2.03884i) q^{58} +(-4.17712 + 7.23499i) q^{59} +(-3.67712 - 6.36897i) q^{61} -4.64575 q^{62} +1.00000 q^{64} +(-8.46863 - 14.6681i) q^{65} +(1.14575 - 1.98450i) q^{67} +(-1.82288 - 3.15731i) q^{68} +(-4.82288 + 8.35347i) q^{70} +15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +(5.96863 - 10.3380i) q^{74} +2.00000 q^{76} +(4.82288 - 8.35347i) q^{77} +(-5.61438 - 9.72439i) q^{79} +(1.82288 - 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} -13.2915 q^{83} -13.2915 q^{85} +(-2.50000 - 4.33013i) q^{86} +(-1.82288 + 3.15731i) q^{88} +(-2.46863 - 4.27579i) q^{89} +12.2915 q^{91} -1.29150 q^{92} +(-2.46863 + 4.27579i) q^{94} +(3.64575 - 6.31463i) q^{95} +13.5830 q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 2 q^{11} - 8 q^{13} - 2 q^{16} - 2 q^{17} - 4 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 6 q^{25} + 4 q^{26} + 20 q^{29} + 4 q^{31} - 2 q^{32} + 4 q^{34} - 14 q^{35} + 8 q^{37} - 4 q^{38} + 2 q^{40} + 12 q^{41} + 20 q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} + 28 q^{49} + 12 q^{50} + 4 q^{52} - 12 q^{53} - 32 q^{55} - 10 q^{58} - 22 q^{59} - 20 q^{61} - 8 q^{62} + 4 q^{64} - 18 q^{65} - 6 q^{67} - 2 q^{68} - 14 q^{70} + 52 q^{71} + 8 q^{74} + 8 q^{76} + 14 q^{77} + 4 q^{79} + 2 q^{80} - 6 q^{82} - 32 q^{83} - 32 q^{85} - 10 q^{86} - 2 q^{88} + 6 q^{89} + 28 q^{91} + 16 q^{92} + 6 q^{94} + 4 q^{95} + 12 q^{97} - 14 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 2 * q^11 - 8 * q^13 - 2 * q^16 - 2 * q^17 - 4 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 6 * q^25 + 4 * q^26 + 20 * q^29 + 4 * q^31 - 2 * q^32 + 4 * q^34 - 14 * q^35 + 8 * q^37 - 4 * q^38 + 2 * q^40 + 12 * q^41 + 20 * q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 + 28 * q^49 + 12 * q^50 + 4 * q^52 - 12 * q^53 - 32 * q^55 - 10 * q^58 - 22 * q^59 - 20 * q^61 - 8 * q^62 + 4 * q^64 - 18 * q^65 - 6 * q^67 - 2 * q^68 - 14 * q^70 + 52 * q^71 + 8 * q^74 + 8 * q^76 + 14 * q^77 + 4 * q^79 + 2 * q^80 - 6 * q^82 - 32 * q^83 - 32 * q^85 - 10 * q^86 - 2 * q^88 + 6 * q^89 + 28 * q^91 + 16 * q^92 + 6 * q^94 + 4 * q^95 + 12 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	0.909174	+	0.416417i	$0.136714\pi$
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	−0.0939588	+	0.995576i	$0.529952\pi$
$6$		0			0
$7$	−2.64575			−1.00000
$7$	−2.64575			−1.00000
$8$	1.00000			0.353553
$9$		0			0
$10$	1.82288	−	3.15731i	0.576444	−	0.998430i
$11$	−1.82288	+	3.15731i	−0.549618	+	0.951966i	0.448683	+	0.893691i	$0.351893\pi$
$11$	−1.82288	+	3.15731i	−0.549618	+	0.951966i	−0.998301	+	0.0582747i	$0.981440\pi$
$12$		0			0
$13$	−4.64575			−1.28850			−0.644250	−	0.764815i	$-0.722830\pi$
$13$	−4.64575			−1.28850			−0.644250	+	0.764815i	$0.722830\pi$
$14$	1.32288	+	2.29129i	0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.82288	+	3.15731i	−0.442112	+	0.765761i	−0.997846	−	0.0655994i	$-0.979104\pi$
$17$	−1.82288	+	3.15731i	−0.442112	+	0.765761i	0.555734	+	0.831360i	$0.312437\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−3.64575			−0.815215
$21$		0			0
$22$	3.64575			0.777277
$23$	0.645751	+	1.11847i	0.134648	+	0.233218i	0.925463	−	0.378838i	$-0.123676\pi$
$23$	0.645751	+	1.11847i	0.134648	+	0.233218i	−0.790815	+	0.612056i	$0.790343\pi$
$24$		0			0
$25$	−4.14575	+	7.18065i	−0.829150	+	1.43613i
$26$	2.32288	+	4.02334i	0.455553	+	0.789042i
$27$		0			0
$28$	1.32288	−	2.29129i	0.250000	−	0.433013i
$29$	2.35425			0.437173			0.218587	−	0.975818i	$-0.429855\pi$
$29$	2.35425			0.437173			0.218587	+	0.975818i	$0.429855\pi$
$30$		0			0
$31$	2.32288	−	4.02334i	0.417201	−	0.722613i	−0.578456	−	0.815714i	$-0.696345\pi$
$31$	2.32288	−	4.02334i	0.417201	−	0.722613i	0.995657	+	0.0931007i	$0.0296779\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.64575			0.625241
$35$	−4.82288	−	8.35347i	−0.815215	−	1.41199i
$36$		0			0
$37$	5.96863	+	10.3380i	0.981236	+	1.69955i	0.657596	+	0.753371i	$0.271573\pi$
$37$	5.96863	+	10.3380i	0.981236	+	1.69955i	0.323640	+	0.946180i	$0.395093\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$	1.82288	+	3.15731i	0.288222	+	0.499215i
$41$	10.9373			1.70811			0.854056	−	0.520181i	$-0.174136\pi$
$41$	10.9373			1.70811			0.854056	+	0.520181i	$0.174136\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	−1.82288	−	3.15731i	−0.274809	−	0.475983i
$45$		0			0
$46$	0.645751	−	1.11847i	0.0952108	−	0.164910i
$47$	−2.46863	−	4.27579i	−0.360086	−	0.623688i	0.627888	−	0.778303i	$-0.283919\pi$
$47$	−2.46863	−	4.27579i	−0.360086	−	0.623688i	−0.987975	+	0.154616i	$0.950586\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$	8.29150			1.17260
$51$		0			0
$52$	2.32288	−	4.02334i	0.322125	−	0.557937i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	−13.2915			−1.79223
$56$	−2.64575			−0.353553
$57$		0			0
$58$	−1.17712	−	2.03884i	−0.154564	−	0.267713i
$59$	−4.17712	+	7.23499i	−0.543815	+	0.941916i	0.454865	+	0.890560i	$0.349687\pi$
$59$	−4.17712	+	7.23499i	−0.543815	+	0.941916i	−0.998680	+	0.0513554i	$0.983646\pi$
$60$		0			0
$61$	−3.67712	−	6.36897i	−0.470808	−	0.815463i	0.528635	−	0.848849i	$-0.322704\pi$
$61$	−3.67712	−	6.36897i	−0.470808	−	0.815463i	−0.999443	+	0.0333867i	$0.989371\pi$
$62$	−4.64575			−0.590011
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.46863	−	14.6681i	−1.05040	−	1.81935i
$66$		0			0
$67$	1.14575	−	1.98450i	0.139976	−	0.242445i	−0.787511	−	0.616300i	$-0.788631\pi$
$67$	1.14575	−	1.98450i	0.139976	−	0.242445i	0.927487	+	0.373855i	$0.121964\pi$
$68$	−1.82288	−	3.15731i	−0.221056	−	0.382880i
$69$		0			0
$70$	−4.82288	+	8.35347i	−0.576444	+	0.998430i
$71$	15.6458			1.85681			0.928405	−	0.371571i	$-0.121181\pi$
$71$	15.6458			1.85681			0.928405	+	0.371571i	$0.121181\pi$
$72$		0			0
$73$	−5.29150	+	9.16515i	−0.619324	+	1.07270i	0.370286	+	0.928918i	$0.379260\pi$
$73$	−5.29150	+	9.16515i	−0.619324	+	1.07270i	−0.989609	+	0.143782i	$0.954074\pi$
$74$	5.96863	−	10.3380i	0.693839	−	1.20176i
$75$		0			0
$76$	2.00000			0.229416
$77$	4.82288	−	8.35347i	0.549618	−	0.951966i
$78$		0			0
$79$	−5.61438	−	9.72439i	−0.631667	−	1.09408i	−0.987211	−	0.159420i	$-0.949038\pi$
$79$	−5.61438	−	9.72439i	−0.631667	−	1.09408i	0.355544	−	0.934660i	$-0.384296\pi$
$80$	1.82288	−	3.15731i	0.203804	−	0.352998i
$81$		0			0
$82$	−5.46863	−	9.47194i	−0.603909	−	1.04600i
$83$	−13.2915			−1.45893			−0.729466	−	0.684017i	$-0.760231\pi$
$83$	−13.2915			−1.45893			−0.729466	+	0.684017i	$0.760231\pi$
$84$		0			0
$85$	−13.2915			−1.44167
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$		0			0
$88$	−1.82288	+	3.15731i	−0.194319	+	0.336571i
$89$	−2.46863	−	4.27579i	−0.261674	−	0.453233i	0.705013	−	0.709194i	$-0.250941\pi$
$89$	−2.46863	−	4.27579i	−0.261674	−	0.453233i	−0.966687	+	0.255962i	$0.917608\pi$
$90$		0			0
$91$	12.2915			1.28850
$92$	−1.29150			−0.134648
$93$		0			0
$94$	−2.46863	+	4.27579i	−0.254619	+	0.441014i
$95$	3.64575	−	6.31463i	0.374046	−	0.647867i
$96$		0			0
$97$	13.5830			1.37915			0.689573	−	0.724217i	$-0.257798\pi$
$97$	13.5830			1.37915			0.689573	+	0.724217i	$0.257798\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$		0			0
$100$	−4.14575	−	7.18065i	−0.414575	−	0.718065i
$101$	−4.17712	+	7.23499i	−0.415639	+	0.719909i	−0.995495	−	0.0948105i	$-0.969775\pi$
$101$	−4.17712	+	7.23499i	−0.415639	+	0.719909i	0.579856	+	0.814719i	$0.303109\pi$
$102$		0			0
$103$	−1.96863	−	3.40976i	−0.193975	−	0.335974i	0.752589	−	0.658490i	$-0.228805\pi$
$103$	−1.96863	−	3.40976i	−0.193975	−	0.335974i	−0.946564	+	0.322516i	$0.895471\pi$
$104$	−4.64575			−0.455553
$105$		0			0
$106$	6.00000			0.582772
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	1.67712	−	2.90486i	0.160639	−	0.278236i	−0.774459	−	0.632624i	$-0.781978\pi$
$109$	1.67712	−	2.90486i	0.160639	−	0.278236i	0.935098	+	0.354389i	$0.115311\pi$
$110$	6.64575	+	11.5108i	0.633648	+	1.09751i
$111$		0			0
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	2.35425			0.221469			0.110735	−	0.993850i	$-0.464680\pi$
$113$	2.35425			0.221469			0.110735	+	0.993850i	$0.464680\pi$
$114$		0			0
$115$	−2.35425	+	4.07768i	−0.219535	+	0.380245i
$116$	−1.17712	+	2.03884i	−0.109293	+	0.189301i
$117$		0			0
$118$	8.35425			0.769071
$119$	4.82288	−	8.35347i	0.442112	−	0.765761i
$120$		0			0
$121$	−1.14575	−	1.98450i	−0.104159	−	0.180409i
$122$	−3.67712	+	6.36897i	−0.332911	+	0.576619i
$123$		0			0
$124$	2.32288	+	4.02334i	0.208600	+	0.361306i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	1.35425			0.120170			0.0600851	−	0.998193i	$-0.480863\pi$
$127$	1.35425			0.120170			0.0600851	+	0.998193i	$0.480863\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.46863	+	14.6681i	−0.742748	+	1.28648i
$131$	7.29150	+	12.6293i	0.637062	+	1.10342i	0.986074	+	0.166305i	$0.0531836\pi$
$131$	7.29150	+	12.6293i	0.637062	+	1.10342i	−0.349013	+	0.937118i	$0.613483\pi$
$132$		0			0
$133$	2.64575	+	4.58258i	0.229416	+	0.397360i
$134$	−2.29150			−0.197956
$135$		0			0
$136$	−1.82288	+	3.15731i	−0.156310	+	0.270737i
$137$	−0.645751	+	1.11847i	−0.0551703	+	0.0955577i	−0.892292	−	0.451460i	$-0.850903\pi$
$137$	−0.645751	+	1.11847i	−0.0551703	+	0.0955577i	0.837121	+	0.547017i	$0.184237\pi$
$138$		0			0
$139$	1.58301			0.134269			0.0671344	−	0.997744i	$-0.478614\pi$
$139$	1.58301			0.134269			0.0671344	+	0.997744i	$0.478614\pi$
$140$	9.64575			0.815215
$141$		0			0
$142$	−7.82288	−	13.5496i	−0.656481	−	1.13706i
$143$	8.46863	−	14.6681i	0.708182	−	1.22661i
$144$		0			0
$145$	4.29150	+	7.43310i	0.356390	+	0.617285i
$146$	10.5830			0.875856
$147$		0			0
$148$	−11.9373			−0.981236
$149$	−11.4686	−	19.8642i	−0.939547	−	1.62734i	−0.766319	−	0.642461i	$-0.777914\pi$
$149$	−11.4686	−	19.8642i	−0.939547	−	1.62734i	−0.173228	−	0.984882i	$-0.555420\pi$
$150$		0			0
$151$	9.61438	−	16.6526i	0.782407	−	1.35517i	−0.148129	−	0.988968i	$-0.547325\pi$
$151$	9.61438	−	16.6526i	0.782407	−	1.35517i	0.930536	−	0.366201i	$-0.119342\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$	−9.64575			−0.777277
$155$	16.9373			1.36043
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	−5.61438	+	9.72439i	−0.446656	+	0.773631i
$159$		0			0
$160$	−3.64575			−0.288222
$161$	−1.70850	−	2.95920i	−0.134648	−	0.233218i
$162$		0			0
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	−5.46863	+	9.47194i	−0.427028	+	0.739634i
$165$		0			0
$166$	6.64575	+	11.5108i	0.515810	+	0.893410i
$167$	−8.58301			−0.664173			−0.332086	−	0.943249i	$-0.607753\pi$
$167$	−8.58301			−0.664173			−0.332086	+	0.943249i	$0.607753\pi$
$168$		0			0
$169$	8.58301			0.660231
$170$	6.64575	+	11.5108i	0.509706	+	0.882836i
$171$		0			0
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	7.29150	+	12.6293i	0.554363	+	0.960184i	0.997953	+	0.0639546i	$0.0203713\pi$
$173$	7.29150	+	12.6293i	0.554363	+	0.960184i	−0.443590	+	0.896230i	$0.646295\pi$
$174$		0			0
$175$	10.9686	−	18.9982i	0.829150	−	1.43613i
$176$	3.64575			0.274809
$177$		0			0
$178$	−2.46863	+	4.27579i	−0.185031	+	0.320484i
$179$	−8.46863	+	14.6681i	−0.632975	+	1.09634i	0.353965	+	0.935259i	$0.384833\pi$
$179$	−8.46863	+	14.6681i	−0.632975	+	1.09634i	−0.986940	+	0.161086i	$0.948500\pi$
$180$		0			0
$181$	−2.70850			−0.201321			−0.100661	−	0.994921i	$-0.532096\pi$
$181$	−2.70850			−0.201321			−0.100661	+	0.994921i	$0.532096\pi$
$182$	−6.14575	−	10.6448i	−0.455553	−	0.789042i
$183$		0			0
$184$	0.645751	+	1.11847i	0.0476054	+	0.0824550i
$185$	−21.7601	+	37.6897i	−1.59984	+	2.77100i
$186$		0			0
$187$	−6.64575	−	11.5108i	−0.485985	−	0.841752i
$188$	4.93725			0.360086
$189$		0			0
$190$	−7.29150			−0.528981
$191$	10.4059	+	18.0235i	0.752943	+	1.30414i	0.946390	+	0.323025i	$0.104700\pi$
$191$	10.4059	+	18.0235i	0.752943	+	1.30414i	−0.193447	+	0.981111i	$0.561967\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	−6.79150	−	11.7632i	−0.487601	−	0.844551i
$195$		0			0
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	4.70850			0.335467			0.167733	−	0.985832i	$-0.446355\pi$
$197$	4.70850			0.335467			0.167733	+	0.985832i	$0.446355\pi$
$198$		0			0
$199$	−3.03137	+	5.25049i	−0.214888	+	0.372198i	−0.953238	−	0.302221i	$-0.902272\pi$
$199$	−3.03137	+	5.25049i	−0.214888	+	0.372198i	0.738350	+	0.674418i	$0.235605\pi$
$200$	−4.14575	+	7.18065i	−0.293149	+	0.507749i
$201$		0			0
$202$	8.35425			0.587803
$203$	−6.22876			−0.437173
$204$		0			0
$205$	19.9373	+	34.5323i	1.39248	+	2.41184i
$206$	−1.96863	+	3.40976i	−0.137161	+	0.237569i
$207$		0			0
$208$	2.32288	+	4.02334i	0.161062	+	0.278968i
$209$	7.29150			0.504364
$210$		0			0
$211$	14.8745			1.02400			0.512002	−	0.858984i	$-0.328904\pi$
$211$	14.8745			1.02400			0.512002	+	0.858984i	$0.328904\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	9.11438	+	15.7866i	0.621595	+	1.07663i
$216$		0			0
$217$	−6.14575	+	10.6448i	−0.417201	+	0.722613i
$218$	−3.35425			−0.227178
$219$		0			0
$220$	6.64575	−	11.5108i	0.448056	−	0.776057i
$221$	8.46863	−	14.6681i	0.569661	−	0.986683i
$222$		0			0
$223$	−13.8745			−0.929106			−0.464553	−	0.885545i	$-0.653785\pi$
$223$	−13.8745			−0.929106			−0.464553	+	0.885545i	$0.653785\pi$
$224$	1.32288	−	2.29129i	0.0883883	−	0.153093i
$225$		0			0
$226$	−1.17712	−	2.03884i	−0.0783011	−	0.135622i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	4.67712	+	8.10102i	0.309073	+	0.535330i	0.978160	−	0.207854i	$-0.0666479\pi$
$229$	4.67712	+	8.10102i	0.309073	+	0.535330i	−0.669087	+	0.743184i	$0.733315\pi$
$230$	4.70850			0.310469
$231$		0			0
$232$	2.35425			0.154564
$233$	9.64575	+	16.7069i	0.631914	+	1.09451i	0.987160	+	0.159735i	$0.0510638\pi$
$233$	9.64575	+	16.7069i	0.631914	+	1.09451i	−0.355246	+	0.934773i	$0.615603\pi$
$234$		0			0
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$	−4.17712	−	7.23499i	−0.271908	−	0.470958i
$237$		0			0
$238$	−9.64575			−0.625241
$239$	−10.9373			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$239$	−10.9373			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	−1.14575	+	1.98450i	−0.0736517	+	0.127568i
$243$		0			0
$244$	7.35425			0.470808
$245$	12.7601	+	22.1012i	0.815215	+	1.41199i
$246$		0			0
$247$	4.64575	+	8.04668i	0.295602	+	0.511998i
$248$	2.32288	−	4.02334i	0.147503	−	0.255482i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	−4.70850			−0.296021
$254$	−0.677124	−	1.17281i	−0.0424866	−	0.0735889i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.93725	−	13.7477i	−0.495112	−	0.857560i	0.504872	−	0.863194i	$-0.331540\pi$
$257$	−7.93725	−	13.7477i	−0.495112	−	0.857560i	−0.999984	+	0.00563467i	$0.998206\pi$
$258$		0			0
$259$	−15.7915	−	27.3517i	−0.981236	−	1.69955i
$260$	16.9373			1.05040
$261$		0			0
$262$	7.29150	−	12.6293i	0.450471	−	0.780238i
$263$	2.46863	−	4.27579i	0.152222	−	0.263656i	−0.779822	−	0.626001i	$-0.784690\pi$
$263$	2.46863	−	4.27579i	0.152222	−	0.263656i	0.932044	+	0.362345i	$0.118024\pi$
$264$		0			0
$265$	−21.8745			−1.34374
$266$	2.64575	−	4.58258i	0.162221	−	0.280976i
$267$		0			0
$268$	1.14575	+	1.98450i	0.0699879	+	0.121223i
$269$	8.35425	−	14.4700i	0.509368	−	0.882250i	−0.490574	−	0.871400i	$-0.663213\pi$
$269$	8.35425	−	14.4700i	0.509368	−	0.882250i	0.999941	−	0.0108507i	$-0.00345395\pi$
$270$		0			0
$271$	−2.61438	−	4.52824i	−0.158812	−	0.275071i	0.775628	−	0.631190i	$-0.217433\pi$
$271$	−2.61438	−	4.52824i	−0.158812	−	0.275071i	−0.934441	+	0.356119i	$0.884100\pi$
$272$	3.64575			0.221056
$273$		0			0
$274$	1.29150			0.0780225
$275$	−15.1144	−	26.1789i	−0.911431	−	1.57865i
$276$		0			0
$277$	1.03137	−	1.78639i	0.0619692	−	0.107334i	−0.833376	−	0.552706i	$-0.813595\pi$
$277$	1.03137	−	1.78639i	0.0619692	−	0.107334i	0.895346	+	0.445372i	$0.146929\pi$
$278$	−0.791503	−	1.37092i	−0.0474712	−	0.0822225i
$279$		0			0
$280$	−4.82288	−	8.35347i	−0.288222	−	0.499215i
$281$	19.5203			1.16448			0.582241	−	0.813017i	$-0.302176\pi$
$281$	19.5203			1.16448			0.582241	+	0.813017i	$0.302176\pi$
$282$		0			0
$283$	1.14575	−	1.98450i	0.0681078	−	0.117966i	−0.829961	−	0.557822i	$-0.811637\pi$
$283$	1.14575	−	1.98450i	0.0681078	−	0.117966i	0.898068	+	0.439856i	$0.144970\pi$
$284$	−7.82288	+	13.5496i	−0.464202	+	0.804022i
$285$		0			0
$286$	−16.9373			−1.00152
$287$	−28.9373			−1.70811
$288$		0			0
$289$	1.85425	+	3.21165i	0.109073	+	0.188921i
$290$	4.29150	−	7.43310i	0.252006	−	0.436487i
$291$		0			0
$292$	−5.29150	−	9.16515i	−0.309662	−	0.536350i
$293$	7.06275			0.412610			0.206305	−	0.978488i	$-0.433856\pi$
$293$	7.06275			0.412610			0.206305	+	0.978488i	$0.433856\pi$
$294$		0			0
$295$	−30.4575			−1.77330
$296$	5.96863	+	10.3380i	0.346919	+	0.600882i
$297$		0			0
$298$	−11.4686	+	19.8642i	−0.664360	+	1.15070i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	−13.2288			−0.762493
$302$	−19.2288			−1.10649
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	13.4059	−	23.2197i	0.767619	−	1.32955i
$306$		0			0
$307$	7.58301			0.432785			0.216392	−	0.976306i	$-0.430571\pi$
$307$	7.58301			0.432785			0.216392	+	0.976306i	$0.430571\pi$
$308$	4.82288	+	8.35347i	0.274809	+	0.475983i
$309$		0			0
$310$	−8.46863	−	14.6681i	−0.480986	−	0.833092i
$311$	6.76013	−	11.7089i	0.383332	−	0.663950i	−0.608204	−	0.793780i	$-0.708110\pi$
$311$	6.76013	−	11.7089i	0.383332	−	0.663950i	0.991536	+	0.129830i	$0.0414433\pi$
$312$		0			0
$313$	−6.35425	−	11.0059i	−0.359163	−	0.622089i	0.628658	−	0.777682i	$-0.283605\pi$
$313$	−6.35425	−	11.0059i	−0.359163	−	0.622089i	−0.987821	+	0.155593i	$0.950271\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	11.2288			0.631667
$317$	−13.4059	−	23.2197i	−0.752949	−	1.30415i	−0.946387	−	0.323034i	$-0.895297\pi$
$317$	−13.4059	−	23.2197i	−0.752949	−	1.30415i	0.193438	−	0.981112i	$-0.438036\pi$
$318$		0			0
$319$	−4.29150	+	7.43310i	−0.240278	+	0.416174i
$320$	1.82288	+	3.15731i	0.101902	+	0.176499i
$321$		0			0
$322$	−1.70850	+	2.95920i	−0.0952108	+	0.164910i
$323$	7.29150			0.405710
$324$		0			0
$325$	19.2601	−	33.3595i	1.06836	−	1.85045i
$326$	0.500000	−	0.866025i	0.0276924	−	0.0479647i
$327$		0			0
$328$	10.9373			0.603909
$329$	6.53137	+	11.3127i	0.360086	+	0.623688i
$330$		0			0
$331$	15.9373	+	27.6041i	0.875991	+	1.51726i	0.855704	+	0.517466i	$0.173125\pi$
$331$	15.9373	+	27.6041i	0.875991	+	1.51726i	0.0202871	+	0.999794i	$0.493542\pi$
$332$	6.64575	−	11.5108i	0.364733	−	0.631736i
$333$		0			0
$334$	4.29150	+	7.43310i	0.234821	+	0.406721i
$335$	8.35425			0.456441
$336$		0			0
$337$	−30.5830			−1.66596			−0.832981	−	0.553301i	$-0.813368\pi$
$337$	−30.5830			−1.66596			−0.832981	+	0.553301i	$0.813368\pi$
$338$	−4.29150	−	7.43310i	−0.233427	−	0.404307i
$339$		0			0
$340$	6.64575	−	11.5108i	0.360416	−	0.624260i
$341$	8.46863	+	14.6681i	0.458602	+	0.794322i
$342$		0			0
$343$	−18.5203			−1.00000
$344$	5.00000			0.269582
$345$		0			0
$346$	7.29150	−	12.6293i	0.391994	−	0.678953i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−1.22876			−0.0657738			−0.0328869	−	0.999459i	$-0.510470\pi$
$349$	−1.22876			−0.0657738			−0.0328869	+	0.999459i	$0.510470\pi$
$350$	−21.9373			−1.17260
$351$		0			0
$352$	−1.82288	−	3.15731i	−0.0971596	−	0.168285i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	28.5203	+	49.3985i	1.51370	+	2.62180i
$356$	4.93725			0.261674
$357$		0			0
$358$	16.9373			0.895162
$359$	−5.58301	−	9.67005i	−0.294660	−	0.510366i	0.680246	−	0.732984i	$-0.261873\pi$
$359$	−5.58301	−	9.67005i	−0.294660	−	0.510366i	−0.974906	+	0.222618i	$0.928540\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	1.35425	+	2.34563i	0.0711777	+	0.123283i
$363$		0			0
$364$	−6.14575	+	10.6448i	−0.322125	+	0.557937i
$365$	−38.5830			−2.01953
$366$		0			0
$367$	−14.9373	+	25.8721i	−0.779718	+	1.35051i	0.152386	+	0.988321i	$0.451304\pi$
$367$	−14.9373	+	25.8721i	−0.779718	+	1.35051i	−0.932104	+	0.362191i	$0.882029\pi$
$368$	0.645751	−	1.11847i	0.0336621	−	0.0583045i
$369$		0			0
$370$	43.5203			2.26251
$371$	7.93725	−	13.7477i	0.412082	−	0.713746i
$372$		0			0
$373$	−2.29150	−	3.96900i	−0.118650	−	0.205507i	0.800583	−	0.599222i	$-0.204523\pi$
$373$	−2.29150	−	3.96900i	−0.118650	−	0.205507i	−0.919233	+	0.393715i	$0.871190\pi$
$374$	−6.64575	+	11.5108i	−0.343644	+	0.595208i
$375$		0			0
$376$	−2.46863	−	4.27579i	−0.127310	−	0.220507i
$377$	−10.9373			−0.563297
$378$		0			0
$379$	25.5830			1.31411			0.657055	−	0.753842i	$-0.271802\pi$
$379$	25.5830			1.31411			0.657055	+	0.753842i	$0.271802\pi$
$380$	3.64575	+	6.31463i	0.187023	+	0.323934i
$381$		0			0
$382$	10.4059	−	18.0235i	0.532411	−	0.922163i
$383$	−10.2915	−	17.8254i	−0.525871	−	0.910836i	−0.999546	−	0.0301357i	$-0.990406\pi$
$383$	−10.2915	−	17.8254i	−0.525871	−	0.910836i	0.473675	−	0.880700i	$-0.342927\pi$
$384$		0			0
$385$	35.1660			1.79223
$386$	−7.00000			−0.356291
$387$		0			0
$388$	−6.79150	+	11.7632i	−0.344786	+	0.597187i
$389$	−9.64575	+	16.7069i	−0.489059	+	0.847075i	−0.999921	−	0.0125878i	$-0.995993\pi$
$389$	−9.64575	+	16.7069i	−0.489059	+	0.847075i	0.510862	+	0.859663i	$0.329326\pi$
$390$		0			0
$391$	−4.70850			−0.238119
$392$	7.00000			0.353553
$393$		0			0
$394$	−2.35425	−	4.07768i	−0.118605	−	0.205430i
$395$	20.4686	−	35.4527i	1.02989	−	1.78382i
$396$		0			0
$397$	8.32288	+	14.4156i	0.417713	+	0.723500i	0.995709	−	0.0925393i	$-0.0294984\pi$
$397$	8.32288	+	14.4156i	0.417713	+	0.723500i	−0.577996	+	0.816040i	$0.696165\pi$
$398$	6.06275			0.303898
$399$		0			0
$400$	8.29150			0.414575
$401$	10.4059	+	18.0235i	0.519645	+	0.900051i	0.999739	+	0.0228345i	$0.00726908\pi$
$401$	10.4059	+	18.0235i	0.519645	+	0.900051i	−0.480094	+	0.877217i	$0.659398\pi$
$402$		0			0
$403$	−10.7915	+	18.6914i	−0.537563	+	0.931086i
$404$	−4.17712	−	7.23499i	−0.207820	−	0.359954i
$405$		0			0
$406$	3.11438	+	5.39426i	0.154564	+	0.267713i
$407$	−43.5203			−2.15722
$408$		0			0
$409$	−7.43725	+	12.8817i	−0.367749	+	0.636959i	−0.989213	−	0.146483i	$-0.953205\pi$
$409$	−7.43725	+	12.8817i	−0.367749	+	0.636959i	0.621465	+	0.783442i	$0.286538\pi$
$410$	19.9373	−	34.5323i	0.984631	−	1.70543i
$411$		0			0
$412$	3.93725			0.193975
$413$	11.0516	−	19.1420i	0.543815	−	0.941916i
$414$		0			0
$415$	−24.2288	−	41.9654i	−1.18934	−	2.06000i
$416$	2.32288	−	4.02334i	0.113888	−	0.197260i
$417$		0			0
$418$	−3.64575	−	6.31463i	−0.178320	−	0.308858i
$419$	28.9373			1.41368			0.706839	−	0.707375i	$-0.250121\pi$
$419$	28.9373			1.41368			0.706839	+	0.707375i	$0.250121\pi$
$420$		0			0
$421$	−14.7085			−0.716848			−0.358424	−	0.933559i	$-0.616686\pi$
$421$	−14.7085			−0.716848			−0.358424	+	0.933559i	$0.616686\pi$
$422$	−7.43725	−	12.8817i	−0.362040	−	0.627071i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−15.1144	−	26.1789i	−0.733155	−	1.26986i
$426$		0			0
$427$	9.72876	+	16.8507i	0.470808	+	0.815463i
$428$	−6.00000			−0.290021
$429$		0			0
$430$	9.11438	−	15.7866i	0.439534	−	0.761296i
$431$	−19.4059	+	33.6120i	−0.934748	+	1.61903i	−0.159666	+	0.987171i	$0.551042\pi$
$431$	−19.4059	+	33.6120i	−0.934748	+	1.61903i	−0.775082	+	0.631861i	$0.782291\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	12.2915			0.590011
$435$		0			0
$436$	1.67712	+	2.90486i	0.0803197	+	0.139118i
$437$	1.29150	−	2.23695i	0.0617809	−	0.107008i
$438$		0			0
$439$	−12.5830	−	21.7944i	−0.600554	−	1.04019i	−0.992737	−	0.120303i	$-0.961613\pi$
$439$	−12.5830	−	21.7944i	−0.600554	−	1.04019i	0.392183	−	0.919887i	$-0.371720\pi$
$440$	−13.2915			−0.633648
$441$		0			0
$442$	−16.9373			−0.805623
$443$	9.64575	+	16.7069i	0.458283	+	0.793770i	0.998870	−	0.0475179i	$-0.0151311\pi$
$443$	9.64575	+	16.7069i	0.458283	+	0.793770i	−0.540587	+	0.841288i	$0.681798\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	6.93725	+	12.0157i	0.328488	+	0.568959i
$447$		0			0
$448$	−2.64575			−0.125000
$449$	2.35425			0.111104			0.0555519	−	0.998456i	$-0.482308\pi$
$449$	2.35425			0.111104			0.0555519	+	0.998456i	$0.482308\pi$
$450$		0			0
$451$	−19.9373	+	34.5323i	−0.938809	+	1.62606i
$452$	−1.17712	+	2.03884i	−0.0553673	+	0.0958989i
$453$		0			0
$454$	6.00000			0.281594
$455$	22.4059	+	38.8081i	1.05040	+	1.81935i
$456$		0			0
$457$	4.14575	+	7.18065i	0.193930	+	0.335897i	0.946549	−	0.322559i	$-0.104543\pi$
$457$	4.14575	+	7.18065i	0.193930	+	0.335897i	−0.752619	+	0.658456i	$0.771210\pi$
$458$	4.67712	−	8.10102i	0.218548	−	0.378536i
$459$		0			0
$460$	−2.35425	−	4.07768i	−0.109767	−	0.190123i
$461$	24.2288			1.12845			0.564223	−	0.825623i	$-0.309176\pi$
$461$	24.2288			1.12845			0.564223	+	0.825623i	$0.309176\pi$
$462$		0			0
$463$	18.7085			0.869458			0.434729	−	0.900561i	$-0.356844\pi$
$463$	18.7085			0.869458			0.434729	+	0.900561i	$0.356844\pi$
$464$	−1.17712	−	2.03884i	−0.0546466	−	0.0946507i
$465$		0			0
$466$	9.64575	−	16.7069i	0.446831	−	0.773934i
$467$	−0.114378	−	0.198109i	−0.00529280	−	0.00916739i	0.863367	−	0.504577i	$-0.168351\pi$
$467$	−0.114378	−	0.198109i	−0.00529280	−	0.00916739i	−0.868660	+	0.495409i	$0.835018\pi$
$468$		0			0
$469$	−3.03137	+	5.25049i	−0.139976	+	0.242445i
$470$	−18.0000			−0.830278
$471$		0			0
$472$	−4.17712	+	7.23499i	−0.192268	+	0.333017i
$473$	−9.11438	+	15.7866i	−0.419080	+	0.725867i
$474$		0			0
$475$	16.5830			0.760880
$476$	4.82288	+	8.35347i	0.221056	+	0.382880i
$477$		0			0
$478$	5.46863	+	9.47194i	0.250129	+	0.433236i
$479$	−1.82288	+	3.15731i	−0.0832893	+	0.144261i	−0.904661	−	0.426132i	$-0.859876\pi$
$479$	−1.82288	+	3.15731i	−0.0832893	+	0.144261i	0.821372	+	0.570393i	$0.193209\pi$
$480$		0			0
$481$	−27.7288	−	48.0276i	−1.26432	−	2.18987i
$482$	5.00000			0.227744
$483$		0			0
$484$	2.29150			0.104159
$485$	24.7601	+	42.8858i	1.12430	+	1.94734i
$486$		0			0
$487$	−11.9373	+	20.6759i	−0.540929	+	0.936916i	0.457922	+	0.888992i	$0.348594\pi$
$487$	−11.9373	+	20.6759i	−0.540929	+	0.936916i	−0.998851	+	0.0479237i	$0.984740\pi$
$488$	−3.67712	−	6.36897i	−0.166456	−	0.288310i
$489$		0			0
$490$	12.7601	−	22.1012i	0.576444	−	0.998430i
$491$	25.7490			1.16204			0.581018	−	0.813890i	$-0.302654\pi$
$491$	25.7490			1.16204			0.581018	+	0.813890i	$0.302654\pi$
$492$		0			0
$493$	−4.29150	+	7.43310i	−0.193280	+	0.334770i
$494$	4.64575	−	8.04668i	0.209022	−	0.362037i
$495$		0			0
$496$	−4.64575			−0.208600
$497$	−41.3948			−1.85681
$498$		0			0
$499$	3.08301	+	5.33992i	0.138014	+	0.239048i	0.926745	−	0.375691i	$-0.122595\pi$
$499$	3.08301	+	5.33992i	0.138014	+	0.239048i	−0.788731	+	0.614739i	$0.789261\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$	3.87451			0.172756			0.0863779	−	0.996262i	$-0.472471\pi$
$503$	3.87451			0.172756			0.0863779	+	0.996262i	$0.472471\pi$
$504$		0			0
$505$	−30.4575			−1.35534
$506$	2.35425	+	4.07768i	0.104659	+	0.181275i
$507$		0			0
$508$	−0.677124	+	1.17281i	−0.0300425	+	0.0520352i
$509$	−4.06275	−	7.03688i	−0.180078	−	0.311904i	0.761829	−	0.647778i	$-0.224302\pi$
$509$	−4.06275	−	7.03688i	−0.180078	−	0.311904i	−0.941907	+	0.335874i	$0.890968\pi$
$510$		0			0
$511$	14.0000	−	24.2487i	0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.93725	+	13.7477i	−0.350097	+	0.606386i
$515$	7.17712	−	12.4311i	0.316262	−	0.547782i
$516$		0			0
$517$	18.0000			0.791639
$518$	−15.7915	+	27.3517i	−0.693839	+	1.20176i
$519$		0			0
$520$	−8.46863	−	14.6681i	−0.371374	−	0.643238i
$521$	4.06275	−	7.03688i	0.177992	−	0.308291i	−0.763201	−	0.646162i	$-0.776373\pi$
$521$	4.06275	−	7.03688i	0.177992	−	0.308291i	0.941193	+	0.337870i	$0.109707\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$	−14.5830			−0.637062
$525$		0			0
$526$	−4.93725			−0.215275
$527$	8.46863	+	14.6681i	0.368899	+	0.638952i
$528$		0			0
$529$	10.6660	−	18.4741i	0.463740	−	0.803221i
$530$	10.9373	+	18.9439i	0.475084	+	0.822870i
$531$		0			0
$532$	−5.29150			−0.229416
$533$	−50.8118			−2.20090
$534$		0			0
$535$	−10.9373	+	18.9439i	−0.472859	+	0.819015i
$536$	1.14575	−	1.98450i	0.0494889	−	0.0857173i
$537$		0			0
$538$	−16.7085			−0.720354
$539$	−12.7601	+	22.1012i	−0.549618	+	0.951966i
$540$		0			0
$541$	−0.583005	−	1.00979i	−0.0250654	−	0.0434145i	0.853221	−	0.521550i	$-0.174646\pi$
$541$	−0.583005	−	1.00979i	−0.0250654	−	0.0434145i	−0.878286	+	0.478136i	$0.841313\pi$
$542$	−2.61438	+	4.52824i	−0.112297	+	0.194504i
$543$		0			0
$544$	−1.82288	−	3.15731i	−0.0781551	−	0.135369i
$545$	12.2288			0.523822
$546$		0			0
$547$	18.2915			0.782088			0.391044	−	0.920372i	$-0.372114\pi$
$547$	18.2915			0.782088			0.391044	+	0.920372i	$0.372114\pi$
$548$	−0.645751	−	1.11847i	−0.0275851	−	0.0477788i
$549$		0			0
$550$	−15.1144	+	26.1789i	−0.644479	+	1.11627i
$551$	−2.35425	−	4.07768i	−0.100294	−	0.173715i
$552$		0			0
$553$	14.8542	+	25.7283i	0.631667	+	1.09408i
$554$	−2.06275			−0.0876377
$555$		0			0
$556$	−0.791503	+	1.37092i	−0.0335672	+	0.0581401i
$557$	2.88562	−	4.99804i	0.122268	−	0.211774i	−0.798394	−	0.602136i	$-0.794317\pi$
$557$	2.88562	−	4.99804i	0.122268	−	0.211774i	0.920662	+	0.390362i	$0.127650\pi$
$558$		0			0
$559$	−23.2288			−0.982472
$560$	−4.82288	+	8.35347i	−0.203804	+	0.352998i
$561$		0			0
$562$	−9.76013	−	16.9050i	−0.411706	−	0.713096i
$563$	−9.22876	+	15.9847i	−0.388946	+	0.673674i	−0.992308	−	0.123793i	$-0.960494\pi$
$563$	−9.22876	+	15.9847i	−0.388946	+	0.673674i	0.603362	+	0.797467i	$0.293827\pi$
$564$		0			0
$565$	4.29150	+	7.43310i	0.180545	+	0.312713i
$566$	−2.29150			−0.0963190
$567$		0			0
$568$	15.6458			0.656481
$569$	8.46863	+	14.6681i	0.355023	+	0.614918i	0.987122	−	0.159970i	$-0.0511396\pi$
$569$	8.46863	+	14.6681i	0.355023	+	0.614918i	−0.632099	+	0.774888i	$0.717806\pi$
$570$		0			0
$571$	−4.64575	+	8.04668i	−0.194419	+	0.336743i	−0.946710	−	0.322088i	$-0.895615\pi$
$571$	−4.64575	+	8.04668i	−0.194419	+	0.336743i	0.752291	+	0.658831i	$0.228949\pi$
$572$	8.46863	+	14.6681i	0.354091	+	0.613304i
$573$		0			0
$574$	14.4686	+	25.0604i	0.603909	+	1.04600i
$575$	−10.7085			−0.446575
$576$		0			0
$577$	16.1458	−	27.9653i	0.672156	−	1.16421i	−0.305135	−	0.952309i	$-0.598702\pi$
$577$	16.1458	−	27.9653i	0.672156	−	1.16421i	0.977291	−	0.211900i	$-0.0679651\pi$
$578$	1.85425	−	3.21165i	0.0771266	−	0.133587i
$579$		0			0
$580$	−8.58301			−0.356390
$581$	35.1660			1.45893
$582$		0			0
$583$	−10.9373	−	18.9439i	−0.452975	−	0.784575i
$584$	−5.29150	+	9.16515i	−0.218964	+	0.379257i
$585$		0			0
$586$	−3.53137	−	6.11652i	−0.145880	−	0.252671i
$587$	11.7712			0.485851			0.242926	−	0.970045i	$-0.421893\pi$
$587$	11.7712			0.485851			0.242926	+	0.970045i	$0.421893\pi$
$588$		0			0
$589$	−9.29150			−0.382850
$590$	15.2288	+	26.3770i	0.626958	+	1.08592i
$591$		0			0
$592$	5.96863	−	10.3380i	0.245309	−	0.424888i
$593$	−20.4686	−	35.4527i	−0.840546	−	1.45587i	−0.889434	−	0.457064i	$-0.848901\pi$
$593$	−20.4686	−	35.4527i	−0.840546	−	1.45587i	0.0488882	−	0.998804i	$-0.484432\pi$
$594$		0			0
$595$	35.1660			1.44167
$596$	22.9373			0.939547
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−4.93725	+	8.55157i	−0.201731	+	0.349408i	−0.949086	−	0.315017i	$-0.897990\pi$
$599$	−4.93725	+	8.55157i	−0.201731	+	0.349408i	0.747355	+	0.664424i	$0.231323\pi$
$600$		0			0
$601$	26.8745			1.09623			0.548117	−	0.836402i	$-0.315345\pi$
$601$	26.8745			1.09623			0.548117	+	0.836402i	$0.315345\pi$
$602$	6.61438	+	11.4564i	0.269582	+	0.466930i
$603$		0			0
$604$	9.61438	+	16.6526i	0.391204	+	0.677584i
$605$	4.17712	−	7.23499i	0.169824	−	0.294144i
$606$		0			0
$607$	−2.70850	−	4.69126i	−0.109935	−	0.190412i	0.805809	−	0.592176i	$-0.201731\pi$
$607$	−2.70850	−	4.69126i	−0.109935	−	0.190412i	−0.915744	+	0.401763i	$0.868397\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	−26.8118			−1.08558
$611$	11.4686	+	19.8642i	0.463971	+	0.803621i
$612$		0			0
$613$	21.1974	−	36.7149i	0.856154	−	1.48290i	−0.0194158	−	0.999811i	$-0.506181\pi$
$613$	21.1974	−	36.7149i	0.856154	−	1.48290i	0.875570	−	0.483091i	$-0.160486\pi$
$614$	−3.79150	−	6.56708i	−0.153013	−	0.265026i
$615$		0			0
$616$	4.82288	−	8.35347i	0.194319	−	0.336571i
$617$	1.52026			0.0612033			0.0306017	−	0.999532i	$-0.490258\pi$
$617$	1.52026			0.0612033			0.0306017	+	0.999532i	$0.490258\pi$
$618$		0			0
$619$	4.14575	−	7.18065i	0.166632	−	0.288615i	−0.770602	−	0.637317i	$-0.780044\pi$
$619$	4.14575	−	7.18065i	0.166632	−	0.288615i	0.937234	+	0.348702i	$0.113378\pi$
$620$	−8.46863	+	14.6681i	−0.340108	+	0.589085i
$621$		0			0
$622$	−13.5203			−0.542113
$623$	6.53137	+	11.3127i	0.261674	+	0.453233i
$624$		0			0
$625$	−1.14575	−	1.98450i	−0.0458301	−	0.0793800i
$626$	−6.35425	+	11.0059i	−0.253967	+	0.439883i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	−43.5203			−1.73527
$630$		0			0
$631$	6.06275			0.241354			0.120677	−	0.992692i	$-0.461493\pi$
$631$	6.06275			0.241354			0.120677	+	0.992692i	$0.461493\pi$
$632$	−5.61438	−	9.72439i	−0.223328	−	0.386815i
$633$		0			0
$634$	−13.4059	+	23.2197i	−0.532416	+	0.922171i
$635$	2.46863	+	4.27579i	0.0979645	+	0.169679i
$636$		0			0
$637$	−32.5203			−1.28850
$638$	8.58301			0.339804
$639$		0			0
$640$	1.82288	−	3.15731i	0.0720555	−	0.124804i
$641$	9.11438	−	15.7866i	0.359996	−	0.623532i	−0.627963	−	0.778243i	$-0.716111\pi$
$641$	9.11438	−	15.7866i	0.359996	−	0.623532i	0.987960	+	0.154711i	$0.0494446\pi$
$642$		0			0
$643$	−3.12549			−0.123257			−0.0616287	−	0.998099i	$-0.519629\pi$
$643$	−3.12549			−0.123257			−0.0616287	+	0.998099i	$0.519629\pi$
$644$	3.41699			0.134648
$645$		0			0
$646$	−3.64575	−	6.31463i	−0.143440	−	0.248446i
$647$	−4.93725	+	8.55157i	−0.194103	+	0.336197i	−0.946606	−	0.322392i	$-0.895513\pi$
$647$	−4.93725	+	8.55157i	−0.194103	+	0.336197i	0.752503	+	0.658589i	$0.228846\pi$
$648$		0			0
$649$	−15.2288	−	26.3770i	−0.597781	−	1.03539i
$650$	−38.5203			−1.51089
$651$		0			0
$652$	−1.00000			−0.0391630
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	−26.5830	+	46.0431i	−1.03868	+	1.79905i
$656$	−5.46863	−	9.47194i	−0.213514	−	0.369817i
$657$		0			0
$658$	6.53137	−	11.3127i	0.254619	−	0.441014i
$659$	−24.2288			−0.943818			−0.471909	−	0.881647i	$-0.656435\pi$
$659$	−24.2288			−0.943818			−0.471909	+	0.881647i	$0.656435\pi$
$660$		0			0
$661$	1.58301	−	2.74185i	0.0615718	−	0.106645i	−0.833596	−	0.552374i	$-0.813722\pi$
$661$	1.58301	−	2.74185i	0.0615718	−	0.106645i	0.895168	+	0.445729i	$0.147055\pi$
$662$	15.9373	−	27.6041i	0.619419	−	1.07287i
$663$		0			0
$664$	−13.2915			−0.515810
$665$	−9.64575	+	16.7069i	−0.374046	+	0.647867i
$666$		0			0
$667$	1.52026	+	2.63317i	0.0588647	+	0.101957i
$668$	4.29150	−	7.43310i	0.166043	−	0.287595i
$669$		0			0
$670$	−4.17712	−	7.23499i	−0.161376	−	0.279512i
$671$	26.8118			1.03506
$672$		0			0
$673$	15.7490			0.607080			0.303540	−	0.952819i	$-0.401831\pi$
$673$	15.7490			0.607080			0.303540	+	0.952819i	$0.401831\pi$
$674$	15.2915	+	26.4857i	0.589007	+	1.02019i
$675$		0			0
$676$	−4.29150	+	7.43310i	−0.165058	+	0.285888i
$677$	22.9373	+	39.7285i	0.881550	+	1.52689i	0.849617	+	0.527400i	$0.176833\pi$
$677$	22.9373	+	39.7285i	0.881550	+	1.52689i	0.0319331	+	0.999490i	$0.489834\pi$
$678$		0			0
$679$	−35.9373			−1.37915
$680$	−13.2915			−0.509706
$681$		0			0
$682$	8.46863	−	14.6681i	0.324280	−	0.561670i
$683$	13.4059	−	23.2197i	0.512962	−	0.888476i	−0.486925	−	0.873444i	$-0.661882\pi$
$683$	13.4059	−	23.2197i	0.512962	−	0.888476i	0.999887	−	0.0150322i	$-0.00478508\pi$
$684$		0			0
$685$	−4.70850			−0.179902
$686$	9.26013	+	16.0390i	0.353553	+	0.612372i
$687$		0			0
$688$	−2.50000	−	4.33013i	−0.0953116	−	0.165085i
$689$	13.9373	−	24.1400i	0.530967	−	0.919662i
$690$		0			0
$691$	19.3745	+	33.5576i	0.737041	+	1.27659i	0.953822	+	0.300372i	$0.0971109\pi$
$691$	19.3745	+	33.5576i	0.737041	+	1.27659i	−0.216781	+	0.976220i	$0.569556\pi$
$692$	−14.5830			−0.554363
$693$		0			0
$694$	−12.0000			−0.455514
$695$	2.88562	+	4.99804i	0.109458	+	0.189587i
$696$		0			0
$697$	−19.9373	+	34.5323i	−0.755177	+	1.30801i
$698$	0.614378	+	1.06413i	0.0232546	+	0.0402781i
$699$		0			0
$700$	10.9686	+	18.9982i	0.414575	+	0.718065i
$701$	−26.5830			−1.00403			−0.502013	−	0.864860i	$-0.667407\pi$
$701$	−26.5830			−1.00403			−0.502013	+	0.864860i	$0.667407\pi$
$702$		0			0
$703$	11.9373	−	20.6759i	0.450222	−	0.779807i
$704$	−1.82288	+	3.15731i	−0.0687022	+	0.118996i
$705$		0			0
$706$	−12.0000			−0.451626
$707$	11.0516	−	19.1420i	0.415639	−	0.719909i
$708$		0			0
$709$	−18.9059	−	32.7459i	−0.710025	−	1.22980i	−0.964847	−	0.262812i	$-0.915350\pi$
$709$	−18.9059	−	32.7459i	−0.710025	−	1.22980i	0.254822	−	0.966988i	$-0.417983\pi$
$710$	28.5203	−	49.3985i	1.07035	−	1.85389i
$711$		0			0
$712$	−2.46863	−	4.27579i	−0.0925157	−	0.160242i
$713$	6.00000			0.224702
$714$		0			0
$715$	61.7490			2.30928
$716$	−8.46863	−	14.6681i	−0.316487	−	0.548172i
$717$		0			0
$718$	−5.58301	+	9.67005i	−0.208356	+	0.360883i
$719$	−11.4686	−	19.8642i	−0.427708	−	0.740811i	0.568961	−	0.822364i	$-0.307345\pi$
$719$	−11.4686	−	19.8642i	−0.427708	−	0.740811i	−0.996669	+	0.0815529i	$0.974012\pi$
$720$		0			0
$721$	5.20850	+	9.02138i	0.193975	+	0.335974i
$722$	−15.0000			−0.558242
$723$		0			0
$724$	1.35425	−	2.34563i	0.0503303	−	0.0871746i
$725$	−9.76013	+	16.9050i	−0.362482	+	0.627837i
$726$		0			0
$727$	−1.22876			−0.0455721			−0.0227860	−	0.999740i	$-0.507254\pi$
$727$	−1.22876			−0.0455721			−0.0227860	+	0.999740i	$0.507254\pi$
$728$	12.2915			0.455553
$729$		0			0
$730$	19.2915	+	33.4139i	0.714011	+	1.23670i
$731$	−9.11438	+	15.7866i	−0.337107	+	0.583887i
$732$		0			0
$733$	−17.6144	−	30.5090i	−0.650602	−	1.12688i	−0.982977	−	0.183728i	$-0.941183\pi$
$733$	−17.6144	−	30.5090i	−0.650602	−	1.12688i	0.332375	−	0.943147i	$-0.392150\pi$
$734$	29.8745			1.10269
$735$		0			0
$736$	−1.29150			−0.0476054
$737$	4.17712	+	7.23499i	0.153866	+	0.266504i
$738$		0			0
$739$	15.7288	−	27.2430i	0.578592	−	1.00215i	−0.417050	−	0.908884i	$-0.636936\pi$
$739$	15.7288	−	27.2430i	0.578592	−	1.00215i	0.995641	−	0.0932664i	$-0.0297308\pi$
$740$	−21.7601	−	37.6897i	−0.799918	−	1.38550i
$741$		0			0
$742$	−15.8745			−0.582772
$743$	−28.9373			−1.06160			−0.530802	−	0.847496i	$-0.678109\pi$
$743$	−28.9373			−1.06160			−0.530802	+	0.847496i	$0.678109\pi$
$744$		0			0
$745$	41.8118	−	72.4201i	1.53186	−	2.65327i
$746$	−2.29150	+	3.96900i	−0.0838979	+	0.145315i
$747$		0			0
$748$	13.2915			0.485985
$749$	−7.93725	−	13.7477i	−0.290021	−	0.502331i
$750$		0			0
$751$	26.2288	+	45.4295i	0.957101	+	1.65775i	0.729485	+	0.683996i	$0.239760\pi$
$751$	26.2288	+	45.4295i	0.957101	+	1.65775i	0.227615	+	0.973751i	$0.426907\pi$
$752$	−2.46863	+	4.27579i	−0.0900216	+	0.155922i
$753$		0			0
$754$	5.46863	+	9.47194i	0.199156	+	0.344948i
$755$	70.1033			2.55132
$756$		0			0
$757$	48.9778			1.78013			0.890064	−	0.455836i	$-0.150660\pi$
$757$	48.9778			1.78013			0.890064	+	0.455836i	$0.150660\pi$
$758$	−12.7915	−	22.1555i	−0.464608	−	0.804725i
$759$		0			0
$760$	3.64575	−	6.31463i	0.132245	−	0.229056i
$761$	−1.29150	−	2.23695i	−0.0468169	−	0.0810893i	0.841667	−	0.539996i	$-0.181574\pi$
$761$	−1.29150	−	2.23695i	−0.0468169	−	0.0810893i	−0.888484	+	0.458907i	$0.848241\pi$
$762$		0			0
$763$	−4.43725	+	7.68555i	−0.160639	+	0.278236i
$764$	−20.8118			−0.752943
$765$		0			0
$766$	−10.2915	+	17.8254i	−0.371847	+	0.644058i
$767$	19.4059	−	33.6120i	0.700706	−	1.21366i
$768$		0			0
$769$	40.5830			1.46346			0.731730	−	0.681594i	$-0.238713\pi$
$769$	40.5830			1.46346			0.731730	+	0.681594i	$0.238713\pi$
$770$	−17.5830	−	30.4547i	−0.633648	−	1.09751i
$771$		0			0
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	23.1660	−	40.1247i	0.833223	−	1.44319i	−0.0622452	−	0.998061i	$-0.519826\pi$
$773$	23.1660	−	40.1247i	0.833223	−	1.44319i	0.895469	−	0.445125i	$-0.146841\pi$
$774$		0			0
$775$	19.2601	+	33.3595i	0.691844	+	1.19831i
$776$	13.5830			0.487601
$777$		0			0
$778$	19.2915			0.691634
$779$	−10.9373	−	18.9439i	−0.391868	−	0.678735i
$780$		0			0
$781$	−28.5203	+	49.3985i	−1.02054	+	1.76762i
$782$	2.35425	+	4.07768i	0.0841878	+	0.145817i
$783$		0			0
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$	14.5830			0.520490
$786$		0			0
$787$	5.85425	−	10.1399i	0.208681	−	0.361447i	−0.742618	−	0.669715i	$-0.766416\pi$
$787$	5.85425	−	10.1399i	0.208681	−	0.361447i	0.951299	+	0.308268i	$0.0997495\pi$
$788$	−2.35425	+	4.07768i	−0.0838666	+	0.145261i
$789$		0			0
$790$	−40.9373			−1.45648
$791$	−6.22876			−0.221469
$792$		0			0
$793$	17.0830	+	29.5886i	0.606635	+	1.05072i
$794$	8.32288	−	14.4156i	0.295368	−	0.511592i
$795$		0			0
$796$	−3.03137	−	5.25049i	−0.107444	−	0.186099i
$797$	−14.8118			−0.524660			−0.262330	−	0.964978i	$-0.584491\pi$
$797$	−14.8118			−0.524660			−0.262330	+	0.964978i	$0.584491\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$	−4.14575	−	7.18065i	−0.146574	−	0.253874i
$801$		0			0
$802$	10.4059	−	18.0235i	0.367444	−	0.636432i
$803$	−19.2915	−	33.4139i	−0.680782	−	1.17915i
$804$		0			0
$805$	6.22876	−	10.7885i	0.219535	−	0.380245i
$806$	21.5830			0.760229
$807$		0			0
$808$	−4.17712	+	7.23499i	−0.146951	+	0.254526i
$809$	−7.70850	+	13.3515i	−0.271016	+	0.469414i	−0.969122	−	0.246580i	$-0.920693\pi$
$809$	−7.70850	+	13.3515i	−0.271016	+	0.469414i	0.698106	+	0.715994i	$0.254026\pi$
$810$		0			0
$811$	−29.2915			−1.02856			−0.514282	−	0.857621i	$-0.671941\pi$
$811$	−29.2915			−1.02856			−0.514282	+	0.857621i	$0.671941\pi$
$812$	3.11438	−	5.39426i	0.109293	−	0.189301i
$813$		0			0
$814$	21.7601	+	37.6897i	0.762692	+	1.32102i
$815$	−1.82288	+	3.15731i	−0.0638525	+	0.110596i
$816$		0			0
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$	14.8745			0.520075
$819$		0			0
$820$	−39.8745			−1.39248
$821$	−10.2915	−	17.8254i	−0.359176	−	0.622111i	0.628647	−	0.777690i	$-0.283609\pi$
$821$	−10.2915	−	17.8254i	−0.359176	−	0.622111i	−0.987823	+	0.155579i	$0.950276\pi$
$822$		0			0
$823$	17.5516	−	30.4003i	0.611811	−	1.05969i	−0.379124	−	0.925346i	$-0.623774\pi$
$823$	17.5516	−	30.4003i	0.611811	−	1.05969i	0.990935	−	0.134342i	$-0.0428922\pi$
$824$	−1.96863	−	3.40976i	−0.0685804	−	0.118785i
$825$		0			0
$826$	−22.1033			−0.769071
$827$	−43.7490			−1.52130			−0.760651	−	0.649161i	$-0.775120\pi$
$827$	−43.7490			−1.52130			−0.760651	+	0.649161i	$0.775120\pi$
$828$		0			0
$829$	14.6458	−	25.3672i	0.508668	−	0.881039i	−0.491282	−	0.871001i	$-0.663471\pi$
$829$	14.6458	−	25.3672i	0.508668	−	0.881039i	0.999950	−	0.0100380i	$-0.00319525\pi$
$830$	−24.2288	+	41.9654i	−0.840992	+	1.45664i
$831$		0			0
$832$	−4.64575			−0.161062
$833$	−12.7601	+	22.1012i	−0.442112	+	0.765761i
$834$		0			0
$835$	−15.6458	−	27.0992i	−0.541444	−	0.937808i
$836$	−3.64575	+	6.31463i	−0.126091	+	0.218396i
$837$		0			0
$838$	−14.4686	−	25.0604i	−0.499810	−	0.865697i
$839$	−49.2915			−1.70173			−0.850866	−	0.525383i	$-0.823922\pi$
$839$	−49.2915			−1.70173			−0.850866	+	0.525383i	$0.823922\pi$
$840$		0			0
$841$	−23.4575			−0.808880
$842$	7.35425	+	12.7379i	0.253444	+	0.438978i
$843$		0			0
$844$	−7.43725	+	12.8817i	−0.256001	+	0.443406i
$845$	15.6458	+	27.0992i	0.538230	+	0.932242i
$846$		0			0
$847$	3.03137	+	5.25049i	0.104159	+	0.180409i
$848$	6.00000			0.206041
$849$		0			0
$850$	−15.1144	+	26.1789i	−0.518419	+	0.897928i
$851$	−7.70850	+	13.3515i	−0.264244	+	0.457684i
$852$		0			0
$853$	47.8745			1.63919			0.819596	−	0.572942i	$-0.194198\pi$
$853$	47.8745			1.63919			0.819596	+	0.572942i	$0.194198\pi$
$854$	9.72876	−	16.8507i	0.332911	−	0.576619i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	13.4059	−	23.2197i	0.457936	−	0.793169i	−0.540916	−	0.841077i	$-0.681922\pi$
$857$	13.4059	−	23.2197i	0.457936	−	0.793169i	0.998852	+	0.0479082i	$0.0152555\pi$
$858$		0			0
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	0.919537	−	0.393003i	$-0.128564\pi$
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	−0.800119	+	0.599841i	$0.795230\pi$
$860$	−18.2288			−0.621595
$861$		0			0
$862$	38.8118			1.32193
$863$	−14.5830	−	25.2585i	−0.496411	−	0.859810i	0.503580	−	0.863949i	$-0.332016\pi$
$863$	−14.5830	−	25.2585i	−0.496411	−	0.859810i	−0.999991	+	0.00413896i	$0.998683\pi$
$864$		0			0
$865$	−26.5830	+	46.0431i	−0.903849	+	1.56551i
$866$	9.50000	+	16.4545i	0.322823	+	0.559146i
$867$		0			0
$868$	−6.14575	−	10.6448i	−0.208600	−	0.361306i
$869$	40.9373			1.38870
$870$		0			0
$871$	−5.32288	+	9.21949i	−0.180359	+	0.312391i
$872$	1.67712	−	2.90486i	0.0567946	−	0.0983711i
$873$		0			0
$874$	−2.58301			−0.0873715
$875$	31.7490			1.07331
$876$		0			0
$877$	−13.3229	−	23.0759i	−0.449882	−	0.779218i	0.548496	−	0.836153i	$-0.315200\pi$
$877$	−13.3229	−	23.0759i	−0.449882	−	0.779218i	−0.998378	+	0.0569353i	$0.981867\pi$
$878$	−12.5830	+	21.7944i	−0.424656	+	0.735526i
$879$		0			0
$880$	6.64575	+	11.5108i	0.224028	+	0.388028i
$881$	−3.87451			−0.130535			−0.0652677	−	0.997868i	$-0.520790\pi$
$881$	−3.87451			−0.130535			−0.0652677	+	0.997868i	$0.520790\pi$
$882$		0			0
$883$	−19.8745			−0.668830			−0.334415	−	0.942426i	$-0.608539\pi$
$883$	−19.8745			−0.668830			−0.334415	+	0.942426i	$0.608539\pi$
$884$	8.46863	+	14.6681i	0.284831	+	0.493341i
$885$		0			0
$886$	9.64575	−	16.7069i	0.324055	−	0.561280i
$887$	−7.93725	−	13.7477i	−0.266507	−	0.461603i	0.701450	−	0.712718i	$-0.252536\pi$
$887$	−7.93725	−	13.7477i	−0.266507	−	0.461603i	−0.967957	+	0.251115i	$0.919203\pi$
$888$		0			0
$889$	−3.58301			−0.120170
$890$	−18.0000			−0.603361
$891$		0			0
$892$	6.93725	−	12.0157i	0.232276	−	0.402315i
$893$	−4.93725	+	8.55157i	−0.165219	+	0.286168i
$894$		0			0
$895$	−61.7490			−2.06404
$896$	1.32288	+	2.29129i	0.0441942	+	0.0765466i
$897$		0			0
$898$	−1.17712	−	2.03884i	−0.0392811	−	0.0680369i
$899$	5.46863	−	9.47194i	0.182389	−	0.315907i
$900$		0			0
$901$	−10.9373	−	18.9439i	−0.364373	−	0.631112i
$902$	39.8745			1.32768
$903$		0			0
$904$	2.35425			0.0783011
$905$	−4.93725	−	8.55157i	−0.164120	−	0.284264i
$906$		0			0
$907$	−18.1458	+	31.4294i	−0.602520	+	1.04359i	0.389918	+	0.920849i	$0.372503\pi$
$907$	−18.1458	+	31.4294i	−0.602520	+	1.04359i	−0.992438	+	0.122745i	$0.960830\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$		0			0
$910$	22.4059	−	38.8081i	0.742748	−	1.28648i
$911$	28.9373			0.958734			0.479367	−	0.877615i	$-0.340866\pi$
$911$	28.9373			0.958734			0.479367	+	0.877615i	$0.340866\pi$
$912$		0			0
$913$	24.2288	−	41.9654i	0.801855	−	1.38885i
$914$	4.14575	−	7.18065i	0.137129	−	0.237515i
$915$		0			0
$916$	−9.35425			−0.309073
$917$	−19.2915	−	33.4139i	−0.637062	−	1.10342i
$918$		0			0
$919$	−14.3856	−	24.9166i	−0.474538	−	0.821924i	0.525037	−	0.851079i	$-0.324051\pi$
$919$	−14.3856	−	24.9166i	−0.474538	−	0.821924i	−0.999575	+	0.0291557i	$0.990718\pi$
$920$	−2.35425	+	4.07768i	−0.0776173	+	0.134437i
$921$		0			0
$922$	−12.1144	−	20.9827i	−0.398966	−	0.691029i
$923$	−72.6863			−2.39250
$924$		0			0
$925$	−98.9778			−3.25437
$926$	−9.35425	−	16.2020i	−0.307400	−	0.532432i
$927$		0			0
$928$	−1.17712	+	2.03884i	−0.0386410	+	0.0669282i
$929$	8.46863	+	14.6681i	0.277847	+	0.481244i	0.970849	−	0.239690i	$-0.0770460\pi$
$929$	8.46863	+	14.6681i	0.277847	+	0.481244i	−0.693003	+	0.720935i	$0.743713\pi$
$930$		0			0
$931$	−7.00000	−	12.1244i	−0.229416	−	0.397360i
$932$	−19.2915			−0.631914
$933$		0			0
$934$	−0.114378	+	0.198109i	−0.00374257	+	0.00648232i
$935$	24.2288	−	41.9654i	0.792365	−	1.37242i
$936$		0			0
$937$	−44.7490			−1.46189			−0.730943	−	0.682438i	$-0.760920\pi$
$937$	−44.7490			−1.46189			−0.730943	+	0.682438i	$0.760920\pi$
$938$	6.06275			0.197956
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	26.6974	−	46.2412i	0.870310	−	1.50742i	0.00863340	−	0.999963i	$-0.497252\pi$
$941$	26.6974	−	46.2412i	0.870310	−	1.50742i	0.861676	−	0.507458i	$-0.169415\pi$
$942$		0			0
$943$	7.06275	+	12.2330i	0.229995	+	0.398362i
$944$	8.35425			0.271908
$945$		0			0
$946$	18.2288			0.592668
$947$	−5.23987	−	9.07572i	−0.170273	−	0.294921i	0.768242	−	0.640159i	$-0.221132\pi$
$947$	−5.23987	−	9.07572i	−0.170273	−	0.294921i	−0.938515	+	0.345238i	$0.887798\pi$
$948$		0			0
$949$	24.5830	−	42.5790i	0.797998	−	1.38217i
$950$	−8.29150	−	14.3613i	−0.269012	−	0.465942i
$951$		0			0
$952$	4.82288	−	8.35347i	0.156310	−	0.270737i
$953$	52.3320			1.69520			0.847600	−	0.530635i	$-0.178047\pi$
$953$	52.3320			1.69520			0.847600	+	0.530635i	$0.178047\pi$
$954$		0			0
$955$	−37.9373	+	65.7093i	−1.22762	+	2.12630i
$956$	5.46863	−	9.47194i	0.176868	−	0.306344i
$957$		0			0
$958$	3.64575			0.117789
$959$	1.70850	−	2.95920i	0.0551703	−	0.0955577i
$960$		0			0
$961$	4.70850	+	8.15536i	0.151887	+	0.263076i
$962$	−27.7288	+	48.0276i	−0.894011	+	1.54847i
$963$		0			0
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$	25.5203			0.821526
$966$		0			0
$967$	36.0627			1.15970			0.579850	−	0.814723i	$-0.303111\pi$
$967$	36.0627			1.15970			0.579850	+	0.814723i	$0.303111\pi$
$968$	−1.14575	−	1.98450i	−0.0368258	−	0.0637842i
$969$		0			0
$970$	24.7601	−	42.8858i	0.795000	−	1.37698i
$971$	4.93725	+	8.55157i	0.158444	+	0.274433i	0.934308	−	0.356467i	$-0.116019\pi$
$971$	4.93725	+	8.55157i	0.158444	+	0.274433i	−0.775864	+	0.630901i	$0.782686\pi$
$972$		0			0
$973$	−4.18824			−0.134269
$974$	23.8745			0.764989
$975$		0			0
$976$	−3.67712	+	6.36897i	−0.117702	+	0.203866i
$977$	25.9373	−	44.9246i	0.829806	−	1.43727i	−0.0683837	−	0.997659i	$-0.521784\pi$
$977$	25.9373	−	44.9246i	0.829806	−	1.43727i	0.898190	−	0.439608i	$-0.144882\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$	−25.5203			−0.815215
$981$		0			0
$982$	−12.8745	−	22.2993i	−0.410842	−	0.711599i
$983$	−10.4059	+	18.0235i	−0.331896	+	0.574861i	−0.982884	−	0.184228i	$-0.941022\pi$
$983$	−10.4059	+	18.0235i	−0.331896	+	0.574861i	0.650988	+	0.759088i	$0.274355\pi$
$984$		0			0
$985$	8.58301	+	14.8662i	0.273477	+	0.473677i
$986$	8.58301			0.273339
$987$		0			0
$988$	−9.29150			−0.295602
$989$	3.22876	+	5.59237i	0.102668	+	0.177827i
$990$		0			0
$991$	13.0314	−	22.5710i	0.413955	−	0.716991i	−0.581363	−	0.813644i	$-0.697480\pi$
$991$	13.0314	−	22.5710i	0.413955	−	0.716991i	0.995318	+	0.0966529i	$0.0308137\pi$
$992$	2.32288	+	4.02334i	0.0737514	+	0.127741i
$993$		0			0
$994$	20.6974	+	35.8489i	0.656481	+	1.13706i
$995$	−22.1033			−0.700721
$996$		0			0
$997$	−11.8431	+	20.5129i	−0.375076	+	0.649650i	−0.990338	−	0.138672i	$-0.955717\pi$
$997$	−11.8431	+	20.5129i	−0.375076	+	0.649650i	0.615263	+	0.788322i	$0.289050\pi$
$998$	3.08301	−	5.33992i	0.0975908	−	0.169032i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.g.g.109.2	✓	4
3.2	odd	2		378.2.g.h.109.1	yes	4
7.2	even	3	inner	378.2.g.g.163.2	yes	4
7.3	odd	6		2646.2.a.bo.1.2		2
7.4	even	3		2646.2.a.bl.1.1		2
9.2	odd	6		1134.2.h.t.109.2		4
9.4	even	3		1134.2.e.t.865.2		4
9.5	odd	6		1134.2.e.q.865.1		4
9.7	even	3		1134.2.h.q.109.1		4
21.2	odd	6		378.2.g.h.163.1	yes	4
21.11	odd	6		2646.2.a.bi.1.2		2
21.17	even	6		2646.2.a.bf.1.1		2
63.2	odd	6		1134.2.e.q.919.1		4
63.16	even	3		1134.2.e.t.919.2		4
63.23	odd	6		1134.2.h.t.541.2		4
63.58	even	3		1134.2.h.q.541.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.g.109.2	✓	4	1.1	even	1	trivial
378.2.g.g.163.2	yes	4	7.2	even	3	inner
378.2.g.h.109.1	yes	4	3.2	odd	2
378.2.g.h.163.1	yes	4	21.2	odd	6
1134.2.e.q.865.1		4	9.5	odd	6
1134.2.e.q.919.1		4	63.2	odd	6
1134.2.e.t.865.2		4	9.4	even	3
1134.2.e.t.919.2		4	63.16	even	3
1134.2.h.q.109.1		4	9.7	even	3
1134.2.h.q.541.1		4	63.58	even	3
1134.2.h.t.109.2		4	9.2	odd	6
1134.2.h.t.541.2		4	63.23	odd	6
2646.2.a.bf.1.1		2	21.17	even	6
2646.2.a.bi.1.2		2	21.11	odd	6
2646.2.a.bl.1.1		2	7.4	even	3
2646.2.a.bo.1.2		2	7.3	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} +(-1.82288 + 3.15731i) q^{11} -4.64575 q^{13} +(1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.82288 + 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} -3.64575 q^{20} +3.64575 q^{22} +(0.645751 + 1.11847i) q^{23} +(-4.14575 + 7.18065i) q^{25} +(2.32288 + 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +2.35425 q^{29} +(2.32288 - 4.02334i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.64575 q^{34} +(-4.82288 - 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.82288 + 3.15731i) q^{40} +10.9373 q^{41} +5.00000 q^{43} +(-1.82288 - 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(-2.46863 - 4.27579i) q^{47} +7.00000 q^{49} +8.29150 q^{50} +(2.32288 - 4.02334i) q^{52} +(-3.00000 + 5.19615i) q^{53} -13.2915 q^{55} -2.64575 q^{56} +(-1.17712 - 2.03884i) q^{58} +(-4.17712 + 7.23499i) q^{59} +(-3.67712 - 6.36897i) q^{61} -4.64575 q^{62} +1.00000 q^{64} +(-8.46863 - 14.6681i) q^{65} +(1.14575 - 1.98450i) q^{67} +(-1.82288 - 3.15731i) q^{68} +(-4.82288 + 8.35347i) q^{70} +15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +(5.96863 - 10.3380i) q^{74} +2.00000 q^{76} +(4.82288 - 8.35347i) q^{77} +(-5.61438 - 9.72439i) q^{79} +(1.82288 - 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} -13.2915 q^{83} -13.2915 q^{85} +(-2.50000 - 4.33013i) q^{86} +(-1.82288 + 3.15731i) q^{88} +(-2.46863 - 4.27579i) q^{89} +12.2915 q^{91} -1.29150 q^{92} +(-2.46863 + 4.27579i) q^{94} +(3.64575 - 6.31463i) q^{95} +13.5830 q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 2 q^{11} - 8 q^{13} - 2 q^{16} - 2 q^{17} - 4 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 6 q^{25} + 4 q^{26} + 20 q^{29} + 4 q^{31} - 2 q^{32} + 4 q^{34} - 14 q^{35} + 8 q^{37} - 4 q^{38} + 2 q^{40} + 12 q^{41} + 20 q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} + 28 q^{49} + 12 q^{50} + 4 q^{52} - 12 q^{53} - 32 q^{55} - 10 q^{58} - 22 q^{59} - 20 q^{61} - 8 q^{62} + 4 q^{64} - 18 q^{65} - 6 q^{67} - 2 q^{68} - 14 q^{70} + 52 q^{71} + 8 q^{74} + 8 q^{76} + 14 q^{77} + 4 q^{79} + 2 q^{80} - 6 q^{82} - 32 q^{83} - 32 q^{85} - 10 q^{86} - 2 q^{88} + 6 q^{89} + 28 q^{91} + 16 q^{92} + 6 q^{94} + 4 q^{95} + 12 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 2 * q^11 - 8 * q^13 - 2 * q^16 - 2 * q^17 - 4 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 6 * q^25 + 4 * q^26 + 20 * q^29 + 4 * q^31 - 2 * q^32 + 4 * q^34 - 14 * q^35 + 8 * q^37 - 4 * q^38 + 2 * q^40 + 12 * q^41 + 20 * q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 + 28 * q^49 + 12 * q^50 + 4 * q^52 - 12 * q^53 - 32 * q^55 - 10 * q^58 - 22 * q^59 - 20 * q^61 - 8 * q^62 + 4 * q^64 - 18 * q^65 - 6 * q^67 - 2 * q^68 - 14 * q^70 + 52 * q^71 + 8 * q^74 + 8 * q^76 + 14 * q^77 + 4 * q^79 + 2 * q^80 - 6 * q^82 - 32 * q^83 - 32 * q^85 - 10 * q^86 - 2 * q^88 + 6 * q^89 + 28 * q^91 + 16 * q^92 + 6 * q^94 + 4 * q^95 + 12 * q^97 - 14 * q^98

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