LMFDB - Embedded newform 378.2.t.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(17,378)]

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([5, 1]))

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

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

chi := DirichletCharacter("378.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (of order $6$, degree $2$, not 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:	$16$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Root			$1.27866 + 1.16834i$ of defining polynomial
Character	$\chi$	$=$	378.17
Dual form			378.2.t.a.89.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.55225 q^{5} +(-1.49384 + 2.18368i) q^{7} +1.00000i q^{8} +(-3.07634 - 1.77612i) q^{10} +3.02237i q^{11} +(0.888944 + 0.513232i) q^{13} +(-2.38554 + 1.14420i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.809204 + 1.40158i) q^{17} +(-7.12643 + 4.11444i) q^{19} +(-1.77612 - 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} -3.35830i q^{23} +7.61848 q^{25} +(0.513232 + 0.888944i) q^{26} +(-2.63804 - 0.201867i) q^{28} +(3.70319 - 2.13804i) q^{29} +(5.18382 - 2.99288i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.40158 + 0.809204i) q^{34} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} -8.22889 q^{38} -3.55225i q^{40} +(0.0472226 - 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +(-2.61745 + 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} +(2.57023 - 4.45176i) q^{47} +(-2.53687 - 6.52413i) q^{49} +(6.59779 + 3.80924i) q^{50} +1.02646i q^{52} +(-2.76235 - 1.59484i) q^{53} -10.7362i q^{55} +(-2.18368 - 1.49384i) q^{56} +4.27608 q^{58} +(4.42036 + 7.65628i) q^{59} +(-4.06195 - 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(-3.15775 - 1.82313i) q^{65} +(0.187838 + 0.325345i) q^{67} -1.61841 q^{68} +(8.47404 - 4.06447i) q^{70} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +5.84647i q^{74} +(-7.12643 - 4.11444i) q^{76} +(-6.59987 - 4.51494i) q^{77} +(-0.462067 + 0.800324i) q^{79} +(1.77612 - 3.07634i) q^{80} +(0.0817920 - 0.0472226i) q^{82} +(5.43209 + 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +6.11799i q^{86} -3.02237 q^{88} +(-2.35495 - 4.07888i) q^{89} +(-2.44867 + 1.17448i) q^{91} +(2.90837 - 1.67915i) q^{92} +(4.45176 - 2.57023i) q^{94} +(25.3148 - 14.6155i) q^{95} +(-13.3330 + 7.69782i) q^{97} +(1.06507 - 6.91850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47}+ \cdots - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.55225			−1.58861			−0.794307	−	0.607516i	$-0.792166\pi$
$5$	−3.55225			−1.58861			−0.794307	+	0.607516i	$0.792166\pi$
$6$		0			0
$7$	−1.49384	+	2.18368i	−0.564619	+	0.825352i
$7$	−1.49384	+	2.18368i	−0.564619	+	0.825352i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.07634	−	1.77612i	−0.972824	−	0.561660i
$11$			3.02237i			0.911279i	0.890164	+	0.455639i	$0.150589\pi$
$11$			3.02237i			0.911279i	−0.890164	+	0.455639i	$0.849411\pi$
$12$		0			0
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	0.618183	−	0.786034i	$-0.287869\pi$
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	−0.371634	+	0.928379i	$0.621202\pi$
$14$	−2.38554	+	1.14420i	−0.637563	+	0.305800i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	−0.947313	−	0.320309i	$-0.896213\pi$
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	0.751052	+	0.660243i	$0.229547\pi$
$18$		0			0
$19$	−7.12643	+	4.11444i	−1.63491	+	0.943918i	−0.652368	+	0.757903i	$0.726224\pi$
$19$	−7.12643	+	4.11444i	−1.63491	+	0.943918i	−0.982547	+	0.186016i	$0.940442\pi$
$20$	−1.77612	−	3.07634i	−0.397154	−	0.687890i
$21$		0			0
$22$	−1.51119	+	2.61745i	−0.322186	+	0.558042i
$23$		−	3.35830i		−	0.700254i	−0.936702	−	0.350127i	$-0.886138\pi$
$23$		−	3.35830i		−	0.700254i	0.936702	−	0.350127i	$-0.113862\pi$
$24$		0			0
$25$	7.61848			1.52370
$26$	0.513232	+	0.888944i	0.100653	+	0.174336i
$27$		0			0
$28$	−2.63804	−	0.201867i	−0.498543	−	0.0381493i
$29$	3.70319	−	2.13804i	0.687666	−	0.397024i	−0.115071	−	0.993357i	$-0.536710\pi$
$29$	3.70319	−	2.13804i	0.687666	−	0.397024i	0.802737	+	0.596333i	$0.203376\pi$
$30$		0			0
$31$	5.18382	−	2.99288i	0.931041	−	0.537537i	0.0439006	−	0.999036i	$-0.486022\pi$
$31$	5.18382	−	2.99288i	0.931041	−	0.537537i	0.887141	+	0.461499i	$0.152688\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.40158	+	0.809204i	−0.240369	+	0.138777i
$35$	5.30650	−	7.75696i	0.896962	−	1.31117i
$36$		0			0
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	0.999752	−	0.0222846i	$-0.00709398\pi$
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	−0.519175	+	0.854668i	$0.673761\pi$
$38$	−8.22889			−1.33490
$39$		0			0
$40$		−	3.55225i		−	0.561660i
$41$	0.0472226	−	0.0817920i	0.00737493	−	0.0127738i	−0.862314	−	0.506373i	$-0.830986\pi$
$41$	0.0472226	−	0.0817920i	0.00737493	−	0.0127738i	0.869689	+	0.493600i	$0.164319\pi$
$42$		0			0
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	0.999267	−	0.0382684i	$-0.0121842\pi$
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	−0.532775	+	0.846257i	$0.678851\pi$
$44$	−2.61745	+	1.51119i	−0.394595	+	0.227820i
$45$		0			0
$46$	1.67915	−	2.90837i	0.247577	−	0.428816i
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	−0.615407	−	0.788210i	$-0.711008\pi$
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	0.990313	+	0.138853i	$0.0443416\pi$
$48$		0			0
$49$	−2.53687	−	6.52413i	−0.362411	−	0.932019i
$50$	6.59779	+	3.80924i	0.933069	+	0.538708i
$51$		0			0
$52$			1.02646i			0.142345i
$53$	−2.76235	−	1.59484i	−0.379438	−	0.219068i	0.298136	−	0.954523i	$-0.403635\pi$
$53$	−2.76235	−	1.59484i	−0.379438	−	0.219068i	−0.677574	+	0.735455i	$0.736968\pi$
$54$		0			0
$55$		−	10.7362i		−	1.44767i
$56$	−2.18368	−	1.49384i	−0.291806	−	0.199623i
$57$		0			0
$58$	4.27608			0.561477
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	0.995989	+	0.0894739i	$0.0285186\pi$
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	−0.420508	+	0.907289i	$0.638148\pi$
$60$		0			0
$61$	−4.06195	−	2.34517i	−0.520080	−	0.300268i	0.216887	−	0.976197i	$-0.430410\pi$
$61$	−4.06195	−	2.34517i	−0.520080	−	0.300268i	−0.736967	+	0.675928i	$0.763743\pi$
$62$	5.98576			0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.15775	−	1.82313i	−0.391671	−	0.226131i
$66$		0			0
$67$	0.187838	+	0.325345i	0.0229480	+	0.0397472i	0.877271	−	0.479995i	$-0.159361\pi$
$67$	0.187838	+	0.325345i	0.0229480	+	0.0397472i	−0.854323	+	0.519742i	$0.826028\pi$
$68$	−1.61841			−0.196261
$69$		0			0
$70$	8.47404	−	4.06447i	1.01284	−	0.485798i
$71$			13.9868i			1.65993i	0.557815	+	0.829966i	$0.311640\pi$
$71$			13.9868i			1.65993i	−0.557815	+	0.829966i	$0.688360\pi$
$72$		0			0
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	0.564974	−	0.825109i	$-0.308886\pi$
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	−0.432079	+	0.901836i	$0.642220\pi$
$74$			5.84647i			0.679638i
$75$		0			0
$76$	−7.12643	−	4.11444i	−0.817457	−	0.471959i
$77$	−6.59987	−	4.51494i	−0.752125	−	0.514525i
$78$		0			0
$79$	−0.462067	+	0.800324i	−0.0519866	+	0.0900434i	−0.890848	−	0.454302i	$-0.849889\pi$
$79$	−0.462067	+	0.800324i	−0.0519866	+	0.0900434i	0.838861	+	0.544346i	$0.183222\pi$
$80$	1.77612	−	3.07634i	0.198577	−	0.343945i
$81$		0			0
$82$	0.0817920	−	0.0472226i	0.00903241	−	0.00521487i
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	0.993369	+	0.114968i	$0.0366765\pi$
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	−0.397119	+	0.917767i	$0.629990\pi$
$84$		0			0
$85$	2.87450	−	4.97877i	0.311783	−	0.540024i
$86$			6.11799i			0.659720i
$87$		0			0
$88$	−3.02237			−0.322186
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	0.713798	−	0.700352i	$-0.246974\pi$
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	−0.963421	+	0.267991i	$0.913640\pi$
$90$		0			0
$91$	−2.44867	+	1.17448i	−0.256691	+	0.123119i
$92$	2.90837	−	1.67915i	0.303219	−	0.175063i
$93$		0			0
$94$	4.45176	−	2.57023i	0.459164	−	0.265099i
$95$	25.3148	−	14.6155i	2.59725	−	1.49952i
$96$		0			0
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.988774	−	0.149417i	$-0.952260\pi$
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.364988	+	0.931012i	$0.618927\pi$
$98$	1.06507	−	6.91850i	0.107588	−	0.698874i
$99$		0			0
$100$	3.80924	+	6.59779i	0.380924	+	0.659779i
$101$	13.7047			1.36367			0.681833	−	0.731508i	$-0.261183\pi$
$101$	13.7047			1.36367			0.681833	+	0.731508i	$0.261183\pi$
$102$		0			0
$103$		−	3.04857i		−	0.300385i	−0.988657	−	0.150192i	$-0.952011\pi$
$103$		−	3.04857i		−	0.300385i	0.988657	−	0.150192i	$-0.0479893\pi$
$104$	−0.513232	+	0.888944i	−0.0503266	+	0.0871682i
$105$		0			0
$106$	−1.59484	−	2.76235i	−0.154905	−	0.268303i
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.935956	−	0.352116i	$-0.885462\pi$
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.163037	+	0.986620i	$0.552129\pi$
$108$		0			0
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	−0.493692	−	0.869637i	$-0.664353\pi$
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	0.999974	−	0.00726875i	$-0.00231373\pi$
$110$	5.36811	−	9.29783i	0.511829	−	0.886514i
$111$		0			0
$112$	−1.14420	−	2.38554i	−0.108116	−	0.225413i
$113$	−10.6520	−	6.14993i	−1.00205	−	0.578537i	−0.0931992	−	0.995647i	$-0.529709\pi$
$113$	−10.6520	−	6.14993i	−1.00205	−	0.578537i	−0.908856	+	0.417111i	$0.863043\pi$
$114$		0			0
$115$			11.9295i			1.11243i
$116$	3.70319	+	2.13804i	0.343833	+	0.198512i
$117$		0			0
$118$			8.84071i			0.813853i
$119$	−1.85178	−	3.86078i	−0.169752	−	0.353917i
$120$		0			0
$121$	1.86528			0.169571
$122$	−2.34517	−	4.06195i	−0.212322	−	0.367752i
$123$		0			0
$124$	5.18382	+	2.99288i	0.465521	+	0.268768i
$125$	−9.30148			−0.831950
$126$		0			0
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.82313	−	3.15775i	−0.159899	−	0.276953i
$131$	−0.372949			−0.0325847			−0.0162923	−	0.999867i	$-0.505186\pi$
$131$	−0.372949			−0.0325847			−0.0162923	+	0.999867i	$0.505186\pi$
$132$		0			0
$133$	1.66114	−	21.7081i	0.144039	−	1.88233i
$134$			0.375675i			0.0324534i
$135$		0			0
$136$	−1.40158	−	0.809204i	−0.120185	−	0.0693887i
$137$			7.06222i			0.603366i	0.953408	+	0.301683i	$0.0975485\pi$
$137$			7.06222i			0.603366i	−0.953408	+	0.301683i	$0.902451\pi$
$138$		0			0
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.928572	−	0.371152i	$-0.121037\pi$
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.142858	+	0.989743i	$0.454371\pi$
$140$	9.37097	+	0.717083i	0.791992	+	0.0606046i
$141$		0			0
$142$	−6.99341	+	12.1129i	−0.586874	+	1.01650i
$143$	−1.55118	+	2.68672i	−0.129716	+	0.224675i
$144$		0			0
$145$	−13.1547	+	7.59485i	−1.09244	+	0.630718i
$146$	0.655556	+	1.13546i	0.0542542	+	0.0939710i
$147$		0			0
$148$	−2.92323	+	5.06319i	−0.240288	+	0.416192i
$149$			10.7021i			0.876753i	0.898791	+	0.438376i	$0.144446\pi$
$149$			10.7021i			0.876753i	−0.898791	+	0.438376i	$0.855554\pi$
$150$		0			0
$151$	16.0013			1.30217			0.651084	−	0.759006i	$-0.274315\pi$
$151$	16.0013			1.30217			0.651084	+	0.759006i	$0.274315\pi$
$152$	−4.11444	−	7.12643i	−0.333726	−	0.578030i
$153$		0			0
$154$	−3.45819	−	7.20999i	−0.278669	−	0.580998i
$155$	−18.4142	+	10.6315i	−1.47907	+	0.853939i
$156$		0			0
$157$	−9.98239	+	5.76334i	−0.796681	+	0.459964i	−0.842309	−	0.538994i	$-0.818804\pi$
$157$	−9.98239	+	5.76334i	−0.796681	+	0.459964i	0.0456280	+	0.998958i	$0.485471\pi$
$158$	−0.800324	+	0.462067i	−0.0636703	+	0.0367601i
$159$		0			0
$160$	3.07634	−	1.77612i	0.243206	−	0.140415i
$161$	7.33344	+	5.01677i	0.577956	+	0.395377i
$162$		0			0
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	0.914801	−	0.403904i	$-0.132347\pi$
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	−0.807192	+	0.590289i	$0.799014\pi$
$164$	0.0944452			0.00737493
$165$		0			0
$166$			10.8642i			0.843225i
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	−0.953058	−	0.302788i	$-0.902083\pi$
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	0.738751	+	0.673979i	$0.235416\pi$
$168$		0			0
$169$	−5.97319	−	10.3459i	−0.459476	−	0.795835i
$170$	4.97877	−	2.87450i	0.381854	−	0.220464i
$171$		0			0
$172$	−3.05899	+	5.29833i	−0.233246	+	0.403994i
$173$	−5.60253	+	9.70387i	−0.425953	+	0.737772i	−0.996509	−	0.0834869i	$-0.973394\pi$
$173$	−5.60253	+	9.70387i	−0.425953	+	0.737772i	0.570556	+	0.821259i	$0.306728\pi$
$174$		0			0
$175$	−11.3808	+	16.6363i	−0.860307	+	1.25758i
$176$	−2.61745	−	1.51119i	−0.197298	−	0.113910i
$177$		0			0
$178$		−	4.70989i		−	0.353021i
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	0.408631	−	0.912700i	$-0.366006\pi$
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	−0.586106	+	0.810235i	$0.699340\pi$
$180$		0			0
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$	−2.70785	−	0.207210i	−0.200719	−	0.0153594i
$183$		0			0
$184$	3.35830			0.247577
$185$	−10.3841	−	17.9857i	−0.763451	−	1.32234i
$186$		0			0
$187$	−4.23610	−	2.44571i	−0.309774	−	0.178848i
$188$	5.14045			0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$	−4.44499	−	2.56632i	−0.321628	−	0.185692i	0.330490	−	0.943810i	$-0.392786\pi$
$191$	−4.44499	−	2.56632i	−0.321628	−	0.185692i	−0.652118	+	0.758117i	$0.726119\pi$
$192$		0			0
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	−0.996009	−	0.0892557i	$-0.971551\pi$
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	0.420707	−	0.907197i	$-0.361782\pi$
$194$	−15.3956			−1.10534
$195$		0			0
$196$	4.38163	−	5.45906i	0.312973	−	0.389933i
$197$		−	4.72572i		−	0.336694i	−0.985728	−	0.168347i	$-0.946157\pi$
$197$		−	4.72572i		−	0.336694i	0.985728	−	0.168347i	$-0.0538428\pi$
$198$		0			0
$199$	1.83679	+	1.06047i	0.130207	+	0.0751749i	0.563689	−	0.825987i	$-0.309382\pi$
$199$	1.83679	+	1.06047i	0.130207	+	0.0751749i	−0.433482	+	0.901162i	$0.642715\pi$
$200$			7.61848i			0.538708i
$201$		0			0
$202$	11.8686	+	6.85234i	0.835072	+	0.482129i
$203$	−0.863200	+	11.2805i	−0.0605848	+	0.791733i
$204$		0			0
$205$	−0.167747	+	0.290545i	−0.0117159	+	0.0202926i
$206$	1.52429	−	2.64014i	0.106202	−	0.183947i
$207$		0			0
$208$	−0.888944	+	0.513232i	−0.0616372	+	0.0355863i
$209$	−12.4354	−	21.5387i	−0.860173	−	1.48986i
$210$		0			0
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.206399	+	0.978468i	$0.566174\pi$
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.744179	+	0.667981i	$0.767159\pi$
$212$		−	3.18968i		−	0.219068i
$213$		0			0
$214$	−13.1267			−0.897324
$215$	−10.8663	−	18.8210i	−0.741076	−	1.28358i
$216$		0			0
$217$	−1.20833	+	15.7907i	−0.0820267	+	1.07194i
$218$	9.15516	−	5.28574i	0.620066	−	0.357995i
$219$		0			0
$220$	9.29783	−	5.36811i	0.626860	−	0.361918i
$221$	−1.43867	+	0.830619i	−0.0967757	+	0.0558735i
$222$		0			0
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.223973	−	0.974595i	$-0.428097\pi$
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.956011	+	0.293331i	$0.0947638\pi$
$224$	0.201867	−	2.63804i	0.0134878	−	0.176261i
$225$		0			0
$226$	−6.14993	−	10.6520i	−0.409087	−	0.708560i
$227$	4.16000			0.276109			0.138054	−	0.990425i	$-0.455915\pi$
$227$	4.16000			0.276109			0.138054	+	0.990425i	$0.455915\pi$
$228$		0			0
$229$			5.96964i			0.394485i	0.980355	+	0.197242i	$0.0631986\pi$
$229$			5.96964i			0.394485i	−0.980355	+	0.197242i	$0.936801\pi$
$230$	−5.96476	+	10.3313i	−0.393305	+	0.681224i
$231$		0			0
$232$	2.13804	+	3.70319i	0.140369	+	0.243126i
$233$	−3.88603	+	2.24360i	−0.254582	+	0.146983i	−0.621861	−	0.783128i	$-0.713623\pi$
$233$	−3.88603	+	2.24360i	−0.254582	+	0.146983i	0.367278	+	0.930111i	$0.380290\pi$
$234$		0			0
$235$	−9.13009	+	15.8138i	−0.595581	+	1.03158i
$236$	−4.42036	+	7.65628i	−0.287741	+	0.498381i
$237$		0			0
$238$	0.326704	−	4.26942i	0.0211771	−	0.276746i
$239$	3.02944	+	1.74905i	0.195958	+	0.113136i	0.594769	−	0.803897i	$-0.297244\pi$
$239$	3.02944	+	1.74905i	0.195958	+	0.113136i	−0.398811	+	0.917033i	$0.630577\pi$
$240$		0			0
$241$			11.5666i			0.745073i	0.928018	+	0.372537i	$0.121512\pi$
$241$			11.5666i			0.745073i	−0.928018	+	0.372537i	$0.878488\pi$
$242$	1.61538	+	0.932639i	0.103840	+	0.0599523i
$243$		0			0
$244$		−	4.69034i		−	0.300268i
$245$	9.01161	+	23.1753i	0.575731	+	1.48062i
$246$		0			0
$247$	−8.44666			−0.537448
$248$	2.99288	+	5.18382i	0.190048	+	0.329173i
$249$		0			0
$250$	−8.05532	−	4.65074i	−0.509463	−	0.294139i
$251$	26.7426			1.68798			0.843988	−	0.536361i	$-0.180202\pi$
$251$	26.7426			1.68798			0.843988	+	0.536361i	$0.180202\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$	0.248691	+	0.143582i	0.0156043	+	0.00900913i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.21227			−0.325133			−0.162566	−	0.986698i	$-0.551977\pi$
$257$	−5.21227			−0.325133			−0.162566	+	0.986698i	$0.551977\pi$
$258$		0			0
$259$	−15.4232	−	1.18021i	−0.958352	−	0.0733348i
$260$		−	3.64626i		−	0.226131i
$261$		0			0
$262$	−0.322983	−	0.186474i	−0.0199540	−	0.0115204i
$263$		−	15.0374i		−	0.927245i	−0.886033	−	0.463622i	$-0.846549\pi$
$263$		−	15.0374i		−	0.927245i	0.886033	−	0.463622i	$-0.153451\pi$
$264$		0			0
$265$	9.81255	+	5.66528i	0.602780	+	0.348015i
$266$	12.2927	−	17.9692i	0.753711	−	1.10176i
$267$		0			0
$268$	−0.187838	+	0.325345i	−0.0114740	+	0.0198736i
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	0.261460	+	0.965214i	$0.415796\pi$
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	−0.966630	+	0.256177i	$0.917537\pi$
$270$		0			0
$271$	8.58661	−	4.95748i	0.521599	−	0.301146i	−0.215989	−	0.976396i	$-0.569298\pi$
$271$	8.58661	−	4.95748i	0.521599	−	0.301146i	0.737589	+	0.675250i	$0.235964\pi$
$272$	−0.809204	−	1.40158i	−0.0490652	−	0.0849834i
$273$		0			0
$274$	−3.53111	+	6.11607i	−0.213322	+	0.369485i
$275$			23.0259i			1.38851i
$276$		0			0
$277$	−8.59443			−0.516389			−0.258195	−	0.966093i	$-0.583128\pi$
$277$	−8.59443			−0.516389			−0.258195	+	0.966093i	$0.583128\pi$
$278$	7.29308	+	12.6320i	0.437410	+	0.757616i
$279$		0			0
$280$	7.75696	+	5.30650i	0.463567	+	0.317124i
$281$	17.9508	−	10.3639i	1.07085	−	0.618258i	0.142440	−	0.989803i	$-0.454505\pi$
$281$	17.9508	−	10.3639i	1.07085	−	0.618258i	0.928415	+	0.371545i	$0.121172\pi$
$282$		0			0
$283$	−2.04997	+	1.18355i	−0.121858	+	0.0703547i	−0.559690	−	0.828702i	$-0.689080\pi$
$283$	−2.04997	+	1.18355i	−0.121858	+	0.0703547i	0.437832	+	0.899057i	$0.355746\pi$
$284$	−12.1129	+	6.99341i	−0.718771	+	0.414983i
$285$		0			0
$286$	−2.68672	+	1.55118i	−0.158869	+	0.0917231i
$287$	0.108064	+	0.225303i	0.00637882	+	0.0132992i
$288$		0			0
$289$	7.19038	+	12.4541i	0.422963	+	0.732594i
$290$	−15.1897			−0.891970
$291$		0			0
$292$			1.31111i			0.0767270i
$293$	8.83774	−	15.3074i	0.516306	−	0.894268i	−0.483515	−	0.875336i	$-0.660640\pi$
$293$	8.83774	−	15.3074i	0.516306	−	0.894268i	0.999821	−	0.0189321i	$-0.00602664\pi$
$294$		0			0
$295$	−15.7022	−	27.1970i	−0.914218	−	1.58347i
$296$	−5.06319	+	2.92323i	−0.294292	+	0.169910i
$297$		0			0
$298$	−5.35107	+	9.26832i	−0.309979	+	0.536899i
$299$	1.72359	−	2.98534i	0.0996777	−	0.172647i
$300$		0			0
$301$	−16.1395	−	1.23502i	−0.930265	−	0.0711855i
$302$	13.8575	+	8.00065i	0.797411	+	0.460386i
$303$		0			0
$304$		−	8.22889i		−	0.471959i
$305$	14.4291	+	8.33063i	0.826206	+	0.477011i
$306$		0			0
$307$			1.28155i			0.0731422i	0.999331	+	0.0365711i	$0.0116435\pi$
$307$			1.28155i			0.0731422i	−0.999331	+	0.0365711i	$0.988356\pi$
$308$	0.610118	−	7.97313i	0.0347647	−	0.454311i
$309$		0			0
$310$	−21.2629			−1.20765
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	0.631839	−	0.775100i	$-0.282300\pi$
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	−0.987175	+	0.159639i	$0.948967\pi$
$312$		0			0
$313$	7.58105	+	4.37692i	0.428507	+	0.247398i	0.698710	−	0.715405i	$-0.253758\pi$
$313$	7.58105	+	4.37692i	0.428507	+	0.247398i	−0.270204	+	0.962803i	$0.587091\pi$
$314$	−11.5267			−0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$	−11.8458	−	6.83920i	−0.665329	−	0.384128i	0.128976	−	0.991648i	$-0.458831\pi$
$317$	−11.8458	−	6.83920i	−0.665329	−	0.384128i	−0.794304	+	0.607520i	$0.792164\pi$
$318$		0			0
$319$	6.46195	+	11.1924i	0.361799	+	0.626655i
$320$	3.55225			0.198577
$321$		0			0
$322$	3.84256	+	8.01137i	0.214137	+	0.446456i
$323$		−	13.3177i		−	0.741017i
$324$		0			0
$325$	6.77240	+	3.91005i	0.375665	+	0.216890i
$326$			2.74773i			0.152182i
$327$		0			0
$328$	0.0817920	+	0.0472226i	0.00451621	+	0.00260743i
$329$	5.88169	+	12.2628i	0.324268	+	0.676068i
$330$		0			0
$331$	5.44858	−	9.43721i	0.299481	−	0.518716i	−0.676536	−	0.736409i	$-0.736520\pi$
$331$	5.44858	−	9.43721i	0.299481	−	0.518716i	0.976017	+	0.217693i	$0.0698532\pi$
$332$	−5.43209	+	9.40866i	−0.298125	+	0.516367i
$333$		0			0
$334$	−4.79685	+	2.76946i	−0.262472	+	0.151538i
$335$	−0.667247	−	1.15570i	−0.0364556	−	0.0631429i
$336$		0			0
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$		−	11.9464i		−	0.649797i
$339$		0			0
$340$	5.74899			0.311783
$341$	9.04559	+	15.6674i	0.489846	+	0.848438i
$342$		0			0
$343$	18.0363	+	4.20631i	0.973867	+	0.227119i
$344$	−5.29833	+	3.05899i	−0.285667	+	0.164930i
$345$		0			0
$346$	−9.70387	+	5.60253i	−0.521683	+	0.301194i
$347$	−14.5166	+	8.38116i	−0.779291	+	0.449924i	−0.836179	−	0.548457i	$-0.815216\pi$
$347$	−14.5166	+	8.38116i	−0.779291	+	0.449924i	0.0568878	+	0.998381i	$0.481882\pi$
$348$		0			0
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	−0.834032	−	0.551716i	$-0.813973\pi$
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	0.0607835	+	0.998151i	$0.480640\pi$
$350$	−18.1742	+	8.71704i	−0.971452	+	0.465945i
$351$		0			0
$352$	−1.51119	−	2.61745i	−0.0805464	−	0.139511i
$353$	35.9137			1.91149			0.955746	−	0.294195i	$-0.0950514\pi$
$353$	35.9137			1.91149			0.955746	+	0.294195i	$0.0950514\pi$
$354$		0			0
$355$		−	49.6847i		−	2.63699i
$356$	2.35495	−	4.07888i	0.124812	−	0.216180i
$357$		0			0
$358$	−1.37089	−	2.37445i	−0.0724538	−	0.125494i
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.323681	−	0.946166i	$-0.395079\pi$
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.981245	+	0.192767i	$0.0617461\pi$
$360$		0			0
$361$	24.3573	−	42.1881i	1.28196	−	2.22043i
$362$	11.1449	−	19.3036i	0.585765	−	1.01457i
$363$		0			0
$364$	−2.24146	−	1.53338i	−0.117485	−	0.0803707i
$365$	−4.03342	−	2.32870i	−0.211119	−	0.121890i
$366$		0			0
$367$			0.358725i			0.0187253i	0.999956	+	0.00936264i	$0.00298026\pi$
$367$			0.358725i			0.0187253i	−0.999956	+	0.00936264i	$0.997020\pi$
$368$	2.90837	+	1.67915i	0.151609	+	0.0875317i
$369$		0			0
$370$		−	20.7681i		−	1.07968i
$371$	7.60913	−	3.64963i	0.395046	−	0.189479i
$372$		0			0
$373$	25.3708			1.31365			0.656826	−	0.754042i	$-0.271898\pi$
$373$	25.3708			1.31365			0.656826	+	0.754042i	$0.271898\pi$
$374$	−2.44571	−	4.23610i	−0.126465	−	0.219044i
$375$		0			0
$376$	4.45176	+	2.57023i	0.229582	+	0.132549i
$377$	4.38924			0.226057
$378$		0			0
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$	25.3148	+	14.6155i	1.29862	+	0.749761i
$381$		0			0
$382$	−2.56632	−	4.44499i	−0.131304	−	0.227426i
$383$	12.5717			0.642385			0.321192	−	0.947014i	$-0.395916\pi$
$383$	12.5717			0.642385			0.321192	+	0.947014i	$0.395916\pi$
$384$		0			0
$385$	23.4444	+	16.0382i	1.19484	+	0.817382i
$386$		−	15.9847i		−	0.813600i
$387$		0			0
$388$	−13.3330	−	7.69782i	−0.676881	−	0.390798i
$389$		−	16.2587i		−	0.824351i	−0.911105	−	0.412175i	$-0.864769\pi$
$389$		−	16.2587i		−	0.824351i	0.911105	−	0.412175i	$-0.135231\pi$
$390$		0			0
$391$	4.70694	+	2.71755i	0.238040	+	0.137432i
$392$	6.52413	−	2.53687i	0.329518	−	0.128131i
$393$		0			0
$394$	2.36286	−	4.09259i	0.119039	−	0.206182i
$395$	1.64138	−	2.84295i	0.0825866	−	0.143044i
$396$		0			0
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	−0.784099	−	0.620636i	$-0.786875\pi$
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	0.145437	+	0.989368i	$0.453541\pi$
$398$	1.06047	+	1.83679i	0.0531567	+	0.0920701i
$399$		0			0
$400$	−3.80924	+	6.59779i	−0.190462	+	0.329890i
$401$		−	16.6464i		−	0.831280i	−0.909529	−	0.415640i	$-0.863558\pi$
$401$		−	16.6464i		−	0.831280i	0.909529	−	0.415640i	$-0.136442\pi$
$402$		0			0
$403$	6.14417			0.306063
$404$	6.85234	+	11.8686i	0.340917	+	0.590485i
$405$		0			0
$406$	−6.38778	+	9.33756i	−0.317020	+	0.463416i
$407$	−15.3028	+	8.83510i	−0.758534	+	0.437940i
$408$		0			0
$409$	−2.43254	+	1.40443i	−0.120282	+	0.0694446i	−0.558934	−	0.829212i	$-0.688789\pi$
$409$	−2.43254	+	1.40443i	−0.120282	+	0.0694446i	0.438652	+	0.898657i	$0.355456\pi$
$410$	−0.290545	+	0.167747i	−0.0143490	+	0.00828441i
$411$		0			0
$412$	2.64014	−	1.52429i	0.130070	−	0.0750962i
$413$	−23.3221	−	1.78465i	−1.14761	−	0.0878169i
$414$		0			0
$415$	−19.2962	−	33.4219i	−0.947211	−	1.64062i
$416$	−1.02646			−0.0503266
$417$		0			0
$418$		−	24.8707i		−	1.21647i
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	−0.623684	−	0.781677i	$-0.714365\pi$
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	0.988794	+	0.149287i	$0.0476980\pi$
$420$		0			0
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$	−23.9160	+	13.8079i	−1.16421	+	0.672160i
$423$		0			0
$424$	1.59484	−	2.76235i	0.0774524	−	0.134151i
$425$	−6.16490	+	10.6779i	−0.299042	+	0.517955i
$426$		0			0
$427$	11.1890	−	5.36668i	0.541474	−	0.259712i
$428$	−11.3681	−	6.56336i	−0.549496	−	0.317252i
$429$		0			0
$430$		−	21.7326i		−	1.04804i
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	0.123109	−	0.992393i	$-0.460714\pi$
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	−0.797883	+	0.602812i	$0.794047\pi$
$432$		0			0
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$	−8.94178	+	13.0710i	−0.429219	+	0.627426i
$435$		0			0
$436$	10.5715			0.506282
$437$	13.8175	+	23.9327i	0.660983	+	1.14486i
$438$		0			0
$439$	28.6955	+	16.5674i	1.36956	+	0.790717i	0.990872	−	0.134806i	$-0.0430412\pi$
$439$	28.6955	+	16.5674i	1.36956	+	0.790717i	0.378690	+	0.925523i	$0.376375\pi$
$440$	10.7362			0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$	−19.2808	−	11.1318i	−0.916060	−	0.528887i	−0.0336837	−	0.999433i	$-0.510724\pi$
$443$	−19.2808	−	11.1318i	−0.916060	−	0.528887i	−0.882376	+	0.470545i	$0.844057\pi$
$444$		0			0
$445$	8.36535	+	14.4892i	0.396556	+	0.686855i
$446$	20.3469			0.963453
$447$		0			0
$448$	1.49384	−	2.18368i	0.0705774	−	0.103169i
$449$			6.80819i			0.321298i	0.987012	+	0.160649i	$0.0513588\pi$
$449$			6.80819i			0.321298i	−0.987012	+	0.160649i	$0.948641\pi$
$450$		0			0
$451$	0.247206	+	0.142724i	0.0116405	+	0.00672062i
$452$		−	12.2999i		−	0.578537i
$453$		0			0
$454$	3.60266	+	2.08000i	0.169081	+	0.0976192i
$455$	8.69830	−	4.17204i	0.407783	−	0.195588i
$456$		0			0
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	−0.987309	−	0.158811i	$-0.949234\pi$
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	0.631189	+	0.775629i	$0.282567\pi$
$458$	−2.98482	+	5.16986i	−0.139471	+	0.241572i
$459$		0			0
$460$	−10.3313	+	5.96476i	−0.481698	+	0.278108i
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	0.868423	−	0.495824i	$-0.165134\pi$
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	−0.863608	+	0.504164i	$0.831801\pi$
$462$		0			0
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	−0.986826	−	0.161785i	$-0.948275\pi$
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	0.633523	+	0.773724i	$0.281608\pi$
$464$			4.27608i			0.198512i
$465$		0			0
$466$	−4.48720			−0.207865
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	0.891495	−	0.453030i	$-0.149657\pi$
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	−0.838083	+	0.545542i	$0.816324\pi$
$468$		0			0
$469$	−0.991047	−	0.0758366i	−0.0457623	−	0.00350181i
$470$	−15.8138	+	9.13009i	−0.729435	+	0.421139i
$471$		0			0
$472$	−7.65628	+	4.42036i	−0.352409	+	0.203463i
$473$	−16.0135	+	9.24541i	−0.736303	+	0.425105i
$474$		0			0
$475$	−54.2925	+	31.3458i	−2.49111	+	1.43824i
$476$	2.41765	−	3.53408i	0.110813	−	0.161984i
$477$		0			0
$478$	1.74905	+	3.02944i	0.0799996	+	0.138563i
$479$	−12.4332			−0.568086			−0.284043	−	0.958812i	$-0.591676\pi$
$479$	−12.4332			−0.568086			−0.284043	+	0.958812i	$0.591676\pi$
$480$		0			0
$481$			6.00119i			0.273631i
$482$	−5.78332	+	10.0170i	−0.263423	+	0.456262i
$483$		0			0
$484$	0.932639	+	1.61538i	0.0423927	+	0.0734263i
$485$	47.3622	−	27.3446i	2.15061	−	1.24165i
$486$		0			0
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	0.0403829	+	0.999184i	$0.487142\pi$
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	−0.885510	+	0.464620i	$0.846191\pi$
$488$	2.34517	−	4.06195i	0.106161	−	0.183876i
$489$		0			0
$490$	−3.78339	+	24.5762i	−0.170916	+	1.11024i
$491$	11.8191	+	6.82377i	0.533389	+	0.307952i	0.742396	−	0.669962i	$-0.233690\pi$
$491$	11.8191	+	6.82377i	0.533389	+	0.307952i	−0.209006	+	0.977914i	$0.567023\pi$
$492$		0			0
$493$			6.92044i			0.311681i
$494$	−7.31502	−	4.22333i	−0.329118	−	0.190017i
$495$		0			0
$496$			5.98576i			0.268768i
$497$	−30.5427	−	20.8941i	−1.37003	−	0.937229i
$498$		0			0
$499$	−21.0019			−0.940175			−0.470088	−	0.882620i	$-0.655778\pi$
$499$	−21.0019			−0.940175			−0.470088	+	0.882620i	$0.655778\pi$
$500$	−4.65074	−	8.05532i	−0.207987	−	0.360245i
$501$		0			0
$502$	23.1598	+	13.3713i	1.03367	+	0.596790i
$503$	−22.3018			−0.994388			−0.497194	−	0.867639i	$-0.665636\pi$
$503$	−22.3018			−0.994388			−0.497194	+	0.867639i	$0.665636\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$	8.79018	+	5.07501i	0.390771	+	0.225612i
$507$		0			0
$508$	0.143582	+	0.248691i	0.00637042	+	0.0110339i
$509$	21.9179			0.971493			0.485746	−	0.874100i	$-0.338548\pi$
$509$	21.9179			0.971493			0.485746	+	0.874100i	$0.338548\pi$
$510$		0			0
$511$	−3.12771	+	1.50017i	−0.138362	+	0.0663636i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.51396	−	2.60614i	−0.199102	−	0.114952i
$515$			10.8293i			0.477196i
$516$		0			0
$517$	13.4549	+	7.76818i	0.591745	+	0.341644i
$518$	−12.7668	−	8.73370i	−0.560941	−	0.383737i
$519$		0			0
$520$	1.82313	−	3.15775i	0.0799495	−	0.138477i
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	−0.408346	−	0.912827i	$-0.633894\pi$
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	0.994705	−	0.102775i	$-0.0327723\pi$
$522$		0			0
$523$	14.8576	−	8.57805i	0.649678	−	0.375092i	−0.138655	−	0.990341i	$-0.544278\pi$
$523$	14.8576	−	8.57805i	0.649678	−	0.375092i	0.788333	+	0.615249i	$0.210945\pi$
$524$	−0.186474	−	0.322983i	−0.00814617	−	0.0141096i
$525$		0			0
$526$	7.51869	−	13.0228i	0.327831	−	0.567819i
$527$			9.68740i			0.421990i
$528$		0			0
$529$	11.7218			0.509644
$530$	5.66528	+	9.81255i	0.246084	+	0.426230i
$531$		0			0
$532$	19.6304	−	9.41547i	0.851084	−	0.408212i
$533$	0.0839566	−	0.0484723i	0.00363656	−	0.00209957i
$534$		0			0
$535$	40.3822	−	23.3147i	1.74588	−	1.00798i
$536$	−0.325345	+	0.187838i	−0.0140527	+	0.00811336i
$537$		0			0
$538$	−20.0323	+	11.5657i	−0.863654	+	0.498631i
$539$	19.7183	−	7.66737i	0.849329	−	0.330257i
$540$		0			0
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	−0.989578	−	0.144000i	$-0.954004\pi$
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	0.370081	−	0.928999i	$-0.379330\pi$
$542$	9.91496			0.425884
$543$		0			0
$544$		−	1.61841i		−	0.0693887i
$545$	−18.7763	+	32.5214i	−0.804286	+	1.39306i
$546$		0			0
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	−0.967972	−	0.251056i	$-0.919222\pi$
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	0.266565	−	0.963817i	$-0.414111\pi$
$548$	−6.11607	+	3.53111i	−0.261265	+	0.150842i
$549$		0			0
$550$	−11.5129	+	19.9410i	−0.490913	+	0.850286i
$551$	−17.5937	+	30.4732i	−0.749516	+	1.29820i
$552$		0			0
$553$	−1.05739	−	2.20456i	−0.0449649	−	0.0937475i
$554$	−7.44299	−	4.29721i	−0.316223	−	0.182571i
$555$		0			0
$556$			14.5862i			0.618591i
$557$	−40.0544	−	23.1254i	−1.69716	−	0.979855i	−0.948434	−	0.316975i	$-0.897333\pi$
$557$	−40.0544	−	23.1254i	−1.69716	−	0.979855i	−0.748725	−	0.662880i	$-0.769334\pi$
$558$		0			0
$559$			6.27990i			0.265611i
$560$	4.06447	+	8.47404i	0.171755	+	0.358094i
$561$		0			0
$562$	20.7278			0.874349
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	0.844440	−	0.535650i	$-0.179933\pi$
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	−0.886106	+	0.463482i	$0.846600\pi$
$564$		0			0
$565$	37.8385	+	21.8461i	1.59188	+	0.919071i
$566$	−2.36710			−0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$	28.5702	+	16.4950i	1.19773	+	0.691508i	0.960048	−	0.279836i	$-0.0902800\pi$
$569$	28.5702	+	16.4950i	1.19773	+	0.691508i	0.237679	+	0.971344i	$0.423613\pi$
$570$		0			0
$571$	−7.40326	−	12.8228i	−0.309817	−	0.536618i	0.668505	−	0.743707i	$-0.266934\pi$
$571$	−7.40326	−	12.8228i	−0.309817	−	0.536618i	−0.978322	+	0.207089i	$0.933601\pi$
$572$	−3.10236			−0.129716
$573$		0			0
$574$	−0.0190654	+	0.249150i	−0.000795775	+	0.0103993i
$575$		−	25.5851i		−	1.06697i
$576$		0			0
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	0.129783	−	0.991542i	$-0.458572\pi$
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	−0.793810	+	0.608166i	$0.791905\pi$
$578$			14.3808i			0.598161i
$579$		0			0
$580$	−13.1547	−	7.59485i	−0.546218	−	0.315359i
$581$	−28.6602	−	2.19312i	−1.18902	−	0.0909861i
$582$		0			0
$583$	4.82020	−	8.34884i	0.199632	−	0.345774i
$584$	−0.655556	+	1.13546i	−0.0271271	+	0.0469855i
$585$		0			0
$586$	15.3074	−	8.83774i	0.632343	−	0.365084i
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.737301	+	0.675565i	$0.236100\pi$
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.216406	+	0.976304i	$0.430567\pi$
$588$		0			0
$589$	−24.6281	+	42.6571i	−1.01478	+	1.75765i
$590$		−	31.4044i		−	1.29290i
$591$		0			0
$592$	−5.84647			−0.240288
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	0.971244	−	0.238086i	$-0.0765200\pi$
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	−0.691810	+	0.722079i	$0.743187\pi$
$594$		0			0
$595$	6.57798	+	13.7145i	0.269671	+	0.562238i
$596$	−9.26832	+	5.35107i	−0.379645	+	0.219188i
$597$		0			0
$598$	2.98534	−	1.72359i	0.122080	−	0.0704827i
$599$	−20.4214	+	11.7903i	−0.834396	+	0.481739i	−0.855355	−	0.518042i	$-0.826661\pi$
$599$	−20.4214	+	11.7903i	−0.834396	+	0.481739i	0.0209595	+	0.999780i	$0.493328\pi$
$600$		0			0
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.293097	−	0.956083i	$-0.405314\pi$
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.974540	+	0.224212i	$0.0719808\pi$
$602$	−13.3597	−	9.13931i	−0.544501	−	0.372490i
$603$		0			0
$604$	8.00065	+	13.8575i	0.325542	+	0.563855i
$605$	−6.62594			−0.269383
$606$		0			0
$607$			19.4569i			0.789732i	0.918739	+	0.394866i	$0.129209\pi$
$607$			19.4569i			0.789732i	−0.918739	+	0.394866i	$0.870791\pi$
$608$	4.11444	−	7.12643i	0.166863	−	0.289015i
$609$		0			0
$610$	8.33063	+	14.4291i	0.337297	+	0.584216i
$611$	4.56958	−	2.63825i	0.184865	−	0.106732i
$612$		0			0
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	0.0253526	+	0.999679i	$0.491929\pi$
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	−0.878423	+	0.477883i	$0.841404\pi$
$614$	−0.640777	+	1.10986i	−0.0258597	+	0.0447902i
$615$		0			0
$616$	4.51494	−	6.59987i	0.181912	−	0.265917i
$617$	−9.63660	−	5.56369i	−0.387955	−	0.223986i	0.293319	−	0.956015i	$-0.405240\pi$
$617$	−9.63660	−	5.56369i	−0.387955	−	0.223986i	−0.681274	+	0.732029i	$0.738574\pi$
$618$		0			0
$619$			10.0619i			0.404422i	0.979342	+	0.202211i	$0.0648127\pi$
$619$			10.0619i			0.404422i	−0.979342	+	0.202211i	$0.935187\pi$
$620$	−18.4142	−	10.6315i	−0.739533	−	0.426969i
$621$		0			0
$622$		−	12.5329i		−	0.502522i
$623$	12.4249	+	0.950773i	0.497792	+	0.0380919i
$624$		0			0
$625$	−5.05121			−0.202048
$626$	4.37692	+	7.58105i	0.174937	+	0.303000i
$627$		0			0
$628$	−9.98239	−	5.76334i	−0.398341	−	0.229982i
$629$	−9.46198			−0.377274
$630$		0			0
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$	−0.800324	−	0.462067i	−0.0318352	−	0.0183800i
$633$		0			0
$634$	−6.83920	−	11.8458i	−0.271619	−	0.470459i
$635$	−1.02008			−0.0404806
$636$		0			0
$637$	1.09325	−	7.10159i	0.0433163	−	0.281375i
$638$			12.9239i			0.511662i
$639$		0			0
$640$	3.07634	+	1.77612i	0.121603	+	0.0702075i
$641$		−	26.6364i		−	1.05207i	−0.850461	−	0.526037i	$-0.823677\pi$
$641$		−	26.6364i		−	1.05207i	0.850461	−	0.526037i	$-0.176323\pi$
$642$		0			0
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.994944	−	0.100429i	$-0.967979\pi$
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.584446	−	0.811433i	$-0.698688\pi$
$644$	−0.677931	+	8.85933i	−0.0267142	+	0.349106i
$645$		0			0
$646$	6.65885	−	11.5335i	0.261989	−	0.453778i
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	0.372611	+	0.927988i	$0.378463\pi$
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	−0.989966	+	0.141303i	$0.954871\pi$
$648$		0			0
$649$	−23.1401	+	13.3600i	−0.908329	+	0.524424i
$650$	3.91005	+	6.77240i	0.153365	+	0.265635i
$651$		0			0
$652$	−1.37386	+	2.37960i	−0.0538046	+	0.0931923i
$653$		−	46.1464i		−	1.80585i	−0.429801	−	0.902924i	$-0.641416\pi$
$653$		−	46.1464i		−	1.80585i	0.429801	−	0.902924i	$-0.358584\pi$
$654$		0			0
$655$	1.32481			0.0517645
$656$	0.0472226	+	0.0817920i	0.00184373	+	0.00319344i
$657$		0			0
$658$	−1.03769	+	13.5607i	−0.0404534	+	0.528652i
$659$	−1.18052	+	0.681575i	−0.0459867	+	0.0265504i	−0.522817	−	0.852445i	$-0.675119\pi$
$659$	−1.18052	+	0.681575i	−0.0459867	+	0.0265504i	0.476830	+	0.878995i	$0.341786\pi$
$660$		0			0
$661$	6.23888	−	3.60202i	0.242664	−	0.140102i	−0.373736	−	0.927535i	$-0.621924\pi$
$661$	6.23888	−	3.60202i	0.242664	−	0.140102i	0.616401	+	0.787433i	$0.288590\pi$
$662$	9.43721	−	5.44858i	0.366788	−	0.211765i
$663$		0			0
$664$	−9.40866	+	5.43209i	−0.365127	+	0.210806i
$665$	−5.90080	+	77.1127i	−0.228823	+	2.99030i
$666$		0			0
$667$	−7.18018	−	12.4364i	−0.278018	−	0.481541i
$668$	−5.53892			−0.214307
$669$		0			0
$670$		−	1.33449i		−	0.0515560i
$671$	7.08797	−	12.2767i	0.273628	−	0.473938i
$672$		0			0
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$	22.1858	−	12.8090i	0.854565	−	0.493383i
$675$		0			0
$676$	5.97319	−	10.3459i	0.229738	−	0.397918i
$677$	−1.20505	+	2.08722i	−0.0463140	+	0.0802182i	−0.888253	−	0.459354i	$-0.848081\pi$
$677$	−1.20505	+	2.08722i	−0.0463140	+	0.0802182i	0.841939	+	0.539573i	$0.181414\pi$
$678$		0			0
$679$	3.10788	−	40.6143i	0.119269	−	1.55863i
$680$	4.97877	+	2.87450i	0.190927	+	0.110232i
$681$		0			0
$682$			18.0912i			0.692747i
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.889529	−	0.456879i	$-0.151033\pi$
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.0490952	+	0.998794i	$0.484366\pi$
$684$		0			0
$685$		−	25.0868i		−	0.958517i
$686$	13.5167	+	12.6609i	0.516070	+	0.483396i
$687$		0			0
$688$	−6.11799			−0.233246
$689$	−1.63705	−	2.83545i	−0.0623666	−	0.108022i
$690$		0			0
$691$	−2.95334	−	1.70511i	−0.112350	−	0.0648655i	0.442772	−	0.896634i	$-0.353995\pi$
$691$	−2.95334	−	1.70511i	−0.112350	−	0.0648655i	−0.555122	+	0.831769i	$0.687328\pi$
$692$	−11.2051			−0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$	−44.8719	−	25.9068i	−1.70209	−	0.982702i
$696$		0			0
$697$	0.0764255	+	0.132373i	0.00289482	+	0.00501398i
$698$	−16.6802			−0.631355
$699$		0			0
$700$	−20.0978	−	1.53792i	−0.759627	−	0.0581280i
$701$			51.4943i			1.94491i	0.233087	+	0.972456i	$0.425117\pi$
$701$			51.4943i			1.94491i	−0.233087	+	0.972456i	$0.574883\pi$
$702$		0			0
$703$	−41.6644	−	24.0550i	−1.57140	−	0.907251i
$704$		−	3.02237i		−	0.113910i
$705$		0			0
$706$	31.1021	+	17.9568i	1.17054	+	0.675814i
$707$	−20.4726	+	29.9266i	−0.769952	+	1.12550i
$708$		0			0
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	−0.945038	−	0.326960i	$-0.893976\pi$
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	0.755675	+	0.654947i	$0.227309\pi$
$710$	24.8424	−	43.0282i	0.932317	−	1.61482i
$711$		0			0
$712$	4.07888	−	2.35495i	0.152863	−	0.0882553i
$713$	−10.0510	−	17.4088i	−0.376412	−	0.651965i
$714$		0			0
$715$	5.51017	−	9.54389i	0.206069	−	0.356921i
$716$		−	2.74178i		−	0.102465i
$717$		0			0
$718$	28.5498			1.06547
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	−0.993526	−	0.113605i	$-0.963760\pi$
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	0.398378	−	0.917221i	$-0.369573\pi$
$720$		0			0
$721$	6.65709	+	4.55409i	0.247923	+	0.169603i
$722$	42.1881	−	24.3573i	1.57008	−	0.906485i
$723$		0			0
$724$	19.3036	−	11.1449i	0.717413	−	0.414198i
$725$	28.2127	−	16.2886i	1.04779	−	0.604943i
$726$		0			0
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	−0.129105	−	0.991631i	$-0.541210\pi$
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	0.794225	+	0.607624i	$0.207877\pi$
$728$	−1.17448	−	2.44867i	−0.0435290	−	0.0907539i
$729$		0			0
$730$	−2.32870	−	4.03342i	−0.0861889	−	0.149284i
$731$	−9.90141			−0.366217
$732$		0			0
$733$		−	8.89115i		−	0.328402i	−0.986427	−	0.164201i	$-0.947495\pi$
$733$		−	8.89115i		−	0.328402i	0.986427	−	0.164201i	$-0.0525046\pi$
$734$	−0.179362	+	0.310665i	−0.00662038	+	0.0114668i
$735$		0			0
$736$	1.67915	+	2.90837i	0.0618943	+	0.107204i
$737$	−0.983312	+	0.567715i	−0.0362207	+	0.0209121i
$738$		0			0
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	0.389539	+	0.921010i	$0.372634\pi$
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	−0.992388	+	0.123154i	$0.960699\pi$
$740$	10.3841	−	17.9857i	0.381726	−	0.661168i
$741$		0			0
$742$	8.41451	+	0.643893i	0.308906	+	0.0236381i
$743$	6.68055	+	3.85702i	0.245086	+	0.141500i	0.617512	−	0.786562i	$-0.288141\pi$
$743$	6.68055	+	3.85702i	0.245086	+	0.141500i	−0.372426	+	0.928062i	$0.621474\pi$
$744$		0			0
$745$		−	38.0166i		−	1.39282i
$746$	21.9718	+	12.6854i	0.804445	+	0.464446i
$747$		0			0
$748$		−	4.89143i		−	0.178848i
$749$	2.64986	−	34.6288i	0.0968236	−	1.26531i
$750$		0			0
$751$	30.7608			1.12248			0.561239	−	0.827654i	$-0.310325\pi$
$751$	30.7608			1.12248			0.561239	+	0.827654i	$0.310325\pi$
$752$	2.57023	+	4.45176i	0.0937265	+	0.162339i
$753$		0			0
$754$	3.80120	+	2.19462i	0.138431	+	0.0799234i
$755$	−56.8406			−2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$	23.3016	+	13.4532i	0.846351	+	0.488641i
$759$		0			0
$760$	14.6155	+	25.3148i	0.530161	+	0.918266i
$761$	37.1917			1.34820			0.674099	−	0.738641i	$-0.264532\pi$
$761$	37.1917			1.34820			0.674099	+	0.738641i	$0.264532\pi$
$762$		0			0
$763$	12.0958	+	25.2187i	0.437899	+	0.912978i
$764$		−	5.13264i		−	0.185692i
$765$		0			0
$766$	10.8874	+	6.28586i	0.393379	+	0.227117i
$767$			9.07468i			0.327668i
$768$		0			0
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	0.704050	−	0.710150i	$-0.251373\pi$
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	−0.262983	+	0.964800i	$0.584706\pi$
$770$	12.2843	+	25.6117i	0.442697	+	0.922981i
$771$		0			0
$772$	7.99235	−	13.8432i	0.287651	−	0.498226i
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	−0.441267	−	0.897376i	$-0.645471\pi$
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	0.997784	−	0.0665393i	$-0.0211958\pi$
$774$		0			0
$775$	39.4928	−	22.8012i	1.41862	−	0.819043i
$776$	−7.69782	−	13.3330i	−0.276336	−	0.478627i
$777$		0			0
$778$	8.12937	−	14.0805i	0.291452	−	0.504810i
$779$			0.777179i			0.0278453i
$780$		0			0
$781$	−42.2734			−1.51266
$782$	2.71755	+	4.70694i	0.0971794	+	0.168320i
$783$		0			0
$784$	6.91850	+	1.06507i	0.247089	+	0.0380381i
$785$	35.4599	−	20.4728i	1.26562	−	0.730706i
$786$		0			0
$787$	−15.8704	+	9.16280i	−0.565720	+	0.326619i	−0.755438	−	0.655220i	$-0.772576\pi$
$787$	−15.8704	+	9.16280i	−0.565720	+	0.326619i	0.189718	+	0.981839i	$0.439243\pi$
$788$	4.09259	−	2.36286i	0.145793	−	0.0841734i
$789$		0			0
$790$	2.84295	−	1.64138i	0.101148	−	0.0583976i
$791$	29.3418	−	14.0735i	1.04328	−	0.500395i
$792$		0			0
$793$	−2.40723	−	4.16945i	−0.0854834	−	0.148062i
$794$	−14.6938			−0.521465
$795$		0			0
$796$			2.12095i			0.0751749i
$797$	−1.07681	+	1.86508i	−0.0381424	+	0.0660646i	−0.884466	−	0.466604i	$-0.845477\pi$
$797$	−1.07681	+	1.86508i	−0.0381424	+	0.0660646i	0.846324	+	0.532668i	$0.178811\pi$
$798$		0			0
$799$	4.15968	+	7.20477i	0.147159	+	0.254886i
$800$	−6.59779	+	3.80924i	−0.233267	+	0.134677i
$801$		0			0
$802$	8.32318	−	14.4162i	0.293902	−	0.509053i
$803$	−1.98133	+	3.43177i	−0.0699197	+	0.121104i
$804$		0			0
$805$	−26.0502	−	17.8208i	−0.918149	−	0.628101i
$806$	5.32101	+	3.07208i	0.187424	+	0.108210i
$807$		0			0
$808$			13.7047i			0.482129i
$809$	17.0147	+	9.82342i	0.598204	+	0.345373i	0.768335	−	0.640048i	$-0.221086\pi$
$809$	17.0147	+	9.82342i	0.598204	+	0.345373i	−0.170131	+	0.985421i	$0.554419\pi$
$810$		0			0
$811$		−	12.3340i		−	0.433105i	−0.976271	−	0.216552i	$-0.930519\pi$
$811$		−	12.3340i		−	0.433105i	0.976271	−	0.216552i	$-0.0694812\pi$
$812$	−10.2008	+	4.89268i	−0.357977	+	0.171699i
$813$		0			0
$814$	−17.6702			−0.619340
$815$	−4.88030	−	8.45293i	−0.170950	−	0.296093i
$816$		0			0
$817$	−43.5994	−	25.1721i	−1.52535	−	0.880661i
$818$	−2.80886			−0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$	19.3763	+	11.1869i	0.676238	+	0.390426i	0.798436	−	0.602079i	$-0.205661\pi$
$821$	19.3763	+	11.1869i	0.676238	+	0.390426i	−0.122198	+	0.992506i	$0.538994\pi$
$822$		0			0
$823$	−13.5033	−	23.3883i	−0.470694	−	0.815266i	0.528744	−	0.848781i	$-0.322663\pi$
$823$	−13.5033	−	23.3883i	−0.470694	−	0.815266i	−0.999438	+	0.0335154i	$0.989330\pi$
$824$	3.04857			0.106202
$825$		0			0
$826$	−19.3052	−	13.2066i	−0.671715	−	0.459517i
$827$		−	26.3189i		−	0.915196i	−0.889159	−	0.457598i	$-0.848710\pi$
$827$		−	26.3189i		−	0.915196i	0.889159	−	0.457598i	$-0.151290\pi$
$828$		0			0
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.909035	−	0.416719i	$-0.136820\pi$
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.0936287	+	0.995607i	$0.470153\pi$
$830$		−	38.5923i		−	1.33956i
$831$		0			0
$832$	−0.888944	−	0.513232i	−0.0308186	−	0.0177931i
$833$	11.1970	+	1.72371i	0.387952	+	0.0597232i
$834$		0			0
$835$	9.83781	−	17.0396i	0.340452	−	0.589679i
$836$	12.4354	−	21.5387i	0.430086	−	0.744932i
$837$		0			0
$838$	12.9447	−	7.47362i	0.447167	−	0.258172i
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	−0.984247	−	0.176799i	$-0.943426\pi$
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	0.339011	−	0.940782i	$-0.389908\pi$
$840$		0			0
$841$	−5.35758	+	9.27960i	−0.184744	+	0.319986i
$842$		−	15.6067i		−	0.537843i
$843$		0			0
$844$	−27.6159			−0.950578
$845$	21.2182	+	36.7511i	0.729930	+	1.26428i
$846$		0			0
$847$	−2.78643	+	4.07316i	−0.0957429	+	0.139956i
$848$	2.76235	−	1.59484i	0.0948594	−	0.0547671i
$849$		0			0
$850$	−10.6779	+	6.16490i	−0.366250	+	0.211454i
$851$	17.0037	−	9.81710i	0.582880	−	0.336526i
$852$		0			0
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	−0.418133	−	0.908386i	$-0.637315\pi$
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	0.577619	+	0.816306i	$0.303982\pi$
$854$	12.3733	+	0.946827i	0.423406	+	0.0323997i
$855$		0			0
$856$	−6.56336	−	11.3681i	−0.224331	−	0.388553i
$857$	−45.4000			−1.55084			−0.775418	−	0.631448i	$-0.782461\pi$
$857$	−45.4000			−1.55084			−0.775418	+	0.631448i	$0.782461\pi$
$858$		0			0
$859$		−	3.88281i		−	0.132480i	−0.997804	−	0.0662399i	$-0.978900\pi$
$859$		−	3.88281i		−	0.132480i	0.997804	−	0.0662399i	$-0.0211003\pi$
$860$	10.8663	−	18.8210i	0.370538	−	0.641791i
$861$		0			0
$862$	−8.08792	−	14.0087i	−0.275476	−	0.477138i
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	−0.804418	−	0.594064i	$-0.797522\pi$
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	0.112266	+	0.993678i	$0.464189\pi$
$864$		0			0
$865$	19.9016	−	34.4706i	0.676674	−	1.17203i
$866$	−13.6250	+	23.5991i	−0.462995	+	0.801931i
$867$		0			0
$868$	−14.2793	+	6.84889i	−0.484670	+	0.232466i
$869$	−2.41887	−	1.39654i	−0.0820547	−	0.0473743i
$870$		0			0
$871$			0.385618i			0.0130662i
$872$	9.15516	+	5.28574i	0.310033	+	0.178998i
$873$		0			0
$874$			27.6351i			0.934770i
$875$	13.8949	−	20.3114i	0.469735	−	0.686651i
$876$		0			0
$877$	32.9591			1.11295			0.556475	−	0.830864i	$-0.312153\pi$
$877$	32.9591			1.11295			0.556475	+	0.830864i	$0.312153\pi$
$878$	16.5674	+	28.6955i	0.559121	+	0.968427i
$879$		0			0
$880$	9.29783	+	5.36811i	0.313430	+	0.180959i
$881$	7.44403			0.250796			0.125398	−	0.992107i	$-0.459979\pi$
$881$	7.44403			0.250796			0.125398	+	0.992107i	$0.459979\pi$
$882$		0			0
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$	−1.43867	−	0.830619i	−0.0483879	−	0.0279368i
$885$		0			0
$886$	−11.1318	−	19.2808i	−0.373980	−	0.647752i
$887$	−12.1275			−0.407203			−0.203602	−	0.979054i	$-0.565265\pi$
$887$	−12.1275			−0.407203			−0.203602	+	0.979054i	$0.565265\pi$
$888$		0			0
$889$	−0.428977	+	0.627073i	−0.0143874	+	0.0210313i
$890$			16.7307i			0.560814i
$891$		0			0
$892$	17.6209	+	10.1734i	0.589992	+	0.340632i
$893$			42.3002i			1.41552i
$894$		0			0
$895$	8.43465	+	4.86975i	0.281939	+	0.162778i
$896$	2.38554	−	1.14420i	0.0796954	−	0.0382249i
$897$		0			0
$898$	−3.40409	+	5.89606i	−0.113596	+	0.196754i
$899$	12.7978	−	22.1664i	0.426830	−	0.739291i
$900$		0			0
$901$	4.47061	−	2.58111i	0.148938	−	0.0859891i
$902$	0.142724	+	0.247206i	0.00475220	+	0.00823105i
$903$		0			0
$904$	6.14993	−	10.6520i	0.204544	−	0.354280i
$905$			79.1792i			2.63201i
$906$		0			0
$907$	−46.1780			−1.53331			−0.766657	−	0.642057i	$-0.778081\pi$
$907$	−46.1780			−1.53331			−0.766657	+	0.642057i	$0.778081\pi$
$908$	2.08000	+	3.60266i	0.0690272	+	0.119559i
$909$		0			0
$910$	9.61897	+	0.736060i	0.318866	+	0.0244002i
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	−0.274098	−	0.961702i	$-0.588379\pi$
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	0.695809	+	0.718227i	$0.255046\pi$
$912$		0			0
$913$	−28.4365	+	16.4178i	−0.941110	+	0.543350i
$914$	−13.1861	+	7.61298i	−0.436156	+	0.251815i
$915$		0			0
$916$	−5.16986	+	2.98482i	−0.170817	+	0.0986212i
$917$	0.557126	−	0.814399i	0.0183979	−	0.0268938i
$918$		0			0
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	0.569904	−	0.821711i	$-0.306980\pi$
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	−0.996575	+	0.0826958i	$0.973647\pi$
$920$	−11.9295			−0.393305
$921$		0			0
$922$			0.206761i			0.00680932i
$923$	−7.17849	+	12.4335i	−0.236283	+	0.409254i
$924$		0			0
$925$	22.2706	+	38.5738i	0.732253	+	1.26830i
$926$	−13.1673	+	7.60217i	−0.432706	+	0.249823i
$927$		0			0
$928$	−2.13804	+	3.70319i	−0.0701846	+	0.121563i
$929$	−6.59673	+	11.4259i	−0.216432	+	0.374870i	−0.953714	−	0.300714i	$-0.902775\pi$
$929$	−6.59673	+	11.4259i	−0.216432	+	0.374870i	0.737283	+	0.675584i	$0.236108\pi$
$930$		0			0
$931$	44.9220	+	36.0559i	1.47226	+	1.18168i
$932$	−3.88603	−	2.24360i	−0.127291	−	0.0734915i
$933$		0			0
$934$			2.30849i			0.0755360i
$935$	15.0477	+	8.68779i	0.492112	+	0.284121i
$936$		0			0
$937$		−	8.86021i		−	0.289451i	−0.989472	−	0.144725i	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$	−0.820353	−	0.561200i	−0.0267855	−	0.0183238i
$939$		0			0
$940$	−18.2602			−0.595581
$941$	2.05919	+	3.56663i	0.0671278	+	0.116269i	0.897636	−	0.440738i	$-0.145283\pi$
$941$	2.05919	+	3.56663i	0.0671278	+	0.116269i	−0.830508	+	0.557007i	$0.811950\pi$
$942$		0			0
$943$	−0.274682	−	0.158588i	−0.00894488	−	0.00516433i
$944$	−8.84071			−0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$	21.4498	+	12.3840i	0.697024	+	0.402427i	0.806238	−	0.591591i	$-0.201500\pi$
$947$	21.4498	+	12.3840i	0.697024	+	0.402427i	−0.109214	+	0.994018i	$0.534833\pi$
$948$		0			0
$949$	0.672905	+	1.16550i	0.0218434	+	0.0378339i
$950$	−62.6916			−2.03398
$951$		0			0
$952$	3.86078	−	1.85178i	0.125129	−	0.0600165i
$953$			9.62625i			0.311825i	0.987771	+	0.155912i	$0.0498317\pi$
$953$			9.62625i			0.311825i	−0.987771	+	0.155912i	$0.950168\pi$
$954$		0			0
$955$	15.7897	+	9.11620i	0.510944	+	0.294993i
$956$			3.49809i			0.113136i
$957$		0			0
$958$	−10.7674	−	6.21659i	−0.347880	−	0.200849i
$959$	−15.4216	−	10.5498i	−0.497989	−	0.340672i
$960$		0			0
$961$	2.41465	−	4.18230i	0.0778920	−	0.134913i
$962$	−3.00060	+	5.19719i	−0.0967431	+	0.167564i
$963$		0			0
$964$	−10.0170	+	5.78332i	−0.322626	+	0.186268i
$965$	28.3908	+	49.1744i	0.913933	+	1.58298i
$966$		0			0
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	−0.773216	−	0.634143i	$-0.781353\pi$
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	0.935792	+	0.352553i	$0.114686\pi$
$968$			1.86528i			0.0599523i
$969$		0			0
$970$	54.6891			1.75596
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	0.588264	−	0.808669i	$-0.299812\pi$
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	−0.994460	+	0.105117i	$0.966478\pi$
$972$		0			0
$973$	−34.7959	+	16.6894i	−1.11550	+	0.535039i
$974$	−32.3033	+	18.6503i	−1.03507	+	0.597595i
$975$		0			0
$976$	4.06195	−	2.34517i	0.130020	−	0.0750671i
$977$	−7.84008	+	4.52647i	−0.250826	+	0.144815i	−0.620143	−	0.784489i	$-0.712925\pi$
$977$	−7.84008	+	4.52647i	−0.250826	+	0.144815i	0.369316	+	0.929304i	$0.379592\pi$
$978$		0			0
$979$	12.3279	−	7.11752i	0.394001	−	0.227477i
$980$	−15.5646	+	19.3920i	−0.497194	+	0.619453i
$981$		0			0
$982$	6.82377	+	11.8191i	0.217755	+	0.377163i
$983$	6.39303			0.203906			0.101953	−	0.994789i	$-0.467491\pi$
$983$	6.39303			0.203906			0.101953	+	0.994789i	$0.467491\pi$
$984$		0			0
$985$			16.7869i			0.534876i
$986$	−3.46022	+	5.99328i	−0.110196	+	0.190865i
$987$		0			0
$988$	−4.22333	−	7.31502i	−0.134362	−	0.232722i
$989$	17.7934	−	10.2730i	0.565797	−	0.326663i
$990$		0			0
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	−0.734881	−	0.678196i	$-0.762762\pi$
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	0.954775	+	0.297328i	$0.0960954\pi$
$992$	−2.99288	+	5.18382i	−0.0950240	+	0.164586i
$993$		0			0
$994$	−16.0037	−	33.3662i	−0.507606	−	1.05831i
$995$	−6.52475	−	3.76706i	−0.206848	−	0.119424i
$996$		0			0
$997$		−	6.92118i		−	0.219196i	−0.993976	−	0.109598i	$-0.965044\pi$
$997$		−	6.92118i		−	0.219196i	0.993976	−	0.109598i	$-0.0349563\pi$
$998$	−18.1882	−	10.5010i	−0.575737	−	0.332402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.t.a.17.5		16
3.2	odd	2		126.2.t.a.59.4	yes	16
4.3	odd	2		3024.2.df.c.17.1		16
7.2	even	3		2646.2.l.a.1097.4		16
7.3	odd	6		2646.2.m.b.881.1		16
7.4	even	3		2646.2.m.a.881.4		16
7.5	odd	6		378.2.l.a.341.1		16
7.6	odd	2		2646.2.t.b.2285.8		16
9.2	odd	6		378.2.l.a.143.5		16
9.4	even	3		1134.2.k.a.647.4		16
9.5	odd	6		1134.2.k.b.647.5		16
9.7	even	3		126.2.l.a.101.2	yes	16
12.11	even	2		1008.2.df.c.689.3		16
21.2	odd	6		882.2.l.b.509.7		16
21.5	even	6		126.2.l.a.5.6	✓	16
21.11	odd	6		882.2.m.a.293.5		16
21.17	even	6		882.2.m.b.293.8		16
21.20	even	2		882.2.t.a.815.1		16
28.19	even	6		3024.2.ca.c.2609.1		16
36.7	odd	6		1008.2.ca.c.353.7		16
36.11	even	6		3024.2.ca.c.2033.1		16
63.2	odd	6		2646.2.t.b.1979.8		16
63.5	even	6		1134.2.k.a.971.4		16
63.11	odd	6		2646.2.m.b.1763.1		16
63.16	even	3		882.2.t.a.803.1		16
63.20	even	6		2646.2.l.a.521.8		16
63.25	even	3		882.2.m.b.587.8		16
63.34	odd	6		882.2.l.b.227.3		16
63.38	even	6		2646.2.m.a.1763.4		16
63.40	odd	6		1134.2.k.b.971.5		16
63.47	even	6	inner	378.2.t.a.89.5		16
63.52	odd	6		882.2.m.a.587.5		16
63.61	odd	6		126.2.t.a.47.4	yes	16
84.47	odd	6		1008.2.ca.c.257.7		16
252.47	odd	6		3024.2.df.c.1601.1		16
252.187	even	6		1008.2.df.c.929.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	21.5	even	6
126.2.l.a.101.2	yes	16	9.7	even	3
126.2.t.a.47.4	yes	16	63.61	odd	6
126.2.t.a.59.4	yes	16	3.2	odd	2
378.2.l.a.143.5		16	9.2	odd	6
378.2.l.a.341.1		16	7.5	odd	6
378.2.t.a.17.5		16	1.1	even	1	trivial
378.2.t.a.89.5		16	63.47	even	6	inner
882.2.l.b.227.3		16	63.34	odd	6
882.2.l.b.509.7		16	21.2	odd	6
882.2.m.a.293.5		16	21.11	odd	6
882.2.m.a.587.5		16	63.52	odd	6
882.2.m.b.293.8		16	21.17	even	6
882.2.m.b.587.8		16	63.25	even	3
882.2.t.a.803.1		16	63.16	even	3
882.2.t.a.815.1		16	21.20	even	2
1008.2.ca.c.257.7		16	84.47	odd	6
1008.2.ca.c.353.7		16	36.7	odd	6
1008.2.df.c.689.3		16	12.11	even	2
1008.2.df.c.929.3		16	252.187	even	6
1134.2.k.a.647.4		16	9.4	even	3
1134.2.k.a.971.4		16	63.5	even	6
1134.2.k.b.647.5		16	9.5	odd	6
1134.2.k.b.971.5		16	63.40	odd	6
2646.2.l.a.521.8		16	63.20	even	6
2646.2.l.a.1097.4		16	7.2	even	3
2646.2.m.a.881.4		16	7.4	even	3
2646.2.m.a.1763.4		16	63.38	even	6
2646.2.m.b.881.1		16	7.3	odd	6
2646.2.m.b.1763.1		16	63.11	odd	6
2646.2.t.b.1979.8		16	63.2	odd	6
2646.2.t.b.2285.8		16	7.6	odd	2
3024.2.ca.c.2033.1		16	36.11	even	6
3024.2.ca.c.2609.1		16	28.19	even	6
3024.2.df.c.17.1		16	4.3	odd	2
3024.2.df.c.1601.1		16	252.47	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.55225 q^{5} +(-1.49384 + 2.18368i) q^{7} +1.00000i q^{8} +(-3.07634 - 1.77612i) q^{10} +3.02237i q^{11} +(0.888944 + 0.513232i) q^{13} +(-2.38554 + 1.14420i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.809204 + 1.40158i) q^{17} +(-7.12643 + 4.11444i) q^{19} +(-1.77612 - 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} -3.35830i q^{23} +7.61848 q^{25} +(0.513232 + 0.888944i) q^{26} +(-2.63804 - 0.201867i) q^{28} +(3.70319 - 2.13804i) q^{29} +(5.18382 - 2.99288i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.40158 + 0.809204i) q^{34} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} -8.22889 q^{38} -3.55225i q^{40} +(0.0472226 - 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +(-2.61745 + 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} +(2.57023 - 4.45176i) q^{47} +(-2.53687 - 6.52413i) q^{49} +(6.59779 + 3.80924i) q^{50} +1.02646i q^{52} +(-2.76235 - 1.59484i) q^{53} -10.7362i q^{55} +(-2.18368 - 1.49384i) q^{56} +4.27608 q^{58} +(4.42036 + 7.65628i) q^{59} +(-4.06195 - 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(-3.15775 - 1.82313i) q^{65} +(0.187838 + 0.325345i) q^{67} -1.61841 q^{68} +(8.47404 - 4.06447i) q^{70} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +5.84647i q^{74} +(-7.12643 - 4.11444i) q^{76} +(-6.59987 - 4.51494i) q^{77} +(-0.462067 + 0.800324i) q^{79} +(1.77612 - 3.07634i) q^{80} +(0.0817920 - 0.0472226i) q^{82} +(5.43209 + 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +6.11799i q^{86} -3.02237 q^{88} +(-2.35495 - 4.07888i) q^{89} +(-2.44867 + 1.17448i) q^{91} +(2.90837 - 1.67915i) q^{92} +(4.45176 - 2.57023i) q^{94} +(25.3148 - 14.6155i) q^{95} +(-13.3330 + 7.69782i) q^{97} +(1.06507 - 6.91850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47}+ \cdots - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

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