LMFDB - Embedded newform 1890.2.bf.e.629.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(629,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("1890.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.3
Character	$\chi$	$=$	1890.629
Dual form			1890.2.bf.e.1259.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16779 + 0.548354i) q^{5} +(-1.29573 - 2.30675i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16779 + 0.548354i) q^{5} +(-1.29573 - 2.30675i) q^{7} +1.00000 q^{8} +(0.609005 - 2.15154i) q^{10} +(2.30587 + 1.33130i) q^{11} +(-1.15988 - 2.00897i) q^{13} +(2.64557 + 0.0312377i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.23248i q^{17} +5.58729i q^{19} +(1.55878 + 1.60318i) q^{20} +(-2.30587 + 1.33130i) q^{22} +(-0.354226 - 0.613538i) q^{23} +(4.39861 - 2.37743i) q^{25} +2.31976 q^{26} +(-1.34984 + 2.27551i) q^{28} +(2.68539 + 1.55041i) q^{29} +(5.32011 - 3.07156i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.26351 - 3.61624i) q^{34} +(4.07379 + 4.29002i) q^{35} -8.09944i q^{37} +(-4.83874 - 2.79365i) q^{38} +(-2.16779 + 0.548354i) q^{40} +(-3.67973 - 6.37348i) q^{41} +(-11.3383 - 6.54616i) q^{43} -2.66259i q^{44} +0.708453 q^{46} +(-4.91158 - 2.83570i) q^{47} +(-3.64216 + 5.97785i) q^{49} +(-0.140390 + 4.99803i) q^{50} +(-1.15988 + 2.00897i) q^{52} -3.40917 q^{53} +(-5.72866 - 1.62153i) q^{55} +(-1.29573 - 2.30675i) q^{56} +(-2.68539 + 1.55041i) q^{58} +(-1.98592 - 3.43972i) q^{59} +(-8.66705 - 5.00392i) q^{61} +6.14313i q^{62} +1.00000 q^{64} +(3.61601 + 3.71900i) q^{65} +(4.96469 - 2.86637i) q^{67} +(6.26351 - 3.61624i) q^{68} +(-5.75216 + 1.38299i) q^{70} -9.75935i q^{71} +4.33252 q^{73} +(7.01432 + 4.04972i) q^{74} +(4.83874 - 2.79365i) q^{76} +(0.0831731 - 7.04406i) q^{77} +(7.29204 - 12.6302i) q^{79} +(0.609005 - 2.15154i) q^{80} +7.35946 q^{82} +(-2.25905 - 1.30426i) q^{83} +(-3.96596 - 15.6785i) q^{85} +(11.3383 - 6.54616i) q^{86} +(2.30587 + 1.33130i) q^{88} -5.66299 q^{89} +(-3.13130 + 5.27864i) q^{91} +(-0.354226 + 0.613538i) q^{92} +(4.91158 - 2.83570i) q^{94} +(-3.06382 - 12.1121i) q^{95} +(-6.43250 + 11.1414i) q^{97} +(-3.35589 - 6.14313i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	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
$5$	−2.16779	+	0.548354i	−0.969465	+	0.245232i
$5$	−2.16779	+	0.548354i	−0.969465	+	0.245232i
$6$		0			0
$7$	−1.29573	−	2.30675i	−0.489740	−	0.871868i
$7$	−1.29573	−	2.30675i	−0.489740	−	0.871868i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.609005	−	2.15154i	0.192584	−	0.680376i
$11$	2.30587	+	1.33130i	0.695246	+	0.401401i	0.805574	−	0.592495i	$-0.201857\pi$
$11$	2.30587	+	1.33130i	0.695246	+	0.401401i	−0.110328	+	0.993895i	$0.535190\pi$
$12$		0			0
$13$	−1.15988	−	2.00897i	−0.321693	−	0.557189i	0.659144	−	0.752016i	$-0.270919\pi$
$13$	−1.15988	−	2.00897i	−0.321693	−	0.557189i	−0.980837	+	0.194828i	$0.937585\pi$
$14$	2.64557	+	0.0312377i	0.707057	+	0.00834862i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			7.23248i			1.75413i	0.480369	+	0.877067i	$0.340503\pi$
$17$			7.23248i			1.75413i	−0.480369	+	0.877067i	$0.659497\pi$
$18$		0			0
$19$			5.58729i			1.28181i	0.767619	+	0.640906i	$0.221441\pi$
$19$			5.58729i			1.28181i	−0.767619	+	0.640906i	$0.778559\pi$
$20$	1.55878	+	1.60318i	0.348555	+	0.358483i
$21$		0			0
$22$	−2.30587	+	1.33130i	−0.491613	+	0.283833i
$23$	−0.354226	−	0.613538i	−0.0738613	−	0.127932i	0.826729	−	0.562600i	$-0.190199\pi$
$23$	−0.354226	−	0.613538i	−0.0738613	−	0.127932i	−0.900591	+	0.434668i	$0.856866\pi$
$24$		0			0
$25$	4.39861	−	2.37743i	0.879723	−	0.475487i
$26$	2.31976			0.454943
$27$		0			0
$28$	−1.34984	+	2.27551i	−0.255095	+	0.430031i
$29$	2.68539	+	1.55041i	0.498664	+	0.287904i	0.728162	−	0.685406i	$-0.240375\pi$
$29$	2.68539	+	1.55041i	0.498664	+	0.287904i	−0.229498	+	0.973309i	$0.573708\pi$
$30$		0			0
$31$	5.32011	−	3.07156i	0.955519	−	0.551669i	0.0607281	−	0.998154i	$-0.480658\pi$
$31$	5.32011	−	3.07156i	0.955519	−	0.551669i	0.894791	+	0.446485i	$0.147324\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−6.26351	−	3.61624i	−1.07418	−	0.620180i
$35$	4.07379	+	4.29002i	0.688595	+	0.725146i
$36$		0			0
$37$		−	8.09944i		−	1.33154i	−0.746157	−	0.665770i	$-0.768103\pi$
$37$		−	8.09944i		−	1.33154i	0.746157	−	0.665770i	$-0.231897\pi$
$38$	−4.83874	−	2.79365i	−0.784947	−	0.453189i
$39$		0			0
$40$	−2.16779	+	0.548354i	−0.342757	+	0.0867025i
$41$	−3.67973	−	6.37348i	−0.574677	−	0.995370i	−0.996077	−	0.0884948i	$-0.971794\pi$
$41$	−3.67973	−	6.37348i	−0.574677	−	0.995370i	0.421400	−	0.906875i	$-0.361539\pi$
$42$		0			0
$43$	−11.3383	−	6.54616i	−1.72907	−	0.998280i	−0.893848	−	0.448371i	$-0.852004\pi$
$43$	−11.3383	−	6.54616i	−1.72907	−	0.998280i	−0.835224	−	0.549909i	$-0.814662\pi$
$44$		−	2.66259i		−	0.401401i
$45$		0			0
$46$	0.708453			0.104456
$47$	−4.91158	−	2.83570i	−0.716428	−	0.413630i	0.0970085	−	0.995284i	$-0.469073\pi$
$47$	−4.91158	−	2.83570i	−0.716428	−	0.413630i	−0.813437	+	0.581654i	$0.802406\pi$
$48$		0			0
$49$	−3.64216	+	5.97785i	−0.520309	+	0.853978i
$50$	−0.140390	+	4.99803i	−0.0198541	+	0.706828i
$51$		0			0
$52$	−1.15988	+	2.00897i	−0.160847	+	0.278594i
$53$	−3.40917			−0.468286			−0.234143	−	0.972202i	$-0.575228\pi$
$53$	−3.40917			−0.468286			−0.234143	+	0.972202i	$0.575228\pi$
$54$		0			0
$55$	−5.72866	−	1.62153i	−0.772453	−	0.218647i
$56$	−1.29573	−	2.30675i	−0.173149	−	0.308252i
$57$		0			0
$58$	−2.68539	+	1.55041i	−0.352608	+	0.203579i
$59$	−1.98592	−	3.43972i	−0.258545	−	0.447814i	0.707307	−	0.706906i	$-0.249910\pi$
$59$	−1.98592	−	3.43972i	−0.258545	−	0.447814i	−0.965852	+	0.259093i	$0.916576\pi$
$60$		0			0
$61$	−8.66705	−	5.00392i	−1.10970	−	0.640687i	−0.170950	−	0.985280i	$-0.554684\pi$
$61$	−8.66705	−	5.00392i	−1.10970	−	0.640687i	−0.938752	+	0.344593i	$0.888017\pi$
$62$			6.14313i			0.780178i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.61601	+	3.71900i	0.448510	+	0.461285i
$66$		0			0
$67$	4.96469	−	2.86637i	0.606534	−	0.350183i	−0.165074	−	0.986281i	$-0.552786\pi$
$67$	4.96469	−	2.86637i	0.606534	−	0.350183i	0.771608	+	0.636099i	$0.219453\pi$
$68$	6.26351	−	3.61624i	0.759562	−	0.438533i
$69$		0			0
$70$	−5.75216	+	1.38299i	−0.687515	+	0.165299i
$71$		−	9.75935i		−	1.15822i	−0.815249	−	0.579111i	$-0.803400\pi$
$71$		−	9.75935i		−	1.15822i	0.815249	−	0.579111i	$-0.196600\pi$
$72$		0			0
$73$	4.33252			0.507083			0.253541	−	0.967325i	$-0.418405\pi$
$73$	4.33252			0.507083			0.253541	+	0.967325i	$0.418405\pi$
$74$	7.01432	+	4.04972i	0.815398	+	0.470770i
$75$		0			0
$76$	4.83874	−	2.79365i	0.555041	−	0.320453i
$77$	0.0831731	−	7.04406i	0.00947846	−	0.802745i
$78$		0			0
$79$	7.29204	−	12.6302i	0.820419	−	1.42101i	−0.0849523	−	0.996385i	$-0.527074\pi$
$79$	7.29204	−	12.6302i	0.820419	−	1.42101i	0.905371	−	0.424622i	$-0.139593\pi$
$80$	0.609005	−	2.15154i	0.0680889	−	0.240549i
$81$		0			0
$82$	7.35946			0.812716
$83$	−2.25905	−	1.30426i	−0.247963	−	0.143162i	0.370868	−	0.928686i	$-0.379060\pi$
$83$	−2.25905	−	1.30426i	−0.247963	−	0.143162i	−0.618831	+	0.785524i	$0.712394\pi$
$84$		0			0
$85$	−3.96596	−	15.6785i	−0.430169	−	1.70057i
$86$	11.3383	−	6.54616i	1.22264	−	0.705891i
$87$		0			0
$88$	2.30587	+	1.33130i	0.245807	+	0.141917i
$89$	−5.66299			−0.600276			−0.300138	−	0.953896i	$-0.597033\pi$
$89$	−5.66299			−0.600276			−0.300138	+	0.953896i	$0.597033\pi$
$90$		0			0
$91$	−3.13130	+	5.27864i	−0.328249	+	0.553352i
$92$	−0.354226	+	0.613538i	−0.0369307	+	0.0639658i
$93$		0			0
$94$	4.91158	−	2.83570i	0.506591	−	0.292481i
$95$	−3.06382	−	12.1121i	−0.314341	−	1.24267i
$96$		0			0
$97$	−6.43250	+	11.1414i	−0.653122	+	1.13124i	0.329239	+	0.944246i	$0.393208\pi$
$97$	−6.43250	+	11.1414i	−0.653122	+	1.13124i	−0.982361	+	0.186993i	$0.940126\pi$
$98$	−3.35589	−	6.14313i	−0.338996	−	0.620550i
$99$		0			0
$100$	−4.25822	−	2.62060i	−0.425822	−	0.262060i
$101$	−2.06435	+	3.57555i	−0.205410	+	0.355781i	−0.950263	−	0.311448i	$-0.899186\pi$
$101$	−2.06435	+	3.57555i	−0.205410	+	0.355781i	0.744853	+	0.667228i	$0.232519\pi$
$102$		0			0
$103$	4.09983	+	7.10111i	0.403968	+	0.699694i	0.994201	−	0.107540i	$-0.0342973\pi$
$103$	4.09983	+	7.10111i	0.403968	+	0.699694i	−0.590233	+	0.807233i	$0.700964\pi$
$104$	−1.15988	−	2.00897i	−0.113736	−	0.196996i
$105$		0			0
$106$	1.70459	−	2.95243i	0.165564	−	0.286765i
$107$	10.5158			1.01660			0.508299	−	0.861180i	$-0.330274\pi$
$107$	10.5158			1.01660			0.508299	+	0.861180i	$0.330274\pi$
$108$		0			0
$109$	7.38448			0.707305			0.353653	−	0.935377i	$-0.384940\pi$
$109$	7.38448			0.707305			0.353653	+	0.935377i	$0.384940\pi$
$110$	4.26862	−	4.15040i	0.406997	−	0.395725i
$111$		0			0
$112$	2.64557	+	0.0312377i	0.249983	+	0.00295168i
$113$	−8.92367	−	15.4563i	−0.839468	−	1.45400i	−0.890340	−	0.455297i	$-0.849533\pi$
$113$	−8.92367	−	15.4563i	−0.839468	−	1.45400i	0.0508712	−	0.998705i	$-0.483800\pi$
$114$		0			0
$115$	1.10432	+	1.13578i	0.102979	+	0.105912i
$116$		−	3.10082i		−	0.287904i
$117$		0			0
$118$	3.97185			0.365638
$119$	16.6835	−	9.37134i	1.52937	−	0.859070i
$120$		0			0
$121$	−1.95531	−	3.38669i	−0.177755	−	0.307881i
$122$	8.66705	−	5.00392i	0.784678	−	0.453034i
$123$		0			0
$124$	−5.32011	−	3.07156i	−0.477760	−	0.275835i
$125$	−8.23159	+	7.56577i	−0.736256	+	0.676703i
$126$		0			0
$127$			16.2541i			1.44232i	0.692770	+	0.721159i	$0.256390\pi$
$127$			16.2541i			1.44232i	−0.692770	+	0.721159i	$0.743610\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−5.02875	+	1.27205i	−0.441051	+	0.111566i
$131$	−1.95598	−	3.38785i	−0.170895	−	0.295998i	0.767838	−	0.640644i	$-0.221332\pi$
$131$	−1.95598	−	3.38785i	−0.170895	−	0.295998i	−0.938733	+	0.344646i	$0.887999\pi$
$132$		0			0
$133$	12.8885	−	7.23963i	1.11757	−	0.627755i
$134$			5.73274i			0.495233i
$135$		0			0
$136$			7.23248i			0.620180i
$137$	−0.467496	+	0.809727i	−0.0399409	+	0.0691796i	−0.885305	−	0.465011i	$-0.846050\pi$
$137$	−0.467496	+	0.809727i	−0.0399409	+	0.0691796i	0.845364	+	0.534191i	$0.179384\pi$
$138$		0			0
$139$	−10.8220	+	6.24810i	−0.917912	+	0.529957i	−0.882968	−	0.469432i	$-0.844459\pi$
$139$	−10.8220	+	6.24810i	−0.917912	+	0.529957i	−0.0349439	+	0.999389i	$0.511125\pi$
$140$	1.67837	−	5.67301i	0.141848	−	0.479457i
$141$		0			0
$142$	8.45184	+	4.87967i	0.709263	+	0.409493i
$143$		−	6.17657i		−	0.516511i
$144$		0			0
$145$	−6.67152	−	1.88841i	−0.554040	−	0.156824i
$146$	−2.16626	+	3.75207i	−0.179281	+	0.310524i
$147$		0			0
$148$	−7.01432	+	4.04972i	−0.576574	+	0.332885i
$149$	−2.62453	+	1.51527i	−0.215010	+	0.124136i	−0.603638	−	0.797259i	$-0.706283\pi$
$149$	−2.62453	+	1.51527i	−0.215010	+	0.124136i	0.388628	+	0.921395i	$0.372949\pi$
$150$		0			0
$151$	−4.75076	+	8.22856i	−0.386612	+	0.669631i	−0.991991	−	0.126306i	$-0.959688\pi$
$151$	−4.75076	+	8.22856i	−0.386612	+	0.669631i	0.605380	+	0.795937i	$0.293021\pi$
$152$			5.58729i			0.453189i
$153$		0			0
$154$	6.05875	+	3.59406i	0.488228	+	0.289618i
$155$	−9.84856	+	9.57581i	−0.791055	+	0.769147i
$156$		0			0
$157$	−3.53933	−	6.13030i	−0.282470	−	0.489252i	0.689523	−	0.724264i	$-0.257820\pi$
$157$	−3.53933	−	6.13030i	−0.282470	−	0.489252i	−0.971992	+	0.235012i	$0.924487\pi$
$158$	7.29204	+	12.6302i	0.580124	+	1.00480i
$159$		0			0
$160$	1.55878	+	1.60318i	0.123233	+	0.126743i
$161$	−0.956295	+	1.61209i	−0.0753666	+	0.127051i
$162$		0			0
$163$		−	18.8251i		−	1.47449i	−0.675624	−	0.737246i	$-0.736126\pi$
$163$		−	18.8251i		−	1.47449i	0.675624	−	0.737246i	$-0.263874\pi$
$164$	−3.67973	+	6.37348i	−0.287339	+	0.497685i
$165$		0			0
$166$	2.25905	−	1.30426i	0.175336	−	0.101231i
$167$	8.32228	−	4.80487i	0.643997	−	0.371812i	−0.142155	−	0.989844i	$-0.545403\pi$
$167$	8.32228	−	4.80487i	0.643997	−	0.371812i	0.786153	+	0.618032i	$0.212070\pi$
$168$		0			0
$169$	3.80935	−	6.59799i	0.293027	−	0.507538i
$170$	15.5609	+	4.40462i	1.19347	+	0.337819i
$171$		0			0
$172$			13.0923i			0.998280i
$173$	−18.9914	−	10.9647i	−1.44389	−	0.833629i	−0.445782	−	0.895142i	$-0.647074\pi$
$173$	−18.9914	−	10.9647i	−1.44389	−	0.833629i	−0.998106	+	0.0615122i	$0.980408\pi$
$174$		0			0
$175$	−11.1836	−	7.06598i	−0.845397	−	0.534138i
$176$	−2.30587	+	1.33130i	−0.173812	+	0.100350i
$177$		0			0
$178$	2.83150	−	4.90430i	0.212230	−	0.367593i
$179$			2.33029i			0.174174i	0.996201	+	0.0870870i	$0.0277558\pi$
$179$			2.33029i			0.174174i	−0.996201	+	0.0870870i	$0.972244\pi$
$180$		0			0
$181$		−	19.7070i		−	1.46481i	−0.680868	−	0.732406i	$-0.738397\pi$
$181$		−	19.7070i		−	1.46481i	0.680868	−	0.732406i	$-0.261603\pi$
$182$	−3.00579	−	5.35110i	−0.222804	−	0.396650i
$183$		0			0
$184$	−0.354226	−	0.613538i	−0.0261139	−	0.0452306i
$185$	4.44137	+	17.5579i	0.326536	+	1.29088i
$186$		0			0
$187$	−9.62856	+	16.6772i	−0.704110	+	1.21955i
$188$			5.67141i			0.413630i
$189$		0			0
$190$	12.0213	+	3.40269i	0.872114	+	0.246857i
$191$	−11.7316	−	6.77323i	−0.848867	−	0.490094i	0.0114013	−	0.999935i	$-0.496371\pi$
$191$	−11.7316	−	6.77323i	−0.848867	−	0.490094i	−0.860268	+	0.509841i	$0.829704\pi$
$192$		0			0
$193$	6.99314	−	4.03749i	0.503378	−	0.290625i	−0.226730	−	0.973958i	$-0.572803\pi$
$193$	6.99314	−	4.03749i	0.503378	−	0.290625i	0.730107	+	0.683333i	$0.239470\pi$
$194$	−6.43250	−	11.1414i	−0.461827	−	0.799907i
$195$		0			0
$196$	6.99805	+	0.165283i	0.499861	+	0.0118059i
$197$	−1.76372			−0.125660			−0.0628299	−	0.998024i	$-0.520013\pi$
$197$	−1.76372			−0.125660			−0.0628299	+	0.998024i	$0.520013\pi$
$198$		0			0
$199$		−	3.39022i		−	0.240327i	−0.992754	−	0.120163i	$-0.961658\pi$
$199$		−	3.39022i		−	0.240327i	0.992754	−	0.120163i	$-0.0383418\pi$
$200$	4.39861	−	2.37743i	0.311029	−	0.168110i
$201$		0			0
$202$	−2.06435	−	3.57555i	−0.145247	−	0.251575i
$203$	0.0968623	−	8.20342i	0.00679840	−	0.575767i
$204$		0			0
$205$	11.4718	+	11.7986i	0.801225	+	0.824047i
$206$	−8.19966			−0.571297
$207$		0			0
$208$	2.31976			0.160847
$209$	−7.43834	+	12.8836i	−0.514520	+	0.891176i
$210$		0			0
$211$	1.09815	+	1.90206i	0.0756000	+	0.130943i	0.901347	−	0.433098i	$-0.142579\pi$
$211$	1.09815	+	1.90206i	0.0756000	+	0.130943i	−0.825747	+	0.564041i	$0.809246\pi$
$212$	1.70459	+	2.95243i	0.117072	+	0.202774i
$213$		0			0
$214$	−5.25789	+	9.10693i	−0.359422	+	0.622537i
$215$	28.1686	+	7.97329i	1.92108	+	0.543774i
$216$		0			0
$217$	−13.9787	−	8.29222i	−0.948939	−	0.562912i
$218$	−3.69224	+	6.39515i	−0.250070	+	0.433134i
$219$		0			0
$220$	1.46004	+	5.77193i	0.0984361	+	0.389144i
$221$	14.5298	−	8.38881i	0.977383	−	0.564292i
$222$		0			0
$223$	4.69564	−	8.13309i	0.314444	−	0.544632i	−0.664875	−	0.746954i	$-0.731515\pi$
$223$	4.69564	−	8.13309i	0.314444	−	0.544632i	0.979319	+	0.202322i	$0.0648487\pi$
$224$	−1.34984	+	2.27551i	−0.0901897	+	0.152039i
$225$		0			0
$226$	17.8473			1.18719
$227$	2.25992	+	1.30477i	0.149996	+	0.0866003i	0.573120	−	0.819472i	$-0.305733\pi$
$227$	2.25992	+	1.30477i	0.149996	+	0.0866003i	−0.423123	+	0.906072i	$0.639066\pi$
$228$		0			0
$229$	2.92097	−	1.68642i	0.193023	−	0.111442i	−0.400374	−	0.916352i	$-0.631120\pi$
$229$	2.92097	−	1.68642i	0.193023	−	0.111442i	0.593397	+	0.804910i	$0.297786\pi$
$230$	−1.53578	+	0.388483i	−0.101266	+	0.0256158i
$231$		0			0
$232$	2.68539	+	1.55041i	0.176304	+	0.101789i
$233$	24.4650			1.60275			0.801377	−	0.598159i	$-0.204101\pi$
$233$	24.4650			1.60275			0.801377	+	0.598159i	$0.204101\pi$
$234$		0			0
$235$	12.2022	+	3.45392i	0.795987	+	0.225309i
$236$	−1.98592	+	3.43972i	−0.129273	+	0.223907i
$237$		0			0
$238$	−0.225926	+	19.1340i	−0.0146446	+	1.24027i
$239$	−14.3027	+	8.25768i	−0.925166	+	0.534145i	−0.885279	−	0.465060i	$-0.846033\pi$
$239$	−14.3027	+	8.25768i	−0.925166	+	0.534145i	−0.0398863	+	0.999204i	$0.512700\pi$
$240$		0			0
$241$	15.4951	+	8.94612i	0.998129	+	0.576270i	0.907694	−	0.419632i	$-0.137841\pi$
$241$	15.4951	+	8.94612i	0.998129	+	0.576270i	0.0904351	+	0.995902i	$0.471174\pi$
$242$	3.91061			0.251384
$243$		0			0
$244$			10.0078i			0.640687i
$245$	4.61746	−	14.9559i	0.294999	−	0.955498i
$246$		0			0
$247$	11.2247	−	6.48059i	0.714212	−	0.412350i
$248$	5.32011	−	3.07156i	0.337827	−	0.195045i
$249$		0			0
$250$	−2.43636	−	10.9117i	−0.154089	−	0.690114i
$251$	4.13340			0.260898			0.130449	−	0.991455i	$-0.458358\pi$
$251$	4.13340			0.260898			0.130449	+	0.991455i	$0.458358\pi$
$252$		0			0
$253$		−	1.88632i		−	0.118592i
$254$	−14.0765	−	8.12704i	−0.883235	−	0.509936i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.85275	+	1.06969i	−0.115571	+	0.0667252i	−0.556671	−	0.830733i	$-0.687922\pi$
$257$	−1.85275	+	1.06969i	−0.115571	+	0.0667252i	0.441100	+	0.897458i	$0.354588\pi$
$258$		0			0
$259$	−18.6834	+	10.4947i	−1.16093	+	0.652109i
$260$	1.41275	−	4.99105i	0.0876149	−	0.309532i
$261$		0			0
$262$	3.91196			0.241681
$263$	−7.24259	+	12.5445i	−0.446597	+	0.773530i	−0.998162	−	0.0606027i	$-0.980698\pi$
$263$	−7.24259	+	12.5445i	−0.446597	+	0.773530i	0.551564	+	0.834132i	$0.314031\pi$
$264$		0			0
$265$	7.39037	−	1.86944i	0.453987	−	0.114839i
$266$	−0.174534	+	14.7816i	−0.0107014	+	0.906315i
$267$		0			0
$268$	−4.96469	−	2.86637i	−0.303267	−	0.175091i
$269$	−12.8786			−0.785219			−0.392610	−	0.919705i	$-0.628428\pi$
$269$	−12.8786			−0.785219			−0.392610	+	0.919705i	$0.628428\pi$
$270$		0			0
$271$			8.07664i			0.490621i	0.969445	+	0.245310i	$0.0788899\pi$
$271$			8.07664i			0.490621i	−0.969445	+	0.245310i	$0.921110\pi$
$272$	−6.26351	−	3.61624i	−0.379781	−	0.219267i
$273$		0			0
$274$	−0.467496	−	0.809727i	−0.0282425	−	0.0489174i
$275$	13.3077	+	0.373800i	0.802485	+	0.0225410i
$276$		0			0
$277$	−9.07801	−	5.24119i	−0.545445	−	0.314913i	0.201838	−	0.979419i	$-0.435309\pi$
$277$	−9.07801	−	5.24119i	−0.545445	−	0.314913i	−0.747283	+	0.664506i	$0.768642\pi$
$278$		−	12.4962i		−	0.749472i
$279$		0			0
$280$	4.07379	+	4.29002i	0.243455	+	0.256378i
$281$	−8.62857	−	4.98171i	−0.514737	−	0.297184i	0.220041	−	0.975491i	$-0.429381\pi$
$281$	−8.62857	−	4.98171i	−0.514737	−	0.297184i	−0.734779	+	0.678307i	$0.762714\pi$
$282$		0			0
$283$	−10.6894	−	18.5146i	−0.635418	−	1.10058i	−0.986426	−	0.164205i	$-0.947494\pi$
$283$	−10.6894	−	18.5146i	−0.635418	−	1.10058i	0.351008	−	0.936373i	$-0.385839\pi$
$284$	−8.45184	+	4.87967i	−0.501525	+	0.289555i
$285$		0			0
$286$	5.34907	+	3.08829i	0.316297	+	0.182614i
$287$	−9.93406	+	16.7465i	−0.586389	+	0.988515i
$288$		0			0
$289$	−35.3087			−2.07698
$290$	4.97118	−	4.83350i	0.291917	−	0.283833i
$291$		0			0
$292$	−2.16626	−	3.75207i	−0.126771	−	0.219573i
$293$	9.94849	−	5.74376i	0.581197	−	0.335554i	−0.180412	−	0.983591i	$-0.557743\pi$
$293$	9.94849	−	5.74376i	0.581197	−	0.335554i	0.761609	+	0.648037i	$0.224410\pi$
$294$		0			0
$295$	6.19125	+	6.36760i	0.360469	+	0.370736i
$296$		−	8.09944i		−	0.470770i
$297$		0			0
$298$		−	3.03055i		−	0.175555i
$299$	−0.821721	+	1.42326i	−0.0475213	+	0.0823094i
$300$		0			0
$301$	−0.408974	+	34.6366i	−0.0235729	+	1.99642i
$302$	−4.75076	−	8.22856i	−0.273376	−	0.473500i
$303$		0			0
$304$	−4.83874	−	2.79365i	−0.277521	−	0.160227i
$305$	21.5323	+	6.09483i	1.23293	+	0.348989i
$306$		0			0
$307$	5.44565			0.310800			0.155400	−	0.987852i	$-0.450333\pi$
$307$	5.44565			0.310800			0.155400	+	0.987852i	$0.450333\pi$
$308$	−6.14192	+	3.45000i	−0.349969	+	0.196582i
$309$		0			0
$310$	−3.36861	−	13.3170i	−0.191324	−	0.756355i
$311$	−1.67706	−	2.90474i	−0.0950971	−	0.164713i	0.814552	−	0.580090i	$-0.196983\pi$
$311$	−1.67706	−	2.90474i	−0.0950971	−	0.164713i	−0.909649	+	0.415378i	$0.863649\pi$
$312$		0			0
$313$	15.6710	−	27.1430i	0.885779	−	1.53421i	0.0409598	−	0.999161i	$-0.486958\pi$
$313$	15.6710	−	27.1430i	0.885779	−	1.53421i	0.844819	−	0.535053i	$-0.179708\pi$
$314$	7.07867			0.399472
$315$		0			0
$316$	−14.5841			−0.820419
$317$	11.8243	−	20.4803i	0.664120	−	1.15029i	−0.315403	−	0.948958i	$-0.602140\pi$
$317$	11.8243	−	20.4803i	0.664120	−	1.15029i	0.979523	−	0.201332i	$-0.0645270\pi$
$318$		0			0
$319$	4.12810	+	7.15008i	0.231129	+	0.400328i
$320$	−2.16779	+	0.548354i	−0.121183	+	0.0306539i
$321$		0			0
$322$	−0.917964	−	1.63422i	−0.0511561	−	0.0910716i
$323$	−40.4100			−2.24847
$324$		0			0
$325$	−9.87807	−	6.07916i	−0.547936	−	0.337211i
$326$	16.3030	+	9.41253i	0.902938	+	0.521312i
$327$		0			0
$328$	−3.67973	−	6.37348i	−0.203179	−	0.351916i
$329$	−0.177162	+	15.0041i	−0.00976724	+	0.827202i
$330$		0			0
$331$	−4.96127	+	8.59317i	−0.272696	+	0.472323i	−0.969551	−	0.244889i	$-0.921249\pi$
$331$	−4.96127	+	8.59317i	−0.272696	+	0.472323i	0.696855	+	0.717212i	$0.254582\pi$
$332$			2.60853i			0.143162i
$333$		0			0
$334$			9.60974i			0.525822i
$335$	−9.19062	+	8.93609i	−0.502137	+	0.488231i
$336$		0			0
$337$	−22.7611	+	13.1411i	−1.23987	+	0.715842i	−0.969069	−	0.246792i	$-0.920624\pi$
$337$	−22.7611	+	13.1411i	−1.23987	+	0.715842i	−0.270806	+	0.962634i	$0.587290\pi$
$338$	3.80935	+	6.59799i	0.207202	+	0.358884i
$339$		0			0
$340$	−11.5950	+	11.2739i	−0.628826	+	0.611411i
$341$	16.3566			0.885762
$342$		0			0
$343$	18.5086	+	0.655869i	0.999373	+	0.0354136i
$344$	−11.3383	−	6.54616i	−0.611319	−	0.352945i
$345$		0			0
$346$	18.9914	−	10.9647i	1.02098	−	0.589465i
$347$	14.0818	+	24.3904i	0.755950	+	1.30934i	0.944901	+	0.327357i	$0.106158\pi$
$347$	14.0818	+	24.3904i	0.755950	+	1.30934i	−0.188951	+	0.981987i	$0.560509\pi$
$348$		0			0
$349$	1.18630	+	0.684908i	0.0635010	+	0.0366623i	0.531414	−	0.847112i	$-0.321661\pi$
$349$	1.18630	+	0.684908i	0.0635010	+	0.0366623i	−0.467913	+	0.883774i	$0.654994\pi$
$350$	11.7111	−	6.15226i	0.625984	−	0.328852i
$351$		0			0
$352$		−	2.66259i		−	0.141917i
$353$	−9.38447	−	5.41813i	−0.499485	−	0.288378i	0.229016	−	0.973423i	$-0.426449\pi$
$353$	−9.38447	−	5.41813i	−0.499485	−	0.288378i	−0.728501	+	0.685045i	$0.759783\pi$
$354$		0			0
$355$	5.35158	+	21.1562i	0.284033	+	1.12285i
$356$	2.83150	+	4.90430i	0.150069	+	0.259927i
$357$		0			0
$358$	−2.01809	−	1.16514i	−0.106659	−	0.0615798i
$359$			5.43488i			0.286842i	0.989662	+	0.143421i	$0.0458103\pi$
$359$			5.43488i			0.286842i	−0.989662	+	0.143421i	$0.954190\pi$
$360$		0			0
$361$	−12.2178			−0.643044
$362$	17.0668	+	9.85352i	0.897011	+	0.517890i
$363$		0			0
$364$	6.13708	+	0.0724640i	0.321671	+	0.00379814i
$365$	−9.39198	+	2.37576i	−0.491599	+	0.124353i
$366$		0			0
$367$	7.28483	−	12.6177i	0.380265	−	0.658639i	−0.610835	−	0.791758i	$-0.709166\pi$
$367$	7.28483	−	12.6177i	0.380265	−	0.658639i	0.991100	+	0.133119i	$0.0424994\pi$
$368$	0.708453			0.0369307
$369$		0			0
$370$	−17.4262	−	4.93260i	−0.905948	−	0.256434i
$371$	4.41737	+	7.86410i	0.229339	+	0.408284i
$372$		0			0
$373$	31.1363	−	17.9766i	1.61218	−	0.930792i	0.623314	−	0.781971i	$-0.285786\pi$
$373$	31.1363	−	17.9766i	1.61218	−	0.930792i	0.988864	−	0.148820i	$-0.0475476\pi$
$374$	−9.62856	−	16.6772i	−0.497881	−	0.862355i
$375$		0			0
$376$	−4.91158	−	2.83570i	−0.253296	−	0.146240i
$377$		−	7.19315i		−	0.370466i
$378$		0			0
$379$	2.04160			0.104870			0.0524348	−	0.998624i	$-0.483302\pi$
$379$	2.04160			0.104870			0.0524348	+	0.998624i	$0.483302\pi$
$380$	−8.95745	+	8.70938i	−0.459508	+	0.446782i
$381$		0			0
$382$	11.7316	−	6.77323i	0.600240	−	0.346549i
$383$	7.15091	−	4.12858i	0.365395	−	0.210961i	−0.306050	−	0.952015i	$-0.599007\pi$
$383$	7.15091	−	4.12858i	0.365395	−	0.210961i	0.671445	+	0.741055i	$0.265674\pi$
$384$		0			0
$385$	3.68234	+	15.3156i	0.187669	+	0.780557i
$386$			8.07499i			0.411006i
$387$		0			0
$388$	12.8650			0.653122
$389$	−15.6859	−	9.05627i	−0.795308	−	0.459171i	0.0465201	−	0.998917i	$-0.485187\pi$
$389$	−15.6859	−	9.05627i	−0.795308	−	0.459171i	−0.841828	+	0.539746i	$0.818520\pi$
$390$		0			0
$391$	4.43740	−	2.56193i	0.224409	−	0.129563i
$392$	−3.64216	+	5.97785i	−0.183957	+	0.301927i
$393$		0			0
$394$	0.881859	−	1.52743i	0.0444274	−	0.0769506i
$395$	−8.88178	+	31.3782i	−0.446891	+	1.57881i
$396$		0			0
$397$	−2.48825			−0.124882			−0.0624409	−	0.998049i	$-0.519889\pi$
$397$	−2.48825			−0.124882			−0.0624409	+	0.998049i	$0.519889\pi$
$398$	2.93602	+	1.69511i	0.147169	+	0.0849683i
$399$		0			0
$400$	−0.140390	+	4.99803i	−0.00701949	+	0.249901i
$401$	−30.2082	+	17.4407i	−1.50853	+	0.870948i	−0.508576	+	0.861017i	$0.669828\pi$
$401$	−30.2082	+	17.4407i	−1.50853	+	0.870948i	−0.999951	+	0.00993115i	$0.996839\pi$
$402$		0			0
$403$	−12.3414	−	7.12530i	−0.614768	−	0.354936i
$404$	4.12869			0.205410
$405$		0			0
$406$	7.05594	+	4.18559i	0.350180	+	0.207728i
$407$	10.7827	−	18.6763i	0.534481	−	0.925748i
$408$		0			0
$409$	7.61870	−	4.39866i	0.376721	−	0.217500i	−0.299670	−	0.954043i	$-0.596877\pi$
$409$	7.61870	−	4.39866i	0.376721	−	0.217500i	0.676391	+	0.736543i	$0.263543\pi$
$410$	−15.9537	+	4.03559i	−0.787899	+	0.199304i
$411$		0			0
$412$	4.09983	−	7.10111i	0.201984	−	0.349847i
$413$	−5.36135	+	9.03798i	−0.263815	+	0.444730i
$414$		0			0
$415$	5.61234	+	1.58861i	0.275499	+	0.0779817i
$416$	−1.15988	+	2.00897i	−0.0568678	+	0.0984980i
$417$		0			0
$418$	−7.43834	−	12.8836i	−0.363821	−	0.630156i
$419$	0.0360658	+	0.0624677i	0.00176193	+	0.00305175i	0.866905	−	0.498473i	$-0.166106\pi$
$419$	0.0360658	+	0.0624677i	0.00176193	+	0.00305175i	−0.865143	+	0.501525i	$0.832772\pi$
$420$		0			0
$421$	3.42682	−	5.93543i	0.167013	−	0.289275i	−0.770355	−	0.637615i	$-0.779921\pi$
$421$	3.42682	−	5.93543i	0.167013	−	0.289275i	0.937368	+	0.348340i	$0.113254\pi$
$422$	−2.19631			−0.106914
$423$		0			0
$424$	−3.40917			−0.165564
$425$	17.1947	+	31.8129i	0.834067	+	1.54315i
$426$		0			0
$427$	−0.312622	+	26.4764i	−0.0151288	+	1.28128i
$428$	−5.25789	−	9.10693i	−0.254150	−	0.440200i
$429$		0			0
$430$	−20.9894	+	20.4081i	−1.01220	+	0.984166i
$431$		−	4.36097i		−	0.210060i	−0.994469	−	0.105030i	$-0.966506\pi$
$431$		−	4.36097i		−	0.210060i	0.994469	−	0.105030i	$-0.0334939\pi$
$432$		0			0
$433$	32.5668			1.56506			0.782530	−	0.622613i	$-0.213929\pi$
$433$	32.5668			1.56506			0.782530	+	0.622613i	$0.213929\pi$
$434$	14.1706	−	7.95984i	0.680213	−	0.382085i
$435$		0			0
$436$	−3.69224	−	6.39515i	−0.176826	−	0.306272i
$437$	3.42802	−	1.97917i	0.163984	−	0.0946764i
$438$		0			0
$439$	26.2998	+	15.1842i	1.25522	+	0.724703i	0.972142	−	0.234393i	$-0.0753101\pi$
$439$	26.2998	+	15.1842i	1.25522	+	0.724703i	0.283081	+	0.959096i	$0.408643\pi$
$440$	−5.72866	−	1.62153i	−0.273103	−	0.0773035i
$441$		0			0
$442$			16.7776i			0.798030i
$443$	−18.8007	+	32.5637i	−0.893246	+	1.54715i	−0.0572857	+	0.998358i	$0.518245\pi$
$443$	−18.8007	+	32.5637i	−0.893246	+	1.54715i	−0.835960	+	0.548790i	$0.815089\pi$
$444$		0			0
$445$	12.2762	−	3.10533i	0.581947	−	0.147207i
$446$	4.69564	+	8.13309i	0.222345	+	0.385113i
$447$		0			0
$448$	−1.29573	−	2.30675i	−0.0612175	−	0.108984i
$449$		−	4.32560i		−	0.204138i	−0.994777	−	0.102069i	$-0.967454\pi$
$449$		−	4.32560i		−	0.204138i	0.994777	−	0.102069i	$-0.0325462\pi$
$450$		0			0
$451$		−	19.5952i		−	0.922703i
$452$	−8.92367	+	15.4563i	−0.419734	+	0.727001i
$453$		0			0
$454$	−2.25992	+	1.30477i	−0.106063	+	0.0612357i
$455$	3.89343	−	13.1600i	0.182527	−	0.616952i
$456$		0			0
$457$	18.5026	+	10.6825i	0.865513	+	0.499704i	0.865855	−	0.500296i	$-0.166775\pi$
$457$	18.5026	+	10.6825i	0.865513	+	0.499704i	−0.000341340		1.00000i	$0.500109\pi$
$458$			3.37284i			0.157603i
$459$		0			0
$460$	0.431452	−	1.52426i	0.0201165	−	0.0710691i
$461$	9.79603	−	16.9672i	0.456246	−	0.790242i	−0.542512	−	0.840048i	$-0.682527\pi$
$461$	9.79603	−	16.9672i	0.456246	−	0.790242i	0.998759	+	0.0498057i	$0.0158602\pi$
$462$		0			0
$463$	−17.7591	+	10.2532i	−0.825335	+	0.476507i	−0.852253	−	0.523130i	$-0.824764\pi$
$463$	−17.7591	+	10.2532i	−0.825335	+	0.476507i	0.0269180	+	0.999638i	$0.491431\pi$
$464$	−2.68539	+	1.55041i	−0.124666	+	0.0719759i
$465$		0			0
$466$	−12.2325	+	21.1873i	−0.566659	+	0.981483i
$467$			14.3203i			0.662663i	0.943514	+	0.331331i	$0.107498\pi$
$467$			14.3203i			0.662663i	−0.943514	+	0.331331i	$0.892502\pi$
$468$		0			0
$469$	−13.0449	−	7.73825i	−0.602357	−	0.357319i
$470$	−9.09230	+	8.84050i	−0.419397	+	0.407782i
$471$		0			0
$472$	−1.98592	−	3.43972i	−0.0914096	−	0.158326i
$473$	−17.4297	−	30.1892i	−0.801421	−	1.38810i
$474$		0			0
$475$	13.2834	+	24.5763i	0.609485	+	1.12764i
$476$	−16.4576	−	9.76266i	−0.754331	−	0.447471i
$477$		0			0
$478$		−	16.5154i		−	0.755395i
$479$	−12.6756	+	21.9548i	−0.579164	+	1.00314i	0.416412	+	0.909176i	$0.363288\pi$
$479$	−12.6756	+	21.9548i	−0.579164	+	1.00314i	−0.995575	+	0.0939651i	$0.970046\pi$
$480$		0			0
$481$	−16.2716	+	9.39439i	−0.741919	+	0.428347i
$482$	−15.4951	+	8.94612i	−0.705784	+	0.407485i
$483$		0			0
$484$	−1.95531	+	3.38669i	−0.0888776	+	0.153940i
$485$	7.83486	−	27.6795i	0.355763	−	1.25686i
$486$		0			0
$487$		−	11.5027i		−	0.521235i	−0.965442	−	0.260618i	$-0.916074\pi$
$487$		−	11.5027i		−	0.521235i	0.965442	−	0.260618i	$-0.0839262\pi$
$488$	−8.66705	−	5.00392i	−0.392339	−	0.226517i
$489$		0			0
$490$	10.6435	+	11.4768i	0.480823	+	0.518469i
$491$	−22.6834	+	13.0963i	−1.02369	+	0.591027i	−0.915170	−	0.403068i	$-0.867944\pi$
$491$	−22.6834	+	13.0963i	−1.02369	+	0.591027i	−0.108518	+	0.994094i	$0.534611\pi$
$492$		0			0
$493$	−11.2133	+	19.4220i	−0.505021	+	0.874722i
$494$			12.9612i			0.583151i
$495$		0			0
$496$			6.14313i			0.275835i
$497$	−22.5123	+	12.6455i	−1.00982	+	0.567228i
$498$		0			0
$499$	9.95558	+	17.2436i	0.445673	+	0.771928i	0.998099	−	0.0616337i	$-0.0196311\pi$
$499$	9.95558	+	17.2436i	0.445673	+	0.771928i	−0.552426	+	0.833562i	$0.686298\pi$
$500$	10.6679	+	3.34588i	0.477085	+	0.149632i
$501$		0			0
$502$	−2.06670	+	3.57963i	−0.0922413	+	0.159767i
$503$		−	29.7206i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$503$		−	29.7206i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$504$		0			0
$505$	2.51440	−	8.88303i	0.111889	−	0.395290i
$506$	1.63360	+	0.943160i	0.0726224	+	0.0419286i
$507$		0			0
$508$	14.0765	−	8.12704i	0.624542	−	0.360579i
$509$	2.08928	+	3.61874i	0.0926057	+	0.160398i	0.908607	−	0.417653i	$-0.137147\pi$
$509$	2.08928	+	3.61874i	0.0926057	+	0.160398i	−0.816001	+	0.578050i	$0.803814\pi$
$510$		0			0
$511$	−5.61378	−	9.99402i	−0.248339	−	0.442109i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	2.13937i		−	0.0943637i
$515$	−12.7815	−	13.1456i	−0.563220	−	0.579262i
$516$		0			0
$517$	−7.55032	−	13.0775i	−0.332063	−	0.575149i
$518$	0.253008	−	21.4276i	0.0111165	−	0.941475i
$519$		0			0
$520$	3.61601	+	3.71900i	0.158572	+	0.163089i
$521$	−2.01258			−0.0881725			−0.0440863	−	0.999028i	$-0.514038\pi$
$521$	−2.01258			−0.0881725			−0.0440863	+	0.999028i	$0.514038\pi$
$522$		0			0
$523$	−40.1926			−1.75750			−0.878750	−	0.477283i	$-0.841622\pi$
$523$	−40.1926			−1.75750			−0.878750	+	0.477283i	$0.841622\pi$
$524$	−1.95598	+	3.38785i	−0.0854473	+	0.147999i
$525$		0			0
$526$	−7.24259	−	12.5445i	−0.315792	−	0.546968i
$527$	22.2150	+	38.4775i	0.967701	+	1.67611i
$528$		0			0
$529$	11.2490	−	19.4839i	0.489089	−	0.847127i
$530$	−2.07621	+	7.33496i	−0.0901846	+	0.318610i
$531$		0			0
$532$	−12.7139	−	7.54193i	−0.551219	−	0.326984i
$533$	−8.53609	+	14.7849i	−0.369739	+	0.640407i
$534$		0			0
$535$	−22.7960	+	5.76638i	−0.985556	+	0.249302i
$536$	4.96469	−	2.86637i	0.214442	−	0.123808i
$537$		0			0
$538$	6.43928	−	11.1532i	0.277617	−	0.480847i
$539$	−16.3566	+	8.93535i	−0.704530	+	0.384873i
$540$		0			0
$541$	−26.0853			−1.12149			−0.560746	−	0.827988i	$-0.689486\pi$
$541$	−26.0853			−1.12149			−0.560746	+	0.827988i	$0.689486\pi$
$542$	−6.99458	−	4.03832i	−0.300443	−	0.173461i
$543$		0			0
$544$	6.26351	−	3.61624i	0.268546	−	0.155045i
$545$	−16.0080	+	4.04931i	−0.685707	+	0.173454i
$546$		0			0
$547$	−26.3226	−	15.1974i	−1.12547	−	0.649792i	−0.182680	−	0.983172i	$-0.558477\pi$
$547$	−26.3226	−	15.1974i	−1.12547	−	0.649792i	−0.942792	+	0.333381i	$0.891811\pi$
$548$	0.934992			0.0399409
$549$		0			0
$550$	−6.97757	+	11.3379i	−0.297525	+	0.483450i
$551$	−8.66258	+	15.0040i	−0.369038	+	0.639193i
$552$		0			0
$553$	−38.5832	−	0.455573i	−1.64072	−	0.0193729i
$554$	9.07801	−	5.24119i	0.385688	−	0.222677i
$555$		0			0
$556$	10.8220	+	6.24810i	0.458956	+	0.264978i
$557$	3.05968			0.129643			0.0648214	−	0.997897i	$-0.479352\pi$
$557$	3.05968			0.129643			0.0648214	+	0.997897i	$0.479352\pi$
$558$		0			0
$559$			30.3711i			1.28456i
$560$	−5.75216	+	1.38299i	−0.243073	+	0.0584421i
$561$		0			0
$562$	8.62857	−	4.98171i	0.363974	−	0.210141i
$563$	13.2448	−	7.64689i	0.558202	−	0.322278i	−0.194222	−	0.980958i	$-0.562218\pi$
$563$	13.2448	−	7.64689i	0.558202	−	0.322278i	0.752423	+	0.658680i	$0.228885\pi$
$564$		0			0
$565$	27.8201	+	28.6126i	1.17040	+	1.20374i
$566$	21.3788			0.898617
$567$		0			0
$568$		−	9.75935i		−	0.409493i
$569$	36.2482	+	20.9279i	1.51960	+	0.877342i	0.999733	+	0.0230961i	$0.00735237\pi$
$569$	36.2482	+	20.9279i	1.51960	+	0.877342i	0.519868	+	0.854246i	$0.325981\pi$
$570$		0			0
$571$	−3.71411	−	6.43303i	−0.155431	−	0.269214i	0.777785	−	0.628530i	$-0.216343\pi$
$571$	−3.71411	−	6.43303i	−0.155431	−	0.269214i	−0.933216	+	0.359317i	$0.883010\pi$
$572$	−5.34907	+	3.08829i	−0.223656	+	0.129128i
$573$		0			0
$574$	−9.53588	−	16.9764i	−0.398020	−	0.708581i
$575$	−3.01675	−	1.85657i	−0.125807	−	0.0774242i
$576$		0			0
$577$	−16.4756			−0.685890			−0.342945	−	0.939356i	$-0.611424\pi$
$577$	−16.4756			−0.685890			−0.342945	+	0.939356i	$0.611424\pi$
$578$	17.6544	−	30.5782i	0.734325	−	1.27189i
$579$		0			0
$580$	1.70035	+	6.72191i	0.0706030	+	0.279112i
$581$	−0.0814843	+	6.90103i	−0.00338054	+	0.286303i
$582$		0			0
$583$	−7.86111	−	4.53862i	−0.325574	−	0.187970i
$584$	4.33252			0.179281
$585$		0			0
$586$			11.4875i			0.474545i
$587$	−9.52825	−	5.50114i	−0.393273	−	0.227056i	0.290304	−	0.956934i	$-0.406243\pi$
$587$	−9.52825	−	5.50114i	−0.393273	−	0.227056i	−0.683577	+	0.729878i	$0.739577\pi$
$588$		0			0
$589$	17.1617	+	29.7250i	0.707137	+	1.22480i
$590$	−8.61013	+	2.17798i	−0.354473	+	0.0896661i
$591$		0			0
$592$	7.01432	+	4.04972i	0.288287	+	0.166442i
$593$		−	33.4327i		−	1.37292i	−0.727170	−	0.686458i	$-0.759165\pi$
$593$		−	33.4327i		−	1.37292i	0.727170	−	0.686458i	$-0.240835\pi$
$594$		0			0
$595$	−31.0275	+	29.4636i	−1.27200	+	1.20789i
$596$	2.62453	+	1.51527i	0.107505	+	0.0620681i
$597$		0			0
$598$	−0.821721	−	1.42326i	−0.0336027	−	0.0582015i
$599$	18.1385	−	10.4723i	0.741120	−	0.427886i	−0.0813566	−	0.996685i	$-0.525925\pi$
$599$	18.1385	−	10.4723i	0.741120	−	0.427886i	0.822476	+	0.568799i	$0.192592\pi$
$600$		0			0
$601$	16.4433	+	9.49353i	0.670735	+	0.387249i	0.796355	−	0.604829i	$-0.206759\pi$
$601$	16.4433	+	9.49353i	0.670735	+	0.387249i	−0.125620	+	0.992078i	$0.540092\pi$
$602$	−29.7917	−	17.6725i	−1.21422	−	0.720277i
$603$		0			0
$604$	9.50152			0.386612
$605$	6.09580	+	6.26943i	0.247829	+	0.254888i
$606$		0			0
$607$	0.824585	+	1.42822i	0.0334689	+	0.0579698i	0.882275	−	0.470735i	$-0.156011\pi$
$607$	0.824585	+	1.42822i	0.0334689	+	0.0579698i	−0.848806	+	0.528705i	$0.822678\pi$
$608$	4.83874	−	2.79365i	0.196237	−	0.113297i
$609$		0			0
$610$	−16.0444	+	15.6001i	−0.649619	+	0.631628i
$611$			13.1563i			0.532247i
$612$		0			0
$613$			9.15196i			0.369644i	0.982772	+	0.184822i	$0.0591709\pi$
$613$			9.15196i			0.369644i	−0.982772	+	0.184822i	$0.940829\pi$
$614$	−2.72283	+	4.71607i	−0.109884	+	0.190325i
$615$		0			0
$616$	0.0831731	−	7.04406i	0.00335114	−	0.283813i
$617$	−9.03988	−	15.6575i	−0.363932	−	0.630349i	0.624672	−	0.780887i	$-0.285233\pi$
$617$	−9.03988	−	15.6575i	−0.363932	−	0.630349i	−0.988604	+	0.150538i	$0.951899\pi$
$618$		0			0
$619$	−1.46056	−	0.843257i	−0.0587050	−	0.0338934i	0.470360	−	0.882475i	$-0.344124\pi$
$619$	−1.46056	−	0.843257i	−0.0587050	−	0.0338934i	−0.529065	+	0.848581i	$0.677457\pi$
$620$	13.2172	+	3.74120i	0.530814	+	0.150250i
$621$		0			0
$622$	3.35411			0.134488
$623$	7.33772	+	13.0631i	0.293979	+	0.523362i
$624$		0			0
$625$	13.6956	−	20.9148i	0.547825	−	0.836593i
$626$	15.6710	+	27.1430i	0.626340	+	1.08485i
$627$		0			0
$628$	−3.53933	+	6.13030i	−0.141235	+	0.244626i
$629$	58.5790			2.33570
$630$		0			0
$631$	7.16980			0.285425			0.142713	−	0.989764i	$-0.454418\pi$
$631$	7.16980			0.285425			0.142713	+	0.989764i	$0.454418\pi$
$632$	7.29204	−	12.6302i	0.290062	−	0.502402i
$633$		0			0
$634$	11.8243	+	20.4803i	0.469604	+	0.813378i
$635$	−8.91300	−	35.2354i	−0.353702	−	1.39828i
$636$		0			0
$637$	16.2338	+	0.383416i	0.643207	+	0.0151915i
$638$	−8.25620			−0.326866
$639$		0			0
$640$	0.609005	−	2.15154i	0.0240731	−	0.0850470i
$641$	−6.85692	−	3.95884i	−0.270832	−	0.156365i	0.358434	−	0.933555i	$-0.383311\pi$
$641$	−6.85692	−	3.95884i	−0.270832	−	0.156365i	−0.629266	+	0.777190i	$0.716644\pi$
$642$		0			0
$643$	18.5820	+	32.1850i	0.732802	+	1.26925i	0.955681	+	0.294404i	$0.0951213\pi$
$643$	18.5820	+	32.1850i	0.732802	+	1.26925i	−0.222879	+	0.974846i	$0.571545\pi$
$644$	1.87426	+	0.0221304i	0.0738562	+	0.000872061i
$645$		0			0
$646$	20.2050	−	34.9961i	0.794954	−	1.37690i
$647$			32.8858i			1.29287i	0.762967	+	0.646437i	$0.223742\pi$
$647$			32.8858i			1.29287i	−0.762967	+	0.646437i	$0.776258\pi$
$648$		0			0
$649$		−	10.5754i		−	0.415121i
$650$	10.2037	−	5.51508i	0.400223	−	0.216319i
$651$		0			0
$652$	−16.3030	+	9.41253i	−0.638474	+	0.368623i
$653$	8.87167	+	15.3662i	0.347175	+	0.601325i	0.985746	−	0.168238i	$-0.0538076\pi$
$653$	8.87167	+	15.3662i	0.347175	+	0.601325i	−0.638571	+	0.769563i	$0.720474\pi$
$654$		0			0
$655$	6.09789	+	6.27158i	0.238264	+	0.245051i
$656$	7.35946			0.287339
$657$		0			0
$658$	−12.9053	−	7.65547i	−0.503103	−	0.298441i
$659$	−31.1902	−	18.0077i	−1.21500	−	0.701479i	−0.251154	−	0.967947i	$-0.580810\pi$
$659$	−31.1902	−	18.0077i	−1.21500	−	0.701479i	−0.963844	+	0.266468i	$0.914143\pi$
$660$		0			0
$661$	−32.5566	+	18.7966i	−1.26630	+	0.731101i	−0.974287	−	0.225312i	$-0.927660\pi$
$661$	−32.5566	+	18.7966i	−1.26630	+	0.731101i	−0.292018	+	0.956413i	$0.594327\pi$
$662$	−4.96127	−	8.59317i	−0.192825	−	0.333983i
$663$		0			0
$664$	−2.25905	−	1.30426i	−0.0876682	−	0.0506153i
$665$	−23.9696	+	22.7614i	−0.929501	+	0.882651i
$666$		0			0
$667$		−	2.19678i		−	0.0850597i
$668$	−8.32228	−	4.80487i	−0.321999	−	0.185906i
$669$		0			0
$670$	−3.14357	−	12.4274i	−0.121447	−	0.480111i
$671$	−13.3234	−	23.0768i	−0.514344	−	0.890870i
$672$		0			0
$673$	10.9840	+	6.34162i	0.423402	+	0.244451i	0.696532	−	0.717526i	$-0.254725\pi$
$673$	10.9840	+	6.34162i	0.423402	+	0.244451i	−0.273130	+	0.961977i	$0.588059\pi$
$674$		−	26.2822i		−	1.01235i
$675$		0			0
$676$	−7.61871			−0.293027
$677$	−16.5374	−	9.54785i	−0.635583	−	0.366954i	0.147328	−	0.989088i	$-0.452933\pi$
$677$	−16.5374	−	9.54785i	−0.635583	−	0.366954i	−0.782911	+	0.622134i	$0.786266\pi$
$678$		0			0
$679$	34.0352	+	0.401873i	1.30615	+	0.0154225i
$680$	−3.96596	−	15.6785i	−0.152088	−	0.601242i
$681$		0			0
$682$	−8.17832	+	14.1653i	−0.313164	+	0.542416i
$683$	6.31366			0.241585			0.120793	−	0.992678i	$-0.461456\pi$
$683$	6.31366			0.241585			0.120793	+	0.992678i	$0.461456\pi$
$684$		0			0
$685$	0.569415	−	2.01167i	0.0217562	−	0.0768620i
$686$	−9.82232	+	15.7010i	−0.375018	+	0.599468i
$687$		0			0
$688$	11.3383	−	6.54616i	0.432268	−	0.249570i
$689$	3.95423	+	6.84894i	0.150644	+	0.260924i
$690$		0			0
$691$	−34.5932	−	19.9724i	−1.31599	−	0.759786i	−0.332908	−	0.942959i	$-0.608030\pi$
$691$	−34.5932	−	19.9724i	−1.31599	−	0.759786i	−0.983081	+	0.183173i	$0.941363\pi$
$692$			21.9294i			0.833629i
$693$		0			0
$694$	−28.1636			−1.06907
$695$	20.0337	−	19.4789i	0.759921	−	0.738876i
$696$		0			0
$697$	46.0960	−	26.6136i	1.74601	−	1.00806i
$698$	−1.18630	+	0.684908i	−0.0449020	+	0.0259242i
$699$		0			0
$700$	−0.527537	+	13.2182i	−0.0199390	+	0.499602i
$701$			8.43098i			0.318434i	0.987244	+	0.159217i	$0.0508969\pi$
$701$			8.43098i			0.318434i	−0.987244	+	0.159217i	$0.949103\pi$
$702$		0			0
$703$	45.2540			1.70679
$704$	2.30587	+	1.33130i	0.0869058	+	0.0501751i
$705$		0			0
$706$	9.38447	−	5.41813i	0.353189	−	0.203914i
$707$	10.9227	+	0.128971i	0.410791	+	0.00485044i
$708$		0			0
$709$	3.49123	−	6.04699i	0.131116	−	0.227100i	−0.792991	−	0.609233i	$-0.791477\pi$
$709$	3.49123	−	6.04699i	0.131116	−	0.227100i	0.924107	+	0.382134i	$0.124811\pi$
$710$	−20.9976	−	5.94350i	−0.788026	−	0.223055i
$711$		0			0
$712$	−5.66299			−0.212230
$713$	−3.76904	−	2.17606i	−0.141152	−	0.0814940i
$714$		0			0
$715$	3.38695	+	13.3895i	0.126665	+	0.500739i
$716$	2.01809	−	1.16514i	0.0754196	−	0.0435435i
$717$		0			0
$718$	−4.70674	−	2.71744i	−0.175654	−	0.101414i
$719$	−29.3256			−1.09366			−0.546830	−	0.837243i	$-0.684166\pi$
$719$	−29.3256			−1.09366			−0.546830	+	0.837243i	$0.684166\pi$
$720$		0			0
$721$	11.0682	−	18.6584i	0.412201	−	0.694875i
$722$	6.10892	−	10.5810i	0.227350	−	0.393783i
$723$		0			0
$724$	−17.0668	+	9.85352i	−0.634283	+	0.366203i
$725$	15.4980	+	0.435323i	0.575580	+	0.0161675i
$726$		0			0
$727$	−14.8721	+	25.7593i	−0.551576	+	0.955358i	0.446585	+	0.894741i	$0.352640\pi$
$727$	−14.8721	+	25.7593i	−0.551576	+	0.955358i	−0.998161	+	0.0606167i	$0.980693\pi$
$728$	−3.13130	+	5.27864i	−0.116054	+	0.195639i
$729$		0			0
$730$	2.63853	−	9.32157i	0.0976562	−	0.345007i
$731$	47.3450	−	82.0039i	1.75112	−	3.03302i
$732$		0			0
$733$	8.26100	+	14.3085i	0.305127	+	0.528496i	0.977290	−	0.211908i	$-0.0679677\pi$
$733$	8.26100	+	14.3085i	0.305127	+	0.528496i	−0.672163	+	0.740404i	$0.734634\pi$
$734$	7.28483	+	12.6177i	0.268888	+	0.465728i
$735$		0			0
$736$	−0.354226	+	0.613538i	−0.0130570	+	0.0226153i
$737$	15.2639			0.562254
$738$		0			0
$739$	−6.19918			−0.228041			−0.114020	−	0.993478i	$-0.536373\pi$
$739$	−6.19918			−0.228041			−0.114020	+	0.993478i	$0.536373\pi$
$740$	12.9849	−	12.6253i	0.477334	−	0.464114i
$741$		0			0
$742$	−9.01920	−	0.106495i	−0.331105	−	0.00390954i
$743$	18.3211	+	31.7331i	0.672137	+	1.16418i	0.977297	+	0.211874i	$0.0679568\pi$
$743$	18.3211	+	31.7331i	0.672137	+	1.16418i	−0.305160	+	0.952301i	$0.598710\pi$
$744$		0			0
$745$	4.85852	−	4.72397i	0.178003	−	0.173073i
$746$			35.9531i			1.31634i
$747$		0			0
$748$	19.2571			0.704110
$749$	−13.6256	−	24.2572i	−0.497869	−	0.886340i
$750$		0			0
$751$	0.432438	+	0.749005i	0.0157799	+	0.0273316i	0.873808	−	0.486272i	$-0.161644\pi$
$751$	0.432438	+	0.749005i	0.0157799	+	0.0273316i	−0.858028	+	0.513604i	$0.828310\pi$
$752$	4.91158	−	2.83570i	0.179107	−	0.103407i
$753$		0			0
$754$	6.22945	+	3.59658i	0.226863	+	0.130980i
$755$	5.78648	−	20.4429i	0.210592	−	0.743993i
$756$		0			0
$757$			43.1842i			1.56956i	0.619777	+	0.784778i	$0.287223\pi$
$757$			43.1842i			1.56956i	−0.619777	+	0.784778i	$0.712777\pi$
$758$	−1.02080	+	1.76807i	−0.0370770	+	0.0642193i
$759$		0			0
$760$	−3.06382	−	12.1121i	−0.111136	−	0.439351i
$761$	−7.49231	−	12.9771i	−0.271596	−	0.470418i	0.697675	−	0.716415i	$-0.254218\pi$
$761$	−7.49231	−	12.9771i	−0.271596	−	0.470418i	−0.969271	+	0.245996i	$0.920885\pi$
$762$		0			0
$763$	−9.56830	−	17.0341i	−0.346396	−	0.616677i
$764$			13.5465i			0.490094i
$765$		0			0
$766$			8.25716i			0.298343i
$767$	−4.60687	+	7.97934i	−0.166344	+	0.288117i
$768$		0			0
$769$	−0.786782	+	0.454249i	−0.0283721	+	0.0163806i	−0.514119	−	0.857719i	$-0.671881\pi$
$769$	−0.786782	+	0.454249i	−0.0283721	+	0.0163806i	0.485747	+	0.874100i	$0.338548\pi$
$770$	−15.1049	−	4.46882i	−0.544343	−	0.161045i
$771$		0			0
$772$	−6.99314	−	4.03749i	−0.251689	−	0.145313i
$773$		−	44.2918i		−	1.59307i	−0.604595	−	0.796533i	$-0.706665\pi$
$773$		−	44.2918i		−	1.59307i	0.604595	−	0.796533i	$-0.293335\pi$
$774$		0			0
$775$	16.0987	−	26.1588i	0.578281	−	0.939653i
$776$	−6.43250	+	11.1414i	−0.230913	+	0.399954i
$777$		0			0
$778$	15.6859	−	9.05627i	0.562367	−	0.324683i
$779$	35.6105	−	20.5597i	1.27588	−	0.736628i
$780$		0			0
$781$	12.9926	−	22.5038i	0.464911	−	0.805249i
$782$			5.12387i			0.183229i
$783$		0			0
$784$	−3.35589	−	6.14313i	−0.119853	−	0.219397i
$785$	11.0341	+	11.3484i	0.393824	+	0.405042i
$786$		0			0
$787$	15.5156	+	26.8737i	0.553070	+	0.957945i	0.998051	+	0.0624052i	$0.0198771\pi$
$787$	15.5156	+	26.8737i	0.553070	+	0.957945i	−0.444981	+	0.895540i	$0.646790\pi$
$788$	0.881859	+	1.52743i	0.0314149	+	0.0544123i
$789$		0			0
$790$	−22.7334	−	23.3809i	−0.808819	−	0.831857i
$791$	−24.0910	+	40.6118i	−0.856577	+	1.44399i
$792$		0			0
$793$			23.2158i			0.824418i
$794$	1.24413	−	2.15489i	0.0441524	−	0.0764742i
$795$		0			0
$796$	−2.93602	+	1.69511i	−0.104064	+	0.0600817i
$797$	15.7354	−	9.08484i	0.557377	−	0.321802i	−0.194715	−	0.980860i	$-0.562378\pi$
$797$	15.7354	−	9.08484i	0.557377	−	0.321802i	0.752092	+	0.659058i	$0.229045\pi$
$798$		0			0
$799$	20.5092	−	35.5229i	0.725562	−	1.25671i
$800$	−4.25822	−	2.62060i	−0.150551	−	0.0926520i
$801$		0			0
$802$		−	34.8815i		−	1.23171i
$803$	9.99022	+	5.76786i	0.352547	+	0.203543i
$804$		0			0
$805$	1.18905	−	4.01906i	0.0419084	−	0.141653i
$806$	12.3414	−	7.12530i	0.434706	−	0.250978i
$807$		0			0
$808$	−2.06435	+	3.57555i	−0.0726234	+	0.125787i
$809$		−	52.2729i		−	1.83782i	−0.394471	−	0.918908i	$-0.629072\pi$
$809$		−	52.2729i		−	1.83782i	0.394471	−	0.918908i	$-0.370928\pi$
$810$		0			0
$811$		−	10.4441i		−	0.366741i	−0.983044	−	0.183370i	$-0.941299\pi$
$811$		−	10.4441i		−	0.366741i	0.983044	−	0.183370i	$-0.0587008\pi$
$812$	−7.15280	+	4.01782i	−0.251014	+	0.140998i
$813$		0			0
$814$	10.7827	+	18.6763i	0.377935	+	0.654603i
$815$	10.3228	+	40.8087i	0.361592	+	1.42947i
$816$		0			0
$817$	36.5753	−	63.3503i	1.27961	−	2.21635i
$818$			8.79732i			0.307591i
$819$		0			0
$820$	4.48195	−	15.8341i	0.156516	−	0.552952i
$821$	−11.0056	−	6.35410i	−0.384099	−	0.221760i	0.295501	−	0.955342i	$-0.404513\pi$
$821$	−11.0056	−	6.35410i	−0.384099	−	0.221760i	−0.679600	+	0.733583i	$0.737847\pi$
$822$		0			0
$823$	−22.4253	+	12.9473i	−0.781697	+	0.451313i	−0.837031	−	0.547155i	$-0.815711\pi$
$823$	−22.4253	+	12.9473i	−0.781697	+	0.451313i	0.0553342	+	0.998468i	$0.482378\pi$
$824$	4.09983	+	7.10111i	0.142824	+	0.247379i
$825$		0			0
$826$	−5.14645	−	9.16205i	−0.179068	−	0.318789i
$827$	−14.3307			−0.498329			−0.249164	−	0.968461i	$-0.580156\pi$
$827$	−14.3307			−0.498329			−0.249164	+	0.968461i	$0.580156\pi$
$828$		0			0
$829$		−	5.00694i		−	0.173898i	−0.996213	−	0.0869490i	$-0.972288\pi$
$829$		−	5.00694i		−	0.173898i	0.996213	−	0.0869490i	$-0.0277117\pi$
$830$	−4.18195	+	4.06613i	−0.145157	+	0.141137i
$831$		0			0
$832$	−1.15988	−	2.00897i	−0.0402116	−	0.0696486i
$833$	−43.2346	−	26.3419i	−1.49799	−	0.912691i
$834$		0			0
$835$	−15.4062	+	14.9795i	−0.533152	+	0.518387i
$836$	14.8767			0.514520
$837$		0			0
$838$	−0.0721315			−0.00249174
$839$	−17.1066	+	29.6295i	−0.590586	+	1.02292i	0.403568	+	0.914950i	$0.367770\pi$
$839$	−17.1066	+	29.6295i	−0.590586	+	1.02292i	−0.994154	+	0.107975i	$0.965564\pi$
$840$		0			0
$841$	−9.69247	−	16.7878i	−0.334223	−	0.578891i
$842$	3.42682	+	5.93543i	0.118096	+	0.204549i
$843$		0			0
$844$	1.09815	−	1.90206i	0.0378000	−	0.0654715i
$845$	−4.63983	+	16.3919i	−0.159615	+	0.563900i
$846$		0			0
$847$	−5.27869	+	8.89864i	−0.181378	+	0.305761i
$848$	1.70459	−	2.95243i	0.0585358	−	0.101387i
$849$		0			0
$850$	−36.1481	−	1.01537i	−1.23987	−	0.0348268i
$851$	−4.96932	+	2.86904i	−0.170346	+	0.0983493i
$852$		0			0
$853$	17.5564	−	30.4086i	0.601119	−	1.04117i	−0.391532	−	0.920164i	$-0.628055\pi$
$853$	17.5564	−	30.4086i	0.601119	−	1.04117i	0.992652	−	0.121005i	$-0.0386117\pi$
$854$	−22.7730	−	13.5090i	−0.779274	−	0.462267i
$855$		0			0
$856$	10.5158			0.359422
$857$	5.45905	+	3.15178i	0.186477	+	0.107663i	0.590332	−	0.807160i	$-0.298997\pi$
$857$	5.45905	+	3.15178i	0.186477	+	0.107663i	−0.403855	+	0.914823i	$0.632330\pi$
$858$		0			0
$859$	28.2571	−	16.3143i	0.964121	−	0.556636i	0.0666823	−	0.997774i	$-0.478759\pi$
$859$	28.2571	−	16.3143i	0.964121	−	0.556636i	0.897439	+	0.441139i	$0.145425\pi$
$860$	−7.17923	−	28.3814i	−0.244810	−	0.967797i
$861$		0			0
$862$	3.77671	+	2.18048i	0.128635	+	0.0742676i
$863$	43.4092			1.47767			0.738834	−	0.673888i	$-0.235377\pi$
$863$	43.4092			1.47767			0.738834	+	0.673888i	$0.235377\pi$
$864$		0			0
$865$	47.1818	+	13.3551i	1.60423	+	0.454087i
$866$	−16.2834	+	28.2037i	−0.553332	+	0.958399i
$867$		0			0
$868$	−0.191897	+	16.2521i	−0.00651341	+	0.551631i
$869$	33.6290	−	19.4157i	1.14079	−	0.658633i
$870$		0			0
$871$	−11.5169	−	6.64929i	−0.390236	−	0.225303i
$872$	7.38448			0.250070
$873$		0			0
$874$			3.95833i			0.133893i
$875$	28.1182	+	9.18499i	0.950570	+	0.310509i
$876$		0			0
$877$	−22.5421	+	13.0147i	−0.761193	+	0.439475i	−0.829724	−	0.558174i	$-0.811502\pi$
$877$	−22.5421	+	13.0147i	−0.761193	+	0.439475i	0.0685308	+	0.997649i	$0.478169\pi$
$878$	−26.2998	+	15.1842i	−0.887577	+	0.512443i
$879$		0			0
$880$	4.26862	−	4.15040i	0.143895	−	0.139910i
$881$	−3.51648			−0.118473			−0.0592366	−	0.998244i	$-0.518867\pi$
$881$	−3.51648			−0.118473			−0.0592366	+	0.998244i	$0.518867\pi$
$882$		0			0
$883$		−	5.38947i		−	0.181370i	−0.995880	−	0.0906851i	$-0.971094\pi$
$883$		−	5.38947i		−	0.181370i	0.995880	−	0.0906851i	$-0.0289057\pi$
$884$	−14.5298	−	8.38881i	−0.488692	−	0.282146i
$885$		0			0
$886$	−18.8007	−	32.5637i	−0.631620	−	1.09400i
$887$	33.1558	−	19.1425i	1.11326	−	0.642742i	0.173589	−	0.984818i	$-0.444464\pi$
$887$	33.1558	−	19.1425i	1.11326	−	0.642742i	0.939672	+	0.342076i	$0.111130\pi$
$888$		0			0
$889$	37.4941	−	21.0609i	1.25751	−	0.706361i
$890$	−3.44879	+	12.1841i	−0.115604	+	0.408413i
$891$		0			0
$892$	−9.39129			−0.314444
$893$	15.8439	−	27.4425i	0.530196	−	0.918327i
$894$		0			0
$895$	−1.27782	−	5.05158i	−0.0427130	−	0.168856i
$896$	2.64557	+	0.0312377i	0.0883822	+	0.00104358i
$897$		0			0
$898$	3.74608	+	2.16280i	0.125008	+	0.0721736i
$899$	19.0487			0.635310
$900$		0			0
$901$		−	24.6568i		−	0.821436i
$902$	16.9700	+	9.79761i	0.565038	+	0.326225i
$903$		0			0
$904$	−8.92367	−	15.4563i	−0.296797	−	0.514067i
$905$	10.8064	+	42.7207i	0.359218	+	1.42008i
$906$		0			0
$907$	−3.01367	−	1.73994i	−0.100067	−	0.0577738i	0.449131	−	0.893466i	$-0.351734\pi$
$907$	−3.01367	−	1.73994i	−0.100067	−	0.0577738i	−0.549198	+	0.835692i	$0.685067\pi$
$908$		−	2.60953i		−	0.0866003i
$909$		0			0
$910$	9.45021	+	9.95182i	0.313271	+	0.329900i
$911$	46.3590	+	26.7654i	1.53594	+	0.886777i	0.999070	+	0.0431128i	$0.0137275\pi$
$911$	46.3590	+	26.7654i	1.53594	+	0.886777i	0.536872	+	0.843664i	$0.319606\pi$
$912$		0			0
$913$	−3.47272	−	6.01493i	−0.114930	−	0.199065i
$914$	−18.5026	+	10.6825i	−0.612010	+	0.353344i
$915$		0			0
$916$	−2.92097	−	1.68642i	−0.0965115	−	0.0557210i
$917$	−5.28050	+	8.90169i	−0.174377	+	0.293960i
$918$		0			0
$919$	−15.2442			−0.502861			−0.251430	−	0.967875i	$-0.580901\pi$
$919$	−15.2442			−0.502861			−0.251430	+	0.967875i	$0.580901\pi$
$920$	1.10432	+	1.13578i	0.0364085	+	0.0374455i
$921$		0			0
$922$	9.79603	+	16.9672i	0.322615	+	0.558786i
$923$	−19.6063	+	11.3197i	−0.645348	+	0.372592i
$924$		0			0
$925$	−19.2559	−	35.6263i	−0.633129	−	1.17139i
$926$		−	20.5064i		−	0.673883i
$927$		0			0
$928$		−	3.10082i		−	0.101789i
$929$	15.7876	−	27.3450i	0.517975	−	0.897159i	−0.481807	−	0.876277i	$-0.660019\pi$
$929$	15.7876	−	27.3450i	0.517975	−	0.897159i	0.999782	−	0.0208818i	$-0.00664736\pi$
$930$		0			0
$931$	−33.4000	−	20.3498i	−1.09464	−	0.666939i
$932$	−12.2325	−	21.1873i	−0.400689	−	0.694013i
$933$		0			0
$934$	−12.4017	−	7.16013i	−0.405796	−	0.234287i
$935$	11.7277	−	41.4324i	0.383537	−	1.35498i
$936$		0			0
$937$	−3.67779			−0.120148			−0.0600741	−	0.998194i	$-0.519134\pi$
$937$	−3.67779			−0.120148			−0.0600741	+	0.998194i	$0.519134\pi$
$938$	13.2240	−	7.42808i	0.431778	−	0.242535i
$939$		0			0
$940$	−3.10994	−	12.2944i	−0.101435	−	0.401000i
$941$	−16.5040	−	28.5858i	−0.538016	−	0.931870i	−0.999011	−	0.0444678i	$-0.985841\pi$
$941$	−16.5040	−	28.5858i	−0.538016	−	0.931870i	0.460995	−	0.887403i	$-0.347493\pi$
$942$		0			0
$943$	−2.60691	+	4.51531i	−0.0848928	+	0.147039i
$944$	3.97185			0.129273
$945$		0			0
$946$	34.8595			1.13338
$947$	3.23974	−	5.61139i	0.105277	−	0.182346i	−0.808574	−	0.588394i	$-0.799760\pi$
$947$	3.23974	−	5.61139i	0.105277	−	0.182346i	0.913851	+	0.406049i	$0.133094\pi$
$948$		0			0
$949$	−5.02520	−	8.70391i	−0.163125	−	0.282541i
$950$	−27.9254	−	0.784399i	−0.906021	−	0.0254493i
$951$		0			0
$952$	16.6835	−	9.37134i	0.540715	−	0.303727i
$953$	16.0190			0.518908			0.259454	−	0.965756i	$-0.416457\pi$
$953$	16.0190			0.518908			0.259454	+	0.965756i	$0.416457\pi$
$954$		0			0
$955$	29.1457	+	8.24987i	0.943133	+	0.266959i
$956$	14.3027	+	8.25768i	0.462583	+	0.267072i
$957$		0			0
$958$	−12.6756	−	21.9548i	−0.409531	−	0.709328i
$959$	2.47358	+	0.0292070i	0.0798762	+	0.000943143i
$960$		0			0
$961$	3.36902	−	5.83531i	0.108678	−	0.188236i
$962$		−	18.7888i		−	0.605774i
$963$		0			0
$964$		−	17.8922i		−	0.576270i
$965$	−12.9457	+	12.5872i	−0.416736	+	0.405195i
$966$		0			0
$967$	−44.9097	+	25.9286i	−1.44420	+	0.833808i	−0.998126	−	0.0611892i	$-0.980511\pi$
$967$	−44.9097	+	25.9286i	−1.44420	+	0.833808i	−0.446072	+	0.894997i	$0.647177\pi$
$968$	−1.95531	−	3.38669i	−0.0628459	−	0.108852i
$969$		0			0
$970$	20.0538	+	20.6250i	0.643887	+	0.662227i
$971$	−12.7024			−0.407638			−0.203819	−	0.979009i	$-0.565335\pi$
$971$	−12.7024			−0.407638			−0.203819	+	0.979009i	$0.565335\pi$
$972$		0			0
$973$	28.4352	+	16.8678i	0.911591	+	0.540758i
$974$	9.96159	+	5.75133i	0.319190	+	0.184284i
$975$		0			0
$976$	8.66705	−	5.00392i	0.277426	−	0.160172i
$977$	6.82737	+	11.8253i	0.218427	+	0.378326i	0.954327	−	0.298763i	$-0.0965742\pi$
$977$	6.82737	+	11.8253i	0.218427	+	0.378326i	−0.735900	+	0.677090i	$0.763241\pi$
$978$		0			0
$979$	−13.0581	−	7.53912i	−0.417340	−	0.240951i
$980$	−15.2609	+	3.47911i	−0.487492	+	0.111136i
$981$		0			0
$982$		−	26.1926i		−	0.835838i
$983$	9.69185	+	5.59559i	0.309122	+	0.178472i	0.646534	−	0.762886i	$-0.276218\pi$
$983$	9.69185	+	5.59559i	0.309122	+	0.178472i	−0.337411	+	0.941357i	$0.609551\pi$
$984$		0			0
$985$	3.82337	−	0.967143i	0.121823	−	0.0308157i
$986$	−11.2133	−	19.4220i	−0.357104	−	0.618522i
$987$		0			0
$988$	−11.2247	−	6.48059i	−0.357106	−	0.206175i
$989$			9.27529i			0.294937i
$990$		0			0
$991$	25.9249			0.823530			0.411765	−	0.911290i	$-0.364912\pi$
$991$	25.9249			0.823530			0.411765	+	0.911290i	$0.364912\pi$
$992$	−5.32011	−	3.07156i	−0.168914	−	0.0975223i
$993$		0			0
$994$	0.304859	−	25.8190i	0.00966955	−	0.818929i
$995$	1.85905	+	7.34929i	0.0589357	+	0.232988i
$996$		0			0
$997$	−9.94358	+	17.2228i	−0.314916	+	0.545451i	−0.979420	−	0.201834i	$-0.935310\pi$
$997$	−9.94358	+	17.2228i	−0.314916	+	0.545451i	0.664503	+	0.747285i	$0.268643\pi$
$998$	−19.9112			−0.630277
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.e.629.3		32
3.2	odd	2		630.2.bf.f.209.6	yes	32
5.4	even	2		1890.2.bf.f.629.15		32
7.6	odd	2	inner	1890.2.bf.e.629.14		32
9.4	even	3		630.2.bf.e.419.6	yes	32
9.5	odd	6		1890.2.bf.f.1259.2		32
15.14	odd	2		630.2.bf.e.209.11	yes	32
21.20	even	2		630.2.bf.f.209.11	yes	32
35.34	odd	2		1890.2.bf.f.629.2		32
45.4	even	6		630.2.bf.f.419.11	yes	32
45.14	odd	6	inner	1890.2.bf.e.1259.14		32
63.13	odd	6		630.2.bf.e.419.11	yes	32
63.41	even	6		1890.2.bf.f.1259.15		32
105.104	even	2		630.2.bf.e.209.6	✓	32
315.104	even	6	inner	1890.2.bf.e.1259.3		32
315.139	odd	6		630.2.bf.f.419.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.6	✓	32	105.104	even	2
630.2.bf.e.209.11	yes	32	15.14	odd	2
630.2.bf.e.419.6	yes	32	9.4	even	3
630.2.bf.e.419.11	yes	32	63.13	odd	6
630.2.bf.f.209.6	yes	32	3.2	odd	2
630.2.bf.f.209.11	yes	32	21.20	even	2
630.2.bf.f.419.6	yes	32	315.139	odd	6
630.2.bf.f.419.11	yes	32	45.4	even	6
1890.2.bf.e.629.3		32	1.1	even	1	trivial
1890.2.bf.e.629.14		32	7.6	odd	2	inner
1890.2.bf.e.1259.3		32	315.104	even	6	inner
1890.2.bf.e.1259.14		32	45.14	odd	6	inner
1890.2.bf.f.629.2		32	35.34	odd	2
1890.2.bf.f.629.15		32	5.4	even	2
1890.2.bf.f.1259.2		32	9.5	odd	6
1890.2.bf.f.1259.15		32	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16779 + 0.548354i) q^{5} +(-1.29573 - 2.30675i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16779 + 0.548354i) q^{5} +(-1.29573 - 2.30675i) q^{7} +1.00000 q^{8} +(0.609005 - 2.15154i) q^{10} +(2.30587 + 1.33130i) q^{11} +(-1.15988 - 2.00897i) q^{13} +(2.64557 + 0.0312377i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.23248i q^{17} +5.58729i q^{19} +(1.55878 + 1.60318i) q^{20} +(-2.30587 + 1.33130i) q^{22} +(-0.354226 - 0.613538i) q^{23} +(4.39861 - 2.37743i) q^{25} +2.31976 q^{26} +(-1.34984 + 2.27551i) q^{28} +(2.68539 + 1.55041i) q^{29} +(5.32011 - 3.07156i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.26351 - 3.61624i) q^{34} +(4.07379 + 4.29002i) q^{35} -8.09944i q^{37} +(-4.83874 - 2.79365i) q^{38} +(-2.16779 + 0.548354i) q^{40} +(-3.67973 - 6.37348i) q^{41} +(-11.3383 - 6.54616i) q^{43} -2.66259i q^{44} +0.708453 q^{46} +(-4.91158 - 2.83570i) q^{47} +(-3.64216 + 5.97785i) q^{49} +(-0.140390 + 4.99803i) q^{50} +(-1.15988 + 2.00897i) q^{52} -3.40917 q^{53} +(-5.72866 - 1.62153i) q^{55} +(-1.29573 - 2.30675i) q^{56} +(-2.68539 + 1.55041i) q^{58} +(-1.98592 - 3.43972i) q^{59} +(-8.66705 - 5.00392i) q^{61} +6.14313i q^{62} +1.00000 q^{64} +(3.61601 + 3.71900i) q^{65} +(4.96469 - 2.86637i) q^{67} +(6.26351 - 3.61624i) q^{68} +(-5.75216 + 1.38299i) q^{70} -9.75935i q^{71} +4.33252 q^{73} +(7.01432 + 4.04972i) q^{74} +(4.83874 - 2.79365i) q^{76} +(0.0831731 - 7.04406i) q^{77} +(7.29204 - 12.6302i) q^{79} +(0.609005 - 2.15154i) q^{80} +7.35946 q^{82} +(-2.25905 - 1.30426i) q^{83} +(-3.96596 - 15.6785i) q^{85} +(11.3383 - 6.54616i) q^{86} +(2.30587 + 1.33130i) q^{88} -5.66299 q^{89} +(-3.13130 + 5.27864i) q^{91} +(-0.354226 + 0.613538i) q^{92} +(4.91158 - 2.83570i) q^{94} +(-3.06382 - 12.1121i) q^{95} +(-6.43250 + 11.1414i) q^{97} +(-3.35589 - 6.14313i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

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