LMFDB - Embedded newform 804.2.j.b.499.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.12
Character	$\chi$	$=$	804.499
Dual form			804.2.j.b.775.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.722396 - 1.21579i) q^{2} +1.00000 q^{3} +(-0.956289 + 1.75656i) q^{4} -1.43594i q^{5} +(-0.722396 - 1.21579i) q^{6} +(-1.39755 + 2.42063i) q^{7} +(2.82643 - 0.106288i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.722396 - 1.21579i) q^{2} +1.00000 q^{3} +(-0.956289 + 1.75656i) q^{4} -1.43594i q^{5} +(-0.722396 - 1.21579i) q^{6} +(-1.39755 + 2.42063i) q^{7} +(2.82643 - 0.106288i) q^{8} +1.00000 q^{9} +(-1.74580 + 1.03732i) q^{10} +(1.49904 - 2.59641i) q^{11} +(-0.956289 + 1.75656i) q^{12} +(-4.37302 + 2.52476i) q^{13} +(3.95256 - 0.0495245i) q^{14} -1.43594i q^{15} +(-2.17102 - 3.35956i) q^{16} +(-4.04917 - 7.01337i) q^{17} +(-0.722396 - 1.21579i) q^{18} +(7.17701 - 4.14365i) q^{19} +(2.52232 + 1.37317i) q^{20} +(-1.39755 + 2.42063i) q^{21} +(-4.23958 + 0.0531208i) q^{22} +(3.65026 - 2.10748i) q^{23} +(2.82643 - 0.106288i) q^{24} +2.93808 q^{25} +(6.22863 + 3.49279i) q^{26} +1.00000 q^{27} +(-2.91552 - 4.76970i) q^{28} +(1.82696 - 3.16439i) q^{29} +(-1.74580 + 1.03732i) q^{30} +(1.72356 - 2.98529i) q^{31} +(-2.51618 + 5.06644i) q^{32} +(1.49904 - 2.59641i) q^{33} +(-5.60168 + 9.98938i) q^{34} +(3.47587 + 2.00680i) q^{35} +(-0.956289 + 1.75656i) q^{36} +(-4.57450 - 7.92326i) q^{37} +(-10.2225 - 5.73238i) q^{38} +(-4.37302 + 2.52476i) q^{39} +(-0.152623 - 4.05858i) q^{40} +(3.52804 + 2.03691i) q^{41} +(3.95256 - 0.0495245i) q^{42} +2.34744 q^{43} +(3.12724 + 5.11606i) q^{44} -1.43594i q^{45} +(-5.19918 - 2.91551i) q^{46} +(-0.474168 - 0.273761i) q^{47} +(-2.17102 - 3.35956i) q^{48} +(-0.406288 - 0.703712i) q^{49} +(-2.12245 - 3.57208i) q^{50} +(-4.04917 - 7.01337i) q^{51} +(-0.253037 - 10.0959i) q^{52} -0.982679i q^{53} +(-0.722396 - 1.21579i) q^{54} +(-3.72828 - 2.15252i) q^{55} +(-3.69279 + 6.99027i) q^{56} +(7.17701 - 4.14365i) q^{57} +(-5.16703 + 0.0647415i) q^{58} +9.80358i q^{59} +(2.52232 + 1.37317i) q^{60} +(-1.22491 + 0.707202i) q^{61} +(-4.87458 + 0.0610772i) q^{62} +(-1.39755 + 2.42063i) q^{63} +(7.97741 - 0.600830i) q^{64} +(3.62541 + 6.27939i) q^{65} +(-4.23958 + 0.0531208i) q^{66} +(1.94133 - 7.95181i) q^{67} +(16.1916 - 0.405817i) q^{68} +(3.65026 - 2.10748i) q^{69} +(-0.0711142 - 5.67563i) q^{70} +(-6.77642 - 3.91237i) q^{71} +(2.82643 - 0.106288i) q^{72} +(-3.06780 - 5.31359i) q^{73} +(-6.32842 + 11.2854i) q^{74} +2.93808 q^{75} +(0.415286 + 16.5694i) q^{76} +(4.18995 + 7.25721i) q^{77} +(6.22863 + 3.49279i) q^{78} +(-3.32083 + 5.75185i) q^{79} +(-4.82413 + 3.11746i) q^{80} +1.00000 q^{81} +(-0.0721815 - 5.76081i) q^{82} +(7.53775 - 4.35192i) q^{83} +(-2.91552 - 4.76970i) q^{84} +(-10.0708 + 5.81437i) q^{85} +(-1.69578 - 2.85400i) q^{86} +(1.82696 - 3.16439i) q^{87} +(3.96095 - 7.49789i) q^{88} +3.05706 q^{89} +(-1.74580 + 1.03732i) q^{90} -14.1139i q^{91} +(0.211216 + 8.42726i) q^{92} +(1.72356 - 2.98529i) q^{93} +(0.00970118 + 0.774252i) q^{94} +(-5.95003 - 10.3058i) q^{95} +(-2.51618 + 5.06644i) q^{96} +(-13.2713 + 7.66220i) q^{97} +(-0.562064 + 1.00232i) q^{98} +(1.49904 - 2.59641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	$ 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.722396	−	1.21579i	−0.510811	−	0.859693i
$2$	−0.722396	−	1.21579i	−0.510811	−	0.859693i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.956289	+	1.75656i	−0.478144	+	0.878281i
$5$		−	1.43594i		−	0.642172i	−0.947050	−	0.321086i	$-0.895952\pi$
$5$		−	1.43594i		−	0.642172i	0.947050	−	0.321086i	$-0.104048\pi$
$6$	−0.722396	−	1.21579i	−0.294917	−	0.496344i
$7$	−1.39755	+	2.42063i	−0.528224	+	0.914911i	0.471235	+	0.882008i	$0.343809\pi$
$7$	−1.39755	+	2.42063i	−0.528224	+	0.914911i	−0.999459	+	0.0329028i	$0.989525\pi$
$8$	2.82643	−	0.106288i	0.999294	−	0.0375784i
$9$	1.00000			0.333333
$10$	−1.74580	+	1.03732i	−0.552071	+	0.328028i
$11$	1.49904	−	2.59641i	0.451976	−	0.782846i	−0.546533	−	0.837438i	$-0.684053\pi$
$11$	1.49904	−	2.59641i	0.451976	−	0.782846i	0.998509	+	0.0545922i	$0.0173859\pi$
$12$	−0.956289	+	1.75656i	−0.276057	+	0.507076i
$13$	−4.37302	+	2.52476i	−1.21286	+	0.700243i	−0.963381	−	0.268137i	$-0.913592\pi$
$13$	−4.37302	+	2.52476i	−1.21286	+	0.700243i	−0.249477	+	0.968381i	$0.580259\pi$
$14$	3.95256	−	0.0495245i	1.05637	−	0.0132360i
$15$		−	1.43594i		−	0.370758i
$16$	−2.17102	−	3.35956i	−0.542756	−	0.839890i
$17$	−4.04917	−	7.01337i	−0.982069	−	1.70099i	−0.654300	−	0.756235i	$-0.727037\pi$
$17$	−4.04917	−	7.01337i	−0.982069	−	1.70099i	−0.327769	−	0.944758i	$-0.606297\pi$
$18$	−0.722396	−	1.21579i	−0.170270	−	0.286564i
$19$	7.17701	−	4.14365i	1.64652	−	0.950618i	0.668079	−	0.744090i	$-0.267117\pi$
$19$	7.17701	−	4.14365i	1.64652	−	0.950618i	0.978441	−	0.206528i	$-0.0662165\pi$
$20$	2.52232	+	1.37317i	0.564007	+	0.307051i
$21$	−1.39755	+	2.42063i	−0.304970	+	0.528224i
$22$	−4.23958	+	0.0531208i	−0.903881	+	0.0113254i
$23$	3.65026	−	2.10748i	0.761131	−	0.439439i	−0.0685704	−	0.997646i	$-0.521844\pi$
$23$	3.65026	−	2.10748i	0.761131	−	0.439439i	0.829702	+	0.558207i	$0.188510\pi$
$24$	2.82643	−	0.106288i	0.576942	−	0.0216959i
$25$	2.93808			0.587615
$26$	6.22863	+	3.49279i	1.22154	+	0.684993i
$27$	1.00000			0.192450
$28$	−2.91552	−	4.76970i	−0.550982	−	0.901389i
$29$	1.82696	−	3.16439i	0.339259	−	0.587613i	−0.645035	−	0.764153i	$-0.723157\pi$
$29$	1.82696	−	3.16439i	0.339259	−	0.587613i	0.984293	+	0.176540i	$0.0564905\pi$
$30$	−1.74580	+	1.03732i	−0.318738	+	0.189387i
$31$	1.72356	−	2.98529i	0.309560	−	0.536174i	−0.668706	−	0.743527i	$-0.733151\pi$
$31$	1.72356	−	2.98529i	0.309560	−	0.536174i	0.978266	+	0.207353i	$0.0664848\pi$
$32$	−2.51618	+	5.06644i	−0.444802	+	0.895629i
$33$	1.49904	−	2.59641i	0.260949	−	0.451976i
$34$	−5.60168	+	9.98938i	−0.960680	+	1.71316i
$35$	3.47587	+	2.00680i	0.587530	+	0.339211i
$36$	−0.956289	+	1.75656i	−0.159381	+	0.292760i
$37$	−4.57450	−	7.92326i	−0.752042	−	1.30258i	−0.946831	−	0.321731i	$-0.895735\pi$
$37$	−4.57450	−	7.92326i	−0.752042	−	1.30258i	0.194789	−	0.980845i	$-0.437598\pi$
$38$	−10.2225	−	5.73238i	−1.65830	−	0.929915i
$39$	−4.37302	+	2.52476i	−0.700243	+	0.404286i
$40$	−0.152623	−	4.05858i	−0.0241318	−	0.641718i
$41$	3.52804	+	2.03691i	0.550987	+	0.318112i	0.749520	−	0.661982i	$-0.230284\pi$
$41$	3.52804	+	2.03691i	0.550987	+	0.318112i	−0.198533	+	0.980094i	$0.563618\pi$
$42$	3.95256	−	0.0495245i	0.609893	−	0.00764180i
$43$	2.34744			0.357982			0.178991	−	0.983851i	$-0.442717\pi$
$43$	2.34744			0.357982			0.178991	+	0.983851i	$0.442717\pi$
$44$	3.12724	+	5.11606i	0.471449	+	0.771275i
$45$		−	1.43594i		−	0.214057i
$46$	−5.19918	−	2.91551i	−0.766577	−	0.429869i
$47$	−0.474168	−	0.273761i	−0.0691645	−	0.0399322i	0.465019	−	0.885301i	$-0.346048\pi$
$47$	−0.474168	−	0.273761i	−0.0691645	−	0.0399322i	−0.534183	+	0.845369i	$0.679381\pi$
$48$	−2.17102	−	3.35956i	−0.313360	−	0.484911i
$49$	−0.406288	−	0.703712i	−0.0580411	−	0.100530i
$50$	−2.12245	−	3.57208i	−0.300160	−	0.505169i
$51$	−4.04917	−	7.01337i	−0.566998	−	0.982069i
$52$	−0.253037	−	10.0959i	−0.0350900	−	1.40005i
$53$		−	0.982679i		−	0.134981i	−0.997720	−	0.0674906i	$-0.978501\pi$
$53$		−	0.982679i		−	0.134981i	0.997720	−	0.0674906i	$-0.0214993\pi$
$54$	−0.722396	−	1.21579i	−0.0983056	−	0.165448i
$55$	−3.72828	−	2.15252i	−0.502721	−	0.290246i
$56$	−3.69279	+	6.99027i	−0.493470	+	0.934114i
$57$	7.17701	−	4.14365i	0.950618	−	0.548840i
$58$	−5.16703	+	0.0647415i	−0.678464	+	0.00850098i
$59$			9.80358i			1.27632i	0.769905	+	0.638158i	$0.220304\pi$
$59$			9.80358i			1.27632i	−0.769905	+	0.638158i	$0.779696\pi$
$60$	2.52232	+	1.37317i	0.325630	+	0.177276i
$61$	−1.22491	+	0.707202i	−0.156834	+	0.0905479i	−0.576363	−	0.817194i	$-0.695529\pi$
$61$	−1.22491	+	0.707202i	−0.156834	+	0.0905479i	0.419529	+	0.907742i	$0.362195\pi$
$62$	−4.87458	+	0.0610772i	−0.619072	+	0.00775681i
$63$	−1.39755	+	2.42063i	−0.176075	+	0.304970i
$64$	7.97741	−	0.600830i	0.997176	−	0.0751037i
$65$	3.62541	+	6.27939i	0.449677	+	0.778863i
$66$	−4.23958	+	0.0531208i	−0.521856	+	0.00653872i
$67$	1.94133	−	7.95181i	0.237171	−	0.971468i
$67$	1.94133	−	7.95181i	0.237171	−	0.971468i
$68$	16.1916	−	0.405817i	1.96352	−	0.0492126i
$69$	3.65026	−	2.10748i	0.439439	−	0.253710i
$70$	−0.0711142	−	5.67563i	−0.00849978	−	0.678368i
$71$	−6.77642	−	3.91237i	−0.804213	−	0.464313i	0.0407292	−	0.999170i	$-0.487032\pi$
$71$	−6.77642	−	3.91237i	−0.804213	−	0.464313i	−0.844942	+	0.534858i	$0.820365\pi$
$72$	2.82643	−	0.106288i	0.333098	−	0.0125261i
$73$	−3.06780	−	5.31359i	−0.359059	−	0.621909i	0.628745	−	0.777612i	$-0.283569\pi$
$73$	−3.06780	−	5.31359i	−0.359059	−	0.621909i	−0.987804	+	0.155703i	$0.950236\pi$
$74$	−6.32842	+	11.2854i	−0.735664	+	1.31190i
$75$	2.93808			0.339260
$76$	0.415286	+	16.5694i	0.0476365	+	1.90064i
$77$	4.18995	+	7.25721i	0.477489	+	0.827036i
$78$	6.22863	+	3.49279i	0.705254	+	0.395481i
$79$	−3.32083	+	5.75185i	−0.373623	+	0.647134i	−0.990120	−	0.140224i	$-0.955218\pi$
$79$	−3.32083	+	5.75185i	−0.373623	+	0.647134i	0.616497	+	0.787357i	$0.288551\pi$
$80$	−4.82413	+	3.11746i	−0.539354	+	0.348543i
$81$	1.00000			0.111111
$82$	−0.0721815	−	5.76081i	−0.00797111	−	0.636175i
$83$	7.53775	−	4.35192i	0.827376	−	0.477686i	−0.0255777	−	0.999673i	$-0.508143\pi$
$83$	7.53775	−	4.35192i	0.827376	−	0.477686i	0.852953	+	0.521987i	$0.174809\pi$
$84$	−2.91552	−	4.76970i	−0.318109	−	0.520417i
$85$	−10.0708	+	5.81437i	−1.09233	+	0.630657i
$86$	−1.69578	−	2.85400i	−0.182861	−	0.307754i
$87$	1.82696	−	3.16439i	0.195871	−	0.339259i
$88$	3.96095	−	7.49789i	0.422239	−	0.799277i
$89$	3.05706			0.324047			0.162024	−	0.986787i	$-0.448198\pi$
$89$	3.05706			0.324047			0.162024	+	0.986787i	$0.448198\pi$
$90$	−1.74580	+	1.03732i	−0.184024	+	0.109343i
$91$		−	14.1139i		−	1.47954i
$92$	0.211216	+	8.42726i	0.0220208	+	0.878603i
$93$	1.72356	−	2.98529i	0.178725	−	0.309560i
$94$	0.00970118	+	0.774252i	0.00100060	+	0.0798580i
$95$	−5.95003	−	10.3058i	−0.610460	−	1.05735i
$96$	−2.51618	+	5.06644i	−0.256807	+	0.517092i
$97$	−13.2713	+	7.66220i	−1.34750	+	0.777979i	−0.987895	−	0.155126i	$-0.950422\pi$
$97$	−13.2713	+	7.66220i	−1.34750	+	0.777979i	−0.359604	+	0.933105i	$0.617088\pi$
$98$	−0.562064	+	1.00232i	−0.0567771	+	0.101250i
$99$	1.49904	−	2.59641i	0.150659	−	0.260949i
$100$	−2.80965	+	5.16092i	−0.280965	+	0.516092i
$101$	−0.647641	−	0.373916i	−0.0644427	−	0.0372060i	0.467432	−	0.884029i	$-0.345179\pi$
$101$	−0.647641	−	0.373916i	−0.0644427	−	0.0372060i	−0.531875	+	0.846823i	$0.678512\pi$
$102$	−5.60168	+	9.98938i	−0.554649	+	0.989096i
$103$	−3.07595	−	1.77590i	−0.303082	−	0.174985i	0.340744	−	0.940156i	$-0.389321\pi$
$103$	−3.07595	−	1.77590i	−0.303082	−	0.174985i	−0.643827	+	0.765171i	$0.722654\pi$
$104$	−12.0917	+	7.60087i	−1.18569	+	0.745326i
$105$	3.47587	+	2.00680i	0.339211	+	0.195843i
$106$	−1.19473	+	0.709883i	−0.116042	+	0.0689499i
$107$			12.2492i			1.18417i	0.805875	+	0.592086i	$0.201695\pi$
$107$			12.2492i			1.18417i	−0.805875	+	0.592086i	$0.798305\pi$
$108$	−0.956289	+	1.75656i	−0.0920189	+	0.169025i
$109$			17.8262i			1.70744i	0.520735	+	0.853719i	$0.325658\pi$
$109$			17.8262i			1.70744i	−0.520735	+	0.853719i	$0.674342\pi$
$110$	0.0762783	+	6.08778i	0.00727285	+	0.580447i
$111$	−4.57450	−	7.92326i	−0.434192	−	0.752042i
$112$	11.1664	−	0.560086i	1.05512	−	0.0529232i
$113$	−14.0310	−	8.10079i	−1.31992	−	0.762059i	−0.336208	−	0.941788i	$-0.609145\pi$
$113$	−14.0310	−	8.10079i	−1.31992	−	0.762059i	−0.983716	+	0.179729i	$0.942478\pi$
$114$	−10.2225	−	5.73238i	−0.957420	−	0.536887i
$115$	−3.02621	−	5.24155i	−0.282196	−	0.488777i
$116$	3.81135	+	6.23525i	0.353875	+	0.578928i
$117$	−4.37302	+	2.52476i	−0.404286	+	0.233414i
$118$	11.9191	−	7.08206i	1.09724	−	0.651957i
$119$	22.6357			2.07501
$120$	−0.152623	−	4.05858i	−0.0139325	−	0.370496i
$121$	1.00579	+	1.74207i	0.0914351	+	0.158370i
$122$	1.74468	+	0.978353i	0.157956	+	0.0885759i
$123$	3.52804	+	2.03691i	0.318112	+	0.183662i
$124$	3.59563	+	5.88234i	0.322897	+	0.528250i
$125$		−	11.3986i		−	1.01952i
$126$	3.95256	−	0.0495245i	0.352122	−	0.00441199i
$127$	−7.94604	−	4.58765i	−0.705097	−	0.407088i	0.104146	−	0.994562i	$-0.466789\pi$
$127$	−7.94604	−	4.58765i	−0.705097	−	0.407088i	−0.809243	+	0.587474i	$0.800122\pi$
$128$	−6.49333	−	9.26481i	−0.573934	−	0.818901i
$129$	2.34744			0.206681
$130$	5.01544	−	8.94394i	0.439883	−	0.784436i
$131$			0.754065i			0.0658829i	0.999457	+	0.0329415i	$0.0104875\pi$
$131$			0.754065i			0.0658829i	−0.999457	+	0.0329415i	$0.989513\pi$
$132$	3.12724	+	5.11606i	0.272191	+	0.445296i
$133$			23.1638i			2.00856i
$134$	−11.0701	+	3.38411i	−0.956314	+	0.292342i
$135$		−	1.43594i		−	0.123586i
$136$	−12.1901	−	19.3924i	−1.04530	−	1.66289i
$137$		−	13.1546i		−	1.12387i	−0.827181	−	0.561935i	$-0.810057\pi$
$137$		−	13.1546i		−	1.12387i	0.827181	−	0.561935i	$-0.189943\pi$
$138$	−5.19918	−	2.91551i	−0.442584	−	0.248185i
$139$	14.5802			1.23668			0.618338	−	0.785912i	$-0.287806\pi$
$139$	14.5802			1.23668			0.618338	+	0.785912i	$0.287806\pi$
$140$	−6.84900	+	4.18651i	−0.578846	+	0.353825i
$141$	−0.474168	−	0.273761i	−0.0399322	−	0.0230548i
$142$	0.138641	+	11.0650i	0.0116345	+	0.928552i
$143$			15.1388i			1.26597i
$144$	−2.17102	−	3.35956i	−0.180919	−	0.279963i
$145$	−4.54388	−	2.62341i	−0.377349	−	0.217862i
$146$	−4.24404	+	7.56832i	−0.351239	+	0.626358i
$147$	−0.406288	−	0.703712i	−0.0335101	−	0.0580411i
$148$	18.2922	−	0.458466i	1.50361	−	0.0376857i
$149$	6.19511			0.507523			0.253762	−	0.967267i	$-0.418332\pi$
$149$	6.19511			0.507523			0.253762	+	0.967267i	$0.418332\pi$
$150$	−2.12245	−	3.57208i	−0.173298	−	0.291659i
$151$	−7.23383	+	4.17645i	−0.588680	+	0.339875i	−0.764576	−	0.644534i	$-0.777051\pi$
$151$	−7.23383	+	4.17645i	−0.588680	+	0.339875i	0.175895	+	0.984409i	$0.443718\pi$
$152$	19.8449	−	12.4746i	1.60963	−	1.01182i
$153$	−4.04917	−	7.01337i	−0.327356	−	0.566998i
$154$	5.79644	−	10.3367i	0.467090	−	0.832953i
$155$	−4.28670	−	2.47493i	−0.344316	−	0.198791i
$156$	−0.253037	−	10.0959i	−0.0202592	−	0.808318i
$157$	10.4662	+	18.1280i	0.835295	+	1.44677i	0.893790	+	0.448485i	$0.148036\pi$
$157$	10.4662	+	18.1280i	0.835295	+	1.44677i	−0.0584958	+	0.998288i	$0.518630\pi$
$158$	9.39199	−	0.117679i	0.747187	−	0.00936206i
$159$		−	0.982679i		−	0.0779315i
$160$	7.27511	+	3.61308i	0.575148	+	0.285639i
$161$			11.7812i			0.928490i
$162$	−0.722396	−	1.21579i	−0.0567568	−	0.0955215i
$163$	3.45100	+	1.99244i	0.270303	+	0.156060i	0.629025	−	0.777385i	$-0.283454\pi$
$163$	3.45100	+	1.99244i	0.270303	+	0.156060i	−0.358722	+	0.933444i	$0.616787\pi$
$164$	−6.95179	+	4.24934i	−0.542843	+	0.331818i
$165$	−3.72828	−	2.15252i	−0.290246	−	0.167574i
$166$	−10.7363	−	6.02051i	−0.833295	−	0.467282i
$167$	15.2756	+	8.81936i	1.18206	+	0.682463i	0.956490	−	0.291764i	$-0.0942423\pi$
$167$	15.2756	+	8.81936i	1.18206	+	0.682463i	0.225570	+	0.974227i	$0.427576\pi$
$168$	−3.69279	+	6.99027i	−0.284905	+	0.539311i
$169$	6.24886	−	10.8234i	0.480682	−	0.832565i
$170$	14.3441	+	8.04368i	1.10015	+	0.616922i
$171$	7.17701	−	4.14365i	0.548840	−	0.316873i
$172$	−2.24483	+	4.12343i	−0.171167	+	0.314409i
$173$	5.53388	+	9.58497i	0.420733	+	0.728732i	0.996011	−	0.0892263i	$-0.0284394\pi$
$173$	5.53388	+	9.58497i	0.420733	+	0.728732i	−0.575278	+	0.817958i	$0.695106\pi$
$174$	−5.16703	+	0.0647415i	−0.391711	+	0.00490804i
$175$	−4.10611	+	7.11199i	−0.310393	+	0.537616i
$176$	−11.9772	+	0.600758i	−0.902817	+	0.0452838i
$177$			9.80358i			0.736882i
$178$	−2.20841	−	3.71674i	−0.165527	−	0.278581i
$179$	−21.6327			−1.61690			−0.808451	−	0.588563i	$-0.799694\pi$
$179$	−21.6327			−1.61690			−0.808451	+	0.588563i	$0.799694\pi$
$180$	2.52232	+	1.37317i	0.188002	+	0.102350i
$181$	0.103727	−	0.179661i	0.00770997	−	0.0133541i	−0.862145	−	0.506662i	$-0.830879\pi$
$181$	0.103727	−	0.179661i	0.00770997	−	0.0133541i	0.869855	+	0.493308i	$0.164212\pi$
$182$	−17.1596	+	10.1958i	−1.27195	+	0.755766i
$183$	−1.22491	+	0.707202i	−0.0905479	+	0.0522779i
$184$	10.0932	−	6.34461i	0.744080	−	0.467731i
$185$	−11.3773	+	6.56870i	−0.836477	+	0.482940i
$186$	−4.87458	+	0.0610772i	−0.357421	+	0.00447840i
$187$	−24.2794			−1.77549
$188$	0.934320	−	0.571111i	0.0681423	−	0.0416526i
$189$	−1.39755	+	2.42063i	−0.101657	+	0.176075i
$190$	−8.23135	+	14.6788i	−0.597165	+	1.06491i
$191$	−0.0494290	−	0.0856136i	−0.00357656	−	0.00619478i	0.864232	−	0.503094i	$-0.167805\pi$
$191$	−0.0494290	−	0.0856136i	−0.00357656	−	0.00619478i	−0.867808	+	0.496899i	$0.834472\pi$
$192$	7.97741	−	0.600830i	0.575720	−	0.0433612i
$193$	−4.27315			−0.307588			−0.153794	−	0.988103i	$-0.549149\pi$
$193$	−4.27315			−0.307588			−0.153794	+	0.988103i	$0.549149\pi$
$194$	18.9028	+	10.6000i	1.35714	+	0.761035i
$195$	3.62541	+	6.27939i	0.259621	+	0.449677i
$196$	1.62464	−	0.0407191i	0.116046	−	0.00290851i
$197$	12.7364	+	7.35337i	0.907431	+	0.523906i	0.879604	−	0.475707i	$-0.157808\pi$
$197$	12.7364	+	7.35337i	0.907431	+	0.523906i	0.0278274	+	0.999613i	$0.491141\pi$
$198$	−4.23958	+	0.0531208i	−0.301294	+	0.00377513i
$199$	21.8300	−	12.6036i	1.54749	−	0.893444i	0.549157	−	0.835719i	$-0.314949\pi$
$199$	21.8300	−	12.6036i	1.54749	−	0.893444i	0.998333	−	0.0577244i	$-0.0183845\pi$
$200$	8.30427	−	0.312282i	0.587200	−	0.0220817i
$201$	1.94133	−	7.95181i	0.136931	−	0.560877i
$202$	0.0132503	+	1.05751i	0.000932290	+	0.0744062i
$203$	5.10654	+	8.84479i	0.358409	+	0.620783i
$204$	16.1916	−	0.405817i	1.13364	−	0.0284129i
$205$	2.92489	−	5.06605i	0.204283	−	0.353828i
$206$	0.0629320	+	5.02261i	0.00438468	+	0.349942i
$207$	3.65026	−	2.10748i	0.253710	−	0.146480i
$208$	17.9760	+	9.21010i	1.24641	+	0.638606i
$209$		−	24.8459i		−	1.71863i
$210$	−0.0711142	−	5.67563i	−0.00490735	−	0.391656i
$211$	0.859699	−	0.496348i	0.0591841	−	0.0341700i	−0.470116	−	0.882605i	$-0.655788\pi$
$211$	0.859699	−	0.496348i	0.0591841	−	0.0341700i	0.529300	+	0.848435i	$0.322455\pi$
$212$	1.72614	+	0.939724i	0.118552	+	0.0645405i
$213$	−6.77642	−	3.91237i	−0.464313	−	0.268071i
$214$	14.8924	−	8.84875i	1.01802	−	0.604888i
$215$		−	3.37079i		−	0.229886i
$216$	2.82643	−	0.106288i	0.192314	−	0.00723197i
$217$	4.81752	+	8.34418i	0.327034	+	0.566440i
$218$	21.6729	−	12.8775i	1.46787	−	0.872178i
$219$	−3.06780	−	5.31359i	−0.207303	−	0.359059i
$220$	7.34636	−	4.49053i	0.495291	−	0.302751i
$221$	35.4142	+	20.4464i	2.38222	+	1.37537i
$222$	−6.32842	+	11.2854i	−0.424736	+	0.757423i
$223$		−	2.50087i		−	0.167471i	−0.996488	−	0.0837354i	$-0.973315\pi$
$223$		−	2.50087i		−	0.167471i	0.996488	−	0.0837354i	$-0.0266851\pi$
$224$	−8.74748	−	13.1713i	−0.584465	−	0.880047i
$225$	2.93808			0.195872
$226$	0.287065	+	22.9107i	0.0190953	+	1.52400i
$227$	16.4750	+	9.51182i	1.09348	+	0.631322i	0.934501	−	0.355960i	$-0.115846\pi$
$227$	16.4750	+	9.51182i	1.09348	+	0.631322i	0.158980	+	0.987282i	$0.449179\pi$
$228$	0.415286	+	16.5694i	0.0275030	+	1.09734i
$229$	19.0569	−	11.0025i	1.25932	−	0.727067i	0.286375	−	0.958118i	$-0.407550\pi$
$229$	19.0569	−	11.0025i	1.25932	−	0.727067i	0.972942	+	0.231051i	$0.0742163\pi$
$230$	−4.18650	+	7.46571i	−0.276050	+	0.492274i
$231$	4.18995	+	7.25721i	0.275679	+	0.477489i
$232$	4.82745	−	9.13812i	0.316937	−	0.599947i
$233$	6.25910	+	3.61369i	0.410047	+	0.236741i	0.690810	−	0.723036i	$-0.257254\pi$
$233$	6.25910	+	3.61369i	0.410047	+	0.236741i	−0.280763	+	0.959777i	$0.590587\pi$
$234$	6.22863	+	3.49279i	0.407178	+	0.228331i
$235$	−0.393104	+	0.680877i	−0.0256433	+	0.0444155i
$236$	−17.2206	−	9.37505i	−1.12097	−	0.610264i
$237$	−3.32083	+	5.75185i	−0.215711	+	0.373623i
$238$	−16.3519	−	27.5202i	−1.05994	−	1.78387i
$239$	−4.93060	+	8.54006i	−0.318934	+	0.552410i	−0.980266	−	0.197683i	$-0.936658\pi$
$239$	−4.93060	+	8.54006i	−0.318934	+	0.552410i	0.661332	+	0.750094i	$0.269992\pi$
$240$	−4.82413	+	3.11746i	−0.311396	+	0.201231i
$241$	24.5140			1.57909			0.789544	−	0.613694i	$-0.210317\pi$
$241$	24.5140			1.57909			0.789544	+	0.613694i	$0.210317\pi$
$242$	1.39142	−	2.48129i	0.0894437	−	0.159503i
$243$	1.00000			0.0641500
$244$	−0.0708774	−	2.82792i	−0.00453746	−	0.181039i
$245$	−1.01049	+	0.583405i	−0.0645577	+	0.0372724i
$246$	−0.0721815	−	5.76081i	−0.00460212	−	0.367296i
$247$	−20.9235	+	36.2405i	−1.33133	+	2.30593i
$248$	4.55422	−	8.62091i	0.289193	−	0.547428i
$249$	7.53775	−	4.35192i	0.477686	−	0.275792i
$250$	−13.8583	+	8.23430i	−0.876476	+	0.520783i
$251$	−7.00168	−	12.1273i	−0.441942	−	0.765466i	0.555891	−	0.831255i	$-0.312377\pi$
$251$	−7.00168	−	12.1273i	−0.441942	−	0.765466i	−0.997834	+	0.0657885i	$0.979044\pi$
$252$	−2.91552	−	4.76970i	−0.183661	−	0.300463i
$253$		−	12.6367i		−	0.794465i
$254$	0.162571	+	12.9748i	0.0102006	+	0.814112i
$255$	−10.0708	+	5.81437i	−0.630657	+	0.364110i
$256$	−6.57331	+	14.5874i	−0.410832	+	0.911711i
$257$	8.10825	−	14.0439i	0.505779	−	0.876035i	−0.494199	−	0.869349i	$-0.664539\pi$
$257$	8.10825	−	14.0439i	0.505779	−	0.876035i	0.999978	−	0.00668565i	$-0.00212812\pi$
$258$	−1.69578	−	2.85400i	−0.105575	−	0.177682i
$259$	25.5723			1.58899
$260$	−14.4971	+	0.363347i	−0.899071	+	0.0225338i
$261$	1.82696	−	3.16439i	0.113086	−	0.195871i
$262$	0.916784	−	0.544733i	0.0566391	−	0.0336537i
$263$		−	15.7737i		−	0.972648i	−0.873779	−	0.486324i	$-0.838337\pi$
$263$		−	15.7737i		−	0.972648i	0.873779	−	0.486324i	$-0.161663\pi$
$264$	3.96095	−	7.49789i	0.243780	−	0.461463i
$265$	−1.41107			−0.0866812
$266$	28.1623	−	16.7334i	1.72674	−	1.02599i
$267$	3.05706			0.187089
$268$	12.1114	+	11.0143i	0.739820	+	0.672805i
$269$	−27.8489			−1.69798			−0.848990	−	0.528409i	$-0.822789\pi$
$269$	−27.8489			−1.69798			−0.848990	+	0.528409i	$0.822789\pi$
$270$	−1.74580	+	1.03732i	−0.106246	+	0.0631291i
$271$	15.6236			0.949067			0.474533	−	0.880238i	$-0.342617\pi$
$271$	15.6236			0.949067			0.474533	+	0.880238i	$0.342617\pi$
$272$	−14.7710	+	28.8297i	−0.895624	+	1.74805i
$273$		−	14.1139i		−	0.854214i
$274$	−15.9932	+	9.50280i	−0.966183	+	0.574085i
$275$	4.40428	−	7.62844i	0.265588	−	0.460012i
$276$	0.211216	+	8.42726i	0.0127137	+	0.507262i
$277$	−18.5054			−1.11188			−0.555941	−	0.831222i	$-0.687642\pi$
$277$	−18.5054			−1.11188			−0.555941	+	0.831222i	$0.687642\pi$
$278$	−10.5327	−	17.7265i	−0.631708	−	1.06316i
$279$	1.72356	−	2.98529i	0.103187	−	0.178725i
$280$	10.0376	+	5.30263i	0.599862	+	0.316893i
$281$	−6.62888	+	3.82719i	−0.395446	+	0.228311i	−0.684517	−	0.728997i	$-0.739987\pi$
$281$	−6.62888	+	3.82719i	−0.395446	+	0.228311i	0.289071	+	0.957308i	$0.406654\pi$
$282$	0.00970118	+	0.774252i	0.000577697	+	0.0461061i
$283$		−	0.663064i		−	0.0394151i	−0.999806	−	0.0197075i	$-0.993726\pi$
$283$		−	0.663064i		−	0.0394151i	0.999806	−	0.0197075i	$-0.00627351\pi$
$284$	13.3525	−	8.16185i	0.792327	−	0.484317i
$285$	−5.95003	−	10.3058i	−0.352449	−	0.610460i
$286$	18.4056	−	10.9362i	1.08835	−	0.646673i
$287$	−9.86121	+	5.69337i	−0.582089	+	0.336069i
$288$	−2.51618	+	5.06644i	−0.148267	+	0.298543i
$289$	−24.2916	+	42.0743i	−1.42892	+	2.47496i
$290$	0.0929650	+	7.41954i	0.00545909	+	0.435691i
$291$	−13.2713	+	7.66220i	−0.777979	+	0.449166i
$292$	12.2674	−	0.307462i	0.717893	−	0.0179929i
$293$	−12.3001			−0.718578			−0.359289	−	0.933226i	$-0.616981\pi$
$293$	−12.3001			−0.718578			−0.359289	+	0.933226i	$0.616981\pi$
$294$	−0.562064	+	1.00232i	−0.0327803	+	0.0584564i
$295$	14.0773			0.819615
$296$	−13.7716	−	21.9083i	−0.800460	−	1.27340i
$297$	1.49904	−	2.59641i	0.0869829	−	0.150659i
$298$	−4.47532	−	7.53195i	−0.259249	−	0.436314i
$299$	−10.6418	+	18.4321i	−0.615429	+	1.06595i
$300$	−2.80965	+	5.16092i	−0.162215	+	0.297966i
$301$	−3.28067	+	5.68228i	−0.189094	+	0.327521i
$302$	10.3034	+	5.77776i	0.592892	+	0.332473i
$303$	−0.647641	−	0.373916i	−0.0372060	−	0.0214809i
$304$	−29.5023	−	15.1156i	−1.69207	−	0.866942i
$305$	1.01550	+	1.75890i	0.0581473	+	0.100714i
$306$	−5.60168	+	9.98938i	−0.320227	+	0.571055i
$307$	−10.5593	+	6.09642i	−0.602651	+	0.347941i	−0.770084	−	0.637943i	$-0.779786\pi$
$307$	−10.5593	+	6.09642i	−0.602651	+	0.347941i	0.167433	+	0.985884i	$0.446452\pi$
$308$	−16.7545	+	0.419926i	−0.954679	+	0.0239275i
$309$	−3.07595	−	1.77590i	−0.174985	−	0.101027i
$310$	0.0877032	+	6.99960i	0.00498121	+	0.397551i
$311$	25.2385			1.43114			0.715571	−	0.698540i	$-0.246166\pi$
$311$	25.2385			1.43114			0.715571	+	0.698540i	$0.246166\pi$
$312$	−12.0917	+	7.60087i	−0.684556	+	0.430314i
$313$		−	14.6562i		−	0.828418i	−0.910182	−	0.414209i	$-0.864058\pi$
$313$		−	14.6562i		−	0.828418i	0.910182	−	0.414209i	$-0.135942\pi$
$314$	14.4791	−	25.8203i	0.817103	−	1.45712i
$315$	3.47587	+	2.00680i	0.195843	+	0.113070i
$316$	−6.92781	−	11.3337i	−0.389720	−	0.637569i
$317$	−1.62348	−	2.81195i	−0.0911836	−	0.157935i	0.816826	−	0.576884i	$-0.195732\pi$
$317$	−1.62348	−	2.81195i	−0.0911836	−	0.157935i	−0.908009	+	0.418950i	$0.862398\pi$
$318$	−1.19473	+	0.709883i	−0.0669972	+	0.0398083i
$319$	−5.47737	−	9.48708i	−0.306674	−	0.531174i
$320$	−0.862756	−	11.4551i	−0.0482295	−	0.640358i
$321$			12.2492i			0.683682i
$322$	14.3235	−	8.51070i	0.798216	−	0.474283i
$323$	−58.1219	−	33.5567i	−3.23399	−	1.86715i
$324$	−0.956289	+	1.75656i	−0.0531271	+	0.0975868i
$325$	−12.8483	+	7.41795i	−0.712694	+	0.411474i
$326$	−0.0706053	−	5.63502i	−0.00391047	−	0.312095i
$327$			17.8262i			0.985789i
$328$	10.1882	+	5.38221i	0.562552	+	0.297183i
$329$	1.32535	−	0.765189i	0.0730687	−	0.0421862i
$330$	0.0762783	+	6.08778i	0.00419898	+	0.335121i
$331$	−15.4094	+	26.6899i	−0.846979	+	1.46701i	0.0369118	+	0.999319i	$0.488248\pi$
$331$	−15.4094	+	26.6899i	−0.846979	+	1.46701i	−0.883891	+	0.467693i	$0.845085\pi$
$332$	0.436159	+	17.4022i	0.0239373	+	0.955071i
$333$	−4.57450	−	7.92326i	−0.250681	−	0.434192i
$334$	−0.312529	−	24.9430i	−0.0171008	−	1.36482i
$335$	−11.4183	−	2.78763i	−0.623849	−	0.152305i
$336$	11.1664	−	0.560086i	0.609175	−	0.0305552i
$337$	−28.8226	+	16.6407i	−1.57007	+	0.906478i	−0.573907	+	0.818920i	$0.694573\pi$
$337$	−28.8226	+	16.6407i	−1.57007	+	0.906478i	−0.996159	+	0.0875578i	$0.972094\pi$
$338$	−17.6731	+	0.221439i	−0.961288	+	0.0120447i
$339$	−14.0310	−	8.10079i	−0.762059	−	0.439975i
$340$	−0.582729	−	23.2502i	−0.0316029	−	1.26092i
$341$	−5.16735	−	8.95011i	−0.279828	−	0.484676i
$342$	−10.2225	−	5.73238i	−0.552767	−	0.309972i
$343$	−17.2945			−0.933813
$344$	6.63488	−	0.249505i	0.357729	−	0.0134524i
$345$	−3.02621	−	5.24155i	−0.162926	−	0.282196i
$346$	7.65565	−	13.6522i	0.411570	−	0.733946i
$347$	1.13184	−	1.96041i	0.0607605	−	0.105240i	−0.834045	−	0.551696i	$-0.813981\pi$
$347$	1.13184	−	1.96041i	0.0607605	−	0.105240i	0.894806	+	0.446456i	$0.147314\pi$
$348$	3.81135	+	6.23525i	0.204310	+	0.334245i
$349$	−31.9706			−1.71135			−0.855675	−	0.517514i	$-0.826858\pi$
$349$	−31.9706			−1.71135			−0.855675	+	0.517514i	$0.826858\pi$
$350$	11.6129	−	0.145507i	0.620736	−	0.00777767i
$351$	−4.37302	+	2.52476i	−0.233414	+	0.134762i
$352$	9.38269	+	14.1278i	0.500099	+	0.753014i
$353$	27.7963	−	16.0482i	1.47945	−	0.854159i	0.479717	−	0.877423i	$-0.340739\pi$
$353$	27.7963	−	16.0482i	1.47945	−	0.854159i	0.999729	+	0.0232642i	$0.00740589\pi$
$354$	11.9191	−	7.08206i	0.633492	−	0.376407i
$355$	−5.61792	+	9.73053i	−0.298168	+	0.516443i
$356$	−2.92343	+	5.36991i	−0.154941	+	0.284605i
$357$	22.6357			1.19801
$358$	15.6274	+	26.3008i	0.825932	+	1.39004i
$359$			10.2156i			0.539156i	0.962979	+	0.269578i	$0.0868843\pi$
$359$			10.2156i			0.539156i	−0.962979	+	0.269578i	$0.913116\pi$
$360$	−0.152623	−	4.05858i	−0.00804393	−	0.213906i
$361$	24.8397	−	43.0236i	1.30735	−	2.26440i
$362$	−0.293361	+	0.00367574i	−0.0154187	+	0.000193193i
$363$	1.00579	+	1.74207i	0.0527901	+	0.0914351i
$364$	24.7920	+	13.4970i	1.29945	+	0.707434i
$365$	−7.63000	+	4.40518i	−0.399372	+	0.230578i
$366$	1.74468	+	0.978353i	0.0911958	+	0.0511393i
$367$	−6.42085	+	11.1212i	−0.335166	+	0.580524i	−0.983517	−	0.180818i	$-0.942126\pi$
$367$	−6.42085	+	11.1212i	−0.335166	+	0.580524i	0.648351	+	0.761342i	$0.275459\pi$
$368$	−15.0050	−	7.68788i	−0.782190	−	0.400758i
$369$	3.52804	+	2.03691i	0.183662	+	0.106037i
$370$	16.2051	+	9.08723i	0.842462	+	0.472423i
$371$	2.37870	+	1.37334i	0.123496	+	0.0713003i
$372$	3.59563	+	5.88234i	0.186425	+	0.304985i
$373$	13.1695	+	7.60340i	0.681890	+	0.393689i	0.800567	−	0.599244i	$-0.204532\pi$
$373$	13.1695	+	7.60340i	0.681890	+	0.393689i	−0.118677	+	0.992933i	$0.537865\pi$
$374$	17.5393	+	29.5187i	0.906938	+	1.52637i
$375$		−	11.3986i		−	0.588621i
$376$	−1.36930	−	0.723368i	−0.0706163	−	0.0373049i
$377$			18.4506i			0.950255i
$378$	3.95256	−	0.0495245i	0.203298	−	0.00254727i
$379$	1.85778	+	3.21777i	0.0954276	+	0.165285i	0.909787	−	0.415075i	$-0.136245\pi$
$379$	1.85778	+	3.21777i	0.0954276	+	0.165285i	−0.814359	+	0.580361i	$0.802911\pi$
$380$	23.7927	−	0.596325i	1.22054	−	0.0305908i
$381$	−7.94604	−	4.58765i	−0.407088	−	0.235032i
$382$	−0.0683808	+	0.121942i	−0.00349867	+	0.00623911i
$383$	1.19984	+	2.07818i	0.0613088	+	0.106190i	0.895051	−	0.445964i	$-0.147139\pi$
$383$	1.19984	+	2.07818i	0.0613088	+	0.106190i	−0.833742	+	0.552154i	$0.813806\pi$
$384$	−6.49333	−	9.26481i	−0.331361	−	0.472793i
$385$	10.4209	−	6.01652i	0.531099	−	0.306630i
$386$	3.08691	+	5.19525i	0.157119	+	0.264431i
$387$	2.34744			0.119327
$388$	−0.767923	−	30.6392i	−0.0389854	−	1.55547i
$389$	−8.27884	−	14.3394i	−0.419754	−	0.727035i	0.576160	−	0.817337i	$-0.304550\pi$
$389$	−8.27884	−	14.3394i	−0.419754	−	0.727035i	−0.995914	+	0.0903012i	$0.971217\pi$
$390$	5.01544	−	8.94394i	0.253967	−	0.452894i
$391$	−29.5611	−	17.0671i	−1.49497	−	0.863119i
$392$	−1.22314	−	1.94581i	−0.0617779	−	0.0982781i
$393$			0.754065i			0.0380375i
$394$	−0.260579	−	20.7968i	−0.0131278	−	1.04773i
$395$	8.25931	+	4.76852i	0.415571	+	0.239930i
$396$	3.12724	+	5.11606i	0.157150	+	0.257092i
$397$	1.06731			0.0535668			0.0267834	−	0.999641i	$-0.491474\pi$
$397$	1.06731			0.0535668			0.0267834	+	0.999641i	$0.491474\pi$
$398$	−31.0932	−	17.4360i	−1.55856	−	0.873985i
$399$			23.1638i			1.15964i
$400$	−6.37864	−	9.87065i	−0.318932	−	0.493532i
$401$			4.93398i			0.246391i	0.992382	+	0.123196i	$0.0393142\pi$
$401$			4.93398i			0.246391i	−0.992382	+	0.123196i	$0.960686\pi$
$402$	−11.0701	+	3.38411i	−0.552128	+	0.168784i
$403$			17.4063i			0.867070i
$404$	1.27614	−	0.780051i	0.0634902	−	0.0388090i
$405$		−	1.43594i		−	0.0713524i
$406$	7.06446	−	12.5979i	0.350603	−	0.625225i
$407$	−27.4293			−1.35962
$408$	−12.1901	−	19.3924i	−0.603502	−	0.960068i
$409$	3.05376	+	1.76309i	0.150999	+	0.0871790i	0.573596	−	0.819139i	$-0.305548\pi$
$409$	3.05376	+	1.76309i	0.150999	+	0.0871790i	−0.422597	+	0.906318i	$0.638881\pi$
$410$	−8.27218	+	0.103648i	−0.408534	+	0.00511882i
$411$		−	13.1546i		−	0.648867i
$412$	6.06098	−	3.70483i	0.298603	−	0.182524i
$413$	−23.7308	−	13.7010i	−1.16772	−	0.674181i
$414$	−5.19918	−	2.91551i	−0.255526	−	0.143290i
$415$	−6.24910	−	10.8238i	−0.306756	−	0.531317i
$416$	−1.78826	−	28.5084i	−0.0876767	−	1.39774i
$417$	14.5802			0.713996
$418$	−30.2074	+	17.9486i	−1.47749	+	0.877894i
$419$	14.4240	−	8.32772i	0.704660	−	0.406836i	−0.104421	−	0.994533i	$-0.533299\pi$
$419$	14.4240	−	8.32772i	0.704660	−	0.406836i	0.809081	+	0.587698i	$0.199966\pi$
$420$	−6.84900	+	4.18651i	−0.334197	+	0.204281i
$421$	−3.05756	−	5.29585i	−0.149017	−	0.258104i	0.781848	−	0.623469i	$-0.214277\pi$
$421$	−3.05756	−	5.29585i	−0.149017	−	0.258104i	−0.930864	+	0.365365i	$0.880944\pi$
$422$	−1.22450	−	0.686654i	−0.0596076	−	0.0334258i
$423$	−0.474168	−	0.273761i	−0.0230548	−	0.0133107i
$424$	−0.104447	−	2.77747i	−0.00507238	−	0.134886i
$425$	−11.8968	−	20.6058i	−0.577079	−	0.999530i
$426$	0.138641	+	11.0650i	0.00671719	+	0.536100i
$427$		−	3.95340i		−	0.191318i
$428$	−21.5164	−	11.7137i	−1.04004	−	0.566205i
$429$			15.1388i			0.730910i
$430$	−4.09817	+	2.43504i	−0.197631	+	0.117428i
$431$	26.4855	+	15.2914i	1.27576	+	0.736562i	0.976066	−	0.217473i	$-0.0697815\pi$
$431$	26.4855	+	15.2914i	1.27576	+	0.736562i	0.299696	+	0.954035i	$0.403115\pi$
$432$	−2.17102	−	3.35956i	−0.104453	−	0.161637i
$433$	2.40368	+	1.38777i	0.115514	+	0.0666918i	0.556644	−	0.830751i	$-0.312089\pi$
$433$	2.40368	+	1.38777i	0.115514	+	0.0666918i	−0.441130	+	0.897443i	$0.645422\pi$
$434$	6.66462	−	11.8849i	0.319912	−	0.570493i
$435$	−4.54388	−	2.62341i	−0.217862	−	0.125783i
$436$	−31.3128	−	17.0470i	−1.49961	−	0.816401i
$437$	17.4653	−	30.2508i	0.835478	−	1.44709i
$438$	−4.24404	+	7.56832i	−0.202788	+	0.361628i
$439$	3.97827	−	2.29686i	0.189872	−	0.109623i	−0.402050	−	0.915618i	$-0.631702\pi$
$439$	3.97827	−	2.29686i	0.189872	−	0.109623i	0.591923	+	0.805995i	$0.298369\pi$
$440$	−10.7665	−	5.68769i	−0.513273	−	0.271150i
$441$	−0.406288	−	0.703712i	−0.0193470	−	0.0335101i
$442$	−0.724553	−	57.8267i	−0.0344635	−	2.75053i
$443$	−17.5037	+	30.3173i	−0.831627	+	1.44042i	0.0651212	+	0.997877i	$0.479257\pi$
$443$	−17.5037	+	30.3173i	−0.831627	+	1.44042i	−0.896748	+	0.442542i	$0.854077\pi$
$444$	18.2922	−	0.458466i	0.868111	−	0.0217578i
$445$		−	4.38975i		−	0.208094i
$446$	−3.04053	+	1.80662i	−0.143974	+	0.0855459i
$447$	6.19511			0.293019
$448$	−9.69443	+	20.1500i	−0.458019	+	0.951998i
$449$	10.3025	−	17.8444i	0.486205	−	0.842131i	−0.513670	−	0.857988i	$-0.671714\pi$
$449$	10.3025	−	17.8444i	0.486205	−	0.842131i	0.999874	+	0.0158569i	$0.00504761\pi$
$450$	−2.12245	−	3.57208i	−0.100053	−	0.168390i
$451$	10.5773	−	6.10681i	0.498066	−	0.287559i
$452$	27.6472	−	16.8996i	1.30042	−	0.794891i
$453$	−7.23383	+	4.17645i	−0.339875	+	0.196227i
$454$	−0.337067	−	26.9014i	−0.0158194	−	1.26254i
$455$	−20.2668			−0.950120
$456$	19.8449	−	12.4746i	0.929323	−	0.584175i
$457$	1.90024	−	3.29131i	0.0888895	−	0.153961i	−0.818152	−	0.575001i	$-0.805002\pi$
$457$	1.90024	−	3.29131i	0.0888895	−	0.153961i	0.907042	+	0.421040i	$0.138335\pi$
$458$	−27.1434	−	15.2210i	−1.26833	−	0.711232i
$459$	−4.04917	−	7.01337i	−0.188999	−	0.327356i
$460$	12.1010	−	0.303294i	0.564214	−	0.0141411i
$461$	−35.2021			−1.63952			−0.819762	−	0.572704i	$-0.805895\pi$
$461$	−35.2021			−1.63952			−0.819762	+	0.572704i	$0.805895\pi$
$462$	5.79644	−	10.3367i	0.269675	−	0.480906i
$463$	12.7930	+	22.1581i	0.594539	+	1.02977i	0.993612	+	0.112853i	$0.0359989\pi$
$463$	12.7930	+	22.1581i	0.594539	+	1.02977i	−0.399072	+	0.916919i	$0.630668\pi$
$464$	−14.5974	+	0.732180i	−0.677665	+	0.0339906i
$465$	−4.28670	−	2.47493i	−0.198791	−	0.114772i
$466$	−0.128057	−	10.2203i	−0.00593214	−	0.473445i
$467$	23.5885	−	13.6188i	1.09154	−	0.630204i	0.157557	−	0.987510i	$-0.449638\pi$
$467$	23.5885	−	13.6188i	1.09154	−	0.630204i	0.933987	+	0.357306i	$0.116305\pi$
$468$	−0.253037	−	10.0959i	−0.0116967	−	0.466682i
$469$	16.5353	+	15.8123i	0.763527	+	0.730143i
$470$	1.11178	−	0.0139303i	0.0512826	−	0.000642558i
$471$	10.4662	+	18.1280i	0.482258	+	0.835295i
$472$	1.04200	+	27.7091i	0.0479620	+	1.27542i
$473$	3.51890	−	6.09491i	0.161799	−	0.280244i
$474$	9.39199	−	0.117679i	0.431389	−	0.00540519i
$475$	21.0866	−	12.1744i	0.967520	−	0.558598i
$476$	−21.6462	+	39.7610i	−0.992154	+	1.82244i
$477$		−	0.982679i		−	0.0449938i
$478$	13.9448	−	0.174724i	0.637818	−	0.00799170i
$479$	3.68804	−	2.12929i	0.168511	−	0.0972897i	−0.413373	−	0.910562i	$-0.635649\pi$
$479$	3.68804	−	2.12929i	0.168511	−	0.0972897i	0.581883	+	0.813272i	$0.302316\pi$
$480$	7.27511	+	3.61308i	0.332062	+	0.164914i
$481$	40.0087	+	23.0990i	1.82424	+	1.05323i
$482$	−17.7088	−	29.8039i	−0.806616	−	1.35753i
$483$			11.7812i			0.536064i
$484$	−4.02188	+	0.100802i	−0.182813	+	0.00458191i
$485$	11.0025	+	19.0568i	0.499596	+	0.865326i
$486$	−0.722396	−	1.21579i	−0.0327685	−	0.0551493i
$487$	−3.61940	−	6.26898i	−0.164011	−	0.284075i	0.772293	−	0.635267i	$-0.219110\pi$
$487$	−3.61940	−	6.26898i	−0.164011	−	0.284075i	−0.936303	+	0.351192i	$0.885776\pi$
$488$	−3.38695	+	2.12905i	−0.153320	+	0.0963775i
$489$	3.45100	+	1.99244i	0.156060	+	0.0901011i
$490$	1.43927	+	0.807091i	0.0650196	+	0.0364606i
$491$		−	24.2098i		−	1.09257i	−0.837599	−	0.546286i	$-0.816041\pi$
$491$		−	24.2098i		−	1.09257i	0.837599	−	0.546286i	$-0.183959\pi$
$492$	−6.95179	+	4.24934i	−0.313411	+	0.191575i
$493$	−29.5908			−1.33270
$494$	59.1759	−	0.741459i	2.66245	−	0.0333598i
$495$	−3.72828	−	2.15252i	−0.167574	−	0.0967488i
$496$	−13.7712	+	0.690738i	−0.618343	+	0.0310151i
$497$	18.9408	−	10.9355i	0.849609	−	0.490522i
$498$	−10.7363	−	6.02051i	−0.481103	−	0.269785i
$499$	18.4103	+	31.8876i	0.824158	+	1.42748i	0.902561	+	0.430562i	$0.141685\pi$
$499$	18.4103	+	31.8876i	0.824158	+	1.42748i	−0.0784028	+	0.996922i	$0.524982\pi$
$500$	20.0224	+	10.9004i	0.895427	+	0.487479i
$501$	15.2756	+	8.81936i	0.682463	+	0.394020i
$502$	−9.68622	+	17.2733i	−0.432317	+	0.770943i
$503$	12.6059	−	21.8340i	0.562069	−	0.973531i	−0.435247	−	0.900311i	$-0.643339\pi$
$503$	12.6059	−	21.8340i	0.562069	−	0.973531i	0.997316	−	0.0732204i	$-0.0233277\pi$
$504$	−3.69279	+	6.99027i	−0.164490	+	0.311371i
$505$	−0.536920	+	0.929973i	−0.0238926	+	0.0413833i
$506$	−15.3636	+	9.12872i	−0.682996	+	0.405821i
$507$	6.24886	−	10.8234i	0.277522	−	0.480682i
$508$	15.6572	−	9.57060i	0.694676	−	0.424627i
$509$	5.69263			0.252321			0.126161	−	0.992010i	$-0.459735\pi$
$509$	5.69263			0.252321			0.126161	+	0.992010i	$0.459735\pi$
$510$	14.3441	+	8.04368i	0.635169	+	0.356180i
$511$	17.1496			0.758655
$512$	22.4837	−	2.54610i	0.993649	−	0.112523i
$513$	7.17701	−	4.14365i	0.316873	−	0.182947i
$514$	−22.9318	+	0.287330i	−1.01148	+	0.0126736i
$515$	−2.55009	+	4.41688i	−0.112370	+	0.194631i
$516$	−2.24483	+	4.12343i	−0.0988232	+	0.181524i
$517$	−1.42159	+	0.820755i	−0.0625214	+	0.0360968i
$518$	−18.4733	−	31.0906i	−0.811672	−	1.36604i
$519$	5.53388	+	9.58497i	0.242911	+	0.420733i
$520$	10.9144	+	17.3629i	0.478627	+	0.761415i
$521$		−	12.7504i		−	0.558604i	−0.960203	−	0.279302i	$-0.909897\pi$
$521$		−	12.7504i		−	0.558604i	0.960203	−	0.279302i	$-0.0901031\pi$
$522$	−5.16703	+	0.0647415i	−0.226155	+	0.00283366i
$523$	−16.4531	+	9.49921i	−0.719445	+	0.415371i	−0.814548	−	0.580096i	$-0.803015\pi$
$523$	−16.4531	+	9.49921i	−0.719445	+	0.415371i	0.0951037	+	0.995467i	$0.469682\pi$
$524$	−1.32456	−	0.721104i	−0.0578638	−	0.0315016i
$525$	−4.10611	+	7.11199i	−0.179205	+	0.310393i
$526$	−19.1775	+	11.3949i	−0.836179	+	0.496839i
$527$	−27.9159			−1.21604
$528$	−11.9772	+	0.600758i	−0.521242	+	0.0261446i
$529$	−2.61708	+	4.53291i	−0.113786	+	0.197083i
$530$	1.01935	+	1.71556i	0.0442777	+	0.0745192i
$531$			9.80358i			0.425439i
$532$	−40.6887	−	22.1513i	−1.76408	−	0.960381i
$533$	−20.5709			−0.891025
$534$	−2.20841	−	3.71674i	−0.0955670	−	0.160839i
$535$	17.5891			0.760442
$536$	4.64185	−	22.6816i	0.200497	−	0.979694i
$537$	−21.6327			−0.933519
$538$	20.1180	+	33.8585i	0.867347	+	1.45974i
$539$	−2.43616			−0.104933
$540$	2.52232	+	1.37317i	0.108543	+	0.0590920i
$541$			10.8008i			0.464362i	0.972673	+	0.232181i	$0.0745862\pi$
$541$			10.8008i			0.464362i	−0.972673	+	0.232181i	$0.925414\pi$
$542$	−11.2864	−	18.9950i	−0.484794	−	0.815906i
$543$	0.103727	−	0.179661i	0.00445135	−	0.00770997i
$544$	45.7213	−	2.86798i	1.96028	−	0.122964i
$545$	25.5973			1.09647
$546$	−17.1596	+	10.1958i	−0.734362	+	0.436342i
$547$	14.4914	−	25.0999i	0.619608	−	1.07319i	−0.369949	−	0.929052i	$-0.620625\pi$
$547$	14.4914	−	25.0999i	0.619608	−	1.07319i	0.989557	−	0.144141i	$-0.0460419\pi$
$548$	23.1068	+	12.5796i	0.987074	+	0.537372i
$549$	−1.22491	+	0.707202i	−0.0522779	+	0.0301826i
$550$	−12.4562	+	0.156073i	−0.531135	+	0.00665498i
$551$		−	30.2812i		−	1.29002i
$552$	10.0932	−	6.34461i	0.429595	−	0.270045i
$553$	−9.28205	−	16.0770i	−0.394713	−	0.683663i
$554$	13.3682	+	22.4987i	0.567961	+	0.955876i
$555$	−11.3773	+	6.56870i	−0.482940	+	0.278826i
$556$	−13.9429	+	25.6110i	−0.591310	+	1.08615i
$557$	−20.3642	+	35.2719i	−0.862860	+	1.49452i	0.00629641	+	0.999980i	$0.497996\pi$
$557$	−20.3642	+	35.2719i	−0.862860	+	1.49452i	−0.869156	+	0.494537i	$0.835338\pi$
$558$	−4.87458	+	0.0610772i	−0.206357	+	0.00258560i
$559$	−10.2654	+	5.92674i	−0.434181	+	0.250674i
$560$	−0.804250	−	16.0342i	−0.0339858	−	0.677569i
$561$	−24.2794			−1.02508
$562$	9.44173	+	5.29458i	0.398275	+	0.223338i
$563$	−36.5872			−1.54196			−0.770982	−	0.636857i	$-0.780234\pi$
$563$	−36.5872			−1.54196			−0.770982	+	0.636857i	$0.780234\pi$
$564$	0.934320	−	0.571111i	0.0393420	−	0.0240481i
$565$	−11.6323	+	20.1477i	−0.489373	+	0.847618i
$566$	−0.806146	+	0.478995i	−0.0338849	+	0.0201337i
$567$	−1.39755	+	2.42063i	−0.0586916	+	0.101657i
$568$	−19.5689	−	10.3378i	−0.821093	−	0.433764i
$569$	−6.07205	+	10.5171i	−0.254554	+	0.440900i	−0.964774	−	0.263079i	$-0.915262\pi$
$569$	−6.07205	+	10.5171i	−0.254554	+	0.440900i	0.710221	+	0.703979i	$0.248595\pi$
$570$	−8.23135	+	14.6788i	−0.344774	+	0.614828i
$571$	17.0741	+	9.85772i	0.714528	+	0.412533i	0.812735	−	0.582633i	$-0.197978\pi$
$571$	17.0741	+	9.85772i	0.714528	+	0.412533i	−0.0982076	+	0.995166i	$0.531311\pi$
$572$	−26.5923	−	14.4771i	−1.11188	−	0.605318i
$573$	−0.0494290	−	0.0856136i	−0.00206493	−	0.00357656i
$574$	14.0456	+	7.87629i	0.586254	+	0.328750i
$575$	10.7247	−	6.19193i	0.447252	−	0.258221i
$576$	7.97741	−	0.600830i	0.332392	−	0.0250346i
$577$	−14.4920	−	8.36696i	−0.603310	−	0.348321i	0.167033	−	0.985951i	$-0.446581\pi$
$577$	−14.4920	−	8.36696i	−0.603310	−	0.348321i	−0.770342	+	0.637630i	$0.779915\pi$
$578$	68.7017	−	0.860814i	2.85761	−	0.0358052i
$579$	−4.27315			−0.177586
$580$	8.95344	−	5.47287i	0.371772	−	0.227249i
$581$			24.3281i			1.00930i
$582$	18.9028	+	10.6000i	0.783545	+	0.439384i
$583$	−2.55143	−	1.47307i	−0.105670	−	0.0610083i
$584$	−9.23570	−	14.6924i	−0.382176	−	0.607977i
$585$	3.62541	+	6.27939i	0.149892	+	0.259621i
$586$	8.88553	+	14.9543i	0.367058	+	0.617757i
$587$	12.9801	+	22.4823i	0.535748	+	0.927942i	0.999127	+	0.0417822i	$0.0133036\pi$
$587$	12.9801	+	22.4823i	0.535748	+	0.927942i	−0.463379	+	0.886160i	$0.653363\pi$
$588$	1.62464	−	0.0407191i	0.0669991	−	0.00167923i
$589$		−	28.5673i		−	1.17709i
$590$	−10.1694	−	17.1151i	−0.418668	−	0.704617i
$591$	12.7364	+	7.35337i	0.523906	+	0.302477i
$592$	−16.6873	+	32.5699i	−0.685845	+	1.33861i
$593$	−11.1499	+	6.43739i	−0.457871	+	0.264352i	−0.711149	−	0.703042i	$-0.751825\pi$
$593$	−11.1499	+	6.43739i	−0.457871	+	0.264352i	0.253277	+	0.967394i	$0.418491\pi$
$594$	−4.23958	+	0.0531208i	−0.173952	+	0.00217957i
$595$		−	32.5035i		−	1.33251i
$596$	−5.92432	+	10.8821i	−0.242669	+	0.445748i
$597$	21.8300	−	12.6036i	0.893444	−	0.515830i
$598$	30.0971	−	0.377109i	1.23076	−	0.0154211i
$599$	−0.550798	+	0.954011i	−0.0225050	+	0.0389798i	−0.877059	−	0.480383i	$-0.840498\pi$
$599$	−0.550798	+	0.954011i	−0.0225050	+	0.0389798i	0.854554	+	0.519363i	$0.173831\pi$
$600$	8.30427	−	0.312282i	0.339020	−	0.0127488i
$601$	−17.4773	−	30.2716i	−0.712915	−	1.23481i	−0.963758	−	0.266778i	$-0.914041\pi$
$601$	−17.4773	−	30.2716i	−0.712915	−	1.23481i	0.250843	−	0.968028i	$-0.419292\pi$
$602$	9.27840	−	0.116256i	0.378159	−	0.00473824i
$603$	1.94133	−	7.95181i	0.0790570	−	0.323823i
$604$	−0.418573	−	16.7006i	−0.0170315	−	0.679536i
$605$	2.50151	−	1.44425i	0.101701	−	0.0587170i
$606$	0.0132503	+	1.05751i	0.000538258	+	0.0429584i
$607$	36.3075	+	20.9621i	1.47368	+	0.850827i	0.999561	−	0.0296358i	$-0.00943475\pi$
$607$	36.3075	+	20.9621i	1.47368	+	0.850827i	0.474115	+	0.880463i	$0.342768\pi$
$608$	2.93490	+	46.7881i	0.119026	+	1.89751i
$609$	5.10654	+	8.84479i	0.206928	+	0.358409i
$610$	1.40486	−	2.50525i	0.0568809	−	0.101435i
$611$	2.76473			0.111849
$612$	16.1916	−	0.405817i	0.654507	−	0.0164042i
$613$	−15.8566	−	27.4644i	−0.640440	−	1.10928i	−0.985335	−	0.170634i	$-0.945419\pi$
$613$	−15.8566	−	27.4644i	−0.640440	−	1.10928i	0.344894	−	0.938642i	$-0.387915\pi$
$614$	15.0400	+	8.43387i	0.606963	+	0.340363i
$615$	2.92489	−	5.06605i	0.117943	−	0.204283i
$616$	12.6140	+	20.0666i	0.508231	+	0.808508i
$617$	11.2658			0.453543			0.226771	−	0.973948i	$-0.427183\pi$
$617$	11.2658			0.453543			0.226771	+	0.973948i	$0.427183\pi$
$618$	0.0629320	+	5.02261i	0.00253150	+	0.202039i
$619$	−24.9841	+	14.4246i	−1.00420	+	0.579772i	−0.909487	−	0.415733i	$-0.863525\pi$
$619$	−24.9841	+	14.4246i	−1.00420	+	0.579772i	−0.0947085	+	0.995505i	$0.530192\pi$
$620$	8.44668	−	5.16311i	0.339227	−	0.207355i
$621$	3.65026	−	2.10748i	0.146480	−	0.0845702i
$622$	−18.2322	−	30.6847i	−0.731043	−	1.23034i
$623$	−4.27239	+	7.39999i	−0.171170	+	0.296474i
$624$	17.9760	+	9.21010i	0.719617	+	0.368699i
$625$	−1.67732			−0.0670928
$626$	−17.8189	+	10.5876i	−0.712185	+	0.423165i
$627$		−	24.8459i		−	0.992250i
$628$	−41.8517	+	1.04895i	−1.67006	+	0.0418575i
$629$	−37.0459	+	64.1653i	−1.47711	+	2.55844i
$630$	−0.0711142	−	5.67563i	−0.00283326	−	0.226123i
$631$	−0.441396	−	0.764520i	−0.0175717	−	0.0304351i	0.857106	−	0.515140i	$-0.172260\pi$
$631$	−0.441396	−	0.764520i	−0.0175717	−	0.0304351i	−0.874678	+	0.484705i	$0.838927\pi$
$632$	−8.77475	+	16.6102i	−0.349041	+	0.660717i
$633$	0.859699	−	0.496348i	0.0341700	−	0.0197280i
$634$	−2.24594	+	4.00514i	−0.0891977	+	0.159065i
$635$	−6.58759	+	11.4100i	−0.261420	+	0.452794i
$636$	1.72614	+	0.939724i	0.0684458	+	0.0372625i
$637$	3.55341	+	2.05156i	0.140791	+	0.0812859i
$638$	−7.57746	+	13.5128i	−0.299995	+	0.534975i
$639$	−6.77642	−	3.91237i	−0.268071	−	0.154771i
$640$	−13.3037	+	9.32403i	−0.525875	+	0.368565i
$641$	−5.84496	−	3.37459i	−0.230862	−	0.133288i	0.380108	−	0.924942i	$-0.375887\pi$
$641$	−5.84496	−	3.37459i	−0.230862	−	0.133288i	−0.610970	+	0.791654i	$0.709220\pi$
$642$	14.8924	−	8.84875i	0.587757	−	0.349232i
$643$			26.8845i			1.06022i	0.847929	+	0.530111i	$0.177850\pi$
$643$			26.8845i			1.06022i	−0.847929	+	0.530111i	$0.822150\pi$
$644$	−20.6944	−	11.2662i	−0.815475	−	0.443952i
$645$		−	3.37079i		−	0.132725i
$646$	1.18914	+	94.9053i	0.0467860	+	3.73400i
$647$	5.21295	+	9.02910i	0.204942	+	0.354970i	0.950114	−	0.311902i	$-0.100966\pi$
$647$	5.21295	+	9.02910i	0.204942	+	0.354970i	−0.745172	+	0.666872i	$0.767633\pi$
$648$	2.82643	−	0.106288i	0.111033	−	0.00417538i
$649$	25.4541	+	14.6959i	0.999159	+	0.576865i
$650$	18.3002	+	10.2621i	0.717793	+	0.402512i
$651$	4.81752	+	8.34418i	0.188813	+	0.327034i
$652$	−6.79999	+	4.15656i	−0.266308	+	0.162783i
$653$	7.61278	−	4.39524i	0.297911	−	0.171999i	−0.343593	−	0.939119i	$-0.611644\pi$
$653$	7.61278	−	4.39524i	0.297911	−	0.171999i	0.641504	+	0.767120i	$0.278311\pi$
$654$	21.6729	−	12.8775i	0.847476	−	0.503552i
$655$	1.08279			0.0423082
$656$	−0.816320	−	16.2748i	−0.0318719	−	0.635426i
$657$	−3.06780	−	5.31359i	−0.119686	−	0.207303i
$658$	−1.88773	−	1.05857i	−0.0735915	−	0.0412675i
$659$	8.25196	+	4.76427i	0.321451	+	0.185590i	0.652039	−	0.758185i	$-0.273914\pi$
$659$	8.25196	+	4.76427i	0.321451	+	0.185590i	−0.330588	+	0.943775i	$0.607247\pi$
$660$	7.34636	−	4.49053i	0.285957	−	0.174793i
$661$			33.4231i			1.30001i	0.759932	+	0.650003i	$0.225232\pi$
$661$			33.4231i			1.30001i	−0.759932	+	0.650003i	$0.774768\pi$
$662$	43.5811	−	0.546059i	1.69383	−	0.0212232i
$663$	35.4142	+	20.4464i	1.37537	+	0.794073i
$664$	20.8424	−	13.1016i	0.808841	−	0.508440i
$665$	33.2619			1.28984
$666$	−6.32842	+	11.2854i	−0.245221	+	0.437299i
$667$		−	15.4011i		−	0.596335i
$668$	−30.0996	+	18.3987i	−1.16459	+	0.711866i
$669$		−	2.50087i		−	0.0966893i
$670$	4.85937	+	15.8960i	0.187734	+	0.614118i
$671$			4.24048i			0.163702i
$672$	−8.74748	−	13.1713i	−0.337441	−	0.508095i
$673$			2.29615i			0.0885103i	0.999020	+	0.0442551i	$0.0140914\pi$
$673$			2.29615i			0.0885103i	−0.999020	+	0.0442551i	$0.985909\pi$
$674$	41.0529	+	23.0210i	1.58130	+	0.886736i
$675$	2.93808			0.113087
$676$	13.0362	+	21.3268i	0.501391	+	0.820260i
$677$	36.2790	+	20.9457i	1.39431	+	0.805008i	0.993789	−	0.111278i	$-0.0354944\pi$
$677$	36.2790	+	20.9457i	1.39431	+	0.805008i	0.400525	+	0.916286i	$0.368828\pi$
$678$	0.287065	+	22.9107i	0.0110247	+	0.879880i
$679$		−	42.8332i		−	1.64379i
$680$	−27.8464	+	17.5043i	−1.06786	+	0.671260i
$681$	16.4750	+	9.51182i	0.631322	+	0.364494i
$682$	−7.14858	+	12.7479i	−0.273733	+	0.488144i
$683$	−2.98899	−	5.17708i	−0.114370	−	0.198095i	0.803157	−	0.595767i	$-0.203152\pi$
$683$	−2.98899	−	5.17708i	−0.114370	−	0.198095i	−0.917528	+	0.397671i	$0.869818\pi$
$684$	0.415286	+	16.5694i	0.0158788	+	0.633547i
$685$	−18.8892			−0.721718
$686$	12.4934	+	21.0264i	0.477002	+	0.802793i
$687$	19.0569	−	11.0025i	0.727067	−	0.419772i
$688$	−5.09636	−	7.88638i	−0.194297	−	0.300665i
$689$	2.48103	+	4.29727i	0.0945198	+	0.163713i
$690$	−4.18650	+	7.46571i	−0.159377	+	0.284215i
$691$	−24.8483	−	14.3462i	−0.945274	−	0.545754i	−0.0536645	−	0.998559i	$-0.517090\pi$
$691$	−24.8483	−	14.3462i	−0.945274	−	0.545754i	−0.891610	+	0.452805i	$0.850423\pi$
$692$	−22.1286	+	0.554618i	−0.841203	+	0.0210834i
$693$	4.18995	+	7.25721i	0.159163	+	0.275679i
$694$	−3.20108	+	0.0401088i	−0.121511	+	0.00152251i
$695$		−	20.9363i		−	0.794159i
$696$	4.82745	−	9.13812i	0.182984	−	0.346380i
$697$		−	32.9913i		−	1.24963i
$698$	23.0955	+	38.8696i	0.874176	+	1.47124i
$699$	6.25910	+	3.61369i	0.236741	+	0.136682i
$700$	−8.56603	−	14.0137i	−0.323765	−	0.529670i
$701$	23.1537	+	13.3678i	0.874502	+	0.504894i	0.868842	−	0.495090i	$-0.164865\pi$
$701$	23.1537	+	13.3678i	0.874502	+	0.504894i	0.00566020	+	0.999984i	$0.498198\pi$
$702$	6.22863	+	3.49279i	0.235085	+	0.131827i
$703$	−65.6624	−	37.9102i	−2.47651	−	1.42981i
$704$	10.3984	−	21.6132i	0.391905	−	0.814580i
$705$	−0.393104	+	0.680877i	−0.0148052	+	0.0256433i
$706$	−39.5911	−	22.2013i	−1.49003	−	0.835556i
$707$	1.81022	−	1.04513i	0.0680803	−	0.0393062i
$708$	−17.2206	−	9.37505i	−0.647190	−	0.352336i
$709$	−5.62639	−	9.74520i	−0.211304	−	0.365989i	0.740819	−	0.671705i	$-0.234438\pi$
$709$	−5.62639	−	9.74520i	−0.211304	−	0.365989i	−0.952123	+	0.305716i	$0.901104\pi$
$710$	15.8886	−	0.199081i	0.596290	−	0.00747136i
$711$	−3.32083	+	5.75185i	−0.124541	+	0.215711i
$712$	8.64056	−	0.324928i	0.323819	−	0.0121772i
$713$		−	14.5294i		−	0.544132i
$714$	−16.3519	−	27.5202i	−0.611955	−	1.02992i
$715$	21.7385			0.812972
$716$	20.6871	−	37.9992i	0.773113	−	1.42010i
$717$	−4.93060	+	8.54006i	−0.184137	+	0.318934i
$718$	12.4200	−	7.37967i	0.463509	−	0.275407i
$719$	14.5587	−	8.40547i	0.542948	−	0.313471i	−0.203325	−	0.979111i	$-0.565175\pi$
$719$	14.5587	−	8.40547i	0.542948	−	0.313471i	0.746273	+	0.665640i	$0.231841\pi$
$720$	−4.82413	+	3.11746i	−0.179785	+	0.116181i
$721$	8.59758	−	4.96382i	0.320191	−	0.184862i
$722$	−70.2517	+	0.880236i	−2.61450	+	0.0327590i
$723$	24.5140			0.911687
$724$	0.216392	+	0.354010i	0.00804215	+	0.0131567i
$725$	5.36776	−	9.29723i	0.199354	−	0.345291i
$726$	1.39142	−	2.48129i	0.0516404	−	0.0920893i
$727$	6.72843	+	11.6540i	0.249544	+	0.432222i	0.963399	−	0.268071i	$-0.0863861\pi$
$727$	6.72843	+	11.6540i	0.249544	+	0.432222i	−0.713856	+	0.700293i	$0.753053\pi$
$728$	−1.50014	−	39.8920i	−0.0555988	−	1.47850i
$729$	1.00000			0.0370370
$730$	10.8676	+	6.09419i	0.402230	+	0.225556i
$731$	−9.50520	−	16.4635i	−0.351563	−	0.608924i
$732$	−0.0708774	−	2.82792i	−0.00261970	−	0.104523i
$733$	9.30274	+	5.37094i	0.343605	+	0.198380i	0.661865	−	0.749623i	$-0.269765\pi$
$733$	9.30274	+	5.37094i	0.343605	+	0.198380i	−0.318260	+	0.948003i	$0.603099\pi$
$734$	18.1595	−	0.227534i	0.670279	−	0.00839842i
$735$	−1.01049	+	0.583405i	−0.0372724	+	0.0215192i
$736$	1.49270	+	23.7966i	0.0550217	+	0.877155i
$737$	−17.7360	−	16.9605i	−0.653314	−	0.624749i
$738$	−0.0721815	−	5.76081i	−0.00265704	−	0.212058i
$739$	17.2547	+	29.8860i	0.634725	+	1.09938i	0.986573	+	0.163318i	$0.0522198\pi$
$739$	17.2547	+	29.8860i	0.634725	+	1.09938i	−0.351849	+	0.936057i	$0.614447\pi$
$740$	−0.658330	−	26.2666i	−0.0242007	−	0.965578i
$741$	−20.9235	+	36.2405i	−0.768643	+	1.33133i
$742$	−0.0486667	−	3.88409i	−0.00178661	−	0.142590i
$743$	39.0200	−	22.5282i	1.43151	−	0.826481i	0.434271	−	0.900782i	$-0.357006\pi$
$743$	39.0200	−	22.5282i	1.43151	−	0.826481i	0.997236	+	0.0743015i	$0.0236727\pi$
$744$	4.55422	−	8.62091i	0.166966	−	0.316058i
$745$		−	8.89581i		−	0.325917i
$746$	−0.269439	−	21.5040i	−0.00986487	−	0.787317i
$747$	7.53775	−	4.35192i	0.275792	−	0.159229i
$748$	23.2181	−	42.6483i	0.848939	−	1.55938i
$749$	−29.6507	−	17.1188i	−1.08341	−	0.625508i
$750$	−13.8583	+	8.23430i	−0.506034	+	0.300674i
$751$		−	22.2839i		−	0.813151i	−0.913617	−	0.406575i	$-0.866723\pi$
$751$		−	22.2839i		−	0.813151i	0.913617	−	0.406575i	$-0.133277\pi$
$752$	0.109713	+	2.18734i	0.00400083	+	0.0797640i
$753$	−7.00168	−	12.1273i	−0.255155	−	0.441942i
$754$	22.4321	−	13.3286i	0.816927	−	0.485401i
$755$	5.99713	+	10.3873i	0.218258	+	0.378034i
$756$	−2.91552	−	4.76970i	−0.106036	−	0.173472i
$757$	14.7374	+	8.50862i	0.535639	+	0.309251i	0.743310	−	0.668948i	$-0.233255\pi$
$757$	14.7374	+	8.50862i	0.535639	+	0.309251i	−0.207671	+	0.978199i	$0.566588\pi$
$758$	2.57007	−	4.58317i	0.0933493	−	0.166468i
$759$		−	12.6367i		−	0.458684i
$760$	−17.9127	−	28.4961i	−0.649763	−	1.03366i
$761$	−21.0326			−0.762432			−0.381216	−	0.924486i	$-0.624495\pi$
$761$	−21.0326			−0.762432			−0.381216	+	0.924486i	$0.624495\pi$
$762$	0.162571	+	12.9748i	0.00588933	+	0.470028i
$763$	−43.1505	−	24.9129i	−1.56215	−	0.901909i
$764$	0.197654	−	0.00495389i	0.00715087	−	0.000179225i
$765$	−10.0708	+	5.81437i	−0.364110	+	0.210219i
$766$	1.65987	−	2.96002i	0.0599736	−	0.106950i
$767$	−24.7517	−	42.8712i	−0.893733	−	1.54799i
$768$	−6.57331	+	14.5874i	−0.237194	+	0.526377i
$769$	9.17747	+	5.29861i	0.330948	+	0.191073i	0.656262	−	0.754533i	$-0.272137\pi$
$769$	9.17747	+	5.29861i	0.330948	+	0.191073i	−0.325314	+	0.945606i	$0.605470\pi$
$770$	−14.8428	−	8.32333i	−0.534899	−	0.299952i
$771$	8.10825	−	14.0439i	0.292012	−	0.505779i
$772$	4.08637	−	7.50606i	0.147072	−	0.270149i
$773$	5.36343	−	9.28974i	0.192909	−	0.334129i	−0.753304	−	0.657673i	$-0.771541\pi$
$773$	5.36343	−	9.28974i	0.192909	−	0.334129i	0.946213	+	0.323544i	$0.104874\pi$
$774$	−1.69578	−	2.85400i	−0.0609537	−	0.102585i
$775$	5.06395	−	8.77101i	0.181902	−	0.315064i
$776$	−36.6961	+	23.0673i	−1.31731	+	0.828066i
$777$	25.5723			0.917402
$778$	−11.4531	+	20.4240i	−0.410612	+	0.732237i
$779$	33.7610			1.20961
$780$	−14.4971	+	0.363347i	−0.519079	+	0.0130099i
$781$	−20.3162	+	11.7296i	−0.726970	+	0.419716i
$782$	0.604801	+	48.2692i	0.0216276	+	1.72610i
$783$	1.82696	−	3.16439i	0.0652904	−	0.113086i
$784$	−1.48210	+	2.89272i	−0.0529322	+	0.103312i
$785$	26.0307	−	15.0288i	0.929077	−	0.536403i
$786$	0.916784	−	0.544733i	0.0327006	−	0.0194300i
$787$	11.9172	+	20.6412i	0.424803	+	0.735781i	0.996402	−	0.0847524i	$-0.0270099\pi$
$787$	11.9172	+	20.6412i	0.424803	+	0.735781i	−0.571599	+	0.820533i	$0.693677\pi$
$788$	−25.0963	+	15.3403i	−0.894019	+	0.546477i
$789$		−	15.7737i		−	0.561559i
$790$	−0.168980	−	13.4863i	−0.00601205	−	0.479822i
$791$	39.2180	−	22.6425i	1.39443	−	0.805075i
$792$	3.96095	−	7.49789i	0.140746	−	0.266426i
$793$	3.57104	−	6.18522i	0.126811	−	0.219643i
$794$	−0.771021	−	1.29763i	−0.0273625	−	0.0460510i
$795$	−1.41107			−0.0500454
$796$	1.26316	+	50.3985i	0.0447714	+	1.78633i
$797$	19.4675	−	33.7186i	0.689573	−	1.19438i	−0.282403	−	0.959296i	$-0.591132\pi$
$797$	19.4675	−	33.7186i	0.689573	−	1.19438i	0.971976	−	0.235080i	$-0.0755351\pi$
$798$	28.1623	−	16.7334i	0.996936	−	0.592358i
$799$			4.43402i			0.156865i
$800$	−7.39273	+	14.8856i	−0.261373	+	0.526285i
$801$	3.05706			0.108016
$802$	5.99868	−	3.56429i	0.211821	−	0.125859i
$803$	−18.3950			−0.649145
$804$	12.1114	+	11.0143i	0.427135	+	0.388444i
$805$	16.9171			0.596250
$806$	21.1624	−	12.5742i	0.745414	−	0.442909i
$807$	−27.8489			−0.980329
$808$	−1.87025	−	0.988010i	−0.0657953	−	0.0347581i
$809$			37.7667i			1.32781i	0.747819	+	0.663903i	$0.231101\pi$
$809$			37.7667i			1.32781i	−0.747819	+	0.663903i	$0.768899\pi$
$810$	−1.74580	+	1.03732i	−0.0613412	+	0.0364476i
$811$	−8.39094	+	14.5335i	−0.294646	+	0.510342i	−0.974902	−	0.222632i	$-0.928535\pi$
$811$	−8.39094	+	14.5335i	−0.294646	+	0.510342i	0.680257	+	0.732974i	$0.261868\pi$
$812$	−20.4198	+	0.511789i	−0.716593	+	0.0179603i
$813$	15.6236			0.547944
$814$	19.8148	+	33.3483i	0.694509	+	1.16886i
$815$	2.86102	−	4.95543i	0.100217	−	0.173581i
$816$	−14.7710	+	28.8297i	−0.517089	+	1.00924i
$817$	16.8476	−	9.72698i	0.589424	−	0.340304i
$818$	−0.0624780	−	4.98637i	−0.00218449	−	0.174344i
$819$		−	14.1139i		−	0.493181i
$820$	6.10180	+	9.98235i	0.213084	+	0.348599i
$821$	13.7942	+	23.8922i	0.481420	+	0.833845i	0.999773	−	0.0213226i	$-0.00678769\pi$
$821$	13.7942	+	23.8922i	0.481420	+	0.833845i	−0.518352	+	0.855167i	$0.673454\pi$
$822$	−15.9932	+	9.50280i	−0.557826	+	0.331448i
$823$	−19.8474	+	11.4589i	−0.691835	+	0.399431i	−0.804299	−	0.594225i	$-0.797459\pi$
$823$	−19.8474	+	11.4589i	−0.691835	+	0.399431i	0.112464	+	0.993656i	$0.464126\pi$
$824$	−8.88271	−	4.69252i	−0.309444	−	0.163472i
$825$	4.40428	−	7.62844i	0.153337	−	0.265588i
$826$	0.485517	+	38.7492i	0.0168933	+	1.34826i
$827$	−7.49359	+	4.32643i	−0.260578	+	0.150445i	−0.624598	−	0.780946i	$-0.714737\pi$
$827$	−7.49359	+	4.32643i	−0.260578	+	0.150445i	0.364020	+	0.931391i	$0.381404\pi$
$828$	0.211216	+	8.42726i	0.00734026	+	0.292868i
$829$	28.9873			1.00677			0.503386	−	0.864062i	$-0.332087\pi$
$829$	28.9873			1.00677			0.503386	+	0.864062i	$0.332087\pi$
$830$	−8.64509	+	15.4166i	−0.300075	+	0.535119i
$831$	−18.5054			−0.641945
$832$	−33.3684	+	22.7685i	−1.15684	+	0.789356i
$833$	−3.29026	+	5.69890i	−0.114001	+	0.197455i
$834$	−10.5327	−	17.7265i	−0.364717	−	0.613817i
$835$	12.6641	−	21.9348i	0.438258	−	0.759086i
$836$	43.6434	+	23.7599i	1.50944	+	0.821752i
$837$	1.72356	−	2.98529i	0.0595749	−	0.103187i
$838$	−20.5446	−	11.5207i	−0.709702	−	0.397975i
$839$	−17.3169	−	9.99794i	−0.597847	−	0.345167i	0.170347	−	0.985384i	$-0.445511\pi$
$839$	−17.3169	−	9.99794i	−0.597847	−	0.345167i	−0.768194	+	0.640217i	$0.778845\pi$
$840$	10.0376	+	5.30263i	0.346330	+	0.182958i
$841$	7.82441	+	13.5523i	0.269807	+	0.467320i
$842$	−4.22987	+	7.54306i	−0.145771	+	0.259951i
$843$	−6.62888	+	3.82719i	−0.228311	+	0.131815i
$844$	0.0497451	+	1.98477i	0.00171230	+	0.0683185i
$845$	−15.5417	−	8.97299i	−0.534650	−	0.308680i
$846$	0.00970118	+	0.774252i	0.000333534	+	0.0266193i
$847$	−5.62254			−0.193193
$848$	−3.30137	+	2.13342i	−0.113369	+	0.0732619i
$849$		−	0.663064i		−	0.0227563i
$850$	−16.4582	+	29.3496i	−0.564511	+	1.00668i
$851$	−33.3962	−	19.2813i	−1.14481	−	0.660954i
$852$	13.3525	−	8.16185i	0.457450	−	0.279620i
$853$	11.1285	+	19.2751i	0.381032	+	0.659968i	0.991210	−	0.132297i	$-0.0422353\pi$
$853$	11.1285	+	19.2751i	0.381032	+	0.659968i	−0.610178	+	0.792265i	$0.708902\pi$
$854$	−4.80650	+	2.85592i	−0.164475	+	0.0977275i
$855$	−5.95003	−	10.3058i	−0.203487	−	0.352449i
$856$	1.30194	+	34.6214i	0.0444993	+	1.18334i
$857$			22.8297i			0.779849i	0.920847	+	0.389925i	$0.127499\pi$
$857$			22.8297i			0.779849i	−0.920847	+	0.389925i	$0.872501\pi$
$858$	18.4056	−	10.9362i	0.628358	−	0.373357i
$859$	−7.39385	−	4.26884i	−0.252275	−	0.145651i	0.368531	−	0.929616i	$-0.379861\pi$
$859$	−7.39385	−	4.26884i	−0.252275	−	0.145651i	−0.620805	+	0.783965i	$0.713194\pi$
$860$	5.92100	+	3.22344i	0.201904	+	0.109919i
$861$	−9.86121	+	5.69337i	−0.336069	+	0.194030i
$862$	−0.541877	−	43.2473i	−0.0184564	−	1.47301i
$863$		−	15.0541i		−	0.512449i	−0.966617	−	0.256225i	$-0.917521\pi$
$863$		−	15.0541i		−	0.512449i	0.966617	−	0.256225i	$-0.0824787\pi$
$864$	−2.51618	+	5.06644i	−0.0856022	+	0.172364i
$865$	13.7634	−	7.94633i	0.467971	−	0.270183i
$866$	−0.0491778	−	3.92489i	−0.00167113	−	0.133373i
$867$	−24.2916	+	42.0743i	−0.824986	+	1.42892i
$868$	−19.2640	+	0.482822i	−0.653863	+	0.0163880i
$869$	9.95609	+	17.2445i	0.337737	+	0.584978i
$870$	0.0929650	+	7.41954i	0.00315181	+	0.251546i
$871$	11.5870	+	39.6748i	0.392609	+	1.34433i
$872$	1.89470	+	50.3844i	0.0641628	+	1.70623i
$873$	−13.2713	+	7.66220i	−0.449166	+	0.259326i
$874$	−49.3954	+	0.618912i	−1.67083	+	0.0209350i
$875$	27.5918	+	15.9301i	0.932772	+	0.538536i
$876$	12.2674	−	0.307462i	0.414476	−	0.0103882i
$877$	−23.5463	−	40.7834i	−0.795102	−	1.37716i	−0.922775	−	0.385340i	$-0.874084\pi$
$877$	−23.5463	−	40.7834i	−0.795102	−	1.37716i	0.127673	−	0.991816i	$-0.459249\pi$
$878$	−5.66638	−	3.17750i	−0.191231	−	0.107235i
$879$	−12.3001			−0.414871
$880$	0.862652	+	17.1986i	0.0290800	+	0.579764i
$881$	−3.34842	−	5.79963i	−0.112811	−	0.195395i	0.804092	−	0.594506i	$-0.202652\pi$
$881$	−3.34842	−	5.79963i	−0.112811	−	0.195395i	−0.916903	+	0.399111i	$0.869319\pi$
$882$	−0.562064	+	1.00232i	−0.0189257	+	0.0337498i
$883$	25.3333	−	43.8786i	0.852534	−	1.47663i	−0.0263791	−	0.999652i	$-0.508398\pi$
$883$	25.3333	−	43.8786i	0.852534	−	1.47663i	0.878914	−	0.476981i	$-0.158269\pi$
$884$	−69.7816	+	42.6546i	−2.34701	+	1.43463i
$885$	14.0773			0.473205
$886$	49.5041	−	0.620274i	1.66312	−	0.0208385i
$887$	−21.4473	+	12.3826i	−0.720130	+	0.415767i	−0.814800	−	0.579742i	$-0.803153\pi$
$887$	−21.4473	+	12.3826i	−0.720130	+	0.415767i	0.0946708	+	0.995509i	$0.469820\pi$
$888$	−13.7716	−	21.9083i	−0.462146	−	0.735195i
$889$	22.2100	−	12.8229i	0.744899	−	0.430067i
$890$	−5.33701	+	3.17114i	−0.178897	+	0.106297i
$891$	1.49904	−	2.59641i	0.0502196	−	0.0869829i
$892$	4.39294	+	2.39156i	0.147086	+	0.0800752i
$893$	−4.53748			−0.151841
$894$	−4.47532	−	7.53195i	−0.149677	−	0.251906i
$895$			31.0632i			1.03833i
$896$	31.5014	−	2.76989i	1.05239	−	0.0925356i
$897$	−10.6418	+	18.4321i	−0.355318	+	0.615429i
$898$	−29.1376	+	0.365086i	−0.972333	+	0.0121831i
$899$	−6.29776	−	10.9080i	−0.210042	−	0.363803i
$900$	−2.80965	+	5.16092i	−0.0936550	+	0.172031i
$901$	−6.89189	+	3.97904i	−0.229602	+	0.132561i
$902$	−15.0656	−	8.44825i	−0.501630	−	0.281296i
$903$	−3.28067	+	5.68228i	−0.109174	+	0.189094i
$904$	−40.5186	−	21.4050i	−1.34763	−	0.711920i
$905$	−0.257982	−	0.148946i	−0.00857560	−	0.00495113i
$906$	10.3034	+	5.77776i	0.342307	+	0.191953i
$907$	28.3767	+	16.3833i	0.942234	+	0.543999i	0.890660	−	0.454670i	$-0.150243\pi$
$907$	28.3767	+	16.3833i	0.942234	+	0.543999i	0.0515742	+	0.998669i	$0.483576\pi$
$908$	−32.4629	+	19.8433i	−1.07732	+	0.658521i
$909$	−0.647641	−	0.373916i	−0.0214809	−	0.0124020i
$910$	14.6406	+	24.6401i	0.485332	+	0.816811i
$911$		−	51.0641i		−	1.69183i	−0.533319	−	0.845914i	$-0.679055\pi$
$911$		−	51.0641i		−	1.69183i	0.533319	−	0.845914i	$-0.320945\pi$
$912$	−29.5023	−	15.1156i	−0.976919	−	0.500529i
$913$		−	26.0947i		−	0.863610i
$914$	−5.37427	+	0.0673382i	−0.177765	+	0.00222735i
$915$	1.01550	+	1.75890i	0.0335714	+	0.0581473i
$916$	1.10270	+	43.9963i	0.0364341	+	1.45368i
$917$	−1.82531	−	1.05384i	−0.0602770	−	0.0348010i
$918$	−5.60168	+	9.98938i	−0.184883	+	0.329699i
$919$	−15.3593	−	26.6030i	−0.506655	−	0.877553i	−0.999970	−	0.00770191i	$-0.997548\pi$
$919$	−15.3593	−	26.6030i	−0.506655	−	0.877553i	0.493315	−	0.869851i	$-0.335785\pi$
$920$	−9.11048	−	14.4932i	−0.300364	−	0.477827i
$921$	−10.5593	+	6.09642i	−0.347941	+	0.200884i
$922$	25.4298	+	42.7983i	0.837487	+	1.40949i
$923$	39.5112			1.30053
$924$	−16.7545	+	0.419926i	−0.551184	+	0.0138146i
$925$	−13.4402	−	23.2791i	−0.441912	−	0.765413i
$926$	17.6980	−	31.5604i	0.581591	−	1.03714i
$927$	−3.07595	−	1.77590i	−0.101027	−	0.0583282i
$928$	11.4352	+	17.2184i	0.375380	+	0.565221i
$929$			12.5734i			0.412519i	0.978497	+	0.206259i	$0.0661291\pi$
$929$			12.5734i			0.412519i	−0.978497	+	0.206259i	$0.933871\pi$
$930$	0.0877032	+	6.99960i	0.00287590	+	0.229526i
$931$	−5.83187	−	3.36703i	−0.191132	−	0.110350i
$932$	−12.3332	+	7.53877i	−0.403987	+	0.246941i
$933$	25.2385			0.826270
$934$	−33.5978	−	18.8405i	−1.09935	−	0.616478i
$935$			34.8638i			1.14017i
$936$	−12.0917	+	7.60087i	−0.395229	+	0.248442i
$937$			3.79923i			0.124115i	0.998073	+	0.0620576i	$0.0197663\pi$
$937$			3.79923i			0.124115i	−0.998073	+	0.0620576i	$0.980234\pi$
$938$	7.27940	−	31.5261i	0.237681	−	1.02936i
$939$		−	14.6562i		−	0.478287i
$940$	−0.820081	−	1.34163i	−0.0267481	−	0.0437591i
$941$		−	9.38299i		−	0.305877i	−0.988236	−	0.152938i	$-0.951126\pi$
$941$		−	9.38299i		−	0.305877i	0.988236	−	0.152938i	$-0.0488736\pi$
$942$	14.4791	−	25.8203i	0.471754	−	0.841271i
$943$	17.1710			0.559165
$944$	32.9357	−	21.2838i	1.07197	−	0.692729i
$945$	3.47587	+	2.00680i	0.113070	+	0.0652811i
$946$	−9.95217	+	0.124698i	−0.323573	+	0.00405429i
$947$			13.8046i			0.448590i	0.974521	+	0.224295i	$0.0720079\pi$
$947$			13.8046i			0.448590i	−0.974521	+	0.224295i	$0.927992\pi$
$948$	−6.92781	−	11.3337i	−0.225005	−	0.368101i
$949$	26.8311	+	15.4910i	0.870975	+	0.502858i
$950$	−30.0343	−	16.8422i	−0.974443	−	0.546432i
$951$	−1.62348	−	2.81195i	−0.0526449	−	0.0911836i
$952$	63.9781	−	2.40590i	2.07354	−	0.0779756i
$953$	−13.8711			−0.449330			−0.224665	−	0.974436i	$-0.572129\pi$
$953$	−13.8711			−0.449330			−0.224665	+	0.974436i	$0.572129\pi$
$954$	−1.19473	+	0.709883i	−0.0386808	+	0.0229833i
$955$	−0.122936	+	0.0709771i	−0.00397812	+	0.00229677i
$956$	−10.2861	−	16.8277i	−0.332675	−	0.544246i
$957$	−5.47737	−	9.48708i	−0.177058	−	0.306674i
$958$	−5.25299	−	2.94569i	−0.169716	−	0.0951708i
$959$	31.8423	+	18.3842i	1.02824	+	0.593655i
$960$	−0.862756	−	11.4551i	−0.0278453	−	0.369711i
$961$	9.55869	+	16.5561i	0.308345	+	0.534069i
$962$	−0.818553	−	65.3288i	−0.0263912	−	2.10629i
$963$			12.2492i			0.394724i
$964$	−23.4425	+	43.0604i	−0.755032	+	1.38688i
$965$			6.13599i			0.197524i
$966$	14.3235	−	8.51070i	0.460850	−	0.273827i
$967$	30.0327	+	17.3394i	0.965788	+	0.557598i	0.897950	−	0.440098i	$-0.145056\pi$
$967$	30.0327	+	17.3394i	0.965788	+	0.557598i	0.0678385	+	0.997696i	$0.478390\pi$
$968$	3.02794	+	4.81694i	0.0973218	+	0.154822i
$969$	−58.1219	−	33.5567i	−1.86715	−	1.07800i
$970$	15.2210	−	27.1432i	0.488715	−	0.871517i
$971$	27.5642	+	15.9142i	0.884577	+	0.510711i	0.872165	−	0.489212i	$-0.162716\pi$
$971$	27.5642	+	15.9142i	0.884577	+	0.510711i	0.0124123	+	0.999923i	$0.496049\pi$
$972$	−0.956289	+	1.75656i	−0.0306730	+	0.0563418i
$973$	−20.3766	+	35.2932i	−0.653242	+	1.13145i
$974$	−5.00713	+	8.92911i	−0.160439	+	0.286107i
$975$	−12.8483	+	7.41795i	−0.411474	+	0.237565i
$976$	5.03520	+	2.57981i	0.161173	+	0.0825776i
$977$	8.11332	+	14.0527i	0.259568	+	0.449585i	0.966126	−	0.258070i	$-0.0830865\pi$
$977$	8.11332	+	14.0527i	0.259568	+	0.449585i	−0.706558	+	0.707655i	$0.749753\pi$
$978$	−0.0706053	−	5.63502i	−0.00225771	−	0.180188i
$979$	4.58264	−	7.93736i	0.146462	−	0.253679i
$980$	−0.0584702	−	2.33289i	−0.00186776	−	0.0745214i
$981$			17.8262i			0.569146i
$982$	−29.4340	+	17.4890i	−0.939276	+	0.558098i
$983$	−15.8827			−0.506579			−0.253290	−	0.967390i	$-0.581513\pi$
$983$	−15.8827			−0.506579			−0.253290	+	0.967390i	$0.581513\pi$
$984$	10.1882	+	5.38221i	0.324790	+	0.171578i
$985$	10.5590	−	18.2887i	0.336437	−	0.582727i
$986$	21.3763	+	35.9762i	0.680759	+	1.14571i
$987$	1.32535	−	0.765189i	0.0421862	−	0.0243562i
$988$	−43.6499	−	71.4098i	−1.38869	−	2.27185i
$989$	8.56877	−	4.94718i	0.272471	−	0.157311i
$990$	0.0762783	+	6.08778i	0.00242428	+	0.193482i
$991$	−30.5677			−0.971014			−0.485507	−	0.874233i	$-0.661365\pi$
$991$	−30.5677			−0.971014			−0.485507	+	0.874233i	$0.661365\pi$
$992$	10.7880	+	16.2438i	0.342520	+	0.515742i
$993$	−15.4094	+	26.6899i	−0.489004	+	0.846979i
$994$	−26.9779	−	15.1283i	−0.855688	−	0.479839i
$995$	−18.0980	−	31.3466i	−0.573744	−	0.993754i
$996$	0.436159	+	17.4022i	0.0138202	+	0.551411i
$997$	36.2194			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$997$	36.2194			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$998$	25.4691	−	45.4185i	0.806209	−	1.43770i
$999$	−4.57450	−	7.92326i	−0.144731	−	0.250681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.b.499.12	yes	68
4.3	odd	2		804.2.j.a.499.24	✓	68
67.38	odd	6		804.2.j.a.775.24	yes	68
268.239	even	6	inner	804.2.j.b.775.12	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.24	✓	68	4.3	odd	2
804.2.j.a.775.24	yes	68	67.38	odd	6
804.2.j.b.499.12	yes	68	1.1	even	1	trivial
804.2.j.b.775.12	yes	68	268.239	even	6	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.722396 - 1.21579i) q^{2} +1.00000 q^{3} +(-0.956289 + 1.75656i) q^{4} -1.43594i q^{5} +(-0.722396 - 1.21579i) q^{6} +(-1.39755 + 2.42063i) q^{7} +(2.82643 - 0.106288i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.722396 - 1.21579i) q^{2} +1.00000 q^{3} +(-0.956289 + 1.75656i) q^{4} -1.43594i q^{5} +(-0.722396 - 1.21579i) q^{6} +(-1.39755 + 2.42063i) q^{7} +(2.82643 - 0.106288i) q^{8} +1.00000 q^{9} +(-1.74580 + 1.03732i) q^{10} +(1.49904 - 2.59641i) q^{11} +(-0.956289 + 1.75656i) q^{12} +(-4.37302 + 2.52476i) q^{13} +(3.95256 - 0.0495245i) q^{14} -1.43594i q^{15} +(-2.17102 - 3.35956i) q^{16} +(-4.04917 - 7.01337i) q^{17} +(-0.722396 - 1.21579i) q^{18} +(7.17701 - 4.14365i) q^{19} +(2.52232 + 1.37317i) q^{20} +(-1.39755 + 2.42063i) q^{21} +(-4.23958 + 0.0531208i) q^{22} +(3.65026 - 2.10748i) q^{23} +(2.82643 - 0.106288i) q^{24} +2.93808 q^{25} +(6.22863 + 3.49279i) q^{26} +1.00000 q^{27} +(-2.91552 - 4.76970i) q^{28} +(1.82696 - 3.16439i) q^{29} +(-1.74580 + 1.03732i) q^{30} +(1.72356 - 2.98529i) q^{31} +(-2.51618 + 5.06644i) q^{32} +(1.49904 - 2.59641i) q^{33} +(-5.60168 + 9.98938i) q^{34} +(3.47587 + 2.00680i) q^{35} +(-0.956289 + 1.75656i) q^{36} +(-4.57450 - 7.92326i) q^{37} +(-10.2225 - 5.73238i) q^{38} +(-4.37302 + 2.52476i) q^{39} +(-0.152623 - 4.05858i) q^{40} +(3.52804 + 2.03691i) q^{41} +(3.95256 - 0.0495245i) q^{42} +2.34744 q^{43} +(3.12724 + 5.11606i) q^{44} -1.43594i q^{45} +(-5.19918 - 2.91551i) q^{46} +(-0.474168 - 0.273761i) q^{47} +(-2.17102 - 3.35956i) q^{48} +(-0.406288 - 0.703712i) q^{49} +(-2.12245 - 3.57208i) q^{50} +(-4.04917 - 7.01337i) q^{51} +(-0.253037 - 10.0959i) q^{52} -0.982679i q^{53} +(-0.722396 - 1.21579i) q^{54} +(-3.72828 - 2.15252i) q^{55} +(-3.69279 + 6.99027i) q^{56} +(7.17701 - 4.14365i) q^{57} +(-5.16703 + 0.0647415i) q^{58} +9.80358i q^{59} +(2.52232 + 1.37317i) q^{60} +(-1.22491 + 0.707202i) q^{61} +(-4.87458 + 0.0610772i) q^{62} +(-1.39755 + 2.42063i) q^{63} +(7.97741 - 0.600830i) q^{64} +(3.62541 + 6.27939i) q^{65} +(-4.23958 + 0.0531208i) q^{66} +(1.94133 - 7.95181i) q^{67} +(16.1916 - 0.405817i) q^{68} +(3.65026 - 2.10748i) q^{69} +(-0.0711142 - 5.67563i) q^{70} +(-6.77642 - 3.91237i) q^{71} +(2.82643 - 0.106288i) q^{72} +(-3.06780 - 5.31359i) q^{73} +(-6.32842 + 11.2854i) q^{74} +2.93808 q^{75} +(0.415286 + 16.5694i) q^{76} +(4.18995 + 7.25721i) q^{77} +(6.22863 + 3.49279i) q^{78} +(-3.32083 + 5.75185i) q^{79} +(-4.82413 + 3.11746i) q^{80} +1.00000 q^{81} +(-0.0721815 - 5.76081i) q^{82} +(7.53775 - 4.35192i) q^{83} +(-2.91552 - 4.76970i) q^{84} +(-10.0708 + 5.81437i) q^{85} +(-1.69578 - 2.85400i) q^{86} +(1.82696 - 3.16439i) q^{87} +(3.96095 - 7.49789i) q^{88} +3.05706 q^{89} +(-1.74580 + 1.03732i) q^{90} -14.1139i q^{91} +(0.211216 + 8.42726i) q^{92} +(1.72356 - 2.98529i) q^{93} +(0.00970118 + 0.774252i) q^{94} +(-5.95003 - 10.3058i) q^{95} +(-2.51618 + 5.06644i) q^{96} +(-13.2713 + 7.66220i) q^{97} +(-0.562064 + 1.00232i) q^{98} +(1.49904 - 2.59641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * q^60 + 6 * q^61 - 34 * q^62 - 4 * q^63 + 16 * q^64 - 22 * q^66 + 18 * q^67 + 34 * q^68 - 56 * q^70 + 36 * q^71 + 6 * q^72 + 6 * q^73 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

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