LMFDB - Embedded newform 841.2.d.i.778.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,1,-1,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.4413675765625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 $ x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			778.1
Root			$-1.00883 - 1.26503i$ of defining polynomial
Character	$\chi$	$=$	841.778
Dual form			841.2.d.i.574.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00883 - 1.26503i) q^{2} +(-0.360046 - 1.57747i) q^{3} +(-0.137526 + 0.602539i) q^{4} +(-1.77950 - 2.23143i) q^{5} +(-1.63232 + 2.04686i) q^{6} +(-0.497572 - 2.18001i) q^{7} +(-2.01463 + 0.970194i) q^{8} +(0.344139 - 0.165729i) q^{9} +(-1.02761 + 4.50225i) q^{10} +(3.25974 + 1.56981i) q^{11} +1.00000 q^{12} +(-3.81657 - 1.83796i) q^{13} +(-2.25581 + 2.82869i) q^{14} +(-2.87930 + 3.61052i) q^{15} +(4.37339 + 2.10612i) q^{16} -6.61803 q^{17} +(-0.556829 - 0.268155i) q^{18} +(-0.412577 + 1.80762i) q^{19} +(1.58925 - 0.765341i) q^{20} +(-3.25974 + 1.56981i) q^{21} +(-1.30266 - 5.70733i) q^{22} +(2.01766 - 2.53006i) q^{23} +(2.25581 + 2.82869i) q^{24} +(-0.700028 + 3.06702i) q^{25} +(1.52518 + 6.68226i) q^{26} +(-3.41182 - 4.27829i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.679710 + 0.852329i) q^{31} +(-0.752558 - 3.29717i) q^{32} +(1.30266 - 5.70733i) q^{33} +(6.67646 + 8.37201i) q^{34} +(-3.97909 + 4.98962i) q^{35} +(0.0525301 + 0.230149i) q^{36} +(7.84582 - 3.77835i) q^{37} +(2.70291 - 1.30165i) q^{38} +(-1.52518 + 6.68226i) q^{39} +(5.74995 + 2.76903i) q^{40} -2.85410 q^{41} +(5.27436 + 2.54000i) q^{42} +(-1.72328 + 2.16093i) q^{43} +(-1.39417 + 1.74823i) q^{44} +(-0.982209 - 0.473007i) q^{45} -5.23607 q^{46} +(6.30678 + 3.03719i) q^{47} +(1.74770 - 7.65718i) q^{48} +(1.80194 - 0.867767i) q^{49} +(4.58608 - 2.20854i) q^{50} +(2.38280 + 10.4397i) q^{51} +(1.63232 - 2.04686i) q^{52} +(-1.24698 - 1.56366i) q^{53} +(-1.97022 + 8.63211i) q^{54} +(-2.29780 - 10.0673i) q^{55} +(3.11745 + 3.90916i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-1.77950 - 2.23143i) q^{60} +(-0.360046 - 1.57747i) q^{61} +(0.392512 - 1.71971i) q^{62} +(-0.532524 - 0.667764i) q^{63} +(2.64115 - 3.31189i) q^{64} +(2.69032 + 11.7870i) q^{65} +(-8.53410 + 4.10981i) q^{66} +(9.43507 - 4.54369i) q^{67} +(0.910148 - 3.98762i) q^{68} +(-4.71753 - 2.27184i) q^{69} +10.3262 q^{70} +(-1.37656 - 0.662915i) q^{71} +(-0.532524 + 0.667764i) q^{72} +(-0.181932 + 0.228135i) q^{73} +(-12.6948 - 6.11350i) q^{74} +5.09017 q^{75} +(-1.03242 - 0.497187i) q^{76} +(1.80023 - 7.88733i) q^{77} +(9.99190 - 4.81184i) q^{78} +(-4.58608 + 2.20854i) q^{79} +(-3.08283 - 13.5068i) q^{80} +(-4.80599 + 6.02652i) q^{81} +(2.87930 + 3.61052i) q^{82} +(-1.76777 + 7.74509i) q^{83} +(-0.497572 - 2.18001i) q^{84} +(11.7768 + 14.7677i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-5.42948 - 6.80835i) q^{89} +(0.392512 + 1.71971i) q^{90} +(-2.10775 + 9.23465i) q^{91} +(1.24698 + 1.56366i) q^{92} +(1.09979 - 1.37910i) q^{93} +(-2.52033 - 11.0423i) q^{94} +(4.76774 - 2.29602i) q^{95} +(-4.93022 + 2.37427i) q^{96} +(3.68546 - 16.1471i) q^{97} +(-2.91560 - 1.40408i) q^{98} +1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} - 7 q^{10} + 5 q^{11} + 12 q^{12} - 4 q^{13} + 5 q^{14} + 7 q^{15} + 3 q^{16} - 66 q^{17} + q^{18} + 3 q^{19} + 8 q^{20} - 5 q^{21} - 5 q^{22}+ \cdots + 30 q^{99}+O(q^{100}) $ 12 * q + q^2 - q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 - 7 * q^10 + 5 * q^11 + 12 * q^12 - 4 * q^13 + 5 * q^14 + 7 * q^15 + 3 * q^16 - 66 * q^17 + q^18 + 3 * q^19 + 8 * q^20 - 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 + 7 * q^26 + 2 * q^27 + 30 * q^28 + 36 * q^30 + 9 * q^31 - 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 + 4 * q^37 + 6 * q^38 - 7 * q^39 + 15 * q^40 + 6 * q^41 + 5 * q^42 + 10 * q^43 + 9 * q^45 - 36 * q^46 + 14 * q^47 + 9 * q^48 + 4 * q^49 - q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 - 5 * q^55 - 10 * q^56 + 36 * q^57 + 6 * q^59 - q^60 - q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 - 10 * q^66 + 12 * q^67 - 3 * q^68 - 6 * q^69 + 30 * q^70 - 12 * q^71 - 5 * q^72 + 14 * q^73 - 17 * q^74 - 6 * q^75 - 9 * q^76 + 5 * q^77 + 11 * q^78 + q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 - 2 * q^85 - 30 * q^88 + 4 * q^89 + 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 + 24 * q^95 - 2 * q^96 + 13 * q^97 - 2 * q^98 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

Coefficient data

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

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

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

$2$	−1.00883	−	1.26503i	−0.713349	−	0.894511i	0.284592	−	0.958649i	$-0.408142\pi$
$2$	−1.00883	−	1.26503i	−0.713349	−	0.894511i	−0.997941	+	0.0641375i	$0.979570\pi$
$3$	−0.360046	−	1.57747i	−0.207873	−	0.910751i	−0.965979	−	0.258620i	$-0.916732\pi$
$3$	−0.360046	−	1.57747i	−0.207873	−	0.910751i	0.758106	−	0.652131i	$-0.226125\pi$
$4$	−0.137526	+	0.602539i	−0.0687628	+	0.301269i
$5$	−1.77950	−	2.23143i	−0.795818	−	0.997924i	−0.999820	−	0.0189540i	$-0.993966\pi$
$5$	−1.77950	−	2.23143i	−0.795818	−	0.997924i	0.204002	−	0.978970i	$-0.434605\pi$
$6$	−1.63232	+	2.04686i	−0.666391	+	0.835628i
$7$	−0.497572	−	2.18001i	−0.188065	−	0.823964i	−0.977636	−	0.210306i	$-0.932554\pi$
$7$	−0.497572	−	2.18001i	−0.188065	−	0.823964i	0.789571	−	0.613659i	$-0.210303\pi$
$8$	−2.01463	+	0.970194i	−0.712278	+	0.343015i
$9$	0.344139	−	0.165729i	0.114713	−	0.0552429i
$10$	−1.02761	+	4.50225i	−0.324959	+	1.42374i
$11$	3.25974	+	1.56981i	0.982847	+	0.473314i	0.855084	−	0.518490i	$-0.173506\pi$
$11$	3.25974	+	1.56981i	0.982847	+	0.473314i	0.127764	+	0.991805i	$0.459220\pi$
$12$	1.00000			0.288675
$13$	−3.81657	−	1.83796i	−1.05852	−	0.509759i	−0.178133	−	0.984006i	$-0.557006\pi$
$13$	−3.81657	−	1.83796i	−1.05852	−	0.509759i	−0.880391	+	0.474248i	$0.842720\pi$
$14$	−2.25581	+	2.82869i	−0.602890	+	0.756000i
$15$	−2.87930	+	3.61052i	−0.743431	+	0.932233i
$16$	4.37339	+	2.10612i	1.09335	+	0.526529i
$17$	−6.61803			−1.60511			−0.802555	−	0.596579i	$-0.796526\pi$
$17$	−6.61803			−1.60511			−0.802555	+	0.596579i	$0.796526\pi$
$18$	−0.556829	−	0.268155i	−0.131246	−	0.0632047i
$19$	−0.412577	+	1.80762i	−0.0946515	+	0.414695i	−0.999949	−	0.0100823i	$-0.996791\pi$
$19$	−0.412577	+	1.80762i	−0.0946515	+	0.414695i	0.905298	+	0.424778i	$0.139648\pi$
$20$	1.58925	−	0.765341i	0.355367	−	0.171136i
$21$	−3.25974	+	1.56981i	−0.711333	+	0.342560i
$22$	−1.30266	−	5.70733i	−0.277728	−	1.21681i
$23$	2.01766	−	2.53006i	0.420710	−	0.527554i	−0.525635	−	0.850710i	$-0.676172\pi$
$23$	2.01766	−	2.53006i	0.420710	−	0.527554i	0.946346	+	0.323156i	$0.104744\pi$
$24$	2.25581	+	2.82869i	0.460465	+	0.577405i
$25$	−0.700028	+	3.06702i	−0.140006	+	0.613405i
$26$	1.52518	+	6.68226i	0.299113	+	1.31050i
$27$	−3.41182	−	4.27829i	−0.656605	−	0.823357i
$28$	1.38197			0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	0.679710	+	0.852329i	0.122079	+	0.153083i	0.839115	−	0.543953i	$-0.183073\pi$
$31$	0.679710	+	0.852329i	0.122079	+	0.153083i	−0.717036	+	0.697036i	$0.754502\pi$
$32$	−0.752558	−	3.29717i	−0.133035	−	0.582863i
$33$	1.30266	−	5.70733i	0.226764	−	0.993518i
$34$	6.67646	+	8.37201i	1.14500	+	1.43579i
$35$	−3.97909	+	4.98962i	−0.672589	+	0.843400i
$36$	0.0525301	+	0.230149i	0.00875501	+	0.0383582i
$37$	7.84582	−	3.77835i	1.28984	−	0.621157i	0.341944	−	0.939720i	$-0.388915\pi$
$37$	7.84582	−	3.77835i	1.28984	−	0.621157i	0.947901	+	0.318564i	$0.103201\pi$
$38$	2.70291	−	1.30165i	0.438469	−	0.211156i
$39$	−1.52518	+	6.68226i	−0.244224	+	1.07002i
$40$	5.74995	+	2.76903i	0.909147	+	0.437822i
$41$	−2.85410			−0.445736			−0.222868	−	0.974849i	$-0.571542\pi$
$41$	−2.85410			−0.445736			−0.222868	+	0.974849i	$0.571542\pi$
$42$	5.27436	+	2.54000i	0.813852	+	0.391930i
$43$	−1.72328	+	2.16093i	−0.262798	+	0.329539i	−0.895671	−	0.444717i	$-0.853304\pi$
$43$	−1.72328	+	2.16093i	−0.262798	+	0.329539i	0.632873	+	0.774256i	$0.281876\pi$
$44$	−1.39417	+	1.74823i	−0.210178	+	0.263555i
$45$	−0.982209	−	0.473007i	−0.146419	−	0.0705117i
$46$	−5.23607			−0.772016
$47$	6.30678	+	3.03719i	0.919939	+	0.443019i	0.833049	−	0.553199i	$-0.186593\pi$
$47$	6.30678	+	3.03719i	0.919939	+	0.443019i	0.0868895	+	0.996218i	$0.472307\pi$
$48$	1.74770	−	7.65718i	0.252259	−	1.10522i
$49$	1.80194	−	0.867767i	0.257420	−	0.123967i
$50$	4.58608	−	2.20854i	0.648570	−	0.312335i
$51$	2.38280	+	10.4397i	0.333659	+	1.46185i
$52$	1.63232	−	2.04686i	0.226362	−	0.283849i
$53$	−1.24698	−	1.56366i	−0.171286	−	0.214786i	0.688778	−	0.724973i	$-0.258148\pi$
$53$	−1.24698	−	1.56366i	−0.171286	−	0.214786i	−0.860064	+	0.510187i	$0.829576\pi$
$54$	−1.97022	+	8.63211i	−0.268113	+	1.17468i
$55$	−2.29780	−	10.0673i	−0.309836	−	1.35748i
$56$	3.11745	+	3.90916i	0.416587	+	0.522383i
$57$	3.00000			0.397360
$58$		0			0
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$	−1.77950	−	2.23143i	−0.229733	−	0.288076i
$61$	−0.360046	−	1.57747i	−0.0460992	−	0.201974i	0.946634	−	0.322311i	$-0.104460\pi$
$61$	−0.360046	−	1.57747i	−0.0460992	−	0.201974i	−0.992733	+	0.120337i	$0.961602\pi$
$62$	0.392512	−	1.71971i	0.0498490	−	0.218403i
$63$	−0.532524	−	0.667764i	−0.0670917	−	0.0841303i
$64$	2.64115	−	3.31189i	0.330143	−	0.413986i
$65$	2.69032	+	11.7870i	0.333693	+	1.46200i
$66$	−8.53410	+	4.10981i	−1.05048	+	0.505882i
$67$	9.43507	−	4.54369i	1.15268	−	0.555100i	0.242840	−	0.970066i	$-0.421921\pi$
$67$	9.43507	−	4.54369i	1.15268	−	0.555100i	0.909837	+	0.414966i	$0.136207\pi$
$68$	0.910148	−	3.98762i	0.110372	−	0.483570i
$69$	−4.71753	−	2.27184i	−0.567924	−	0.273498i
$70$	10.3262			1.23422
$71$	−1.37656	−	0.662915i	−0.163367	−	0.0786736i	0.350413	−	0.936595i	$-0.386041\pi$
$71$	−1.37656	−	0.662915i	−0.163367	−	0.0786736i	−0.513781	+	0.857922i	$0.671755\pi$
$72$	−0.532524	+	0.667764i	−0.0627585	+	0.0786967i
$73$	−0.181932	+	0.228135i	−0.0212935	+	0.0267012i	−0.792364	−	0.610048i	$-0.791150\pi$
$73$	−0.181932	+	0.228135i	−0.0212935	+	0.0267012i	0.771071	+	0.636750i	$0.219721\pi$
$74$	−12.6948	−	6.11350i	−1.47574	−	0.710679i
$75$	5.09017			0.587762
$76$	−1.03242	−	0.497187i	−0.118427	−	0.0570312i
$77$	1.80023	−	7.88733i	0.205155	−	0.898845i
$78$	9.99190	−	4.81184i	1.13136	−	0.544834i
$79$	−4.58608	+	2.20854i	−0.515975	+	0.248480i	−0.673703	−	0.739002i	$-0.735297\pi$
$79$	−4.58608	+	2.20854i	−0.515975	+	0.248480i	0.157728	+	0.987483i	$0.449583\pi$
$80$	−3.08283	−	13.5068i	−0.344671	−	1.51010i
$81$	−4.80599	+	6.02652i	−0.533999	+	0.669613i
$82$	2.87930	+	3.61052i	0.317965	+	0.398716i
$83$	−1.76777	+	7.74509i	−0.194038	+	0.850134i	0.780365	+	0.625324i	$0.215033\pi$
$83$	−1.76777	+	7.74509i	−0.194038	+	0.850134i	−0.974403	+	0.224810i	$0.927824\pi$
$84$	−0.497572	−	2.18001i	−0.0542895	−	0.237858i
$85$	11.7768	+	14.7677i	1.27737	+	1.60178i
$86$	4.47214			0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	−5.42948	−	6.80835i	−0.575523	−	0.721683i	0.405819	−	0.913954i	$-0.366986\pi$
$89$	−5.42948	−	6.80835i	−0.575523	−	0.721683i	−0.981342	+	0.192270i	$0.938415\pi$
$90$	0.392512	+	1.71971i	0.0413744	+	0.181273i
$91$	−2.10775	+	9.23465i	−0.220952	+	0.968054i
$92$	1.24698	+	1.56366i	0.130007	+	0.163023i
$93$	1.09979	−	1.37910i	0.114043	−	0.143006i
$94$	−2.52033	−	11.0423i	−0.259952	−	1.13892i
$95$	4.76774	−	2.29602i	0.489160	−	0.235567i
$96$	−4.93022	+	2.37427i	−0.503189	+	0.242323i
$97$	3.68546	−	16.1471i	0.374202	−	1.63948i	−0.340636	−	0.940195i	$-0.610643\pi$
$97$	3.68546	−	16.1471i	0.374202	−	1.63948i	0.714838	−	0.699290i	$-0.246500\pi$
$98$	−2.91560	−	1.40408i	−0.294520	−	0.141833i
$99$	1.38197			0.138893
$100$	−1.75173	−	0.843588i	−0.175173	−	0.0843588i
$101$	1.00883	−	1.26503i	0.100382	−	0.125875i	−0.729103	−	0.684404i	$-0.760063\pi$
$101$	1.00883	−	1.26503i	0.100382	−	0.125875i	0.829485	+	0.558529i	$0.188634\pi$
$102$	10.8027	−	13.5462i	1.06963	−	1.34127i
$103$	11.8751	+	5.71874i	1.17009	+	0.563484i	0.915008	−	0.403437i	$-0.132184\pi$
$103$	11.8751	+	5.71874i	1.17009	+	0.563484i	0.255078	+	0.966920i	$0.417899\pi$
$104$	9.47214			0.928819
$105$	9.30362	+	4.48039i	0.907940	+	0.437241i
$106$	−0.720093	+	3.15493i	−0.0699416	+	0.306434i
$107$	−10.1233	+	4.87515i	−0.978661	+	0.471298i	−0.853644	−	0.520856i	$-0.825613\pi$
$107$	−10.1233	+	4.87515i	−0.978661	+	0.471298i	−0.125017	+	0.992155i	$0.539898\pi$
$108$	3.04705	−	1.46738i	0.293202	−	0.141199i
$109$	3.69786	+	16.2014i	0.354191	+	1.55181i	0.767396	+	0.641173i	$0.221552\pi$
$109$	3.69786	+	16.2014i	0.354191	+	1.55181i	−0.413205	+	0.910638i	$0.635591\pi$
$110$	−10.4174	+	13.0630i	−0.993260	+	1.24551i
$111$	−8.78508	−	11.0161i	−0.833843	−	1.04561i
$112$	2.41526	−	10.5820i	0.228221	−	0.999902i
$113$	2.21281	+	9.69495i	0.208164	+	0.912024i	0.965788	+	0.259333i	$0.0835028\pi$
$113$	2.21281	+	9.69495i	0.208164	+	0.912024i	−0.757624	+	0.652691i	$0.773640\pi$
$114$	−3.02648	−	3.79509i	−0.283456	−	0.355443i
$115$	−9.23607			−0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	5.13510	+	6.43922i	0.472725	+	0.592778i
$119$	3.29295	+	14.4273i	0.301864	+	1.32255i
$120$	2.29780	−	10.0673i	0.209760	−	0.919018i
$121$	1.30320	+	1.63416i	0.118473	+	0.148560i
$122$	−1.63232	+	2.04686i	−0.147783	+	0.185314i
$123$	1.02761	+	4.50225i	0.0926564	+	0.405954i
$124$	−0.607039	+	0.292334i	−0.0545137	+	0.0262524i
$125$	−4.76774	+	2.29602i	−0.426440	+	0.205363i
$126$	−0.307516	+	1.34732i	−0.0273957	+	0.120029i
$127$	1.75173	+	0.843588i	0.155441	+	0.0748563i	0.509987	−	0.860182i	$-0.329650\pi$
$127$	1.75173	+	0.843588i	0.155441	+	0.0748563i	−0.354546	+	0.935039i	$0.615365\pi$
$128$	−13.6180			−1.20368
$129$	4.02926	+	1.94039i	0.354756	+	0.170842i
$130$	12.1969	−	15.2944i	1.06974	−	1.34141i
$131$	−0.826896	+	1.03689i	−0.0722462	+	0.0905939i	−0.816641	−	0.577146i	$-0.804167\pi$
$131$	−0.826896	+	1.03689i	−0.0722462	+	0.0905939i	0.744395	+	0.667739i	$0.232738\pi$
$132$	3.25974	+	1.56981i	0.283724	+	0.136634i
$133$	4.14590			0.359495
$134$	−15.2663	−	7.35184i	−1.31880	−	0.635103i
$135$	−3.47534	+	15.2265i	−0.299110	+	1.31048i
$136$	13.3329	−	6.42077i	1.14328	−	0.550577i
$137$	−12.4821	+	6.01107i	−1.06642	+	0.513560i	−0.882951	−	0.469465i	$-0.844447\pi$
$137$	−12.4821	+	6.01107i	−1.06642	+	0.513560i	−0.183468	+	0.983026i	$0.558732\pi$
$138$	1.88523	+	8.25972i	0.160481	+	0.703114i
$139$	9.17042	−	11.4993i	0.777824	−	0.975361i	−0.222175	−	0.975007i	$-0.571316\pi$
$139$	9.17042	−	11.4993i	0.777824	−	0.975361i	1.00000		0.000354328i	$-0.000112786\pi$
$140$	−2.45921	−	3.08376i	−0.207841	−	0.260625i
$141$	2.52033	−	11.0423i	0.212250	−	0.929927i
$142$	0.550102	+	2.41015i	0.0461635	+	0.202256i
$143$	−9.55575	−	11.9825i	−0.799092	−	1.00203i
$144$	1.85410			0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	−2.01766	−	2.53006i	−0.166413	−	0.208676i
$148$	1.19760	+	5.24703i	0.0984421	+	0.431303i
$149$	−1.64264	+	7.19688i	−0.134570	+	0.589592i	0.862005	+	0.506900i	$0.169209\pi$
$149$	−1.64264	+	7.19688i	−0.134570	+	0.589592i	−0.996575	+	0.0826915i	$0.973648\pi$
$150$	−5.13510	−	6.43922i	−0.419280	−	0.525760i
$151$	11.4262	−	14.3280i	0.929853	−	1.16600i	−0.0560077	−	0.998430i	$-0.517837\pi$
$151$	11.4262	−	14.3280i	0.929853	−	1.16600i	0.985860	−	0.167568i	$-0.0535914\pi$
$152$	−0.922549	−	4.04195i	−0.0748286	−	0.327846i
$153$	−2.27753	+	1.09680i	−0.184127	+	0.0886710i
$154$	−11.7938	+	5.67961i	−0.950374	+	0.457676i
$155$	0.692364	−	3.03345i	0.0556120	−	0.243652i
$156$	−3.81657	−	1.83796i	−0.305570	−	0.147155i
$157$	−5.56231			−0.443920			−0.221960	−	0.975056i	$-0.571245\pi$
$157$	−5.56231			−0.443920			−0.221960	+	0.975056i	$0.571245\pi$
$158$	7.42044	+	3.57350i	0.590339	+	0.284292i
$159$	−2.01766	+	2.53006i	−0.160010	+	0.200647i
$160$	−6.01822	+	7.54661i	−0.475782	+	0.596612i
$161$	−6.51947	−	3.13961i	−0.513806	−	0.247436i
$162$	12.4721			0.979904
$163$	−20.7533	−	9.99427i	−1.62553	−	0.782812i	−0.999997	−	0.00261030i	$-0.999169\pi$
$163$	−20.7533	−	9.99427i	−1.62553	−	0.782812i	−0.625528	−	0.780201i	$-0.715117\pi$
$164$	0.392512	−	1.71971i	0.0306500	−	0.134287i
$165$	−15.0536	+	7.24942i	−1.17192	+	0.564366i
$166$	11.5811	−	5.57719i	0.898871	−	0.432874i
$167$	−4.33296	−	18.9839i	−0.335294	−	1.46902i	−0.808724	−	0.588189i	$-0.799841\pi$
$167$	−4.33296	−	18.9839i	−0.335294	−	1.46902i	0.473429	−	0.880832i	$-0.343016\pi$
$168$	5.04414	−	6.32515i	0.389164	−	0.487996i
$169$	3.08270	+	3.86559i	0.237131	+	0.297353i
$170$	6.80075	−	29.7960i	0.521594	−	2.28525i
$171$	0.157590	+	0.690448i	0.0120512	+	0.0527999i
$172$	−1.06505	−	1.33553i	−0.0812091	−	0.101833i
$173$	−7.09017			−0.539056			−0.269528	−	0.962993i	$-0.586868\pi$
$173$	−7.09017			−0.539056			−0.269528	+	0.962993i	$0.586868\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	10.9499	+	13.7308i	0.825381	+	1.03500i
$177$	1.83270	+	8.02957i	0.137754	+	0.603540i
$178$	−3.13536	+	13.7369i	−0.235005	+	1.02962i
$179$	−9.97584	−	12.5093i	−0.745629	−	0.934989i	0.253851	−	0.967243i	$-0.418303\pi$
$179$	−9.97584	−	12.5093i	−0.745629	−	0.934989i	−0.999480	+	0.0322542i	$0.989731\pi$
$180$	0.420084	−	0.526768i	0.0313112	−	0.0392630i
$181$	2.65785	+	11.6448i	0.197556	+	0.865551i	0.972385	+	0.233381i	$0.0749788\pi$
$181$	2.65785	+	11.6448i	0.197556	+	0.865551i	−0.774829	+	0.632171i	$0.782164\pi$
$182$	13.8085	−	6.64981i	1.02355	−	0.492916i
$183$	−2.35877	+	1.13592i	−0.174365	+	0.0839698i
$184$	−1.61018	+	7.05464i	−0.118704	+	0.520075i
$185$	−22.3928	−	10.7838i	−1.64635	−	0.792840i
$186$	−2.85410			−0.209273
$187$	−21.5730	−	10.3890i	−1.57758	−	0.759721i
$188$	−2.69737	+	3.38239i	−0.196726	+	0.246686i
$189$	−7.62906	+	9.56654i	−0.554933	+	0.695864i
$190$	−7.71437	−	3.71505i	−0.559659	−	0.269518i
$191$	−12.0344			−0.870782			−0.435391	−	0.900242i	$-0.643390\pi$
$191$	−12.0344			−0.870782			−0.435391	+	0.900242i	$0.643390\pi$
$192$	−6.17533	−	2.97388i	−0.445666	−	0.214622i
$193$	−0.785024	+	3.43941i	−0.0565072	+	0.247574i	−0.995291	−	0.0969328i	$-0.969097\pi$
$193$	−0.785024	+	3.43941i	−0.0565072	+	0.247574i	0.938784	+	0.344507i	$0.111954\pi$
$194$	−24.1445	+	11.6274i	−1.73347	+	0.834797i
$195$	17.6250	−	8.48777i	1.26215	−	0.607822i
$196$	0.275051	+	1.20508i	0.0196465	+	0.0860769i
$197$	−12.2879	+	15.4085i	−0.875474	+	1.09781i	0.119007	+	0.992893i	$0.462029\pi$
$197$	−12.2879	+	15.4085i	−0.875474	+	1.09781i	−0.994481	+	0.104916i	$0.966543\pi$
$198$	−1.39417	−	1.74823i	−0.0990790	−	0.124241i
$199$	−0.190056	+	0.832688i	−0.0134727	+	0.0590277i	−0.981217	−	0.192905i	$-0.938209\pi$
$199$	−0.190056	+	0.832688i	−0.0134727	+	0.0590277i	0.967745	+	0.251933i	$0.0810662\pi$
$200$	−1.56531	−	6.85807i	−0.110684	−	0.484939i
$201$	−10.5646	−	13.2476i	−0.745168	−	0.934411i
$202$	−2.61803			−0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	5.07888	+	6.36872i	0.354725	+	0.444811i
$206$	−4.74553	−	20.7915i	−0.330637	−	1.44862i
$207$	0.275051	−	1.20508i	0.0191174	−	0.0837587i
$208$	−12.8204	−	16.0763i	−0.888934	−	1.11469i
$209$	−4.18250	+	5.24469i	−0.289309	+	0.362782i
$210$	−3.71793	−	16.2893i	−0.256561	−	1.12407i
$211$	−17.7063	+	8.52689i	−1.21895	+	0.587015i	−0.929019	−	0.370032i	$-0.879347\pi$
$211$	−17.7063	+	8.52689i	−1.21895	+	0.587015i	−0.289931	+	0.957048i	$0.593632\pi$
$212$	1.11366	−	0.536310i	0.0764864	−	0.0368339i
$213$	−0.550102	+	2.41015i	−0.0376924	+	0.165141i
$214$	16.3799	+	7.88815i	1.11971	+	0.539223i
$215$	7.88854			0.537994
$216$	11.0243	+	5.30903i	0.750110	+	0.361234i
$217$	1.51988	−	1.90587i	0.103176	−	0.129379i
$218$	16.7647	−	21.0223i	1.13545	−	1.42381i
$219$	0.425380	+	0.204852i	0.0287445	+	0.0138426i
$220$	6.38197			0.430272
$221$	25.2582	+	12.1637i	1.69905	+	0.818218i
$222$	−5.07312	+	22.2268i	−0.340485	+	1.49176i
$223$	−16.5114	+	7.95146i	−1.10568	+	0.532469i	−0.895441	−	0.445180i	$-0.853140\pi$
$223$	−16.5114	+	7.95146i	−1.10568	+	0.532469i	−0.210242	+	0.977649i	$0.567425\pi$
$224$	−6.81340	+	3.28116i	−0.455240	+	0.219232i
$225$	0.267387	+	1.17150i	0.0178258	+	0.0780999i
$226$	10.0321	−	12.5798i	0.667322	−	0.836796i
$227$	9.28286	+	11.6403i	0.616125	+	0.772596i	0.987793	−	0.155769i	$-0.0497857\pi$
$227$	9.28286	+	11.6403i	0.616125	+	0.772596i	−0.371669	+	0.928365i	$0.621214\pi$
$228$	−0.412577	+	1.80762i	−0.0273235	+	0.119712i
$229$	−3.49540	−	15.3144i	−0.230983	−	1.01200i	−0.948827	−	0.315798i	$-0.897728\pi$
$229$	−3.49540	−	15.3144i	−0.230983	−	1.01200i	0.717844	−	0.696204i	$-0.245129\pi$
$230$	9.31760	+	11.6839i	0.614384	+	0.770414i
$231$	−13.0902			−0.861270
$232$		0			0
$233$	10.7639			0.705169			0.352584	−	0.935780i	$-0.385303\pi$
$233$	10.7639			0.705169			0.352584	+	0.935780i	$0.385303\pi$
$234$	1.63232	+	2.04686i	0.106708	+	0.133808i
$235$	−4.44568	−	19.4778i	−0.290004	−	1.27059i
$236$	0.700028	−	3.06702i	0.0455680	−	0.199646i
$237$	5.13510	+	6.43922i	0.333561	+	0.418272i
$238$	14.9290	−	18.7204i	0.967704	−	1.21346i
$239$	−3.28055	−	14.3730i	−0.212201	−	0.929713i	−0.963068	−	0.269259i	$-0.913221\pi$
$239$	−3.28055	−	14.3730i	−0.212201	−	0.929713i	0.750867	−	0.660454i	$-0.229636\pi$
$240$	−20.1965	+	9.72611i	−1.30368	+	0.627818i
$241$	−24.0131	+	11.5641i	−1.54682	+	0.744908i	−0.995969	−	0.0896982i	$-0.971410\pi$
$241$	−24.0131	+	11.5641i	−1.54682	+	0.744908i	−0.550848	+	0.834606i	$0.685695\pi$
$242$	0.752558	−	3.29717i	0.0483763	−	0.211950i
$243$	−3.55367	−	1.71136i	−0.227968	−	0.109784i
$244$	1.00000			0.0640184
$245$	−5.14291	−	2.47670i	−0.328569	−	0.158230i
$246$	4.65880	−	5.84195i	0.297034	−	0.372469i
$247$	4.89695	−	6.14058i	0.311586	−	0.390716i
$248$	−2.19629	−	1.05768i	−0.139464	−	0.0671625i
$249$	12.8541			0.814596
$250$	7.71437	+	3.71505i	0.487900	+	0.234960i
$251$	−2.59292	+	11.3603i	−0.163664	+	0.717057i	0.824778	+	0.565456i	$0.191300\pi$
$251$	−2.59292	+	11.3603i	−0.163664	+	0.717057i	−0.988442	+	0.151601i	$0.951557\pi$
$252$	0.475589	−	0.229032i	0.0299593	−	0.0144276i
$253$	10.5487	−	5.08000i	0.663193	−	0.319377i
$254$	−0.700028	−	3.06702i	−0.0439237	−	0.192442i
$255$	19.0553	−	23.8946i	1.19329	−	1.49634i
$256$	8.45596	+	10.6034i	0.528497	+	0.662715i
$257$	0.182392	−	0.799110i	0.0113773	−	0.0498471i	−0.968921	−	0.247372i	$-0.920433\pi$
$257$	0.182392	−	0.799110i	0.0113773	−	0.0498471i	0.980298	+	0.197525i	$0.0632903\pi$
$258$	−1.61018	−	7.05464i	−0.100245	−	0.439203i
$259$	−12.1407	−	15.2239i	−0.754385	−	0.945969i
$260$	−7.47214			−0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	−2.05240	−	2.57363i	−0.126556	−	0.158697i	0.714516	−	0.699619i	$-0.246647\pi$
$263$	−2.05240	−	2.57363i	−0.126556	−	0.158697i	−0.841073	+	0.540922i	$0.818075\pi$
$264$	2.91284	+	12.7620i	0.179273	+	0.785445i
$265$	−1.27019	+	5.56509i	−0.0780275	+	0.341861i
$266$	−4.18250	−	5.24469i	−0.256445	−	0.321572i
$267$	−8.78508	+	11.0161i	−0.537638	+	0.674177i
$268$	1.44019	+	6.30987i	0.0879733	+	0.385436i
$269$	5.40581	−	2.60330i	0.329598	−	0.158726i	−0.261765	−	0.965132i	$-0.584304\pi$
$269$	5.40581	−	2.60330i	0.329598	−	0.158726i	0.591363	+	0.806406i	$0.298590\pi$
$270$	22.7679	−	10.9645i	1.38561	−	0.667276i
$271$	2.71038	−	11.8750i	0.164644	−	0.721352i	−0.823436	−	0.567409i	$-0.807946\pi$
$271$	2.71038	−	11.8750i	0.164644	−	0.721352i	0.988080	−	0.153943i	$-0.0491971\pi$
$272$	−28.9433	−	13.9383i	−1.75494	−	0.845136i
$273$	15.3262			0.927586
$274$	20.1965	+	9.72611i	1.22011	+	0.587576i
$275$	−7.09654	+	8.89878i	−0.427937	+	0.536617i
$276$	2.01766	−	2.53006i	0.121449	−	0.152292i
$277$	21.2791	+	10.2475i	1.27854	+	0.615711i	0.945014	−	0.327030i	$-0.106048\pi$
$277$	21.2791	+	10.2475i	1.27854	+	0.615711i	0.333524	+	0.942742i	$0.391762\pi$
$278$	−23.7984			−1.42733
$279$	0.375171	+	0.180673i	0.0224609	+	0.0108166i
$280$	3.17549	−	13.9127i	0.189772	−	0.831444i
$281$	15.4287	−	7.43009i	0.920402	−	0.443242i	0.0871871	−	0.996192i	$-0.472212\pi$
$281$	15.4287	−	7.43009i	0.920402	−	0.443242i	0.833214	+	0.552950i	$0.186498\pi$
$282$	−16.5114	+	7.95146i	−0.983238	+	0.473502i
$283$	0.169991	+	0.744779i	0.0101049	+	0.0442725i	0.979729	−	0.200327i	$-0.0642006\pi$
$283$	0.169991	+	0.744779i	0.0101049	+	0.0442725i	−0.969624	+	0.244600i	$0.921343\pi$
$284$	0.588744	−	0.738262i	0.0349355	−	0.0438078i
$285$	−5.33851	−	6.69428i	−0.316226	−	0.396535i
$286$	−5.51816	+	24.1766i	−0.326295	+	1.42959i
$287$	1.42012	+	6.22196i	0.0838271	+	0.367270i
$288$	−0.805422	−	1.00997i	−0.0474599	−	0.0595129i
$289$	26.7984			1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	−0.112440	−	0.140995i	−0.00658006	−	0.00825113i
$293$	−3.88792	−	17.0341i	−0.227134	−	0.995141i	−0.951963	−	0.306212i	$-0.900938\pi$
$293$	−3.88792	−	17.0341i	−0.227134	−	0.995141i	0.724829	−	0.688929i	$-0.241919\pi$
$294$	−1.16513	+	5.10479i	−0.0679520	+	0.297717i
$295$	9.05798	+	11.3583i	0.527376	+	0.661308i
$296$	−12.1407	+	15.2239i	−0.705663	+	0.884873i
$297$	−4.40555	−	19.3020i	−0.255636	−	1.12001i
$298$	10.7614	−	5.18243i	0.623392	−	0.300210i
$299$	−12.3507	+	5.94777i	−0.714257	+	0.343968i
$300$	−0.700028	+	3.06702i	−0.0404161	+	0.177075i
$301$	5.56829	+	2.68155i	0.320951	+	0.154562i
$302$	−29.6525			−1.70631
$303$	−2.35877	−	1.13592i	−0.135508	−	0.0652570i
$304$	−5.61141	+	7.03648i	−0.321836	+	0.403570i
$305$	−2.87930	+	3.61052i	−0.164868	+	0.206738i
$306$	3.68512	+	1.77466i	0.210664	+	0.101450i
$307$	3.18034			0.181512			0.0907558	−	0.995873i	$-0.471072\pi$
$307$	3.18034			0.181512			0.0907558	+	0.995873i	$0.471072\pi$
$308$	4.50484	+	2.16942i	0.256687	+	0.123614i
$309$	4.74553	−	20.7915i	0.269964	−	1.18279i
$310$	−4.53588	+	2.18436i	−0.257620	+	0.124063i
$311$	8.18996	−	3.94408i	0.464410	−	0.223648i	−0.187021	−	0.982356i	$-0.559883\pi$
$311$	8.18996	−	3.94408i	0.464410	−	0.223648i	0.651431	+	0.758708i	$0.274169\pi$
$312$	−3.41041	−	14.9420i	−0.193076	−	0.845923i
$313$	−15.0200	+	18.8345i	−0.848979	+	1.06459i	0.148157	+	0.988964i	$0.452666\pi$
$313$	−15.0200	+	18.8345i	−0.848979	+	1.06459i	−0.997137	+	0.0756224i	$0.975906\pi$
$314$	5.61141	+	7.03648i	0.316670	+	0.397092i
$315$	−0.542438	+	2.37658i	−0.0305629	+	0.133905i
$316$	−0.700028	−	3.06702i	−0.0393797	−	0.172534i
$317$	8.91079	+	11.1738i	0.500480	+	0.627582i	0.966337	−	0.257278i	$-0.0828256\pi$
$317$	8.91079	+	11.1738i	0.500480	+	0.627582i	−0.465858	+	0.884860i	$0.654254\pi$
$318$	5.23607			0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	11.3353	+	14.2140i	0.632672	+	0.793346i
$322$	2.60532	+	11.4147i	0.145189	+	0.636114i
$323$	2.73045	−	11.9629i	0.151926	−	0.665631i
$324$	−2.97026	−	3.72459i	−0.165015	−	0.206922i
$325$	8.30877	−	10.4189i	0.460888	−	0.577935i
$326$	8.29347	+	36.3361i	0.459333	+	2.01247i
$327$	24.2257	−	11.6665i	1.33969	−	0.645159i
$328$	5.74995	−	2.76903i	0.317488	−	0.152894i
$329$	3.48300	−	15.2600i	0.192024	−	0.841313i
$330$	24.3572	+	11.7298i	1.34082	+	0.645704i
$331$	−1.18034			−0.0648773			−0.0324387	−	0.999474i	$-0.510327\pi$
$331$	−1.18034			−0.0648773			−0.0324387	+	0.999474i	$0.510327\pi$
$332$	−4.42360	−	2.13030i	−0.242777	−	0.116915i
$333$	2.07388	−	2.60056i	0.113648	−	0.142510i
$334$	−19.6440	+	24.6328i	−1.07487	+	1.34785i
$335$	−26.9286	−	12.9682i	−1.47127	−	0.708526i
$336$	−17.5623			−0.958102
$337$	−21.6853	−	10.4431i	−1.18127	−	0.568872i	−0.262992	−	0.964798i	$-0.584709\pi$
$337$	−21.6853	−	10.4431i	−1.18127	−	0.568872i	−0.918282	+	0.395926i	$0.870424\pi$
$338$	1.78017	−	7.79942i	0.0968283	−	0.424233i
$339$	14.4967	−	6.98126i	0.787355	−	0.379170i
$340$	−10.5177	+	5.06506i	−0.570402	+	0.274691i
$341$	0.877683	+	3.84538i	0.0475292	+	0.208239i
$342$	0.714456	−	0.895899i	0.0386333	−	0.0484447i
$343$	−12.5475	−	15.7341i	−0.677501	−	0.849559i
$344$	1.37526	−	6.02539i	0.0741488	−	0.324867i
$345$	3.32541	+	14.5696i	0.179034	+	0.784400i
$346$	7.15276	+	8.96928i	0.384535	+	0.482191i
$347$	8.12461			0.436152			0.218076	−	0.975932i	$-0.430022\pi$
$347$	8.12461			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	−7.09654	−	8.89878i	−0.379326	−	0.475660i
$351$	5.15811	+	22.5992i	0.275320	+	1.20625i
$352$	2.72278	−	11.9293i	0.145125	−	0.635833i
$353$	13.1710	+	16.5159i	0.701021	+	0.879052i	0.997099	−	0.0761116i	$-0.0242505\pi$
$353$	13.1710	+	16.5159i	0.701021	+	0.879052i	−0.296079	+	0.955164i	$0.595679\pi$
$354$	8.30877	−	10.4189i	0.441606	−	0.553757i
$355$	0.970343	+	4.25135i	0.0515004	+	0.225638i
$356$	4.84898	−	2.33515i	0.256996	−	0.123763i
$357$	21.5730	−	10.3890i	1.14177	−	0.549846i
$358$	−5.76074	+	25.2395i	−0.304465	+	1.33395i
$359$	25.4398	+	12.2512i	1.34266	+	0.646592i	0.960701	−	0.277586i	$-0.0895344\pi$
$359$	25.4398	+	12.2512i	1.34266	+	0.646592i	0.381962	+	0.924178i	$0.375249\pi$
$360$	2.43769			0.128478
$361$	14.0212	+	6.75223i	0.737955	+	0.355381i
$362$	12.0497	−	15.1099i	0.633319	−	0.794157i
$363$	2.10862	−	2.64413i	0.110674	−	0.138781i
$364$	−5.27436	−	2.54000i	−0.276452	−	0.133132i
$365$	0.832816			0.0435916
$366$	3.81657	+	1.83796i	0.199495	+	0.0960718i
$367$	1.39532	−	6.11330i	0.0728351	−	0.319111i	−0.925365	−	0.379076i	$-0.876242\pi$
$367$	1.39532	−	6.11330i	0.0728351	−	0.319111i	0.998200	+	0.0599650i	$0.0190989\pi$
$368$	14.1526	−	6.81553i	0.737755	−	0.355284i
$369$	−0.982209	+	0.473007i	−0.0511318	+	0.0246238i
$370$	8.94863	+	39.2065i	0.465217	+	2.03825i
$371$	−2.78833	+	3.49646i	−0.144763	+	0.181527i
$372$	0.679710	+	0.852329i	0.0352413	+	0.0441912i
$373$	−4.09037	+	17.9211i	−0.211791	+	0.927919i	0.751558	+	0.659668i	$0.229303\pi$
$373$	−4.09037	+	17.9211i	−0.211791	+	0.927919i	−0.963349	+	0.268251i	$0.913554\pi$
$374$	8.62105	+	37.7713i	0.445784	+	1.95311i
$375$	5.33851	+	6.69428i	0.275679	+	0.345691i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	−23.5107	−	29.4815i	−1.20766	−	1.51436i	−0.798609	−	0.601851i	$-0.794430\pi$
$379$	−23.5107	−	29.4815i	−1.20766	−	1.51436i	−0.409054	−	0.912510i	$-0.634141\pi$
$380$	0.727757	+	3.18851i	0.0373331	+	0.163567i
$381$	0.700028	−	3.06702i	0.0358635	−	0.157128i
$382$	12.1407	+	15.2239i	0.621171	+	0.778924i
$383$	−13.8077	+	17.3144i	−0.705543	+	0.884722i	−0.997424	−	0.0717321i	$-0.977147\pi$
$383$	−13.8077	+	17.3144i	−0.705543	+	0.884722i	0.291881	+	0.956455i	$0.405719\pi$
$384$	4.90312	+	21.4820i	0.250212	+	1.09625i
$385$	−20.8035	+	10.0184i	−1.06025	+	0.510587i
$386$	5.14291	−	2.47670i	0.261767	−	0.126061i
$387$	−0.234922	+	1.02926i	−0.0119417	+	0.0523202i
$388$	9.22238	+	4.44126i	0.468195	+	0.225471i
$389$	21.1246			1.07106			0.535530	−	0.844516i	$-0.320112\pi$
$389$	21.1246			1.07106			0.535530	+	0.844516i	$0.320112\pi$
$390$	−28.5179	−	13.7335i	−1.44406	−	0.695423i
$391$	−13.3529	+	16.7440i	−0.675286	+	0.846782i
$392$	−2.78833	+	3.49646i	−0.140832	+	0.176598i
$393$	1.93339	+	0.931070i	0.0975265	+	0.0469663i
$394$	31.8885			1.60652
$395$	13.0892	+	6.30340i	0.658587	+	0.317159i
$396$	−0.190056	+	0.832688i	−0.00955065	+	0.0418441i
$397$	28.7808	−	13.8601i	1.44447	−	0.695618i	0.462842	−	0.886441i	$-0.346830\pi$
$397$	28.7808	−	13.8601i	1.44447	−	0.695618i	0.981625	+	0.190822i	$0.0611154\pi$
$398$	1.24511	−	0.599613i	0.0624116	−	0.0300559i
$399$	−1.49272	−	6.54002i	−0.0747293	−	0.327410i
$400$	−9.52101	+	11.9390i	−0.476050	+	0.596948i
$401$	−20.6181	−	25.8543i	−1.02962	−	1.29110i	−0.955859	−	0.293826i	$-0.905071\pi$
$401$	−20.6181	−	25.8543i	−1.02962	−	1.29110i	−0.0737604	−	0.997276i	$-0.523500\pi$
$402$	−6.10072	+	26.7290i	−0.304276	+	1.33312i
$403$	−1.02761	−	4.50225i	−0.0511889	−	0.224273i
$404$	0.623490	+	0.781831i	0.0310198	+	0.0388976i
$405$	22.0000			1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	−14.9290	−	18.7204i	−0.739096	−	0.926797i
$409$	−0.129861	−	0.568960i	−0.00642124	−	0.0281333i	0.971616	−	0.236564i	$-0.0760214\pi$
$409$	−0.129861	−	0.568960i	−0.00642124	−	0.0281333i	−0.978037	+	0.208431i	$0.933164\pi$
$410$	2.93290	−	12.8499i	0.144846	−	0.634610i
$411$	13.9764	+	17.5259i	0.689405	+	0.864487i
$412$	−5.07888	+	6.36872i	−0.250219	+	0.313764i
$413$	2.53273	+	11.0966i	0.124627	+	0.546028i
$414$	−1.80194	+	0.867767i	−0.0885604	+	0.0426484i
$415$	20.4284	−	9.83778i	1.00279	−	0.482917i
$416$	−3.18789	+	13.9670i	−0.156299	+	0.684791i
$417$	−21.4416	−	10.3257i	−1.05000	−	0.505653i
$418$	10.8541			0.530891
$419$	−2.30856	−	1.11174i	−0.112780	−	0.0543122i	0.376643	−	0.926359i	$-0.377078\pi$
$419$	−2.30856	−	1.11174i	−0.112780	−	0.0543122i	−0.489423	+	0.872046i	$0.662793\pi$
$420$	−3.97909	+	4.98962i	−0.194160	+	0.243469i
$421$	−1.22551	+	1.53674i	−0.0597275	+	0.0748959i	−0.810798	−	0.585326i	$-0.800966\pi$
$421$	−1.22551	+	1.53674i	−0.0597275	+	0.0748959i	0.751070	+	0.660222i	$0.229538\pi$
$422$	28.6493	+	13.7968i	1.39463	+	0.671618i
$423$	2.67376			0.130003
$424$	4.02926	+	1.94039i	0.195678	+	0.0942335i
$425$	4.63281	−	20.2977i	0.224724	−	0.984582i
$426$	3.60388	−	1.73553i	0.174608	−	0.0840869i
$427$	−3.25974	+	1.56981i	−0.157750	+	0.0759682i
$428$	−1.54525	−	6.77016i	−0.0746923	−	0.327248i
$429$	−15.4615	+	19.3881i	−0.746490	+	0.936069i
$430$	−7.95818	−	9.97924i	−0.383778	−	0.481242i
$431$	7.69850	−	33.7293i	0.370824	−	1.62468i	−0.353647	−	0.935379i	$-0.615058\pi$
$431$	7.69850	−	33.7293i	0.370824	−	1.62468i	0.724470	−	0.689306i	$-0.242084\pi$
$432$	−5.91067	−	25.8963i	−0.284377	−	1.24594i
$433$	7.86722	+	9.86518i	0.378074	+	0.474090i	0.934067	−	0.357097i	$-0.116233\pi$
$433$	7.86722	+	9.86518i	0.378074	+	0.474090i	−0.555993	+	0.831187i	$0.687662\pi$
$434$	−3.94427			−0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	3.74094	+	4.69099i	0.178953	+	0.224400i
$438$	−0.169991	−	0.744779i	−0.00812248	−	0.0355869i
$439$	0.679963	−	2.97911i	0.0324529	−	0.142185i	−0.956106	−	0.293021i	$-0.905339\pi$
$439$	0.679963	−	2.97911i	0.0324529	−	0.142185i	0.988559	+	0.150836i	$0.0481965\pi$
$440$	14.3965	+	18.0526i	0.686326	+	0.860625i
$441$	0.476304	−	0.597266i	0.0226811	−	0.0284412i
$442$	−10.0937	−	44.2234i	−0.480108	−	2.10349i
$443$	11.7938	−	5.67961i	0.560342	−	0.269847i	−0.132201	−	0.991223i	$-0.542204\pi$
$443$	11.7938	−	5.67961i	0.560342	−	0.269847i	0.692543	+	0.721376i	$0.256490\pi$
$444$	7.84582	−	3.77835i	0.372346	−	0.179312i
$445$	−5.53056	+	24.2310i	−0.262174	+	1.14866i
$446$	26.7160	+	12.8657i	1.26504	+	0.609210i
$447$	11.9443			0.564945
$448$	−8.53410	−	4.10981i	−0.403198	−	0.194170i
$449$	8.80655	−	11.0431i	0.415607	−	0.521155i	−0.529326	−	0.848418i	$-0.677555\pi$
$449$	8.80655	−	11.0431i	0.415607	−	0.521155i	0.944933	+	0.327264i	$0.106127\pi$
$450$	1.21223	−	1.52009i	0.0571452	−	0.0716579i
$451$	−9.30362	−	4.48039i	−0.438090	−	0.210973i
$452$	−6.14590			−0.289079
$453$	−26.7160	−	12.8657i	−1.25523	−	0.604485i
$454$	5.36057	−	23.4862i	0.251584	−	1.10226i
$455$	24.3572	−	11.7298i	1.14188	−	0.549902i
$456$	−6.04388	+	2.91058i	−0.283031	+	0.136300i
$457$	−1.17754	−	5.15912i	−0.0550828	−	0.241333i	0.939890	−	0.341477i	$-0.110927\pi$
$457$	−1.17754	−	5.15912i	−0.0550828	−	0.241333i	−0.994973	+	0.100143i	$0.968070\pi$
$458$	−15.8469	+	19.8713i	−0.740476	+	0.928527i
$459$	22.5795	+	28.3139i	1.05392	+	1.32158i
$460$	1.27019	−	5.56509i	0.0592231	−	0.259474i
$461$	−1.77543	−	7.77867i	−0.0826901	−	0.362289i	0.916607	−	0.399791i	$-0.130917\pi$
$461$	−1.77543	−	7.77867i	−0.0826901	−	0.362289i	−0.999297	+	0.0375018i	$0.988060\pi$
$462$	13.2057	+	16.5595i	0.614386	+	0.770416i
$463$	−2.70820			−0.125861			−0.0629305	−	0.998018i	$-0.520045\pi$
$463$	−2.70820			−0.125861			−0.0629305	+	0.998018i	$0.520045\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	−10.8590	−	13.6167i	−0.503031	−	0.630781i
$467$	0.0124007	+	0.0543309i	0.000573834	+	0.00251413i	0.975214	−	0.221264i	$-0.0710181\pi$
$467$	0.0124007	+	0.0543309i	0.000573834	+	0.00251413i	−0.974640	+	0.223778i	$0.928161\pi$
$468$	0.222521	−	0.974928i	0.0102860	−	0.0450661i
$469$	−14.5999	−	18.3077i	−0.674160	−	0.845370i
$470$	−20.1551	+	25.2737i	−0.929685	+	1.16579i
$471$	2.00269	+	8.77435i	0.0922790	+	0.404301i
$472$	10.2548	−	4.93845i	0.472015	−	0.227311i
$473$	−9.00969	+	4.33884i	−0.414266	+	0.199500i
$474$	2.96537	−	12.9921i	0.136204	−	0.596748i
$475$	−5.25519	−	2.53076i	−0.241124	−	0.116119i
$476$	−9.14590			−0.419202
$477$	−0.688279	−	0.331458i	−0.0315141	−	0.0151764i
$478$	−14.8728	+	18.6499i	−0.680266	+	0.853026i
$479$	6.97083	−	8.74114i	0.318505	−	0.399393i	−0.596645	−	0.802505i	$-0.703500\pi$
$479$	6.97083	−	8.74114i	0.318505	−	0.399393i	0.915151	+	0.403112i	$0.132072\pi$
$480$	14.0714	+	6.77641i	0.642267	+	0.309299i
$481$	−36.8885			−1.68197
$482$	38.8539	+	18.7111i	1.76975	+	0.852266i
$483$	−2.60532	+	11.4147i	−0.118546	+	0.519385i
$484$	−1.16387	+	0.560489i	−0.0529031	+	0.0254768i
$485$	−42.5893	+	20.5099i	−1.93388	+	0.931307i
$486$	1.42012	+	6.22196i	0.0644180	+	0.282234i
$487$	13.9897	−	17.5425i	0.633933	−	0.794926i	−0.356297	−	0.934373i	$-0.615961\pi$
$487$	13.9897	−	17.5425i	0.633933	−	0.794926i	0.990230	+	0.139446i	$0.0445323\pi$
$488$	2.25581	+	2.82869i	0.102116	+	0.128049i
$489$	−8.29347	+	36.3361i	−0.375044	+	1.64317i
$490$	2.05522	+	9.00450i	0.0928453	+	0.406782i
$491$	15.6649	+	19.6432i	0.706949	+	0.886486i	0.997521	−	0.0703673i	$-0.0224171\pi$
$491$	15.6649	+	19.6432i	0.706949	+	0.886486i	−0.290572	+	0.956853i	$0.593846\pi$
$492$	−2.85410			−0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	−2.45921	−	3.08376i	−0.110533	−	0.138605i
$496$	1.17754	+	5.15912i	0.0528729	+	0.231651i
$497$	−0.760222	+	3.33075i	−0.0341006	+	0.149405i
$498$	−12.9676	−	16.2608i	−0.581091	−	0.728665i
$499$	−22.2504	+	27.9012i	−0.996066	+	1.24903i	−0.0276681	+	0.999617i	$0.508808\pi$
$499$	−22.2504	+	27.9012i	−0.996066	+	1.24903i	−0.968398	+	0.249410i	$0.919763\pi$
$500$	−0.727757	−	3.18851i	−0.0325463	−	0.142595i
$501$	−28.3864	+	13.6702i	−1.26821	+	0.610739i
$502$	16.9870	−	8.18049i	0.758165	−	0.365113i
$503$	4.28809	−	18.7874i	0.191197	−	0.837687i	−0.784774	−	0.619783i	$-0.787221\pi$
$503$	4.28809	−	18.7874i	0.191197	−	0.837687i	0.975970	−	0.217904i	$-0.0699221\pi$
$504$	1.72070	+	0.828644i	0.0766460	+	0.0369107i
$505$	−4.61803			−0.205500
$506$	−17.0682	−	8.21961i	−0.758774	−	0.365406i
$507$	4.98792	−	6.25465i	0.221521	−	0.277779i
$508$	−0.749202	+	0.939469i	−0.0332404	+	0.0416822i
$509$	−10.3050	−	4.96263i	−0.456761	−	0.219965i	0.191332	−	0.981525i	$-0.438719\pi$
$509$	−10.3050	−	4.96263i	−0.456761	−	0.219965i	−0.648094	+	0.761561i	$0.724433\pi$
$510$	−49.4508			−2.18972
$511$	0.587860	+	0.283099i	0.0260054	+	0.0125235i
$512$	−1.17754	+	5.15912i	−0.0520402	+	0.228003i
$513$	9.14114	−	4.40214i	0.403591	−	0.194359i
$514$	−1.19490	+	0.575433i	−0.0527047	+	0.0253813i
$515$	−8.37080	−	36.6749i	−0.368862	−	1.61609i
$516$	−1.72328	+	2.16093i	−0.0758633	+	0.0951296i
$517$	15.7907	+	19.8009i	0.694472	+	0.870840i
$518$	−7.01087	+	30.7166i	−0.308040	+	1.34961i
$519$	2.55279	+	11.1845i	0.112055	+	0.490945i
$520$	−16.8557	−	21.1364i	−0.739171	−	0.926891i
$521$	−7.09017			−0.310626			−0.155313	−	0.987865i	$-0.549639\pi$
$521$	−7.09017			−0.310626			−0.155313	+	0.987865i	$0.549639\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	−0.511050	−	0.640836i	−0.0223253	−	0.0279951i
$525$	−2.53273	−	11.0966i	−0.110537	−	0.484295i
$526$	−1.18520	+	5.19270i	−0.0516772	+	0.226412i
$527$	−4.49834	−	5.64074i	−0.195951	−	0.245715i
$528$	17.7173	−	22.2168i	0.771048	−	0.966864i
$529$	2.78771	+	12.2138i	0.121205	+	0.531033i
$530$	8.32141	−	4.00738i	0.361459	−	0.174069i
$531$	−1.75173	+	0.843588i	−0.0760185	+	0.0366086i
$532$	−0.570167	+	2.49806i	−0.0247199	+	0.108305i
$533$	10.8929	+	5.24573i	0.471822	+	0.227218i
$534$	22.7984			0.986582
$535$	28.8931	+	13.9142i	1.24916	+	0.601562i
$536$	−14.5999	+	18.3077i	−0.630619	+	0.790772i
$537$	−16.1412	+	20.2405i	−0.696546	+	0.873441i
$538$	−8.74679	−	4.21223i	−0.377101	−	0.181602i
$539$	7.23607			0.311680
$540$	−8.69658	−	4.18805i	−0.374241	−	0.180225i
$541$	−7.69850	+	33.7293i	−0.330984	+	1.45014i	0.486244	+	0.873823i	$0.338367\pi$
$541$	−7.69850	+	33.7293i	−0.330984	+	1.45014i	−0.817228	+	0.576314i	$0.804490\pi$
$542$	−17.7565	+	8.55107i	−0.762706	+	0.367300i
$543$	17.4123	−	8.38534i	0.747235	−	0.359849i
$544$	4.98046	+	21.8208i	0.213535	+	0.935559i
$545$	29.5718	−	37.0819i	1.26672	−	1.58842i
$546$	−15.4615	−	19.3881i	−0.661693	−	0.829736i
$547$	−2.14021	+	9.37689i	−0.0915089	+	0.400927i	−0.999850	−	0.0173027i	$-0.994492\pi$
$547$	−2.14021	+	9.37689i	−0.0915089	+	0.400927i	0.908341	+	0.418230i	$0.137349\pi$
$548$	−1.90529	−	8.34763i	−0.0813901	−	0.356593i
$549$	−0.385338	−	0.483198i	−0.0164458	−	0.0206224i
$550$	18.4164			0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	7.09654	+	8.89878i	0.301776	+	0.378415i
$554$	−8.50359	−	37.2567i	−0.361283	−	1.58288i
$555$	−8.94863	+	39.2065i	−0.379848	+	1.66422i
$556$	5.66763	+	7.10698i	0.240361	+	0.301403i
$557$	20.2675	−	25.4147i	0.858762	−	1.07685i	−0.137502	−	0.990501i	$-0.543907\pi$
$557$	20.2675	−	25.4147i	0.858762	−	1.07685i	0.996265	−	0.0863525i	$-0.0275211\pi$
$558$	−0.149926	−	0.656869i	−0.00634688	−	0.0278075i
$559$	10.5487	−	5.08000i	0.446164	−	0.214861i
$560$	−27.9109	+	13.4412i	−1.17945	+	0.567993i
$561$	−8.62105	+	37.7713i	−0.363981	+	1.59470i
$562$	−24.9642	−	12.0221i	−1.05305	−	0.507123i
$563$	−45.3951			−1.91318			−0.956588	−	0.291443i	$-0.905865\pi$
$563$	−45.3951			−1.91318			−0.956588	+	0.291443i	$0.905865\pi$
$564$	6.30678	+	3.03719i	0.265563	+	0.127889i
$565$	17.6959	−	22.1899i	0.744471	−	0.933537i
$566$	0.770676	−	0.966397i	0.0323939	−	0.0406207i
$567$	15.5292	+	7.47845i	0.652163	+	0.314065i
$568$	3.41641			0.143349
$569$	−14.3653	−	6.91796i	−0.602224	−	0.290016i	0.107823	−	0.994170i	$-0.465612\pi$
$569$	−14.3653	−	6.91796i	−0.602224	−	0.290016i	−0.710047	+	0.704154i	$0.751326\pi$
$570$	−3.08283	+	13.5068i	−0.129125	+	0.565736i
$571$	−3.15932	+	1.52145i	−0.132213	+	0.0636706i	−0.498821	−	0.866705i	$-0.666233\pi$
$571$	−3.15932	+	1.52145i	−0.132213	+	0.0636706i	0.366608	+	0.930376i	$0.380519\pi$
$572$	8.53410	−	4.10981i	0.356829	−	0.171840i
$573$	4.33296	+	18.9839i	0.181012	+	0.793065i
$574$	6.43830	−	8.07338i	0.268730	−	0.336976i
$575$	6.34734	+	7.95931i	0.264702	+	0.331926i
$576$	0.360046	−	1.57747i	0.0150019	−	0.0657278i
$577$	1.61018	+	7.05464i	0.0670325	+	0.293689i	0.997322	−	0.0731380i	$-0.0233013\pi$
$577$	1.61018	+	7.05464i	0.0670325	+	0.293689i	−0.930289	+	0.366827i	$0.880444\pi$
$578$	−27.0349	−	33.9007i	−1.12451	−	1.41009i
$579$	5.70820			0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	27.0349	+	33.9007i	1.12063	+	1.40523i
$583$	−1.61018	−	7.05464i	−0.0666867	−	0.292174i
$584$	0.145190	−	0.636117i	0.00600799	−	0.0263227i
$585$	2.87930	+	3.61052i	0.119044	+	0.149277i
$586$	−17.6264	+	22.1028i	−0.728139	+	0.913057i
$587$	−9.87592	−	43.2692i	−0.407623	−	1.78591i	−0.595110	−	0.803645i	$-0.702891\pi$
$587$	−9.87592	−	43.2692i	−0.407623	−	1.78591i	0.187487	−	0.982267i	$-0.439966\pi$
$588$	1.80194	−	0.867767i	0.0743107	−	0.0357861i
$589$	−1.82112	+	0.877003i	−0.0750378	+	0.0361363i
$590$	5.23071	−	22.9172i	0.215345	−	0.943487i
$591$	28.7306	+	13.8359i	1.18182	+	0.569134i
$592$	42.2705			1.73731
$593$	31.1396	+	14.9960i	1.27875	+	0.615813i	0.945068	−	0.326873i	$-0.105995\pi$
$593$	31.1396	+	14.9960i	1.27875	+	0.615813i	0.333680	+	0.942686i	$0.391709\pi$
$594$	−19.9731	+	25.0455i	−0.819508	+	1.02763i
$595$	26.3338	−	33.0215i	1.07958	−	1.35375i
$596$	−4.11050	−	1.97951i	−0.168372	−	0.0810839i
$597$	1.38197			0.0565601
$598$	19.9838	+	9.62369i	0.817198	+	0.393542i
$599$	10.0288	−	43.9389i	0.409764	−	1.79530i	−0.175530	−	0.984474i	$-0.556164\pi$
$599$	10.0288	−	43.9389i	0.409764	−	1.79530i	0.585294	−	0.810821i	$-0.300979\pi$
$600$	−10.2548	+	4.93845i	−0.418650	+	0.201611i
$601$	36.1821	−	17.4244i	1.47590	−	0.710754i	0.489027	−	0.872269i	$-0.337352\pi$
$601$	36.1821	−	17.4244i	1.47590	−	0.710754i	0.986870	+	0.161514i	$0.0516378\pi$
$602$	−2.22521	−	9.74928i	−0.0906928	−	0.397351i
$603$	2.49396	−	3.12733i	0.101562	−	0.127355i
$604$	7.06179	+	8.85521i	0.287340	+	0.360313i
$605$	1.32746	−	5.81599i	0.0539690	−	0.236454i
$606$	0.942614	+	4.12986i	0.0382911	+	0.167764i
$607$	−22.4324	−	28.1293i	−0.910501	−	1.14173i	−0.989453	−	0.144854i	$-0.953729\pi$
$607$	−22.4324	−	28.1293i	−0.910501	−	1.14173i	0.0789516	−	0.996878i	$-0.474843\pi$
$608$	6.27051			0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	−18.4880	−	23.1832i	−0.747945	−	0.937893i
$612$	−0.347646	−	1.52314i	−0.0140527	−	0.0615691i
$613$	8.79870	−	38.5496i	0.355376	−	1.55701i	−0.409183	−	0.912452i	$-0.634186\pi$
$613$	8.79870	−	38.5496i	0.355376	−	1.55701i	0.764559	−	0.644553i	$-0.222957\pi$
$614$	−3.20841	−	4.02323i	−0.129481	−	0.162364i
$615$	8.21781	−	10.3048i	0.331374	−	0.415530i
$616$	4.02544	+	17.6366i	0.162190	+	0.710599i
$617$	−7.37023	+	3.54932i	−0.296714	+	0.142890i	−0.576318	−	0.817225i	$-0.695511\pi$
$617$	−7.37023	+	3.54932i	−0.296714	+	0.142890i	0.279604	+	0.960115i	$0.409797\pi$
$618$	−31.0894	+	14.9718i	−1.25060	+	0.602256i
$619$	−5.55062	+	24.3189i	−0.223098	+	0.977458i	0.732032	+	0.681271i	$0.238572\pi$
$619$	−5.55062	+	24.3189i	−0.223098	+	0.977458i	−0.955130	+	0.296187i	$0.904285\pi$
$620$	1.73255	+	0.834352i	0.0695809	+	0.0335084i
$621$	−17.7082			−0.710606
$622$	−13.2516	−	6.38165i	−0.531342	−	0.255881i
$623$	−12.1407	+	15.2239i	−0.486406	+	0.609934i
$624$	−20.7438	+	26.0119i	−0.830418	+	1.04131i
$625$	27.7794	+	13.3779i	1.11118	+	0.535114i
$626$	38.9787			1.55790
$627$	9.77921	+	4.70942i	0.390544	+	0.188076i
$628$	0.764959	−	3.35150i	0.0305252	−	0.133740i
$629$	−51.9239	+	25.0052i	−2.07034	+	0.997024i
$630$	3.55367	−	1.71136i	0.141581	−	0.0681820i
$631$	−5.16577	−	22.6327i	−0.205646	−	0.900995i	−0.967425	−	0.253158i	$-0.918531\pi$
$631$	−5.16577	−	22.6327i	−0.205646	−	0.900995i	0.761779	−	0.647837i	$-0.224326\pi$
$632$	7.09654	−	8.89878i	0.282285	−	0.353974i
$633$	19.8260	+	24.8610i	0.788011	+	0.988135i
$634$	5.14571	−	22.5448i	0.204362	−	0.895370i
$635$	−1.23480	−	5.41002i	−0.0490016	−	0.214690i
$636$	−1.24698	−	1.56366i	−0.0494460	−	0.0620033i
$637$	−8.47214			−0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	24.2333	+	30.3876i	0.957907	+	1.20118i
$641$	−6.44071	−	28.2186i	−0.254393	−	1.11457i	−0.927146	−	0.374700i	$-0.877746\pi$
$641$	−6.44071	−	28.2186i	−0.254393	−	1.11457i	0.672753	−	0.739867i	$-0.265111\pi$
$642$	6.54577	−	28.6789i	0.258341	−	1.13186i
$643$	−6.59876	−	8.27459i	−0.260230	−	0.326318i	0.634502	−	0.772921i	$-0.281205\pi$
$643$	−6.59876	−	8.27459i	−0.260230	−	0.326318i	−0.894732	+	0.446603i	$0.852634\pi$
$644$	2.78833	−	3.49646i	0.109876	−	0.137780i
$645$	−2.84024	−	12.4439i	−0.111834	−	0.489979i
$646$	−17.8879	+	8.61437i	−0.703791	+	0.338928i
$647$	35.5632	−	17.1263i	1.39813	−	0.673305i	0.425351	−	0.905029i	$-0.360151\pi$
$647$	35.5632	−	17.1263i	1.39813	−	0.673305i	0.972782	+	0.231724i	$0.0744365\pi$
$648$	3.83539	−	16.8039i	0.150668	−	0.660120i
$649$	−16.5926	−	7.99058i	−0.651317	−	0.313658i
$650$	−21.5623			−0.845743
$651$	−3.55367	−	1.71136i	−0.139279	−	0.0670733i
$652$	8.87604	−	11.1302i	0.347613	−	0.435893i
$653$	−17.4659	+	21.9016i	−0.683494	+	0.857075i	−0.995671	−	0.0929495i	$-0.970370\pi$
$653$	−17.4659	+	21.9016i	−0.683494	+	0.857075i	0.312177	+	0.950024i	$0.398942\pi$
$654$	−39.1981	−	18.8768i	−1.53277	−	0.738141i
$655$	3.78522			0.147901
$656$	−12.4821	−	6.01107i	−0.487345	−	0.234693i
$657$	−0.0248013	+	0.108662i	−0.000967592	+	0.00423930i
$658$	−22.8182	+	10.9886i	−0.889544	+	0.428382i
$659$	22.4740	−	10.8229i	0.875463	−	0.421601i	0.0584978	−	0.998288i	$-0.481369\pi$
$659$	22.4740	−	10.8229i	0.875463	−	0.421601i	0.816965	+	0.576687i	$0.195655\pi$
$660$	−2.29780	−	10.0673i	−0.0894419	−	0.391871i
$661$	11.5039	−	14.4255i	0.447450	−	0.561085i	−0.506039	−	0.862510i	$-0.668891\pi$
$661$	11.5039	−	14.4255i	0.447450	−	0.561085i	0.953490	+	0.301425i	$0.0974624\pi$
$662$	1.19076	+	1.49317i	0.0462802	+	0.0580335i
$663$	10.0937	−	44.2234i	0.392007	−	1.71749i
$664$	−3.95285	−	17.3186i	−0.153400	−	0.672090i
$665$	−7.37764	−	9.25127i	−0.286093	−	0.358749i
$666$	−5.38197			−0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	18.4880	+	23.1832i	0.714788	+	0.896316i
$670$	10.7613	+	47.1482i	0.415744	+	1.82149i
$671$	1.30266	−	5.70733i	0.0502886	−	0.220329i
$672$	7.62906	+	9.56654i	0.294298	+	0.369037i
$673$	1.54135	−	1.93279i	0.0594147	−	0.0745037i	−0.751236	−	0.660034i	$-0.770542\pi$
$673$	1.54135	−	1.93279i	0.0594147	−	0.0745037i	0.810651	+	0.585530i	$0.199113\pi$
$674$	8.66592	+	37.9679i	0.333799	+	1.46247i
$675$	15.5100	−	7.46921i	0.596980	−	0.287490i
$676$	−2.75312	+	1.32583i	−0.105889	+	0.0509935i
$677$	−2.85557	+	12.5111i	−0.109748	+	0.480839i	0.889945	+	0.456068i	$0.150743\pi$
$677$	−2.85557	+	12.5111i	−0.109748	+	0.480839i	−0.999693	+	0.0247710i	$0.992114\pi$
$678$	−23.4562	−	11.2959i	−0.900831	−	0.433817i
$679$	−37.0344			−1.42125
$680$	−38.0534	−	18.3255i	−1.45928	−	0.702752i
$681$	15.0200	−	18.8345i	0.575567	−	0.721738i
$682$	3.97909	−	4.98962i	0.152367	−	0.191062i
$683$	−12.7450	−	6.13768i	−0.487674	−	0.234852i	0.173854	−	0.984771i	$-0.444378\pi$
$683$	−12.7450	−	6.13768i	−0.487674	−	0.234852i	−0.661529	+	0.749920i	$0.730092\pi$
$684$	−0.437694			−0.0167357
$685$	35.6252	+	17.1562i	1.36117	+	0.655505i
$686$	−7.24579	+	31.7459i	−0.276646	+	1.21206i
$687$	−22.8994	+	11.0278i	−0.873666	+	0.420736i
$688$	−12.0878	+	5.82116i	−0.460842	+	0.221930i
$689$	1.88523	+	8.25972i	0.0718215	+	0.314670i
$690$	15.0762	−	18.9050i	0.573941	−	0.719699i
$691$	−26.0823	−	32.7062i	−0.992219	−	1.24420i	−0.969660	−	0.244457i	$-0.921390\pi$
$691$	−26.0823	−	32.7062i	−0.992219	−	1.24420i	−0.0225587	−	0.999746i	$-0.507181\pi$
$692$	0.975079	−	4.27210i	0.0370669	−	0.162401i
$693$	−0.687628	−	3.01269i	−0.0261208	−	0.114443i
$694$	−8.19633	−	10.2779i	−0.311129	−	0.390143i
$695$	−41.9787			−1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	−13.5911	−	17.0427i	−0.514429	−	0.645074i
$699$	−3.87552	−	16.9797i	−0.146585	−	0.642233i
$700$	−0.967415	+	4.23852i	−0.0365649	+	0.160201i
$701$	−24.2814	−	30.4479i	−0.917094	−	1.15000i	−0.988298	−	0.152538i	$-0.951255\pi$
$701$	−24.2814	−	30.4479i	−0.917094	−	1.15000i	0.0712034	−	0.997462i	$-0.477316\pi$
$702$	23.3850	−	29.3238i	0.882609	−	1.10676i
$703$	3.59280	+	15.7411i	0.135505	+	0.593686i
$704$	13.8085	−	6.64981i	0.520426	−	0.250624i
$705$	−29.1249	+	14.0258i	−1.09691	+	0.528243i
$706$	7.60584	−	33.3234i	0.286250	−	1.25414i
$707$	−3.25974	−	1.56981i	−0.122595	−	0.0590386i
$708$	−5.09017			−0.191300
$709$	3.14746	+	1.51574i	0.118206	+	0.0569248i	0.492052	−	0.870566i	$-0.336247\pi$
$709$	3.14746	+	1.51574i	0.118206	+	0.0569248i	−0.373846	+	0.927491i	$0.621961\pi$
$710$	4.39917	−	5.51639i	0.165098	−	0.207026i
$711$	−1.21223	+	1.52009i	−0.0454623	+	0.0570079i
$712$	17.5438	+	8.44864i	0.657481	+	0.316626i
$713$	3.52786			0.132120
$714$	−34.9059	−	16.8098i	−1.30632	−	0.629091i
$715$	−9.73365	+	42.6459i	−0.364018	+	1.59487i
$716$	8.90927	−	4.29048i	0.332955	−	0.160343i
$717$	−21.4918	+	10.3499i	−0.802626	+	0.386524i
$718$	−10.1663	−	44.5415i	−0.379403	−	1.66227i
$719$	−18.3971	+	23.0692i	−0.686094	+	0.860335i	−0.995900	−	0.0904651i	$-0.971165\pi$
$719$	−18.3971	+	23.0692i	−0.686094	+	0.860335i	0.309805	+	0.950800i	$0.399736\pi$
$720$	−3.29938	−	4.13729i	−0.122961	−	0.154188i
$721$	6.55817	−	28.7332i	0.244239	−	1.07008i
$722$	−5.60315	−	24.5490i	−0.208528	−	0.913620i
$723$	26.8878	+	33.7162i	0.999966	+	1.25392i
$724$	−7.38197			−0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	28.6458	+	35.9207i	1.06241	+	1.33222i	0.940542	+	0.339678i	$0.110318\pi$
$727$	28.6458	+	35.9207i	1.06241	+	1.33222i	0.121872	+	0.992546i	$0.461110\pi$
$728$	−4.71307	−	20.6493i	−0.174678	−	0.765314i
$729$	−6.56583	+	28.7668i	−0.243179	+	1.06544i
$730$	−0.840168	−	1.05354i	−0.0310960	−	0.0389931i
$731$	11.4047	−	14.3011i	0.421820	−	0.528945i
$732$	−0.360046	−	1.57747i	−0.0133077	−	0.0583048i
$733$	−33.4983	+	16.1319i	−1.23729	+	0.595847i	−0.934075	−	0.357076i	$-0.883774\pi$
$733$	−33.4983	+	16.1319i	−1.23729	+	0.595847i	−0.303214	+	0.952923i	$0.598060\pi$
$734$	−9.14114	+	4.40214i	−0.337406	+	0.162486i
$735$	−2.05522	+	9.00450i	−0.0758079	+	0.332136i
$736$	−9.86045	−	4.74854i	−0.363461	−	0.175034i
$737$	37.8885			1.39564
$738$	1.58925	+	0.765341i	0.0585010	+	0.0281726i
$739$	5.03087	−	6.30851i	0.185063	−	0.232062i	−0.680642	−	0.732616i	$-0.738299\pi$
$739$	5.03087	−	6.30851i	0.185063	−	0.232062i	0.865705	+	0.500554i	$0.166870\pi$
$740$	9.57723	−	12.0095i	0.352066	−	0.441477i
$741$	−11.4497	−	5.51388i	−0.420615	−	0.202558i
$742$	7.23607			0.265644
$743$	−27.7173	−	13.3480i	−1.01685	−	0.489690i	−0.150227	−	0.988652i	$-0.548000\pi$
$743$	−27.7173	−	13.3480i	−1.01685	−	0.489690i	−0.866624	+	0.498962i	$0.833715\pi$
$744$	−0.877683	+	3.84538i	−0.0321774	+	0.140978i
$745$	18.9824	−	9.14145i	0.695462	−	0.334917i
$746$	26.7972	−	12.9049i	0.981115	−	0.472480i
$747$	0.675227	+	2.95836i	0.0247053	+	0.108241i
$748$	9.22664	−	11.5698i	0.337359	−	0.423035i
$749$	15.6649	+	19.6432i	0.572384	+	0.717747i
$750$	3.08283	−	13.5068i	0.112569	−	0.493197i
$751$	6.11313	+	26.7834i	0.223071	+	0.977338i	0.955151	+	0.296120i	$0.0956927\pi$
$751$	6.11313	+	26.7834i	0.223071	+	0.977338i	−0.732080	+	0.681219i	$0.761450\pi$
$752$	21.1854	+	26.5656i	0.772551	+	0.968749i
$753$	18.8541			0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	−4.71502	−	5.91245i	−0.171484	−	0.215034i
$757$	10.4537	+	45.8009i	0.379948	+	1.66466i	0.697626	+	0.716462i	$0.254240\pi$
$757$	10.4537	+	45.8009i	0.379948	+	1.66466i	−0.317678	+	0.948199i	$0.602903\pi$
$758$	−13.5767	+	59.4834i	−0.493128	+	2.16054i
$759$	−11.8116	−	14.8112i	−0.428732	−	0.537614i
$760$	−7.37764	+	9.25127i	−0.267615	+	0.335579i
$761$	−11.0812	−	48.5498i	−0.401692	−	1.75993i	−0.620544	−	0.784172i	$-0.713088\pi$
$761$	−11.0812	−	48.5498i	−0.401692	−	1.75993i	0.218852	−	0.975758i	$-0.429769\pi$
$762$	−4.58608	+	2.20854i	−0.166136	+	0.0800070i
$763$	33.4792	−	16.1227i	1.21203	−	0.583681i
$764$	1.65504	−	7.25122i	0.0598773	−	0.262340i
$765$	6.50029	+	3.13038i	0.235019	+	0.113179i
$766$	35.8328			1.29469
$767$	19.4270	+	9.35553i	0.701467	+	0.337809i
$768$	13.6820	−	17.1567i	0.493708	−	0.619090i
$769$	15.8121	−	19.8278i	0.570200	−	0.715008i	−0.410207	−	0.911993i	$-0.634543\pi$
$769$	15.8121	−	19.8278i	0.570200	−	0.715008i	0.980407	+	0.196985i	$0.0631149\pi$
$770$	33.6608	+	16.2102i	1.21305	+	0.584175i
$771$	−1.32624			−0.0477633
$772$	−1.96442	−	0.946014i	−0.0707010	−	0.0340478i
$773$	3.11529	−	13.6490i	0.112049	−	0.490920i	−0.887497	−	0.460813i	$-0.847558\pi$
$773$	3.11529	−	13.6490i	0.112049	−	0.490920i	0.999547	−	0.0301073i	$-0.00958490\pi$
$774$	1.53904	−	0.741162i	0.0553196	−	0.0266405i
$775$	−3.08993	+	1.48803i	−0.110994	+	0.0534517i
$776$	8.24094	+	36.1059i	0.295832	+	1.29613i
$777$	−19.6440	+	24.6328i	−0.704726	+	0.883698i
$778$	−21.3111	−	26.7233i	−0.764040	−	0.958075i
$779$	1.17754	−	5.15912i	0.0421896	−	0.184845i
$780$	2.69032	+	11.7870i	0.0963288	+	0.422044i
$781$	−3.44657	−	4.32186i	−0.123328	−	0.154648i
$782$	34.6525			1.23917
$783$		0			0
$784$	9.70820			0.346722
$785$	9.89814	+	12.4119i	0.353280	+	0.442999i
$786$	−0.772623	−	3.38508i	−0.0275585	−	0.120742i
$787$	5.64328	−	24.7248i	0.201161	−	0.881345i	−0.769070	−	0.639165i	$-0.779280\pi$
$787$	5.64328	−	24.7248i	0.201161	−	0.881345i	0.970231	−	0.242181i	$-0.0778626\pi$
$788$	−7.59432	−	9.52297i	−0.270536	−	0.339242i
$789$	−3.32086	+	4.16422i	−0.118226	+	0.148250i
$790$	−5.23071	−	22.9172i	−0.186100	−	0.815358i
$791$	20.0340	−	9.64787i	0.712327	−	0.343039i
$792$	−2.78415	+	1.34077i	−0.0989304	+	0.0476423i
$793$	−1.52518	+	6.68226i	−0.0541608	+	0.237294i
$794$	−46.5683	−	22.4261i	−1.65265	−	0.795873i
$795$	9.23607			0.327570
$796$	−0.475589	−	0.229032i	−0.0168568	−	0.00811781i
$797$	12.9808	−	16.2775i	0.459805	−	0.576577i	−0.496837	−	0.867844i	$-0.665505\pi$
$797$	12.9808	−	16.2775i	0.459805	−	0.576577i	0.956642	+	0.291267i	$0.0940767\pi$
$798$	−6.76742	+	8.48608i	−0.239564	+	0.300404i
$799$	−41.7385	−	20.1002i	−1.47660	−	0.711094i
$800$	10.6393			0.376157
$801$	−2.99684	−	1.44320i	−0.105888	−	0.0509930i
$802$	−11.9063	+	52.1651i	−0.420427	+	1.84201i
$803$	−0.951178	+	0.458063i	−0.0335663	+	0.0161647i
$804$	9.43507	−	4.54369i	0.332749	−	0.160244i
$805$	4.59561	+	20.1347i	0.161974	+	0.709654i
$806$	−4.65880	+	5.84195i	−0.164099	+	0.205774i
$807$	−6.05297	−	7.59018i	−0.213074	−	0.267187i
$808$	−0.805088	+	3.52732i	−0.0283229	+	0.124091i
$809$	−3.35314	−	14.6911i	−0.117890	−	0.516511i	−0.999045	−	0.0436836i	$-0.986091\pi$
$809$	−3.35314	−	14.6911i	−0.117890	−	0.516511i	0.881155	−	0.472827i	$-0.156766\pi$
$810$	−22.1942	−	27.8307i	−0.779825	−	0.977870i
$811$	−25.6525			−0.900780			−0.450390	−	0.892832i	$-0.648715\pi$
$811$	−25.6525			−0.900780			−0.450390	+	0.892832i	$0.648715\pi$
$812$		0			0
$813$	−19.7082			−0.691197
$814$	−31.7847	−	39.8568i	−1.11405	−	1.39698i
$815$	14.6291	+	64.0943i	0.512436	+	2.24513i
$816$	−11.5664	+	50.6755i	−0.404903	+	1.77400i
$817$	−3.19514	−	4.00658i	−0.111784	−	0.140173i
$818$	−0.588744	+	0.738262i	−0.0205849	+	0.0258127i
$819$	0.805088	+	3.52732i	0.0281321	+	0.123255i
$820$	−4.53588	+	2.18436i	−0.158400	+	0.0762812i
$821$	−31.9091	+	15.3666i	−1.11363	+	0.536298i	−0.897920	−	0.440158i	$-0.854922\pi$
$821$	−31.9091	+	15.3666i	−1.11363	+	0.536298i	−0.215714	+	0.976456i	$0.569208\pi$
$822$	8.07095	−	35.3611i	0.281507	−	1.23336i
$823$	−3.12829	−	1.50650i	−0.109045	−	0.0525134i	0.378566	−	0.925574i	$-0.376417\pi$
$823$	−3.12829	−	1.50650i	−0.109045	−	0.0525134i	−0.487611	+	0.873061i	$0.662132\pi$
$824$	−29.4721			−1.02671
$825$	16.5926	+	7.99058i	0.577681	+	0.278196i
$826$	11.4824	−	14.3985i	0.399525	−	0.500989i
$827$	34.9369	−	43.8095i	1.21488	−	1.52341i	0.431172	−	0.902270i	$-0.358100\pi$
$827$	34.9369	−	43.8095i	1.21488	−	1.52341i	0.783703	−	0.621135i	$-0.213328\pi$
$828$	0.688279	+	0.331458i	0.0239193	+	0.0115190i
$829$	8.20163			0.284854			0.142427	−	0.989805i	$-0.454509\pi$
$829$	8.20163			0.284854			0.142427	+	0.989805i	$0.454509\pi$
$830$	−33.0538	−	15.9179i	−1.14731	−	0.552517i
$831$	8.50359	−	37.2567i	0.294986	−	1.29242i
$832$	−16.1672	+	7.78573i	−0.560498	+	0.269922i
$833$	−11.9253	+	5.74291i	−0.413187	+	0.198980i
$834$	8.56852	+	37.5411i	0.296704	+	1.29994i
$835$	−34.6507	+	43.4506i	−1.19914	+	1.50367i
$836$	−2.58493	−	3.24139i	−0.0894015	−	0.112106i
$837$	1.32746	−	5.81599i	0.0458838	−	0.201030i
$838$	0.922549	+	4.04195i	0.0318689	+	0.139627i
$839$	2.00438	+	2.51342i	0.0691990	+	0.0867728i	0.815226	−	0.579143i	$-0.196613\pi$
$839$	2.00438	+	2.51342i	0.0691990	+	0.0867728i	−0.746027	+	0.665915i	$0.768041\pi$
$840$	−23.0902			−0.796687
$841$		0			0
$842$	3.18034			0.109602
$843$	−17.2758	−	21.6631i	−0.595010	−	0.746118i
$844$	−2.70272	−	11.8414i	−0.0930313	−	0.407597i
$845$	3.14009	−	13.7577i	0.108023	−	0.473278i
$846$	−2.69737	−	3.38239i	−0.0927373	−	0.116289i
$847$	2.91404	−	3.65409i	0.100128	−	0.125556i
$848$	−2.16028	−	9.46480i	−0.0741843	−	0.325023i
$849$	1.11366	−	0.536310i	0.0382207	−	0.0184061i
$850$	−30.3509	+	14.6162i	−1.04103	+	0.501332i
$851$	6.27072	−	27.4738i	0.214957	−	0.941790i
$852$	−1.37656	−	0.662915i	−0.0471601	−	0.0227111i
$853$	−45.0000			−1.54077			−0.770385	−	0.637579i	$-0.779936\pi$
$853$	−45.0000			−1.54077			−0.770385	+	0.637579i	$0.779936\pi$
$854$	5.27436	+	2.54000i	0.180485	+	0.0869170i
$855$	1.26025	−	1.58031i	0.0430997	−	0.0540453i
$856$	15.6649	−	19.6432i	0.535417	−	0.671391i
$857$	26.7351	+	12.8750i	0.913255	+	0.439800i	0.830658	−	0.556783i	$-0.187964\pi$
$857$	26.7351	+	12.8750i	0.913255	+	0.439800i	0.0825967	+	0.996583i	$0.473679\pi$
$858$	40.1246			1.36983
$859$	−17.3813	−	8.37040i	−0.593043	−	0.285594i	0.113191	−	0.993573i	$-0.463893\pi$
$859$	−17.3813	−	8.37040i	−0.593043	−	0.285594i	−0.706233	+	0.707979i	$0.749607\pi$
$860$	−1.08488	+	4.75315i	−0.0369940	+	0.162081i
$861$	9.30362	−	4.48039i	0.317066	−	0.152691i
$862$	−50.4351	+	24.2883i	−1.71783	+	0.827261i
$863$	5.50576	+	24.1223i	0.187418	+	0.821133i	0.977971	+	0.208739i	$0.0669360\pi$
$863$	5.50576	+	24.1223i	0.187418	+	0.821133i	−0.790553	+	0.612393i	$0.790207\pi$
$864$	−11.5387	+	14.4690i	−0.392553	+	0.492246i
$865$	12.6170	+	15.8212i	0.428990	+	0.537937i
$866$	4.54308	−	19.9045i	0.154380	−	0.676383i
$867$	−9.64866	−	42.2735i	−0.327686	−	1.43568i
$868$	0.939336	+	1.17789i	0.0318831	+	0.0399802i
$869$	−18.4164			−0.624734
$870$		0			0
$871$	−44.3607			−1.50310
$872$	−23.1683	−	29.0521i	−0.784577	−	0.983829i
$873$	−1.40772	−	6.16763i	−0.0476441	−	0.208743i
$874$	2.16028	−	9.46480i	0.0730725	−	0.320152i
$875$	7.37764	+	9.25127i	0.249410	+	0.312750i
$876$	−0.181932	+	0.228135i	−0.00614691	+	0.00770798i
$877$	−1.47265	−	6.45211i	−0.0497279	−	0.217872i	0.943959	−	0.330064i	$-0.107070\pi$
$877$	−1.47265	−	6.45211i	−0.0497279	−	0.217872i	−0.993687	+	0.112191i	$0.964213\pi$
$878$	−4.45464	+	2.14524i	−0.150337	+	0.0723983i
$879$	−25.4708	+	12.2661i	−0.859110	+	0.413726i
$880$	11.1538	−	48.8679i	0.375994	−	1.64734i
$881$	26.3718	+	12.7000i	0.888489	+	0.427874i	0.821718	−	0.569894i	$-0.193016\pi$
$881$	26.3718	+	12.7000i	0.888489	+	0.427874i	0.0667713	+	0.997768i	$0.478730\pi$
$882$	−1.23607			−0.0416206
$883$	−35.7567	−	17.2195i	−1.20331	−	0.579483i	−0.278691	−	0.960381i	$-0.589901\pi$
$883$	−35.7567	−	17.2195i	−1.20331	−	0.579483i	−0.924617	+	0.380898i	$0.875615\pi$
$884$	−10.8027	+	13.5462i	−0.363335	+	0.455608i
$885$	14.6561	−	18.3782i	0.492660	−	0.617776i
$886$	−19.0828	−	9.18981i	−0.641100	−	0.308738i
$887$	20.0689			0.673847			0.336924	−	0.941532i	$-0.390614\pi$
$887$	20.0689			0.673847			0.336924	+	0.941532i	$0.390614\pi$
$888$	28.3864	+	13.6702i	0.952587	+	0.458742i
$889$	0.967415	−	4.23852i	0.0324461	−	0.142155i
$890$	36.2323	−	17.4485i	1.21451	−	0.584876i
$891$	−25.1267	+	12.1004i	−0.841776	+	0.405378i
$892$	−2.52033	−	11.0423i	−0.0843867	−	0.369722i
$893$	−8.09210	+	10.1472i	−0.270792	+	0.339562i
$894$	−12.0497	−	15.1099i	−0.403003	−	0.505349i
$895$	−10.1616	+	44.5207i	−0.339663	+	1.48816i
$896$	6.77595	+	29.6874i	0.226369	+	0.991786i
$897$	13.8292	+	17.3413i	0.461744	+	0.579009i
$898$	−22.8541			−0.762651
$899$		0			0
$900$	−0.742646			−0.0247549
$901$	8.25255	+	10.3484i	0.274932	+	0.344754i
$902$	3.71793	+	16.2893i	0.123793	+	0.542374i
$903$	2.22521	−	9.74928i	0.0740503	−	0.324436i
$904$	−13.8640	−	17.3849i	−0.461109	−	0.578212i
$905$	21.2549	−	26.6528i	0.706536	−	0.885968i
$906$	10.6763	+	46.7758i	0.354695	+	1.55402i
$907$	−12.8263	+	6.17680i	−0.425889	+	0.205097i	−0.634535	−	0.772894i	$-0.718808\pi$
$907$	−12.8263	+	6.17680i	−0.425889	+	0.205097i	0.208647	+	0.977991i	$0.433094\pi$
$908$	−8.29038	+	3.99244i	−0.275126	+	0.132494i
$909$	0.137526	−	0.602539i	0.00456143	−	0.0199849i
$910$	−39.4108	−	18.9792i	−1.30645	−	0.629155i
$911$	6.94427			0.230074			0.115037	−	0.993361i	$-0.463301\pi$
$911$	6.94427			0.230074			0.115037	+	0.993361i	$0.463301\pi$
$912$	13.1202	+	6.31835i	0.434453	+	0.209221i
$913$	−17.9207	+	22.4719i	−0.593090	+	0.743712i
$914$	−5.33851	+	6.69428i	−0.176582	+	0.221427i
$915$	6.73216	+	3.24204i	0.222558	+	0.107178i
$916$	9.70820			0.320768
$917$	2.67188	+	1.28671i	0.0882331	+	0.0424908i
$918$	13.0390	−	57.1276i	0.430351	−	1.88549i
$919$	28.2048	−	13.5827i	0.930390	−	0.448052i	0.0936208	−	0.995608i	$-0.470156\pi$
$919$	28.2048	−	13.5827i	0.930390	−	0.448052i	0.836769	+	0.547556i	$0.184442\pi$
$920$	18.6072	−	8.96077i	0.613462	−	0.295428i
$921$	−1.14507	−	5.01688i	−0.0377313	−	0.165312i
$922$	−8.04915	+	10.0933i	−0.265085	+	0.332406i
$923$	4.03531	+	5.06012i	0.132824	+	0.166556i
$924$	1.80023	−	7.88733i	0.0592233	−	0.259474i
$925$	6.09599	+	26.7083i	0.200435	+	0.878162i
$926$	2.73211	+	3.42596i	0.0897827	+	0.112584i
$927$	5.03444			0.165353
$928$		0			0
$929$	27.6525			0.907248			0.453624	−	0.891193i	$-0.350131\pi$
$929$	27.6525			0.907248			0.453624	+	0.891193i	$0.350131\pi$
$930$	5.07888	+	6.36872i	0.166543	+	0.208839i
$931$	0.825153	+	3.61523i	0.0270433	+	0.118484i
$932$	−1.48032	+	6.48568i	−0.0484893	+	0.212446i
$933$	−9.17042	−	11.4993i	−0.300226	−	0.376471i
$934$	0.0562200	−	0.0704977i	0.00183958	−	0.00230676i
$935$	15.2069	+	66.6260i	0.497320	+	2.17890i
$936$	3.25974	−	1.56981i	0.106548	−	0.0513107i
$937$	22.2111	−	10.6963i	0.725605	−	0.349433i	−0.0343487	−	0.999410i	$-0.510936\pi$
$937$	22.2111	−	10.6963i	0.725605	−	0.349433i	0.759954	+	0.649977i	$0.225221\pi$
$938$	−8.43099	+	36.9386i	−0.275282	+	1.20609i
$939$	35.1186	+	16.9122i	1.14605	+	0.551910i
$940$	12.3475			0.402732
$941$	−0.800550	−	0.385525i	−0.0260972	−	0.0125677i	0.420790	−	0.907158i	$-0.361753\pi$
$941$	−0.800550	−	0.385525i	−0.0260972	−	0.0125677i	−0.446887	+	0.894590i	$0.647467\pi$
$942$	9.07945	−	11.3853i	0.295824	−	0.370952i
$943$	−5.75859	+	7.22105i	−0.187526	+	0.235150i
$944$	−22.2613	−	10.7205i	−0.724544	−	0.348922i
$945$	34.9230			1.13604
$946$	14.5780	+	7.02039i	0.473971	+	0.228252i
$947$	−3.10763	+	13.6154i	−0.100984	+	0.442441i	0.899005	+	0.437937i	$0.144291\pi$
$947$	−3.10763	+	13.6154i	−0.100984	+	0.442441i	−0.999990	+	0.00450408i	$0.998566\pi$
$948$	−4.58608	+	2.20854i	−0.148949	+	0.0717301i
$949$	1.11366	−	0.536310i	0.0361509	−	0.0174094i
$950$	2.10008	+	9.20107i	0.0681357	+	0.298522i
$951$	14.4180	−	18.0795i	0.467534	−	0.586270i
$952$	−20.6314	−	25.8709i	−0.668667	−	0.838482i
$953$	7.92869	−	34.7378i	0.256835	−	1.12527i	−0.667778	−	0.744361i	$-0.732754\pi$
$953$	7.92869	−	34.7378i	0.256835	−	1.12527i	0.924613	−	0.380908i	$-0.124389\pi$
$954$	0.275051	+	1.20508i	0.00890510	+	0.0390158i
$955$	21.4153	+	26.8540i	0.692984	+	0.868974i
$956$	9.11146			0.294686
$957$		0			0
$958$	−18.0902			−0.584467
$959$	19.3149	+	24.2201i	0.623711	+	0.782109i
$960$	4.35302	+	19.0718i	0.140493	+	0.615541i
$961$	6.63369	−	29.0641i	0.213990	−	0.937551i
$962$	37.2142	+	46.6651i	1.19983	+	1.50454i
$963$	−2.67589	+	3.35546i	−0.0862294	+	0.108128i
$964$	−3.66540	−	16.0591i	−0.118054	−	0.517230i
$965$	9.07175	−	4.36872i	0.292030	−	0.140634i
$966$	17.0682	−	8.21961i	0.549160	−	0.264462i
$967$	3.68546	−	16.1471i	0.118516	−	0.519254i	−0.880464	−	0.474113i	$-0.842769\pi$
$967$	3.68546	−	16.1471i	0.118516	−	0.519254i	0.998981	−	0.0451416i	$-0.0143739\pi$
$968$	−4.21091	−	2.02787i	−0.135344	−	0.0651782i
$969$	−19.8541			−0.637806
$970$	68.9109	+	33.1857i	2.21259	+	1.06553i
$971$	11.5387	−	14.4690i	0.370293	−	0.464333i	−0.561418	−	0.827532i	$-0.689744\pi$
$971$	11.5387	−	14.4690i	0.370293	−	0.464333i	0.931712	+	0.363199i	$0.118316\pi$
$972$	1.51988	−	1.90587i	0.0487501	−	0.0611307i
$973$	−29.6316	−	14.2698i	−0.949944	−	0.457469i
$974$	−36.3050			−1.16329
$975$	−19.4270	−	9.35553i	−0.622161	−	0.299617i
$976$	1.74770	−	7.65718i	0.0559426	−	0.245100i
$977$	−5.59932	+	2.69649i	−0.179138	+	0.0862684i	−0.521303	−	0.853371i	$-0.674554\pi$
$977$	−5.59932	+	2.69649i	−0.179138	+	0.0862684i	0.342165	+	0.939640i	$0.388840\pi$
$978$	54.3329	−	26.1653i	1.73737	−	0.836675i
$979$	−7.01087	−	30.7166i	−0.224068	−	0.981708i
$980$	2.19959	−	2.75820i	0.0702632	−	0.0881073i
$981$	3.95762	+	4.96269i	0.126357	+	0.158447i
$982$	9.04603	−	39.6332i	0.288670	−	1.26475i
$983$	−1.54525	−	6.77016i	−0.0492857	−	0.215935i	0.944288	−	0.329120i	$-0.106752\pi$
$983$	−1.54525	−	6.77016i	−0.0492857	−	0.215935i	−0.993574	+	0.113185i	$0.963895\pi$
$984$	−6.43830	−	8.07338i	−0.205246	−	0.257370i
$985$	56.2492			1.79225
$986$		0			0
$987$	−25.3262			−0.806143
$988$	3.02648	+	3.79509i	0.0962853	+	0.120738i
$989$	1.99029	+	8.72002i	0.0632875	+	0.277281i
$990$	−1.42012	+	6.22196i	−0.0451344	+	0.197747i
$991$	24.0994	+	30.2197i	0.765543	+	0.959961i	0.999926	−	0.0121834i	$-0.00387818\pi$
$991$	24.0994	+	30.2197i	0.765543	+	0.959961i	−0.234382	+	0.972144i	$0.575307\pi$
$992$	2.29876	−	2.88255i	0.0729856	−	0.0915210i
$993$	0.424977	+	1.86195i	0.0134862	+	0.0590871i
$994$	4.98043	−	2.39845i	0.157970	−	0.0760742i
$995$	2.19629	−	1.05768i	0.0696270	−	0.0335306i
$996$	−1.76777	+	7.74509i	−0.0560138	+	0.245413i
$997$	−25.3084	−	12.1879i	−0.801524	−	0.385994i	−0.0121654	−	0.999926i	$-0.503872\pi$
$997$	−25.3084	−	12.1879i	−0.801524	−	0.385994i	−0.789359	+	0.613932i	$0.789587\pi$
$998$	57.7426			1.82781
$999$	−42.9334	−	20.6756i	−1.35835	−	0.654148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.i.778.1		12
29.2	odd	28		841.2.e.j.270.1		24
29.3	odd	28		841.2.e.j.651.4		24
29.4	even	14		841.2.d.g.645.1		12
29.5	even	14		841.2.d.g.571.1		12
29.6	even	14		841.2.d.g.574.2		12
29.7	even	7	inner	841.2.d.i.190.2		12
29.8	odd	28		841.2.b.b.840.1		4
29.9	even	14		841.2.a.c.1.2	yes	2
29.10	odd	28		841.2.e.j.196.1		24
29.11	odd	28		841.2.e.j.236.1		24
29.12	odd	4		841.2.e.j.63.4		24
29.13	even	14		841.2.d.g.605.1		12
29.14	odd	28		841.2.e.j.267.4		24
29.15	odd	28		841.2.e.j.267.1		24
29.16	even	7	inner	841.2.d.i.605.2		12
29.17	odd	4		841.2.e.j.63.1		24
29.18	odd	28		841.2.e.j.236.4		24
29.19	odd	28		841.2.e.j.196.4		24
29.20	even	7		841.2.a.a.1.1	✓	2
29.21	odd	28		841.2.b.b.840.4		4
29.22	even	14		841.2.d.g.190.1		12
29.23	even	7	inner	841.2.d.i.574.1		12
29.24	even	7	inner	841.2.d.i.571.2		12
29.25	even	7	inner	841.2.d.i.645.2		12
29.26	odd	28		841.2.e.j.651.1		24
29.27	odd	28		841.2.e.j.270.4		24
29.28	even	2		841.2.d.g.778.2		12
87.20	odd	14		7569.2.a.l.1.2		2
87.38	odd	14		7569.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.1	✓	2	29.20	even	7
841.2.a.c.1.2	yes	2	29.9	even	14
841.2.b.b.840.1		4	29.8	odd	28
841.2.b.b.840.4		4	29.21	odd	28
841.2.d.g.190.1		12	29.22	even	14
841.2.d.g.571.1		12	29.5	even	14
841.2.d.g.574.2		12	29.6	even	14
841.2.d.g.605.1		12	29.13	even	14
841.2.d.g.645.1		12	29.4	even	14
841.2.d.g.778.2		12	29.28	even	2
841.2.d.i.190.2		12	29.7	even	7	inner
841.2.d.i.571.2		12	29.24	even	7	inner
841.2.d.i.574.1		12	29.23	even	7	inner
841.2.d.i.605.2		12	29.16	even	7	inner
841.2.d.i.645.2		12	29.25	even	7	inner
841.2.d.i.778.1		12	1.1	even	1	trivial
841.2.e.j.63.1		24	29.17	odd	4
841.2.e.j.63.4		24	29.12	odd	4
841.2.e.j.196.1		24	29.10	odd	28
841.2.e.j.196.4		24	29.19	odd	28
841.2.e.j.236.1		24	29.11	odd	28
841.2.e.j.236.4		24	29.18	odd	28
841.2.e.j.267.1		24	29.15	odd	28
841.2.e.j.267.4		24	29.14	odd	28
841.2.e.j.270.1		24	29.2	odd	28
841.2.e.j.270.4		24	29.27	odd	28
841.2.e.j.651.1		24	29.26	odd	28
841.2.e.j.651.4		24	29.3	odd	28
7569.2.a.d.1.1		2	87.38	odd	14
7569.2.a.l.1.2		2	87.20	odd	14

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00883 - 1.26503i) q^{2} +(-0.360046 - 1.57747i) q^{3} +(-0.137526 + 0.602539i) q^{4} +(-1.77950 - 2.23143i) q^{5} +(-1.63232 + 2.04686i) q^{6} +(-0.497572 - 2.18001i) q^{7} +(-2.01463 + 0.970194i) q^{8} +(0.344139 - 0.165729i) q^{9} +(-1.02761 + 4.50225i) q^{10} +(3.25974 + 1.56981i) q^{11} +1.00000 q^{12} +(-3.81657 - 1.83796i) q^{13} +(-2.25581 + 2.82869i) q^{14} +(-2.87930 + 3.61052i) q^{15} +(4.37339 + 2.10612i) q^{16} -6.61803 q^{17} +(-0.556829 - 0.268155i) q^{18} +(-0.412577 + 1.80762i) q^{19} +(1.58925 - 0.765341i) q^{20} +(-3.25974 + 1.56981i) q^{21} +(-1.30266 - 5.70733i) q^{22} +(2.01766 - 2.53006i) q^{23} +(2.25581 + 2.82869i) q^{24} +(-0.700028 + 3.06702i) q^{25} +(1.52518 + 6.68226i) q^{26} +(-3.41182 - 4.27829i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.679710 + 0.852329i) q^{31} +(-0.752558 - 3.29717i) q^{32} +(1.30266 - 5.70733i) q^{33} +(6.67646 + 8.37201i) q^{34} +(-3.97909 + 4.98962i) q^{35} +(0.0525301 + 0.230149i) q^{36} +(7.84582 - 3.77835i) q^{37} +(2.70291 - 1.30165i) q^{38} +(-1.52518 + 6.68226i) q^{39} +(5.74995 + 2.76903i) q^{40} -2.85410 q^{41} +(5.27436 + 2.54000i) q^{42} +(-1.72328 + 2.16093i) q^{43} +(-1.39417 + 1.74823i) q^{44} +(-0.982209 - 0.473007i) q^{45} -5.23607 q^{46} +(6.30678 + 3.03719i) q^{47} +(1.74770 - 7.65718i) q^{48} +(1.80194 - 0.867767i) q^{49} +(4.58608 - 2.20854i) q^{50} +(2.38280 + 10.4397i) q^{51} +(1.63232 - 2.04686i) q^{52} +(-1.24698 - 1.56366i) q^{53} +(-1.97022 + 8.63211i) q^{54} +(-2.29780 - 10.0673i) q^{55} +(3.11745 + 3.90916i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-1.77950 - 2.23143i) q^{60} +(-0.360046 - 1.57747i) q^{61} +(0.392512 - 1.71971i) q^{62} +(-0.532524 - 0.667764i) q^{63} +(2.64115 - 3.31189i) q^{64} +(2.69032 + 11.7870i) q^{65} +(-8.53410 + 4.10981i) q^{66} +(9.43507 - 4.54369i) q^{67} +(0.910148 - 3.98762i) q^{68} +(-4.71753 - 2.27184i) q^{69} +10.3262 q^{70} +(-1.37656 - 0.662915i) q^{71} +(-0.532524 + 0.667764i) q^{72} +(-0.181932 + 0.228135i) q^{73} +(-12.6948 - 6.11350i) q^{74} +5.09017 q^{75} +(-1.03242 - 0.497187i) q^{76} +(1.80023 - 7.88733i) q^{77} +(9.99190 - 4.81184i) q^{78} +(-4.58608 + 2.20854i) q^{79} +(-3.08283 - 13.5068i) q^{80} +(-4.80599 + 6.02652i) q^{81} +(2.87930 + 3.61052i) q^{82} +(-1.76777 + 7.74509i) q^{83} +(-0.497572 - 2.18001i) q^{84} +(11.7768 + 14.7677i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-5.42948 - 6.80835i) q^{89} +(0.392512 + 1.71971i) q^{90} +(-2.10775 + 9.23465i) q^{91} +(1.24698 + 1.56366i) q^{92} +(1.09979 - 1.37910i) q^{93} +(-2.52033 - 11.0423i) q^{94} +(4.76774 - 2.29602i) q^{95} +(-4.93022 + 2.37427i) q^{96} +(3.68546 - 16.1471i) q^{97} +(-2.91560 - 1.40408i) q^{98} +1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} - 7 q^{10} + 5 q^{11} + 12 q^{12} - 4 q^{13} + 5 q^{14} + 7 q^{15} + 3 q^{16} - 66 q^{17} + q^{18} + 3 q^{19} + 8 q^{20} - 5 q^{21} - 5 q^{22}+ \cdots + 30 q^{99}+O(q^{100}) \) 12 * q + q^2 - q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 - 7 * q^10 + 5 * q^11 + 12 * q^12 - 4 * q^13 + 5 * q^14 + 7 * q^15 + 3 * q^16 - 66 * q^17 + q^18 + 3 * q^19 + 8 * q^20 - 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 + 7 * q^26 + 2 * q^27 + 30 * q^28 + 36 * q^30 + 9 * q^31 - 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 + 4 * q^37 + 6 * q^38 - 7 * q^39 + 15 * q^40 + 6 * q^41 + 5 * q^42 + 10 * q^43 + 9 * q^45 - 36 * q^46 + 14 * q^47 + 9 * q^48 + 4 * q^49 - q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 - 5 * q^55 - 10 * q^56 + 36 * q^57 + 6 * q^59 - q^60 - q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 - 10 * q^66 + 12 * q^67 - 3 * q^68 - 6 * q^69 + 30 * q^70 - 12 * q^71 - 5 * q^72 + 14 * q^73 - 17 * q^74 - 6 * q^75 - 9 * q^76 + 5 * q^77 + 11 * q^78 + q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 - 2 * q^85 - 30 * q^88 + 4 * q^89 + 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 + 24 * q^95 - 2 * q^96 + 13 * q^97 - 2 * q^98 + 30 * q^99

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