LMFDB - Embedded newform 841.2.e.j.267.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.4
Character	$\chi$	$=$	841.267
Dual form			841.2.e.j.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	1.26503	+	1.00883i	0.894511	+	0.713349i	0.958649	−	0.284592i	$-0.0918582\pi$
$2$	1.26503	+	1.00883i	0.894511	+	0.713349i	−0.0641375	+	0.997941i	$0.520430\pi$
$3$	1.57747	+	0.360046i	0.910751	+	0.207873i	0.652131	−	0.758106i	$-0.273875\pi$
$3$	1.57747	+	0.360046i	0.910751	+	0.207873i	0.258620	+	0.965979i	$0.416732\pi$
$4$	0.137526	+	0.602539i	0.0687628	+	0.301269i
$5$	1.77950	−	2.23143i	0.795818	−	0.997924i	−0.204002	−	0.978970i	$-0.565395\pi$
$5$	1.77950	−	2.23143i	0.795818	−	0.997924i	0.999820	−	0.0189540i	$-0.00603359\pi$
$6$	1.63232	+	2.04686i	0.666391	+	0.835628i
$7$	−0.497572	+	2.18001i	−0.188065	+	0.823964i	0.789571	+	0.613659i	$0.210303\pi$
$7$	−0.497572	+	2.18001i	−0.188065	+	0.823964i	−0.977636	+	0.210306i	$0.932554\pi$
$8$	0.970194	−	2.01463i	0.343015	−	0.712278i
$9$	−0.344139	−	0.165729i	−0.114713	−	0.0552429i
$10$	4.50225	−	1.02761i	1.42374	−	0.324959i
$11$	−1.56981	−	3.25974i	−0.473314	−	0.982847i	−0.991805	−	0.127764i	$-0.959220\pi$
$11$	−1.56981	−	3.25974i	−0.473314	−	0.982847i	0.518490	−	0.855084i	$-0.326494\pi$
$12$			1.00000i			0.288675i
$13$	3.81657	−	1.83796i	1.05852	−	0.509759i	0.178133	−	0.984006i	$-0.442994\pi$
$13$	3.81657	−	1.83796i	1.05852	−	0.509759i	0.880391	+	0.474248i	$0.157280\pi$
$14$	−2.82869	+	2.25581i	−0.756000	+	0.602890i
$15$	3.61052	−	2.87930i	0.932233	−	0.743431i
$16$	4.37339	−	2.10612i	1.09335	−	0.526529i
$17$			6.61803i			1.60511i	0.596579	+	0.802555i	$0.296526\pi$
$17$			6.61803i			1.60511i	−0.596579	+	0.802555i	$0.703474\pi$
$18$	−0.268155	−	0.556829i	−0.0632047	−	0.131246i
$19$	−1.80762	+	0.412577i	−0.414695	+	0.0946515i	−0.424778	−	0.905298i	$-0.639648\pi$
$19$	−1.80762	+	0.412577i	−0.414695	+	0.0946515i	0.0100823	+	0.999949i	$0.496791\pi$
$20$	1.58925	+	0.765341i	0.355367	+	0.171136i
$21$	−1.56981	+	3.25974i	−0.342560	+	0.711333i
$22$	1.30266	−	5.70733i	0.277728	−	1.21681i
$23$	2.01766	+	2.53006i	0.420710	+	0.527554i	0.946346	−	0.323156i	$-0.104744\pi$
$23$	2.01766	+	2.53006i	0.420710	+	0.527554i	−0.525635	+	0.850710i	$0.676172\pi$
$24$	2.25581	−	2.82869i	0.460465	−	0.577405i
$25$	−0.700028	−	3.06702i	−0.140006	−	0.613405i
$26$	6.68226	+	1.52518i	1.31050	+	0.299113i
$27$	−4.27829	−	3.41182i	−0.823357	−	0.656605i
$28$	−1.38197			−0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	−0.852329	−	0.679710i	−0.153083	−	0.122079i	0.543953	−	0.839115i	$-0.316927\pi$
$31$	−0.852329	−	0.679710i	−0.153083	−	0.122079i	−0.697036	+	0.717036i	$0.745498\pi$
$32$	3.29717	+	0.752558i	0.582863	+	0.133035i
$33$	−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
$37$	−3.77835	+	7.84582i	−0.621157	+	1.28984i	0.318564	+	0.947901i	$0.396799\pi$
$37$	−3.77835	+	7.84582i	−0.621157	+	1.28984i	−0.939720	+	0.341944i	$0.888915\pi$
$38$	−2.70291	−	1.30165i	−0.438469	−	0.211156i
$39$	6.68226	−	1.52518i	1.07002	−	0.244224i
$40$	−2.76903	−	5.74995i	−0.437822	−	0.909147i
$41$		−	2.85410i		−	0.445736i	−0.974849	−	0.222868i	$-0.928458\pi$
$41$		−	2.85410i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$42$	−5.27436	+	2.54000i	−0.813852	+	0.391930i
$43$	−2.16093	+	1.72328i	−0.329539	+	0.262798i	−0.774256	−	0.632873i	$-0.781876\pi$
$43$	−2.16093	+	1.72328i	−0.329539	+	0.262798i	0.444717	+	0.895671i	$0.353304\pi$
$44$	1.74823	−	1.39417i	0.263555	−	0.210178i
$45$	−0.982209	+	0.473007i	−0.146419	+	0.0705117i
$46$			5.23607i			0.772016i
$47$	3.03719	+	6.30678i	0.443019	+	0.919939i	0.996218	+	0.0868895i	$0.0276927\pi$
$47$	3.03719	+	6.30678i	0.443019	+	0.919939i	−0.553199	+	0.833049i	$0.686593\pi$
$48$	7.65718	−	1.74770i	1.10522	−	0.252259i
$49$	1.80194	+	0.867767i	0.257420	+	0.123967i
$50$	2.20854	−	4.58608i	0.312335	−	0.648570i
$51$	−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	−0.860064	−	0.510187i	$-0.829576\pi$
$53$	−1.24698	+	1.56366i	−0.171286	+	0.214786i	0.688778	+	0.724973i	$0.258148\pi$
$54$	−1.97022	−	8.63211i	−0.268113	−	1.17468i
$55$	−10.0673	−	2.29780i	−1.35748	−	0.309836i
$56$	3.90916	+	3.11745i	0.522383	+	0.416587i
$57$	−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	$0.607501\pi$
$60$	2.23143	+	1.77950i	0.288076	+	0.229733i
$61$	1.57747	+	0.360046i	0.201974	+	0.0460992i	0.322311	−	0.946634i	$-0.395540\pi$
$61$	1.57747	+	0.360046i	0.201974	+	0.0460992i	−0.120337	+	0.992733i	$0.538398\pi$
$62$	−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
$66$	4.10981	−	8.53410i	0.505882	−	1.05048i
$67$	−9.43507	−	4.54369i	−1.15268	−	0.555100i	−0.242840	−	0.970066i	$-0.578079\pi$
$67$	−9.43507	−	4.54369i	−1.15268	−	0.555100i	−0.909837	+	0.414966i	$0.863793\pi$
$68$	−3.98762	+	0.910148i	−0.483570	+	0.110372i
$69$	2.27184	+	4.71753i	0.273498	+	0.567924i
$70$			10.3262i			1.23422i
$71$	1.37656	−	0.662915i	0.163367	−	0.0786736i	−0.350413	−	0.936595i	$-0.613959\pi$
$71$	1.37656	−	0.662915i	0.163367	−	0.0786736i	0.513781	+	0.857922i	$0.328245\pi$
$72$	−0.667764	+	0.532524i	−0.0786967	+	0.0627585i
$73$	0.228135	−	0.181932i	0.0267012	−	0.0212935i	−0.610048	−	0.792364i	$-0.708850\pi$
$73$	0.228135	−	0.181932i	0.0267012	−	0.0212935i	0.636750	+	0.771071i	$0.280279\pi$
$74$	−12.6948	+	6.11350i	−1.47574	+	0.710679i
$75$		−	5.09017i		−	0.587762i
$76$	−0.497187	−	1.03242i	−0.0570312	−	0.118427i
$77$	7.88733	−	1.80023i	0.898845	−	0.205155i
$78$	9.99190	+	4.81184i	1.13136	+	0.544834i
$79$	−2.20854	+	4.58608i	−0.248480	+	0.515975i	−0.987483	−	0.157728i	$-0.949583\pi$
$79$	−2.20854	+	4.58608i	−0.248480	+	0.515975i	0.739002	+	0.673703i	$0.235297\pi$
$80$	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	−0.974403	−	0.224810i	$-0.927824\pi$
$83$	−1.76777	−	7.74509i	−0.194038	−	0.850134i	0.780365	−	0.625324i	$-0.215033\pi$
$84$	−2.18001	−	0.497572i	−0.237858	−	0.0542895i
$85$	14.7677	+	11.7768i	1.60178	+	1.27737i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	6.80835	+	5.42948i	0.721683	+	0.575523i	0.913954	−	0.405819i	$-0.133014\pi$
$89$	6.80835	+	5.42948i	0.721683	+	0.575523i	−0.192270	+	0.981342i	$0.561585\pi$
$90$	−1.71971	−	0.392512i	−0.181273	−	0.0413744i
$91$	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
$95$	−2.29602	+	4.76774i	−0.235567	+	0.489160i
$96$	4.93022	+	2.37427i	0.503189	+	0.242323i
$97$	−16.1471	+	3.68546i	−1.63948	+	0.374202i	−0.940195	−	0.340636i	$-0.889357\pi$
$97$	−16.1471	+	3.68546i	−1.63948	+	0.374202i	−0.699290	+	0.714838i	$0.746500\pi$
$98$	1.40408	+	2.91560i	0.141833	+	0.294520i
$99$			1.38197i			0.138893i
$100$	1.75173	−	0.843588i	0.175173	−	0.0843588i
$101$	1.26503	−	1.00883i	0.125875	−	0.100382i	−0.558529	−	0.829485i	$-0.688634\pi$
$101$	1.26503	−	1.00883i	0.125875	−	0.100382i	0.684404	+	0.729103i	$0.260063\pi$
$102$	−13.5462	+	10.8027i	−1.34127	+	1.06963i
$103$	11.8751	−	5.71874i	1.17009	−	0.563484i	0.255078	−	0.966920i	$-0.417899\pi$
$103$	11.8751	−	5.71874i	1.17009	−	0.563484i	0.915008	+	0.403437i	$0.132184\pi$
$104$		−	9.47214i		−	0.928819i
$105$	4.48039	+	9.30362i	0.437241	+	0.907940i
$106$	−3.15493	+	0.720093i	−0.306434	+	0.0699416i
$107$	−10.1233	−	4.87515i	−0.978661	−	0.471298i	−0.125017	−	0.992155i	$-0.539898\pi$
$107$	−10.1233	−	4.87515i	−0.978661	−	0.471298i	−0.853644	+	0.520856i	$0.825613\pi$
$108$	1.46738	−	3.04705i	0.141199	−	0.293202i
$109$	−3.69786	+	16.2014i	−0.354191	+	1.55181i	0.413205	+	0.910638i	$0.364409\pi$
$109$	−3.69786	+	16.2014i	−0.354191	+	1.55181i	−0.767396	+	0.641173i	$0.778448\pi$
$110$	−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
$113$	9.69495	+	2.21281i	0.912024	+	0.208164i	0.652691	−	0.757624i	$-0.273640\pi$
$113$	9.69495	+	2.21281i	0.912024	+	0.208164i	0.259333	+	0.965788i	$0.416497\pi$
$114$	−3.79509	−	3.02648i	−0.355443	−	0.283456i
$115$	9.23607			0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	−6.43922	−	5.13510i	−0.592778	−	0.472725i
$119$	−14.4273	−	3.29295i	−1.32255	−	0.301864i
$120$	−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
$124$	0.292334	−	0.607039i	0.0262524	−	0.0545137i
$125$	4.76774	+	2.29602i	0.426440	+	0.205363i
$126$	1.34732	−	0.307516i	0.120029	−	0.0273957i
$127$	−0.843588	−	1.75173i	−0.0748563	−	0.155441i	0.860182	−	0.509987i	$-0.170350\pi$
$127$	−0.843588	−	1.75173i	−0.0748563	−	0.155441i	−0.935039	+	0.354546i	$0.884635\pi$
$128$		−	13.6180i		−	1.20368i
$129$	−4.02926	+	1.94039i	−0.354756	+	0.170842i
$130$	15.2944	−	12.1969i	1.34141	−	1.06974i
$131$	1.03689	−	0.826896i	0.0905939	−	0.0722462i	−0.577146	−	0.816641i	$-0.695833\pi$
$131$	1.03689	−	0.826896i	0.0905939	−	0.0722462i	0.667739	+	0.744395i	$0.267262\pi$
$132$	3.25974	−	1.56981i	0.283724	−	0.136634i
$133$		−	4.14590i		−	0.359495i
$134$	−7.35184	−	15.2663i	−0.635103	−	1.31880i
$135$	−15.2265	+	3.47534i	−1.31048	+	0.299110i
$136$	13.3329	+	6.42077i	1.14328	+	0.550577i
$137$	−6.01107	+	12.4821i	−0.513560	+	1.06642i	0.469465	+	0.882951i	$0.344447\pi$
$137$	−6.01107	+	12.4821i	−0.513560	+	1.06642i	−0.983026	+	0.183468i	$0.941268\pi$
$138$	−1.88523	+	8.25972i	−0.160481	+	0.703114i
$139$	9.17042	+	11.4993i	0.777824	+	0.975361i	1.00000		0.000354328i	$0.000112786\pi$
$139$	9.17042	+	11.4993i	0.777824	+	0.975361i	−0.222175	+	0.975007i	$0.571316\pi$
$140$	−2.45921	+	3.08376i	−0.207841	+	0.260625i
$141$	2.52033	+	11.0423i	0.212250	+	0.929927i
$142$	2.41015	+	0.550102i	0.202256	+	0.0461635i
$143$	−11.9825	−	9.55575i	−1.00203	−	0.799092i
$144$	−1.85410			−0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	2.53006	+	2.01766i	0.208676	+	0.166413i
$148$	−5.24703	−	1.19760i	−0.431303	−	0.0984421i
$149$	1.64264	+	7.19688i	0.134570	+	0.589592i	0.996575	+	0.0826915i	$0.0263516\pi$
$149$	1.64264	+	7.19688i	0.134570	+	0.589592i	−0.862005	+	0.506900i	$0.830791\pi$
$150$	5.13510	−	6.43922i	0.419280	−	0.525760i
$151$	−11.4262	−	14.3280i	−0.929853	−	1.16600i	−0.985860	−	0.167568i	$-0.946409\pi$
$151$	−11.4262	−	14.3280i	−0.929853	−	1.16600i	0.0560077	−	0.998430i	$-0.482163\pi$
$152$	−0.922549	+	4.04195i	−0.0748286	+	0.327846i
$153$	1.09680	−	2.27753i	0.0886710	−	0.184127i
$154$	11.7938	+	5.67961i	0.950374	+	0.457676i
$155$	−3.03345	+	0.692364i	−0.243652	+	0.0556120i
$156$	1.83796	+	3.81657i	0.147155	+	0.305570i
$157$		−	5.56231i		−	0.443920i	−0.975056	−	0.221960i	$-0.928755\pi$
$157$		−	5.56231i		−	0.443920i	0.975056	−	0.221960i	$-0.0712455\pi$
$158$	−7.42044	+	3.57350i	−0.590339	+	0.284292i
$159$	−2.53006	+	2.01766i	−0.200647	+	0.160010i
$160$	7.54661	−	6.01822i	0.596612	−	0.475782i
$161$	−6.51947	+	3.13961i	−0.513806	+	0.247436i
$162$		−	12.4721i		−	0.979904i
$163$	−9.99427	−	20.7533i	−0.782812	−	1.62553i	−0.780201	−	0.625528i	$-0.784883\pi$
$163$	−9.99427	−	20.7533i	−0.782812	−	1.62553i	−0.00261030	−	0.999997i	$-0.500831\pi$
$164$	1.71971	−	0.392512i	0.134287	−	0.0306500i
$165$	−15.0536	−	7.24942i	−1.17192	−	0.564366i
$166$	5.57719	−	11.5811i	0.432874	−	0.898871i
$167$	4.33296	−	18.9839i	0.335294	−	1.46902i	−0.473429	−	0.880832i	$-0.656984\pi$
$167$	4.33296	−	18.9839i	0.335294	−	1.46902i	0.808724	−	0.588189i	$-0.200159\pi$
$168$	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
$171$	0.690448	+	0.157590i	0.0527999	+	0.0120512i
$172$	−1.33553	−	1.06505i	−0.101833	−	0.0812091i
$173$	7.09017			0.539056			0.269528	−	0.962993i	$-0.413132\pi$
$173$	7.09017			0.539056			0.269528	+	0.962993i	$0.413132\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	−13.7308	−	10.9499i	−1.03500	−	0.825381i
$177$	−8.02957	−	1.83270i	−0.603540	−	0.137754i
$178$	3.13536	+	13.7369i	0.235005	+	1.02962i
$179$	9.97584	−	12.5093i	0.745629	−	0.934989i	−0.253851	−	0.967243i	$-0.581697\pi$
$179$	9.97584	−	12.5093i	0.745629	−	0.934989i	0.999480	+	0.0322542i	$0.0102686\pi$
$180$	−0.420084	−	0.526768i	−0.0313112	−	0.0392630i
$181$	2.65785	−	11.6448i	0.197556	−	0.865551i	−0.774829	−	0.632171i	$-0.782164\pi$
$181$	2.65785	−	11.6448i	0.197556	−	0.865551i	0.972385	−	0.233381i	$-0.0749788\pi$
$182$	−6.64981	+	13.8085i	−0.492916	+	1.02355i
$183$	2.35877	+	1.13592i	0.174365	+	0.0839698i
$184$	7.05464	−	1.61018i	0.520075	−	0.118704i
$185$	10.7838	+	22.3928i	0.792840	+	1.64635i
$186$		−	2.85410i		−	0.209273i
$187$	21.5730	−	10.3890i	1.57758	−	0.759721i
$188$	−3.38239	+	2.69737i	−0.246686	+	0.196726i
$189$	9.56654	−	7.62906i	0.695864	−	0.554933i
$190$	−7.71437	+	3.71505i	−0.559659	+	0.269518i
$191$			12.0344i			0.870782i	0.900242	+	0.435391i	$0.143390\pi$
$191$			12.0344i			0.870782i	−0.900242	+	0.435391i	$0.856610\pi$
$192$	−2.97388	−	6.17533i	−0.214622	−	0.445666i
$193$	−3.43941	+	0.785024i	−0.247574	+	0.0565072i	−0.344507	−	0.938784i	$-0.611954\pi$
$193$	−3.43941	+	0.785024i	−0.247574	+	0.0565072i	0.0969328	+	0.995291i	$0.469097\pi$
$194$	−24.1445	−	11.6274i	−1.73347	−	0.834797i
$195$	8.48777	−	17.6250i	0.607822	−	1.26215i
$196$	−0.275051	+	1.20508i	−0.0196465	+	0.0860769i
$197$	−12.2879	−	15.4085i	−0.875474	−	1.09781i	−0.994481	−	0.104916i	$-0.966543\pi$
$197$	−12.2879	−	15.4085i	−0.875474	−	1.09781i	0.119007	−	0.992893i	$-0.462029\pi$
$198$	−1.39417	+	1.74823i	−0.0990790	+	0.124241i
$199$	−0.190056	−	0.832688i	−0.0134727	−	0.0590277i	0.967745	−	0.251933i	$-0.0810662\pi$
$199$	−0.190056	−	0.832688i	−0.0134727	−	0.0590277i	−0.981217	+	0.192905i	$0.938209\pi$
$200$	−6.85807	−	1.56531i	−0.484939	−	0.110684i
$201$	−13.2476	−	10.5646i	−0.934411	−	0.745168i
$202$	2.61803			0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	−6.36872	−	5.07888i	−0.444811	−	0.354725i
$206$	20.7915	+	4.74553i	1.44862	+	0.330637i
$207$	−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
$211$	8.52689	−	17.7063i	0.587015	−	1.21895i	−0.370032	−	0.929019i	$-0.620653\pi$
$211$	8.52689	−	17.7063i	0.587015	−	1.21895i	0.957048	−	0.289931i	$-0.0936323\pi$
$212$	−1.11366	−	0.536310i	−0.0764864	−	0.0368339i
$213$	2.41015	−	0.550102i	0.165141	−	0.0376924i
$214$	−7.88815	−	16.3799i	−0.539223	−	1.11971i
$215$			7.88854i			0.537994i
$216$	−11.0243	+	5.30903i	−0.750110	+	0.361234i
$217$	1.90587	−	1.51988i	0.129379	−	0.103176i
$218$	−21.0223	+	16.7647i	−1.42381	+	1.13545i
$219$	0.425380	−	0.204852i	0.0287445	−	0.0138426i
$220$		−	6.38197i		−	0.430272i
$221$	12.1637	+	25.2582i	0.818218	+	1.69905i
$222$	−22.2268	+	5.07312i	−1.49176	+	0.340485i
$223$	−16.5114	−	7.95146i	−1.10568	−	0.532469i	−0.210242	−	0.977649i	$-0.567425\pi$
$223$	−16.5114	−	7.95146i	−1.10568	−	0.532469i	−0.895441	+	0.445180i	$0.853140\pi$
$224$	−3.28116	+	6.81340i	−0.219232	+	0.455240i
$225$	−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	−0.371669	−	0.928365i	$-0.621214\pi$
$227$	9.28286	−	11.6403i	0.616125	−	0.772596i	0.987793	+	0.155769i	$0.0497857\pi$
$228$	−0.412577	−	1.80762i	−0.0273235	−	0.119712i
$229$	−15.3144	−	3.49540i	−1.01200	−	0.230983i	−0.315798	−	0.948827i	$-0.602272\pi$
$229$	−15.3144	−	3.49540i	−1.01200	−	0.230983i	−0.696204	+	0.717844i	$0.745129\pi$
$230$	11.6839	+	9.31760i	0.770414	+	0.614384i
$231$	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	$0.385303\pi$
$234$	−2.04686	−	1.63232i	−0.133808	−	0.106708i
$235$	19.4778	+	4.44568i	1.27059	+	0.290004i
$236$	−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	0.750867	+	0.660454i	$0.229636\pi$
$239$	−3.28055	+	14.3730i	−0.212201	+	0.929713i	−0.963068	+	0.269259i	$0.913221\pi$
$240$	9.72611	−	20.1965i	0.627818	−	1.30368i
$241$	24.0131	+	11.5641i	1.54682	+	0.744908i	0.995969	−	0.0896982i	$-0.0285903\pi$
$241$	24.0131	+	11.5641i	1.54682	+	0.744908i	0.550848	+	0.834606i	$0.314305\pi$
$242$	−3.29717	+	0.752558i	−0.211950	+	0.0483763i
$243$	1.71136	+	3.55367i	0.109784	+	0.227968i
$244$			1.00000i			0.0640184i
$245$	5.14291	−	2.47670i	0.328569	−	0.158230i
$246$	5.84195	−	4.65880i	0.372469	−	0.297034i
$247$	−6.14058	+	4.89695i	−0.390716	+	0.311586i
$248$	−2.19629	+	1.05768i	−0.139464	+	0.0671625i
$249$		−	12.8541i		−	0.814596i
$250$	3.71505	+	7.71437i	0.234960	+	0.487900i
$251$	−11.3603	+	2.59292i	−0.717057	+	0.163664i	−0.565456	−	0.824778i	$-0.691300\pi$
$251$	−11.3603	+	2.59292i	−0.717057	+	0.163664i	−0.151601	+	0.988442i	$0.548443\pi$
$252$	0.475589	+	0.229032i	0.0299593	+	0.0144276i
$253$	5.08000	−	10.5487i	0.319377	−	0.663193i
$254$	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	0.980298	−	0.197525i	$-0.0632903\pi$
$257$	0.182392	+	0.799110i	0.0113773	+	0.0498471i	−0.968921	+	0.247372i	$0.920433\pi$
$258$	−7.05464	−	1.61018i	−0.439203	−	0.100245i
$259$	−15.2239	−	12.1407i	−0.945969	−	0.754385i
$260$	7.47214			0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	2.57363	+	2.05240i	0.158697	+	0.126556i	0.699619	−	0.714516i	$-0.253353\pi$
$263$	2.57363	+	2.05240i	0.158697	+	0.126556i	−0.540922	+	0.841073i	$0.681925\pi$
$264$	−12.7620	−	2.91284i	−0.785445	−	0.179273i
$265$	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
$269$	−2.60330	+	5.40581i	−0.158726	+	0.329598i	−0.965132	−	0.261765i	$-0.915696\pi$
$269$	−2.60330	+	5.40581i	−0.158726	+	0.329598i	0.806406	+	0.591363i	$0.201410\pi$
$270$	−22.7679	−	10.9645i	−1.38561	−	0.667276i
$271$	−11.8750	+	2.71038i	−0.721352	+	0.164644i	−0.567409	−	0.823436i	$-0.692054\pi$
$271$	−11.8750	+	2.71038i	−0.721352	+	0.164644i	−0.153943	+	0.988080i	$0.549197\pi$
$272$	13.9383	+	28.9433i	0.845136	+	1.75494i
$273$			15.3262i			0.927586i
$274$	−20.1965	+	9.72611i	−1.22011	+	0.587576i
$275$	−8.89878	+	7.09654i	−0.536617	+	0.427937i
$276$	−2.53006	+	2.01766i	−0.152292	+	0.121449i
$277$	21.2791	−	10.2475i	1.27854	−	0.615711i	0.333524	−	0.942742i	$-0.391762\pi$
$277$	21.2791	−	10.2475i	1.27854	−	0.615711i	0.945014	+	0.327030i	$0.106048\pi$
$278$			23.7984i			1.42733i
$279$	0.180673	+	0.375171i	0.0108166	+	0.0224609i
$280$	13.9127	−	3.17549i	0.831444	−	0.189772i
$281$	15.4287	+	7.43009i	0.920402	+	0.443242i	0.833214	−	0.552950i	$-0.186498\pi$
$281$	15.4287	+	7.43009i	0.920402	+	0.443242i	0.0871871	+	0.996192i	$0.472212\pi$
$282$	−7.95146	+	16.5114i	−0.473502	+	0.983238i
$283$	−0.169991	+	0.744779i	−0.0101049	+	0.0442725i	−0.979729	−	0.200327i	$-0.935799\pi$
$283$	−0.169991	+	0.744779i	−0.0101049	+	0.0442725i	0.969624	+	0.244600i	$0.0786566\pi$
$284$	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
$287$	6.22196	+	1.42012i	0.367270	+	0.0838271i
$288$	−1.00997	−	0.805422i	−0.0595129	−	0.0474599i
$289$	−26.7984			−1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	0.140995	+	0.112440i	0.00825113	+	0.00658006i
$293$	17.0341	+	3.88792i	0.995141	+	0.227134i	0.688929	−	0.724829i	$-0.258081\pi$
$293$	17.0341	+	3.88792i	0.995141	+	0.227134i	0.306212	+	0.951963i	$0.400938\pi$
$294$	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
$298$	−5.18243	+	10.7614i	−0.300210	+	0.623392i
$299$	12.3507	+	5.94777i	0.714257	+	0.343968i
$300$	3.06702	−	0.700028i	0.177075	−	0.0404161i
$301$	−2.68155	−	5.56829i	−0.154562	−	0.320951i
$302$		−	29.6525i		−	1.70631i
$303$	2.35877	−	1.13592i	0.135508	−	0.0652570i
$304$	−7.03648	+	5.61141i	−0.403570	+	0.321836i
$305$	3.61052	−	2.87930i	0.206738	−	0.164868i
$306$	3.68512	−	1.77466i	0.210664	−	0.101450i
$307$		−	3.18034i		−	0.181512i	−0.995873	−	0.0907558i	$-0.971072\pi$
$307$		−	3.18034i		−	0.181512i	0.995873	−	0.0907558i	$-0.0289283\pi$
$308$	2.16942	+	4.50484i	0.123614	+	0.256687i
$309$	20.7915	−	4.74553i	1.18279	−	0.269964i
$310$	−4.53588	−	2.18436i	−0.257620	−	0.124063i
$311$	3.94408	−	8.18996i	0.223648	−	0.464410i	−0.758708	−	0.651431i	$-0.774169\pi$
$311$	3.94408	−	8.18996i	0.223648	−	0.464410i	0.982356	+	0.187021i	$0.0598833\pi$
$312$	3.41041	−	14.9420i	0.193076	−	0.845923i
$313$	−15.0200	−	18.8345i	−0.848979	−	1.06459i	−0.997137	−	0.0756224i	$-0.975906\pi$
$313$	−15.0200	−	18.8345i	−0.848979	−	1.06459i	0.148157	−	0.988964i	$-0.452666\pi$
$314$	5.61141	−	7.03648i	0.316670	−	0.397092i
$315$	−0.542438	−	2.37658i	−0.0305629	−	0.133905i
$316$	−3.06702	−	0.700028i	−0.172534	−	0.0393797i
$317$	11.1738	+	8.91079i	0.627582	+	0.500480i	0.884860	−	0.465858i	$-0.154254\pi$
$317$	11.1738	+	8.91079i	0.627582	+	0.500480i	−0.257278	+	0.966337i	$0.582826\pi$
$318$	−5.23607			−0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	−14.2140	−	11.3353i	−0.793346	−	0.632672i
$322$	−11.4147	−	2.60532i	−0.636114	−	0.145189i
$323$	−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
$327$	−11.6665	+	24.2257i	−0.645159	+	1.33969i
$328$	−5.74995	−	2.76903i	−0.317488	−	0.152894i
$329$	−15.2600	+	3.48300i	−0.841313	+	0.192024i
$330$	−11.7298	−	24.3572i	−0.645704	−	1.34082i
$331$		−	1.18034i		−	0.0648773i	−0.999474	−	0.0324387i	$-0.989673\pi$
$331$		−	1.18034i		−	0.0648773i	0.999474	−	0.0324387i	$-0.0103274\pi$
$332$	4.42360	−	2.13030i	0.242777	−	0.116915i
$333$	2.60056	−	2.07388i	0.142510	−	0.113648i
$334$	24.6328	−	19.6440i	1.34785	−	1.07487i
$335$	−26.9286	+	12.9682i	−1.47127	+	0.708526i
$336$			17.5623i			0.958102i
$337$	−10.4431	−	21.6853i	−0.568872	−	1.18127i	−0.964798	−	0.262992i	$-0.915291\pi$
$337$	−10.4431	−	21.6853i	−0.568872	−	1.18127i	0.395926	−	0.918282i	$-0.370424\pi$
$338$	7.79942	−	1.78017i	0.424233	−	0.0968283i
$339$	14.4967	+	6.98126i	0.787355	+	0.379170i
$340$	−5.06506	+	10.5177i	−0.274691	+	0.570402i
$341$	−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
$345$	14.5696	+	3.32541i	0.784400	+	0.179034i
$346$	8.96928	+	7.15276i	0.482191	+	0.384535i
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	8.89878	+	7.09654i	0.475660	+	0.379326i
$351$	−22.5992	−	5.15811i	−1.20625	−	0.275320i
$352$	−2.72278	−	11.9293i	−0.145125	−	0.635833i
$353$	−13.1710	+	16.5159i	−0.701021	+	0.879052i	−0.997099	−	0.0761116i	$-0.975749\pi$
$353$	−13.1710	+	16.5159i	−0.701021	+	0.879052i	0.296079	+	0.955164i	$0.404321\pi$
$354$	−8.30877	−	10.4189i	−0.441606	−	0.553757i
$355$	0.970343	−	4.25135i	0.0515004	−	0.225638i
$356$	−2.33515	+	4.84898i	−0.123763	+	0.256996i
$357$	−21.5730	−	10.3890i	−1.14177	−	0.549846i
$358$	25.2395	−	5.76074i	1.33395	−	0.304465i
$359$	−12.2512	−	25.4398i	−0.646592	−	1.34266i	−0.924178	−	0.381962i	$-0.875249\pi$
$359$	−12.2512	−	25.4398i	−0.646592	−	1.34266i	0.277586	−	0.960701i	$-0.410466\pi$
$360$			2.43769i			0.128478i
$361$	−14.0212	+	6.75223i	−0.737955	+	0.355381i
$362$	15.1099	−	12.0497i	0.794157	−	0.633319i
$363$	−2.64413	+	2.10862i	−0.138781	+	0.110674i
$364$	−5.27436	+	2.54000i	−0.276452	+	0.133132i
$365$		−	0.832816i		−	0.0435916i
$366$	1.83796	+	3.81657i	0.0960718	+	0.199495i
$367$	6.11330	−	1.39532i	0.319111	−	0.0728351i	−0.0599650	−	0.998200i	$-0.519099\pi$
$367$	6.11330	−	1.39532i	0.319111	−	0.0728351i	0.379076	+	0.925365i	$0.376242\pi$
$368$	14.1526	+	6.81553i	0.737755	+	0.355284i
$369$	−0.473007	+	0.982209i	−0.0246238	+	0.0511318i
$370$	−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	−0.963349	−	0.268251i	$-0.913554\pi$
$373$	−4.09037	−	17.9211i	−0.211791	−	0.927919i	0.751558	−	0.659668i	$-0.229303\pi$
$374$	37.7713	+	8.62105i	1.95311	+	0.445784i
$375$	6.69428	+	5.33851i	0.345691	+	0.275679i
$376$	15.6525			0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	29.4815	+	23.5107i	1.51436	+	1.20766i	0.912510	+	0.409054i	$0.134141\pi$
$379$	29.4815	+	23.5107i	1.51436	+	1.20766i	0.601851	+	0.798609i	$0.294430\pi$
$380$	−3.18851	−	0.727757i	−0.163567	−	0.0373331i
$381$	−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	$-0.0228527\pi$
$383$	13.8077	+	17.3144i	0.705543	+	0.884722i	−0.291881	+	0.956455i	$0.594281\pi$
$384$	4.90312	−	21.4820i	0.250212	−	1.09625i
$385$	10.0184	−	20.8035i	0.510587	−	1.06025i
$386$	−5.14291	−	2.47670i	−0.261767	−	0.126061i
$387$	1.02926	−	0.234922i	0.0523202	−	0.0119417i
$388$	−4.44126	−	9.22238i	−0.225471	−	0.468195i
$389$			21.1246i			1.07106i	0.844516	+	0.535530i	$0.179888\pi$
$389$			21.1246i			1.07106i	−0.844516	+	0.535530i	$0.820112\pi$
$390$	28.5179	−	13.7335i	1.44406	−	0.695423i
$391$	−16.7440	+	13.3529i	−0.846782	+	0.675286i
$392$	3.49646	−	2.78833i	0.176598	−	0.140832i
$393$	1.93339	−	0.931070i	0.0975265	−	0.0469663i
$394$		−	31.8885i		−	1.60652i
$395$	6.30340	+	13.0892i	0.317159	+	0.658587i
$396$	−0.832688	+	0.190056i	−0.0418441	+	0.00955065i
$397$	28.7808	+	13.8601i	1.44447	+	0.695618i	0.981625	−	0.190822i	$-0.0611154\pi$
$397$	28.7808	+	13.8601i	1.44447	+	0.695618i	0.462842	+	0.886441i	$0.346830\pi$
$398$	0.599613	−	1.24511i	0.0300559	−	0.0624116i
$399$	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	−0.0737604	+	0.997276i	$0.523500\pi$
$401$	−20.6181	+	25.8543i	−1.02962	+	1.29110i	−0.955859	+	0.293826i	$0.905071\pi$
$402$	−6.10072	−	26.7290i	−0.304276	−	1.33312i
$403$	−4.50225	−	1.02761i	−0.224273	−	0.0511889i
$404$	0.781831	+	0.623490i	0.0388976	+	0.0310198i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	18.7204	+	14.9290i	0.926797	+	0.739096i
$409$	0.568960	+	0.129861i	0.0281333	+	0.00642124i	0.236564	−	0.971616i	$-0.423979\pi$
$409$	0.568960	+	0.129861i	0.0281333	+	0.00642124i	−0.208431	+	0.978037i	$0.566836\pi$
$410$	−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
$414$	0.867767	−	1.80194i	0.0426484	−	0.0885604i
$415$	−20.4284	−	9.83778i	−1.00279	−	0.482917i
$416$	13.9670	−	3.18789i	0.684791	−	0.156299i
$417$	10.3257	+	21.4416i	0.505653	+	1.05000i
$418$			10.8541i			0.530891i
$419$	2.30856	−	1.11174i	0.112780	−	0.0543122i	−0.376643	−	0.926359i	$-0.622922\pi$
$419$	2.30856	−	1.11174i	0.112780	−	0.0543122i	0.489423	+	0.872046i	$0.337207\pi$
$420$	−4.98962	+	3.97909i	−0.243469	+	0.194160i
$421$	1.53674	−	1.22551i	0.0748959	−	0.0597275i	−0.585326	−	0.810798i	$-0.699034\pi$
$421$	1.53674	−	1.22551i	0.0748959	−	0.0597275i	0.660222	+	0.751070i	$0.270462\pi$
$422$	28.6493	−	13.7968i	1.39463	−	0.671618i
$423$		−	2.67376i		−	0.130003i
$424$	1.94039	+	4.02926i	0.0942335	+	0.195678i
$425$	20.2977	−	4.63281i	0.984582	−	0.224724i
$426$	3.60388	+	1.73553i	0.174608	+	0.0840869i
$427$	−1.56981	+	3.25974i	−0.0759682	+	0.157750i
$428$	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	0.724470	+	0.689306i	$0.242084\pi$
$431$	7.69850	+	33.7293i	0.370824	+	1.62468i	−0.353647	+	0.935379i	$0.615058\pi$
$432$	−25.8963	−	5.91067i	−1.24594	−	0.284377i
$433$	9.86518	+	7.86722i	0.474090	+	0.378074i	0.831187	−	0.555993i	$-0.187662\pi$
$433$	9.86518	+	7.86722i	0.474090	+	0.378074i	−0.357097	+	0.934067i	$0.616233\pi$
$434$	3.94427			0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	−4.69099	−	3.74094i	−0.224400	−	0.178953i
$438$	0.744779	+	0.169991i	0.0355869	+	0.00812248i
$439$	−0.679963	−	2.97911i	−0.0324529	−	0.142185i	0.956106	−	0.293021i	$-0.0946607\pi$
$439$	−0.679963	−	2.97911i	−0.0324529	−	0.142185i	−0.988559	+	0.150836i	$0.951804\pi$
$440$	−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
$443$	−5.67961	+	11.7938i	−0.269847	+	0.560342i	−0.991223	−	0.132201i	$-0.957796\pi$
$443$	−5.67961	+	11.7938i	−0.269847	+	0.560342i	0.721376	+	0.692543i	$0.243510\pi$
$444$	−7.84582	−	3.77835i	−0.372346	−	0.179312i
$445$	24.2310	−	5.53056i	1.14866	−	0.262174i
$446$	−12.8657	−	26.7160i	−0.609210	−	1.26504i
$447$			11.9443i			0.564945i
$448$	8.53410	−	4.10981i	0.403198	−	0.194170i
$449$	11.0431	−	8.80655i	0.521155	−	0.415607i	−0.327264	−	0.944933i	$-0.606127\pi$
$449$	11.0431	−	8.80655i	0.521155	−	0.415607i	0.848418	+	0.529326i	$0.177555\pi$
$450$	−1.52009	+	1.21223i	−0.0716579	+	0.0571452i
$451$	−9.30362	+	4.48039i	−0.438090	+	0.210973i
$452$			6.14590i			0.289079i
$453$	−12.8657	−	26.7160i	−0.604485	−	1.25523i
$454$	23.4862	−	5.36057i	1.10226	−	0.251584i
$455$	24.3572	+	11.7298i	1.14188	+	0.549902i
$456$	−2.91058	+	6.04388i	−0.136300	+	0.283031i
$457$	1.17754	−	5.15912i	0.0550828	−	0.241333i	−0.939890	−	0.341477i	$-0.889073\pi$
$457$	1.17754	−	5.15912i	0.0550828	−	0.241333i	0.994973	+	0.100143i	$0.0319301\pi$
$458$	−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
$461$	−7.77867	−	1.77543i	−0.362289	−	0.0826901i	0.0375018	−	0.999297i	$-0.488060\pi$
$461$	−7.77867	−	1.77543i	−0.362289	−	0.0826901i	−0.399791	+	0.916607i	$0.630917\pi$
$462$	16.5595	+	13.2057i	0.770416	+	0.614386i
$463$	2.70820			0.125861			0.0629305	−	0.998018i	$-0.479955\pi$
$463$	2.70820			0.125861			0.0629305	+	0.998018i	$0.479955\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	13.6167	+	10.8590i	0.630781	+	0.503031i
$467$	−0.0543309	−	0.0124007i	−0.00251413	−	0.000573834i	0.221264	−	0.975214i	$-0.428982\pi$
$467$	−0.0543309	−	0.0124007i	−0.00251413	−	0.000573834i	−0.223778	+	0.974640i	$0.571839\pi$
$468$	−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
$472$	−4.93845	+	10.2548i	−0.227311	+	0.472015i
$473$	9.00969	+	4.33884i	0.414266	+	0.199500i
$474$	−12.9921	+	2.96537i	−0.596748	+	0.136204i
$475$	2.53076	+	5.25519i	0.116119	+	0.241124i
$476$		−	9.14590i		−	0.419202i
$477$	0.688279	−	0.331458i	0.0315141	−	0.0151764i
$478$	−18.6499	+	14.8728i	−0.853026	+	0.680266i
$479$	−8.74114	+	6.97083i	−0.399393	+	0.318505i	−0.802505	−	0.596645i	$-0.796500\pi$
$479$	−8.74114	+	6.97083i	−0.399393	+	0.318505i	0.403112	+	0.915151i	$0.367928\pi$
$480$	14.0714	−	6.77641i	0.642267	−	0.309299i
$481$			36.8885i			1.68197i
$482$	18.7111	+	38.8539i	0.852266	+	1.76975i
$483$	−11.4147	+	2.60532i	−0.519385	+	0.118546i
$484$	−1.16387	−	0.560489i	−0.0529031	−	0.0254768i
$485$	−20.5099	+	42.5893i	−0.931307	+	1.93388i
$486$	−1.42012	+	6.22196i	−0.0644180	+	0.282234i
$487$	13.9897	+	17.5425i	0.633933	+	0.794926i	0.990230	−	0.139446i	$-0.0445323\pi$
$487$	13.9897	+	17.5425i	0.633933	+	0.794926i	−0.356297	+	0.934373i	$0.615961\pi$
$488$	2.25581	−	2.82869i	0.102116	−	0.128049i
$489$	−8.29347	−	36.3361i	−0.375044	−	1.64317i
$490$	9.00450	+	2.05522i	0.406782	+	0.0928453i
$491$	19.6432	+	15.6649i	0.886486	+	0.706949i	0.956853	−	0.290572i	$-0.0938457\pi$
$491$	19.6432	+	15.6649i	0.886486	+	0.706949i	−0.0703673	+	0.997521i	$0.522417\pi$
$492$	2.85410			0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	3.08376	+	2.45921i	0.138605	+	0.110533i
$496$	−5.15912	−	1.17754i	−0.231651	−	0.0528729i
$497$	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	0.968398	+	0.249410i	$0.0802367\pi$
$499$	22.2504	+	27.9012i	0.996066	+	1.24903i	0.0276681	+	0.999617i	$0.491192\pi$
$500$	−0.727757	+	3.18851i	−0.0325463	+	0.142595i
$501$	13.6702	−	28.3864i	0.610739	−	1.26821i
$502$	−16.9870	−	8.18049i	−0.758165	−	0.365113i
$503$	−18.7874	+	4.28809i	−0.837687	+	0.191197i	−0.619783	−	0.784774i	$-0.712779\pi$
$503$	−18.7874	+	4.28809i	−0.837687	+	0.191197i	−0.217904	+	0.975970i	$0.569922\pi$
$504$	−0.828644	−	1.72070i	−0.0369107	−	0.0766460i
$505$		−	4.61803i		−	0.205500i
$506$	17.0682	−	8.21961i	0.758774	−	0.365406i
$507$	6.25465	−	4.98792i	0.277779	−	0.221521i
$508$	0.939469	−	0.749202i	0.0416822	−	0.0332404i
$509$	−10.3050	+	4.96263i	−0.456761	+	0.219965i	−0.648094	−	0.761561i	$-0.724433\pi$
$509$	−10.3050	+	4.96263i	−0.456761	+	0.219965i	0.191332	+	0.981525i	$0.438719\pi$
$510$			49.4508i			2.18972i
$511$	0.283099	+	0.587860i	0.0125235	+	0.0260054i
$512$	−5.15912	+	1.17754i	−0.228003	+	0.0520402i
$513$	9.14114	+	4.40214i	0.403591	+	0.194359i
$514$	−0.575433	+	1.19490i	−0.0253813	+	0.0527047i
$515$	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
$519$	11.1845	+	2.55279i	0.490945	+	0.112055i
$520$	−21.1364	−	16.8557i	−0.926891	−	0.739171i
$521$	7.09017			0.310626			0.155313	−	0.987865i	$-0.450361\pi$
$521$	7.09017			0.310626			0.155313	+	0.987865i	$0.450361\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	0.640836	+	0.511050i	0.0279951	+	0.0223253i
$525$	11.0966	+	2.53273i	0.484295	+	0.110537i
$526$	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
$530$	−4.00738	+	8.32141i	−0.174069	+	0.361459i
$531$	1.75173	+	0.843588i	0.0760185	+	0.0366086i
$532$	2.49806	−	0.570167i	0.108305	−	0.0247199i
$533$	−5.24573	−	10.8929i	−0.227218	−	0.471822i
$534$			22.7984i			0.986582i
$535$	−28.8931	+	13.9142i	−1.24916	+	0.601562i
$536$	−18.3077	+	14.5999i	−0.790772	+	0.630619i
$537$	20.2405	−	16.1412i	0.873441	−	0.696546i
$538$	−8.74679	+	4.21223i	−0.377101	+	0.181602i
$539$		−	7.23607i		−	0.311680i
$540$	−4.18805	−	8.69658i	−0.180225	−	0.374241i
$541$	−33.7293	+	7.69850i	−1.45014	+	0.330984i	−0.873823	−	0.486244i	$-0.838367\pi$
$541$	−33.7293	+	7.69850i	−1.45014	+	0.330984i	−0.576314	+	0.817228i	$0.695510\pi$
$542$	−17.7565	−	8.55107i	−0.762706	−	0.367300i
$543$	8.38534	−	17.4123i	0.359849	−	0.747235i
$544$	−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	0.908341	−	0.418230i	$-0.137349\pi$
$547$	−2.14021	−	9.37689i	−0.0915089	−	0.400927i	−0.999850	+	0.0173027i	$0.994492\pi$
$548$	−8.34763	−	1.90529i	−0.356593	−	0.0813901i
$549$	−0.483198	−	0.385338i	−0.0206224	−	0.0164458i
$550$	−18.4164			−0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	−8.89878	−	7.09654i	−0.378415	−	0.301776i
$554$	37.2567	+	8.50359i	1.58288	+	0.361283i
$555$	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	−0.996265	−	0.0863525i	$-0.972479\pi$
$557$	−20.2675	−	25.4147i	−0.858762	−	1.07685i	0.137502	−	0.990501i	$-0.456093\pi$
$558$	−0.149926	+	0.656869i	−0.00634688	+	0.0278075i
$559$	−5.08000	+	10.5487i	−0.214861	+	0.446164i
$560$	27.9109	+	13.4412i	1.17945	+	0.567993i
$561$	37.7713	−	8.62105i	1.59470	−	0.363981i
$562$	12.0221	+	24.9642i	0.507123	+	1.05305i
$563$		−	45.3951i		−	1.91318i	−0.291443	−	0.956588i	$-0.594135\pi$
$563$		−	45.3951i		−	1.91318i	0.291443	−	0.956588i	$-0.405865\pi$
$564$	−6.30678	+	3.03719i	−0.265563	+	0.127889i
$565$	22.1899	−	17.6959i	0.933537	−	0.744471i
$566$	−0.966397	+	0.770676i	−0.0406207	+	0.0323939i
$567$	15.5292	−	7.47845i	0.652163	−	0.314065i
$568$		−	3.41641i		−	0.143349i
$569$	−6.91796	−	14.3653i	−0.290016	−	0.602224i	0.704154	−	0.710047i	$-0.251326\pi$
$569$	−6.91796	−	14.3653i	−0.290016	−	0.602224i	−0.994170	+	0.107823i	$0.965612\pi$
$570$	−13.5068	+	3.08283i	−0.565736	+	0.129125i
$571$	−3.15932	−	1.52145i	−0.132213	−	0.0636706i	0.366608	−	0.930376i	$-0.380519\pi$
$571$	−3.15932	−	1.52145i	−0.132213	−	0.0636706i	−0.498821	+	0.866705i	$0.666233\pi$
$572$	4.10981	−	8.53410i	0.171840	−	0.356829i
$573$	−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
$577$	7.05464	+	1.61018i	0.293689	+	0.0670325i	0.366827	−	0.930289i	$-0.380444\pi$
$577$	7.05464	+	1.61018i	0.293689	+	0.0670325i	−0.0731380	+	0.997322i	$0.523301\pi$
$578$	−33.9007	−	27.0349i	−1.41009	−	1.12451i
$579$	−5.70820			−0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	−33.9007	−	27.0349i	−1.40523	−	1.12063i
$583$	7.05464	+	1.61018i	0.292174	+	0.0666867i
$584$	−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	0.187487	+	0.982267i	$0.439966\pi$
$587$	−9.87592	+	43.2692i	−0.407623	+	1.78591i	−0.595110	+	0.803645i	$0.702891\pi$
$588$	−0.867767	+	1.80194i	−0.0357861	+	0.0743107i
$589$	1.82112	+	0.877003i	0.0750378	+	0.0361363i
$590$	−22.9172	+	5.23071i	−0.943487	+	0.215345i
$591$	−13.8359	−	28.7306i	−0.569134	−	1.18182i
$592$			42.2705i			1.73731i
$593$	−31.1396	+	14.9960i	−1.27875	+	0.615813i	−0.945068	−	0.326873i	$-0.894005\pi$
$593$	−31.1396	+	14.9960i	−1.27875	+	0.615813i	−0.333680	+	0.942686i	$0.608291\pi$
$594$	−25.0455	+	19.9731i	−1.02763	+	0.819508i
$595$	−33.0215	+	26.3338i	−1.35375	+	1.07958i
$596$	−4.11050	+	1.97951i	−0.168372	+	0.0810839i
$597$		−	1.38197i		−	0.0565601i
$598$	9.62369	+	19.9838i	0.393542	+	0.817198i
$599$	43.9389	−	10.0288i	1.79530	−	0.409764i	0.810821	−	0.585294i	$-0.199021\pi$
$599$	43.9389	−	10.0288i	1.79530	−	0.409764i	0.984474	+	0.175530i	$0.0561638\pi$
$600$	−10.2548	−	4.93845i	−0.418650	−	0.201611i
$601$	17.4244	−	36.1821i	0.710754	−	1.47590i	−0.161514	−	0.986870i	$-0.551638\pi$
$601$	17.4244	−	36.1821i	0.710754	−	1.47590i	0.872269	−	0.489027i	$-0.162648\pi$
$602$	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
$606$	4.12986	+	0.942614i	0.167764	+	0.0382911i
$607$	−28.1293	−	22.4324i	−1.14173	−	0.910501i	−0.144854	−	0.989453i	$-0.546271\pi$
$607$	−28.1293	−	22.4324i	−1.14173	−	0.910501i	−0.996878	+	0.0789516i	$0.974843\pi$
$608$	−6.27051			−0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	23.1832	+	18.4880i	0.937893	+	0.747945i
$612$	1.52314	+	0.347646i	0.0615691	+	0.0140527i
$613$	−8.79870	−	38.5496i	−0.355376	−	1.55701i	−0.764559	−	0.644553i	$-0.777043\pi$
$613$	−8.79870	−	38.5496i	−0.355376	−	1.55701i	0.409183	−	0.912452i	$-0.365814\pi$
$614$	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
$617$	3.54932	−	7.37023i	0.142890	−	0.296714i	−0.817225	−	0.576318i	$-0.804489\pi$
$617$	3.54932	−	7.37023i	0.142890	−	0.296714i	0.960115	+	0.279604i	$0.0902032\pi$
$618$	31.0894	+	14.9718i	1.25060	+	0.602256i
$619$	24.3189	−	5.55062i	0.977458	−	0.223098i	0.296187	−	0.955130i	$-0.404285\pi$
$619$	24.3189	−	5.55062i	0.977458	−	0.223098i	0.681271	+	0.732032i	$0.261428\pi$
$620$	−0.834352	−	1.73255i	−0.0335084	−	0.0695809i
$621$		−	17.7082i		−	0.710606i
$622$	13.2516	−	6.38165i	0.531342	−	0.255881i
$623$	−15.2239	+	12.1407i	−0.609934	+	0.486406i
$624$	26.0119	−	20.7438i	1.04131	−	0.830418i
$625$	27.7794	−	13.3779i	1.11118	−	0.535114i
$626$		−	38.9787i		−	1.55790i
$627$	4.70942	+	9.77921i	0.188076	+	0.390544i
$628$	3.35150	−	0.764959i	0.133740	−	0.0305252i
$629$	−51.9239	−	25.0052i	−2.07034	−	0.997024i
$630$	1.71136	−	3.55367i	0.0681820	−	0.141581i
$631$	5.16577	−	22.6327i	0.205646	−	0.900995i	−0.761779	−	0.647837i	$-0.775674\pi$
$631$	5.16577	−	22.6327i	0.205646	−	0.900995i	0.967425	−	0.253158i	$-0.0814692\pi$
$632$	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
$635$	−5.41002	−	1.23480i	−0.214690	−	0.0490016i
$636$	−1.56366	−	1.24698i	−0.0620033	−	0.0494460i
$637$	8.47214			0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	−30.3876	−	24.2333i	−1.20118	−	0.957907i
$641$	28.2186	+	6.44071i	1.11457	+	0.254393i	0.739867	−	0.672753i	$-0.234889\pi$
$641$	28.2186	+	6.44071i	1.11457	+	0.254393i	0.374700	+	0.927146i	$0.377746\pi$
$642$	−6.54577	−	28.6789i	−0.258341	−	1.13186i
$643$	6.59876	−	8.27459i	0.260230	−	0.326318i	−0.634502	−	0.772921i	$-0.718795\pi$
$643$	6.59876	−	8.27459i	0.260230	−	0.326318i	0.894732	+	0.446603i	$0.147366\pi$
$644$	−2.78833	−	3.49646i	−0.109876	−	0.137780i
$645$	−2.84024	+	12.4439i	−0.111834	+	0.489979i
$646$	8.61437	−	17.8879i	0.338928	−	0.703791i
$647$	−35.5632	−	17.1263i	−1.39813	−	0.673305i	−0.425351	−	0.905029i	$-0.639849\pi$
$647$	−35.5632	−	17.1263i	−1.39813	−	0.673305i	−0.972782	+	0.231724i	$0.925564\pi$
$648$	−16.8039	+	3.83539i	−0.660120	+	0.150668i
$649$	7.99058	+	16.5926i	0.313658	+	0.651317i
$650$		−	21.5623i		−	0.845743i
$651$	3.55367	−	1.71136i	0.139279	−	0.0670733i
$652$	11.1302	−	8.87604i	0.435893	−	0.347613i
$653$	21.9016	−	17.4659i	0.857075	−	0.683494i	−0.0929495	−	0.995671i	$-0.529630\pi$
$653$	21.9016	−	17.4659i	0.857075	−	0.683494i	0.950024	+	0.312177i	$0.101058\pi$
$654$	−39.1981	+	18.8768i	−1.53277	+	0.738141i
$655$		−	3.78522i		−	0.147901i
$656$	−6.01107	−	12.4821i	−0.234693	−	0.487345i
$657$	−0.108662	+	0.0248013i	−0.00423930	+	0.000967592i
$658$	−22.8182	−	10.9886i	−0.889544	−	0.428382i
$659$	10.8229	−	22.4740i	0.421601	−	0.875463i	−0.576687	−	0.816965i	$-0.695655\pi$
$659$	10.8229	−	22.4740i	0.421601	−	0.875463i	0.998288	−	0.0584978i	$-0.0186311\pi$
$660$	2.29780	−	10.0673i	0.0894419	−	0.391871i
$661$	11.5039	+	14.4255i	0.447450	+	0.561085i	0.953490	−	0.301425i	$-0.0974624\pi$
$661$	11.5039	+	14.4255i	0.447450	+	0.561085i	−0.506039	+	0.862510i	$0.668891\pi$
$662$	1.19076	−	1.49317i	0.0462802	−	0.0580335i
$663$	10.0937	+	44.2234i	0.392007	+	1.71749i
$664$	−17.3186	−	3.95285i	−0.672090	−	0.153400i
$665$	−9.25127	−	7.37764i	−0.358749	−	0.286093i
$666$	5.38197			0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	−23.1832	−	18.4880i	−0.896316	−	0.714788i
$670$	−47.1482	−	10.7613i	−1.82149	−	0.415744i
$671$	−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	$-0.229458\pi$
$673$	−1.54135	−	1.93279i	−0.0594147	−	0.0745037i	−0.810651	+	0.585530i	$0.800887\pi$
$674$	8.66592	−	37.9679i	0.333799	−	1.46247i
$675$	−7.46921	+	15.5100i	−0.287490	+	0.596980i
$676$	2.75312	+	1.32583i	0.105889	+	0.0509935i
$677$	12.5111	−	2.85557i	0.480839	−	0.109748i	0.0247710	−	0.999693i	$-0.492114\pi$
$677$	12.5111	−	2.85557i	0.480839	−	0.109748i	0.456068	+	0.889945i	$0.349257\pi$
$678$	11.2959	+	23.4562i	0.433817	+	0.900831i
$679$		−	37.0344i		−	1.42125i
$680$	38.0534	−	18.3255i	1.45928	−	0.702752i
$681$	18.8345	−	15.0200i	0.721738	−	0.575567i
$682$	−4.98962	+	3.97909i	−0.191062	+	0.152367i
$683$	−12.7450	+	6.13768i	−0.487674	+	0.234852i	−0.661529	−	0.749920i	$-0.730092\pi$
$683$	−12.7450	+	6.13768i	−0.487674	+	0.234852i	0.173854	+	0.984771i	$0.444378\pi$
$684$			0.437694i			0.0167357i
$685$	17.1562	+	35.6252i	0.655505	+	1.36117i
$686$	−31.7459	+	7.24579i	−1.21206	+	0.276646i
$687$	−22.8994	−	11.0278i	−0.873666	−	0.420736i
$688$	−5.82116	+	12.0878i	−0.221930	+	0.460842i
$689$	−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	−0.0225587	+	0.999746i	$0.507181\pi$
$691$	−26.0823	+	32.7062i	−0.992219	+	1.24420i	−0.969660	+	0.244457i	$0.921390\pi$
$692$	0.975079	+	4.27210i	0.0370669	+	0.162401i
$693$	−3.01269	−	0.687628i	−0.114443	−	0.0261208i
$694$	−10.2779	−	8.19633i	−0.390143	−	0.311129i
$695$	41.9787			1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	17.0427	+	13.5911i	0.645074	+	0.514429i
$699$	16.9797	+	3.87552i	0.642233	+	0.146585i
$700$	0.967415	+	4.23852i	0.0365649	+	0.160201i
$701$	24.2814	−	30.4479i	0.917094	−	1.15000i	−0.0712034	−	0.997462i	$-0.522684\pi$
$701$	24.2814	−	30.4479i	0.917094	−	1.15000i	0.988298	−	0.152538i	$-0.0487446\pi$
$702$	−23.3850	−	29.3238i	−0.882609	−	1.10676i
$703$	3.59280	−	15.7411i	0.135505	−	0.593686i
$704$	−6.64981	+	13.8085i	−0.250624	+	0.520426i
$705$	29.1249	+	14.0258i	1.09691	+	0.528243i
$706$	−33.3234	+	7.60584i	−1.25414	+	0.286250i
$707$	1.56981	+	3.25974i	0.0590386	+	0.122595i
$708$		−	5.09017i		−	0.191300i
$709$	−3.14746	+	1.51574i	−0.118206	+	0.0569248i	−0.492052	−	0.870566i	$-0.663753\pi$
$709$	−3.14746	+	1.51574i	−0.118206	+	0.0569248i	0.373846	+	0.927491i	$0.378039\pi$
$710$	5.51639	−	4.39917i	0.207026	−	0.165098i
$711$	1.52009	−	1.21223i	0.0570079	−	0.0454623i
$712$	17.5438	−	8.44864i	0.657481	−	0.316626i
$713$		−	3.52786i		−	0.132120i
$714$	−16.8098	−	34.9059i	−0.629091	−	1.30632i
$715$	−42.6459	+	9.73365i	−1.59487	+	0.364018i
$716$	8.90927	+	4.29048i	0.332955	+	0.160343i
$717$	−10.3499	+	21.4918i	−0.386524	+	0.802626i
$718$	10.1663	−	44.5415i	0.379403	−	1.66227i
$719$	−18.3971	−	23.0692i	−0.686094	−	0.860335i	0.309805	−	0.950800i	$-0.399736\pi$
$719$	−18.3971	−	23.0692i	−0.686094	−	0.860335i	−0.995900	+	0.0904651i	$0.971165\pi$
$720$	−3.29938	+	4.13729i	−0.122961	+	0.154188i
$721$	6.55817	+	28.7332i	0.244239	+	1.07008i
$722$	−24.5490	−	5.60315i	−0.913620	−	0.208528i
$723$	33.7162	+	26.8878i	1.25392	+	0.999966i
$724$	7.38197			0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	−35.9207	−	28.6458i	−1.33222	−	1.06241i	−0.992546	−	0.121872i	$-0.961110\pi$
$727$	−35.9207	−	28.6458i	−1.33222	−	1.06241i	−0.339678	−	0.940542i	$-0.610318\pi$
$728$	20.6493	+	4.71307i	0.765314	+	0.174678i
$729$	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
$733$	16.1319	−	33.4983i	0.595847	−	1.23729i	−0.357076	−	0.934075i	$-0.616226\pi$
$733$	16.1319	−	33.4983i	0.595847	−	1.23729i	0.952923	−	0.303214i	$-0.0980595\pi$
$734$	9.14114	+	4.40214i	0.337406	+	0.162486i
$735$	9.00450	−	2.05522i	0.332136	−	0.0758079i
$736$	4.74854	+	9.86045i	0.175034	+	0.363461i
$737$			37.8885i			1.39564i
$738$	−1.58925	+	0.765341i	−0.0585010	+	0.0281726i
$739$	6.30851	−	5.03087i	0.232062	−	0.185063i	−0.500554	−	0.865705i	$-0.666870\pi$
$739$	6.30851	−	5.03087i	0.232062	−	0.185063i	0.732616	+	0.680642i	$0.238299\pi$
$740$	−12.0095	+	9.57723i	−0.441477	+	0.352066i
$741$	−11.4497	+	5.51388i	−0.420615	+	0.202558i
$742$		−	7.23607i		−	0.265644i
$743$	−13.3480	−	27.7173i	−0.489690	−	1.01685i	−0.988652	−	0.150227i	$-0.952000\pi$
$743$	−13.3480	−	27.7173i	−0.489690	−	1.01685i	0.498962	−	0.866624i	$-0.333715\pi$
$744$	−3.84538	+	0.877683i	−0.140978	+	0.0321774i
$745$	18.9824	+	9.14145i	0.695462	+	0.334917i
$746$	12.9049	−	26.7972i	0.472480	−	0.981115i
$747$	−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
$751$	26.7834	+	6.11313i	0.977338	+	0.223071i	0.681219	−	0.732080i	$-0.261450\pi$
$751$	26.7834	+	6.11313i	0.977338	+	0.223071i	0.296120	+	0.955151i	$0.404307\pi$
$752$	26.5656	+	21.1854i	0.968749	+	0.772551i
$753$	−18.8541			−0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	5.91245	+	4.71502i	0.215034	+	0.171484i
$757$	−45.8009	−	10.4537i	−1.66466	−	0.379948i	−0.716462	−	0.697626i	$-0.754240\pi$
$757$	−45.8009	−	10.4537i	−1.66466	−	0.379948i	−0.948199	+	0.317678i	$0.897097\pi$
$758$	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	0.218852	+	0.975758i	$0.429769\pi$
$761$	−11.0812	+	48.5498i	−0.401692	+	1.75993i	−0.620544	+	0.784172i	$0.713088\pi$
$762$	2.20854	−	4.58608i	0.0800070	−	0.166136i
$763$	−33.4792	−	16.1227i	−1.21203	−	0.583681i
$764$	−7.25122	+	1.65504i	−0.262340	+	0.0598773i
$765$	−3.13038	−	6.50029i	−0.113179	−	0.235019i
$766$			35.8328i			1.29469i
$767$	−19.4270	+	9.35553i	−0.701467	+	0.337809i
$768$	17.1567	−	13.6820i	0.619090	−	0.493708i
$769$	−19.8278	+	15.8121i	−0.715008	+	0.570200i	−0.911993	−	0.410207i	$-0.865457\pi$
$769$	−19.8278	+	15.8121i	−0.715008	+	0.570200i	0.196985	+	0.980407i	$0.436885\pi$
$770$	33.6608	−	16.2102i	1.21305	−	0.584175i

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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