LMFDB - Embedded newform 338.2.c.h.315.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,2,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.69894358832$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.3
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.2.c.h.191.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.02446 + 1.77441i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.60388 q^{5} +(1.02446 - 1.77441i) q^{6} +(0.554958 - 0.961216i) q^{7} +1.00000 q^{8} +(-0.599031 + 1.03755i) q^{9} +(-1.80194 - 3.12105i) q^{10} +(-1.17845 - 2.04113i) q^{11} -2.04892 q^{12} -1.10992 q^{14} +(3.69202 + 6.39477i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.98039 + 5.16218i) q^{17} +1.19806 q^{18} +(0.455927 - 0.789689i) q^{19} +(-1.80194 + 3.12105i) q^{20} +2.27413 q^{21} +(-1.17845 + 2.04113i) q^{22} +(-1.69202 - 2.93067i) q^{23} +(1.02446 + 1.77441i) q^{24} +7.98792 q^{25} +3.69202 q^{27} +(0.554958 + 0.961216i) q^{28} +(1.89008 + 3.27372i) q^{29} +(3.69202 - 6.39477i) q^{30} -8.49396 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.41454 - 4.18211i) q^{33} +5.96077 q^{34} +(2.00000 - 3.46410i) q^{35} +(-0.599031 - 1.03755i) q^{36} +(2.44504 + 4.23494i) q^{37} -0.911854 q^{38} +3.60388 q^{40} +(-3.59299 - 6.22324i) q^{41} +(-1.13706 - 1.96945i) q^{42} +(0.257865 - 0.446635i) q^{43} +2.35690 q^{44} +(-2.15883 + 3.73921i) q^{45} +(-1.69202 + 2.93067i) q^{46} -6.98792 q^{47} +(1.02446 - 1.77441i) q^{48} +(2.88404 + 4.99531i) q^{49} +(-3.99396 - 6.91774i) q^{50} -12.2131 q^{51} -3.38404 q^{53} +(-1.84601 - 3.19738i) q^{54} +(-4.24698 - 7.35598i) q^{55} +(0.554958 - 0.961216i) q^{56} +1.86831 q^{57} +(1.89008 - 3.27372i) q^{58} +(5.07338 - 8.78735i) q^{59} -7.38404 q^{60} +(0.219833 - 0.380761i) q^{61} +(4.24698 + 7.35598i) q^{62} +(0.664874 + 1.15160i) q^{63} +1.00000 q^{64} -4.82908 q^{66} +(1.07338 + 1.85914i) q^{67} +(-2.98039 - 5.16218i) q^{68} +(3.46681 - 6.00469i) q^{69} -4.00000 q^{70} +(0.307979 - 0.533434i) q^{71} +(-0.599031 + 1.03755i) q^{72} -6.32304 q^{73} +(2.44504 - 4.23494i) q^{74} +(8.18329 + 14.1739i) q^{75} +(0.455927 + 0.789689i) q^{76} -2.61596 q^{77} -15.4819 q^{79} +(-1.80194 - 3.12105i) q^{80} +(5.57942 + 9.66383i) q^{81} +(-3.59299 + 6.22324i) q^{82} +0.911854 q^{83} +(-1.13706 + 1.96945i) q^{84} +(-10.7409 + 18.6039i) q^{85} -0.515729 q^{86} +(-3.87263 + 6.70758i) q^{87} +(-1.17845 - 2.04113i) q^{88} +(1.87531 + 3.24814i) q^{89} +4.31767 q^{90} +3.38404 q^{92} +(-8.70171 - 15.0718i) q^{93} +(3.49396 + 6.05171i) q^{94} +(1.64310 - 2.84594i) q^{95} -2.04892 q^{96} +(-7.33728 + 12.7085i) q^{97} +(2.88404 - 4.99531i) q^{98} +2.82371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{7} + 6 q^{8} - 8 q^{9} - 2 q^{10} - 3 q^{11} + 6 q^{12} - 8 q^{14} + 12 q^{15} - 3 q^{16} - 5 q^{17} + 16 q^{18} - q^{19} - 2 q^{20} - 8 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^7 + 6 * q^8 - 8 * q^9 - 2 * q^10 - 3 * q^11 + 6 * q^12 - 8 * q^14 + 12 * q^15 - 3 * q^16 - 5 * q^17 + 16 * q^18 - q^19 - 2 * q^20 - 8 * q^21 - 3 * q^22 - 3 * q^24 + 10 * q^25 + 12 * q^27 + 4 * q^28 + 10 * q^29 + 12 * q^30 - 32 * q^31 - 3 * q^32 + 4 * q^33 + 10 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 + 2 * q^38 + 4 * q^40 - 7 * q^41 + 4 * q^42 - 11 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^47 - 3 * q^48 - 3 * q^49 - 5 * q^50 - 32 * q^51 - 6 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 + 10 * q^58 + 3 * q^59 - 24 * q^60 + 4 * q^61 + 16 * q^62 + 6 * q^63 + 6 * q^64 - 8 * q^66 - 21 * q^67 - 5 * q^68 + 14 * q^69 - 24 * q^70 + 12 * q^71 - 8 * q^72 + 2 * q^73 + 14 * q^74 + 23 * q^75 - q^76 - 36 * q^77 - 36 * q^79 - 2 * q^80 + 25 * q^81 - 7 * q^82 - 2 * q^83 + 4 * q^84 - 36 * q^85 + 22 * q^86 + 10 * q^87 - 3 * q^88 - 25 * q^89 - 8 * q^90 + 2 * q^93 + 2 * q^94 + 18 * q^95 + 6 * q^96 - 23 * q^97 - 3 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.02446	+	1.77441i	0.591471	+	1.02446i	0.994034	+	0.109066i	$0.0347861\pi$
$3$	1.02446	+	1.77441i	0.591471	+	1.02446i	−0.402563	+	0.915392i	$0.631881\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.60388			1.61170			0.805851	−	0.592118i	$-0.201708\pi$
$5$	3.60388			1.61170			0.805851	+	0.592118i	$0.201708\pi$
$6$	1.02446	−	1.77441i	0.418234	−	0.724402i
$7$	0.554958	−	0.961216i	0.209754	−	0.363305i	−0.741883	−	0.670530i	$-0.766067\pi$
$7$	0.554958	−	0.961216i	0.209754	−	0.363305i	0.951637	+	0.307224i	$0.0994002\pi$
$8$	1.00000			0.353553
$9$	−0.599031	+	1.03755i	−0.199677	+	0.345851i
$10$	−1.80194	−	3.12105i	−0.569823	−	0.986962i
$11$	−1.17845	−	2.04113i	−0.355315	−	0.615424i	0.631856	−	0.775085i	$-0.282293\pi$
$11$	−1.17845	−	2.04113i	−0.355315	−	0.615424i	−0.987172	+	0.159661i	$0.948960\pi$
$12$	−2.04892			−0.591471
$13$		0			0
$13$		0			0
$14$	−1.10992			−0.296638
$15$	3.69202	+	6.39477i	0.953276	+	1.65112i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.98039	+	5.16218i	−0.722850	+	1.25201i	0.237003	+	0.971509i	$0.423835\pi$
$17$	−2.98039	+	5.16218i	−0.722850	+	1.25201i	−0.959853	+	0.280504i	$0.909499\pi$
$18$	1.19806			0.282386
$19$	0.455927	−	0.789689i	0.104597	−	0.181167i	−0.808977	−	0.587841i	$-0.799978\pi$
$19$	0.455927	−	0.789689i	0.104597	−	0.181167i	0.913573	+	0.406674i	$0.133311\pi$
$20$	−1.80194	+	3.12105i	−0.402926	+	0.697887i
$21$	2.27413			0.496255
$22$	−1.17845	+	2.04113i	−0.251246	+	0.435171i
$23$	−1.69202	−	2.93067i	−0.352811	−	0.611086i	0.633930	−	0.773391i	$-0.281441\pi$
$23$	−1.69202	−	2.93067i	−0.352811	−	0.611086i	−0.986741	+	0.162304i	$0.948107\pi$
$24$	1.02446	+	1.77441i	0.209117	+	0.362201i
$25$	7.98792			1.59758
$26$		0			0
$27$	3.69202			0.710530
$28$	0.554958	+	0.961216i	0.104877	+	0.181653i
$29$	1.89008	+	3.27372i	0.350980	+	0.607915i	0.986421	−	0.164234i	$-0.0525153\pi$
$29$	1.89008	+	3.27372i	0.350980	+	0.607915i	−0.635442	+	0.772149i	$0.719182\pi$
$30$	3.69202	−	6.39477i	0.674068	−	1.16752i
$31$	−8.49396			−1.52556			−0.762780	−	0.646658i	$-0.776166\pi$
$31$	−8.49396			−1.52556			−0.762780	+	0.646658i	$0.776166\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.41454	−	4.18211i	0.420318	−	0.728012i
$34$	5.96077			1.02226
$35$	2.00000	−	3.46410i	0.338062	−	0.585540i
$36$	−0.599031	−	1.03755i	−0.0998385	−	0.172925i
$37$	2.44504	+	4.23494i	0.401962	+	0.696219i	0.993963	−	0.109718i	$-0.0349949\pi$
$37$	2.44504	+	4.23494i	0.401962	+	0.696219i	−0.592000	+	0.805938i	$0.701662\pi$
$38$	−0.911854			−0.147922
$39$		0			0
$40$	3.60388			0.569823
$41$	−3.59299	−	6.22324i	−0.561131	−	0.971907i	−0.997398	−	0.0720900i	$-0.977033\pi$
$41$	−3.59299	−	6.22324i	−0.561131	−	0.971907i	0.436267	−	0.899817i	$-0.356300\pi$
$42$	−1.13706	−	1.96945i	−0.175453	−	0.303893i
$43$	0.257865	−	0.446635i	0.0393240	−	0.0681112i	−0.845694	−	0.533669i	$-0.820813\pi$
$43$	0.257865	−	0.446635i	0.0393240	−	0.0681112i	0.885018	+	0.465558i	$0.154146\pi$
$44$	2.35690			0.355315
$45$	−2.15883	+	3.73921i	−0.321820	+	0.557408i
$46$	−1.69202	+	2.93067i	−0.249475	+	0.432103i
$47$	−6.98792			−1.01929			−0.509646	−	0.860384i	$-0.670224\pi$
$47$	−6.98792			−1.01929			−0.509646	+	0.860384i	$0.670224\pi$
$48$	1.02446	−	1.77441i	0.147868	−	0.256115i
$49$	2.88404	+	4.99531i	0.412006	+	0.713616i
$50$	−3.99396	−	6.91774i	−0.564831	−	0.978316i
$51$	−12.2131			−1.71018
$52$		0			0
$53$	−3.38404			−0.464834			−0.232417	−	0.972616i	$-0.574663\pi$
$53$	−3.38404			−0.464834			−0.232417	+	0.972616i	$0.574663\pi$
$54$	−1.84601	−	3.19738i	−0.251210	−	0.435109i
$55$	−4.24698	−	7.35598i	−0.572663	−	0.991881i
$56$	0.554958	−	0.961216i	0.0741594	−	0.128448i
$57$	1.86831			0.247464
$58$	1.89008	−	3.27372i	0.248180	−	0.429861i
$59$	5.07338	−	8.78735i	0.660497	−	1.14401i	−0.319988	−	0.947422i	$-0.603679\pi$
$59$	5.07338	−	8.78735i	0.660497	−	1.14401i	0.980485	−	0.196593i	$-0.0629878\pi$
$60$	−7.38404			−0.953276
$61$	0.219833	−	0.380761i	0.0281467	−	0.0487515i	−0.851609	−	0.524178i	$-0.824373\pi$
$61$	0.219833	−	0.380761i	0.0281467	−	0.0487515i	0.879756	+	0.475426i	$0.157706\pi$
$62$	4.24698	+	7.35598i	0.539367	+	0.934211i
$63$	0.664874	+	1.15160i	0.0837663	+	0.145087i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.82908			−0.594419
$67$	1.07338	+	1.85914i	0.131134	+	0.227130i	0.924114	−	0.382117i	$-0.124805\pi$
$67$	1.07338	+	1.85914i	0.131134	+	0.227130i	−0.792980	+	0.609248i	$0.791472\pi$
$68$	−2.98039	−	5.16218i	−0.361425	−	0.626006i
$69$	3.46681	−	6.00469i	0.417355	−	0.722880i
$70$	−4.00000			−0.478091
$71$	0.307979	−	0.533434i	0.0365503	−	0.0633070i	−0.847172	−	0.531319i	$-0.821696\pi$
$71$	0.307979	−	0.533434i	0.0365503	−	0.0633070i	0.883722	+	0.468012i	$0.155030\pi$
$72$	−0.599031	+	1.03755i	−0.0705965	+	0.122277i
$73$	−6.32304			−0.740056			−0.370028	−	0.929021i	$-0.620652\pi$
$73$	−6.32304			−0.740056			−0.370028	+	0.929021i	$0.620652\pi$
$74$	2.44504	−	4.23494i	0.284230	−	0.492301i
$75$	8.18329	+	14.1739i	0.944925	+	1.63666i
$76$	0.455927	+	0.789689i	0.0522984	+	0.0905835i
$77$	−2.61596			−0.298116
$78$		0			0
$79$	−15.4819			−1.74185			−0.870924	−	0.491418i	$-0.836479\pi$
$79$	−15.4819			−1.74185			−0.870924	+	0.491418i	$0.836479\pi$
$80$	−1.80194	−	3.12105i	−0.201463	−	0.348944i
$81$	5.57942	+	9.66383i	0.619935	+	1.07376i
$82$	−3.59299	+	6.22324i	−0.396779	+	0.687242i
$83$	0.911854			0.100089			0.0500445	−	0.998747i	$-0.484064\pi$
$83$	0.911854			0.100089			0.0500445	+	0.998747i	$0.484064\pi$
$84$	−1.13706	+	1.96945i	−0.124064	+	0.214885i
$85$	−10.7409	+	18.6039i	−1.16502	+	2.01787i
$86$	−0.515729			−0.0556125
$87$	−3.87263	+	6.70758i	−0.415189	+	0.719128i
$88$	−1.17845	−	2.04113i	−0.125623	−	0.217585i
$89$	1.87531	+	3.24814i	0.198783	+	0.344302i	0.948134	−	0.317871i	$-0.102968\pi$
$89$	1.87531	+	3.24814i	0.198783	+	0.344302i	−0.749351	+	0.662173i	$0.769634\pi$
$90$	4.31767			0.455122
$91$		0			0
$92$	3.38404			0.352811
$93$	−8.70171	−	15.0718i	−0.902325	−	1.56287i
$94$	3.49396	+	6.05171i	0.360374	+	0.624187i
$95$	1.64310	−	2.84594i	0.168579	−	0.291987i
$96$	−2.04892			−0.209117
$97$	−7.33728	+	12.7085i	−0.744988	+	1.29036i	0.205212	+	0.978717i	$0.434212\pi$
$97$	−7.33728	+	12.7085i	−0.744988	+	1.29036i	−0.950200	+	0.311640i	$0.899122\pi$
$98$	2.88404	−	4.99531i	0.291332	−	0.504602i
$99$	2.82371			0.283793
$100$	−3.99396	+	6.91774i	−0.399396	+	0.691774i
$101$	−4.38404	−	7.59339i	−0.436229	−	0.755570i	0.561166	−	0.827703i	$-0.310353\pi$
$101$	−4.38404	−	7.59339i	−0.436229	−	0.755570i	−0.997395	+	0.0721329i	$0.977019\pi$
$102$	6.10656	+	10.5769i	0.604640	+	1.04727i
$103$	18.8116			1.85356			0.926782	−	0.375599i	$-0.122563\pi$
$103$	18.8116			1.85356			0.926782	+	0.375599i	$0.122563\pi$
$104$		0			0
$105$	8.19567			0.799815
$106$	1.69202	+	2.93067i	0.164344	+	0.284652i
$107$	−9.02595	−	15.6334i	−0.872572	−	1.51134i	−0.859327	−	0.511426i	$-0.829117\pi$
$107$	−9.02595	−	15.6334i	−0.872572	−	1.51134i	−0.0132443	−	0.999912i	$-0.504216\pi$
$108$	−1.84601	+	3.19738i	−0.177632	+	0.307668i
$109$	−6.09783			−0.584067			−0.292033	−	0.956408i	$-0.594332\pi$
$109$	−6.09783			−0.584067			−0.292033	+	0.956408i	$0.594332\pi$
$110$	−4.24698	+	7.35598i	−0.404934	+	0.701366i
$111$	−5.00969	+	8.67704i	−0.475499	+	0.823588i
$112$	−1.10992			−0.104877
$113$	6.10052	−	10.5664i	0.573889	−	0.994005i	−0.422272	−	0.906469i	$-0.638767\pi$
$113$	6.10052	−	10.5664i	0.573889	−	0.994005i	0.996161	−	0.0875358i	$-0.0278992\pi$
$114$	−0.934157	−	1.61801i	−0.0874918	−	0.151540i
$115$	−6.09783	−	10.5618i	−0.568626	−	0.984889i
$116$	−3.78017			−0.350980
$117$		0			0
$118$	−10.1468			−0.934084
$119$	3.30798	+	5.72959i	0.303242	+	0.525230i
$120$	3.69202	+	6.39477i	0.337034	+	0.583760i
$121$	2.72252	−	4.71554i	0.247502	−	0.428686i
$122$	−0.439665			−0.0398054
$123$	7.36174	−	12.7509i	0.663786	−	1.14971i
$124$	4.24698	−	7.35598i	0.381390	−	0.660587i
$125$	10.7681			0.963127
$126$	0.664874	−	1.15160i	0.0592317	−	0.102592i
$127$	−5.71379	−	9.89658i	−0.507017	−	0.878179i	−0.999967	−	0.00812161i	$-0.997415\pi$
$127$	−5.71379	−	9.89658i	−0.507017	−	0.878179i	0.492950	−	0.870058i	$-0.335919\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.05669			0.0930361
$130$		0			0
$131$	2.29590			0.200593			0.100297	−	0.994958i	$-0.468021\pi$
$131$	2.29590			0.200593			0.100297	+	0.994958i	$0.468021\pi$
$132$	2.41454	+	4.18211i	0.210159	+	0.364006i
$133$	−0.506041	−	0.876488i	−0.0438793	−	0.0760012i
$134$	1.07338	−	1.85914i	0.0927256	−	0.160605i
$135$	13.3056			1.14516
$136$	−2.98039	+	5.16218i	−0.255566	+	0.442653i
$137$	4.54019	−	7.86384i	0.387894	−	0.671853i	−0.604272	−	0.796778i	$-0.706536\pi$
$137$	4.54019	−	7.86384i	0.387894	−	0.671853i	0.992166	+	0.124925i	$0.0398692\pi$
$138$	−6.93362			−0.590229
$139$	−9.45257	+	16.3723i	−0.801757	+	1.38868i	0.116702	+	0.993167i	$0.462768\pi$
$139$	−9.45257	+	16.3723i	−0.801757	+	1.38868i	−0.918459	+	0.395517i	$0.870566\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$	−7.15883	−	12.3995i	−0.602883	−	1.04422i
$142$	−0.615957			−0.0516900
$143$		0			0
$144$	1.19806			0.0998385
$145$	6.81163	+	11.7981i	0.565675	+	0.979777i
$146$	3.16152	+	5.47592i	0.261649	+	0.453190i
$147$	−5.90917	+	10.2350i	−0.487380	+	0.844167i
$148$	−4.89008			−0.401962
$149$	9.34481	−	16.1857i	0.765557	−	1.32598i	−0.174395	−	0.984676i	$-0.555797\pi$
$149$	9.34481	−	16.1857i	0.765557	−	1.32598i	0.939952	−	0.341308i	$-0.110870\pi$
$150$	8.18329	−	14.1739i	0.668163	−	1.15729i
$151$	0.317667			0.0258514			0.0129257	−	0.999916i	$-0.495886\pi$
$151$	0.317667			0.0258514			0.0129257	+	0.999916i	$0.495886\pi$
$152$	0.455927	−	0.789689i	0.0369806	−	0.0640522i
$153$	−3.57069	−	6.18461i	−0.288673	−	0.499996i
$154$	1.30798	+	2.26549i	0.105400	+	0.182558i
$155$	−30.6112			−2.45875
$156$		0			0
$157$	18.8901			1.50759			0.753796	−	0.657108i	$-0.228220\pi$
$157$	18.8901			1.50759			0.753796	+	0.657108i	$0.228220\pi$
$158$	7.74094	+	13.4077i	0.615836	+	1.06666i
$159$	−3.46681	−	6.00469i	−0.274936	−	0.476203i
$160$	−1.80194	+	3.12105i	−0.142456	+	0.246740i
$161$	−3.75600			−0.296015
$162$	5.57942	−	9.66383i	0.438360	−	0.759262i
$163$	−2.16637	+	3.75226i	−0.169683	+	0.293899i	−0.938308	−	0.345800i	$-0.887608\pi$
$163$	−2.16637	+	3.75226i	−0.169683	+	0.293899i	0.768625	+	0.639699i	$0.220941\pi$
$164$	7.18598			0.561131
$165$	8.70171	−	15.0718i	0.677427	−	1.17334i
$166$	−0.455927	−	0.789689i	−0.0353868	−	0.0612917i
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	0.998808	+	0.0488118i	$0.0155435\pi$
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	−0.457132	+	0.889399i	$0.651123\pi$
$168$	2.27413			0.175453
$169$		0			0
$170$	21.4819			1.64758
$171$	0.546229	+	0.946096i	0.0417712	+	0.0723498i
$172$	0.257865	+	0.446635i	0.0196620	+	0.0340556i
$173$	5.49396	−	9.51582i	0.417698	−	0.723474i	−0.578010	−	0.816030i	$-0.696170\pi$
$173$	5.49396	−	9.51582i	0.417698	−	0.723474i	0.995707	+	0.0925559i	$0.0295037\pi$
$174$	7.74525			0.587166
$175$	4.43296	−	7.67811i	0.335100	−	0.580411i
$176$	−1.17845	+	2.04113i	−0.0888289	+	0.153856i
$177$	20.7899			1.56266
$178$	1.87531	−	3.24814i	0.140561	−	0.243458i
$179$	−2.32759	−	4.03151i	−0.173972	−	0.301329i	0.765833	−	0.643040i	$-0.222327\pi$
$179$	−2.32759	−	4.03151i	−0.173972	−	0.301329i	−0.939805	+	0.341711i	$0.888994\pi$
$180$	−2.15883	−	3.73921i	−0.160910	−	0.278704i
$181$	−1.06638			−0.0792631			−0.0396315	−	0.999214i	$-0.512618\pi$
$181$	−1.06638			−0.0792631			−0.0396315	+	0.999214i	$0.512618\pi$
$182$		0			0
$183$	0.900837			0.0665918
$184$	−1.69202	−	2.93067i	−0.124737	−	0.216052i
$185$	8.81163	+	15.2622i	0.647844	+	1.12210i
$186$	−8.70171	+	15.0718i	−0.638040	+	1.10512i
$187$	14.0489			1.02736
$188$	3.49396	−	6.05171i	0.254823	−	0.441367i
$189$	2.04892	−	3.54883i	0.149037	−	0.258139i
$190$	−3.28621			−0.238407
$191$	−0.445042	+	0.770835i	−0.0322021	+	0.0557757i	−0.881677	−	0.471853i	$-0.843585\pi$
$191$	−0.445042	+	0.770835i	−0.0322021	+	0.0557757i	0.849475	+	0.527629i	$0.176919\pi$
$192$	1.02446	+	1.77441i	0.0739339	+	0.128057i
$193$	8.10872	+	14.0447i	0.583678	+	1.01096i	0.995039	+	0.0994879i	$0.0317205\pi$
$193$	8.10872	+	14.0447i	0.583678	+	1.01096i	−0.411360	+	0.911473i	$0.634946\pi$
$194$	14.6746			1.05357
$195$		0			0
$196$	−5.76809			−0.412006
$197$	−5.73556	−	9.93428i	−0.408642	−	0.707788i	0.586096	−	0.810242i	$-0.300664\pi$
$197$	−5.73556	−	9.93428i	−0.408642	−	0.707788i	−0.994738	+	0.102453i	$0.967331\pi$
$198$	−1.41185	−	2.44540i	−0.100336	−	0.173787i
$199$	1.89977	−	3.29050i	0.134671	−	0.233258i	−0.790801	−	0.612074i	$-0.790335\pi$
$199$	1.89977	−	3.29050i	0.134671	−	0.233258i	0.925472	+	0.378816i	$0.123669\pi$
$200$	7.98792			0.564831
$201$	−2.19926	+	3.80923i	−0.155124	+	0.268682i
$202$	−4.38404	+	7.59339i	−0.308460	+	0.534269i
$203$	4.19567			0.294478
$204$	6.10656	−	10.5769i	0.427545	−	0.740530i
$205$	−12.9487	−	22.4278i	−0.904376	−	1.56642i
$206$	−9.40581	−	16.2913i	−0.655334	−	1.13507i
$207$	4.05429			0.281793
$208$		0			0
$209$	−2.14914			−0.148659
$210$	−4.09783	−	7.09766i	−0.282777	−	0.489785i
$211$	12.5233	+	21.6909i	0.862137	+	1.49326i	0.869862	+	0.493295i	$0.164208\pi$
$211$	12.5233	+	21.6909i	0.862137	+	1.49326i	−0.00772527	+	0.999970i	$0.502459\pi$
$212$	1.69202	−	2.93067i	0.116209	−	0.201279i
$213$	1.26205			0.0864739
$214$	−9.02595	+	15.6334i	−0.617001	+	1.06868i
$215$	0.929312	−	1.60962i	0.0633786	−	0.109775i
$216$	3.69202			0.251210
$217$	−4.71379	+	8.16453i	−0.319993	+	0.554244i
$218$	3.04892	+	5.28088i	0.206499	+	0.357666i
$219$	−6.47770	−	11.2197i	−0.437722	−	0.758157i
$220$	8.49396			0.572663
$221$		0			0
$222$	10.0194			0.672457
$223$	6.49396	+	11.2479i	0.434868	+	0.753213i	0.997285	−	0.0736407i	$-0.0234618\pi$
$223$	6.49396	+	11.2479i	0.434868	+	0.753213i	−0.562417	+	0.826854i	$0.690128\pi$
$224$	0.554958	+	0.961216i	0.0370797	+	0.0642239i
$225$	−4.78501	+	8.28788i	−0.319001	+	0.552526i
$226$	−12.2010			−0.811602
$227$	−6.90246	+	11.9554i	−0.458132	+	0.793509i	−0.998862	−	0.0476877i	$-0.984815\pi$
$227$	−6.90246	+	11.9554i	−0.458132	+	0.793509i	0.540730	+	0.841196i	$0.318148\pi$
$228$	−0.934157	+	1.61801i	−0.0618660	+	0.107155i
$229$	11.5603			0.763928			0.381964	−	0.924177i	$-0.375248\pi$
$229$	11.5603			0.763928			0.381964	+	0.924177i	$0.375248\pi$
$230$	−6.09783	+	10.5618i	−0.402079	+	0.696422i
$231$	−2.67994	−	4.64179i	−0.176327	−	0.305407i
$232$	1.89008	+	3.27372i	0.124090	+	0.214930i
$233$	9.77479			0.640368			0.320184	−	0.947355i	$-0.396255\pi$
$233$	9.77479			0.640368			0.320184	+	0.947355i	$0.396255\pi$
$234$		0			0
$235$	−25.1836			−1.64280
$236$	5.07338	+	8.78735i	0.330249	+	0.572007i
$237$	−15.8605	−	27.4713i	−1.03025	−	1.78445i
$238$	3.30798	−	5.72959i	0.214424	−	0.371394i
$239$	0.944378			0.0610867			0.0305434	−	0.999533i	$-0.490276\pi$
$239$	0.944378			0.0610867			0.0305434	+	0.999533i	$0.490276\pi$
$240$	3.69202	−	6.39477i	0.238319	−	0.412781i
$241$	−0.109916	+	0.190381i	−0.00708033	+	0.0122635i	−0.869544	−	0.493856i	$-0.835587\pi$
$241$	−0.109916	+	0.190381i	−0.00708033	+	0.0122635i	0.862464	+	0.506119i	$0.168920\pi$
$242$	−5.44504			−0.350021
$243$	−5.89373	+	10.2082i	−0.378083	+	0.654859i
$244$	0.219833	+	0.380761i	0.0140733	+	0.0243757i
$245$	10.3937	+	18.0025i	0.664031	+	1.15014i
$246$	−14.7235			−0.938735
$247$		0			0
$248$	−8.49396			−0.539367
$249$	0.934157	+	1.61801i	0.0591998	+	0.102537i
$250$	−5.38404	−	9.32544i	−0.340517	−	0.589792i
$251$	−8.12714	+	14.0766i	−0.512980	+	0.888508i	0.486906	+	0.873454i	$0.338125\pi$
$251$	−8.12714	+	14.0766i	−0.512980	+	0.888508i	−0.999887	+	0.0150539i	$0.995208\pi$
$252$	−1.32975			−0.0837663
$253$	−3.98792	+	6.90728i	−0.250718	+	0.434257i
$254$	−5.71379	+	9.89658i	−0.358515	+	0.620967i
$255$	−44.0146			−2.75630
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.2186	+	19.4312i	0.699799	+	1.21209i	0.968536	+	0.248874i	$0.0800606\pi$
$257$	11.2186	+	19.4312i	0.699799	+	1.21209i	−0.268737	+	0.963214i	$0.586606\pi$
$258$	−0.528344	−	0.915118i	−0.0328932	−	0.0569727i
$259$	5.42758			0.337254
$260$		0			0
$261$	−4.52888			−0.280330
$262$	−1.14795	−	1.98831i	−0.0709205	−	0.122838i
$263$	5.24698	+	9.08804i	0.323543	+	0.560392i	0.981216	−	0.192911i	$-0.0617928\pi$
$263$	5.24698	+	9.08804i	0.323543	+	0.560392i	−0.657674	+	0.753303i	$0.728459\pi$
$264$	2.41454	−	4.18211i	0.148605	−	0.257391i
$265$	−12.1957			−0.749174
$266$	−0.506041	+	0.876488i	−0.0310274	+	0.0537409i
$267$	−3.84236	+	6.65517i	−0.235149	+	0.407290i
$268$	−2.14675			−0.131134
$269$	−13.2078	+	22.8765i	−0.805291	+	1.39480i	0.110804	+	0.993842i	$0.464657\pi$
$269$	−13.2078	+	22.8765i	−0.805291	+	1.39480i	−0.916095	+	0.400962i	$0.868676\pi$
$270$	−6.65279	−	11.5230i	−0.404876	−	0.701266i
$271$	−11.0151	−	19.0787i	−0.669118	−	1.15895i	−0.978151	−	0.207895i	$-0.933339\pi$
$271$	−11.0151	−	19.0787i	−0.669118	−	1.15895i	0.309034	−	0.951051i	$-0.399994\pi$
$272$	5.96077			0.361425
$273$		0			0
$274$	−9.08038			−0.548566
$275$	−9.41335	−	16.3044i	−0.567646	−	0.983192i
$276$	3.46681	+	6.00469i	0.208678	+	0.361440i
$277$	−1.08815	+	1.88472i	−0.0653804	+	0.113242i	−0.896863	−	0.442309i	$-0.854159\pi$
$277$	−1.08815	+	1.88472i	−0.0653804	+	0.113242i	0.831482	+	0.555551i	$0.187493\pi$
$278$	18.9051			1.13386
$279$	5.08815	−	8.81293i	0.304619	−	0.527616i
$280$	2.00000	−	3.46410i	0.119523	−	0.207020i
$281$	−25.0030			−1.49155			−0.745776	−	0.666196i	$-0.767921\pi$
$281$	−25.0030			−1.49155			−0.745776	+	0.666196i	$0.767921\pi$
$282$	−7.15883	+	12.3995i	−0.426302	+	0.738377i
$283$	8.15764	+	14.1294i	0.484921	+	0.839908i	0.999850	−	0.0173249i	$-0.00551495\pi$
$283$	8.15764	+	14.1294i	0.484921	+	0.839908i	−0.514929	+	0.857233i	$0.672182\pi$
$284$	0.307979	+	0.533434i	0.0182752	+	0.0316535i
$285$	6.73317			0.398839
$286$		0			0
$287$	−7.97584			−0.470799
$288$	−0.599031	−	1.03755i	−0.0352982	−	0.0611384i
$289$	−9.26540	−	16.0481i	−0.545023	−	0.944008i
$290$	6.81163	−	11.7981i	0.399992	−	0.692807i
$291$	−30.0670			−1.76256
$292$	3.16152	−	5.47592i	0.185014	−	0.320454i
$293$	−0.939001	+	1.62640i	−0.0548570	+	0.0950152i	−0.892150	−	0.451740i	$-0.850804\pi$
$293$	−0.939001	+	1.62640i	−0.0548570	+	0.0950152i	0.837293	+	0.546755i	$0.184137\pi$
$294$	11.8183			0.689259
$295$	18.2838	−	31.6685i	1.06452	−	1.84381i
$296$	2.44504	+	4.23494i	0.142115	+	0.246151i
$297$	−4.35086	−	7.53590i	−0.252462	−	0.437277i
$298$	−18.6896			−1.08266
$299$		0			0
$300$	−16.3666			−0.944925
$301$	−0.286208	−	0.495727i	−0.0164968	−	0.0285732i
$302$	−0.158834	−	0.275108i	−0.00913985	−	0.0158307i
$303$	8.98254	−	15.5582i	0.516034	−	0.893796i
$304$	−0.911854			−0.0522984
$305$	0.792249	−	1.37222i	0.0453640	−	0.0785728i
$306$	−3.57069	+	6.18461i	−0.204123	+	0.353551i
$307$	23.9801			1.36862			0.684310	−	0.729192i	$-0.260104\pi$
$307$	23.9801			1.36862			0.684310	+	0.729192i	$0.260104\pi$
$308$	1.30798	−	2.26549i	0.0745290	−	0.129088i
$309$	19.2717	+	33.3796i	1.09633	+	1.89890i
$310$	15.3056	+	26.5101i	0.869299	+	1.50567i
$311$	−5.38404			−0.305301			−0.152651	−	0.988280i	$-0.548781\pi$
$311$	−5.38404			−0.305301			−0.152651	+	0.988280i	$0.548781\pi$
$312$		0			0
$313$	18.9487			1.07104			0.535522	−	0.844522i	$-0.320115\pi$
$313$	18.9487			1.07104			0.535522	+	0.844522i	$0.320115\pi$
$314$	−9.44504	−	16.3593i	−0.533015	−	0.923208i
$315$	2.39612	+	4.15021i	0.135006	+	0.233838i
$316$	7.74094	−	13.4077i	0.435462	−	0.754242i
$317$	11.5013			0.645975			0.322987	−	0.946403i	$-0.395313\pi$
$317$	11.5013			0.645975			0.322987	+	0.946403i	$0.395313\pi$
$318$	−3.46681	+	6.00469i	−0.194409	+	0.336727i
$319$	4.45473	−	7.71582i	0.249417	−	0.432003i
$320$	3.60388			0.201463
$321$	18.4934	−	32.0316i	1.03220	−	1.78783i
$322$	1.87800	+	3.25280i	0.104657	+	0.181271i
$323$	2.71768	+	4.70715i	0.151216	+	0.261913i
$324$	−11.1588			−0.619935
$325$		0			0
$326$	4.33273			0.239968
$327$	−6.24698	−	10.8201i	−0.345459	−	0.598352i
$328$	−3.59299	−	6.22324i	−0.198390	−	0.343621i
$329$	−3.87800	+	6.71690i	−0.213801	+	0.370315i
$330$	−17.4034			−0.958027
$331$	−17.3056	+	29.9742i	−0.951201	+	1.64753i	−0.208369	+	0.978050i	$0.566816\pi$
$331$	−17.3056	+	29.9742i	−0.951201	+	1.64753i	−0.742832	+	0.669478i	$0.766518\pi$
$332$	−0.455927	+	0.789689i	−0.0250222	+	0.0433398i
$333$	−5.85862			−0.321051
$334$	7.00000	−	12.1244i	0.383023	−	0.663415i
$335$	3.86831	+	6.70012i	0.211349	+	0.366066i
$336$	−1.13706	−	1.96945i	−0.0620319	−	0.107442i
$337$	1.95407			0.106445			0.0532224	−	0.998583i	$-0.483051\pi$
$337$	1.95407			0.106445			0.0532224	+	0.998583i	$0.483051\pi$
$338$		0			0
$339$	24.9989			1.35776
$340$	−10.7409	−	18.6039i	−0.582509	−	1.00894i
$341$	10.0097	+	17.3373i	0.542055	+	0.938867i
$342$	0.546229	−	0.946096i	0.0295367	−	0.0511590i
$343$	14.1715			0.765189
$344$	0.257865	−	0.446635i	0.0139031	−	0.0240809i
$345$	12.4940	−	21.6402i	0.672652	−	1.16507i
$346$	−10.9879			−0.590714
$347$	3.20775	−	5.55599i	0.172201	−	0.298261i	−0.766988	−	0.641661i	$-0.778245\pi$
$347$	3.20775	−	5.55599i	0.172201	−	0.298261i	0.939189	+	0.343400i	$0.111579\pi$
$348$	−3.87263	−	6.70758i	−0.207595	−	0.359564i
$349$	−0.542877	−	0.940290i	−0.0290595	−	0.0503326i	0.851130	−	0.524955i	$-0.175918\pi$
$349$	−0.542877	−	0.940290i	−0.0290595	−	0.0503326i	−0.880189	+	0.474623i	$0.842585\pi$
$350$	−8.86592			−0.473903
$351$		0			0
$352$	2.35690			0.125623
$353$	−2.14460	−	3.71455i	−0.114145	−	0.197706i	0.803292	−	0.595585i	$-0.203080\pi$
$353$	−2.14460	−	3.71455i	−0.114145	−	0.197706i	−0.917438	+	0.397879i	$0.869746\pi$
$354$	−10.3949	−	18.0045i	−0.552484	−	0.956931i
$355$	1.10992	−	1.92243i	0.0589082	−	0.102032i
$356$	−3.75063			−0.198783
$357$	−6.77777	+	11.7394i	−0.358718	+	0.621318i
$358$	−2.32759	+	4.03151i	−0.123017	+	0.213072i
$359$	−15.5060			−0.818378			−0.409189	−	0.912450i	$-0.634188\pi$
$359$	−15.5060			−0.818378			−0.409189	+	0.912450i	$0.634188\pi$
$360$	−2.15883	+	3.73921i	−0.113781	+	0.197074i
$361$	9.08426	+	15.7344i	0.478119	+	0.828126i
$362$	0.533188	+	0.923508i	0.0280237	+	0.0485385i
$363$	11.1564			0.585561
$364$		0			0
$365$	−22.7875			−1.19275
$366$	−0.450419	−	0.780148i	−0.0235438	−	0.0407790i
$367$	−8.71379	−	15.0927i	−0.454856	−	0.787834i	0.543824	−	0.839199i	$-0.316976\pi$
$367$	−8.71379	−	15.0927i	−0.454856	−	0.787834i	−0.998680	+	0.0513654i	$0.983643\pi$
$368$	−1.69202	+	2.93067i	−0.0882027	+	0.152772i
$369$	8.60925			0.448180
$370$	8.81163	−	15.2622i	0.458095	−	0.793443i
$371$	−1.87800	+	3.25280i	−0.0975010	+	0.168877i
$372$	17.4034			0.902325
$373$	−4.09783	+	7.09766i	−0.212178	+	0.367503i	−0.952396	−	0.304864i	$-0.901389\pi$
$373$	−4.09783	+	7.09766i	−0.212178	+	0.367503i	0.740218	+	0.672367i	$0.234722\pi$
$374$	−7.02446	−	12.1667i	−0.363226	−	0.629126i
$375$	11.0315	+	19.1070i	0.569662	+	0.986684i
$376$	−6.98792			−0.360374
$377$		0			0
$378$	−4.09783			−0.210770
$379$	7.52379	+	13.0316i	0.386471	+	0.669388i	0.991972	−	0.126457i	$-0.0403605\pi$
$379$	7.52379	+	13.0316i	0.386471	+	0.669388i	−0.605501	+	0.795845i	$0.707027\pi$
$380$	1.64310	+	2.84594i	0.0842895	+	0.145994i
$381$	11.7071	−	20.2773i	0.599772	−	1.03884i
$382$	0.890084			0.0455406
$383$	5.56033	−	9.63078i	0.284120	−	0.492110i	−0.688276	−	0.725449i	$-0.741632\pi$
$383$	5.56033	−	9.63078i	0.284120	−	0.492110i	0.972395	+	0.233339i	$0.0749653\pi$
$384$	1.02446	−	1.77441i	0.0522792	−	0.0905502i
$385$	−9.42758			−0.480474
$386$	8.10872	−	14.0447i	0.412723	−	0.714857i
$387$	0.308938	+	0.535096i	0.0157042	+	0.0272005i
$388$	−7.33728	−	12.7085i	−0.372494	−	0.645179i
$389$	−8.04354			−0.407824			−0.203912	−	0.978989i	$-0.565366\pi$
$389$	−8.04354			−0.407824			−0.203912	+	0.978989i	$0.565366\pi$
$390$		0			0
$391$	20.1715			1.02012
$392$	2.88404	+	4.99531i	0.145666	+	0.252301i
$393$	2.35205	+	4.07387i	0.118645	+	0.205500i
$394$	−5.73556	+	9.93428i	−0.288953	+	0.500482i
$395$	−55.7948			−2.80734
$396$	−1.41185	+	2.44540i	−0.0709483	+	0.122886i
$397$	10.9541	−	18.9730i	0.549769	−	0.952228i	−0.448521	−	0.893772i	$-0.648049\pi$
$397$	10.9541	−	18.9730i	0.549769	−	0.952228i	0.998290	−	0.0584554i	$-0.0186175\pi$
$398$	−3.79954			−0.190454
$399$	1.03684	−	1.79585i	0.0519067	−	0.0899051i
$400$	−3.99396	−	6.91774i	−0.199698	−	0.345887i
$401$	−8.72132	−	15.1058i	−0.435522	−	0.754347i	0.561816	−	0.827262i	$-0.310103\pi$
$401$	−8.72132	−	15.1058i	−0.435522	−	0.754347i	−0.997338	+	0.0729157i	$0.976770\pi$
$402$	4.39852			0.219378
$403$		0			0
$404$	8.76809			0.436229
$405$	20.1075	+	34.8273i	0.999151	+	1.73058i
$406$	−2.09783	−	3.63356i	−0.104114	−	0.180330i
$407$	5.76271	−	9.98130i	0.285647	−	0.494755i
$408$	−12.2131			−0.604640
$409$	8.71648	−	15.0974i	0.431002	−	0.746518i	−0.565958	−	0.824434i	$-0.691493\pi$
$409$	8.71648	−	15.0974i	0.431002	−	0.746518i	0.996960	+	0.0779166i	$0.0248268\pi$
$410$	−12.9487	+	22.4278i	−0.639490	+	1.10763i
$411$	18.6049			0.917714
$412$	−9.40581	+	16.2913i	−0.463391	+	0.802617i
$413$	−5.63102	−	9.75322i	−0.277085	−	0.479924i
$414$	−2.02715	−	3.51112i	−0.0996288	−	0.172562i
$415$	3.28621			0.161314
$416$		0			0
$417$	−38.7351			−1.89687
$418$	1.07457	+	1.86121i	0.0525591	+	0.0910350i
$419$	−4.98792	−	8.63933i	−0.243676	−	0.422059i	0.718083	−	0.695958i	$-0.245020\pi$
$419$	−4.98792	−	8.63933i	−0.243676	−	0.422059i	−0.961758	+	0.273899i	$0.911687\pi$
$420$	−4.09783	+	7.09766i	−0.199954	+	0.346330i
$421$	0.615957			0.0300199			0.0150100	−	0.999887i	$-0.495222\pi$
$421$	0.615957			0.0300199			0.0150100	+	0.999887i	$0.495222\pi$
$422$	12.5233	−	21.6909i	0.609623	−	1.05590i
$423$	4.18598	−	7.25033i	0.203529	−	0.352523i
$424$	−3.38404			−0.164344
$425$	−23.8071	+	41.2351i	−1.15481	+	2.00019i
$426$	−0.631023	−	1.09296i	−0.0305731	−	0.0529542i
$427$	−0.243996	−	0.422613i	−0.0118078	−	0.0204517i
$428$	18.0519			0.872572
$429$		0			0
$430$	−1.85862			−0.0896308
$431$	7.39612	+	12.8105i	0.356259	+	0.617058i	0.987333	−	0.158665i	$-0.0507188\pi$
$431$	7.39612	+	12.8105i	0.356259	+	0.617058i	−0.631074	+	0.775723i	$0.717385\pi$
$432$	−1.84601	−	3.19738i	−0.0888162	−	0.153834i
$433$	−8.26606	+	14.3172i	−0.397242	+	0.688043i	−0.993384	−	0.114836i	$-0.963366\pi$
$433$	−8.26606	+	14.3172i	−0.397242	+	0.688043i	0.596143	+	0.802878i	$0.296699\pi$
$434$	9.42758			0.452538
$435$	−13.9565	+	24.1733i	−0.669161	+	1.15902i
$436$	3.04892	−	5.28088i	0.146017	−	0.252908i
$437$	−3.08575			−0.147612
$438$	−6.47770	+	11.2197i	−0.309516	+	0.536098i
$439$	−1.75063	−	3.03218i	−0.0835529	−	0.144718i	0.821221	−	0.570611i	$-0.193293\pi$
$439$	−1.75063	−	3.03218i	−0.0835529	−	0.144718i	−0.904774	+	0.425893i	$0.859960\pi$
$440$	−4.24698	−	7.35598i	−0.202467	−	0.350683i
$441$	−6.91053			−0.329073
$442$		0			0
$443$	17.4077			0.827066			0.413533	−	0.910489i	$-0.364295\pi$
$443$	17.4077			0.827066			0.413533	+	0.910489i	$0.364295\pi$
$444$	−5.00969	−	8.67704i	−0.237749	−	0.411794i
$445$	6.75840	+	11.7059i	0.320379	+	0.554912i
$446$	6.49396	−	11.2479i	0.307498	−	0.532602i
$447$	38.2935			1.81122
$448$	0.554958	−	0.961216i	0.0262193	−	0.0454132i
$449$	−17.0749	+	29.5745i	−0.805813	+	1.39571i	0.109928	+	0.993940i	$0.464938\pi$
$449$	−17.0749	+	29.5745i	−0.805813	+	1.39571i	−0.915741	+	0.401769i	$0.868395\pi$
$450$	9.57002			0.451135
$451$	−8.46830	+	14.6675i	−0.398757	+	0.690667i
$452$	6.10052	+	10.5664i	0.286944	+	0.497002i
$453$	0.325437	+	0.563673i	0.0152904	+	0.0264837i
$454$	13.8049			0.647897
$455$		0			0
$456$	1.86831			0.0874918
$457$	−4.70171	−	8.14360i	−0.219937	−	0.380942i	0.734852	−	0.678228i	$-0.237252\pi$
$457$	−4.70171	−	8.14360i	−0.219937	−	0.380942i	−0.954788	+	0.297286i	$0.903918\pi$
$458$	−5.78017	−	10.0115i	−0.270089	−	0.467809i
$459$	−11.0036	+	19.0589i	−0.513606	+	0.889592i
$460$	12.1957			0.568626
$461$	0.366585	−	0.634943i	0.0170735	−	0.0295722i	−0.857362	−	0.514713i	$-0.827898\pi$
$461$	0.366585	−	0.634943i	0.0170735	−	0.0295722i	0.874436	+	0.485141i	$0.161232\pi$
$462$	−2.67994	+	4.64179i	−0.124682	+	0.215956i
$463$	7.24267			0.336595			0.168298	−	0.985736i	$-0.446173\pi$
$463$	7.24267			0.336595			0.168298	+	0.985736i	$0.446173\pi$
$464$	1.89008	−	3.27372i	0.0877449	−	0.151979i
$465$	−31.3599	−	54.3169i	−1.45428	−	2.51889i
$466$	−4.88740	−	8.46522i	−0.226404	−	0.392144i
$467$	30.2446			1.39955			0.699776	−	0.714362i	$-0.253283\pi$
$467$	30.2446			1.39955			0.699776	+	0.714362i	$0.253283\pi$
$468$		0			0
$469$	2.38271			0.110024
$470$	12.5918	+	21.8096i	0.580816	+	1.00600i
$471$	19.3521	+	33.5188i	0.891698	+	1.54447i
$472$	5.07338	−	8.78735i	0.233521	−	0.404470i
$473$	−1.21552			−0.0558897
$474$	−15.8605	+	27.4713i	−0.728499	+	1.26180i
$475$	3.64191	−	6.30797i	0.167102	−	0.289429i
$476$	−6.61596			−0.303242
$477$	2.02715	−	3.51112i	0.0928167	−	0.160763i
$478$	−0.472189	−	0.817855i	−0.0215974	−	0.0374078i
$479$	18.3599	+	31.8002i	0.838884	+	1.45299i	0.890828	+	0.454340i	$0.150125\pi$
$479$	18.3599	+	31.8002i	0.838884	+	1.45299i	−0.0519439	+	0.998650i	$0.516542\pi$
$480$	−7.38404			−0.337034
$481$		0			0
$482$	0.219833			0.0100131
$483$	−3.84787	−	6.66471i	−0.175084	−	0.303255i
$484$	2.72252	+	4.71554i	0.123751	+	0.214343i
$485$	−26.4426	+	45.8000i	−1.20070	+	2.07967i
$486$	11.7875			0.534690
$487$	14.3274	−	24.8157i	0.649234	−	1.12451i	−0.334072	−	0.942548i	$-0.608423\pi$
$487$	14.3274	−	24.8157i	0.649234	−	1.12451i	0.983306	−	0.181959i	$-0.0582439\pi$
$488$	0.219833	−	0.380761i	0.00995135	−	0.0172362i
$489$	−8.87741			−0.401450
$490$	10.3937	−	18.0025i	0.469541	−	0.813269i
$491$	−15.2148	−	26.3527i	−0.686632	−	1.18928i	−0.972921	−	0.231138i	$-0.925755\pi$
$491$	−15.2148	−	26.3527i	−0.686632	−	1.18928i	0.286289	−	0.958143i	$-0.407578\pi$
$492$	7.36174	+	12.7509i	0.331893	+	0.574855i
$493$	−22.5327			−1.01482
$494$		0			0
$495$	10.1763			0.457390
$496$	4.24698	+	7.35598i	0.190695	+	0.330293i
$497$	−0.341830	−	0.592068i	−0.0153332	−	0.0265579i
$498$	0.934157	−	1.61801i	0.0418606	−	0.0725046i
$499$	15.9715			0.714984			0.357492	−	0.933916i	$-0.383632\pi$
$499$	15.9715			0.714984			0.357492	+	0.933916i	$0.383632\pi$
$500$	−5.38404	+	9.32544i	−0.240782	+	0.417046i
$501$	−14.3424	+	24.8418i	−0.640772	+	1.10985i
$502$	16.2543			0.725464
$503$	20.9855	−	36.3480i	0.935698	−	1.62068i	0.162314	−	0.986739i	$-0.448104\pi$
$503$	20.9855	−	36.3480i	0.935698	−	1.62068i	0.773384	−	0.633938i	$-0.218563\pi$
$504$	0.664874	+	1.15160i	0.0296159	+	0.0512962i
$505$	−15.7995	−	27.3656i	−0.703071	−	1.21775i
$506$	7.97584			0.354569
$507$		0			0
$508$	11.4276			0.507017
$509$	−0.457123	−	0.791761i	−0.0202616	−	0.0350942i	0.855717	−	0.517444i	$-0.173117\pi$
$509$	−0.457123	−	0.791761i	−0.0202616	−	0.0350942i	−0.875978	+	0.482350i	$0.839783\pi$
$510$	22.0073	+	38.1178i	0.974499	+	1.68788i
$511$	−3.50902	+	6.07781i	−0.155230	+	0.268866i
$512$	1.00000			0.0441942
$513$	1.68329	−	2.91555i	0.0743192	−	0.128725i
$514$	11.2186	−	19.4312i	0.494833	−	0.857076i
$515$	67.7948			2.98739
$516$	−0.528344	+	0.915118i	−0.0232590	+	0.0402858i
$517$	8.23490	+	14.2633i	0.362170	+	0.627298i
$518$	−2.71379	−	4.70043i	−0.119237	−	0.206525i
$519$	22.5133			0.988226
$520$		0			0
$521$	−3.31096			−0.145056			−0.0725279	−	0.997366i	$-0.523107\pi$
$521$	−3.31096			−0.145056			−0.0725279	+	0.997366i	$0.523107\pi$
$522$	2.26444	+	3.92212i	0.0991118	+	0.171667i
$523$	0.425428	+	0.736862i	0.0186026	+	0.0322207i	0.875177	−	0.483803i	$-0.160745\pi$
$523$	0.425428	+	0.736862i	0.0186026	+	0.0322207i	−0.856574	+	0.516024i	$0.827412\pi$
$524$	−1.14795	+	1.98831i	−0.0501484	+	0.0868595i
$525$	18.1655			0.792809
$526$	5.24698	−	9.08804i	0.228779	−	0.396257i
$527$	25.3153	−	43.8473i	1.10275	−	1.91002i
$528$	−4.82908			−0.210159
$529$	5.77413	−	10.0011i	0.251049	−	0.434830i
$530$	6.09783	+	10.5618i	0.264873	+	0.458774i
$531$	6.07822	+	10.5278i	0.263772	+	0.456867i
$532$	1.01208			0.0438793
$533$		0			0
$534$	7.68473			0.332551
$535$	−32.5284	−	56.3408i	−1.40633	−	2.43583i
$536$	1.07338	+	1.85914i	0.0463628	+	0.0803027i
$537$	4.76905	−	8.26023i	0.205799	−	0.356455i
$538$	26.4155			1.13885
$539$	6.79739	−	11.7734i	0.292784	−	0.507117i
$540$	−6.65279	+	11.5230i	−0.286291	+	0.495870i
$541$	−40.8853			−1.75780			−0.878898	−	0.477010i	$-0.841721\pi$
$541$	−40.8853			−1.75780			−0.878898	+	0.477010i	$0.841721\pi$
$542$	−11.0151	+	19.0787i	−0.473138	+	0.819498i
$543$	−1.09246	−	1.89219i	−0.0468819	−	0.0812018i
$544$	−2.98039	−	5.16218i	−0.127783	−	0.221327i
$545$	−21.9758			−0.941341
$546$		0			0
$547$	−2.39075			−0.102221			−0.0511105	−	0.998693i	$-0.516276\pi$
$547$	−2.39075			−0.102221			−0.0511105	+	0.998693i	$0.516276\pi$
$548$	4.54019	+	7.86384i	0.193947	+	0.335926i
$549$	0.263373	+	0.456176i	0.0112405	+	0.0194691i
$550$	−9.41335	+	16.3044i	−0.401386	+	0.695222i
$551$	3.44696			0.146845
$552$	3.46681	−	6.00469i	0.147557	−	0.255577i
$553$	−8.59179	+	14.8814i	−0.365360	+	0.632822i
$554$	2.17629			0.0924618
$555$	−18.0543	+	31.2710i	−0.766362	+	1.32738i
$556$	−9.45257	−	16.3723i	−0.400878	−	0.694342i
$557$	−13.5754	−	23.5133i	−0.575208	−	0.996290i	−0.996019	−	0.0891414i	$-0.971588\pi$
$557$	−13.5754	−	23.5133i	−0.575208	−	0.996290i	0.420811	−	0.907148i	$-0.361746\pi$
$558$	−10.1763			−0.430797
$559$		0			0
$560$	−4.00000			−0.169031
$561$	14.3925	+	24.9286i	0.607653	+	1.05249i
$562$	12.5015	+	21.6532i	0.527344	+	0.913386i
$563$	3.26205	−	5.65003i	0.137479	−	0.238120i	−0.789063	−	0.614312i	$-0.789433\pi$
$563$	3.26205	−	5.65003i	0.137479	−	0.238120i	0.926542	+	0.376192i	$0.122767\pi$
$564$	14.3177			0.602883
$565$	21.9855	−	38.0800i	0.924938	−	1.60204i
$566$	8.15764	−	14.1294i	0.342891	−	0.593905i
$567$	12.3854			0.520137
$568$	0.307979	−	0.533434i	0.0129225	−	0.0223824i
$569$	−3.65010	−	6.32217i	−0.153020	−	0.265039i	0.779316	−	0.626631i	$-0.215567\pi$
$569$	−3.65010	−	6.32217i	−0.153020	−	0.265039i	−0.932336	+	0.361592i	$0.882233\pi$
$570$	−3.36658	−	5.83110i	−0.141011	−	0.244238i
$571$	−43.6722			−1.82762			−0.913812	−	0.406138i	$-0.866875\pi$
$571$	−43.6722			−1.82762			−0.913812	+	0.406138i	$0.866875\pi$
$572$		0			0
$573$	−1.82371			−0.0761865
$574$	3.98792	+	6.90728i	0.166452	+	0.288304i
$575$	−13.5157	−	23.4099i	−0.563645	−	0.976262i
$576$	−0.599031	+	1.03755i	−0.0249596	+	0.0432313i
$577$	16.8528			0.701590			0.350795	−	0.936452i	$-0.385911\pi$
$577$	16.8528			0.701590			0.350795	+	0.936452i	$0.385911\pi$
$578$	−9.26540	+	16.0481i	−0.385390	+	0.667515i
$579$	−16.6141	+	28.7765i	−0.690458	+	1.19591i
$580$	−13.6233			−0.565675
$581$	0.506041	−	0.876488i	0.0209941	−	0.0363629i
$582$	15.0335	+	26.0388i	0.623158	+	1.07934i
$583$	3.98792	+	6.90728i	0.165163	+	0.286070i
$584$	−6.32304			−0.261649
$585$		0			0
$586$	1.87800			0.0775796
$587$	11.0913	+	19.2106i	0.457785	+	0.792907i	0.998844	−	0.0480776i	$-0.0153095\pi$
$587$	11.0913	+	19.2106i	0.457785	+	0.792907i	−0.541058	+	0.840985i	$0.681976\pi$
$588$	−5.90917	−	10.2350i	−0.243690	−	0.422083i
$589$	−3.87263	+	6.70758i	−0.159569	+	0.276381i
$590$	−36.5676			−1.50547
$591$	11.7517	−	20.3545i	0.483400	−	0.837273i
$592$	2.44504	−	4.23494i	0.100491	−	0.174055i
$593$	3.98493			0.163642			0.0818208	−	0.996647i	$-0.473926\pi$
$593$	3.98493			0.163642			0.0818208	+	0.996647i	$0.473926\pi$
$594$	−4.35086	+	7.53590i	−0.178518	+	0.309202i
$595$	11.9215	+	20.6487i	0.488736	+	0.846515i
$596$	9.34481	+	16.1857i	0.382779	+	0.662992i
$597$	7.78495			0.318617
$598$		0			0
$599$	33.2379			1.35806			0.679032	−	0.734109i	$-0.262400\pi$
$599$	33.2379			1.35806			0.679032	+	0.734109i	$0.262400\pi$
$600$	8.18329	+	14.1739i	0.334082	+	0.578646i
$601$	−4.89858	−	8.48458i	−0.199817	−	0.346093i	0.748652	−	0.662963i	$-0.230701\pi$
$601$	−4.89858	−	8.48458i	−0.199817	−	0.346093i	−0.948469	+	0.316870i	$0.897368\pi$
$602$	−0.286208	+	0.495727i	−0.0116650	+	0.0202043i
$603$	−2.57194			−0.104738
$604$	−0.158834	+	0.275108i	−0.00646285	+	0.0111940i
$605$	9.81163	−	16.9942i	0.398899	−	0.690914i
$606$	−17.9651			−0.729782
$607$	12.1129	−	20.9802i	0.491647	−	0.851558i	−0.508306	−	0.861176i	$-0.669728\pi$
$607$	12.1129	−	20.9802i	0.491647	−	0.851558i	0.999954	+	0.00961799i	$0.00306155\pi$
$608$	0.455927	+	0.789689i	0.0184903	+	0.0320261i
$609$	4.29829	+	7.44486i	0.174175	+	0.301681i
$610$	−1.58450			−0.0641545
$611$		0			0
$612$	7.14138			0.288673
$613$	7.52781	+	13.0386i	0.304045	+	0.526622i	0.977048	−	0.213018i	$-0.0683292\pi$
$613$	7.52781	+	13.0386i	0.304045	+	0.526622i	−0.673003	+	0.739640i	$0.734996\pi$
$614$	−11.9901	−	20.7674i	−0.483880	−	0.838105i
$615$	26.5308	−	45.9527i	1.06982	−	1.85299i
$616$	−2.61596			−0.105400
$617$	1.00939	−	1.74832i	0.0406366	−	0.0703847i	−0.844992	−	0.534779i	$-0.820395\pi$
$617$	1.00939	−	1.74832i	0.0406366	−	0.0703847i	0.885628	+	0.464395i	$0.153728\pi$
$618$	19.2717	−	33.3796i	0.775223	−	1.34273i
$619$	−7.84309			−0.315240			−0.157620	−	0.987500i	$-0.550382\pi$
$619$	−7.84309			−0.315240			−0.157620	+	0.987500i	$0.550382\pi$
$620$	15.3056	−	26.5101i	0.614687	−	1.06467i
$621$	−6.24698	−	10.8201i	−0.250683	−	0.434195i
$622$	2.69202	+	4.66272i	0.107940	+	0.186958i
$623$	4.16288			0.166782
$624$		0			0
$625$	−1.13275			−0.0453101
$626$	−9.47434	−	16.4100i	−0.378671	−	0.655877i
$627$	−2.20171	−	3.81347i	−0.0879278	−	0.152295i
$628$	−9.44504	+	16.3593i	−0.376898	+	0.652807i
$629$	−29.1487			−1.16223
$630$	2.39612	−	4.15021i	0.0954639	−	0.165348i
$631$	−12.2664	+	21.2460i	−0.488316	+	0.845788i	−0.999910	−	0.0134394i	$-0.995722\pi$
$631$	−12.2664	+	21.2460i	−0.488316	+	0.845788i	0.511594	+	0.859227i	$0.329055\pi$
$632$	−15.4819			−0.615836
$633$	−25.6591	+	44.4429i	−1.01986	+	1.76645i
$634$	−5.75063	−	9.96038i	−0.228387	−	0.395577i
$635$	−20.5918	−	35.6660i	−0.817160	−	1.41536i
$636$	6.93362			0.274936
$637$		0			0
$638$	−8.90946			−0.352729
$639$	0.368977	+	0.639088i	0.0145965	+	0.0252819i
$640$	−1.80194	−	3.12105i	−0.0712278	−	0.123370i
$641$	20.8007	−	36.0279i	0.821580	−	1.42302i	−0.0829254	−	0.996556i	$-0.526426\pi$
$641$	20.8007	−	36.0279i	0.821580	−	1.42302i	0.904505	−	0.426462i	$-0.140240\pi$
$642$	−36.9869			−1.45975
$643$	−22.7059	+	39.3278i	−0.895433	+	1.55094i	−0.0621650	+	0.998066i	$0.519801\pi$
$643$	−22.7059	+	39.3278i	−0.895433	+	1.55094i	−0.833268	+	0.552869i	$0.813533\pi$
$644$	1.87800	−	3.25280i	0.0740037	−	0.128178i
$645$	3.80817			0.149946
$646$	2.71768	−	4.70715i	0.106926	−	0.185200i
$647$	−17.9172	−	31.0336i	−0.704399	−	1.22005i	−0.966908	−	0.255125i	$-0.917883\pi$
$647$	−17.9172	−	31.0336i	−0.704399	−	1.22005i	0.262509	−	0.964930i	$-0.415450\pi$
$648$	5.57942	+	9.66383i	0.219180	+	0.379631i
$649$	−23.9148			−0.938740
$650$		0			0
$651$	−19.3163			−0.757067
$652$	−2.16637	−	3.75226i	−0.0848415	−	0.146950i
$653$	−9.27950	−	16.0726i	−0.363135	−	0.628968i	0.625340	−	0.780352i	$-0.284960\pi$
$653$	−9.27950	−	16.0726i	−0.363135	−	0.628968i	−0.988475	+	0.151384i	$0.951627\pi$
$654$	−6.24698	+	10.8201i	−0.244276	+	0.423099i
$655$	8.27413			0.323297
$656$	−3.59299	+	6.22324i	−0.140283	+	0.242977i
$657$	3.78770	−	6.56049i	0.147772	−	0.255949i
$658$	7.75600			0.302361
$659$	1.98762	−	3.44266i	0.0774268	−	0.134107i	−0.824712	−	0.565553i	$-0.808663\pi$
$659$	1.98762	−	3.44266i	0.0774268	−	0.134107i	0.902139	+	0.431445i	$0.141996\pi$
$660$	8.70171	+	15.0718i	0.338714	+	0.586669i
$661$	−0.615957	−	1.06687i	−0.0239580	−	0.0414964i	0.853798	−	0.520605i	$-0.174293\pi$
$661$	−0.615957	−	1.06687i	−0.0239580	−	0.0414964i	−0.877756	+	0.479108i	$0.840960\pi$
$662$	34.6112			1.34520
$663$		0			0
$664$	0.911854			0.0353868
$665$	−1.82371	−	3.15875i	−0.0707204	−	0.122491i
$666$	2.92931	+	5.07372i	0.113509	+	0.196603i
$667$	6.39612	−	11.0784i	0.247659	−	0.428958i
$668$	−14.0000			−0.541676
$669$	−13.3056	+	23.0460i	−0.514424	+	0.891008i
$670$	3.86831	−	6.70012i	0.149446	−	0.258848i
$671$	−1.03624			−0.0400038
$672$	−1.13706	+	1.96945i	−0.0438632	+	0.0759732i
$673$	18.4128	+	31.8919i	0.709762	+	1.22934i	0.964945	+	0.262451i	$0.0845308\pi$
$673$	18.4128	+	31.8919i	0.709762	+	1.22934i	−0.255184	+	0.966893i	$0.582136\pi$
$674$	−0.977033	−	1.69227i	−0.0376339	−	0.0651839i
$675$	29.4916			1.13513
$676$		0			0
$677$	−25.9215			−0.996246			−0.498123	−	0.867106i	$-0.665977\pi$
$677$	−25.9215			−0.996246			−0.498123	+	0.867106i	$0.665977\pi$
$678$	−12.4995	−	21.6497i	−0.480039	−	0.831452i
$679$	8.14377	+	14.1054i	0.312529	+	0.541316i
$680$	−10.7409	+	18.6039i	−0.411896	+	0.713425i
$681$	−28.2851			−1.08389
$682$	10.0097	−	17.3373i	0.383291	−	0.663879i
$683$	−18.7736	+	32.5168i	−0.718352	+	1.24422i	0.243301	+	0.969951i	$0.421770\pi$
$683$	−18.7736	+	32.5168i	−0.718352	+	1.24422i	−0.961653	+	0.274271i	$0.911564\pi$
$684$	−1.09246			−0.0417712
$685$	16.3623	−	28.3403i	0.625170	−	1.08283i
$686$	−7.08575	−	12.2729i	−0.270535	−	0.468581i
$687$	11.8431	+	20.5128i	0.451842	+	0.782613i
$688$	−0.515729			−0.0196620
$689$		0			0
$690$	−24.9879			−0.951274
$691$	−22.6274	−	39.1919i	−0.860788	−	1.49093i	−0.871169	−	0.490983i	$-0.836638\pi$
$691$	−22.6274	−	39.1919i	−0.860788	−	1.49093i	0.0103812	−	0.999946i	$-0.496695\pi$
$692$	5.49396	+	9.51582i	0.208849	+	0.361737i
$693$	1.56704	−	2.71419i	0.0595269	−	0.103104i
$694$	−6.41550			−0.243529
$695$	−34.0659	+	59.0039i	−1.29219	+	2.23814i
$696$	−3.87263	+	6.70758i	−0.146791	+	0.254250i
$697$	42.8340			1.62245
$698$	−0.542877	+	0.940290i	−0.0205482	+	0.0355905i
$699$	10.0139	+	17.3445i	0.378759	+	0.656030i
$700$	4.43296	+	7.67811i	0.167550	+	0.290205i
$701$	36.0823			1.36281			0.681405	−	0.731907i	$-0.261369\pi$
$701$	36.0823			1.36281			0.681405	+	0.731907i	$0.261369\pi$
$702$		0			0
$703$	4.45904			0.168176
$704$	−1.17845	−	2.04113i	−0.0444144	−	0.0769280i
$705$	−25.7995	−	44.6861i	−0.971667	−	1.68298i
$706$	−2.14460	+	3.71455i	−0.0807129	+	0.139799i
$707$	−9.73184			−0.366004
$708$	−10.3949	+	18.0045i	−0.390665	+	0.676652i
$709$	9.53319	−	16.5120i	0.358026	−	0.620120i	−0.629605	−	0.776916i	$-0.716783\pi$
$709$	9.53319	−	16.5120i	0.358026	−	0.620120i	0.987631	+	0.156796i	$0.0501165\pi$
$710$	−2.21983			−0.0833088
$711$	9.27413	−	16.0633i	0.347807	−	0.602419i
$712$	1.87531	+	3.24814i	0.0702804	+	0.121729i
$713$	14.3720	+	24.8930i	0.538234	+	0.932249i
$714$	13.5555			0.507304
$715$		0			0
$716$	4.65519			0.173972
$717$	0.967476	+	1.67572i	0.0361311	+	0.0625808i
$718$	7.75302	+	13.4286i	0.289340	+	0.501152i
$719$	7.65279	−	13.2550i	0.285401	−	0.494329i	−0.687305	−	0.726369i	$-0.741207\pi$
$719$	7.65279	−	13.2550i	0.285401	−	0.494329i	0.972706	+	0.232040i	$0.0745399\pi$
$720$	4.31767			0.160910
$721$	10.4397	−	18.0820i	0.388793	−	0.673410i
$722$	9.08426	−	15.7344i	0.338081	−	0.585574i
$723$	−0.450419			−0.0167513
$724$	0.533188	−	0.923508i	0.0198158	−	0.0343219i
$725$	15.0978	+	26.1502i	0.560720	+	0.971195i
$726$	−5.57822	−	9.66176i	−0.207027	−	0.358582i
$727$	3.46250			0.128417			0.0642085	−	0.997937i	$-0.479548\pi$
$727$	3.46250			0.128417			0.0642085	+	0.997937i	$0.479548\pi$
$728$		0			0
$729$	9.32496			0.345369
$730$	11.3937	+	19.7345i	0.421701	+	0.730407i
$731$	1.53707	+	2.66229i	0.0568507	+	0.0984683i
$732$	−0.450419	+	0.780148i	−0.0166480	+	0.0288351i
$733$	−26.0930			−0.963769			−0.481884	−	0.876235i	$-0.660047\pi$
$733$	−26.0930			−0.963769			−0.481884	+	0.876235i	$0.660047\pi$
$734$	−8.71379	+	15.0927i	−0.321632	+	0.557083i
$735$	−21.2959	+	36.8856i	−0.785511	+	1.36054i
$736$	3.38404			0.124737
$737$	2.52984	−	4.38180i	0.0931877	−	0.161406i
$738$	−4.30463	−	7.45583i	−0.158455	−	0.274453i
$739$	13.2497	+	22.9491i	0.487397	+	0.844196i	0.999895	−	0.0144922i	$-0.00461316\pi$
$739$	13.2497	+	22.9491i	0.487397	+	0.844196i	−0.512498	+	0.858688i	$0.671280\pi$
$740$	−17.6233			−0.647844
$741$		0			0
$742$	3.75600			0.137887
$743$	0.207751	+	0.359835i	0.00762164	+	0.0132011i	0.869811	−	0.493385i	$-0.164241\pi$
$743$	0.207751	+	0.359835i	0.00762164	+	0.0132011i	−0.862189	+	0.506586i	$0.830907\pi$
$744$	−8.70171	−	15.0718i	−0.319020	−	0.552559i
$745$	33.6775	−	58.3312i	1.23385	−	2.13709i
$746$	8.19567			0.300065
$747$	−0.546229	+	0.946096i	−0.0199855	+	0.0346159i
$748$	−7.02446	+	12.1667i	−0.256840	+	0.444859i
$749$	−20.0361			−0.732103
$750$	11.0315	−	19.1070i	0.402812	−	0.697691i
$751$	−1.45473	−	2.51967i	−0.0530839	−	0.0919440i	0.838262	−	0.545267i	$-0.183572\pi$
$751$	−1.45473	−	2.51967i	−0.0530839	−	0.0919440i	−0.891346	+	0.453323i	$0.850238\pi$
$752$	3.49396	+	6.05171i	0.127412	+	0.220683i
$753$	−33.3037			−1.21365
$754$		0			0
$755$	1.14483			0.0416647
$756$	2.04892	+	3.54883i	0.0745184	+	0.129070i
$757$	−6.18598	−	10.7144i	−0.224833	−	0.389423i	0.731436	−	0.681910i	$-0.238850\pi$
$757$	−6.18598	−	10.7144i	−0.224833	−	0.389423i	−0.956269	+	0.292487i	$0.905517\pi$
$758$	7.52379	−	13.0316i	0.273277	−	0.473329i
$759$	−16.3418			−0.593171
$760$	1.64310	−	2.84594i	0.0596017	−	0.103233i
$761$	−21.2153	+	36.7459i	−0.769053	+	1.33204i	0.169023	+	0.985612i	$0.445939\pi$
$761$	−21.2153	+	36.7459i	−0.769053	+	1.33204i	−0.938077	+	0.346428i	$0.887395\pi$
$762$	−23.4142			−0.848206
$763$	−3.38404	+	5.86133i	−0.122511	+	0.212195i
$764$	−0.445042	−	0.770835i	−0.0161010	−	0.0278878i
$765$	−12.8683	−	22.2886i	−0.465255	−	0.805845i
$766$	−11.1207			−0.401806
$767$		0			0
$768$	−2.04892			−0.0739339
$769$	−6.66703	−	11.5476i	−0.240419	−	0.416418i	0.720415	−	0.693544i	$-0.243952\pi$
$769$	−6.66703	−	11.5476i	−0.240419	−	0.416418i	−0.960834	+	0.277125i	$0.910618\pi$
$770$	4.71379	+	8.16453i	0.169873	+	0.294229i
$771$	−22.9861	+	39.8130i	−0.827823	+	1.43383i
$772$	−16.2174			−0.583678
$773$	2.92692	−	5.06957i	0.105274	−	0.182340i	−0.808576	−	0.588392i	$-0.799761\pi$
$773$	2.92692	−	5.06957i	0.105274	−	0.182340i	0.913850	+	0.406052i	$0.133095\pi$
$774$	0.308938	−	0.535096i	0.0111045	−	0.0192336i
$775$	−67.8491			−2.43721
$776$	−7.33728	+	12.7085i	−0.263393	+	0.456210i
$777$	5.56033	+	9.63078i	0.199476	+	0.345502i
$778$	4.02177	+	6.96591i	0.144187	+	0.249740i
$779$	−6.55257			−0.234770
$780$		0			0
$781$	−1.45175			−0.0519476
$782$	−10.0858	−	17.4690i	−0.360666	−	0.624691i
$783$	6.97823	+	12.0866i	0.249382	+	0.431942i
$784$	2.88404	−	4.99531i	0.103002	−	0.178404i
$785$	68.0775			2.42979
$786$	2.35205	−	4.07387i	0.0838949	−	0.145310i
$787$	11.6482	−	20.1754i	0.415215	−	0.719174i	−0.580236	−	0.814448i	$-0.697040\pi$
$787$	11.6482	−	20.1754i	0.415215	−	0.719174i	0.995451	+	0.0952749i	$0.0303730\pi$
$788$	11.4711			0.408642
$789$	−10.7506	+	18.6206i	−0.382732	+	0.662912i
$790$	27.8974	+	48.3197i	0.992544	+	1.71914i
$791$	−6.77107	−	11.7278i	−0.240752	−	0.416994i
$792$	2.82371			0.100336
$793$		0			0
$794$	−21.9081			−0.777491
$795$	−12.4940	−	21.6402i	−0.443115	−	0.767498i
$796$	1.89977	+	3.29050i	0.0673356	+	0.116629i
$797$	−17.9051	+	31.0126i	−0.634233	+	1.09852i	0.352444	+	0.935833i	$0.385351\pi$
$797$	−17.9051	+	31.0126i	−0.634233	+	1.09852i	−0.986677	+	0.162691i	$0.947983\pi$
$798$	−2.07367			−0.0734072
$799$	20.8267	−	36.0729i	0.736795	−	1.27617i
$800$	−3.99396	+	6.91774i	−0.141208	+	0.244579i
$801$	−4.49349			−0.158769
$802$	−8.72132	+	15.1058i	−0.307961	+	0.533404i
$803$	7.45138	+	12.9062i	0.262953	+	0.455449i
$804$	−2.19926	−	3.80923i	−0.0775619	−	0.134341i
$805$	−13.5362			−0.477087
$806$		0			0
$807$	−54.1232			−1.90523
$808$	−4.38404	−	7.59339i	−0.154230	−	0.267134i
$809$	−14.1872	−	24.5729i	−0.498795	−	0.863938i	0.501204	−	0.865329i	$-0.332890\pi$
$809$	−14.1872	−	24.5729i	−0.498795	−	0.863938i	−0.999999	+	0.00139133i	$0.999557\pi$
$810$	20.1075	−	34.8273i	0.706506	−	1.22370i
$811$	5.20344			0.182717			0.0913587	−	0.995818i	$-0.470879\pi$
$811$	5.20344			0.182717			0.0913587	+	0.995818i	$0.470879\pi$
$812$	−2.09783	+	3.63356i	−0.0736196	+	0.127513i
$813$	22.5690	−	39.0906i	0.791528	−	1.37097i
$814$	−11.5254			−0.403966
$815$	−7.80731	+	13.5227i	−0.273478	+	0.473678i
$816$	6.10656	+	10.5769i	0.213772	+	0.370265i
$817$	−0.235135	−	0.407266i	−0.00822633	−	0.0142484i
$818$	−17.4330			−0.609529
$819$		0			0
$820$	25.8974			0.904376
$821$	2.82669	+	4.89597i	0.0986522	+	0.170871i	0.911127	−	0.412126i	$-0.135214\pi$
$821$	2.82669	+	4.89597i	0.0986522	+	0.170871i	−0.812475	+	0.582996i	$0.801880\pi$
$822$	−9.30247	−	16.1124i	−0.324461	−	0.561983i
$823$	−19.5308	+	33.8283i	−0.680801	+	1.17918i	0.293936	+	0.955825i	$0.405035\pi$
$823$	−19.5308	+	33.8283i	−0.680801	+	1.17918i	−0.974737	+	0.223356i	$0.928299\pi$
$824$	18.8116			0.655334
$825$	19.2872	−	33.4064i	0.671493	−	1.16306i
$826$	−5.63102	+	9.75322i	−0.195928	+	0.339358i
$827$	−5.40283			−0.187875			−0.0939374	−	0.995578i	$-0.529945\pi$
$827$	−5.40283			−0.187875			−0.0939374	+	0.995578i	$0.529945\pi$
$828$	−2.02715	+	3.51112i	−0.0704482	+	0.122020i
$829$	4.19269	+	7.26194i	0.145618	+	0.252218i	0.929603	−	0.368562i	$-0.120150\pi$
$829$	4.19269	+	7.26194i	0.145618	+	0.252218i	−0.783985	+	0.620779i	$0.786816\pi$
$830$	−1.64310	−	2.84594i	−0.0570330	−	0.0987840i
$831$	−4.45904			−0.154682
$832$		0			0
$833$	−34.3822			−1.19127
$834$	19.3675	+	33.5456i	0.670643	+	1.16159i
$835$	25.2271	+	43.6947i	0.873021	+	1.51212i
$836$	1.07457	−	1.86121i	0.0371649	−	0.0643714i
$837$	−31.3599			−1.08396
$838$	−4.98792	+	8.63933i	−0.172305	+	0.298441i
$839$	1.99031	−	3.44732i	0.0687132	−	0.119015i	−0.829622	−	0.558326i	$-0.811444\pi$
$839$	1.99031	−	3.44732i	0.0687132	−	0.119015i	0.898335	+	0.439311i	$0.144777\pi$
$840$	8.19567			0.282777
$841$	7.35517	−	12.7395i	0.253626	−	0.439294i
$842$	−0.307979	−	0.533434i	−0.0106136	−	0.0183834i
$843$	−25.6145	−	44.3657i	−0.882211	−	1.52803i
$844$	−25.0465			−0.862137
$845$		0			0
$846$	−8.37196			−0.287834
$847$	−3.02177	−	5.23386i	−0.103829	−	0.179838i
$848$	1.69202	+	2.93067i	0.0581043	+	0.100640i
$849$	−16.7143	+	28.9501i	−0.573634	+	0.993563i
$850$	47.6142			1.63315
$851$	8.27413	−	14.3312i	0.283633	−	0.491267i
$852$	−0.631023	+	1.09296i	−0.0216185	+	0.0374443i
$853$	6.29350			0.215485			0.107743	−	0.994179i	$-0.465638\pi$
$853$	6.29350			0.215485			0.107743	+	0.994179i	$0.465638\pi$
$854$	−0.243996	+	0.422613i	−0.00834936	+	0.0144615i
$855$	1.96854	+	3.40961i	0.0673227	+	0.116606i
$856$	−9.02595	−	15.6334i	−0.308501	−	0.534339i
$857$	4.37627			0.149491			0.0747453	−	0.997203i	$-0.476186\pi$
$857$	4.37627			0.149491			0.0747453	+	0.997203i	$0.476186\pi$
$858$		0			0
$859$	15.0261			0.512683			0.256342	−	0.966586i	$-0.417483\pi$
$859$	15.0261			0.512683			0.256342	+	0.966586i	$0.417483\pi$
$860$	0.929312	+	1.60962i	0.0316893	+	0.0548875i
$861$	−8.17092	−	14.1524i	−0.278464	−	0.482314i
$862$	7.39612	−	12.8105i	0.251913	−	0.436326i
$863$	6.21121			0.211432			0.105716	−	0.994396i	$-0.466287\pi$
$863$	6.21121			0.211432			0.105716	+	0.994396i	$0.466287\pi$
$864$	−1.84601	+	3.19738i	−0.0628026	+	0.108777i
$865$	19.7995	−	34.2938i	0.673205	−	1.16602i
$866$	16.5321			0.561784
$867$	18.9840	−	32.8813i	0.644732	−	1.11671i
$868$	−4.71379	−	8.16453i	−0.159997	−	0.277122i
$869$	18.2446	+	31.6006i	0.618905	+	1.07198i
$870$	27.9129			0.946337
$871$		0			0
$872$	−6.09783			−0.206499
$873$	−8.79052	−	15.2256i	−0.297514	−	0.515309i
$874$	1.54288	+	2.67234i	0.0521886	+	0.0903933i
$875$	5.97584	−	10.3505i	0.202020	−	0.349909i
$876$	12.9554			0.437722
$877$	−19.1099	+	33.0993i	−0.645296	+	1.11769i	0.338937	+	0.940809i	$0.389933\pi$
$877$	−19.1099	+	33.0993i	−0.645296	+	1.11769i	−0.984233	+	0.176876i	$0.943401\pi$
$878$	−1.75063	+	3.03218i	−0.0590808	+	0.102331i
$879$	−3.84787			−0.129785
$880$	−4.24698	+	7.35598i	−0.143166	+	0.247970i
$881$	−13.3916	−	23.1949i	−0.451174	−	0.781456i	0.547286	−	0.836946i	$-0.315661\pi$
$881$	−13.3916	−	23.1949i	−0.451174	−	0.781456i	−0.998459	+	0.0554902i	$0.982328\pi$
$882$	3.45526	+	5.98469i	0.116345	+	0.201515i
$883$	−34.4956			−1.16087			−0.580435	−	0.814307i	$-0.697117\pi$
$883$	−34.4956			−1.16087			−0.580435	+	0.814307i	$0.697117\pi$
$884$		0			0
$885$	74.9241			2.51854
$886$	−8.70387	−	15.0755i	−0.292412	−	0.506473i
$887$	11.9933	+	20.7730i	0.402695	+	0.697489i	0.994050	−	0.108923i	$-0.0347400\pi$
$887$	11.9933	+	20.7730i	0.402695	+	0.697489i	−0.591355	+	0.806411i	$0.701407\pi$
$888$	−5.00969	+	8.67704i	−0.168114	+	0.291182i
$889$	−12.6837			−0.425396
$890$	6.75840	−	11.7059i	0.226542	−	0.392382i
$891$	13.1501	−	22.7766i	0.440545	−	0.763046i
$892$	−12.9879			−0.434868
$893$	−3.18598	+	5.51828i	−0.106615	+	0.184662i
$894$	−19.1468	−	33.1631i	−0.640363	−	1.10914i
$895$	−8.38835	−	14.5291i	−0.280392	−	0.485653i
$896$	−1.10992			−0.0370797
$897$		0			0
$898$	34.1497			1.13959
$899$	−16.0543	−	27.8069i	−0.535441	−	0.927410i
$900$	−4.78501	−	8.28788i	−0.159500	−	0.276263i
$901$	10.0858	−	17.4690i	0.336005	−	0.581978i
$902$	16.9366			0.563927
$903$	0.586417	−	1.01570i	0.0195147	−	0.0338005i
$904$	6.10052	−	10.5664i	0.202900	−	0.351434i
$905$	−3.84309			−0.127748
$906$	0.325437	−	0.563673i	0.0108119	−	0.0187268i
$907$	−11.9635	−	20.7213i	−0.397240	−	0.688040i	0.596144	−	0.802877i	$-0.296699\pi$
$907$	−11.9635	−	20.7213i	−0.397240	−	0.688040i	−0.993384	+	0.114837i	$0.963365\pi$
$908$	−6.90246	−	11.9554i	−0.229066	−	0.396754i
$909$	10.5047			0.348419
$910$		0			0
$911$	−35.8866			−1.18898			−0.594488	−	0.804104i	$-0.702645\pi$
$911$	−35.8866			−1.18898			−0.594488	+	0.804104i	$0.702645\pi$
$912$	−0.934157	−	1.61801i	−0.0309330	−	0.0535776i
$913$	−1.07457	−	1.86121i	−0.0355632	−	0.0615972i
$914$	−4.70171	+	8.14360i	−0.155519	+	0.269366i
$915$	3.24651			0.107326
$916$	−5.78017	+	10.0115i	−0.190982	+	0.330791i
$917$	1.27413	−	2.20685i	0.0420754	−	0.0728767i
$918$	22.0073			0.726349
$919$	−16.6233	+	28.7923i	−0.548351	+	0.949771i	0.450037	+	0.893010i	$0.351411\pi$
$919$	−16.6233	+	28.7923i	−0.548351	+	0.949771i	−0.998388	+	0.0567612i	$0.981923\pi$
$920$	−6.09783	−	10.5618i	−0.201040	−	0.348211i
$921$	24.5667	+	42.5507i	0.809499	+	1.40209i
$922$	−0.733169			−0.0241456
$923$		0			0
$924$	5.35988			0.176327
$925$	19.5308	+	33.8283i	0.642169	+	1.11227i
$926$	−3.62133	−	6.27233i	−0.119004	−	0.206122i
$927$	−11.2687	+	19.5180i	−0.370114	+	0.641057i
$928$	−3.78017			−0.124090
$929$	−27.1292	+	46.9891i	−0.890079	+	1.54166i	−0.0502995	+	0.998734i	$0.516018\pi$
$929$	−27.1292	+	46.9891i	−0.890079	+	1.54166i	−0.839779	+	0.542928i	$0.817316\pi$
$930$	−31.3599	+	54.3169i	−1.02833	+	1.78112i
$931$	5.25965			0.172378
$932$	−4.88740	+	8.46522i	−0.160092	+	0.277287i
$933$	−5.51573	−	9.55352i	−0.180577	−	0.312768i
$934$	−15.1223	−	26.1926i	−0.494817	−	0.857047i
$935$	50.6305			1.65580
$936$		0			0
$937$	16.5265			0.539897			0.269948	−	0.962875i	$-0.412993\pi$
$937$	16.5265			0.539897			0.269948	+	0.962875i	$0.412993\pi$
$938$	−1.19136	−	2.06349i	−0.0388992	−	0.0673754i
$939$	19.4121	+	33.6228i	0.633492	+	1.09724i
$940$	12.5918	−	21.8096i	0.410699	−	0.711352i
$941$	41.7017			1.35944			0.679718	−	0.733473i	$-0.262102\pi$
$941$	41.7017			1.35944			0.679718	+	0.733473i	$0.262102\pi$
$942$	19.3521	−	33.5188i	0.630526	−	1.09210i
$943$	−12.1588	+	21.0597i	−0.395946	+	0.685799i
$944$	−10.1468			−0.330249
$945$	7.38404	−	12.7895i	0.240203	−	0.416044i
$946$	0.607760	+	1.05267i	0.0197600	+	0.0342253i
$947$	1.50053	+	2.59900i	0.0487608	+	0.0844561i	0.889376	−	0.457177i	$-0.151139\pi$
$947$	1.50053	+	2.59900i	0.0487608	+	0.0844561i	−0.840615	+	0.541633i	$0.817806\pi$
$948$	31.7211			1.03025
$949$		0			0
$950$	−7.28382			−0.236318
$951$	11.7826	+	20.4080i	0.382076	+	0.661775i
$952$	3.30798	+	5.72959i	0.107212	+	0.185697i
$953$	−19.0725	+	33.0345i	−0.617818	+	1.07009i	0.372065	+	0.928207i	$0.378650\pi$
$953$	−19.0725	+	33.0345i	−0.617818	+	1.07009i	−0.989883	+	0.141886i	$0.954683\pi$
$954$	−4.05429			−0.131263
$955$	−1.60388	+	2.77799i	−0.0519002	+	0.0898938i
$956$	−0.472189	+	0.817855i	−0.0152717	+	0.0264513i
$957$	18.2547			0.590092
$958$	18.3599	−	31.8002i	0.593181	−	1.02742i
$959$	−5.03923	−	8.72820i	−0.162725	−	0.281848i
$960$	3.69202	+	6.39477i	0.119159	+	0.206390i
$961$	41.1473			1.32733
$962$		0			0
$963$	21.6273			0.696930
$964$	−0.109916	−	0.190381i	−0.00354016	−	0.00613174i
$965$	29.2228	+	50.6154i	0.940716	+	1.62937i
$966$	−3.84787	+	6.66471i	−0.123803	+	0.214433i
$967$	26.8793			0.864381			0.432190	−	0.901782i	$-0.357741\pi$
$967$	26.8793			0.864381			0.432190	+	0.901782i	$0.357741\pi$
$968$	2.72252	−	4.71554i	0.0875051	−	0.151563i
$969$	−5.56829	+	9.64457i	−0.178879	+	0.309828i
$970$	52.8853			1.69804
$971$	−1.56824	+	2.71626i	−0.0503271	+	0.0871691i	−0.890092	−	0.455782i	$-0.849360\pi$
$971$	−1.56824	+	2.71626i	−0.0503271	+	0.0871691i	0.839764	+	0.542951i	$0.182693\pi$
$972$	−5.89373	−	10.2082i	−0.189042	−	0.327430i
$973$	10.4916	+	18.1719i	0.336344	+	0.582565i
$974$	−28.6547			−0.918156
$975$		0			0
$976$	−0.439665			−0.0140733
$977$	17.9432	+	31.0785i	0.574053	+	0.994289i	0.996144	+	0.0877357i	$0.0279631\pi$
$977$	17.9432	+	31.0785i	0.574053	+	0.994289i	−0.422091	+	0.906554i	$0.638704\pi$
$978$	4.43871	+	7.68806i	0.141934	+	0.245837i
$979$	4.41992	−	7.65552i	0.141261	−	0.244672i
$980$	−20.7875			−0.664031
$981$	3.65279	−	6.32682i	0.116625	−	0.202000i
$982$	−15.2148	+	26.3527i	−0.485522	+	0.840949i
$983$	30.4370			0.970790			0.485395	−	0.874295i	$-0.338676\pi$
$983$	30.4370			0.970790			0.485395	+	0.874295i	$0.338676\pi$
$984$	7.36174	−	12.7509i	0.234684	−	0.406484i
$985$	−20.6703	−	35.8019i	−0.658609	−	1.14074i
$986$	11.2664	+	19.5139i	0.358794	+	0.621449i
$987$	−15.8914			−0.505829
$988$		0			0
$989$	−1.74525			−0.0554957
$990$	−5.08815	−	8.81293i	−0.161712	−	0.280093i
$991$	−15.7235	−	27.2339i	−0.499473	−	0.865112i	0.500527	−	0.865721i	$-0.333140\pi$
$991$	−15.7235	−	27.2339i	−0.499473	−	0.865112i	−1.00000		0.000608632i	$0.999806\pi$
$992$	4.24698	−	7.35598i	0.134842	−	0.233553i
$993$	−70.9154			−2.25043
$994$	−0.341830	+	0.592068i	−0.0108422	+	0.0187792i
$995$	6.84654	−	11.8586i	0.217050	−	0.375942i
$996$	−1.86831			−0.0591998
$997$	−9.55496	+	16.5497i	−0.302609	+	0.524133i	−0.976726	−	0.214491i	$-0.931191\pi$
$997$	−9.55496	+	16.5497i	−0.302609	+	0.524133i	0.674117	+	0.738624i	$0.264524\pi$
$998$	−7.98576	−	13.8317i	−0.252785	−	0.437836i
$999$	9.02715	+	15.6355i	0.285606	+	0.494685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.c.h.315.3		6
13.2	odd	12		338.2.b.d.337.1		6
13.3	even	3		338.2.a.h.1.1	yes	3
13.4	even	6		338.2.c.i.191.3		6
13.5	odd	4		338.2.e.e.23.3		12
13.6	odd	12		338.2.e.e.147.6		12
13.7	odd	12		338.2.e.e.147.3		12
13.8	odd	4		338.2.e.e.23.6		12
13.9	even	3	inner	338.2.c.h.191.3		6
13.10	even	6		338.2.a.g.1.1	✓	3
13.11	odd	12		338.2.b.d.337.4		6
13.12	even	2		338.2.c.i.315.3		6
39.2	even	12		3042.2.b.n.1351.6		6
39.11	even	12		3042.2.b.n.1351.1		6
39.23	odd	6		3042.2.a.bi.1.3		3
39.29	odd	6		3042.2.a.z.1.1		3
52.3	odd	6		2704.2.a.w.1.3		3
52.11	even	12		2704.2.f.m.337.6		6
52.15	even	12		2704.2.f.m.337.5		6
52.23	odd	6		2704.2.a.v.1.3		3
65.29	even	6		8450.2.a.bn.1.3		3
65.49	even	6		8450.2.a.bx.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.2.a.g.1.1	✓	3	13.10	even	6
338.2.a.h.1.1	yes	3	13.3	even	3
338.2.b.d.337.1		6	13.2	odd	12
338.2.b.d.337.4		6	13.11	odd	12
338.2.c.h.191.3		6	13.9	even	3	inner
338.2.c.h.315.3		6	1.1	even	1	trivial
338.2.c.i.191.3		6	13.4	even	6
338.2.c.i.315.3		6	13.12	even	2
338.2.e.e.23.3		12	13.5	odd	4
338.2.e.e.23.6		12	13.8	odd	4
338.2.e.e.147.3		12	13.7	odd	12
338.2.e.e.147.6		12	13.6	odd	12
2704.2.a.v.1.3		3	52.23	odd	6
2704.2.a.w.1.3		3	52.3	odd	6
2704.2.f.m.337.5		6	52.15	even	12
2704.2.f.m.337.6		6	52.11	even	12
3042.2.a.z.1.1		3	39.29	odd	6
3042.2.a.bi.1.3		3	39.23	odd	6
3042.2.b.n.1351.1		6	39.11	even	12
3042.2.b.n.1351.6		6	39.2	even	12
8450.2.a.bn.1.3		3	65.29	even	6
8450.2.a.bx.1.3		3	65.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.02446 + 1.77441i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.60388 q^{5} +(1.02446 - 1.77441i) q^{6} +(0.554958 - 0.961216i) q^{7} +1.00000 q^{8} +(-0.599031 + 1.03755i) q^{9} +(-1.80194 - 3.12105i) q^{10} +(-1.17845 - 2.04113i) q^{11} -2.04892 q^{12} -1.10992 q^{14} +(3.69202 + 6.39477i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.98039 + 5.16218i) q^{17} +1.19806 q^{18} +(0.455927 - 0.789689i) q^{19} +(-1.80194 + 3.12105i) q^{20} +2.27413 q^{21} +(-1.17845 + 2.04113i) q^{22} +(-1.69202 - 2.93067i) q^{23} +(1.02446 + 1.77441i) q^{24} +7.98792 q^{25} +3.69202 q^{27} +(0.554958 + 0.961216i) q^{28} +(1.89008 + 3.27372i) q^{29} +(3.69202 - 6.39477i) q^{30} -8.49396 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.41454 - 4.18211i) q^{33} +5.96077 q^{34} +(2.00000 - 3.46410i) q^{35} +(-0.599031 - 1.03755i) q^{36} +(2.44504 + 4.23494i) q^{37} -0.911854 q^{38} +3.60388 q^{40} +(-3.59299 - 6.22324i) q^{41} +(-1.13706 - 1.96945i) q^{42} +(0.257865 - 0.446635i) q^{43} +2.35690 q^{44} +(-2.15883 + 3.73921i) q^{45} +(-1.69202 + 2.93067i) q^{46} -6.98792 q^{47} +(1.02446 - 1.77441i) q^{48} +(2.88404 + 4.99531i) q^{49} +(-3.99396 - 6.91774i) q^{50} -12.2131 q^{51} -3.38404 q^{53} +(-1.84601 - 3.19738i) q^{54} +(-4.24698 - 7.35598i) q^{55} +(0.554958 - 0.961216i) q^{56} +1.86831 q^{57} +(1.89008 - 3.27372i) q^{58} +(5.07338 - 8.78735i) q^{59} -7.38404 q^{60} +(0.219833 - 0.380761i) q^{61} +(4.24698 + 7.35598i) q^{62} +(0.664874 + 1.15160i) q^{63} +1.00000 q^{64} -4.82908 q^{66} +(1.07338 + 1.85914i) q^{67} +(-2.98039 - 5.16218i) q^{68} +(3.46681 - 6.00469i) q^{69} -4.00000 q^{70} +(0.307979 - 0.533434i) q^{71} +(-0.599031 + 1.03755i) q^{72} -6.32304 q^{73} +(2.44504 - 4.23494i) q^{74} +(8.18329 + 14.1739i) q^{75} +(0.455927 + 0.789689i) q^{76} -2.61596 q^{77} -15.4819 q^{79} +(-1.80194 - 3.12105i) q^{80} +(5.57942 + 9.66383i) q^{81} +(-3.59299 + 6.22324i) q^{82} +0.911854 q^{83} +(-1.13706 + 1.96945i) q^{84} +(-10.7409 + 18.6039i) q^{85} -0.515729 q^{86} +(-3.87263 + 6.70758i) q^{87} +(-1.17845 - 2.04113i) q^{88} +(1.87531 + 3.24814i) q^{89} +4.31767 q^{90} +3.38404 q^{92} +(-8.70171 - 15.0718i) q^{93} +(3.49396 + 6.05171i) q^{94} +(1.64310 - 2.84594i) q^{95} -2.04892 q^{96} +(-7.33728 + 12.7085i) q^{97} +(2.88404 - 4.99531i) q^{98} +2.82371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{7} + 6 q^{8} - 8 q^{9} - 2 q^{10} - 3 q^{11} + 6 q^{12} - 8 q^{14} + 12 q^{15} - 3 q^{16} - 5 q^{17} + 16 q^{18} - q^{19} - 2 q^{20} - 8 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^7 + 6 * q^8 - 8 * q^9 - 2 * q^10 - 3 * q^11 + 6 * q^12 - 8 * q^14 + 12 * q^15 - 3 * q^16 - 5 * q^17 + 16 * q^18 - q^19 - 2 * q^20 - 8 * q^21 - 3 * q^22 - 3 * q^24 + 10 * q^25 + 12 * q^27 + 4 * q^28 + 10 * q^29 + 12 * q^30 - 32 * q^31 - 3 * q^32 + 4 * q^33 + 10 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 + 2 * q^38 + 4 * q^40 - 7 * q^41 + 4 * q^42 - 11 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^47 - 3 * q^48 - 3 * q^49 - 5 * q^50 - 32 * q^51 - 6 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 + 10 * q^58 + 3 * q^59 - 24 * q^60 + 4 * q^61 + 16 * q^62 + 6 * q^63 + 6 * q^64 - 8 * q^66 - 21 * q^67 - 5 * q^68 + 14 * q^69 - 24 * q^70 + 12 * q^71 - 8 * q^72 + 2 * q^73 + 14 * q^74 + 23 * q^75 - q^76 - 36 * q^77 - 36 * q^79 - 2 * q^80 + 25 * q^81 - 7 * q^82 - 2 * q^83 + 4 * q^84 - 36 * q^85 + 22 * q^86 + 10 * q^87 - 3 * q^88 - 25 * q^89 - 8 * q^90 + 2 * q^93 + 2 * q^94 + 18 * q^95 + 6 * q^96 - 23 * q^97 - 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more