LMFDB - Embedded newform 338.3.d.f.239.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(99,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0] 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:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.1
Root			$-3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.239
Dual form			338.3.d.f.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} -4.77574 q^{3} -2.00000i q^{4} +(5.88981 - 5.88981i) q^{5} +(4.77574 - 4.77574i) q^{6} +(-0.251956 - 0.251956i) q^{7} +(2.00000 + 2.00000i) q^{8} +13.8077 q^{9} +11.7796i q^{10} +(0.523787 + 0.523787i) q^{11} +9.55149i q^{12} +0.503913 q^{14} +(-28.1282 + 28.1282i) q^{15} -4.00000 q^{16} -2.88063i q^{17} +(-13.8077 + 13.8077i) q^{18} +(-7.68297 + 7.68297i) q^{19} +(-11.7796 - 11.7796i) q^{20} +(1.20328 + 1.20328i) q^{21} -1.04757 q^{22} -22.8951i q^{23} +(-9.55149 - 9.55149i) q^{24} -44.3798i q^{25} -22.9605 q^{27} +(-0.503913 + 0.503913i) q^{28} +30.4185 q^{29} -56.2565i q^{30} +(-14.8631 + 14.8631i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.50147 - 2.50147i) q^{33} +(2.88063 + 2.88063i) q^{34} -2.96795 q^{35} -27.6155i q^{36} +(-29.4864 - 29.4864i) q^{37} -15.3659i q^{38} +23.5593 q^{40} +(18.2202 - 18.2202i) q^{41} -2.40656 q^{42} -29.3186i q^{43} +(1.04757 - 1.04757i) q^{44} +(81.3249 - 81.3249i) q^{45} +(22.8951 + 22.8951i) q^{46} +(-21.2000 - 21.2000i) q^{47} +19.1030 q^{48} -48.8730i q^{49} +(44.3798 + 44.3798i) q^{50} +13.7571i q^{51} -85.8410 q^{53} +(22.9605 - 22.9605i) q^{54} +6.17002 q^{55} -1.00783i q^{56} +(36.6919 - 36.6919i) q^{57} +(-30.4185 + 30.4185i) q^{58} +(-70.7628 - 70.7628i) q^{59} +(56.2565 + 56.2565i) q^{60} +15.4640 q^{61} -29.7263i q^{62} +(-3.47895 - 3.47895i) q^{63} +8.00000i q^{64} +5.00295 q^{66} +(-49.2169 + 49.2169i) q^{67} -5.76126 q^{68} +109.341i q^{69} +(2.96795 - 2.96795i) q^{70} +(-68.9636 + 68.9636i) q^{71} +(27.6155 + 27.6155i) q^{72} +(-50.9541 - 50.9541i) q^{73} +58.9729 q^{74} +211.947i q^{75} +(15.3659 + 15.3659i) q^{76} -0.263943i q^{77} +105.981 q^{79} +(-23.5593 + 23.5593i) q^{80} -14.6162 q^{81} +36.4405i q^{82} +(27.2221 - 27.2221i) q^{83} +(2.40656 - 2.40656i) q^{84} +(-16.9664 - 16.9664i) q^{85} +(29.3186 + 29.3186i) q^{86} -145.271 q^{87} +2.09515i q^{88} +(60.1398 + 60.1398i) q^{89} +162.650i q^{90} -45.7902 q^{92} +(70.9825 - 70.9825i) q^{93} +42.4001 q^{94} +90.5025i q^{95} +(-19.1030 + 19.1030i) q^{96} +(-14.3732 + 14.3732i) q^{97} +(48.8730 + 48.8730i) q^{98} +(7.23232 + 7.23232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9} - 42 q^{11} + 20 q^{14} - 60 q^{15} - 32 q^{16} - 84 q^{18} - 22 q^{19} + 12 q^{20} + 102 q^{21} + 84 q^{22} + 72 q^{27} - 20 q^{28} + 12 q^{29}+ \cdots - 252 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9 - 42 * q^11 + 20 * q^14 - 60 * q^15 - 32 * q^16 - 84 * q^18 - 22 * q^19 + 12 * q^20 + 102 * q^21 + 84 * q^22 + 72 * q^27 - 20 * q^28 + 12 * q^29 - 32 * q^31 + 32 * q^32 - 54 * q^33 + 60 * q^34 + 156 * q^35 - 32 * q^37 - 24 * q^40 + 12 * q^41 - 204 * q^42 - 84 * q^44 + 102 * q^45 + 108 * q^46 - 60 * q^47 + 88 * q^50 - 132 * q^53 - 72 * q^54 + 324 * q^55 + 294 * q^57 - 12 * q^58 - 234 * q^59 + 120 * q^60 - 72 * q^61 + 156 * q^63 + 108 * q^66 + 14 * q^67 - 120 * q^68 - 156 * q^70 - 162 * q^71 + 168 * q^72 - 166 * q^73 + 64 * q^74 + 44 * q^76 - 96 * q^79 + 24 * q^80 + 24 * q^81 + 240 * q^83 + 204 * q^84 + 234 * q^85 - 132 * q^86 - 720 * q^87 - 210 * q^89 - 216 * q^92 + 444 * q^93 + 120 * q^94 - 146 * q^97 + 16 * q^98 - 252 * q^99

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−4.77574			−1.59191			−0.795957	−	0.605353i	$-0.793032\pi$
$3$	−4.77574			−1.59191			−0.795957	+	0.605353i	$0.793032\pi$
$4$		−	2.00000i		−	0.500000i
$5$	5.88981	−	5.88981i	1.17796	−	1.17796i	0.197700	−	0.980263i	$-0.436653\pi$
$5$	5.88981	−	5.88981i	1.17796	−	1.17796i	0.980263	−	0.197700i	$-0.0633472\pi$
$6$	4.77574	−	4.77574i	0.795957	−	0.795957i
$7$	−0.251956	−	0.251956i	−0.0359938	−	0.0359938i	0.688881	−	0.724875i	$-0.258102\pi$
$7$	−0.251956	−	0.251956i	−0.0359938	−	0.0359938i	−0.724875	+	0.688881i	$0.758102\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	13.8077			1.53419
$10$			11.7796i			1.17796i
$11$	0.523787	+	0.523787i	0.0476170	+	0.0476170i	0.730514	−	0.682897i	$-0.239280\pi$
$11$	0.523787	+	0.523787i	0.0476170	+	0.0476170i	−0.682897	+	0.730514i	$0.739280\pi$
$12$			9.55149i			0.795957i
$13$		0			0
$13$		0			0
$14$	0.503913			0.0359938
$15$	−28.1282	+	28.1282i	−1.87522	+	1.87522i
$16$	−4.00000			−0.250000
$17$		−	2.88063i		−	0.169449i	−0.996404	−	0.0847244i	$-0.972999\pi$
$17$		−	2.88063i		−	0.169449i	0.996404	−	0.0847244i	$-0.0270010\pi$
$18$	−13.8077	+	13.8077i	−0.767096	+	0.767096i
$19$	−7.68297	+	7.68297i	−0.404367	+	0.404367i	−0.879769	−	0.475402i	$-0.842303\pi$
$19$	−7.68297	+	7.68297i	−0.404367	+	0.404367i	0.475402	+	0.879769i	$0.342303\pi$
$20$	−11.7796	−	11.7796i	−0.588981	−	0.588981i
$21$	1.20328	+	1.20328i	0.0572990	+	0.0572990i
$22$	−1.04757			−0.0476170
$23$		−	22.8951i		−	0.995440i	−0.867338	−	0.497720i	$-0.834171\pi$
$23$		−	22.8951i		−	0.995440i	0.867338	−	0.497720i	$-0.165829\pi$
$24$	−9.55149	−	9.55149i	−0.397979	−	0.397979i
$25$		−	44.3798i		−	1.77519i
$26$		0			0
$27$	−22.9605			−0.850388
$28$	−0.503913	+	0.503913i	−0.0179969	+	0.0179969i
$29$	30.4185			1.04891			0.524457	−	0.851437i	$-0.324268\pi$
$29$	30.4185			1.04891			0.524457	+	0.851437i	$0.324268\pi$
$30$		−	56.2565i		−	1.87522i
$31$	−14.8631	+	14.8631i	−0.479456	+	0.479456i	−0.904958	−	0.425502i	$-0.860098\pi$
$31$	−14.8631	+	14.8631i	−0.479456	+	0.479456i	0.425502	+	0.904958i	$0.360098\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−2.50147	−	2.50147i	−0.0758023	−	0.0758023i
$34$	2.88063	+	2.88063i	0.0847244	+	0.0847244i
$35$	−2.96795			−0.0847986
$36$		−	27.6155i		−	0.767096i
$37$	−29.4864	−	29.4864i	−0.796931	−	0.796931i	0.185680	−	0.982610i	$-0.440551\pi$
$37$	−29.4864	−	29.4864i	−0.796931	−	0.796931i	−0.982610	+	0.185680i	$0.940551\pi$
$38$		−	15.3659i		−	0.404367i
$39$		0			0
$40$	23.5593			0.588981
$41$	18.2202	−	18.2202i	0.444396	−	0.444396i	−0.449090	−	0.893486i	$-0.648252\pi$
$41$	18.2202	−	18.2202i	0.444396	−	0.444396i	0.893486	+	0.449090i	$0.148252\pi$
$42$	−2.40656			−0.0572990
$43$		−	29.3186i		−	0.681828i	−0.940095	−	0.340914i	$-0.889264\pi$
$43$		−	29.3186i		−	0.681828i	0.940095	−	0.340914i	$-0.110736\pi$
$44$	1.04757	−	1.04757i	0.0238085	−	0.0238085i
$45$	81.3249	−	81.3249i	1.80722	−	1.80722i
$46$	22.8951	+	22.8951i	0.497720	+	0.497720i
$47$	−21.2000	−	21.2000i	−0.451065	−	0.451065i	0.444643	−	0.895708i	$-0.353330\pi$
$47$	−21.2000	−	21.2000i	−0.451065	−	0.451065i	−0.895708	+	0.444643i	$0.853330\pi$
$48$	19.1030			0.397979
$49$		−	48.8730i		−	0.997409i
$50$	44.3798	+	44.3798i	0.887596	+	0.887596i
$51$			13.7571i			0.269748i
$52$		0			0
$53$	−85.8410			−1.61964			−0.809821	−	0.586678i	$-0.800436\pi$
$53$	−85.8410			−1.61964			−0.809821	+	0.586678i	$0.800436\pi$
$54$	22.9605	−	22.9605i	0.425194	−	0.425194i
$55$	6.17002			0.112182
$56$		−	1.00783i		−	0.0179969i
$57$	36.6919	−	36.6919i	0.643718	−	0.643718i
$58$	−30.4185	+	30.4185i	−0.524457	+	0.524457i
$59$	−70.7628	−	70.7628i	−1.19937	−	1.19937i	−0.974355	−	0.225015i	$-0.927757\pi$
$59$	−70.7628	−	70.7628i	−1.19937	−	1.19937i	−0.225015	−	0.974355i	$-0.572243\pi$
$60$	56.2565	+	56.2565i	0.937608	+	0.937608i
$61$	15.4640			0.253509			0.126754	−	0.991934i	$-0.459544\pi$
$61$	15.4640			0.253509			0.126754	+	0.991934i	$0.459544\pi$
$62$		−	29.7263i		−	0.479456i
$63$	−3.47895	−	3.47895i	−0.0552214	−	0.0552214i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	5.00295			0.0758023
$67$	−49.2169	+	49.2169i	−0.734581	+	0.734581i	−0.971524	−	0.236943i	$-0.923855\pi$
$67$	−49.2169	+	49.2169i	−0.734581	+	0.734581i	0.236943	+	0.971524i	$0.423855\pi$
$68$	−5.76126			−0.0847244
$69$			109.341i			1.58466i
$70$	2.96795	−	2.96795i	0.0423993	−	0.0423993i
$71$	−68.9636	+	68.9636i	−0.971318	+	0.971318i	−0.999600	−	0.0282816i	$-0.990996\pi$
$71$	−68.9636	+	68.9636i	−0.971318	+	0.971318i	0.0282816	+	0.999600i	$0.490996\pi$
$72$	27.6155	+	27.6155i	0.383548	+	0.383548i
$73$	−50.9541	−	50.9541i	−0.698001	−	0.698001i	0.265978	−	0.963979i	$-0.414305\pi$
$73$	−50.9541	−	50.9541i	−0.698001	−	0.698001i	−0.963979	+	0.265978i	$0.914305\pi$
$74$	58.9729			0.796931
$75$			211.947i			2.82595i
$76$	15.3659	+	15.3659i	0.202183	+	0.202183i
$77$		−	0.263943i		−	0.00342783i
$78$		0			0
$79$	105.981			1.34153			0.670767	−	0.741669i	$-0.265965\pi$
$79$	105.981			1.34153			0.670767	+	0.741669i	$0.265965\pi$
$80$	−23.5593	+	23.5593i	−0.294491	+	0.294491i
$81$	−14.6162			−0.180447
$82$			36.4405i			0.444396i
$83$	27.2221	−	27.2221i	0.327977	−	0.327977i	−0.523840	−	0.851817i	$-0.675501\pi$
$83$	27.2221	−	27.2221i	0.327977	−	0.327977i	0.851817	+	0.523840i	$0.175501\pi$
$84$	2.40656	−	2.40656i	0.0286495	−	0.0286495i
$85$	−16.9664	−	16.9664i	−0.199604	−	0.199604i
$86$	29.3186	+	29.3186i	0.340914	+	0.340914i
$87$	−145.271			−1.66978
$88$			2.09515i			0.0238085i
$89$	60.1398	+	60.1398i	0.675728	+	0.675728i	0.959031	−	0.283303i	$-0.0914301\pi$
$89$	60.1398	+	60.1398i	0.675728	+	0.675728i	−0.283303	+	0.959031i	$0.591430\pi$
$90$			162.650i			1.80722i
$91$		0			0
$92$	−45.7902			−0.497720
$93$	70.9825	−	70.9825i	0.763253	−	0.763253i
$94$	42.4001			0.451065
$95$			90.5025i			0.952658i
$96$	−19.1030	+	19.1030i	−0.198989	+	0.198989i
$97$	−14.3732	+	14.3732i	−0.148177	+	0.148177i	−0.777303	−	0.629126i	$-0.783413\pi$
$97$	−14.3732	+	14.3732i	−0.148177	+	0.148177i	0.629126	+	0.777303i	$0.283413\pi$
$98$	48.8730	+	48.8730i	0.498704	+	0.498704i
$99$	7.23232	+	7.23232i	0.0730537	+	0.0730537i
$100$	−88.7596			−0.887596
$101$			27.8238i			0.275484i	0.990468	+	0.137742i	$0.0439844\pi$
$101$			27.8238i			0.275484i	−0.990468	+	0.137742i	$0.956016\pi$
$102$	−13.7571	−	13.7571i	−0.134874	−	0.134874i
$103$		−	68.0852i		−	0.661021i	−0.943802	−	0.330511i	$-0.892779\pi$
$103$		−	68.0852i		−	0.661021i	0.943802	−	0.330511i	$-0.107221\pi$
$104$		0			0
$105$	14.1742			0.134992
$106$	85.8410	−	85.8410i	0.809821	−	0.809821i
$107$	−128.599			−1.20186			−0.600930	−	0.799301i	$-0.705203\pi$
$107$	−128.599			−1.20186			−0.600930	+	0.799301i	$0.705203\pi$
$108$			45.9210i			0.425194i
$109$	30.5407	−	30.5407i	0.280190	−	0.280190i	−0.552995	−	0.833185i	$-0.686515\pi$
$109$	30.5407	−	30.5407i	0.280190	−	0.280190i	0.833185	+	0.552995i	$0.186515\pi$
$110$	−6.17002	+	6.17002i	−0.0560911	+	0.0560911i
$111$	140.820	+	140.820i	1.26865	+	1.26865i
$112$	1.00783	+	1.00783i	0.00899844	+	0.00899844i
$113$	46.1413			0.408330			0.204165	−	0.978936i	$-0.434552\pi$
$113$	46.1413			0.408330			0.204165	+	0.978936i	$0.434552\pi$
$114$			73.3838i			0.643718i
$115$	−134.848	−	134.848i	−1.17259	−	1.17259i
$116$		−	60.8370i		−	0.524457i
$117$		0			0
$118$	141.526			1.19937
$119$	−0.725793	+	0.725793i	−0.00609910	+	0.00609910i
$120$	−112.513			−0.937608
$121$		−	120.451i		−	0.995465i
$122$	−15.4640	+	15.4640i	−0.126754	+	0.126754i
$123$	−87.0151	+	87.0151i	−0.707440	+	0.707440i
$124$	29.7263	+	29.7263i	0.239728	+	0.239728i
$125$	−114.143	−	114.143i	−0.913147	−	0.913147i
$126$	6.95789			0.0552214
$127$		−	230.649i		−	1.81613i	−0.418824	−	0.908067i	$-0.637558\pi$
$127$		−	230.649i		−	1.81613i	0.418824	−	0.908067i	$-0.362442\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			140.018i			1.08541i
$130$		0			0
$131$	162.262			1.23864			0.619321	−	0.785138i	$-0.287408\pi$
$131$	162.262			1.23864			0.619321	+	0.785138i	$0.287408\pi$
$132$	−5.00295	+	5.00295i	−0.0379011	+	0.0379011i
$133$	3.87155			0.0291094
$134$		−	98.4338i		−	0.734581i
$135$	−135.233	+	135.233i	−1.00173	+	1.00173i
$136$	5.76126	−	5.76126i	0.0423622	−	0.0423622i
$137$	73.0740	+	73.0740i	0.533387	+	0.533387i	0.921579	−	0.388192i	$-0.126900\pi$
$137$	73.0740	+	73.0740i	0.533387	+	0.533387i	−0.388192	+	0.921579i	$0.626900\pi$
$138$	−109.341	−	109.341i	−0.792328	−	0.792328i
$139$	−25.5784			−0.184017			−0.0920087	−	0.995758i	$-0.529329\pi$
$139$	−25.5784			−0.184017			−0.0920087	+	0.995758i	$0.529329\pi$
$140$			5.93590i			0.0423993i
$141$	101.246	+	101.246i	0.718056	+	0.718056i
$142$		−	137.927i		−	0.971318i
$143$		0			0
$144$	−55.2309			−0.383548
$145$	179.159	−	179.159i	1.23558	−	1.23558i
$146$	101.908			0.698001
$147$			233.405i			1.58779i
$148$	−58.9729	+	58.9729i	−0.398465	+	0.398465i
$149$	−19.0235	+	19.0235i	−0.127674	+	0.127674i	−0.768056	−	0.640382i	$-0.778776\pi$
$149$	−19.0235	+	19.0235i	−0.127674	+	0.127674i	0.640382	+	0.768056i	$0.278776\pi$
$150$	−211.947	−	211.947i	−1.41298	−	1.41298i
$151$	109.697	+	109.697i	0.726468	+	0.726468i	0.969914	−	0.243446i	$-0.0782780\pi$
$151$	109.697	+	109.697i	0.726468	+	0.726468i	−0.243446	+	0.969914i	$0.578278\pi$
$152$	−30.7319			−0.202183
$153$		−	39.7749i		−	0.259967i
$154$	0.263943	+	0.263943i	0.00171392	+	0.00171392i
$155$			175.082i			1.12956i
$156$		0			0
$157$	−142.680			−0.908790			−0.454395	−	0.890800i	$-0.650145\pi$
$157$	−142.680			−0.908790			−0.454395	+	0.890800i	$0.650145\pi$
$158$	−105.981	+	105.981i	−0.670767	+	0.670767i
$159$	409.955			2.57833
$160$		−	47.1185i		−	0.294491i
$161$	−5.76857	+	5.76857i	−0.0358296	+	0.0358296i
$162$	14.6162	−	14.6162i	0.0902233	−	0.0902233i
$163$	−18.7836	−	18.7836i	−0.115237	−	0.115237i	0.647137	−	0.762374i	$-0.275966\pi$
$163$	−18.7836	−	18.7836i	−0.115237	−	0.115237i	−0.762374	+	0.647137i	$0.775966\pi$
$164$	−36.4405	−	36.4405i	−0.222198	−	0.222198i
$165$	−29.4664			−0.178584
$166$			54.4441i			0.327977i
$167$	5.32150	+	5.32150i	0.0318653	+	0.0318653i	0.722860	−	0.690995i	$-0.242827\pi$
$167$	5.32150	+	5.32150i	0.0318653	+	0.0318653i	−0.690995	+	0.722860i	$0.742827\pi$
$168$			4.81312i			0.0286495i
$169$		0			0
$170$	33.9327			0.199604
$171$	−106.084	+	106.084i	−0.620376	+	0.620376i
$172$	−58.6372			−0.340914
$173$		−	28.8293i		−	0.166643i	−0.996523	−	0.0833216i	$-0.973447\pi$
$173$		−	28.8293i		−	0.166643i	0.996523	−	0.0833216i	$-0.0265529\pi$
$174$	145.271	−	145.271i	0.834891	−	0.834891i
$175$	−11.1818	+	11.1818i	−0.0638958	+	0.0638958i
$176$	−2.09515	−	2.09515i	−0.0119043	−	0.0119043i
$177$	337.945	+	337.945i	1.90929	+	1.90929i
$178$	−120.280			−0.675728
$179$			212.098i			1.18491i	0.805605	+	0.592453i	$0.201840\pi$
$179$			212.098i			1.18491i	−0.805605	+	0.592453i	$0.798160\pi$
$180$	−162.650	−	162.650i	−0.903610	−	0.903610i
$181$		−	112.088i		−	0.619270i	−0.950856	−	0.309635i	$-0.899793\pi$
$181$		−	112.088i		−	0.619270i	0.950856	−	0.309635i	$-0.100207\pi$
$182$		0			0
$183$	−73.8523			−0.403564
$184$	45.7902	−	45.7902i	0.248860	−	0.248860i
$185$	−347.339			−1.87751
$186$			141.965i			0.763253i
$187$	1.50884	−	1.50884i	0.00806865	−	0.00806865i
$188$	−42.4001	+	42.4001i	−0.225532	+	0.225532i
$189$	5.78504	+	5.78504i	0.0306087	+	0.0306087i
$190$	−90.5025	−	90.5025i	−0.476329	−	0.476329i
$191$	265.048			1.38769			0.693843	−	0.720126i	$-0.255916\pi$
$191$	265.048			1.38769			0.693843	+	0.720126i	$0.255916\pi$
$192$		−	38.2060i		−	0.198989i
$193$	112.568	+	112.568i	0.583256	+	0.583256i	0.935796	−	0.352541i	$-0.114682\pi$
$193$	112.568	+	112.568i	0.583256	+	0.583256i	−0.352541	+	0.935796i	$0.614682\pi$
$194$		−	28.7464i		−	0.148177i
$195$		0			0
$196$	−97.7461			−0.498704
$197$	−212.704	+	212.704i	−1.07972	+	1.07972i	−0.0831819	+	0.996534i	$0.526508\pi$
$197$	−212.704	+	212.704i	−1.07972	+	1.07972i	−0.996534	+	0.0831819i	$0.973492\pi$
$198$	−14.4646			−0.0730537
$199$		−	187.319i		−	0.941301i	−0.882320	−	0.470650i	$-0.844019\pi$
$199$		−	187.319i		−	0.941301i	0.882320	−	0.470650i	$-0.155981\pi$
$200$	88.7596	−	88.7596i	0.443798	−	0.443798i
$201$	235.047	−	235.047i	1.16939	−	1.16939i
$202$	−27.8238	−	27.8238i	−0.137742	−	0.137742i
$203$	−7.66414	−	7.66414i	−0.0377544	−	0.0377544i
$204$	27.5143			0.134874
$205$		−	214.627i		−	1.04696i
$206$	68.0852	+	68.0852i	0.330511	+	0.330511i
$207$		−	316.130i		−	1.52720i
$208$		0			0
$209$	−8.04849			−0.0385095
$210$	−14.1742	+	14.1742i	−0.0674961	+	0.0674961i
$211$	169.813			0.804801			0.402401	−	0.915464i	$-0.368176\pi$
$211$	169.813			0.804801			0.402401	+	0.915464i	$0.368176\pi$
$212$			171.682i			0.809821i
$213$	329.353	−	329.353i	1.54626	−	1.54626i
$214$	128.599	−	128.599i	0.600930	−	0.600930i
$215$	−172.681	−	172.681i	−0.803168	−	0.803168i
$216$	−45.9210	−	45.9210i	−0.212597	−	0.212597i
$217$	7.48972			0.0345148
$218$			61.0814i			0.280190i
$219$	243.344	+	243.344i	1.11116	+	1.11116i
$220$		−	12.3400i		−	0.0560911i
$221$		0			0
$222$	−281.639			−1.26865
$223$	170.054	−	170.054i	0.762572	−	0.762572i	−0.214215	−	0.976787i	$-0.568719\pi$
$223$	170.054	−	170.054i	0.762572	−	0.762572i	0.976787	+	0.214215i	$0.0687192\pi$
$224$	−2.01565			−0.00899844
$225$		−	612.784i		−	2.72349i
$226$	−46.1413	+	46.1413i	−0.204165	+	0.204165i
$227$	63.9791	−	63.9791i	0.281846	−	0.281846i	−0.551999	−	0.833845i	$-0.686135\pi$
$227$	63.9791	−	63.9791i	0.281846	−	0.281846i	0.833845	+	0.551999i	$0.186135\pi$
$228$	−73.3838	−	73.3838i	−0.321859	−	0.321859i
$229$	−248.887	−	248.887i	−1.08684	−	1.08684i	−0.995852	−	0.0909923i	$-0.970996\pi$
$229$	−248.887	−	248.887i	−1.08684	−	1.08684i	−0.0909923	−	0.995852i	$-0.529004\pi$
$230$	269.696			1.17259
$231$			1.26053i			0.00545682i
$232$	60.8370	+	60.8370i	0.262228	+	0.262228i
$233$			384.870i			1.65180i	0.563815	+	0.825901i	$0.309333\pi$
$233$			384.870i			1.65180i	−0.563815	+	0.825901i	$0.690667\pi$
$234$		0			0
$235$	−249.728			−1.06267
$236$	−141.526	+	141.526i	−0.599685	+	0.599685i
$237$	−506.139			−2.13561
$238$		−	1.45159i		−	0.00609910i
$239$	−210.628	+	210.628i	−0.881290	+	0.881290i	−0.993666	−	0.112375i	$-0.964154\pi$
$239$	−210.628	+	210.628i	−0.881290	+	0.881290i	0.112375	+	0.993666i	$0.464154\pi$
$240$	112.513	−	112.513i	0.468804	−	0.468804i
$241$	132.472	+	132.472i	0.549675	+	0.549675i	0.926347	−	0.376672i	$-0.122932\pi$
$241$	132.472	+	132.472i	0.549675	+	0.549675i	−0.376672	+	0.926347i	$0.622932\pi$
$242$	120.451	+	120.451i	0.497733	+	0.497733i
$243$	276.447			1.13764
$244$		−	30.9281i		−	0.126754i
$245$	−287.853	−	287.853i	−1.17491	−	1.17491i
$246$		−	174.030i		−	0.707440i
$247$		0			0
$248$	−59.4525			−0.239728
$249$	−130.006	+	130.006i	−0.522111	+	0.522111i
$250$	228.287			0.913147
$251$		−	100.518i		−	0.400471i	−0.979748	−	0.200236i	$-0.935829\pi$
$251$		−	100.518i		−	0.400471i	0.979748	−	0.200236i	$-0.0641708\pi$
$252$	−6.95789	+	6.95789i	−0.0276107	+	0.0276107i
$253$	11.9922	−	11.9922i	0.0473999	−	0.0473999i
$254$	230.649	+	230.649i	0.908067	+	0.908067i
$255$	81.0270	+	81.0270i	0.317753	+	0.317753i
$256$	16.0000			0.0625000
$257$			69.5049i			0.270447i	0.990815	+	0.135223i	$0.0431752\pi$
$257$			69.5049i			0.270447i	−0.990815	+	0.135223i	$0.956825\pi$
$258$	−140.018	−	140.018i	−0.542706	−	0.542706i
$259$			14.8586i			0.0573691i
$260$		0			0
$261$	420.010			1.60924
$262$	−162.262	+	162.262i	−0.619321	+	0.619321i
$263$	259.178			0.985469			0.492735	−	0.870180i	$-0.335997\pi$
$263$	259.178			0.985469			0.492735	+	0.870180i	$0.335997\pi$
$264$		−	10.0059i		−	0.0379011i
$265$	−505.587	+	505.587i	−1.90788	+	1.90788i
$266$	−3.87155	+	3.87155i	−0.0145547	+	0.0145547i
$267$	−287.212	−	287.212i	−1.07570	−	1.07570i
$268$	98.4338	+	98.4338i	0.367290	+	0.367290i
$269$	42.0112			0.156176			0.0780878	−	0.996946i	$-0.475119\pi$
$269$	42.0112			0.156176			0.0780878	+	0.996946i	$0.475119\pi$
$270$		−	270.466i		−	1.00173i
$271$	−222.800	−	222.800i	−0.822139	−	0.822139i	0.164275	−	0.986415i	$-0.447471\pi$
$271$	−222.800	−	222.800i	−0.822139	−	0.822139i	−0.986415	+	0.164275i	$0.947471\pi$
$272$			11.5225i			0.0423622i
$273$		0			0
$274$	−146.148			−0.533387
$275$	23.2456	−	23.2456i	0.0845294	−	0.0845294i
$276$	218.682			0.792328
$277$		−	189.673i		−	0.684739i	−0.939565	−	0.342370i	$-0.888771\pi$
$277$		−	189.673i		−	0.684739i	0.939565	−	0.342370i	$-0.111229\pi$
$278$	25.5784	−	25.5784i	0.0920087	−	0.0920087i
$279$	−205.226	+	205.226i	−0.735577	+	0.735577i
$280$	−5.93590	−	5.93590i	−0.0211997	−	0.0211997i
$281$	32.8661	+	32.8661i	0.116961	+	0.116961i	0.763165	−	0.646204i	$-0.223644\pi$
$281$	32.8661	+	32.8661i	0.116961	+	0.116961i	−0.646204	+	0.763165i	$0.723644\pi$
$282$	−202.492			−0.718056
$283$		−	526.965i		−	1.86207i	−0.364934	−	0.931033i	$-0.618909\pi$
$283$		−	526.965i		−	1.86207i	0.364934	−	0.931033i	$-0.381091\pi$
$284$	137.927	+	137.927i	0.485659	+	0.485659i
$285$		−	432.217i		−	1.51655i
$286$		0			0
$287$	−9.18141			−0.0319910
$288$	55.2309	−	55.2309i	0.191774	−	0.191774i
$289$	280.702			0.971287
$290$			358.319i			1.23558i
$291$	68.6426	−	68.6426i	0.235885	−	0.235885i
$292$	−101.908	+	101.908i	−0.349001	+	0.349001i
$293$	−96.8335	−	96.8335i	−0.330490	−	0.330490i	0.522283	−	0.852772i	$-0.325081\pi$
$293$	−96.8335	−	96.8335i	−0.330490	−	0.330490i	−0.852772	+	0.522283i	$0.825081\pi$
$294$	−233.405	−	233.405i	−0.793895	−	0.793895i
$295$	−833.560			−2.82563
$296$		−	117.946i		−	0.398465i
$297$	−12.0264	−	12.0264i	−0.0404930	−	0.0404930i
$298$		−	38.0469i		−	0.127674i
$299$		0			0
$300$	423.893			1.41298
$301$	−7.38701	+	7.38701i	−0.0245416	+	0.0245416i
$302$	−219.393			−0.726468
$303$		−	132.880i		−	0.438546i
$304$	30.7319	−	30.7319i	0.101092	−	0.101092i
$305$	91.0803	−	91.0803i	0.298624	−	0.298624i
$306$	39.7749	+	39.7749i	0.129983	+	0.129983i
$307$	306.038	+	306.038i	0.996866	+	0.996866i	0.999995	−	0.00312957i	$-0.000996174\pi$
$307$	306.038	+	306.038i	0.996866	+	0.996866i	−0.00312957	+	0.999995i	$0.500996\pi$
$308$	−0.527886			−0.00171392
$309$			325.157i			1.05229i
$310$	−175.082	−	175.082i	−0.564781	−	0.564781i
$311$		−	138.274i		−	0.444611i	−0.974977	−	0.222305i	$-0.928642\pi$
$311$		−	138.274i		−	0.444611i	0.974977	−	0.222305i	$-0.0713582\pi$
$312$		0			0
$313$	525.434			1.67870			0.839352	−	0.543589i	$-0.182935\pi$
$313$	525.434			1.67870			0.839352	+	0.543589i	$0.182935\pi$
$314$	142.680	−	142.680i	0.454395	−	0.454395i
$315$	−40.9807			−0.130097
$316$		−	211.962i		−	0.670767i
$317$	−24.3899	+	24.3899i	−0.0769397	+	0.0769397i	−0.744529	−	0.667590i	$-0.767326\pi$
$317$	−24.3899	+	24.3899i	−0.0769397	+	0.0769397i	0.667590	+	0.744529i	$0.267326\pi$
$318$	−409.955	+	409.955i	−1.28917	+	1.28917i
$319$	15.9328	+	15.9328i	0.0499462	+	0.0499462i
$320$	47.1185	+	47.1185i	0.147245	+	0.147245i
$321$	614.156			1.91326
$322$		−	11.5371i		−	0.0358296i
$323$	22.1318	+	22.1318i	0.0685194	+	0.0685194i
$324$			29.2323i			0.0902233i
$325$		0			0
$326$	37.5671			0.115237
$327$	−145.855	+	145.855i	−0.446039	+	0.446039i
$328$	72.8809			0.222198
$329$			10.6830i			0.0324710i
$330$	29.4664	−	29.4664i	0.0892922	−	0.0892922i
$331$	−15.6801	+	15.6801i	−0.0473718	+	0.0473718i	−0.730396	−	0.683024i	$-0.760664\pi$
$331$	−15.6801	+	15.6801i	−0.0473718	+	0.0473718i	0.683024	+	0.730396i	$0.260664\pi$
$332$	−54.4441	−	54.4441i	−0.163988	−	0.163988i
$333$	−407.141	−	407.141i	−1.22264	−	1.22264i
$334$	−10.6430			−0.0318653
$335$			579.757i			1.73062i
$336$	−4.81312	−	4.81312i	−0.0143248	−	0.0143248i
$337$			544.688i			1.61629i	0.588987	+	0.808143i	$0.299527\pi$
$337$			544.688i			1.61629i	−0.588987	+	0.808143i	$0.700473\pi$
$338$		0			0
$339$	−220.359			−0.650026
$340$	−33.9327	+	33.9327i	−0.0998021	+	0.0998021i
$341$	−15.5702			−0.0456605
$342$		−	212.169i		−	0.620376i
$343$	−24.6597	+	24.6597i	−0.0718943	+	0.0718943i
$344$	58.6372	−	58.6372i	0.170457	−	0.170457i
$345$	643.999	+	643.999i	1.86666	+	1.86666i
$346$	28.8293	+	28.8293i	0.0833216	+	0.0833216i
$347$	−640.601			−1.84611			−0.923057	−	0.384663i	$-0.874317\pi$
$347$	−640.601			−1.84611			−0.923057	+	0.384663i	$0.874317\pi$
$348$			290.542i			0.834891i
$349$	−42.7706	−	42.7706i	−0.122552	−	0.122552i	0.643171	−	0.765723i	$-0.277619\pi$
$349$	−42.7706	−	42.7706i	−0.122552	−	0.122552i	−0.765723	+	0.643171i	$0.777619\pi$
$350$		−	22.3635i		−	0.0638958i
$351$		0			0
$352$	4.19030			0.0119043
$353$	207.432	−	207.432i	0.587625	−	0.587625i	−0.349362	−	0.936988i	$-0.613602\pi$
$353$	207.432	−	207.432i	0.587625	−	0.587625i	0.936988	+	0.349362i	$0.113602\pi$
$354$	−675.890			−1.90929
$355$			812.365i			2.28835i
$356$	120.280	−	120.280i	0.337864	−	0.337864i
$357$	3.46620	−	3.46620i	0.00970925	−	0.00970925i
$358$	−212.098	−	212.098i	−0.592453	−	0.592453i
$359$	118.752	+	118.752i	0.330785	+	0.330785i	0.852885	−	0.522099i	$-0.174851\pi$
$359$	118.752	+	118.752i	0.330785	+	0.330785i	−0.522099	+	0.852885i	$0.674851\pi$
$360$	325.300			0.903610
$361$			242.944i			0.672975i
$362$	112.088	+	112.088i	0.309635	+	0.309635i
$363$			575.245i			1.58470i
$364$		0			0
$365$	−600.220			−1.64444
$366$	73.8523	−	73.8523i	0.201782	−	0.201782i
$367$	−102.316			−0.278789			−0.139395	−	0.990237i	$-0.544516\pi$
$367$	−102.316			−0.278789			−0.139395	+	0.990237i	$0.544516\pi$
$368$			91.5805i			0.248860i
$369$	251.580	−	251.580i	0.681789	−	0.681789i
$370$	347.339	−	347.339i	0.938755	−	0.938755i
$371$	21.6282	+	21.6282i	0.0582970	+	0.0582970i
$372$	−141.965	−	141.965i	−0.381626	−	0.381626i
$373$	604.616			1.62095			0.810477	−	0.585770i	$-0.199208\pi$
$373$	604.616			1.62095			0.810477	+	0.585770i	$0.199208\pi$
$374$			3.01767i			0.00806865i
$375$	545.119	+	545.119i	1.45365	+	1.45365i
$376$		−	84.8001i		−	0.225532i
$377$		0			0
$378$	−11.5701			−0.0306087
$379$	271.338	−	271.338i	0.715931	−	0.715931i	−0.251838	−	0.967769i	$-0.581035\pi$
$379$	271.338	−	271.338i	0.715931	−	0.715931i	0.967769	+	0.251838i	$0.0810350\pi$
$380$	181.005			0.476329
$381$			1101.52i			2.89113i
$382$	−265.048	+	265.048i	−0.693843	+	0.693843i
$383$	289.692	−	289.692i	0.756377	−	0.756377i	−0.219284	−	0.975661i	$-0.570372\pi$
$383$	289.692	−	289.692i	0.756377	−	0.756377i	0.975661	+	0.219284i	$0.0703722\pi$
$384$	38.2060	+	38.2060i	0.0994947	+	0.0994947i
$385$	−1.55458	−	1.55458i	−0.00403786	−	0.00403786i
$386$	−225.137			−0.583256
$387$		−	404.823i		−	1.04605i
$388$	28.7464	+	28.7464i	0.0740885	+	0.0740885i
$389$			43.6909i			0.112316i	0.998422	+	0.0561579i	$0.0178850\pi$
$389$			43.6909i			0.112316i	−0.998422	+	0.0561579i	$0.982115\pi$
$390$		0			0
$391$	−65.9523			−0.168676
$392$	97.7461	−	97.7461i	0.249352	−	0.249352i
$393$	−774.922			−1.97181
$394$		−	425.408i		−	1.07972i
$395$	624.209	−	624.209i	1.58028	−	1.58028i
$396$	14.4646	−	14.4646i	0.0365268	−	0.0365268i
$397$	193.785	+	193.785i	0.488122	+	0.488122i	0.907713	−	0.419591i	$-0.137826\pi$
$397$	193.785	+	193.785i	0.488122	+	0.488122i	−0.419591	+	0.907713i	$0.637826\pi$
$398$	187.319	+	187.319i	0.470650	+	0.470650i
$399$	−18.4895			−0.0463396
$400$			177.519i			0.443798i
$401$	63.0185	+	63.0185i	0.157153	+	0.157153i	0.781304	−	0.624151i	$-0.214555\pi$
$401$	63.0185	+	63.0185i	0.157153	+	0.157153i	−0.624151	+	0.781304i	$0.714555\pi$
$402$			470.095i			1.16939i
$403$		0			0
$404$	55.6477			0.137742
$405$	−86.0865	+	86.0865i	−0.212559	+	0.212559i
$406$	15.3283			0.0377544
$407$		−	30.8893i		−	0.0758950i
$408$	−27.5143	+	27.5143i	−0.0674370	+	0.0674370i
$409$	−516.276	+	516.276i	−1.26229	+	1.26229i	−0.312307	+	0.949981i	$0.601102\pi$
$409$	−516.276	+	516.276i	−1.26229	+	1.26229i	−0.949981	+	0.312307i	$0.898898\pi$
$410$	214.627	+	214.627i	0.523482	+	0.523482i
$411$	−348.983	−	348.983i	−0.849107	−	0.849107i
$412$	−136.170			−0.330511
$413$			35.6583i			0.0863397i
$414$	316.130	+	316.130i	0.763598	+	0.763598i
$415$		−	320.666i		−	0.772688i
$416$		0			0
$417$	122.156			0.292940
$418$	8.04849	−	8.04849i	0.0192548	−	0.0192548i
$419$	260.975			0.622851			0.311426	−	0.950271i	$-0.399194\pi$
$419$	260.975			0.622851			0.311426	+	0.950271i	$0.399194\pi$
$420$		−	28.3484i		−	0.0674961i
$421$	103.038	−	103.038i	0.244745	−	0.244745i	−0.574065	−	0.818810i	$-0.694634\pi$
$421$	103.038	−	103.038i	0.244745	−	0.244745i	0.818810	+	0.574065i	$0.194634\pi$
$422$	−169.813	+	169.813i	−0.402401	+	0.402401i
$423$	−292.724	−	292.724i	−0.692020	−	0.692020i
$424$	−171.682	−	171.682i	−0.404910	−	0.404910i
$425$	−127.842			−0.300804
$426$			658.705i			1.54626i
$427$	−3.89626	−	3.89626i	−0.00912474	−	0.00912474i
$428$			257.198i			0.600930i
$429$		0			0
$430$	345.362			0.803168
$431$	96.3288	−	96.3288i	0.223501	−	0.223501i	−0.586470	−	0.809971i	$-0.699483\pi$
$431$	96.3288	−	96.3288i	0.223501	−	0.223501i	0.809971	+	0.586470i	$0.199483\pi$
$432$	91.8419			0.212597
$433$			201.358i			0.465031i	0.972593	+	0.232516i	$0.0746956\pi$
$433$			201.358i			0.465031i	−0.972593	+	0.232516i	$0.925304\pi$
$434$	−7.48972	+	7.48972i	−0.0172574	+	0.0172574i
$435$	−855.619	+	855.619i	−1.96694	+	1.96694i
$436$	−61.0814	−	61.0814i	−0.140095	−	0.140095i
$437$	175.902	+	175.902i	0.402523	+	0.402523i
$438$	−486.687			−1.11116
$439$			74.3517i			0.169366i	0.996408	+	0.0846830i	$0.0269878\pi$
$439$			74.3517i			0.169366i	−0.996408	+	0.0846830i	$0.973012\pi$
$440$	12.3400	+	12.3400i	0.0280455	+	0.0280455i
$441$		−	674.826i		−	1.53022i
$442$		0			0
$443$	130.644			0.294908			0.147454	−	0.989069i	$-0.452892\pi$
$443$	130.644			0.294908			0.147454	+	0.989069i	$0.452892\pi$
$444$	281.639	−	281.639i	0.634323	−	0.634323i
$445$	708.424			1.59196
$446$			340.107i			0.762572i
$447$	90.8512	−	90.8512i	0.203246	−	0.203246i
$448$	2.01565	−	2.01565i	0.00449922	−	0.00449922i
$449$	−509.691	−	509.691i	−1.13517	−	1.13517i	−0.989305	−	0.145864i	$-0.953404\pi$
$449$	−509.691	−	509.691i	−1.13517	−	1.13517i	−0.145864	−	0.989305i	$-0.546596\pi$
$450$	612.784	+	612.784i	1.36174	+	1.36174i
$451$	19.0871			0.0423216
$452$		−	92.2826i		−	0.204165i
$453$	−523.883	−	523.883i	−1.15647	−	1.15647i
$454$			127.958i			0.281846i
$455$		0			0
$456$	146.768			0.321859
$457$	256.408	−	256.408i	0.561069	−	0.561069i	−0.368542	−	0.929611i	$-0.620143\pi$
$457$	256.408	−	256.408i	0.561069	−	0.561069i	0.929611	+	0.368542i	$0.120143\pi$
$458$	497.774			1.08684
$459$			66.1406i			0.144097i
$460$	−269.696	+	269.696i	−0.586295	+	0.586295i
$461$	611.809	−	611.809i	1.32713	−	1.32713i	0.419274	−	0.907860i	$-0.362285\pi$
$461$	611.809	−	611.809i	1.32713	−	1.32713i	0.907860	−	0.419274i	$-0.137715\pi$
$462$	−1.26053	−	1.26053i	−0.00272841	−	0.00272841i
$463$	−163.492	−	163.492i	−0.353114	−	0.353114i	0.508153	−	0.861267i	$-0.330328\pi$
$463$	−163.492	−	163.492i	−0.353114	−	0.353114i	−0.861267	+	0.508153i	$0.830328\pi$
$464$	−121.674			−0.262228
$465$		−	836.147i		−	1.79817i
$466$	−384.870	−	384.870i	−0.825901	−	0.825901i
$467$		−	242.866i		−	0.520056i	−0.965601	−	0.260028i	$-0.916268\pi$
$467$		−	242.866i		−	0.520056i	0.965601	−	0.260028i	$-0.0837318\pi$
$468$		0			0
$469$	24.8010			0.0528807
$470$	249.728	−	249.728i	0.531337	−	0.531337i
$471$	681.403			1.44672
$472$		−	283.051i		−	0.599685i
$473$	15.3567	−	15.3567i	0.0324666	−	0.0324666i
$474$	506.139	−	506.139i	1.06780	−	1.06780i
$475$	340.969	+	340.969i	0.717829	+	0.717829i
$476$	1.45159	+	1.45159i	0.00304955	+	0.00304955i
$477$	−1185.27			−2.48484
$478$		−	421.257i		−	0.881290i
$479$	158.062	+	158.062i	0.329983	+	0.329983i	0.852580	−	0.522597i	$-0.175037\pi$
$479$	158.062	+	158.062i	0.329983	+	0.329983i	−0.522597	+	0.852580i	$0.675037\pi$
$480$			225.026i			0.468804i
$481$		0			0
$482$	−264.943			−0.549675
$483$	27.5492	−	27.5492i	0.0570377	−	0.0570377i
$484$	−240.903			−0.497733
$485$			169.311i			0.349094i
$486$	−276.447	+	276.447i	−0.568822	+	0.568822i
$487$	15.2557	−	15.2557i	0.0313258	−	0.0313258i	−0.691270	−	0.722596i	$-0.742949\pi$
$487$	15.2557	−	15.2557i	0.0313258	−	0.0313258i	0.722596	+	0.691270i	$0.242949\pi$
$488$	30.9281	+	30.9281i	0.0633772	+	0.0633772i
$489$	89.7055	+	89.7055i	0.183447	+	0.183447i
$490$	575.706			1.17491
$491$			58.3092i			0.118756i	0.998236	+	0.0593780i	$0.0189117\pi$
$491$			58.3092i			0.118756i	−0.998236	+	0.0593780i	$0.981088\pi$
$492$	174.030	+	174.030i	0.353720	+	0.353720i
$493$		−	87.6244i		−	0.177737i
$494$		0			0
$495$	85.1940			0.172109
$496$	59.4525	−	59.4525i	0.119864	−	0.119864i
$497$	34.7516			0.0699228
$498$		−	260.011i		−	0.522111i
$499$	−625.494	+	625.494i	−1.25350	+	1.25350i	−0.299353	+	0.954142i	$0.596771\pi$
$499$	−625.494	+	625.494i	−1.25350	+	1.25350i	−0.954142	+	0.299353i	$0.903229\pi$
$500$	−228.287	+	228.287i	−0.456573	+	0.456573i
$501$	−25.4141	−	25.4141i	−0.0507268	−	0.0507268i
$502$	100.518	+	100.518i	0.200236	+	0.200236i
$503$	−10.5141			−0.0209029			−0.0104514	−	0.999945i	$-0.503327\pi$
$503$	−10.5141			−0.0209029			−0.0104514	+	0.999945i	$0.503327\pi$
$504$		−	13.9158i		−	0.0276107i
$505$	163.877	+	163.877i	0.324509	+	0.324509i
$506$			23.9843i			0.0473999i
$507$		0			0
$508$	−461.298			−0.908067
$509$	−72.0472	+	72.0472i	−0.141547	+	0.141547i	−0.774329	−	0.632783i	$-0.781913\pi$
$509$	−72.0472	+	72.0472i	−0.141547	+	0.141547i	0.632783	+	0.774329i	$0.281913\pi$
$510$	−162.054			−0.317753
$511$			25.6764i			0.0502474i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	176.405	−	176.405i	0.343869	−	0.343869i
$514$	−69.5049	−	69.5049i	−0.135223	−	0.135223i
$515$	−401.009	−	401.009i	−0.778658	−	0.778658i
$516$	280.036			0.542706
$517$		−	22.2086i		−	0.0429567i
$518$	−14.8586	−	14.8586i	−0.0286845	−	0.0286845i
$519$			137.681i			0.265282i
$520$		0			0
$521$	170.985			0.328185			0.164093	−	0.986445i	$-0.447530\pi$
$521$	170.985			0.328185			0.164093	+	0.986445i	$0.447530\pi$
$522$	−420.010	+	420.010i	−0.804618	+	0.804618i
$523$	−835.390			−1.59730			−0.798652	−	0.601793i	$-0.794453\pi$
$523$	−835.390			−1.59730			−0.798652	+	0.601793i	$0.794453\pi$
$524$		−	324.524i		−	0.619321i
$525$	53.4013	−	53.4013i	0.101717	−	0.101717i
$526$	−259.178	+	259.178i	−0.492735	+	0.492735i
$527$	42.8152	+	42.8152i	0.0812432	+	0.0812432i
$528$	10.0059	+	10.0059i	0.0189506	+	0.0189506i
$529$	4.81369			0.00909960
$530$		−	1011.17i		−	1.90788i
$531$	−977.074	−	977.074i	−1.84006	−	1.84006i
$532$		−	7.74309i		−	0.0145547i
$533$		0			0
$534$	574.424			1.07570
$535$	−757.425	+	757.425i	−1.41575	+	1.41575i
$536$	−196.868			−0.367290
$537$		−	1012.93i		−	1.88627i
$538$	−42.0112	+	42.0112i	−0.0780878	+	0.0780878i
$539$	25.5991	−	25.5991i	0.0474937	−	0.0474937i
$540$	270.466	+	270.466i	0.500863	+	0.500863i
$541$	−503.966	−	503.966i	−0.931545	−	0.931545i	0.0662572	−	0.997803i	$-0.478894\pi$
$541$	−503.966	−	503.966i	−0.931545	−	0.931545i	−0.997803	+	0.0662572i	$0.978894\pi$
$542$	445.599			0.822139
$543$			535.303i			0.985825i
$544$	−11.5225	−	11.5225i	−0.0211811	−	0.0211811i
$545$		−	359.758i		−	0.660107i
$546$		0			0
$547$	−249.081			−0.455359			−0.227680	−	0.973736i	$-0.573114\pi$
$547$	−249.081			−0.455359			−0.227680	+	0.973736i	$0.573114\pi$
$548$	146.148	−	146.148i	0.266694	−	0.266694i
$549$	213.523			0.388931
$550$			46.4912i			0.0845294i
$551$	−233.704	+	233.704i	−0.424146	+	0.424146i
$552$	−218.682	+	218.682i	−0.396164	+	0.396164i
$553$	−26.7026	−	26.7026i	−0.0482868	−	0.0482868i
$554$	189.673	+	189.673i	0.342370	+	0.342370i
$555$	1658.80			2.98883
$556$			51.1568i			0.0920087i
$557$	462.831	+	462.831i	0.830936	+	0.830936i	0.987645	−	0.156709i	$-0.0500884\pi$
$557$	462.831	+	462.831i	0.830936	+	0.830936i	−0.156709	+	0.987645i	$0.550088\pi$
$558$		−	410.452i		−	0.735577i
$559$		0			0
$560$	11.8718			0.0211997
$561$	−7.20582	+	7.20582i	−0.0128446	+	0.0128446i
$562$	−65.7322			−0.116961
$563$		−	956.407i		−	1.69877i	−0.527774	−	0.849385i	$-0.676973\pi$
$563$		−	956.407i		−	1.69877i	0.527774	−	0.849385i	$-0.323027\pi$
$564$	202.492	−	202.492i	0.359028	−	0.359028i
$565$	271.764	−	271.764i	0.480997	−	0.480997i
$566$	526.965	+	526.965i	0.931033	+	0.931033i
$567$	3.68264	+	3.68264i	0.00649495	+	0.00649495i
$568$	−275.854			−0.485659
$569$			325.258i			0.571630i	0.958285	+	0.285815i	$0.0922643\pi$
$569$			325.258i			0.571630i	−0.958285	+	0.285815i	$0.907736\pi$
$570$	432.217	+	432.217i	0.758275	+	0.758275i
$571$		−	218.946i		−	0.383442i	−0.981449	−	0.191721i	$-0.938593\pi$
$571$		−	218.946i		−	0.383442i	0.981449	−	0.191721i	$-0.0614069\pi$
$572$		0			0
$573$	−1265.80			−2.20908
$574$	9.18141	−	9.18141i	0.0159955	−	0.0159955i
$575$	−1016.08			−1.76710
$576$			110.462i			0.191774i
$577$	478.578	−	478.578i	0.829425	−	0.829425i	−0.158012	−	0.987437i	$-0.550508\pi$
$577$	478.578	−	478.578i	0.829425	−	0.829425i	0.987437	+	0.158012i	$0.0505084\pi$
$578$	−280.702	+	280.702i	−0.485644	+	0.485644i
$579$	−537.597	−	537.597i	−0.928493	−	0.928493i
$580$	−358.319	−	358.319i	−0.617791	−	0.617791i
$581$	−13.7175			−0.0236102
$582$			137.285i			0.235885i
$583$	−44.9624	−	44.9624i	−0.0771225	−	0.0771225i
$584$		−	203.816i		−	0.349001i
$585$		0			0
$586$	193.667			0.330490
$587$	−175.333	+	175.333i	−0.298694	+	0.298694i	−0.840502	−	0.541808i	$-0.817740\pi$
$587$	−175.333	+	175.333i	−0.298694	+	0.298694i	0.541808	+	0.840502i	$0.317740\pi$
$588$	466.810			0.793895
$589$		−	228.386i		−	0.387752i
$590$	833.560	−	833.560i	1.41281	−	1.41281i
$591$	1015.82	−	1015.82i	1.71882	−	1.71882i
$592$	117.946	+	117.946i	0.199233	+	0.199233i
$593$	107.905	+	107.905i	0.181964	+	0.181964i	0.792211	−	0.610247i	$-0.208930\pi$
$593$	107.905	+	107.905i	0.181964	+	0.181964i	−0.610247	+	0.792211i	$0.708930\pi$
$594$	24.0528			0.0404930
$595$			8.54957i			0.0143690i
$596$	38.0469	+	38.0469i	0.0638371	+	0.0638371i
$597$			894.587i			1.49847i
$598$		0			0
$599$	788.030			1.31558			0.657788	−	0.753203i	$-0.271492\pi$
$599$	788.030			1.31558			0.657788	+	0.753203i	$0.271492\pi$
$600$	−423.893	+	423.893i	−0.706488	+	0.706488i
$601$	383.052			0.637358			0.318679	−	0.947863i	$-0.396761\pi$
$601$	383.052			0.637358			0.318679	+	0.947863i	$0.396761\pi$
$602$		−	14.7740i		−	0.0245416i
$603$	−679.574	+	679.574i	−1.12699	+	1.12699i
$604$	219.393	−	219.393i	0.363234	−	0.363234i
$605$	−709.436	−	709.436i	−1.17262	−	1.17262i
$606$	132.880	+	132.880i	0.219273	+	0.219273i
$607$	237.780			0.391730			0.195865	−	0.980631i	$-0.437249\pi$
$607$	237.780			0.391730			0.195865	+	0.980631i	$0.437249\pi$
$608$			61.4638i			0.101092i
$609$	36.6020	+	36.6020i	0.0601017	+	0.0601017i
$610$			182.161i			0.298624i
$611$		0			0
$612$	−79.5499			−0.129983
$613$	−309.811	+	309.811i	−0.505401	+	0.505401i	−0.913111	−	0.407710i	$-0.866327\pi$
$613$	−309.811	+	309.811i	−0.505401	+	0.505401i	0.407710	+	0.913111i	$0.366327\pi$
$614$	−612.075			−0.996866
$615$			1025.01i			1.66668i
$616$	0.527886	−	0.527886i	0.000856959	−	0.000856959i
$617$	−81.8203	+	81.8203i	−0.132610	+	0.132610i	−0.770296	−	0.637686i	$-0.779892\pi$
$617$	−81.8203	+	81.8203i	−0.132610	+	0.132610i	0.637686	+	0.770296i	$0.279892\pi$
$618$	−325.157	−	325.157i	−0.526145	−	0.526145i
$619$	471.622	+	471.622i	0.761910	+	0.761910i	0.976667	−	0.214757i	$-0.0688961\pi$
$619$	471.622	+	471.622i	0.761910	+	0.761910i	−0.214757	+	0.976667i	$0.568896\pi$
$620$	350.164			0.564781
$621$			525.683i			0.846510i
$622$	138.274	+	138.274i	0.222305	+	0.222305i
$623$		−	30.3052i		−	0.0486440i
$624$		0			0
$625$	−235.071			−0.376114
$626$	−525.434	+	525.434i	−0.839352	+	0.839352i
$627$	38.4375			0.0613038
$628$			285.360i			0.454395i
$629$	−84.9395	+	84.9395i	−0.135039	+	0.135039i
$630$	40.9807	−	40.9807i	0.0650487	−	0.0650487i
$631$	601.949	+	601.949i	0.953960	+	0.953960i	0.998986	−	0.0450262i	$-0.0143371\pi$
$631$	601.949	+	601.949i	0.953960	+	0.953960i	−0.0450262	+	0.998986i	$0.514337\pi$
$632$	211.962	+	211.962i	0.335383	+	0.335383i
$633$	−810.984			−1.28118
$634$		−	48.7798i		−	0.0769397i
$635$	−1358.48	−	1358.48i	−2.13934	−	2.13934i
$636$		−	819.909i		−	1.28917i
$637$		0			0
$638$	−31.8657			−0.0499462
$639$	−952.231	+	952.231i	−1.49019	+	1.49019i
$640$	−94.2370			−0.147245
$641$			29.2054i			0.0455622i	0.999740	+	0.0227811i	$0.00725207\pi$
$641$			29.2054i			0.0455622i	−0.999740	+	0.0227811i	$0.992748\pi$
$642$	−614.156	+	614.156i	−0.956630	+	0.956630i
$643$	144.515	−	144.515i	0.224752	−	0.224752i	−0.585744	−	0.810496i	$-0.699198\pi$
$643$	144.515	−	144.515i	0.224752	−	0.224752i	0.810496	+	0.585744i	$0.199198\pi$
$644$	11.5371	+	11.5371i	0.0179148	+	0.0179148i
$645$	824.681	+	824.681i	1.27857	+	1.27857i
$646$	−44.2636			−0.0685194
$647$			1057.30i			1.63415i	0.576528	+	0.817077i	$0.304407\pi$
$647$			1057.30i			1.63415i	−0.576528	+	0.817077i	$0.695593\pi$
$648$	−29.2323	−	29.2323i	−0.0451116	−	0.0451116i
$649$		−	74.1294i		−	0.114221i
$650$		0			0
$651$	−35.7690			−0.0549447
$652$	−37.5671	+	37.5671i	−0.0576183	+	0.0576183i
$653$	76.1010			0.116541			0.0582703	−	0.998301i	$-0.481441\pi$
$653$	76.1010			0.116541			0.0582703	+	0.998301i	$0.481441\pi$
$654$		−	291.709i		−	0.446039i
$655$	955.693	−	955.693i	1.45907	−	1.45907i
$656$	−72.8809	+	72.8809i	−0.111099	+	0.111099i
$657$	−703.560	−	703.560i	−1.07087	−	1.07087i
$658$	−10.6830	−	10.6830i	−0.0162355	−	0.0162355i
$659$	−843.635			−1.28017			−0.640087	−	0.768302i	$-0.721102\pi$
$659$	−843.635			−1.28017			−0.640087	+	0.768302i	$0.721102\pi$
$660$			58.9329i			0.0892922i
$661$	592.287	+	592.287i	0.896046	+	0.896046i	0.995084	−	0.0990373i	$-0.0315763\pi$
$661$	592.287	+	592.287i	0.896046	+	0.896046i	−0.0990373	+	0.995084i	$0.531576\pi$
$662$		−	31.3602i		−	0.0473718i
$663$		0			0
$664$	108.888			0.163988
$665$	22.8027	−	22.8027i	0.0342898	−	0.0342898i
$666$	814.281			1.22264
$667$		−	696.435i		−	1.04413i
$668$	10.6430	−	10.6430i	0.0159326	−	0.0159326i
$669$	−812.132	+	812.132i	−1.21395	+	1.21395i
$670$	−579.757	−	579.757i	−0.865308	−	0.865308i
$671$	8.09987	+	8.09987i	0.0120713	+	0.0120713i
$672$	9.62623			0.0143248
$673$		−	386.500i		−	0.574294i	−0.957887	−	0.287147i	$-0.907293\pi$
$673$		−	386.500i		−	0.574294i	0.957887	−	0.287147i	$-0.0927068\pi$
$674$	−544.688	−	544.688i	−0.808143	−	0.808143i
$675$			1018.98i			1.50960i
$676$		0			0
$677$	328.683			0.485500			0.242750	−	0.970089i	$-0.421951\pi$
$677$	328.683			0.485500			0.242750	+	0.970089i	$0.421951\pi$
$678$	220.359	−	220.359i	0.325013	−	0.325013i
$679$	7.24283			0.0106669
$680$		−	67.8654i		−	0.0998021i
$681$	−305.548	+	305.548i	−0.448675	+	0.448675i
$682$	15.5702	−	15.5702i	0.0228303	−	0.0228303i
$683$	571.567	+	571.567i	0.836848	+	0.836848i	0.988443	−	0.151595i	$-0.0484410\pi$
$683$	571.567	+	571.567i	0.836848	+	0.836848i	−0.151595	+	0.988443i	$0.548441\pi$
$684$	212.169	+	212.169i	0.310188	+	0.310188i
$685$	860.785			1.25662
$686$		−	49.3195i		−	0.0718943i
$687$	1188.62	+	1188.62i	1.73016	+	1.73016i
$688$			117.274i			0.170457i
$689$		0			0
$690$	−1288.00			−1.86666
$691$	570.418	−	570.418i	0.825497	−	0.825497i	−0.161393	−	0.986890i	$-0.551599\pi$
$691$	570.418	−	570.418i	0.825497	−	0.825497i	0.986890	+	0.161393i	$0.0515988\pi$
$692$	−57.6586			−0.0833216
$693$		−	3.64446i		−	0.00525896i
$694$	640.601	−	640.601i	0.923057	−	0.923057i
$695$	−150.652	+	150.652i	−0.216766	+	0.216766i
$696$	−290.542	−	290.542i	−0.417445	−	0.417445i
$697$	−52.4857	−	52.4857i	−0.0753023	−	0.0753023i
$698$	85.5412			0.122552
$699$		−	1838.04i		−	2.62953i
$700$	22.3635	+	22.3635i	0.0319479	+	0.0319479i
$701$		−	1080.31i		−	1.54110i	−0.637378	−	0.770552i	$-0.719981\pi$
$701$		−	1080.31i		−	1.54110i	0.637378	−	0.770552i	$-0.280019\pi$
$702$		0			0
$703$	453.087			0.644505
$704$	−4.19030	+	4.19030i	−0.00595213	+	0.00595213i
$705$	1192.64			1.69169
$706$			414.863i			0.587625i
$707$	7.01040	−	7.01040i	0.00991570	−	0.00991570i
$708$	675.890	−	675.890i	0.954647	−	0.954647i
$709$	−558.528	−	558.528i	−0.787769	−	0.787769i	0.193359	−	0.981128i	$-0.438062\pi$
$709$	−558.528	−	558.528i	−0.787769	−	0.787769i	−0.981128	+	0.193359i	$0.938062\pi$
$710$	−812.365	−	812.365i	−1.14418	−	1.14418i
$711$	1463.36			2.05817
$712$			240.559i			0.337864i
$713$	340.293	+	340.293i	0.477269	+	0.477269i
$714$			6.93240i			0.00970925i
$715$		0			0
$716$	424.196			0.592453
$717$	1005.91	−	1005.91i	1.40294	−	1.40294i
$718$	−237.504			−0.330785
$719$		−	809.099i		−	1.12531i	−0.826691	−	0.562656i	$-0.809780\pi$
$719$		−	809.099i		−	1.12531i	0.826691	−	0.562656i	$-0.190220\pi$
$720$	−325.300	+	325.300i	−0.451805	+	0.451805i
$721$	−17.1545	+	17.1545i	−0.0237926	+	0.0237926i
$722$	−242.944	−	242.944i	−0.336487	−	0.336487i
$723$	−632.651	−	632.651i	−0.875036	−	0.875036i
$724$	−224.176			−0.309635
$725$		−	1349.97i		−	1.86202i
$726$	−575.245	−	575.245i	−0.792348	−	0.792348i
$727$		−	1368.53i		−	1.88243i	−0.337808	−	0.941215i	$-0.609685\pi$
$727$		−	1368.53i		−	1.88243i	0.337808	−	0.941215i	$-0.390315\pi$
$728$		0			0
$729$	−1188.70			−1.63059
$730$	600.220	−	600.220i	0.822219	−	0.822219i
$731$	−84.4560			−0.115535
$732$			147.705i			0.201782i
$733$	−204.408	+	204.408i	−0.278865	+	0.278865i	−0.832656	−	0.553791i	$-0.813181\pi$
$733$	−204.408	+	204.408i	−0.278865	+	0.278865i	0.553791	+	0.832656i	$0.313181\pi$
$734$	102.316	−	102.316i	0.139395	−	0.139395i
$735$	1374.71	+	1374.71i	1.87036	+	1.87036i
$736$	−91.5805	−	91.5805i	−0.124430	−	0.124430i
$737$	−51.5584			−0.0699571
$738$			503.160i			0.681789i
$739$	171.597	+	171.597i	0.232202	+	0.232202i	0.813611	−	0.581409i	$-0.197498\pi$
$739$	171.597	+	171.597i	0.232202	+	0.232202i	−0.581409	+	0.813611i	$0.697498\pi$
$740$			694.678i			0.938755i
$741$		0			0
$742$	−43.2564			−0.0582970
$743$	−63.8290	+	63.8290i	−0.0859071	+	0.0859071i	−0.748755	−	0.662847i	$-0.769348\pi$
$743$	−63.8290	+	63.8290i	−0.0859071	+	0.0859071i	0.662847	+	0.748755i	$0.269348\pi$
$744$	283.930			0.381626
$745$			224.089i			0.300791i
$746$	−604.616	+	604.616i	−0.810477	+	0.810477i
$747$	375.875	−	375.875i	0.503179	−	0.503179i
$748$	−3.01767	−	3.01767i	−0.00403432	−	0.00403432i
$749$	32.4014	+	32.4014i	0.0432595	+	0.0432595i
$750$	−1090.24			−1.45365
$751$		−	392.268i		−	0.522328i	−0.965294	−	0.261164i	$-0.915894\pi$
$751$		−	392.268i		−	0.522328i	0.965294	−	0.261164i	$-0.0841063\pi$
$752$	84.8001	+	84.8001i	0.112766	+	0.112766i
$753$			480.050i			0.637516i
$754$		0			0
$755$	1292.19			1.71150
$756$	11.5701	−	11.5701i	0.0153043	−	0.0153043i
$757$	−357.655			−0.472463			−0.236232	−	0.971697i	$-0.575912\pi$
$757$	−357.655			−0.472463			−0.236232	+	0.971697i	$0.575912\pi$
$758$			542.676i			0.715931i
$759$	−57.2715	+	57.2715i	−0.0754566	+	0.0754566i
$760$	−181.005	+	181.005i	−0.238165	+	0.238165i
$761$	589.776	+	589.776i	0.775001	+	0.775001i	0.978976	−	0.203975i	$-0.0653860\pi$
$761$	589.776	+	589.776i	0.775001	+	0.775001i	−0.203975	+	0.978976i	$0.565386\pi$
$762$	−1101.52	−	1101.52i	−1.44557	−	1.44557i
$763$	−15.3899			−0.0201702
$764$		−	530.096i		−	0.693843i
$765$	−234.267	−	234.267i	−0.306231	−	0.306231i
$766$			579.385i			0.756377i
$767$		0			0
$768$	−76.4119			−0.0994947
$769$	−589.722	+	589.722i	−0.766869	+	0.766869i	−0.977554	−	0.210685i	$-0.932430\pi$
$769$	−589.722	+	589.722i	−0.766869	+	0.766869i	0.210685	+	0.977554i	$0.432430\pi$
$770$	3.10915			0.00403786
$771$		−	331.937i		−	0.430528i
$772$	225.137	−	225.137i	0.291628	−	0.291628i
$773$	−633.332	+	633.332i	−0.819317	+	0.819317i	−0.986009	−	0.166692i	$-0.946691\pi$
$773$	−633.332	+	633.332i	−0.819317	+	0.819317i	0.166692	+	0.986009i	$0.446691\pi$
$774$	404.823	+	404.823i	0.523027	+	0.523027i
$775$	659.623	+	659.623i	0.851126	+	0.851126i
$776$	−57.4927			−0.0740885
$777$		−	70.9608i		−	0.0913267i
$778$	−43.6909	−	43.6909i	−0.0561579	−	0.0561579i
$779$			279.971i			0.359398i
$780$		0			0
$781$	−72.2445			−0.0925026
$782$	65.9523	−	65.9523i	0.0843380	−	0.0843380i
$783$	−698.423			−0.891984
$784$			195.492i			0.249352i
$785$	−840.359	+	840.359i	−1.07052	+	1.07052i
$786$	774.922	−	774.922i	0.985906	−	0.985906i
$787$	−670.541	−	670.541i	−0.852021	−	0.852021i	0.138361	−	0.990382i	$-0.455817\pi$
$787$	−670.541	−	670.541i	−0.852021	−	0.852021i	−0.990382	+	0.138361i	$0.955817\pi$
$788$	425.408	+	425.408i	0.539858	+	0.539858i
$789$	−1237.77			−1.56878
$790$			1248.42i			1.58028i
$791$	−11.6256	−	11.6256i	−0.0146973	−	0.0146973i
$792$			28.9293i			0.0365268i
$793$		0			0
$794$	−387.569			−0.488122
$795$	2414.56	−	2414.56i	3.03718	−	3.03718i
$796$	−374.638			−0.470650
$797$		−	384.489i		−	0.482421i	−0.970473	−	0.241210i	$-0.922456\pi$
$797$		−	384.489i		−	0.482421i	0.970473	−	0.241210i	$-0.0775444\pi$
$798$	18.4895	−	18.4895i	0.0231698	−	0.0231698i
$799$	−61.0694	+	61.0694i	−0.0764323	+	0.0764323i
$800$	−177.519	−	177.519i	−0.221899	−	0.221899i
$801$	830.394	+	830.394i	1.03670	+	1.03670i
$802$	−126.037			−0.157153
$803$		−	53.3782i		−	0.0664735i
$804$	−470.095	−	470.095i	−0.584695	−	0.584695i
$805$			67.9516i			0.0844119i
$806$		0			0
$807$	−200.635			−0.248618
$808$	−55.6477	+	55.6477i	−0.0688709	+	0.0688709i
$809$	15.5780			0.0192558			0.00962791	−	0.999954i	$-0.496935\pi$
$809$	15.5780			0.0192558			0.00962791	+	0.999954i	$0.496935\pi$
$810$		−	172.173i		−	0.212559i
$811$	488.921	−	488.921i	0.602861	−	0.602861i	−0.338209	−	0.941071i	$-0.609821\pi$
$811$	488.921	−	488.921i	0.602861	−	0.602861i	0.941071	+	0.338209i	$0.109821\pi$
$812$	−15.3283	+	15.3283i	−0.0188772	+	0.0188772i
$813$	1064.03	+	1064.03i	1.30878	+	1.30878i
$814$	30.8893	+	30.8893i	0.0379475	+	0.0379475i
$815$	−221.263			−0.271489
$816$		−	55.0286i		−	0.0674370i
$817$	225.254	+	225.254i	0.275709	+	0.275709i
$818$		−	1032.55i		−	1.26229i
$819$		0			0
$820$	−429.255			−0.523482
$821$	279.870	−	279.870i	0.340890	−	0.340890i	−0.515812	−	0.856702i	$-0.672510\pi$
$821$	279.870	−	279.870i	0.340890	−	0.340890i	0.856702	+	0.515812i	$0.172510\pi$
$822$	697.966			0.849107
$823$			459.551i			0.558385i	0.960235	+	0.279192i	$0.0900667\pi$
$823$			459.551i			0.558385i	−0.960235	+	0.279192i	$0.909933\pi$
$824$	136.170	−	136.170i	0.165255	−	0.165255i
$825$	−111.015	+	111.015i	−0.134564	+	0.134564i
$826$	−35.6583	−	35.6583i	−0.0431699	−	0.0431699i
$827$	−1019.38	−	1019.38i	−1.23263	−	1.23263i	−0.962951	−	0.269678i	$-0.913083\pi$
$827$	−1019.38	−	1019.38i	−1.23263	−	1.23263i	−0.269678	−	0.962951i	$-0.586917\pi$
$828$	−632.259			−0.763598
$829$			137.402i			0.165744i	0.996560	+	0.0828722i	$0.0264093\pi$
$829$			137.402i			0.165744i	−0.996560	+	0.0828722i	$0.973591\pi$
$830$	320.666	+	320.666i	0.386344	+	0.386344i
$831$			905.828i			1.09005i
$832$		0			0
$833$	−140.785			−0.169010
$834$	−122.156	+	122.156i	−0.146470	+	0.146470i
$835$	62.6853			0.0750722
$836$			16.0970i			0.0192548i
$837$	341.265	−	341.265i	0.407724	−	0.407724i
$838$	−260.975	+	260.975i	−0.311426	+	0.311426i
$839$	382.590	+	382.590i	0.456007	+	0.456007i	0.897342	−	0.441335i	$-0.145495\pi$
$839$	382.590	+	382.590i	0.456007	+	0.456007i	−0.441335	+	0.897342i	$0.645495\pi$
$840$	28.3484	+	28.3484i	0.0337480	+	0.0337480i
$841$	84.2851			0.100220
$842$			206.076i			0.244745i
$843$	−156.960	−	156.960i	−0.186192	−	0.186192i
$844$		−	339.626i		−	0.402401i
$845$		0			0
$846$	585.449			0.692020
$847$	−30.3485	+	30.3485i	−0.0358306	+	0.0358306i
$848$	343.364			0.404910
$849$			2516.65i			2.96425i
$850$	127.842	−	127.842i	0.150402	−	0.150402i
$851$	−675.095	+	675.095i	−0.793297	+	0.793297i
$852$	−658.705	−	658.705i	−0.773128	−	0.773128i
$853$	549.575	+	549.575i	0.644285	+	0.644285i	0.951606	−	0.307321i	$-0.0994325\pi$
$853$	549.575	+	549.575i	0.644285	+	0.644285i	−0.307321	+	0.951606i	$0.599433\pi$
$854$	7.79253			0.00912474
$855$			1249.63i			1.46156i
$856$	−257.198	−	257.198i	−0.300465	−	0.300465i
$857$			908.454i			1.06004i	0.847985	+	0.530020i	$0.177816\pi$
$857$			908.454i			1.06004i	−0.847985	+	0.530020i	$0.822184\pi$
$858$		0			0
$859$	−383.134			−0.446023			−0.223012	−	0.974816i	$-0.571589\pi$
$859$	−383.134			−0.446023			−0.223012	+	0.974816i	$0.571589\pi$
$860$	−345.362	+	345.362i	−0.401584	+	0.401584i
$861$	43.8480			0.0509269
$862$			192.658i			0.223501i
$863$	320.195	−	320.195i	0.371026	−	0.371026i	−0.496825	−	0.867851i	$-0.665501\pi$
$863$	320.195	−	320.195i	0.371026	−	0.371026i	0.867851	+	0.496825i	$0.165501\pi$
$864$	−91.8419	+	91.8419i	−0.106299	+	0.106299i
$865$	−169.799	−	169.799i	−0.196299	−	0.196299i
$866$	−201.358	−	201.358i	−0.232516	−	0.232516i
$867$	−1340.56			−1.54621
$868$		−	14.9794i		−	0.0172574i
$869$	55.5116	+	55.5116i	0.0638798	+	0.0638798i
$870$		−	1711.24i		−	1.96694i
$871$		0			0
$872$	122.163			0.140095
$873$	−198.461	+	198.461i	−0.227332	+	0.227332i
$874$	−351.805			−0.402523
$875$			57.5183i			0.0657352i
$876$	486.687	−	486.687i	0.555579	−	0.555579i
$877$	−1068.79	+	1068.79i	−1.21868	+	1.21868i	−0.250591	+	0.968093i	$0.580625\pi$
$877$	−1068.79	+	1068.79i	−1.21868	+	1.21868i	−0.968093	+	0.250591i	$0.919375\pi$
$878$	−74.3517	−	74.3517i	−0.0846830	−	0.0846830i
$879$	462.452	+	462.452i	0.526111	+	0.526111i
$880$	−24.6801			−0.0280455
$881$			1160.78i			1.31758i	0.752329	+	0.658788i	$0.228931\pi$
$881$			1160.78i			1.31758i	−0.752329	+	0.658788i	$0.771069\pi$
$882$	674.826	+	674.826i	0.765108	+	0.765108i
$883$			1327.78i			1.50371i	0.659328	+	0.751856i	$0.270841\pi$
$883$			1327.78i			1.50371i	−0.659328	+	0.751856i	$0.729159\pi$
$884$		0			0
$885$	3980.87			4.49815
$886$	−130.644	+	130.644i	−0.147454	+	0.147454i
$887$	497.255			0.560604			0.280302	−	0.959912i	$-0.409565\pi$
$887$	497.255			0.560604			0.280302	+	0.959912i	$0.409565\pi$
$888$			563.279i			0.634323i
$889$	−58.1135	+	58.1135i	−0.0653695	+	0.0653695i
$890$	−708.424	+	708.424i	−0.795982	+	0.795982i
$891$	−7.65577	−	7.65577i	−0.00859233	−	0.00859233i
$892$	−340.107	−	340.107i	−0.381286	−	0.381286i
$893$	325.758			0.364791
$894$			181.702i			0.203246i
$895$	1249.22	+	1249.22i	1.39578	+	1.39578i
$896$			4.03130i			0.00449922i
$897$		0			0
$898$	1019.38			1.13517
$899$	−452.114	+	452.114i	−0.502908	+	0.502908i
$900$	−1225.57			−1.36174
$901$			247.276i			0.274446i
$902$	−19.0871	+	19.0871i	−0.0211608	+	0.0211608i
$903$	35.2785	−	35.2785i	0.0390681	−	0.0390681i
$904$	92.2826	+	92.2826i	0.102082	+	0.102082i
$905$	−660.176	−	660.176i	−0.729477	−	0.729477i
$906$	1047.77			1.15647
$907$			967.599i			1.06681i	0.845859	+	0.533406i	$0.179088\pi$
$907$			967.599i			1.06681i	−0.845859	+	0.533406i	$0.820912\pi$
$908$	−127.958	−	127.958i	−0.140923	−	0.140923i
$909$			384.184i			0.422645i
$910$		0			0
$911$	−760.079			−0.834335			−0.417168	−	0.908830i	$-0.636977\pi$
$911$	−760.079			−0.834335			−0.417168	+	0.908830i	$0.636977\pi$
$912$	−146.768	+	146.768i	−0.160929	+	0.160929i
$913$	28.5171			0.0312345
$914$			512.817i			0.561069i
$915$	−434.976	+	434.976i	−0.475384	+	0.475384i
$916$	−497.774	+	497.774i	−0.543422	+	0.543422i
$917$	−40.8830	−	40.8830i	−0.0445834	−	0.0445834i
$918$	−66.1406	−	66.1406i	−0.0720486	−	0.0720486i
$919$	416.498			0.453208			0.226604	−	0.973987i	$-0.427238\pi$
$919$	416.498			0.453208			0.226604	+	0.973987i	$0.427238\pi$
$920$		−	539.392i		−	0.586295i
$921$	−1461.56	−	1461.56i	−1.58692	−	1.58692i
$922$			1223.62i			1.32713i
$923$		0			0
$924$	2.52105			0.00272841
$925$	−1308.60	+	1308.60i	−1.41470	+	1.41470i
$926$	326.983			0.353114
$927$		−	940.102i		−	1.01413i
$928$	121.674	−	121.674i	0.131114	−	0.131114i
$929$	295.541	−	295.541i	0.318128	−	0.318128i	−0.529920	−	0.848048i	$-0.677778\pi$
$929$	295.541	−	295.541i	0.318128	−	0.318128i	0.848048	+	0.529920i	$0.177778\pi$
$930$	836.147	+	836.147i	0.899083	+	0.899083i
$931$	375.490	+	375.490i	0.403319	+	0.403319i
$932$	769.740			0.825901
$933$			660.361i			0.707783i
$934$	242.866	+	242.866i	0.260028	+	0.260028i
$935$		−	17.7735i		−	0.0190091i
$936$		0			0
$937$	−140.819			−0.150287			−0.0751436	−	0.997173i	$-0.523942\pi$
$937$	−140.819			−0.150287			−0.0751436	+	0.997173i	$0.523942\pi$
$938$	−24.8010	+	24.8010i	−0.0264403	+	0.0264403i
$939$	−2509.34			−2.67235
$940$			499.457i			0.531337i
$941$	−1032.31	+	1032.31i	−1.09704	+	1.09704i	−0.102281	+	0.994756i	$0.532614\pi$
$941$	−1032.31	+	1032.31i	−1.09704	+	1.09704i	−0.994756	+	0.102281i	$0.967386\pi$
$942$	−681.403	+	681.403i	−0.723358	+	0.723358i
$943$	−417.154	−	417.154i	−0.442369	−	0.442369i
$944$	283.051	+	283.051i	0.299842	+	0.299842i
$945$	68.1456			0.0721118
$946$			30.7134i			0.0324666i
$947$	341.629	+	341.629i	0.360749	+	0.360749i	0.864088	−	0.503340i	$-0.167896\pi$
$947$	341.629	+	341.629i	0.360749	+	0.360749i	−0.503340	+	0.864088i	$0.667896\pi$
$948$			1012.28i			1.06780i
$949$		0			0
$950$	−681.937			−0.717829
$951$	116.480	−	116.480i	0.122481	−	0.122481i
$952$	−2.90317			−0.00304955
$953$			857.938i			0.900250i	0.892966	+	0.450125i	$0.148621\pi$
$953$			857.938i			0.900250i	−0.892966	+	0.450125i	$0.851379\pi$
$954$	1185.27	−	1185.27i	1.24242	−	1.24242i
$955$	1561.08	−	1561.08i	1.63464	−	1.63464i
$956$	421.257	+	421.257i	0.440645	+	0.440645i
$957$	−76.0911	−	76.0911i	−0.0795100	−	0.0795100i
$958$	−316.124			−0.329983
$959$		−	36.8229i		−	0.0383972i
$960$	−225.026	−	225.026i	−0.234402	−	0.234402i
$961$			519.175i			0.540244i
$962$		0			0
$963$	−1775.66			−1.84389
$964$	264.943	−	264.943i	0.274837	−	0.274837i
$965$	1326.01			1.37411
$966$			55.0984i			0.0570377i
$967$	911.551	−	911.551i	0.942658	−	0.942658i	−0.0557845	−	0.998443i	$-0.517766\pi$
$967$	911.551	−	911.551i	0.942658	−	0.942658i	0.998443	+	0.0557845i	$0.0177660\pi$
$968$	240.903	−	240.903i	0.248866	−	0.248866i
$969$	−105.696	−	105.696i	−0.109077	−	0.109077i
$970$	−169.311	−	169.311i	−0.174547	−	0.174547i
$971$	1074.01			1.10609			0.553043	−	0.833153i	$-0.313467\pi$
$971$	1074.01			1.10609			0.553043	+	0.833153i	$0.313467\pi$
$972$		−	552.895i		−	0.568822i
$973$	6.44465	+	6.44465i	0.00662348	+	0.00662348i
$974$			30.5113i			0.0313258i
$975$		0			0
$976$	−61.8562			−0.0633772
$977$	561.757	−	561.757i	0.574981	−	0.574981i	−0.358535	−	0.933516i	$-0.616724\pi$
$977$	561.757	−	561.757i	0.574981	−	0.574981i	0.933516	+	0.358535i	$0.116724\pi$
$978$	−179.411			−0.183447
$979$			63.0009i			0.0643523i
$980$	−575.706	+	575.706i	−0.587455	+	0.587455i
$981$	421.698	−	421.698i	0.429865	−	0.429865i
$982$	−58.3092	−	58.3092i	−0.0593780	−	0.0593780i
$983$	1275.63	+	1275.63i	1.29769	+	1.29769i	0.929916	+	0.367773i	$0.119880\pi$
$983$	1275.63	+	1275.63i	1.29769	+	1.29769i	0.367773	+	0.929916i	$0.380120\pi$
$984$	−348.061			−0.353720
$985$			2505.57i			2.54373i
$986$	87.6244	+	87.6244i	0.0888686	+	0.0888686i
$987$		−	51.0191i		−	0.0516911i
$988$		0			0
$989$	−671.253			−0.678719
$990$	−85.1940	+	85.1940i	−0.0860545	+	0.0860545i
$991$	−1129.33			−1.13959			−0.569795	−	0.821787i	$-0.692977\pi$
$991$	−1129.33			−1.13959			−0.569795	+	0.821787i	$0.692977\pi$
$992$			118.905i			0.119864i
$993$	74.8840	−	74.8840i	0.0754119	−	0.0754119i
$994$	−34.7516	+	34.7516i	−0.0349614	+	0.0349614i
$995$	−1103.27	−	1103.27i	−1.10882	−	1.10882i
$996$	260.011	+	260.011i	0.261055	+	0.261055i
$997$	−7.14438			−0.00716588			−0.00358294	−	0.999994i	$-0.501140\pi$
$997$	−7.14438			−0.00716588			−0.00358294	+	0.999994i	$0.501140\pi$
$998$		−	1250.99i		−	1.25350i
$999$	677.023	+	677.023i	0.677701	+	0.677701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.d.f.239.1		8
13.2	odd	12		338.3.f.h.319.2		8
13.3	even	3		338.3.f.i.19.2		8
13.4	even	6		338.3.f.h.249.2		8
13.5	odd	4		338.3.d.g.99.1		8
13.6	odd	12		26.3.f.b.11.2	✓	8
13.7	odd	12		338.3.f.i.89.2		8
13.8	odd	4	inner	338.3.d.f.99.1		8
13.9	even	3		338.3.f.j.249.2		8
13.10	even	6		26.3.f.b.19.2	yes	8
13.11	odd	12		338.3.f.j.319.2		8
13.12	even	2		338.3.d.g.239.1		8
39.23	odd	6		234.3.bb.f.19.2		8
39.32	even	12		234.3.bb.f.37.2		8
52.19	even	12		208.3.bd.f.193.1		8
52.23	odd	6		208.3.bd.f.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.2	✓	8	13.6	odd	12
26.3.f.b.19.2	yes	8	13.10	even	6
208.3.bd.f.97.1		8	52.23	odd	6
208.3.bd.f.193.1		8	52.19	even	12
234.3.bb.f.19.2		8	39.23	odd	6
234.3.bb.f.37.2		8	39.32	even	12
338.3.d.f.99.1		8	13.8	odd	4	inner
338.3.d.f.239.1		8	1.1	even	1	trivial
338.3.d.g.99.1		8	13.5	odd	4
338.3.d.g.239.1		8	13.12	even	2
338.3.f.h.249.2		8	13.4	even	6
338.3.f.h.319.2		8	13.2	odd	12
338.3.f.i.19.2		8	13.3	even	3
338.3.f.i.89.2		8	13.7	odd	12
338.3.f.j.249.2		8	13.9	even	3
338.3.f.j.319.2		8	13.11	odd	12

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -4.77574 q^{3} -2.00000i q^{4} +(5.88981 - 5.88981i) q^{5} +(4.77574 - 4.77574i) q^{6} +(-0.251956 - 0.251956i) q^{7} +(2.00000 + 2.00000i) q^{8} +13.8077 q^{9} +11.7796i q^{10} +(0.523787 + 0.523787i) q^{11} +9.55149i q^{12} +0.503913 q^{14} +(-28.1282 + 28.1282i) q^{15} -4.00000 q^{16} -2.88063i q^{17} +(-13.8077 + 13.8077i) q^{18} +(-7.68297 + 7.68297i) q^{19} +(-11.7796 - 11.7796i) q^{20} +(1.20328 + 1.20328i) q^{21} -1.04757 q^{22} -22.8951i q^{23} +(-9.55149 - 9.55149i) q^{24} -44.3798i q^{25} -22.9605 q^{27} +(-0.503913 + 0.503913i) q^{28} +30.4185 q^{29} -56.2565i q^{30} +(-14.8631 + 14.8631i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.50147 - 2.50147i) q^{33} +(2.88063 + 2.88063i) q^{34} -2.96795 q^{35} -27.6155i q^{36} +(-29.4864 - 29.4864i) q^{37} -15.3659i q^{38} +23.5593 q^{40} +(18.2202 - 18.2202i) q^{41} -2.40656 q^{42} -29.3186i q^{43} +(1.04757 - 1.04757i) q^{44} +(81.3249 - 81.3249i) q^{45} +(22.8951 + 22.8951i) q^{46} +(-21.2000 - 21.2000i) q^{47} +19.1030 q^{48} -48.8730i q^{49} +(44.3798 + 44.3798i) q^{50} +13.7571i q^{51} -85.8410 q^{53} +(22.9605 - 22.9605i) q^{54} +6.17002 q^{55} -1.00783i q^{56} +(36.6919 - 36.6919i) q^{57} +(-30.4185 + 30.4185i) q^{58} +(-70.7628 - 70.7628i) q^{59} +(56.2565 + 56.2565i) q^{60} +15.4640 q^{61} -29.7263i q^{62} +(-3.47895 - 3.47895i) q^{63} +8.00000i q^{64} +5.00295 q^{66} +(-49.2169 + 49.2169i) q^{67} -5.76126 q^{68} +109.341i q^{69} +(2.96795 - 2.96795i) q^{70} +(-68.9636 + 68.9636i) q^{71} +(27.6155 + 27.6155i) q^{72} +(-50.9541 - 50.9541i) q^{73} +58.9729 q^{74} +211.947i q^{75} +(15.3659 + 15.3659i) q^{76} -0.263943i q^{77} +105.981 q^{79} +(-23.5593 + 23.5593i) q^{80} -14.6162 q^{81} +36.4405i q^{82} +(27.2221 - 27.2221i) q^{83} +(2.40656 - 2.40656i) q^{84} +(-16.9664 - 16.9664i) q^{85} +(29.3186 + 29.3186i) q^{86} -145.271 q^{87} +2.09515i q^{88} +(60.1398 + 60.1398i) q^{89} +162.650i q^{90} -45.7902 q^{92} +(70.9825 - 70.9825i) q^{93} +42.4001 q^{94} +90.5025i q^{95} +(-19.1030 + 19.1030i) q^{96} +(-14.3732 + 14.3732i) q^{97} +(48.8730 + 48.8730i) q^{98} +(7.23232 + 7.23232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9} - 42 q^{11} + 20 q^{14} - 60 q^{15} - 32 q^{16} - 84 q^{18} - 22 q^{19} + 12 q^{20} + 102 q^{21} + 84 q^{22} + 72 q^{27} - 20 q^{28} + 12 q^{29}+ \cdots - 252 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9 - 42 * q^11 + 20 * q^14 - 60 * q^15 - 32 * q^16 - 84 * q^18 - 22 * q^19 + 12 * q^20 + 102 * q^21 + 84 * q^22 + 72 * q^27 - 20 * q^28 + 12 * q^29 - 32 * q^31 + 32 * q^32 - 54 * q^33 + 60 * q^34 + 156 * q^35 - 32 * q^37 - 24 * q^40 + 12 * q^41 - 204 * q^42 - 84 * q^44 + 102 * q^45 + 108 * q^46 - 60 * q^47 + 88 * q^50 - 132 * q^53 - 72 * q^54 + 324 * q^55 + 294 * q^57 - 12 * q^58 - 234 * q^59 + 120 * q^60 - 72 * q^61 + 156 * q^63 + 108 * q^66 + 14 * q^67 - 120 * q^68 - 156 * q^70 - 162 * q^71 + 168 * q^72 - 166 * q^73 + 64 * q^74 + 44 * q^76 - 96 * q^79 + 24 * q^80 + 24 * q^81 + 240 * q^83 + 204 * q^84 + 234 * q^85 - 132 * q^86 - 720 * q^87 - 210 * q^89 - 216 * q^92 + 444 * q^93 + 120 * q^94 - 146 * q^97 + 16 * q^98 - 252 * q^99

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