LMFDB - Embedded newform 513.2.f.h.163.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(163,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,1,0,-3,5,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 8x^{10} - x^{9} + 41x^{8} - 7x^{7} + 91x^{6} + 9x^{5} + 135x^{4} - 12x^{3} + 45x^{2} + 9x + 9 $ x^12 - x^11 + 8x^10 - x^9 + 41x^8 - 7x^7 + 91x^6 + 9x^5 + 135x^4 - 12x^3 + 45x^2 + 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.6
Root			$1.24972 + 2.16459i$ of defining polynomial
Character	$\chi$	$=$	513.163
Dual form			513.2.f.h.406.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24972 - 2.16459i) q^{2} +(-2.12362 - 3.67822i) q^{4} +(0.535221 - 0.927030i) q^{5} -0.193560 q^{7} -5.61687 q^{8} +(-1.33776 - 2.31706i) q^{10} +0.571729 q^{11} +(-2.84366 - 4.92536i) q^{13} +(-0.241896 + 0.418977i) q^{14} +(-2.77229 + 4.80175i) q^{16} +(-1.02257 + 1.77114i) q^{17} +(-1.50783 - 4.08980i) q^{19} -4.54643 q^{20} +(0.714503 - 1.23756i) q^{22} +(0.777117 + 1.34601i) q^{23} +(1.92708 + 3.33780i) q^{25} -14.2151 q^{26} +(0.411048 + 0.711956i) q^{28} +(3.04941 + 5.28174i) q^{29} +5.86981 q^{31} +(1.31234 + 2.27304i) q^{32} +(2.55586 + 4.42688i) q^{34} +(-0.103597 + 0.179436i) q^{35} +9.36668 q^{37} +(-10.7371 - 1.84730i) q^{38} +(-3.00627 + 5.20701i) q^{40} +(-0.964779 + 1.67105i) q^{41} +(1.60603 - 2.78173i) q^{43} +(-1.21414 - 2.10294i) q^{44} +3.88473 q^{46} +(5.30880 + 9.19512i) q^{47} -6.96253 q^{49} +9.63326 q^{50} +(-12.0777 + 20.9192i) q^{52} +(-3.84829 - 6.66544i) q^{53} +(0.306001 - 0.530010i) q^{55} +1.08720 q^{56} +15.2437 q^{58} +(5.89826 - 10.2161i) q^{59} +(-4.01155 - 6.94820i) q^{61} +(7.33564 - 12.7057i) q^{62} -4.52893 q^{64} -6.08794 q^{65} +(3.37013 + 5.83724i) q^{67} +8.68621 q^{68} +(0.258936 + 0.448490i) q^{70} +(-3.50280 + 6.06703i) q^{71} +(4.03676 - 6.99188i) q^{73} +(11.7058 - 20.2750i) q^{74} +(-11.8411 + 14.2313i) q^{76} -0.110664 q^{77} +(2.44019 - 4.22653i) q^{79} +(2.96758 + 5.14000i) q^{80} +(2.41142 + 4.17669i) q^{82} +6.02879 q^{83} +(1.09460 + 1.89591i) q^{85} +(-4.01419 - 6.95278i) q^{86} -3.21133 q^{88} +(8.79523 + 15.2338i) q^{89} +(0.550418 + 0.953351i) q^{91} +(3.30061 - 5.71682i) q^{92} +26.5382 q^{94} +(-4.59839 - 0.791145i) q^{95} +(3.79512 - 6.57333i) q^{97} +(-8.70125 + 15.0710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) $ 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.24972	−	2.16459i	0.883689	−	1.53059i	0.0364791	−	0.999334i	$-0.488386\pi$
$2$	1.24972	−	2.16459i	0.883689	−	1.53059i	0.847209	−	0.531259i	$-0.178281\pi$
$3$		0			0
$3$		0			0
$4$	−2.12362	−	3.67822i	−1.06181	−	1.83911i
$5$	0.535221	−	0.927030i	0.239358	−	0.414580i	−0.721172	−	0.692756i	$-0.756396\pi$
$5$	0.535221	−	0.927030i	0.239358	−	0.414580i	0.960530	+	0.278175i	$0.0897297\pi$
$6$		0			0
$7$	−0.193560			−0.0731588			−0.0365794	−	0.999331i	$-0.511646\pi$
$7$	−0.193560			−0.0731588			−0.0365794	+	0.999331i	$0.511646\pi$
$8$	−5.61687			−1.98586
$9$		0			0
$10$	−1.33776	−	2.31706i	−0.423036	−	0.732720i
$11$	0.571729			0.172383			0.0861914	−	0.996279i	$-0.472530\pi$
$11$	0.571729			0.172383			0.0861914	+	0.996279i	$0.472530\pi$
$12$		0			0
$13$	−2.84366	−	4.92536i	−0.788688	−	1.36605i	−0.926771	−	0.375627i	$-0.877427\pi$
$13$	−2.84366	−	4.92536i	−0.788688	−	1.36605i	0.138083	−	0.990421i	$-0.455906\pi$
$14$	−0.241896	+	0.418977i	−0.0646495	+	0.111976i
$15$		0			0
$16$	−2.77229	+	4.80175i	−0.693074	+	1.20044i
$17$	−1.02257	+	1.77114i	−0.248010	+	0.429565i	−0.962973	−	0.269596i	$-0.913110\pi$
$17$	−1.02257	+	1.77114i	−0.248010	+	0.429565i	0.714964	+	0.699161i	$0.246443\pi$
$18$		0			0
$19$	−1.50783	−	4.08980i	−0.345919	−	0.938264i
$19$	−1.50783	−	4.08980i	−0.345919	−	0.938264i
$20$	−4.54643			−1.01661
$21$		0			0
$22$	0.714503	−	1.23756i	0.152333	−	0.263848i
$23$	0.777117	+	1.34601i	0.162040	+	0.280662i	0.935600	−	0.353061i	$-0.114859\pi$
$23$	0.777117	+	1.34601i	0.162040	+	0.280662i	−0.773560	+	0.633723i	$0.781526\pi$
$24$		0			0
$25$	1.92708	+	3.33780i	0.385415	+	0.667559i
$26$	−14.2151			−2.78782
$27$		0			0
$28$	0.411048	+	0.711956i	0.0776808	+	0.134547i
$29$	3.04941	+	5.28174i	0.566262	+	0.980794i	0.996931	+	0.0782841i	$0.0249441\pi$
$29$	3.04941	+	5.28174i	0.566262	+	0.980794i	−0.430670	+	0.902510i	$0.641723\pi$
$30$		0			0
$31$	5.86981			1.05425			0.527124	−	0.849788i	$-0.323270\pi$
$31$	5.86981			1.05425			0.527124	+	0.849788i	$0.323270\pi$
$32$	1.31234	+	2.27304i	0.231991	+	0.401820i
$33$		0			0
$34$	2.55586	+	4.42688i	0.438327	+	0.759204i
$35$	−0.103597	+	0.179436i	−0.0175111	+	0.0303302i
$36$		0			0
$37$	9.36668			1.53987			0.769937	−	0.638120i	$-0.220288\pi$
$37$	9.36668			1.53987			0.769937	+	0.638120i	$0.220288\pi$
$38$	−10.7371	−	1.84730i	−1.74179	−	0.299671i
$39$		0			0
$40$	−3.00627	+	5.20701i	−0.475332	+	0.823300i
$41$	−0.964779	+	1.67105i	−0.150673	+	0.260974i	−0.931475	−	0.363805i	$-0.881477\pi$
$41$	−0.964779	+	1.67105i	−0.150673	+	0.260974i	0.780802	+	0.624779i	$0.214811\pi$
$42$		0			0
$43$	1.60603	−	2.78173i	0.244917	−	0.424209i	−0.717191	−	0.696877i	$-0.754572\pi$
$43$	1.60603	−	2.78173i	0.244917	−	0.424209i	0.962108	+	0.272667i	$0.0879058\pi$
$44$	−1.21414	−	2.10294i	−0.183038	−	0.317031i
$45$		0			0
$46$	3.88473			0.572772
$47$	5.30880	+	9.19512i	0.774368	+	1.34125i	0.935149	+	0.354255i	$0.115266\pi$
$47$	5.30880	+	9.19512i	0.774368	+	1.34125i	−0.160780	+	0.986990i	$0.551401\pi$
$48$		0			0
$49$	−6.96253			−0.994648
$50$	9.63326			1.36235
$51$		0			0
$52$	−12.0777	+	20.9192i	−1.67488	+	2.90097i
$53$	−3.84829	−	6.66544i	−0.528604	−	0.915569i	−0.999444	−	0.0333501i	$-0.989382\pi$
$53$	−3.84829	−	6.66544i	−0.528604	−	0.915569i	0.470840	−	0.882219i	$-0.343951\pi$
$54$		0			0
$55$	0.306001	−	0.530010i	0.0412612	−	0.0714665i
$56$	1.08720			0.145283
$57$		0			0
$58$	15.2437			2.00160
$59$	5.89826	−	10.2161i	0.767888	−	1.33002i	−0.170818	−	0.985303i	$-0.554641\pi$
$59$	5.89826	−	10.2161i	0.767888	−	1.33002i	0.938706	−	0.344718i	$-0.112026\pi$
$60$		0			0
$61$	−4.01155	−	6.94820i	−0.513626	−	0.889626i	−0.999875	−	0.0158062i	$-0.994969\pi$
$61$	−4.01155	−	6.94820i	−0.513626	−	0.889626i	0.486249	−	0.873820i	$-0.338365\pi$
$62$	7.33564	−	12.7057i	0.931628	−	1.61363i
$63$		0			0
$64$	−4.52893			−0.566117
$65$	−6.08794			−0.755116
$66$		0			0
$67$	3.37013	+	5.83724i	0.411727	+	0.713132i	0.995079	−	0.0990878i	$-0.0315925\pi$
$67$	3.37013	+	5.83724i	0.411727	+	0.713132i	−0.583352	+	0.812220i	$0.698259\pi$
$68$	8.68621			1.05336
$69$		0			0
$70$	0.258936	+	0.448490i	0.0309488	+	0.0536049i
$71$	−3.50280	+	6.06703i	−0.415706	+	0.720024i	−0.995502	−	0.0947376i	$-0.969799\pi$
$71$	−3.50280	+	6.06703i	−0.415706	+	0.720024i	0.579796	+	0.814761i	$0.303132\pi$
$72$		0			0
$73$	4.03676	−	6.99188i	0.472467	−	0.818337i	−0.527036	−	0.849843i	$-0.676697\pi$
$73$	4.03676	−	6.99188i	0.472467	−	0.818337i	0.999504	+	0.0315056i	$0.0100302\pi$
$74$	11.7058	−	20.2750i	1.36077	−	2.35692i
$75$		0			0
$76$	−11.8411	+	14.2313i	−1.35827	+	1.63244i
$77$	−0.110664			−0.0126113
$78$		0			0
$79$	2.44019	−	4.22653i	0.274542	−	0.475522i	−0.695477	−	0.718548i	$-0.744807\pi$
$79$	2.44019	−	4.22653i	0.274542	−	0.475522i	0.970020	+	0.243027i	$0.0781403\pi$
$80$	2.96758	+	5.14000i	0.331786	+	0.574669i
$81$		0			0
$82$	2.41142	+	4.17669i	0.266296	+	0.461239i
$83$	6.02879			0.661746			0.330873	−	0.943675i	$-0.392657\pi$
$83$	6.02879			0.661746			0.330873	+	0.943675i	$0.392657\pi$
$84$		0			0
$85$	1.09460	+	1.89591i	0.118726	+	0.205640i
$86$	−4.01419	−	6.95278i	−0.432861	−	0.749738i
$87$		0			0
$88$	−3.21133			−0.342328
$89$	8.79523	+	15.2338i	0.932293	+	1.61478i	0.779392	+	0.626537i	$0.215528\pi$
$89$	8.79523	+	15.2338i	0.932293	+	1.61478i	0.152901	+	0.988242i	$0.451138\pi$
$90$		0			0
$91$	0.550418	+	0.953351i	0.0576994	+	0.0999384i
$92$	3.30061	−	5.71682i	0.344112	−	0.596020i
$93$		0			0
$94$	26.5382			2.73720
$95$	−4.59839	−	0.791145i	−0.471785	−	0.0811697i
$96$		0			0
$97$	3.79512	−	6.57333i	0.385336	−	0.667421i	−0.606480	−	0.795099i	$-0.707419\pi$
$97$	3.79512	−	6.57333i	0.385336	−	0.667421i	0.991816	+	0.127678i	$0.0407524\pi$
$98$	−8.70125	+	15.0710i	−0.878959	+	1.52240i
$99$		0			0
$100$	8.18477	−	14.1764i	0.818477	−	1.41764i
$101$	3.62114	+	6.27200i	0.360317	+	0.624087i	0.988013	−	0.154371i	$-0.0493352\pi$
$101$	3.62114	+	6.27200i	0.360317	+	0.624087i	−0.627696	+	0.778459i	$0.716002\pi$
$102$		0			0
$103$	4.75198			0.468227			0.234113	−	0.972209i	$-0.424781\pi$
$103$	4.75198			0.468227			0.234113	+	0.972209i	$0.424781\pi$
$104$	15.9724	+	27.6651i	1.56623	+	2.71278i
$105$		0			0
$106$	−19.2372			−1.86848
$107$	3.66421			0.354233			0.177117	−	0.984190i	$-0.443323\pi$
$107$	3.66421			0.354233			0.177117	+	0.984190i	$0.443323\pi$
$108$		0			0
$109$	−6.16947	+	10.6858i	−0.590928	+	1.02352i	0.403180	+	0.915121i	$0.367905\pi$
$109$	−6.16947	+	10.6858i	−0.590928	+	1.02352i	−0.994108	+	0.108397i	$0.965428\pi$
$110$	−0.764834	−	1.32473i	−0.0729241	−	0.126308i
$111$		0			0
$112$	0.536605	−	0.929427i	0.0507044	−	0.0878226i
$113$	−16.6031			−1.56189			−0.780943	−	0.624602i	$-0.785261\pi$
$113$	−16.6031			−1.56189			−0.780943	+	0.624602i	$0.785261\pi$
$114$		0			0
$115$	1.66372			0.155143
$116$	12.9516	−	22.4328i	1.20253	−	2.08283i
$117$		0			0
$118$	−14.7424	−	25.5346i	−1.35715	−	2.35065i
$119$	0.197929	−	0.342822i	0.0181441	−	0.0314265i
$120$		0			0
$121$	−10.6731			−0.970284
$122$	−20.0533			−1.81554
$123$		0			0
$124$	−12.4653	−	21.5905i	−1.11941	−	1.93888i
$125$	9.47786			0.847725
$126$		0			0
$127$	1.78674	+	3.09472i	0.158547	+	0.274612i	0.934345	−	0.356370i	$-0.115986\pi$
$127$	1.78674	+	3.09472i	0.158547	+	0.274612i	−0.775798	+	0.630982i	$0.782652\pi$
$128$	−8.28459	+	14.3493i	−0.732262	+	1.26831i
$129$		0			0
$130$	−7.60824	+	13.1779i	−0.667287	+	1.15577i
$131$	4.88169	−	8.45533i	0.426515	−	0.738746i	−0.570046	−	0.821613i	$-0.693074\pi$
$131$	4.88169	−	8.45533i	0.426515	−	0.738746i	0.996561	+	0.0828675i	$0.0264078\pi$
$132$		0			0
$133$	0.291855	+	0.791621i	0.0253070	+	0.0686422i
$134$	16.8469			1.45535
$135$		0			0
$136$	5.74364	−	9.94828i	0.492513	−	0.853058i
$137$	11.2337	+	19.4574i	0.959763	+	1.66236i	0.723071	+	0.690774i	$0.242730\pi$
$137$	11.2337	+	19.4574i	0.959763	+	1.66236i	0.236692	+	0.971585i	$0.423937\pi$
$138$		0			0
$139$	−9.25493	−	16.0300i	−0.784993	−	1.35965i	−0.929003	−	0.370072i	$-0.879333\pi$
$139$	−9.25493	−	16.0300i	−0.784993	−	1.35965i	0.144010	−	0.989576i	$-0.454000\pi$
$140$	0.880006			0.0743741
$141$		0			0
$142$	8.75507	+	15.1642i	0.734709	+	1.27255i
$143$	−1.62580	−	2.81597i	−0.135956	−	0.235483i
$144$		0			0
$145$	6.52844			0.542157
$146$	−10.0897	−	17.4758i	−0.835028	−	1.44631i
$147$		0			0
$148$	−19.8913	−	34.4527i	−1.63505	−	2.83200i
$149$	−7.44955	+	12.9030i	−0.610291	+	1.05706i	0.380900	+	0.924616i	$0.375614\pi$
$149$	−7.44955	+	12.9030i	−0.610291	+	1.05706i	−0.991191	+	0.132439i	$0.957719\pi$
$150$		0			0
$151$	−8.14617			−0.662926			−0.331463	−	0.943468i	$-0.607542\pi$
$151$	−8.14617			−0.662926			−0.331463	+	0.943468i	$0.607542\pi$
$152$	8.46927	+	22.9719i	0.686949	+	1.86326i
$153$		0			0
$154$	−0.138299	+	0.239541i	−0.0111445	+	0.0193028i
$155$	3.14165	−	5.44149i	0.252343	−	0.437071i
$156$		0			0
$157$	−4.69850	+	8.13804i	−0.374981	+	0.649486i	−0.990324	−	0.138773i	$-0.955684\pi$
$157$	−4.69850	+	8.13804i	−0.374981	+	0.649486i	0.615343	+	0.788259i	$0.289017\pi$
$158$	−6.09912	−	10.5640i	−0.485220	−	0.840426i
$159$		0			0
$160$	2.80956			0.222116
$161$	−0.150419	−	0.260533i	−0.0118547	−	0.0205329i
$162$		0			0
$163$	−4.38809			−0.343702			−0.171851	−	0.985123i	$-0.554975\pi$
$163$	−4.38809			−0.343702			−0.171851	+	0.985123i	$0.554975\pi$
$164$	8.19530			0.639946
$165$		0			0
$166$	7.53432	−	13.0498i	0.584777	−	1.01286i
$167$	−8.58819	−	14.8752i	−0.664574	−	1.15108i	−0.979401	−	0.201926i	$-0.935280\pi$
$167$	−8.58819	−	14.8752i	−0.664574	−	1.15108i	0.314827	−	0.949149i	$-0.398054\pi$
$168$		0			0
$169$	−9.67275	+	16.7537i	−0.744058	+	1.28875i
$170$	5.47180			0.419668
$171$		0			0
$172$	−13.6424			−1.04022
$173$	−3.79450	+	6.57226i	−0.288490	+	0.499680i	−0.973450	−	0.228902i	$-0.926487\pi$
$173$	−3.79450	+	6.57226i	−0.288490	+	0.499680i	0.684959	+	0.728581i	$0.259820\pi$
$174$		0			0
$175$	−0.373005	−	0.646063i	−0.0281965	−	0.0488378i
$176$	−1.58500	+	2.74530i	−0.119474	+	0.206935i
$177$		0			0
$178$	43.9665			3.29543
$179$	23.5346			1.75906			0.879530	−	0.475844i	$-0.157857\pi$
$179$	23.5346			1.75906			0.879530	+	0.475844i	$0.157857\pi$
$180$		0			0
$181$	1.22414	+	2.12028i	0.0909897	+	0.157599i	0.907928	−	0.419127i	$-0.137664\pi$
$181$	1.22414	+	2.12028i	0.0909897	+	0.157599i	−0.816938	+	0.576725i	$0.804330\pi$
$182$	2.75148			0.203953
$183$		0			0
$184$	−4.36497	−	7.56034i	−0.321790	−	0.557356i
$185$	5.01325	−	8.68320i	0.368581	−	0.638401i
$186$		0			0
$187$	−0.584633	+	1.01261i	−0.0427526	+	0.0740496i
$188$	22.5478	−	39.0539i	1.64447	−	2.84830i
$189$		0			0
$190$	−7.45922	+	8.96489i	−0.541148	+	0.650382i
$191$	−15.8473			−1.14667			−0.573334	−	0.819322i	$-0.694350\pi$
$191$	−15.8473			−1.14667			−0.573334	+	0.819322i	$0.694350\pi$
$192$		0			0
$193$	9.00617	−	15.5992i	0.648279	−	1.12285i	−0.335255	−	0.942127i	$-0.608823\pi$
$193$	9.00617	−	15.5992i	0.648279	−	1.12285i	0.983534	−	0.180724i	$-0.0578441\pi$
$194$	−9.48569	−	16.4297i	−0.681033	−	1.17958i
$195$		0			0
$196$	14.7858	+	25.6097i	1.05613	+	1.82927i
$197$	−15.0865			−1.07487			−0.537433	−	0.843306i	$-0.680606\pi$
$197$	−15.0865			−1.07487			−0.537433	+	0.843306i	$0.680606\pi$
$198$		0			0
$199$	8.82097	+	15.2784i	0.625302	+	1.08305i	0.988482	+	0.151336i	$0.0483576\pi$
$199$	8.82097	+	15.2784i	0.625302	+	1.08305i	−0.363180	+	0.931719i	$0.618309\pi$
$200$	−10.8241	−	18.7480i	−0.765382	−	1.32568i
$201$		0			0
$202$	18.1017			1.27363
$203$	−0.590244	−	1.02233i	−0.0414270	−	0.0717536i
$204$		0			0
$205$	1.03274	+	1.78876i	0.0721297	+	0.124932i
$206$	5.93867	−	10.2861i	0.413767	−	0.716665i
$207$		0			0
$208$	31.5338			2.18648
$209$	−0.862069	−	2.33826i	−0.0596305	−	0.161741i
$210$		0			0
$211$	−7.92083	+	13.7193i	−0.545292	+	0.944474i	0.453296	+	0.891360i	$0.350248\pi$
$211$	−7.92083	+	13.7193i	−0.545292	+	0.944474i	−0.998588	+	0.0531140i	$0.983085\pi$
$212$	−16.3446	+	28.3098i	−1.12255	+	1.94432i
$213$		0			0
$214$	4.57926	−	7.93151i	0.313032	−	0.542187i
$215$	−1.71916	−	2.97768i	−0.117246	−	0.203076i
$216$		0			0
$217$	−1.13616			−0.0771275
$218$	15.4203	+	26.7087i	1.04439	+	1.80894i
$219$		0			0
$220$	−2.59932			−0.175246
$221$	11.6313			0.782409
$222$		0			0
$223$	−7.99178	+	13.8422i	−0.535169	+	0.926940i	0.463986	+	0.885843i	$0.346419\pi$
$223$	−7.99178	+	13.8422i	−0.535169	+	0.926940i	−0.999155	+	0.0410976i	$0.986915\pi$
$224$	−0.254016	−	0.439969i	−0.0169722	−	0.0293966i
$225$		0			0
$226$	−20.7493	+	35.9388i	−1.38022	+	2.39061i
$227$	9.49687			0.630330			0.315165	−	0.949037i	$-0.397940\pi$
$227$	9.49687			0.630330			0.315165	+	0.949037i	$0.397940\pi$
$228$		0			0
$229$	−12.4620			−0.823513			−0.411757	−	0.911294i	$-0.635085\pi$
$229$	−12.4620			−0.823513			−0.411757	+	0.911294i	$0.635085\pi$
$230$	2.07919	−	3.60126i	0.137098	−	0.237460i
$231$		0			0
$232$	−17.1281	−	29.6668i	−1.12452	−	1.94772i
$233$	0.398235	−	0.689764i	0.0260893	−	0.0451879i	−0.852686	−	0.522424i	$-0.825028\pi$
$233$	0.398235	−	0.689764i	0.0260893	−	0.0451879i	0.878775	+	0.477236i	$0.158361\pi$
$234$		0			0
$235$	11.3655			0.741405
$236$	−50.1027			−3.26141
$237$		0			0
$238$	−0.494712	−	0.856867i	−0.0320674	−	0.0555424i
$239$	−7.61127			−0.492332			−0.246166	−	0.969228i	$-0.579171\pi$
$239$	−7.61127			−0.492332			−0.246166	+	0.969228i	$0.579171\pi$
$240$		0			0
$241$	13.9134	+	24.0987i	0.896240	+	1.55233i	0.832263	+	0.554381i	$0.187045\pi$
$241$	13.9134	+	24.0987i	0.896240	+	1.55233i	0.0639766	+	0.997951i	$0.479622\pi$
$242$	−13.3385	+	23.1029i	−0.857429	+	1.48511i
$243$		0			0
$244$	−17.0380	+	29.5107i	−1.09075	+	1.88923i
$245$	−3.72649	+	6.45448i	−0.238077	+	0.412361i
$246$		0			0
$247$	−15.8560	+	19.0566i	−1.00889	+	1.21254i
$248$	−32.9700			−2.09359
$249$		0			0
$250$	11.8447	−	20.5156i	0.749125	−	1.29752i
$251$	−4.03898	−	6.99572i	−0.254938	−	0.441566i	0.709940	−	0.704262i	$-0.248722\pi$
$251$	−4.03898	−	6.99572i	−0.254938	−	0.441566i	−0.964879	+	0.262696i	$0.915389\pi$
$252$		0			0
$253$	0.444300	+	0.769551i	0.0279329	+	0.0483812i
$254$	8.93172			0.560426
$255$		0			0
$256$	16.1780	+	28.0211i	1.01112	+	1.75132i
$257$	0.186398	+	0.322850i	0.0116272	+	0.0201388i	0.871780	−	0.489897i	$-0.162966\pi$
$257$	0.186398	+	0.322850i	0.0116272	+	0.0201388i	−0.860153	+	0.510036i	$0.829632\pi$
$258$		0			0
$259$	−1.81301			−0.112655
$260$	12.9285	+	22.3928i	0.801790	+	1.38874i
$261$		0			0
$262$	−12.2015	−	21.1337i	−0.753813	−	1.30564i
$263$	5.57101	−	9.64928i	0.343523	−	0.595000i	−0.641561	−	0.767072i	$-0.721713\pi$
$263$	5.57101	−	9.64928i	0.343523	−	0.595000i	0.985084	+	0.172072i	$0.0550462\pi$
$264$		0			0
$265$	−8.23875			−0.506103
$266$	2.07827	+	0.357563i	0.127427	+	0.0219236i
$267$		0			0
$268$	14.3138	−	24.7922i	0.874352	−	1.51442i
$269$	−12.3204	+	21.3396i	−0.751191	+	1.30110i	0.196055	+	0.980593i	$0.437187\pi$
$269$	−12.3204	+	21.3396i	−0.751191	+	1.30110i	−0.947246	+	0.320508i	$0.896146\pi$
$270$		0			0
$271$	−0.0196243	+	0.0339902i	−0.00119209	+	0.00206476i	−0.866621	−	0.498967i	$-0.833713\pi$
$271$	−0.0196243	+	0.0339902i	−0.00119209	+	0.00206476i	0.865429	+	0.501032i	$0.167046\pi$
$272$	−5.66973	−	9.82026i	−0.343778	−	0.595441i
$273$		0			0
$274$	56.1563			3.39253
$275$	1.10177	+	1.90831i	0.0664390	+	0.115076i
$276$		0			0
$277$	−8.82444			−0.530209			−0.265105	−	0.964220i	$-0.585407\pi$
$277$	−8.82444			−0.530209			−0.265105	+	0.964220i	$0.585407\pi$
$278$	−46.2645			−2.77476
$279$		0			0
$280$	0.581892	−	1.00787i	0.0347747	−	0.0602316i
$281$	0.708321	+	1.22685i	0.0422549	+	0.0731876i	0.886379	−	0.462960i	$-0.153213\pi$
$281$	0.708321	+	1.22685i	0.0422549	+	0.0731876i	−0.844124	+	0.536147i	$0.819879\pi$
$282$		0			0
$283$	−6.65237	+	11.5223i	−0.395443	+	0.684927i	−0.993158	−	0.116782i	$-0.962742\pi$
$283$	−6.65237	+	11.5223i	−0.395443	+	0.684927i	0.597715	+	0.801709i	$0.296075\pi$
$284$	29.7545			1.76560
$285$		0			0
$286$	−8.12721			−0.480572
$287$	0.186742	−	0.323447i	0.0110231	−	0.0190925i
$288$		0			0
$289$	6.40870	+	11.1002i	0.376982	+	0.652953i
$290$	8.15875	−	14.1314i	0.479098	−	0.829822i
$291$		0			0
$292$	−34.2902			−2.00668
$293$	−16.5875			−0.969051			−0.484526	−	0.874777i	$-0.661008\pi$
$293$	−16.5875			−0.969051			−0.484526	+	0.874777i	$0.661008\pi$
$294$		0			0
$295$	−6.31374	−	10.9357i	−0.367600	−	0.636702i
$296$	−52.6114			−3.05798
$297$		0			0
$298$	18.6198	+	32.2504i	1.07861	+	1.86822i
$299$	4.41971	−	7.65516i	0.255598	−	0.442709i
$300$		0			0
$301$	−0.310863	+	0.538431i	−0.0179178	+	0.0310346i
$302$	−10.1805	+	17.6331i	−0.585820	+	1.01467i
$303$		0			0
$304$	23.8184	+	4.09791i	1.36608	+	0.235031i
$305$	−8.58826			−0.491762
$306$		0			0
$307$	15.6001	−	27.0201i	0.890342	−	1.54212i	0.0508769	−	0.998705i	$-0.483798\pi$
$307$	15.6001	−	27.0201i	0.890342	−	1.54212i	0.839465	−	0.543413i	$-0.182868\pi$
$308$	0.235008	+	0.407046i	0.0133908	+	0.0231936i
$309$		0			0
$310$	−7.85238	−	13.6007i	−0.445985	−	0.772469i
$311$	16.1732			0.917101			0.458550	−	0.888668i	$-0.348369\pi$
$311$	16.1732			0.917101			0.458550	+	0.888668i	$0.348369\pi$
$312$		0			0
$313$	−4.98259	−	8.63010i	−0.281633	−	0.487802i	0.690154	−	0.723662i	$-0.257543\pi$
$313$	−4.98259	−	8.63010i	−0.281633	−	0.487802i	−0.971787	+	0.235860i	$0.924209\pi$
$314$	11.7437	+	20.3406i	0.662733	+	1.14789i
$315$		0			0
$316$	−20.7281			−1.16605
$317$	−5.38021	−	9.31879i	−0.302183	−	0.523395i	0.674448	−	0.738323i	$-0.264382\pi$
$317$	−5.38021	−	9.31879i	−0.302183	−	0.523395i	−0.976630	+	0.214927i	$0.931049\pi$
$318$		0			0
$319$	1.74344	+	3.01972i	0.0976137	+	0.169072i
$320$	−2.42398	+	4.19846i	−0.135505	+	0.234701i
$321$		0			0
$322$	−0.751928			−0.0419033
$323$	8.78548	+	1.51153i	0.488837	+	0.0841036i
$324$		0			0
$325$	10.9599	−	18.9831i	0.607945	−	1.05299i
$326$	−5.48391	+	9.49841i	−0.303726	+	0.526068i
$327$		0			0
$328$	5.41904	−	9.38605i	0.299216	−	0.518258i
$329$	−1.02757	−	1.77981i	−0.0566518	−	0.0981238i
$330$		0			0
$331$	−3.66316			−0.201346			−0.100673	−	0.994920i	$-0.532100\pi$
$331$	−3.66316			−0.201346			−0.100673	+	0.994920i	$0.532100\pi$
$332$	−12.8029	−	22.1752i	−0.702649	−	1.21702i
$333$		0			0
$334$	−42.9315			−2.34910
$335$	7.21506			0.394201
$336$		0			0
$337$	4.89465	−	8.47779i	0.266629	−	0.461814i	−0.701360	−	0.712807i	$-0.747424\pi$
$337$	4.89465	−	8.47779i	0.266629	−	0.461814i	0.967989	+	0.250992i	$0.0807569\pi$
$338$	24.1765	+	41.8750i	1.31503	+	2.27770i
$339$		0			0
$340$	4.64904	−	8.05237i	0.252130	−	0.436701i
$341$	3.35594			0.181734
$342$		0			0
$343$	2.70259			0.145926
$344$	−9.02086	+	15.6246i	−0.486372	+	0.842422i
$345$		0			0
$346$	9.48415	+	16.4270i	0.509871	+	0.883123i
$347$	1.22366	−	2.11944i	0.0656895	−	0.113778i	−0.831310	−	0.555809i	$-0.812409\pi$
$347$	1.22366	−	2.11944i	0.0656895	−	0.113778i	0.897000	+	0.442031i	$0.145742\pi$
$348$		0			0
$349$	10.1049			0.540905			0.270453	−	0.962733i	$-0.412827\pi$
$349$	10.1049			0.540905			0.270453	+	0.962733i	$0.412827\pi$
$350$	−1.86461			−0.0996677
$351$		0			0
$352$	0.750302	+	1.29956i	0.0399912	+	0.0692668i
$353$	−9.94896			−0.529529			−0.264765	−	0.964313i	$-0.585294\pi$
$353$	−9.94896			−0.529529			−0.264765	+	0.964313i	$0.585294\pi$
$354$		0			0
$355$	3.74954	+	6.49440i	0.199005	+	0.344687i
$356$	37.3555	−	64.7016i	1.97984	−	3.42918i
$357$		0			0
$358$	29.4118	−	50.9427i	1.55446	−	2.69240i
$359$	−0.112962	+	0.195656i	−0.00596191	+	0.0103263i	−0.868991	−	0.494828i	$-0.835231\pi$
$359$	−0.112962	+	0.195656i	−0.00596191	+	0.0103263i	0.863029	+	0.505154i	$0.168564\pi$
$360$		0			0
$361$	−14.4529	+	12.3334i	−0.760679	+	0.649128i
$362$	6.11936			0.321626
$363$		0			0
$364$	2.33776	−	4.04911i	0.122532	−	0.212231i
$365$	−4.32112	−	7.48440i	−0.226178	−	0.391751i
$366$		0			0
$367$	−3.09327	−	5.35770i	−0.161467	−	0.279670i	0.773928	−	0.633274i	$-0.218289\pi$
$367$	−3.09327	−	5.35770i	−0.161467	−	0.279670i	−0.935395	+	0.353604i	$0.884956\pi$
$368$	−8.61759			−0.449223
$369$		0			0
$370$	−12.5304	−	21.7032i	−0.651422	−	1.12830i
$371$	0.744875	+	1.29016i	0.0386720	+	0.0669819i
$372$		0			0
$373$	14.4281			0.747059			0.373530	−	0.927618i	$-0.378147\pi$
$373$	14.4281			0.747059			0.373530	+	0.927618i	$0.378147\pi$
$374$	1.46126	+	2.53098i	0.0755599	+	0.130874i
$375$		0			0
$376$	−29.8188	−	51.6478i	−1.53779	−	2.66353i
$377$	17.3430	−	30.0389i	0.893208	−	1.54708i
$378$		0			0
$379$	−16.6715			−0.856358			−0.428179	−	0.903694i	$-0.640845\pi$
$379$	−16.6715			−0.856358			−0.428179	+	0.903694i	$0.640845\pi$
$380$	6.85523	+	18.5940i	0.351666	+	0.953851i
$381$		0			0
$382$	−19.8047	+	34.3028i	−1.01330	+	1.75508i
$383$	14.8521	−	25.7246i	0.758908	−	1.31447i	−0.184500	−	0.982833i	$-0.559067\pi$
$383$	14.8521	−	25.7246i	0.758908	−	1.31447i	0.943408	−	0.331635i	$-0.107600\pi$
$384$		0			0
$385$	−0.0592296	+	0.102589i	−0.00301862	+	0.00522840i
$386$	−22.5105	−	38.9893i	−1.14575	−	1.98450i
$387$		0			0
$388$	−32.2376			−1.63661
$389$	−13.1780	−	22.8249i	−0.668150	−	1.15727i	−0.978421	−	0.206622i	$-0.933753\pi$
$389$	−13.1780	−	22.8249i	−0.668150	−	1.15727i	0.310271	−	0.950648i	$-0.399580\pi$
$390$		0			0
$391$	−3.17863			−0.160750
$392$	39.1076			1.97523
$393$		0			0
$394$	−18.8539	+	32.6560i	−0.949847	+	1.64518i
$395$	−2.61208	−	4.52425i	−0.131428	−	0.227640i
$396$		0			0
$397$	5.54142	−	9.59802i	0.278116	−	0.481711i	−0.692801	−	0.721129i	$-0.743623\pi$
$397$	5.54142	−	9.59802i	0.278116	−	0.481711i	0.970916	+	0.239418i	$0.0769568\pi$
$398$	44.0951			2.21029
$399$		0			0
$400$	−21.3697			−1.06849
$401$	−13.0893	+	22.6713i	−0.653647	+	1.13215i	0.328584	+	0.944475i	$0.393429\pi$
$401$	−13.0893	+	22.6713i	−0.653647	+	1.13215i	−0.982231	+	0.187676i	$0.939905\pi$
$402$		0			0
$403$	−16.6917	−	28.9109i	−0.831474	−	1.44015i
$404$	15.3799	−	26.6387i	0.765177	−	1.32533i
$405$		0			0
$406$	−2.95057			−0.146434
$407$	5.35520			0.265448
$408$		0			0
$409$	−5.40845	−	9.36771i	−0.267431	−	0.463204i	0.700767	−	0.713390i	$-0.252841\pi$
$409$	−5.40845	−	9.36771i	−0.267431	−	0.463204i	−0.968198	+	0.250187i	$0.919508\pi$
$410$	5.16256			0.254961
$411$		0			0
$412$	−10.0914	−	17.4788i	−0.497168	−	0.861120i
$413$	−1.14167	+	1.97742i	−0.0561777	+	0.0973026i
$414$		0			0
$415$	3.22673	−	5.58887i	0.158394	−	0.274347i
$416$	7.46368	−	12.9275i	0.365937	−	0.633821i
$417$		0			0
$418$	−6.13870	−	1.05615i	−0.300254	−	0.0516582i
$419$	12.5477			0.612996			0.306498	−	0.951871i	$-0.400843\pi$
$419$	12.5477			0.612996			0.306498	+	0.951871i	$0.400843\pi$
$420$		0			0
$421$	−3.97623	+	6.88704i	−0.193790	+	0.335654i	−0.946503	−	0.322695i	$-0.895411\pi$
$421$	−3.97623	+	6.88704i	−0.193790	+	0.335654i	0.752713	+	0.658348i	$0.228745\pi$
$422$	19.7977	+	34.2906i	0.963737	+	1.66924i
$423$		0			0
$424$	21.6154	+	37.4389i	1.04974	+	1.81819i
$425$	−7.88229			−0.382347
$426$		0			0
$427$	0.776475	+	1.34489i	0.0375762	+	0.0650840i
$428$	−7.78141	−	13.4778i	−0.376128	−	0.651474i
$429$		0			0
$430$	−8.59392			−0.414435
$431$	0.516348	+	0.894341i	0.0248716	+	0.0430789i	0.878193	−	0.478306i	$-0.158749\pi$
$431$	0.516348	+	0.894341i	0.0248716	+	0.0430789i	−0.853322	+	0.521385i	$0.825416\pi$
$432$		0			0
$433$	8.22588	+	14.2476i	0.395310	+	0.684698i	0.993141	−	0.116925i	$-0.0373037\pi$
$433$	8.22588	+	14.2476i	0.395310	+	0.684698i	−0.597830	+	0.801623i	$0.703970\pi$
$434$	−1.41989	+	2.45932i	−0.0681567	+	0.118051i
$435$		0			0
$436$	52.4065			2.50982
$437$	4.33314	−	5.20780i	0.207282	−	0.249123i
$438$		0			0
$439$	12.4617	−	21.5842i	0.594763	−	1.03016i	−0.398818	−	0.917030i	$-0.630579\pi$
$439$	12.4617	−	21.5842i	0.594763	−	1.03016i	0.993580	−	0.113129i	$-0.0360873\pi$
$440$	−1.71877	+	2.97699i	−0.0819391	+	0.141923i
$441$		0			0
$442$	14.5360	−	25.1771i	0.691406	−	1.19755i
$443$	0.348840	+	0.604209i	0.0165739	+	0.0287069i	0.874193	−	0.485578i	$-0.161391\pi$
$443$	0.348840	+	0.604209i	0.0165739	+	0.0287069i	−0.857619	+	0.514285i	$0.828057\pi$
$444$		0			0
$445$	18.8296			0.892607
$446$	19.9750	+	34.5978i	0.945846	+	1.63825i
$447$		0			0
$448$	0.876620			0.0414164
$449$	−19.7227			−0.930771			−0.465385	−	0.885108i	$-0.654084\pi$
$449$	−19.7227			−0.930771			−0.465385	+	0.885108i	$0.654084\pi$
$450$		0			0
$451$	−0.551592	+	0.955385i	−0.0259735	+	0.0449873i
$452$	35.2586	+	61.0698i	1.65843	+	2.87248i
$453$		0			0
$454$	11.8685	−	20.5568i	0.557015	−	0.964779i
$455$	1.17838			0.0552433
$456$		0			0
$457$	20.7346			0.969924			0.484962	−	0.874535i	$-0.338833\pi$
$457$	20.7346			0.969924			0.484962	+	0.874535i	$0.338833\pi$
$458$	−15.5741	+	26.9751i	−0.727729	+	1.26046i
$459$		0			0
$460$	−3.53311	−	6.11952i	−0.164732	−	0.285324i
$461$	−10.9954	+	19.0445i	−0.512105	+	0.886992i	0.487797	+	0.872957i	$0.337801\pi$
$461$	−10.9954	+	19.0445i	−0.512105	+	0.886992i	−0.999902	+	0.0140344i	$0.995533\pi$
$462$		0			0
$463$	−10.1268			−0.470631			−0.235316	−	0.971919i	$-0.575612\pi$
$463$	−10.1268			−0.470631			−0.235316	+	0.971919i	$0.575612\pi$
$464$	−33.8155			−1.56984
$465$		0			0
$466$	−0.995369	−	1.72403i	−0.0461096	−	0.0798641i
$467$	−37.7532			−1.74701			−0.873506	−	0.486814i	$-0.838159\pi$
$467$	−37.7532			−1.74701			−0.873506	+	0.486814i	$0.838159\pi$
$468$		0			0
$469$	−0.652322	−	1.12985i	−0.0301214	−	0.0521718i
$470$	14.2038	−	24.6017i	0.655171	−	1.13479i
$471$		0			0
$472$	−33.1297	+	57.3824i	−1.52492	+	2.64124i
$473$	0.918214	−	1.59039i	0.0422195	−	0.0731264i
$474$		0			0
$475$	10.7452	−	12.9142i	0.493024	−	0.592543i
$476$	−1.68130			−0.0770623
$477$		0			0
$478$	−9.51199	+	16.4752i	−0.435068	+	0.753560i
$479$	−21.3890	−	37.0469i	−0.977289	−	1.69271i	−0.672164	−	0.740402i	$-0.734635\pi$
$479$	−21.3890	−	37.0469i	−0.977289	−	1.69271i	−0.305125	−	0.952312i	$-0.598698\pi$
$480$		0			0
$481$	−26.6356	−	46.1343i	−1.21448	−	2.10354i
$482$	69.5516			3.16799
$483$		0			0
$484$	22.6657	+	39.2581i	1.03026	+	1.78446i
$485$	−4.06245	−	7.03637i	−0.184466	−	0.319505i
$486$		0			0
$487$	40.8764			1.85229			0.926144	−	0.377170i	$-0.123103\pi$
$487$	40.8764			1.85229			0.926144	+	0.377170i	$0.123103\pi$
$488$	22.5323	+	39.0272i	1.01999	+	1.76668i
$489$		0			0
$490$	9.31418	+	16.1326i	0.420772	+	0.728798i
$491$	−14.7667	+	25.5766i	−0.666410	+	1.15426i	0.312491	+	0.949921i	$0.398837\pi$
$491$	−14.7667	+	25.5766i	−0.666410	+	1.15426i	−0.978901	+	0.204335i	$0.934497\pi$
$492$		0			0
$493$	−12.4729			−0.561753
$494$	21.4340	+	58.1371i	0.964361	+	2.61571i
$495$		0			0
$496$	−16.2728	+	28.1854i	−0.730672	+	1.26556i
$497$	0.678002	−	1.17433i	0.0304125	−	0.0526760i
$498$		0			0
$499$	−5.40313	+	9.35849i	−0.241877	+	0.418944i	−0.961249	−	0.275682i	$-0.911096\pi$
$499$	−5.40313	+	9.35849i	−0.241877	+	0.418944i	0.719372	+	0.694625i	$0.244430\pi$
$500$	−20.1274	−	34.8617i	−0.900124	−	1.55906i
$501$		0			0
$502$	−20.1905			−0.901145
$503$	−18.1255	−	31.3943i	−0.808175	−	1.39980i	−0.914126	−	0.405429i	$-0.867122\pi$
$503$	−18.1255	−	31.3943i	−0.808175	−	1.39980i	0.105951	−	0.994371i	$-0.466211\pi$
$504$		0			0
$505$	7.75244			0.344979
$506$	2.22101			0.0987360
$507$		0			0
$508$	7.58871	−	13.1440i	0.336695	−	0.583172i
$509$	16.8203	+	29.1336i	0.745546	+	1.29132i	0.949939	+	0.312435i	$0.101145\pi$
$509$	16.8203	+	29.1336i	0.745546	+	1.29132i	−0.204393	+	0.978889i	$0.565522\pi$
$510$		0			0
$511$	−0.781355	+	1.35335i	−0.0345651	+	0.0598685i
$512$	47.7337			2.10955
$513$		0			0
$514$	0.931782			0.0410991
$515$	2.54336	−	4.40523i	0.112074	−	0.194118i
$516$		0			0
$517$	3.03520	+	5.25711i	0.133488	+	0.231208i
$518$	−2.26577	+	3.92443i	−0.0995521	+	0.172429i
$519$		0			0
$520$	34.1951			1.49956
$521$	−11.4164			−0.500162			−0.250081	−	0.968225i	$-0.580457\pi$
$521$	−11.4164			−0.500162			−0.250081	+	0.968225i	$0.580457\pi$
$522$		0			0
$523$	8.31606	+	14.4038i	0.363636	+	0.629836i	0.988556	−	0.150853i	$-0.0482019\pi$
$523$	8.31606	+	14.4038i	0.363636	+	0.629836i	−0.624920	+	0.780688i	$0.714869\pi$
$524$	−41.4674			−1.81151
$525$		0			0
$526$	−13.9245	−	24.1179i	−0.607135	−	1.05159i
$527$	−6.00229	+	10.3963i	−0.261464	+	0.452869i
$528$		0			0
$529$	10.2922	−	17.8266i	0.447486	−	0.775068i
$530$	−10.2962	+	17.8335i	−0.447237	+	0.774637i
$531$		0			0
$532$	2.29197	−	2.75461i	0.0993694	−	0.119427i
$533$	10.9740			0.475337
$534$		0			0
$535$	1.96116	−	3.39684i	0.0847885	−	0.146858i
$536$	−18.9296	−	32.7870i	−0.817633	−	1.41618i
$537$		0			0
$538$	30.7943	+	53.3373i	1.32764	+	2.29954i
$539$	−3.98068			−0.171460
$540$		0			0
$541$	−3.67947	−	6.37302i	−0.158193	−	0.273998i	0.776024	−	0.630703i	$-0.217233\pi$
$541$	−3.67947	−	6.37302i	−0.158193	−	0.273998i	−0.934217	+	0.356705i	$0.883900\pi$
$542$	0.0490498	+	0.0849568i	0.00210687	+	0.00364921i
$543$		0			0
$544$	−5.36783			−0.230144
$545$	6.60406	+	11.4386i	0.282887	+	0.489974i
$546$		0			0
$547$	19.3523	+	33.5191i	0.827443	+	1.43317i	0.900038	+	0.435812i	$0.143539\pi$
$547$	19.3523	+	33.5191i	0.827443	+	1.43317i	−0.0725944	+	0.997362i	$0.523128\pi$
$548$	47.7124	−	82.6403i	2.03817	−	3.53022i
$549$		0			0
$550$	5.50761			0.234845
$551$	17.0033	−	20.4354i	0.724363	−	0.870579i
$552$		0			0
$553$	−0.472322	+	0.818086i	−0.0200852	+	0.0347886i
$554$	−11.0281	+	19.1013i	−0.468540	+	0.811535i
$555$		0			0
$556$	−39.3079	+	68.0834i	−1.66703	+	2.88738i
$557$	7.68267	+	13.3068i	0.325525	+	0.563826i	0.981619	−	0.190854i	$-0.0611256\pi$
$557$	7.68267	+	13.3068i	0.325525	+	0.563826i	−0.656093	+	0.754680i	$0.727792\pi$
$558$		0			0
$559$	−18.2680			−0.772654
$560$	−0.574404	−	0.994898i	−0.0242730	−	0.0420421i
$561$		0			0
$562$	3.54082			0.149361
$563$	32.6963			1.37799			0.688993	−	0.724768i	$-0.258053\pi$
$563$	32.6963			1.37799			0.688993	+	0.724768i	$0.258053\pi$
$564$		0			0
$565$	−8.88631	+	15.3915i	−0.373850	+	0.647527i
$566$	16.6273	+	28.7993i	0.698896	+	1.21052i
$567$		0			0
$568$	19.6748	−	34.0777i	0.825535	−	1.42987i
$569$	−20.7445			−0.869655			−0.434827	−	0.900514i	$-0.643191\pi$
$569$	−20.7445			−0.869655			−0.434827	+	0.900514i	$0.643191\pi$
$570$		0			0
$571$	16.9043			0.707421			0.353710	−	0.935355i	$-0.384920\pi$
$571$	16.9043			0.707421			0.353710	+	0.935355i	$0.384920\pi$
$572$	−6.90517	+	11.9601i	−0.288720	+	0.500077i
$573$		0			0
$574$	−0.466753	−	0.808440i	−0.0194819	−	0.0337436i
$575$	−2.99513	+	5.18772i	−0.124906	+	0.216343i
$576$		0			0
$577$	−17.8528			−0.743221			−0.371610	−	0.928389i	$-0.621194\pi$
$577$	−17.8528			−0.743221			−0.371610	+	0.928389i	$0.621194\pi$
$578$	32.0364			1.33254
$579$		0			0
$580$	−13.8639	−	24.0130i	−0.575668	−	0.997087i
$581$	−1.16693			−0.0484125
$582$		0			0
$583$	−2.20018	−	3.81083i	−0.0911222	−	0.157828i
$584$	−22.6740	+	39.2724i	−0.938255	+	1.62511i
$585$		0			0
$586$	−20.7298	+	35.9050i	−0.856340	+	1.48322i
$587$	9.49336	−	16.4430i	0.391833	−	0.678675i	−0.600858	−	0.799355i	$-0.705174\pi$
$587$	9.49336	−	16.4430i	0.391833	−	0.678675i	0.992691	+	0.120681i	$0.0385078\pi$
$588$		0			0
$589$	−8.85066	−	24.0063i	−0.364685	−	0.989164i
$590$	−31.5617			−1.29938
$591$		0			0
$592$	−25.9672	+	44.9765i	−1.06725	+	1.84852i
$593$	19.1067	+	33.0938i	0.784618	+	1.35900i	0.929227	+	0.369510i	$0.120474\pi$
$593$	19.1067	+	33.0938i	0.784618	+	1.35900i	−0.144609	+	0.989489i	$0.546192\pi$
$594$		0			0
$595$	−0.211871	−	0.366971i	−0.00868586	−	0.0150444i
$596$	63.2801			2.59206
$597$		0			0
$598$	−11.0468	−	19.1337i	−0.451739	−	0.782434i
$599$	−19.8987	−	34.4656i	−0.813041	−	1.40823i	−0.910726	−	0.413010i	$-0.864477\pi$
$599$	−19.8987	−	34.4656i	−0.813041	−	1.40823i	0.0976858	−	0.995217i	$-0.468856\pi$
$600$		0			0
$601$	37.9672			1.54871			0.774357	−	0.632748i	$-0.218073\pi$
$601$	37.9672			1.54871			0.774357	+	0.632748i	$0.218073\pi$
$602$	0.776986	+	1.34578i	0.0316676	+	0.0548499i
$603$		0			0
$604$	17.2994	+	29.9634i	0.703902	+	1.21919i
$605$	−5.71248	+	9.89431i	−0.232245	+	0.402261i
$606$		0			0
$607$	13.4994			0.547924			0.273962	−	0.961740i	$-0.411666\pi$
$607$	13.4994			0.547924			0.273962	+	0.961740i	$0.411666\pi$
$608$	7.31748	−	8.79455i	0.296763	−	0.356666i
$609$		0			0
$610$	−10.7330	+	18.5900i	−0.434565	+	0.752688i
$611$	30.1928	−	52.2955i	1.22147	−	2.11565i
$612$		0			0
$613$	−1.53078	+	2.65140i	−0.0618278	+	0.107089i	−0.895282	−	0.445499i	$-0.853026\pi$
$613$	−1.53078	+	2.65140i	−0.0618278	+	0.107089i	0.833455	+	0.552588i	$0.186360\pi$
$614$	−38.9915	−	67.5353i	−1.57357	−	2.72550i
$615$		0			0
$616$	0.621584			0.0250443
$617$	−5.51398	−	9.55050i	−0.221985	−	0.384489i	0.733426	−	0.679769i	$-0.237920\pi$
$617$	−5.51398	−	9.55050i	−0.221985	−	0.384489i	−0.955411	+	0.295281i	$0.904587\pi$
$618$		0			0
$619$	−7.94478			−0.319328			−0.159664	−	0.987171i	$-0.551041\pi$
$619$	−7.94478			−0.319328			−0.159664	+	0.987171i	$0.551041\pi$
$620$	−26.6867			−1.07176
$621$		0			0
$622$	20.2121	−	35.0084i	0.810431	−	1.40371i
$623$	−1.70240	−	2.94865i	−0.0682054	−	0.118135i
$624$		0			0
$625$	−4.56264	+	7.90272i	−0.182505	+	0.316109i
$626$	−24.9074			−0.995502
$627$		0			0
$628$	39.9113			1.59264
$629$	−9.57809	+	16.5897i	−0.381904	+	0.661476i
$630$		0			0
$631$	−4.27495	−	7.40443i	−0.170183	−	0.294766i	0.768301	−	0.640089i	$-0.221103\pi$
$631$	−4.27495	−	7.40443i	−0.170183	−	0.294766i	−0.938484	+	0.345323i	$0.887769\pi$
$632$	−13.7062	+	23.7399i	−0.545204	+	0.944321i
$633$		0			0
$634$	−26.8951			−1.06814
$635$	3.82520			0.151798
$636$		0			0
$637$	19.7990	+	34.2930i	0.784467	+	1.35874i
$638$	8.71526			0.345040
$639$		0			0
$640$	8.86818	+	15.3601i	0.350545	+	0.607163i
$641$	17.3272	−	30.0116i	0.684384	−	1.18539i	−0.289247	−	0.957255i	$-0.593405\pi$
$641$	17.3272	−	30.0116i	0.684384	−	1.18539i	0.973630	−	0.228132i	$-0.0732619\pi$
$642$		0			0
$643$	18.9184	−	32.7677i	0.746069	−	1.29223i	−0.203624	−	0.979049i	$-0.565272\pi$
$643$	18.9184	−	32.7677i	0.746069	−	1.29223i	0.949693	−	0.313181i	$-0.101395\pi$
$644$	−0.638865	+	1.10655i	−0.0251748	+	0.0436040i
$645$		0			0
$646$	14.2513	−	17.1279i	0.560708	−	0.673890i
$647$	7.50137			0.294909			0.147455	−	0.989069i	$-0.452892\pi$
$647$	7.50137			0.294909			0.147455	+	0.989069i	$0.452892\pi$
$648$		0			0
$649$	3.37220	−	5.84083i	0.132371	−	0.229273i
$650$	−27.3937	−	47.4472i	−1.07447	−	1.86103i
$651$		0			0
$652$	9.31865	+	16.1404i	0.364947	+	0.632106i
$653$	25.0757			0.981287			0.490644	−	0.871360i	$-0.336762\pi$
$653$	25.0757			0.981287			0.490644	+	0.871360i	$0.336762\pi$
$654$		0			0
$655$	−5.22556	−	9.05094i	−0.204180	−	0.353649i
$656$	−5.34930	−	9.26526i	−0.208855	−	0.361748i
$657$		0			0
$658$	−5.13672			−0.200250
$659$	7.74250	+	13.4104i	0.301605	+	0.522395i	0.976500	−	0.215519i	$-0.0691443\pi$
$659$	7.74250	+	13.4104i	0.301605	+	0.522395i	−0.674895	+	0.737914i	$0.735811\pi$
$660$		0			0
$661$	2.87978	+	4.98792i	0.112010	+	0.194008i	0.916581	−	0.399850i	$-0.130938\pi$
$661$	2.87978	+	4.98792i	0.112010	+	0.194008i	−0.804570	+	0.593857i	$0.797604\pi$
$662$	−4.57794	+	7.92923i	−0.177927	+	0.308178i
$663$		0			0
$664$	−33.8629			−1.31414
$665$	0.890063	+	0.153134i	0.0345152	+	0.00593828i
$666$		0			0
$667$	−4.73950	+	8.20906i	−0.183514	+	0.317856i
$668$	−36.4761	+	63.1785i	−1.41130	+	2.44445i
$669$		0			0
$670$	9.01683	−	15.6176i	0.348351	−	0.603361i
$671$	−2.29352	−	3.97249i	−0.0885403	−	0.153356i
$672$		0			0
$673$	−12.5871			−0.485198			−0.242599	−	0.970127i	$-0.578000\pi$
$673$	−12.5871			−0.485198			−0.242599	+	0.970127i	$0.578000\pi$
$674$	−12.2339	−	21.1898i	−0.471233	−	0.816200i
$675$		0			0
$676$	82.1651			3.16019
$677$	−12.0664			−0.463749			−0.231875	−	0.972746i	$-0.574486\pi$
$677$	−12.0664			−0.463749			−0.231875	+	0.972746i	$0.574486\pi$
$678$		0			0
$679$	−0.734582	+	1.27233i	−0.0281907	+	0.0488277i
$680$	−6.14824	−	10.6491i	−0.235774	−	0.408373i
$681$		0			0
$682$	4.19400	−	7.26422i	0.160597	−	0.278161i
$683$	36.8458			1.40987			0.704933	−	0.709274i	$-0.250977\pi$
$683$	36.8458			1.40987			0.704933	+	0.709274i	$0.250977\pi$
$684$		0			0
$685$	24.0501			0.918908
$686$	3.37749	−	5.84998i	0.128953	−	0.223353i
$687$		0			0
$688$	8.90478	+	15.4235i	0.339492	+	0.588017i
$689$	−21.8864	+	37.9084i	−0.833807	+	1.44420i
$690$		0			0
$691$	−41.0406			−1.56126			−0.780629	−	0.624995i	$-0.785101\pi$
$691$	−41.0406			−1.56126			−0.780629	+	0.624995i	$0.785101\pi$
$692$	32.2323			1.22529
$693$		0			0
$694$	−3.05848	−	5.29744i	−0.116098	−	0.201088i
$695$	−19.8137			−0.751578
$696$		0			0
$697$	−1.97311	−	3.41752i	−0.0747368	−	0.129448i
$698$	12.6284	−	21.8730i	0.477992	−	0.827906i
$699$		0			0
$700$	−1.58424	+	2.74399i	−0.0598787	+	0.103713i
$701$	18.0662	−	31.2916i	0.682352	−	1.18187i	−0.291909	−	0.956446i	$-0.594290\pi$
$701$	18.0662	−	31.2916i	0.682352	−	1.18187i	0.974261	−	0.225423i	$-0.0723763\pi$
$702$		0			0
$703$	−14.1233	−	38.3079i	−0.532672	−	1.44481i
$704$	−2.58932			−0.0975887
$705$		0			0
$706$	−12.4335	+	21.5354i	−0.467939	+	0.810494i
$707$	−0.700907	−	1.21401i	−0.0263603	−	0.0456574i
$708$		0			0
$709$	−14.4051	−	24.9503i	−0.540994	−	0.937030i	−0.998847	−	0.0480019i	$-0.984715\pi$
$709$	−14.4051	−	24.9503i	−0.540994	−	0.937030i	0.457853	−	0.889028i	$-0.348619\pi$
$710$	18.7436			0.703434
$711$		0			0
$712$	−49.4017	−	85.5662i	−1.85141	−	3.20673i
$713$	4.56153	+	7.90080i	0.170831	+	0.295887i
$714$		0			0
$715$	−3.48065			−0.130169
$716$	−49.9786	−	86.5655i	−1.86779	−	3.23510i
$717$		0			0
$718$	0.282343	+	0.489032i	0.0105369	+	0.0182505i
$719$	2.58283	−	4.47360i	0.0963235	−	0.166837i	−0.813837	−	0.581094i	$-0.802625\pi$
$719$	2.58283	−	4.47360i	0.0963235	−	0.166837i	0.910160	+	0.414256i	$0.135958\pi$
$720$		0			0
$721$	−0.919793			−0.0342549
$722$	8.63461	+	46.6979i	0.321347	+	1.73792i
$723$		0			0
$724$	5.19923	−	9.00532i	0.193228	−	0.334680i
$725$	−11.7529	+	20.3566i	−0.436492	+	0.756026i
$726$		0			0
$727$	5.32376	−	9.22103i	0.197447	−	0.341989i	−0.750253	−	0.661151i	$-0.770068\pi$
$727$	5.32376	−	9.22103i	0.197447	−	0.341989i	0.947700	+	0.319162i	$0.103401\pi$
$728$	−3.09162	−	5.35485i	−0.114583	−	0.198464i
$729$		0			0
$730$	−21.6008			−0.799482
$731$	3.28456	+	5.68902i	0.121484	+	0.210416i
$732$		0			0
$733$	−31.4643			−1.16216			−0.581080	−	0.813846i	$-0.697370\pi$
$733$	−31.4643			−1.16216			−0.581080	+	0.813846i	$0.697370\pi$
$734$	−15.4629			−0.570747
$735$		0			0
$736$	−2.03968	+	3.53283i	−0.0751837	+	0.130222i
$737$	1.92680	+	3.33732i	0.0709746	+	0.122932i
$738$		0			0
$739$	−2.36895	+	4.10314i	−0.0871433	+	0.150937i	−0.906302	−	0.422630i	$-0.861107\pi$
$739$	−2.36895	+	4.10314i	−0.0871433	+	0.150937i	0.819159	+	0.573566i	$0.194440\pi$
$740$	−42.5849			−1.56545
$741$		0			0
$742$	3.72356			0.136696
$743$	−21.0744	+	36.5020i	−0.773145	+	1.33913i	0.162685	+	0.986678i	$0.447984\pi$
$743$	−21.0744	+	36.5020i	−0.773145	+	1.33913i	−0.935831	+	0.352449i	$0.885349\pi$
$744$		0			0
$745$	7.97432	+	13.8119i	0.292156	+	0.506030i
$746$	18.0312	−	31.2309i	0.660168	−	1.14344i
$747$		0			0
$748$	4.96616			0.181581
$749$	−0.709245			−0.0259152
$750$		0			0
$751$	22.5468	+	39.0522i	0.822745	+	1.42504i	0.903630	+	0.428313i	$0.140892\pi$
$751$	22.5468	+	39.0522i	0.822745	+	1.42504i	−0.0808849	+	0.996723i	$0.525775\pi$
$752$	−58.8703			−2.14678
$753$		0			0
$754$	−43.3478	−	75.0806i	−1.57863	−	2.73428i
$755$	−4.36000	+	7.55174i	−0.158677	+	0.274836i
$756$		0			0
$757$	21.0271	−	36.4201i	0.764244	−	1.32371i	−0.176401	−	0.984318i	$-0.556446\pi$
$757$	21.0271	−	36.4201i	0.764244	−	1.32371i	0.940645	−	0.339391i	$-0.110221\pi$
$758$	−20.8348	+	36.0869i	−0.756753	+	1.31074i
$759$		0			0
$760$	25.8285	+	4.44376i	0.936899	+	0.161192i
$761$	4.42852			0.160534			0.0802668	−	0.996773i	$-0.474423\pi$
$761$	4.42852			0.160534			0.0802668	+	0.996773i	$0.474423\pi$
$762$		0			0
$763$	1.19416	−	2.06835i	0.0432316	−	0.0748793i
$764$	33.6536	+	58.2898i	1.21755	+	2.10885i
$765$		0			0
$766$	−37.1221	−	64.2974i	−1.34128	−	2.32316i
$767$	−67.0905			−2.42250
$768$		0			0
$769$	−2.09080	−	3.62136i	−0.0753960	−	0.130590i	0.825862	−	0.563872i	$-0.190689\pi$
$769$	−2.09080	−	3.62136i	−0.0753960	−	0.130590i	−0.901258	+	0.433282i	$0.857355\pi$
$770$	0.148041	+	0.256415i	0.00533504	+	0.00924055i
$771$		0			0
$772$	−76.5028			−2.75340
$773$	−10.7251	−	18.5764i	−0.385754	−	0.668146i	0.606119	−	0.795374i	$-0.292725\pi$
$773$	−10.7251	−	18.5764i	−0.385754	−	0.668146i	−0.991874	+	0.127228i	$0.959392\pi$
$774$		0			0
$775$	11.3116	+	19.5922i	0.406324	+	0.703773i
$776$	−21.3167	+	36.9215i	−0.765224	+	1.32541i
$777$		0			0
$778$	−65.8754			−2.36175
$779$	8.28896	+	1.42610i	0.296983	+	0.0510954i
$780$		0			0
$781$	−2.00265	+	3.46870i	−0.0716605	+	0.124120i
$782$	−3.97241	+	6.88041i	−0.142053	+	0.246043i
$783$		0			0
$784$	19.3022	−	33.4324i	0.689364	−	1.19401i
$785$	5.02947	+	8.71129i	0.179509	+	0.310919i
$786$		0			0
$787$	−0.147232			−0.00524825			−0.00262412	−	0.999997i	$-0.500835\pi$
$787$	−0.147232			−0.00524825			−0.00262412	+	0.999997i	$0.500835\pi$
$788$	32.0379	+	55.4913i	1.14130	+	1.97680i
$789$		0			0
$790$	−13.0575			−0.464565
$791$	3.21369			0.114266
$792$		0			0
$793$	−22.8149	+	39.5166i	−0.810182	+	1.40328i
$794$	−13.8505	−	23.9897i	−0.491535	−	0.851364i
$795$		0			0
$796$	37.4648	−	64.8910i	1.32790	−	2.30000i
$797$	−9.20825			−0.326173			−0.163087	−	0.986612i	$-0.552145\pi$
$797$	−9.20825			−0.326173			−0.163087	+	0.986612i	$0.552145\pi$
$798$		0			0
$799$	−21.7145			−0.768203
$800$	−5.05795	+	8.76063i	−0.178826	+	0.309735i
$801$		0			0
$802$	32.7160	+	56.6657i	1.15524	+	2.00094i
$803$	2.30793	−	3.99746i	0.0814452	−	0.141067i
$804$		0			0
$805$	−0.322029			−0.0113500
$806$	−83.4402			−2.93905
$807$		0			0
$808$	−20.3395	−	35.2290i	−0.715540	−	1.23935i
$809$	−44.5084			−1.56483			−0.782417	−	0.622755i	$-0.786013\pi$
$809$	−44.5084			−1.56483			−0.782417	+	0.622755i	$0.786013\pi$
$810$		0			0
$811$	−9.73582	−	16.8629i	−0.341871	−	0.592137i	0.642909	−	0.765942i	$-0.277727\pi$
$811$	−9.73582	−	16.8629i	−0.341871	−	0.592137i	−0.984780	+	0.173805i	$0.944394\pi$
$812$	−2.50691	+	4.34209i	−0.0879752	+	0.152378i
$813$		0			0
$814$	6.69253	−	11.5918i	0.234573	−	0.406292i
$815$	−2.34860	+	4.06789i	−0.0822679	+	0.142492i
$816$		0			0
$817$	−13.7983	−	2.37398i	−0.482742	−	0.0830550i
$818$	−27.0363			−0.945302
$819$		0			0
$820$	4.38630	−	7.59729i	0.153176	−	0.265309i
$821$	−1.67892	−	2.90798i	−0.0585949	−	0.101489i	0.835240	−	0.549886i	$-0.185329\pi$
$821$	−1.67892	−	2.90798i	−0.0585949	−	0.101489i	−0.893835	+	0.448396i	$0.851995\pi$
$822$		0			0
$823$	16.4823	+	28.5481i	0.574535	+	0.995125i	0.996092	+	0.0883224i	$0.0281506\pi$
$823$	16.4823	+	28.5481i	0.574535	+	0.995125i	−0.421557	+	0.906802i	$0.638516\pi$
$824$	−26.6913			−0.929834
$825$		0			0
$826$	2.85354	+	4.94247i	0.0992872	+	0.171970i
$827$	19.6587	+	34.0498i	0.683599	+	1.18403i	0.973875	+	0.227086i	$0.0729198\pi$
$827$	19.6587	+	34.0498i	0.683599	+	1.18403i	−0.290275	+	0.956943i	$0.593747\pi$
$828$		0			0
$829$	−34.4755			−1.19738			−0.598692	−	0.800980i	$-0.704313\pi$
$829$	−34.4755			−1.19738			−0.598692	+	0.800980i	$0.704313\pi$
$830$	−8.06506	−	13.9691i	−0.279942	−	0.484874i
$831$		0			0
$832$	12.8787	+	22.3066i	0.446489	+	0.773342i
$833$	7.11968	−	12.3316i	0.246682	−	0.427266i
$834$		0			0
$835$	−18.3863			−0.636284
$836$	−6.76991	+	8.13645i	−0.234142	+	0.281405i
$837$		0			0
$838$	15.6812	−	27.1606i	0.541697	−	0.938247i
$839$	−15.2482	+	26.4107i	−0.526426	+	0.911797i	0.473100	+	0.881009i	$0.343135\pi$
$839$	−15.2482	+	26.4107i	−0.526426	+	0.911797i	−0.999526	+	0.0307883i	$0.990198\pi$
$840$		0			0
$841$	−4.09782	+	7.09764i	−0.141304	+	0.244746i
$842$	9.93839	+	17.2138i	0.342500	+	0.593227i
$843$		0			0
$844$	67.2834			2.31599
$845$	10.3541	+	17.9339i	0.356193	+	0.616944i
$846$		0			0
$847$	2.06589			0.0709848
$848$	42.6744			1.46545
$849$		0			0
$850$	−9.85068	+	17.0619i	−0.337876	+	0.585218i
$851$	7.27901	+	12.6076i	0.249521	+	0.432184i
$852$		0			0
$853$	−11.9320	+	20.6669i	−0.408545	+	0.707621i	−0.994727	−	0.102558i	$-0.967297\pi$
$853$	−11.9320	+	20.6669i	−0.408545	+	0.707621i	0.586182	+	0.810180i	$0.300631\pi$
$854$	3.88152			0.132823
$855$		0			0
$856$	−20.5814			−0.703458
$857$	17.7312	−	30.7114i	0.605688	−	1.04908i	−0.386255	−	0.922392i	$-0.626231\pi$
$857$	17.7312	−	30.7114i	0.605688	−	1.04908i	0.991942	−	0.126690i	$-0.0404353\pi$
$858$		0			0
$859$	17.8160	+	30.8582i	0.607875	+	1.05287i	0.991590	+	0.129418i	$0.0413110\pi$
$859$	17.8160	+	30.8582i	0.607875	+	1.05287i	−0.383715	+	0.923451i	$0.625356\pi$
$860$	−7.30170	+	12.6469i	−0.248986	+	0.431256i
$861$		0			0
$862$	2.58117			0.0879151
$863$	−25.5558			−0.869931			−0.434965	−	0.900447i	$-0.643239\pi$
$863$	−25.5558			−0.869931			−0.434965	+	0.900447i	$0.643239\pi$
$864$		0			0
$865$	4.06179	+	7.03522i	0.138105	+	0.239205i
$866$	41.1203			1.39733
$867$		0			0
$868$	2.41277	+	4.17905i	0.0818949	+	0.141846i
$869$	1.39513	−	2.41643i	0.0473264	−	0.0819717i
$870$		0			0
$871$	19.1670	−	33.1982i	0.649448	−	1.12488i
$872$	34.6531	−	60.0210i	1.17350	−	2.03257i
$873$		0			0
$874$	−5.85750	−	15.8878i	−0.198133	−	0.537412i
$875$	−1.83453			−0.0620185
$876$		0			0
$877$	4.75134	−	8.22956i	0.160441	−	0.277892i	−0.774586	−	0.632469i	$-0.782042\pi$
$877$	4.75134	−	8.22956i	0.160441	−	0.277892i	0.935027	+	0.354577i	$0.115375\pi$
$878$	−31.1473	−	53.9487i	−1.05117	−	1.82068i
$879$		0			0
$880$	1.69665	+	2.93869i	0.0571941	+	0.0990631i
$881$	0.392087			0.0132097			0.00660487	−	0.999978i	$-0.497898\pi$
$881$	0.392087			0.0132097			0.00660487	+	0.999978i	$0.497898\pi$
$882$		0			0
$883$	2.32394	+	4.02518i	0.0782068	+	0.135458i	0.902476	−	0.430739i	$-0.141747\pi$
$883$	2.32394	+	4.02518i	0.0782068	+	0.135458i	−0.824269	+	0.566198i	$0.808414\pi$
$884$	−24.7006	−	42.7827i	−0.830771	−	1.43894i
$885$		0			0
$886$	1.74382			0.0585847
$887$	19.4700	+	33.7231i	0.653740	+	1.13231i	0.982208	+	0.187796i	$0.0601344\pi$
$887$	19.4700	+	33.7231i	0.653740	+	1.13231i	−0.328468	+	0.944515i	$0.606532\pi$
$888$		0			0
$889$	−0.345841	−	0.599014i	−0.0115991	−	0.0200903i
$890$	23.5318	−	40.7582i	0.788787	−	1.36622i
$891$		0			0
$892$	67.8861			2.27299
$893$	29.6014	−	35.5766i	0.990574	−	1.19053i
$894$		0			0
$895$	12.5962	−	21.8173i	0.421045	−	0.729271i
$896$	1.60356	−	2.77746i	0.0535713	−	0.0927883i
$897$		0			0
$898$	−24.6479	+	42.6914i	−0.822512	+	1.42463i
$899$	17.8995	+	31.0028i	0.596981	+	1.03400i
$900$		0			0
$901$	15.7406			0.524396
$902$	1.37868	+	2.38794i	0.0459049	+	0.0795096i
$903$		0			0
$904$	93.2573			3.10169
$905$	2.62074			0.0871165
$906$		0			0
$907$	21.6183	−	37.4440i	0.717823	−	1.24331i	−0.244037	−	0.969766i	$-0.578472\pi$
$907$	21.6183	−	37.4440i	0.717823	−	1.24331i	0.961860	−	0.273541i	$-0.0881948\pi$
$908$	−20.1678	−	34.9316i	−0.669291	−	1.15925i
$909$		0			0
$910$	1.47265	−	2.55070i	0.0488179	−	0.0845550i
$911$	36.6276			1.21353			0.606763	−	0.794883i	$-0.292468\pi$
$911$	36.6276			1.21353			0.606763	+	0.794883i	$0.292468\pi$
$912$		0			0
$913$	3.44683			0.114074
$914$	25.9125	−	44.8818i	0.857110	−	1.48456i
$915$		0			0
$916$	26.4646	+	45.8380i	0.874415	+	1.51453i
$917$	−0.944899	+	1.63661i	−0.0312033	+	0.0540457i
$918$		0			0
$919$	−25.3513			−0.836262			−0.418131	−	0.908387i	$-0.637315\pi$
$919$	−25.3513			−0.836262			−0.418131	+	0.908387i	$0.637315\pi$
$920$	−9.34489			−0.308092
$921$		0			0
$922$	27.4823	+	47.6008i	0.905082	+	1.56765i
$923$	39.8430			1.31145
$924$		0			0
$925$	18.0503	+	31.2641i	0.593491	+	1.02796i
$926$	−12.6557	+	21.9203i	−0.415891	+	0.720345i
$927$		0			0
$928$	−8.00372	+	13.8628i	−0.262735	+	0.455070i
$929$	−11.9781	+	20.7467i	−0.392989	+	0.680676i	−0.992842	−	0.119433i	$-0.961892\pi$
$929$	−11.9781	+	20.7467i	−0.392989	+	0.680676i	0.599854	+	0.800110i	$0.295226\pi$
$930$		0			0
$931$	10.4983	+	28.4754i	0.344068	+	0.933242i
$932$	−3.38280			−0.110807
$933$		0			0
$934$	−47.1811	+	81.7201i	−1.54381	+	2.67396i
$935$	0.625815	+	1.08394i	0.0204664	+	0.0354488i
$936$		0			0
$937$	−3.49569	−	6.05471i	−0.114199	−	0.197799i	0.803260	−	0.595628i	$-0.203097\pi$
$937$	−3.49569	−	6.05471i	−0.114199	−	0.197799i	−0.917459	+	0.397830i	$0.869764\pi$
$938$	−3.26089			−0.106472
$939$		0			0
$940$	−24.1361	−	41.8049i	−0.787232	−	1.36353i
$941$	−18.4128	−	31.8919i	−0.600241	−	1.03965i	−0.992784	−	0.119914i	$-0.961738\pi$
$941$	−18.4128	−	31.8919i	−0.600241	−	1.03965i	0.392543	−	0.919733i	$-0.371595\pi$
$942$		0			0
$943$	−2.99899			−0.0976604
$944$	32.7034	+	56.6440i	1.06441	+	1.84360i
$945$		0			0
$946$	−2.29503	−	3.97511i	−0.0746178	−	0.129242i
$947$	6.62804	−	11.4801i	0.215382	−	0.373053i	−0.738009	−	0.674791i	$-0.764234\pi$
$947$	6.62804	−	11.4801i	0.215382	−	0.373053i	0.953391	+	0.301738i	$0.0975669\pi$
$948$		0			0
$949$	−45.9166			−1.49052
$950$	−14.5253	−	39.3981i	−0.471263	−	1.27824i
$951$		0			0
$952$	−1.11174	+	1.92559i	−0.0360317	+	0.0624087i
$953$	11.9032	−	20.6169i	0.385582	−	0.667847i	−0.606268	−	0.795260i	$-0.707334\pi$
$953$	11.9032	−	20.6169i	0.385582	−	0.667847i	0.991850	+	0.127413i	$0.0406675\pi$
$954$		0			0
$955$	−8.48179	+	14.6909i	−0.274464	+	0.475386i
$956$	16.1635	+	27.9959i	0.522763	+	0.905453i
$957$		0			0
$958$	−106.921			−3.45448
$959$	−2.17440	−	3.76617i	−0.0702151	−	0.121616i
$960$		0			0
$961$	3.45467			0.111441
$962$	−133.149			−4.29289
$963$		0			0
$964$	59.0935	−	102.353i	1.90327	−	3.29657i
$965$	−9.64059	−	16.6980i	−0.310341	−	0.537527i
$966$		0			0
$967$	−18.2018	+	31.5265i	−0.585332	+	1.01382i	0.409502	+	0.912309i	$0.365702\pi$
$967$	−18.2018	+	31.5265i	−0.585332	+	1.01382i	−0.994834	+	0.101515i	$0.967631\pi$
$968$	59.9496			1.92685
$969$		0			0
$970$	−20.3078			−0.652043
$971$	10.1594	−	17.5965i	0.326029	−	0.564699i	−0.655691	−	0.755029i	$-0.727623\pi$
$971$	10.1594	−	17.5965i	0.326029	−	0.564699i	0.981720	+	0.190330i	$0.0609559\pi$
$972$		0			0
$973$	1.79138	+	3.10277i	0.0574291	+	0.0994701i
$974$	51.0843	−	88.4806i	1.63685	−	2.83510i
$975$		0			0
$976$	44.4848			1.42392
$977$	43.5229			1.39242			0.696210	−	0.717838i	$-0.254868\pi$
$977$	43.5229			1.39242			0.696210	+	0.717838i	$0.254868\pi$
$978$		0			0
$979$	5.02849	+	8.70960i	0.160711	+	0.278360i
$980$	31.6547			1.01117
$981$		0			0
$982$	36.9085	+	63.9274i	1.17780	+	2.04001i
$983$	−1.90199	+	3.29435i	−0.0606642	+	0.105073i	−0.894762	−	0.446542i	$-0.852655\pi$
$983$	−1.90199	+	3.29435i	−0.0606642	+	0.105073i	0.834098	+	0.551616i	$0.185989\pi$
$984$		0			0
$985$	−8.07459	+	13.9856i	−0.257278	+	0.445618i
$986$	−15.5877	+	26.9988i	−0.496415	+	0.859816i
$987$		0			0
$988$	103.766	+	17.8528i	3.30125	+	0.567974i
$989$	4.99230			0.158746
$990$		0			0
$991$	−19.5767	+	33.9079i	−0.621875	+	1.07712i	0.367262	+	0.930118i	$0.380295\pi$
$991$	−19.5767	+	33.9079i	−0.621875	+	1.07712i	−0.989136	+	0.147001i	$0.953038\pi$
$992$	7.70318	+	13.3423i	0.244576	+	0.423618i
$993$		0			0
$994$	−1.69463	−	2.93519i	−0.0537504	−	0.0930984i
$995$	18.8847			0.598684
$996$		0			0
$997$	18.7197	+	32.4234i	0.592858	+	1.02686i	0.993845	+	0.110776i	$0.0353336\pi$
$997$	18.7197	+	32.4234i	0.592858	+	1.02686i	−0.400988	+	0.916083i	$0.631333\pi$
$998$	13.5048	+	23.3911i	0.427488	+	0.740431i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.f.h.163.6	yes	12
3.2	odd	2		513.2.f.f.163.1	✓	12
19.7	even	3	inner	513.2.f.h.406.6	yes	12
19.8	odd	6		9747.2.a.br.1.6		6
19.11	even	3		9747.2.a.bl.1.1		6
57.8	even	6		9747.2.a.bm.1.1		6
57.11	odd	6		9747.2.a.bs.1.6		6
57.26	odd	6		513.2.f.f.406.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.f.f.163.1	✓	12	3.2	odd	2
513.2.f.f.406.1	yes	12	57.26	odd	6
513.2.f.h.163.6	yes	12	1.1	even	1	trivial
513.2.f.h.406.6	yes	12	19.7	even	3	inner
9747.2.a.bl.1.1		6	19.11	even	3
9747.2.a.bm.1.1		6	57.8	even	6
9747.2.a.br.1.6		6	19.8	odd	6
9747.2.a.bs.1.6		6	57.11	odd	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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24972 - 2.16459i) q^{2} +(-2.12362 - 3.67822i) q^{4} +(0.535221 - 0.927030i) q^{5} -0.193560 q^{7} -5.61687 q^{8} +(-1.33776 - 2.31706i) q^{10} +0.571729 q^{11} +(-2.84366 - 4.92536i) q^{13} +(-0.241896 + 0.418977i) q^{14} +(-2.77229 + 4.80175i) q^{16} +(-1.02257 + 1.77114i) q^{17} +(-1.50783 - 4.08980i) q^{19} -4.54643 q^{20} +(0.714503 - 1.23756i) q^{22} +(0.777117 + 1.34601i) q^{23} +(1.92708 + 3.33780i) q^{25} -14.2151 q^{26} +(0.411048 + 0.711956i) q^{28} +(3.04941 + 5.28174i) q^{29} +5.86981 q^{31} +(1.31234 + 2.27304i) q^{32} +(2.55586 + 4.42688i) q^{34} +(-0.103597 + 0.179436i) q^{35} +9.36668 q^{37} +(-10.7371 - 1.84730i) q^{38} +(-3.00627 + 5.20701i) q^{40} +(-0.964779 + 1.67105i) q^{41} +(1.60603 - 2.78173i) q^{43} +(-1.21414 - 2.10294i) q^{44} +3.88473 q^{46} +(5.30880 + 9.19512i) q^{47} -6.96253 q^{49} +9.63326 q^{50} +(-12.0777 + 20.9192i) q^{52} +(-3.84829 - 6.66544i) q^{53} +(0.306001 - 0.530010i) q^{55} +1.08720 q^{56} +15.2437 q^{58} +(5.89826 - 10.2161i) q^{59} +(-4.01155 - 6.94820i) q^{61} +(7.33564 - 12.7057i) q^{62} -4.52893 q^{64} -6.08794 q^{65} +(3.37013 + 5.83724i) q^{67} +8.68621 q^{68} +(0.258936 + 0.448490i) q^{70} +(-3.50280 + 6.06703i) q^{71} +(4.03676 - 6.99188i) q^{73} +(11.7058 - 20.2750i) q^{74} +(-11.8411 + 14.2313i) q^{76} -0.110664 q^{77} +(2.44019 - 4.22653i) q^{79} +(2.96758 + 5.14000i) q^{80} +(2.41142 + 4.17669i) q^{82} +6.02879 q^{83} +(1.09460 + 1.89591i) q^{85} +(-4.01419 - 6.95278i) q^{86} -3.21133 q^{88} +(8.79523 + 15.2338i) q^{89} +(0.550418 + 0.953351i) q^{91} +(3.30061 - 5.71682i) q^{92} +26.5382 q^{94} +(-4.59839 - 0.791145i) q^{95} +(3.79512 - 6.57333i) q^{97} +(-8.70125 + 15.0710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} + q^{10} - 4 q^{11} - 5 q^{13} + 2 q^{14} + 3 q^{16} + 10 q^{17} - 9 q^{19} - 2 q^{20} - 4 q^{22} + 3 q^{23} - 5 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) \) 12 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 + q^10 - 4 * q^11 - 5 * q^13 + 2 * q^14 + 3 * q^16 + 10 * q^17 - 9 * q^19 - 2 * q^20 - 4 * q^22 + 3 * q^23 - 5 * q^25 - 2 * q^26 - 2 * q^28 - 6 * q^29 - 4 * q^31 + 8 * q^32 + 4 * q^34 + 3 * q^35 + 26 * q^37 - 10 * q^38 - 6 * q^40 - 13 * q^41 - 3 * q^43 - 20 * q^44 - 10 * q^46 + 18 * q^47 + 26 * q^49 + 6 * q^50 - 22 * q^52 - q^53 - 6 * q^55 + 48 * q^56 + 28 * q^58 + 11 * q^59 - 13 * q^61 + 22 * q^62 - 72 * q^65 + 9 * q^67 - 10 * q^68 - 30 * q^70 - 6 * q^71 - 15 * q^73 + 43 * q^74 - 33 * q^76 - 58 * q^77 - 13 * q^79 + q^80 + 4 * q^82 - 16 * q^83 - 3 * q^85 - 7 * q^86 - 30 * q^88 + 29 * q^89 + 22 * q^91 + 21 * q^92 + 36 * q^94 + 22 * q^95 + 20 * q^97 - 59 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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