LMFDB - Embedded newform 117.3.n.a.38.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.5
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38552 + 2.39980i) q^{2} +(0.210571 + 2.99260i) q^{3} +(-1.83936 - 3.18586i) q^{4} +(-2.12220 - 3.67577i) q^{5} +(-7.47339 - 3.64100i) q^{6} +(-4.71279 - 2.72093i) q^{7} -0.890291 q^{8} +(-8.91132 + 1.26031i) q^{9} +11.7615 q^{10} +(-6.06300 + 10.5014i) q^{11} +(9.14670 - 6.17531i) q^{12} +(3.21938 - 12.5951i) q^{13} +(13.0594 - 7.53984i) q^{14} +(10.5532 - 7.12492i) q^{15} +(8.59095 - 14.8800i) q^{16} +15.7681i q^{17} +(9.32237 - 23.1316i) q^{18} +16.0835i q^{19} +(-7.80699 + 13.5221i) q^{20} +(7.15029 - 14.6765i) q^{21} +(-16.8009 - 29.1000i) q^{22} +(-29.1372 + 16.8223i) q^{23} +(-0.187469 - 2.66429i) q^{24} +(3.49249 - 6.04918i) q^{25} +(25.7651 + 25.1766i) q^{26} +(-5.64806 - 26.4026i) q^{27} +20.0191i q^{28} +(-2.73504 - 1.57907i) q^{29} +(2.47662 + 35.1974i) q^{30} +(-8.66585 + 5.00323i) q^{31} +(22.0254 + 38.1491i) q^{32} +(-32.7033 - 15.9329i) q^{33} +(-37.8404 - 21.8472i) q^{34} +23.0975i q^{35} +(20.4063 + 26.0721i) q^{36} +54.7483i q^{37} +(-38.5972 - 22.2841i) q^{38} +(38.3699 + 6.98217i) q^{39} +(1.88938 + 3.27250i) q^{40} +(-17.0319 - 29.5002i) q^{41} +(25.3136 + 37.4938i) q^{42} +(-40.0900 + 69.4379i) q^{43} +44.6081 q^{44} +(23.5442 + 30.0813i) q^{45} -93.2311i q^{46} +(8.29612 - 14.3693i) q^{47} +(46.3388 + 22.5760i) q^{48} +(-9.69307 - 16.7889i) q^{49} +(9.67788 + 16.7626i) q^{50} +(-47.1878 + 3.32031i) q^{51} +(-46.0477 + 12.9103i) q^{52} -16.8893i q^{53} +(71.1866 + 23.0273i) q^{54} +51.4677 q^{55} +(4.19576 + 2.42242i) q^{56} +(-48.1315 + 3.38671i) q^{57} +(7.57892 - 4.37569i) q^{58} +(-7.70351 - 13.3429i) q^{59} +(-42.1102 - 20.5158i) q^{60} +(22.7829 - 39.4612i) q^{61} -27.7284i q^{62} +(45.4264 + 18.3075i) q^{63} -53.3392 q^{64} +(-53.1287 + 14.8956i) q^{65} +(83.5469 - 56.4059i) q^{66} +(-43.2647 + 24.9789i) q^{67} +(50.2351 - 29.0033i) q^{68} +(-56.4780 - 83.6536i) q^{69} +(-55.4294 - 32.0022i) q^{70} +95.5531 q^{71} +(7.93367 - 1.12204i) q^{72} +47.3627i q^{73} +(-131.385 - 75.8552i) q^{74} +(18.8382 + 9.17786i) q^{75} +(51.2399 - 29.5833i) q^{76} +(57.1473 - 32.9940i) q^{77} +(-69.9183 + 82.4061i) q^{78} +(0.426027 - 0.737900i) q^{79} -72.9271 q^{80} +(77.8233 - 22.4620i) q^{81} +94.3926 q^{82} +(14.8880 - 25.7868i) q^{83} +(-59.9091 + 4.21543i) q^{84} +(57.9600 - 33.4632i) q^{85} +(-111.091 - 192.416i) q^{86} +(4.14962 - 8.51738i) q^{87} +(5.39784 - 9.34933i) q^{88} -87.0977 q^{89} +(-104.810 + 14.8231i) q^{90} +(-49.4426 + 50.5982i) q^{91} +(107.187 + 61.8847i) q^{92} +(-16.7975 - 24.8799i) q^{93} +(22.9890 + 39.8180i) q^{94} +(59.1192 - 34.1325i) q^{95} +(-109.527 + 73.9462i) q^{96} +(84.6758 + 48.8876i) q^{97} +53.7199 q^{98} +(40.7943 - 101.223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.38552	+	2.39980i	−0.692762	+	1.19990i	0.278167	+	0.960533i	$0.410273\pi$
$2$	−1.38552	+	2.39980i	−0.692762	+	1.19990i	−0.970929	+	0.239367i	$0.923060\pi$
$3$	0.210571	+	2.99260i	0.0701902	+	0.997534i
$3$	0.210571	+	2.99260i	0.0701902	+	0.997534i
$4$	−1.83936	−	3.18586i	−0.459840	−	0.796466i
$5$	−2.12220	−	3.67577i	−0.424441	−	0.735153i	0.571927	−	0.820304i	$-0.306196\pi$
$5$	−2.12220	−	3.67577i	−0.424441	−	0.735153i	−0.996368	+	0.0851512i	$0.972863\pi$
$6$	−7.47339	−	3.64100i	−1.24557	−	0.606833i
$7$	−4.71279	−	2.72093i	−0.673256	−	0.388704i	0.124053	−	0.992276i	$-0.460411\pi$
$7$	−4.71279	−	2.72093i	−0.673256	−	0.388704i	−0.797309	+	0.603571i	$0.793744\pi$
$8$	−0.890291			−0.111286
$9$	−8.91132	+	1.26031i	−0.990147	+	0.140034i
$10$	11.7615			1.17615
$11$	−6.06300	+	10.5014i	−0.551182	+	0.954675i	0.447008	+	0.894530i	$0.352490\pi$
$11$	−6.06300	+	10.5014i	−0.551182	+	0.954675i	−0.998190	+	0.0601452i	$0.980844\pi$
$12$	9.14670	−	6.17531i	0.762225	−	0.514610i
$13$	3.21938	−	12.5951i	0.247645	−	0.968851i
$13$	3.21938	−	12.5951i	0.247645	−	0.968851i
$14$	13.0594	−	7.53984i	0.932813	−	0.538560i
$15$	10.5532	−	7.12492i	0.703549	−	0.474995i
$16$	8.59095	−	14.8800i	0.536935	−	0.929998i
$17$			15.7681i			0.927538i	0.885956	+	0.463769i	$0.153503\pi$
$17$			15.7681i			0.927538i	−0.885956	+	0.463769i	$0.846497\pi$
$18$	9.32237	−	23.1316i	0.517909	−	1.28509i
$19$			16.0835i			0.846501i	0.906013	+	0.423250i	$0.139111\pi$
$19$			16.0835i			0.846501i	−0.906013	+	0.423250i	$0.860889\pi$
$20$	−7.80699	+	13.5221i	−0.390350	+	0.676105i
$21$	7.15029	−	14.6765i	0.340490	−	0.698879i
$22$	−16.8009	−	29.1000i	−0.763676	−	1.32273i
$23$	−29.1372	+	16.8223i	−1.26683	+	0.731406i	−0.974387	−	0.224876i	$-0.927802\pi$
$23$	−29.1372	+	16.8223i	−1.26683	+	0.731406i	−0.292446	+	0.956282i	$0.594469\pi$
$24$	−0.187469	−	2.66429i	−0.00781121	−	0.111012i
$25$	3.49249	−	6.04918i	0.139700	−	0.241967i
$26$	25.7651	+	25.1766i	0.990965	+	0.968332i
$27$	−5.64806	−	26.4026i	−0.209187	−	0.977876i
$28$			20.0191i			0.714967i
$29$	−2.73504	−	1.57907i	−0.0943116	−	0.0544508i	0.452102	−	0.891966i	$-0.350674\pi$
$29$	−2.73504	−	1.57907i	−0.0943116	−	0.0544508i	−0.546414	+	0.837515i	$0.684007\pi$
$30$	2.47662	+	35.1974i	0.0825540	+	1.17325i
$31$	−8.66585	+	5.00323i	−0.279544	+	0.161395i	−0.633217	−	0.773974i	$-0.718266\pi$
$31$	−8.66585	+	5.00323i	−0.279544	+	0.161395i	0.353673	+	0.935369i	$0.384933\pi$
$32$	22.0254	+	38.1491i	0.688293	+	1.19216i
$33$	−32.7033	−	15.9329i	−0.991008	−	0.482814i
$34$	−37.8404	−	21.8472i	−1.11295	−	0.642563i
$35$			23.0975i			0.659928i
$36$	20.4063	+	26.0721i	0.566841	+	0.724225i
$37$			54.7483i			1.47968i	0.672780	+	0.739842i	$0.265100\pi$
$37$			54.7483i			1.47968i	−0.672780	+	0.739842i	$0.734900\pi$
$38$	−38.5972	−	22.2841i	−1.01572	−	0.586424i
$39$	38.3699	+	6.98217i	0.983844	+	0.179030i
$40$	1.88938	+	3.27250i	0.0472345	+	0.0818126i
$41$	−17.0319	−	29.5002i	−0.415413	−	0.719516i	0.580059	−	0.814575i	$-0.303030\pi$
$41$	−17.0319	−	29.5002i	−0.415413	−	0.719516i	−0.995472	+	0.0950584i	$0.969696\pi$
$42$	25.3136	+	37.4938i	0.602706	+	0.892710i
$43$	−40.0900	+	69.4379i	−0.932325	+	1.61483i	−0.152990	+	0.988228i	$0.548890\pi$
$43$	−40.0900	+	69.4379i	−0.932325	+	1.61483i	−0.779335	+	0.626607i	$0.784443\pi$
$44$	44.6081			1.01382
$45$	23.5442	+	30.0813i	0.523205	+	0.668473i
$46$		−	93.2311i		−	2.02676i
$47$	8.29612	−	14.3693i	0.176513	−	0.305730i	−0.764171	−	0.645014i	$-0.776852\pi$
$47$	8.29612	−	14.3693i	0.176513	−	0.305730i	0.940684	+	0.339284i	$0.110185\pi$
$48$	46.3388	+	22.5760i	0.965392	+	0.470334i
$49$	−9.69307	−	16.7889i	−0.197818	−	0.342630i
$50$	9.67788	+	16.7626i	0.193558	+	0.335251i
$51$	−47.1878	+	3.32031i	−0.925250	+	0.0651040i
$52$	−46.0477	+	12.9103i	−0.885533	+	0.248276i
$53$		−	16.8893i		−	0.318667i	−0.987225	−	0.159333i	$-0.949066\pi$
$53$		−	16.8893i		−	0.318667i	0.987225	−	0.159333i	$-0.0509344\pi$
$54$	71.1866	+	23.0273i	1.31827	+	0.426432i
$55$	51.4677			0.935777
$56$	4.19576	+	2.42242i	0.0749242	+	0.0432575i
$57$	−48.1315	+	3.38671i	−0.844413	+	0.0594160i
$58$	7.57892	−	4.37569i	0.130671	−	0.0754430i
$59$	−7.70351	−	13.3429i	−0.130568	−	0.226150i	0.793328	−	0.608795i	$-0.208347\pi$
$59$	−7.70351	−	13.3429i	−0.130568	−	0.226150i	−0.923896	+	0.382645i	$0.875013\pi$
$60$	−42.1102	−	20.5158i	−0.701836	−	0.341931i
$61$	22.7829	−	39.4612i	0.373491	−	0.646905i	−0.616609	−	0.787270i	$-0.711494\pi$
$61$	22.7829	−	39.4612i	0.373491	−	0.646905i	0.990100	+	0.140364i	$0.0448274\pi$
$62$		−	27.7284i		−	0.447232i
$63$	45.4264	+	18.3075i	0.721054	+	0.290596i
$64$	−53.3392			−0.833425
$65$	−53.1287	+	14.8956i	−0.817364	+	0.229163i
$66$	83.5469	−	56.4059i	1.26586	−	0.854635i
$67$	−43.2647	+	24.9789i	−0.645742	+	0.372819i	−0.786823	−	0.617179i	$-0.788276\pi$
$67$	−43.2647	+	24.9789i	−0.645742	+	0.372819i	0.141081	+	0.989998i	$0.454942\pi$
$68$	50.2351	−	29.0033i	0.738752	−	0.426519i
$69$	−56.4780	−	83.6536i	−0.818522	−	1.21237i
$70$	−55.4294	−	32.0022i	−0.791848	−	0.457174i
$71$	95.5531			1.34582			0.672909	−	0.739725i	$-0.265044\pi$
$71$	95.5531			1.34582			0.672909	+	0.739725i	$0.265044\pi$
$72$	7.93367	−	1.12204i	0.110190	−	0.0155839i
$73$			47.3627i			0.648804i	0.945919	+	0.324402i	$0.105163\pi$
$73$			47.3627i			0.648804i	−0.945919	+	0.324402i	$0.894837\pi$
$74$	−131.385	−	75.8552i	−1.77547	−	1.02507i
$75$	18.8382	+	9.17786i	0.251176	+	0.122372i
$76$	51.2399	−	29.5833i	0.674209	−	0.389255i
$77$	57.1473	−	32.9940i	0.742173	−	0.428494i
$78$	−69.9183	+	82.4061i	−0.896388	+	1.05649i
$79$	0.426027	−	0.737900i	0.00539275	−	0.00934051i	−0.863316	−	0.504663i	$-0.831617\pi$
$79$	0.426027	−	0.737900i	0.00539275	−	0.00934051i	0.868709	+	0.495322i	$0.164950\pi$
$80$	−72.9271			−0.911588
$81$	77.8233	−	22.4620i	0.960781	−	0.277309i
$82$	94.3926			1.15113
$83$	14.8880	−	25.7868i	0.179374	−	0.310685i	−0.762292	−	0.647233i	$-0.775926\pi$
$83$	14.8880	−	25.7868i	0.179374	−	0.310685i	0.941666	+	0.336548i	$0.109260\pi$
$84$	−59.9091	+	4.21543i	−0.713203	+	0.0501837i
$85$	57.9600	−	33.4632i	0.681882	−	0.393685i
$86$	−111.091	−	192.416i	−1.29176	−	2.23739i
$87$	4.14962	−	8.51738i	0.0476968	−	0.0979009i
$88$	5.39784	−	9.34933i	0.0613391	−	0.106242i
$89$	−87.0977			−0.978626			−0.489313	−	0.872108i	$-0.662752\pi$
$89$	−87.0977			−0.978626			−0.489313	+	0.872108i	$0.662752\pi$
$90$	−104.810	+	14.8231i	−1.16456	+	0.164701i
$91$	−49.4426	+	50.5982i	−0.543325	+	0.556024i
$92$	107.187	+	61.8847i	1.16508	+	0.672659i
$93$	−16.7975	−	24.8799i	−0.180618	−	0.267526i
$94$	22.9890	+	39.8180i	0.244563	+	0.423596i
$95$	59.1192	−	34.1325i	0.622308	−	0.359290i
$96$	−109.527	+	73.9462i	−1.14091	+	0.770273i
$97$	84.6758	+	48.8876i	0.872946	+	0.503996i	0.868326	−	0.495994i	$-0.165196\pi$
$97$	84.6758	+	48.8876i	0.872946	+	0.503996i	0.00462004	+	0.999989i	$0.498529\pi$
$98$	53.7199			0.548163
$99$	40.7943	−	101.223i	0.412064	−	1.02245i
$100$	−25.6958			−0.256958
$101$	154.337	+	89.1066i	1.52809	+	0.882243i	0.999442	+	0.0334025i	$0.0106343\pi$
$101$	154.337	+	89.1066i	1.52809	+	0.882243i	0.528648	+	0.848841i	$0.322699\pi$
$102$	57.4117	−	117.842i	0.562860	−	1.15531i
$103$	47.4632	+	82.2087i	0.460808	+	0.798142i	0.999001	−	0.0446788i	$-0.0142264\pi$
$103$	47.4632	+	82.2087i	0.460808	+	0.798142i	−0.538194	+	0.842821i	$0.680893\pi$
$104$	−2.86618	+	11.2133i	−0.0275595	+	0.107820i
$105$	−69.1216	+	4.86365i	−0.658301	+	0.0463205i
$106$	40.5310	+	23.4006i	0.382368	+	0.220760i
$107$			105.123i			0.982456i	0.871031	+	0.491228i	$0.163452\pi$
$107$			105.123i			0.982456i	−0.871031	+	0.491228i	$0.836548\pi$
$108$	−73.7264	+	66.5579i	−0.682652	+	0.616276i
$109$		−	107.467i		−	0.985934i	−0.870048	−	0.492967i	$-0.835912\pi$
$109$		−	107.467i		−	0.985934i	0.870048	−	0.492967i	$-0.164088\pi$
$110$	−71.3098	+	123.512i	−0.648271	+	1.12284i
$111$	−163.840	+	11.5284i	−1.47604	+	0.103859i
$112$	−80.9747	+	46.7508i	−0.722989	+	0.417418i
$113$	−128.924	+	74.4341i	−1.14092	+	0.658709i	−0.946658	−	0.322241i	$-0.895564\pi$
$113$	−128.924	+	74.4341i	−1.14092	+	0.658709i	−0.194260	+	0.980950i	$0.562231\pi$
$114$	58.5600	−	120.198i	0.513684	−	1.05437i
$115$	123.670	+	71.4009i	1.07539	+	0.620878i
$116$			11.6179i			0.100155i
$117$	−12.8153	+	116.296i	−0.109532	+	0.993983i
$118$	42.6936			0.361810
$119$	42.9040	−	74.3120i	0.360538	−	0.624470i
$120$	−9.39545	+	6.34325i	−0.0782954	+	0.0528604i
$121$	−13.0200	−	22.5513i	−0.107603	−	0.186375i
$122$	63.1327	+	109.349i	0.517481	+	0.896303i
$123$	84.6958	−	57.1816i	0.688584	−	0.464891i
$124$	31.8792	+	18.4055i	0.257090	+	0.148431i
$125$	−135.757			−1.08606
$126$	−106.874	+	83.6487i	−0.848205	+	0.663879i
$127$	−106.144			−0.835779			−0.417890	−	0.908498i	$-0.637230\pi$
$127$	−106.144			−0.835779			−0.417890	+	0.908498i	$0.637230\pi$
$128$	−14.1987	+	24.5929i	−0.110927	+	0.192132i
$129$	−216.242	−	105.352i	−1.67629	−	0.816680i
$130$	37.8646	−	148.136i	0.291266	−	1.13951i
$131$	192.702	−	111.256i	1.47100	−	0.849285i	0.471535	−	0.881848i	$-0.343700\pi$
$131$	192.702	−	111.256i	1.47100	−	0.849285i	0.999470	+	0.0325629i	$0.0103669\pi$
$132$	9.39316	+	133.494i	0.0711603	+	1.01132i
$133$	43.7621	−	75.7982i	0.329039	−	0.569912i
$134$		−	138.436i		−	1.03310i
$135$	−85.0636	+	76.7928i	−0.630101	+	0.568835i
$136$		−	14.0382i		−	0.103222i
$137$	−35.2366	+	61.0315i	−0.257201	+	0.445486i	−0.965491	−	0.260436i	$-0.916134\pi$
$137$	−35.2366	+	61.0315i	−0.257201	+	0.445486i	0.708290	+	0.705922i	$0.249467\pi$
$138$	279.004	−	19.6317i	2.02176	−	0.142259i
$139$	17.2904	+	29.9478i	0.124391	+	0.215452i	0.921495	−	0.388391i	$-0.126969\pi$
$139$	17.2904	+	29.9478i	0.124391	+	0.215452i	−0.797104	+	0.603843i	$0.793636\pi$
$140$	73.5854	−	42.4846i	0.525610	−	0.303461i
$141$	44.7485	+	21.8012i	0.317365	+	0.154619i
$142$	−132.391	+	229.308i	−0.932333	+	1.61485i
$143$	112.747	+	110.172i	0.788441	+	0.770433i
$144$	−57.8034	+	143.427i	−0.401413	+	0.996024i
$145$			13.4045i			0.0924446i
$146$	−113.661	−	65.6222i	−0.778499	−	0.449467i
$147$	48.2014	−	32.5427i	0.327900	−	0.221379i
$148$	174.421	−	100.702i	1.17852	−	0.680418i
$149$	−97.8456	−	169.474i	−0.656682	−	1.13741i	−0.981469	−	0.191620i	$-0.938626\pi$
$149$	−97.8456	−	169.474i	−0.656682	−	1.13741i	0.324787	−	0.945787i	$-0.394707\pi$
$150$	−48.1258	+	32.4917i	−0.320839	+	0.216611i
$151$	221.816	+	128.065i	1.46898	+	0.848114i	0.999395	−	0.0347746i	$-0.0110713\pi$
$151$	221.816	+	128.065i	1.46898	+	0.848114i	0.469582	+	0.882889i	$0.344405\pi$
$152$		−	14.3190i		−	0.0942040i
$153$	−19.8727	−	140.515i	−0.129887	−	0.918398i
$154$			182.856i			1.18738i
$155$	36.7814	+	21.2358i	0.237300	+	0.137005i
$156$	−48.3318	−	135.084i	−0.309819	−	0.865923i
$157$	109.330	+	189.365i	0.696369	+	1.20615i	0.969717	+	0.244231i	$0.0785356\pi$
$157$	109.330	+	189.365i	0.696369	+	1.20615i	−0.273348	+	0.961915i	$0.588131\pi$
$158$	1.18054	+	2.04476i	0.00747179	+	0.0129415i
$159$	50.5430	−	3.55640i	0.317881	−	0.0223673i
$160$	93.4847	−	161.920i	0.584280	−	1.01200i
$161$	183.090			1.13720
$162$	−53.9217	+	217.882i	−0.332850	+	1.34495i
$163$		−	305.896i		−	1.87666i	−0.345740	−	0.938330i	$-0.612372\pi$
$163$		−	305.896i		−	1.87666i	0.345740	−	0.938330i	$-0.387628\pi$
$164$	−62.6556	+	108.523i	−0.382047	+	0.661724i
$165$	10.8376	+	154.022i	0.0656824	+	0.933469i
$166$	41.2555	+	71.4566i	0.248527	+	0.430461i
$167$	−140.615	−	243.553i	−0.842008	−	1.45840i	−0.888195	−	0.459467i	$-0.848040\pi$
$167$	−140.615	−	243.553i	−0.842008	−	1.45840i	0.0461872	−	0.998933i	$-0.485293\pi$
$168$	−6.36584	+	13.0663i	−0.0378919	+	0.0777757i
$169$	−148.271	−	81.0966i	−0.877344	−	0.479861i
$170$			185.457i			1.09092i
$171$	−20.2702	−	143.325i	−0.118539	−	0.838160i
$172$	294.959			1.71488
$173$	−173.528	−	100.186i	−1.00305	−	0.579111i	−0.0939003	−	0.995582i	$-0.529933\pi$
$173$	−173.528	−	100.186i	−1.00305	−	0.579111i	−0.909149	+	0.416471i	$0.863267\pi$
$174$	14.6906	+	21.7593i	0.0844287	+	0.125053i
$175$	−32.9188	+	19.0057i	−0.188107	+	0.108604i
$176$	104.174	+	180.435i	0.591898	+	1.02520i
$177$	38.3078	−	25.8631i	0.216428	−	0.146119i
$178$	120.676	−	209.017i	0.677956	−	1.17425i
$179$			31.5946i			0.176506i	0.996098	+	0.0882529i	$0.0281284\pi$
$179$			31.5946i			0.176506i	−0.996098	+	0.0882529i	$0.971872\pi$
$180$	52.5286	−	130.339i	0.291825	−	0.724106i
$181$	−249.188			−1.37673			−0.688366	−	0.725364i	$-0.741672\pi$
$181$	−249.188			−1.37673			−0.688366	+	0.725364i	$0.741672\pi$
$182$	−52.9216	−	188.757i	−0.290778	−	1.03713i
$183$	122.889	+	59.8709i	0.671525	+	0.327163i
$184$	25.9406	−	14.9768i	0.140981	−	0.0813956i
$185$	201.242	−	116.187i	1.08780	−	0.628039i
$186$	82.9801	−	5.83879i	0.446129	−	0.0313913i
$187$	−165.588	−	95.6023i	−0.885497	−	0.511242i
$188$	−61.0381			−0.324671
$189$	−45.2216	+	139.798i	−0.239268	+	0.739673i
$190$			189.166i			0.995609i
$191$	−27.7883	−	16.0436i	−0.145488	−	0.0839978i	0.425489	−	0.904964i	$-0.360102\pi$
$191$	−27.7883	−	16.0436i	−0.145488	−	0.0839978i	−0.570977	+	0.820966i	$0.693436\pi$
$192$	−11.2317	−	159.623i	−0.0584983	−	0.831370i
$193$	−281.909	+	162.761i	−1.46067	+	0.843319i	−0.999042	−	0.0437545i	$-0.986068\pi$
$193$	−281.909	+	162.761i	−1.46067	+	0.843319i	−0.461629	+	0.887073i	$0.652735\pi$
$194$	−234.641	+	135.470i	−1.20949	+	0.698299i
$195$	−55.7640	−	155.856i	−0.285969	−	0.799263i
$196$	−35.6580	+	61.7616i	−0.181929	+	0.315110i
$197$	39.4908			0.200461			0.100231	−	0.994964i	$-0.468042\pi$
$197$	39.4908			0.200461			0.100231	+	0.994964i	$0.468042\pi$
$198$	186.393	+	238.145i	0.941379	+	1.20275i
$199$	−166.261			−0.835482			−0.417741	−	0.908566i	$-0.637178\pi$
$199$	−166.261			−0.835482			−0.417741	+	0.908566i	$0.637178\pi$
$200$	−3.10934	+	5.38553i	−0.0155467	+	0.0269276i
$201$	−83.8621	−	124.214i	−0.417225	−	0.617981i
$202$	−427.676	+	246.919i	−2.11721	+	1.22237i
$203$	8.59310	+	14.8837i	0.0423306	+	0.0733187i
$204$	97.3732	+	144.226i	0.477320	+	0.706992i
$205$	−72.2905	+	125.211i	−0.352636	+	0.610784i
$206$	−263.046			−1.27692
$207$	238.449	−	186.631i	1.15193	−	0.901600i
$208$	−159.757	−	156.108i	−0.768061	−	0.750519i
$209$	−168.900	−	97.5144i	−0.808133	−	0.466576i
$210$	84.0979	−	172.617i	0.400466	−	0.821984i
$211$	−51.4269	−	89.0741i	−0.243730	−	0.422152i	0.718044	−	0.695998i	$-0.245038\pi$
$211$	−51.4269	−	89.0741i	−0.243730	−	0.422152i	−0.961774	+	0.273846i	$0.911704\pi$
$212$	−53.8071	+	31.0655i	−0.253807	+	0.146536i
$213$	20.1207	+	285.952i	0.0944633	+	1.34250i
$214$	−252.274	−	145.650i	−1.17885	−	0.680609i
$215$	340.317			1.58287
$216$	5.02842	+	23.5060i	0.0232797	+	0.108824i
$217$	54.4538			0.250939
$218$	257.899	+	148.898i	1.18302	+	0.683018i
$219$	−141.738	+	9.97319i	−0.647204	+	0.0455397i
$220$	−94.6676	−	163.969i	−0.430307	−	0.745314i
$221$	198.601	+	50.7636i	0.898646	+	0.229700i
$222$	199.338	−	409.156i	0.897921	−	1.84304i
$223$	−134.735	−	77.7894i	−0.604194	−	0.348831i	0.166496	−	0.986042i	$-0.446755\pi$
$223$	−134.735	−	77.7894i	−0.604194	−	0.348831i	−0.770690	+	0.637211i	$0.780088\pi$
$224$		−	239.718i		−	1.07017i
$225$	−23.4989	+	58.3078i	−0.104440	+	0.259146i
$226$		−	412.521i		−	1.82532i
$227$	123.515	−	213.934i	0.544119	−	0.942442i	−0.454543	−	0.890725i	$-0.650197\pi$
$227$	123.515	−	213.934i	0.544119	−	0.942442i	0.998662	−	0.0517169i	$-0.0164693\pi$
$228$	99.3208	+	147.111i	0.435617	+	0.645224i
$229$	−143.484	+	82.8404i	−0.626567	+	0.361749i	−0.779421	−	0.626500i	$-0.784487\pi$
$229$	−143.484	+	82.8404i	−0.626567	+	0.361749i	0.152854	+	0.988249i	$0.451153\pi$
$230$	−342.696	+	197.856i	−1.48998	+	0.860242i
$231$	110.772	+	164.072i	0.479530	+	0.710267i
$232$	2.43498	+	1.40584i	0.0104956	+	0.00605964i
$233$		−	224.070i		−	0.961673i	−0.876810	−	0.480837i	$-0.840333\pi$
$233$		−	224.070i		−	0.961673i	0.876810	−	0.480837i	$-0.159667\pi$
$234$	−261.331	−	191.885i	−1.11680	−	0.820022i
$235$	−70.4242			−0.299678
$236$	−28.3390	+	49.0846i	−0.120081	+	0.207986i
$237$	2.29795	+	1.11955i	0.00969599	+	0.00472383i
$238$	118.889	+	205.922i	0.499534	+	0.865219i
$239$	178.007	+	308.318i	0.744801	+	1.29003i	0.950288	+	0.311373i	$0.100789\pi$
$239$	178.007	+	308.318i	0.744801	+	1.29003i	−0.205487	+	0.978660i	$0.565878\pi$
$240$	−15.3563	−	218.242i	−0.0639846	−	0.909340i
$241$	333.428	+	192.505i	1.38352	+	0.798774i	0.992574	−	0.121640i	$-0.0388154\pi$
$241$	333.428	+	192.505i	1.38352	+	0.798774i	0.390944	+	0.920415i	$0.372149\pi$
$242$	72.1582			0.298174
$243$	83.6071	+	228.164i	0.344062	+	0.938947i
$244$	−167.624			−0.686984
$245$	−41.1413	+	71.2589i	−0.167924	+	0.290853i
$246$	19.8763	+	282.479i	0.0807980	+	1.14829i
$247$	202.573	+	51.7789i	0.820133	+	0.209631i
$248$	7.71513	−	4.45433i	0.0311094	−	0.0179610i
$249$	80.3046	+	39.1240i	0.322509	+	0.157124i
$250$	188.095	−	325.791i	0.752381	−	1.30316i
$251$			229.103i			0.912761i	0.889785	+	0.456381i	$0.150854\pi$
$251$			229.103i			0.912761i	−0.889785	+	0.456381i	$0.849146\pi$
$252$	−25.2302	−	178.396i	−0.100120	−	0.707922i
$253$		−	407.976i		−	1.61255i
$254$	147.065	−	254.724i	0.578996	−	1.00285i
$255$	112.347	+	166.405i	0.440575	+	0.652568i
$256$	−146.024	−	252.921i	−0.570405	−	0.987971i
$257$	−137.301	+	79.2710i	−0.534247	+	0.308448i	−0.742744	−	0.669575i	$-0.766476\pi$
$257$	−137.301	+	79.2710i	−0.534247	+	0.308448i	0.208497	+	0.978023i	$0.433143\pi$
$258$	552.431	−	372.969i	2.14121	−	1.44562i
$259$	148.966	−	258.017i	0.575160	−	0.996206i
$260$	145.178	+	141.862i	0.558377	+	0.545624i
$261$	26.3629	+	10.6246i	0.101007	+	0.0407075i
$262$			616.593i			2.35341i
$263$	−48.6838	−	28.1076i	−0.185110	−	0.106873i	0.404581	−	0.914502i	$-0.367417\pi$
$263$	−48.6838	−	28.1076i	−0.185110	−	0.106873i	−0.589691	+	0.807629i	$0.700751\pi$
$264$	29.1154	+	14.1849i	0.110286	+	0.0537306i
$265$	−62.0812	+	35.8426i	−0.234269	+	0.135255i
$266$	121.267	+	210.041i	0.455891	+	0.789627i
$267$	−18.3402	−	260.649i	−0.0686900	−	0.976213i
$268$	159.159	+	91.8903i	0.593876	+	0.342874i
$269$		−	342.033i		−	1.27150i	−0.771895	−	0.635750i	$-0.780691\pi$
$269$		−	342.033i		−	1.27150i	0.771895	−	0.635750i	$-0.219309\pi$
$270$	−66.4295	−	310.534i	−0.246035	−	1.15013i
$271$			216.315i			0.798209i	0.916905	+	0.399104i	$0.130679\pi$
$271$			216.315i			0.798209i	−0.916905	+	0.399104i	$0.869321\pi$
$272$	234.629	+	135.463i	0.862608	+	0.498027i
$273$	−161.831	−	137.307i	−0.592789	−	0.502957i
$274$	−97.6423	−	169.121i	−0.356359	−	0.617232i
$275$	42.3500	+	73.3524i	0.154000	+	0.266736i
$276$	−162.626	+	333.800i	−0.589223	+	1.20942i
$277$	97.1805	−	168.322i	0.350832	−	0.607659i	−0.635563	−	0.772049i	$-0.719232\pi$
$277$	97.1805	−	168.322i	0.350832	−	0.607659i	0.986395	+	0.164390i	$0.0525654\pi$
$278$	−95.8251			−0.344695
$279$	70.9186	−	55.5070i	0.254188	−	0.198950i
$280$		−	20.5635i		−	0.0734410i
$281$	−150.967	+	261.483i	−0.537249	+	0.930543i	0.461802	+	0.886983i	$0.347203\pi$
$281$	−150.967	+	261.483i	−0.537249	+	0.930543i	−0.999051	+	0.0435595i	$0.986130\pi$
$282$	−114.319	+	77.1813i	−0.405385	+	0.273692i
$283$	4.18445	+	7.24767i	0.0147860	+	0.0256102i	0.873324	−	0.487140i	$-0.161960\pi$
$283$	4.18445	+	7.24767i	0.0147860	+	0.0256102i	−0.858538	+	0.512750i	$0.828627\pi$
$284$	−175.756	−	304.419i	−0.618861	−	1.07190i
$285$	114.594	+	169.733i	0.402083	+	0.595554i
$286$	−420.605	+	117.924i	−1.47065	+	0.412323i
$287$			185.371i			0.645891i
$288$	−244.355	−	312.200i	−0.848454	−	1.08403i
$289$	40.3657			0.139674
$290$	−32.1680	−	18.5722i	−0.110924	−	0.0640422i
$291$	−128.471	+	263.695i	−0.441480	+	0.906169i
$292$	150.891	−	87.1169i	0.516750	−	0.298346i
$293$	110.255	+	190.968i	0.376298	+	0.651767i	0.990520	−	0.137366i	$-0.0438636\pi$
$293$	110.255	+	190.968i	0.376298	+	0.651767i	−0.614223	+	0.789133i	$0.710530\pi$
$294$	11.3118	+	160.762i	0.0384756	+	0.546811i
$295$	−32.6969	+	56.6326i	−0.110837	+	0.191975i
$296$		−	48.7420i		−	0.164669i
$297$	311.510	+	100.767i	1.04885	+	0.339281i
$298$	542.270			1.81970
$299$	118.075	+	421.142i	0.394900	+	1.40850i
$300$	−5.41078	−	76.8973i	−0.0180359	−	0.256324i
$301$	377.871	−	218.164i	1.25539	−	0.724798i
$302$	−614.662	+	354.875i	−2.03530	+	1.17508i
$303$	−234.162	+	480.633i	−0.772810	+	1.58625i
$304$	239.322	+	138.173i	0.787244	+	0.454516i
$305$	−193.400			−0.634099
$306$	364.742	+	146.996i	1.19197	+	0.480381i
$307$			253.268i			0.824978i	0.910963	+	0.412489i	$0.135341\pi$
$307$			253.268i			0.824978i	−0.910963	+	0.412489i	$0.864659\pi$
$308$	−210.229	−	121.376i	−0.682561	−	0.394077i
$309$	−236.023	+	159.349i	−0.763830	+	0.515693i
$310$	−101.923	+	58.8454i	−0.328784	+	0.189824i
$311$	−311.732	+	179.979i	−1.00235	+	0.578709i	−0.908944	−	0.416918i	$-0.863110\pi$
$311$	−311.732	+	179.979i	−1.00235	+	0.578709i	−0.0934101	+	0.995628i	$0.529777\pi$
$312$	−34.1604	−	6.21616i	−0.109488	−	0.0199236i
$313$	−34.7019	+	60.1055i	−0.110869	+	0.192030i	−0.916121	−	0.400902i	$-0.868697\pi$
$313$	−34.7019	+	60.1055i	−0.110869	+	0.192030i	0.805252	+	0.592933i	$0.202030\pi$
$314$	−605.917			−1.92967
$315$	−29.1099	−	205.829i	−0.0924125	−	0.653426i
$316$	−3.13447			−0.00991920
$317$	115.467	−	199.995i	0.364249	−	0.630898i	−0.624406	−	0.781100i	$-0.714659\pi$
$317$	115.467	−	199.995i	0.364249	−	0.630898i	0.988655	+	0.150202i	$0.0479924\pi$
$318$	−61.4940	+	126.221i	−0.193377	+	0.396920i
$319$	33.1651	−	19.1479i	0.103966	−	0.0600246i
$320$	113.197	+	196.062i	0.353740	+	0.612695i
$321$	−314.591	+	22.1358i	−0.980033	+	0.0689588i
$322$	−253.675	+	439.379i	−0.787812	+	1.36453i
$323$	−253.607			−0.785161
$324$	−214.706	−	206.618i	−0.662672	−	0.637711i
$325$	−64.9461	−	63.4628i	−0.199834	−	0.195270i
$326$	734.088	+	423.826i	2.25180	+	1.30008i
$327$	321.605	−	22.6293i	0.983502	−	0.0692029i
$328$	15.1634	+	26.2637i	0.0462298	+	0.0800724i
$329$	−78.1957	+	45.1463i	−0.237677	+	0.137223i
$330$	−384.639	−	187.394i	−1.16557	−	0.567860i
$331$	−131.121	−	75.7027i	−0.396136	−	0.228709i	0.288680	−	0.957426i	$-0.406784\pi$
$331$	−131.121	−	75.7027i	−0.396136	−	0.228709i	−0.684815	+	0.728717i	$0.740117\pi$
$332$	−109.538			−0.329933
$333$	−68.9997	−	487.880i	−0.207206	−	1.46510i
$334$	779.304			2.33324
$335$	183.633	+	106.021i	0.548159	+	0.316480i
$336$	−156.957	−	232.481i	−0.467135	−	0.691907i
$337$	−177.923	−	308.171i	−0.527960	−	0.914454i	−0.999469	−	0.0325925i	$-0.989624\pi$
$337$	−177.923	−	308.171i	−0.527960	−	0.914454i	0.471508	−	0.881862i	$-0.343710\pi$
$338$	400.049	−	243.460i	1.18358	−	0.720295i
$339$	−249.899	−	370.144i	−0.737166	−	1.09187i
$340$	−213.218	−	123.102i	−0.627113	−	0.362064i
$341$		−	121.338i		−	0.355831i
$342$	372.037	+	149.936i	1.08783	+	0.438411i
$343$			372.148i			1.08498i
$344$	35.6918	−	61.8199i	0.103755	−	0.179709i
$345$	−187.633	+	385.130i	−0.543864	+	1.11632i
$346$	480.853	−	277.621i	1.38975	−	0.802372i
$347$	144.234	−	83.2734i	0.415659	−	0.239981i	−0.277559	−	0.960709i	$-0.589525\pi$
$347$	144.234	−	83.2734i	0.415659	−	0.239981i	0.693218	+	0.720728i	$0.256192\pi$
$348$	−34.7678	+	2.44639i	−0.0999076	+	0.00702987i
$349$	215.596	+	124.474i	0.617754	+	0.356660i	0.775994	−	0.630740i	$-0.217249\pi$
$349$	215.596	+	124.474i	0.617754	+	0.356660i	−0.158240	+	0.987401i	$0.550582\pi$
$350$		−	105.331i		−	0.300947i
$351$	−350.726	−	13.8625i	−0.999220	−	0.0394942i
$352$	−534.160			−1.51750
$353$	−27.8453	+	48.2294i	−0.0788818	+	0.136627i	−0.902768	−	0.430128i	$-0.858468\pi$
$353$	−27.8453	+	48.2294i	−0.0788818	+	0.136627i	0.823886	+	0.566756i	$0.191802\pi$
$354$	8.99002	+	127.765i	0.0253955	+	0.360918i
$355$	−202.783	−	351.231i	−0.571221	−	0.989383i
$356$	160.204	+	277.481i	0.450011	+	0.779442i
$357$	231.420	+	112.747i	0.648236	+	0.315817i
$358$	−75.8206	−	43.7750i	−0.211789	−	0.122277i
$359$	−114.632			−0.319310			−0.159655	−	0.987173i	$-0.551038\pi$
$359$	−114.632			−0.319310			−0.159655	+	0.987173i	$0.551038\pi$
$360$	−20.9612	−	26.7811i	−0.0582256	−	0.0743920i
$361$	102.321			0.283437
$362$	345.257	−	598.002i	0.953748	−	1.65194i
$363$	64.7455	−	43.7123i	0.178362	−	0.120420i
$364$	252.141	+	64.4490i	0.692696	+	0.177058i
$365$	174.094	−	100.513i	0.476970	−	0.275379i
$366$	−313.944	+	211.957i	−0.857771	+	0.579116i
$367$	−16.7960	+	29.0915i	−0.0457657	+	0.0792684i	−0.888001	−	0.459842i	$-0.847906\pi$
$367$	−16.7960	+	29.0915i	−0.0457657	+	0.0792684i	0.842235	+	0.539110i	$0.181239\pi$
$368$			578.080i			1.57087i
$369$	188.956	+	241.420i	0.512076	+	0.654255i
$370$			643.921i			1.74033i
$371$	−45.9547	+	79.5959i	−0.123867	+	0.214544i
$372$	−48.3674	+	99.2774i	−0.130020	+	0.266875i
$373$	272.986	+	472.826i	0.731867	+	1.26763i	0.956084	+	0.293092i	$0.0946842\pi$
$373$	272.986	+	472.826i	0.731867	+	1.26763i	−0.224217	+	0.974539i	$0.571982\pi$
$374$	458.853	−	264.919i	1.22688	−	0.708339i
$375$	−28.5865	−	406.268i	−0.0762307	−	1.08338i
$376$	−7.38596	+	12.7929i	−0.0196435	+	0.0340236i
$377$	−28.6937	+	29.3643i	−0.0761105	+	0.0778894i
$378$	−272.832	−	302.217i	−0.721777	−	0.799515i
$379$		−	50.5254i		−	0.133312i	−0.997776	−	0.0666562i	$-0.978767\pi$
$379$		−	50.5254i		−	0.133312i	0.997776	−	0.0666562i	$-0.0212331\pi$
$380$	−217.483	−	125.564i	−0.572324	−	0.330431i
$381$	−22.3508	−	317.646i	−0.0586635	−	0.833718i
$382$	77.0027	−	44.4575i	0.201578	−	0.116381i
$383$	−178.238	−	308.718i	−0.465374	−	0.806052i	0.533844	−	0.845583i	$-0.320747\pi$
$383$	−178.238	−	308.718i	−0.465374	−	0.806052i	−0.999218	+	0.0395310i	$0.987414\pi$
$384$	−76.5865	−	37.3125i	−0.199444	−	0.0971681i
$385$	−242.557	−	140.040i	−0.630017	−	0.363741i
$386$		−	902.035i		−	2.33688i
$387$	269.742	−	669.309i	0.697007	−	1.72948i
$388$		−	359.687i		−	0.927029i
$389$	−91.0937	−	52.5930i	−0.234174	−	0.135200i	0.378322	−	0.925674i	$-0.376501\pi$
$389$	−91.0937	−	52.5930i	−0.234174	−	0.135200i	−0.612496	+	0.790474i	$0.709835\pi$
$390$	451.286	+	82.1205i	1.15714	+	0.210565i
$391$	−265.257	−	459.439i	−0.678407	−	1.17504i
$392$	8.62965	+	14.9470i	0.0220144	+	0.0381301i
$393$	373.523	+	553.252i	0.950440	+	1.40776i
$394$	−54.7155	+	94.7701i	−0.138872	+	0.240533i
$395$	−3.61647			−0.00915561
$396$	−397.517	+	56.2200i	−1.00383	+	0.141970i
$397$		−	461.341i		−	1.16207i	−0.813879	−	0.581034i	$-0.802648\pi$
$397$		−	461.341i		−	1.16207i	0.813879	−	0.581034i	$-0.197352\pi$
$398$	230.359	−	398.993i	0.578791	−	1.00249i
$399$	236.049	+	115.002i	0.591601	+	0.288225i
$400$	−60.0077	−	103.936i	−0.150019	−	0.259841i
$401$	118.899	+	205.939i	0.296506	+	0.513563i	0.975334	−	0.220734i	$-0.0708452\pi$
$401$	118.899	+	205.939i	0.296506	+	0.513563i	−0.678828	+	0.734297i	$0.737512\pi$
$402$	414.282	−	29.1505i	1.03055	−	0.0725136i
$403$	35.1174	+	125.254i	0.0871399	+	0.310805i
$404$		−	655.596i		−	1.62276i
$405$	−247.722	−	238.391i	−0.611659	−	0.588620i
$406$	−47.6238			−0.117300
$407$	−574.936	−	331.939i	−1.41262	−	0.815576i
$408$	42.0108	−	2.95604i	0.102968	−	0.00724520i
$409$	−85.7896	+	49.5307i	−0.209755	+	0.121102i	−0.601197	−	0.799101i	$-0.705309\pi$
$409$	−85.7896	+	49.5307i	−0.209755	+	0.121102i	0.391443	+	0.920202i	$0.371976\pi$
$410$	−200.320	−	346.965i	−0.488587	−	0.846257i
$411$	−190.063	−	92.5976i	−0.462440	−	0.225298i
$412$	174.604	−	302.422i	0.423795	−	0.734035i
$413$			83.8429i			0.203009i
$414$	117.500	+	830.812i	0.283816	+	2.00679i
$415$	−126.382			−0.304534
$416$	551.398	−	154.595i	1.32548	−	0.371622i
$417$	−85.9811	+	58.0494i	−0.206190	+	0.139207i
$418$	468.030	−	270.217i	1.11969	−	0.646453i
$419$	−503.726	+	290.826i	−1.20221	+	0.694096i	−0.961046	−	0.276388i	$-0.910863\pi$
$419$	−503.726	+	290.826i	−1.20221	+	0.694096i	−0.241164	+	0.970484i	$0.577529\pi$
$420$	142.634	+	211.266i	0.339605	+	0.503014i
$421$	−427.771	−	246.974i	−1.01608	−	0.586636i	−0.103116	−	0.994669i	$-0.532881\pi$
$421$	−427.771	−	246.974i	−1.01608	−	0.586636i	−0.912967	+	0.408034i	$0.866215\pi$
$422$	285.013			0.675387
$423$	−55.8196	+	138.505i	−0.131961	+	0.327435i
$424$			15.0364i			0.0354633i
$425$	95.3843	+	55.0701i	0.224434	+	0.129577i
$426$	−714.106	−	347.909i	−1.67631	−	0.816687i
$427$	−214.743	+	123.982i	−0.502910	+	0.290355i
$428$	334.907	−	193.358i	0.782492	−	0.451772i
$429$	−305.960	+	360.606i	−0.713192	+	0.840573i
$430$	−471.517	+	816.692i	−1.09655	+	1.89928i
$431$	644.759			1.49596			0.747980	−	0.663721i	$-0.231024\pi$
$431$	644.759			1.49596			0.747980	+	0.663721i	$0.231024\pi$
$432$	−441.393	−	142.781i	−1.02174	−	0.330511i
$433$	754.246			1.74191			0.870954	−	0.491365i	$-0.163502\pi$
$433$	754.246			1.74191			0.870954	+	0.491365i	$0.163502\pi$
$434$	−75.4471	+	130.678i	−0.173841	+	0.301102i
$435$	−40.1142	+	2.82259i	−0.0922166	+	0.00648871i
$436$	−342.374	+	197.670i	−0.785262	+	0.453371i
$437$	−270.562	−	468.628i	−0.619136	−	1.07238i
$438$	172.447	−	353.960i	0.393715	−	0.808128i
$439$	−287.814	+	498.509i	−0.655613	+	1.13556i	0.326126	+	0.945326i	$0.394257\pi$
$439$	−287.814	+	498.509i	−0.655613	+	1.13556i	−0.981740	+	0.190229i	$0.939077\pi$
$440$	−45.8213			−0.104139
$441$	107.537	+	137.395i	0.243848	+	0.311553i
$442$	−396.989	+	406.268i	−0.898165	+	0.919158i
$443$	−382.267	−	220.702i	−0.862906	−	0.498199i	0.00207857	−	0.999998i	$-0.499338\pi$
$443$	−382.267	−	220.702i	−0.862906	−	0.498199i	−0.864984	+	0.501799i	$0.832672\pi$
$444$	338.088	+	500.767i	0.761460	+	1.12785i
$445$	184.839	+	320.151i	0.415369	+	0.719440i
$446$	373.358	−	215.558i	0.837126	−	0.483315i
$447$	486.564	−	328.499i	1.08851	−	0.734897i
$448$	251.377	+	145.132i	0.561108	+	0.323956i
$449$	−597.799			−1.33140			−0.665701	−	0.746219i	$-0.731867\pi$
$449$	−597.799			−1.33140			−0.665701	+	0.746219i	$0.731867\pi$
$450$	−107.369	−	137.180i	−0.238597	−	0.304843i
$451$	413.058			0.915872
$452$	474.274	+	273.822i	1.04928	+	0.605801i
$453$	−336.540	+	690.772i	−0.742915	+	1.52488i
$454$	342.266	+	592.823i	0.753890	+	1.30578i
$455$	290.914	+	74.3596i	0.639372	+	0.163428i
$456$	42.8511	−	3.01516i	0.0939717	−	0.00661220i
$457$	−303.229	−	175.069i	−0.663520	−	0.383084i	0.130097	−	0.991501i	$-0.458471\pi$
$457$	−303.229	−	175.069i	−0.663520	−	0.383084i	−0.793617	+	0.608418i	$0.791805\pi$
$458$		−	459.110i		−	1.00242i
$459$	416.321	−	89.0594i	0.907016	−	0.194029i
$460$		−	525.328i		−	1.14202i
$461$	−114.056	+	197.550i	−0.247409	+	0.428525i	−0.962806	−	0.270193i	$-0.912913\pi$
$461$	−114.056	+	197.550i	−0.247409	+	0.428525i	0.715397	+	0.698718i	$0.246246\pi$
$462$	−547.216	+	38.5041i	−1.18445	+	0.0833423i
$463$	−141.391	+	81.6320i	−0.305380	+	0.176311i	−0.644857	−	0.764303i	$-0.723083\pi$
$463$	−141.391	+	81.6320i	−0.305380	+	0.176311i	0.339477	+	0.940614i	$0.389750\pi$
$464$	−46.9931	+	27.1315i	−0.101278	+	0.0584731i
$465$	−55.8051	+	114.544i	−0.120011	+	0.246331i
$466$	537.723	+	310.454i	1.15391	+	0.666211i
$467$			64.3434i			0.137780i	0.997624	+	0.0688902i	$0.0219458\pi$
$467$			64.3434i			0.137780i	−0.997624	+	0.0688902i	$0.978054\pi$
$468$	394.075	−	173.082i	0.842041	−	0.369834i
$469$	271.863			0.579666
$470$	97.5745	−	169.004i	0.207605	−	0.359583i
$471$	−543.672	+	367.056i	−1.15429	+	0.779311i
$472$	6.85837	+	11.8790i	0.0145304	+	0.0251675i
$473$	−486.131	−	842.004i	−1.02776	−	1.78014i
$474$	−5.87056	+	3.96346i	−0.0123851	+	0.00836172i
$475$	97.2920	+	56.1716i	0.204825	+	0.118256i
$476$	−315.664			−0.663159
$477$	21.2857	+	150.506i	0.0446242	+	0.315527i
$478$	−986.535			−2.06388
$479$	−270.481	+	468.487i	−0.564679	+	0.978053i	0.432400	+	0.901682i	$0.357667\pi$
$479$	−270.481	+	468.487i	−0.564679	+	0.978053i	−0.997079	+	0.0763711i	$0.975667\pi$
$480$	504.248	+	245.667i	1.05052	+	0.511806i
$481$	689.559	+	176.256i	1.43359	+	0.366436i
$482$	−923.945	+	533.440i	−1.91690	+	1.10672i
$483$	38.5533	+	547.915i	0.0798206	+	1.13440i
$484$	−47.8969	+	82.9599i	−0.0989606	+	0.171405i
$485$		−	414.998i		−	0.855666i
$486$	−663.388	−	115.487i	−1.36500	−	0.237627i
$487$			491.385i			1.00900i	0.863411	+	0.504502i	$0.168324\pi$
$487$			491.385i			1.00900i	−0.863411	+	0.504502i	$0.831676\pi$
$488$	−20.2835	+	35.1320i	−0.0415645	+	0.0719917i
$489$	915.424	−	64.4126i	1.87203	−	0.131723i
$490$	−114.005	−	197.462i	−0.232663	−	0.402984i
$491$	267.027	−	154.168i	0.543843	−	0.313988i	−0.202792	−	0.979222i	$-0.565002\pi$
$491$	267.027	−	154.168i	0.543843	−	0.313988i	0.746635	+	0.665234i	$0.231668\pi$
$492$	−337.959	−	164.652i	−0.686908	−	0.334658i
$493$	24.8991	−	43.1264i	0.0505052	−	0.0874776i
$494$	−404.929	+	414.393i	−0.819694	+	0.838853i
$495$	−458.645	+	64.8652i	−0.926556	+	0.131041i
$496$			171.930i			0.346633i
$497$	−450.322	−	259.993i	−0.906080	−	0.523126i
$498$	−205.154	+	138.508i	−0.411955	+	0.278128i
$499$	−367.158	+	211.979i	−0.735788	+	0.424807i	−0.820536	−	0.571595i	$-0.806325\pi$
$499$	−367.158	+	211.979i	−0.735788	+	0.424807i	0.0847480	+	0.996402i	$0.472991\pi$
$500$	249.707	+	432.504i	0.499413	+	0.865009i
$501$	699.247	−	472.090i	1.39570	−	0.942296i
$502$	−549.802	−	317.428i	−1.09522	−	0.632327i
$503$			774.682i			1.54012i	0.637970	+	0.770061i	$0.279774\pi$
$503$			774.682i			1.54012i	−0.637970	+	0.770061i	$0.720226\pi$
$504$	−40.4427	−	16.2990i	−0.0802435	−	0.0323393i
$505$		−	756.410i		−	1.49784i
$506$	979.060	+	565.261i	1.93490	+	1.11712i
$507$	211.468	−	460.793i	0.417097	−	0.908862i
$508$	195.237	+	338.160i	0.384324	+	0.665669i
$509$	−32.4011	−	56.1204i	−0.0636565	−	0.110256i	0.832441	−	0.554114i	$-0.186943\pi$
$509$	−32.4011	−	56.1204i	−0.0636565	−	0.110256i	−0.896097	+	0.443858i	$0.853610\pi$
$510$	−554.997	+	39.0517i	−1.08823	+	0.0765719i
$511$	128.871	−	223.210i	0.252193	−	0.436811i
$512$	695.689			1.35877
$513$	424.647	−	90.8406i	0.827772	−	0.177077i
$514$		−	439.328i		−	0.854724i
$515$	201.453	−	348.927i	0.391171	−	0.677529i
$516$	62.1098	+	882.696i	0.120368	+	1.71065i
$517$	100.599	+	174.242i	0.194582	+	0.337025i
$518$	412.793	+	714.979i	0.796899	+	1.38027i
$519$	263.277	−	540.395i	0.507278	−	1.04122i
$520$	47.3000	−	13.2614i	0.0909615	−	0.0255028i
$521$			345.592i			0.663323i	0.943398	+	0.331662i	$0.107609\pi$
$521$			345.592i			0.663323i	−0.943398	+	0.331662i	$0.892391\pi$
$522$	−62.0235	+	48.5450i	−0.118819	+	0.0929980i
$523$	−199.085			−0.380660			−0.190330	−	0.981720i	$-0.560956\pi$
$523$	−199.085			−0.380660			−0.190330	+	0.981720i	$0.560956\pi$
$524$	−708.894	−	409.280i	−1.35285	−	0.781070i
$525$	−63.8081	−	94.5108i	−0.121539	−	0.180021i
$526$	134.905	−	77.8876i	0.256474	−	0.148075i
$527$	−78.8917	−	136.644i	−0.149700	−	0.259287i
$528$	−518.033	+	349.745i	−0.981123	+	0.662396i
$529$	301.483	−	522.184i	0.569911	−	0.987115i
$530$		−	198.643i		−	0.374799i
$531$	85.4646	+	109.194i	0.160950	+	0.205638i
$532$	−321.977			−0.605220
$533$	−426.389	+	119.546i	−0.799979	+	0.224289i
$534$	650.916	+	317.123i	1.21894	+	0.593862i
$535$	386.407	−	223.092i	0.722256	−	0.416994i
$536$	38.5182	−	22.2385i	0.0718623	−	0.0414897i
$537$	−94.5499	+	6.65288i	−0.176071	+	0.0123890i
$538$	820.811	+	473.896i	1.52567	+	0.880847i
$539$	235.076			0.436134
$540$	401.114	+	129.752i	0.742803	+	0.240281i
$541$		−	228.668i		−	0.422676i	−0.977413	−	0.211338i	$-0.932218\pi$
$541$		−	228.668i		−	0.422676i	0.977413	−	0.211338i	$-0.0677820\pi$
$542$	−519.112	−	299.709i	−0.957771	−	0.552969i
$543$	−52.4718	−	745.722i	−0.0966331	−	1.37334i
$544$	−601.540	+	347.299i	−1.10577	+	0.638418i
$545$	−395.023	+	228.067i	−0.724813	+	0.418471i
$546$	553.731	−	198.120i	1.01416	−	0.362857i
$547$	268.854	−	465.670i	0.491507	−	0.851315i	−0.508445	−	0.861094i	$-0.669779\pi$
$547$	268.854	−	465.670i	0.491507	−	0.851315i	0.999952	+	0.00977902i	$0.00311281\pi$
$548$	259.251			0.473085
$549$	−153.293	+	380.365i	−0.279222	+	0.692832i
$550$	−234.708			−0.426742
$551$	25.3971	−	43.9890i	0.0460927	−	0.0798348i
$552$	50.2819	+	74.4761i	0.0910903	+	0.134920i
$553$	−4.01555	+	2.31838i	−0.00726140	+	0.00419237i
$554$	269.292	+	466.427i	0.486087	+	0.841927i
$555$	390.078	+	577.772i	0.702842	+	1.04103i
$556$	63.6065	−	110.170i	0.114400	−	0.198147i
$557$	906.914			1.62821			0.814106	−	0.580717i	$-0.197228\pi$
$557$	906.914			1.62821			0.814106	+	0.580717i	$0.197228\pi$
$558$	34.9463	+	247.097i	0.0626278	+	0.442826i
$559$	745.510	+	728.483i	1.33365	+	1.30319i
$560$	343.690	+	198.430i	0.613732	+	0.354338i
$561$	251.232	−	515.670i	0.447828	−	0.919198i
$562$	−418.337	−	724.581i	−0.744372	−	1.28929i
$563$	621.955	−	359.086i	1.10472	−	0.637808i	0.167260	−	0.985913i	$-0.446508\pi$
$563$	621.955	−	359.086i	1.10472	−	0.637808i	0.937456	+	0.348105i	$0.113175\pi$
$564$	−12.8528	−	182.663i	−0.0227887	−	0.323870i
$565$	547.205	+	315.929i	0.968504	+	0.559166i
$566$	−23.1906			−0.0409728
$567$	−427.882	−	105.893i	−0.754642	−	0.186760i
$568$	−85.0701			−0.149771
$569$	560.036	+	323.337i	0.984246	+	0.568255i	0.903549	−	0.428484i	$-0.140952\pi$
$569$	560.036	+	323.337i	0.984246	+	0.568255i	0.0806964	+	0.996739i	$0.474286\pi$
$570$	−566.098	+	39.8327i	−0.993154	+	0.0698820i
$571$	−198.171	−	343.243i	−0.347060	−	0.601126i	0.638665	−	0.769484i	$-0.279487\pi$
$571$	−198.171	−	343.243i	−0.347060	−	0.601126i	−0.985726	+	0.168358i	$0.946153\pi$
$572$	143.611	−	561.842i	0.251067	−	0.982242i
$573$	42.1606	−	86.5375i	0.0735787	−	0.151025i
$574$	−444.853	−	256.836i	−0.775005	−	0.447449i
$575$			235.008i			0.408709i
$576$	475.323	−	67.2238i	0.825213	−	0.116708i
$577$			850.646i			1.47426i	0.675753	+	0.737128i	$0.263819\pi$
$577$			850.646i			1.47426i	−0.675753	+	0.737128i	$0.736181\pi$
$578$	−55.9277	+	96.8697i	−0.0967608	+	0.167595i
$579$	−546.439	−	809.370i	−0.943764	−	1.39788i
$580$	42.7048	−	24.6556i	0.0736290	−	0.0425097i
$581$	−140.328	+	81.0186i	−0.241529	+	0.139447i
$582$	−454.816	−	673.660i	−0.781471	−	1.15749i
$583$	177.362	+	102.400i	0.304223	+	0.175643i
$584$		−	42.1666i		−	0.0722030i
$585$	454.674	−	199.698i	0.777220	−	0.341364i
$586$	−611.046			−1.04274
$587$	−295.418	+	511.678i	−0.503267	+	0.871684i	0.496726	+	0.867907i	$0.334535\pi$
$587$	−295.418	+	511.678i	−0.503267	+	0.871684i	−0.999993	+	0.00377645i	$0.998798\pi$
$588$	−192.336	−	93.7051i	−0.327102	−	0.159362i
$589$	−80.4696	−	139.377i	−0.136621	−	0.236634i
$590$	−90.6046	−	156.932i	−0.153567	−	0.265986i
$591$	8.31561	+	118.180i	0.0140704	+	0.199967i
$592$	814.654	+	470.340i	1.37610	+	0.794494i
$593$	−140.528			−0.236979			−0.118489	−	0.992955i	$-0.537805\pi$
$593$	−140.528			−0.236979			−0.118489	+	0.992955i	$0.537805\pi$
$594$	−673.424	+	607.946i	−1.13371	+	1.02348i
$595$	−364.205			−0.612108
$596$	−359.946	+	623.445i	−0.603937	+	1.04605i
$597$	−35.0097	−	497.553i	−0.0586427	−	0.833422i
$598$	−1174.25	−	300.146i	−1.96363	−	0.501917i
$599$	−142.441	+	82.2383i	−0.237798	+	0.137293i	−0.614164	−	0.789178i	$-0.710507\pi$
$599$	−142.441	+	82.2383i	−0.237798	+	0.137293i	0.376366	+	0.926471i	$0.377173\pi$
$600$	−16.7715	−	8.17097i	−0.0279525	−	0.0136183i
$601$	328.043	−	568.187i	0.545828	−	0.945403i	−0.452726	−	0.891650i	$-0.649548\pi$
$601$	328.043	−	568.187i	0.545828	−	0.945403i	0.998554	−	0.0537528i	$-0.0171183\pi$
$602$			1209.09i			2.00845i
$603$	354.065	−	277.122i	0.587172	−	0.459572i
$604$		−	942.232i		−	1.55999i
$605$	−55.2622	+	95.7170i	−0.0913426	+	0.158210i
$606$	−828.985	−	1227.87i	−1.36796	−	2.02619i
$607$	−105.406	−	182.569i	−0.173651	−	0.300772i	0.766043	−	0.642790i	$-0.222223\pi$
$607$	−105.406	−	182.569i	−0.173651	−	0.300772i	−0.939694	+	0.342017i	$0.888890\pi$
$608$	−613.571	+	354.245i	−1.00916	+	0.582641i
$609$	−42.7315	+	28.8498i	−0.0701666	+	0.0473724i
$610$	267.961	−	464.122i	0.439280	−	0.760856i
$611$	−154.274	−	150.750i	−0.252494	−	0.246727i
$612$	−411.108	+	321.769i	−0.671746	+	0.525766i
$613$			365.386i			0.596063i	0.954556	+	0.298031i	$0.0963300\pi$
$613$			365.386i			0.596063i	−0.954556	+	0.298031i	$0.903670\pi$
$614$	−607.793	−	350.910i	−0.989891	−	0.571514i
$615$	−389.928	−	189.971i	−0.634029	−	0.308896i
$616$	−50.8778	+	29.3743i	−0.0825938	+	0.0476855i
$617$	282.695	+	489.641i	0.458176	+	0.793584i	0.998865	−	0.0476389i	$-0.0151697\pi$
$617$	282.695	+	489.641i	0.458176	+	0.793584i	−0.540689	+	0.841223i	$0.681836\pi$
$618$	−55.3897	−	787.191i	−0.0896273	−	1.27377i
$619$	−347.565	−	200.667i	−0.561494	−	0.324179i	0.192251	−	0.981346i	$-0.438421\pi$
$619$	−347.565	−	200.667i	−0.561494	−	0.324179i	−0.753745	+	0.657167i	$0.771755\pi$
$620$		−	156.241i		−	0.252001i
$621$	608.723	+	674.284i	0.980230	+	1.08580i
$622$		−	997.459i		−	1.60363i
$623$	410.473	+	236.987i	0.658866	+	0.380396i
$624$	433.529	−	510.960i	0.694757	−	0.818845i
$625$	200.793	+	347.783i	0.321268	+	0.556453i
$626$	−96.1607	−	166.555i	−0.153611	−	0.266063i
$627$	256.256	−	525.984i	0.408702	−	0.838889i
$628$	402.194	−	696.620i	0.640436	−	1.10927i
$629$	−863.279			−1.37246
$630$	534.281	+	215.323i	0.848065	+	0.341783i
$631$		−	514.107i		−	0.814750i	−0.913261	−	0.407375i	$-0.866444\pi$
$631$		−	514.107i		−	0.814750i	0.913261	−	0.407375i	$-0.133556\pi$
$632$	−0.379288	+	0.656946i	−0.000600139	+	0.00103947i
$633$	255.734	−	172.657i	0.404003	−	0.272759i
$634$	319.965	+	554.195i	0.504676	+	0.874124i
$635$	225.259	+	390.160i	0.354739	+	0.614426i
$636$	−104.297	−	154.482i	−0.163989	−	0.242896i
$637$	−242.663	+	68.0350i	−0.380946	+	0.106805i
$638$			106.119i			0.166331i
$639$	−851.505	+	120.426i	−1.33256	+	0.188461i
$640$	120.530			0.188329
$641$	−281.654	−	162.613i	−0.439398	−	0.253686i	0.263944	−	0.964538i	$-0.414976\pi$
$641$	−281.654	−	162.613i	−0.439398	−	0.253686i	−0.703342	+	0.710851i	$0.748310\pi$
$642$	382.752	−	785.624i	0.596186	−	1.22371i
$643$	−802.944	+	463.580i	−1.24875	+	0.720964i	−0.970859	−	0.239650i	$-0.922967\pi$
$643$	−802.944	+	463.580i	−1.24875	+	0.720964i	−0.277887	+	0.960614i	$0.589634\pi$
$644$	−336.768	−	583.299i	−0.522931	−	0.905744i
$645$	71.6607	+	1018.43i	0.111102	+	1.57896i
$646$	351.379	−	608.606i	0.543930	−	0.942115i
$647$			905.944i			1.40022i	0.714034	+	0.700111i	$0.246866\pi$
$647$			905.944i			1.40022i	−0.714034	+	0.700111i	$0.753134\pi$
$648$	−69.2854	+	19.9977i	−0.106922	+	0.0308607i
$649$	186.826			0.287867
$650$	242.282	−	67.9284i	0.372742	−	0.104505i
$651$	11.4664	+	162.959i	0.0176135	+	0.250320i
$652$	−974.542	+	562.652i	−1.49470	+	0.862963i
$653$	377.429	−	217.909i	0.577993	−	0.333704i	−0.182343	−	0.983235i	$-0.558368\pi$
$653$	377.429	−	217.909i	0.577993	−	0.333704i	0.760335	+	0.649531i	$0.225035\pi$
$654$	−391.286	+	803.142i	−0.598297	+	1.22805i
$655$	−817.904	−	472.217i	−1.24871	−	0.720942i
$656$	−585.282			−0.892198
$657$	−59.6915	−	422.064i	−0.0908547	−	0.642411i
$658$		−	250.205i		−	0.380251i
$659$	290.348	+	167.632i	0.440588	+	0.254374i	0.703847	−	0.710351i	$-0.251464\pi$
$659$	290.348	+	167.632i	0.440588	+	0.254374i	−0.263259	+	0.964725i	$0.584797\pi$
$660$	470.760	−	317.829i	0.713273	−	0.481560i
$661$	594.164	−	343.041i	0.898886	−	0.518972i	0.0220476	−	0.999757i	$-0.492981\pi$
$661$	594.164	−	343.041i	0.898886	−	0.518972i	0.876839	+	0.480785i	$0.159648\pi$
$662$	363.343	−	209.776i	0.548856	−	0.316882i
$663$	−110.096	+	605.022i	−0.166057	+	0.912552i
$664$	−13.2547	+	22.9578i	−0.0199619	+	0.0345750i
$665$	−371.489			−0.558630
$666$	1266.41	+	510.384i	1.90152	+	0.766343i
$667$	106.255			0.159303
$668$	−517.284	+	895.962i	−0.774377	+	1.34126i
$669$	204.421	−	419.589i	0.305563	−	0.627188i
$670$	−508.857	+	293.789i	−0.759488	+	0.438490i
$671$	276.266	+	478.507i	0.411723	+	0.713125i
$672$	717.381	−	50.4776i	1.06753	−	0.0751155i
$673$	−29.2868	+	50.7262i	−0.0435168	+	0.0753733i	−0.886963	−	0.461840i	$-0.847190\pi$
$673$	−29.2868	+	50.7262i	−0.0435168	+	0.0753733i	0.843447	+	0.537213i	$0.180523\pi$
$674$	986.065			1.46300
$675$	−179.440	−	58.0450i	−0.265837	−	0.0859925i
$676$	14.3614	+	621.537i	0.0212447	+	0.919434i
$677$	406.058	+	234.438i	0.599790	+	0.346289i	0.768959	−	0.639298i	$-0.220775\pi$
$677$	406.058	+	234.438i	0.599790	+	0.346289i	−0.169169	+	0.985587i	$0.554108\pi$
$678$	1234.51	−	86.8649i	1.82081	−	0.128119i
$679$	−266.040	−	460.794i	−0.391811	−	0.678636i
$680$	−51.6013	+	29.7920i	−0.0758842	+	0.0438118i
$681$	666.229	+	324.583i	0.978309	+	0.476627i
$682$	291.188	+	168.117i	0.426962	+	0.246507i
$683$	228.933			0.335187			0.167594	−	0.985856i	$-0.446400\pi$
$683$	228.933			0.335187			0.167594	+	0.985856i	$0.446400\pi$
$684$	−419.331	+	328.205i	−0.613057	+	0.479831i
$685$	299.117			0.436667
$686$	−893.080	−	515.620i	−1.30187	−	0.751633i
$687$	−278.122	−	411.946i	−0.404835	−	0.599630i
$688$	688.823	+	1193.08i	1.00120	+	1.73412i
$689$	−212.722	−	54.3732i	−0.308740	−	0.0789160i
$690$	−664.264	−	983.889i	−0.962702	−	1.42593i
$691$	−570.410	−	329.327i	−0.825485	−	0.476594i	0.0268190	−	0.999640i	$-0.491462\pi$
$691$	−570.410	−	329.327i	−0.825485	−	0.476594i	−0.852304	+	0.523046i	$0.824796\pi$
$692$			737.113i			1.06519i
$693$	−467.676	+	366.044i	−0.674856	+	0.528201i
$694$			461.509i			0.664999i
$695$	73.3875	−	127.111i	0.105594	−	0.182893i
$696$	−3.69437	+	7.58295i	−0.00530800	+	0.0108950i
$697$	465.163	−	268.562i	0.667378	−	0.385311i
$698$	−597.428	+	344.925i	−0.855913	+	0.494162i
$699$	670.552	−	47.1825i	0.959301	−	0.0675000i
$700$	121.099	+	69.9165i	0.172998	+	0.0998807i
$701$		−	652.751i		−	0.931171i	−0.885003	−	0.465585i	$-0.845844\pi$
$701$		−	652.751i		−	0.931171i	0.885003	−	0.465585i	$-0.154156\pi$
$702$	519.207	−	822.466i	0.739611	−	1.17160i
$703$	−880.546			−1.25255
$704$	323.396	−	560.138i	0.459369	−	0.795651i
$705$	−14.8293	−	210.752i	−0.0210344	−	0.298938i
$706$	−77.1606	−	133.646i	−0.109293	−	0.189300i
$707$	−484.906	−	839.881i	−0.685864	−	1.18795i
$708$	−152.858	−	74.4716i	−0.215901	−	0.105186i
$709$	715.213	+	412.928i	1.00876	+	0.582409i	0.910829	−	0.412784i	$-0.135443\pi$
$709$	715.213	+	412.928i	1.00876	+	0.582409i	0.0979335	+	0.995193i	$0.468777\pi$
$710$	1123.85			1.58288
$711$	−2.86648	+	7.11259i	−0.00403162	+	0.0100036i
$712$	77.5423			0.108908
$713$	168.332	−	291.560i	0.236090	−	0.408920i
$714$	−591.208	+	399.149i	−0.828023	+	0.559032i
$715$	165.694	−	648.239i	0.231740	−	0.906628i
$716$	100.656	−	58.1137i	0.140581	−	0.0811644i
$717$	−885.189	+	597.628i	−1.23457	+	0.833512i
$718$	158.826	−	275.094i	0.221206	−	0.383140i
$719$		−	584.633i		−	0.813120i	−0.913624	−	0.406560i	$-0.866728\pi$
$719$		−	584.633i		−	0.813120i	0.913624	−	0.406560i	$-0.133272\pi$
$720$	649.876	−	91.9105i	0.902606	−	0.127653i
$721$		−	516.576i		−	0.716472i
$722$	−141.768	+	245.549i	−0.196354	+	0.340096i
$723$	−505.879	+	1038.35i	−0.699695	+	1.43617i
$724$	458.347	+	793.880i	0.633076	+	1.09652i
$725$	−19.1042	+	11.0298i	−0.0263506	+	0.0152135i
$726$	15.1944	+	215.941i	0.0209289	+	0.297439i
$727$	−308.393	+	534.153i	−0.424200	+	0.734735i	−0.996345	−	0.0854166i	$-0.972778\pi$
$727$	−308.393	+	534.153i	−0.424200	+	0.734735i	0.572146	+	0.820152i	$0.306111\pi$
$728$	44.0183	−	45.0471i	0.0604647	−	0.0618779i
$729$	−665.199	+	298.247i	−0.912481	+	0.409118i
$730$			557.055i			0.763089i
$731$	−1094.91	−	632.145i	−1.49782	−	0.864767i
$732$	−35.2967	−	501.632i	−0.0482195	−	0.685289i
$733$	107.053	−	61.8072i	0.146048	−	0.0843209i	−0.425195	−	0.905102i	$-0.639795\pi$
$733$	107.053	−	61.8072i	0.146048	−	0.0843209i	0.571243	+	0.820781i	$0.306461\pi$
$734$	−46.5425	−	80.6141i	−0.0634095	−	0.109828i
$735$	−221.913	−	108.115i	−0.301922	−	0.147095i
$736$	−1283.51	−	741.037i	−1.74391	−	1.00684i
$737$		−	605.789i		−	0.821965i
$738$	−841.163	+	118.964i	−1.13979	+	0.161197i
$739$		−	1132.78i		−	1.53285i	−0.642333	−	0.766426i	$-0.722033\pi$
$739$		−	1132.78i		−	1.53285i	0.642333	−	0.766426i	$-0.277967\pi$
$740$	−740.313	−	427.420i	−1.00042	−	0.577594i
$741$	−112.298	+	617.123i	−0.151549	+	0.832824i
$742$	−127.343	−	220.564i	−0.171621	−	0.297256i
$743$	92.8768	+	160.867i	0.125002	+	0.216511i	0.921734	−	0.387823i	$-0.126773\pi$
$743$	92.8768	+	160.867i	0.125002	+	0.216511i	−0.796731	+	0.604333i	$0.793439\pi$
$744$	14.9546	+	22.1504i	0.0201003	+	0.0297720i
$745$	−415.297	+	719.315i	−0.557446	+	0.965524i
$746$	−1512.92			−2.02804
$747$	−100.173	+	248.558i	−0.134100	+	0.332742i
$748$			703.387i			0.940358i
$749$	286.032	−	495.422i	0.381885	−	0.661444i
$750$	1014.57	+	494.292i	1.35276	+	0.659056i
$751$	−501.698	−	868.967i	−0.668041	−	1.15708i	−0.978451	−	0.206478i	$-0.933800\pi$
$751$	−501.698	−	868.967i	−0.668041	−	1.15708i	0.310411	−	0.950603i	$-0.399533\pi$
$752$	−142.543	−	246.892i	−0.189552	−	0.328314i
$753$	−685.614	+	48.2424i	−0.910510	+	0.0640669i
$754$	−30.7127	−	109.544i	−0.0407330	−	0.145284i
$755$		−	1087.12i		−	1.43990i
$756$	528.556	−	113.069i	0.699149	−	0.149562i
$757$	210.311			0.277822			0.138911	−	0.990305i	$-0.455640\pi$
$757$	210.311			0.277822			0.138911	+	0.990305i	$0.455640\pi$
$758$	121.251	+	70.0042i	0.159961	+	0.0923538i
$759$	1220.91	−	85.9077i	1.60858	−	0.113185i
$760$	−52.6333	+	30.3879i	−0.0692544	+	0.0399840i
$761$	698.104	+	1209.15i	0.917351	+	1.58890i	0.803422	+	0.595409i	$0.203010\pi$
$761$	698.104	+	1209.15i	0.917351	+	1.58890i	0.113929	+	0.993489i	$0.463657\pi$
$762$	793.255	+	386.470i	1.04102	+	0.507178i
$763$	−292.410	+	506.469i	−0.383237	+	0.663786i
$764$			118.040i			0.154502i
$765$	−474.326	+	371.249i	−0.620034	+	0.485293i
$766$	987.815			1.28958
$767$	−192.855	+	54.0704i	−0.251440	+	0.0704960i
$768$	726.142	−	490.248i	0.945497	−	0.638344i
$769$	854.200	−	493.173i	1.11079	−	0.641317i	0.171759	−	0.985139i	$-0.445055\pi$
$769$	854.200	−	493.173i	1.11079	−	0.641317i	0.939035	+	0.343822i	$0.111722\pi$
$770$	672.137	−	388.058i	0.872905	−	0.503972i
$771$	−266.138	−	394.196i	−0.345186	−	0.511279i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38552 + 2.39980i) q^{2} +(0.210571 + 2.99260i) q^{3} +(-1.83936 - 3.18586i) q^{4} +(-2.12220 - 3.67577i) q^{5} +(-7.47339 - 3.64100i) q^{6} +(-4.71279 - 2.72093i) q^{7} -0.890291 q^{8} +(-8.91132 + 1.26031i) q^{9} +11.7615 q^{10} +(-6.06300 + 10.5014i) q^{11} +(9.14670 - 6.17531i) q^{12} +(3.21938 - 12.5951i) q^{13} +(13.0594 - 7.53984i) q^{14} +(10.5532 - 7.12492i) q^{15} +(8.59095 - 14.8800i) q^{16} +15.7681i q^{17} +(9.32237 - 23.1316i) q^{18} +16.0835i q^{19} +(-7.80699 + 13.5221i) q^{20} +(7.15029 - 14.6765i) q^{21} +(-16.8009 - 29.1000i) q^{22} +(-29.1372 + 16.8223i) q^{23} +(-0.187469 - 2.66429i) q^{24} +(3.49249 - 6.04918i) q^{25} +(25.7651 + 25.1766i) q^{26} +(-5.64806 - 26.4026i) q^{27} +20.0191i q^{28} +(-2.73504 - 1.57907i) q^{29} +(2.47662 + 35.1974i) q^{30} +(-8.66585 + 5.00323i) q^{31} +(22.0254 + 38.1491i) q^{32} +(-32.7033 - 15.9329i) q^{33} +(-37.8404 - 21.8472i) q^{34} +23.0975i q^{35} +(20.4063 + 26.0721i) q^{36} +54.7483i q^{37} +(-38.5972 - 22.2841i) q^{38} +(38.3699 + 6.98217i) q^{39} +(1.88938 + 3.27250i) q^{40} +(-17.0319 - 29.5002i) q^{41} +(25.3136 + 37.4938i) q^{42} +(-40.0900 + 69.4379i) q^{43} +44.6081 q^{44} +(23.5442 + 30.0813i) q^{45} -93.2311i q^{46} +(8.29612 - 14.3693i) q^{47} +(46.3388 + 22.5760i) q^{48} +(-9.69307 - 16.7889i) q^{49} +(9.67788 + 16.7626i) q^{50} +(-47.1878 + 3.32031i) q^{51} +(-46.0477 + 12.9103i) q^{52} -16.8893i q^{53} +(71.1866 + 23.0273i) q^{54} +51.4677 q^{55} +(4.19576 + 2.42242i) q^{56} +(-48.1315 + 3.38671i) q^{57} +(7.57892 - 4.37569i) q^{58} +(-7.70351 - 13.3429i) q^{59} +(-42.1102 - 20.5158i) q^{60} +(22.7829 - 39.4612i) q^{61} -27.7284i q^{62} +(45.4264 + 18.3075i) q^{63} -53.3392 q^{64} +(-53.1287 + 14.8956i) q^{65} +(83.5469 - 56.4059i) q^{66} +(-43.2647 + 24.9789i) q^{67} +(50.2351 - 29.0033i) q^{68} +(-56.4780 - 83.6536i) q^{69} +(-55.4294 - 32.0022i) q^{70} +95.5531 q^{71} +(7.93367 - 1.12204i) q^{72} +47.3627i q^{73} +(-131.385 - 75.8552i) q^{74} +(18.8382 + 9.17786i) q^{75} +(51.2399 - 29.5833i) q^{76} +(57.1473 - 32.9940i) q^{77} +(-69.9183 + 82.4061i) q^{78} +(0.426027 - 0.737900i) q^{79} -72.9271 q^{80} +(77.8233 - 22.4620i) q^{81} +94.3926 q^{82} +(14.8880 - 25.7868i) q^{83} +(-59.9091 + 4.21543i) q^{84} +(57.9600 - 33.4632i) q^{85} +(-111.091 - 192.416i) q^{86} +(4.14962 - 8.51738i) q^{87} +(5.39784 - 9.34933i) q^{88} -87.0977 q^{89} +(-104.810 + 14.8231i) q^{90} +(-49.4426 + 50.5982i) q^{91} +(107.187 + 61.8847i) q^{92} +(-16.7975 - 24.8799i) q^{93} +(22.9890 + 39.8180i) q^{94} +(59.1192 - 34.1325i) q^{95} +(-109.527 + 73.9462i) q^{96} +(84.6758 + 48.8876i) q^{97} +53.7199 q^{98} +(40.7943 - 101.223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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