LMFDB - Embedded newform 222.3.l.d.193.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,3,Mod(97,222)] 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("222.97"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	222.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,8,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.04906186880$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 318 x^{13} + 8876 x^{12} - 14732 x^{11} + 38482 x^{10} + 1520688 x^{9} + \cdots + 4 $ x^16 - 4x^15 + 8x^14 + 318x^13 + 8876x^12 - 14732x^11 + 38482x^10 + 1520688x^9 + 22685392x^8 + 15961410x^7 + 5199688x^6 - 6131200x^5 + 2764889x^4 - 258648x^3 + 12800x^2 - 320*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.2
Root			$0.0303820 - 0.0303820i$ of defining polynomial
Character	$\chi$	$=$	222.193
Dual form			222.3.l.d.199.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.32452 - 0.354905i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.749275 - 1.29778i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +1.93924 q^{10} +13.9681i q^{11} +(1.73205 + 3.00000i) q^{12} +(18.1732 - 4.86949i) q^{13} +(1.49855 - 1.49855i) q^{14} +(2.29414 + 0.614713i) q^{15} +(2.00000 + 3.46410i) q^{16} +(5.39402 - 20.1307i) q^{17} +(1.09808 + 4.09808i) q^{18} +(-22.1889 + 5.94550i) q^{19} +(2.64905 + 0.709810i) q^{20} +(2.24783 - 1.29778i) q^{21} +(-5.11266 + 19.0807i) q^{22} +(0.638443 + 0.638443i) q^{23} +(1.26795 + 4.73205i) q^{24} +(-20.0222 + 11.5598i) q^{25} +26.6074 q^{26} +5.19615i q^{27} +(2.59557 - 1.49855i) q^{28} +(-18.4700 + 18.4700i) q^{29} +(2.90885 + 1.67943i) q^{30} +(29.2146 - 29.2146i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-12.0967 + 20.9521i) q^{33} +(14.7367 - 25.5248i) q^{34} +(0.531843 - 1.98486i) q^{35} +6.00000i q^{36} +(-7.20452 - 36.2918i) q^{37} -32.4868 q^{38} +(31.4769 + 8.43421i) q^{39} +(3.35886 + 1.93924i) q^{40} +(12.2618 + 7.07934i) q^{41} +(3.54561 - 0.950043i) q^{42} +(-59.2758 - 59.2758i) q^{43} +(-13.9681 + 24.1934i) q^{44} +(2.90885 + 2.90885i) q^{45} +(0.638443 + 1.10582i) q^{46} -3.69578 q^{47} +6.92820i q^{48} +(23.3772 + 40.4905i) q^{49} +(-31.5821 + 8.46239i) q^{50} +(25.5248 - 25.5248i) q^{51} +(36.3464 + 9.73898i) q^{52} +(-26.2884 - 45.5328i) q^{53} +(-1.90192 + 7.09808i) q^{54} +(4.95733 + 18.5010i) q^{55} +(4.09412 - 1.09702i) q^{56} +(-38.4323 - 10.2979i) q^{57} +(-31.9909 + 18.4700i) q^{58} +(-2.55567 + 9.53789i) q^{59} +(3.35886 + 3.35886i) q^{60} +(-14.0922 - 52.5927i) q^{61} +(50.6011 - 29.2146i) q^{62} +4.49565 q^{63} +8.00000i q^{64} +(22.3426 - 12.8995i) q^{65} +(-24.1934 + 24.1934i) q^{66} +(-57.1834 - 33.0149i) q^{67} +(29.4735 - 29.4735i) q^{68} +(0.404757 + 1.51057i) q^{69} +(1.45302 - 2.51671i) q^{70} +(-56.4797 + 97.8256i) q^{71} +(-2.19615 + 8.19615i) q^{72} -124.914i q^{73} +(3.44216 - 52.2126i) q^{74} -40.0445 q^{75} +(-44.3778 - 11.8910i) q^{76} +(18.1275 + 10.4659i) q^{77} +(39.9111 + 23.0427i) q^{78} +(-11.6945 + 3.13354i) q^{79} +(3.87847 + 3.87847i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(14.1587 + 14.1587i) q^{82} +(59.4411 + 102.955i) q^{83} +5.19113 q^{84} -28.5780i q^{85} +(-59.2758 - 102.669i) q^{86} +(-43.7004 + 11.7095i) q^{87} +(-27.9361 + 27.9361i) q^{88} +(-8.89198 - 2.38260i) q^{89} +(2.90885 + 5.03828i) q^{90} +(7.29718 - 27.2334i) q^{91} +(0.467373 + 1.74426i) q^{92} +(69.1224 - 18.5213i) q^{93} +(-5.04853 - 1.35275i) q^{94} +(-27.2796 + 15.7499i) q^{95} +(-2.53590 + 9.46410i) q^{96} +(-49.1179 - 49.1179i) q^{97} +(17.1133 + 63.8676i) q^{98} +(-36.2901 + 20.9521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	1.32452	−	0.354905i	0.264905	−	0.0709810i	−0.123922	−	0.992292i	$-0.539547\pi$
$5$	1.32452	−	0.354905i	0.264905	−	0.0709810i	0.388826	+	0.921311i	$0.372881\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	0.749275	−	1.29778i	0.107039	−	0.185398i	−0.807530	−	0.589826i	$-0.799196\pi$
$7$	0.749275	−	1.29778i	0.107039	−	0.185398i	0.914570	+	0.404429i	$0.132530\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	1.93924			0.193924
$11$			13.9681i			1.26982i	0.772585	+	0.634912i	$0.218963\pi$
$11$			13.9681i			1.26982i	−0.772585	+	0.634912i	$0.781037\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	18.1732	−	4.86949i	1.39794	−	0.374576i	0.520334	−	0.853963i	$-0.325808\pi$
$13$	18.1732	−	4.86949i	1.39794	−	0.374576i	0.877604	+	0.479387i	$0.159141\pi$
$14$	1.49855	−	1.49855i	0.107039	−	0.107039i
$15$	2.29414	+	0.614713i	0.152943	+	0.0409809i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	5.39402	−	20.1307i	0.317295	−	1.18416i	−0.604539	−	0.796576i	$-0.706643\pi$
$17$	5.39402	−	20.1307i	0.317295	−	1.18416i	0.921834	−	0.387586i	$-0.126691\pi$
$18$	1.09808	+	4.09808i	0.0610042	+	0.227671i
$19$	−22.1889	+	5.94550i	−1.16784	+	0.312921i	−0.790092	−	0.612988i	$-0.789967\pi$
$19$	−22.1889	+	5.94550i	−1.16784	+	0.312921i	−0.377746	+	0.925909i	$0.623301\pi$
$20$	2.64905	+	0.709810i	0.132452	+	0.0354905i
$21$	2.24783	−	1.29778i	0.107039	−	0.0617992i
$22$	−5.11266	+	19.0807i	−0.232394	+	0.867305i
$23$	0.638443	+	0.638443i	0.0277584	+	0.0277584i	0.720850	−	0.693091i	$-0.243752\pi$
$23$	0.638443	+	0.638443i	0.0277584	+	0.0277584i	−0.693091	+	0.720850i	$0.743752\pi$
$24$	1.26795	+	4.73205i	0.0528312	+	0.197169i
$25$	−20.0222	+	11.5598i	−0.800889	+	0.462394i
$26$	26.6074			1.02336
$27$			5.19615i			0.192450i
$28$	2.59557	−	1.49855i	0.0926988	−	0.0535197i
$29$	−18.4700	+	18.4700i	−0.636895	+	0.636895i	−0.949788	−	0.312893i	$-0.898702\pi$
$29$	−18.4700	+	18.4700i	−0.636895	+	0.636895i	0.312893	+	0.949788i	$0.398702\pi$
$30$	2.90885	+	1.67943i	0.0969618	+	0.0559809i
$31$	29.2146	−	29.2146i	0.942406	−	0.942406i	−0.0560238	−	0.998429i	$-0.517842\pi$
$31$	29.2146	−	29.2146i	0.942406	−	0.942406i	0.998429	+	0.0560238i	$0.0178423\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−12.0967	+	20.9521i	−0.366566	+	0.634912i
$34$	14.7367	−	25.5248i	0.433433	−	0.750728i
$35$	0.531843	−	1.98486i	0.0151955	−	0.0567104i
$36$			6.00000i			0.166667i
$37$	−7.20452	−	36.2918i	−0.194717	−	0.980860i
$37$	−7.20452	−	36.2918i	−0.194717	−	0.980860i
$38$	−32.4868			−0.854917
$39$	31.4769	+	8.43421i	0.807100	+	0.216262i
$40$	3.35886	+	1.93924i	0.0839714	+	0.0484809i
$41$	12.2618	+	7.07934i	0.299068	+	0.172667i	0.642024	−	0.766685i	$-0.278095\pi$
$41$	12.2618	+	7.07934i	0.299068	+	0.172667i	−0.342956	+	0.939351i	$0.611428\pi$
$42$	3.54561	−	0.950043i	0.0844193	−	0.0226201i
$43$	−59.2758	−	59.2758i	−1.37851	−	1.37851i	−0.847145	−	0.531361i	$-0.821681\pi$
$43$	−59.2758	−	59.2758i	−1.37851	−	1.37851i	−0.531361	−	0.847145i	$-0.678319\pi$
$44$	−13.9681	+	24.1934i	−0.317456	+	0.549849i
$45$	2.90885	+	2.90885i	0.0646412	+	0.0646412i
$46$	0.638443	+	1.10582i	0.0138792	+	0.0240395i
$47$	−3.69578			−0.0786337			−0.0393168	−	0.999227i	$-0.512518\pi$
$47$	−3.69578			−0.0786337			−0.0393168	+	0.999227i	$0.512518\pi$
$48$			6.92820i			0.144338i
$49$	23.3772	+	40.4905i	0.477085	+	0.826336i
$50$	−31.5821	+	8.46239i	−0.631641	+	0.169248i
$51$	25.5248	−	25.5248i	0.500485	−	0.500485i
$52$	36.3464	+	9.73898i	0.698969	+	0.187288i
$53$	−26.2884	−	45.5328i	−0.496007	−	0.859109i	0.503983	−	0.863714i	$-0.331868\pi$
$53$	−26.2884	−	45.5328i	−0.496007	−	0.859109i	−0.999989	+	0.00460487i	$0.998534\pi$
$54$	−1.90192	+	7.09808i	−0.0352208	+	0.131446i
$55$	4.95733	+	18.5010i	0.0901333	+	0.336382i
$56$	4.09412	−	1.09702i	0.0731092	−	0.0195896i
$57$	−38.4323	−	10.2979i	−0.674252	−	0.180665i
$58$	−31.9909	+	18.4700i	−0.551567	+	0.318447i
$59$	−2.55567	+	9.53789i	−0.0433164	+	0.161659i	−0.984196	−	0.177082i	$-0.943334\pi$
$59$	−2.55567	+	9.53789i	−0.0433164	+	0.161659i	0.940880	+	0.338741i	$0.110001\pi$
$60$	3.35886	+	3.35886i	0.0559809	+	0.0559809i
$61$	−14.0922	−	52.5927i	−0.231019	−	0.862175i	−0.979903	−	0.199474i	$-0.936077\pi$
$61$	−14.0922	−	52.5927i	−0.231019	−	0.862175i	0.748884	−	0.662701i	$-0.230590\pi$
$62$	50.6011	−	29.2146i	0.816147	−	0.471203i
$63$	4.49565			0.0713596
$64$			8.00000i			0.125000i
$65$	22.3426	−	12.8995i	0.343732	−	0.198454i
$66$	−24.1934	+	24.1934i	−0.366566	+	0.366566i
$67$	−57.1834	−	33.0149i	−0.853484	−	0.492759i	0.00834107	−	0.999965i	$-0.497345\pi$
$67$	−57.1834	−	33.0149i	−0.853484	−	0.492759i	−0.861825	+	0.507206i	$0.830678\pi$
$68$	29.4735	−	29.4735i	0.433433	−	0.433433i
$69$	0.404757	+	1.51057i	0.00586604	+	0.0218924i
$70$	1.45302	−	2.51671i	0.0207575	−	0.0359530i
$71$	−56.4797	+	97.8256i	−0.795488	+	1.37783i	0.127041	+	0.991898i	$0.459452\pi$
$71$	−56.4797	+	97.8256i	−0.795488	+	1.37783i	−0.922529	+	0.385928i	$0.873881\pi$
$72$	−2.19615	+	8.19615i	−0.0305021	+	0.113835i
$73$		−	124.914i		−	1.71115i	−0.517676	−	0.855577i	$-0.673203\pi$
$73$		−	124.914i		−	1.71115i	0.517676	−	0.855577i	$-0.326797\pi$
$74$	3.44216	−	52.2126i	0.0465157	−	0.705575i
$75$	−40.0445			−0.533926
$76$	−44.3778	−	11.8910i	−0.583919	−	0.156461i
$77$	18.1275	+	10.4659i	0.235422	+	0.135921i
$78$	39.9111	+	23.0427i	0.511681	+	0.295419i
$79$	−11.6945	+	3.13354i	−0.148032	+	0.0396651i	−0.332074	−	0.943253i	$-0.607748\pi$
$79$	−11.6945	+	3.13354i	−0.148032	+	0.0396651i	0.184042	+	0.982918i	$0.441082\pi$
$80$	3.87847	+	3.87847i	0.0484809	+	0.0484809i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	14.1587	+	14.1587i	0.172667	+	0.172667i
$83$	59.4411	+	102.955i	0.716158	+	1.24042i	0.962511	+	0.271242i	$0.0874343\pi$
$83$	59.4411	+	102.955i	0.716158	+	1.24042i	−0.246353	+	0.969180i	$0.579232\pi$
$84$	5.19113			0.0617992
$85$		−	28.5780i		−	0.336212i
$86$	−59.2758	−	102.669i	−0.689253	−	1.19382i
$87$	−43.7004	+	11.7095i	−0.502303	+	0.134592i
$88$	−27.9361	+	27.9361i	−0.317456	+	0.317456i
$89$	−8.89198	−	2.38260i	−0.0999099	−	0.0267708i	0.208518	−	0.978019i	$-0.433136\pi$
$89$	−8.89198	−	2.38260i	−0.0999099	−	0.0267708i	−0.308428	+	0.951248i	$0.599803\pi$
$90$	2.90885	+	5.03828i	0.0323206	+	0.0559809i
$91$	7.29718	−	27.2334i	0.0801888	−	0.299269i
$92$	0.467373	+	1.74426i	0.00508014	+	0.0189593i
$93$	69.1224	−	18.5213i	0.743252	−	0.199154i
$94$	−5.04853	−	1.35275i	−0.0537078	−	0.0143910i
$95$	−27.2796	+	15.7499i	−0.287154	+	0.165789i
$96$	−2.53590	+	9.46410i	−0.0264156	+	0.0985844i
$97$	−49.1179	−	49.1179i	−0.506370	−	0.506370i	0.407040	−	0.913410i	$-0.366561\pi$
$97$	−49.1179	−	49.1179i	−0.506370	−	0.506370i	−0.913410	+	0.407040i	$0.866561\pi$
$98$	17.1133	+	63.8676i	0.174625	+	0.651710i
$99$	−36.2901	+	20.9521i	−0.366566	+	0.211637i
$100$	−46.2394			−0.462394
$101$			116.875i			1.15718i	0.815620	+	0.578588i	$0.196396\pi$
$101$			116.875i			1.15718i	−0.815620	+	0.578588i	$0.803604\pi$
$102$	44.2102	−	25.5248i	0.433433	−	0.250243i
$103$	18.6974	−	18.6974i	0.181528	−	0.181528i	−0.610493	−	0.792022i	$-0.709029\pi$
$103$	18.6974	−	18.6974i	0.181528	−	0.181528i	0.792022	+	0.610493i	$0.209029\pi$
$104$	46.0854	+	26.6074i	0.443128	+	0.255840i
$105$	2.51671	−	2.51671i	0.0239686	−	0.0239686i
$106$	−19.2444	−	71.8211i	−0.181551	−	0.677558i
$107$	35.5463	−	61.5681i	0.332209	−	0.575402i	−0.650736	−	0.759304i	$-0.725540\pi$
$107$	35.5463	−	61.5681i	0.332209	−	0.575402i	0.982945	+	0.183902i	$0.0588728\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	12.0351	−	44.9155i	0.110414	−	0.412069i	−0.888489	−	0.458897i	$-0.848245\pi$
$109$	12.0351	−	44.9155i	0.110414	−	0.412069i	0.998903	+	0.0468281i	$0.0149113\pi$
$110$			27.0874i			0.246249i
$111$	20.6228	−	60.6770i	0.185791	−	0.546640i
$112$	5.99420			0.0535197
$113$	20.2852	+	5.43540i	0.179515	+	0.0481009i	0.347457	−	0.937696i	$-0.387045\pi$
$113$	20.2852	+	5.43540i	0.179515	+	0.0481009i	−0.167942	+	0.985797i	$0.553712\pi$
$114$	−48.7303	−	28.1344i	−0.427458	−	0.246793i
$115$	1.07222	+	0.619046i	0.00932364	+	0.00538301i
$116$	−50.4608	+	13.5209i	−0.435007	+	0.116560i
$117$	39.9111	+	39.9111i	0.341120	+	0.341120i
$118$	−6.98222	+	12.0936i	−0.0591713	+	0.102488i
$119$	−22.0837	−	22.0837i	−0.185578	−	0.185578i
$120$	3.35886	+	5.81771i	0.0279905	+	0.0484809i
$121$	−74.1065			−0.612450
$122$		−	77.0010i		−	0.631156i
$123$	12.2618	+	21.2380i	0.0996892	+	0.172667i
$124$	79.8157	−	21.3866i	0.643675	−	0.172472i
$125$	−46.6577	+	46.6577i	−0.373262	+	0.373262i
$126$	6.14118	+	1.64552i	0.0487395	+	0.0130597i
$127$	113.781	+	197.074i	0.895913	+	1.55177i	0.832671	+	0.553768i	$0.186810\pi$
$127$	113.781	+	197.074i	0.895913	+	1.55177i	0.0632414	+	0.997998i	$0.479856\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−37.5793	−	140.248i	−0.291313	−	1.08719i
$130$	35.2421	−	9.44309i	0.271093	−	0.0726392i
$131$	168.276	+	45.0895i	1.28455	+	0.344195i	0.835589	−	0.549356i	$-0.185127\pi$
$131$	168.276	+	45.0895i	1.28455	+	0.344195i	0.448963	+	0.893550i	$0.351793\pi$
$132$	−41.9042	+	24.1934i	−0.317456	+	0.183283i
$133$	−8.90964	+	33.2512i	−0.0669898	+	0.250009i
$134$	−66.0297	−	66.0297i	−0.492759	−	0.492759i
$135$	1.84414	+	6.88242i	0.0136603	+	0.0509809i
$136$	51.0495	−	29.4735i	0.375364	−	0.216717i
$137$	54.3456			0.396684			0.198342	−	0.980133i	$-0.436444\pi$
$137$	54.3456			0.396684			0.198342	+	0.980133i	$0.436444\pi$
$138$			2.21163i			0.0160263i
$139$	−121.362	+	70.0682i	−0.873106	+	0.504088i	−0.868379	−	0.495901i	$-0.834838\pi$
$139$	−121.362	+	70.0682i	−0.873106	+	0.504088i	−0.00472668	+	0.999989i	$0.501505\pi$
$140$	2.90604	−	2.90604i	0.0207575	−	0.0207575i
$141$	−5.54367	−	3.20064i	−0.0393168	−	0.0226996i
$142$	−112.959	+	112.959i	−0.795488	+	0.795488i
$143$	68.0173	+	253.844i	0.475646	+	1.77513i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$	−17.9088	+	31.0189i	−0.123509	+	0.213924i
$146$	45.7218	−	170.636i	0.313163	−	1.16874i
$147$			80.9809i			0.550890i
$148$	23.8132	−	70.0638i	0.160900	−	0.473404i
$149$	149.593			1.00398			0.501992	−	0.864872i	$-0.332601\pi$
$149$	149.593			1.00398			0.501992	+	0.864872i	$0.332601\pi$
$150$	−54.7018	−	14.6573i	−0.364678	−	0.0977153i
$151$	115.225	+	66.5254i	0.763081	+	0.440565i	0.830401	−	0.557166i	$-0.188111\pi$
$151$	115.225	+	66.5254i	0.763081	+	0.440565i	−0.0673196	+	0.997731i	$0.521445\pi$
$152$	−56.2689	−	32.4868i	−0.370190	−	0.213729i
$153$	60.3922	−	16.1820i	0.394720	−	0.105765i
$154$	20.9318	+	20.9318i	0.135921	+	0.135921i
$155$	28.3270	−	49.0638i	0.182755	−	0.316540i
$156$	46.0854	+	46.0854i	0.295419	+	0.295419i
$157$	−40.8748	−	70.7973i	−0.260349	−	0.450938i	0.705985	−	0.708226i	$-0.250504\pi$
$157$	−40.8748	−	70.7973i	−0.260349	−	0.450938i	−0.966335	+	0.257288i	$0.917171\pi$
$158$	−17.1220			−0.108367
$159$		−	91.0655i		−	0.572739i
$160$	3.87847	+	6.71771i	0.0242404	+	0.0419857i
$161$	1.30693	−	0.350191i	0.00811758	−	0.00217510i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	141.671	+	37.9607i	0.869149	+	0.232888i	0.665720	−	0.746202i	$-0.268125\pi$
$163$	141.671	+	37.9607i	0.869149	+	0.232888i	0.203429	+	0.979090i	$0.434791\pi$
$164$	14.1587	+	24.5235i	0.0863334	+	0.149534i
$165$	−8.58635	+	32.0447i	−0.0520385	+	0.194210i
$166$	43.5139	+	162.396i	0.262132	+	0.978290i
$167$	−116.880	+	31.3178i	−0.699879	+	0.187532i	−0.591176	−	0.806542i	$-0.701336\pi$
$167$	−116.880	+	31.3178i	−0.699879	+	0.187532i	−0.108702	+	0.994074i	$0.534670\pi$
$168$	7.09122	+	1.90009i	0.0422096	+	0.0113100i
$169$	160.195	−	92.4883i	0.947896	−	0.547268i
$170$	10.4603	−	39.0383i	0.0615310	−	0.229637i
$171$	−48.7303	−	48.7303i	−0.284972	−	0.284972i
$172$	−43.3929	−	161.944i	−0.252284	−	0.941537i
$173$	−39.7628	+	22.9571i	−0.229843	+	0.132700i	−0.610500	−	0.792017i	$-0.709031\pi$
$173$	−39.7628	+	22.9571i	−0.229843	+	0.132700i	0.380657	+	0.924716i	$0.375698\pi$
$174$	−63.9818			−0.367711
$175$			34.6460i			0.197977i
$176$	−48.3868	+	27.9361i	−0.274925	+	0.158728i
$177$	−12.0936	+	12.0936i	−0.0683252	+	0.0683252i
$178$	−11.2746	−	6.50938i	−0.0633403	−	0.0365696i
$179$	−108.822	+	108.822i	−0.607946	+	0.607946i	−0.942409	−	0.334463i	$-0.891445\pi$
$179$	−108.822	+	108.822i	−0.607946	+	0.607946i	0.334463	+	0.942409i	$0.391445\pi$
$180$	2.12943	+	7.94714i	0.0118302	+	0.0441508i
$181$	−75.2695	+	130.371i	−0.415854	+	0.720280i	−0.995518	−	0.0945758i	$-0.969851\pi$
$181$	−75.2695	+	130.371i	−0.415854	+	0.720280i	0.579664	+	0.814856i	$0.303184\pi$
$182$	19.9363	−	34.5306i	0.109540	−	0.189729i
$183$	24.4083	−	91.0932i	0.133379	−	0.497777i
$184$			2.55377i			0.0138792i
$185$	−22.4227	−	45.5124i	−0.121204	−	0.246013i
$186$	101.202			0.544098
$187$	281.187	+	75.3439i	1.50368	+	0.402909i
$188$	−6.40128	−	3.69578i	−0.0340494	−	0.0196584i
$189$	6.74348	+	3.89335i	0.0356798	+	0.0205997i
$190$	−43.0296	+	11.5297i	−0.226471	+	0.0606828i
$191$	234.534	+	234.534i	1.22793	+	1.22793i	0.964746	+	0.263184i	$0.0847725\pi$
$191$	234.534	+	234.534i	1.22793	+	1.22793i	0.263184	+	0.964746i	$0.415228\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	220.924	+	220.924i	1.14468	+	1.14468i	0.987582	+	0.157102i	$0.0502152\pi$
$193$	220.924	+	220.924i	1.14468	+	1.14468i	0.157102	+	0.987582i	$0.449785\pi$
$194$	−49.1179	−	85.0747i	−0.253185	−	0.438529i
$195$	44.6852			0.229155
$196$			93.5087i			0.477085i
$197$	−67.6691	−	117.206i	−0.343498	−	0.594956i	0.641582	−	0.767055i	$-0.278279\pi$
$197$	−67.6691	−	117.206i	−0.343498	−	0.594956i	−0.985080	+	0.172099i	$0.944945\pi$
$198$	−57.2421	+	15.3380i	−0.289102	+	0.0774646i
$199$	−84.6582	+	84.6582i	−0.425418	+	0.425418i	−0.887064	−	0.461646i	$-0.847259\pi$
$199$	−84.6582	+	84.6582i	−0.425418	+	0.425418i	0.461646	+	0.887064i	$0.347259\pi$
$200$	−63.1641	−	16.9248i	−0.315821	−	0.0846239i
$201$	−57.1834	−	99.0446i	−0.284495	−	0.492759i
$202$	−42.7791	+	159.654i	−0.211778	+	0.790366i
$203$	10.1309	+	37.8091i	0.0499060	+	0.186252i
$204$	69.7349	−	18.6854i	0.341838	−	0.0915952i
$205$	18.7535	+	5.02498i	0.0914804	+	0.0245121i
$206$	32.3849	−	18.6974i	0.157208	−	0.0907642i
$207$	−0.701059	+	2.61639i	−0.00338676	+	0.0126396i
$208$	53.2148	+	53.2148i	0.255840	+	0.255840i
$209$	−83.0471	−	309.936i	−0.397355	−	1.48295i
$210$	4.35907	−	2.51671i	0.0207575	−	0.0119843i
$211$	73.7146			0.349358			0.174679	−	0.984625i	$-0.444111\pi$
$211$	73.7146			0.349358			0.174679	+	0.984625i	$0.444111\pi$
$212$		−	105.153i		−	0.496007i
$213$	−169.439	+	97.8256i	−0.795488	+	0.459275i
$214$	71.0927	−	71.0927i	0.332209	−	0.332209i
$215$	−99.5494	−	57.4749i	−0.463020	−	0.267325i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−16.0244	−	59.8039i	−0.0738452	−	0.275594i
$218$	32.8805	−	56.9506i	0.150828	−	0.261241i
$219$	108.179	−	187.371i	0.493967	−	0.855577i
$220$	−9.91466	+	37.0020i	−0.0450666	+	0.168191i
$221$		−	392.106i		−	1.77423i
$222$	50.3807	−	75.3378i	0.226940	−	0.339360i
$223$	180.708			0.810348			0.405174	−	0.914239i	$-0.367211\pi$
$223$	180.708			0.810348			0.405174	+	0.914239i	$0.367211\pi$
$224$	8.18823	+	2.19403i	0.0365546	+	0.00979478i
$225$	−60.0667	−	34.6795i	−0.266963	−	0.154131i
$226$	25.7206	+	14.8498i	0.113808	+	0.0657070i
$227$	−205.897	+	55.1699i	−0.907034	+	0.243039i	−0.682035	−	0.731320i	$-0.738905\pi$
$227$	−205.897	+	55.1699i	−0.907034	+	0.243039i	−0.225000	+	0.974359i	$0.572238\pi$
$228$	−56.2689	−	56.2689i	−0.246793	−	0.246793i
$229$	−125.275	+	216.982i	−0.547051	+	0.947520i	0.451424	+	0.892310i	$0.350916\pi$
$229$	−125.275	+	216.982i	−0.547051	+	0.947520i	−0.998475	+	0.0552104i	$0.982417\pi$
$230$	1.23809	+	1.23809i	0.00538301	+	0.00538301i
$231$	18.1275	+	31.3978i	0.0784740	+	0.135921i
$232$	−73.8798			−0.318447
$233$		−	237.554i		−	1.01954i	−0.860310	−	0.509772i	$-0.829730\pi$
$233$		−	237.554i		−	1.01954i	0.860310	−	0.509772i	$-0.170270\pi$
$234$	39.9111	+	69.1280i	0.170560	+	0.295419i
$235$	−4.89515	+	1.31165i	−0.0208304	+	0.00558149i
$236$	−13.9644	+	13.9644i	−0.0591713	+	0.0591713i
$237$	−20.2555	−	5.42745i	−0.0854664	−	0.0229006i
$238$	−22.0837	−	38.2501i	−0.0927888	−	0.160715i
$239$	−24.5883	+	91.7648i	−0.102880	+	0.383953i	−0.998096	−	0.0616791i	$-0.980354\pi$
$239$	−24.5883	+	91.7648i	−0.102880	+	0.383953i	0.895216	+	0.445632i	$0.147021\pi$
$240$	2.45885	+	9.17656i	0.0102452	+	0.0382357i
$241$	−15.1791	+	4.06724i	−0.0629840	+	0.0168765i	−0.290173	−	0.956974i	$-0.593713\pi$
$241$	−15.1791	+	4.06724i	−0.0629840	+	0.0168765i	0.227189	+	0.973851i	$0.427046\pi$
$242$	−101.231	−	27.1249i	−0.418311	−	0.112086i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$	28.1843	−	105.185i	0.115510	−	0.431088i
$245$	45.3339	+	45.3339i	0.185036	+	0.185036i
$246$	8.97624	+	33.4998i	0.0364888	+	0.136178i
$247$	−374.292	+	216.098i	−1.51535	+	0.874889i
$248$	116.858			0.471203
$249$			205.910i			0.826948i
$250$	−80.8135	+	46.6577i	−0.323254	+	0.186631i
$251$	−115.250	+	115.250i	−0.459164	+	0.459164i	−0.898381	−	0.439217i	$-0.855256\pi$
$251$	−115.250	+	115.250i	−0.459164	+	0.459164i	0.439217	+	0.898381i	$0.355256\pi$
$252$	7.78670	+	4.49565i	0.0308996	+	0.0178399i
$253$	−8.91781	+	8.91781i	−0.0352482	+	0.0352482i
$254$	83.2934	+	310.855i	0.327927	+	1.22384i
$255$	24.7493	−	42.8670i	0.0970559	−	0.168106i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	27.8872	−	104.077i	0.108511	−	0.404967i	−0.890209	−	0.455552i	$-0.849442\pi$
$257$	27.8872	−	104.077i	0.108511	−	0.404967i	0.998720	+	0.0505848i	$0.0161085\pi$
$258$		−	205.337i		−	0.795881i
$259$	−52.4971	−	17.8427i	−0.202691	−	0.0688905i
$260$	51.5980			0.198454
$261$	−75.6913	−	20.2814i	−0.290005	−	0.0777066i
$262$	213.366	+	123.187i	0.814373	+	0.470179i
$263$	−436.840	−	252.210i	−1.66099	−	0.958972i	−0.972245	−	0.233965i	$-0.924830\pi$
$263$	−436.840	−	252.210i	−1.66099	−	0.958972i	−0.688742	−	0.725006i	$-0.741837\pi$
$264$	−66.0975	+	17.7108i	−0.250369	+	0.0670863i
$265$	−50.9793	−	50.9793i	−0.192375	−	0.192375i
$266$	−24.3416	+	42.1609i	−0.0915097	+	0.158499i
$267$	−11.2746	−	11.2746i	−0.0422269	−	0.0422269i
$268$	−66.0297	−	114.367i	−0.246380	−	0.426742i
$269$	−75.2286			−0.279660			−0.139830	−	0.990176i	$-0.544656\pi$
$269$	−75.2286			−0.279660			−0.139830	+	0.990176i	$0.544656\pi$
$270$			10.0766i			0.0373206i
$271$	−199.152	−	344.942i	−0.734879	−	1.27285i	−0.954777	−	0.297324i	$-0.903906\pi$
$271$	−199.152	−	344.942i	−0.734879	−	1.27285i	0.219898	−	0.975523i	$-0.429428\pi$
$272$	80.5230	−	21.5761i	0.296040	−	0.0793238i
$273$	34.5306	−	34.5306i	0.126486	−	0.126486i
$274$	74.2375	+	19.8919i	0.270940	+	0.0725981i
$275$	−161.468	−	279.672i	−0.587158	−	1.01699i
$276$	−0.809513	+	3.02114i	−0.00293302	+	0.0109462i
$277$	−85.5864	−	319.413i	−0.308976	−	1.15311i	−0.929468	−	0.368902i	$-0.879734\pi$
$277$	−85.5864	−	319.413i	−0.308976	−	1.15311i	0.620492	−	0.784213i	$-0.286933\pi$
$278$	−191.430	+	51.2935i	−0.688597	+	0.184509i
$279$	119.724	+	32.0798i	0.429117	+	0.114981i
$280$	5.03342	−	2.90604i	0.0179765	−	0.0103787i
$281$	130.378	−	486.578i	0.463979	−	1.73160i	−0.196271	−	0.980550i	$-0.562883\pi$
$281$	130.378	−	486.578i	0.463979	−	1.73160i	0.660251	−	0.751045i	$-0.270450\pi$
$282$	−6.40128	−	6.40128i	−0.0226996	−	0.0226996i
$283$	77.9355	+	290.859i	0.275390	+	1.02777i	0.955579	+	0.294734i	$0.0952310\pi$
$283$	77.9355	+	290.859i	0.275390	+	1.02777i	−0.680189	+	0.733037i	$0.738102\pi$
$284$	−195.651	+	112.959i	−0.688913	+	0.397744i
$285$	−54.5593			−0.191436
$286$			371.653i			1.29949i
$287$	18.3749	−	10.6087i	0.0640240	−	0.0369643i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$	−125.870	−	72.6711i	−0.435537	−	0.251457i
$290$	−35.8176	+	35.8176i	−0.123509	+	0.123509i
$291$	−31.1395	−	116.214i	−0.107009	−	0.399361i
$292$	124.914	−	216.358i	0.427788	−	0.740951i
$293$	162.762	−	281.913i	0.555503	−	0.962160i	−0.442361	−	0.896837i	$-0.645859\pi$
$293$	162.762	−	281.913i	0.555503	−	0.962160i	0.997864	−	0.0653227i	$-0.0208077\pi$
$294$	−29.6411	+	110.622i	−0.100820	+	0.376265i
$295$			13.5402i			0.0458989i
$296$	58.1746	−	86.9926i	0.196536	−	0.293894i
$297$	−72.5801			−0.244378
$298$	204.349	+	54.7550i	0.685733	+	0.183742i
$299$	14.7114	+	8.49365i	0.0492021	+	0.0284069i
$300$	−69.3590	−	40.0445i	−0.231197	−	0.133482i
$301$	−121.341	+	32.5132i	−0.403126	+	0.108017i
$302$	133.051	+	133.051i	0.440565	+	0.440565i
$303$	−101.216	+	175.312i	−0.334048	+	0.578588i
$304$	−64.9737	−	64.9737i	−0.213729	−	0.213729i
$305$	−37.3308	−	64.6588i	−0.122396	−	0.211996i
$306$	88.4204			0.288955
$307$		−	274.523i		−	0.894213i	−0.894481	−	0.447107i	$-0.852454\pi$
$307$		−	274.523i		−	0.894213i	0.894481	−	0.447107i	$-0.147546\pi$
$308$	20.9318	+	36.2550i	0.0679605	+	0.117711i
$309$	44.2386	−	11.8537i	0.143167	−	0.0383615i
$310$	56.6540	−	56.6540i	0.182755	−	0.182755i
$311$	238.416	+	63.8833i	0.766610	+	0.205413i	0.620873	−	0.783911i	$-0.286778\pi$
$311$	238.416	+	63.8833i	0.766610	+	0.205413i	0.145737	+	0.989323i	$0.453445\pi$
$312$	46.0854	+	79.8222i	0.147709	+	0.255840i
$313$	−5.83011	+	21.7583i	−0.0186265	+	0.0695152i	−0.974614	−	0.223894i	$-0.928123\pi$
$313$	−5.83011	+	21.7583i	−0.0186265	+	0.0695152i	0.955987	+	0.293409i	$0.0947898\pi$
$314$	−29.9225	−	111.672i	−0.0952944	−	0.355644i
$315$	5.95459	−	1.59553i	0.0189035	−	0.00506517i
$316$	−23.3891	−	6.26708i	−0.0740160	−	0.0198325i
$317$	−533.610	+	308.080i	−1.68331	+	0.971860i	−0.723876	+	0.689930i	$0.757641\pi$
$317$	−533.610	+	308.080i	−1.68331	+	0.971860i	−0.959435	+	0.281930i	$0.909025\pi$
$318$	33.3323	−	124.398i	0.104819	−	0.391188i
$319$	−257.989	−	257.989i	−0.808744	−	0.808744i
$320$	2.83924	+	10.5962i	0.00887262	+	0.0331131i
$321$	106.639	−	61.5681i	0.332209	−	0.191801i
$322$	1.91348			0.00594248
$323$			478.750i			1.48220i
$324$	−15.5885	+	9.00000i	−0.0481125	+	0.0277778i
$325$	−307.577	+	307.577i	−0.946391	+	0.946391i
$326$	179.632	+	103.711i	0.551019	+	0.318131i
$327$	56.9506	−	56.9506i	0.174161	−	0.174161i
$328$	10.3649	+	38.6822i	0.0316002	+	0.117934i
$329$	−2.76916	+	4.79632i	−0.00841689	+	0.0145785i
$330$	−23.4583	+	40.6310i	−0.0710859	+	0.123124i
$331$	81.6470	−	304.711i	0.246668	−	0.920576i	−0.725870	−	0.687832i	$-0.758563\pi$
$331$	81.6470	−	304.711i	0.246668	−	0.920576i	0.972538	−	0.232744i	$-0.0747706\pi$
$332$			237.764i			0.716158i
$333$	83.4821	−	73.1556i	0.250697	−	0.219686i
$334$	−171.124			−0.512347
$335$	−87.4579	−	23.4343i	−0.261068	−	0.0699530i
$336$	8.99130	+	5.19113i	0.0267598	+	0.0154498i
$337$	435.090	+	251.200i	1.29107	+	0.745399i	0.978844	−	0.204609i	$-0.0655922\pi$
$337$	435.090	+	251.200i	1.29107	+	0.745399i	0.312226	+	0.950008i	$0.398926\pi$
$338$	252.683	−	67.7062i	0.747582	−	0.200314i
$339$	25.7206	+	25.7206i	0.0758720	+	0.0758720i
$340$	28.5780	−	49.4985i	0.0840529	−	0.145584i
$341$	408.071	+	408.071i	1.19669	+	1.19669i
$342$	−48.7303	−	84.4033i	−0.142486	−	0.246793i
$343$	143.493			0.418346
$344$		−	237.103i		−	0.689253i
$345$	1.07222	+	1.85714i	0.00310788	+	0.00538301i
$346$	−62.7199	+	16.8057i	−0.181271	+	0.0485715i
$347$	−95.3180	+	95.3180i	−0.274692	+	0.274692i	−0.830986	−	0.556294i	$-0.812223\pi$
$347$	−95.3180	+	95.3180i	−0.274692	+	0.274692i	0.556294	+	0.830986i	$0.312223\pi$
$348$	−87.4008	−	23.4190i	−0.251152	−	0.0672959i
$349$	−143.406	−	248.386i	−0.410905	−	0.711708i	0.584084	−	0.811693i	$-0.301454\pi$
$349$	−143.406	−	248.386i	−0.410905	−	0.711708i	−0.994989	+	0.0999854i	$0.968120\pi$
$350$	−12.6813	+	47.3273i	−0.0362323	+	0.135221i
$351$	25.3026	+	94.4307i	0.0720872	+	0.269033i
$352$	−76.3229	+	20.4506i	−0.216826	+	0.0580984i
$353$	84.2935	+	22.5864i	0.238792	+	0.0639841i	0.376230	−	0.926526i	$-0.377220\pi$
$353$	84.2935	+	22.5864i	0.238792	+	0.0639841i	−0.137438	+	0.990510i	$0.543887\pi$
$354$	−20.9467	+	12.0936i	−0.0591713	+	0.0341626i
$355$	−40.0898	+	149.617i	−0.112929	+	0.421457i
$356$	−13.0188	−	13.0188i	−0.0365696	−	0.0365696i
$357$	−14.0005	−	52.2507i	−0.0392172	−	0.146360i
$358$	−188.486	+	108.822i	−0.526496	+	0.303973i
$359$	−12.4041			−0.0345517			−0.0172759	−	0.999851i	$-0.505499\pi$
$359$	−12.4041			−0.0345517			−0.0172759	+	0.999851i	$0.505499\pi$
$360$			11.6354i			0.0323206i
$361$	144.364	−	83.3486i	0.399900	−	0.230883i
$362$	−150.539	+	150.539i	−0.415854	+	0.415854i
$363$	−111.160	−	64.1781i	−0.306225	−	0.176799i
$364$	39.8725	−	39.8725i	0.109540	−	0.109540i
$365$	−44.3326	−	165.452i	−0.121459	−	0.453292i
$366$	66.6848	−	115.502i	0.182199	−	0.315578i
$367$	129.064	−	223.545i	0.351672	−	0.609114i	−0.634870	−	0.772619i	$-0.718947\pi$
$367$	129.064	−	223.545i	0.351672	−	0.609114i	0.986543	+	0.163505i	$0.0522798\pi$
$368$	−0.934745	+	3.48852i	−0.00254007	+	0.00947967i
$369$			42.4760i			0.115111i
$370$	−13.9713	−	70.3784i	−0.0377602	−	0.190212i
$371$	−78.7889			−0.212369
$372$	138.245	+	37.0426i	0.371626	+	0.0995769i
$373$	505.950	+	292.110i	1.35643	+	0.783137i	0.989141	−	0.146968i	$-0.0469514\pi$
$373$	505.950	+	292.110i	1.35643	+	0.783137i	0.367293	+	0.930105i	$0.380285\pi$
$374$	356.531	+	205.843i	0.953292	+	0.550383i
$375$	−110.393	+	29.5798i	−0.294382	+	0.0788795i
$376$	−7.39156	−	7.39156i	−0.0196584	−	0.0196584i
$377$	−245.719	+	425.597i	−0.651774	+	1.12890i
$378$	7.78670	+	7.78670i	0.0205997	+	0.0205997i
$379$	−75.9432	−	131.537i	−0.200378	−	0.347064i	0.748272	−	0.663392i	$-0.230884\pi$
$379$	−75.9432	−	131.537i	−0.200378	−	0.347064i	−0.948650	+	0.316327i	$0.897550\pi$
$380$	−62.9996			−0.165789
$381$			394.149i			1.03451i
$382$	234.534	+	406.226i	0.613965	+	1.06342i
$383$	498.670	−	133.618i	1.30201	−	0.348872i	0.459800	−	0.888022i	$-0.347921\pi$
$383$	498.670	−	133.618i	1.30201	−	0.348872i	0.842210	+	0.539150i	$0.181254\pi$
$384$	−13.8564	+	13.8564i	−0.0360844	+	0.0360844i
$385$	27.7247	+	7.42881i	0.0720122	+	0.0192956i
$386$	220.924	+	382.652i	0.572342	+	0.991326i
$387$	65.0893	−	242.917i	0.168189	−	0.627692i
$388$	−35.9568	−	134.193i	−0.0926721	−	0.345857i
$389$	509.566	−	136.538i	1.30994	−	0.350997i	0.464738	−	0.885448i	$-0.346148\pi$
$389$	509.566	−	136.538i	1.30994	−	0.350997i	0.845199	+	0.534452i	$0.179482\pi$
$390$	61.0411	+	16.3559i	0.156516	+	0.0419382i
$391$	16.2961	−	9.40856i	0.0416780	−	0.0240628i
$392$	−34.2266	+	127.735i	−0.0873126	+	0.325855i
$393$	213.366	+	213.366i	0.542915	+	0.542915i
$394$	−49.5372	−	184.875i	−0.125729	−	0.469227i
$395$	−14.3776	+	8.30089i	−0.0363989	+	0.0210149i
$396$	−83.8083			−0.211637
$397$			664.112i			1.67283i	0.548099	+	0.836413i	$0.315352\pi$
$397$			664.112i			1.67283i	−0.548099	+	0.836413i	$0.684648\pi$
$398$	−146.632	+	84.6582i	−0.368423	+	0.212709i
$399$	−42.1609	+	42.1609i	−0.105666	+	0.105666i
$400$	−80.0889	−	46.2394i	−0.200222	−	0.115598i
$401$	485.976	−	485.976i	1.21191	−	1.21191i	0.241513	−	0.970398i	$-0.422356\pi$
$401$	485.976	−	485.976i	1.21191	−	1.21191i	0.970398	−	0.241513i	$-0.0776436\pi$
$402$	−41.8612	−	156.228i	−0.104132	−	0.388627i
$403$	388.662	−	673.182i	0.964421	−	1.67043i
$404$	−116.875	+	202.433i	−0.289294	+	0.501072i
$405$	−3.19414	+	11.9207i	−0.00788677	+	0.0294338i
$406$			55.3563i			0.136346i
$407$	506.926	−	100.633i	1.24552	−	0.247256i
$408$	102.099			0.250243
$409$	−334.801	−	89.7095i	−0.818583	−	0.219339i	−0.174856	−	0.984594i	$-0.555946\pi$
$409$	−334.801	−	89.7095i	−0.818583	−	0.219339i	−0.643727	+	0.765255i	$0.722613\pi$
$410$	23.7785	+	13.7285i	0.0579963	+	0.0334842i
$411$	81.5185	+	47.0647i	0.198342	+	0.114513i
$412$	51.0823	−	13.6875i	0.123986	−	0.0332220i
$413$	10.4632	+	10.4632i	0.0253346	+	0.0253346i
$414$	−1.91533	+	3.31745i	−0.00462640	+	0.00801316i
$415$	115.270	+	115.270i	0.277760	+	0.277760i
$416$	53.2148	+	92.1707i	0.127920	+	0.221564i
$417$	−242.723			−0.582070
$418$		−	453.778i		−	1.08559i
$419$	82.7667	+	143.356i	0.197534	+	0.342139i	0.947728	−	0.319079i	$-0.103373\pi$
$419$	82.7667	+	143.356i	0.197534	+	0.342139i	−0.750194	+	0.661217i	$0.770040\pi$
$420$	6.87577	−	1.84236i	0.0163709	−	0.00438657i
$421$	−79.2329	+	79.2329i	−0.188202	+	0.188202i	−0.794918	−	0.606717i	$-0.792486\pi$
$421$	−79.2329	+	79.2329i	−0.188202	+	0.188202i	0.606717	+	0.794918i	$0.292486\pi$
$422$	100.696	+	26.9814i	0.238616	+	0.0639370i
$423$	−5.54367	−	9.60192i	−0.0131056	−	0.0226996i
$424$	38.4888	−	143.642i	0.0907755	−	0.338779i
$425$	124.708	+	465.416i	0.293430	+	1.09510i
$426$	−267.265	+	71.6133i	−0.627382	+	0.168106i
$427$	−78.8128	−	21.1178i	−0.184573	−	0.0494563i
$428$	123.136	−	71.0927i	0.287701	−	0.166104i
$429$	−117.809	+	439.671i	−0.274614	+	1.02487i
$430$	−114.950	−	114.950i	−0.267325	−	0.267325i
$431$	147.013	+	548.659i	0.341097	+	1.27299i	0.897107	+	0.441814i	$0.145665\pi$
$431$	147.013	+	548.659i	0.341097	+	1.27299i	−0.556010	+	0.831176i	$0.687668\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$	373.987			0.863712			0.431856	−	0.901942i	$-0.357859\pi$
$433$	373.987			0.863712			0.431856	+	0.901942i	$0.357859\pi$
$434$		−	87.5590i		−	0.201749i
$435$	−53.7264	+	31.0189i	−0.123509	+	0.0713079i
$436$	65.7609	−	65.7609i	0.150828	−	0.150828i
$437$	−17.9622	−	10.3705i	−0.0411035	−	0.0237311i
$438$	216.358	−	216.358i	0.493967	−	0.493967i
$439$	86.4365	+	322.585i	0.196894	+	0.734818i	0.991768	+	0.128044i	$0.0408700\pi$
$439$	86.4365	+	322.585i	0.196894	+	0.734818i	−0.794874	+	0.606774i	$0.792463\pi$
$440$	−27.0874	+	46.9167i	−0.0615622	+	0.106629i
$441$	−70.1315	+	121.471i	−0.159028	+	0.275445i
$442$	143.521	−	535.627i	0.324707	−	1.21182i
$443$		−	211.523i		−	0.477478i	−0.971084	−	0.238739i	$-0.923266\pi$
$443$		−	211.523i		−	0.477478i	0.971084	−	0.238739i	$-0.0767340\pi$
$444$	96.3968	−	84.4728i	0.217110	−	0.190254i
$445$	−12.6232			−0.0283668
$446$	246.851	+	66.1436i	0.553478	+	0.148304i
$447$	224.390	+	129.552i	0.501992	+	0.289825i
$448$	10.3823	+	5.99420i	0.0231747	+	0.0133799i
$449$	−740.743	+	198.482i	−1.64976	+	0.442053i	−0.959546	−	0.281550i	$-0.909151\pi$
$449$	−740.743	+	198.482i	−1.64976	+	0.442053i	−0.690216	+	0.723603i	$0.742485\pi$
$450$	−69.3590	−	69.3590i	−0.154131	−	0.154131i
$451$	−98.8846	+	171.273i	−0.219256	+	0.379763i
$452$	29.6996	+	29.6996i	0.0657070	+	0.0657070i
$453$	115.225	+	199.576i	0.254360	+	0.440565i
$454$	−301.454			−0.663995
$455$		−	38.6611i		−	0.0849695i
$456$	−56.2689	−	97.4605i	−0.123397	−	0.213729i
$457$	−645.459	+	172.950i	−1.41238	+	0.378447i	−0.882775	−	0.469796i	$-0.844327\pi$
$457$	−645.459	+	172.950i	−1.41238	+	0.378447i	−0.529607	+	0.848243i	$0.677661\pi$
$458$	−250.549	+	250.549i	−0.547051	+	0.547051i
$459$	104.602	+	28.0281i	0.227892	+	0.0610635i
$460$	1.23809	+	2.14444i	0.00269150	+	0.00466182i
$461$	−33.7914	+	126.111i	−0.0733001	+	0.273560i	−0.992842	−	0.119431i	$-0.961893\pi$
$461$	−33.7914	+	126.111i	−0.0733001	+	0.273560i	0.919542	+	0.392991i	$0.128560\pi$
$462$	13.2703	+	49.5253i	0.0287235	+	0.107198i
$463$	−277.140	+	74.2594i	−0.598575	+	0.160388i	−0.545369	−	0.838196i	$-0.683610\pi$
$463$	−277.140	+	74.2594i	−0.598575	+	0.160388i	−0.0532055	+	0.998584i	$0.516944\pi$
$464$	−100.922	−	27.0419i	−0.217504	−	0.0582799i
$465$	84.9809	−	49.0638i	0.182755	−	0.105513i
$466$	86.9507	−	324.504i	0.186589	−	0.696361i
$467$	−501.603	−	501.603i	−1.07410	−	1.07410i	−0.997026	−	0.0770711i	$-0.975443\pi$
$467$	−501.603	−	501.603i	−1.07410	−	1.07410i	−0.0770711	−	0.997026i	$-0.524557\pi$
$468$	29.2169	+	109.039i	0.0624294	+	0.232990i
$469$	−85.6922	+	49.4744i	−0.182713	+	0.105489i
$470$	−7.16699			−0.0152489
$471$		−	141.595i		−	0.300625i
$472$	−24.1871	+	13.9644i	−0.0512439	+	0.0295857i
$473$	827.967	−	827.967i	1.75046	−	1.75046i
$474$	−25.6830	−	14.8281i	−0.0541835	−	0.0312829i
$475$	375.543	−	375.543i	0.790616	−	0.790616i
$476$	−16.1664	−	60.3339i	−0.0339631	−	0.126752i
$477$	78.8651	−	136.598i	0.165336	−	0.286370i
$478$	−67.1765	+	116.353i	−0.140537	+	0.243417i
$479$	88.6134	−	330.710i	0.184997	−	0.690417i	−0.809634	−	0.586934i	$-0.800335\pi$
$479$	88.6134	−	330.710i	0.184997	−	0.690417i	0.994631	−	0.103483i	$-0.0329987\pi$
$480$			13.4354i			0.0279905i
$481$	−307.652	−	624.455i	−0.639608	−	1.29824i
$482$	−22.2238			−0.0461075
$483$	2.26367	+	0.606548i	0.00468669	+	0.00125579i
$484$	−128.356	−	74.1065i	−0.265199	−	0.153113i
$485$	−82.4899	−	47.6256i	−0.170082	−	0.0981971i
$486$	−21.2942	+	5.70577i	−0.0438153	+	0.0117403i
$487$	−100.998	−	100.998i	−0.207389	−	0.207389i	0.595768	−	0.803157i	$-0.296848\pi$
$487$	−100.998	−	100.998i	−0.207389	−	0.207389i	−0.803157	+	0.595768i	$0.796848\pi$
$488$	77.0010	−	133.370i	0.157789	−	0.273299i
$489$	179.632	+	179.632i	0.367346	+	0.367346i
$490$	45.3339	+	78.5205i	0.0925181	+	0.160246i
$491$	−713.681			−1.45352			−0.726762	−	0.686889i	$-0.758976\pi$
$491$	−713.681			−1.45352			−0.726762	+	0.686889i	$0.758976\pi$
$492$			49.0471i			0.0996892i
$493$	272.187	+	471.441i	0.552103	+	0.956270i
$494$	−590.389	+	158.194i	−1.19512	+	0.320231i
$495$	−40.6310	+	40.6310i	−0.0820829	+	0.0820829i
$496$	159.631	+	42.7731i	0.321838	+	0.0862361i
$497$	84.6376	+	146.597i	0.170297	+	0.294963i
$498$	−75.3683	+	281.278i	−0.151342	+	0.564816i
$499$	−121.753	−	454.388i	−0.243994	−	0.910597i	−0.973886	−	0.227036i	$-0.927097\pi$
$499$	−121.753	−	454.388i	−0.243994	−	0.910597i	0.729893	−	0.683562i	$-0.239570\pi$
$500$	−127.471	+	34.1558i	−0.254942	+	0.0683116i
$501$	−202.442	−	54.2441i	−0.404075	−	0.108272i
$502$	−199.619	+	115.250i	−0.397648	+	0.229582i
$503$	−225.082	+	840.018i	−0.447479	+	1.67002i	0.261827	+	0.965115i	$0.415675\pi$
$503$	−225.082	+	840.018i	−0.447479	+	1.67002i	−0.709306	+	0.704900i	$0.750992\pi$
$504$	8.99130	+	8.99130i	0.0178399	+	0.0178399i
$505$	41.4794	+	154.803i	0.0821374	+	0.306541i
$506$	−15.4461	+	8.91781i	−0.0305259	+	0.0176241i
$507$	320.389			0.631931
$508$			455.124i			0.895913i
$509$	−679.206	+	392.140i	−1.33439	+	0.770412i	−0.985969	−	0.166926i	$-0.946616\pi$
$509$	−679.206	+	392.140i	−1.33439	+	0.770412i	−0.348423	+	0.937338i	$0.613283\pi$
$510$	49.4985	−	49.4985i	0.0970559	−	0.0970559i
$511$	−162.112	−	93.5951i	−0.317244	−	0.183161i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−30.8937	−	115.297i	−0.0602217	−	0.224751i
$514$	76.1894	−	131.964i	0.148228	−	0.256739i
$515$	18.1294	−	31.4010i	0.0352026	−	0.0609728i
$516$	75.1587	−	280.496i	0.145656	−	0.543597i
$517$		−	51.6229i		−	0.0998508i
$518$	−65.1814	−	43.5888i	−0.125833	−	0.0841482i
$519$	−79.5256			−0.153229
$520$	70.4842	+	18.8862i	0.135547	+	0.0363196i
$521$	81.1657	+	46.8610i	0.155788	+	0.0899444i	0.575868	−	0.817543i	$-0.304664\pi$
$521$	81.1657	+	46.8610i	0.155788	+	0.0899444i	−0.420079	+	0.907487i	$0.637998\pi$
$522$	−95.9727	−	55.4099i	−0.183856	−	0.106149i
$523$	−133.022	+	35.6430i	−0.254343	+	0.0681511i	−0.383738	−	0.923442i	$-0.625363\pi$
$523$	−133.022	+	35.6430i	−0.254343	+	0.0681511i	0.129394	+	0.991593i	$0.458697\pi$
$524$	246.374	+	246.374i	0.470179	+	0.470179i
$525$	−30.0043	+	51.9690i	−0.0571511	+	0.0989886i
$526$	−504.419	−	504.419i	−0.958972	−	0.958972i
$527$	−430.527	−	745.695i	−0.816940	−	1.41498i
$528$	−96.7735			−0.183283
$529$		−	528.185i		−	0.998459i
$530$	−50.9793	−	88.2988i	−0.0961874	−	0.166601i
$531$	−28.6137	+	7.66701i	−0.0538864	+	0.0144388i
$532$	−48.6832	+	48.6832i	−0.0915097	+	0.0915097i
$533$	257.308	+	68.9455i	0.482755	+	0.129354i
$534$	−11.2746	−	19.5281i	−0.0211134	−	0.0365696i
$535$	25.2311	−	94.1639i	0.0471610	−	0.176007i
$536$	−48.3371	−	180.397i	−0.0901812	−	0.336561i
$537$	−257.476	+	68.9906i	−0.479472	+	0.128474i
$538$	−102.764	−	27.5356i	−0.191011	−	0.0511814i
$539$	−565.573	+	326.534i	−1.04930	+	0.605814i
$540$	−3.68828	+	13.7648i	−0.00683015	+	0.0254905i
$541$	242.843	+	242.843i	0.448878	+	0.448878i	0.894982	−	0.446103i	$-0.147189\pi$
$541$	242.843	+	242.843i	0.448878	+	0.448878i	−0.446103	+	0.894982i	$0.647189\pi$
$542$	−145.789	−	544.094i	−0.268984	−	1.00386i
$543$	−225.809	+	130.371i	−0.415854	+	0.240093i
$544$	117.894			0.216717
$545$		−	63.7630i		−	0.116996i
$546$	59.8088	−	34.5306i	0.109540	−	0.0632429i
$547$	−168.273	+	168.273i	−0.307630	+	0.307630i	−0.843989	−	0.536360i	$-0.819799\pi$
$547$	−168.273	+	168.273i	−0.307630	+	0.307630i	0.536360	+	0.843989i	$0.319799\pi$
$548$	94.1294	+	54.3456i	0.171769	+	0.0991709i
$549$	115.502	−	115.502i	0.210385	−	0.210385i
$550$	−118.203	−	441.140i	−0.214915	−	0.802073i
$551$	300.015	−	519.642i	0.544492	−	0.943088i
$552$	−2.21163	+	3.83066i	−0.00400658	+	0.00693960i
$553$	−4.69577	+	17.5249i	−0.00849145	+	0.0316905i
$554$		−	467.653i		−	0.844139i
$555$	5.78087	−	87.6872i	0.0104160	−	0.157995i
$556$	−280.273			−0.504088
$557$	11.7595	+	3.15095i	0.0211122	+	0.00565700i	0.269360	−	0.963040i	$-0.413188\pi$
$557$	11.7595	+	3.15095i	0.0211122	+	0.00565700i	−0.248247	+	0.968697i	$0.579855\pi$
$558$	151.803	+	87.6437i	0.272049	+	0.157068i
$559$	−1365.87	−	788.587i	−2.44342	−	1.41071i
$560$	7.93946	−	2.12737i	0.0141776	−	0.00379888i
$561$	356.531	+	356.531i	0.635528	+	0.635528i
$562$	356.200	−	616.956i	0.633808	−	1.09779i
$563$	623.589	+	623.589i	1.10762	+	1.10762i	0.993463	+	0.114154i	$0.0364158\pi$
$563$	623.589	+	623.589i	1.10762	+	1.10762i	0.114154	+	0.993463i	$0.463584\pi$
$564$	−6.40128	−	11.0873i	−0.0113498	−	0.0196584i
$565$	28.7973			0.0509686
$566$			425.847i			0.752380i
$567$	6.74348	+	11.6800i	0.0118933	+	0.0205997i
$568$	−308.611	+	82.6920i	−0.543328	+	0.145584i
$569$	605.403	−	605.403i	1.06398	−	1.06398i	0.0661686	−	0.997808i	$-0.478922\pi$
$569$	605.403	−	605.403i	1.06398	−	1.06398i	0.997808	−	0.0661686i	$-0.0210775\pi$
$570$	−74.5294	−	19.9701i	−0.130753	−	0.0350352i
$571$	106.177	+	183.903i	0.185949	+	0.322073i	0.943896	−	0.330243i	$-0.107131\pi$
$571$	106.177	+	183.903i	0.185949	+	0.322073i	−0.757947	+	0.652316i	$0.773798\pi$
$572$	−136.035	+	507.688i	−0.237823	+	0.887567i
$573$	148.689	+	554.915i	0.259492	+	0.968437i
$574$	28.9836	−	7.76614i	0.0504941	−	0.0135299i
$575$	−20.1634	−	5.40275i	−0.0350667	−	0.00939609i
$576$	−20.7846	+	12.0000i	−0.0360844	+	0.0208333i
$577$	34.7926	−	129.848i	0.0602991	−	0.225039i	−0.929200	−	0.369577i	$-0.879503\pi$
$577$	34.7926	−	129.848i	0.0602991	−	0.225039i	0.989499	+	0.144537i	$0.0461694\pi$
$578$	−145.342	−	145.342i	−0.251457	−	0.251457i
$579$	140.060	+	522.712i	0.241900	+	0.902784i
$580$	−62.0379	+	35.8176i	−0.106962	+	0.0617545i
$581$	178.151			0.306628
$582$		−	170.149i		−	0.292353i
$583$	636.004	−	367.197i	1.09092	−	0.629841i
$584$	249.828	−	249.828i	0.427788	−	0.427788i
$585$	67.0278	+	38.6985i	0.114577	+	0.0661513i
$586$	325.525	−	325.525i	0.555503	−	0.555503i
$587$	−73.8136	−	275.476i	−0.125747	−	0.469295i	0.874118	−	0.485713i	$-0.161440\pi$
$587$	−73.8136	−	275.476i	−0.125747	−	0.469295i	−0.999865	+	0.0164188i	$0.994773\pi$
$588$	−80.9809	+	140.263i	−0.137723	+	0.238543i
$589$	−474.545	+	821.935i	−0.805678	+	1.39548i
$590$	−4.95605	+	18.4962i	−0.00840008	+	0.0313495i
$591$		−	234.413i		−	0.396637i
$592$	111.309	−	97.5408i	0.188023	−	0.164765i
$593$	906.533			1.52872			0.764362	−	0.644788i	$-0.223054\pi$
$593$	906.533			1.52872			0.764362	+	0.644788i	$0.223054\pi$
$594$	−99.1463	−	26.5662i	−0.166913	−	0.0447242i
$595$	−37.0880	−	21.4128i	−0.0623328	−	0.0359879i
$596$	259.104	+	149.593i	0.434737	+	0.250996i
$597$	−200.304	+	53.6712i	−0.335517	+	0.0899015i
$598$	16.9873	+	16.9873i	0.0284069	+	0.0284069i
$599$	106.739	−	184.877i	0.178195	−	0.308644i	−0.763067	−	0.646319i	$-0.776307\pi$
$599$	106.739	−	184.877i	0.178195	−	0.308644i	0.941262	+	0.337676i	$0.109641\pi$
$600$	−80.0889	−	80.0889i	−0.133482	−	0.133482i
$601$	28.0498	+	48.5838i	0.0466720	+	0.0808382i	0.888418	−	0.459036i	$-0.151805\pi$
$601$	28.0498	+	48.5838i	0.0466720	+	0.0808382i	−0.841746	+	0.539874i	$0.818472\pi$
$602$	−177.656			−0.295109
$603$		−	198.089i		−	0.328506i
$604$	133.051	+	230.451i	0.220283	+	0.381541i
$605$	−98.1558	+	26.3008i	−0.162241	+	0.0434723i
$606$	−202.433	+	202.433i	−0.334048	+	0.334048i
$607$	247.641	+	66.3553i	0.407976	+	0.109317i	0.456970	−	0.889482i	$-0.348935\pi$
$607$	247.641	+	66.3553i	0.407976	+	0.109317i	−0.0489939	+	0.998799i	$0.515601\pi$
$608$	−64.9737	−	112.538i	−0.106865	−	0.185095i
$609$	−17.5473	+	65.4872i	−0.0288132	+	0.107532i
$610$	−27.3280	−	101.990i	−0.0448001	−	0.167196i
$611$	−67.1641	+	17.9966i	−0.109925	+	0.0294543i
$612$	120.784	+	32.3641i	0.197360	+	0.0528825i
$613$	−408.760	+	235.998i	−0.666818	+	0.384988i	−0.794870	−	0.606780i	$-0.792461\pi$
$613$	−408.760	+	235.998i	−0.666818	+	0.384988i	0.128052	+	0.991768i	$0.459128\pi$
$614$	100.483	−	375.006i	0.163652	−	0.610759i
$615$	23.7785	+	23.7785i	0.0386642	+	0.0386642i
$616$	15.3232	+	57.1868i	0.0248753	+	0.0928358i
$617$	−878.806	+	507.379i	−1.42432	+	0.822332i	−0.996664	−	0.0816086i	$-0.973994\pi$
$617$	−878.806	+	507.379i	−1.42432	+	0.822332i	−0.427657	+	0.903941i	$0.640661\pi$
$618$	64.7698			0.104805
$619$			732.033i			1.18261i	0.806450	+	0.591303i	$0.201386\pi$
$619$			732.033i			1.18261i	−0.806450	+	0.591303i	$0.798614\pi$
$620$	98.1275	−	56.6540i	0.158270	−	0.0913773i
$621$	−3.31745	+	3.31745i	−0.00534211	+	0.00534211i
$622$	302.299	+	174.532i	0.486011	+	0.280599i
$623$	−9.75464	+	9.75464i	−0.0156575	+	0.0156575i
$624$	33.7368	+	125.908i	0.0540654	+	0.201775i
$625$	243.756	−	422.198i	0.390009	−	0.675516i
$626$	−15.9282	+	27.5884i	−0.0254443	+	0.0440709i
$627$	143.842	−	536.825i	0.229413	−	0.856180i
$628$		−	163.499i		−	0.260349i
$629$	−769.442	−	50.7262i	−1.22328	−	0.0806459i
$630$	8.71813			0.0138383
$631$	563.240	+	150.920i	0.892615	+	0.239176i	0.675842	−	0.737046i	$-0.263780\pi$
$631$	563.240	+	150.920i	0.892615	+	0.239176i	0.216773	+	0.976222i	$0.430447\pi$
$632$	−29.6561	−	17.1220i	−0.0469243	−	0.0270917i
$633$	110.572	+	63.8387i	0.174679	+	0.100851i
$634$	−841.689	+	225.530i	−1.32759	+	0.355725i
$635$	220.648	+	220.648i	0.347477	+	0.347477i
$636$	91.0655	−	157.730i	0.143185	−	0.248003i
$637$	622.006	+	622.006i	0.976461	+	0.976461i
$638$	−257.989	−	446.851i	−0.404372	−	0.700393i
$639$	−338.878			−0.530325
$640$			15.5139i			0.0242404i
$641$	−193.846	−	335.751i	−0.302411	−	0.523792i	0.674270	−	0.738485i	$-0.264458\pi$
$641$	−193.846	−	335.751i	−0.302411	−	0.523792i	−0.976682	+	0.214693i	$0.931125\pi$
$642$	168.207	−	45.0709i	0.262005	−	0.0702040i
$643$	819.425	−	819.425i	1.27438	−	1.27438i	0.330610	−	0.943767i	$-0.392746\pi$
$643$	819.425	−	819.425i	1.27438	−	1.27438i	0.943767	−	0.330610i	$-0.107254\pi$
$644$	2.61386	+	0.700382i	0.00405879	+	0.00108755i
$645$	−99.5494	−	172.425i	−0.154340	−	0.267325i
$646$	−175.235	+	653.984i	−0.271261	+	1.01236i
$647$	−64.2870	−	239.923i	−0.0993617	−	0.370823i	0.898283	−	0.439418i	$-0.144815\pi$
$647$	−64.2870	−	239.923i	−0.0993617	−	0.370823i	−0.997645	+	0.0685946i	$0.978149\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$	−133.226	−	35.6977i	−0.205278	−	0.0550042i
$650$	−532.739	+	307.577i	−0.819599	+	0.473196i
$651$	27.7551	−	103.583i	0.0426346	−	0.159114i
$652$	207.421	+	207.421i	0.318131	+	0.318131i
$653$	48.4545	+	180.835i	0.0742029	+	0.276929i	0.993051	−	0.117681i	$-0.0375462\pi$
$653$	48.4545	+	180.835i	0.0742029	+	0.276929i	−0.918848	+	0.394611i	$0.870880\pi$
$654$	98.6414	−	56.9506i	0.150828	−	0.0870804i
$655$	238.888			0.364715
$656$			56.6347i			0.0863334i
$657$	324.537	−	187.371i	0.493967	−	0.285192i
$658$	−5.53832	+	5.53832i	−0.00841689	+	0.00841689i
$659$	−81.8758	−	47.2710i	−0.124242	−	0.0717314i	0.436591	−	0.899660i	$-0.356186\pi$
$659$	−81.8758	−	47.2710i	−0.124242	−	0.0717314i	−0.560833	+	0.827929i	$0.689519\pi$
$660$	−46.9167	+	46.9167i	−0.0710859	+	0.0710859i
$661$	256.821	+	958.469i	0.388534	+	1.45003i	0.832520	+	0.553995i	$0.186897\pi$
$661$	256.821	+	958.469i	0.388534	+	1.45003i	−0.443986	+	0.896033i	$0.646436\pi$
$662$	223.064	−	386.358i	0.336954	−	0.583622i
$663$	339.574	−	588.159i	0.512177	−	0.887117i
$664$	−87.0278	+	324.792i	−0.131066	+	0.489145i
$665$			47.2041i			0.0709836i
$666$	140.815	−	69.3758i	0.211435	−	0.104168i
$667$	−23.5840			−0.0353584
$668$	−233.760	−	62.6357i	−0.349939	−	0.0937660i
$669$	271.062	+	156.497i	0.405174	+	0.233927i
$670$	−110.892	−	64.0236i	−0.165511	−	0.0955576i
$671$	734.617	−	196.840i	1.09481	−	0.293353i
$672$	10.3823	+	10.3823i	0.0154498	+	0.0154498i
$673$	17.1498	−	29.7044i	0.0254827	−	0.0441373i	−0.853003	−	0.521906i	$-0.825221\pi$
$673$	17.1498	−	29.7044i	0.0254827	−	0.0441373i	0.878486	+	0.477769i	$0.158554\pi$
$674$	502.399	+	502.399i	0.745399	+	0.745399i
$675$	−60.0667	−	104.039i	−0.0889877	−	0.154131i
$676$	369.953			0.547268
$677$		−	394.492i		−	0.582705i	−0.956616	−	0.291353i	$-0.905895\pi$
$677$		−	394.492i		−	0.582705i	0.956616	−	0.291353i	$-0.0941053\pi$
$678$	25.7206	+	44.5494i	0.0379360	+	0.0657070i
$679$	−100.547	+	26.9415i	−0.148081	+	0.0396783i
$680$	57.1560	−	57.1560i	0.0840529	−	0.0840529i
$681$	−356.624	−	95.5570i	−0.523677	−	0.140319i
$682$	408.071	+	706.799i	0.598344	+	1.03636i
$683$	−149.381	+	557.497i	−0.218713	+	0.816247i	0.766114	+	0.642705i	$0.222188\pi$
$683$	−149.381	+	557.497i	−0.218713	+	0.816247i	−0.984826	+	0.173542i	$0.944479\pi$
$684$	−35.6730	−	133.134i	−0.0521535	−	0.194640i
$685$	71.9820	−	19.2875i	0.105083	−	0.0281570i
$686$	196.015	+	52.5220i	0.285736	+	0.0765627i
$687$	−375.824	+	216.982i	−0.547051	+	0.315840i
$688$	86.7858	−	323.889i	0.126142	−	0.470769i
$689$	−699.465	−	699.465i	−1.01519	−	1.01519i
$690$	0.784919	+	2.92936i	0.00113756	+	0.00424544i
$691$	−181.521	+	104.801i	−0.262693	+	0.151666i	−0.625562	−	0.780174i	$-0.715130\pi$
$691$	−181.521	+	104.801i	−0.262693	+	0.151666i	0.362869	+	0.931840i	$0.381797\pi$
$692$	−91.8282			−0.132700
$693$			62.7955i			0.0906140i
$694$	−165.096	+	95.3180i	−0.237890	+	0.137346i
$695$	−135.879	+	135.879i	−0.195509	+	0.195509i
$696$	−110.820	−	63.9818i	−0.159224	−	0.0919279i
$697$	208.653	−	208.653i	0.299358	−	0.299358i
$698$	−104.980	−	391.792i	−0.150402	−	0.561306i
$699$	205.728	−	356.331i	0.294317	−	0.509772i
$700$	−34.6460	+	60.0087i	−0.0494943	+	0.0857267i
$701$	−178.464	+	666.038i	−0.254586	+	0.950126i	0.713735	+	0.700416i	$0.247002\pi$
$701$	−178.464	+	666.038i	−0.254586	+	0.950126i	−0.968321	+	0.249710i	$0.919665\pi$
$702$			138.256i			0.196946i
$703$	375.634	+	762.441i	0.534329	+	1.08455i
$704$	−111.744			−0.158728
$705$	−8.47864	−	2.27185i	−0.0120264	−	0.00322248i
$706$	106.880	+	61.7072i	0.151388	+	0.0874039i
$707$	151.678	+	87.5714i	0.214538	+	0.123863i
$708$	−33.0402	+	8.85310i	−0.0466670	+	0.0125044i
$709$	1.60724	+	1.60724i	0.00226692	+	0.00226692i	0.708239	−	0.705972i	$-0.249490\pi$
$709$	1.60724	+	1.60724i	0.00226692	+	0.00226692i	−0.705972	+	0.708239i	$0.749490\pi$
$710$	−109.527	+	189.707i	−0.154264	+	0.267193i
$711$	−25.6830	−	25.6830i	−0.0361223	−	0.0361223i
$712$	−13.0188	−	22.5492i	−0.0182848	−	0.0316702i
$713$	37.3037			0.0523193
$714$		−	76.5003i		−	0.107143i
$715$	180.181	+	312.083i	0.252001	+	0.436479i
$716$	−297.308	+	79.6634i	−0.415235	+	0.111262i
$717$	−116.353	+	116.353i	−0.162278	+	0.162278i
$718$	−16.9443	−	4.54021i	−0.0235993	−	0.00632341i
$719$	−485.769	−	841.376i	−0.675617	−	1.17020i	−0.976288	−	0.216475i	$-0.930544\pi$
$719$	−485.769	−	841.376i	−0.675617	−	1.17020i	0.300671	−	0.953728i	$-0.402789\pi$
$720$	−4.25886	+	15.8943i	−0.00591508	+	0.0220754i
$721$	−10.2557	−	38.2747i	−0.0142242	−	0.0530856i
$722$	227.713	−	61.0154i	0.315392	−	0.0845089i
$723$	−26.2910	−	7.04466i	−0.0363638	−	0.00974366i
$724$	−260.741	+	150.539i	−0.360140	+	0.207927i
$725$	156.300	−	583.319i	0.215586	−	0.804578i
$726$	−128.356	−	128.356i	−0.176799	−	0.176799i
$727$	−31.9264	−	119.151i	−0.0439152	−	0.163894i	0.940486	−	0.339833i	$-0.110371\pi$
$727$	−31.9264	−	119.151i	−0.0439152	−	0.163894i	−0.984401	+	0.175939i	$0.943704\pi$
$728$	69.0612	−	39.8725i	0.0948643	−	0.0547700i
$729$	−27.0000			−0.0370370
$730$		−	242.238i		−	0.331833i
$731$	−1513.00	+	873.531i	−2.06977	+	1.19498i
$732$	133.370	−	133.370i	0.182199	−	0.182199i
$733$	−576.430	−	332.802i	−0.786398	−	0.454027i	0.0522951	−	0.998632i	$-0.483346\pi$
$733$	−576.430	−	332.802i	−0.786398	−	0.454027i	−0.838693	+	0.544605i	$0.816680\pi$
$734$	258.127	−	258.127i	0.351672	−	0.351672i
$735$	28.7405	+	107.261i	0.0391027	+	0.145933i
$736$	−2.55377	+	4.42326i	−0.00346980	+	0.00600987i
$737$	461.153	−	798.741i	0.625717	−	1.08377i
$738$	−15.5473	+	58.0233i	−0.0210668	+	0.0786224i
$739$		−	77.7912i		−	0.105265i	−0.998614	−	0.0526327i	$-0.983239\pi$
$739$		−	77.7912i		−	0.105265i	0.998614	−	0.0526327i	$-0.0167613\pi$
$740$	6.67517	−	101.252i	0.00902050	−	0.136828i
$741$	−748.584			−1.01023
$742$	−107.628	−	28.8387i	−0.145051	−	0.0388662i
$743$	423.232	+	244.353i	0.569625	+	0.328873i	0.757000	−	0.653415i	$-0.226664\pi$
$743$	423.232	+	244.353i	0.569625	+	0.328873i	−0.187374	+	0.982289i	$0.559998\pi$
$744$	175.287	+	101.202i	0.235601	+	0.136025i
$745$	198.140	−	53.0915i	0.265960	−	0.0712637i
$746$	584.221	+	584.221i	0.783137	+	0.783137i
$747$	−178.323	+	308.865i	−0.238719	+	0.413474i
$748$	411.687	+	411.687i	0.550383	+	0.550383i
$749$	−53.2680	−	92.2628i	−0.0711188	−	0.123181i
$750$	−161.627			−0.215503
$751$		−	596.769i		−	0.794632i	−0.917682	−	0.397316i	$-0.869942\pi$
$751$		−	596.769i		−	0.794632i	0.917682	−	0.397316i	$-0.130058\pi$
$752$	−7.39156	−	12.8026i	−0.00982921	−	0.0170247i
$753$	−272.685	+	73.0657i	−0.362131	+	0.0970328i
$754$	−491.437	+	491.437i	−0.651774	+	0.651774i
$755$	176.229	+	47.2203i	0.233415	+	0.0625435i
$756$	7.78670	+	13.4870i	0.0102999	+	0.0178399i
$757$	−243.026	+	906.986i	−0.321039	+	1.19813i	0.597196	+	0.802095i	$0.296281\pi$
$757$	−243.026	+	906.986i	−0.321039	+	1.19813i	−0.918235	+	0.396037i	$0.870385\pi$
$758$	−55.5942	−	207.481i	−0.0733433	−	0.273721i
$759$	−21.0998	+	5.65366i	−0.0277994	+	0.00744883i
$760$	−86.0591	−	23.0595i	−0.113236	−	0.0303414i
$761$	1168.67	−	674.732i	1.53570	−	0.886639i	0.536621	−	0.843823i	$-0.319700\pi$
$761$	1168.67	−	674.732i	1.53570	−	0.886639i	0.999083	−	0.0428159i	$-0.0136329\pi$
$762$	−144.268	+	538.417i	−0.189329	+	0.706584i
$763$	−49.2730	−	49.2730i	−0.0645780	−	0.0645780i
$764$	171.691	+	640.760i	0.224727	+	0.838691i
$765$	74.2478	−	42.8670i	0.0970559	−	0.0560353i
$766$	730.103			0.953137
$767$			185.779i			0.242215i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$	−45.9299	+	45.9299i	−0.0597268	+	0.0597268i	−0.736339	−	0.676612i	$-0.763447\pi$
$769$	−45.9299	+	45.9299i	−0.0597268	+	0.0597268i	0.676612	+	0.736339i	$0.263447\pi$
$770$	35.1535	+	20.2959i	0.0456539	+	0.0263583i
$771$	131.964	−	131.964i	0.171159	−	0.171159i
$772$	161.728	+	603.576i	0.209492	+	0.781834i
$773$	−399.245	+	691.512i	−0.516487	+	0.894582i	0.483329	+	0.875439i	$0.339427\pi$
$773$	−399.245	+	691.512i	−0.516487	+	0.894582i	−0.999817	+	0.0191438i	$0.993906\pi$
$774$	177.827	−	308.006i	0.229751	−	0.397941i
$775$	−247.225	+	922.657i	−0.319000	+	1.19052i
$776$		−	196.472i		−	0.253185i
$777$	−63.2934	−	72.2278i	−0.0814587	−	0.0929572i
$778$	746.056			0.958941
$779$	−314.166	−	84.1804i	−0.403294	−	0.108062i
$780$	77.3970	+	44.6852i	0.0992270	+	0.0572887i
$781$	−1366.43	−	788.911i	−1.74959	−	1.01013i
$782$	25.7047	−	6.88754i	0.0328704	−	0.00880760i
$783$	−95.9727	−	95.9727i	−0.122570	−	0.122570i
$784$	−93.5087	+	161.962i	−0.119271	+	0.206584i
$785$	−79.2660	−	79.2660i	−0.100976	−	0.100976i
$786$	213.366	+	369.560i	0.271458	+	0.470179i
$787$	1258.44			1.59903			0.799514	−	0.600647i	$-0.205090\pi$
$787$	1258.44			1.59903			0.799514	+	0.600647i	$0.205090\pi$
$788$		−	270.676i		−	0.343498i
$789$	−436.840	−	756.629i	−0.553662	−	0.958972i
$790$	−22.6785	+	6.07668i	−0.0287069	+	0.00769199i
$791$	22.2532	−	22.2532i	0.0281330	−	0.0281330i
$792$	−114.484	−	30.6760i	−0.144551	−	0.0387323i
$793$	−512.199	−	887.155i	−0.645901	−	1.11873i
$794$	−243.082	+	907.194i	−0.306149	+	1.14256i
$795$	−32.3196	−	120.618i	−0.0406536	−	0.151721i
$796$	−231.291	+	61.9741i	−0.290566	+	0.0778569i
$797$	408.382	+	109.426i	0.512399	+	0.137297i	0.505749	−	0.862681i	$-0.331216\pi$
$797$	408.382	+	109.426i	0.512399	+	0.137297i	0.00665070	+	0.999978i	$0.497883\pi$
$798$	−73.0248	+	42.1609i	−0.0915097	+	0.0528332i
$799$	−19.9351	+	74.3988i	−0.0249501	+	0.0931149i
$800$	−92.4787	−	92.4787i	−0.115598	−	0.115598i
$801$	−7.14780	−	26.6759i	−0.00892359	−	0.0333033i
$802$	841.735	−	485.976i	1.04955	−	0.605955i
$803$	1744.81			2.17286
$804$		−	228.734i		−	0.284495i
$805$	1.60677	−	0.927672i	0.00199599	−	0.00115239i
$806$	777.324	−	777.324i	0.964421	−	0.964421i
$807$	−112.843	−	65.1499i	−0.139830	−	0.0807309i
$808$	−233.749	+	233.749i	−0.289294	+	0.289294i
$809$	311.751	+	1163.47i	0.385353	+	1.43816i	0.837610	+	0.546269i	$0.183952\pi$
$809$	311.751	+	1163.47i	0.385353	+	1.43816i	−0.452257	+	0.891888i	$0.649381\pi$
$810$	−8.72656	+	15.1148i	−0.0107735	+	0.0186603i
$811$	−393.816	+	682.109i	−0.485593	+	0.841071i	−0.999863	−	0.0165570i	$-0.994729\pi$
$811$	−393.816	+	682.109i	−0.485593	+	0.841071i	0.514270	+	0.857628i	$0.328063\pi$
$812$	−20.2618	+	75.6181i	−0.0249530	+	0.0931258i
$813$		−	689.883i		−	0.848565i
$814$	729.308	+	48.0803i	0.895956	+	0.0590668i
$815$	201.119			0.246772
$816$	139.470	+	37.3708i	0.170919	+	0.0457976i
$817$	1667.69	+	962.841i	2.04124	+	1.17851i
$818$	−424.510	−	245.091i	−0.518961	−	0.299622i
$819$	81.7003	−	21.8915i	0.0997562	−	0.0267296i
$820$	27.4570	+	27.4570i	0.0334842	+	0.0334842i
$821$	−578.734	+	1002.40i	−0.704914	+	1.22095i	0.261809	+	0.965120i	$0.415681\pi$
$821$	−578.734	+	1002.40i	−0.704914	+	1.22095i	−0.966723	+	0.255827i	$0.917652\pi$
$822$	94.1294	+	94.1294i	0.114513	+	0.114513i
$823$	−408.823	−	708.102i	−0.496747	−	0.860391i	0.503246	−	0.864143i	$-0.332139\pi$
$823$	−408.823	−	708.102i	−0.496747	−	0.860391i	−0.999993	+	0.00375214i	$0.998806\pi$
$824$	74.7897			0.0907642
$825$		−	559.343i		−	0.677992i
$826$	10.4632	+	18.1228i	0.0126673	+	0.0219404i
$827$	−679.357	+	182.033i	−0.821471	+	0.220113i	−0.644990	−	0.764191i	$-0.723138\pi$
$827$	−679.357	+	182.033i	−0.821471	+	0.220113i	−0.176482	+	0.984304i	$0.556472\pi$
$828$	−3.83066	+	3.83066i	−0.00462640	+	0.00462640i
$829$	240.750	+	64.5088i	0.290410	+	0.0778152i	0.401083	−	0.916042i	$-0.368634\pi$
$829$	240.750	+	64.5088i	0.290410	+	0.0778152i	−0.110673	+	0.993857i	$0.535301\pi$
$830$	115.270	+	199.654i	0.138880	+	0.240547i
$831$	148.240	−	553.239i	0.178387	−	0.665751i
$832$	38.9559	+	145.385i	0.0468220	+	0.174742i
$833$	941.200	−	252.194i	1.12989	−	0.302754i
$834$	−331.566	−	88.8429i	−0.397562	−	0.106526i
$835$	−143.695	+	82.9624i	−0.172090	+	0.0993561i
$836$	166.094	−	619.872i	0.198677	−	0.741474i
$837$	151.803	+	151.803i	0.181366	+	0.181366i
$838$	60.5894	+	226.123i	0.0723024	+	0.269836i
$839$	−469.749	+	271.210i	−0.559892	+	0.323254i	−0.753102	−	0.657904i	$-0.771443\pi$
$839$	−469.749	+	271.210i	−0.559892	+	0.323254i	0.193210	+	0.981157i	$0.438110\pi$
$840$	10.0668			0.0119843
$841$			158.722i			0.188730i
$842$	−137.235	+	79.2329i	−0.162987	+	0.0941008i
$843$	616.956	−	616.956i	0.731858	−	0.731858i
$844$	127.677	+	73.7146i	0.151277	+	0.0873396i
$845$	179.357	−	179.357i	0.212256	−	0.212256i
$846$	−4.05825	−	15.1456i	−0.00479699	−	0.0179026i
$847$	−55.5262	+	96.1742i	−0.0655563	+	0.113547i
$848$	105.153	−	182.131i	0.124002	−	0.214777i
$849$	−134.988	+	503.783i	−0.158997	+	0.593384i
$850$			681.417i			0.801667i
$851$	18.5706	−	27.7699i	0.0218221	−	0.0326321i
$852$	−391.303			−0.459275
$853$	546.268	+	146.372i	0.640408	+	0.171597i	0.564388	−	0.825510i	$-0.309112\pi$
$853$	546.268	+	146.372i	0.640408	+	0.171597i	0.0760196	+	0.997106i	$0.475779\pi$
$854$	−99.9306	−	57.6950i	−0.117015	−	0.0675585i
$855$	−81.8389	−	47.2497i	−0.0957181	−	0.0552628i
$856$	194.229	−	52.0434i	0.226903	−	0.0607984i
$857$	58.7016	+	58.7016i	0.0684966	+	0.0684966i	0.740525	−	0.672029i	$-0.234577\pi$
$857$	58.7016	+	58.7016i	0.0684966	+	0.0684966i	−0.672029	+	0.740525i	$0.734577\pi$
$858$	−321.861	+	557.480i	−0.375130	+	0.649744i
$859$	151.639	+	151.639i	0.176530	+	0.176530i	0.789841	−	0.613311i	$-0.210163\pi$
$859$	151.639	+	151.639i	0.176530	+	0.176530i	−0.613311	+	0.789841i	$0.710163\pi$
$860$	−114.950	−	199.099i	−0.133662	−	0.231510i
$861$	36.7498			0.0426827
$862$			803.292i			0.931893i
$863$	−652.876	−	1130.81i	−0.756520	−	1.31033i	−0.944615	−	0.328180i	$-0.893565\pi$
$863$	−652.876	−	1130.81i	−0.756520	−	1.31033i	0.188096	−	0.982151i	$-0.439768\pi$
$864$	−28.3923	+	7.60770i	−0.0328615	+	0.00880520i
$865$	−44.5192	+	44.5192i	−0.0514672	+	0.0514672i
$866$	510.876	+	136.889i	0.589927	+	0.158070i
$867$	−125.870	−	218.013i	−0.145179	−	0.251457i
$868$	32.0488	−	119.608i	0.0369226	−	0.137797i
$869$	−43.7695	−	163.350i	−0.0503676	−	0.187975i
$870$	−84.7453	+	22.7074i	−0.0974084	+	0.0261005i
$871$	−1199.97	−	321.531i	−1.37769	−	0.369152i
$872$	113.901	−	65.7609i	0.130621	−	0.0754139i
$873$	53.9352	−	201.289i	0.0617814	−	0.230571i
$874$	−20.7410	−	20.7410i	−0.0237311	−	0.0237311i
$875$	25.5921	+	95.5111i	0.0292481	+	0.109155i
$876$	374.743	−	216.358i	0.427788	−	0.246984i
$877$	1496.69			1.70660			0.853301	−	0.521418i	$-0.174597\pi$
$877$	1496.69			1.70660			0.853301	+	0.521418i	$0.174597\pi$
$878$			472.298i			0.537924i
$879$	488.287	−	281.913i	0.555503	−	0.320720i
$880$	−54.1747	+	54.1747i	−0.0615622	+	0.0615622i
$881$	−116.677	−	67.3633i	−0.132437	−	0.0764623i	0.432318	−	0.901721i	$-0.357696\pi$
$881$	−116.677	−	67.3633i	−0.132437	−	0.0764623i	−0.564755	+	0.825259i	$0.691029\pi$
$882$	−140.263	+	140.263i	−0.159028	+	0.159028i
$883$	−386.464	−	1442.30i	−0.437671	−	1.63341i	−0.734591	−	0.678510i	$-0.762626\pi$
$883$	−386.464	−	1442.30i	−0.437671	−	1.63341i	0.296920	−	0.954902i	$-0.404041\pi$
$884$	392.106	−	679.147i	0.443559	−	0.768266i
$885$	−11.7261	+	20.3103i	−0.0132499	+	0.0229494i
$886$	77.4226	−	288.945i	0.0873845	−	0.326123i
$887$		−	417.497i		−	0.470684i	−0.971913	−	0.235342i	$-0.924379\pi$
$887$		−	417.497i		−	0.470684i	0.971913	−	0.235342i	$-0.0756210\pi$
$888$	162.600	−	80.1083i	0.183108	−	0.0902121i
$889$	341.013			0.383592
$890$	−17.2436	−	4.62042i	−0.0193749	−	0.00519148i
$891$	−108.870	−	62.8562i	−0.122189	−	0.0705457i
$892$	312.995	+	180.708i	0.350891	+	0.202587i
$893$	82.0054	−	21.9733i	0.0918314	−	0.0246061i
$894$	259.104	+	259.104i	0.289825	+	0.289825i
$895$	−105.516	+	182.759i	−0.117895	+	0.204200i
$896$	11.9884	+	11.9884i	0.0133799	+	0.0133799i
$897$	14.7114	+	25.4810i	0.0164007	+	0.0284069i
$898$	−1084.52			−1.20771
$899$			1079.18i			1.20043i
$900$	−69.3590	−	120.133i	−0.0770656	−	0.133482i
$901$	−1058.41	+	283.600i	−1.17470	+	0.314761i
$902$	−197.769	+	197.769i	−0.219256	+	0.219256i
$903$	−210.169	−	56.3145i	−0.232745	−	0.0623638i
$904$	29.6996	+	51.4412i	0.0328535	+	0.0569040i
$905$	−53.4270	+	199.392i	−0.0590354	+	0.220323i
$906$	84.3508	+	314.801i	0.0931024	+	0.347463i
$907$	−327.735	+	87.8163i	−0.361340	+	0.0968206i	−0.434921	−	0.900469i	$-0.643224\pi$
$907$	−327.735	+	87.8163i	−0.361340	+	0.0968206i	0.0735816	+	0.997289i	$0.476557\pi$
$908$	−411.794	−	110.340i	−0.453517	−	0.121520i
$909$	−303.649	+	175.312i	−0.334048	+	0.192863i
$910$	14.1510	−	52.8121i	0.0155505	−	0.0580352i
$911$	778.915	+	778.915i	0.855011	+	0.855011i	0.990745	−	0.135734i	$-0.0433393\pi$
$911$	778.915	+	778.915i	0.855011	+	0.855011i	−0.135734	+	0.990745i	$0.543339\pi$
$912$	−41.1917	−	153.729i	−0.0451663	−	0.168563i
$913$	−1438.08	+	830.276i	−1.57512	+	0.909394i
$914$	−945.017			−1.03394
$915$		−	129.318i		−	0.141331i
$916$	−433.964	+	250.549i	−0.473760	+	0.273525i
$917$	184.602	−	184.602i	0.201310	−	0.201310i
$918$	132.631	+	76.5743i	0.144478	+	0.0834142i
$919$	631.174	−	631.174i	0.686805	−	0.686805i	−0.274719	−	0.961525i	$-0.588585\pi$
$919$	631.174	−	631.174i	0.686805	−	0.686805i	0.961525	+	0.274719i	$0.0885849\pi$
$920$	0.906346	+	3.38253i	0.000985159	+	0.00367666i
$921$	237.744	−	411.785i	0.258137	−	0.447107i
$922$	−92.3197	+	159.902i	−0.100130	+	0.173430i
$923$	−550.054	+	2052.83i	−0.595942	+	2.22409i
$924$			72.5100i			0.0784740i
$925$	563.778	+	643.360i	0.609490	+	0.695524i
$926$	−405.761			−0.438187
$927$	76.6235	+	20.5312i	0.0826575	+	0.0221480i
$928$	−127.964	−	73.8798i	−0.137892	−	0.0796119i
$929$	−1517.59	−	876.182i	−1.63358	−	0.943146i	−0.982978	−	0.183723i	$-0.941185\pi$
$929$	−1517.59	−	876.182i	−1.63358	−	0.943146i	−0.650598	−	0.759422i	$-0.725482\pi$
$930$	134.045	−	35.9172i	0.144134	−	0.0386206i
$931$	−759.450	−	759.450i	−0.815736	−	0.815736i
$932$	237.554	−	411.455i	0.254886	−	0.441475i
$933$	302.299	+	302.299i	0.324008	+	0.324008i
$934$	−501.603	−	868.802i	−0.537048	−	0.930195i
$935$	399.179			0.426929
$936$			159.644i			0.170560i
$937$	425.437	+	736.878i	0.454041	+	0.786423i	0.998633	−	0.0522788i	$-0.0166484\pi$
$937$	425.437	+	736.878i	0.454041	+	0.786423i	−0.544591	+	0.838702i	$0.683315\pi$
$938$	−135.167	+	36.2178i	−0.144101	+	0.0386117i
$939$	−27.5884	+	27.5884i	−0.0293806	+	0.0293806i
$940$	−9.79030	−	2.62330i	−0.0104152	−	0.00279075i
$941$	438.511	+	759.523i	0.466005	+	0.807145i	0.999246	−	0.0388187i	$-0.0123595\pi$
$941$	438.511	+	759.523i	0.466005	+	0.807145i	−0.533241	+	0.845963i	$0.679026\pi$
$942$	51.8272	−	193.422i	0.0550183	−	0.205331i
$943$	3.30869	+	12.3482i	0.00350868	+	0.0130946i
$944$	−38.1516	+	10.2227i	−0.0404148	+	0.0108291i
$945$	10.3137	+	2.76354i	0.0109139	+	0.00292438i
$946$	1434.08	−	827.967i	1.51594	−	0.875230i
$947$	261.898	−	977.418i	0.276556	−	1.03212i	−0.678236	−	0.734844i	$-0.737255\pi$
$947$	261.898	−	977.418i	0.276556	−	1.03212i	0.954792	−	0.297276i	$-0.0960781\pi$
$948$	−29.6561	−	29.6561i	−0.0312829	−	0.0312829i
$949$	−608.269	−	2270.09i	−0.640957	−	2.39209i
$950$	650.459	−	375.543i	0.684694	−	0.395308i
$951$	−1067.22			−1.12221
$952$		−	88.3349i		−	0.0927888i
$953$	73.8173	−	42.6185i	0.0774579	−	0.0447203i	−0.460771	−	0.887519i	$-0.652427\pi$
$953$	73.8173	−	42.6185i	0.0774579	−	0.0447203i	0.538229	+	0.842799i	$0.319094\pi$
$954$	157.730	−	157.730i	0.165336	−	0.165336i
$955$	393.884	+	227.409i	0.412444	+	0.238124i
$956$	−134.353	+	134.353i	−0.140537	+	0.140537i
$957$	−163.559	−	610.409i	−0.170908	−	0.637836i
$958$	242.096	−	419.323i	0.252710	−	0.437707i
$959$	40.7199	−	70.5289i	0.0424607	−	0.0735442i
$960$	−4.91771	+	18.3531i	−0.00512261	+	0.0191178i
$961$		−	745.983i		−	0.776257i
$962$	−191.693	−	965.630i	−0.199266	−	1.00377i
$963$	213.278			0.221472
$964$	−30.3583	−	8.13448i	−0.0314920	−	0.00843825i
$965$	371.026	+	214.212i	0.384483	+	0.221981i
$966$	2.87022	+	1.65712i	0.00297124	+	0.00171545i
$967$	−1373.59	+	368.051i	−1.42046	+	0.380612i	−0.885648	−	0.464358i	$-0.846285\pi$
$967$	−1373.59	+	368.051i	−1.42046	+	0.380612i	−0.534814	+	0.844970i	$0.679618\pi$
$968$	−148.213	−	148.213i	−0.153113	−	0.153113i
$969$	−414.609	+	718.124i	−0.427873	+	0.741098i
$970$	−95.2512	−	95.2512i	−0.0981971	−	0.0981971i
$971$	−912.651	−	1580.76i	−0.939908	−	1.62797i	−0.765639	−	0.643271i	$-0.777577\pi$
$971$	−912.651	−	1580.76i	−0.939908	−	1.62797i	−0.174269	−	0.984698i	$-0.555756\pi$
$972$	−31.1769			−0.0320750
$973$			210.002i			0.215829i
$974$	−100.998	−	174.934i	−0.103694	−	0.179604i
$975$	−727.736	+	194.996i	−0.746395	+	0.199996i
$976$	154.002	−	154.002i	0.157789	−	0.157789i
$977$	−1256.88	−	336.780i	−1.28647	−	0.344709i	−0.450151	−	0.892952i	$-0.648630\pi$
$977$	−1256.88	−	336.780i	−1.28647	−	0.344709i	−0.836319	+	0.548244i	$0.815297\pi$
$978$	179.632	+	311.132i	0.183673	+	0.318131i
$979$	33.2803	−	124.204i	0.0339941	−	0.126868i
$980$	33.1867	+	123.854i	0.0338640	+	0.126382i
$981$	134.747	−	36.1052i	0.137356	−	0.0368045i
$982$	−974.906	−	261.225i	−0.992776	−	0.266014i
$983$	−534.456	+	308.568i	−0.543699	+	0.313905i	−0.746577	−	0.665299i	$-0.768304\pi$
$983$	−534.456	+	308.568i	−0.543699	+	0.313905i	0.202878	+	0.979204i	$0.434971\pi$
$984$	−17.9525	+	66.9996i	−0.0182444	+	0.0680890i
$985$	−131.226	−	131.226i	−0.133225	−	0.133225i
$986$	199.254	+	743.628i	0.202084	+	0.754186i
$987$	−8.30748	+	4.79632i	−0.00841689	+	0.00485950i
$988$	−864.390			−0.874889
$989$		−	75.6884i		−	0.0765302i
$990$	−70.3750	+	40.6310i	−0.0710859	+	0.0410414i
$991$	733.968	−	733.968i	0.740634	−	0.740634i	−0.232066	−	0.972700i	$-0.574549\pi$
$991$	733.968	−	733.968i	0.740634	−	0.740634i	0.972700	+	0.232066i	$0.0745485\pi$
$992$	202.405	+	116.858i	0.204037	+	0.117801i
$993$	386.358	−	386.358i	0.389081	−	0.389081i
$994$	61.9590	+	231.234i	0.0623330	+	0.232630i
$995$	−82.0861	+	142.177i	−0.0824986	+	0.142892i
$996$	−205.910	+	356.647i	−0.206737	+	0.358079i
$997$	379.480	−	1416.24i	0.380622	−	1.42050i	−0.464332	−	0.885661i	$-0.653706\pi$
$997$	379.480	−	1416.24i	0.380622	−	1.42050i	0.844954	−	0.534839i	$-0.179628\pi$
$998$		−	665.270i		−	0.666604i
$999$	188.578	−	37.4358i	0.188767	−	0.0374733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.3.l.d.193.2	✓	16
37.14	odd	12	inner	222.3.l.d.199.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.3.l.d.193.2	✓	16	1.1	even	1	trivial
222.3.l.d.199.2	yes	16	37.14	odd	12	inner

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:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	222.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.32452 - 0.354905i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.749275 - 1.29778i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +1.93924 q^{10} +13.9681i q^{11} +(1.73205 + 3.00000i) q^{12} +(18.1732 - 4.86949i) q^{13} +(1.49855 - 1.49855i) q^{14} +(2.29414 + 0.614713i) q^{15} +(2.00000 + 3.46410i) q^{16} +(5.39402 - 20.1307i) q^{17} +(1.09808 + 4.09808i) q^{18} +(-22.1889 + 5.94550i) q^{19} +(2.64905 + 0.709810i) q^{20} +(2.24783 - 1.29778i) q^{21} +(-5.11266 + 19.0807i) q^{22} +(0.638443 + 0.638443i) q^{23} +(1.26795 + 4.73205i) q^{24} +(-20.0222 + 11.5598i) q^{25} +26.6074 q^{26} +5.19615i q^{27} +(2.59557 - 1.49855i) q^{28} +(-18.4700 + 18.4700i) q^{29} +(2.90885 + 1.67943i) q^{30} +(29.2146 - 29.2146i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-12.0967 + 20.9521i) q^{33} +(14.7367 - 25.5248i) q^{34} +(0.531843 - 1.98486i) q^{35} +6.00000i q^{36} +(-7.20452 - 36.2918i) q^{37} -32.4868 q^{38} +(31.4769 + 8.43421i) q^{39} +(3.35886 + 1.93924i) q^{40} +(12.2618 + 7.07934i) q^{41} +(3.54561 - 0.950043i) q^{42} +(-59.2758 - 59.2758i) q^{43} +(-13.9681 + 24.1934i) q^{44} +(2.90885 + 2.90885i) q^{45} +(0.638443 + 1.10582i) q^{46} -3.69578 q^{47} +6.92820i q^{48} +(23.3772 + 40.4905i) q^{49} +(-31.5821 + 8.46239i) q^{50} +(25.5248 - 25.5248i) q^{51} +(36.3464 + 9.73898i) q^{52} +(-26.2884 - 45.5328i) q^{53} +(-1.90192 + 7.09808i) q^{54} +(4.95733 + 18.5010i) q^{55} +(4.09412 - 1.09702i) q^{56} +(-38.4323 - 10.2979i) q^{57} +(-31.9909 + 18.4700i) q^{58} +(-2.55567 + 9.53789i) q^{59} +(3.35886 + 3.35886i) q^{60} +(-14.0922 - 52.5927i) q^{61} +(50.6011 - 29.2146i) q^{62} +4.49565 q^{63} +8.00000i q^{64} +(22.3426 - 12.8995i) q^{65} +(-24.1934 + 24.1934i) q^{66} +(-57.1834 - 33.0149i) q^{67} +(29.4735 - 29.4735i) q^{68} +(0.404757 + 1.51057i) q^{69} +(1.45302 - 2.51671i) q^{70} +(-56.4797 + 97.8256i) q^{71} +(-2.19615 + 8.19615i) q^{72} -124.914i q^{73} +(3.44216 - 52.2126i) q^{74} -40.0445 q^{75} +(-44.3778 - 11.8910i) q^{76} +(18.1275 + 10.4659i) q^{77} +(39.9111 + 23.0427i) q^{78} +(-11.6945 + 3.13354i) q^{79} +(3.87847 + 3.87847i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(14.1587 + 14.1587i) q^{82} +(59.4411 + 102.955i) q^{83} +5.19113 q^{84} -28.5780i q^{85} +(-59.2758 - 102.669i) q^{86} +(-43.7004 + 11.7095i) q^{87} +(-27.9361 + 27.9361i) q^{88} +(-8.89198 - 2.38260i) q^{89} +(2.90885 + 5.03828i) q^{90} +(7.29718 - 27.2334i) q^{91} +(0.467373 + 1.74426i) q^{92} +(69.1224 - 18.5213i) q^{93} +(-5.04853 - 1.35275i) q^{94} +(-27.2796 + 15.7499i) q^{95} +(-2.53590 + 9.46410i) q^{96} +(-49.1179 - 49.1179i) q^{97} +(17.1133 + 63.8676i) q^{98} +(-36.2901 + 20.9521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Introduction

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