LMFDB - Embedded newform 171.2.x.a.110.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.3
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80901 + 1.51794i) q^{2} +(-0.419122 + 1.68058i) q^{3} +(0.621081 - 3.52233i) q^{4} +(-1.22473 + 3.36492i) q^{5} +(-1.79282 - 3.67638i) q^{6} +(0.850912 + 1.47382i) q^{7} +(1.86164 + 3.22446i) q^{8} +(-2.64867 - 1.40873i) q^{9} +O(q^{10})$	\(q+(-1.80901 + 1.51794i) q^{2} +(-0.419122 + 1.68058i) q^{3} +(0.621081 - 3.52233i) q^{4} +(-1.22473 + 3.36492i) q^{5} +(-1.79282 - 3.67638i) q^{6} +(0.850912 + 1.47382i) q^{7} +(1.86164 + 3.22446i) q^{8} +(-2.64867 - 1.40873i) q^{9} +(-2.89220 - 7.94624i) q^{10} -0.0685816i q^{11} +(5.65923 + 2.52006i) q^{12} +(0.947862 + 2.60423i) q^{13} +(-3.77648 - 1.37453i) q^{14} +(-5.14169 - 3.46856i) q^{15} +(-1.54034 - 0.560636i) q^{16} +(2.40059 - 6.59558i) q^{17} +(6.92985 - 1.47211i) q^{18} +(-3.88520 - 1.97616i) q^{19} +(11.0917 + 6.40378i) q^{20} +(-2.83351 + 0.812310i) q^{21} +(0.104103 + 0.124065i) q^{22} +(2.95636 + 0.521285i) q^{23} +(-6.19920 + 1.77719i) q^{24} +(-5.99249 - 5.02830i) q^{25} +(-5.66776 - 3.27228i) q^{26} +(3.47760 - 3.86087i) q^{27} +(5.71977 - 2.08182i) q^{28} +(-1.00498 + 5.69952i) q^{29} +(14.5664 - 1.53011i) q^{30} +2.56914i q^{31} +(-3.35999 + 1.22294i) q^{32} +(0.115257 + 0.0287441i) q^{33} +(5.66899 + 15.5754i) q^{34} +(-6.00143 + 1.05821i) q^{35} +(-6.60706 + 8.45455i) q^{36} +7.77355i q^{37} +(10.0281 - 2.32260i) q^{38} +(-4.77388 + 0.501464i) q^{39} +(-13.1300 + 2.31518i) q^{40} +(-8.32894 + 6.98881i) q^{41} +(3.89281 - 5.77057i) q^{42} +(0.683977 + 3.87902i) q^{43} +(-0.241567 - 0.0425947i) q^{44} +(7.98418 - 7.18725i) q^{45} +(-6.13936 + 3.54456i) q^{46} +(-0.713950 - 0.125889i) q^{47} +(1.58778 - 2.35368i) q^{48} +(2.05190 - 3.55399i) q^{49} +18.4731 q^{50} +(10.0782 + 6.79873i) q^{51} +(9.76164 - 1.72124i) q^{52} +(6.47151 + 5.43024i) q^{53} +(-0.430456 + 12.2631i) q^{54} +(0.230771 + 0.0839939i) q^{55} +(-3.16818 + 5.48746i) q^{56} +(4.94947 - 5.70112i) q^{57} +(-6.83351 - 11.8360i) q^{58} +(-1.93552 - 10.9769i) q^{59} +(-15.4108 + 15.9564i) q^{60} +(-1.83166 + 0.666669i) q^{61} +(-3.89981 - 4.64761i) q^{62} +(-0.177564 - 5.10238i) q^{63} +(5.86110 - 10.1517i) q^{64} -9.92389 q^{65} +(-0.252132 + 0.122954i) q^{66} +(-5.17654 + 6.16916i) q^{67} +(-21.7408 - 12.5521i) q^{68} +(-2.11513 + 4.74990i) q^{69} +(9.25034 - 11.0241i) q^{70} +(4.92220 - 4.13021i) q^{71} +(-0.388478 - 11.1631i) q^{72} +(1.28461 + 7.28540i) q^{73} +(-11.7998 - 14.0624i) q^{74} +(10.9620 - 7.96337i) q^{75} +(-9.37372 + 12.4576i) q^{76} +(0.101077 - 0.0583569i) q^{77} +(7.87480 - 8.15361i) q^{78} +(3.66753 - 10.0764i) q^{79} +(3.77299 - 4.49647i) q^{80} +(5.03094 + 7.46255i) q^{81} +(4.45854 - 25.2857i) q^{82} +(-0.302529 + 0.174665i) q^{83} +(1.10138 + 10.4850i) q^{84} +(19.2535 + 16.1556i) q^{85} +(-7.12545 - 5.97896i) q^{86} +(-9.15727 - 4.07774i) q^{87} +(0.221138 - 0.127674i) q^{88} +(-0.881834 + 5.00113i) q^{89} +(-3.53366 + 25.1213i) q^{90} +(-3.03162 + 3.61295i) q^{91} +(3.67227 - 10.0895i) q^{92} +(-4.31764 - 1.07678i) q^{93} +(1.48263 - 0.855999i) q^{94} +(11.4080 - 10.6531i) q^{95} +(-0.646991 - 6.15927i) q^{96} +(2.44747 + 2.91678i) q^{97} +(1.68284 + 9.54387i) q^{98} +(-0.0966132 + 0.181650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.80901	+	1.51794i	−1.27916	+	1.07335i	−0.285805	+	0.958288i	$0.592261\pi$
$2$	−1.80901	+	1.51794i	−1.27916	+	1.07335i	−0.993359	+	0.115058i	$0.963295\pi$
$3$	−0.419122	+	1.68058i	−0.241980	+	0.970281i
$3$	−0.419122	+	1.68058i	−0.241980	+	0.970281i
$4$	0.621081	−	3.52233i	0.310540	−	1.76116i
$5$	−1.22473	+	3.36492i	−0.547716	+	1.50484i	0.289070	+	0.957308i	$0.406654\pi$
$5$	−1.22473	+	3.36492i	−0.547716	+	1.50484i	−0.836786	+	0.547529i	$0.815568\pi$
$6$	−1.79282	−	3.67638i	−0.731915	−	1.50088i
$7$	0.850912	+	1.47382i	0.321614	+	0.557052i	0.980821	−	0.194909i	$-0.0624412\pi$
$7$	0.850912	+	1.47382i	0.321614	+	0.557052i	−0.659207	+	0.751962i	$0.729108\pi$
$8$	1.86164	+	3.22446i	0.658190	+	1.14002i
$9$	−2.64867	−	1.40873i	−0.882891	−	0.469578i
$10$	−2.89220	−	7.94624i	−0.914592	−	2.51282i
$11$		−	0.0685816i		−	0.0206781i	−0.999947	−	0.0103391i	$-0.996709\pi$
$11$		−	0.0685816i		−	0.0206781i	0.999947	−	0.0103391i	$-0.00329108\pi$
$12$	5.65923	+	2.52006i	1.63368	+	0.727478i
$13$	0.947862	+	2.60423i	0.262890	+	0.722283i	0.998969	+	0.0453885i	$0.0144526\pi$
$13$	0.947862	+	2.60423i	0.262890	+	0.722283i	−0.736080	+	0.676895i	$0.763325\pi$
$14$	−3.77648	−	1.37453i	−1.00931	−	0.367358i
$15$	−5.14169	−	3.46856i	−1.32758	−	0.895579i
$16$	−1.54034	−	0.560636i	−0.385084	−	0.140159i
$17$	2.40059	−	6.59558i	0.582230	−	1.59966i	−0.202132	−	0.979358i	$-0.564787\pi$
$17$	2.40059	−	6.59558i	0.582230	−	1.59966i	0.784361	−	0.620304i	$-0.212991\pi$
$18$	6.92985	−	1.47211i	1.63338	−	0.346980i
$19$	−3.88520	−	1.97616i	−0.891326	−	0.453363i
$19$	−3.88520	−	1.97616i	−0.891326	−	0.453363i
$20$	11.0917	+	6.40378i	2.48018	+	1.43193i
$21$	−2.83351	+	0.812310i	−0.618322	+	0.177261i
$22$	0.104103	+	0.124065i	0.0221948	+	0.0264507i
$23$	2.95636	+	0.521285i	0.616443	+	0.108696i	0.473146	−	0.880984i	$-0.343118\pi$
$23$	2.95636	+	0.521285i	0.616443	+	0.108696i	0.143297	+	0.989680i	$0.454229\pi$
$24$	−6.19920	+	1.77719i	−1.26541	+	0.362767i
$25$	−5.99249	−	5.02830i	−1.19850	−	1.00566i
$26$	−5.66776	−	3.27228i	−1.11154	−	0.641747i
$27$	3.47760	−	3.86087i	0.669265	−	0.743024i
$28$	5.71977	−	2.08182i	1.08093	−	0.393428i
$29$	−1.00498	+	5.69952i	−0.186620	+	1.05837i	0.737236	+	0.675635i	$0.236130\pi$
$29$	−1.00498	+	5.69952i	−0.186620	+	1.05837i	−0.923856	+	0.382739i	$0.874981\pi$
$30$	14.5664	−	1.53011i	2.65946	−	0.279358i
$31$			2.56914i			0.461432i	0.973021	+	0.230716i	$0.0741068\pi$
$31$			2.56914i			0.461432i	−0.973021	+	0.230716i	$0.925893\pi$
$32$	−3.35999	+	1.22294i	−0.593967	+	0.216186i
$33$	0.115257	+	0.0287441i	0.0200636	+	0.00500370i
$34$	5.66899	+	15.5754i	0.972224	+	2.67116i
$35$	−6.00143	+	1.05821i	−1.01443	+	0.178871i
$36$	−6.60706	+	8.45455i	−1.10118	+	1.40909i
$37$			7.77355i			1.27796i	0.769221	+	0.638982i	$0.220644\pi$
$37$			7.77355i			1.27796i	−0.769221	+	0.638982i	$0.779356\pi$
$38$	10.0281	−	2.32260i	1.62677	−	0.376775i
$39$	−4.77388	+	0.501464i	−0.764432	+	0.0802985i
$40$	−13.1300	+	2.31518i	−2.07604	+	0.366062i
$41$	−8.32894	+	6.98881i	−1.30076	+	1.09147i	−0.310749	+	0.950492i	$0.600580\pi$
$41$	−8.32894	+	6.98881i	−1.30076	+	1.09147i	−0.990013	+	0.140977i	$0.954976\pi$
$42$	3.89281	−	5.77057i	0.600673	−	0.890419i
$43$	0.683977	+	3.87902i	0.104305	+	0.591546i	0.991495	+	0.130141i	$0.0415431\pi$
$43$	0.683977	+	3.87902i	0.104305	+	0.591546i	−0.887190	+	0.461404i	$0.847346\pi$
$44$	−0.241567	−	0.0425947i	−0.0364175	−	0.00642139i
$45$	7.98418	−	7.18725i	1.19021	−	1.07141i
$46$	−6.13936	+	3.54456i	−0.905200	+	0.522617i
$47$	−0.713950	−	0.125889i	−0.104140	−	0.0183627i	0.121335	−	0.992612i	$-0.461282\pi$
$47$	−0.713950	−	0.125889i	−0.104140	−	0.0183627i	−0.225475	+	0.974249i	$0.572394\pi$
$48$	1.58778	−	2.35368i	0.229176	−	0.339724i
$49$	2.05190	−	3.55399i	0.293128	−	0.507713i
$50$	18.4731			2.61250
$51$	10.0782	+	6.79873i	1.41123	+	0.952013i
$52$	9.76164	−	1.72124i	1.35370	−	0.238693i
$53$	6.47151	+	5.43024i	0.888930	+	0.745901i	0.967995	−	0.250969i	$-0.0807492\pi$
$53$	6.47151	+	5.43024i	0.888930	+	0.745901i	−0.0790654	+	0.996869i	$0.525194\pi$
$54$	−0.430456	+	12.2631i	−0.0585776	+	1.66880i
$55$	0.230771	+	0.0839939i	0.0311172	+	0.0113257i
$56$	−3.16818	+	5.48746i	−0.423366	+	0.733292i
$57$	4.94947	−	5.70112i	0.655573	−	0.755132i
$58$	−6.83351	−	11.8360i	−0.897284	−	1.55414i
$59$	−1.93552	−	10.9769i	−0.251983	−	1.42907i	−0.803699	−	0.595036i	$-0.797138\pi$
$59$	−1.93552	−	10.9769i	−0.251983	−	1.42907i	0.551716	−	0.834032i	$-0.313973\pi$
$60$	−15.4108	+	15.9564i	−1.98953	+	2.05997i
$61$	−1.83166	+	0.666669i	−0.234520	+	0.0853582i	−0.456607	−	0.889669i	$-0.650935\pi$
$61$	−1.83166	+	0.666669i	−0.234520	+	0.0853582i	0.222087	+	0.975027i	$0.428713\pi$
$62$	−3.89981	−	4.64761i	−0.495276	−	0.590247i
$63$	−0.177564	−	5.10238i	−0.0223710	−	0.642840i
$64$	5.86110	−	10.1517i	0.732638	−	1.26897i
$65$	−9.92389			−1.23091
$66$	−0.252132	+	0.122954i	−0.0310353	+	0.0151346i
$67$	−5.17654	+	6.16916i	−0.632415	+	0.753683i	−0.983152	−	0.182791i	$-0.941487\pi$
$67$	−5.17654	+	6.16916i	−0.632415	+	0.753683i	0.350737	+	0.936474i	$0.385931\pi$
$68$	−21.7408	−	12.5521i	−2.63646	−	1.52216i
$69$	−2.11513	+	4.74990i	−0.254632	+	0.571821i
$70$	9.25034	−	11.0241i	1.10563	−	1.31764i
$71$	4.92220	−	4.13021i	0.584157	−	0.490166i	−0.302152	−	0.953260i	$-0.597705\pi$
$71$	4.92220	−	4.13021i	0.584157	−	0.490166i	0.886309	+	0.463093i	$0.153261\pi$
$72$	−0.388478	−	11.1631i	−0.0457826	−	1.31558i
$73$	1.28461	+	7.28540i	0.150353	+	0.852692i	0.962912	+	0.269814i	$0.0869623\pi$
$73$	1.28461	+	7.28540i	0.150353	+	0.852692i	−0.812560	+	0.582878i	$0.801927\pi$
$74$	−11.7998	−	14.0624i	−1.37170	−	1.63473i
$75$	10.9620	−	7.96337i	1.26579	−	0.919530i
$76$	−9.37372	+	12.4576i	−1.07524	+	1.42898i
$77$	0.101077	−	0.0583569i	0.0115188	−	0.00665038i
$78$	7.87480	−	8.15361i	0.891645	−	0.923215i
$79$	3.66753	−	10.0764i	0.412629	−	1.13369i	−0.543159	−	0.839630i	$-0.682772\pi$
$79$	3.66753	−	10.0764i	0.412629	−	1.13369i	0.955787	−	0.294058i	$-0.0950060\pi$
$80$	3.77299	−	4.49647i	0.421833	−	0.502721i
$81$	5.03094	+	7.46255i	0.558993	+	0.829172i
$82$	4.45854	−	25.2857i	0.492364	−	2.79233i
$83$	−0.302529	+	0.174665i	−0.0332069	+	0.0191720i	−0.516512	−	0.856280i	$-0.672770\pi$
$83$	−0.302529	+	0.174665i	−0.0332069	+	0.0191720i	0.483305	+	0.875452i	$0.339436\pi$
$84$	1.10138	+	10.4850i	0.120171	+	1.14401i
$85$	19.2535	+	16.1556i	2.08834	+	1.75232i
$86$	−7.12545	−	5.97896i	−0.768357	−	0.644728i
$87$	−9.15727	−	4.07774i	−0.981762	−	0.437179i
$88$	0.221138	−	0.127674i	0.0235734	−	0.0136101i
$89$	−0.881834	+	5.00113i	−0.0934743	+	0.530119i	0.901730	+	0.432300i	$0.142298\pi$
$89$	−0.881834	+	5.00113i	−0.0934743	+	0.530119i	−0.995204	+	0.0978191i	$0.968813\pi$
$90$	−3.53366	+	25.1213i	−0.372480	+	2.64802i
$91$	−3.03162	+	3.61295i	−0.317801	+	0.378740i
$92$	3.67227	−	10.0895i	0.382861	−	1.05190i
$93$	−4.31764	−	1.07678i	−0.447719	−	0.111657i
$94$	1.48263	−	0.855999i	0.152922	−	0.0882896i
$95$	11.4080	−	10.6531i	1.17043	−	1.09299i
$96$	−0.646991	−	6.15927i	−0.0660332	−	0.628628i
$97$	2.44747	+	2.91678i	0.248503	+	0.296154i	0.875848	−	0.482587i	$-0.160303\pi$
$97$	2.44747	+	2.91678i	0.248503	+	0.296154i	−0.627345	+	0.778741i	$0.715859\pi$
$98$	1.68284	+	9.54387i	0.169993	+	0.964077i
$99$	−0.0966132	+	0.181650i	−0.00970999	+	0.0182565i
$100$	−21.4331	+	17.9845i	−2.14331	+	1.79845i
$101$	−3.71031	+	4.42177i	−0.369189	+	0.439983i	−0.918371	−	0.395720i	$-0.870495\pi$
$101$	−3.71031	+	4.42177i	−0.369189	+	0.439983i	0.549182	+	0.835703i	$0.314939\pi$
$102$	−28.5517	+	2.99917i	−2.82704	+	0.296962i
$103$	−9.35292	−	5.39991i	−0.921571	−	0.532069i	−0.0374351	−	0.999299i	$-0.511919\pi$
$103$	−9.35292	−	5.39991i	−0.921571	−	0.532069i	−0.884136	+	0.467230i	$0.845252\pi$
$104$	−6.63265	+	7.90448i	−0.650384	+	0.775098i
$105$	0.736923	−	10.5294i	0.0719163	−	1.02756i
$106$	−19.9498			−1.93770
$107$	5.99297	−	10.3801i	0.579362	−	1.00348i	−0.416191	−	0.909277i	$-0.636635\pi$
$107$	5.99297	−	10.3801i	0.579362	−	1.00348i	0.995553	−	0.0942068i	$-0.0300315\pi$
$108$	−11.4394	−	14.6472i	−1.10075	−	1.40942i
$109$	1.67453	+	1.99563i	0.160391	+	0.191146i	0.840255	−	0.542192i	$-0.182406\pi$
$109$	1.67453	+	1.99563i	0.160391	+	0.191146i	−0.679864	+	0.733338i	$0.737961\pi$
$110$	−0.544966	+	0.198351i	−0.0519604	+	0.0189121i
$111$	−13.0641	−	3.25807i	−1.23998	−	0.309242i
$112$	−0.484411	−	2.74723i	−0.0457725	−	0.259589i
$113$	9.89206	+	17.1335i	0.930567	+	1.61179i	0.782355	+	0.622833i	$0.214018\pi$
$113$	9.89206	+	17.1335i	0.930567	+	1.61179i	0.148212	+	0.988956i	$0.452648\pi$
$114$	−0.299681	+	17.8264i	−0.0280677	+	1.66959i
$115$	−5.37482	+	9.30947i	−0.501205	+	0.868112i
$116$	19.4514	+	7.07973i	1.80602	+	0.657336i
$117$	1.15809	−	8.23304i	0.107065	−	0.761144i
$118$	20.1636	+	16.9193i	1.85621	+	1.55755i
$119$	11.7634	−	2.07421i	1.07835	−	0.190142i
$120$	1.61225	−	23.0364i	0.147178	−	2.10292i
$121$	10.9953			0.999572
$122$	2.30152	−	3.98636i	0.208370	−	0.360908i
$123$	−8.25438	−	16.9266i	−0.744273	−	1.52622i
$124$	9.04936	+	1.59565i	0.812656	+	0.143293i
$125$	8.75336	−	5.05376i	0.782924	−	0.452022i
$126$	8.06632	+	8.96073i	0.718605	+	0.798285i
$127$	1.09837	+	0.193673i	0.0974648	+	0.0171857i	0.222168	−	0.975008i	$-0.428687\pi$
$127$	1.09837	+	0.193673i	0.0974648	+	0.0171857i	−0.124703	+	0.992194i	$0.539798\pi$
$128$	3.56512	+	20.2188i	0.315115	+	1.78710i
$129$	−6.80567	−	0.476310i	−0.599206	−	0.0419368i
$130$	17.9524	−	15.0639i	1.57453	−	1.32119i
$131$	0.0109927	−	0.00193831i	0.000960439	−	0.000169351i	−0.173168	−	0.984892i	$-0.555400\pi$
$131$	0.0109927	−	0.00193831i	0.000960439	−	0.000169351i	0.174128	+	0.984723i	$0.444289\pi$
$132$	0.172830	−	0.388119i	0.0150429	−	0.0337814i
$133$	−0.393447	−	7.40763i	−0.0341162	−	0.642323i
$134$		−	19.0178i		−	1.64288i
$135$	8.73237	+	16.4304i	0.751563	+	1.41410i
$136$	25.7362	−	4.53799i	2.20686	−	0.389129i
$137$	−1.11583	−	3.06570i	−0.0953314	−	0.261921i	0.882857	−	0.469643i	$-0.155617\pi$
$137$	−1.11583	−	3.06570i	−0.0953314	−	0.261921i	−0.978188	+	0.207722i	$0.933395\pi$
$138$	−3.38376	−	11.8033i	−0.288045	−	1.00476i
$139$	8.02855	−	2.92215i	0.680973	−	0.247854i	0.0217075	−	0.999764i	$-0.493090\pi$
$139$	8.02855	−	2.92215i	0.680973	−	0.247854i	0.659265	+	0.751911i	$0.270868\pi$
$140$			21.7962i			1.84212i
$141$	0.510798	−	1.14708i	0.0430169	−	0.0966019i
$142$	−2.63489	+	14.9432i	−0.221115	+	1.25401i
$143$	0.178602	−	0.0650059i	0.0149355	−	0.00543606i
$144$	3.29006	+	3.65486i	0.274171	+	0.304572i
$145$	−17.9476	−	10.3620i	−1.49047	−	0.860521i
$146$	−13.3827	−	11.2294i	−1.10756	−	0.929352i
$147$	5.11276	+	4.93793i	0.421693	+	0.407274i
$148$	27.3810	+	4.82801i	2.25070	+	0.396860i
$149$	0.600370	+	0.715493i	0.0491842	+	0.0586155i	0.790076	−	0.613009i	$-0.210041\pi$
$149$	0.600370	+	0.715493i	0.0491842	+	0.0586155i	−0.740891	+	0.671625i	$0.765597\pi$
$150$	−7.74250	+	31.0455i	−0.632172	+	2.53486i
$151$	−10.8642	−	6.27247i	−0.884119	−	0.510447i	−0.0121050	−	0.999927i	$-0.503853\pi$
$151$	−10.8642	−	6.27247i	−0.884119	−	0.510447i	−0.872014	+	0.489480i	$0.837187\pi$
$152$	−0.860791	−	16.2066i	−0.0698194	−	1.31453i
$153$	−15.6498	+	14.0877i	−1.26521	+	1.13893i
$154$	−0.0942672	+	0.258997i	−0.00759627	+	0.0208706i
$155$	−8.64496	−	3.14651i	−0.694380	−	0.252734i
$156$	−1.19864	+	17.1266i	−0.0959683	+	1.37122i
$157$	−10.9534	−	3.98670i	−0.874174	−	0.318173i	−0.134318	−	0.990938i	$-0.542884\pi$
$157$	−10.9534	−	3.98670i	−0.874174	−	0.318173i	−0.739856	+	0.672765i	$0.765106\pi$
$158$	8.66085	+	23.7955i	0.689020	+	1.89307i
$159$	−11.8383	+	8.59993i	−0.938837	+	0.682019i
$160$		−	12.8038i		−	1.01223i
$161$	1.74732	+	4.80071i	0.137708	+	0.378349i
$162$	−20.4287	−	5.86317i	−1.60503	−	0.460654i
$163$	8.85463	+	15.3367i	0.693548	+	1.20126i	0.970668	+	0.240425i	$0.0772868\pi$
$163$	8.85463	+	15.3367i	0.693548	+	1.20126i	−0.277120	+	0.960835i	$0.589380\pi$
$164$	19.4439	+	33.6778i	1.51831	+	2.62980i
$165$	−0.237880	+	0.352625i	−0.0185189	+	0.0274518i
$166$	0.282147	−	0.775192i	0.0218989	−	0.0601666i
$167$	0.198247	−	1.12432i	0.0153408	−	0.0870022i	−0.976176	−	0.216980i	$-0.930379\pi$
$167$	0.198247	−	1.12432i	0.0153408	−	0.0870022i	0.991517	+	0.129978i	$0.0414905\pi$
$168$	−7.89423	−	7.62429i	−0.609053	−	0.588227i
$169$	4.07501	−	3.41934i	0.313462	−	0.263026i
$170$	−59.3530			−4.55217
$171$	7.50673	+	10.7074i	0.574054	+	0.818817i
$172$	14.0880			1.07420
$173$	0.683168	−	0.573246i	0.0519403	−	0.0435831i	−0.616448	−	0.787396i	$-0.711429\pi$
$173$	0.683168	−	0.573246i	0.0519403	−	0.0435831i	0.668388	+	0.743813i	$0.266984\pi$
$174$	22.7554	−	6.52351i	1.72508	−	0.494546i
$175$	2.31173	−	13.1105i	0.174751	−	0.991061i
$176$	−0.0384493	+	0.105639i	−0.00289823	+	0.00796281i
$177$	19.2587	+	1.34786i	1.44757	+	0.101312i
$178$	−5.99617	−	10.3857i	−0.449432	−	0.778439i
$179$	7.40214	+	12.8209i	0.553262	+	0.958278i	0.998036	+	0.0626353i	$0.0199505\pi$
$179$	7.40214	+	12.8209i	0.553262	+	0.958278i	−0.444774	+	0.895643i	$0.646716\pi$
$180$	−20.3570	−	32.5868i	−1.51732	−	2.42887i
$181$	2.14356	+	5.88939i	0.159330	+	0.437755i	0.993511	−	0.113735i	$-0.0362816\pi$
$181$	2.14356	+	5.88939i	0.159330	+	0.437755i	−0.834181	+	0.551490i	$0.814059\pi$
$182$		−	11.1377i		−	0.825580i
$183$	−0.352699	−	3.35765i	−0.0260723	−	0.248205i
$184$	3.82281	+	10.5031i	0.281822	+	0.774298i
$185$	−26.1574	−	9.52051i	−1.92313	−	0.699962i
$186$	9.44515	−	4.60601i	0.692552	−	0.337729i
$187$	−0.452335	−	0.164637i	−0.0330780	−	0.0120394i
$188$	−0.886841	+	2.43658i	−0.0646795	+	0.177706i
$189$	8.64936	+	1.84011i	0.629148	+	0.133848i
$190$	−4.46632	+	36.5882i	−0.324021	+	2.65439i
$191$	16.6733	+	9.62632i	1.20644	+	0.696536i	0.961979	−	0.273124i	$-0.0880570\pi$
$191$	16.6733	+	9.62632i	1.20644	+	0.696536i	0.244457	+	0.969660i	$0.421390\pi$
$192$	14.6042	+	14.1048i	1.05397	+	1.01793i
$193$	−8.89893	−	10.6053i	−0.640559	−	0.763388i	0.343900	−	0.939006i	$-0.388252\pi$
$193$	−8.89893	−	10.6053i	−0.640559	−	0.763388i	−0.984458	+	0.175618i	$0.943808\pi$
$194$	−8.85498	−	1.56137i	−0.635751	−	0.112100i
$195$	4.15932	−	16.6779i	0.297855	−	1.19433i
$196$	−11.2439	−	9.43477i	−0.803137	−	0.673912i
$197$	10.1316	+	5.84947i	0.721845	+	0.416757i	0.815431	−	0.578854i	$-0.196500\pi$
$197$	10.1316	+	5.84947i	0.721845	+	0.416757i	−0.0935863	+	0.995611i	$0.529833\pi$
$198$	−0.100960	−	0.475260i	−0.00717491	−	0.0337753i
$199$	−5.06800	+	1.84460i	−0.359261	+	0.130760i	−0.515343	−	0.856984i	$-0.672336\pi$
$199$	−5.06800	+	1.84460i	−0.359261	+	0.130760i	0.156083	+	0.987744i	$0.450113\pi$
$200$	5.05766	−	28.6834i	0.357630	−	2.02822i
$201$	−8.19814	−	11.2852i	−0.578252	−	0.795997i
$202$		−	13.6311i		−	0.959078i
$203$	−9.25523	+	3.36863i	−0.649590	+	0.236431i
$204$	30.2067	−	31.2762i	2.11490	−	2.18977i
$205$	−13.3161	−	36.5856i	−0.930035	−	2.55525i
$206$	25.1163	−	4.42868i	1.74993	−	0.308561i
$207$	−7.09607	−	5.54543i	−0.493211	−	0.385434i
$208$		−	4.54279i		−	0.314986i
$209$	−0.135528	+	0.266453i	−0.00937470	+	0.0184309i
$210$	14.6499	+	20.1664i	1.01094	+	1.39161i
$211$	−1.39187	+	0.245425i	−0.0958204	+	0.0168957i	−0.221353	−	0.975194i	$-0.571047\pi$
$211$	−1.39187	+	0.245425i	−0.0958204	+	0.0168957i	0.125532	+	0.992090i	$0.459936\pi$
$212$	23.1464	−	19.4221i	1.58970	−	1.33392i
$213$	4.87814	+	10.0032i	0.334245	+	0.685408i
$214$	4.91506	+	27.8747i	0.335987	+	1.90548i
$215$	−13.8903	−	2.44923i	−0.947310	−	0.167036i
$216$	18.9232	+	4.02583i	1.28756	+	0.273923i
$217$	−3.78646	+	2.18611i	−0.257042	+	0.148403i
$218$	−6.05848	−	1.06827i	−0.410332	−	0.0723526i
$219$	−12.7821	−	0.894584i	−0.863733	−	0.0604504i
$220$	0.439182	−	0.760685i	0.0296096	−	0.0512854i
$221$	19.4518			1.30847
$222$	28.5786	−	13.9366i	1.91807	−	0.935361i
$223$	7.70442	−	1.35850i	0.515926	−	0.0909716i	0.0903779	−	0.995908i	$-0.471193\pi$
$223$	7.70442	−	1.35850i	0.515926	−	0.0909716i	0.425548	+	0.904936i	$0.360081\pi$
$224$	−4.66144	−	3.91141i	−0.311456	−	0.261342i
$225$	8.78862	+	21.7601i	0.585908	+	1.45068i
$226$	−43.9025	−	15.9792i	−2.92035	−	1.06292i
$227$	13.4006	−	23.2105i	0.889428	−	1.54053i	0.0488758	−	0.998805i	$-0.484436\pi$
$227$	13.4006	−	23.2105i	0.889428	−	1.54053i	0.840553	−	0.541730i	$-0.182231\pi$
$228$	−17.0072	−	20.9745i	−1.12633	−	1.38907i
$229$	4.04261	+	7.00201i	0.267143	+	0.462706i	0.968123	−	0.250476i	$-0.0805870\pi$
$229$	4.04261	+	7.00201i	0.267143	+	0.462706i	−0.700980	+	0.713181i	$0.747254\pi$
$230$	−4.40810	−	24.9996i	−0.290662	−	1.64842i
$231$	0.0557095	+	0.194326i	0.00366542	+	0.0127857i
$232$	−20.2488	+	7.36995i	−1.32940	+	0.483861i
$233$	5.38901	+	6.42237i	0.353046	+	0.420743i	0.913115	−	0.407702i	$-0.133670\pi$
$233$	5.38901	+	6.42237i	0.353046	+	0.420743i	−0.560069	+	0.828446i	$0.689225\pi$
$234$	10.4023	+	16.6516i	0.680017	+	1.08855i
$235$	1.29800	−	2.24820i	0.0846722	−	0.146657i
$236$	−39.8662			−2.59507
$237$	15.3971	+	10.3868i	1.00015	+	0.674696i
$238$	−18.1316	+	21.6084i	−1.17530	+	1.40066i
$239$	−17.2827	−	9.97818i	−1.11793	−	0.645435i	−0.177056	−	0.984201i	$-0.556657\pi$
$239$	−17.2827	−	9.97818i	−1.11793	−	0.645435i	−0.940871	+	0.338766i	$0.889991\pi$
$240$	5.97532	+	8.22537i	0.385706	+	0.530945i
$241$	4.31692	−	5.14471i	0.278078	−	0.331400i	−0.608870	−	0.793270i	$-0.708377\pi$
$241$	4.31692	−	5.14471i	0.278078	−	0.331400i	0.886948	+	0.461870i	$0.152821\pi$
$242$	−19.8906	+	16.6902i	−1.27862	+	1.07289i
$243$	−14.6500	+	5.32716i	−0.939796	+	0.341737i
$244$	1.21062	+	6.86575i	0.0775018	+	0.439534i
$245$	9.44587	+	11.2572i	0.603475	+	0.719193i
$246$	40.6258	+	18.0907i	2.59021	+	1.15342i
$247$	1.46375	−	11.9911i	0.0931363	−	0.762974i
$248$	−8.28409	+	4.78282i	−0.526040	+	0.303710i
$249$	−0.166742	−	0.581629i	−0.0105668	−	0.0368593i
$250$	−8.16363	+	22.4294i	−0.516313	+	1.41856i
$251$	15.1000	−	17.9955i	0.953103	−	1.13586i	−0.0375279	−	0.999296i	$-0.511948\pi$
$251$	15.1000	−	17.9955i	0.953103	−	1.13586i	0.990631	−	0.136568i	$-0.0436073\pi$
$252$	−18.0825	−	2.54355i	−1.13909	−	0.160229i
$253$	0.0357506	−	0.202752i	0.00224762	−	0.0127469i
$254$	−2.28095	+	1.31691i	−0.143120	+	0.0826302i
$255$	−35.2203	+	25.5858i	−2.20558	+	1.60225i
$256$	−19.1808	−	16.0946i	−1.19880	−	1.00591i
$257$	6.19757	+	5.20038i	0.386594	+	0.324391i	0.815285	−	0.579061i	$-0.196581\pi$
$257$	6.19757	+	5.20038i	0.386594	+	0.324391i	−0.428691	+	0.903451i	$0.641025\pi$
$258$	13.0345	−	9.46894i	0.811495	−	0.589511i
$259$	−11.4568	+	6.61461i	−0.711893	+	0.411012i
$260$	−6.16354	+	34.9552i	−0.382247	+	2.16783i
$261$	10.6910	−	13.6804i	0.661754	−	0.846797i
$262$	−0.0169437	+	0.0201927i	−0.00104679	+	0.00124751i
$263$	−6.23810	+	17.1390i	−0.384658	+	1.05684i	0.584714	+	0.811240i	$0.301207\pi$
$263$	−6.23810	+	17.1390i	−0.384658	+	1.05684i	−0.969372	+	0.245599i	$0.921015\pi$
$264$	0.121882	+	0.425151i	0.00750134	+	0.0261662i
$265$	−26.1982	+	15.1255i	−1.60934	+	0.929153i
$266$	11.9561	+	12.8033i	0.733075	+	0.785018i
$267$	−8.03519	−	3.57808i	−0.491745	−	0.218975i
$268$	18.5147	+	22.0650i	1.13097	+	1.34783i
$269$	−1.90392	−	10.7977i	−0.116084	−	0.658347i	−0.986208	−	0.165513i	$-0.947072\pi$
$269$	−1.90392	−	10.7977i	−0.116084	−	0.658347i	0.870123	−	0.492834i	$-0.164039\pi$
$270$	−40.7373	−	16.4675i	−2.47919	−	1.00218i
$271$	7.63501	−	6.40653i	0.463794	−	0.389169i	−0.380731	−	0.924686i	$-0.624328\pi$
$271$	7.63501	−	6.40653i	0.463794	−	0.389169i	0.844525	+	0.535517i	$0.179883\pi$
$272$	−7.39544	+	8.81354i	−0.448414	+	0.534399i
$273$	−4.80121	−	6.60914i	−0.290583	−	0.400003i
$274$	6.67210	+	3.85214i	0.403076	+	0.232716i
$275$	−0.344848	+	0.410974i	−0.0207951	+	0.0247827i
$276$	15.4170	+	10.4003i	0.927996	+	0.626022i
$277$	−5.65714			−0.339905			−0.169952	−	0.985452i	$-0.554361\pi$
$277$	−5.65714			−0.339905			−0.169952	+	0.985452i	$0.554361\pi$
$278$	−10.0881	+	17.4731i	−0.605043	+	1.04796i
$279$	3.61924	−	6.80482i	0.216678	−	0.407394i
$280$	−14.5847	−	17.3813i	−0.871601	−	1.03873i
$281$	8.00493	−	2.91356i	0.477534	−	0.173808i	−0.0920282	−	0.995756i	$-0.529335\pi$
$281$	8.00493	−	2.91356i	0.477534	−	0.173808i	0.569562	+	0.821948i	$0.307113\pi$
$282$	0.817167	+	2.85045i	0.0486616	+	0.169742i
$283$	2.85192	+	16.1740i	0.169529	+	0.961446i	0.944271	+	0.329169i	$0.106769\pi$
$283$	2.85192	+	16.1740i	0.169529	+	0.961446i	−0.774742	+	0.632277i	$0.782120\pi$
$284$	−11.4909	−	19.9028i	−0.681858	−	1.18101i
$285$	13.1220	+	23.6369i	0.777283	+	1.40013i
$286$	−0.224418	+	0.388704i	−0.0132701	+	0.0229845i
$287$	−17.3875	−	6.32852i	−1.02635	−	0.373560i
$288$	10.6223	+	1.49417i	0.625925	+	0.0880448i
$289$	−24.7160	−	20.7392i	−1.45388	−	1.21995i
$290$	48.1963	−	8.49832i	2.83019	−	0.499038i
$291$	−5.92765	+	2.89067i	−0.347485	+	0.169454i
$292$	26.4594			1.54842
$293$	11.7033	−	20.2707i	0.683714	−	1.18423i	−0.290125	−	0.956989i	$-0.593697\pi$
$293$	11.7033	−	20.2707i	0.683714	−	1.18423i	0.973839	−	0.227238i	$-0.0729696\pi$
$294$	−16.7445	−	1.17190i	−0.976560	−	0.0683468i
$295$	39.3068	+	6.93085i	2.28853	+	0.403530i
$296$	−25.0655	+	14.4716i	−1.45690	+	0.841143i
$297$	−0.264784	−	0.238499i	−0.0153643	−	0.0138391i
$298$	−2.17215	−	0.383009i	−0.125829	−	0.0221871i
$299$	1.44467	+	8.19314i	0.0835475	+	0.473821i
$300$	−21.2413	−	43.5577i	−1.22636	−	2.51480i
$301$	−5.13499	+	4.30877i	−0.295976	+	0.248353i
$302$	29.1748	−	5.14430i	1.67882	−	0.296021i
$303$	−5.87605	−	8.08872i	−0.337571	−	0.464685i
$304$	4.87660	+	5.22214i	0.279692	+	0.299510i
$305$		−	6.97986i		−	0.399666i
$306$	6.92632	−	49.2403i	0.395951	−	2.81488i
$307$	0.718463	−	0.126684i	0.0410048	−	0.00723026i	−0.153108	−	0.988209i	$-0.548928\pi$
$307$	0.718463	−	0.126684i	0.0410048	−	0.00723026i	0.194113	+	0.980979i	$0.437817\pi$
$308$	−0.142775	−	0.392271i	−0.00813535	−	0.0223517i
$309$	12.9950	−	13.4551i	0.739259	−	0.765433i
$310$	20.4150	−	7.43046i	1.15950	−	0.422022i
$311$			4.00327i			0.227005i	0.993538	+	0.113502i	$0.0362069\pi$
$311$			4.00327i			0.227005i	−0.993538	+	0.113502i	$0.963793\pi$
$312$	−10.5042	−	14.4596i	−0.594683	−	0.818614i
$313$	−0.440938	+	2.50068i	−0.0249233	+	0.141347i	−0.994730	−	0.102527i	$-0.967307\pi$
$313$	−0.440938	+	2.50068i	−0.0249233	+	0.141347i	0.969807	+	0.243874i	$0.0784183\pi$
$314$	25.8663	−	9.41457i	1.45972	−	0.531295i
$315$	17.3866	+	5.65155i	0.979622	+	0.318429i
$316$	−33.2147	−	19.1765i	−1.86847	−	1.07876i
$317$	24.5334	+	20.5860i	1.37793	+	1.15622i	0.969970	+	0.243226i	$0.0782055\pi$
$317$	24.5334	+	20.5860i	1.37793	+	1.15622i	0.407964	+	0.912998i	$0.366239\pi$
$318$	8.36140	−	33.5272i	0.468884	−	1.88011i
$319$	0.390882	+	0.0689230i	0.0218852	+	0.00385895i
$320$	26.9815	+	32.1552i	1.50831	+	1.79753i
$321$	14.9328	+	14.4222i	0.833468	+	0.804967i
$322$	−10.4481	−	6.03222i	−0.582250	−	0.336162i
$323$	−22.3607	+	20.8812i	−1.24418	+	1.16186i
$324$	29.4101	−	13.0858i	1.63390	−	0.726986i
$325$	7.41478	−	20.3719i	0.411298	−	1.13003i
$326$	−39.2983	−	14.3034i	−2.17653	−	0.792192i
$327$	−4.05563	+	1.97776i	−0.224277	+	0.109371i
$328$	−38.0406	−	13.8456i	−2.10044	−	0.764498i
$329$	−0.421971	−	1.15935i	−0.0232640	−	0.0639173i
$330$	−0.104937	−	0.998990i	−0.00577661	−	0.0549926i
$331$			25.6998i			1.41259i	0.707919	+	0.706293i	$0.249634\pi$
$331$			25.6998i			1.41259i	−0.707919	+	0.706293i	$0.750366\pi$
$332$	0.427333	+	1.17409i	0.0234529	+	0.0644364i
$333$	10.9509	−	20.5896i	0.600104	−	1.12830i
$334$	1.34801	+	2.33483i	0.0737600	+	0.127756i
$335$	−14.4189	−	24.9742i	−0.787786	−	1.36449i
$336$	4.81996	+	0.337336i	0.262950	+	0.0184032i
$337$	−4.70694	+	12.9322i	−0.256404	+	0.704463i	0.742979	+	0.669315i	$0.233412\pi$
$337$	−4.70694	+	12.9322i	−0.256404	+	0.704463i	−0.999382	+	0.0351479i	$0.988810\pi$
$338$	−2.18138	+	12.3712i	−0.118652	+	0.672907i
$339$	−32.9402	+	9.44331i	−1.78907	+	0.512890i
$340$	68.8633	−	57.7832i	3.73464	−	3.13373i
$341$	0.176196			0.00954154
$342$	−29.8330	−	7.97507i	−1.61318	−	0.431242i
$343$	18.8967			1.02033
$344$	−11.2344	+	9.42681i	−0.605720	+	0.508259i
$345$	−13.3926	−	12.9346i	−0.721031	−	0.696376i
$346$	−0.365705	+	2.07402i	−0.0196604	+	0.111500i
$347$	0.882518	−	2.42470i	0.0473761	−	0.130165i	−0.913748	−	0.406281i	$-0.866825\pi$
$347$	0.882518	−	2.42470i	0.0473761	−	0.130165i	0.961124	+	0.276117i	$0.0890476\pi$
$348$	−20.0505	+	29.7223i	−1.07482	+	1.59328i
$349$	2.91543	+	5.04967i	0.156059	+	0.270303i	0.933444	−	0.358723i	$-0.116788\pi$
$349$	2.91543	+	5.04967i	0.156059	+	0.270303i	−0.777385	+	0.629025i	$0.783454\pi$
$350$	15.7190	+	27.2261i	0.840216	+	1.45530i
$351$	13.3509	+	5.39690i	0.712616	+	0.288065i
$352$	0.0838708	+	0.230433i	0.00447033	+	0.0122821i
$353$			15.5640i			0.828389i	0.910188	+	0.414195i	$0.135937\pi$
$353$			15.5640i			0.828389i	−0.910188	+	0.414195i	$0.864063\pi$
$354$	−36.8852	+	26.7953i	−1.96042	+	1.42415i
$355$	7.86947	+	21.6212i	0.417668	+	1.14753i
$356$	17.0679	+	6.21222i	0.904598	+	0.329247i
$357$	−1.44444	+	20.6386i	−0.0764480	+	1.09231i
$358$	−32.8519	−	11.9571i	−1.73628	−	0.631953i
$359$	3.60821	−	9.91347i	0.190434	−	0.523213i	−0.807326	−	0.590105i	$-0.799086\pi$
$359$	3.60821	−	9.91347i	0.190434	−	0.523213i	0.997760	+	0.0668923i	$0.0213084\pi$
$360$	38.0387	+	12.3646i	2.00481	+	0.651670i
$361$	11.1896	+	15.3556i	0.588924	+	0.808189i
$362$	−12.8175	−	7.40017i	−0.673671	−	0.388944i
$363$	−4.60837	+	18.4784i	−0.241877	+	0.969866i
$364$	10.8431	+	12.9223i	0.568333	+	0.677312i
$365$	−26.0881	−	4.60003i	−1.36551	−	0.240777i
$366$	5.73476	+	5.53866i	0.299761	+	0.289510i
$367$	8.48054	+	7.11602i	0.442681	+	0.371453i	0.836711	−	0.547644i	$-0.184475\pi$
$367$	8.48054	+	7.11602i	0.442681	+	0.371453i	−0.394031	+	0.919097i	$0.628920\pi$
$368$	−4.26153	−	2.46039i	−0.222148	−	0.128257i
$369$	31.9060	−	6.77782i	1.66096	−	0.352839i
$370$	61.7705	−	22.4826i	3.21130	−	1.16882i
$371$	−2.49653	+	14.1585i	−0.129613	+	0.735073i
$372$	−6.47439	+	14.5394i	−0.335682	+	0.753831i
$373$		−	31.3106i		−	1.62120i	−0.585599	−	0.810601i	$-0.699141\pi$
$373$		−	31.3106i		−	1.62120i	0.585599	−	0.810601i	$-0.300859\pi$
$374$	1.06819	−	0.388788i	0.0552347	−	0.0201038i
$375$	4.82449	+	16.8288i	0.249136	+	0.869037i
$376$	−0.923196	−	2.53646i	−0.0476102	−	0.130808i
$377$	−15.7954	+	2.78516i	−0.813506	+	0.143443i
$378$	−18.4400	+	9.80043i	−0.948450	+	0.504080i
$379$		−	27.4978i		−	1.41247i	−0.707979	−	0.706234i	$-0.750393\pi$
$379$		−	27.4978i		−	1.41247i	0.707979	−	0.706234i	$-0.249607\pi$
$380$	−30.4385	−	46.7990i	−1.56146	−	2.40074i
$381$	−0.785834	+	1.76473i	−0.0402595	+	0.0904097i
$382$	−44.7743	+	7.89492i	−2.29085	+	0.403939i
$383$	−14.5449	+	12.2046i	−0.743211	+	0.623628i	−0.933698	−	0.358062i	$-0.883438\pi$
$383$	−14.5449	+	12.2046i	−0.743211	+	0.623628i	0.190487	+	0.981690i	$0.438993\pi$
$384$	−35.4734	−	2.48269i	−1.81024	−	0.126694i
$385$	0.0725740	+	0.411587i	0.00369871	+	0.0209764i
$386$	32.1965	+	5.67711i	1.63876	+	0.288957i
$387$	3.65288	−	11.2378i	0.185686	−	0.571250i
$388$	11.7939	−	6.80922i	0.598745	−	0.345686i
$389$	−27.3570	−	4.82378i	−1.38706	−	0.244575i	−0.570242	−	0.821477i	$-0.693150\pi$
$389$	−27.3570	−	4.82378i	−1.38706	−	0.244575i	−0.816813	+	0.576902i	$0.804262\pi$
$390$	17.7917	+	36.4840i	0.900919	+	1.84744i
$391$	10.5352	−	18.2475i	0.532788	−	0.922815i
$392$	15.2796			0.771736
$393$	−0.00134981	+	0.0192865i	−6.80890e−5	+	0.000972876i
$394$	−27.2073	+	4.79738i	−1.37068	+	0.241688i
$395$	29.4147	+	24.6818i	1.48001	+	1.24188i
$396$	0.579826	+	0.453122i	0.0291374	+	0.0227703i
$397$	15.9016	+	5.78772i	0.798080	+	0.290477i	0.708690	−	0.705520i	$-0.249286\pi$
$397$	15.9016	+	5.78772i	0.798080	+	0.290477i	0.0893892	+	0.995997i	$0.471509\pi$
$398$	6.36807	−	11.0298i	0.319203	−	0.552875i
$399$	12.6140	+	2.44349i	0.631490	+	0.122327i
$400$	6.41140	+	11.1049i	0.320570	+	0.555243i
$401$	−0.579010	−	3.28373i	−0.0289144	−	0.163982i	0.966932	−	0.255036i	$-0.0820874\pi$
$401$	−0.579010	−	3.28373i	−0.0289144	−	0.163982i	−0.995846	+	0.0910545i	$0.970976\pi$
$402$	31.9608	+	7.97076i	1.59406	+	0.397545i
$403$	−6.69064	+	2.43519i	−0.333284	+	0.121306i
$404$	13.2705	+	15.8152i	0.660233	+	0.786835i
$405$	−31.2724	+	7.78909i	−1.55394	+	0.387043i
$406$	11.6294	−	20.1428i	0.577159	−	0.999669i
$407$	0.533123			0.0264259
$408$	−3.16018	+	45.1536i	−0.156452	+	2.23544i
$409$	14.4682	−	17.2425i	0.715405	−	0.852587i	−0.278771	−	0.960358i	$-0.589927\pi$
$409$	14.4682	−	17.2425i	0.715405	−	0.852587i	0.994176	+	0.107771i	$0.0343714\pi$
$410$	79.6237	+	45.9708i	3.93233	+	2.27033i
$411$	5.61982	−	0.590324i	0.277205	−	0.0291186i
$412$	−24.8292	+	29.5903i	−1.22325	+	1.45781i
$413$	14.5310	−	12.1930i	0.715024	−	0.599977i
$414$	21.2545	−	0.739662i	1.04460	−	0.0363524i
$415$	−0.217218	−	1.23190i	−0.0106628	−	0.0604718i
$416$	−6.36961	−	7.59100i	−0.312296	−	0.372179i
$417$	1.54596	+	14.7173i	0.0757059	+	0.720711i
$418$	−0.159287	−	0.687741i	−0.00779100	−	0.0336385i
$419$	6.84253	−	3.95053i	0.334279	−	0.192996i	−0.323460	−	0.946242i	$-0.604846\pi$
$419$	6.84253	−	3.95053i	0.334279	−	0.192996i	0.657739	+	0.753246i	$0.271513\pi$
$420$	−36.6302	−	9.13528i	−1.78737	−	0.445756i
$421$	−0.951687	+	2.61474i	−0.0463824	+	0.127435i	−0.960721	−	0.277516i	$-0.910489\pi$
$421$	−0.951687	+	2.61474i	−0.0463824	+	0.127435i	0.914339	+	0.404950i	$0.132711\pi$
$422$	2.14537	−	2.55675i	0.104435	−	0.124461i
$423$	1.71368	+	1.33920i	0.0833218	+	0.0651143i
$424$	−5.46195	+	30.9762i	−0.265256	+	1.50434i
$425$	−47.5501	+	27.4530i	−2.30652	+	1.33167i
$426$	−24.0089	−	10.6912i	−1.16323	−	0.517989i
$427$	−2.54113	−	2.13226i	−0.122974	−	0.103187i
$428$	−32.8400	−	27.5561i	−1.58738	−	1.33197i
$429$	0.0343912	+	0.327400i	0.00166042	+	0.0158070i
$430$	28.8455	−	16.6539i	1.39105	−	0.803124i
$431$	2.52762	−	14.3348i	0.121751	−	0.690485i	−0.861434	−	0.507870i	$-0.830433\pi$
$431$	2.52762	−	14.3348i	0.121751	−	0.690485i	0.983185	−	0.182614i	$-0.0584560\pi$
$432$	−7.52121	+	3.99736i	−0.361865	+	0.192323i
$433$	−21.0433	+	25.0784i	−1.01128	+	1.20519i	−0.0326658	+	0.999466i	$0.510400\pi$
$433$	−21.0433	+	25.0784i	−1.01128	+	1.20519i	−0.978610	+	0.205725i	$0.934045\pi$
$434$	3.53136	−	9.70232i	0.169511	−	0.465726i
$435$	24.9364	−	25.8193i	1.19561	−	1.23794i
$436$	8.06926	−	4.65879i	0.386448	−	0.223116i
$437$	−10.4559	−	7.86754i	−0.500173	−	0.376356i
$438$	24.4809	−	17.7841i	1.16974	−	0.849759i
$439$	−1.20863	−	1.44038i	−0.0576845	−	0.0687458i	0.736431	−	0.676513i	$-0.236510\pi$
$439$	−1.20863	−	1.44038i	−0.0576845	−	0.0687458i	−0.794115	+	0.607767i	$0.792065\pi$
$440$	0.158779	+	0.900479i	0.00756948	+	0.0429287i
$441$	−10.4414	+	6.52279i	−0.497211	+	0.310609i
$442$	−35.1886	+	29.5267i	−1.67375	+	1.40444i
$443$	12.5216	−	14.9226i	0.594917	−	0.708994i	−0.381626	−	0.924317i	$-0.624636\pi$
$443$	12.5216	−	14.9226i	0.594917	−	0.708994i	0.976543	+	0.215322i	$0.0690802\pi$
$444$	−19.5898	+	43.9923i	−0.929691	+	2.08778i
$445$	−15.7484	−	9.09234i	−0.746545	−	0.431018i
$446$	−11.8753	+	14.1524i	−0.562310	+	0.670134i
$447$	−1.45407	+	0.709089i	−0.0687751	+	0.0335387i
$448$	19.9491			0.942507
$449$	−1.89892	+	3.28902i	−0.0896154	+	0.155218i	−0.907349	−	0.420379i	$-0.861897\pi$
$449$	−1.89892	+	3.28902i	−0.0896154	+	0.155218i	0.817733	+	0.575597i	$0.195230\pi$
$450$	−48.9293	−	26.0237i	−2.30655	−	1.22677i
$451$	0.479304	+	0.571212i	0.0225695	+	0.0268973i
$452$	66.4937	−	24.2017i	3.12760	−	1.13835i
$453$	15.0948	−	15.6293i	0.709216	−	0.734326i
$454$	10.9903	+	62.3293i	0.515802	+	2.92526i
$455$	−8.44436	−	14.6261i	−0.395878	−	0.685680i
$456$	27.5971	+	5.34591i	1.29235	+	0.250345i
$457$	6.13044	−	10.6182i	0.286770	−	0.496700i	−0.686267	−	0.727350i	$-0.740752\pi$
$457$	6.13044	−	10.6182i	0.286770	−	0.496700i	0.973037	+	0.230650i	$0.0740851\pi$
$458$	−17.9418	−	6.53027i	−0.838363	−	0.305139i
$459$	−17.1163	−	32.2052i	−0.798922	−	1.50321i
$460$	29.4528	+	24.7138i	1.37324	+	1.15229i
$461$	−30.9667	+	5.46026i	−1.44226	+	0.254310i	−0.839390	−	0.543529i	$-0.817088\pi$
$461$	−30.9667	+	5.46026i	−1.44226	+	0.254310i	−0.602871	+	0.797839i	$0.705977\pi$
$462$	−0.395755	−	0.266975i	−0.0184122	−	0.0124208i
$463$	18.1595			0.843941			0.421971	−	0.906609i	$-0.361339\pi$
$463$	18.1595			0.843941			0.421971	+	0.906609i	$0.361339\pi$
$464$	4.74336	−	8.21574i	0.220205	−	0.381406i
$465$	8.91124	−	13.2097i	0.413249	−	0.612587i
$466$	−19.4975	−	3.43794i	−0.903206	−	0.159260i
$467$	−33.3722	+	19.2674i	−1.54428	+	0.891591i	−0.545719	+	0.837968i	$0.683744\pi$
$467$	−33.3722	+	19.2674i	−1.54428	+	0.891591i	−0.998561	+	0.0536229i	$0.982923\pi$
$468$	−28.2802	−	9.19255i	−1.30725	−	0.424926i
$469$	−13.4970	−	2.37989i	−0.623234	−	0.109893i
$470$	1.06454	+	6.03731i	0.0491036	+	0.278480i
$471$	11.2908	−	16.7371i	0.520250	−	0.771203i
$472$	31.7912	−	26.6760i	1.46331	−	1.22786i
$473$	0.266030	−	0.0469082i	0.0122321	−	0.00215684i
$474$	−43.6201	+	4.58200i	−2.00354	+	0.210458i
$475$	13.3453	+	31.3781i	0.612323	+	1.43972i
$476$		−	42.7228i		−	1.95820i
$477$	−9.49115	−	23.4996i	−0.434570	−	1.07597i
$478$	46.4109	−	8.18350i	2.12279	−	0.374304i
$479$	6.27057	+	17.2282i	0.286510	+	0.787179i	0.996548	+	0.0830160i	$0.0264553\pi$
$479$	6.27057	+	17.2282i	0.286510	+	0.787179i	−0.710039	+	0.704163i	$0.751323\pi$
$480$	21.5178	+	5.36638i	0.982151	+	0.244940i
$481$	−20.2441	+	7.36826i	−0.923052	+	0.335964i
$482$			15.8597i			0.722388i
$483$	−8.80030	+	0.924413i	−0.400428	+	0.0420623i
$484$	6.82897	−	38.7290i	0.310408	−	1.76041i
$485$	−12.8122	+	4.66326i	−0.581772	+	0.211748i
$486$	18.4156	−	31.8747i	0.835350	−	1.44586i
$487$	−4.94599	−	2.85557i	−0.224124	−	0.129398i	0.383734	−	0.923444i	$-0.374638\pi$
$487$	−4.94599	−	2.85557i	−0.224124	−	0.129398i	−0.607859	+	0.794045i	$0.707971\pi$
$488$	−5.55953	−	4.66500i	−0.251668	−	0.211175i
$489$	−29.4856	+	8.45294i	−1.33339	+	0.382255i
$490$	−34.1754	−	6.02604i	−1.54389	−	0.272229i
$491$	1.35643	+	1.61653i	0.0612149	+	0.0729531i	0.795783	−	0.605582i	$-0.207060\pi$
$491$	1.35643	+	1.61653i	0.0612149	+	0.0729531i	−0.734568	+	0.678535i	$0.762615\pi$
$492$	−64.7476	+	18.5618i	−2.91905	+	0.836833i
$493$	35.1791	+	20.3106i	1.58439	+	0.914746i
$494$	15.5538	+	23.9139i	0.699799	+	1.07594i
$495$	−0.492913	−	0.547568i	−0.0221548	−	0.0246113i
$496$	1.44035	−	3.95734i	0.0646738	−	0.177690i
$497$	10.2756	+	3.74000i	0.460922	+	0.167762i
$498$	1.18452	+	0.799070i	0.0530794	+	0.0358072i
$499$	−5.97530	−	2.17483i	−0.267491	−	0.0973587i	0.204793	−	0.978805i	$-0.434348\pi$
$499$	−5.97530	−	2.17483i	−0.267491	−	0.0973587i	−0.472284	+	0.881447i	$0.656570\pi$
$500$	−12.3644	−	33.9710i	−0.552954	−	1.51923i
$501$	1.80641	+	0.804395i	0.0807044	+	0.0359377i
$502$			55.4749i			2.47596i
$503$	0.199225	+	0.547365i	0.00888299	+	0.0244058i	0.944055	−	0.329788i	$-0.106977\pi$
$503$	0.199225	+	0.547365i	0.00888299	+	0.0244058i	−0.935172	+	0.354194i	$0.884755\pi$
$504$	16.1218	−	10.0713i	0.718124	−	0.448614i
$505$	−10.3348	−	17.9004i	−0.459892	−	0.796556i
$506$	0.243092	+	0.421047i	0.0108067	+	0.0187178i
$507$	4.03853	+	8.28149i	0.179358	+	0.367794i
$508$	1.36436	−	3.74854i	0.0605336	−	0.166315i
$509$	2.67718	−	15.1830i	0.118664	−	0.672976i	−0.866207	−	0.499686i	$-0.833449\pi$
$509$	2.67718	−	15.1830i	0.118664	−	0.672976i	0.984871	−	0.173291i	$-0.0554400\pi$
$510$	24.8762	−	99.7473i	1.10154	−	4.41689i
$511$	−9.64430	+	8.09253i	−0.426639	+	0.357992i
$512$	18.0675			0.798477
$513$	−21.1409	+	8.12792i	−0.933393	+	0.358857i
$514$	−19.1053			−0.842700
$515$	29.6251	−	24.8584i	1.30544	−	1.09539i
$516$	−5.90459	+	23.6759i	−0.259935	+	1.04228i
$517$	−0.00863364	+	0.0489638i	−0.000379707	+	0.00215343i
$518$	10.6850	−	29.3567i	0.469470	−	1.28986i
$519$	0.677053	+	1.38838i	0.0297193	+	0.0609430i
$520$	−18.4747	−	31.9992i	−0.810170	−	1.40326i
$521$	−9.57944	−	16.5921i	−0.419683	−	0.726912i	0.576225	−	0.817291i	$-0.304525\pi$
$521$	−9.57944	−	16.5921i	−0.419683	−	0.726912i	−0.995907	+	0.0903794i	$0.971192\pi$
$522$	1.42598	+	40.9763i	0.0624136	+	1.79348i
$523$	−3.22775	−	8.86817i	−0.141140	−	0.387778i	0.848902	−	0.528550i	$-0.177264\pi$
$523$	−3.22775	−	8.86817i	−0.141140	−	0.387778i	−0.990042	+	0.140771i	$0.955042\pi$
$524$		−	0.0399238i		−	0.00174408i
$525$	21.0643	+	9.37995i	0.919321	+	0.409374i
$526$	−14.7312	−	40.4738i	−0.642313	−	1.76474i
$527$	16.9450	+	6.16747i	0.738135	+	0.268659i
$528$	−0.161419	−	0.108892i	−0.00702485	−	0.00473894i
$529$	−13.1446	−	4.78425i	−0.571505	−	0.208011i
$530$	24.4331	−	67.1295i	1.06131	−	2.91592i
$531$	−10.3369	+	31.8008i	−0.448585	+	1.38004i
$532$	−26.3365	−	3.21489i	−1.14183	−	0.139383i
$533$	−26.0951	−	15.0660i	−1.13031	−	0.652583i
$534$	19.9670	−	5.72416i	0.864058	−	0.247708i
$535$	27.5885	+	32.8787i	1.19275	+	1.42147i
$536$	−29.5290	−	5.20677i	−1.27546	−	0.224898i
$537$	−24.6489	+	7.06635i	−1.06368	+	0.304935i
$538$	19.8345	+	16.6431i	0.855125	+	0.717535i
$539$	−0.243738	−	0.140722i	−0.0104986	−	0.00606135i
$540$	63.2966	−	20.5537i	2.72385	−	0.884489i
$541$	25.2382	−	9.18594i	1.08507	−	0.394934i	0.263280	−	0.964720i	$-0.415196\pi$
$541$	25.2382	−	9.18594i	1.08507	−	0.394934i	0.821794	+	0.569785i	$0.192974\pi$
$542$	−4.08708	+	23.1790i	−0.175555	+	0.995622i
$543$	−10.7960	+	1.13405i	−0.463300	+	0.0486666i
$544$			25.0968i			1.07602i
$545$	−8.76597	+	3.19055i	−0.375493	+	0.136668i
$546$	18.7177	+	4.66805i	0.801045	+	0.199774i
$547$	−3.74695	−	10.2947i	−0.160208	−	0.440168i	0.833452	−	0.552591i	$-0.186361\pi$
$547$	−3.74695	−	10.2947i	−0.160208	−	0.440168i	−0.993660	+	0.112423i	$0.964139\pi$
$548$	−11.4914	+	2.02625i	−0.490889	+	0.0865570i
$549$	5.79062	+	0.814529i	0.247138	+	0.0347633i
$550$		−	1.26692i		−	0.0540215i
$551$	15.1677	−	20.1578i	0.646167	−	0.858750i
$552$	−19.2535	+	2.02245i	−0.819482	+	0.0860812i
$553$	17.9716	−	3.16888i	0.764231	−	0.134755i
$554$	10.2338	−	8.58720i	0.434794	−	0.364835i
$555$	26.9631	−	39.9692i	1.14452	−	1.69660i
$556$	−5.30639	−	30.0940i	−0.225041	−	1.27627i
$557$	−17.4664	−	3.07981i	−0.740077	−	0.130496i	−0.209115	−	0.977891i	$-0.567058\pi$
$557$	−17.4664	−	3.07981i	−0.740077	−	0.130496i	−0.530962	+	0.847396i	$0.678169\pi$
$558$	3.78207	+	17.8038i	0.160108	+	0.753694i
$559$	−9.45355	+	5.45801i	−0.399843	+	0.230849i
$560$	9.83748	+	1.73461i	0.415710	+	0.0733008i
$561$	0.466268	−	0.691181i	0.0196858	−	0.0291817i
$562$	−10.0584	+	17.4217i	−0.424288	+	0.734888i
$563$	−19.1862			−0.808602			−0.404301	−	0.914626i	$-0.632485\pi$
$563$	−19.1862			−0.808602			−0.404301	+	0.914626i	$0.632485\pi$
$564$	−3.72316	−	2.51163i	−0.156773	−	0.105759i
$565$	−69.7681	+	12.3020i	−2.93517	+	0.517549i
$566$	−29.7104	−	24.9300i	−1.24882	−	1.04788i
$567$	−6.71759	+	13.7647i	−0.282112	+	0.578062i
$568$	22.4811	+	8.18244i	0.943285	+	0.343327i
$569$	4.66952	−	8.08785i	0.195757	−	0.339060i	−0.751392	−	0.659856i	$-0.770617\pi$
$569$	4.66952	−	8.08785i	0.195757	−	0.339060i	0.947148	+	0.320796i	$0.103950\pi$
$570$	−59.6173	−	22.8409i	−2.49709	−	0.956701i
$571$	−15.2479	−	26.4101i	−0.638105	−	1.10523i	−0.985848	−	0.167640i	$-0.946385\pi$
$571$	−15.2479	−	26.4101i	−0.638105	−	1.10523i	0.347743	−	0.937590i	$-0.386948\pi$
$572$	−0.118045	−	0.669469i	−0.00493573	−	0.0279919i
$573$	−23.1659	+	23.9861i	−0.967769	+	1.00203i
$574$	41.0604	−	14.9448i	1.71383	−	0.623782i
$575$	−15.0948	−	17.9892i	−0.629495	−	0.750203i
$576$	−29.8252	+	18.6319i	−1.24272	+	0.776328i
$577$	9.96919	−	17.2671i	0.415023	−	0.718841i	−0.580408	−	0.814326i	$-0.697107\pi$
$577$	9.96919	−	17.2671i	0.415023	−	0.718841i	0.995431	+	0.0954852i	$0.0304403\pi$
$578$	76.1925			3.16919
$579$	21.5528	−	10.5104i	0.895704	−	0.436797i
$580$	−47.6454	+	56.7816i	−1.97837	+	2.35773i
$581$	−0.514851	−	0.297249i	−0.0213596	−	0.0123320i
$582$	6.33533	−	14.2271i	0.262608	−	0.589731i
$583$	0.372414	−	0.443826i	0.0154238	−	0.0183814i
$584$	−21.1000	+	17.7050i	−0.873124	+	0.732638i
$585$	26.2852	+	13.9801i	1.08676	+	0.578007i
$586$	9.59833	+	54.4348i	0.396503	+	2.24868i
$587$	−28.1528	−	33.5512i	−1.16199	−	1.38481i	−0.908716	−	0.417414i	$-0.862936\pi$
$587$	−28.1528	−	33.5512i	−1.16199	−	1.38481i	−0.253276	−	0.967394i	$-0.581508\pi$
$588$	20.5684	−	14.9419i	0.848228	−	0.616196i
$589$	5.07705	−	9.98163i	0.209196	−	0.411286i
$590$	−81.6270	+	47.1274i	−3.36053	+	1.94020i
$591$	−14.0769	+	14.5752i	−0.579044	+	0.599546i
$592$	4.35814	−	11.9739i	0.179118	−	0.492123i
$593$	21.7722	−	25.9471i	0.894077	−	1.06552i	−0.103408	−	0.994639i	$-0.532975\pi$
$593$	21.7722	−	25.9471i	0.894077	−	1.06552i	0.997485	−	0.0708804i	$-0.0225809\pi$
$594$	0.841025	+	0.0295213i	0.0345077	+	0.00121127i
$595$	−7.42746	+	42.1232i	−0.304496	+	1.72688i
$596$	2.89308	−	1.67032i	0.118505	−	0.0684190i
$597$	−0.975882	−	9.29027i	−0.0399402	−	0.380226i
$598$	−15.0501	−	12.6285i	−0.615445	−	0.516420i
$599$	23.5890	+	19.7935i	0.963820	+	0.808741i	0.981570	−	0.191101i	$-0.0612059\pi$
$599$	23.5890	+	19.7935i	0.963820	+	0.808741i	−0.0177500	+	0.999842i	$0.505650\pi$
$600$	46.0849	+	20.5216i	1.88141	+	0.837792i
$601$	12.5543	−	7.24824i	0.512101	−	0.295662i	−0.221596	−	0.975139i	$-0.571127\pi$
$601$	12.5543	−	7.24824i	0.512101	−	0.295662i	0.733697	+	0.679477i	$0.237793\pi$
$602$	2.74880	−	15.5892i	0.112033	−	0.635369i
$603$	22.4017	−	9.04772i	0.912266	−	0.368452i
$604$	−28.8413	+	34.3717i	−1.17353	+	1.39856i
$605$	−13.4663	+	36.9983i	−0.547482	+	1.50419i
$606$	22.9080	+	5.71308i	0.930575	+	0.232078i
$607$	−10.7115	+	6.18431i	−0.434768	+	0.251013i	−0.701376	−	0.712792i	$-0.747430\pi$
$607$	−10.7115	+	6.18431i	−0.434768	+	0.251013i	0.266608	+	0.963805i	$0.414097\pi$
$608$	15.4709	+	1.88854i	0.627429	+	0.0765903i
$609$	−1.78216	−	16.9660i	−0.0722169	−	0.687496i
$610$	10.5950	+	12.6267i	0.428980	+	0.511238i
$611$	−0.348883	−	1.97861i	−0.0141143	−	0.0800461i
$612$	39.9018	+	63.8733i	1.61293	+	2.58193i
$613$	28.4226	−	23.8494i	1.14798	−	0.963268i	0.148308	−	0.988941i	$-0.452617\pi$
$613$	28.4226	−	23.8494i	1.14798	−	0.963268i	0.999670	+	0.0256733i	$0.00817296\pi$
$614$	−1.10741	+	1.31976i	−0.0446913	+	0.0532611i
$615$	67.0660	−	7.04483i	2.70436	−	0.284075i
$616$	0.376338	+	0.217279i	0.0151631	+	0.00875442i
$617$	−19.6829	+	23.4572i	−0.792404	+	0.944350i	−0.999422	−	0.0339871i	$-0.989179\pi$
$617$	−19.6829	+	23.4572i	−0.792404	+	0.944350i	0.207019	+	0.978337i	$0.433624\pi$
$618$	−3.08406	+	44.0660i	−0.124059	+	1.77259i
$619$	22.8389			0.917974			0.458987	−	0.888443i	$-0.348212\pi$
$619$	22.8389			0.917974			0.458987	+	0.888443i	$0.348212\pi$
$620$	−16.4522	+	28.4961i	−0.660738	+	1.14443i
$621$	12.2936	−	9.60127i	0.493327	−	0.385286i
$622$	−6.07673	−	7.24196i	−0.243654	−	0.290376i
$623$	−8.12114	+	2.95585i	−0.325367	+	0.118424i
$624$	7.63451	+	1.90398i	0.305625	+	0.0762204i
$625$	−0.506966	−	2.87515i	−0.0202787	−	0.115006i
$626$	−2.99823	−	5.19308i	−0.119833	−	0.207557i
$627$	−0.390992	−	0.339442i	−0.0156147	−	0.0135560i
$628$	−20.8454	+	36.1053i	−0.831821	+	1.44076i
$629$	51.2711	+	18.6611i	2.04431	+	0.744069i
$630$	−40.0312	+	16.1680i	−1.59488	+	0.644150i
$631$	19.6728	+	16.5075i	0.783164	+	0.657152i	0.944043	−	0.329822i	$-0.106989\pi$
$631$	19.6728	+	16.5075i	0.783164	+	0.657152i	−0.160880	+	0.986974i	$0.551433\pi$
$632$	39.3187	−	6.93294i	1.56401	−	0.275778i
$633$	0.170910	−	2.44201i	0.00679305	−	0.0970612i
$634$	−75.6295			−3.00363
$635$	−1.99690	+	3.45874i	−0.0792447	+	0.137256i
$636$	22.9392	+	47.0395i	0.909599	+	1.86524i
$637$	11.2003	+	1.97492i	0.443773	+	0.0782492i
$638$	−0.811731	+	0.468653i	−0.0321367	+	0.0185542i
$639$	−18.8557	+	4.00552i	−0.745919	+	0.158456i
$640$	−72.4008	−	12.7662i	−2.86189	−	0.504629i
$641$	−0.122614	−	0.695380i	−0.00484297	−	0.0274658i	0.982291	−	0.187364i	$-0.0599945\pi$
$641$	−0.122614	−	0.695380i	−0.00484297	−	0.0274658i	−0.987133	+	0.159898i	$0.948883\pi$
$642$	−48.9056	−	3.42277i	−1.93015	−	0.135086i
$643$	34.0799	−	28.5965i	1.34398	−	1.12773i	0.363397	−	0.931634i	$-0.381617\pi$
$643$	34.0799	−	28.5965i	1.34398	−	1.12773i	0.980584	−	0.196100i	$-0.0628276\pi$
$644$	17.9949	−	3.17299i	0.709098	−	0.125033i
$645$	9.93785	−	22.3172i	0.391302	−	0.878737i
$646$	8.75444	−	71.7165i	0.344439	−	2.82165i
$647$			9.57031i			0.376248i	0.982145	+	0.188124i	$0.0602407\pi$
$647$			9.57031i			0.376248i	−0.982145	+	0.188124i	$0.939759\pi$
$648$	−14.6969	+	30.1146i	−0.577347	+	1.18301i
$649$	−0.752812	+	0.132741i	−0.0295504	+	0.00521054i
$650$	17.5100	+	48.1083i	0.686798	+	1.88696i
$651$	−2.08694	−	7.27968i	−0.0817937	−	0.285313i
$652$	59.5202	−	21.6636i	2.33099	−	0.848411i
$653$		−	26.2999i		−	1.02919i	−0.857432	−	0.514597i	$-0.827942\pi$
$653$		−	26.2999i		−	1.02919i	0.857432	−	0.514597i	$-0.172058\pi$
$654$	4.33456	−	9.73400i	0.169495	−	0.380630i
$655$	−0.00694086	+	0.0393636i	−0.000271202	+	0.00153806i
$656$	16.7475	−	6.09560i	0.653881	−	0.237993i
$657$	6.86067	−	21.1063i	0.267660	−	0.823436i
$658$	2.52318	+	1.45676i	0.0983638	+	0.0567904i
$659$	17.1070	+	14.3545i	0.666394	+	0.559171i	0.911996	−	0.410200i	$-0.134541\pi$
$659$	17.1070	+	14.3545i	0.666394	+	0.559171i	−0.245602	+	0.969371i	$0.578986\pi$
$660$	1.09432	+	1.05690i	0.0425963	+	0.0411397i
$661$	−8.11331	−	1.43060i	−0.315571	−	0.0556437i	0.0136193	−	0.999907i	$-0.495665\pi$
$661$	−8.11331	−	1.43060i	−0.315571	−	0.0556437i	−0.329190	+	0.944264i	$0.606776\pi$
$662$	−39.0107	−	46.4911i	−1.51619	−	1.80693i
$663$	−8.15269	+	32.6903i	−0.316624	+	1.26959i
$664$	−1.12640	−	0.650328i	−0.0437128	−	0.0252376i
$665$	25.4080	+	7.74844i	0.985278	+	0.300471i
$666$	11.4436	+	53.8696i	0.443429	+	2.08740i
$667$	−5.94215	+	16.3259i	−0.230081	+	0.632143i
$668$	−3.83708	−	1.39658i	−0.148461	−	0.0540354i
$669$	−0.946035	+	13.5172i	−0.0365758	+	0.522606i
$670$	63.9932	+	23.2916i	2.47227	+	0.899833i
$671$	0.0457212	+	0.125618i	0.00176505	+	0.00484943i
$672$	8.52714	−	6.19455i	0.328942	−	0.238960i
$673$		−	21.7657i		−	0.839008i	−0.907754	−	0.419504i	$-0.862204\pi$
$673$		−	21.7657i		−	0.839008i	0.907754	−	0.419504i	$-0.137796\pi$
$674$	−11.1154	−	30.5394i	−0.428150	−	1.17633i
$675$	−40.2531	+	5.64979i	−1.54934	+	0.217460i
$676$	−9.51312	−	16.4772i	−0.365889	−	0.633738i
$677$	−17.5825	−	30.4538i	−0.675751	−	1.17043i	−0.976249	−	0.216652i	$-0.930486\pi$
$677$	−17.5825	−	30.4538i	−0.675751	−	1.17043i	0.300498	−	0.953782i	$-0.402847\pi$
$678$	45.2548	−	67.0843i	1.73800	−	2.57636i
$679$	−2.21623	+	6.08905i	−0.0850512	+	0.233676i
$680$	−16.2499	+	92.1580i	−0.623157	+	3.53410i
$681$	33.3905	+	32.2487i	1.27953	+	1.23577i
$682$	−0.318740	+	0.267455i	−0.0122052	+	0.0102414i
$683$	−14.9200			−0.570898			−0.285449	−	0.958394i	$-0.592143\pi$
$683$	−14.9200			−0.570898			−0.285449	+	0.958394i	$0.592143\pi$
$684$	42.3773	−	19.7910i	1.62034	−	0.756727i
$685$	11.6824			0.446363
$686$	−34.1843	+	28.6841i	−1.30516	+	1.09516i
$687$	−13.4618	+	3.85922i	−0.513598	+	0.147238i
$688$	1.12117	−	6.35846i	0.0427441	−	0.242414i
$689$	−8.00749	+	22.0004i	−0.305061	+	0.838149i
$690$	43.8612	+	3.06973i	1.66977	+	0.116863i
$691$	18.1022	+	31.3539i	0.688640	+	1.19276i	0.972278	+	0.233828i	$0.0751253\pi$
$691$	18.1022	+	31.3539i	0.688640	+	1.19276i	−0.283638	+	0.958931i	$0.591541\pi$
$692$	−1.59486	−	2.76237i	−0.0606274	−	0.105010i
$693$	−0.349929	+	0.0121776i	−0.0132927	+	0.000462590i
$694$	2.08406	+	5.72592i	0.0791100	+	0.217353i
$695$			30.5943i			1.16051i
$696$	−3.89905	−	37.1185i	−0.147793	−	1.40697i
$697$	26.1008	+	71.7115i	0.988640	+	2.71627i
$698$	−12.9391	−	4.70946i	−0.489753	−	0.178256i
$699$	−13.0519	+	6.36488i	−0.493670	+	0.240742i
$700$	−44.7437	−	16.2854i	−1.69115	−	0.615529i
$701$	−14.0704	+	38.6582i	−0.531433	+	1.46010i	0.325933	+	0.945393i	$0.394322\pi$
$701$	−14.0704	+	38.6582i	−0.531433	+	1.46010i	−0.857366	+	0.514707i	$0.827901\pi$
$702$	−32.3440	+	10.5028i	−1.22075	+	0.396401i
$703$	15.3618	−	30.2018i	0.579382	−	1.13908i
$704$	−0.696221	−	0.401963i	−0.0262398	−	0.0151496i
$705$	3.23426	+	3.12366i	0.121809	+	0.117644i
$706$	−23.6253	−	28.1555i	−0.889148	−	1.05965i
$707$	−9.67405	−	1.70580i	−0.363830	−	0.0641531i
$708$	16.7088	−	66.9983i	0.627956	−	2.51795i
$709$	−21.7969	−	18.2898i	−0.818600	−	0.686887i	0.134044	−	0.990975i	$-0.457204\pi$
$709$	−21.7969	−	18.2898i	−0.818600	−	0.686887i	−0.952644	+	0.304089i	$0.901648\pi$
$710$	−47.0556	−	27.1676i	−1.76597	−	1.01958i
$711$	−23.9091	+	21.5226i	−0.896661	+	0.807162i
$712$	−17.7676	+	6.46688i	−0.665869	+	0.242356i
$713$	−1.33926	+	7.59530i	−0.0501556	+	0.284446i
$714$	−28.7152	−	39.5281i	−1.07464	−	1.47930i
$715$			0.680596i			0.0254529i
$716$	49.7567	−	18.1099i	1.85949	−	0.676800i
$717$	24.0127	−	24.8629i	0.896770	−	0.928520i
$718$	8.52077	+	23.4106i	0.317992	+	0.873677i
$719$	12.7557	−	2.24917i	0.475706	−	0.0838798i	0.0693456	−	0.997593i	$-0.477909\pi$
$719$	12.7557	−	2.24917i	0.475706	−	0.0838798i	0.406360	+	0.913713i	$0.366798\pi$
$720$	−16.3278	+	6.59455i	−0.608499	+	0.245764i
$721$		−	18.3794i		−	0.684484i
$722$	−43.5509	−	10.7933i	−1.62080	−	0.401687i
$723$	6.83676	+	9.41118i	0.254262	+	0.350006i
$724$	22.0757	−	3.89253i	0.820436	−	0.144665i
$725$	34.6812	−	29.1010i	1.28803	−	1.08078i
$726$	−19.7126	−	40.4229i	−0.731602	−	1.50024i
$727$	0.223512	+	1.26760i	0.00828960	+	0.0470126i	0.988672	−	0.150092i	$-0.0479571\pi$
$727$	0.223512	+	1.26760i	0.00828960	+	0.0470126i	−0.980382	+	0.197105i	$0.936846\pi$
$728$	−17.2936	−	3.04933i	−0.640943	−	0.113016i
$729$	−2.81257	−	26.8531i	−0.104169	−	0.994560i
$730$	54.1762	−	31.2787i	2.00515	−	1.15768i
$731$	27.2264	+	4.80074i	1.00700	+	0.177562i
$732$	−12.0458	−	0.843053i	−0.445226	−	0.0311602i
$733$	22.0489	−	38.1898i	0.814395	−	1.41057i	−0.0953663	−	0.995442i	$-0.530402\pi$
$733$	22.0489	−	38.1898i	0.814395	−	1.41057i	0.909761	−	0.415131i	$-0.136264\pi$
$734$	−26.1431			−0.964959
$735$	−22.8775	+	11.1564i	−0.843849	+	0.411510i
$736$	−10.5708	+	1.86392i	−0.389646	+	0.0687050i
$737$	0.423091	+	0.355015i	0.0155847	+	0.0130772i
$738$	−47.4300	+	60.6926i	−1.74592	+	2.23412i
$739$	−38.0632	−	13.8539i	−1.40018	−	0.509623i	−0.471947	−	0.881627i	$-0.656449\pi$
$739$	−38.0632	−	13.8539i	−1.40018	−	0.509623i	−0.928231	+	0.372003i	$0.878671\pi$
$740$	−49.7802	+	86.2218i	−1.82996	+	3.16958i
$741$	19.5384	+	7.48567i	0.717762	+	0.274993i
$742$	−16.9755	−	29.4025i	−0.623191	−	1.07940i
$743$	7.14422	+	40.5169i	0.262096	+	1.48642i	0.777179	+	0.629279i	$0.216650\pi$
$743$	7.14422	+	40.5169i	0.262096	+	1.48642i	−0.515083	+	0.857140i	$0.672239\pi$
$744$	−4.56585	−	15.9266i	−0.167392	−	0.583899i
$745$	−3.14287	+	1.14391i	−0.115146	+	0.0419096i
$746$	47.5276	+	56.6412i	1.74011	+	2.07378i
$747$	1.04736	−	0.0364483i	0.0383208	−	0.00133357i
$748$	−0.860840	+	1.49102i	−0.0314754	+	0.0545170i
$749$	20.3979			0.745324
$750$	−34.2727	−	23.1202i	−1.25146	−	0.844232i
$751$	21.3166	−	25.4041i	0.777854	−	0.927010i	−0.220981	−	0.975278i	$-0.570926\pi$
$751$	21.3166	−	25.4041i	0.777854	−	0.927010i	0.998834	+	0.0482683i	$0.0153703\pi$
$752$	1.02914	+	0.594177i	0.0375290	+	0.0216674i
$753$	23.9140	+	32.9190i	0.871475	+	1.19963i
$754$	24.3464	−	29.0149i	0.886644	−	1.05666i
$755$	34.4121	−	28.8752i	1.25239	−	1.05088i
$756$	11.8534	−	29.3230i	0.431105	−	1.06647i
$757$	5.09501	+	28.8952i	0.185181	+	1.05021i	0.925722	+	0.378204i	$0.123458\pi$
$757$	5.09501	+	28.8952i	0.185181	+	1.05021i	−0.740541	+	0.672011i	$0.765431\pi$
$758$	41.7400	+	49.7438i	1.51607	+	1.80678i
$759$	0.325756	+	0.145059i	0.0118242	+	0.00526532i
$760$	55.5880	+	16.9522i	2.01639	+	0.614920i
$761$	26.0608	−	15.0462i	0.944704	−	0.545425i	0.0532721	−	0.998580i	$-0.483035\pi$
$761$	26.0608	−	15.0462i	0.944704	−	0.545425i	0.891432	+	0.453155i	$0.149702\pi$
$762$	−1.25717	−	4.38526i	−0.0455424	−	0.158861i
$763$	−1.51632	+	4.16606i	−0.0548945	+	0.150821i
$764$	44.2625	−	52.7500i	1.60136	−	1.90843i
$765$	−28.2373	−	69.9140i	−1.02092	−	2.52775i
$766$	7.78601	−	44.1566i	0.281320	−	1.59544i
$767$	26.7517	−	15.4451i	0.965948	−	0.557690i
$768$	35.0873	−	25.4892i	1.26610	−	0.919761i
$769$	−21.5219	−	18.0590i	−0.776098	−	0.651224i	0.166164	−	0.986098i	$-0.446862\pi$
$769$	−21.5219	−	18.0590i	−0.776098	−	0.651224i	−0.942263	+	0.334874i	$0.891306\pi$
$770$	−0.756052	−	0.634403i	−0.0272462	−	0.0228623i
$771$	−11.3372	+	8.23590i	−0.408298	+	0.296609i
$772$	−42.8824	+	24.7581i	−1.54337	+	0.891065i
$773$	1.25029	−	7.09077i	0.0449700	−	0.255037i	−0.954032	−	0.299705i	$-0.903112\pi$
$773$	1.25029	−	7.09077i	0.0449700	−	0.255037i	0.999002	+	0.0446676i	$0.0142229\pi$
$774$	10.4502	+	25.8742i	0.375625	+	0.930028i
$775$	12.9184	−	15.3956i	0.464043	−	0.553025i
$776$	−4.84872	+	13.3217i	−0.174059	+	0.478223i
$777$	−6.31454	−	22.0264i	−0.226533	−	0.790193i
$778$	56.8113	−	32.8000i	2.03678	−	1.17594i
$779$	46.1706	−	10.6936i	1.65423	−	0.383137i
$780$	−56.1616	−	25.0088i	−2.01091	−	0.895458i
$781$	−0.283257	−	0.337572i	−0.0101357	−	0.0120793i
$782$	8.64032	+	49.0017i	0.308977	+	1.75230i
$783$	18.5102	+	23.7007i	0.661499	+	0.846996i
$784$	−5.15311	+	4.32397i	−0.184040	+	0.154428i
$785$	26.8298	−	31.9746i	0.957598	−	1.14122i
$786$	−0.0268339	−	0.0369384i	−0.000957135	−	0.00131755i
$787$	−4.88523	−	2.82049i	−0.174140	−	0.100540i	0.410397	−	0.911907i	$-0.365390\pi$
$787$	−4.88523	−	2.82049i	−0.174140	−	0.100540i	−0.584536	+	0.811368i	$0.698724\pi$
$788$	26.8963	−	32.0537i	0.958140	−	1.14187i
$789$	−26.1889	−	17.6670i	−0.932351	−	0.628960i
$790$	−90.6771			−3.22614
$791$	−16.8345	+	29.1583i	−0.598567	+	1.03675i
$792$	−0.765582	+	0.0266424i	−0.0272038	+	0.000946698i
$793$	−3.47232	−	4.13814i	−0.123306	−	0.146950i
$794$	−37.5516	+	13.6677i	−1.33266	+	0.485048i
$795$	−14.4394	−	50.3674i	−0.512111	−	1.78635i
$796$	3.34965	+	18.9968i	0.118725	+	0.673323i
$797$	5.82703	+	10.0927i	0.206404	+	0.357502i	0.950579	−	0.310482i	$-0.100491\pi$
$797$	5.82703	+	10.0927i	0.206404	+	0.357502i	−0.744175	+	0.667985i	$0.767157\pi$
$798$	−26.5279	+	14.7270i	−0.939078	+	0.521330i
$799$	−2.54421	+	4.40670i	−0.0900077	+	0.155898i
$800$	26.2840	+	9.56658i	0.929279	+	0.338230i
$801$	9.38095	−	12.0041i	0.331460	−	0.424144i
$802$	6.03194	+	5.06140i	0.212995	+	0.178724i
$803$	0.499644	−	0.0881008i	0.0176321	−	0.00310901i
$804$	−44.8418	+	21.8675i	−1.58145	+	0.771207i
$805$	−18.2940			−0.644779
$806$	8.40696	−	14.5613i	0.296122	−	0.512899i
$807$	18.9443	+	1.32586i	0.666872	+	0.0466726i
$808$	−21.1651	−	3.73197i	−0.744585	−	0.131290i
$809$	−35.8631	+	20.7056i	−1.26088	+	0.727970i	−0.973245	−	0.229770i	$-0.926203\pi$
$809$	−35.8631	+	20.7056i	−1.26088	+	0.727970i	−0.287636	+	0.957740i	$0.592869\pi$
$810$	44.7488	−	61.5602i	1.57231	−	2.16301i
$811$	−33.4287	−	5.89438i	−1.17384	−	0.206980i	−0.447479	−	0.894294i	$-0.647678\pi$
$811$	−33.4287	−	5.89438i	−1.17384	−	0.206980i	−0.726360	+	0.687315i	$0.758789\pi$
$812$	6.11715	+	34.6921i	0.214670	+	1.21745i
$813$	7.56667	+	15.5163i	0.265375	+	0.544182i
$814$	−0.964425	+	0.809248i	−0.0338031	+	0.0283641i
$815$	−62.4512	+	11.0118i	−2.18757	+	0.385727i
$816$	−11.7122	−	16.1225i	−0.410010	−	0.564402i
$817$	5.00820	−	16.4224i	0.175215	−	0.574548i
$818$			53.1537i			1.85847i
$819$	13.1195	−	5.29877i	0.458431	−	0.185154i
$820$	−137.137	+	24.1809i	−4.78902	+	0.844434i
$821$	5.39189	+	14.8141i	0.188178	+	0.517016i	0.997525	−	0.0703158i	$-0.0224007\pi$
$821$	5.39189	+	14.8141i	0.188178	+	0.517016i	−0.809346	+	0.587332i	$0.800178\pi$
$822$	−9.27023	+	9.59845i	−0.323336	+	0.334784i
$823$	−24.3559	+	8.86482i	−0.848993	+	0.309008i	−0.729630	−	0.683842i	$-0.760308\pi$
$823$	−24.3559	+	8.86482i	−0.848993	+	0.309008i	−0.119364	+	0.992851i	$0.538085\pi$
$824$		−	40.2108i		−	1.40081i
$825$	−0.546140	−	0.751793i	−0.0190142	−	0.0261741i
$826$	−7.77856	+	44.1144i	−0.270651	+	1.53494i
$827$	7.92236	−	2.88350i	0.275487	−	0.100269i	−0.200582	−	0.979677i	$-0.564283\pi$
$827$	7.92236	−	2.88350i	0.275487	−	0.100269i	0.476069	+	0.879408i	$0.342061\pi$
$828$	−23.9401	+	21.5505i	−0.831974	+	0.748932i
$829$	23.0878	+	13.3297i	0.801871	+	0.462960i	0.844125	−	0.536146i	$-0.180121\pi$
$829$	23.0878	+	13.3297i	0.801871	+	0.462960i	−0.0422540	+	0.999107i	$0.513454\pi$
$830$	2.26291	+	1.89880i	0.0785466	+	0.0659084i
$831$	2.37103	−	9.50726i	0.0822502	−	0.329803i
$832$	31.9929	+	5.64122i	1.10916	+	0.195574i
$833$	−18.5149	−	22.0652i	−0.641502	−	0.764512i
$834$	−25.1367	−	24.2771i	−0.870412	−	0.840648i
$835$	3.54043	+	2.04407i	0.122522	+	0.0707379i
$836$	0.854360	+	0.642864i	0.0295487	+	0.0222339i
$837$	9.91912	+	8.93446i	0.342855	+	0.308820i
$838$	−6.38153	+	17.5331i	−0.220446	+	0.605671i
$839$	−28.8043	−	10.4839i	−0.994433	−	0.361944i	−0.206998	−	0.978341i	$-0.566369\pi$
$839$	−28.8043	−	10.4839i	−0.994433	−	0.361944i	−0.787435	+	0.616397i	$0.788592\pi$
$840$	35.3234	−	17.2257i	1.21877	−	0.594345i
$841$	−4.22345	−	1.53721i	−0.145636	−	0.0530073i
$842$	−2.24741	−	6.17470i	−0.0774507	−	0.212794i
$843$	1.54141	+	14.6740i	0.0530890	+	0.505400i
$844$			5.05506i			0.174002i
$845$	6.51501	+	17.8998i	0.224123	+	0.615773i
$846$	−5.13289	+	0.178626i	−0.176472	+	0.00614128i
$847$	9.35603	+	16.2051i	0.321477	+	0.556814i
$848$	−6.92390	−	11.9925i	−0.237768	−	0.411826i
$849$	−28.3770	−	1.98603i	−0.973896	−	0.0681604i
$850$	44.3465	−	121.841i	1.52107	−	4.17911i
$851$	−4.05224	+	22.9814i	−0.138909	+	0.787792i
$852$	38.2642	−	10.9696i	1.31091	−	0.375812i
$853$	−23.2450	+	19.5049i	−0.795895	+	0.667835i	−0.947197	−	0.320653i	$-0.896098\pi$
$853$	−23.2450	+	19.5049i	−0.795895	+	0.667835i	0.151302	+	0.988488i	$0.451653\pi$
$854$	7.83357			0.268059
$855$	−45.2233	+	12.1458i	−1.54661	+	0.415379i
$856$	44.6270			1.52532
$857$	−25.2851	+	21.2167i	−0.863722	+	0.724749i	−0.962766	−	0.270334i	$-0.912866\pi$
$857$	−25.2851	+	21.2167i	−0.863722	+	0.724749i	0.0990448	+	0.995083i	$0.468421\pi$
$858$	−0.559188	−	0.540066i	−0.0190903	−	0.0184376i
$859$	−0.135644	+	0.769277i	−0.00462812	+	0.0262474i	−0.987034	−	0.160509i	$-0.948686\pi$
$859$	−0.135644	+	0.769277i	−0.00462812	+	0.0262474i	0.982406	+	0.186756i	$0.0597975\pi$
$860$	−17.2540	+	47.4049i	−0.588356	+	1.61649i
$861$	17.9230	−	26.5685i	0.610815	−	0.905453i
$862$	17.1869	+	29.7686i	0.585389	+	1.01392i
$863$	−12.6819	−	21.9656i	−0.431695	−	0.747718i	0.565324	−	0.824869i	$-0.308751\pi$
$863$	−12.6819	−	21.9656i	−0.431695	−	0.747718i	−0.997019	+	0.0771505i	$0.975418\pi$
$864$	−6.96311	+	17.2253i	−0.236890	+	0.586018i
$865$	1.09223	+	3.00088i	0.0371369	+	0.102033i
$866$		−	77.3096i		−	2.62709i
$867$	45.2129	−	32.8449i	1.53551	−	1.11547i
$868$	5.34850	+	14.6949i	0.181540	+	0.498777i
$869$	−0.691058	−	0.251525i	−0.0234426	−	0.00853239i
$870$	−5.91809	+	84.5595i	−0.200642	+	2.86683i
$871$	−20.9725	−	7.63338i	−0.710628	−	0.258647i
$872$	−3.31744	+	9.11459i	−0.112343	+	0.308659i
$873$	−2.37358	−	11.1734i	−0.0803334	−	0.378163i
$874$	30.8573	−	1.63894i	1.04376	−	0.0554381i
$875$	14.8967	+	8.60060i	0.503599	+	0.290753i
$876$	−11.0897	+	44.4671i	−0.374687	+	1.50240i
$877$	0.474465	+	0.565445i	0.0160215	+	0.0190937i	0.773996	−	0.633191i	$-0.218255\pi$
$877$	0.474465	+	0.565445i	0.0160215	+	0.0190937i	−0.757974	+	0.652285i	$0.773811\pi$
$878$	4.37283	+	0.771048i	0.147576	+	0.0260216i
$879$	29.1613	+	28.1642i	0.983588	+	0.949954i
$880$	−0.308375	−	0.258758i	−0.0103953	−	0.00872272i
$881$	−13.3201	−	7.69035i	−0.448765	−	0.259095i	0.258544	−	0.966000i	$-0.416757\pi$
$881$	−13.3201	−	7.69035i	−0.448765	−	0.259095i	−0.707308	+	0.706905i	$0.750091\pi$
$882$	8.98747	−	27.6493i	0.302624	−	0.930999i
$883$	−40.2488	+	14.6494i	−1.35448	+	0.492990i	−0.914343	−	0.404940i	$-0.867292\pi$
$883$	−40.2488	+	14.6494i	−1.35448	+	0.492990i	−0.440137	+	0.897931i	$0.645070\pi$
$884$	12.0812	−	68.5157i	0.406333	−	2.30443i
$885$	−28.1222	+	63.1532i	−0.945316	+	2.12287i
$886$			46.0021i			1.54547i
$887$	23.9094	−	8.70231i	0.802799	−	0.292195i	0.0921532	−	0.995745i	$-0.470625\pi$
$887$	23.9094	−	8.70231i	0.802799	−	0.292195i	0.710646	+	0.703550i	$0.248403\pi$
$888$	−13.8151	−	48.1898i	−0.463603	−	1.61714i
$889$	0.649179	+	1.78360i	0.0217728	+	0.0598202i
$890$	42.2906	−	7.45698i	1.41759	−	0.249959i
$891$	0.511793	−	0.345030i	0.0171457	−	0.0115589i
$892$		−	27.9812i		−	0.936880i
$893$	2.52506	+	1.89998i	0.0844979	+	0.0635805i
$894$	1.55407	−	3.48994i	0.0519760	−	0.116721i
$895$	−52.2069	+	9.20548i	−1.74508	+	0.307705i
$896$	−26.7653	+	22.4587i	−0.894165	+	0.750294i
$897$	−14.3747	−	1.00605i	−0.479957	−	0.0335909i
$898$	−1.55738	−	8.83232i	−0.0519703	−	0.294738i
$899$	−14.6429	−	2.58193i	−0.488367	−	0.0861124i
$900$	82.1047	−	17.4416i	2.73682	−	0.581385i
$901$	51.3510	−	29.6475i	1.71075	−	0.987702i
$902$	−1.73413	−	0.305774i	−0.0577402	−	0.0101812i
$903$	−5.08902	−	10.4356i	−0.169352	−	0.347276i
$904$	−36.8309	+	63.7930i	−1.22498	+	2.12172i
$905$	−22.4426			−0.746017
$906$	−3.58241	+	51.1865i	−0.119017	+	1.70056i
$907$	15.4501	−	2.72428i	0.513013	−	0.0904581i	0.0888522	−	0.996045i	$-0.471680\pi$
$907$	15.4501	−	2.72428i	0.513013	−	0.0904581i	0.424161	+	0.905587i	$0.360569\pi$
$908$	−73.4321	−	61.6168i	−2.43693	−	2.04483i
$909$	16.0565	−	6.48500i	0.532560	−	0.215094i
$910$	37.4774	+	13.6407i	1.24236	+	0.452183i
$911$	−0.772381	+	1.33780i	−0.0255901	+	0.0443234i	−0.878537	−	0.477675i	$-0.841480\pi$
$911$	−0.772381	+	1.33780i	−0.0255901	+	0.0443234i	0.852947	+	0.521998i	$0.174813\pi$
$912$	−10.8201	+	6.00678i	−0.358289	+	0.198905i
$913$	0.0119788	+	0.0207479i	0.000396441	+	0.000686656i
$914$	5.02782	+	28.5142i	0.166305	+	0.943164i
$915$	11.7302	+	2.92542i	0.387788	+	0.0967113i
$916$	27.1741	−	9.89058i	0.897859	−	0.326794i
$917$	0.0122106	+	0.0145520i	0.000403229	+	0.000480549i
$918$	79.8491	+	32.2779i	2.63541	+	1.06533i
$919$	−9.28314	+	16.0789i	−0.306222	+	0.530393i	−0.977533	−	0.210784i	$-0.932398\pi$
$919$	−9.28314	+	16.0789i	−0.306222	+	0.530393i	0.671310	+	0.741176i	$0.265732\pi$
$920$	−40.0240			−1.31955
$921$	−0.0882209	+	1.26053i	−0.00290698	+	0.0415358i
$922$	47.7307	−	56.8832i	1.57193	−	1.87335i
$923$	15.4216	+	8.90366i	0.507608	+	0.293067i
$924$	0.719081	−	0.0755347i	0.0236560	−	0.00248491i
$925$	39.0877	−	46.5829i	1.28520	−	1.53164i
$926$	−32.8506	+	27.5650i	−1.07954	+	0.905841i
$927$	17.1658	+	27.4784i	0.563799	+	0.902509i
$928$	−3.59343	−	20.3793i	−0.117960	−	0.668984i
$929$	−4.09919	−	4.88523i	−0.134490	−	0.160279i	0.694596	−	0.719400i	$-0.255583\pi$
$929$	−4.09919	−	4.88523i	−0.134490	−	0.160279i	−0.829086	+	0.559121i	$0.811139\pi$
$930$	3.93107	+	37.4233i	0.128905	+	1.22716i
$931$	−14.9953	+	9.75308i	−0.491451	+	0.319644i
$932$	25.9687	−	14.9930i	0.850633	−	0.491113i
$933$	−6.72780	−	1.67786i	−0.220258	−	0.0549306i
$934$	31.1238	−	85.5120i	1.01840	−	2.79804i
$935$	1.10798	−	1.32044i	0.0362347	−	0.0431829i
$936$	28.7030	−	11.5928i	0.938188	−	0.378921i
$937$	−4.16870	+	23.6419i	−0.136186	+	0.772347i	0.837841	+	0.545914i	$0.183817\pi$
$937$	−4.16870	+	23.6419i	−0.136186	+	0.772347i	−0.974027	+	0.226433i	$0.927294\pi$
$938$	28.0288	−	16.1824i	0.915172	−	0.528375i
$939$	−4.01778	−	1.78912i	−0.131115	−	0.0583858i
$940$	−7.11274	−	5.96830i	−0.231992	−	0.194664i
$941$	−0.813201	−	0.682357i	−0.0265096	−	0.0222442i	0.629437	−	0.777052i	$-0.283286\pi$
$941$	−0.813201	−	0.682357i	−0.0265096	−	0.0222442i	−0.655946	+	0.754808i	$0.727730\pi$
$942$	4.98076	+	47.4162i	0.162282	+	1.54490i
$943$	−28.2665	+	16.3197i	−0.920483	+	0.531441i
$944$	−3.17269	+	17.9932i	−0.103262	+	0.585629i
$945$	−16.7850	+	26.8508i	−0.546015	+	0.873455i
$946$	−0.410047	+	0.488675i	−0.0133318	+	0.0158882i
$947$	10.1404	−	27.8606i	0.329520	−	0.905349i	−0.658713	−	0.752394i	$-0.728899\pi$
$947$	10.1404	−	27.8606i	0.329520	−	0.905349i	0.988233	−	0.152955i	$-0.0488788\pi$
$948$	46.1486	−	47.7825i	1.49884	−	1.55190i
$949$	−17.7552	+	10.2510i	−0.576359	+	0.332761i
$950$	−71.7718	−	36.5059i	−2.32858	−	1.18441i
$951$	−44.8788	+	32.6022i	−1.45529	+	1.05720i
$952$	28.5874	+	34.0692i	0.926524	+	1.10419i
$953$	−6.61263	−	37.5021i	−0.214204	−	1.21481i	−0.882282	−	0.470721i	$-0.843994\pi$
$953$	−6.61263	−	37.5021i	−0.214204	−	1.21481i	0.668078	−	0.744091i	$-0.267117\pi$
$954$	52.8405	+	28.1040i	1.71077	+	0.909899i
$955$	−52.8120	+	44.3146i	−1.70896	+	1.43399i
$956$	−45.8804	+	54.6781i	−1.48388	+	1.76842i
$957$	−0.279658	+	0.628020i	−0.00904005	+	0.0203010i
$958$	−37.4950	−	21.6477i	−1.21141	−	0.699407i
$959$	3.56883	−	4.25317i	0.115244	−	0.137342i
$960$	−65.3479	+	31.8674i	−2.10909	+	1.02852i
$961$	24.3995			0.787081
$962$	25.4373	−	44.0586i	0.820130	−	1.42051i
$963$	−30.4962	+	19.0511i	−0.982727	+	0.613912i
$964$	−15.4402	−	18.4009i	−0.497295	−	0.592653i
$965$	46.5848	−	16.9555i	1.49962	−	0.545817i
$966$	14.5166	−	15.0306i	0.467065	−	0.483602i
$967$	7.73515	+	43.8682i	0.248746	+	1.41071i	0.811630	+	0.584172i	$0.198580\pi$
$967$	7.73515	+	43.8682i	0.248746	+	1.41071i	−0.562884	+	0.826536i	$0.690308\pi$
$968$	20.4693	+	35.4539i	0.657908	+	1.13953i
$969$	−25.7205	−	46.3307i	−0.826262	−	1.48836i
$970$	16.0989	−	27.8840i	0.516903	−	0.895303i
$971$	−47.0073	−	17.1093i	−1.50854	−	0.549063i	−0.550282	−	0.834979i	$-0.685480\pi$
$971$	−47.0073	−	17.1093i	−1.50854	−	0.549063i	−0.958255	+	0.285916i	$0.907702\pi$
$972$	9.66517	+	54.9105i	0.310010	+	1.76126i
$973$	11.1383	+	9.34616i	0.357078	+	0.299624i
$974$	13.2819	−	2.34197i	0.425581	−	0.0750414i
$975$	31.1289	+	20.9994i	0.996923	+	0.672520i
$976$	3.19512			0.102273
$977$	10.2848	−	17.8137i	0.329039	−	0.569912i	−0.653283	−	0.757114i	$-0.726609\pi$
$977$	10.2848	−	17.8137i	0.329039	−	0.569912i	0.982321	+	0.187202i	$0.0599420\pi$
$978$	40.5087	−	60.0488i	1.29533	−	1.92015i
$979$	0.342985	+	0.0604776i	0.0109619	+	0.00193287i
$980$	45.5180	−	26.2798i	1.45402	−	0.839479i
$981$	−1.62397	−	7.64473i	−0.0518495	−	0.244077i
$982$	−4.90760	−	0.865342i	−0.156608	−	0.0276142i
$983$	−2.52803	−	14.3371i	−0.0806315	−	0.457284i	−0.998214	−	0.0597387i	$-0.980973\pi$
$983$	−2.52803	−	14.3371i	−0.0806315	−	0.457284i	0.917583	−	0.397545i	$-0.130138\pi$
$984$	39.2123	−	58.1271i	1.25004	−	1.85303i
$985$	−32.0914	+	26.9279i	−1.02252	+	0.857995i
$986$	−94.4697	+	16.6576i	−3.00853	+	0.530485i
$987$	2.12524	−	0.223243i	0.0676472	−	0.00710589i
$988$	−41.3274	−	12.6032i	−1.31480	−	0.400963i
$989$			11.8243i			0.375992i
$990$	1.72286	+	0.242344i	0.0547561	+	0.00770219i
$991$	16.0707	−	2.83370i	0.510503	−	0.0900155i	0.0875375	−	0.996161i	$-0.472100\pi$
$991$	16.0707	−	2.83370i	0.510503	−	0.0900155i	0.422966	+	0.906146i	$0.360989\pi$
$992$	−3.14190	−	8.63229i	−0.0997553	−	0.274075i
$993$	−43.1904	−	10.7713i	−1.37061	−	0.341818i
$994$	−24.2657	+	8.83199i	−0.769661	+	0.280134i
$995$		−	19.3125i		−	0.612249i
$996$	−2.15225	+	0.226079i	−0.0681966	+	0.00716360i
$997$	−6.82225	+	38.6909i	−0.216063	+	1.22535i	0.662989	+	0.748629i	$0.269287\pi$
$997$	−6.82225	+	38.6909i	−0.216063	+	1.22535i	−0.879052	+	0.476725i	$0.841824\pi$
$998$	14.1106	−	5.13585i	0.446664	−	0.162573i
$999$	30.0127	+	27.0333i	0.949558	+	0.855297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.3	yes	108
3.2	odd	2		513.2.bo.a.224.16		108
9.4	even	3		513.2.cd.a.395.3		108
9.5	odd	6		171.2.bd.a.167.16	yes	108
19.14	odd	18		171.2.bd.a.128.16	yes	108
57.14	even	18		513.2.cd.a.413.3		108
171.14	even	18	inner	171.2.x.a.14.3	✓	108
171.166	odd	18		513.2.bo.a.71.16		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.3	✓	108	171.14	even	18	inner
171.2.x.a.110.3	yes	108	1.1	even	1	trivial
171.2.bd.a.128.16	yes	108	19.14	odd	18
171.2.bd.a.167.16	yes	108	9.5	odd	6
513.2.bo.a.71.16		108	171.166	odd	18
513.2.bo.a.224.16		108	3.2	odd	2
513.2.cd.a.395.3		108	9.4	even	3
513.2.cd.a.413.3		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80901 + 1.51794i) q^{2} +(-0.419122 + 1.68058i) q^{3} +(0.621081 - 3.52233i) q^{4} +(-1.22473 + 3.36492i) q^{5} +(-1.79282 - 3.67638i) q^{6} +(0.850912 + 1.47382i) q^{7} +(1.86164 + 3.22446i) q^{8} +(-2.64867 - 1.40873i) q^{9} +O(q^{10})\)	\(q+(-1.80901 + 1.51794i) q^{2} +(-0.419122 + 1.68058i) q^{3} +(0.621081 - 3.52233i) q^{4} +(-1.22473 + 3.36492i) q^{5} +(-1.79282 - 3.67638i) q^{6} +(0.850912 + 1.47382i) q^{7} +(1.86164 + 3.22446i) q^{8} +(-2.64867 - 1.40873i) q^{9} +(-2.89220 - 7.94624i) q^{10} -0.0685816i q^{11} +(5.65923 + 2.52006i) q^{12} +(0.947862 + 2.60423i) q^{13} +(-3.77648 - 1.37453i) q^{14} +(-5.14169 - 3.46856i) q^{15} +(-1.54034 - 0.560636i) q^{16} +(2.40059 - 6.59558i) q^{17} +(6.92985 - 1.47211i) q^{18} +(-3.88520 - 1.97616i) q^{19} +(11.0917 + 6.40378i) q^{20} +(-2.83351 + 0.812310i) q^{21} +(0.104103 + 0.124065i) q^{22} +(2.95636 + 0.521285i) q^{23} +(-6.19920 + 1.77719i) q^{24} +(-5.99249 - 5.02830i) q^{25} +(-5.66776 - 3.27228i) q^{26} +(3.47760 - 3.86087i) q^{27} +(5.71977 - 2.08182i) q^{28} +(-1.00498 + 5.69952i) q^{29} +(14.5664 - 1.53011i) q^{30} +2.56914i q^{31} +(-3.35999 + 1.22294i) q^{32} +(0.115257 + 0.0287441i) q^{33} +(5.66899 + 15.5754i) q^{34} +(-6.00143 + 1.05821i) q^{35} +(-6.60706 + 8.45455i) q^{36} +7.77355i q^{37} +(10.0281 - 2.32260i) q^{38} +(-4.77388 + 0.501464i) q^{39} +(-13.1300 + 2.31518i) q^{40} +(-8.32894 + 6.98881i) q^{41} +(3.89281 - 5.77057i) q^{42} +(0.683977 + 3.87902i) q^{43} +(-0.241567 - 0.0425947i) q^{44} +(7.98418 - 7.18725i) q^{45} +(-6.13936 + 3.54456i) q^{46} +(-0.713950 - 0.125889i) q^{47} +(1.58778 - 2.35368i) q^{48} +(2.05190 - 3.55399i) q^{49} +18.4731 q^{50} +(10.0782 + 6.79873i) q^{51} +(9.76164 - 1.72124i) q^{52} +(6.47151 + 5.43024i) q^{53} +(-0.430456 + 12.2631i) q^{54} +(0.230771 + 0.0839939i) q^{55} +(-3.16818 + 5.48746i) q^{56} +(4.94947 - 5.70112i) q^{57} +(-6.83351 - 11.8360i) q^{58} +(-1.93552 - 10.9769i) q^{59} +(-15.4108 + 15.9564i) q^{60} +(-1.83166 + 0.666669i) q^{61} +(-3.89981 - 4.64761i) q^{62} +(-0.177564 - 5.10238i) q^{63} +(5.86110 - 10.1517i) q^{64} -9.92389 q^{65} +(-0.252132 + 0.122954i) q^{66} +(-5.17654 + 6.16916i) q^{67} +(-21.7408 - 12.5521i) q^{68} +(-2.11513 + 4.74990i) q^{69} +(9.25034 - 11.0241i) q^{70} +(4.92220 - 4.13021i) q^{71} +(-0.388478 - 11.1631i) q^{72} +(1.28461 + 7.28540i) q^{73} +(-11.7998 - 14.0624i) q^{74} +(10.9620 - 7.96337i) q^{75} +(-9.37372 + 12.4576i) q^{76} +(0.101077 - 0.0583569i) q^{77} +(7.87480 - 8.15361i) q^{78} +(3.66753 - 10.0764i) q^{79} +(3.77299 - 4.49647i) q^{80} +(5.03094 + 7.46255i) q^{81} +(4.45854 - 25.2857i) q^{82} +(-0.302529 + 0.174665i) q^{83} +(1.10138 + 10.4850i) q^{84} +(19.2535 + 16.1556i) q^{85} +(-7.12545 - 5.97896i) q^{86} +(-9.15727 - 4.07774i) q^{87} +(0.221138 - 0.127674i) q^{88} +(-0.881834 + 5.00113i) q^{89} +(-3.53366 + 25.1213i) q^{90} +(-3.03162 + 3.61295i) q^{91} +(3.67227 - 10.0895i) q^{92} +(-4.31764 - 1.07678i) q^{93} +(1.48263 - 0.855999i) q^{94} +(11.4080 - 10.6531i) q^{95} +(-0.646991 - 6.15927i) q^{96} +(2.44747 + 2.91678i) q^{97} +(1.68284 + 9.54387i) q^{98} +(-0.0966132 + 0.181650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

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