LMFDB - Embedded newform 77.2.n.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	77.19
Dual form			77.2.n.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.476751 + 0.0501086i) q^{2} +(-1.66384 - 1.49813i) q^{3} +(-1.73151 + 0.368045i) q^{4} +(-0.547175 - 1.22898i) q^{5} +(0.868306 + 0.630861i) q^{6} +(-1.63770 - 2.07796i) q^{7} +(1.71889 - 0.558501i) q^{8} +(0.210388 + 2.00171i) q^{9} +O(q^{10})$	\(q+(-0.476751 + 0.0501086i) q^{2} +(-1.66384 - 1.49813i) q^{3} +(-1.73151 + 0.368045i) q^{4} +(-0.547175 - 1.22898i) q^{5} +(0.868306 + 0.630861i) q^{6} +(-1.63770 - 2.07796i) q^{7} +(1.71889 - 0.558501i) q^{8} +(0.210388 + 2.00171i) q^{9} +(0.322449 + 0.558497i) q^{10} +(-1.74880 + 2.81810i) q^{11} +(3.43234 + 1.98166i) q^{12} +(3.83820 - 2.78861i) q^{13} +(0.884901 + 0.908608i) q^{14} +(-0.930750 + 2.86455i) q^{15} +(2.44281 - 1.08761i) q^{16} +(0.179716 - 1.70988i) q^{17} +(-0.200606 - 0.943776i) q^{18} +(-2.20796 - 0.469315i) q^{19} +(1.39976 + 1.92660i) q^{20} +(-0.388179 + 5.91088i) q^{21} +(0.692533 - 1.43116i) q^{22} +(-0.646028 + 1.11895i) q^{23} +(-3.69666 - 1.64586i) q^{24} +(2.13467 - 2.37079i) q^{25} +(-1.69013 + 1.52180i) q^{26} +(-1.29924 + 1.78825i) q^{27} +(3.60049 + 2.99527i) q^{28} +(-6.79788 - 2.20877i) q^{29} +(0.300197 - 1.41232i) q^{30} +(3.83290 - 8.60884i) q^{31} +(-4.24053 + 2.44827i) q^{32} +(7.13159 - 2.06893i) q^{33} +0.824195i q^{34} +(-1.65766 + 3.14971i) q^{35} +(-1.10101 - 3.38856i) q^{36} +(1.75162 + 1.94538i) q^{37} +(1.07616 + 0.113109i) q^{38} +(-10.5638 - 1.11030i) q^{39} +(-1.62692 - 1.80687i) q^{40} +(0.669247 + 2.05973i) q^{41} +(-0.111121 - 2.83747i) q^{42} -5.22507i q^{43} +(1.99089 - 5.52322i) q^{44} +(2.34493 - 1.35385i) q^{45} +(0.251925 - 0.565834i) q^{46} +(1.32038 - 6.21190i) q^{47} +(-5.69383 - 1.85004i) q^{48} +(-1.63586 + 6.80617i) q^{49} +(-0.898911 + 1.23724i) q^{50} +(-2.86064 + 2.57573i) q^{51} +(-5.61956 + 6.24116i) q^{52} +(9.96520 + 4.43679i) q^{53} +(0.529807 - 0.917653i) q^{54} +(4.42028 + 0.607243i) q^{55} +(-3.97557 - 2.65713i) q^{56} +(2.97059 + 4.08866i) q^{57} +(3.35158 + 0.712400i) q^{58} +(1.22060 + 5.74247i) q^{59} +(0.557323 - 5.30257i) q^{60} +(-5.43033 + 2.41774i) q^{61} +(-1.39596 + 4.29633i) q^{62} +(3.81493 - 3.71539i) q^{63} +(-2.42761 + 1.76376i) q^{64} +(-5.52731 - 3.19119i) q^{65} +(-3.29632 + 1.34372i) q^{66} +(-0.828067 - 1.43425i) q^{67} +(0.318133 + 3.02683i) q^{68} +(2.75122 - 0.893925i) q^{69} +(0.632462 - 1.58469i) q^{70} +(12.6618 + 9.19936i) q^{71} +(1.47959 + 3.32322i) q^{72} +(8.45880 - 1.79797i) q^{73} +(-0.932569 - 0.839689i) q^{74} +(-7.10350 + 0.746608i) q^{75} +3.99584 q^{76} +(8.71993 - 0.981260i) q^{77} +5.09196 q^{78} +(4.43547 - 0.466187i) q^{79} +(-2.67330 - 2.40705i) q^{80} +(10.7470 - 2.28435i) q^{81} +(-0.422275 - 0.948444i) q^{82} +(-6.53096 - 4.74502i) q^{83} +(-1.50333 - 10.3776i) q^{84} +(-2.19974 + 0.714740i) q^{85} +(0.261821 + 2.49106i) q^{86} +(8.00156 + 13.8591i) q^{87} +(-1.43209 + 5.82071i) q^{88} +(-2.96156 - 1.70986i) q^{89} +(-1.05011 + 0.762950i) q^{90} +(-12.0805 - 3.40871i) q^{91} +(0.706781 - 2.17525i) q^{92} +(-19.2744 + 8.58154i) q^{93} +(-0.318223 + 3.02769i) q^{94} +(0.631361 + 2.97032i) q^{95} +(10.7234 + 2.27932i) q^{96} +(-3.90871 - 5.37988i) q^{97} +(0.438850 - 3.32682i) q^{98} +(-6.00895 - 2.90770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.476751	+	0.0501086i	−0.337114	+	0.0354321i	−0.271573	−	0.962418i	$-0.587544\pi$
$2$	−0.476751	+	0.0501086i	−0.337114	+	0.0354321i	−0.0655408	+	0.997850i	$0.520877\pi$
$3$	−1.66384	−	1.49813i	−0.960617	−	0.864943i	0.0302832	−	0.999541i	$-0.490359\pi$
$3$	−1.66384	−	1.49813i	−0.960617	−	0.864943i	−0.990900	+	0.134598i	$0.957026\pi$
$4$	−1.73151	+	0.368045i	−0.865757	+	0.184022i
$5$	−0.547175	−	1.22898i	−0.244704	−	0.549615i	0.748881	−	0.662705i	$-0.230592\pi$
$5$	−0.547175	−	1.22898i	−0.244704	−	0.549615i	−0.993585	+	0.113090i	$0.963925\pi$
$6$	0.868306	+	0.630861i	0.354484	+	0.257548i
$7$	−1.63770	−	2.07796i	−0.618993	−	0.785396i
$7$	−1.63770	−	2.07796i	−0.618993	−	0.785396i
$8$	1.71889	−	0.558501i	0.607719	−	0.197460i
$9$	0.210388	+	2.00171i	0.0701294	+	0.667237i
$10$	0.322449	+	0.558497i	0.101967	+	0.176612i
$11$	−1.74880	+	2.81810i	−0.527284	+	0.849689i
$11$	−1.74880	+	2.81810i	−0.527284	+	0.849689i
$12$	3.43234	+	1.98166i	0.990830	+	0.572056i
$13$	3.83820	−	2.78861i	1.06452	−	0.773423i	0.0896047	−	0.995977i	$-0.471440\pi$
$13$	3.83820	−	2.78861i	1.06452	−	0.773423i	0.974920	+	0.222555i	$0.0714396\pi$
$14$	0.884901	+	0.908608i	0.236500	+	0.242836i
$15$	−0.930750	+	2.86455i	−0.240319	+	0.739624i
$16$	2.44281	−	1.08761i	0.610704	−	0.271903i
$17$	0.179716	−	1.70988i	0.0435876	−	0.414708i	−0.950872	−	0.309585i	$-0.899810\pi$
$17$	0.179716	−	1.70988i	0.0435876	−	0.414708i	0.994459	−	0.105123i	$-0.0335235\pi$
$18$	−0.200606	−	0.943776i	−0.0472832	−	0.222450i
$19$	−2.20796	−	0.469315i	−0.506540	−	0.107668i	−0.0524487	−	0.998624i	$-0.516703\pi$
$19$	−2.20796	−	0.469315i	−0.506540	−	0.107668i	−0.454091	+	0.890955i	$0.650036\pi$
$20$	1.39976	+	1.92660i	0.312996	+	0.430802i
$21$	−0.388179	+	5.91088i	−0.0847076	+	1.28986i
$22$	0.692533	−	1.43116i	0.147649	−	0.305125i
$23$	−0.646028	+	1.11895i	−0.134706	+	0.233318i	−0.925485	−	0.378784i	$-0.876342\pi$
$23$	−0.646028	+	1.11895i	−0.134706	+	0.233318i	0.790779	+	0.612102i	$0.209676\pi$
$24$	−3.69666	−	1.64586i	−0.754577	−	0.335959i
$25$	2.13467	−	2.37079i	0.426935	−	0.474159i
$26$	−1.69013	+	1.52180i	−0.331462	+	0.298450i
$27$	−1.29924	+	1.78825i	−0.250039	+	0.344149i
$28$	3.60049	+	2.99527i	0.680428	+	0.566054i
$29$	−6.79788	−	2.20877i	−1.26234	−	0.410158i	−0.400009	−	0.916511i	$-0.630993\pi$
$29$	−6.79788	−	2.20877i	−1.26234	−	0.410158i	−0.862326	+	0.506354i	$0.830993\pi$
$30$	0.300197	−	1.41232i	0.0548083	−	0.257853i
$31$	3.83290	−	8.60884i	0.688409	−	1.54619i	−0.142506	−	0.989794i	$-0.545516\pi$
$31$	3.83290	−	8.60884i	0.688409	−	1.54619i	0.830915	−	0.556399i	$-0.187817\pi$
$32$	−4.24053	+	2.44827i	−0.749627	+	0.432798i
$33$	7.13159	−	2.06893i	1.24145	−	0.360155i
$34$			0.824195i			0.141348i
$35$	−1.65766	+	3.14971i	−0.280195	+	0.532398i
$36$	−1.10101	−	3.38856i	−0.183502	−	0.564760i
$37$	1.75162	+	1.94538i	0.287965	+	0.319818i	0.869719	−	0.493547i	$-0.164300\pi$
$37$	1.75162	+	1.94538i	0.287965	+	0.319818i	−0.581754	+	0.813365i	$0.697633\pi$
$38$	1.07616	+	0.113109i	0.174577	+	0.0183487i
$39$	−10.5638	−	1.11030i	−1.69157	−	0.177791i
$40$	−1.62692	−	1.80687i	−0.257238	−	0.285692i
$41$	0.669247	+	2.05973i	0.104519	+	0.321676i	0.989617	−	0.143728i	$-0.0459091\pi$
$41$	0.669247	+	2.05973i	0.104519	+	0.321676i	−0.885098	+	0.465404i	$0.845909\pi$
$42$	−0.111121	−	2.83747i	−0.0171463	−	0.437831i
$43$		−	5.22507i		−	0.796816i	−0.917208	−	0.398408i	$-0.869563\pi$
$43$		−	5.22507i		−	0.796816i	0.917208	−	0.398408i	$-0.130437\pi$
$44$	1.99089	−	5.52322i	0.300138	−	0.832656i
$45$	2.34493	−	1.35385i	0.349562	−	0.201820i
$46$	0.251925	−	0.565834i	0.0371444	−	0.0834276i
$47$	1.32038	−	6.21190i	0.192597	−	0.906099i	−0.770603	−	0.637315i	$-0.780045\pi$
$47$	1.32038	−	6.21190i	0.192597	−	0.906099i	0.963201	−	0.268784i	$-0.0866217\pi$
$48$	−5.69383	−	1.85004i	−0.821833	−	0.267030i
$49$	−1.63586	+	6.80617i	−0.233694	+	0.972310i
$50$	−0.898911	+	1.23724i	−0.127125	+	0.174973i
$51$	−2.86064	+	2.57573i	−0.400570	+	0.360675i
$52$	−5.61956	+	6.24116i	−0.779293	+	0.865493i
$53$	9.96520	+	4.43679i	1.36883	+	0.609440i	0.953820	−	0.300378i	$-0.0971129\pi$
$53$	9.96520	+	4.43679i	1.36883	+	0.609440i	0.415006	+	0.909819i	$0.363780\pi$
$54$	0.529807	−	0.917653i	0.0720976	−	0.124877i
$55$	4.42028	+	0.607243i	0.596030	+	0.0818806i
$56$	−3.97557	−	2.65713i	−0.531258	−	0.355074i
$57$	2.97059	+	4.08866i	0.393464	+	0.541556i
$58$	3.35158	+	0.712400i	0.440084	+	0.0935427i
$59$	1.22060	+	5.74247i	0.158908	+	0.747605i	0.983359	+	0.181672i	$0.0581508\pi$
$59$	1.22060	+	5.74247i	0.158908	+	0.747605i	−0.824451	+	0.565934i	$0.808516\pi$
$60$	0.557323	−	5.30257i	0.0719501	−	0.684559i
$61$	−5.43033	+	2.41774i	−0.695282	+	0.309560i	−0.723777	−	0.690034i	$-0.757595\pi$
$61$	−5.43033	+	2.41774i	−0.695282	+	0.309560i	0.0284944	+	0.999594i	$0.490929\pi$
$62$	−1.39596	+	4.29633i	−0.177288	+	0.545635i
$63$	3.81493	−	3.71539i	0.480636	−	0.468095i
$64$	−2.42761	+	1.76376i	−0.303452	+	0.220470i
$65$	−5.52731	−	3.19119i	−0.685578	−	0.395819i
$66$	−3.29632	+	1.34372i	−0.405750	+	0.165400i
$67$	−0.828067	−	1.43425i	−0.101164	−	0.175222i	0.811000	−	0.585046i	$-0.198923\pi$
$67$	−0.828067	−	1.43425i	−0.101164	−	0.175222i	−0.912165	+	0.409824i	$0.865590\pi$
$68$	0.318133	+	3.02683i	0.0385793	+	0.367057i
$69$	2.75122	−	0.893925i	0.331208	−	0.107616i
$70$	0.632462	−	1.58469i	0.0755937	−	0.189407i
$71$	12.6618	+	9.19936i	1.50268	+	1.09176i	0.969297	+	0.245892i	$0.0790808\pi$
$71$	12.6618	+	9.19936i	1.50268	+	1.09176i	0.533386	+	0.845872i	$0.320919\pi$
$72$	1.47959	+	3.32322i	0.174372	+	0.391645i
$73$	8.45880	−	1.79797i	0.990028	−	0.210437i	0.315692	−	0.948862i	$-0.397763\pi$
$73$	8.45880	−	1.79797i	0.990028	−	0.210437i	0.674336	+	0.738425i	$0.264430\pi$
$74$	−0.932569	−	0.839689i	−0.108409	−	0.0976118i
$75$	−7.10350	+	0.746608i	−0.820241	+	0.0862108i
$76$	3.99584			0.458354
$77$	8.71993	−	0.981260i	0.993728	−	0.111825i
$78$	5.09196			0.576551
$79$	4.43547	−	0.466187i	0.499029	−	0.0524501i	0.148329	−	0.988938i	$-0.452610\pi$
$79$	4.43547	−	0.466187i	0.499029	−	0.0524501i	0.350700	+	0.936488i	$0.385944\pi$
$80$	−2.67330	−	2.40705i	−0.298883	−	0.269116i
$81$	10.7470	−	2.28435i	1.19411	−	0.253816i
$82$	−0.422275	−	0.948444i	−0.0466324	−	0.104738i
$83$	−6.53096	−	4.74502i	−0.716866	−	0.520833i	0.168516	−	0.985699i	$-0.446103\pi$
$83$	−6.53096	−	4.74502i	−0.716866	−	0.520833i	−0.885381	+	0.464866i	$0.846103\pi$
$84$	−1.50333	−	10.3776i	−0.164027	−	1.13229i
$85$	−2.19974	+	0.714740i	−0.238596	+	0.0775244i
$86$	0.261821	+	2.49106i	0.0282329	+	0.268618i
$87$	8.00156	+	13.8591i	0.857858	+	1.48585i
$88$	−1.43209	+	5.82071i	−0.152661	+	0.620490i
$89$	−2.96156	−	1.70986i	−0.313925	−	0.181245i	0.334756	−	0.942305i	$-0.391346\pi$
$89$	−2.96156	−	1.70986i	−0.313925	−	0.181245i	−0.648682	+	0.761060i	$0.724679\pi$
$90$	−1.05011	+	0.762950i	−0.110691	+	0.0804220i
$91$	−12.0805	−	3.40871i	−1.26638	−	0.357330i
$92$	0.706781	−	2.17525i	0.0736871	−	0.226785i
$93$	−19.2744	+	8.58154i	−1.99867	+	0.889864i
$94$	−0.318223	+	3.02769i	−0.0328222	+	0.312283i
$95$	0.631361	+	2.97032i	0.0647763	+	0.304749i
$96$	10.7234	+	2.27932i	1.09445	+	0.232633i
$97$	−3.90871	−	5.37988i	−0.396869	−	0.546244i	0.563085	−	0.826399i	$-0.309614\pi$
$97$	−3.90871	−	5.37988i	−0.396869	−	0.546244i	−0.959955	+	0.280155i	$0.909614\pi$
$98$	0.438850	−	3.32682i	0.0443306	−	0.336060i
$99$	−6.00895	−	2.90770i	−0.603922	−	0.292235i
$100$	−2.82366	+	4.89072i	−0.282366	+	0.489072i
$101$	−11.4880	−	5.11478i	−1.14310	−	0.508940i	−0.254248	−	0.967139i	$-0.581828\pi$
$101$	−11.4880	−	5.11478i	−1.14310	−	0.508940i	−0.888850	+	0.458199i	$0.848495\pi$
$102$	1.23475	−	1.37133i	0.122258	−	0.135782i
$103$	−5.41512	+	4.87579i	−0.533567	+	0.480426i	−0.891310	−	0.453394i	$-0.850213\pi$
$103$	−5.41512	+	4.87579i	−0.533567	+	0.480426i	0.357743	+	0.933820i	$0.383546\pi$
$104$	5.03999	−	6.93696i	0.494212	−	0.680225i
$105$	7.47673	−	2.75722i	0.729654	−	0.269077i
$106$	−4.97324	−	1.61590i	−0.483044	−	0.156951i
$107$	2.28550	−	10.7524i	0.220948	−	1.03948i	−0.718166	−	0.695872i	$-0.755018\pi$
$107$	2.28550	−	10.7524i	0.220948	−	1.03948i	0.939114	−	0.343606i	$-0.111649\pi$
$108$	1.59149	−	3.57456i	0.153142	−	0.343962i
$109$	−1.08789	+	0.628095i	−0.104201	+	0.0601606i	−0.551195	−	0.834377i	$-0.685828\pi$
$109$	−1.08789	+	0.628095i	−0.104201	+	0.0601606i	0.446994	+	0.894537i	$0.352495\pi$
$110$	−2.13780	−	0.0680100i	−0.203831	−	0.00648450i
$111$		−	5.86094i		−	0.556296i
$112$	−6.26062	−	3.29489i	−0.591573	−	0.311338i
$113$	1.78776	+	5.50216i	0.168178	+	0.517600i	0.999256	−	0.0385560i	$-0.0122758\pi$
$113$	1.78776	+	5.50216i	0.168178	+	0.517600i	−0.831078	+	0.556156i	$0.812276\pi$
$114$	−1.62111	−	1.80042i	−0.151831	−	0.168625i
$115$	1.72866	+	0.181689i	0.161198	+	0.0169426i
$116$	12.5836	+	1.32259i	1.16835	+	0.122799i
$117$	6.38951	+	7.09627i	0.590711	+	0.656051i
$118$	−0.869669	−	2.67657i	−0.0800595	−	0.246398i
$119$	−3.84740	+	2.42684i	−0.352690	+	0.222468i
$120$			5.44367i			0.496937i
$121$	−4.88337	−	9.85661i	−0.443943	−	0.896055i
$122$	2.46777	−	1.42477i	0.223421	−	0.128992i
$123$	1.97222	−	4.42967i	0.177829	−	0.399410i
$124$	−3.46829	+	16.3170i	−0.311461	+	1.46531i
$125$	−10.4789	−	3.40479i	−0.937260	−	0.304534i
$126$	−1.63260	+	1.96248i	−0.145443	+	0.174831i
$127$	9.98641	−	13.7451i	0.886150	−	1.21968i	−0.0885291	−	0.996074i	$-0.528217\pi$
$127$	9.98641	−	13.7451i	0.886150	−	1.21968i	0.974679	−	0.223607i	$-0.0717834\pi$
$128$	8.34667	−	7.51538i	0.737749	−	0.664272i
$129$	−7.82782	+	8.69367i	−0.689201	+	0.765435i
$130$	2.79506	+	1.24444i	0.245143	+	0.109145i
$131$	8.03158	−	13.9111i	0.701723	−	1.21542i	−0.266139	−	0.963935i	$-0.585748\pi$
$131$	8.03158	−	13.9111i	0.701723	−	1.21542i	0.967861	−	0.251485i	$-0.0809188\pi$
$132$	−11.5870	+	6.20713i	−1.00852	+	0.540261i
$133$	2.64076	+	5.35665i	0.228983	+	0.464480i
$134$	0.466650	+	0.642289i	0.0403124	+	0.0554853i
$135$	2.90863	+	0.618247i	0.250335	+	0.0532103i
$136$	−0.646060	−	3.03947i	−0.0553992	−	0.260633i
$137$	1.66973	−	15.8864i	0.142654	−	1.35726i	−0.655675	−	0.755043i	$-0.727616\pi$
$137$	1.66973	−	15.8864i	0.142654	−	1.35726i	0.798329	−	0.602222i	$-0.205718\pi$
$138$	−1.26685	+	0.564039i	−0.107842	+	0.0480142i
$139$	−2.74665	+	8.45333i	−0.232968	+	0.717002i	0.764416	+	0.644723i	$0.223027\pi$
$139$	−2.74665	+	8.45333i	−0.232968	+	0.717002i	−0.997384	+	0.0722792i	$0.976973\pi$
$140$	1.71102	−	6.06385i	0.144608	−	0.512489i
$141$	−11.5031	+	8.35750i	−0.968736	+	0.703828i
$142$	−6.49751	−	3.75134i	−0.545259	−	0.314806i
$143$	1.14634	+	15.6932i	0.0958615	+	1.31233i
$144$	2.69102	+	4.66099i	0.224252	+	0.388416i
$145$	1.00511	+	9.56301i	0.0834701	+	0.794165i
$146$	−3.94265	+	1.28104i	−0.326296	+	0.106020i
$147$	12.9183	−	8.87364i	1.06548	−	0.731885i
$148$	−3.74895	−	2.72377i	−0.308162	−	0.223892i
$149$	4.26354	+	9.57606i	0.349282	+	0.784501i	0.999690	+	0.0249154i	$0.00793164\pi$
$149$	4.26354	+	9.57606i	0.349282	+	0.784501i	−0.650407	+	0.759586i	$0.725402\pi$
$150$	3.34919	−	0.711892i	0.273460	−	0.0581258i
$151$	4.51938	+	4.06927i	0.367782	+	0.331152i	0.832212	−	0.554457i	$-0.187074\pi$
$151$	4.51938	+	4.06927i	0.367782	+	0.331152i	−0.464430	+	0.885610i	$0.653741\pi$
$152$	−4.05734	+	0.426444i	−0.329094	+	0.0345892i
$153$	3.46051			0.279765
$154$	−4.10807	+	0.904760i	−0.331037	+	0.0729077i
$155$	−12.6773			−1.01827
$156$	18.7001	−	1.96546i	1.49720	−	0.157363i
$157$	13.5757	+	12.2236i	1.08346	+	0.975551i	0.999781	−	0.0209413i	$-0.00666632\pi$
$157$	13.5757	+	12.2236i	1.08346	+	0.975551i	0.0836789	+	0.996493i	$0.473333\pi$
$158$	−2.09126	+	0.444510i	−0.166371	+	0.0353633i
$159$	−9.93360	−	22.3112i	−0.787786	−	1.76940i
$160$	5.32918	+	3.87188i	0.421309	+	0.306099i
$161$	3.38314	−	0.490090i	0.266629	−	0.0386245i
$162$	−5.00918	+	1.62758i	−0.393559	+	0.127875i
$163$	0.782182	+	7.44196i	0.0612652	+	0.582900i	0.981491	+	0.191511i	$0.0613386\pi$
$163$	0.782182	+	7.44196i	0.0612652	+	0.582900i	−0.920225	+	0.391389i	$0.871995\pi$
$164$	−1.91688	−	3.32014i	−0.149683	−	0.259259i
$165$	−6.44490	−	7.63249i	−0.501735	−	0.594188i
$166$	3.35141	+	1.93494i	0.260120	+	0.150180i
$167$	−4.96710	+	3.60881i	−0.384365	+	0.279258i	−0.763143	−	0.646230i	$-0.776345\pi$
$167$	−4.96710	+	3.60881i	−0.384365	+	0.279258i	0.378777	+	0.925488i	$0.376345\pi$
$168$	2.63399	+	10.3769i	0.203217	+	0.800598i
$169$	2.93818	−	9.04278i	0.226014	−	0.695599i
$170$	1.01292	−	0.450979i	0.0776871	−	0.0345885i
$171$	0.474906	−	4.51843i	0.0363170	−	0.345533i
$172$	1.92306	+	9.04729i	0.146632	+	0.689849i
$173$	−4.83393	−	1.02748i	−0.367517	−	0.0781181i	0.0204515	−	0.999791i	$-0.493490\pi$
$173$	−4.83393	−	1.02748i	−0.367517	−	0.0781181i	−0.387968	+	0.921673i	$0.626823\pi$
$174$	−4.50922	−	6.20640i	−0.341843	−	0.470506i
$175$	−8.42238	−	0.553114i	−0.636672	−	0.0418115i
$176$	−1.20701	+	8.78611i	−0.0909816	+	0.662278i
$177$	6.57206	−	11.3831i	0.493986	−	0.855609i
$178$	1.49761	+	0.666778i	0.112250	+	0.0499771i
$179$	−4.74927	+	5.27460i	−0.354977	+	0.394242i	−0.894013	−	0.448040i	$-0.852122\pi$
$179$	−4.74927	+	5.27460i	−0.354977	+	0.394242i	0.539036	+	0.842283i	$0.318789\pi$
$180$	−3.56201	+	3.20725i	−0.265497	+	0.239054i
$181$	−0.179772	+	0.247434i	−0.0133623	+	0.0183916i	−0.815646	−	0.578551i	$-0.803618\pi$
$181$	−0.179772	+	0.247434i	−0.0133623	+	0.0183916i	0.802284	+	0.596943i	$0.203618\pi$
$182$	5.93018	+	1.01977i	0.439574	+	0.0755906i
$183$	12.6573	+	4.11259i	0.935652	+	0.304012i
$184$	−0.485514	+	2.28416i	−0.0357925	+	0.168391i
$185$	1.43237	−	3.21716i	0.105310	−	0.236531i
$186$	8.75911	−	5.05707i	0.642249	−	0.370803i
$187$	4.50434	+	3.49671i	0.329390	+	0.255705i
$188$			11.2420i			0.819904i
$189$	5.84368	−	0.228850i	0.425065	−	0.0166464i
$190$	−0.449841	−	1.38447i	−0.0326349	−	0.100440i
$191$	13.5964	+	15.1004i	0.983802	+	1.09262i	0.995695	+	0.0926939i	$0.0295478\pi$
$191$	13.5964	+	15.1004i	0.983802	+	1.09262i	−0.0118923	+	0.999929i	$0.503786\pi$
$192$	6.68149	+	0.702253i	0.482195	+	0.0506808i
$193$	−13.1251	−	1.37951i	−0.944769	−	0.0992992i	−0.380400	−	0.924822i	$-0.624214\pi$
$193$	−13.1251	−	1.37951i	−0.944769	−	0.0992992i	−0.564369	+	0.825523i	$0.690880\pi$
$194$	2.13306	+	2.36900i	0.153145	+	0.170085i
$195$	4.41573	+	13.5902i	0.316217	+	0.973216i
$196$	0.327538	−	12.3871i	0.0233956	−	0.884789i
$197$		−	5.08391i		−	0.362214i	−0.983463	−	0.181107i	$-0.942032\pi$
$197$		−	5.08391i		−	0.362214i	0.983463	−	0.181107i	$-0.0579680\pi$
$198$	3.01047	+	1.08515i	0.213945	+	0.0771184i
$199$	−4.75397	+	2.74471i	−0.337000	+	0.194567i	−0.658945	−	0.752191i	$-0.728997\pi$
$199$	−4.75397	+	2.74471i	−0.337000	+	0.194567i	0.321945	+	0.946758i	$0.395664\pi$
$200$	2.34518	−	5.26735i	0.165829	−	0.372458i
$201$	−0.770924	+	3.62691i	−0.0543768	+	0.255823i
$202$	5.73321	+	1.86283i	0.403387	+	0.131068i
$203$	6.54318	+	17.7431i	0.459241	+	1.24532i
$204$	4.00526	−	5.51276i	0.280424	−	0.385971i
$205$	2.16516	−	1.94952i	0.151222	−	0.136161i
$206$	2.33734	−	2.59588i	0.162851	−	0.180864i
$207$	−2.37574	−	1.05775i	−0.165125	−	0.0735184i
$208$	6.34308	−	10.9865i	0.439814	−	0.761779i
$209$	5.18386	−	5.40150i	0.358575	−	0.373629i
$210$	−3.42638	+	1.68916i	−0.236443	+	0.116563i
$211$	−4.70461	−	6.47533i	−0.323878	−	0.445780i	0.615768	−	0.787928i	$-0.288846\pi$
$211$	−4.70461	−	6.47533i	−0.323878	−	0.445780i	−0.939646	+	0.342147i	$0.888846\pi$
$212$	−18.8878	−	4.01473i	−1.29722	−	0.275733i
$213$	−7.28543	−	34.2753i	−0.499190	−	2.34850i
$214$	−0.550827	+	5.24077i	−0.0376537	+	0.358251i
$215$	−6.42149	+	2.85903i	−0.437942	+	0.194984i
$216$	−1.23451	+	3.79943i	−0.0839977	+	0.258518i
$217$	−24.1660	+	6.13409i	−1.64049	+	0.416409i
$218$	0.487181	−	0.353958i	0.0329960	−	0.0239730i
$219$	−16.7677	−	9.68081i	−1.13305	−	0.654169i
$220$	−7.87727	+	0.575410i	−0.531085	+	0.0387941i
$221$	−4.07842	−	7.06404i	−0.274344	−	0.475179i
$222$	0.293683	+	2.79421i	0.0197107	+	0.187535i
$223$	12.3285	−	4.00577i	0.825577	−	0.268246i	0.134396	−	0.990928i	$-0.457091\pi$
$223$	12.3285	−	4.00577i	0.825577	−	0.268246i	0.691181	+	0.722682i	$0.257091\pi$
$224$	12.0322	+	4.80213i	0.803932	+	0.320856i
$225$	5.19476	+	3.77421i	0.346317	+	0.251614i
$226$	−1.12802	−	2.53358i	−0.0750349	−	0.168531i
$227$	−18.8823	+	4.01356i	−1.25326	+	0.266389i	−0.786276	−	0.617875i	$-0.787994\pi$
$227$	−18.8823	+	4.01356i	−1.25326	+	0.266389i	−0.466987	+	0.884264i	$0.654660\pi$
$228$	−6.64842	−	5.98627i	−0.440303	−	0.396450i
$229$	6.30813	−	0.663011i	0.416853	−	0.0438130i	0.106219	−	0.994343i	$-0.466125\pi$
$229$	6.30813	−	0.663011i	0.416853	−	0.0438130i	0.310634	+	0.950530i	$0.399459\pi$
$230$	−0.833243			−0.0549424
$231$	−15.9786	−	11.4309i	−1.05131	−	0.752097i
$232$	−12.9184			−0.848135
$233$	−17.1569	+	1.80326i	−1.12398	+	0.118135i	−0.648231	−	0.761444i	$-0.724491\pi$
$233$	−17.1569	+	1.80326i	−1.12398	+	0.118135i	−0.475752	+	0.879579i	$0.657824\pi$
$234$	−3.40179	−	3.06299i	−0.222382	−	0.200234i
$235$	−8.35675	+	1.77628i	−0.545134	+	0.115872i
$236$	−4.22697	−	9.49393i	−0.275152	−	0.618002i
$237$	−8.07831	−	5.86923i	−0.524742	−	0.381248i
$238$	1.71265	−	1.34979i	0.111014	−	0.0874937i
$239$	26.9545	−	8.75806i	1.74354	−	0.566512i	0.748250	−	0.663417i	$-0.230894\pi$
$239$	26.9545	−	8.75806i	1.74354	−	0.566512i	0.995294	+	0.0969048i	$0.0308942\pi$
$240$	0.841871	+	8.00987i	0.0543425	+	0.517035i
$241$	3.43595	+	5.95124i	0.221329	+	0.383353i	0.955212	−	0.295923i	$-0.0956271\pi$
$241$	3.43595	+	5.95124i	0.221329	+	0.383353i	−0.733883	+	0.679276i	$0.762294\pi$
$242$	2.82205	+	4.45445i	0.181408	+	0.286343i
$243$	−15.5607	−	8.98399i	−0.998221	−	0.576323i
$244$	8.51286	−	6.18495i	0.544980	−	0.395951i
$245$	9.25972	−	1.71374i	0.591582	−	0.109487i
$246$	−0.718293	+	2.21068i	−0.0457967	+	0.140948i
$247$	−9.78331	+	4.35581i	−0.622497	+	0.277154i
$248$	1.78029	−	16.9383i	0.113048	−	1.07558i
$249$	3.75782	+	17.6791i	0.238142	+	1.12037i
$250$	5.16643	+	1.09816i	0.326754	+	0.0694536i
$251$	5.68440	+	7.82391i	0.358796	+	0.493841i	0.949813	−	0.312819i	$-0.101273\pi$
$251$	5.68440	+	7.82391i	0.358796	+	0.493841i	−0.591017	+	0.806659i	$0.701273\pi$
$252$	−5.23817	+	7.83731i	−0.329974	+	0.493704i
$253$	−2.02354	−	3.77740i	−0.127219	−	0.237483i
$254$	−4.07228	+	7.05340i	−0.255518	+	0.442570i
$255$	4.73078	+	2.10628i	0.296253	+	0.131900i
$256$	0.413011	−	0.458695i	0.0258132	−	0.0286685i
$257$	8.08338	−	7.27830i	0.504227	−	0.454008i	−0.377335	−	0.926077i	$-0.623159\pi$
$257$	8.08338	−	7.27830i	0.504227	−	0.454008i	0.881562	+	0.472069i	$0.156493\pi$
$258$	3.29629	−	4.53696i	0.205218	−	0.282459i
$259$	1.17378	−	6.82576i	0.0729351	−	0.424132i
$260$	10.7451	+	3.49130i	0.666384	+	0.216521i
$261$	2.99112	−	14.0721i	0.185145	−	0.871041i
$262$	−3.13200	+	7.03459i	−0.193496	+	0.434598i
$263$	−4.03337	+	2.32867i	−0.248708	+	0.143592i	−0.619173	−	0.785255i	$-0.712532\pi$
$263$	−4.03337	+	2.32867i	−0.248708	+	0.143592i	0.370464	+	0.928847i	$0.379199\pi$
$264$	11.1029	−	7.53927i	0.683337	−	0.464010i
$265$		−	14.6747i		−	0.901459i
$266$	−1.52740	−	2.42146i	−0.0936507	−	0.148470i
$267$	2.36598	+	7.28173i	0.144795	+	0.445634i
$268$	1.96168	+	2.17867i	0.119829	+	0.133083i
$269$	17.3909	+	1.82785i	1.06034	+	0.111446i	0.618607	−	0.785701i	$-0.287697\pi$
$269$	17.3909	+	1.82785i	1.06034	+	0.111446i	0.441733	+	0.897147i	$0.354364\pi$
$270$	−1.41767	−	0.149003i	−0.0862767	−	0.00906804i
$271$	20.9858	+	23.3071i	1.27480	+	1.41580i	0.863537	+	0.504285i	$0.168244\pi$
$271$	20.9858	+	23.3071i	1.27480	+	1.41580i	0.411259	+	0.911519i	$0.365089\pi$
$272$	−1.42068	−	4.37239i	−0.0861412	−	0.265115i
$273$	14.9933	+	23.7696i	0.907433	+	1.43860i
$274$			7.65752i			0.462608i
$275$	2.94801	+	10.1618i	0.177772	+	0.612778i
$276$	−4.43477	+	2.56041i	−0.266942	+	0.154119i
$277$	−5.85537	+	13.1514i	−0.351815	+	0.790190i	0.647782	+	0.761826i	$0.275697\pi$
$277$	−5.85537	+	13.1514i	−0.351815	+	0.790190i	−0.999598	+	0.0283648i	$0.990970\pi$
$278$	0.885886	−	4.16777i	0.0531319	−	0.249966i
$279$	18.0388	+	5.86116i	1.07995	+	0.350899i
$280$	−1.09021	+	6.33980i	−0.0651526	+	0.378875i
$281$	−14.6231	+	20.1270i	−0.872340	+	1.20067i	0.106143	+	0.994351i	$0.466150\pi$
$281$	−14.6231	+	20.1270i	−0.872340	+	1.20067i	−0.978484	+	0.206323i	$0.933850\pi$
$282$	5.06534	−	4.56085i	0.301637	−	0.271595i
$283$	4.06765	−	4.51758i	0.241797	−	0.268542i	−0.610016	−	0.792389i	$-0.708837\pi$
$283$	4.06765	−	4.51758i	0.241797	−	0.268542i	0.851812	+	0.523847i	$0.175504\pi$
$284$	−25.3099	−	11.2687i	−1.50187	−	0.668675i
$285$	3.39943	−	5.88799i	0.201365	−	0.348774i
$286$	−1.33288	−	7.42430i	−0.0788148	−	0.439008i
$287$	3.18402	−	4.76390i	0.187947	−	0.281204i
$288$	−5.79289	−	7.97323i	−0.341350	−	0.469827i
$289$	13.7371	+	2.91991i	0.808065	+	0.171759i
$290$	−0.958378	−	4.50881i	−0.0562779	−	0.264767i
$291$	−1.55628	+	14.8070i	−0.0912306	+	0.868001i
$292$	−13.9848	+	6.22643i	−0.818398	+	0.364374i
$293$	6.38521	−	19.6517i	0.373028	−	1.14806i	−0.571772	−	0.820413i	$-0.693744\pi$
$293$	6.38521	−	19.6517i	0.373028	−	1.14806i	0.944800	−	0.327649i	$-0.106256\pi$
$294$	−5.71417	+	4.87784i	−0.333257	+	0.284481i
$295$	6.38947	−	4.64222i	0.372009	−	0.270281i
$296$	4.09734	+	2.36560i	0.238153	+	0.137498i
$297$	−2.76735	−	6.78868i	−0.160578	−	0.393919i
$298$	−2.51249	−	4.35176i	−0.145545	−	0.252091i
$299$	0.640745	+	6.09628i	0.0370553	+	0.352557i
$300$	12.0250	−	3.90717i	0.694265	−	0.225580i
$301$	−10.8575	+	8.55712i	−0.625816	+	0.493224i
$302$	−2.35853	−	1.71357i	−0.135718	−	0.0986048i
$303$	11.4516	+	25.7206i	0.657875	+	1.47761i
$304$	−5.90406	+	1.25495i	−0.338621	+	0.0719761i
$305$	5.94268	+	5.35081i	0.340277	+	0.306387i
$306$	−1.64980	+	0.173401i	−0.0943128	+	0.00991267i
$307$	29.1596			1.66423			0.832114	−	0.554605i	$-0.187131\pi$
$307$	29.1596			1.66423			0.832114	+	0.554605i	$0.187131\pi$
$308$	−14.7375	+	4.90839i	−0.839749	+	0.279681i
$309$	16.3144			0.928096
$310$	6.04393	−	0.635242i	0.343272	−	0.0360793i
$311$	−17.2188	−	15.5039i	−0.976389	−	0.879145i	0.0162972	−	0.999867i	$-0.494812\pi$
$311$	−17.2188	−	15.5039i	−0.976389	−	0.879145i	−0.992686	+	0.120723i	$0.961479\pi$
$312$	−18.7782	+	3.99142i	−1.06310	+	0.225970i
$313$	−5.04239	−	11.3254i	−0.285013	−	0.640150i	0.713132	−	0.701030i	$-0.247276\pi$
$313$	−5.04239	−	11.3254i	−0.285013	−	0.640150i	−0.998145	+	0.0608800i	$0.980609\pi$
$314$	−7.08474	−	5.14737i	−0.399815	−	0.290483i
$315$	−6.65355	−	2.65549i	−0.374885	−	0.149620i
$316$	−7.50850	+	2.43966i	−0.422386	+	0.137242i
$317$	0.0495311	+	0.471257i	0.00278194	+	0.0264684i	0.995825	−	0.0912850i	$-0.0290974\pi$
$317$	0.0495311	+	0.471257i	0.00278194	+	0.0264684i	−0.993043	+	0.117753i	$0.962431\pi$
$318$	5.85384	+	10.1391i	0.328267	+	0.568575i
$319$	18.1127	−	15.2944i	1.01412	−	0.856323i
$320$	3.49595	+	2.01839i	0.195430	+	0.112831i
$321$	−19.9112	+	14.4664i	−1.11134	+	0.807433i
$322$	−1.58836	+	0.403176i	−0.0885158	+	0.0224681i
$323$	−1.19928	+	3.69101i	−0.0667298	+	0.205373i
$324$	−17.7679	+	7.91076i	−0.987103	+	0.439487i
$325$	1.58207	−	15.0524i	0.0877573	−	0.834955i
$326$	−0.745812	−	3.50877i	−0.0413067	−	0.194333i
$327$	2.75104	+	0.584752i	0.152133	+	0.0323368i
$328$	2.30072	+	3.16667i	0.127036	+	0.174850i
$329$	−15.0705	+	7.42955i	−0.830863	+	0.409604i
$330$	3.45507	+	3.31585i	0.190195	+	0.182532i
$331$	9.30467	−	16.1162i	0.511431	−	0.885824i	−0.488481	−	0.872574i	$-0.662449\pi$
$331$	9.30467	−	16.1162i	0.511431	−	0.885824i	0.999912	−	0.0132499i	$-0.00421769\pi$
$332$	13.0548	+	5.81238i	0.716477	+	0.318996i
$333$	−3.52556	+	3.91553i	−0.193199	+	0.214570i
$334$	2.18724	−	1.96940i	0.119680	−	0.107761i
$335$	−1.30957	+	1.80246i	−0.0715492	+	0.0984790i
$336$	5.48049	+	14.8614i	0.298985	+	0.810754i
$337$	−19.6425	−	6.38222i	−1.06999	−	0.347662i	−0.279508	−	0.960143i	$-0.590171\pi$
$337$	−19.6425	−	6.38222i	−1.06999	−	0.347662i	−0.790485	+	0.612481i	$0.790171\pi$
$338$	−0.947659	+	4.45839i	−0.0515459	+	0.242504i
$339$	5.26839	−	11.8330i	0.286140	−	0.642680i
$340$	3.54583	−	2.04719i	0.192300	−	0.111024i
$341$	17.5576	+	25.8567i	0.950796	+	1.40022i
$342$			2.17796i			0.117771i
$343$	16.8220	−	7.74723i	0.908304	−	0.418311i
$344$	−2.91821	−	8.98132i	−0.157339	−	0.484240i
$345$	−2.60401	−	2.89205i	−0.140195	−	0.155702i
$346$	2.35607	+	0.247633i	0.126663	+	0.0133128i
$347$	5.19698	+	0.546225i	0.278989	+	0.0293229i	0.242989	−	0.970029i	$-0.421872\pi$
$347$	5.19698	+	0.546225i	0.278989	+	0.0293229i	0.0359992	+	0.999352i	$0.488539\pi$
$348$	−18.9556	−	21.0523i	−1.01613	−	1.12852i
$349$	4.91483	+	15.1263i	0.263085	+	0.809692i	0.992128	+	0.125224i	$0.0399651\pi$
$349$	4.91483	+	15.1263i	0.263085	+	0.809692i	−0.729044	+	0.684467i	$0.760035\pi$
$350$	4.04310	−	0.158336i	0.216113	−	0.00846340i
$351$			10.4867i			0.559740i
$352$	0.516383	−	16.2318i	0.0275233	−	0.865158i
$353$	1.53593	−	0.886769i	0.0817493	−	0.0471980i	−0.458568	−	0.888659i	$-0.651638\pi$
$353$	1.53593	−	0.886769i	0.0817493	−	0.0471980i	0.540317	+	0.841461i	$0.318304\pi$
$354$	−2.56284	+	5.75624i	−0.136214	+	0.305941i
$355$	4.37755	−	20.5948i	0.232336	−	1.09306i
$356$	5.75730	+	1.87066i	0.305136	+	0.0991447i
$357$	10.0372	+	1.72602i	0.531223	+	0.0913507i
$358$	1.99992	−	2.75265i	0.105699	−	0.145482i
$359$	12.0024	−	10.8070i	0.633461	−	0.570371i	−0.288584	−	0.957455i	$-0.593184\pi$
$359$	12.0024	−	10.8070i	0.633461	−	0.570371i	0.922044	+	0.387084i	$0.126518\pi$
$360$	3.27456	−	3.63676i	0.172584	−	0.191674i
$361$	−12.7026	−	5.65554i	−0.668555	−	0.297660i
$362$	0.0733077	−	0.126973i	0.00385297	−	0.00667354i
$363$	−6.64130	+	23.7157i	−0.348578	+	1.24475i
$364$	22.1721	+	1.45608i	1.16213	+	0.0763195i
$365$	−6.83811	−	9.41185i	−0.357923	−	0.492639i
$366$	−6.24044	−	1.32645i	−0.326193	−	0.0693345i
$367$	0.530577	+	2.49617i	0.0276959	+	0.130299i	0.989824	−	0.142300i	$-0.0454499\pi$
$367$	0.530577	+	2.49617i	0.0276959	+	0.130299i	−0.962128	+	0.272600i	$0.912117\pi$
$368$	−0.361140	+	3.43602i	−0.0188257	+	0.179115i
$369$	−3.98218	+	1.77298i	−0.207304	+	0.0922978i
$370$	−0.521678	+	1.60556i	−0.0271208	+	0.0834692i
$371$	−7.10055	−	27.9735i	−0.368642	−	1.45231i
$372$	30.2156	−	21.9529i	1.56661	−	1.13821i
$373$	−3.69579	−	2.13376i	−0.191361	−	0.110482i	0.401259	−	0.915965i	$-0.368573\pi$
$373$	−3.69579	−	2.13376i	−0.191361	−	0.110482i	−0.592619	+	0.805483i	$0.701906\pi$
$374$	−2.32266	−	1.44136i	−0.120102	−	0.0745307i
$375$	12.3343	+	21.3637i	0.636943	+	1.10322i
$376$	−1.19977	−	11.4150i	−0.0618732	−	0.588684i
$377$	−32.2510	+	10.4790i	−1.66101	+	0.539696i
$378$	−2.77451	+	0.401923i	−0.142706	+	0.0206727i
$379$	−12.7744	−	9.28115i	−0.656177	−	0.476740i	0.209193	−	0.977874i	$-0.432916\pi$
$379$	−12.7744	−	9.28115i	−0.656177	−	0.476740i	−0.865370	+	0.501134i	$0.832916\pi$
$380$	−2.18642	−	4.91078i	−0.112161	−	0.251918i
$381$	−37.2077	+	7.90873i	−1.90621	+	0.405177i
$382$	−7.23877	−	6.51781i	−0.370368	−	0.333480i
$383$	−11.4956	+	1.20823i	−0.587397	+	0.0617379i	−0.393565	−	0.919297i	$-0.628758\pi$
$383$	−11.4956	+	1.20823i	−0.587397	+	0.0617379i	−0.193832	+	0.981035i	$0.562092\pi$
$384$	−25.1465			−1.28325
$385$	−5.97727	−	10.1797i	−0.304630	−	0.518803i
$386$	6.32656			0.322013
$387$	10.4591	−	1.09929i	0.531665	−	0.0558803i
$388$	8.74803	+	7.87676i	0.444114	+	0.399882i
$389$	−7.63724	+	1.62335i	−0.387224	+	0.0823069i	−0.397410	−	0.917641i	$-0.630091\pi$
$389$	−7.63724	+	1.62335i	−0.387224	+	0.0823069i	0.0101863	+	0.999948i	$0.496758\pi$
$390$	−2.78619	−	6.25789i	−0.141084	−	0.316881i
$391$	1.79718	+	1.30573i	0.0908872	+	0.0660334i
$392$	0.989393	+	12.6127i	0.0499719	+	0.637037i
$393$	−34.2038	+	11.1135i	−1.72536	+	0.560602i
$394$	0.254747	+	2.42376i	0.0128340	+	0.122107i
$395$	−2.99991	−	5.19600i	−0.150942	−	0.261439i
$396$	11.4747	+	2.82317i	0.576628	+	0.141870i
$397$	11.7867	+	6.80506i	0.591558	+	0.341536i	0.765713	−	0.643182i	$-0.222386\pi$
$397$	11.7867	+	6.80506i	0.591558	+	0.341536i	−0.174155	+	0.984718i	$0.555719\pi$
$398$	2.12893	−	1.54676i	0.106713	−	0.0775319i
$399$	3.63115	−	12.8688i	0.181785	−	0.644245i
$400$	2.63611	−	8.11311i	0.131805	−	0.405655i
$401$	−2.69796	+	1.20121i	−0.134730	+	0.0599856i	−0.472994	−	0.881066i	$-0.656827\pi$
$401$	−2.69796	+	1.20121i	−0.134730	+	0.0599856i	0.338264	+	0.941051i	$0.390160\pi$
$402$	0.185800	−	1.76777i	0.00926684	−	0.0881681i
$403$	−9.29529	−	43.7309i	−0.463032	−	2.17839i
$404$	21.7741	+	4.62823i	1.08330	+	0.230263i
$405$	−8.68790	−	11.9579i	−0.431705	−	0.594191i
$406$	−4.00855	−	8.13115i	−0.198941	−	0.403542i
$407$	−8.54551	+	1.53417i	−0.423585	+	0.0760460i
$408$	−3.47858	+	6.02507i	−0.172215	+	0.298285i
$409$	3.24171	+	1.44330i	0.160292	+	0.0713668i	0.485315	−	0.874340i	$-0.338705\pi$
$409$	3.24171	+	1.44330i	0.160292	+	0.0713668i	−0.325022	+	0.945706i	$0.605372\pi$
$410$	−0.934556	+	1.03793i	−0.0461545	+	0.0512597i
$411$	−26.5780	+	23.9309i	−1.31099	+	1.18042i
$412$	7.58184	−	10.4355i	0.373531	−	0.514121i
$413$	9.93365	−	11.9408i	0.488803	−	0.587569i
$414$	1.18564	+	0.385237i	0.0582709	+	0.0189334i
$415$	−2.25793	+	10.6227i	−0.110838	+	0.521450i
$416$	−9.44872	+	21.2222i	−0.463262	+	1.04050i
$417$	17.2341	−	9.95014i	0.843959	−	0.487260i
$418$	−2.20075	+	2.83493i	−0.107642	+	0.138661i
$419$			38.0166i			1.85723i	0.371042	+	0.928616i	$0.379001\pi$
$419$			38.0166i			1.85723i	−0.371042	+	0.928616i	$0.620999\pi$
$420$	−11.9313	+	7.52594i	−0.582187	+	0.367228i
$421$	−1.56677	−	4.82203i	−0.0763598	−	0.235011i	0.905590	−	0.424155i	$-0.139429\pi$
$421$	−1.56677	−	4.82203i	−0.0763598	−	0.235011i	−0.981949	+	0.189144i	$0.939429\pi$
$422$	2.56740	+	2.85138i	0.124979	+	0.138803i
$423$	12.7122	+	1.33611i	0.618089	+	0.0649638i
$424$	19.6070	+	2.06078i	0.952202	+	0.100080i
$425$	−3.67015	−	4.07611i	−0.178028	−	0.197721i
$426$	5.19082	+	15.9757i	0.251496	+	0.774026i
$427$	13.9172	+	7.32448i	0.673502	+	0.354457i
$428$			19.4592i			0.940595i
$429$	21.6030	−	27.8282i	1.04300	−	1.34356i
$430$	2.91819	−	1.68482i	0.140728	−	0.0812491i
$431$	4.10689	−	9.22423i	0.197822	−	0.444315i	−0.787210	−	0.616684i	$-0.788475\pi$
$431$	4.10689	−	9.22423i	0.197822	−	0.444315i	0.985032	+	0.172369i	$0.0551421\pi$
$432$	−1.22888	+	5.78143i	−0.0591245	+	0.278159i
$433$	−26.2664	−	8.53446i	−1.26228	−	0.410140i	−0.399975	−	0.916526i	$-0.630981\pi$
$433$	−26.2664	−	8.53446i	−1.26228	−	0.410140i	−0.862307	+	0.506386i	$0.830981\pi$
$434$	11.2138	−	4.13536i	0.538280	−	0.198504i
$435$	12.6543	−	17.4171i	0.606725	−	0.835085i
$436$	1.65253	−	1.48795i	0.0791420	−	0.0712598i
$437$	1.95154	−	2.16741i	0.0933549	−	0.103681i
$438$	8.47909	+	3.77514i	0.405147	+	0.180383i
$439$	−14.9509	+	25.8957i	−0.713567	+	1.23593i	0.249943	+	0.968261i	$0.419588\pi$
$439$	−14.9509	+	25.8957i	−0.713567	+	1.23593i	−0.963510	+	0.267674i	$0.913745\pi$
$440$	7.93711	−	1.42495i	0.378387	−	0.0679316i
$441$	−13.9682	−	1.84258i	−0.665150	−	0.0877418i
$442$	2.29836	+	3.16342i	0.109322	+	0.150469i
$443$	−0.876401	−	0.186285i	−0.0416391	−	0.00885066i	0.187045	−	0.982351i	$-0.440109\pi$
$443$	−0.876401	−	0.186285i	−0.0416391	−	0.00885066i	−0.228684	+	0.973501i	$0.573442\pi$
$444$	2.15709	+	10.1483i	0.102371	+	0.481617i
$445$	−0.480882	+	4.57528i	−0.0227960	+	0.216889i
$446$	−5.67690	+	2.52752i	−0.268809	+	0.119681i
$447$	7.25231	−	22.3203i	0.343023	−	1.05571i
$448$	7.64074	+	2.15597i	0.360991	+	0.101860i
$449$	9.91637	−	7.20467i	0.467982	−	0.340009i	−0.328672	−	0.944444i	$-0.606601\pi$
$449$	9.91637	−	7.20467i	0.467982	−	0.340009i	0.796654	+	0.604435i	$0.206601\pi$
$450$	−2.66573	−	1.53906i	−0.125664	−	0.0725519i
$451$	−6.97491	−	1.71606i	−0.328436	−	0.0808061i
$452$	−5.12057	−	8.86909i	−0.240852	−	0.417167i
$453$	−1.42324	−	13.5412i	−0.0668696	−	0.636221i
$454$	8.80105	−	2.85963i	0.413054	−	0.134209i
$455$	2.42091	+	16.7118i	0.113494	+	0.783459i
$456$	7.38963	+	5.36888i	0.346051	+	0.251421i
$457$	13.0224	+	29.2487i	0.609160	+	1.36820i	0.910035	+	0.414532i	$0.136055\pi$
$457$	13.0224	+	29.2487i	0.609160	+	1.36820i	−0.300875	+	0.953664i	$0.597279\pi$
$458$	−2.97419	+	0.632183i	−0.138975	+	0.0295400i
$459$	2.82421	+	2.54293i	0.131823	+	0.118694i
$460$	−3.06006	+	0.321625i	−0.142676	+	0.0149959i
$461$	9.89306			0.460766			0.230383	−	0.973100i	$-0.426002\pi$
$461$	9.89306			0.460766			0.230383	+	0.973100i	$0.426002\pi$
$462$	8.19060	+	4.64903i	0.381061	+	0.216292i
$463$	3.79441			0.176341			0.0881706	−	0.996105i	$-0.471898\pi$
$463$	3.79441			0.176341			0.0881706	+	0.996105i	$0.471898\pi$
$464$	−19.0082	+	1.99785i	−0.882436	+	0.0927477i
$465$	21.0930	+	18.9922i	0.978164	+	0.880743i
$466$	8.08920	−	1.71941i	0.374725	−	0.0796502i
$467$	3.96774	+	8.91169i	0.183605	+	0.412384i	0.981775	−	0.190049i	$-0.0608647\pi$
$467$	3.96774	+	8.91169i	0.183605	+	0.412384i	−0.798169	+	0.602433i	$0.794198\pi$
$468$	−13.6753	−	9.93567i	−0.632140	−	0.459277i
$469$	−1.62420	+	4.06957i	−0.0749985	+	0.187915i
$470$	3.89509	−	1.26559i	0.179667	−	0.0583773i
$471$	−4.27525	−	40.6763i	−0.196993	−	1.87426i
$472$	5.30525	+	9.18896i	0.244194	+	0.422956i
$473$	14.7248	+	9.13763i	0.677046	+	0.420149i
$474$	4.14544	+	2.39337i	0.190406	+	0.109931i
$475$	−5.82591	+	4.23277i	−0.267311	+	0.194213i
$476$	5.76864	−	5.61812i	0.264405	−	0.257506i
$477$	−6.78462	+	20.8809i	−0.310646	+	0.956071i
$478$	−12.4118	+	5.52607i	−0.567700	+	0.252756i
$479$	−0.632139	+	6.01440i	−0.0288832	+	0.274805i	0.970543	+	0.240929i	$0.0774519\pi$
$479$	−0.632139	+	6.01440i	−0.0288832	+	0.274805i	−0.999426	+	0.0338765i	$0.989215\pi$
$480$	−3.06633	−	14.4260i	−0.139958	−	0.658452i
$481$	12.1480	+	2.58213i	0.553900	+	0.117735i
$482$	−1.93630	−	2.66509i	−0.0881962	−	0.121392i
$483$	−6.36322	−	4.25294i	−0.289536	−	0.193516i
$484$	12.0833	+	15.2696i	0.549241	+	0.694071i
$485$	−4.47299	+	7.74745i	−0.203108	+	0.351793i
$486$	7.86877	+	3.50340i	0.356935	+	0.158918i
$487$	−0.662221	+	0.735471i	−0.0300081	+	0.0333274i	−0.757962	−	0.652299i	$-0.773805\pi$
$487$	−0.662221	+	0.735471i	−0.0300081	+	0.0333274i	0.727954	+	0.685626i	$0.240471\pi$
$488$	−7.98382	+	7.18867i	−0.361411	+	0.325416i
$489$	9.84758	−	13.5540i	0.445323	−	0.612934i
$490$	−4.32871	+	1.28102i	−0.195551	+	0.0578705i
$491$	−21.1985	−	6.88780i	−0.956674	−	0.310842i	−0.211249	−	0.977432i	$-0.567753\pi$
$491$	−21.1985	−	6.88780i	−0.956674	−	0.310842i	−0.745425	+	0.666590i	$0.767753\pi$
$492$	−1.78461	+	8.39591i	−0.0804562	+	0.378517i
$493$	−4.99842	+	11.2266i	−0.225118	+	0.505623i
$494$	4.44594	−	2.56687i	0.200032	−	0.115489i
$495$	−0.285550	+	8.97588i	−0.0128345	+	0.403436i
$496$		−	25.1985i		−	1.13145i
$497$	−1.62039	−	41.3766i	−0.0726845	−	1.85600i
$498$	−2.67742	−	8.24025i	−0.119978	−	0.369254i
$499$	9.95293	+	11.0539i	0.445554	+	0.494838i	0.923525	−	0.383537i	$-0.125294\pi$
$499$	9.95293	+	11.0539i	0.445554	+	0.494838i	−0.477971	+	0.878376i	$0.658628\pi$
$500$	19.3974	+	2.03875i	0.867480	+	0.0911759i
$501$	13.6709	+	1.43687i	0.610770	+	0.0641945i
$502$	−3.10209	−	3.44522i	−0.138453	−	0.153768i
$503$	−10.2972	−	31.6916i	−0.459130	−	1.41306i	−0.866217	−	0.499668i	$-0.833455\pi$
$503$	−10.2972	−	31.6916i	−0.459130	−	1.41306i	0.407087	−	0.913389i	$-0.366545\pi$
$504$	4.48239	−	8.51698i	0.199662	−	0.379376i
$505$			16.9171i			0.752803i
$506$	1.15401	+	1.69948i	0.0513019	+	0.0755512i
$507$	−18.4359	+	10.6440i	−0.818766	+	0.472715i
$508$	−12.2328	+	27.4753i	−0.542742	+	1.21902i
$509$	6.87795	−	32.3582i	0.304860	−	1.43425i	−0.512779	−	0.858520i	$-0.671384\pi$
$509$	6.87795	−	32.3582i	0.304860	−	1.43425i	0.817639	−	0.575731i	$-0.195283\pi$
$510$	−2.36095	−	0.767119i	−0.104545	−	0.0339686i
$511$	−17.5891	−	14.6325i	−0.778097	−	0.647305i
$512$	−13.3774	+	18.4124i	−0.591203	+	0.813722i
$513$	3.70791	−	3.33862i	0.163708	−	0.147404i
$514$	−3.48905	+	3.87499i	−0.153896	+	0.170918i
$515$	8.95525	+	3.98713i	0.394615	+	0.175694i
$516$	10.3543	−	17.9342i	0.455823	−	0.789509i
$517$	15.1967	+	14.5844i	0.668349	+	0.641419i
$518$	−0.217571	+	3.31300i	−0.00955954	+	0.145565i
$519$	6.50357	+	8.95140i	0.285475	+	0.392923i
$520$	−11.2831	−	2.39830i	−0.494797	−	0.105172i
$521$	3.04272	+	14.3149i	0.133304	+	0.627146i	0.993175	+	0.116634i	$0.0372105\pi$
$521$	3.04272	+	14.3149i	0.133304	+	0.627146i	−0.859871	+	0.510511i	$0.829456\pi$
$522$	−0.720886	+	6.85877i	−0.0315523	+	0.300200i
$523$	−19.1486	+	8.52553i	−0.837312	+	0.372795i	−0.780168	−	0.625571i	$-0.784866\pi$
$523$	−19.1486	+	8.52553i	−0.837312	+	0.372795i	−0.0571444	+	0.998366i	$0.518200\pi$
$524$	−8.78689	+	27.0433i	−0.383857	+	1.18139i
$525$	13.1848	+	13.5381i	0.575434	+	0.590850i
$526$	1.80623	−	1.31230i	0.0787553	−	0.0572191i
$527$	−14.0313	−	8.10097i	−0.611212	−	0.352884i
$528$	15.1710	−	12.8104i	0.660232	−	0.557502i
$529$	10.6653	+	18.4728i	0.463709	+	0.803167i
$530$	0.735328	+	6.99618i	0.0319406	+	0.303895i
$531$	−11.2380	+	3.65143i	−0.487686	+	0.158459i
$532$	−6.54399	−	8.30320i	−0.283718	−	0.359989i
$533$	8.31250	+	6.03938i	0.360054	+	0.261595i
$534$	−1.49286	−	3.35302i	−0.0646023	−	0.145099i
$535$	−14.4651	+	3.07464i	−0.625379	+	0.132928i
$536$	−2.22439	−	2.00285i	−0.0960789	−	0.0865098i
$537$	15.8040	−	1.66107i	0.681995	−	0.0716805i
$538$	−8.38271			−0.361404
$539$	−16.3197	−	16.5127i	−0.702938	−	0.711251i
$540$	−5.26387			−0.226521
$541$	−9.11322	+	0.957838i	−0.391808	+	0.0411807i	−0.298384	−	0.954446i	$-0.596448\pi$
$541$	−9.11322	+	0.957838i	−0.391808	+	0.0411807i	−0.0934235	+	0.995626i	$0.529781\pi$
$542$	−11.1729	−	10.0601i	−0.479916	−	0.432119i
$543$	0.669798	−	0.142370i	0.0287438	−	0.00610968i
$544$	3.42417	+	7.69082i	0.146810	+	0.329741i
$545$	1.36718	+	0.993315i	0.0585636	+	0.0425489i
$546$	−8.33911	−	10.5809i	−0.356881	−	0.452821i
$547$	6.99390	−	2.27246i	0.299038	−	0.0971632i	−0.155655	−	0.987811i	$-0.549749\pi$
$547$	6.99390	−	2.27246i	0.299038	−	0.0971632i	0.454693	+	0.890648i	$0.349749\pi$
$548$	2.95574	+	28.1220i	0.126263	+	1.20131i
$549$	−5.98209	−	10.3613i	−0.255309	−	0.442209i
$550$	−1.91466	−	4.69692i	−0.0816414	−	0.200277i
$551$	13.9728	+	8.06721i	0.595262	+	0.343675i
$552$	4.22978	−	3.07311i	0.180031	−	0.130800i
$553$	−8.23270	−	8.45327i	−0.350090	−	0.359469i
$554$	2.13256	−	6.56334i	0.0906038	−	0.278850i
$555$	−7.20296	+	3.20696i	−0.305748	+	0.136128i
$556$	1.64467	−	15.6480i	0.0697494	−	0.663621i
$557$	1.66437	+	7.83025i	0.0705217	+	0.331778i	0.999239	−	0.0390107i	$-0.0124206\pi$
$557$	1.66437	+	7.83025i	0.0705217	+	0.331778i	−0.928717	+	0.370789i	$0.879087\pi$
$558$	−8.89372	−	1.89042i	−0.376501	−	0.0800278i
$559$	−14.5707	−	20.0549i	−0.616276	−	0.848231i
$560$	−0.623689	+	9.49703i	−0.0263557	+	0.401323i
$561$	−2.25597	−	12.5660i	−0.0952472	−	0.530538i
$562$	5.96304	−	10.3283i	0.251536	−	0.435673i
$563$	23.8442	+	10.6161i	1.00491	+	0.447417i	0.842147	−	0.539248i	$-0.181291\pi$
$563$	23.8442	+	10.6161i	1.00491	+	0.447417i	0.162768	+	0.986664i	$0.447958\pi$
$564$	16.8419	−	18.7048i	0.709170	−	0.787614i
$565$	5.78380	−	5.20776i	0.243326	−	0.219092i
$566$	−1.71289	+	2.35759i	−0.0719980	+	0.0990968i
$567$	−22.3472	−	18.5908i	−0.938494	−	0.780740i
$568$	26.9021	+	8.74104i	1.12879	+	0.366766i
$569$	6.30186	−	29.6479i	0.264188	−	1.24291i	−0.623267	−	0.782009i	$-0.714195\pi$
$569$	6.30186	−	29.6479i	0.264188	−	1.24291i	0.887454	−	0.460896i	$-0.152472\pi$
$570$	−1.32565	+	2.97745i	−0.0555252	+	0.124712i
$571$	0.104033	−	0.0600632i	0.00435363	−	0.00251357i	−0.497822	−	0.867279i	$-0.665867\pi$
$571$	0.104033	−	0.0600632i	0.00435363	−	0.00251357i	0.502175	+	0.864766i	$0.332533\pi$
$572$	−7.76069	−	26.7510i	−0.324491	−	1.11852i
$573$		−	45.4937i		−	1.90053i
$574$	−1.27927	+	2.43074i	−0.0533958	+	0.101457i
$575$	1.27375	+	3.92020i	0.0531190	+	0.163483i
$576$	−4.04129	−	4.48830i	−0.168387	−	0.187013i
$577$	5.40811	+	0.568416i	0.225143	+	0.0236635i	0.216428	−	0.976299i	$-0.430559\pi$
$577$	5.40811	+	0.568416i	0.225143	+	0.0236635i	0.00871466	+	0.999962i	$0.497226\pi$
$578$	−6.69549	−	0.703725i	−0.278496	−	0.0292711i
$579$	19.7714	+	21.9584i	0.821673	+	0.912560i
$580$	−5.25999	−	16.1886i	−0.218409	−	0.672194i
$581$	0.835796	+	21.3420i	0.0346746	+	0.885416i
$582$		−	7.13723i		−	0.295848i
$583$	−29.9305	+	20.3238i	−1.23960	+	0.841728i
$584$	13.5356	−	7.81476i	0.560106	−	0.323377i
$585$	5.22496	−	11.7355i	0.216026	−	0.485202i
$586$	−2.05944	+	9.68890i	−0.0850747	+	0.400245i
$587$	−1.05526	−	0.342876i	−0.0435554	−	0.0141520i	0.287158	−	0.957883i	$-0.407289\pi$
$587$	−1.05526	−	0.342876i	−0.0435554	−	0.0141520i	−0.330714	+	0.943731i	$0.607289\pi$
$588$	−19.1023	+	20.1193i	−0.787767	+	0.829708i
$589$	−12.5031	+	17.2091i	−0.515183	+	0.709088i
$590$	−2.81357	+	2.53335i	−0.115833	+	0.104296i
$591$	−7.61634	+	8.45880i	−0.313294	+	0.347949i
$592$	6.39471	+	2.84711i	0.262821	+	0.117015i
$593$	−1.02128	+	1.76892i	−0.0419391	+	0.0726407i	−0.886233	−	0.463240i	$-0.846687\pi$
$593$	−1.02128	+	1.76892i	−0.0419391	+	0.0726407i	0.844294	+	0.535880i	$0.180020\pi$
$594$	1.65951	+	3.09784i	0.0680904	+	0.127106i
$595$	5.08773	+	3.40045i	0.208576	+	0.139405i
$596$	−10.9068	−	15.0119i	−0.446760	−	0.614912i
$597$	12.0217	+	2.55530i	0.492017	+	0.104582i
$598$	−0.610952	−	2.87430i	−0.0249837	−	0.117539i
$599$	0.520794	−	4.95502i	0.0212790	−	0.202457i	−0.978717	−	0.205214i	$-0.934211\pi$
$599$	0.520794	−	4.95502i	0.0212790	−	0.202457i	0.999996	+	0.00275728i	$0.000877669\pi$
$600$	−11.7931	+	5.25065i	−0.481453	+	0.214357i
$601$	−4.24531	+	13.0657i	−0.173170	+	0.532961i	−0.999545	−	0.0301581i	$-0.990399\pi$
$601$	−4.24531	+	13.0657i	−0.173170	+	0.532961i	0.826375	+	0.563119i	$0.190399\pi$
$602$	4.74754	−	4.62367i	0.193495	−	0.188447i
$603$	2.69675	−	1.95930i	0.109820	−	0.0797889i
$604$	−9.32305	−	5.38266i	−0.379349	−	0.219017i
$605$	−9.44147	+	11.3948i	−0.383850	+	0.463266i
$606$	−6.74837	−	11.6885i	−0.274134	−	0.474814i
$607$	0.360664	+	3.43149i	0.0146389	+	0.139280i	0.999400	−	0.0346319i	$-0.0110259\pi$
$607$	0.360664	+	3.43149i	0.0146389	+	0.139280i	−0.984761	+	0.173912i	$0.944359\pi$
$608$	10.5119	−	3.41553i	0.426315	−	0.138518i
$609$	15.6945	−	39.3241i	0.635975	−	1.59349i
$610$	−3.10130	−	2.25323i	−0.125568	−	0.0912305i
$611$	−12.2547	−	27.5245i	−0.495773	−	1.11352i
$612$	−5.99192	+	1.27362i	−0.242209	+	0.0514831i
$613$	16.2494	+	14.6310i	0.656306	+	0.590941i	0.928514	−	0.371298i	$-0.121087\pi$
$613$	16.2494	+	14.6310i	0.656306	+	0.590941i	−0.272208	+	0.962238i	$0.587754\pi$
$614$	−13.9019	+	1.46115i	−0.561034	+	0.0589671i
$615$	−6.52311			−0.263037
$616$	14.4406	−	6.55677i	0.581826	−	0.264180i
$617$	13.9890			0.563177			0.281589	−	0.959535i	$-0.409139\pi$
$617$	13.9890			0.563177			0.281589	+	0.959535i	$0.409139\pi$
$618$	−7.77792	+	0.817493i	−0.312874	+	0.0328844i
$619$	−3.29546	−	2.96725i	−0.132456	−	0.119264i	0.600240	−	0.799820i	$-0.295072\pi$
$619$	−3.29546	−	2.96725i	−0.132456	−	0.119264i	−0.732696	+	0.680556i	$0.761738\pi$
$620$	21.9510	−	4.66582i	0.881572	−	0.187384i
$621$	−1.16162	−	2.60904i	−0.0466143	−	0.104697i
$622$	8.98597	+	6.52869i	0.360304	+	0.261776i
$623$	1.29714	+	8.95426i	0.0519687	+	0.358745i
$624$	−27.0131	+	8.77708i	−1.08139	+	0.351364i
$625$	−0.117969	−	1.12240i	−0.00471877	−	0.0448961i
$626$	2.97147	+	5.14673i	0.118764	+	0.205705i
$627$	−16.7172	+	1.22114i	−0.667622	+	0.0487677i
$628$	−28.0054	−	16.1689i	−1.11754	−	0.645210i
$629$	3.64116	−	2.64546i	0.145183	−	0.105481i
$630$	3.30515	+	0.932606i	0.131680	+	0.0371559i
$631$	10.8219	−	33.3063i	0.430812	−	1.32590i	−0.466506	−	0.884518i	$-0.654488\pi$
$631$	10.8219	−	33.3063i	0.430812	−	1.32590i	0.897318	−	0.441384i	$-0.145512\pi$
$632$	7.36371	−	3.27854i	0.292913	−	0.130413i
$633$	−1.87317	+	17.8220i	−0.0744517	+	0.708361i
$634$	−0.0472280	−	0.222190i	−0.00187566	−	0.00882431i
$635$	−22.3567	−	4.75207i	−0.887199	−	0.188580i
$636$	25.4117	+	34.9762i	1.00764	+	1.38690i
$637$	12.7010	+	30.6852i	0.503233	+	1.21579i
$638$	−7.86886	+	8.19923i	−0.311531	+	0.324611i
$639$	−15.7506	+	27.2808i	−0.623083	+	1.07921i
$640$	−13.8033	−	6.14563i	−0.545624	−	0.242927i
$641$	−3.96926	+	4.40831i	−0.156776	+	0.174118i	−0.816416	−	0.577464i	$-0.804042\pi$
$641$	−3.96926	+	4.40831i	−0.156776	+	0.174118i	0.659640	+	0.751582i	$0.270709\pi$
$642$	8.76781	−	7.89458i	0.346038	−	0.311574i
$643$	−19.4192	+	26.7283i	−0.765820	+	1.05406i	0.230888	+	0.972980i	$0.425837\pi$
$643$	−19.4192	+	26.7283i	−0.765820	+	1.05406i	−0.996708	+	0.0810798i	$0.974163\pi$
$644$	−5.67759	+	2.09375i	−0.223728	+	0.0825052i
$645$	14.9675	+	4.86323i	0.589345	+	0.191490i
$646$	0.386807	−	1.81979i	0.0152187	−	0.0715985i
$647$	−1.89752	+	4.26189i	−0.0745990	+	0.167552i	−0.946996	−	0.321247i	$-0.895898\pi$
$647$	−1.89752	+	4.26189i	−0.0745990	+	0.167552i	0.872397	+	0.488799i	$0.162565\pi$
$648$	17.1971	−	9.92875i	0.675566	−	0.390038i
$649$	−18.3174	−	6.60268i	−0.719022	−	0.259178i
$650$			7.25551i			0.284584i
$651$	49.3979	+	25.9976i	1.93606	+	1.01893i
$652$	−4.09333	−	12.5980i	−0.160307	−	0.493375i
$653$	6.77002	+	7.51886i	0.264931	+	0.294236i	0.860903	−	0.508770i	$-0.169900\pi$
$653$	6.77002	+	7.51886i	0.264931	+	0.294236i	−0.595971	+	0.803006i	$0.703233\pi$
$654$	−1.34086	−	0.140930i	−0.0524319	−	0.00551081i
$655$	−21.4911	−	2.25881i	−0.839727	−	0.0882588i
$656$	3.87503	+	4.30366i	0.151295	+	0.168030i
$657$	5.37866	+	16.5538i	0.209841	+	0.645825i
$658$	6.81259	−	4.29721i	0.265582	−	0.167523i
$659$		−	16.3262i		−	0.635978i	−0.948094	−	0.317989i	$-0.896992\pi$
$659$		−	16.3262i		−	0.635978i	0.948094	−	0.317989i	$-0.103008\pi$
$660$	13.9685	+	10.8437i	0.543724	+	0.422092i
$661$	6.68945	−	3.86215i	0.260189	−	0.150220i	−0.364232	−	0.931308i	$-0.618668\pi$
$661$	6.68945	−	3.86215i	0.260189	−	0.150220i	0.624421	+	0.781088i	$0.285335\pi$
$662$	−3.62845	+	8.14964i	−0.141024	+	0.316745i
$663$	−3.79698	+	17.8634i	−0.147463	+	0.693757i
$664$	−13.8761	−	4.50861i	−0.538497	−	0.174968i
$665$	5.13824	−	6.17645i	0.199252	−	0.239512i
$666$	1.48461	−	2.04339i	0.0575276	−	0.0791799i
$667$	6.86312	−	6.17958i	0.265741	−	0.239274i
$668$	7.27240	−	8.07682i	0.281377	−	0.312501i
$669$	−26.5138	−	11.8047i	−1.02508	−	0.456395i
$670$	0.534018	−	0.924946i	0.0206309	−	0.0357338i
$671$	2.68315	−	19.5314i	0.103582	−	0.754000i
$672$	−12.8254	−	26.0156i	−0.494749	−	1.00358i
$673$	17.4921	+	24.0759i	0.674272	+	0.928056i	0.999848	−	0.0174600i	$-0.00555797\pi$
$673$	17.4921	+	24.0759i	0.674272	+	0.928056i	−0.325575	+	0.945516i	$0.605558\pi$
$674$	9.68437	+	2.05848i	0.373028	+	0.0792896i
$675$	1.46612	+	6.89755i	0.0564310	+	0.265487i
$676$	−1.75935	+	16.7391i	−0.0676673	+	0.643811i
$677$	27.7050	−	12.3351i	1.06479	−	0.474075i	0.201869	−	0.979413i	$-0.435299\pi$
$677$	27.7050	−	12.3351i	1.06479	−	0.474075i	0.862922	+	0.505337i	$0.168632\pi$
$678$	−1.91878	+	5.90538i	−0.0736901	+	0.226795i
$679$	−4.77788	+	16.9328i	−0.183358	+	0.649821i
$680$	−3.38193	+	2.45712i	−0.129691	+	0.0942261i
$681$	37.4299	+	21.6102i	1.43432	+	0.828104i
$682$	−9.66623	−	11.4474i	−0.370139	−	0.438344i
$683$	−21.1679	−	36.6639i	−0.809968	−	1.40291i	−0.912885	−	0.408216i	$-0.866151\pi$
$683$	−21.1679	−	36.6639i	−0.809968	−	1.40291i	0.102918	−	0.994690i	$-0.467182\pi$
$684$	0.840677	+	7.99851i	0.0321441	+	0.305831i
$685$	−20.4376	+	6.64058i	−0.780881	+	0.253724i
$686$	−7.63172	+	4.53643i	−0.291380	+	0.173202i
$687$	−11.4890	−	8.34723i	−0.438332	−	0.318467i
$688$	−5.68285	−	12.7639i	−0.216657	−	0.486619i
$689$	50.6209	−	10.7598i	1.92850	−	0.409916i
$690$	1.38638	+	1.24830i	0.0527786	+	0.0475221i
$691$	20.8523	−	2.19166i	0.793257	−	0.0833747i	0.300773	−	0.953696i	$-0.402755\pi$
$691$	20.8523	−	2.19166i	0.793257	−	0.0833747i	0.492485	+	0.870321i	$0.336089\pi$
$692$	8.74818			0.332556
$693$	3.79877	+	17.2483i	0.144303	+	0.655210i
$694$	−2.50504			−0.0950900
$695$	11.8918	−	1.24988i	0.451083	−	0.0474107i
$696$	21.4941	+	19.3534i	0.814733	+	0.733589i
$697$	3.64218	−	0.774169i	0.137957	−	0.0293237i
$698$	−3.10111	−	6.96520i	−0.117379	−	0.263637i
$699$	31.2477	+	22.7028i	1.18190	+	0.858699i
$700$	14.7870	−	2.14209i	0.558898	−	0.0809633i
$701$	−0.357284	+	0.116089i	−0.0134944	+	0.00438461i	−0.315756	−	0.948840i	$-0.602258\pi$
$701$	−0.357284	+	0.116089i	−0.0134944	+	0.00438461i	0.302262	+	0.953225i	$0.402258\pi$
$702$	−0.525475	−	4.99956i	−0.0198328	−	0.188696i
$703$	−2.95451	−	5.11737i	−0.111432	−	0.193005i
$704$	−0.725044	−	9.92573i	−0.0273261	−	0.374090i
$705$	16.5654	+	9.56402i	0.623888	+	0.360202i
$706$	−0.687821	+	0.499732i	−0.0258865	+	0.0188076i
$707$	8.18559	+	32.2481i	0.307851	+	1.21282i
$708$	−7.19011	+	22.1289i	−0.270221	+	0.831654i
$709$	32.0770	−	14.2816i	1.20468	−	0.536358i	0.296537	−	0.955021i	$-0.404168\pi$
$709$	32.0770	−	14.2816i	1.20468	−	0.536358i	0.908141	+	0.418664i	$0.137501\pi$
$710$	−1.05503	+	10.0379i	−0.0395945	+	0.376717i
$711$	1.86634	+	8.78045i	0.0699933	+	0.329293i
$712$	−6.04556	−	1.28502i	−0.226567	−	0.0481583i
$713$	7.15672	+	9.85038i	0.268021	+	0.368900i
$714$	−4.87172	−	0.319935i	−0.182319	−	0.0119733i
$715$	18.6593	−	9.99573i	0.697817	−	0.373819i
$716$	6.28215	−	10.8810i	0.234775	−	0.406642i
$717$	−57.9686	−	25.8093i	−2.16488	−	0.963866i
$718$	−5.18062	+	5.75366i	−0.193339	+	0.214725i
$719$	−3.31620	+	2.98592i	−0.123673	+	0.111356i	−0.728647	−	0.684890i	$-0.759850\pi$
$719$	−3.31620	+	2.98592i	−0.123673	+	0.111356i	0.604974	+	0.796246i	$0.293184\pi$
$720$	4.25578	−	5.85758i	0.158604	−	0.218299i
$721$	19.0001	+	3.26731i	0.707600	+	0.121681i
$722$	6.33935	+	2.05978i	0.235926	+	0.0766570i
$723$	3.19885	−	15.0494i	0.118966	−	0.559693i
$724$	0.220210	−	0.494600i	0.00818404	−	0.0183817i
$725$	−19.7478	+	11.4014i	−0.733414	+	0.423437i
$726$	1.97789	−	11.6393i	0.0734064	−	0.431974i
$727$			43.6196i			1.61776i	0.587972	+	0.808881i	$0.299926\pi$
$727$			43.6196i			1.61776i	−0.587972	+	0.808881i	$0.700074\pi$
$728$	−22.6688	+	0.887753i	−0.840160	+	0.0329023i
$729$	2.24577	+	6.91178i	0.0831768	+	0.255992i
$730$	3.73169	+	4.14446i	0.138116	+	0.153393i
$731$	−8.93427	−	0.939030i	−0.330446	−	0.0347313i
$732$	−23.4298	−	2.46258i	−0.865992	−	0.0910194i
$733$	0.631219	+	0.701040i	0.0233146	+	0.0258935i	0.754689	−	0.656082i	$-0.227788\pi$
$733$	0.631219	+	0.701040i	0.0233146	+	0.0258935i	−0.731375	+	0.681976i	$0.761121\pi$
$734$	−0.378033	−	1.16347i	−0.0139535	−	0.0429443i
$735$	−17.9741	−	11.0208i	−0.662983	−	0.406510i
$736$		−	6.32661i		−	0.233202i
$737$	5.49000	+	0.174654i	0.202227	+	0.00643345i
$738$	1.80967	−	1.04481i	0.0666149	−	0.0384601i
$739$	7.40288	−	16.6271i	0.272319	−	0.611640i	−0.724677	−	0.689089i	$-0.758011\pi$
$739$	7.40288	−	16.6271i	0.272319	−	0.611640i	0.996996	+	0.0774494i	$0.0246776\pi$
$740$	−1.29612	+	6.09774i	−0.0476462	+	0.224158i
$741$	22.8034	+	7.40927i	0.837704	+	0.272186i
$742$	4.78690	+	12.9806i	0.175733	+	0.476532i
$743$	17.1565	−	23.6138i	0.629410	−	0.866308i	−0.368586	−	0.929594i	$-0.620158\pi$
$743$	17.1565	−	23.6138i	0.629410	−	0.866308i	0.997995	+	0.0632858i	$0.0201580\pi$
$744$	−28.3378	+	25.5155i	−1.03892	+	0.935444i
$745$	9.43584	−	10.4796i	0.345702	−	0.383941i
$746$	1.86889	+	0.832084i	0.0684250	+	0.0304648i
$747$	8.12412	−	14.0714i	0.297246	−	0.514845i
$748$	−9.08627	−	4.39681i	−0.332227	−	0.160763i
$749$	−26.0862	+	12.8601i	−0.953168	+	0.469899i
$750$	−6.95092	−	9.56712i	−0.253812	−	0.349342i
$751$	−12.2614	−	2.60623i	−0.447424	−	0.0951028i	−0.0213109	−	0.999773i	$-0.506784\pi$
$751$	−12.2614	−	2.60623i	−0.447424	−	0.0951028i	−0.426113	+	0.904670i	$0.640117\pi$
$752$	−3.53069	−	16.6106i	−0.128751	−	0.605726i
$753$	2.26328	−	21.5337i	0.0824785	−	0.784730i
$754$	14.8506	−	6.61193i	0.540828	−	0.240792i
$755$	2.52814	−	7.78081i	0.0920084	−	0.283173i
$756$	−10.0342	+	2.54699i	−0.364940	+	0.0926333i
$757$	−41.0708	+	29.8397i	−1.49274	+	1.08454i	−0.519582	+	0.854421i	$0.673912\pi$
$757$	−41.0708	+	29.8397i	−1.49274	+	1.08454i	−0.973162	+	0.230122i	$0.926088\pi$
$758$	6.55528	+	3.78469i	0.238098	+	0.137466i
$759$	−2.29217	+	9.31650i	−0.0832005	+	0.338168i
$760$	2.74417	+	4.75304i	0.0995414	+	0.172411i
$761$	−0.0948176	−	0.902129i	−0.00343713	−	0.0327021i	0.992669	−	0.120865i	$-0.0385669\pi$
$761$	−0.0948176	−	0.902129i	−0.00343713	−	0.0327021i	−0.996106	+	0.0881633i	$0.971900\pi$
$762$	17.3425	−	5.63492i	0.628253	−	0.204132i
$763$	3.08680	+	1.23197i	0.111750	+	0.0446002i
$764$	−29.1000	−	21.1424i	−1.05280	−	0.764905i
$765$	−1.89350	−	4.25288i	−0.0684597	−	0.153763i
$766$	5.41999	−	1.15205i	0.195832	−	0.0416254i
$767$	20.6984	+	18.6369i	0.747377	+	0.672941i
$768$	−1.37437	+	0.144452i	−0.0495932	+	0.00521246i
$769$	−29.9499			−1.08002			−0.540011	−	0.841658i	$-0.681580\pi$
$769$	−29.9499			−1.08002			−0.540011	+	0.841658i	$0.681580\pi$
$770$	3.35976	+	4.55365i	0.121077	+	0.164102i
$771$	−24.3532			−0.877061
$772$	23.2341	−	2.44200i	0.836214	−	0.0878896i
$773$	−23.5557	−	21.2096i	−0.847238	−	0.762857i	0.126152	−	0.992011i	$-0.459737\pi$
$773$	−23.5557	−	21.2096i	−0.847238	−	0.762857i	−0.973390	+	0.229154i	$0.926404\pi$
$774$	−4.93130	+	1.04818i	−0.177252	+	0.0376760i
$775$	−12.2278	−	27.4641i	−0.439235	−	0.986539i
$776$	−9.72331	−	7.06440i	−0.349046	−	0.253597i
$777$	−12.1788	+	9.59848i	−0.436913	+	0.344344i
$778$	3.55972	−	1.15662i	0.127622	−	0.0414670i
$779$	−0.511004	−	4.86188i	−0.0183086	−	0.174195i
$780$	−12.6477	−	21.9065i	−0.452861	−	0.784378i
$781$	−48.0678	+	19.5944i	−1.72000	+	0.701144i
$782$	−0.922235	−	0.532453i	−0.0329791	−	0.0190405i
$783$	12.7819	−	9.28659i	0.456788	−	0.331876i
$784$	3.40637	+	18.4054i	0.121656	+	0.657336i
$785$	7.59424	−	23.3727i	0.271050	−	0.834207i
$786$	15.7498	−	7.01228i	0.561778	−	0.250120i
$787$	3.41827	−	32.5227i	0.121848	−	1.15931i	−0.747207	−	0.664592i	$-0.768605\pi$
$787$	3.41827	−	32.5227i	0.121848	−	1.15931i	0.869055	−	0.494716i	$-0.164728\pi$
$788$	1.87111	+	8.80286i	0.0666554	+	0.313589i
$789$	10.1995	+	2.16797i	0.363112	+	0.0771819i
$790$	1.69058	+	2.32688i	0.0601480	+	0.0827866i
$791$	8.50547	−	12.7258i	0.302420	−	0.452477i
$792$	−11.9527	−	1.64202i	−0.424720	−	0.0583466i
$793$	−14.1005	+	24.4229i	−0.500725	+	0.867281i
$794$	−5.96032	−	2.65371i	−0.211524	−	0.0941765i
$795$	−21.9845	+	24.4163i	−0.779711	+	0.865957i
$796$	7.22139	−	6.50217i	0.255955	−	0.230463i
$797$	6.92321	−	9.52899i	0.245233	−	0.337534i	−0.668602	−	0.743621i	$-0.733107\pi$
$797$	6.92321	−	9.52899i	0.245233	−	0.337534i	0.913835	+	0.406087i	$0.133107\pi$
$798$	−1.08632	+	6.31716i	−0.0384552	+	0.223625i
$799$	−10.3843	−	3.37408i	−0.367372	−	0.119366i
$800$	−3.24780	+	15.2797i	−0.114827	+	0.540219i
$801$	2.79957	−	6.28793i	0.0989179	−	0.222173i
$802$	1.22607	−	0.707870i	0.0432939	−	0.0249958i
$803$	−9.72591	+	26.9820i	−0.343220	+	0.952176i
$804$		−	6.56379i		−	0.231487i
$805$	−2.45348	−	3.88963i	−0.0864738	−	0.137092i
$806$	6.62284	+	20.3830i	0.233279	+	0.717960i
$807$	−26.1972	−	29.0950i	−0.922186	−	1.02419i
$808$	−22.6032	−	2.37569i	−0.795178	−	0.0835765i
$809$	11.2347	+	1.18082i	0.394992	+	0.0415153i	0.299943	−	0.953957i	$-0.403032\pi$
$809$	11.2347	+	1.18082i	0.394992	+	0.0415153i	0.0950493	+	0.995473i	$0.469699\pi$
$810$	4.74116	+	5.26559i	0.166587	+	0.185014i
$811$	−10.5026	−	32.3237i	−0.368797	−	1.13504i	−0.947569	−	0.319550i	$-0.896468\pi$
$811$	−10.5026	−	32.3237i	−0.368797	−	1.13504i	0.578773	−	0.815489i	$-0.303532\pi$
$812$	−17.8598	−	28.3142i	−0.626758	−	0.993632i
$813$		−	70.2185i		−	2.46267i
$814$	3.99721	−	1.15962i	0.140102	−	0.0406447i
$815$	8.71800	−	5.03334i	0.305378	−	0.176310i
$816$	−4.18662	+	9.40330i	−0.146561	+	0.329181i
$817$	−2.45221	+	11.5367i	−0.0857919	+	0.403619i
$818$	−1.61781	−	0.525659i	−0.0565655	−	0.0183792i
$819$	4.28167	−	24.8988i	0.149614	−	0.870033i
$820$	−3.03150	+	4.17250i	−0.105865	+	0.145710i
$821$	4.72384	−	4.25337i	0.164863	−	0.148443i	−0.582570	−	0.812781i	$-0.697953\pi$
$821$	4.72384	−	4.25337i	0.164863	−	0.148443i	0.747433	+	0.664337i	$0.231286\pi$
$822$	11.4719	−	12.7409i	0.400129	−	0.444389i
$823$	3.02512	+	1.34687i	0.105449	+	0.0469490i	0.458783	−	0.888548i	$-0.348285\pi$
$823$	3.02512	+	1.34687i	0.105449	+	0.0469490i	−0.353334	+	0.935497i	$0.614952\pi$
$824$	−6.58485	+	11.4053i	−0.229394	+	0.397322i
$825$	10.3186	−	21.3240i	0.359248	−	0.742408i
$826$	−4.13754	+	6.19056i	−0.143964	+	0.215397i
$827$	15.5137	+	21.3528i	0.539464	+	0.742508i	0.988536	−	0.150988i	$-0.0482454\pi$
$827$	15.5137	+	21.3528i	0.539464	+	0.742508i	−0.449072	+	0.893496i	$0.648245\pi$
$828$	4.50292	+	0.957125i	0.156487	+	0.0332624i
$829$	3.39584	+	15.9762i	0.117942	+	0.554875i	0.996948	+	0.0780643i	$0.0248740\pi$
$829$	3.39584	+	15.9762i	0.117942	+	0.554875i	−0.879006	+	0.476811i	$0.841793\pi$
$830$	0.544182	−	5.17755i	0.0188888	−	0.179715i
$831$	29.4448	−	13.1097i	1.02143	−	0.454770i
$832$	−4.39920	+	13.5394i	−0.152515	+	0.469393i
$833$	11.3438	+	4.02031i	0.393039	+	0.139295i
$834$	−7.71781	+	5.60732i	−0.267246	+	0.194166i
$835$	7.15301	+	4.12979i	0.247540	+	0.142917i
$836$	−6.98793	+	11.2607i	−0.241683	+	0.389458i
$837$	10.4149	+	18.0391i	0.359991	+	0.623523i
$838$	−1.90496	−	18.1245i	−0.0658057	−	0.626099i
$839$	12.9356	−	4.20302i	0.446586	−	0.145104i	−0.0770864	−	0.997024i	$-0.524562\pi$
$839$	12.9356	−	4.20302i	0.446586	−	0.145104i	0.523672	+	0.851920i	$0.324562\pi$
$840$	11.3118	−	8.91512i	0.390293	−	0.307601i
$841$	17.8711	+	12.9841i	0.616244	+	0.447727i
$842$	0.988585	+	2.22040i	0.0340689	+	0.0765200i
$843$	54.4832	−	11.5808i	1.87650	−	0.398862i
$844$	10.5293	+	9.48063i	0.362434	+	0.326337i
$845$	−12.7211	+	1.33704i	−0.437618	+	0.0459955i
$846$	−6.12752			−0.210668
$847$	−12.4842	+	26.2897i	−0.428961	+	0.903323i
$848$	29.1686			1.00166
$849$	−13.5358	+	1.42267i	−0.464548	+	0.0488260i
$850$	1.95400	+	1.75939i	0.0670215	+	0.0603465i
$851$	−3.30838	+	0.703218i	−0.113410	+	0.0241060i
$852$	25.2297	+	56.6668i	0.864354	+	1.94137i
$853$	34.7523	+	25.2490i	1.18989	+	0.864509i	0.993253	−	0.115966i	$-0.0369965\pi$
$853$	34.7523	+	25.2490i	1.18989	+	0.864509i	0.196642	+	0.980475i	$0.436996\pi$
$854$	−7.00208	−	2.79458i	−0.239606	−	0.0956287i
$855$	−5.81289	+	1.88872i	−0.198797	+	0.0645930i
$856$	−2.07673	−	19.7587i	−0.0709810	−	0.675339i
$857$	−21.1712	−	36.6696i	−0.723195	−	1.25261i	−0.959713	−	0.280984i	$-0.909339\pi$
$857$	−21.1712	−	36.6696i	−0.723195	−	1.25261i	0.236517	−	0.971627i	$-0.423994\pi$
$858$	−8.90483	+	14.3496i	−0.304006	+	0.489889i
$859$	−31.2199	−	18.0248i	−1.06521	−	0.614999i	−0.138341	−	0.990385i	$-0.544177\pi$
$859$	−31.2199	−	18.0248i	−1.06521	−	0.614999i	−0.926869	+	0.375386i	$0.877510\pi$
$860$	10.0666	−	7.31385i	0.343270	−	0.249400i
$861$	−12.4346	+	3.15629i	−0.423770	+	0.107566i
$862$	−1.49575	+	4.60345i	−0.0509455	+	0.156794i
$863$	−1.20477	+	0.536396i	−0.0410107	+	0.0182591i	−0.427140	−	0.904186i	$-0.640479\pi$
$863$	−1.20477	+	0.536396i	−0.0410107	+	0.0182591i	0.386129	+	0.922445i	$0.373812\pi$
$864$	1.13134	−	10.7640i	0.0384891	−	0.366199i
$865$	1.38225	+	6.50299i	0.0469980	+	0.221108i
$866$	12.9502	+	2.75265i	0.440065	+	0.0935387i
$867$	−18.4819	−	25.4382i	−0.627679	−	0.863925i
$868$	39.5862	−	19.5154i	1.34364	−	0.662397i
$869$	−6.44301	+	13.3149i	−0.218564	+	0.451676i
$870$	−5.16019	+	8.93770i	−0.174947	+	0.303017i
$871$	−7.17787	−	3.19579i	−0.243213	−	0.108285i
$872$	−1.51917	+	1.68721i	−0.0514457	+	0.0571363i
$873$	9.94662	−	8.95597i	0.336642	−	0.303114i
$874$	−0.821794	+	1.13110i	−0.0277976	+	0.0382601i
$875$	10.0863	+	27.3508i	0.340978	+	0.924625i
$876$	32.5964	+	10.5912i	1.10133	+	0.357844i
$877$	−3.95621	+	18.6125i	−0.133592	+	0.628499i	0.859498	+	0.511139i	$0.170776\pi$
$877$	−3.95621	+	18.6125i	−0.133592	+	0.628499i	−0.993089	+	0.117360i	$0.962557\pi$
$878$	5.83026	−	13.0950i	0.196762	−	0.441934i
$879$	−40.0646	+	23.1313i	−1.35135	+	0.780200i
$880$	11.4584	−	3.32416i	0.386261	−	0.112057i
$881$			10.2750i			0.346172i	0.984907	+	0.173086i	$0.0553738\pi$
$881$			10.2750i			0.346172i	−0.984907	+	0.173086i	$0.944626\pi$
$882$	6.75166	+	0.178527i	0.227340	+	0.00601133i
$883$	14.1063	+	43.4148i	0.474716	+	1.46103i	0.846341	+	0.532642i	$0.178801\pi$
$883$	14.1063	+	43.4148i	0.474716	+	1.46103i	−0.371625	+	0.928383i	$0.621199\pi$
$884$	9.66173	+	10.7304i	0.324959	+	0.360904i
$885$	−17.5857	−	1.84833i	−0.591136	−	0.0621309i
$886$	0.427160	+	0.0448963i	0.0143507	+	0.00150832i
$887$	−17.3010	−	19.2147i	−0.580911	−	0.645167i	0.379025	−	0.925386i	$-0.376259\pi$
$887$	−17.3010	−	19.2147i	−0.580911	−	0.645167i	−0.959936	+	0.280220i	$0.909593\pi$
$888$	−3.27334	−	10.0743i	−0.109846	−	0.338072i
$889$	−44.9166	+	1.75902i	−1.50645	+	0.0589957i
$890$		−	2.20537i		−	0.0739241i
$891$	−12.3569	+	34.2810i	−0.413971	+	1.14846i
$892$	−19.8727	+	11.4735i	−0.665386	+	0.384161i
$893$	−5.83068	+	13.0959i	−0.195116	+	0.438238i
$894$	−2.33911	+	11.0046i	−0.0782315	+	0.368050i
$895$	9.08104	+	2.95061i	0.303546	+	0.0986280i
$896$	−29.2860	−	5.03612i	−0.978378	−	0.168245i
$897$	8.06691	−	11.1031i	0.269346	−	0.370723i
$898$	−4.36663	+	3.93173i	−0.145716	+	0.131203i
$899$	−45.0705	+	50.0559i	−1.50319	+	1.66946i
$900$	−10.3839	−	4.62320i	−0.346129	−	0.154107i
$901$	9.37731	−	16.2420i	0.312404	−	0.541099i
$902$	3.41129	+	0.468631i	0.113583	+	0.0156037i
$903$	30.8848	+	2.02826i	1.02778	+	0.0674964i
$904$	6.14592	+	8.45914i	0.204410	+	0.281347i
$905$	0.402457	+	0.0855449i	0.0133781	+	0.00284361i
$906$	1.35706	+	6.38447i	0.0450853	+	0.212110i
$907$	4.42027	−	42.0560i	0.146773	−	1.39645i	−0.634821	−	0.772659i	$-0.718926\pi$
$907$	4.42027	−	42.0560i	0.146773	−	1.39645i	0.781593	−	0.623788i	$-0.214407\pi$
$908$	31.2178	−	13.8991i	1.03600	−	0.461257i
$909$	7.82138	−	24.0717i	0.259419	−	0.798409i
$910$	−1.99157	−	7.84604i	−0.0660200	−	0.260094i
$911$	3.78224	−	2.74796i	0.125311	−	0.0910440i	−0.523364	−	0.852109i	$-0.675323\pi$
$911$	3.78224	−	2.74796i	0.125311	−	0.0910440i	0.648676	+	0.761065i	$0.275323\pi$
$912$	11.7035	+	6.75700i	0.387540	+	0.223747i
$913$	24.7933	−	10.1068i	0.820538	−	0.334486i
$914$	−7.67403	−	13.2918i	−0.253834	−	0.439654i
$915$	−1.87146	−	17.8058i	−0.0618686	−	0.588641i
$916$	−10.6786	+	3.46969i	−0.352831	+	0.114642i
$917$	−42.0601	+	6.09293i	−1.38895	+	0.201206i
$918$	−1.47387	−	1.07083i	−0.0486448	−	0.0353425i
$919$	0.615244	+	1.38186i	0.0202950	+	0.0455834i	0.923409	−	0.383818i	$-0.125391\pi$
$919$	0.615244	+	1.38186i	0.0202950	+	0.0455834i	−0.903114	+	0.429402i	$0.858724\pi$
$920$	3.07284	−	0.653152i	0.101309	−	0.0215338i
$921$	−48.5169	−	43.6848i	−1.59869	−	1.43946i
$922$	−4.71653	+	0.495727i	−0.155331	+	0.0163259i
$923$	74.2521			2.44404
$924$	31.8742	+	13.9119i	1.04859	+	0.457668i
$925$	8.35123			0.274587
$926$	−1.80899	+	0.190132i	−0.0594471	+	0.00624814i
$927$	−10.8992	−	9.81369i	−0.357977	−	0.322324i
$928$	34.2343	−	7.27673i	1.12380	−	0.238870i
$929$	13.3886	+	30.0713i	0.439266	+	0.986609i	0.988539	+	0.150965i	$0.0482382\pi$
$929$	13.3886	+	30.0713i	0.439266	+	0.986609i	−0.549273	+	0.835643i	$0.685095\pi$
$930$	−11.0078	−	7.99763i	−0.360960	−	0.262252i
$931$	6.80615	−	14.2600i	0.223062	−	0.467352i
$932$	29.0437	−	9.43686i	0.951357	−	0.309115i
$933$	5.42253	+	51.5919i	0.177526	+	1.68904i
$934$	−2.33818	−	4.04984i	−0.0765075	−	0.132515i
$935$	1.83271	−	7.44903i	0.0599360	−	0.243609i
$936$	14.9461	+	8.62916i	0.488530	+	0.282053i
$937$	−3.45765	+	2.51213i	−0.112956	+	0.0820677i	−0.642829	−	0.766009i	$-0.722240\pi$
$937$	−3.45765	+	2.51213i	−0.112956	+	0.0820677i	0.529873	+	0.848077i	$0.322240\pi$
$938$	0.570418	−	2.02156i	0.0186248	−	0.0660063i
$939$	−8.57716	+	26.3978i	−0.279905	+	0.861459i
$940$	13.8161	−	6.15132i	0.450631	−	0.200634i
$941$	−5.93535	+	56.4710i	−0.193487	+	1.84090i	0.279877	+	0.960036i	$0.409706\pi$
$941$	−5.93535	+	56.4710i	−0.193487	+	1.84090i	−0.473363	+	0.880867i	$0.656960\pi$
$942$	4.07646	+	19.1782i	0.132818	+	0.624860i
$943$	−2.73709	−	0.581787i	−0.0891320	−	0.0189456i
$944$	9.22727	+	12.7002i	0.300322	+	0.413358i
$945$	−3.47877	−	7.05652i	−0.113164	−	0.229549i
$946$	−7.47793	−	3.61854i	−0.243128	−	0.117649i
$947$	24.2402	−	41.9853i	0.787701	−	1.36434i	−0.139670	−	0.990198i	$-0.544604\pi$
$947$	24.2402	−	41.9853i	0.787701	−	1.36434i	0.927372	−	0.374141i	$-0.122062\pi$
$948$	16.1478	+	7.18948i	0.524458	+	0.233504i
$949$	27.4527	−	30.4893i	0.891152	−	0.989725i
$950$	2.56541	−	2.30991i	0.0832330	−	0.0749433i
$951$	0.623591	−	0.858299i	0.0202213	−	0.0278322i
$952$	−5.25786	+	6.32024i	−0.170408	+	0.204840i
$953$	−47.5305	−	15.4436i	−1.53967	−	0.500268i	−0.588381	−	0.808584i	$-0.700235\pi$
$953$	−47.5305	−	15.4436i	−1.53967	−	0.500268i	−0.951284	+	0.308316i	$0.900235\pi$
$954$	2.18826	−	10.2950i	0.0708476	−	0.333312i
$955$	11.1183	−	24.9722i	0.359781	−	0.808082i
$956$	−43.4488	+	25.0852i	−1.40523	+	0.811313i
$957$	−53.0495	−	1.68767i	−1.71485	−	0.0545546i
$958$		−	2.89905i		−	0.0936640i
$959$	−35.7458	+	22.5475i	−1.15429	+	0.728098i
$960$	−2.79290	−	8.59565i	−0.0901403	−	0.277423i
$961$	−38.6779	−	42.9562i	−1.24767	−	1.38568i
$962$	−5.92095	−	0.622317i	−0.190899	−	0.0200643i
$963$	22.0041	+	2.31273i	0.709073	+	0.0745266i
$964$	−8.13973	−	9.04008i	−0.262163	−	0.291161i
$965$	5.48637	+	16.8853i	0.176613	+	0.543558i
$966$	3.24678	+	1.70874i	0.104463	+	0.0549779i
$967$			39.0758i			1.25659i	0.777974	+	0.628297i	$0.216248\pi$
$967$			39.0758i			1.25659i	−0.777974	+	0.628297i	$0.783752\pi$
$968$	−13.8989	−	14.2150i	−0.446727	−	0.456889i
$969$	7.52500	−	4.34456i	0.241738	−	0.139567i
$970$	1.74429	−	3.91774i	0.0560058	−	0.125791i
$971$	−2.16127	+	10.1680i	−0.0693585	+	0.326306i	−0.999124	−	0.0418460i	$-0.986676\pi$
$971$	−2.16127	+	10.1680i	−0.0693585	+	0.326306i	0.929766	+	0.368152i	$0.120009\pi$
$972$	30.2501	+	9.82887i	0.970274	+	0.315261i
$973$	22.0639	−	8.13660i	0.707336	−	0.260847i
$974$	0.278861	−	0.383820i	0.00893530	−	0.0122984i
$975$	−25.1826	+	22.6745i	−0.806490	+	0.726167i
$976$	−10.6357	+	11.8122i	−0.340441	+	0.378098i
$977$	42.5630	+	18.9503i	1.36171	+	0.606273i	0.952044	−	0.305962i	$-0.0989782\pi$
$977$	42.5630	+	18.9503i	1.36171	+	0.606273i	0.409667	+	0.912235i	$0.365645\pi$
$978$	−4.01567	+	6.95535i	−0.128407	+	0.222407i
$979$	9.99775	−	5.35577i	0.319530	−	0.171171i
$980$	−15.4026	+	6.37535i	−0.492018	+	0.203653i
$981$	−1.48614	−	2.04550i	−0.0474489	−	0.0653078i
$982$	10.4515	+	2.22154i	0.333522	+	0.0708923i
$983$	−1.02012	−	4.79929i	−0.0325368	−	0.153074i	0.958880	−	0.283811i	$-0.0915989\pi$
$983$	−1.02012	−	4.79929i	−0.0325368	−	0.153074i	−0.991417	+	0.130737i	$0.958266\pi$
$984$	0.916047	−	8.71560i	0.0292025	−	0.277843i
$985$	−6.24800	+	2.78179i	−0.199078	+	0.0886352i
$986$	1.82045	−	5.60278i	0.0579751	−	0.178429i
$987$	36.2052	+	10.2159i	1.15243	+	0.325177i
$988$	15.3368	−	11.1428i	0.487929	−	0.354501i
$989$	5.84661	+	3.37554i	0.185911	+	0.107336i
$990$	−0.313632	−	4.29357i	−0.00996788	−	0.136459i
$991$	4.78069	+	8.28040i	0.151864	+	0.263036i	0.931913	−	0.362683i	$-0.118139\pi$
$991$	4.78069	+	8.28040i	0.151864	+	0.263036i	−0.780049	+	0.625719i	$0.784806\pi$
$992$	4.82324	+	45.8900i	0.153138	+	1.45701i
$993$	−39.6255	+	12.8751i	−1.25748	+	0.408579i
$994$	2.84585	+	19.6452i	0.0902648	+	0.623107i
$995$	5.97443	+	4.34068i	0.189402	+	0.137609i
$996$	−13.0134	−	29.2286i	−0.412346	−	0.926145i
$997$	38.7403	−	8.23451i	1.22692	−	0.260790i	0.451520	−	0.892261i	$-0.350882\pi$
$997$	38.7403	−	8.23451i	1.22692	−	0.260790i	0.775399	+	0.631472i	$0.217549\pi$
$998$	−5.29896	−	4.77121i	−0.167736	−	0.151030i
$999$	−5.75459	+	0.604832i	−0.182067	+	0.0191360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.19.3	✓	48
3.2	odd	2		693.2.cg.a.19.4		48
7.2	even	3		539.2.m.a.195.8		48
7.3	odd	6	inner	77.2.n.a.52.4	yes	48
7.4	even	3		539.2.s.d.129.4		48
7.5	odd	6		539.2.m.a.195.7		48
7.6	odd	2		539.2.s.d.19.3		48
11.2	odd	10		847.2.i.b.362.11		48
11.3	even	5		847.2.r.d.215.3		48
11.4	even	5		847.2.r.c.40.3		48
11.5	even	5		847.2.r.a.838.4		48
11.6	odd	10		847.2.r.d.838.3		48
11.7	odd	10	inner	77.2.n.a.40.4	yes	48
11.8	odd	10		847.2.r.a.215.4		48
11.9	even	5		847.2.i.b.362.14		48
11.10	odd	2		847.2.r.c.481.4		48
21.17	even	6		693.2.cg.a.514.3		48
33.29	even	10		693.2.cg.a.271.3		48
77.3	odd	30		847.2.r.d.94.3		48
77.10	even	6		847.2.r.c.360.3		48
77.17	even	30		847.2.r.d.717.3		48
77.18	odd	30		539.2.s.d.227.3		48
77.24	even	30		847.2.i.b.241.14		48
77.31	odd	30		847.2.i.b.241.11		48
77.38	odd	30		847.2.r.a.717.4		48
77.40	even	30		539.2.m.a.293.8		48
77.51	odd	30		539.2.m.a.293.7		48
77.52	even	30		847.2.r.a.94.4		48
77.59	odd	30		847.2.r.c.766.4		48
77.62	even	10		539.2.s.d.117.4		48
77.73	even	30	inner	77.2.n.a.73.3	yes	48
231.227	odd	30		693.2.cg.a.73.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.3	✓	48	1.1	even	1	trivial
77.2.n.a.40.4	yes	48	11.7	odd	10	inner
77.2.n.a.52.4	yes	48	7.3	odd	6	inner
77.2.n.a.73.3	yes	48	77.73	even	30	inner
539.2.m.a.195.7		48	7.5	odd	6
539.2.m.a.195.8		48	7.2	even	3
539.2.m.a.293.7		48	77.51	odd	30
539.2.m.a.293.8		48	77.40	even	30
539.2.s.d.19.3		48	7.6	odd	2
539.2.s.d.117.4		48	77.62	even	10
539.2.s.d.129.4		48	7.4	even	3
539.2.s.d.227.3		48	77.18	odd	30
693.2.cg.a.19.4		48	3.2	odd	2
693.2.cg.a.73.4		48	231.227	odd	30
693.2.cg.a.271.3		48	33.29	even	10
693.2.cg.a.514.3		48	21.17	even	6
847.2.i.b.241.11		48	77.31	odd	30
847.2.i.b.241.14		48	77.24	even	30
847.2.i.b.362.11		48	11.2	odd	10
847.2.i.b.362.14		48	11.9	even	5
847.2.r.a.94.4		48	77.52	even	30
847.2.r.a.215.4		48	11.8	odd	10
847.2.r.a.717.4		48	77.38	odd	30
847.2.r.a.838.4		48	11.5	even	5
847.2.r.c.40.3		48	11.4	even	5
847.2.r.c.360.3		48	77.10	even	6
847.2.r.c.481.4		48	11.10	odd	2
847.2.r.c.766.4		48	77.59	odd	30
847.2.r.d.94.3		48	77.3	odd	30
847.2.r.d.215.3		48	11.3	even	5
847.2.r.d.717.3		48	77.17	even	30
847.2.r.d.838.3		48	11.6	odd	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.476751 + 0.0501086i) q^{2} +(-1.66384 - 1.49813i) q^{3} +(-1.73151 + 0.368045i) q^{4} +(-0.547175 - 1.22898i) q^{5} +(0.868306 + 0.630861i) q^{6} +(-1.63770 - 2.07796i) q^{7} +(1.71889 - 0.558501i) q^{8} +(0.210388 + 2.00171i) q^{9} +O(q^{10})\)	\(q+(-0.476751 + 0.0501086i) q^{2} +(-1.66384 - 1.49813i) q^{3} +(-1.73151 + 0.368045i) q^{4} +(-0.547175 - 1.22898i) q^{5} +(0.868306 + 0.630861i) q^{6} +(-1.63770 - 2.07796i) q^{7} +(1.71889 - 0.558501i) q^{8} +(0.210388 + 2.00171i) q^{9} +(0.322449 + 0.558497i) q^{10} +(-1.74880 + 2.81810i) q^{11} +(3.43234 + 1.98166i) q^{12} +(3.83820 - 2.78861i) q^{13} +(0.884901 + 0.908608i) q^{14} +(-0.930750 + 2.86455i) q^{15} +(2.44281 - 1.08761i) q^{16} +(0.179716 - 1.70988i) q^{17} +(-0.200606 - 0.943776i) q^{18} +(-2.20796 - 0.469315i) q^{19} +(1.39976 + 1.92660i) q^{20} +(-0.388179 + 5.91088i) q^{21} +(0.692533 - 1.43116i) q^{22} +(-0.646028 + 1.11895i) q^{23} +(-3.69666 - 1.64586i) q^{24} +(2.13467 - 2.37079i) q^{25} +(-1.69013 + 1.52180i) q^{26} +(-1.29924 + 1.78825i) q^{27} +(3.60049 + 2.99527i) q^{28} +(-6.79788 - 2.20877i) q^{29} +(0.300197 - 1.41232i) q^{30} +(3.83290 - 8.60884i) q^{31} +(-4.24053 + 2.44827i) q^{32} +(7.13159 - 2.06893i) q^{33} +0.824195i q^{34} +(-1.65766 + 3.14971i) q^{35} +(-1.10101 - 3.38856i) q^{36} +(1.75162 + 1.94538i) q^{37} +(1.07616 + 0.113109i) q^{38} +(-10.5638 - 1.11030i) q^{39} +(-1.62692 - 1.80687i) q^{40} +(0.669247 + 2.05973i) q^{41} +(-0.111121 - 2.83747i) q^{42} -5.22507i q^{43} +(1.99089 - 5.52322i) q^{44} +(2.34493 - 1.35385i) q^{45} +(0.251925 - 0.565834i) q^{46} +(1.32038 - 6.21190i) q^{47} +(-5.69383 - 1.85004i) q^{48} +(-1.63586 + 6.80617i) q^{49} +(-0.898911 + 1.23724i) q^{50} +(-2.86064 + 2.57573i) q^{51} +(-5.61956 + 6.24116i) q^{52} +(9.96520 + 4.43679i) q^{53} +(0.529807 - 0.917653i) q^{54} +(4.42028 + 0.607243i) q^{55} +(-3.97557 - 2.65713i) q^{56} +(2.97059 + 4.08866i) q^{57} +(3.35158 + 0.712400i) q^{58} +(1.22060 + 5.74247i) q^{59} +(0.557323 - 5.30257i) q^{60} +(-5.43033 + 2.41774i) q^{61} +(-1.39596 + 4.29633i) q^{62} +(3.81493 - 3.71539i) q^{63} +(-2.42761 + 1.76376i) q^{64} +(-5.52731 - 3.19119i) q^{65} +(-3.29632 + 1.34372i) q^{66} +(-0.828067 - 1.43425i) q^{67} +(0.318133 + 3.02683i) q^{68} +(2.75122 - 0.893925i) q^{69} +(0.632462 - 1.58469i) q^{70} +(12.6618 + 9.19936i) q^{71} +(1.47959 + 3.32322i) q^{72} +(8.45880 - 1.79797i) q^{73} +(-0.932569 - 0.839689i) q^{74} +(-7.10350 + 0.746608i) q^{75} +3.99584 q^{76} +(8.71993 - 0.981260i) q^{77} +5.09196 q^{78} +(4.43547 - 0.466187i) q^{79} +(-2.67330 - 2.40705i) q^{80} +(10.7470 - 2.28435i) q^{81} +(-0.422275 - 0.948444i) q^{82} +(-6.53096 - 4.74502i) q^{83} +(-1.50333 - 10.3776i) q^{84} +(-2.19974 + 0.714740i) q^{85} +(0.261821 + 2.49106i) q^{86} +(8.00156 + 13.8591i) q^{87} +(-1.43209 + 5.82071i) q^{88} +(-2.96156 - 1.70986i) q^{89} +(-1.05011 + 0.762950i) q^{90} +(-12.0805 - 3.40871i) q^{91} +(0.706781 - 2.17525i) q^{92} +(-19.2744 + 8.58154i) q^{93} +(-0.318223 + 3.02769i) q^{94} +(0.631361 + 2.97032i) q^{95} +(10.7234 + 2.27932i) q^{96} +(-3.90871 - 5.37988i) q^{97} +(0.438850 - 3.32682i) q^{98} +(-6.00895 - 2.90770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

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