LMFDB - Embedded newform 171.2.x.a.110.14

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			110.14
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28121 - 1.07506i) q^{2} +(0.658438 - 1.60202i) q^{3} +(0.138440 - 0.785130i) q^{4} +(-0.199661 + 0.548565i) q^{5} +(-0.878670 - 2.76037i) q^{6} +(-1.25763 - 2.17828i) q^{7} +(1.00580 + 1.74210i) q^{8} +(-2.13292 - 2.10966i) q^{9} +O(q^{10})$	\(q+(1.28121 - 1.07506i) q^{2} +(0.658438 - 1.60202i) q^{3} +(0.138440 - 0.785130i) q^{4} +(-0.199661 + 0.548565i) q^{5} +(-0.878670 - 2.76037i) q^{6} +(-1.25763 - 2.17828i) q^{7} +(1.00580 + 1.74210i) q^{8} +(-2.13292 - 2.10966i) q^{9} +(0.333933 + 0.917472i) q^{10} +0.404547i q^{11} +(-1.16664 - 0.738742i) q^{12} +(2.33106 + 6.40453i) q^{13} +(-3.95307 - 1.43880i) q^{14} +(0.747346 + 0.681056i) q^{15} +(4.65983 + 1.69604i) q^{16} +(1.57381 - 4.32400i) q^{17} +(-5.00072 - 0.409890i) q^{18} +(-3.47008 + 2.63790i) q^{19} +(0.403054 + 0.232703i) q^{20} +(-4.31772 + 0.580486i) q^{21} +(0.434912 + 0.518308i) q^{22} +(-6.06451 - 1.06934i) q^{23} +(3.45314 - 0.464249i) q^{24} +(3.56916 + 2.99488i) q^{25} +(9.87182 + 5.69950i) q^{26} +(-4.78410 + 2.02790i) q^{27} +(-1.88434 + 0.685845i) q^{28} +(0.264049 - 1.49750i) q^{29} +(1.68968 + 0.0691324i) q^{30} -2.99963i q^{31} +(4.01296 - 1.46060i) q^{32} +(0.648091 + 0.266369i) q^{33} +(-2.63218 - 7.23187i) q^{34} +(1.44603 - 0.254974i) q^{35} +(-1.95164 + 1.38256i) q^{36} +7.01209i q^{37} +(-1.60999 + 7.11024i) q^{38} +(11.7950 + 0.482587i) q^{39} +(-1.15648 + 0.203918i) q^{40} +(3.94971 - 3.31420i) q^{41} +(-4.90783 + 5.38553i) q^{42} +(-0.105574 - 0.598738i) q^{43} +(0.317622 + 0.0560053i) q^{44} +(1.58314 - 0.748828i) q^{45} +(-8.91949 + 5.14967i) q^{46} +(-4.36769 - 0.770141i) q^{47} +(5.78529 - 6.34840i) q^{48} +(0.336719 - 0.583215i) q^{49} +7.79251 q^{50} +(-5.89086 - 5.36835i) q^{51} +(5.35110 - 0.943543i) q^{52} +(-2.63029 - 2.20707i) q^{53} +(-3.94931 + 7.74135i) q^{54} +(-0.221920 - 0.0807723i) q^{55} +(2.52986 - 4.38185i) q^{56} +(1.94113 + 7.29603i) q^{57} +(-1.27160 - 2.20247i) q^{58} +(-1.31593 - 7.46301i) q^{59} +(0.638180 - 0.492479i) q^{60} +(-10.7552 + 3.91458i) q^{61} +(-3.22478 - 3.84315i) q^{62} +(-1.91300 + 7.29928i) q^{63} +(-1.38769 + 2.40355i) q^{64} -3.97872 q^{65} +(1.11670 - 0.355463i) q^{66} +(1.54091 - 1.83638i) q^{67} +(-3.17702 - 1.83425i) q^{68} +(-5.70620 + 9.01136i) q^{69} +(1.57855 - 1.88124i) q^{70} +(5.10921 - 4.28714i) q^{71} +(1.52994 - 5.83767i) q^{72} +(-2.34660 - 13.3082i) q^{73} +(7.53841 + 8.98393i) q^{74} +(7.14793 - 3.74592i) q^{75} +(1.59070 + 3.08966i) q^{76} +(0.881218 - 0.508771i) q^{77} +(15.6307 - 12.0621i) q^{78} +(-0.472257 + 1.29752i) q^{79} +(-1.86078 + 2.21759i) q^{80} +(0.0986944 + 8.99946i) q^{81} +(1.49743 - 8.49234i) q^{82} +(-11.3968 + 6.57996i) q^{83} +(-0.141987 + 3.47034i) q^{84} +(2.05776 + 1.72667i) q^{85} +(-0.778940 - 0.653608i) q^{86} +(-2.22516 - 1.40902i) q^{87} +(-0.704762 + 0.406895i) q^{88} +(-1.53648 + 8.71380i) q^{89} +(1.22330 - 2.66138i) q^{90} +(11.0193 - 13.1323i) q^{91} +(-1.67914 + 4.61339i) q^{92} +(-4.80547 - 1.97507i) q^{93} +(-6.42386 + 3.70882i) q^{94} +(-0.754220 - 2.43025i) q^{95} +(0.302380 - 7.39055i) q^{96} +(-2.35590 - 2.80765i) q^{97} +(-0.195584 - 1.10921i) q^{98} +(0.853455 - 0.862866i) 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 $

$2$	1.28121	−	1.07506i	0.905949	−	0.760182i	−0.0653946	−	0.997859i	$-0.520831\pi$
$2$	1.28121	−	1.07506i	0.905949	−	0.760182i	0.971344	+	0.237678i	$0.0763862\pi$
$3$	0.658438	−	1.60202i	0.380149	−	0.924925i
$3$	0.658438	−	1.60202i	0.380149	−	0.924925i
$4$	0.138440	−	0.785130i	0.0692198	−	0.392565i
$5$	−0.199661	+	0.548565i	−0.0892912	+	0.245326i	−0.976298	−	0.216431i	$-0.930558\pi$
$5$	−0.199661	+	0.548565i	−0.0892912	+	0.245326i	0.887007	+	0.461757i	$0.152781\pi$
$6$	−0.878670	−	2.76037i	−0.358715	−	1.12692i
$7$	−1.25763	−	2.17828i	−0.475341	−	0.823314i	0.524261	−	0.851558i	$-0.324342\pi$
$7$	−1.25763	−	2.17828i	−0.475341	−	0.823314i	−0.999601	+	0.0282440i	$0.991008\pi$
$8$	1.00580	+	1.74210i	0.355605	+	0.615927i
$9$	−2.13292	−	2.10966i	−0.710973	−	0.703219i
$10$	0.333933	+	0.917472i	0.105599	+	0.290130i
$11$			0.404547i			0.121975i	0.998139	+	0.0609877i	$0.0194250\pi$
$11$			0.404547i			0.121975i	−0.998139	+	0.0609877i	$0.980575\pi$
$12$	−1.16664	−	0.738742i	−0.336779	−	0.213256i
$13$	2.33106	+	6.40453i	0.646519	+	1.77630i	0.630203	+	0.776430i	$0.282972\pi$
$13$	2.33106	+	6.40453i	0.646519	+	1.77630i	0.0163159	+	0.999867i	$0.494806\pi$
$14$	−3.95307	−	1.43880i	−1.05650	−	0.384536i
$15$	0.747346	+	0.681056i	0.192964	+	0.175848i
$16$	4.65983	+	1.69604i	1.16496	+	0.424010i
$17$	1.57381	−	4.32400i	0.381704	−	1.04872i	−0.588935	−	0.808181i	$-0.700452\pi$
$17$	1.57381	−	4.32400i	0.381704	−	1.04872i	0.970639	−	0.240542i	$-0.0773253\pi$
$18$	−5.00072	−	0.409890i	−1.17868	−	0.0966119i
$19$	−3.47008	+	2.63790i	−0.796091	+	0.605176i
$19$	−3.47008	+	2.63790i	−0.796091	+	0.605176i
$20$	0.403054	+	0.232703i	0.0901255	+	0.0520340i
$21$	−4.31772	+	0.580486i	−0.942204	+	0.126672i
$22$	0.434912	+	0.518308i	0.0927235	+	0.110504i
$23$	−6.06451	−	1.06934i	−1.26454	−	0.222972i	−0.499136	−	0.866524i	$-0.666349\pi$
$23$	−6.06451	−	1.06934i	−1.26454	−	0.222972i	−0.765403	+	0.643552i	$0.777460\pi$
$24$	3.45314	−	0.464249i	0.704869	−	0.0947644i
$25$	3.56916	+	2.99488i	0.713833	+	0.598977i
$26$	9.87182	+	5.69950i	1.93602	+	1.11776i
$27$	−4.78410	+	2.02790i	−0.920701	+	0.390269i
$28$	−1.88434	+	0.685845i	−0.356107	+	0.129612i
$29$	0.264049	−	1.49750i	0.0490327	−	0.278078i	−0.950427	−	0.310948i	$-0.899354\pi$
$29$	0.264049	−	1.49750i	0.0490327	−	0.278078i	0.999460	+	0.0328698i	$0.0104647\pi$
$30$	1.68968	+	0.0691324i	0.308492	+	0.0126218i
$31$		−	2.99963i		−	0.538750i	−0.963035	−	0.269375i	$-0.913183\pi$
$31$		−	2.99963i		−	0.538750i	0.963035	−	0.269375i	$-0.0868171\pi$
$32$	4.01296	−	1.46060i	0.709398	−	0.258200i
$33$	0.648091	+	0.266369i	0.112818	+	0.0463689i
$34$	−2.63218	−	7.23187i	−0.451416	−	1.24025i
$35$	1.44603	−	0.254974i	0.244424	−	0.0430985i
$36$	−1.95164	+	1.38256i	−0.325273	+	0.230427i
$37$			7.01209i			1.15278i	0.817175	+	0.576390i	$0.195539\pi$
$37$			7.01209i			1.15278i	−0.817175	+	0.576390i	$0.804461\pi$
$38$	−1.60999	+	7.11024i	−0.261174	+	1.15343i
$39$	11.7950	+	0.482587i	1.88872	+	0.0772758i
$40$	−1.15648	+	0.203918i	−0.182855	+	0.0322423i
$41$	3.94971	−	3.31420i	0.616841	−	0.517591i	−0.279968	−	0.960009i	$-0.590324\pi$
$41$	3.94971	−	3.31420i	0.616841	−	0.517591i	0.896809	+	0.442418i	$0.145879\pi$
$42$	−4.90783	+	5.38553i	−0.757295	+	0.831005i
$43$	−0.105574	−	0.598738i	−0.0160998	−	0.0913066i	0.975699	−	0.219115i	$-0.0703169\pi$
$43$	−0.105574	−	0.598738i	−0.0160998	−	0.0913066i	−0.991799	+	0.127808i	$0.959206\pi$
$44$	0.317622	+	0.0560053i	0.0478833	+	0.00844312i
$45$	1.58314	−	0.748828i	0.236001	−	0.111629i
$46$	−8.91949	+	5.14967i	−1.31511	+	0.759278i
$47$	−4.36769	−	0.770141i	−0.637093	−	0.112337i	−0.154233	−	0.988034i	$-0.549291\pi$
$47$	−4.36769	−	0.770141i	−0.637093	−	0.112337i	−0.482860	+	0.875698i	$0.660402\pi$
$48$	5.78529	−	6.34840i	0.835035	−	0.916312i
$49$	0.336719	−	0.583215i	0.0481028	−	0.0833164i
$50$	7.79251			1.10203
$51$	−5.89086	−	5.36835i	−0.824886	−	0.751719i
$52$	5.35110	−	0.943543i	0.742064	−	0.130846i
$53$	−2.63029	−	2.20707i	−0.361297	−	0.303165i	0.444010	−	0.896022i	$-0.353555\pi$
$53$	−2.63029	−	2.20707i	−0.361297	−	0.303165i	−0.805308	+	0.592857i	$0.798000\pi$
$54$	−3.94931	+	7.74135i	−0.537433	+	1.05346i
$55$	−0.221920	−	0.0807723i	−0.0299237	−	0.0108913i
$56$	2.52986	−	4.38185i	0.338067	−	0.585550i
$57$	1.94113	+	7.29603i	0.257110	+	0.966382i
$58$	−1.27160	−	2.20247i	−0.166969	−	0.289198i
$59$	−1.31593	−	7.46301i	−0.171320	−	0.971602i	−0.942307	−	0.334751i	$-0.891348\pi$
$59$	−1.31593	−	7.46301i	−0.171320	−	0.971602i	0.770987	−	0.636851i	$-0.219763\pi$
$60$	0.638180	−	0.492479i	0.0823887	−	0.0635787i
$61$	−10.7552	+	3.91458i	−1.37706	+	0.501211i	−0.921287	−	0.388883i	$-0.872861\pi$
$61$	−10.7552	+	3.91458i	−1.37706	+	0.501211i	−0.455778	+	0.890094i	$0.650639\pi$
$62$	−3.22478	−	3.84315i	−0.409548	−	0.488080i
$63$	−1.91300	+	7.29928i	−0.241016	+	0.919623i
$64$	−1.38769	+	2.40355i	−0.173461	+	0.300443i
$65$	−3.97872			−0.493500
$66$	1.11670	−	0.355463i	0.137456	−	0.0437545i
$67$	1.54091	−	1.83638i	0.188252	−	0.224349i	−0.663661	−	0.748033i	$-0.730998\pi$
$67$	1.54091	−	1.83638i	0.188252	−	0.224349i	0.851913	+	0.523684i	$0.175443\pi$
$68$	−3.17702	−	1.83425i	−0.385271	−	0.222436i
$69$	−5.70620	+	9.01136i	−0.686946	+	1.08484i
$70$	1.57855	−	1.88124i	0.188673	−	0.224852i
$71$	5.10921	−	4.28714i	0.606352	−	0.508790i	−0.287128	−	0.957892i	$-0.592701\pi$
$71$	5.10921	−	4.28714i	0.606352	−	0.508790i	0.893480	+	0.449102i	$0.148256\pi$
$72$	1.52994	−	5.83767i	0.180305	−	0.687976i
$73$	−2.34660	−	13.3082i	−0.274649	−	1.55761i	−0.740075	−	0.672524i	$-0.765210\pi$
$73$	−2.34660	−	13.3082i	−0.274649	−	1.55761i	0.465426	−	0.885087i	$-0.345901\pi$
$74$	7.53841	+	8.98393i	0.876323	+	1.04436i
$75$	7.14793	−	3.74592i	0.825372	−	0.432541i
$76$	1.59070	+	3.08966i	0.182466	+	0.354408i
$77$	0.881218	−	0.508771i	0.100424	−	0.0579799i
$78$	15.6307	−	12.0621i	1.76982	−	1.36576i
$79$	−0.472257	+	1.29752i	−0.0531331	+	0.145982i	−0.963420	−	0.267996i	$-0.913639\pi$
$79$	−0.472257	+	1.29752i	−0.0531331	+	0.145982i	0.910287	+	0.413978i	$0.135861\pi$
$80$	−1.86078	+	2.21759i	−0.208041	+	0.247934i
$81$	0.0986944	+	8.99946i	0.0109660	+	0.999940i
$82$	1.49743	−	8.49234i	0.165363	−	0.937822i
$83$	−11.3968	+	6.57996i	−1.25096	+	0.722245i	−0.971301	−	0.237853i	$-0.923556\pi$
$83$	−11.3968	+	6.57996i	−1.25096	+	0.722245i	−0.279664	+	0.960098i	$0.590223\pi$
$84$	−0.141987	+	3.47034i	−0.0154920	+	0.378645i
$85$	2.05776	+	1.72667i	0.223196	+	0.187284i
$86$	−0.778940	−	0.653608i	−0.0839953	−	0.0704804i
$87$	−2.22516	−	1.40902i	−0.238562	−	0.151063i
$88$	−0.704762	+	0.406895i	−0.0751279	+	0.0433751i
$89$	−1.53648	+	8.71380i	−0.162866	+	0.923661i	0.788371	+	0.615201i	$0.210925\pi$
$89$	−1.53648	+	8.71380i	−0.162866	+	0.923661i	−0.951237	+	0.308461i	$0.900186\pi$
$90$	1.22330	−	2.66138i	0.128947	−	0.280534i
$91$	11.0193	−	13.1323i	1.15513	−	1.37663i
$92$	−1.67914	+	4.61339i	−0.175062	+	0.480979i
$93$	−4.80547	−	1.97507i	−0.498304	−	0.204805i
$94$	−6.42386	+	3.70882i	−0.662570	+	0.382535i
$95$	−0.754220	−	2.43025i	−0.0773813	−	0.249339i
$96$	0.302380	−	7.39055i	0.0308616	−	0.754295i
$97$	−2.35590	−	2.80765i	−0.239206	−	0.285074i	0.633064	−	0.774099i	$-0.281797\pi$
$97$	−2.35590	−	2.80765i	−0.239206	−	0.285074i	−0.872270	+	0.489025i	$0.837353\pi$
$98$	−0.195584	−	1.10921i	−0.0197570	−	0.112047i
$99$	0.853455	−	0.862866i	0.0857754	−	0.0867213i
$100$	2.84549	−	2.38765i	0.284549	−	0.238765i
$101$	5.71285	−	6.80830i	0.568449	−	0.677452i	−0.402863	−	0.915260i	$-0.631985\pi$
$101$	5.71285	−	6.80830i	0.568449	−	0.677452i	0.971312	+	0.237809i	$0.0764292\pi$
$102$	−13.3187	−	0.544928i	−1.31875	−	0.0539559i
$103$	−0.240253	−	0.138710i	−0.0236728	−	0.0136675i	0.488117	−	0.872778i	$-0.337684\pi$
$103$	−0.240253	−	0.138710i	−0.0236728	−	0.0136675i	−0.511790	+	0.859111i	$0.671017\pi$
$104$	−8.81277	+	10.5026i	−0.864163	+	1.02987i
$105$	0.543648	−	2.48445i	0.0530546	−	0.242458i
$106$	−5.74267			−0.557777
$107$	2.99056	−	5.17980i	0.289108	−	0.500750i	−0.684489	−	0.729023i	$-0.739975\pi$
$107$	2.99056	−	5.17980i	0.289108	−	0.500750i	0.973597	+	0.228273i	$0.0733079\pi$
$108$	0.929854	+	4.03688i	0.0894752	+	0.388449i
$109$	5.96323	+	7.10670i	0.571174	+	0.680698i	0.971871	−	0.235512i	$-0.0756767\pi$
$109$	5.96323	+	7.10670i	0.571174	+	0.680698i	−0.400698	+	0.916210i	$0.631232\pi$
$110$	−0.371160	+	0.135091i	−0.0353888	+	0.0128805i
$111$	11.2335	+	4.61702i	1.06624	+	0.438228i
$112$	−2.16590	−	12.2834i	−0.204658	−	1.16068i
$113$	−10.0435	−	17.3958i	−0.944812	−	1.63646i	−0.756128	−	0.654424i	$-0.772911\pi$
$113$	−10.0435	−	17.3958i	−0.944812	−	1.63646i	−0.188684	−	0.982038i	$-0.560422\pi$
$114$	10.3307	+	7.26088i	0.967555	+	0.680044i
$115$	1.79745	−	3.11327i	0.167613	−	0.290314i
$116$	−1.13917	−	0.414626i	−0.105770	−	0.0384970i
$117$	8.53940	−	18.5781i	0.789468	−	1.71754i
$118$	−9.70916	−	8.14695i	−0.893801	−	0.749988i
$119$	−11.3982	+	2.00980i	−1.04487	+	0.184238i
$120$	−0.434787	+	1.98696i	−0.0396905	+	0.181384i
$121$	10.8363			0.985122
$122$	−9.57125	+	16.5779i	−0.866540	+	1.50089i
$123$	−2.70877	−	8.50970i	−0.244241	−	0.767293i
$124$	−2.35510	−	0.415268i	−0.211494	−	0.0372922i
$125$	−4.88331	+	2.81938i	−0.436777	+	0.252173i
$126$	5.39621	+	11.4085i	0.480733	+	1.01635i
$127$	14.8487	+	2.61823i	1.31761	+	0.232331i	0.787877	−	0.615833i	$-0.211180\pi$
$127$	14.8487	+	2.61823i	1.31761	+	0.232331i	0.529735	+	0.848163i	$0.322291\pi$
$128$	2.28917	+	12.9825i	0.202336	+	1.14751i
$129$	−1.02870	−	0.225101i	−0.0905721	−	0.0198190i
$130$	−5.09756	+	4.27736i	−0.447086	+	0.375149i
$131$	8.30606	−	1.46458i	0.725704	−	0.127961i	0.201420	−	0.979505i	$-0.435444\pi$
$131$	8.30606	−	1.46458i	0.725704	−	0.127961i	0.524283	+	0.851544i	$0.324333\pi$
$132$	0.298856	−	0.471960i	0.0260120	−	0.0410788i
$133$	10.1102	+	4.24131i	0.876665	+	0.367768i
$134$		−	4.00935i		−	0.346355i
$135$	−0.157233	−	3.02928i	−0.0135325	−	0.260719i
$136$	9.11579	−	1.60736i	0.781672	−	0.137830i
$137$	5.33163	+	14.6485i	0.455512	+	1.25151i	0.928793	+	0.370598i	$0.120847\pi$
$137$	5.33163	+	14.6485i	0.455512	+	1.25151i	−0.473281	+	0.880911i	$0.656931\pi$
$138$	2.37693	+	17.6799i	0.202338	+	1.50501i
$139$	5.28626	−	1.92404i	0.448375	−	0.163195i	−0.107957	−	0.994156i	$-0.534431\pi$
$139$	5.28626	−	1.92404i	0.448375	−	0.163195i	0.556331	+	0.830961i	$0.312209\pi$
$140$		−	1.17062i		−	0.0989355i
$141$	−4.10963	+	6.49002i	−0.346093	+	0.546559i
$142$	1.93703	−	10.9854i	0.162552	−	0.921876i
$143$	−2.59093	+	0.943022i	−0.216665	+	0.0788595i
$144$	−6.36098	−	13.4482i	−0.530082	−	1.12068i
$145$	0.768753	+	0.443840i	0.0638415	+	0.0368589i
$146$	−17.3136	−	14.5279i	−1.43289	−	1.20233i
$147$	−0.712612	−	0.923441i	−0.0587752	−	0.0761641i
$148$	5.50540	+	0.970751i	0.452541	+	0.0797952i
$149$	13.0336	+	15.5328i	1.06775	+	1.27250i	0.960503	+	0.278268i	$0.0897605\pi$
$149$	13.0336	+	15.5328i	1.06775	+	1.27250i	0.107251	+	0.994232i	$0.465795\pi$
$150$	5.13088	−	12.4837i	0.418935	−	1.01929i
$151$	−0.772652	−	0.446091i	−0.0628775	−	0.0363023i	0.468232	−	0.883606i	$-0.344891\pi$
$151$	−0.772652	−	0.446091i	−0.0628775	−	0.0363023i	−0.531109	+	0.847303i	$0.678225\pi$
$152$	−8.08572	−	3.39203i	−0.655839	−	0.275130i
$153$	−12.4790	+	5.90255i	−1.00886	+	0.477193i
$154$	0.582062	−	1.59920i	0.0469039	−	0.128867i
$155$	1.64549	+	0.598911i	0.132169	+	0.0481057i
$156$	2.01179	−	9.19382i	0.161072	−	0.736095i
$157$	−6.33046	−	2.30410i	−0.505226	−	0.183887i	0.0768172	−	0.997045i	$-0.475524\pi$
$157$	−6.33046	−	2.30410i	−0.505226	−	0.183887i	−0.582043	+	0.813158i	$0.697746\pi$
$158$	0.789848	+	2.17009i	0.0628369	+	0.172643i
$159$	−5.26765	+	2.76054i	−0.417751	+	0.218925i
$160$			2.49299i			0.197089i
$161$	5.29761	+	14.5551i	0.417510	+	1.14710i
$162$	9.80140	+	11.4241i	0.770071	+	0.897559i
$163$	7.41814	+	12.8486i	0.581034	+	1.00638i	0.995357	+	0.0962505i	$0.0306850\pi$
$163$	7.41814	+	12.8486i	0.581034	+	1.00638i	−0.414323	+	0.910130i	$0.635982\pi$
$164$	−2.05528	−	3.55985i	−0.160491	−	0.277978i
$165$	−0.275519	+	0.302336i	−0.0214491	+	0.0235369i
$166$	−7.52784	+	20.6826i	−0.584273	+	1.60528i
$167$	0.834702	−	4.73383i	0.0645912	−	0.366315i	−0.935330	−	0.353776i	$-0.884898\pi$
$167$	0.834702	−	4.73383i	0.0645912	−	0.366315i	0.999921	−	0.0125388i	$-0.00399133\pi$
$168$	−5.35405	−	6.93806i	−0.413074	−	0.535283i
$169$	−25.6256	+	21.5024i	−1.97120	+	1.65403i
$170$	4.49269			0.344574
$171$	12.9665	+	1.69425i	0.991571	+	0.129562i
$172$	−0.484702			−0.0369582
$173$	−6.00586	+	5.03951i	−0.456617	+	0.383147i	−0.841884	−	0.539658i	$-0.818554\pi$
$173$	−6.00586	+	5.03951i	−0.456617	+	0.383147i	0.385268	+	0.922805i	$0.374109\pi$
$174$	−4.36566	+	0.586931i	−0.330960	+	0.0444951i
$175$	2.03501	−	11.5411i	0.153832	−	0.872426i
$176$	−0.686127	+	1.88512i	−0.0517188	+	0.142096i
$177$	−12.8223	−	2.80578i	−0.963786	−	0.210896i
$178$	7.39931	+	12.8160i	0.554602	+	0.960599i
$179$	−0.189879	−	0.328881i	−0.0141923	−	0.0245817i	0.858842	−	0.512240i	$-0.171184\pi$
$179$	−0.189879	−	0.328881i	−0.0141923	−	0.0245817i	−0.873034	+	0.487659i	$0.837851\pi$
$180$	−0.368757	−	1.34664i	−0.0274856	−	0.100373i
$181$	−4.35197	−	11.9569i	−0.323479	−	0.888752i	−0.989720	−	0.143015i	$-0.954320\pi$
$181$	−4.35197	−	11.9569i	−0.323479	−	0.888752i	0.666241	−	0.745736i	$-0.267902\pi$
$182$		−	28.6715i		−	2.12527i
$183$	−0.810416	+	19.8076i	−0.0599076	+	1.46422i
$184$	−4.23681	−	11.6406i	−0.312342	−	0.858153i
$185$	−3.84658	−	1.40004i	−0.282807	−	0.102933i
$186$	−8.28011	+	2.63569i	−0.607127	+	0.193258i
$187$	1.74926	+	0.636678i	0.127918	+	0.0465585i
$188$	−1.20932	+	3.32259i	−0.0881989	+	0.242325i
$189$	10.4340	+	7.87078i	0.758960	+	0.572515i
$190$	−3.57898	−	2.30282i	−0.259646	−	0.167064i
$191$	16.9778	+	9.80211i	1.22847	+	0.709256i	0.966709	−	0.255878i	$-0.0823645\pi$
$191$	16.9778	+	9.80211i	1.22847	+	0.709256i	0.261758	+	0.965134i	$0.415698\pi$
$192$	2.93682	+	3.80569i	0.211946	+	0.274652i
$193$	0.0560858	+	0.0668404i	0.00403714	+	0.00481128i	0.768059	−	0.640379i	$-0.221223\pi$
$193$	0.0560858	+	0.0668404i	0.00403714	+	0.00481128i	−0.764022	+	0.645190i	$0.776778\pi$
$194$	−6.03679	−	1.06445i	−0.433416	−	0.0764230i
$195$	−2.61974	+	6.37398i	−0.187603	+	0.456450i
$196$	−0.411284	−	0.345108i	−0.0293774	−	0.0246506i
$197$	12.6355	+	7.29511i	0.900242	+	0.519755i	0.877279	−	0.479981i	$-0.159357\pi$
$197$	12.6355	+	7.29511i	0.900242	+	0.519755i	0.0229632	+	0.999736i	$0.492690\pi$
$198$	0.165819	−	2.02302i	0.0117843	−	0.143770i
$199$	8.66420	−	3.15351i	0.614189	−	0.223547i	−0.0161461	−	0.999870i	$-0.505140\pi$
$199$	8.66420	−	3.15351i	0.614189	−	0.223547i	0.630335	+	0.776323i	$0.282917\pi$
$200$	−1.62752	+	9.23012i	−0.115083	+	0.652668i
$201$	−1.92732	−	3.67770i	−0.135943	−	0.259405i
$202$		−	14.8645i		−	1.04586i
$203$	−3.59405	+	1.30813i	−0.252253	+	0.0918125i
$204$	−5.03038	+	3.88190i	−0.352197	+	0.271788i
$205$	1.02945	+	2.82839i	0.0718998	+	0.197543i
$206$	−0.456935	+	0.0805699i	−0.0318362	+	0.00561357i
$207$	10.6792	+	15.0749i	0.742255	+	1.04777i
$208$			33.7976i			2.34344i
$209$	−1.06716	−	1.40381i	−0.0738167	−	0.0971036i
$210$	−1.97441	−	3.76755i	−0.136247	−	0.259985i
$211$	−6.98414	+	1.23149i	−0.480808	+	0.0847794i	−0.408799	−	0.912625i	$-0.634052\pi$
$211$	−6.98414	+	1.23149i	−0.480808	+	0.0847794i	−0.0720091	+	0.997404i	$0.522941\pi$
$212$	−2.09697	+	1.75957i	−0.144021	+	0.120848i
$213$	−3.50397	−	11.0079i	−0.240088	−	0.754246i
$214$	−1.73707	−	9.85142i	−0.118744	−	0.673429i
$215$	0.349525	+	0.0616307i	0.0238374	+	0.00420318i
$216$	−8.34467	−	6.29473i	−0.567783	−	0.428302i
$217$	−6.53405	+	3.77244i	−0.443560	+	0.256090i
$218$	15.2802	+	2.69432i	1.03491	+	0.182482i
$219$	−22.8651	−	5.00335i	−1.54508	−	0.338095i
$220$	−0.0941393	+	0.163054i	−0.00634687	+	0.0109931i
$221$	31.3618			2.10962
$222$	19.3560	−	6.16131i	1.29909	−	0.413520i
$223$	13.6087	−	2.39958i	0.911306	−	0.160688i	0.301710	−	0.953400i	$-0.402443\pi$
$223$	13.6087	−	2.39958i	0.911306	−	0.160688i	0.609596	+	0.792712i	$0.291332\pi$
$224$	−8.22843	−	6.90448i	−0.549785	−	0.461325i
$225$	−1.29456	−	13.9176i	−0.0863041	−	0.927837i
$226$	−31.5693	−	11.4903i	−2.09996	−	0.764323i
$227$	4.85622	−	8.41122i	0.322319	−	0.558272i	−0.658647	−	0.752452i	$-0.728871\pi$
$227$	4.85622	−	8.41122i	0.322319	−	0.558272i	0.980966	+	0.194179i	$0.0622044\pi$
$228$	5.99706	−	0.513984i	0.397165	−	0.0340394i
$229$	1.12422	+	1.94720i	0.0742903	+	0.128675i	0.900777	−	0.434281i	$-0.142998\pi$
$229$	1.12422	+	1.94720i	0.0742903	+	0.128675i	−0.826487	+	0.562956i	$0.809664\pi$
$230$	−1.04405	−	5.92111i	−0.0688427	−	0.390426i
$231$	−0.234834	−	1.74672i	−0.0154509	−	0.114926i
$232$	2.87437	−	1.04619i	0.188712	−	0.0686855i
$233$	−18.5722	−	22.1335i	−1.21671	−	1.45002i	−0.855715	−	0.517447i	$-0.826882\pi$
$233$	−18.5722	−	22.1335i	−1.21671	−	1.45002i	−0.360992	−	0.932569i	$-0.617562\pi$
$234$	−9.03181	−	32.9827i	−0.590428	−	2.15615i
$235$	1.29453	−	2.24219i	0.0844459	−	0.146265i
$236$	−6.04161			−0.393275
$237$	1.76769	+	1.61090i	0.114824	+	0.104639i
$238$	−12.4427	+	14.8287i	−0.806543	+	0.961200i
$239$	−8.75151	−	5.05269i	−0.566088	−	0.326831i	0.189497	−	0.981881i	$-0.439314\pi$
$239$	−8.75151	−	5.05269i	−0.566088	−	0.326831i	−0.755585	+	0.655050i	$0.772647\pi$
$240$	2.32741	+	4.44114i	0.150233	+	0.286674i
$241$	−4.27935	+	5.09993i	−0.275657	+	0.328516i	−0.886056	−	0.463579i	$-0.846565\pi$
$241$	−4.27935	+	5.09993i	−0.275657	+	0.328516i	0.610398	+	0.792095i	$0.291009\pi$
$242$	13.8836	−	11.6497i	0.892471	−	0.748872i
$243$	14.4823	+	5.76747i	0.929038	+	0.369983i
$244$	1.58451	+	8.98618i	0.101438	+	0.575281i
$245$	0.252701	+	0.301158i	0.0161445	+	0.0192403i
$246$	−12.6189	−	7.99059i	−0.804553	−	0.509461i
$247$	−24.9835	−	16.0751i	−1.58966	−	1.02284i
$248$	5.22567	−	3.01704i	0.331830	−	0.191582i
$249$	3.03711	+	22.5904i	0.192469	+	1.43161i
$250$	−3.22553	+	8.86206i	−0.204000	+	0.560486i
$251$	12.9843	−	15.4741i	0.819561	−	0.976714i	−0.180416	−	0.983590i	$-0.557744\pi$
$251$	12.9843	−	15.4741i	0.819561	−	0.976714i	0.999976	+	0.00687624i	$0.00218879\pi$
$252$	5.46605	+	2.51246i	0.344329	+	0.158270i
$253$	0.432597	−	2.45338i	0.0271971	−	0.154243i
$254$	21.8390	−	12.6088i	1.37030	−	0.791145i
$255$	4.12106	−	2.15967i	0.258071	−	0.135244i
$256$	12.6378	+	10.6044i	0.789861	+	0.662772i
$257$	−12.8250	−	10.7615i	−0.800004	−	0.671283i	0.148196	−	0.988958i	$-0.452654\pi$
$257$	−12.8250	−	10.7615i	−0.800004	−	0.671283i	−0.948200	+	0.317675i	$0.897098\pi$
$258$	−1.55998	+	0.817515i	−0.0971198	+	0.0508963i
$259$	15.2743	−	8.81863i	0.949100	−	0.547963i
$260$	−0.550813	+	3.12381i	−0.0341600	+	0.193731i
$261$	−3.72240	+	2.63699i	−0.230411	+	0.163225i
$262$	9.06726	−	10.8059i	0.560177	−	0.667593i
$263$	0.131317	−	0.360791i	0.00809736	−	0.0222473i	−0.935578	−	0.353120i	$-0.885121\pi$
$263$	0.131317	−	0.360791i	0.00809736	−	0.0222473i	0.943675	+	0.330873i	$0.107343\pi$
$264$	0.187810	+	1.39696i	0.0115589	+	0.0859767i
$265$	1.73589	−	1.00222i	0.106635	−	0.0615656i
$266$	17.5129	−	5.43506i	1.07378	−	0.333245i
$267$	12.9480	+	8.19896i	0.792404	+	0.501768i
$268$	−1.22847	−	1.46404i	−0.0750410	−	0.0894304i
$269$	5.48235	+	31.0919i	0.334265	+	1.89571i	0.434375	+	0.900732i	$0.356969\pi$
$269$	5.48235	+	31.0919i	0.334265	+	1.89571i	−0.100110	+	0.994976i	$0.531920\pi$
$270$	−3.45811	−	3.71210i	−0.210454	−	0.225911i
$271$	−7.01972	+	5.89025i	−0.426418	+	0.357807i	−0.830598	−	0.556872i	$-0.812001\pi$
$271$	−7.01972	+	5.89025i	−0.426418	+	0.357807i	0.404180	+	0.914679i	$0.367557\pi$
$272$	14.6673	−	17.4799i	0.889338	−	1.05987i
$273$	−13.7826	−	26.2998i	−0.834161	−	1.59174i
$274$	22.5790	+	13.0360i	1.36405	+	0.787532i
$275$	−1.21157	+	1.44389i	−0.0730604	+	0.0870700i
$276$	6.28513	+	5.72764i	0.378320	+	0.344763i
$277$	12.7744			0.767542			0.383771	−	0.923428i	$-0.374625\pi$
$277$	12.7744			0.767542			0.383771	+	0.923428i	$0.374625\pi$
$278$	4.70433	−	8.14814i	0.282147	−	0.488693i
$279$	−6.32820	+	6.39798i	−0.378859	+	0.383037i
$280$	1.89861	+	2.26268i	0.113464	+	0.135221i
$281$	−2.26386	+	0.823978i	−0.135051	+	0.0491544i	−0.408661	−	0.912686i	$-0.634004\pi$
$281$	−2.26386	+	0.823978i	−0.135051	+	0.0491544i	0.273611	+	0.961841i	$0.411782\pi$
$282$	1.71188	+	12.7332i	0.101941	+	0.758248i
$283$	−4.81731	−	27.3203i	−0.286359	−	1.62402i	−0.700390	−	0.713761i	$-0.746990\pi$
$283$	−4.81731	−	27.3203i	−0.286359	−	1.62402i	0.414030	−	0.910263i	$-0.364121\pi$
$284$	−2.65864	−	4.60491i	−0.157761	−	0.273251i
$285$	−4.38991	−	0.391896i	−0.260036	−	0.0232139i
$286$	−2.30571	+	3.99361i	−0.136340	+	0.236147i
$287$	−12.1865	−	4.43554i	−0.719349	−	0.261822i
$288$	−11.6407	−	5.35063i	−0.685934	−	0.315289i
$289$	−3.19732	−	2.68287i	−0.188078	−	0.157816i
$290$	1.46209	−	0.257805i	0.0858566	−	0.0151388i
$291$	−6.04913	+	1.92553i	−0.354606	+	0.112877i
$292$	−10.7736			−0.630475
$293$	15.6142	−	27.0446i	0.912193	−	1.57996i	0.101233	−	0.994863i	$-0.467721\pi$
$293$	15.6142	−	27.0446i	0.912193	−	1.57996i	0.810960	−	0.585101i	$-0.198945\pi$
$294$	−1.90576	−	0.417018i	−0.111146	−	0.0243210i
$295$	4.35669	+	0.768201i	0.253656	+	0.0447264i
$296$	−12.2158	+	7.05278i	−0.710028	+	0.409935i
$297$	−0.820379	−	1.93539i	−0.0476032	−	0.112303i
$298$	33.3975	+	5.88888i	1.93466	+	0.341133i
$299$	−7.28813	−	41.3330i	−0.421483	−	2.39035i
$300$	−1.95148	−	6.13064i	−0.112669	−	0.353952i
$301$	−1.17145	+	0.982961i	−0.0675211	+	0.0566569i
$302$	−1.46950	+	0.259112i	−0.0845602	+	0.0149102i
$303$	−7.14547	−	13.6349i	−0.410497	−	0.783306i
$304$	−20.6440	+	6.40679i	−1.18401	+	0.367454i
$305$		−	6.68152i		−	0.382583i
$306$	−9.64252	+	20.9780i	−0.551226	+	1.19923i
$307$	−11.1605	+	1.96789i	−0.636961	+	0.112313i	−0.482798	−	0.875732i	$-0.660379\pi$
$307$	−11.1605	+	1.96789i	−0.636961	+	0.112313i	−0.154164	+	0.988045i	$0.549268\pi$
$308$	−0.277456	−	0.762305i	−0.0158095	−	0.0434363i
$309$	−0.380407	+	0.293557i	−0.0216406	+	0.0166999i
$310$	2.75208	−	1.00168i	0.156308	−	0.0568913i
$311$			24.3216i			1.37915i	0.724214	+	0.689576i	$0.242203\pi$
$311$			24.3216i			1.37915i	−0.724214	+	0.689576i	$0.757797\pi$
$312$	11.0228	+	21.0335i	0.624041	+	1.19079i
$313$	−2.25649	+	12.7972i	−0.127545	+	0.723341i	0.852219	+	0.523185i	$0.175256\pi$
$313$	−2.25649	+	12.7972i	−0.127545	+	0.723341i	−0.979764	+	0.200157i	$0.935855\pi$
$314$	−10.5877	+	3.85360i	−0.597497	+	0.217471i
$315$	−3.62217	−	2.50679i	−0.204086	−	0.141242i
$316$	0.953339	+	0.550411i	0.0536295	+	0.0309630i
$317$	2.68688	+	2.25456i	0.150910	+	0.126629i	0.715117	−	0.699005i	$-0.246373\pi$
$317$	2.68688	+	2.25456i	0.150910	+	0.126629i	−0.564207	+	0.825634i	$0.690818\pi$
$318$	−3.78119	+	9.19986i	−0.212039	+	0.515902i
$319$	0.605807	+	0.106820i	0.0339187	+	0.00598078i
$320$	−1.04143	−	1.24113i	−0.0582179	−	0.0693814i
$321$	−6.32903	−	8.20150i	−0.353252	−	0.457763i
$322$	22.4349	+	12.9528i	1.25025	+	0.721831i
$323$	5.94505	+	19.1562i	0.330791	+	1.06588i
$324$	7.07941	+	1.16839i	0.393301	+	0.0649108i
$325$	−10.8609	+	29.8401i	−0.602454	+	1.65523i
$326$	23.3172	+	8.48676i	1.29142	+	0.470038i
$327$	15.3115	−	4.87388i	0.846726	−	0.269526i
$328$	9.74631	+	3.54737i	0.538150	+	0.195871i
$329$	3.81536	+	10.4826i	0.210348	+	0.577926i
$330$	−0.0279673	+	0.683555i	−0.00153955	+	0.0376284i
$331$		−	14.5165i		−	0.797901i	−0.916973	−	0.398950i	$-0.869375\pi$
$331$		−	14.5165i		−	0.797901i	0.916973	−	0.398950i	$-0.130625\pi$
$332$	3.58835	+	9.85892i	0.196937	+	0.541079i
$333$	14.7931	−	14.9562i	0.810657	−	0.819596i
$334$	−4.01972	−	6.96236i	−0.219949	−	0.380964i
$335$	0.699714	+	1.21194i	0.0382295	+	0.0662154i
$336$	−21.1044	−	4.61806i	−1.15134	−	0.251936i
$337$	−3.62311	+	9.95441i	−0.197363	+	0.542251i	−0.998411	−	0.0563492i	$-0.982054\pi$
$337$	−3.62311	+	9.95441i	−0.197363	+	0.542251i	0.801048	+	0.598600i	$0.204276\pi$
$338$	−9.71528	+	55.0981i	−0.528441	+	2.99694i
$339$	−34.4814	+	4.63577i	−1.87277	+	0.251781i
$340$	1.64054	−	1.37657i	0.0889705	−	0.0746551i
$341$	1.21349			0.0657143
$342$	18.4341	−	11.7691i	0.996804	−	0.636398i
$343$	−19.3007			−1.04214
$344$	0.936876	−	0.786133i	0.0505130	−	0.0423854i
$345$	−3.80401	−	4.92944i	−0.204801	−	0.265392i
$346$	−2.27696	+	12.9133i	−0.122410	+	0.694224i
$347$	−12.5772	+	34.5556i	−0.675179	+	1.85504i	−0.186826	+	0.982393i	$0.559820\pi$
$347$	−12.5772	+	34.5556i	−0.675179	+	1.85504i	−0.488353	+	0.872646i	$0.662402\pi$
$348$	−1.41431	+	1.55197i	−0.0758151	+	0.0831944i
$349$	−10.4080	−	18.0272i	−0.557129	−	0.964976i	−0.997734	−	0.0672748i	$-0.978570\pi$
$349$	−10.4080	−	18.0272i	−0.557129	−	0.964976i	0.440606	−	0.897701i	$-0.354764\pi$
$350$	−9.80012	−	16.9743i	−0.523838	−	0.907315i
$351$	−24.1398	−	25.9128i	−1.28848	−	1.38312i
$352$	0.590881	+	1.62343i	0.0314940	+	0.0865292i
$353$			0.532095i			0.0283205i	0.999900	+	0.0141603i	$0.00450751\pi$
$353$			0.532095i			0.0283205i	−0.999900	+	0.0141603i	$0.995492\pi$
$354$	−19.4444	+	10.1900i	−1.03346	+	0.541592i
$355$	1.33166	+	3.65871i	0.0706772	+	0.194184i
$356$	6.62876	+	2.41267i	0.351324	+	0.127871i
$357$	−4.28524	+	19.5834i	−0.226799	+	1.03646i
$358$	−0.596841	−	0.217232i	−0.0315440	−	0.0114811i
$359$	−9.26844	+	25.4648i	−0.489170	+	1.34398i	0.412264	+	0.911064i	$0.364738\pi$
$359$	−9.26844	+	25.4648i	−0.489170	+	1.34398i	−0.901433	+	0.432918i	$0.857484\pi$
$360$	2.89687	+	2.00483i	0.152678	+	0.105664i
$361$	5.08294	−	18.3075i	0.267523	−	0.963551i
$362$	−18.4302	−	10.6407i	−0.968669	−	0.559261i
$363$	7.13505	−	17.3600i	0.374493	−	0.911164i
$364$	−8.78502	−	10.4696i	−0.460460	−	0.548755i
$365$	7.76895	+	1.36988i	0.406646	+	0.0717026i
$366$	20.2560	+	26.2488i	1.05880	+	1.37205i
$367$	−17.6986	−	14.8509i	−0.923857	−	0.775208i	0.0508471	−	0.998706i	$-0.483808\pi$
$367$	−17.6986	−	14.8509i	−0.923857	−	0.775208i	−0.974704	+	0.223498i	$0.928252\pi$
$368$	−26.4460	−	15.2686i	−1.37859	−	0.795930i
$369$	−15.4162	−	1.26361i	−0.802537	−	0.0657809i
$370$	−6.43340	+	2.34156i	−0.334456	+	0.121732i
$371$	−1.49970	+	8.50519i	−0.0778603	+	0.441568i
$372$	−2.21595	+	3.49949i	−0.114892	+	0.181440i
$373$			25.0670i			1.29792i	0.760823	+	0.648959i	$0.224795\pi$
$373$			25.0670i			1.29792i	−0.760823	+	0.648959i	$0.775205\pi$
$374$	2.92563	−	1.06484i	0.151281	−	0.0550616i
$375$	1.30134	+	9.67954i	0.0672010	+	0.499849i
$376$	−3.05137	−	8.38358i	−0.157363	−	0.432350i
$377$	10.2063	−	1.79964i	0.525650	−	0.0926862i
$378$	21.8296	−	1.13306i	1.12280	−	0.0582781i
$379$			19.7225i			1.01308i	0.862217	+	0.506538i	$0.169075\pi$
$379$			19.7225i			1.01308i	−0.862217	+	0.506538i	$0.830925\pi$
$380$	−2.01248	+	0.255718i	−0.103238	+	0.0131180i
$381$	13.9714	−	22.0640i	0.715777	−	1.13037i
$382$	32.2898	−	5.69357i	1.65209	−	0.291308i
$383$	−16.3804	+	13.7448i	−0.836999	+	0.702325i	−0.956887	−	0.290462i	$-0.906191\pi$
$383$	−16.3804	+	13.7448i	−0.836999	+	0.702325i	0.119888	+	0.992787i	$0.461747\pi$
$384$	22.3055	+	4.88090i	1.13827	+	0.249077i
$385$	0.103149	+	0.584987i	0.00525696	+	0.0298137i
$386$	0.143715	+	0.0253408i	0.00731489	+	0.00128981i
$387$	−1.03795	+	1.49978i	−0.0527620	+	0.0762383i
$388$	−2.53052	+	1.46100i	−0.128468	+	0.0741710i
$389$	−25.6112	−	4.51595i	−1.29854	−	0.228968i	−0.518706	−	0.854953i	$-0.673586\pi$
$389$	−25.6112	−	4.51595i	−1.29854	−	0.228968i	−0.779835	+	0.625985i	$0.784697\pi$
$390$	3.49598	+	10.9828i	0.177026	+	0.556134i
$391$	−14.1682	+	24.5400i	−0.716515	+	1.24104i
$392$	1.35469			0.0684224
$393$	3.12273	−	14.2708i	0.157521	−	0.719866i
$394$	24.0313	−	4.23738i	1.21068	−	0.213476i
$395$	−0.617480	−	0.518127i	−0.0310688	−	0.0260698i
$396$	−0.559310	−	0.789528i	−0.0281064	−	0.0396753i
$397$	2.93642	+	1.06877i	0.147375	+	0.0536400i	0.414654	−	0.909979i	$-0.363903\pi$
$397$	2.93642	+	1.06877i	0.147375	+	0.0536400i	−0.267280	+	0.963619i	$0.586125\pi$
$398$	7.71042	−	13.3548i	0.386488	−	0.669417i
$399$	13.4516	−	13.4041i	0.673421	−	0.671043i
$400$	11.5523	+	20.0091i	0.577613	+	1.00045i
$401$	−1.57136	−	8.91162i	−0.0784700	−	0.445025i	−0.998576	−	0.0533550i	$-0.983009\pi$
$401$	−1.57136	−	8.91162i	−0.0784700	−	0.445025i	0.920106	−	0.391670i	$-0.128103\pi$
$402$	−6.42304	−	2.63990i	−0.320352	−	0.131666i
$403$	19.2112	−	6.99232i	0.956980	−	0.348312i
$404$	−4.55452	−	5.42787i	−0.226596	−	0.270046i
$405$	−4.95649	−	1.74270i	−0.246290	−	0.0865956i
$406$	−3.19840	+	5.53980i	−0.158734	+	0.274935i
$407$	−2.83672			−0.140611
$408$	3.42716	−	15.6620i	0.169670	−	0.775384i
$409$	24.5093	−	29.2091i	1.21191	−	1.44430i	0.350366	−	0.936613i	$-0.386057\pi$
$409$	24.5093	−	29.2091i	1.21191	−	1.44430i	0.861543	−	0.507684i	$-0.169498\pi$
$410$	4.35962	+	2.51703i	0.215306	+	0.124307i
$411$	26.9778	+	1.10378i	1.33072	+	0.0544455i
$412$	−0.142166	+	0.169427i	−0.00700401	+	0.00834705i
$413$	−14.6016	+	12.2522i	−0.718498	+	0.602891i
$414$	29.8886	+	7.83323i	1.46894	+	0.384982i
$415$	−1.33403	−	7.56566i	−0.0654850	−	0.371384i
$416$	18.7089	+	22.2964i	0.917279	+	1.09317i
$417$	0.398325	−	9.73554i	0.0195060	−	0.476752i
$418$	−2.87643	−	0.651315i	−0.140691	−	0.0318569i
$419$	−10.2452	+	5.91508i	−0.500512	+	0.288971i	−0.728925	−	0.684594i	$-0.759980\pi$
$419$	−10.2452	+	5.91508i	−0.500512	+	0.288971i	0.228413	+	0.973564i	$0.426646\pi$
$420$	−1.87535	−	0.770781i	−0.0915079	−	0.0376102i
$421$	−1.20018	+	3.29748i	−0.0584934	+	0.160709i	−0.965497	−	0.260413i	$-0.916141\pi$
$421$	−1.20018	+	3.29748i	−0.0584934	+	0.160709i	0.907004	+	0.421122i	$0.138364\pi$
$422$	−7.62419	+	9.08616i	−0.371140	+	0.442307i
$423$	7.69120	+	10.8570i	0.373959	+	0.527884i
$424$	1.19940	−	6.80211i	0.0582478	−	0.330340i
$425$	18.5670	−	10.7197i	0.900634	−	0.519981i
$426$	−16.3234	−	10.3364i	−0.790872	−	0.500798i
$427$	22.0532	+	18.5048i	1.06723	+	0.895511i
$428$	−3.65280	−	3.06507i	−0.176565	−	0.148156i
$429$	−0.195229	+	4.77164i	−0.00942575	+	0.230377i
$430$	0.514071	−	0.296799i	0.0247907	−	0.0143129i
$431$	0.452949	−	2.56880i	0.0218178	−	0.123735i	−0.971954	−	0.235173i	$-0.924434\pi$
$431$	0.452949	−	2.56880i	0.0218178	−	0.123735i	0.993771	+	0.111438i	$0.0355456\pi$
$432$	−25.7325	+	1.33563i	−1.23806	+	0.0642606i
$433$	3.13200	−	3.73257i	0.150514	−	0.179376i	−0.685519	−	0.728055i	$-0.740425\pi$
$433$	3.13200	−	3.73257i	0.150514	−	0.179376i	0.836033	+	0.548679i	$0.184869\pi$
$434$	−4.31587	+	11.8578i	−0.207169	+	0.569191i
$435$	1.21722	−	0.939315i	0.0583610	−	0.0450367i
$436$	6.40523	−	3.69806i	0.306755	−	0.177105i
$437$	23.8652	−	12.2869i	1.14163	−	0.587763i
$438$	−34.6738	+	18.1710i	−1.65678	+	0.868246i
$439$	−10.5687	−	12.5953i	−0.504418	−	0.601142i	0.452405	−	0.891813i	$-0.350566\pi$
$439$	−10.5687	−	12.5953i	−0.504418	−	0.601142i	−0.956823	+	0.290670i	$0.906122\pi$
$440$	−0.0824944	−	0.467849i	−0.00393276	−	0.0223038i
$441$	−1.94858	+	0.533588i	−0.0927895	+	0.0254090i
$442$	40.1809	−	33.7158i	1.91121	−	1.60370i
$443$	−10.5311	+	12.5505i	−0.500349	+	0.596293i	−0.955818	−	0.293959i	$-0.905027\pi$
$443$	−10.5311	+	12.5505i	−0.500349	+	0.596293i	0.455469	+	0.890252i	$0.349472\pi$
$444$	5.18012	−	8.18057i	0.245838	−	0.388233i
$445$	−4.47331	−	2.58267i	−0.212055	−	0.122430i
$446$	14.8559	−	17.7045i	0.703445	−	0.838334i
$447$	33.4657	−	10.6527i	1.58287	−	0.503853i
$448$	6.98081			0.329812
$449$	12.6656	−	21.9375i	0.597728	−	1.03529i	−0.395428	−	0.918497i	$-0.629404\pi$
$449$	12.6656	−	21.9375i	0.597728	−	1.03529i	0.993156	−	0.116798i	$-0.0372629\pi$
$450$	−16.6208	−	16.4395i	−0.783512	−	0.774967i
$451$	1.34075	+	1.59784i	0.0631334	+	0.0752394i
$452$	−15.0484	+	5.47717i	−0.707817	+	0.257625i
$453$	−1.22339	+	0.944078i	−0.0574798	+	0.0443567i
$454$	−2.82074	−	15.9972i	−0.132384	−	0.750787i
$455$	5.00377	+	8.66679i	0.234580	+	0.406305i
$456$	−10.7580	+	10.7200i	−0.503791	+	0.502011i
$457$	10.8524	−	18.7969i	0.507654	−	0.879282i	−0.492307	−	0.870422i	$-0.663846\pi$
$457$	10.8524	−	18.7969i	0.507654	−	0.879282i	0.999961	−	0.00886020i	$-0.00282033\pi$
$458$	3.53371	+	1.28616i	0.165119	+	0.0600985i
$459$	1.23937	+	23.8780i	0.0578490	+	1.11453i
$460$	−2.19549	−	1.84223i	−0.102365	−	0.0858945i
$461$	−22.9177	+	4.04101i	−1.06738	+	0.188208i	−0.679630	−	0.733555i	$-0.737860\pi$
$461$	−22.9177	+	4.04101i	−1.06738	+	0.188208i	−0.387753	+	0.921763i	$0.626749\pi$
$462$	−2.17870	−	1.98545i	−0.101362	−	0.0923714i
$463$	25.0104			1.16233			0.581165	−	0.813785i	$-0.302597\pi$
$463$	25.0104			1.16233			0.581165	+	0.813785i	$0.302597\pi$
$464$	3.77024	−	6.53024i	0.175029	−	0.303159i
$465$	2.04292	−	2.24176i	0.0947381	−	0.103959i
$466$	−47.5897	−	8.39135i	−2.20455	−	0.388722i
$467$	13.6784	−	7.89724i	0.632961	−	0.365440i	−0.148937	−	0.988847i	$-0.547585\pi$
$467$	13.6784	−	7.89724i	0.632961	−	0.365440i	0.781898	+	0.623406i	$0.214252\pi$
$468$	−13.4040	−	9.27648i	−0.619601	−	0.428806i
$469$	−5.93805	−	1.04704i	−0.274194	−	0.0483477i
$470$	−0.751930	−	4.26441i	−0.0346840	−	0.196703i
$471$	−7.85942	+	8.62440i	−0.362143	+	0.397392i
$472$	11.6778	−	9.79881i	0.537513	−	0.451027i
$473$	0.242217	−	0.0427094i	0.0111372	−	0.00196378i
$474$	3.99659	+	0.163518i	0.183569	+	0.00751064i
$475$	−20.2855	−	0.977385i	−0.930763	−	0.0448455i
$476$			9.22728i			0.422931i
$477$	0.954024	+	10.2565i	0.0436818	+	0.469613i
$478$	−16.6444	+	2.93486i	−0.761298	+	0.134237i
$479$	8.78811	+	24.1451i	0.401539	+	1.10322i	0.961525	+	0.274717i	$0.0885842\pi$
$479$	8.78811	+	24.1451i	0.401539	+	1.10322i	−0.559986	+	0.828502i	$0.689194\pi$
$480$	3.99382	+	1.64148i	0.182292	+	0.0749230i
$481$	−44.9091	+	16.3456i	−2.04768	+	0.745295i
$482$			11.1346i			0.507168i
$483$	26.8056	+	1.09674i	1.21970	+	0.0499033i
$484$	1.50018	−	8.50794i	0.0681900	−	0.386724i
$485$	2.01056	−	0.731785i	0.0912949	−	0.0332286i
$486$	24.7552	−	8.17999i	1.12292	−	0.371052i
$487$	−17.2791	−	9.97610i	−0.782991	−	0.452060i	0.0544981	−	0.998514i	$-0.482644\pi$
$487$	−17.2791	−	9.97610i	−0.782991	−	0.452060i	−0.837489	+	0.546454i	$0.815977\pi$
$488$	−17.6372	−	14.7994i	−0.798400	−	0.669938i
$489$	25.4681	−	3.42399i	1.15171	−	0.154838i
$490$	0.647525	+	0.114176i	0.0292522	+	0.00515795i
$491$	−27.0303	−	32.2134i	−1.21986	−	1.45377i	−0.851716	−	0.524003i	$-0.824438\pi$
$491$	−27.0303	−	32.2134i	−1.21986	−	1.45377i	−0.368143	−	0.929769i	$-0.620006\pi$
$492$	−7.05622	+	0.948656i	−0.318119	+	0.0427687i
$493$	−6.05961	−	3.49851i	−0.272911	−	0.157565i
$494$	−49.2907	+	6.26318i	−2.21769	+	0.281794i
$495$	0.302936	+	0.640456i	0.0136160	+	0.0287864i
$496$	5.08750	−	13.9778i	0.228435	−	0.627621i
$497$	−15.7641	−	5.73767i	−0.707117	−	0.257370i
$498$	28.1772	+	25.6779i	1.26265	+	1.15065i
$499$	−5.31693	−	1.93520i	−0.238018	−	0.0866316i	0.220257	−	0.975442i	$-0.429310\pi$
$499$	−5.31693	−	1.93520i	−0.238018	−	0.0866316i	−0.458275	+	0.888810i	$0.651533\pi$
$500$	1.53754	+	4.22435i	0.0687608	+	0.188919i
$501$	−7.03408	−	4.45414i	−0.314259	−	0.198996i
$502$		−	33.7843i		−	1.50787i
$503$	−1.26270	−	3.46923i	−0.0563009	−	0.154685i	0.908354	−	0.418202i	$-0.137340\pi$
$503$	−1.26270	−	3.46923i	−0.0563009	−	0.154685i	−0.964655	+	0.263517i	$0.915117\pi$
$504$	−14.6402	+	4.00900i	−0.652126	+	0.178575i
$505$	2.59416	+	4.49322i	0.115439	+	0.199946i
$506$	−2.08328	−	3.60835i	−0.0926132	−	0.160411i
$507$	17.5744	+	55.2107i	0.780507	+	2.45199i
$508$	4.11131	−	11.2957i	0.182410	−	0.501167i
$509$	0.901032	−	5.11001i	0.0399376	−	0.226497i	−0.958306	−	0.285745i	$-0.907759\pi$
$509$	0.901032	−	5.11001i	0.0399376	−	0.226497i	0.998243	+	0.0592476i	$0.0188702\pi$
$510$	2.95816	−	7.19737i	0.130989	−	0.318705i
$511$	−26.0380	+	21.8484i	−1.15185	+	0.966518i
$512$	1.22629			0.0541947
$513$	11.2518	−	19.6570i	0.496780	−	0.867876i
$514$	−28.0008			−1.23506
$515$	0.124061	−	0.104099i	0.00546676	−	0.00458716i
$516$	−0.319146	+	0.776502i	−0.0140496	+	0.0341836i
$517$	0.311558	−	1.76693i	0.0137023	−	0.0777097i
$518$	10.0890	−	27.7193i	0.443285	−	1.21792i
$519$	4.11890	+	12.9397i	0.180800	+	0.567989i
$520$	−4.00181	−	6.93134i	−0.175491	−	0.303960i
$521$	18.4067	+	31.8814i	0.806413	+	1.39675i	0.915333	+	0.402698i	$0.131928\pi$
$521$	18.4067	+	31.8814i	0.806413	+	1.39675i	−0.108919	+	0.994051i	$0.534739\pi$
$522$	−1.93424	+	7.38032i	−0.0846595	+	0.323028i
$523$	−2.82677	−	7.76649i	−0.123606	−	0.339605i	0.862421	−	0.506192i	$-0.168947\pi$
$523$	−2.82677	−	7.76649i	−0.123606	−	0.339605i	−0.986027	+	0.166587i	$0.946725\pi$
$524$		−	6.72409i		−	0.293743i
$525$	−17.1491	−	10.8592i	−0.748450	−	0.473935i
$526$	−0.219627	−	0.603421i	−0.00957621	−	0.0263104i
$527$	−12.9704	−	4.72084i	−0.565000	−	0.205643i
$528$	2.56822	+	2.34042i	0.111768	+	0.101854i
$529$	14.0219	+	5.10356i	0.609648	+	0.221894i
$530$	1.14659	−	3.15023i	0.0498046	−	0.136837i
$531$	−12.9376	+	18.6942i	−0.561445	+	0.811258i
$532$	4.72963	−	7.35065i	0.205056	−	0.318691i
$533$	30.4329	+	17.5704i	1.31819	+	0.761060i
$534$	25.4034	−	3.41530i	1.09931	−	0.147795i
$535$	2.24436	+	2.67472i	0.0970320	+	0.115638i
$536$	4.74901	+	0.837379i	0.205126	+	0.0361693i
$537$	−0.651897	+	0.0876427i	−0.0281314	+	0.00378206i
$538$	40.4497	+	33.9413i	1.74391	+	1.46331i
$539$	0.235938	+	0.136219i	0.0101626	+	0.00586735i
$540$	−2.40015	−	0.295924i	−0.103286	−	0.0127345i
$541$	−10.7032	+	3.89566i	−0.460168	+	0.167487i	−0.561693	−	0.827346i	$-0.689850\pi$
$541$	−10.7032	+	3.89566i	−0.460168	+	0.167487i	0.101526	+	0.994833i	$0.467628\pi$
$542$	−2.66135	+	15.0932i	−0.114315	+	0.648310i
$543$	−22.0207	−	0.900966i	−0.944999	−	0.0386641i
$544$		−	19.6507i		−	0.842518i
$545$	−5.08911	+	1.85228i	−0.217993	+	0.0793431i
$546$	−45.9322	−	18.8784i	−1.96572	−	0.807920i
$547$	0.617530	+	1.69665i	0.0264037	+	0.0725435i	0.952194	−	0.305493i	$-0.0988214\pi$
$547$	0.617530	+	1.69665i	0.0264037	+	0.0725435i	−0.925790	+	0.378037i	$0.876599\pi$
$548$	12.2391	−	2.15809i	0.522829	−	0.0921889i
$549$	31.1984	+	14.3403i	1.33152	+	0.612031i
$550$			3.15244i			0.134420i
$551$	3.03398	+	5.89297i	0.129252	+	0.251049i
$552$	−21.4380	−	0.877126i	−0.912464	−	0.0373330i
$553$	3.42028	−	0.603088i	0.145445	−	0.0256459i
$554$	16.3667	−	13.7333i	0.695354	−	0.583471i
$555$	−4.77563	+	5.24045i	−0.202714	+	0.222445i
$556$	−0.778795	−	4.41677i	−0.0330283	−	0.187313i
$557$	−2.75569	−	0.485903i	−0.116763	−	0.0205884i	0.114962	−	0.993370i	$-0.463326\pi$
$557$	−2.75569	−	0.485903i	−0.116763	−	0.0205884i	−0.231724	+	0.972782i	$0.574437\pi$
$558$	−1.22952	+	15.0003i	−0.0520497	+	0.635014i
$559$	3.58853	−	2.07184i	0.151779	−	0.0876296i
$560$	7.17070	+	1.26439i	0.303018	+	0.0534302i
$561$	2.17175	−	2.38313i	0.0916912	−	0.100616i
$562$	−2.01465	+	3.48947i	−0.0849828	+	0.147195i
$563$	−36.2091			−1.52603			−0.763017	−	0.646379i	$-0.776283\pi$
$563$	−36.2091			−1.52603			−0.763017	+	0.646379i	$0.776283\pi$
$564$	4.52658	+	4.12507i	0.190603	+	0.173697i
$565$	11.5480	−	2.03623i	0.485829	−	0.0856648i
$566$	−35.5429	−	29.8241i	−1.49398	−	1.25360i
$567$	19.4793	−	11.5330i	0.818052	−	0.484340i
$568$	12.6075	+	4.58876i	0.528999	+	0.192540i
$569$	7.47528	−	12.9476i	0.313380	−	0.542790i	−0.665712	−	0.746209i	$-0.731872\pi$
$569$	7.47528	−	12.9476i	0.313380	−	0.542790i	0.979092	+	0.203419i	$0.0652053\pi$
$570$	−6.04569	+	4.21732i	−0.253226	+	0.176644i
$571$	−7.37174	−	12.7682i	−0.308498	−	0.534334i	0.669536	−	0.742779i	$-0.266493\pi$
$571$	−7.37174	−	12.7682i	−0.308498	−	0.534334i	−0.978034	+	0.208446i	$0.933160\pi$
$572$	0.381707	+	2.16477i	0.0159600	+	0.0905136i
$573$	26.8819	−	20.7446i	1.12301	−	0.866617i
$574$	−20.3820	+	7.41842i	−0.850726	+	0.309639i
$575$	−18.4427	−	21.9792i	−0.769114	−	0.916594i
$576$	8.03048	−	2.19903i	0.334604	−	0.0916261i
$577$	−18.2291	+	31.5737i	−0.758886	+	1.31443i	0.184533	+	0.982826i	$0.440923\pi$
$577$	−18.2291	+	31.5737i	−0.758886	+	1.31443i	−0.943419	+	0.331603i	$0.892411\pi$
$578$	−6.98067			−0.290358
$579$	0.144009	−	0.0458401i	0.00598479	−	0.00190505i
$580$	0.454898	−	0.542126i	0.0188886	−	0.0225106i
$581$	28.6661	+	16.5504i	1.18927	+	0.686625i
$582$	−5.68012	+	8.97017i	−0.235448	+	0.371826i
$583$	0.892863	−	1.06407i	0.0369786	−	0.0440694i
$584$	20.8241	−	17.4735i	0.861707	−	0.723058i
$585$	8.48629	+	8.39374i	0.350865	+	0.347038i
$586$	−9.06955	−	51.4360i	−0.374660	−	2.12480i
$587$	−1.91259	−	2.27934i	−0.0789410	−	0.0940782i	0.725128	−	0.688614i	$-0.241780\pi$
$587$	−1.91259	−	2.27934i	−0.0789410	−	0.0940782i	−0.804069	+	0.594535i	$0.797336\pi$
$588$	−0.823675	+	0.431652i	−0.0339678	+	0.0178010i
$589$	7.91274	+	10.4090i	0.326039	+	0.428894i
$590$	6.40767	−	3.69947i	0.263800	−	0.152305i
$591$	20.0066	−	15.4389i	0.822961	−	0.635072i
$592$	−11.8928	+	32.6751i	−0.488790	+	1.34294i
$593$	1.72884	−	2.06035i	0.0709948	−	0.0846083i	−0.729378	−	0.684111i	$-0.760190\pi$
$593$	1.72884	−	2.06035i	0.0709948	−	0.0846083i	0.800373	+	0.599503i	$0.204635\pi$
$594$	−3.13174	−	1.59768i	−0.128497	−	0.0655536i
$595$	1.17326	−	6.65391i	0.0480991	−	0.272784i
$596$	13.9997	−	8.08272i	0.573449	−	0.331081i
$597$	0.652856	−	15.9566i	0.0267196	−	0.653060i
$598$	−53.7731	−	45.1210i	−2.19894	−	1.84513i
$599$	18.1064	+	15.1931i	0.739809	+	0.620773i	0.932786	−	0.360430i	$-0.117370\pi$
$599$	18.1064	+	15.1931i	0.739809	+	0.620773i	−0.192978	+	0.981203i	$0.561814\pi$
$600$	13.7152	+	8.68477i	0.559920	+	0.354554i
$601$	−13.4725	+	7.77837i	−0.549556	+	0.317286i	−0.748943	−	0.662634i	$-0.769438\pi$
$601$	−13.4725	+	7.77837i	−0.549556	+	0.317286i	0.199387	+	0.979921i	$0.436105\pi$
$602$	−0.444124	+	2.51875i	−0.0181011	+	0.102657i
$603$	−7.16076	+	0.666068i	−0.291609	+	0.0271244i
$604$	−0.457205	+	0.544875i	−0.0186034	+	0.0221707i
$605$	−2.16360	+	5.94444i	−0.0879627	+	0.241676i
$606$	−23.8132	−	9.78734i	−0.967344	−	0.397583i
$607$	−4.10356	+	2.36919i	−0.166558	+	0.0961626i	−0.580962	−	0.813931i	$-0.697324\pi$
$607$	−4.10356	+	2.36919i	−0.166558	+	0.0961626i	0.414404	+	0.910093i	$0.363990\pi$
$608$	−10.0724	+	15.6542i	−0.408489	+	0.634862i
$609$	−0.270815	+	6.61905i	−0.0109740	+	0.268217i
$610$	−7.18304	−	8.56041i	−0.290833	−	0.346601i
$611$	−5.24894	−	29.7682i	−0.212350	−	1.20429i
$612$	2.90669	+	10.6147i	0.117496	+	0.429076i
$613$	29.7951	−	25.0010i	1.20341	−	1.00978i	0.203885	−	0.978995i	$-0.434643\pi$
$613$	29.7951	−	25.0010i	1.20341	−	1.00978i	0.999526	−	0.0307869i	$-0.00980132\pi$
$614$	−12.1833	+	14.5194i	−0.491676	+	0.585957i
$615$	5.20895	+	0.213122i	0.210045	+	0.00859389i
$616$	1.77266	+	1.02345i	0.0714227	+	0.0412359i
$617$	4.98288	−	5.93837i	0.200603	−	0.239070i	−0.656359	−	0.754449i	$-0.727904\pi$
$617$	4.98288	−	5.93837i	0.200603	−	0.239070i	0.856962	+	0.515379i	$0.172349\pi$
$618$	−0.171789	+	0.785068i	−0.00691035	+	0.0315801i
$619$	26.3144			1.05767			0.528833	−	0.848726i	$-0.322630\pi$
$619$	26.3144			1.05767			0.528833	+	0.848726i	$0.322630\pi$
$620$	0.698024	−	1.20901i	0.0280333	−	0.0485551i
$621$	31.1818	−	7.18239i	1.25128	−	0.288219i
$622$	26.1472	+	31.1610i	1.04841	+	1.24944i
$623$	20.9135	−	7.61188i	0.837880	−	0.304963i
$624$	54.1443	+	22.2536i	2.16751	+	0.890857i
$625$	3.47371	+	19.7004i	0.138949	+	0.788016i
$626$	10.8667	+	18.8217i	0.434322	+	0.752268i
$627$	−2.95158	+	0.785280i	−0.117875	+	0.0313610i
$628$	−2.68540	+	4.65126i	−0.107159	+	0.185605i
$629$	30.3202	+	11.0357i	1.20895	+	0.440021i
$630$	−7.33570	+	0.682341i	−0.292261	+	0.0271851i
$631$	−4.47423	−	3.75433i	−0.178116	−	0.149457i	0.549371	−	0.835579i	$-0.314867\pi$
$631$	−4.47423	−	3.75433i	−0.178116	−	0.149457i	−0.727487	+	0.686121i	$0.759312\pi$
$632$	−2.73540	+	0.482326i	−0.108809	+	0.0191859i
$633$	−2.62575	+	11.9996i	−0.104364	+	0.476940i
$634$	5.86624			0.232978
$635$	−4.40099	+	7.62273i	−0.174648	+	0.302499i
$636$	1.43814	+	4.51796i	0.0570258	+	0.179149i
$637$	4.52013	+	0.797021i	0.179094	+	0.0315791i
$638$	0.891002	−	0.514420i	0.0352751	−	0.0203661i
$639$	−19.9419	−	1.63456i	−0.788891	−	0.0646623i
$640$	−7.57882	−	1.33635i	−0.299579	−	0.0528239i
$641$	0.555772	+	3.15194i	0.0219517	+	0.124494i	0.993814	−	0.111054i	$-0.0354226\pi$
$641$	0.555772	+	3.15194i	0.0219517	+	0.124494i	−0.971863	+	0.235548i	$0.924311\pi$
$642$	−16.9259	−	3.70373i	−0.668012	−	0.146174i
$643$	−30.3291	+	25.4492i	−1.19606	+	1.00362i	−0.196331	+	0.980538i	$0.562903\pi$
$643$	−30.3291	+	25.4492i	−1.19606	+	1.00362i	−0.999734	+	0.0230796i	$0.992653\pi$
$644$	12.1610	−	2.14432i	0.479211	−	0.0844979i
$645$	0.328874	−	0.519366i	0.0129494	−	0.0204500i
$646$	28.2109	+	18.1517i	1.10994	+	0.714170i
$647$			27.5631i			1.08362i	0.840502	+	0.541808i	$0.182260\pi$
$647$			27.5631i			1.08362i	−0.840502	+	0.541808i	$0.817740\pi$
$648$	−15.5787	+	9.22363i	−0.611990	+	0.362338i
$649$	3.01914	−	0.532355i	0.118512	−	0.0208968i
$650$	18.1648	+	49.9074i	0.712482	+	1.95753i
$651$	1.74124	+	12.9516i	0.0682447	+	0.507613i
$652$	11.1148	−	4.04545i	0.435289	−	0.158432i
$653$		−	13.3174i		−	0.521149i	−0.965454	−	0.260574i	$-0.916088\pi$
$653$		−	13.3174i		−	0.521149i	0.965454	−	0.260574i	$-0.0839119\pi$
$654$	14.3774	−	22.7052i	0.562202	−	0.887843i
$655$	−0.854980	+	4.84883i	−0.0334068	+	0.189460i
$656$	24.0260	−	8.74475i	0.938057	−	0.341425i
$657$	−23.0707	+	33.3359i	−0.900074	+	1.30056i
$658$	16.1577	+	9.32866i	0.629893	+	0.363669i
$659$	−8.52225	−	7.15102i	−0.331980	−	0.278564i	0.461526	−	0.887127i	$-0.347302\pi$
$659$	−8.52225	−	7.15102i	−0.331980	−	0.278564i	−0.793506	+	0.608562i	$0.791746\pi$
$660$	0.199231	+	0.258174i	0.00775504	+	0.0100494i
$661$	2.27762	+	0.401606i	0.0885892	+	0.0156207i	0.217767	−	0.976001i	$-0.430123\pi$
$661$	2.27762	+	0.401606i	0.0885892	+	0.0156207i	−0.129178	+	0.991621i	$0.541234\pi$
$662$	−15.6061	−	18.5987i	−0.606550	−	0.722858i
$663$	20.6498	−	50.2421i	0.801971	−	1.95124i
$664$	−22.9260	−	13.2363i	−0.889700	−	0.513668i
$665$	−4.34525	+	4.69927i	−0.168501	+	0.182230i
$666$	2.87418	−	35.0655i	0.111372	−	1.35876i
$667$	−3.20266	+	8.79923i	−0.124007	+	0.340707i
$668$	−3.60112	−	1.31070i	−0.139331	−	0.0507125i
$669$	5.11631	−	23.3814i	0.197808	−	0.903976i
$670$	2.19939	+	0.800511i	0.0849697	+	0.0309264i
$671$	−1.58363	−	4.35099i	−0.0611354	−	0.167968i
$672$	−16.4790	+	8.63593i	−0.635691	+	0.333138i
$673$		−	16.1918i		−	0.624147i	−0.950058	−	0.312073i	$-0.898977\pi$
$673$		−	16.1918i		−	0.624147i	0.950058	−	0.312073i	$-0.101023\pi$
$674$	6.05963	+	16.6487i	0.233408	+	0.641284i
$675$	−23.1486	−	7.08993i	−0.890988	−	0.272892i
$676$	13.3346	+	23.0962i	0.512869	+	0.888316i
$677$	−21.0773	−	36.5070i	−0.810068	−	1.40308i	−0.912816	−	0.408371i	$-0.866097\pi$
$677$	−21.0773	−	36.5070i	−0.810068	−	1.40308i	0.102748	−	0.994707i	$-0.467236\pi$
$678$	−39.1941	+	43.0090i	−1.50524	+	1.65175i
$679$	−3.15301	+	8.66282i	−0.121001	+	0.332449i
$680$	−0.938329	+	5.32153i	−0.0359833	+	0.204071i
$681$	−10.2774	−	13.3180i	−0.393831	−	0.510347i
$682$	1.55473	−	1.30458i	0.0595338	−	0.0499548i
$683$	13.0918			0.500945			0.250472	−	0.968124i	$-0.419414\pi$
$683$	13.0918			0.500945			0.250472	+	0.968124i	$0.419414\pi$
$684$	3.12528	−	9.94582i	0.119498	−	0.380288i
$685$	−9.10020			−0.347701
$686$	−24.7282	+	20.7494i	−0.944128	+	0.792217i
$687$	3.85967	−	0.518904i	0.147256	−	0.0197974i
$688$	0.523528	−	2.96907i	0.0199593	−	0.113195i
$689$	8.00391	−	21.9906i	0.304925	−	0.837773i
$690$	−10.1732	−	2.22609i	−0.387286	−	0.0847459i
$691$	13.9770	+	24.2089i	0.531710	+	0.920949i	0.999315	+	0.0370110i	$0.0117836\pi$
$691$	13.9770	+	24.2089i	0.531710	+	0.920949i	−0.467605	+	0.883938i	$0.654883\pi$
$692$	3.12522	+	5.41305i	0.118803	+	0.205773i
$693$	−2.95290	−	0.773899i	−0.112171	−	0.0293980i
$694$	21.0353	+	57.7940i	0.798489	+	2.19383i
$695$			3.28401i			0.124570i
$696$	0.216587	−	5.29365i	0.00820970	−	0.200655i
$697$	−8.11451	−	22.2944i	−0.307359	−	0.844462i
$698$	−32.7152	−	11.9073i	−1.23829	−	0.450700i
$699$	−47.6870	+	15.1795i	−1.80369	+	0.574141i
$700$	−8.77955	−	3.19550i	−0.331836	−	0.120778i
$701$	5.74896	−	15.7951i	0.217135	−	0.596574i	−0.782526	−	0.622618i	$-0.786069\pi$
$701$	5.74896	−	15.7951i	0.217135	−	0.596574i	0.999661	+	0.0260446i	$0.00829119\pi$
$702$	−58.7858	−	7.24794i	−2.21873	−	0.273556i
$703$	−18.4972	−	24.3325i	−0.697635	−	0.917718i
$704$	−0.972347	−	0.561385i	−0.0366467	−	0.0211580i
$705$	−2.73966	−	3.55021i	−0.103182	−	0.133708i
$706$	0.572034	+	0.681723i	0.0215288	+	0.0256570i
$707$	−22.0151	−	3.88185i	−0.827962	−	0.145992i
$708$	−3.97802	+	9.67877i	−0.149503	+	0.363750i
$709$	25.8623	+	21.7010i	0.971278	+	0.814999i	0.982751	−	0.184935i	$-0.0592075\pi$
$709$	25.8623	+	21.7010i	0.971278	+	0.814999i	−0.0114728	+	0.999934i	$0.503652\pi$
$710$	5.63946	+	3.25595i	0.211645	+	0.122193i
$711$	3.74460	−	1.77120i	0.140433	−	0.0664250i
$712$	−16.7257	+	6.08767i	−0.626824	+	0.228145i
$713$	−3.20762	+	18.1913i	−0.120126	+	0.681270i
$714$	15.5630	+	29.6972i	0.582432	+	1.11139i
$715$		−	1.60958i		−	0.0601948i
$716$	−0.284501	+	0.103550i	−0.0106323	+	0.00386984i
$717$	−13.8568	+	10.6932i	−0.517492	+	0.399345i
$718$	15.5014	+	42.5898i	0.578508	+	1.58944i
$719$	21.8362	−	3.85031i	0.814352	−	0.143592i	0.249065	−	0.968487i	$-0.419877\pi$
$719$	21.8362	−	3.85031i	0.814352	−	0.143592i	0.565287	+	0.824895i	$0.308766\pi$
$720$	8.64723	−	0.804335i	0.322263	−	0.0299758i
$721$			0.697785i			0.0259869i
$722$	−13.1693	−	28.9201i	−0.490112	−	1.07630i
$723$	5.35250	+	10.2136i	0.199061	+	0.379847i
$724$	−9.99023	+	1.76155i	−0.371284	+	0.0654674i
$725$	5.42726	−	4.55401i	0.201563	−	0.169132i
$726$	−9.52157	−	29.9124i	−0.353379	−	1.11015i
$727$	−1.60278	−	9.08980i	−0.0594437	−	0.337122i	0.940553	−	0.339647i	$-0.110307\pi$
$727$	−1.60278	−	9.08980i	−0.0594437	−	0.337122i	−0.999997	+	0.00252468i	$0.999196\pi$
$728$	33.9610	+	5.98823i	1.25868	+	0.221939i
$729$	18.7753	−	19.4033i	0.695380	−	0.718642i
$730$	11.4263	−	6.59699i	0.422907	−	0.244166i
$731$	−2.75509	−	0.485797i	−0.101901	−	0.0179678i
$732$	15.4393	+	3.37843i	0.570653	+	0.124870i
$733$	−3.07982	+	5.33441i	−0.113756	+	0.197031i	−0.917282	−	0.398239i	$-0.869621\pi$
$733$	−3.07982	+	5.33441i	−0.113756	+	0.197031i	0.803526	+	0.595270i	$0.202955\pi$
$734$	−38.6411			−1.42627
$735$	0.648848	−	0.206538i	0.0239331	−	0.00761828i
$736$	−25.8985	+	4.56661i	−0.954633	+	0.168328i
$737$	0.742901	+	0.623368i	0.0273651	+	0.0229621i
$738$	−21.1098	+	14.9544i	−0.777064	+	0.550480i
$739$	41.0076	+	14.9256i	1.50849	+	0.549045i	0.958243	−	0.285956i	$-0.0923112\pi$
$739$	41.0076	+	14.9256i	1.50849	+	0.549045i	0.550247	+	0.835002i	$0.314533\pi$
$740$	−1.63173	+	2.82625i	−0.0599838	+	0.103895i
$741$	−42.2027	+	29.4395i	−1.55036	+	1.08149i
$742$	7.22217	+	12.5092i	0.265134	+	0.459226i
$743$	5.37307	+	30.4722i	0.197119	+	1.11792i	0.909369	+	0.415991i	$0.136565\pi$
$743$	5.37307	+	30.4722i	0.197119	+	1.11792i	−0.712250	+	0.701926i	$0.752324\pi$
$744$	−1.39258	−	10.3582i	−0.0510543	−	0.379748i
$745$	−11.1231	+	4.04847i	−0.407518	+	0.148324i
$746$	26.9485	+	32.1160i	0.986654	+	1.17585i
$747$	38.1900	+	10.0089i	1.39730	+	0.366205i
$748$	0.742042	−	1.28525i	0.0271317	−	0.0469935i
$749$	−15.0441			−0.549699
$750$	12.0734	+	11.0025i	0.440857	+	0.401753i
$751$	28.3565	−	33.7940i	1.03474	−	1.23316i	0.0627816	−	0.998027i	$-0.480003\pi$
$751$	28.3565	−	33.7940i	1.03474	−	1.23316i	0.971963	−	0.235133i	$-0.0755527\pi$
$752$	−19.0465	−	10.9965i	−0.694555	−	0.401001i
$753$	−16.2404	−	30.9897i	−0.591832	−	1.12933i
$754$	11.1416	−	13.2781i	0.405754	−	0.483558i
$755$	0.398978	−	0.334782i	0.0145203	−	0.0121840i
$756$	7.62406	−	7.10240i	0.277285	−	0.258312i
$757$	2.66165	+	15.0949i	0.0967392	+	0.548635i	0.994201	+	0.107542i	$0.0342980\pi$
$757$	2.66165	+	15.0949i	0.0967392	+	0.548635i	−0.897461	+	0.441093i	$0.854591\pi$
$758$	21.2029	+	25.2686i	0.770123	+	0.917797i
$759$	−3.64552	−	2.30842i	−0.132324	−	0.0837905i
$760$	3.47515	−	3.75829i	0.126057	−	0.136327i
$761$	−23.7318	+	13.7015i	−0.860276	+	0.496680i	−0.864105	−	0.503312i	$-0.832115\pi$
$761$	−23.7318	+	13.7015i	−0.860276	+	0.496680i	0.00382896	+	0.999993i	$0.498781\pi$
$762$	−5.81983	−	43.2886i	−0.210830	−	1.56818i
$763$	7.98085	−	21.9272i	0.288926	−	0.793819i
$764$	10.0463	−	11.9727i	0.363463	−	0.433159i
$765$	−0.746366	−	8.02402i	−0.0269849	−	0.290109i
$766$	−6.21020	+	35.2198i	−0.224384	+	1.27254i
$767$	44.7296	−	25.8246i	1.61509	−	0.932473i
$768$	25.3096	−	13.2636i	0.913280	−	0.478610i
$769$	11.6063	+	9.73884i	0.418534	+	0.351191i	0.827605	−	0.561311i	$-0.189703\pi$
$769$	11.6063	+	9.73884i	0.418534	+	0.351191i	−0.409071	+	0.912502i	$0.634147\pi$
$770$	0.761051	+	0.638597i	0.0274264	+	0.0230135i
$771$	−25.6846	+	13.4602i	−0.925008	+	0.484756i
$772$	0.0602429	−	0.0347813i	0.00216819	−	0.00125181i
$773$	−2.17005	+	12.3070i	−0.0780513	+	0.442651i	0.920590	+	0.390531i	$0.127709\pi$
$773$	−2.17005	+	12.3070i	−0.0780513	+	0.442651i	−0.998641	+	0.0521193i	$0.983402\pi$
$774$	0.282527	+	3.03739i	0.0101552	+	0.109177i
$775$	8.98355	−	10.7062i	0.322699	−	0.384577i
$776$	2.52165	−	6.92817i	0.0905219	−	0.248707i
$777$	−4.07042	−	30.2762i	−0.146025	−	1.08615i
$778$	−37.6682	+	21.7477i	−1.35047	+	0.779694i
$779$	−4.96328	+	21.9195i	−0.177828	+	0.785347i
$780$	4.64173	+	2.93925i	0.166201	+	0.105242i
$781$	1.73435	+	2.06692i	0.0620598	+	0.0739600i
$782$	8.22961	+	46.6724i	0.294290	+	1.66900i
$783$	1.77353	+	7.69964i	0.0633808	+	0.275163i
$784$	2.55821	−	2.14659i	0.0913647	−	0.0766641i
$785$	2.52790	−	3.01263i	0.0902245	−	0.107525i
$786$	−11.3411	−	21.6409i	−0.404523	−	0.771907i
$787$	5.00564	+	2.89001i	0.178432	+	0.103018i	0.586556	−	0.809909i	$-0.300484\pi$
$787$	5.00564	+	2.89001i	0.178432	+	0.103018i	−0.408124	+	0.912927i	$0.633817\pi$
$788$	7.47686	−	8.91058i	0.266352	−	0.317426i
$789$	−0.491529	−	0.447931i	−0.0174989	−	0.0159468i
$790$	−1.34814			−0.0479645
$791$	−25.2620	+	43.7551i	−0.898215	+	1.55575i
$792$	2.36161	+	0.618933i	0.0839161	+	0.0219928i
$793$	−50.1421	−	59.7570i	−1.78060	−	2.12203i
$794$	4.91115	−	1.78751i	0.174290	−	0.0634364i
$795$	−0.462593	−	3.44082i	−0.0164065	−	0.122033i
$796$	−1.27645	−	7.23910i	−0.0452425	−	0.256583i
$797$	−15.0976	−	26.1497i	−0.534783	−	0.926271i	−0.999174	−	0.0406406i	$-0.987060\pi$
$797$	−15.0976	−	26.1497i	−0.534783	−	0.926271i	0.464391	−	0.885630i	$-0.346273\pi$
$798$	2.82408	−	31.6346i	0.0999714	−	1.11985i
$799$	−10.2040	+	17.6738i	−0.360991	+	0.625255i
$800$	18.6972	+	6.80524i	0.661047	+	0.240602i
$801$	21.6603	−	15.3444i	0.765330	−	0.542168i
$802$	−11.5938	−	9.72832i	−0.409390	−	0.343519i
$803$	5.38380	−	0.949310i	0.189990	−	0.0335004i
$804$	−3.15429	+	1.00406i	−0.111243	+	0.0354104i
$805$	−9.04212			−0.318693
$806$	17.0964	−	29.6118i	0.602195	−	1.04303i
$807$	53.4196	+	11.6893i	1.88046	+	0.411482i
$808$	17.6068	+	3.10455i	0.619404	+	0.109218i
$809$	11.2366	−	6.48747i	0.395059	−	0.228087i	−0.289291	−	0.957241i	$-0.593419\pi$
$809$	11.2366	−	6.48747i	0.395059	−	0.228087i	0.684350	+	0.729154i	$0.260086\pi$
$810$	−8.22380	+	3.09576i	−0.288955	+	0.108774i
$811$	55.4307	+	9.77392i	1.94643	+	0.343209i	0.999780	+	0.0209574i	$0.00667145\pi$
$811$	55.4307	+	9.77392i	1.94643	+	0.343209i	0.946654	+	0.322251i	$0.104440\pi$
$812$	0.529491	+	3.00289i	0.0185815	+	0.105381i
$813$	4.81423	+	15.1241i	0.168842	+	0.530425i
$814$	−3.63442	+	3.04964i	−0.127386	+	0.106890i
$815$	−8.52941	+	1.50396i	−0.298772	+	0.0526816i
$816$	−18.3455	−	35.0067i	−0.642221	−	1.22548i
$817$	1.94576	+	1.79918i	0.0680735	+	0.0629452i
$818$		−	63.7719i		−	2.22973i
$819$	−51.2078	+	4.76317i	−1.78934	+	0.166439i
$820$	2.36317	−	0.416690i	0.0825254	−	0.0145515i
$821$	−4.62750	−	12.7139i	−0.161501	−	0.443720i	0.832376	−	0.554211i	$-0.186980\pi$
$821$	−4.62750	−	12.7139i	−0.161501	−	0.443720i	−0.993877	+	0.110491i	$0.964758\pi$
$822$	35.7507	−	27.5885i	1.24695	−	0.962261i
$823$	−4.57724	+	1.66598i	−0.159552	+	0.0580724i	−0.420562	−	0.907264i	$-0.638167\pi$
$823$	−4.57724	+	1.66598i	−0.159552	+	0.0580724i	0.261009	+	0.965336i	$0.415945\pi$
$824$		−	0.558060i		−	0.0194409i
$825$	1.51540	+	2.89167i	0.0527594	+	0.100675i
$826$	−5.53582	+	31.3952i	−0.192616	+	1.09238i
$827$	−22.6833	+	8.25604i	−0.788775	+	0.287091i	−0.704827	−	0.709380i	$-0.748975\pi$
$827$	−22.6833	+	8.25604i	−0.788775	+	0.287091i	−0.0839482	+	0.996470i	$0.526753\pi$
$828$	13.3141	−	6.29759i	0.462698	−	0.218856i
$829$	45.1860	+	26.0882i	1.56938	+	0.906080i	0.996242	+	0.0866187i	$0.0276062\pi$
$829$	45.1860	+	26.0882i	1.56938	+	0.906080i	0.573135	+	0.819461i	$0.305727\pi$
$830$	−9.84271	−	8.25901i	−0.341645	−	0.286675i
$831$	8.41117	−	20.4649i	0.291780	−	0.709919i
$832$	−18.6284	−	3.28468i	−0.645822	−	0.113876i
$833$	−1.99189	−	2.37384i	−0.0690148	−	0.0822487i
$834$	−9.95595	−	12.9015i	−0.344746	−	0.446741i
$835$	2.43015	+	1.40305i	0.0840990	+	0.0485546i
$836$	−1.24991	+	0.643513i	−0.0432290	+	0.0222563i
$837$	6.08295	+	14.3506i	0.210257	+	0.496028i
$838$	−6.76718	+	18.5927i	−0.233768	+	0.642273i
$839$	−9.47505	−	3.44864i	−0.327115	−	0.119060i	0.173242	−	0.984879i	$-0.444576\pi$
$839$	−9.47505	−	3.44864i	−0.327115	−	0.119060i	−0.500357	+	0.865819i	$0.666798\pi$
$840$	4.87497	−	1.55178i	0.168203	−	0.0535415i
$841$	25.0783	+	9.12776i	0.864769	+	0.314750i
$842$	2.00730	+	5.51502i	0.0691762	+	0.190060i
$843$	−0.170584	+	4.16928i	−0.00587523	+	0.143598i
$844$			5.65394i			0.194617i
$845$	−6.67904	−	18.3505i	−0.229766	−	0.631276i
$846$	21.5259	+	5.64153i	0.740076	+	0.193960i
$847$	−13.6281	−	23.6046i	−0.468268	−	0.811065i
$848$	−8.51340	−	14.7456i	−0.292352	−	0.506368i
$849$	−46.9395	−	10.2713i	−1.61096	−	0.352510i
$850$	12.2639	−	33.6948i	0.420648	−	1.15572i
$851$	7.49829	−	42.5249i	0.257038	−	1.45773i
$852$	−9.12769	+	1.22715i	−0.312710	+	0.0420415i
$853$	3.07507	−	2.58029i	0.105288	−	0.0883475i	−0.588624	−	0.808407i	$-0.700330\pi$
$853$	3.07507	−	2.58029i	0.105288	−	0.0883475i	0.693912	+	0.720060i	$0.255886\pi$
$854$	48.1485			1.64761
$855$	−3.51831	+	6.77468i	−0.120324	+	0.231689i
$856$	12.0317			0.411234
$857$	−14.4590	+	12.1326i	−0.493911	+	0.414441i	−0.855426	−	0.517926i	$-0.826704\pi$
$857$	−14.4590	+	12.1326i	−0.493911	+	0.414441i	0.361514	+	0.932367i	$0.382260\pi$
$858$	4.87967	+	6.32334i	0.166589	+	0.215875i
$859$	−5.24029	+	29.7192i	−0.178796	+	1.01400i	0.754874	+	0.655870i	$0.227698\pi$
$859$	−5.24029	+	29.7192i	−0.178796	+	1.01400i	−0.933670	+	0.358135i	$0.883413\pi$
$860$	0.0967763	−	0.265891i	0.00330004	−	0.00906680i
$861$	−15.1299	+	16.6025i	−0.515626	+	0.565813i
$862$	−2.18129	−	3.77811i	−0.0742952	−	0.128683i
$863$	2.77666	+	4.80931i	0.0945184	+	0.163711i	0.909408	−	0.415906i	$-0.136536\pi$
$863$	2.77666	+	4.80931i	0.0945184	+	0.163711i	−0.814889	+	0.579617i	$0.803202\pi$
$864$	−16.2365	+	15.1255i	−0.552376	+	0.514581i
$865$	−1.56536	−	4.30080i	−0.0532239	−	0.146231i
$866$		−	8.14928i		−	0.276924i
$867$	−6.40324	+	3.35566i	−0.217466	+	0.113964i
$868$	2.05728	+	5.65234i	0.0698287	+	0.191853i
$869$	−0.524906	−	0.191050i	−0.0178062	−	0.00648093i
$870$	0.549684	−	2.51204i	0.0186360	−	0.0851660i
$871$	15.3531	+	5.58807i	0.520219	+	0.189344i
$872$	−6.38276	+	17.5365i	−0.216148	+	0.593861i
$873$	−0.898238	+	10.9586i	−0.0304008	+	0.370894i
$874$	17.3670	−	41.3985i	0.587449	−	1.40033i
$875$	12.2828	+	7.09149i	0.415235	+	0.239736i
$876$	−7.09372	+	17.2594i	−0.239674	+	0.583142i
$877$	−22.9693	−	27.3737i	−0.775617	−	0.924344i	0.223110	−	0.974793i	$-0.428379\pi$
$877$	−22.9693	−	27.3737i	−0.775617	−	0.924344i	−0.998727	+	0.0504489i	$0.983935\pi$
$878$	−27.0815	−	4.77519i	−0.913955	−	0.161155i
$879$	−33.0450	−	42.8215i	−1.11458	−	1.44433i
$880$	−0.897117	−	0.752771i	−0.0302418	−	0.0253759i
$881$	−12.2972	−	7.09981i	−0.414305	−	0.239199i	0.278333	−	0.960485i	$-0.410218\pi$
$881$	−12.2972	−	7.09981i	−0.414305	−	0.239199i	−0.692638	+	0.721286i	$0.743551\pi$
$882$	−1.92289	+	2.77847i	−0.0647471	+	0.0935561i
$883$	3.10982	−	1.13188i	0.104654	−	0.0380909i	−0.289163	−	0.957280i	$-0.593377\pi$
$883$	3.10982	−	1.13188i	0.104654	−	0.0380909i	0.393816	+	0.919189i	$0.371155\pi$
$884$	4.34172	−	24.6231i	0.146028	−	0.828164i
$885$	4.09928	−	6.47367i	0.137796	−	0.217610i
$886$			27.4014i			0.920567i
$887$	38.9812	−	14.1880i	1.30886	−	0.476386i	0.408988	−	0.912540i	$-0.365882\pi$
$887$	38.9812	−	14.1880i	1.30886	−	0.476386i	0.899872	+	0.436154i	$0.143660\pi$
$888$	3.25535	+	24.2137i	0.109243	+	0.812559i
$889$	−12.9710	−	35.6375i	−0.435033	−	1.19524i
$890$	−8.50775	+	1.50015i	−0.285180	+	0.0502850i
$891$	−3.64070	+	0.0399265i	−0.121968	+	0.00133759i
$892$		−	11.0168i		−	0.368870i
$893$	17.1878	−	8.84909i	0.575168	−	0.296123i
$894$	31.4242	−	49.6259i	1.05098	−	1.65974i
$895$	0.218324	−	0.0384964i	0.00729777	−	0.00128679i
$896$	25.4007	−	21.3137i	0.848578	−	0.712042i
$897$	−71.0150	−	15.5395i	−2.37112	−	0.518849i
$898$	−7.35685	−	41.7228i	−0.245501	−	1.39231i
$899$	−4.49194	−	0.792050i	−0.149815	−	0.0264163i
$900$	−11.1063	−	0.910342i	−0.370210	−	0.0303447i
$901$	−13.6829	+	7.89984i	−0.455844	+	0.263182i
$902$	3.43555	+	0.605780i	0.114391	+	0.0201703i
$903$	0.803396	+	2.52390i	0.0267353	+	0.0839901i
$904$	20.2036	−	34.9936i	0.671960	−	1.16387i
$905$	7.42807			0.246917
$906$	−0.552471	+	2.52477i	−0.0183546	+	0.0838800i
$907$	18.6843	−	3.29455i	0.620403	−	0.109394i	0.145393	−	0.989374i	$-0.453555\pi$
$907$	18.6843	−	3.29455i	0.620403	−	0.109394i	0.475010	+	0.879980i	$0.342444\pi$
$908$	−5.93161	−	4.97721i	−0.196847	−	0.165175i
$909$	−26.5482	+	2.46942i	−0.880549	+	0.0819056i
$910$	15.7282	+	5.72459i	0.521384	+	0.189768i
$911$	−8.73004	+	15.1209i	−0.289239	+	0.500977i	−0.973628	−	0.228140i	$-0.926736\pi$
$911$	−8.73004	+	15.1209i	−0.289239	+	0.500977i	0.684389	+	0.729117i	$0.260069\pi$
$912$	−3.32899	+	37.2905i	−0.110234	+	1.23481i
$913$	−2.66190	−	4.61055i	−0.0880961	−	0.152587i
$914$	−6.30363	−	35.7497i	−0.208506	−	1.18249i
$915$	−10.7039	−	4.39937i	−0.353861	−	0.145439i
$916$	1.68444	−	0.613086i	0.0556555	−	0.0202569i
$917$	−13.6362	−	16.2510i	−0.450309	−	0.536657i
$918$	27.2581	+	29.2602i	0.899652	+	0.965730i
$919$	−20.9664	+	36.3149i	−0.691619	+	1.19792i	0.279689	+	0.960091i	$0.409769\pi$
$919$	−20.9664	+	36.3149i	−0.691619	+	1.19792i	−0.971307	+	0.237828i	$0.923565\pi$
$920$	7.23152			0.238416
$921$	−4.19587	+	19.1750i	−0.138259	+	0.631838i
$922$	−25.0180	+	29.8152i	−0.823923	+	0.981913i
$923$	39.3670	+	22.7285i	1.29578	+	0.748119i
$924$	−1.40391	−	0.0574404i	−0.0461853	−	0.00188965i
$925$	−21.0004	+	25.0273i	−0.690489	+	0.822892i
$926$	32.0434	−	26.8876i	1.05301	−	0.883583i
$927$	0.219809	+	0.802708i	0.00721949	+	0.0263644i
$928$	−1.12762	−	6.39507i	−0.0370160	−	0.209928i
$929$	9.16238	+	10.9193i	0.300608	+	0.358251i	0.895112	−	0.445842i	$-0.147096\pi$
$929$	9.16238	+	10.9193i	0.300608	+	0.358251i	−0.594503	+	0.804093i	$0.702651\pi$
$930$	0.207372	−	5.06842i	0.00679999	−	0.166200i
$931$	0.370021	+	2.91204i	0.0121269	+	0.0954381i
$932$	−19.9488	+	11.5175i	−0.653446	+	0.377267i
$933$	38.9636	+	16.0143i	1.27561	+	0.524283i
$934$	9.03487	−	24.8231i	0.295630	−	0.812236i
$935$	−0.698518	+	0.832462i	−0.0228440	+	0.0272244i
$936$	40.9539	−	3.80939i	1.33862	−	0.124514i
$937$	−5.18260	+	29.3920i	−0.169308	+	0.960194i	0.775203	+	0.631713i	$0.217648\pi$
$937$	−5.18260	+	29.3920i	−0.169308	+	0.960194i	−0.944511	+	0.328481i	$0.893463\pi$
$938$	−8.73349	+	5.04228i	−0.285159	+	0.164636i
$939$	19.0156	+	12.0411i	0.620551	+	0.392947i
$940$	−1.58120	−	1.32678i	−0.0515730	−	0.0432749i
$941$	34.8696	+	29.2590i	1.13672	+	0.953817i	0.999326	−	0.0366997i	$-0.0116845\pi$
$941$	34.8696	+	29.2590i	1.13672	+	0.953817i	0.137389	+	0.990517i	$0.456129\pi$
$942$	−0.797791	+	19.4990i	−0.0259934	+	0.635311i
$943$	−27.4971	+	15.8754i	−0.895427	+	0.516975i
$944$	6.52555	−	37.0083i	0.212389	−	1.20452i
$945$	−6.40090	+	4.15222i	−0.208221	+	0.135072i
$946$	0.264415	−	0.315118i	0.00859688	−	0.0102454i
$947$	−19.6062	+	53.8677i	−0.637118	+	1.75047i	0.0234784	+	0.999724i	$0.492526\pi$
$947$	−19.6062	+	53.8677i	−0.637118	+	1.75047i	−0.660596	+	0.750742i	$0.729696\pi$
$948$	1.50948	−	1.16486i	0.0490257	−	0.0378327i
$949$	79.7629	−	46.0511i	2.58921	−	1.49488i
$950$	−27.0407	+	20.5559i	−0.877315	+	0.666921i
$951$	5.38099	−	2.81994i	0.174491	−	0.0914429i
$952$	−14.9656	−	17.8353i	−0.485038	−	0.578046i
$953$	−3.12608	−	17.7289i	−0.101264	−	0.574294i	−0.992647	−	0.121044i	$-0.961376\pi$
$953$	−3.12608	−	17.7289i	−0.101264	−	0.574294i	0.891384	−	0.453250i	$-0.149735\pi$
$954$	12.2487	+	12.1151i	0.396565	+	0.392240i
$955$	−8.76689	+	7.35629i	−0.283690	+	0.238044i
$956$	−5.17857	+	6.17158i	−0.167487	+	0.199603i
$957$	0.570014	−	0.900179i	0.0184259	−	0.0290987i
$958$	37.2168	+	21.4871i	1.20242	+	0.694218i
$959$	25.2035	−	30.0363i	0.813862	−	0.969923i
$960$	−2.67403	+	0.851186i	−0.0863041	+	0.0274719i
$961$	22.0022			0.709748
$962$	−39.9654	+	69.2221i	−1.28854	+	2.23181i
$963$	−17.3062	+	4.73904i	−0.557685	+	0.152714i
$964$	3.41168	+	4.06588i	0.109883	+	0.130953i
$965$	−0.0478645	+	0.0174212i	−0.00154081	+	0.000560809i
$966$	35.5226	−	27.4125i	1.14292	−	0.881982i
$967$	−1.26590	−	7.17925i	−0.0407085	−	0.230869i	0.957665	−	0.287886i	$-0.0929523\pi$
$967$	−1.26590	−	7.17925i	−0.0407085	−	0.230869i	−0.998373	+	0.0570165i	$0.981841\pi$
$968$	10.8992	+	18.8780i	0.350315	+	0.606763i
$969$	34.6030	+	3.08907i	1.11161	+	0.0992353i
$970$	1.78923	−	3.09904i	0.0574488	−	0.0995042i
$971$	5.85755	+	2.13197i	0.187978	+	0.0684183i	0.434294	−	0.900771i	$-0.356998\pi$
$971$	5.85755	+	2.13197i	0.187978	+	0.0684183i	−0.246316	+	0.969190i	$0.579220\pi$
$972$	6.53314	−	10.5720i	0.209550	−	0.339098i
$973$	−10.8393	−	9.09524i	−0.347491	−	0.291580i
$974$	−32.8630	+	5.79463i	−1.05300	+	0.185672i
$975$	40.6531	+	37.0472i	1.30194	+	1.18646i
$976$	−56.7568			−1.81674
$977$	7.86310	−	13.6193i	0.251563	−	0.435719i	−0.712394	−	0.701780i	$-0.752389\pi$
$977$	7.86310	−	13.6193i	0.251563	−	0.435719i	0.963956	+	0.266061i	$0.0857222\pi$
$978$	28.9489	−	31.7665i	0.925682	−	1.01578i
$979$	−3.52514	−	0.621577i	−0.112664	−	0.0198657i
$980$	0.271432	−	0.156711i	0.00867057	−	0.00500596i
$981$	2.27361	−	27.7384i	0.0725907	−	0.885618i
$982$	−69.2627	−	12.2129i	−2.21026	−	0.389729i
$983$	1.40366	+	7.96055i	0.0447698	+	0.253902i	0.998976	−	0.0452483i	$-0.0144079\pi$
$983$	1.40366	+	7.96055i	0.0447698	+	0.253902i	−0.954206	+	0.299150i	$0.903297\pi$
$984$	12.1003	−	13.2780i	0.385743	−	0.423288i
$985$	−6.52466	+	5.47484i	−0.207893	+	0.174443i
$986$	−11.5247	+	2.03212i	−0.367022	+	0.0647158i
$987$	19.3055	+	0.789875i	0.614502	+	0.0251420i
$988$	−16.0798	+	17.3899i	−0.511566	+	0.553245i
$989$			3.74395i			0.119051i
$990$	1.07665	+	0.494882i	0.0342182	+	0.0157284i
$991$	−46.4300	+	8.18687i	−1.47490	+	0.260064i	−0.852538	−	0.522666i	$-0.824938\pi$
$991$	−46.4300	+	8.18687i	−1.47490	+	0.260064i	−0.622361	+	0.782730i	$0.713827\pi$
$992$	−4.38126	−	12.0374i	−0.139105	−	0.382188i
$993$	−23.2557	−	9.55823i	−0.737998	−	0.303321i
$994$	−26.3654	+	9.59623i	−0.836260	+	0.304374i
$995$			5.38251i			0.170637i
$996$	18.1569	+	0.742879i	0.575323	+	0.0235390i
$997$	−0.765922	+	4.34376i	−0.0242570	+	0.137568i	−0.994531	−	0.104440i	$-0.966695\pi$
$997$	−0.765922	+	4.34376i	−0.0242570	+	0.137568i	0.970274	+	0.242008i	$0.0778061\pi$
$998$	−8.89254	+	3.23662i	−0.281488	+	0.102453i
$999$	−14.2198	−	33.5465i	−0.449894	−	1.06137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.14	yes	108
3.2	odd	2		513.2.bo.a.224.5		108
9.4	even	3		513.2.cd.a.395.14		108
9.5	odd	6		171.2.bd.a.167.5	yes	108
19.14	odd	18		171.2.bd.a.128.5	yes	108
57.14	even	18		513.2.cd.a.413.14		108
171.14	even	18	inner	171.2.x.a.14.14	✓	108
171.166	odd	18		513.2.bo.a.71.5		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.14	✓	108	171.14	even	18	inner
171.2.x.a.110.14	yes	108	1.1	even	1	trivial
171.2.bd.a.128.5	yes	108	19.14	odd	18
171.2.bd.a.167.5	yes	108	9.5	odd	6
513.2.bo.a.71.5		108	171.166	odd	18
513.2.bo.a.224.5		108	3.2	odd	2
513.2.cd.a.395.14		108	9.4	even	3
513.2.cd.a.413.14		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)

\(f(q)\)	\(=\)	\(q+(1.28121 - 1.07506i) q^{2} +(0.658438 - 1.60202i) q^{3} +(0.138440 - 0.785130i) q^{4} +(-0.199661 + 0.548565i) q^{5} +(-0.878670 - 2.76037i) q^{6} +(-1.25763 - 2.17828i) q^{7} +(1.00580 + 1.74210i) q^{8} +(-2.13292 - 2.10966i) q^{9} +O(q^{10})\)	\(q+(1.28121 - 1.07506i) q^{2} +(0.658438 - 1.60202i) q^{3} +(0.138440 - 0.785130i) q^{4} +(-0.199661 + 0.548565i) q^{5} +(-0.878670 - 2.76037i) q^{6} +(-1.25763 - 2.17828i) q^{7} +(1.00580 + 1.74210i) q^{8} +(-2.13292 - 2.10966i) q^{9} +(0.333933 + 0.917472i) q^{10} +0.404547i q^{11} +(-1.16664 - 0.738742i) q^{12} +(2.33106 + 6.40453i) q^{13} +(-3.95307 - 1.43880i) q^{14} +(0.747346 + 0.681056i) q^{15} +(4.65983 + 1.69604i) q^{16} +(1.57381 - 4.32400i) q^{17} +(-5.00072 - 0.409890i) q^{18} +(-3.47008 + 2.63790i) q^{19} +(0.403054 + 0.232703i) q^{20} +(-4.31772 + 0.580486i) q^{21} +(0.434912 + 0.518308i) q^{22} +(-6.06451 - 1.06934i) q^{23} +(3.45314 - 0.464249i) q^{24} +(3.56916 + 2.99488i) q^{25} +(9.87182 + 5.69950i) q^{26} +(-4.78410 + 2.02790i) q^{27} +(-1.88434 + 0.685845i) q^{28} +(0.264049 - 1.49750i) q^{29} +(1.68968 + 0.0691324i) q^{30} -2.99963i q^{31} +(4.01296 - 1.46060i) q^{32} +(0.648091 + 0.266369i) q^{33} +(-2.63218 - 7.23187i) q^{34} +(1.44603 - 0.254974i) q^{35} +(-1.95164 + 1.38256i) q^{36} +7.01209i q^{37} +(-1.60999 + 7.11024i) q^{38} +(11.7950 + 0.482587i) q^{39} +(-1.15648 + 0.203918i) q^{40} +(3.94971 - 3.31420i) q^{41} +(-4.90783 + 5.38553i) q^{42} +(-0.105574 - 0.598738i) q^{43} +(0.317622 + 0.0560053i) q^{44} +(1.58314 - 0.748828i) q^{45} +(-8.91949 + 5.14967i) q^{46} +(-4.36769 - 0.770141i) q^{47} +(5.78529 - 6.34840i) q^{48} +(0.336719 - 0.583215i) q^{49} +7.79251 q^{50} +(-5.89086 - 5.36835i) q^{51} +(5.35110 - 0.943543i) q^{52} +(-2.63029 - 2.20707i) q^{53} +(-3.94931 + 7.74135i) q^{54} +(-0.221920 - 0.0807723i) q^{55} +(2.52986 - 4.38185i) q^{56} +(1.94113 + 7.29603i) q^{57} +(-1.27160 - 2.20247i) q^{58} +(-1.31593 - 7.46301i) q^{59} +(0.638180 - 0.492479i) q^{60} +(-10.7552 + 3.91458i) q^{61} +(-3.22478 - 3.84315i) q^{62} +(-1.91300 + 7.29928i) q^{63} +(-1.38769 + 2.40355i) q^{64} -3.97872 q^{65} +(1.11670 - 0.355463i) q^{66} +(1.54091 - 1.83638i) q^{67} +(-3.17702 - 1.83425i) q^{68} +(-5.70620 + 9.01136i) q^{69} +(1.57855 - 1.88124i) q^{70} +(5.10921 - 4.28714i) q^{71} +(1.52994 - 5.83767i) q^{72} +(-2.34660 - 13.3082i) q^{73} +(7.53841 + 8.98393i) q^{74} +(7.14793 - 3.74592i) q^{75} +(1.59070 + 3.08966i) q^{76} +(0.881218 - 0.508771i) q^{77} +(15.6307 - 12.0621i) q^{78} +(-0.472257 + 1.29752i) q^{79} +(-1.86078 + 2.21759i) q^{80} +(0.0986944 + 8.99946i) q^{81} +(1.49743 - 8.49234i) q^{82} +(-11.3968 + 6.57996i) q^{83} +(-0.141987 + 3.47034i) q^{84} +(2.05776 + 1.72667i) q^{85} +(-0.778940 - 0.653608i) q^{86} +(-2.22516 - 1.40902i) q^{87} +(-0.704762 + 0.406895i) q^{88} +(-1.53648 + 8.71380i) q^{89} +(1.22330 - 2.66138i) q^{90} +(11.0193 - 13.1323i) q^{91} +(-1.67914 + 4.61339i) q^{92} +(-4.80547 - 1.97507i) q^{93} +(-6.42386 + 3.70882i) q^{94} +(-0.754220 - 2.43025i) q^{95} +(0.302380 - 7.39055i) q^{96} +(-2.35590 - 2.80765i) q^{97} +(-0.195584 - 1.10921i) q^{98} +(0.853455 - 0.862866i) 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

L-functions

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