LMFDB - Embedded newform 171.2.x.a.110.7

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			110.7
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788568 + 0.661687i) q^{2} +(-0.897794 - 1.48120i) q^{3} +(-0.163287 + 0.926044i) q^{4} +(0.446483 - 1.22670i) q^{5} +(1.68807 + 0.573972i) q^{6} +(-0.947545 - 1.64120i) q^{7} +(-1.51339 - 2.62127i) q^{8} +(-1.38793 + 2.65963i) q^{9} +O(q^{10})$	\(q+(-0.788568 + 0.661687i) q^{2} +(-0.897794 - 1.48120i) q^{3} +(-0.163287 + 0.926044i) q^{4} +(0.446483 - 1.22670i) q^{5} +(1.68807 + 0.573972i) q^{6} +(-0.947545 - 1.64120i) q^{7} +(-1.51339 - 2.62127i) q^{8} +(-1.38793 + 2.65963i) q^{9} +(0.459610 + 1.26277i) q^{10} -5.09241i q^{11} +(1.51826 - 0.589536i) q^{12} +(0.188944 + 0.519120i) q^{13} +(1.83316 + 0.667217i) q^{14} +(-2.21784 + 0.439993i) q^{15} +(1.16063 + 0.422436i) q^{16} +(1.79639 - 4.93555i) q^{17} +(-0.665367 - 3.01568i) q^{18} +(-1.28875 - 4.16403i) q^{19} +(1.06307 + 0.613766i) q^{20} +(-1.58025 + 2.87696i) q^{21} +(3.36958 + 4.01571i) q^{22} +(-4.43591 - 0.782171i) q^{23} +(-2.52392 + 4.59500i) q^{24} +(2.52477 + 2.11854i) q^{25} +(-0.492490 - 0.284339i) q^{26} +(5.18554 - 0.331993i) q^{27} +(1.67454 - 0.609484i) q^{28} +(-0.744354 + 4.22144i) q^{29} +(1.45778 - 1.81448i) q^{30} +9.56154i q^{31} +(4.49373 - 1.63559i) q^{32} +(-7.54289 + 4.57193i) q^{33} +(1.84921 + 5.08067i) q^{34} +(-2.43632 + 0.429589i) q^{35} +(-2.23631 - 1.71957i) q^{36} -0.822439i q^{37} +(3.77155 + 2.43087i) q^{38} +(0.599289 - 0.745928i) q^{39} +(-3.89122 + 0.686127i) q^{40} +(-4.69226 + 3.93727i) q^{41} +(-0.657519 - 3.31431i) q^{42} +(-0.620272 - 3.51774i) q^{43} +(4.71579 + 0.831522i) q^{44} +(2.64289 + 2.89006i) q^{45} +(4.01557 - 2.31839i) q^{46} +(6.74036 + 1.18851i) q^{47} +(-0.416295 - 2.09839i) q^{48} +(1.70432 - 2.95196i) q^{49} -3.39277 q^{50} +(-8.92335 + 1.77028i) q^{51} +(-0.511580 + 0.0902054i) q^{52} +(-3.87285 - 3.24971i) q^{53} +(-3.86947 + 3.69300i) q^{54} +(-6.24686 - 2.27367i) q^{55} +(-2.86801 + 4.96755i) q^{56} +(-5.01074 + 5.64734i) q^{57} +(-2.20630 - 3.82142i) q^{58} +(1.14034 + 6.46720i) q^{59} +(-0.0453088 - 2.12567i) q^{60} +(2.20421 - 0.802266i) q^{61} +(-6.32675 - 7.53992i) q^{62} +(5.68011 - 0.242254i) q^{63} +(-3.69649 + 6.40251i) q^{64} +0.721165 q^{65} +(2.92290 - 8.59632i) q^{66} +(10.0012 - 11.9190i) q^{67} +(4.27721 + 2.46945i) q^{68} +(2.82398 + 7.27272i) q^{69} +(1.63695 - 1.95084i) q^{70} +(0.276935 - 0.232376i) q^{71} +(9.07210 - 0.386921i) q^{72} +(0.920520 + 5.22053i) q^{73} +(0.544197 + 0.648549i) q^{74} +(0.871259 - 5.64172i) q^{75} +(4.06651 - 0.513512i) q^{76} +(-8.35764 + 4.82529i) q^{77} +(0.0209902 + 0.984757i) q^{78} +(4.77547 - 13.1205i) q^{79} +(1.03640 - 1.23514i) q^{80} +(-5.14729 - 7.38278i) q^{81} +(1.09492 - 6.20962i) q^{82} +(6.96872 - 4.02339i) q^{83} +(-2.40616 - 1.93315i) q^{84} +(-5.25239 - 4.40727i) q^{85} +(2.81677 + 2.36355i) q^{86} +(6.92109 - 2.68744i) q^{87} +(-13.3486 + 7.70681i) q^{88} +(-0.457076 + 2.59221i) q^{89} +(-3.99641 - 0.530242i) q^{90} +(0.672944 - 0.801984i) q^{91} +(1.44865 - 3.98014i) q^{92} +(14.1626 - 8.58429i) q^{93} +(-6.10165 + 3.52279i) q^{94} +(-5.68342 - 0.278252i) q^{95} +(-6.45709 - 5.18772i) q^{96} +(1.47879 + 1.76235i) q^{97} +(0.609306 + 3.45555i) q^{98} +(13.5439 + 7.06791i) 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 $

$2$	−0.788568	+	0.661687i	−0.557602	+	0.467884i	−0.877506	−	0.479567i	$-0.840794\pi$
$2$	−0.788568	+	0.661687i	−0.557602	+	0.467884i	0.319904	+	0.947450i	$0.396349\pi$
$3$	−0.897794	−	1.48120i	−0.518342	−	0.855174i
$3$	−0.897794	−	1.48120i	−0.518342	−	0.855174i
$4$	−0.163287	+	0.926044i	−0.0816433	+	0.463022i
$5$	0.446483	−	1.22670i	0.199673	−	0.548597i	−0.798931	−	0.601423i	$-0.794601\pi$
$5$	0.446483	−	1.22670i	0.199673	−	0.548597i	0.998604	+	0.0528259i	$0.0168228\pi$
$6$	1.68807	+	0.573972i	0.689150	+	0.234323i
$7$	−0.947545	−	1.64120i	−0.358138	−	0.620314i	0.629511	−	0.776991i	$-0.283255\pi$
$7$	−0.947545	−	1.64120i	−0.358138	−	0.620314i	−0.987650	+	0.156677i	$0.949922\pi$
$8$	−1.51339	−	2.62127i	−0.535065	−	0.926759i
$9$	−1.38793	+	2.65963i	−0.462644	+	0.886544i
$10$	0.459610	+	1.26277i	0.145342	+	0.399323i
$11$		−	5.09241i		−	1.53542i	−0.640799	−	0.767709i	$-0.721397\pi$
$11$		−	5.09241i		−	1.53542i	0.640799	−	0.767709i	$-0.278603\pi$
$12$	1.51826	−	0.589536i	0.438284	−	0.170185i
$13$	0.188944	+	0.519120i	0.0524037	+	0.143978i	0.963133	−	0.269026i	$-0.0867018\pi$
$13$	0.188944	+	0.519120i	0.0524037	+	0.143978i	−0.910729	+	0.413004i	$0.864480\pi$
$14$	1.83316	+	0.667217i	0.489933	+	0.178321i
$15$	−2.21784	+	0.439993i	−0.572645	+	0.113606i
$16$	1.16063	+	0.422436i	0.290158	+	0.105609i
$17$	1.79639	−	4.93555i	0.435689	−	1.19705i	−0.506580	−	0.862193i	$-0.669091\pi$
$17$	1.79639	−	4.93555i	0.435689	−	1.19705i	0.942270	−	0.334854i	$-0.108687\pi$
$18$	−0.665367	−	3.01568i	−0.156828	−	0.710802i
$19$	−1.28875	−	4.16403i	−0.295660	−	0.955293i
$19$	−1.28875	−	4.16403i	−0.295660	−	0.955293i
$20$	1.06307	+	0.613766i	0.237711	+	0.137242i
$21$	−1.58025	+	2.87696i	−0.344838	+	0.627805i
$22$	3.36958	+	4.01571i	0.718397	+	0.856152i
$23$	−4.43591	−	0.782171i	−0.924952	−	0.163094i	−0.309167	−	0.951008i	$-0.600050\pi$
$23$	−4.43591	−	0.782171i	−0.924952	−	0.163094i	−0.615785	+	0.787914i	$0.711161\pi$
$24$	−2.52392	+	4.59500i	−0.515194	+	0.937951i
$25$	2.52477	+	2.11854i	0.504955	+	0.423707i
$26$	−0.492490	−	0.284339i	−0.0965853	−	0.0557635i
$27$	5.18554	−	0.331993i	0.997957	−	0.0638920i
$28$	1.67454	−	0.609484i	0.316459	−	0.115182i
$29$	−0.744354	+	4.22144i	−0.138223	+	0.783902i	0.834338	+	0.551253i	$0.185850\pi$
$29$	−0.744354	+	4.22144i	−0.138223	+	0.783902i	−0.972561	+	0.232648i	$0.925261\pi$
$30$	1.45778	−	1.81448i	0.266154	−	0.331278i
$31$			9.56154i			1.71730i	0.512560	+	0.858651i	$0.328697\pi$
$31$			9.56154i			1.71730i	−0.512560	+	0.858651i	$0.671303\pi$
$32$	4.49373	−	1.63559i	0.794388	−	0.289133i
$33$	−7.54289	+	4.57193i	−1.31305	+	0.795871i
$34$	1.84921	+	5.08067i	0.317137	+	0.871328i
$35$	−2.43632	+	0.429589i	−0.411813	+	0.0726138i
$36$	−2.23631	−	1.71957i	−0.372718	−	0.286595i
$37$		−	0.822439i		−	0.135208i	−0.997712	−	0.0676041i	$-0.978465\pi$
$37$		−	0.822439i		−	0.135208i	0.997712	−	0.0676041i	$-0.0215355\pi$
$38$	3.77155	+	2.43087i	0.611827	+	0.394339i
$39$	0.599289	−	0.745928i	0.0959631	−	0.119444i
$40$	−3.89122	+	0.686127i	−0.615256	+	0.108486i
$41$	−4.69226	+	3.93727i	−0.732808	+	0.614899i	−0.930896	−	0.365285i	$-0.880971\pi$
$41$	−4.69226	+	3.93727i	−0.732808	+	0.614899i	0.198088	+	0.980184i	$0.436527\pi$
$42$	−0.657519	−	3.31431i	−0.101457	−	0.511409i
$43$	−0.620272	−	3.51774i	−0.0945906	−	0.536450i	−0.994872	−	0.101142i	$-0.967750\pi$
$43$	−0.620272	−	3.51774i	−0.0945906	−	0.536450i	0.900281	−	0.435308i	$-0.143361\pi$
$44$	4.71579	+	0.831522i	0.710933	+	0.125357i
$45$	2.64289	+	2.89006i	0.393978	+	0.430824i
$46$	4.01557	−	2.31839i	0.592064	−	0.341828i
$47$	6.74036	+	1.18851i	0.983182	+	0.173362i	0.642057	−	0.766657i	$-0.278081\pi$
$47$	6.74036	+	1.18851i	0.983182	+	0.173362i	0.341125	+	0.940018i	$0.389192\pi$
$48$	−0.416295	−	2.09839i	−0.0600871	−	0.302877i
$49$	1.70432	−	2.95196i	0.243474	−	0.421709i
$50$	−3.39277			−0.479810
$51$	−8.92335	+	1.77028i	−1.24952	+	0.247889i
$52$	−0.511580	+	0.0902054i	−0.0709434	+	0.0125092i
$53$	−3.87285	−	3.24971i	−0.531977	−	0.446382i	0.336806	−	0.941574i	$-0.390653\pi$
$53$	−3.87285	−	3.24971i	−0.531977	−	0.446382i	−0.868783	+	0.495192i	$0.835098\pi$
$54$	−3.86947	+	3.69300i	−0.526569	+	0.502554i
$55$	−6.24686	−	2.27367i	−0.842326	−	0.306582i
$56$	−2.86801	+	4.96755i	−0.383255	+	0.663816i
$57$	−5.01074	+	5.64734i	−0.663689	+	0.748009i
$58$	−2.20630	−	3.82142i	−0.289701	−	0.501778i
$59$	1.14034	+	6.46720i	0.148460	+	0.841958i	0.964524	+	0.263996i	$0.0850406\pi$
$59$	1.14034	+	6.46720i	0.148460	+	0.841958i	−0.816064	+	0.577962i	$0.803848\pi$
$60$	−0.0453088	−	2.12567i	−0.00584934	−	0.274422i
$61$	2.20421	−	0.802266i	0.282220	−	0.102720i	−0.197032	−	0.980397i	$-0.563130\pi$
$61$	2.20421	−	0.802266i	0.282220	−	0.102720i	0.479252	+	0.877677i	$0.340908\pi$
$62$	−6.32675	−	7.53992i	−0.803498	−	0.957571i
$63$	5.68011	−	0.242254i	0.715626	−	0.0305211i
$64$	−3.69649	+	6.40251i	−0.462061	+	0.800313i
$65$	0.721165			0.0894495
$66$	2.92290	−	8.59632i	0.359784	−	1.05813i
$67$	10.0012	−	11.9190i	1.22184	−	1.45613i	0.372713	−	0.927947i	$-0.378428\pi$
$67$	10.0012	−	11.9190i	1.22184	−	1.45613i	0.849128	−	0.528187i	$-0.177128\pi$
$68$	4.27721	+	2.46945i	0.518688	+	0.299465i
$69$	2.82398	+	7.27272i	0.339968	+	0.875533i
$70$	1.63695	−	1.95084i	0.195653	−	0.233170i
$71$	0.276935	−	0.232376i	0.0328661	−	0.0275780i	−0.626207	−	0.779657i	$-0.715393\pi$
$71$	0.276935	−	0.232376i	0.0328661	−	0.0275780i	0.659073	+	0.752079i	$0.270949\pi$
$72$	9.07210	−	0.386921i	1.06916	−	0.0455991i
$73$	0.920520	+	5.22053i	0.107739	+	0.611017i	0.990091	+	0.140427i	$0.0448476\pi$
$73$	0.920520	+	5.22053i	0.107739	+	0.611017i	−0.882352	+	0.470589i	$0.844041\pi$
$74$	0.544197	+	0.648549i	0.0632617	+	0.0753923i
$75$	0.871259	−	5.64172i	0.100604	−	0.651449i
$76$	4.06651	−	0.513512i	0.466461	−	0.0589039i
$77$	−8.35764	+	4.82529i	−0.952441	+	0.549892i
$78$	0.0209902	+	0.984757i	0.00237667	+	0.111502i
$79$	4.77547	−	13.1205i	0.537282	−	1.47617i	−0.312954	−	0.949768i	$-0.601318\pi$
$79$	4.77547	−	13.1205i	0.537282	−	1.47617i	0.850236	−	0.526402i	$-0.176459\pi$
$80$	1.03640	−	1.23514i	0.115873	−	0.138093i
$81$	−5.14729	−	7.38278i	−0.571921	−	0.820308i
$82$	1.09492	−	6.20962i	0.120914	−	0.685738i
$83$	6.96872	−	4.02339i	0.764917	−	0.441625i	−0.0661417	−	0.997810i	$-0.521069\pi$
$83$	6.96872	−	4.02339i	0.764917	−	0.441625i	0.831058	+	0.556185i	$0.187736\pi$
$84$	−2.40616	−	1.93315i	−0.262534	−	0.210924i
$85$	−5.25239	−	4.40727i	−0.569701	−	0.478036i
$86$	2.81677	+	2.36355i	0.303740	+	0.254868i
$87$	6.92109	−	2.68744i	0.742019	−	0.288124i
$88$	−13.3486	+	7.70681i	−1.42296	+	0.821548i
$89$	−0.457076	+	2.59221i	−0.0484500	+	0.274773i	−0.999403	−	0.0345634i	$-0.988996\pi$
$89$	−0.457076	+	2.59221i	−0.0484500	+	0.274773i	0.950953	+	0.309337i	$0.100107\pi$
$90$	−3.99641	−	0.530242i	−0.421258	−	0.0558924i
$91$	0.672944	−	0.801984i	0.0705437	−	0.0840708i
$92$	1.44865	−	3.98014i	0.151032	−	0.414958i
$93$	14.1626	−	8.58429i	1.46859	−	0.890149i
$94$	−6.10165	+	3.52279i	−0.629337	+	0.363348i
$95$	−5.68342	−	0.278252i	−0.583107	−	0.0285480i
$96$	−6.45709	−	5.18772i	−0.659023	−	0.529469i
$97$	1.47879	+	1.76235i	0.150148	+	0.178939i	0.835876	−	0.548919i	$-0.184960\pi$
$97$	1.47879	+	1.76235i	0.150148	+	0.178939i	−0.685728	+	0.727858i	$0.740516\pi$
$98$	0.609306	+	3.45555i	0.0615492	+	0.349063i
$99$	13.5439	+	7.06791i	1.36122	+	0.710352i
$100$	−2.37412	+	1.99212i	−0.237412	+	0.199212i
$101$	5.31701	−	6.33656i	0.529062	−	0.630512i	−0.433637	−	0.901088i	$-0.642770\pi$
$101$	5.31701	−	6.33656i	0.529062	−	0.630512i	0.962699	+	0.270576i	$0.0872143\pi$
$102$	5.86530	−	7.30046i	0.580751	−	0.722853i
$103$	−12.1267	−	7.00135i	−1.19488	−	0.689864i	−0.235470	−	0.971882i	$-0.575663\pi$
$103$	−12.1267	−	7.00135i	−1.19488	−	0.689864i	−0.959409	+	0.282018i	$0.908996\pi$
$104$	1.07481	−	1.28091i	0.105394	−	0.125603i
$105$	2.82362	+	3.22300i	0.275557	+	0.314533i
$106$	5.20430			0.505486
$107$	−1.26663	+	2.19386i	−0.122449	+	0.212089i	−0.920733	−	0.390193i	$-0.872408\pi$
$107$	−1.26663	+	2.19386i	−0.122449	+	0.212089i	0.798284	+	0.602282i	$0.205742\pi$
$108$	−0.539289	+	4.85625i	−0.0518931	+	0.467293i
$109$	7.35992	+	8.77121i	0.704953	+	0.840130i	0.993077	−	0.117463i	$-0.0374761\pi$
$109$	7.35992	+	8.77121i	0.704953	+	0.840130i	−0.288124	+	0.957593i	$0.593032\pi$
$110$	6.43053	−	2.34052i	0.613127	−	0.223160i
$111$	−1.21820	+	0.738381i	−0.115626	+	0.0700840i
$112$	−0.406452	−	2.30510i	−0.0384061	−	0.217812i
$113$	3.04325	+	5.27107i	0.286285	+	0.495860i	0.972920	−	0.231142i	$-0.0742463\pi$
$113$	3.04325	+	5.27107i	0.286285	+	0.495860i	−0.686635	+	0.727002i	$0.740913\pi$
$114$	0.214534	−	7.76886i	0.0200929	−	0.727620i
$115$	−2.94005	+	5.09231i	−0.274161	+	0.474861i
$116$	−3.78770	−	1.37861i	−0.351679	−	0.128001i
$117$	−1.64291	−	0.217981i	−0.151887	−	0.0201523i
$118$	−5.17850	−	4.34528i	−0.476720	−	0.400015i
$119$	−9.80237	+	1.72842i	−0.898582	+	0.158444i
$120$	4.50981	+	5.14769i	0.411687	+	0.469918i
$121$	−14.9326			−1.35751
$122$	−1.20732	+	2.09114i	−0.109306	+	0.189323i
$123$	10.0446	+	3.41533i	0.905690	+	0.307950i
$124$	−8.85441	−	1.56127i	−0.795149	−	0.140206i
$125$	9.37875	−	5.41482i	0.838861	−	0.484316i
$126$	−4.31886	+	3.94949i	−0.384754	+	0.351848i
$127$	−3.06101	−	0.539739i	−0.271621	−	0.0478941i	0.0361787	−	0.999345i	$-0.488481\pi$
$127$	−3.06101	−	0.539739i	−0.271621	−	0.0478941i	−0.307799	+	0.951451i	$0.599593\pi$
$128$	0.339294	+	1.92423i	0.0299896	+	0.170080i
$129$	−4.65361	+	4.07695i	−0.409728	+	0.358956i
$130$	−0.568688	+	0.477186i	−0.0498772	+	0.0418519i
$131$	−12.7315	+	2.24491i	−1.11236	+	0.196139i	−0.699483	−	0.714649i	$-0.746587\pi$
$131$	−12.7315	+	2.24491i	−1.11236	+	0.196139i	−0.412875	+	0.910788i	$0.635475\pi$
$132$	−3.00216	−	7.73159i	−0.261304	−	0.672948i
$133$	−5.61283	+	6.06070i	−0.486695	+	0.525529i
$134$			16.0166i			1.38362i
$135$	1.90800	−	6.50933i	0.164214	−	0.560234i
$136$	−15.6561	+	2.76059i	−1.34250	+	0.236718i
$137$	2.91352	+	8.00484i	0.248919	+	0.683900i	0.999727	+	0.0233786i	$0.00744232\pi$
$137$	2.91352	+	8.00484i	0.248919	+	0.683900i	−0.750808	+	0.660521i	$0.770335\pi$
$138$	−7.03917	−	3.86645i	−0.599214	−	0.329134i
$139$	2.98108	−	1.08503i	0.252852	−	0.0920307i	−0.212484	−	0.977164i	$-0.568155\pi$
$139$	2.98108	−	1.08503i	0.252852	−	0.0920307i	0.465337	+	0.885134i	$0.345933\pi$
$140$		−	2.32629i		−	0.196607i
$141$	−4.29103	−	11.0509i	−0.361370	−	0.930652i
$142$	−0.0646218	+	0.366489i	−0.00542294	+	0.0307550i
$143$	2.64357	−	0.962180i	0.221066	−	0.0804616i
$144$	−2.73440	+	2.50054i	−0.227867	+	0.208379i
$145$	4.84610	+	2.79790i	0.402447	+	0.232353i
$146$	−4.18025	−	3.50765i	−0.345960	−	0.290295i
$147$	−5.90258	+	0.125814i	−0.486837	+	0.0103770i
$148$	0.761615	+	0.134293i	0.0626044	+	0.0110388i
$149$	−11.6236	−	13.8524i	−0.952240	−	1.13483i	−0.990767	−	0.135577i	$-0.956711\pi$
$149$	−11.6236	−	13.8524i	−0.952240	−	1.13483i	0.0385273	−	0.999258i	$-0.487733\pi$
$150$	3.04601	+	5.02538i	0.248705	+	0.410320i
$151$	11.2859	+	6.51591i	0.918432	+	0.530257i	0.883135	−	0.469120i	$-0.155429\pi$
$151$	11.2859	+	6.51591i	0.918432	+	0.530257i	0.0352977	+	0.999377i	$0.488762\pi$
$152$	−8.96466	+	9.67997i	−0.727130	+	0.785150i
$153$	10.6335	+	11.6280i	0.859666	+	0.940064i
$154$	3.39774	−	9.33521i	0.273798	−	0.752253i
$155$	11.7291	+	4.26906i	0.942107	+	0.342899i
$156$	0.592906	+	0.676769i	0.0474705	+	0.0541849i
$157$	20.6617	+	7.52026i	1.64899	+	0.600182i	0.988576	−	0.150724i	$-0.0481603\pi$
$157$	20.6617	+	7.52026i	1.64899	+	0.600182i	0.660410	+	0.750905i	$0.270383\pi$
$158$	4.91588	+	13.5063i	0.391086	+	1.07450i
$159$	−1.33646	+	8.65405i	−0.105988	+	0.686311i
$160$		−	6.24273i		−	0.493531i
$161$	2.91953	+	8.02135i	0.230091	+	0.632171i
$162$	8.94408	+	2.41592i	0.702713	+	0.189813i
$163$	2.41860	+	4.18914i	0.189439	+	0.328119i	0.945063	−	0.326887i	$-0.106000\pi$
$163$	2.41860	+	4.18914i	0.189439	+	0.328119i	−0.755624	+	0.655006i	$0.772666\pi$
$164$	−2.87991	−	4.98815i	−0.224883	−	0.389509i
$165$	2.24062	+	11.2942i	0.174432	+	0.879249i
$166$	−2.83308	+	7.78383i	−0.219890	+	0.604143i
$167$	0.334515	−	1.89713i	0.0258855	−	0.146804i	−0.969126	−	0.246567i	$-0.920697\pi$
$167$	0.334515	−	1.89713i	0.0258855	−	0.146804i	0.995011	+	0.0997631i	$0.0318085\pi$
$168$	9.93284	−	0.211719i	0.766335	−	0.0163345i
$169$	9.72479	−	8.16007i	0.748061	−	0.627698i
$170$	7.05810			0.541332
$171$	12.8635	+	2.35178i	0.983695	+	0.179845i
$172$	3.35886			0.256111
$173$	0.541085	−	0.454024i	0.0411379	−	0.0345188i	−0.621987	−	0.783028i	$-0.713674\pi$
$173$	0.541085	−	0.454024i	0.0411379	−	0.0345188i	0.663125	+	0.748509i	$0.269230\pi$
$174$	−3.67951	+	6.69883i	−0.278943	+	0.507837i
$175$	1.08460	−	6.15106i	0.0819879	−	0.464977i
$176$	2.15121	−	5.91041i	0.162154	−	0.445514i
$177$	8.55545	−	7.49529i	0.643067	−	0.563381i
$178$	−1.35480	−	2.34657i	−0.101546	−	0.175883i
$179$	−10.1185	−	17.5257i	−0.756288	−	1.30993i	−0.944731	−	0.327846i	$-0.893677\pi$
$179$	−10.1185	−	17.5257i	−0.756288	−	1.30993i	0.188443	−	0.982084i	$-0.439656\pi$
$180$	−3.10787	+	1.97552i	−0.231647	+	0.147247i
$181$	4.39983	+	12.0884i	0.327037	+	0.898527i	0.988858	+	0.148865i	$0.0475618\pi$
$181$	4.39983	+	12.0884i	0.327037	+	0.898527i	−0.661821	+	0.749662i	$0.730216\pi$
$182$			1.07770i			0.0798843i
$183$	−3.16725	−	2.54461i	−0.234130	−	0.188103i
$184$	4.66299	+	12.8115i	0.343760	+	0.944474i
$185$	−1.00889	−	0.367205i	−0.0741748	−	0.0269974i
$186$	−5.48805	+	16.1405i	−0.402403	+	1.18348i
$187$	−25.1338	−	9.14797i	−1.83797	−	0.668966i
$188$	−2.20122	+	6.04780i	−0.160540	+	0.441081i
$189$	−5.45840	−	8.19591i	−0.397040	−	0.596164i
$190$	4.66588	−	3.54123i	0.338498	−	0.256908i
$191$	3.19381	+	1.84395i	0.231096	+	0.133423i	0.611078	−	0.791571i	$-0.290736\pi$
$191$	3.19381	+	1.84395i	0.231096	+	0.133423i	−0.379982	+	0.924994i	$0.624070\pi$
$192$	12.8021	−	0.272878i	0.923912	−	0.0196933i
$193$	−10.9517	−	13.0518i	−0.788324	−	0.939488i	0.210953	−	0.977496i	$-0.432343\pi$
$193$	−10.9517	−	13.0518i	−0.788324	−	0.939488i	−0.999277	+	0.0380081i	$0.987899\pi$
$194$	−2.33225	−	0.411238i	−0.167446	−	0.0295252i
$195$	−0.647458	−	1.06819i	−0.0463654	−	0.0764948i
$196$	2.45536	+	2.06029i	0.175383	+	0.147163i
$197$	13.7412	+	7.93351i	0.979022	+	0.565239i	0.901975	−	0.431789i	$-0.142117\pi$
$197$	13.7412	+	7.93351i	0.979022	+	0.565239i	0.0770476	+	0.997027i	$0.475451\pi$
$198$	−15.3571	+	3.38832i	−1.09138	+	0.240797i
$199$	−16.9852	+	6.18211i	−1.20405	+	0.438238i	−0.864636	−	0.502399i	$-0.832451\pi$
$199$	−16.9852	+	6.18211i	−1.20405	+	0.438238i	−0.339414	+	0.940637i	$0.610229\pi$
$200$	1.73229	−	9.82430i	0.122491	−	0.694683i
$201$	−26.6334	−	4.11304i	−1.87858	−	0.290112i
$202$			8.51501i			0.599114i
$203$	7.63352	−	2.77838i	0.535768	−	0.195004i
$204$	−0.182297	−	8.55248i	−0.0127633	−	0.598794i
$205$	2.73484	+	7.51392i	0.191010	+	0.524795i
$206$	14.1954	−	2.50304i	0.989043	−	0.174395i
$207$	8.23703	−	10.7123i	0.572513	−	0.744557i
$208$			0.682324i			0.0473106i
$209$	−21.2049	+	6.56285i	−1.46677	+	0.453962i
$210$	−4.35924	−	0.673204i	−0.300816	−	0.0464555i
$211$	26.2753	−	4.63304i	1.80887	−	0.318952i	0.835723	−	0.549152i	$-0.185049\pi$
$211$	26.2753	−	4.63304i	1.80887	−	0.318952i	0.973143	+	0.230200i	$0.0739381\pi$
$212$	3.64176	−	3.05580i	0.250117	−	0.209873i
$213$	−0.592827	−	0.201571i	−0.0406198	−	0.0138114i
$214$	−0.452829	−	2.56812i	−0.0309548	−	0.175553i
$215$	−4.59215	−	0.809720i	−0.313182	−	0.0552225i
$216$	−8.71799	−	13.0903i	−0.593184	−	0.890680i
$217$	15.6924	−	9.05999i	1.06527	−	0.615032i
$218$	−11.6076	−	2.04673i	−0.786166	−	0.138622i
$219$	6.90623	−	6.05044i	0.466680	−	0.408851i
$220$	3.12555	−	5.41361i	0.210724	−	0.364985i
$221$	2.90156			0.195180
$222$	0.472057	−	1.38833i	0.0316824	−	0.0931787i
$223$	−11.3279	+	1.99741i	−0.758570	+	0.133756i	−0.539538	−	0.841961i	$-0.681401\pi$
$223$	−11.3279	+	1.99741i	−0.758570	+	0.133756i	−0.219032	+	0.975718i	$0.570290\pi$
$224$	−6.94233	−	5.82531i	−0.463854	−	0.389220i
$225$	−9.13875	+	3.77459i	−0.609250	+	0.251639i
$226$	−5.88761	−	2.14291i	−0.391638	−	0.142545i
$227$	−10.4898	+	18.1688i	−0.696230	+	1.20591i	0.273534	+	0.961862i	$0.411807\pi$
$227$	−10.4898	+	18.1688i	−0.696230	+	1.20591i	−0.969764	+	0.244044i	$0.921526\pi$
$228$	−4.41150	−	5.56230i	−0.292159	−	0.368373i
$229$	3.77433	+	6.53733i	0.249415	+	0.431999i	0.963364	−	0.268199i	$-0.0864284\pi$
$229$	3.77433	+	6.53733i	0.249415	+	0.431999i	−0.713949	+	0.700198i	$0.753095\pi$
$230$	−1.05109	−	5.96103i	−0.0693068	−	0.393059i
$231$	14.6507	+	8.04726i	0.963943	+	0.529471i
$232$	12.1920	−	4.43754i	0.800447	−	0.291339i
$233$	−18.0687	−	21.5335i	−1.18372	−	1.41070i	−0.890695	−	0.454600i	$-0.849782\pi$
$233$	−18.0687	−	21.5335i	−1.18372	−	1.41070i	−0.293026	−	0.956104i	$-0.594662\pi$
$234$	1.43978	−	0.915200i	0.0941214	−	0.0598285i
$235$	4.46739	−	7.73775i	0.291421	−	0.504755i
$236$	−6.17512			−0.401966
$237$	−23.7215	+	4.70606i	−1.54088	+	0.305691i
$238$	6.58616	−	7.84909i	0.426918	−	0.508781i
$239$	23.2383	+	13.4166i	1.50316	+	0.867848i	0.999993	+	0.00365777i	$0.00116431\pi$
$239$	23.2383	+	13.4166i	1.50316	+	0.867848i	0.503164	+	0.864191i	$0.332169\pi$
$240$	−2.75997	−	0.426226i	−0.178155	−	0.0275128i
$241$	3.68705	−	4.39406i	0.237504	−	0.283046i	−0.634106	−	0.773246i	$-0.718632\pi$
$241$	3.68705	−	4.39406i	0.237504	−	0.283046i	0.871610	+	0.490200i	$0.163076\pi$
$242$	11.7754	−	9.88071i	0.756949	−	0.635156i
$243$	−6.31419	+	14.2524i	−0.405055	+	0.914292i
$244$	0.383016	+	2.17219i	0.0245201	+	0.139060i
$245$	−2.86023	−	3.40868i	−0.182733	−	0.217773i
$246$	−10.1807	+	3.95315i	−0.649099	+	0.252044i
$247$	1.91813	−	1.45579i	0.122047	−	0.0926294i
$248$	25.0634	−	14.4703i	1.59153	−	0.918868i
$249$	−12.2159	−	6.70992i	−0.774154	−	0.425224i
$250$	−3.81286	+	10.4758i	−0.241147	+	0.662545i
$251$	2.87033	−	3.42072i	0.181173	−	0.215914i	−0.667812	−	0.744330i	$-0.732769\pi$
$251$	2.87033	−	3.42072i	0.181173	−	0.215914i	0.848986	+	0.528415i	$0.177214\pi$
$252$	−0.703148	+	5.29959i	−0.0442941	+	0.333843i
$253$	−3.98313	+	22.5895i	−0.250418	+	1.42019i
$254$	2.77095	−	1.59981i	0.173865	−	0.100381i
$255$	−1.81251	+	11.7367i	−0.113504	+	0.734979i
$256$	−12.8675	−	10.7971i	−0.804218	−	0.674819i
$257$	−10.9885	−	9.22043i	−0.685442	−	0.575154i	0.232149	−	0.972680i	$-0.425424\pi$
$257$	−10.9885	−	9.22043i	−0.685442	−	0.575154i	−0.917591	+	0.397526i	$0.869869\pi$
$258$	0.972021	−	6.29419i	0.0605154	−	0.391859i
$259$	−1.34978	+	0.779298i	−0.0838715	+	0.0484232i
$260$	−0.117757	+	0.667831i	−0.00730295	+	0.0414171i
$261$	−10.1944	−	7.83878i	−0.631016	−	0.485208i
$262$	8.55425	−	10.1946i	0.528483	−	0.629822i
$263$	−3.25822	+	8.95187i	−0.200910	+	0.551996i	−0.998702	−	0.0509370i	$-0.983779\pi$
$263$	−3.25822	+	8.95187i	−0.200910	+	0.551996i	0.797792	+	0.602933i	$0.206001\pi$
$264$	23.3996	+	12.8528i	1.44015	+	0.791038i
$265$	−5.71558	+	3.29989i	−0.351105	+	0.202711i
$266$	0.415815	−	8.49322i	0.0254953	−	0.520753i
$267$	4.24995	−	1.65025i	0.260093	−	0.100993i
$268$	9.40443	+	11.2078i	0.574467	+	0.684623i
$269$	1.18735	+	6.73379i	0.0723940	+	0.410567i	0.999371	+	0.0354497i	$0.0112863\pi$
$269$	1.18735	+	6.73379i	0.0723940	+	0.410567i	−0.926977	+	0.375117i	$0.877603\pi$
$270$	2.80256	+	6.39555i	0.170558	+	0.389221i
$271$	21.5952	−	18.1205i	1.31182	−	1.10074i	0.323843	−	0.946111i	$-0.395025\pi$
$271$	21.5952	−	18.1205i	1.31182	−	1.10074i	0.987972	−	0.154633i	$-0.0494195\pi$
$272$	4.16990	−	4.96950i	0.252838	−	0.301320i
$273$	−1.79207	−	0.276752i	−0.108461	−	0.0167498i
$274$	−7.59421	−	4.38452i	−0.458783	−	0.264879i
$275$	10.7885	−	12.8572i	0.650568	−	0.775317i
$276$	−7.19598	+	1.42759i	−0.433147	+	0.0859311i
$277$	2.96624			0.178224			0.0891120	−	0.996022i	$-0.471597\pi$
$277$	2.96624			0.178224			0.0891120	+	0.996022i	$0.471597\pi$
$278$	−1.63284	+	2.82816i	−0.0979313	+	0.169622i
$279$	−25.4302	−	13.2708i	−1.52246	−	0.794499i
$280$	4.81317	+	5.73612i	0.287642	+	0.342799i
$281$	12.7465	−	4.63936i	0.760395	−	0.276761i	0.0674220	−	0.997725i	$-0.478523\pi$
$281$	12.7465	−	4.63936i	0.760395	−	0.276761i	0.692973	+	0.720963i	$0.256300\pi$
$282$	10.6960	+	5.87505i	0.636937	+	0.349854i
$283$	1.10490	+	6.26623i	0.0656798	+	0.372489i	0.999876	+	0.0157297i	$0.00500711\pi$
$283$	1.10490	+	6.26623i	0.0656798	+	0.372489i	−0.934197	+	0.356759i	$0.883882\pi$
$284$	0.169971	+	0.294398i	0.0100859	+	0.0174693i
$285$	4.69039	+	8.66812i	0.277835	+	0.513455i
$286$	−1.44797	+	2.50796i	−0.0856204	+	0.148299i
$287$	10.9080	+	3.97018i	0.643877	+	0.234352i
$288$	−1.88694	+	14.2218i	−0.111189	+	0.838026i
$289$	−8.10988	−	6.80500i	−0.477052	−	0.400294i
$290$	−5.67282	+	1.00027i	−0.333119	+	0.0587379i
$291$	1.28275	−	3.77261i	0.0751963	−	0.221154i
$292$	−4.98475			−0.291710
$293$	6.15574	−	10.6621i	0.359622	−	0.622884i	−0.628275	−	0.777991i	$-0.716239\pi$
$293$	6.15574	−	10.6621i	0.359622	−	0.622884i	0.987898	+	0.155107i	$0.0495722\pi$
$294$	4.57134	−	4.00488i	0.266606	−	0.233569i
$295$	8.44246	+	1.48863i	0.491539	+	0.0866716i
$296$	−2.15584	+	1.24467i	−0.125305	+	0.0723451i
$297$	−1.69064	−	26.4069i	−0.0981010	−	1.53228i
$298$	18.3319	+	3.23242i	1.06194	+	0.187249i
$299$	−0.432099	−	2.45056i	−0.0249890	−	0.141719i
$300$	5.08222	+	1.72804i	0.293422	+	0.0997685i
$301$	−5.18556	+	4.35121i	−0.298891	+	0.250799i
$302$	−13.2112	+	2.32949i	−0.760218	+	0.134047i
$303$	−14.1593	−	2.18664i	−0.813432	−	0.125619i
$304$	0.263265	−	5.37732i	0.0150993	−	0.308410i
$305$		−	3.06210i		−	0.175335i
$306$	−16.0793	−	2.13340i	−0.919192	−	0.121958i
$307$	4.09615	−	0.722262i	0.233780	−	0.0412217i	−0.0555308	−	0.998457i	$-0.517685\pi$
$307$	4.09615	−	0.722262i	0.233780	−	0.0412217i	0.289310	+	0.957235i	$0.406574\pi$
$308$	−3.10374	−	8.52745i	−0.176852	−	0.485897i
$309$	0.516846	+	24.2479i	0.0294023	+	1.37941i
$310$	−12.0740	+	4.39458i	−0.685758	+	0.249595i
$311$			15.4430i			0.875692i	0.899050	+	0.437846i	$0.144259\pi$
$311$			15.4430i			0.875692i	−0.899050	+	0.437846i	$0.855741\pi$
$312$	−2.86224	−	0.442020i	−0.162042	−	0.0250244i
$313$	1.18388	−	6.71411i	0.0669168	−	0.379504i	−0.932896	−	0.360146i	$-0.882727\pi$
$313$	1.18388	−	6.71411i	0.0669168	−	0.379504i	0.999813	−	0.0193578i	$-0.00616215\pi$
$314$	−21.2692	+	7.74137i	−1.20029	+	0.436871i
$315$	2.23890	−	7.07595i	0.126147	−	0.398685i
$316$	11.3704	+	6.56470i	0.639634	+	0.369293i
$317$	−7.21033	−	6.05018i	−0.404972	−	0.339812i	0.417439	−	0.908705i	$-0.362928\pi$
$317$	−7.21033	−	6.05018i	−0.404972	−	0.339812i	−0.822412	+	0.568893i	$0.807372\pi$
$318$	−4.67239	−	7.70863i	−0.262014	−	0.432278i
$319$	21.4973	+	3.79055i	1.20362	+	0.212230i
$320$	6.20354	+	7.39309i	0.346788	+	0.413286i
$321$	4.38673	−	0.0935035i	0.244843	−	0.00521886i
$322$	−7.60988	−	4.39356i	−0.424082	−	0.244844i
$323$	−22.8669	−	1.11953i	−1.27235	−	0.0622922i
$324$	7.67726	−	3.56111i	0.426515	−	0.197840i
$325$	−0.622733	+	1.71095i	−0.0345430	+	0.0949062i
$326$	−4.67913	−	1.70307i	−0.259153	−	0.0943240i
$327$	6.38426	−	18.7763i	0.353051	−	1.03833i
$328$	17.4219	+	6.34105i	0.961963	+	0.350126i
$329$	−4.43622	−	12.1884i	−0.244577	−	0.671969i
$330$	−9.24008	−	7.42362i	−0.508650	−	0.408657i
$331$			34.6632i			1.90526i	0.304130	+	0.952631i	$0.401634\pi$
$331$			34.6632i			1.90526i	−0.304130	+	0.952631i	$0.598366\pi$
$332$	2.58794	+	7.11031i	0.142032	+	0.390229i
$333$	2.18739	+	1.14149i	0.119868	+	0.0625532i
$334$	0.991518	+	1.71736i	0.0542534	+	0.0939697i
$335$	−10.1556	−	17.5901i	−0.554862	−	0.961049i
$336$	−3.04942	+	2.67155i	−0.166359	+	0.145745i
$337$	−0.256198	+	0.703897i	−0.0139560	+	0.0383437i	−0.946475	−	0.322777i	$-0.895384\pi$
$337$	−0.256198	+	0.703897i	−0.0139560	+	0.0383437i	0.932519	+	0.361121i	$0.117606\pi$
$338$	−2.26925	+	12.8695i	−0.123431	+	0.700011i
$339$	5.07531	−	9.24001i	0.275653	−	0.501848i
$340$	4.93898	−	4.14429i	0.267854	−	0.224756i
$341$	48.6912			2.63678
$342$	−11.6999	+	6.65707i	−0.632657	+	0.359973i
$343$	−19.7253			−1.06507
$344$	−8.28223	+	6.94962i	−0.446548	+	0.374698i
$345$	10.1823	−	0.217037i	0.548197	−	0.0116849i
$346$	−0.126260	+	0.716058i	−0.00678780	+	0.0384955i
$347$	4.90061	−	13.4643i	0.263078	−	0.722802i	−0.735878	−	0.677115i	$-0.763230\pi$
$347$	4.90061	−	13.4643i	0.263078	−	0.722802i	0.998956	−	0.0456870i	$-0.0145477\pi$
$348$	1.35857	+	6.84806i	0.0728271	+	0.367095i
$349$	−0.0568119	−	0.0984011i	−0.00304107	−	0.00526729i	0.864501	−	0.502631i	$-0.167635\pi$
$349$	−0.0568119	−	0.0984011i	−0.00304107	−	0.00526729i	−0.867542	+	0.497364i	$0.834301\pi$
$350$	3.21480	+	5.56820i	0.171838	+	0.297633i
$351$	1.15212	+	2.62919i	0.0614957	+	0.140336i
$352$	−8.32907	−	22.8839i	−0.443941	−	1.21972i
$353$			4.23792i			0.225562i	0.993620	+	0.112781i	$0.0359758\pi$
$353$			4.23792i			0.225562i	−0.993620	+	0.112781i	$0.964024\pi$
$354$	−1.78702	+	11.5716i	−0.0949789	+	0.615023i
$355$	−0.161409	−	0.443468i	−0.00856671	−	0.0235368i
$356$	−2.32587	−	0.846546i	−0.123271	−	0.0448668i
$357$	11.3607	+	12.9675i	0.601270	+	0.686315i
$358$	19.5756	+	7.12494i	1.03460	+	0.376565i
$359$	−11.5267	+	31.6692i	−0.608354	+	1.67144i	0.125470	+	0.992097i	$0.459956\pi$
$359$	−11.5267	+	31.6692i	−0.608354	+	1.67144i	−0.733824	+	0.679340i	$0.762266\pi$
$360$	3.57590	−	11.3015i	0.188466	−	0.595642i
$361$	−15.6782	+	10.7328i	−0.825170	+	0.564884i
$362$	−11.4683	−	6.62125i	−0.602762	−	0.348005i
$363$	13.4064	+	22.1182i	0.703653	+	1.16091i
$364$	0.632790	+	0.754130i	0.0331672	+	0.0395271i
$365$	6.81502	+	1.20167i	0.356714	+	0.0628984i
$366$	4.18133	−	0.0891254i	0.218561	−	0.00465866i
$367$	−27.0849	−	22.7269i	−1.41382	−	1.18633i	−0.954555	−	0.298035i	$-0.903669\pi$
$367$	−27.0849	−	22.7269i	−1.41382	−	1.18633i	−0.459263	−	0.888300i	$-0.651887\pi$
$368$	−4.81805	−	2.78170i	−0.251158	−	0.145006i
$369$	−3.95917	−	17.9444i	−0.206106	−	0.934146i
$370$	1.03855	−	0.378001i	0.0539917	−	0.0196514i
$371$	−1.66371	+	9.43535i	−0.0863754	+	0.489859i
$372$	5.63687	+	14.5169i	0.292258	+	0.752665i
$373$			24.3603i			1.26133i	0.776055	+	0.630665i	$0.217218\pi$
$373$			24.3603i			1.26133i	−0.776055	+	0.630665i	$0.782782\pi$
$374$	25.8728	−	9.41694i	1.33785	−	0.486938i
$375$	−16.4406	−	9.03044i	−0.848991	−	0.466330i
$376$	−7.08540	−	19.4670i	−0.365402	−	1.00393i
$377$	−2.33207	+	0.411208i	−0.120108	+	0.0211783i
$378$	9.72744	+	2.85128i	0.500326	+	0.146654i
$379$		−	4.56637i		−	0.234559i	−0.993099	−	0.117279i	$-0.962583\pi$
$379$		−	4.56637i		−	0.234559i	0.993099	−	0.117279i	$-0.0374173\pi$
$380$	1.18570	−	5.21766i	0.0608251	−	0.267661i
$381$	1.94869	+	5.01856i	0.0998346	+	0.257108i
$382$	−3.73865	+	0.659225i	−0.191286	+	0.0337289i
$383$	−3.81663	+	3.20253i	−0.195021	+	0.163642i	−0.735069	−	0.677992i	$-0.762850\pi$
$383$	−3.81663	+	3.20253i	−0.195021	+	0.163642i	0.540048	+	0.841634i	$0.318406\pi$
$384$	2.54556	−	2.23013i	0.129903	−	0.113806i
$385$	2.18764	+	12.4067i	0.111492	+	0.632305i
$386$	17.2724	+	3.04559i	0.879142	+	0.155016i
$387$	10.2168	+	3.23268i	0.519349	+	0.164327i
$388$	−1.87348	+	1.08165i	−0.0951115	+	0.0549126i
$389$	7.24832	+	1.27807i	0.367505	+	0.0648010i	0.354351	−	0.935113i	$-0.384702\pi$
$389$	7.24832	+	1.27807i	0.367505	+	0.0648010i	0.0131536	+	0.999913i	$0.495813\pi$
$390$	1.21737	+	0.413928i	0.0616441	+	0.0209601i
$391$	−11.8291	+	20.4886i	−0.598223	+	1.03615i
$392$	−10.3172			−0.521097
$393$	14.7555	+	16.8425i	0.744315	+	0.849593i
$394$	−16.0854	+	2.83629i	−0.810371	+	0.142890i
$395$	−13.9627	−	11.7161i	−0.702542	−	0.589503i
$396$	−8.75674	+	11.3882i	−0.440043	+	0.572278i
$397$	−24.9352	−	9.07567i	−1.25146	−	0.455495i	−0.370567	−	0.928806i	$-0.620837\pi$
$397$	−24.9352	−	9.07567i	−1.25146	−	0.455495i	−0.880896	+	0.473311i	$0.843059\pi$
$398$	9.30338	−	16.1139i	0.466336	−	0.807718i
$399$	14.0163	+	2.87249i	0.701693	+	0.143805i
$400$	2.03539	+	3.52540i	0.101769	+	0.176270i
$401$	−2.83041	−	16.0521i	−0.141344	−	0.801602i	−0.970230	−	0.242185i	$-0.922136\pi$
$401$	−2.83041	−	16.0521i	−0.141344	−	0.801602i	0.828886	−	0.559417i	$-0.188975\pi$
$402$	23.7238	−	14.3796i	1.18324	−	0.717189i
$403$	−4.96358	+	1.80660i	−0.247254	+	0.0899930i
$404$	4.99974	+	5.95846i	0.248746	+	0.296445i
$405$	−11.3546	+	3.01791i	−0.564216	+	0.149961i
$406$	−4.18114	+	7.24194i	−0.207506	+	0.359412i
$407$	−4.18819			−0.207601
$408$	18.1449	+	20.7114i	0.898307	+	1.02537i
$409$	−13.2654	+	15.8091i	−0.655934	+	0.781711i	−0.986796	−	0.161968i	$-0.948216\pi$
$409$	−13.2654	+	15.8091i	−0.655934	+	0.781711i	0.330863	+	0.943679i	$0.392660\pi$
$410$	−7.12848	−	4.11563i	−0.352050	−	0.203256i
$411$	9.24106	−	11.5022i	0.455828	−	0.567363i
$412$	8.46369	−	10.0866i	0.416976	−	0.496933i
$413$	9.53342	−	7.99949i	0.469109	−	0.393629i
$414$	0.592732	+	13.8977i	0.0291312	+	0.683036i
$415$	−1.82409	−	10.3449i	−0.0895409	−	0.507812i
$416$	1.69813	+	2.02375i	0.0832577	+	0.0992226i
$417$	−4.28354	−	3.44146i	−0.209766	−	0.168529i
$418$	12.3790	−	19.2063i	0.605475	−	0.939410i
$419$	−32.3192	+	18.6595i	−1.57889	+	0.911575i	−0.583880	+	0.811840i	$0.698466\pi$
$419$	−32.3192	+	18.6595i	−1.57889	+	0.911575i	−0.995014	+	0.0997349i	$0.968201\pi$
$420$	−3.44570	+	2.08853i	−0.168133	+	0.101910i
$421$	−0.617360	+	1.69618i	−0.0300883	+	0.0826668i	−0.953827	−	0.300356i	$-0.902895\pi$
$421$	−0.617360	+	1.69618i	−0.0300883	+	0.0826668i	0.923739	+	0.383023i	$0.125117\pi$
$422$	−17.6542	+	21.0395i	−0.859395	+	1.02419i
$423$	−12.5161	+	16.2773i	−0.608556	+	0.791430i
$424$	−2.65723	+	15.0699i	−0.129046	+	0.731858i
$425$	14.9916	−	8.65543i	0.727201	−	0.419850i
$426$	0.600862	−	0.233313i	0.0291118	−	0.0113041i
$427$	−3.40526	−	2.85736i	−0.164792	−	0.138277i
$428$	−1.82479	−	1.53118i	−0.0882046	−	0.0740125i
$429$	−3.79857	−	3.05182i	−0.183396	−	0.147343i
$430$	4.15701	−	2.40005i	0.200469	−	0.115741i
$431$	−3.09931	+	17.5771i	−0.149289	+	0.846658i	0.814534	+	0.580115i	$0.196993\pi$
$431$	−3.09931	+	17.5771i	−0.149289	+	0.846658i	−0.963823	+	0.266543i	$0.914119\pi$
$432$	6.15874	+	1.80523i	0.296313	+	0.0868543i
$433$	8.99091	−	10.7149i	0.432076	−	0.514928i	−0.505444	−	0.862859i	$-0.668671\pi$
$433$	8.99091	−	10.7149i	0.432076	−	0.514928i	0.937520	+	0.347932i	$0.113116\pi$
$434$	−6.37962	+	17.5279i	−0.306231	+	0.841364i
$435$	−0.206543	−	9.69001i	−0.00990300	−	0.464600i
$436$	−9.32431	+	5.38339i	−0.446554	+	0.257818i
$437$	2.45981	+	19.4793i	0.117669	+	0.931821i
$438$	−1.44254	+	9.34095i	−0.0689270	+	0.446328i
$439$	−4.96718	−	5.91965i	−0.237070	−	0.282529i	0.634371	−	0.773028i	$-0.281259\pi$
$439$	−4.96718	−	5.91965i	−0.237070	−	0.282529i	−0.871442	+	0.490499i	$0.836815\pi$
$440$	3.49404	+	19.8157i	0.166572	+	0.944675i
$441$	5.48566	+	8.62997i	0.261222	+	0.410951i
$442$	−2.28808	+	1.91993i	−0.108833	+	0.0913215i
$443$	−2.77933	+	3.31228i	−0.132050	+	0.157371i	−0.828018	−	0.560702i	$-0.810531\pi$
$443$	−2.77933	+	3.31228i	−0.132050	+	0.157371i	0.695968	+	0.718073i	$0.254976\pi$
$444$	−0.484858	−	1.24868i	−0.0230103	−	0.0592595i
$445$	2.97579	+	1.71807i	0.141066	+	0.0814444i
$446$	7.61114	−	9.07060i	0.360398	−	0.429505i
$447$	−10.0827	+	29.6535i	−0.476895	+	1.40256i
$448$	14.0104			0.661927
$449$	16.3492	−	28.3177i	0.771568	−	1.33640i	−0.165135	−	0.986271i	$-0.552806\pi$
$449$	16.3492	−	28.3177i	0.771568	−	1.33640i	0.936703	−	0.350124i	$-0.113861\pi$
$450$	4.70893	−	9.02351i	0.221981	−	0.425372i
$451$	20.0502	+	23.8949i	0.944127	+	1.12517i
$452$	−5.37816	+	1.95749i	−0.252968	+	0.0920726i
$453$	−0.481010	−	22.5666i	−0.0225998	−	1.06027i
$454$	−3.75017	−	21.2683i	−0.176004	−	0.998170i
$455$	−0.683336	−	1.18357i	−0.0320353	−	0.0554868i
$456$	22.3864	+	4.58786i	1.04834	+	0.214846i
$457$	2.41382	−	4.18086i	0.112914	−	0.195573i	−0.804030	−	0.594589i	$-0.797315\pi$
$457$	2.41382	−	4.18086i	0.112914	−	0.195573i	0.916944	+	0.399016i	$0.130648\pi$
$458$	−7.30199	−	2.65771i	−0.341200	−	0.124186i
$459$	7.67670	−	26.1899i	0.358318	−	1.22244i
$460$	−4.23564	−	3.55412i	−0.197488	−	0.165712i
$461$	19.8871	−	3.50664i	0.926236	−	0.163320i	0.309869	−	0.950779i	$-0.399715\pi$
$461$	19.8871	−	3.50664i	0.926236	−	0.163320i	0.616367	+	0.787459i	$0.288604\pi$
$462$	−16.8778	+	3.34835i	−0.785227	+	0.155779i
$463$	−40.6046			−1.88706			−0.943529	−	0.331290i	$-0.892516\pi$
$463$	−40.6046			−1.88706			−0.943529	+	0.331290i	$0.892516\pi$
$464$	−2.64721	+	4.58510i	−0.122894	+	0.212858i
$465$	−4.20701	−	21.2060i	−0.195095	−	0.983404i
$466$	28.4969	+	5.02476i	1.32009	+	0.232768i
$467$	−7.04539	+	4.06766i	−0.326022	+	0.188229i	−0.654074	−	0.756431i	$-0.726941\pi$
$467$	−7.04539	+	4.06766i	−0.326022	+	0.188229i	0.328052	+	0.944660i	$0.393608\pi$
$468$	0.470125	−	1.48581i	0.0217315	−	0.0686818i
$469$	−29.0380	−	5.12018i	−1.34085	−	0.236428i
$470$	1.59713	+	9.05776i	0.0736700	+	0.417803i
$471$	−7.41095	−	37.3559i	−0.341478	−	1.72127i
$472$	15.2265	−	12.7766i	0.700857	−	0.588089i
$473$	−17.9138	+	3.15868i	−0.823675	+	0.145236i
$474$	15.5921	−	19.4073i	0.716168	−	0.891405i
$475$	5.56784	−	13.2435i	0.255470	−	0.607653i
$476$		−	9.35966i		−	0.428999i
$477$	14.0183	−	5.78999i	0.641853	−	0.265105i
$478$	−27.2025	+	4.79654i	−1.24422	+	0.219389i
$479$	4.64845	+	12.7715i	0.212393	+	0.583545i	0.999444	−	0.0333431i	$-0.0106154\pi$
$479$	4.64845	+	12.7715i	0.212393	+	0.583545i	−0.787051	+	0.616888i	$0.788393\pi$
$480$	−9.24675	+	5.60468i	−0.422055	+	0.255818i
$481$	0.426944	−	0.155395i	0.0194670	−	0.00708540i
$482$			5.90469i			0.268951i
$483$	9.26012	−	11.5259i	0.421350	−	0.524449i
$484$	2.43829	−	13.8282i	0.110832	−	0.628557i
$485$	2.82213	−	1.02717i	0.128146	−	0.0466414i
$486$	−4.45147	−	15.4170i	−0.201923	−	0.699330i
$487$	−0.548867	−	0.316888i	−0.0248715	−	0.0143596i	0.487513	−	0.873116i	$-0.337904\pi$
$487$	−0.548867	−	0.316888i	−0.0248715	−	0.0143596i	−0.512384	+	0.858756i	$0.671238\pi$
$488$	−5.43879	−	4.56369i	−0.246202	−	0.206588i
$489$	4.03357	−	7.34343i	0.182404	−	0.332081i
$490$	4.51097	+	0.795405i	0.203785	+	0.0359327i
$491$	−3.33772	−	3.97775i	−0.150629	−	0.179513i	0.685453	−	0.728117i	$-0.259604\pi$
$491$	−3.33772	−	3.97775i	−0.150629	−	0.179513i	−0.836083	+	0.548604i	$0.815160\pi$
$492$	−4.80290	+	8.74406i	−0.216531	+	0.394213i
$493$	19.4980	+	11.2572i	0.878145	+	0.506997i
$494$	−0.549299	+	2.41719i	−0.0247141	+	0.108754i
$495$	14.7173	−	13.4586i	0.661495	−	0.604921i
$496$	−4.03913	+	11.0974i	−0.181362	+	0.498289i
$497$	−0.643783	−	0.234318i	−0.0288776	−	0.0105106i
$498$	14.0730	−	2.79190i	0.630625	−	0.125108i
$499$	−0.197698	−	0.0719561i	−0.00885017	−	0.00322120i	0.337591	−	0.941293i	$-0.390388\pi$
$499$	−0.197698	−	0.0719561i	−0.00885017	−	0.00322120i	−0.346441	+	0.938072i	$0.612610\pi$
$500$	3.48294	+	9.56930i	0.155762	+	0.427952i
$501$	−3.11036	+	1.20775i	−0.138961	+	0.0539581i
$502$			4.59673i			0.205162i
$503$	10.5560	+	29.0023i	0.470668	+	1.29315i	0.917216	+	0.398390i	$0.130431\pi$
$503$	10.5560	+	29.0023i	0.470668	+	1.29315i	−0.446548	+	0.894760i	$0.647347\pi$
$504$	−9.23124	−	14.5225i	−0.411192	−	0.646883i
$505$	−5.39911	−	9.35154i	−0.240257	−	0.416138i
$506$	−11.8062	−	20.4489i	−0.524849	−	0.909066i
$507$	−20.8176	−	7.07834i	−0.924542	−	0.314360i
$508$	0.999644	−	2.74650i	0.0443520	−	0.121856i
$509$	3.08959	−	17.5219i	0.136944	−	0.776646i	−0.836543	−	0.547902i	$-0.815427\pi$
$509$	3.08959	−	17.5219i	0.136944	−	0.776646i	0.973486	−	0.228745i	$-0.0734621\pi$
$510$	−6.33672	−	10.4545i	−0.280595	−	0.462933i
$511$	7.69568	−	6.45744i	0.340437	−	0.285660i
$512$	13.3834			0.591467
$513$	−8.06530	−	21.1649i	−0.356092	−	0.934451i
$514$	14.7662			0.651309
$515$	−14.0029	+	11.7498i	−0.617042	+	0.517760i
$516$	−3.01557	−	4.97516i	−0.132753	−	0.219019i
$517$	6.05236	−	34.3246i	0.266182	−	1.50960i
$518$	0.548745	−	1.50766i	0.0241105	−	0.0662430i
$519$	−1.15829	−	0.393837i	−0.0508431	−	0.0172875i
$520$	−1.09140	−	1.89037i	−0.0478613	−	0.0828982i
$521$	14.9254	+	25.8516i	0.653895	+	1.13258i	0.982170	+	0.187997i	$0.0601997\pi$
$521$	14.9254	+	25.8516i	0.653895	+	1.13258i	−0.328274	+	0.944582i	$0.606467\pi$
$522$	13.2258	−	0.564074i	0.578877	−	0.0246888i
$523$	−15.1156	−	41.5297i	−0.660958	−	1.81597i	−0.572529	−	0.819885i	$-0.694038\pi$
$523$	−15.1156	−	41.5297i	−0.660958	−	1.81597i	−0.0884291	−	0.996082i	$-0.528185\pi$
$524$		−	12.1565i		−	0.531060i
$525$	−10.0847	+	3.91588i	−0.440133	+	0.170903i
$526$	−3.35402	−	9.21508i	−0.146242	−	0.401797i
$527$	47.1914	+	17.1763i	2.05569	+	0.748211i
$528$	−10.6859	+	2.11995i	−0.465043	+	0.0922588i
$529$	−2.54738	−	0.927172i	−0.110756	−	0.0403118i
$530$	2.32363	−	6.38411i	0.100932	−	0.277308i
$531$	−18.7831	−	5.94314i	−0.815117	−	0.257910i
$532$	−4.69598	−	6.18737i	−0.203596	−	0.268256i
$533$	−2.93049	−	1.69192i	−0.126934	−	0.0732852i
$534$	−2.25943	+	4.11347i	−0.0977750	+	0.178007i
$535$	2.12569	+	2.53329i	0.0919014	+	0.109524i
$536$	−46.3786	−	8.17780i	−2.00325	−	0.353227i
$537$	−16.8748	+	30.7219i	−0.728202	+	1.32575i
$538$	−5.39197	−	4.52440i	−0.232464	−	0.195061i
$539$	−15.0326	−	8.67907i	−0.647499	−	0.373834i
$540$	5.71638	+	2.82977i	0.245994	+	0.121774i
$541$	27.4781	−	10.0012i	1.18138	−	0.429986i	0.324689	−	0.945821i	$-0.394740\pi$
$541$	27.4781	−	10.0012i	1.18138	−	0.429986i	0.856688	+	0.515834i	$0.172518\pi$
$542$	−5.03917	+	28.5785i	−0.216451	+	1.22755i
$543$	13.9553	−	17.3700i	0.598879	−	0.745417i
$544$		−	25.1172i		−	1.07689i
$545$	14.0457	−	5.11223i	0.601653	−	0.218984i
$546$	1.59629	−	0.967551i	0.0683149	−	0.0414074i
$547$	0.732656	+	2.01296i	0.0313261	+	0.0860678i	0.954370	−	0.298627i	$-0.0965288\pi$
$547$	0.732656	+	2.01296i	0.0313261	+	0.0860678i	−0.923044	+	0.384695i	$0.874307\pi$
$548$	−7.88858	+	1.39097i	−0.336983	+	0.0594192i
$549$	−0.925557	+	6.97588i	−0.0395018	+	0.297723i
$550$			17.2773i			0.736708i
$551$	18.5375	−	2.34088i	0.789723	−	0.0997249i
$552$	14.7900	−	18.4089i	0.629504	−	0.783535i
$553$	−26.0583	+	4.59478i	−1.10811	+	0.195390i
$554$	−2.33908	+	1.96272i	−0.0993780	+	0.0833881i
$555$	0.361867	+	1.82404i	0.0153604	+	0.0774262i
$556$	0.518011	+	2.93779i	0.0219686	+	0.124590i
$557$	0.460074	+	0.0811235i	0.0194940	+	0.00343731i	0.183387	−	0.983041i	$-0.441294\pi$
$557$	0.460074	+	0.0811235i	0.0194940	+	0.00343731i	−0.163893	+	0.986478i	$0.552405\pi$
$558$	28.8345	−	6.36193i	1.22066	−	0.269322i
$559$	1.70893	−	0.986652i	0.0722801	−	0.0417309i
$560$	−3.00914	−	0.530593i	−0.127160	−	0.0224217i
$561$	9.01500	+	45.4413i	0.380614	+	1.91853i
$562$	−6.98171	+	12.0927i	−0.294506	+	0.510099i
$563$	34.7538			1.46470			0.732350	−	0.680929i	$-0.238424\pi$
$563$	34.7538			1.46470			0.732350	+	0.680929i	$0.238424\pi$
$564$	10.9343	−	2.16923i	0.460416	−	0.0913409i
$565$	7.82478	−	1.37972i	0.329191	−	0.0580452i
$566$	−5.01758	−	4.21025i	−0.210904	−	0.176970i
$567$	−7.23929	+	15.4432i	−0.304022	+	0.648555i
$568$	−1.02823	−	0.374246i	−0.0431436	−	0.0157030i
$569$	1.65136	−	2.86024i	0.0692287	−	0.119908i	−0.829333	−	0.558754i	$-0.811280\pi$
$569$	1.65136	−	2.86024i	0.0692287	−	0.119908i	0.898562	+	0.438847i	$0.144613\pi$
$570$	−9.43428	−	3.73183i	−0.395158	−	0.156309i
$571$	−16.4743	−	28.5343i	−0.689428	−	1.19412i	−0.972023	−	0.234885i	$-0.924529\pi$
$571$	−16.4743	−	28.5343i	−0.689428	−	1.19412i	0.282595	−	0.959239i	$-0.408805\pi$
$572$	0.459362	+	2.60517i	0.0192069	+	0.108928i
$573$	−0.136122	−	6.38617i	−0.00568657	−	0.266786i
$574$	−11.2287	+	4.08691i	−0.468677	+	0.170584i
$575$	−9.54262	−	11.3725i	−0.397955	−	0.474264i
$576$	−11.8978	−	18.7175i	−0.495743	−	0.779898i
$577$	−12.2898	+	21.2865i	−0.511630	+	0.886169i	0.488279	+	0.872687i	$0.337625\pi$
$577$	−12.2898	+	21.2865i	−0.511630	+	0.886169i	−0.999909	+	0.0134815i	$0.995709\pi$
$578$	10.8980			0.453296
$579$	−9.49994	+	27.9396i	−0.394804	+	1.16113i
$580$	−3.38228	+	4.03085i	−0.140442	+	0.167372i
$581$	−13.2064	−	7.62469i	−0.547892	−	0.316326i
$582$	1.48475	+	3.82374i	0.0615449	+	0.158499i
$583$	−16.5488	+	19.7221i	−0.685383	+	0.816807i
$584$	12.2913	−	10.3136i	0.508618	−	0.426781i
$585$	−1.00093	+	1.91803i	−0.0413833	+	0.0793009i
$586$	2.20073	+	12.4809i	0.0909112	+	0.515583i
$587$	29.8376	+	35.5590i	1.23153	+	1.46768i	0.835547	+	0.549419i	$0.185151\pi$
$587$	29.8376	+	35.5590i	1.23153	+	1.46768i	0.395981	+	0.918259i	$0.370405\pi$
$588$	0.847303	−	5.48660i	0.0349422	−	0.226263i
$589$	39.8145	−	12.3225i	1.64053	−	0.507738i
$590$	−7.64247	+	4.41238i	−0.314635	+	0.181655i
$591$	−0.585658	−	27.4762i	−0.0240908	−	1.13022i
$592$	0.347427	−	0.954549i	0.0142792	−	0.0392317i
$593$	13.8322	−	16.4846i	0.568020	−	0.676940i	−0.403203	−	0.915110i	$-0.632103\pi$
$593$	13.8322	−	16.4846i	0.568020	−	0.676940i	0.971223	+	0.238171i	$0.0765477\pi$
$594$	18.8063	+	19.7049i	0.771630	+	0.808503i
$595$	−2.25633	+	12.7963i	−0.0925006	+	0.524597i
$596$	14.7259	−	8.50202i	0.603198	−	0.348256i
$597$	24.4062	+	19.6083i	0.998879	+	0.802515i
$598$	1.96224	+	1.64652i	0.0802421	+	0.0673311i
$599$	17.5885	+	14.7585i	0.718648	+	0.603017i	0.927011	−	0.375034i	$-0.122369\pi$
$599$	17.5885	+	14.7585i	0.718648	+	0.603017i	−0.208363	+	0.978052i	$0.566814\pi$
$600$	−16.1070	+	6.25432i	−0.657567	+	0.255332i
$601$	8.75623	−	5.05541i	0.357174	−	0.206215i	−0.310666	−	0.950519i	$-0.600552\pi$
$601$	8.75623	−	5.05541i	0.357174	−	0.206215i	0.667840	+	0.744304i	$0.267219\pi$
$602$	1.21003	−	6.86244i	0.0493173	−	0.279692i
$603$	17.8191	+	43.1422i	0.725650	+	1.75689i
$604$	−7.87685	+	9.38727i	−0.320505	+	0.381963i
$605$	−6.66714	+	18.3178i	−0.271058	+	0.744725i
$606$	12.6125	−	7.64472i	0.512346	−	0.310546i
$607$	−23.3384	+	13.4744i	−0.947277	+	0.546911i	−0.892234	−	0.451573i	$-0.850863\pi$
$607$	−23.3384	+	13.4744i	−0.947277	+	0.546911i	−0.0550432	+	0.998484i	$0.517530\pi$
$608$	−12.6019	−	16.6042i	−0.511076	−	0.673388i
$609$	−10.9687	−	8.81240i	−0.444473	−	0.357096i
$610$	2.02615	+	2.41468i	0.0820366	+	0.0977674i
$611$	0.656574	+	3.72361i	0.0265621	+	0.150641i
$612$	−12.5043	+	7.94839i	−0.505457	+	0.321295i
$613$	22.9952	−	19.2953i	0.928768	−	0.779329i	−0.0468276	−	0.998903i	$-0.514911\pi$
$613$	22.9952	−	19.2953i	0.928768	−	0.779329i	0.975596	+	0.219574i	$0.0704667\pi$
$614$	−2.75218	+	3.27992i	−0.111069	+	0.132367i
$615$	8.67433	−	10.7968i	0.349783	−	0.435370i
$616$	25.2968	+	14.6051i	1.01924	+	0.588456i
$617$	−15.8259	+	18.8605i	−0.637125	+	0.759296i	−0.983913	−	0.178648i	$-0.942828\pi$
$617$	−15.8259	+	18.8605i	−0.637125	+	0.759296i	0.346788	+	0.937943i	$0.387272\pi$
$618$	−16.4521	−	18.7791i	−0.661800	−	0.755407i
$619$	−40.0436			−1.60949			−0.804743	−	0.593623i	$-0.797697\pi$
$619$	−40.0436			−1.60949			−0.804743	+	0.593623i	$0.797697\pi$
$620$	−5.86855	+	10.1646i	−0.235687	+	0.408221i
$621$	−23.2623	−	2.58329i	−0.933483	−	0.103664i
$622$	−10.2184	−	12.1779i	−0.409722	−	0.488288i
$623$	4.68742	−	1.70608i	0.187798	−	0.0683528i
$624$	1.01066	−	0.612586i	0.0404588	−	0.0245231i
$625$	0.406681	+	2.30640i	0.0162672	+	0.0922560i
$626$	3.50907	+	6.07789i	0.140251	+	0.242922i
$627$	28.7586	+	25.5167i	1.14851	+	1.01904i
$628$	−10.3379	+	17.9057i	−0.412526	+	0.714516i
$629$	−4.05919	−	1.47742i	−0.161851	−	0.0589088i
$630$	2.91655	+	7.06132i	0.116198	+	0.281330i
$631$	12.0925	+	10.1469i	0.481397	+	0.403940i	0.850931	−	0.525277i	$-0.176038\pi$
$631$	12.0925	+	10.1469i	0.481397	+	0.403940i	−0.369534	+	0.929217i	$0.620483\pi$
$632$	−41.6195	+	7.33864i	−1.65554	+	0.291916i
$633$	−30.4523	−	34.7596i	−1.21037	−	1.38157i
$634$	9.68917			0.384806
$635$	−2.02879	+	3.51396i	−0.0805099	+	0.139447i
$636$	−7.79581	−	2.65071i	−0.309124	−	0.105107i
$637$	1.85444	+	0.326988i	0.0734757	+	0.0129557i
$638$	−19.4602	+	11.2354i	−0.770438	+	0.444813i
$639$	0.233668	+	1.05907i	0.00924377	+	0.0418961i
$640$	2.51194	+	0.442923i	0.0992933	+	0.0175081i
$641$	−3.66739	−	20.7988i	−0.144853	−	0.821503i	−0.967485	−	0.252929i	$-0.918606\pi$
$641$	−3.66739	−	20.7988i	−0.144853	−	0.821503i	0.822632	−	0.568574i	$-0.192505\pi$
$642$	−3.39737	+	2.97638i	−0.134083	+	0.117468i
$643$	4.26135	−	3.57570i	0.168051	−	0.141012i	−0.554883	−	0.831928i	$-0.687237\pi$
$643$	4.26135	−	3.57570i	0.168051	−	0.141012i	0.722935	+	0.690916i	$0.242793\pi$
$644$	−7.90485	+	1.39384i	−0.311495	+	0.0549249i
$645$	2.92345	+	7.52888i	0.115111	+	0.296449i
$646$	18.7729	−	14.2479i	0.738609	−	0.560576i
$647$		−	19.5668i		−	0.769252i	−0.923073	−	0.384626i	$-0.874330\pi$
$647$		−	19.5668i		−	0.769252i	0.923073	−	0.384626i	$-0.125670\pi$
$648$	−11.5624	+	24.6655i	−0.454214	+	0.968952i
$649$	32.9336	−	5.80708i	1.29276	−	0.227948i
$650$	−0.641043	−	1.76125i	−0.0251438	−	0.0690820i
$651$	−27.5082	−	15.1096i	−1.07813	−	0.592191i
$652$	−4.27426	+	1.55570i	−0.167393	+	0.0609260i
$653$			25.3016i			0.990127i	0.868857	+	0.495064i	$0.164855\pi$
$653$			25.3016i			0.990127i	−0.868857	+	0.495064i	$0.835145\pi$
$654$	7.38961	+	19.0308i	0.288956	+	0.744162i
$655$	−2.93057	+	16.6201i	−0.114507	+	0.649400i
$656$	−7.10923	+	2.58755i	−0.277569	+	0.101027i
$657$	−15.1623	−	4.79749i	−0.591538	−	0.187168i
$658$	11.5632	+	6.67601i	0.450780	+	0.260258i
$659$	−26.3078	−	22.0749i	−1.02481	−	0.859915i	−0.0345826	−	0.999402i	$-0.511010\pi$
$659$	−26.3078	−	22.0749i	−1.02481	−	0.859915i	−0.990224	+	0.139487i	$0.955455\pi$
$660$	−10.8248	+	0.230731i	−0.421353	+	0.00898118i
$661$	18.1920	+	3.20774i	0.707587	+	0.124767i	0.515849	−	0.856679i	$-0.327476\pi$
$661$	18.1920	+	3.20774i	0.707587	+	0.124767i	0.191738	+	0.981446i	$0.438588\pi$
$662$	−22.9362	−	27.3343i	−0.891440	−	1.06238i
$663$	−2.60500	−	4.29780i	−0.101170	−	0.166913i
$664$	−21.0928	−	12.1779i	−0.818560	−	0.472596i
$665$	4.92863	+	9.59126i	0.191124	+	0.371933i
$666$	−2.48021	+	0.547223i	−0.0961063	+	0.0212045i
$667$	6.60378	−	18.1437i	0.255699	−	0.702528i
$668$	1.70220	+	0.619551i	0.0658602	+	0.0239712i
$669$	13.1287	+	14.9856i	0.507583	+	0.579378i
$670$	19.6476	+	7.15113i	0.759051	+	0.276272i
$671$	−4.08547	−	11.2247i	−0.157718	−	0.433326i
$672$	−2.39569	+	15.5129i	−0.0924156	+	0.598425i
$673$		−	22.9356i		−	0.884104i	−0.896989	−	0.442052i	$-0.854251\pi$
$673$		−	22.9356i		−	0.884104i	0.896989	−	0.442052i	$-0.145749\pi$
$674$	−0.263730	−	0.724593i	−0.0101585	−	0.0279103i
$675$	13.7956	+	10.1475i	0.530995	+	0.390579i
$676$	5.96866	+	10.3380i	0.229564	+	0.397616i
$677$	17.1278	+	29.6662i	0.658274	+	1.14016i	0.981062	+	0.193693i	$0.0620465\pi$
$677$	17.1278	+	29.6662i	0.658274	+	1.14016i	−0.322788	+	0.946471i	$0.604620\pi$
$678$	2.11177	+	10.6446i	0.0811019	+	0.408805i
$679$	1.49114	−	4.09688i	0.0572248	−	0.157224i
$680$	−3.60375	+	20.4379i	−0.138197	+	0.783756i
$681$	36.3294	−	0.774364i	1.39214	−	0.0296737i
$682$	−38.3963	+	32.2184i	−1.47027	+	1.23370i
$683$	−20.2934			−0.776507			−0.388254	−	0.921553i	$-0.626922\pi$
$683$	−20.2934			−0.776507			−0.388254	+	0.921553i	$0.626922\pi$
$684$	−4.27828	+	11.5281i	−0.163584	+	0.440790i
$685$	11.1204			0.424888
$686$	15.5547	−	13.0520i	0.593883	−	0.498327i
$687$	6.29455	−	11.4597i	0.240152	−	0.437216i
$688$	0.766110	−	4.34483i	0.0292077	−	0.165645i
$689$	0.955235	−	2.62449i	0.0363916	−	0.0999850i
$690$	−7.88584	+	6.90866i	−0.300209	+	0.263008i
$691$	18.5303	+	32.0954i	0.704925	+	1.22097i	0.966719	+	0.255842i	$0.0823527\pi$
$691$	18.5303	+	32.0954i	0.704925	+	1.22097i	−0.261793	+	0.965124i	$0.584314\pi$
$692$	0.332095	+	0.575205i	0.0126243	+	0.0218660i
$693$	−1.23366	−	28.9254i	−0.0468627	−	1.09879i
$694$	5.04470	+	13.8602i	0.191494	+	0.526126i
$695$		−	4.14134i		−	0.157090i
$696$	−17.5188	−	14.0749i	−0.664050	−	0.533508i
$697$	11.0035	+	30.2318i	0.416786	+	1.14511i
$698$	0.109911	+	0.0400043i	0.00416018	+	0.00151418i
$699$	−15.6735	+	46.0961i	−0.592825	+	1.74351i
$700$	5.51906	+	2.00877i	0.208601	+	0.0759244i
$701$	−0.0851016	+	0.233815i	−0.00321424	+	0.00883106i	−0.941289	−	0.337601i	$-0.890385\pi$
$701$	−0.0851016	+	0.233815i	−0.00321424	+	0.00883106i	0.938075	+	0.346432i	$0.112607\pi$
$702$	−2.64822	−	1.31095i	−0.0999508	−	0.0494786i
$703$	−3.42466	+	1.05992i	−0.129163	+	0.0399757i
$704$	32.6042	+	18.8240i	1.22882	+	0.709457i
$705$	−15.4720	+	0.329787i	−0.582709	+	0.0124205i
$706$	−2.80418	−	3.34189i	−0.105537	−	0.125774i
$707$	−15.4376	−	2.72207i	−0.580593	−	0.102374i
$708$	5.54399	+	9.14661i	0.208356	+	0.343751i
$709$	9.22851	+	7.74364i	0.346584	+	0.290819i	0.799417	−	0.600777i	$-0.205142\pi$
$709$	9.22851	+	7.74364i	0.346584	+	0.290819i	−0.452833	+	0.891596i	$0.649586\pi$
$710$	0.420719	+	0.242902i	0.0157893	+	0.00911597i
$711$	28.2677	+	30.9113i	1.06012	+	1.15927i
$712$	7.48662	−	2.72491i	0.280573	−	0.102120i
$713$	7.47876	−	42.4142i	0.280082	−	1.58842i
$714$	−17.5391	−	2.70859i	−0.656385	−	0.101367i
$715$		−	3.67246i		−	0.137342i
$716$	17.8818	−	6.50843i	0.668273	−	0.243231i
$717$	−0.990426	−	46.4660i	−0.0369881	−	1.73530i
$718$	−11.8656	−	32.6004i	−0.442819	−	1.21664i
$719$	45.5717	−	8.03553i	1.69954	−	0.299675i	0.762006	−	0.647570i	$-0.224215\pi$
$719$	45.5717	−	8.03553i	1.69954	−	0.299675i	0.937533	+	0.347896i	$0.113104\pi$
$720$	1.84656	+	4.47074i	0.0688171	+	0.166615i
$721$			26.5364i			0.988267i
$722$	5.26160	−	18.8376i	0.195817	−	0.701064i
$723$	−9.81871	−	1.51632i	−0.365162	−	0.0563925i
$724$	−11.9129	+	2.10056i	−0.442738	+	0.0780667i
$725$	−10.8226	+	9.08125i	−0.401942	+	0.337269i
$726$	−25.2072	−	8.57089i	−0.935527	−	0.318095i
$727$	1.99292	+	11.3024i	0.0739133	+	0.419183i	0.999203	+	0.0399215i	$0.0127108\pi$
$727$	1.99292	+	11.3024i	0.0739133	+	0.419183i	−0.925290	+	0.379261i	$0.876178\pi$
$728$	−3.12065	−	0.550254i	−0.115659	−	0.0203938i
$729$	26.7796	−	3.44312i	0.991836	−	0.127523i
$730$	−6.16924	+	3.56181i	−0.228334	+	0.131829i
$731$	−18.4762	−	3.25786i	−0.683368	−	0.120496i
$732$	2.87359	−	2.51751i	0.106211	−	0.0930498i
$733$	−4.59735	+	7.96285i	−0.169807	+	0.294115i	−0.938352	−	0.345681i	$-0.887648\pi$
$733$	−4.59735	+	7.96285i	−0.169807	+	0.294115i	0.768545	+	0.639796i	$0.220981\pi$
$734$	36.3964			1.34341
$735$	−2.48106	+	7.29688i	−0.0915154	+	0.269149i
$736$	−21.2131	+	3.74045i	−0.781926	+	0.137875i
$737$	−60.6962	−	50.9302i	−2.23577	−	1.87604i
$738$	14.9956	+	11.5306i	0.551997	+	0.424448i
$739$	−15.7479	−	5.73176i	−0.579295	−	0.210846i	0.0357194	−	0.999362i	$-0.488628\pi$
$739$	−15.7479	−	5.73176i	−0.579295	−	0.210846i	−0.615015	+	0.788516i	$0.710850\pi$
$740$	0.504786	−	0.874314i	0.0185563	−	0.0321404i
$741$	−3.87840	−	1.53414i	−0.142477	−	0.0563581i
$742$	−4.93131	−	8.54127i	−0.181034	−	0.313560i
$743$	−3.31059	−	18.7753i	−0.121454	−	0.688798i	−0.983351	−	0.181715i	$-0.941835\pi$
$743$	−3.31059	−	18.7753i	−0.121454	−	0.688798i	0.861897	−	0.507083i	$-0.169276\pi$
$744$	−43.9353	−	24.1326i	−1.61075	−	0.884744i
$745$	−22.1825	+	8.07377i	−0.812704	+	0.295800i
$746$	−16.1189	−	19.2098i	−0.590156	−	0.703320i
$747$	1.02864	+	24.1184i	0.0376360	+	0.882447i
$748$	12.5754	−	21.7813i	0.459804	−	0.796403i
$749$	4.80075			0.175415
$750$	18.9399	−	3.75744i	0.691587	−	0.137202i
$751$	−10.5101	+	12.5255i	−0.383520	+	0.457062i	−0.922922	−	0.384987i	$-0.874206\pi$
$751$	−10.5101	+	12.5255i	−0.383520	+	0.457062i	0.539402	+	0.842049i	$0.318650\pi$
$752$	7.32101	+	4.22679i	0.266970	+	0.154135i
$753$	−7.64375	−	1.18044i	−0.278554	−	0.0430175i
$754$	1.56691	−	1.86737i	0.0570635	−	0.0680056i
$755$	13.0320	−	10.9352i	0.474284	−	0.397971i
$756$	8.48106	−	3.71643i	0.308453	−	0.135165i
$757$	1.53487	+	8.70469i	0.0557858	+	0.316377i	0.999913	−	0.0132048i	$-0.00420333\pi$
$757$	1.53487	+	8.70469i	0.0557858	+	0.316377i	−0.944127	+	0.329582i	$0.893092\pi$
$758$	3.02151	+	3.60089i	0.109746	+	0.130790i
$759$	37.0357	−	14.3809i	1.34431	−	0.521992i
$760$	7.87187	+	15.3189i	0.285543	+	0.555675i
$761$	−2.25718	+	1.30318i	−0.0818227	+	0.0472404i	−0.540353	−	0.841438i	$-0.681709\pi$
$761$	−2.25718	+	1.30318i	−0.0818227	+	0.0472404i	0.458530	+	0.888679i	$0.348376\pi$
$762$	−4.85739	−	2.66805i	−0.175965	−	0.0966532i
$763$	7.42143	−	20.3902i	0.268674	−	0.738175i
$764$	−2.22908	+	2.65652i	−0.0806454	+	0.0961094i
$765$	19.0117	−	7.85242i	0.687369	−	0.283905i
$766$	0.890598	−	5.05083i	0.0321786	−	0.182494i
$767$	−3.14179	+	1.81391i	−0.113444	+	0.0654966i
$768$	−4.44036	+	28.7530i	−0.160228	+	1.03753i
$769$	21.1464	+	17.7439i	0.762558	+	0.639862i	0.938791	−	0.344486i	$-0.111947\pi$
$769$	21.1464	+	17.7439i	0.762558	+	0.639862i	−0.176233	+	0.984348i	$0.556391\pi$
$770$	−9.93448	−	8.33602i	−0.358014	−	0.300409i
$771$	−3.79194	+	24.5542i	−0.136564	+	0.884299i
$772$	13.8748	−	8.01062i	0.499365	−	0.288309i
$773$	2.94101	−	16.6793i	0.105781	−	0.599912i	−0.885125	−	0.465353i	$-0.845927\pi$
$773$	2.94101	−	16.6793i	0.105781	−	0.599912i	0.990906	−	0.134558i	$-0.0429616\pi$
$774$	−10.1957	+	4.21113i	−0.366475	+	0.151366i
$775$	−20.2565	+	24.1407i	−0.727634	+	0.867160i
$776$	2.38161	−	6.54342i	0.0854949	−	0.234895i
$777$	2.36613	+	1.29966i	0.0848844	+	0.0466249i
$778$	−6.56148	+	3.78827i	−0.235241	+	0.135816i
$779$	22.4421	+	14.4645i	0.804071	+	0.518245i
$780$	1.09491	−	0.425153i	0.0392042	−	0.0152229i
$781$	−1.18335	−	1.41027i	−0.0423437	−	0.0504633i
$782$	−4.22899	−	23.9838i	−0.151229	−	0.857660i
$783$	−2.45839	+	22.1376i	−0.0878556	+	0.791132i
$784$	3.22510	−	2.70618i	0.115182	−	0.0966492i
$785$	18.4502	−	21.9881i	0.658516	−	0.784789i
$786$	−22.7802	−	3.51797i	−0.812542	−	0.125482i
$787$	12.1246	+	7.00013i	0.432195	+	0.249528i	0.700281	−	0.713867i	$-0.253058\pi$
$787$	12.1246	+	7.00013i	0.432195	+	0.249528i	−0.268087	+	0.963395i	$0.586391\pi$
$788$	−9.59054	+	11.4296i	−0.341649	+	0.407161i
$789$	16.1848	−	3.21086i	0.576193	−	0.114310i
$790$	18.7630			0.667558
$791$	5.76724	−	9.98915i	0.205059	−	0.355173i
$792$	−1.97036	−	46.1988i	−0.0700137	−	1.64160i
$793$	0.832945	+	0.992665i	0.0295787	+	0.0352506i
$794$	25.6684	−	9.34252i	0.910936	−	0.331554i
$795$	10.0192	+	5.50332i	0.355345	+	0.195183i
$796$	−2.95145	−	16.7385i	−0.104611	−	0.593281i
$797$	−1.47817	−	2.56026i	−0.0523594	−	0.0906892i	0.838658	−	0.544659i	$-0.183341\pi$
$797$	−1.47817	−	2.56026i	−0.0523594	−	0.0906892i	−0.891017	+	0.453970i	$0.850007\pi$
$798$	−12.9535	+	7.00925i	−0.458549	+	0.248125i
$799$	17.9743	−	31.1324i	0.635884	−	1.10138i
$800$	14.8107	+	5.39066i	0.523638	+	0.190589i
$801$	−6.25993	−	4.81346i	−0.221184	−	0.170075i
$802$	12.8534	+	10.7853i	0.453870	+	0.380842i
$803$	26.5850	−	4.68766i	0.938166	−	0.165424i
$804$	8.15774	−	23.9921i	0.287701	−	0.846138i
$805$	11.1433			0.392750
$806$	2.71872	−	4.70896i	0.0957629	−	0.165866i
$807$	8.90813	−	7.80427i	0.313581	−	0.274723i
$808$	−24.6566	−	4.34762i	−0.867415	−	0.152949i
$809$	17.0663	−	9.85324i	0.600019	−	0.346421i	−0.169030	−	0.985611i	$-0.554063\pi$
$809$	17.0663	−	9.85324i	0.600019	−	0.346421i	0.769049	+	0.639190i	$0.220730\pi$
$810$	6.95699	−	9.89304i	0.244444	−	0.347606i
$811$	18.0689	+	3.18603i	0.634484	+	0.111877i	0.481634	−	0.876373i	$-0.340044\pi$
$811$	18.0689	+	3.18603i	0.634484	+	0.111877i	0.152850	+	0.988249i	$0.451155\pi$
$812$	1.32645	+	7.52265i	0.0465492	+	0.263993i
$813$	−46.2282	−	15.7184i	−1.62130	−	0.551268i
$814$	3.30268	−	2.77127i	0.115759	−	0.0971331i
$815$	6.21868	−	1.09652i	0.217831	−	0.0384095i
$816$	−11.1046	−	1.71489i	−0.388737	−	0.0600333i
$817$	−13.8486	+	7.11632i	−0.484500	+	0.248969i
$818$		−	21.2441i		−	0.742784i
$819$	1.19898	+	2.90288i	0.0418958	+	0.101435i
$820$	−7.40479	+	1.30566i	−0.258586	+	0.0455958i
$821$	14.7938	+	40.6457i	0.516308	+	1.41855i	0.874559	+	0.484920i	$0.161151\pi$
$821$	14.7938	+	40.6457i	0.516308	+	1.41855i	−0.358250	+	0.933626i	$0.616627\pi$
$822$	0.323669	+	15.1850i	0.0112893	+	0.529637i
$823$	30.4212	−	11.0724i	1.06042	−	0.385960i	0.247831	−	0.968803i	$-0.420282\pi$
$823$	30.4212	−	11.0724i	1.06042	−	0.385960i	0.812585	+	0.582843i	$0.198060\pi$
$824$			42.3831i			1.47649i
$825$	−28.7299	−	4.43680i	−1.00025	−	0.154470i
$826$	−2.22459	+	12.6163i	−0.0774035	+	0.438977i
$827$	−19.2831	+	7.01846i	−0.670538	+	0.244056i	−0.654779	−	0.755820i	$-0.727239\pi$
$827$	−19.2831	+	7.01846i	−0.670538	+	0.244056i	−0.0157585	+	0.999876i	$0.505016\pi$
$828$	8.57507	+	9.37704i	0.298004	+	0.325875i
$829$	2.74471	+	1.58466i	0.0953277	+	0.0550375i	0.546906	−	0.837194i	$-0.315806\pi$
$829$	2.74471	+	1.58466i	0.0953277	+	0.0550375i	−0.451578	+	0.892231i	$0.649139\pi$
$830$	8.28351	+	6.95069i	0.287525	+	0.241262i
$831$	−2.66307	−	4.39360i	−0.0923809	−	0.152412i
$832$	−4.02210	−	0.709204i	−0.139441	−	0.0245872i
$833$	−11.5079	−	13.7146i	−0.398726	−	0.475184i
$834$	5.65504	−	0.120538i	0.195818	−	0.00417388i
$835$	−2.17785	−	1.25738i	−0.0753677	−	0.0435136i
$836$	−2.61501	−	20.7083i	−0.0904421	−	0.716212i
$837$	3.17436	+	49.5817i	0.109722	+	1.71379i
$838$	13.1391	−	36.0994i	0.453883	−	1.24703i
$839$	−9.41918	−	3.42830i	−0.325186	−	0.118358i	0.174268	−	0.984698i	$-0.444244\pi$
$839$	−9.41918	−	3.42830i	−0.325186	−	0.118358i	−0.499455	+	0.866340i	$0.666466\pi$
$840$	4.17512	−	12.2791i	0.144055	−	0.423671i
$841$	9.98458	+	3.63409i	0.344296	+	0.125313i
$842$	−0.635512	−	1.74605i	−0.0219012	−	0.0601730i
$843$	−18.3156	−	14.7150i	−0.630823	−	0.506813i
$844$			25.0886i			0.863585i
$845$	−5.66801	−	15.5727i	−0.194986	−	0.535718i
$846$	−0.900654	−	21.1175i	−0.0309651	−	0.726036i
$847$	14.1493	+	24.5073i	0.486176	+	0.842082i
$848$	−3.12216	−	5.40774i	−0.107216	−	0.185703i
$849$	8.28958	−	7.26237i	0.284498	−	0.249244i
$850$	−6.09474	+	16.7452i	−0.209048	+	0.574355i
$851$	−0.643288	+	3.64827i	−0.0220516	+	0.125061i
$852$	0.283465	−	0.516070i	0.00971134	−	0.0176803i
$853$	26.1211	−	21.9182i	0.894368	−	0.750464i	−0.0747131	−	0.997205i	$-0.523804\pi$
$853$	26.1211	−	21.9182i	0.894368	−	0.750464i	0.969081	+	0.246741i	$0.0793596\pi$
$854$	4.57596			0.156586
$855$	8.62824	−	14.7296i	0.295080	−	0.503742i
$856$	7.66761			0.262074
$857$	−44.0054	+	36.9249i	−1.50319	+	1.26133i	−0.627349	+	0.778738i	$0.715860\pi$
$857$	−44.0054	+	36.9249i	−1.50319	+	1.26133i	−0.875846	+	0.482591i	$0.839696\pi$
$858$	5.01478	−	0.106891i	0.171202	−	0.00364918i
$859$	−5.71944	+	32.4366i	−0.195145	+	1.10672i	0.717068	+	0.697004i	$0.245484\pi$
$859$	−5.71944	+	32.4366i	−0.195145	+	1.10672i	−0.912212	+	0.409718i	$0.865627\pi$
$860$	1.49967	−	4.12032i	0.0511385	−	0.140502i
$861$	−3.91247	−	19.7213i	−0.133337	−	0.672101i
$862$	−9.18651	−	15.9115i	−0.312894	−	0.541948i
$863$	3.45960	+	5.99221i	0.117766	+	0.203977i	0.918882	−	0.394532i	$-0.129093\pi$
$863$	3.45960	+	5.99221i	0.117766	+	0.203977i	−0.801116	+	0.598509i	$0.795760\pi$
$864$	22.7594	−	9.97328i	0.774291	−	0.339298i
$865$	−0.315367	−	0.866463i	−0.0107228	−	0.0294606i
$866$			14.3986i			0.489286i
$867$	−2.79859	+	18.1219i	−0.0950450	+	0.615451i
$868$	5.82760	+	16.0112i	0.197802	+	0.543455i
$869$	−66.8149	−	24.3186i	−2.26654	−	0.824953i
$870$	6.57463	+	7.50456i	0.222901	+	0.254429i
$871$	8.07704	+	2.93980i	0.273680	+	0.0996114i
$872$	11.8533	−	32.5666i	0.401403	−	1.10285i
$873$	−6.73965	+	1.48701i	−0.228103	+	0.0503276i
$874$	−14.8289	−	13.7331i	−0.501596	−	0.464530i
$875$	−17.7736	−	10.2616i	−0.600856	−	0.346905i
$876$	4.47528	+	7.38343i	0.151206	+	0.249463i
$877$	−32.8270	−	39.1217i	−1.10849	−	1.32104i	−0.942232	−	0.334962i	$-0.891277\pi$
$877$	−32.8270	−	39.1217i	−1.10849	−	1.32104i	−0.166256	−	0.986083i	$-0.553168\pi$
$878$	7.83391	+	1.38133i	0.264382	+	0.0466176i
$879$	−21.3193	+	0.454422i	−0.719082	+	0.0153273i
$880$	−6.28982	−	5.27779i	−0.212030	−	0.177914i
$881$	−5.69677	−	3.28903i	−0.191929	−	0.110810i	0.400956	−	0.916097i	$-0.368678\pi$
$881$	−5.69677	−	3.28903i	−0.191929	−	0.110810i	−0.592885	+	0.805287i	$0.702011\pi$
$882$	−10.0362	−	3.17553i	−0.337935	−	0.106926i
$883$	−10.4353	+	3.79815i	−0.351177	+	0.127818i	−0.511585	−	0.859233i	$-0.670941\pi$
$883$	−10.4353	+	3.79815i	−0.351177	+	0.127818i	0.160408	+	0.987051i	$0.448719\pi$
$884$	−0.473786	+	2.68697i	−0.0159351	+	0.0903727i
$885$	−5.37462	−	13.8415i	−0.180666	−	0.465277i
$886$		−	4.45100i		−	0.149534i
$887$	−25.8607	+	9.41252i	−0.868317	+	0.316042i	−0.737485	−	0.675363i	$-0.763987\pi$
$887$	−25.8607	+	9.41252i	−0.868317	+	0.316042i	−0.130832	+	0.991405i	$0.541765\pi$
$888$	3.77911	+	2.07577i	0.126819	+	0.0696584i
$889$	2.01463	+	5.53515i	0.0675685	+	0.185643i
$890$	−3.48344	+	0.614224i	−0.116765	+	0.0205888i
$891$	−37.5961	+	26.2121i	−1.25952	+	0.878138i
$892$		−	10.8163i		−	0.362155i
$893$	−3.73768	−	29.5987i	−0.125077	−	0.990483i
$894$	−11.6704	−	30.0554i	−0.390318	−	1.00520i
$895$	−26.0165	+	4.58740i	−0.869634	+	0.153340i
$896$	2.83654	−	2.38014i	0.0947623	−	0.0795150i
$897$	−3.24184	+	2.84012i	−0.108242	+	0.0948290i
$898$	5.84498	+	33.1485i	0.195049	+	1.10618i
$899$	−40.3635	−	7.11717i	−1.34620	−	0.237371i
$900$	−2.00320	−	9.07922i	−0.0667734	−	0.302641i
$901$	−22.9963	+	13.2769i	−0.766117	+	0.442318i
$902$	−31.6219	−	5.57579i	−1.05289	−	0.185654i
$903$	11.1006	+	3.77439i	0.369405	+	0.125604i
$904$	9.21126	−	15.9544i	0.306362	−	0.530635i
$905$	16.7933			0.558230
$906$	15.3114	+	17.4771i	0.508686	+	0.580636i
$907$	30.7635	−	5.42444i	1.02149	−	0.180115i	0.362273	−	0.932072i	$-0.382001\pi$
$907$	30.7635	−	5.42444i	1.02149	−	0.180115i	0.659213	+	0.751957i	$0.270890\pi$
$908$	−15.1123	−	12.6807i	−0.501519	−	0.420824i
$909$	9.47329	+	22.9360i	0.314209	+	0.760739i
$910$	1.32201	+	0.481173i	0.0438243	+	0.0159507i
$911$	22.3311	−	38.6787i	0.739864	−	1.28148i	−0.212693	−	0.977119i	$-0.568223\pi$
$911$	22.3311	−	38.6787i	0.739864	−	1.28148i	0.952556	−	0.304362i	$-0.0984434\pi$
$912$	−8.20126	+	4.43777i	−0.271571	+	0.146949i
$913$	−20.4887	−	35.4876i	−0.678079	−	1.17447i
$914$	0.862960	+	4.89409i	0.0285442	+	0.161882i
$915$	−4.53560	+	2.74914i	−0.149942	+	0.0908837i
$916$	−6.67016	+	2.42774i	−0.220388	+	0.0802148i
$917$	15.7480	+	18.7678i	0.520046	+	0.619767i
$918$	11.2759	+	25.7321i	0.372160	+	0.849285i
$919$	21.0986	−	36.5438i	0.695978	−	1.20547i	−0.273872	−	0.961766i	$-0.588305\pi$
$919$	21.0986	−	36.5438i	0.695978	−	1.20547i	0.969850	−	0.243703i	$-0.0783621\pi$
$920$	17.7978			0.586775
$921$	−4.74732	−	5.41879i	−0.156429	−	0.178555i
$922$	−13.3621	+	15.9243i	−0.440056	+	0.524439i
$923$	0.172956	+	0.0998563i	0.00569292	+	0.00328681i
$924$	−9.84438	+	12.2532i	−0.323856	+	0.403099i
$925$	1.74237	−	2.07647i	0.0572887	−	0.0682740i
$926$	32.0195	−	26.8676i	1.05223	−	0.882923i
$927$	35.4520	−	22.5352i	1.16440	−	0.740152i
$928$	3.55960	+	20.1875i	0.116850	+	0.662687i
$929$	18.2757	+	21.7801i	0.599606	+	0.714583i	0.977422	−	0.211298i	$-0.0677690\pi$
$929$	18.2757	+	21.7801i	0.599606	+	0.714583i	−0.377815	+	0.925881i	$0.623325\pi$
$930$	17.3492	+	13.9386i	0.568904	+	0.457066i
$931$	−14.4885	−	3.29247i	−0.474841	−	0.107906i
$932$	22.8913	−	13.2163i	0.749831	−	0.432915i
$933$	22.8742	−	13.8646i	0.748869	−	0.453908i
$934$	2.86425	−	7.86947i	0.0937212	−	0.257497i
$935$	−22.4436	+	26.7473i	−0.733985	+	0.874729i
$936$	1.91498	+	4.63640i	0.0625931	+	0.151546i
$937$	4.63709	−	26.2982i	0.151487	−	0.859126i	−0.810440	−	0.585821i	$-0.800772\pi$
$937$	4.63709	−	26.2982i	0.151487	−	0.859126i	0.961927	−	0.273305i	$-0.0881168\pi$
$938$	26.2864	−	15.1764i	0.858280	−	0.495528i
$939$	−11.0079	+	4.27432i	−0.359228	+	0.139487i
$940$	6.43604	+	5.40048i	0.209920	+	0.176144i
$941$	−11.4393	−	9.59873i	−0.372911	−	0.312910i	0.437001	−	0.899461i	$-0.356041\pi$
$941$	−11.4393	−	9.59873i	−0.372911	−	0.312910i	−0.809912	+	0.586552i	$0.800485\pi$
$942$	30.5620	+	24.5539i	0.995762	+	0.800010i
$943$	23.8941	−	13.7953i	0.778099	−	0.449235i
$944$	−1.40846	+	7.98776i	−0.0458414	+	0.259980i
$945$	−12.4910	+	3.03649i	−0.406332	+	0.0987770i
$946$	12.0362	−	14.3441i	0.391329	−	0.466368i
$947$	−0.470350	+	1.29228i	−0.0152843	+	0.0419933i	−0.947100	−	0.320938i	$-0.896002\pi$
$947$	−0.470350	+	1.29228i	−0.0152843	+	0.0419933i	0.931816	+	0.362931i	$0.118224\pi$
$948$	−0.484612	−	22.7356i	−0.0157395	−	0.738418i
$949$	−2.53615	+	1.46425i	−0.0823270	+	0.0475315i
$950$	4.37244	+	14.1276i	0.141861	+	0.458359i
$951$	−2.48817	+	16.1118i	−0.0806843	+	0.522461i
$952$	19.3655	+	23.0789i	0.627639	+	0.747992i
$953$	2.83477	+	16.0768i	0.0918272	+	0.520778i	0.995674	+	0.0929206i	$0.0296203\pi$
$953$	2.83477	+	16.0768i	0.0918272	+	0.520778i	−0.903846	+	0.427857i	$0.859269\pi$
$954$	−7.22321	+	13.8415i	−0.233860	+	0.448136i
$955$	3.68795	−	3.09456i	0.119339	−	0.100138i
$956$	−16.2189	+	19.3289i	−0.524556	+	0.625141i
$957$	−13.6856	−	35.2450i	−0.442391	−	1.13931i
$958$	−12.1164	−	6.99538i	−0.391462	−	0.226011i
$959$	10.3768	−	12.3666i	0.335085	−	0.399339i
$960$	5.38118	−	15.8262i	0.173677	−	0.510788i
$961$	−60.4230			−1.94913
$962$	−0.233852	+	0.405043i	−0.00753969	+	0.0130591i
$963$	−4.07688	−	6.41369i	−0.131376	−	0.206678i
$964$	3.46705	+	4.13187i	0.111666	+	0.133078i
$965$	−20.9004	+	7.60712i	−0.672808	+	0.244882i
$966$	0.324337	+	15.2163i	0.0104354	+	0.489576i
$967$	1.18925	+	6.74459i	0.0382438	+	0.216891i	0.997940	−	0.0641464i	$-0.0204325\pi$
$967$	1.18925	+	6.74459i	0.0382438	+	0.216891i	−0.959697	+	0.281038i	$0.909321\pi$
$968$	22.5989	+	39.1424i	0.726355	+	1.25808i
$969$	18.8715	+	34.8756i	0.606240	+	1.12037i
$970$	−1.54577	+	2.67736i	−0.0496318	+	0.0859648i
$971$	5.18519	+	1.88725i	0.166401	+	0.0605648i	0.423877	−	0.905720i	$-0.360669\pi$
$971$	5.18519	+	1.88725i	0.166401	+	0.0605648i	−0.257477	+	0.966285i	$0.582891\pi$
$972$	−12.1673	−	8.17445i	−0.390267	−	0.262196i
$973$	−4.60545	−	3.86443i	−0.147644	−	0.123888i
$974$	0.642500	−	0.113290i	0.0205870	−	0.00363005i
$975$	3.09335	−	0.613682i	0.0990664	−	0.0196535i
$976$	2.89718			0.0927365
$977$	2.48980	−	4.31246i	0.0796557	−	0.137968i	−0.823446	−	0.567395i	$-0.807951\pi$
$977$	2.48980	−	4.31246i	0.0796557	−	0.137968i	0.903101	+	0.429427i	$0.141285\pi$
$978$	1.67831	+	8.45975i	0.0536665	+	0.270513i
$979$	13.2006	+	2.32762i	0.421892	+	0.0743910i
$980$	3.62363	−	2.09210i	0.115753	−	0.0668298i
$981$	−33.5433	+	7.40085i	−1.07095	+	0.236291i
$982$	5.26405	+	0.928194i	0.167983	+	0.0296198i
$983$	6.20132	+	35.1694i	0.197791	+	1.12173i	0.908387	+	0.418130i	$0.137314\pi$
$983$	6.20132	+	35.1694i	0.197791	+	1.12173i	−0.710596	+	0.703601i	$0.751574\pi$
$984$	−6.24888	−	31.4983i	−0.199207	−	1.00413i
$985$	15.8673	−	13.3142i	0.505573	−	0.424226i
$986$	−22.8242	+	4.02453i	−0.726871	+	0.128167i
$987$	−14.0707	+	17.5136i	−0.447876	+	0.557465i
$988$	1.03492	+	2.01398i	0.0329251	+	0.0640733i
$989$			16.0895i			0.511618i
$990$	−2.70021	+	20.3513i	−0.0858182	+	0.646808i
$991$	−46.6422	+	8.22428i	−1.48164	+	0.261253i	−0.855232	−	0.518245i	$-0.826586\pi$
$991$	−46.6422	+	8.22428i	−1.48164	+	0.261253i	−0.626405	+	0.779497i	$0.715475\pi$
$992$	15.6387	+	42.9670i	0.496530	+	1.36420i
$993$	51.3433	−	31.1204i	1.62933	−	0.987576i
$994$	0.662712	−	0.241207i	0.0210200	−	0.00765064i
$995$			23.5960i			0.748043i
$996$	8.20838	−	10.2169i	0.260093	−	0.323734i
$997$	−2.55812	+	14.5078i	−0.0810166	+	0.459468i	0.917129	+	0.398591i	$0.130501\pi$
$997$	−2.55812	+	14.5078i	−0.0810166	+	0.459468i	−0.998145	+	0.0608768i	$0.980610\pi$
$998$	0.203511	−	0.0740718i	0.00644202	−	0.00234470i
$999$	−0.273044	−	4.26479i	−0.00863872	−	0.134932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.7	yes	108
3.2	odd	2		513.2.bo.a.224.12		108
9.4	even	3		513.2.cd.a.395.7		108
9.5	odd	6		171.2.bd.a.167.12	yes	108
19.14	odd	18		171.2.bd.a.128.12	yes	108
57.14	even	18		513.2.cd.a.413.7		108
171.14	even	18	inner	171.2.x.a.14.7	✓	108
171.166	odd	18		513.2.bo.a.71.12		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.7	✓	108	171.14	even	18	inner
171.2.x.a.110.7	yes	108	1.1	even	1	trivial
171.2.bd.a.128.12	yes	108	19.14	odd	18
171.2.bd.a.167.12	yes	108	9.5	odd	6
513.2.bo.a.71.12		108	171.166	odd	18
513.2.bo.a.224.12		108	3.2	odd	2
513.2.cd.a.395.7		108	9.4	even	3
513.2.cd.a.413.7		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)

\(f(q)\)	\(=\)	\(q+(-0.788568 + 0.661687i) q^{2} +(-0.897794 - 1.48120i) q^{3} +(-0.163287 + 0.926044i) q^{4} +(0.446483 - 1.22670i) q^{5} +(1.68807 + 0.573972i) q^{6} +(-0.947545 - 1.64120i) q^{7} +(-1.51339 - 2.62127i) q^{8} +(-1.38793 + 2.65963i) q^{9} +O(q^{10})\)	\(q+(-0.788568 + 0.661687i) q^{2} +(-0.897794 - 1.48120i) q^{3} +(-0.163287 + 0.926044i) q^{4} +(0.446483 - 1.22670i) q^{5} +(1.68807 + 0.573972i) q^{6} +(-0.947545 - 1.64120i) q^{7} +(-1.51339 - 2.62127i) q^{8} +(-1.38793 + 2.65963i) q^{9} +(0.459610 + 1.26277i) q^{10} -5.09241i q^{11} +(1.51826 - 0.589536i) q^{12} +(0.188944 + 0.519120i) q^{13} +(1.83316 + 0.667217i) q^{14} +(-2.21784 + 0.439993i) q^{15} +(1.16063 + 0.422436i) q^{16} +(1.79639 - 4.93555i) q^{17} +(-0.665367 - 3.01568i) q^{18} +(-1.28875 - 4.16403i) q^{19} +(1.06307 + 0.613766i) q^{20} +(-1.58025 + 2.87696i) q^{21} +(3.36958 + 4.01571i) q^{22} +(-4.43591 - 0.782171i) q^{23} +(-2.52392 + 4.59500i) q^{24} +(2.52477 + 2.11854i) q^{25} +(-0.492490 - 0.284339i) q^{26} +(5.18554 - 0.331993i) q^{27} +(1.67454 - 0.609484i) q^{28} +(-0.744354 + 4.22144i) q^{29} +(1.45778 - 1.81448i) q^{30} +9.56154i q^{31} +(4.49373 - 1.63559i) q^{32} +(-7.54289 + 4.57193i) q^{33} +(1.84921 + 5.08067i) q^{34} +(-2.43632 + 0.429589i) q^{35} +(-2.23631 - 1.71957i) q^{36} -0.822439i q^{37} +(3.77155 + 2.43087i) q^{38} +(0.599289 - 0.745928i) q^{39} +(-3.89122 + 0.686127i) q^{40} +(-4.69226 + 3.93727i) q^{41} +(-0.657519 - 3.31431i) q^{42} +(-0.620272 - 3.51774i) q^{43} +(4.71579 + 0.831522i) q^{44} +(2.64289 + 2.89006i) q^{45} +(4.01557 - 2.31839i) q^{46} +(6.74036 + 1.18851i) q^{47} +(-0.416295 - 2.09839i) q^{48} +(1.70432 - 2.95196i) q^{49} -3.39277 q^{50} +(-8.92335 + 1.77028i) q^{51} +(-0.511580 + 0.0902054i) q^{52} +(-3.87285 - 3.24971i) q^{53} +(-3.86947 + 3.69300i) q^{54} +(-6.24686 - 2.27367i) q^{55} +(-2.86801 + 4.96755i) q^{56} +(-5.01074 + 5.64734i) q^{57} +(-2.20630 - 3.82142i) q^{58} +(1.14034 + 6.46720i) q^{59} +(-0.0453088 - 2.12567i) q^{60} +(2.20421 - 0.802266i) q^{61} +(-6.32675 - 7.53992i) q^{62} +(5.68011 - 0.242254i) q^{63} +(-3.69649 + 6.40251i) q^{64} +0.721165 q^{65} +(2.92290 - 8.59632i) q^{66} +(10.0012 - 11.9190i) q^{67} +(4.27721 + 2.46945i) q^{68} +(2.82398 + 7.27272i) q^{69} +(1.63695 - 1.95084i) q^{70} +(0.276935 - 0.232376i) q^{71} +(9.07210 - 0.386921i) q^{72} +(0.920520 + 5.22053i) q^{73} +(0.544197 + 0.648549i) q^{74} +(0.871259 - 5.64172i) q^{75} +(4.06651 - 0.513512i) q^{76} +(-8.35764 + 4.82529i) q^{77} +(0.0209902 + 0.984757i) q^{78} +(4.77547 - 13.1205i) q^{79} +(1.03640 - 1.23514i) q^{80} +(-5.14729 - 7.38278i) q^{81} +(1.09492 - 6.20962i) q^{82} +(6.96872 - 4.02339i) q^{83} +(-2.40616 - 1.93315i) q^{84} +(-5.25239 - 4.40727i) q^{85} +(2.81677 + 2.36355i) q^{86} +(6.92109 - 2.68744i) q^{87} +(-13.3486 + 7.70681i) q^{88} +(-0.457076 + 2.59221i) q^{89} +(-3.99641 - 0.530242i) q^{90} +(0.672944 - 0.801984i) q^{91} +(1.44865 - 3.98014i) q^{92} +(14.1626 - 8.58429i) q^{93} +(-6.10165 + 3.52279i) q^{94} +(-5.68342 - 0.278252i) q^{95} +(-6.45709 - 5.18772i) q^{96} +(1.47879 + 1.76235i) q^{97} +(0.609306 + 3.45555i) q^{98} +(13.5439 + 7.06791i) 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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