LMFDB - Embedded newform 171.2.x.a.14.5

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			14.5
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28119 - 1.07504i) q^{2} +(1.71187 - 0.263611i) q^{3} +(0.138425 + 0.785049i) q^{4} +(0.287058 + 0.788686i) q^{5} +(-2.47662 - 1.50260i) q^{6} +(1.60000 - 2.77129i) q^{7} +(-1.00586 + 1.74220i) q^{8} +(2.86102 - 0.902536i) q^{9} +O(q^{10})$	\(q+(-1.28119 - 1.07504i) q^{2} +(1.71187 - 0.263611i) q^{3} +(0.138425 + 0.785049i) q^{4} +(0.287058 + 0.788686i) q^{5} +(-2.47662 - 1.50260i) q^{6} +(1.60000 - 2.77129i) q^{7} +(-1.00586 + 1.74220i) q^{8} +(2.86102 - 0.902536i) q^{9} +(0.480097 - 1.31905i) q^{10} -0.779960i q^{11} +(0.443914 + 1.30741i) q^{12} +(0.150878 - 0.414534i) q^{13} +(-5.02916 + 1.83046i) q^{14} +(0.699313 + 1.27446i) q^{15} +(4.65980 - 1.69603i) q^{16} +(0.0888182 + 0.244026i) q^{17} +(-4.63577 - 1.91940i) q^{18} +(-4.35307 + 0.225372i) q^{19} +(-0.579421 + 0.334529i) q^{20} +(2.00846 - 5.16587i) q^{21} +(-0.838491 + 0.999275i) q^{22} +(-5.41417 + 0.954665i) q^{23} +(-1.26264 + 3.24758i) q^{24} +(3.29060 - 2.76114i) q^{25} +(-0.638944 + 0.368895i) q^{26} +(4.65978 - 2.29922i) q^{27} +(2.39708 + 0.872464i) q^{28} +(-0.519224 - 2.94466i) q^{29} +(0.474148 - 2.38461i) q^{30} +6.02187i q^{31} +(-4.01259 - 1.46046i) q^{32} +(-0.205606 - 1.33519i) q^{33} +(0.148546 - 0.408126i) q^{34} +(2.64497 + 0.466380i) q^{35} +(1.10457 + 2.12111i) q^{36} +11.1767i q^{37} +(5.81938 + 4.39100i) q^{38} +(0.149008 - 0.749402i) q^{39} +(-1.66279 - 0.293194i) q^{40} +(6.93325 + 5.81769i) q^{41} +(-8.12675 + 4.45926i) q^{42} +(-1.51015 + 8.56448i) q^{43} +(0.612307 - 0.107966i) q^{44} +(1.53310 + 1.99737i) q^{45} +(7.96287 + 4.59737i) q^{46} +(0.169371 - 0.0298646i) q^{47} +(7.52990 - 4.13176i) q^{48} +(-1.62002 - 2.80596i) q^{49} -7.18422 q^{50} +(0.216373 + 0.394328i) q^{51} +(0.346314 + 0.0610645i) q^{52} +(-0.860313 + 0.721888i) q^{53} +(-8.44182 - 2.06374i) q^{54} +(0.615144 - 0.223894i) q^{55} +(3.21875 + 5.57504i) q^{56} +(-7.39249 + 1.53332i) q^{57} +(-2.50042 + 4.33085i) q^{58} +(0.264850 - 1.50204i) q^{59} +(-0.903710 + 0.725412i) q^{60} +(-3.82725 - 1.39301i) q^{61} +(6.47377 - 7.71514i) q^{62} +(2.07645 - 9.37277i) q^{63} +(-1.38804 - 2.40415i) q^{64} +0.370248 q^{65} +(-1.17197 + 1.93167i) q^{66} +(-4.63066 - 5.51861i) q^{67} +(-0.179278 + 0.103506i) q^{68} +(-9.01672 + 3.06150i) q^{69} +(-2.88732 - 3.44098i) q^{70} +(7.53727 + 6.32452i) q^{71} +(-1.30538 + 5.89228i) q^{72} +(0.479455 - 2.71912i) q^{73} +(12.0154 - 14.3194i) q^{74} +(4.90522 - 5.59416i) q^{75} +(-0.779503 - 3.38617i) q^{76} +(-2.16149 - 1.24794i) q^{77} +(-0.996547 + 0.799933i) q^{78} +(-1.20161 - 3.30139i) q^{79} +(2.67527 + 3.18826i) q^{80} +(7.37086 - 5.16434i) q^{81} +(-2.62852 - 14.9071i) q^{82} +(-10.2281 - 5.90517i) q^{83} +(4.33348 + 0.861654i) q^{84} +(-0.166964 + 0.140099i) q^{85} +(11.1420 - 9.34923i) q^{86} +(-1.66509 - 4.90402i) q^{87} +(1.35884 + 0.784529i) q^{88} +(1.74018 + 9.86906i) q^{89} +(0.183072 - 4.20715i) q^{90} +(-0.907387 - 1.08138i) q^{91} +(-1.49892 - 4.11824i) q^{92} +(1.58743 + 10.3087i) q^{93} +(-0.249101 - 0.143819i) q^{94} +(-1.42733 - 3.36851i) q^{95} +(-7.25404 - 1.44237i) q^{96} +(-7.42282 + 8.84617i) q^{97} +(-0.940980 + 5.33656i) q^{98} +(-0.703942 - 2.23148i) 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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.28119	−	1.07504i	−0.905936	−	0.760171i	0.0654054	−	0.997859i	$-0.479166\pi$
$2$	−1.28119	−	1.07504i	−0.905936	−	0.760171i	−0.971342	+	0.237688i	$0.923610\pi$
$3$	1.71187	−	0.263611i	0.988350	−	0.152196i
$3$	1.71187	−	0.263611i	0.988350	−	0.152196i
$4$	0.138425	+	0.785049i	0.0692126	+	0.392524i
$5$	0.287058	+	0.788686i	0.128376	+	0.352711i	0.987184	−	0.159587i	$-0.0510164\pi$
$5$	0.287058	+	0.788686i	0.128376	+	0.352711i	−0.858807	+	0.512299i	$0.828794\pi$
$6$	−2.47662	−	1.50260i	−1.01108	−	0.613435i
$7$	1.60000	−	2.77129i	0.604745	−	1.04745i	−0.387347	−	0.921934i	$-0.626609\pi$
$7$	1.60000	−	2.77129i	0.604745	−	1.04745i	0.992092	−	0.125514i	$-0.0400581\pi$
$8$	−1.00586	+	1.74220i	−0.355625	+	0.615960i
$9$	2.86102	−	0.902536i	0.953673	−	0.300845i
$10$	0.480097	−	1.31905i	0.151820	−	0.417122i
$11$		−	0.779960i		−	0.235167i	−0.993063	−	0.117583i	$-0.962485\pi$
$11$		−	0.779960i		−	0.235167i	0.993063	−	0.117583i	$-0.0375148\pi$
$12$	0.443914	+	1.30741i	0.128147	+	0.377418i
$13$	0.150878	−	0.414534i	0.0418460	−	0.114971i	−0.917010	−	0.398865i	$-0.869404\pi$
$13$	0.150878	−	0.414534i	0.0418460	−	0.114971i	0.958856	+	0.283894i	$0.0916264\pi$
$14$	−5.02916	+	1.83046i	−1.34410	+	0.489212i
$15$	0.699313	+	1.27446i	0.180562	+	0.329064i
$16$	4.65980	−	1.69603i	1.16495	−	0.424007i
$17$	0.0888182	+	0.244026i	0.0215416	+	0.0591850i	0.949997	−	0.312258i	$-0.101085\pi$
$17$	0.0888182	+	0.244026i	0.0215416	+	0.0591850i	−0.928456	+	0.371443i	$0.878863\pi$
$18$	−4.63577	−	1.91940i	−1.09266	−	0.452408i
$19$	−4.35307	+	0.225372i	−0.998662	+	0.0517039i
$19$	−4.35307	+	0.225372i	−0.998662	+	0.0517039i
$20$	−0.579421	+	0.334529i	−0.129562	+	0.0748029i
$21$	2.00846	−	5.16587i	0.438282	−	1.12729i
$22$	−0.838491	+	0.999275i	−0.178767	+	0.213046i
$23$	−5.41417	+	0.954665i	−1.12893	+	0.199061i	−0.706760	−	0.707454i	$-0.749844\pi$
$23$	−5.41417	+	0.954665i	−1.12893	+	0.199061i	−0.422173	+	0.906515i	$0.638733\pi$
$24$	−1.26264	+	3.24758i	−0.257735	+	0.662909i
$25$	3.29060	−	2.76114i	0.658120	−	0.552228i
$26$	−0.638944	+	0.368895i	−0.125307	+	0.0723462i
$27$	4.65978	−	2.29922i	0.896776	−	0.442485i
$28$	2.39708	+	0.872464i	0.453005	+	0.164880i
$29$	−0.519224	−	2.94466i	−0.0964174	−	0.546810i	−0.994304	−	0.106583i	$-0.966009\pi$
$29$	−0.519224	−	2.94466i	−0.0964174	−	0.546810i	0.897886	−	0.440227i	$-0.145102\pi$
$30$	0.474148	−	2.38461i	0.0865672	−	0.435369i
$31$			6.02187i			1.08156i	0.841164	+	0.540780i	$0.181871\pi$
$31$			6.02187i			1.08156i	−0.841164	+	0.540780i	$0.818129\pi$
$32$	−4.01259	−	1.46046i	−0.709332	−	0.258176i
$33$	−0.205606	−	1.33519i	−0.0357914	−	0.232427i
$34$	0.148546	−	0.408126i	0.0254754	−	0.0699931i
$35$	2.64497	+	0.466380i	0.447082	+	0.0788326i
$36$	1.10457	+	2.12111i	0.184095	+	0.353518i
$37$			11.1767i			1.83743i	0.394920	+	0.918715i	$0.370772\pi$
$37$			11.1767i			1.83743i	−0.394920	+	0.918715i	$0.629228\pi$
$38$	5.81938	+	4.39100i	0.944028	+	0.712313i
$39$	0.149008	−	0.749402i	0.0238604	−	0.120000i
$40$	−1.66279	−	0.293194i	−0.262910	−	0.0463581i
$41$	6.93325	+	5.81769i	1.08279	+	0.908570i	0.996150	−	0.0876691i	$-0.0279418\pi$
$41$	6.93325	+	5.81769i	1.08279	+	0.908570i	0.0866423	+	0.996239i	$0.472386\pi$
$42$	−8.12675	+	4.45926i	−1.25399	+	0.688079i
$43$	−1.51015	+	8.56448i	−0.230296	+	1.30607i	0.622003	+	0.783015i	$0.286319\pi$
$43$	−1.51015	+	8.56448i	−0.230296	+	1.30607i	−0.852298	+	0.523056i	$0.824792\pi$
$44$	0.612307	−	0.107966i	0.0923087	−	0.0162765i
$45$	1.53310	+	1.99737i	0.228541	+	0.297750i
$46$	7.96287	+	4.59737i	1.17406	+	0.677845i
$47$	0.169371	−	0.0298646i	0.0247052	−	0.00435620i	−0.161282	−	0.986908i	$-0.551563\pi$
$47$	0.169371	−	0.0298646i	0.0247052	−	0.00435620i	0.185987	+	0.982552i	$0.440452\pi$
$48$	7.52990	−	4.13176i	1.08685	−	0.596368i
$49$	−1.62002	−	2.80596i	−0.231432	−	0.400852i
$50$	−7.18422			−1.01600
$51$	0.216373	+	0.394328i	0.0302983	+	0.0552170i
$52$	0.346314	+	0.0610645i	0.0480251	+	0.00846813i
$53$	−0.860313	+	0.721888i	−0.118173	+	0.0991590i	−0.699959	−	0.714183i	$-0.746799\pi$
$53$	−0.860313	+	0.721888i	−0.118173	+	0.0991590i	0.581786	+	0.813342i	$0.302354\pi$
$54$	−8.44182	−	2.06374i	−1.14879	−	0.280839i
$55$	0.615144	−	0.223894i	0.0829460	−	0.0301899i
$56$	3.21875	+	5.57504i	0.430124	+	0.744997i
$57$	−7.39249	+	1.53332i	−0.979159	+	0.203094i
$58$	−2.50042	+	4.33085i	−0.328321	+	0.568669i
$59$	0.264850	−	1.50204i	0.0344805	−	0.195549i	−0.962702	−	0.270565i	$-0.912790\pi$
$59$	0.264850	−	1.50204i	0.0344805	−	0.195549i	0.997182	+	0.0750159i	$0.0239008\pi$
$60$	−0.903710	+	0.725412i	−0.116668	+	0.0936503i
$61$	−3.82725	−	1.39301i	−0.490029	−	0.178356i	0.0851748	−	0.996366i	$-0.472855\pi$
$61$	−3.82725	−	1.39301i	−0.490029	−	0.178356i	−0.575204	+	0.818010i	$0.695077\pi$
$62$	6.47377	−	7.71514i	0.822170	−	0.979824i
$63$	2.07645	−	9.37277i	0.261609	−	1.18086i
$64$	−1.38804	−	2.40415i	−0.173505	−	0.300519i
$65$	0.370248			0.0459236
$66$	−1.17197	+	1.93167i	−0.144260	+	0.237772i
$67$	−4.63066	−	5.51861i	−0.565725	−	0.674205i	0.405023	−	0.914307i	$-0.367264\pi$
$67$	−4.63066	−	5.51861i	−0.565725	−	0.674205i	−0.970748	+	0.240102i	$0.922819\pi$
$68$	−0.179278	+	0.103506i	−0.0217406	+	0.0125519i
$69$	−9.01672	+	3.06150i	−1.08549	+	0.368561i
$70$	−2.88732	−	3.44098i	−0.345101	−	0.411276i
$71$	7.53727	+	6.32452i	0.894509	+	0.750582i	0.969109	−	0.246631i	$-0.0793236\pi$
$71$	7.53727	+	6.32452i	0.894509	+	0.750582i	−0.0746001	+	0.997214i	$0.523768\pi$
$72$	−1.30538	+	5.89228i	−0.153841	+	0.694412i
$73$	0.479455	−	2.71912i	0.0561159	−	0.318249i	−0.943809	−	0.330491i	$-0.892786\pi$
$73$	0.479455	−	2.71912i	0.0561159	−	0.318249i	0.999925	+	0.0122418i	$0.00389678\pi$
$74$	12.0154	−	14.3194i	1.39676	−	1.66459i
$75$	4.90522	−	5.59416i	0.566406	−	0.645958i
$76$	−0.779503	−	3.38617i	−0.0894151	−	0.388421i
$77$	−2.16149	−	1.24794i	−0.246325	−	0.142216i
$78$	−0.996547	+	0.799933i	−0.112837	+	0.0905746i
$79$	−1.20161	−	3.30139i	−0.135191	−	0.371435i	0.853562	−	0.520991i	$-0.174438\pi$
$79$	−1.20161	−	3.30139i	−0.135191	−	0.371435i	−0.988753	+	0.149557i	$0.952215\pi$
$80$	2.67527	+	3.18826i	0.299104	+	0.356458i
$81$	7.37086	−	5.16434i	0.818984	−	0.573816i
$82$	−2.62852	−	14.9071i	−0.290272	−	1.64621i
$83$	−10.2281	−	5.90517i	−1.12267	−	0.648176i	−0.180592	−	0.983558i	$-0.557801\pi$
$83$	−10.2281	−	5.90517i	−1.12267	−	0.648176i	−0.942082	+	0.335382i	$0.891135\pi$
$84$	4.33348	+	0.861654i	0.472822	+	0.0940141i
$85$	−0.166964	+	0.140099i	−0.0181098	+	0.0151959i
$86$	11.1420	−	9.34923i	1.20147	−	1.00815i
$87$	−1.66509	−	4.90402i	−0.178516	−	0.525766i
$88$	1.35884	+	0.784529i	0.144853	+	0.0836311i
$89$	1.74018	+	9.86906i	0.184459	+	1.04612i	0.926649	+	0.375928i	$0.122676\pi$
$89$	1.74018	+	9.86906i	0.184459	+	1.04612i	−0.742190	+	0.670190i	$0.766213\pi$
$90$	0.183072	−	4.20715i	0.0192975	−	0.443472i
$91$	−0.907387	−	1.08138i	−0.0951200	−	0.113360i
$92$	−1.49892	−	4.11824i	−0.156273	−	0.429356i
$93$	1.58743	+	10.3087i	0.164609	+	1.06896i
$94$	−0.249101	−	0.143819i	−0.0256928	−	0.0148338i
$95$	−1.42733	−	3.36851i	−0.146441	−	0.345602i
$96$	−7.25404	−	1.44237i	−0.740362	−	0.147211i
$97$	−7.42282	+	8.84617i	−0.753673	+	0.898193i	−0.997430	−	0.0716436i	$-0.977176\pi$
$97$	−7.42282	+	8.84617i	−0.753673	+	0.898193i	0.243757	+	0.969836i	$0.421620\pi$
$98$	−0.940980	+	5.33656i	−0.0950533	+	0.539074i
$99$	−0.703942	−	2.23148i	−0.0707488	−	0.224272i
$100$	2.62313	+	2.20107i	0.262313	+	0.220107i
$101$	−12.2833	−	14.6387i	−1.22224	−	1.45661i	−0.848602	−	0.529032i	$-0.822555\pi$
$101$	−12.2833	−	14.6387i	−1.22224	−	1.45661i	−0.373637	−	0.927575i	$-0.621889\pi$
$102$	0.146705	−	0.737819i	0.0145260	−	0.0730550i
$103$	1.41055	−	0.814379i	0.138985	−	0.0802431i	−0.428895	−	0.903354i	$-0.641097\pi$
$103$	1.41055	−	0.814379i	0.138985	−	0.0802431i	0.567880	+	0.823111i	$0.307764\pi$
$104$	0.570438	+	0.679821i	0.0559360	+	0.0666619i
$105$	4.65080	+	0.101141i	0.453871	+	0.00987031i
$106$	1.87828			0.182435
$107$	−9.03967	−	15.6572i	−0.873898	−	1.51364i	−0.857932	−	0.513763i	$-0.828251\pi$
$107$	−9.03967	−	15.6572i	−0.873898	−	1.51364i	−0.0159655	−	0.999873i	$-0.505082\pi$
$108$	2.45003	+	3.33989i	0.235754	+	0.321381i
$109$	2.43728	−	2.90464i	0.233450	−	0.278214i	−0.636583	−	0.771208i	$-0.719653\pi$
$109$	2.43728	−	2.90464i	0.233450	−	0.278214i	0.870033	+	0.492993i	$0.164097\pi$
$110$	−1.02881	−	0.374456i	−0.0980932	−	0.0357030i
$111$	2.94628	+	19.1330i	0.279649	+	1.81603i
$112$	2.75551	−	15.6273i	0.260372	−	1.47664i
$113$	−3.35007	+	5.80250i	−0.315148	+	0.545853i	−0.979469	−	0.201595i	$-0.935388\pi$
$113$	−3.35007	+	5.80250i	−0.315148	+	0.545853i	0.664321	+	0.747448i	$0.268721\pi$
$114$	11.1196	+	5.98278i	1.04144	+	0.560338i
$115$	−2.30711	−	3.99604i	−0.215140	−	0.372633i
$116$	2.23983	−	0.815232i	0.207963	−	0.0756924i
$117$	0.0575331	−	1.32216i	0.00531894	−	0.122234i
$118$	−1.95408	+	1.63967i	−0.179887	+	0.150944i
$119$	0.818376	+	0.144302i	0.0750204	+	0.0132281i
$120$	−2.92377	−	0.0635831i	−0.266902	−	0.00580431i
$121$	10.3917			0.944697
$122$	3.40588	+	5.89916i	0.308354	+	0.534085i
$123$	13.4025	+	8.13147i	1.20846	+	0.733190i
$124$	−4.72746	+	0.833579i	−0.424538	+	0.0748576i
$125$	6.75655	+	3.90090i	0.604324	+	0.348907i
$126$	−12.7365	+	9.77599i	−1.13465	+	0.870914i
$127$	−19.1529	+	3.37718i	−1.69955	+	0.299676i	−0.937536	−	0.347889i	$-0.886899\pi$
$127$	−19.1529	+	3.37718i	−1.69955	+	0.299676i	−0.762010	+	0.647565i	$0.775788\pi$
$128$	−2.28923	+	12.9828i	−0.202341	+	1.14753i
$129$	−0.327496	+	15.0594i	−0.0288344	+	1.32591i
$130$	−0.474357	−	0.398032i	−0.0416038	−	0.0349097i
$131$	12.3035	+	2.16944i	1.07496	+	0.189545i	0.682987	−	0.730431i	$-0.260681\pi$
$131$	12.3035	+	2.16944i	1.07496	+	0.189545i	0.391976	+	0.919976i	$0.371792\pi$
$132$	1.01973	−	0.346235i	0.0887561	−	0.0301359i
$133$	−6.34036	+	12.4242i	−0.549779	+	1.07731i
$134$			12.0485i			1.04083i
$135$	3.15099	+	3.01510i	0.271194	+	0.259498i
$136$	−0.514480	−	0.0907167i	−0.0441163	−	0.00777889i
$137$	4.97031	−	13.6558i	0.424642	−	1.16669i	−0.524380	−	0.851484i	$-0.675703\pi$
$137$	4.97031	−	13.6558i	0.424642	−	1.16669i	0.949022	−	0.315210i	$-0.102075\pi$
$138$	14.8433	+	5.77101i	1.26355	+	0.491261i
$139$	9.78293	+	3.56070i	0.829778	+	0.302014i	0.721768	−	0.692135i	$-0.243330\pi$
$139$	9.78293	+	3.56070i	0.829778	+	0.302014i	0.108010	+	0.994150i	$0.465552\pi$
$140$			2.14099i			0.180947i
$141$	0.282068	−	0.0957723i	0.0237544	−	0.00806548i
$142$	−2.85752	−	16.2058i	−0.239798	−	1.35996i
$143$	−0.323320	−	0.117679i	−0.0270373	−	0.00984079i
$144$	11.8010	−	9.05801i	0.983421	−	0.754834i
$145$	2.17337	−	1.25480i	0.180488	−	0.104205i
$146$	−3.53745	+	2.96827i	−0.292761	+	0.245656i
$147$	−3.51296	−	4.37640i	−0.289744	−	0.360959i
$148$	−8.77422	+	1.54713i	−0.721236	+	0.127173i
$149$	−7.12610	+	8.49256i	−0.583793	+	0.695737i	−0.974400	−	0.224820i	$-0.927821\pi$
$149$	−7.12610	+	8.49256i	−0.583793	+	0.695737i	0.390607	+	0.920557i	$0.372265\pi$
$150$	−12.2985	+	1.89384i	−1.00417	+	0.154631i
$151$	−4.12164	+	2.37963i	−0.335414	+	0.193652i	−0.658242	−	0.752806i	$-0.728700\pi$
$151$	−4.12164	+	2.37963i	−0.335414	+	0.193652i	0.322828	+	0.946458i	$0.395366\pi$
$152$	3.98593	−	7.81060i	0.323301	−	0.633523i
$153$	0.474353	+	0.618001i	0.0383491	+	0.0499625i
$154$	1.42769	+	3.92254i	0.115046	+	0.316088i
$155$	−4.74937	+	1.72863i	−0.381478	+	0.138847i
$156$	0.608943	+	0.0132427i	0.0487545	+	0.00106026i
$157$	−2.68063	+	0.975668i	−0.213937	+	0.0778668i	−0.446766	−	0.894651i	$-0.647424\pi$
$157$	−2.68063	+	0.975668i	−0.213937	+	0.0778668i	0.232828	+	0.972518i	$0.425202\pi$
$158$	−2.00965	+	5.52147i	−0.159879	+	0.439265i
$159$	−1.28245	+	1.46257i	−0.101705	+	0.115989i
$160$		−	3.58391i		−	0.283333i
$161$	−6.01705	+	16.5317i	−0.474210	+	1.30288i
$162$	−14.9953	−	1.30750i	−1.17815	−	0.102727i
$163$	9.29688	−	16.1027i	0.728188	−	1.26126i	−0.229460	−	0.973318i	$-0.573696\pi$
$163$	9.29688	−	16.1027i	0.728188	−	1.26126i	0.957648	−	0.287941i	$-0.0929706\pi$
$164$	−3.60743	+	6.24825i	−0.281693	+	0.487907i
$165$	0.994028	−	0.545437i	0.0773849	−	0.0424622i
$166$	6.75573	+	18.5612i	0.524347	+	1.44063i
$167$	−4.43378	−	25.1452i	−0.343097	−	1.94580i	−0.324240	−	0.945975i	$-0.605109\pi$
$167$	−4.43378	−	25.1452i	−0.343097	−	1.94580i	−0.0188565	−	0.999822i	$-0.506003\pi$
$168$	6.97974	+	8.69527i	0.538499	+	0.670855i
$169$	9.80950	+	8.23115i	0.754577	+	0.633165i
$170$	0.364525			0.0279578
$171$	−12.2508	+	4.57359i	−0.936843	+	0.349751i
$172$	−6.93258			−0.528604
$173$	3.87445	+	3.25105i	0.294569	+	0.247173i	0.778080	−	0.628166i	$-0.216194\pi$
$173$	3.87445	+	3.25105i	0.294569	+	0.247173i	−0.483510	+	0.875339i	$0.660638\pi$
$174$	−3.13874	+	8.07301i	−0.237947	+	0.612013i
$175$	−2.38694	−	13.5370i	−0.180436	−	1.02330i
$176$	−1.32283	−	3.63446i	−0.0997124	−	0.273958i
$177$	0.0574362	−	2.64111i	0.00431717	−	0.198518i
$178$	8.38017	−	14.5149i	0.628120	−	1.08794i
$179$	11.9053	−	20.6206i	0.889845	−	1.54126i	0.0497877	−	0.998760i	$-0.484146\pi$
$179$	11.9053	−	20.6206i	0.889845	−	1.54126i	0.840058	−	0.542497i	$-0.182521\pi$
$180$	−1.35581	+	1.48004i	−0.101056	+	0.110316i
$181$	−2.03798	+	5.59931i	−0.151482	+	0.416194i	−0.992102	−	0.125431i	$-0.959969\pi$
$181$	−2.03798	+	5.59931i	−0.151482	+	0.416194i	0.840620	+	0.541625i	$0.182191\pi$
$182$			2.36093i			0.175004i
$183$	−6.91898	−	1.37574i	−0.511466	−	0.101698i
$184$	3.78267	−	10.3928i	0.278862	−	0.766168i
$185$	−8.81487	+	3.20835i	−0.648082	+	0.235883i
$186$	9.04848	−	14.9139i	0.663467	−	1.09354i
$187$	0.190331	−	0.0692747i	0.0139184	−	0.00506587i
$188$	0.0468903	+	0.128830i	0.00341983	+	0.00939590i
$189$	1.08387	−	16.5924i	0.0788397	−	1.20692i
$190$	−1.79262	+	5.85014i	−0.130050	+	0.424414i
$191$	12.8102	−	7.39595i	0.926911	−	0.535152i	0.0410778	−	0.999156i	$-0.486921\pi$
$191$	12.8102	−	7.39595i	0.926911	−	0.535152i	0.885833	+	0.464004i	$0.153588\pi$
$192$	−3.00991	−	3.74970i	−0.217221	−	0.270612i
$193$	12.2129	−	14.5547i	0.879102	−	1.04767i	−0.119393	−	0.992847i	$-0.538095\pi$
$193$	12.2129	−	14.5547i	0.879102	−	1.04767i	0.998496	−	0.0548265i	$-0.0174606\pi$
$194$	19.0200	−	3.35375i	1.36556	−	0.240785i
$195$	0.633817	−	0.0976012i	0.0453886	−	0.00698937i
$196$	1.97857	−	1.66021i	0.141326	−	0.118587i
$197$	−15.3913	+	8.88617i	−1.09658	+	0.633113i	−0.935322	−	0.353798i	$-0.884890\pi$
$197$	−15.3913	+	8.88617i	−1.09658	+	0.633113i	−0.161263	+	0.986912i	$0.551557\pi$
$198$	−1.49706	+	3.61571i	−0.106391	+	0.256958i
$199$	−14.7880	−	5.38237i	−1.04829	−	0.381546i	−0.240273	−	0.970705i	$-0.577237\pi$
$199$	−14.7880	−	5.38237i	−1.04829	−	0.381546i	−0.808017	+	0.589159i	$0.799459\pi$
$200$	1.50058	+	8.51019i	0.106107	+	0.601761i
$201$	−9.38186	−	8.22646i	−0.661746	−	0.580250i
$202$			31.9601i			2.24870i
$203$	−8.99127	−	3.27256i	−0.631064	−	0.229688i
$204$	−0.279615	+	0.224449i	−0.0195770	+	0.0157145i
$205$	−2.59808	+	7.13818i	−0.181458	+	0.498552i
$206$	−2.68267	−	0.473026i	−0.186910	−	0.0329573i
$207$	−14.6284	+	7.61780i	−1.01675	+	0.529473i
$208$		−	2.18754i		−	0.151678i
$209$	0.175781	+	3.39522i	0.0121590	+	0.234852i
$210$	−5.84981	−	5.12939i	−0.403675	−	0.353962i
$211$	−6.16204	−	1.08653i	−0.424212	−	0.0748001i	−0.0425335	−	0.999095i	$-0.513543\pi$
$211$	−6.16204	−	1.08653i	−0.424212	−	0.0748001i	−0.381679	+	0.924295i	$0.624654\pi$
$212$	−0.685807	−	0.575460i	−0.0471014	−	0.0395228i
$213$	14.5701	+	8.83987i	0.998324	+	0.605698i
$214$	−5.25063	+	29.7778i	−0.358926	+	2.03557i
$215$	−7.18819	+	1.26747i	−0.490231	+	0.0864409i
$216$	−0.681384	+	10.4310i	−0.0463623	+	0.709736i
$217$	16.6883	+	9.63501i	1.13288	+	0.654067i
$218$	−6.24524	+	1.10120i	−0.422981	+	0.0745829i
$219$	0.103976	−	4.78118i	0.00702605	−	0.323082i
$220$	0.260919	+	0.451925i	0.0175912	+	0.0304688i
$221$	0.114558			0.00770598
$222$	16.7941	−	27.6804i	1.12715	−	1.85778i
$223$	−18.0587	−	3.18423i	−1.20930	−	0.213232i	−0.467584	−	0.883949i	$-0.654875\pi$
$223$	−18.0587	−	3.18423i	−1.20930	−	0.213232i	−0.741713	+	0.670717i	$0.765987\pi$
$224$	−10.4675	+	8.78330i	−0.699391	+	0.586859i
$225$	6.92244	−	10.8696i	0.461496	−	0.724637i
$226$	10.5300	−	3.83261i	0.700446	−	0.254941i
$227$	10.4219	+	18.0512i	0.691725	+	1.19810i	0.971272	+	0.237971i	$0.0764824\pi$
$227$	10.4219	+	18.0512i	0.691725	+	1.19810i	−0.279547	+	0.960132i	$0.590184\pi$
$228$	−2.22704	−	5.59121i	−0.147489	−	0.370287i
$229$	−2.78708	+	4.82737i	−0.184176	+	0.319002i	−0.943298	−	0.331946i	$-0.892295\pi$
$229$	−2.78708	+	4.82737i	−0.184176	+	0.319002i	0.759123	+	0.650947i	$0.225628\pi$
$230$	−1.34007	+	7.59992i	−0.0883617	+	0.501124i
$231$	−4.02917	−	1.56652i	−0.265100	−	0.103070i
$232$	5.65245	+	2.05732i	0.371102	+	0.135070i
$233$	8.33802	−	9.93686i	0.546242	−	0.650986i	−0.420333	−	0.907370i	$-0.638087\pi$
$233$	8.33802	−	9.93686i	0.546242	−	0.650986i	0.966575	+	0.256384i	$0.0825312\pi$
$234$	−1.49509	+	1.63208i	−0.0977372	+	0.106693i
$235$	0.0721730	+	0.125007i	0.00470805	+	0.00815458i
$236$	1.21583			0.0791441
$237$	−2.92728	−	5.33480i	−0.190147	−	0.346532i
$238$	−0.893362	−	1.06467i	−0.0579080	−	0.0690121i
$239$	−1.34830	+	0.778443i	−0.0872145	+	0.0503533i	−0.542973	−	0.839750i	$-0.682701\pi$
$239$	−1.34830	+	0.778443i	−0.0872145	+	0.0503533i	0.455759	+	0.890103i	$0.349368\pi$
$240$	5.42018	+	4.75267i	0.349871	+	0.306784i
$241$	14.9283	+	17.7908i	0.961615	+	1.14601i	0.989227	+	0.146390i	$0.0467653\pi$
$241$	14.9283	+	17.7908i	0.961615	+	1.14601i	−0.0276118	+	0.999619i	$0.508790\pi$
$242$	−13.3137	−	11.1715i	−0.855835	−	0.718131i
$243$	11.2566	−	10.7837i	0.722111	−	0.691777i
$244$	0.563789	−	3.19740i	0.0360929	−	0.204693i
$245$	1.74798	−	2.08317i	0.111675	−	0.133089i
$246$	−8.42937	−	24.8261i	−0.537437	−	1.58286i
$247$	−0.563357	+	1.83850i	−0.0358456	+	0.116981i
$248$	−10.4913	−	6.05715i	−0.666197	−	0.384629i
$249$	−19.0658	−	7.41268i	−1.20825	−	0.469759i
$250$	−4.46277	−	12.2614i	−0.282251	−	0.775477i
$251$	−1.22580	−	1.46086i	−0.0773721	−	0.0922085i	0.725970	−	0.687727i	$-0.241391\pi$
$251$	−1.22580	−	1.46086i	−0.0773721	−	0.0922085i	−0.803342	+	0.595518i	$0.796947\pi$
$252$	7.64551	+	0.332690i	0.481622	+	0.0209575i
$253$	0.744600	+	4.22284i	0.0468126	+	0.265488i
$254$	28.1691	+	16.2634i	1.76749	+	1.02046i
$255$	−0.248889	+	0.283846i	−0.0155861	+	0.0177751i
$256$	12.6369	−	10.6036i	0.789804	−	0.662724i
$257$	−5.80431	+	4.87040i	−0.362063	+	0.303807i	−0.805612	−	0.592443i	$-0.798164\pi$
$257$	−5.80431	+	4.87040i	−0.362063	+	0.303807i	0.443549	+	0.896250i	$0.353719\pi$
$258$	16.6091	−	18.9418i	1.03404	−	1.17927i
$259$	30.9737	+	17.8827i	1.92461	+	1.11118i
$260$	0.0512516	+	0.290662i	0.00317849	+	0.0180261i
$261$	−4.14317	−	7.95612i	−0.256456	−	0.492472i
$262$	−13.4309	−	16.0063i	−0.829761	−	0.988870i
$263$	−0.709409	−	1.94909i	−0.0437440	−	0.120186i	0.915897	−	0.401413i	$-0.131481\pi$
$263$	−0.709409	−	1.94909i	−0.0437440	−	0.120186i	−0.959641	+	0.281227i	$0.909259\pi$
$264$	2.53298	+	0.984809i	0.155894	+	0.0606108i
$265$	−0.816304	−	0.471293i	−0.0501451	−	0.0289513i
$266$	21.4797	−	9.10157i	1.31701	−	0.558053i
$267$	5.58056	+	16.4358i	0.341525	+	1.00586i
$268$	3.69137	−	4.39921i	0.225486	−	0.268724i
$269$	1.35352	−	7.67620i	0.0825257	−	0.468026i	−0.915337	−	0.402688i	$-0.868076\pi$
$269$	1.35352	−	7.67620i	0.0825257	−	0.468026i	0.997863	−	0.0653387i	$-0.0208128\pi$
$270$	−0.795653	−	7.25036i	−0.0484219	−	0.441243i
$271$	3.03110	+	2.54340i	0.184126	+	0.154500i	0.730192	−	0.683242i	$-0.239431\pi$
$271$	3.03110	+	2.54340i	0.184126	+	0.154500i	−0.546066	+	0.837742i	$0.683875\pi$
$272$	0.827750	+	0.986474i	0.0501897	+	0.0598138i
$273$	−1.83839	−	1.61199i	−0.111265	−	0.0975621i
$274$	−21.0485	+	12.1523i	−1.27158	+	0.734150i
$275$	−2.15358	−	2.56654i	−0.129866	−	0.154768i
$276$	−3.65157	−	6.65477i	−0.219798	−	0.400570i
$277$	−3.07137			−0.184541			−0.0922704	−	0.995734i	$-0.529412\pi$
$277$	−3.07137			−0.184541			−0.0922704	+	0.995734i	$0.529412\pi$
$278$	−8.70586	−	15.0790i	−0.522143	−	0.904378i
$279$	5.43495	+	17.2287i	0.325382	+	1.03145i
$280$	−3.47299	+	4.13895i	−0.207551	+	0.247350i
$281$	−13.1737	−	4.79485i	−0.785880	−	0.286037i	−0.0822576	−	0.996611i	$-0.526213\pi$
$281$	−13.1737	−	4.79485i	−0.785880	−	0.286037i	−0.703622	+	0.710574i	$0.748435\pi$
$282$	−0.464342	−	0.180534i	−0.0276511	−	0.0107506i
$283$	0.318679	−	1.80732i	0.0189435	−	0.107434i	−0.973870	−	0.227107i	$-0.927073\pi$
$283$	0.318679	−	1.80732i	0.0189435	−	0.107434i	0.992813	+	0.119673i	$0.0381845\pi$
$284$	−3.92171	+	6.79260i	−0.232710	+	0.403066i
$285$	−3.33139	−	5.39020i	−0.197334	−	0.319288i
$286$	0.287723	+	0.498351i	0.0170134	+	0.0294681i
$287$	27.2157	−	9.90571i	1.60649	−	0.584716i
$288$	−12.7982	−	0.556908i	−0.754142	−	0.0328161i
$289$	12.9711	−	10.8840i	0.763006	−	0.640238i
$290$	−4.13345	−	0.728839i	−0.242725	−	0.0427989i
$291$	−10.3750	+	17.1003i	−0.608192	+	1.00243i
$292$	2.20101			0.128804
$293$	8.42099	+	14.5856i	0.491959	+	0.852098i	0.999957	−	0.00925986i	$-0.00294755\pi$
$293$	8.42099	+	14.5856i	0.491959	+	0.852098i	−0.507998	+	0.861358i	$0.669614\pi$
$294$	−0.204064	+	9.38357i	−0.0119012	+	0.547261i
$295$	1.26066	−	0.222289i	0.0733987	−	0.0129422i
$296$	−19.4719	−	11.2421i	−1.13178	−	0.653435i
$297$	−1.79330	−	3.63445i	−0.104058	−	0.210892i
$298$	18.2597	−	3.21968i	1.05776	−	0.186511i
$299$	−0.421138	+	2.38839i	−0.0243551	+	0.138124i
$300$	5.07069	+	3.07646i	0.292757	+	0.177620i
$301$	21.3184	+	17.8883i	1.22877	+	1.03106i
$302$	7.83880	+	1.38219i	0.451072	+	0.0795362i
$303$	−24.8865	−	21.8216i	−1.42969	−	1.25362i
$304$	−19.9022	+	8.43312i	−1.14147	+	0.483672i
$305$		−	3.41837i		−	0.195735i
$306$	0.0566439	−	1.30173i	0.00323812	−	0.0744147i
$307$	−19.9765	−	3.52240i	−1.14012	−	0.201034i	−0.428463	−	0.903559i	$-0.640945\pi$
$307$	−19.9765	−	3.52240i	−1.14012	−	0.201034i	−0.711659	+	0.702525i	$0.752056\pi$
$308$	0.680488	−	1.86962i	0.0387744	−	0.106532i
$309$	2.20000	−	1.76595i	0.125153	−	0.100461i
$310$	7.94318	+	2.89108i	0.451142	+	0.164202i
$311$			25.9637i			1.47226i	0.676838	+	0.736132i	$0.263350\pi$
$311$			25.9637i			1.47226i	−0.676838	+	0.736132i	$0.736650\pi$
$312$	1.15572	+	1.01339i	0.0654300	+	0.0573721i
$313$	−4.47146	−	25.3589i	−0.252742	−	1.43337i	−0.801804	−	0.597588i	$-0.796126\pi$
$313$	−4.47146	−	25.3589i	−0.252742	−	1.43337i	0.549062	−	0.835782i	$-0.314985\pi$
$314$	4.48327	+	1.63178i	0.253005	+	0.0920864i
$315$	7.98824	−	1.05286i	0.450086	−	0.0593219i
$316$	2.42542	−	1.40031i	0.136440	−	0.0787738i
$317$	−18.3982	+	15.4379i	−1.03335	+	0.867080i	−0.991245	−	0.132033i	$-0.957849\pi$
$317$	−18.3982	+	15.4379i	−1.03335	+	0.867080i	−0.0421005	+	0.999113i	$0.513405\pi$
$318$	3.21538	−	0.495135i	0.180310	−	0.0277658i
$319$	−2.29672	+	0.404974i	−0.128592	+	0.0226742i
$320$	1.49767	−	1.78486i	0.0837226	−	0.0997767i
$321$	−19.6022	−	24.4201i	−1.09409	−	1.36300i
$322$	25.4813	−	14.7116i	1.42001	−	0.819846i
$323$	−0.441628	−	1.04224i	−0.0245729	−	0.0579921i
$324$	5.07457	+	5.07161i	0.281921	+	0.281756i
$325$	−0.648107	−	1.78066i	−0.0359505	−	0.0987732i
$326$	−29.2221	+	10.6360i	−1.61846	+	0.589073i
$327$	3.40663	−	5.61487i	0.188387	−	0.310503i
$328$	−17.1094	+	6.22732i	−0.944710	+	0.343846i
$329$	0.188230	−	0.517158i	0.0103775	−	0.0285118i
$330$	−1.85990	−	0.369816i	−0.102384	−	0.0203577i
$331$		−	15.9956i		−	0.879198i	−0.898194	−	0.439599i	$-0.855121\pi$
$331$		−	15.9956i		−	0.879198i	0.898194	−	0.439599i	$-0.144879\pi$
$332$	3.22002	−	8.84694i	0.176722	−	0.485539i
$333$	10.0873	+	31.9766i	0.552782	+	1.75231i
$334$	−21.3517	+	36.9823i	−1.16831	+	2.02358i
$335$	3.02318	−	5.23630i	0.165174	−	0.286090i
$336$	0.597570	−	27.4783i	0.0326001	−	1.49907i
$337$	7.65615	+	21.0351i	0.417057	+	1.14585i	0.953362	+	0.301830i	$0.0975975\pi$
$337$	7.65615	+	21.0351i	0.417057	+	1.14585i	−0.536305	+	0.844024i	$0.680180\pi$
$338$	−3.71896	−	21.0913i	−0.202285	−	1.14721i
$339$	−4.20530	+	10.8163i	−0.228401	+	0.587458i
$340$	−0.133097	−	0.111682i	−0.00721819	−	0.00605678i
$341$	4.69682			0.254347
$342$	20.6124	+	7.31052i	1.11459	+	0.395308i
$343$	12.0319			0.649660
$344$	−13.4020	−	11.2456i	−0.722589	−	0.606324i
$345$	−5.00288	−	6.23253i	−0.269346	−	0.335548i
$346$	−1.46888	−	8.33041i	−0.0789672	−	0.447845i
$347$	−6.33828	−	17.4143i	−0.340257	−	0.934848i	−0.985320	−	0.170718i	$-0.945391\pi$
$347$	−6.33828	−	17.4143i	−0.340257	−	0.934848i	0.645063	−	0.764129i	$-0.276831\pi$
$348$	3.61940	−	1.98602i	0.194020	−	0.106462i
$349$	16.7886	−	29.0788i	0.898675	−	1.55655i	0.0694867	−	0.997583i	$-0.477864\pi$
$349$	16.7886	−	29.0788i	0.898675	−	1.55655i	0.829189	−	0.558969i	$-0.188803\pi$
$350$	−11.4948	+	19.9095i	−0.614422	+	1.06421i
$351$	−0.250046	−	2.27854i	−0.0133465	−	0.121619i
$352$	−1.13910	+	3.12966i	−0.0607144	+	0.166811i
$353$			22.2320i			1.18329i	0.806199	+	0.591645i	$0.201521\pi$
$353$			22.2320i			1.18329i	−0.806199	+	0.591645i	$0.798479\pi$
$354$	−2.91290	+	3.32202i	−0.154819	+	0.176563i
$355$	−2.82443	+	7.76005i	−0.149905	+	0.411861i
$356$	−7.50681	+	2.73225i	−0.397860	+	0.144809i
$357$	1.43899	+	0.0312937i	0.0761597	+	0.00165624i
$358$	−37.4210	+	13.6201i	−1.97776	+	0.719846i
$359$	1.40113	+	3.84956i	0.0739486	+	0.203172i	0.971160	−	0.238430i	$-0.0766326\pi$
$359$	1.40113	+	3.84956i	0.0739486	+	0.203172i	−0.897211	+	0.441602i	$0.854410\pi$
$360$	−5.02188	+	0.661890i	−0.264677	+	0.0348847i
$361$	18.8984	−	1.96212i	0.994653	−	0.103269i
$362$	8.63054	−	4.98285i	0.453611	−	0.261893i
$363$	17.7892	−	2.73935i	0.933691	−	0.143779i
$364$	0.723332	−	0.862033i	0.0379129	−	0.0451828i
$365$	2.28217	−	0.402407i	0.119454	−	0.0210630i
$366$	7.38552	+	9.20079i	0.386047	+	0.480933i
$367$	1.15739	−	0.971168i	0.0604154	−	0.0506946i	−0.612080	−	0.790796i	$-0.709667\pi$
$367$	1.15739	−	0.971168i	0.0604154	−	0.0506946i	0.672495	+	0.740101i	$0.265222\pi$
$368$	−23.6098	+	13.6311i	−1.23075	+	0.710572i
$369$	25.0868	+	10.3870i	1.30597	+	0.540726i
$370$	14.7426	+	5.36588i	0.766432	+	0.278959i
$371$	0.624056	+	3.53920i	0.0323994	+	0.183746i
$372$	−7.87307	+	2.67319i	−0.408200	+	0.138598i
$373$		−	25.6009i		−	1.32556i	−0.748813	−	0.662781i	$-0.769376\pi$
$373$		−	25.6009i		−	1.32556i	0.748813	−	0.662781i	$-0.230624\pi$
$374$	−0.318322	−	0.115860i	−0.0164601	−	0.00599097i
$375$	12.5947	+	4.89674i	0.650386	+	0.252867i
$376$	−0.118333	+	0.325117i	−0.00610255	+	0.0167666i
$377$	−1.29900	−	0.229049i	−0.0669020	−	0.0117966i
$378$	−19.2262	+	20.0927i	−0.988886	+	1.03346i
$379$			7.24022i			0.371905i	0.982559	+	0.185953i	$0.0595371\pi$
$379$			7.24022i			0.371905i	−0.982559	+	0.185953i	$0.940463\pi$
$380$	2.44687	−	1.58681i	0.125522	−	0.0814018i
$381$	−31.8971	+	10.8302i	−1.63414	+	0.554848i
$382$	−24.3632	−	4.29589i	−1.24653	−	0.219797i
$383$	16.2182	+	13.6087i	0.828712	+	0.695372i	0.954995	−	0.296622i	$-0.0958603\pi$
$383$	16.2182	+	13.6087i	0.828712	+	0.695372i	−0.126283	+	0.991994i	$0.540305\pi$
$384$	−0.496449	+	22.8284i	−0.0253343	+	1.16496i
$385$	0.363758	−	2.06297i	0.0185388	−	0.105139i
$386$	−31.2940	+	5.51797i	−1.59282	+	0.280857i
$387$	3.40919	+	25.8661i	0.173299	+	1.31485i
$388$	−7.97218	−	4.60274i	−0.404726	−	0.233669i
$389$	−18.6075	+	3.28100i	−0.943438	+	0.166354i	−0.624150	−	0.781304i	$-0.714555\pi$
$389$	−18.6075	+	3.28100i	−0.943438	+	0.166354i	−0.319287	+	0.947658i	$0.603444\pi$
$390$	−0.916964	−	0.556336i	−0.0464323	−	0.0281711i
$391$	−0.713840	−	1.23641i	−0.0361004	−	0.0625278i
$392$	6.51806			0.329212
$393$	21.6339	+	0.470472i	1.09129	+	0.0237322i
$394$	29.2722	+	5.16147i	1.47471	+	0.260031i
$395$	2.25883	−	1.89538i	0.113654	−	0.0953669i
$396$	1.65438	−	0.861522i	0.0831356	−	0.0432931i
$397$	−28.9900	+	10.5515i	−1.45496	+	0.529564i	−0.943973	−	0.330022i	$-0.892944\pi$
$397$	−28.9900	+	10.5515i	−1.45496	+	0.529564i	−0.510991	+	0.859586i	$0.670721\pi$
$398$	13.1598	+	22.7935i	0.659643	+	1.14254i
$399$	−7.57873	+	22.9400i	−0.379411	+	1.14844i
$400$	10.6506	−	18.4473i	0.532528	−	0.922365i
$401$	−0.467484	+	2.65123i	−0.0233450	+	0.132396i	−0.994253	−	0.107057i	$-0.965857\pi$
$401$	−0.467484	+	2.65123i	−0.0233450	+	0.132396i	0.970908	+	0.239454i	$0.0769683\pi$
$402$	3.17612	+	20.6255i	0.158410	+	1.02871i
$403$	2.49627	+	0.908567i	0.124348	+	0.0452589i
$404$	9.79178	−	11.6694i	0.487159	−	0.580574i
$405$	6.18891	+	4.33083i	0.307530	+	0.215201i
$406$	8.00136	+	13.8588i	0.397101	+	0.687799i
$407$	8.71735			0.432103
$408$	−0.904638	−	0.0196731i	−0.0447863	−	0.000973965i
$409$	−10.2383	−	12.2015i	−0.506250	−	0.603325i	0.451023	−	0.892513i	$-0.351059\pi$
$409$	−10.2383	−	12.2015i	−0.506250	−	0.603325i	−0.957273	+	0.289187i	$0.906615\pi$
$410$	11.0025	−	6.35229i	0.543374	−	0.313717i
$411$	4.90872	−	24.6872i	0.242129	−	1.21773i
$412$	0.834582	+	0.994616i	0.0411169	+	0.0490012i
$413$	−3.73882	−	3.13724i	−0.183975	−	0.154374i
$414$	26.9312	+	5.96638i	1.32360	+	0.293231i
$415$	1.72128	−	9.76185i	0.0844942	−	0.479190i
$416$	−1.21082	+	1.44300i	−0.0593654	+	0.0707490i
$417$	17.6858	+	3.51658i	0.866076	+	0.172207i
$418$	3.42480	−	4.53889i	0.167513	−	0.222004i
$419$	0.375319	+	0.216691i	0.0183355	+	0.0105860i	0.509140	−	0.860684i	$-0.329964\pi$
$419$	0.375319	+	0.216691i	0.0183355	+	0.0105860i	−0.490804	+	0.871270i	$0.663297\pi$
$420$	0.564387	+	3.66510i	0.0275393	+	0.178839i
$421$	−6.14272	−	16.8770i	−0.299378	−	0.822535i	−0.994604	−	0.103743i	$-0.966918\pi$
$421$	−6.14272	−	16.8770i	−0.299378	−	0.822535i	0.695226	−	0.718791i	$-0.255304\pi$
$422$	6.72666	+	8.01652i	0.327449	+	0.390238i
$423$	0.457619	−	0.238306i	0.0222502	−	0.0115868i
$424$	−0.392319	−	2.22495i	−0.0190527	−	0.108053i
$425$	0.966055	+	0.557752i	0.0468606	+	0.0270550i
$426$	−9.16372	−	26.9890i	−0.443984	−	1.30762i
$427$	−9.98403	+	8.37760i	−0.483161	+	0.405420i
$428$	11.0403	−	9.26393i	0.533654	−	0.447789i
$429$	−0.584504	−	0.116221i	−0.0282201	−	0.00561118i
$430$	10.5720	+	6.10375i	0.509827	+	0.294349i
$431$	−0.549611	−	3.11700i	−0.0264738	−	0.150141i	0.968705	−	0.248213i	$-0.0798434\pi$
$431$	−0.549611	−	3.11700i	−0.0264738	−	0.150141i	−0.995179	+	0.0980727i	$0.968732\pi$
$432$	17.8141	−	18.6170i	0.857082	−	0.895713i
$433$	3.90711	+	4.65631i	0.187764	+	0.223768i	0.851712	−	0.524011i	$-0.175565\pi$
$433$	3.90711	+	4.65631i	0.187764	+	0.223768i	−0.663948	+	0.747779i	$0.731120\pi$
$434$	−11.0228	−	30.2849i	−0.529112	−	1.45372i
$435$	3.38975	−	2.72097i	0.162526	−	0.130461i
$436$	2.61767	+	1.51131i	0.125364	+	0.0723787i
$437$	23.3531	−	5.37592i	1.11713	−	0.257165i
$438$	−5.27319	+	6.01381i	−0.251963	+	0.287351i
$439$	16.8473	−	20.0778i	0.804077	−	0.958262i	−0.195672	−	0.980669i	$-0.562689\pi$
$439$	16.8473	−	20.0778i	0.804077	−	0.958262i	0.999749	+	0.0224073i	$0.00713308\pi$
$440$	−0.228680	+	1.29691i	−0.0109019	+	0.0618277i
$441$	−7.16740	−	6.56579i	−0.341305	−	0.312656i
$442$	−0.146770	−	0.123154i	−0.00698113	−	0.00585786i
$443$	16.4675	+	19.6252i	0.782396	+	0.932423i	0.999039	−	0.0438279i	$-0.0139553\pi$
$443$	16.4675	+	19.6252i	0.782396	+	0.932423i	−0.216643	+	0.976251i	$0.569511\pi$
$444$	−14.6125	+	4.96147i	−0.693479	+	0.235461i
$445$	−7.28406	+	4.20545i	−0.345297	+	0.199358i
$446$	19.7133	+	23.4934i	0.933454	+	1.11245i
$447$	−9.96025	+	16.4167i	−0.471104	+	0.776483i
$448$	−8.88347			−0.419704
$449$	0.803181	+	1.39115i	0.0379044	+	0.0656524i	0.884355	−	0.466814i	$-0.154598\pi$
$449$	0.803181	+	1.39115i	0.0379044	+	0.0656524i	−0.846451	+	0.532467i	$0.821265\pi$
$450$	−20.5542	+	6.48401i	−0.968934	+	0.305659i
$451$	4.53757	−	5.40766i	0.213666	−	0.254637i
$452$	−5.01898	−	1.82676i	−0.236073	−	0.0859235i
$453$	−6.42843	+	5.16013i	−0.302034	+	0.242444i
$454$	6.05348	−	34.3310i	0.284104	−	1.61123i
$455$	0.592398	−	1.02606i	0.0277720	−	0.0481026i
$456$	4.76445	−	14.4215i	0.223116	−	0.675348i
$457$	−11.6118	−	20.1122i	−0.543175	−	0.940807i	−0.998719	−	0.0505939i	$-0.983889\pi$
$457$	−11.6118	−	20.1122i	−0.543175	−	0.940807i	0.455544	−	0.890213i	$-0.349445\pi$
$458$	8.76041	−	3.18853i	0.409347	−	0.148990i
$459$	0.974943	+	0.932896i	0.0455065	+	0.0435438i
$460$	2.81772	−	2.36435i	0.131377	−	0.110238i
$461$	−19.0370	−	3.35674i	−0.886642	−	0.156339i	−0.288262	−	0.957551i	$-0.593078\pi$
$461$	−19.0370	−	3.35674i	−0.886642	−	0.156339i	−0.598380	+	0.801213i	$0.704189\pi$
$462$	3.47805	+	6.33854i	0.161813	+	0.294896i
$463$	−19.9589			−0.927567			−0.463784	−	0.885949i	$-0.653508\pi$
$463$	−19.9589			−0.927567			−0.463784	+	0.885949i	$0.653508\pi$
$464$	−7.41371	−	12.8409i	−0.344173	−	0.596125i
$465$	−7.67463	+	4.21117i	−0.355902	+	0.195289i
$466$	−21.3651	+	3.76725i	−0.989720	+	0.174514i
$467$	10.8432	+	6.26031i	0.501762	+	0.289692i	0.729441	−	0.684044i	$-0.239780\pi$
$467$	10.8432	+	6.26031i	0.501762	+	0.289692i	−0.227679	+	0.973736i	$0.573114\pi$
$468$	1.04592	−	0.137854i	0.0483479	−	0.00637231i
$469$	−22.7027	+	4.00310i	−1.04831	+	0.184846i
$470$	0.0419212	−	0.237747i	0.00193368	−	0.0109665i
$471$	−4.33169	+	2.37686i	−0.199594	+	0.109520i
$472$	2.35044	+	1.97226i	0.108188	+	0.0907805i
$473$	6.67996	+	1.17786i	0.307145	+	0.0541579i
$474$	−1.98475	+	9.98182i	−0.0911626	+	0.458480i
$475$	−13.7019	+	12.7610i	−0.628687	+	0.585517i
$476$			0.662440i			0.0303629i
$477$	−1.80984	+	2.84180i	−0.0828670	+	0.130117i
$478$	2.56429	+	0.452153i	0.117288	+	0.0206810i
$479$	9.18108	−	25.2248i	0.419494	−	1.15255i	−0.532498	−	0.846431i	$-0.678747\pi$
$479$	9.18108	−	25.2248i	0.419494	−	1.15255i	0.951993	−	0.306121i	$-0.0990311\pi$
$480$	−0.944757	−	6.13520i	−0.0431221	−	0.280033i
$481$	4.63310	+	1.68631i	0.211251	+	0.0768891i
$482$		−	38.8419i		−	1.76920i
$483$	−5.94249	+	29.8863i	−0.270393	+	1.35987i
$484$	1.43847	+	8.15796i	0.0653849	+	0.370816i
$485$	−9.10764	−	3.31491i	−0.413557	−	0.150522i
$486$	−26.0148	+	1.71465i	−1.18006	+	0.0777781i
$487$	6.50890	−	3.75791i	0.294946	−	0.170287i	−0.345224	−	0.938520i	$-0.612197\pi$
$487$	6.50890	−	3.75791i	0.294946	−	0.170287i	0.640170	+	0.768233i	$0.278864\pi$
$488$	6.27656	−	5.26666i	0.284127	−	0.238410i
$489$	11.6702	−	30.0165i	0.527747	−	1.35739i
$490$	−4.47899	+	0.789766i	−0.202340	+	0.0356780i
$491$	4.27476	−	5.09446i	0.192917	−	0.229910i	−0.660911	−	0.750464i	$-0.729830\pi$
$491$	4.27476	−	5.09446i	0.192917	−	0.229910i	0.853829	+	0.520554i	$0.174275\pi$
$492$	−4.52836	+	11.6472i	−0.204154	+	0.525095i
$493$	0.672458	−	0.388244i	0.0302860	−	0.0174856i
$494$	2.69823	−	1.74982i	0.121399	−	0.0787283i
$495$	1.55787	−	1.19575i	0.0700209	−	0.0537452i
$496$	10.2133	+	28.0607i	0.458589	+	1.25996i
$497$	29.5867	−	10.7687i	1.32715	−	0.483042i
$498$	16.4579	+	29.9936i	0.737496	+	1.34404i
$499$	−36.2660	+	13.1998i	−1.62349	+	0.590902i	−0.984043	−	0.177933i	$-0.943059\pi$
$499$	−36.2660	+	13.1998i	−1.62349	+	0.590902i	−0.639447	+	0.768835i	$0.720837\pi$
$500$	−2.12712	+	5.84421i	−0.0951276	+	0.261361i
$501$	−14.2186	−	41.8767i	−0.635241	−	1.87091i
$502$			3.18942i			0.142351i
$503$	−4.70303	+	12.9215i	−0.209698	+	0.576140i	−0.999297	−	0.0374828i	$-0.988066\pi$
$503$	−4.70303	+	12.9215i	−0.209698	+	0.576140i	0.789600	+	0.613622i	$0.210288\pi$
$504$	14.2406	+	13.0453i	0.634326	+	0.581082i
$505$	8.01932	−	13.8899i	0.356855	−	0.618091i
$506$	3.58576	−	6.21072i	0.159407	−	0.276100i
$507$	18.9624	+	11.5048i	0.842152	+	0.510946i
$508$	−5.30249	−	14.5685i	−0.235260	−	0.646372i
$509$	1.42928	+	8.10587i	0.0633519	+	0.359286i	0.999960	+	0.00890848i	$0.00283570\pi$
$509$	1.42928	+	8.10587i	0.0633519	+	0.359286i	−0.936608	+	0.350378i	$0.886053\pi$
$510$	0.624021	−	0.0960927i	0.0276321	−	0.00425505i
$511$	−6.76834	−	5.67931i	−0.299414	−	0.251238i
$512$	−1.22324			−0.0540599
$513$	−19.7662	+	11.0589i	−0.872698	+	0.488260i
$514$	12.6723			0.558951
$515$	1.04720	+	0.878704i	0.0461451	+	0.0387203i
$516$	−11.8677	+	1.82750i	−0.522446	+	0.0804512i
$517$	−0.0232932	−	0.132102i	−0.00102443	−	0.00580985i
$518$	−20.4585	−	56.2092i	−0.898893	−	2.46969i
$519$	7.48958	+	4.54404i	0.328756	+	0.199461i
$520$	−0.372417	+	0.645045i	−0.0163315	+	0.0282871i
$521$	15.2031	−	26.3325i	0.666059	−	1.15365i	−0.312938	−	0.949774i	$-0.601313\pi$
$521$	15.2031	−	26.3325i	0.666059	−	1.15365i	0.978997	−	0.203875i	$-0.0653535\pi$
$522$	−3.24500	+	14.6474i	−0.142030	+	0.641098i
$523$	4.91167	−	13.4947i	0.214772	−	0.590082i	−0.784787	−	0.619766i	$-0.787228\pi$
$523$	4.91167	−	13.4947i	0.214772	−	0.590082i	0.999559	+	0.0296833i	$0.00944989\pi$
$524$			9.95916i			0.435068i
$525$	−7.65465	−	22.5445i	−0.334076	−	0.983921i
$526$	−1.18647	+	3.25979i	−0.0517324	+	0.142134i
$527$	−1.46949	+	0.534852i	−0.0640121	+	0.0232985i
$528$	−3.22261	−	5.87302i	−0.140246	−	0.255590i
$529$	6.78894	−	2.47097i	0.295171	−	0.107434i
$530$	0.539177	+	1.48138i	0.0234203	+	0.0643469i
$531$	−0.597902	−	4.53639i	−0.0259468	−	0.196863i
$532$	−10.6313	−	3.25766i	−0.460924	−	0.141238i
$533$	3.45770	−	1.99630i	0.149770	−	0.0864696i
$534$	10.5195	−	27.0567i	0.455224	−	1.17086i
$535$	9.75368	−	11.6240i	0.421688	−	0.502549i
$536$	14.2723	−	2.51659i	0.616469	−	0.108700i
$537$	14.9446	−	38.4382i	0.644906	−	1.65873i
$538$	−9.98637	+	8.37956i	−0.430543	+	0.361268i
$539$	−2.18854	+	1.26355i	−0.0942671	+	0.0544251i
$540$	−1.93082	+	2.89105i	−0.0830893	+	0.124411i
$541$	14.4424	+	5.25662i	0.620929	+	0.226000i	0.633279	−	0.773924i	$-0.281709\pi$
$541$	14.4424	+	5.25662i	0.620929	+	0.226000i	−0.0123492	+	0.999924i	$0.503931\pi$
$542$	−1.14915	−	6.51713i	−0.0493601	−	0.279935i
$543$	−2.01273	+	10.1225i	−0.0863745	+	0.434400i
$544$		−	1.10889i		−	0.0475434i
$545$	2.99049	+	1.08845i	0.128099	+	0.0466241i
$546$	0.622367	+	4.04162i	0.0266348	+	0.172965i
$547$	−10.8609	+	29.8401i	−0.464379	+	1.27587i	0.457782	+	0.889065i	$0.348644\pi$
$547$	−10.8609	+	29.8401i	−0.464379	+	1.27587i	−0.922161	+	0.386807i	$0.873578\pi$
$548$	11.4085	+	2.01162i	0.487346	+	0.0859323i
$549$	−12.2071	−	0.531184i	−0.520985	−	0.0226704i
$550$			5.60340i			0.238930i
$551$	2.92386	+	12.7013i	0.124561	+	0.541094i
$552$	3.73580	−	18.7883i	0.159006	−	0.799684i
$553$	−11.0717	−	1.95223i	−0.470815	−	0.0830174i
$554$	3.93500	+	3.30186i	0.167182	+	0.140282i
$555$	−14.2442	+	7.81599i	−0.604632	+	0.331770i
$556$	−1.44111	+	8.17297i	−0.0611169	+	0.346611i
$557$	30.6193	−	5.39901i	1.29738	−	0.228763i	0.518037	−	0.855358i	$-0.326663\pi$
$557$	30.6193	−	5.39901i	1.29738	−	0.228763i	0.779345	+	0.626595i	$0.215552\pi$
$558$	11.5584	−	27.9160i	0.489306	−	1.18178i
$559$	3.32242	+	1.91820i	0.140523	+	0.0811312i
$560$	13.1160	−	2.31271i	0.554253	−	0.0977298i
$561$	0.307560	−	0.168763i	0.0129852	−	0.00712516i
$562$	11.7234	+	20.3055i	0.494520	+	0.856534i
$563$	3.97217			0.167407			0.0837035	−	0.996491i	$-0.473325\pi$
$563$	3.97217			0.167407			0.0837035	+	0.996491i	$0.473325\pi$
$564$	0.114231	+	0.208180i	0.00481000	+	0.00876596i
$565$	−5.53802	−	0.976502i	−0.232986	−	0.0410817i
$566$	−2.35123	+	1.97292i	−0.0988297	+	0.0829280i
$567$	−2.51848	−	28.6897i	−0.105766	−	1.20486i
$568$	−18.6000	+	6.76984i	−0.780438	+	0.284056i
$569$	−16.6420	−	28.8248i	−0.697669	−	1.20840i	−0.969272	−	0.245990i	$-0.920887\pi$
$569$	−16.6420	−	28.8248i	−0.697669	−	1.20840i	0.271603	−	0.962409i	$-0.412446\pi$
$570$	−1.52657	+	10.4872i	−0.0639411	+	0.439262i
$571$	−11.6552	+	20.1875i	−0.487756	+	0.844819i	−0.999901	−	0.0140804i	$-0.995518\pi$
$571$	−11.6552	+	20.1875i	−0.487756	+	0.844819i	0.512144	+	0.858899i	$0.328851\pi$
$572$	0.0476279	−	0.270111i	0.00199142	−	0.0112939i
$573$	19.9797	−	16.0378i	0.834665	−	0.669990i
$574$	−45.5175	−	16.5670i	−1.89986	−	0.691494i
$575$	−15.1799	+	18.0907i	−0.633046	+	0.754435i
$576$	−6.14104	−	5.62557i	−0.255877	−	0.234399i
$577$	1.37276	+	2.37769i	0.0571486	+	0.0989843i	0.893184	−	0.449691i	$-0.148466\pi$
$577$	1.37276	+	2.37769i	0.0571486	+	0.0989843i	−0.836036	+	0.548675i	$0.815132\pi$
$578$	−28.3192			−1.17792
$579$	17.0701	−	28.1353i	0.709410	−	1.16926i
$580$	1.28592	+	1.53250i	0.0533951	+	0.0636338i
$581$	−32.7298	+	18.8966i	−1.35786	+	0.783962i
$582$	31.6758	−	10.7551i	1.31300	−	0.445812i
$583$	0.563044	+	0.671010i	0.0233189	+	0.0277904i
$584$	4.25498	+	3.57036i	0.176073	+	0.147742i
$585$	1.05929	−	0.334162i	0.0437961	−	0.0138159i
$586$	4.89127	−	27.7398i	0.202057	−	1.14592i
$587$	12.1977	−	14.5366i	0.503452	−	0.599991i	−0.453133	−	0.891443i	$-0.649694\pi$
$587$	12.1977	−	14.5366i	0.503452	−	0.599991i	0.956586	+	0.291452i	$0.0941383\pi$
$588$	2.94940	−	3.36365i	0.121631	−	0.138714i
$589$	−1.35716	−	26.2136i	−0.0559208	−	1.08011i
$590$	−1.85412	−	1.07047i	−0.0763328	−	0.0440707i
$591$	−24.0055	+	19.2693i	−0.987453	+	0.792633i
$592$	18.9559	+	52.0810i	0.779084	+	2.14051i
$593$	24.3015	+	28.9613i	0.997941	+	1.18930i	0.981895	+	0.189429i	$0.0606635\pi$
$593$	24.3015	+	28.9613i	0.997941	+	1.18930i	0.0160465	+	0.999871i	$0.494892\pi$
$594$	−1.60963	+	6.58428i	−0.0660441	+	0.270156i
$595$	0.121113	+	0.686865i	0.00496514	+	0.0281587i
$596$	−7.65350	−	4.41875i	−0.313500	−	0.180999i
$597$	−26.7339	−	5.31568i	−1.09415	−	0.217556i
$598$	3.10718	−	2.60724i	0.127062	−	0.106618i
$599$	0.907017	−	0.761078i	0.0370597	−	0.0310968i	−0.624070	−	0.781369i	$-0.714522\pi$
$599$	0.907017	−	0.761078i	0.0370597	−	0.0310968i	0.661129	+	0.750272i	$0.270077\pi$
$600$	4.81217	+	14.1728i	0.196456	+	0.578602i
$601$	−7.88914	−	4.55480i	−0.321805	−	0.185794i	0.330392	−	0.943844i	$-0.392819\pi$
$601$	−7.88914	−	4.55480i	−0.321805	−	0.185794i	−0.652197	+	0.758050i	$0.726152\pi$
$602$	−8.08220	−	45.8364i	−0.329406	−	1.86815i
$603$	−18.2291	−	11.6095i	−0.742348	−	0.472775i
$604$	−2.43866	−	2.90629i	−0.0992279	−	0.118255i
$605$	2.98301	+	8.19576i	0.121277	+	0.333205i
$606$	8.42501	+	54.7116i	0.342243	+	2.22251i
$607$	−4.96410	−	2.86602i	−0.201487	−	0.116328i	0.395862	−	0.918310i	$-0.370446\pi$
$607$	−4.96410	−	2.86602i	−0.201487	−	0.116328i	−0.597349	+	0.801982i	$0.703779\pi$
$608$	17.7962	+	5.45317i	0.721732	+	0.221155i
$609$	−16.2546	−	3.23201i	−0.658669	−	0.130967i
$610$	−3.67490	+	4.37958i	−0.148792	+	0.177324i
$611$	0.0131744	−	0.0747157i	0.000532979	−	0.00302267i
$612$	−0.419499	+	0.457937i	−0.0169572	+	0.0185110i
$613$	−8.39829	−	7.04700i	−0.339204	−	0.284626i	0.457234	−	0.889347i	$-0.348840\pi$
$613$	−8.39829	−	7.04700i	−0.339204	−	0.284626i	−0.796438	+	0.604721i	$0.793285\pi$
$614$	21.8069	+	25.9885i	0.880057	+	1.04881i
$615$	−2.56589	+	12.9045i	−0.103467	+	0.520361i
$616$	4.34831	−	2.51050i	0.175199	−	0.101151i
$617$	22.6024	+	26.9365i	0.909937	+	1.08442i	0.996108	+	0.0881406i	$0.0280925\pi$
$617$	22.6024	+	26.9365i	0.909937	+	1.08442i	−0.0861708	+	0.996280i	$0.527463\pi$
$618$	−4.71708	−	0.102582i	−0.189749	−	0.00412645i
$619$	25.7176			1.03368			0.516838	−	0.856083i	$-0.327109\pi$
$619$	25.7176			1.03368			0.516838	+	0.856083i	$0.327109\pi$
$620$	−2.01449	−	3.48920i	−0.0809038	−	0.140130i
$621$	−23.0339	+	16.8969i	−0.924318	+	0.678050i
$622$	27.9121	−	33.2643i	1.11917	−	1.33378i
$623$	30.1343	+	10.9680i	1.20731	+	0.439423i
$624$	−0.576658	−	3.74478i	−0.0230848	−	0.149911i
$625$	2.59253	−	14.7030i	0.103701	−	0.588119i
$626$	−21.5331	+	37.2965i	−0.860638	+	1.49067i
$627$	1.19593	+	5.76585i	0.0477609	+	0.230266i
$628$	−1.13701	−	1.96936i	−0.0453718	−	0.0785862i
$629$	−2.72739	+	0.992690i	−0.108748	+	0.0395812i
$630$	−11.3663	−	7.23879i	−0.452844	−	0.288400i
$631$	−25.0217	+	20.9957i	−0.996098	+	0.835825i	−0.986439	−	0.164128i	$-0.947519\pi$
$631$	−25.0217	+	20.9957i	−0.996098	+	0.835825i	−0.00965891	+	0.999953i	$0.503075\pi$
$632$	6.96031	+	1.22729i	0.276866	+	0.0488190i
$633$	−10.8351	−	0.235629i	−0.430655	−	0.00936543i
$634$	40.1680			1.59527
$635$	−8.16154	−	14.1362i	−0.323881	−	0.560978i
$636$	−1.32571	−	0.804329i	−0.0525679	−	0.0318937i
$637$	−1.40759	+	0.248196i	−0.0557708	+	0.00983390i
$638$	3.37789	+	1.95023i	0.133732	+	0.0772103i
$639$	27.2724	+	11.2919i	1.07888	+	0.446701i
$640$	−10.8965	+	1.92135i	−0.430723	+	0.0759481i
$641$	1.88358	−	10.6823i	0.0743971	−	0.421927i	−0.924748	−	0.380581i	$-0.875724\pi$
$641$	1.88358	−	10.6823i	0.0743971	−	0.421927i	0.999145	−	0.0413464i	$-0.0131647\pi$
$642$	−1.13867	+	52.3599i	−0.0449397	+	2.06648i
$643$	9.98334	+	8.37701i	0.393704	+	0.330357i	0.818054	−	0.575141i	$-0.195053\pi$
$643$	9.98334	+	8.37701i	0.393704	+	0.330357i	−0.424350	+	0.905498i	$0.639497\pi$
$644$	−13.8111	−	2.43527i	−0.544233	−	0.0959630i
$645$	−11.9712	+	4.06463i	−0.471364	+	0.160045i
$646$	−0.554650	+	1.81008i	−0.0218224	+	0.0712167i
$647$			25.5417i			1.00415i	0.864825	+	0.502074i	$0.167429\pi$
$647$			25.5417i			1.00415i	−0.864825	+	0.502074i	$0.832571\pi$
$648$	1.58327	+	18.0361i	0.0621966	+	0.708524i
$649$	−1.17153	−	0.206572i	−0.0459866	−	0.00810867i
$650$	−1.08394	+	2.97810i	−0.0425156	+	0.116811i
$651$	31.1082	+	12.0947i	1.21923	+	0.474029i
$652$	13.9283	+	5.06949i	0.545474	+	0.198536i
$653$			13.5130i			0.528805i	0.964412	+	0.264402i	$0.0851747\pi$
$653$			13.5130i			0.528805i	−0.964412	+	0.264402i	$0.914825\pi$
$654$	−10.4008	+	3.53143i	−0.406702	+	0.138090i
$655$	1.82082	+	10.3264i	0.0711452	+	0.403484i
$656$	42.1745	+	15.3503i	1.64664	+	0.599328i
$657$	−1.08238	−	8.21219i	−0.0422275	−	0.320388i
$658$	−0.797126	+	0.460221i	−0.0310752	+	0.0179413i
$659$	−17.4099	+	14.6086i	−0.678192	+	0.569071i	−0.915478	−	0.402369i	$-0.868187\pi$
$659$	−17.4099	+	14.6086i	−0.678192	+	0.569071i	0.237285	+	0.971440i	$0.423742\pi$
$660$	0.565793	+	0.704858i	0.0220235	+	0.0274365i
$661$	25.3483	−	4.46958i	0.985933	−	0.173847i	0.342640	−	0.939467i	$-0.388679\pi$
$661$	25.3483	−	4.46958i	0.985933	−	0.173847i	0.643293	+	0.765620i	$0.277568\pi$
$662$	−17.1960	+	20.4934i	−0.668341	+	0.796497i
$663$	0.196108	−	0.0301986i	0.00761621	−	0.00117282i
$664$	20.5759	−	11.8795i	0.798501	−	0.461015i
$665$	−11.6188	−	1.43408i	−0.450560	−	0.0556113i
$666$	21.4525	−	51.8124i	0.831268	−	2.00769i
$667$	5.62233	+	15.4472i	0.217698	+	0.598119i
$668$	19.1265	−	6.96147i	0.740026	−	0.269347i
$669$	−31.7535	−	0.690542i	−1.22766	−	0.0266979i
$670$	−9.50251	+	3.45863i	−0.367114	+	0.133619i
$671$	−1.08649	+	2.98510i	−0.0419434	+	0.115239i
$672$	−15.6037	+	17.7952i	−0.601926	+	0.686466i
$673$		−	0.522437i		−	0.0201385i	−0.999949	−	0.0100692i	$-0.996795\pi$
$673$		−	0.522437i		−	0.0201385i	0.999949	−	0.0100692i	$-0.00320519\pi$
$674$	12.8047	−	35.1806i	0.493218	−	1.35511i
$675$	8.98500	−	20.4321i	0.345833	−	0.786433i
$676$	−5.10397	+	8.84034i	−0.196307	+	0.340013i
$677$	−10.2593	+	17.7696i	−0.394297	+	0.682942i	−0.993011	−	0.118021i	$-0.962345\pi$
$677$	−10.2593	+	17.7696i	−0.394297	+	0.682942i	0.598714	+	0.800963i	$0.295678\pi$
$678$	17.0157	−	9.33676i	0.653485	−	0.358576i
$679$	12.6387	+	34.7247i	0.485031	+	1.33261i
$680$	−0.0761388	−	0.431804i	−0.00291979	−	0.0165589i
$681$	22.5995	+	28.1541i	0.866013	+	1.07887i
$682$	−6.01750	−	5.04929i	−0.230422	−	0.193347i
$683$	−45.4076			−1.73747			−0.868737	−	0.495274i	$-0.835068\pi$
$683$	−45.4076			−1.73747			−0.868737	+	0.495274i	$0.835068\pi$
$684$	−5.28631	−	8.98438i	−0.202127	−	0.343526i
$685$	12.1969			0.466020
$686$	−15.4151	−	12.9348i	−0.588551	−	0.493853i
$687$	−3.49859	+	8.99855i	−0.133479	+	0.343316i
$688$	7.48861	+	42.4700i	0.285501	+	1.61916i
$689$	0.169445	+	0.465546i	0.00645533	+	0.0177359i
$690$	−0.290612	+	13.3634i	−0.0110634	+	0.508734i
$691$	−5.50192	+	9.52960i	−0.209303	+	0.362523i	−0.951495	−	0.307664i	$-0.900453\pi$
$691$	−5.50192	+	9.52960i	−0.209303	+	0.362523i	0.742192	+	0.670187i	$0.233786\pi$
$692$	−2.01591	+	3.49166i	−0.0766334	+	0.132733i
$693$	−7.31039	−	1.61955i	−0.277699	−	0.0615217i
$694$	−10.6006	+	29.1249i	−0.402393	+	1.10557i
$695$			8.73779i			0.331443i
$696$	10.2186	+	2.03183i	0.387336	+	0.0770164i
$697$	−0.803868	+	2.20861i	−0.0304487	+	0.0836571i
$698$	−52.7704	+	19.2068i	−1.99739	+	0.726990i
$699$	11.6542	−	19.2086i	0.440801	−	0.726538i
$700$	10.2968	−	3.74773i	0.389183	−	0.141651i
$701$	12.0049	+	32.9832i	0.453419	+	1.24576i	0.930303	+	0.366793i	$0.119544\pi$
$701$	12.0049	+	32.9832i	0.453419	+	1.24576i	−0.476883	+	0.878967i	$0.658234\pi$
$702$	−2.12917	+	3.18804i	−0.0803604	+	0.120325i
$703$	−2.51890	−	48.6527i	−0.0950023	−	1.83497i
$704$	−1.87514	+	1.08261i	−0.0706721	+	0.0408026i
$705$	0.156504	+	0.194971i	0.00589429	+	0.00734304i
$706$	23.9004	−	28.4833i	0.899502	−	1.07198i
$707$	−60.2215	+	10.6187i	−2.26486	+	0.399356i
$708$	2.08135	−	0.320507i	0.0782221	−	0.0120454i
$709$	−1.56712	+	1.31497i	−0.0588545	+	0.0493848i	−0.671740	−	0.740787i	$-0.734453\pi$
$709$	−1.56712	+	1.31497i	−0.0588545	+	0.0493848i	0.612886	+	0.790171i	$0.290009\pi$
$710$	11.9610	−	6.90569i	0.448889	−	0.259166i
$711$	−6.41744	−	8.36083i	−0.240673	−	0.313556i
$712$	−18.9442	−	6.89513i	−0.709965	−	0.258406i
$713$	−5.74887	−	32.6034i	−0.215297	−	1.22101i
$714$	−1.80998	−	1.58708i	−0.0677368	−	0.0593948i
$715$		−	0.288778i		−	0.0107997i
$716$	17.8362	+	6.49184i	0.666569	+	0.242611i
$717$	−2.10292	+	1.68802i	−0.0785349	+	0.0630404i
$718$	2.34334	−	6.43828i	0.0874528	−	0.240275i
$719$	23.5419	+	4.15108i	0.877966	+	0.154809i	0.594425	−	0.804151i	$-0.297380\pi$
$719$	23.5419	+	4.15108i	0.877966	+	0.154809i	0.283541	+	0.958960i	$0.408491\pi$
$720$	10.5315	+	6.70715i	0.392486	+	0.249961i
$721$		−	5.21204i		−	0.194106i
$722$	−26.3218	−	17.8028i	−0.979595	−	0.662551i
$723$	30.2452	+	26.5204i	1.12483	+	0.986304i
$724$	−4.67784	−	0.824830i	−0.173851	−	0.0306545i
$725$	−9.83919	−	8.25606i	−0.365418	−	0.306622i
$726$	−25.7362	−	15.6146i	−0.955161	−	0.579510i
$727$	0.423760	−	2.40326i	0.0157164	−	0.0891321i	−0.975941	−	0.218036i	$-0.930035\pi$
$727$	0.423760	−	2.40326i	0.0157164	−	0.0891321i	0.991657	+	0.128904i	$0.0411460\pi$
$728$	2.79668	−	0.493130i	0.103652	−	0.0182766i
$729$	16.4272	−	21.4277i	0.608413	−	0.793620i
$730$	−3.35649	−	1.93787i	−0.124229	−	0.0717237i
$731$	−2.22409	+	0.392166i	−0.0822608	+	0.0145048i
$732$	0.122265	−	5.62217i	0.00451905	−	0.207801i
$733$	21.0743	+	36.5018i	0.778398	+	1.34823i	0.932864	+	0.360227i	$0.117301\pi$
$733$	21.0743	+	36.5018i	0.778398	+	1.34823i	−0.154466	+	0.987998i	$0.549366\pi$
$734$	−2.52688			−0.0932690
$735$	2.44318	−	4.02690i	0.0901181	−	0.148535i
$736$	23.1191	+	4.07652i	0.852182	+	0.150263i
$737$	−4.30429	+	3.61173i	−0.158551	+	0.133040i
$738$	−20.9744	−	40.2771i	−0.772080	−	1.48262i
$739$	−35.9105	+	13.0704i	−1.32099	+	0.480801i	−0.903776	−	0.428007i	$-0.859216\pi$
$739$	−35.9105	+	13.0704i	−1.32099	+	0.480801i	−0.417215	+	0.908808i	$0.636994\pi$
$740$	−3.73891	−	6.47599i	−0.137445	−	0.238062i
$741$	−0.479749	+	3.29578i	−0.0176240	+	0.121073i
$742$	3.00526	−	5.20526i	0.110327	−	0.191091i
$743$	1.58897	−	9.01148i	0.0582936	−	0.330599i	−0.941689	−	0.336484i	$-0.890762\pi$
$743$	1.58897	−	9.01148i	0.0582936	−	0.330599i	0.999983	+	0.00588497i	$0.00187325\pi$
$744$	−19.5565	−	7.60345i	−0.716975	−	0.278756i
$745$	−8.74357	−	3.18240i	−0.320340	−	0.116594i
$746$	−27.5220	+	32.7995i	−1.00765	+	1.20087i
$747$	−34.5923	−	7.66362i	−1.26567	−	0.280397i
$748$	0.0807305	+	0.139829i	0.00295180	+	0.00511267i
$749$	−57.8540			−2.11394
$750$	−10.8719	−	19.8135i	−0.396987	−	0.723486i
$751$	−18.8612	−	22.4779i	−0.688255	−	0.820230i	0.302888	−	0.953026i	$-0.402049\pi$
$751$	−18.8612	−	22.4779i	−0.688255	−	0.820230i	−0.991143	+	0.132796i	$0.957605\pi$
$752$	0.738582	−	0.426420i	0.0269333	−	0.0155500i
$753$	−2.48352	−	2.17767i	−0.0905045	−	0.0793586i
$754$	1.41803	+	1.68994i	0.0516415	+	0.0615439i
$755$	−3.05993	−	2.56759i	−0.111362	−	0.0934441i
$756$	13.1758	−	1.44591i	0.479201	−	0.0525874i
$757$	3.30448	−	18.7406i	0.120103	−	0.681139i	−0.863993	−	0.503504i	$-0.832044\pi$
$757$	3.30448	−	18.7406i	0.120103	−	0.681139i	0.984096	−	0.177636i	$-0.0568448\pi$
$758$	7.78355	−	9.27608i	0.282711	−	0.336922i
$759$	2.38785	+	7.03268i	0.0866733	+	0.255270i
$760$	7.30430	+	0.901549i	0.264955	+	0.0327026i
$761$	19.6162	+	11.3254i	0.711087	+	0.410546i	0.811463	−	0.584403i	$-0.198671\pi$
$761$	19.6162	+	11.3254i	0.711087	+	0.410546i	−0.100376	+	0.994950i	$0.532005\pi$
$762$	52.5091	+	20.4153i	1.90220	+	0.739567i
$763$	−4.14994	−	11.4019i	−0.150238	−	0.412775i
$764$	7.57943	+	9.03282i	0.274214	+	0.326796i
$765$	−0.351242	+	0.551518i	−0.0126992	+	0.0199402i
$766$	−6.14862	−	34.8706i	−0.222159	−	1.25993i
$767$	−0.582685	−	0.336413i	−0.0210395	−	0.0121472i
$768$	18.8375	−	21.4832i	0.679739	−	0.775208i
$769$	−1.63106	+	1.36862i	−0.0588174	+	0.0493537i	−0.671722	−	0.740803i	$-0.734445\pi$
$769$	−1.63106	+	1.36862i	−0.0588174	+	0.0493537i	0.612905	+	0.790157i	$0.290001\pi$
$770$	−2.68383	+	2.25200i	−0.0967184	+	0.0811564i
$771$	−8.65236	+	9.86758i	−0.311607	+	0.355372i
$772$	13.1168	+	7.57296i	0.472082	+	0.272557i
$773$	−8.33893	−	47.2924i	−0.299931	−	1.70099i	−0.646457	−	0.762951i	$-0.723750\pi$
$773$	−8.33893	−	47.2924i	−0.299931	−	1.70099i	0.346526	−	0.938040i	$-0.387361\pi$
$774$	23.4394	−	36.8044i	0.842512	−	1.32291i
$775$	16.6272	+	19.8156i	0.597268	+	0.711796i
$776$	−7.94547	−	21.8300i	−0.285226	−	0.783652i
$777$	57.7372	+	22.4479i	2.07131	+	0.805314i
$778$	27.3669	+	15.8003i	0.981151	+	0.566468i
$779$	−31.4921	−	23.7622i	−1.12832	−	0.851371i
$780$	0.164358	+	0.484067i	0.00588496	+	0.0173324i
$781$	4.93287	−	5.87877i	0.176512	−	0.210359i
$782$	−0.414629	+	2.35148i	−0.0148271	+	0.0840887i
$783$	−9.18991	−	12.5277i	−0.328420	−	0.447703i
$784$	−12.3080	−	10.3276i	−0.439571	−	0.368844i
$785$	−1.53899	−	1.83410i	−0.0549290	−	0.0654618i
$786$	−27.2113	−	23.8602i	−0.970596	−	0.851064i
$787$	−14.4809	+	8.36057i	−0.516190	+	0.298022i	−0.735374	−	0.677661i	$-0.762994\pi$
$787$	−14.4809	+	8.36057i	−0.516190	+	0.298022i	0.219185	+	0.975683i	$0.429660\pi$
$788$	−9.10662	−	10.8528i	−0.324410	−	0.386617i
$789$	−1.72822	−	3.14958i	−0.0615262	−	0.112128i
$790$	−4.93160			−0.175458
$791$	10.7203	+	18.5680i	0.381169	+	0.660203i
$792$	4.59575	+	1.01815i	0.163303	+	0.0361783i
$793$	−1.15489	+	1.37635i	−0.0410115	+	0.0488756i
$794$	48.4849	+	17.6470i	1.72066	+	0.626270i
$795$	−1.52165	−	0.591608i	−0.0539672	−	0.0209822i
$796$	2.17840	−	12.3543i	0.0772113	−	0.437887i
$797$	2.54200	−	4.40287i	0.0900421	−	0.155958i	−0.817486	−	0.575948i	$-0.804633\pi$
$797$	2.54200	−	4.40287i	0.0900421	−	0.155958i	0.907529	+	0.419990i	$0.137966\pi$
$798$	34.3713	−	21.2430i	1.21673	−	0.751995i
$799$	0.0223309	+	0.0386783i	0.000790012	+	0.00136834i
$800$	−17.2364	+	6.27353i	−0.609398	+	0.221803i
$801$	13.8859	+	26.6650i	0.490633	+	0.942161i
$802$	3.44913	−	2.89416i	0.121793	−	0.102196i
$803$	−2.12081	−	0.373956i	−0.0748417	−	0.0131966i
$804$	5.15948	−	8.50397i	0.181961	−	0.299912i
$805$	−14.7656			−0.520418
$806$	−2.22144	−	3.84764i	−0.0782467	−	0.135527i
$807$	0.293529	−	13.4975i	0.0103327	−	0.475134i
$808$	37.8589	−	6.67554i	1.33187	−	0.234845i
$809$	−40.9606	−	23.6486i	−1.44010	−	0.831440i	−0.442241	−	0.896896i	$-0.645816\pi$
$809$	−40.9606	−	23.6486i	−1.44010	−	0.831440i	−0.997855	+	0.0654562i	$0.979150\pi$
$810$	−3.27333	−	12.2020i	−0.115013	−	0.428733i
$811$	16.1200	−	2.84238i	0.566048	−	0.0998095i	0.116701	−	0.993167i	$-0.462768\pi$
$811$	16.1200	−	2.84238i	0.566048	−	0.0998095i	0.449347	+	0.893358i	$0.351657\pi$
$812$	1.32450	−	7.51159i	0.0464807	−	0.263605i
$813$	5.85933	+	3.55494i	0.205496	+	0.124677i
$814$	−11.1686	−	9.37153i	−0.391458	−	0.328472i
$815$	15.3687	+	2.70992i	0.538342	+	0.0949243i
$816$	1.67705	+	1.47051i	0.0587084	+	0.0514783i
$817$	4.64359	−	37.6221i	0.162459	−	1.31623i
$818$			26.6390i			0.931410i
$819$	−3.57204	−	2.27490i	−0.124817	−	0.0794916i
$820$	−5.96346	−	1.05152i	−0.208253	−	0.0367206i
$821$	−6.75726	+	18.5654i	−0.235830	+	0.647938i	0.764166	+	0.645020i	$0.223151\pi$
$821$	−6.75726	+	18.5654i	−0.235830	+	0.647938i	−0.999996	+	0.00291789i	$0.999071\pi$
$822$	−32.8288	+	26.3519i	−1.14504	+	0.919127i
$823$	27.2972	+	9.93538i	0.951521	+	0.346325i	0.770705	−	0.637192i	$-0.219904\pi$
$823$	27.2972	+	9.93538i	0.951521	+	0.346325i	0.180816	+	0.983517i	$0.442126\pi$
$824$			3.27660i			0.114146i
$825$	−4.36322	−	3.82588i	−0.151908	−	0.133200i
$826$	1.41745	+	8.03878i	0.0493196	+	0.279705i
$827$	−33.5724	−	12.2193i	−1.16743	−	0.424908i	−0.315681	−	0.948865i	$-0.602233\pi$
$827$	−33.5724	−	12.2193i	−1.16743	−	0.424908i	−0.851744	+	0.523957i	$0.824455\pi$
$828$	−8.00528	−	10.4295i	−0.278203	−	0.362451i
$829$	−14.2428	+	8.22307i	−0.494672	+	0.285599i	−0.726511	−	0.687155i	$-0.758859\pi$
$829$	−14.2428	+	8.22307i	−0.494672	+	0.285599i	0.231839	+	0.972754i	$0.425526\pi$
$830$	−12.6997	+	10.6563i	−0.440813	+	0.369886i
$831$	−5.25780	+	0.809646i	−0.182391	+	0.0280863i
$832$	−1.20603	+	0.212655i	−0.0418114	+	0.00737248i
$833$	0.540840	−	0.644549i	0.0187390	−	0.0223323i
$834$	−18.8783	−	23.5184i	−0.653703	−	0.814375i
$835$	18.5590	−	10.7150i	0.642259	−	0.370808i
$836$	−2.64108	+	0.607981i	−0.0913437	+	0.0210275i
$837$	13.8456	+	28.0606i	0.478574	+	0.969917i
$838$	−0.247902	−	0.681105i	−0.00856364	−	0.0235284i
$839$	41.5963	−	15.1398i	1.43606	−	0.522685i	0.497401	−	0.867521i	$-0.334288\pi$
$839$	41.5963	−	15.1398i	1.43606	−	0.522685i	0.938663	+	0.344836i	$0.112066\pi$
$840$	−4.85425	+	8.00087i	−0.167488	+	0.276056i
$841$	18.8496	−	6.86070i	0.649987	−	0.236576i
$842$	−10.2735	+	28.2263i	−0.354049	+	0.972742i
$843$	−23.8158	−	4.73544i	−0.820258	−	0.163097i
$844$		−	4.98791i		−	0.171691i
$845$	−3.67590	+	10.0994i	−0.126455	+	0.347431i
$846$	−0.842485	−	0.186645i	−0.0289652	−	0.00641699i
$847$	16.6267	−	28.7983i	0.571300	−	0.989521i
$848$	−2.78454	+	4.82297i	−0.0956216	+	0.165622i
$849$	0.0691097	−	3.17791i	0.00237184	−	0.109065i
$850$	−0.638089	−	1.75314i	−0.0218863	−	0.0601321i
$851$	−10.6700	−	60.5123i	−0.365761	−	2.07434i
$852$	−4.92286	+	12.6619i	−0.168655	+	0.433788i
$853$	12.0891	+	10.1439i	0.413922	+	0.347322i	0.825845	−	0.563897i	$-0.190698\pi$
$853$	12.0891	+	10.1439i	0.413922	+	0.347322i	−0.411923	+	0.911218i	$0.635143\pi$
$854$	21.7977			0.745902
$855$	−7.12383	−	8.34915i	−0.243630	−	0.285535i
$856$	36.3705			1.24312
$857$	−0.330437	−	0.277270i	−0.0112875	−	0.00947136i	0.637126	−	0.770759i	$-0.280123\pi$
$857$	−0.330437	−	0.277270i	−0.0112875	−	0.00947136i	−0.648414	+	0.761288i	$0.724567\pi$
$858$	0.623916	+	0.777267i	0.0213002	+	0.0265355i
$859$	−1.64693	−	9.34019i	−0.0561924	−	0.318683i	0.943735	−	0.330702i	$-0.107285\pi$
$859$	−1.64693	−	9.34019i	−0.0561924	−	0.318683i	−0.999928	+	0.0120185i	$0.996174\pi$
$860$	−1.99005	−	5.46763i	−0.0678603	−	0.186445i
$861$	43.9786	−	24.1317i	1.49879	−	0.822405i
$862$	−2.64676	+	4.58431i	−0.0901488	+	0.156142i
$863$	−5.99619	+	10.3857i	−0.204113	+	0.353534i	−0.949850	−	0.312707i	$-0.898764\pi$
$863$	−5.99619	+	10.3857i	−0.204113	+	0.353534i	0.745737	+	0.666241i	$0.232098\pi$
$864$	−22.0557	+	2.42039i	−0.750351	+	0.0823434i
$865$	−1.45187	+	3.98897i	−0.0493649	+	0.135629i
$866$		−	10.1659i		−	0.345452i
$867$	19.3357	−	22.0514i	0.656676	−	0.748905i
$868$	−5.25387	+	14.4349i	−0.178328	+	0.489952i
$869$	−2.57495	+	0.937205i	−0.0873492	+	0.0317925i
$870$	−7.26807	−	0.158058i	−0.246411	−	0.00535868i
$871$	−2.98631	+	1.08693i	−0.101187	+	0.0368292i
$872$	2.60890	+	7.16789i	0.0883485	+	0.242735i
$873$	−13.2528	+	32.0084i	−0.448541	+	1.08332i
$874$	−35.6991	−	18.2180i	−1.20754	−	0.616235i
$875$	21.6210	−	12.4829i	0.730924	−	0.421999i
$876$	3.76785	−	0.580210i	0.127304	−	0.0196035i
$877$	−27.5732	+	32.8605i	−0.931082	+	1.10962i	0.0626728	+	0.998034i	$0.480038\pi$
$877$	−27.5732	+	32.8605i	−0.931082	+	1.10962i	−0.993755	+	0.111586i	$0.964407\pi$
$878$	−43.1691	+	7.61187i	−1.45689	+	0.256888i
$879$	18.2606	+	22.7488i	0.615914	+	0.767298i
$880$	2.48672	−	2.08660i	0.0838272	−	0.0703394i
$881$	6.08179	−	3.51133i	0.204901	−	0.118300i	−0.394039	−	0.919094i	$-0.628922\pi$
$881$	6.08179	−	3.51133i	0.204901	−	0.118300i	0.598939	+	0.800794i	$0.295589\pi$
$882$	2.12428	+	16.1173i	0.0715281	+	0.542697i
$883$	19.6164	+	7.13978i	0.660143	+	0.240273i	0.650298	−	0.759679i	$-0.274644\pi$
$883$	19.6164	+	7.13978i	0.660143	+	0.240273i	0.00984518	+	0.999952i	$0.496866\pi$
$884$	0.0158577	+	0.0899333i	0.000533351	+	0.00302479i
$885$	2.09950	−	0.712855i	0.0705739	−	0.0239624i
$886$		−	42.8469i		−	1.43947i
$887$	51.6484	+	18.7985i	1.73418	+	0.631191i	0.998914	−	0.0465830i	$-0.0148332\pi$
$887$	51.6484	+	18.7985i	1.73418	+	0.631191i	0.735270	+	0.677774i	$0.237055\pi$
$888$	−36.2970	−	14.1121i	−1.21805	−	0.473571i
$889$	−21.2856	+	58.4817i	−0.713896	+	1.96141i
$890$	13.8533	+	2.44271i	0.464363	+	0.0818798i
$891$	−4.02798	−	5.74898i	−0.134942	−	0.192598i
$892$		−	14.6177i		−	0.489437i
$893$	−0.730551	+	0.168174i	−0.0244470	+	0.00562773i
$894$	30.4096	−	10.3252i	1.01705	−	0.345325i
$895$	19.6807	+	3.47024i	0.657854	+	0.115997i
$896$	32.3164	+	27.1167i	1.07962	+	0.905906i
$897$	−0.0913294	+	4.19964i	−0.00304940	+	0.140222i
$898$	0.466522	−	2.64578i	0.0155680	−	0.0882907i
$899$	17.7324	−	3.12670i	0.591408	−	0.104281i
$900$	9.49137	+	3.92983i	0.316379	+	0.130994i
$901$	−0.252571	−	0.145822i	−0.00841436	−	0.00485803i
$902$	−11.6269	+	2.05014i	−0.387135	+	0.0682623i
$903$	41.2099	+	25.0027i	1.37138	+	0.832037i
$904$	−6.73940	−	11.6730i	−0.224149	−	0.388238i
$905$	−5.00112			−0.166243
$906$	13.7834	+	0.299747i	0.457922	+	0.00995841i
$907$	−27.4952	−	4.84814i	−0.912963	−	0.160980i	−0.302614	−	0.953113i	$-0.597859\pi$
$907$	−27.4952	−	4.84814i	−0.912963	−	0.160980i	−0.610348	+	0.792133i	$0.708971\pi$
$908$	−12.7285	+	10.6804i	−0.422409	+	0.354443i
$909$	−48.3549	−	30.7955i	−1.60383	−	1.02142i
$910$	−1.86203	+	0.677725i	−0.0617258	+	0.0224664i
$911$	−11.6746	−	20.2209i	−0.386796	−	0.669950i	0.605221	−	0.796058i	$-0.293085\pi$
$911$	−11.6746	−	20.2209i	−0.386796	−	0.669950i	−0.992017	+	0.126108i	$0.959751\pi$
$912$	−31.8470	+	19.6829i	−1.05456	+	0.651764i
$913$	−4.60580	+	7.97747i	−0.152430	+	0.264016i
$914$	−6.74461	+	38.2506i	−0.223092	+	1.26522i
$915$	−0.901119	−	5.85182i	−0.0297901	−	0.193455i
$916$	−4.17552	−	1.51977i	−0.137963	−	0.0502145i
$917$	25.6978	−	30.6254i	0.848616	−	1.01134i
$918$	−0.246181	−	2.24332i	−0.00812520	−	0.0740406i
$919$	2.51276	+	4.35224i	0.0828885	+	0.143567i	0.904489	−	0.426496i	$-0.140252\pi$
$919$	2.51276	+	4.35224i	0.0828885	+	0.143567i	−0.821601	+	0.570063i	$0.806919\pi$
$920$	9.28252			0.306036
$921$	−35.1258	−	0.763880i	−1.15744	−	0.0251707i
$922$	20.7813	+	24.7662i	0.684397	+	0.815633i
$923$	3.75893	−	2.17022i	0.123727	−	0.0714337i
$924$	0.672056	−	3.37994i	0.0221090	−	0.111192i
$925$	30.8603	+	36.7779i	1.01468	+	1.20925i
$926$	25.5710	+	21.4567i	0.840317	+	0.705109i
$927$	3.30059	−	3.60302i	0.108406	−	0.118339i
$928$	−2.21714	+	12.5740i	−0.0727813	+	0.412763i
$929$	−2.93469	+	3.49742i	−0.0962839	+	0.114747i	−0.812035	−	0.583609i	$-0.801640\pi$
$929$	−2.93469	+	3.49742i	−0.0962839	+	0.114747i	0.715751	+	0.698356i	$0.246085\pi$
$930$	14.3598	+	2.85526i	0.470877	+	0.0936276i
$931$	7.68446	+	11.8494i	0.251848	+	0.388350i
$932$	8.95511	+	5.17024i	0.293335	+	0.169357i
$933$	6.84430	+	44.4465i	0.224072	+	1.45511i
$934$	−7.16203	−	19.6775i	−0.234349	−	0.643868i
$935$	0.109272	+	0.130225i	0.00357358	+	0.00425882i
$936$	2.24560	+	1.43014i	0.0733996	+	0.0467456i
$937$	7.45191	+	42.2619i	0.243443	+	1.38064i	0.824081	+	0.566473i	$0.191692\pi$
$937$	7.45191	+	42.2619i	0.243443	+	1.38064i	−0.580637	+	0.814162i	$0.697197\pi$
$938$	33.3899	+	19.2777i	1.09022	+	0.629439i
$939$	−14.3394	−	42.2325i	−0.467950	−	1.37821i
$940$	−0.0881463	+	0.0739635i	−0.00287502	+	0.00241242i
$941$	−19.7454	+	16.5683i	−0.643680	+	0.540112i	−0.905146	−	0.425101i	$-0.860239\pi$
$941$	−19.7454	+	16.5683i	−0.643680	+	0.540112i	0.261466	+	0.965213i	$0.415794\pi$
$942$	8.10494	+	1.61156i	0.264073	+	0.0525074i
$943$	−43.0918	−	24.8790i	−1.40326	−	0.810173i
$944$	−1.31335	−	7.44839i	−0.0427460	−	0.242424i
$945$	13.3973	−	3.90815i	0.435814	−	0.127132i
$946$	−7.29203	−	8.69030i	−0.237084	−	0.282546i
$947$	13.0443	+	35.8390i	0.423883	+	1.16461i	0.949467	+	0.313868i	$0.101625\pi$
$947$	13.0443	+	35.8390i	0.423883	+	1.16461i	−0.525583	+	0.850742i	$0.676153\pi$
$948$	3.78287	−	3.03652i	0.122862	−	0.0986217i
$949$	−1.05483	−	0.609005i	−0.0342412	−	0.0197692i
$950$	31.2734	−	1.61912i	1.01464	−	0.0525312i
$951$	−27.4258	+	31.2777i	−0.889342	+	1.01425i
$952$	−1.07457	+	1.28063i	−0.0348271	+	0.0415053i
$953$	−1.52894	+	8.67103i	−0.0495271	+	0.280882i	−0.999506	−	0.0314322i	$-0.989993\pi$
$953$	−1.52894	+	8.67103i	−0.0495271	+	0.280882i	0.949979	+	0.312315i	$0.101104\pi$
$954$	5.37380	−	1.69522i	0.173983	−	0.0548847i
$955$	9.51035	+	7.98013i	0.307748	+	0.258231i
$956$	−0.797755	−	0.950727i	−0.0258012	−	0.0307487i
$957$	−3.82494	+	1.29870i	−0.123643	+	0.0419811i
$958$	−38.8805	+	22.4477i	−1.25617	+	0.725251i
$959$	−29.8916	−	35.6235i	−0.965252	−	1.15034i
$960$	2.09332	−	3.45025i	0.0675616	−	0.111357i
$961$	−5.26291			−0.169771
$962$	−4.12301	−	7.14126i	−0.132931	−	0.230243i
$963$	−39.9938	−	36.6368i	−1.28878	−	1.18061i
$964$	−11.9002	+	14.1821i	−0.383280	+	0.456776i
$965$	14.9849	+	5.45407i	0.482382	+	0.175573i
$966$	39.7425	−	31.9015i	1.27870	−	1.02642i
$967$	10.2613	−	58.1945i	0.329980	−	1.87141i	−0.142098	−	0.989853i	$-0.545385\pi$
$967$	10.2613	−	58.1945i	0.329980	−	1.87141i	0.472078	−	0.881557i	$-0.343504\pi$
$968$	−10.4525	+	18.1043i	−0.335957	+	0.581895i
$969$	−1.03076	−	1.66777i	−0.0331127	−	0.0535766i
$970$	8.10492	+	14.0381i	0.260233	+	0.450737i
$971$	−26.2207	+	9.54356i	−0.841463	+	0.306267i	−0.726555	−	0.687109i	$-0.758880\pi$
$971$	−26.2207	+	9.54356i	−0.841463	+	0.306267i	−0.114908	+	0.993376i	$0.536657\pi$
$972$	10.0240	+	7.34424i	0.321518	+	0.235566i
$973$	25.5204	−	21.4142i	0.818148	−	0.686508i
$974$	−12.3790	−	2.18276i	−0.396650	−	0.0699401i
$975$	−1.57888	−	2.87741i	−0.0505645	−	0.0921510i
$976$	−20.1968			−0.646484
$977$	−12.2752	−	21.2613i	−0.392719	−	0.680209i	0.600088	−	0.799934i	$-0.295132\pi$
$977$	−12.2752	−	21.2613i	−0.392719	−	0.680209i	−0.992807	+	0.119725i	$0.961799\pi$
$978$	−47.2208	+	25.9107i	−1.50995	+	0.828533i
$979$	7.69747	−	1.35727i	0.246012	−	0.0433786i
$980$	1.87735	+	1.08389i	0.0599698	+	0.0346236i
$981$	4.35157	−	10.5100i	0.138935	−	0.335558i
$982$	−10.9535	+	1.93141i	−0.349542	+	0.0616336i
$983$	10.1109	−	57.3419i	0.322488	−	1.82892i	−0.204280	−	0.978913i	$-0.565485\pi$
$983$	10.1109	−	57.3419i	0.322488	−	1.82892i	0.526768	−	0.850009i	$-0.323404\pi$
$984$	−27.6476	+	15.1706i	−0.881373	+	0.483622i
$985$	−11.4266	−	9.58806i	−0.364082	−	0.305501i
$986$	−1.27892	−	0.225509i	−0.0407292	−	0.00718166i
$987$	0.185898	−	0.934928i	0.00591719	−	0.0297591i
$988$	−1.52129	−	0.187769i	−0.0483987	−	0.00597372i
$989$		−	47.8113i		−	1.52031i
$990$	−3.28141	−	0.142789i	−0.104290	−	0.00453812i
$991$	32.7961	+	5.78284i	1.04180	+	0.183698i	0.668270	−	0.743919i	$-0.267035\pi$
$991$	32.7961	+	5.78284i	1.04180	+	0.183698i	0.373533	+	0.927617i	$0.378146\pi$
$992$	8.79472	−	24.1633i	0.279233	−	0.767185i
$993$	−4.21661	−	27.3825i	−0.133810	−	0.868956i
$994$	−49.4829	−	18.0103i	−1.56950	−	0.571253i
$995$		−	13.2081i		−	0.418725i
$996$	3.18012	−	15.9937i	0.100766	−	0.506779i
$997$	6.35284	+	36.0287i	0.201196	+	1.14104i	0.903314	+	0.428980i	$0.141127\pi$
$997$	6.35284	+	36.0287i	0.201196	+	1.14104i	−0.702118	+	0.712061i	$0.747762\pi$
$998$	60.6539	+	22.0762i	1.91996	+	0.698810i
$999$	25.6976	+	52.0808i	0.813036	+	1.64776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.5	✓	108
3.2	odd	2		513.2.bo.a.71.14		108
9.2	odd	6		171.2.bd.a.128.14	yes	108
9.7	even	3		513.2.cd.a.413.5		108
19.15	odd	18		171.2.bd.a.167.14	yes	108
57.53	even	18		513.2.cd.a.395.5		108
171.34	odd	18		513.2.bo.a.224.14		108
171.110	even	18	inner	171.2.x.a.110.5	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.5	✓	108	1.1	even	1	trivial
171.2.x.a.110.5	yes	108	171.110	even	18	inner
171.2.bd.a.128.14	yes	108	9.2	odd	6
171.2.bd.a.167.14	yes	108	19.15	odd	18
513.2.bo.a.71.14		108	3.2	odd	2
513.2.bo.a.224.14		108	171.34	odd	18
513.2.cd.a.395.5		108	57.53	even	18
513.2.cd.a.413.5		108	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.28119 - 1.07504i) q^{2} +(1.71187 - 0.263611i) q^{3} +(0.138425 + 0.785049i) q^{4} +(0.287058 + 0.788686i) q^{5} +(-2.47662 - 1.50260i) q^{6} +(1.60000 - 2.77129i) q^{7} +(-1.00586 + 1.74220i) q^{8} +(2.86102 - 0.902536i) q^{9} +O(q^{10})\)	\(q+(-1.28119 - 1.07504i) q^{2} +(1.71187 - 0.263611i) q^{3} +(0.138425 + 0.785049i) q^{4} +(0.287058 + 0.788686i) q^{5} +(-2.47662 - 1.50260i) q^{6} +(1.60000 - 2.77129i) q^{7} +(-1.00586 + 1.74220i) q^{8} +(2.86102 - 0.902536i) q^{9} +(0.480097 - 1.31905i) q^{10} -0.779960i q^{11} +(0.443914 + 1.30741i) q^{12} +(0.150878 - 0.414534i) q^{13} +(-5.02916 + 1.83046i) q^{14} +(0.699313 + 1.27446i) q^{15} +(4.65980 - 1.69603i) q^{16} +(0.0888182 + 0.244026i) q^{17} +(-4.63577 - 1.91940i) q^{18} +(-4.35307 + 0.225372i) q^{19} +(-0.579421 + 0.334529i) q^{20} +(2.00846 - 5.16587i) q^{21} +(-0.838491 + 0.999275i) q^{22} +(-5.41417 + 0.954665i) q^{23} +(-1.26264 + 3.24758i) q^{24} +(3.29060 - 2.76114i) q^{25} +(-0.638944 + 0.368895i) q^{26} +(4.65978 - 2.29922i) q^{27} +(2.39708 + 0.872464i) q^{28} +(-0.519224 - 2.94466i) q^{29} +(0.474148 - 2.38461i) q^{30} +6.02187i q^{31} +(-4.01259 - 1.46046i) q^{32} +(-0.205606 - 1.33519i) q^{33} +(0.148546 - 0.408126i) q^{34} +(2.64497 + 0.466380i) q^{35} +(1.10457 + 2.12111i) q^{36} +11.1767i q^{37} +(5.81938 + 4.39100i) q^{38} +(0.149008 - 0.749402i) q^{39} +(-1.66279 - 0.293194i) q^{40} +(6.93325 + 5.81769i) q^{41} +(-8.12675 + 4.45926i) q^{42} +(-1.51015 + 8.56448i) q^{43} +(0.612307 - 0.107966i) q^{44} +(1.53310 + 1.99737i) q^{45} +(7.96287 + 4.59737i) q^{46} +(0.169371 - 0.0298646i) q^{47} +(7.52990 - 4.13176i) q^{48} +(-1.62002 - 2.80596i) q^{49} -7.18422 q^{50} +(0.216373 + 0.394328i) q^{51} +(0.346314 + 0.0610645i) q^{52} +(-0.860313 + 0.721888i) q^{53} +(-8.44182 - 2.06374i) q^{54} +(0.615144 - 0.223894i) q^{55} +(3.21875 + 5.57504i) q^{56} +(-7.39249 + 1.53332i) q^{57} +(-2.50042 + 4.33085i) q^{58} +(0.264850 - 1.50204i) q^{59} +(-0.903710 + 0.725412i) q^{60} +(-3.82725 - 1.39301i) q^{61} +(6.47377 - 7.71514i) q^{62} +(2.07645 - 9.37277i) q^{63} +(-1.38804 - 2.40415i) q^{64} +0.370248 q^{65} +(-1.17197 + 1.93167i) q^{66} +(-4.63066 - 5.51861i) q^{67} +(-0.179278 + 0.103506i) q^{68} +(-9.01672 + 3.06150i) q^{69} +(-2.88732 - 3.44098i) q^{70} +(7.53727 + 6.32452i) q^{71} +(-1.30538 + 5.89228i) q^{72} +(0.479455 - 2.71912i) q^{73} +(12.0154 - 14.3194i) q^{74} +(4.90522 - 5.59416i) q^{75} +(-0.779503 - 3.38617i) q^{76} +(-2.16149 - 1.24794i) q^{77} +(-0.996547 + 0.799933i) q^{78} +(-1.20161 - 3.30139i) q^{79} +(2.67527 + 3.18826i) q^{80} +(7.37086 - 5.16434i) q^{81} +(-2.62852 - 14.9071i) q^{82} +(-10.2281 - 5.90517i) q^{83} +(4.33348 + 0.861654i) q^{84} +(-0.166964 + 0.140099i) q^{85} +(11.1420 - 9.34923i) q^{86} +(-1.66509 - 4.90402i) q^{87} +(1.35884 + 0.784529i) q^{88} +(1.74018 + 9.86906i) q^{89} +(0.183072 - 4.20715i) q^{90} +(-0.907387 - 1.08138i) q^{91} +(-1.49892 - 4.11824i) q^{92} +(1.58743 + 10.3087i) q^{93} +(-0.249101 - 0.143819i) q^{94} +(-1.42733 - 3.36851i) q^{95} +(-7.25404 - 1.44237i) q^{96} +(-7.42282 + 8.84617i) q^{97} +(-0.940980 + 5.33656i) q^{98} +(-0.703942 - 2.23148i) 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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