LMFDB - Embedded newform 99.2.p.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	99.2
Dual form			99.2.p.a.50.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.148911 + 0.165382i) q^{2} +(-1.37407 - 1.05449i) q^{3} +(0.203880 - 1.93979i) q^{4} +(0.397470 + 0.357884i) q^{5} +(-0.0302197 - 0.384271i) q^{6} +(-1.30165 - 2.92356i) q^{7} +(0.711251 - 0.516754i) q^{8} +(0.776111 + 2.89787i) q^{9} +O(q^{10})$	\(q+(0.148911 + 0.165382i) q^{2} +(-1.37407 - 1.05449i) q^{3} +(0.203880 - 1.93979i) q^{4} +(0.397470 + 0.357884i) q^{5} +(-0.0302197 - 0.384271i) q^{6} +(-1.30165 - 2.92356i) q^{7} +(0.711251 - 0.516754i) q^{8} +(0.776111 + 2.89787i) q^{9} +0.119027i q^{10} +(3.12205 - 1.11928i) q^{11} +(-2.32563 + 2.45041i) q^{12} +(0.183129 + 0.861553i) q^{13} +(0.289675 - 0.650620i) q^{14} +(-0.168766 - 0.910883i) q^{15} +(-3.62433 - 0.770375i) q^{16} +(1.83995 + 5.66278i) q^{17} +(-0.363685 + 0.559880i) q^{18} +(2.50028 + 3.44134i) q^{19} +(0.775255 - 0.698043i) q^{20} +(-1.29430 + 5.38973i) q^{21} +(0.650017 + 0.349660i) q^{22} +(-3.19429 + 1.84423i) q^{23} +(-1.52222 - 0.0399516i) q^{24} +(-0.492741 - 4.68811i) q^{25} +(-0.115216 + 0.158581i) q^{26} +(1.98934 - 4.80026i) q^{27} +(-5.93647 + 1.92887i) q^{28} +(-2.17094 + 0.966564i) q^{29} +(0.125513 - 0.163551i) q^{30} +(7.08615 - 1.50621i) q^{31} +(-1.29145 - 2.23686i) q^{32} +(-5.47017 - 1.75421i) q^{33} +(-0.662535 + 1.14754i) q^{34} +(0.528926 - 1.62787i) q^{35} +(5.77949 - 0.914674i) q^{36} +(-0.636941 - 0.462765i) q^{37} +(-0.196818 + 0.925955i) q^{38} +(0.656866 - 1.37694i) q^{39} +(0.467639 + 0.0491508i) q^{40} +(9.17098 + 4.08318i) q^{41} +(-1.08410 + 0.588536i) q^{42} +(3.73912 + 2.15878i) q^{43} +(-1.53464 - 6.28432i) q^{44} +(-0.728620 + 1.42957i) q^{45} +(-0.780668 - 0.253654i) q^{46} +(-1.89502 + 0.199174i) q^{47} +(4.16771 + 4.88036i) q^{48} +(-2.16898 + 2.40889i) q^{49} +(0.701957 - 0.779602i) q^{50} +(3.44312 - 9.72123i) q^{51} +(1.70857 - 0.179578i) q^{52} +(-9.64245 - 3.13302i) q^{53} +(1.09011 - 0.385810i) q^{54} +(1.64149 + 0.672452i) q^{55} +(-2.43656 - 1.40675i) q^{56} +(0.193303 - 7.36514i) q^{57} +(-0.483129 - 0.215103i) q^{58} +(-11.0642 - 1.16290i) q^{59} +(-1.80133 + 0.141659i) q^{60} +(-0.383703 + 1.80518i) q^{61} +(1.30431 + 0.947634i) q^{62} +(7.46186 - 6.04102i) q^{63} +(-2.11237 + 6.50122i) q^{64} +(-0.235548 + 0.407980i) q^{65} +(-0.524454 - 1.16589i) q^{66} +(-0.337099 - 0.583872i) q^{67} +(11.3597 - 2.41458i) q^{68} +(6.33388 + 0.834257i) q^{69} +(0.347983 - 0.154932i) q^{70} +(4.21053 - 1.36808i) q^{71} +(2.04949 + 1.66005i) q^{72} +(0.0544863 - 0.0749940i) q^{73} +(-0.0183144 - 0.174250i) q^{74} +(-4.26650 + 6.96136i) q^{75} +(7.18523 - 4.14840i) q^{76} +(-7.33610 - 7.67059i) q^{77} +(0.325536 - 0.0964069i) q^{78} +(-11.5129 + 10.3663i) q^{79} +(-1.16486 - 1.60329i) q^{80} +(-7.79530 + 4.49814i) q^{81} +(0.690373 + 2.12475i) q^{82} +(-13.9274 - 2.96037i) q^{83} +(10.1911 + 3.60953i) q^{84} +(-1.29529 + 2.90927i) q^{85} +(0.199771 + 0.939851i) q^{86} +(4.00224 + 0.961106i) q^{87} +(1.64217 - 2.40942i) q^{88} +4.58327i q^{89} +(-0.344926 + 0.0923784i) q^{90} +(2.28043 - 1.65683i) q^{91} +(2.92616 + 6.57226i) q^{92} +(-11.3251 - 5.40263i) q^{93} +(-0.315129 - 0.283743i) q^{94} +(-0.237813 + 2.26264i) q^{95} +(-0.584202 + 4.43541i) q^{96} +(6.55256 + 7.27736i) q^{97} -0.721373 q^{98} +(5.66658 + 8.17862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.148911	+	0.165382i	0.105296	+	0.116943i	0.793489	−	0.608585i	$-0.208262\pi$
$2$	0.148911	+	0.165382i	0.105296	+	0.116943i	−0.688193	+	0.725528i	$0.741596\pi$
$3$	−1.37407	−	1.05449i	−0.793317	−	0.608809i
$3$	−1.37407	−	1.05449i	−0.793317	−	0.608809i
$4$	0.203880	−	1.93979i	0.101940	−	0.969895i
$5$	0.397470	+	0.357884i	0.177754	+	0.160051i	0.753205	−	0.657786i	$-0.228507\pi$
$5$	0.397470	+	0.357884i	0.177754	+	0.160051i	−0.575451	+	0.817836i	$0.695173\pi$
$6$	−0.0302197	−	0.384271i	−0.0123371	−	0.156878i
$7$	−1.30165	−	2.92356i	−0.491978	−	1.10500i	−0.973525	−	0.228581i	$-0.926592\pi$
$7$	−1.30165	−	2.92356i	−0.491978	−	1.10500i	0.481547	−	0.876420i	$-0.340075\pi$
$8$	0.711251	−	0.516754i	0.251465	−	0.182700i
$9$	0.776111	+	2.89787i	0.258704	+	0.965957i
$10$			0.119027i			0.0376398i
$11$	3.12205	−	1.11928i	0.941334	−	0.337475i
$11$	3.12205	−	1.11928i	0.941334	−	0.337475i
$12$	−2.32563	+	2.45041i	−0.671351	+	0.707372i
$13$	0.183129	+	0.861553i	0.0507908	+	0.238952i	0.996219	−	0.0868790i	$-0.0276894\pi$
$13$	0.183129	+	0.861553i	0.0507908	+	0.238952i	−0.945428	+	0.325831i	$0.894356\pi$
$14$	0.289675	−	0.650620i	0.0774188	−	0.173885i
$15$	−0.168766	−	0.910883i	−0.0435752	−	0.235189i
$16$	−3.62433	−	0.770375i	−0.906082	−	0.192594i
$17$	1.83995	+	5.66278i	0.446253	+	1.37342i	0.881104	+	0.472923i	$0.156801\pi$
$17$	1.83995	+	5.66278i	0.446253	+	1.37342i	−0.434851	+	0.900502i	$0.643199\pi$
$18$	−0.363685	+	0.559880i	−0.0857214	+	0.131965i
$19$	2.50028	+	3.44134i	0.573604	+	0.789497i	0.992976	−	0.118317i	$-0.0377498\pi$
$19$	2.50028	+	3.44134i	0.573604	+	0.789497i	−0.419372	+	0.907814i	$0.637750\pi$
$20$	0.775255	−	0.698043i	0.173352	−	0.156087i
$21$	−1.29430	+	5.38973i	−0.282440	+	1.17614i
$22$	0.650017	+	0.349660i	0.138584	+	0.0745477i
$23$	−3.19429	+	1.84423i	−0.666056	+	0.384548i	−0.794581	−	0.607159i	$-0.792309\pi$
$23$	−3.19429	+	1.84423i	−0.666056	+	0.384548i	0.128524	+	0.991706i	$0.458976\pi$
$24$	−1.52222	−	0.0399516i	−0.310721	−	0.00815509i
$25$	−0.492741	−	4.68811i	−0.0985481	−	0.937623i
$26$	−0.115216	+	0.158581i	−0.0225957	+	0.0311003i
$27$	1.98934	−	4.80026i	0.382849	−	0.923811i
$28$	−5.93647	+	1.92887i	−1.12189	+	0.364523i
$29$	−2.17094	+	0.966564i	−0.403133	+	0.179486i	−0.598279	−	0.801288i	$-0.704149\pi$
$29$	−2.17094	+	0.966564i	−0.403133	+	0.179486i	0.195146	+	0.980774i	$0.437482\pi$
$30$	0.125513	−	0.163551i	0.0229154	−	0.0298603i
$31$	7.08615	−	1.50621i	1.27271	−	0.270523i	0.478458	−	0.878111i	$-0.341196\pi$
$31$	7.08615	−	1.50621i	1.27271	−	0.270523i	0.794253	+	0.607588i	$0.207863\pi$
$32$	−1.29145	−	2.23686i	−0.228298	−	0.395424i
$33$	−5.47017	−	1.75421i	−0.952234	−	0.305368i
$34$	−0.662535	+	1.14754i	−0.113624	+	0.196802i
$35$	0.528926	−	1.62787i	0.0894048	−	0.275160i
$36$	5.77949	−	0.914674i	0.963249	−	0.152446i
$37$	−0.636941	−	0.462765i	−0.104713	−	0.0760781i	0.534197	−	0.845360i	$-0.320614\pi$
$37$	−0.636941	−	0.462765i	−0.104713	−	0.0760781i	−0.638909	+	0.769282i	$0.720614\pi$
$38$	−0.196818	+	0.925955i	−0.0319281	+	0.150210i
$39$	0.656866	−	1.37694i	0.105183	−	0.220486i
$40$	0.467639	+	0.0491508i	0.0739402	+	0.00777143i
$41$	9.17098	+	4.08318i	1.43227	+	0.637686i	0.968668	−	0.248359i	$-0.0798912\pi$
$41$	9.17098	+	4.08318i	1.43227	+	0.637686i	0.463599	+	0.886045i	$0.346558\pi$
$42$	−1.08410	+	0.588536i	−0.167281	+	0.0908131i
$43$	3.73912	+	2.15878i	0.570210	+	0.329211i	0.757233	−	0.653144i	$-0.226551\pi$
$43$	3.73912	+	2.15878i	0.570210	+	0.329211i	−0.187023	+	0.982356i	$0.559884\pi$
$44$	−1.53464	−	6.28432i	−0.231356	−	0.947397i
$45$	−0.728620	+	1.42957i	−0.108616	+	0.213108i
$46$	−0.780668	−	0.253654i	−0.115103	−	0.0373993i
$47$	−1.89502	+	0.199174i	−0.276417	+	0.0290526i	−0.241723	−	0.970345i	$-0.577712\pi$
$47$	−1.89502	+	0.199174i	−0.276417	+	0.0290526i	−0.0346943	+	0.999398i	$0.511046\pi$
$48$	4.16771	+	4.88036i	0.601558	+	0.704419i
$49$	−2.16898	+	2.40889i	−0.309854	+	0.344127i
$50$	0.701957	−	0.779602i	0.0992717	−	0.110252i
$51$	3.44312	−	9.72123i	0.482133	−	1.36124i
$52$	1.70857	−	0.179578i	0.236936	−	0.0249029i
$53$	−9.64245	−	3.13302i	−1.32449	−	0.430353i	−0.440457	−	0.897774i	$-0.645183\pi$
$53$	−9.64245	−	3.13302i	−1.32449	−	0.430353i	−0.884035	+	0.467420i	$0.845183\pi$
$54$	1.09011	−	0.385810i	0.148346	−	0.0525020i
$55$	1.64149	+	0.672452i	0.221339	+	0.0906734i
$56$	−2.43656	−	1.40675i	−0.325599	−	0.187985i
$57$	0.193303	−	7.36514i	0.0256037	−	0.975537i
$58$	−0.483129	−	0.215103i	−0.0634380	−	0.0282444i
$59$	−11.0642	−	1.16290i	−1.44044	−	0.151396i	−0.648135	−	0.761525i	$-0.724451\pi$
$59$	−11.0642	−	1.16290i	−1.44044	−	0.151396i	−0.792302	+	0.610129i	$0.791117\pi$
$60$	−1.80133	+	0.141659i	−0.232551	+	0.0182882i
$61$	−0.383703	+	1.80518i	−0.0491282	+	0.231130i	−0.995861	−	0.0908905i	$-0.971029\pi$
$61$	−0.383703	+	1.80518i	−0.0491282	+	0.231130i	0.946733	+	0.322020i	$0.104362\pi$
$62$	1.30431	+	0.947634i	0.165647	+	0.120350i
$63$	7.46186	−	6.04102i	0.940106	−	0.761097i
$64$	−2.11237	+	6.50122i	−0.264047	+	0.812653i
$65$	−0.235548	+	0.407980i	−0.0292161	+	0.0506037i
$66$	−0.524454	−	1.16589i	−0.0645558	−	0.143511i
$67$	−0.337099	−	0.583872i	−0.0411832	−	0.0713314i	0.844699	−	0.535241i	$-0.179779\pi$
$67$	−0.337099	−	0.583872i	−0.0411832	−	0.0713314i	−0.885882	+	0.463910i	$0.846446\pi$
$68$	11.3597	−	2.41458i	1.37757	−	0.292811i
$69$	6.33388	+	0.834257i	0.762510	+	0.100433i
$70$	0.347983	−	0.154932i	0.0415920	−	0.0185179i
$71$	4.21053	−	1.36808i	0.499698	−	0.162362i	−0.0483139	−	0.998832i	$-0.515385\pi$
$71$	4.21053	−	1.36808i	0.499698	−	0.162362i	0.548012	+	0.836470i	$0.315385\pi$
$72$	2.04949	+	1.66005i	0.241535	+	0.195639i
$73$	0.0544863	−	0.0749940i	0.00637714	−	0.00877738i	−0.805817	−	0.592165i	$-0.798273\pi$
$73$	0.0544863	−	0.0749940i	0.00637714	−	0.00877738i	0.812194	+	0.583388i	$0.198273\pi$
$74$	−0.0183144	−	0.174250i	−0.00212900	−	0.0202561i
$75$	−4.26650	+	6.96136i	−0.492653	+	0.803829i
$76$	7.18523	−	4.14840i	0.824203	−	0.475854i
$77$	−7.33610	−	7.67059i	−0.836026	−	0.874145i
$78$	0.325536	−	0.0964069i	0.0368597	−	0.0109159i
$79$	−11.5129	+	10.3663i	−1.29531	+	1.16630i	−0.319519	+	0.947580i	$0.603521\pi$
$79$	−11.5129	+	10.3663i	−1.29531	+	1.16630i	−0.975788	+	0.218719i	$0.929812\pi$
$80$	−1.16486	−	1.60329i	−0.130235	−	0.179253i
$81$	−7.79530	+	4.49814i	−0.866145	+	0.499793i
$82$	0.690373	+	2.12475i	0.0762390	+	0.234639i
$83$	−13.9274	−	2.96037i	−1.52873	−	0.324943i	−0.634635	−	0.772812i	$-0.718850\pi$
$83$	−13.9274	−	2.96037i	−1.52873	−	0.324943i	−0.894099	+	0.447869i	$0.852183\pi$
$84$	10.1911	+	3.60953i	1.11194	+	0.393832i
$85$	−1.29529	+	2.90927i	−0.140494	+	0.315555i
$86$	0.199771	+	0.939851i	0.0215419	+	0.101347i
$87$	4.00224	+	0.961106i	0.429085	+	0.103041i
$88$	1.64217	−	2.40942i	0.175056	−	0.256845i
$89$			4.58327i			0.485826i	0.970048	+	0.242913i	$0.0781029\pi$
$89$			4.58327i			0.485826i	−0.970048	+	0.242913i	$0.921897\pi$
$90$	−0.344926	+	0.0923784i	−0.0363584	+	0.00973754i
$91$	2.28043	−	1.65683i	0.239054	−	0.173683i
$92$	2.92616	+	6.57226i	0.305073	+	0.685205i
$93$	−11.3251	−	5.40263i	−1.17436	−	0.560227i
$94$	−0.315129	−	0.283743i	−0.0325031	−	0.0292659i
$95$	−0.237813	+	2.26264i	−0.0243991	+	0.232142i
$96$	−0.584202	+	4.43541i	−0.0596248	+	0.452687i
$97$	6.55256	+	7.27736i	0.665312	+	0.738904i	0.977458	−	0.211130i	$-0.0677144\pi$
$97$	6.55256	+	7.27736i	0.665312	+	0.738904i	−0.312146	+	0.950034i	$0.601048\pi$
$98$	−0.721373			−0.0728696
$99$	5.66658	+	8.17862i	0.569513	+	0.821982i
$100$	−9.19441			−0.919441
$101$	7.15791	+	7.94967i	0.712239	+	0.791022i	0.985274	−	0.170983i	$-0.0546942\pi$
$101$	7.15791	+	7.94967i	0.712239	+	0.791022i	−0.273035	+	0.962004i	$0.588027\pi$
$102$	2.12044	−	0.878166i	0.209955	−	0.0869514i
$103$	0.392106	−	3.73064i	0.0386354	−	0.367591i	−0.958073	−	0.286523i	$-0.907500\pi$
$103$	0.392106	−	3.73064i	0.0386354	−	0.367591i	0.996709	−	0.0810676i	$-0.0258330\pi$
$104$	0.575461	+	0.518148i	0.0564286	+	0.0508085i
$105$	−2.44334	+	1.67905i	−0.238446	+	0.163858i
$106$	−0.917719	−	2.06123i	−0.0891368	−	0.200205i
$107$	0.664192	−	0.482564i	0.0642098	−	0.0466512i	−0.555217	−	0.831705i	$-0.687365\pi$
$107$	0.664192	−	0.482564i	0.0642098	−	0.0466512i	0.619427	+	0.785054i	$0.287365\pi$
$108$	−8.90591	−	4.83758i	−0.856972	−	0.465497i
$109$		−	0.344350i		−	0.0329828i	−0.999864	−	0.0164914i	$-0.994750\pi$
$109$		−	0.344350i		−	0.0329828i	0.999864	−	0.0164914i	$-0.00524961\pi$
$110$	0.133225	+	0.371610i	0.0127025	+	0.0354316i
$111$	0.387219	+	1.30752i	0.0367532	+	0.124104i
$112$	2.46538	+	11.5987i	0.232956	+	1.09597i
$113$	−5.95347	+	13.3717i	−0.560056	+	1.25791i	0.382531	+	0.923943i	$0.375053\pi$
$113$	−5.95347	+	13.3717i	−0.560056	+	1.25791i	−0.942586	+	0.333963i	$0.891614\pi$
$114$	1.24685	−	1.06478i	0.116778	−	0.0997259i
$115$	−1.92966	−	0.410161i	−0.179941	−	0.0382477i
$116$	1.43232	+	4.40823i	0.132988	+	0.409294i
$117$	−2.35454	+	1.19934i	−0.217677	+	0.110879i
$118$	−1.45526	−	2.00299i	−0.133967	−	0.184390i
$119$	14.1605	−	12.7502i	1.29809	−	1.16880i
$120$	−0.590737	−	0.560656i	−0.0539267	−	0.0511806i
$121$	8.49443	−	6.98889i	0.772221	−	0.635354i
$122$	−0.355683	+	0.205354i	−0.0322020	+	0.0185918i
$123$	−8.29586	−	15.2813i	−0.748013	−	1.37786i
$124$	−1.47700	−	14.0527i	−0.132639	−	1.26197i
$125$	3.05383	−	4.20324i	0.273143	−	0.375949i
$126$	2.11023	+	0.334486i	0.187994	+	0.0297984i
$127$	13.3595	−	4.34077i	1.18546	−	0.385181i	0.351070	−	0.936349i	$-0.385818\pi$
$127$	13.3595	−	4.34077i	1.18546	−	0.385181i	0.834394	+	0.551168i	$0.185818\pi$
$128$	−6.10894	+	2.71987i	−0.539959	+	0.240405i
$129$	−2.86139	−	6.90916i	−0.251931	−	0.608318i
$130$	−0.102548	+	0.0217973i	−0.00899409	+	0.00191175i
$131$	1.07963	+	1.86997i	0.0943274	+	0.163380i	0.909328	−	0.416081i	$-0.136597\pi$
$131$	1.07963	+	1.86997i	0.0943274	+	0.163380i	−0.815000	+	0.579461i	$0.803263\pi$
$132$	−4.51805	+	10.2533i	−0.393246	+	0.892438i
$133$	6.80646	−	11.7891i	0.590195	−	1.02225i
$134$	0.0463645	−	0.142695i	0.00400528	−	0.0123270i
$135$	2.50864	−	1.19601i	0.215909	−	0.102936i
$136$	4.23492	+	3.07685i	0.363142	+	0.263838i
$137$	−0.150225	+	0.706754i	−0.0128346	+	0.0603821i	−0.984099	−	0.177622i	$-0.943160\pi$
$137$	−0.150225	+	0.706754i	−0.0128346	+	0.0603821i	0.971264	+	0.238004i	$0.0764930\pi$
$138$	0.805213	+	1.17174i	0.0685443	+	0.0997453i
$139$	−18.0949	−	1.90185i	−1.53479	−	0.161313i	−0.700907	−	0.713252i	$-0.747221\pi$
$139$	−18.0949	−	1.90185i	−1.53479	−	0.161313i	−0.833884	+	0.551939i	$0.813888\pi$
$140$	−3.04988	−	1.35789i	−0.257762	−	0.114763i
$141$	2.81391	+	1.72460i	0.236974	+	0.145237i
$142$	0.853251	+	0.492625i	0.0716033	+	0.0413402i
$143$	1.53606	+	2.48484i	0.128451	+	0.207793i
$144$	−0.580434	−	11.1007i	−0.0483695	−	0.925061i
$145$	−1.20880	−	0.392763i	−0.100385	−	0.0326172i
$146$	0.0205163	−	0.00215635i	0.00169794	−	0.000178461i
$147$	5.52046	−	1.02282i	0.455320	−	0.0843605i
$148$	−1.02753	+	1.14118i	−0.0844621	+	0.0938047i
$149$	15.2390	−	16.9247i	1.24843	−	1.38652i	0.356533	−	0.934283i	$-0.383959\pi$
$149$	15.2390	−	16.9247i	1.24843	−	1.38652i	0.891897	−	0.452239i	$-0.149375\pi$
$150$	−1.78662	+	0.331019i	−0.145877	+	0.0270276i
$151$	−11.3594	+	1.19392i	−0.924412	+	0.0971596i	−0.554760	−	0.832011i	$-0.687190\pi$
$151$	−11.3594	+	1.19392i	−0.924412	+	0.0971596i	−0.369652	+	0.929170i	$0.620523\pi$
$152$	3.55665	+	1.15563i	0.288482	+	0.0937336i
$153$	−14.9820	+	9.72687i	−1.21122	+	0.786371i
$154$	0.176155	−	2.35550i	0.0141949	−	0.189811i
$155$	3.35558	+	1.93735i	0.269527	+	0.155611i
$156$	−2.53705	−	1.55491i	−0.203126	−	0.124493i
$157$	−18.1548	−	8.08304i	−1.44891	−	0.645097i	−0.476671	−	0.879082i	$-0.658157\pi$
$157$	−18.1548	−	8.08304i	−1.44891	−	0.645097i	−0.972240	+	0.233985i	$0.924823\pi$
$158$	−3.42880	−	0.360382i	−0.272781	−	0.0286704i
$159$	9.94562	+	14.4728i	0.788739	+	1.14777i
$160$	0.287222	−	1.35127i	0.0227069	−	0.106828i
$161$	9.54956	+	6.93816i	0.752611	+	0.546804i
$162$	−1.90472	−	0.619384i	−0.149649	−	0.0486634i
$163$	3.18523	−	9.80313i	0.249486	−	0.767840i	−0.745380	−	0.666640i	$-0.767732\pi$
$163$	3.18523	−	9.80313i	0.249486	−	0.767840i	0.994866	−	0.101200i	$-0.0322683\pi$
$164$	9.79030	−	16.9573i	0.764494	−	1.32414i
$165$	−1.54643	−	2.65493i	−0.120389	−	0.206686i
$166$	−1.58435	−	2.74418i	−0.122970	−	0.212990i
$167$	11.5938	−	2.46433i	0.897153	−	0.190696i	0.263817	−	0.964573i	$-0.415018\pi$
$167$	11.5938	−	2.46433i	0.897153	−	0.190696i	0.633336	+	0.773877i	$0.281685\pi$
$168$	1.86459	+	4.50229i	0.143856	+	0.347359i
$169$	11.1674	−	4.97203i	0.859027	−	0.382464i
$170$	−0.674025	+	0.219004i	−0.0516954	+	0.0167969i
$171$	−8.03206	+	9.91635i	−0.614227	+	0.758322i
$172$	4.94991	−	6.81297i	0.377427	−	0.519484i
$173$	1.65458	+	15.7423i	0.125796	+	1.19687i	0.857223	+	0.514946i	$0.172188\pi$
$173$	1.65458	+	15.7423i	0.125796	+	1.19687i	−0.731427	+	0.681920i	$0.761145\pi$
$174$	0.437028	+	0.805019i	0.0331310	+	0.0610284i
$175$	−13.0646	+	7.54285i	−0.987590	+	0.570186i
$176$	−12.1776	+	1.65148i	−0.917922	+	0.124485i
$177$	13.9767	+	13.2650i	1.05055	+	0.997056i
$178$	−0.757992	+	0.682499i	−0.0568139	+	0.0511555i
$179$	4.11815	+	5.66815i	0.307805	+	0.423658i	0.934695	−	0.355450i	$-0.115672\pi$
$179$	4.11815	+	5.66815i	0.307805	+	0.423658i	−0.626890	+	0.779108i	$0.715672\pi$
$180$	2.62452	+	1.70483i	0.195620	+	0.127071i
$181$	−3.74044	−	11.5119i	−0.278025	−	0.855673i	−0.988403	−	0.151853i	$-0.951476\pi$
$181$	−3.74044	−	11.5119i	−0.278025	−	0.855673i	0.710378	−	0.703820i	$-0.248524\pi$
$182$	0.613591	+	0.130423i	0.0454824	+	0.00966758i
$183$	2.43078	−	2.07583i	0.179688	−	0.153450i
$184$	−1.31893	+	2.96237i	−0.0972330	+	0.218389i
$185$	−0.0875491	−	0.411886i	−0.00643674	−	0.0302825i
$186$	−0.792933	−	2.67748i	−0.0581407	−	0.196323i
$187$	12.0826	+	15.6201i	0.883570	+	1.14225i
$188$			3.71654i			0.271057i
$189$	−16.6233	+	0.432314i	−1.20917	+	0.0314462i
$190$	−0.409614	+	0.297602i	−0.0297165	+	0.0215903i
$191$	−8.25925	−	18.5506i	−0.597618	−	1.34227i	−0.918600	−	0.395187i	$-0.870680\pi$
$191$	−8.25925	−	18.5506i	−0.597618	−	1.34227i	0.320982	−	0.947085i	$-0.395987\pi$
$192$	9.75800	−	6.70563i	0.704223	−	0.483937i
$193$	4.22233	+	3.80181i	0.303930	+	0.273660i	0.806956	−	0.590611i	$-0.201113\pi$
$193$	4.22233	+	3.80181i	0.303930	+	0.273660i	−0.503026	+	0.864271i	$0.667780\pi$
$194$	−0.227798	+	2.16736i	−0.0163550	+	0.155607i
$195$	0.753868	−	0.312210i	0.0539856	−	0.0223578i
$196$	4.23053	+	4.69848i	0.302181	+	0.335606i
$197$	−16.4596			−1.17270			−0.586350	−	0.810058i	$-0.699436\pi$
$197$	−16.4596			−1.17270			−0.586350	+	0.810058i	$0.699436\pi$
$198$	−0.508783	+	2.15504i	−0.0361577	+	0.153152i
$199$	13.9772			0.990818			0.495409	−	0.868660i	$-0.335018\pi$
$199$	13.9772			0.990818			0.495409	+	0.868660i	$0.335018\pi$
$200$	−2.77306	−	3.07980i	−0.196085	−	0.217775i
$201$	−0.152490	+	1.15775i	−0.0107558	+	0.0816611i
$202$	−0.248843	+	2.36759i	−0.0175086	+	0.166583i
$203$	5.65161	+	5.08873i	0.396665	+	0.357159i
$204$	−18.1551	−	8.66089i	−1.27111	−	0.606384i
$205$	2.18389	+	4.90509i	0.152529	+	0.342586i
$206$	0.675371	−	0.490686i	0.0470554	−	0.0341877i
$207$	−7.82346	−	7.82533i	−0.543768	−	0.543898i
$208$		−	3.26363i		−	0.226292i
$209$	11.6578	+	7.94554i	0.806389	+	0.549604i
$210$	−0.641526	−	0.154057i	−0.0442695	−	0.0106310i
$211$	2.23574	+	10.5183i	0.153915	+	0.724112i	0.985631	+	0.168911i	$0.0540252\pi$
$211$	2.23574	+	10.5183i	0.153915	+	0.724112i	−0.831716	+	0.555201i	$0.812641\pi$
$212$	−8.04330	+	18.0656i	−0.552416	+	1.24075i
$213$	−7.22817	−	2.56012i	−0.495266	−	0.175416i
$214$	0.178713	+	0.0379866i	0.0122166	+	0.00259671i
$215$	0.713596	+	2.19622i	0.0486668	+	0.149781i
$216$	−1.06563	−	4.44219i	−0.0725072	−	0.302253i
$217$	−13.6272	−	18.7562i	−0.925074	−	1.27325i
$218$	0.0569495	−	0.0512775i	0.00385711	−	0.00347295i
$219$	−0.153948	+	0.0455915i	−0.0104028	+	0.00308079i
$220$	1.63908	−	3.04705i	0.110507	−	0.205432i
$221$	−4.54183	+	2.62223i	−0.305517	+	0.176390i
$222$	−0.158579	+	0.258743i	−0.0106431	+	0.0173657i
$223$	1.71464	+	16.3137i	0.114821	+	1.09245i	0.888503	+	0.458871i	$0.151746\pi$
$223$	1.71464	+	16.3137i	0.114821	+	1.09245i	−0.773682	+	0.633574i	$0.781587\pi$
$224$	−4.85856	+	6.68724i	−0.324626	+	0.446810i
$225$	13.2031	−	5.06639i	0.880208	−	0.337760i
$226$	−3.09798	+	1.00660i	−0.206075	+	0.0669578i
$227$	−13.8406	+	6.16224i	−0.918634	+	0.409002i	−0.810905	−	0.585178i	$-0.801025\pi$
$227$	−13.8406	+	6.16224i	−0.918634	+	0.409002i	−0.107729	+	0.994180i	$0.534358\pi$
$228$	−14.2474	−	1.87657i	−0.943558	−	0.124279i
$229$	−6.93316	+	1.47369i	−0.458156	+	0.0973841i	−0.431208	−	0.902253i	$-0.641912\pi$
$229$	−6.93316	+	1.47369i	−0.458156	+	0.0973841i	−0.0269485	+	0.999637i	$0.508579\pi$
$230$	−0.219513	−	0.380208i	−0.0144743	−	0.0250702i
$231$	1.99174	+	18.2757i	0.131047	+	1.20245i
$232$	−1.04461	+	1.80931i	−0.0685817	+	0.118787i
$233$	6.69692	−	20.6110i	0.438730	−	1.35027i	−0.450486	−	0.892784i	$-0.648749\pi$
$233$	6.69692	−	20.6110i	0.438730	−	1.35027i	0.889216	−	0.457488i	$-0.151251\pi$
$234$	−0.548967	−	0.210804i	−0.0358871	−	0.0137807i
$235$	−0.824495	−	0.599031i	−0.0537841	−	0.0390764i
$236$	−4.51154	+	21.2251i	−0.293676	+	1.38164i
$237$	26.7507	−	2.10371i	1.73764	−	0.136651i
$238$	4.21730	+	0.443256i	0.273367	+	0.0287320i
$239$	−16.9181	−	7.53244i	−1.09434	−	0.487233i	−0.221463	−	0.975169i	$-0.571083\pi$
$239$	−16.9181	−	7.53244i	−1.09434	−	0.487233i	−0.872880	+	0.487936i	$0.837750\pi$
$240$	−0.0900583	+	3.43135i	−0.00581324	+	0.221493i
$241$	9.56117	+	5.52014i	0.615889	+	0.355584i	0.775267	−	0.631634i	$-0.217615\pi$
$241$	9.56117	+	5.52014i	0.615889	+	0.355584i	−0.159378	+	0.987218i	$0.550949\pi$
$242$	2.42075	+	0.364106i	0.155612	+	0.0234056i
$243$	15.4545	+	2.03932i	0.991406	+	0.130822i
$244$	3.42344	+	1.11234i	0.219164	+	0.0712106i
$245$	−1.72421	+	0.181221i	−0.110156	+	0.0115778i
$246$	1.29191	−	3.64754i	0.0823689	−	0.232558i
$247$	−2.50702	+	2.78433i	−0.159518	+	0.177163i
$248$	4.26169	−	4.73309i	0.270618	−	0.300551i
$249$	16.0155	+	18.7540i	1.01494	+	1.18849i
$250$	1.14989	−	0.120858i	0.0727255	−	0.00764375i
$251$	−18.6948	−	6.07431i	−1.18001	−	0.383407i	−0.347636	−	0.937629i	$-0.613016\pi$
$251$	−18.6948	−	6.07431i	−1.18001	−	0.383407i	−0.832369	+	0.554223i	$0.813016\pi$
$252$	−10.1970	−	15.7061i	−0.642350	−	0.989391i
$253$	−7.90855	+	9.33308i	−0.497206	+	0.586766i
$254$	2.70726	+	1.56304i	0.169869	+	0.0980738i
$255$	4.84761	−	2.63166i	0.303569	−	0.164801i
$256$	11.1301	+	4.95544i	0.695631	+	0.309715i
$257$	26.1815	+	2.75179i	1.63316	+	0.171652i	0.876246	−	0.481864i	$-0.160040\pi$
$257$	26.1815	+	2.75179i	1.63316	+	0.171652i	0.756913	+	0.653516i	$0.226707\pi$
$258$	0.716562	−	1.50207i	0.0446112	−	0.0935150i
$259$	−0.523844	+	2.46449i	−0.0325501	+	0.153136i
$260$	0.743373	+	0.540092i	0.0461020	+	0.0334951i
$261$	−4.48587	−	5.54094i	−0.277668	−	0.342975i
$262$	−0.148491	+	0.457010i	−0.00917384	+	0.0282342i
$263$	1.31836	−	2.28347i	0.0812936	−	0.140805i	−0.822512	−	0.568747i	$-0.807428\pi$
$263$	1.31836	−	2.28347i	0.0812936	−	0.140805i	0.903806	+	0.427943i	$0.140762\pi$
$264$	−4.79715	+	1.57905i	−0.295244	+	0.0971839i
$265$	−2.71133	−	4.69616i	−0.166556	−	0.288483i
$266$	2.96327	−	0.629863i	0.181690	−	0.0386194i
$267$	4.83300	−	6.29771i	0.295775	−	0.385414i
$268$	−1.20132	+	0.534861i	−0.0733821	+	0.0326718i
$269$	3.48174	−	1.13129i	0.212285	−	0.0689757i	−0.200944	−	0.979603i	$-0.564401\pi$
$269$	3.48174	−	1.13129i	0.212285	−	0.0689757i	0.413229	+	0.910627i	$0.364401\pi$
$270$	0.571363	+	0.236786i	0.0347720	+	0.0144103i
$271$	−6.37358	+	8.77249i	−0.387168	+	0.532891i	−0.957466	−	0.288547i	$-0.906828\pi$
$271$	−6.37358	+	8.77249i	−0.387168	+	0.532891i	0.570298	+	0.821438i	$0.306828\pi$
$272$	−2.30611	−	21.9412i	−0.139829	−	1.33038i
$273$	−4.88057	−	0.128094i	−0.295385	−	0.00775260i
$274$	−0.139255	+	0.0803988i	−0.00841269	+	0.00485707i
$275$	−6.78567	−	14.0850i	−0.409191	−	0.849359i
$276$	2.90963	−	12.1163i	0.175139	−	0.729316i
$277$	−0.148105	+	0.133354i	−0.00889876	+	0.00801248i	−0.673568	−	0.739125i	$-0.735239\pi$
$277$	−0.148105	+	0.133354i	−0.00889876	+	0.00801248i	0.664669	+	0.747138i	$0.268572\pi$
$278$	−2.38000	−	3.27579i	−0.142743	−	0.196469i
$279$	9.86443	+	19.3658i	0.590568	+	1.15940i
$280$	−0.465007	−	1.43115i	−0.0277895	−	0.0855273i
$281$	−7.46681	−	1.58712i	−0.445433	−	0.0946797i	−0.0202659	−	0.999795i	$-0.506451\pi$
$281$	−7.46681	−	1.58712i	−0.445433	−	0.0946797i	−0.425167	+	0.905115i	$0.639785\pi$
$282$	0.133804	+	0.722182i	0.00796790	+	0.0430053i
$283$	0.229559	−	0.515598i	0.0136459	−	0.0306491i	−0.906594	−	0.422004i	$-0.861327\pi$
$283$	0.229559	−	0.515598i	0.0136459	−	0.0306491i	0.920240	+	0.391355i	$0.127993\pi$
$284$	−1.79535	−	8.44647i	−0.106535	−	0.501206i
$285$	2.71270	−	2.85824i	0.160686	−	0.169308i
$286$	−0.182214	+	0.624057i	−0.0107745	+	0.0369012i
$287$		−	32.1268i		−	1.89638i
$288$	5.47981	−	5.47850i	0.322901	−	0.322824i
$289$	−14.9283	+	10.8461i	−0.878137	+	0.638004i
$290$	−0.115048	−	0.258401i	−0.00675583	−	0.0151738i
$291$	−1.32976	−	16.9092i	−0.0779521	−	0.991233i
$292$	−0.134364	−	0.120982i	−0.00786305	−	0.00707992i
$293$	−0.534278	+	5.08332i	−0.0312129	+	0.296971i	0.967768	+	0.251842i	$0.0810364\pi$
$293$	−0.534278	+	5.08332i	−0.0312129	+	0.296971i	−0.998981	+	0.0451285i	$0.985630\pi$
$294$	0.991213	+	0.760679i	0.0578087	+	0.0443637i
$295$	−3.98151	−	4.42192i	−0.231813	−	0.257454i
$296$	−0.692160			−0.0402310
$297$	0.838000	−	17.2133i	0.0486257	−	0.998817i
$298$	5.06830			0.293599
$299$	−2.17387	−	2.41432i	−0.125718	−	0.139624i
$300$	12.6337	+	9.69540i	0.729408	+	0.559764i
$301$	1.44429	−	13.7415i	0.0832475	−	0.792048i
$302$	−1.88899	−	1.70085i	−0.108699	−	0.0978730i
$303$	−1.45261	−	18.4713i	−0.0834504	−	1.06115i
$304$	−6.41071	−	14.3987i	−0.367680	−	0.825822i
$305$	−0.798556	+	0.580185i	−0.0457252	+	0.0332213i
$306$	−3.83963	−	1.02932i	−0.219497	−	0.0588422i
$307$		−	2.87711i		−	0.164205i	−0.996624	−	0.0821026i	$-0.973836\pi$
$307$		−	2.87711i		−	0.164205i	0.996624	−	0.0821026i	$-0.0261635\pi$
$308$	−16.3750	+	12.6666i	−0.933053	+	0.721747i
$309$	−4.47270	+	4.71267i	−0.254443	+	0.268095i
$310$	0.179280	+	0.843446i	0.0101824	+	0.0479045i
$311$	1.10271	−	2.47674i	0.0625292	−	0.140443i	−0.879578	−	0.475755i	$-0.842175\pi$
$311$	1.10271	−	2.47674i	0.0625292	−	0.140443i	0.942107	+	0.335312i	$0.108842\pi$
$312$	−0.244341	−	1.31879i	−0.0138331	−	0.0746615i
$313$	10.9007	+	2.31701i	0.616144	+	0.130965i	0.505402	−	0.862884i	$-0.331344\pi$
$313$	10.9007	+	2.31701i	0.616144	+	0.130965i	0.110742	+	0.993849i	$0.464677\pi$
$314$	−1.36666	−	4.20614i	−0.0771249	−	0.237366i
$315$	5.12785	+	0.269354i	0.288922	+	0.0151764i
$316$	17.7612	+	24.4462i	0.999144	+	1.37520i
$317$	4.64579	−	4.18309i	0.260933	−	0.234946i	−0.528271	−	0.849076i	$-0.677160\pi$
$317$	4.64579	−	4.18309i	0.260933	−	0.234946i	0.789205	+	0.614130i	$0.210493\pi$
$318$	−0.912537	+	3.79999i	−0.0511725	+	0.213093i
$319$	−5.69593	+	5.44755i	−0.318911	+	0.305004i
$320$	−3.16629	+	1.82806i	−0.177001	+	0.102191i
$321$	−1.42150	−	0.0373083i	−0.0793404	−	0.00208235i
$322$	0.274585	+	2.61250i	0.0153020	+	0.145589i
$323$	−14.8872	+	20.4904i	−0.828343	+	1.14012i
$324$	7.13613	+	16.0383i	0.396452	+	0.891018i
$325$	3.94882	−	1.28305i	0.219041	−	0.0711708i
$326$	2.09558	−	0.933013i	0.116063	−	0.0516748i
$327$	−0.363113	+	0.473160i	−0.0200802	+	0.0261658i
$328$	8.63287	−	1.83497i	0.476670	−	0.101319i
$329$	3.04895	+	5.28094i	0.168094	+	0.291148i
$330$	0.208798	−	0.651100i	0.0114940	−	0.0358419i
$331$	−1.55234	+	2.68873i	−0.0853242	+	0.147786i	−0.905529	−	0.424284i	$-0.860526\pi$
$331$	−1.55234	+	2.68873i	−0.0853242	+	0.147786i	0.820205	+	0.572070i	$0.193859\pi$
$332$	−8.58202	+	26.4127i	−0.470999	+	1.44959i
$333$	0.846696	−	2.20493i	0.0463986	−	0.120829i
$334$	2.13400	+	1.55044i	0.116767	+	0.0848363i
$335$	0.0749717	−	0.352714i	0.00409614	−	0.0192708i
$336$	8.84309	−	18.5371i	0.482430	−	1.01128i
$337$	13.3023	+	1.39813i	0.724622	+	0.0761608i	0.459656	−	0.888097i	$-0.347973\pi$
$337$	13.3023	+	1.39813i	0.724622	+	0.0761608i	0.264966	+	0.964258i	$0.414639\pi$
$338$	2.48523	+	1.10649i	0.135179	+	0.0601854i
$339$	22.2808	−	12.0958i	1.21013	−	0.656951i
$340$	5.37929	+	3.10574i	0.291733	+	0.168432i
$341$	20.4375	−	12.6338i	1.10675	−	0.684161i
$342$	−2.83605	+	0.148291i	−0.153356	+	0.00801868i
$343$	−11.4394	−	3.71689i	−0.617671	−	0.200693i
$344$	3.77501	−	0.396769i	0.203535	−	0.0213924i
$345$	2.21896	+	2.59839i	0.119465	+	0.139892i
$346$	−2.35712	+	2.61784i	−0.126719	+	0.140736i
$347$	−1.88487	+	2.09336i	−0.101185	+	0.112377i	−0.791610	−	0.611027i	$-0.790757\pi$
$347$	−1.88487	+	2.09336i	−0.101185	+	0.112377i	0.690425	+	0.723404i	$0.257424\pi$
$348$	2.68032	−	7.56755i	0.143680	−	0.405664i
$349$	−26.7592	+	2.81251i	−1.43239	+	0.150550i	−0.788719	−	0.614754i	$-0.789255\pi$
$349$	−26.7592	+	2.81251i	−1.43239	+	0.150550i	−0.643669	+	0.765304i	$0.722589\pi$
$350$	−3.19291	−	1.03744i	−0.170668	−	0.0554535i
$351$	4.49999	+	0.834857i	0.240191	+	0.0445614i
$352$	−6.53564	−	5.53809i	−0.348351	−	0.295181i
$353$	−1.73418	−	1.00123i	−0.0923011	−	0.0532901i	0.453139	−	0.891440i	$-0.350304\pi$
$353$	−1.73418	−	1.00123i	−0.0923011	−	0.0532901i	−0.545440	+	0.838150i	$0.683637\pi$
$354$	−0.112510	+	4.28680i	−0.00597984	+	0.227841i
$355$	2.16318	+	0.963108i	0.114809	+	0.0511165i
$356$	8.89058	+	0.934437i	0.471200	+	0.0495251i
$357$	−32.9023	+	2.58749i	−1.74137	+	0.136944i
$358$	−0.324174	+	1.52512i	−0.0171331	+	0.0806051i
$359$	2.02249	+	1.46942i	0.106743	+	0.0775532i	0.639876	−	0.768478i	$-0.278986\pi$
$359$	2.02249	+	1.46942i	0.106743	+	0.0775532i	−0.533133	+	0.846031i	$0.678986\pi$
$360$	0.220507	+	1.39330i	0.0116217	+	0.0734335i
$361$	0.279902	−	0.861450i	0.0147317	−	0.0453395i
$362$	1.34687	−	2.33285i	0.0707901	−	0.122612i
$363$	−19.0416	+	0.645924i	−0.999425	+	0.0339022i
$364$	−2.74897	−	4.76135i	−0.144085	−	0.249562i
$365$	0.0484958	−	0.0103081i	0.00253839	−	0.000539551i
$366$	0.705275	+	0.0928940i	0.0368653	+	0.00485565i
$367$	−12.1115	+	5.39240i	−0.632217	+	0.281481i	−0.697719	−	0.716371i	$-0.745802\pi$
$367$	−12.1115	+	5.39240i	−0.632217	+	0.281481i	0.0655024	+	0.997852i	$0.479135\pi$
$368$	12.9979	−	4.22328i	0.677563	−	0.220154i
$369$	−4.71484	+	29.7453i	−0.245445	+	1.54848i
$370$	0.0550817	−	0.0758135i	0.00286356	−	0.00394135i
$371$	3.39154	+	32.2683i	0.176080	+	1.67529i
$372$	−12.7889	+	20.8668i	−0.663075	+	1.08190i
$373$	27.5050	−	15.8800i	1.42416	−	0.822238i	0.427507	−	0.904012i	$-0.359392\pi$
$373$	27.5050	−	15.8800i	1.42416	−	0.822238i	0.996651	+	0.0817746i	$0.0260588\pi$
$374$	−0.784048	+	4.32426i	−0.0405421	+	0.223602i
$375$	−8.62843	+	2.55530i	−0.445570	+	0.131955i
$376$	−1.24491	+	1.12092i	−0.0642013	+	0.0578071i
$377$	−1.23031	−	1.69337i	−0.0633641	−	0.0872131i
$378$	−2.54688	−	2.68482i	−0.130998	−	0.138092i
$379$	7.34658	+	22.6104i	0.377368	+	1.16142i	0.941867	+	0.335986i	$0.109070\pi$
$379$	7.34658	+	22.6104i	0.377368	+	1.16142i	−0.564498	+	0.825434i	$0.690930\pi$
$380$	4.34056	+	0.922614i	0.222666	+	0.0473291i
$381$	−22.9341	−	8.12294i	−1.17495	−	0.416151i
$382$	1.83805	−	4.12832i	0.0940426	−	0.211223i
$383$	3.70805	+	17.4450i	0.189472	+	0.891397i	0.965440	+	0.260625i	$0.0839285\pi$
$383$	3.70805	+	17.4450i	0.189472	+	0.891397i	−0.775968	+	0.630772i	$0.782738\pi$
$384$	11.2621	+	2.70451i	0.574719	+	0.138014i
$385$	−0.170702	−	5.67430i	−0.00869976	−	0.289189i
$386$			1.26443i			0.0643578i
$387$	−3.35390	+	12.5109i	−0.170488	+	0.635967i
$388$	15.4525	−	11.2269i	0.784481	−	0.569959i
$389$	−10.0542	−	22.5821i	−0.509769	−	1.14496i	−0.966806	−	0.255512i	$-0.917756\pi$
$389$	−10.0542	−	22.5821i	−0.509769	−	1.14496i	0.457037	−	0.889448i	$-0.348911\pi$
$390$	0.163893	+	0.0781851i	0.00829906	+	0.00395906i
$391$	−16.3208	−	14.6953i	−0.825377	−	0.743173i
$392$	−0.297881	+	2.83415i	−0.0150453	+	0.143146i
$393$	0.488381	−	3.70791i	0.0246356	−	0.187039i
$394$	−2.45102	−	2.72213i	−0.123480	−	0.137139i
$395$	−8.28598			−0.416913
$396$	17.0201	−	9.32452i	0.855292	−	0.468575i
$397$	−4.07143			−0.204339			−0.102170	−	0.994767i	$-0.532578\pi$
$397$	−4.07143			−0.204339			−0.102170	+	0.994767i	$0.532578\pi$
$398$	2.08136	+	2.31158i	0.104329	+	0.115869i
$399$	−21.7840	+	9.02171i	−1.09057	+	0.451651i
$400$	−1.82575	+	17.3709i	−0.0912875	+	0.868543i
$401$	−18.8206	−	16.9462i	−0.939857	−	0.846251i	0.0484344	−	0.998826i	$-0.484577\pi$
$401$	−18.8206	−	16.9462i	−0.939857	−	0.846251i	−0.988292	+	0.152575i	$0.951243\pi$
$402$	−0.214178	+	0.147182i	−0.0106822	+	0.00734076i
$403$	2.59536	+	5.82926i	0.129284	+	0.290376i
$404$	16.8800	−	12.2641i	0.839813	−	0.610160i
$405$	−4.70821	−	1.00194i	−0.233953	−	0.0497867i
$406$			1.69245i			0.0839946i
$407$	−2.50653	−	0.731862i	−0.124244	−	0.0362771i
$408$	−2.57456	−	8.69347i	−0.127460	−	0.430391i
$409$	−1.86286	−	8.76406i	−0.0921124	−	0.433355i	−0.999903	−	0.0139310i	$-0.995565\pi$
$409$	−1.86286	−	8.76406i	−0.0921124	−	0.433355i	0.907791	−	0.419424i	$-0.137768\pi$
$410$	−0.486011	+	1.09160i	−0.0240024	+	0.0539102i
$411$	0.951683	−	0.812716i	0.0469431	−	0.0400883i
$412$	−7.15672	−	1.52121i	−0.352586	−	0.0749445i
$413$	11.0020	+	33.8605i	0.541371	+	1.66617i
$414$	0.129173	−	2.45914i	0.00634849	−	0.120860i
$415$	−4.47627	−	6.16106i	−0.219732	−	0.302435i
$416$	1.69067	−	1.52229i	0.0828919	−	0.0746362i
$417$	22.8581	+	21.6941i	1.11937	+	1.06237i
$418$	0.421926	+	3.11118i	0.0206371	+	0.152173i
$419$	−2.71746	+	1.56893i	−0.132757	+	0.0766471i	−0.564908	−	0.825154i	$-0.691088\pi$
$419$	−2.71746	+	1.56893i	−0.132757	+	0.0766471i	0.432151	+	0.901801i	$0.357755\pi$
$420$	2.75885	+	5.08190i	0.134618	+	0.247971i
$421$	−3.00840	−	28.6230i	−0.146620	−	1.39500i	−0.782230	−	0.622990i	$-0.785918\pi$
$421$	−3.00840	−	28.6230i	−0.146620	−	1.39500i	0.635609	−	0.772011i	$-0.280749\pi$
$422$	−1.40662	+	1.93605i	−0.0684732	+	0.0942453i
$423$	−2.04793	−	5.33694i	−0.0995736	−	0.259491i
$424$	−8.47720	+	2.75441i	−0.411689	+	0.133766i
$425$	25.6411	−	11.4162i	1.24378	−	0.553765i
$426$	−0.652956	−	1.57664i	−0.0316358	−	0.0763885i
$427$	5.77700	−	1.22794i	0.279569	−	0.0594242i
$428$	−0.800656	−	1.38678i	−0.0387012	−	0.0670324i
$429$	0.509595	−	5.03409i	0.0246035	−	0.243048i
$430$	−0.256954	+	0.445058i	−0.0123914	+	0.0214626i
$431$	−8.71998	+	26.8373i	−0.420027	+	1.29271i	0.487650	+	0.873039i	$0.337854\pi$
$431$	−8.71998	+	26.8373i	−0.420027	+	1.29271i	−0.907677	+	0.419670i	$0.862146\pi$
$432$	−10.9080	+	15.8652i	−0.524813	+	0.763314i
$433$	0.815921	+	0.592801i	0.0392107	+	0.0284882i	0.607218	−	0.794535i	$-0.292285\pi$
$433$	0.815921	+	0.592801i	0.0392107	+	0.0284882i	−0.568007	+	0.823024i	$0.692285\pi$
$434$	1.07271	−	5.04670i	0.0514917	−	0.242249i
$435$	1.24681	+	1.81435i	0.0597798	+	0.0869913i
$436$	−0.667967	−	0.0702062i	−0.0319898	−	0.00336227i
$437$	−14.3332	−	6.38157i	−0.685652	−	0.305272i
$438$	−0.0304646	−	0.0186712i	−0.00145565	−	0.000892145i
$439$	−30.7703	−	17.7652i	−1.46859	−	0.847888i	−0.469205	−	0.883089i	$-0.655459\pi$
$439$	−30.7703	−	17.7652i	−1.46859	−	0.847888i	−0.999380	+	0.0352012i	$0.988793\pi$
$440$	1.51501	−	0.369967i	0.0722251	−	0.0176375i
$441$	−8.66402	−	4.41584i	−0.412573	−	0.210278i
$442$	−1.11000	−	0.360661i	−0.0527973	−	0.0171549i
$443$	18.7712	−	1.97294i	0.891849	−	0.0937371i	0.352492	−	0.935815i	$-0.385334\pi$
$443$	18.7712	−	1.97294i	0.891849	−	0.0937371i	0.539356	+	0.842078i	$0.318668\pi$
$444$	2.61525	−	0.484547i	0.124114	−	0.0229956i
$445$	−1.64028	+	1.82171i	−0.0777566	+	0.0863575i
$446$	−2.44267	+	2.71286i	−0.115664	+	0.128458i
$447$	−38.7863	+	7.18621i	−1.83453	+	0.339896i
$448$	21.7563	−	2.28668i	1.02789	−	0.108035i
$449$	3.71574	+	1.20732i	0.175356	+	0.0569768i	0.395379	−	0.918518i	$-0.370613\pi$
$449$	3.71574	+	1.20732i	0.175356	+	0.0569768i	−0.220023	+	0.975495i	$0.570613\pi$
$450$	2.80398	+	1.42912i	0.132181	+	0.0673695i
$451$	33.2025	+	2.48303i	1.56345	+	0.116922i
$452$	24.7245	+	14.2747i	1.16294	+	0.671426i
$453$	16.8675	+	10.3378i	0.792503	+	0.485712i
$454$	−3.08015	−	1.37137i	−0.144558	−	0.0643615i
$455$	1.49936	+	0.157589i	0.0702909	+	0.00738787i
$456$	−3.66848	−	5.33835i	−0.171792	−	0.249991i
$457$	5.69308	−	26.7839i	0.266311	−	1.25290i	−0.618067	−	0.786125i	$-0.712084\pi$
$457$	5.69308	−	26.7839i	0.266311	−	1.25290i	0.884378	−	0.466771i	$-0.154583\pi$
$458$	−1.27615	−	0.927174i	−0.0596304	−	0.0433240i
$459$	30.8431	+	2.43297i	1.43963	+	0.113561i
$460$	−1.18904	+	3.65950i	−0.0554395	+	0.170625i
$461$	−2.42545	+	4.20100i	−0.112964	+	0.195660i	−0.916964	−	0.398970i	$-0.869368\pi$
$461$	−2.42545	+	4.20100i	−0.112964	+	0.195660i	0.804000	+	0.594629i	$0.202701\pi$
$462$	−2.72589	+	3.05085i	−0.126820	+	0.141939i
$463$	16.3454	+	28.3111i	0.759637	+	1.31573i	0.943036	+	0.332691i	$0.107956\pi$
$463$	16.3454	+	28.3111i	0.759637	+	1.31573i	−0.183400	+	0.983038i	$0.558710\pi$
$464$	8.61281	−	1.83071i	0.399840	−	0.0849886i
$465$	−2.56788	−	6.20046i	−0.119083	−	0.287539i
$466$	4.40594	−	1.96165i	0.204101	−	0.0908718i
$467$	23.1944	−	7.53631i	1.07331	−	0.348739i	0.281533	−	0.959552i	$-0.409157\pi$
$467$	23.1944	−	7.53631i	1.07331	−	0.348739i	0.791775	+	0.610813i	$0.209157\pi$
$468$	1.84643	+	4.81183i	0.0853513	+	0.222427i
$469$	−1.26820	+	1.74553i	−0.0585600	+	0.0806009i
$470$	−0.0237072	−	0.225559i	−0.00109353	−	0.0104043i
$471$	16.4224	+	30.2507i	0.756705	+	1.39388i
$472$	−8.47035	+	4.89036i	−0.389880	+	0.225097i
$473$	14.0900	+	2.55471i	0.647859	+	0.117466i
$474$	4.33138	+	4.11082i	0.198947	+	0.188816i
$475$	14.9014	−	13.4173i	0.683723	−	0.615627i
$476$	−21.8456	−	30.0678i	−1.00129	−	1.37816i
$477$	1.59548	−	30.3741i	0.0730520	−	1.39074i
$478$	−1.27356	−	3.91962i	−0.0582514	−	0.179279i
$479$	−22.8097	−	4.84835i	−1.04220	−	0.221527i	−0.345150	−	0.938548i	$-0.612172\pi$
$479$	−22.8097	−	4.84835i	−1.04220	−	0.221527i	−0.697052	+	0.717021i	$0.745505\pi$
$480$	−1.81956	+	1.55387i	−0.0830513	+	0.0709239i
$481$	0.282054	−	0.633504i	0.0128606	−	0.0288853i
$482$	0.510828	+	2.40326i	0.0232676	+	0.109465i
$483$	−5.80551	−	19.6034i	−0.264160	−	0.891985i
$484$	−11.8251	−	17.9023i	−0.537506	−	0.813741i
$485$			5.23759i			0.237827i
$486$	1.96408	+	2.85958i	0.0890923	+	0.129713i
$487$	−4.01884	+	2.91986i	−0.182111	+	0.132311i	−0.675106	−	0.737721i	$-0.735902\pi$
$487$	−4.01884	+	2.91986i	−0.182111	+	0.132311i	0.492995	+	0.870032i	$0.335902\pi$
$488$	0.659926	+	1.48222i	0.0298734	+	0.0670968i
$489$	−14.7140	+	10.1114i	−0.665390	+	0.457251i
$490$	−0.286724	−	0.258168i	−0.0129529	−	0.0116628i
$491$	1.81851	−	17.3020i	0.0820682	−	0.780827i	−0.873652	−	0.486551i	$-0.838255\pi$
$491$	1.81851	−	17.3020i	0.0820682	−	0.780827i	0.955720	−	0.294276i	$-0.0950785\pi$
$492$	−31.3338	+	12.9767i	−1.41264	+	0.585034i
$493$	−9.46785	−	10.5151i	−0.426410	−	0.473577i
$494$	−0.833803			−0.0375146
$495$	−0.674697	+	5.27874i	−0.0303254	+	0.237262i
$496$	−26.8429			−1.20528
$497$	−9.48032	−	10.5290i	−0.425250	−	0.472288i
$498$	−0.716701	+	5.44137i	−0.0321161	+	0.243834i
$499$	1.12880	−	10.7398i	0.0505321	−	0.480781i	−0.939766	−	0.341819i	$-0.888957\pi$
$499$	1.12880	−	10.7398i	0.0505321	−	0.480781i	0.990298	−	0.138961i	$-0.0443764\pi$
$500$	−7.53078	−	6.78075i	−0.336787	−	0.303244i
$501$	−18.5292	−	8.83934i	−0.827824	−	0.394913i
$502$	−1.77928	−	3.99632i	−0.0794130	−	0.178365i
$503$	22.5838	−	16.4081i	1.00696	−	0.731599i	0.0433908	−	0.999058i	$-0.486184\pi$
$503$	22.5838	−	16.4081i	1.00696	−	0.731599i	0.963569	+	0.267459i	$0.0861839\pi$
$504$	2.18553	−	8.15263i	0.0973514	−	0.363147i
$505$			5.72146i			0.254602i
$506$	−2.72120	+	0.0818625i	−0.120972	+	0.00363923i
$507$	−20.5876	−	4.94395i	−0.914328	−	0.219569i
$508$	−5.69644	−	26.7996i	−0.252738	−	1.18904i
$509$	12.2879	−	27.5991i	0.544652	−	1.22331i	−0.406234	−	0.913769i	$-0.633158\pi$
$509$	12.2879	−	27.5991i	0.544652	−	1.22331i	0.950886	−	0.309540i	$-0.100175\pi$
$510$	1.15709	+	0.409826i	0.0512369	+	0.0181474i
$511$	−0.290171	−	0.0616778i	−0.0128364	−	0.00272847i
$512$	4.97068	+	15.2982i	0.219675	+	0.676091i
$513$	21.4932	−	5.15600i	0.948950	−	0.227643i
$514$	3.44362	+	4.73974i	0.151892	+	0.209061i
$515$	1.49099	−	1.34249i	0.0657007	−	0.0591572i
$516$	−13.9857	+	4.14184i	−0.615686	+	0.182335i
$517$	−5.69342	+	2.74289i	−0.250396	+	0.120632i
$518$	−0.485590	+	0.280355i	−0.0213356	+	0.0123181i
$519$	14.3266	−	23.3757i	0.628867	−	1.02608i
$520$	0.0432921	+	0.411896i	0.00189848	+	0.0180629i
$521$	−1.84317	+	2.53691i	−0.0807507	+	0.111144i	−0.847481	−	0.530825i	$-0.821882\pi$
$521$	−1.84317	+	2.53691i	−0.0807507	+	0.111144i	0.766731	+	0.641969i	$0.221882\pi$
$522$	0.248379	−	1.56699i	0.0108712	−	0.0685853i
$523$	−9.10633	+	2.95883i	−0.398192	+	0.129380i	−0.501266	−	0.865293i	$-0.667132\pi$
$523$	−9.10633	+	2.95883i	−0.398192	+	0.129380i	0.103074	+	0.994674i	$0.467132\pi$
$524$	3.84746	−	1.71300i	0.168077	−	0.0748327i
$525$	25.9054	+	3.41209i	1.13061	+	0.148916i
$526$	0.573963	−	0.122000i	0.0250260	−	0.00531944i
$527$	21.5675	+	37.3559i	0.939493	+	1.62725i
$528$	18.4743	+	10.5719i	0.803991	+	0.460083i
$529$	−4.69766	+	8.13658i	−0.204246	+	0.353764i
$530$	0.372915	−	1.14772i	0.0161984	−	0.0498536i
$531$	−5.21713	−	32.9652i	−0.226404	−	1.43057i
$532$	−21.4807	−	15.6067i	−0.931308	−	0.676635i
$533$	−1.83841	+	8.64904i	−0.0796303	+	0.374631i
$534$	1.76122	−	0.138505i	0.0762153	−	0.00599369i
$535$	0.436698	+	0.0458988i	0.0188801	+	0.00198438i
$536$	−0.541480	−	0.241082i	−0.0233884	−	0.0104132i
$537$	0.318385	−	12.1310i	0.0137393	−	0.523489i
$538$	0.705564	+	0.407357i	0.0304190	+	0.0175624i
$539$	−4.07544	+	9.94838i	−0.175542	+	0.428507i
$540$	−1.80854	−	5.11008i	−0.0778273	−	0.219903i
$541$	12.3285	+	4.00578i	0.530045	+	0.172222i	0.561799	−	0.827274i	$-0.310109\pi$
$541$	12.3285	+	4.00578i	0.530045	+	0.172222i	−0.0317543	+	0.999496i	$0.510109\pi$
$542$	−2.39991	+	0.252241i	−0.103085	+	0.0108347i
$543$	−6.99955	+	19.7624i	−0.300379	+	0.848084i
$544$	10.2906	−	11.4289i	0.441207	−	0.490010i
$545$	0.123237	−	0.136869i	0.00527891	−	0.00586282i
$546$	−0.705585	−	0.826234i	−0.0301963	−	0.0353596i
$547$	38.1211	−	4.00669i	1.62994	−	0.171314i	0.755062	−	0.655653i	$-0.227607\pi$
$547$	38.1211	−	4.00669i	1.62994	−	0.171314i	0.874880	+	0.484340i	$0.160940\pi$
$548$	1.34033	+	0.435498i	0.0572559	+	0.0186036i
$549$	−5.52898	+	0.289099i	−0.235971	+	0.0123384i
$550$	1.31895	−	3.21964i	0.0562404	−	0.137286i
$551$	−8.75423	−	5.05426i	−0.372943	−	0.215319i
$552$	4.93608	−	2.67969i	0.210094	−	0.114055i
$553$	45.2923	+	20.1654i	1.92602	+	0.857521i
$554$	−0.0441089	−	0.00463603i	−0.00187401	−	0.000196966i
$555$	−0.314031	+	0.658278i	−0.0133299	+	0.0279424i
$556$	−7.37839	+	34.7126i	−0.312913	+	1.47214i
$557$	−20.0026	−	14.5328i	−0.847538	−	0.615773i	0.0769278	−	0.997037i	$-0.475489\pi$
$557$	−20.0026	−	14.5328i	−0.847538	−	0.615773i	−0.924466	+	0.381264i	$0.875489\pi$
$558$	−1.73383	+	4.51518i	−0.0733990	+	0.191143i
$559$	−1.17516	+	3.61678i	−0.0497042	+	0.152974i
$560$	−3.17107	+	5.49245i	−0.134002	+	0.232099i
$561$	−0.131156	−	34.2040i	−0.00553742	−	1.44409i
$562$	−0.849409	−	1.47122i	−0.0358301	−	0.0620596i
$563$	−30.7670	+	6.53972i	−1.29667	+	0.275616i	−0.804017	−	0.594607i	$-0.797308\pi$
$563$	−30.7670	+	6.53972i	−1.29667	+	0.275616i	−0.492657	+	0.870223i	$0.663974\pi$
$564$	3.91905	−	5.10678i	0.165022	−	0.215034i
$565$	−7.15185	+	3.18421i	−0.300881	+	0.133961i
$566$	0.119455	−	0.0388131i	0.00502105	−	0.00163144i
$567$	23.2973	+	16.9350i	0.978396	+	0.711204i
$568$	2.28778	−	3.14886i	0.0959931	−	0.132123i
$569$	2.39430	+	22.7803i	0.100374	+	0.954998i	0.922580	+	0.385807i	$0.126077\pi$
$569$	2.39430	+	22.7803i	0.100374	+	0.954998i	−0.822205	+	0.569191i	$0.807256\pi$
$570$	0.876653	+	0.0230084i	0.0367190	+	0.000963715i
$571$	−14.2974	+	8.25459i	−0.598326	+	0.345444i	−0.768383	−	0.639990i	$-0.778938\pi$
$571$	−14.2974	+	8.25459i	−0.598326	+	0.345444i	0.170057	+	0.985434i	$0.445605\pi$
$572$	5.13324	−	2.47301i	0.214632	−	0.103402i
$573$	−8.21261	+	34.1990i	−0.343087	+	1.42868i
$574$	5.31320	−	4.78403i	0.221769	−	0.199682i
$575$	10.2199	+	14.0665i	0.426199	+	0.586613i
$576$	−20.4791	−	1.07572i	−0.853297	−	0.0448216i
$577$	3.22929	+	9.93872i	0.134437	+	0.413754i	0.995502	−	0.0947405i	$-0.0302021\pi$
$577$	3.22929	+	9.93872i	0.134437	+	0.413754i	−0.861065	+	0.508495i	$0.830202\pi$
$578$	−4.01674	−	0.853785i	−0.167074	−	0.0355128i
$579$	−1.79280	−	9.67633i	−0.0745064	−	0.402134i
$580$	−1.00833	+	2.26474i	−0.0418686	+	0.0940383i
$581$	9.47386	+	44.5710i	0.393042	+	1.84912i
$582$	2.59846	−	2.73788i	0.107710	−	0.113489i
$583$	−33.6110	+	1.01113i	−1.39202	+	0.0418766i
$584$		−	0.0814955i		−	0.00337231i
$585$	−1.36509	−	0.365948i	−0.0564393	−	0.0151301i
$586$	−0.920251	+	0.668602i	−0.0380152	+	0.0276197i
$587$	9.74504	+	21.8877i	0.402221	+	0.903403i	0.995170	+	0.0981633i	$0.0312967\pi$
$587$	9.74504	+	21.8877i	0.402221	+	0.903403i	−0.592949	+	0.805240i	$0.702037\pi$
$588$	−0.858535	−	10.9171i	−0.0354054	−	0.450212i
$589$	22.9007	+	20.6199i	0.943608	+	0.849629i
$590$	0.138416	−	1.31694i	0.00569851	−	0.0542177i
$591$	22.6166	+	17.3565i	0.930322	+	0.713950i
$592$	1.95198	+	2.16790i	0.0802260	+	0.0891000i
$593$	−34.0556			−1.39850			−0.699248	−	0.714880i	$-0.746481\pi$
$593$	−34.0556			−1.39850			−0.699248	+	0.714880i	$0.746481\pi$
$594$	2.97156	−	2.42466i	0.121925	−	0.0994850i
$595$	10.1914			0.417808
$596$	−29.7233	−	33.0111i	−1.21751	−	1.35219i
$597$	−19.2056	−	14.7388i	−0.786033	−	0.603219i
$598$	0.0755740	−	0.719038i	0.00309045	−	0.0294037i
$599$	−28.6823	−	25.8256i	−1.17193	−	1.05521i	−0.997509	−	0.0705342i	$-0.977530\pi$
$599$	−28.6823	−	25.8256i	−1.17193	−	1.05521i	−0.174416	−	0.984672i	$-0.555804\pi$
$600$	0.562759	+	7.15600i	0.0229746	+	0.292143i
$601$	5.99885	+	13.4736i	0.244698	+	0.549601i	0.993584	−	0.113098i	$-0.0360774\pi$
$601$	5.99885	+	13.4736i	0.244698	+	0.549601i	−0.748886	+	0.662699i	$0.769411\pi$
$602$	2.48767	−	1.80740i	0.101390	−	0.0736642i
$603$	1.43036	−	1.43002i	0.0582488	−	0.0582349i
$604$			22.2782i			0.906486i
$605$	5.87750	+	0.262142i	0.238954	+	0.0106576i
$606$	2.83852	−	2.99081i	0.115307	−	0.121494i
$607$	−3.39430	−	15.9689i	−0.137770	−	0.648159i	−0.991786	−	0.127911i	$-0.959173\pi$
$607$	−3.39430	−	15.9689i	−0.137770	−	0.648159i	0.854015	−	0.520248i	$-0.174160\pi$
$608$	4.46880	−	10.0371i	0.181234	−	0.407058i
$609$	−2.39968	−	12.9518i	−0.0972397	−	0.524834i
$610$	−0.214866	−	0.0456712i	−0.00869968	−	0.00184917i
$611$	−0.518632	−	1.59618i	−0.0209816	−	0.0645747i
$612$	15.8136	+	31.0450i	0.639225	+	1.25492i
$613$	9.77045	+	13.4479i	0.394625	+	0.543155i	0.959385	−	0.282101i	$-0.0910312\pi$
$613$	9.77045	+	13.4479i	0.394625	+	0.543155i	−0.564760	+	0.825255i	$0.691031\pi$
$614$	0.475823	−	0.428433i	0.0192026	−	0.0172901i
$615$	2.17155	−	9.04280i	0.0875655	−	0.364641i
$616$	−9.18161	−	1.66475i	−0.369938	−	0.0670748i
$617$	−25.5162	+	14.7318i	−1.02724	+	0.593080i	−0.916194	−	0.400735i	$-0.868755\pi$
$617$	−25.5162	+	14.7318i	−1.02724	+	0.593080i	−0.111051	+	0.993815i	$0.535422\pi$
$618$	−1.44543	−	0.0379362i	−0.0581436	−	0.00152602i
$619$	4.61802	+	43.9375i	0.185614	+	1.76600i	0.550394	+	0.834905i	$0.314477\pi$
$619$	4.61802	+	43.9375i	0.185614	+	1.76600i	−0.364780	+	0.931094i	$0.618856\pi$
$620$	4.44218	−	6.11413i	0.178402	−	0.245550i
$621$	2.49823	+	19.0022i	0.100250	+	0.762534i
$622$	0.573815	−	0.186444i	0.0230079	−	0.00747571i
$623$	13.3994	−	5.96582i	0.536838	−	0.239015i
$624$	−3.44146	+	4.48444i	−0.137769	+	0.179521i
$625$	−20.3366	+	4.32267i	−0.813462	+	0.172907i
$626$	1.24004	+	2.14781i	0.0495620	+	0.0858438i
$627$	−7.64014	−	23.2107i	−0.305118	−	0.926947i
$628$	−19.3808	+	33.5685i	−0.773378	+	1.33953i
$629$	1.44860	−	4.45832i	0.0577593	−	0.177765i
$630$	0.719047	+	0.888166i	0.0286475	+	0.0353854i
$631$	9.62953	+	6.99627i	0.383346	+	0.278517i	0.762723	−	0.646725i	$-0.223862\pi$
$631$	9.62953	+	6.99627i	0.383346	+	0.278517i	−0.379378	+	0.925242i	$0.623862\pi$
$632$	−2.83176	+	13.3224i	−0.112641	+	0.529936i
$633$	8.01940	−	16.8104i	0.318743	−	0.668155i
$634$	1.38362	+	0.145424i	0.0549505	+	0.00577553i
$635$	6.86350	+	3.05583i	0.272370	+	0.121267i
$636$	30.1019	−	16.3417i	1.19362	−	0.647990i
$637$	−2.47259	−	1.42755i	−0.0979676	−	0.0565616i
$638$	−1.74912	−	0.130807i	−0.0692481	−	0.00517869i
$639$	7.23237	+	11.1398i	0.286108	+	0.440683i
$640$	−3.40152	−	1.10522i	−0.134457	−	0.0436877i
$641$	−0.424548	+	0.0446218i	−0.0167686	+	0.00176245i	−0.112909	−	0.993605i	$-0.536017\pi$
$641$	−0.424548	+	0.0446218i	−0.0167686	+	0.00176245i	0.0961404	+	0.995368i	$0.469350\pi$
$642$	−0.205507	−	0.240647i	−0.00811071	−	0.00949757i
$643$	19.7755	−	21.9629i	0.779870	−	0.866133i	−0.213983	−	0.976837i	$-0.568644\pi$
$643$	19.7755	−	21.9629i	0.779870	−	0.866133i	0.993853	+	0.110704i	$0.0353105\pi$
$644$	15.4055	−	17.1096i	0.607063	−	0.674212i
$645$	1.33536	−	3.77023i	0.0525798	−	0.148453i
$646$	−5.60561	+	0.589174i	−0.220550	+	0.0231807i
$647$	−12.2213	−	3.97095i	−0.480470	−	0.156114i	0.0587611	−	0.998272i	$-0.481285\pi$
$647$	−12.2213	−	3.97095i	−0.480470	−	0.156114i	−0.539231	+	0.842158i	$0.681285\pi$
$648$	−3.21998	+	7.22756i	−0.126493	+	0.283925i
$649$	−35.8446	+	8.75331i	−1.40703	+	0.343597i
$650$	0.800217	+	0.462005i	0.0313871	+	0.0181213i
$651$	−1.05355	+	40.1420i	−0.0412920	+	1.57329i
$652$	−18.3666	−	8.17734i	−0.719292	−	0.320249i
$653$	10.4284	+	1.09606i	0.408093	+	0.0428923i	0.306351	−	0.951919i	$-0.400892\pi$
$653$	10.4284	+	1.09606i	0.408093	+	0.0428923i	0.101742	+	0.994811i	$0.467558\pi$
$654$	−0.132324	+	0.0104062i	−0.00517427	+	0.000406913i
$655$	−0.240112	+	1.12964i	−0.00938194	+	0.0441386i
$656$	−30.0931	−	21.8639i	−1.17494	−	0.853642i
$657$	0.259610	+	0.0996906i	0.0101284	+	0.00388930i
$658$	−0.419352	+	1.29063i	−0.0163480	+	0.0503141i
$659$	10.1911	−	17.6516i	0.396990	−	0.687607i	−0.596363	−	0.802715i	$-0.703388\pi$
$659$	10.1911	−	17.6516i	0.396990	−	0.687607i	0.993353	+	0.115108i	$0.0367214\pi$
$660$	−5.46529	+	2.45846i	−0.212736	+	0.0956953i
$661$	−2.66875	−	4.62241i	−0.103802	−	0.179791i	0.809446	−	0.587194i	$-0.199768\pi$
$661$	−2.66875	−	4.62241i	−0.103802	−	0.179791i	−0.913248	+	0.407403i	$0.866434\pi$
$662$	−0.675828	+	0.143652i	−0.0262668	+	0.00558318i
$663$	9.00588	+	1.18619i	0.349760	+	0.0460680i
$664$	−11.4357	+	5.09149i	−0.443790	+	0.197588i
$665$	6.92451	−	2.24991i	0.268521	−	0.0872477i
$666$	0.490739	−	0.188310i	0.0190157	−	0.00729685i
$667$	5.15205	−	7.09119i	0.199488	−	0.274572i
$668$	−2.41655	−	22.9919i	−0.0934990	−	0.889584i
$669$	14.8466	−	24.2241i	0.574001	−	0.936559i
$670$	0.0694968	−	0.0401240i	0.00268490	−	0.00155013i
$671$	0.822560	+	6.06535i	0.0317546	+	0.234150i
$672$	13.7276	−	4.06541i	0.529553	−	0.156826i
$673$	22.3581	−	20.1313i	0.861840	−	0.776005i	−0.114231	−	0.993454i	$-0.536440\pi$
$673$	22.3581	−	20.1313i	0.861840	−	0.776005i	0.976072	+	0.217450i	$0.0697738\pi$
$674$	1.74963	+	2.40816i	0.0673933	+	0.0927589i
$675$	−23.4844	−	6.96098i	−0.903915	−	0.267928i
$676$	−7.36788	−	22.6760i	−0.283380	−	0.872154i
$677$	−26.3994	−	5.61137i	−1.01461	−	0.215662i	−0.329543	−	0.944141i	$-0.606895\pi$
$677$	−26.3994	−	5.61137i	−1.01461	−	0.215662i	−0.685069	+	0.728478i	$0.740228\pi$
$678$	5.31828	+	1.88366i	0.204247	+	0.0723414i
$679$	12.7466	−	28.6294i	0.489170	−	1.09869i
$680$	0.582101	+	2.73857i	0.0223225	+	0.105019i
$681$	25.5159	+	6.12744i	0.977772	+	0.234804i
$682$	5.13278	+	1.49868i	0.196544	+	0.0573874i
$683$		−	19.1623i		−	0.733224i	−0.930374	−	0.366612i	$-0.880518\pi$
$683$		−	19.1623i		−	0.733224i	0.930374	−	0.366612i	$-0.119482\pi$
$684$	17.5980	+	17.6023i	0.672878	+	0.673039i
$685$	−0.312646	+	0.227151i	−0.0119456	+	0.00867898i
$686$	−1.08875	−	2.44537i	−0.0415685	−	0.0933645i
$687$	11.0806	+	5.28599i	0.422751	+	0.201673i
$688$	−11.8887	−	10.7047i	−0.453253	−	0.408111i
$689$	0.933454	−	8.88122i	0.0355618	−	0.338348i
$690$	−0.0992994	+	0.753906i	−0.00378026	+	0.0287007i
$691$	−4.07683	−	4.52777i	−0.155090	−	0.172245i	0.660593	−	0.750744i	$-0.270305\pi$
$691$	−4.07683	−	4.52777i	−0.155090	−	0.172245i	−0.815683	+	0.578500i	$0.803638\pi$
$692$	30.8741			1.17366
$693$	16.5347	−	27.2123i	0.628103	−	1.03371i
$694$	−0.626882			−0.0237961
$695$	−6.51155	−	7.23181i	−0.246997	−	0.274318i
$696$	3.34325	−	1.38459i	0.126726	−	0.0524826i
$697$	−6.24803	+	59.4461i	−0.236661	+	2.25168i
$698$	−4.44988	−	4.00669i	−0.168430	−	0.151655i
$699$	−30.9361	+	21.2590i	−1.17011	+	0.804091i
$700$	11.9679	+	26.8804i	0.452345	+	1.01598i
$701$	−20.3206	+	14.7638i	−0.767499	+	0.557621i	−0.901201	−	0.433401i	$-0.857313\pi$
$701$	−20.3206	+	14.7638i	−0.767499	+	0.557621i	0.133702	+	0.991022i	$0.457313\pi$
$702$	0.532026	+	0.868538i	0.0200800	+	0.0327808i
$703$		−	3.34897i		−	0.126309i
$704$	0.681732	+	22.6615i	0.0256937	+	0.854087i
$705$	0.501239	+	1.69253i	0.0188778	+	0.0637443i
$706$	−0.0926527	−	0.435897i	−0.00348703	−	0.0164052i
$707$	13.9242	−	31.2743i	0.523674	−	1.17619i
$708$	28.5808	−	24.4074i	1.07413	−	0.917285i
$709$	−5.60465	−	1.19131i	−0.210487	−	0.0447404i	0.101461	−	0.994840i	$-0.467648\pi$
$709$	−5.60465	−	1.19131i	−0.210487	−	0.0447404i	−0.311948	+	0.950099i	$0.600982\pi$
$710$	0.162840	+	0.501168i	0.00611126	+	0.0188085i
$711$	−38.9755	−	25.3176i	−1.46170	−	0.949484i
$712$	2.36842	+	3.25985i	0.0887603	+	0.122168i
$713$	−19.8575	+	17.8797i	−0.743668	+	0.669601i
$714$	−5.32744	−	5.05616i	−0.199374	−	0.189222i
$715$	−0.278748	+	1.53738i	−0.0104246	+	0.0574948i
$716$	11.8346	−	6.83273i	0.442281	−	0.255351i
$717$	15.3038	+	28.1900i	0.571529	+	1.05278i
$718$	0.0581538	+	0.553297i	0.00217028	+	0.0206489i
$719$	6.16104	−	8.47994i	0.229768	−	0.316248i	−0.678530	−	0.734573i	$-0.737383\pi$
$719$	6.16104	−	8.47994i	0.229768	−	0.316248i	0.908298	+	0.418325i	$0.137383\pi$
$720$	3.74207	−	4.61994i	0.139459	−	0.172175i
$721$	−11.4171	+	3.70965i	−0.425196	+	0.138155i
$722$	0.184149	−	0.0819884i	0.00685332	−	0.00305129i
$723$	−7.31675	−	17.6672i	−0.272113	−	0.657049i
$724$	−23.0933	+	4.90863i	−0.858255	+	0.182428i
$725$	5.60107	+	9.70134i	0.208019	+	0.360299i
$726$	−2.94233	−	3.05296i	−0.109200	−	0.113306i
$727$	17.0164	−	29.4732i	0.631102	−	1.09310i	−0.356225	−	0.934400i	$-0.615936\pi$
$727$	17.0164	−	29.4732i	0.631102	−	1.09310i	0.987327	−	0.158700i	$-0.0507304\pi$
$728$	0.765784	−	2.35684i	0.0283818	−	0.0873503i
$729$	−19.0850	−	19.0987i	−0.706853	−	0.707360i
$730$	0.00892634	+	0.00648536i	0.000330379	+	0.000240034i
$731$	−5.34491	+	25.1458i	−0.197689	+	0.930052i
$732$	−3.53108	−	5.13841i	−0.130513	−	0.189921i
$733$	29.4641	+	3.09680i	1.08828	+	0.114383i	0.631636	−	0.775265i	$-0.282384\pi$
$733$	29.4641	+	3.09680i	1.08828	+	0.114383i	0.456646	+	0.889648i	$0.349051\pi$
$734$	−2.69535	−	1.20005i	−0.0994871	−	0.0442945i
$735$	2.56027	+	1.56915i	0.0944369	+	0.0578788i
$736$	8.25054	+	4.76345i	0.304119	+	0.175583i
$737$	−1.70596	−	1.44557i	−0.0628397	−	0.0532484i
$738$	−5.62144	+	3.64965i	−0.206928	+	0.134346i
$739$	25.4725	+	8.27651i	0.937020	+	0.304456i	0.737430	−	0.675423i	$-0.236039\pi$
$739$	25.4725	+	8.27651i	0.937020	+	0.304456i	0.199590	+	0.979880i	$0.436039\pi$
$740$	−0.816822	+	0.0858515i	−0.0300270	+	0.00315596i
$741$	6.38086	−	1.18223i	0.234407	−	0.0434302i
$742$	−4.83158	+	5.36601i	−0.177373	+	0.196992i
$743$	16.5430	−	18.3729i	0.606904	−	0.674035i	−0.358880	−	0.933384i	$-0.616841\pi$
$743$	16.5430	−	18.3729i	0.606904	−	0.674035i	0.965784	+	0.259348i	$0.0835078\pi$
$744$	−10.8468	+	2.00967i	−0.397664	+	0.0736781i
$745$	12.1141	−	1.27325i	0.443827	−	0.0466481i
$746$	6.72208	+	2.18414i	0.246113	+	0.0799669i
$747$	−2.23047	−	42.6575i	−0.0816087	−	1.56076i
$748$	32.7631	−	20.2531i	1.19794	−	0.740528i
$749$	−2.27535	−	1.31367i	−0.0831394	−	0.0480006i
$750$	−1.70747	−	1.04648i	−0.0623479	−	0.0382120i
$751$	−6.74831	−	3.00454i	−0.246249	−	0.109637i	0.279901	−	0.960029i	$-0.409698\pi$
$751$	−6.74831	−	3.00454i	−0.246249	−	0.109637i	−0.526150	+	0.850392i	$0.676365\pi$
$752$	7.02161	+	0.738001i	0.256052	+	0.0269121i
$753$	19.2826	+	28.0599i	0.702697	+	1.02256i
$754$	0.0968478	−	0.455633i	0.00352699	−	0.0165932i
$755$	−4.94229	−	3.59079i	−0.179868	−	0.130682i
$756$	−2.55056	+	32.3338i	−0.0927628	+	1.17597i
$757$	0.0920305	−	0.283241i	0.00334491	−	0.0102946i	−0.949370	−	0.314160i	$-0.898277\pi$
$757$	0.0920305	−	0.283241i	0.00334491	−	0.0102946i	0.952715	+	0.303865i	$0.0982772\pi$
$758$	−2.64538	+	4.58194i	−0.0960846	+	0.166423i
$759$	20.7085	−	4.48479i	0.751670	−	0.162787i
$760$	1.00008	+	1.73219i	0.0362768	+	0.0628333i
$761$	−24.8141	+	5.27440i	−0.899511	+	0.191197i	−0.634386	−	0.773017i	$-0.718747\pi$
$761$	−24.8141	+	5.27440i	−0.899511	+	0.191197i	−0.265126	+	0.964214i	$0.585413\pi$
$762$	−2.07175	−	5.00249i	−0.0750516	−	0.181221i
$763$	−1.00673	+	0.448224i	−0.0364460	+	0.0162268i
$764$	−37.6681	+	12.2391i	−1.36278	+	0.442795i
$765$	−9.43598	−	1.49567i	−0.341159	−	0.0540760i
$766$	−2.33292	+	3.21099i	−0.0842920	+	0.116018i
$767$	−1.02428	−	9.74536i	−0.0369846	−	0.351885i
$768$	−10.0680	−	18.5457i	−0.363299	−	0.669209i
$769$	−9.05193	+	5.22613i	−0.326421	+	0.188459i	−0.654251	−	0.756278i	$-0.727016\pi$
$769$	−9.05193	+	5.22613i	−0.326421	+	0.188459i	0.327830	+	0.944737i	$0.393683\pi$
$770$	0.913010	−	0.873197i	0.0329026	−	0.0314678i
$771$	−33.0734	−	31.3892i	−1.19111	−	1.13046i
$772$	8.23555	−	7.41532i	0.296404	−	0.266883i
$773$	5.51171	+	7.58622i	0.198243	+	0.272857i	0.896552	−	0.442939i	$-0.146064\pi$
$773$	5.51171	+	7.58622i	0.198243	+	0.272857i	−0.698309	+	0.715796i	$0.746064\pi$
$774$	−2.56852	+	1.30834i	−0.0923236	+	0.0470273i
$775$	−10.5529	−	32.4785i	−0.379072	−	1.16666i
$776$	8.42112	+	1.78996i	0.302301	+	0.0642560i
$777$	3.31857	−	2.83399i	0.119053	−	0.101669i
$778$	2.23750	−	5.02552i	0.0802184	−	0.180174i
$779$	8.87840	+	41.7696i	0.318102	+	1.49655i
$780$	−0.451922	−	1.52600i	−0.0161814	−	0.0546395i
$781$	11.6142	−	8.98399i	0.415590	−	0.321472i
$782$		−	4.88746i		−	0.174775i
$783$	0.321022	+	12.3439i	0.0114724	+	0.441135i
$784$	9.71683	−	7.05969i	0.347030	−	0.252132i
$785$	−4.32321	−	9.71008i	−0.154302	−	0.346568i
$786$	0.685948	−	0.471379i	0.0244670	−	0.0168135i
$787$	6.51938	+	5.87007i	0.232391	+	0.209246i	0.777096	−	0.629382i	$-0.216692\pi$
$787$	6.51938	+	5.87007i	0.232391	+	0.209246i	−0.544705	+	0.838627i	$0.683359\pi$
$788$	−3.35579	+	31.9282i	−0.119545	+	1.13739i
$789$	−4.21940	+	1.74744i	−0.150215	+	0.0622104i
$790$	−1.23387	−	1.37035i	−0.0438992	−	0.0487550i
$791$	46.8423			1.66552
$792$	8.25669	+	2.88882i	0.293389	+	0.102650i
$793$	−1.62553			−0.0577242
$794$	−0.606280	−	0.673343i	−0.0215161	−	0.0238960i
$795$	−1.22650	+	9.31189i	−0.0434995	+	0.330259i
$796$	2.84967	−	27.1128i	0.101004	−	0.960989i
$797$	−16.2068	−	14.5926i	−0.574073	−	0.516897i	0.330167	−	0.943923i	$-0.392895\pi$
$797$	−16.2068	−	14.5926i	−0.574073	−	0.516897i	−0.904240	+	0.427025i	$0.859562\pi$
$798$	−4.73591	−	2.25926i	−0.167649	−	0.0799770i
$799$	−4.61462	−	10.3646i	−0.163253	−	0.366673i
$800$	−9.85029	+	7.15665i	−0.348260	+	0.253026i
$801$	−13.2817	+	3.55712i	−0.469286	+	0.125685i
$802$		−	5.63607i		−	0.199017i
$803$	0.0861700	−	0.295120i	0.00304087	−	0.0104146i
$804$	2.21469	+	0.531841i	0.0781062	+	0.0187566i
$805$	1.31261	+	6.17535i	0.0462634	+	0.217652i
$806$	−0.577581	+	1.29727i	−0.0203444	+	0.0456943i
$807$	−5.97706	−	2.11699i	−0.210403	−	0.0745216i
$808$	9.19909	+	1.95533i	0.323623	+	0.0687882i
$809$	−2.71969	−	8.37033i	−0.0956190	−	0.294285i	0.891795	−	0.452439i	$-0.149446\pi$
$809$	−2.71969	−	8.37033i	−0.0956190	−	0.294285i	−0.987415	+	0.158154i	$0.949446\pi$
$810$	−0.535402	−	0.927855i	−0.0188121	−	0.0326015i
$811$	−24.6647	−	33.9480i	−0.866094	−	1.19208i	−0.980082	−	0.198594i	$-0.936363\pi$
$811$	−24.6647	−	33.9480i	−0.866094	−	1.19208i	0.113988	−	0.993482i	$-0.463637\pi$
$812$	11.0233	−	9.92544i	0.386843	−	0.348315i
$813$	18.0082	−	5.33310i	0.631575	−	0.187040i
$814$	−0.252212	−	0.523518i	−0.00884004	−	0.0183493i
$815$	4.77442	−	2.75651i	0.167240	−	0.0965563i
$816$	−19.9680	+	32.5804i	−0.699019	+	1.14054i
$817$	1.91974	+	18.2651i	0.0671633	+	0.639016i
$818$	1.17202	−	1.61315i	0.0409787	−	0.0564024i
$819$	6.57114	+	5.32251i	0.229614	+	0.185983i
$820$	9.96009	−	3.23623i	0.347822	−	0.113014i
$821$	31.8328	−	14.1729i	1.11097	−	0.494637i	0.232580	−	0.972577i	$-0.425283\pi$
$821$	31.8328	−	14.1729i	1.11097	−	0.494637i	0.878392	+	0.477940i	$0.158616\pi$
$822$	0.276125	+	0.0363693i	0.00963096	+	0.00126853i
$823$	−14.2424	+	3.02732i	−0.496459	+	0.105526i	−0.449335	−	0.893363i	$-0.648339\pi$
$823$	−14.2424	+	3.02732i	−0.496459	+	0.105526i	−0.0471242	+	0.998889i	$0.515006\pi$
$824$	−1.64894	−	2.85604i	−0.0574435	−	0.0994950i
$825$	−5.52854	+	26.5091i	−0.192479	+	0.922930i
$826$	−3.96162	+	6.86173i	−0.137842	+	0.238750i
$827$	−14.8117	+	45.5858i	−0.515054	+	1.58517i	0.268131	+	0.963383i	$0.413594\pi$
$827$	−14.8117	+	45.5858i	−0.515054	+	1.58517i	−0.783184	+	0.621790i	$0.786406\pi$
$828$	−16.7745	+	13.5804i	−0.582955	+	0.471952i
$829$	10.6108	+	7.70918i	0.368527	+	0.267751i	0.756600	−	0.653878i	$-0.226859\pi$
$829$	10.6108	+	7.70918i	0.368527	+	0.267751i	−0.388073	+	0.921629i	$0.626859\pi$
$830$	0.352365	−	1.65775i	0.0122308	−	0.0575412i
$831$	0.344126	−	0.0270626i	0.0119376	−	0.000938792i
$832$	−5.98798	−	0.629362i	−0.207596	−	0.0218192i
$833$	−17.6318	−	7.85019i	−0.610906	−	0.271993i
$834$	−0.184004	+	7.01083i	−0.00637154	+	0.242765i
$835$	5.49012	+	3.16972i	0.189994	+	0.109693i
$836$	17.7895	−	20.9938i	0.615261	−	0.726085i
$837$	6.86658	−	37.0117i	0.237344	−	1.27931i
$838$	−0.664133	−	0.215790i	−0.0229421	−	0.00745434i
$839$	27.7651	−	2.91823i	0.958559	−	0.100749i	0.387690	−	0.921790i	$-0.373273\pi$
$839$	27.7651	−	2.91823i	0.958559	−	0.100749i	0.570869	+	0.821041i	$0.306606\pi$
$840$	−0.870175	+	2.45683i	−0.0300239	+	0.0847688i
$841$	−15.6261	+	17.3545i	−0.538830	+	0.598431i
$842$	4.28576	−	4.75982i	0.147697	−	0.164034i
$843$	8.58629	+	10.0545i	0.295728	+	0.346294i
$844$	20.8592	−	2.19239i	0.718003	−	0.0754651i
$845$	6.21810	+	2.02038i	0.213909	+	0.0695033i
$846$	0.577677	−	1.13342i	0.0198609	−	0.0389678i
$847$	−31.4892	−	15.7368i	−1.08198	−	0.540725i
$848$	32.5338	+	18.7834i	1.11721	+	0.645024i
$849$	−0.859120	+	0.466398i	−0.0294849	+	0.0160067i
$850$	5.70628	+	2.54060i	0.195724	+	0.0871418i
$851$	2.88802	+	0.303543i	0.0990001	+	0.0104053i
$852$	−6.43977	+	13.4992i	−0.220623	+	0.462474i
$853$	0.697099	−	3.27959i	0.0238682	−	0.112291i	−0.964601	−	0.263714i	$-0.915052\pi$
$853$	0.697099	−	3.27959i	0.0238682	−	0.112291i	0.988469	+	0.151423i	$0.0483857\pi$
$854$	1.06334	+	0.772561i	0.0363867	+	0.0264365i
$855$	−6.74141	+	1.06691i	−0.230551	+	0.0364875i
$856$	0.223040	−	0.686447i	0.00762336	−	0.0234623i
$857$	5.78843	−	10.0259i	0.197729	−	0.342477i	−0.750063	−	0.661367i	$-0.769977\pi$
$857$	5.78843	−	10.0259i	0.197729	−	0.342477i	0.947792	+	0.318890i	$0.103310\pi$
$858$	0.908433	−	0.665353i	0.0310134	−	0.0227148i
$859$	−17.2606	−	29.8962i	−0.588923	−	1.02005i	−0.994374	−	0.105928i	$-0.966219\pi$
$859$	−17.2606	−	29.8962i	−0.588923	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$860$	4.40570	−	0.936459i	0.150233	−	0.0319330i
$861$	−33.8773	+	44.1443i	−1.15454	+	1.50443i
$862$	−5.73692	+	2.55424i	−0.195400	+	0.0869979i
$863$	23.6801	−	7.69412i	0.806079	−	0.261911i	0.123143	−	0.992389i	$-0.460703\pi$
$863$	23.6801	−	7.69412i	0.806079	−	0.261911i	0.682936	+	0.730478i	$0.260703\pi$
$864$	−13.3066	+	1.74943i	−0.452701	+	0.0595167i
$865$	−4.97627	+	6.84925i	−0.169198	+	0.232882i
$866$	0.0234607	+	0.223214i	0.000797227	+	0.00758511i
$867$	31.9496	+	0.838539i	1.08506	+	0.0284783i
$868$	−39.1614	+	22.6098i	−1.32922	+	0.767428i
$869$	−24.3412	+	45.2503i	−0.825720	+	1.53501i
$870$	−0.114398	+	0.476376i	−0.00387845	+	0.0161507i
$871$	0.441304	−	0.397352i	0.0149530	−	0.0134638i
$872$	−0.177944	−	0.244919i	−0.00602596	−	0.00829402i
$873$	−16.0033	+	24.6365i	−0.541631	+	0.833820i
$874$	−1.07898	−	3.32075i	−0.0364970	−	0.112326i
$875$	−16.2634	−	3.45690i	−0.549804	−	0.116865i
$876$	0.0570509	+	0.307922i	0.00192757	+	0.0104037i
$877$	−16.5596	+	37.1936i	−0.559179	+	1.25594i	0.383902	+	0.923374i	$0.374580\pi$
$877$	−16.5596	+	37.1936i	−0.559179	+	1.25594i	−0.943081	+	0.332563i	$0.892086\pi$
$878$	−1.64398	−	7.73430i	−0.0554815	−	0.261020i
$879$	6.09443	−	6.42142i	0.205560	−	0.216589i
$880$	−5.43128	−	3.70175i	−0.183088	−	0.124786i
$881$			15.5331i			0.523323i	0.965160	+	0.261661i	$0.0842703\pi$
$881$			15.5331i			0.523323i	−0.965160	+	0.261661i	$0.915730\pi$
$882$	−0.559865	−	2.09044i	−0.0188516	−	0.0703889i
$883$	−11.1691	+	8.11482i	−0.375870	+	0.273086i	−0.759641	−	0.650343i	$-0.774625\pi$
$883$	−11.1691	+	8.11482i	−0.375870	+	0.273086i	0.383771	+	0.923428i	$0.374625\pi$
$884$	4.16058	+	9.34482i	0.139936	+	0.314300i
$885$	0.808000	+	10.2745i	0.0271606	+	0.345372i
$886$	3.12153	+	2.81064i	0.104870	+	0.0944253i
$887$	3.28428	−	31.2478i	0.110275	−	1.04920i	−0.789770	−	0.613403i	$-0.789800\pi$
$887$	3.28428	−	31.2478i	0.110275	−	1.04920i	0.900046	−	0.435796i	$-0.143533\pi$
$888$	0.951074	+	0.729875i	0.0319159	+	0.0244930i
$889$	−30.0799	−	33.4071i	−1.00885	−	1.12044i
$890$	−0.545534			−0.0182864
$891$	−19.3027	+	22.7685i	−0.646664	+	0.762775i
$892$	31.9947			1.07126
$893$	−5.42350	−	6.02341i	−0.181491	−	0.201566i
$894$	−6.96417	−	5.34446i	−0.232917	−	0.178745i
$895$	−0.391696	+	3.72674i	−0.0130930	+	0.124571i
$896$	15.9034	+	14.3195i	0.531296	+	0.478381i
$897$	0.441160	+	5.60975i	0.0147299	+	0.187304i
$898$	0.353645	+	0.794300i	0.0118013	+	0.0265061i
$899$	−13.9278	+	10.1191i	−0.464516	+	0.337491i
$900$	−7.13588	−	26.6442i	−0.237863	−	0.888140i
$901$		−	60.3676i		−	2.01114i
$902$	4.53357	+	5.86086i	0.150951	+	0.195145i
$903$	−16.4748	+	17.3587i	−0.548247	+	0.577663i
$904$	2.67548	+	12.5871i	0.0889850	+	0.418641i
$905$	2.63321	−	5.91428i	0.0875308	−	0.196597i
$906$	0.802064	+	4.32899i	0.0266468	+	0.143821i
$907$	45.3069	+	9.63029i	1.50439	+	0.319768i	0.885103	−	0.465395i	$-0.154088\pi$
$907$	45.3069	+	9.63029i	1.50439	+	0.319768i	0.619289	+	0.785163i	$0.287421\pi$
$908$	9.13162	+	28.1042i	0.303044	+	0.932672i
$909$	−17.4818	+	26.9125i	−0.579834	+	0.892632i
$910$	0.197208	+	0.271434i	0.00653738	+	0.00899794i
$911$	14.4923	−	13.0489i	0.480151	−	0.432330i	−0.393176	−	0.919463i	$-0.628624\pi$
$911$	14.4923	−	13.0489i	0.480151	−	0.432330i	0.873328	+	0.487133i	$0.161957\pi$
$912$	−6.37451	+	26.5448i	−0.211081	+	0.878985i
$913$	−46.7957	+	6.34625i	−1.54871	+	0.210030i
$914$	5.27734	−	3.04687i	0.174559	−	0.100782i
$915$	1.70907	+	0.0448557i	0.0565000	+	0.00148288i
$916$	1.44511	+	13.7493i	0.0477479	+	0.454290i
$917$	4.06166	−	5.59040i	0.134128	−	0.184611i
$918$	4.19050	+	5.46320i	0.138307	+	0.180312i
$919$	51.8032	−	16.8319i	1.70883	−	0.555232i	0.718691	−	0.695329i	$-0.244742\pi$
$919$	51.8032	−	16.8319i	1.70883	−	0.555232i	0.990138	+	0.140097i	$0.0447415\pi$
$920$	−1.58442	+	0.705430i	−0.0522368	+	0.0232573i
$921$	−3.03387	+	3.95333i	−0.0999695	+	0.130267i
$922$	−1.05595	+	0.224448i	−0.0347757	+	0.00739181i
$923$	1.94975	+	3.37706i	0.0641767	+	0.111157i
$924$	35.8571	−	0.137495i	1.17961	−	0.00452326i
$925$	−1.85565	+	3.21408i	−0.0610133	+	0.105678i
$926$	−2.24815	+	6.91908i	−0.0738787	+	0.227375i
$927$	11.1152	−	1.75912i	0.365072	−	0.0577770i
$928$	4.96572	+	3.60781i	0.163008	+	0.118432i
$929$	3.27981	−	15.4303i	0.107607	−	0.506251i	−0.891025	−	0.453955i	$-0.850013\pi$
$929$	3.27981	−	15.4303i	0.107607	−	0.506251i	0.998632	−	0.0522962i	$-0.0166540\pi$
$930$	0.643061	−	1.34800i	0.0210868	−	0.0442026i
$931$	−13.7129	−	1.44128i	−0.449421	−	0.0472361i
$932$	−38.6156	−	17.1928i	−1.26490	−	0.563169i
$933$	−4.12689	+	2.24040i	−0.135108	+	0.0733474i
$934$	4.70027	+	2.71370i	0.153798	+	0.0887950i
$935$	−0.787682	+	10.5327i	−0.0257600	+	0.344456i
$936$	−1.05490	+	2.06975i	−0.0344806	+	0.0676519i
$937$	−26.3765	−	8.57025i	−0.861683	−	0.279978i	−0.155352	−	0.987859i	$-0.549651\pi$
$937$	−26.3765	−	8.57025i	−0.861683	−	0.279978i	−0.706331	+	0.707882i	$0.749651\pi$
$938$	−0.477528	+	0.0501902i	−0.0155918	+	0.00163877i
$939$	−12.5350	−	14.6784i	−0.409065	−	0.479011i
$940$	−1.33009	+	1.47722i	−0.0433828	+	0.0481815i
$941$	−6.20656	+	6.89308i	−0.202328	+	0.224708i	−0.835766	−	0.549085i	$-0.814976\pi$
$941$	−6.20656	+	6.89308i	−0.202328	+	0.224708i	0.633438	+	0.773793i	$0.281643\pi$
$942$	−2.55745	+	7.22063i	−0.0833261	+	0.235261i
$943$	−36.8251	+	3.87048i	−1.19919	+	0.126040i
$944$	39.2045	+	12.7383i	1.27600	+	0.414596i
$945$	−6.76197	−	5.77737i	−0.219967	−	0.187938i
$946$	1.67565	+	2.71066i	0.0544801	+	0.0881313i
$947$	4.44675	+	2.56733i	0.144500	+	0.0834270i	0.570507	−	0.821293i	$-0.306747\pi$
$947$	4.44675	+	2.56733i	0.144500	+	0.0834270i	−0.426007	+	0.904720i	$0.640080\pi$
$948$	1.37316	−	52.3195i	0.0445983	−	1.69926i
$949$	0.0745893	+	0.0332093i	0.00242127	+	0.00107802i
$950$	4.43796	+	0.466449i	0.143987	+	0.0151336i
$951$	−10.7946	+	0.848907i	−0.350040	+	0.0275277i
$952$	3.48296	−	16.3860i	0.112883	−	0.531074i
$953$	33.1526	+	24.0868i	1.07392	+	0.780248i	0.976613	−	0.215006i	$-0.0689772\pi$
$953$	33.1526	+	24.0868i	1.07392	+	0.780248i	0.0973068	+	0.995254i	$0.468977\pi$
$954$	5.26093	−	4.25918i	0.170329	−	0.137896i
$955$	3.35615	−	10.3292i	0.108602	−	0.334244i
$956$	−18.0606	+	31.2819i	−0.584122	+	1.01173i
$957$	13.5710	−	1.47900i	0.438687	−	0.0478093i
$958$	−2.59478	−	4.49429i	−0.0838336	−	0.145204i
$959$	2.26178	−	0.480756i	0.0730366	−	0.0155244i
$960$	6.27835	+	0.826942i	0.202633	+	0.0266894i
$961$	19.6250	−	8.73759i	0.633063	−	0.281858i
$962$	0.146771	−	0.0476889i	0.00473210	−	0.00153755i
$963$	1.91389	+	1.55022i	0.0616743	+	0.0499551i
$964$	12.6572	−	17.4212i	0.407663	−	0.561099i
$965$	0.317647	+	3.02221i	0.0102254	+	0.0972883i
$966$	2.37755	−	3.87929i	0.0764964	−	0.124814i
$967$	13.7225	−	7.92268i	0.441285	−	0.254776i	−0.262857	−	0.964835i	$-0.584665\pi$
$967$	13.7225	−	7.92268i	0.441285	−	0.254776i	0.704143	+	0.710059i	$0.251332\pi$
$968$	2.43013	−	9.36038i	0.0781074	−	0.300854i
$969$	42.0628	−	12.4568i	1.35125	−	0.400171i
$970$	−0.866205	+	0.779935i	−0.0278122	+	0.0250422i
$971$	−1.51662	−	2.08745i	−0.0486708	−	0.0669896i	0.783988	−	0.620776i	$-0.213182\pi$
$971$	−1.51662	−	2.08745i	−0.0486708	−	0.0669896i	−0.832659	+	0.553786i	$0.813182\pi$
$972$	7.10671	−	29.5627i	0.227948	−	0.948223i
$973$	17.9931	+	55.3771i	0.576833	+	1.77531i
$974$	−1.08134	−	0.229846i	−0.0346484	−	0.00736475i
$975$	−6.77890	−	2.40099i	−0.217099	−	0.0768932i
$976$	2.78133	−	6.24698i	0.0890283	−	0.199961i
$977$	−6.37823	−	30.0072i	−0.204058	−	0.960015i	−0.954300	−	0.298852i	$-0.903396\pi$
$977$	−6.37823	−	30.0072i	−0.204058	−	0.960015i	0.750242	−	0.661163i	$-0.229937\pi$
$978$	−3.86332	−	0.927744i	−0.123535	−	0.0296660i
$979$	5.12995	+	14.3092i	0.163954	+	0.457324i
$980$			3.38155i			0.108020i
$981$	0.997883	−	0.267254i	0.0318599	−	0.00853277i
$982$	3.13224	−	2.27570i	0.0999537	−	0.0726206i
$983$	14.3155	+	32.1531i	0.456593	+	1.02553i	0.984365	+	0.176139i	$0.0563609\pi$
$983$	14.3155	+	32.1531i	0.456593	+	1.02553i	−0.527772	+	0.849386i	$0.676972\pi$
$984$	−13.7971	−	6.58188i	−0.439835	−	0.209823i
$985$	−6.54221	−	5.89063i	−0.208452	−	0.187691i
$986$	0.329148	−	3.13163i	0.0104822	−	0.0997314i
$987$	1.37923	−	10.4714i	0.0439013	−	0.333310i
$988$	4.88988	+	5.43077i	0.155568	+	0.172776i
$989$	−15.9251			−0.506390
$990$	−0.973480	+	0.674479i	−0.0309392	+	0.0214363i
$991$	−2.21717			−0.0704307			−0.0352154	−	0.999380i	$-0.511212\pi$
$991$	−2.21717			−0.0704307			−0.0352154	+	0.999380i	$0.511212\pi$
$992$	−12.5206	−	13.9055i	−0.397529	−	0.441500i
$993$	4.96825	−	2.05757i	0.157663	−	0.0652949i
$994$	0.329581	−	3.13575i	0.0104537	−	0.0994601i
$995$	5.55552	+	5.00222i	0.176122	+	0.158581i
$996$	39.6441	−	27.2432i	1.25617	−	0.863233i
$997$	13.9619	+	31.3590i	0.442178	+	0.993149i	0.987887	+	0.155174i	$0.0495939\pi$
$997$	13.9619	+	31.3590i	0.442178	+	0.993149i	−0.545709	+	0.837975i	$0.683739\pi$
$998$	1.94427	−	1.41259i	0.0615447	−	0.0447149i
$999$	−3.48849	+	2.13689i	−0.110371	+	0.0676081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.2.7	✓	80
3.2	odd	2		297.2.t.a.35.4		80
9.2	odd	6		891.2.k.a.728.9		80
9.4	even	3		297.2.t.a.233.4		80
9.5	odd	6	inner	99.2.p.a.68.7	yes	80
9.7	even	3		891.2.k.a.728.12		80
11.6	odd	10	inner	99.2.p.a.83.7	yes	80
33.17	even	10		297.2.t.a.116.4		80
99.50	even	30	inner	99.2.p.a.50.7	yes	80
99.61	odd	30		891.2.k.a.809.9		80
99.83	even	30		891.2.k.a.809.12		80
99.94	odd	30		297.2.t.a.17.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.7	✓	80	1.1	even	1	trivial
99.2.p.a.50.7	yes	80	99.50	even	30	inner
99.2.p.a.68.7	yes	80	9.5	odd	6	inner
99.2.p.a.83.7	yes	80	11.6	odd	10	inner
297.2.t.a.17.4		80	99.94	odd	30
297.2.t.a.35.4		80	3.2	odd	2
297.2.t.a.116.4		80	33.17	even	10
297.2.t.a.233.4		80	9.4	even	3
891.2.k.a.728.9		80	9.2	odd	6
891.2.k.a.728.12		80	9.7	even	3
891.2.k.a.809.9		80	99.61	odd	30
891.2.k.a.809.12		80	99.83	even	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.148911 + 0.165382i) q^{2} +(-1.37407 - 1.05449i) q^{3} +(0.203880 - 1.93979i) q^{4} +(0.397470 + 0.357884i) q^{5} +(-0.0302197 - 0.384271i) q^{6} +(-1.30165 - 2.92356i) q^{7} +(0.711251 - 0.516754i) q^{8} +(0.776111 + 2.89787i) q^{9} +O(q^{10})\)	\(q+(0.148911 + 0.165382i) q^{2} +(-1.37407 - 1.05449i) q^{3} +(0.203880 - 1.93979i) q^{4} +(0.397470 + 0.357884i) q^{5} +(-0.0302197 - 0.384271i) q^{6} +(-1.30165 - 2.92356i) q^{7} +(0.711251 - 0.516754i) q^{8} +(0.776111 + 2.89787i) q^{9} +0.119027i q^{10} +(3.12205 - 1.11928i) q^{11} +(-2.32563 + 2.45041i) q^{12} +(0.183129 + 0.861553i) q^{13} +(0.289675 - 0.650620i) q^{14} +(-0.168766 - 0.910883i) q^{15} +(-3.62433 - 0.770375i) q^{16} +(1.83995 + 5.66278i) q^{17} +(-0.363685 + 0.559880i) q^{18} +(2.50028 + 3.44134i) q^{19} +(0.775255 - 0.698043i) q^{20} +(-1.29430 + 5.38973i) q^{21} +(0.650017 + 0.349660i) q^{22} +(-3.19429 + 1.84423i) q^{23} +(-1.52222 - 0.0399516i) q^{24} +(-0.492741 - 4.68811i) q^{25} +(-0.115216 + 0.158581i) q^{26} +(1.98934 - 4.80026i) q^{27} +(-5.93647 + 1.92887i) q^{28} +(-2.17094 + 0.966564i) q^{29} +(0.125513 - 0.163551i) q^{30} +(7.08615 - 1.50621i) q^{31} +(-1.29145 - 2.23686i) q^{32} +(-5.47017 - 1.75421i) q^{33} +(-0.662535 + 1.14754i) q^{34} +(0.528926 - 1.62787i) q^{35} +(5.77949 - 0.914674i) q^{36} +(-0.636941 - 0.462765i) q^{37} +(-0.196818 + 0.925955i) q^{38} +(0.656866 - 1.37694i) q^{39} +(0.467639 + 0.0491508i) q^{40} +(9.17098 + 4.08318i) q^{41} +(-1.08410 + 0.588536i) q^{42} +(3.73912 + 2.15878i) q^{43} +(-1.53464 - 6.28432i) q^{44} +(-0.728620 + 1.42957i) q^{45} +(-0.780668 - 0.253654i) q^{46} +(-1.89502 + 0.199174i) q^{47} +(4.16771 + 4.88036i) q^{48} +(-2.16898 + 2.40889i) q^{49} +(0.701957 - 0.779602i) q^{50} +(3.44312 - 9.72123i) q^{51} +(1.70857 - 0.179578i) q^{52} +(-9.64245 - 3.13302i) q^{53} +(1.09011 - 0.385810i) q^{54} +(1.64149 + 0.672452i) q^{55} +(-2.43656 - 1.40675i) q^{56} +(0.193303 - 7.36514i) q^{57} +(-0.483129 - 0.215103i) q^{58} +(-11.0642 - 1.16290i) q^{59} +(-1.80133 + 0.141659i) q^{60} +(-0.383703 + 1.80518i) q^{61} +(1.30431 + 0.947634i) q^{62} +(7.46186 - 6.04102i) q^{63} +(-2.11237 + 6.50122i) q^{64} +(-0.235548 + 0.407980i) q^{65} +(-0.524454 - 1.16589i) q^{66} +(-0.337099 - 0.583872i) q^{67} +(11.3597 - 2.41458i) q^{68} +(6.33388 + 0.834257i) q^{69} +(0.347983 - 0.154932i) q^{70} +(4.21053 - 1.36808i) q^{71} +(2.04949 + 1.66005i) q^{72} +(0.0544863 - 0.0749940i) q^{73} +(-0.0183144 - 0.174250i) q^{74} +(-4.26650 + 6.96136i) q^{75} +(7.18523 - 4.14840i) q^{76} +(-7.33610 - 7.67059i) q^{77} +(0.325536 - 0.0964069i) q^{78} +(-11.5129 + 10.3663i) q^{79} +(-1.16486 - 1.60329i) q^{80} +(-7.79530 + 4.49814i) q^{81} +(0.690373 + 2.12475i) q^{82} +(-13.9274 - 2.96037i) q^{83} +(10.1911 + 3.60953i) q^{84} +(-1.29529 + 2.90927i) q^{85} +(0.199771 + 0.939851i) q^{86} +(4.00224 + 0.961106i) q^{87} +(1.64217 - 2.40942i) q^{88} +4.58327i q^{89} +(-0.344926 + 0.0923784i) q^{90} +(2.28043 - 1.65683i) q^{91} +(2.92616 + 6.57226i) q^{92} +(-11.3251 - 5.40263i) q^{93} +(-0.315129 - 0.283743i) q^{94} +(-0.237813 + 2.26264i) q^{95} +(-0.584202 + 4.43541i) q^{96} +(6.55256 + 7.27736i) q^{97} -0.721373 q^{98} +(5.66658 + 8.17862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

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