LMFDB - Embedded newform 483.2.q.f.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	483.85
Dual form			483.2.q.f.358.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83093 + 2.11301i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.827862 - 5.75791i) q^{4} +(0.00406880 + 0.00890943i) q^{5} +(-0.397900 + 2.76745i) q^{6} +(0.959493 - 0.281733i) q^{7} +(8.97813 + 5.76989i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.83093 + 2.11301i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.827862 - 5.75791i) q^{4} +(0.00406880 + 0.00890943i) q^{5} +(-0.397900 + 2.76745i) q^{6} +(0.959493 - 0.281733i) q^{7} +(8.97813 + 5.76989i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.0262754 - 0.00771515i) q^{10} +(-0.139370 - 0.160842i) q^{11} +(-3.80940 - 4.39628i) q^{12} +(-5.04352 - 1.48091i) q^{13} +(-1.16146 + 2.54325i) q^{14} +(0.00823969 + 0.00529533i) q^{15} +(-17.4672 + 5.12883i) q^{16} +(0.956315 - 6.65132i) q^{17} +(1.16146 + 2.54325i) q^{18} +(-0.502886 - 3.49765i) q^{19} +(0.0479313 - 0.0308035i) q^{20} +(0.654861 - 0.755750i) q^{21} +0.595036 q^{22} +(2.98626 + 3.75263i) q^{23} +10.6723 q^{24} +(3.27424 - 3.77868i) q^{25} +(12.3635 - 7.94555i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-2.41652 - 5.29144i) q^{28} +(-0.511412 + 3.55695i) q^{29} +(-0.0262754 + 0.00771515i) q^{30} +(-3.22598 - 2.07321i) q^{31} +(12.2771 - 26.8831i) q^{32} +(-0.204203 - 0.0599594i) q^{33} +(12.3033 + 14.1988i) q^{34} +(0.00641406 + 0.00740222i) q^{35} +(-5.58148 - 1.63887i) q^{36} +(3.75906 - 8.23120i) q^{37} +(8.31132 + 5.34136i) q^{38} +(-5.04352 + 1.48091i) q^{39} +(-0.0148762 + 0.103467i) q^{40} +(-0.766098 - 1.67752i) q^{41} +(0.397900 + 2.76745i) q^{42} +(4.72369 - 3.03573i) q^{43} +(-0.810731 + 0.935634i) q^{44} +0.00979454 q^{45} +(-13.3970 - 0.560813i) q^{46} -7.79141 q^{47} +(-11.9215 + 13.7581i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.98946 + 13.8370i) q^{50} +(-2.79147 - 6.11247i) q^{51} +(-4.35161 + 30.2661i) q^{52} +(-3.42206 + 1.00481i) q^{53} +(2.35207 + 1.51158i) q^{54} +(0.000865938 - 0.00189614i) q^{55} +(10.2400 + 3.00674i) q^{56} +(-2.31403 - 2.67053i) q^{57} +(-6.57950 - 7.59315i) q^{58} +(3.27745 + 0.962346i) q^{59} +(0.0236687 - 0.0518272i) q^{60} +(11.9691 + 7.69206i) q^{61} +(10.2873 - 3.02062i) q^{62} +(0.142315 - 0.989821i) q^{63} +(19.2008 + 42.0438i) q^{64} +(-0.00732700 - 0.0509604i) q^{65} +(0.500576 - 0.321701i) q^{66} +(2.09577 - 2.41864i) q^{67} -39.0894 q^{68} +(4.54103 + 1.54242i) q^{69} -0.0273847 q^{70} +(7.26092 - 8.37955i) q^{71} +(8.97813 - 5.76989i) q^{72} +(0.0244627 + 0.170142i) q^{73} +(10.5100 + 23.0137i) q^{74} +(0.711561 - 4.94901i) q^{75} +(-19.7228 + 5.79115i) q^{76} +(-0.179039 - 0.115061i) q^{77} +(6.10516 - 13.3684i) q^{78} +(0.216588 + 0.0635960i) q^{79} +(-0.116766 - 0.134755i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(4.94729 + 1.45266i) q^{82} +(0.677185 - 1.48283i) q^{83} +(-4.89367 - 3.14497i) q^{84} +(0.0631505 - 0.0185427i) q^{85} +(-2.23423 + 15.5394i) q^{86} +(1.49280 + 3.26879i) q^{87} +(-0.323243 - 2.24820i) q^{88} +(-6.06999 + 3.90095i) q^{89} +(-0.0179331 + 0.0206959i) q^{90} -5.25644 q^{91} +(19.1351 - 20.3013i) q^{92} -3.83473 q^{93} +(14.2655 - 16.4633i) q^{94} +(0.0291159 - 0.0187117i) q^{95} +(-4.20595 - 29.2530i) q^{96} +(-4.98120 - 10.9073i) q^{97} +(-0.397900 + 2.76745i) q^{98} +(-0.204203 + 0.0599594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−1.83093	+	2.11301i	−1.29466	+	1.49412i	−0.533066	+	0.846074i	$0.678960\pi$
$2$	−1.83093	+	2.11301i	−1.29466	+	1.49412i	−0.761599	+	0.648049i	$0.775585\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.827862	−	5.75791i	−0.413931	−	2.87895i
$5$	0.00406880	+	0.00890943i	0.00181962	+	0.00398442i	0.910540	−	0.413422i	$-0.135666\pi$
$5$	0.00406880	+	0.00890943i	0.00181962	+	0.00398442i	−0.908720	+	0.417406i	$0.862939\pi$
$6$	−0.397900	+	2.76745i	−0.162442	+	1.12981i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	8.97813	+	5.76989i	3.17425	+	2.03996i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.0262754	−	0.00771515i	−0.00830901	−	0.00243975i
$11$	−0.139370	−	0.160842i	−0.0420216	−	0.0484955i	0.734350	−	0.678771i	$-0.237487\pi$
$11$	−0.139370	−	0.160842i	−0.0420216	−	0.0484955i	−0.776371	+	0.630276i	$0.782942\pi$
$12$	−3.80940	−	4.39628i	−1.09968	−	1.26910i
$13$	−5.04352	−	1.48091i	−1.39882	−	0.410731i	−0.506541	−	0.862216i	$-0.669076\pi$
$13$	−5.04352	−	1.48091i	−1.39882	−	0.410731i	−0.892279	+	0.451485i	$0.850894\pi$
$14$	−1.16146	+	2.54325i	−0.310414	+	0.679712i
$15$	0.00823969	+	0.00529533i	0.00212748	+	0.00136725i
$16$	−17.4672	+	5.12883i	−4.36680	+	1.28221i
$17$	0.956315	−	6.65132i	0.231940	−	1.61318i	−0.457753	−	0.889080i	$-0.651345\pi$
$17$	0.956315	−	6.65132i	0.231940	−	1.61318i	0.689693	−	0.724102i	$-0.257745\pi$
$18$	1.16146	+	2.54325i	0.273760	+	0.599450i
$19$	−0.502886	−	3.49765i	−0.115370	−	0.802416i	−0.962549	−	0.271108i	$-0.912610\pi$
$19$	−0.502886	−	3.49765i	−0.115370	−	0.802416i	0.847179	−	0.531308i	$-0.178299\pi$
$20$	0.0479313	−	0.0308035i	0.0107178	−	0.00688788i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	0.595036			0.126862
$23$	2.98626	+	3.75263i	0.622679	+	0.782477i
$23$	2.98626	+	3.75263i	0.622679	+	0.782477i
$24$	10.6723			2.17848
$25$	3.27424	−	3.77868i	0.654848	−	0.755735i
$26$	12.3635	−	7.94555i	2.42468	−	1.55825i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	−2.41652	−	5.29144i	−0.456679	−	0.999987i
$29$	−0.511412	+	3.55695i	−0.0949669	+	0.660509i	0.885618	+	0.464414i	$0.153735\pi$
$29$	−0.511412	+	3.55695i	−0.0949669	+	0.660509i	−0.980585	+	0.196095i	$0.937174\pi$
$30$	−0.0262754	+	0.00771515i	−0.00479721	+	0.00140859i
$31$	−3.22598	−	2.07321i	−0.579404	−	0.372360i	0.217870	−	0.975978i	$-0.430089\pi$
$31$	−3.22598	−	2.07321i	−0.579404	−	0.372360i	−0.797274	+	0.603618i	$0.793725\pi$
$32$	12.2771	−	26.8831i	2.17031	−	4.75231i
$33$	−0.204203	−	0.0599594i	−0.0355472	−	0.0104376i
$34$	12.3033	+	14.1988i	2.11001	+	2.43508i
$35$	0.00641406	+	0.00740222i	0.00108417	+	0.00125120i
$36$	−5.58148	−	1.63887i	−0.930247	−	0.273145i
$37$	3.75906	−	8.23120i	0.617986	−	1.35320i	−0.298989	−	0.954257i	$-0.596649\pi$
$37$	3.75906	−	8.23120i	0.617986	−	1.35320i	0.916975	−	0.398945i	$-0.130623\pi$
$38$	8.31132	+	5.34136i	1.34827	+	0.866483i
$39$	−5.04352	+	1.48091i	−0.807609	+	0.237135i
$40$	−0.0148762	+	0.103467i	−0.00235214	+	0.0163595i
$41$	−0.766098	−	1.67752i	−0.119644	−	0.261985i	0.840329	−	0.542077i	$-0.182362\pi$
$41$	−0.766098	−	1.67752i	−0.119644	−	0.261985i	−0.959973	+	0.280093i	$0.909635\pi$
$42$	0.397900	+	2.76745i	0.0613972	+	0.427027i
$43$	4.72369	−	3.03573i	0.720357	−	0.462945i	−0.128404	−	0.991722i	$-0.540985\pi$
$43$	4.72369	−	3.03573i	0.720357	−	0.462945i	0.848761	+	0.528777i	$0.177349\pi$
$44$	−0.810731	+	0.935634i	−0.122222	+	0.141052i
$45$	0.00979454			0.00146008
$46$	−13.3970	−	0.560813i	−1.97528	−	0.0826873i
$47$	−7.79141			−1.13649			−0.568247	−	0.822858i	$-0.692378\pi$
$47$	−7.79141			−1.13649			−0.568247	+	0.822858i	$0.692378\pi$
$48$	−11.9215	+	13.7581i	−1.72072	+	1.98581i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	1.98946	+	13.8370i	0.281352	+	1.95685i
$51$	−2.79147	−	6.11247i	−0.390884	−	0.855917i
$52$	−4.35161	+	30.2661i	−0.603459	+	4.19715i
$53$	−3.42206	+	1.00481i	−0.470056	+	0.138021i	−0.508178	−	0.861252i	$-0.669681\pi$
$53$	−3.42206	+	1.00481i	−0.470056	+	0.138021i	0.0381220	+	0.999273i	$0.487862\pi$
$54$	2.35207	+	1.51158i	0.320076	+	0.205700i
$55$	0.000865938	−	0.00189614i	0.000116763	−	0.000255675i
$56$	10.2400	+	3.00674i	1.36838	+	0.401792i
$57$	−2.31403	−	2.67053i	−0.306501	−	0.353720i
$58$	−6.57950	−	7.59315i	−0.863931	−	0.997030i
$59$	3.27745	+	0.962346i	0.426688	+	0.125287i	0.488024	−	0.872830i	$-0.337718\pi$
$59$	3.27745	+	0.962346i	0.426688	+	0.125287i	−0.0613360	+	0.998117i	$0.519536\pi$
$60$	0.0236687	−	0.0518272i	0.00305561	−	0.00669086i
$61$	11.9691	+	7.69206i	1.53248	+	0.984867i	0.989405	+	0.145185i	$0.0463777\pi$
$61$	11.9691	+	7.69206i	1.53248	+	0.984867i	0.543078	+	0.839682i	$0.317259\pi$
$62$	10.2873	−	3.02062i	1.30649	−	0.383619i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	19.2008	+	42.0438i	2.40010	+	5.25548i
$65$	−0.00732700	−	0.0509604i	−0.000908802	−	0.00632086i
$66$	0.500576	−	0.321701i	0.0616167	−	0.0395987i
$67$	2.09577	−	2.41864i	0.256039	−	0.295484i	−0.613148	−	0.789968i	$-0.710097\pi$
$67$	2.09577	−	2.41864i	0.256039	−	0.295484i	0.869187	+	0.494483i	$0.164643\pi$
$68$	−39.0894			−4.74028
$69$	4.54103	+	1.54242i	0.546676	+	0.185685i
$70$	−0.0273847			−0.00327309
$71$	7.26092	−	8.37955i	0.861713	−	0.994469i	−0.138279	−	0.990393i	$-0.544157\pi$
$71$	7.26092	−	8.37955i	0.861713	−	0.994469i	0.999992	−	0.00407612i	$-0.00129747\pi$
$72$	8.97813	−	5.76989i	1.05808	−	0.679988i
$73$	0.0244627	+	0.170142i	0.00286315	+	0.0199136i	0.991203	−	0.132351i	$-0.0422525\pi$
$73$	0.0244627	+	0.170142i	0.00286315	+	0.0199136i	−0.988340	+	0.152264i	$0.951343\pi$
$74$	10.5100	+	23.0137i	1.22176	+	2.67529i
$75$	0.711561	−	4.94901i	0.0821639	−	0.571463i
$76$	−19.7228	+	5.79115i	−2.26236	+	0.664290i
$77$	−0.179039	−	0.115061i	−0.0204034	−	0.0131124i
$78$	6.10516	−	13.3684i	0.691273	−	1.51368i
$79$	0.216588	+	0.0635960i	0.0243681	+	0.00715511i	0.293894	−	0.955838i	$-0.405049\pi$
$79$	0.216588	+	0.0635960i	0.0243681	+	0.00715511i	−0.269526	+	0.962993i	$0.586867\pi$
$80$	−0.116766	−	0.134755i	−0.0130548	−	0.0150660i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	4.94729	+	1.45266i	0.546337	+	0.160419i
$83$	0.677185	−	1.48283i	0.0743307	−	0.162762i	−0.868819	−	0.495130i	$-0.835120\pi$
$83$	0.677185	−	1.48283i	0.0743307	−	0.162762i	0.943150	+	0.332368i	$0.107848\pi$
$84$	−4.89367	−	3.14497i	−0.533943	−	0.343144i
$85$	0.0631505	−	0.0185427i	0.00684963	−	0.00201123i
$86$	−2.23423	+	15.5394i	−0.240924	+	1.67566i
$87$	1.49280	+	3.26879i	0.160045	+	0.350451i
$88$	−0.323243	−	2.24820i	−0.0344578	−	0.239659i
$89$	−6.06999	+	3.90095i	−0.643418	+	0.413500i	−0.821256	−	0.570560i	$-0.806726\pi$
$89$	−6.06999	+	3.90095i	−0.643418	+	0.413500i	0.177838	+	0.984060i	$0.443090\pi$
$90$	−0.0179331	+	0.0206959i	−0.00189032	+	0.00218154i
$91$	−5.25644			−0.551025
$92$	19.1351	−	20.3013i	1.99497	−	2.11656i
$93$	−3.83473			−0.397643
$94$	14.2655	−	16.4633i	1.47138	−	1.69806i
$95$	0.0291159	−	0.0187117i	0.00298723	−	0.00191978i
$96$	−4.20595	−	29.2530i	−0.429268	−	2.98562i
$97$	−4.98120	−	10.9073i	−0.505764	−	1.10747i	−0.974553	−	0.224159i	$-0.928037\pi$
$97$	−4.98120	−	10.9073i	−0.505764	−	1.10747i	0.468788	−	0.883311i	$-0.344691\pi$
$98$	−0.397900	+	2.76745i	−0.0401939	+	0.279555i
$99$	−0.204203	+	0.0599594i	−0.0205232	+	0.00602615i
$100$	−24.4679	−	15.7246i	−2.44679	−	1.57246i
$101$	−2.73161	+	5.98139i	−0.271805	+	0.595170i	−0.995480	−	0.0949708i	$-0.969724\pi$
$101$	−2.73161	+	5.98139i	−0.271805	+	0.595170i	0.723675	+	0.690141i	$0.242451\pi$
$102$	18.0267	+	5.29311i	1.78491	+	0.524096i
$103$	0.738585	+	0.852372i	0.0727749	+	0.0839867i	0.790969	−	0.611856i	$-0.209577\pi$
$103$	0.738585	+	0.852372i	0.0727749	+	0.0839867i	−0.718195	+	0.695842i	$0.755031\pi$
$104$	−36.7366	−	42.3963i	−3.60232	−	4.15730i
$105$	0.00939779	+	0.00275944i	0.000917131	+	0.000269294i
$106$	4.14239	−	9.07057i	0.402344	−	0.881011i
$107$	3.50798	+	2.25444i	0.339130	+	0.217945i	0.699109	−	0.715015i	$-0.253580\pi$
$107$	3.50798	+	2.25444i	0.339130	+	0.217945i	−0.359980	+	0.932960i	$0.617216\pi$
$108$	−5.58148	+	1.63887i	−0.537078	+	0.157700i
$109$	−2.61186	+	18.1659i	−0.250171	+	1.73997i	0.347004	+	0.937864i	$0.387199\pi$
$109$	−2.61186	+	18.1659i	−0.250171	+	1.73997i	−0.597175	+	0.802111i	$0.703710\pi$
$110$	0.00242108	+	0.00530143i	0.000230841	+	0.000505472i
$111$	−1.28780	−	8.95683i	−0.122232	−	0.850145i
$112$	−15.3147	+	9.84216i	−1.44710	+	0.929996i
$113$	1.15178	−	1.32922i	0.108350	−	0.125043i	−0.698984	−	0.715137i	$-0.746364\pi$
$113$	1.15178	−	1.32922i	0.108350	−	0.125043i	0.807334	+	0.590095i	$0.200910\pi$
$114$	9.87968			0.925317
$115$	−0.0212833	+	0.0418746i	−0.00198468	+	0.00390483i
$116$	20.9040			1.94088
$117$	−3.44224	+	3.97255i	−0.318235	+	0.367263i
$118$	−8.03423	+	5.16329i	−0.739611	+	0.475319i
$119$	−0.956315	−	6.65132i	−0.0876653	−	0.609725i
$120$	0.0434235	+	0.0950843i	0.00396401	+	0.00867997i
$121$	1.55902	−	10.8432i	0.141729	−	0.985746i
$122$	−38.1679	+	11.2071i	−3.45556	+	1.01464i
$123$	−1.55142	−	0.997037i	−0.139887	−	0.0898998i
$124$	−9.26670	+	20.2913i	−0.832175	+	1.82221i
$125$	0.0939770	+	0.0275941i	0.00840556	+	0.00246810i
$126$	1.83093	+	2.11301i	0.163112	+	0.188242i
$127$	−1.19557	−	1.37976i	−0.106089	−	0.122434i	0.700222	−	0.713926i	$-0.253085\pi$
$127$	−1.19557	−	1.37976i	−0.106089	−	0.122434i	−0.806311	+	0.591492i	$0.798539\pi$
$128$	−67.2808	−	19.7554i	−5.94684	−	1.74615i
$129$	2.33258	−	5.10764i	0.205372	−	0.449703i
$130$	0.121095	+	0.0778230i	0.0106207	+	0.00682553i
$131$	−7.10362	+	2.08581i	−0.620646	+	0.182238i	−0.576914	−	0.816805i	$-0.695743\pi$
$131$	−7.10362	+	2.08581i	−0.620646	+	0.182238i	−0.0437324	+	0.999043i	$0.513925\pi$
$132$	−0.176189	+	1.22542i	−0.0153353	+	0.106659i
$133$	−1.46792	−	3.21429i	−0.127285	−	0.278715i
$134$	1.27341	+	8.85674i	0.110006	+	0.765106i
$135$	0.00823969	−	0.00529533i	0.000709160	−	0.000455749i
$136$	46.9633	−	54.1985i	4.02707	−	4.64749i
$137$	−13.9863			−1.19493			−0.597463	−	0.801896i	$-0.703825\pi$
$137$	−13.9863			−1.19493			−0.597463	+	0.801896i	$0.703825\pi$
$138$	−11.5735	+	6.77117i	−0.985198	+	0.576400i
$139$	17.7315			1.50397			0.751984	−	0.659181i	$-0.229097\pi$
$139$	17.7315			1.50397			0.751984	+	0.659181i	$0.229097\pi$
$140$	0.0373113	−	0.0430596i	0.00315338	−	0.00363920i
$141$	−6.55455	+	4.21235i	−0.551993	+	0.354744i
$142$	4.41180	+	30.6848i	0.370230	+	2.57501i
$143$	0.464723	+	1.01760i	0.0388621	+	0.0850961i
$144$	−2.59079	+	18.0193i	−0.215899	+	1.50161i
$145$	−0.0337712	+	0.00991613i	−0.00280455	+	0.000823489i
$146$	−0.404301	−	0.259829i	−0.0334602	−	0.0215036i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−50.5065	−	14.8300i	−4.15161	−	1.21902i
$149$	8.66890	+	10.0044i	0.710184	+	0.819596i	0.990090	−	0.140431i	$-0.0448488\pi$
$149$	8.66890	+	10.0044i	0.710184	+	0.819596i	−0.279906	+	0.960027i	$0.590303\pi$
$150$	9.15449	+	10.5648i	0.747461	+	0.862615i
$151$	−2.93708	−	0.862403i	−0.239016	−	0.0701814i	0.160031	−	0.987112i	$-0.448841\pi$
$151$	−2.93708	−	0.862403i	−0.239016	−	0.0701814i	−0.399047	+	0.916931i	$0.630659\pi$
$152$	15.6661	−	34.3040i	1.27069	−	2.78242i
$153$	−5.65298	−	3.63295i	−0.457017	−	0.293707i
$154$	0.570933	−	0.167641i	0.0460071	−	0.0135089i
$155$	0.00534527	−	0.0371772i	0.000429342	−	0.00298614i
$156$	12.7023	+	27.8141i	1.01700	+	2.22691i
$157$	−0.0309873	−	0.215521i	−0.00247305	−	0.0172005i	0.988548	−	0.150910i	$-0.0482203\pi$
$157$	−0.0309873	−	0.215521i	−0.00247305	−	0.0172005i	−0.991021	+	0.133709i	$0.957311\pi$
$158$	−0.530937	+	0.341213i	−0.0422391	+	0.0271454i
$159$	−2.33558	+	2.69540i	−0.185223	+	0.213759i
$160$	0.289466			0.0228843
$161$	3.92254	+	2.75929i	0.309139	+	0.217463i
$162$	2.79591			0.219667
$163$	7.73901	−	8.93130i	0.606166	−	0.699553i	−0.366853	−	0.930279i	$-0.619565\pi$
$163$	7.73901	−	8.93130i	0.606166	−	0.699553i	0.973019	+	0.230726i	$0.0741101\pi$
$164$	−9.02479	+	5.79988i	−0.704718	+	0.452895i
$165$	−0.000296657	−	0.00206329i	−2.30947e−5	−	0.000160627i
$166$	1.89335	+	4.14586i	0.146952	+	0.321781i
$167$	0.555227	−	3.86169i	0.0429648	−	0.298826i	−0.956997	−	0.290097i	$-0.906312\pi$
$167$	0.555227	−	3.86169i	0.0429648	−	0.298826i	0.999962	−	0.00872913i	$-0.00277860\pi$
$168$	10.2400	−	3.00674i	0.790034	−	0.231975i
$169$	12.3077	+	7.90966i	0.946744	+	0.608436i
$170$	−0.0764435	+	0.167388i	−0.00586295	+	0.0128381i
$171$	−3.39048	−	0.995536i	−0.259277	−	0.0761305i
$172$	−21.3900	−	24.6854i	−1.63098	−	1.88225i
$173$	3.53310	+	4.07742i	0.268617	+	0.310000i	0.873992	−	0.485940i	$-0.161523\pi$
$173$	3.53310	+	4.07742i	0.268617	+	0.310000i	−0.605376	+	0.795940i	$0.706977\pi$
$174$	−9.64020	−	2.83062i	−0.730822	−	0.214589i
$175$	2.07704	−	4.54807i	0.157009	−	0.343802i
$176$	3.25933	+	2.09465i	0.245681	+	0.157890i
$177$	3.27745	−	0.962346i	0.246348	−	0.0723344i
$178$	2.87101	−	19.9683i	0.215191	−	1.49669i
$179$	9.19435	+	20.1328i	0.687218	+	1.50480i	0.854810	+	0.518942i	$0.173674\pi$
$179$	9.19435	+	20.1328i	0.687218	+	1.50480i	−0.167591	+	0.985857i	$0.553599\pi$
$180$	−0.00810853	−	0.0563961i	−0.000604374	−	0.00420351i
$181$	−1.04832	+	0.673714i	−0.0779209	+	0.0500767i	−0.579021	−	0.815313i	$-0.696565\pi$
$181$	−1.04832	+	0.673714i	−0.0779209	+	0.0500767i	0.501100	+	0.865389i	$0.332929\pi$
$182$	9.62419	−	11.1069i	0.713392	−	0.823298i
$183$	14.2277			1.05174
$184$	5.15878	+	50.9220i	0.380310	+	3.75402i
$185$	0.0886302			0.00651622
$186$	7.02114	−	8.10283i	0.514815	−	0.594128i
$187$	−1.20309	+	0.773179i	−0.0879786	+	0.0565404i
$188$	6.45021	+	44.8622i	0.470430	+	3.27191i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	−0.0137714	+	0.0957820i	−0.000999081	+	0.00694876i
$191$	−4.22411	+	1.24031i	−0.305646	+	0.0897458i	−0.430959	−	0.902371i	$-0.641825\pi$
$191$	−4.22411	+	1.24031i	−0.305646	+	0.0897458i	0.125313	+	0.992117i	$0.460006\pi$
$192$	38.8833	+	24.9888i	2.80616	+	1.80341i
$193$	−10.7922	+	23.6315i	−0.776837	+	1.70104i	−0.0658501	+	0.997830i	$0.520976\pi$
$193$	−10.7922	+	23.6315i	−0.776837	+	1.70104i	−0.710987	+	0.703206i	$0.751751\pi$
$194$	32.1675	+	9.44522i	2.30949	+	0.678128i
$195$	−0.0337151	−	0.0389093i	−0.00241439	−	0.00278636i
$196$	−3.80940	−	4.39628i	−0.272100	−	0.314020i
$197$	−6.89179	−	2.02361i	−0.491020	−	0.144176i	0.0268438	−	0.999640i	$-0.491454\pi$
$197$	−6.89179	−	2.02361i	−0.491020	−	0.144176i	−0.517864	+	0.855463i	$0.673273\pi$
$198$	0.247187	−	0.541264i	0.0175668	−	0.0384660i
$199$	−7.67769	−	4.93415i	−0.544257	−	0.349773i	0.239445	−	0.970910i	$-0.423035\pi$
$199$	−7.67769	−	4.93415i	−0.544257	−	0.349773i	−0.783702	+	0.621137i	$0.786671\pi$
$200$	51.1991	−	15.0334i	3.62032	−	1.06302i
$201$	0.455454	−	3.16775i	0.0321252	−	0.223436i
$202$	−7.63733	−	16.7234i	−0.537361	−	1.17666i
$203$	0.511412	+	3.55695i	0.0358941	+	0.249649i
$204$	−32.8841	+	21.1333i	−2.30235	+	1.47963i
$205$	0.0118287	−	0.0136510i	0.000826149	−	0.000953427i
$206$	−3.15337			−0.219706
$207$	4.65405	−	1.15750i	0.323479	−	0.0804519i
$208$	95.6915			6.63501
$209$	−0.492480	+	0.568353i	−0.0340656	+	0.0393138i
$210$	−0.0230374	+	0.0148053i	−0.00158973	+	0.00102166i
$211$	0.813900	+	5.66080i	0.0560312	+	0.389706i	0.998469	+	0.0553228i	$0.0176188\pi$
$211$	0.813900	+	5.66080i	0.0560312	+	0.389706i	−0.942437	+	0.334383i	$0.891472\pi$
$212$	8.61857	+	18.8720i	0.591926	+	1.29614i
$213$	1.57795	−	10.9749i	0.108119	−	0.751986i
$214$	−11.1865	+	3.28467i	−0.764696	+	0.224535i
$215$	0.0462664	+	0.0297336i	0.00315534	+	0.00202782i
$216$	4.43344	−	9.70788i	0.301657	−	0.660538i
$217$	−3.67940	−	1.08037i	−0.249774	−	0.0733403i
$218$	−33.6025	−	38.7794i	−2.27585	−	2.62647i
$219$	0.112565	+	0.129907i	0.00760644	+	0.00877831i
$220$	−0.0116347	−	0.00341625i	−0.000784409	−	0.000230323i
$221$	−14.6732	+	32.1298i	−0.987026	+	2.16129i
$222$	21.2837	+	13.6782i	1.42847	+	0.918022i
$223$	−16.1660	+	4.74676i	−1.08255	+	0.317866i	−0.773900	−	0.633308i	$-0.781697\pi$
$223$	−16.1660	+	4.74676i	−1.08255	+	0.317866i	−0.308653	+	0.951175i	$0.599878\pi$
$224$	4.20595	−	29.2530i	0.281022	−	1.95455i
$225$	−2.07704	−	4.54807i	−0.138469	−	0.303205i
$226$	0.699832	+	4.86744i	0.0465522	+	0.323777i
$227$	−17.2712	+	11.0995i	−1.14633	+	0.736700i	−0.968904	−	0.247435i	$-0.920412\pi$
$227$	−17.2712	+	11.0995i	−1.14633	+	0.736700i	−0.177423	+	0.984135i	$0.556776\pi$
$228$	−13.4610	+	15.5348i	−0.891475	+	1.02882i
$229$	−14.6048			−0.965115			−0.482558	−	0.875864i	$-0.660292\pi$
$229$	−14.6048			−0.965115			−0.482558	+	0.875864i	$0.660292\pi$
$230$	−0.0495131	−	0.121641i	−0.00326480	−	0.00802079i
$231$	−0.212824			−0.0140028
$232$	−25.1147	+	28.9839i	−1.64886	+	1.90289i
$233$	−19.5686	+	12.5760i	−1.28198	+	0.823879i	−0.991131	−	0.132890i	$-0.957574\pi$
$233$	−19.5686	+	12.5760i	−1.28198	+	0.823879i	−0.290850	+	0.956769i	$0.593938\pi$
$234$	−2.09154	−	14.5469i	−0.136728	−	0.950964i
$235$	−0.0317017	−	0.0694170i	−0.00206799	−	0.00452827i
$236$	2.82782	−	19.6679i	0.184076	−	1.28027i
$237$	0.216588	−	0.0635960i	0.0140689	−	0.00413101i
$238$	15.8052	+	10.1574i	1.02450	+	0.658407i
$239$	4.90535	−	10.7412i	0.317301	−	0.694791i	−0.682032	−	0.731322i	$-0.738904\pi$
$239$	4.90535	−	10.7412i	0.317301	−	0.694791i	0.999333	+	0.0365311i	$0.0116308\pi$
$240$	−0.171083	−	0.0502346i	−0.0110434	−	0.00324263i
$241$	−8.75820	−	10.1075i	−0.564165	−	0.651081i	0.399959	−	0.916533i	$-0.369024\pi$
$241$	−8.75820	−	10.1075i	−0.564165	−	0.651081i	−0.964124	+	0.265452i	$0.914479\pi$
$242$	20.0573	+	23.1474i	1.28933	+	1.48797i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	34.3814	−	75.2848i	2.20104	−	4.81961i
$245$	0.00823969	+	0.00529533i	0.000526415	+	0.000338306i
$246$	4.94729	−	1.45266i	0.315428	−	0.0926180i
$247$	−2.64339	+	18.3852i	−0.168195	+	1.16982i
$248$	−17.0011	−	37.2271i	−1.07957	−	2.36393i
$249$	−0.231993	−	1.61355i	−0.0147020	−	0.102254i
$250$	−0.230372	+	0.148051i	−0.0145700	+	0.00936358i
$251$	−9.23341	+	10.6559i	−0.582808	+	0.672596i	−0.968206	−	0.250154i	$-0.919519\pi$
$251$	−9.23341	+	10.6559i	−0.582808	+	0.672596i	0.385398	+	0.922750i	$0.374064\pi$
$252$	−5.81712			−0.366444
$253$	0.187383	−	1.00332i	0.0117807	−	0.0630781i
$254$	5.10444			0.320281
$255$	0.0431007	−	0.0497408i	0.00269907	−	0.00311489i
$256$	87.1633	−	56.0165i	5.44771	−	3.50103i
$257$	−0.746589	−	5.19264i	−0.0465709	−	0.323908i	−0.999768	−	0.0215570i	$-0.993138\pi$
$257$	−0.746589	−	5.19264i	−0.0465709	−	0.323908i	0.953197	−	0.302351i	$-0.0977714\pi$
$258$	6.52169	+	14.2805i	0.406023	+	0.889066i
$259$	1.28780	−	8.95683i	0.0800199	−	0.556550i
$260$	−0.287359	+	0.0843763i	−0.0178213	+	0.00523280i
$261$	3.02307	+	1.94281i	0.187123	+	0.120257i
$262$	8.59891	−	18.8290i	0.531242	−	1.16326i
$263$	25.8099	+	7.57848i	1.59151	+	0.467309i	0.953167	−	0.302444i	$-0.0978026\pi$
$263$	25.8099	+	7.57848i	1.59151	+	0.467309i	0.638342	+	0.769753i	$0.279621\pi$
$264$	−1.48740	−	1.71655i	−0.0915432	−	0.105646i
$265$	−0.0228759	−	0.0264002i	−0.00140526	−	0.00162175i
$266$	9.47949	+	2.78343i	0.581225	+	0.170663i
$267$	−2.99739	+	6.56337i	−0.183437	+	0.401672i
$268$	−15.6613	−	10.0649i	−0.956668	−	0.614813i
$269$	25.3774	−	7.45148i	1.54729	−	0.454325i	0.607000	−	0.794702i	$-0.292373\pi$
$269$	25.3774	−	7.45148i	1.54729	−	0.454325i	0.940289	+	0.340377i	$0.110555\pi$
$270$	−0.00389724	+	0.0271059i	−0.000237179	+	0.00164961i
$271$	7.67665	+	16.8095i	0.466323	+	1.02111i	0.986000	+	0.166743i	$0.0533249\pi$
$271$	7.67665	+	16.8095i	0.466323	+	1.02111i	−0.519677	+	0.854363i	$0.673948\pi$
$272$	17.4093	+	121.085i	1.05560	+	7.34184i
$273$	−4.42200	+	2.84185i	−0.267632	+	0.171996i
$274$	25.6079	−	29.5531i	1.54703	−	1.78537i
$275$	−1.06410			−0.0641676
$276$	5.12175	−	27.4237i	0.308293	−	1.65071i
$277$	6.07041			0.364735			0.182368	−	0.983230i	$-0.441624\pi$
$277$	6.07041			0.364735			0.182368	+	0.983230i	$0.441624\pi$
$278$	−32.4652	+	37.4669i	−1.94713	+	2.24711i
$279$	−3.22598	+	2.07321i	−0.193135	+	0.124120i
$280$	0.0148762	+	0.103467i	0.000889025	+	0.00618331i
$281$	7.38887	+	16.1794i	0.440783	+	0.965180i	0.991454	+	0.130458i	$0.0416447\pi$
$281$	7.38887	+	16.1794i	0.440783	+	0.965180i	−0.550671	+	0.834722i	$0.685628\pi$
$282$	3.10020	−	21.5624i	0.184614	−	1.28402i
$283$	29.1627	−	8.56295i	1.73354	−	0.509014i	0.745944	−	0.666009i	$-0.231999\pi$
$283$	29.1627	−	8.56295i	1.73354	−	0.509014i	0.987600	+	0.156994i	$0.0501804\pi$
$284$	−54.2597	−	34.8706i	−3.21972	−	2.06919i
$285$	0.0143776	−	0.0314825i	0.000851655	−	0.00186486i
$286$	−3.00108	−	0.881196i	−0.177457	−	0.0521062i
$287$	−1.20768	−	1.39374i	−0.0712870	−	0.0822696i
$288$	−19.3537	−	22.3353i	−1.14042	−	1.31612i
$289$	−27.0141	−	7.93206i	−1.58906	−	0.466592i
$290$	0.0408800	−	0.0895146i	0.00240055	−	0.00525648i
$291$	−10.0874	−	6.48277i	−0.591333	−	0.380027i
$292$	0.959410	−	0.281708i	0.0561452	−	0.0164857i
$293$	3.60938	−	25.1038i	0.210862	−	1.46658i	−0.559424	−	0.828881i	$-0.688978\pi$
$293$	3.60938	−	25.1038i	0.210862	−	1.46658i	0.770287	−	0.637698i	$-0.220113\pi$
$294$	1.16146	+	2.54325i	0.0677379	+	0.148325i
$295$	0.00476133	+	0.0331158i	0.000277216	+	0.00192808i
$296$	81.2425	−	52.2114i	4.72212	−	3.03472i
$297$	−0.139370	+	0.160842i	−0.00808707	+	0.00933297i
$298$	−37.0117			−2.14403
$299$	−9.50396	−	23.3488i	−0.549628	−	1.35030i
$300$	−29.0850			−1.67922
$301$	3.67709	−	4.24358i	0.211944	−	0.244596i
$302$	7.19985	−	4.62706i	0.414305	−	0.266258i
$303$	0.935807	+	6.50868i	0.0537607	+	0.373914i
$304$	26.7229	+	58.5150i	1.53266	+	3.35606i
$305$	−0.0198321	+	0.137935i	−0.00113558	+	0.00789814i
$306$	18.0267	−	5.29311i	1.03052	−	0.302587i
$307$	14.6406	+	9.40893i	0.835582	+	0.536996i	0.887047	−	0.461679i	$-0.152753\pi$
$307$	14.6406	+	9.40893i	0.835582	+	0.536996i	−0.0514652	+	0.998675i	$0.516389\pi$
$308$	−0.514293	+	1.12614i	−0.0293045	+	0.0641680i
$309$	1.08216	+	0.317752i	0.0615622	+	0.0180763i
$310$	0.0687688	+	0.0793635i	0.00390581	+	0.00450754i
$311$	−0.992576	−	1.14549i	−0.0562838	−	0.0649550i	0.726910	−	0.686733i	$-0.240956\pi$
$311$	−0.992576	−	1.14549i	−0.0562838	−	0.0649550i	−0.783193	+	0.621778i	$0.786410\pi$
$312$	−53.8260	−	15.8047i	−3.04730	−	0.894768i
$313$	−13.2861	+	29.0924i	−0.750972	+	1.64440i	0.0136388	+	0.999907i	$0.495659\pi$
$313$	−13.2861	+	29.0924i	−0.750972	+	1.64440i	−0.764611	+	0.644492i	$0.777069\pi$
$314$	0.512133	+	0.329128i	0.0289014	+	0.0185738i
$315$	0.00939779	−	0.00275944i	0.000529506	−	0.000155477i
$316$	0.186875	−	1.29974i	0.0105125	−	0.0731163i
$317$	−8.67181	−	18.9886i	−0.487057	−	1.06651i	−0.980462	−	0.196707i	$-0.936975\pi$
$317$	−8.67181	−	18.9886i	−0.487057	−	1.06651i	0.493405	−	0.869800i	$-0.335752\pi$
$318$	−1.41912	−	9.87019i	−0.0795803	−	0.553493i
$319$	0.643381	−	0.413476i	0.0360224	−	0.0231502i
$320$	−0.296462	+	0.342136i	−0.0165727	+	0.0191260i
$321$	4.16995			0.232744
$322$	−13.0123	+	3.23627i	−0.725148	+	0.180350i
$323$	−23.7449			−1.32120
$324$	−3.80940	+	4.39628i	−0.211633	+	0.244238i
$325$	−22.1096	+	14.2090i	−1.22642	+	0.788171i
$326$	4.70230	+	32.7052i	0.260436	+	1.81137i
$327$	7.62398	+	16.6942i	0.421607	+	0.923190i
$328$	2.80099	−	19.4813i	0.154659	−	1.07567i
$329$	−7.47580	+	2.19509i	−0.412154	+	0.121019i
$330$	0.00490292	+	0.00315091i	0.000269897	+	0.000173452i
$331$	5.97382	−	13.0808i	0.328351	−	0.718988i	−0.671405	−	0.741091i	$-0.734309\pi$
$331$	5.97382	−	13.0808i	0.328351	−	0.718988i	0.999756	+	0.0221026i	$0.00703604\pi$
$332$	−9.09860	−	2.67159i	−0.499351	−	0.146623i
$333$	−5.92579	−	6.83873i	−0.324731	−	0.374760i
$334$	7.14320	+	8.24369i	0.390858	+	0.451075i
$335$	0.0300760	+	0.00883111i	0.00164323	+	0.000482495i
$336$	−7.56247	+	16.5595i	−0.412567	+	0.903395i
$337$	17.7193	+	11.3875i	0.965234	+	0.620318i	0.925442	−	0.378890i	$-0.123694\pi$
$337$	17.7193	+	11.3875i	0.965234	+	0.620318i	0.0397924	+	0.999208i	$0.487330\pi$
$338$	−39.2477	+	11.5242i	−2.13479	+	0.626832i
$339$	0.250306	−	1.74091i	0.0135947	−	0.0945535i
$340$	−0.159047	−	0.348264i	−0.00862552	−	0.0188873i
$341$	0.116146	+	0.807816i	0.00628968	+	0.0437457i
$342$	8.31132	−	5.34136i	0.449425	−	0.288828i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	59.9258			3.23098
$345$	0.00473448	+	0.0467338i	0.000254896	+	0.00251606i
$346$	−15.0845			−0.810947
$347$	9.29482	−	10.7268i	0.498972	−	0.575845i	−0.449269	−	0.893397i	$-0.648315\pi$
$347$	9.29482	−	10.7268i	0.498972	−	0.575845i	0.948241	+	0.317552i	$0.102861\pi$
$348$	17.5855	−	11.3015i	0.942684	−	0.605826i
$349$	2.87441	+	19.9919i	0.153864	+	1.07014i	0.909665	+	0.415343i	$0.136339\pi$
$349$	2.87441	+	19.9919i	0.153864	+	1.07014i	−0.755801	+	0.654801i	$0.772752\pi$
$350$	5.80721	+	12.7160i	0.310408	+	0.679699i
$351$	−0.748069	+	5.20294i	−0.0399290	+	0.277712i
$352$	−6.03498	+	1.77203i	−0.321666	+	0.0944495i
$353$	5.00794	+	3.21841i	0.266546	+	0.171299i	0.667086	−	0.744980i	$-0.267541\pi$
$353$	5.00794	+	3.21841i	0.266546	+	0.171299i	−0.400540	+	0.916279i	$0.631178\pi$
$354$	−3.96734	+	8.68727i	−0.210862	+	0.461723i
$355$	0.104200	+	0.0305959i	0.00553037	+	0.00162386i
$356$	27.4864	+	31.7210i	1.45678	+	1.68121i
$357$	−4.40048	−	5.07842i	−0.232898	−	0.268779i
$358$	−59.3751	−	17.4341i	−3.13807	−	0.921420i
$359$	8.13416	−	17.8113i	0.429305	−	0.940046i	−0.564134	−	0.825683i	$-0.690790\pi$
$359$	8.13416	−	17.8113i	0.429305	−	0.940046i	0.993439	−	0.114363i	$-0.0364828\pi$
$360$	0.0879366	+	0.0565134i	0.00463467	+	0.00297852i
$361$	6.24969	−	1.83508i	0.328931	−	0.0965829i
$362$	0.495838	−	3.44863i	0.0260607	−	0.181256i
$363$	−4.55075	−	9.96475i	−0.238852	−	0.523014i
$364$	4.35161	+	30.2661i	0.228086	+	1.58637i
$365$	−0.00141633		0.000910223i	−7.41343e−5		4.76433e-5i
$366$	−26.0499	+	30.0632i	−1.36165	+	1.57143i
$367$	−4.56978			−0.238540			−0.119270	−	0.992862i	$-0.538055\pi$
$367$	−4.56978			−0.238540			−0.119270	+	0.992862i	$0.538055\pi$
$368$	−71.4083	−	50.2319i	−3.72241	−	2.61852i
$369$	−1.84418			−0.0960040
$370$	−0.162276	+	0.187276i	−0.00843632	+	0.00973603i
$371$	−3.00035	+	1.92821i	−0.155771	+	0.100108i
$372$	3.17463	+	22.0800i	0.164597	+	1.14480i
$373$	14.4110	+	31.5558i	0.746176	+	1.63390i	0.773120	+	0.634260i	$0.218695\pi$
$373$	14.4110	+	31.5558i	0.746176	+	1.63390i	−0.0269437	+	0.999637i	$0.508577\pi$
$374$	0.569042	−	3.95778i	0.0294245	−	0.204652i
$375$	0.0939770	−	0.0275941i	0.00485295	−	0.00142496i
$376$	−69.9523	−	44.9556i	−3.60751	−	2.31841i
$377$	7.84684	−	17.1822i	0.404133	−	0.884927i
$378$	2.68266	+	0.787699i	0.137981	+	0.0405149i
$379$	7.45638	+	8.60512i	0.383008	+	0.442015i	0.914216	−	0.405226i	$-0.132807\pi$
$379$	7.45638	+	8.60512i	0.383008	+	0.442015i	−0.531208	+	0.847241i	$0.678262\pi$
$380$	−0.131844	−	0.152156i	−0.00676346	−	0.00780545i
$381$	−1.75173	−	0.514353i	−0.0897437	−	0.0263511i
$382$	5.11327	−	11.1965i	0.261618	−	0.572863i
$383$	20.0362	+	12.8765i	1.02380	+	0.657956i	0.940929	−	0.338604i	$-0.109955\pi$
$383$	20.0362	+	12.8765i	1.02380	+	0.657956i	0.0828710	+	0.996560i	$0.473591\pi$
$384$	−67.2808	+	19.7554i	−3.43341	+	1.00814i
$385$	0.000296657	−	0.00206329i	1.51190e−5	−	0.000105155i
$386$	−30.1739	−	66.0717i	−1.53581	−	3.36296i
$387$	−0.799107	−	5.55791i	−0.0406209	−	0.282525i
$388$	−58.6795	+	37.7110i	−2.97900	+	1.91449i
$389$	−2.00490	+	2.31378i	−0.101653	+	0.117313i	−0.804296	−	0.594229i	$-0.797457\pi$
$389$	−2.00490	+	2.31378i	−0.101653	+	0.117313i	0.702644	+	0.711542i	$0.252003\pi$
$390$	0.143946			0.00728898
$391$	27.8157	−	16.2739i	1.40670	−	0.823006i
$392$	10.6723			0.539033
$393$	−4.84827	+	5.59520i	−0.244563	+	0.282241i
$394$	16.8943	−	10.8573i	0.851123	−	0.546984i
$395$	0.000314650		0.00218844i	1.58317e−5		0.000110112i
$396$	0.514293	+	1.12614i	0.0258442	+	0.0565908i
$397$	0.169283	−	1.17739i	0.00849608	−	0.0590915i	−0.985132	−	0.171797i	$-0.945043\pi$
$397$	0.169283	−	1.17739i	0.00849608	−	0.0590915i	0.993628	+	0.112706i	$0.0359517\pi$
$398$	24.4832	−	7.18893i	1.22723	−	0.360348i
$399$	−2.97267	−	1.91042i	−0.148820	−	0.0956406i
$400$	−37.8116	+	82.7959i	−1.89058	+	4.13980i
$401$	8.50615	+	2.49763i	0.424777	+	0.124726i	0.487132	−	0.873328i	$-0.338043\pi$
$401$	8.50615	+	2.49763i	0.424777	+	0.124726i	−0.0623553	+	0.998054i	$0.519861\pi$
$402$	5.85958	+	6.76231i	0.292249	+	0.337273i
$403$	13.2001	+	15.2337i	0.657542	+	0.758844i
$404$	36.7017	+	10.7766i	1.82598	+	0.536155i
$405$	0.00406880	−	0.00890943i	0.000202180	−	0.000442713i
$406$	−8.45223	−	5.43192i	−0.419477	−	0.269581i
$407$	−1.84782	+	0.542569i	−0.0915930	+	0.0268941i
$408$	10.2061	−	70.9850i	0.505277	−	3.51428i
$409$	−2.18943	−	4.79419i	−0.108261	−	0.237058i	0.847746	−	0.530402i	$-0.177959\pi$
$409$	−2.18943	−	4.79419i	−0.108261	−	0.237058i	−0.956007	+	0.293344i	$0.905232\pi$
$410$	0.00718720	+	0.0499881i	0.000354951	+	0.00246874i
$411$	−11.7660	+	7.56154i	−0.580373	+	0.372983i
$412$	4.29643	−	4.95835i	0.211670	−	0.244280i
$413$	3.41581			0.168081
$414$	−6.07544	+	11.9534i	−0.298592	+	0.587475i
$415$	0.0159665			0.000783764
$416$	−101.731	+	117.404i	−4.98779	+	5.75621i
$417$	14.9167	−	9.58639i	0.730474	−	0.469447i
$418$	−0.299236	−	2.08123i	−0.0146361	−	0.101796i
$419$	−14.8625	−	32.5443i	−0.726079	−	1.58989i	−0.805184	−	0.593025i	$-0.797934\pi$
$419$	−14.8625	−	32.5443i	−0.726079	−	1.58989i	0.0791054	−	0.996866i	$-0.474794\pi$
$420$	0.00810853	−	0.0563961i	0.000395656	−	0.00275185i
$421$	−6.43562	+	1.88967i	−0.313653	+	0.0920968i	−0.434770	−	0.900541i	$-0.643170\pi$
$421$	−6.43562	+	1.88967i	−0.313653	+	0.0920968i	0.121117	+	0.992638i	$0.461352\pi$
$422$	−13.4515	−	8.64476i	−0.654810	−	0.420821i
$423$	−3.23667	+	7.08732i	−0.157372	+	0.344597i
$424$	−36.5213	−	10.7236i	−1.77363	−	0.520785i
$425$	−22.0020	−	25.3916i	−1.06725	−	1.23167i
$426$	20.3009	+	23.4285i	0.983581	+	1.13511i
$427$	13.6513	+	4.00840i	0.660635	+	0.193980i
$428$	10.0768	−	22.0650i	0.487078	−	1.06655i
$429$	0.941107	+	0.604813i	0.0454371	+	0.0292006i
$430$	−0.147538	+	0.0433211i	−0.00711492	+	0.00208913i
$431$	−3.63963	+	25.3142i	−0.175315	+	1.21934i	0.692117	+	0.721785i	$0.256678\pi$
$431$	−3.63963	+	25.3142i	−0.175315	+	1.21934i	−0.867432	+	0.497556i	$0.834231\pi$
$432$	7.56247	+	16.5595i	0.363850	+	0.796719i
$433$	−0.612710	−	4.26149i	−0.0294449	−	0.204794i	0.969788	−	0.243948i	$-0.0784427\pi$
$433$	−0.612710	−	4.26149i	−0.0294449	−	0.204794i	−0.999233	+	0.0391542i	$0.987534\pi$
$434$	9.01956	−	5.79652i	0.432953	−	0.278242i
$435$	−0.0230491	+	0.0266001i	−0.00110512	+	0.00127538i
$436$	106.760			5.11286
$437$	11.6236	−	12.3321i	0.556034	−	0.589922i
$438$	−0.480594			−0.0229637
$439$	19.4544	−	22.4516i	0.928507	−	1.07155i	−0.0687568	−	0.997633i	$-0.521903\pi$
$439$	19.4544	−	22.4516i	0.928507	−	1.07155i	0.997264	−	0.0739211i	$-0.0235513\pi$
$440$	0.0187150	−	0.0120274i	0.000892203	−	0.000573384i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−41.0249	−	89.8321i	−1.95136	−	4.27288i
$443$	2.29569	−	15.9669i	0.109072	−	0.758611i	−0.859726	−	0.510756i	$-0.829365\pi$
$443$	2.29569	−	15.9669i	0.109072	−	0.758611i	0.968797	−	0.247854i	$-0.0797255\pi$
$444$	−50.5065	+	14.8300i	−2.39693	+	0.703803i
$445$	−0.0594528	−	0.0382080i	−0.00281833	−	0.00181123i
$446$	19.5689	−	42.8498i	0.926612	−	2.02900i
$447$	12.7016	+	3.72951i	0.600763	+	0.176400i
$448$	30.2681	+	34.9313i	1.43003	+	1.65035i
$449$	−2.49683	−	2.88150i	−0.117833	−	0.135986i	0.693768	−	0.720198i	$-0.255949\pi$
$449$	−2.49683	−	2.88150i	−0.117833	−	0.135986i	−0.811601	+	0.584212i	$0.801404\pi$
$450$	13.4130	+	3.93842i	0.632296	+	0.185659i
$451$	−0.163044	+	0.357017i	−0.00767744	+	0.0168113i
$452$	−8.60707	−	5.53143i	−0.404842	−	0.260176i
$453$	−2.93708	+	0.862403i	−0.137996	+	0.0405192i
$454$	8.16898	−	56.8165i	0.383389	−	2.66653i
$455$	−0.0213874	−	0.0468319i	−0.00100266	−	0.00219551i
$456$	−5.36696	−	37.3281i	−0.251331	−	1.74805i
$457$	−16.9069	+	10.8654i	−0.790872	+	0.508263i	−0.872625	−	0.488390i	$-0.837584\pi$
$457$	−16.9069	+	10.8654i	−0.790872	+	0.508263i	0.0817534	+	0.996653i	$0.473948\pi$
$458$	26.7405	−	30.8602i	1.24950	−	1.44200i
$459$	−6.71971			−0.313649
$460$	0.258730	+	0.0878808i	0.0120633	+	0.00409746i
$461$	32.0611			1.49323			0.746617	−	0.665254i	$-0.231677\pi$
$461$	32.0611			1.49323			0.746617	+	0.665254i	$0.231677\pi$
$462$	0.389666	−	0.449699i	0.0181289	−	0.0209219i
$463$	21.9755	−	14.1228i	1.02129	−	0.656343i	0.0809986	−	0.996714i	$-0.474189\pi$
$463$	21.9755	−	14.1228i	1.02129	−	0.656343i	0.940291	+	0.340371i	$0.110553\pi$
$464$	−9.31006	−	64.7529i	−0.432209	−	3.00608i
$465$	−0.0156028	−	0.0341653i	−0.000723561	−	0.00158438i
$466$	9.25563	−	64.3743i	0.428759	−	2.98208i
$467$	9.08488	−	2.66756i	0.420398	−	0.123440i	−0.0646898	−	0.997905i	$-0.520606\pi$
$467$	9.08488	−	2.66756i	0.420398	−	0.123440i	0.485088	+	0.874465i	$0.338788\pi$
$468$	25.7233	+	16.5314i	1.18906	+	0.764162i
$469$	1.32946	−	2.91112i	0.0613889	−	0.134423i
$470$	0.204722	+	0.0601119i	0.00944314	+	0.00277276i
$471$	−0.142588	−	0.164555i	−0.00657009	−	0.00758229i
$472$	23.8727	+	27.5506i	1.09883	+	1.26812i
$473$	−1.14661	−	0.336676i	−0.0527213	−	0.0154804i
$474$	−0.262179	+	0.574093i	−0.0120423	+	0.0263690i
$475$	−14.8631	−	9.55191i	−0.681964	−	0.438272i
$476$	−37.5060	+	11.0127i	−1.71908	+	0.504768i
$477$	−0.507570	+	3.53022i	−0.0232400	+	0.161638i
$478$	13.7149	+	30.0315i	0.627305	+	1.37361i
$479$	1.76427	+	12.2707i	0.0806113	+	0.560664i	0.989600	+	0.143844i	$0.0459464\pi$
$479$	1.76427	+	12.2707i	0.0806113	+	0.560664i	−0.908989	+	0.416820i	$0.863145\pi$
$480$	0.243515	−	0.156497i	0.0111149	−	0.00714309i
$481$	−31.1486	+	35.9474i	−1.42025	+	1.63906i
$482$	37.3929			1.70320
$483$	4.79164	+	0.200583i	0.218027	+	0.00912685i
$484$	−63.7248			−2.89658
$485$	0.0769104	−	0.0887593i	0.00349232	−	0.00403035i
$486$	2.35207	−	1.51158i	0.106692	−	0.0685668i
$487$	−4.10758	−	28.5689i	−0.186132	−	1.29458i	−0.841907	−	0.539622i	$-0.818567\pi$
$487$	−4.10758	−	28.5689i	−0.186132	−	1.29458i	0.655775	−	0.754956i	$-0.272342\pi$
$488$	63.0775	+	138.120i	2.85538	+	6.25242i
$489$	1.68185	−	11.6975i	0.0760558	−	0.528980i
$490$	−0.0262754	+	0.00771515i	−0.00118700	+	0.000348535i
$491$	12.5222	+	8.04755i	0.565121	+	0.363181i	0.791793	−	0.610790i	$-0.209148\pi$
$491$	12.5222	+	8.04755i	0.565121	+	0.363181i	−0.226672	+	0.973971i	$0.572784\pi$
$492$	−4.45648	+	9.75834i	−0.200914	+	0.439940i
$493$	23.1693	+	6.80313i	1.04349	+	0.306398i
$494$	−34.0082	−	39.2476i	−1.53010	−	1.76583i
$495$	−0.00136507	−	0.00157537i	−6.13551e−5	−	7.08076e-5i
$496$	66.9821	+	19.6677i	3.00758	+	0.883106i
$497$	4.60601	−	10.0858i	0.206608	−	0.452408i
$498$	3.83421	+	2.46409i	0.171815	+	0.110419i
$499$	25.2340	−	7.40938i	1.12963	−	0.331689i	0.337068	−	0.941480i	$-0.390565\pi$
$499$	25.2340	−	7.40938i	1.12963	−	0.331689i	0.792562	+	0.609791i	$0.208747\pi$
$500$	0.0810845	−	0.563955i	0.00362621	−	0.0252208i
$501$	−1.62070	−	3.54884i	−0.0724075	−	0.158550i
$502$	−5.61031	−	39.0205i	−0.250400	−	1.74157i
$503$	9.72914	−	6.25254i	0.433801	−	0.278787i	−0.305461	−	0.952204i	$-0.598811\pi$
$503$	9.72914	−	6.25254i	0.433801	−	0.278787i	0.739262	+	0.673417i	$0.235174\pi$
$504$	6.98888	−	8.06560i	0.311310	−	0.359270i
$505$	−0.0644051			−0.00286599
$506$	1.77694	+	2.23295i	0.0789944	+	0.0992668i
$507$	14.6302			0.649748
$508$	−6.95475	+	8.02621i	−0.308567	+	0.356105i
$509$	−7.23329	+	4.64856i	−0.320610	+	0.206044i	−0.691039	−	0.722817i	$-0.742847\pi$
$509$	−7.23329	+	4.64856i	−0.320610	+	0.206044i	0.370429	+	0.928861i	$0.379211\pi$
$510$	0.0261884	+	0.182144i	0.00115964	+	0.00806548i
$511$	0.0714064	+	0.156358i	0.00315883	+	0.00691688i
$512$	−21.2683	+	147.924i	−0.939935	+	6.53739i
$513$	−3.39048	+	0.995536i	−0.149693	+	0.0439540i
$514$	12.3390	+	7.92982i	0.544252	+	0.349769i
$515$	−0.00458900	+	0.0100485i	−0.000202215	+	0.000442790i
$516$	−31.3404	−	9.20237i	−1.37968	−	0.405112i
$517$	1.08589	+	1.25318i	0.0477573	+	0.0551149i
$518$	16.5680	+	19.1205i	0.727956	+	0.840106i
$519$	5.17665	+	1.52000i	0.227230	+	0.0667207i
$520$	0.228253	−	0.499805i	0.0100096	−	0.0219179i
$521$	−0.322688	−	0.207379i	−0.0141372	−	0.00908543i	0.533553	−	0.845767i	$-0.320856\pi$
$521$	−0.322688	−	0.207379i	−0.0141372	−	0.00908543i	−0.547690	+	0.836681i	$0.684493\pi$
$522$	−9.64020	+	2.83062i	−0.421940	+	0.123893i
$523$	3.90179	−	27.1376i	0.170613	−	1.18664i	−0.706979	−	0.707235i	$-0.749942\pi$
$523$	3.90179	−	27.1376i	0.170613	−	1.18664i	0.877592	−	0.479408i	$-0.159148\pi$
$524$	17.8907	+	39.1752i	0.781560	+	1.71138i
$525$	−0.711561	−	4.94901i	−0.0310550	−	0.215993i
$526$	−63.2696	+	40.6609i	−2.75869	+	1.77290i
$527$	−16.8747	+	19.4744i	−0.735072	+	0.848318i
$528$	3.87438			0.168611
$529$	−5.16447	+	22.4127i	−0.224542	+	0.974464i
$530$	0.0976681			0.00424243
$531$	2.23688	−	2.58150i	0.0970725	−	0.112028i
$532$	−17.2924	+	11.1131i	−0.749719	+	0.481815i
$533$	1.37957	+	9.59513i	0.0597559	+	0.415611i
$534$	−8.38044	−	18.3506i	−0.362657	−	0.794108i
$535$	−0.00581253	+	0.0404270i	−0.000251298	+	0.00174781i
$536$	32.7714	−	9.62254i	1.41551	−	0.415630i
$537$	18.6194	+	11.9660i	0.803487	+	0.516370i
$538$	−30.7193	+	67.2659i	−1.32440	+	2.90004i
$539$	−0.204203	−	0.0599594i	−0.00879564	−	0.00258263i
$540$	−0.0373113	−	0.0430596i	−0.00160562	−	0.00185299i
$541$	−13.2589	−	15.3016i	−0.570045	−	0.657867i	0.395389	−	0.918514i	$-0.370610\pi$
$541$	−13.2589	−	15.3016i	−0.570045	−	0.657867i	−0.965434	+	0.260646i	$0.916064\pi$
$542$	−49.5741	−	14.5563i	−2.12939	−	0.625245i
$543$	−0.517665	+	1.13353i	−0.0222151	+	0.0486443i
$544$	−167.067	−	107.368i	−7.16295	−	4.60335i
$545$	−0.172475	+	0.0506431i	−0.00738800	+	0.00216931i
$546$	2.09154	−	14.5469i	0.0895094	−	0.622552i
$547$	3.45164	+	7.55804i	0.147582	+	0.323159i	0.968957	−	0.247229i	$-0.0795201\pi$
$547$	3.45164	+	7.55804i	0.147582	+	0.323159i	−0.821375	+	0.570388i	$0.806793\pi$
$548$	11.5787	+	80.5315i	0.494617	+	3.44014i
$549$	11.9691	−	7.69206i	0.510828	−	0.328289i
$550$	1.94829	−	2.24845i	0.0830755	−	0.0958742i
$551$	12.6982			0.540960
$552$	31.8703	+	40.0493i	1.35649	+	1.70461i
$553$	0.225732			0.00959910
$554$	−11.1145	+	12.8268i	−0.472210	+	0.544959i
$555$	0.0745605	−	0.0479171i	0.00316492	−	0.00203397i
$556$	−14.6793	−	102.096i	−0.622539	−	4.32985i
$557$	−9.81620	−	21.4945i	−0.415926	−	0.910750i	−0.995404	−	0.0957625i	$-0.969471\pi$
$557$	−9.81620	−	21.4945i	−0.415926	−	0.910750i	0.579479	−	0.814987i	$-0.303256\pi$
$558$	1.52584	−	10.6124i	0.0645939	−	0.449261i
$559$	−28.3197	+	8.31541i	−1.19780	+	0.351704i
$560$	−0.150000	−	0.0963994i	−0.00633868	−	0.00407362i
$561$	−0.594091	+	1.30088i	−0.0250826	+	0.0549231i
$562$	−47.7157	−	14.0106i	−2.01276	−	0.591001i
$563$	24.8778	+	28.7105i	1.04847	+	1.21000i	0.977150	+	0.212551i	$0.0681773\pi$
$563$	24.8778	+	28.7105i	1.04847	+	1.21000i	0.0713249	+	0.997453i	$0.477277\pi$
$564$	29.6806	+	34.2533i	1.24978	+	1.44232i
$565$	0.0165290	+	0.00485335i	0.000695380	+	0.000204182i
$566$	−35.3014	+	77.2992i	−1.48383	+	3.24913i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	113.539	−	33.3379i	4.76397	−	1.39883i
$569$	−4.95600	+	34.4697i	−0.207766	+	1.44505i	0.572658	+	0.819794i	$0.305912\pi$
$569$	−4.95600	+	34.4697i	−0.207766	+	1.44505i	−0.780424	+	0.625251i	$0.784997\pi$
$570$	0.0401985	+	0.0880223i	0.00168373	+	0.00368685i
$571$	0.494121	+	3.43668i	0.0206783	+	0.143821i	0.997545	−	0.0700284i	$-0.0223090\pi$
$571$	0.494121	+	3.43668i	0.0206783	+	0.143821i	−0.976867	+	0.213849i	$0.931400\pi$
$572$	5.47453	−	3.51827i	0.228901	−	0.147106i
$573$	−2.88299	+	3.32714i	−0.120438	+	0.138993i
$574$	5.15615			0.215214
$575$	23.9577	+	1.00290i	0.999106	+	0.0418237i
$576$	46.2207			1.92586
$577$	11.3424	−	13.0898i	0.472190	−	0.544937i	−0.468829	−	0.883289i	$-0.655324\pi$
$577$	11.3424	−	13.0898i	0.472190	−	0.544937i	0.941020	+	0.338352i	$0.109869\pi$
$578$	66.2215	−	42.5580i	2.75445	−	1.77018i
$579$	3.69723	+	25.7148i	0.153652	+	1.06867i
$580$	0.0850541	+	0.186242i	0.00353168	+	0.00773329i
$581$	0.231993	−	1.61355i	0.00962470	−	0.0669413i
$582$	32.1675	−	9.44522i	1.33339	−	0.391517i
$583$	0.638546	+	0.410369i	0.0264459	+	0.0169957i
$584$	−0.762072	+	1.66870i	−0.0315347	+	0.0690515i
$585$	−0.0493989	−	0.0145048i	−0.00204239	−	0.000599701i
$586$	46.4360	+	53.5900i	1.91825	+	2.21378i
$587$	−24.8872	−	28.7214i	−1.02721	−	1.18546i	−0.982463	−	0.186460i	$-0.940298\pi$
$587$	−24.8872	−	28.7214i	−1.02721	−	1.18546i	−0.0447433	−	0.998999i	$-0.514247\pi$
$588$	−5.58148	−	1.63887i	−0.230176	−	0.0675859i
$589$	−5.62908	+	12.3260i	−0.231942	+	0.507882i
$590$	−0.0786917	−	0.0505721i	−0.00323968	−	0.00208202i
$591$	−6.89179	+	2.02361i	−0.283490	+	0.0832403i
$592$	−23.4439	+	163.056i	−0.963537	+	6.70155i
$593$	−18.0139	−	39.4449i	−0.739741	−	1.61981i	−0.783980	−	0.620786i	$-0.786814\pi$
$593$	−18.0139	−	39.4449i	−0.739741	−	1.61981i	0.0442393	−	0.999021i	$-0.485914\pi$
$594$	−0.0846825	−	0.588980i	−0.00347457	−	0.0241661i
$595$	0.0553684	−	0.0355831i	0.00226988	−	0.00145876i
$596$	50.4280	−	58.1970i	2.06561	−	2.38384i
$597$	−9.12649			−0.373522
$598$	66.7374	+	22.6682i	2.72910	+	0.926972i
$599$	−9.21798			−0.376637			−0.188318	−	0.982108i	$-0.560304\pi$
$599$	−9.21798			−0.376637			−0.188318	+	0.982108i	$0.560304\pi$
$600$	34.9437	−	40.3272i	1.42657	−	1.64635i
$601$	−9.69276	+	6.22916i	−0.395376	+	0.254093i	−0.723189	−	0.690650i	$-0.757325\pi$
$601$	−9.69276	+	6.22916i	−0.395376	+	0.254093i	0.327813	+	0.944743i	$0.393688\pi$
$602$	2.23423	+	15.5394i	0.0910605	+	0.633340i
$603$	−1.32946	−	2.91112i	−0.0541399	−	0.118550i
$604$	−2.53414	+	17.6254i	−0.103113	+	0.717166i
$605$	0.102950	−	0.0302289i	0.00418552	−	0.00122898i
$606$	−15.4663	−	9.93958i	−0.628275	−	0.403768i
$607$	8.26025	−	18.0874i	0.335273	−	0.734146i	−0.664642	−	0.747162i	$-0.731416\pi$
$607$	8.26025	−	18.0874i	0.335273	−	0.734146i	0.999915	+	0.0130159i	$0.00414321\pi$
$608$	−100.202	−	29.4219i	−4.06372	−	1.19322i
$609$	2.35326	+	2.71581i	0.0953589	+	0.110050i
$610$	−0.255147	−	0.294455i	−0.0103306	−	0.0119221i
$611$	39.2961	+	11.5384i	1.58975	+	0.466793i
$612$	−16.2383	+	35.5569i	−0.656395	+	1.43730i
$613$	29.1646	+	18.7429i	1.17795	+	0.757020i	0.975007	−	0.222172i	$-0.0713147\pi$
$613$	29.1646	+	18.7429i	1.17795	+	0.757020i	0.202938	+	0.979192i	$0.434951\pi$
$614$	−46.6870	+	13.7086i	−1.88414	+	0.553232i
$615$	0.00257061	−	0.0178790i	0.000103657	−	0.000720951i
$616$	−0.943542	−	2.06607i	−0.0380164	−	0.0832443i
$617$	−5.24132	−	36.4541i	−0.211007	−	1.46759i	−0.769802	−	0.638283i	$-0.779645\pi$
$617$	−5.24132	−	36.4541i	−0.211007	−	1.46759i	0.558795	−	0.829306i	$-0.311264\pi$
$618$	−2.65278	+	1.70484i	−0.106711	+	0.0685787i
$619$	18.7952	−	21.6908i	0.755443	−	0.871828i	−0.239641	−	0.970862i	$-0.577030\pi$
$619$	18.7952	−	21.6908i	0.755443	−	0.871828i	0.995084	+	0.0990339i	$0.0315752\pi$
$620$	−0.218488			−0.00877468
$621$	3.28944	−	3.48992i	0.132001	−	0.140046i
$622$	4.23778			0.169919
$623$	−4.72509	+	5.45305i	−0.189307	+	0.218472i
$624$	80.5008	−	51.7347i	3.22261	−	2.07105i
$625$	−3.55767	−	24.7441i	−0.142307	−	0.989764i
$626$	−37.1466	−	81.3397i	−1.48468	−	3.25099i
$627$	−0.107026	+	0.744384i	−0.00427422	+	0.0297278i
$628$	−1.21530	+	0.356843i	−0.0484956	+	0.0142396i
$629$	−51.1535	−	32.8743i	−2.03962	−	1.31079i
$630$	−0.0113760	+	0.0249100i	−0.000453231	+	0.000992437i
$631$	20.3813	+	5.98449i	0.811366	+	0.238239i	0.660994	−	0.750391i	$-0.270135\pi$
$631$	20.3813	+	5.98449i	0.811366	+	0.238239i	0.150372	+	0.988629i	$0.451953\pi$
$632$	1.57761	+	1.82066i	0.0627541	+	0.0724221i
$633$	3.74516	+	4.32214i	0.148857	+	0.171790i
$634$	56.0006	+	16.4433i	2.22407	+	0.653045i
$635$	0.00742833	−	0.0162658i	0.000294784	−	0.000645487i
$636$	17.4534	+	11.2166i	0.692072	+	0.444768i
$637$	−5.04352	+	1.48091i	−0.199831	+	0.0586758i
$638$	−0.304309	+	2.11651i	−0.0120477	+	0.0837936i
$639$	−4.60601	−	10.0858i	−0.182211	−	0.398986i
$640$	−0.0977425	−	0.679814i	−0.00386361	−	0.0268720i
$641$	−4.90075	+	3.14952i	−0.193568	+	0.124399i	−0.633835	−	0.773468i	$-0.718520\pi$
$641$	−4.90075	+	3.14952i	−0.193568	+	0.124399i	0.440267	+	0.897867i	$0.354884\pi$
$642$	−7.63489	+	8.81114i	−0.301325	+	0.347748i
$643$	−13.2953			−0.524317			−0.262159	−	0.965025i	$-0.584434\pi$
$643$	−13.2953			−0.524317			−0.262159	+	0.965025i	$0.584434\pi$
$644$	12.6404	−	24.8699i	0.498103	−	0.980012i
$645$	0.0549970			0.00216551
$646$	43.4753	−	50.1732i	1.71051	−	1.97404i
$647$	3.37624	−	2.16978i	0.132734	−	0.0853029i	−0.472589	−	0.881283i	$-0.656680\pi$
$647$	3.37624	−	2.16978i	0.132734	−	0.0853029i	0.605323	+	0.795980i	$0.293044\pi$
$648$	−1.51883	−	10.5637i	−0.0596652	−	0.414981i
$649$	−0.301993	−	0.661272i	−0.0118543	−	0.0259572i
$650$	10.4575	−	72.7333i	0.410176	−	2.85284i
$651$	−3.67940	+	1.08037i	−0.144207	+	0.0423430i
$652$	−57.8324	−	37.1666i	−2.26489	−	1.45556i
$653$	−10.5409	+	23.0813i	−0.412497	+	0.903243i	0.583352	+	0.812220i	$0.301741\pi$
$653$	−10.5409	+	23.0813i	−0.412497	+	0.903243i	−0.995849	+	0.0910229i	$0.970986\pi$
$654$	−49.2339	−	14.4564i	−1.92520	−	0.565289i
$655$	−0.0474866	−	0.0548024i	−0.00185545	−	0.00214131i
$656$	21.9853	+	25.3724i	0.858383	+	0.990626i
$657$	0.164929	+	0.0484275i	0.00643449	+	0.00188934i
$658$	9.04944	−	19.8155i	0.352784	−	0.772489i
$659$	7.89226	+	5.07205i	0.307439	+	0.197579i	0.685258	−	0.728301i	$-0.259689\pi$
$659$	7.89226	+	5.07205i	0.307439	+	0.197579i	−0.377819	+	0.925879i	$0.623326\pi$
$660$	−0.0116347	+	0.00341625i	−0.000452879	+	0.000132977i
$661$	−4.99083	+	34.7120i	−0.194121	+	1.35014i	0.626836	+	0.779151i	$0.284349\pi$
$661$	−4.99083	+	34.7120i	−0.194121	+	1.35014i	−0.820957	+	0.570990i	$0.806560\pi$
$662$	16.7023	+	36.5729i	0.649152	+	1.42145i
$663$	5.02681	+	34.9623i	0.195225	+	1.35782i
$664$	14.6356	−	9.40574i	0.567972	−	0.365013i
$665$	0.0226648	−	0.0261566i	0.000878905	−	0.00101431i
$666$	25.3000			0.980356
$667$	−14.8751	+	8.70285i	−0.575967	+	0.336976i
$668$	−22.6949			−0.878092
$669$	−11.0334	+	12.7332i	−0.426575	+	0.492294i
$670$	−0.0737273	+	0.0473817i	−0.00284833	+	0.00183051i
$671$	−0.430927	−	2.99717i	−0.0166358	−	0.115704i
$672$	−12.2771	−	26.8831i	−0.473600	−	1.03704i
$673$	−0.416405	+	2.89616i	−0.0160512	+	0.111639i	−0.996272	−	0.0862690i	$-0.972506\pi$
$673$	−0.416405	+	2.89616i	−0.0160512	+	0.111639i	0.980221	+	0.197908i	$0.0634146\pi$
$674$	−56.5049	+	16.5913i	−2.17649	+	0.639074i
$675$	−4.20619	−	2.70315i	−0.161896	−	0.104044i
$676$	35.3540	−	77.4146i	1.35977	−	2.97748i
$677$	−37.5925	−	11.0382i	−1.44480	−	0.424231i	−0.536980	−	0.843595i	$-0.680435\pi$
$677$	−37.5925	−	11.0382i	−1.44480	−	0.424231i	−0.907818	+	0.419364i	$0.862253\pi$
$678$	3.22027	+	3.71639i	0.123674	+	0.142727i
$679$	−7.85237	−	9.06212i	−0.301346	−	0.347772i
$680$	0.673962	+	0.197893i	0.0258453	+	0.00758886i
$681$	−8.52858	+	18.6750i	−0.326816	+	0.715627i
$682$	−1.91958	−	1.23364i	−0.0735044	−	0.0472384i
$683$	9.47492	−	2.78209i	0.362548	−	0.106454i	−0.0953851	−	0.995440i	$-0.530408\pi$
$683$	9.47492	−	2.78209i	0.362548	−	0.106454i	0.457933	+	0.888987i	$0.348590\pi$
$684$	−2.92535	+	20.3463i	−0.111854	+	0.777958i
$685$	−0.0569073	−	0.124610i	−0.00217431	−	0.00476108i
$686$	0.397900	+	2.76745i	0.0151919	+	0.105662i
$687$	−12.2864	+	7.89598i	−0.468755	+	0.301250i
$688$	−66.9399	+	77.2528i	−2.55206	+	2.94524i
$689$	18.7472			0.714213
$690$	−0.107417	−	0.0755624i	−0.00408931	−	0.00287661i
$691$	25.2649			0.961122			0.480561	−	0.876961i	$-0.340433\pi$
$691$	25.2649			0.961122			0.480561	+	0.876961i	$0.340433\pi$
$692$	20.5525	−	23.7188i	0.781288	−	0.901654i
$693$	−0.179039	+	0.115061i	−0.00680112	+	0.00437082i
$694$	5.64762	+	39.2801i	0.214381	+	1.49105i
$695$	0.0721460	+	0.157978i	0.00273665	+	0.00599244i
$696$	−5.45795	+	37.9609i	−0.206883	+	1.43890i
$697$	−11.8904	+	3.49132i	−0.450379	+	0.132243i
$698$	−47.5060	−	30.5303i	−1.79813	−	1.15559i
$699$	−9.66306	+	21.1591i	−0.365490	+	0.800312i
$700$	−27.9069	−	8.19420i	−1.05478	−	0.309712i
$701$	2.28950	+	2.64222i	0.0864731	+	0.0997953i	0.797337	−	0.603534i	$-0.206241\pi$
$701$	2.28950	+	2.64222i	0.0864731	+	0.0997953i	−0.710864	+	0.703329i	$0.751696\pi$
$702$	−9.62419	−	11.1069i	−0.363241	−	0.419203i
$703$	−30.6803	−	9.00854i	−1.15713	−	0.339763i
$704$	4.08638	−	8.94792i	0.154011	−	0.337238i
$705$	−0.0641988	−	0.0412581i	−0.00241787	−	0.00155387i
$706$	−15.9697	+	4.68914i	−0.601029	+	0.176478i
$707$	−0.935807	+	6.50868i	−0.0351946	+	0.244784i
$708$	−8.25438	−	18.0746i	−0.310218	−	0.679284i
$709$	3.14338	+	21.8627i	0.118052	+	0.821070i	0.959697	+	0.281038i	$0.0906788\pi$
$709$	3.14338	+	21.8627i	0.118052	+	0.821070i	−0.841644	+	0.540032i	$0.818412\pi$
$710$	−0.255433	+	0.164157i	−0.00958623	+	0.00616070i
$711$	0.147823	−	0.170597i	0.00554380	−	0.00639788i
$712$	−77.0052			−2.88589
$713$	−1.85363	−	18.2971i	−0.0694190	−	0.685231i
$714$	18.7877			0.703113
$715$	−0.00717538	+	0.00828083i	−0.000268344	+	0.000309686i
$716$	108.311	−	69.6074i	4.04778	−	2.60135i
$717$	−1.68050	−	11.6881i	−0.0627593	−	0.436501i
$718$	22.7424	+	49.7989i	0.848739	+	1.85848i
$719$	5.21378	−	36.2626i	0.194441	−	1.35237i	−0.625636	−	0.780115i	$-0.715161\pi$
$719$	5.21378	−	36.2626i	0.194441	−	1.35237i	0.820077	−	0.572253i	$-0.193930\pi$
$720$	−0.171083	+	0.0502346i	−0.00637590	+	0.00187213i
$721$	0.948808	+	0.609762i	0.0353354	+	0.0227087i
$722$	−7.56523	+	16.5655i	−0.281549	+	0.616506i
$723$	−12.8324	−	3.76793i	−0.477242	−	0.140131i
$724$	4.74704	+	5.47838i	0.176422	+	0.203602i
$725$	11.7661	+	13.5788i	0.436981	+	0.504303i
$726$	29.3877	+	8.62901i	1.09068	+	0.320253i
$727$	−1.27675	+	2.79569i	−0.0473520	+	0.103686i	−0.931829	−	0.362897i	$-0.881788\pi$
$727$	−1.27675	+	2.79569i	−0.0473520	+	0.103686i	0.884477	+	0.466583i	$0.154515\pi$
$728$	−47.1930	−	30.3291i	−1.74909	−	1.12407i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.000669904	−	0.00465928i	2.47943e−5	−	0.000172448i
$731$	−15.6743	−	34.3219i	−0.579735	−	1.26944i
$732$	−11.7785	−	81.9216i	−0.435347	−	3.02791i
$733$	5.68517	−	3.65364i	0.209987	−	0.134950i	−0.431420	−	0.902151i	$-0.641987\pi$
$733$	5.68517	−	3.65364i	0.209987	−	0.134950i	0.641407	+	0.767201i	$0.278351\pi$
$734$	8.36695	−	9.65598i	0.308830	−	0.356409i
$735$	0.00979454			0.000361277
$736$	137.545	−	34.2086i	5.06998	−	1.26095i
$737$	−0.681105			−0.0250888
$738$	3.37656	−	3.89676i	0.124293	−	0.143442i
$739$	−15.8459	+	10.1835i	−0.582901	+	0.374608i	−0.798609	−	0.601850i	$-0.794430\pi$
$739$	−15.8459	+	10.1835i	−0.582901	+	0.374608i	0.215708	+	0.976458i	$0.430794\pi$
$740$	−0.0733736	−	0.510324i	−0.00269727	−	0.0187599i
$741$	7.71603	+	16.8957i	0.283455	+	0.620680i
$742$	1.41912	−	9.87019i	0.0520975	−	0.362346i
$743$	−28.4411	+	8.35106i	−1.04340	+	0.306371i	−0.758149	−	0.652081i	$-0.773896\pi$
$743$	−28.4411	+	8.35106i	−1.04340	+	0.306371i	−0.285254	+	0.958452i	$0.592078\pi$
$744$	−34.4287	−	22.1260i	−1.26222	−	0.811178i
$745$	−0.0538619	+	0.117941i	−0.00197335	+	0.00432103i
$746$	−93.0633	−	27.3259i	−3.40729	−	1.00047i
$747$	−1.06752	−	1.23198i	−0.0390583	−	0.0450757i
$748$	5.44788	+	6.28719i	0.199194	+	0.229883i
$749$	4.00104	+	1.17481i	0.146195	+	0.0429266i
$750$	−0.113759	+	0.249097i	−0.00415389	+	0.00909575i
$751$	16.6708	+	10.7137i	0.608325	+	0.390947i	0.808229	−	0.588869i	$-0.200426\pi$
$751$	16.6708	+	10.7137i	0.608325	+	0.390947i	−0.199903	+	0.979816i	$0.564063\pi$
$752$	136.094	−	39.9608i	4.96284	−	1.45722i
$753$	−2.00661	+	13.9563i	−0.0731250	+	0.508595i
$754$	21.9391	+	48.0398i	0.798974	+	1.74951i
$755$	−0.00426685	−	0.0296766i	−0.000155287	−	0.00108004i
$756$	−4.89367	+	3.14497i	−0.177981	+	0.114381i
$757$	−8.55594	+	9.87408i	−0.310971	+	0.358880i	−0.889624	−	0.456694i	$-0.849033\pi$
$757$	−8.55594	+	9.87408i	−0.310971	+	0.358880i	0.578653	+	0.815574i	$0.303579\pi$
$758$	−31.8348			−1.15629
$759$	−0.384798	−	0.945353i	−0.0139673	−	0.0343141i
$760$	0.369371			0.0133985
$761$	12.1230	−	13.9907i	0.439460	−	0.507164i	−0.492206	−	0.870478i	$-0.663809\pi$
$761$	12.1230	−	13.9907i	0.439460	−	0.507164i	0.931667	+	0.363314i	$0.118355\pi$
$762$	4.29413	−	2.75967i	0.155560	−	0.0999722i
$763$	2.61186	+	18.1659i	0.0945556	+	0.657649i
$764$	10.6386	+	23.2952i	0.384890	+	0.842792i
$765$	0.00936667	−	0.0651466i	0.000338653	−	0.00235538i
$766$	−63.8929	+	18.7607i	−2.30854	+	0.677850i
$767$	−15.1047	−	9.70722i	−0.545400	−	0.350507i
$768$	43.0417	−	94.2481i	1.55313	−	3.40089i
$769$	41.7010	+	12.2445i	1.50378	+	0.441548i	0.926908	−	0.375289i	$-0.122457\pi$
$769$	41.7010	+	12.2445i	1.50378	+	0.441548i	0.576868	+	0.816837i	$0.304275\pi$
$770$	0.00381660	+	0.00440459i	0.000137541	+	0.000158730i
$771$	−3.43542	−	3.96469i	−0.123724	−	0.142785i
$772$	145.003	+	42.5766i	5.21876	+	1.53237i
$773$	−5.04920	+	11.0562i	−0.181607	+	0.397664i	−0.978439	−	0.206537i	$-0.933780\pi$
$773$	−5.04920	+	11.0562i	−0.181607	+	0.397664i	0.796832	+	0.604201i	$0.206508\pi$
$774$	13.2070	+	8.48764i	0.474717	+	0.305082i
$775$	−18.3967	+	5.40174i	−0.660827	+	0.194036i
$776$	18.2121	−	126.668i	0.653778	−	4.54712i
$777$	−3.75906	−	8.23120i	−0.134856	−	0.295293i
$778$	−1.21820	−	8.47275i	−0.0436745	−	0.303763i
$779$	−5.48213	+	3.52315i	−0.196418	+	0.126230i
$780$	−0.196125	+	0.226340i	−0.00702240	+	0.00810428i
$781$	−2.35973			−0.0844379
$782$	−16.5419	+	88.5713i	−0.591536	+	3.16730i
$783$	3.59353			0.128422
$784$	−11.9215	+	13.7581i	−0.425767	+	0.491362i
$785$	0.00179409	−	0.00115299i	6.40338e−5	−	4.11520e-5i
$786$	−2.94585	−	20.4889i	−0.105075	−	0.730814i
$787$	−14.4540	−	31.6498i	−0.515229	−	1.12819i	−0.971214	−	0.238207i	$-0.923440\pi$
$787$	−14.4540	−	31.6498i	−0.515229	−	1.12819i	0.455986	−	0.889987i	$-0.349287\pi$
$788$	−5.94632	+	41.3576i	−0.211829	+	1.47330i
$789$	25.8099	−	7.57848i	0.918858	−	0.269801i
$790$	−0.00520029	−	0.00334202i	−0.000185018	−	0.000118904i
$791$	0.730639	−	1.59988i	0.0259785	−	0.0568850i
$792$	−2.17932	−	0.639906i	−0.0774387	−	0.0227381i
$793$	−48.9750	−	56.5201i	−1.73915	−	2.00709i
$794$	2.17789	+	2.51342i	0.0772904	+	0.0891979i
$795$	−0.0335175	−	0.00984162i	−0.00118874	−	0.000349046i
$796$	−22.0543	+	48.2922i	−0.781695	+	1.71167i
$797$	32.4906	+	20.8805i	1.15088	+	0.739624i	0.969813	−	0.243848i	$-0.0784098\pi$
$797$	32.4906	+	20.8805i	1.15088	+	0.739624i	0.181063	+	0.983471i	$0.442046\pi$
$798$	9.47949	−	2.78343i	0.335570	−	0.0985323i
$799$	−7.45104	+	51.8231i	−0.263599	+	1.83337i
$800$	−61.3844	−	134.413i	−2.17027	−	4.75222i
$801$	1.02686	+	7.14197i	0.0362823	+	0.252349i
$802$	−20.8517	+	13.4006i	−0.736299	+	0.473191i
$803$	0.0239565	−	0.0276473i	0.000845408	−	0.000975653i
$804$	−18.6167			−0.656559
$805$	−0.00862373	+	0.0461746i	−0.000303946	+	0.00162744i
$806$	−56.3573			−1.98510
$807$	17.3203	−	19.9887i	0.609702	−	0.703634i
$808$	−59.0367	+	37.9406i	−2.07690	+	1.33474i
$809$	2.97443	+	20.6876i	0.104575	+	0.727337i	0.972881	+	0.231307i	$0.0743003\pi$
$809$	2.97443	+	20.6876i	0.104575	+	0.727337i	−0.868305	+	0.496030i	$0.834791\pi$
$810$	0.0113760	+	0.0249100i	0.000399712	+	0.000875247i
$811$	−2.76170	+	19.2081i	−0.0969765	+	0.674486i	0.882110	+	0.471043i	$0.156122\pi$
$811$	−2.76170	+	19.2081i	−0.0969765	+	0.674486i	−0.979087	+	0.203443i	$0.934787\pi$
$812$	20.0572	−	5.88933i	0.703870	−	0.206675i
$813$	15.5459	+	9.99075i	0.545219	+	0.350391i
$814$	2.23678	−	4.89786i	0.0783991	−	0.171670i
$815$	0.111061	+	0.0326105i	0.00389031	+	0.00114230i
$816$	80.1090	+	92.4507i	2.80438	+	3.23642i
$817$	−12.9934	−	14.9952i	−0.454582	−	0.524616i
$818$	14.1389	+	4.15155i	0.494354	+	0.145156i
$819$	−2.18360	+	4.78143i	−0.0763013	+	0.167077i
$820$	−0.0883937	−	0.0568072i	−0.00308684	−	0.00198379i
$821$	−36.8364	+	10.8161i	−1.28560	+	0.377486i	−0.851962	−	0.523603i	$-0.824588\pi$
$821$	−36.8364	+	10.8161i	−1.28560	+	0.377486i	−0.433635	+	0.901088i	$0.642769\pi$
$822$	5.56512	−	38.7063i	0.194106	−	1.35004i
$823$	−7.29918	−	15.9830i	−0.254433	−	0.557131i	0.738711	−	0.674022i	$-0.235435\pi$
$823$	−7.29918	−	15.9830i	−0.254433	−	0.557131i	−0.993145	+	0.116890i	$0.962707\pi$
$824$	1.71301	+	11.9143i	0.0596756	+	0.415053i
$825$	−0.895177	+	0.575295i	−0.0311661	+	0.0200292i
$826$	−6.25412	+	7.21764i	−0.217609	+	0.251134i
$827$	−2.96639			−0.103151			−0.0515757	−	0.998669i	$-0.516424\pi$
$827$	−2.96639			−0.103151			−0.0515757	+	0.998669i	$0.516424\pi$
$828$	−10.5177	−	25.8393i	−0.365515	−	0.897979i
$829$	−23.9535			−0.831940			−0.415970	−	0.909378i	$-0.636558\pi$
$829$	−23.9535			−0.831940			−0.415970	+	0.909378i	$0.636558\pi$
$830$	−0.0292336	+	0.0337373i	−0.00101471	+	0.00117104i
$831$	5.10675	−	3.28191i	0.177151	−	0.113848i
$832$	−34.5763	−	240.483i	−1.19872	−	8.33726i
$833$	−2.79147	−	6.11247i	−0.0967187	−	0.211784i
$834$	−7.05537	+	49.0712i	−0.244307	+	1.69920i
$835$	0.0366646	−	0.0107657i	0.00126883	−	0.000372562i
$836$	3.68023	+	2.36514i	0.127283	+	0.0818000i
$837$	−1.59301	+	3.48820i	−0.0550624	+	0.120570i
$838$	95.9784	+	28.1818i	3.31552	+	0.973525i
$839$	4.14991	+	4.78925i	0.143271	+	0.165343i	0.822850	−	0.568259i	$-0.192383\pi$
$839$	4.14991	+	4.78925i	0.143271	+	0.165343i	−0.679579	+	0.733602i	$0.737837\pi$
$840$	0.0684529	+	0.0789989i	0.00236185	+	0.00272572i
$841$	15.4349	+	4.53211i	0.532240	+	0.156280i
$842$	7.79030	−	17.0584i	0.268471	−	0.587870i
$843$	14.9631	+	9.61623i	0.515358	+	0.331200i
$844$	31.9206	−	9.37273i	1.09875	−	0.322623i
$845$	−0.0203931	+	0.141837i	−0.000701544	+	0.00487935i
$846$	−9.04944	−	19.8155i	−0.311126	−	0.681271i
$847$	−1.55902	−	10.8432i	−0.0535685	−	0.372577i
$848$	54.6203	−	35.1023i	1.87567	−	1.20542i
$849$	19.9038	−	22.9702i	0.683095	−	0.788334i
$850$	93.9368			3.22201
$851$	42.1142	−	10.4742i	1.44366	−	0.359049i
$852$	−64.4986			−2.20969
$853$	10.2054	−	11.7777i	0.349428	−	0.403261i	−0.553642	−	0.832755i	$-0.686762\pi$
$853$	10.2054	−	11.7777i	0.349428	−	0.403261i	0.903070	+	0.429494i	$0.141308\pi$
$854$	−33.4645	+	21.5063i	−1.14513	+	0.735931i
$855$	−0.00492554	−	0.0342579i	−0.000168450	−	0.00117160i
$856$	18.4872	+	40.4814i	0.631880	+	1.38362i
$857$	1.75806	−	12.2276i	0.0600543	−	0.417687i	−0.937511	−	0.347954i	$-0.886876\pi$
$857$	1.75806	−	12.2276i	0.0600543	−	0.417687i	0.997566	−	0.0697323i	$-0.0222145\pi$
$858$	−3.00108	+	0.881196i	−0.102455	+	0.0300835i
$859$	−17.9475	−	11.5341i	−0.612360	−	0.393540i	0.197381	−	0.980327i	$-0.436756\pi$
$859$	−17.9475	−	11.5341i	−0.612360	−	0.393540i	−0.809741	+	0.586787i	$0.800393\pi$
$860$	0.132901	−	0.291013i	0.00453189	−	0.00992347i
$861$	−1.76947	−	0.519564i	−0.0603035	−	0.0177067i
$862$	−46.8252	−	54.0391i	−1.59487	−	1.84058i
$863$	16.6730	+	19.2416i	0.567555	+	0.654993i	0.964882	−	0.262684i	$-0.0846076\pi$
$863$	16.6730	+	19.2416i	0.567555	+	0.654993i	−0.397327	+	0.917677i	$0.630062\pi$
$864$	−28.3567	−	8.32628i	−0.964715	−	0.283266i
$865$	−0.0219520	+	0.0480681i	−0.000746389	+	0.00163436i
$866$	10.1264	+	6.50784i	0.344109	+	0.221145i
$867$	−27.0141	+	7.93206i	−0.917447	+	0.269387i
$868$	−3.17463	+	22.0800i	−0.107754	+	0.749446i
$869$	−0.0199570	−	0.0436998i	−0.000676995	−	0.00148241i
$870$	−0.0140049	−	0.0974059i	−0.000474809	−	0.00330237i
$871$	−14.1518	+	9.09483i	−0.479516	+	0.308166i
$872$	−128.265	+	148.025i	−4.34359	+	5.01277i
$873$	−11.9909			−0.405831
$874$	4.77563	+	47.1400i	0.161538	+	1.59453i
$875$	0.0979445			0.00331113
$876$	0.654804	−	0.755685i	0.0221238	−	0.0255322i
$877$	−9.30846	+	5.98218i	−0.314324	+	0.202004i	−0.688285	−	0.725441i	$-0.741636\pi$
$877$	−9.30846	+	5.98218i	−0.314324	+	0.202004i	0.373960	+	0.927445i	$0.378000\pi$
$878$	11.8207	+	82.2146i	0.398928	+	2.77461i
$879$	−10.5357	−	23.0700i	−0.355361	−	0.778133i
$880$	−0.00540053	+	0.0375615i	−0.000182052	+	0.00126620i
$881$	33.4113	−	9.81044i	1.12565	−	0.330522i	0.334656	−	0.942340i	$-0.391380\pi$
$881$	33.4113	−	9.81044i	1.12565	−	0.330522i	0.790998	+	0.611818i	$0.209562\pi$
$882$	2.35207	+	1.51158i	0.0791983	+	0.0508977i
$883$	11.7216	−	25.6668i	0.394464	−	0.863756i	−0.603338	−	0.797486i	$-0.706163\pi$
$883$	11.7216	−	25.6668i	0.394464	−	0.863756i	0.997802	−	0.0662698i	$-0.0211098\pi$
$884$	197.148	+	57.8878i	6.63080	+	1.94698i
$885$	0.0219092	+	0.0252846i	0.000736471	+	0.000849933i
$886$	29.5349	+	34.0851i	0.992246	+	1.14511i
$887$	−14.1135	−	4.14411i	−0.473886	−	0.139145i	0.0360641	−	0.999349i	$-0.488518\pi$
$887$	−14.1135	−	4.14411i	−0.473886	−	0.139145i	−0.509950	+	0.860204i	$0.670336\pi$
$888$	40.1179	−	87.8460i	1.34627	−	2.94792i
$889$	−1.53586	−	0.987037i	−0.0515111	−	0.0331042i
$890$	0.189588	−	0.0556680i	0.00635500	−	0.00186600i
$891$	−0.0302880	+	0.210658i	−0.00101469	+	0.00705729i
$892$	40.7146	+	89.1525i	1.36322	+	2.98505i
$893$	3.91819	+	27.2516i	0.131117	+	0.911942i
$894$	−31.1362	+	20.0100i	−1.04135	+	0.669235i
$895$	−0.141962	+	0.163833i	−0.00474527	+	0.00547633i
$896$	−70.1212			−2.34258
$897$	−20.6186	−	14.5041i	−0.688434	−	0.484277i
$898$	10.6601			0.355734
$899$	9.02413	−	10.4144i	0.300971	−	0.347340i
$900$	−24.4679	+	15.7246i	−0.815596	+	0.524152i
$901$	3.41072	+	23.7221i	0.113628	+	0.790298i
$902$	−0.455856	−	0.998186i	−0.0151784	−	0.0332360i
$903$	0.799107	−	5.55791i	0.0265926	−	0.184956i
$904$	18.0103	−	5.28830i	0.599014	−	0.175886i
$905$	−0.0102678	−	0.00659872i	−0.000341313	−	0.000219349i
$906$	3.55532	−	7.78507i	0.118118	−	0.258642i
$907$	15.7786	+	4.63302i	0.523920	+	0.153837i	0.532989	−	0.846122i	$-0.321069\pi$
$907$	15.7786	+	4.63302i	0.523920	+	0.153837i	−0.00906898	+	0.999959i	$0.502887\pi$
$908$	78.2080	+	90.2569i	2.59542	+	2.99528i
$909$	4.30611	+	4.96951i	0.142825	+	0.164828i
$910$	0.138115	+	0.0405542i	0.00457847	+	0.00134436i
$911$	−16.5654	+	36.2732i	−0.548836	+	1.20178i	0.408487	+	0.912764i	$0.366057\pi$
$911$	−16.5654	+	36.2732i	−0.548836	+	1.20178i	−0.957323	+	0.289020i	$0.906671\pi$
$912$	54.1163	+	34.7784i	1.79197	+	1.15163i
$913$	−0.332880	+	0.0977423i	−0.0110167	+	0.00323480i
$914$	7.99670	−	55.6183i	0.264507	−	1.83969i
$915$	0.0578895	+	0.126760i	0.00191377	+	0.00419057i
$916$	12.0908	+	84.0933i	0.399491	+	2.77852i
$917$	−6.22823	+	4.00264i	−0.205674	+	0.132179i
$918$	12.3033	−	14.1988i	0.406071	−	0.468631i
$919$	−44.9184			−1.48172			−0.740861	−	0.671658i	$-0.765582\pi$
$919$	−44.9184			−1.48172			−0.740861	+	0.671658i	$0.765582\pi$
$920$	−0.432696	+	0.253153i	−0.0142656	+	0.00834621i
$921$	17.4033			0.573458
$922$	−58.7017	+	67.7454i	−1.93324	+	2.23108i
$923$	−49.0299	+	31.5096i	−1.61384	+	1.03715i
$924$	0.176189	+	1.22542i	0.00579618	+	0.0403134i
$925$	−18.7950	−	41.1552i	−0.617974	−	1.35318i
$926$	−10.3941	+	72.2924i	−0.341571	+	2.37568i
$927$	1.08216	−	0.317752i	0.0355429	−	0.0104363i
$928$	89.3432	+	57.4174i	2.93284	+	1.88482i
$929$	17.0745	−	37.3880i	0.560197	−	1.22666i	−0.391658	−	0.920111i	$-0.628098\pi$
$929$	17.0745	−	37.3880i	0.560197	−	1.22666i	0.951855	−	0.306549i	$-0.0991743\pi$
$930$	0.100759	+	0.0295856i	0.00330402	+	0.000970149i
$931$	−2.31403	−	2.67053i	−0.0758392	−	0.0875231i
$932$	88.6113	+	102.263i	2.90256	+	3.34973i
$933$	−1.45431	−	0.427023i	−0.0476119	−	0.0139801i
$934$	−10.9972	+	24.0805i	−0.359840	+	0.787940i
$935$	−0.0117837	−	0.00757293i	−0.000385369	−	0.000247661i
$936$	−53.8260	+	15.8047i	−1.75936	+	0.516594i
$937$	3.21390	−	22.3532i	0.104994	−	0.730246i	−0.867520	−	0.497402i	$-0.834288\pi$
$937$	3.21390	−	22.3532i	0.104994	−	0.730246i	0.972514	−	0.232845i	$-0.0748034\pi$
$938$	3.71706	+	8.13922i	0.121366	+	0.265755i
$939$	4.55160	+	31.6571i	0.148536	+	1.03309i
$940$	−0.373452	+	0.240003i	−0.0121807	+	0.00782804i
$941$	−14.4195	+	16.6410i	−0.470062	+	0.542481i	−0.940429	−	0.339990i	$-0.889576\pi$
$941$	−14.4195	+	16.6410i	−0.470062	+	0.542481i	0.470367	+	0.882471i	$0.344122\pi$
$942$	0.608774			0.0198349
$943$	4.00735	−	7.88440i	0.130497	−	0.256752i
$944$	−62.1836			−2.02390
$945$	0.00641406	−	0.00740222i	0.000208649	−	0.000240794i
$946$	2.81077	−	1.80637i	0.0913860	−	0.0587302i
$947$	−2.92353	−	20.3336i	−0.0950020	−	0.660753i	−0.980559	−	0.196223i	$-0.937132\pi$
$947$	−2.92353	−	20.3336i	−0.0950020	−	0.660753i	0.885557	−	0.464530i	$-0.153777\pi$
$948$	−0.545485	−	1.19445i	−0.0177165	−	0.0387938i
$949$	0.128587	−	0.894342i	0.00417411	−	0.0290316i
$950$	47.3965	−	13.9169i	1.53775	−	0.451523i
$951$	−17.5612	−	11.2859i	−0.569461	−	0.365971i
$952$	29.7915	−	65.2342i	0.965547	−	2.11425i
$953$	−55.3993	−	16.2667i	−1.79456	−	0.526930i	−0.797484	−	0.603340i	$-0.793836\pi$
$953$	−55.3993	−	16.2667i	−1.79456	−	0.526930i	−0.997076	+	0.0764098i	$0.975654\pi$
$954$	−6.53007	−	7.53610i	−0.211419	−	0.243990i
$955$	−0.0282375	−	0.0325879i	−0.000913745	−	0.00105452i
$956$	−65.9078	−	19.3523i	−2.13161	−	0.625898i
$957$	0.317704	−	0.695676i	0.0102699	−	0.0224880i
$958$	−29.1584	−	18.7390i	−0.942066	−	0.605429i
$959$	−13.4197	+	3.94038i	−0.433345	+	0.127242i
$960$	−0.0644274	+	0.448102i	−0.00207939	+	0.0144624i
$961$	−6.76911	−	14.8223i	−0.218358	−	0.478138i
$962$	−18.9262	−	131.634i	−0.610204	−	4.24406i
$963$	3.50798	−	2.25444i	0.113043	−	0.0726485i
$964$	−50.9475	+	58.7965i	−1.64091	+	1.89371i
$965$	−0.254455			−0.00819118
$966$	−9.19699	+	9.75751i	−0.295908	+	0.313943i
$967$	51.1756			1.64570			0.822848	−	0.568262i	$-0.192384\pi$
$967$	51.1756			1.64570			0.822848	+	0.568262i	$0.192384\pi$
$968$	76.5611	−	88.3563i	2.46077	−	2.83988i
$969$	−19.9755	+	12.8375i	−0.641705	+	0.412399i
$970$	0.0467315	+	0.325025i	0.00150046	+	0.0104359i
$971$	−15.0724	−	33.0039i	−0.483696	−	1.05915i	−0.981431	−	0.191817i	$-0.938562\pi$
$971$	−15.0724	−	33.0039i	−0.483696	−	1.05915i	0.497735	−	0.867329i	$-0.334165\pi$
$972$	−0.827862	+	5.75791i	−0.0265537	+	0.184685i
$973$	17.0133	−	4.99555i	0.545421	−	0.160150i
$974$	67.8869	+	43.6283i	2.17524	+	1.39794i
$975$	−10.9178	+	23.9067i	−0.349650	+	0.765626i
$976$	−248.517	−	72.9713i	−7.95485	−	2.33575i
$977$	6.16834	+	7.11864i	0.197343	+	0.227746i	0.845793	−	0.533512i	$-0.179128\pi$
$977$	6.16834	+	7.11864i	0.197343	+	0.227746i	−0.648450	+	0.761257i	$0.724582\pi$
$978$	21.6376	+	24.9711i	0.691894	+	0.798488i
$979$	1.47341	+	0.432632i	0.0470904	+	0.0138270i
$980$	0.0236687	−	0.0518272i	0.000756068	−	0.00165556i
$981$	15.4393	+	9.92221i	0.492937	+	0.316792i
$982$	−39.9319	+	11.7251i	−1.27428	+	0.374162i
$983$	−7.19015	+	50.0086i	−0.229330	+	1.59503i	0.471611	+	0.881807i	$0.343673\pi$
$983$	−7.19015	+	50.0086i	−0.229330	+	1.59503i	−0.700941	+	0.713219i	$0.747237\pi$
$984$	−8.17605	−	17.9030i	−0.260643	−	0.570728i
$985$	−0.0100121	−	0.0696356i	−0.000319012	−	0.00221877i
$986$	−56.7965	+	36.5009i	−1.80877	+	1.16243i
$987$	−5.10229	+	5.88836i	−0.162408	+	0.187428i
$988$	108.049			3.43748
$989$	25.4982	+	8.66078i	0.810795	+	0.275397i
$990$	0.00582811			0.000185229
$991$	1.64195	−	1.89491i	0.0521581	−	0.0601937i	−0.729071	−	0.684438i	$-0.760048\pi$
$991$	1.64195	−	1.89491i	0.0521581	−	0.0601937i	0.781229	+	0.624244i	$0.214593\pi$
$992$	−95.3402	+	61.2714i	−3.02705	+	1.94537i
$993$	−2.04654	−	14.2340i	−0.0649450	−	0.451702i
$994$	12.8780	+	28.1989i	0.408465	+	0.894414i
$995$	0.0127215	−	0.0884799i	0.000403298	−	0.00280500i
$996$	−9.09860	+	2.67159i	−0.288300	+	0.0846526i
$997$	42.3234	+	27.1996i	1.34040	+	0.861421i	0.996972	−	0.0777598i	$-0.0247767\pi$
$997$	42.3234	+	27.1996i	1.34040	+	0.861421i	0.343424	+	0.939180i	$0.388413\pi$
$998$	−30.5457	+	66.8858i	−0.966908	+	2.11723i
$999$	−8.68239	−	2.54938i	−0.274699	−	0.0806588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.85.1	✓	80
23.13	even	11	inner	483.2.q.f.358.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.85.1	✓	80	1.1	even	1	trivial
483.2.q.f.358.1	yes	80	23.13	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83093 + 2.11301i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.827862 - 5.75791i) q^{4} +(0.00406880 + 0.00890943i) q^{5} +(-0.397900 + 2.76745i) q^{6} +(0.959493 - 0.281733i) q^{7} +(8.97813 + 5.76989i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.83093 + 2.11301i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.827862 - 5.75791i) q^{4} +(0.00406880 + 0.00890943i) q^{5} +(-0.397900 + 2.76745i) q^{6} +(0.959493 - 0.281733i) q^{7} +(8.97813 + 5.76989i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.0262754 - 0.00771515i) q^{10} +(-0.139370 - 0.160842i) q^{11} +(-3.80940 - 4.39628i) q^{12} +(-5.04352 - 1.48091i) q^{13} +(-1.16146 + 2.54325i) q^{14} +(0.00823969 + 0.00529533i) q^{15} +(-17.4672 + 5.12883i) q^{16} +(0.956315 - 6.65132i) q^{17} +(1.16146 + 2.54325i) q^{18} +(-0.502886 - 3.49765i) q^{19} +(0.0479313 - 0.0308035i) q^{20} +(0.654861 - 0.755750i) q^{21} +0.595036 q^{22} +(2.98626 + 3.75263i) q^{23} +10.6723 q^{24} +(3.27424 - 3.77868i) q^{25} +(12.3635 - 7.94555i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-2.41652 - 5.29144i) q^{28} +(-0.511412 + 3.55695i) q^{29} +(-0.0262754 + 0.00771515i) q^{30} +(-3.22598 - 2.07321i) q^{31} +(12.2771 - 26.8831i) q^{32} +(-0.204203 - 0.0599594i) q^{33} +(12.3033 + 14.1988i) q^{34} +(0.00641406 + 0.00740222i) q^{35} +(-5.58148 - 1.63887i) q^{36} +(3.75906 - 8.23120i) q^{37} +(8.31132 + 5.34136i) q^{38} +(-5.04352 + 1.48091i) q^{39} +(-0.0148762 + 0.103467i) q^{40} +(-0.766098 - 1.67752i) q^{41} +(0.397900 + 2.76745i) q^{42} +(4.72369 - 3.03573i) q^{43} +(-0.810731 + 0.935634i) q^{44} +0.00979454 q^{45} +(-13.3970 - 0.560813i) q^{46} -7.79141 q^{47} +(-11.9215 + 13.7581i) q^{48} +(0.841254 - 0.540641i) q^{49} +(1.98946 + 13.8370i) q^{50} +(-2.79147 - 6.11247i) q^{51} +(-4.35161 + 30.2661i) q^{52} +(-3.42206 + 1.00481i) q^{53} +(2.35207 + 1.51158i) q^{54} +(0.000865938 - 0.00189614i) q^{55} +(10.2400 + 3.00674i) q^{56} +(-2.31403 - 2.67053i) q^{57} +(-6.57950 - 7.59315i) q^{58} +(3.27745 + 0.962346i) q^{59} +(0.0236687 - 0.0518272i) q^{60} +(11.9691 + 7.69206i) q^{61} +(10.2873 - 3.02062i) q^{62} +(0.142315 - 0.989821i) q^{63} +(19.2008 + 42.0438i) q^{64} +(-0.00732700 - 0.0509604i) q^{65} +(0.500576 - 0.321701i) q^{66} +(2.09577 - 2.41864i) q^{67} -39.0894 q^{68} +(4.54103 + 1.54242i) q^{69} -0.0273847 q^{70} +(7.26092 - 8.37955i) q^{71} +(8.97813 - 5.76989i) q^{72} +(0.0244627 + 0.170142i) q^{73} +(10.5100 + 23.0137i) q^{74} +(0.711561 - 4.94901i) q^{75} +(-19.7228 + 5.79115i) q^{76} +(-0.179039 - 0.115061i) q^{77} +(6.10516 - 13.3684i) q^{78} +(0.216588 + 0.0635960i) q^{79} +(-0.116766 - 0.134755i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(4.94729 + 1.45266i) q^{82} +(0.677185 - 1.48283i) q^{83} +(-4.89367 - 3.14497i) q^{84} +(0.0631505 - 0.0185427i) q^{85} +(-2.23423 + 15.5394i) q^{86} +(1.49280 + 3.26879i) q^{87} +(-0.323243 - 2.24820i) q^{88} +(-6.06999 + 3.90095i) q^{89} +(-0.0179331 + 0.0206959i) q^{90} -5.25644 q^{91} +(19.1351 - 20.3013i) q^{92} -3.83473 q^{93} +(14.2655 - 16.4633i) q^{94} +(0.0291159 - 0.0187117i) q^{95} +(-4.20595 - 29.2530i) q^{96} +(-4.98120 - 10.9073i) q^{97} +(-0.397900 + 2.76745i) q^{98} +(-0.204203 + 0.0599594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

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