LMFDB - Embedded newform 471.2.q.b.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	471.37
Dual form			471.2.q.b.331.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.369506 + 0.193932i) q^{2} +(-0.996757 + 0.0804666i) q^{3} +(-1.03720 + 1.50265i) q^{4} +(0.841882 - 0.876493i) q^{5} +(0.352702 - 0.223035i) q^{6} +(-0.419250 - 0.607388i) q^{7} +(0.192443 - 1.58491i) q^{8} +(0.987050 - 0.160411i) q^{9} +O(q^{10})$	\(q+(-0.369506 + 0.193932i) q^{2} +(-0.996757 + 0.0804666i) q^{3} +(-1.03720 + 1.50265i) q^{4} +(0.841882 - 0.876493i) q^{5} +(0.352702 - 0.223035i) q^{6} +(-0.419250 - 0.607388i) q^{7} +(0.192443 - 1.58491i) q^{8} +(0.987050 - 0.160411i) q^{9} +(-0.141101 + 0.487136i) q^{10} +(2.89699 - 1.83194i) q^{11} +(0.912928 - 1.58124i) q^{12} +(0.750048 + 1.29912i) q^{13} +(0.272707 + 0.143128i) q^{14} +(-0.768624 + 0.941394i) q^{15} +(-1.05866 - 2.79146i) q^{16} +(-1.32284 + 1.37722i) q^{17} +(-0.333612 + 0.250693i) q^{18} +(2.97926 + 2.23877i) q^{19} +(0.443857 + 2.17416i) q^{20} +(0.466765 + 0.571683i) q^{21} +(-0.715181 + 1.23873i) q^{22} +(2.53675 + 6.68885i) q^{23} +(-0.0642866 + 1.59526i) q^{24} +(0.141857 + 3.52014i) q^{25} +(-0.529087 - 0.334574i) q^{26} +(-0.970942 + 0.239316i) q^{27} +1.34754 q^{28} +(10.1917 - 2.51202i) q^{29} +(0.101445 - 0.496911i) q^{30} +(1.51147 + 0.504602i) q^{31} +(3.32260 + 2.94357i) q^{32} +(-2.74018 + 2.05911i) q^{33} +(0.221710 - 0.765430i) q^{34} +(-0.885330 - 0.143880i) q^{35} +(-0.782731 + 1.64957i) q^{36} +(-5.04281 - 5.25012i) q^{37} +(-1.53502 - 0.249465i) q^{38} +(-0.852151 - 1.23455i) q^{39} +(-1.22715 - 1.50298i) q^{40} +(-1.49247 + 3.93531i) q^{41} +(-0.283339 - 0.120720i) q^{42} +(3.16356 + 0.255389i) q^{43} +(-0.251998 + 6.25326i) q^{44} +(0.690381 - 1.00019i) q^{45} +(-2.23452 - 1.97961i) q^{46} +(3.24976 + 11.2195i) q^{47} +(1.27985 + 2.69722i) q^{48} +(2.28908 - 6.03582i) q^{49} +(-0.735082 - 1.27320i) q^{50} +(1.20773 - 1.47920i) q^{51} +(-2.73008 - 0.220395i) q^{52} +(9.20522 - 3.92198i) q^{53} +(0.312358 - 0.276725i) q^{54} +(0.833238 - 4.08147i) q^{55} +(-1.04334 + 0.547585i) q^{56} +(-3.14975 - 1.99178i) q^{57} +(-3.27872 + 2.90469i) q^{58} +(-0.474176 - 3.90519i) q^{59} +(-0.617365 - 2.13139i) q^{60} +(-8.36197 - 6.28361i) q^{61} +(-0.656354 + 0.106668i) q^{62} +(-0.511252 - 0.532270i) q^{63} +(3.99885 + 0.985628i) q^{64} +(1.77012 + 0.436296i) q^{65} +(0.613186 - 1.29226i) q^{66} +(-1.44545 + 11.9044i) q^{67} +(-0.697426 - 3.41622i) q^{68} +(-3.06675 - 6.46303i) q^{69} +(0.355037 - 0.118529i) q^{70} +(2.50201 - 1.06601i) q^{71} +(-0.0642866 - 1.59526i) q^{72} +(14.5620 - 1.17557i) q^{73} +(2.88151 + 0.961990i) q^{74} +(-0.424650 - 3.49731i) q^{75} +(-6.45419 + 2.15473i) q^{76} +(-2.32726 - 0.991553i) q^{77} +(0.554294 + 0.290916i) q^{78} +(-14.6639 - 7.69622i) q^{79} +(-3.33796 - 1.42217i) q^{80} +(0.948536 - 0.316668i) q^{81} +(-0.211706 - 1.74356i) q^{82} +(-4.31439 - 1.44035i) q^{83} +(-1.34317 + 0.108432i) q^{84} +(0.0934490 + 2.31891i) q^{85} +(-1.21848 + 0.519146i) q^{86} +(-9.95649 + 3.32397i) q^{87} +(-2.34596 - 4.94401i) q^{88} +(1.13009 + 5.53555i) q^{89} +(-0.0611314 + 0.503462i) q^{90} +(0.474613 - 1.00023i) q^{91} +(-12.6821 - 3.12586i) q^{92} +(-1.54717 - 0.381343i) q^{93} +(-3.37661 - 3.51543i) q^{94} +(4.47045 - 0.726519i) q^{95} +(-3.54869 - 2.66667i) q^{96} +(-3.47843 - 12.0089i) q^{97} +(0.324706 + 2.67419i) q^{98} +(2.56561 - 2.27293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{29}{39}\right)$

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 $

$2$	−0.369506	+	0.193932i	−0.261280	+	0.137130i	−0.590277	−	0.807201i	$-0.700982\pi$
$2$	−0.369506	+	0.193932i	−0.261280	+	0.137130i	0.328997	+	0.944331i	$0.393289\pi$
$3$	−0.996757	+	0.0804666i	−0.575478	+	0.0464574i
$3$	−0.996757	+	0.0804666i	−0.575478	+	0.0464574i
$4$	−1.03720	+	1.50265i	−0.518602	+	0.751325i
$5$	0.841882	−	0.876493i	0.376501	−	0.391979i	−0.505811	−	0.862645i	$-0.668807\pi$
$5$	0.841882	−	0.876493i	0.376501	−	0.391979i	0.882312	+	0.470665i	$0.155986\pi$
$6$	0.352702	−	0.223035i	0.143990	−	0.0910539i
$7$	−0.419250	−	0.607388i	−0.158461	−	0.229571i	0.735709	−	0.677298i	$-0.236849\pi$
$7$	−0.419250	−	0.607388i	−0.158461	−	0.229571i	−0.894170	+	0.447727i	$0.852234\pi$
$8$	0.192443	−	1.58491i	0.0680388	−	0.560350i
$9$	0.987050	−	0.160411i	0.329017	−	0.0534704i
$10$	−0.141101	+	0.487136i	−0.0446200	+	0.154046i
$11$	2.89699	−	1.83194i	0.873474	−	0.552352i	−0.0208441	−	0.999783i	$-0.506635\pi$
$11$	2.89699	−	1.83194i	0.873474	−	0.552352i	0.894318	+	0.447431i	$0.147661\pi$
$12$	0.912928	−	1.58124i	0.263540	−	0.456464i
$13$	0.750048	+	1.29912i	0.208026	+	0.360311i	0.951093	−	0.308906i	$-0.0999629\pi$
$13$	0.750048	+	1.29912i	0.208026	+	0.360311i	−0.743067	+	0.669217i	$0.766630\pi$
$14$	0.272707	+	0.143128i	0.0728839	+	0.0382524i
$15$	−0.768624	+	0.941394i	−0.198458	+	0.243067i
$16$	−1.05866	−	2.79146i	−0.264665	−	0.697864i
$17$	−1.32284	+	1.37722i	−0.320835	+	0.334025i	−0.862016	−	0.506882i	$-0.830798\pi$
$17$	−1.32284	+	1.37722i	−0.320835	+	0.334025i	0.541180	+	0.840906i	$0.317978\pi$
$18$	−0.333612	+	0.250693i	−0.0786331	+	0.0590889i
$19$	2.97926	+	2.23877i	0.683489	+	0.513609i	0.884831	−	0.465912i	$-0.154274\pi$
$19$	2.97926	+	2.23877i	0.683489	+	0.513609i	−0.201342	+	0.979521i	$0.564530\pi$
$20$	0.443857	+	2.17416i	0.0992495	+	0.486156i
$21$	0.466765	+	0.571683i	0.101856	+	0.124751i
$22$	−0.715181	+	1.23873i	−0.152477	+	0.264098i
$23$	2.53675	+	6.68885i	0.528948	+	1.39472i	0.887325	+	0.461144i	$0.152561\pi$
$23$	2.53675	+	6.68885i	0.528948	+	1.39472i	−0.358377	+	0.933577i	$0.616670\pi$
$24$	−0.0642866	+	1.59526i	−0.0131224	+	0.325630i
$25$	0.141857	+	3.52014i	0.0283713	+	0.704028i
$26$	−0.529087	−	0.334574i	−0.103763	−	0.0656154i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	1.34754			0.254661
$29$	10.1917	−	2.51202i	1.89255	−	0.466471i	0.892671	−	0.450709i	$-0.148829\pi$
$29$	10.1917	−	2.51202i	1.89255	−	0.466471i	0.999876	−	0.0157621i	$-0.00501743\pi$
$30$	0.101445	−	0.496911i	0.0185212	−	0.0907231i
$31$	1.51147	+	0.504602i	0.271467	+	0.0906291i	0.449143	−	0.893460i	$-0.351729\pi$
$31$	1.51147	+	0.504602i	0.271467	+	0.0906291i	−0.177675	+	0.984089i	$0.556858\pi$
$32$	3.32260	+	2.94357i	0.587359	+	0.520354i
$33$	−2.74018	+	2.05911i	−0.477005	+	0.358446i
$34$	0.221710	−	0.765430i	0.0380229	−	0.131270i
$35$	−0.885330	−	0.143880i	−0.149648	−	0.0243202i
$36$	−0.782731	+	1.64957i	−0.130455	+	0.274928i
$37$	−5.04281	−	5.25012i	−0.829033	−	0.863115i	0.163316	−	0.986574i	$-0.447781\pi$
$37$	−5.04281	−	5.25012i	−0.829033	−	0.863115i	−0.992350	+	0.123459i	$0.960601\pi$
$38$	−1.53502	−	0.249465i	−0.249013	−	0.0404686i
$39$	−0.852151	−	1.23455i	−0.136453	−	0.197687i
$40$	−1.22715	−	1.50298i	−0.194029	−	0.237642i
$41$	−1.49247	+	3.93531i	−0.233084	+	0.614593i	−0.999619	−	0.0276105i	$-0.991210\pi$
$41$	−1.49247	+	3.93531i	−0.233084	+	0.614593i	0.766535	+	0.642203i	$0.221979\pi$
$42$	−0.283339	−	0.120720i	−0.0437202	−	0.0186274i
$43$	3.16356	+	0.255389i	0.482438	+	0.0389464i	0.319294	−	0.947656i	$-0.396554\pi$
$43$	3.16356	+	0.255389i	0.482438	+	0.0389464i	0.163144	+	0.986602i	$0.447836\pi$
$44$	−0.251998	+	6.25326i	−0.0379901	+	0.942714i
$45$	0.690381	−	1.00019i	0.102916	−	0.149099i
$46$	−2.23452	−	1.97961i	−0.329462	−	0.291878i
$47$	3.24976	+	11.2195i	0.474026	+	1.63653i	0.740043	+	0.672559i	$0.234805\pi$
$47$	3.24976	+	11.2195i	0.474026	+	1.63653i	−0.266017	+	0.963968i	$0.585708\pi$
$48$	1.27985	+	2.69722i	0.184730	+	0.389310i
$49$	2.28908	−	6.03582i	0.327012	−	0.862260i
$50$	−0.735082	−	1.27320i	−0.103956	−	0.180058i
$51$	1.20773	−	1.47920i	0.169116	−	0.207129i
$52$	−2.73008	−	0.220395i	−0.378593	−	0.0305632i
$53$	9.20522	−	3.92198i	1.26443	−	0.538725i	0.347469	−	0.937692i	$-0.387041\pi$
$53$	9.20522	−	3.92198i	1.26443	−	0.538725i	0.916966	+	0.398966i	$0.130631\pi$
$54$	0.312358	−	0.276725i	0.0425065	−	0.0376575i
$55$	0.833238	−	4.08147i	0.112354	−	0.550345i
$56$	−1.04334	+	0.547585i	−0.139422	+	0.0731742i
$57$	−3.14975	−	1.99178i	−0.417194	−	0.263818i
$58$	−3.27872	+	2.90469i	−0.430517	+	0.381405i
$59$	−0.474176	−	3.90519i	−0.0617324	−	0.508412i	−0.990476	−	0.137688i	$-0.956033\pi$
$59$	−0.474176	−	3.90519i	−0.0617324	−	0.508412i	0.928743	−	0.370724i	$-0.120890\pi$
$60$	−0.617365	−	2.13139i	−0.0797015	−	0.275161i
$61$	−8.36197	−	6.28361i	−1.07064	−	0.804534i	−0.0891445	−	0.996019i	$-0.528413\pi$
$61$	−8.36197	−	6.28361i	−1.07064	−	0.804534i	−0.981496	+	0.191485i	$0.938670\pi$
$62$	−0.656354	+	0.106668i	−0.0833570	+	0.0135468i
$63$	−0.511252	−	0.532270i	−0.0644117	−	0.0670597i
$64$	3.99885	+	0.985628i	0.499856	+	0.123204i
$65$	1.77012	+	0.436296i	0.219557	+	0.0541158i
$66$	0.613186	−	1.29226i	0.0754780	−	0.159066i
$67$	−1.44545	+	11.9044i	−0.176590	+	1.45435i	0.587492	+	0.809230i	$0.300116\pi$
$67$	−1.44545	+	11.9044i	−0.176590	+	1.45435i	−0.764082	+	0.645120i	$0.776808\pi$
$68$	−0.697426	−	3.41622i	−0.0845754	−	0.414278i
$69$	−3.06675	−	6.46303i	−0.369193	−	0.778058i
$70$	0.355037	−	0.118529i	0.0424351	−	0.0141669i
$71$	2.50201	−	1.06601i	0.296935	−	0.126512i	−0.238362	−	0.971176i	$-0.576610\pi$
$71$	2.50201	−	1.06601i	0.296935	−	0.126512i	0.535296	+	0.844665i	$0.320200\pi$
$72$	−0.0642866	−	1.59526i	−0.00757625	−	0.188003i
$73$	14.5620	−	1.17557i	1.70436	−	0.137590i	0.810439	−	0.585822i	$-0.199228\pi$
$73$	14.5620	−	1.17557i	1.70436	−	0.137590i	0.893917	+	0.448233i	$0.147946\pi$
$74$	2.88151	+	0.961990i	0.334969	+	0.111829i
$75$	−0.424650	−	3.49731i	−0.0490344	−	0.403834i
$76$	−6.45419	+	2.15473i	−0.740347	+	0.247164i
$77$	−2.32726	−	0.991553i	−0.265216	−	0.112998i
$78$	0.554294	+	0.290916i	0.0627614	+	0.0329397i
$79$	−14.6639	−	7.69622i	−1.64982	−	0.865892i	−0.993804	−	0.111146i	$-0.964548\pi$
$79$	−14.6639	−	7.69622i	−1.64982	−	0.865892i	−0.656016	−	0.754747i	$-0.727760\pi$
$80$	−3.33796	−	1.42217i	−0.373195	−	0.159004i
$81$	0.948536	−	0.316668i	0.105393	−	0.0351853i
$82$	−0.211706	−	1.74356i	−0.0233790	−	0.192544i
$83$	−4.31439	−	1.44035i	−0.473566	−	0.158099i	0.0698599	−	0.997557i	$-0.477745\pi$
$83$	−4.31439	−	1.44035i	−0.473566	−	0.158099i	−0.543426	+	0.839457i	$0.682873\pi$
$84$	−1.34317	+	0.108432i	−0.146552	+	0.0118309i
$85$	0.0934490	+	2.31891i	0.0101360	+	0.251522i
$86$	−1.21848	+	0.519146i	−0.131392	+	0.0559809i
$87$	−9.95649	+	3.32397i	−1.06745	+	0.356367i
$88$	−2.34596	−	4.94401i	−0.250080	−	0.527033i
$89$	1.13009	+	5.53555i	0.119789	+	0.586768i	0.994729	+	0.102536i	$0.0326957\pi$
$89$	1.13009	+	5.53555i	0.119789	+	0.586768i	−0.874940	+	0.484232i	$0.839099\pi$
$90$	−0.0611314	+	0.503462i	−0.00644381	+	0.0530696i
$91$	0.474613	−	1.00023i	0.0497529	−	0.104852i
$92$	−12.6821	−	3.12586i	−1.32220	−	0.325894i
$93$	−1.54717	−	0.381343i	−0.160434	−	0.0395434i
$94$	−3.37661	−	3.51543i	−0.348271	−	0.362588i
$95$	4.47045	−	0.726519i	0.458659	−	0.0745393i
$96$	−3.54869	−	2.66667i	−0.362186	−	0.272165i
$97$	−3.47843	−	12.0089i	−0.353181	−	1.21932i	−0.918823	−	0.394670i	$-0.870859\pi$
$97$	−3.47843	−	12.0089i	−0.353181	−	1.21932i	0.565642	−	0.824651i	$-0.308628\pi$
$98$	0.324706	+	2.67419i	0.0328003	+	0.270134i
$99$	2.56561	−	2.27293i	0.257853	−	0.228438i
$100$	−5.43667	−	3.43794i	−0.543667	−	0.343794i
$101$	3.71461	−	1.94958i	0.369617	−	0.193990i	−0.269680	−	0.962950i	$-0.586918\pi$
$101$	3.71461	−	1.94958i	0.369617	−	0.193990i	0.639297	+	0.768960i	$0.279225\pi$
$102$	−0.159399	+	0.780788i	−0.0157829	+	0.0773096i
$103$	0.110297	−	0.0977142i	0.0108678	−	0.00962807i	−0.657671	−	0.753305i	$-0.728458\pi$
$103$	0.110297	−	0.0977142i	0.0108678	−	0.00962807i	0.668539	+	0.743677i	$0.266920\pi$
$104$	2.20333	−	0.938751i	0.216054	−	0.0920521i
$105$	0.894037	+	0.0721741i	0.0872490	+	0.00704347i
$106$	−2.64079	+	3.23438i	−0.256496	+	0.314150i
$107$	−0.159416	−	0.276116i	−0.0154113	−	0.0266932i	0.858217	−	0.513287i	$-0.171572\pi$
$107$	−0.159416	−	0.276116i	−0.0154113	−	0.0266932i	−0.873628	+	0.486594i	$0.838239\pi$
$108$	0.647458	−	1.70721i	0.0623016	−	0.164276i
$109$	−3.21205	−	6.76926i	−0.307659	−	0.648377i	0.689453	−	0.724331i	$-0.257851\pi$
$109$	−3.21205	−	6.76926i	−0.307659	−	0.648377i	−0.997111	+	0.0759536i	$0.975800\pi$
$110$	0.483639	+	1.66972i	0.0461132	+	0.159201i
$111$	5.44892	+	4.82732i	0.517189	+	0.458189i
$112$	−1.25165	+	1.81333i	−0.118270	+	0.171344i
$113$	0.314938	−	7.81510i	0.0296268	−	0.735182i	−0.914302	−	0.405033i	$-0.867260\pi$
$113$	0.314938	−	7.81510i	0.0296268	−	0.735182i	0.943929	−	0.330149i	$-0.107099\pi$
$114$	1.55012	+	0.125138i	0.145182	+	0.0117203i
$115$	7.99837	+	3.40779i	0.745852	+	0.317778i
$116$	−6.79616	+	17.9200i	−0.631008	+	1.66383i
$117$	0.948728	+	1.16198i	0.0877099	+	0.107425i
$118$	0.932549	+	1.35103i	0.0858481	+	0.124372i
$119$	1.39111	+	0.226077i	0.127522	+	0.0207244i
$120$	1.34411	+	1.39936i	0.122700	+	0.127744i
$121$	0.320897	−	0.676276i	0.0291724	−	0.0614796i
$122$	4.30838	+	0.700180i	0.390063	+	0.0633914i
$123$	1.17097	−	4.04265i	0.105582	−	0.364513i
$124$	−2.32594	+	1.74783i	−0.208876	+	0.156960i
$125$	7.75321	+	6.86874i	0.693468	+	0.614359i
$126$	0.292135	+	0.0975288i	0.0260254	+	0.00868856i
$127$	−3.45127	+	16.9054i	−0.306251	+	1.50012i	0.477274	+	0.878755i	$0.341625\pi$
$127$	−3.45127	+	16.9054i	−0.306251	+	1.50012i	−0.783524	+	0.621361i	$0.786580\pi$
$128$	−10.2887	+	2.53593i	−0.909398	+	0.224147i
$129$	−3.17385			−0.279442
$130$	−0.738681	+	0.182069i	−0.0647866	+	0.0159685i
$131$	−9.20863	−	5.82318i	−0.804562	−	0.508774i	0.0677628	−	0.997701i	$-0.478414\pi$
$131$	−9.20863	−	5.82318i	−0.804562	−	0.508774i	−0.872324	+	0.488928i	$0.837388\pi$
$132$	−0.251998	−	6.25326i	−0.0219336	−	0.544276i
$133$	0.110747	−	2.74817i	0.00960303	−	0.238297i
$134$	−1.77453	−	4.67905i	−0.153296	−	0.404208i
$135$	−0.607661	+	1.05250i	−0.0522991	+	0.0905847i
$136$	1.92820	+	2.36161i	0.165342	+	0.202507i
$137$	−0.572279	−	2.80321i	−0.0488931	−	0.239494i	0.947999	−	0.318273i	$-0.103103\pi$
$137$	−0.572279	−	2.80321i	−0.0488931	−	0.239494i	−0.996892	+	0.0787791i	$0.974898\pi$
$138$	2.38657	+	1.79339i	0.203158	+	0.152663i
$139$	−5.67019	+	4.26087i	−0.480939	+	0.361402i	−0.813390	−	0.581718i	$-0.802381\pi$
$139$	−5.67019	+	4.26087i	−0.480939	+	0.361402i	0.332451	+	0.943120i	$0.392124\pi$
$140$	1.13447	−	1.18111i	0.0958802	−	0.0998218i
$141$	−4.14201	−	10.9216i	−0.348820	−	0.919764i
$142$	−0.717776	+	0.879116i	−0.0602344	+	0.0737738i
$143$	4.55279	+	2.38949i	0.380724	+	0.199819i
$144$	−1.49273	−	2.58549i	−0.124394	−	0.215457i
$145$	6.37842	−	11.0478i	0.529699	−	0.917466i
$146$	−5.15277	+	3.25842i	−0.426446	+	0.269668i
$147$	−1.79598	+	6.20044i	−0.148130	+	0.511404i
$148$	13.1195	−	2.13213i	1.07842	−	0.175260i
$149$	2.04484	−	16.8408i	0.167520	−	1.37965i	−0.630112	−	0.776505i	$-0.716991\pi$
$149$	2.04484	−	16.8408i	0.167520	−	1.37965i	0.797631	−	0.603145i	$-0.206086\pi$
$150$	0.835149	+	1.20992i	0.0681896	+	0.0987897i
$151$	−1.65661	+	1.04758i	−0.134813	+	0.0852505i	−0.600170	−	0.799873i	$-0.704900\pi$
$151$	−1.65661	+	1.04758i	−0.134813	+	0.0852505i	0.465357	+	0.885123i	$0.345926\pi$
$152$	4.12159	−	4.29103i	0.334305	−	0.348048i
$153$	−1.08479	+	1.57158i	−0.0876997	+	0.127055i
$154$	1.05223	−	0.0849447i	0.0847911	−	0.00684504i
$155$	1.71476	−	0.899974i	0.137733	−	0.0722876i
$156$	2.73896			0.219292
$157$	10.6984	+	6.52252i	0.853829	+	0.520554i
$157$	10.6984	+	6.52252i	0.853829	+	0.520554i
$158$	6.91094			0.549805
$159$	−8.85978	+	4.64997i	−0.702626	+	0.368767i
$160$	5.37726	−	0.434097i	0.425110	−	0.0343184i
$161$	2.99920	−	4.34509i	0.236370	−	0.342441i
$162$	−0.289078	+	0.300962i	−0.0227121	+	0.0236458i
$163$	−18.1434	+	11.4732i	−1.42110	+	0.898651i	−0.999965	−	0.00834591i	$-0.997343\pi$
$163$	−18.1434	+	11.4732i	−1.42110	+	0.898651i	−0.421138	+	0.906997i	$0.638369\pi$
$164$	−4.36540	−	6.32438i	−0.340881	−	0.493851i
$165$	−0.502114	+	4.13528i	−0.0390895	+	0.321931i
$166$	1.87352	−	0.304477i	0.145413	−	0.0236320i
$167$	−1.10403	+	3.81157i	−0.0854327	+	0.294948i	−0.991846	−	0.127445i	$-0.959322\pi$
$167$	−1.10403	+	3.81157i	−0.0854327	+	0.294948i	0.906413	+	0.422393i	$0.138810\pi$
$168$	0.995891	−	0.629763i	0.0768347	−	0.0485873i
$169$	5.37486	−	9.30953i	0.413451	−	0.716117i
$170$	−0.484240	−	0.838729i	−0.0371395	−	0.0643276i
$171$	3.29980	+	1.73187i	0.252342	+	0.132440i
$172$	−3.66502	+	4.48883i	−0.279455	+	0.342270i
$173$	4.62305	+	12.1900i	0.351484	+	0.926788i	0.987851	+	0.155402i	$0.0496672\pi$
$173$	4.62305	+	12.1900i	0.351484	+	0.926788i	−0.636367	+	0.771386i	$0.719564\pi$
$174$	3.03436	−	3.15910i	0.230034	−	0.239491i
$175$	2.07862	−	1.56198i	0.157129	−	0.118074i
$176$	−8.18071	−	6.14741i	−0.616644	−	0.463378i
$177$	0.786875	+	3.85437i	0.0591451	+	0.289712i
$178$	−1.49109	−	1.82626i	−0.111762	−	0.136884i
$179$	7.53870	−	13.0574i	0.563469	−	0.975957i	−0.433721	−	0.901047i	$-0.642800\pi$
$179$	7.53870	−	13.0574i	0.563469	−	0.975957i	0.997190	−	0.0749101i	$-0.0238670\pi$
$180$	0.786869	+	2.07480i	0.0586497	+	0.154647i
$181$	−0.487661	+	12.1012i	−0.0362476	+	0.899474i	0.874129	+	0.485694i	$0.161433\pi$
$181$	−0.487661	+	12.1012i	−0.0362476	+	0.899474i	−0.910377	+	0.413781i	$0.864208\pi$
$182$	0.0186031	+	0.461631i	0.00137895	+	0.0342184i
$183$	8.84047	+	5.59038i	0.653506	+	0.413252i
$184$	11.0894	−	2.73329i	0.817521	−	0.201501i
$185$	−8.84715			−0.650455
$186$	0.645642	−	0.159136i	0.0473408	−	0.0116685i
$187$	−1.30925	+	6.41315i	−0.0957421	+	0.468976i
$188$	−20.2296	−	6.75363i	−1.47540	−	0.492559i
$189$	0.552424	+	0.489405i	0.0401830	+	0.0355990i
$190$	−1.51096	+	1.13541i	−0.109617	+	0.0823716i
$191$	6.65467	−	22.9746i	0.481515	−	1.66238i	−0.240612	−	0.970621i	$-0.577348\pi$
$191$	6.65467	−	22.9746i	0.481515	−	1.66238i	0.722127	−	0.691761i	$-0.243165\pi$
$192$	−4.06519	−	0.660658i	−0.293380	−	0.0476789i
$193$	2.47335	−	5.21247i	0.178036	−	0.375202i	−0.794740	−	0.606950i	$-0.792393\pi$
$193$	2.47335	−	5.21247i	0.178036	−	0.375202i	0.972776	+	0.231747i	$0.0744443\pi$
$194$	3.61421	+	3.76279i	0.259485	+	0.270152i
$195$	−1.79949	−	0.292445i	−0.128864	−	0.0209424i
$196$	6.69548	+	9.70007i	0.478248	+	0.692862i
$197$	3.34921	+	4.10204i	0.238621	+	0.292258i	0.880007	−	0.474960i	$-0.157538\pi$
$197$	3.34921	+	4.10204i	0.238621	+	0.292258i	−0.641386	+	0.767219i	$0.721640\pi$
$198$	−0.507214	+	1.33741i	−0.0360461	+	0.0950457i
$199$	2.84451	+	1.21193i	0.201642	+	0.0859116i	0.490427	−	0.871482i	$-0.336841\pi$
$199$	2.84451	+	1.21193i	0.201642	+	0.0859116i	−0.288785	+	0.957394i	$0.593251\pi$
$200$	5.60640	+	0.452595i	0.396432	+	0.0320033i
$201$	0.482861	−	11.9821i	0.0340584	−	0.845150i
$202$	−0.994484	+	1.44076i	−0.0699717	+	0.101371i
$203$	−5.79863	−	5.13714i	−0.406984	−	0.360556i
$204$	0.970056	+	3.34902i	0.0679175	+	0.234479i
$205$	2.19279	+	4.62121i	0.153151	+	0.322759i
$206$	−0.0218053	+	0.0574959i	−0.00151925	+	0.00400593i
$207$	3.57686	+	6.19531i	0.248609	+	0.430604i
$208$	2.83239	−	3.46905i	0.196391	−	0.240535i
$209$	12.7322	+	1.02785i	0.880703	+	0.0710977i
$210$	−0.344348	+	0.146713i	−0.0237623	+	0.0101242i
$211$	−3.35384	+	2.97125i	−0.230888	+	0.204549i	−0.770632	−	0.637280i	$-0.780059\pi$
$211$	−3.35384	+	2.97125i	−0.230888	+	0.204549i	0.539744	+	0.841829i	$0.318521\pi$
$212$	−3.65434	+	17.9001i	−0.250981	+	1.22939i
$213$	−2.40812	+	1.26388i	−0.165002	+	0.0865997i
$214$	0.112453	+	0.0711108i	0.00768711	+	0.00486103i
$215$	2.88719	−	2.55783i	0.196905	−	0.174442i
$216$	0.192443	+	1.58491i	0.0130941	+	0.107839i
$217$	−0.327193	−	1.12960i	−0.0222113	−	0.0766823i
$218$	2.49964	+	1.87836i	0.169297	+	0.127219i
$219$	−14.4202	+	2.34351i	−0.974428	+	0.158360i
$220$	5.26878	+	5.48538i	0.355221	+	0.369824i
$221$	−2.78136	−	0.685545i	−0.187095	−	0.0461147i
$222$	−2.94958	−	0.727005i	−0.197963	−	0.0487934i
$223$	2.74661	−	5.78835i	0.183926	−	0.387617i	−0.790454	−	0.612521i	$-0.790156\pi$
$223$	2.74661	−	5.78835i	0.183926	−	0.387617i	0.974381	+	0.224904i	$0.0722068\pi$
$224$	0.394888	−	3.25220i	0.0263846	−	0.217297i
$225$	0.704689	+	3.45180i	0.0469793	+	0.230120i
$226$	1.39922	+	2.94880i	0.0930749	+	0.196151i
$227$	−8.15141	+	2.72134i	−0.541028	+	0.180622i	−0.574031	−	0.818834i	$-0.694621\pi$
$227$	−8.15141	+	2.72134i	−0.541028	+	0.180622i	0.0330030	+	0.999455i	$0.489493\pi$
$228$	6.25988	−	2.66709i	0.414571	−	0.176632i
$229$	0.746634	+	18.5275i	0.0493390	+	1.22433i	0.814372	+	0.580343i	$0.197082\pi$
$229$	0.746634	+	18.5275i	0.0493390	+	1.22433i	−0.765033	+	0.643991i	$0.777277\pi$
$230$	−3.61632	+	0.291939i	−0.238453	+	0.0192499i
$231$	2.39950	+	0.801071i	0.157876	+	0.0527066i
$232$	−2.02001	−	16.6363i	−0.132620	−	1.09223i
$233$	−2.80541	+	0.936582i	−0.183788	+	0.0613575i	−0.407073	−	0.913396i	$-0.633450\pi$
$233$	−2.80541	+	0.936582i	−0.183788	+	0.0613575i	0.223284	+	0.974753i	$0.428322\pi$
$234$	−0.575905	−	0.245370i	−0.0376481	−	0.0160404i
$235$	12.5697	+	6.59708i	0.819956	+	0.430346i
$236$	6.35995	+	3.33796i	0.413997	+	0.217283i
$237$	15.2357	+	6.49131i	0.989663	+	0.421656i
$238$	−0.557865	+	0.186243i	−0.0361610	+	0.0120723i
$239$	−0.0980438	−	0.807464i	−0.00634193	−	0.0522305i	0.989194	−	0.146610i	$-0.0468363\pi$
$239$	−0.0980438	−	0.807464i	−0.00634193	−	0.0522305i	−0.995536	+	0.0943797i	$0.969913\pi$
$240$	3.44157	+	1.14897i	0.222152	+	0.0741654i
$241$	−23.6931	+	1.91270i	−1.52620	+	0.123208i	−0.814869	−	0.579645i	$-0.803191\pi$
$241$	−23.6931	+	1.91270i	−1.52620	+	0.123208i	−0.711335	+	0.702853i	$0.751909\pi$
$242$	0.0125780	+	0.312120i	0.000808544	+	0.0200638i
$243$	−0.919979	+	0.391967i	−0.0590167	+	0.0251447i
$244$	18.1151	−	6.04772i	1.15970	−	0.387166i
$245$	−3.36321	−	7.08782i	−0.214868	−	0.452824i
$246$	0.351318	+	1.72087i	0.0223992	+	0.109719i
$247$	−0.673844	+	5.54960i	−0.0428757	+	0.353113i
$248$	1.09062	−	2.29843i	0.0692544	−	0.145951i
$249$	4.41630	+	1.08852i	0.279872	+	0.0689821i
$250$	−4.19692	−	1.03445i	−0.265436	−	0.0654242i
$251$	15.5794	+	16.2198i	0.983360	+	1.02379i	0.999714	+	0.0239203i	$0.00761480\pi$
$251$	15.5794	+	16.2198i	0.983360	+	1.02379i	−0.0163535	+	0.999866i	$0.505206\pi$
$252$	1.33009	−	0.216160i	0.0837877	−	0.0136168i
$253$	19.6025	+	14.7303i	1.23240	+	0.926088i
$254$	−2.00323	−	6.91597i	−0.125694	−	0.433946i
$255$	−0.279741	−	2.30388i	−0.0175181	−	0.144274i
$256$	−2.85560	+	2.52984i	−0.178475	+	0.158115i
$257$	−12.5143	−	7.91355i	−0.780620	−	0.493634i	0.0837525	−	0.996487i	$-0.473309\pi$
$257$	−12.5143	−	7.91355i	−0.780620	−	0.493634i	−0.864372	+	0.502853i	$0.832284\pi$
$258$	1.17276	−	0.615509i	0.0730126	−	0.0383199i
$259$	−1.07466	+	5.26406i	−0.0667764	+	0.327093i
$260$	−2.49158	+	2.20735i	−0.154521	+	0.136894i
$261$	9.65674	−	4.11435i	0.597737	−	0.254672i
$262$	4.53194	+	0.365856i	0.279984	+	0.0226027i
$263$	−11.3086	+	13.8505i	−0.697316	+	0.854057i	−0.994924	−	0.100632i	$-0.967914\pi$
$263$	−11.3086	+	13.8505i	−0.697316	+	0.854057i	0.297608	+	0.954688i	$0.403811\pi$
$264$	2.73618	+	4.73920i	0.168400	+	0.291678i
$265$	4.31213	−	11.3702i	0.264892	−	0.698463i
$266$	0.492035	+	1.03694i	0.0301686	+	0.0635790i
$267$	−1.57185	−	5.42667i	−0.0961959	−	0.332107i
$268$	−16.3889	−	14.5193i	−1.00111	−	0.886906i
$269$	−3.22701	+	4.67513i	−0.196754	+	0.285048i	−0.908926	−	0.416958i	$-0.863096\pi$
$269$	−3.22701	+	4.67513i	−0.196754	+	0.285048i	0.712172	+	0.702005i	$0.247712\pi$
$270$	0.0204213	−	0.506749i	0.00124280	−	0.0308397i
$271$	12.3246	+	0.994942i	0.748664	+	0.0604384i	0.448909	−	0.893578i	$-0.351813\pi$
$271$	12.3246	+	0.994942i	0.748664	+	0.0604384i	0.299756	+	0.954016i	$0.403095\pi$
$272$	5.24488	+	2.23464i	0.318018	+	0.135495i
$273$	−0.392589	+	1.03517i	−0.0237606	+	0.0626515i
$274$	0.755090	+	0.924818i	0.0456167	+	0.0558703i
$275$	6.85965	+	9.93792i	0.413652	+	0.599279i
$276$	12.8925	+	2.09524i	0.776039	+	0.126119i
$277$	−9.21101	−	9.58967i	−0.553436	−	0.576188i	0.384444	−	0.923148i	$-0.374393\pi$
$277$	−9.21101	−	9.58967i	−0.553436	−	0.576188i	−0.937880	+	0.346961i	$0.887214\pi$
$278$	1.26885	−	2.67404i	0.0761005	−	0.160378i
$279$	1.57284	+	0.255611i	0.0941633	+	0.0153030i
$280$	−0.398412	+	1.37548i	−0.0238097	+	0.0822006i
$281$	6.22429	−	4.67725i	0.371310	−	0.279021i	−0.398663	−	0.917097i	$-0.630526\pi$
$281$	6.22429	−	4.67725i	0.371310	−	0.279021i	0.769973	+	0.638076i	$0.220269\pi$
$282$	3.64854	+	3.23232i	0.217267	+	0.192482i
$283$	17.1295	+	5.71866i	1.01824	+	0.339939i	0.776308	−	0.630354i	$-0.217090\pi$
$283$	17.1295	+	5.71866i	1.01824	+	0.339939i	0.241934	+	0.970293i	$0.422218\pi$
$284$	−0.993263	+	4.86532i	−0.0589393	+	0.288704i
$285$	−4.39750	+	1.08389i	−0.260485	+	0.0642038i
$286$	−2.14568			−0.126877
$287$	3.01598	−	0.743372i	0.178028	−	0.0438798i
$288$	3.75176	+	2.37247i	0.221074	+	0.139799i
$289$	0.537686	+	13.3425i	0.0316286	+	0.784855i
$290$	−0.214356	+	5.31919i	−0.0125874	+	0.312353i
$291$	4.43346	+	11.6901i	0.259894	+	0.685285i
$292$	−13.3373	+	23.1009i	−0.780508	+	1.35188i
$293$	2.05620	+	2.51839i	0.120124	+	0.147126i	0.831166	−	0.556024i	$-0.187674\pi$
$293$	2.05620	+	2.51839i	0.120124	+	0.147126i	−0.711042	+	0.703150i	$0.751776\pi$
$294$	−0.538836	−	2.63940i	−0.0314256	−	0.153933i
$295$	−3.82207	−	2.87210i	−0.222529	−	0.167220i
$296$	−9.29143	+	6.98206i	−0.540053	+	0.405824i
$297$	−2.37439	+	2.47200i	−0.137776	+	0.143440i
$298$	2.51038	+	6.61932i	0.145422	+	0.383447i
$299$	−6.78694	+	8.31249i	−0.392499	+	0.480724i
$300$	5.69568	+	2.98932i	0.328840	+	0.172589i
$301$	−1.17120	−	2.02858i	−0.0675069	−	0.116925i
$302$	0.408968	−	0.708354i	0.0235335	−	0.0407612i
$303$	−3.54569	+	2.24216i	−0.203694	+	0.128809i
$304$	3.09540	−	10.6866i	0.177534	−	0.612917i
$305$	−12.5473	+	2.03914i	−0.718458	+	0.116761i
$306$	0.0960548	−	0.791083i	0.00549109	−	0.0452232i
$307$	−7.88264	−	11.4200i	−0.449886	−	0.651773i	0.530769	−	0.847517i	$-0.321903\pi$
$307$	−7.88264	−	11.4200i	−0.449886	−	0.651773i	−0.980655	+	0.195744i	$0.937288\pi$
$308$	3.90380	−	2.46862i	0.222440	−	0.140662i
$309$	−0.102076	+	0.106273i	−0.00580691	+	0.00604564i
$310$	−0.459079	+	0.665091i	−0.0260739	+	0.0377746i
$311$	−21.4399	+	1.73081i	−1.21575	+	0.0981451i	−0.671644	−	0.740874i	$-0.734412\pi$
$311$	−21.4399	+	1.73081i	−1.21575	+	0.0981451i	−0.544102	+	0.839019i	$0.683129\pi$
$312$	−2.12065	+	1.11300i	−0.120058	+	0.0630113i
$313$	−14.2723			−0.806718			−0.403359	−	0.915042i	$-0.632157\pi$
$313$	−14.2723			−0.806718			−0.403359	+	0.915042i	$0.632157\pi$
$314$	−5.21806	−	0.335344i	−0.294472	−	0.0189246i
$315$	−0.896945			−0.0505371
$316$	26.7742	−	14.0522i	1.50617	−	0.790498i
$317$	−23.3101	+	1.88178i	−1.30922	+	0.105691i	−0.715293	−	0.698825i	$-0.753707\pi$
$317$	−23.3101	+	1.88178i	−1.30922	+	0.105691i	−0.593931	+	0.804516i	$0.702425\pi$
$318$	2.37196	−	3.43638i	0.133013	−	0.192703i
$319$	24.9233	−	25.9479i	1.39544	−	1.45280i
$320$	4.23046	−	2.67518i	0.236490	−	0.149547i
$321$	0.181117	+	0.262393i	0.0101090	+	0.0146454i
$322$	−0.265571	+	2.18717i	−0.0147997	+	0.121886i
$323$	−7.02436	+	1.14157i	−0.390846	+	0.0635186i
$324$	−0.507985	+	1.75377i	−0.0282214	+	0.0974316i
$325$	−4.46668	+	2.82456i	−0.247767	+	0.156678i
$326$	4.47908	−	7.75800i	0.248073	−	0.429676i
$327$	3.74634	+	6.48884i	0.207173	+	0.358834i
$328$	5.94990	+	3.12275i	0.328528	+	0.172425i
$329$	5.45211	−	6.67762i	0.300584	−	0.368149i
$330$	−0.616427	−	1.62539i	−0.0339332	−	0.0894745i
$331$	2.33760	−	2.43370i	0.128486	−	0.133768i	−0.653851	−	0.756623i	$-0.726848\pi$
$331$	2.33760	−	2.43370i	0.128486	−	0.133768i	0.782337	+	0.622855i	$0.214027\pi$
$332$	6.63925	−	4.98907i	0.364376	−	0.273811i
$333$	−5.81969	−	4.37321i	−0.318917	−	0.239651i
$334$	−0.331236	−	1.62250i	−0.0181244	−	0.0887793i
$335$	9.21719	+	11.2890i	0.503589	+	0.616784i
$336$	1.10168	−	1.90817i	0.0601017	−	0.104099i
$337$	−2.76858	−	7.30016i	−0.150814	−	0.397665i	0.838223	−	0.545327i	$-0.183594\pi$
$337$	−2.76858	−	7.30016i	−0.150814	−	0.397665i	−0.989038	+	0.147662i	$0.952825\pi$
$338$	−0.180630	+	4.48228i	−0.00982495	+	0.243804i
$339$	0.314938	+	7.81510i	0.0171051	+	0.424458i
$340$	−3.58144	−	2.26477i	−0.194231	−	0.122824i
$341$	5.30310	−	1.30710i	0.287179	−	0.0707833i
$342$	−1.55516			−0.0840935
$343$	−9.64188	+	2.37651i	−0.520613	+	0.128319i
$344$	1.01357	−	4.96481i	0.0546482	−	0.267684i
$345$	−8.24664	−	2.75313i	−0.443984	−	0.148224i
$346$	−4.07227	−	3.60772i	−0.218927	−	0.193952i
$347$	14.7846	−	11.1099i	0.793679	−	0.596411i	−0.124663	−	0.992199i	$-0.539785\pi$
$347$	14.7846	−	11.1099i	0.793679	−	0.596411i	0.918342	+	0.395788i	$0.129529\pi$
$348$	5.33216	−	18.4088i	0.285834	−	0.986813i
$349$	9.73429	+	1.58198i	0.521065	+	0.0846813i	0.415255	−	0.909705i	$-0.363692\pi$
$349$	9.73429	+	1.58198i	0.521065	+	0.0846813i	0.105810	+	0.994386i	$0.466257\pi$
$350$	−0.465143	+	0.980269i	−0.0248630	+	0.0523976i
$351$	−1.03915	−	1.08187i	−0.0554658	−	0.0577461i
$352$	15.0180	+	2.44066i	0.800461	+	0.130088i
$353$	−7.40674	−	10.7305i	−0.394221	−	0.571128i	0.574742	−	0.818335i	$-0.305103\pi$
$353$	−7.40674	−	10.7305i	−0.394221	−	0.571128i	−0.968963	+	0.247207i	$0.920487\pi$
$354$	−1.03824	−	1.27161i	−0.0551817	−	0.0675854i
$355$	1.17205	−	3.09045i	0.0622062	−	0.164024i
$356$	−9.49014	−	4.04337i	−0.502976	−	0.214298i
$357$	−1.40479	−	0.113406i	−0.0743492	−	0.00600209i
$358$	−0.253349	+	6.28678i	−0.0133899	+	0.332267i
$359$	2.58335	−	3.74263i	0.136344	−	0.197528i	−0.748864	−	0.662724i	$-0.769400\pi$
$359$	2.58335	−	3.74263i	0.136344	−	0.197528i	0.885208	+	0.465195i	$0.154016\pi$
$360$	−1.45235	−	1.28667i	−0.0765456	−	0.0678135i
$361$	−1.42222	−	4.91008i	−0.0748538	−	0.258425i
$362$	−2.16661	−	4.56603i	−0.113874	−	0.239985i
$363$	−0.265439	+	0.699904i	−0.0139319	+	0.0367354i
$364$	1.01072	+	1.75062i	0.0529760	+	0.0917572i
$365$	11.2291	−	13.7532i	0.587760	−	0.719875i
$366$	−4.35075	−	0.351229i	−0.227418	−	0.0183590i
$367$	−34.3825	+	14.6490i	−1.79475	+	0.764671i	−0.811019	+	0.585020i	$0.801087\pi$
$367$	−34.3825	+	14.6490i	−1.79475	+	0.764671i	−0.983730	+	0.179652i	$0.942503\pi$
$368$	15.9861	−	14.1624i	0.833332	−	0.738268i
$369$	−0.841872	+	4.12376i	−0.0438261	+	0.214674i
$370$	3.26907	−	1.71574i	0.169951	−	0.0891971i
$371$	−6.24145	−	3.94685i	−0.324040	−	0.204910i
$372$	2.17776	−	1.92932i	0.112911	−	0.100031i
$373$	−2.13273	−	17.5647i	−0.110429	−	0.909463i	−0.937649	−	0.347585i	$-0.887002\pi$
$373$	−2.13273	−	17.5647i	−0.110429	−	0.909463i	0.827220	−	0.561879i	$-0.189921\pi$
$374$	−0.759935	−	2.62360i	−0.0392953	−	0.135663i
$375$	−8.28077	−	6.22259i	−0.427617	−	0.321333i
$376$	18.4072	−	2.99147i	0.949281	−	0.154273i
$377$	10.9077	+	11.3561i	0.561773	+	0.584868i
$378$	−0.299035	−	0.0737055i	−0.0153807	−	0.00379100i
$379$	2.56491	+	0.632194i	0.131751	+	0.0324736i	0.304640	−	0.952468i	$-0.401464\pi$
$379$	2.56491	+	0.632194i	0.131751	+	0.0324736i	−0.172889	+	0.984941i	$0.555310\pi$
$380$	−3.54507	+	7.47108i	−0.181858	+	0.383258i
$381$	2.07976	−	17.1283i	0.106549	−	0.877511i
$382$	1.99656	+	9.77978i	0.102153	+	0.500377i
$383$	−13.9524	−	29.4040i	−0.712934	−	1.50248i	−0.858328	−	0.513102i	$-0.828496\pi$
$383$	−13.9524	−	29.4040i	−0.712934	−	1.50248i	0.145394	−	0.989374i	$-0.453555\pi$
$384$	10.0512	−	3.35560i	0.512926	−	0.171240i
$385$	−2.82837	+	1.20506i	−0.144147	+	0.0614153i
$386$	0.0969463	+	2.40570i	0.00493444	+	0.122447i
$387$	3.16356	−	0.255389i	0.160813	−	0.0129821i
$388$	21.6530	+	7.22885i	1.09927	+	0.366989i
$389$	−0.826184	−	6.80424i	−0.0418892	−	0.344988i	−0.998552	−	0.0537912i	$-0.982869\pi$
$389$	−0.826184	−	6.80424i	−0.0418892	−	0.344988i	0.956663	−	0.291197i	$-0.0940536\pi$
$390$	0.721635	−	0.240917i	0.0365414	−	0.0121993i
$391$	−12.5677	−	5.35460i	−0.635577	−	0.270794i
$392$	−9.12571	−	4.78954i	−0.460918	−	0.241908i
$393$	9.64734	+	5.06331i	0.486644	+	0.255410i
$394$	−2.03307	−	0.866209i	−0.102424	−	0.0436390i
$395$	−19.0910	+	6.37351i	−0.960571	+	0.320686i
$396$	0.754359	+	6.21270i	0.0379079	+	0.312200i
$397$	−30.4845	−	10.1772i	−1.52997	−	0.510779i	−0.577757	−	0.816209i	$-0.696072\pi$
$397$	−30.4845	−	10.1772i	−1.52997	−	0.510779i	−0.952215	+	0.305430i	$0.901200\pi$
$398$	−1.28609	+	0.103824i	−0.0644661	+	0.00520424i
$399$	0.110747	+	2.74817i	0.00554431	+	0.137581i
$400$	9.67613	−	4.12261i	0.483807	−	0.206131i
$401$	−28.8681	+	9.63757i	−1.44160	+	0.481277i	−0.926645	−	0.375939i	$-0.877320\pi$
$401$	−28.8681	+	9.63757i	−1.44160	+	0.481277i	−0.514957	+	0.857216i	$0.672192\pi$
$402$	2.14528	+	4.52109i	0.106997	+	0.225491i
$403$	0.478133	+	2.34205i	0.0238175	+	0.116666i
$404$	−0.923277	+	7.60387i	−0.0459347	+	0.378307i
$405$	0.520999	−	1.09798i	0.0258887	−	0.0545592i
$406$	3.13888	+	0.773664i	0.155780	+	0.0383963i
$407$	−24.2269	−	5.97139i	−1.20088	−	0.295991i
$408$	−2.11198	−	2.19880i	−0.104558	−	0.108857i
$409$	−31.8009	+	5.16815i	−1.57245	+	0.255549i	−0.883209	−	0.468979i	$-0.844622\pi$
$409$	−31.8009	+	5.16815i	−1.57245	+	0.255549i	−0.689246	+	0.724528i	$0.742058\pi$
$410$	−1.70645	−	1.28231i	−0.0842754	−	0.0633288i
$411$	0.795987	+	2.74807i	0.0392632	+	0.135552i
$412$	0.0324302	+	0.267087i	0.00159772	+	0.0131584i
$413$	−2.17317	+	1.92526i	−0.106934	+	0.0947357i
$414$	−2.52314	−	1.59553i	−0.124005	−	0.0784162i
$415$	−4.89467	+	2.56892i	−0.240270	+	0.126103i
$416$	−1.33194	+	6.52428i	−0.0653038	+	0.319879i
$417$	5.30894	−	4.70331i	0.259980	−	0.230322i
$418$	−4.90394	+	2.08938i	−0.239860	+	0.102195i
$419$	20.2040	+	1.63104i	0.987032	+	0.0796815i	0.563427	−	0.826166i	$-0.309483\pi$
$419$	20.2040	+	1.63104i	0.987032	+	0.0796815i	0.423605	+	0.905847i	$0.360765\pi$
$420$	−1.03575	+	1.26856i	−0.0505395	+	0.0618996i
$421$	−10.0344	−	17.3800i	−0.489045	−	0.847051i	0.510876	−	0.859655i	$-0.329321\pi$
$421$	−10.0344	−	17.3800i	−0.489045	−	0.847051i	−0.999921	+	0.0126039i	$0.995988\pi$
$422$	0.663046	−	1.74831i	0.0322766	−	0.0851063i
$423$	5.00740	+	10.5529i	0.243468	+	0.513099i
$424$	−4.44450	−	15.3442i	−0.215844	−	0.745180i
$425$	−5.03566	−	4.46120i	−0.244265	−	0.216400i
$426$	0.644709	−	0.934022i	0.0312362	−	0.0452535i
$427$	−0.310838	+	7.71336i	−0.0150425	+	0.373276i
$428$	0.580253	+	0.0468429i	0.0280476	+	0.00226424i
$429$	−4.73030	−	2.01539i	−0.228381	−	0.0973041i
$430$	−0.570790	+	1.50505i	−0.0275259	+	0.0725799i
$431$	10.1035	+	12.3746i	0.486670	+	0.596063i	0.958311	−	0.285728i	$-0.0922355\pi$
$431$	10.1035	+	12.3746i	0.486670	+	0.596063i	−0.471641	+	0.881791i	$0.656338\pi$
$432$	1.69594	+	2.45699i	0.0815958	+	0.118212i
$433$	20.8673	+	3.39127i	1.00282	+	0.162974i	0.639582	−	0.768723i	$-0.279107\pi$
$433$	20.8673	+	3.39127i	1.00282	+	0.162974i	0.363237	+	0.931697i	$0.381672\pi$
$434$	0.339965	+	0.353941i	0.0163188	+	0.0169897i
$435$	−5.46877	+	11.5252i	−0.262207	+	0.552590i
$436$	13.5034	+	2.19451i	0.646695	+	0.105098i
$437$	−7.41716	+	25.6070i	−0.354811	+	1.22495i
$438$	4.87387	−	3.66247i	0.232882	−	0.175000i
$439$	12.1639	+	10.7763i	0.580551	+	0.514323i	0.901503	−	0.432772i	$-0.142464\pi$
$439$	12.1639	+	10.7763i	0.580551	+	0.514323i	−0.320952	+	0.947095i	$0.604003\pi$
$440$	−6.30841	−	2.10606i	−0.300742	−	0.100402i
$441$	1.29123	−	6.32485i	0.0614870	−	0.301183i
$442$	1.16068	−	0.286082i	0.0552079	−	0.0136075i
$443$	−7.81501			−0.371302			−0.185651	−	0.982616i	$-0.559439\pi$
$443$	−7.81501			−0.371302			−0.185651	+	0.982616i	$0.559439\pi$
$444$	−12.9054	+	3.18090i	−0.612464	+	0.150959i
$445$	5.80328	+	3.66977i	0.275102	+	0.173964i
$446$	0.107657	+	2.67148i	0.00509771	+	0.126498i
$447$	−0.683090	+	16.9507i	−0.0323091	+	0.801741i
$448$	−1.07786	−	2.84208i	−0.0509240	−	0.134276i
$449$	8.83284	−	15.2989i	0.416848	−	0.722001i	−0.578773	−	0.815489i	$-0.696468\pi$
$449$	8.83284	−	15.2989i	0.416848	−	0.722001i	0.995620	+	0.0934876i	$0.0298015\pi$
$450$	−0.929799	−	1.13880i	−0.0438311	−	0.0536834i
$451$	2.88561	+	14.1347i	0.135878	+	0.665575i
$452$	11.4167	+	8.57909i	0.536996	+	0.403527i
$453$	1.56694	−	1.17748i	0.0736214	−	0.0553229i
$454$	2.48424	−	2.58637i	0.116591	−	0.121384i
$455$	−0.477122	−	1.25807i	−0.0223678	−	0.0589791i
$456$	−3.76294	+	4.60876i	−0.176216	+	0.215825i
$457$	−26.3070	−	13.8070i	−1.23059	−	0.645863i	−0.281105	−	0.959677i	$-0.590701\pi$
$457$	−26.3070	−	13.8070i	−1.23059	−	0.645863i	−0.949485	+	0.313814i	$0.898393\pi$
$458$	−3.86896	−	6.70124i	−0.180785	−	0.313128i
$459$	0.954808	−	1.65378i	0.0445666	−	0.0771916i
$460$	−13.4167	+	8.48418i	−0.625555	+	0.395577i
$461$	−1.31569	+	4.54229i	−0.0612778	+	0.211555i	−0.985315	−	0.170748i	$-0.945382\pi$
$461$	−1.31569	+	4.54229i	−0.0612778	+	0.211555i	0.924037	+	0.382303i	$0.124869\pi$
$462$	−1.04198	+	0.169339i	−0.0484774	+	0.00787834i
$463$	0.895277	−	7.37327i	0.0416070	−	0.342665i	−0.957008	−	0.290060i	$-0.906325\pi$
$463$	0.895277	−	7.37327i	0.0416070	−	0.342665i	0.998615	−	0.0526046i	$-0.0167523\pi$
$464$	−17.8017	−	25.7902i	−0.826424	−	1.19728i
$465$	−1.63678	+	1.03504i	−0.0759038	+	0.0479987i
$466$	0.854981	−	0.890129i	0.0396062	−	0.0412344i
$467$	2.78739	−	4.03823i	0.128985	−	0.186867i	−0.753170	−	0.657826i	$-0.771476\pi$
$467$	2.78739	−	4.03823i	0.128985	−	0.186867i	0.882155	+	0.470958i	$0.156092\pi$
$468$	−2.73008	+	0.220395i	−0.126198	+	0.0101877i
$469$	7.83657	−	4.11295i	0.361859	−	0.189918i
$470$	−5.92395			−0.273252
$471$	−11.1886	−	5.64051i	−0.515543	−	0.259901i
$472$	−6.28062			−0.289089
$473$	9.63264	−	5.05560i	0.442909	−	0.232457i
$474$	−6.88853	+	0.556100i	−0.316401	+	0.0255425i
$475$	−7.45815	+	10.8050i	−0.342203	+	0.495767i
$476$	−1.78258	+	1.85586i	−0.0817042	+	0.0850631i
$477$	8.45689	−	5.34781i	0.387214	−	0.244859i
$478$	0.192820	+	0.279349i	0.00881940	+	0.0127771i
$479$	2.51627	−	20.7233i	0.114971	−	0.946873i	−0.815056	−	0.579382i	$-0.803294\pi$
$479$	2.51627	−	20.7233i	0.114971	−	0.946873i	0.930027	−	0.367491i	$-0.119783\pi$
$480$	−5.32489	+	0.865379i	−0.243047	+	0.0394990i
$481$	3.03819	−	10.4891i	0.138530	−	0.478260i
$482$	8.38378	−	5.30158i	0.381871	−	0.241480i
$483$	−2.63984	+	4.57233i	−0.120117	+	0.208048i
$484$	0.683370	+	1.18363i	0.0310623	+	0.0538014i
$485$	−13.4542	−	7.06128i	−0.610922	−	0.320636i
$486$	0.263923	−	0.323247i	0.0119718	−	0.0146628i
$487$	4.43702	+	11.6995i	0.201061	+	0.530153i	0.997185	−	0.0749797i	$-0.0238892\pi$
$487$	4.43702	+	11.6995i	0.201061	+	0.530153i	−0.796124	+	0.605133i	$0.793120\pi$
$488$	−11.5682	+	12.0437i	−0.523666	+	0.545194i
$489$	17.1614	−	12.8959i	0.776064	−	0.583175i
$490$	2.61728	+	1.96676i	0.118236	+	0.0888490i
$491$	4.23162	+	20.7279i	0.190970	+	0.935435i	0.956432	+	0.291954i	$0.0943054\pi$
$491$	4.23162	+	20.7279i	0.190970	+	0.935435i	−0.765462	+	0.643481i	$0.777490\pi$
$492$	4.86015	+	5.95260i	0.219112	+	0.268364i
$493$	−10.0223	+	17.3592i	−0.451383	+	0.781818i
$494$	−0.827254	−	2.18129i	−0.0372199	−	0.0981408i
$495$	0.167734	−	4.16227i	0.00753908	−	0.187080i
$496$	−0.191555	−	4.75340i	−0.00860109	−	0.213434i
$497$	−1.69645	−	1.07277i	−0.0760962	−	0.0481203i
$498$	−1.84295	+	0.454245i	−0.0825844	+	0.0203552i
$499$	−12.2380			−0.547849			−0.273924	−	0.961751i	$-0.588322\pi$
$499$	−12.2380			−0.547849			−0.273924	+	0.961751i	$0.588322\pi$
$500$	−18.3630	+	4.52607i	−0.821217	+	0.202412i
$501$	0.793750	−	3.88804i	0.0354621	−	0.173705i
$502$	−8.90220	−	2.97199i	−0.397324	−	0.132646i
$503$	−29.4278	−	26.0708i	−1.31212	−	1.16244i	−0.975304	−	0.220867i	$-0.929111\pi$
$503$	−29.4278	−	26.0708i	−1.31212	−	1.16244i	−0.336817	−	0.941570i	$-0.609350\pi$
$504$	−0.941987	+	0.707857i	−0.0419594	+	0.0315305i
$505$	1.41847	−	4.89714i	0.0631213	−	0.217920i
$506$	−10.0999	−	1.64140i	−0.448996	−	0.0729689i
$507$	−4.60832	+	9.71183i	−0.204663	+	0.431318i
$508$	−21.8233	−	22.7205i	−0.968252	−	1.00806i
$509$	31.8419	+	5.17481i	1.41137	+	0.229370i	0.817841	−	0.575445i	$-0.195171\pi$
$509$	31.8419	+	5.17481i	1.41137	+	0.229370i	0.593527	+	0.804814i	$0.297735\pi$
$510$	0.550160	+	0.797044i	0.0243615	+	0.0352937i
$511$	−6.81915	−	8.35194i	−0.301661	−	0.369468i
$512$	8.07975	−	21.3045i	0.357078	−	0.941537i
$513$	−3.42846	−	1.46073i	−0.151370	−	0.0644929i
$514$	6.15879	+	0.497189i	0.271652	+	0.0219300i
$515$	0.00721096	−	0.178938i	0.000317753	−	0.00788495i
$516$	3.29193	−	4.76919i	0.144919	−	0.209952i
$517$	29.9679	+	26.5493i	1.31799	+	1.16764i
$518$	−0.623772	−	2.15351i	−0.0274070	−	0.0946198i
$519$	−5.58895	−	11.7785i	−0.245328	−	0.517017i
$520$	1.03214	−	2.72152i	0.0452622	−	0.119347i
$521$	11.5810	+	20.0590i	0.507375	+	0.878799i	0.999964	+	0.00853679i	$0.00271738\pi$
$521$	11.5810	+	20.0590i	0.507375	+	0.878799i	−0.492589	+	0.870262i	$0.663949\pi$
$522$	−2.77032	+	3.39302i	−0.121253	+	0.148509i
$523$	−3.33937	−	0.269582i	−0.146021	−	0.0117880i	0.00724011	−	0.999974i	$-0.497695\pi$
$523$	−3.33937	−	0.269582i	−0.146021	−	0.0117880i	−0.153261	+	0.988186i	$0.548977\pi$
$524$	18.3014	−	7.79751i	0.799502	−	0.340636i
$525$	−1.94619	+	1.72417i	−0.0849386	+	0.0752491i
$526$	1.49253	−	7.31091i	0.0650776	−	0.318771i
$527$	−2.69437	+	1.41412i	−0.117369	+	0.0615998i
$528$	8.64885	+	5.46920i	0.376393	+	0.238016i
$529$	−21.0899	+	18.6840i	−0.916950	+	0.812347i
$530$	0.611674	+	5.03759i	0.0265694	+	0.218819i
$531$	−1.09447	−	3.77855i	−0.0474960	−	0.163975i
$532$	4.01467	+	3.01683i	0.174058	+	0.130796i
$533$	−6.23187	+	1.01278i	−0.269932	+	0.0438682i
$534$	1.63321	+	1.70035i	0.0706760	+	0.0735815i
$535$	−0.376223	−	0.0927307i	−0.0162656	−	0.00400910i
$536$	18.5892	+	4.58182i	0.802930	+	0.197905i
$537$	−6.46357	+	13.6217i	−0.278924	+	0.587819i
$538$	0.285743	−	2.35330i	0.0123192	−	0.101458i
$539$	−4.42583	−	21.6792i	−0.190634	−	0.933788i
$540$	−0.951269	−	2.00476i	−0.0409361	−	0.0862710i
$541$	13.8773	−	4.63293i	0.596633	−	0.199185i	−0.00228294	−	0.999997i	$-0.500727\pi$
$541$	13.8773	−	4.63293i	0.596633	−	0.199185i	0.598916	+	0.800812i	$0.295598\pi$
$542$	−4.74695	+	2.02249i	−0.203899	+	0.0868732i
$543$	−0.487661	−	12.1012i	−0.0209275	−	0.519312i
$544$	−8.44920	+	0.682090i	−0.362257	+	0.0292444i
$545$	−8.63737	−	2.88358i	−0.369984	−	0.123519i
$546$	−0.0556887	−	0.458637i	−0.00238326	−	0.0196279i
$547$	10.5332	−	3.51649i	0.450367	−	0.150354i	−0.0824318	−	0.996597i	$-0.526269\pi$
$547$	10.5332	−	3.51649i	0.450367	−	0.150354i	0.532798	+	0.846242i	$0.321140\pi$
$548$	4.80581	+	2.04756i	0.205294	+	0.0874676i
$549$	−9.26164	−	4.86088i	−0.395277	−	0.207458i
$550$	−4.46195	−	2.34181i	−0.190258	−	0.0998553i
$551$	35.9875	+	15.3328i	1.53312	+	0.653201i
$552$	−10.8335	+	3.61675i	−0.461104	+	0.153939i
$553$	1.47325	+	12.1333i	0.0626491	+	0.515962i
$554$	5.26326	+	1.75713i	0.223614	+	0.0746535i
$555$	8.81846	−	0.711900i	0.374323	−	0.0302185i
$556$	−0.521452	−	12.9397i	−0.0221145	−	0.548766i
$557$	36.8044	−	15.6809i	1.55945	−	0.664420i	0.571701	−	0.820462i	$-0.306284\pi$
$557$	36.8044	−	15.6809i	1.55945	−	0.664420i	0.987751	+	0.156041i	$0.0498733\pi$
$558$	−0.630743	+	0.210573i	−0.0267015	+	0.00891427i
$559$	2.04104	+	4.30140i	0.0863267	+	0.181930i
$560$	0.535628	+	2.62368i	0.0226344	+	0.110871i
$561$	0.788964	−	6.49771i	0.0333101	−	0.274333i
$562$	−1.39284	+	2.93536i	−0.0587536	+	0.123821i
$563$	24.7861	+	6.10922i	1.04461	+	0.257473i	0.724044	−	0.689754i	$-0.242281\pi$
$563$	24.7861	+	6.10922i	1.04461	+	0.257473i	0.320565	+	0.947227i	$0.396127\pi$
$564$	20.7074	+	5.10393i	0.871941	+	0.214914i
$565$	−6.58473	−	6.85543i	−0.277022	−	0.288410i
$566$	−7.43847	+	1.20887i	−0.312662	+	0.0508125i
$567$	−0.590014	−	0.443367i	−0.0247783	−	0.0186196i
$568$	−1.20803	−	4.17061i	−0.0506879	−	0.174995i
$569$	0.839228	+	6.91167i	0.0351823	+	0.289752i	0.999672	+	0.0256299i	$0.00815914\pi$
$569$	0.839228	+	6.91167i	0.0351823	+	0.289752i	−0.964489	+	0.264122i	$0.914918\pi$
$570$	1.41470	−	1.25331i	0.0592553	−	0.0524956i
$571$	−39.1592	−	24.7628i	−1.63876	−	1.03629i	−0.950451	−	0.310874i	$-0.899378\pi$
$571$	−39.1592	−	24.7628i	−1.63876	−	1.03629i	−0.688310	−	0.725416i	$-0.741647\pi$
$572$	−8.31274	+	4.36286i	−0.347573	+	0.182421i
$573$	−4.78440	+	23.4356i	−0.199871	+	0.979034i
$574$	−0.970257	+	0.859573i	−0.0404978	+	0.0358779i
$575$	−23.1858	+	9.87855i	−0.966915	+	0.411964i
$576$	4.10517	+	0.331404i	0.171049	+	0.0138085i
$577$	−18.3029	+	22.4169i	−0.761958	+	0.933229i	−0.999270	−	0.0382047i	$-0.987836\pi$
$577$	−18.3029	+	22.4169i	−0.761958	+	0.933229i	0.237312	+	0.971433i	$0.423734\pi$
$578$	−2.78622	−	4.82587i	−0.115891	−	0.200730i
$579$	−2.04590	+	5.39459i	−0.0850247	+	0.224192i
$580$	9.98518	+	21.0433i	0.414612	+	0.873776i
$581$	0.933952	+	3.22438i	0.0387468	+	0.133770i
$582$	−3.90526	−	3.45976i	−0.161878	−	0.143412i
$583$	19.4826	−	28.2254i	0.806885	−	1.16897i
$584$	0.939189	−	23.3057i	0.0388639	−	0.964398i
$585$	1.81719	+	0.146698i	0.0751314	+	0.00606523i
$586$	−1.24817	−	0.531796i	−0.0515615	−	0.0219683i
$587$	12.2093	−	32.1933i	0.503932	−	1.32876i	−0.405952	−	0.913894i	$-0.633060\pi$
$587$	12.2093	−	32.1933i	0.503932	−	1.32876i	0.909883	−	0.414864i	$-0.136171\pi$
$588$	−7.45430	−	9.12986i	−0.307410	−	0.376509i
$589$	3.37337	+	4.88717i	0.138997	+	0.201372i
$590$	1.96927	+	0.320037i	0.0810734	+	0.0131757i
$591$	−3.66843	−	3.81924i	−0.150899	−	0.157102i
$592$	−9.31687	+	19.6349i	−0.382921	+	0.806989i
$593$	−8.74523	−	1.42124i	−0.359124	−	0.0583633i	−0.0218272	−	0.999762i	$-0.506948\pi$
$593$	−8.74523	−	1.42124i	−0.359124	−	0.0583633i	−0.337296	+	0.941398i	$0.609512\pi$
$594$	0.397952	−	1.37389i	0.0163282	−	0.0563714i
$595$	1.36930	−	1.02896i	0.0561359	−	0.0421834i
$596$	23.1849	+	20.5400i	0.949689	+	0.841351i
$597$	−2.93281	−	0.979114i	−0.120032	−	0.0400725i
$598$	0.895758	−	4.38771i	0.0366303	−	0.179427i
$599$	36.3585	−	8.96157i	1.48557	−	0.366160i	0.588662	−	0.808379i	$-0.299655\pi$
$599$	36.3585	−	8.96157i	1.48557	−	0.366160i	0.896907	+	0.442220i	$0.145809\pi$
$600$	−5.62464			−0.229625
$601$	28.2464	−	6.96212i	1.15220	−	0.283991i	0.383460	−	0.923557i	$-0.374732\pi$
$601$	28.2464	−	6.96212i	1.15220	−	0.283991i	0.768736	+	0.639566i	$0.220886\pi$
$602$	0.826170	+	0.522439i	0.0336722	+	0.0212930i
$603$	0.482861	+	11.9821i	0.0196636	+	0.487948i
$604$	0.144102	−	3.57585i	0.00586343	−	0.145499i
$605$	−0.322593	−	0.850608i	−0.0131153	−	0.0345821i
$606$	0.875327	−	1.51611i	0.0355577	−	0.0615878i
$607$	8.29193	+	10.1558i	0.336559	+	0.412210i	0.914961	−	0.403542i	$-0.132221\pi$
$607$	8.29193	+	10.1558i	0.336559	+	0.412210i	−0.578402	+	0.815752i	$0.696324\pi$
$608$	3.30893	+	16.2082i	0.134195	+	0.657330i
$609$	6.19319	+	4.65388i	0.250961	+	0.188585i
$610$	4.24086	−	3.18680i	0.171707	−	0.129030i
$611$	−12.1380	+	12.6370i	−0.491050	+	0.511237i
$612$	−1.23640	−	3.26011i	−0.0499783	−	0.131782i
$613$	6.37082	−	7.80284i	0.257315	−	0.315154i	−0.629750	−	0.776798i	$-0.716843\pi$
$613$	6.37082	−	7.80284i	0.257315	−	0.315154i	0.887065	+	0.461644i	$0.152740\pi$
$614$	5.12738	+	2.69105i	0.206924	+	0.108602i
$615$	−2.55753	−	4.42978i	−0.103130	−	0.178626i
$616$	−2.01939	+	3.49768i	−0.0813634	+	0.140926i
$617$	−27.8136	+	17.5883i	−1.11973	+	0.708077i	−0.960255	−	0.279124i	$-0.909956\pi$
$617$	−27.8136	+	17.5883i	−1.11973	+	0.708077i	−0.159479	+	0.987201i	$0.550982\pi$
$618$	0.0171081	−	0.0590641i	0.000688190	−	0.00237591i
$619$	9.12301	−	1.48263i	0.366685	−	0.0595921i	0.0257226	−	0.999669i	$-0.491811\pi$
$619$	9.12301	−	1.48263i	0.366685	−	0.0595921i	0.340962	+	0.940077i	$0.389247\pi$
$620$	−0.426208	+	3.51014i	−0.0171169	+	0.140970i
$621$	−4.06378	−	5.88740i	−0.163074	−	0.236253i
$622$	7.58651	−	4.79742i	0.304191	−	0.192359i
$623$	2.88844	−	3.00718i	0.115723	−	0.120480i
$624$	−2.54407	+	3.68572i	−0.101844	+	0.147547i
$625$	−5.01017	+	0.404462i	−0.200407	+	0.0161785i
$626$	5.27369	−	2.76785i	0.210779	−	0.110625i
$627$	−12.7736			−0.510128
$628$	−20.8975	+	9.31083i	−0.833903	+	0.371542i
$629$	13.9014			0.554285
$630$	0.331426	−	0.173946i	0.0132043	−	0.00693017i
$631$	24.6888	−	1.99309i	0.982846	−	0.0793435i	0.421416	−	0.906868i	$-0.361533\pi$
$631$	24.6888	−	1.99309i	0.982846	−	0.0793435i	0.561430	+	0.827524i	$0.310251\pi$
$632$	−15.0198	+	21.7599i	−0.597455	+	0.865563i
$633$	3.10388	−	3.23148i	0.123368	−	0.128440i
$634$	8.24826	−	5.21589i	0.327580	−	0.207149i
$635$	11.9119	+	17.2574i	0.472711	+	0.684839i
$636$	2.20212	−	18.1361i	0.0873199	−	0.719144i
$637$	9.55818	−	1.55336i	0.378709	−	0.0615462i
$638$	−4.17718	+	14.4213i	−0.165376	+	0.570944i
$639$	2.29861	−	1.45356i	0.0909318	−	0.0575018i
$640$	−6.43913	+	11.1529i	−0.254529	+	0.440857i
$641$	−13.3724	−	23.1617i	−0.528178	−	0.914832i	−0.999460	−	0.0328493i	$-0.989542\pi$
$641$	−13.3724	−	23.1617i	−0.528178	−	0.914832i	0.471282	−	0.881983i	$-0.343791\pi$
$642$	−0.117810	−	0.0618315i	−0.00464959	−	0.00244029i
$643$	−9.67626	+	11.8513i	−0.381594	+	0.467368i	−0.929312	−	0.369295i	$-0.879599\pi$
$643$	−9.67626	+	11.8513i	−0.381594	+	0.467368i	0.547718	+	0.836663i	$0.315497\pi$
$644$	3.41836	+	9.01348i	0.134702	+	0.355181i
$645$	−2.67201	+	2.78186i	−0.105210	+	0.109535i
$646$	2.37415	−	1.78406i	0.0934098	−	0.0701929i
$647$	7.61075	+	5.71911i	0.299210	+	0.224841i	0.739734	−	0.672899i	$-0.234951\pi$
$647$	7.61075	+	5.71911i	0.299210	+	0.224841i	−0.440525	+	0.897740i	$0.645208\pi$
$648$	−0.319351	−	1.56429i	−0.0125453	−	0.0614509i
$649$	−8.52776	−	10.4446i	−0.334744	−	0.409987i
$650$	1.10269	−	1.90992i	0.0432512	−	0.0749133i
$651$	0.417027	+	1.09961i	0.0163446	+	0.0430971i
$652$	1.57823	−	39.1633i	0.0618081	−	1.53375i
$653$	1.21809	+	30.2266i	0.0476676	+	1.18286i	0.829185	+	0.558975i	$0.188805\pi$
$653$	1.21809	+	30.2266i	0.0476676	+	1.18286i	−0.781517	+	0.623884i	$0.785554\pi$
$654$	−2.64268	−	1.67113i	−0.103337	−	0.0653464i
$655$	−12.8566	+	3.16886i	−0.502347	+	0.123818i
$656$	12.5653			0.490591
$657$	14.1849	−	3.49626i	0.553405	−	0.136402i
$658$	−0.719584	+	3.52475i	−0.0280523	+	0.137409i
$659$	17.1089	+	5.71180i	0.666469	+	0.222500i	0.629717	−	0.776824i	$-0.283171\pi$
$659$	17.1089	+	5.71180i	0.666469	+	0.222500i	0.0367519	+	0.999324i	$0.488299\pi$
$660$	−5.69309	−	5.04363i	−0.221603	−	0.196323i
$661$	36.0132	−	27.0622i	1.40075	−	1.05260i	0.410719	−	0.911762i	$-0.365278\pi$
$661$	36.0132	−	27.0622i	1.40075	−	1.05260i	0.990033	−	0.140835i	$-0.0449786\pi$
$662$	−0.391786	+	1.35260i	−0.0152272	+	0.0525703i
$663$	2.82751	+	0.459515i	0.109811	+	0.0178461i
$664$	−3.11311	+	6.56073i	−0.120812	+	0.254606i
$665$	−2.31551	−	2.41071i	−0.0897918	−	0.0934832i
$666$	2.99851	+	0.487306i	0.116190	+	0.0188827i
$667$	42.6562	+	61.7982i	1.65166	+	2.39284i
$668$	−4.58234	−	5.61235i	−0.177296	−	0.217148i
$669$	−2.27193	+	5.99059i	−0.0878380	+	0.231610i
$670$	−5.59510	−	2.38385i	−0.216157	−	0.0920961i
$671$	−35.7357	−	2.88489i	−1.37956	−	0.111370i
$672$	−0.131915	+	3.27343i	−0.00508872	+	0.126275i
$673$	21.2889	−	30.8423i	0.820626	−	1.18888i	−0.158846	−	0.987303i	$-0.550777\pi$
$673$	21.2889	−	30.8423i	0.820626	−	1.18888i	0.979472	−	0.201579i	$-0.0646073\pi$
$674$	2.43874	+	2.16053i	0.0939367	+	0.0832206i
$675$	−0.980159	−	3.38390i	−0.0377263	−	0.130246i
$676$	8.41413	+	17.7324i	0.323621	+	0.682016i
$677$	−0.643437	+	1.69660i	−0.0247293	+	0.0652058i	−0.946812	−	0.321786i	$-0.895717\pi$
$677$	−0.643437	+	1.69660i	−0.0247293	+	0.0652058i	0.922083	+	0.386992i	$0.126486\pi$
$678$	−1.63196	−	2.82665i	−0.0626752	−	0.108557i
$679$	−5.83574	+	7.14749i	−0.223955	+	0.274295i
$680$	3.69325	+	0.298150i	0.141630	+	0.0114335i
$681$	7.90600	−	3.36843i	0.302959	−	0.129079i
$682$	−1.70604	+	1.51142i	−0.0653276	+	0.0578752i
$683$	−0.208250	+	1.02008i	−0.00796847	+	0.0390321i	−0.983581	−	0.180470i	$-0.942238\pi$
$683$	−0.208250	+	1.02008i	−0.00796847	+	0.0390321i	0.975612	+	0.219502i	$0.0704433\pi$
$684$	−6.02497	+	3.16215i	−0.230370	+	0.120908i
$685$	−2.93878	−	1.85837i	−0.112285	−	0.0710048i
$686$	3.10185	−	2.74800i	0.118429	−	0.104919i
$687$	−2.23506	−	18.4074i	−0.0852729	−	0.702286i
$688$	−2.63622	−	9.10130i	−0.100505	−	0.346984i
$689$	11.9995	+	9.01702i	0.457144	+	0.343521i
$690$	3.58110	−	0.581985i	0.136330	−	0.0221558i
$691$	17.2765	+	17.9867i	0.657229	+	0.684248i	0.963504	−	0.267695i	$-0.0862621\pi$
$691$	17.2765	+	17.9867i	0.657229	+	0.684248i	−0.306275	+	0.951943i	$0.599083\pi$
$692$	−23.1123	−	5.69668i	−0.878600	−	0.216555i
$693$	−2.45618	−	0.605394i	−0.0933025	−	0.0229970i
$694$	−3.30843	+	6.97237i	−0.125586	+	0.264668i
$695$	−1.03901	+	8.55703i	−0.0394119	+	0.324587i
$696$	3.35213	+	16.4198i	0.127062	+	0.622392i
$697$	−3.44550	−	7.26123i	−0.130508	−	0.275039i
$698$	−3.90367	+	1.30324i	−0.147756	+	0.0493282i
$699$	2.72095	−	1.15929i	0.102916	−	0.0438482i
$700$	0.191157	+	4.74352i	0.00722507	+	0.179288i
$701$	21.6937	−	1.75130i	0.819360	−	0.0661456i	0.336325	−	0.941746i	$-0.390816\pi$
$701$	21.6937	−	1.75130i	0.819360	−	0.0661456i	0.483036	+	0.875601i	$0.339534\pi$
$702$	0.593782	+	0.198233i	0.0224108	+	0.00748184i
$703$	−3.27004	−	26.9312i	−0.123332	−	1.01573i
$704$	13.3902	−	4.47032i	0.504663	−	0.168481i
$705$	−13.0598	−	5.56425i	−0.491860	−	0.209562i
$706$	4.81782	+	2.52859i	0.181321	+	0.0951646i
$707$	−2.74150	−	1.43885i	−0.103105	−	0.0541135i
$708$	−6.60792	−	2.81537i	−0.248341	−	0.105808i
$709$	−45.7704	+	15.2804i	−1.71894	+	0.573868i	−0.993441	−	0.114350i	$-0.963521\pi$
$709$	−45.7704	+	15.2804i	−1.71894	+	0.573868i	−0.725504	+	0.688218i	$0.758393\pi$
$710$	0.166256	+	1.36924i	0.00623946	+	0.0513866i
$711$	−15.7086	−	5.24430i	−0.589118	−	0.196677i
$712$	8.99083	−	0.725815i	0.336946	−	0.0272011i
$713$	0.459002	+	11.3900i	0.0171898	+	0.426559i
$714$	0.541069	−	0.230528i	0.0202490	−	0.00862730i
$715$	5.92729	−	1.97882i	0.221668	−	0.0740036i
$716$	11.8016	+	24.8712i	0.441045	+	0.929482i
$717$	0.162700	+	0.796956i	0.00607613	+	0.0297629i
$718$	−0.228749	+	1.88392i	−0.00853683	+	0.0703071i
$719$	−5.28439	+	11.1366i	−0.197074	+	0.415326i	−0.977798	−	0.209551i	$-0.932800\pi$
$719$	−5.28439	+	11.1366i	−0.197074	+	0.415326i	0.780723	+	0.624877i	$0.214851\pi$
$720$	−3.52286	−	0.868308i	−0.131289	−	0.0323599i
$721$	−0.105592	−	0.0260262i	−0.00393246	−	0.000969264i
$722$	1.47774	+	1.53849i	0.0549957	+	0.0572566i
$723$	23.4623	−	3.81300i	0.872573	−	0.141807i
$724$	−17.6780	−	13.2842i	−0.656999	−	0.493703i
$725$	10.2884	+	35.5198i	0.382102	+	1.31917i
$726$	−0.0376524	−	0.310095i	−0.00139741	−	0.0115087i
$727$	−31.6903	+	28.0752i	−1.17533	+	1.04125i	−0.176956	+	0.984219i	$0.556625\pi$
$727$	−31.6903	+	28.0752i	−1.17533	+	1.04125i	−0.998372	+	0.0570309i	$0.981837\pi$
$728$	−1.49393	−	0.944705i	−0.0553688	−	0.0350131i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−1.48205	+	7.25957i	−0.0548532	+	0.268689i
$731$	−4.53660	+	4.01908i	−0.167792	+	0.148651i
$732$	−17.5698	+	7.48577i	−0.649397	+	0.276682i
$733$	27.6883	+	2.23523i	1.02269	+	0.0825601i	0.580416	−	0.814320i	$-0.302890\pi$
$733$	27.6883	+	2.23523i	1.02269	+	0.0825601i	0.442274	+	0.896880i	$0.354172\pi$
$734$	9.86361	−	12.0807i	0.364072	−	0.445908i
$735$	3.92264	+	6.79421i	0.144689	+	0.250608i
$736$	−11.2605	+	29.6915i	−0.415067	+	1.09444i
$737$	17.6207	+	37.1348i	0.649066	+	1.36788i
$738$	−0.488651	−	1.68702i	−0.0179875	−	0.0621000i
$739$	0.533584	+	0.472714i	0.0196282	+	0.0173891i	0.672880	−	0.739752i	$-0.265057\pi$
$739$	0.533584	+	0.472714i	0.0196282	+	0.0173891i	−0.653252	+	0.757141i	$0.726596\pi$
$740$	9.17630	−	13.2942i	0.337328	−	0.488704i
$741$	0.225101	−	5.58583i	0.00826930	−	0.205201i
$742$	3.07167	+	0.247971i	0.112765	+	0.00910329i
$743$	40.6012	+	17.2985i	1.48951	+	0.634622i	0.974868	−	0.222782i	$-0.0715137\pi$
$743$	40.6012	+	17.2985i	1.48951	+	0.634622i	0.514644	+	0.857404i	$0.327924\pi$
$744$	−0.902136	+	2.37874i	−0.0330739	+	0.0872087i
$745$	−13.0393	−	15.9702i	−0.477723	−	0.585104i
$746$	4.19440	+	6.07663i	0.153568	+	0.222481i
$747$	−4.48957	−	0.729626i	−0.164265	−	0.0266956i
$748$	−8.27876	−	8.61910i	−0.302701	−	0.315145i
$749$	−0.100875	+	0.212589i	−0.00368588	+	0.00776783i
$750$	4.26655	+	0.693381i	0.155792	+	0.0253187i
$751$	1.89780	−	6.55195i	0.0692515	−	0.239084i	−0.918424	−	0.395596i	$-0.870538\pi$
$751$	1.89780	−	6.55195i	0.0692515	−	0.239084i	0.987676	+	0.156512i	$0.0500251\pi$
$752$	27.8783	−	20.9492i	1.01662	−	0.763937i
$753$	−16.8340	−	14.9136i	−0.613465	−	0.543482i
$754$	−6.23274	−	2.08080i	−0.226983	−	0.0757781i
$755$	−0.476478	+	2.33394i	−0.0173408	+	0.0849408i
$756$	−1.30838	+	0.322487i	−0.0475854	+	0.0117287i
$757$	20.0695			0.729437			0.364718	−	0.931118i	$-0.381165\pi$
$757$	20.0695			0.729437			0.364718	+	0.931118i	$0.381165\pi$
$758$	−1.07035	+	0.263818i	−0.0388769	+	0.00958231i
$759$	−20.7242	−	13.1052i	−0.752242	−	0.475689i
$760$	−0.291161	−	7.22508i	−0.0105615	−	0.262081i
$761$	0.285559	−	7.08608i	0.0103515	−	0.256870i	−0.985724	−	0.168367i	$-0.946151\pi$
$761$	0.285559	−	7.08608i	0.0103515	−	0.256870i	0.996076	−	0.0885033i	$-0.0282084\pi$
$762$	2.55324	+	6.73235i	0.0924942	+	0.243887i
$763$	−2.76491	+	4.78897i	−0.100097	+	0.173372i
$764$	27.6205	+	33.8290i	0.999275	+	1.22389i
$765$	0.464219	+	2.27389i	0.0167839	+	0.0822128i
$766$	10.8579	+	8.15915i	0.392310	+	0.294802i
$767$	4.71765	−	3.54509i	0.170345	−	0.128006i
$768$	2.64277	−	2.75142i	0.0953628	−	0.0992832i
$769$	−14.0335	−	37.0032i	−0.506060	−	1.33437i	−0.908102	−	0.418750i	$-0.862469\pi$
$769$	−14.0335	−	37.0032i	−0.506060	−	1.33437i	0.402042	−	0.915621i	$-0.368301\pi$
$770$	0.811400	−	0.993785i	0.0292408	−	0.0358135i
$771$	13.1105	+	6.88091i	0.472162	+	0.247810i
$772$	5.26716	+	9.12298i	0.189569	+	0.328343i
$773$	9.72854	−	16.8503i	0.349911	−	0.606064i	−0.636322	−	0.771424i	$-0.719545\pi$
$773$	9.72854	−	16.8503i	0.349911	−	0.606064i	0.986233	+	0.165359i	$0.0528784\pi$
$774$	−1.11942	+	0.707881i	−0.0402369	+	0.0254443i
$775$	−1.56186	+	5.39215i	−0.0561035	+	0.193692i
$776$	−19.7025	+	3.20196i	−0.707277	+	0.114944i
$777$	0.647599	−	5.33346i	0.0232325	−	0.191337i
$778$	1.62484	+	2.35398i	0.0582532	+	0.0843943i
$779$	−13.2567	+	8.38304i	−0.474971	+	0.300353i
$780$	2.30588	−	2.40068i	0.0825638	−	0.0859580i
$781$	5.29544	−	7.67176i	0.189486	−	0.274517i
$782$	5.68227	−	0.458720i	0.203197	−	0.0164038i
$783$	−9.29436	+	4.87806i	−0.332153	+	0.174327i
$784$	−19.2721			−0.688289
$785$	14.7238	−	3.88591i	0.525514	−	0.138694i
$786$	−4.54668			−0.162175
$787$	−38.8262	+	20.3776i	−1.38400	+	0.726381i	−0.981933	−	0.189227i	$-0.939402\pi$
$787$	−38.8262	+	20.3776i	−1.38400	+	0.726381i	−0.402071	+	0.915609i	$0.631709\pi$
$788$	−9.63774	+	0.778039i	−0.343330	+	0.0277165i
$789$	10.1574	−	14.7155i	0.361613	−	0.523886i
$790$	5.81820	−	6.05739i	0.207002	−	0.215512i
$791$	−4.87883	+	3.08519i	−0.173471	+	0.109697i
$792$	−3.10866	−	4.50367i	−0.110461	−	0.160031i
$793$	1.89129	−	15.5762i	0.0671618	−	0.553127i
$794$	13.2379	−	2.15136i	0.469794	−	0.0763490i
$795$	−3.38323	+	11.6803i	−0.119991	+	0.414256i
$796$	−4.77145	+	3.01728i	−0.169119	+	0.106945i
$797$	5.05416	−	8.75406i	0.179028	−	0.310085i	−0.762520	−	0.646964i	$-0.776038\pi$
$797$	5.05416	−	8.75406i	0.179028	−	0.310085i	0.941548	+	0.336880i	$0.109372\pi$
$798$	−0.573879	−	0.993987i	−0.0203151	−	0.0351868i
$799$	−19.7506	−	10.3659i	−0.698725	−	0.366719i
$800$	−9.89043	+	12.1136i	−0.349680	+	0.428280i
$801$	2.00342	+	5.28259i	0.0707875	+	0.186651i
$802$	8.79788	−	9.15956i	0.310664	−	0.323435i
$803$	40.0324	−	30.0824i	1.41271	−	1.06159i
$804$	17.5040	+	13.1534i	0.617320	+	0.463886i
$805$	−1.28346	−	6.28682i	−0.0452362	−	0.221581i
$806$	−0.630871	−	0.772676i	−0.0222215	−	0.0272164i
$807$	2.84035	−	4.91963i	0.0999851	−	0.173179i
$808$	−2.37505	−	6.26250i	−0.0835541	−	0.220314i
$809$	−0.207166	+	5.14078i	−0.00728358	+	0.180740i	0.991452	+	0.130471i	$0.0416489\pi$
$809$	−0.207166	+	5.14078i	−0.00728358	+	0.180740i	−0.998736	+	0.0502691i	$0.983992\pi$
$810$	0.0204213	+	0.506749i	0.000717531	+	0.0178053i
$811$	−26.5364	−	16.7806i	−0.931820	−	0.589248i	−0.0199836	−	0.999800i	$-0.506361\pi$
$811$	−26.5364	−	16.7806i	−0.931820	−	0.589248i	−0.911837	+	0.410553i	$0.865336\pi$
$812$	13.7337	−	3.38505i	0.481958	−	0.118792i
$813$	−12.3647			−0.433648
$814$	10.1100	−	2.49189i	0.354356	−	0.0873409i
$815$	−5.21845	+	25.5617i	−0.182794	+	0.895386i
$816$	−5.40769	−	1.80535i	−0.189307	−	0.0632000i
$817$	8.85331	+	7.84335i	0.309738	+	0.274404i
$818$	10.7484	−	8.07686i	0.375807	−	0.282401i
$819$	0.308019	−	1.06341i	0.0107631	−	0.0371584i
$820$	−9.21843	−	1.49814i	−0.321922	−	0.0523173i
$821$	−5.75772	+	12.1341i	−0.200946	+	0.423485i	−0.978760	−	0.205010i	$-0.934277\pi$
$821$	−5.75772	+	12.1341i	−0.200946	+	0.423485i	0.777814	+	0.628495i	$0.216329\pi$
$822$	−0.827059	−	0.861059i	−0.0288470	−	0.0300329i
$823$	4.09358	+	0.665271i	0.142693	+	0.0231899i	0.231338	−	0.972873i	$-0.425690\pi$
$823$	4.09358	+	0.665271i	0.142693	+	0.0231899i	−0.0886451	+	0.996063i	$0.528254\pi$
$824$	−0.133642	−	0.193615i	−0.00465566	−	0.00674488i
$825$	−7.63708	−	9.35372i	−0.265889	−	0.325655i
$826$	0.429629	−	1.13284i	0.0149487	−	0.0394165i
$827$	−35.8252	−	15.2637i	−1.24576	−	0.530770i	−0.334422	−	0.942423i	$-0.608541\pi$
$827$	−35.8252	−	15.2637i	−1.24576	−	0.530770i	−0.911340	+	0.411653i	$0.864951\pi$
$828$	−13.0193	−	1.05103i	−0.452452	−	0.0365257i
$829$	−1.47234	+	36.5359i	−0.0511366	+	1.26894i	0.746329	+	0.665578i	$0.231815\pi$
$829$	−1.47234	+	36.5359i	−0.0511366	+	1.26894i	−0.797465	+	0.603365i	$0.793826\pi$
$830$	1.31041	−	1.89846i	0.0454851	−	0.0658965i
$831$	9.95279	+	8.81740i	0.345258	+	0.305872i
$832$	1.71888	+	5.93426i	0.0595914	+	0.205733i
$833$	5.28456	+	11.1370i	0.183099	+	0.385873i
$834$	−1.04956	+	2.76747i	−0.0363434	+	0.0958297i
$835$	2.41134	+	4.17657i	0.0834479	+	0.144536i
$836$	−14.7504	+	18.0659i	−0.510152	+	0.624823i
$837$	−1.58831	−	0.128221i	−0.0548999	−	0.00443198i
$838$	−7.78182	+	3.31552i	−0.268818	+	0.114533i
$839$	7.07733	−	6.26997i	0.244337	−	0.216463i	−0.532062	−	0.846705i	$-0.678583\pi$
$839$	7.07733	−	6.26997i	0.244337	−	0.216463i	0.776399	+	0.630242i	$0.217044\pi$
$840$	0.286440	−	1.40308i	0.00988313	−	0.0484108i
$841$	71.8818	−	37.7265i	2.47868	−	1.30091i
$842$	7.07829	+	4.47604i	0.243934	+	0.154254i
$843$	−5.82775	+	5.16293i	−0.200718	+	0.177821i
$844$	−0.986122	−	8.12144i	−0.0339437	−	0.279552i
$845$	−3.63473	−	12.5485i	−0.125039	−	0.431683i
$846$	−3.89680	−	2.92826i	−0.133975	−	0.100675i
$847$	−0.545297	+	0.0886194i	−0.0187366	+	0.00304500i
$848$	−20.6932	−	21.5439i	−0.710608	−	0.739822i
$849$	−17.5341	−	4.32177i	−0.601769	−	0.148323i
$850$	2.72587	+	0.671867i	0.0934966	+	0.0230448i
$851$	22.3250	−	47.0488i	0.765289	−	1.61281i
$852$	0.598546	−	4.92947i	0.0205058	−	0.168881i
$853$	−4.39244	−	21.5156i	−0.150394	−	0.736680i	−0.983115	−	0.182987i	$-0.941423\pi$
$853$	−4.39244	−	21.5156i	−0.150394	−	0.736680i	0.832721	−	0.553693i	$-0.186782\pi$
$854$	−1.38101	−	2.91041i	−0.0472571	−	0.0995922i
$855$	4.29602	−	1.43422i	0.146921	−	0.0490494i
$856$	−0.468298	+	0.199523i	−0.0160061	+	0.00681956i
$857$	1.08144	+	26.8358i	0.0369415	+	0.916693i	0.906332	+	0.422567i	$0.138871\pi$
$857$	1.08144	+	26.8358i	0.0369415	+	0.916693i	−0.869390	+	0.494126i	$0.835488\pi$
$858$	2.13872	−	0.172655i	0.0730148	−	0.00589436i
$859$	−2.49762	−	0.833827i	−0.0852176	−	0.0284498i	0.273740	−	0.961804i	$-0.411739\pi$
$859$	−2.49762	−	0.833827i	−0.0852176	−	0.0284498i	−0.358957	+	0.933354i	$0.616868\pi$
$860$	0.848913	+	6.99143i	0.0289477	+	0.238406i
$861$	−2.94638	+	0.983647i	−0.100412	+	0.0335226i
$862$	−6.13313	−	2.61308i	−0.208895	−	0.0890020i
$863$	32.4802	+	17.0469i	1.10564	+	0.580284i	0.915842	−	0.401539i	$-0.131525\pi$
$863$	32.4802	+	17.0469i	1.10564	+	0.580284i	0.189797	+	0.981823i	$0.439217\pi$
$864$	−3.93050	−	2.06288i	−0.133718	−	0.0701807i
$865$	14.5765	+	6.21047i	0.495616	+	0.211162i
$866$	−8.36826	+	2.79374i	−0.284365	+	0.0949350i
$867$	−1.60957	−	13.2560i	−0.0546639	−	0.450198i
$868$	2.03676	+	0.679971i	0.0691322	+	0.0230797i
$869$	−56.5802	+	4.56763i	−1.91935	+	0.154946i
$870$	−0.214356	−	5.31919i	−0.00726734	−	0.180337i
$871$	−16.5494	+	7.05102i	−0.560754	+	0.238915i
$872$	−11.3468	+	3.78812i	−0.384251	+	0.128282i
$873$	−5.35975	−	11.2954i	−0.181400	−	0.382292i
$874$	−2.22532	−	10.9004i	−0.0752727	−	0.368710i
$875$	0.921462	−	7.58892i	0.0311511	−	0.256552i
$876$	11.4352	−	24.0992i	0.386361	−	0.814238i
$877$	−1.74385	−	0.429819i	−0.0588855	−	0.0145140i	0.209763	−	0.977752i	$-0.432731\pi$
$877$	−1.74385	−	0.429819i	−0.0588855	−	0.0145140i	−0.268648	+	0.963238i	$0.586577\pi$
$878$	−6.58449	−	1.62293i	−0.222216	−	0.0547712i
$879$	−2.25218	−	2.34477i	−0.0759641	−	0.0790870i
$880$	−12.2754	+	1.99494i	−0.413802	+	0.0672494i
$881$	−25.2144	−	18.9474i	−0.849496	−	0.638355i	0.0841893	−	0.996450i	$-0.473170\pi$
$881$	−25.2144	−	18.9474i	−0.849496	−	0.638355i	−0.933685	+	0.358095i	$0.883426\pi$
$882$	0.749472	+	2.58748i	0.0252360	+	0.0871249i
$883$	1.91371	+	15.7608i	0.0644013	+	0.530393i	0.988831	+	0.149040i	$0.0476184\pi$
$883$	1.91371	+	15.7608i	0.0644013	+	0.530393i	−0.924430	+	0.381352i	$0.875458\pi$
$884$	3.91498	−	3.46837i	0.131675	−	0.116654i
$885$	4.04078	+	2.55524i	0.135829	+	0.0858933i
$886$	2.88769	−	1.51558i	0.0970139	−	0.0509168i
$887$	9.20791	−	45.1033i	0.309171	−	1.51442i	−0.467203	−	0.884150i	$-0.654738\pi$
$887$	9.20791	−	45.1033i	0.309171	−	1.51442i	0.776374	−	0.630272i	$-0.217057\pi$
$888$	8.69948	−	7.70706i	0.291935	−	0.258632i
$889$	11.7151	−	4.99134i	0.392912	−	0.167404i
$890$	−2.85603	−	0.230562i	−0.0957343	−	0.00772847i
$891$	2.16778	−	2.65505i	0.0726233	−	0.0889475i
$892$	5.84908	+	10.1309i	0.195842	+	0.339208i
$893$	−15.4359	+	40.7012i	−0.516544	+	1.36201i
$894$	−3.03487	−	6.39585i	−0.101501	−	0.213909i
$895$	−5.09803	−	17.6004i	−0.170408	−	0.588317i
$896$	5.85381	+	5.18603i	0.195562	+	0.173253i
$897$	6.09605	−	8.83166i	0.203541	−	0.294880i
$898$	−0.296840	+	7.36601i	−0.00990568	+	0.245807i
$899$	16.6720	+	1.34590i	0.556041	+	0.0448882i
$900$	−5.91775	−	2.52132i	−0.197258	−	0.0840439i
$901$	−6.77559	+	17.8657i	−0.225727	+	0.595194i
$902$	−3.80741	−	4.66323i	−0.126773	−	0.155268i
$903$	1.33064	+	1.92776i	0.0442808	+	0.0641518i
$904$	−12.3256	−	2.00311i	−0.409944	−	0.0666224i
$905$	10.1960	+	10.6152i	0.338928	+	0.352861i
$906$	−0.350643	+	0.738965i	−0.0116493	+	0.0245505i
$907$	−3.92865	−	0.638468i	−0.130449	−	0.0212000i	0.0948363	−	0.995493i	$-0.469767\pi$
$907$	−3.92865	−	0.638468i	−0.130449	−	0.0212000i	−0.225285	+	0.974293i	$0.572331\pi$
$908$	4.36546	−	15.0713i	0.144873	−	0.500159i
$909$	3.35377	−	2.52020i	0.111238	−	0.0835896i
$910$	0.420278	+	0.372334i	0.0139321	+	0.0123427i
$911$	−21.0106	−	7.01437i	−0.696112	−	0.232396i	−0.0534774	−	0.998569i	$-0.517031\pi$
$911$	−21.0106	−	7.01437i	−0.696112	−	0.232396i	−0.642635	+	0.766173i	$0.722159\pi$
$912$	−2.22545	+	10.9010i	−0.0736922	+	0.360968i
$913$	−15.1374	+	3.73103i	−0.500974	+	0.123479i
$914$	12.3982			0.410096
$915$	12.3426	−	3.04217i	0.408032	−	0.100571i
$916$	−28.6148	−	18.0949i	−0.945461	−	0.597873i
$917$	0.323782	+	8.03458i	0.0106922	+	0.265325i
$918$	−0.0320876	+	0.796247i	−0.00105905	+	0.0262801i
$919$	6.21416	+	16.3854i	0.204986	+	0.540504i	0.997602	−	0.0692177i	$-0.0220503\pi$
$919$	6.21416	+	16.3854i	0.204986	+	0.540504i	−0.792615	+	0.609722i	$0.791281\pi$
$920$	6.94026	−	12.0209i	0.228814	−	0.396317i
$921$	8.77601	+	10.7487i	0.289179	+	0.354180i
$922$	−0.394738	−	1.93355i	−0.0130000	−	0.0636782i
$923$	3.26150	+	2.45086i	0.107354	+	0.0806711i
$924$	−3.69250	+	2.77474i	−0.121474	+	0.0912821i
$925$	17.7658	−	18.4962i	0.584136	−	0.608150i
$926$	1.09910	+	2.89809i	0.0361186	+	0.0952370i
$927$	0.0931938	−	0.114142i	0.00306089	−	0.00374890i
$928$	41.2572	+	21.6535i	1.35433	+	0.710809i
$929$	7.61318	+	13.1864i	0.249780	+	0.432632i	0.963465	−	0.267835i	$-0.0863082\pi$
$929$	7.61318	+	13.1864i	0.249780	+	0.432632i	−0.713684	+	0.700467i	$0.752975\pi$
$930$	0.404073	−	0.699875i	0.0132501	−	0.0229498i
$931$	20.3326	−	12.8576i	0.666374	−	0.421389i
$932$	1.50242	−	5.18697i	0.0492136	−	0.169905i
$933$	21.2311	−	3.45039i	0.695075	−	0.112961i
$934$	−0.246816	+	2.03271i	−0.00807607	+	0.0665124i
$935$	4.51884	+	6.54667i	0.147782	+	0.214099i
$936$	2.02421	−	1.28003i	0.0661634	−	0.0418392i
$937$	−14.3478	+	14.9377i	−0.468723	+	0.487992i	−0.913036	−	0.407880i	$-0.866268\pi$
$937$	−14.3478	+	14.9377i	−0.468723	+	0.487992i	0.444313	+	0.895872i	$0.353448\pi$
$938$	−2.09803	+	3.03952i	−0.0685030	+	0.0992438i
$939$	14.2260	−	1.14844i	0.464249	−	0.0374780i
$940$	−22.9505	+	12.0453i	−0.748561	+	0.392875i
$941$	−36.8610			−1.20163			−0.600817	−	0.799386i	$-0.705158\pi$
$941$	−36.8610			−1.20163			−0.600817	+	0.799386i	$0.705158\pi$
$942$	5.22812	−	0.0856225i	0.170341	−	0.00278973i
$943$	−30.1087			−0.980475
$944$	−10.3992	+	5.45791i	−0.338464	+	0.177640i
$945$	0.894037	−	0.0721741i	0.0290830	−	0.00234782i
$946$	−2.57888	+	3.73615i	−0.0838465	+	0.121473i
$947$	28.4596	−	29.6296i	0.924814	−	0.962833i	−0.0745949	−	0.997214i	$-0.523766\pi$
$947$	28.4596	−	29.6296i	0.924814	−	0.962833i	0.999409	+	0.0343806i	$0.0109458\pi$
$948$	−25.5567	+	16.1611i	−0.830042	+	0.524887i
$949$	12.4494	+	18.0361i	0.404125	+	0.585476i
$950$	0.660399	−	5.43888i	0.0214262	−	0.176460i
$951$	23.0831	−	3.75136i	0.748519	−	0.121646i
$952$	0.626020	−	2.16127i	0.0202894	−	0.0700472i
$953$	6.74445	−	4.26493i	0.218474	−	0.138155i	−0.420746	−	0.907179i	$-0.638232\pi$
$953$	6.74445	−	4.26493i	0.218474	−	0.138155i	0.639220	+	0.769024i	$0.279257\pi$
$954$	−2.08776	+	3.61610i	−0.0675937	+	0.117076i
$955$	−14.5346	−	25.1747i	−0.470328	−	0.814633i
$956$	1.31503	+	0.690179i	0.0425310	+	0.0223220i
$957$	−22.7545	+	27.8692i	−0.735549	+	0.900884i
$958$	3.08913	+	8.14537i	0.0998053	+	0.263165i
$959$	−1.46271	+	1.52284i	−0.0472332	+	0.0491750i
$960$	−4.00148	+	3.00692i	−0.129147	+	0.0970478i
$961$	−22.7528	−	17.0976i	−0.733962	−	0.551537i
$962$	0.911530	+	4.46497i	0.0293889	+	0.143956i
$963$	−0.201644	−	0.246969i	−0.00649787	−	0.00795845i
$964$	21.7004	−	37.5862i	0.698923	−	1.21057i
$965$	−2.48642	−	6.55616i	−0.0800408	−	0.211050i
$966$	0.0887154	−	2.20145i	0.00285437	−	0.0708305i
$967$	1.53147	+	38.0031i	0.0492488	+	1.22210i	0.815193	+	0.579189i	$0.196631\pi$
$967$	1.53147	+	38.0031i	0.0492488	+	1.22210i	−0.765944	+	0.642907i	$0.777728\pi$
$968$	−1.01008	−	0.638737i	−0.0324652	−	0.0205298i
$969$	6.90972	−	1.70309i	0.221972	−	0.0547112i
$970$	6.34079			0.203590
$971$	−19.6697	+	4.84814i	−0.631230	+	0.155584i	−0.541934	−	0.840421i	$-0.682308\pi$
$971$	−19.6697	+	4.84814i	−0.631230	+	0.155584i	−0.0892960	+	0.996005i	$0.528462\pi$
$972$	0.365218	−	1.78896i	0.0117144	−	0.0573808i
$973$	4.96522	+	1.65764i	0.159178	+	0.0531414i
$974$	−3.90840	−	3.46254i	−0.125233	−	0.110947i
$975$	4.22492	−	3.17482i	0.135306	−	0.101676i
$976$	−8.68795	+	29.9943i	−0.278094	+	0.960093i
$977$	−27.6042	−	4.48612i	−0.883137	−	0.143524i	−0.298104	−	0.954533i	$-0.596354\pi$
$977$	−27.6042	−	4.48612i	−0.883137	−	0.143524i	−0.585033	+	0.811010i	$0.698918\pi$
$978$	−3.84030	+	8.09326i	−0.122799	+	0.258794i
$979$	13.4147	+	13.9662i	0.428735	+	0.446361i
$980$	14.1388	+	2.29779i	0.451649	+	0.0734001i
$981$	−4.25632	−	6.16635i	−0.135894	−	0.196876i
$982$	−5.58339	−	6.83841i	−0.178173	−	0.218223i
$983$	−5.55338	+	14.6431i	−0.177125	+	0.467041i	−0.993949	−	0.109847i	$-0.964964\pi$
$983$	−5.55338	+	14.6431i	−0.177125	+	0.467041i	0.816823	+	0.576888i	$0.195733\pi$
$984$	−6.18188	−	2.63385i	−0.197071	−	0.0839642i
$985$	6.41505	+	0.517876i	0.204400	+	0.0165009i
$986$	0.336814	−	8.35796i	0.0107263	−	0.266172i
$987$	−4.89710	+	7.09468i	−0.155877	+	0.225826i
$988$	−7.64020	−	6.76863i	−0.243067	−	0.215339i
$989$	6.31688	+	21.8084i	0.200865	+	0.693467i
$990$	0.745218	+	1.57051i	0.0236846	+	0.0499142i
$991$	−0.487363	+	1.28507i	−0.0154816	+	0.0408217i	−0.942534	−	0.334110i	$-0.891564\pi$
$991$	−0.487363	+	1.28507i	−0.0154816	+	0.0408217i	0.927053	+	0.374931i	$0.122334\pi$
$992$	3.53667	+	6.12570i	0.112289	+	0.194491i
$993$	−2.13419	+	2.61391i	−0.0677265	+	0.0829499i
$994$	0.834892	+	0.0673994i	0.0264812	+	0.00213778i
$995$	3.45699	−	1.47289i	0.109594	−	0.0466936i
$996$	−6.21627	+	5.50713i	−0.196970	+	0.174500i
$997$	−9.03355	+	44.2493i	−0.286095	+	1.40139i	0.541801	+	0.840507i	$0.317743\pi$
$997$	−9.03355	+	44.2493i	−0.286095	+	1.40139i	−0.827896	+	0.560881i	$0.810462\pi$
$998$	4.52201	−	2.37334i	0.143142	−	0.0751266i
$999$	6.15271	+	3.89074i	0.194663	+	0.123098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.37.6	✓	336
157.17	even	39	inner	471.2.q.b.331.6	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.37.6	✓	336	1.1	even	1	trivial
471.2.q.b.331.6	yes	336	157.17	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.369506 + 0.193932i) q^{2} +(-0.996757 + 0.0804666i) q^{3} +(-1.03720 + 1.50265i) q^{4} +(0.841882 - 0.876493i) q^{5} +(0.352702 - 0.223035i) q^{6} +(-0.419250 - 0.607388i) q^{7} +(0.192443 - 1.58491i) q^{8} +(0.987050 - 0.160411i) q^{9} +O(q^{10})\)	\(q+(-0.369506 + 0.193932i) q^{2} +(-0.996757 + 0.0804666i) q^{3} +(-1.03720 + 1.50265i) q^{4} +(0.841882 - 0.876493i) q^{5} +(0.352702 - 0.223035i) q^{6} +(-0.419250 - 0.607388i) q^{7} +(0.192443 - 1.58491i) q^{8} +(0.987050 - 0.160411i) q^{9} +(-0.141101 + 0.487136i) q^{10} +(2.89699 - 1.83194i) q^{11} +(0.912928 - 1.58124i) q^{12} +(0.750048 + 1.29912i) q^{13} +(0.272707 + 0.143128i) q^{14} +(-0.768624 + 0.941394i) q^{15} +(-1.05866 - 2.79146i) q^{16} +(-1.32284 + 1.37722i) q^{17} +(-0.333612 + 0.250693i) q^{18} +(2.97926 + 2.23877i) q^{19} +(0.443857 + 2.17416i) q^{20} +(0.466765 + 0.571683i) q^{21} +(-0.715181 + 1.23873i) q^{22} +(2.53675 + 6.68885i) q^{23} +(-0.0642866 + 1.59526i) q^{24} +(0.141857 + 3.52014i) q^{25} +(-0.529087 - 0.334574i) q^{26} +(-0.970942 + 0.239316i) q^{27} +1.34754 q^{28} +(10.1917 - 2.51202i) q^{29} +(0.101445 - 0.496911i) q^{30} +(1.51147 + 0.504602i) q^{31} +(3.32260 + 2.94357i) q^{32} +(-2.74018 + 2.05911i) q^{33} +(0.221710 - 0.765430i) q^{34} +(-0.885330 - 0.143880i) q^{35} +(-0.782731 + 1.64957i) q^{36} +(-5.04281 - 5.25012i) q^{37} +(-1.53502 - 0.249465i) q^{38} +(-0.852151 - 1.23455i) q^{39} +(-1.22715 - 1.50298i) q^{40} +(-1.49247 + 3.93531i) q^{41} +(-0.283339 - 0.120720i) q^{42} +(3.16356 + 0.255389i) q^{43} +(-0.251998 + 6.25326i) q^{44} +(0.690381 - 1.00019i) q^{45} +(-2.23452 - 1.97961i) q^{46} +(3.24976 + 11.2195i) q^{47} +(1.27985 + 2.69722i) q^{48} +(2.28908 - 6.03582i) q^{49} +(-0.735082 - 1.27320i) q^{50} +(1.20773 - 1.47920i) q^{51} +(-2.73008 - 0.220395i) q^{52} +(9.20522 - 3.92198i) q^{53} +(0.312358 - 0.276725i) q^{54} +(0.833238 - 4.08147i) q^{55} +(-1.04334 + 0.547585i) q^{56} +(-3.14975 - 1.99178i) q^{57} +(-3.27872 + 2.90469i) q^{58} +(-0.474176 - 3.90519i) q^{59} +(-0.617365 - 2.13139i) q^{60} +(-8.36197 - 6.28361i) q^{61} +(-0.656354 + 0.106668i) q^{62} +(-0.511252 - 0.532270i) q^{63} +(3.99885 + 0.985628i) q^{64} +(1.77012 + 0.436296i) q^{65} +(0.613186 - 1.29226i) q^{66} +(-1.44545 + 11.9044i) q^{67} +(-0.697426 - 3.41622i) q^{68} +(-3.06675 - 6.46303i) q^{69} +(0.355037 - 0.118529i) q^{70} +(2.50201 - 1.06601i) q^{71} +(-0.0642866 - 1.59526i) q^{72} +(14.5620 - 1.17557i) q^{73} +(2.88151 + 0.961990i) q^{74} +(-0.424650 - 3.49731i) q^{75} +(-6.45419 + 2.15473i) q^{76} +(-2.32726 - 0.991553i) q^{77} +(0.554294 + 0.290916i) q^{78} +(-14.6639 - 7.69622i) q^{79} +(-3.33796 - 1.42217i) q^{80} +(0.948536 - 0.316668i) q^{81} +(-0.211706 - 1.74356i) q^{82} +(-4.31439 - 1.44035i) q^{83} +(-1.34317 + 0.108432i) q^{84} +(0.0934490 + 2.31891i) q^{85} +(-1.21848 + 0.519146i) q^{86} +(-9.95649 + 3.32397i) q^{87} +(-2.34596 - 4.94401i) q^{88} +(1.13009 + 5.53555i) q^{89} +(-0.0611314 + 0.503462i) q^{90} +(0.474613 - 1.00023i) q^{91} +(-12.6821 - 3.12586i) q^{92} +(-1.54717 - 0.381343i) q^{93} +(-3.37661 - 3.51543i) q^{94} +(4.47045 - 0.726519i) q^{95} +(-3.54869 - 2.66667i) q^{96} +(-3.47843 - 12.0089i) q^{97} +(0.324706 + 2.67419i) q^{98} +(2.56561 - 2.27293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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