LMFDB - Embedded newform 73.2.g.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(2,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("73.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.g (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	73.16
Dual form			73.2.g.a.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.352058 + 1.99662i) q^{2} +(-0.860978 + 1.49126i) q^{3} +(-1.98316 - 0.721811i) q^{4} +(-0.0610770 - 0.346385i) q^{5} +(-2.67436 - 2.24405i) q^{6} +(0.956032 - 1.65590i) q^{7} +(0.111947 - 0.193897i) q^{8} +(0.0174332 + 0.0301951i) q^{9} +O(q^{10})$	\(q+(-0.352058 + 1.99662i) q^{2} +(-0.860978 + 1.49126i) q^{3} +(-1.98316 - 0.721811i) q^{4} +(-0.0610770 - 0.346385i) q^{5} +(-2.67436 - 2.24405i) q^{6} +(0.956032 - 1.65590i) q^{7} +(0.111947 - 0.193897i) q^{8} +(0.0174332 + 0.0301951i) q^{9} +0.713101 q^{10} +(-0.0281794 - 0.159813i) q^{11} +(2.78386 - 2.33594i) q^{12} +(2.13983 + 1.79553i) q^{13} +(2.96962 + 2.49180i) q^{14} +(0.569135 + 0.207148i) q^{15} +(-2.88564 - 2.42134i) q^{16} +(2.75830 + 4.77752i) q^{17} +(-0.0664257 + 0.0241770i) q^{18} +(1.22918 - 6.97101i) q^{19} +(-0.128899 + 0.731022i) q^{20} +(1.64625 + 2.85138i) q^{21} +0.329007 q^{22} +(-0.0372373 - 0.211183i) q^{23} +(0.192767 + 0.333883i) q^{24} +(4.58221 - 1.66779i) q^{25} +(-4.33834 + 3.64030i) q^{26} -5.22591 q^{27} +(-3.09121 + 2.59383i) q^{28} +(1.36239 - 7.72647i) q^{29} +(-0.613964 + 1.06342i) q^{30} +(-5.51116 + 2.00590i) q^{31} +(6.19344 - 5.19691i) q^{32} +(0.262585 + 0.0955731i) q^{33} +(-10.5100 + 3.82532i) q^{34} +(-0.631969 - 0.230018i) q^{35} +(-0.0127776 - 0.0724652i) q^{36} +(-1.27068 - 7.20636i) q^{37} +(13.4857 + 4.90840i) q^{38} +(-4.51995 + 1.64513i) q^{39} +(-0.0740005 - 0.0269340i) q^{40} +(-7.91913 + 6.64494i) q^{41} +(-6.27270 + 2.28308i) q^{42} +(-1.72634 + 2.99011i) q^{43} +(-0.0594708 + 0.337276i) q^{44} +(0.00939437 - 0.00788281i) q^{45} +0.434762 q^{46} +(5.31758 - 4.46198i) q^{47} +(6.09532 - 2.21852i) q^{48} +(1.67200 + 2.89600i) q^{49} +(1.71674 + 9.73609i) q^{50} -9.49935 q^{51} +(-2.94759 - 5.10538i) q^{52} +(0.0886539 - 0.502781i) q^{53} +(1.83982 - 10.4341i) q^{54} +(-0.0536358 + 0.0195218i) q^{55} +(-0.214049 - 0.370745i) q^{56} +(9.33728 + 7.83491i) q^{57} +(14.9472 + 5.44033i) q^{58} +(-3.20623 - 2.69035i) q^{59} +(-0.979163 - 0.821615i) q^{60} +(3.53117 - 2.96301i) q^{61} +(-2.06477 - 11.7099i) q^{62} +0.0666667 q^{63} +(4.42886 + 7.67101i) q^{64} +(0.491251 - 0.850871i) q^{65} +(-0.283268 + 0.490635i) q^{66} +(1.79431 + 1.50560i) q^{67} +(-2.02169 - 11.4655i) q^{68} +(0.346989 + 0.126294i) q^{69} +(0.681748 - 1.18082i) q^{70} +(-0.379215 + 2.15064i) q^{71} +0.00780635 q^{72} +(-8.24477 + 2.24138i) q^{73} +14.8357 q^{74} +(-1.45808 + 8.26919i) q^{75} +(-7.46940 + 12.9374i) q^{76} +(-0.291575 - 0.106125i) q^{77} +(-1.69341 - 9.60381i) q^{78} +(2.68141 + 2.24997i) q^{79} +(-0.662469 + 1.14743i) q^{80} +(4.44709 - 7.70259i) q^{81} +(-10.4794 - 18.1509i) q^{82} -3.66682 q^{83} +(-1.20661 - 6.84302i) q^{84} +(1.48639 - 1.24723i) q^{85} +(-5.36235 - 4.49954i) q^{86} +(10.3492 + 8.68400i) q^{87} +(-0.0341420 - 0.0124267i) q^{88} +(-11.9564 - 10.0326i) q^{89} +(0.0124316 + 0.0215322i) q^{90} +(5.01897 - 1.82676i) q^{91} +(-0.0785868 + 0.445688i) q^{92} +(1.75368 - 9.94560i) q^{93} +(7.03678 + 12.1881i) q^{94} -2.48973 q^{95} +(2.41752 + 13.7104i) q^{96} +(5.50716 + 9.53867i) q^{97} +(-6.37084 + 2.31880i) q^{98} +(0.00433433 - 0.00363694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{4} - 12 q^{5} + 3 q^{6} + 3 q^{7} + 15 q^{8} - 9 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 + 3 * q^6 + 3 * q^7 + 15 * q^8 - 9 * q^9	\( 30 q - 6 q^{2} - 6 q^{4} - 12 q^{5} + 3 q^{6} + 3 q^{7} + 15 q^{8} - 9 q^{9} + 6 q^{10} - 3 q^{11} - 33 q^{12} - 30 q^{13} + 15 q^{15} - 24 q^{16} - 6 q^{17} + 33 q^{18} - 57 q^{20} + 15 q^{21} - 12 q^{22} + 33 q^{24} + 12 q^{25} - 12 q^{26} - 12 q^{27} - 6 q^{28} + 30 q^{30} + 3 q^{31} + 69 q^{32} - 6 q^{33} + 21 q^{34} + 12 q^{35} - 54 q^{36} + 27 q^{37} + 45 q^{38} - 57 q^{39} + 42 q^{40} - 24 q^{41} + 33 q^{42} - 9 q^{43} - 27 q^{44} + 45 q^{45} - 24 q^{46} + 12 q^{47} + 48 q^{48} + 24 q^{49} - 90 q^{50} + 18 q^{51} + 21 q^{52} - 6 q^{53} + 63 q^{54} - 30 q^{55} - 6 q^{56} + 27 q^{57} + 57 q^{58} + 9 q^{59} - 45 q^{60} + 15 q^{61} - 27 q^{62} - 72 q^{63} - 33 q^{64} + 6 q^{65} - 42 q^{66} - 6 q^{67} - 36 q^{68} - 24 q^{69} - 60 q^{70} - 66 q^{71} - 54 q^{72} - 30 q^{73} - 18 q^{74} + 63 q^{75} + 6 q^{76} - 27 q^{77} - 84 q^{78} - 33 q^{79} + 54 q^{80} + 57 q^{81} - 48 q^{82} + 84 q^{83} + 54 q^{84} - 69 q^{85} - 9 q^{86} - 54 q^{87} + 3 q^{88} - 6 q^{89} + 69 q^{90} + 102 q^{91} + 57 q^{92} - 42 q^{93} + 18 q^{94} - 12 q^{95} - 102 q^{96} + 33 q^{97} - 9 q^{98} - 57 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 + 3 * q^6 + 3 * q^7 + 15 * q^8 - 9 * q^9 + 6 * q^10 - 3 * q^11 - 33 * q^12 - 30 * q^13 + 15 * q^15 - 24 * q^16 - 6 * q^17 + 33 * q^18 - 57 * q^20 + 15 * q^21 - 12 * q^22 + 33 * q^24 + 12 * q^25 - 12 * q^26 - 12 * q^27 - 6 * q^28 + 30 * q^30 + 3 * q^31 + 69 * q^32 - 6 * q^33 + 21 * q^34 + 12 * q^35 - 54 * q^36 + 27 * q^37 + 45 * q^38 - 57 * q^39 + 42 * q^40 - 24 * q^41 + 33 * q^42 - 9 * q^43 - 27 * q^44 + 45 * q^45 - 24 * q^46 + 12 * q^47 + 48 * q^48 + 24 * q^49 - 90 * q^50 + 18 * q^51 + 21 * q^52 - 6 * q^53 + 63 * q^54 - 30 * q^55 - 6 * q^56 + 27 * q^57 + 57 * q^58 + 9 * q^59 - 45 * q^60 + 15 * q^61 - 27 * q^62 - 72 * q^63 - 33 * q^64 + 6 * q^65 - 42 * q^66 - 6 * q^67 - 36 * q^68 - 24 * q^69 - 60 * q^70 - 66 * q^71 - 54 * q^72 - 30 * q^73 - 18 * q^74 + 63 * q^75 + 6 * q^76 - 27 * q^77 - 84 * q^78 - 33 * q^79 + 54 * q^80 + 57 * q^81 - 48 * q^82 + 84 * q^83 + 54 * q^84 - 69 * q^85 - 9 * q^86 - 54 * q^87 + 3 * q^88 - 6 * q^89 + 69 * q^90 + 102 * q^91 + 57 * q^92 - 42 * q^93 + 18 * q^94 - 12 * q^95 - 102 * q^96 + 33 * q^97 - 9 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.352058	+	1.99662i	−0.248942	+	1.41182i	0.562213	+	0.826992i	$0.309950\pi$
$2$	−0.352058	+	1.99662i	−0.248942	+	1.41182i	−0.811156	+	0.584831i	$0.801161\pi$
$3$	−0.860978	+	1.49126i	−0.497086	+	0.860978i	−0.999994	−	0.00336156i	$-0.998930\pi$
$3$	−0.860978	+	1.49126i	−0.497086	+	0.860978i	0.502908	+	0.864340i	$0.332263\pi$
$4$	−1.98316	−	0.721811i	−0.991579	−	0.360905i
$5$	−0.0610770	−	0.346385i	−0.0273145	−	0.154908i	0.968100	−	0.250564i	$-0.0806161\pi$
$5$	−0.0610770	−	0.346385i	−0.0273145	−	0.154908i	−0.995414	+	0.0956563i	$0.969505\pi$
$6$	−2.67436	−	2.24405i	−1.09180	−	0.916131i
$7$	0.956032	−	1.65590i	0.361346	−	0.625870i	−0.626836	−	0.779151i	$-0.715651\pi$
$7$	0.956032	−	1.65590i	0.361346	−	0.625870i	0.988183	+	0.153281i	$0.0489839\pi$
$8$	0.111947	−	0.193897i	0.0395792	−	0.0685531i
$9$	0.0174332	+	0.0301951i	0.00581106	+	0.0100650i
$10$	0.713101			0.225502
$11$	−0.0281794	−	0.159813i	−0.00849642	−	0.0481856i	0.980265	−	0.197689i	$-0.0633436\pi$
$11$	−0.0281794	−	0.159813i	−0.00849642	−	0.0481856i	−0.988761	+	0.149503i	$0.952232\pi$
$12$	2.78386	−	2.33594i	0.803632	−	0.674327i
$13$	2.13983	+	1.79553i	0.593483	+	0.497991i	0.889343	−	0.457240i	$-0.151162\pi$
$13$	2.13983	+	1.79553i	0.593483	+	0.497991i	−0.295860	+	0.955231i	$0.595606\pi$
$14$	2.96962	+	2.49180i	0.793663	+	0.665963i
$15$	0.569135	+	0.207148i	0.146950	+	0.0534854i
$16$	−2.88564	−	2.42134i	−0.721411	−	0.605335i
$17$	2.75830	+	4.77752i	0.668987	+	1.15872i	0.978188	+	0.207722i	$0.0666050\pi$
$17$	2.75830	+	4.77752i	0.668987	+	1.15872i	−0.309201	+	0.950997i	$0.600062\pi$
$18$	−0.0664257	+	0.0241770i	−0.0156567	+	0.00569856i
$19$	1.22918	−	6.97101i	0.281993	−	1.59926i	−0.433842	−	0.900989i	$-0.642842\pi$
$19$	1.22918	−	6.97101i	0.281993	−	1.59926i	0.715834	−	0.698270i	$-0.246047\pi$
$20$	−0.128899	+	0.731022i	−0.0288227	+	0.163461i
$21$	1.64625	+	2.85138i	0.359240	+	0.622223i
$22$	0.329007			0.0701446
$23$	−0.0372373	−	0.211183i	−0.00776451	−	0.0440347i	0.980679	−	0.195622i	$-0.0626726\pi$
$23$	−0.0372373	−	0.211183i	−0.00776451	−	0.0440347i	−0.988444	+	0.151587i	$0.951561\pi$
$24$	0.192767	+	0.333883i	0.0393485	+	0.0681536i
$25$	4.58221	−	1.66779i	0.916442	−	0.333558i
$26$	−4.33834	+	3.64030i	−0.850819	+	0.713922i
$27$	−5.22591			−1.00573
$28$	−3.09121	+	2.59383i	−0.584183	+	0.490188i
$29$	1.36239	−	7.72647i	0.252989	−	1.43477i	−0.548194	−	0.836351i	$-0.684685\pi$
$29$	1.36239	−	7.72647i	0.252989	−	1.43477i	0.801183	−	0.598419i	$-0.204204\pi$
$30$	−0.613964	+	1.06342i	−0.112094	+	0.194153i
$31$	−5.51116	+	2.00590i	−0.989834	+	0.360270i	−0.785656	−	0.618664i	$-0.787674\pi$
$31$	−5.51116	+	2.00590i	−0.989834	+	0.360270i	−0.204178	+	0.978934i	$0.565452\pi$
$32$	6.19344	−	5.19691i	1.09486	−	0.918692i
$33$	0.262585	+	0.0955731i	0.0457102	+	0.0166371i
$34$	−10.5100	+	3.82532i	−1.80244	+	0.656036i
$35$	−0.631969	−	0.230018i	−0.106822	−	0.0388801i
$36$	−0.0127776	−	0.0724652i	−0.00212959	−	0.0120775i
$37$	−1.27068	−	7.20636i	−0.208898	−	1.18472i	−0.891187	−	0.453636i	$-0.850127\pi$
$37$	−1.27068	−	7.20636i	−0.208898	−	1.18472i	0.682289	−	0.731082i	$-0.260984\pi$
$38$	13.4857	+	4.90840i	2.18767	+	0.796247i
$39$	−4.51995	+	1.64513i	−0.723772	+	0.263431i
$40$	−0.0740005	−	0.0269340i	−0.0117005	−	0.00425864i
$41$	−7.91913	+	6.64494i	−1.23676	+	1.03777i	−0.238990	+	0.971022i	$0.576816\pi$
$41$	−7.91913	+	6.64494i	−1.23676	+	1.03777i	−0.997770	+	0.0667430i	$0.978739\pi$
$42$	−6.27270	+	2.28308i	−0.967898	+	0.352286i
$43$	−1.72634	+	2.99011i	−0.263265	+	0.455988i	−0.967108	−	0.254368i	$-0.918133\pi$
$43$	−1.72634	+	2.99011i	−0.263265	+	0.455988i	0.703843	+	0.710356i	$0.251466\pi$
$44$	−0.0594708	+	0.337276i	−0.00896556	+	0.0508462i
$45$	0.00939437	−	0.00788281i	0.00140043	−	0.00117510i
$46$	0.434762			0.0641022
$47$	5.31758	−	4.46198i	0.775649	−	0.650847i	−0.166500	−	0.986041i	$-0.553247\pi$
$47$	5.31758	−	4.46198i	0.775649	−	0.650847i	0.942149	+	0.335195i	$0.108802\pi$
$48$	6.09532	−	2.21852i	0.879784	−	0.320215i
$49$	1.67200	+	2.89600i	0.238858	+	0.413714i
$50$	1.71674	+	9.73609i	0.242783	+	1.37689i
$51$	−9.49935			−1.33018
$52$	−2.94759	−	5.10538i	−0.408758	−	0.707989i
$53$	0.0886539	−	0.502781i	0.0121775	−	0.0690623i	−0.978113	−	0.208073i	$-0.933281\pi$
$53$	0.0886539	−	0.502781i	0.0121775	−	0.0690623i	0.990291	+	0.139010i	$0.0443921\pi$
$54$	1.83982	−	10.4341i	0.250368	−	1.41991i
$55$	−0.0536358	+	0.0195218i	−0.00723225	+	0.00263232i
$56$	−0.214049	−	0.370745i	−0.0286036	−	0.0495428i
$57$	9.33728	+	7.83491i	1.23675	+	1.03776i
$58$	14.9472	+	5.44033i	1.96266	+	0.714351i
$59$	−3.20623	−	2.69035i	−0.417416	−	0.350253i	0.409763	−	0.912192i	$-0.365611\pi$
$59$	−3.20623	−	2.69035i	−0.417416	−	0.350253i	−0.827179	+	0.561939i	$0.810056\pi$
$60$	−0.979163	−	0.821615i	−0.126409	−	0.106070i
$61$	3.53117	−	2.96301i	0.452120	−	0.379374i	−0.388102	−	0.921617i	$-0.626869\pi$
$61$	3.53117	−	2.96301i	0.452120	−	0.379374i	0.840222	+	0.542243i	$0.182425\pi$
$62$	−2.06477	−	11.7099i	−0.262226	−	1.48716i
$63$	0.0666667			0.00839921
$64$	4.42886	+	7.67101i	0.553608	+	0.958877i
$65$	0.491251	−	0.850871i	0.0609322	−	0.105538i
$66$	−0.283268	+	0.490635i	−0.0348679	+	0.0603930i
$67$	1.79431	+	1.50560i	0.219209	+	0.183939i	0.745779	−	0.666194i	$-0.232078\pi$
$67$	1.79431	+	1.50560i	0.219209	+	0.183939i	−0.526569	+	0.850132i	$0.676522\pi$
$68$	−2.02169	−	11.4655i	−0.245165	−	1.39040i
$69$	0.346989	+	0.126294i	0.0417726	+	0.0152040i
$70$	0.681748	−	1.18082i	0.0814844	−	0.141135i
$71$	−0.379215	+	2.15064i	−0.0450046	+	0.255234i	−0.999006	−	0.0445672i	$-0.985809\pi$
$71$	−0.379215	+	2.15064i	−0.0450046	+	0.255234i	0.954002	+	0.299801i	$0.0969202\pi$
$72$	0.00780635			0.000919987
$73$	−8.24477	+	2.24138i	−0.964977	+	0.262334i
$73$	−8.24477	+	2.24138i	−0.964977	+	0.262334i
$74$	14.8357			1.72462
$75$	−1.45808	+	8.26919i	−0.168365	+	0.954844i
$76$	−7.46940	+	12.9374i	−0.856799	+	1.48402i
$77$	−0.291575	−	0.106125i	−0.0332281	−	0.0120940i
$78$	−1.69341	−	9.60381i	−0.191741	−	1.08742i
$79$	2.68141	+	2.24997i	0.301683	+	0.253142i	0.781044	−	0.624476i	$-0.214687\pi$
$79$	2.68141	+	2.24997i	0.301683	+	0.253142i	−0.479362	+	0.877618i	$0.659132\pi$
$80$	−0.662469	+	1.14743i	−0.0740663	+	0.128287i
$81$	4.44709	−	7.70259i	0.494121	−	0.855843i
$82$	−10.4794	−	18.1509i	−1.15726	−	2.00443i
$83$	−3.66682			−0.402486			−0.201243	−	0.979541i	$-0.564498\pi$
$83$	−3.66682			−0.402486			−0.201243	+	0.979541i	$0.564498\pi$
$84$	−1.20661	−	6.84302i	−0.131652	−	0.746635i
$85$	1.48639	−	1.24723i	0.161222	−	0.135281i
$86$	−5.36235	−	4.49954i	−0.578237	−	0.485198i
$87$	10.3492	+	8.68400i	1.10955	+	0.931022i
$88$	−0.0341420	−	0.0124267i	−0.00363955	−	0.00132469i
$89$	−11.9564	−	10.0326i	−1.26737	−	1.06345i	−0.994856	−	0.101299i	$-0.967700\pi$
$89$	−11.9564	−	10.0326i	−1.26737	−	1.06345i	−0.272515	−	0.962152i	$-0.587855\pi$
$90$	0.0124316	+	0.0215322i	0.00131041	+	0.00226969i
$91$	5.01897	−	1.82676i	0.526131	−	0.191496i
$92$	−0.0785868	+	0.445688i	−0.00819324	+	0.0464662i
$93$	1.75368	−	9.94560i	0.181848	−	1.03131i
$94$	7.03678	+	12.1881i	0.725788	+	1.25710i
$95$	−2.48973			−0.255440
$96$	2.41752	+	13.7104i	0.246737	+	1.39932i
$97$	5.50716	+	9.53867i	0.559167	+	0.968506i	0.997566	+	0.0697252i	$0.0222123\pi$
$97$	5.50716	+	9.53867i	0.559167	+	0.968506i	−0.438399	+	0.898780i	$0.644454\pi$
$98$	−6.37084	+	2.31880i	−0.643552	+	0.234234i
$99$	0.00433433	−	0.00363694i	0.000435617	−	0.000365526i
$100$	−10.2911			−1.02911
$101$	−6.12624	+	5.14052i	−0.609583	+	0.511501i	−0.894510	−	0.447048i	$-0.852475\pi$
$101$	−6.12624	+	5.14052i	−0.609583	+	0.511501i	0.284927	+	0.958549i	$0.408031\pi$
$102$	3.34432	−	18.9666i	0.331137	−	1.87797i
$103$	−6.78665	+	11.7548i	−0.668709	+	1.15824i	0.309557	+	0.950881i	$0.399819\pi$
$103$	−6.78665	+	11.7548i	−0.668709	+	1.15824i	−0.978265	+	0.207357i	$0.933514\pi$
$104$	0.587697	−	0.213904i	0.0576284	−	0.0209750i
$105$	0.887127	−	0.744388i	0.0865748	−	0.0726449i
$106$	0.972651	+	0.354016i	0.0944722	+	0.0343851i
$107$	−14.9715	+	5.44919i	−1.44735	+	0.526793i	−0.941850	−	0.336033i	$-0.890915\pi$
$107$	−14.9715	+	5.44919i	−1.44735	+	0.526793i	−0.505501	+	0.862826i	$0.668692\pi$
$108$	10.3638	+	3.77211i	0.997257	+	0.362972i
$109$	1.96361	+	11.1362i	0.188079	+	1.06665i	0.921935	+	0.387346i	$0.126608\pi$
$109$	1.96361	+	11.1362i	0.188079	+	1.06665i	−0.733855	+	0.679306i	$0.762281\pi$
$110$	−0.0200948	−	0.113963i	−0.00191596	−	0.0108660i
$111$	11.8406	+	4.30961i	1.12386	+	0.409050i
$112$	−6.76826	+	2.46345i	−0.639540	+	0.232774i
$113$	6.32826	+	2.30330i	0.595313	+	0.216676i	0.622065	−	0.782966i	$-0.286294\pi$
$113$	6.32826	+	2.30330i	0.595313	+	0.216676i	−0.0267517	+	0.999642i	$0.508516\pi$
$114$	−18.9306	+	15.8846i	−1.77301	+	1.48773i
$115$	−0.0708763	+	0.0257969i	−0.00660925	+	0.00240557i
$116$	−8.27888	+	14.3394i	−0.768674	+	1.33138i
$117$	−0.0169123	+	0.0959144i	−0.00156354	+	0.00886729i
$118$	6.50037	−	5.45446i	0.598408	−	0.502124i
$119$	10.5481			0.966943
$120$	0.103878	−	0.0871643i	0.00948275	−	0.00795697i
$121$	10.3119	−	3.75321i	0.937443	−	0.341201i
$122$	4.67282	+	8.09356i	0.423057	+	0.732756i
$123$	−3.09112	−	17.5306i	−0.278717	−	1.58068i
$124$	12.3774			1.11152
$125$	−1.73688	−	3.00837i	−0.155352	−	0.269077i
$126$	−0.0234705	+	0.133108i	−0.00209092	+	0.0118582i
$127$	2.52842	−	14.3394i	0.224361	−	1.27241i	−0.639543	−	0.768755i	$-0.720876\pi$
$127$	2.52842	−	14.3394i	0.224361	−	1.27241i	0.863904	−	0.503657i	$-0.168012\pi$
$128$	−1.68056	+	0.611675i	−0.148542	+	0.0540649i
$129$	−2.97269	−	5.14885i	−0.261731	−	0.453331i
$130$	1.52592	+	1.28040i	0.133832	+	0.112298i
$131$	−9.35997	−	3.40675i	−0.817784	−	0.297649i	−0.100949	−	0.994892i	$-0.532188\pi$
$131$	−9.35997	−	3.40675i	−0.817784	−	0.297649i	−0.716835	+	0.697242i	$0.754410\pi$
$132$	−0.451762	−	0.379073i	−0.0393208	−	0.0329941i
$133$	−10.3681	−	8.69990i	−0.899032	−	0.754377i
$134$	−3.63781	+	3.05249i	−0.314259	+	0.263695i
$135$	0.319183	+	1.81017i	0.0274709	+	0.155795i
$136$	1.23513			0.105912
$137$	−1.89546	−	3.28304i	−0.161940	−	0.280489i	0.773624	−	0.633645i	$-0.218442\pi$
$137$	−1.89546	−	3.28304i	−0.161940	−	0.280489i	−0.935564	+	0.353156i	$0.885108\pi$
$138$	−0.374321	+	0.648342i	−0.0318643	+	0.0551906i
$139$	8.82943	−	15.2930i	0.748903	−	1.29714i	−0.199446	−	0.979909i	$-0.563914\pi$
$139$	8.82943	−	15.2930i	0.748903	−	1.29714i	0.948349	−	0.317229i	$-0.102752\pi$
$140$	1.08726	+	0.912324i	0.0918907	+	0.0771054i
$141$	2.07564	+	11.7716i	0.174801	+	0.991344i
$142$	−4.16050	−	1.51430i	−0.349141	−	0.127077i
$143$	0.226651	−	0.392571i	0.0189535	−	0.0328285i
$144$	0.0228068	−	0.129344i	0.00190057	−	0.0107787i
$145$	−2.75954			−0.229168
$146$	−1.57255	−	17.2508i	−0.130146	−	1.42768i
$147$	−5.75824			−0.474931
$148$	−2.68167	+	15.2085i	−0.220432	+	1.25013i
$149$	7.20547	−	12.4802i	0.590295	−	1.02242i	−0.403897	−	0.914804i	$-0.632345\pi$
$149$	7.20547	−	12.4802i	0.590295	−	1.02242i	0.994192	−	0.107617i	$-0.0343220\pi$
$150$	−15.9971	−	5.82246i	−1.30616	−	0.475402i
$151$	−2.59394	−	14.7110i	−0.211092	−	1.19716i	−0.887561	−	0.460690i	$-0.847602\pi$
$151$	−2.59394	−	14.7110i	−0.211092	−	1.19716i	0.676469	−	0.736471i	$-0.263509\pi$
$152$	−1.21406	−	1.01872i	−0.0984732	−	0.0826288i
$153$	−0.0961719	+	0.166575i	−0.00777504	+	0.0134668i
$154$	0.314542	−	0.544802i	0.0253465	−	0.0439014i
$155$	1.03142	+	1.78647i	0.0828454	+	0.143493i
$156$	10.1513			0.812751
$157$	1.63897	+	9.29508i	0.130804	+	0.741829i	0.977690	+	0.210053i	$0.0673638\pi$
$157$	1.63897	+	9.29508i	0.130804	+	0.741829i	−0.846886	+	0.531775i	$0.821525\pi$
$158$	−5.43635	+	4.56164i	−0.432493	+	0.362905i
$159$	0.673447	+	0.565089i	0.0534078	+	0.0448145i
$160$	−2.17841	−	1.82790i	−0.172218	−	0.144508i
$161$	−0.385298	−	0.140237i	−0.0303657	−	0.0110522i
$162$	13.8135	+	11.5909i	1.08529	+	0.910668i
$163$	1.21403	+	2.10277i	0.0950904	+	0.164701i	0.909646	−	0.415384i	$-0.136353\pi$
$163$	1.21403	+	2.10277i	0.0950904	+	0.164701i	−0.814556	+	0.580085i	$0.803019\pi$
$164$	20.5013	−	7.46185i	1.60088	−	0.582673i
$165$	0.0170672	−	0.0967927i	0.00132868	−	0.00753530i
$166$	1.29093	−	7.32125i	0.100196	−	0.568239i
$167$	5.99946	+	10.3914i	0.464252	+	0.804108i	0.999167	−	0.0407976i	$-0.0129899\pi$
$167$	5.99946	+	10.3914i	0.464252	+	0.804108i	−0.534915	+	0.844906i	$0.679657\pi$
$168$	0.737168			0.0568737
$169$	−0.902480	−	5.11822i	−0.0694215	−	0.393709i
$170$	1.96695	+	3.40685i	0.150858	+	0.261294i
$171$	0.231919	−	0.0844116i	0.0177353	−	0.00645512i
$172$	5.58191	−	4.68378i	0.425616	−	0.357135i
$173$	−12.4672			−0.947860			−0.473930	−	0.880563i	$-0.657165\pi$
$173$	−12.4672			−0.947860			−0.473930	+	0.880563i	$0.657165\pi$
$174$	−20.9821	+	17.6061i	−1.59065	+	1.33472i
$175$	1.61906	−	9.18213i	0.122389	−	0.694104i
$176$	−0.305647	+	0.529397i	−0.0230390	+	0.0399048i
$177$	6.77249	−	2.46499i	0.509052	−	0.185280i
$178$	24.2406	−	20.3402i	1.81691	−	1.52457i
$179$	19.4673	+	7.08552i	1.45506	+	0.529597i	0.943998	−	0.329950i	$-0.107032\pi$
$179$	19.4673	+	7.08552i	1.45506	+	0.529597i	0.511057	+	0.859547i	$0.329254\pi$
$180$	−0.0243204	+	0.00885190i	−0.00181274	+	0.000659782i
$181$	16.4254	+	5.97836i	1.22089	+	0.444368i	0.870469	−	0.492224i	$-0.163816\pi$
$181$	16.4254	+	5.97836i	1.22089	+	0.444368i	0.350422	+	0.936592i	$0.386038\pi$
$182$	1.88037	+	10.6641i	0.139382	+	0.790475i
$183$	1.37834	+	7.81697i	0.101890	+	0.577847i
$184$	−0.0451165	−	0.0164211i	−0.00332603	−	0.00121058i
$185$	−2.41856	+	0.880285i	−0.177816	+	0.0647198i
$186$	19.2402	+	7.00285i	1.41076	+	0.513474i
$187$	0.685785	−	0.575442i	0.0501495	−	0.0420805i
$188$	−13.7663	+	5.01053i	−1.00401	+	0.365430i
$189$	−4.99614	+	8.65356i	−0.363415	+	0.629454i
$190$	0.876527	−	4.97103i	0.0635900	−	0.360637i
$191$	13.8943	−	11.6587i	1.00535	−	0.843592i	0.0176368	−	0.999844i	$-0.494386\pi$
$191$	13.8943	−	11.6587i	1.00535	−	0.843592i	0.987717	+	0.156252i	$0.0499413\pi$
$192$	−15.2526			−1.10076
$193$	−11.7956	+	9.89770i	−0.849067	+	0.712452i	−0.959584	−	0.281422i	$-0.909194\pi$
$193$	−11.7956	+	9.89770i	−0.849067	+	0.712452i	0.110517	+	0.993874i	$0.464749\pi$
$194$	−20.9839	+	7.63753i	−1.50656	+	0.548343i
$195$	0.845912	+	1.46516i	0.0605770	+	0.104923i
$196$	−1.22549	−	6.95009i	−0.0875348	−	0.496435i
$197$	9.69904			0.691028			0.345514	−	0.938414i	$-0.387705\pi$
$197$	9.69904			0.691028			0.345514	+	0.938414i	$0.387705\pi$
$198$	0.00573564	+	0.00993442i	0.000407614	+	0.000706008i
$199$	−4.09424	+	23.2196i	−0.290233	+	1.64599i	0.395738	+	0.918363i	$0.370489\pi$
$199$	−4.09424	+	23.2196i	−0.290233	+	1.64599i	−0.685971	+	0.727629i	$0.740622\pi$
$200$	0.189584	−	1.07518i	0.0134056	−	0.0760269i
$201$	−3.79010	+	1.37948i	−0.267333	+	0.0973013i
$202$	−8.10688	−	14.0415i	−0.570398	−	0.987958i
$203$	−11.4918	−	9.64273i	−0.806563	−	0.676787i
$204$	18.8387	+	6.85673i	1.31897	+	0.480067i
$205$	2.78538	+	2.33721i	0.194539	+	0.163238i
$206$	−21.0806	−	17.6887i	−1.46876	−	1.23243i
$207$	0.00572754	−	0.00480598i	0.000398092	−	0.000334038i
$208$	−1.82719	−	10.3625i	−0.126693	−	0.718513i
$209$	−1.14870			−0.0794571
$210$	1.17394	+	2.03332i	0.0810095	+	0.140313i
$211$	−12.7325	+	22.0534i	−0.876543	+	1.51822i	−0.0214333	+	0.999770i	$0.506823\pi$
$211$	−12.7325	+	22.0534i	−0.876543	+	1.51822i	−0.855110	+	0.518447i	$0.826510\pi$
$212$	−0.538727	+	0.933103i	−0.0369999	+	0.0640858i
$213$	−2.88066	−	2.41716i	−0.197379	−	0.165621i
$214$	−5.60911	−	31.8109i	−0.383431	−	2.17455i
$215$	1.14117	+	0.415352i	0.0778271	+	0.0283268i
$216$	−0.585023	+	1.01329i	−0.0398058	+	0.0689457i
$217$	−1.94729	+	11.0436i	−0.132190	+	0.749689i
$218$	−22.9260			−1.55274
$219$	3.75608	−	14.2249i	0.253813	−	0.961227i
$220$	0.120459			0.00812137
$221$	−2.67589	+	15.1757i	−0.180000	+	1.02083i
$222$	−12.7732	+	22.1239i	−0.857282	+	1.48486i
$223$	10.0687	+	3.66469i	0.674248	+	0.245406i	0.656376	−	0.754434i	$-0.272089\pi$
$223$	10.0687	+	3.66469i	0.674248	+	0.245406i	0.0178720	+	0.999840i	$0.494311\pi$
$224$	−2.68442	−	15.2241i	−0.179360	−	1.01720i
$225$	0.130242	+	0.109286i	0.00868277	+	0.00728571i
$226$	−6.82673	+	11.8242i	−0.454107	+	0.786536i
$227$	1.85253	−	3.20868i	0.122957	−	0.212968i	−0.797975	−	0.602690i	$-0.794096\pi$
$227$	1.85253	−	3.20868i	0.122957	−	0.212968i	0.920933	+	0.389722i	$0.127429\pi$
$228$	−12.8620	−	22.2776i	−0.851805	−	1.47537i
$229$	−7.77252			−0.513623			−0.256811	−	0.966462i	$-0.582672\pi$
$229$	−7.77252			−0.513623			−0.256811	+	0.966462i	$0.582672\pi$
$230$	−0.0265539	−	0.150595i	−0.00175092	−	0.00992994i
$231$	0.409299	−	0.343443i	0.0269299	−	0.0225969i
$232$	−1.34563	−	1.12912i	−0.0883449	−	0.0741302i
$233$	−15.8157	−	13.2709i	−1.03612	−	0.869406i	−0.0445516	−	0.999007i	$-0.514186\pi$
$233$	−15.8157	−	13.2709i	−1.03612	−	0.869406i	−0.991566	+	0.129601i	$0.958630\pi$
$234$	−0.185550	−	0.0675348i	−0.0121298	−	0.00441489i
$235$	−1.87034	−	1.56940i	−0.122008	−	0.102377i
$236$	4.41654	+	7.64967i	0.287492	+	0.497951i
$237$	−5.66393	+	2.06150i	−0.367912	+	0.133909i
$238$	−3.71354	+	21.0606i	−0.240713	+	1.36515i
$239$	2.13161	−	12.0890i	0.137883	−	0.781971i	−0.834926	−	0.550362i	$-0.814490\pi$
$239$	2.13161	−	12.0890i	0.137883	−	0.781971i	0.972809	−	0.231609i	$-0.0743990\pi$
$240$	−1.14074	−	1.97583i	−0.0736347	−	0.127539i
$241$	2.53885			0.163542			0.0817709	−	0.996651i	$-0.473942\pi$
$241$	2.53885			0.163542			0.0817709	+	0.996651i	$0.473942\pi$
$242$	3.86336	+	21.9102i	0.248346	+	1.40844i
$243$	−0.181162	−	0.313781i	−0.0116215	−	0.0201291i
$244$	−9.14160	+	3.32727i	−0.585231	+	0.213007i
$245$	0.901008	−	0.756035i	0.0575633	−	0.0483013i
$246$	36.0902			2.30103
$247$	15.1469	−	12.7098i	0.963775	−	0.808703i
$248$	−0.228018	+	1.29315i	−0.0144792	+	0.0821154i
$249$	3.15706	−	5.46818i	0.200070	−	0.346532i
$250$	6.61806	−	2.40878i	0.418563	−	0.152344i
$251$	−3.88440	+	3.25940i	−0.245181	+	0.205731i	−0.757094	−	0.653306i	$-0.773382\pi$
$251$	−3.88440	+	3.25940i	−0.245181	+	0.205731i	0.511913	+	0.859037i	$0.328937\pi$
$252$	−0.132211	−	0.0481207i	−0.00832848	−	0.00303132i
$253$	−0.0327006	+	0.0119020i	−0.00205587	+	0.000748275i
$254$	27.7401	+	10.0966i	1.74057	+	0.633515i
$255$	0.580192	+	3.29043i	0.0363330	+	0.206055i
$256$	2.44663	+	13.8755i	0.152914	+	0.867220i
$257$	2.87182	+	1.04526i	0.179139	+	0.0652013i	0.430032	−	0.902813i	$-0.358502\pi$
$257$	2.87182	+	1.04526i	0.179139	+	0.0652013i	−0.250893	+	0.968015i	$0.580724\pi$
$258$	11.3268	−	4.12263i	0.705178	−	0.256664i
$259$	−13.1478	−	4.78540i	−0.816964	−	0.297351i
$260$	−1.58840	+	1.33282i	−0.0985081	+	0.0826581i
$261$	0.257053	−	0.0935595i	0.0159112	−	0.00579119i
$262$	10.0972	−	17.4889i	0.623809	−	1.08047i
$263$	−4.23165	+	23.9989i	−0.260935	+	1.47983i	0.519432	+	0.854512i	$0.326143\pi$
$263$	−4.23165	+	23.9989i	−0.260935	+	1.47983i	−0.780367	+	0.625322i	$0.784968\pi$
$264$	0.0479269	−	0.0402155i	0.00294970	−	0.00247509i
$265$	−0.179570			−0.0110309
$266$	21.0206	−	17.6384i	1.28885	−	1.08148i
$267$	25.2553	−	9.19218i	1.54560	−	0.562552i
$268$	−2.47163	−	4.28100i	−0.150979	−	0.261503i
$269$	−1.76587	−	10.0148i	−0.107667	−	0.610611i	−0.990121	−	0.140213i	$-0.955221\pi$
$269$	−1.76587	−	10.0148i	−0.107667	−	0.610611i	0.882454	−	0.470399i	$-0.155890\pi$
$270$	−3.72660			−0.226794
$271$	9.55425	+	16.5484i	0.580379	+	1.00525i	0.995434	+	0.0954500i	$0.0304290\pi$
$271$	9.55425	+	16.5484i	0.580379	+	1.00525i	−0.415055	+	0.909796i	$0.636238\pi$
$272$	3.60853	−	20.4650i	0.218799	−	1.24087i
$273$	−1.59706	+	9.05737i	−0.0966584	+	0.548177i
$274$	7.22228	−	2.62870i	0.436314	−	0.158805i
$275$	−0.395659	−	0.685302i	−0.0238591	−	0.0413252i
$276$	−0.596974	−	0.500921i	−0.0359336	−	0.0301519i
$277$	−21.2037	−	7.71751i	−1.27401	−	0.463700i	−0.385560	−	0.922683i	$-0.625992\pi$
$277$	−21.2037	−	7.71751i	−1.27401	−	0.463700i	−0.888445	+	0.458982i	$0.848214\pi$
$278$	27.4259	+	23.0130i	1.64489	+	1.38023i
$279$	−0.156645	−	0.131441i	−0.00937811	−	0.00786917i
$280$	−0.115347	+	0.0967874i	−0.00689329	+	0.00578415i
$281$	−1.40798	−	7.98504i	−0.0839929	−	0.476348i	−0.997569	−	0.0696805i	$-0.977802\pi$
$281$	−1.40798	−	7.98504i	−0.0839929	−	0.476348i	0.913576	−	0.406667i	$-0.133309\pi$
$282$	−24.2341			−1.44312
$283$	−2.72482	−	4.71953i	−0.161974	−	0.280547i	0.773603	−	0.633671i	$-0.218453\pi$
$283$	−2.72482	−	4.71953i	−0.161974	−	0.280547i	−0.935577	+	0.353124i	$0.885119\pi$
$284$	2.30440	−	3.99133i	0.136741	−	0.236842i
$285$	2.14360	−	3.71282i	0.126976	−	0.219929i
$286$	0.704021	+	0.590744i	0.0416296	+	0.0349314i
$287$	3.43239	+	19.4660i	0.202607	+	1.14904i
$288$	0.264893	+	0.0964130i	0.0156089	+	0.00568119i
$289$	−6.71647	+	11.6333i	−0.395086	+	0.684309i
$290$	0.971519	−	5.50976i	0.0570495	−	0.323544i
$291$	−18.9662			−1.11182
$292$	17.9685	+	1.50614i	1.05153	+	0.0881403i
$293$	−31.2915			−1.82807			−0.914035	−	0.405634i	$-0.867051\pi$
$293$	−31.2915			−1.82807			−0.914035	+	0.405634i	$0.867051\pi$
$294$	2.02723	−	11.4970i	0.118231	−	0.670519i
$295$	−0.736068	+	1.27491i	−0.0428555	+	0.0742280i
$296$	−1.53954	−	0.560348i	−0.0894841	−	0.0325695i
$297$	0.147263	+	0.835170i	0.00854507	+	0.0484615i
$298$	22.3815	+	18.7803i	1.29653	+	1.08792i
$299$	0.299505	−	0.518758i	0.0173208	−	0.0300005i
$300$	8.86039	−	15.3466i	0.511555	−	0.886039i
$301$	3.30088	+	5.71729i	0.190260	+	0.329539i
$302$	30.2854			1.74273
$303$	−2.39129	−	13.5617i	−0.137376	−	0.779098i
$304$	−20.4262	+	17.1396i	−1.17152	+	0.983023i
$305$	−1.24201	−	1.04217i	−0.0711175	−	0.0596746i
$306$	−0.298728	−	0.250663i	−0.0170771	−	0.0143294i
$307$	−16.1661	−	5.88399i	−0.922649	−	0.335817i	−0.163357	−	0.986567i	$-0.552232\pi$
$307$	−16.1661	−	5.88399i	−0.922649	−	0.335817i	−0.759292	+	0.650750i	$0.774455\pi$
$308$	0.501637	+	0.420924i	0.0285834	+	0.0239844i
$309$	−11.6863	−	20.2413i	−0.664811	−	1.15149i
$310$	−3.93001	+	1.43041i	−0.223210	+	0.0812417i
$311$	0.183336	−	1.03975i	0.0103960	−	0.0589589i	−0.979168	−	0.203050i	$-0.934915\pi$
$311$	0.183336	−	1.03975i	0.0103960	−	0.0589589i	0.989564	+	0.144091i	$0.0460258\pi$
$312$	−0.187008	+	1.06057i	−0.0105872	+	0.0600432i
$313$	−2.80127	−	4.85194i	−0.158337	−	0.274248i	0.775932	−	0.630817i	$-0.217280\pi$
$313$	−2.80127	−	4.85194i	−0.158337	−	0.274248i	−0.934269	+	0.356569i	$0.883947\pi$
$314$	−19.1358			−1.07989
$315$	−0.00407180	−	0.0230923i	−0.000229420	−	0.00130110i
$316$	−3.69361	−	6.39753i	−0.207782	−	0.359889i
$317$	11.6766	−	4.24992i	0.655821	−	0.238699i	0.00739000	−	0.999973i	$-0.497648\pi$
$317$	11.6766	−	4.24992i	0.655821	−	0.238699i	0.648431	+	0.761273i	$0.275425\pi$
$318$	−1.36536	+	1.14567i	−0.0765656	+	0.0642462i
$319$	−1.27319			−0.0712847
$320$	2.38662	−	2.00261i	0.133416	−	0.111949i
$321$	4.76401	−	27.0180i	0.265901	−	1.50800i
$322$	0.415647	−	0.719921i	0.0231631	−	0.0401196i
$323$	36.6946	−	13.3557i	2.04174	−	0.743133i
$324$	−14.3791	+	12.0655i	−0.798839	+	0.670305i
$325$	12.7997	+	4.65872i	0.710002	+	0.258420i
$326$	−4.62583	+	1.68367i	−0.256201	+	0.0932496i
$327$	−18.2975	−	6.65975i	−1.01186	−	0.368285i
$328$	0.401916	+	2.27938i	0.0221921	+	0.125858i
$329$	−2.30480	−	13.0712i	−0.127068	−	0.720637i
$330$	0.187250	+	0.0681533i	0.0103077	+	0.00375171i
$331$	2.48357	−	0.903945i	0.136509	−	0.0496853i	−0.272862	−	0.962053i	$-0.587970\pi$
$331$	2.48357	−	0.903945i	0.136509	−	0.0496853i	0.409371	+	0.912368i	$0.365748\pi$
$332$	7.27189	+	2.64675i	0.399097	+	0.145259i
$333$	0.195445	−	0.163998i	0.0107103	−	0.00898703i
$334$	−22.8598	+	8.32027i	−1.25083	+	0.455265i
$335$	0.411927	−	0.713478i	0.0225060	−	0.0389815i
$336$	2.15369	−	12.2142i	0.117494	−	0.666339i
$337$	−22.2984	+	18.7106i	−1.21467	+	1.01923i	−0.215583	+	0.976485i	$0.569165\pi$
$337$	−22.2984	+	18.7106i	−1.21467	+	1.01923i	−0.999086	+	0.0427432i	$0.986390\pi$
$338$	10.5369			0.573129
$339$	−8.88331	+	7.45398i	−0.482475	+	0.404845i
$340$	−3.84801	+	1.40056i	−0.208688	+	0.0759561i
$341$	0.475871	+	0.824232i	0.0257698	+	0.0446347i
$342$	0.0868889	+	0.492772i	0.00469842	+	0.0266460i
$343$	19.7784			1.06793
$344$	0.386517	+	0.669467i	0.0208396	+	0.0360953i
$345$	0.0225532	−	0.127905i	0.00121422	−	0.00688619i
$346$	4.38916	−	24.8922i	0.235963	−	1.33821i
$347$	−14.6299	+	5.32486i	−0.785376	+	0.285853i	−0.703412	−	0.710782i	$-0.748341\pi$
$347$	−14.6299	+	5.32486i	−0.785376	+	0.285853i	−0.0819635	+	0.996635i	$0.526119\pi$
$348$	−14.2559	−	24.6919i	−0.764195	−	1.32362i
$349$	11.2430	+	9.43403i	0.601826	+	0.504992i	0.892032	−	0.451972i	$-0.149279\pi$
$349$	11.2430	+	9.43403i	0.601826	+	0.504992i	−0.290206	+	0.956964i	$0.593724\pi$
$350$	17.7632	+	6.46528i	0.949484	+	0.345584i
$351$	−11.1826	−	9.38329i	−0.596881	−	0.500843i
$352$	−1.00506	−	0.843348i	−0.0535701	−	0.0449506i
$353$	7.88763	−	6.61851i	0.419816	−	0.352268i	−0.408277	−	0.912858i	$-0.633870\pi$
$353$	7.88763	−	6.61851i	0.419816	−	0.352268i	0.828093	+	0.560591i	$0.189426\pi$
$354$	2.53733	+	14.3899i	0.134858	+	0.764815i
$355$	0.768109			0.0407670
$356$	16.4697	+	28.5264i	0.872894	+	1.51190i
$357$	−9.08169	+	15.7299i	−0.480654	+	0.832517i
$358$	−21.0007	+	36.3743i	−1.10992	+	1.92244i
$359$	23.5804	+	19.7863i	1.24453	+	1.04428i	0.997156	+	0.0753614i	$0.0240110\pi$
$359$	23.5804	+	19.7863i	1.24453	+	1.04428i	0.247371	+	0.968921i	$0.420433\pi$
$360$	−0.000476788	−	0.00270400i	−2.51289e−5	−	0.000142513i
$361$	−29.2299	−	10.6388i	−1.53842	−	0.559938i
$362$	−17.7192	+	30.6905i	−0.931300	+	1.61306i
$363$	−3.28129	+	18.6091i	−0.172223	+	0.976724i
$364$	−11.2720			−0.590812
$365$	1.27995	+	2.71896i	0.0669955	+	0.142317i
$366$	−16.0928			−0.841183
$367$	1.94414	−	11.0258i	0.101483	−	0.575540i	−0.891084	−	0.453839i	$-0.850054\pi$
$367$	1.94414	−	11.0258i	0.101483	−	0.575540i	0.992567	−	0.121701i	$-0.0388348\pi$
$368$	−0.403893	+	0.699563i	−0.0210544	+	0.0364673i
$369$	−0.338700	−	0.123277i	−0.0176320	−	0.00641754i
$370$	−0.906120	−	5.13886i	−0.0471069	−	0.267157i
$371$	−0.747798	−	0.627477i	−0.0388237	−	0.0325770i
$372$	−10.6567	+	18.4579i	−0.552522	+	0.956996i
$373$	−3.61889	+	6.26810i	−0.187379	+	0.324550i	−0.944376	−	0.328869i	$-0.893333\pi$
$373$	−3.61889	+	6.26810i	−0.187379	+	0.324550i	0.756997	+	0.653419i	$0.226666\pi$
$374$	0.907502	+	1.57184i	0.0469258	+	0.0812779i
$375$	5.98168			0.308893
$376$	−0.269881	−	1.53057i	−0.0139180	−	0.0789331i
$377$	16.7884	−	14.0872i	0.864648	−	0.725526i
$378$	−15.5189	−	13.0219i	−0.798208	−	0.669776i
$379$	8.90708	+	7.47393i	0.457526	+	0.383910i	0.842220	−	0.539134i	$-0.181248\pi$
$379$	8.90708	+	7.47393i	0.457526	+	0.383910i	−0.384694	+	0.923044i	$0.625693\pi$
$380$	4.93752	+	1.79711i	0.253289	+	0.0921898i
$381$	19.2068	+	16.1164i	0.983993	+	0.825668i
$382$	18.3863	+	31.8461i	0.940727	+	1.62939i
$383$	10.0408	−	3.65456i	0.513062	−	0.186739i	−0.0724975	−	0.997369i	$-0.523097\pi$
$383$	10.0408	−	3.65456i	0.513062	−	0.186739i	0.585560	+	0.810629i	$0.300875\pi$
$384$	0.534763	−	3.03279i	0.0272895	−	0.154767i
$385$	−0.0189514	+	0.107479i	−0.000965854	+	0.00547763i
$386$	−15.6092	−	27.0359i	−0.794487	−	1.37609i
$387$	−0.120383			−0.00611939
$388$	−4.03645	−	22.8918i	−0.204919	−	1.16216i
$389$	11.5545	+	20.0129i	0.585834	+	1.01469i	0.994771	+	0.102131i	$0.0325662\pi$
$389$	11.5545	+	20.0129i	0.585834	+	1.01469i	−0.408937	+	0.912563i	$0.634100\pi$
$390$	−3.22318	+	1.17314i	−0.163212	+	0.0594044i
$391$	0.906220	−	0.760409i	0.0458295	−	0.0384555i
$392$	0.748702			0.0378151
$393$	13.1391	−	11.0250i	0.662778	−	0.556137i
$394$	−3.41462	+	19.3653i	−0.172026	+	0.975609i
$395$	0.615584	−	1.06622i	0.0309734	−	0.0536475i
$396$	−0.0112208	+	0.00408405i	−0.000563869	+	0.000205231i
$397$	−0.878819	+	0.737417i	−0.0441067	+	0.0370099i	−0.664575	−	0.747222i	$-0.731387\pi$
$397$	−0.878819	+	0.737417i	−0.0441067	+	0.0370099i	0.620468	+	0.784232i	$0.286943\pi$
$398$	−44.9192	−	16.3493i	−2.25160	−	0.819515i
$399$	21.9005	−	7.97114i	1.09640	−	0.399056i
$400$	−17.2609	−	6.28246i	−0.863046	−	0.314123i
$401$	−3.95384	−	22.4234i	−0.197445	−	1.11977i	−0.908893	−	0.417030i	$-0.863071\pi$
$401$	−3.95384	−	22.4234i	−0.197445	−	1.11977i	0.711447	−	0.702739i	$-0.248040\pi$
$402$	−1.41997	−	8.05304i	−0.0708216	−	0.401649i
$403$	−15.3946	−	5.60318i	−0.766861	−	0.279114i
$404$	15.8598	−	5.77249i	0.789053	−	0.287192i
$405$	−2.93967	−	1.06995i	−0.146074	−	0.0531664i
$406$	23.2986	−	19.5499i	1.15629	−	0.970244i
$407$	−1.11587	+	0.406142i	−0.0553114	+	0.0201317i
$408$	−1.06342	+	1.84190i	−0.0526472	+	0.0911877i
$409$	−1.45345	+	8.24291i	−0.0718684	+	0.407586i	0.927557	+	0.373682i	$0.121905\pi$
$409$	−1.45345	+	8.24291i	−0.0718684	+	0.407586i	−0.999425	+	0.0339034i	$0.989206\pi$
$410$	−5.64714	+	4.73851i	−0.278892	+	0.234018i
$411$	6.52780			0.321993
$412$	21.9438	−	18.4130i	1.08109	−	0.907144i
$413$	−7.52020	+	2.73713i	−0.370045	+	0.134685i
$414$	0.00757928	+	0.0131277i	0.000372501	+	0.000645191i
$415$	0.223958	+	1.27013i	0.0109937	+	0.0623483i
$416$	22.5841			1.10728
$417$	15.2039	+	26.3339i	0.744538	+	1.28958i
$418$	0.404408	−	2.29351i	0.0197803	−	0.112179i
$419$	−2.82128	+	16.0003i	−0.137829	+	0.781664i	0.835020	+	0.550220i	$0.185456\pi$
$419$	−2.82128	+	16.0003i	−0.137829	+	0.781664i	−0.972848	+	0.231444i	$0.925655\pi$
$420$	−2.29662	+	0.835902i	−0.112064	+	0.0407878i
$421$	−9.09149	−	15.7469i	−0.443092	−	0.767458i	0.554825	−	0.831967i	$-0.312785\pi$
$421$	−9.09149	−	15.7469i	−0.443092	−	0.767458i	−0.997917	+	0.0645090i	$0.979452\pi$
$422$	−39.5496	−	33.1861i	−1.92525	−	1.61547i
$423$	0.227432	+	0.0827786i	0.0110581	+	0.00402483i
$424$	−0.0875635	−	0.0734745i	−0.00425246	−	0.00356824i
$425$	20.6070	+	17.2913i	0.999587	+	0.838753i
$426$	5.84030	−	4.90060i	0.282964	−	0.237435i
$427$	−1.53052	−	8.67999i	−0.0740669	−	0.420054i
$428$	33.6242			1.62529
$429$	0.390283	+	0.675991i	0.0188431	+	0.0326371i
$430$	−1.23106	+	2.13225i	−0.0593668	+	0.102826i
$431$	0.0414026	−	0.0717115i	0.00199429	−	0.00345422i	−0.865027	−	0.501726i	$-0.832699\pi$
$431$	0.0414026	−	0.0717115i	0.00199429	−	0.00345422i	0.867021	+	0.498272i	$0.166032\pi$
$432$	15.0801	+	12.6537i	0.725542	+	0.608802i
$433$	−0.496678	−	2.81680i	−0.0238688	−	0.135367i	0.970545	−	0.240921i	$-0.0774495\pi$
$433$	−0.496678	−	2.81680i	−0.0238688	−	0.135367i	−0.994414	+	0.105554i	$0.966338\pi$
$434$	−21.3643	−	7.77598i	−1.02552	−	0.373259i
$435$	2.37591	−	4.11519i	0.113916	−	0.197308i
$436$	4.14406	−	23.5021i	0.198465	−	1.12555i
$437$	−1.51793			−0.0726125
$438$	27.0793	+	12.5074i	1.29390	+	0.597629i
$439$	−4.76226			−0.227290			−0.113645	−	0.993521i	$-0.536253\pi$
$439$	−4.76226			−0.227290			−0.113645	+	0.993521i	$0.536253\pi$
$440$	−0.00221912	+	0.0125853i	−0.000105792	+	0.000599979i
$441$	−0.0582966	+	0.100973i	−0.00277603	+	0.00480823i
$442$	−29.3581	−	10.6855i	−1.39642	−	0.508256i
$443$	5.57020	+	31.5902i	0.264648	+	1.50089i	0.770035	+	0.638001i	$0.220238\pi$
$443$	5.57020	+	31.5902i	0.264648	+	1.50089i	−0.505387	+	0.862893i	$0.668650\pi$
$444$	−20.3710	−	17.0933i	−0.966764	−	0.811211i
$445$	−2.74487	+	4.75426i	−0.130119	+	0.225373i
$446$	−10.8618	+	18.8131i	−0.514319	+	0.890826i
$447$	12.4075	+	21.4904i	0.586855	+	1.01646i
$448$	16.9365			0.800176
$449$	−1.02172	−	5.79446i	−0.0482179	−	0.273457i	0.951161	−	0.308695i	$-0.0998923\pi$
$449$	−1.02172	−	5.79446i	−0.0482179	−	0.273457i	−0.999379	+	0.0352377i	$0.988781\pi$
$450$	−0.264054	+	0.221568i	−0.0124476	+	0.0104448i
$451$	1.28511	+	1.07833i	0.0605133	+	0.0507767i
$452$	−10.8874	−	9.13561i	−0.512100	−	0.429703i
$453$	24.1712	+	8.79758i	1.13566	+	0.413346i
$454$	5.75432	+	4.82845i	0.270064	+	0.226610i
$455$	−0.939303	−	1.62692i	−0.0440352	−	0.0762712i
$456$	2.56445	−	0.933382i	0.120091	−	0.0437096i
$457$	2.37170	−	13.4506i	0.110943	−	0.629190i	−0.877736	−	0.479145i	$-0.840947\pi$
$457$	2.37170	−	13.4506i	0.110943	−	0.629190i	0.988679	−	0.150046i	$-0.0479420\pi$
$458$	2.73638	−	15.5188i	0.127863	−	0.725144i
$459$	−14.4146	−	24.9669i	−0.672817	−	1.16535i
$460$	0.159179			0.00742177
$461$	−5.78438	−	32.8048i	−0.269405	−	1.52787i	−0.756190	−	0.654352i	$-0.772941\pi$
$461$	−5.78438	−	32.8048i	−0.269405	−	1.52787i	0.486785	−	0.873522i	$-0.338170\pi$
$462$	0.541627	+	0.938126i	0.0251988	+	0.0436456i
$463$	−1.26102	+	0.458973i	−0.0586045	+	0.0213303i	−0.371156	−	0.928571i	$-0.621039\pi$
$463$	−1.26102	+	0.458973i	−0.0586045	+	0.0213303i	0.312552	+	0.949901i	$0.398816\pi$
$464$	−22.6398	+	18.9970i	−1.05103	+	0.881916i
$465$	−3.55211			−0.164725
$466$	32.0650	−	26.9057i	1.48538	−	1.24638i
$467$	−5.08618	+	28.8452i	−0.235360	+	1.33479i	0.606493	+	0.795089i	$0.292576\pi$
$467$	−5.08618	+	28.8452i	−0.235360	+	1.33479i	−0.841854	+	0.539706i	$0.818535\pi$
$468$	0.102772	−	0.178006i	0.00475063	−	0.00822833i
$469$	4.20854	−	1.53178i	0.194332	−	0.0707311i
$470$	3.79197	−	3.18184i	0.174911	−	0.146767i
$471$	−15.2725	−	5.55873i	−0.703719	−	0.256133i
$472$	−0.880578	+	0.320504i	−0.0405319	+	0.0147524i
$473$	0.526508	+	0.191633i	0.0242089	+	0.00881130i
$474$	−2.12200	−	12.0345i	−0.0974669	−	0.552762i
$475$	−5.99382	−	33.9926i	−0.275015	−	1.55969i
$476$	−20.9186	−	7.61373i	−0.958801	−	0.348975i
$477$	0.0167271	−	0.00608815i	0.000765879	−	0.000278757i
$478$	23.3866	+	8.51204i	1.06968	+	0.389331i
$479$	−7.42958	+	6.23416i	−0.339466	+	0.284846i	−0.796544	−	0.604581i	$-0.793341\pi$
$479$	−7.42958	+	6.23416i	−0.339466	+	0.284846i	0.457077	+	0.889427i	$0.348896\pi$
$480$	4.60143	−	1.67478i	0.210026	−	0.0764431i
$481$	10.2202	−	17.7019i	0.466002	−	0.807139i
$482$	−0.893823	+	5.06912i	−0.0407125	+	0.230892i
$483$	0.540862	−	0.453837i	0.0246101	−	0.0206503i
$484$	−23.1592			−1.05269
$485$	2.96769	−	2.49019i	0.134756	−	0.113074i
$486$	0.690281	−	0.251242i	0.0313118	−	0.0113965i
$487$	−2.86108	−	4.95554i	−0.129648	−	0.224557i	0.793892	−	0.608059i	$-0.208051\pi$
$487$	−2.86108	−	4.95554i	−0.129648	−	0.224557i	−0.923540	+	0.383502i	$0.874718\pi$
$488$	−0.179216	−	1.01638i	−0.00811273	−	0.0460096i
$489$	−4.18102			−0.189072
$490$	1.19231	+	2.06514i	0.0538630	+	0.0932934i
$491$	−3.20663	+	18.1857i	−0.144713	+	0.820708i	0.822884	+	0.568209i	$0.192364\pi$
$491$	−3.20663	+	18.1857i	−0.144713	+	0.820708i	−0.967597	+	0.252499i	$0.918748\pi$
$492$	−6.52360	+	36.9972i	−0.294107	+	1.66796i
$493$	40.6713	−	14.8031i	1.83174	−	0.666699i
$494$	20.0440	+	34.7172i	0.901821	+	1.56200i
$495$	−0.00152451	−	0.00127921i	−6.85215e−5	−	5.74963e-5i
$496$	20.7602	+	7.55610i	0.932161	+	0.339279i
$497$	3.19869	+	2.68402i	0.143481	+	0.120395i
$498$	9.80641	+	8.22855i	0.439436	+	0.368730i
$499$	−0.0161325	+	0.0135368i	−0.000722189	+	0.000605989i	−0.643149	−	0.765741i	$-0.722372\pi$
$499$	−0.0161325	+	0.0135368i	−0.000722189	+	0.000605989i	0.642426	+	0.766347i	$0.277928\pi$
$500$	1.27304	+	7.21978i	0.0569322	+	0.322878i
$501$	−20.6616			−0.923093
$502$	−5.14025	−	8.90317i	−0.229420	−	0.397368i
$503$	10.2243	−	17.7091i	0.455881	−	0.789609i	−0.542857	−	0.839825i	$-0.682658\pi$
$503$	10.2243	−	17.7091i	0.455881	−	0.789609i	0.998738	+	0.0502158i	$0.0159909\pi$
$504$	0.00746312	−	0.0129265i	0.000332434	−	0.000575792i
$505$	2.15477	+	1.80807i	0.0958860	+	0.0804579i
$506$	−0.0122513	−	0.0694808i	−0.000544639	−	0.00308880i
$507$	8.40960	+	3.06084i	0.373483	+	0.135937i
$508$	−15.3645	+	26.6122i	−0.681692	+	1.18072i
$509$	0.996070	−	5.64900i	0.0441500	−	0.250387i	−0.954743	−	0.297433i	$-0.903870\pi$
$509$	0.996070	−	5.64900i	0.0441500	−	0.250387i	0.998893	+	0.0470457i	$0.0149806\pi$
$510$	−6.77400			−0.299958
$511$	−4.17077	+	15.7953i	−0.184504	+	0.698744i
$512$	−32.1423			−1.42050
$513$	−6.42357	+	36.4298i	−0.283607	+	1.60842i
$514$	−3.09803	+	5.36594i	−0.136648	+	0.236681i
$515$	4.48620	+	1.63284i	0.197686	+	0.0719517i
$516$	2.17882	+	12.3567i	0.0959171	+	0.543973i
$517$	−0.862931	−	0.724085i	−0.0379516	−	0.0318452i
$518$	14.1834	−	24.5664i	0.623183	−	1.07939i
$519$	10.7339	−	18.5917i	0.471168	−	0.816087i
$520$	−0.109988	−	0.190505i	−0.00482329	−	0.00835418i
$521$	23.5644			1.03237			0.516187	−	0.856476i	$-0.327351\pi$
$521$	23.5644			1.03237			0.516187	+	0.856476i	$0.327351\pi$
$522$	0.0963053	+	0.546175i	0.00421517	+	0.0239054i
$523$	0.117193	−	0.0983364i	0.00512448	−	0.00429995i	−0.640222	−	0.768190i	$-0.721158\pi$
$523$	0.117193	−	0.0983364i	0.00512448	−	0.00429995i	0.645346	+	0.763890i	$0.276713\pi$
$524$	16.1033	+	13.5122i	0.703475	+	0.590285i
$525$	12.2989	+	10.3200i	0.536770	+	0.450404i
$526$	−46.4268	−	16.8980i	−2.02431	−	0.736787i
$527$	−24.7847	−	20.7968i	−1.07964	−	0.905923i
$528$	−0.526311	−	0.911598i	−0.0229048	−	0.0396722i
$529$	21.5697	−	7.85074i	0.937814	−	0.341336i
$530$	0.0632192	−	0.358534i	0.00274606	−	0.0155737i
$531$	0.0253406	−	0.143714i	0.00109969	−	0.00623665i
$532$	14.2820	+	24.7371i	0.619202	+	1.07249i
$533$	−28.8768			−1.25079
$534$	9.46196	+	53.6614i	0.409459	+	2.32216i
$535$	2.80193	+	4.85309i	0.121138	+	0.209817i
$536$	0.492799	−	0.179364i	0.0212857	−	0.00774736i
$537$	−27.3273	+	22.9303i	−1.17926	+	0.989516i
$538$	20.6174			0.888878
$539$	0.415703	−	0.348816i	0.0179056	−	0.0150246i
$540$	0.673613	−	3.82025i	0.0289877	−	0.164397i
$541$	9.09656	−	15.7557i	0.391092	−	0.677391i	−0.601502	−	0.798871i	$-0.705431\pi$
$541$	9.09656	−	15.7557i	0.391092	−	0.677391i	0.992594	+	0.121480i	$0.0387642\pi$
$542$	−36.4046	+	13.2502i	−1.56371	+	0.569144i
$543$	−23.0572	+	19.3473i	−0.989479	+	0.830271i
$544$	41.9117	+	15.2546i	1.79695	+	0.654036i
$545$	3.73747	−	1.36033i	0.160096	−	0.0582700i
$546$	−17.5219	−	6.37744i	−0.749867	−	0.272929i
$547$	−5.08582	−	28.8431i	−0.217454	−	1.23324i	−0.876597	−	0.481225i	$-0.840192\pi$
$547$	−5.08582	−	28.8431i	−0.217454	−	1.23324i	0.659144	−	0.752017i	$-0.270919\pi$
$548$	1.38927	+	7.87894i	0.0593467	+	0.336572i
$549$	0.151028	+	0.0549696i	0.00644571	+	0.00234605i
$550$	1.50758	−	0.548715i	0.0642835	−	0.0233973i
$551$	−52.1867	−	18.9944i	−2.22323	−	0.809189i
$552$	0.0633323	−	0.0531421i	0.00269560	−	0.00226188i
$553$	6.28924	−	2.28910i	0.267446	−	0.0973423i
$554$	22.8738	−	39.6187i	0.971817	−	1.68324i
$555$	0.769598	−	4.36461i	0.0326676	−	0.185267i
$556$	−28.5488	+	23.9553i	−1.21074	+	1.01593i
$557$	9.11623			0.386267			0.193133	−	0.981172i	$-0.438135\pi$
$557$	9.11623			0.386267			0.193133	+	0.981172i	$0.438135\pi$
$558$	0.317586	−	0.266486i	0.0134445	−	0.0112813i
$559$	−9.06294	+	3.29864i	−0.383321	+	0.139518i
$560$	1.26668	+	2.19396i	0.0535272	+	0.0927118i
$561$	0.267686	+	1.51812i	0.0113017	+	0.0640953i
$562$	16.4388			0.693428
$563$	15.3008	+	26.5017i	0.644851	+	1.11691i	0.984336	+	0.176303i	$0.0564139\pi$
$563$	15.3008	+	26.5017i	0.644851	+	1.11691i	−0.339485	+	0.940612i	$0.610253\pi$
$564$	4.38050	−	24.8431i	0.184452	−	1.04608i
$565$	0.411316	−	2.33269i	0.0173042	−	0.0981371i
$566$	10.3824	−	3.77889i	0.436405	−	0.158838i
$567$	−8.50313	−	14.7279i	−0.357098	−	0.618512i
$568$	0.374551	+	0.314286i	0.0157158	+	0.0131871i
$569$	−42.7919	−	15.5750i	−1.79393	−	0.652937i	−0.998926	−	0.0463337i	$-0.985246\pi$
$569$	−42.7919	−	15.5750i	−1.79393	−	0.652937i	−0.795004	−	0.606604i	$-0.792532\pi$
$570$	6.65842	+	5.58708i	0.278891	+	0.234017i
$571$	−16.7110	−	14.0222i	−0.699334	−	0.586811i	0.222250	−	0.974990i	$-0.428660\pi$
$571$	−16.7110	−	14.0222i	−0.699334	−	0.586811i	−0.921584	+	0.388179i	$0.873104\pi$
$572$	−0.732847	+	0.614932i	−0.0306419	+	0.0257116i
$573$	5.42343	+	30.7578i	0.226567	+	1.28493i
$574$	−40.0747			−1.67268
$575$	−0.522838	−	0.905582i	−0.0218039	−	0.0377654i
$576$	−0.154418	+	0.267460i	−0.00643409	+	0.0111442i
$577$	0.825769	−	1.43027i	0.0343772	−	0.0595431i	−0.848325	−	0.529476i	$-0.822389\pi$
$577$	0.825769	−	1.43027i	0.0343772	−	0.0595431i	0.882702	+	0.469933i	$0.155722\pi$
$578$	−20.8626	−	17.5058i	−0.867770	−	0.728145i
$579$	−4.60425	−	26.1120i	−0.191346	−	1.08518i
$580$	5.47261	+	1.99187i	0.227238	+	0.0827078i
$581$	−3.50560	+	6.07188i	−0.145437	+	0.251904i
$582$	6.67719	−	37.8682i	0.276778	−	1.56969i
$583$	−0.0828494			−0.00343127
$584$	−0.488376	+	1.84956i	−0.0202092	+	0.0765352i
$585$	0.0342562			0.00141632
$586$	11.0164	−	62.4773i	0.455085	−	2.58091i
$587$	6.05045	−	10.4797i	0.249729	−	0.432543i	−0.713722	−	0.700429i	$-0.752992\pi$
$587$	6.05045	−	10.4797i	0.249729	−	0.432543i	0.963451	+	0.267886i	$0.0863252\pi$
$588$	11.4195	+	4.15635i	0.470932	+	0.171405i
$589$	7.20894	+	40.8840i	0.297039	+	1.68459i
$590$	−2.28637	−	1.91849i	−0.0941282	−	0.0789829i
$591$	−8.35066	+	14.4638i	−0.343500	+	0.594960i
$592$	−13.7823	+	23.8717i	−0.566451	+	0.981121i
$593$	23.0381	+	39.9031i	0.946059	+	1.63862i	0.753616	+	0.657315i	$0.228308\pi$
$593$	23.0381	+	39.9031i	0.946059	+	1.63862i	0.192443	+	0.981308i	$0.438359\pi$
$594$	−1.71936			−0.0705463
$595$	−0.644246	−	3.65370i	−0.0264115	−	0.149787i
$596$	−23.2980	+	19.5493i	−0.954321	+	0.800771i
$597$	−31.1013	−	26.0971i	−1.27289	−	1.06808i
$598$	0.930318	+	0.780630i	0.0380436	+	0.0319223i
$599$	33.6502	+	12.2477i	1.37491	+	0.500427i	0.920632	−	0.390433i	$-0.127675\pi$
$599$	33.6502	+	12.2477i	1.37491	+	0.500427i	0.454279	+	0.890859i	$0.349897\pi$
$600$	1.44015	+	1.20843i	0.0587938	+	0.0493338i
$601$	15.6425	+	27.0937i	0.638072	+	1.10517i	0.985855	+	0.167599i	$0.0536013\pi$
$601$	15.6425	+	27.0937i	0.638072	+	1.10517i	−0.347783	+	0.937575i	$0.613065\pi$
$602$	−12.5774	+	4.57778i	−0.512615	+	0.186577i
$603$	−0.0141814	+	0.0804267i	−0.000577511	+	0.00327523i
$604$	−5.47433	+	31.0465i	−0.222747	+	1.26326i
$605$	−1.92987	−	3.34264i	−0.0784605	−	0.135898i
$606$	27.9194			1.13415
$607$	−4.76640	−	27.0316i	−0.193462	−	1.09718i	−0.914591	−	0.404379i	$-0.867488\pi$
$607$	−4.76640	−	27.0316i	−0.193462	−	1.09718i	0.721129	−	0.692801i	$-0.243623\pi$
$608$	−28.6149	−	49.5624i	−1.16049	−	2.01002i
$609$	24.2740	−	8.83500i	0.983630	−	0.358012i
$610$	2.51808	−	2.11292i	0.101954	−	0.0855497i
$611$	19.3904			0.784450
$612$	0.310959	−	0.260926i	0.0125698	−	0.0105473i
$613$	1.08385	−	6.14684i	0.0437764	−	0.248268i	−0.955065	−	0.296397i	$-0.904215\pi$
$613$	1.08385	−	6.14684i	0.0437764	−	0.248268i	0.998841	+	0.0481289i	$0.0153258\pi$
$614$	17.4395	−	30.2061i	0.703801	−	1.21902i
$615$	−5.88354	+	2.14143i	−0.237247	+	0.0863509i
$616$	−0.0532182	+	0.0446554i	−0.00214422	+	0.00179922i
$617$	−24.3733	−	8.87116i	−0.981233	−	0.357140i	−0.198913	−	0.980017i	$-0.563741\pi$
$617$	−24.3733	−	8.87116i	−0.981233	−	0.357140i	−0.782319	+	0.622878i	$0.785963\pi$
$618$	44.5284	−	16.2070i	1.79120	−	0.651942i
$619$	−34.4402	−	12.5352i	−1.38427	−	0.503833i	−0.460800	−	0.887504i	$-0.652437\pi$
$619$	−34.4402	−	12.5352i	−1.38427	−	0.503833i	−0.923470	+	0.383671i	$0.874660\pi$
$620$	−0.755973	−	4.28733i	−0.0303606	−	0.172184i
$621$	0.194599	+	1.10362i	0.00780897	+	0.0442869i
$622$	2.01144	+	0.732105i	0.0806515	+	0.0293547i
$623$	−28.0436	+	10.2070i	−1.12354	+	0.408936i
$624$	17.0264	+	6.19710i	0.681601	+	0.248083i
$625$	17.7413	−	14.8867i	0.709652	−	0.595469i
$626$	10.6737	−	3.88491i	0.426607	−	0.155272i
$627$	0.989004	−	1.71301i	0.0394970	−	0.0684109i
$628$	3.45894	−	19.6167i	0.138027	−	0.782790i
$629$	30.9236	−	25.9480i	1.23301	−	1.03461i
$630$	0.0475401			0.00189404
$631$	−30.3060	+	25.4298i	−1.20646	+	1.01234i	−0.207043	+	0.978332i	$0.566384\pi$
$631$	−30.3060	+	25.4298i	−1.20646	+	1.01234i	−0.999421	+	0.0340116i	$0.989172\pi$
$632$	0.736440	−	0.268042i	0.0292940	−	0.0106621i
$633$	−21.9249	−	37.9750i	−0.871435	−	1.50937i
$634$	4.37465	+	24.8099i	0.173740	+	0.985326i
$635$	−5.12136			−0.203235
$636$	−0.927665	−	1.60676i	−0.0367843	−	0.0637123i
$637$	−1.62205	+	9.19909i	−0.0642679	+	0.364481i
$638$	0.448235	−	2.54207i	0.0177458	−	0.100641i
$639$	−0.0715497	+	0.0260419i	−0.00283046	+	0.00103020i
$640$	0.314519	+	0.544762i	0.0124324	+	0.0215336i
$641$	14.5420	+	12.2022i	0.574376	+	0.481959i	0.883095	−	0.469195i	$-0.155456\pi$
$641$	14.5420	+	12.2022i	0.574376	+	0.481959i	−0.308719	+	0.951153i	$0.599900\pi$
$642$	52.2675	+	19.0238i	2.06283	+	0.750810i
$643$	22.2511	+	18.6709i	0.877496	+	0.736307i	0.965663	−	0.259799i	$-0.0836564\pi$
$643$	22.2511	+	18.6709i	0.877496	+	0.736307i	−0.0881667	+	0.996106i	$0.528101\pi$
$644$	0.662882	+	0.556224i	0.0261212	+	0.0219183i
$645$	−1.60192	+	1.34417i	−0.0630755	+	0.0529266i
$646$	13.7477	+	77.9671i	0.540896	+	3.06757i
$647$	12.1693			0.478425			0.239212	−	0.970967i	$-0.423111\pi$
$647$	12.1693			0.478425			0.239212	+	0.970967i	$0.423111\pi$
$648$	−0.995675	−	1.72456i	−0.0391138	−	0.0677471i
$649$	−0.339604	+	0.588211i	−0.0133306	+	0.0230893i
$650$	−13.8079	+	23.9161i	−0.541592	+	0.938065i
$651$	−14.7923	−	12.4122i	−0.579756	−	0.486473i
$652$	−0.889820	−	5.04642i	−0.0348480	−	0.197633i
$653$	28.6472	+	10.4267i	1.12105	+	0.408030i	0.835036	−	0.550195i	$-0.185446\pi$
$653$	28.6472	+	10.4267i	1.12105	+	0.408030i	0.286017	+	0.958225i	$0.407669\pi$
$654$	19.7388	−	34.1886i	0.771847	−	1.33688i
$655$	−0.608368	+	3.45022i	−0.0237709	+	0.134811i
$656$	38.9414			1.52041
$657$	−0.211411	−	0.209877i	−0.00824794	−	0.00818810i
$658$	26.9096			1.04904
$659$	−5.18946	+	29.4309i	−0.202153	+	1.14646i	0.699705	+	0.714432i	$0.253315\pi$
$659$	−5.18946	+	29.4309i	−0.202153	+	1.14646i	−0.901858	+	0.432033i	$0.857796\pi$
$660$	−0.103713	+	0.179636i	−0.00403702	+	0.00699232i
$661$	33.4989	+	12.1926i	1.30296	+	0.474238i	0.897959	−	0.440080i	$-0.145050\pi$
$661$	33.4989	+	12.1926i	1.30296	+	0.474238i	0.404998	+	0.914317i	$0.367272\pi$
$662$	0.930474	+	5.27698i	0.0361639	+	0.205096i
$663$	−20.3270	−	17.0564i	−0.789437	−	0.662416i
$664$	−0.410489	+	0.710988i	−0.0159301	+	0.0275917i
$665$	−2.38026	+	4.12273i	−0.0923025	+	0.159873i
$666$	0.258633	+	0.447966i	0.0100218	+	0.0173583i
$667$	−1.68243			−0.0651441
$668$	−4.39728	−	24.9382i	−0.170136	−	0.964888i
$669$	−14.1339	+	11.8598i	−0.546448	+	0.458525i
$670$	1.27952	+	1.07365i	0.0494322	+	0.0414786i
$671$	−0.573035	−	0.480833i	−0.0221218	−	0.0185624i
$672$	25.0143	+	9.10446i	0.964947	+	0.351212i
$673$	25.9142	+	21.7446i	0.998920	+	0.838193i	0.986834	−	0.161734i	$-0.0517085\pi$
$673$	25.9142	+	21.7446i	0.998920	+	0.838193i	0.0120855	+	0.999927i	$0.496153\pi$
$674$	−29.5075	−	51.1085i	−1.13659	−	1.96863i
$675$	−23.9462	+	8.71571i	−0.921690	+	0.335468i
$676$	−1.90462	+	10.8017i	−0.0732547	+	0.415448i
$677$	−1.86386	+	10.5705i	−0.0716340	+	0.406256i	0.927814	+	0.373042i	$0.121685\pi$
$677$	−1.86386	+	10.5705i	−0.0716340	+	0.406256i	−0.999448	+	0.0332141i	$0.989426\pi$
$678$	−11.7553	−	20.3608i	−0.451460	−	0.781952i
$679$	21.0601			0.808212
$680$	−0.0754381	−	0.427831i	−0.00289292	−	0.0164066i
$681$	3.18998	+	5.52521i	0.122240	+	0.211727i
$682$	−1.81321	+	0.659955i	−0.0694315	+	0.0252710i
$683$	9.13799	−	7.66768i	0.349655	−	0.293396i	−0.450996	−	0.892526i	$-0.648931\pi$
$683$	9.13799	−	7.66768i	0.349655	−	0.293396i	0.800652	+	0.599130i	$0.204487\pi$
$684$	−0.520861			−0.0199156
$685$	−1.02142	+	0.857077i	−0.0390266	+	0.0327472i
$686$	−6.96315	+	39.4900i	−0.265854	+	1.50773i
$687$	6.69197	−	11.5908i	0.255315	−	0.442218i
$688$	12.2217	−	4.44833i	0.465948	−	0.169591i
$689$	1.09246	−	0.916687i	0.0416196	−	0.0349230i
$690$	0.247438	+	0.0900602i	0.00941981	+	0.00342853i
$691$	17.7744	−	6.46937i	0.676171	−	0.246106i	0.0189686	−	0.999820i	$-0.493962\pi$
$691$	17.7744	−	6.46937i	0.676171	−	0.246106i	0.657203	+	0.753714i	$0.271740\pi$
$692$	24.7243	+	8.99892i	0.939878	+	0.342088i
$693$	−0.00187863	−	0.0106542i	−7.13632e−5	−	0.000404721i
$694$	−5.48114	−	31.0851i	−0.208061	−	1.17997i
$695$	−5.83655	−	2.12433i	−0.221393	−	0.0805804i
$696$	2.84236	−	1.03454i	0.107739	−	0.0392140i
$697$	−53.5897	−	19.5050i	−2.02985	−	0.738806i
$698$	−22.7944	+	19.1267i	−0.862779	+	0.723958i
$699$	33.4073	−	12.1593i	1.26358	−	0.459905i
$700$	−9.83860	+	17.0410i	−0.371864	+	0.644088i
$701$	−2.34223	+	13.2834i	−0.0884647	+	0.501708i	0.908090	+	0.418774i	$0.137540\pi$
$701$	−2.34223	+	13.2834i	−0.0884647	+	0.501708i	−0.996555	+	0.0829340i	$0.973571\pi$
$702$	22.6718	−	19.0239i	0.855691	−	0.718010i
$703$	−51.7975			−1.95358
$704$	1.10113	−	0.923956i	0.0415003	−	0.0348229i
$705$	3.95071	−	1.43794i	0.148792	−	0.0541560i
$706$	10.4377	+	18.0787i	0.392829	+	0.680400i
$707$	2.65529	+	15.0589i	0.0998626	+	0.566349i
$708$	−15.2102			−0.571634
$709$	−22.5947	−	39.1352i	−0.848562	−	1.46975i	−0.882492	−	0.470328i	$-0.844136\pi$
$709$	−22.5947	−	39.1352i	−0.848562	−	1.46975i	0.0339298	−	0.999424i	$-0.489198\pi$
$710$	−0.270419	+	1.53362i	−0.0101486	+	0.0575558i
$711$	−0.0211927	+	0.120190i	−0.000794789	+	0.00450747i
$712$	−3.28377	+	1.19519i	−0.123064	+	0.0447917i
$713$	0.628833	+	1.08917i	0.0235500	+	0.0407897i
$714$	−28.2094	−	23.6705i	−1.05571	−	0.885847i
$715$	−0.149824	−	0.0545314i	−0.00560309	−	0.00203936i
$716$	−33.4924	−	28.1034i	−1.25167	−	1.05027i
$717$	16.1925	+	13.5871i	0.604720	+	0.507421i
$718$	−47.8074	+	40.1152i	−1.78416	+	1.49709i
$719$	−2.42907	−	13.7759i	−0.0905889	−	0.513755i	−0.996010	−	0.0892407i	$-0.971556\pi$
$719$	−2.42907	−	13.7759i	−0.0905889	−	0.513755i	0.905421	−	0.424514i	$-0.139555\pi$
$720$	−0.0461958			−0.00172161
$721$	12.9765	+	22.4760i	0.483271	+	0.837050i
$722$	31.5323	−	54.6156i	1.17351	−	2.03258i
$723$	−2.18590	+	3.78608i	−0.0812944	+	0.140806i
$724$	−28.2589	−	23.7121i	−1.05023	−	0.881252i
$725$	−6.64339	−	37.6765i	−0.246729	−	1.39927i
$726$	−36.0001	−	13.1030i	−1.33609	−	0.486296i
$727$	3.24320	−	5.61738i	0.120284	−	0.208337i	−0.799596	−	0.600538i	$-0.794953\pi$
$727$	3.24320	−	5.61738i	0.120284	−	0.208337i	0.919879	+	0.392201i	$0.128286\pi$
$728$	0.207654	−	1.17766i	0.00769617	−	0.0436472i
$729$	27.3065			1.01135
$730$	−5.87935	+	1.59833i	−0.217605	+	0.0591570i
$731$	−19.0471			−0.704483
$732$	2.90890	−	16.4972i	0.107516	−	0.609754i
$733$	3.03958	−	5.26471i	0.112270	−	0.194457i	−0.804415	−	0.594067i	$-0.797521\pi$
$733$	3.03958	−	5.26471i	0.112270	−	0.194457i	0.916685	+	0.399611i	$0.130855\pi$
$734$	21.3298	+	7.76341i	0.787297	+	0.286553i
$735$	0.351696	+	1.99456i	0.0129725	+	0.0735706i
$736$	−1.32813	−	1.11443i	−0.0489554	−	0.0410785i
$737$	0.190053	−	0.329181i	0.00700069	−	0.0121255i
$738$	0.365379	−	0.632855i	0.0134498	−	0.0232957i
$739$	−10.0817	−	17.4620i	−0.370862	−	0.642351i	0.618837	−	0.785520i	$-0.287604\pi$
$739$	−10.0817	−	17.4620i	−0.370862	−	0.642351i	−0.989698	+	0.143168i	$0.954271\pi$
$740$	5.43179			0.199677
$741$	5.91238	+	33.5308i	0.217197	+	1.23178i
$742$	1.51610	−	1.27216i	0.0556578	−	0.0467024i
$743$	−24.1056	−	20.2270i	−0.884350	−	0.742058i	0.0827186	−	0.996573i	$-0.473640\pi$
$743$	−24.1056	−	20.2270i	−0.884350	−	0.742058i	−0.967069	+	0.254515i	$0.918084\pi$
$744$	−1.73211	−	1.45341i	−0.0635021	−	0.0532846i
$745$	−4.76305	−	1.73361i	−0.174505	−	0.0635145i
$746$	−11.2410	−	9.43228i	−0.411561	−	0.345340i
$747$	−0.0639243	−	0.110720i	−0.00233887	−	0.00405104i
$748$	−1.77538	+	0.646185i	−0.0649143	+	0.0236269i
$749$	−5.28997	+	30.0009i	−0.193291	+	1.09621i
$750$	−2.10590	+	11.9431i	−0.0768965	+	0.436102i
$751$	14.2023	+	24.5990i	0.518248	+	0.897632i	0.999775	+	0.0212006i	$0.00674888\pi$
$751$	14.2023	+	24.5990i	0.518248	+	0.897632i	−0.481527	+	0.876431i	$0.659918\pi$
$752$	−26.1486			−0.953542
$753$	−1.51622	−	8.59892i	−0.0552542	−	0.313362i
$754$	22.2162	+	38.4796i	0.809066	+	1.40134i
$755$	−4.93722	+	1.79700i	−0.179684	+	0.0653996i
$756$	16.1544	−	13.5551i	0.587528	−	0.492995i
$757$	−22.0087			−0.799918			−0.399959	−	0.916533i	$-0.630976\pi$
$757$	−22.0087			−0.799918			−0.399959	+	0.916533i	$0.630976\pi$
$758$	−18.0584	+	15.1528i	−0.655911	+	0.550374i
$759$	0.0104055	−	0.0590124i	0.000377695	−	0.00214201i
$760$	−0.278717	+	0.482752i	−0.0101101	+	0.0175112i
$761$	−12.3893	+	4.50934i	−0.449112	+	0.163464i	−0.556667	−	0.830736i	$-0.687920\pi$
$761$	−12.3893	+	4.50934i	−0.449112	+	0.163464i	0.107555	+	0.994199i	$0.465698\pi$
$762$	−38.9402	+	32.6747i	−1.41065	+	1.18368i
$763$	20.3176	+	7.39501i	0.735547	+	0.267717i
$764$	−35.9699	+	13.0920i	−1.30134	+	0.473651i
$765$	0.0635728	+	0.0231386i	0.00229848	+	0.000836578i
$766$	3.76182	+	21.3343i	0.135920	+	0.770841i
$767$	−2.03019	−	11.5138i	−0.0733059	−	0.415739i
$768$	−22.7985	−	8.29797i	−0.822669	−	0.299427i
$769$	−12.9524	+	4.71428i	−0.467074	+	0.170001i	−0.564827	−	0.825210i	$-0.691057\pi$
$769$	−12.9524	+	4.71428i	−0.467074	+	0.170001i	0.0977523	+	0.995211i	$0.468835\pi$
$770$	−0.207922	−	0.0756776i	−0.00749300	−	0.00272723i
$771$	−4.03132	+	3.38268i	−0.145184	+	0.121824i
$772$	30.5368	−	11.1145i	1.09905	−	0.400020i
$773$	6.63470	−	11.4916i	0.238633	−	0.413325i	−0.721689	−	0.692218i	$-0.756634\pi$
$773$	6.63470	−	11.4916i	0.238633	−	0.413325i	0.960322	+	0.278892i	$0.0899672\pi$
$774$	0.0423816	−	0.240358i	0.00152338	−	0.00863949i
$775$	−21.9079	+	18.3829i	−0.786954	+	0.660333i
$776$	2.46603			0.0885254
$777$	18.4562	−	15.4866i	0.662114	−	0.555579i
$778$	−44.0260	+	16.0241i	−1.57841	+	0.574493i
$779$	36.5879	+	63.3721i	1.31090	+	2.27054i
$780$	−0.620008	−	3.51624i	−0.0221998	−	0.125902i
$781$	0.354387			0.0126810
$782$	1.19921	+	2.07708i	0.0428835	+	0.0742764i
$783$	−7.11970	+	40.3778i	−0.254437	+	1.44299i
$784$	2.18739	−	12.4053i	0.0781210	−	0.443046i
$785$	3.11957	−	1.13543i	0.111342	−	0.0405253i
$786$	17.3870	+	30.1152i	0.620173	+	1.07417i
$787$	13.5180	+	11.3429i	0.481863	+	0.404331i	0.851100	−	0.525004i	$-0.175936\pi$
$787$	13.5180	+	11.3429i	0.481863	+	0.404331i	−0.369236	+	0.929336i	$0.620381\pi$
$788$	−19.2347	−	7.00087i	−0.685209	−	0.249396i
$789$	−32.1451	−	26.9730i	−1.14440	−	0.960263i
$790$	1.91212	+	1.60446i	0.0680302	+	0.0570841i
$791$	9.86405	−	8.27692i	0.350725	−	0.294293i
$792$	−0.000219978	−	0.00124756i	−7.81659e−6	−	4.43301e-5i
$793$	12.8763			0.457251
$794$	−1.16295	−	2.01428i	−0.0412714	−	0.0714841i
$795$	0.154606	−	0.267786i	0.00548332	−	0.00949738i
$796$	24.8797	−	43.0928i	0.881836	−	1.52738i
$797$	−3.66576	−	3.07594i	−0.129848	−	0.108955i	0.575551	−	0.817766i	$-0.304788\pi$
$797$	−3.66576	−	3.07594i	−0.129848	−	0.108955i	−0.705399	+	0.708811i	$0.749232\pi$
$798$	8.20508	+	46.5333i	0.290457	+	1.64726i
$799$	35.9847	+	13.0974i	1.27305	+	0.463351i
$800$	19.7123	−	34.1427i	0.696934	−	1.20713i
$801$	0.0944977	−	0.535923i	0.00333891	−	0.0189359i
$802$	46.1629			1.63007
$803$	0.590536	+	1.25446i	0.0208396	+	0.0442691i
$804$	8.51209			0.300198
$805$	−0.0250431	+	0.142026i	−0.000882653	+	0.00500577i
$806$	16.6072	−	28.7646i	0.584964	−	1.01319i
$807$	16.4550	+	5.98913i	0.579243	+	0.210827i
$808$	0.310922	+	1.76333i	0.0109382	+	0.0620336i
$809$	−7.63616	−	6.40750i	−0.268473	−	0.225276i	0.498605	−	0.866829i	$-0.333846\pi$
$809$	−7.63616	−	6.40750i	−0.268473	−	0.225276i	−0.767078	+	0.641554i	$0.778290\pi$
$810$	3.17123	−	5.49272i	0.111426	−	0.192995i
$811$	−13.6097	+	23.5727i	−0.477900	+	0.827748i	−0.999679	−	0.0253330i	$-0.991935\pi$
$811$	−13.6097	+	23.5727i	−0.477900	+	0.827748i	0.521779	+	0.853081i	$0.325269\pi$
$812$	15.8298	+	27.4179i	0.555515	+	0.962181i
$813$	−32.9040			−1.15399
$814$	−0.418062	−	2.37094i	−0.0146530	−	0.0831016i
$815$	0.654217	−	0.548953i	0.0229162	−	0.0192290i
$816$	27.4117	+	23.0012i	0.959603	+	0.805202i
$817$	18.7221	+	15.7097i	0.655005	+	0.549614i
$818$	−15.9463	−	5.80396i	−0.557548	−	0.202931i
$819$	0.142656	+	0.119702i	0.00498479	+	0.00418274i
$820$	−3.83683	−	6.64558i	−0.133988	−	0.232074i
$821$	34.5652	−	12.5807i	1.20633	−	0.439070i	0.340904	−	0.940098i	$-0.389267\pi$
$821$	34.5652	−	12.5807i	1.20633	−	0.439070i	0.865431	+	0.501028i	$0.167045\pi$
$822$	−2.29816	+	13.0335i	−0.0801577	+	0.454597i
$823$	8.60891	−	48.8236i	0.300088	−	1.70188i	−0.345683	−	0.938351i	$-0.612353\pi$
$823$	8.60891	−	48.8236i	0.300088	−	1.70188i	0.645771	−	0.763531i	$-0.276536\pi$
$824$	1.51949	+	2.63183i	0.0529339	+	0.0916841i
$825$	1.36262			0.0474402
$826$	−2.81746	−	15.9786i	−0.0980319	−	0.555966i
$827$	1.76912	+	3.06421i	0.0615184	+	0.106553i	0.895144	−	0.445776i	$-0.147072\pi$
$827$	1.76912	+	3.06421i	0.0615184	+	0.106553i	−0.833626	+	0.552329i	$0.813739\pi$
$828$	−0.0148276	+	0.00539681i	−0.000515295	+	0.000187552i
$829$	29.9857	−	25.1610i	1.04145	−	0.873877i	0.0492779	−	0.998785i	$-0.484308\pi$
$829$	29.9857	−	25.1610i	1.04145	−	0.873877i	0.992168	+	0.124908i	$0.0398636\pi$
$830$	−2.61482			−0.0907616
$831$	29.7647	−	24.9756i	1.03253	−	0.866392i
$832$	−4.29654	+	24.3669i	−0.148956	+	0.844769i
$833$	−9.22378	+	15.9761i	−0.319585	+	0.553538i
$834$	−57.9315	+	21.0853i	−2.00600	+	0.730125i
$835$	3.23298	−	2.71279i	0.111882	−	0.0938801i
$836$	2.27805	+	0.829143i	0.0787880	+	0.0286765i
$837$	28.8008	−	10.4826i	0.995502	−	0.362333i
$838$	−30.9532	−	11.2660i	−1.06926	−	0.389179i
$839$	−0.275624	−	1.56314i	−0.00951561	−	0.0539657i	0.979680	−	0.200566i	$-0.0642780\pi$
$839$	−0.275624	−	1.56314i	−0.00951561	−	0.0539657i	−0.989196	+	0.146600i	$0.953167\pi$
$840$	−0.0450240	−	0.255344i	−0.00155347	−	0.00881019i
$841$	−30.5912	−	11.1343i	−1.05487	−	0.383941i
$842$	34.6413	−	12.6084i	1.19382	−	0.434515i
$843$	13.1200	+	4.77529i	0.451877	+	0.164470i
$844$	41.1690	−	34.5449i	1.41709	−	1.18908i
$845$	−1.71775	+	0.625210i	−0.0590924	+	0.0215079i
$846$	−0.245347	+	0.424953i	−0.00843519	+	0.0146102i
$847$	3.64355	−	20.6636i	0.125194	−	0.710009i
$848$	−1.47323	+	1.23619i	−0.0505909	+	0.0424508i
$849$	9.38406			0.322060
$850$	−41.7791	+	35.0568i	−1.43301	+	1.20244i
$851$	−1.47455	+	0.536691i	−0.0505468	+	0.0183975i
$852$	3.96807	+	6.87290i	0.135944	+	0.235462i
$853$	−4.13333	−	23.4413i	−0.141522	−	0.802613i	−0.970094	−	0.242730i	$-0.921957\pi$
$853$	−4.13333	−	23.4413i	−0.141522	−	0.802613i	0.828572	−	0.559883i	$-0.189154\pi$
$854$	17.8695			0.611480
$855$	−0.0434038	−	0.0751776i	−0.00148438	−	0.00257102i
$856$	−0.619430	+	3.51296i	−0.0211717	+	0.120070i
$857$	−3.81753	+	21.6503i	−0.130404	+	0.739559i	0.847546	+	0.530722i	$0.178079\pi$
$857$	−3.81753	+	21.6503i	−0.130404	+	0.739559i	−0.977950	+	0.208837i	$0.933032\pi$
$858$	−1.48710	+	0.541259i	−0.0507687	+	0.0184783i
$859$	15.2806	+	26.4668i	0.521367	+	0.903034i	0.999691	+	0.0248510i	$0.00791113\pi$
$859$	15.2806	+	26.4668i	0.521367	+	0.903034i	−0.478324	+	0.878183i	$0.658756\pi$
$860$	−1.96331	−	1.64742i	−0.0669485	−	0.0561764i
$861$	−31.9841	−	11.6413i	−1.09002	−	0.396733i
$862$	0.128604	+	0.107912i	0.00438028	+	0.00367549i
$863$	6.33612	+	5.31664i	0.215684	+	0.180981i	0.744228	−	0.667925i	$-0.232817\pi$
$863$	6.33612	+	5.31664i	0.215684	+	0.180981i	−0.528544	+	0.848906i	$0.677262\pi$
$864$	−32.3663	+	27.1586i	−1.10112	+	0.923953i
$865$	0.761456	+	4.31843i	0.0258903	+	0.146831i
$866$	5.79894			0.197056
$867$	−11.5655	−	20.0320i	−0.392784	−	0.680321i
$868$	11.8332	−	20.4957i	0.401644	−	0.695668i
$869$	0.284015	−	0.491929i	0.00963456	−	0.0166876i
$870$	7.38001	+	6.19257i	0.250206	+	0.209948i
$871$	1.13616	+	6.44347i	0.0384973	+	0.218329i
$872$	2.37909	+	0.865920i	0.0805663	+	0.0293237i
$873$	−0.192014	+	0.332579i	−0.00649870	+	0.0112561i
$874$	0.534400	−	3.03073i	0.0180763	−	0.102516i
$875$	−6.64207			−0.224543
$876$	−17.7166	+	25.4990i	−0.598587	+	0.861530i
$877$	29.4106			0.993124			0.496562	−	0.868001i	$-0.334595\pi$
$877$	29.4106			0.993124			0.496562	+	0.868001i	$0.334595\pi$
$878$	1.67659	−	9.50843i	0.0565823	−	0.320894i
$879$	26.9413	−	46.6637i	0.908708	−	1.57393i
$880$	0.202043	+	0.0735376i	0.00681086	+	0.00247895i
$881$	0.586989	+	3.32898i	0.0197762	+	0.112156i	0.993098	−	0.117288i	$-0.0374202\pi$
$881$	0.586989	+	3.32898i	0.0197762	+	0.112156i	−0.973322	+	0.229445i	$0.926309\pi$
$882$	−0.181080	−	0.151944i	−0.00609729	−	0.00511624i
$883$	10.7862	−	18.6823i	0.362985	−	0.628709i	−0.625465	−	0.780252i	$-0.715091\pi$
$883$	10.7862	−	18.6823i	0.362985	−	0.628709i	0.988451	+	0.151543i	$0.0484242\pi$
$884$	16.2607	−	28.1644i	0.546907	−	0.947270i
$885$	−1.26748	−	2.19533i	−0.0426058	−	0.0737954i
$886$	−65.0345			−2.18488
$887$	−3.67601	−	20.8477i	−0.123428	−	0.699998i	−0.982229	−	0.187687i	$-0.939901\pi$
$887$	−3.67601	−	20.8477i	−0.123428	−	0.699998i	0.858800	−	0.512310i	$-0.171210\pi$
$888$	2.16114	−	1.81341i	0.0725230	−	0.0608540i
$889$	−21.3272	−	17.8957i	−0.715293	−	0.600202i
$890$	−8.52609	−	7.15424i	−0.285795	−	0.239811i
$891$	−1.35629	−	0.493651i	−0.0454376	−	0.0165379i
$892$	−17.3225	−	14.5353i	−0.580001	−	0.486679i
$893$	−24.5683	−	42.5535i	−0.822145	−	1.42400i
$894$	−47.2764	+	17.2072i	−1.58116	+	0.575494i
$895$	1.26531	−	7.17594i	0.0422947	−	0.239865i
$896$	−0.593802	+	3.36762i	−0.0198375	+	0.112504i
$897$	0.515734	+	0.893278i	0.0172199	+	0.0298257i
$898$	11.9290			0.398077
$899$	7.99019	+	45.3146i	0.266488	+	1.51133i
$900$	−0.179406	−	0.310740i	−0.00598020	−	0.0103580i
$901$	2.64658	−	0.963277i	0.0881704	−	0.0320914i
$902$	−2.60545	+	2.18623i	−0.0867521	+	0.0727936i
$903$	−11.3679			−0.378302
$904$	1.15503	−	0.969187i	0.0384158	−	0.0322347i
$905$	1.06760	−	6.05465i	0.0354882	−	0.201263i
$906$	−26.0751	+	45.1633i	−0.866286	+	1.50045i
$907$	25.2109	−	9.17603i	0.837115	−	0.304685i	0.112340	−	0.993670i	$-0.464166\pi$
$907$	25.2109	−	9.17603i	0.837115	−	0.304685i	0.724776	+	0.688985i	$0.241943\pi$
$908$	−5.98993	+	5.02615i	−0.198783	+	0.166799i
$909$	−0.262018	−	0.0953669i	−0.00869060	−	0.00316312i
$910$	3.57903	−	1.30266i	0.118644	−	0.0431828i
$911$	−3.78209	−	1.37657i	−0.125306	−	0.0456077i	0.278606	−	0.960405i	$-0.410128\pi$
$911$	−3.78209	−	1.37657i	−0.125306	−	0.0456077i	−0.403912	+	0.914798i	$0.632350\pi$
$912$	−7.97306	−	45.2175i	−0.264014	−	1.49730i
$913$	0.103329	+	0.586008i	0.00341969	+	0.0193940i
$914$	26.0207	+	9.47075i	0.860687	+	0.313264i
$915$	2.62349	−	0.954874i	0.0867301	−	0.0315672i
$916$	15.4141	+	5.61029i	0.509298	+	0.185369i
$917$	−14.5897	+	12.2422i	−0.481793	+	0.404272i
$918$	54.9241	−	19.9907i	1.81277	−	0.659793i
$919$	−28.6521	+	49.6270i	−0.945147	+	1.63704i	−0.189690	+	0.981844i	$0.560748\pi$
$919$	−28.6521	+	49.6270i	−0.945147	+	1.63704i	−0.755457	+	0.655198i	$0.772585\pi$
$920$	−0.00293243	+	0.0166306i	−9.66792e−5	+	0.000548295i
$921$	22.6932	−	19.0419i	0.747767	−	0.627451i
$922$	67.5352			2.22415
$923$	−4.67300	+	3.92111i	−0.153814	+	0.129065i
$924$	−1.05960	+	0.385665i	−0.0348584	+	0.0126874i
$925$	−17.8412	−	30.9018i	−0.586614	−	1.01605i
$926$	−0.472443	−	2.67936i	−0.0155254	−	0.0880491i
$927$	−0.473251			−0.0155436
$928$	−31.7159	−	54.9336i	−1.04113	−	1.80328i
$929$	−0.317516	+	1.80072i	−0.0104174	+	0.0590797i	−0.989573	−	0.144030i	$-0.953994\pi$
$929$	−0.317516	+	1.80072i	−0.0104174	+	0.0590797i	0.979156	+	0.203110i	$0.0651049\pi$
$930$	1.25055	−	7.09221i	0.0410071	−	0.232563i
$931$	22.2432	−	8.09586i	0.728991	−	0.265331i
$932$	21.7859	+	37.7342i	0.713619	+	1.23603i
$933$	1.39269	+	1.16860i	0.0455946	+	0.0382584i
$934$	−55.8022	−	20.3103i	−1.82590	−	0.664574i
$935$	−0.241210	−	0.202399i	−0.00788840	−	0.00661916i
$936$	0.0167043	+	0.0140166i	0.000545997	+	0.000458145i
$937$	14.4370	−	12.1141i	0.471635	−	0.395749i	−0.375755	−	0.926719i	$-0.622617\pi$
$937$	14.4370	−	12.1141i	0.471635	−	0.395749i	0.847391	+	0.530970i	$0.178172\pi$
$938$	1.57674	+	8.94212i	0.0514823	+	0.291971i
$939$	9.64733			0.314829
$940$	2.57637	+	4.46241i	0.0840321	+	0.145548i
$941$	8.19494	−	14.1941i	0.267147	−	0.462713i	−0.700977	−	0.713184i	$-0.747252\pi$
$941$	8.19494	−	14.1941i	0.267147	−	0.462713i	0.968124	+	0.250471i	$0.0805856\pi$
$942$	16.4755	−	28.5364i	0.536800	−	0.929765i
$943$	1.69819	+	1.42495i	0.0553006	+	0.0464027i
$944$	2.73779	+	15.5268i	0.0891073	+	0.505353i
$945$	3.30261	+	1.20205i	0.107434	+	0.0391028i
$946$	−0.567980	+	0.983770i	−0.0184666	+	0.0319851i
$947$	1.19781	−	6.79311i	0.0389236	−	0.220747i	−0.959141	−	0.282927i	$-0.908694\pi$
$947$	1.19781	−	6.79311i	0.0389236	−	0.220747i	0.998065	+	0.0621809i	$0.0198056\pi$
$948$	12.7205			0.413142
$949$	−21.6669	−	10.0076i	−0.703338	−	0.324859i
$950$	69.9805			2.27047
$951$	−3.71554	+	21.0719i	−0.120485	+	0.683302i
$952$	1.18083	−	2.04525i	0.0382708	−	0.0662870i
$953$	15.9979	+	5.82276i	0.518223	+	0.188618i	0.587872	−	0.808954i	$-0.299966\pi$
$953$	15.9979	+	5.82276i	0.518223	+	0.188618i	−0.0696494	+	0.997572i	$0.522188\pi$
$954$	0.00626683	+	0.0355409i	0.000202896	+	0.00115068i
$955$	−4.88701	−	4.10069i	−0.158140	−	0.132695i
$956$	−12.9533	+	22.4357i	−0.418939	+	0.725623i
$957$	1.09619	−	1.89865i	0.0354346	−	0.0613746i
$958$	−9.83160	−	17.0288i	−0.317645	−	0.550177i
$959$	−7.24849			−0.234066
$960$	0.931583	+	5.28327i	0.0300667	+	0.170517i
$961$	2.60188	−	2.18324i	0.0839316	−	0.0704269i
$962$	31.7459	+	26.6380i	1.02353	+	0.858844i
$963$	−0.425540	−	0.357070i	−0.0137128	−	0.0115064i
$964$	−5.03495	−	1.83257i	−0.162165	−	0.0590231i
$965$	4.14885	+	3.48130i	0.133556	+	0.112067i
$966$	0.715725	+	1.23967i	0.0230281	+	0.0398858i
$967$	−1.12154	+	0.408206i	−0.0360662	+	0.0131270i	−0.359990	−	0.932956i	$-0.617220\pi$
$967$	−1.12154	+	0.408206i	−0.0360662	+	0.0131270i	0.323924	+	0.946083i	$0.394998\pi$
$968$	0.426642	−	2.41961i	0.0137128	−	0.0777691i
$969$	−11.6764	+	66.2201i	−0.375100	+	2.12730i
$970$	3.92716	+	6.80204i	0.126093	+	0.218400i
$971$	28.4728			0.913735			0.456868	−	0.889535i	$-0.348971\pi$
$971$	28.4728			0.913735			0.456868	+	0.889535i	$0.348971\pi$
$972$	0.132782	+	0.753042i	0.00425897	+	0.0241538i
$973$	−16.8825	−	29.2413i	−0.541227	−	0.937432i
$974$	10.9016	−	3.96786i	0.349310	−	0.127138i
$975$	−17.9677	+	15.0767i	−0.575425	+	0.482839i
$976$	−17.3642			−0.555813
$977$	−35.4226	+	29.7231i	−1.13327	+	0.950926i	−0.999198	−	0.0400459i	$-0.987250\pi$
$977$	−35.4226	+	29.7231i	−1.13327	+	0.950926i	−0.134071	+	0.990972i	$0.542805\pi$
$978$	1.47196	−	8.34791i	0.0470681	−	0.266937i
$979$	−1.26642	+	2.19350i	−0.0404749	+	0.0701045i
$980$	−2.33255	+	0.848980i	−0.0745107	+	0.0271197i
$981$	−0.302026	+	0.253430i	−0.00964295	+	0.00809140i
$982$	−35.1810	−	12.8048i	−1.12267	−	0.408618i
$983$	2.15051	−	0.782723i	0.0685908	−	0.0249650i	−0.307497	−	0.951549i	$-0.599491\pi$
$983$	2.15051	−	0.782723i	0.0685908	−	0.0249650i	0.376088	+	0.926584i	$0.377269\pi$
$984$	−3.74518	−	1.36313i	−0.119392	−	0.0434552i
$985$	−0.592388	−	3.35960i	−0.0188751	−	0.107046i
$986$	15.2376	+	86.4166i	0.485263	+	2.75206i
$987$	21.4769	+	7.81694i	0.683616	+	0.248816i
$988$	−39.2128	+	14.2723i	−1.24752	+	0.454062i
$989$	0.695746	+	0.253231i	0.0221234	+	0.00805228i
$990$	0.00309082	−	0.00259350i	9.82326e−5	−	8.24269e-5i
$991$	−46.6297	+	16.9718i	−1.48124	+	0.539128i	−0.951127	−	0.308799i	$-0.900073\pi$
$991$	−46.6297	+	16.9718i	−1.48124	+	0.539128i	−0.530114	+	0.847927i	$0.677851\pi$
$992$	−23.7085	+	41.0644i	−0.752747	+	1.30380i
$993$	−0.790283	+	4.48192i	−0.0250789	+	0.142229i
$994$	−6.48509	+	5.44164i	−0.205695	+	0.172598i
$995$	8.29297			0.262905
$996$	−10.2079	+	8.56547i	−0.323451	+	0.271407i
$997$	2.24903	−	0.818579i	0.0712274	−	0.0259247i	−0.306161	−	0.951980i	$-0.599044\pi$
$997$	2.24903	−	0.818579i	0.0712274	−	0.0259247i	0.377388	+	0.926055i	$0.376822\pi$
$998$	−0.0213482	−	0.0369762i	−0.000675765	−	0.00117046i
$999$	6.64043	+	37.6598i	0.210094	+	1.19150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.g.a.16.2	✓	30
3.2	odd	2		657.2.z.b.235.4		30
73.18	even	18		5329.2.a.k.1.4		15
73.32	even	9	inner	73.2.g.a.32.2	yes	30
73.55	even	9		5329.2.a.l.1.4		15
219.32	odd	18		657.2.z.b.397.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.g.a.16.2	✓	30	1.1	even	1	trivial
73.2.g.a.32.2	yes	30	73.32	even	9	inner
657.2.z.b.235.4		30	3.2	odd	2
657.2.z.b.397.4		30	219.32	odd	18
5329.2.a.k.1.4		15	73.18	even	18
5329.2.a.l.1.4		15	73.55	even	9

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.g (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.352058 + 1.99662i) q^{2} +(-0.860978 + 1.49126i) q^{3} +(-1.98316 - 0.721811i) q^{4} +(-0.0610770 - 0.346385i) q^{5} +(-2.67436 - 2.24405i) q^{6} +(0.956032 - 1.65590i) q^{7} +(0.111947 - 0.193897i) q^{8} +(0.0174332 + 0.0301951i) q^{9} +O(q^{10})\)	\(q+(-0.352058 + 1.99662i) q^{2} +(-0.860978 + 1.49126i) q^{3} +(-1.98316 - 0.721811i) q^{4} +(-0.0610770 - 0.346385i) q^{5} +(-2.67436 - 2.24405i) q^{6} +(0.956032 - 1.65590i) q^{7} +(0.111947 - 0.193897i) q^{8} +(0.0174332 + 0.0301951i) q^{9} +0.713101 q^{10} +(-0.0281794 - 0.159813i) q^{11} +(2.78386 - 2.33594i) q^{12} +(2.13983 + 1.79553i) q^{13} +(2.96962 + 2.49180i) q^{14} +(0.569135 + 0.207148i) q^{15} +(-2.88564 - 2.42134i) q^{16} +(2.75830 + 4.77752i) q^{17} +(-0.0664257 + 0.0241770i) q^{18} +(1.22918 - 6.97101i) q^{19} +(-0.128899 + 0.731022i) q^{20} +(1.64625 + 2.85138i) q^{21} +0.329007 q^{22} +(-0.0372373 - 0.211183i) q^{23} +(0.192767 + 0.333883i) q^{24} +(4.58221 - 1.66779i) q^{25} +(-4.33834 + 3.64030i) q^{26} -5.22591 q^{27} +(-3.09121 + 2.59383i) q^{28} +(1.36239 - 7.72647i) q^{29} +(-0.613964 + 1.06342i) q^{30} +(-5.51116 + 2.00590i) q^{31} +(6.19344 - 5.19691i) q^{32} +(0.262585 + 0.0955731i) q^{33} +(-10.5100 + 3.82532i) q^{34} +(-0.631969 - 0.230018i) q^{35} +(-0.0127776 - 0.0724652i) q^{36} +(-1.27068 - 7.20636i) q^{37} +(13.4857 + 4.90840i) q^{38} +(-4.51995 + 1.64513i) q^{39} +(-0.0740005 - 0.0269340i) q^{40} +(-7.91913 + 6.64494i) q^{41} +(-6.27270 + 2.28308i) q^{42} +(-1.72634 + 2.99011i) q^{43} +(-0.0594708 + 0.337276i) q^{44} +(0.00939437 - 0.00788281i) q^{45} +0.434762 q^{46} +(5.31758 - 4.46198i) q^{47} +(6.09532 - 2.21852i) q^{48} +(1.67200 + 2.89600i) q^{49} +(1.71674 + 9.73609i) q^{50} -9.49935 q^{51} +(-2.94759 - 5.10538i) q^{52} +(0.0886539 - 0.502781i) q^{53} +(1.83982 - 10.4341i) q^{54} +(-0.0536358 + 0.0195218i) q^{55} +(-0.214049 - 0.370745i) q^{56} +(9.33728 + 7.83491i) q^{57} +(14.9472 + 5.44033i) q^{58} +(-3.20623 - 2.69035i) q^{59} +(-0.979163 - 0.821615i) q^{60} +(3.53117 - 2.96301i) q^{61} +(-2.06477 - 11.7099i) q^{62} +0.0666667 q^{63} +(4.42886 + 7.67101i) q^{64} +(0.491251 - 0.850871i) q^{65} +(-0.283268 + 0.490635i) q^{66} +(1.79431 + 1.50560i) q^{67} +(-2.02169 - 11.4655i) q^{68} +(0.346989 + 0.126294i) q^{69} +(0.681748 - 1.18082i) q^{70} +(-0.379215 + 2.15064i) q^{71} +0.00780635 q^{72} +(-8.24477 + 2.24138i) q^{73} +14.8357 q^{74} +(-1.45808 + 8.26919i) q^{75} +(-7.46940 + 12.9374i) q^{76} +(-0.291575 - 0.106125i) q^{77} +(-1.69341 - 9.60381i) q^{78} +(2.68141 + 2.24997i) q^{79} +(-0.662469 + 1.14743i) q^{80} +(4.44709 - 7.70259i) q^{81} +(-10.4794 - 18.1509i) q^{82} -3.66682 q^{83} +(-1.20661 - 6.84302i) q^{84} +(1.48639 - 1.24723i) q^{85} +(-5.36235 - 4.49954i) q^{86} +(10.3492 + 8.68400i) q^{87} +(-0.0341420 - 0.0124267i) q^{88} +(-11.9564 - 10.0326i) q^{89} +(0.0124316 + 0.0215322i) q^{90} +(5.01897 - 1.82676i) q^{91} +(-0.0785868 + 0.445688i) q^{92} +(1.75368 - 9.94560i) q^{93} +(7.03678 + 12.1881i) q^{94} -2.48973 q^{95} +(2.41752 + 13.7104i) q^{96} +(5.50716 + 9.53867i) q^{97} +(-6.37084 + 2.31880i) q^{98} +(0.00433433 - 0.00363694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{4} - 12 q^{5} + 3 q^{6} + 3 q^{7} + 15 q^{8} - 9 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 + 3 * q^6 + 3 * q^7 + 15 * q^8 - 9 * q^9	\( 30 q - 6 q^{2} - 6 q^{4} - 12 q^{5} + 3 q^{6} + 3 q^{7} + 15 q^{8} - 9 q^{9} + 6 q^{10} - 3 q^{11} - 33 q^{12} - 30 q^{13} + 15 q^{15} - 24 q^{16} - 6 q^{17} + 33 q^{18} - 57 q^{20} + 15 q^{21} - 12 q^{22} + 33 q^{24} + 12 q^{25} - 12 q^{26} - 12 q^{27} - 6 q^{28} + 30 q^{30} + 3 q^{31} + 69 q^{32} - 6 q^{33} + 21 q^{34} + 12 q^{35} - 54 q^{36} + 27 q^{37} + 45 q^{38} - 57 q^{39} + 42 q^{40} - 24 q^{41} + 33 q^{42} - 9 q^{43} - 27 q^{44} + 45 q^{45} - 24 q^{46} + 12 q^{47} + 48 q^{48} + 24 q^{49} - 90 q^{50} + 18 q^{51} + 21 q^{52} - 6 q^{53} + 63 q^{54} - 30 q^{55} - 6 q^{56} + 27 q^{57} + 57 q^{58} + 9 q^{59} - 45 q^{60} + 15 q^{61} - 27 q^{62} - 72 q^{63} - 33 q^{64} + 6 q^{65} - 42 q^{66} - 6 q^{67} - 36 q^{68} - 24 q^{69} - 60 q^{70} - 66 q^{71} - 54 q^{72} - 30 q^{73} - 18 q^{74} + 63 q^{75} + 6 q^{76} - 27 q^{77} - 84 q^{78} - 33 q^{79} + 54 q^{80} + 57 q^{81} - 48 q^{82} + 84 q^{83} + 54 q^{84} - 69 q^{85} - 9 q^{86} - 54 q^{87} + 3 q^{88} - 6 q^{89} + 69 q^{90} + 102 q^{91} + 57 q^{92} - 42 q^{93} + 18 q^{94} - 12 q^{95} - 102 q^{96} + 33 q^{97} - 9 q^{98} - 57 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 + 3 * q^6 + 3 * q^7 + 15 * q^8 - 9 * q^9 + 6 * q^10 - 3 * q^11 - 33 * q^12 - 30 * q^13 + 15 * q^15 - 24 * q^16 - 6 * q^17 + 33 * q^18 - 57 * q^20 + 15 * q^21 - 12 * q^22 + 33 * q^24 + 12 * q^25 - 12 * q^26 - 12 * q^27 - 6 * q^28 + 30 * q^30 + 3 * q^31 + 69 * q^32 - 6 * q^33 + 21 * q^34 + 12 * q^35 - 54 * q^36 + 27 * q^37 + 45 * q^38 - 57 * q^39 + 42 * q^40 - 24 * q^41 + 33 * q^42 - 9 * q^43 - 27 * q^44 + 45 * q^45 - 24 * q^46 + 12 * q^47 + 48 * q^48 + 24 * q^49 - 90 * q^50 + 18 * q^51 + 21 * q^52 - 6 * q^53 + 63 * q^54 - 30 * q^55 - 6 * q^56 + 27 * q^57 + 57 * q^58 + 9 * q^59 - 45 * q^60 + 15 * q^61 - 27 * q^62 - 72 * q^63 - 33 * q^64 + 6 * q^65 - 42 * q^66 - 6 * q^67 - 36 * q^68 - 24 * q^69 - 60 * q^70 - 66 * q^71 - 54 * q^72 - 30 * q^73 - 18 * q^74 + 63 * q^75 + 6 * q^76 - 27 * q^77 - 84 * q^78 - 33 * q^79 + 54 * q^80 + 57 * q^81 - 48 * q^82 + 84 * q^83 + 54 * q^84 - 69 * q^85 - 9 * q^86 - 54 * q^87 + 3 * q^88 - 6 * q^89 + 69 * q^90 + 102 * q^91 + 57 * q^92 - 42 * q^93 + 18 * q^94 - 12 * q^95 - 102 * q^96 + 33 * q^97 - 9 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more