LMFDB - Embedded newform 171.2.x.a.110.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.16
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42288 - 1.19394i) q^{2} +(-1.62073 - 0.610926i) q^{3} +(0.251804 - 1.42805i) q^{4} +(0.629748 - 1.73022i) q^{5} +(-3.03552 + 1.06578i) q^{6} +(-1.66649 - 2.88644i) q^{7} +(0.510719 + 0.884592i) q^{8} +(2.25354 + 1.98029i) q^{9} +O(q^{10})$	\(q+(1.42288 - 1.19394i) q^{2} +(-1.62073 - 0.610926i) q^{3} +(0.251804 - 1.42805i) q^{4} +(0.629748 - 1.73022i) q^{5} +(-3.03552 + 1.06578i) q^{6} +(-1.66649 - 2.88644i) q^{7} +(0.510719 + 0.884592i) q^{8} +(2.25354 + 1.98029i) q^{9} +(-1.16972 - 3.21378i) q^{10} -2.01233i q^{11} +(-1.28054 + 2.16066i) q^{12} +(-0.355101 - 0.975632i) q^{13} +(-5.81744 - 2.11738i) q^{14} +(-2.07769 + 2.41949i) q^{15} +(4.50811 + 1.64082i) q^{16} +(-2.49671 + 6.85966i) q^{17} +(5.57087 + 0.127133i) q^{18} +(4.33498 - 0.456034i) q^{19} +(-2.31227 - 1.33499i) q^{20} +(0.937526 + 5.69624i) q^{21} +(-2.40260 - 2.86331i) q^{22} +(5.68790 + 1.00293i) q^{23} +(-0.287319 - 1.74570i) q^{24} +(1.23315 + 1.03473i) q^{25} +(-1.67011 - 0.964239i) q^{26} +(-2.44257 - 4.58627i) q^{27} +(-4.54161 + 1.65301i) q^{28} +(-0.250256 + 1.41927i) q^{29} +(-0.0675790 + 5.92328i) q^{30} -3.08283i q^{31} +(6.45386 - 2.34901i) q^{32} +(-1.22938 + 3.26144i) q^{33} +(4.63749 + 12.7414i) q^{34} +(-6.04364 + 1.06566i) q^{35} +(3.39541 - 2.71953i) q^{36} +2.56367i q^{37} +(5.62368 - 5.82458i) q^{38} +(-0.0205155 + 1.79818i) q^{39} +(1.85216 - 0.326586i) q^{40} +(-6.61929 + 5.55425i) q^{41} +(8.13495 + 6.98572i) q^{42} +(-0.553471 - 3.13889i) q^{43} +(-2.87371 - 0.506713i) q^{44} +(4.84550 - 2.65203i) q^{45} +(9.29064 - 5.36395i) q^{46} +(-8.65752 - 1.52655i) q^{47} +(-6.30401 - 5.41344i) q^{48} +(-2.05435 + 3.55824i) q^{49} +2.99003 q^{50} +(8.23725 - 9.59236i) q^{51} +(-1.48267 + 0.261435i) q^{52} +(-4.17870 - 3.50634i) q^{53} +(-8.95121 - 3.60944i) q^{54} +(-3.48177 - 1.26726i) q^{55} +(1.70221 - 2.94832i) q^{56} +(-7.30444 - 1.90924i) q^{57} +(1.33844 + 2.31825i) q^{58} +(1.40063 + 7.94334i) q^{59} +(2.93199 + 3.57629i) q^{60} +(10.4732 - 3.81194i) q^{61} +(-3.68071 - 4.38650i) q^{62} +(1.96050 - 9.80483i) q^{63} +(1.58107 - 2.73850i) q^{64} -1.91168 q^{65} +(2.14470 + 6.10846i) q^{66} +(-5.53209 + 6.59289i) q^{67} +(9.16728 + 5.29273i) q^{68} +(-8.60584 - 5.10036i) q^{69} +(-7.32705 + 8.73204i) q^{70} +(4.33638 - 3.63865i) q^{71} +(-0.600825 + 3.00484i) q^{72} +(-2.19677 - 12.4585i) q^{73} +(3.06087 + 3.64780i) q^{74} +(-1.36645 - 2.43038i) q^{75} +(0.440324 - 6.30541i) q^{76} +(-5.80846 + 3.35352i) q^{77} +(2.11772 + 2.58309i) q^{78} +(-3.44685 + 9.47013i) q^{79} +(5.67794 - 6.76671i) q^{80} +(1.15688 + 8.92534i) q^{81} +(-2.78704 + 15.8061i) q^{82} +(-7.44260 + 4.29699i) q^{83} +(8.37060 + 0.0955007i) q^{84} +(10.2964 + 8.63972i) q^{85} +(-4.53517 - 3.80546i) q^{86} +(1.27267 - 2.14737i) q^{87} +(1.78009 - 1.02773i) q^{88} +(-1.35261 + 7.67105i) q^{89} +(3.72821 - 9.55876i) q^{90} +(-2.22433 + 2.65085i) q^{91} +(2.86447 - 7.87007i) q^{92} +(-1.88338 + 4.99643i) q^{93} +(-14.1412 + 8.16445i) q^{94} +(1.94091 - 7.78765i) q^{95} +(-11.8950 - 0.135711i) q^{96} +(-10.2106 - 12.1685i) q^{97} +(1.32522 + 7.51572i) q^{98} +(3.98500 - 4.53486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.42288	−	1.19394i	1.00613	−	0.844243i	0.0183074	−	0.999832i	$-0.494172\pi$
$2$	1.42288	−	1.19394i	1.00613	−	0.844243i	0.987822	+	0.155590i	$0.0497278\pi$
$3$	−1.62073	−	0.610926i	−0.935730	−	0.352718i
$3$	−1.62073	−	0.610926i	−0.935730	−	0.352718i
$4$	0.251804	−	1.42805i	0.125902	−	0.714026i
$5$	0.629748	−	1.73022i	0.281632	−	0.773778i	−0.715536	−	0.698576i	$-0.753818\pi$
$5$	0.629748	−	1.73022i	0.281632	−	0.773778i	0.997168	−	0.0752020i	$-0.0239602\pi$
$6$	−3.03552	+	1.06578i	−1.23924	+	0.435103i
$7$	−1.66649	−	2.88644i	−0.629872	−	1.09097i	−0.987577	−	0.157136i	$-0.949774\pi$
$7$	−1.66649	−	2.88644i	−0.629872	−	1.09097i	0.357705	−	0.933835i	$-0.383560\pi$
$8$	0.510719	+	0.884592i	0.180567	+	0.312750i
$9$	2.25354	+	1.98029i	0.751180	+	0.660098i
$10$	−1.16972	−	3.21378i	−0.369898	−	1.01629i
$11$		−	2.01233i		−	0.606740i	−0.952873	−	0.303370i	$-0.901888\pi$
$11$		−	2.01233i		−	0.606740i	0.952873	−	0.303370i	$-0.0981118\pi$
$12$	−1.28054	+	2.16066i	−0.369660	+	0.623728i
$13$	−0.355101	−	0.975632i	−0.0984873	−	0.270592i	0.880658	−	0.473752i	$-0.157101\pi$
$13$	−0.355101	−	0.975632i	−0.0984873	−	0.270592i	−0.979145	+	0.203161i	$0.934879\pi$
$14$	−5.81744	−	2.11738i	−1.55478	−	0.565893i
$15$	−2.07769	+	2.41949i	−0.536457	+	0.624710i
$16$	4.50811	+	1.64082i	1.12703	+	0.410204i
$17$	−2.49671	+	6.85966i	−0.605542	+	1.66371i	0.134307	+	0.990940i	$0.457119\pi$
$17$	−2.49671	+	6.85966i	−0.605542	+	1.66371i	−0.739849	+	0.672773i	$0.765103\pi$
$18$	5.57087	+	0.127133i	1.31307	+	0.0299656i
$19$	4.33498	−	0.456034i	0.994512	−	0.104621i
$19$	4.33498	−	0.456034i	0.994512	−	0.104621i
$20$	−2.31227	−	1.33499i	−0.517039	−	0.298513i
$21$	0.937526	+	5.69624i	0.204585	+	1.24302i
$22$	−2.40260	−	2.86331i	−0.512236	−	0.610459i
$23$	5.68790	+	1.00293i	1.18601	+	0.209125i	0.731642	−	0.681689i	$-0.238754\pi$
$23$	5.68790	+	1.00293i	1.18601	+	0.209125i	0.454367	+	0.890815i	$0.349866\pi$
$24$	−0.287319	−	1.74570i	−0.0586487	−	0.356339i
$25$	1.23315	+	1.03473i	0.246629	+	0.206947i
$26$	−1.67011	−	0.964239i	−0.327536	−	0.189103i
$27$	−2.44257	−	4.58627i	−0.470073	−	0.882628i
$28$	−4.54161	+	1.65301i	−0.858284	+	0.312390i
$29$	−0.250256	+	1.41927i	−0.0464715	+	0.263553i	−0.999187	−	0.0403102i	$-0.987165\pi$
$29$	−0.250256	+	1.41927i	−0.0464715	+	0.263553i	0.952716	+	0.303863i	$0.0982765\pi$
$30$	−0.0675790	+	5.92328i	−0.0123382	+	1.08144i
$31$		−	3.08283i		−	0.553692i	−0.960914	−	0.276846i	$-0.910711\pi$
$31$		−	3.08283i		−	0.553692i	0.960914	−	0.276846i	$-0.0892892\pi$
$32$	6.45386	−	2.34901i	1.14089	−	0.415251i
$33$	−1.22938	+	3.26144i	−0.214008	+	0.567745i
$34$	4.63749	+	12.7414i	0.795324	+	2.18513i
$35$	−6.04364	+	1.06566i	−1.02156	+	0.180129i
$36$	3.39541	−	2.71953i	0.565902	−	0.453254i
$37$			2.56367i			0.421465i	0.977544	+	0.210733i	$0.0675849\pi$
$37$			2.56367i			0.421465i	−0.977544	+	0.210733i	$0.932415\pi$
$38$	5.62368	−	5.82458i	0.912282	−	0.944872i
$39$	−0.0205155	+	1.79818i	−0.00328511	+	0.287939i
$40$	1.85216	−	0.326586i	0.292853	−	0.0516378i
$41$	−6.61929	+	5.55425i	−1.03376	+	0.867428i	−0.991294	−	0.131670i	$-0.957966\pi$
$41$	−6.61929	+	5.55425i	−1.03376	+	0.867428i	−0.0424664	+	0.999098i	$0.513522\pi$
$42$	8.13495	+	6.98572i	1.25525	+	1.07792i
$43$	−0.553471	−	3.13889i	−0.0844035	−	0.478676i	−0.997484	−	0.0708960i	$-0.977414\pi$
$43$	−0.553471	−	3.13889i	−0.0844035	−	0.478676i	0.913080	−	0.407780i	$-0.133697\pi$
$44$	−2.87371	−	0.506713i	−0.433228	−	0.0763898i
$45$	4.84550	−	2.65203i	0.722325	−	0.395341i
$46$	9.29064	−	5.36395i	1.36983	−	0.790872i
$47$	−8.65752	−	1.52655i	−1.26283	−	0.222671i	−0.498155	−	0.867088i	$-0.665989\pi$
$47$	−8.65752	−	1.52655i	−1.26283	−	0.222671i	−0.764674	+	0.644417i	$0.777100\pi$
$48$	−6.30401	−	5.41344i	−0.909905	−	0.781363i
$49$	−2.05435	+	3.55824i	−0.293479	+	0.508320i
$50$	2.99003			0.422854
$51$	8.23725	−	9.59236i	1.15345	−	1.34320i
$52$	−1.48267	+	0.261435i	−0.205609	+	0.0362544i
$53$	−4.17870	−	3.50634i	−0.573988	−	0.481633i	0.308978	−	0.951069i	$-0.400013\pi$
$53$	−4.17870	−	3.50634i	−0.573988	−	0.481633i	−0.882967	+	0.469436i	$0.844457\pi$
$54$	−8.95121	−	3.60944i	−1.21811	−	0.491182i
$55$	−3.48177	−	1.26726i	−0.469482	−	0.170877i
$56$	1.70221	−	2.94832i	0.227468	−	0.393986i
$57$	−7.30444	−	1.90924i	−0.967496	−	0.252885i
$58$	1.33844	+	2.31825i	0.175746	+	0.304401i
$59$	1.40063	+	7.94334i	0.182346	+	1.03414i	0.929318	+	0.369280i	$0.120396\pi$
$59$	1.40063	+	7.94334i	0.182346	+	1.03414i	−0.746972	+	0.664855i	$0.768493\pi$
$60$	2.93199	+	3.57629i	0.378518	+	0.461697i
$61$	10.4732	−	3.81194i	1.34096	−	0.488069i	0.430845	−	0.902426i	$-0.358216\pi$
$61$	10.4732	−	3.81194i	1.34096	−	0.488069i	0.910115	+	0.414357i	$0.135993\pi$
$62$	−3.68071	−	4.38650i	−0.467450	−	0.557086i
$63$	1.96050	−	9.80483i	0.247000	−	1.23529i
$64$	1.58107	−	2.73850i	0.197634	−	0.342312i
$65$	−1.91168			−0.237115
$66$	2.14470	+	6.10846i	0.263994	+	0.751899i
$67$	−5.53209	+	6.59289i	−0.675852	+	0.805449i	−0.989568	−	0.144068i	$-0.953982\pi$
$67$	−5.53209	+	6.59289i	−0.675852	+	0.805449i	0.313716	+	0.949517i	$0.398426\pi$
$68$	9.16728	+	5.29273i	1.11170	+	0.641838i
$69$	−8.60584	−	5.10036i	−1.03602	−	0.614012i
$70$	−7.32705	+	8.73204i	−0.875750	+	1.04368i
$71$	4.33638	−	3.63865i	0.514633	−	0.431829i	−0.348123	−	0.937449i	$-0.613181\pi$
$71$	4.33638	−	3.63865i	0.514633	−	0.431829i	0.862756	+	0.505620i	$0.168736\pi$
$72$	−0.600825	+	3.00484i	−0.0708079	+	0.354123i
$73$	−2.19677	−	12.4585i	−0.257112	−	1.45816i	−0.790592	−	0.612343i	$-0.790227\pi$
$73$	−2.19677	−	12.4585i	−0.257112	−	1.45816i	0.533480	−	0.845813i	$-0.320884\pi$
$74$	3.06087	+	3.64780i	0.355819	+	0.424048i
$75$	−1.36645	−	2.43038i	−0.157784	−	0.280637i
$76$	0.440324	−	6.30541i	0.0505087	−	0.723280i
$77$	−5.80846	+	3.35352i	−0.661936	+	0.382169i
$78$	2.11772	+	2.58309i	0.239785	+	0.292477i
$79$	−3.44685	+	9.47013i	−0.387800	+	1.06547i	0.580189	+	0.814482i	$0.302979\pi$
$79$	−3.44685	+	9.47013i	−0.387800	+	1.06547i	−0.967989	+	0.250991i	$0.919244\pi$
$80$	5.67794	−	6.76671i	0.634813	−	0.756541i
$81$	1.15688	+	8.92534i	0.128542	+	0.991704i
$82$	−2.78704	+	15.8061i	−0.307777	+	1.74549i
$83$	−7.44260	+	4.29699i	−0.816932	+	0.471656i	−0.849357	−	0.527818i	$-0.823010\pi$
$83$	−7.44260	+	4.29699i	−0.816932	+	0.471656i	0.0324254	+	0.999474i	$0.489677\pi$
$84$	8.37060	+	0.0955007i	0.913308	+	0.0104200i
$85$	10.2964	+	8.63972i	1.11680	+	0.937109i
$86$	−4.53517	−	3.80546i	−0.489039	−	0.410353i
$87$	1.27267	−	2.14737i	0.136445	−	0.230223i
$88$	1.78009	−	1.02773i	0.189758	−	0.109557i
$89$	−1.35261	+	7.67105i	−0.143377	+	0.813130i	0.825280	+	0.564724i	$0.191018\pi$
$89$	−1.35261	+	7.67105i	−0.143377	+	0.813130i	−0.968656	+	0.248405i	$0.920094\pi$
$90$	3.72821	−	9.55876i	0.392988	−	1.00758i
$91$	−2.22433	+	2.65085i	−0.233173	+	0.277885i
$92$	2.86447	−	7.87007i	0.298642	−	0.820512i
$93$	−1.88338	+	4.99643i	−0.195297	+	0.518106i
$94$	−14.1412	+	8.16445i	−1.45856	+	0.842098i
$95$	1.94091	−	7.78765i	0.199133	−	0.798996i
$96$	−11.8950	−	0.135711i	−1.21403	−	0.0138510i
$97$	−10.2106	−	12.1685i	−1.03673	−	1.23552i	−0.971347	−	0.237664i	$-0.923618\pi$
$97$	−10.2106	−	12.1685i	−1.03673	−	1.23552i	−0.0653807	−	0.997860i	$-0.520826\pi$
$98$	1.32522	+	7.51572i	0.133868	+	0.759202i
$99$	3.98500	−	4.53486i	0.400508	−	0.455771i
$100$	1.78816	−	1.50045i	0.178816	−	0.150045i
$101$	3.65665	−	4.35782i	0.363850	−	0.433620i	−0.552798	−	0.833315i	$-0.686440\pi$
$101$	3.65665	−	4.35782i	0.363850	−	0.433620i	0.916648	+	0.399696i	$0.130884\pi$
$102$	0.267925	−	23.4836i	0.0265286	−	2.32522i
$103$	−3.51204	−	2.02767i	−0.346051	−	0.199793i	0.316894	−	0.948461i	$-0.397360\pi$
$103$	−3.51204	−	2.02767i	−0.346051	−	0.199793i	−0.662945	+	0.748668i	$0.730694\pi$
$104$	0.681679	−	0.812393i	0.0668441	−	0.0796617i
$105$	10.4461	+	1.96507i	1.01944	+	0.191771i
$106$	−10.1322			−0.984122
$107$	−1.89059	+	3.27459i	−0.182770	+	0.316567i	−0.942823	−	0.333295i	$-0.891840\pi$
$107$	−1.89059	+	3.27459i	−0.182770	+	0.316567i	0.760053	+	0.649861i	$0.225173\pi$
$108$	−7.16448	+	2.33328i	−0.689403	+	0.224520i
$109$	−4.65575	−	5.54851i	−0.445940	−	0.531451i	0.495510	−	0.868602i	$-0.334981\pi$
$109$	−4.65575	−	5.54851i	−0.445940	−	0.531451i	−0.941450	+	0.337151i	$0.890537\pi$
$110$	−6.46718	+	2.35386i	−0.616621	+	0.224432i
$111$	1.56621	−	4.15502i	0.148658	−	0.394377i
$112$	−2.77658	−	15.7468i	−0.262362	−	1.48793i
$113$	7.23693	+	12.5347i	0.680793	+	1.17917i	0.974739	+	0.223346i	$0.0716981\pi$
$113$	7.23693	+	12.5347i	0.680793	+	1.17917i	−0.293946	+	0.955822i	$0.594969\pi$
$114$	−12.6729	+	6.00443i	−1.18692	+	0.562367i
$115$	5.31723	−	9.20972i	0.495834	−	0.858810i
$116$	1.96378	+	0.714759i	0.182333	+	0.0663637i
$117$	1.13180	−	2.90183i	0.104635	−	0.268274i
$118$	11.4768	+	9.63017i	1.05652	+	0.886529i
$119$	23.9607	−	4.22492i	2.19648	−	0.387298i
$120$	−3.20138	−	0.602225i	−0.292244	−	0.0549754i
$121$	6.95053			0.631867
$122$	10.3509	−	17.9283i	0.937129	−	1.62316i
$123$	14.1213	−	4.95804i	1.27328	−	0.447052i
$124$	−4.40244	−	0.776269i	−0.395351	−	0.0697110i
$125$	10.5398	−	6.08514i	0.942707	−	0.544272i
$126$	−8.91681	−	16.2918i	−0.794373	−	1.45139i
$127$	−1.28938	−	0.227353i	−0.114414	−	0.0201743i	0.116148	−	0.993232i	$-0.462945\pi$
$127$	−1.28938	−	0.227353i	−0.114414	−	0.0201743i	−0.230562	+	0.973058i	$0.574056\pi$
$128$	1.36533	+	7.74316i	0.120679	+	0.684406i
$129$	−1.02060	+	5.42542i	−0.0898589	+	0.477682i
$130$	−2.72009	+	2.28243i	−0.238568	+	0.200182i
$131$	5.10663	−	0.900436i	0.446168	−	0.0786715i	0.0539498	−	0.998544i	$-0.482819\pi$
$131$	5.10663	−	0.900436i	0.446168	−	0.0786715i	0.392218	+	0.919872i	$0.371708\pi$
$132$	4.34795	+	2.57687i	0.378440	+	0.224288i
$133$	−8.54049	−	11.7527i	−0.740555	−	1.01909i
$134$			15.9859i			1.38097i
$135$	−9.47345	+	1.33799i	−0.815345	+	0.115155i
$136$	−7.34312	+	1.29479i	−0.629667	+	0.111027i
$137$	4.70095	+	12.9158i	0.401629	+	1.10347i	0.961480	+	0.274874i	$0.0886362\pi$
$137$	4.70095	+	12.9158i	0.401629	+	1.10347i	−0.559851	+	0.828593i	$0.689142\pi$
$138$	−18.3346	+	3.01764i	−1.56075	+	0.256878i
$139$	−4.91514	+	1.78896i	−0.416896	+	0.151738i	−0.541947	−	0.840412i	$-0.682313\pi$
$139$	−4.91514	+	1.78896i	−0.416896	+	0.151738i	0.125051	+	0.992150i	$0.460091\pi$
$140$			8.89897i			0.752100i
$141$	13.0989	+	7.76323i	1.10313	+	0.653782i
$142$	1.82582	−	10.3547i	0.153219	−	0.868951i
$143$	−1.96329	+	0.714580i	−0.164179	+	0.0597561i
$144$	6.90990	+	12.6250i	0.575825	+	1.05208i
$145$	2.29806	+	1.32678i	0.190843	+	0.110183i
$146$	−18.0004	−	15.1041i	−1.48973	−	1.25003i
$147$	5.50337	−	4.51189i	0.453910	−	0.372135i
$148$	3.66106	+	0.645544i	0.300937	+	0.0530634i
$149$	1.95002	+	2.32394i	0.159752	+	0.190385i	0.839983	−	0.542613i	$-0.182565\pi$
$149$	1.95002	+	2.32394i	0.159752	+	0.190385i	−0.680231	+	0.732998i	$0.738121\pi$
$150$	−4.84603	−	1.82669i	−0.395677	−	0.149148i
$151$	−15.6433	−	9.03169i	−1.27304	−	0.734988i	−0.297478	−	0.954729i	$-0.596146\pi$
$151$	−15.6433	−	9.03169i	−1.27304	−	0.734988i	−0.975558	+	0.219740i	$0.929479\pi$
$152$	2.61736	+	3.60178i	0.212296	+	0.292143i
$153$	−19.2106	+	10.5143i	−1.55308	+	0.850030i
$154$	−4.26086	+	11.7066i	−0.343350	+	0.943345i
$155$	−5.33397	−	1.94141i	−0.428435	−	0.155937i
$156$	2.56273	+	0.482086i	0.205182	+	0.0385977i
$157$	21.8184	+	7.94124i	1.74130	+	0.633780i	0.999328	−	0.0366550i	$-0.0116703\pi$
$157$	21.8184	+	7.94124i	1.74130	+	0.633780i	0.741968	+	0.670435i	$0.233892\pi$
$158$	6.40231	+	17.5902i	0.509340	+	1.39940i
$159$	4.63043	+	8.23572i	0.367217	+	0.653135i
$160$		−	12.6459i		−	0.999744i
$161$	−6.58391	−	18.0891i	−0.518884	−	1.42562i
$162$	12.3024	+	11.3185i	0.966569	+	0.889262i
$163$	−1.87789	−	3.25259i	−0.147087	−	0.254763i	0.783062	−	0.621943i	$-0.213657\pi$
$163$	−1.87789	−	3.25259i	−0.147087	−	0.254763i	−0.930150	+	0.367180i	$0.880323\pi$
$164$	6.26499	+	10.8513i	0.489214	+	0.847343i
$165$	4.86881	+	4.18099i	0.379036	+	0.325490i
$166$	−5.45960	+	15.0001i	−0.423747	+	1.16424i
$167$	−0.900611	+	5.10762i	−0.0696914	+	0.395239i	0.929930	+	0.367736i	$0.119867\pi$
$167$	−0.900611	+	5.10762i	−0.0696914	+	0.395239i	−0.999622	+	0.0275037i	$0.991244\pi$
$168$	−4.56003	+	3.73851i	−0.351814	+	0.288432i
$169$	9.13282	−	7.66334i	0.702524	−	0.589488i
$170$	24.9659			1.91480
$171$	10.6721	+	7.55684i	0.816118	+	0.577886i
$172$	−4.62186			−0.352414
$173$	0.795445	−	0.667458i	0.0604766	−	0.0507459i	−0.612048	−	0.790820i	$-0.709654\pi$
$173$	0.795445	−	0.667458i	0.0604766	−	0.0507459i	0.672525	+	0.740074i	$0.265210\pi$
$174$	−0.752977	−	4.57495i	−0.0570830	−	0.346826i
$175$	0.931671	−	5.28377i	0.0704277	−	0.399415i
$176$	3.30186	−	9.07179i	0.248887	−	0.683812i
$177$	2.58276	−	13.7297i	0.194132	−	1.03199i
$178$	7.23416	+	12.5299i	0.542223	+	0.939158i
$179$	5.29472	+	9.17073i	0.395746	+	0.685453i	0.993196	−	0.116454i	$-0.0371527\pi$
$179$	5.29472	+	9.17073i	0.395746	+	0.685453i	−0.597450	+	0.801906i	$0.703819\pi$
$180$	−2.56712	−	7.58743i	−0.191342	−	0.565533i
$181$	8.27035	+	22.7226i	0.614730	+	1.68896i	0.719528	+	0.694464i	$0.244358\pi$
$181$	8.27035	+	22.7226i	0.614730	+	1.68896i	−0.104798	+	0.994494i	$0.533419\pi$
$182$			6.42756i			0.476443i
$183$	−19.3031	−	0.220230i	−1.42693	−	0.0162799i
$184$	2.01774	+	5.54368i	0.148749	+	0.408686i
$185$	4.43572	+	1.61447i	0.326120	+	0.118698i
$186$	3.28561	+	9.35797i	0.240913	+	0.686160i
$187$	13.8039	+	5.02421i	1.00944	+	0.367406i
$188$	−4.36000	+	11.9790i	−0.317986	+	0.873658i
$189$	−9.16747	+	14.6933i	−0.666835	+	1.06878i
$190$	−6.53630	−	13.3982i	−0.474193	−	0.972009i
$191$	−9.40161	−	5.42802i	−0.680277	−	0.392758i	0.119683	−	0.992812i	$-0.461812\pi$
$191$	−9.40161	−	5.42802i	−0.680277	−	0.392758i	−0.799959	+	0.600054i	$0.795146\pi$
$192$	−4.23551	+	3.47245i	−0.305672	+	0.250602i
$193$	1.57956	+	1.88245i	0.113699	+	0.135502i	0.819892	−	0.572518i	$-0.194033\pi$
$193$	1.57956	+	1.88245i	0.113699	+	0.135502i	−0.706193	+	0.708020i	$0.749589\pi$
$194$	−29.0569	−	5.12352i	−2.08616	−	0.367847i
$195$	3.09832	+	1.16790i	0.221875	+	0.0836347i
$196$	4.56406	+	3.82970i	0.326004	+	0.273550i
$197$	−14.2423	−	8.22281i	−1.01472	−	0.585851i	−0.102153	−	0.994769i	$-0.532573\pi$
$197$	−14.2423	−	8.22281i	−1.01472	−	0.585851i	−0.912571	+	0.408918i	$0.865906\pi$
$198$	0.255834	−	11.2104i	0.0181813	−	0.796690i
$199$	−12.8946	+	4.69326i	−0.914077	+	0.332697i	−0.755879	−	0.654711i	$-0.772790\pi$
$199$	−12.8946	+	4.69326i	−0.914077	+	0.332697i	−0.158197	+	0.987408i	$0.550568\pi$
$200$	−0.285524	+	1.61929i	−0.0201896	+	0.114501i
$201$	12.9938	−	7.30560i	0.916512	−	0.515297i
$202$		−	10.5665i		−	0.743455i
$203$	4.51370	−	1.64285i	0.316799	−	0.115306i
$204$	−11.6242	−	14.1786i	−0.813859	−	0.992702i
$205$	5.44158	+	14.9506i	0.380056	+	1.04420i
$206$	−7.41813	+	1.30802i	−0.516846	+	0.0911338i
$207$	10.8318	+	13.5238i	0.752862	+	0.939972i
$208$		−	4.98091i		−	0.345364i
$209$	−0.917691	−	8.72340i	−0.0634780	−	0.603410i
$210$	17.2098	−	9.67600i	1.18759	−	0.667708i
$211$	7.95554	−	1.40278i	0.547682	−	0.0965712i	0.107041	−	0.994255i	$-0.465862\pi$
$211$	7.95554	−	1.40278i	0.547682	−	0.0965712i	0.440641	+	0.897683i	$0.354751\pi$
$212$	−6.05946	+	5.08449i	−0.416165	+	0.349204i
$213$	−9.25105	+	3.24807i	−0.633871	+	0.222554i
$214$	1.21958	+	6.91660i	0.0833690	+	0.472809i
$215$	−5.77951	−	1.01908i	−0.394159	−	0.0695010i
$216$	2.80951	−	4.50297i	0.191163	−	0.306388i
$217$	−8.89839	+	5.13749i	−0.604062	+	0.348755i
$218$	−13.2492	−	2.33618i	−0.897346	−	0.158226i
$219$	−4.05084	+	21.5339i	−0.273731	+	1.45513i
$220$	−2.68644	+	4.65305i	−0.181120	+	0.313709i
$221$	7.57909			0.509825
$222$	−2.73231	−	7.78207i	−0.183381	−	0.522298i
$223$	−15.5123	+	2.73524i	−1.03878	+	0.183165i	−0.666925	−	0.745125i	$-0.732390\pi$
$223$	−15.5123	+	2.73524i	−1.03878	+	0.183165i	−0.371857	+	0.928290i	$0.621279\pi$
$224$	−17.5355	−	14.7141i	−1.17164	−	0.983125i
$225$	0.729870	+	4.77380i	0.0486580	+	0.318253i
$226$	25.2630	+	9.19498i	1.68047	+	0.611641i
$227$	13.8297	−	23.9537i	0.917909	−	1.58986i	0.115323	−	0.993328i	$-0.463210\pi$
$227$	13.8297	−	23.9537i	0.917909	−	1.58986i	0.802586	−	0.596537i	$-0.203457\pi$
$228$	−4.56578	+	9.95037i	−0.302376	+	0.658979i
$229$	−4.51331	−	7.81728i	−0.298248	−	0.516580i	0.677487	−	0.735534i	$-0.263069\pi$
$229$	−4.51331	−	7.81728i	−0.298248	−	0.516580i	−0.975735	+	0.218954i	$0.929735\pi$
$230$	−3.43005	−	19.4528i	−0.226171	−	1.28268i
$231$	11.4627	−	1.88661i	0.754191	−	0.124130i
$232$	−1.38329	+	0.503476i	−0.0908174	+	0.0330548i
$233$	−13.7138	−	16.3435i	−0.898420	−	1.07070i	−0.997140	−	0.0755804i	$-0.975919\pi$
$233$	−13.7138	−	16.3435i	−0.898420	−	1.07070i	0.0987193	−	0.995115i	$-0.468525\pi$
$234$	−1.85419	−	5.48026i	−0.121212	−	0.358256i
$235$	−8.09333	+	14.0181i	−0.527951	+	0.914437i
$236$	11.6962			0.761358
$237$	11.3720	−	13.2428i	0.738688	−	0.860210i
$238$	29.0490	−	34.6192i	1.88297	−	2.24403i
$239$	−7.11510	−	4.10790i	−0.460237	−	0.265718i	0.251907	−	0.967752i	$-0.418942\pi$
$239$	−7.11510	−	4.10790i	−0.460237	−	0.265718i	−0.712144	+	0.702033i	$0.752276\pi$
$240$	−13.3364	+	7.49822i	−0.860860	+	0.484008i
$241$	−15.7245	+	18.7397i	−1.01290	+	1.20713i	−0.0347155	+	0.999397i	$0.511052\pi$
$241$	−15.7245	+	18.7397i	−1.01290	+	1.20713i	−0.978186	+	0.207732i	$0.933392\pi$
$242$	9.88978	−	8.29851i	0.635739	−	0.533449i
$243$	3.57773	−	15.1723i	0.229511	−	0.973306i
$244$	−2.80645	−	15.9162i	−0.179665	−	1.01893i
$245$	4.86281	+	5.79527i	0.310673	+	0.370246i
$246$	14.1734	−	23.9147i	0.903661	−	1.52475i
$247$	−1.98428	−	4.06740i	−0.126256	−	0.258803i
$248$	2.72704	−	1.57446i	0.173167	−	0.0999783i
$249$	14.6876	−	2.41739i	0.930789	−	0.153196i
$250$	7.73156	−	21.2423i	0.488987	−	1.34348i
$251$	−8.54330	+	10.1815i	−0.539248	+	0.642651i	−0.965019	−	0.262180i	$-0.915559\pi$
$251$	−8.54330	+	10.1815i	−0.539248	+	0.642651i	0.425771	+	0.904831i	$0.360003\pi$
$252$	−13.5082	−	5.26860i	−0.850934	−	0.331890i
$253$	2.01822	−	11.4459i	0.126885	−	0.719599i
$254$	−2.10608	+	1.21595i	−0.132147	+	0.0762953i
$255$	−11.4095	−	20.2930i	−0.714491	−	1.27080i
$256$	16.0323	+	13.4527i	1.00202	+	0.840791i
$257$	−15.4469	−	12.9615i	−0.963551	−	0.808516i	0.0179757	−	0.999838i	$-0.494278\pi$
$257$	−15.4469	−	12.9615i	−0.963551	−	0.808516i	−0.981527	+	0.191323i	$0.938722\pi$
$258$	5.02543	+	8.93827i	0.312870	+	0.556472i
$259$	7.39988	−	4.27232i	0.459806	−	0.265469i
$260$	−0.481369	+	2.72998i	−0.0298533	+	0.169306i
$261$	−3.37454	+	2.70281i	−0.208879	+	0.167300i
$262$	6.19106	−	7.37822i	0.382485	−	0.455828i
$263$	−7.51651	+	20.6514i	−0.463488	+	1.27342i	0.459358	+	0.888251i	$0.348080\pi$
$263$	−7.51651	+	20.6514i	−0.463488	+	1.27342i	−0.922845	+	0.385170i	$0.874143\pi$
$264$	−3.51292	+	0.578180i	−0.216205	+	0.0355845i
$265$	−8.69827	+	5.02195i	−0.534331	+	0.308496i
$266$	−26.1841	−	6.52582i	−1.60545	−	0.400124i
$267$	6.87866	−	11.6064i	0.420967	−	0.710298i
$268$	8.02199	+	9.56023i	0.490021	+	0.583984i
$269$	−1.76467	−	10.0079i	−0.107594	−	0.610194i	−0.990153	−	0.139992i	$-0.955292\pi$
$269$	−1.76467	−	10.0079i	−0.107594	−	0.610194i	0.882559	−	0.470202i	$-0.155819\pi$
$270$	−11.8821	+	13.2145i	−0.723123	+	0.804210i
$271$	11.1890	−	9.38869i	0.679683	−	0.570322i	−0.236230	−	0.971697i	$-0.575912\pi$
$271$	11.1890	−	9.38869i	0.679683	−	0.570322i	0.915914	+	0.401375i	$0.131468\pi$
$272$	−22.5109	+	26.8274i	−1.36492	+	1.62665i
$273$	5.22451	−	2.93742i	0.316202	−	0.177781i
$274$	22.1095	+	12.7649i	1.33569	+	0.771158i
$275$	2.08222	−	2.48150i	0.125563	−	0.149640i
$276$	−9.45057	+	11.0053i	−0.568858	+	0.662441i
$277$	8.81336			0.529543			0.264772	−	0.964311i	$-0.414703\pi$
$277$	8.81336			0.529543			0.264772	+	0.964311i	$0.414703\pi$
$278$	−4.85774	+	8.41386i	−0.291348	+	0.504629i
$279$	6.10490	−	6.94727i	0.365491	−	0.415922i
$280$	−4.02927	−	4.80190i	−0.240795	−	0.286968i
$281$	1.36960	−	0.498492i	0.0817032	−	0.0297376i	−0.300845	−	0.953673i	$-0.597269\pi$
$281$	1.36960	−	0.498492i	0.0817032	−	0.0297376i	0.382548	+	0.923935i	$0.375047\pi$
$282$	27.9070	−	4.59313i	1.66184	−	0.273517i
$283$	−5.63746	−	31.9716i	−0.335112	−	1.90052i	−0.426120	−	0.904666i	$-0.640120\pi$
$283$	−5.63746	−	31.9716i	−0.335112	−	1.90052i	0.0910081	−	0.995850i	$-0.470991\pi$
$284$	−4.10427	−	7.10880i	−0.243544	−	0.421830i
$285$	−7.90336	+	11.4359i	−0.468155	+	0.677406i
$286$	−1.94037	+	3.36081i	−0.114736	+	0.198729i
$287$	27.0629	+	9.85011i	1.59748	+	0.581433i
$288$	19.1958	+	7.48694i	1.13112	+	0.441172i
$289$	−27.7986	−	23.3258i	−1.63521	−	1.37211i
$290$	4.85396	−	0.855885i	0.285035	−	0.0502593i
$291$	9.11456	+	25.9598i	0.534305	+	1.52179i
$292$	−18.3445			−1.07353
$293$	0.195948	−	0.339392i	0.0114474	−	0.0198275i	−0.860245	−	0.509881i	$-0.829689\pi$
$293$	0.195948	−	0.339392i	0.0114474	−	0.0198275i	0.871692	+	0.490053i	$0.163023\pi$
$294$	2.44372	−	12.9906i	0.142520	−	0.757626i
$295$	14.6258	+	2.57892i	0.851545	+	0.150150i
$296$	−2.26780	+	1.30932i	−0.131813	+	0.0761025i
$297$	−9.22908	+	4.91525i	−0.535525	+	0.285212i
$298$	5.54929	+	0.978490i	0.321462	+	0.0566824i
$299$	−1.04129	−	5.90543i	−0.0602192	−	0.341520i
$300$	−3.81480	+	1.33939i	−0.220247	+	0.0773295i
$301$	−8.13786	+	6.82847i	−0.469058	+	0.393587i
$302$	−33.0419	+	5.82618i	−1.90135	+	0.335259i
$303$	−8.58875	+	4.82892i	−0.493411	+	0.277414i
$304$	20.2908	+	5.05705i	1.16376	+	0.290042i
$305$		−	20.5215i		−	1.17506i
$306$	−14.7810	+	37.8969i	−0.844971	+	2.16642i
$307$	−5.80729	+	1.02398i	−0.331440	+	0.0584417i	−0.336892	−	0.941543i	$-0.609376\pi$
$307$	−5.80729	+	1.02398i	−0.331440	+	0.0584417i	0.00545214	+	0.999985i	$0.498265\pi$
$308$	3.32640	+	9.13922i	0.189539	+	0.520755i
$309$	4.45331	+	5.43191i	0.253340	+	0.309011i
$310$	−9.90752	+	3.60604i	−0.562709	+	0.204810i
$311$			2.19354i			0.124384i	0.998064	+	0.0621921i	$0.0198092\pi$
$311$			2.19354i			0.124384i	−0.998064	+	0.0621921i	$0.980191\pi$
$312$	−1.60113	+	0.900216i	−0.0906461	+	0.0509647i
$313$	−3.72184	+	21.1076i	−0.210371	+	1.19307i	0.678390	+	0.734702i	$0.262678\pi$
$313$	−3.72184	+	21.1076i	−0.210371	+	1.19307i	−0.888761	+	0.458371i	$0.848433\pi$
$314$	40.5263	−	14.7504i	2.28703	−	0.832412i
$315$	−15.7299	−	9.56668i	−0.886279	−	0.539021i
$316$	12.6559	+	7.30690i	0.711951	+	0.411045i
$317$	−7.32717	−	6.14822i	−0.411535	−	0.345319i	0.413397	−	0.910551i	$-0.364342\pi$
$317$	−7.32717	−	6.14822i	−0.411535	−	0.345319i	−0.824932	+	0.565232i	$0.808787\pi$
$318$	16.4215	+	6.19000i	0.920872	+	0.347118i
$319$	2.85605	+	0.503598i	0.159908	+	0.0281961i
$320$	−3.74252	−	4.46016i	−0.209213	−	0.249331i
$321$	5.06466	−	4.15222i	0.282682	−	0.231755i
$322$	−30.9654	−	17.8779i	−1.72564	−	0.996297i
$323$	−7.69495	+	30.8751i	−0.428159	+	1.71793i
$324$	13.0372	+	0.595354i	0.724286	+	0.0330752i
$325$	0.571626	−	1.57053i	0.0317081	−	0.0871174i
$326$	−6.55541	−	2.38597i	−0.363070	−	0.132147i
$327$	4.15599	+	11.8370i	0.229827	+	0.654585i
$328$	−8.29384	−	3.01871i	−0.457951	−	0.166680i
$329$	10.0213	+	27.5334i	0.552494	+	1.51796i
$330$	11.9196	+	0.135991i	0.656152	+	0.00748607i
$331$		−	7.67688i		−	0.421959i	−0.977490	−	0.210980i	$-0.932335\pi$
$331$		−	7.67688i		−	0.421959i	0.977490	−	0.210980i	$-0.0676654\pi$
$332$	4.26225	+	11.7104i	0.233921	+	0.642693i
$333$	−5.07682	+	5.77734i	−0.278208	+	0.316596i
$334$	4.81672	+	8.34281i	0.263559	+	0.456498i
$335$	7.92332	+	13.7236i	0.432897	+	0.749800i
$336$	−5.12002	+	27.2176i	−0.279320	+	1.48484i
$337$	−2.77732	+	7.63062i	−0.151290	+	0.415667i	−0.992066	−	0.125717i	$-0.959877\pi$
$337$	−2.77732	+	7.63062i	−0.151290	+	0.415667i	0.840776	+	0.541383i	$0.182099\pi$
$338$	3.84535	−	21.8081i	0.209159	−	1.18620i
$339$	−4.07133	−	24.7367i	−0.221124	−	1.34351i
$340$	14.9307	−	12.5283i	0.809729	−	0.679443i
$341$	−6.20366			−0.335947
$342$	24.2076	−	1.98939i	1.30900	−	0.107574i
$343$	−9.63662			−0.520329
$344$	2.49397	−	2.09269i	0.134466	−	0.112830i
$345$	−14.2443	+	11.6780i	−0.766885	+	0.628725i
$346$	0.334920	−	1.89943i	0.0180054	−	0.102114i
$347$	4.50145	−	12.3676i	0.241650	−	0.663929i	−0.758278	−	0.651932i	$-0.773959\pi$
$347$	4.50145	−	12.3676i	0.241650	−	0.663929i	0.999928	−	0.0119971i	$-0.00381890\pi$
$348$	−2.74610	−	2.35816i	−0.147206	−	0.126411i
$349$	−2.14047	−	3.70740i	−0.114577	−	0.198452i	0.803034	−	0.595933i	$-0.203218\pi$
$349$	−2.14047	−	3.70740i	−0.114577	−	0.198452i	−0.917610	+	0.397481i	$0.869884\pi$
$350$	−4.98284	−	8.63053i	−0.266344	−	0.461321i
$351$	−3.60715	+	4.01164i	−0.192535	+	0.214125i
$352$	−4.72698	−	12.9873i	−0.251949	−	0.692225i
$353$		−	23.1211i		−	1.23061i	−0.788288	−	0.615307i	$-0.789032\pi$
$353$		−	23.1211i		−	1.23061i	0.788288	−	0.615307i	$-0.210968\pi$
$354$	−12.7175	−	22.6194i	−0.675926	−	1.20221i
$355$	−3.56484	−	9.79432i	−0.189202	−	0.519829i
$356$	10.6141	+	3.86320i	0.562544	+	0.204749i
$357$	−41.4150	−	7.79076i	−2.19191	−	0.412331i
$358$	18.4831	+	6.72728i	0.976860	+	0.355548i
$359$	1.03497	−	2.84356i	0.0546238	−	0.150078i	−0.909380	−	0.415967i	$-0.863443\pi$
$359$	1.03497	−	2.84356i	0.0546238	−	0.150078i	0.964004	+	0.265889i	$0.0856655\pi$
$360$	4.82066	+	2.93185i	0.254071	+	0.154522i
$361$	18.5841	−	3.95380i	0.978109	−	0.208095i
$362$	38.8971	+	22.4573i	2.04439	+	1.18033i
$363$	−11.2649	−	4.24626i	−0.591256	−	0.222871i
$364$	3.22546	+	3.84396i	0.169060	+	0.201478i
$365$	−22.9393	−	4.04482i	−1.20070	−	0.211716i
$366$	−27.7290	+	22.7334i	−1.44942	+	1.18829i
$367$	22.1772	+	18.6089i	1.15764	+	0.971376i	0.999870	−	0.0160993i	$-0.00512480\pi$
$367$	22.1772	+	18.6089i	1.15764	+	0.971376i	0.157771	+	0.987476i	$0.449569\pi$
$368$	23.9960	+	13.8541i	1.25088	+	0.722195i
$369$	−25.9159	−	0.591428i	−1.34913	−	0.0307885i
$370$	8.23908	−	2.99878i	0.428329	−	0.155899i
$371$	−3.15710	+	17.9048i	−0.163909	+	0.929572i
$372$	6.66093	+	3.94769i	0.345353	+	0.204678i
$373$		−	5.02370i		−	0.260117i	−0.991506	−	0.130059i	$-0.958483\pi$
$373$		−	5.02370i		−	0.260117i	0.991506	−	0.130059i	$-0.0415166\pi$
$374$	25.6399	−	9.33216i	1.32581	−	0.482555i
$375$	−20.7997	+	3.42336i	−1.07409	+	0.176782i
$376$	−3.07118	−	8.43801i	−0.158384	−	0.435157i
$377$	1.47356	−	0.259828i	0.0758920	−	0.0133818i
$378$	4.49865	+	31.8522i	0.231386	+	1.63830i
$379$			10.9355i			0.561718i	0.959749	+	0.280859i	$0.0906193\pi$
$379$			10.9355i			0.561718i	−0.959749	+	0.280859i	$0.909381\pi$
$380$	−10.6324	−	4.73268i	−0.545433	−	0.242781i
$381$	1.95085	+	1.15619i	0.0999449	+	0.0592336i
$382$	−19.8581	+	3.50152i	−1.01603	+	0.179153i
$383$	3.19500	−	2.68092i	0.163257	−	0.136989i	−0.557500	−	0.830177i	$-0.688239\pi$
$383$	3.19500	−	2.68092i	0.163257	−	0.136989i	0.720756	+	0.693189i	$0.243795\pi$
$384$	2.51767	−	13.3837i	0.128479	−	0.682984i
$385$	2.14445	+	12.1618i	0.109291	+	0.619822i
$386$	4.49506	+	0.792600i	0.228793	+	0.0403423i
$387$	4.96865	−	8.16964i	0.252571	−	0.415286i
$388$	−19.9483	+	11.5172i	−1.01272	+	0.584696i
$389$	9.04539	+	1.59495i	0.458619	+	0.0808670i	0.398185	−	0.917305i	$-0.369640\pi$
$389$	9.04539	+	1.59495i	0.458619	+	0.0808670i	0.0604345	+	0.998172i	$0.480751\pi$
$390$	5.80294	−	2.03743i	0.293843	−	0.103169i
$391$	−21.0808	+	36.5130i	−1.06610	+	1.84654i
$392$	−4.19678			−0.211970
$393$	−8.82657	−	1.66041i	−0.445241	−	0.0837564i
$394$	−30.0827	+	5.30439i	−1.51554	+	0.267231i
$395$	14.2148	+	11.9276i	0.715222	+	0.600143i
$396$	−5.47258	−	6.83269i	−0.275008	−	0.343355i
$397$	34.6905	+	12.6263i	1.74106	+	0.633696i	0.999316	−	0.0369820i	$-0.0117744\pi$
$397$	34.6905	+	12.6263i	1.74106	+	0.633696i	0.741749	+	0.670678i	$0.233997\pi$
$398$	−12.7441	+	22.0734i	−0.638802	+	1.10644i
$399$	6.66184	+	24.2655i	0.333509	+	1.21480i
$400$	3.86135	+	6.68805i	0.193067	+	0.334403i
$401$	−4.78032	−	27.1106i	−0.238718	−	1.35384i	−0.834641	−	0.550795i	$-0.814325\pi$
$401$	−4.78032	−	27.1106i	−0.238718	−	1.35384i	0.595923	−	0.803042i	$-0.296786\pi$
$402$	9.76619	−	25.9088i	0.487093	−	1.29221i
$403$	−3.00770	+	1.09471i	−0.149824	+	0.0545316i
$404$	−5.30244	−	6.31921i	−0.263806	−	0.314392i
$405$	16.1713	+	3.61906i	0.803560	+	0.179833i
$406$	4.46099	−	7.72666i	0.221395	−	0.383468i
$407$	5.15895			0.255720
$408$	12.6922	+	2.38759i	0.628360	+	0.118204i
$409$	−8.63679	+	10.2929i	−0.427062	+	0.508952i	−0.936072	−	0.351808i	$-0.885567\pi$
$409$	−8.63679	+	10.2929i	−0.427062	+	0.508952i	0.509011	+	0.860760i	$0.330011\pi$
$410$	25.5928	+	14.7760i	1.26394	+	0.729736i
$411$	0.271591	−	23.8049i	0.0133966	−	1.17421i
$412$	−3.77997	+	4.50479i	−0.186226	+	0.221935i
$413$	20.5938	−	17.2803i	1.01336	−	0.850307i
$414$	31.5590	+	6.31031i	1.55104	+	0.310135i
$415$	2.74777	+	15.5834i	0.134883	+	0.764957i
$416$	−4.58354	−	5.46245i	−0.224727	−	0.267819i
$417$	9.05904	+	0.103355i	0.443623	+	0.00506132i
$418$	−11.7210	−	11.3167i	−0.573292	−	0.553518i
$419$	−28.4986	+	16.4537i	−1.39225	+	0.803814i	−0.993564	−	0.113275i	$-0.963866\pi$
$419$	−28.4986	+	16.4537i	−1.39225	+	0.803814i	−0.398683	+	0.917089i	$0.630532\pi$
$420$	5.43661	−	14.4228i	0.265279	−	0.703762i
$421$	9.94232	−	27.3163i	0.484559	−	1.33131i	−0.420987	−	0.907067i	$-0.638316\pi$
$421$	9.94232	−	27.3163i	0.484559	−	1.33131i	0.905546	−	0.424248i	$-0.139462\pi$
$422$	9.64496	−	11.4944i	0.469510	−	0.559540i
$423$	−16.4870	−	20.5846i	−0.801627	−	1.00086i
$424$	0.967541	−	5.48720i	0.0469880	−	0.266482i
$425$	−10.1767	+	5.87554i	−0.493644	+	0.285005i
$426$	−9.28514	+	15.6668i	−0.449867	+	0.759060i
$427$	−28.4564	−	23.8778i	−1.37710	−	1.15553i
$428$	4.20023	+	3.52441i	0.203026	+	0.170359i
$429$	3.61852	+	0.0412839i	0.174704	+	0.00199321i
$430$	−9.44029	+	5.45035i	−0.455251	+	0.262839i
$431$	6.81517	−	38.6508i	0.328275	−	1.86174i	−0.157306	−	0.987550i	$-0.550281\pi$
$431$	6.81517	−	38.6508i	0.328275	−	1.86174i	0.485581	−	0.874192i	$-0.338608\pi$
$432$	−3.48614	−	24.6832i	−0.167727	−	1.18757i
$433$	21.1600	−	25.2175i	1.01689	−	1.21188i	0.0397614	−	0.999209i	$-0.487340\pi$
$433$	21.1600	−	25.2175i	1.01689	−	1.21188i	0.977124	−	0.212668i	$-0.0682154\pi$
$434$	−6.52751	+	17.9342i	−0.313330	+	0.860868i
$435$	−2.91397	−	3.55430i	−0.139714	−	0.170416i
$436$	−9.09590	+	5.25152i	−0.435614	+	0.251502i
$437$	25.1143	+	1.75380i	1.20138	+	0.0838957i
$438$	19.9463	+	35.4767i	0.953073	+	1.69514i
$439$	−2.47542	−	2.95009i	−0.118145	−	0.140800i	0.703730	−	0.710467i	$-0.251516\pi$
$439$	−2.47542	−	2.95009i	−0.118145	−	0.140800i	−0.821875	+	0.569667i	$0.807072\pi$
$440$	−0.657199	−	3.72716i	−0.0313307	−	0.177685i
$441$	−11.6759	+	3.95041i	−0.555996	+	0.188115i
$442$	10.7841	−	9.04897i	0.512949	−	0.430416i
$443$	20.1469	−	24.0101i	0.957207	−	1.14075i	−0.0327611	−	0.999463i	$-0.510430\pi$
$443$	20.1469	−	24.0101i	0.957207	−	1.14075i	0.989968	−	0.141292i	$-0.0451255\pi$
$444$	−5.53921	−	3.28289i	−0.262879	−	0.155799i
$445$	12.4208	+	7.17115i	0.588802	+	0.339945i
$446$	−18.8065	+	22.4127i	−0.890513	+	1.06127i
$447$	−1.74070	−	4.95780i	−0.0823323	−	0.234496i
$448$	−10.5393			−0.497937
$449$	−6.48937	+	11.2399i	−0.306252	+	0.530444i	−0.977539	−	0.210753i	$-0.932408\pi$
$449$	−6.48937	+	11.2399i	−0.306252	+	0.530444i	0.671287	+	0.741197i	$0.265742\pi$
$450$	6.73815	+	5.92113i	0.317639	+	0.279125i
$451$	11.1770	+	13.3202i	0.526303	+	0.627223i
$452$	19.7225	−	7.17842i	0.927670	−	0.337644i
$453$	19.8360	+	24.1949i	0.931974	+	1.13677i
$454$	−8.92129	−	50.5951i	−0.418697	−	2.37455i
$455$	3.18579	+	5.51795i	0.149352	+	0.258685i
$456$	−2.04162	−	7.43653i	−0.0956075	−	0.348247i
$457$	1.27172	−	2.20269i	0.0594886	−	0.103037i	−0.834747	−	0.550633i	$-0.814386\pi$
$457$	1.27172	−	2.20269i	0.0594886	−	0.103037i	0.894236	+	0.447596i	$0.147720\pi$
$458$	−15.7553	−	5.73444i	−0.736195	−	0.267953i
$459$	37.5586	−	5.30461i	1.75309	−	0.247598i
$460$	−11.8131	−	9.91233i	−0.550787	−	0.462165i
$461$	19.3059	−	3.40415i	0.899166	−	0.158547i	0.295086	−	0.955471i	$-0.404652\pi$
$461$	19.3059	−	3.40415i	0.899166	−	0.158547i	0.604080	+	0.796924i	$0.293541\pi$
$462$	14.0576	−	16.3702i	0.654018	−	0.761611i
$463$	11.1887			0.519984			0.259992	−	0.965611i	$-0.416280\pi$
$463$	11.1887			0.519984			0.259992	+	0.965611i	$0.416280\pi$
$464$	−3.45695	+	5.98762i	−0.160485	+	0.277968i
$465$	7.45887	+	6.40515i	0.345897	+	0.297032i
$466$	−39.0262	−	6.88137i	−1.80785	−	0.318773i
$467$	−12.7064	+	7.33603i	−0.587981	+	0.339471i	−0.764299	−	0.644862i	$-0.776915\pi$
$467$	−12.7064	+	7.33603i	−0.587981	+	0.339471i	0.176318	+	0.984333i	$0.443581\pi$
$468$	−3.85897	−	2.34697i	−0.178381	−	0.108489i
$469$	28.2491	+	4.98108i	1.30442	+	0.230005i
$470$	5.22086	+	29.6090i	0.240820	+	1.36576i
$471$	−30.5102	−	26.2000i	−1.40584	−	1.20723i
$472$	−6.31129	+	5.29580i	−0.290501	+	0.243759i
$473$	−6.31648	+	1.11377i	−0.290432	+	0.0512110i
$474$	0.369885	−	32.4203i	0.0169894	−	1.48911i
$475$	5.81754	+	3.92319i	0.266927	+	0.180008i
$476$		−	35.2810i		−	1.61710i
$477$	−2.47327	−	16.1767i	−0.113243	−	0.740682i
$478$	−15.0285	+	2.64993i	−0.687389	+	0.121205i
$479$	−1.26216	−	3.46776i	−0.0576697	−	0.158446i	0.907512	−	0.420026i	$-0.137979\pi$
$479$	−1.26216	−	3.46776i	−0.0576697	−	0.158446i	−0.965182	+	0.261579i	$0.915757\pi$
$480$	−7.72569	+	20.4956i	−0.352628	+	0.935490i
$481$	2.50120	−	0.910362i	0.114045	−	0.0415089i
$482$			45.4384i			2.06966i
$483$	−0.380377	+	33.3399i	−0.0173077	+	1.51702i
$484$	1.75017	−	9.92573i	0.0795533	−	0.451169i
$485$	−27.4843	+	10.0035i	−1.24800	+	0.454234i
$486$	−13.0242	−	25.8600i	−0.590788	−	1.17303i
$487$	−26.5090	−	15.3050i	−1.20124	−	0.693534i	−0.240407	−	0.970672i	$-0.577281\pi$
$487$	−26.5090	−	15.3050i	−1.20124	−	0.693534i	−0.960830	+	0.277138i	$0.910614\pi$
$488$	8.72089	+	7.31770i	0.394776	+	0.331257i
$489$	1.05645	+	6.41883i	0.0477745	+	0.290269i
$490$	13.8384	+	2.44008i	0.625155	+	0.110232i
$491$	−4.36948	−	5.20734i	−0.197192	−	0.235004i	0.658383	−	0.752683i	$-0.271241\pi$
$491$	−4.36948	−	5.20734i	−0.197192	−	0.235004i	−0.855575	+	0.517679i	$0.826796\pi$
$492$	−3.52454	−	21.4145i	−0.158898	−	0.965438i
$493$	−9.11093	−	5.26020i	−0.410336	−	0.236907i
$494$	−7.67962	−	3.41833i	−0.345522	−	0.153798i
$495$	−5.33676	−	9.75075i	−0.239869	−	0.438263i
$496$	5.05835	−	13.8977i	0.227127	−	0.624026i
$497$	−17.7293	−	6.45292i	−0.795266	−	0.289453i
$498$	18.0125	−	20.9758i	0.807160	−	0.939946i
$499$	2.92874	+	1.06598i	0.131109	+	0.0477196i	0.406741	−	0.913543i	$-0.366665\pi$
$499$	2.92874	+	1.06598i	0.131109	+	0.0477196i	−0.275633	+	0.961263i	$0.588887\pi$
$500$	−6.03595	−	16.5836i	−0.269936	−	0.741642i
$501$	4.58002	−	7.72787i	0.204620	−	0.345256i
$502$			24.6873i			1.10185i
$503$	13.2963	+	36.5314i	0.592854	+	1.62885i	0.765183	+	0.643813i	$0.222649\pi$
$503$	13.2963	+	36.5314i	0.592854	+	1.62885i	−0.172329	+	0.985040i	$0.555129\pi$
$504$	9.67454	−	3.27327i	0.430938	−	0.145803i
$505$	−5.23722	−	9.07114i	−0.233053	−	0.403660i
$506$	−10.7940	−	18.6958i	−0.479854	−	0.831131i
$507$	−19.4836	+	6.84075i	−0.865296	+	0.303808i
$508$	−0.649344	+	1.78406i	−0.0288100	+	0.0791547i
$509$	−0.768996	+	4.36119i	−0.0340852	+	0.193307i	−0.997096	−	0.0761566i	$-0.975735\pi$
$509$	−0.768996	+	4.36119i	−0.0340852	+	0.193307i	0.963011	+	0.269463i	$0.0868462\pi$
$510$	−40.4630	−	15.2523i	−1.79173	−	0.675383i
$511$	−32.2998	+	27.1027i	−1.42886	+	1.19895i
$512$	23.1484			1.02303
$513$	−12.6800	−	18.7675i	−0.559835	−	0.828604i
$514$	−37.4543			−1.65204
$515$	−5.72002	+	4.79967i	−0.252054	+	0.211499i
$516$	7.49080	+	2.82362i	0.329764	+	0.124303i
$517$	−3.07193	+	17.4218i	−0.135103	+	0.766209i
$518$	5.42826	−	14.9140i	0.238504	−	0.655284i
$519$	−1.69697	+	0.595812i	−0.0744887	+	0.0261532i
$520$	−0.976332	−	1.69106i	−0.0428150	−	0.0741577i
$521$	5.51847	+	9.55828i	0.241769	+	0.418756i	0.961218	−	0.275789i	$-0.0889391\pi$
$521$	5.51847	+	9.55828i	0.241769	+	0.418756i	−0.719449	+	0.694545i	$0.755606\pi$
$522$	−1.57458	+	7.87478i	−0.0689176	+	0.344670i
$523$	6.63357	+	18.2256i	0.290066	+	0.796949i	0.996056	+	0.0887276i	$0.0282801\pi$
$523$	6.63357	+	18.2256i	0.290066	+	0.796949i	−0.705990	+	0.708222i	$0.749498\pi$
$524$		−	7.51926i		−	0.328481i
$525$	−4.73798	+	7.99439i	−0.206782	+	0.348904i
$526$	13.9615	+	38.3588i	0.608748	+	1.67252i
$527$	21.1472	+	7.69693i	0.921185	+	0.335284i
$528$	−10.8936	+	12.6857i	−0.474084	+	0.552076i
$529$	9.73338	+	3.54266i	0.423190	+	0.154029i
$530$	−6.38071	+	17.5308i	−0.277160	+	0.761491i
$531$	−12.5738	+	20.6743i	−0.545656	+	0.897188i
$532$	−18.9340	+	9.23690i	−0.820891	+	0.400471i
$533$	7.76941	+	4.48567i	0.336531	+	0.194296i
$534$	−4.06977	−	24.7272i	−0.176116	−	1.07005i
$535$	4.47517	+	5.33330i	0.193478	+	0.230578i
$536$	−8.65736	−	1.52653i	−0.373941	−	0.0659359i
$537$	−2.97869	−	18.0980i	−0.128540	−	0.780985i
$538$	−14.4598	−	12.1332i	−0.623405	−	0.523099i
$539$	7.16034	+	4.13403i	0.308418	+	0.178065i
$540$	−0.474742	+	13.8655i	−0.0204296	+	0.596676i
$541$	−12.3864	+	4.50828i	−0.532533	+	0.193826i	−0.594269	−	0.804266i	$-0.702559\pi$
$541$	−12.3864	+	4.50828i	−0.532533	+	0.193826i	0.0617360	+	0.998093i	$0.480336\pi$
$542$	4.71110	−	26.7180i	0.202359	−	1.14764i
$543$	0.477809	−	41.8798i	0.0205047	−	1.79723i
$544$			50.1361i			2.14957i
$545$	−12.5321	+	4.56131i	−0.536815	+	0.195385i
$546$	3.92676	−	10.4174i	0.168050	−	0.445822i
$547$	7.71585	+	21.1991i	0.329906	+	0.906409i	0.988135	+	0.153591i	$0.0490838\pi$
$547$	7.71585	+	21.1991i	0.329906	+	0.906409i	−0.658229	+	0.752818i	$0.728694\pi$
$548$	19.6281	−	3.46096i	0.838471	−	0.147845i
$549$	31.1506	+	12.1497i	1.32947	+	0.518536i
$550$		−	6.01692i		−	0.256562i
$551$	−0.437618	+	6.26665i	−0.0186431	+	0.266968i
$552$	0.116572	−	10.2175i	0.00496164	−	0.434886i
$553$	33.0791	−	5.83273i	1.40667	−	0.248033i
$554$	12.5404	−	10.5226i	0.532789	−	0.447063i
$555$	−6.20278	−	5.32651i	−0.263293	−	0.226098i
$556$	1.31708	+	7.46954i	0.0558567	+	0.316779i
$557$	−6.75730	−	1.19149i	−0.286316	−	0.0504853i	0.0286456	−	0.999590i	$-0.490881\pi$
$557$	−6.75730	−	1.19149i	−0.286316	−	0.0504853i	−0.314962	+	0.949104i	$0.601992\pi$
$558$	0.391930	−	17.1740i	0.0165917	−	0.727035i
$559$	−2.86586	+	1.65461i	−0.121213	+	0.0699824i
$560$	−28.9939	−	5.11241i	−1.22522	−	0.216039i
$561$	−19.3030	−	16.5760i	−0.814973	−	0.699841i
$562$	1.35360	−	2.34451i	0.0570983	−	0.0988972i
$563$	14.3595			0.605181			0.302590	−	0.953121i	$-0.402149\pi$
$563$	14.3595			0.605181			0.302590	+	0.953121i	$0.402149\pi$
$564$	14.3847	−	16.7511i	0.605704	−	0.705349i
$565$	26.2453	−	4.62775i	1.10415	−	0.194691i
$566$	−46.1936	−	38.7611i	−1.94166	−	1.62925i
$567$	23.8345	−	18.2132i	1.00096	−	0.764883i
$568$	5.43339	+	1.97759i	0.227980	+	0.0829780i
$569$	−10.6542	+	18.4536i	−0.446647	+	0.773616i	−0.998165	−	0.0605472i	$-0.980715\pi$
$569$	−10.6542	+	18.4536i	−0.446647	+	0.773616i	0.551518	+	0.834163i	$0.314049\pi$
$570$	2.40827	+	25.7081i	0.100871	+	1.07679i
$571$	−0.953898	−	1.65220i	−0.0399194	−	0.0691424i	0.845375	−	0.534173i	$-0.179377\pi$
$571$	−0.953898	−	1.65220i	−0.0399194	−	0.0691424i	−0.885295	+	0.465030i	$0.846043\pi$
$572$	0.526092	+	2.98362i	0.0219970	+	0.124751i
$573$	11.9214	+	14.5411i	0.498022	+	0.607461i
$574$	50.2678	−	18.2960i	2.09814	−	0.763659i
$575$	5.97625	+	7.12221i	0.249227	+	0.297017i
$576$	8.98603	−	3.04032i	0.374418	−	0.126680i
$577$	−15.3988	+	26.6715i	−0.641061	+	1.11035i	0.344135	+	0.938920i	$0.388172\pi$
$577$	−15.3988	+	26.6715i	−0.641061	+	1.11035i	−0.985196	+	0.171430i	$0.945161\pi$
$578$	−67.4038			−2.80363
$579$	−1.41001	−	4.01594i	−0.0585980	−	0.166897i
$580$	2.47338	−	2.94766i	0.102701	−	0.122395i
$581$	24.8060	+	14.3217i	1.02913	+	0.594166i
$582$	43.9634	+	26.0555i	1.82234	+	1.08003i
$583$	−7.05592	+	8.40892i	−0.292226	+	0.348262i
$584$	9.89875	−	8.30603i	0.409613	−	0.343706i
$585$	−4.30805	−	3.78569i	−0.178116	−	0.156519i
$586$	−0.126403	−	0.716864i	−0.00522164	−	0.0296134i
$587$	−6.60180	−	7.86771i	−0.272485	−	0.324735i	0.612397	−	0.790551i	$-0.290206\pi$
$587$	−6.60180	−	7.86771i	−0.272485	−	0.324735i	−0.884882	+	0.465815i	$0.845761\pi$
$588$	−5.05745	−	8.99521i	−0.208566	−	0.370956i
$589$	−1.40588	−	13.3640i	−0.0579281	−	0.550654i
$590$	23.8898	−	13.7928i	0.983528	−	0.567840i
$591$	18.0595	+	22.0280i	0.742867	+	0.906110i
$592$	−4.20652	+	11.5573i	−0.172887	+	0.475002i
$593$	5.84464	−	6.96537i	0.240011	−	0.286033i	−0.632571	−	0.774503i	$-0.718000\pi$
$593$	5.84464	−	6.96537i	0.240011	−	0.286033i	0.872581	+	0.488469i	$0.162445\pi$
$594$	−7.26337	+	18.0128i	−0.298020	+	0.739073i
$595$	7.77919	−	44.1180i	0.318915	−	1.80866i
$596$	3.80973	−	2.19955i	0.156053	−	0.0900971i
$597$	23.7660	+	0.271147i	0.972677	+	0.0110973i
$598$	−8.53236	−	7.15950i	−0.348914	−	0.292774i
$599$	−9.99737	−	8.38879i	−0.408482	−	0.342757i	0.415279	−	0.909694i	$-0.363684\pi$
$599$	−9.99737	−	8.38879i	−0.408482	−	0.342757i	−0.823761	+	0.566937i	$0.808128\pi$
$600$	1.45202	−	2.45000i	0.0592786	−	0.100021i
$601$	−3.33374	+	1.92474i	−0.135986	+	0.0785117i	−0.566450	−	0.824096i	$-0.691683\pi$
$601$	−3.33374	+	1.92474i	−0.135986	+	0.0785117i	0.430463	+	0.902608i	$0.358350\pi$
$602$	−3.42642	+	19.4322i	−0.139651	+	0.791998i
$603$	−25.5226	+	3.90217i	−1.03936	+	0.158909i
$604$	−16.8368	+	20.0653i	−0.685079	+	0.816445i
$605$	4.37709	−	12.0259i	0.177954	−	0.488924i
$606$	−6.45534	+	17.1254i	−0.262230	+	0.695673i
$607$	27.0590	−	15.6225i	1.09829	−	0.634098i	0.162519	−	0.986705i	$-0.448038\pi$
$607$	27.0590	−	15.6225i	1.09829	−	0.634098i	0.935771	+	0.352607i	$0.114705\pi$
$608$	26.9061	−	13.1261i	1.09119	−	0.532334i
$609$	−8.31915	−	0.0949136i	−0.337109	−	0.00384609i
$610$	−24.5015	−	29.1997i	−0.992036	−	1.18226i
$611$	1.58494	+	8.98863i	0.0641197	+	0.363641i
$612$	10.1777	+	30.0813i	0.411408	+	1.21596i
$613$	−15.2044	+	12.7580i	−0.614101	+	0.515292i	−0.895943	−	0.444169i	$-0.853499\pi$
$613$	−15.2044	+	12.7580i	−0.614101	+	0.515292i	0.281842	+	0.959461i	$0.409055\pi$
$614$	−7.04051	+	8.39056i	−0.284132	+	0.338615i
$615$	0.314380	−	27.5553i	0.0126770	−	1.11114i
$616$	−5.93299	−	3.42541i	−0.239047	−	0.138014i
$617$	9.67497	−	11.5302i	0.389500	−	0.464188i	−0.535289	−	0.844669i	$-0.679797\pi$
$617$	9.67497	−	11.5302i	0.389500	−	0.464188i	0.924789	+	0.380481i	$0.124242\pi$
$618$	12.8219	+	2.41198i	0.515772	+	0.0970242i
$619$	−6.02193			−0.242042			−0.121021	−	0.992650i	$-0.538617\pi$
$619$	−6.02193			−0.242042			−0.121021	+	0.992650i	$0.538617\pi$
$620$	−4.11554	+	7.12833i	−0.165284	+	0.286281i
$621$	−9.29338	−	28.5359i	−0.372930	−	1.14511i
$622$	2.61895	+	3.12115i	0.105010	+	0.125147i
$623$	24.3961	−	8.87946i	0.977410	−	0.355748i
$624$	−3.04296	+	8.07271i	−0.121816	+	0.323167i
$625$	−2.49357	−	14.1417i	−0.0997427	−	0.565669i
$626$	19.9055	+	34.4773i	0.795583	+	1.37799i
$627$	−3.84202	+	14.6989i	−0.153435	+	0.587019i
$628$	16.8345	−	29.1582i	0.671768	−	1.16354i
$629$	−17.5859	−	6.40075i	−0.701197	−	0.255215i
$630$	−33.8038	+	5.16828i	−1.34678	+	0.205909i
$631$	29.0095	+	24.3418i	1.15485	+	0.969033i	0.999822	−	0.0188777i	$-0.00600933\pi$
$631$	29.0095	+	24.3418i	1.15485	+	0.969033i	0.155026	+	0.987910i	$0.450454\pi$
$632$	−10.1376	+	1.78753i	−0.403251	+	0.0711040i
$633$	−13.7508	−	2.58672i	−0.546545	−	0.102813i
$634$	−17.7663			−0.705590
$635$	−1.20536	+	2.08774i	−0.0478331	+	0.0828494i
$636$	12.9270	−	4.53871i	0.512589	−	0.179972i
$637$	4.20103	+	0.740755i	0.166451	+	0.0293498i
$638$	4.66508	−	2.69339i	0.184692	−	0.106632i
$639$	16.9778	+	0.387452i	0.671631	+	0.0153273i
$640$	14.2572	+	2.51393i	0.563565	+	0.0993717i
$641$	−4.09124	−	23.2026i	−0.161594	−	0.916447i	−0.952507	−	0.304518i	$-0.901505\pi$
$641$	−4.09124	−	23.2026i	−0.161594	−	0.916447i	0.790912	−	0.611929i	$-0.209606\pi$
$642$	2.24891	−	11.9550i	0.0887575	−	0.471827i
$643$	−11.3449	+	9.51952i	−0.447400	+	0.375413i	−0.838470	−	0.544948i	$-0.816549\pi$
$643$	−11.3449	+	9.51952i	−0.447400	+	0.375413i	0.391070	+	0.920361i	$0.372105\pi$
$644$	−27.4901	+	4.84724i	−1.08326	+	0.191008i
$645$	8.74445	+	5.18251i	0.344312	+	0.204061i
$646$	25.9140	+	53.1189i	1.01957	+	2.08993i
$647$			15.6034i			0.613433i	0.951801	+	0.306716i	$0.0992303\pi$
$647$			15.6034i			0.613433i	−0.951801	+	0.306716i	$0.900770\pi$
$648$	−7.30444	+	5.58171i	−0.286945	+	0.219270i
$649$	15.9846	−	2.81852i	0.627451	−	0.110637i
$650$	−1.06176	−	2.91717i	−0.0416457	−	0.114421i
$651$	17.5605	−	2.89023i	0.688251	−	0.113277i
$652$	−5.11773	+	1.86270i	−0.200426	+	0.0729491i
$653$		−	18.6660i		−	0.730459i	−0.930918	−	0.365229i	$-0.880991\pi$
$653$		−	18.6660i		−	0.730459i	0.930918	−	0.365229i	$-0.119009\pi$
$654$	20.0461	+	11.8806i	0.783864	+	0.464567i
$655$	1.65794	−	9.40263i	0.0647810	−	0.367391i
$656$	−38.9540	+	14.1781i	−1.52090	+	0.553561i
$657$	19.7210	−	32.4259i	0.769388	−	1.26506i
$658$	47.1323	+	27.2119i	1.83741	+	1.06083i
$659$	1.37276	+	1.15188i	0.0534752	+	0.0448710i	0.669134	−	0.743142i	$-0.266665\pi$
$659$	1.37276	+	1.15188i	0.0534752	+	0.0448710i	−0.615658	+	0.788013i	$0.711110\pi$
$660$	7.19666	−	5.90013i	0.280130	−	0.229662i
$661$	17.2956	+	3.04967i	0.672719	+	0.118619i	0.499565	−	0.866276i	$-0.333493\pi$
$661$	17.2956	+	3.04967i	0.672719	+	0.118619i	0.173154	+	0.984895i	$0.444604\pi$
$662$	−9.16573	−	10.9233i	−0.356236	−	0.424546i
$663$	−12.2837	−	4.63026i	−0.477058	−	0.179824i
$664$	−7.60216	−	4.38911i	−0.295021	−	0.170330i
$665$	−25.7131	+	7.37570i	−0.997110	+	0.286018i
$666$	−0.325928	+	14.2819i	−0.0126295	+	0.553412i
$667$	−2.84687	+	7.82170i	−0.110231	+	0.302857i
$668$	7.06717	+	2.57224i	0.273437	+	0.0995229i
$669$	26.8123	+	5.04379i	1.03662	+	0.195004i
$670$	27.6591	+	10.0671i	1.06856	+	0.388925i
$671$	−7.67088	−	21.0756i	−0.296131	−	0.813614i
$672$	19.4312	+	34.5605i	0.749575	+	1.33320i
$673$		−	27.5490i		−	1.06194i	−0.847392	−	0.530968i	$-0.821828\pi$
$673$		−	27.5490i		−	1.06194i	0.847392	−	0.530968i	$-0.178172\pi$
$674$	5.15870	+	14.1734i	0.198706	+	0.545940i
$675$	1.73352	−	8.18295i	0.0667231	−	0.314962i
$676$	−8.64398	−	14.9718i	−0.332461	−	0.575839i
$677$	6.64844	+	11.5154i	0.255520	+	0.442574i	0.965037	−	0.262115i	$-0.0844199\pi$
$677$	6.64844	+	11.5154i	0.255520	+	0.442574i	−0.709516	+	0.704689i	$0.751087\pi$
$678$	−35.3271	−	30.3364i	−1.35673	−	1.16506i
$679$	−18.1078	+	49.7509i	−0.694915	+	1.90926i
$680$	−2.38405	+	13.5206i	−0.0914240	+	0.518491i
$681$	−37.0482	+	30.3736i	−1.41969	+	1.16392i
$682$	−8.82708	+	7.40680i	−0.338006	+	0.283621i
$683$	22.0982			0.845566			0.422783	−	0.906231i	$-0.361053\pi$
$683$	22.0982			0.845566			0.422783	+	0.906231i	$0.361053\pi$
$684$	13.4788	−	13.3375i	0.515376	−	0.509973i
$685$	25.3075			0.966950
$686$	−13.7118	+	11.5055i	−0.523518	+	0.439284i
$687$	2.53908	+	15.4270i	0.0968720	+	0.588577i
$688$	2.65523	−	15.0586i	0.101230	−	0.574103i
$689$	−1.93704	+	5.32198i	−0.0737954	+	0.202751i
$690$	−6.32502	+	33.6232i	−0.240789	+	1.28002i
$691$	−11.6378	−	20.1573i	−0.442724	−	0.766821i	0.555166	−	0.831739i	$-0.312655\pi$
$691$	−11.6378	−	20.1573i	−0.442724	−	0.766821i	−0.997891	+	0.0649186i	$0.979321\pi$
$692$	−0.752868	−	1.30401i	−0.0286198	−	0.0495709i
$693$	−19.7305	−	3.94517i	−0.749501	−	0.149865i
$694$	−8.36117	−	22.9721i	−0.317386	−	0.872010i
$695$			9.63086i			0.365319i
$696$	2.54953	+	0.0290877i	0.0966396	+	0.00110257i
$697$	−21.5738	−	59.2735i	−0.817165	−	2.24514i
$698$	−7.47204	−	2.71960i	−0.282821	−	0.102938i
$699$	12.2417	+	34.8665i	0.463025	+	1.31877i
$700$	−7.31090	−	2.66095i	−0.276326	−	0.100574i
$701$	7.58127	−	20.8294i	0.286341	−	0.786715i	−0.710230	−	0.703970i	$-0.751409\pi$
$701$	7.58127	−	20.8294i	0.286341	−	0.786715i	0.996571	−	0.0827450i	$-0.0263687\pi$
$702$	−0.342897	+	10.0148i	−0.0129418	+	0.377984i
$703$	1.16912	+	11.1135i	0.0440943	+	0.419152i
$704$	−5.51075	−	3.18164i	−0.207694	−	0.119912i
$705$	21.6811	−	17.7751i	0.816558	−	0.669448i
$706$	−27.6052	−	32.8986i	−1.03894	−	1.23816i
$707$	−18.6723	−	3.29244i	−0.702246	−	0.123825i
$708$	−18.9564	−	7.14551i	−0.712425	−	0.268545i
$709$	−24.2283	−	20.3300i	−0.909915	−	0.763509i	0.0621881	−	0.998064i	$-0.480192\pi$
$709$	−24.2283	−	20.3300i	−0.909915	−	0.763509i	−0.972103	+	0.234555i	$0.924637\pi$
$710$	−16.7662	−	9.67995i	−0.629223	−	0.363282i
$711$	−26.5212	+	14.5155i	−0.994624	+	0.544376i
$712$	−7.47655	+	2.72124i	−0.280196	+	0.101983i
$713$	3.09186	−	17.5348i	0.115791	−	0.656684i
$714$	−68.2304	+	38.3617i	−2.55346	+	1.43565i
$715$			3.84693i			0.143867i
$716$	14.4295	−	5.25192i	0.539256	−	0.196273i
$717$	9.02203	+	11.0046i	0.336934	+	0.410974i
$718$	−1.92240	−	5.28175i	−0.0717433	−	0.197113i
$719$	31.0491	−	5.47480i	1.15794	−	0.204176i	0.438499	−	0.898732i	$-0.355510\pi$
$719$	31.0491	−	5.47480i	1.15794	−	0.204176i	0.719438	+	0.694556i	$0.244399\pi$
$720$	26.1955	−	4.00505i	0.976250	−	0.149260i
$721$			13.5164i			0.503376i
$722$	21.7223	−	27.8140i	0.808421	−	1.03513i
$723$	36.9337	−	20.7655i	1.37358	−	0.772277i
$724$	34.5316	−	6.08885i	1.28336	−	0.226290i
$725$	−1.77717	+	1.49122i	−0.0660025	+	0.0553827i
$726$	−21.0985	+	7.40774i	−0.783037	+	0.274927i
$727$	6.35871	+	36.0620i	0.235831	+	1.33747i	0.840856	+	0.541260i	$0.182052\pi$
$727$	6.35871	+	36.0620i	0.235831	+	1.33747i	−0.605024	+	0.796207i	$0.706837\pi$
$728$	−3.48093	−	0.613782i	−0.129012	−	0.0227483i
$729$	−15.0677	+	22.4046i	−0.558063	+	0.829798i
$730$	−37.4692	+	21.6329i	−1.38680	+	0.800668i
$731$	22.9136	+	4.04028i	0.847489	+	0.149435i
$732$	−5.17510	+	27.5104i	−0.191277	+	1.01681i
$733$	14.7002	−	25.4615i	0.542964	−	0.940442i	−0.455768	−	0.890099i	$-0.650635\pi$
$733$	14.7002	−	25.4615i	0.542964	−	0.940442i	0.998732	−	0.0503430i	$-0.0160314\pi$
$734$	53.7734			1.98481
$735$	−4.34083	−	12.3634i	−0.160114	−	0.456031i
$736$	39.0648	−	6.88817i	1.43995	−	0.253901i
$737$	13.2671	+	11.1324i	0.488698	+	0.410067i
$738$	−37.5813	+	30.1004i	−1.38339	+	1.10801i
$739$	−45.1726	−	16.4415i	−1.66170	−	0.604810i	−0.671072	−	0.741392i	$-0.734166\pi$
$739$	−45.1726	−	16.4415i	−1.66170	−	0.604810i	−0.990629	+	0.136583i	$0.956388\pi$
$740$	3.42248	−	5.92791i	0.125813	−	0.217914i
$741$	0.731096	+	7.80441i	0.0268575	+	0.286702i
$742$	16.8851	+	29.2458i	0.619871	+	1.07365i
$743$	−0.262367	−	1.48796i	−0.00962530	−	0.0545878i	0.979617	−	0.200875i	$-0.0643786\pi$
$743$	−0.262367	−	1.48796i	−0.00962530	−	0.0545878i	−0.989242	+	0.146288i	$0.953268\pi$
$744$	−5.38168	+	0.885754i	−0.197302	+	0.0324733i
$745$	5.24895	−	1.91046i	0.192307	−	0.0699939i
$746$	−5.99799	−	7.14813i	−0.219602	−	0.261712i
$747$	−25.2815	−	5.05510i	−0.925002	−	0.184957i
$748$	10.6507	−	18.4476i	0.389429	−	0.674510i
$749$	12.6025			0.460487
$750$	−25.5083	+	29.7046i	−0.931430	+	1.08466i
$751$	15.4593	−	18.4237i	0.564118	−	0.672290i	−0.406295	−	0.913742i	$-0.633179\pi$
$751$	15.4593	−	18.4237i	0.564118	−	0.672290i	0.970413	+	0.241452i	$0.0776237\pi$
$752$	−36.5242	−	21.0873i	−1.33190	−	0.768973i
$753$	20.0665	−	11.2822i	0.731265	−	0.411145i
$754$	1.78648	−	2.12904i	0.0650596	−	0.0775350i
$755$	−25.4782	+	21.3787i	−0.927245	+	0.778051i
$756$	18.6744	+	16.7915i	0.679180	+	0.610700i
$757$	−2.26718	−	12.8578i	−0.0824019	−	0.467325i	−0.997887	−	0.0649728i	$-0.979304\pi$
$757$	−2.26718	−	12.8578i	−0.0824019	−	0.467325i	0.915485	−	0.402352i	$-0.131807\pi$
$758$	13.0563	+	15.5599i	0.474226	+	0.565161i
$759$	−10.2636	+	17.3178i	−0.372545	+	0.628595i
$760$	7.88015	−	2.26039i	0.285843	−	0.0819931i
$761$	−27.7682	+	16.0320i	−1.00660	+	0.581159i	−0.910193	−	0.414183i	$-0.864067\pi$
$761$	−27.7682	+	16.0320i	−1.00660	+	0.581159i	−0.0964035	+	0.995342i	$0.530734\pi$
$762$	4.15625	−	0.684064i	0.150565	−	0.0247810i
$763$	−8.25668	+	22.6850i	−0.298912	+	0.821254i
$764$	−10.1189	+	12.0592i	−0.366088	+	0.436286i
$765$	6.09420	+	39.8599i	0.220336	+	1.44114i
$766$	1.34525	−	7.62927i	0.0486057	−	0.275657i
$767$	7.25241	−	4.18718i	0.261869	−	0.151190i
$768$	−17.7654	−	31.5977i	−0.641054	−	1.14018i
$769$	−1.31313

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42288 - 1.19394i) q^{2} +(-1.62073 - 0.610926i) q^{3} +(0.251804 - 1.42805i) q^{4} +(0.629748 - 1.73022i) q^{5} +(-3.03552 + 1.06578i) q^{6} +(-1.66649 - 2.88644i) q^{7} +(0.510719 + 0.884592i) q^{8} +(2.25354 + 1.98029i) q^{9} +O(q^{10})\)	\(q+(1.42288 - 1.19394i) q^{2} +(-1.62073 - 0.610926i) q^{3} +(0.251804 - 1.42805i) q^{4} +(0.629748 - 1.73022i) q^{5} +(-3.03552 + 1.06578i) q^{6} +(-1.66649 - 2.88644i) q^{7} +(0.510719 + 0.884592i) q^{8} +(2.25354 + 1.98029i) q^{9} +(-1.16972 - 3.21378i) q^{10} -2.01233i q^{11} +(-1.28054 + 2.16066i) q^{12} +(-0.355101 - 0.975632i) q^{13} +(-5.81744 - 2.11738i) q^{14} +(-2.07769 + 2.41949i) q^{15} +(4.50811 + 1.64082i) q^{16} +(-2.49671 + 6.85966i) q^{17} +(5.57087 + 0.127133i) q^{18} +(4.33498 - 0.456034i) q^{19} +(-2.31227 - 1.33499i) q^{20} +(0.937526 + 5.69624i) q^{21} +(-2.40260 - 2.86331i) q^{22} +(5.68790 + 1.00293i) q^{23} +(-0.287319 - 1.74570i) q^{24} +(1.23315 + 1.03473i) q^{25} +(-1.67011 - 0.964239i) q^{26} +(-2.44257 - 4.58627i) q^{27} +(-4.54161 + 1.65301i) q^{28} +(-0.250256 + 1.41927i) q^{29} +(-0.0675790 + 5.92328i) q^{30} -3.08283i q^{31} +(6.45386 - 2.34901i) q^{32} +(-1.22938 + 3.26144i) q^{33} +(4.63749 + 12.7414i) q^{34} +(-6.04364 + 1.06566i) q^{35} +(3.39541 - 2.71953i) q^{36} +2.56367i q^{37} +(5.62368 - 5.82458i) q^{38} +(-0.0205155 + 1.79818i) q^{39} +(1.85216 - 0.326586i) q^{40} +(-6.61929 + 5.55425i) q^{41} +(8.13495 + 6.98572i) q^{42} +(-0.553471 - 3.13889i) q^{43} +(-2.87371 - 0.506713i) q^{44} +(4.84550 - 2.65203i) q^{45} +(9.29064 - 5.36395i) q^{46} +(-8.65752 - 1.52655i) q^{47} +(-6.30401 - 5.41344i) q^{48} +(-2.05435 + 3.55824i) q^{49} +2.99003 q^{50} +(8.23725 - 9.59236i) q^{51} +(-1.48267 + 0.261435i) q^{52} +(-4.17870 - 3.50634i) q^{53} +(-8.95121 - 3.60944i) q^{54} +(-3.48177 - 1.26726i) q^{55} +(1.70221 - 2.94832i) q^{56} +(-7.30444 - 1.90924i) q^{57} +(1.33844 + 2.31825i) q^{58} +(1.40063 + 7.94334i) q^{59} +(2.93199 + 3.57629i) q^{60} +(10.4732 - 3.81194i) q^{61} +(-3.68071 - 4.38650i) q^{62} +(1.96050 - 9.80483i) q^{63} +(1.58107 - 2.73850i) q^{64} -1.91168 q^{65} +(2.14470 + 6.10846i) q^{66} +(-5.53209 + 6.59289i) q^{67} +(9.16728 + 5.29273i) q^{68} +(-8.60584 - 5.10036i) q^{69} +(-7.32705 + 8.73204i) q^{70} +(4.33638 - 3.63865i) q^{71} +(-0.600825 + 3.00484i) q^{72} +(-2.19677 - 12.4585i) q^{73} +(3.06087 + 3.64780i) q^{74} +(-1.36645 - 2.43038i) q^{75} +(0.440324 - 6.30541i) q^{76} +(-5.80846 + 3.35352i) q^{77} +(2.11772 + 2.58309i) q^{78} +(-3.44685 + 9.47013i) q^{79} +(5.67794 - 6.76671i) q^{80} +(1.15688 + 8.92534i) q^{81} +(-2.78704 + 15.8061i) q^{82} +(-7.44260 + 4.29699i) q^{83} +(8.37060 + 0.0955007i) q^{84} +(10.2964 + 8.63972i) q^{85} +(-4.53517 - 3.80546i) q^{86} +(1.27267 - 2.14737i) q^{87} +(1.78009 - 1.02773i) q^{88} +(-1.35261 + 7.67105i) q^{89} +(3.72821 - 9.55876i) q^{90} +(-2.22433 + 2.65085i) q^{91} +(2.86447 - 7.87007i) q^{92} +(-1.88338 + 4.99643i) q^{93} +(-14.1412 + 8.16445i) q^{94} +(1.94091 - 7.78765i) q^{95} +(-11.8950 - 0.135711i) q^{96} +(-10.2106 - 12.1685i) q^{97} +(1.32522 + 7.51572i) q^{98} +(3.98500 - 4.53486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

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