LMFDB - Embedded newform 567.2.bd.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245063 + 0.0432112i) q^{2} +(-1.82120 + 0.662861i) q^{4} +(-1.99870 + 0.727467i) q^{5} +(0.302346 - 2.62842i) q^{7} +(0.848674 - 0.489982i) q^{8} +O(q^{10})$	\(q+(-0.245063 + 0.0432112i) q^{2} +(-1.82120 + 0.662861i) q^{4} +(-1.99870 + 0.727467i) q^{5} +(0.302346 - 2.62842i) q^{7} +(0.848674 - 0.489982i) q^{8} +(0.458373 - 0.264642i) q^{10} +(0.489168 - 1.34398i) q^{11} +(1.30709 + 3.59121i) q^{13} +(0.0394834 + 0.657193i) q^{14} +(2.78250 - 2.33479i) q^{16} +(-0.109097 - 0.188961i) q^{17} +(2.56992 + 1.48374i) q^{19} +(3.15782 - 2.64972i) q^{20} +(-0.0618021 + 0.350497i) q^{22} +(7.61556 + 1.34283i) q^{23} +(-0.364628 + 0.305959i) q^{25} +(-0.475500 - 0.823590i) q^{26} +(1.19165 + 4.98728i) q^{28} +(1.78349 - 4.90009i) q^{29} +(1.32486 + 3.64001i) q^{31} +(-1.84082 + 2.19380i) q^{32} +(0.0349009 + 0.0415932i) q^{34} +(1.30779 + 5.47337i) q^{35} +6.01251 q^{37} +(-0.693906 - 0.252561i) q^{38} +(-1.33980 + 1.59671i) q^{40} +(10.0627 - 3.66253i) q^{41} +(1.29579 + 7.34878i) q^{43} +2.77190i q^{44} -1.92432 q^{46} +(5.51793 + 2.00836i) q^{47} +(-6.81717 - 1.58938i) q^{49} +(0.0761360 - 0.0907353i) q^{50} +(-4.76094 - 5.67387i) q^{52} +(-12.1036 - 6.98800i) q^{53} +3.04206i q^{55} +(-1.03129 - 2.37882i) q^{56} +(-0.225328 + 1.27790i) q^{58} +(1.21070 + 1.01590i) q^{59} +(1.45500 - 3.99757i) q^{61} +(-0.481963 - 0.834784i) q^{62} +(-3.27598 + 5.67416i) q^{64} +(-5.22497 - 6.22688i) q^{65} +(2.59043 - 14.6911i) q^{67} +(0.323942 + 0.271820i) q^{68} +(-0.557002 - 1.28481i) q^{70} +(4.29452 + 2.47944i) q^{71} -2.46806i q^{73} +(-1.47344 + 0.259808i) q^{74} +(-5.66384 - 0.998688i) q^{76} +(-3.38464 - 1.69209i) q^{77} +(-0.675969 - 3.83361i) q^{79} +(-3.86290 + 6.69073i) q^{80} +(-2.30773 + 1.33237i) q^{82} +(0.141502 + 0.0515026i) q^{83} +(0.355515 + 0.298313i) q^{85} +(-0.635099 - 1.74492i) q^{86} +(-0.243381 - 1.38028i) q^{88} +(-3.40271 + 5.89366i) q^{89} +(9.83439 - 2.34980i) q^{91} +(-14.7595 + 2.60251i) q^{92} +(-1.43902 - 0.253739i) q^{94} +(-6.21587 - 1.09603i) q^{95} +(12.2644 - 2.16255i) q^{97} +(1.73932 + 0.0949204i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.245063	+	0.0432112i	−0.173286	+	0.0305549i	−0.259618	−	0.965711i	$-0.583597\pi$
$2$	−0.245063	+	0.0432112i	−0.173286	+	0.0305549i	0.0863320	+	0.996266i	$0.472485\pi$
$3$		0			0
$3$		0			0
$4$	−1.82120	+	0.662861i	−0.910598	+	0.331431i
$5$	−1.99870	+	0.727467i	−0.893846	+	0.325333i	−0.747784	−	0.663942i	$-0.768882\pi$
$5$	−1.99870	+	0.727467i	−0.893846	+	0.325333i	−0.146062	+	0.989275i	$0.546660\pi$
$6$		0			0
$7$	0.302346	−	2.62842i	0.114276	−	0.993449i
$7$	0.302346	−	2.62842i	0.114276	−	0.993449i
$8$	0.848674	−	0.489982i	0.300052	−	0.173235i
$9$		0			0
$10$	0.458373	−	0.264642i	0.144950	−	0.0836870i
$11$	0.489168	−	1.34398i	0.147490	−	0.405225i	−0.843845	−	0.536588i	$-0.819713\pi$
$11$	0.489168	−	1.34398i	0.147490	−	0.405225i	0.991334	+	0.131363i	$0.0419353\pi$
$12$		0			0
$13$	1.30709	+	3.59121i	0.362522	+	0.996021i	0.978135	+	0.207972i	$0.0666864\pi$
$13$	1.30709	+	3.59121i	0.362522	+	0.996021i	−0.615613	+	0.788049i	$0.711091\pi$
$14$	0.0394834	+	0.657193i	0.0105524	+	0.175642i
$15$		0			0
$16$	2.78250	−	2.33479i	0.695625	−	0.583699i
$17$	−0.109097	−	0.188961i	−0.0264599	−	0.0458299i	0.852492	−	0.522740i	$-0.175090\pi$
$17$	−0.109097	−	0.188961i	−0.0264599	−	0.0458299i	−0.878952	+	0.476910i	$0.841757\pi$
$18$		0			0
$19$	2.56992	+	1.48374i	0.589579	+	0.340394i	0.764931	−	0.644112i	$-0.222773\pi$
$19$	2.56992	+	1.48374i	0.589579	+	0.340394i	−0.175352	+	0.984506i	$0.556106\pi$
$20$	3.15782	−	2.64972i	0.706109	−	0.592496i
$21$		0			0
$22$	−0.0618021	+	0.350497i	−0.0131762	+	0.0747262i
$23$	7.61556	+	1.34283i	1.58795	+	0.279999i	0.896709	−	0.442621i	$-0.145951\pi$
$23$	7.61556	+	1.34283i	1.58795	+	0.279999i	0.691246	+	0.722620i	$0.257062\pi$
$24$		0			0
$25$	−0.364628	+	0.305959i	−0.0729256	+	0.0611919i
$26$	−0.475500	−	0.823590i	−0.0932532	−	0.161519i
$27$		0			0
$28$	1.19165	+	4.98728i	0.225200	+	0.942508i
$29$	1.78349	−	4.90009i	0.331185	−	0.909924i	−0.656619	−	0.754223i	$-0.728014\pi$
$29$	1.78349	−	4.90009i	0.331185	−	0.909924i	0.987804	−	0.155702i	$-0.0497638\pi$
$30$		0			0
$31$	1.32486	+	3.64001i	0.237951	+	0.653766i	0.999981	+	0.00622334i	$0.00198096\pi$
$31$	1.32486	+	3.64001i	0.237951	+	0.653766i	−0.762029	+	0.647543i	$0.775797\pi$
$32$	−1.84082	+	2.19380i	−0.325413	+	0.387813i
$33$		0			0
$34$	0.0349009	+	0.0415932i	0.00598545	+	0.00713318i
$35$	1.30779	+	5.47337i	0.221057	+	0.925168i
$36$		0			0
$37$	6.01251			0.988450			0.494225	−	0.869334i	$-0.335452\pi$
$37$	6.01251			0.988450			0.494225	+	0.869334i	$0.335452\pi$
$38$	−0.693906	−	0.252561i	−0.112566	−	0.0409708i
$39$		0			0
$40$	−1.33980	+	1.59671i	−0.211841	+	0.252462i
$41$	10.0627	−	3.66253i	1.57153	−	0.571990i	0.598190	−	0.801354i	$-0.295887\pi$
$41$	10.0627	−	3.66253i	1.57153	−	0.571990i	0.973341	+	0.229364i	$0.0736646\pi$
$42$		0			0
$43$	1.29579	+	7.34878i	0.197606	+	1.12068i	0.908659	+	0.417540i	$0.137108\pi$
$43$	1.29579	+	7.34878i	0.197606	+	1.12068i	−0.711053	+	0.703139i	$0.751781\pi$
$44$			2.77190i			0.417880i
$45$		0			0
$46$	−1.92432			−0.283725
$47$	5.51793	+	2.00836i	0.804873	+	0.292950i	0.711504	−	0.702682i	$-0.248014\pi$
$47$	5.51793	+	2.00836i	0.804873	+	0.292950i	0.0933687	+	0.995632i	$0.470236\pi$
$48$		0			0
$49$	−6.81717	−	1.58938i	−0.973882	−	0.227055i
$50$	0.0761360	−	0.0907353i	0.0107673	−	0.0128319i
$51$		0			0
$52$	−4.76094	−	5.67387i	−0.660224	−	0.786824i
$53$	−12.1036	−	6.98800i	−1.66255	−	0.959875i	−0.971490	−	0.237080i	$-0.923810\pi$
$53$	−12.1036	−	6.98800i	−1.66255	−	0.959875i	−0.691063	−	0.722795i	$-0.742857\pi$
$54$		0			0
$55$			3.04206i			0.410192i
$56$	−1.03129	−	2.37882i	−0.137811	−	0.317883i
$57$		0			0
$58$	−0.225328	+	1.27790i	−0.0295870	+	0.167796i
$59$	1.21070	+	1.01590i	0.157620	+	0.132259i	0.718187	−	0.695850i	$-0.244972\pi$
$59$	1.21070	+	1.01590i	0.157620	+	0.132259i	−0.560567	+	0.828109i	$0.689417\pi$
$60$		0			0
$61$	1.45500	−	3.99757i	0.186293	−	0.511837i	−0.811026	−	0.585010i	$-0.801090\pi$
$61$	1.45500	−	3.99757i	0.186293	−	0.511837i	0.997319	+	0.0731735i	$0.0233127\pi$
$62$	−0.481963	−	0.834784i	−0.0612093	−	0.106018i
$63$		0			0
$64$	−3.27598	+	5.67416i	−0.409497	+	0.709270i
$65$	−5.22497	−	6.22688i	−0.648078	−	0.772349i
$66$		0			0
$67$	2.59043	−	14.6911i	0.316471	−	1.79480i	−0.247376	−	0.968920i	$-0.579568\pi$
$67$	2.59043	−	14.6911i	0.316471	−	1.79480i	0.563848	−	0.825879i	$-0.309321\pi$
$68$	0.323942	+	0.271820i	0.0392838	+	0.0329630i
$69$		0			0
$70$	−0.557002	−	1.28481i	−0.0665745	−	0.153564i
$71$	4.29452	+	2.47944i	0.509666	+	0.294256i	0.732696	−	0.680556i	$-0.238262\pi$
$71$	4.29452	+	2.47944i	0.509666	+	0.294256i	−0.223031	+	0.974811i	$0.571595\pi$
$72$		0			0
$73$		−	2.46806i		−	0.288864i	−0.989515	−	0.144432i	$-0.953864\pi$
$73$		−	2.46806i		−	0.288864i	0.989515	−	0.144432i	$-0.0461355\pi$
$74$	−1.47344	+	0.259808i	−0.171284	+	0.0302020i
$75$		0			0
$76$	−5.66384	−	0.998688i	−0.649687	−	0.114557i
$77$	−3.38464	−	1.69209i	−0.385716	−	0.192831i
$78$		0			0
$79$	−0.675969	−	3.83361i	−0.0760524	−	0.431315i	−0.998931	−	0.0462239i	$-0.985281\pi$
$79$	−0.675969	−	3.83361i	−0.0760524	−	0.431315i	0.922879	−	0.385091i	$-0.125830\pi$
$80$	−3.86290	+	6.69073i	−0.431885	+	0.748047i
$81$		0			0
$82$	−2.30773	+	1.33237i	−0.254847	+	0.147136i
$83$	0.141502	+	0.0515026i	0.0155319	+	0.00565315i	0.349774	−	0.936834i	$-0.386258\pi$
$83$	0.141502	+	0.0515026i	0.0155319	+	0.00565315i	−0.334243	+	0.942487i	$0.608480\pi$
$84$		0			0
$85$	0.355515	+	0.298313i	0.0385610	+	0.0323566i
$86$	−0.635099	−	1.74492i	−0.0684845	−	0.188160i
$87$		0			0
$88$	−0.243381	−	1.38028i	−0.0259445	−	0.147139i
$89$	−3.40271	+	5.89366i	−0.360686	+	0.624727i	−0.988074	−	0.153980i	$-0.950791\pi$
$89$	−3.40271	+	5.89366i	−0.360686	+	0.624727i	0.627388	+	0.778707i	$0.284124\pi$
$90$		0			0
$91$	9.83439	−	2.34980i	1.03092	−	0.246326i
$92$	−14.7595	+	2.60251i	−1.53879	+	0.271330i
$93$		0			0
$94$	−1.43902	−	0.253739i	−0.148424	−	0.0261712i
$95$	−6.21587	−	1.09603i	−0.637735	−	0.112450i
$96$		0			0
$97$	12.2644	−	2.16255i	1.24526	−	0.219573i	0.488092	−	0.872792i	$-0.337693\pi$
$97$	12.2644	−	2.16255i	1.24526	−	0.219573i	0.757169	+	0.653219i	$0.226582\pi$
$98$	1.73932	+	0.0949204i	0.175697	+	0.00958841i
$99$		0			0
$100$	0.461251	−	0.798910i	0.0461251	−	0.0798910i
$101$	1.45464	+	8.24969i	0.144742	+	0.820874i	0.967574	+	0.252589i	$0.0812820\pi$
$101$	1.45464	+	8.24969i	0.144742	+	0.820874i	−0.822831	+	0.568286i	$0.807607\pi$
$102$		0			0
$103$	−0.0733066	−	0.201408i	−0.00722311	−	0.0198453i	0.936029	−	0.351924i	$-0.114472\pi$
$103$	−0.0733066	−	0.201408i	−0.00722311	−	0.0198453i	−0.943252	+	0.332078i	$0.892250\pi$
$104$	2.86892	+	2.40731i	0.281321	+	0.236056i
$105$		0			0
$106$	3.26809	+	1.18949i	0.317425	+	0.115533i
$107$	−15.3166	+	8.84302i	−1.48071	+	0.854887i	−0.999761	−	0.0218632i	$-0.993040\pi$
$107$	−15.3166	+	8.84302i	−1.48071	+	0.854887i	−0.480946	+	0.876750i	$0.659707\pi$
$108$		0			0
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	−0.887936	−	0.459967i	$-0.847861\pi$
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	0.842311	+	0.538992i	$0.181195\pi$
$110$	−0.131451	−	0.745497i	−0.0125334	−	0.0710804i
$111$		0			0
$112$	−5.29554	−	8.01949i	−0.500382	−	0.757771i
$113$	13.8921	+	2.44955i	1.30686	+	0.230434i	0.783346	−	0.621586i	$-0.213511\pi$
$113$	13.8921	+	2.44955i	1.30686	+	0.230434i	0.523510	+	0.852020i	$0.324622\pi$
$114$		0			0
$115$	−16.1981	+	2.85616i	−1.51048	+	0.266338i
$116$			10.1062i			0.938340i
$117$		0			0
$118$	−0.340597	−	0.196644i	−0.0313545	−	0.0181025i
$119$	−0.529655	+	0.229621i	−0.0485534	+	0.0210493i
$120$		0			0
$121$	6.85950	+	5.75580i	0.623591	+	0.523255i
$122$	−0.183826	+	1.04253i	−0.0166428	+	0.0943862i
$123$		0			0
$124$	−4.82565	−	5.75099i	−0.433356	−	0.516454i
$125$	5.82364	−	10.0868i	0.520882	−	0.902194i
$126$		0			0
$127$	−2.41898	−	4.18980i	−0.214650	−	0.371785i	0.738514	−	0.674238i	$-0.235528\pi$
$127$	−2.41898	−	4.18980i	−0.214650	−	0.371785i	−0.953164	+	0.302453i	$0.902194\pi$
$128$	2.51659	−	6.91427i	0.222437	−	0.611141i
$129$		0			0
$130$	1.54952	+	1.30020i	0.135902	+	0.114035i
$131$	−0.622917	+	3.53274i	−0.0544246	+	0.308657i	−0.999853	−	0.0171742i	$-0.994533\pi$
$131$	−0.622917	+	3.53274i	−0.0544246	+	0.308657i	0.945428	+	0.325831i	$0.105644\pi$
$132$		0			0
$133$	4.67690	−	6.30622i	0.405539	−	0.546818i
$134$			3.71217i			0.320683i
$135$		0			0
$136$	−0.185175	−	0.106911i	−0.0158787	−	0.00916755i
$137$	−2.29835	−	2.73907i	−0.196361	−	0.234014i	0.658875	−	0.752252i	$-0.271033\pi$
$137$	−2.29835	−	2.73907i	−0.196361	−	0.234014i	−0.855236	+	0.518238i	$0.826588\pi$
$138$		0			0
$139$	−3.85722	+	4.59686i	−0.327165	+	0.389900i	−0.904405	−	0.426674i	$-0.859685\pi$
$139$	−3.85722	+	4.59686i	−0.327165	+	0.389900i	0.577240	+	0.816574i	$0.304130\pi$
$140$	−6.00983	−	9.10120i	−0.507923	−	0.769191i
$141$		0			0
$142$	−1.15957	−	0.422048i	−0.0973087	−	0.0354175i
$143$	5.46589			0.457081
$144$		0			0
$145$			11.0912i			0.921078i
$146$	0.106648	+	0.604829i	0.00882623	+	0.0500560i
$147$		0			0
$148$	−10.9500	+	3.98546i	−0.900081	+	0.327603i
$149$	−3.58546	+	4.27298i	−0.293732	+	0.350057i	−0.892647	−	0.450756i	$-0.851154\pi$
$149$	−3.58546	+	4.27298i	−0.293732	+	0.350057i	0.598915	+	0.800813i	$0.295599\pi$
$150$		0			0
$151$	−1.49517	−	0.544196i	−0.121675	−	0.0442861i	0.280465	−	0.959864i	$-0.409511\pi$
$151$	−1.49517	−	0.544196i	−0.121675	−	0.0442861i	−0.402140	+	0.915578i	$0.631734\pi$
$152$	2.90803			0.235872
$153$		0			0
$154$	0.902567	+	0.268413i	0.0727309	+	0.0216293i
$155$	−5.29598	−	6.31151i	−0.425384	−	0.506952i
$156$		0			0
$157$	−15.9051	+	18.9549i	−1.26936	+	1.51277i	−0.513412	+	0.858143i	$0.671619\pi$
$157$	−15.9051	+	18.9549i	−1.26936	+	1.51277i	−0.755952	+	0.654627i	$0.772826\pi$
$158$	0.331310	+	0.910266i	0.0263576	+	0.0724169i
$159$		0			0
$160$	2.08332	−	5.72388i	0.164701	−	0.452513i
$161$	5.83205	−	19.6109i	0.459630	−	1.54555i
$162$		0			0
$163$	−6.48707	−	11.2359i	−0.508107	−	0.880066i	−0.999956	−	0.00938604i	$-0.997012\pi$
$163$	−6.48707	−	11.2359i	−0.508107	−	0.880066i	0.491849	−	0.870680i	$-0.336321\pi$
$164$	−15.8984	+	13.3404i	−1.24146	+	1.04171i
$165$		0			0
$166$	−0.0369024	−	0.00650690i	−0.00286419	−	0.000505033i
$167$	−1.43124	+	8.11696i	−0.110753	+	0.628110i	0.878013	+	0.478637i	$0.158869\pi$
$167$	−1.43124	+	8.11696i	−0.110753	+	0.628110i	−0.988766	+	0.149473i	$0.952242\pi$
$168$		0			0
$169$	−1.22969	+	1.03183i	−0.0945915	+	0.0793717i
$170$	−0.100014	−	0.0577432i	−0.00767073	−	0.00442870i
$171$		0			0
$172$	−7.23111	−	12.5246i	−0.551367	−	0.954995i
$173$	18.0347	−	15.1329i	1.37115	−	1.15053i	0.398793	−	0.917041i	$-0.369429\pi$
$173$	18.0347	−	15.1329i	1.37115	−	1.15053i	0.972359	−	0.233491i	$-0.0750151\pi$
$174$		0			0
$175$	0.693946	+	1.05090i	0.0524574	+	0.0794407i
$176$	−1.77680	−	4.88173i	−0.133932	−	0.367974i
$177$		0			0
$178$	0.579205	−	1.59135i	0.0434133	−	0.119277i
$179$	7.22926	−	4.17381i	0.540340	−	0.311965i	−0.204877	−	0.978788i	$-0.565679\pi$
$179$	7.22926	−	4.17381i	0.540340	−	0.311965i	0.745217	+	0.666822i	$0.232346\pi$
$180$		0			0
$181$	−3.60525	+	2.08149i	−0.267976	+	0.154716i	−0.627967	−	0.778240i	$-0.716113\pi$
$181$	−3.60525	+	2.08149i	−0.267976	+	0.154716i	0.359992	+	0.932956i	$0.382780\pi$
$182$	−2.30851	+	1.00080i	−0.171118	+	0.0741846i
$183$		0			0
$184$	7.12109	−	2.59187i	0.524974	−	0.191075i
$185$	−12.0172	+	4.37390i	−0.883522	+	0.321576i
$186$		0			0
$187$	−0.307327	+	0.0541900i	−0.0224740	+	0.00396277i
$188$	−11.3805			−0.830009
$189$		0			0
$190$	1.57064			0.113946
$191$	0.952580	−	0.167966i	0.0689263	−	0.0121536i	−0.139079	−	0.990281i	$-0.544414\pi$
$191$	0.952580	−	0.167966i	0.0689263	−	0.0121536i	0.208005	+	0.978128i	$0.433303\pi$
$192$		0			0
$193$	6.76620	−	2.46270i	0.487042	−	0.177269i	−0.0868148	−	0.996224i	$-0.527669\pi$
$193$	6.76620	−	2.46270i	0.487042	−	0.177269i	0.573857	+	0.818956i	$0.305447\pi$
$194$	−2.91211	+	1.05992i	−0.209077	+	0.0760978i
$195$		0			0
$196$	13.4690	−	1.62426i	0.962068	−	0.116019i
$197$	−6.90426	+	3.98617i	−0.491908	+	0.284003i	−0.725366	−	0.688364i	$-0.758329\pi$
$197$	−6.90426	+	3.98617i	−0.491908	+	0.284003i	0.233458	+	0.972367i	$0.424996\pi$
$198$		0			0
$199$	−3.69994	+	2.13616i	−0.262282	+	0.151428i	−0.625375	−	0.780324i	$-0.715054\pi$
$199$	−3.69994	+	2.13616i	−0.262282	+	0.151428i	0.363093	+	0.931753i	$0.381721\pi$
$200$	−0.159536	+	0.438321i	−0.0112809	+	0.0309940i
$201$		0			0
$202$	−0.712958	−	1.95884i	−0.0501635	−	0.137823i
$203$	−12.3403	−	6.16927i	−0.866117	−	0.432998i
$204$		0			0
$205$	−17.4480	+	14.6406i	−1.21862	+	1.02254i
$206$	0.0266678	+	0.0461900i	0.00185804	+	0.00321821i
$207$		0			0
$208$	12.0217	+	6.94074i	0.833556	+	0.481254i
$209$	3.25124	−	2.72811i	0.224893	−	0.188708i
$210$		0			0
$211$	3.70699	−	21.0234i	0.255199	−	1.44731i	−0.540361	−	0.841433i	$-0.681712\pi$
$211$	3.70699	−	21.0234i	0.255199	−	1.44731i	0.795560	−	0.605875i	$-0.207177\pi$
$212$	26.6750	+	4.70353i	1.83205	+	0.323040i
$213$		0			0
$214$	3.37140	−	2.82894i	0.230464	−	0.193383i
$215$	−7.93589	−	13.7454i	−0.541223	−	0.937426i
$216$		0			0
$217$	9.96805	−	2.38174i	0.676675	−	0.161683i
$218$	0.0810826	−	0.222773i	0.00549161	−	0.0150881i
$219$		0			0
$220$	−2.01647	−	5.54020i	−0.135950	−	0.373520i
$221$	0.536000	−	0.638779i	0.0360552	−	0.0429689i
$222$		0			0
$223$	7.92110	+	9.44000i	0.530436	+	0.632149i	0.963015	−	0.269447i	$-0.0868408\pi$
$223$	7.92110	+	9.44000i	0.530436	+	0.632149i	−0.432579	+	0.901596i	$0.642396\pi$
$224$	5.20966	+	5.50172i	0.348085	+	0.367599i
$225$		0			0
$226$	−3.51028			−0.233500
$227$	17.5438	+	6.38541i	1.16442	+	0.423815i	0.850675	−	0.525692i	$-0.176194\pi$
$227$	17.5438	+	6.38541i	1.16442	+	0.423815i	0.313746	+	0.949507i	$0.398416\pi$
$228$		0			0
$229$	−12.4826	+	14.8762i	−0.824872	+	0.983044i	−0.999999	−	0.00150162i	$-0.999522\pi$
$229$	−12.4826	+	14.8762i	−0.824872	+	0.983044i	0.175127	+	0.984546i	$0.443966\pi$
$230$	3.84613	−	1.39988i	0.253607	−	0.0923052i
$231$		0			0
$232$	−0.887358	−	5.03246i	−0.0582579	−	0.330397i
$233$		−	13.1872i		−	0.863923i	−0.901892	−	0.431961i	$-0.857822\pi$
$233$		−	13.1872i		−	0.863923i	0.901892	−	0.431961i	$-0.142178\pi$
$234$		0			0
$235$	−12.4897			−0.814739
$236$	−2.87833	−	1.04763i	−0.187363	−	0.0681947i
$237$		0			0
$238$	0.119877	−	0.0791586i	0.00777044	−	0.00513109i
$239$	−10.0464	+	11.9729i	−0.649849	+	0.774460i	−0.985891	−	0.167387i	$-0.946467\pi$
$239$	−10.0464	+	11.9729i	−0.649849	+	0.774460i	0.336043	+	0.941847i	$0.390911\pi$
$240$		0			0
$241$	4.17444	+	4.97490i	0.268899	+	0.320462i	0.883549	−	0.468338i	$-0.155147\pi$
$241$	4.17444	+	4.97490i	0.268899	+	0.320462i	−0.614650	+	0.788800i	$0.710703\pi$
$242$	−1.92972	−	1.11413i	−0.124047	−	0.0716187i
$243$		0			0
$244$			8.24483i			0.527821i
$245$	14.7817	−	1.78257i	0.944369	−	0.113884i
$246$		0			0
$247$	−1.96931	+	11.1685i	−0.125304	+	0.710634i
$248$	2.90791	+	2.44003i	0.184653	+	0.154942i
$249$		0			0
$250$	−0.991293	+	2.72356i	−0.0626949	+	0.172253i
$251$	11.9045	+	20.6191i	0.751403	+	1.30147i	0.947143	+	0.320812i	$0.103956\pi$
$251$	11.9045	+	20.6191i	0.751403	+	1.30147i	−0.195740	+	0.980656i	$0.562711\pi$
$252$		0			0
$253$	5.53002	−	9.57828i	0.347670	−	0.602182i
$254$	0.773849	+	0.922238i	0.0485556	+	0.0578663i
$255$		0			0
$256$	1.95752	−	11.1017i	0.122345	−	0.693853i
$257$	23.2700	+	19.5258i	1.45154	+	1.21799i	0.931446	+	0.363880i	$0.118548\pi$
$257$	23.2700	+	19.5258i	1.45154	+	1.21799i	0.520096	+	0.854108i	$0.325896\pi$
$258$		0			0
$259$	1.81786	−	15.8034i	0.112956	−	0.981975i
$260$	13.6433	+	7.87694i	0.846119	+	0.488507i
$261$		0			0
$262$		−	0.892661i		−	0.0551488i
$263$	−15.2337	+	2.68611i	−0.939348	+	0.165632i	−0.622302	−	0.782778i	$-0.713802\pi$
$263$	−15.2337	+	2.68611i	−0.939348	+	0.165632i	−0.317047	+	0.948410i	$0.602691\pi$
$264$		0			0
$265$	29.2749	+	5.16196i	1.79835	+	0.317097i
$266$	−0.873636	+	1.74751i	−0.0535660	+	0.107147i
$267$		0			0
$268$	5.02045	+	28.4724i	0.306673	+	1.73923i
$269$	−0.343714	+	0.595329i	−0.0209566	+	0.0362979i	−0.876314	−	0.481741i	$-0.840005\pi$
$269$	−0.343714	+	0.595329i	−0.0209566	+	0.0362979i	0.855357	+	0.518039i	$0.173338\pi$
$270$		0			0
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	−0.298131	−	0.954525i	$-0.596363\pi$
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	0.677578	+	0.735451i	$0.263030\pi$
$272$	−0.744748	−	0.271066i	−0.0451570	−	0.0164358i
$273$		0			0
$274$	0.681599	+	0.571929i	0.0411769	+	0.0345515i
$275$	0.232838	+	0.639718i	0.0140407	+	0.0385765i
$276$		0			0
$277$	2.15820	+	12.2398i	0.129674	+	0.735417i	0.978421	+	0.206619i	$0.0662461\pi$
$277$	2.15820	+	12.2398i	0.129674	+	0.735417i	−0.848748	+	0.528798i	$0.822643\pi$
$278$	0.746626	−	1.29319i	0.0447797	−	0.0775607i
$279$		0			0
$280$	3.79174	+	4.00431i	0.226600	+	0.239303i
$281$	−2.05517	+	0.362382i	−0.122601	+	0.0216179i	−0.234612	−	0.972089i	$-0.575382\pi$
$281$	−2.05517	+	0.362382i	−0.122601	+	0.0216179i	0.112011	+	0.993707i	$0.464271\pi$
$282$		0			0
$283$	19.9337	+	3.51484i	1.18493	+	0.208936i	0.731175	−	0.682189i	$-0.238972\pi$
$283$	19.9337	+	3.51484i	1.18493	+	0.208936i	0.453758	+	0.891125i	$0.350083\pi$
$284$	−9.46469	−	1.66888i	−0.561626	−	0.0990298i
$285$		0			0
$286$	−1.33949	+	0.236188i	−0.0792055	+	0.0139661i
$287$	−6.58424	−	27.5564i	−0.388655	−	1.62660i
$288$		0			0
$289$	8.47620	−	14.6812i	0.498600	−	0.863600i
$290$	−0.479266	−	2.71805i	−0.0281435	−	0.159610i
$291$		0			0
$292$	1.63598	+	4.49482i	0.0957384	+	0.263039i
$293$	−21.6520	−	18.1682i	−1.26493	−	1.06140i	−0.995139	−	0.0984780i	$-0.968603\pi$
$293$	−21.6520	−	18.1682i	−1.26493	−	1.06140i	−0.269786	−	0.962920i	$-0.586953\pi$
$294$		0			0
$295$	−3.15887	−	1.14973i	−0.183916	−	0.0669401i
$296$	5.10266	−	2.94602i	0.296586	−	0.171234i
$297$		0			0
$298$	0.694022	−	1.20208i	0.0402036	−	0.0696347i
$299$	5.13186	+	29.1043i	0.296783	+	1.68314i
$300$		0			0
$301$	19.7074	−	1.18400i	1.13592	−	0.0682448i
$302$	0.389925	+	0.0687543i	0.0224377	+	0.00395637i
$303$		0			0
$304$	10.6150	−	1.87172i	0.608814	−	0.107350i
$305$			9.04841i			0.518111i
$306$		0			0
$307$	−1.71807	−	0.991927i	−0.0980553	−	0.0566122i	0.450170	−	0.892943i	$-0.351363\pi$
$307$	−1.71807	−	0.991927i	−0.0980553	−	0.0566122i	−0.548226	+	0.836330i	$0.684697\pi$
$308$	7.28571	+	0.838072i	0.415142	+	0.0477536i
$309$		0			0
$310$	1.57058	+	1.31787i	0.0892028	+	0.0748500i
$311$	2.35895	−	13.3783i	0.133764	−	0.758612i	−0.841949	−	0.539557i	$-0.818592\pi$
$311$	2.35895	−	13.3783i	0.133764	−	0.758612i	0.975713	−	0.219054i	$-0.0702973\pi$
$312$		0			0
$313$	−9.40882	−	11.2130i	−0.531818	−	0.633796i	0.431515	−	0.902106i	$-0.357979\pi$
$313$	−9.40882	−	11.2130i	−0.531818	−	0.633796i	−0.963333	+	0.268310i	$0.913535\pi$
$314$	3.07868	−	5.33243i	0.173740	−	0.300927i
$315$		0			0
$316$	3.77222	+	6.53368i	0.212204	+	0.367548i
$317$	6.46638	−	17.7662i	0.363188	−	0.997850i	−0.614707	−	0.788755i	$-0.710726\pi$
$317$	6.46638	−	17.7662i	0.363188	−	0.997850i	0.977895	−	0.209095i	$-0.0670519\pi$
$318$		0			0
$319$	−5.71319	−	4.79394i	−0.319877	−	0.268409i
$320$	2.41993	−	13.7241i	0.135278	−	0.767201i
$321$		0			0
$322$	−0.581809	+	5.05791i	−0.0324229	+	0.281866i
$323$		−	0.647487i		−	0.0360271i
$324$		0			0
$325$	−1.57537	−	0.909538i	−0.0873856	−	0.0504521i
$326$	2.07526	+	2.47320i	0.114938	+	0.136978i
$327$		0			0
$328$	6.74539	−	8.03884i	0.372452	−	0.443871i
$329$	6.94714	−	13.8962i	0.383008	−	0.766123i
$330$		0			0
$331$	−11.1300	−	4.05098i	−0.611760	−	0.222662i	0.0175134	−	0.999847i	$-0.494425\pi$
$331$	−11.1300	−	4.05098i	−0.611760	−	0.222662i	−0.629273	+	0.777184i	$0.716647\pi$
$332$	−0.291842			−0.0160169
$333$		0			0
$334$		−	2.05101i		−	0.112226i
$335$	5.50977	+	31.2475i	0.301031	+	1.70723i
$336$		0			0
$337$	19.6990	−	7.16984i	1.07307	−	0.390566i	0.255747	−	0.966744i	$-0.417679\pi$
$337$	19.6990	−	7.16984i	1.07307	−	0.390566i	0.817324	+	0.576178i	$0.195456\pi$
$338$	0.256765	−	0.306000i	0.0139662	−	0.0166442i
$339$		0			0
$340$	−0.845203	−	0.307629i	−0.0458376	−	0.0166835i
$341$	5.54018			0.300018
$342$		0			0
$343$	−6.23871	+	17.4378i	−0.336858	+	0.941555i
$344$	4.70047	+	5.60181i	0.253433	+	0.302029i
$345$		0			0
$346$	−3.76572	+	4.48781i	−0.202446	+	0.241266i
$347$	−10.4749	−	28.7796i	−0.562323	−	1.54497i	−0.816222	−	0.577738i	$-0.803935\pi$
$347$	−10.4749	−	28.7796i	−0.562323	−	1.54497i	0.253899	−	0.967231i	$-0.418287\pi$
$348$		0			0
$349$	−6.58819	+	18.1009i	−0.352658	+	0.968919i	0.628855	+	0.777523i	$0.283524\pi$
$349$	−6.58819	+	18.1009i	−0.352658	+	0.968919i	−0.981513	+	0.191397i	$0.938698\pi$
$350$	−0.215471	−	0.227551i	−0.0115174	−	0.0121631i
$351$		0			0
$352$	2.04795	+	3.54715i	0.109156	+	0.189064i
$353$	14.1346	−	11.8604i	0.752311	−	0.631264i	−0.183802	−	0.982963i	$-0.558841\pi$
$353$	14.1346	−	11.8604i	0.752311	−	0.631264i	0.936113	+	0.351700i	$0.114396\pi$
$354$		0			0
$355$	−10.3872	−	1.83154i	−0.551294	−	0.0972079i
$356$	2.29032	−	12.9890i	0.121387	−	0.688418i
$357$		0			0
$358$	−1.59127	+	1.33523i	−0.0841011	+	0.0705692i
$359$	0.675231	+	0.389845i	0.0356373	+	0.0205752i	0.517713	−	0.855554i	$-0.326784\pi$
$359$	0.675231	+	0.389845i	0.0356373	+	0.0205752i	−0.482075	+	0.876130i	$0.660117\pi$
$360$		0			0
$361$	−5.09702	−	8.82829i	−0.268264	−	0.464647i
$362$	0.793568	−	0.665883i	0.0417090	−	0.0349980i
$363$		0			0
$364$	−16.3528	+	10.7983i	−0.857118	+	0.565984i
$365$	1.79543	+	4.93291i	0.0939771	+	0.258200i
$366$		0			0
$367$	−8.50857	+	23.3771i	−0.444144	+	1.22027i	0.492599	+	0.870256i	$0.336047\pi$
$367$	−8.50857	+	23.3771i	−0.444144	+	1.22027i	−0.936743	+	0.350018i	$0.886175\pi$
$368$	24.3255	−	14.0444i	1.26806	−	0.732113i
$369$		0			0
$370$	2.75597	−	1.59116i	0.143276	−	0.0827205i
$371$	−22.0268	+	29.7005i	−1.14358	+	1.54197i
$372$		0			0
$373$	22.5973	−	8.22473i	1.17004	−	0.425860i	0.317367	−	0.948303i	$-0.397201\pi$
$373$	22.5973	−	8.22473i	1.17004	−	0.425860i	0.852675	+	0.522442i	$0.174979\pi$
$374$	0.0729728	−	0.0265599i	0.00377333	−	0.00137338i
$375$		0			0
$376$	5.66699	−	0.999243i	0.292253	−	0.0515320i
$377$	19.9284			1.02637
$378$		0			0
$379$	−30.5872			−1.57116			−0.785579	−	0.618761i	$-0.787635\pi$
$379$	−30.5872			−1.57116			−0.785579	+	0.618761i	$0.787635\pi$
$380$	12.0468	−	2.12418i	0.617989	−	0.108968i
$381$		0			0
$382$	−0.226184	+	0.0823242i	−0.0115726	+	0.00421207i
$383$	−33.8267	+	12.3119i	−1.72846	+	0.629109i	−0.998519	−	0.0543988i	$-0.982676\pi$
$383$	−33.8267	+	12.3119i	−1.72846	+	0.629109i	−0.729943	+	0.683508i	$0.760454\pi$
$384$		0			0
$385$	7.99582	+	0.919755i	0.407505	+	0.0468751i
$386$	−1.55173	+	0.895891i	−0.0789809	+	0.0455997i
$387$		0			0
$388$	−20.9024	+	12.0680i	−1.06116	+	0.612661i
$389$	−8.34439	+	22.9260i	−0.423077	+	1.16240i	0.526859	+	0.849953i	$0.323369\pi$
$389$	−8.34439	+	22.9260i	−0.423077	+	1.16240i	−0.949937	+	0.312443i	$0.898853\pi$
$390$		0			0
$391$	−0.577092	−	1.58555i	−0.0291848	−	0.0801845i
$392$	−6.56433	+	1.99143i	−0.331549	+	0.100582i
$393$		0			0
$394$	1.51973	−	1.27520i	0.0765629	−	0.0642439i
$395$	4.13988	+	7.17049i	0.208300	+	0.360786i
$396$		0			0
$397$	5.85723	+	3.38167i	0.293966	+	0.169721i	0.639729	−	0.768601i	$-0.279047\pi$
$397$	5.85723	+	3.38167i	0.293966	+	0.169721i	−0.345763	+	0.938322i	$0.612380\pi$
$398$	0.814412	−	0.683373i	0.0408228	−	0.0342544i
$399$		0			0
$400$	−0.300226	+	1.70266i	−0.0150113	+	0.0851332i
$401$	0.948178	+	0.167189i	0.0473497	+	0.00834904i	0.197273	−	0.980349i	$-0.436792\pi$
$401$	0.948178	+	0.167189i	0.0473497	+	0.00834904i	−0.149923	+	0.988698i	$0.547903\pi$
$402$		0			0
$403$	−11.3403	+	9.51567i	−0.564902	+	0.474009i
$404$	−8.11759	−	14.0601i	−0.403865	−	0.699515i
$405$		0			0
$406$	3.29072	+	0.978623i	0.163316	+	0.0485682i
$407$	2.94113	−	8.08068i	0.145786	−	0.400545i
$408$		0			0
$409$	−9.93846	−	27.3057i	−0.491425	−	1.35018i	−0.899376	−	0.437176i	$-0.855979\pi$
$409$	−9.93846	−	27.3057i	−0.491425	−	1.35018i	0.407951	−	0.913004i	$-0.366244\pi$
$410$	3.64321	−	4.34181i	0.179925	−	0.214427i
$411$		0			0
$412$	0.267011	+	0.318212i	0.0131547	+	0.0156772i
$413$	3.03626	−	2.87508i	0.149405	−	0.141474i
$414$		0			0
$415$	−0.320287			−0.0157223
$416$	−10.2845	−	3.74325i	−0.504239	−	0.183528i
$417$		0			0
$418$	−0.678873	+	0.809050i	−0.0332048	+	0.0395719i
$419$	−22.8869	+	8.33016i	−1.11810	+	0.406955i	−0.833958	−	0.551828i	$-0.813931\pi$
$419$	−22.8869	+	8.33016i	−1.11810	+	0.406955i	−0.284141	+	0.958782i	$0.591708\pi$
$420$		0			0
$421$	2.03579	+	11.5455i	0.0992181	+	0.562694i	0.993373	+	0.114936i	$0.0366663\pi$
$421$	2.03579	+	11.5455i	0.0992181	+	0.562694i	−0.894155	+	0.447758i	$0.852223\pi$
$422$			5.31223i			0.258595i
$423$		0			0
$424$	−13.6960			−0.665135
$425$	0.0975943	+	0.0355214i	0.00473402	+	0.00172304i
$426$		0			0
$427$	−10.0674	−	5.03299i	−0.487195	−	0.243564i
$428$	22.0328	−	26.2576i	1.06499	−	1.26921i
$429$		0			0
$430$	2.53875	+	3.02556i	0.122429	+	0.145905i
$431$	22.9443	+	13.2469i	1.10519	+	0.638082i	0.937579	−	0.347772i	$-0.113062\pi$
$431$	22.9443	+	13.2469i	1.10519	+	0.638082i	0.167610	+	0.985853i	$0.446395\pi$
$432$		0			0
$433$		−	23.5474i		−	1.13161i	−0.824538	−	0.565807i	$-0.808565\pi$
$433$		−	23.5474i		−	1.13161i	0.824538	−	0.565807i	$-0.191435\pi$
$434$	−2.33988	+	1.01441i	−0.112318	+	0.0486931i
$435$		0			0
$436$	0.320620	−	1.81833i	0.0153549	−	0.0870821i
$437$	17.5790	+	14.7505i	0.840915	+	0.705612i
$438$		0			0
$439$	1.42802	−	3.92345i	0.0681557	−	0.187256i	−0.900939	−	0.433946i	$-0.857121\pi$
$439$	1.42802	−	3.92345i	0.0681557	−	0.187256i	0.969094	+	0.246690i	$0.0793430\pi$
$440$	1.49056	+	2.58172i	0.0710595	+	0.123079i
$441$		0			0
$442$	−0.103751	+	0.179702i	−0.00493494	+	0.00854757i
$443$	−1.56064	−	1.85990i	−0.0741482	−	0.0883663i	0.727695	−	0.685901i	$-0.240592\pi$
$443$	−1.56064	−	1.85990i	−0.0741482	−	0.0883663i	−0.801843	+	0.597534i	$0.796147\pi$
$444$		0			0
$445$	2.51355	−	14.2550i	0.119153	−	0.675753i
$446$	−2.34908	−	1.97111i	−0.111232	−	0.0933350i
$447$		0			0
$448$	13.9236	+	10.3262i	0.657828	+	0.487867i
$449$	−10.0967	−	5.82936i	−0.476495	−	0.275104i	0.242460	−	0.970161i	$-0.422046\pi$
$449$	−10.0967	−	5.82936i	−0.476495	−	0.275104i	−0.718955	+	0.695057i	$0.755379\pi$
$450$		0			0
$451$		−	15.3157i		−	0.721186i
$452$	−26.9239	+	4.74741i	−1.26639	+	0.223299i
$453$		0			0
$454$	−4.57525	−	0.806740i	−0.214727	−	0.0378622i
$455$	−17.9466	+	11.8507i	−0.841349	+	0.555571i
$456$		0			0
$457$	−3.68876	−	20.9200i	−0.172553	−	0.978597i	−0.940930	−	0.338600i	$-0.890047\pi$
$457$	−3.68876	−	20.9200i	−0.172553	−	0.978597i	0.768377	−	0.639997i	$-0.221064\pi$
$458$	2.41620	−	4.18498i	0.112902	−	0.195551i
$459$		0			0
$460$	27.6067	−	15.9387i	1.28717	−	0.743147i
$461$	−25.2929	−	9.20586i	−1.17801	−	0.428760i	−0.322510	−	0.946566i	$-0.604527\pi$
$461$	−25.2929	−	9.20586i	−1.17801	−	0.428760i	−0.855498	+	0.517806i	$0.826749\pi$
$462$		0			0
$463$	18.3826	+	15.4248i	0.854311	+	0.716852i	0.960735	−	0.277469i	$-0.0894956\pi$
$463$	18.3826	+	15.4248i	0.854311	+	0.716852i	−0.106424	+	0.994321i	$0.533940\pi$
$464$	−6.47816	−	17.7986i	−0.300741	−	0.826279i
$465$		0			0
$466$	0.569835	+	3.23170i	0.0263971	+	0.149705i
$467$	−3.09488	+	5.36049i	−0.143214	+	0.248054i	−0.928705	−	0.370819i	$-0.879077\pi$
$467$	−3.09488	+	5.36049i	−0.143214	+	0.248054i	0.785491	+	0.618873i	$0.212410\pi$
$468$		0			0
$469$	−37.8311	−	11.2505i	−1.74688	−	0.519500i
$470$	3.06076	−	0.539695i	0.141183	−	0.0248943i
$471$		0			0
$472$	1.52527	+	0.268946i	0.0702061	+	0.0123792i
$473$	10.5105	+	1.85328i	0.483271	+	0.0852138i
$474$		0			0
$475$	−1.39103	+	0.245276i	−0.0638248	+	0.0112540i
$476$	0.812399	−	0.769272i	0.0372362	−	0.0352595i
$477$		0			0
$478$	1.94464	−	3.36822i	0.0889459	−	0.154059i
$479$	−2.79921	−	15.8751i	−0.127899	−	0.725353i	−0.979543	−	0.201233i	$-0.935505\pi$
$479$	−2.79921	−	15.8751i	−0.127899	−	0.725353i	0.851644	−	0.524121i	$-0.175606\pi$
$480$		0			0
$481$	7.85890	+	21.5922i	0.358335	+	0.984518i
$482$	−1.23797	−	1.03878i	−0.0563881	−	0.0473152i
$483$		0			0
$484$	−16.3078	−	5.93555i	−0.741263	−	0.269798i
$485$	−22.9397	+	13.2442i	−1.04164	+	0.601390i
$486$		0			0
$487$	−13.0260	+	22.5617i	−0.590265	+	1.02237i	0.403931	+	0.914789i	$0.367643\pi$
$487$	−13.0260	+	22.5617i	−0.590265	+	1.02237i	−0.994196	+	0.107580i	$0.965690\pi$
$488$	−0.723921	−	4.10556i	−0.0327704	−	0.185850i
$489$		0			0
$490$	−3.54542	+	1.07558i	−0.160166	+	0.0485897i
$491$	−10.3899	−	1.83203i	−0.468892	−	0.0826783i	−0.0657902	−	0.997833i	$-0.520957\pi$
$491$	−10.3899	−	1.83203i	−0.468892	−	0.0826783i	−0.403102	+	0.915155i	$0.632068\pi$
$492$		0			0
$493$	−1.12050	+	0.197575i	−0.0504648	+	0.00889831i
$494$		−	2.82208i		−	0.126971i
$495$		0			0
$496$	12.1851	+	7.03507i	0.547127	+	0.315884i
$497$	7.81544	−	10.5381i	0.350570	−	0.472700i
$498$		0			0
$499$	−6.18372	−	5.18876i	−0.276822	−	0.232281i	0.493798	−	0.869577i	$-0.335608\pi$
$499$	−6.18372	−	5.18876i	−0.276822	−	0.232281i	−0.770619	+	0.637296i	$0.780053\pi$
$500$	−3.91982	+	22.2304i	−0.175299	+	0.994173i
$501$		0			0
$502$	−3.80832	−	4.53858i	−0.169974	−	0.202567i
$503$	15.6629	−	27.1289i	0.698373	−	1.20962i	−0.270658	−	0.962676i	$-0.587241\pi$
$503$	15.6629	−	27.1289i	0.698373	−	1.20962i	0.969030	−	0.246941i	$-0.0794255\pi$
$504$		0			0
$505$	−8.90877	−	15.4304i	−0.396435	−	0.686646i
$506$	−0.941315	+	2.58624i	−0.0418465	+	0.114972i
$507$		0			0
$508$	7.18270	+	6.02700i	0.318681	+	0.267405i
$509$	−7.03911	+	39.9208i	−0.312003	+	1.76946i	0.276552	+	0.960999i	$0.410808\pi$
$509$	−7.03911	+	39.9208i	−0.312003	+	1.76946i	−0.588555	+	0.808457i	$0.700303\pi$
$510$		0			0
$511$	−6.48709	−	0.746206i	−0.286972	−	0.0330102i
$512$			17.5212i			0.774336i
$513$		0			0
$514$	−6.54634	−	3.77953i	−0.288747	−	0.166708i
$515$	0.293036	+	0.349227i	0.0129127	+	0.0153888i
$516$		0			0
$517$	5.39839	−	6.43355i	0.237421	−	0.282947i
$518$	0.237395	+	3.95138i	0.0104305	+	0.173614i
$519$		0			0
$520$	−7.48536	−	2.72445i	−0.328255	−	0.119475i
$521$	−23.4014			−1.02523			−0.512616	−	0.858618i	$-0.671324\pi$
$521$	−23.4014			−1.02523			−0.512616	+	0.858618i	$0.671324\pi$
$522$		0			0
$523$		−	14.0156i		−	0.612858i	−0.951894	−	0.306429i	$-0.900866\pi$
$523$		−	14.0156i		−	0.612858i	0.951894	−	0.306429i	$-0.0991342\pi$
$524$	−1.20726	−	6.84672i	−0.0527395	−	0.299100i
$525$		0			0
$526$	3.61714	−	1.31653i	0.157715	−	0.0574035i
$527$	0.543284	−	0.647461i	0.0236658	−	0.0282038i
$528$		0			0
$529$	34.5807	+	12.5863i	1.50351	+	0.547232i
$530$	−7.39726			−0.321316
$531$		0			0
$532$	−4.33741	+	14.5850i	−0.188050	+	0.632340i
$533$	26.3058	+	31.3500i	1.13943	+	1.35792i
$534$		0			0
$535$	24.1802	−	28.8168i	1.04540	−	1.24586i
$536$	−4.99993	−	13.7372i	−0.215964	−	0.593356i
$537$		0			0
$538$	0.0585066	−	0.160745i	0.00252240	−	0.00693023i
$539$	−5.47084	+	8.38466i	−0.235646	+	0.361153i
$540$		0			0
$541$	−11.9247	−	20.6542i	−0.512683	−	0.887993i	−0.999892	−	0.0147075i	$-0.995318\pi$
$541$	−11.9247	−	20.6542i	−0.512683	−	0.887993i	0.487209	−	0.873285i	$-0.338015\pi$
$542$	−1.37494	+	1.15372i	−0.0590589	+	0.0495563i
$543$		0			0
$544$	0.615371	+	0.108506i	0.0263838	+	0.00465218i
$545$	0.351870	−	1.99555i	0.0150724	−	0.0854801i
$546$		0			0
$547$	−0.534982	+	0.448903i	−0.0228742	+	0.0191937i	−0.654153	−	0.756362i	$-0.726975\pi$
$547$	−0.534982	+	0.448903i	−0.0228742	+	0.0191937i	0.631279	+	0.775556i	$0.282530\pi$
$548$	6.00137	+	3.46489i	0.256366	+	0.148013i
$549$		0			0
$550$	−0.0847030	−	0.146710i	−0.00361175	−	0.00625573i
$551$	11.8539	−	9.94659i	0.504993	−	0.423739i
$552$		0			0
$553$	−10.2807	+	0.617654i	−0.437180	+	0.0262653i
$554$	−1.05779	−	2.90626i	−0.0449413	−	0.123475i
$555$		0			0
$556$	3.97768	−	10.9286i	0.168691	−	0.463475i
$557$	−9.63238	+	5.56126i	−0.408137	+	0.235638i	−0.689989	−	0.723820i	$-0.742385\pi$
$557$	−9.63238	+	5.56126i	−0.408137	+	0.235638i	0.281852	+	0.959458i	$0.409051\pi$
$558$		0			0
$559$	−24.6973	+	14.2590i	−1.04458	+	0.603090i
$560$	16.4181	+	12.1762i	0.693792	+	0.514539i
$561$		0			0
$562$	0.487987	−	0.177613i	0.0205845	−	0.00749214i
$563$	−10.5579	+	3.84276i	−0.444962	+	0.161953i	−0.554777	−	0.831999i	$-0.687196\pi$
$563$	−10.5579	+	3.84276i	−0.444962	+	0.161953i	0.109815	+	0.993952i	$0.464974\pi$
$564$		0			0
$565$	−29.5481	+	5.21012i	−1.24310	+	0.219191i
$566$	−5.03688			−0.211716
$567$		0			0
$568$	4.85953			0.203901
$569$	−35.5984	+	6.27695i	−1.49236	+	0.263143i	−0.859505	−	0.511127i	$-0.829228\pi$
$569$	−35.5984	+	6.27695i	−1.49236	+	0.263143i	−0.632855	+	0.774270i	$0.718117\pi$
$570$		0			0
$571$	−18.7772	+	6.83434i	−0.785802	+	0.286008i	−0.703590	−	0.710607i	$-0.748421\pi$
$571$	−18.7772	+	6.83434i	−0.785802	+	0.286008i	−0.0822119	+	0.996615i	$0.526198\pi$
$572$	−9.95446	+	3.62313i	−0.416217	+	0.151491i
$573$		0			0
$574$	2.80430	+	6.46853i	0.117049	+	0.269991i
$575$	−3.18770	+	1.84042i	−0.132936	+	0.0767508i
$576$		0			0
$577$	26.4773	−	15.2867i	1.10226	−	0.636393i	0.165450	−	0.986218i	$-0.447092\pi$
$577$	26.4773	−	15.2867i	1.10226	−	0.636393i	0.936815	+	0.349825i	$0.113759\pi$
$578$	−1.44281	+	3.96408i	−0.0600129	+	0.164884i
$579$		0			0
$580$	−7.35196	−	20.1993i	−0.305273	−	0.838732i
$581$	0.178153	−	0.356356i	0.00739103	−	0.0147841i
$582$		0			0
$583$	−15.3124	+	12.8486i	−0.634175	+	0.532136i
$584$	−1.20930	−	2.09458i	−0.0500414	−	0.0866742i
$585$		0			0
$586$	6.09118	+	3.51674i	0.251624	+	0.145275i
$587$	23.6386	−	19.8352i	0.975671	−	0.818685i	−0.00775999	−	0.999970i	$-0.502470\pi$
$587$	23.6386	−	19.8352i	0.975671	−	0.818685i	0.983431	+	0.181285i	$0.0580257\pi$
$588$		0			0
$589$	−1.99607	+	11.3203i	−0.0822467	+	0.466444i
$590$	0.823803	+	0.145259i	0.0339154	+	0.00598021i
$591$		0			0
$592$	16.7298	−	14.0380i	0.687591	−	0.576957i
$593$	−15.8362	−	27.4292i	−0.650316	−	1.12638i	−0.983046	−	0.183358i	$-0.941303\pi$
$593$	−15.8362	−	27.4292i	−0.650316	−	1.12638i	0.332730	−	0.943022i	$-0.392030\pi$
$594$		0			0
$595$	0.891579	−	0.844250i	0.0365512	−	0.0346109i
$596$	3.69743	−	10.1586i	0.151453	−	0.416113i
$597$		0			0
$598$	−2.51526	−	6.91062i	−0.102857	−	0.282596i
$599$	9.55357	−	11.3855i	0.390348	−	0.465199i	−0.534703	−	0.845040i	$-0.679577\pi$
$599$	9.55357	−	11.3855i	0.390348	−	0.465199i	0.925052	+	0.379841i	$0.124021\pi$
$600$		0			0
$601$	−11.0892	−	13.2156i	−0.452338	−	0.539075i	0.490890	−	0.871221i	$-0.336672\pi$
$601$	−11.0892	−	13.2156i	−0.452338	−	0.539075i	−0.943228	+	0.332146i	$0.892227\pi$
$602$	−4.77840	+	1.14174i	−0.194753	+	0.0465338i
$603$		0			0
$604$	3.08372			0.125475
$605$	−17.8972	−	6.51406i	−0.727626	−	0.264834i
$606$		0			0
$607$	−26.1323	+	31.1432i	−1.06068	+	1.26407i	−0.0974887	+	0.995237i	$0.531081\pi$
$607$	−26.1323	+	31.1432i	−1.06068	+	1.26407i	−0.963188	+	0.268829i	$0.913363\pi$
$608$	−7.98578	+	2.90659i	−0.323866	+	0.117878i
$609$		0			0
$610$	−0.390993	−	2.21743i	−0.0158308	−	0.0897812i
$611$			22.4411i			0.907871i
$612$		0			0
$613$	28.1248			1.13595			0.567975	−	0.823046i	$-0.307727\pi$
$613$	28.1248			1.13595			0.567975	+	0.823046i	$0.307727\pi$
$614$	0.463897	+	0.168845i	0.0187214	+	0.00681402i
$615$		0			0
$616$	−3.70155	+	0.222385i	−0.149140	+	0.00896015i
$617$	−2.77984	+	3.31289i	−0.111912	+	0.133372i	−0.819092	−	0.573661i	$-0.805523\pi$
$617$	−2.77984	+	3.31289i	−0.111912	+	0.133372i	0.707180	+	0.707033i	$0.249967\pi$
$618$		0			0
$619$	9.94128	+	11.8476i	0.399574	+	0.476193i	0.927890	−	0.372854i	$-0.121621\pi$
$619$	9.94128	+	11.8476i	0.399574	+	0.476193i	−0.528316	+	0.849048i	$0.677176\pi$
$620$	13.8287	+	7.98399i	0.555373	+	0.320645i
$621$		0			0
$622$			3.38045i			0.135544i
$623$	14.4622	+	10.7257i	0.579417	+	0.429715i
$624$		0			0
$625$	−3.88859	+	22.0533i	−0.155544	+	0.882131i
$626$	2.79028	+	2.34132i	0.111522	+	0.0935781i
$627$		0			0
$628$	16.4018	−	45.0635i	0.654503	−	1.79823i
$629$	−0.655946	−	1.13613i	−0.0261543	−	0.0453006i
$630$		0			0
$631$	−17.0661	+	29.5593i	−0.679389	+	1.17674i	0.295776	+	0.955257i	$0.404422\pi$
$631$	−17.0661	+	29.5593i	−0.679389	+	1.17674i	−0.975165	+	0.221479i	$0.928911\pi$
$632$	−2.45208	−	2.92227i	−0.0975384	−	0.116242i
$633$		0			0
$634$	−0.816969	+	4.63326i	−0.0324460	+	0.184010i
$635$	7.88276	+	6.61442i	0.312818	+	0.262485i
$636$		0			0
$637$	−3.20287	−	26.5593i	−0.126903	−	1.05232i
$638$	1.60724	+	0.927943i	0.0636314	+	0.0367376i
$639$		0			0
$640$			15.6503i			0.618632i
$641$	−3.26804	+	0.576243i	−0.129080	+	0.0227602i	−0.237815	−	0.971311i	$-0.576431\pi$
$641$	−3.26804	+	0.576243i	−0.129080	+	0.0227602i	0.108735	+	0.994071i	$0.465320\pi$
$642$		0			0
$643$	−24.9953	−	4.40734i	−0.985717	−	0.173808i	−0.342521	−	0.939510i	$-0.611281\pi$
$643$	−24.9953	−	4.40734i	−0.985717	−	0.173808i	−0.643196	+	0.765702i	$0.722392\pi$
$644$	2.37799	+	39.5811i	0.0937060	+	1.55972i
$645$		0			0
$646$	0.0279787	+	0.158675i	0.00110081	+	0.00624298i
$647$	−0.170073	+	0.294574i	−0.00668625	+	0.0115809i	−0.869349	−	0.494198i	$-0.835462\pi$
$647$	−0.170073	+	0.294574i	−0.00668625	+	0.0115809i	0.862663	+	0.505779i	$0.168795\pi$
$648$		0			0
$649$	1.95759	−	1.13021i	0.0768420	−	0.0443648i
$650$	0.425366	+	0.154821i	0.0166842	+	0.00607256i
$651$		0			0
$652$	19.2621	+	16.1628i	0.754362	+	0.632985i
$653$	9.61429	+	26.4150i	0.376236	+	1.03370i	0.972903	+	0.231212i	$0.0742690\pi$
$653$	9.61429	+	26.4150i	0.376236	+	1.03370i	−0.596667	+	0.802489i	$0.703509\pi$
$654$		0			0
$655$	−1.32493	−	7.51404i	−0.0517692	−	0.293598i
$656$	19.4482	−	33.6853i	0.759326	−	1.31519i
$657$		0			0
$658$	−1.10201	+	3.70564i	−0.0429610	+	0.144461i
$659$	−29.0041	+	5.11420i	−1.12984	+	0.199221i	−0.707157	−	0.707057i	$-0.750022\pi$
$659$	−29.0041	+	5.11420i	−1.12984	+	0.199221i	−0.422682	+	0.906278i	$0.638911\pi$
$660$		0			0
$661$	−0.798762	−	0.140843i	−0.0310682	−	0.00547817i	0.158092	−	0.987424i	$-0.449466\pi$
$661$	−0.798762	−	0.140843i	−0.0310682	−	0.00547817i	−0.189161	+	0.981946i	$0.560577\pi$
$662$	2.90260	+	0.511806i	0.112813	+	0.0198919i
$663$		0			0
$664$	0.145325	−	0.0256247i	0.00563969	−	0.000994430i
$665$	−4.76015	+	16.0065i	−0.184591	+	0.620707i
$666$		0			0
$667$	20.1622	−	34.9220i	0.780685	−	1.35219i
$668$	−2.77385	−	15.7313i	−0.107324	−	0.608662i
$669$		0			0
$670$	−2.70048	−	7.41951i	−0.104329	−	0.286641i
$671$	−4.66091	−	3.91097i	−0.179933	−	0.150981i
$672$		0			0
$673$	12.2309	+	4.45168i	0.471466	+	0.171600i	0.566816	−	0.823844i	$-0.308175\pi$
$673$	12.2309	+	4.45168i	0.471466	+	0.171600i	−0.0953502	+	0.995444i	$0.530397\pi$
$674$	−4.51767	+	2.60828i	−0.174014	+	0.100467i
$675$		0			0
$676$	1.55554	−	2.69428i	0.0598286	−	0.103626i
$677$	−2.28800	−	12.9759i	−0.0879349	−	0.498704i	−0.996685	−	0.0813620i	$-0.974073\pi$
$677$	−2.28800	−	12.9759i	−0.0879349	−	0.498704i	0.908750	−	0.417341i	$-0.137038\pi$
$678$		0			0
$679$	−1.97599	−	32.8898i	−0.0758314	−	1.26220i
$680$	0.447885	+	0.0789741i	0.0171756	+	0.00302852i
$681$		0			0
$682$	−1.35769	+	0.239398i	−0.0519887	+	0.00916702i
$683$		−	6.25312i		−	0.239269i	−0.992818	−	0.119635i	$-0.961828\pi$
$683$		−	6.25312i		−	0.239269i	0.992818	−	0.119635i	$-0.0381723\pi$
$684$		0			0
$685$	6.58629	+	3.80260i	0.251649	+	0.145290i
$686$	0.775365	−	4.54295i	0.0296036	−	0.173451i
$687$		0			0
$688$	20.7634	+	17.4226i	0.791598	+	0.664230i
$689$	9.27486	−	52.6003i	0.353344	−	2.00391i
$690$		0			0
$691$	−3.35901	−	4.00311i	−0.127783	−	0.152286i	0.698359	−	0.715747i	$-0.253914\pi$
$691$	−3.35901	−	4.00311i	−0.127783	−	0.152286i	−0.826142	+	0.563462i	$0.809469\pi$
$692$	−22.8137	+	39.5145i	−0.867246	+	1.50211i
$693$		0			0
$694$	3.81061	+	6.60018i	0.144649	+	0.250539i
$695$	4.36537	−	11.9937i	0.165588	−	0.454949i
$696$		0			0
$697$	−1.78989	−	1.50189i	−0.0677968	−	0.0568883i
$698$	0.832360	−	4.72055i	0.0315053	−	0.178675i
$699$		0			0
$700$	−1.96041	−	1.45391i	−0.0740967	−	0.0549526i
$701$		−	21.7945i		−	0.823166i	−0.911372	−	0.411583i	$-0.864976\pi$
$701$		−	21.7945i		−	0.823166i	0.911372	−	0.411583i	$-0.135024\pi$
$702$		0			0
$703$	15.4517	+	8.92101i	0.582770	+	0.336462i
$704$	6.02344	+	7.17846i	0.227017	+	0.270548i
$705$		0			0
$706$	−2.95137	+	3.51731i	−0.111076	+	0.132376i
$707$	22.1234	−	1.32915i	0.832038	−	0.0499879i
$708$		0			0
$709$	−16.2367	−	5.90968i	−0.609783	−	0.221943i	0.0186255	−	0.999827i	$-0.494071\pi$
$709$	−16.2367	−	5.90968i	−0.609783	−	0.221943i	−0.628408	+	0.777884i	$0.716293\pi$
$710$	2.62465			0.0985015
$711$		0			0
$712$			6.66907i			0.249934i
$713$	5.20161	+	29.4998i	0.194802	+	1.10478i
$714$		0			0
$715$	−10.9247	+	3.97626i	−0.408560	+	0.148704i
$716$	−10.3992	+	12.3933i	−0.388638	+	0.463160i
$717$		0			0
$718$	−0.182320	−	0.0663590i	−0.00680411	−	0.00247649i
$719$	−24.2323			−0.903713			−0.451857	−	0.892091i	$-0.649238\pi$
$719$	−24.2323			−0.903713			−0.451857	+	0.892091i	$0.649238\pi$
$720$		0			0
$721$	−0.551549	+	0.131786i	−0.0205408	+	0.00490795i
$722$	1.63057	+	1.94324i	0.0606836	+	0.0723199i
$723$		0			0
$724$	5.18612	−	6.18058i	0.192741	−	0.229699i
$725$	0.848919	+	2.33239i	0.0315281	+	0.0866227i
$726$		0			0
$727$	4.28953	−	11.7854i	0.159090	−	0.437095i	−0.834380	−	0.551189i	$-0.814174\pi$
$727$	4.28953	−	11.7854i	0.159090	−	0.437095i	0.993470	+	0.114094i	$0.0363965\pi$
$728$	7.19483	−	6.81289i	0.266658	−	0.252502i
$729$		0			0
$730$	−0.653150	−	1.13129i	−0.0241742	−	0.0418709i
$731$	1.24727	−	1.04658i	0.0461319	−	0.0387093i
$732$		0			0
$733$	−17.9357	−	3.16255i	−0.662471	−	0.116812i	−0.167704	−	0.985837i	$-0.553635\pi$
$733$	−17.9357	−	3.16255i	−0.662471	−	0.116812i	−0.494767	+	0.869026i	$0.664747\pi$
$734$	1.07498	−	6.09652i	0.0396783	−	0.225027i
$735$		0			0
$736$	−16.9648	+	14.2351i	−0.625329	+	0.524713i
$737$	−18.4773	−	10.6679i	−0.680621	−	0.392956i
$738$		0			0
$739$	24.1785	+	41.8783i	0.889420	+	1.54052i	0.840563	+	0.541714i	$0.182224\pi$
$739$	24.1785	+	41.8783i	0.889420	+	1.54052i	0.0488568	+	0.998806i	$0.484442\pi$
$740$	18.9864	−	15.9315i	0.697954	−	0.585653i
$741$		0			0
$742$	4.11457	−	8.23029i	0.151051	−	0.302143i
$743$	−11.3965	−	31.3117i	−0.418098	−	1.14872i	−0.952780	−	0.303662i	$-0.901791\pi$
$743$	−11.3965	−	31.3117i	−0.418098	−	1.14872i	0.534682	−	0.845053i	$-0.320431\pi$
$744$		0			0
$745$	4.05780	−	11.1487i	0.148666	−	0.408457i
$746$	−5.18235	+	2.99203i	−0.189739	+	0.109546i
$747$		0			0
$748$	0.523782	−	0.302406i	0.0191514	−	0.0110570i
$749$	18.6123	+	42.9320i	0.680077	+	1.56870i
$750$		0			0
$751$	−31.1058	+	11.3216i	−1.13507	+	0.413130i	−0.840129	−	0.542387i	$-0.817521\pi$
$751$	−31.1058	+	11.3216i	−1.13507	+	0.413130i	−0.294937	+	0.955517i	$0.595299\pi$
$752$	20.0428	−	7.29497i	0.730884	−	0.266020i
$753$		0			0
$754$	−4.88372	+	0.861131i	−0.177854	+	0.0313605i
$755$	3.38427			0.123166
$756$		0			0
$757$	37.7148			1.37077			0.685384	−	0.728182i	$-0.259635\pi$
$757$	37.7148			1.37077			0.685384	+	0.728182i	$0.259635\pi$
$758$	7.49579	−	1.32171i	0.272259	−	0.0480067i
$759$		0			0
$760$	−5.81228	+	2.11550i	−0.210834	+	0.0767371i
$761$	−5.51061	+	2.00570i	−0.199760	+	0.0727065i	−0.439962	−	0.898016i	$-0.645008\pi$
$761$	−5.51061	+	2.00570i	−0.199760	+	0.0727065i	0.240203	+	0.970723i	$0.422786\pi$
$762$		0			0
$763$	2.02456	+	1.50148i	0.0732939	+	0.0543572i
$764$	−1.62350	+	0.937327i	−0.0587361	+	0.0339113i
$765$		0			0
$766$	7.75765	−	4.47888i	0.280295	−	0.161829i
$767$	−2.06581	+	5.67576i	−0.0745920	+	0.204940i
$768$		0			0
$769$	−6.33820	−	17.4141i	−0.228561	−	0.627967i	0.771404	−	0.636346i	$-0.219555\pi$
$769$	−6.33820	−	17.4141i	−0.228561	−	0.627967i	−0.999965	+	0.00837935i	$0.997333\pi$
$770$	−1.99922	+	0.120111i	−0.0720470	+	0.00432851i
$771$		0			0
$772$	−10.6902	+	8.97011i	−0.384747	+	0.322841i
$773$	3.16361	+	5.47954i	0.113787	+	0.197085i	0.917294	−	0.398210i	$-0.130368\pi$
$773$	3.16361	+	5.47954i	0.113787	+	0.197085i	−0.803507	+	0.595295i	$0.797035\pi$
$774$		0			0
$775$	−1.59678	−	0.921900i	−0.0573579	−	0.0331156i
$776$	9.34888	−	7.84464i	0.335605	−	0.281606i
$777$		0			0
$778$	1.05424	−	5.97889i	0.0377963	−	0.214354i
$779$	31.2946	+	5.51808i	1.12124	+	0.197706i
$780$		0			0
$781$	5.43306	−	4.55888i	0.194410	−	0.163129i
$782$	0.209937	+	0.363622i	0.00750733	+	0.0130031i
$783$		0			0
$784$	−22.6797	+	11.4942i	−0.809988	+	0.410509i
$785$	18.0004	−	49.4557i	0.642462	−	1.76515i
$786$		0			0
$787$	16.1802	+	44.4547i	0.576762	+	1.58464i	0.793605	+	0.608434i	$0.208202\pi$
$787$	16.1802	+	44.4547i	0.576762	+	1.58464i	−0.216843	+	0.976206i	$0.569576\pi$
$788$	9.93173	−	11.8362i	0.353803	−	0.421646i
$789$		0			0
$790$	−1.32438	−	1.57833i	−0.0471192	−	0.0561545i
$791$	10.6386	−	35.7736i	0.378267	−	1.27196i
$792$		0			0
$793$	16.2579			0.577336
$794$	−1.58152	−	0.575625i	−0.0561259	−	0.0204282i
$795$		0			0
$796$	5.32234	−	6.34291i	0.188645	−	0.224819i
$797$	14.8436	−	5.40264i	0.525788	−	0.191371i	−0.0654686	−	0.997855i	$-0.520854\pi$
$797$	14.8436	−	5.40264i	0.525788	−	0.191371i	0.591257	+	0.806483i	$0.298632\pi$
$798$		0			0
$799$	−0.222486	−	1.26178i	−0.00787100	−	0.0446386i
$800$		−	1.36314i		−	0.0481942i
$801$		0			0
$802$	−0.239588			−0.00846013
$803$	−3.31702	−	1.20729i	−0.117055	−	0.0426045i
$804$		0			0
$805$	2.60976	+	43.4389i	0.0919821	+	1.53102i
$806$	2.36791	−	2.82197i	0.0834061	−	0.0993995i
$807$		0			0
$808$	5.27672	+	6.28855i	0.185634	+	0.221230i
$809$	43.3139	+	25.0073i	1.52284	+	0.879210i	0.999635	+	0.0269998i	$0.00859536\pi$
$809$	43.3139	+	25.0073i	1.52284	+	0.879210i	0.523200	+	0.852210i	$0.324738\pi$
$810$		0			0
$811$			43.1499i			1.51520i	0.652720	+	0.757600i	$0.273628\pi$
$811$			43.1499i			1.51520i	−0.652720	+	0.757600i	$0.726372\pi$
$812$	26.5634	+	3.05558i	0.932193	+	0.107230i
$813$		0			0
$814$	−0.371585	+	2.10737i	−0.0130241	+	0.0738631i
$815$	21.1395	+	17.7381i	0.740484	+	0.621340i
$816$		0			0
$817$	−7.57363	+	20.8084i	−0.264968	+	0.727993i
$818$	3.61546	+	6.26216i	0.126412	+	0.218951i
$819$		0			0
$820$	22.0715	−	38.2290i	0.770770	−	1.33501i
$821$	−19.4758	−	23.2104i	−0.679711	−	0.810048i	0.310359	−	0.950619i	$-0.399551\pi$
$821$	−19.4758	−	23.2104i	−0.679711	−	0.810048i	−0.990071	+	0.140571i	$0.955106\pi$
$822$		0			0
$823$	3.77527	−	21.4106i	0.131598	−	0.746327i	−0.845571	−	0.533862i	$-0.820740\pi$
$823$	3.77527	−	21.4106i	0.131598	−	0.746327i	0.977169	−	0.212464i	$-0.0681489\pi$
$824$	−0.160900	−	0.135011i	−0.00560521	−	0.00470333i
$825$		0			0
$826$	−0.619840	+	0.835777i	−0.0215670	+	0.0290804i
$827$	−6.80237	−	3.92735i	−0.236541	−	0.136567i	0.377045	−	0.926195i	$-0.376940\pi$
$827$	−6.80237	−	3.92735i	−0.236541	−	0.136567i	−0.613586	+	0.789628i	$0.710274\pi$
$828$		0			0
$829$		−	4.06084i		−	0.141039i	−0.997510	−	0.0705193i	$-0.977534\pi$
$829$		−	4.06084i		−	0.141039i	0.997510	−	0.0705193i	$-0.0224656\pi$
$830$	0.0784905	−	0.0138400i	0.00272444	−	0.000480393i
$831$		0			0
$832$	−24.6591	−	4.34806i	−0.854900	−	0.150742i
$833$	0.443401	+	1.46158i	0.0153629	+	0.0506407i
$834$		0			0
$835$	−3.04421	−	17.2646i	−0.105349	−	0.597465i
$836$	−4.11279	+	7.12355i	−0.142244	+	0.246373i
$837$		0			0
$838$	5.24878	−	3.03038i	0.181316	−	0.104683i
$839$	−16.0171	−	5.82975i	−0.552971	−	0.201265i	0.0503948	−	0.998729i	$-0.483952\pi$
$839$	−16.0171	−	5.82975i	−0.552971	−	0.201265i	−0.603366	+	0.797464i	$0.706174\pi$
$840$		0			0
$841$	1.38521	+	1.16233i	0.0477660	+	0.0400804i
$842$	−0.997791	−	2.74141i	−0.0343862	−	0.0944752i
$843$		0			0
$844$	7.18442	+	40.7449i	0.247298	+	1.40250i
$845$	1.70716	−	2.95688i	0.0587280	−	0.101720i
$846$		0			0
$847$	17.2026	−	16.2894i	0.591088	−	0.559710i
$848$	−49.9937	+	8.81524i	−1.71679	+	0.302717i
$849$		0			0
$850$	−0.0254517	−	0.00448782i	−0.000872985	−	0.000153931i
$851$	45.7886	+	8.07377i	1.56961	+	0.276765i
$852$		0			0
$853$	−23.9922	+	4.23048i	−0.821478	+	0.144849i	−0.568563	−	0.822640i	$-0.692500\pi$
$853$	−23.9922	+	4.23048i	−0.821478	+	0.144849i	−0.252915	+	0.967488i	$0.581389\pi$
$854$	2.68462	+	0.798376i	0.0918660	+	0.0273199i
$855$		0			0
$856$	−8.66584	+	15.0097i	−0.296192	+	0.513020i
$857$	−9.37979	−	53.1954i	−0.320407	−	1.81712i	−0.540157	−	0.841565i	$-0.681635\pi$
$857$	−9.37979	−	53.1954i	−0.320407	−	1.81712i	0.219749	−	0.975556i	$-0.429476\pi$
$858$		0			0
$859$	−9.38266	−	25.7786i	−0.320132	−	0.879556i	−0.990498	−	0.137525i	$-0.956085\pi$
$859$	−9.38266	−	25.7786i	−0.320132	−	0.879556i	0.670366	−	0.742031i	$-0.266137\pi$
$860$	23.5641	+	19.7726i	0.803529	+	0.674241i
$861$		0			0
$862$	−6.19522	−	2.25488i	−0.211010	−	0.0768014i
$863$	−13.4069	+	7.74047i	−0.456376	+	0.263489i	−0.710519	−	0.703678i	$-0.751540\pi$
$863$	−13.4069	+	7.74047i	−0.456376	+	0.263489i	0.254143	+	0.967167i	$0.418207\pi$
$864$		0			0
$865$	−25.0372	+	43.3658i	−0.851292	+	1.47448i
$866$	1.01751	+	5.77059i	0.0345764	+	0.196092i
$867$		0			0
$868$	−16.5750	+	10.9450i	−0.562593	+	0.371499i
$869$	−5.48295	−	0.966792i	−0.185996	−	0.0327962i
$870$		0			0
$871$	56.1445	−	9.89980i	1.90239	−	0.335442i
$872$			0.933598i			0.0316156i
$873$		0			0
$874$	−4.94534	−	2.85519i	−0.167278	−	0.0965783i
$875$	−24.7517	−	18.3567i	−0.836760	−	0.620569i
$876$		0			0
$877$	27.8754	+	23.3902i	0.941285	+	0.789832i	0.977808	−	0.209501i	$-0.0671839\pi$
$877$	27.8754	+	23.3902i	0.941285	+	0.789832i	−0.0365234	+	0.999333i	$0.511628\pi$
$878$	−0.180418	+	1.02320i	−0.00608880	+	0.0345313i
$879$		0			0
$880$	7.10260	+	8.46454i	0.239428	+	0.285340i
$881$	−16.4076	+	28.4188i	−0.552787	+	0.957455i	0.445285	+	0.895389i	$0.353102\pi$
$881$	−16.4076	+	28.4188i	−0.552787	+	0.957455i	−0.998072	+	0.0620663i	$0.980231\pi$
$882$		0			0
$883$	−4.24994	−	7.36111i	−0.143022	−	0.247721i	0.785611	−	0.618720i	$-0.212349\pi$
$883$	−4.24994	−	7.36111i	−0.143022	−	0.247721i	−0.928633	+	0.370999i	$0.879015\pi$
$884$	−0.552738	+	1.51864i	−0.0185906	+	0.0510773i
$885$		0			0
$886$	0.462823	+	0.388355i	0.0155488	+	0.0130470i
$887$	1.37491	−	7.79748i	0.0461648	−	0.261814i	−0.952986	−	0.303014i	$-0.902007\pi$
$887$	1.37491	−	7.79748i	0.0461648	−	0.261814i	0.999151	+	0.0412003i	$0.0131182\pi$
$888$		0			0
$889$	−11.7439	+	5.09133i	−0.393878	+	0.170758i
$890$			3.60199i			0.120739i
$891$		0			0
$892$	−20.6833	−	11.9415i	−0.692528	−	0.399831i
$893$	11.2007	+	13.3485i	0.374818	+	0.446691i
$894$		0			0
$895$	−11.4128	+	13.6012i	−0.381488	+	0.454640i
$896$	−17.4127	−	8.70515i	−0.581718	−	0.290819i
$897$		0			0
$898$	2.72623	+	0.992267i	0.0909755	+	0.0331124i
$899$	20.1993			0.673683
$900$		0			0
$901$			3.04948i			0.101593i
$902$	0.661808	+	3.75330i	0.0220358	+	0.124971i
$903$		0			0
$904$	12.9901	−	4.72800i	0.432044	−	0.157251i
$905$	5.69159	−	6.78297i	0.189195	−	0.225474i
$906$		0			0
$907$	34.6469	+	12.6104i	1.15043	+	0.418722i	0.845670	−	0.533706i	$-0.179201\pi$
$907$	34.6469	+	12.6104i	1.15043	+	0.418722i	0.304761	+	0.952429i	$0.401423\pi$
$908$	−36.1833			−1.20079
$909$		0			0
$910$	3.88596	−	3.67967i	0.128818	−	0.121980i
$911$	3.62967	+	4.32568i	0.120256	+	0.143316i	0.822814	−	0.568311i	$-0.192403\pi$
$911$	3.62967	+	4.32568i	0.120256	+	0.143316i	−0.702557	+	0.711627i	$0.747959\pi$
$912$		0			0
$913$	0.138437	−	0.164983i	0.00458159	−	0.00546013i
$914$	1.80796	+	4.96732i	0.0598019	+	0.164304i
$915$		0			0
$916$	12.8724	−	35.3666i	0.425316	−	1.16855i
$917$	9.09719	+	2.70540i	0.300416	+	0.0893401i
$918$		0			0
$919$	10.6179	+	18.3908i	0.350253	+	0.606655i	0.986294	−	0.165000i	$-0.0527624\pi$
$919$	10.6179	+	18.3908i	0.350253	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$920$	−12.3474	+	10.3607i	−0.407083	+	0.341583i
$921$		0			0
$922$	6.59615	+	1.16308i	0.217233	+	0.0383040i
$923$	−3.29085	+	18.6634i	−0.108320	+	0.614312i
$924$		0			0
$925$	−2.19233	+	1.83958i	−0.0720834	+	0.0604851i
$926$	−5.17141	−	2.98572i	−0.169943	−	0.0981167i
$927$		0			0
$928$	7.46675	+	12.9328i	0.245108	+	0.424539i
$929$	30.4946	−	25.5880i	1.00050	−	0.839515i	0.0134422	−	0.999910i	$-0.495721\pi$
$929$	30.4946	−	25.5880i	1.00050	−	0.839515i	0.987053	+	0.160395i	$0.0512766\pi$
$930$		0			0
$931$	−15.1613	−	14.1995i	−0.496893	−	0.465370i
$932$	8.74129	+	24.0165i	0.286331	+	0.786687i
$933$		0			0
$934$	0.526807	−	1.44739i	0.0172376	−	0.0473600i
$935$	0.574833	−	0.331880i	0.0187990	−	0.0108536i
$936$		0			0
$937$	2.26157	−	1.30572i	0.0738824	−	0.0426560i	−0.462604	−	0.886565i	$-0.653085\pi$
$937$	2.26157	−	1.30572i	0.0738824	−	0.0426560i	0.536486	+	0.843909i	$0.319751\pi$
$938$	9.75714	+	1.12236i	0.318582	+	0.0366463i
$939$		0			0
$940$	22.7462	−	8.27895i	0.741900	−	0.270029i
$941$	27.9161	−	10.1606i	0.910038	−	0.331227i	0.155770	−	0.987793i	$-0.450214\pi$
$941$	27.9161	−	10.1606i	0.910038	−	0.331227i	0.754268	+	0.656566i	$0.227992\pi$
$942$		0			0
$943$	81.5513	−	14.3797i	2.65568	−	0.468267i
$944$	5.74070			0.186844
$945$		0			0
$946$	−2.65581			−0.0863477
$947$	−17.0572	+	3.00765i	−0.554285	+	0.0977355i	−0.443773	−	0.896139i	$-0.646360\pi$
$947$	−17.0572	+	3.00765i	−0.554285	+	0.0977355i	−0.110513	+	0.993875i	$0.535249\pi$
$948$		0			0
$949$	8.86330	−	3.22598i	0.287715	−	0.104720i
$950$	0.330291	−	0.120216i	0.0107161	−	0.00390033i
$951$		0			0
$952$	−0.336994	+	0.454395i	−0.0109220	+	0.0147270i
$953$	16.8568	−	9.73226i	0.546044	−	0.315259i	−0.201481	−	0.979492i	$-0.564575\pi$
$953$	16.8568	−	9.73226i	0.546044	−	0.315259i	0.747525	+	0.664234i	$0.231242\pi$
$954$		0			0
$955$	−1.78173	+	1.02868i	−0.0576555	+	0.0332874i
$956$	10.3602	−	28.4643i	0.335071	−	0.920601i
$957$		0			0
$958$	1.37197	+	3.76945i	0.0443262	+	0.121785i
$959$	−7.89431	+	5.21288i	−0.254921	+	0.168333i
$960$		0			0
$961$	12.2529	−	10.2814i	0.395255	−	0.331659i
$962$	−2.85895	−	4.95184i	−0.0921762	−	0.159654i
$963$		0			0
$964$	−10.9001	−	6.29320i	−0.351070	−	0.202690i
$965$	−11.7321	+	9.84438i	−0.377669	+	0.316902i
$966$		0			0
$967$	3.08674	−	17.5057i	0.0992627	−	0.562947i	−0.894095	−	0.447878i	$-0.852180\pi$
$967$	3.08674	−	17.5057i	0.0992627	−	0.562947i	0.993357	−	0.115069i	$-0.0367089\pi$
$968$	8.64172	+	1.52377i	0.277755	+	0.0489758i
$969$		0			0
$970$	5.04937	−	4.23692i	0.162125	−	0.136039i
$971$	15.6634	+	27.1298i	0.502662	+	0.870636i	0.999995	+	0.00307625i	$0.000979204\pi$
$971$	15.6634	+	27.1298i	0.502662	+	0.870636i	−0.497334	+	0.867559i	$0.665687\pi$
$972$		0			0
$973$	10.9163	+	11.5282i	0.349959	+	0.369578i
$974$	2.21727	−	6.09191i	0.0710461	−	0.195197i
$975$		0			0
$976$	−5.28498	−	14.5204i	−0.169168	−	0.464786i
$977$	0.137449	−	0.163806i	0.00439739	−	0.00524061i	−0.763841	−	0.645404i	$-0.776689\pi$
$977$	0.137449	−	0.163806i	0.00439739	−	0.00524061i	0.768239	+	0.640164i	$0.221133\pi$
$978$		0			0
$979$	6.25646	+	7.45616i	0.199957	+	0.238300i
$980$	−25.7388	+	13.0446i	−0.822196	+	0.416696i
$981$		0			0
$982$	2.62536			0.0837785
$983$	18.2660	+	6.64828i	0.582595	+	0.212047i	0.616469	−	0.787379i	$-0.288562\pi$
$983$	18.2660	+	6.64828i	0.582595	+	0.212047i	−0.0338747	+	0.999426i	$0.510785\pi$
$984$		0			0
$985$	10.8997	−	12.9898i	0.347294	−	0.413889i
$986$	0.266056	−	0.0968364i	0.00847295	−	0.00308390i
$987$		0			0
$988$	−3.81667	−	21.6454i	−0.121424	−	0.688632i
$989$			57.7051i			1.83492i
$990$		0			0
$991$	−28.1667			−0.894746			−0.447373	−	0.894348i	$-0.647640\pi$
$991$	−28.1667			−0.894746			−0.447373	+	0.894348i	$0.647640\pi$
$992$	−10.4243	−	3.79413i	−0.330971	−	0.120464i
$993$		0			0
$994$	−1.45991	+	2.92022i	−0.0463055	+	0.0926239i
$995$	5.84108	−	6.96113i	0.185175	−	0.220683i
$996$		0			0
$997$	−21.5307	−	25.6593i	−0.681883	−	0.812637i	0.308465	−	0.951236i	$-0.400185\pi$
$997$	−21.5307	−	25.6593i	−0.681883	−	0.812637i	−0.990349	+	0.138599i	$0.955740\pi$
$998$	1.73961	+	1.00437i	0.0550665	+	0.0317927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.10		132
3.2	odd	2		189.2.bd.a.185.13	yes	132
7.5	odd	6		567.2.ba.a.341.13		132
21.5	even	6		189.2.ba.a.131.10	yes	132
27.7	even	9		189.2.ba.a.101.10	✓	132
27.20	odd	18		567.2.ba.a.143.13		132
189.47	even	18	inner	567.2.bd.a.467.10		132
189.61	odd	18		189.2.bd.a.47.13	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.10	✓	132	27.7	even	9
189.2.ba.a.131.10	yes	132	21.5	even	6
189.2.bd.a.47.13	yes	132	189.61	odd	18
189.2.bd.a.185.13	yes	132	3.2	odd	2
567.2.ba.a.143.13		132	27.20	odd	18
567.2.ba.a.341.13		132	7.5	odd	6
567.2.bd.a.17.10		132	1.1	even	1	trivial
567.2.bd.a.467.10		132	189.47	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.245063 + 0.0432112i) q^{2} +(-1.82120 + 0.662861i) q^{4} +(-1.99870 + 0.727467i) q^{5} +(0.302346 - 2.62842i) q^{7} +(0.848674 - 0.489982i) q^{8} +O(q^{10})\)	\(q+(-0.245063 + 0.0432112i) q^{2} +(-1.82120 + 0.662861i) q^{4} +(-1.99870 + 0.727467i) q^{5} +(0.302346 - 2.62842i) q^{7} +(0.848674 - 0.489982i) q^{8} +(0.458373 - 0.264642i) q^{10} +(0.489168 - 1.34398i) q^{11} +(1.30709 + 3.59121i) q^{13} +(0.0394834 + 0.657193i) q^{14} +(2.78250 - 2.33479i) q^{16} +(-0.109097 - 0.188961i) q^{17} +(2.56992 + 1.48374i) q^{19} +(3.15782 - 2.64972i) q^{20} +(-0.0618021 + 0.350497i) q^{22} +(7.61556 + 1.34283i) q^{23} +(-0.364628 + 0.305959i) q^{25} +(-0.475500 - 0.823590i) q^{26} +(1.19165 + 4.98728i) q^{28} +(1.78349 - 4.90009i) q^{29} +(1.32486 + 3.64001i) q^{31} +(-1.84082 + 2.19380i) q^{32} +(0.0349009 + 0.0415932i) q^{34} +(1.30779 + 5.47337i) q^{35} +6.01251 q^{37} +(-0.693906 - 0.252561i) q^{38} +(-1.33980 + 1.59671i) q^{40} +(10.0627 - 3.66253i) q^{41} +(1.29579 + 7.34878i) q^{43} +2.77190i q^{44} -1.92432 q^{46} +(5.51793 + 2.00836i) q^{47} +(-6.81717 - 1.58938i) q^{49} +(0.0761360 - 0.0907353i) q^{50} +(-4.76094 - 5.67387i) q^{52} +(-12.1036 - 6.98800i) q^{53} +3.04206i q^{55} +(-1.03129 - 2.37882i) q^{56} +(-0.225328 + 1.27790i) q^{58} +(1.21070 + 1.01590i) q^{59} +(1.45500 - 3.99757i) q^{61} +(-0.481963 - 0.834784i) q^{62} +(-3.27598 + 5.67416i) q^{64} +(-5.22497 - 6.22688i) q^{65} +(2.59043 - 14.6911i) q^{67} +(0.323942 + 0.271820i) q^{68} +(-0.557002 - 1.28481i) q^{70} +(4.29452 + 2.47944i) q^{71} -2.46806i q^{73} +(-1.47344 + 0.259808i) q^{74} +(-5.66384 - 0.998688i) q^{76} +(-3.38464 - 1.69209i) q^{77} +(-0.675969 - 3.83361i) q^{79} +(-3.86290 + 6.69073i) q^{80} +(-2.30773 + 1.33237i) q^{82} +(0.141502 + 0.0515026i) q^{83} +(0.355515 + 0.298313i) q^{85} +(-0.635099 - 1.74492i) q^{86} +(-0.243381 - 1.38028i) q^{88} +(-3.40271 + 5.89366i) q^{89} +(9.83439 - 2.34980i) q^{91} +(-14.7595 + 2.60251i) q^{92} +(-1.43902 - 0.253739i) q^{94} +(-6.21587 - 1.09603i) q^{95} +(12.2644 - 2.16255i) q^{97} +(1.73932 + 0.0949204i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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