LMFDB - Embedded newform 567.2.bd.a.467.10

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			467.10
Character	$\chi$	$=$	567.467
Dual form			567.2.bd.a.17.10

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

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	0.0863320	−	0.996266i	$-0.472485\pi$
$2$	−0.245063	−	0.0432112i	−0.173286	−	0.0305549i	−0.259618	+	0.965711i	$0.583597\pi$
$3$		0			0
$3$		0			0
$4$	−1.82120	−	0.662861i	−0.910598	−	0.331431i
$5$	−1.99870	−	0.727467i	−0.893846	−	0.325333i	−0.146062	−	0.989275i	$-0.546660\pi$
$5$	−1.99870	−	0.727467i	−0.893846	−	0.325333i	−0.747784	+	0.663942i	$0.768882\pi$
$6$		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	0.991334	−	0.131363i	$-0.0419353\pi$
$11$	0.489168	+	1.34398i	0.147490	+	0.405225i	−0.843845	+	0.536588i	$0.819713\pi$
$12$		0			0
$13$	1.30709	−	3.59121i	0.362522	−	0.996021i	−0.615613	−	0.788049i	$-0.711091\pi$
$13$	1.30709	−	3.59121i	0.362522	−	0.996021i	0.978135	−	0.207972i	$-0.0666864\pi$
$14$	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	−0.878952	−	0.476910i	$-0.841757\pi$
$17$	−0.109097	+	0.188961i	−0.0264599	+	0.0458299i	0.852492	+	0.522740i	$0.175090\pi$
$18$		0			0
$19$	2.56992	−	1.48374i	0.589579	−	0.340394i	−0.175352	−	0.984506i	$-0.556106\pi$
$19$	2.56992	−	1.48374i	0.589579	−	0.340394i	0.764931	+	0.644112i	$0.222773\pi$
$20$	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	0.691246	−	0.722620i	$-0.257062\pi$
$23$	7.61556	−	1.34283i	1.58795	−	0.279999i	0.896709	+	0.442621i	$0.145951\pi$
$24$		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	0.987804	+	0.155702i	$0.0497638\pi$
$29$	1.78349	+	4.90009i	0.331185	+	0.909924i	−0.656619	+	0.754223i	$0.728014\pi$
$30$		0			0
$31$	1.32486	−	3.64001i	0.237951	−	0.653766i	−0.762029	−	0.647543i	$-0.775797\pi$
$31$	1.32486	−	3.64001i	0.237951	−	0.653766i	0.999981	−	0.00622334i	$-0.00198096\pi$
$32$	−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	0.973341	−	0.229364i	$-0.0736646\pi$
$41$	10.0627	+	3.66253i	1.57153	+	0.571990i	0.598190	+	0.801354i	$0.295887\pi$
$42$		0			0
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	−0.711053	−	0.703139i	$-0.751781\pi$
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	0.908659	−	0.417540i	$-0.137108\pi$
$44$		−	2.77190i		−	0.417880i
$45$		0			0
$46$	−1.92432			−0.283725
$47$	5.51793	−	2.00836i	0.804873	−	0.292950i	0.0933687	−	0.995632i	$-0.470236\pi$
$47$	5.51793	−	2.00836i	0.804873	−	0.292950i	0.711504	+	0.702682i	$0.248014\pi$
$48$		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	−0.691063	+	0.722795i	$0.742857\pi$
$53$	−12.1036	+	6.98800i	−1.66255	+	0.959875i	−0.971490	+	0.237080i	$0.923810\pi$
$54$		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	−0.560567	−	0.828109i	$-0.689417\pi$
$59$	1.21070	−	1.01590i	0.157620	−	0.132259i	0.718187	+	0.695850i	$0.244972\pi$
$60$		0			0
$61$	1.45500	+	3.99757i	0.186293	+	0.511837i	0.997319	−	0.0731735i	$-0.0233127\pi$
$61$	1.45500	+	3.99757i	0.186293	+	0.511837i	−0.811026	+	0.585010i	$0.801090\pi$
$62$	−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	0.563848	+	0.825879i	$0.309321\pi$
$67$	2.59043	+	14.6911i	0.316471	+	1.79480i	−0.247376	+	0.968920i	$0.579568\pi$
$68$	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	−0.223031	−	0.974811i	$-0.571595\pi$
$71$	4.29452	−	2.47944i	0.509666	−	0.294256i	0.732696	+	0.680556i	$0.238262\pi$
$72$		0			0
$73$			2.46806i			0.288864i	0.989515	+	0.144432i	$0.0461355\pi$
$73$			2.46806i			0.288864i	−0.989515	+	0.144432i	$0.953864\pi$
$74$	−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	0.922879	+	0.385091i	$0.125830\pi$
$79$	−0.675969	+	3.83361i	−0.0760524	+	0.431315i	−0.998931	+	0.0462239i	$0.985281\pi$
$80$	−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	−0.334243	−	0.942487i	$-0.608480\pi$
$83$	0.141502	−	0.0515026i	0.0155319	−	0.00565315i	0.349774	+	0.936834i	$0.386258\pi$
$84$		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	0.627388	−	0.778707i	$-0.284124\pi$
$89$	−3.40271	−	5.89366i	−0.360686	−	0.624727i	−0.988074	+	0.153980i	$0.950791\pi$
$90$		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	0.757169	−	0.653219i	$-0.226582\pi$
$97$	12.2644	+	2.16255i	1.24526	+	0.219573i	0.488092	+	0.872792i	$0.337693\pi$
$98$	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	−0.822831	−	0.568286i	$-0.807607\pi$
$101$	1.45464	−	8.24969i	0.144742	−	0.820874i	0.967574	−	0.252589i	$-0.0812820\pi$
$102$		0			0
$103$	−0.0733066	+	0.201408i	−0.00722311	+	0.0198453i	−0.943252	−	0.332078i	$-0.892250\pi$
$103$	−0.0733066	+	0.201408i	−0.00722311	+	0.0198453i	0.936029	+	0.351924i	$0.114472\pi$
$104$	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	−0.480946	−	0.876750i	$-0.659707\pi$
$107$	−15.3166	−	8.84302i	−1.48071	−	0.854887i	−0.999761	+	0.0218632i	$0.993040\pi$
$108$		0			0
$109$	−0.476343	−	0.825050i	−0.0456254	−	0.0790255i	0.842311	−	0.538992i	$-0.181195\pi$
$109$	−0.476343	−	0.825050i	−0.0456254	−	0.0790255i	−0.887936	+	0.459967i	$0.847861\pi$
$110$	−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	0.523510	−	0.852020i	$-0.324622\pi$
$113$	13.8921	−	2.44955i	1.30686	−	0.230434i	0.783346	+	0.621586i	$0.213511\pi$
$114$		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	−0.953164	−	0.302453i	$-0.902194\pi$
$127$	−2.41898	+	4.18980i	−0.214650	+	0.371785i	0.738514	+	0.674238i	$0.235528\pi$
$128$	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	0.945428	−	0.325831i	$-0.105644\pi$
$131$	−0.622917	−	3.53274i	−0.0544246	−	0.308657i	−0.999853	+	0.0171742i	$0.994533\pi$
$132$		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	−0.855236	−	0.518238i	$-0.826588\pi$
$137$	−2.29835	+	2.73907i	−0.196361	+	0.234014i	0.658875	+	0.752252i	$0.271033\pi$
$138$		0			0
$139$	−3.85722	−	4.59686i	−0.327165	−	0.389900i	0.577240	−	0.816574i	$-0.304130\pi$
$139$	−3.85722	−	4.59686i	−0.327165	−	0.389900i	−0.904405	+	0.426674i	$0.859685\pi$
$140$	−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	0.598915	−	0.800813i	$-0.295599\pi$
$149$	−3.58546	−	4.27298i	−0.293732	−	0.350057i	−0.892647	+	0.450756i	$0.851154\pi$
$150$		0			0
$151$	−1.49517	+	0.544196i	−0.121675	+	0.0442861i	−0.402140	−	0.915578i	$-0.631734\pi$
$151$	−1.49517	+	0.544196i	−0.121675	+	0.0442861i	0.280465	+	0.959864i	$0.409511\pi$
$152$	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	−0.755952	−	0.654627i	$-0.772826\pi$
$157$	−15.9051	−	18.9549i	−1.26936	−	1.51277i	−0.513412	−	0.858143i	$-0.671619\pi$
$158$	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	0.491849	+	0.870680i	$0.336321\pi$
$163$	−6.48707	+	11.2359i	−0.508107	+	0.880066i	−0.999956	+	0.00938604i	$0.997012\pi$
$164$	−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	−0.988766	−	0.149473i	$-0.952242\pi$
$167$	−1.43124	−	8.11696i	−0.110753	−	0.628110i	0.878013	−	0.478637i	$-0.158869\pi$
$168$		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	0.972359	+	0.233491i	$0.0750151\pi$
$173$	18.0347	+	15.1329i	1.37115	+	1.15053i	0.398793	+	0.917041i	$0.369429\pi$
$174$		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	0.745217	−	0.666822i	$-0.232346\pi$
$179$	7.22926	+	4.17381i	0.540340	+	0.311965i	−0.204877	+	0.978788i	$0.565679\pi$
$180$		0			0
$181$	−3.60525	−	2.08149i	−0.267976	−	0.154716i	0.359992	−	0.932956i	$-0.382780\pi$
$181$	−3.60525	−	2.08149i	−0.267976	−	0.154716i	−0.627967	+	0.778240i	$0.716113\pi$
$182$	−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	0.208005	−	0.978128i	$-0.433303\pi$
$191$	0.952580	+	0.167966i	0.0689263	+	0.0121536i	−0.139079	+	0.990281i	$0.544414\pi$
$192$		0			0
$193$	6.76620	+	2.46270i	0.487042	+	0.177269i	0.573857	−	0.818956i	$-0.305447\pi$
$193$	6.76620	+	2.46270i	0.487042	+	0.177269i	−0.0868148	+	0.996224i	$0.527669\pi$
$194$	−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	0.233458	−	0.972367i	$-0.424996\pi$
$197$	−6.90426	−	3.98617i	−0.491908	−	0.284003i	−0.725366	+	0.688364i	$0.758329\pi$
$198$		0			0
$199$	−3.69994	−	2.13616i	−0.262282	−	0.151428i	0.363093	−	0.931753i	$-0.381721\pi$
$199$	−3.69994	−	2.13616i	−0.262282	−	0.151428i	−0.625375	+	0.780324i	$0.715054\pi$
$200$	−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	0.795560	+	0.605875i	$0.207177\pi$
$211$	3.70699	+	21.0234i	0.255199	+	1.44731i	−0.540361	+	0.841433i	$0.681712\pi$
$212$	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	−0.432579	−	0.901596i	$-0.642396\pi$
$223$	7.92110	−	9.44000i	0.530436	−	0.632149i	0.963015	+	0.269447i	$0.0868408\pi$
$224$	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	0.313746	−	0.949507i	$-0.398416\pi$
$227$	17.5438	−	6.38541i	1.16442	−	0.423815i	0.850675	+	0.525692i	$0.176194\pi$
$228$		0			0
$229$	−12.4826	−	14.8762i	−0.824872	−	0.983044i	0.175127	−	0.984546i	$-0.443966\pi$
$229$	−12.4826	−	14.8762i	−0.824872	−	0.983044i	−0.999999	+	0.00150162i	$0.999522\pi$
$230$	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	$0.142178\pi$
$233$			13.1872i			0.863923i	−0.901892	+	0.431961i	$0.857822\pi$
$234$		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	0.336043	−	0.941847i	$-0.390911\pi$
$239$	−10.0464	−	11.9729i	−0.649849	−	0.774460i	−0.985891	+	0.167387i	$0.946467\pi$
$240$		0			0
$241$	4.17444	−	4.97490i	0.268899	−	0.320462i	−0.614650	−	0.788800i	$-0.710703\pi$
$241$	4.17444	−	4.97490i	0.268899	−	0.320462i	0.883549	+	0.468338i	$0.155147\pi$
$242$	−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	−0.195740	−	0.980656i	$-0.562711\pi$
$251$	11.9045	−	20.6191i	0.751403	−	1.30147i	0.947143	−	0.320812i	$-0.103956\pi$
$252$		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	0.520096	−	0.854108i	$-0.325896\pi$
$257$	23.2700	−	19.5258i	1.45154	−	1.21799i	0.931446	−	0.363880i	$-0.118548\pi$
$258$		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	−0.317047	−	0.948410i	$-0.602691\pi$
$263$	−15.2337	−	2.68611i	−0.939348	−	0.165632i	−0.622302	+	0.782778i	$0.713802\pi$
$264$		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	0.855357	−	0.518039i	$-0.173338\pi$
$269$	−0.343714	−	0.595329i	−0.0209566	−	0.0362979i	−0.876314	+	0.481741i	$0.840005\pi$
$270$		0			0
$271$	6.24649	+	3.60641i	0.379447	+	0.219074i	0.677578	−	0.735451i	$-0.263030\pi$
$271$	6.24649	+	3.60641i	0.379447	+	0.219074i	−0.298131	+	0.954525i	$0.596363\pi$
$272$	−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	−0.848748	−	0.528798i	$-0.822643\pi$
$277$	2.15820	−	12.2398i	0.129674	−	0.735417i	0.978421	−	0.206619i	$-0.0662461\pi$
$278$	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	0.112011	−	0.993707i	$-0.464271\pi$
$281$	−2.05517	−	0.362382i	−0.122601	−	0.0216179i	−0.234612	+	0.972089i	$0.575382\pi$
$282$		0			0
$283$	19.9337	−	3.51484i	1.18493	−	0.208936i	0.453758	−	0.891125i	$-0.350083\pi$
$283$	19.9337	−	3.51484i	1.18493	−	0.208936i	0.731175	+	0.682189i	$0.238972\pi$
$284$	−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	−0.269786	+	0.962920i	$0.586953\pi$
$293$	−21.6520	+	18.1682i	−1.26493	+	1.06140i	−0.995139	+	0.0984780i	$0.968603\pi$
$294$		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	−0.548226	−	0.836330i	$-0.684697\pi$
$307$	−1.71807	+	0.991927i	−0.0980553	+	0.0566122i	0.450170	+	0.892943i	$0.351363\pi$
$308$	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	0.975713	+	0.219054i	$0.0702973\pi$
$311$	2.35895	+	13.3783i	0.133764	+	0.758612i	−0.841949	+	0.539557i	$0.818592\pi$
$312$		0			0
$313$	−9.40882	+	11.2130i	−0.531818	+	0.633796i	−0.963333	−	0.268310i	$-0.913535\pi$
$313$	−9.40882	+	11.2130i	−0.531818	+	0.633796i	0.431515	+	0.902106i	$0.357979\pi$
$314$	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	0.977895	+	0.209095i	$0.0670519\pi$
$317$	6.46638	+	17.7662i	0.363188	+	0.997850i	−0.614707	+	0.788755i	$0.710726\pi$
$318$		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	−0.629273	−	0.777184i	$-0.716647\pi$
$331$	−11.1300	+	4.05098i	−0.611760	+	0.222662i	0.0175134	+	0.999847i	$0.494425\pi$
$332$	−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	0.817324	−	0.576178i	$-0.195456\pi$
$337$	19.6990	+	7.16984i	1.07307	+	0.390566i	0.255747	+	0.966744i	$0.417679\pi$
$338$	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	0.253899	+	0.967231i	$0.418287\pi$
$347$	−10.4749	+	28.7796i	−0.562323	+	1.54497i	−0.816222	+	0.577738i	$0.803935\pi$
$348$		0			0
$349$	−6.58819	−	18.1009i	−0.352658	−	0.968919i	−0.981513	−	0.191397i	$-0.938698\pi$
$349$	−6.58819	−	18.1009i	−0.352658	−	0.968919i	0.628855	−	0.777523i	$-0.283524\pi$
$350$	−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	0.936113	−	0.351700i	$-0.114396\pi$
$353$	14.1346	+	11.8604i	0.752311	+	0.631264i	−0.183802	+	0.982963i	$0.558841\pi$
$354$		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	−0.482075	−	0.876130i	$-0.660117\pi$
$359$	0.675231	−	0.389845i	0.0356373	−	0.0205752i	0.517713	+	0.855554i	$0.326784\pi$
$360$		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	−0.936743	−	0.350018i	$-0.886175\pi$
$367$	−8.50857	−	23.3771i	−0.444144	−	1.22027i	0.492599	−	0.870256i	$-0.336047\pi$
$368$	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	0.852675	−	0.522442i	$-0.174979\pi$
$373$	22.5973	+	8.22473i	1.17004	+	0.425860i	0.317367	+	0.948303i	$0.397201\pi$
$374$	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	−0.729943	−	0.683508i	$-0.760454\pi$
$383$	−33.8267	−	12.3119i	−1.72846	−	0.629109i	−0.998519	+	0.0543988i	$0.982676\pi$
$384$		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	−0.949937	−	0.312443i	$-0.898853\pi$
$389$	−8.34439	−	22.9260i	−0.423077	−	1.16240i	0.526859	−	0.849953i	$-0.323369\pi$
$390$		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	−0.345763	−	0.938322i	$-0.612380\pi$
$397$	5.85723	−	3.38167i	0.293966	−	0.169721i	0.639729	+	0.768601i	$0.279047\pi$
$398$	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	−0.149923	−	0.988698i	$-0.547903\pi$
$401$	0.948178	−	0.167189i	0.0473497	−	0.00834904i	0.197273	+	0.980349i	$0.436792\pi$
$402$		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	0.407951	+	0.913004i	$0.366244\pi$
$409$	−9.93846	+	27.3057i	−0.491425	+	1.35018i	−0.899376	+	0.437176i	$0.855979\pi$
$410$	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	−0.284141	−	0.958782i	$-0.591708\pi$
$419$	−22.8869	−	8.33016i	−1.11810	−	0.406955i	−0.833958	+	0.551828i	$0.813931\pi$
$420$		0			0
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	−0.894155	−	0.447758i	$-0.852223\pi$
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	0.993373	−	0.114936i	$-0.0366663\pi$
$422$		−	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	0.167610	−	0.985853i	$-0.446395\pi$
$431$	22.9443	−	13.2469i	1.10519	−	0.638082i	0.937579	+	0.347772i	$0.113062\pi$
$432$		0			0
$433$			23.5474i			1.13161i	0.824538	+	0.565807i	$0.191435\pi$
$433$			23.5474i			1.13161i	−0.824538	+	0.565807i	$0.808565\pi$
$434$	−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	0.969094	−	0.246690i	$-0.0793430\pi$
$439$	1.42802	+	3.92345i	0.0681557	+	0.187256i	−0.900939	+	0.433946i	$0.857121\pi$
$440$	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	−0.801843	−	0.597534i	$-0.796147\pi$
$443$	−1.56064	+	1.85990i	−0.0741482	+	0.0883663i	0.727695	+	0.685901i	$0.240592\pi$
$444$		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	−0.718955	−	0.695057i	$-0.755379\pi$
$449$	−10.0967	+	5.82936i	−0.476495	+	0.275104i	0.242460	+	0.970161i	$0.422046\pi$
$450$		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	0.768377	+	0.639997i	$0.221064\pi$
$457$	−3.68876	+	20.9200i	−0.172553	+	0.978597i	−0.940930	+	0.338600i	$0.890047\pi$
$458$	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	−0.855498	−	0.517806i	$-0.826749\pi$
$461$	−25.2929	+	9.20586i	−1.17801	+	0.428760i	−0.322510	+	0.946566i	$0.604527\pi$
$462$		0			0
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	−0.106424	−	0.994321i	$-0.533940\pi$
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	0.960735	+	0.277469i	$0.0894956\pi$
$464$	−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	0.785491	−	0.618873i	$-0.212410\pi$
$467$	−3.09488	−	5.36049i	−0.143214	−	0.248054i	−0.928705	+	0.370819i	$0.879077\pi$
$468$		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	0.851644	+	0.524121i	$0.175606\pi$
$479$	−2.79921	+	15.8751i	−0.127899	+	0.725353i	−0.979543	+	0.201233i	$0.935505\pi$
$480$		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	−0.994196	−	0.107580i	$-0.965690\pi$
$487$	−13.0260	−	22.5617i	−0.590265	−	1.02237i	0.403931	−	0.914789i	$-0.367643\pi$
$488$	−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	−0.403102	−	0.915155i	$-0.632068\pi$
$491$	−10.3899	+	1.83203i	−0.468892	+	0.0826783i	−0.0657902	+	0.997833i	$0.520957\pi$
$492$		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	−0.770619	−	0.637296i	$-0.780053\pi$
$499$	−6.18372	+	5.18876i	−0.276822	+	0.232281i	0.493798	+	0.869577i	$0.335608\pi$
$500$	−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	0.969030	+	0.246941i	$0.0794255\pi$
$503$	15.6629	+	27.1289i	0.698373	+	1.20962i	−0.270658	+	0.962676i	$0.587241\pi$
$504$		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	−0.588555	−	0.808457i	$-0.700303\pi$
$509$	−7.03911	−	39.9208i	−0.312003	−	1.76946i	0.276552	−	0.960999i	$-0.410808\pi$
$510$		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	$0.0991342\pi$
$523$			14.0156i			0.612858i	−0.951894	+	0.306429i	$0.900866\pi$
$524$	−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	0.487209	+	0.873285i	$0.338015\pi$
$541$	−11.9247	+	20.6542i	−0.512683	+	0.887993i	−0.999892	+	0.0147075i	$0.995318\pi$
$542$	−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	0.631279	−	0.775556i	$-0.282530\pi$
$547$	−0.534982	−	0.448903i	−0.0228742	−	0.0191937i	−0.654153	+	0.756362i	$0.726975\pi$
$548$	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	0.281852	−	0.959458i	$-0.409051\pi$
$557$	−9.63238	−	5.56126i	−0.408137	−	0.235638i	−0.689989	+	0.723820i	$0.742385\pi$
$558$		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	0.109815	−	0.993952i	$-0.464974\pi$
$563$	−10.5579	−	3.84276i	−0.444962	−	0.161953i	−0.554777	+	0.831999i	$0.687196\pi$
$564$		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	−0.632855	−	0.774270i	$-0.718117\pi$
$569$	−35.5984	−	6.27695i	−1.49236	−	0.263143i	−0.859505	+	0.511127i	$0.829228\pi$
$570$		0			0
$571$	−18.7772	−	6.83434i	−0.785802	−	0.286008i	−0.0822119	−	0.996615i	$-0.526198\pi$
$571$	−18.7772	−	6.83434i	−0.785802	−	0.286008i	−0.703590	+	0.710607i	$0.748421\pi$
$572$	−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	0.936815	−	0.349825i	$-0.113759\pi$
$577$	26.4773	+	15.2867i	1.10226	+	0.636393i	0.165450	+	0.986218i	$0.447092\pi$
$578$	−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	0.983431	−	0.181285i	$-0.0580257\pi$
$587$	23.6386	+	19.8352i	0.975671	+	0.818685i	−0.00775999	+	0.999970i	$0.502470\pi$
$588$		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	0.332730	+	0.943022i	$0.392030\pi$
$593$	−15.8362	+	27.4292i	−0.650316	+	1.12638i	−0.983046	+	0.183358i	$0.941303\pi$
$594$		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	0.925052	−	0.379841i	$-0.124021\pi$
$599$	9.55357	+	11.3855i	0.390348	+	0.465199i	−0.534703	+	0.845040i	$0.679577\pi$
$600$		0			0
$601$	−11.0892	+	13.2156i	−0.452338	+	0.539075i	−0.943228	−	0.332146i	$-0.892227\pi$
$601$	−11.0892	+	13.2156i	−0.452338	+	0.539075i	0.490890	+	0.871221i	$0.336672\pi$
$602$	−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	−0.963188	−	0.268829i	$-0.913363\pi$
$607$	−26.1323	−	31.1432i	−1.06068	−	1.26407i	−0.0974887	−	0.995237i	$-0.531081\pi$
$608$	−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	0.707180	−	0.707033i	$-0.249967\pi$
$617$	−2.77984	−	3.31289i	−0.111912	−	0.133372i	−0.819092	+	0.573661i	$0.805523\pi$
$618$		0			0
$619$	9.94128	−	11.8476i	0.399574	−	0.476193i	−0.528316	−	0.849048i	$-0.677176\pi$
$619$	9.94128	−	11.8476i	0.399574	−	0.476193i	0.927890	+	0.372854i	$0.121621\pi$
$620$	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	−0.975165	−	0.221479i	$-0.928911\pi$
$631$	−17.0661	−	29.5593i	−0.679389	−	1.17674i	0.295776	−	0.955257i	$-0.404422\pi$
$632$	−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	0.108735	−	0.994071i	$-0.465320\pi$
$641$	−3.26804	−	0.576243i	−0.129080	−	0.0227602i	−0.237815	+	0.971311i	$0.576431\pi$
$642$		0			0
$643$	−24.9953	+	4.40734i	−0.985717	+	0.173808i	−0.643196	−	0.765702i	$-0.722392\pi$
$643$	−24.9953	+	4.40734i	−0.985717	+	0.173808i	−0.342521	+	0.939510i	$0.611281\pi$
$644$	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	0.862663	−	0.505779i	$-0.168795\pi$
$647$	−0.170073	−	0.294574i	−0.00668625	−	0.0115809i	−0.869349	+	0.494198i	$0.835462\pi$
$648$		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	−0.596667	−	0.802489i	$-0.703509\pi$
$653$	9.61429	−	26.4150i	0.376236	−	1.03370i	0.972903	−	0.231212i	$-0.0742690\pi$
$654$		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	−0.422682	−	0.906278i	$-0.638911\pi$
$659$	−29.0041	−	5.11420i	−1.12984	−	0.199221i	−0.707157	+	0.707057i	$0.750022\pi$
$660$		0			0
$661$	−0.798762	+	0.140843i	−0.0310682	+	0.00547817i	−0.189161	−	0.981946i	$-0.560577\pi$
$661$	−0.798762	+	0.140843i	−0.0310682	+	0.00547817i	0.158092	+	0.987424i	$0.449466\pi$
$662$	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	−0.0953502	−	0.995444i	$-0.530397\pi$
$673$	12.2309	−	4.45168i	0.471466	−	0.171600i	0.566816	+	0.823844i	$0.308175\pi$
$674$	−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	0.908750	+	0.417341i	$0.137038\pi$
$677$	−2.28800	+	12.9759i	−0.0879349	+	0.498704i	−0.996685	+	0.0813620i	$0.974073\pi$
$678$		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	$0.0381723\pi$
$683$			6.25312i			0.239269i	−0.992818	+	0.119635i	$0.961828\pi$
$684$		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	−0.826142	−	0.563462i	$-0.809469\pi$
$691$	−3.35901	+	4.00311i	−0.127783	+	0.152286i	0.698359	+	0.715747i	$0.253914\pi$
$692$	−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	$0.135024\pi$
$701$			21.7945i			0.823166i	−0.911372	+	0.411583i	$0.864976\pi$
$702$		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	−0.628408	−	0.777884i	$-0.716293\pi$
$709$	−16.2367	+	5.90968i	−0.609783	+	0.221943i	0.0186255	+	0.999827i	$0.494071\pi$
$710$	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	0.993470	−	0.114094i	$-0.0363965\pi$
$727$	4.28953	+	11.7854i	0.159090	+	0.437095i	−0.834380	+	0.551189i	$0.814174\pi$
$728$	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	−0.494767	−	0.869026i	$-0.664747\pi$
$733$	−17.9357	+	3.16255i	−0.662471	+	0.116812i	−0.167704	+	0.985837i	$0.553635\pi$
$734$	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	0.0488568	−	0.998806i	$-0.484442\pi$
$739$	24.1785	−	41.8783i	0.889420	−	1.54052i	0.840563	−	0.541714i	$-0.182224\pi$
$740$	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	0.534682	+	0.845053i	$0.320431\pi$
$743$	−11.3965	+	31.3117i	−0.418098	+	1.14872i	−0.952780	+	0.303662i	$0.901791\pi$
$744$		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	−0.294937	−	0.955517i	$-0.595299\pi$
$751$	−31.1058	−	11.3216i	−1.13507	−	0.413130i	−0.840129	+	0.542387i	$0.817521\pi$
$752$	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	0.240203	−	0.970723i	$-0.422786\pi$
$761$	−5.51061	−	2.00570i	−0.199760	−	0.0727065i	−0.439962	+	0.898016i	$0.645008\pi$
$762$		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	−0.999965	−	0.00837935i	$-0.997333\pi$
$769$	−6.33820	+	17.4141i	−0.228561	+	0.627967i	0.771404	+	0.636346i	$0.219555\pi$
$770$	−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	−0.803507	−	0.595295i	$-0.797035\pi$
$773$	3.16361	−	5.47954i	0.113787	−	0.197085i	0.917294	+	0.398210i	$0.130368\pi$
$774$		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	−0.216843	−	0.976206i	$-0.569576\pi$
$787$	16.1802	−	44.4547i	0.576762	−	1.58464i	0.793605	−	0.608434i	$-0.208202\pi$
$788$	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	0.591257	−	0.806483i	$-0.298632\pi$
$797$	14.8436	+	5.40264i	0.525788	+	0.191371i	−0.0654686	+	0.997855i	$0.520854\pi$
$798$		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	0.523200	−	0.852210i	$-0.324738\pi$
$809$	43.3139	−	25.0073i	1.52284	−	0.879210i	0.999635	−	0.0269998i	$-0.00859536\pi$
$810$		0			0
$811$		−	43.1499i		−	1.51520i	−0.652720	−	0.757600i	$-0.726372\pi$
$811$		−	43.1499i		−	1.51520i	0.652720	−	0.757600i	$-0.273628\pi$
$812$	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	−0.990071	−	0.140571i	$-0.955106\pi$
$821$	−19.4758	+	23.2104i	−0.679711	+	0.810048i	0.310359	+	0.950619i	$0.399551\pi$
$822$		0			0
$823$	3.77527	+	21.4106i	0.131598	+	0.746327i	0.977169	+	0.212464i	$0.0681489\pi$
$823$	3.77527	+	21.4106i	0.131598	+	0.746327i	−0.845571	+	0.533862i	$0.820740\pi$
$824$	−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	−0.613586	−	0.789628i	$-0.710274\pi$
$827$	−6.80237	+	3.92735i	−0.236541	+	0.136567i	0.377045	+	0.926195i	$0.376940\pi$
$828$		0			0
$829$			4.06084i			0.141039i	0.997510	+	0.0705193i	$0.0224656\pi$
$829$			4.06084i			0.141039i	−0.997510	+	0.0705193i	$0.977534\pi$
$830$	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	−0.603366	−	0.797464i	$-0.706174\pi$
$839$	−16.0171	+	5.82975i	−0.552971	+	0.201265i	0.0503948	+	0.998729i	$0.483952\pi$
$840$		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	−0.252915	−	0.967488i	$-0.581389\pi$
$853$	−23.9922	−	4.23048i	−0.821478	−	0.144849i	−0.568563	+	0.822640i	$0.692500\pi$
$854$	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	0.219749	+	0.975556i	$0.429476\pi$
$857$	−9.37979	+	53.1954i	−0.320407	+	1.81712i	−0.540157	+	0.841565i	$0.681635\pi$
$858$		0			0
$859$	−9.38266	+	25.7786i	−0.320132	+	0.879556i	0.670366	+	0.742031i	$0.266137\pi$
$859$	−9.38266	+	25.7786i	−0.320132	+	0.879556i	−0.990498	+	0.137525i	$0.956085\pi$
$860$	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	0.254143	−	0.967167i	$-0.418207\pi$
$863$	−13.4069	−	7.74047i	−0.456376	−	0.263489i	−0.710519	+	0.703678i	$0.751540\pi$
$864$		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	−0.0365234	−	0.999333i	$-0.511628\pi$
$877$	27.8754	−	23.3902i	0.941285	−	0.789832i	0.977808	+	0.209501i	$0.0671839\pi$
$878$	−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	−0.998072	−	0.0620663i	$-0.980231\pi$
$881$	−16.4076	−	28.4188i	−0.552787	−	0.957455i	0.445285	−	0.895389i	$-0.353102\pi$
$882$		0			0
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	−0.928633	−	0.370999i	$-0.879015\pi$
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	0.785611	+	0.618720i	$0.212349\pi$
$884$	−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	0.999151	−	0.0412003i	$-0.0131182\pi$
$887$	1.37491	+	7.79748i	0.0461648	+	0.261814i	−0.952986	+	0.303014i	$0.902007\pi$
$888$		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	0.304761	−	0.952429i	$-0.401423\pi$
$907$	34.6469	−	12.6104i	1.15043	−	0.418722i	0.845670	+	0.533706i	$0.179201\pi$
$908$	−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	−0.702557	−	0.711627i	$-0.747959\pi$
$911$	3.62967	−	4.32568i	0.120256	−	0.143316i	0.822814	+	0.568311i	$0.192403\pi$
$912$		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	−0.636041	−	0.771655i	$-0.719429\pi$
$919$	10.6179	−	18.3908i	0.350253	−	0.606655i	0.986294	+	0.165000i	$0.0527624\pi$
$920$	−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	0.987053	−	0.160395i	$-0.0512766\pi$
$929$	30.4946	+	25.5880i	1.00050	+	0.839515i	0.0134422	+	0.999910i	$0.495721\pi$
$930$		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	0.536486	−	0.843909i	$-0.319751\pi$
$937$	2.26157	+	1.30572i	0.0738824	+	0.0426560i	−0.462604	+	0.886565i	$0.653085\pi$
$938$	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	0.754268	−	0.656566i	$-0.227992\pi$
$941$	27.9161	+	10.1606i	0.910038	+	0.331227i	0.155770	+	0.987793i	$0.450214\pi$
$942$		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	−0.110513	−	0.993875i	$-0.535249\pi$
$947$	−17.0572	−	3.00765i	−0.554285	−	0.0977355i	−0.443773	+	0.896139i	$0.646360\pi$
$948$		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	0.747525	−	0.664234i	$-0.231242\pi$
$953$	16.8568	+	9.73226i	0.546044	+	0.315259i	−0.201481	+	0.979492i	$0.564575\pi$
$954$		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	0.993357	+	0.115069i	$0.0367089\pi$
$967$	3.08674	+	17.5057i	0.0992627	+	0.562947i	−0.894095	+	0.447878i	$0.852180\pi$
$968$	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	−0.497334	−	0.867559i	$-0.665687\pi$
$971$	15.6634	−	27.1298i	0.502662	−	0.870636i	0.999995	−	0.00307625i	$-0.000979204\pi$
$972$		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	0.768239	−	0.640164i	$-0.221133\pi$
$977$	0.137449	+	0.163806i	0.00439739	+	0.00524061i	−0.763841	+	0.645404i	$0.776689\pi$
$978$		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	−0.0338747	−	0.999426i	$-0.510785\pi$
$983$	18.2660	−	6.64828i	0.582595	−	0.212047i	0.616469	+	0.787379i	$0.288562\pi$
$984$		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	−0.990349	−	0.138599i	$-0.955740\pi$
$997$	−21.5307	+	25.6593i	−0.681883	+	0.812637i	0.308465	+	0.951236i	$0.400185\pi$
$998$	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.467.10		132
3.2	odd	2		189.2.bd.a.47.13	yes	132
7.3	odd	6		567.2.ba.a.143.13		132
21.17	even	6		189.2.ba.a.101.10	✓	132
27.4	even	9		189.2.ba.a.131.10	yes	132
27.23	odd	18		567.2.ba.a.341.13		132
189.31	odd	18		189.2.bd.a.185.13	yes	132
189.185	even	18	inner	567.2.bd.a.17.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.10	✓	132	21.17	even	6
189.2.ba.a.131.10	yes	132	27.4	even	9
189.2.bd.a.47.13	yes	132	3.2	odd	2
189.2.bd.a.185.13	yes	132	189.31	odd	18
567.2.ba.a.143.13		132	7.3	odd	6
567.2.ba.a.341.13		132	27.23	odd	18
567.2.bd.a.17.10		132	189.185	even	18	inner
567.2.bd.a.467.10		132	1.1	even	1	trivial

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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