LMFDB - Embedded newform 369.2.u.a.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.2
Character	$\chi$	$=$	369.118
Dual form			369.2.u.a.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415383 + 0.571726i) q^{2} +(0.463706 - 1.42714i) q^{4} +(-2.26179 - 0.734900i) q^{5} +(-4.85225 + 0.768522i) q^{7} +(2.35276 - 0.764458i) q^{8} +O(q^{10})$	\(q+(0.415383 + 0.571726i) q^{2} +(0.463706 - 1.42714i) q^{4} +(-2.26179 - 0.734900i) q^{5} +(-4.85225 + 0.768522i) q^{7} +(2.35276 - 0.764458i) q^{8} +(-0.519348 - 1.59839i) q^{10} +(-1.51881 - 0.773870i) q^{11} +(0.621065 - 3.92125i) q^{13} +(-2.45493 - 2.45493i) q^{14} +(-1.01364 - 0.736453i) q^{16} +(1.24719 - 2.44775i) q^{17} +(-0.150964 - 0.953149i) q^{19} +(-2.09761 + 2.88712i) q^{20} +(-0.188445 - 1.18979i) q^{22} +(-5.46604 + 3.97131i) q^{23} +(0.530527 + 0.385451i) q^{25} +(2.49986 - 1.27374i) q^{26} +(-1.15323 + 7.28122i) q^{28} +(-0.230233 - 0.451858i) q^{29} +(0.182364 + 0.561259i) q^{31} -5.83311i q^{32} +(1.91751 - 0.303703i) q^{34} +(11.5396 + 1.82769i) q^{35} +(1.31461 - 4.04595i) q^{37} +(0.482233 - 0.482233i) q^{38} -5.88325 q^{40} +(4.01905 + 4.98470i) q^{41} +(3.16632 + 4.35807i) q^{43} +(-1.80870 + 1.80870i) q^{44} +(-4.54100 - 1.47546i) q^{46} +(4.96501 + 0.786381i) q^{47} +(16.2964 - 5.29501i) q^{49} +0.463426i q^{50} +(-5.30819 - 2.70466i) q^{52} +(-3.46320 - 6.79691i) q^{53} +(2.86650 + 2.86650i) q^{55} +(-10.8287 + 5.51749i) q^{56} +(0.162704 - 0.319325i) q^{58} +(6.81790 - 4.95350i) q^{59} +(0.408684 - 0.562505i) q^{61} +(-0.245135 + 0.337400i) q^{62} +(1.30766 - 0.950072i) q^{64} +(-4.28645 + 8.41262i) q^{65} +(-3.63545 + 1.85235i) q^{67} +(-2.91496 - 2.91496i) q^{68} +(3.74841 + 7.35666i) q^{70} +(-6.47886 - 3.30115i) q^{71} +9.72685i q^{73} +(2.85924 - 0.929024i) q^{74} +(-1.43028 - 0.226534i) q^{76} +(7.96437 + 2.58778i) q^{77} +(6.15477 - 6.15477i) q^{79} +(1.75142 + 2.41063i) q^{80} +(-1.18044 + 4.36836i) q^{82} -4.81920 q^{83} +(-4.61974 + 4.61974i) q^{85} +(-1.17638 + 3.62054i) q^{86} +(-4.16498 - 0.659667i) q^{88} +(3.63773 - 0.576160i) q^{89} +19.5042i q^{91} +(3.13298 + 9.64234i) q^{92} +(1.61279 + 3.16528i) q^{94} +(-0.359020 + 2.26677i) q^{95} +(-3.63700 + 1.85314i) q^{97} +(9.79653 + 7.11760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.415383	+	0.571726i	0.293720	+	0.404272i	0.930218	−	0.367007i	$-0.119618\pi$
$2$	0.415383	+	0.571726i	0.293720	+	0.404272i	−0.636498	+	0.771279i	$0.719618\pi$
$3$		0			0
$3$		0			0
$4$	0.463706	−	1.42714i	0.231853	−	0.713571i
$5$	−2.26179	−	0.734900i	−1.01150	−	0.328657i	−0.244050	−	0.969763i	$-0.578476\pi$
$5$	−2.26179	−	0.734900i	−1.01150	−	0.328657i	−0.767453	+	0.641105i	$0.778476\pi$
$6$		0			0
$7$	−4.85225	+	0.768522i	−1.83398	+	0.290474i	−0.975110	−	0.221720i	$-0.928833\pi$
$7$	−4.85225	+	0.768522i	−1.83398	+	0.290474i	−0.858870	+	0.512194i	$0.828833\pi$
$8$	2.35276	−	0.764458i	0.831826	−	0.270277i
$9$		0			0
$10$	−0.519348	−	1.59839i	−0.164232	−	0.505455i
$11$	−1.51881	−	0.773870i	−0.457937	−	0.233331i	0.209776	−	0.977750i	$-0.432727\pi$
$11$	−1.51881	−	0.773870i	−0.457937	−	0.233331i	−0.667713	+	0.744419i	$0.732727\pi$
$12$		0			0
$13$	0.621065	−	3.92125i	0.172253	−	1.08756i	−0.738393	−	0.674371i	$-0.764415\pi$
$13$	0.621065	−	3.92125i	0.172253	−	1.08756i	0.910645	−	0.413189i	$-0.135585\pi$
$14$	−2.45493	−	2.45493i	−0.656108	−	0.656108i
$15$		0			0
$16$	−1.01364	−	0.736453i	−0.253410	−	0.184113i
$17$	1.24719	−	2.44775i	0.302488	−	0.593667i	−0.688864	−	0.724890i	$-0.741890\pi$
$17$	1.24719	−	2.44775i	0.302488	−	0.593667i	0.991353	+	0.131223i	$0.0418905\pi$
$18$		0			0
$19$	−0.150964	−	0.953149i	−0.0346335	−	0.218667i	0.964301	−	0.264807i	$-0.0853082\pi$
$19$	−0.150964	−	0.953149i	−0.0346335	−	0.218667i	−0.998935	+	0.0461393i	$0.985308\pi$
$20$	−2.09761	+	2.88712i	−0.469040	+	0.645579i
$21$		0			0
$22$	−0.188445	−	1.18979i	−0.0401766	−	0.253665i
$23$	−5.46604	+	3.97131i	−1.13975	+	0.828075i	−0.987084	−	0.160203i	$-0.948785\pi$
$23$	−5.46604	+	3.97131i	−1.13975	+	0.828075i	−0.152664	+	0.988278i	$0.548785\pi$
$24$		0			0
$25$	0.530527	+	0.385451i	0.106105	+	0.0770902i
$26$	2.49986	−	1.27374i	0.490264	−	0.249802i
$27$		0			0
$28$	−1.15323	+	7.28122i	−0.217940	+	1.37602i
$29$	−0.230233	−	0.451858i	−0.0427532	−	0.0839080i	0.868642	−	0.495441i	$-0.164993\pi$
$29$	−0.230233	−	0.451858i	−0.0427532	−	0.0839080i	−0.911395	+	0.411533i	$0.864993\pi$
$30$		0			0
$31$	0.182364	+	0.561259i	0.0327536	+	0.100805i	0.966097	−	0.258180i	$-0.0831228\pi$
$31$	0.182364	+	0.561259i	0.0327536	+	0.100805i	−0.933343	+	0.358985i	$0.883123\pi$
$32$		−	5.83311i		−	1.03116i
$33$		0			0
$34$	1.91751	−	0.303703i	0.328850	−	0.0520847i
$35$	11.5396	+	1.82769i	1.95054	+	0.308936i
$36$		0			0
$37$	1.31461	−	4.04595i	0.216120	−	0.665150i	−0.782952	−	0.622082i	$-0.786287\pi$
$37$	1.31461	−	4.04595i	0.216120	−	0.665150i	0.999072	−	0.0430675i	$-0.0137130\pi$
$38$	0.482233	−	0.482233i	0.0782285	−	0.0782285i
$39$		0			0
$40$	−5.88325			−0.930223
$41$	4.01905	+	4.98470i	0.627670	+	0.778479i
$41$	4.01905	+	4.98470i	0.627670	+	0.778479i
$42$		0			0
$43$	3.16632	+	4.35807i	0.482860	+	0.664599i	0.979051	−	0.203614i	$-0.0652686\pi$
$43$	3.16632	+	4.35807i	0.482860	+	0.664599i	−0.496192	+	0.868213i	$0.665269\pi$
$44$	−1.80870	+	1.80870i	−0.272672	+	0.272672i
$45$		0			0
$46$	−4.54100	−	1.47546i	−0.669535	−	0.217545i
$47$	4.96501	+	0.786381i	0.724221	+	0.114705i	0.507652	−	0.861562i	$-0.330513\pi$
$47$	4.96501	+	0.786381i	0.724221	+	0.114705i	0.216569	+	0.976267i	$0.430513\pi$
$48$		0			0
$49$	16.2964	−	5.29501i	2.32805	−	0.756430i
$50$			0.463426i			0.0655384i
$51$		0			0
$52$	−5.30819	−	2.70466i	−0.736114	−	0.375069i
$53$	−3.46320	−	6.79691i	−0.475707	−	0.933628i	−0.996785	−	0.0801188i	$-0.974470\pi$
$53$	−3.46320	−	6.79691i	−0.475707	−	0.933628i	0.521078	−	0.853509i	$-0.325530\pi$
$54$		0			0
$55$	2.86650	+	2.86650i	0.386519	+	0.386519i
$56$	−10.8287	+	5.51749i	−1.44704	+	0.737306i
$57$		0			0
$58$	0.162704	−	0.319325i	0.0213641	−	0.0419294i
$59$	6.81790	−	4.95350i	0.887616	−	0.644890i	−0.0476396	−	0.998865i	$-0.515170\pi$
$59$	6.81790	−	4.95350i	0.887616	−	0.644890i	0.935255	+	0.353974i	$0.115170\pi$
$60$		0			0
$61$	0.408684	−	0.562505i	0.0523266	−	0.0720214i	−0.782052	−	0.623213i	$-0.785827\pi$
$61$	0.408684	−	0.562505i	0.0523266	−	0.0720214i	0.834378	+	0.551192i	$0.185827\pi$
$62$	−0.245135	+	0.337400i	−0.0311322	+	0.0428499i
$63$		0			0
$64$	1.30766	−	0.950072i	0.163458	−	0.118759i
$65$	−4.28645	+	8.41262i	−0.531668	+	1.04346i
$66$		0			0
$67$	−3.63545	+	1.85235i	−0.444141	+	0.226301i	−0.661734	−	0.749738i	$-0.730179\pi$
$67$	−3.63545	+	1.85235i	−0.444141	+	0.226301i	0.217594	+	0.976039i	$0.430179\pi$
$68$	−2.91496	−	2.91496i	−0.353491	−	0.353491i
$69$		0			0
$70$	3.74841	+	7.35666i	0.448020	+	0.879289i
$71$	−6.47886	−	3.30115i	−0.768900	−	0.391774i	0.0251057	−	0.999685i	$-0.492008\pi$
$71$	−6.47886	−	3.30115i	−0.768900	−	0.391774i	−0.794005	+	0.607911i	$0.792008\pi$
$72$		0			0
$73$			9.72685i			1.13844i	0.822185	+	0.569221i	$0.192755\pi$
$73$			9.72685i			1.13844i	−0.822185	+	0.569221i	$0.807245\pi$
$74$	2.85924	−	0.929024i	0.332380	−	0.107997i
$75$		0			0
$76$	−1.43028	−	0.226534i	−0.164065	−	0.0259853i
$77$	7.96437	+	2.58778i	0.907624	+	0.294905i
$78$		0			0
$79$	6.15477	−	6.15477i	0.692465	−	0.692465i	−0.270309	−	0.962774i	$-0.587126\pi$
$79$	6.15477	−	6.15477i	0.692465	−	0.692465i	0.962774	+	0.270309i	$0.0871257\pi$
$80$	1.75142	+	2.41063i	0.195815	+	0.269516i
$81$		0			0
$82$	−1.18044	+	4.36836i	−0.130358	+	0.482405i
$83$	−4.81920			−0.528976			−0.264488	−	0.964389i	$-0.585203\pi$
$83$	−4.81920			−0.528976			−0.264488	+	0.964389i	$0.585203\pi$
$84$		0			0
$85$	−4.61974	+	4.61974i	−0.501081	+	0.501081i
$86$	−1.17638	+	3.62054i	−0.126853	+	0.390413i
$87$		0			0
$88$	−4.16498	−	0.659667i	−0.443988	−	0.0703208i
$89$	3.63773	−	0.576160i	0.385598	−	0.0610728i	0.0393741	−	0.999225i	$-0.487464\pi$
$89$	3.63773	−	0.576160i	0.385598	−	0.0610728i	0.346224	+	0.938152i	$0.387464\pi$
$90$		0			0
$91$			19.5042i			2.04460i
$92$	3.13298	+	9.64234i	0.326636	+	1.00528i
$93$		0			0
$94$	1.61279	+	3.16528i	0.166346	+	0.326473i
$95$	−0.359020	+	2.26677i	−0.0368347	+	0.232565i
$96$		0			0
$97$	−3.63700	+	1.85314i	−0.369281	+	0.188158i	−0.628776	−	0.777586i	$-0.716444\pi$
$97$	−3.63700	+	1.85314i	−0.369281	+	0.188158i	0.259495	+	0.965744i	$0.416444\pi$
$98$	9.79653	+	7.11760i	0.989599	+	0.718986i
$99$		0			0
$100$	0.796102	−	0.578402i	0.0796102	−	0.0578402i
$101$	−1.63009	−	10.2920i	−0.162200	−	1.02409i	−0.925693	−	0.378274i	$-0.876518\pi$
$101$	−1.63009	−	10.2920i	−0.162200	−	1.02409i	0.763494	−	0.645815i	$-0.223482\pi$
$102$		0			0
$103$	−0.240884	+	0.331548i	−0.0237350	+	0.0326684i	−0.820720	−	0.571331i	$-0.806427\pi$
$103$	−0.240884	+	0.331548i	−0.0237350	+	0.0326684i	0.796985	+	0.604000i	$0.206427\pi$
$104$	−1.53641	−	9.70054i	−0.150658	−	0.951216i
$105$		0			0
$106$	2.44742	−	4.80333i	0.237714	−	0.466540i
$107$	−11.3095	−	8.21683i	−1.09333	−	0.794351i	−0.113372	−	0.993553i	$-0.536165\pi$
$107$	−11.3095	−	8.21683i	−1.09333	−	0.794351i	−0.979959	+	0.199202i	$0.936165\pi$
$108$		0			0
$109$	−10.8428	−	10.8428i	−1.03855	−	1.03855i	−0.999226	−	0.0393244i	$-0.987479\pi$
$109$	−10.8428	−	10.8428i	−1.03855	−	1.03855i	−0.0393244	−	0.999226i	$-0.512521\pi$
$110$	−0.448157	+	2.82955i	−0.0427301	+	0.269787i
$111$		0			0
$112$	5.48442	+	2.79445i	0.518229	+	0.264051i
$113$	2.49191	+	7.66931i	0.234419	+	0.721468i	0.997198	+	0.0748085i	$0.0238345\pi$
$113$	2.49191	+	7.66931i	0.234419	+	0.721468i	−0.762779	+	0.646660i	$0.776165\pi$
$114$		0			0
$115$	15.2815	−	4.96527i	1.42501	−	0.463014i
$116$	−0.751626	+	0.119046i	−0.0697867	+	0.0110531i
$117$		0			0
$118$	5.66409	+	1.84037i	0.521422	+	0.169420i
$119$	−4.17054	+	12.8356i	−0.382313	+	1.17664i
$120$		0			0
$121$	−4.75774	−	6.54847i	−0.432522	−	0.595315i
$122$	0.491360			0.0444856
$123$		0			0
$124$	0.885560			0.0795256
$125$	6.07264	+	8.35827i	0.543153	+	0.747586i
$126$		0			0
$127$	3.32547	−	10.2347i	0.295087	−	0.908186i	−0.688105	−	0.725612i	$-0.741557\pi$
$127$	3.32547	−	10.2347i	0.295087	−	0.908186i	0.983192	−	0.182574i	$-0.0584430\pi$
$128$	−10.0089	−	3.25208i	−0.884668	−	0.287446i
$129$		0			0
$130$	−6.59024	+	1.04379i	−0.578002	+	0.0915465i
$131$	15.4682	−	5.02592i	1.35146	−	0.439116i	0.458278	−	0.888809i	$-0.348466\pi$
$131$	15.4682	−	5.02592i	1.35146	−	0.439116i	0.893184	+	0.449692i	$0.148466\pi$
$132$		0			0
$133$	1.46503	+	4.50890i	0.127034	+	0.390972i
$134$	−2.56914	−	1.30904i	−0.221940	−	0.113084i
$135$		0			0
$136$	1.06314	−	6.71240i	0.0911634	−	0.575583i
$137$	−12.5397	−	12.5397i	−1.07134	−	1.07134i	−0.997252	−	0.0740834i	$-0.976397\pi$
$137$	−12.5397	−	12.5397i	−1.07134	−	1.07134i	−0.0740834	−	0.997252i	$-0.523603\pi$
$138$		0			0
$139$	1.72343	+	1.25214i	0.146179	+	0.106206i	0.658471	−	0.752606i	$-0.271203\pi$
$139$	1.72343	+	1.25214i	0.146179	+	0.106206i	−0.512292	+	0.858811i	$0.671203\pi$
$140$	7.95934	−	15.6211i	0.672687	−	1.32022i
$141$		0			0
$142$	−0.803861	−	5.07538i	−0.0674585	−	0.425916i
$143$	−3.97782	+	5.47500i	−0.332642	+	0.457842i
$144$		0			0
$145$	0.188669	+	1.19121i	0.0156681	+	0.0989243i
$146$	−5.56110	+	4.04037i	−0.460240	+	0.334384i
$147$		0			0
$148$	−5.16455	−	3.75226i	−0.424523	−	0.308434i
$149$	1.35193	−	0.688843i	0.110754	−	0.0564322i	−0.397736	−	0.917500i	$-0.630204\pi$
$149$	1.35193	−	0.688843i	0.110754	−	0.0564322i	0.508490	+	0.861068i	$0.330204\pi$
$150$		0			0
$151$	0.327873	−	2.07011i	0.0266819	−	0.168463i	−0.970749	−	0.240096i	$-0.922821\pi$
$151$	0.327873	−	2.07011i	0.0266819	−	0.168463i	0.997431	+	0.0716330i	$0.0228210\pi$
$152$	−1.08382	−	2.12713i	−0.0879098	−	0.172533i
$153$		0			0
$154$	1.82877	+	5.62836i	0.147366	+	0.453546i
$155$		−	1.40347i		−	0.112729i
$156$		0			0
$157$	−6.82911	+	1.08163i	−0.545023	+	0.0863231i	−0.422874	−	0.906189i	$-0.638979\pi$
$157$	−6.82911	+	1.08163i	−0.545023	+	0.0863231i	−0.122149	+	0.992512i	$0.538979\pi$
$158$	6.07543	+	0.962253i	0.483335	+	0.0765528i
$159$		0			0
$160$	−4.28675	+	13.1933i	−0.338898	+	1.04302i
$161$	23.4706	−	23.4706i	1.84974	−	1.84974i
$162$		0			0
$163$	−7.72291			−0.604905			−0.302453	−	0.953164i	$-0.597805\pi$
$163$	−7.72291			−0.604905			−0.302453	+	0.953164i	$0.597805\pi$
$164$	8.97753	−	3.42432i	0.701028	−	0.267394i
$165$		0			0
$166$	−2.00182	−	2.75526i	−0.155371	−	0.213850i
$167$	−13.4205	+	13.4205i	−1.03851	+	1.03851i	−0.0392793	+	0.999228i	$0.512506\pi$
$167$	−13.4205	+	13.4205i	−1.03851	+	1.03851i	−0.999228	+	0.0392793i	$0.987494\pi$
$168$		0			0
$169$	−2.62676	−	0.853486i	−0.202059	−	0.0656528i
$170$	−4.56019	−	0.722263i	−0.349750	−	0.0553950i
$171$		0			0
$172$	7.68783	−	2.49793i	0.586191	−	0.190465i
$173$			12.9720i			0.986242i	0.869961	+	0.493121i	$0.164144\pi$
$173$			12.9720i			0.986242i	−0.869961	+	0.493121i	$0.835856\pi$
$174$		0			0
$175$	−2.87048	−	1.46258i	−0.216988	−	0.110561i
$176$	0.969604	+	1.90295i	0.0730867	+	0.143441i
$177$		0			0
$178$	1.84046	+	1.84046i	0.137948	+	0.137948i
$179$	−0.493180	+	0.251288i	−0.0368620	+	0.0187821i	−0.472324	−	0.881425i	$-0.656585\pi$
$179$	−0.493180	+	0.251288i	−0.0368620	+	0.0187821i	0.435462	+	0.900207i	$0.356585\pi$
$180$		0			0
$181$	10.9072	−	21.4065i	0.810723	−	1.59113i	0.00415439	−	0.999991i	$-0.498678\pi$
$181$	10.9072	−	21.4065i	0.810723	−	1.59113i	0.806568	−	0.591141i	$-0.201322\pi$
$182$	−11.1511	+	8.10173i	−0.826573	+	0.600540i
$183$		0			0
$184$	−9.82438	+	13.5221i	−0.724263	+	0.996862i
$185$	−5.94673	+	8.18497i	−0.437212	+	0.601771i
$186$		0			0
$187$	−3.78848	+	2.75249i	−0.277041	+	0.201282i
$188$	3.42458	−	6.72112i	0.249763	−	0.490188i
$189$		0			0
$190$	−1.44510	+	0.736316i	−0.104839	+	0.0534180i
$191$	−8.79132	−	8.79132i	−0.636118	−	0.636118i	0.313478	−	0.949596i	$-0.398506\pi$
$191$	−8.79132	−	8.79132i	−0.636118	−	0.636118i	−0.949596	+	0.313478i	$0.898506\pi$
$192$		0			0
$193$	−1.47698	−	2.89873i	−0.106315	−	0.208655i	0.831720	−	0.555195i	$-0.187357\pi$
$193$	−1.47698	−	2.89873i	−0.106315	−	0.208655i	−0.938035	+	0.346540i	$0.887357\pi$
$194$	−2.57024	−	1.30960i	−0.184533	−	0.0940240i
$195$		0			0
$196$		−	25.7125i		−	1.83661i
$197$	12.8789	−	4.18462i	0.917586	−	0.298142i	0.188110	−	0.982148i	$-0.439764\pi$
$197$	12.8789	−	4.18462i	0.917586	−	0.298142i	0.729476	+	0.684006i	$0.239764\pi$
$198$		0			0
$199$	−9.16208	−	1.45113i	−0.649483	−	0.102868i	−0.177004	−	0.984210i	$-0.556641\pi$
$199$	−9.16208	−	1.45113i	−0.649483	−	0.102868i	−0.472479	+	0.881342i	$0.656641\pi$
$200$	1.54286	+	0.501307i	0.109097	+	0.0354478i
$201$		0			0
$202$	5.20708	−	5.20708i	0.366369	−	0.366369i
$203$	1.46441	+	2.01559i	0.102782	+	0.141467i
$204$		0			0
$205$	−5.42699	−	14.2279i	−0.379037	−	0.993722i
$206$	−0.289614			−0.0201784
$207$		0			0
$208$	−3.51735	+	3.51735i	−0.243885	+	0.243885i
$209$	−0.508329	+	1.56448i	−0.0351618	+	0.108217i
$210$		0			0
$211$	26.8855	+	4.25824i	1.85087	+	0.293149i	0.980095	−	0.198529i	$-0.0636163\pi$
$211$	26.8855	+	4.25824i	1.85087	+	0.293149i	0.870777	+	0.491678i	$0.163616\pi$
$212$	−11.3061	+	1.79070i	−0.776504	+	0.122986i
$213$		0			0
$214$		−	9.87907i		−	0.675320i
$215$	−3.95881	−	12.1840i	−0.269989	−	0.830940i
$216$		0			0
$217$	−1.31622	−	2.58322i	−0.0893506	−	0.175360i
$218$	1.69519	−	10.7030i	0.114813	−	0.724900i
$219$		0			0
$220$	5.42012	−	2.76169i	0.365424	−	0.186193i
$221$	−8.82366	−	6.41077i	−0.593544	−	0.431235i
$222$		0			0
$223$	−7.71095	+	5.60233i	−0.516363	+	0.375160i	−0.815232	−	0.579134i	$-0.803391\pi$
$223$	−7.71095	+	5.60233i	−0.516363	+	0.375160i	0.298869	+	0.954294i	$0.403391\pi$
$224$	4.48287	+	28.3037i	0.299524	+	1.89112i
$225$		0			0
$226$	−3.34965	+	4.61040i	−0.222815	+	0.306679i
$227$	0.238184	+	1.50383i	0.0158088	+	0.0998130i	0.994331	−	0.106328i	$-0.0339094\pi$
$227$	0.238184	+	1.50383i	0.0158088	+	0.0998130i	−0.978522	+	0.206141i	$0.933909\pi$
$228$		0			0
$229$	−6.69218	+	13.1341i	−0.442232	+	0.867929i	0.557066	+	0.830468i	$0.311927\pi$
$229$	−6.69218	+	13.1341i	−0.442232	+	0.867929i	−0.999298	+	0.0374606i	$0.988073\pi$
$230$	9.18648	+	6.67437i	0.605738	+	0.440095i
$231$		0			0
$232$	−0.887110	−	0.887110i	−0.0582416	−	0.0582416i
$233$	2.32886	−	14.7039i	0.152569	−	0.963282i	−0.786009	−	0.618215i	$-0.787856\pi$
$233$	2.32886	−	14.7039i	0.152569	−	0.963282i	0.938578	−	0.345067i	$-0.112144\pi$
$234$		0			0
$235$	−10.6519	−	5.42741i	−0.694853	−	0.354045i
$236$	−3.90784	−	12.0271i	−0.254379	−	0.782897i
$237$		0			0
$238$	−9.07083	+	2.94729i	−0.587974	+	0.191044i
$239$	13.2085	−	2.09203i	0.854390	−	0.135322i	0.286150	−	0.958185i	$-0.407625\pi$
$239$	13.2085	−	2.09203i	0.854390	−	0.135322i	0.568240	+	0.822863i	$0.307625\pi$
$240$		0			0
$241$	−3.79971	−	1.23460i	−0.244761	−	0.0795276i	0.184068	−	0.982914i	$-0.441073\pi$
$241$	−3.79971	−	1.23460i	−0.244761	−	0.0795276i	−0.428828	+	0.903386i	$0.641073\pi$
$242$	1.76765	−	5.44025i	0.113629	−	0.349713i
$243$		0			0
$244$	−0.613265	−	0.844087i	−0.0392603	−	0.0540372i
$245$	−40.7502			−2.60344
$246$		0			0
$247$	−3.83130			−0.243780
$248$	0.858118	+	1.18110i	0.0544905	+	0.0749998i
$249$		0			0
$250$	−2.25617	+	6.94378i	−0.142693	+	0.439163i
$251$	25.9816	+	8.44194i	1.63995	+	0.532851i	0.976527	−	0.215397i	$-0.0691045\pi$
$251$	25.9816	+	8.44194i	1.63995	+	0.532851i	0.663420	+	0.748248i	$0.269104\pi$
$252$		0			0
$253$	11.3751	−	1.80164i	0.715148	−	0.113268i
$254$	7.23281	−	2.35008i	0.453827	−	0.147457i
$255$		0			0
$256$	−3.29719	−	10.1477i	−0.206074	−	0.634231i
$257$	6.68063	+	3.40395i	0.416726	+	0.212333i	0.649766	−	0.760135i	$-0.274867\pi$
$257$	6.68063	+	3.40395i	0.416726	+	0.212333i	−0.233039	+	0.972467i	$0.574867\pi$
$258$		0			0
$259$	−3.26941	+	20.6423i	−0.203152	+	1.28265i
$260$	10.0184	+	10.0184i	0.621312	+	0.621312i
$261$		0			0
$262$	9.29868	+	6.75588i	0.574474	+	0.417380i
$263$	−5.41178	+	10.6212i	−0.333705	+	0.654933i	−0.995501	−	0.0947511i	$-0.969794\pi$
$263$	−5.41178	+	10.6212i	−0.333705	+	0.654933i	0.661796	+	0.749684i	$0.269794\pi$
$264$		0			0
$265$	2.83798	+	17.9183i	0.174336	+	1.10071i
$266$	−1.96931	+	2.71052i	−0.120746	+	0.166193i
$267$		0			0
$268$	0.957790	+	6.04725i	0.0585063	+	0.369394i
$269$	17.1372	−	12.4509i	1.04488	−	0.759147i	0.0736443	−	0.997285i	$-0.476537\pi$
$269$	17.1372	−	12.4509i	1.04488	−	0.759147i	0.971231	+	0.238138i	$0.0765370\pi$
$270$		0			0
$271$	−3.10054	−	2.25267i	−0.188344	−	0.136840i	0.489617	−	0.871937i	$-0.337136\pi$
$271$	−3.10054	−	2.25267i	−0.188344	−	0.136840i	−0.677962	+	0.735097i	$0.737136\pi$
$272$	−3.06686	+	1.56264i	−0.185956	+	0.0947491i
$273$		0			0
$274$	1.96049	−	12.3780i	0.118437	−	0.747784i
$275$	−0.507479	−	0.995984i	−0.0306022	−	0.0600601i
$276$		0			0
$277$	0.360907	+	1.11076i	0.0216848	+	0.0667389i	0.961313	−	0.275457i	$-0.0888293\pi$
$277$	0.360907	+	1.11076i	0.0216848	+	0.0667389i	−0.939629	+	0.342196i	$0.888829\pi$
$278$			1.50545i			0.0902909i
$279$		0			0
$280$	28.5470	−	4.52140i	1.70601	−	0.270205i
$281$	−17.4781	−	2.76826i	−1.04266	−	0.165140i	−0.388460	−	0.921466i	$-0.626993\pi$
$281$	−17.4781	−	2.76826i	−1.04266	−	0.165140i	−0.654196	+	0.756325i	$0.726993\pi$
$282$		0			0
$283$	2.28989	−	7.04757i	0.136120	−	0.418934i	−0.859643	−	0.510896i	$-0.829314\pi$
$283$	2.28989	−	7.04757i	0.136120	−	0.418934i	0.995763	+	0.0919616i	$0.0293137\pi$
$284$	−7.71549	+	7.71549i	−0.457830	+	0.457830i
$285$		0			0
$286$	−4.78252			−0.282796
$287$	−23.3323	−	21.0983i	−1.37726	−	1.24539i
$288$		0			0
$289$	5.55635	+	7.64766i	0.326844	+	0.449862i
$290$	−0.602674	+	0.602674i	−0.0353902	+	0.0353902i
$291$		0			0
$292$	13.8816	+	4.51040i	0.812359	+	0.263951i
$293$	−10.2251	−	1.61950i	−0.597357	−	0.0946120i	−0.149568	−	0.988751i	$-0.547788\pi$
$293$	−10.2251	−	1.61950i	−0.597357	−	0.0946120i	−0.447789	+	0.894139i	$0.647788\pi$
$294$		0			0
$295$	−19.0610	+	6.19329i	−1.10977	+	0.360587i
$296$		−	10.5241i		−	0.611701i
$297$		0			0
$298$	0.955399	+	0.486800i	0.0553448	+	0.0281996i
$299$	12.1777	+	23.9002i	0.704257	+	1.38218i
$300$		0			0
$301$	−18.7131	−	18.7131i	−1.07860	−	1.07860i
$302$	1.31973	−	0.672435i	0.0759418	−	0.0386943i
$303$		0			0
$304$	−0.548926	+	1.07733i	−0.0314831	+	0.0617890i
$305$	−1.33774	+	0.971927i	−0.0765989	+	0.0556524i
$306$		0			0
$307$	−0.807435	+	1.11134i	−0.0460827	+	0.0634274i	−0.831437	−	0.555620i	$-0.812481\pi$
$307$	−0.807435	+	1.11134i	−0.0460827	+	0.0634274i	0.785354	+	0.619047i	$0.212481\pi$
$308$	7.38626	−	10.1663i	0.420871	−	0.579279i
$309$		0			0
$310$	0.802400	−	0.582978i	0.0455733	−	0.0331109i
$311$	−5.51590	+	10.8256i	−0.312778	+	0.613862i	−0.992861	−	0.119273i	$-0.961944\pi$
$311$	−5.51590	+	10.8256i	−0.312778	+	0.613862i	0.680083	+	0.733135i	$0.261944\pi$
$312$		0			0
$313$	26.8319	−	13.6715i	1.51663	−	0.772761i	0.519950	−	0.854197i	$-0.325951\pi$
$313$	26.8319	−	13.6715i	1.51663	−	0.772761i	0.996679	+	0.0814357i	$0.0259505\pi$
$314$	−3.45509	−	3.45509i	−0.194982	−	0.194982i
$315$		0			0
$316$	−5.92972	−	11.6377i	−0.333573	−	0.654673i
$317$	7.54815	+	3.84597i	0.423946	+	0.216011i	0.652929	−	0.757419i	$-0.273540\pi$
$317$	7.54815	+	3.84597i	0.423946	+	0.216011i	−0.228983	+	0.973430i	$0.573540\pi$
$318$		0			0
$319$			0.864455i			0.0484002i
$320$	−3.65586	+	1.18786i	−0.204369	+	0.0664035i
$321$		0			0
$322$	23.1680	+	3.66946i	1.29110	+	0.204491i
$323$	−2.52135	−	0.819237i	−0.140292	−	0.0455836i
$324$		0			0
$325$	1.84094	−	1.84094i	0.102117	−	0.102117i
$326$	−3.20797	−	4.41539i	−0.177673	−	0.244546i
$327$		0			0
$328$	13.2665	+	8.65541i	0.732517	+	0.477915i
$329$	−24.6959			−1.36153
$330$		0			0
$331$	−7.38632	+	7.38632i	−0.405989	+	0.405989i	−0.880337	−	0.474348i	$-0.842684\pi$
$331$	−7.38632	+	7.38632i	−0.405989	+	0.405989i	0.474348	+	0.880337i	$0.342684\pi$
$332$	−2.23469	+	6.87768i	−0.122645	+	0.377462i
$333$		0			0
$334$	−13.2475	−	2.09820i	−0.724870	−	0.114808i
$335$	9.58391	−	1.51794i	0.523625	−	0.0829341i
$336$		0			0
$337$		−	22.8689i		−	1.24575i	−0.782321	−	0.622875i	$-0.785964\pi$
$337$		−	22.8689i		−	1.24575i	0.782321	−	0.622875i	$-0.214036\pi$
$338$	−0.603152	−	1.85631i	−0.0328072	−	0.100970i
$339$		0			0
$340$	4.45082	+	8.73522i	0.241379	+	0.473734i
$341$	0.157366	−	0.993570i	0.00852184	−	0.0538048i
$342$		0			0
$343$	−44.3638	+	22.6045i	−2.39542	+	1.22053i
$344$	10.7812	+	7.83297i	0.581281	+	0.422325i
$345$		0			0
$346$	−7.41643	+	5.38835i	−0.398710	+	0.289680i
$347$	−0.261536	−	1.65127i	−0.0140400	−	0.0886450i	0.979673	−	0.200599i	$-0.0642890\pi$
$347$	−0.261536	−	1.65127i	−0.0140400	−	0.0886450i	−0.993713	+	0.111954i	$0.964289\pi$
$348$		0			0
$349$	−20.3042	+	27.9463i	−1.08686	+	1.49593i	−0.235116	+	0.971967i	$0.575547\pi$
$349$	−20.3042	+	27.9463i	−1.08686	+	1.49593i	−0.851741	+	0.523963i	$0.824453\pi$
$350$	−0.356153	−	2.24866i	−0.0190372	−	0.120196i
$351$		0			0
$352$	−4.51407	+	8.85936i	−0.240601	+	0.472206i
$353$	20.7152	+	15.0505i	1.10256	+	0.801055i	0.981476	−	0.191587i	$-0.0613636\pi$
$353$	20.7152	+	15.0505i	1.10256	+	0.801055i	0.121082	+	0.992642i	$0.461364\pi$
$354$		0			0
$355$	12.2278	+	12.2278i	0.648985	+	0.648985i
$356$	0.864577	−	5.45872i	0.0458225	−	0.289312i
$357$		0			0
$358$	−0.348527	−	0.177583i	−0.0184202	−	0.00938556i
$359$	8.16247	+	25.1215i	0.430799	+	1.32586i	0.897331	+	0.441358i	$0.145503\pi$
$359$	8.16247	+	25.1215i	0.430799	+	1.32586i	−0.466532	+	0.884504i	$0.654497\pi$
$360$		0			0
$361$	17.1844	−	5.58354i	0.904441	−	0.293871i
$362$	16.7693	−	2.65600i	0.881375	−	0.139596i
$363$		0			0
$364$	27.8353	+	9.04423i	1.45897	+	0.474047i
$365$	7.14826	−	22.0001i	0.374157	−	1.15154i
$366$		0			0
$367$	11.8091	+	16.2538i	0.616429	+	0.848442i	0.997087	−	0.0762741i	$-0.0243024\pi$
$367$	11.8091	+	16.2538i	0.616429	+	0.848442i	−0.380658	+	0.924716i	$0.624302\pi$
$368$	8.46528			0.441283
$369$		0			0
$370$	−7.14974			−0.371697
$371$	22.0279	+	30.3188i	1.14363	+	1.57407i
$372$		0			0
$373$	−2.37421	+	7.30705i	−0.122932	+	0.378345i	−0.993519	−	0.113670i	$-0.963739\pi$
$373$	−2.37421	+	7.30705i	−0.122932	+	0.378345i	0.870587	+	0.492015i	$0.163739\pi$
$374$	−3.14735	−	1.02264i	−0.162745	−	0.0528792i
$375$		0			0
$376$	12.2826	−	1.94538i	0.633428	−	0.100325i
$377$	−1.91484	+	0.622169i	−0.0986193	+	0.0320433i
$378$		0			0
$379$	7.20512	+	22.1751i	0.370102	+	1.13906i	0.946724	+	0.322046i	$0.104371\pi$
$379$	7.20512	+	22.1751i	0.370102	+	1.13906i	−0.576622	+	0.817011i	$0.695629\pi$
$380$	3.06852	+	1.56349i	0.157412	+	0.0802052i
$381$		0			0
$382$	1.37446	−	8.67800i	0.0703235	−	0.444005i
$383$	11.5251	+	11.5251i	0.588904	+	0.588904i	0.937335	−	0.348430i	$-0.113285\pi$
$383$	11.5251	+	11.5251i	0.588904	+	0.588904i	−0.348430	+	0.937335i	$0.613285\pi$
$384$		0			0
$385$	−16.1120	−	11.7060i	−0.821142	−	0.596594i
$386$	1.04377	−	2.04851i	0.0531265	−	0.104267i
$387$		0			0
$388$	0.958199	+	6.04983i	0.0486452	+	0.307134i
$389$	0.170988	−	0.235345i	0.00866943	−	0.0119325i	−0.804660	−	0.593735i	$-0.797653\pi$
$389$	0.170988	−	0.235345i	0.00866943	−	0.0119325i	0.813330	+	0.581803i	$0.197653\pi$
$390$		0			0
$391$	2.90358	+	18.3325i	0.146840	+	0.927114i
$392$	34.2936	−	24.9158i	1.73209	−	1.25844i
$393$		0			0
$394$	7.74216	+	5.62500i	0.390044	+	0.283384i
$395$	−18.4439	+	9.39765i	−0.928014	+	0.472847i
$396$		0			0
$397$	4.42708	−	27.9515i	0.222189	−	1.40284i	−0.584272	−	0.811558i	$-0.698620\pi$
$397$	4.42708	−	27.9515i	0.222189	−	1.40284i	0.806461	−	0.591287i	$-0.201380\pi$
$398$	−2.97613	−	5.84098i	−0.149180	−	0.292782i
$399$		0			0
$400$	−0.253898	−	0.781417i	−0.0126949	−	0.0390708i
$401$		−	6.77610i		−	0.338382i	−0.985583	−	0.169191i	$-0.945885\pi$
$401$		−	6.77610i		−	0.338382i	0.985583	−	0.169191i	$-0.0541155\pi$
$402$		0			0
$403$	2.31410	−	0.366517i	0.115273	−	0.0182575i
$404$	−15.4440	−	2.44609i	−0.768367	−	0.121697i
$405$		0			0
$406$	−0.544074	+	1.67449i	−0.0270019	+	0.0831034i
$407$	−5.12767	+	5.12767i	−0.254169	+	0.254169i
$408$		0			0
$409$	16.9059			0.835945			0.417972	−	0.908460i	$-0.362741\pi$
$409$	16.9059			0.835945			0.417972	+	0.908460i	$0.362741\pi$
$410$	5.88021	−	9.01280i	0.290403	−	0.445111i
$411$		0			0
$412$	0.361467	+	0.497517i	0.0178082	+	0.0245109i
$413$	−29.2753	+	29.2753i	−1.44055	+	1.44055i
$414$		0			0
$415$	10.9000	+	3.54163i	0.535061	+	0.173852i
$416$	−22.8731	−	3.62274i	−1.12145	−	0.177620i
$417$		0			0
$418$	−1.10560	+	0.359232i	−0.0540768	+	0.0175706i
$419$			12.2920i			0.600504i	0.953860	+	0.300252i	$0.0970708\pi$
$419$			12.2920i			0.600504i	−0.953860	+	0.300252i	$0.902929\pi$
$420$		0			0
$421$	25.9576	+	13.2260i	1.26509	+	0.644597i	0.952283	−	0.305218i	$-0.0987293\pi$
$421$	25.9576	+	13.2260i	1.26509	+	0.644597i	0.312811	+	0.949815i	$0.398729\pi$
$422$	8.73323	+	17.1399i	0.425127	+	0.834359i
$423$		0			0
$424$	−13.3440	−	13.3440i	−0.648043	−	0.648043i
$425$	1.60516	−	0.817868i	0.0778616	−	0.0396724i
$426$		0			0
$427$	−1.55074	+	3.04350i	−0.0750456	+	0.147285i
$428$	−16.9709	+	12.3301i	−0.820318	+	0.595996i
$429$		0			0
$430$	5.32147	−	7.32437i	0.256624	−	0.353213i
$431$	−5.05984	+	6.96427i	−0.243724	+	0.335457i	−0.913301	−	0.407285i	$-0.866475\pi$
$431$	−5.05984	+	6.96427i	−0.243724	+	0.335457i	0.669577	+	0.742743i	$0.266475\pi$
$432$		0			0
$433$	9.57821	−	6.95897i	0.460299	−	0.334427i	−0.333349	−	0.942803i	$-0.608179\pi$
$433$	9.57821	−	6.95897i	0.460299	−	0.334427i	0.793649	+	0.608376i	$0.208179\pi$
$434$	0.930161	−	1.82554i	0.0446491	−	0.0876289i
$435$		0			0
$436$	−20.5021	+	10.4463i	−0.981871	+	0.500288i
$437$	4.61043	+	4.61043i	0.220547	+	0.220547i
$438$		0			0
$439$	−13.8074	−	27.0986i	−0.658993	−	1.29335i	−0.942445	−	0.334360i	$-0.891480\pi$
$439$	−13.8074	−	27.0986i	−0.658993	−	1.29335i	0.283453	−	0.958986i	$-0.408520\pi$
$440$	8.93551	+	4.55287i	0.425984	+	0.217050i
$441$		0			0
$442$		−	7.70765i		−	0.366615i
$443$	12.6998	−	4.12642i	0.603387	−	0.196052i	0.00863630	−	0.999963i	$-0.497251\pi$
$443$	12.6998	−	4.12642i	0.603387	−	0.196052i	0.594750	+	0.803911i	$0.297251\pi$
$444$		0			0
$445$	−8.65119	−	1.37021i	−0.410106	−	0.0649544i
$446$	−6.40600	−	2.08144i	−0.303333	−	0.0985588i
$447$		0			0
$448$	−5.61496	+	5.61496i	−0.265282	+	0.265282i
$449$	−14.7829	−	20.3470i	−0.697649	−	0.960232i	−0.999975	−	0.00702734i	$-0.997763\pi$
$449$	−14.7829	−	20.3470i	−0.697649	−	0.960232i	0.302326	−	0.953205i	$-0.402237\pi$
$450$		0			0
$451$	−2.24664	−	10.6810i	−0.105790	−	0.502949i
$452$	12.1007			0.569169
$453$		0			0
$454$	−0.760844	+	0.760844i	−0.0357082	+	0.0357082i
$455$	14.3336	−	44.1144i	0.671972	−	2.06812i
$456$		0			0
$457$	−31.7784	−	5.03321i	−1.48653	−	0.235444i	−0.640245	−	0.768170i	$-0.721167\pi$
$457$	−31.7784	−	5.03321i	−1.48653	−	0.235444i	−0.846287	+	0.532727i	$0.821167\pi$
$458$	−10.2890	+	1.62961i	−0.480771	+	0.0761467i
$459$		0			0
$460$		−	24.1114i		−	1.12420i
$461$	−9.09817	−	28.0013i	−0.423744	−	1.30415i	−0.904192	−	0.427126i	$-0.859526\pi$
$461$	−9.09817	−	28.0013i	−0.423744	−	1.30415i	0.480448	−	0.877023i	$-0.340474\pi$
$462$		0			0
$463$	9.31629	+	18.2842i	0.432965	+	0.849741i	0.999667	+	0.0258181i	$0.00821907\pi$
$463$	9.31629	+	18.2842i	0.432965	+	0.849741i	−0.566702	+	0.823923i	$0.691781\pi$
$464$	−0.0993985	+	0.627578i	−0.00461446	+	0.0291346i
$465$		0			0
$466$	9.37396	−	4.77627i	0.434240	−	0.221256i
$467$	−19.9773	−	14.5143i	−0.924437	−	0.671643i	0.0201872	−	0.999796i	$-0.493574\pi$
$467$	−19.9773	−	14.5143i	−0.924437	−	0.671643i	−0.944625	+	0.328153i	$0.893574\pi$
$468$		0			0
$469$	16.2165	−	11.7820i	0.748811	−	0.544043i
$470$	−1.32163	−	8.34443i	−0.0609621	−	0.384900i
$471$		0			0
$472$	12.2541	−	16.8664i	0.564043	−	0.776339i
$473$	−1.43645	−	9.06939i	−0.0660480	−	0.417011i
$474$		0			0
$475$	0.287302	−	0.563861i	0.0131823	−	0.0258717i
$476$	16.3843	+	11.9039i	0.750974	+	0.545615i
$477$		0			0
$478$	6.68268	+	6.68268i	0.305659	+	0.305659i
$479$	4.53834	−	28.6540i	0.207362	−	1.30923i	−0.635917	−	0.771757i	$-0.719378\pi$
$479$	4.53834	−	28.6540i	0.207362	−	1.30923i	0.843279	−	0.537476i	$-0.180622\pi$
$480$		0			0
$481$	−15.0487	−	7.66771i	−0.686163	−	0.349617i
$482$	−0.872483	−	2.68523i	−0.0397405	−	0.122309i
$483$		0			0
$484$	−11.5518	+	3.75340i	−0.525081	+	0.170609i
$485$	9.58800	−	1.51859i	0.435369	−	0.0689557i
$486$		0			0
$487$	−25.0893	−	8.15201i	−1.13691	−	0.369403i	−0.320709	−	0.947178i	$-0.603921\pi$
$487$	−25.0893	−	8.15201i	−1.13691	−	0.369403i	−0.816196	+	0.577775i	$0.803921\pi$
$488$	0.531524	−	1.63586i	0.0240609	−	0.0740520i
$489$		0			0
$490$	−16.9270	−	23.2980i	−0.764682	−	1.05250i
$491$	−17.4748			−0.788628			−0.394314	−	0.918976i	$-0.629018\pi$
$491$	−17.4748			−0.788628			−0.394314	+	0.918976i	$0.629018\pi$
$492$		0			0
$493$	−1.39318			−0.0627457
$494$	−1.59146	−	2.19045i	−0.0716031	−	0.0985532i
$495$		0			0
$496$	0.228489	−	0.703217i	0.0102595	−	0.0315754i
$497$	33.9741	+	11.0389i	1.52395	+	0.495160i
$498$		0			0
$499$	6.24219	−	0.988666i	0.279439	−	0.0442588i	−0.0151419	−	0.999885i	$-0.504820\pi$
$499$	6.24219	−	0.988666i	0.279439	−	0.0442588i	0.294581	+	0.955627i	$0.404820\pi$
$500$	14.7444	−	4.79073i	0.659388	−	0.214248i
$501$		0			0
$502$	5.96586	+	18.3610i	0.266269	+	0.819493i
$503$	−9.88764	−	5.03800i	−0.440868	−	0.224634i	0.219444	−	0.975625i	$-0.429576\pi$
$503$	−9.88764	−	5.03800i	−0.440868	−	0.224634i	−0.660312	+	0.750992i	$0.729576\pi$
$504$		0			0
$505$	−3.87665	+	24.4762i	−0.172509	+	1.08918i
$506$	5.75509	+	5.75509i	0.255845	+	0.255845i
$507$		0			0
$508$	−13.0644	−	9.49183i	−0.579638	−	0.421132i
$509$	−9.54403	+	18.7312i	−0.423032	+	0.830247i	0.576878	+	0.816830i	$0.304271\pi$
$509$	−9.54403	+	18.7312i	−0.423032	+	0.830247i	−0.999910	+	0.0134165i	$0.995729\pi$
$510$		0			0
$511$	−7.47530	−	47.1972i	−0.330688	−	2.08788i
$512$	−7.93954	+	10.9278i	−0.350881	+	0.482947i
$513$		0			0
$514$	0.828895	+	5.23344i	0.0365610	+	0.230837i
$515$	0.788484	−	0.572867i	0.0347447	−	0.0252435i
$516$		0			0
$517$	−6.93233	−	5.03663i	−0.304884	−	0.221511i
$518$	−13.1598	+	6.70525i	−0.578208	+	0.294612i
$519$		0			0
$520$	−3.65388	+	23.0697i	−0.160233	+	1.01167i
$521$	4.33618	+	8.51023i	0.189971	+	0.372840i	0.966272	−	0.257523i	$-0.0829062\pi$
$521$	4.33618	+	8.51023i	0.189971	+	0.372840i	−0.776301	+	0.630363i	$0.782906\pi$
$522$		0			0
$523$	3.08324	+	9.48924i	0.134821	+	0.414936i	0.995562	−	0.0941069i	$-0.0299996\pi$
$523$	3.08324	+	9.48924i	0.134821	+	0.414936i	−0.860741	+	0.509043i	$0.830000\pi$
$524$		−	24.4058i		−	1.06617i
$525$		0			0
$526$	−8.32040	+	1.31782i	−0.362787	+	0.0574598i
$527$	1.60127	+	0.253616i	0.0697522	+	0.0110477i
$528$		0			0
$529$	6.99889	−	21.5404i	0.304300	−	0.936538i
$530$	−9.06551	+	9.06551i	−0.393780	+	0.393780i
$531$		0			0
$532$	7.11419			0.308439
$533$	22.0424	−	12.6639i	0.954761	−	0.548534i
$534$		0			0
$535$	19.5412	+	26.8961i	0.844838	+	1.16282i
$536$	−7.13729	+	7.13729i	−0.308284	+	0.308284i
$537$		0			0
$538$	14.2370	+	4.62590i	0.613803	+	0.199437i
$539$	−28.8486	−	4.56918i	−1.24260	−	0.196808i
$540$		0			0
$541$	−4.63179	+	1.50496i	−0.199136	+	0.0647032i	−0.406887	−	0.913479i	$-0.633386\pi$
$541$	−4.63179	+	1.50496i	−0.199136	+	0.0647032i	0.207751	+	0.978182i	$0.433386\pi$
$542$		−	2.70838i		−	0.116335i
$543$		0			0
$544$	−14.2780	−	7.27501i	−0.612164	−	0.311913i
$545$	16.5557	+	32.4925i	0.709170	+	1.39182i
$546$		0			0
$547$	14.2161	+	14.2161i	0.607837	+	0.607837i	0.942380	−	0.334543i	$-0.108582\pi$
$547$	14.2161	+	14.2161i	0.607837	+	0.607837i	−0.334543	+	0.942380i	$0.608582\pi$
$548$	−23.7106	+	12.0812i	−1.01287	+	0.516081i
$549$		0			0
$550$	0.358632	−	0.703855i	0.0152921	−	0.0300125i
$551$	−0.395931	+	0.287661i	−0.0168672	+	0.0122548i
$552$		0			0
$553$	−25.1344	+	34.5946i	−1.06882	+	1.47111i
$554$	−0.485134	+	0.667730i	−0.0206114	+	0.0283691i
$555$		0			0
$556$	2.58615	−	1.87895i	0.109677	−	0.0796852i
$557$	−9.22663	+	18.1083i	−0.390945	+	0.767273i	−0.999659	−	0.0261171i	$-0.991686\pi$
$557$	−9.22663	+	18.1083i	−0.390945	+	0.767273i	0.608714	+	0.793390i	$0.291686\pi$
$558$		0			0
$559$	19.0556	−	9.70931i	0.805965	−	0.410660i
$560$	−10.3510	−	10.3510i	−0.437408	−	0.437408i
$561$		0			0
$562$	−5.67742	−	11.1426i	−0.239488	−	0.470021i
$563$	−14.3215	−	7.29719i	−0.603581	−	0.307540i	0.125366	−	0.992111i	$-0.459990\pi$
$563$	−14.3215	−	7.29719i	−0.603581	−	0.307540i	−0.728946	+	0.684571i	$0.759990\pi$
$564$		0			0
$565$		−	19.1777i		−	0.806811i
$566$	4.98046	−	1.61825i	0.209345	−	0.0680202i
$567$		0			0
$568$	−17.7668	−	2.81398i	−0.745478	−	0.118072i
$569$	−13.6249	−	4.42700i	−0.571186	−	0.185590i	0.00916232	−	0.999958i	$-0.497084\pi$
$569$	−13.6249	−	4.42700i	−0.571186	−	0.185590i	−0.580348	+	0.814369i	$0.697084\pi$
$570$		0			0
$571$	−5.79685	+	5.79685i	−0.242591	+	0.242591i	−0.817921	−	0.575330i	$-0.804873\pi$
$571$	−5.79685	+	5.79685i	−0.242591	+	0.242591i	0.575330	+	0.817921i	$0.304873\pi$
$572$	5.96906	+	8.21570i	0.249579	+	0.343516i
$573$		0			0
$574$	2.37061	−	22.1036i	0.0989472	−	0.922586i
$575$	−4.43063			−0.184770
$576$		0			0
$577$	−3.49886	+	3.49886i	−0.145660	+	0.145660i	−0.776176	−	0.630516i	$-0.782843\pi$
$577$	−3.49886	+	3.49886i	−0.145660	+	0.145660i	0.630516	+	0.776176i	$0.282843\pi$
$578$	−2.06435	+	6.35342i	−0.0858657	+	0.264268i
$579$		0			0
$580$	1.78751	+	0.283113i	0.0742222	+	0.0117556i
$581$	23.3840	−	3.70366i	0.970132	−	0.153654i
$582$		0			0
$583$			13.0033i			0.538540i
$584$	7.43577	+	22.8849i	0.307694	+	0.946986i
$585$		0			0
$586$	−3.32143	−	6.51867i	−0.137207	−	0.269284i
$587$	−1.58441	+	10.0036i	−0.0653955	+	0.412891i	0.933174	+	0.359425i	$0.117027\pi$
$587$	−1.58441	+	10.0036i	−0.0653955	+	0.412891i	−0.998570	+	0.0534665i	$0.982973\pi$
$588$		0			0
$589$	0.507433	−	0.258550i	0.0209084	−	0.0106534i
$590$	−11.4585	−	8.32508i	−0.471738	−	0.342738i
$591$		0			0
$592$	−4.31219	+	3.13299i	−0.177230	+	0.128765i
$593$	−2.36683	−	14.9436i	−0.0971942	−	0.613660i	−0.987417	−	0.158136i	$-0.949452\pi$
$593$	−2.36683	−	14.9436i	−0.0971942	−	0.613660i	0.890223	−	0.455525i	$-0.150548\pi$
$594$		0			0
$595$	18.8658	−	25.9665i	0.773421	−	1.06452i
$596$	−0.356178	−	2.24882i	−0.0145896	−	0.0921151i
$597$		0			0
$598$	−8.60592	+	16.8901i	−0.351922	+	0.690686i
$599$	−2.65199	−	1.92679i	−0.108358	−	0.0787264i	0.532287	−	0.846564i	$-0.321333\pi$
$599$	−2.65199	−	1.92679i	−0.108358	−	0.0787264i	−0.640644	+	0.767838i	$0.721333\pi$
$600$		0			0
$601$	−5.05364	−	5.05364i	−0.206142	−	0.206142i	0.596483	−	0.802626i	$-0.296564\pi$
$601$	−5.05364	−	5.05364i	−0.206142	−	0.206142i	−0.802626	+	0.596483i	$0.796564\pi$
$602$	2.92566	−	18.4719i	0.119241	−	0.752857i
$603$		0			0
$604$	−2.80230	−	1.42784i	−0.114024	−	0.0580981i
$605$	5.94854	+	18.3077i	0.241843	+	0.744315i
$606$		0			0
$607$	−32.2830	+	10.4894i	−1.31033	+	0.425751i	−0.879163	−	0.476522i	$-0.841897\pi$
$607$	−32.2830	+	10.4894i	−1.31033	+	0.425751i	−0.431165	+	0.902273i	$0.641897\pi$
$608$	−5.55983	+	0.880590i	−0.225481	+	0.0357126i
$609$		0			0
$610$	−1.11135	−	0.361100i	−0.0449973	−	0.0146205i
$611$	6.16719	−	18.9807i	0.249498	−	0.767876i
$612$		0			0
$613$	9.06342	+	12.4747i	0.366068	+	0.503849i	0.951827	−	0.306636i	$-0.0992034\pi$
$613$	9.06342	+	12.4747i	0.366068	+	0.503849i	−0.585759	+	0.810485i	$0.699203\pi$
$614$	−0.970776			−0.0391773
$615$		0			0
$616$	20.7165			0.834691
$617$	0.427082	+	0.587827i	0.0171937	+	0.0236650i	0.817527	−	0.575890i	$-0.195344\pi$
$617$	0.427082	+	0.587827i	0.0171937	+	0.0236650i	−0.800334	+	0.599555i	$0.795344\pi$
$618$		0			0
$619$	7.59558	−	23.3768i	0.305292	−	0.939593i	−0.674276	−	0.738480i	$-0.735544\pi$
$619$	7.59558	−	23.3768i	0.305292	−	0.939593i	0.979568	−	0.201113i	$-0.0644559\pi$
$620$	−2.00295	−	0.650798i	−0.0804404	−	0.0261367i
$621$		0			0
$622$	−8.48048	+	1.34318i	−0.340036	+	0.0538564i
$623$	−17.2084	+	5.59135i	−0.689440	+	0.224013i
$624$		0			0
$625$	−8.60576	−	26.4858i	−0.344230	−	1.05943i
$626$	18.9619	+	9.66157i	0.757870	+	0.386154i
$627$		0			0
$628$	−1.62307	+	10.2477i	−0.0647676	+	0.408927i
$629$	−8.26391	−	8.26391i	−0.329503	−	0.329503i
$630$		0			0
$631$	−11.0214	−	8.00754i	−0.438756	−	0.318775i	0.346384	−	0.938093i	$-0.387409\pi$
$631$	−11.0214	−	8.00754i	−0.438756	−	0.318775i	−0.785141	+	0.619318i	$0.787409\pi$
$632$	9.77562	−	19.1857i	0.388853	−	0.763168i
$633$		0			0
$634$	0.936532	+	5.91303i	0.0371944	+	0.234836i
$635$	−15.0430	+	20.7049i	−0.596964	+	0.821650i
$636$		0			0
$637$	−10.6420	−	67.1907i	−0.421650	−	2.66219i
$638$	−0.494232	+	0.359080i	−0.0195668	+	0.0142161i
$639$		0			0
$640$	20.2480	+	14.7110i	0.800373	+	0.581505i
$641$	8.46013	−	4.31065i	0.334155	−	0.170260i	−0.278860	−	0.960332i	$-0.589957\pi$
$641$	8.46013	−	4.31065i	0.334155	−	0.170260i	0.613015	+	0.790071i	$0.289957\pi$
$642$		0			0
$643$	6.20230	−	39.1598i	0.244595	−	1.54431i	−0.493579	−	0.869701i	$-0.664312\pi$
$643$	6.20230	−	39.1598i	0.244595	−	1.54431i	0.738174	−	0.674610i	$-0.235688\pi$
$644$	−22.6124	−	44.3793i	−0.891053	−	1.74879i
$645$		0			0
$646$	−0.578949	−	1.78182i	−0.0227784	−	0.0701048i
$647$		−	40.5997i		−	1.59614i	−0.602564	−	0.798070i	$-0.705854\pi$
$647$		−	40.5997i		−	1.59614i	0.602564	−	0.798070i	$-0.294146\pi$
$648$		0			0
$649$	−14.1884	+	2.24723i	−0.556945	+	0.0882114i
$650$	1.81721	+	0.287818i	0.0712769	+	0.0112892i
$651$		0			0
$652$	−3.58117	+	11.0217i	−0.140249	+	0.431643i
$653$	6.90831	−	6.90831i	0.270343	−	0.270343i	−0.558895	−	0.829238i	$-0.688775\pi$
$653$	6.90831	−	6.90831i	0.270343	−	0.270343i	0.829238	+	0.558895i	$0.188775\pi$
$654$		0			0
$655$	−38.6793			−1.51133
$656$	−0.402874	−	8.01253i	−0.0157296	−	0.312837i
$657$		0			0
$658$	−10.2582	−	14.1193i	−0.399908	−	0.550426i
$659$	27.6241	−	27.6241i	1.07608	−	1.07608i	0.0792258	−	0.996857i	$-0.474755\pi$
$659$	27.6241	−	27.6241i	1.07608	−	1.07608i	0.996857	−	0.0792258i	$-0.0252448\pi$
$660$		0			0
$661$	35.4354	+	11.5137i	1.37828	+	0.447829i	0.902102	−	0.431522i	$-0.142023\pi$
$661$	35.4354	+	11.5137i	1.37828	+	0.447829i	0.476174	+	0.879351i	$0.342023\pi$
$662$	−7.29110	−	1.15480i	−0.283377	−	0.0448825i
$663$		0			0
$664$	−11.3384	+	3.68408i	−0.440016	+	0.142970i
$665$		−	11.2748i		−	0.437220i
$666$		0			0
$667$	3.05293	+	1.55555i	0.118210	+	0.0602310i
$668$	12.9298	+	25.3761i	0.500267	+	0.981830i
$669$		0			0
$670$	4.84885	+	4.84885i	0.187327	+	0.187327i
$671$	−1.05602	+	0.538068i	−0.0407671	+	0.0207719i
$672$		0			0
$673$	−14.5486	+	28.5532i	−0.560807	+	1.10065i	0.420337	+	0.907368i	$0.361912\pi$
$673$	−14.5486	+	28.5532i	−0.560807	+	1.10065i	−0.981144	+	0.193277i	$0.938088\pi$
$674$	13.0748	−	9.49938i	0.503621	−	0.365902i
$675$		0			0
$676$	−2.43609	+	3.35299i	−0.0936958	+	0.128961i
$677$	21.5287	−	29.6318i	0.827417	−	1.13884i	−0.160982	−	0.986957i	$-0.551466\pi$
$677$	21.5287	−	29.6318i	0.827417	−	1.13884i	0.988398	−	0.151884i	$-0.0485340\pi$
$678$		0			0
$679$	16.2235	−	11.7870i	0.622600	−	0.452345i
$680$	−7.33754	+	14.4007i	−0.281382	+	0.552243i
$681$		0			0
$682$	0.633417	−	0.322742i	0.0242548	−	0.0123584i
$683$	32.2175	+	32.2175i	1.23277	+	1.23277i	0.962896	+	0.269874i	$0.0869821\pi$
$683$	32.2175	+	32.2175i	1.23277	+	1.23277i	0.269874	+	0.962896i	$0.413018\pi$
$684$		0			0
$685$	19.1467	+	37.5775i	0.731557	+	1.43576i
$686$	−31.3515	−	15.9744i	−1.19701	−	0.609906i
$687$		0			0
$688$		−	6.74936i		−	0.257317i
$689$	−28.8033	+	9.35875i	−1.09732	+	0.356540i
$690$		0			0
$691$	12.3380	+	1.95415i	0.469360	+	0.0743394i	0.386635	−	0.922233i	$-0.373637\pi$
$691$	12.3380	+	1.95415i	0.469360	+	0.0743394i	0.0827257	+	0.996572i	$0.473637\pi$
$692$	18.5129	+	6.01520i	0.703754	+	0.228663i
$693$		0			0
$694$	0.835439	−	0.835439i	0.0317128	−	0.0317128i
$695$	−2.97783	−	4.09864i	−0.112956	−	0.155470i
$696$		0			0
$697$	17.2138	−	3.62076i	0.652020	−	0.137146i
$698$	−24.4116			−0.923994
$699$		0			0
$700$	−3.41838	+	3.41838i	−0.129202	+	0.129202i
$701$	−10.2823	+	31.6458i	−0.388358	+	1.19524i	0.545656	+	0.838009i	$0.316280\pi$
$701$	−10.2823	+	31.6458i	−0.388358	+	1.19524i	−0.934015	+	0.357235i	$0.883720\pi$
$702$		0			0
$703$	−4.05485	−	0.642225i	−0.152932	−	0.0242220i
$704$	−2.72132	+	0.431014i	−0.102564	+	0.0162445i
$705$		0			0
$706$			18.0951i			0.681019i
$707$	15.8192	+	48.6865i	0.594943	+	1.83105i
$708$		0			0
$709$	12.6452	+	24.8176i	0.474901	+	0.932046i	0.996868	+	0.0790803i	$0.0251983\pi$
$709$	12.6452	+	24.8176i	0.474901	+	0.932046i	−0.521967	+	0.852966i	$0.674802\pi$
$710$	−1.91173	+	12.0702i	−0.0717460	+	0.452986i
$711$		0			0
$712$	8.11825	−	4.13646i	0.304244	−	0.155020i
$713$	−3.22574	−	2.34364i	−0.120805	−	0.0877700i
$714$		0			0
$715$	13.0206	−	9.45999i	0.486941	−	0.353784i
$716$	0.129932	+	0.820361i	0.00485580	+	0.0306583i
$717$		0			0
$718$	−10.9721	+	15.1018i	−0.409474	+	0.563593i
$719$	−4.62484	−	29.2001i	−0.172477	−	1.08898i	−0.910289	−	0.413973i	$-0.864141\pi$
$719$	−4.62484	−	29.2001i	−0.172477	−	1.08898i	0.737812	−	0.675006i	$-0.235859\pi$
$720$		0			0
$721$	0.914029	−	1.79388i	0.0340402	−	0.0668077i
$722$	10.3304	+	7.50545i	0.384456	+	0.279324i
$723$		0			0
$724$	−25.4924	−	25.4924i	−0.947417	−	0.947417i
$725$	0.0520240	−	0.328467i	0.00193212	−	0.0121989i
$726$		0			0
$727$	12.9250	+	6.58561i	0.479361	+	0.244247i	0.676937	−	0.736041i	$-0.263307\pi$
$727$	12.9250	+	6.58561i	0.479361	+	0.244247i	−0.197576	+	0.980288i	$0.563307\pi$
$728$	14.9102	+	45.8887i	0.552607	+	1.70075i
$729$		0			0
$730$	15.5473	−	5.05162i	0.575431	−	0.186969i
$731$	14.6165	−	2.31502i	0.540610	−	0.0856242i
$732$		0			0
$733$	42.4622	+	13.7968i	1.56838	+	0.509596i	0.959029	−	0.283307i	$-0.0914316\pi$
$733$	42.4622	+	13.7968i	1.56838	+	0.509596i	0.609347	+	0.792904i	$0.291432\pi$
$734$	−4.38743	+	13.5031i	−0.161943	+	0.498410i
$735$		0			0
$736$	23.1651	+	31.8840i	0.853877	+	1.17526i
$737$	6.95502			0.256191
$738$		0			0
$739$	−2.65655			−0.0977228			−0.0488614	−	0.998806i	$-0.515559\pi$
$739$	−2.65655			−0.0977228			−0.0488614	+	0.998806i	$0.515559\pi$
$740$	8.92358	+	12.2823i	0.328037	+	0.451505i
$741$		0			0
$742$	−8.18403	+	25.1879i	−0.300445	+	0.924676i
$743$	29.1554	+	9.47315i	1.06961	+	0.347536i	0.790334	−	0.612676i	$-0.209907\pi$
$743$	29.1554	+	9.47315i	1.06961	+	0.347536i	0.279272	+	0.960212i	$0.409907\pi$
$744$		0			0
$745$	−3.56401	+	0.564484i	−0.130575	+	0.0206811i
$746$	−5.16384	+	1.67783i	−0.189062	+	0.0614298i
$747$		0			0
$748$	2.17146	+	6.68305i	0.0793963	+	0.244357i
$749$	61.1914	+	31.1786i	2.23588	+	1.13924i
$750$		0			0
$751$	7.92192	−	50.0170i	0.289075	−	1.82515i	−0.233268	−	0.972412i	$-0.574942\pi$
$751$	7.92192	−	50.0170i	0.289075	−	1.82515i	0.522343	−	0.852735i	$-0.325058\pi$
$752$	−4.45360	−	4.45360i	−0.162406	−	0.162406i
$753$		0			0
$754$	−1.15110	−	0.836325i	−0.0419207	−	0.0304572i
$755$	−2.26290	+	4.44120i	−0.0823554	+	0.161632i
$756$		0			0
$757$	4.53435	+	28.6288i	0.164804	+	1.04053i	0.921957	+	0.387293i	$0.126590\pi$
$757$	4.53435	+	28.6288i	0.164804	+	1.04053i	−0.757153	+	0.653238i	$0.773410\pi$
$758$	−9.68519	+	13.3305i	−0.351782	+	0.484186i
$759$		0			0
$760$	0.888158	+	5.60761i	0.0322169	+	0.203409i
$761$	−31.5410	+	22.9159i	−1.14336	+	0.830700i	−0.987584	−	0.157092i	$-0.949788\pi$
$761$	−31.5410	+	22.9159i	−1.14336	+	0.830700i	−0.155777	+	0.987792i	$0.549788\pi$
$762$		0			0
$763$	60.9449	+	44.2791i	2.20635	+	1.60301i
$764$	−16.6231	+	8.46987i	−0.601401	+	0.306429i
$765$		0			0
$766$	−1.80186	+	11.3765i	−0.0651040	+	0.411051i
$767$	−15.1895	−	29.8112i	−0.548463	−	1.07642i
$768$		0			0
$769$	−0.817089	−	2.51474i	−0.0294650	−	0.0906839i	0.935243	−	0.354008i	$-0.115181\pi$
$769$	−0.817089	−	2.51474i	−0.0294650	−	0.0906839i	−0.964708	+	0.263324i	$0.915181\pi$
$770$		−	14.0741i		−	0.507196i
$771$		0			0
$772$	−4.82179	+	0.763696i	−0.173540	+	0.0274860i
$773$	20.6803	+	3.27543i	0.743817	+	0.117809i	0.516829	−	0.856089i	$-0.327112\pi$
$773$	20.6803	+	3.27543i	0.743817	+	0.117809i	0.226988	+	0.973898i	$0.427112\pi$
$774$		0			0
$775$	−0.119589	+	0.368056i	−0.00429575	+	0.0132210i
$776$	−7.14034	+	7.14034i	−0.256323	+	0.256323i
$777$		0			0
$778$	0.205578			0.00737034
$779$	4.14443	−	4.58326i	0.148490	−	0.164213i
$780$		0			0
$781$	7.28548	+	10.0276i	0.260695	+	0.358816i
$782$	−9.27507	+	9.27507i	−0.331676	+	0.331676i
$783$		0			0
$784$	−20.4182	−	6.63427i	−0.729220	−	0.236938i
$785$	16.2409	+	2.57231i	0.579663	+	0.0918095i
$786$		0			0
$787$	21.2772	−	6.91338i	0.758450	−	0.246435i	0.0958369	−	0.995397i	$-0.469447\pi$
$787$	21.2772	−	6.91338i	0.758450	−	0.246435i	0.662613	+	0.748962i	$0.269447\pi$
$788$		−	20.3205i		−	0.723888i
$789$		0			0
$790$	−13.0342	−	6.64125i	−0.463735	−	0.236285i
$791$	−17.9854	−	35.2984i	−0.639488	−	1.25507i
$792$		0			0
$793$	−1.95191	−	1.95191i	−0.0693142	−	0.0693142i
$794$	17.8195	−	9.07951i	0.632392	−	0.322220i
$795$		0			0
$796$	−6.31948	+	12.4027i	−0.223988	+	0.439602i
$797$	16.2691	−	11.8202i	0.576279	−	0.418691i	−0.261101	−	0.965311i	$-0.584086\pi$
$797$	16.2691	−	11.8202i	0.576279	−	0.418691i	0.837381	+	0.546620i	$0.184086\pi$
$798$		0			0
$799$	8.11718	−	11.1723i	0.287165	−	0.395249i
$800$	2.24838	−	3.09463i	0.0794921	−	0.109412i
$801$		0			0
$802$	3.87407	−	2.81468i	0.136798	−	0.0993897i
$803$	7.52732	−	14.7732i	0.265633	−	0.521335i
$804$		0			0
$805$	−70.3340	+	35.8370i	−2.47895	+	1.26309i
$806$	1.17079	+	1.17079i	0.0412392	+	0.0412392i
$807$		0			0
$808$	−11.7030	−	22.9684i	−0.411710	−	0.808026i
$809$	8.18594	+	4.17095i	0.287802	+	0.146643i	0.591932	−	0.805988i	$-0.298365\pi$
$809$	8.18594	+	4.17095i	0.287802	+	0.146643i	−0.304129	+	0.952631i	$0.598365\pi$
$810$		0			0
$811$			18.4060i			0.646324i	0.946344	+	0.323162i	$0.104746\pi$
$811$			18.4060i			0.646324i	−0.946344	+	0.323162i	$0.895254\pi$
$812$	3.55559	−	1.15528i	0.124777	−	0.0405425i
$813$		0			0
$814$	−5.06158	−	0.801675i	−0.177408	−	0.0280987i
$815$	17.4676	+	5.67557i	0.611863	+	0.198806i
$816$		0			0
$817$	3.67589	−	3.67589i	0.128603	−	0.128603i
$818$	7.02245	+	9.66557i	0.245534	+	0.337949i
$819$		0			0
$820$	−22.8218	+	1.14749i	−0.796972	+	0.0400722i
$821$	−18.0353			−0.629436			−0.314718	−	0.949185i	$-0.601910\pi$
$821$	−18.0353			−0.629436			−0.314718	+	0.949185i	$0.601910\pi$
$822$		0			0
$823$	−31.4518	+	31.4518i	−1.09634	+	1.09634i	−0.101506	+	0.994835i	$0.532366\pi$
$823$	−31.4518	+	31.4518i	−1.09634	+	1.09634i	−0.994835	+	0.101506i	$0.967634\pi$
$824$	−0.313287	+	0.964199i	−0.0109139	+	0.0335895i
$825$		0			0
$826$	−28.8980	−	4.57699i	−1.00549	−	0.159254i
$827$	−44.3599	+	7.02591i	−1.54254	+	0.244315i	−0.868992	−	0.494826i	$-0.835232\pi$
$827$	−44.3599	+	7.02591i	−1.54254	+	0.244315i	−0.673551	+	0.739141i	$0.735232\pi$
$828$		0			0
$829$			45.0253i			1.56379i	0.623409	+	0.781896i	$0.285747\pi$
$829$			45.0253i			1.56379i	−0.623409	+	0.781896i	$0.714253\pi$
$830$	2.50284	+	7.70296i	0.0868750	+	0.267374i
$831$		0			0
$832$	−2.91333	−	5.71773i	−0.101001	−	0.198227i
$833$	7.36382	−	46.4933i	0.255141	−	1.61090i
$834$		0			0
$835$	40.2170	−	20.4916i	1.39177	−	0.709140i
$836$	1.99701	+	1.45091i	0.0690681	+	0.0501809i
$837$		0			0
$838$	−7.02766	+	5.10590i	−0.242767	+	0.176380i
$839$	−1.71160	−	10.8066i	−0.0590911	−	0.373087i	−0.999458	−	0.0329242i	$-0.989518\pi$
$839$	−1.71160	−	10.8066i	−0.0590911	−	0.373087i	0.940367	−	0.340162i	$-0.110482\pi$
$840$		0			0
$841$	16.8946	−	23.2534i	0.582573	−	0.801842i
$842$	3.22067	+	20.3345i	0.110992	+	0.700773i
$843$		0			0
$844$	18.5441	−	36.3948i	0.638314	−	1.25276i
$845$	5.31395	+	3.86081i	0.182806	+	0.132816i
$846$		0			0
$847$	28.1184	+	28.1184i	0.966160	+	0.966160i
$848$	−1.49517	+	9.44011i	−0.0513442	+	0.324175i
$849$		0			0
$850$	1.13435	+	0.577982i	0.0389080	+	0.0198246i
$851$	8.88201	+	27.3360i	0.304471	+	0.937067i
$852$		0			0
$853$	15.9051	−	5.16789i	0.544581	−	0.176945i	−0.0237905	−	0.999717i	$-0.507573\pi$
$853$	15.9051	−	5.16789i	0.544581	−	0.176945i	0.568372	+	0.822772i	$0.307573\pi$
$854$	−2.38420	+	0.377621i	−0.0815857	+	0.0129219i
$855$		0			0
$856$	−32.8900	−	10.6866i	−1.12416	−	0.365260i
$857$	−3.43704	+	10.5781i	−0.117407	+	0.361341i	−0.992441	−	0.122719i	$-0.960839\pi$
$857$	−3.43704	+	10.5781i	−0.117407	+	0.361341i	0.875034	+	0.484061i	$0.160839\pi$
$858$		0			0
$859$	−27.8427	−	38.3222i	−0.949981	−	1.30754i	−0.951536	−	0.307538i	$-0.900495\pi$
$859$	−27.8427	−	38.3222i	−0.949981	−	1.30754i	0.00155429	−	0.999999i	$-0.499505\pi$
$860$	−19.2240			−0.655532
$861$		0			0
$862$	−6.08343			−0.207203
$863$	8.28362	+	11.4014i	0.281978	+	0.388109i	0.926388	−	0.376571i	$-0.122897\pi$
$863$	8.28362	+	11.4014i	0.281978	+	0.388109i	−0.644410	+	0.764680i	$0.722897\pi$
$864$		0			0
$865$	9.53311	−	29.3399i	0.324136	−	0.997587i
$866$	7.95726	+	2.58547i	0.270399	+	0.0878578i
$867$		0			0
$868$	−4.29696	+	0.680572i	−0.145848	+	0.0231001i
$869$	−14.1109	+	4.58490i	−0.478679	+	0.155532i
$870$		0			0
$871$	5.00569	+	15.4059i	0.169611	+	0.522010i
$872$	−33.7993	−	17.2216i	−1.14459	−	0.583198i
$873$		0			0
$874$	−0.720807	+	4.55100i	−0.0243817	+	0.153940i
$875$	−35.8895	−	35.8895i	−1.21329	−	1.21329i
$876$		0			0
$877$	28.6207	+	20.7942i	0.966453	+	0.702169i	0.954640	−	0.297761i	$-0.0962398\pi$
$877$	28.6207	+	20.7942i	0.966453	+	0.702169i	0.0118127	+	0.999930i	$0.496240\pi$
$878$	9.75761	−	19.1504i	0.329303	−	0.646294i
$879$		0			0
$880$	−0.794558	−	5.01664i	−0.0267846	−	0.169111i
$881$	12.7504	−	17.5494i	0.429572	−	0.591256i	−0.538283	−	0.842764i	$-0.680927\pi$
$881$	12.7504	−	17.5494i	0.429572	−	0.591256i	0.967855	+	0.251509i	$0.0809267\pi$
$882$		0			0
$883$	−0.504234	−	3.18361i	−0.0169688	−	0.107137i	0.977750	−	0.209773i	$-0.0672724\pi$
$883$	−0.504234	−	3.18361i	−0.0169688	−	0.107137i	−0.994719	+	0.102636i	$0.967272\pi$
$884$	−13.2407	+	9.61990i	−0.445332	+	0.323552i
$885$		0			0
$886$	7.63448	+	5.54677i	0.256485	+	0.186347i
$887$	12.8950	−	6.57032i	0.432971	−	0.220610i	−0.223901	−	0.974612i	$-0.571879\pi$
$887$	12.8950	−	6.57032i	0.432971	−	0.220610i	0.656872	+	0.754002i	$0.271879\pi$
$888$		0			0
$889$	−8.27040	+	52.2172i	−0.277380	+	1.75131i
$890$	−2.81018	−	5.51528i	−0.0941973	−	0.184873i
$891$		0			0
$892$	4.41971	+	13.6025i	0.147983	+	0.455444i
$893$		−	4.85111i		−	0.162336i
$894$		0			0
$895$	1.30014	−	0.205922i	0.0434589	−	0.00688321i
$896$	51.0649	+	8.08789i	1.70596	+	0.270197i
$897$		0			0
$898$	5.49230	−	16.9036i	0.183281	−	0.564080i
$899$	0.211623	−	0.211623i	0.00705803	−	0.00705803i
$900$		0			0
$901$	−20.9564			−0.698160
$902$	5.17340	−	5.72118i	0.172255	−	0.190495i
$903$		0			0
$904$	11.7257	+	16.1391i	0.389992	+	0.536778i
$905$	−40.4013	+	40.4013i	−1.34299	+	1.34299i
$906$		0			0
$907$	−40.1252	−	13.0375i	−1.33233	−	0.432902i	−0.445621	−	0.895222i	$-0.647017\pi$
$907$	−40.1252	−	13.0375i	−1.33233	−	0.432902i	−0.886713	+	0.462320i	$0.847017\pi$
$908$	2.25663	+	0.357415i	0.0748890	+	0.0118612i
$909$		0			0
$910$	31.1753	−	10.1295i	1.03345	−	0.335789i
$911$			46.8754i			1.55305i	0.630087	+	0.776525i	$0.283019\pi$
$911$			46.8754i			1.55305i	−0.630087	+	0.776525i	$0.716981\pi$
$912$		0			0
$913$	7.31943	+	3.72944i	0.242238	+	0.123426i
$914$	−10.3226	−	20.2593i	−0.341442	−	0.670118i
$915$		0			0
$916$	15.6411	+	15.6411i	0.516796	+	0.516796i
$917$	−71.1930	+	36.2747i	−2.35100	+	1.19790i
$918$		0			0
$919$	11.8130	−	23.1843i	0.389675	−	0.764780i	−0.609942	−	0.792446i	$-0.708807\pi$
$919$	11.8130	−	23.1843i	0.389675	−	0.764780i	0.999617	+	0.0276656i	$0.00880735\pi$
$920$	32.1581	−	23.3642i	1.06022	−	0.770295i
$921$		0			0
$922$	12.2298	−	16.8329i	0.402768	−	0.554363i
$923$	−16.9684	+	23.3550i	−0.558522	+	0.768740i
$924$		0			0
$925$	2.25695	−	1.63977i	0.0742080	−	0.0539153i
$926$	−6.58375	+	12.9213i	−0.216355	+	0.424622i
$927$		0			0
$928$	−2.63574	+	1.34298i	−0.0865224	+	0.0440853i
$929$	−25.6662	−	25.6662i	−0.842079	−	0.842079i	0.147050	−	0.989129i	$-0.453022\pi$
$929$	−25.6662	−	25.6662i	−0.842079	−	0.842079i	−0.989129	+	0.147050i	$0.953022\pi$
$930$		0			0
$931$	−7.50710	−	14.7335i	−0.246035	−	0.482871i
$932$	−19.9046	−	10.1419i	−0.651997	−	0.332209i
$933$		0			0
$934$		−	17.4505i		−	0.570999i
$935$	10.5916	−	3.44141i	0.346381	−	0.112546i
$936$		0			0
$937$	11.0570	+	1.75125i	0.361216	+	0.0572110i	0.334405	−	0.942430i	$-0.391465\pi$
$937$	11.0570	+	1.75125i	0.361216	+	0.0572110i	0.0268112	+	0.999641i	$0.491465\pi$
$938$	13.4722	+	4.37737i	0.439882	+	0.142926i
$939$		0			0
$940$	−12.6850	+	12.6850i	−0.413740	+	0.413740i
$941$	9.08708	+	12.5073i	0.296230	+	0.407726i	0.931025	−	0.364954i	$-0.118915\pi$
$941$	9.08708	+	12.5073i	0.296230	+	0.407726i	−0.634795	+	0.772681i	$0.718915\pi$
$942$		0			0
$943$	−41.7641	−	11.2857i	−1.36003	−	0.367512i
$944$	−10.5589			−0.343664
$945$		0			0
$946$	4.58853	−	4.58853i	0.149186	−	0.149186i
$947$	11.7171	−	36.0615i	0.380755	−	1.17184i	−0.558758	−	0.829330i	$-0.688722\pi$
$947$	11.7171	−	36.0615i	0.380755	−	1.17184i	0.939513	−	0.342512i	$-0.111278\pi$
$948$		0			0
$949$	38.1414	+	6.04101i	1.23812	+	0.196100i
$950$	0.441715	−	0.0699607i	0.0143311	−	0.00226983i
$951$		0			0
$952$			33.3873i			1.08209i
$953$	10.8163	+	33.2891i	0.350373	+	1.07834i	0.958644	+	0.284609i	$0.0918637\pi$
$953$	10.8163	+	33.2891i	0.350373	+	1.07834i	−0.608270	+	0.793730i	$0.708136\pi$
$954$		0			0
$955$	13.4234	+	26.3449i	0.434370	+	0.852499i
$956$	3.13927	−	19.8205i	0.101531	−	0.641042i
$957$		0			0
$958$	18.2674	−	9.30769i	0.590192	−	0.300718i
$959$	70.4826	+	51.2086i	2.27600	+	1.65361i
$960$		0			0
$961$	24.7978	−	18.0166i	0.799928	−	0.581182i
$962$	−1.86716	−	11.7888i	−0.0601997	−	0.380086i
$963$		0			0
$964$	−3.52390	+	4.85023i	−0.113497	+	0.156215i
$965$	1.21034	+	7.64176i	0.0389621	+	0.245997i
$966$		0			0
$967$	8.63244	−	16.9421i	0.277601	−	0.544822i	−0.709542	−	0.704663i	$-0.751098\pi$
$967$	8.63244	−	16.9421i	0.277601	−	0.544822i	0.987143	+	0.159841i	$0.0510982\pi$
$968$	−16.1999	−	11.7699i	−0.520683	−	0.378298i
$969$		0			0
$970$	4.85092	+	4.85092i	0.155754	+	0.155754i
$971$	5.92738	−	37.4240i	0.190219	−	1.20099i	−0.689067	−	0.724698i	$-0.741979\pi$
$971$	5.92738	−	37.4240i	0.190219	−	1.20099i	0.879286	−	0.476295i	$-0.158021\pi$
$972$		0			0
$973$	−9.32482	−	4.75123i	−0.298940	−	0.152318i
$974$	−5.76097	−	17.7304i	−0.184593	−	0.568120i
$975$		0			0
$976$	−0.828517	+	0.269202i	−0.0265202	+	0.00861693i
$977$	−21.7408	+	3.44341i	−0.695551	+	0.110164i	−0.494191	−	0.869353i	$-0.664536\pi$
$977$	−21.7408	+	3.44341i	−0.695551	+	0.110164i	−0.201359	+	0.979517i	$0.564536\pi$
$978$		0			0
$979$	−5.97088	−	1.94006i	−0.190830	−	0.0620044i
$980$	−18.8961	+	58.1563i	−0.603615	+	1.85774i
$981$		0			0
$982$	−7.25876	−	9.99082i	−0.231636	−	0.318820i
$983$	12.0990			0.385900			0.192950	−	0.981209i	$-0.438195\pi$
$983$	12.0990			0.385900			0.192950	+	0.981209i	$0.438195\pi$
$984$		0			0
$985$	−32.2047			−1.02613
$986$	−0.578705	−	0.796518i	−0.0184297	−	0.0253663i
$987$		0			0
$988$	−1.77660	+	5.46780i	−0.0565211	+	0.173954i
$989$	−34.6145	−	11.2469i	−1.10068	−	0.357632i
$990$		0			0
$991$	−37.0961	+	5.87545i	−1.17840	+	0.186640i	−0.714750	−	0.699380i	$-0.753459\pi$
$991$	−37.0961	+	5.87545i	−1.17840	+	0.186640i	−0.463647	+	0.886020i	$0.653459\pi$
$992$	3.27389	−	1.06375i	0.103946	−	0.0337741i
$993$		0			0
$994$	7.80108	+	24.0092i	0.247435	+	0.761527i
$995$	19.6563	+	10.0154i	0.623145	+	0.317508i
$996$		0			0
$997$	−1.20345	+	7.59830i	−0.0381137	+	0.240641i	−0.999389	−	0.0349491i	$-0.988873\pi$
$997$	−1.20345	+	7.59830i	−0.0381137	+	0.240641i	0.961275	+	0.275590i	$0.0888731\pi$
$998$	3.15815	+	3.15815i	0.0999694	+	0.0999694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.118.2		24
3.2	odd	2		41.2.g.a.36.2	yes	24
12.11	even	2		656.2.bs.d.241.2		24
41.8	even	20	inner	369.2.u.a.172.2		24
123.8	odd	20		41.2.g.a.8.2	✓	24
123.89	even	40		1681.2.a.m.1.14		24
123.116	even	40		1681.2.a.m.1.13		24
492.131	even	20		656.2.bs.d.49.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.2	✓	24	123.8	odd	20
41.2.g.a.36.2	yes	24	3.2	odd	2
369.2.u.a.118.2		24	1.1	even	1	trivial
369.2.u.a.172.2		24	41.8	even	20	inner
656.2.bs.d.49.2		24	492.131	even	20
656.2.bs.d.241.2		24	12.11	even	2
1681.2.a.m.1.13		24	123.116	even	40
1681.2.a.m.1.14		24	123.89	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415383 + 0.571726i) q^{2} +(0.463706 - 1.42714i) q^{4} +(-2.26179 - 0.734900i) q^{5} +(-4.85225 + 0.768522i) q^{7} +(2.35276 - 0.764458i) q^{8} +O(q^{10})\)	\(q+(0.415383 + 0.571726i) q^{2} +(0.463706 - 1.42714i) q^{4} +(-2.26179 - 0.734900i) q^{5} +(-4.85225 + 0.768522i) q^{7} +(2.35276 - 0.764458i) q^{8} +(-0.519348 - 1.59839i) q^{10} +(-1.51881 - 0.773870i) q^{11} +(0.621065 - 3.92125i) q^{13} +(-2.45493 - 2.45493i) q^{14} +(-1.01364 - 0.736453i) q^{16} +(1.24719 - 2.44775i) q^{17} +(-0.150964 - 0.953149i) q^{19} +(-2.09761 + 2.88712i) q^{20} +(-0.188445 - 1.18979i) q^{22} +(-5.46604 + 3.97131i) q^{23} +(0.530527 + 0.385451i) q^{25} +(2.49986 - 1.27374i) q^{26} +(-1.15323 + 7.28122i) q^{28} +(-0.230233 - 0.451858i) q^{29} +(0.182364 + 0.561259i) q^{31} -5.83311i q^{32} +(1.91751 - 0.303703i) q^{34} +(11.5396 + 1.82769i) q^{35} +(1.31461 - 4.04595i) q^{37} +(0.482233 - 0.482233i) q^{38} -5.88325 q^{40} +(4.01905 + 4.98470i) q^{41} +(3.16632 + 4.35807i) q^{43} +(-1.80870 + 1.80870i) q^{44} +(-4.54100 - 1.47546i) q^{46} +(4.96501 + 0.786381i) q^{47} +(16.2964 - 5.29501i) q^{49} +0.463426i q^{50} +(-5.30819 - 2.70466i) q^{52} +(-3.46320 - 6.79691i) q^{53} +(2.86650 + 2.86650i) q^{55} +(-10.8287 + 5.51749i) q^{56} +(0.162704 - 0.319325i) q^{58} +(6.81790 - 4.95350i) q^{59} +(0.408684 - 0.562505i) q^{61} +(-0.245135 + 0.337400i) q^{62} +(1.30766 - 0.950072i) q^{64} +(-4.28645 + 8.41262i) q^{65} +(-3.63545 + 1.85235i) q^{67} +(-2.91496 - 2.91496i) q^{68} +(3.74841 + 7.35666i) q^{70} +(-6.47886 - 3.30115i) q^{71} +9.72685i q^{73} +(2.85924 - 0.929024i) q^{74} +(-1.43028 - 0.226534i) q^{76} +(7.96437 + 2.58778i) q^{77} +(6.15477 - 6.15477i) q^{79} +(1.75142 + 2.41063i) q^{80} +(-1.18044 + 4.36836i) q^{82} -4.81920 q^{83} +(-4.61974 + 4.61974i) q^{85} +(-1.17638 + 3.62054i) q^{86} +(-4.16498 - 0.659667i) q^{88} +(3.63773 - 0.576160i) q^{89} +19.5042i q^{91} +(3.13298 + 9.64234i) q^{92} +(1.61279 + 3.16528i) q^{94} +(-0.359020 + 2.26677i) q^{95} +(-3.63700 + 1.85314i) q^{97} +(9.79653 + 7.11760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

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