LMFDB - Embedded newform 729.2.g.b.379.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,63] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			379.6
Character	$\chi$	$=$	729.379
Dual form			729.2.g.b.352.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.194062 + 0.648213i) q^{2} +(1.28846 - 0.847431i) q^{4} +(-0.373572 - 0.866038i) q^{5} +(0.0849292 - 1.45818i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(-3.65505 - 4.90959i) q^{11} +(3.60053 + 3.81633i) q^{13} +(0.961691 - 0.227925i) q^{14} +(0.579298 - 1.34296i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(-1.21524 - 0.799275i) q^{20} +(2.47315 - 3.32202i) q^{22} +(0.00607888 + 0.104370i) q^{23} +(2.82074 - 2.98981i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(-0.498884 - 0.118238i) q^{29} +(-7.30038 - 3.66639i) q^{31} +(5.74406 + 0.671384i) q^{32} +(-0.0186811 + 0.00938202i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(2.45747 - 0.287237i) q^{38} +(0.648337 - 2.16560i) q^{40} +(1.25791 - 4.20171i) q^{41} +(-1.36737 + 0.159822i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(-5.01303 + 2.51764i) q^{47} +(4.83360 + 0.564967i) q^{49} +(2.48543 + 1.24823i) q^{50} +(7.87320 + 1.86598i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(2.40241 - 2.54641i) q^{56} +(-0.0201713 - 0.346328i) q^{58} +(3.37359 - 4.53152i) q^{59} +(-1.43519 - 0.943940i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(1.96003 - 4.54387i) q^{65} +(2.66387 - 0.631349i) q^{67} +(0.0326960 + 0.0346557i) q^{68} +(-0.556652 - 0.747714i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(-0.227062 + 3.89850i) q^{74} +(-2.23352 - 5.17789i) q^{76} +(-7.46947 + 4.91275i) q^{77} +(3.61740 + 12.0829i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(5.11210 + 17.0756i) q^{83} +(0.0243456 - 0.0160123i) q^{85} +(-0.368953 - 0.855329i) q^{86} +(0.852982 - 14.6451i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(0.0962791 + 0.129325i) q^{92} +(-2.60480 - 2.76093i) q^{94} +(-3.35585 + 0.795351i) q^{95} +(-2.77706 + 6.43795i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.194062	+	0.648213i	0.137223	+	0.458356i	0.998784	−	0.0492977i	$-0.0156983\pi$
$2$	0.194062	+	0.648213i	0.137223	+	0.458356i	−0.861561	+	0.507653i	$0.830513\pi$
$3$		0			0
$3$		0			0
$4$	1.28846	−	0.847431i	0.644228	−	0.423715i
$5$	−0.373572	−	0.866038i	−0.167067	−	0.387304i	0.814030	−	0.580823i	$-0.197269\pi$
$5$	−0.373572	−	0.866038i	−0.167067	−	0.387304i	−0.981097	+	0.193519i	$0.938010\pi$
$6$		0			0
$7$	0.0849292	−	1.45818i	0.0321002	−	0.551139i	−0.943471	−	0.331455i	$-0.892460\pi$
$7$	0.0849292	−	1.45818i	0.0321002	−	0.551139i	0.975571	−	0.219684i	$-0.0705026\pi$
$8$	1.83603	+	1.54061i	0.649133	+	0.544688i
$9$		0			0
$10$	0.488880	−	0.410219i	0.154598	−	0.129723i
$11$	−3.65505	−	4.90959i	−1.10204	−	1.48030i	−0.860183	−	0.509985i	$-0.829651\pi$
$11$	−3.65505	−	4.90959i	−1.10204	−	1.48030i	−0.241857	−	0.970312i	$-0.577756\pi$
$12$		0			0
$13$	3.60053	+	3.81633i	0.998606	+	1.05846i	0.998290	+	0.0584608i	$0.0186193\pi$
$13$	3.60053	+	3.81633i	0.998606	+	1.05846i	0.000316539		1.00000i	$0.499899\pi$
$14$	0.961691	−	0.227925i	0.257023	−	0.0609155i
$15$		0			0
$16$	0.579298	−	1.34296i	0.144825	−	0.335741i
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	0.985451	−	0.169957i	$-0.0543630\pi$
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	−0.984150	+	0.177337i	$0.943252\pi$
$18$		0			0
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	−0.821156	−	0.570704i	$-0.806670\pi$
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	0.966826	−	0.255434i	$-0.0822184\pi$
$20$	−1.21524	−	0.799275i	−0.271736	−	0.178723i
$21$		0			0
$22$	2.47315	−	3.32202i	0.527277	−	0.708256i
$23$	0.00607888	+	0.104370i	0.00126753	+	0.0217627i	0.998883	−	0.0472600i	$-0.0150489\pi$
$23$	0.00607888	+	0.104370i	0.00126753	+	0.0217627i	−0.997615	+	0.0690227i	$0.978012\pi$
$24$		0			0
$25$	2.82074	−	2.98981i	0.564149	−	0.597963i
$26$	−1.77507	+	3.07451i	−0.348120	+	0.602961i
$27$		0			0
$28$	−1.12628	−	1.95077i	−0.212846	−	0.368661i
$29$	−0.498884	−	0.118238i	−0.0926405	−	0.0219562i	0.184034	−	0.982920i	$-0.441084\pi$
$29$	−0.498884	−	0.118238i	−0.0926405	−	0.0219562i	−0.276675	+	0.960964i	$0.589232\pi$
$30$		0			0
$31$	−7.30038	−	3.66639i	−1.31119	−	0.658503i	−0.350611	−	0.936521i	$-0.614026\pi$
$31$	−7.30038	−	3.66639i	−1.31119	−	0.658503i	−0.960576	+	0.278019i	$0.910322\pi$
$32$	5.74406	+	0.671384i	1.01542	+	0.118685i
$33$		0			0
$34$	−0.0186811	+	0.00938202i	−0.00320379	+	0.00160900i
$35$	−1.29456	+	0.471183i	−0.218821	+	0.0796444i
$36$		0			0
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.746874	−	0.664965i	$-0.231554\pi$
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.144707	+	0.989475i	$0.453776\pi$
$38$	2.45747	−	0.287237i	0.398654	−	0.0465960i
$39$		0			0
$40$	0.648337	−	2.16560i	0.102511	−	0.342411i
$41$	1.25791	−	4.20171i	0.196452	−	0.656197i	−0.801827	−	0.597557i	$-0.796138\pi$
$41$	1.25791	−	4.20171i	0.196452	−	0.656197i	0.998279	−	0.0586403i	$-0.0186765\pi$
$42$		0			0
$43$	−1.36737	+	0.159822i	−0.208522	+	0.0243727i	−0.219712	−	0.975565i	$-0.570512\pi$
$43$	−1.36737	+	0.159822i	−0.208522	+	0.0243727i	0.0111907	+	0.999937i	$0.496438\pi$
$44$	−8.86991	−	3.22838i	−1.33719	−	0.486697i
$45$		0			0
$46$	−0.0664745	+	0.0241947i	−0.00980113	+	0.00356732i
$47$	−5.01303	+	2.51764i	−0.731225	+	0.367235i	−0.775131	−	0.631801i	$-0.782316\pi$
$47$	−5.01303	+	2.51764i	−0.731225	+	0.367235i	0.0439058	+	0.999036i	$0.486020\pi$
$48$		0			0
$49$	4.83360	+	0.564967i	0.690514	+	0.0807095i
$50$	2.48543	+	1.24823i	0.351493	+	0.176527i
$51$		0			0
$52$	7.87320	+	1.86598i	1.09182	+	0.258765i
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	0.977382	+	0.211481i	$0.0678288\pi$
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	−0.305543	+	0.952178i	$0.598838\pi$
$54$		0			0
$55$	−2.88646	+	4.99950i	−0.389211	+	0.674132i
$56$	2.40241	−	2.54641i	0.321036	−	0.340278i
$57$		0			0
$58$	−0.0201713	−	0.346328i	−0.00264863	−	0.0454752i
$59$	3.37359	−	4.53152i	0.439204	−	0.589953i	−0.526314	−	0.850290i	$-0.676426\pi$
$59$	3.37359	−	4.53152i	0.439204	−	0.589953i	0.965518	+	0.260337i	$0.0838337\pi$
$60$		0			0
$61$	−1.43519	−	0.943940i	−0.183757	−	0.120859i	0.454297	−	0.890850i	$-0.349890\pi$
$61$	−1.43519	−	0.943940i	−0.183757	−	0.120859i	−0.638055	+	0.769991i	$0.720261\pi$
$62$	0.959872	−	5.44370i	0.121904	−	0.691351i
$63$		0			0
$64$	0.171556	+	0.972942i	0.0214445	+	0.121618i
$65$	1.96003	−	4.54387i	0.243112	−	0.563597i
$66$		0			0
$67$	2.66387	−	0.631349i	0.325444	−	0.0771315i	−0.0646466	−	0.997908i	$-0.520592\pi$
$67$	2.66387	−	0.631349i	0.325444	−	0.0771315i	0.390090	+	0.920777i	$0.372444\pi$
$68$	0.0326960	+	0.0346557i	0.00396497	+	0.00420262i
$69$		0			0
$70$	−0.556652	−	0.747714i	−0.0665327	−	0.0893689i
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	−0.736191	−	0.676774i	$-0.763377\pi$
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	0.538654	+	0.842527i	$0.318933\pi$
$72$		0			0
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	0.187736	−	0.982219i	$-0.439885\pi$
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	−0.934697	+	0.355445i	$0.884329\pi$
$74$	−0.227062	+	3.89850i	−0.0263954	+	0.453191i
$75$		0			0
$76$	−2.23352	−	5.17789i	−0.256203	−	0.593944i
$77$	−7.46947	+	4.91275i	−0.851225	+	0.559860i
$78$		0			0
$79$	3.61740	+	12.0829i	0.406989	+	1.35944i	0.878570	+	0.477614i	$0.158498\pi$
$79$	3.61740	+	12.0829i	0.406989	+	1.35944i	−0.471581	+	0.881823i	$0.656316\pi$
$80$	−1.37947			−0.154229
$81$		0			0
$82$	2.96771			0.327729
$83$	5.11210	+	17.0756i	0.561126	+	1.87429i	0.479313	+	0.877644i	$0.340886\pi$
$83$	5.11210	+	17.0756i	0.561126	+	1.87429i	0.0818133	+	0.996648i	$0.473929\pi$
$84$		0			0
$85$	0.0243456	−	0.0160123i	0.00264065	−	0.00173678i
$86$	−0.368953	−	0.855329i	−0.0397852	−	0.0922325i
$87$		0			0
$88$	0.852982	−	14.6451i	0.0909282	−	1.56118i
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.999173	−	0.0406545i	$-0.0129443\pi$
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.133468	+	0.991053i	$0.457389\pi$
$90$		0			0
$91$	5.87068	−	4.92609i	0.615415	−	0.516394i
$92$	0.0962791	+	0.129325i	0.0100378	+	0.0134831i
$93$		0			0
$94$	−2.60480	−	2.76093i	−0.268665	−	0.284768i
$95$	−3.35585	+	0.795351i	−0.344303	+	0.0816013i
$96$		0			0
$97$	−2.77706	+	6.43795i	−0.281968	+	0.653675i	−0.999062	−	0.0433014i	$-0.986212\pi$
$97$	−2.77706	+	6.43795i	−0.281968	+	0.653675i	0.717094	+	0.696976i	$0.245472\pi$
$98$	0.571800	+	3.24284i	0.0577605	+	0.327576i
$99$		0			0
$100$	1.10074	−	6.24263i	0.110074	−	0.624263i
$101$	−7.26104	−	4.77566i	−0.722501	−	0.475196i	0.134237	−	0.990949i	$-0.457142\pi$
$101$	−7.26104	−	4.77566i	−0.722501	−	0.475196i	−0.856737	+	0.515753i	$0.827512\pi$
$102$		0			0
$103$	−3.06205	+	4.11304i	−0.301712	+	0.405270i	−0.926962	−	0.375155i	$-0.877590\pi$
$103$	−3.06205	+	4.11304i	−0.301712	+	0.405270i	0.625250	+	0.780425i	$0.284997\pi$
$104$	0.731181	+	12.5539i	0.0716982	+	1.23101i
$105$		0			0
$106$	−4.54221	+	4.81446i	−0.441178	+	0.467622i
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	−0.518676	−	0.854971i	$-0.673575\pi$
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	0.999765	+	0.0217011i	$0.00690820\pi$
$108$		0			0
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	0.991240	+	0.132071i	$0.0421627\pi$
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	−0.381243	+	0.924475i	$0.624504\pi$
$110$	−3.80089	−	0.900828i	−0.362401	−	0.0858906i
$111$		0			0
$112$	−1.90908	−	0.958776i	−0.180391	−	0.0905958i
$113$	5.70803	+	0.667173i	0.536966	+	0.0627623i	0.380254	−	0.924882i	$-0.375836\pi$
$113$	5.70803	+	0.667173i	0.536966	+	0.0627623i	0.156712	+	0.987644i	$0.449911\pi$
$114$		0			0
$115$	0.0881178	−	0.0442544i	0.00821703	−	0.00412675i
$116$	−0.742989	+	0.270426i	−0.0689848	+	0.0251084i
$117$		0			0
$118$	3.59207	+	1.30741i	0.330677	+	0.120357i
$119$	0.0448216	−	0.00523889i	0.00410879	−	0.000480248i
$120$		0			0
$121$	−7.58981	+	25.3517i	−0.689983	+	2.30470i
$122$	0.333357	−	1.11349i	0.0301808	−	0.100811i
$123$		0			0
$124$	−12.5132	+	1.46259i	−1.12372	+	0.131344i
$125$	−8.07451	−	2.93888i	−0.722206	−	0.262862i
$126$		0			0
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.743814	−	0.668387i	$-0.766985\pi$
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.140163	+	0.990128i	$0.544763\pi$
$128$	9.73866	−	4.89094i	0.860784	−	0.432302i
$129$		0			0
$130$	3.32576	+	0.388726i	0.291689	+	0.0340935i
$131$	−12.7466	−	6.40157i	−1.11367	−	0.559308i	−0.205817	−	0.978590i	$-0.565985\pi$
$131$	−12.7466	−	6.40157i	−1.11367	−	0.559308i	−0.907856	+	0.419283i	$0.862282\pi$
$132$		0			0
$133$	−5.19705	−	1.23172i	−0.450641	−	0.106804i
$134$	0.926205	+	1.60423i	0.0800119	+	0.138585i
$135$		0			0
$136$	−0.0370239	+	0.0641273i	−0.00317478	+	0.00549887i
$137$	3.66191	−	3.88140i	0.312858	−	0.331610i	−0.551795	−	0.833980i	$-0.686057\pi$
$137$	3.66191	−	3.88140i	0.312858	−	0.331610i	0.864653	+	0.502370i	$0.167538\pi$
$138$		0			0
$139$	0.238054	+	4.08722i	0.0201915	+	0.346674i	0.993240	+	0.116075i	$0.0370314\pi$
$139$	0.238054	+	4.08722i	0.0201915	+	0.346674i	−0.973049	+	0.230599i	$0.925932\pi$
$140$	−1.26869	+	1.70415i	−0.107224	+	0.144027i
$141$		0			0
$142$	−1.22834	−	0.807895i	−0.103080	−	0.0677971i
$143$	5.57652	−	31.6260i	0.466332	−	2.64470i
$144$		0			0
$145$	0.0839709	+	0.476223i	0.00697341	+	0.0395482i
$146$	2.23277	−	5.17615i	0.184786	−	0.428381i
$147$		0			0
$148$	8.66041	−	2.05255i	0.711881	−	0.168719i
$149$	−12.9539	−	13.7303i	−1.06122	−	1.12483i	−0.991872	−	0.127237i	$-0.959389\pi$
$149$	−12.9539	−	13.7303i	−1.06122	−	1.12483i	−0.0693495	−	0.997592i	$-0.522092\pi$
$150$		0			0
$151$	−1.83951	−	2.47089i	−0.149697	−	0.201078i	0.720949	−	0.692988i	$-0.243706\pi$
$151$	−1.83951	−	2.47089i	−0.149697	−	0.201078i	−0.870646	+	0.491910i	$0.836299\pi$
$152$	6.71362	−	5.63340i	0.544547	−	0.456929i
$153$		0			0
$154$	−4.63405	−	3.88843i	−0.373422	−	0.313338i
$155$	−0.448012	+	7.69206i	−0.0359852	+	0.617841i
$156$		0			0
$157$	−1.35800	−	3.14820i	−0.108380	−	0.251254i	0.855391	−	0.517982i	$-0.173317\pi$
$157$	−1.35800	−	3.14820i	−0.108380	−	0.251254i	−0.963772	+	0.266728i	$0.914057\pi$
$158$	−7.13032	+	4.68968i	−0.567257	+	0.373091i
$159$		0			0
$160$	−1.56438	−	5.22538i	−0.123675	−	0.413103i
$161$	0.152707			0.0120350
$162$		0			0
$163$	−19.7151			−1.54420			−0.772101	−	0.635500i	$-0.780794\pi$
$163$	−19.7151			−1.54420			−0.772101	+	0.635500i	$0.780794\pi$
$164$	−1.93990	−	6.47971i	−0.151481	−	0.505980i
$165$		0			0
$166$	−10.0766	+	6.62746i	−0.782093	+	0.514391i
$167$	7.66118	+	17.7606i	0.592840	+	1.37436i	0.905441	+	0.424473i	$0.139540\pi$
$167$	7.66118	+	17.7606i	0.592840	+	1.37436i	−0.312601	+	0.949885i	$0.601200\pi$
$168$		0			0
$169$	−0.844740	+	14.5036i	−0.0649800	+	1.11566i
$170$	0.0151039	+	0.0126737i	0.00115842	+	0.000972029i
$171$		0			0
$172$	−1.62635	+	1.36467i	−0.124008	+	0.104055i
$173$	3.68287	+	4.94696i	0.280004	+	0.376110i	0.919769	−	0.392460i	$-0.128376\pi$
$173$	3.68287	+	4.94696i	0.280004	+	0.376110i	−0.639765	+	0.768570i	$0.720969\pi$
$174$		0			0
$175$	−4.12011	−	4.36707i	−0.311451	−	0.330119i
$176$	−8.71077	+	2.06449i	−0.656599	+	0.155617i
$177$		0			0
$178$	−3.73829	+	8.66632i	−0.280196	+	0.649568i
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	0.998997	−	0.0447821i	$-0.0142593\pi$
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	−0.954066	+	0.299596i	$0.903148\pi$
$180$		0			0
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	0.571244	+	0.820780i	$0.306461\pi$
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	−0.817517	+	0.575904i	$0.804650\pi$
$182$	4.33243	+	2.84948i	0.321141	+	0.211218i
$183$		0			0
$184$	−0.149633	+	0.200992i	−0.0110311	+	0.0148173i
$185$	−0.316504	−	5.43416i	−0.0232698	−	0.399528i
$186$		0			0
$187$	0.129768	−	0.137546i	0.00948960	−	0.0100584i
$188$	−4.32554	+	7.49206i	−0.315473	+	0.546415i
$189$		0			0
$190$	−1.16680	−	2.02096i	−0.0846486	−	0.146616i
$191$	19.3906	+	4.59566i	1.40306	+	0.332530i	0.861339	−	0.508031i	$-0.169626\pi$
$191$	19.3906	+	4.59566i	1.40306	+	0.332530i	0.541717	+	0.840561i	$0.317774\pi$
$192$		0			0
$193$	−9.57740	−	4.80995i	−0.689396	−	0.346228i	0.0693698	−	0.997591i	$-0.477901\pi$
$193$	−9.57740	−	4.80995i	−0.689396	−	0.346228i	−0.758766	+	0.651363i	$0.774197\pi$
$194$	−4.71208	−	0.550763i	−0.338308	−	0.0395425i
$195$		0			0
$196$	6.70665	−	3.36821i	0.479047	−	0.240586i
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.976679	−	0.214707i	$-0.931120\pi$
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.610169	+	0.792272i	$0.708898\pi$
$198$		0			0
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	0.0342781	−	0.999412i	$-0.489087\pi$
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	−0.616151	+	0.787628i	$0.711309\pi$
$200$	9.78509	−	1.14371i	0.691910	−	0.0808727i
$201$		0			0
$202$	1.68655	−	5.63347i	0.118665	−	0.396370i
$203$	−0.214781	+	0.717420i	−0.0150747	+	0.0503530i
$204$		0			0
$205$	−4.10876	+	0.480245i	−0.286968	+	0.0335418i
$206$	−3.26035	−	1.18667i	−0.227160	−	0.0826793i
$207$		0			0
$208$	7.21098	−	2.62458i	0.499991	−	0.181982i
$209$	−20.0005	+	10.0446i	−1.38346	+	0.694802i
$210$		0			0
$211$	7.22885	+	0.844932i	0.497655	+	0.0581675i	0.361218	−	0.932481i	$-0.382361\pi$
$211$	7.22885	+	0.844932i	0.497655	+	0.0581675i	0.136437	+	0.990649i	$0.456435\pi$
$212$	13.4810	+	6.77041i	0.925878	+	0.464994i
$213$		0			0
$214$	6.55294	+	1.55308i	0.447950	+	0.106166i
$215$	0.649223	+	1.12449i	0.0442766	+	0.0766894i
$216$		0			0
$217$	−5.96626	+	10.3339i	−0.405016	+	0.701508i
$218$	−5.91432	+	6.26881i	−0.400568	+	0.424578i
$219$		0			0
$220$	0.517650	+	8.88771i	0.0349000	+	0.599210i
$221$	−0.0967980	+	0.130022i	−0.00651134	+	0.00874624i
$222$		0			0
$223$	−0.625341	−	0.411293i	−0.0418759	−	0.0275422i	0.528398	−	0.848997i	$-0.322793\pi$
$223$	−0.625341	−	0.411293i	−0.0418759	−	0.0275422i	−0.570274	+	0.821454i	$0.693163\pi$
$224$	1.46684	−	8.31884i	0.0980071	−	0.555826i
$225$		0			0
$226$	0.675242	+	3.82949i	0.0449164	+	0.254734i
$227$	−3.01257	+	6.98392i	−0.199951	+	0.463539i	−0.988460	−	0.151485i	$-0.951594\pi$
$227$	−3.01257	+	6.98392i	−0.199951	+	0.463539i	0.788508	+	0.615024i	$0.210854\pi$
$228$		0			0
$229$	−15.1813	+	3.59803i	−1.00321	+	0.237765i	−0.699216	−	0.714910i	$-0.746468\pi$
$229$	−15.1813	+	3.59803i	−1.00321	+	0.237765i	−0.303991	+	0.952675i	$0.598319\pi$
$230$	0.0457866	+	0.0485310i	0.00301908	+	0.00320004i
$231$		0			0
$232$	−0.733806	−	0.985673i	−0.0481768	−	0.0647126i
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	−0.127647	−	0.991820i	$-0.540742\pi$
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	0.954586	+	0.297935i	$0.0962979\pi$
$234$		0			0
$235$	4.05310	+	3.40095i	0.264395	+	0.221854i
$236$	0.506574	−	8.69755i	0.0329752	−	0.566162i
$237$		0			0
$238$	0.0120941	+	0.0280372i	0.000783943	+	0.00181738i
$239$	16.1641	−	10.6313i	1.04557	−	0.687682i	0.0941436	−	0.995559i	$-0.469989\pi$
$239$	16.1641	−	10.6313i	1.04557	−	0.687682i	0.951426	+	0.307876i	$0.0996184\pi$
$240$		0			0
$241$	−1.65339	−	5.52271i	−0.106504	−	0.355749i	0.888079	−	0.459691i	$-0.152040\pi$
$241$	−1.65339	−	5.52271i	−0.106504	−	0.355749i	−0.994583	+	0.103941i	$0.966855\pi$
$242$	−17.9062			−1.15105
$243$		0			0
$244$	−2.64910			−0.169591
$245$	−1.31642	−	4.39714i	−0.0841027	−	0.280923i
$246$		0			0
$247$	16.0290	−	10.5425i	1.01990	−	0.670800i
$248$	−7.75521	−	17.9786i	−0.492457	−	1.14164i
$249$		0			0
$250$	0.338063	−	5.80433i	0.0213810	−	0.367098i
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	0.972813	−	0.231591i	$-0.0743930\pi$
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	−0.0591449	+	0.998249i	$0.518837\pi$
$252$		0			0
$253$	0.490197	−	0.411324i	0.0308184	−	0.0258597i
$254$	−4.28355	−	5.75380i	−0.268774	−	0.361026i
$255$		0			0
$256$	6.41622	+	6.80080i	0.401014	+	0.425050i
$257$	17.6323	−	4.17892i	1.09987	−	0.260674i	0.359683	−	0.933075i	$-0.382885\pi$
$257$	17.6323	−	4.17892i	1.09987	−	0.260674i	0.740187	+	0.672401i	$0.234737\pi$
$258$		0			0
$259$	3.33891	−	7.74046i	0.207470	−	0.480969i
$260$	−1.32520	−	7.51557i	−0.0821853	−	0.466096i
$261$		0			0
$262$	1.67595	−	9.50479i	0.103541	−	0.587208i
$263$	7.24297	+	4.76377i	0.446621	+	0.293747i	0.752827	−	0.658218i	$-0.228690\pi$
$263$	7.24297	+	4.76377i	0.446621	+	0.293747i	−0.306207	+	0.951965i	$0.599060\pi$
$264$		0			0
$265$	5.50953	−	7.40059i	0.338448	−	0.454615i
$266$	−0.210132	−	3.60782i	−0.0128840	−	0.221210i
$267$		0			0
$268$	2.89726	−	3.07091i	0.176978	−	0.187586i
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	−0.643607	−	0.765356i	$-0.722563\pi$
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	0.984621	+	0.174702i	$0.0558962\pi$
$270$		0			0
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	0.978147	−	0.207912i	$-0.0666669\pi$
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	−0.669131	+	0.743144i	$0.733334\pi$
$272$	0.0439683	+	0.0104207i	0.00266597	+	0.000631847i
$273$		0			0
$274$	3.22661	+	1.62046i	0.194926	+	0.0978957i
$275$	−24.9887	−	2.92076i	−1.50688	−	0.176129i
$276$		0			0
$277$	−1.16354	+	0.584354i	−0.0699106	+	0.0351104i	−0.483411	−	0.875394i	$-0.660602\pi$
$277$	−1.16354	+	0.584354i	−0.0699106	+	0.0351104i	0.413500	+	0.910504i	$0.364306\pi$
$278$	−2.60319	+	0.947485i	−0.156129	+	0.0568264i
$279$		0			0
$280$	−3.10276	−	1.12931i	−0.185425	−	0.0674894i
$281$	−6.36648	+	0.744134i	−0.379792	+	0.0443913i	−0.303847	−	0.952721i	$-0.598271\pi$
$281$	−6.36648	+	0.744134i	−0.379792	+	0.0443913i	−0.0759447	+	0.997112i	$0.524197\pi$
$282$		0			0
$283$	5.48286	−	18.3140i	0.325922	−	1.08866i	−0.625361	−	0.780336i	$-0.715048\pi$
$283$	5.48286	−	18.3140i	0.325922	−	1.08866i	0.951283	−	0.308319i	$-0.0997666\pi$
$284$	−0.961030	+	3.21006i	−0.0570267	+	0.190482i
$285$		0			0
$286$	21.5826	−	2.52264i	1.27620	−	0.149167i
$287$	−6.02001	−	2.19110i	−0.355350	−	0.129337i
$288$		0			0
$289$	15.9739	−	5.81402i	0.939640	−	0.342001i
$290$	−0.292398	+	0.146848i	−0.0171702	+	0.00862320i
$291$		0			0
$292$	−12.7611	−	1.49156i	−0.746787	−	0.0872869i
$293$	1.63183	+	0.819535i	0.0953324	+	0.0478777i	0.495826	−	0.868422i	$-0.334865\pi$
$293$	1.63183	+	0.819535i	0.0953324	+	0.0478777i	−0.400494	+	0.916299i	$0.631161\pi$
$294$		0			0
$295$	−5.18474	−	1.22881i	−0.301868	−	0.0715439i
$296$	6.91625	+	11.9793i	0.401999	+	0.696283i
$297$		0			0
$298$	6.38629	−	11.0614i	0.369948	−	0.640769i
$299$	−0.376425	+	0.398987i	−0.0217692	+	0.0230740i
$300$		0			0
$301$	0.116920	+	2.00744i	0.00673916	+	0.115707i
$302$	1.24468	−	1.67190i	0.0716234	−	0.0962069i
$303$		0			0
$304$	−4.46825	−	2.93881i	−0.256272	−	0.168553i
$305$	−0.281340	+	1.59556i	−0.0161095	+	0.0913614i
$306$		0			0
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	−0.964483	−	0.264145i	$-0.914910\pi$
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	0.815975	−	0.578087i	$-0.196201\pi$
$308$	−5.46087	+	12.6597i	−0.311162	+	0.721355i
$309$		0			0
$310$	−5.07303	+	1.20233i	−0.288129	+	0.0682878i
$311$	14.1776	+	15.0274i	0.803937	+	0.852123i	0.991497	−	0.130130i	$-0.0415394\pi$
$311$	14.1776	+	15.0274i	0.803937	+	0.852123i	−0.187560	+	0.982253i	$0.560058\pi$
$312$		0			0
$313$	13.3306	+	17.9062i	0.753492	+	1.01212i	0.999086	+	0.0427428i	$0.0136096\pi$
$313$	13.3306	+	17.9062i	0.753492	+	1.01212i	−0.245594	+	0.969373i	$0.578983\pi$
$314$	1.77717	−	1.49122i	0.100291	−	0.0841545i
$315$		0			0
$316$	14.9003	+	12.5028i	0.838208	+	0.703340i
$317$	0.660533	−	11.3409i	0.0370992	−	0.636969i	−0.927593	−	0.373591i	$-0.878126\pi$
$317$	0.660533	−	11.3409i	0.0370992	−	0.636969i	0.964693	−	0.263378i	$-0.0848367\pi$
$318$		0			0
$319$	1.24295	+	2.88148i	0.0695918	+	0.161332i
$320$	0.778516	−	0.512038i	0.0435204	−	0.0286238i
$321$		0			0
$322$	0.0296346	+	0.0989865i	0.00165147	+	0.00551630i
$323$	0.112971			0.00628586
$324$		0			0
$325$	21.5663			1.19628
$326$	−3.82594	−	12.7795i	−0.211899	−	0.707794i
$327$		0			0
$328$	8.78275	−	5.77650i	0.484946	−	0.318954i
$329$	3.24541	+	7.52371i	0.178925	+	0.414795i
$330$		0			0
$331$	−0.837706	+	14.3829i	−0.0460445	+	0.790553i	0.893698	+	0.448670i	$0.148102\pi$
$331$	−0.837706	+	14.3829i	−0.0460445	+	0.790553i	−0.939742	+	0.341884i	$0.888935\pi$
$332$	21.0571	+	17.6690i	1.15566	+	0.969714i
$333$		0			0
$334$	−10.0259	+	8.41273i	−0.548593	+	0.460324i
$335$	−1.54192	−	2.07116i	−0.0842441	−	0.113159i
$336$		0			0
$337$	6.79901	+	7.20653i	0.370366	+	0.392565i	0.885573	−	0.464501i	$-0.153766\pi$
$337$	6.79901	+	7.20653i	0.370366	+	0.392565i	−0.515207	+	0.857066i	$0.672285\pi$
$338$	−9.56536	+	2.26703i	−0.520287	+	0.123310i
$339$		0			0
$340$	0.0177988	−	0.0412624i	0.000965278	−	0.00223777i
$341$	8.68281	+	49.2427i	0.470201	+	2.66664i
$342$		0			0
$343$	3.00981	−	17.0695i	0.162514	−	0.921665i
$344$	−2.75675	−	1.81314i	−0.148634	−	0.0977580i
$345$		0			0
$346$	−2.49197	+	3.34730i	−0.133969	+	0.179952i
$347$	−0.196427	−	3.37252i	−0.0105448	−	0.181046i	−0.999468	−	0.0326179i	$-0.989616\pi$
$347$	−0.196427	−	3.37252i	−0.0105448	−	0.181046i	0.988923	−	0.148428i	$-0.0474215\pi$
$348$		0			0
$349$	0.912656	−	0.967359i	0.0488534	−	0.0517815i	−0.702486	−	0.711698i	$-0.747927\pi$
$349$	0.912656	−	0.967359i	0.0488534	−	0.0517815i	0.751339	+	0.659916i	$0.229408\pi$
$350$	2.03123	−	3.51819i	0.108574	−	0.188055i
$351$		0			0
$352$	−17.6986	−	30.6549i	−0.943340	−	1.63391i
$353$	−11.4757	−	2.71979i	−0.610789	−	0.144760i	−0.0864312	−	0.996258i	$-0.527546\pi$
$353$	−11.4757	−	2.71979i	−0.610789	−	0.144760i	−0.524357	+	0.851498i	$0.675694\pi$
$354$		0			0
$355$	1.83136	+	0.919745i	0.0971987	+	0.0488150i
$356$	21.3657	+	2.49729i	1.13238	+	0.132356i
$357$		0			0
$358$	−2.09321	+	1.05125i	−0.110630	+	0.0555603i
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.949058	−	0.315102i	$-0.897961\pi$
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.524477	+	0.851425i	$0.675739\pi$
$360$		0			0
$361$	5.28976	+	1.92531i	0.278408	+	0.101332i
$362$	−12.8232	+	1.49882i	−0.673972	+	0.0787760i
$363$		0			0
$364$	3.38960	−	11.3220i	0.177663	−	0.593437i
$365$	−2.25362	+	7.52763i	−0.117960	+	0.394014i
$366$		0			0
$367$	7.97273	−	0.931879i	0.416173	−	0.0486437i	0.0945701	−	0.995518i	$-0.469852\pi$
$367$	7.97273	−	0.931879i	0.416173	−	0.0486437i	0.321603	+	0.946875i	$0.395778\pi$
$368$	0.143687	+	0.0522978i	0.00749021	+	0.00272621i
$369$		0			0
$370$	3.46107	−	1.25973i	0.179933	−	0.0654901i
$371$	12.7684	−	6.41256i	0.662905	−	0.332923i
$372$		0			0
$373$	2.97358	+	0.347562i	0.153966	+	0.0179961i	0.192727	−	0.981252i	$-0.438267\pi$
$373$	2.97358	+	0.347562i	0.153966	+	0.0179961i	−0.0387606	+	0.999249i	$0.512341\pi$
$374$	0.114342	+	0.0574249i	0.00591251	+	0.00296937i
$375$		0			0
$376$	−13.0827	−	3.10067i	−0.674691	−	0.159905i
$377$	−1.34501	−	2.32963i	−0.0692716	−	0.119982i
$378$		0			0
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	−0.428992	−	0.903308i	$-0.641131\pi$
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	0.996784	−	0.0801362i	$-0.0255355\pi$
$380$	−3.64986	+	3.86863i	−0.187234	+	0.198456i
$381$		0			0
$382$	0.784019	+	13.4611i	0.0401139	+	0.688729i
$383$	−8.57378	+	11.5166i	−0.438100	+	0.588470i	−0.965259	−	0.261297i	$-0.915850\pi$
$383$	−8.57378	+	11.5166i	−0.438100	+	0.588470i	0.527159	+	0.849767i	$0.323257\pi$
$384$		0			0
$385$	7.04501	+	4.63358i	0.359047	+	0.236149i
$386$	1.25926	−	7.14162i	0.0640947	−	0.363499i
$387$		0			0
$388$	1.87760	+	10.6484i	0.0953206	+	0.540590i
$389$	7.22054	−	16.7391i	0.366096	−	0.848706i	−0.631228	−	0.775597i	$-0.717449\pi$
$389$	7.22054	−	16.7391i	0.366096	−	0.848706i	0.997324	−	0.0731085i	$-0.0232919\pi$
$390$		0			0
$391$	−0.00314292		0.000744886i	−0.000158944		3.76705e-5i
$392$	8.00422	+	8.48398i	0.404274	+	0.428506i
$393$		0			0
$394$	−9.57698	−	12.8641i	−0.482481	−	0.648085i
$395$	9.11293	−	7.64665i	0.458521	−	0.384745i
$396$		0			0
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	0.669061	−	0.743208i	$-0.266697\pi$
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	−0.615735	+	0.787953i	$0.711141\pi$
$398$	0.343666	−	5.90052i	0.0172264	−	0.295766i
$399$		0			0
$400$	−2.38116	−	5.52015i	−0.119058	−	0.276007i
$401$	18.4528	−	12.1366i	0.921490	−	0.606074i	0.00234714	−	0.999997i	$-0.499253\pi$
$401$	18.4528	−	12.1366i	0.921490	−	0.606074i	0.919143	+	0.393923i	$0.128883\pi$
$402$		0			0
$403$	−12.2930	−	41.0616i	−0.612360	−	2.04542i
$404$	−13.4026			−0.666803
$405$		0			0
$406$	−0.506722			−0.0251482
$407$	−10.1313	−	33.8408i	−0.502189	−	1.67743i
$408$		0			0
$409$	−0.482395	+	0.317276i	−0.0238529	+	0.0156883i	−0.561379	−	0.827559i	$-0.689729\pi$
$409$	−0.482395	+	0.317276i	−0.0238529	+	0.0156883i	0.537527	+	0.843247i	$0.319359\pi$
$410$	−1.10866	−	2.57015i	−0.0547526	−	0.126931i
$411$		0			0
$412$	−0.459793	+	7.89435i	−0.0226524	+	0.388927i
$413$	−6.32124	−	5.30415i	−0.311048	−	0.261000i
$414$		0			0
$415$	12.8784	−	10.8062i	0.632175	−	0.530458i
$416$	18.1194	+	24.3386i	0.888377	+	1.19330i
$417$		0			0
$418$	−10.3924	−	11.0153i	−0.508309	−	0.538776i
$419$	12.2911	−	2.91303i	0.600457	−	0.142311i	0.0808646	−	0.996725i	$-0.474232\pi$
$419$	12.2911	−	2.91303i	0.600457	−	0.142311i	0.519593	+	0.854414i	$0.326084\pi$
$420$		0			0
$421$	8.48642	−	19.6737i	0.413603	−	0.958839i	−0.576319	−	0.817225i	$-0.695511\pi$
$421$	8.48642	−	19.6737i	0.413603	−	0.958839i	0.989922	−	0.141614i	$-0.0452292\pi$
$422$	0.855151	+	4.84980i	0.0416281	+	0.236085i
$423$		0			0
$424$	−4.07126	+	23.0892i	−0.197718	+	1.12131i
$425$	0.106100	+	0.0697829i	0.00514659	+	0.00338497i
$426$		0			0
$427$	−1.49832	+	2.01259i	−0.0725088	+	0.0973963i
$428$	−0.892458	−	15.3229i	−0.0431386	−	0.740661i
$429$		0			0
$430$	−0.602917	+	0.639055i	−0.0290752	+	0.0308179i
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	−0.807145	−	0.590353i	$-0.798989\pi$
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	0.914833	+	0.403832i	$0.132322\pi$
$432$		0			0
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	0.735182	−	0.677870i	$-0.237097\pi$
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	−0.954644	+	0.297751i	$0.903763\pi$
$434$	−7.85636	−	1.86199i	−0.377118	−	0.0893785i
$435$		0			0
$436$	17.5533	+	8.81562i	0.840652	+	0.422191i
$437$	0.379703	+	0.0443809i	0.0181637	+	0.00212303i
$438$		0			0
$439$	2.54563	−	1.27847i	0.121496	−	0.0610178i	−0.387013	−	0.922074i	$-0.626493\pi$
$439$	2.54563	−	1.27847i	0.121496	−	0.0610178i	0.508509	+	0.861057i	$0.330197\pi$
$440$	−13.0019	+	4.73230i	−0.619841	+	0.225604i
$441$		0			0
$442$	−0.103067	−	0.0375133i	−0.00490239	−	0.00178432i
$443$	−12.2879	+	1.43625i	−0.583816	+	0.0682383i	−0.402874	−	0.915255i	$-0.631989\pi$
$443$	−12.2879	+	1.43625i	−0.583816	+	0.0682383i	−0.180942	+	0.983494i	$0.557915\pi$
$444$		0			0
$445$	3.77320	−	12.6033i	0.178867	−	0.597456i
$446$	0.145250	−	0.485170i	0.00687781	−	0.0229735i
$447$		0			0
$448$	1.43329	−	0.167528i	0.0677167	−	0.00791495i
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.693495	−	0.720461i	$-0.256070\pi$
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.0681449	+	0.997675i	$0.478292\pi$
$450$		0			0
$451$	−25.2264	+	9.18166i	−1.18786	+	0.432347i
$452$	7.91993	−	3.97754i	0.372522	−	0.187088i
$453$		0			0
$454$	−5.11169	−	0.597471i	−0.239903	−	0.0280407i
$455$	−6.45930	−	3.24398i	−0.302817	−	0.152080i
$456$		0			0
$457$	0.860915	+	0.204041i	0.0402719	+	0.00954461i	0.250702	−	0.968064i	$-0.419338\pi$
$457$	0.860915	+	0.204041i	0.0402719	+	0.00954461i	−0.210431	+	0.977609i	$0.567487\pi$
$458$	−5.27840	−	9.14246i	−0.246644	−	0.427199i
$459$		0			0
$460$	0.0760334	−	0.131694i	0.00354507	−	0.00614025i
$461$	−10.4527	+	11.0792i	−0.486831	+	0.516011i	−0.923493	−	0.383615i	$-0.874679\pi$
$461$	−10.4527	+	11.0792i	−0.486831	+	0.516011i	0.436662	+	0.899626i	$0.356161\pi$
$462$		0			0
$463$	−1.95582	−	33.5801i	−0.0908945	−	1.56060i	−0.668145	−	0.744031i	$-0.732912\pi$
$463$	−1.95582	−	33.5801i	−0.0908945	−	1.56060i	0.577251	−	0.816567i	$-0.304126\pi$
$464$	−0.447792	+	0.601489i	−0.0207882	+	0.0279234i
$465$		0			0
$466$	9.31525	+	6.12674i	0.431521	+	0.283816i
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	0.907890	+	0.419207i	$0.137692\pi$
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	−0.996515	+	0.0834093i	$0.973419\pi$
$468$		0			0
$469$	−0.694378	−	3.93802i	−0.0320634	−	0.181841i
$470$	−1.41799	+	3.28726i	−0.0654069	+	0.151630i
$471$		0			0
$472$	13.1753	−	3.12260i	0.606442	−	0.143729i
$473$	5.78246	+	6.12905i	0.265878	+	0.281814i
$474$		0			0
$475$	−8.97541	−	12.0561i	−0.411820	−	0.553170i
$476$	0.0533110	−	0.0447333i	0.00244351	−	0.00205035i
$477$		0			0
$478$	10.0282	+	8.41465i	0.458679	+	0.384877i
$479$	−0.693250	+	11.9026i	−0.0316754	+	0.543846i	0.944723	+	0.327869i	$0.106331\pi$
$479$	−0.693250	+	11.9026i	−0.0316754	+	0.543846i	−0.976399	+	0.215977i	$0.930706\pi$
$480$		0			0
$481$	11.9935	+	27.8042i	0.546859	+	1.26776i
$482$	3.25903	−	2.14350i	0.148445	−	0.0976337i
$483$		0			0
$484$	11.7047	+	39.0964i	0.532032	+	1.77711i
$485$	6.61294			0.300278
$486$		0			0
$487$	38.2435			1.73298			0.866489	−	0.499196i	$-0.166371\pi$
$487$	38.2435			1.73298			0.866489	+	0.499196i	$0.166371\pi$
$488$	−1.18081	−	3.94417i	−0.0534526	−	0.178544i
$489$		0			0
$490$	2.59481	−	1.70663i	0.117222	−	0.0770979i
$491$	−1.67921	−	3.89284i	−0.0757815	−	0.175681i	0.876114	−	0.482104i	$-0.160127\pi$
$491$	−1.67921	−	3.89284i	−0.0757815	−	0.175681i	−0.951896	+	0.306423i	$0.900868\pi$
$492$		0			0
$493$	0.000921013	−	0.0158132i	4.14803e−5	−	0.000712190i
$494$	9.94438	+	8.34432i	0.447419	+	0.375429i
$495$		0			0
$496$	−9.15292	+	7.68021i	−0.410978	+	0.344852i
$497$	1.89522	+	2.54572i	0.0850121	+	0.114191i
$498$		0			0
$499$	−25.6682	−	27.2067i	−1.14906	−	1.21794i	−0.972313	−	0.233682i	$-0.924923\pi$
$499$	−25.6682	−	27.2067i	−1.14906	−	1.21794i	−0.176752	−	0.984255i	$-0.556559\pi$
$500$	−12.8942	+	3.05597i	−0.576644	+	0.136667i
$501$		0			0
$502$	−5.06420	+	11.7401i	−0.226026	+	0.523988i
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	0.983455	−	0.181154i	$-0.0579833\pi$
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	−0.986104	+	0.166132i	$0.946872\pi$
$504$		0			0
$505$	−1.42338	+	8.07239i	−0.0633396	+	0.359217i
$506$	0.361754	+	0.237929i	0.0160819	+	0.0105773i
$507$		0			0
$508$	−9.76284	+	13.1138i	−0.433156	+	0.581830i
$509$	−0.363632	−	6.24332i	−0.0161177	−	0.276730i	−0.996732	−	0.0807816i	$-0.974258\pi$
$509$	−0.363632	−	6.24332i	−0.0161177	−	0.276730i	0.980614	−	0.195949i	$-0.0627787\pi$
$510$		0			0
$511$	−8.35080	+	8.85134i	−0.369418	+	0.391560i
$512$	7.73462	−	13.3968i	0.341825	−	0.592059i
$513$		0			0
$514$	6.13058	+	10.6185i	0.270408	+	0.468361i
$515$	4.70595	+	1.11533i	0.207369	+	0.0491473i
$516$		0			0
$517$	30.6834	+	15.4098i	1.34946	+	0.677722i
$518$	5.66542	+	0.662193i	0.248924	+	0.0290951i
$519$		0			0
$520$	10.5990	−	5.32302i	0.464797	−	0.233430i
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.895119	−	0.445827i	$-0.852910\pi$
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.399129	+	0.916895i	$0.630687\pi$
$522$		0			0
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.137870	−	0.990450i	$-0.544026\pi$
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.742264	+	0.670108i	$0.766248\pi$
$524$	−21.8483	+	2.55370i	−0.954447	+	0.111559i
$525$		0			0
$526$	−1.68235	+	5.61945i	−0.0733541	+	0.245020i
$527$	0.0723866	−	0.241788i	0.00315321	−	0.0105325i
$528$		0			0
$529$	22.8336	−	2.66887i	0.992766	−	0.116038i
$530$	5.86635	+	2.13518i	0.254818	+	0.0927461i
$531$		0			0
$532$	−7.73997	+	2.81712i	−0.335570	+	0.122138i
$533$	20.5643	−	10.3278i	0.890737	−	0.447345i
$534$		0			0
$535$	−9.32379	−	1.08979i	−0.403102	−	0.0471159i
$536$	5.86360	+	2.94481i	0.253269	+	0.127196i
$537$		0			0
$538$	7.36492	+	1.74552i	0.317524	+	0.0752547i
$539$	−14.8933	−	25.7960i	−0.641500	−	1.11111i
$540$		0			0
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	−0.861955	−	0.506985i	$-0.830760\pi$
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	0.870039	+	0.492983i	$0.164093\pi$
$542$	−4.72422	+	5.00738i	−0.202922	+	0.215085i
$543$		0			0
$544$	0.0103888	+	0.178368i	0.000445415	+	0.00764748i
$545$	7.17386	−	9.63616i	0.307294	−	0.412768i
$546$		0			0
$547$	5.57872	+	3.66918i	0.238529	+	0.156883i	0.663146	−	0.748490i	$-0.269221\pi$
$547$	5.57872	+	3.66918i	0.238529	+	0.156883i	−0.424617	+	0.905373i	$0.639591\pi$
$548$	1.42899	−	8.10422i	0.0610436	−	0.346195i
$549$		0			0
$550$	−2.95609	−	16.7648i	−0.126048	−	0.714854i
$551$	−0.742553	+	1.72143i	−0.0316338	+	0.0733355i
$552$		0			0
$553$	17.9263	−	4.24861i	0.762304	−	0.180669i
$554$	−0.604586	−	0.640823i	−0.0256864	−	0.0272260i
$555$		0			0
$556$	3.77036	+	5.06448i	0.159899	+	0.214782i
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	−0.690290	−	0.723533i	$-0.742517\pi$
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	0.592674	+	0.805443i	$0.298072\pi$
$558$		0			0
$559$	−5.53318	−	4.64289i	−0.234028	−	0.196373i
$560$	−0.117157	+	2.01151i	−0.00495079	+	0.0850017i
$561$		0			0
$562$	−1.71785	−	3.98242i	−0.0724631	−	0.167988i
$563$	−27.4131	+	18.0299i	−1.15533	+	0.759870i	−0.974664	−	0.223675i	$-0.928194\pi$
$563$	−27.4131	+	18.0299i	−1.15533	+	0.759870i	−0.180662	+	0.983545i	$0.557824\pi$
$564$		0			0
$565$	−1.55456	−	5.19261i	−0.0654010	−	0.218455i
$566$	12.9354			0.543715
$567$		0			0
$568$	−5.20773			−0.218511
$569$	7.49905	+	25.0486i	0.314376	+	1.05009i	0.958482	+	0.285154i	$0.0920446\pi$
$569$	7.49905	+	25.0486i	0.314376	+	1.05009i	−0.644105	+	0.764937i	$0.722770\pi$
$570$		0			0
$571$	0.669019	−	0.440021i	0.0279976	−	0.0184143i	−0.535433	−	0.844578i	$-0.679852\pi$
$571$	0.669019	−	0.440021i	0.0279976	−	0.0184143i	0.563431	+	0.826163i	$0.309481\pi$
$572$	−19.6158	−	45.4744i	−0.820176	−	1.90138i
$573$		0			0
$574$	0.252046	−	4.32745i	0.0105202	−	0.180624i
$575$	0.329195	+	0.276227i	0.0137284	+	0.0115195i
$576$		0			0
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.369395	+	0.929273i	$0.620435\pi$
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.979300	+	0.202416i	$0.935121\pi$
$578$	6.86864	+	9.22619i	0.285698	+	0.383759i
$579$		0			0
$580$	0.511759	+	0.542433i	0.0212496	+	0.0225233i
$581$	25.3334	−	6.00414i	1.05101	−	0.249094i
$582$		0			0
$583$	23.7148	−	54.9772i	0.982168	−	2.27692i
$584$	−3.46737	−	19.6644i	−0.143481	−	0.813721i
$585$		0			0
$586$	−0.214557	+	1.21681i	−0.00886326	+	0.0502661i
$587$	11.1494	+	7.33310i	0.460186	+	0.302669i	0.758352	−	0.651845i	$-0.226005\pi$
$587$	11.1494	+	7.33310i	0.460186	+	0.302669i	−0.298166	+	0.954514i	$0.596375\pi$
$588$		0			0
$589$	−17.8383	+	23.9610i	−0.735015	+	0.987297i
$590$	−0.209634	−	3.59928i	−0.00863051	−	0.148180i
$591$		0			0
$592$	5.79259	−	6.13978i	0.238074	−	0.252344i
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	−0.259644	−	0.965704i	$-0.583605\pi$
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	0.966147	−	0.257994i	$-0.0830615\pi$
$594$		0			0
$595$	−0.0212812	−	0.0368601i	−0.000872443	−	0.00151112i
$596$	−28.3260	−	6.71338i	−1.16028	−	0.274991i
$597$		0			0
$598$	−0.331679	−	0.166575i	−0.0135633	−	0.00681177i
$599$	−39.7896	−	4.65074i	−1.62576	−	0.190024i	−0.746169	−	0.665757i	$-0.768109\pi$
$599$	−39.7896	−	4.65074i	−1.62576	−	0.190024i	−0.879590	+	0.475733i	$0.842183\pi$
$600$		0			0
$601$	−38.5925	+	19.3819i	−1.57422	+	0.790603i	−0.999613	−	0.0278267i	$-0.991141\pi$
$601$	−38.5925	+	19.3819i	−1.57422	+	0.790603i	−0.574607	+	0.818430i	$0.694845\pi$
$602$	−1.27856	+	0.465357i	−0.0521101	+	0.0189665i
$603$		0			0
$604$	−4.46403	−	1.62477i	−0.181639	−	0.0661111i
$605$	24.7909	−	2.89764i	1.00789	−	0.117806i
$606$		0			0
$607$	−5.05347	+	16.8798i	−0.205114	+	0.685129i	0.792090	+	0.610404i	$0.208993\pi$
$607$	−5.05347	+	16.8798i	−0.205114	+	0.685129i	−0.997204	+	0.0747248i	$0.976192\pi$
$608$	6.06495	−	20.2583i	0.245966	−	0.821585i
$609$		0			0
$610$	−1.08886	+	0.127269i	−0.0440866	+	0.00515298i
$611$	−27.6577	−	10.0666i	−1.11891	−	0.407250i
$612$		0			0
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.240641	−	0.970614i	$-0.422642\pi$
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.808241	+	0.588852i	$0.200420\pi$
$614$	9.06077	−	4.55049i	0.365663	−	0.183643i
$615$		0			0
$616$	−21.2828	−	2.48760i	−0.857507	−	0.100228i
$617$	−3.94054	−	1.97901i	−0.158640	−	0.0796720i	0.367708	−	0.929941i	$-0.380143\pi$
$617$	−3.94054	−	1.97901i	−0.158640	−	0.0796720i	−0.526348	+	0.850269i	$0.676439\pi$
$618$		0			0
$619$	−24.3417	−	5.76908i	−0.978375	−	0.231879i	−0.289834	−	0.957077i	$-0.593600\pi$
$619$	−24.3417	−	5.76908i	−0.978375	−	0.231879i	−0.688541	+	0.725198i	$0.741748\pi$
$620$	5.94125	+	10.2905i	0.238606	+	0.413278i
$621$		0			0
$622$	−6.98959	+	12.1063i	−0.280257	+	0.485420i
$623$	13.9816	−	14.8196i	0.560160	−	0.593735i
$624$		0			0
$625$	−0.723768	−	12.4266i	−0.0289507	−	0.497065i
$626$	−9.02002	+	12.1160i	−0.360513	+	0.484252i
$627$		0			0
$628$	−4.41761	−	2.90551i	−0.176282	−	0.115942i
$629$	−0.0309624	+	0.175596i	−0.00123455	+	0.00700148i
$630$		0			0
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	0.993924	+	0.110066i	$0.0351062\pi$
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	−0.896339	+	0.443370i	$0.853783\pi$
$632$	−11.9735	+	27.7576i	−0.476279	+	1.10414i
$633$		0			0
$634$	7.47951	−	1.77268i	0.297049	−	0.0704020i
$635$	6.86161	+	7.27288i	0.272295	+	0.288616i
$636$		0			0
$637$	15.2474	+	20.4808i	0.604124	+	0.811479i
$638$	−1.62660	+	1.36488i	−0.0643978	+	0.0540362i
$639$		0			0
$640$	−7.87383	−	6.60693i	−0.311241	−	0.261162i
$641$	1.98908	−	34.1512i	0.0785639	−	1.34889i	−0.696750	−	0.717314i	$-0.745371\pi$
$641$	1.98908	−	34.1512i	0.0785639	−	1.34889i	0.775314	−	0.631576i	$-0.217592\pi$
$642$		0			0
$643$	−5.34174	−	12.3835i	−0.210658	−	0.488359i	0.779825	−	0.625998i	$-0.215308\pi$
$643$	−5.34174	−	12.3835i	−0.210658	−	0.488359i	−0.990483	+	0.137639i	$0.956049\pi$
$644$	0.196756	−	0.129409i	0.00775328	−	0.00509941i
$645$		0			0
$646$	0.0219233	+	0.0732290i	0.000862562	+	0.00288116i
$647$	−3.19249			−0.125510			−0.0627548	−	0.998029i	$-0.519989\pi$
$647$	−3.19249			−0.125510			−0.0627548	+	0.998029i	$0.519989\pi$
$648$		0			0
$649$	−34.5785			−1.35733
$650$	4.18520	+	13.9795i	0.164157	+	0.548323i
$651$		0			0
$652$	−25.4020	+	16.7071i	−0.994818	+	0.654302i
$653$	12.7409	+	29.5367i	0.498589	+	1.15586i	0.962819	+	0.270146i	$0.0870718\pi$
$653$	12.7409	+	29.5367i	0.498589	+	1.15586i	−0.464230	+	0.885715i	$0.653669\pi$
$654$		0			0
$655$	−0.782235	+	13.4305i	−0.0305645	+	0.524772i
$656$	−4.91404	−	4.12337i	−0.191861	−	0.160991i
$657$		0			0
$658$	−4.24715	+	3.56378i	−0.165571	+	0.138931i
$659$	−8.71506	−	11.7064i	−0.339490	−	0.456015i	0.599289	−	0.800532i	$-0.295450\pi$
$659$	−8.71506	−	11.7064i	−0.339490	−	0.456015i	−0.938780	+	0.344518i	$0.888042\pi$
$660$		0			0
$661$	5.34701	+	5.66750i	0.207975	+	0.220440i	0.822962	−	0.568097i	$-0.192320\pi$
$661$	5.34701	+	5.66750i	0.207975	+	0.220440i	−0.614987	+	0.788537i	$0.710839\pi$
$662$	−9.48572	+	2.24816i	−0.368673	+	0.0873771i
$663$		0			0
$664$	−16.9209	+	39.2270i	−0.656658	+	1.52230i
$665$	0.874754	+	4.96098i	0.0339215	+	0.192378i
$666$		0			0
$667$	0.00930786	−	0.0527875i	0.000360402	−	0.00204394i
$668$	24.9220	+	16.3914i	0.964260	+	0.634204i
$669$		0			0
$670$	1.04332	−	1.40143i	0.0403071	−	0.0541418i
$671$	0.611343	+	10.4963i	0.0236006	+	0.405207i
$672$		0			0
$673$	−5.50205	+	5.83183i	−0.212088	+	0.224801i	−0.824681	−	0.565598i	$-0.808645\pi$
$673$	−5.50205	+	5.83183i	−0.212088	+	0.224801i	0.612592	+	0.790399i	$0.290127\pi$
$674$	−3.35193	+	5.80572i	−0.129112	+	0.223628i
$675$		0			0
$676$	11.2024	+	19.4031i	0.430862	+	0.746274i
$677$	−8.28940	−	1.96462i	−0.318588	−	0.0755067i	0.0682108	−	0.997671i	$-0.478271\pi$
$677$	−8.28940	−	1.96462i	−0.318588	−	0.0755067i	−0.386798	+	0.922164i	$0.626419\pi$
$678$		0			0
$679$	9.15182	+	4.59622i	0.351215	+	0.176387i
$680$	0.0693678	+	0.00810794i	0.00266013	+	0.000310925i
$681$		0			0
$682$	−30.2347	+	15.1844i	−1.15775	+	0.581443i
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	−0.0695940	−	0.997575i	$-0.522170\pi$
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	0.587917	+	0.808921i	$0.299948\pi$
$684$		0			0
$685$	−4.72942	−	1.72137i	−0.180702	−	0.0657701i
$686$	11.6487	−	1.36154i	0.444751	−	0.0519839i
$687$		0			0
$688$	−0.577478	+	1.92891i	−0.0220161	+	0.0735390i
$689$	−14.7199	+	49.1680i	−0.560785	+	1.87315i
$690$		0			0
$691$	−36.2228	+	4.23384i	−1.37798	+	0.161063i	−0.772610	−	0.634881i	$-0.781049\pi$
$691$	−36.2228	+	4.23384i	−1.37798	+	0.161063i	−0.605371	+	0.795944i	$0.706975\pi$
$692$	8.93742	+	3.25296i	0.339750	+	0.123659i
$693$		0			0
$694$	2.14799	−	0.781805i	0.0815366	−	0.0296769i
$695$	3.45076	−	1.73304i	0.130895	−	0.0657378i
$696$		0			0
$697$	0.134588	+	0.0157311i	0.00509789	+	0.000595857i
$698$	0.804166	+	0.403867i	0.0304381	+	0.0152866i
$699$		0			0
$700$	−9.00937	−	2.13526i	−0.340522	−	0.0807053i
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	0.941807	−	0.336153i	$-0.109126\pi$
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	−0.762021	+	0.647553i	$0.775793\pi$
$702$		0			0
$703$	10.5517	−	18.2761i	0.397966	−	0.689298i
$704$	4.14970	−	4.39842i	0.156398	−	0.165772i
$705$		0			0
$706$	−0.463995	−	7.96648i	−0.0174627	−	0.299823i
$707$	−7.58044	+	10.1823i	−0.285092	+	0.382945i
$708$		0			0
$709$	−9.99222	−	6.57198i	−0.375266	−	0.246816i	0.347840	−	0.937554i	$-0.386915\pi$
$709$	−9.99222	−	6.57198i	−0.375266	−	0.246816i	−0.723105	+	0.690738i	$0.757286\pi$
$710$	−0.240792	+	1.36560i	−0.00903677	+	0.0512501i
$711$		0			0
$712$	5.80535	+	32.9238i	0.217565	+	1.23387i
$713$	0.338284	−	0.784231i	0.0126688	−	0.0293697i
$714$		0			0
$715$	−29.4725	+	6.98512i	−1.10221	+	0.261229i
$716$	3.66357	+	3.88316i	0.136914	+	0.145120i
$717$		0			0
$718$	−12.0052	−	16.1257i	−0.448029	−	0.601807i
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	−0.284135	−	0.958784i	$-0.591706\pi$
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	0.894879	+	0.446310i	$0.147262\pi$
$720$		0			0
$721$	5.73749	+	4.81433i	0.213675	+	0.179295i
$722$	−0.221472	+	3.80252i	−0.00824232	+	0.141515i
$723$		0			0
$724$	11.6546	+	27.0185i	0.433141	+	1.00413i
$725$	−1.76073	+	1.15805i	−0.0653920	+	0.0430090i
$726$		0			0
$727$	2.26034	+	7.55006i	0.0838313	+	0.280016i	0.989619	−	0.143716i	$-0.0459051\pi$
$727$	2.26034	+	7.55006i	0.0838313	+	0.280016i	−0.905788	+	0.423732i	$0.860720\pi$
$728$	18.3679			0.680760
$729$		0			0
$730$	−5.31685			−0.196785
$731$	−0.0121984	−	0.0407456i	−0.000451175	−	0.00150703i
$732$		0			0
$733$	−29.0944	+	19.1357i	−1.07463	+	0.706794i	−0.958112	−	0.286395i	$-0.907543\pi$
$733$	−29.0944	+	19.1357i	−1.07463	+	0.706794i	−0.116516	+	0.993189i	$0.537173\pi$
$734$	2.15126	+	4.98718i	0.0794045	+	0.184080i
$735$		0			0
$736$	−0.0351552	+	0.603591i	−0.00129584	+	0.0222487i
$737$	−12.8363	−	10.7709i	−0.472829	−	0.396751i
$738$		0			0
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.237772	−	0.971321i	$-0.423583\pi$
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.997853	−	0.0654916i	$-0.0208615\pi$
$740$	−5.01288	−	6.73346i	−0.184277	−	0.247527i
$741$		0			0
$742$	6.63457	+	7.03224i	0.243563	+	0.258161i
$743$	−20.7769	+	4.92421i	−0.762229	+	0.180652i	−0.593305	−	0.804978i	$-0.702177\pi$
$743$	−20.7769	+	4.92421i	−0.762229	+	0.180652i	−0.168924	+	0.985629i	$0.554029\pi$
$744$		0			0
$745$	−7.05175	+	16.3478i	−0.258356	+	0.598937i
$746$	0.351765	+	1.99496i	0.0128790	+	0.0730407i
$747$		0			0
$748$	0.0506397	−	0.287192i	0.00185157	−	0.0105008i
$749$	−12.1460	−	7.98854i	−0.443805	−	0.291895i
$750$		0			0
$751$	2.70404	−	3.63215i	0.0986718	−	0.132539i	−0.750045	−	0.661387i	$-0.769968\pi$
$751$	2.70404	−	3.63215i	0.0986718	−	0.132539i	0.848717	+	0.528848i	$0.177376\pi$
$752$	0.477058	+	8.19078i	0.0173965	+	0.298687i
$753$		0			0
$754$	1.24908	−	1.32395i	0.0454887	−	0.0482152i
$755$	−1.45269	+	2.51614i	−0.0528689	+	0.0915716i
$756$		0			0
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	−0.997529	−	0.0702583i	$-0.977618\pi$
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	0.437919	−	0.899014i	$-0.355716\pi$
$758$	14.5555	+	3.44973i	0.528681	+	0.125300i
$759$		0			0
$760$	−7.38676	−	3.70977i	−0.267946	−	0.134567i
$761$	−3.55461	−	0.415474i	−0.128854	−	0.0150609i	0.0514212	−	0.998677i	$-0.483625\pi$
$761$	−3.55461	−	0.415474i	−0.128854	−	0.0150609i	−0.180276	+	0.983616i	$0.557699\pi$
$762$		0			0
$763$	16.6255	−	8.34966i	0.601885	−	0.302278i
$764$	28.8785	−	10.5109i	1.04479	−	0.380271i
$765$		0			0
$766$	−9.12904	−	3.32270i	−0.329846	−	0.120054i
$767$	29.4405	−	3.44110i	1.06303	−	0.124251i
$768$		0			0
$769$	4.18876	−	13.9914i	0.151051	−	0.504544i	−0.848652	−	0.528952i	$-0.822585\pi$
$769$	4.18876	−	13.9914i	0.151051	−	0.504544i	0.999702	+	0.0244085i	$0.00777023\pi$
$770$	−1.63637	+	5.46587i	−0.0589708	+	0.196976i
$771$		0			0
$772$	−16.4162	+	1.91877i	−0.590831	+	0.0690582i
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.657184	−	0.753730i	$-0.271747\pi$
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.0189442	+	0.999821i	$0.493970\pi$
$774$		0			0
$775$	−31.5543	+	11.4848i	−1.13346	+	0.412547i
$776$	−15.0171	+	7.54188i	−0.539083	+	0.270738i
$777$		0			0
$778$	12.2517	+	1.43202i	0.439246	+	0.0513404i
$779$	−14.3319	−	7.19773i	−0.513492	−	0.257885i
$780$		0			0
$781$	12.9408	+	3.06702i	0.463057	+	0.109747i
$782$	−0.00109277	−	0.00189273i	−3.90772e−5	−	6.76838e-5i
$783$		0			0
$784$	3.55882	−	6.16407i	0.127101	−	0.220145i
$785$	−2.21915	+	2.35216i	−0.0792049	+	0.0839523i
$786$		0			0
$787$	0.787575	+	13.5221i	0.0280740	+	0.482012i	0.982817	+	0.184581i	$0.0590928\pi$
$787$	0.787575	+	13.5221i	0.0280740	+	0.482012i	−0.954743	+	0.297431i	$0.903870\pi$
$788$	−21.8274	+	29.3193i	−0.777568	+	1.04446i
$789$		0			0
$790$	6.72513	+	4.42319i	0.239269	+	0.157370i
$791$	1.45763	−	8.26666i	0.0518275	−	0.293929i
$792$		0			0
$793$	−1.56505	−	8.87585i	−0.0555766	−	0.315191i
$794$	−0.371719	+	0.861743i	−0.0131918	+	0.0305821i
$795$		0			0
$796$	−13.1079	+	3.10662i	−0.464595	+	0.110111i
$797$	−20.5872	−	21.8212i	−0.729237	−	0.772946i	0.251588	−	0.967834i	$-0.419047\pi$
$797$	−20.5872	−	21.8212i	−0.729237	−	0.772946i	−0.980825	+	0.194888i	$0.937566\pi$
$798$		0			0
$799$	−0.103495	−	0.139018i	−0.00366138	−	0.00491809i
$800$	18.2098	−	15.2799i	0.643814	−	0.540225i
$801$		0			0
$802$	11.4481	+	9.60610i	0.404247	+	0.339203i
$803$	−2.96497	+	50.9066i	−0.104632	+	1.79645i
$804$		0			0
$805$	−0.0570470	−	0.132250i	−0.00201064	−	0.00466120i
$806$	24.2310	−	15.9370i	0.853502	−	0.561357i
$807$		0			0
$808$	−5.97404	−	19.9547i	−0.210166	−	0.702003i
$809$	−48.8577			−1.71774			−0.858872	−	0.512190i	$-0.828834\pi$
$809$	−48.8577			−1.71774			−0.858872	+	0.512190i	$0.828834\pi$
$810$		0			0
$811$	−14.0558			−0.493566			−0.246783	−	0.969071i	$-0.579373\pi$
$811$	−14.0558			−0.493566			−0.246783	+	0.969071i	$0.579373\pi$
$812$	0.331227	+	1.10638i	0.0116238	+	0.0388262i
$813$		0			0
$814$	19.9699	−	13.1344i	0.699946	−	0.460362i
$815$	7.36500	+	17.0740i	0.257985	+	0.598075i
$816$		0			0
$817$	−0.292699	+	5.02544i	−0.0102402	+	0.175818i
$818$	−0.299277	−	0.251123i	−0.0104640	−	0.00878032i
$819$		0			0
$820$	−4.88698	+	4.10067i	−0.170661	+	0.143201i
$821$	−19.2557	−	25.8649i	−0.672030	−	0.902692i	0.327075	−	0.944998i	$-0.393937\pi$
$821$	−19.2557	−	25.8649i	−0.672030	−	0.902692i	−0.999105	+	0.0423060i	$0.986530\pi$
$822$		0			0
$823$	22.7018	+	24.0626i	0.791337	+	0.838768i	0.989966	−	0.141307i	$-0.0451304\pi$
$823$	22.7018	+	24.0626i	0.791337	+	0.838768i	−0.198629	+	0.980075i	$0.563649\pi$
$824$	−11.9586	+	2.83424i	−0.416597	+	0.0987353i
$825$		0			0
$826$	2.21150	−	5.12684i	0.0769481	−	0.178386i
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	−0.829604	−	0.558352i	$-0.811434\pi$
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	0.588605	−	0.808421i	$-0.299677\pi$
$828$		0			0
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	0.885797	+	0.464073i	$0.153612\pi$
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	−0.991099	+	0.133125i	$0.957499\pi$
$830$	9.50395	+	6.25085i	0.329887	+	0.216970i
$831$		0			0
$832$	−3.09538	+	4.15782i	−0.107313	+	0.144146i
$833$	0.00874210	+	0.150096i	0.000302896	+	0.00520052i
$834$		0			0
$835$	12.5194	−	13.2697i	0.433250	−	0.459218i
$836$	−17.2576	+	29.8911i	−0.596868	+	1.03381i
$837$		0			0
$838$	4.27349	+	7.40191i	0.147625	+	0.255695i
$839$	38.4211	+	9.10598i	1.32645	+	0.314373i	0.831971	−	0.554819i	$-0.187212\pi$
$839$	38.4211	+	9.10598i	1.32645	+	0.314373i	0.494474	+	0.869192i	$0.335361\pi$
$840$		0			0
$841$	−25.6804	−	12.8972i	−0.885532	−	0.444731i
$842$	14.3997	+	1.68308i	0.496245	+	0.0580027i
$843$		0			0
$844$	10.0301	−	5.03730i	0.345250	−	0.173391i
$845$	12.8763	−	4.68657i	0.442957	−	0.161223i
$846$		0			0
$847$	36.3227	+	13.2204i	1.24806	+	0.454258i
$848$	14.2104	−	1.66096i	0.487987	−	0.0570375i
$849$		0			0
$850$	−0.0246442	+	0.0823174i	−0.000845289	+	0.00282346i
$851$	−0.173050	+	0.578029i	−0.00593209	+	0.0198146i
$852$		0			0
$853$	31.1073	−	3.63592i	1.06509	−	0.124491i	0.434551	−	0.900647i	$-0.356907\pi$
$853$	31.1073	−	3.63592i	1.06509	−	0.124491i	0.630541	+	0.776156i	$0.282833\pi$
$854$	−1.59536	−	0.580662i	−0.0545920	−	0.0198699i
$855$		0			0
$856$	22.4160	−	8.15875i	0.766162	−	0.278860i
$857$	−31.5874	+	15.8638i	−1.07901	+	0.541897i	−0.897284	−	0.441453i	$-0.854463\pi$
$857$	−31.5874	+	15.8638i	−1.07901	+	0.541897i	−0.181721	+	0.983350i	$0.558167\pi$
$858$		0			0
$859$	−28.0616	−	3.27993i	−0.957450	−	0.111910i	−0.377007	−	0.926211i	$-0.623047\pi$
$859$	−28.0616	−	3.27993i	−0.957450	−	0.111910i	−0.580443	+	0.814301i	$0.697121\pi$
$860$	1.78942	+	0.898680i	0.0610187	+	0.0306447i
$861$		0			0
$862$	2.94391	+	0.697720i	0.100270	+	0.0237644i
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	0.896715	−	0.442608i	$-0.145947\pi$
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	−0.831668	+	0.555274i	$0.812613\pi$
$864$		0			0
$865$	2.90843	−	5.03755i	0.0988896	−	0.171282i
$866$	4.24099	−	4.49518i	0.144115	−	0.152752i
$867$		0			0
$868$	1.06997	+	18.3707i	0.0363172	+	0.623543i
$869$	46.1005	−	61.9237i	1.56385	−	2.10062i
$870$		0			0
$871$	12.0008	+	7.89303i	0.406631	+	0.267445i
$872$	−5.30110	+	30.0640i	−0.179518	+	1.01810i
$873$		0			0
$874$	0.0449177	+	0.254741i	0.00151936	+	0.00861674i
$875$	−4.97117	+	11.5245i	−0.168056	+	0.389598i
$876$		0			0
$877$	−33.3655	+	7.90777i	−1.12667	+	0.267026i	−0.751374	−	0.659877i	$-0.770608\pi$
$877$	−33.3655	+	7.90777i	−1.12667	+	0.267026i	−0.375300	+	0.926904i	$0.622460\pi$
$878$	1.32273	+	1.40201i	0.0446399	+	0.0473156i
$879$		0			0
$880$	5.04203	+	6.77262i	0.169967	+	0.228305i
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.331059	+	0.943610i	$0.607406\pi$
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.986762	+	0.162173i	$0.948150\pi$
$882$		0			0
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.0409344	−	0.999162i	$-0.513033\pi$
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.991091	+	0.133190i	$0.957478\pi$
$884$	−0.0145351	+	0.249558i	−0.000488867	+	0.00839353i
$885$		0			0
$886$	−3.31561	−	7.68646i	−0.111390	−	0.258232i
$887$	19.1315	−	12.5830i	0.642374	−	0.422496i	−0.186095	−	0.982532i	$-0.559583\pi$
$887$	19.1315	−	12.5830i	0.642374	−	0.422496i	0.828468	+	0.560036i	$0.189213\pi$
$888$		0			0
$889$	4.44106	+	14.8342i	0.148948	+	0.497523i
$890$	8.90188			0.298392
$891$		0			0
$892$	−1.15427			−0.0386477
$893$	5.88306	+	19.6508i	0.196869	+	0.657588i
$894$		0			0
$895$	2.72791	−	1.79417i	0.0911839	−	0.0599726i
$896$	−6.30476	−	14.6161i	−0.210627	−	0.488289i
$897$		0			0
$898$	−0.675702	+	11.6014i	−0.0225485	+	0.387142i
$899$	3.20854	+	2.69228i	0.107011	+	0.0897927i
$900$		0			0
$901$	−0.231513	+	0.194262i	−0.00771281	+	0.00647182i
$902$	−10.8472	−	14.5703i	−0.361171	−	0.485136i
$903$		0			0
$904$	9.45224	+	10.0188i	0.314377	+	0.333220i
$905$	17.5110	−	4.15018i	0.582085	−	0.137957i
$906$		0			0
$907$	−9.48338	+	21.9850i	−0.314891	+	0.729998i	0.685108	+	0.728441i	$0.259755\pi$
$907$	−9.48338	+	21.9850i	−0.314891	+	0.729998i	−0.999999	+	0.00155714i	$0.999504\pi$
$908$	2.03683	+	11.5514i	0.0675944	+	0.383347i
$909$		0			0
$910$	0.849285	−	4.81654i	0.0281535	−	0.159667i
$911$	−25.7190	−	16.9157i	−0.852110	−	0.560441i	0.0466357	−	0.998912i	$-0.485150\pi$
$911$	−25.7190	−	16.9157i	−0.852110	−	0.560441i	−0.898746	+	0.438470i	$0.855520\pi$
$912$		0			0
$913$	65.1492	−	87.5106i	2.15612	−	2.89618i
$914$	0.0348093	+	0.597652i	0.00115139	+	0.0197686i
$915$		0			0
$916$	−16.5113	+	17.5010i	−0.545550	+	0.578249i
$917$	−10.4172	+	18.0431i	−0.344006	+	0.595835i
$918$		0			0
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	0.958824	+	0.284002i	$0.0916623\pi$
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	−0.233459	+	0.972367i	$0.575004\pi$
$920$	0.229965	+	0.0545028i	0.00758173	+	0.00179690i
$921$		0			0
$922$	−9.21017	−	4.62552i	−0.303321	−	0.152333i
$923$	−11.3231	−	1.32348i	−0.372705	−	0.0435629i
$924$		0			0
$925$	21.1993	−	10.6467i	0.697029	−	0.350061i
$926$	21.3875	−	7.78440i	0.702836	−	0.255811i
$927$		0			0
$928$	−2.78624	−	1.01411i	−0.0914627	−	0.0332897i
$929$	−28.1444	+	3.28960i	−0.923386	+	0.107928i	−0.564481	−	0.825446i	$-0.690924\pi$
$929$	−28.1444	+	3.28960i	−0.923386	+	0.107928i	−0.358905	+	0.933374i	$0.616850\pi$
$930$		0			0
$931$	5.10363	−	17.0473i	0.167265	−	0.558703i
$932$	7.28805	−	24.3438i	0.238728	−	0.797407i
$933$		0			0
$934$	−7.41232	+	0.866376i	−0.242539	+	0.0283487i
$935$	−0.167598	−	0.0610008i	−0.00548105	−	0.00199494i
$936$		0			0
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	−0.129979	−	0.991517i	$-0.541491\pi$
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	0.537765	+	0.843095i	$0.319269\pi$
$938$	2.41792	−	1.21432i	0.0789479	−	0.0396491i
$939$		0			0
$940$	8.10431	+	0.947258i	0.264333	+	0.0308961i
$941$	12.6023	+	6.32910i	0.410822	+	0.206323i	0.642193	−	0.766543i	$-0.278025\pi$
$941$	12.6023	+	6.32910i	0.410822	+	0.206323i	−0.231371	+	0.972866i	$0.574321\pi$
$942$		0			0
$943$	0.446181	+	0.105747i	0.0145296	+	0.00344359i
$944$	−4.13135	−	7.15571i	−0.134464	−	0.232898i
$945$		0			0
$946$	−2.85077	+	4.93768i	−0.0926866	+	0.160538i
$947$	16.6076	−	17.6030i	0.539673	−	0.572020i	−0.398946	−	0.916974i	$-0.630624\pi$
$947$	16.6076	−	17.6030i	0.539673	−	0.572020i	0.938620	+	0.344954i	$0.112105\pi$
$948$		0			0
$949$	−2.54159	−	43.6374i	−0.0825035	−	1.41653i
$950$	6.07311	−	8.15760i	0.197038	−	0.264667i
$951$		0			0
$952$	0.0903646	+	0.0594338i	0.00292874	+	0.00192626i
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	−0.979271	−	0.202555i	$-0.935075\pi$
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	0.989492	+	0.144590i	$0.0461865\pi$
$954$		0			0
$955$	−3.26378	−	18.5098i	−0.105613	−	0.598964i
$956$	11.8175	−	27.3959i	0.382204	−	0.886048i
$957$		0			0
$958$	−7.84998	+	1.86048i	−0.253621	+	0.0601094i
$959$	−5.34876	−	5.66936i	−0.172721	−	0.183073i
$960$		0			0
$961$	21.3412	+	28.6662i	0.688425	+	0.924716i
$962$	−15.6955	+	13.1701i	−0.506044	+	0.424621i
$963$		0			0
$964$	−6.81044	−	5.71464i	−0.219350	−	0.184056i
$965$	−0.587749	+	10.0913i	−0.0189203	+	0.324849i
$966$		0			0
$967$	−0.751265	−	1.74163i	−0.0241591	−	0.0560070i	0.905709	−	0.423899i	$-0.139339\pi$
$967$	−0.751265	−	1.74163i	−0.0241591	−	0.0560070i	−0.929869	+	0.367892i	$0.880080\pi$
$968$	−52.9922	+	34.8535i	−1.70323	+	1.12023i
$969$		0			0
$970$	1.28332	+	4.28659i	0.0412050	+	0.137634i
$971$	27.1629			0.871698			0.435849	−	0.900020i	$-0.356448\pi$
$971$	27.1629			0.871698			0.435849	+	0.900020i	$0.356448\pi$
$972$		0			0
$973$	5.98012			0.191714
$974$	7.42161	+	24.7899i	0.237804	+	0.794320i
$975$		0			0
$976$	−2.09908	+	1.38059i	−0.0671899	+	0.0441915i
$977$	10.1432	+	23.5146i	0.324510	+	0.752298i	0.999890	+	0.0148287i	$0.00472028\pi$
$977$	10.1432	+	23.5146i	0.324510	+	0.752298i	−0.675380	+	0.737470i	$0.736020\pi$
$978$		0			0
$979$	4.96419	−	85.2319i	0.158656	−	2.72402i
$980$	−5.42241	−	4.54994i	−0.173213	−	0.145343i
$981$		0			0
$982$	2.19751	−	1.84393i	0.0701255	−	0.0588423i
$983$	17.3432	+	23.2960i	0.553163	+	0.743026i	0.987482	−	0.157733i	$-0.0504184\pi$
$983$	17.3432	+	23.2960i	0.553163	+	0.743026i	−0.434319	+	0.900759i	$0.643011\pi$
$984$		0			0
$985$	15.3409	+	16.2604i	0.488802	+	0.518100i
$986$	0.0104290	−	0.00247173i	0.000332128	−	7.87158e-5i
$987$		0			0
$988$	11.7187	−	27.1670i	0.372821	−	0.864297i
$989$	−0.0249928	−	0.141741i	−0.000794725	−	0.00450711i
$990$		0			0
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	−0.705671	−	0.708539i	$-0.749354\pi$
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	0.905449	−	0.424456i	$-0.139534\pi$
$992$	−39.4722	−	25.9613i	−1.25324	−	0.824272i
$993$		0			0
$994$	−1.28238	+	1.72253i	−0.0406745	+	0.0546354i
$995$	0.479040	+	8.22481i	0.0151866	+	0.260744i
$996$		0			0
$997$	10.4130	−	11.0372i	0.329784	−	0.349550i	−0.541172	−	0.840912i	$-0.682019\pi$
$997$	10.4130	−	11.0372i	0.329784	−	0.349550i	0.870956	+	0.491362i	$0.163501\pi$
$998$	12.6545	−	21.9182i	0.400571	−	0.693809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.379.6		144
3.2	odd	2		729.2.g.c.379.3		144
9.2	odd	6		729.2.g.d.622.3		144
9.4	even	3		243.2.g.a.208.3		144
9.5	odd	6		81.2.g.a.16.6	✓	144
9.7	even	3		729.2.g.a.622.6		144
81.5	odd	54		729.2.g.d.109.3		144
81.7	even	27		6561.2.a.d.1.27		72
81.22	even	27		243.2.g.a.118.3		144
81.32	odd	54		729.2.g.c.352.3		144
81.49	even	27	inner	729.2.g.b.352.6		144
81.59	odd	54		81.2.g.a.76.6	yes	144
81.74	odd	54		6561.2.a.c.1.46		72
81.76	even	27		729.2.g.a.109.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.6	✓	144	9.5	odd	6
81.2.g.a.76.6	yes	144	81.59	odd	54
243.2.g.a.118.3		144	81.22	even	27
243.2.g.a.208.3		144	9.4	even	3
729.2.g.a.109.6		144	81.76	even	27
729.2.g.a.622.6		144	9.7	even	3
729.2.g.b.352.6		144	81.49	even	27	inner
729.2.g.b.379.6		144	1.1	even	1	trivial
729.2.g.c.352.3		144	81.32	odd	54
729.2.g.c.379.3		144	3.2	odd	2
729.2.g.d.109.3		144	81.5	odd	54
729.2.g.d.622.3		144	9.2	odd	6
6561.2.a.c.1.46		72	81.74	odd	54
6561.2.a.d.1.27		72	81.7	even	27

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.194062 + 0.648213i) q^{2} +(1.28846 - 0.847431i) q^{4} +(-0.373572 - 0.866038i) q^{5} +(0.0849292 - 1.45818i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(-3.65505 - 4.90959i) q^{11} +(3.60053 + 3.81633i) q^{13} +(0.961691 - 0.227925i) q^{14} +(0.579298 - 1.34296i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(-1.21524 - 0.799275i) q^{20} +(2.47315 - 3.32202i) q^{22} +(0.00607888 + 0.104370i) q^{23} +(2.82074 - 2.98981i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(-0.498884 - 0.118238i) q^{29} +(-7.30038 - 3.66639i) q^{31} +(5.74406 + 0.671384i) q^{32} +(-0.0186811 + 0.00938202i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(2.45747 - 0.287237i) q^{38} +(0.648337 - 2.16560i) q^{40} +(1.25791 - 4.20171i) q^{41} +(-1.36737 + 0.159822i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(-5.01303 + 2.51764i) q^{47} +(4.83360 + 0.564967i) q^{49} +(2.48543 + 1.24823i) q^{50} +(7.87320 + 1.86598i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(2.40241 - 2.54641i) q^{56} +(-0.0201713 - 0.346328i) q^{58} +(3.37359 - 4.53152i) q^{59} +(-1.43519 - 0.943940i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(1.96003 - 4.54387i) q^{65} +(2.66387 - 0.631349i) q^{67} +(0.0326960 + 0.0346557i) q^{68} +(-0.556652 - 0.747714i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(-0.227062 + 3.89850i) q^{74} +(-2.23352 - 5.17789i) q^{76} +(-7.46947 + 4.91275i) q^{77} +(3.61740 + 12.0829i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(5.11210 + 17.0756i) q^{83} +(0.0243456 - 0.0160123i) q^{85} +(-0.368953 - 0.855329i) q^{86} +(0.852982 - 14.6451i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(0.0962791 + 0.129325i) q^{92} +(-2.60480 - 2.76093i) q^{94} +(-3.35585 + 0.795351i) q^{95} +(-2.77706 + 6.43795i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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