LMFDB - Embedded newform 729.2.k.a.4.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90833 - 0.0246729i) q^{2} +(1.72970 - 0.0902694i) q^{3} +(1.64178 + 0.0424604i) q^{4} +(0.325467 + 0.0997352i) q^{5} +(-3.30306 + 0.129587i) q^{6} +(0.868282 - 2.16517i) q^{7} +(0.682106 + 0.0264688i) q^{8} +(2.98370 - 0.312277i) q^{9} +O(q^{10})$	\(q+(-1.90833 - 0.0246729i) q^{2} +(1.72970 - 0.0902694i) q^{3} +(1.64178 + 0.0424604i) q^{4} +(0.325467 + 0.0997352i) q^{5} +(-3.30306 + 0.129587i) q^{6} +(0.868282 - 2.16517i) q^{7} +(0.682106 + 0.0264688i) q^{8} +(2.98370 - 0.312277i) q^{9} +(-0.618636 - 0.198358i) q^{10} +(-5.40157 - 3.07222i) q^{11} +(2.84361 - 0.0747585i) q^{12} +(-1.97878 - 4.42900i) q^{13} +(-1.71039 + 4.11044i) q^{14} +(0.571962 + 0.143132i) q^{15} +(-4.58129 - 0.237126i) q^{16} +(-4.50309 - 2.04690i) q^{17} +(-5.70159 + 0.522311i) q^{18} +(2.34282 + 3.41591i) q^{19} +(0.530108 + 0.177562i) q^{20} +(1.30641 - 3.82347i) q^{21} +(10.2322 + 5.99607i) q^{22} +(-0.672522 + 2.05174i) q^{23} +(1.18223 - 0.0157903i) q^{24} +(-4.04559 - 2.73640i) q^{25} +(3.66689 + 8.50080i) q^{26} +(5.13271 - 0.809482i) q^{27} +(1.51746 - 3.51786i) q^{28} +(-5.39631 + 3.45010i) q^{29} +(-1.08796 - 0.287255i) q^{30} +(-1.34259 - 4.94660i) q^{31} +(7.37436 + 0.477357i) q^{32} +(-9.62041 - 4.82641i) q^{33} +(8.54286 + 4.01727i) q^{34} +(0.498541 - 0.618094i) q^{35} +(4.91183 - 0.386000i) q^{36} +(1.42422 + 0.279707i) q^{37} +(-4.38659 - 6.57649i) q^{38} +(-3.82249 - 7.48220i) q^{39} +(0.219363 + 0.0766447i) q^{40} +(-1.31883 + 0.499417i) q^{41} +(-2.58740 + 7.26421i) q^{42} +(7.05209 - 3.09619i) q^{43} +(-8.73772 - 5.27324i) q^{44} +(1.00224 + 0.195944i) q^{45} +(1.33402 - 3.89881i) q^{46} +(-2.79504 + 10.2980i) q^{47} +(-7.94564 + 0.00339465i) q^{48} +(1.12639 + 1.07654i) q^{49} +(7.65279 + 5.32177i) q^{50} +(-7.97375 - 3.13403i) q^{51} +(-3.06066 - 7.35544i) q^{52} +(7.20515 - 7.63701i) q^{53} +(-9.81487 + 1.41812i) q^{54} +(-1.45162 - 1.53863i) q^{55} +(0.649569 - 1.45390i) q^{56} +(4.36072 + 5.69701i) q^{57} +(10.3831 - 6.45078i) q^{58} +(-6.97807 + 1.18396i) q^{59} +(0.932955 + 0.259276i) q^{60} +(-1.34763 + 2.48011i) q^{61} +(2.44005 + 9.47286i) q^{62} +(1.91456 - 6.73138i) q^{63} +(-4.91367 - 0.381921i) q^{64} +(-0.202300 - 1.63884i) q^{65} +(18.2398 + 9.44773i) q^{66} +(-0.0407420 + 0.0211253i) q^{67} +(-7.30614 - 3.55176i) q^{68} +(-0.978050 + 3.60960i) q^{69} +(-0.966630 + 1.16723i) q^{70} +(1.52525 + 1.18216i) q^{71} +(2.04347 - 0.134031i) q^{72} +(0.476852 - 0.152897i) q^{73} +(-2.71097 - 0.568912i) q^{74} +(-7.24465 - 4.36795i) q^{75} +(3.70134 + 5.70764i) q^{76} +(-11.3420 + 9.02780i) q^{77} +(7.10996 + 14.3728i) q^{78} +(3.05305 - 16.0950i) q^{79} +(-1.46741 - 0.534092i) q^{80} +(8.80497 - 1.86349i) q^{81} +(2.52908 - 0.920511i) q^{82} +(-1.35923 - 8.33750i) q^{83} +(2.30719 - 6.22182i) q^{84} +(-1.26146 - 1.11532i) q^{85} +(-13.5341 + 5.73456i) q^{86} +(-9.02254 + 6.45475i) q^{87} +(-3.60313 - 2.23855i) q^{88} +(4.15787 + 1.69868i) q^{89} +(-1.90777 - 0.398654i) q^{90} +(-11.3077 + 0.438790i) q^{91} +(-1.19125 + 3.33995i) q^{92} +(-2.76880 - 8.43493i) q^{93} +(5.58794 - 19.5830i) q^{94} +(0.421823 + 1.34543i) q^{95} +(12.7985 + 0.160004i) q^{96} +(2.50255 - 10.8718i) q^{97} +(-2.12296 - 2.08219i) q^{98} +(-17.0761 - 7.47979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

Coefficient data

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

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

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

$2$	−1.90833	−	0.0246729i	−1.34939	−	0.0174464i	−0.665154	−	0.746706i	$-0.731634\pi$
$2$	−1.90833	−	0.0246729i	−1.34939	−	0.0174464i	−0.684237	+	0.729259i	$0.739865\pi$
$3$	1.72970	−	0.0902694i	0.998641	−	0.0521171i
$3$	1.72970	−	0.0902694i	0.998641	−	0.0521171i
$4$	1.64178	+	0.0424604i	0.820888	+	0.0212302i
$5$	0.325467	+	0.0997352i	0.145553	+	0.0446030i	0.364916	−	0.931040i	$-0.381098\pi$
$5$	0.325467	+	0.0997352i	0.145553	+	0.0446030i	−0.219363	+	0.975643i	$0.570398\pi$
$6$	−3.30306	+	0.129587i	−1.34847	+	0.0529037i
$7$	0.868282	−	2.16517i	0.328180	−	0.818359i	−0.668997	−	0.743265i	$-0.733276\pi$
$7$	0.868282	−	2.16517i	0.328180	−	0.818359i	0.997176	−	0.0750937i	$-0.0239256\pi$
$8$	0.682106	+	0.0264688i	0.241161	+	0.00935814i
$9$	2.98370	−	0.312277i	0.994568	−	0.104092i
$10$	−0.618636	−	0.198358i	−0.195630	−	0.0627262i
$11$	−5.40157	−	3.07222i	−1.62864	−	0.926308i	−0.987266	−	0.159076i	$-0.949148\pi$
$11$	−5.40157	−	3.07222i	−1.62864	−	0.926308i	−0.641370	−	0.767232i	$-0.721633\pi$
$12$	2.84361	−	0.0747585i	0.820879	−	0.0215809i
$13$	−1.97878	−	4.42900i	−0.548815	−	1.22838i	−0.949961	−	0.312368i	$-0.898878\pi$
$13$	−1.97878	−	4.42900i	−0.548815	−	1.22838i	0.401146	−	0.916014i	$-0.368612\pi$
$14$	−1.71039	+	4.11044i	−0.457120	+	1.09856i
$15$	0.571962	+	0.143132i	0.147680	+	0.0369565i
$16$	−4.58129	−	0.237126i	−1.14532	−	0.0592814i
$17$	−4.50309	−	2.04690i	−1.09216	−	0.496447i	−0.214984	−	0.976618i	$-0.568970\pi$
$17$	−4.50309	−	2.04690i	−1.09216	−	0.496447i	−0.877175	+	0.480171i	$0.840575\pi$
$18$	−5.70159	+	0.522311i	−1.34388	+	0.123110i
$19$	2.34282	+	3.41591i	0.537480	+	0.783664i	0.994382	−	0.105853i	$-0.0337571\pi$
$19$	2.34282	+	3.41591i	0.537480	+	0.783664i	−0.456902	+	0.889517i	$0.651041\pi$
$20$	0.530108	+	0.177562i	0.118536	+	0.0397041i
$21$	1.30641	−	3.82347i	0.285083	−	0.834350i
$22$	10.2322	+	5.99607i	2.18151	+	1.27837i
$23$	−0.672522	+	2.05174i	−0.140231	+	0.427818i	−0.995980	−	0.0895716i	$-0.971450\pi$
$23$	−0.672522	+	2.05174i	−0.140231	+	0.427818i	0.855750	+	0.517390i	$0.173096\pi$
$24$	1.18223	−	0.0157903i	0.241321	−	0.00322318i
$25$	−4.04559	−	2.73640i	−0.809118	−	0.547280i
$26$	3.66689	+	8.50080i	0.719136	+	1.66714i
$27$	5.13271	−	0.809482i	0.987791	−	0.155785i
$28$	1.51746	−	3.51786i	0.286773	−	0.664813i
$29$	−5.39631	+	3.45010i	−1.00207	+	0.640668i	−0.934097	−	0.357020i	$-0.883793\pi$
$29$	−5.39631	+	3.45010i	−1.00207	+	0.640668i	−0.0679725	+	0.997687i	$0.521653\pi$
$30$	−1.08796	−	0.287255i	−0.198633	−	0.0524453i
$31$	−1.34259	−	4.94660i	−0.241136	−	0.888436i	−0.977340	−	0.211676i	$-0.932108\pi$
$31$	−1.34259	−	4.94660i	−0.241136	−	0.888436i	0.736204	−	0.676760i	$-0.236616\pi$
$32$	7.37436	+	0.477357i	1.30361	+	0.0843856i
$33$	−9.62041	−	4.82641i	−1.67470	−	0.840170i
$34$	8.54286	+	4.01727i	1.46509	+	0.688956i
$35$	0.498541	−	0.618094i	0.0842688	−	0.104477i
$36$	4.91183	−	0.386000i	0.818638	−	0.0643334i
$37$	1.42422	+	0.279707i	0.234140	+	0.0459835i	0.308406	−	0.951255i	$-0.400205\pi$
$37$	1.42422	+	0.279707i	0.234140	+	0.0459835i	−0.0742660	+	0.997238i	$0.523661\pi$
$38$	−4.38659	−	6.57649i	−0.711598	−	1.06685i
$39$	−3.82249	−	7.48220i	−0.612089	−	1.19811i
$40$	0.219363	+	0.0766447i	0.0346843	+	0.0121186i
$41$	−1.31883	+	0.499417i	−0.205967	+	0.0779958i	−0.454970	−	0.890507i	$-0.650350\pi$
$41$	−1.31883	+	0.499417i	−0.205967	+	0.0779958i	0.249003	+	0.968503i	$0.419897\pi$
$42$	−2.58740	+	7.26421i	−0.399245	+	1.12089i
$43$	7.05209	−	3.09619i	1.07543	−	0.472165i	0.212333	−	0.977197i	$-0.431894\pi$
$43$	7.05209	−	3.09619i	1.07543	−	0.472165i	0.863100	+	0.505032i	$0.168519\pi$
$44$	−8.73772	−	5.27324i	−1.31726	−	0.794971i
$45$	1.00224	+	0.195944i	0.149405	+	0.0292097i
$46$	1.33402	−	3.89881i	0.196690	−	0.574848i
$47$	−2.79504	+	10.2980i	−0.407699	+	1.50212i	0.402202	+	0.915551i	$0.368245\pi$
$47$	−2.79504	+	10.2980i	−0.407699	+	1.50212i	−0.809901	+	0.586566i	$0.800479\pi$
$48$	−7.94564	+	0.00339465i	−1.14685	+	0.000489975i
$49$	1.12639	+	1.07654i	0.160913	+	0.153792i
$50$	7.65279	+	5.32177i	1.08227	+	0.752611i
$51$	−7.97375	−	3.13403i	−1.11655	−	0.438852i
$52$	−3.06066	−	7.35544i	−0.424437	−	1.02002i
$53$	7.20515	−	7.63701i	0.989703	−	1.04902i	−0.00909235	−	0.999959i	$-0.502894\pi$
$53$	7.20515	−	7.63701i	0.989703	−	1.04902i	0.998796	−	0.0490655i	$-0.0156243\pi$
$54$	−9.81487	+	1.41812i	−1.33563	+	0.192982i
$55$	−1.45162	−	1.53863i	−0.195737	−	0.207469i
$56$	0.649569	−	1.45390i	0.0868024	−	0.194285i
$57$	4.36072	+	5.69701i	0.577591	+	0.754587i
$58$	10.3831	−	6.45078i	1.36336	−	0.847029i
$59$	−6.97807	+	1.18396i	−0.908467	+	0.154139i	−0.602700	−	0.797968i	$-0.705909\pi$
$59$	−6.97807	+	1.18396i	−0.908467	+	0.154139i	−0.305767	+	0.952107i	$0.598913\pi$
$60$	0.932955	+	0.259276i	0.120444	+	0.0334724i
$61$	−1.34763	+	2.48011i	−0.172546	+	0.317546i	−0.950472	−	0.310811i	$-0.899400\pi$
$61$	−1.34763	+	2.48011i	−0.172546	+	0.317546i	0.777926	+	0.628356i	$0.216272\pi$
$62$	2.44005	+	9.47286i	0.309887	+	1.20305i
$63$	1.91456	−	6.73138i	0.241212	−	0.848074i
$64$	−4.91367	−	0.381921i	−0.614209	−	0.0477401i
$65$	−0.202300	−	1.63884i	−0.0250923	−	0.203274i
$66$	18.2398	+	9.44773i	2.24517	+	1.16294i
$67$	−0.0407420	+	0.0211253i	−0.00497743	+	0.00258087i	−0.462801	−	0.886462i	$-0.653156\pi$
$67$	−0.0407420	+	0.0211253i	−0.00497743	+	0.00258087i	0.457824	+	0.889043i	$0.348629\pi$
$68$	−7.30614	−	3.55176i	−0.886000	−	0.430714i
$69$	−0.978050	+	3.60960i	−0.117743	+	0.434545i
$70$	−0.966630	+	1.16723i	−0.115534	+	0.139510i
$71$	1.52525	+	1.18216i	0.181014	+	0.140297i	0.699078	−	0.715045i	$-0.253594\pi$
$71$	1.52525	+	1.18216i	0.181014	+	0.140297i	−0.518064	+	0.855342i	$0.673347\pi$
$72$	2.04347	−	0.134031i	0.240825	−	0.0157957i
$73$	0.476852	−	0.152897i	0.0558113	−	0.0178952i	−0.277289	−	0.960787i	$-0.589436\pi$
$73$	0.476852	−	0.152897i	0.0558113	−	0.0178952i	0.333101	+	0.942891i	$0.391905\pi$
$74$	−2.71097	−	0.568912i	−0.315144	−	0.0661347i
$75$	−7.24465	−	4.36795i	−0.836541	−	0.504367i
$76$	3.70134	+	5.70764i	0.424573	+	0.654711i
$77$	−11.3420	+	9.02780i	−1.29254	+	1.02881i
$78$	7.10996	+	14.3728i	0.805045	+	1.62740i
$79$	3.05305	−	16.0950i	0.343494	−	1.81083i	−0.209682	−	0.977770i	$-0.567243\pi$
$79$	3.05305	−	16.0950i	0.343494	−	1.81083i	0.553176	−	0.833064i	$-0.313416\pi$
$80$	−1.46741	−	0.534092i	−0.164061	−	0.0597133i
$81$	8.80497	−	1.86349i	0.978330	−	0.207054i
$82$	2.52908	−	0.920511i	0.279291	−	0.101653i
$83$	−1.35923	−	8.33750i	−0.149195	−	0.915159i	−0.949087	−	0.315015i	$-0.897990\pi$
$83$	−1.35923	−	8.33750i	−0.149195	−	0.915159i	0.799892	−	0.600144i	$-0.204890\pi$
$84$	2.30719	−	6.22182i	0.251735	−	0.678856i
$85$	−1.26146	−	1.11532i	−0.136824	−	0.120973i
$86$	−13.5341	+	5.73456i	−1.45942	+	0.618373i
$87$	−9.02254	+	6.45475i	−0.967318	+	0.692022i
$88$	−3.60313	−	2.23855i	−0.384095	−	0.238630i
$89$	4.15787	+	1.69868i	0.440733	+	0.180059i	0.587694	−	0.809083i	$-0.300036\pi$
$89$	4.15787	+	1.69868i	0.440733	+	0.180059i	−0.146961	+	0.989142i	$0.546949\pi$
$90$	−1.90777	−	0.398654i	−0.201097	−	0.0420219i
$91$	−11.3077	+	0.438790i	−1.18537	+	0.0459977i
$92$	−1.19125	+	3.33995i	−0.124196	+	0.348214i
$93$	−2.76880	−	8.43493i	−0.287111	−	0.874661i
$94$	5.58794	−	19.5830i	0.576352	−	2.01983i
$95$	0.421823	+	1.34543i	0.0432781	+	0.138038i
$96$	12.7985	+	0.160004i	1.30624	+	0.0163303i
$97$	2.50255	−	10.8718i	0.254095	−	1.10386i	−0.676103	−	0.736807i	$-0.736333\pi$
$97$	2.50255	−	10.8718i	0.254095	−	1.10386i	0.930199	−	0.367056i	$-0.119634\pi$
$98$	−2.12296	−	2.08219i	−0.214452	−	0.210333i
$99$	−17.0761	−	7.47979i	−1.71621	−	0.751747i
$100$	−6.52576	−	4.66433i	−0.652576	−	0.466433i
$101$	1.80844	−	12.0738i	0.179946	−	1.20139i	−0.695662	−	0.718370i	$-0.744889\pi$
$101$	1.80844	−	12.0738i	0.179946	−	1.20139i	0.875608	−	0.483023i	$-0.160461\pi$
$102$	15.1392	+	6.17750i	1.49900	+	0.611663i
$103$	0.900115	+	2.52369i	0.0886910	+	0.248666i	0.977987	−	0.208666i	$-0.0669121\pi$
$103$	0.900115	+	2.52369i	0.0886910	+	0.248666i	−0.889296	+	0.457332i	$0.848805\pi$
$104$	−1.23251	−	3.07342i	−0.120857	−	0.301374i
$105$	0.806530	−	1.11412i	0.0787092	−	0.108727i
$106$	−13.9382	+	14.3961i	−1.35380	+	1.39828i
$107$	−1.15154	−	19.7711i	−0.111323	−	1.91135i	−0.344294	−	0.938862i	$-0.611882\pi$
$107$	−1.15154	−	19.7711i	−0.111323	−	1.91135i	0.232971	−	0.972484i	$-0.425155\pi$
$108$	8.46113	−	1.11105i	0.814173	−	0.106911i
$109$	−0.590001	+	10.1299i	−0.0565119	+	0.970271i	0.844248	+	0.535953i	$0.180048\pi$
$109$	−0.590001	+	10.1299i	−0.0565119	+	0.970271i	−0.900760	+	0.434318i	$0.856989\pi$
$110$	2.73221	+	2.97203i	0.260506	+	0.283372i
$111$	2.48871	+	0.355245i	0.236218	+	0.0337183i
$112$	−4.49126	+	9.71339i	−0.424385	+	0.917829i
$113$	3.72156	−	2.73339i	0.350095	−	0.257136i	−0.402783	−	0.915295i	$-0.631957\pi$
$113$	3.72156	−	2.73339i	0.350095	−	0.257136i	0.752878	+	0.658160i	$0.228665\pi$
$114$	−8.18112	−	10.9794i	−0.766232	−	1.02831i
$115$	−0.423515	+	0.600700i	−0.0394930	+	0.0560156i
$116$	−9.00602	+	5.43516i	−0.836188	+	0.504642i
$117$	−7.28717	−	12.5969i	−0.673699	−	1.16458i
$118$	13.3457	−	2.08722i	1.22857	−	0.192144i
$119$	−8.34185	+	7.97268i	−0.764696	+	0.730854i
$120$	0.386350	+	0.112770i	0.0352688	+	0.0102945i
$121$	14.1158	+	23.7352i	1.28325	+	2.15775i
$122$	2.63291	−	4.69961i	0.238372	−	0.425483i
$123$	−2.23610	+	0.982890i	−0.201622	+	0.0886242i
$124$	−1.99419	−	8.17822i	−0.179084	−	0.734426i
$125$	−2.11234	−	2.61889i	−0.188934	−	0.234241i
$126$	−3.81969	+	12.7984i	−0.340285	+	1.14018i
$127$	0.159797	+	8.23911i	0.0141797	+	0.731103i	0.937679	+	0.347503i	$0.112970\pi$
$127$	0.159797	+	8.23911i	0.0141797	+	0.731103i	−0.923499	+	0.383600i	$0.874684\pi$
$128$	−5.35163	−	0.485642i	−0.473022	−	0.0429251i
$129$	11.9185	−	5.99206i	1.04936	−	0.527572i
$130$	0.345620	+	3.13244i	0.0303129	+	0.274734i
$131$	13.1703	−	1.19515i	1.15069	−	0.104421i	0.501577	−	0.865113i	$-0.332753\pi$
$131$	13.1703	−	1.19515i	1.15069	−	0.104421i	0.649113	+	0.760692i	$0.275140\pi$
$132$	−15.5896	−	8.33236i	−1.35690	−	0.725239i
$133$	9.43027	−	2.10664i	0.817708	−	0.182669i
$134$	0.0782703	−	0.0393088i	0.00676152	−	0.00339576i
$135$	1.75126	+	0.248453i	0.150725	+	0.0213834i
$136$	−3.01740	−	1.51540i	−0.258740	−	0.129944i
$137$	12.9530	+	3.24734i	1.10665	+	0.277439i	0.753053	−	0.657960i	$-0.228580\pi$
$137$	12.9530	+	3.24734i	1.10665	+	0.277439i	0.353596	+	0.935398i	$0.384959\pi$
$138$	1.95550	−	6.86418i	0.166463	−	0.584318i
$139$	11.7264	+	1.67897i	0.994622	+	0.142409i	0.619860	−	0.784712i	$-0.287189\pi$
$139$	11.7264	+	1.67897i	0.994622	+	0.142409i	0.374762	+	0.927121i	$0.377724\pi$
$140$	0.844737	−	0.993603i	0.0713933	−	0.0839748i
$141$	−3.90499	+	18.0647i	−0.328859	+	1.52132i
$142$	−2.88152	−	2.29358i	−0.241812	−	0.192473i
$143$	−2.91830	+	30.0028i	−0.244041	+	2.50896i
$144$	−13.7432	+	0.723120i	−1.14527	+	0.0602600i
$145$	−2.10042	+	0.584691i	−0.174430	+	0.0485559i
$146$	−0.913763	+	0.280011i	−0.0756236	+	0.0231739i
$147$	2.04550	+	1.76041i	0.168710	+	0.145196i
$148$	2.32637	+	0.519688i	0.191226	+	0.0427181i
$149$	9.62703	−	2.41351i	0.788677	−	0.197723i	0.172165	−	0.985068i	$-0.444924\pi$
$149$	9.62703	−	2.41351i	0.788677	−	0.197723i	0.616512	+	0.787346i	$0.288545\pi$
$150$	13.7174	+	8.51423i	1.12002	+	0.695184i
$151$	−13.1173	−	15.4289i	−1.06747	−	1.25559i	−0.965390	−	0.260809i	$-0.916011\pi$
$151$	−13.1173	−	15.4289i	−1.06747	−	1.25559i	−0.102078	−	0.994776i	$-0.532549\pi$
$152$	1.50764	+	2.39203i	0.122285	+	0.194019i
$153$	−14.0751	−	4.70114i	−1.13790	−	0.380065i
$154$	21.8669	−	16.9482i	1.76209	−	1.36572i
$155$	0.0563827	−	1.74386i	0.00452877	−	0.140070i
$156$	−5.95798	−	12.4464i	−0.477020	−	0.996509i
$157$	−1.15808	+	9.38163i	−0.0924245	+	0.748735i	0.872939	+	0.487829i	$0.162211\pi$
$157$	−1.15808	+	9.38163i	−0.0924245	+	0.748735i	−0.965364	+	0.260907i	$0.915978\pi$
$158$	−6.22332	+	30.6393i	−0.495101	+	2.43753i
$159$	11.7733	−	13.8601i	0.933686	−	1.09918i
$160$	2.35250	+	0.890847i	0.185981	+	0.0704277i
$161$	3.85844	+	3.23762i	0.304088	+	0.255160i
$162$	−16.8487	+	3.33890i	−1.32376	+	0.262329i
$163$	−8.20001	+	6.88062i	−0.642274	+	0.538932i	−0.904716	−	0.426016i	$-0.859917\pi$
$163$	−8.20001	+	6.88062i	−0.642274	+	0.538932i	0.262441	+	0.964948i	$0.415472\pi$
$164$	−2.18643	+	0.763932i	−0.170731	+	0.0596531i
$165$	−2.64976	−	2.53033i	−0.206284	−	0.196986i
$166$	2.38815	+	15.9442i	0.185356	+	1.23751i
$167$	6.24540	−	12.2377i	0.483284	−	0.946984i	−0.512795	−	0.858511i	$-0.671390\pi$
$167$	6.24540	−	12.2377i	0.483284	−	0.946984i	0.996079	−	0.0884726i	$-0.0281986\pi$
$168$	0.992316	−	2.57343i	0.0765588	−	0.198545i
$169$	−7.02674	+	7.84468i	−0.540518	+	0.603437i
$170$	2.37975	+	2.15951i	0.182519	+	0.165627i
$171$	8.05699	+	9.46046i	0.616133	+	0.723460i
$172$	11.7094	−	4.78382i	0.892834	−	0.364763i
$173$	3.07978	+	0.522544i	0.234151	+	0.0397283i	0.283171	−	0.959070i	$-0.408614\pi$
$173$	3.07978	+	0.522544i	0.234151	+	0.0397283i	−0.0490193	+	0.998798i	$0.515610\pi$
$174$	17.3772	−	12.0952i	1.31736	−	0.916932i
$175$	−9.43749	+	6.38344i	−0.713407	+	0.482542i
$176$	24.0177	+	15.3556i	1.81040	+	1.15747i
$177$	−11.9631	+	2.67780i	−0.899199	+	0.201276i
$178$	−7.89266	−	3.34422i	−0.591580	−	0.250660i
$179$	6.95867	+	14.5528i	0.520115	+	1.08773i	0.979861	+	0.199679i	$0.0639898\pi$
$179$	6.95867	+	14.5528i	0.520115	+	1.08773i	−0.459746	+	0.888050i	$0.652060\pi$
$180$	1.63713	+	0.364252i	0.122025	+	0.0271498i
$181$	10.4104	+	2.89794i	0.773800	+	0.215402i	0.632495	−	0.774564i	$-0.282031\pi$
$181$	10.4104	+	2.89794i	0.773800	+	0.215402i	0.141304	+	0.989966i	$0.454870\pi$
$182$	21.5896	−	0.558361i	1.60033	−	0.0413885i
$183$	−2.10711	+	4.41149i	−0.155762	+	0.326107i
$184$	−0.513039	+	1.38171i	−0.0378217	+	0.101861i
$185$	0.435638	+	0.233080i	0.0320287	+	0.0171364i
$186$	5.07566	+	16.1649i	0.372165	+	1.18527i
$187$	18.0352	+	24.8910i	1.31887	+	1.82021i
$188$	−5.02609	+	16.7883i	−0.366566	+	1.22441i
$189$	2.70397	−	11.8161i	0.196685	−	0.859493i
$190$	−0.771780	−	2.57792i	−0.0559908	−	0.187022i
$191$	5.08765	−	6.65259i	0.368129	−	0.481364i	−0.572931	−	0.819604i	$-0.694194\pi$
$191$	5.08765	−	6.65259i	0.368129	−	0.481364i	0.941060	+	0.338240i	$0.109831\pi$
$192$	−8.53364	−	0.217053i	−0.615862	−	0.0156644i
$193$	10.1853	−	4.78964i	0.733157	−	0.344766i	−0.0224884	−	0.999747i	$-0.507159\pi$
$193$	10.1853	−	4.78964i	0.733157	−	0.344766i	0.755645	+	0.654981i	$0.227323\pi$
$194$	−5.04393	+	20.6852i	−0.362133	+	1.48511i
$195$	−0.497856	−	2.81644i	−0.0356522	−	0.201690i
$196$	1.80357	+	1.81527i	0.128827	+	0.129662i
$197$	12.2618	−	2.40815i	0.873619	−	0.171573i	0.264245	−	0.964456i	$-0.414877\pi$
$197$	12.2618	−	2.40815i	0.873619	−	0.171573i	0.609375	+	0.792882i	$0.291421\pi$
$198$	32.4022	+	14.6952i	2.30272	+	1.04434i
$199$	6.78696	−	3.74489i	0.481115	−	0.265468i	−0.223963	−	0.974598i	$-0.571900\pi$
$199$	6.78696	−	3.74489i	0.481115	−	0.265468i	0.705078	+	0.709130i	$0.250912\pi$
$200$	−2.68709	−	1.97360i	−0.190006	−	0.139554i
$201$	−0.0685643	+	0.0402182i	−0.00483615	+	0.00283677i
$202$	−3.74899	+	22.9962i	−0.263778	+	1.61801i
$203$	2.78455	+	14.6796i	0.195437	+	1.03031i
$204$	−12.9580	−	5.48395i	−0.907244	−	0.383953i
$205$	−0.479045	+	0.0310095i	−0.0334580	+	0.00216580i
$206$	−1.65545	−	4.83823i	−0.115341	−	0.337096i
$207$	−1.36589	+	6.33181i	−0.0949361	+	0.440091i
$208$	8.01513	+	20.7597i	0.555750	+	1.43943i
$209$	−2.16048	−	25.6490i	−0.149444	−	1.77418i
$210$	−1.56661	+	2.10620i	−0.108106	+	0.145342i
$211$	−8.94938	+	13.4171i	−0.616101	+	0.923674i	0.383899	+	0.923375i	$0.374581\pi$
$211$	−8.94938	+	13.4171i	−0.616101	+	0.923674i	−1.00000		0.000299476i	$0.999905\pi$
$212$	12.1535	−	12.2323i	0.834706	−	0.840119i
$213$	2.74494	+	1.90710i	0.188080	+	0.130672i
$214$	1.70970	+	37.7582i	0.116872	+	2.58110i
$215$	2.60402	−	0.304366i	0.177593	−	0.0207576i
$216$	3.52248	−	0.416296i	0.239674	−	0.0283253i
$217$	−11.8760	−	1.38811i	−0.806195	−	0.0942307i
$218$	1.37585	−	19.3167i	0.0931844	−	1.30829i
$219$	0.811008	−	0.307510i	0.0548028	−	0.0207796i
$220$	−2.31791	−	2.58772i	−0.156273	−	0.174464i
$221$	−0.155107	+	23.9945i	−0.0104336	+	1.61405i
$222$	−4.74051	−	0.739327i	−0.318162	−	0.0496204i
$223$	−10.9348	+	9.66798i	−0.732247	+	0.647416i	−0.944014	−	0.329904i	$-0.892983\pi$
$223$	−10.9348	+	9.66798i	−0.732247	+	0.647416i	0.211767	+	0.977320i	$0.432078\pi$
$224$	7.43658	−	15.5523i	0.496878	−	1.03913i
$225$	−12.9253	−	6.90126i	−0.861690	−	0.460084i
$226$	−7.16940	+	5.12438i	−0.476902	+	0.340869i
$227$	6.31727	+	12.3786i	0.419292	+	0.821593i	0.999972	+	0.00746157i	$0.00237511\pi$
$227$	6.31727	+	12.3786i	0.419292	+	0.821593i	−0.580680	+	0.814132i	$0.697213\pi$
$228$	6.91743	+	9.53837i	0.458118	+	0.631694i
$229$	−5.59412	−	7.31484i	−0.369670	−	0.483378i	0.571840	−	0.820365i	$-0.306230\pi$
$229$	−5.59412	−	7.31484i	−0.369670	−	0.483378i	−0.941509	+	0.336987i	$0.890592\pi$
$230$	0.823026	−	1.13588i	0.0542687	−	0.0748979i
$231$	−18.8032	+	16.6392i	−1.23716	+	1.09478i
$232$	−3.77217	+	2.21050i	−0.247655	+	0.145126i
$233$	1.00814	+	4.65409i	0.0660455	+	0.304900i	0.998393	−	0.0566626i	$-0.0180459\pi$
$233$	1.00814	+	4.65409i	0.0660455	+	0.304900i	−0.932348	+	0.361562i	$0.882243\pi$
$234$	13.5955	+	24.2188i	0.888766	+	1.58323i
$235$	−1.93677	+	3.07289i	−0.126341	+	0.200453i
$236$	−11.5067	+	1.64751i	−0.749022	+	0.107244i
$237$	3.82795	−	28.1151i	0.248652	−	1.82628i
$238$	16.1157	−	15.0087i	1.04463	−	0.972867i
$239$	−5.66761	−	10.4304i	−0.366607	−	0.674686i	0.628021	−	0.778196i	$-0.283865\pi$
$239$	−5.66761	−	10.4304i	−0.366607	−	0.674686i	−0.994628	+	0.103510i	$0.966993\pi$
$240$	−2.58638	−	0.791356i	−0.166950	−	0.0510818i
$241$	−7.79823	+	13.1125i	−0.502328	+	0.844648i	−0.999739	−	0.0228670i	$-0.992721\pi$
$241$	−7.79823	+	13.1125i	−0.502328	+	0.844648i	0.497410	+	0.867515i	$0.334284\pi$
$242$	−26.3519	−	45.6429i	−1.69397	−	2.93404i
$243$	15.0617	−	4.01809i	0.966209	−	0.257760i
$244$	−2.31781	+	4.01456i	−0.148383	+	0.257006i
$245$	0.259234	+	0.462720i	0.0165618	+	0.0295621i
$246$	4.29146	−	1.82050i	0.273613	−	0.116071i
$247$	10.4931	−	17.1357i	0.667663	−	1.09032i
$248$	−0.784857	−	3.40964i	−0.0498385	−	0.216512i
$249$	−3.10368	−	14.2987i	−0.196688	−	0.906140i
$250$	3.96642	+	5.04982i	0.250859	+	0.319379i
$251$	−4.77507	−	9.06525i	−0.301400	−	0.572194i	0.686529	−	0.727103i	$-0.259134\pi$
$251$	−4.77507	−	9.06525i	−0.301400	−	0.572194i	−0.987929	+	0.154909i	$0.950492\pi$
$252$	3.42909	−	10.9701i	0.216013	−	0.691053i
$253$	9.93608	−	9.01651i	0.624676	−	0.566863i
$254$	−0.101663	−	15.7269i	−0.00637889	−	0.986791i
$255$	−2.28262	−	1.81529i	−0.142943	−	0.113678i
$256$	20.0050	+	2.07646i	1.25031	+	0.129779i
$257$	−22.4584	+	2.91979i	−1.40091	+	0.182131i	−0.791717	−	0.610887i	$-0.790813\pi$
$257$	−22.4584	+	2.91979i	−1.40091	+	0.182131i	−0.609197	+	0.793019i	$0.708508\pi$
$258$	−22.8922	+	11.1408i	−1.42521	+	0.693593i
$259$	1.84223	−	2.84081i	0.114471	−	0.176519i
$260$	−0.262546	−	2.69920i	−0.0162824	−	0.167398i
$261$	−15.0236	+	11.9792i	−0.929937	+	0.741495i
$262$	−25.1627	+	1.95580i	−1.55455	+	0.120829i
$263$	0.104457	+	0.514275i	0.00644111	+	0.0317115i	0.983081	−	0.183169i	$-0.0586357\pi$
$263$	0.104457	+	0.514275i	0.00644111	+	0.0317115i	−0.976640	+	0.214881i	$0.931064\pi$
$264$	−6.43439	−	3.54676i	−0.396009	−	0.218288i
$265$	3.10671	−	1.76699i	0.190844	−	0.108545i
$266$	−18.0480	+	3.78748i	−1.10660	+	0.232225i
$267$	7.34519	+	2.56287i	0.449518	+	0.156845i
$268$	−0.0677862	+	0.0329531i	−0.00414070	+	0.00201293i
$269$	8.84745	−	11.8842i	0.539438	−	0.724591i	−0.445923	−	0.895071i	$-0.647124\pi$
$269$	8.84745	−	11.8842i	0.539438	−	0.724591i	0.985361	+	0.170480i	$0.0545318\pi$
$270$	−3.33585	−	0.517338i	−0.203013	−	0.0314842i
$271$	−13.9394	−	18.7238i	−0.846757	−	1.13739i	−0.989052	−	0.147568i	$-0.952855\pi$
$271$	−13.9394	−	18.7238i	−0.846757	−	1.13739i	0.142295	−	0.989824i	$-0.454552\pi$
$272$	20.1446	+	10.4452i	1.22144	+	0.633336i
$273$	−19.5193	+	1.77971i	−1.18136	+	0.107713i
$274$	−24.6384	−	6.51657i	−1.48846	−	0.393681i
$275$	13.4457	+	27.2098i	0.810808	+	1.64081i
$276$	−1.75900	+	5.88463i	−0.105880	+	0.354213i
$277$	−13.9370	+	9.69179i	−0.837391	+	0.582323i	−0.909798	−	0.415052i	$-0.863763\pi$
$277$	−13.9370	+	9.69179i	−0.837391	+	0.582323i	0.0724066	+	0.997375i	$0.476932\pi$
$278$	−22.3364	−	3.49335i	−1.33965	−	0.209518i
$279$	−5.55060	−	14.3399i	−0.332306	−	0.858509i
$280$	0.356418	−	0.408409i	0.0213000	−	0.0244071i
$281$	13.0719	−	26.4533i	0.779805	−	1.57807i	−0.0357271	−	0.999362i	$-0.511375\pi$
$281$	13.0719	−	26.4533i	0.779805	−	1.57807i	0.815532	−	0.578711i	$-0.196444\pi$
$282$	7.89770	−	34.3771i	0.470301	−	2.04712i
$283$	11.6415	−	10.0277i	0.692017	−	0.596085i	−0.234600	−	0.972092i	$-0.575378\pi$
$283$	11.6415	−	10.0277i	0.692017	−	0.596085i	0.926617	+	0.376007i	$0.122703\pi$
$284$	2.45393	+	2.00561i	0.145614	+	0.119011i
$285$	0.851076	+	2.28910i	0.0504134	+	0.135595i
$286$	6.30934	−	57.1832i	0.373079	−	3.38131i
$287$	−0.0637927	+	3.28913i	−0.00376556	+	0.194151i
$288$	22.1520	−	0.878554i	1.30532	−	0.0517693i
$289$	4.91010	+	5.62636i	0.288830	+	0.330962i
$290$	4.02271	−	1.06396i	0.236222	−	0.0624778i
$291$	3.34726	−	19.0308i	0.196220	−	1.11561i
$292$	0.789376	−	0.230774i	0.0461948	−	0.0135051i
$293$	−2.37020	+	28.1387i	−0.138469	+	1.64388i	0.494119	+	0.869394i	$0.335491\pi$
$293$	−2.37020	+	28.1387i	−0.138469	+	1.64388i	−0.632588	+	0.774489i	$0.718007\pi$
$294$	−3.86004	−	3.40992i	−0.225122	−	0.198870i
$295$	−2.38921	−	0.310618i	−0.139105	−	0.0180849i
$296$	0.964062	+	0.228487i	0.0560350	+	0.0132805i
$297$	−30.2116	−	11.3963i	−1.75306	−	0.661282i
$298$	−18.4311	+	4.36824i	−1.06768	+	0.253046i
$299$	10.4179	−	1.08135i	0.602485	−	0.0625363i
$300$	−11.7086	−	7.47880i	−0.675998	−	0.431789i
$301$	−0.580601	−	17.9574i	−0.0334653	−	1.03505i
$302$	24.6514	+	29.7670i	1.41853	+	1.71290i
$303$	2.03815	−	21.0473i	0.117089	−	1.20914i
$304$	−9.92312	−	16.2048i	−0.569130	−	0.929410i
$305$	−0.685962	+	0.672787i	−0.0392781	+	0.0385237i
$306$	26.7439	+	9.31859i	1.52884	+	0.532708i
$307$	−11.1420	+	16.2454i	−0.635905	+	0.927172i	−0.999991	−	0.00419337i	$-0.998665\pi$
$307$	−11.1420	+	16.2454i	−0.635905	+	0.927172i	0.364086	+	0.931365i	$0.381381\pi$
$308$	−19.0043	+	14.3400i	−1.08287	+	0.817099i
$309$	1.78474	+	4.28396i	0.101530	+	0.243706i
$310$	−0.150623	+	3.32646i	−0.00855480	+	0.188930i
$311$	−0.436710	−	6.13131i	−0.0247635	−	0.347675i	−0.994590	−	0.103879i	$-0.966875\pi$
$311$	−0.436710	−	6.13131i	−0.0247635	−	0.347675i	0.969826	−	0.243796i	$-0.0783928\pi$
$312$	−2.40930	−	5.20483i	−0.136400	−	0.294665i
$313$	9.34726	+	25.1739i	0.528338	+	1.42291i	0.874633	+	0.484785i	$0.161102\pi$
$313$	9.34726	+	25.1739i	0.528338	+	1.42291i	−0.346295	+	0.938126i	$0.612560\pi$
$314$	2.44146	−	17.8747i	0.137780	−	1.00872i
$315$	1.29448	−	1.99989i	0.0729357	−	0.112681i
$316$	5.69582	−	26.2948i	0.320415	−	1.47920i
$317$	8.42259	+	25.6958i	0.473060	+	1.44322i	0.854804	+	0.518952i	$0.173677\pi$
$317$	8.42259	+	25.6958i	0.473060	+	1.44322i	−0.381744	+	0.924268i	$0.624676\pi$
$318$	−22.8094	+	26.1592i	−1.27908	+	1.46693i
$319$	39.7480	−	2.05734i	2.22546	−	0.115189i
$320$	−1.56115	−	0.614369i	−0.0872707	−	0.0343442i
$321$	−3.77654	−	34.0941i	−0.210786	−	1.90295i
$322$	−7.28330	−	6.27364i	−0.405882	−	0.349616i
$323$	−3.55787	−	20.1777i	−0.197965	−	1.12272i
$324$	14.5349	−	2.68556i	0.807495	−	0.149198i
$325$	−4.11417	+	23.3326i	−0.228213	+	1.29426i
$326$	15.8181	−	12.9282i	0.876082	−	0.716025i
$327$	−0.106100	+	17.5750i	−0.00586737	+	0.971898i
$328$	−0.912801	+	0.305747i	−0.0504010	+	0.0168821i
$329$	19.8701	+	14.9933i	1.09547	+	0.826608i
$330$	4.99418	+	4.89408i	0.274921	+	0.269410i
$331$	10.0075	−	5.35432i	0.550062	−	0.294300i	−0.173185	−	0.984889i	$-0.555406\pi$
$331$	10.0075	−	5.35432i	0.550062	−	0.294300i	0.723247	+	0.690589i	$0.242649\pi$
$332$	−1.87754	−	13.7460i	−0.103043	−	0.754411i
$333$	4.33678	+	0.389812i	0.237654	+	0.0213615i
$334$	−12.2202	+	23.1995i	−0.668660	+	1.26942i
$335$	−0.0153671	+	0.00281218i	−0.000839594	+	0.000153646i
$336$	−6.89170	+	17.2066i	−0.375973	+	0.938699i
$337$	−11.7862	−	12.1735i	−0.642038	−	0.663132i	0.316336	−	0.948647i	$-0.397547\pi$
$337$	−11.7862	−	12.1735i	−0.642038	−	0.663132i	−0.958374	+	0.285515i	$0.907835\pi$
$338$	13.6029	−	14.7969i	0.739899	−	0.804843i
$339$	6.19043	−	5.06388i	0.336218	−	0.275032i
$340$	−2.02367	−	1.88466i	−0.109749	−	0.102210i
$341$	−7.94494	+	30.8442i	−0.430243	+	1.67030i
$342$	−15.1420	−	18.2525i	−0.818783	−	0.986980i
$343$	18.1747	−	8.26142i	0.981342	−	0.446075i
$344$	4.89222	−	1.92527i	0.263771	−	0.103804i
$345$	−0.678327	+	1.07726i	−0.0365199	+	0.0579977i
$346$	−5.86434	−	1.07317i	−0.315269	−	0.0576941i
$347$	1.87183	−	2.38310i	0.100485	−	0.127932i	−0.733568	−	0.679616i	$-0.762146\pi$
$347$	1.87183	−	2.38310i	0.100485	−	0.127932i	0.834053	+	0.551684i	$0.186015\pi$
$348$	−15.0871	+	10.2142i	−0.808751	+	0.547536i
$349$	−7.49201	−	26.2558i	−0.401038	−	1.40544i	−0.856942	−	0.515413i	$-0.827639\pi$
$349$	−7.49201	−	26.2558i	−0.401038	−	1.40544i	0.455904	−	0.890029i	$-0.349316\pi$
$350$	18.1673	−	11.9488i	0.971085	−	0.638692i
$351$	−13.7417	−	21.1310i	−0.733478	−	1.12789i
$352$	−38.3666	−	25.2341i	−2.04495	−	1.34498i
$353$	−3.58220	+	11.4256i	−0.190661	+	0.608126i	0.809129	+	0.587632i	$0.199940\pi$
$353$	−3.58220	+	11.4256i	−0.190661	+	0.608126i	−0.999790	+	0.0204940i	$0.993476\pi$
$354$	22.8955	−	4.81497i	1.21688	−	0.255913i
$355$	0.378516	+	0.536876i	0.0200896	+	0.0284944i
$356$	6.75416	+	2.96539i	0.357970	+	0.157165i
$357$	−13.7092	+	14.5433i	−0.725567	+	0.769714i
$358$	−12.9204	−	27.9433i	−0.682862	−	1.47685i
$359$	−32.2205	−	17.7785i	−1.70053	−	0.938315i	−0.965545	−	0.260237i	$-0.916199\pi$
$359$	−32.2205	−	17.7785i	−1.70053	−	0.938315i	−0.734989	−	0.678079i	$-0.762813\pi$
$360$	0.678448	+	0.160183i	0.0357573	+	0.00844238i
$361$	0.663711	−	1.71905i	0.0349322	−	0.0904766i
$362$	−19.7950	−	5.78707i	−1.04040	−	0.304161i
$363$	26.5586	+	39.7805i	1.39397	+	2.08794i
$364$	−18.5833	+	0.240265i	−0.974030	+	0.0125933i
$365$	0.170449	−	0.00220375i	0.00892169	−	0.000115349i
$366$	4.12990	−	8.36658i	0.215873	−	0.437328i
$367$	8.75097	+	2.55835i	0.456797	+	0.133545i	0.500943	−	0.865480i	$-0.332987\pi$
$367$	8.75097	+	2.55835i	0.456797	+	0.133545i	−0.0441460	+	0.999025i	$0.514057\pi$
$368$	3.56754	−	9.24016i	0.185971	−	0.481676i
$369$	−3.77904	+	1.90195i	−0.196729	+	0.0990117i
$370$	−0.825589	−	0.455541i	−0.0429203	−	0.0236824i
$371$	−10.2794	−	22.2315i	−0.533678	−	1.15420i
$372$	−4.18759	−	13.9658i	−0.217117	−	0.724094i
$373$	19.8348	+	8.70841i	1.02701	+	0.450904i	0.846342	−	0.532640i	$-0.178800\pi$
$373$	19.8348	+	8.70841i	1.02701	+	0.450904i	0.180666	+	0.983544i	$0.442175\pi$
$374$	−33.8030	−	47.9451i	−1.74791	−	2.47918i
$375$	−3.89012	−	4.33921i	−0.200885	−	0.224076i
$376$	−2.17909	+	6.95034i	−0.112378	+	0.358436i
$377$	25.9586	+	17.0732i	1.33694	+	0.879316i
$378$	−5.45160	+	22.4822i	−0.280400	+	1.15636i
$379$	−24.6215	+	16.1938i	−1.26472	+	0.831821i	−0.991497	−	0.130130i	$-0.958461\pi$
$379$	−24.6215	+	16.1938i	−1.26472	+	0.831821i	−0.273225	+	0.961950i	$0.588090\pi$
$380$	0.635410	+	2.22680i	0.0325959	+	0.114232i
$381$	1.02014	+	14.2367i	0.0522634	+	0.729370i
$382$	−9.87304	+	12.5698i	−0.505149	+	0.643126i
$383$	−5.74254	−	1.05088i	−0.293430	−	0.0536977i	0.0312818	−	0.999511i	$-0.490041\pi$
$383$	−5.74254	−	1.05088i	−0.293430	−	0.0536977i	−0.324712	+	0.945813i	$0.605267\pi$
$384$	−9.30054	−	0.356924i	−0.474616	−	0.0182142i
$385$	−4.59182	+	1.80705i	−0.234021	+	0.0920960i
$386$	−19.5551	+	8.88890i	−0.995331	+	0.452433i
$387$	20.0745	−	11.4403i	1.02044	−	0.581545i
$388$	4.57025	−	17.7428i	0.232019	−	0.900753i
$389$	−6.35779	−	5.92105i	−0.322353	−	0.300209i	0.503614	−	0.863929i	$-0.332004\pi$
$389$	−6.35779	−	5.92105i	−0.322353	−	0.300209i	−0.825966	+	0.563720i	$0.809370\pi$
$390$	0.880582	+	5.38698i	0.0445900	+	0.272780i
$391$	7.22815	−	7.86259i	0.365543	−	0.397628i
$392$	0.739824	+	0.764130i	0.0373667	+	0.0385944i
$393$	22.6727	−	3.25612i	1.14368	−	0.164250i
$394$	−23.4590	+	4.29300i	−1.18185	+	0.216278i
$395$	2.59891	−	4.93390i	0.130765	−	0.248252i
$396$	−27.7175	−	13.0052i	−1.39286	−	0.653536i
$397$	−3.41893	−	25.0310i	−0.171591	−	1.25627i	−0.852040	−	0.523476i	$-0.824635\pi$
$397$	−3.41893	−	25.0310i	−0.171591	−	1.25627i	0.680449	−	0.732795i	$-0.261785\pi$
$398$	−13.0441	+	6.97902i	−0.653844	+	0.349826i
$399$	16.1214	−	4.49511i	0.807077	−	0.225037i
$400$	17.8851	+	13.4955i	0.894256	+	0.674777i
$401$	−21.6863	+	7.26393i	−1.08296	+	0.362743i	−0.802213	−	0.597038i	$-0.796344\pi$
$401$	−21.6863	+	7.26393i	−1.08296	+	0.362743i	−0.280749	+	0.959781i	$0.590583\pi$
$402$	0.131836	−	0.0750578i	0.00657536	−	0.00374354i
$403$	−19.2518	+	15.7346i	−0.959000	+	0.783794i
$404$	3.48171	−	19.7458i	0.173221	−	0.982388i
$405$	3.05158	+	0.271663i	0.151634	+	0.0134990i
$406$	−4.95165	−	28.0822i	−0.245746	−	1.39370i
$407$	−6.83368	−	5.88636i	−0.338733	−	0.291776i
$408$	−5.35598	−	2.34880i	−0.265161	−	0.116283i
$409$	−0.261397	−	0.102869i	−0.0129253	−	0.00508657i	0.359729	−	0.933057i	$-0.382869\pi$
$409$	−0.261397	−	0.102869i	−0.0129253	−	0.00508657i	−0.372654	+	0.927970i	$0.621552\pi$
$410$	0.914940	−	0.0473569i	0.0451857	−	0.00233879i
$411$	22.6979	+	4.44765i	1.11960	+	0.219386i
$412$	1.37063	+	4.18155i	0.0675261	+	0.206010i
$413$	−3.49544	+	16.1367i	−0.171999	+	0.794037i
$414$	2.76280	−	12.0495i	0.135784	−	0.592199i
$415$	0.389158	−	2.84914i	0.0191030	−	0.139859i
$416$	−12.4780	−	33.6056i	−0.611786	−	1.64765i
$417$	20.4347	+	1.84558i	1.00069	+	0.0903782i
$418$	3.49007	+	48.9999i	0.170705	+	2.39667i
$419$	1.47678	−	32.6144i	0.0721456	−	1.59332i	−0.566663	−	0.823950i	$-0.691766\pi$
$419$	1.47678	−	32.6144i	0.0721456	−	1.59332i	0.638808	−	0.769366i	$-0.279428\pi$
$420$	1.37145	−	1.79489i	0.0669197	−	0.0875815i
$421$	−31.8561	+	24.0376i	−1.55257	+	1.17152i	−0.635970	+	0.771714i	$0.719400\pi$
$421$	−31.8561	+	24.0376i	−1.55257	+	1.17152i	−0.916600	+	0.399805i	$0.869078\pi$
$422$	17.4094	−	25.3835i	0.847476	−	1.23565i
$423$	−5.12375	+	31.5990i	−0.249125	+	1.53640i
$424$	5.11682	−	5.01854i	0.248495	−	0.243722i
$425$	12.6165	+	20.6032i	0.611989	+	0.999401i
$426$	−5.19119	−	3.70709i	−0.251514	−	0.179609i
$427$	4.19975	+	5.07128i	0.203240	+	0.245417i
$428$	−1.05107	−	32.5086i	−0.0508056	−	1.57136i
$429$	−2.33945	+	52.1592i	−0.112950	+	2.51827i
$430$	−4.97683	+	0.516582i	−0.240004	+	0.0249118i
$431$	16.1667	−	3.83159i	0.778725	−	0.184561i	0.178014	−	0.984028i	$-0.443033\pi$
$431$	16.1667	−	3.83159i	0.778725	−	0.184561i	0.600710	+	0.799467i	$0.294885\pi$
$432$	−23.7064	+	2.49137i	−1.14057	+	0.119866i
$433$	15.3720	+	3.64324i	0.738733	+	0.175083i	0.582721	−	0.812672i	$-0.301988\pi$
$433$	15.3720	+	3.64324i	0.738733	+	0.175083i	0.156012	+	0.987755i	$0.450136\pi$
$434$	22.6291	+	2.94198i	1.08623	+	0.141219i
$435$	−3.58030	+	1.20094i	−0.171662	+	0.0575807i
$436$	−1.39877	+	16.6060i	−0.0669890	+	0.795284i
$437$	−8.58418	+	2.50959i	−0.410637	+	0.120050i
$438$	−1.55526	+	0.566820i	−0.0743130	+	0.0270837i
$439$	−16.6431	+	4.40191i	−0.794333	+	0.210092i	−0.630288	−	0.776361i	$-0.717063\pi$
$439$	−16.6431	+	4.40191i	−0.794333	+	0.210092i	−0.164045	+	0.986453i	$0.552454\pi$
$440$	−0.949435	−	1.08793i	−0.0452626	−	0.0518651i
$441$	3.69700	+	2.86034i	0.176048	+	0.136207i
$442$	0.888011	−	45.7856i	0.0422384	−	2.17780i
$443$	−2.15412	+	19.5233i	−0.102345	+	0.927581i	0.827958	+	0.560790i	$0.189502\pi$
$443$	−2.15412	+	19.5233i	−0.102345	+	0.927581i	−0.930303	+	0.366791i	$0.880456\pi$
$444$	4.07082	+	0.688904i	0.193193	+	0.0326939i
$445$	1.18383	+	0.967548i	0.0561189	+	0.0458662i
$446$	21.1057	−	18.1799i	0.999383	−	0.860842i
$447$	16.4340	−	5.04367i	0.777300	−	0.238557i
$448$	−5.09337	+	10.3073i	−0.240639	+	0.486976i
$449$	14.9236	−	17.1005i	0.704286	−	0.807023i	−0.284131	−	0.958786i	$-0.591705\pi$
$449$	14.9236	−	17.1005i	0.704286	−	0.807023i	0.988417	+	0.151763i	$0.0484950\pi$
$450$	24.4955	+	13.4888i	1.15473	+	0.635867i
$451$	8.65808	+	1.35410i	0.407693	+	0.0637620i
$452$	6.22603	−	4.32959i	0.292848	−	0.203647i
$453$	−24.0817	−	25.5032i	−1.13145	−	1.19825i
$454$	−11.7500	−	23.7782i	−0.551455	−	1.11597i
$455$	−3.72404	−	0.984963i	−0.174586	−	0.0461758i
$456$	2.82368	+	4.00139i	0.132231	+	0.187382i
$457$	8.26707	+	4.28660i	0.386717	+	0.200519i	0.642622	−	0.766183i	$-0.277847\pi$
$457$	8.26707	+	4.28660i	0.386717	+	0.200519i	−0.255905	+	0.966702i	$0.582373\pi$
$458$	10.4949	+	14.0971i	0.490396	+	0.658716i
$459$	−24.7700	−	6.86100i	−1.15616	−	0.320244i
$460$	−0.720822	+	0.968232i	−0.0336085	+	0.0451441i
$461$	21.6978	−	10.5480i	1.01057	−	0.491270i	0.143600	−	0.989636i	$-0.454132\pi$
$461$	21.6978	−	10.5480i	1.01057	−	0.491270i	0.866967	+	0.498366i	$0.166066\pi$
$462$	36.2933	−	31.2891i	1.68852	−	1.45570i
$463$	−28.7988	+	6.04359i	−1.33839	+	0.280870i	−0.819063	−	0.573703i	$-0.805506\pi$
$463$	−28.7988	+	6.04359i	−1.33839	+	0.280870i	−0.519332	+	0.854573i	$0.673819\pi$
$464$	25.5401	−	14.5263i	1.18567	−	0.674366i
$465$	−0.0598920	−	3.02143i	−0.00277743	−	0.140116i
$466$	−1.80903	−	8.90641i	−0.0838018	−	0.412582i
$467$	−37.7389	+	2.93330i	−1.74635	+	0.135737i	−0.910577	−	0.413340i	$-0.864362\pi$
$467$	−37.7389	+	2.93330i	−1.74635	+	0.135737i	−0.835772	+	0.549077i	$0.814979\pi$
$468$	−11.4290	−	20.9907i	−0.528307	−	0.970294i
$469$	0.0103645	+	0.106556i	0.000478587	+	0.00492031i
$470$	3.77180	−	5.81630i	0.173980	−	0.268286i
$471$	−1.15625	+	16.3319i	−0.0532770	+	0.752535i
$472$	−4.79112	+	0.622888i	−0.220529	+	0.0286707i
$473$	−47.6045	−	4.94122i	−2.18886	−	0.227198i
$474$	−7.99867	+	53.5585i	−0.367391	+	2.46002i
$475$	−0.130774	−	20.2303i	−0.00600032	−	0.928228i
$476$	−14.0340	+	12.7351i	−0.643246	+	0.583714i
$477$	19.1132	−	25.0366i	0.875131	−	1.14635i
$478$	10.5583	+	20.0444i	0.482926	+	0.916812i
$479$	1.39671	+	1.77821i	0.0638172	+	0.0812484i	0.817275	−	0.576248i	$-0.195484\pi$
$479$	1.39671	+	1.77821i	0.0638172	+	0.0812484i	−0.753458	+	0.657496i	$0.771615\pi$
$480$	4.14953	+	1.32854i	0.189399	+	0.0606392i
$481$	−1.57939	−	6.86132i	−0.0720140	−	0.312849i
$482$	15.2051	−	24.8305i	0.692574	−	1.13100i
$483$	6.96620	+	5.25180i	0.316973	+	0.238965i
$484$	22.1671	+	39.5673i	1.00760	+	1.79851i
$485$	1.89880	−	3.28881i	0.0862200	−	0.149337i
$486$	−28.8418	+	7.29621i	−1.30829	+	0.330963i
$487$	−13.1822	−	22.8322i	−0.597343	−	1.03463i	−0.993212	−	0.116321i	$-0.962890\pi$
$487$	−13.1822	−	22.8322i	−0.597343	−	1.03463i	0.395869	−	0.918307i	$-0.370443\pi$
$488$	−0.984870	+	1.65603i	−0.0445830	+	0.0749648i
$489$	−13.5624	+	12.6416i	−0.613314	+	0.571673i
$490$	−0.483286	−	0.889417i	−0.0218327	−	0.0401798i
$491$	12.2683	−	11.4256i	0.553661	−	0.515628i	−0.354049	−	0.935227i	$-0.615195\pi$
$491$	12.2683	−	11.4256i	0.553661	−	0.515628i	0.907710	+	0.419599i	$0.137829\pi$
$492$	−3.71290	+	1.51874i	−0.167391	+	0.0684700i
$493$	31.3621	−	4.49037i	1.41248	−	0.202236i
$494$	−20.4471	+	32.4416i	−0.919960	+	1.45962i
$495$	−4.81169	−	4.13751i	−0.216270	−	0.185967i
$496$	4.97782	+	22.9802i	0.223511	+	1.03184i
$497$	3.88393	−	2.27599i	0.174218	−	0.102092i
$498$	5.57005	+	27.3631i	0.249600	+	1.22617i
$499$	−2.39162	+	3.30074i	−0.107063	+	0.147762i	−0.859931	−	0.510411i	$-0.829493\pi$
$499$	−2.39162	+	3.30074i	−0.107063	+	0.147762i	0.752867	+	0.658172i	$0.228670\pi$
$500$	−3.35679	−	4.38932i	−0.150120	−	0.196297i
$501$	9.69796	−	21.7313i	0.433273	−	0.970884i
$502$	8.88874	+	17.4173i	0.396724	+	0.777372i
$503$	−8.82633	+	6.30868i	−0.393546	+	0.281290i	−0.761000	−	0.648752i	$-0.775291\pi$
$503$	−8.82633	+	6.30868i	−0.393546	+	0.281290i	0.367454	+	0.930042i	$0.380230\pi$
$504$	1.48410	−	4.54084i	0.0661072	−	0.202265i
$505$	1.79277	−	3.74927i	0.0797774	−	0.166840i
$506$	−19.1838	+	16.9613i	−0.852822	+	0.754022i
$507$	−11.4460	+	14.2032i	−0.508334	+	0.630787i
$508$	−0.0874846	+	13.5336i	−0.00388150	+	0.600454i
$509$	−19.4854	−	21.7536i	−0.863676	−	0.964212i	0.135973	−	0.990713i	$-0.456584\pi$
$509$	−19.4854	−	21.7536i	−0.863676	−	0.964212i	−0.999649	+	0.0265010i	$0.991563\pi$
$510$	4.31119	+	3.52048i	0.190903	+	0.155890i
$511$	0.0829944	−	1.16523i	0.00367146	−	0.0515465i
$512$	−27.4503	−	3.20848i	−1.21314	−	0.141796i
$513$	14.7901	+	15.6364i	0.653001	+	0.690365i
$514$	42.9300	−	5.01779i	1.89356	−	0.221325i
$515$	0.0412570	+	0.911149i	0.00181800	+	0.0401500i
$516$	19.8219	−	9.33156i	0.872610	−	0.410799i
$517$	46.7353	−	47.0384i	2.05542	−	2.06875i
$518$	−3.58568	+	5.37574i	−0.157546	+	0.236197i
$519$	5.37426	+	0.625833i	0.235904	+	0.0274710i
$520$	−0.0946119	−	1.12322i	−0.00414901	−	0.0492565i
$521$	10.2251	+	26.4836i	0.447969	+	1.16027i	0.954543	+	0.298072i	$0.0963436\pi$
$521$	10.2251	+	26.4836i	0.447969	+	1.16027i	−0.506575	+	0.862196i	$0.669089\pi$
$522$	28.9655	−	22.4896i	1.26779	−	0.984343i
$523$	6.77300	+	19.7948i	0.296163	+	0.865568i	0.989446	+	0.144903i	$0.0462870\pi$
$523$	6.77300	+	19.7948i	0.296163	+	0.865568i	−0.693283	+	0.720665i	$0.743836\pi$
$524$	21.6733	−	1.40296i	0.946805	−	0.0612886i
$525$	−15.7478	+	11.8933i	−0.687289	+	0.519067i
$526$	−0.186650	−	0.983982i	−0.00813833	−	0.0429037i
$527$	−4.07943	+	25.0231i	−0.177703	+	1.09002i
$528$	42.9294	+	24.3924i	1.86826	+	1.06154i
$529$	14.7799	+	10.8554i	0.642603	+	0.471975i
$530$	−5.97223	+	3.29534i	−0.259417	+	0.143140i
$531$	−20.4508	+	5.71169i	−0.887487	+	0.247866i
$532$	15.5718	−	3.05821i	0.675125	−	0.132590i
$533$	4.82159	+	4.85286i	0.208846	+	0.210201i
$534$	−13.9538	−	5.07202i	−0.603840	−	0.219488i
$535$	1.59709	−	6.54969i	0.0690482	−	0.283168i
$536$	−0.0283495	+	0.0133313i	−0.00122451	+	0.000575825i
$537$	13.3501	+	24.5438i	0.576098	+	1.05914i
$538$	−17.1770	+	22.4606i	−0.740555	+	0.968346i
$539$	−2.77692	−	9.27555i	−0.119610	−	0.399526i
$540$	2.86463	+	0.482263i	0.123274	+	0.0207533i
$541$	−8.58630	+	28.6802i	−0.369154	+	1.23306i	0.548659	+	0.836046i	$0.315139\pi$
$541$	−8.58630	+	28.6802i	−0.369154	+	1.23306i	−0.917813	+	0.397014i	$0.870047\pi$
$542$	26.1389	+	36.0752i	1.12276	+	1.54956i
$543$	18.2684	+	4.07281i	0.783974	+	0.174781i
$544$	−32.2303	−	17.2442i	−1.38186	−	0.739338i
$545$	−1.20234	+	3.23811i	−0.0515024	+	0.138705i
$546$	37.2931	−	2.91468i	1.59600	−	0.124737i
$547$	0.311757	−	0.00806282i	0.0133298	−	0.000344741i	−0.0191884	−	0.999816i	$-0.506108\pi$
$547$	0.311757	−	0.00806282i	0.0133298	−	0.000344741i	0.0325182	+	0.999471i	$0.489647\pi$
$548$	21.1280	+	5.88139i	0.902545	+	0.251240i
$549$	−3.24644	+	7.82075i	−0.138555	+	0.333781i
$550$	−24.9875	−	52.2570i	−1.06547	−	2.22824i
$551$	−24.4278	−	10.3504i	−1.04066	−	0.440940i
$552$	−0.762675	+	2.43624i	−0.0324616	+	0.103693i
$553$	−32.1977	−	20.5854i	−1.36918	−	0.875380i
$554$	26.8354	−	18.1512i	1.14013	−	0.771172i
$555$	0.774562	+	0.363832i	0.0328783	+	0.0154438i
$556$	19.1809	+	3.25440i	0.813450	+	0.138017i
$557$	−9.31690	+	3.80637i	−0.394770	+	0.161281i	−0.566888	−	0.823795i	$-0.691853\pi$
$557$	−9.31690	+	3.80637i	−0.394770	+	0.161281i	0.172118	+	0.985076i	$0.444939\pi$
$558$	10.2386	+	27.5022i	0.433432	+	1.16426i
$559$	−27.6676	−	25.1070i	−1.17021	−	1.06191i
$560$	−2.43052	+	2.71345i	−0.102708	+	0.114664i
$561$	33.4424	+	41.4258i	1.41194	+	1.74900i
$562$	−25.5982	+	50.1591i	−1.07979	+	2.11583i
$563$	0.759424	+	5.07022i	0.0320059	+	0.213684i	0.999183	−	0.0404200i	$-0.0128696\pi$
$563$	0.759424	+	5.07022i	0.0320059	+	0.213684i	−0.967177	+	0.254104i	$0.918219\pi$
$564$	−7.17815	+	29.4924i	−0.302254	+	1.24185i
$565$	1.48386	−	0.518456i	0.0624265	−	0.0218116i
$566$	−22.4633	+	18.8489i	−0.944202	+	0.792279i
$567$	3.61042	−	20.6823i	0.151623	−	0.868576i
$568$	1.00909	+	0.846730i	0.0423406	+	0.0355280i
$569$	7.30195	+	2.76511i	0.306114	+	0.115919i	0.502422	−	0.864623i	$-0.332443\pi$
$569$	7.30195	+	2.76511i	0.306114	+	0.115919i	−0.196308	+	0.980542i	$0.562895\pi$
$570$	−1.56765	−	4.38936i	−0.0656618	−	0.183850i
$571$	−1.27200	+	6.26244i	−0.0532316	+	0.262075i	−0.997805	−	0.0662262i	$-0.978904\pi$
$571$	−1.27200	+	6.26244i	−0.0532316	+	0.262075i	0.944573	+	0.328301i	$0.106476\pi$
$572$	−6.06513	+	49.1339i	−0.253596	+	2.05439i
$573$	8.19957	−	11.9662i	0.342542	−	0.499896i
$574$	0.202890	−	6.27517i	0.00846846	−	0.261921i
$575$	8.33514	−	6.46022i	0.347599	−	0.269410i
$576$	−14.7802	+	0.394891i	−0.615842	+	0.0164538i
$577$	14.2538	+	22.6152i	0.593395	+	0.941485i	0.999616	+	0.0277100i	$0.00882148\pi$
$577$	14.2538	+	22.6152i	0.593395	+	0.941485i	−0.406221	+	0.913775i	$0.633154\pi$
$578$	−9.23127	−	10.8581i	−0.383970	−	0.451637i
$579$	17.1852	−	9.20405i	0.714192	−	0.382507i
$580$	−3.47324	+	0.870746i	−0.144218	+	0.0361558i
$581$	−19.2323	−	4.29633i	−0.797892	−	0.178242i
$582$	−6.85722	+	36.2344i	−0.284241	+	1.50197i
$583$	−62.3817	+	19.1161i	−2.58359	+	0.791708i
$584$	0.329311	−	0.0916699i	0.0136270	−	0.00379333i
$585$	−1.11538	−	4.82665i	−0.0461152	−	0.199557i
$586$	5.21739	−	53.6395i	0.215528	−	2.21583i
$587$	−21.2926	−	16.9481i	−0.878839	−	0.699524i	0.0758532	−	0.997119i	$-0.475832\pi$
$587$	−21.2926	−	16.9481i	−0.878839	−	0.699524i	−0.954692	+	0.297595i	$0.903816\pi$
$588$	3.28350	+	2.97706i	0.135409	+	0.122772i
$589$	13.7517	−	16.1752i	0.566630	−	0.666486i
$590$	4.55174	+	0.651711i	0.187392	+	0.0268305i
$591$	20.9919	−	5.27223i	0.863490	−	0.216871i
$592$	−6.45841	−	1.61913i	−0.265439	−	0.0665460i
$593$	−26.6154	−	13.3668i	−1.09296	−	0.548907i	−0.191382	−	0.981516i	$-0.561297\pi$
$593$	−26.6154	−	13.3668i	−1.09296	−	0.548907i	−0.901582	+	0.432609i	$0.857593\pi$
$594$	57.3725	+	22.4933i	2.35402	+	0.922913i
$595$	−3.51015	+	1.76286i	−0.143902	+	0.0722704i
$596$	15.9079	−	3.55368i	0.651613	−	0.145564i
$597$	11.4013	−	7.09017i	0.466626	−	0.290181i
$598$	−19.9075	+	1.80654i	−0.814079	+	0.0738748i
$599$	−3.32801	−	30.1626i	−0.135979	−	1.23241i	−0.847902	−	0.530154i	$-0.822134\pi$
$599$	−3.32801	−	30.1626i	−0.135979	−	1.23241i	0.711923	−	0.702258i	$-0.247825\pi$
$600$	−4.82601	−	3.17116i	−0.197021	−	0.129462i
$601$	23.4871	+	2.13137i	0.958059	+	0.0869405i	0.558263	−	0.829664i	$-0.311468\pi$
$601$	23.4871	+	2.13137i	0.958059	+	0.0869405i	0.399796	+	0.916604i	$0.369081\pi$
$602$	0.664915	+	34.2829i	0.0270999	+	1.39727i
$603$	−0.114965	+	0.0757545i	−0.00468174	+	0.00308496i
$604$	−20.8805	−	25.8878i	−0.849615	−	1.05336i
$605$	2.22698	+	9.13287i	0.0905396	+	0.371304i
$606$	−4.40876	+	40.1149i	−0.179094	+	1.62956i
$607$	14.4719	−	25.8317i	0.587397	−	1.04848i	−0.403644	−	0.914916i	$-0.632256\pi$
$607$	14.4719	−	25.8317i	0.587397	−	1.04848i	0.991041	−	0.133559i	$-0.0426406\pi$
$608$	15.6462	+	26.3085i	0.634536	+	1.06695i
$609$	6.14155	+	25.1399i	0.248868	+	1.01872i
$610$	1.32564	−	1.26697i	0.0536736	−	0.0512983i
$611$	51.1406	−	7.99824i	2.06893	−	0.323574i
$612$	−22.9085	−	8.31585i	−0.926021	−	0.336148i
$613$	39.0663	−	23.5766i	1.57787	−	0.952251i	0.588231	−	0.808693i	$-0.299825\pi$
$613$	39.0663	−	23.5766i	1.57787	−	0.952251i	0.989642	−	0.143558i	$-0.0458544\pi$
$614$	21.6633	−	30.7266i	0.874260	−	1.24002i
$615$	−0.825803	+	0.0968802i	−0.0332996	+	0.00390659i
$616$	−7.97538	+	5.85770i	−0.321337	+	0.236014i
$617$	−11.6966	+	25.2965i	−0.470886	+	1.01840i	0.515941	+	0.856624i	$0.327442\pi$
$617$	−11.6966	+	25.2965i	−0.470886	+	1.01840i	−0.986828	+	0.161776i	$0.948278\pi$
$618$	−3.30017	−	8.21924i	−0.132752	−	0.330626i
$619$	20.4990	+	22.2983i	0.823926	+	0.896245i	0.996047	−	0.0888307i	$-0.0283130\pi$
$619$	20.4990	+	22.2983i	0.823926	+	0.896245i	−0.172121	+	0.985076i	$0.555062\pi$
$620$	0.166613	−	2.86063i	0.00669132	−	0.114886i
$621$	−1.79101	+	11.0754i	−0.0718709	+	0.444441i
$622$	0.682108	+	11.7113i	0.0273500	+	0.469582i
$623$	7.28813	−	7.52758i	0.291993	−	0.301586i
$624$	15.7377	+	35.1845i	0.630013	+	1.40851i
$625$	8.66325	+	21.6029i	0.346530	+	0.864118i
$626$	−17.2165	−	48.2706i	−0.688111	−	1.92928i
$627$	−6.05230	−	44.1699i	−0.241705	−	1.76398i
$628$	−2.29965	+	15.3534i	−0.0917659	+	0.612666i
$629$	−5.84083	−	4.17478i	−0.232889	−	0.166459i
$630$	−2.51964	+	3.78451i	−0.100385	+	0.150778i
$631$	10.4475	+	10.2468i	0.415909	+	0.407920i	0.877809	−	0.479012i	$-0.159005\pi$
$631$	10.4475	+	10.2468i	0.415909	+	0.407920i	−0.461900	+	0.886932i	$0.652832\pi$
$632$	2.50852	−	10.8977i	0.0997834	−	0.433488i
$633$	−14.2686	+	24.0155i	−0.567124	+	0.954528i
$634$	−15.4391	−	49.2438i	−0.613164	−	1.95572i
$635$	−0.769721	+	2.69749i	−0.0305454	+	0.107047i
$636$	19.9177	−	22.2553i	0.789787	−	0.882480i
$637$	2.53912	−	7.11903i	0.100604	−	0.282066i
$638$	−75.9030	+	2.94538i	−3.00503	+	0.116609i
$639$	4.92007	+	3.05091i	0.194635	+	0.120692i
$640$	−1.69334	−	0.691807i	−0.0669353	−	0.0273461i
$641$	30.3519	+	18.8570i	1.19883	+	0.744807i	0.973324	−	0.229435i	$-0.0736878\pi$
$641$	30.3519	+	18.8570i	1.19883	+	0.744807i	0.225504	+	0.974242i	$0.427597\pi$
$642$	6.36567	+	65.1559i	0.251233	+	2.57150i
$643$	9.73680	−	4.12560i	0.383982	−	0.162698i	−0.189570	−	0.981867i	$-0.560709\pi$
$643$	9.73680	−	4.12560i	0.383982	−	0.162698i	0.573551	+	0.819170i	$0.305565\pi$
$644$	6.19723	+	5.47928i	0.244205	+	0.215914i
$645$	4.47669	−	0.761524i	0.176269	−	0.0299850i
$646$	6.29174	+	38.5934i	0.247545	+	1.51844i
$647$	3.53983	−	1.28839i	0.139165	−	0.0506520i	−0.271499	−	0.962439i	$-0.587519\pi$
$647$	3.53983	−	1.28839i	0.139165	−	0.0506520i	0.410664	+	0.911787i	$0.365297\pi$
$648$	6.05524	−	1.03804i	0.237872	−	0.0407780i
$649$	41.3299	+	15.0429i	1.62234	+	0.590484i
$650$	8.42687	−	44.4248i	0.330529	−	1.74248i
$651$	−20.6672	−	1.32896i	−0.810011	−	0.0520861i
$652$	−13.7547	+	10.9483i	−0.538677	+	0.428767i
$653$	14.8862	+	22.9551i	0.582540	+	0.898304i	0.999946	−	0.0104161i	$-0.00331561\pi$
$653$	14.8862	+	22.9551i	0.582540	+	0.898304i	−0.417405	+	0.908720i	$0.637060\pi$
$654$	0.636100	−	33.5362i	0.0248735	−	1.31137i
$655$	4.40568	+	0.924556i	0.172144	+	0.0361254i
$656$	6.16037	−	1.97524i	0.240522	−	0.0771203i
$657$	1.37504	−	0.605108i	0.0536454	−	0.0236075i
$658$	−37.5487	−	29.1024i	−1.46380	−	1.13453i
$659$	6.26048	−	7.55966i	0.243874	−	0.294483i	−0.634041	−	0.773299i	$-0.718605\pi$
$659$	6.26048	−	7.55966i	0.243874	−	0.294483i	0.877915	+	0.478817i	$0.158934\pi$
$660$	−4.24287	−	4.26674i	−0.165154	−	0.166083i
$661$	−1.92429	−	0.935463i	−0.0748464	−	0.0363853i	0.399407	−	0.916774i	$-0.369216\pi$
$661$	−1.92429	−	0.935463i	−0.0748464	−	0.0363853i	−0.474253	+	0.880388i	$0.657282\pi$
$662$	−19.2297	+	9.97089i	−0.747384	+	0.387530i
$663$	1.89768	+	41.5173i	0.0736999	+	1.61240i
$664$	−0.706456	−	5.72303i	−0.0274158	−	0.222097i
$665$	3.27935	+	0.254891i	0.127168	+	0.00988425i
$666$	−8.26638	−	0.850889i	−0.320316	−	0.0329713i
$667$	−3.44959	−	13.3921i	−0.133568	−	0.518545i
$668$	10.7732	−	19.8264i	0.416826	−	0.767107i
$669$	−18.0411	+	17.7098i	−0.697511	+	0.684699i
$670$	0.0293948	−	0.00498740i	0.00113562	−	0.000192680i
$671$	14.8987	−	9.25629i	0.575160	−	0.357335i
$672$	11.4591	−	27.5720i	0.442046	−	1.06361i
$673$	2.24520	−	5.02532i	0.0865463	−	0.193712i	−0.864594	−	0.502471i	$-0.832424\pi$
$673$	2.24520	−	5.02532i	0.0865463	−	0.193712i	0.951140	+	0.308760i	$0.0999139\pi$
$674$	22.1917	+	23.5218i	0.854791	+	0.906026i
$675$	−22.9799	−	10.7703i	−0.884497	−	0.414550i
$676$	−11.8694	+	12.5808i	−0.456516	+	0.483879i
$677$	18.2073	+	43.7561i	0.699762	+	1.68168i	0.731187	+	0.682177i	$0.238967\pi$
$677$	18.2073	+	43.7561i	0.699762	+	1.68168i	−0.0314246	+	0.999506i	$0.510004\pi$
$678$	−11.9383	+	9.51081i	−0.458488	+	0.365260i
$679$	−21.3664	−	14.8582i	−0.819967	−	0.570207i
$680$	−0.830925	−	0.794152i	−0.0318645	−	0.0304543i
$681$	12.0444	+	20.8409i	0.461541	+	0.798624i
$682$	15.9226	−	58.6647i	0.609707	−	2.24639i
$683$	−6.32011	+	18.4712i	−0.241832	+	0.706782i	0.756757	+	0.653696i	$0.226782\pi$
$683$	−6.32011	+	18.4712i	−0.241832	+	0.706782i	−0.998590	+	0.0530863i	$0.983094\pi$
$684$	12.8261	+	15.8741i	0.490417	+	0.606960i
$685$	3.89189	+	2.34877i	0.148702	+	0.0897419i
$686$	−34.8871	+	15.3171i	−1.33200	+	0.584808i
$687$	−10.3364	−	12.1475i	−0.394359	−	0.463455i
$688$	−33.0418	+	12.5123i	−1.25971	+	0.477028i
$689$	−48.0817	−	16.7996i	−1.83177	−	0.640014i
$690$	1.32105	−	2.03903i	0.0502915	−	0.0776245i
$691$	−10.5480	−	15.8139i	−0.401267	−	0.601590i	0.575002	−	0.818152i	$-0.305001\pi$
$691$	−10.5480	−	15.8139i	−0.401267	−	0.601590i	−0.976269	+	0.216562i	$0.930516\pi$
$692$	5.03412	+	0.988669i	0.191369	+	0.0375836i
$693$	−31.0219	+	30.4781i	−1.17842	+	1.15777i
$694$	−3.63086	+	4.50156i	−0.137826	+	0.170877i
$695$	3.64911	+	1.71599i	0.138419	+	0.0650911i
$696$	−6.32518	+	4.16401i	−0.239755	+	0.157836i
$697$	6.96107	+	0.450604i	0.263669	+	0.0170678i
$698$	13.6494	+	50.2896i	0.516638	+	1.90349i
$699$	2.16390	+	7.95917i	0.0818462	+	0.301043i
$700$	−15.7653	+	10.0795i	−0.595872	+	0.380967i
$701$	0.0922438	−	0.213845i	0.00348400	−	0.00807682i	−0.916465	−	0.400114i	$-0.868970\pi$
$701$	0.0922438	−	0.213845i	0.00348400	−	0.00807682i	0.919949	+	0.392038i	$0.128230\pi$
$702$	25.7023	+	40.6639i	0.970072	+	1.53476i
$703$	2.38122	+	5.52030i	0.0898096	+	0.208202i
$704$	25.3682	+	17.1588i	0.956100	+	0.646698i
$705$	−3.07263	+	5.49000i	−0.115722	+	0.206765i
$706$	7.11792	−	21.7155i	0.267886	−	0.817273i
$707$	−24.5717	−	14.3991i	−0.924115	−	0.541533i
$708$	−19.7544	+	3.88840i	−0.742415	+	0.146135i
$709$	−8.78585	−	2.94286i	−0.329960	−	0.110522i	0.147787	−	0.989019i	$-0.452785\pi$
$709$	−8.78585	−	2.94286i	−0.329960	−	0.110522i	−0.477747	+	0.878498i	$0.658546\pi$
$710$	−0.709087	−	1.03387i	−0.0266116	−	0.0388006i
$711$	4.08326	−	48.9762i	0.153134	−	1.83675i
$712$	2.79114	+	1.26873i	0.104603	+	0.0475477i
$713$	11.0521	+	0.572051i	0.413904	+	0.0214235i
$714$	26.5204	−	27.4152i	0.992503	−	1.02599i
$715$	−3.94215	+	9.47385i	−0.147428	+	0.354302i
$716$	10.8067	+	24.1879i	0.403864	+	0.903946i
$717$	−10.7448	−	17.5298i	−0.401271	−	0.654663i
$718$	61.0487	+	34.7223i	2.27832	+	1.29582i
$719$	26.1854	+	8.39601i	0.976550	+	0.313118i	0.750407	−	0.660976i	$-0.229857\pi$
$719$	26.1854	+	8.39601i	0.976550	+	0.313118i	0.226143	+	0.974094i	$0.427388\pi$
$720$	−4.54509	−	1.13533i	−0.169385	−	0.0423114i
$721$	6.24578	+	0.242365i	0.232605	+	0.00902613i
$722$	−1.30899	+	3.26415i	−0.0487157	+	0.121479i
$723$	−12.3049	+	23.3845i	−0.457625	+	0.869680i
$724$	16.9685	+	5.19979i	0.630630	+	0.193249i
$725$	31.2721	+	0.808774i	1.16142	+	0.0300371i
$726$	−49.7010	−	76.5696i	−1.84458	−	2.84176i
$727$	−8.22637	−	0.106359i	−0.305099	−	0.00394466i	−0.139773	−	0.990184i	$-0.544637\pi$
$727$	−8.22637	−	0.106359i	−0.305099	−	0.00394466i	−0.165326	+	0.986239i	$0.552868\pi$
$728$	−7.72465			−0.286295
$729$	25.6895	−	8.30968i	0.951462	−	0.307766i
$730$	−0.325326			−0.0120409
$731$	−38.0938	−	0.492517i	−1.40895	−	0.0182164i
$732$	−3.64672	+	7.15321i	−0.134786	+	0.264390i
$733$	24.6810	+	0.638313i	0.911614	+	0.0235766i	0.478817	−	0.877915i	$-0.341066\pi$
$733$	24.6810	+	0.638313i	0.911614	+	0.0235766i	0.432797	+	0.901491i	$0.357527\pi$
$734$	−16.6366	−	5.09808i	−0.614068	−	0.188174i
$735$	0.490165	+	0.776964i	0.0180800	+	0.0286588i
$736$	−5.93884	+	14.8093i	−0.218908	+	0.545877i
$737$	0.284972	+	0.0110582i	0.0104971	+	0.000407335i
$738$	7.25858	−	3.53631i	0.267192	−	0.130173i
$739$	−7.72722	−	2.47763i	−0.284250	−	0.0911412i	0.159781	−	0.987152i	$-0.448921\pi$
$739$	−7.72722	−	2.47763i	−0.284250	−	0.0911412i	−0.444031	+	0.896011i	$0.646452\pi$
$740$	0.705323	+	0.401162i	0.0259282	+	0.0147470i
$741$	16.6031	−	30.5867i	0.609931	−	1.12363i
$742$	19.0679	+	42.6786i	0.700004	+	1.56678i
$743$	14.0677	−	33.8078i	0.516094	−	1.24029i	−0.425935	−	0.904754i	$-0.640055\pi$
$743$	14.0677	−	33.8078i	0.516094	−	1.24029i	0.942028	−	0.335534i	$-0.108917\pi$
$744$	−1.66535	−	5.82680i	−0.0610547	−	0.213621i
$745$	3.37399	+	0.174636i	0.123613	+	0.00639818i
$746$	−37.6365	−	17.1079i	−1.37797	−	0.626364i
$747$	−6.65916	−	24.4522i	−0.243646	−	0.894658i
$748$	28.5529	+	41.6312i	1.04400	+	1.52219i
$749$	−43.8078	−	14.6736i	−1.60070	−	0.536162i
$750$	7.31656	+	8.37662i	0.267163	+	0.305871i
$751$	−34.3195	−	20.1113i	−1.25234	−	0.733871i	−0.278350	−	0.960480i	$-0.589788\pi$
$751$	−34.3195	−	20.1113i	−1.25234	−	0.733871i	−0.973986	+	0.226609i	$0.927236\pi$
$752$	15.2468	−	46.5153i	0.555994	−	1.69624i
$753$	−9.07774	−	15.2491i	−0.330811	−	0.555708i
$754$	−49.1163	−	33.2218i	−1.78871	−	1.20987i
$755$	−2.73043	−	6.32985i	−0.0993705	−	0.230367i
$756$	4.94103	−	19.2845i	0.179703	−	0.701372i
$757$	7.22038	−	16.7387i	0.262429	−	0.608379i	−0.735151	−	0.677903i	$-0.762889\pi$
$757$	7.22038	−	16.7387i	0.262429	−	0.608379i	0.997580	+	0.0695243i	$0.0221481\pi$
$758$	47.3855	−	30.2956i	1.72112	−	1.10039i
$759$	16.3725	−	16.4928i	0.594284	−	0.598649i
$760$	0.252116	+	0.928889i	0.00914520	+	0.0336944i
$761$	39.1917	+	2.53696i	1.42070	+	0.0919647i	0.755718	−	0.654897i	$-0.227288\pi$
$761$	39.1917	+	2.53696i	1.42070	+	0.0919647i	0.664980	+	0.746861i	$0.268440\pi$
$762$	−1.59550	−	27.1935i	−0.0577989	−	0.985118i
$763$	21.4208	+	10.0731i	0.775484	+	0.364670i
$764$	8.63525	−	10.7060i	0.312412	−	0.387331i
$765$	−4.11210	−	2.93385i	−0.148673	−	0.106073i
$766$	10.9327	+	2.14712i	0.395015	+	0.0775785i
$767$	19.0518	+	28.5630i	0.687922	+	1.03135i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90833 - 0.0246729i) q^{2} +(1.72970 - 0.0902694i) q^{3} +(1.64178 + 0.0424604i) q^{4} +(0.325467 + 0.0997352i) q^{5} +(-3.30306 + 0.129587i) q^{6} +(0.868282 - 2.16517i) q^{7} +(0.682106 + 0.0264688i) q^{8} +(2.98370 - 0.312277i) q^{9} +O(q^{10})\)	\(q+(-1.90833 - 0.0246729i) q^{2} +(1.72970 - 0.0902694i) q^{3} +(1.64178 + 0.0424604i) q^{4} +(0.325467 + 0.0997352i) q^{5} +(-3.30306 + 0.129587i) q^{6} +(0.868282 - 2.16517i) q^{7} +(0.682106 + 0.0264688i) q^{8} +(2.98370 - 0.312277i) q^{9} +(-0.618636 - 0.198358i) q^{10} +(-5.40157 - 3.07222i) q^{11} +(2.84361 - 0.0747585i) q^{12} +(-1.97878 - 4.42900i) q^{13} +(-1.71039 + 4.11044i) q^{14} +(0.571962 + 0.143132i) q^{15} +(-4.58129 - 0.237126i) q^{16} +(-4.50309 - 2.04690i) q^{17} +(-5.70159 + 0.522311i) q^{18} +(2.34282 + 3.41591i) q^{19} +(0.530108 + 0.177562i) q^{20} +(1.30641 - 3.82347i) q^{21} +(10.2322 + 5.99607i) q^{22} +(-0.672522 + 2.05174i) q^{23} +(1.18223 - 0.0157903i) q^{24} +(-4.04559 - 2.73640i) q^{25} +(3.66689 + 8.50080i) q^{26} +(5.13271 - 0.809482i) q^{27} +(1.51746 - 3.51786i) q^{28} +(-5.39631 + 3.45010i) q^{29} +(-1.08796 - 0.287255i) q^{30} +(-1.34259 - 4.94660i) q^{31} +(7.37436 + 0.477357i) q^{32} +(-9.62041 - 4.82641i) q^{33} +(8.54286 + 4.01727i) q^{34} +(0.498541 - 0.618094i) q^{35} +(4.91183 - 0.386000i) q^{36} +(1.42422 + 0.279707i) q^{37} +(-4.38659 - 6.57649i) q^{38} +(-3.82249 - 7.48220i) q^{39} +(0.219363 + 0.0766447i) q^{40} +(-1.31883 + 0.499417i) q^{41} +(-2.58740 + 7.26421i) q^{42} +(7.05209 - 3.09619i) q^{43} +(-8.73772 - 5.27324i) q^{44} +(1.00224 + 0.195944i) q^{45} +(1.33402 - 3.89881i) q^{46} +(-2.79504 + 10.2980i) q^{47} +(-7.94564 + 0.00339465i) q^{48} +(1.12639 + 1.07654i) q^{49} +(7.65279 + 5.32177i) q^{50} +(-7.97375 - 3.13403i) q^{51} +(-3.06066 - 7.35544i) q^{52} +(7.20515 - 7.63701i) q^{53} +(-9.81487 + 1.41812i) q^{54} +(-1.45162 - 1.53863i) q^{55} +(0.649569 - 1.45390i) q^{56} +(4.36072 + 5.69701i) q^{57} +(10.3831 - 6.45078i) q^{58} +(-6.97807 + 1.18396i) q^{59} +(0.932955 + 0.259276i) q^{60} +(-1.34763 + 2.48011i) q^{61} +(2.44005 + 9.47286i) q^{62} +(1.91456 - 6.73138i) q^{63} +(-4.91367 - 0.381921i) q^{64} +(-0.202300 - 1.63884i) q^{65} +(18.2398 + 9.44773i) q^{66} +(-0.0407420 + 0.0211253i) q^{67} +(-7.30614 - 3.55176i) q^{68} +(-0.978050 + 3.60960i) q^{69} +(-0.966630 + 1.16723i) q^{70} +(1.52525 + 1.18216i) q^{71} +(2.04347 - 0.134031i) q^{72} +(0.476852 - 0.152897i) q^{73} +(-2.71097 - 0.568912i) q^{74} +(-7.24465 - 4.36795i) q^{75} +(3.70134 + 5.70764i) q^{76} +(-11.3420 + 9.02780i) q^{77} +(7.10996 + 14.3728i) q^{78} +(3.05305 - 16.0950i) q^{79} +(-1.46741 - 0.534092i) q^{80} +(8.80497 - 1.86349i) q^{81} +(2.52908 - 0.920511i) q^{82} +(-1.35923 - 8.33750i) q^{83} +(2.30719 - 6.22182i) q^{84} +(-1.26146 - 1.11532i) q^{85} +(-13.5341 + 5.73456i) q^{86} +(-9.02254 + 6.45475i) q^{87} +(-3.60313 - 2.23855i) q^{88} +(4.15787 + 1.69868i) q^{89} +(-1.90777 - 0.398654i) q^{90} +(-11.3077 + 0.438790i) q^{91} +(-1.19125 + 3.33995i) q^{92} +(-2.76880 - 8.43493i) q^{93} +(5.58794 - 19.5830i) q^{94} +(0.421823 + 1.34543i) q^{95} +(12.7985 + 0.160004i) q^{96} +(2.50255 - 10.8718i) q^{97} +(-2.12296 - 2.08219i) q^{98} +(-17.0761 - 7.47979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

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