LMFDB - Embedded newform 729.2.k.a.4.11

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			4.11
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27606 - 0.0294274i) q^{2} +(-1.57284 - 0.725368i) q^{3} +(3.18025 + 0.0822491i) q^{4} +(-3.48668 - 1.06845i) q^{5} +(3.55854 + 1.69727i) q^{6} +(0.216487 - 0.539838i) q^{7} +(-2.68694 - 0.104265i) q^{8} +(1.94768 + 2.28178i) q^{9} +O(q^{10})$	\(q+(-2.27606 - 0.0294274i) q^{2} +(-1.57284 - 0.725368i) q^{3} +(3.18025 + 0.0822491i) q^{4} +(-3.48668 - 1.06845i) q^{5} +(3.55854 + 1.69727i) q^{6} +(0.216487 - 0.539838i) q^{7} +(-2.68694 - 0.104265i) q^{8} +(1.94768 + 2.28178i) q^{9} +(7.90445 + 2.53446i) q^{10} +(-0.775368 - 0.441001i) q^{11} +(-4.94238 - 2.43622i) q^{12} +(-1.68337 - 3.76779i) q^{13} +(-0.508623 + 1.22233i) q^{14} +(4.70899 + 4.20963i) q^{15} +(-0.241559 - 0.0125030i) q^{16} +(-6.45469 - 2.93401i) q^{17} +(-4.36589 - 5.25079i) q^{18} +(-2.98512 - 4.35242i) q^{19} +(-11.0006 - 3.68471i) q^{20} +(-0.732082 + 0.692049i) q^{21} +(1.75181 + 1.02656i) q^{22} +(1.64220 - 5.01006i) q^{23} +(4.15050 + 2.11301i) q^{24} +(6.87379 + 4.64937i) q^{25} +(3.72057 + 8.62526i) q^{26} +(-1.40827 - 5.00168i) q^{27} +(0.732883 - 1.69901i) q^{28} +(-6.32489 + 4.04378i) q^{29} +(-10.5941 - 9.71995i) q^{30} +(-1.11447 - 4.10614i) q^{31} +(5.91612 + 0.382962i) q^{32} +(0.899646 + 1.25605i) q^{33} +(14.6049 + 6.86794i) q^{34} +(-1.33161 + 1.65094i) q^{35} +(6.00644 + 7.41683i) q^{36} +(3.07552 + 0.604013i) q^{37} +(6.66624 + 9.99420i) q^{38} +(-0.0853574 + 7.14722i) q^{39} +(9.25709 + 3.23440i) q^{40} +(-0.830224 + 0.314390i) q^{41} +(1.68663 - 1.55360i) q^{42} +(-9.55271 + 4.19408i) q^{43} +(-2.42959 - 1.46627i) q^{44} +(-4.35297 - 10.0369i) q^{45} +(-3.88518 + 11.3549i) q^{46} +(1.89759 - 6.99145i) q^{47} +(0.370866 + 0.194885i) q^{48} +(4.81590 + 4.60277i) q^{49} +(-15.5083 - 10.7845i) q^{50} +(8.02398 + 9.29677i) q^{51} +(-5.04363 - 12.1210i) q^{52} +(7.68328 - 8.14380i) q^{53} +(3.05812 + 11.4256i) q^{54} +(2.23227 + 2.36607i) q^{55} +(-0.637973 + 1.42794i) q^{56} +(1.53803 + 9.01099i) q^{57} +(14.5148 - 9.01776i) q^{58} +(-2.86711 + 0.486461i) q^{59} +(14.6295 + 13.7750i) q^{60} +(2.14494 - 3.94744i) q^{61} +(2.41578 + 9.37862i) q^{62} +(1.65344 - 0.557457i) q^{63} +(-12.9719 - 1.00825i) q^{64} +(1.84367 + 14.9357i) q^{65} +(-2.01068 - 2.88533i) q^{66} +(-0.561233 + 0.291008i) q^{67} +(-20.2862 - 9.86179i) q^{68} +(-6.21707 + 6.68885i) q^{69} +(3.07941 - 3.71845i) q^{70} +(11.3548 + 8.80061i) q^{71} +(-4.99539 - 6.33408i) q^{72} +(-6.26361 + 2.00834i) q^{73} +(-6.98230 - 1.46527i) q^{74} +(-7.43890 - 12.2988i) q^{75} +(-9.13545 - 14.0873i) q^{76} +(-0.405926 + 0.323102i) q^{77} +(0.404602 - 16.2650i) q^{78} +(-2.36594 + 12.4727i) q^{79} +(0.828882 + 0.301688i) q^{80} +(-1.41307 + 8.88838i) q^{81} +(1.89889 - 0.691140i) q^{82} +(2.06384 + 12.6595i) q^{83} +(-2.38512 + 2.14067i) q^{84} +(19.3706 + 17.1265i) q^{85} +(21.8660 - 9.26487i) q^{86} +(12.8813 - 1.77237i) q^{87} +(2.03738 + 1.26578i) q^{88} +(-0.183718 - 0.0750572i) q^{89} +(9.61227 + 22.9726i) q^{90} +(-2.39843 + 0.0930698i) q^{91} +(5.63468 - 15.7982i) q^{92} +(-1.22557 + 7.26673i) q^{93} +(-4.52477 + 15.8571i) q^{94} +(5.75783 + 18.3649i) q^{95} +(-9.02735 - 4.89370i) q^{96} +(-0.943971 + 4.10088i) q^{97} +(-10.8258 - 10.6179i) q^{98} +(-0.503902 - 2.62815i) 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 $

$2$	−2.27606	−	0.0294274i	−1.60942	−	0.0208083i	−0.797035	−	0.603934i	$-0.793599\pi$
$2$	−2.27606	−	0.0294274i	−1.60942	−	0.0208083i	−0.812382	+	0.583125i	$0.801830\pi$
$3$	−1.57284	−	0.725368i	−0.908082	−	0.418791i
$3$	−1.57284	−	0.725368i	−0.908082	−	0.418791i
$4$	3.18025	+	0.0822491i	1.59012	+	0.0411246i
$5$	−3.48668	−	1.06845i	−1.55929	−	0.477826i	−0.610047	−	0.792365i	$-0.708849\pi$
$5$	−3.48668	−	1.06845i	−1.55929	−	0.477826i	−0.949244	+	0.314540i	$0.898150\pi$
$6$	3.55854	+	1.69727i	1.45277	+	0.692906i
$7$	0.216487	−	0.539838i	0.0818243	−	0.204040i	−0.881613	−	0.471972i	$-0.843542\pi$
$7$	0.216487	−	0.539838i	0.0818243	−	0.204040i	0.963438	+	0.267933i	$0.0863405\pi$
$8$	−2.68694	−	0.104265i	−0.949975	−	0.0368634i
$9$	1.94768	+	2.28178i	0.649227	+	0.760594i
$10$	7.90445	+	2.53446i	2.49961	+	0.801467i
$11$	−0.775368	−	0.441001i	−0.233782	−	0.132967i	0.373010	−	0.927827i	$-0.378326\pi$
$11$	−0.775368	−	0.441001i	−0.233782	−	0.132967i	−0.606792	+	0.794861i	$0.707544\pi$
$12$	−4.94238	−	2.43622i	−1.42674	−	0.703275i
$13$	−1.68337	−	3.76779i	−0.466883	−	1.04500i	−0.982173	−	0.187982i	$-0.939805\pi$
$13$	−1.68337	−	3.76779i	−0.466883	−	1.04500i	0.515290	−	0.857016i	$-0.327684\pi$
$14$	−0.508623	+	1.22233i	−0.135935	+	0.326682i
$15$	4.70899	+	4.20963i	1.21586	+	1.08692i
$16$	−0.241559	−	0.0125030i	−0.0603899	−	0.00312576i
$17$	−6.45469	−	2.93401i	−1.56549	−	0.711603i	−0.571453	−	0.820635i	$-0.693620\pi$
$17$	−6.45469	−	2.93401i	−1.56549	−	0.711603i	−0.994038	+	0.109032i	$0.965225\pi$
$18$	−4.36589	−	5.25079i	−1.02905	−	1.23762i
$19$	−2.98512	−	4.35242i	−0.684834	−	0.998513i	−0.998795	−	0.0490770i	$-0.984372\pi$
$19$	−2.98512	−	4.35242i	−0.684834	−	0.998513i	0.313961	−	0.949436i	$-0.398344\pi$
$20$	−11.0006	−	3.68471i	−2.45982	−	0.823927i
$21$	−0.732082	+	0.692049i	−0.159753	+	0.151018i
$22$	1.75181	+	1.02656i	0.373486	+	0.218864i
$23$	1.64220	−	5.01006i	0.342423	−	1.04467i	−0.622608	−	0.782534i	$-0.713927\pi$
$23$	1.64220	−	5.01006i	0.342423	−	1.04467i	0.965031	−	0.262137i	$-0.0844271\pi$
$24$	4.15050	+	2.11301i	0.847218	+	0.431317i
$25$	6.87379	+	4.64937i	1.37476	+	0.929874i
$26$	3.72057	+	8.62526i	0.729664	+	1.69155i
$27$	−1.40827	−	5.00168i	−0.271022	−	0.962573i
$28$	0.732883	−	1.69901i	0.138502	−	0.321083i
$29$	−6.32489	+	4.04378i	−1.17450	+	0.750912i	−0.973502	−	0.228680i	$-0.926559\pi$
$29$	−6.32489	+	4.04378i	−1.17450	+	0.750912i	−0.201000	+	0.979591i	$0.564419\pi$
$30$	−10.5941	−	9.71995i	−1.93420	−	1.77461i
$31$	−1.11447	−	4.10614i	−0.200166	−	0.737485i	−0.991944	−	0.126677i	$-0.959569\pi$
$31$	−1.11447	−	4.10614i	−0.200166	−	0.737485i	0.791778	−	0.610808i	$-0.209155\pi$
$32$	5.91612	+	0.382962i	1.04583	+	0.0676988i
$33$	0.899646	+	1.25605i	0.156608	+	0.218651i
$34$	14.6049	+	6.86794i	2.50472	+	1.17784i
$35$	−1.33161	+	1.65094i	−0.225083	+	0.279059i
$36$	6.00644	+	7.41683i	1.00107	+	1.23614i
$37$	3.07552	+	0.604013i	0.505613	+	0.0992992i	0.439013	−	0.898481i	$-0.355328\pi$
$37$	3.07552	+	0.604013i	0.505613	+	0.0992992i	0.0665999	+	0.997780i	$0.478785\pi$
$38$	6.66624	+	9.99420i	1.08141	+	1.62127i
$39$	−0.0853574	+	7.14722i	−0.0136681	+	1.14447i
$40$	9.25709	+	3.23440i	1.46367	+	0.511403i
$41$	−0.830224	+	0.314390i	−0.129659	+	0.0490995i	−0.418118	−	0.908393i	$-0.637310\pi$
$41$	−0.830224	+	0.314390i	−0.129659	+	0.0490995i	0.288458	+	0.957492i	$0.406857\pi$
$42$	1.68663	−	1.55360i	0.260252	−	0.239726i
$43$	−9.55271	+	4.19408i	−1.45678	+	0.639592i	−0.971986	−	0.235039i	$-0.924478\pi$
$43$	−9.55271	+	4.19408i	−1.45678	+	0.639592i	−0.484789	+	0.874631i	$0.661104\pi$
$44$	−2.42959	−	1.46627i	−0.366274	−	0.221048i
$45$	−4.35297	−	10.0369i	−0.648903	−	1.49621i
$46$	−3.88518	+	11.3549i	−0.572839	+	1.67419i
$47$	1.89759	−	6.99145i	0.276792	−	1.01981i	−0.680985	−	0.732297i	$-0.738448\pi$
$47$	1.89759	−	6.99145i	0.276792	−	1.01981i	0.957778	−	0.287510i	$-0.0928275\pi$
$48$	0.370866	+	0.194885i	0.0535299	+	0.0281292i
$49$	4.81590	+	4.60277i	0.687986	+	0.657538i
$50$	−15.5083	−	10.7845i	−2.19321	−	1.52516i
$51$	8.02398	+	9.29677i	1.12358	+	1.30181i
$52$	−5.04363	−	12.1210i	−0.699426	−	1.68088i
$53$	7.68328	−	8.14380i	1.05538	−	1.11864i	0.0626793	−	0.998034i	$-0.480035\pi$
$53$	7.68328	−	8.14380i	1.05538	−	1.11864i	0.992701	−	0.120604i	$-0.0384830\pi$
$54$	3.05812	+	11.4256i	0.416157	+	1.55482i
$55$	2.23227	+	2.36607i	0.301000	+	0.319041i
$56$	−0.637973	+	1.42794i	−0.0852527	+	0.190816i
$57$	1.53803	+	9.01099i	0.203717	+	1.19353i
$58$	14.5148	−	9.01776i	1.90589	−	1.18409i
$59$	−2.86711	+	0.486461i	−0.373267	+	0.0633319i	−0.350887	−	0.936418i	$-0.614120\pi$
$59$	−2.86711	+	0.486461i	−0.373267	+	0.0633319i	−0.0223792	+	0.999750i	$0.507124\pi$
$60$	14.6295	+	13.7750i	1.88866	+	1.77834i
$61$	2.14494	−	3.94744i	0.274631	−	0.505418i	−0.704223	−	0.709979i	$-0.748704\pi$
$61$	2.14494	−	3.94744i	0.274631	−	0.505418i	0.978854	+	0.204561i	$0.0655768\pi$
$62$	2.41578	+	9.37862i	0.306804	+	1.19109i
$63$	1.65344	−	0.557457i	0.208314	−	0.0702330i
$64$	−12.9719	−	1.00825i	−1.62148	−	0.126032i
$65$	1.84367	+	14.9357i	0.228679	+	1.85254i
$66$	−2.01068	−	2.88533i	−0.247498	−	0.355159i
$67$	−0.561233	+	0.291008i	−0.0685655	+	0.0355522i	−0.494254	−	0.869318i	$-0.664559\pi$
$67$	−0.561233	+	0.291008i	−0.0685655	+	0.0355522i	0.425688	+	0.904870i	$0.360032\pi$
$68$	−20.2862	−	9.86179i	−2.46006	−	1.19592i
$69$	−6.21707	+	6.68885i	−0.748447	+	0.805243i
$70$	3.07941	−	3.71845i	0.368060	−	0.444439i
$71$	11.3548	+	8.80061i	1.34756	+	1.04444i	0.994040	+	0.109014i	$0.0347694\pi$
$71$	11.3548	+	8.80061i	1.34756	+	1.04444i	0.353523	+	0.935426i	$0.384984\pi$
$72$	−4.99539	−	6.33408i	−0.588712	−	0.746479i
$73$	−6.26361	+	2.00834i	−0.733100	+	0.235059i	−0.648349	−	0.761343i	$-0.724540\pi$
$73$	−6.26361	+	2.00834i	−0.733100	+	0.235059i	−0.0847506	+	0.996402i	$0.527009\pi$
$74$	−6.98230	−	1.46527i	−0.811676	−	0.170335i
$75$	−7.43890	−	12.2988i	−0.858970	−	1.42014i
$76$	−9.13545	−	14.0873i	−1.04791	−	1.61592i
$77$	−0.405926	+	0.323102i	−0.0462596	+	0.0368209i
$78$	0.404602	−	16.2650i	0.0458122	−	1.84165i
$79$	−2.36594	+	12.4727i	−0.266189	+	1.40329i	0.554627	+	0.832099i	$0.312861\pi$
$79$	−2.36594	+	12.4727i	−0.266189	+	1.40329i	−0.820815	+	0.571194i	$0.806480\pi$
$80$	0.828882	+	0.301688i	0.0926718	+	0.0337298i
$81$	−1.41307	+	8.88838i	−0.157007	+	0.987597i
$82$	1.89889	−	0.691140i	0.209697	−	0.0763236i
$83$	2.06384	+	12.6595i	0.226536	+	1.38957i	0.814258	+	0.580503i	$0.197144\pi$
$83$	2.06384	+	12.6595i	0.226536	+	1.38957i	−0.587722	+	0.809063i	$0.699975\pi$
$84$	−2.38512	+	2.14067i	−0.260238	+	0.233567i
$85$	19.3706	+	17.1265i	2.10103	+	1.85763i
$86$	21.8660	−	9.26487i	2.35787	−	0.999057i
$87$	12.8813	−	1.77237i	1.38102	−	0.190018i
$88$	2.03738	+	1.26578i	0.217186	+	0.134933i
$89$	−0.183718	−	0.0750572i	−0.0194741	−	0.00795605i	0.368442	−	0.929651i	$-0.379891\pi$
$89$	−0.183718	−	0.0750572i	−0.0194741	−	0.00795605i	−0.387916	+	0.921695i	$0.626805\pi$
$90$	9.61227	+	22.9726i	1.01322	+	2.42152i
$91$	−2.39843	+	0.0930698i	−0.251423	+	0.00975637i
$92$	5.63468	−	15.7982i	0.587456	−	1.64707i
$93$	−1.22557	+	7.26673i	−0.127086	+	0.753525i
$94$	−4.52477	+	15.8571i	−0.466695	+	1.63554i
$95$	5.75783	+	18.3649i	0.590741	+	1.88420i
$96$	−9.02735	−	4.89370i	−0.921350	−	0.499462i
$97$	−0.943971	+	4.10088i	−0.0958458	+	0.416381i	−0.999940	−	0.0109517i	$-0.996514\pi$
$97$	−0.943971	+	4.10088i	−0.0958458	+	0.416381i	0.904094	+	0.427333i	$0.140547\pi$
$98$	−10.8258	−	10.6179i	−1.09357	−	1.07257i
$99$	−0.503902	−	2.62815i	−0.0506441	−	0.264139i
$100$	21.4779	+	15.3515i	2.14779	+	1.53515i
$101$	−1.28087	+	8.55161i	−0.127452	+	0.850917i	0.829047	+	0.559179i	$0.188884\pi$
$101$	−1.28087	+	8.55161i	−0.127452	+	0.850917i	−0.956498	+	0.291738i	$0.905767\pi$
$102$	−17.9895	−	21.3961i	−1.78122	−	2.11853i
$103$	−0.592376	−	1.66087i	−0.0583686	−	0.163650i	0.909139	−	0.416494i	$-0.136741\pi$
$103$	−0.592376	−	1.66087i	−0.0583686	−	0.163650i	−0.967507	+	0.252844i	$0.918634\pi$
$104$	4.13026	+	10.2993i	0.405005	+	1.00993i
$105$	3.29195	−	1.63076i	0.321262	−	0.159146i
$106$	−17.7273	+	18.3097i	−1.72182	+	1.77839i
$107$	−0.744112	−	12.7759i	−0.0719360	−	1.23509i	−0.820350	−	0.571862i	$-0.806221\pi$
$107$	−0.744112	−	12.7759i	−0.0719360	−	1.23509i	0.748414	−	0.663232i	$-0.230816\pi$
$108$	−4.06726	−	16.0224i	−0.391372	−	1.54176i
$109$	0.996814	−	17.1146i	0.0954775	−	1.63929i	−0.522178	−	0.852837i	$-0.674880\pi$
$109$	0.996814	−	17.1146i	0.0954775	−	1.63929i	0.617655	−	0.786449i	$-0.288083\pi$
$110$	−5.01116	−	5.45101i	−0.477795	−	0.519733i
$111$	−4.39919	−	3.18091i	−0.417553	−	0.301918i
$112$	−0.0590440	+	0.127696i	−0.00557914	+	0.0120662i
$113$	5.68242	−	4.17359i	0.534557	−	0.392618i	−0.291184	−	0.956667i	$-0.594049\pi$
$113$	5.68242	−	4.17359i	0.534557	−	0.392618i	0.825741	+	0.564049i	$0.190757\pi$
$114$	−3.23548	−	20.5548i	−0.303031	−	1.92513i
$115$	−11.0788	+	15.7139i	−1.03311	+	1.46533i
$116$	−20.4473	+	12.3400i	−1.89848	+	1.14574i
$117$	5.31862	−	11.1795i	0.491706	−	1.03355i
$118$	6.54004	−	1.02284i	0.602059	−	0.0941604i
$119$	−2.98125	+	2.84931i	−0.273291	+	0.261196i
$120$	−12.2138	−	11.8020i	−1.11497	−	1.07737i
$121$	−5.21598	−	8.77050i	−0.474180	−	0.797319i
$122$	−4.99817	+	8.92148i	−0.452513	+	0.807713i
$123$	1.53386	+	0.107731i	0.138304	+	0.00971376i
$124$	−3.20658	−	13.1502i	−0.287959	−	1.18092i
$125$	−7.55182	−	9.36279i	−0.675456	−	0.837434i
$126$	−3.77973	+	1.22015i	−0.336725	+	0.108700i
$127$	0.194158	+	10.0108i	0.0172288	+	0.888311i	0.904354	+	0.426783i	$0.140353\pi$
$127$	0.194158	+	10.0108i	0.0172288	+	0.888311i	−0.887125	+	0.461528i	$0.847301\pi$
$128$	17.6866	+	1.60499i	1.56329	+	0.141863i
$129$	18.0672	+	0.332589i	1.59073	+	0.0292828i
$130$	−3.75679	−	34.0488i	−0.329492	−	2.98627i
$131$	3.04934	−	0.276717i	0.266422	−	0.0241768i	0.0436480	−	0.999047i	$-0.486102\pi$
$131$	3.04934	−	0.276717i	0.266422	−	0.0241768i	0.222774	+	0.974870i	$0.428489\pi$
$132$	2.75779	+	4.06855i	0.240034	+	0.354122i
$133$	−2.99584	+	0.669243i	−0.259772	+	0.0580307i
$134$	1.28596	−	0.645835i	0.111090	−	0.0557916i
$135$	−0.433857	+	18.9439i	−0.0373405	+	1.63043i
$136$	17.0374	+	8.55651i	1.46095	+	0.733715i
$137$	−4.03052	−	1.01046i	−0.344350	−	0.0863292i	0.0671394	−	0.997744i	$-0.478613\pi$
$137$	−4.03052	−	1.01046i	−0.344350	−	0.0863292i	−0.411490	+	0.911414i	$0.634991\pi$
$138$	14.3473	−	15.0413i	1.22132	−	1.28040i
$139$	1.95688	+	0.280183i	0.165980	+	0.0237648i	0.224224	−	0.974538i	$-0.428015\pi$
$139$	1.95688	+	0.280183i	0.165980	+	0.0237648i	−0.0582441	+	0.998302i	$0.518550\pi$
$140$	−4.37064	+	5.14087i	−0.369386	+	0.434483i
$141$	−8.05599	+	9.62001i	−0.678437	+	0.810151i
$142$	−25.5851	−	20.3648i	−2.14706	−	1.70898i
$143$	−0.356369	+	3.66379i	−0.0298011	+	0.306382i
$144$	−0.441952	−	0.575538i	−0.0368293	−	0.0479615i
$145$	26.3734	−	7.34155i	2.19020	−	0.609683i
$146$	14.3154	−	4.38679i	1.18475	−	0.363053i
$147$	−4.23596	−	10.7327i	−0.349376	−	0.885221i
$148$	9.73125	+	2.17387i	0.799904	+	0.178691i
$149$	5.50895	−	1.38110i	0.451311	−	0.113144i	−0.0108488	−	0.999941i	$-0.503453\pi$
$149$	5.50895	−	1.38110i	0.451311	−	0.113144i	0.462159	+	0.886797i	$0.347075\pi$
$150$	16.5694	+	28.2116i	1.35289	+	2.30347i
$151$	8.17195	+	9.61207i	0.665024	+	0.782219i	0.986335	−	0.164754i	$-0.0526831\pi$
$151$	8.17195	+	9.61207i	0.665024	+	0.782219i	−0.321311	+	0.946974i	$0.604123\pi$
$152$	7.56703	+	12.0059i	0.613767	+	0.973808i
$153$	−5.87689	−	20.4427i	−0.475119	−	1.65270i
$154$	0.933420	−	0.723455i	0.0752171	−	0.0582976i
$155$	−0.501394	+	15.5076i	−0.0402729	+	1.24560i
$156$	−0.859310	+	22.7229i	−0.0687999	+	1.81929i
$157$	−0.0387438	+	0.313866i	−0.00309209	+	0.0250492i	−0.993934	−	0.109977i	$-0.964922\pi$
$157$	−0.0387438	+	0.313866i	−0.00309209	+	0.0250492i	0.990842	+	0.135026i	$0.0431117\pi$
$158$	5.75205	−	28.3191i	0.457609	−	2.25294i
$159$	−17.9919	+	7.23573i	−1.42685	+	0.573831i
$160$	−20.2184	−	7.65635i	−1.59841	−	0.605287i
$161$	−2.34911	−	1.97114i	−0.185136	−	0.155347i
$162$	3.47779	−	20.1889i	0.273241	−	1.58619i
$163$	16.2581	−	13.6422i	1.27343	−	1.06854i	0.279317	−	0.960199i	$-0.409892\pi$
$163$	16.2581	−	13.6422i	1.27343	−	1.06854i	0.994114	−	0.108337i	$-0.0345525\pi$
$164$	−2.66618	+	0.931554i	−0.208193	+	0.0727421i
$165$	−1.79475	−	5.34068i	−0.139721	−	0.415772i
$166$	−4.32488	−	28.8746i	−0.335676	−	2.24110i
$167$	1.37322	−	2.69079i	0.106263	−	0.208220i	−0.831476	−	0.555560i	$-0.812504\pi$
$167$	1.37322	−	2.69079i	0.106263	−	0.208220i	0.937739	+	0.347341i	$0.112915\pi$
$168$	2.03921	−	1.78316i	0.157329	−	0.137574i
$169$	−2.68884	+	3.00183i	−0.206834	+	0.230910i
$170$	−43.5846	−	39.5509i	−3.34279	−	3.03342i
$171$	4.11720	−	15.2885i	0.314850	−	1.16914i
$172$	−30.7250	+	12.5525i	−2.34276	+	0.957121i
$173$	−14.3970	−	2.44273i	−1.09459	−	0.185718i	−0.408155	−	0.912913i	$-0.633828\pi$
$173$	−14.3970	−	2.44273i	−1.09459	−	0.185718i	−0.686431	+	0.727195i	$0.740824\pi$
$174$	−29.3708	+	3.65496i	−2.22659	+	0.277082i
$175$	3.99799	−	2.70421i	0.302220	−	0.204419i
$176$	0.181784	+	0.116222i	0.0137025	+	0.00876059i
$177$	4.86239	+	1.31459i	0.365480	+	0.0988103i
$178$	0.415945	+	0.176241i	0.0311764	+	0.0132098i
$179$	4.00097	+	8.36731i	0.299046	+	0.625402i	0.995764	−	0.0919430i	$-0.0293077\pi$
$179$	4.00097	+	8.36731i	0.299046	+	0.625402i	−0.696718	+	0.717345i	$0.745357\pi$
$180$	−13.0180	−	32.2777i	−0.970306	−	2.40584i
$181$	−15.0470	−	4.18862i	−1.11844	−	0.311338i	−0.340851	−	0.940117i	$-0.610715\pi$
$181$	−15.0470	−	4.18862i	−1.11844	−	0.311338i	−0.777584	+	0.628780i	$0.783555\pi$
$182$	5.46170	−	0.141253i	0.404848	−	0.0104704i
$183$	−6.23700	+	4.65284i	−0.461052	+	0.343948i
$184$	−4.93487	+	13.2905i	−0.363803	+	0.979788i
$185$	−10.0780	−	5.39205i	−0.740950	−	0.396431i
$186$	3.00331	−	16.5034i	0.220213	−	1.21009i
$187$	3.71085	+	5.12146i	0.271365	+	0.374518i
$188$	6.60986	−	22.0785i	0.482073	−	1.61024i
$189$	−3.00497	−	0.322559i	−0.218579	−	0.0234627i
$190$	−12.5647	−	41.9691i	−0.911542	−	3.04476i
$191$	−4.13537	+	5.40739i	−0.299225	+	0.391265i	−0.919481	−	0.393134i	$-0.871391\pi$
$191$	−4.13537	+	5.40739i	−0.299225	+	0.391265i	0.620256	+	0.784399i	$0.287029\pi$
$192$	19.6714	+	10.9952i	1.41966	+	0.793510i
$193$	−21.0612	+	9.90401i	−1.51602	+	0.712906i	−0.990454	−	0.137846i	$-0.955982\pi$
$193$	−21.0612	+	9.90401i	−1.51602	+	0.712906i	−0.525567	+	0.850752i	$0.676147\pi$
$194$	2.26921	−	9.30607i	0.162920	−	0.668137i
$195$	7.93406	−	24.8289i	0.568170	−	1.77803i
$196$	14.9372	+	15.0340i	1.06694	+	1.07386i
$197$	−13.6086	+	2.67265i	−0.969576	+	0.190418i	−0.652338	−	0.757928i	$-0.726212\pi$
$197$	−13.6086	+	2.67265i	−0.969576	+	0.190418i	−0.317237	+	0.948346i	$0.602755\pi$
$198$	1.06957	+	5.99666i	0.0760111	+	0.426164i
$199$	−3.03929	+	1.67701i	−0.215449	+	0.118880i	−0.587167	−	0.809466i	$-0.699757\pi$
$199$	−3.03929	+	1.67701i	−0.215449	+	0.118880i	0.371717	+	0.928346i	$0.378769\pi$
$200$	−17.9847	−	13.2093i	−1.27171	−	0.934035i
$201$	1.09382	−	0.0506093i	0.0771521	−	0.00356971i
$202$	3.16699	−	19.4263i	0.222829	−	1.36683i
$203$	0.813734	+	4.28984i	0.0571129	+	0.301088i
$204$	24.7536	+	30.2260i	1.73310	+	2.11624i
$205$	3.23064	−	0.209126i	0.225637	−	0.0146060i
$206$	1.29941	+	3.79766i	0.0905341	+	0.264596i
$207$	14.6304	−	6.01086i	1.01688	−	0.417784i
$208$	0.359525	+	0.931193i	0.0249286	+	0.0645666i
$209$	0.395150	+	4.69117i	0.0273331	+	0.324495i
$210$	−7.54067	+	3.61484i	−0.520356	+	0.249447i
$211$	7.32804	−	10.9864i	0.504483	−	0.756334i	−0.488756	−	0.872420i	$-0.662549\pi$
$211$	7.32804	−	10.9864i	0.504483	−	0.756334i	0.993239	+	0.116086i	$0.0370349\pi$
$212$	25.1046	−	25.2674i	1.72419	−	1.73537i
$213$	−11.4756	−	22.0784i	−0.786296	−	1.51279i
$214$	1.31768	+	29.1006i	0.0900748	+	1.98928i
$215$	37.7884	−	4.41683i	2.57715	−	0.301226i
$216$	3.26243	+	13.5860i	0.221980	+	0.924412i
$217$	−2.45792	−	0.287290i	−0.166855	−	0.0195025i
$218$	−2.77245	+	38.9246i	−0.187774	+	2.63631i
$219$	11.3085	+	1.38461i	0.764156	+	0.0935630i
$220$	6.90457	+	7.70829i	0.465506	+	0.519693i
$221$	−0.189138	+	29.2590i	−0.0127228	+	1.96817i
$222$	9.91921	+	7.36939i	0.665734	+	0.494601i
$223$	−2.96540	+	2.62185i	−0.198578	+	0.175572i	−0.755824	−	0.654775i	$-0.772763\pi$
$223$	−2.96540	+	2.62185i	−0.198578	+	0.175572i	0.557246	+	0.830347i	$0.311858\pi$
$224$	1.48750	−	3.11084i	0.0993877	−	0.207852i
$225$	2.77910	+	24.7400i	0.185273	+	1.64933i
$226$	−13.0563	+	9.33212i	−0.868495	+	0.620763i
$227$	5.50240	+	10.7818i	0.365207	+	0.715616i	0.998289	−	0.0584691i	$-0.0186219\pi$
$227$	5.50240	+	10.7818i	0.365207	+	0.715616i	−0.633082	+	0.774085i	$0.718210\pi$
$228$	4.15018	+	28.7837i	0.274852	+	1.90625i
$229$	−9.50207	−	12.4249i	−0.627915	−	0.821058i	0.366069	−	0.930588i	$-0.380703\pi$
$229$	−9.50207	−	12.4249i	−0.627915	−	0.821058i	−0.993984	+	0.109529i	$0.965066\pi$
$230$	25.6785	−	35.4397i	1.69319	−	2.33682i
$231$	0.872827	−	0.213744i	0.0574278	−	0.0140633i
$232$	17.4162	−	10.2059i	1.14343	−	0.670051i
$233$	−1.23763	−	5.71353i	−0.0810798	−	0.374306i	0.918707	−	0.394939i	$-0.129234\pi$
$233$	−1.23763	−	5.71353i	−0.0810798	−	0.374306i	−0.999787	+	0.0206331i	$0.993432\pi$
$234$	−12.4345	+	25.2888i	−0.812867	+	1.65318i
$235$	−14.0863	+	22.3495i	−0.918890	+	1.45792i
$236$	−9.15815	+	1.31125i	−0.596145	+	0.0853551i
$237$	12.7686	−	17.9015i	0.829408	−	1.16283i
$238$	6.86934	−	6.39747i	0.445273	−	0.414686i
$239$	10.4612	+	19.2522i	0.676676	+	1.24532i	0.958291	+	0.285794i	$0.0922575\pi$
$239$	10.4612	+	19.2522i	0.676676	+	1.24532i	−0.281615	+	0.959527i	$0.590870\pi$
$240$	−1.08487	−	1.07575i	−0.0700279	−	0.0694396i
$241$	9.61534	−	16.1679i	0.619379	−	1.04146i	−0.374094	−	0.927391i	$-0.622046\pi$
$241$	9.61534	−	16.1679i	0.619379	−	1.04146i	0.993472	−	0.114074i	$-0.0363901\pi$
$242$	11.6138	+	20.1157i	0.746563	+	1.29308i
$243$	8.66988	−	12.9550i	0.556173	−	0.831066i
$244$	7.14610	−	12.3774i	0.457482	−	0.792383i
$245$	−11.8737	−	21.1939i	−0.758581	−	1.35403i
$246$	−3.48799	−	0.290339i	−0.222386	−	0.0185113i
$247$	−11.3739	+	18.5741i	−0.723706	+	1.18184i
$248$	2.56639	+	11.1491i	0.162966	+	0.707971i
$249$	5.93673	−	21.4085i	0.376225	−	1.35671i
$250$	16.9129	+	21.5325i	1.06966	+	1.36183i
$251$	−5.15547	−	9.78743i	−0.325411	−	0.617777i	0.666385	−	0.745607i	$-0.267841\pi$
$251$	−5.15547	−	9.78743i	−0.325411	−	0.617777i	−0.991796	+	0.127831i	$0.959199\pi$
$252$	5.30420	−	1.63686i	0.334133	−	0.103112i
$253$	−3.48275	+	3.16043i	−0.218959	+	0.198695i
$254$	−0.147326	−	22.7908i	−0.00924404	−	1.43002i
$255$	−18.0439	−	40.9881i	−1.12995	−	2.56677i
$256$	−14.3255	−	1.48695i	−0.895345	−	0.0929344i
$257$	21.8254	−	2.83749i	1.36143	−	0.176998i	0.586964	−	0.809613i	$-0.300323\pi$
$257$	21.8254	−	2.83749i	1.36143	−	0.176998i	0.774466	+	0.632615i	$0.218018\pi$
$258$	−41.1122	−	1.28866i	−2.55953	−	0.0802286i
$259$	0.991880	−	1.52952i	0.0616324	−	0.0950400i
$260$	4.63489	+	47.6508i	0.287444	+	2.95518i
$261$	−21.5459	−	6.55602i	−1.33366	−	0.405807i
$262$	−6.94862	+	0.540089i	−0.429287	+	0.0333668i
$263$	−0.427612	−	2.10526i	−0.0263677	−	0.129816i	0.964653	−	0.263522i	$-0.0848842\pi$
$263$	−0.427612	−	2.10526i	−0.0263677	−	0.129816i	−0.991021	+	0.133706i	$0.957312\pi$
$264$	−2.28633	−	3.46874i	−0.140714	−	0.213486i
$265$	−35.4904	+	20.1856i	−2.18016	+	1.23999i
$266$	6.83841	−	1.43508i	0.419290	−	0.0879902i
$267$	0.234516	+	0.251317i	0.0143522	+	0.0153803i
$268$	−1.80879	+	0.879315i	−0.110490	+	0.0537127i
$269$	−9.53469	+	12.8073i	−0.581340	+	0.780875i	−0.991355	−	0.131203i	$-0.958116\pi$
$269$	−9.53469	+	12.8073i	−0.581340	+	0.780875i	0.410015	+	0.912079i	$0.365523\pi$
$270$	1.54495	−	43.1047i	0.0940229	−	2.62327i
$271$	13.3836	+	17.9773i	0.812996	+	1.09204i	0.994088	+	0.108577i	$0.0346294\pi$
$271$	13.3836	+	17.9773i	0.812996	+	1.09204i	−0.181092	+	0.983466i	$0.557963\pi$
$272$	1.52251	+	0.789442i	0.0923155	+	0.0478670i
$273$	3.83986	+	1.59336i	0.232399	+	0.0964344i
$274$	9.14396	+	2.41847i	0.552407	+	0.146105i
$275$	−3.27934	−	6.63632i	−0.197752	−	0.400185i
$276$	−20.3220	+	20.7609i	−1.22324	+	1.24966i
$277$	0.923268	−	0.642042i	0.0554738	−	0.0385766i	−0.542863	−	0.839821i	$-0.682660\pi$
$277$	0.923268	−	0.642042i	0.0554738	−	0.0385766i	0.598337	+	0.801245i	$0.295828\pi$
$278$	−4.44572	−	0.695298i	−0.266637	−	0.0417012i
$279$	7.19869	−	10.5405i	0.430974	−	0.631040i
$280$	3.75009	−	4.29712i	0.224111	−	0.256802i
$281$	5.60073	−	11.3341i	0.334112	−	0.676133i	−0.663276	−	0.748375i	$-0.730834\pi$
$281$	5.60073	−	11.3341i	0.334112	−	0.676133i	0.997387	+	0.0722419i	$0.0230153\pi$
$282$	18.6190	−	21.6586i	1.10875	−	1.28975i
$283$	8.04028	−	6.92568i	0.477945	−	0.411689i	−0.380353	−	0.924842i	$-0.624197\pi$
$283$	8.04028	−	6.92568i	0.477945	−	0.411689i	0.858297	+	0.513153i	$0.171522\pi$
$284$	35.3871	+	28.9220i	2.09984	+	1.71621i
$285$	4.26517	−	33.0618i	0.252647	−	1.95841i
$286$	0.918933	−	8.32852i	0.0543376	−	0.492476i
$287$	−0.0100126	+	0.516248i	−0.000591026	+	0.0304731i
$288$	10.6489	+	14.2452i	0.627492	+	0.839406i
$289$	21.8767	+	25.0679i	1.28686	+	1.47458i
$290$	−60.2436	+	15.9337i	−3.53762	+	0.935659i
$291$	4.45937	−	5.76532i	0.261413	−	0.337969i
$292$	−20.0850	+	5.87186i	−1.17539	+	0.343624i
$293$	−1.98905	+	23.6138i	−0.116202	+	1.37953i	0.661050	+	0.750342i	$0.270111\pi$
$293$	−1.98905	+	23.6138i	−0.116202	+	1.37953i	−0.777252	+	0.629190i	$0.783387\pi$
$294$	9.32546	+	24.5530i	0.543872	+	1.43196i
$295$	10.5165	+	1.36723i	0.612293	+	0.0796034i
$296$	−8.20076	−	1.94362i	−0.476659	−	0.112970i
$297$	−1.11382	+	4.49919i	−0.0646302	+	0.261069i
$298$	−12.5793	+	2.98136i	−0.728701	+	0.172705i
$299$	−21.6413	+	2.24631i	−1.25155	+	0.129907i
$300$	−22.6460	−	39.7250i	−1.30747	−	2.29352i
$301$	0.196091	+	6.06488i	0.0113025	+	0.349574i
$302$	−18.3170	−	22.1181i	−1.05402	−	1.27275i
$303$	8.21768	−	12.5213i	0.472093	−	0.719327i
$304$	0.666667	+	1.08869i	0.0382360	+	0.0624407i
$305$	−11.6964	+	11.4717i	−0.669731	+	0.656868i
$306$	12.7746	+	46.7018i	0.730274	+	2.66976i
$307$	−16.5753	+	24.1673i	−0.946001	+	1.37930i	−0.0208170	+	0.999783i	$0.506627\pi$
$307$	−16.5753	+	24.1673i	−0.946001	+	1.37930i	−0.925184	+	0.379519i	$0.876089\pi$
$308$	−1.31752	+	0.994158i	−0.0750727	+	0.0566474i
$309$	−0.273024	+	3.04198i	−0.0155318	+	0.173052i
$310$	1.59755	−	35.2814i	0.0907346	−	2.00385i
$311$	−0.393987	−	5.53150i	−0.0223409	−	0.313662i	−0.996237	−	0.0866687i	$-0.972378\pi$
$311$	−0.393987	−	5.53150i	−0.0223409	−	0.313662i	0.973896	−	0.226994i	$-0.0728897\pi$
$312$	0.974557	−	19.1952i	0.0551734	−	1.08671i
$313$	−1.36363	−	3.67251i	−0.0770772	−	0.207583i	0.893160	−	0.449739i	$-0.148483\pi$
$313$	−1.36363	−	3.67251i	−0.0770772	−	0.207583i	−0.970237	+	0.242156i	$0.922145\pi$
$314$	0.0974195	−	0.713237i	0.00549770	−	0.0402503i
$315$	−6.36064	+	0.177056i	−0.358381	+	0.00997600i
$316$	−8.55013	+	39.4718i	−0.480983	+	2.22046i
$317$	−1.93523	−	5.90403i	−0.108693	−	0.331603i	0.881331	−	0.472499i	$-0.156648\pi$
$317$	−1.93523	−	5.90403i	−0.108693	−	0.331603i	−0.990024	+	0.140896i	$0.955002\pi$
$318$	41.1635	−	15.9395i	2.30833	−	0.893843i
$319$	6.68743	−	0.346139i	0.374424	−	0.0193800i
$320$	44.1515	+	17.3752i	2.46814	+	0.971305i
$321$	−8.09686	+	20.6343i	−0.451923	+	1.15169i
$322$	5.28870	+	4.55555i	0.294728	+	0.253871i
$323$	6.49798	+	36.8519i	0.361557	+	2.05049i
$324$	−5.22497	+	28.1510i	−0.290276	+	1.56395i
$325$	5.94674	−	33.7256i	0.329866	−	1.87076i
$326$	−37.4058	+	30.5719i	−2.07172	+	1.69322i
$327$	−13.9822	+	26.1956i	−0.773220	+	1.44862i
$328$	2.26354	−	0.758183i	0.124983	−	0.0418636i
$329$	−3.36345	−	2.53795i	−0.185433	−	0.139922i
$330$	3.92779	+	12.2085i	0.216218	+	0.672057i
$331$	12.3622	−	6.61413i	0.679486	−	0.363546i	−0.0955841	−	0.995421i	$-0.530472\pi$
$331$	12.3622	−	6.61413i	0.679486	−	0.363546i	0.775070	+	0.631876i	$0.217715\pi$
$332$	5.52228	+	40.4302i	0.303075	+	2.21890i
$333$	4.61192	+	8.19411i	0.252732	+	0.449034i
$334$	−3.20471	+	6.08399i	−0.175354	+	0.332901i
$335$	2.26777	−	0.415001i	0.123901	−	0.0226739i
$336$	0.185494	−	0.158018i	0.0101195	−	0.00862058i
$337$	−20.6316	−	21.3094i	−1.12387	−	1.16080i	−0.985368	−	0.170438i	$-0.945482\pi$
$337$	−20.6316	−	21.3094i	−1.12387	−	1.16080i	−0.138506	−	0.990362i	$-0.544230\pi$
$338$	6.20830	−	6.75322i	0.337687	−	0.367327i
$339$	−11.9650	+	2.44256i	−0.649847	+	0.132662i
$340$	60.1946	+	56.0597i	3.26451	+	3.04026i
$341$	−0.946685	+	3.67526i	−0.0512659	+	0.199026i
$342$	−9.82089	+	34.6764i	−0.531053	+	1.87509i
$343$	7.23378	−	3.28816i	0.390587	−	0.177544i
$344$	26.1048	−	10.2732i	1.40748	−	0.553895i
$345$	28.8236	−	16.6793i	1.55181	−	0.897981i
$346$	32.6966	+	5.98347i	1.75778	+	0.321674i
$347$	−7.68321	+	9.78182i	−0.412456	+	0.525115i	−0.947520	−	0.319696i	$-0.896419\pi$
$347$	−7.68321	+	9.78182i	−0.412456	+	0.525115i	0.535064	+	0.844812i	$0.320288\pi$
$348$	41.1115	−	4.57710i	2.20381	−	0.245358i
$349$	0.938725	+	3.28977i	0.0502488	+	0.176097i	0.982702	−	0.185193i	$-0.0592911\pi$
$349$	0.938725	+	3.28977i	0.0502488	+	0.176097i	−0.932453	+	0.361290i	$0.882336\pi$
$350$	−9.17924	+	6.03728i	−0.490651	+	0.322706i
$351$	−16.4746	+	13.7257i	−0.879352	+	0.732626i
$352$	−4.41828	−	2.90595i	−0.235495	−	0.154888i
$353$	10.4893	−	33.4563i	0.558290	−	1.78070i	−0.0640446	−	0.997947i	$-0.520400\pi$
$353$	10.4893	−	33.4563i	0.558290	−	1.78070i	0.622334	−	0.782751i	$-0.286184\pi$
$354$	−11.0284	−	3.13516i	−0.586153	−	0.166632i
$355$	−30.1874	−	42.8169i	−1.60218	−	2.27249i
$356$	−0.578096	−	0.253811i	−0.0306390	−	0.0134520i
$357$	6.75584	−	2.31902i	0.357557	−	0.122736i
$358$	−8.86021	−	19.1622i	−0.468276	−	1.01276i
$359$	−26.8209	−	14.7992i	−1.41555	−	0.781070i	−0.423382	−	0.905951i	$-0.639157\pi$
$359$	−26.8209	−	14.7992i	−1.41555	−	0.781070i	−0.992172	+	0.124882i	$0.960145\pi$
$360$	10.6497	+	27.4222i	0.561287	+	1.44528i
$361$	−3.18919	+	8.26022i	−0.167852	+	0.434748i
$362$	34.1246	+	9.97634i	1.79355	+	0.524345i
$363$	1.84209	+	17.5781i	0.0966846	+	0.922614i
$364$	−7.63524	+	0.0987167i	−0.400195	+	0.00517416i
$365$	23.9850	−	0.310104i	1.25543	−	0.0162316i
$366$	14.3327	−	10.4066i	0.749182	−	0.543962i
$367$	22.4101	+	6.55161i	1.16980	+	0.341991i	0.807384	−	0.590026i	$-0.200882\pi$
$367$	22.4101	+	6.55161i	1.16980	+	0.341991i	0.362415	+	0.932017i	$0.381952\pi$
$368$	−0.459331	+	1.18970i	−0.0239443	+	0.0620172i
$369$	−2.33438	−	1.28206i	−0.121523	−	0.0667413i
$370$	22.7795	+	12.5692i	1.18425	+	0.653441i
$371$	−2.73301	−	5.91076i	−0.141891	−	0.306871i
$372$	−4.49530	+	23.0092i	−0.233070	+	1.19297i
$373$	0.552597	+	0.242616i	0.0286124	+	0.0125622i	0.416264	−	0.909244i	$-0.363339\pi$
$373$	0.552597	+	0.242616i	0.0286124	+	0.0125622i	−0.387652	+	0.921806i	$0.626714\pi$
$374$	−8.29541	−	11.7660i	−0.428946	−	0.608403i
$375$	5.08638	+	20.2041i	0.262659	+	1.04333i
$376$	−5.82768	+	18.5877i	−0.300540	+	0.958588i
$377$	25.8833	+	17.0237i	1.33306	+	0.876764i
$378$	6.82999	+	0.822592i	0.351297	+	0.0423096i
$379$	−21.3041	+	14.0119i	−1.09432	+	0.719745i	−0.962433	−	0.271519i	$-0.912474\pi$
$379$	−21.3041	+	14.0119i	−1.09432	+	0.719745i	−0.131887	+	0.991265i	$0.542104\pi$
$380$	16.8008	+	58.8787i	0.861865	+	3.02041i
$381$	6.95610	−	15.8862i	0.356372	−	0.813875i
$382$	9.57147	−	12.1858i	0.489719	−	0.623482i
$383$	10.3045	+	1.88573i	0.526537	+	0.0963561i	0.436712	−	0.899601i	$-0.356143\pi$
$383$	10.3045	+	1.88573i	0.526537	+	0.0963561i	0.0898248	+	0.995958i	$0.471369\pi$
$384$	−26.6540	−	15.3537i	−1.36018	−	0.783514i
$385$	1.76055	−	0.692843i	0.0897261	−	0.0353106i
$386$	48.2281	−	21.9223i	2.45474	−	1.11582i
$387$	−28.1756	−	13.6285i	−1.43225	−	0.692774i
$388$	−3.33936	+	12.9642i	−0.169530	+	0.658156i
$389$	−24.0277	−	22.3772i	−1.21826	−	1.13457i	−0.986837	−	0.161715i	$-0.948297\pi$
$389$	−24.0277	−	22.3772i	−1.21826	−	1.13457i	−0.231418	−	0.972854i	$-0.574336\pi$
$390$	−18.7890	+	56.2785i	−0.951420	+	2.84977i
$391$	−25.2995	+	27.5201i	−1.27945	+	1.39175i
$392$	−12.4601	−	12.8695i	−0.629330	−	0.650007i
$393$	−4.99686	−	1.77666i	−0.252058	−	0.0896207i
$394$	31.0527	−	5.68264i	1.56441	−	0.286287i
$395$	21.5758	−	40.9606i	1.08559	−	2.06095i
$396$	−1.38637	−	8.39962i	−0.0696677	−	0.422097i
$397$	4.67663	+	34.2390i	0.234713	+	1.71841i	0.610768	+	0.791809i	$0.290861\pi$
$397$	4.67663	+	34.2390i	0.234713	+	1.71841i	−0.376055	+	0.926597i	$0.622720\pi$
$398$	6.96695	−	3.72753i	0.349221	−	0.186844i
$399$	5.19744	+	1.12047i	0.260197	+	0.0560937i
$400$	−1.60230	−	1.20904i	−0.0801149	−	0.0604521i
$401$	26.3519	−	8.82670i	1.31595	−	0.440784i	0.429275	−	0.903174i	$-0.358769\pi$
$401$	26.3519	−	8.82670i	1.31595	−	0.440784i	0.886677	+	0.462389i	$0.153008\pi$
$402$	−2.49109	+	0.0830016i	−0.124244	+	0.00413974i
$403$	−13.5950	+	11.1113i	−0.677217	+	0.553492i
$404$	−4.77686	+	27.0909i	−0.237657	+	1.34782i
$405$	14.4237	−	29.4811i	0.716720	−	1.46493i
$406$	−1.72587	−	9.78788i	−0.0856533	−	0.485764i
$407$	−2.11829	−	1.82464i	−0.105000	−	0.0904441i
$408$	−20.5906	−	25.8165i	−1.01939	−	1.27811i
$409$	5.14808	+	2.02596i	0.254556	+	0.100177i	0.490037	−	0.871702i	$-0.336983\pi$
$409$	5.14808	+	2.02596i	0.254556	+	0.100177i	−0.235481	+	0.971879i	$0.575666\pi$
$410$	−7.35927	+	0.380913i	−0.363449	+	0.0188120i
$411$	5.60642	+	4.51290i	0.276544	+	0.222605i
$412$	−1.74730	−	5.33069i	−0.0860832	−	0.262624i
$413$	−0.358082	+	1.65309i	−0.0176201	+	0.0813433i
$414$	−33.4765	+	13.2505i	−1.64528	+	0.651229i
$415$	6.33015	−	46.3449i	0.310735	−	2.27498i
$416$	−8.51609	−	22.9354i	−0.417536	−	1.12450i
$417$	−2.87463	−	1.86014i	−0.140771	−	0.0910914i
$418$	−0.761336	−	10.6890i	−0.0372381	−	0.522816i
$419$	−0.352260	+	7.77957i	−0.0172090	+	0.380057i	0.972131	+	0.234436i	$0.0753244\pi$
$419$	−0.352260	+	7.77957i	−0.0172090	+	0.380057i	−0.989341	+	0.145620i	$0.953482\pi$
$420$	10.6034	−	4.91547i	0.517391	−	0.239850i
$421$	4.75181	−	3.58556i	0.231589	−	0.174750i	−0.480166	−	0.877178i	$-0.659423\pi$
$421$	4.75181	−	3.58556i	0.231589	−	0.174750i	0.711755	+	0.702428i	$0.247901\pi$
$422$	−17.0023	+	24.7900i	−0.827661	+	1.20676i
$423$	19.6489	−	9.28722i	0.955361	−	0.451560i
$424$	−21.4936	+	21.0808i	−1.04382	+	1.02377i
$425$	−30.7268	−	50.1780i	−1.49047	−	2.43399i
$426$	25.4695	+	50.5894i	1.23400	+	2.45106i
$427$	−1.66663	−	2.01249i	−0.0806538	−	0.0973911i
$428$	−1.31565	−	40.6918i	−0.0635945	−	1.96691i
$429$	3.21811	−	5.50408i	0.155372	−	0.265739i
$430$	−86.1387	+	8.94096i	−4.15398	+	0.431171i
$431$	7.26698	−	1.72231i	0.350038	−	0.0829606i	−0.0518356	−	0.998656i	$-0.516507\pi$
$431$	7.26698	−	1.72231i	0.350038	−	0.0829606i	0.401874	+	0.915695i	$0.368359\pi$
$432$	0.277645	+	1.22581i	0.0133582	+	0.0589768i
$433$	−26.8153	−	6.35534i	−1.28866	−	0.305418i	−0.471519	−	0.881856i	$-0.656294\pi$
$433$	−26.8153	−	6.35534i	−1.28866	−	0.305418i	−0.817141	+	0.576438i	$0.804442\pi$
$434$	5.58592	+	0.726219i	0.268133	+	0.0348596i
$435$	−46.8067	−	7.58334i	−2.24421	−	0.363593i
$436$	4.57778	−	54.3468i	0.219236	−	2.60274i
$437$	−26.7081	+	7.80811i	−1.27762	+	0.373513i
$438$	−25.6980	−	3.48422i	−1.22790	−	0.166483i
$439$	−14.2071	+	3.75761i	−0.678068	+	0.179341i	−0.578491	−	0.815689i	$-0.696358\pi$
$439$	−14.2071	+	3.75761i	−0.678068	+	0.179341i	−0.0995773	+	0.995030i	$0.531749\pi$
$440$	−5.75128	−	6.59023i	−0.274181	−	0.314177i
$441$	−1.12268	+	19.9536i	−0.0534609	+	0.950170i
$442$	1.29150	−	66.5895i	0.0614305	−	3.16734i
$443$	0.566310	−	5.13261i	0.0269062	−	0.243858i	−0.973008	−	0.230771i	$-0.925875\pi$
$443$	0.566310	−	5.13261i	0.0269062	−	0.243858i	0.999914	−	0.0130870i	$-0.00416585\pi$
$444$	−13.7289	−	10.4779i	−0.651544	−	0.497259i
$445$	0.560372	+	0.457994i	0.0265642	+	0.0217110i
$446$	6.82657	−	5.88023i	0.323248	−	0.278437i
$447$	−9.66653	−	1.82376i	−0.457211	−	0.0862607i
$448$	−3.35253	+	6.78443i	−0.158392	+	0.320534i
$449$	7.32085	−	8.38876i	0.345492	−	0.395890i	−0.554222	−	0.832369i	$-0.686984\pi$
$449$	7.32085	−	8.38876i	0.345492	−	0.395890i	0.899715	+	0.436478i	$0.143774\pi$
$450$	−5.59737	−	56.3914i	−0.263862	−	2.65832i
$451$	0.782375	+	0.122361i	0.0368406	+	0.00576177i
$452$	18.4148	−	12.8057i	0.866159	−	0.602328i
$453$	−5.88092	−	21.0460i	−0.276310	−	0.988826i
$454$	−12.2065	−	24.7020i	−0.572880	−	1.15932i
$455$	8.46199	+	2.23809i	0.396704	+	0.104923i
$456$	−3.19306	−	24.3723i	−0.149529	−	1.14134i
$457$	15.5962	+	8.08689i	0.729562	+	0.378289i	0.784440	−	0.620204i	$-0.212950\pi$
$457$	15.5962	+	8.08689i	0.729562	+	0.378289i	−0.0548785	+	0.998493i	$0.517477\pi$
$458$	21.2617	+	28.5594i	0.993492	+	1.33449i
$459$	−5.58506	+	36.4161i	−0.260688	+	1.69976i
$460$	−36.5259	+	49.0628i	−1.70303	+	2.28757i
$461$	7.53602	−	3.66351i	0.350988	−	0.170627i	−0.253311	−	0.967385i	$-0.581519\pi$
$461$	7.53602	−	3.66351i	0.350988	−	0.170627i	0.604298	+	0.796758i	$0.293454\pi$
$462$	−1.99290	+	0.460809i	−0.0927179	+	0.0214388i
$463$	−17.9163	+	3.75984i	−0.832641	+	0.174734i	−0.602193	−	0.798350i	$-0.705706\pi$
$463$	−17.9163	+	3.75984i	−0.832641	+	0.174734i	−0.230448	+	0.973085i	$0.574019\pi$
$464$	1.57840	−	0.897734i	0.0732752	−	0.0416762i
$465$	12.0373	−	24.0273i	0.558217	−	1.11424i
$466$	2.64878	+	13.0408i	0.122703	+	0.604101i
$467$	−36.7474	+	2.85623i	−1.70047	+	0.132171i	−0.890703	−	0.454586i	$-0.849787\pi$
$467$	−36.7474	+	2.85623i	−1.70047	+	0.132171i	−0.809763	+	0.586757i	$0.800404\pi$
$468$	17.8340	−	35.1163i	0.824378	−	1.62325i
$469$	0.0355975	+	0.365974i	0.00164374	+	0.0168991i
$470$	32.7190	−	50.4542i	1.50921	−	2.32728i
$471$	0.288606	−	0.465558i	0.0132983	−	0.0214518i
$472$	7.75447	−	1.00815i	0.356929	−	0.0464039i
$473$	9.25646	+	0.960796i	0.425613	+	0.0441774i
$474$	−29.5888	+	40.3692i	−1.35906	+	1.85422i
$475$	−0.283113	−	43.7965i	−0.0129901	−	2.00952i
$476$	−9.71546	+	8.81631i	−0.445307	+	0.404095i
$477$	33.5470	+	1.67004i	1.53601	+	0.0764659i
$478$	−23.2437	−	44.1270i	−1.06314	−	2.01832i
$479$	22.4772	+	28.6167i	1.02701	+	1.30753i	0.950587	+	0.310457i	$0.100482\pi$
$479$	22.4772	+	28.6167i	1.02701	+	1.30753i	0.0764243	+	0.997075i	$0.475650\pi$
$480$	26.2468	+	26.7081i	1.19800	+	1.21905i
$481$	−2.90145	−	12.6047i	−0.132295	−	0.574726i
$482$	−22.3609	+	36.5161i	−1.01851	+	1.66326i
$483$	2.26498	+	4.80426i	0.103060	+	0.218601i
$484$	−15.8667	−	28.3214i	−0.721216	−	1.28734i
$485$	7.67291	−	13.2899i	0.348409	−	0.603462i
$486$	−20.1144	+	29.2313i	−0.912407	+	1.32596i
$487$	−2.63582	−	4.56537i	−0.119440	−	0.206877i	0.800106	−	0.599859i	$-0.204777\pi$
$487$	−2.63582	−	4.56537i	−0.119440	−	0.206877i	−0.919546	+	0.392982i	$0.871443\pi$
$488$	−6.17489	+	10.3829i	−0.279524	+	0.470011i
$489$	−35.4670	+	9.66389i	−1.60387	+	0.437016i
$490$	26.4015	+	48.5881i	1.19270	+	2.19498i
$491$	21.7778	−	20.2818i	0.982816	−	0.915304i	−0.0135985	−	0.999908i	$-0.504329\pi$
$491$	21.7778	−	20.2818i	0.982816	−	0.915304i	0.996415	+	0.0846036i	$0.0269624\pi$
$492$	4.86920	+	0.468769i	0.219520	+	0.0211338i
$493$	52.6897	−	7.54403i	2.37302	−	0.339766i
$494$	26.4343	−	41.9409i	1.18934	−	1.88701i
$495$	−1.05110	+	9.70192i	−0.0472435	+	0.436069i
$496$	0.217873	+	1.00581i	0.00978277	+	0.0451623i
$497$	7.20906	−	4.22452i	0.323371	−	0.189496i
$498$	−14.1424	+	48.5524i	−0.633734	+	2.17569i
$499$	10.1728	−	14.0398i	0.455396	−	0.628506i	−0.518615	−	0.855008i	$-0.673552\pi$
$499$	10.1728	−	14.0398i	0.455396	−	0.628506i	0.974011	+	0.226502i	$0.0727291\pi$
$500$	−23.2466	−	30.3971i	−1.03962	−	1.35940i
$501$	−4.11168	+	3.23611i	−0.183696	+	0.144579i
$502$	11.4461	+	22.4285i	0.510866	+	1.00103i
$503$	6.76094	−	4.83243i	0.301455	−	0.215467i	−0.420697	−	0.907201i	$-0.638215\pi$
$503$	6.76094	−	4.83243i	0.301455	−	0.215467i	0.722153	+	0.691734i	$0.243153\pi$
$504$	−4.50081	+	1.32546i	−0.200482	+	0.0590405i
$505$	13.6030	−	28.4482i	0.605324	−	1.26593i
$506$	8.01996	−	7.09084i	0.356530	−	0.315226i
$507$	6.40656	−	2.77102i	0.284525	−	0.123065i
$508$	−0.205904	+	31.8526i	−0.00913552	+	1.41323i
$509$	15.1918	+	16.9601i	0.673363	+	0.751745i	0.979764	−	0.200158i	$-0.0641454\pi$
$509$	15.1918	+	16.9601i	0.673363	+	0.751745i	−0.306401	+	0.951903i	$0.599125\pi$
$510$	39.8628	+	93.8223i	1.76516	+	4.15452i
$511$	−0.271807	+	3.81611i	−0.0120240	+	0.168815i
$512$	−2.71634	−	0.317494i	−0.120046	−	0.0140314i
$513$	−17.5655	+	21.0600i	−0.775537	+	0.929822i
$514$	−49.7594	+	5.81604i	−2.19479	+	0.256534i
$515$	0.290873	+	6.42384i	0.0128174	+	0.283068i
$516$	57.4308	+	2.54373i	2.52825	+	0.111981i
$517$	−4.55457	+	4.58410i	−0.200310	+	0.201609i
$518$	−2.30259	+	3.45210i	−0.101170	+	0.151677i
$519$	20.8724	+	14.2852i	0.916197	+	0.627050i
$520$	−3.39656	−	40.3235i	−0.148949	−	1.76830i
$521$	−9.00821	−	23.3318i	−0.394657	−	1.02219i	−0.977749	−	0.209780i	$-0.932725\pi$
$521$	−9.00821	−	23.3318i	−0.394657	−	1.02219i	0.583092	−	0.812406i	$-0.301843\pi$
$522$	48.8468	+	15.5559i	2.13797	+	0.680864i
$523$	−4.76430	−	13.9242i	−0.208328	−	0.608863i	0.791669	−	0.610950i	$-0.209212\pi$
$523$	−4.76430	−	13.9242i	−0.208328	−	0.608863i	−0.999998	+	0.00208698i	$0.999336\pi$
$524$	9.72041	−	0.629222i	0.424638	−	0.0274877i
$525$	−8.24976	+	1.35328i	−0.360049	+	0.0590620i
$526$	0.911317	+	4.80428i	0.0397353	+	0.209477i
$527$	−4.85390	+	29.7738i	−0.211439	+	1.29697i
$528$	−0.201613	−	0.314660i	−0.00877410	−	0.0136938i
$529$	−3.86668	−	2.83997i	−0.168116	−	0.123477i
$530$	81.3723	−	44.8993i	3.53459	−	1.95030i
$531$	−6.69423	−	5.59466i	−0.290505	−	0.242788i
$532$	−9.58256	+	1.88195i	−0.415457	+	0.0815930i
$533$	2.58213	+	2.59888i	0.111845	+	0.112570i
$534$	−0.526378	−	0.578913i	−0.0227786	−	0.0250520i
$535$	−11.0559	+	45.3406i	−0.477990	+	1.96024i
$536$	1.53834	−	0.723402i	0.0664461	−	0.0312462i
$537$	−0.223519	−	16.0627i	−0.00964556	−	0.693155i
$538$	22.0784	−	28.8696i	0.951867	−	1.24466i
$539$	−1.70427	−	5.69265i	−0.0734081	−	0.245200i
$540$	−2.93789	+	60.2107i	−0.126427	+	2.59105i
$541$	8.91689	−	29.7845i	0.383367	−	1.28054i	−0.520918	−	0.853607i	$-0.674410\pi$
$541$	8.91689	−	29.7845i	0.383367	−	1.28054i	0.904285	−	0.426929i	$-0.140405\pi$
$542$	−29.9329	−	41.3112i	−1.28573	−	1.77447i
$543$	20.6283	+	17.5027i	0.885246	+	0.751111i
$544$	−37.0631	−	19.8299i	−1.58907	−	0.850199i
$545$	−21.7617	+	58.6082i	−0.932170	+	2.51050i
$546$	−8.69286	−	3.73957i	−0.372020	−	0.160039i
$547$	−21.1092	+	0.545937i	−0.902564	+	0.0233426i	−0.474352	−	0.880335i	$-0.657317\pi$
$547$	−21.1092	+	0.545937i	−0.902564	+	0.0233426i	−0.428213	+	0.903678i	$0.640857\pi$
$548$	−12.7349	−	3.54501i	−0.544009	−	0.151435i
$549$	13.1849	−	2.79408i	0.562716	−	0.119248i
$550$	7.26868	+	15.2012i	0.309938	+	0.648179i
$551$	36.4808	+	15.4574i	1.55413	+	0.658506i
$552$	17.4023	−	17.3243i	0.740690	−	0.737371i
$553$	6.22107	+	3.97741i	0.264547	+	0.169137i
$554$	−2.12031	+	1.43416i	−0.0900831	+	0.0609314i
$555$	11.9399	+	15.7911i	0.506822	+	0.670296i
$556$	6.20031	+	1.05200i	0.262952	+	0.0446148i
$557$	−29.3607	+	11.9952i	−1.24405	+	0.508251i	−0.902125	−	0.431476i	$-0.857993\pi$
$557$	−29.3607	+	11.9952i	−1.24405	+	0.508251i	−0.341927	+	0.939727i	$0.611079\pi$
$558$	−16.6948	+	23.7789i	−0.706748	+	1.00664i
$559$	31.8832	+	28.9324i	1.34852	+	1.22371i
$560$	0.342305	−	0.382151i	0.0144650	−	0.0161488i
$561$	−2.12165	−	10.7470i	−0.0895762	−	0.453739i
$562$	−13.0811	+	25.6322i	−0.551794	+	1.08123i
$563$	−5.87295	−	39.2101i	−0.247515	−	1.65251i	−0.667229	−	0.744852i	$-0.732520\pi$
$563$	−5.87295	−	39.2101i	−0.247515	−	1.65251i	0.419714	−	0.907656i	$-0.362130\pi$
$564$	−26.4113	+	29.9314i	−1.11212	+	1.26034i
$565$	−24.2721	+	8.48059i	−1.02113	+	0.356781i
$566$	−18.5039	+	15.5267i	−0.777779	+	0.652634i
$567$	4.49237	+	2.68704i	0.188662	+	0.112845i
$568$	−29.5919	−	24.8306i	−1.24165	−	1.04187i
$569$	−19.8221	−	7.50625i	−0.830984	−	0.314678i	−0.0982233	−	0.995164i	$-0.531316\pi$
$569$	−19.8221	−	7.50625i	−0.830984	−	0.314678i	−0.732761	+	0.680486i	$0.761769\pi$
$570$	−10.6807	+	75.1250i	−0.447365	+	3.14664i
$571$	−5.30982	+	26.1418i	−0.222209	+	1.09400i	0.702018	+	0.712159i	$0.252282\pi$
$571$	−5.30982	+	26.1418i	−0.222209	+	1.09400i	−0.924227	+	0.381843i	$0.875290\pi$
$572$	−1.43469	+	11.6225i	−0.0599872	+	0.485959i
$573$	10.4266	−	5.50532i	0.435579	−	0.229988i
$574$	0.0379811	−	1.17472i	0.00158530	−	0.0490317i
$575$	34.5818	−	26.8029i	1.44216	−	1.11776i
$576$	−22.9644	−	31.5627i	−0.956852	−	1.31511i
$577$	1.99178	+	3.16018i	0.0829189	+	0.131560i	0.884885	−	0.465810i	$-0.154237\pi$
$577$	1.99178	+	3.16018i	0.0829189	+	0.131560i	−0.801966	+	0.597370i	$0.796212\pi$
$578$	−49.0549	−	57.6998i	−2.04042	−	2.39999i
$579$	40.3101	−	0.300331i	1.67523	−	0.0124813i
$580$	84.4779	−	21.1788i	3.50775	−	0.879400i
$581$	7.28090	+	1.62649i	0.302063	+	0.0674780i
$582$	−10.3194	+	12.9910i	−0.427755	+	0.538494i
$583$	−9.54879	+	2.92611i	−0.395471	+	0.121187i
$584$	17.0393	−	4.74322i	0.705092	−	0.196276i
$585$	−30.4891	+	33.2968i	−1.26057	+	1.37665i
$586$	5.22209	−	53.6878i	0.215723	−	2.21782i
$587$	11.6198	+	9.24894i	0.479601	+	0.381745i	0.832596	−	0.553880i	$-0.186853\pi$
$587$	11.6198	+	9.24894i	0.479601	+	0.381745i	−0.352996	+	0.935625i	$0.614837\pi$
$588$	−12.5886	−	34.4812i	−0.519147	−	1.42198i
$589$	−14.5448	+	17.1080i	−0.599308	+	0.704923i
$590$	−23.8959	−	3.42138i	−0.983778	−	0.140856i
$591$	23.3429	+	5.66761i	0.960200	+	0.233134i
$592$	−0.735370	−	0.184359i	−0.0302235	−	0.00757709i
$593$	−17.2978	−	8.68729i	−0.710337	−	0.356744i	0.0566618	−	0.998393i	$-0.481954\pi$
$593$	−17.2978	−	8.68729i	−0.710337	−	0.356744i	−0.766998	+	0.641649i	$0.778251\pi$
$594$	2.66751	−	10.2076i	0.109449	−	0.418825i
$595$	13.4390	−	6.74932i	0.550946	−	0.276695i
$596$	17.6334	−	3.93914i	0.722293	−	0.161354i
$597$	5.99677	−	0.433071i	0.245432	−	0.0177244i
$598$	49.3230	−	4.47589i	2.01697	−	0.183033i
$599$	3.44747	+	31.2453i	0.140860	+	1.27665i	0.832345	+	0.554257i	$0.186998\pi$
$599$	3.44747	+	31.2453i	0.140860	+	1.27665i	−0.691486	+	0.722390i	$0.743044\pi$
$600$	18.7055	+	33.8216i	0.763649	+	1.38076i
$601$	22.0073	+	1.99709i	0.897698	+	0.0814629i	0.529525	−	0.848294i	$-0.322370\pi$
$601$	22.0073	+	1.99709i	0.897698	+	0.0814629i	0.368173	+	0.929757i	$0.379983\pi$
$602$	−0.267841	−	13.8098i	−0.0109164	−	0.562846i
$603$	−1.75712	−	0.713822i	−0.0715554	−	0.0290691i
$604$	25.1982	+	31.2409i	1.02530	+	1.27117i
$605$	8.81562	+	36.1530i	0.358406	+	1.46983i
$606$	−19.0724	+	28.2573i	−0.774763	+	1.14787i
$607$	−3.28573	+	5.86486i	−0.133364	+	0.238047i	−0.930941	−	0.365168i	$-0.881011\pi$
$607$	−3.28573	+	5.86486i	−0.133364	+	0.238047i	0.797578	+	0.603216i	$0.206114\pi$
$608$	−15.9935	−	26.8926i	−0.648624	−	1.09064i
$609$	1.83184	−	7.33751i	0.0742298	−	0.297331i
$610$	26.9592	−	25.7661i	1.09154	−	1.04324i
$611$	−29.5367	+	4.61945i	−1.19493	+	0.186883i
$612$	−17.0086	−	65.4963i	−0.687531	−	2.64753i
$613$	32.4285	−	19.5707i	1.30977	−	0.790452i	0.322058	−	0.946720i	$-0.395625\pi$
$613$	32.4285	−	19.5707i	1.30977	−	0.790452i	0.987715	+	0.156268i	$0.0499462\pi$
$614$	38.4375	−	54.5185i	1.55121	−	2.20019i
$615$	−5.23298	−	2.01448i	−0.211014	−	0.0812316i
$616$	1.12439	−	0.825831i	0.0453028	−	0.0332737i
$617$	−5.57570	+	12.0587i	−0.224469	+	0.485467i	−0.986845	−	0.161668i	$-0.948313\pi$
$617$	−5.57570	+	12.0587i	−0.224469	+	0.485467i	0.762376	+	0.647135i	$0.224033\pi$
$618$	0.710937	−	6.91569i	0.0285981	−	0.278190i
$619$	21.9255	+	23.8500i	0.881260	+	0.958611i	0.999409	−	0.0343846i	$-0.0109471\pi$
$619$	21.9255	+	23.8500i	0.881260	+	0.958611i	−0.118149	+	0.992996i	$0.537696\pi$
$620$	−2.87004	+	49.2767i	−0.115264	+	1.97900i
$621$	−27.3714	−	1.15825i	−1.09838	−	0.0464788i
$622$	0.733960	+	12.6016i	0.0294291	+	0.505278i
$623$	−0.0802913	+	0.0829293i	−0.00321680	+	0.00332249i
$624$	0.109981	−	1.72541i	0.00440275	−	0.0690717i
$625$	0.883226	+	2.20244i	0.0353290	+	0.0880976i
$626$	2.99564	+	8.39899i	0.119730	+	0.335691i
$627$	2.78131	−	7.66511i	0.111075	−	0.306115i
$628$	−0.149030	+	0.994984i	−0.00594695	+	0.0397042i
$629$	−18.0794	−	12.9224i	−0.720871	−	0.515248i
$630$	14.4824	−	0.215814i	0.576992	−	0.00859825i
$631$	−19.5513	−	19.1758i	−0.778325	−	0.763375i	0.197880	−	0.980226i	$-0.436594\pi$
$631$	−19.5513	−	19.1758i	−0.778325	−	0.763375i	−0.976205	+	0.216851i	$0.930421\pi$
$632$	7.65759	−	33.2668i	0.304603	−	1.32328i
$633$	−19.4950	+	11.9644i	−0.774858	+	0.475541i
$634$	4.23095	+	13.4949i	0.168033	+	0.535950i
$635$	10.0190	−	35.1118i	0.397593	−	1.39337i
$636$	−57.8137	+	21.5316i	−2.29246	+	0.853784i
$637$	9.23534	−	25.8935i	0.365918	−	1.02594i
$638$	−15.2312	+	0.591039i	−0.603008	+	0.0233994i
$639$	2.03440	+	43.0499i	0.0804796	+	1.70303i
$640$	−59.9525	−	24.4933i	−2.36983	−	0.968183i
$641$	−20.2184	−	12.5613i	−0.798580	−	0.496142i	0.0664932	−	0.997787i	$-0.478819\pi$
$641$	−20.2184	−	12.5613i	−0.798580	−	0.496142i	−0.865074	+	0.501645i	$0.832728\pi$
$642$	19.0362	−	46.7266i	0.751297	−	1.84415i
$643$	−2.83136	+	1.19968i	−0.111658	+	0.0473107i	−0.445247	−	0.895408i	$-0.646884\pi$
$643$	−2.83136	+	1.19968i	−0.111658	+	0.0473107i	0.333589	+	0.942718i	$0.391740\pi$
$644$	−7.30862	−	6.46191i	−0.288000	−	0.254635i
$645$	−62.6392	−	20.4635i	−2.46642	−	0.805751i
$646$	−13.7053	−	84.0683i	−0.539229	−	3.30762i
$647$	−17.0681	+	6.21229i	−0.671017	+	0.244230i	−0.654986	−	0.755641i	$-0.727325\pi$
$647$	−17.0681	+	6.21229i	−0.671017	+	0.244230i	−0.0160315	+	0.999871i	$0.505103\pi$
$648$	4.72357	−	23.7352i	0.185559	−	0.932405i
$649$	2.43760	+	0.887213i	0.0956841	+	0.0348262i
$650$	−14.5276	+	76.5865i	−0.569818	+	3.00397i
$651$	3.65754	+	2.23476i	0.143350	+	0.0875872i
$652$	52.8268	−	42.0482i	2.06886	−	1.64673i
$653$	−14.0919	−	21.7303i	−0.551457	−	0.850373i	0.447580	−	0.894244i	$-0.352286\pi$
$653$	−14.0919	−	21.7303i	−0.551457	−	0.850373i	−0.999037	+	0.0438711i	$0.986031\pi$
$654$	32.5953	−	59.2113i	1.27458	−	2.31535i
$655$	−10.9277	−	2.29324i	−0.426982	−	0.0896045i
$656$	0.204479	−	0.0655636i	0.00798357	−	0.00255983i
$657$	−16.7821	−	10.3806i	−0.654733	−	0.404985i
$658$	7.58072	+	5.87550i	0.295527	+	0.229051i
$659$	−6.03694	+	7.28973i	−0.235166	+	0.283968i	−0.874566	−	0.484907i	$-0.838854\pi$
$659$	−6.03694	+	7.28973i	−0.235166	+	0.283968i	0.639400	+	0.768874i	$0.279183\pi$
$660$	−5.26847	−	17.1323i	−0.205075	−	0.666874i
$661$	7.00789	+	3.40677i	0.272576	+	0.132508i	0.568447	−	0.822720i	$-0.307544\pi$
$661$	7.00789	+	3.40677i	0.272576	+	0.132508i	−0.295872	+	0.955228i	$0.595610\pi$
$662$	−28.3316	+	14.6904i	−1.10114	+	0.570958i
$663$	21.5210	−	45.8826i	0.835806	−	1.78193i
$664$	−4.22545	−	34.2306i	−0.163979	−	1.32840i
$665$	11.1606	+	0.867470i	0.432789	+	0.0336390i
$666$	−10.2559	−	18.7860i	−0.397407	−	0.727942i
$667$	9.87286	+	38.3288i	0.382279	+	1.48410i
$668$	4.58849	−	8.44444i	0.177534	−	0.326725i
$669$	6.56592	−	1.97277i	0.253853	−	0.0762715i
$670$	−5.17378	+	0.877833i	−0.199881	+	0.0339136i
$671$	−3.40394	+	2.11480i	−0.131408	+	0.0816409i
$672$	−4.59611	+	3.81389i	−0.177299	+	0.147124i
$673$	15.1369	−	33.8800i	0.583483	−	1.30598i	−0.346387	−	0.938092i	$-0.612592\pi$
$673$	15.1369	−	33.8800i	0.583483	−	1.30598i	0.929871	−	0.367887i	$-0.119919\pi$
$674$	46.3316	+	49.1087i	1.78463	+	1.89160i
$675$	13.5745	−	40.9280i	0.522483	−	1.57532i
$676$	−8.79808	+	9.32542i	−0.338388	+	0.358670i
$677$	0.934524	+	2.24587i	0.0359167	+	0.0863157i	0.940209	−	0.340598i	$-0.110630\pi$
$677$	0.934524	+	2.24587i	0.0359167	+	0.0863157i	−0.904292	+	0.426914i	$0.859601\pi$
$678$	27.3048	−	5.20731i	1.04864	−	0.199986i
$679$	2.00945	+	1.39738i	0.0771158	+	0.0536265i
$680$	−50.2618	−	48.0374i	−1.92745	−	1.84215i
$681$	−0.833625	−	20.9494i	−0.0319446	−	0.802784i
$682$	2.26286	−	8.33724i	0.0866495	−	0.319250i
$683$	−1.88875	+	5.52009i	−0.0722711	+	0.211220i	−0.976371	−	0.216101i	$-0.930666\pi$
$683$	−1.88875	+	5.52009i	−0.0722711	+	0.211220i	0.904100	+	0.427321i	$0.140543\pi$
$684$	14.3512	−	48.2827i	0.548731	−	1.84613i
$685$	12.9735	+	7.82955i	0.495692	+	0.299152i
$686$	−16.5613	+	7.27117i	−0.632312	+	0.277614i
$687$	5.93269	+	26.4349i	0.226346	+	1.00855i
$688$	2.35999	−	0.893683i	0.0899737	−	0.0340713i
$689$	−43.6180	−	15.2400i	−1.66171	−	0.580597i
$690$	−66.0951	+	37.1148i	−2.51620	+	1.41294i
$691$	−20.7823	−	31.1574i	−0.790597	−	1.18528i	−0.979133	−	0.203218i	$-0.934860\pi$
$691$	−20.7823	−	31.1574i	−0.790597	−	1.18528i	0.188536	−	0.982066i	$-0.439626\pi$
$692$	−45.5852	−	8.95264i	−1.73289	−	0.340328i
$693$	−1.52786	−	0.296934i	−0.0580388	−	0.0112796i
$694$	17.7753	−	22.0379i	0.674741	−	0.836547i
$695$	−6.52364	−	3.06773i	−0.247456	−	0.116366i
$696$	−34.7960	+	3.41917i	−1.31894	+	0.129603i
$697$	6.28126	+	0.406599i	0.237920	+	0.0154010i
$698$	−2.03978	−	7.51533i	−0.0772070	−	0.284460i
$699$	−2.19782	+	9.88424i	−0.0831290	+	0.373856i
$700$	12.9370	−	8.27121i	0.488973	−	0.312622i
$701$	2.82508	−	6.54926i	0.106702	−	0.247362i	−0.856497	−	0.516151i	$-0.827364\pi$
$701$	2.82508	−	6.54926i	0.106702	−	0.247362i	0.963199	+	0.268789i	$0.0866235\pi$
$702$	37.9012	−	30.7558i	1.43049	−	1.16080i
$703$	−6.55190	−	15.1890i	−0.247110	−	0.572865i
$704$	9.61332	+	6.50237i	0.362316	+	0.245067i
$705$	38.3672	−	24.9345i	1.44499	−	0.939087i
$706$	−24.8588	+	75.8398i	−0.935574	+	2.85427i
$707$	4.33920	+	2.54278i	0.163192	+	0.0956309i
$708$	15.3555	+	4.58063i	0.577094	+	0.172151i
$709$	−19.3570	−	6.48372i	−0.726967	−	0.243501i	−0.0701347	−	0.997538i	$-0.522343\pi$
$709$	−19.3570	−	6.48372i	−0.726967	−	0.243501i	−0.656833	+	0.754036i	$0.728104\pi$
$710$	67.4484	+	98.3422i	2.53129	+	3.69072i
$711$	−33.0682	+	18.8944i	−1.24015	+	0.708595i
$712$	0.485814	+	0.220829i	0.0182066	+	0.00827593i
$713$	−22.4022	−	1.15953i	−0.838970	−	0.0434248i
$714$	−15.4449	+	5.07943i	−0.578012	+	0.190093i
$715$	5.15713	−	12.3937i	0.192866	−	0.463499i
$716$	12.0359	+	26.9392i	0.449801	+	1.00676i
$717$	−2.48884	−	37.8689i	−0.0929473	−	1.41424i
$718$	60.6105	+	34.4730i	2.26196	+	1.28652i
$719$	−48.4728	−	15.5422i	−1.80773	−	0.579625i	−0.807777	−	0.589488i	$-0.799330\pi$
$719$	−48.4728	−	15.5422i	−1.80773	−	0.579625i	−0.999951	+	0.00986279i	$0.996861\pi$
$720$	0.926011	+	2.47892i	0.0345104	+	0.0923840i
$721$	−1.02484	−	0.0397685i	−0.0381671	−	0.00148106i
$722$	7.50187	−	18.7069i	0.279191	−	0.696199i
$723$	−26.8511	+	18.4549i	−0.998603	+	0.686346i
$724$	−47.5087	−	14.5585i	−1.76565	−	0.541061i
$725$	−62.2770	−	1.61064i	−2.31291	−	0.0598176i
$726$	−3.67542	−	40.0631i	−0.136408	−	1.48688i
$727$	37.7593	+	0.488193i	1.40041	+	0.0181061i	0.709436	−	0.704770i	$-0.248950\pi$
$727$	37.7593	+	0.488193i	1.40041	+	0.0181061i	0.690978	+	0.722876i	$0.257180\pi$
$728$	6.45412			0.239206
$729$	−23.0336	+	14.0874i	−0.853095	+	0.521756i
$730$	−54.6004			−2.02085
$731$	73.9653	+	0.956303i	2.73570	+	0.0353702i
$732$	−20.2179	+	14.2842i	−0.747275	+	0.527959i
$733$	35.1210	+	0.908318i	1.29723	+	0.0335495i	0.668286	−	0.743905i	$-0.267028\pi$
$733$	35.1210	+	0.908318i	1.29723	+	0.0335495i	0.628939	+	0.777454i	$0.283489\pi$
$734$	−50.8140	−	15.5713i	−1.87558	−	0.574748i
$735$	3.30204	+	41.9476i	0.121798	+	1.54726i
$736$	11.6341	−	29.0112i	0.428840	−	1.06937i
$737$	0.563497	+	0.0218662i	0.0207567	+	0.000805453i
$738$	5.27547	+	2.98674i	0.194193	+	0.109943i
$739$	42.7991	+	13.7230i	1.57439	+	0.504808i	0.958998	−	0.283413i	$-0.0914669\pi$
$739$	42.7991	+	13.7230i	1.57439	+	0.504808i	0.615392	+	0.788221i	$0.288998\pi$
$740$	−31.6071	−	17.9770i	−1.16190	−	0.660846i
$741$	31.3625	−	20.9638i	1.15213	−	0.770125i
$742$	6.04655	+	13.5337i	0.221976	+	0.496836i
$743$	4.83963	−	11.6307i	0.177549	−	0.426689i	−0.809498	−	0.587123i	$-0.800260\pi$
$743$	4.83963	−	11.6307i	0.177549	−	0.426689i	0.987047	+	0.160434i	$0.0512893\pi$
$744$	4.05070	−	19.3975i	0.148506	−	0.711145i
$745$	−20.6836	−	1.07057i	−0.757788	−	0.0392228i
$746$	−1.25060	−	0.568469i	−0.0457879	−	0.0208131i
$747$	−24.8666	+	29.3660i	−0.909823	+	1.07445i
$748$	11.3802	+	16.5927i	0.416101	+	0.606690i
$749$	−7.05801	−	2.36412i	−0.257894	−	0.0863829i
$750$	−10.9823	−	46.1353i	−0.401018	−	1.68462i
$751$	−8.24538	−	4.83181i	−0.300878	−	0.176315i	0.347403	−	0.937716i	$-0.387063\pi$
$751$	−8.24538	−	4.83181i	−0.300878	−	0.176315i	−0.648282	+	0.761401i	$0.724512\pi$
$752$	−0.545796	+	1.66513i	−0.0199031	+	0.0607209i
$753$	1.00927	+	19.1337i	0.0367800	+	0.697272i
$754$	−58.4109	−	39.5086i	−2.12720	−	1.43882i
$755$	−18.2230	−	42.2455i	−0.663201	−	1.53747i
$756$	−9.53001	−	1.27297i	−0.346603	−	0.0462976i
$757$	4.79985	−	11.1273i	0.174453	−	0.404429i	−0.808446	−	0.588570i	$-0.799691\pi$
$757$	4.79985	−	11.1273i	0.174453	−	0.404429i	0.982900	+	0.184141i	$0.0589504\pi$
$758$	48.9018	−	31.2651i	1.77619	−	1.13560i
$759$	7.77031	−	2.44459i	0.282044	−	0.0887329i
$760$	−13.5561	−	49.9458i	−0.491731	−	1.81172i
$761$	−30.3017	−	1.96149i	−1.09844	−	0.0711040i	−0.495285	−	0.868731i	$-0.664936\pi$
$761$	−30.3017	−	1.96149i	−1.09844	−	0.0711040i	−0.603151	+	0.797627i	$0.706089\pi$
$762$	−16.3000	+	35.9532i	−0.590486	+	1.30245i
$763$	−9.02334	−	4.24321i	−0.326667	−	0.153615i
$764$	−13.5963	+	16.8567i	−0.491895	+	0.609854i
$765$	−1.35118	+	77.5564i	−0.0488521	+	2.80406i
$766$	−23.3982	−	4.59526i	−0.845412	−	0.166033i
$767$	6.65930	+	9.98380i	0.240453	+	0.360494i

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)

\(f(q)\)	\(=\)	\(q+(-2.27606 - 0.0294274i) q^{2} +(-1.57284 - 0.725368i) q^{3} +(3.18025 + 0.0822491i) q^{4} +(-3.48668 - 1.06845i) q^{5} +(3.55854 + 1.69727i) q^{6} +(0.216487 - 0.539838i) q^{7} +(-2.68694 - 0.104265i) q^{8} +(1.94768 + 2.28178i) q^{9} +O(q^{10})\)	\(q+(-2.27606 - 0.0294274i) q^{2} +(-1.57284 - 0.725368i) q^{3} +(3.18025 + 0.0822491i) q^{4} +(-3.48668 - 1.06845i) q^{5} +(3.55854 + 1.69727i) q^{6} +(0.216487 - 0.539838i) q^{7} +(-2.68694 - 0.104265i) q^{8} +(1.94768 + 2.28178i) q^{9} +(7.90445 + 2.53446i) q^{10} +(-0.775368 - 0.441001i) q^{11} +(-4.94238 - 2.43622i) q^{12} +(-1.68337 - 3.76779i) q^{13} +(-0.508623 + 1.22233i) q^{14} +(4.70899 + 4.20963i) q^{15} +(-0.241559 - 0.0125030i) q^{16} +(-6.45469 - 2.93401i) q^{17} +(-4.36589 - 5.25079i) q^{18} +(-2.98512 - 4.35242i) q^{19} +(-11.0006 - 3.68471i) q^{20} +(-0.732082 + 0.692049i) q^{21} +(1.75181 + 1.02656i) q^{22} +(1.64220 - 5.01006i) q^{23} +(4.15050 + 2.11301i) q^{24} +(6.87379 + 4.64937i) q^{25} +(3.72057 + 8.62526i) q^{26} +(-1.40827 - 5.00168i) q^{27} +(0.732883 - 1.69901i) q^{28} +(-6.32489 + 4.04378i) q^{29} +(-10.5941 - 9.71995i) q^{30} +(-1.11447 - 4.10614i) q^{31} +(5.91612 + 0.382962i) q^{32} +(0.899646 + 1.25605i) q^{33} +(14.6049 + 6.86794i) q^{34} +(-1.33161 + 1.65094i) q^{35} +(6.00644 + 7.41683i) q^{36} +(3.07552 + 0.604013i) q^{37} +(6.66624 + 9.99420i) q^{38} +(-0.0853574 + 7.14722i) q^{39} +(9.25709 + 3.23440i) q^{40} +(-0.830224 + 0.314390i) q^{41} +(1.68663 - 1.55360i) q^{42} +(-9.55271 + 4.19408i) q^{43} +(-2.42959 - 1.46627i) q^{44} +(-4.35297 - 10.0369i) q^{45} +(-3.88518 + 11.3549i) q^{46} +(1.89759 - 6.99145i) q^{47} +(0.370866 + 0.194885i) q^{48} +(4.81590 + 4.60277i) q^{49} +(-15.5083 - 10.7845i) q^{50} +(8.02398 + 9.29677i) q^{51} +(-5.04363 - 12.1210i) q^{52} +(7.68328 - 8.14380i) q^{53} +(3.05812 + 11.4256i) q^{54} +(2.23227 + 2.36607i) q^{55} +(-0.637973 + 1.42794i) q^{56} +(1.53803 + 9.01099i) q^{57} +(14.5148 - 9.01776i) q^{58} +(-2.86711 + 0.486461i) q^{59} +(14.6295 + 13.7750i) q^{60} +(2.14494 - 3.94744i) q^{61} +(2.41578 + 9.37862i) q^{62} +(1.65344 - 0.557457i) q^{63} +(-12.9719 - 1.00825i) q^{64} +(1.84367 + 14.9357i) q^{65} +(-2.01068 - 2.88533i) q^{66} +(-0.561233 + 0.291008i) q^{67} +(-20.2862 - 9.86179i) q^{68} +(-6.21707 + 6.68885i) q^{69} +(3.07941 - 3.71845i) q^{70} +(11.3548 + 8.80061i) q^{71} +(-4.99539 - 6.33408i) q^{72} +(-6.26361 + 2.00834i) q^{73} +(-6.98230 - 1.46527i) q^{74} +(-7.43890 - 12.2988i) q^{75} +(-9.13545 - 14.0873i) q^{76} +(-0.405926 + 0.323102i) q^{77} +(0.404602 - 16.2650i) q^{78} +(-2.36594 + 12.4727i) q^{79} +(0.828882 + 0.301688i) q^{80} +(-1.41307 + 8.88838i) q^{81} +(1.89889 - 0.691140i) q^{82} +(2.06384 + 12.6595i) q^{83} +(-2.38512 + 2.14067i) q^{84} +(19.3706 + 17.1265i) q^{85} +(21.8660 - 9.26487i) q^{86} +(12.8813 - 1.77237i) q^{87} +(2.03738 + 1.26578i) q^{88} +(-0.183718 - 0.0750572i) q^{89} +(9.61227 + 22.9726i) q^{90} +(-2.39843 + 0.0930698i) q^{91} +(5.63468 - 15.7982i) q^{92} +(-1.22557 + 7.26673i) q^{93} +(-4.52477 + 15.8571i) q^{94} +(5.75783 + 18.3649i) q^{95} +(-9.02735 - 4.89370i) q^{96} +(-0.943971 + 4.10088i) q^{97} +(-10.8258 - 10.6179i) q^{98} +(-0.503902 - 2.62815i) 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

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