LMFDB - Embedded newform 273.2.k.b.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6040683.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} - 2x^{3} + 25x^{2} - 5x + 1 $ x^6 + 5x^4 - 2x^3 + 25x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.3
Root			$-1.16503 + 2.01789i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.b.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16503 + 2.01789i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.71459 + 2.96975i) q^{4} +0.900885 q^{5} +(-1.16503 + 2.01789i) q^{6} +(-0.500000 + 0.866025i) q^{7} -3.33006 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.16503 + 2.01789i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.71459 + 2.96975i) q^{4} +0.900885 q^{5} +(-1.16503 + 2.01789i) q^{6} +(-0.500000 + 0.866025i) q^{7} -3.33006 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.04956 + 1.81789i) q^{10} +(-1.45044 - 2.51224i) q^{11} -3.42917 q^{12} +(1.54956 - 3.25559i) q^{13} -2.33006 q^{14} +(0.450443 + 0.780189i) q^{15} +(-0.450443 - 0.780189i) q^{16} +(-0.834971 + 1.44621i) q^{17} -2.33006 q^{18} +(1.83006 - 3.16975i) q^{19} +(-1.54465 + 2.67540i) q^{20} -1.00000 q^{21} +(3.37962 - 5.85367i) q^{22} +(2.21459 + 3.83578i) q^{23} +(-1.66503 - 2.88392i) q^{24} -4.18841 q^{25} +(8.37470 - 0.666022i) q^{26} -1.00000 q^{27} +(-1.71459 - 2.96975i) q^{28} +(-2.66503 - 4.61597i) q^{29} +(-1.04956 + 1.81789i) q^{30} +6.56100 q^{31} +(-2.28050 + 3.94994i) q^{32} +(1.45044 - 2.51224i) q^{33} -3.89106 q^{34} +(-0.450443 + 0.780189i) q^{35} +(-1.71459 - 2.96975i) q^{36} +(-4.30879 - 7.46304i) q^{37} +8.52829 q^{38} +(3.59420 - 0.285839i) q^{39} -3.00000 q^{40} +(3.66012 + 6.33951i) q^{41} +(-1.16503 - 2.01789i) q^{42} +(2.21459 - 3.83578i) q^{43} +9.94764 q^{44} +(-0.450443 + 0.780189i) q^{45} +(-5.16012 + 8.93759i) q^{46} +6.95746 q^{47} +(0.450443 - 0.780189i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-4.87962 - 8.45174i) q^{50} -1.66994 q^{51} +(7.01144 + 10.1838i) q^{52} -0.141653 q^{53} +(-1.16503 - 2.01789i) q^{54} +(-1.30668 - 2.26324i) q^{55} +(1.66503 - 2.88392i) q^{56} +3.66012 q^{57} +(6.20967 - 10.7555i) q^{58} +(-4.74288 + 8.21490i) q^{59} -3.08929 q^{60} +(1.25923 - 2.18105i) q^{61} +(7.64376 + 13.2394i) q^{62} +(-0.500000 - 0.866025i) q^{63} -12.4292 q^{64} +(1.39597 - 2.93291i) q^{65} +6.75923 q^{66} +(-0.00491189 - 0.00850764i) q^{67} +(-2.86326 - 4.95931i) q^{68} +(-2.21459 + 3.83578i) q^{69} -2.09911 q^{70} +(-7.04465 + 12.2017i) q^{71} +(1.66503 - 2.88392i) q^{72} -2.57083 q^{73} +(10.0397 - 17.3893i) q^{74} +(-2.09420 - 3.62727i) q^{75} +(6.27559 + 10.8696i) q^{76} +2.90089 q^{77} +(4.76414 + 6.91970i) q^{78} -9.41935 q^{79} +(-0.405797 - 0.702861i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.52829 + 14.7714i) q^{82} +1.58065 q^{83} +(1.71459 - 2.96975i) q^{84} +(-0.752213 + 1.30287i) q^{85} +10.3202 q^{86} +(2.66503 - 4.61597i) q^{87} +(4.83006 + 8.36591i) q^{88} +(-4.16012 - 7.20553i) q^{89} -2.09911 q^{90} +(2.04465 + 2.96975i) q^{91} -15.1884 q^{92} +(3.28050 + 5.68199i) q^{93} +(8.10565 + 14.0394i) q^{94} +(1.64867 - 2.85558i) q^{95} -4.56100 q^{96} +(3.85133 - 6.67069i) q^{97} +(1.16503 - 2.01789i) q^{98} +2.90089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.16503	+	2.01789i	0.823800	+	1.42686i	0.902833	+	0.429992i	$0.141484\pi$
$2$	1.16503	+	2.01789i	0.823800	+	1.42686i	−0.0790327	+	0.996872i	$0.525183\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.71459	+	2.96975i	−0.857293	+	1.48488i
$5$	0.900885			0.402888			0.201444	−	0.979500i	$-0.435437\pi$
$5$	0.900885			0.402888			0.201444	+	0.979500i	$0.435437\pi$
$6$	−1.16503	+	2.01789i	−0.475621	+	0.823800i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−3.33006			−1.17735
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.04956	+	1.81789i	0.331899	+	0.574866i
$11$	−1.45044	−	2.51224i	−0.437325	−	0.757469i	0.560157	−	0.828386i	$-0.310741\pi$
$11$	−1.45044	−	2.51224i	−0.437325	−	0.757469i	−0.997482	+	0.0709174i	$0.977407\pi$
$12$	−3.42917			−0.989917
$13$	1.54956	−	3.25559i	0.429770	−	0.902938i
$13$	1.54956	−	3.25559i	0.429770	−	0.902938i
$14$	−2.33006			−0.622734
$15$	0.450443	+	0.780189i	0.116304	+	0.201444i
$16$	−0.450443	−	0.780189i	−0.112611	−	0.195047i
$17$	−0.834971	+	1.44621i	−0.202510	+	0.350758i	−0.949337	−	0.314261i	$-0.898243\pi$
$17$	−0.834971	+	1.44621i	−0.202510	+	0.350758i	0.746826	+	0.665019i	$0.231577\pi$
$18$	−2.33006			−0.549200
$19$	1.83006	−	3.16975i	0.419844	−	0.727192i	−0.576079	−	0.817394i	$-0.695418\pi$
$19$	1.83006	−	3.16975i	0.419844	−	0.727192i	0.995923	+	0.0902023i	$0.0287514\pi$
$20$	−1.54465	+	2.67540i	−0.345393	+	0.598239i
$21$	−1.00000			−0.218218
$22$	3.37962	−	5.85367i	0.720537	−	1.24801i
$23$	2.21459	+	3.83578i	0.461773	+	0.799815i	0.999049	−	0.0435916i	$-0.0138800\pi$
$23$	2.21459	+	3.83578i	0.461773	+	0.799815i	−0.537276	+	0.843406i	$0.680547\pi$
$24$	−1.66503	−	2.88392i	−0.339873	−	0.588677i
$25$	−4.18841			−0.837681
$26$	8.37470	−	0.666022i	1.64241	−	0.130618i
$27$	−1.00000			−0.192450
$28$	−1.71459	−	2.96975i	−0.324026	−	0.561230i
$29$	−2.66503	−	4.61597i	−0.494884	−	0.857163i	0.505099	−	0.863061i	$-0.331456\pi$
$29$	−2.66503	−	4.61597i	−0.494884	−	0.857163i	−0.999983	+	0.00589795i	$0.998123\pi$
$30$	−1.04956	+	1.81789i	−0.191622	+	0.331899i
$31$	6.56100			1.17839			0.589195	−	0.807991i	$-0.299445\pi$
$31$	6.56100			1.17839			0.589195	+	0.807991i	$0.299445\pi$
$32$	−2.28050	+	3.94994i	−0.403139	+	0.698258i
$33$	1.45044	−	2.51224i	0.252490	−	0.437325i
$34$	−3.89106			−0.667311
$35$	−0.450443	+	0.780189i	−0.0761387	+	0.131876i
$36$	−1.71459	−	2.96975i	−0.285764	−	0.494959i
$37$	−4.30879	−	7.46304i	−0.708361	−	1.22692i	−0.965465	−	0.260533i	$-0.916102\pi$
$37$	−4.30879	−	7.46304i	−0.708361	−	1.22692i	0.257104	−	0.966384i	$-0.417232\pi$
$38$	8.52829			1.38347
$39$	3.59420	−	0.285839i	0.575533	−	0.0457709i
$40$	−3.00000			−0.474342
$41$	3.66012	+	6.33951i	0.571614	+	0.990065i	0.996400	+	0.0847713i	$0.0270160\pi$
$41$	3.66012	+	6.33951i	0.571614	+	0.990065i	−0.424786	+	0.905294i	$0.639651\pi$
$42$	−1.16503	−	2.01789i	−0.179768	−	0.311367i
$43$	2.21459	−	3.83578i	0.337721	−	0.584951i	−0.646282	−	0.763098i	$-0.723677\pi$
$43$	2.21459	−	3.83578i	0.337721	−	0.584951i	0.984004	+	0.178148i	$0.0570105\pi$
$44$	9.94764			1.49966
$45$	−0.450443	+	0.780189i	−0.0671480	+	0.116304i
$46$	−5.16012	+	8.93759i	−0.760818	+	1.31778i
$47$	6.95746			1.01485			0.507425	−	0.861696i	$-0.330597\pi$
$47$	6.95746			1.01485			0.507425	+	0.861696i	$0.330597\pi$
$48$	0.450443	−	0.780189i	0.0650158	−	0.112611i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−4.87962	−	8.45174i	−0.690082	−	1.19526i
$51$	−1.66994			−0.233839
$52$	7.01144	+	10.1838i	0.972312	+	1.41224i
$53$	−0.141653			−0.0194575			−0.00972874	−	0.999953i	$-0.503097\pi$
$53$	−0.141653			−0.0194575			−0.00972874	+	0.999953i	$0.503097\pi$
$54$	−1.16503	−	2.01789i	−0.158540	−	0.274600i
$55$	−1.30668	−	2.26324i	−0.176193	−	0.305175i
$56$	1.66503	−	2.88392i	0.222499	−	0.385379i
$57$	3.66012			0.484794
$58$	6.20967	−	10.7555i	0.815370	−	1.41226i
$59$	−4.74288	+	8.21490i	−0.617470	+	1.06949i	0.372476	+	0.928042i	$0.378509\pi$
$59$	−4.74288	+	8.21490i	−0.617470	+	1.06949i	−0.989946	+	0.141447i	$0.954824\pi$
$60$	−3.08929			−0.398826
$61$	1.25923	−	2.18105i	0.161228	−	0.279255i	−0.774081	−	0.633086i	$-0.781788\pi$
$61$	1.25923	−	2.18105i	0.161228	−	0.279255i	0.935309	+	0.353831i	$0.115121\pi$
$62$	7.64376	+	13.2394i	0.970759	+	1.68140i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	−12.4292			−1.55365
$65$	1.39597	−	2.93291i	0.173149	−	0.363783i
$66$	6.75923			0.832004
$67$	−0.00491189	−	0.00850764i	−0.000600083	−	0.00103937i	0.865725	−	0.500520i	$-0.166858\pi$
$67$	−0.00491189	−	0.00850764i	−0.000600083	−	0.00103937i	−0.866325	+	0.499480i	$0.833524\pi$
$68$	−2.86326	−	4.95931i	−0.347221	−	0.601405i
$69$	−2.21459	+	3.83578i	−0.266605	+	0.461773i
$70$	−2.09911			−0.250892
$71$	−7.04465	+	12.2017i	−0.836046	+	1.44807i	0.0571306	+	0.998367i	$0.481805\pi$
$71$	−7.04465	+	12.2017i	−0.836046	+	1.44807i	−0.893176	+	0.449707i	$0.851528\pi$
$72$	1.66503	−	2.88392i	0.196226	−	0.339873i
$73$	−2.57083			−0.300892			−0.150446	−	0.988618i	$-0.548071\pi$
$73$	−2.57083			−0.300892			−0.150446	+	0.988618i	$0.548071\pi$
$74$	10.0397	−	17.3893i	1.16710	−	2.02147i
$75$	−2.09420	−	3.62727i	−0.241818	−	0.418841i
$76$	6.27559	+	10.8696i	0.719859	+	1.24683i
$77$	2.90089			0.330587
$78$	4.76414	+	6.91970i	0.539433	+	0.783501i
$79$	−9.41935			−1.05976			−0.529880	−	0.848073i	$-0.677763\pi$
$79$	−9.41935			−1.05976			−0.529880	+	0.848073i	$0.677763\pi$
$80$	−0.405797	−	0.702861i	−0.0453695	−	0.0785822i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.52829	+	14.7714i	−0.941792	+	1.63123i
$83$	1.58065			0.173499			0.0867494	−	0.996230i	$-0.472352\pi$
$83$	1.58065			0.173499			0.0867494	+	0.996230i	$0.472352\pi$
$84$	1.71459	−	2.96975i	0.187077	−	0.324026i
$85$	−0.752213	+	1.30287i	−0.0815889	+	0.141316i
$86$	10.3202			1.11286
$87$	2.66503	−	4.61597i	0.285721	−	0.494884i
$88$	4.83006	+	8.36591i	0.514886	+	0.891809i
$89$	−4.16012	−	7.20553i	−0.440972	−	0.763785i	0.556790	−	0.830653i	$-0.312033\pi$
$89$	−4.16012	−	7.20553i	−0.440972	−	0.763785i	−0.997762	+	0.0668680i	$0.978699\pi$
$90$	−2.09911			−0.221266
$91$	2.04465	+	2.96975i	0.214337	+	0.311315i
$92$	−15.1884			−1.58350
$93$	3.28050	+	5.68199i	0.340172	+	0.589195i
$94$	8.10565	+	14.0394i	0.836034	+	1.44805i
$95$	1.64867	−	2.85558i	0.169150	−	0.292977i
$96$	−4.56100			−0.465505
$97$	3.85133	−	6.67069i	0.391043	−	0.677306i	−0.601544	−	0.798839i	$-0.705448\pi$
$97$	3.85133	−	6.67069i	0.391043	−	0.677306i	0.992587	+	0.121533i	$0.0387810\pi$
$98$	1.16503	−	2.01789i	0.117686	−	0.203838i
$99$	2.90089			0.291550
$100$	7.18139	−	12.4385i	0.718139	−	1.24385i
$101$	−9.20476	−	15.9431i	−0.915908	−	1.58640i	−0.805566	−	0.592506i	$-0.798139\pi$
$101$	−9.20476	−	15.9431i	−0.915908	−	1.58640i	−0.110342	−	0.993894i	$-0.535195\pi$
$102$	−1.94553	−	3.36976i	−0.192636	−	0.333656i
$103$	8.05658			0.793838			0.396919	−	0.917854i	$-0.370079\pi$
$103$	8.05658			0.793838			0.396919	+	0.917854i	$0.370079\pi$
$104$	−5.16012	+	10.8413i	−0.505991	+	1.06308i
$105$	−0.900885			−0.0879174
$106$	−0.165029	−	0.285839i	−0.0160291	−	0.0277632i
$107$	−1.81370	−	3.14142i	−0.175337	−	0.303693i	0.764941	−	0.644101i	$-0.222768\pi$
$107$	−1.81370	−	3.14142i	−0.175337	−	0.303693i	−0.940278	+	0.340408i	$0.889435\pi$
$108$	1.71459	−	2.96975i	0.164986	−	0.285764i
$109$	−8.84852			−0.847535			−0.423767	−	0.905771i	$-0.639293\pi$
$109$	−8.84852			−0.847535			−0.423767	+	0.905771i	$0.639293\pi$
$110$	3.04465	−	5.27348i	0.290296	−	0.502807i
$111$	4.30879	−	7.46304i	0.408972	−	0.708361i
$112$	0.900885			0.0851256
$113$	3.18139	−	5.51032i	0.299280	−	0.518368i	−0.676692	−	0.736266i	$-0.736587\pi$
$113$	3.18139	−	5.51032i	0.299280	−	0.518368i	0.975971	+	0.217899i	$0.0699203\pi$
$114$	4.26414	+	7.38571i	0.399374	+	0.691736i
$115$	1.99509	+	3.45559i	0.186043	+	0.322236i
$116$	18.2777			1.69704
$117$	2.04465	+	2.96975i	0.189028	+	0.274554i
$118$	−22.1024			−2.03469
$119$	−0.834971	−	1.44621i	−0.0765416	−	0.132574i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	1.29243	−	2.23856i	0.117494	−	0.203505i
$122$	5.86817			0.531279
$123$	−3.66012	+	6.33951i	−0.330022	+	0.571614i
$124$	−11.2494	+	19.4845i	−1.01023	+	1.74976i
$125$	−8.27770			−0.740380
$126$	1.16503	−	2.01789i	0.103789	−	0.179768i
$127$	−5.53973	−	9.59510i	−0.491572	−	0.851427i	0.508381	−	0.861132i	$-0.330244\pi$
$127$	−5.53973	−	9.59510i	−0.491572	−	0.851427i	−0.999953	+	0.00970477i	$0.996911\pi$
$128$	−9.91935	−	17.1808i	−0.876755	−	1.51858i
$129$	4.42917			0.389967
$130$	7.54465	−	0.600009i	0.661709	−	0.0526243i
$131$	−6.90089			−0.602933			−0.301467	−	0.953477i	$-0.597476\pi$
$131$	−6.90089			−0.602933			−0.301467	+	0.953477i	$0.597476\pi$
$132$	4.97382	+	8.61491i	0.432915	+	0.749831i
$133$	1.83006	+	3.16975i	0.158686	+	0.274853i
$134$	0.0114450	−	0.0198233i	0.000988697	−	0.00171247i
$135$	−0.900885			−0.0775358
$136$	2.78050	−	4.81597i	0.238426	−	0.412966i
$137$	−6.25923	+	10.8413i	−0.534762	+	0.926236i	0.464412	+	0.885619i	$0.346266\pi$
$137$	−6.25923	+	10.8413i	−0.534762	+	0.926236i	−0.999175	+	0.0406165i	$0.987068\pi$
$138$	−10.3202			−0.878517
$139$	−1.66503	+	2.88392i	−0.141226	+	0.244611i	−0.927959	−	0.372683i	$-0.878438\pi$
$139$	−1.66503	+	2.88392i	−0.141226	+	0.244611i	0.786733	+	0.617294i	$0.211771\pi$
$140$	−1.54465	−	2.67540i	−0.130546	−	0.226113i
$141$	3.47873	+	6.02534i	0.292962	+	0.507425i
$142$	−32.8289			−2.75494
$143$	−10.4264	+	0.829187i	−0.871897	+	0.0693401i
$144$	0.900885			0.0750738
$145$	−2.40089	−	4.15845i	−0.199383	−	0.345341i
$146$	−2.99509	−	5.18764i	−0.247875	−	0.429333i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	29.5512			2.42909
$149$	−7.83708	+	13.5742i	−0.642039	+	1.11204i	0.342939	+	0.939358i	$0.388578\pi$
$149$	−7.83708	+	13.5742i	−0.642039	+	1.11204i	−0.984977	+	0.172685i	$0.944756\pi$
$150$	4.87962	−	8.45174i	0.398419	−	0.690082i
$151$	8.46189			0.688619			0.344309	−	0.938856i	$-0.388113\pi$
$151$	8.46189			0.688619			0.344309	+	0.938856i	$0.388113\pi$
$152$	−6.09420	+	10.5555i	−0.494305	+	0.856162i
$153$	−0.834971	−	1.44621i	−0.0675034	−	0.116919i
$154$	3.37962	+	5.85367i	0.272337	+	0.471702i
$155$	5.91071			0.474760
$156$	−5.31370	+	11.1640i	−0.425437	+	0.893834i
$157$	−24.7396			−1.97443			−0.987217	−	0.159382i	$-0.949050\pi$
$157$	−24.7396			−1.97443			−0.987217	+	0.159382i	$0.949050\pi$
$158$	−10.9738	−	19.0072i	−0.873030	−	1.51213i
$159$	−0.0708263	−	0.122675i	−0.00561689	−	0.00972874i
$160$	−2.05447	+	3.55845i	−0.162420	+	0.281320i
$161$	−4.42917			−0.349068
$162$	1.16503	−	2.01789i	0.0915334	−	0.158540i
$163$	12.3583	−	21.4053i	0.967980	−	1.67659i	0.266596	−	0.963808i	$-0.414101\pi$
$163$	12.3583	−	21.4053i	0.967980	−	1.67659i	0.701385	−	0.712783i	$-0.252566\pi$
$164$	−25.1024			−1.96016
$165$	1.30668	−	2.26324i	0.101725	−	0.176193i
$166$	1.84150	+	3.18958i	0.142928	+	0.247559i
$167$	5.35835	+	9.28093i	0.414641	+	0.718180i	0.995391	−	0.0959025i	$-0.0305737\pi$
$167$	5.35835	+	9.28093i	0.414641	+	0.718180i	−0.580749	+	0.814082i	$0.697240\pi$
$168$	3.33006			0.256920
$169$	−8.19774	−	10.0895i	−0.630596	−	0.776112i
$170$	−3.50540			−0.268852
$171$	1.83006	+	3.16975i	0.139948	+	0.242397i
$172$	7.59420	+	13.1535i	0.579053	+	1.00295i
$173$	3.64376	−	6.31118i	0.277030	−	0.479830i	−0.693615	−	0.720346i	$-0.743983\pi$
$173$	3.64376	−	6.31118i	0.277030	−	0.479830i	0.970645	+	0.240516i	$0.0773165\pi$
$174$	12.4193			0.941508
$175$	2.09420	−	3.62727i	0.158307	−	0.274196i
$176$	−1.30668	+	2.26324i	−0.0984949	+	0.170598i
$177$	−9.48575			−0.712993
$178$	9.69332	−	16.7893i	0.726545	−	1.25841i
$179$	8.55609	+	14.8196i	0.639512	+	1.10767i	0.985540	+	0.169443i	$0.0541970\pi$
$179$	8.55609	+	14.8196i	0.639512	+	1.10767i	−0.346028	+	0.938224i	$0.612470\pi$
$180$	−1.54465	−	2.67540i	−0.115131	−	0.199413i
$181$	15.3529			1.14118			0.570588	−	0.821237i	$-0.306715\pi$
$181$	15.3529			1.14118			0.570588	+	0.821237i	$0.306715\pi$
$182$	−3.61056	+	7.58572i	−0.267633	+	0.562291i
$183$	2.51846			0.186170
$184$	−7.37470	−	12.7734i	−0.543670	−	0.941665i
$185$	−3.88172	−	6.72334i	−0.285390	−	0.494310i
$186$	−7.64376	+	13.2394i	−0.560468	+	0.970759i
$187$	4.84431			0.354251
$188$	−11.9292	+	20.6619i	−0.870024	+	1.50693i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	7.68301			0.557384
$191$	−11.7756	+	20.3959i	−0.852052	+	1.47580i	0.0273017	+	0.999627i	$0.491309\pi$
$191$	−11.7756	+	20.3959i	−0.852052	+	1.47580i	−0.879353	+	0.476170i	$0.842025\pi$
$192$	−6.21459	−	10.7640i	−0.448499	−	0.776823i
$193$	5.84199	+	10.1186i	0.420516	+	0.728355i	0.995990	−	0.0894654i	$-0.0285158\pi$
$193$	5.84199	+	10.1186i	0.420516	+	0.728355i	−0.575474	+	0.817820i	$0.695183\pi$
$194$	17.9476			1.28857
$195$	3.23796	−	0.257508i	0.231875	−	0.0184406i
$196$	3.42917			0.244941
$197$	11.4738	+	19.8732i	0.817476	+	1.41591i	0.907536	+	0.419973i	$0.137961\pi$
$197$	11.4738	+	19.8732i	0.817476	+	1.41591i	−0.0900607	+	0.995936i	$0.528706\pi$
$198$	3.37962	+	5.85367i	0.240179	+	0.416002i
$199$	−13.9357	+	24.1374i	−0.987876	+	1.71105i	−0.359492	+	0.933148i	$0.617050\pi$
$199$	−13.9357	+	24.1374i	−0.987876	+	1.71105i	−0.628384	+	0.777903i	$0.716283\pi$
$200$	13.9476			0.986247
$201$	0.00491189	−	0.00850764i	0.000346458	−	0.000600083i
$202$	21.4476	−	37.1484i	1.50905	−	2.61375i
$203$	5.33006			0.374097
$204$	2.86326	−	4.95931i	0.200468	−	0.347221i
$205$	3.29734	+	5.71117i	0.230297	+	0.398885i
$206$	9.38615	+	16.2573i	0.653964	+	1.13270i
$207$	−4.42917			−0.307849
$208$	−3.23796	+	0.257508i	−0.224512	+	0.0178550i
$209$	−10.6176			−0.734433
$210$	−1.04956	−	1.81789i	−0.0724263	−	0.125446i
$211$	3.40299	+	5.89416i	0.234272	+	0.405770i	0.959061	−	0.283200i	$-0.0913961\pi$
$211$	3.40299	+	5.89416i	0.234272	+	0.405770i	−0.724789	+	0.688971i	$0.758063\pi$
$212$	0.242876	−	0.420673i	0.0166808	−	0.0288919i
$213$	−14.0893			−0.965382
$214$	4.22603	−	7.31970i	0.288886	−	0.500365i
$215$	1.99509	−	3.45559i	0.136064	−	0.235670i
$216$	3.33006			0.226582
$217$	−3.28050	+	5.68199i	−0.222695	+	0.385719i
$218$	−10.3088	−	17.8553i	−0.698199	−	1.20932i
$219$	−1.28541	−	2.22640i	−0.0868602	−	0.150446i
$220$	8.96168			0.604196
$221$	3.41444	+	4.95931i	0.229680	+	0.333599i
$222$	20.0795			1.34765
$223$	10.2592	+	17.7695i	0.687009	+	1.18993i	0.972801	+	0.231643i	$0.0744101\pi$
$223$	10.2592	+	17.7695i	0.687009	+	1.18993i	−0.285792	+	0.958292i	$0.592257\pi$
$224$	−2.28050	−	3.94994i	−0.152372	−	0.263917i
$225$	2.09420	−	3.62727i	0.139614	−	0.241818i
$226$	14.8256			0.986186
$227$	−0.752213	+	1.30287i	−0.0499261	+	0.0864745i	−0.889908	−	0.456139i	$-0.849232\pi$
$227$	−0.752213	+	1.30287i	−0.0499261	+	0.0864745i	0.839982	+	0.542614i	$0.182565\pi$
$228$	−6.27559	+	10.8696i	−0.415611	+	0.719859i
$229$	25.8148			1.70589			0.852946	−	0.521999i	$-0.174813\pi$
$229$	25.8148			1.70589			0.852946	+	0.521999i	$0.174813\pi$
$230$	−4.64867	+	8.05174i	−0.306524	+	0.530916i
$231$	1.45044	+	2.51224i	0.0954321	+	0.165293i
$232$	8.87470	+	15.3714i	0.582653	+	1.00918i
$233$	−24.0369			−1.57471			−0.787356	−	0.616499i	$-0.788551\pi$
$233$	−24.0369			−1.57471			−0.787356	+	0.616499i	$0.788551\pi$
$234$	−3.61056	+	7.58572i	−0.236030	+	0.495894i
$235$	6.26787			0.408871
$236$	−16.2641	−	28.1703i	−1.05871	−	1.83373i
$237$	−4.70967	−	8.15740i	−0.305926	−	0.529880i
$238$	1.94553	−	3.36976i	0.126110	−	0.218429i
$239$	24.6601			1.59513			0.797565	−	0.603233i	$-0.206121\pi$
$239$	24.6601			1.59513			0.797565	+	0.603233i	$0.206121\pi$
$240$	0.405797	−	0.702861i	0.0261941	−	0.0453695i
$241$	1.98316	−	3.43493i	0.127746	−	0.221263i	−0.795057	−	0.606535i	$-0.792559\pi$
$241$	1.98316	−	3.43493i	0.127746	−	0.221263i	0.922803	+	0.385272i	$0.125892\pi$
$242$	6.02289			0.387166
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.31813	+	7.47922i	0.276440	+	0.478808i
$245$	−0.450443	−	0.780189i	−0.0287777	−	0.0498445i
$246$	−17.0566			−1.08749
$247$	−7.48364	−	10.8696i	−0.476173	−	0.691619i
$248$	−21.8485			−1.38738
$249$	0.790325	+	1.36888i	0.0500848	+	0.0867494i
$250$	−9.64376	−	16.7035i	−0.609925	−	1.05642i
$251$	9.47873	−	16.4176i	0.598292	−	1.03627i	−0.394781	−	0.918775i	$-0.629180\pi$
$251$	9.47873	−	16.4176i	0.598292	−	1.03627i	0.993073	−	0.117497i	$-0.0374871\pi$
$252$	3.42917			0.216018
$253$	6.42426	−	11.1271i	0.403890	−	0.699558i
$254$	12.9079	−	22.3571i	0.809914	−	1.40281i
$255$	−1.50443			−0.0942108
$256$	10.6835	−	18.5044i	0.667718	−	1.15652i
$257$	−7.57293	−	13.1167i	−0.472387	−	0.818198i	0.527114	−	0.849795i	$-0.323274\pi$
$257$	−7.57293	−	13.1167i	−0.472387	−	0.818198i	−0.999501	+	0.0315969i	$0.989941\pi$
$258$	5.16012	+	8.93759i	0.321255	+	0.556430i
$259$	8.61758			0.535470
$260$	6.31651	+	9.17443i	0.391733	+	0.568974i
$261$	5.33006			0.329922
$262$	−8.03973	−	13.9252i	−0.496696	−	0.860303i
$263$	−3.74730	−	6.49052i	−0.231068	−	0.400222i	0.727054	−	0.686580i	$-0.240889\pi$
$263$	−3.74730	−	6.49052i	−0.231068	−	0.400222i	−0.958123	+	0.286358i	$0.907555\pi$
$264$	−4.83006	+	8.36591i	−0.297270	+	0.514886i
$265$	−0.127613			−0.00783918
$266$	−4.26414	+	7.38571i	−0.261451	+	0.452847i
$267$	4.16012	−	7.20553i	0.254595	−	0.440972i
$268$	0.0336875			0.00205779
$269$	−4.23796	+	7.34037i	−0.258393	+	0.447550i	−0.965812	−	0.259245i	$-0.916526\pi$
$269$	−4.23796	+	7.34037i	−0.258393	+	0.447550i	0.707418	+	0.706795i	$0.249860\pi$
$270$	−1.04956	−	1.81789i	−0.0638740	−	0.110633i
$271$	−0.825147	−	1.42920i	−0.0501241	−	0.0868175i	0.839875	−	0.542780i	$-0.182628\pi$
$271$	−0.825147	−	1.42920i	−0.0501241	−	0.0868175i	−0.889999	+	0.455963i	$0.849295\pi$
$272$	1.50443			0.0912192
$273$	−1.54956	+	3.25559i	−0.0937835	+	0.197037i
$274$	−29.1688			−1.76215
$275$	6.07504	+	10.5223i	0.366339	+	0.634517i
$276$	−7.59420	−	13.1535i	−0.457117	−	0.791750i
$277$	−16.2679	+	28.1768i	−0.977442	+	1.69298i	−0.305812	+	0.952092i	$0.598928\pi$
$277$	−16.2679	+	28.1768i	−0.977442	+	1.69298i	−0.671630	+	0.740887i	$0.734405\pi$
$278$	−7.75923			−0.465368
$279$	−3.28050	+	5.68199i	−0.196398	+	0.340172i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	16.2777			0.971046			0.485523	−	0.874224i	$-0.338629\pi$
$281$	16.2777			0.971046			0.485523	+	0.874224i	$0.338629\pi$
$282$	−8.10565	+	14.0394i	−0.482684	+	0.836034i
$283$	−12.7543	−	22.0911i	−0.758166	−	1.31318i	−0.943785	−	0.330560i	$-0.892762\pi$
$283$	−12.7543	−	22.0911i	−0.758166	−	1.31318i	0.185619	−	0.982622i	$-0.440571\pi$
$284$	−24.1573	−	41.8417i	−1.43347	−	2.48285i
$285$	3.29734			0.195318
$286$	−13.8202	−	20.0732i	−0.817208	−	1.18696i
$287$	−7.32023			−0.432100
$288$	−2.28050	−	3.94994i	−0.134380	−	0.232753i
$289$	7.10565	+	12.3073i	0.417979	+	0.723961i
$290$	5.59420	−	9.68944i	0.328503	−	0.568984i
$291$	7.70266			0.451538
$292$	4.40790	−	7.63472i	0.257953	−	0.446788i
$293$	5.19985	−	9.00641i	0.303779	−	0.526160i	−0.673210	−	0.739451i	$-0.735085\pi$
$293$	5.19985	−	9.00641i	0.303779	−	0.526160i	0.976989	+	0.213291i	$0.0684184\pi$
$294$	2.33006			0.135892
$295$	−4.27279	+	7.40068i	−0.248771	+	0.430884i
$296$	14.3485	+	24.8524i	0.833991	+	1.44451i
$297$	1.45044	+	2.51224i	0.0841632	+	0.145775i
$298$	−36.5217			−2.11565
$299$	15.9193	−	1.26603i	0.920640	−	0.0732165i
$300$	14.3628			0.829235
$301$	2.21459	+	3.83578i	0.127647	+	0.221091i
$302$	9.85835	+	17.0752i	0.567284	+	0.982565i
$303$	9.20476	−	15.9431i	0.528800	−	0.915908i
$304$	−3.29734			−0.189116
$305$	1.13442	−	1.96488i	0.0649569	−	0.112509i
$306$	1.94553	−	3.36976i	0.111219	−	0.192636i
$307$	30.3670			1.73314			0.866568	−	0.499059i	$-0.166321\pi$
$307$	30.3670			1.73314			0.866568	+	0.499059i	$0.166321\pi$
$308$	−4.97382	+	8.61491i	−0.283410	+	0.490880i
$309$	4.02829	+	6.97720i	0.229161	+	0.396919i
$310$	6.88615	+	11.9272i	0.391107	+	0.677417i
$311$	15.8485			0.898687			0.449344	−	0.893359i	$-0.351658\pi$
$311$	15.8485			0.898687			0.449344	+	0.893359i	$0.351658\pi$
$312$	−11.9689	+	0.951862i	−0.677606	+	0.0538885i
$313$	20.7027			1.17018			0.585092	−	0.810967i	$-0.301059\pi$
$313$	20.7027			1.17018			0.585092	+	0.810967i	$0.301059\pi$
$314$	−28.8223	−	49.9218i	−1.62654	−	2.81725i
$315$	−0.450443	−	0.780189i	−0.0253796	−	0.0439587i
$316$	16.1503	−	27.9731i	0.908525	−	1.57361i
$317$	−12.9705			−0.728497			−0.364249	−	0.931302i	$-0.618674\pi$
$317$	−12.9705			−0.728497			−0.364249	+	0.931302i	$0.618674\pi$
$318$	0.165029	−	0.285839i	0.00925439	−	0.0160291i
$319$	−7.73094	+	13.3904i	−0.432850	+	0.749718i
$320$	−11.1973			−0.625946
$321$	1.81370	−	3.14142i	0.101231	−	0.175337i
$322$	−5.16012	−	8.93759i	−0.287562	−	0.498072i
$323$	3.05609	+	5.29330i	0.170045	+	0.294527i
$324$	3.42917			0.190510
$325$	−6.49018	+	13.6357i	−0.360010	+	0.756375i
$326$	57.5914			3.18969
$327$	−4.42426	−	7.66305i	−0.244662	−	0.423767i
$328$	−12.1884	−	21.1109i	−0.672992	−	1.16566i
$329$	−3.47873	+	6.02534i	−0.191789	+	0.332188i
$330$	6.08929			0.335204
$331$	−13.2359	+	22.9252i	−0.727508	+	1.26008i	0.230425	+	0.973090i	$0.425988\pi$
$331$	−13.2359	+	22.9252i	−0.727508	+	1.26008i	−0.957933	+	0.286991i	$0.907345\pi$
$332$	−2.71016	+	4.69414i	−0.148739	+	0.257624i
$333$	8.61758			0.472240
$334$	−12.4853	+	21.6251i	−0.683163	+	1.18327i
$335$	−0.00442505	−	0.00766441i	−0.000241766	−	0.000418751i
$336$	0.450443	+	0.780189i	0.0245737	+	0.0425628i
$337$	7.02289			0.382561			0.191281	−	0.981535i	$-0.438736\pi$
$337$	7.02289			0.382561			0.191281	+	0.981535i	$0.438736\pi$
$338$	10.8088	−	28.2967i	0.587921	−	1.53913i
$339$	6.36277			0.345578
$340$	−2.57947	−	4.46777i	−0.139891	−	0.242299i
$341$	−9.51636	−	16.4828i	−0.515340	−	0.892594i
$342$	−4.26414	+	7.38571i	−0.230579	+	0.399374i
$343$	1.00000			0.0539949
$344$	−7.37470	+	12.7734i	−0.397617	+	0.688694i
$345$	−1.99509	+	3.45559i	−0.107412	+	0.186043i
$346$	16.9804			0.912869
$347$	6.72161	−	11.6422i	0.360835	−	0.624984i	−0.627264	−	0.778807i	$-0.715825\pi$
$347$	6.72161	−	11.6422i	0.360835	−	0.624984i	0.988098	+	0.153823i	$0.0491585\pi$
$348$	9.13885	+	15.8290i	0.489894	+	0.848521i
$349$	−0.632316	−	1.09520i	−0.0338471	−	0.0586249i	0.848606	−	0.529026i	$-0.177443\pi$
$349$	−0.632316	−	1.09520i	−0.0338471	−	0.0586249i	−0.882453	+	0.470401i	$0.844109\pi$
$350$	9.75923			0.521653
$351$	−1.54956	+	3.25559i	−0.0827093	+	0.173771i
$352$	13.2309			0.705212
$353$	−8.99720	−	15.5836i	−0.478872	−	0.829431i	0.520834	−	0.853658i	$-0.325621\pi$
$353$	−8.99720	−	15.5836i	−0.478872	−	0.829431i	−0.999706	+	0.0242266i	$0.992288\pi$
$354$	−11.0512	−	19.1412i	−0.587364	−	1.01734i
$355$	−6.34642	+	10.9923i	−0.336833	+	0.583411i
$356$	28.5315			1.51217
$357$	0.834971	−	1.44621i	0.0441913	−	0.0765416i
$358$	−19.9362	+	34.5305i	−1.05366	+	1.82499i
$359$	23.7167			1.25172			0.625860	−	0.779936i	$-0.284748\pi$
$359$	23.7167			1.25172			0.625860	+	0.779936i	$0.284748\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	2.80177	+	4.85281i	0.147462	+	0.255411i
$362$	17.8866	+	30.9806i	0.940101	+	1.62830i
$363$	2.58487			0.135670
$364$	−12.3251	+	0.980192i	−0.646013	+	0.0513760i
$365$	−2.31602			−0.121226
$366$	2.93409	+	5.08199i	0.153367	+	0.265640i
$367$	−11.5021	−	19.9222i	−0.600405	−	1.03993i	−0.992760	−	0.120118i	$-0.961673\pi$
$367$	−11.5021	−	19.9222i	−0.600405	−	1.03993i	0.392354	−	0.919814i	$-0.371661\pi$
$368$	1.99509	−	3.45559i	0.104001	−	0.180135i
$369$	−7.32023			−0.381076
$370$	9.04465	−	15.6658i	0.470209	−	0.814425i
$371$	0.0708263	−	0.122675i	0.00367712	−	0.00636895i
$372$	−22.4988			−1.16651
$373$	−3.27116	+	5.66582i	−0.169374	+	0.293365i	−0.938200	−	0.346093i	$-0.887508\pi$
$373$	−3.27116	+	5.66582i	−0.169374	+	0.293365i	0.768826	+	0.639458i	$0.220841\pi$
$374$	5.64376	+	9.77528i	0.291832	+	0.505468i
$375$	−4.13885	−	7.16870i	−0.213729	−	0.370190i
$376$	−23.1688			−1.19484
$377$	−19.1573	+	1.52354i	−0.986652	+	0.0784663i
$378$	2.33006			0.119845
$379$	4.93360	+	8.54524i	0.253422	+	0.438940i	0.964466	−	0.264208i	$-0.0851106\pi$
$379$	4.93360	+	8.54524i	0.253422	+	0.438940i	−0.711044	+	0.703148i	$0.751777\pi$
$380$	5.65358	+	9.79230i	0.290023	+	0.502334i
$381$	5.53973	−	9.59510i	0.283809	−	0.491572i
$382$	−54.8756			−2.80768
$383$	−9.71669	+	16.8298i	−0.496500	+	0.859963i	−0.999992	−	0.00403684i	$-0.998715\pi$
$383$	−9.71669	+	16.8298i	−0.496500	+	0.859963i	0.503492	+	0.864000i	$0.332048\pi$
$384$	9.91935	−	17.1808i	0.506195	−	0.876755i
$385$	2.61336			0.133189
$386$	−13.6122	+	23.5770i	−0.692842	+	1.20004i
$387$	2.21459	+	3.83578i	0.112574	+	0.194984i
$388$	13.2069	+	22.8750i	0.670477	+	1.16130i
$389$	23.9804			1.21585			0.607926	−	0.793994i	$-0.292002\pi$
$389$	23.9804			1.21585			0.607926	+	0.793994i	$0.292002\pi$
$390$	4.29195	+	6.23385i	0.217331	+	0.315663i
$391$	−7.39646			−0.374055
$392$	1.66503	+	2.88392i	0.0840967	+	0.145660i
$393$	−3.45044	−	5.97634i	−0.174052	−	0.301467i
$394$	−26.7347	+	46.3058i	−1.34687	+	2.33285i
$395$	−8.48575			−0.426964
$396$	−4.97382	+	8.61491i	−0.249944	+	0.432915i
$397$	−19.1573	+	33.1814i	−0.961478	+	1.66533i	−0.242684	+	0.970105i	$0.578028\pi$
$397$	−19.1573	+	33.1814i	−0.961478	+	1.66533i	−0.718794	+	0.695223i	$0.755305\pi$
$398$	−64.9420			−3.25525
$399$	−1.83006	+	3.16975i	−0.0916175	+	0.158686i
$400$	1.88664	+	3.26775i	0.0943318	+	0.163387i
$401$	−4.46680	−	7.73672i	−0.223061	−	0.386354i	0.732675	−	0.680579i	$-0.238272\pi$
$401$	−4.46680	−	7.73672i	−0.223061	−	0.386354i	−0.955736	+	0.294225i	$0.904938\pi$
$402$	0.0228900			0.00114165
$403$	10.1667	−	21.3599i	0.506437	−	1.06401i
$404$	63.1295			3.14081
$405$	−0.450443	−	0.780189i	−0.0223827	−	0.0387679i
$406$	6.20967	+	10.7555i	0.308181	+	0.533785i
$407$	−12.4993	+	21.6494i	−0.619568	+	1.07312i
$408$	5.56100			0.275311
$409$	−0.962374	+	1.66688i	−0.0475863	+	0.0824220i	−0.888837	−	0.458223i	$-0.848486\pi$
$409$	−0.962374	+	1.66688i	−0.0475863	+	0.0824220i	0.841251	+	0.540645i	$0.181820\pi$
$410$	−7.68301	+	13.3074i	−0.379437	+	0.657204i
$411$	−12.5185			−0.617490
$412$	−13.8137	+	23.9260i	−0.680552	+	1.17875i
$413$	−4.74288	−	8.21490i	−0.233382	−	0.404229i
$414$	−5.16012	−	8.93759i	−0.253606	−	0.439258i
$415$	1.42398			0.0699006
$416$	9.32563	+	13.5450i	0.457227	+	0.664100i
$417$	−3.33006			−0.163074
$418$	−12.3698	−	21.4251i	−0.605026	−	1.04794i
$419$	10.7380	+	18.5987i	0.524584	+	0.908606i	0.999590	+	0.0286236i	$0.00911240\pi$
$419$	10.7380	+	18.5987i	0.524584	+	0.908606i	−0.475006	+	0.879982i	$0.657554\pi$
$420$	1.54465	−	2.67540i	0.0753710	−	0.130546i
$421$	−34.8050			−1.69629			−0.848146	−	0.529762i	$-0.822281\pi$
$421$	−34.8050			−1.69629			−0.848146	+	0.529762i	$0.822281\pi$
$422$	−7.92917	+	13.7337i	−0.385986	+	0.668548i
$423$	−3.47873	+	6.02534i	−0.169142	+	0.292962i
$424$	0.471711			0.0229083
$425$	3.49720	−	6.05732i	0.169639	−	0.293823i
$426$	−16.4144	−	28.4306i	−0.795282	−	1.37747i
$427$	1.25923	+	2.18105i	0.0609385	+	0.105549i
$428$	12.4390			0.601262
$429$	−5.93128	−	8.61491i	−0.286365	−	0.415932i
$430$	9.29734			0.448358
$431$	−12.0397	−	20.8534i	−0.579934	−	1.00447i	−0.995486	−	0.0949053i	$-0.969745\pi$
$431$	−12.0397	−	20.8534i	−0.579934	−	1.00447i	0.415553	−	0.909569i	$-0.363588\pi$
$432$	0.450443	+	0.780189i	0.0216719	+	0.0375369i
$433$	−0.938998	+	1.62639i	−0.0451253	+	0.0781594i	−0.887706	−	0.460411i	$-0.847702\pi$
$433$	−0.938998	+	1.62639i	−0.0451253	+	0.0781594i	0.842581	+	0.538570i	$0.181035\pi$
$434$	−15.2875			−0.733824
$435$	2.40089	−	4.15845i	0.115114	−	0.199383i
$436$	15.1716	−	26.2779i	0.726586	−	1.25848i
$437$	16.2113			0.775491
$438$	2.99509	−	5.18764i	0.143111	−	0.247875i
$439$	11.2499	+	19.4854i	0.536928	+	0.929987i	0.999067	+	0.0431795i	$0.0137487\pi$
$439$	11.2499	+	19.4854i	0.536928	+	0.929987i	−0.462139	+	0.886807i	$0.652918\pi$
$440$	4.35133	+	7.53672i	0.207441	+	0.359299i
$441$	1.00000			0.0476190
$442$	−6.02942	+	12.6677i	−0.286790	+	0.602541i
$443$	16.4988			0.783882			0.391941	−	0.919990i	$-0.371804\pi$
$443$	16.4988			0.783882			0.391941	+	0.919990i	$0.371804\pi$
$444$	14.7756	+	25.5921i	0.701218	+	1.21455i
$445$	−3.74779	−	6.49136i	−0.177662	−	0.307720i
$446$	−23.9046	+	41.4040i	−1.13192	+	1.96054i
$447$	−15.6742			−0.741362
$448$	6.21459	−	10.7640i	0.293612	−	0.508550i
$449$	16.9591	−	29.3740i	0.800349	−	1.38624i	−0.119038	−	0.992890i	$-0.537981\pi$
$449$	16.9591	−	29.3740i	0.800349	−	1.38624i	0.919387	−	0.393355i	$-0.128686\pi$
$450$	9.75923			0.460055
$451$	10.6176	−	18.3902i	0.499962	−	0.865960i
$452$	10.9095	+	18.8959i	0.513141	+	0.888786i
$453$	4.23094	+	7.32821i	0.198787	+	0.344309i
$454$	−3.50540			−0.164517
$455$	1.84199	+	2.67540i	0.0863539	+	0.125425i
$456$	−12.1884			−0.570774
$457$	2.28099	+	3.95079i	0.106700	+	0.184810i	0.914432	−	0.404741i	$-0.132638\pi$
$457$	2.28099	+	3.95079i	0.106700	+	0.184810i	−0.807731	+	0.589551i	$0.799305\pi$
$458$	30.0750	+	52.0915i	1.40531	+	2.43408i
$459$	0.834971	−	1.44621i	0.0389731	−	0.0675034i
$460$	−13.6830			−0.637974
$461$	2.87519	−	4.97998i	0.133911	−	0.231941i	−0.791270	−	0.611467i	$-0.790580\pi$
$461$	2.87519	−	4.97998i	0.133911	−	0.231941i	0.925181	+	0.379526i	$0.123913\pi$
$462$	−3.37962	+	5.85367i	−0.157234	+	0.272337i
$463$	−19.3726			−0.900321			−0.450160	−	0.892948i	$-0.648633\pi$
$463$	−19.3726			−0.900321			−0.450160	+	0.892948i	$0.648633\pi$
$464$	−2.40089	+	4.15845i	−0.111458	+	0.193051i
$465$	2.95535	+	5.11882i	0.137051	+	0.237380i
$466$	−28.0037	−	48.5039i	−1.29725	−	2.24690i
$467$	−27.7723			−1.28515			−0.642574	−	0.766223i	$-0.722134\pi$
$467$	−27.7723			−1.28515			−0.642574	+	0.766223i	$0.722134\pi$
$468$	−12.3251	+	0.980192i	−0.569730	+	0.0453094i
$469$	0.00982378			0.000453620
$470$	7.30226	+	12.6479i	0.336828	+	0.583403i
$471$	−12.3698	−	21.4251i	−0.569970	−	0.987217i
$472$	15.7941	−	27.3561i	0.726980	−	1.25917i
$473$	−12.8485			−0.590776
$474$	10.9738	−	19.0072i	0.504044	−	0.873030i
$475$	−7.66503	+	13.2762i	−0.351696	+	0.609155i
$476$	5.72652			0.262475
$477$	0.0708263	−	0.122675i	0.00324291	−	0.00561689i
$478$	28.7298	+	49.7614i	1.31407	+	2.27603i
$479$	5.94553	+	10.2980i	0.271658	+	0.470526i	0.969287	−	0.245934i	$-0.0790946\pi$
$479$	5.94553	+	10.2980i	0.271658	+	0.470526i	−0.697628	+	0.716460i	$0.745761\pi$
$480$	−4.10894			−0.187547
$481$	−30.9733	+	2.46324i	−1.41226	+	0.112314i
$482$	9.24174			0.420950
$483$	−2.21459	−	3.83578i	−0.100767	−	0.174534i
$484$	4.43198	+	7.67641i	0.201454	+	0.348928i
$485$	3.46960	−	6.00953i	0.157547	−	0.272879i
$486$	2.33006			0.105694
$487$	11.1367	−	19.2894i	0.504654	−	0.874086i	−0.495332	−	0.868704i	$-0.664953\pi$
$487$	11.1367	−	19.2894i	0.504654	−	0.874086i	0.999986	−	0.00538221i	$-0.00171322\pi$
$488$	−4.19332	+	7.26304i	−0.189823	+	0.328782i
$489$	24.7167			1.11773
$490$	1.04956	−	1.81789i	0.0474142	−	0.0821238i
$491$	−3.09420	−	5.35932i	−0.139639	−	0.241863i	0.787721	−	0.616033i	$-0.211261\pi$
$491$	−3.09420	−	5.35932i	−0.139639	−	0.241863i	−0.927360	+	0.374170i	$0.877928\pi$
$492$	−12.5512	−	21.7393i	−0.565851	−	0.980082i
$493$	8.90089			0.400876
$494$	13.2151	−	27.7646i	0.594574	−	1.24919i
$495$	2.61336			0.117462
$496$	−2.95535	−	5.11882i	−0.132699	−	0.229842i
$497$	−7.04465	−	12.2017i	−0.315996	−	0.547320i
$498$	−1.84150	+	3.18958i	−0.0825198	+	0.142928i
$499$	18.4236			0.824752			0.412376	−	0.911014i	$-0.364699\pi$
$499$	18.4236			0.824752			0.412376	+	0.911014i	$0.364699\pi$
$500$	14.1928	−	24.5827i	0.634723	−	1.09937i
$501$	−5.35835	+	9.28093i	−0.239393	+	0.414641i
$502$	44.1720			1.97149
$503$	−11.7637	+	20.3753i	−0.524516	+	0.908488i	0.475077	+	0.879944i	$0.342420\pi$
$503$	−11.7637	+	20.3753i	−0.524516	+	0.908488i	−0.999593	+	0.0285434i	$0.990913\pi$
$504$	1.66503	+	2.88392i	0.0741663	+	0.128460i
$505$	−8.29243	−	14.3629i	−0.369008	−	0.639141i
$506$	29.9378			1.33090
$507$	4.63885	−	12.1442i	0.206019	−	0.539342i
$508$	37.9934			1.68569
$509$	−2.29734	−	3.97912i	−0.101828	−	0.176371i	0.810610	−	0.585587i	$-0.199136\pi$
$509$	−2.29734	−	3.97912i	−0.101828	−	0.176371i	−0.912438	+	0.409215i	$0.865802\pi$
$510$	−1.75270	−	3.03576i	−0.0776108	−	0.134426i
$511$	1.28541	−	2.22640i	0.0568633	−	0.0984902i
$512$	10.1089			0.446756
$513$	−1.83006	+	3.16975i	−0.0807991	+	0.139948i
$514$	17.6454	−	30.5627i	0.778304	−	1.34806i
$515$	7.25805			0.319828
$516$	−7.59420	+	13.1535i	−0.334316	+	0.579053i
$517$	−10.0914	−	17.4788i	−0.443819	−	0.768717i
$518$	10.0397	+	17.3893i	0.441121	+	0.764043i
$519$	7.28752			0.319887
$520$	−4.64867	+	9.76677i	−0.203858	+	0.428301i
$521$	−2.95325			−0.129384			−0.0646920	−	0.997905i	$-0.520607\pi$
$521$	−2.95325			−0.129384			−0.0646920	+	0.997905i	$0.520607\pi$
$522$	6.20967	+	10.7555i	0.271790	+	0.470754i
$523$	−11.1716	−	19.3497i	−0.488498	−	0.846104i	0.511414	−	0.859334i	$-0.329122\pi$
$523$	−11.1716	−	19.3497i	−0.488498	−	0.846104i	−0.999912	+	0.0132305i	$0.995788\pi$
$524$	11.8322	−	20.4939i	0.516891	−	0.895281i
$525$	4.18841			0.182797
$526$	8.73143	−	15.1233i	0.380708	−	0.659406i
$527$	−5.47824	+	9.48860i	−0.238636	+	0.413330i
$528$	−2.61336			−0.113732
$529$	1.69121	−	2.92926i	0.0735309	−	0.127359i
$530$	−0.148672	−	0.257508i	−0.00645792	−	0.0111854i
$531$	−4.74288	−	8.21490i	−0.205823	−	0.356496i
$532$	−12.5512			−0.544163
$533$	26.3104	−	2.09241i	1.13963	−	0.0906324i
$534$	19.3866			0.838942
$535$	−1.63394	−	2.83006i	−0.0706412	−	0.122354i
$536$	0.0163569	+	0.0283310i	0.000706510	+	0.00122371i
$537$	−8.55609	+	14.8196i	−0.369223	+	0.639512i
$538$	−19.7494			−0.851457
$539$	−1.45044	+	2.51224i	−0.0624750	+	0.108210i
$540$	1.54465	−	2.67540i	0.0664710	−	0.115131i
$541$	−2.66994			−0.114790			−0.0573949	−	0.998352i	$-0.518279\pi$
$541$	−2.66994			−0.114790			−0.0573949	+	0.998352i	$0.518279\pi$
$542$	1.92264	−	3.33011i	0.0825845	−	0.143041i
$543$	7.67647	+	13.2960i	0.329429	+	0.570588i
$544$	−3.80830	−	6.59617i	−0.163280	−	0.282809i
$545$	−7.97150			−0.341462
$546$	−8.37470	+	0.666022i	−0.358404	+	0.0285031i
$547$	−12.1973			−0.521517			−0.260759	−	0.965404i	$-0.583973\pi$
$547$	−12.1973			−0.521517			−0.260759	+	0.965404i	$0.583973\pi$
$548$	−21.4640	−	37.1767i	−0.916896	−	1.58811i
$549$	1.25923	+	2.18105i	0.0537427	+	0.0930851i
$550$	−14.1552	+	24.5175i	−0.603580	+	1.04543i
$551$	−19.5086			−0.831096
$552$	7.37470	−	12.7734i	0.313888	−	0.543670i
$553$	4.70967	−	8.15740i	0.200276	−	0.346888i
$554$	−75.8102			−3.22087
$555$	3.88172	−	6.72334i	0.164770	−	0.285390i
$556$	−5.70967	−	9.88945i	−0.242144	−	0.419406i
$557$	−10.9951	−	19.0441i	−0.465877	−	0.806922i	0.533364	−	0.845886i	$-0.320928\pi$
$557$	−10.9951	−	19.0441i	−0.465877	−	0.806922i	−0.999241	+	0.0389636i	$0.987594\pi$
$558$	−15.2875			−0.647172
$559$	−9.05609	−	13.1535i	−0.383032	−	0.556336i
$560$	0.811594			0.0342961
$561$	2.42215	+	4.19529i	0.102263	+	0.177125i
$562$	18.9640	+	32.8466i	0.799948	+	1.38555i
$563$	11.1454	−	19.3044i	0.469722	−	0.813582i	−0.529679	−	0.848198i	$-0.677688\pi$
$563$	11.1454	−	19.3044i	0.469722	−	0.813582i	0.999401	+	0.0346162i	$0.0110209\pi$
$564$	−23.8583			−1.00462
$565$	2.86606	−	4.96417i	0.120576	−	0.208844i
$566$	29.7183	−	51.4736i	1.24915	−	2.16360i
$567$	1.00000			0.0419961
$568$	23.4591	−	40.6323i	0.984321	−	1.70489i
$569$	−14.3932	−	24.9297i	−0.603393	−	1.04511i	−0.992303	−	0.123832i	$-0.960482\pi$
$569$	−14.3932	−	24.9297i	−0.603393	−	1.04511i	0.388910	−	0.921276i	$-0.372852\pi$
$570$	3.84150	+	6.65368i	0.160903	+	0.278692i
$571$	18.4432			0.771824			0.385912	−	0.922535i	$-0.373887\pi$
$571$	18.4432			0.771824			0.385912	+	0.922535i	$0.373887\pi$
$572$	15.4144	−	32.3854i	0.644510	−	1.35410i
$573$	−23.5512			−0.983865
$574$	−8.52829	−	14.7714i	−0.355964	−	0.616548i
$575$	−9.27559	−	16.0658i	−0.386819	−	0.669990i
$576$	6.21459	−	10.7640i	0.258941	−	0.448499i
$577$	−1.10894			−0.0461657			−0.0230829	−	0.999734i	$-0.507348\pi$
$577$	−1.10894			−0.0461657			−0.0230829	+	0.999734i	$0.507348\pi$
$578$	−16.5566	+	28.6768i	−0.688663	+	1.19280i
$579$	−5.84199	+	10.1186i	−0.242785	+	0.420516i
$580$	16.4661			0.683718
$581$	−0.790325	+	1.36888i	−0.0327882	+	0.0567908i
$582$	8.97382	+	15.5431i	0.371977	+	0.644283i
$583$	0.205459	+	0.355865i	0.00850924	+	0.0147384i
$584$	8.56100			0.354257
$585$	1.84199	+	2.67540i	0.0761569	+	0.110614i
$586$	24.2319			1.00101
$587$	−12.3894	−	21.4591i	−0.511367	−	0.885713i	−0.999913	−	0.0131755i	$-0.995806\pi$
$587$	−12.3894	−	21.4591i	−0.511367	−	0.885713i	0.488546	−	0.872538i	$-0.337527\pi$
$588$	1.71459	+	2.96975i	0.0707084	+	0.122470i
$589$	12.0070	−	20.7968i	0.494741	−	0.856916i
$590$	−19.9117			−0.819751
$591$	−11.4738	+	19.8732i	−0.471970	+	0.817476i
$592$	−3.88172	+	6.72334i	−0.159538	+	0.276328i
$593$	14.7157			0.604302			0.302151	−	0.953260i	$-0.402295\pi$
$593$	14.7157			0.604302			0.302151	+	0.953260i	$0.402295\pi$
$594$	−3.37962	+	5.85367i	−0.138667	+	0.240179i
$595$	−0.752213	−	1.30287i	−0.0308377	−	0.0534125i
$596$	−26.8747	−	46.5484i	−1.10083	−	1.90669i
$597$	−27.8714			−1.14070
$598$	21.1012	+	30.6485i	0.862893	+	1.25331i
$599$	−10.8018			−0.441348			−0.220674	−	0.975348i	$-0.570826\pi$
$599$	−10.8018			−0.441348			−0.220674	+	0.975348i	$0.570826\pi$
$600$	6.97382	+	12.0790i	0.284705	+	0.493123i
$601$	0.450443	+	0.780189i	0.0183739	+	0.0318246i	0.875066	−	0.484003i	$-0.160818\pi$
$601$	0.450443	+	0.780189i	0.0183739	+	0.0318246i	−0.856692	+	0.515828i	$0.827484\pi$
$602$	−5.16012	+	8.93759i	−0.210311	+	0.364269i
$603$	0.00982378			0.000400055
$604$	−14.5086	+	25.1297i	−0.590348	+	1.02251i
$605$	1.16433	−	2.01668i	0.0473369	−	0.0819899i
$606$	42.8953			1.74250
$607$	5.71621	−	9.90076i	0.232014	−	0.401860i	−0.726387	−	0.687286i	$-0.758802\pi$
$607$	5.71621	−	9.90076i	0.232014	−	0.401860i	0.958401	+	0.285426i	$0.0921352\pi$
$608$	8.34690	+	14.4573i	0.338512	+	0.586319i
$609$	2.66503	+	4.61597i	0.107992	+	0.187048i
$610$	5.28655			0.214046
$611$	10.7810	−	22.6507i	0.436152	−	0.916347i
$612$	5.72652			0.231481
$613$	−1.67156	−	2.89523i	−0.0675138	−	0.116937i	0.830293	−	0.557328i	$-0.188173\pi$
$613$	−1.67156	−	2.89523i	−0.0675138	−	0.116937i	−0.897806	+	0.440391i	$0.854840\pi$
$614$	35.3784	+	61.2772i	1.42776	+	2.47295i
$615$	−3.29734	+	5.71117i	−0.132962	+	0.230297i
$616$	−9.66012			−0.389217
$617$	4.11056	−	7.11970i	0.165485	−	0.286628i	−0.771342	−	0.636420i	$-0.780414\pi$
$617$	4.11056	−	7.11970i	0.165485	−	0.286628i	0.936827	+	0.349792i	$0.113748\pi$
$618$	−9.38615	+	16.2573i	−0.377566	+	0.653964i
$619$	−1.98035			−0.0795971			−0.0397985	−	0.999208i	$-0.512672\pi$
$619$	−1.98035			−0.0795971			−0.0397985	+	0.999208i	$0.512672\pi$
$620$	−10.1344	+	17.5533i	−0.407008	+	0.704959i
$621$	−2.21459	−	3.83578i	−0.0888683	−	0.153924i
$622$	18.4640	+	31.9806i	0.740339	+	1.28230i
$623$	8.32023			0.333343
$624$	−1.84199	−	2.67540i	−0.0737386	−	0.107102i
$625$	13.4848			0.539391
$626$	24.1192	+	41.7757i	0.963997	+	1.66969i
$627$	−5.30879	−	9.19509i	−0.212013	−	0.367217i
$628$	42.4182	−	73.4704i	1.69267	−	2.93179i
$629$	14.3909			0.573801
$630$	1.04956	−	1.81789i	0.0418154	−	0.0724263i
$631$	−6.20757	+	10.7518i	−0.247119	+	0.428023i	−0.962725	−	0.270481i	$-0.912817\pi$
$631$	−6.20757	+	10.7518i	−0.247119	+	0.428023i	0.715606	+	0.698504i	$0.246151\pi$
$632$	31.3670			1.24771
$633$	−3.40299	+	5.89416i	−0.135257	+	0.234272i
$634$	−15.1110	−	26.1731i	−0.600136	−	1.03947i
$635$	−4.99066	−	8.64408i	−0.198048	−	0.343030i
$636$	0.485751			0.0192613
$637$	−3.59420	+	0.285839i	−0.142408	+	0.0113254i
$638$	−36.0271			−1.42633
$639$	−7.04465	−	12.2017i	−0.278682	−	0.482691i
$640$	−8.93619	−	15.4779i	−0.353234	−	0.611819i
$641$	5.78541	−	10.0206i	0.228510	−	0.395791i	−0.728857	−	0.684666i	$-0.759948\pi$
$641$	5.78541	−	10.0206i	0.228510	−	0.395791i	0.957367	+	0.288875i	$0.0932813\pi$
$642$	8.45206			0.333576
$643$	−1.17977	+	2.04341i	−0.0465254	+	0.0805843i	−0.888350	−	0.459166i	$-0.848148\pi$
$643$	−1.17977	+	2.04341i	−0.0465254	+	0.0805843i	0.841825	+	0.539751i	$0.181482\pi$
$644$	7.59420	−	13.1535i	0.299254	−	0.518322i
$645$	3.99018			0.157113
$646$	−7.12087	+	12.3337i	−0.280167	+	0.485263i
$647$	−4.76414	−	8.25174i	−0.187298	−	0.324409i	0.757051	−	0.653356i	$-0.226640\pi$
$647$	−4.76414	−	8.25174i	−0.187298	−	0.324409i	−0.944348	+	0.328947i	$0.893306\pi$
$648$	1.66503	+	2.88392i	0.0654085	+	0.113291i
$649$	27.5171			1.08014
$650$	−35.0767	+	2.78957i	−1.37582	+	0.109416i
$651$	−6.56100			−0.257146
$652$	42.3789	+	73.4024i	1.65969	+	2.87466i
$653$	7.67437	+	13.2924i	0.300321	+	0.520172i	0.976209	−	0.216833i	$-0.0695728\pi$
$653$	7.67437	+	13.2924i	0.300321	+	0.520172i	−0.675887	+	0.737005i	$0.736239\pi$
$654$	10.3088	−	17.8553i	0.403106	−	0.698199i
$655$	−6.21690			−0.242915
$656$	3.29734	−	5.71117i	0.128740	−	0.222984i
$657$	1.28541	−	2.22640i	0.0501487	−	0.0868602i
$658$	−16.2113			−0.631982
$659$	−12.2478	+	21.2138i	−0.477106	+	0.826372i	−0.999656	−	0.0262369i	$-0.991648\pi$
$659$	−12.2478	+	21.2138i	−0.477106	+	0.826372i	0.522550	+	0.852609i	$0.324981\pi$
$660$	4.48084	+	7.76104i	0.174416	+	0.302098i
$661$	−0.323039	−	0.559520i	−0.0125648	−	0.0217628i	0.859675	−	0.510842i	$-0.170666\pi$
$661$	−0.323039	−	0.559520i	−0.0125648	−	0.0217628i	−0.872239	+	0.489079i	$0.837333\pi$
$662$	−61.6806			−2.39729
$663$	−2.58767	+	5.43665i	−0.100497	+	0.211142i
$664$	−5.26366			−0.204270
$665$	1.64867	+	2.85558i	0.0639328	+	0.110735i
$666$	10.0397	+	17.3893i	0.389032	+	0.673823i
$667$	11.8039	−	20.4449i	0.457048	−	0.791630i
$668$	−36.7494			−1.42188
$669$	−10.2592	+	17.7695i	−0.396645	+	0.687009i
$670$	0.0103106	−	0.0178585i	0.000398334	−	0.000689935i
$671$	−7.30578			−0.282036
$672$	2.28050	−	3.94994i	0.0879722	−	0.152372i
$673$	21.1851	+	36.6937i	0.816626	+	1.41444i	0.908154	+	0.418636i	$0.137492\pi$
$673$	21.1851	+	36.6937i	0.816626	+	1.41444i	−0.0915281	+	0.995802i	$0.529175\pi$
$674$	8.18187	+	14.1714i	0.315154	+	0.545863i
$675$	4.18841			0.161212
$676$	44.0189	−	7.04602i	1.69303	−	0.271001i
$677$	25.7723			0.990510			0.495255	−	0.868748i	$-0.335075\pi$
$677$	25.7723			0.990510			0.495255	+	0.868748i	$0.335075\pi$
$678$	7.41282	+	12.8394i	0.284688	+	0.493093i
$679$	3.85133	+	6.67069i	0.147800	+	0.255998i
$680$	2.50491	−	4.33863i	0.0960590	−	0.166379i
$681$	−1.50443			−0.0576497
$682$	22.1737	−	38.4059i	0.849074	−	1.47064i
$683$	−5.68630	+	9.84896i	−0.217580	+	0.376860i	−0.954068	−	0.299591i	$-0.903150\pi$
$683$	−5.68630	+	9.84896i	−0.217580	+	0.376860i	0.736487	+	0.676451i	$0.236483\pi$
$684$	−12.5512			−0.479906
$685$	−5.63885	+	9.76677i	−0.215449	+	0.373169i
$686$	1.16503	+	2.01789i	0.0444810	+	0.0770434i
$687$	12.9074	+	22.3563i	0.492449	+	0.852946i
$688$	−3.99018			−0.152124
$689$	−0.219499	+	0.461163i	−0.00836224	+	0.0175689i
$690$	−9.29734			−0.353944
$691$	−7.27116	−	12.5940i	−0.276608	−	0.479099i	0.693931	−	0.720041i	$-0.255877\pi$
$691$	−7.27116	−	12.5940i	−0.276608	−	0.479099i	−0.970540	+	0.240942i	$0.922544\pi$
$692$	12.4951	+	21.6421i	0.474992	+	0.822710i
$693$	−1.45044	+	2.51224i	−0.0550978	+	0.0954321i
$694$	31.3235			1.18902
$695$	−1.50000	+	2.59808i	−0.0568982	+	0.0985506i
$696$	−8.87470	+	15.3714i	−0.336395	+	0.582653i
$697$	−12.2244			−0.463031
$698$	1.47333	−	2.55189i	0.0557665	−	0.0965903i
$699$	−12.0185	−	20.8166i	−0.454580	−	0.787356i
$700$	7.18139	+	12.4385i	0.271431	+	0.470132i
$701$	−5.69844			−0.215227			−0.107614	−	0.994193i	$-0.534321\pi$
$701$	−5.69844			−0.215227			−0.107614	+	0.994193i	$0.534321\pi$
$702$	−8.37470	+	0.666022i	−0.316083	+	0.0251374i
$703$	−31.5414			−1.18960
$704$	18.0278	+	31.2251i	0.679448	+	1.17684i
$705$	3.13394	+	5.42814i	0.118031	+	0.204435i
$706$	20.9640	−	36.3107i	0.788990	−	1.36657i
$707$	18.4095			0.692361
$708$	16.2641	−	28.1703i	0.611244	−	1.05871i
$709$	−20.4313	+	35.3880i	−0.767313	+	1.32902i	0.171702	+	0.985149i	$0.445073\pi$
$709$	−20.4313	+	35.3880i	−0.767313	+	1.32902i	−0.939015	+	0.343876i	$0.888260\pi$
$710$	−29.5750			−1.10993
$711$	4.70967	−	8.15740i	0.176627	−	0.305926i
$712$	13.8534	+	23.9949i	0.519179	+	0.899245i
$713$	14.5299	+	25.1665i	0.544149	+	0.942494i
$714$	3.89106			0.145619
$715$	−9.39296	+	0.747002i	−0.351277	+	0.0279363i
$716$	−58.6806			−2.19300
$717$	12.3301	+	21.3563i	0.460474	+	0.797565i
$718$	27.6306	+	47.8577i	1.03117	+	1.78603i
$719$	−13.7842	+	23.8750i	−0.514065	+	0.890387i	0.485802	+	0.874069i	$0.338528\pi$
$719$	−13.7842	+	23.8750i	−0.514065	+	0.890387i	−0.999867	+	0.0163178i	$0.994806\pi$
$720$	0.811594			0.0302463
$721$	−4.02829	+	6.97720i	−0.150021	+	0.259845i
$722$	−6.52829	+	11.3073i	−0.242958	+	0.420815i
$723$	3.96631			0.147509
$724$	−26.3240	+	45.5944i	−0.978322	+	1.69450i
$725$	11.1622	+	19.3335i	0.414555	+	0.718030i
$726$	3.01144	+	5.21598i	0.111765	+	0.193583i
$727$	9.72652			0.360737			0.180368	−	0.983599i	$-0.442271\pi$
$727$	9.72652			0.360737			0.180368	+	0.983599i	$0.442271\pi$
$728$	−6.80879	−	9.88945i	−0.252351	−	0.366527i
$729$	1.00000			0.0370370
$730$	−2.69823	−	4.67347i	−0.0998660	−	0.172973i
$731$	3.69823	+	6.40552i	0.136784	+	0.236917i
$732$	−4.31813	+	7.47922i	−0.159603	+	0.276440i
$733$	52.3843			1.93486			0.967429	−	0.253144i	$-0.0814647\pi$
$733$	52.3843			1.93486			0.967429	+	0.253144i	$0.0814647\pi$
$734$	26.8006	−	46.4200i	0.989228	−	1.71339i
$735$	0.450443	−	0.780189i	0.0166148	−	0.0287777i
$736$	−20.2015			−0.744636
$737$	−0.0142488	+	0.0246797i	−0.000524862	+	0.000909088i
$738$	−8.52829	−	14.7714i	−0.313931	−	0.543744i
$739$	−26.4161	−	45.7540i	−0.971730	−	1.68309i	−0.690328	−	0.723497i	$-0.742534\pi$
$739$	−26.4161	−	45.7540i	−0.971730	−	1.68309i	−0.281403	−	0.959590i	$-0.590800\pi$
$740$	26.6222			0.978652
$741$	5.67156	−	11.9158i	0.208350	−	0.437739i
$742$	0.330059			0.0121168
$743$	9.23586	+	15.9970i	0.338831	+	0.586872i	0.984213	−	0.176988i	$-0.0566353\pi$
$743$	9.23586	+	15.9970i	0.338831	+	0.586872i	−0.645382	+	0.763860i	$0.723302\pi$
$744$	−10.9243	−	18.9214i	−0.400503	−	0.693691i
$745$	−7.06031	+	12.2288i	−0.258670	+	0.448029i
$746$	−15.2440			−0.558123
$747$	−0.790325	+	1.36888i	−0.0289165	+	0.0500848i
$748$	−8.30599	+	14.3864i	−0.303697	+	0.526019i
$749$	3.62740			0.132542
$750$	9.64376	−	16.7035i	0.352140	−	0.609925i
$751$	−9.04184	−	15.6609i	−0.329941	−	0.571475i	0.652558	−	0.757738i	$-0.273696\pi$
$751$	−9.04184	−	15.6609i	−0.329941	−	0.571475i	−0.982500	+	0.186263i	$0.940362\pi$
$752$	−3.13394	−	5.42814i	−0.114283	−	0.197944i
$753$	18.9575			0.690848
$754$	−25.3932	−	36.8824i	−0.924765	−	1.34318i
$755$	7.62319			0.277436
$756$	1.71459	+	2.96975i	0.0623589	+	0.108009i
$757$	−20.3932	−	35.3220i	−0.741202	−	1.28380i	−0.951948	−	0.306259i	$-0.900923\pi$
$757$	−20.3932	−	35.3220i	−0.741202	−	1.28380i	0.210746	−	0.977541i	$-0.432411\pi$
$758$	−11.4956	+	19.9109i	−0.417538	+	0.723197i
$759$	12.8485			0.466372
$760$	−5.49018	+	9.50926i	−0.199150	+	0.344937i
$761$	9.24779	−	16.0176i	0.335232	−	0.580639i	−0.648297	−	0.761387i	$-0.724519\pi$
$761$	9.24779	−	16.0176i	0.335232	−	0.580639i	0.983529	+	0.180748i	$0.0578520\pi$
$762$	25.8158			0.935208
$763$	4.42426	−	7.66305i	0.160169	−	0.277421i
$764$	−40.3805	−	69.9411i	−1.46092	−	2.53038i
$765$	−0.752213	−	1.30287i	−0.0271963	−	0.0471054i
$766$	−45.2809			−1.63607
$767$	19.3950	+	28.1703i	0.700313	+	1.01717i
$768$	21.3670			0.771015
$769$	25.2580	+	43.7482i	0.910829	+	1.57760i	0.812896	+	0.582408i	$0.197889\pi$
$769$	25.2580	+	43.7482i	0.910829	+	1.57760i	0.0979321	+	0.995193i	$0.468777\pi$
$770$	3.04465	+	5.27348i	0.109721	+	0.190043i
$771$	7.57293	−	13.1167i	0.272733	−	0.472387i
$772$	−40.0664			−1.44202

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16503 + 2.01789i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.71459 + 2.96975i) q^{4} +0.900885 q^{5} +(-1.16503 + 2.01789i) q^{6} +(-0.500000 + 0.866025i) q^{7} -3.33006 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.16503 + 2.01789i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.71459 + 2.96975i) q^{4} +0.900885 q^{5} +(-1.16503 + 2.01789i) q^{6} +(-0.500000 + 0.866025i) q^{7} -3.33006 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.04956 + 1.81789i) q^{10} +(-1.45044 - 2.51224i) q^{11} -3.42917 q^{12} +(1.54956 - 3.25559i) q^{13} -2.33006 q^{14} +(0.450443 + 0.780189i) q^{15} +(-0.450443 - 0.780189i) q^{16} +(-0.834971 + 1.44621i) q^{17} -2.33006 q^{18} +(1.83006 - 3.16975i) q^{19} +(-1.54465 + 2.67540i) q^{20} -1.00000 q^{21} +(3.37962 - 5.85367i) q^{22} +(2.21459 + 3.83578i) q^{23} +(-1.66503 - 2.88392i) q^{24} -4.18841 q^{25} +(8.37470 - 0.666022i) q^{26} -1.00000 q^{27} +(-1.71459 - 2.96975i) q^{28} +(-2.66503 - 4.61597i) q^{29} +(-1.04956 + 1.81789i) q^{30} +6.56100 q^{31} +(-2.28050 + 3.94994i) q^{32} +(1.45044 - 2.51224i) q^{33} -3.89106 q^{34} +(-0.450443 + 0.780189i) q^{35} +(-1.71459 - 2.96975i) q^{36} +(-4.30879 - 7.46304i) q^{37} +8.52829 q^{38} +(3.59420 - 0.285839i) q^{39} -3.00000 q^{40} +(3.66012 + 6.33951i) q^{41} +(-1.16503 - 2.01789i) q^{42} +(2.21459 - 3.83578i) q^{43} +9.94764 q^{44} +(-0.450443 + 0.780189i) q^{45} +(-5.16012 + 8.93759i) q^{46} +6.95746 q^{47} +(0.450443 - 0.780189i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-4.87962 - 8.45174i) q^{50} -1.66994 q^{51} +(7.01144 + 10.1838i) q^{52} -0.141653 q^{53} +(-1.16503 - 2.01789i) q^{54} +(-1.30668 - 2.26324i) q^{55} +(1.66503 - 2.88392i) q^{56} +3.66012 q^{57} +(6.20967 - 10.7555i) q^{58} +(-4.74288 + 8.21490i) q^{59} -3.08929 q^{60} +(1.25923 - 2.18105i) q^{61} +(7.64376 + 13.2394i) q^{62} +(-0.500000 - 0.866025i) q^{63} -12.4292 q^{64} +(1.39597 - 2.93291i) q^{65} +6.75923 q^{66} +(-0.00491189 - 0.00850764i) q^{67} +(-2.86326 - 4.95931i) q^{68} +(-2.21459 + 3.83578i) q^{69} -2.09911 q^{70} +(-7.04465 + 12.2017i) q^{71} +(1.66503 - 2.88392i) q^{72} -2.57083 q^{73} +(10.0397 - 17.3893i) q^{74} +(-2.09420 - 3.62727i) q^{75} +(6.27559 + 10.8696i) q^{76} +2.90089 q^{77} +(4.76414 + 6.91970i) q^{78} -9.41935 q^{79} +(-0.405797 - 0.702861i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.52829 + 14.7714i) q^{82} +1.58065 q^{83} +(1.71459 - 2.96975i) q^{84} +(-0.752213 + 1.30287i) q^{85} +10.3202 q^{86} +(2.66503 - 4.61597i) q^{87} +(4.83006 + 8.36591i) q^{88} +(-4.16012 - 7.20553i) q^{89} -2.09911 q^{90} +(2.04465 + 2.96975i) q^{91} -15.1884 q^{92} +(3.28050 + 5.68199i) q^{93} +(8.10565 + 14.0394i) q^{94} +(1.64867 - 2.85558i) q^{95} -4.56100 q^{96} +(3.85133 - 6.67069i) q^{97} +(1.16503 - 2.01789i) q^{98} +2.90089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

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