LMFDB - Embedded newform 273.2.k.d.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:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 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			$1.32555 + 2.29591i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.d.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.78804 - 8.29313i) q^{10} +(1.63695 + 2.83527i) q^{11} -3.65109 q^{12} +(0.910836 + 3.48861i) q^{13} +2.37720 q^{14} +(-2.01415 - 3.48861i) q^{15} +(-1.01415 - 1.75656i) q^{16} +(0.188601 - 0.326667i) q^{17} -2.37720 q^{18} +(1.77389 - 3.07247i) q^{19} +(7.35384 - 12.7372i) q^{20} +1.00000 q^{21} +(-3.89135 + 6.74002i) q^{22} +(-0.948344 - 1.64258i) q^{23} +(-1.96249 - 3.39914i) q^{24} +11.2272 q^{25} +(-6.09944 + 6.02172i) q^{26} -1.00000 q^{27} +(1.82555 + 3.16194i) q^{28} +(4.33969 + 7.51657i) q^{29} +(4.78804 - 8.29313i) q^{30} +6.33048 q^{31} +(-1.51415 + 2.62258i) q^{32} +(-1.63695 + 2.83527i) q^{33} +0.896688 q^{34} +(-2.01415 + 3.48861i) q^{35} +(-1.82555 - 3.16194i) q^{36} +(-2.01415 - 3.48861i) q^{37} +8.43380 q^{38} +(-2.56580 + 2.53311i) q^{39} +15.8110 q^{40} +(-3.75441 - 6.50282i) q^{41} +(1.18860 + 2.05872i) q^{42} +(4.32555 - 7.49207i) q^{43} -11.9533 q^{44} +(2.01415 - 3.48861i) q^{45} +(2.25441 - 3.90475i) q^{46} -12.1239 q^{47} +(1.01415 - 1.75656i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(13.3446 + 23.1136i) q^{50} +0.377203 q^{51} +(-12.6935 - 3.48861i) q^{52} +7.75441 q^{53} +(-1.18860 - 2.05872i) q^{54} +(-6.59410 - 11.4213i) q^{55} +(-1.96249 + 3.39914i) q^{56} +3.54778 q^{57} +(-10.3163 + 17.8684i) q^{58} +(1.05166 - 1.82152i) q^{59} +14.7077 q^{60} +(-3.87720 + 6.71551i) q^{61} +(7.52442 + 13.0327i) q^{62} +(0.500000 + 0.866025i) q^{63} -11.2555 q^{64} +(-3.66912 - 14.0531i) q^{65} -7.78270 q^{66} +(-2.79191 - 4.83574i) q^{67} +(0.688601 + 1.19269i) q^{68} +(0.948344 - 1.64258i) q^{69} -9.57608 q^{70} +(-1.99612 + 3.45739i) q^{71} +(1.96249 - 3.39914i) q^{72} +7.50106 q^{73} +(4.78804 - 8.29313i) q^{74} +(5.61359 + 9.72302i) q^{75} +(6.47664 + 11.2179i) q^{76} +3.27389 q^{77} +(-8.26468 - 2.27141i) q^{78} -1.16283 q^{79} +(4.08529 + 7.07593i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.92498 - 15.4585i) q^{82} +15.1805 q^{83} +(-1.82555 + 3.16194i) q^{84} +(-0.759742 + 1.31591i) q^{85} +20.5654 q^{86} +(-4.33969 + 7.51657i) q^{87} +(-6.42498 - 11.1284i) q^{88} +(-3.17939 - 5.50686i) q^{89} +9.57608 q^{90} +(3.47664 + 0.955496i) q^{91} +6.92498 q^{92} +(3.16524 + 5.48236i) q^{93} +(-14.4104 - 24.9596i) q^{94} +(-7.14576 + 12.3768i) q^{95} -3.02830 q^{96} +(-2.48585 + 4.30562i) q^{97} +(1.18860 - 2.05872i) q^{98} -3.27389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 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 $

$2$	1.18860	+	2.05872i	0.840468	+	1.45573i	0.889499	+	0.456936i	$0.151053\pi$
$2$	1.18860	+	2.05872i	0.840468	+	1.45573i	−0.0490313	+	0.998797i	$0.515613\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.82555	+	3.16194i	−0.912773	+	1.58097i
$5$	−4.02830			−1.80151			−0.900754	−	0.434329i	$-0.856986\pi$
$5$	−4.02830			−1.80151			−0.900754	+	0.434329i	$0.856986\pi$
$6$	−1.18860	+	2.05872i	−0.485245	+	0.840468i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−3.92498			−1.38769
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.78804	−	8.29313i	−1.51411	−	2.62252i
$11$	1.63695	+	2.83527i	0.493558	+	0.854867i	0.999972	−	0.00742317i	$-0.00236289\pi$
$11$	1.63695	+	2.83527i	0.493558	+	0.854867i	−0.506415	+	0.862290i	$0.669030\pi$
$12$	−3.65109			−1.05398
$13$	0.910836	+	3.48861i	0.252620	+	0.967565i
$13$	0.910836	+	3.48861i	0.252620	+	0.967565i
$14$	2.37720			0.635334
$15$	−2.01415	−	3.48861i	−0.520051	−	0.900754i
$16$	−1.01415	−	1.75656i	−0.253537	−	0.439139i
$17$	0.188601	−	0.326667i	0.0457426	−	0.0792284i	−0.842248	−	0.539091i	$-0.818768\pi$
$17$	0.188601	−	0.326667i	0.0457426	−	0.0792284i	0.887990	+	0.459862i	$0.152101\pi$
$18$	−2.37720			−0.560312
$19$	1.77389	−	3.07247i	0.406958	−	0.704873i	−0.587589	−	0.809160i	$-0.699923\pi$
$19$	1.77389	−	3.07247i	0.406958	−	0.704873i	0.994547	+	0.104287i	$0.0332561\pi$
$20$	7.35384	−	12.7372i	1.64437	−	2.84813i
$21$	1.00000			0.218218
$22$	−3.89135	+	6.74002i	−0.829639	+	1.43698i
$23$	−0.948344	−	1.64258i	−0.197743	−	0.342502i	0.750053	−	0.661378i	$-0.230028\pi$
$23$	−0.948344	−	1.64258i	−0.197743	−	0.342502i	−0.947796	+	0.318876i	$0.896695\pi$
$24$	−1.96249	−	3.39914i	−0.400592	−	0.693846i
$25$	11.2272			2.24543
$26$	−6.09944	+	6.02172i	−1.19620	+	1.18096i
$27$	−1.00000			−0.192450
$28$	1.82555	+	3.16194i	0.344996	+	0.597550i
$29$	4.33969	+	7.51657i	0.805861	+	1.39579i	0.915708	+	0.401844i	$0.131631\pi$
$29$	4.33969	+	7.51657i	0.805861	+	1.39579i	−0.109847	+	0.993948i	$0.535036\pi$
$30$	4.78804	−	8.29313i	0.874172	−	1.51411i
$31$	6.33048			1.13699			0.568494	−	0.822687i	$-0.307526\pi$
$31$	6.33048			1.13699			0.568494	+	0.822687i	$0.307526\pi$
$32$	−1.51415	+	2.62258i	−0.267666	+	0.463611i
$33$	−1.63695	+	2.83527i	−0.284956	+	0.493558i
$34$	0.896688			0.153781
$35$	−2.01415	+	3.48861i	−0.340453	+	0.589682i
$36$	−1.82555	−	3.16194i	−0.304258	−	0.526990i
$37$	−2.01415	−	3.48861i	−0.331124	−	0.573523i	0.651609	−	0.758555i	$-0.274094\pi$
$37$	−2.01415	−	3.48861i	−0.331124	−	0.573523i	−0.982733	+	0.185032i	$0.940761\pi$
$38$	8.43380			1.36814
$39$	−2.56580	+	2.53311i	−0.410858	+	0.405622i
$40$	15.8110			2.49994
$41$	−3.75441	−	6.50282i	−0.586340	−	1.01557i	−0.994707	−	0.102752i	$-0.967235\pi$
$41$	−3.75441	−	6.50282i	−0.586340	−	1.01557i	0.408367	−	0.912818i	$-0.366098\pi$
$42$	1.18860	+	2.05872i	0.183405	+	0.317667i
$43$	4.32555	−	7.49207i	0.659640	−	1.14253i	−0.321069	−	0.947056i	$-0.604042\pi$
$43$	4.32555	−	7.49207i	0.659640	−	1.14253i	0.980709	−	0.195474i	$-0.0626244\pi$
$44$	−11.9533			−1.80202
$45$	2.01415	−	3.48861i	0.300251	−	0.520051i
$46$	2.25441	−	3.90475i	0.332394	−	0.575723i
$47$	−12.1239			−1.76845			−0.884223	−	0.467064i	$-0.845312\pi$
$47$	−12.1239			−1.76845			−0.884223	+	0.467064i	$0.845312\pi$
$48$	1.01415	−	1.75656i	0.146380	−	0.253537i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	13.3446	+	23.1136i	1.88722	+	3.26875i
$51$	0.377203			0.0528190
$52$	−12.6935	−	3.48861i	−1.76028	−	0.483783i
$53$	7.75441			1.06515			0.532575	−	0.846383i	$-0.321225\pi$
$53$	7.75441			1.06515			0.532575	+	0.846383i	$0.321225\pi$
$54$	−1.18860	−	2.05872i	−0.161748	−	0.280156i
$55$	−6.59410	−	11.4213i	−0.889148	−	1.54005i
$56$	−1.96249	+	3.39914i	−0.262249	+	0.454229i
$57$	3.54778			0.469915
$58$	−10.3163	+	17.8684i	−1.35460	+	2.34624i
$59$	1.05166	−	1.82152i	0.136914	−	0.237142i	−0.789413	−	0.613862i	$-0.789615\pi$
$59$	1.05166	−	1.82152i	0.136914	−	0.237142i	0.926327	+	0.376720i	$0.122948\pi$
$60$	14.7077			1.89875
$61$	−3.87720	+	6.71551i	−0.496425	+	0.859833i	−0.999991	−	0.00412320i	$-0.998688\pi$
$61$	−3.87720	+	6.71551i	−0.496425	+	0.859833i	0.503567	+	0.863956i	$0.332021\pi$
$62$	7.52442	+	13.0327i	0.955602	+	1.65515i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	−11.2555			−1.40693
$65$	−3.66912	−	14.0531i	−0.455098	−	1.74308i
$66$	−7.78270			−0.957984
$67$	−2.79191	−	4.83574i	−0.341087	−	0.590779i	0.643548	−	0.765406i	$-0.277462\pi$
$67$	−2.79191	−	4.83574i	−0.341087	−	0.590779i	−0.984635	+	0.174626i	$0.944128\pi$
$68$	0.688601	+	1.19269i	0.0835052	+	0.144635i
$69$	0.948344	−	1.64258i	0.114167	−	0.197743i
$70$	−9.57608			−1.14456
$71$	−1.99612	+	3.45739i	−0.236896	+	0.410317i	−0.959822	−	0.280609i	$-0.909464\pi$
$71$	−1.99612	+	3.45739i	−0.236896	+	0.410317i	0.722926	+	0.690926i	$0.242797\pi$
$72$	1.96249	−	3.39914i	0.231282	−	0.400592i
$73$	7.50106			0.877933			0.438966	−	0.898503i	$-0.355345\pi$
$73$	7.50106			0.877933			0.438966	+	0.898503i	$0.355345\pi$
$74$	4.78804	−	8.29313i	0.556598	−	0.964056i
$75$	5.61359	+	9.72302i	0.648201	+	1.12272i
$76$	6.47664	+	11.2179i	0.742922	+	1.28678i
$77$	3.27389			0.373094
$78$	−8.26468	−	2.27141i	−0.935791	−	0.257186i
$79$	−1.16283			−0.130828			−0.0654142	−	0.997858i	$-0.520837\pi$
$79$	−1.16283			−0.130828			−0.0654142	+	0.997858i	$0.520837\pi$
$80$	4.08529	+	7.07593i	0.456749	+	0.791113i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.92498	−	15.4585i	0.985600	−	1.70711i
$83$	15.1805			1.66627			0.833135	−	0.553069i	$-0.186543\pi$
$83$	15.1805			1.66627			0.833135	+	0.553069i	$0.186543\pi$
$84$	−1.82555	+	3.16194i	−0.199183	+	0.344996i
$85$	−0.759742	+	1.31591i	−0.0824056	+	0.142731i
$86$	20.5654			2.21762
$87$	−4.33969	+	7.51657i	−0.465264	+	0.805861i
$88$	−6.42498	−	11.1284i	−0.684906	−	1.18629i
$89$	−3.17939	−	5.50686i	−0.337015	−	0.583726i	0.646855	−	0.762613i	$-0.276084\pi$
$89$	−3.17939	−	5.50686i	−0.337015	−	0.583726i	−0.983870	+	0.178886i	$0.942751\pi$
$90$	9.57608			1.00941
$91$	3.47664	+	0.955496i	0.364451	+	0.100163i
$92$	6.92498			0.721979
$93$	3.16524	+	5.48236i	0.328220	+	0.568494i
$94$	−14.4104	−	24.9596i	−1.48632	−	2.57439i
$95$	−7.14576	+	12.3768i	−0.733139	+	1.26983i
$96$	−3.02830			−0.309074
$97$	−2.48585	+	4.30562i	−0.252400	+	0.437170i	−0.964186	−	0.265227i	$-0.914553\pi$
$97$	−2.48585	+	4.30562i	−0.252400	+	0.437170i	0.711786	+	0.702396i	$0.247887\pi$
$98$	1.18860	−	2.05872i	0.120067	−	0.207962i
$99$	−3.27389			−0.329038
$100$	−20.4957	+	35.4996i	−2.04957	+	3.54996i
$101$	−2.94834	−	5.10668i	−0.293371	−	0.508134i	0.681233	−	0.732066i	$-0.261444\pi$
$101$	−2.94834	−	5.10668i	−0.293371	−	0.508134i	−0.974605	+	0.223932i	$0.928111\pi$
$102$	0.448344	+	0.776554i	0.0443927	+	0.0768903i
$103$	10.5654			1.04104			0.520520	−	0.853849i	$-0.325738\pi$
$103$	10.5654			1.04104			0.520520	+	0.853849i	$0.325738\pi$
$104$	−3.57502	−	13.6927i	−0.350559	−	1.34268i
$105$	−4.02830			−0.393121
$106$	9.21690	+	15.9641i	0.895224	+	1.55057i
$107$	6.20275	+	10.7435i	0.599642	+	1.03861i	0.992874	+	0.119172i	$0.0380239\pi$
$107$	6.20275	+	10.7435i	0.599642	+	1.03861i	−0.393231	+	0.919440i	$0.628643\pi$
$108$	1.82555	−	3.16194i	0.175663	−	0.304258i
$109$	−12.1316			−1.16200			−0.580999	−	0.813905i	$-0.697338\pi$
$109$	−12.1316			−1.16200			−0.580999	+	0.813905i	$0.697338\pi$
$110$	15.6755	−	27.1508i	1.49460	−	2.58873i
$111$	2.01415	−	3.48861i	0.191174	−	0.331124i
$112$	−2.02830			−0.191656
$113$	5.33582	−	9.24191i	0.501952	−	0.869406i	−0.498046	−	0.867151i	$-0.665949\pi$
$113$	5.33582	−	9.24191i	0.501952	−	0.869406i	0.999997	−	0.00225510i	$-0.000717821\pi$
$114$	4.21690	+	7.30388i	0.394949	+	0.684071i
$115$	3.82021	+	6.61680i	0.356236	+	0.617020i
$116$	−31.6893			−2.94227
$117$	−3.47664	−	0.955496i	−0.321415	−	0.0883357i
$118$	5.00000			0.460287
$119$	−0.188601	−	0.326667i	−0.0172891	−	0.0299455i
$120$	7.90550	+	13.6927i	0.721670	+	1.24997i
$121$	0.140820	−	0.243908i	0.0128018	−	0.0221734i
$122$	−18.4338			−1.66892
$123$	3.75441	−	6.50282i	0.338523	−	0.586340i
$124$	−11.5566	+	20.0166i	−1.03781	+	1.79754i
$125$	−25.0849			−2.24366
$126$	−1.18860	+	2.05872i	−0.105889	+	0.183405i
$127$	−3.66524	−	6.34838i	−0.325238	−	0.563328i	0.656323	−	0.754480i	$-0.272111\pi$
$127$	−3.66524	−	6.34838i	−0.325238	−	0.563328i	−0.981560	+	0.191152i	$0.938778\pi$
$128$	−10.3500	−	17.9267i	−0.914817	−	1.58451i
$129$	8.65109			0.761686
$130$	24.5703	−	24.2573i	2.15496	−	2.12750i
$131$	11.4239			0.998113			0.499056	−	0.866570i	$-0.333680\pi$
$131$	11.4239			0.998113			0.499056	+	0.866570i	$0.333680\pi$
$132$	−5.97664	−	10.3518i	−0.520200	−	0.901012i
$133$	−1.77389	−	3.07247i	−0.153816	−	0.266417i
$134$	6.63695	−	11.4955i	0.573345	−	0.993062i
$135$	4.02830			0.346701
$136$	−0.740258	+	1.28216i	−0.0634766	+	0.109945i
$137$	1.59556	−	2.76359i	0.136318	−	0.236110i	−0.789782	−	0.613387i	$-0.789806\pi$
$137$	1.59556	−	2.76359i	0.136318	−	0.236110i	0.926100	+	0.377278i	$0.123140\pi$
$138$	4.50881			0.383816
$139$	−2.68860	+	4.65679i	−0.228044	+	0.394984i	−0.957228	−	0.289333i	$-0.906566\pi$
$139$	−2.68860	+	4.65679i	−0.228044	+	0.394984i	0.729184	+	0.684317i	$0.239900\pi$
$140$	−7.35384	−	12.7372i	−0.621513	−	1.07649i
$141$	−6.06193	−	10.4996i	−0.510507	−	0.884223i
$142$	−9.49039			−0.796416
$143$	−8.40016	+	8.29313i	−0.702457	+	0.693506i
$144$	2.02830			0.169025
$145$	−17.4816	−	30.2790i	−1.45177	−	2.51453i
$146$	8.91577	+	15.4426i	0.737875	+	1.27804i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	14.7077			1.20896
$149$	5.01415	−	8.68476i	0.410775	−	0.711483i	−0.584200	−	0.811610i	$-0.698592\pi$
$149$	5.01415	−	8.68476i	0.410775	−	0.711483i	0.994975	+	0.100127i	$0.0319248\pi$
$150$	−13.3446	+	23.1136i	−1.08958	+	1.88722i
$151$	−9.71544			−0.790631			−0.395315	−	0.918545i	$-0.629365\pi$
$151$	−9.71544			−0.790631			−0.395315	+	0.918545i	$0.629365\pi$
$152$	−6.96249	+	12.0594i	−0.564733	+	0.978146i
$153$	0.188601	+	0.326667i	0.0152475	+	0.0264095i
$154$	3.89135	+	6.74002i	0.313574	+	0.543126i
$155$	−25.5011			−2.04829
$156$	−3.32555	−	12.7372i	−0.266257	−	1.01979i
$157$	17.5761			1.40272			0.701362	−	0.712805i	$-0.252576\pi$
$157$	17.5761			1.40272			0.701362	+	0.712805i	$0.252576\pi$
$158$	−1.38214	−	2.39394i	−0.109957	−	0.190451i
$159$	3.87720	+	6.71551i	0.307482	+	0.532575i
$160$	6.09944	−	10.5645i	0.482203	−	0.835200i
$161$	−1.89669			−0.149480
$162$	1.18860	−	2.05872i	0.0933853	−	0.161748i
$163$	2.74559	−	4.75551i	0.215052	−	0.372480i	−0.738237	−	0.674541i	$-0.764341\pi$
$163$	2.74559	−	4.75551i	0.215052	−	0.372480i	0.953289	+	0.302061i	$0.0976747\pi$
$164$	27.4154			2.14078
$165$	6.59410	−	11.4213i	0.513350	−	0.889148i
$166$	18.0435	+	31.2523i	1.40045	+	2.42565i
$167$	−2.21836	−	3.84231i	−0.171662	−	0.297327i	0.767339	−	0.641241i	$-0.221580\pi$
$167$	−2.21836	−	3.84231i	−0.171662	−	0.297327i	−0.939001	+	0.343914i	$0.888247\pi$
$168$	−3.92498			−0.302819
$169$	−11.3408	+	6.35510i	−0.872366	+	0.488854i
$170$	−3.61212			−0.277037
$171$	1.77389	+	3.07247i	0.135653	+	0.234958i
$172$	15.7930	+	27.3542i	1.20420	+	2.08574i
$173$	−11.0800	+	19.1910i	−0.842393	+	1.45907i	0.0454728	+	0.998966i	$0.485521\pi$
$173$	−11.0800	+	19.1910i	−0.842393	+	1.45907i	−0.887866	+	0.460102i	$0.847813\pi$
$174$	−20.6327			−1.56416
$175$	5.61359	−	9.72302i	0.424347	−	0.734991i
$176$	3.32021	−	5.75077i	0.250270	−	0.433481i
$177$	2.10331			0.158095
$178$	7.55805	−	13.0909i	0.566500	−	0.981207i
$179$	0.970242	+	1.68051i	0.0725193	+	0.125607i	0.900005	−	0.435880i	$-0.143563\pi$
$179$	0.970242	+	1.68051i	0.0725193	+	0.125607i	−0.827486	+	0.561487i	$0.810229\pi$
$180$	7.35384	+	12.7372i	0.548123	+	0.949377i
$181$	−8.50106			−0.631879			−0.315939	−	0.948779i	$-0.602320\pi$
$181$	−8.50106			−0.631879			−0.315939	+	0.948779i	$0.602320\pi$
$182$	2.16524	+	8.29313i	0.160498	+	0.614727i
$183$	−7.75441			−0.573222
$184$	3.72223	+	6.44710i	0.274407	+	0.475286i
$185$	8.11359	+	14.0531i	0.596523	+	1.03321i
$186$	−7.52442	+	13.0327i	−0.551717	+	0.955602i
$187$	1.23492			0.0903064
$188$	22.1327	−	38.3349i	1.61419	−	2.79586i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	−33.9738			−2.46472
$191$	−0.325547	+	0.563863i	−0.0235557	+	0.0407997i	−0.877563	−	0.479461i	$-0.840832\pi$
$191$	−0.325547	+	0.563863i	−0.0235557	+	0.0407997i	0.854007	+	0.520261i	$0.174165\pi$
$192$	−5.62773	−	9.74752i	−0.406147	−	0.703467i
$193$	−9.53217	−	16.5102i	−0.686141	−	1.18843i	−0.973077	−	0.230481i	$-0.925970\pi$
$193$	−9.53217	−	16.5102i	−0.686141	−	1.18843i	0.286936	−	0.957950i	$-0.407363\pi$
$194$	−11.8187			−0.848537
$195$	10.3358	−	10.2041i	0.740163	−	0.730732i
$196$	3.65109			0.260792
$197$	−12.3549	−	21.3993i	−0.880250	−	1.52464i	−0.851062	−	0.525065i	$-0.824041\pi$
$197$	−12.3549	−	21.3993i	−0.880250	−	1.52464i	−0.0291881	−	0.999574i	$-0.509292\pi$
$198$	−3.89135	−	6.74002i	−0.276546	−	0.478992i
$199$	−6.57220	+	11.3834i	−0.465891	+	0.806947i	−0.999241	−	0.0389475i	$-0.987599\pi$
$199$	−6.57220	+	11.3834i	−0.465891	+	0.806947i	0.533350	+	0.845895i	$0.320933\pi$
$200$	−44.0665			−3.11597
$201$	2.79191	−	4.83574i	0.196926	−	0.341087i
$202$	7.00881	−	12.1396i	0.493138	−	0.854141i
$203$	8.67939			0.609174
$204$	−0.688601	+	1.19269i	−0.0482117	+	0.0835052i
$205$	15.1239	+	26.1953i	1.05630	+	1.82956i
$206$	12.5581	+	21.7512i	0.874961	+	1.51548i
$207$	1.89669			0.131829
$208$	5.20421	−	5.13790i	0.360847	−	0.356249i
$209$	11.6150			0.803430
$210$	−4.78804	−	8.29313i	−0.330406	−	0.572280i
$211$	9.79831	+	16.9712i	0.674544	+	1.16834i	0.976602	+	0.215054i	$0.0689929\pi$
$211$	9.79831	+	16.9712i	0.674544	+	1.16834i	−0.302058	+	0.953289i	$0.597674\pi$
$212$	−14.1560	+	24.5190i	−0.972240	+	1.68397i
$213$	−3.99225			−0.273544
$214$	−14.7452	+	25.5394i	−1.00796	+	1.74584i
$215$	−17.4246	+	30.1803i	−1.18835	+	2.05828i
$216$	3.92498			0.267061
$217$	3.16524	−	5.48236i	0.214871	−	0.372167i
$218$	−14.4196	−	24.9756i	−0.976622	−	1.69156i
$219$	3.75053	+	6.49611i	0.253437	+	0.438966i
$220$	48.1514			3.24636
$221$	1.31140	+	0.360416i	0.0882142	+	0.0242442i
$222$	9.57608			0.642704
$223$	13.9338	+	24.1340i	0.933076	+	1.61613i	0.778029	+	0.628228i	$0.216219\pi$
$223$	13.9338	+	24.1340i	0.933076	+	1.61613i	0.155046	+	0.987907i	$0.450447\pi$
$224$	1.51415	+	2.62258i	0.101168	+	0.175229i
$225$	−5.61359	+	9.72302i	−0.374239	+	0.648201i
$226$	25.3687			1.68750
$227$	−6.01521	+	10.4186i	−0.399243	+	0.691510i	−0.993633	−	0.112667i	$-0.964061\pi$
$227$	−6.01521	+	10.4186i	−0.399243	+	0.691510i	0.594389	+	0.804177i	$0.297394\pi$
$228$	−6.47664	+	11.2179i	−0.428926	+	0.742922i
$229$	−9.19887			−0.607879			−0.303939	−	0.952691i	$-0.598302\pi$
$229$	−9.19887			−0.607879			−0.303939	+	0.952691i	$0.598302\pi$
$230$	−9.08141	+	15.7295i	−0.598811	+	1.03717i
$231$	1.63695	+	2.83527i	0.107703	+	0.186547i
$232$	−17.0332	−	29.5024i	−1.11829	−	1.93693i
$233$	−12.4522			−0.815772			−0.407886	−	0.913033i	$-0.633734\pi$
$233$	−12.4522			−0.815772			−0.407886	+	0.913033i	$0.633734\pi$
$234$	−2.16524	−	8.29313i	−0.141546	−	0.542139i
$235$	48.8385			3.18587
$236$	3.83969	+	6.65055i	0.249943	+	0.432914i
$237$	−0.581414	−	1.00704i	−0.0377669	−	0.0654142i
$238$	0.448344	−	0.776554i	0.0290618	−	0.0503365i
$239$	−3.24559			−0.209940			−0.104970	−	0.994475i	$-0.533475\pi$
$239$	−3.24559			−0.209940			−0.104970	+	0.994475i	$0.533475\pi$
$240$	−4.08529	+	7.07593i	−0.263704	+	0.456749i
$241$	−4.71302	+	8.16319i	−0.303592	+	0.525838i	−0.976947	−	0.213482i	$-0.931519\pi$
$241$	−4.71302	+	8.16319i	−0.303592	+	0.525838i	0.673354	+	0.739320i	$0.264853\pi$
$242$	0.669517			0.0430382
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−14.1560	−	24.5190i	−0.906247	−	1.56967i
$245$	2.01415	+	3.48861i	0.128679	+	0.222879i
$246$	17.8500			1.13807
$247$	12.3344	+	3.38989i	0.784816	+	0.215694i
$248$	−24.8470			−1.57779
$249$	7.59023	+	13.1467i	0.481011	+	0.833135i
$250$	−29.8159	−	51.6427i	−1.88573	−	3.26617i
$251$	5.99466	−	10.3831i	0.378380	−	0.655373i	−0.612447	−	0.790512i	$-0.709815\pi$
$251$	5.99466	−	10.3831i	0.378380	−	0.655373i	0.990827	+	0.135139i	$0.0431480\pi$
$252$	−3.65109			−0.229997
$253$	3.10477	−	5.37763i	0.195195	−	0.338088i
$254$	8.71302	−	15.0914i	0.546704	−	0.946919i
$255$	−1.51948			−0.0951538
$256$	13.3485	−	23.1203i	0.834282	−	1.44502i
$257$	−7.29831	−	12.6410i	−0.455256	−	0.788527i	0.543447	−	0.839444i	$-0.317119\pi$
$257$	−7.29831	−	12.6410i	−0.455256	−	0.788527i	−0.998703	+	0.0509168i	$0.983786\pi$
$258$	10.2827	+	17.8102i	0.640173	+	1.10881i
$259$	−4.02830			−0.250306
$260$	51.1333	+	14.0531i	3.17115	+	0.871539i
$261$	−8.67939			−0.537241
$262$	13.5785	+	23.5186i	0.838882	+	1.45299i
$263$	−11.3266	−	19.6183i	−0.698429	−	1.20971i	−0.969011	−	0.247017i	$-0.920550\pi$
$263$	−11.3266	−	19.6183i	−0.698429	−	1.20971i	0.270583	−	0.962697i	$-0.412784\pi$
$264$	6.42498	−	11.1284i	0.395430	−	0.684906i
$265$	−31.2370			−1.91888
$266$	4.21690	−	7.30388i	0.258555	−	0.447830i
$267$	3.17939	−	5.50686i	0.194575	−	0.337015i
$268$	20.3871			1.24534
$269$	13.9947	−	24.2395i	0.853270	−	1.47791i	−0.0249713	−	0.999688i	$-0.507949\pi$
$269$	13.9947	−	24.2395i	0.853270	−	1.47791i	0.878241	−	0.478218i	$-0.158717\pi$
$270$	4.78804	+	8.29313i	0.291391	+	0.504704i
$271$	3.80365	+	6.58811i	0.231055	+	0.400199i	0.958119	−	0.286371i	$-0.0924489\pi$
$271$	3.80365	+	6.58811i	0.231055	+	0.400199i	−0.727064	+	0.686570i	$0.759116\pi$
$272$	−0.765079			−0.0463897
$273$	0.910836	+	3.48861i	0.0551263	+	0.211140i
$274$	7.58595			0.458284
$275$	18.3783	+	31.8321i	1.10825	+	1.91955i
$276$	3.46249	+	5.99721i	0.208418	+	0.360990i
$277$	3.44447	−	5.96599i	0.206958	−	0.358462i	−0.743797	−	0.668406i	$-0.766977\pi$
$277$	3.44447	−	5.96599i	0.206958	−	0.358462i	0.950755	+	0.309944i	$0.100310\pi$
$278$	−12.7827			−0.766656
$279$	−3.16524	+	5.48236i	−0.189498	+	0.328220i
$280$	7.90550	−	13.6927i	0.472444	−	0.818297i
$281$	10.8062			0.644642			0.322321	−	0.946630i	$-0.395537\pi$
$281$	10.8062			0.644642			0.322321	+	0.946630i	$0.395537\pi$
$282$	14.4104	−	24.9596i	0.858129	−	1.48632i
$283$	3.81246	+	6.60337i	0.226627	+	0.392530i	0.956806	−	0.290726i	$-0.0938968\pi$
$283$	3.81246	+	6.60337i	0.226627	+	0.392530i	−0.730179	+	0.683256i	$0.760563\pi$
$284$	−7.28804	−	12.6233i	−0.432466	−	0.749052i
$285$	−14.2915			−0.846556
$286$	−27.0577	−	7.43634i	−1.59995	−	0.439720i
$287$	−7.50881			−0.443231
$288$	−1.51415	−	2.62258i	−0.0892220	−	0.154537i
$289$	8.42886	+	14.5992i	0.495815	+	0.858777i
$290$	41.5573	−	71.9793i	2.44033	−	4.22677i
$291$	−4.97170			−0.291446
$292$	−13.6935	+	23.7179i	−0.801354	+	1.38799i
$293$	11.1458	−	19.3050i	0.651142	−	1.12781i	−0.331704	−	0.943384i	$-0.607624\pi$
$293$	11.1458	−	19.3050i	0.651142	−	1.12781i	0.982846	−	0.184428i	$-0.0590431\pi$
$294$	2.37720			0.138641
$295$	−4.23638	+	7.33763i	−0.246652	+	0.427213i
$296$	7.90550	+	13.6927i	0.459498	+	0.795874i
$297$	−1.63695	−	2.83527i	−0.0949852	−	0.164519i
$298$	23.8393			1.38097
$299$	4.86653	−	4.80452i	0.281439	−	0.277853i
$300$	−40.9914			−2.36664
$301$	−4.32555	−	7.49207i	−0.249320	−	0.431836i
$302$	−11.5478	−	20.0013i	−0.664500	−	1.15095i
$303$	2.94834	−	5.10668i	0.169378	−	0.293371i
$304$	−7.19595			−0.412716
$305$	15.6185	−	27.0521i	0.894314	−	1.54900i
$306$	−0.448344	+	0.776554i	−0.0256301	+	0.0443927i
$307$	−28.2448			−1.61202			−0.806008	−	0.591905i	$-0.798376\pi$
$307$	−28.2448			−1.61202			−0.806008	+	0.591905i	$0.798376\pi$
$308$	−5.97664	+	10.3518i	−0.340551	+	0.589851i
$309$	5.28270	+	9.14991i	0.300522	+	0.520520i
$310$	−30.3106	−	52.4995i	−1.72153	−	2.98177i
$311$	−2.66177			−0.150935			−0.0754675	−	0.997148i	$-0.524045\pi$
$311$	−2.66177			−0.150935			−0.0754675	+	0.997148i	$0.524045\pi$
$312$	10.0707	−	9.94242i	0.570143	−	0.562879i
$313$	−22.4826			−1.27079			−0.635397	−	0.772186i	$-0.719163\pi$
$313$	−22.4826			−1.27079			−0.635397	+	0.772186i	$0.719163\pi$
$314$	20.8910	+	36.1842i	1.17894	+	2.04199i
$315$	−2.01415	−	3.48861i	−0.113484	−	0.196561i
$316$	2.12280	−	3.67679i	0.119417	−	0.206836i
$317$	18.8315			1.05768			0.528842	−	0.848720i	$-0.322626\pi$
$317$	18.8315			1.05768			0.528842	+	0.848720i	$0.322626\pi$
$318$	−9.21690	+	15.9641i	−0.516858	+	0.895224i
$319$	−14.2077	+	24.6084i	−0.795478	+	1.37781i
$320$	45.3404			2.53460
$321$	−6.20275	+	10.7435i	−0.346204	+	0.599642i
$322$	−2.25441	−	3.90475i	−0.125633	−	0.217603i
$323$	−0.669117	−	1.15894i	−0.0372306	−	0.0644854i
$324$	3.65109			0.202839
$325$	10.2261	+	39.1672i	0.567242	+	2.17260i
$326$	13.0537			0.722976
$327$	−6.06580	−	10.5063i	−0.335440	−	0.580999i
$328$	14.7360	+	25.5235i	0.813659	+	1.40930i
$329$	−6.06193	+	10.4996i	−0.334205	+	0.578860i
$330$	31.3510			1.72582
$331$	8.91577	−	15.4426i	0.490055	−	0.848800i	−0.509879	−	0.860246i	$-0.670310\pi$
$331$	8.91577	−	15.4426i	0.490055	−	0.848800i	0.999934	+	0.0114455i	$0.00364329\pi$
$332$	−27.7126	+	47.9997i	−1.52093	+	2.63432i
$333$	4.02830			0.220749
$334$	5.27349	−	9.13395i	0.288553	−	0.499788i
$335$	11.2467	+	19.4798i	0.614470	+	1.06429i
$336$	−1.01415	−	1.75656i	−0.0553263	−	0.0958280i
$337$	7.57608			0.412695			0.206348	−	0.978479i	$-0.433842\pi$
$337$	7.57608			0.412695			0.206348	+	0.978479i	$0.433842\pi$
$338$	−26.5630	−	15.7937i	−1.44484	−	0.859066i
$339$	10.6716			0.579604
$340$	−2.77389	−	4.80452i	−0.150435	−	0.260562i
$341$	10.3627	+	17.9486i	0.561169	+	0.971974i
$342$	−4.21690	+	7.30388i	−0.228024	+	0.394949i
$343$	−1.00000			−0.0539949
$344$	−16.9777	+	29.4062i	−0.915376	+	1.58548i
$345$	−3.82021	+	6.61680i	−0.205673	+	0.356236i
$346$	−52.6786			−2.83202
$347$	−3.94407	+	6.83133i	−0.211729	+	0.366725i	−0.952256	−	0.305302i	$-0.901243\pi$
$347$	−3.94407	+	6.83133i	−0.211729	+	0.366725i	0.740527	+	0.672027i	$0.234576\pi$
$348$	−15.8446	−	27.4437i	−0.849361	−	1.47114i
$349$	5.86693	+	10.1618i	0.314050	+	0.543950i	0.979235	−	0.202728i	$-0.0649809\pi$
$349$	5.86693	+	10.1618i	0.314050	+	0.543950i	−0.665185	+	0.746678i	$0.731648\pi$
$350$	26.6893			1.42660
$351$	−0.910836	−	3.48861i	−0.0486168	−	0.186208i
$352$	−9.91431			−0.528435
$353$	6.26855	+	10.8575i	0.333641	+	0.577884i	0.983223	−	0.182408i	$-0.0583892\pi$
$353$	6.26855	+	10.8575i	0.333641	+	0.577884i	−0.649581	+	0.760292i	$0.725056\pi$
$354$	2.50000	+	4.33013i	0.132874	+	0.230144i
$355$	8.04098	−	13.9274i	0.426771	−	0.739189i
$356$	23.2165			1.23047
$357$	0.188601	−	0.326667i	0.00998185	−	0.0172891i
$358$	−2.30646	+	3.99491i	−0.121900	+	0.211138i
$359$	−5.01762			−0.264820			−0.132410	−	0.991195i	$-0.542272\pi$
$359$	−5.01762			−0.264820			−0.132410	+	0.991195i	$0.542272\pi$
$360$	−7.90550	+	13.6927i	−0.416656	+	0.721670i
$361$	3.20662	+	5.55404i	0.168770	+	0.292318i
$362$	−10.1044	−	17.5013i	−0.531074	−	0.919847i
$363$	0.281641			0.0147823
$364$	−9.36799	+	9.24862i	−0.491016	+	0.484760i
$365$	−30.2165			−1.58160
$366$	−9.21690	−	15.9641i	−0.481775	−	0.834459i
$367$	−11.8549	−	20.5333i	−0.618821	−	1.07183i	−0.989701	−	0.143149i	$-0.954277\pi$
$367$	−11.8549	−	20.5333i	−0.618821	−	1.07183i	0.370880	−	0.928681i	$-0.379056\pi$
$368$	−1.92352	+	3.33164i	−0.100271	+	0.173674i
$369$	7.50881			0.390893
$370$	−19.2876	+	33.4072i	−1.00272	+	1.73676i
$371$	3.87720	−	6.71551i	0.201294	−	0.348652i
$372$	−23.1132			−1.19836
$373$	4.97664	−	8.61979i	0.257681	−	0.446316i	−0.707940	−	0.706273i	$-0.750375\pi$
$373$	4.97664	−	8.61979i	0.257681	−	0.446316i	0.965620	+	0.259957i	$0.0837084\pi$
$374$	1.46783	+	2.54235i	0.0758996	+	0.131462i
$375$	−12.5424	−	21.7242i	−0.647689	−	1.12183i
$376$	47.5860			2.45406
$377$	−22.2696	+	21.9859i	−1.14694	+	1.13233i
$378$	−2.37720			−0.122270
$379$	13.9250	+	24.1188i	0.715278	+	1.23890i	0.962852	+	0.270029i	$0.0870334\pi$
$379$	13.9250	+	24.1188i	0.715278	+	1.23890i	−0.247574	+	0.968869i	$0.579633\pi$
$380$	−26.0898	−	45.1889i	−1.33838	−	2.31814i
$381$	3.66524	−	6.34838i	0.187776	−	0.325238i
$382$	−1.54778			−0.0791914
$383$	3.45222	−	5.97942i	0.176400	−	0.305534i	−0.764245	−	0.644926i	$-0.776888\pi$
$383$	3.45222	−	5.97942i	0.176400	−	0.305534i	0.940645	+	0.339392i	$0.110221\pi$
$384$	10.3500	−	17.9267i	0.528170	−	0.914817i
$385$	−13.1882			−0.672133
$386$	22.6599	−	39.2481i	1.15336	−	1.99768i
$387$	4.32555	+	7.49207i	0.219880	+	0.380843i
$388$	−9.07608	−	15.7202i	−0.460768	−	0.798074i
$389$	−28.3764			−1.43874			−0.719370	−	0.694627i	$-0.755570\pi$
$389$	−28.3764			−1.43874			−0.719370	+	0.694627i	$0.755570\pi$
$390$	33.2926	+	9.14991i	1.68584	+	0.463324i
$391$	−0.715436			−0.0361812
$392$	1.96249	+	3.39914i	0.0991208	+	0.171682i
$393$	5.71196	+	9.89341i	0.288130	+	0.499056i
$394$	29.3701	−	50.8705i	1.47964	−	2.56282i
$395$	4.68422			0.235689
$396$	5.97664	−	10.3518i	0.300337	−	0.520200i
$397$	2.38360	−	4.12852i	0.119630	−	0.207204i	−0.799991	−	0.600011i	$-0.795163\pi$
$397$	2.38360	−	4.12852i	0.119630	−	0.207204i	0.919621	+	0.392807i	$0.128496\pi$
$398$	−31.2469			−1.56627
$399$	1.77389	−	3.07247i	0.0888056	−	0.153816i
$400$	−11.3860	−	19.7212i	−0.569301	−	0.986058i
$401$	4.13307	+	7.15869i	0.206396	+	0.357488i	0.950577	−	0.310490i	$-0.100493\pi$
$401$	4.13307	+	7.15869i	0.206396	+	0.357488i	−0.744181	+	0.667978i	$0.767160\pi$
$402$	13.2739			0.662041
$403$	5.76603	+	22.0846i	0.287226	+	1.10011i
$404$	21.5294			1.07113
$405$	2.01415	+	3.48861i	0.100084	+	0.173350i
$406$	10.3163	+	17.8684i	0.511991	+	0.886795i
$407$	6.59410	−	11.4213i	0.326857	−	0.566134i
$408$	−1.48052			−0.0732964
$409$	−10.7169	+	18.5622i	−0.529916	+	0.917842i	0.469474	+	0.882946i	$0.344443\pi$
$409$	−10.7169	+	18.5622i	−0.529916	+	0.917842i	−0.999391	+	0.0348962i	$0.988890\pi$
$410$	−35.9525	+	62.2715i	−1.77557	+	3.07537i
$411$	3.19112			0.157407
$412$	−19.2876	+	33.4072i	−0.950234	+	1.64585i
$413$	−1.05166	−	1.82152i	−0.0517486	−	0.0896312i
$414$	2.25441	+	3.90475i	0.110798	+	0.191908i
$415$	−61.1514			−3.00180
$416$	−10.5283	−	2.89353i	−0.516192	−	0.141867i
$417$	−5.37720			−0.263323
$418$	13.8057	+	23.9121i	0.675257	+	1.16958i
$419$	1.14576	+	1.98451i	0.0559739	+	0.0969496i	0.892655	−	0.450741i	$-0.148840\pi$
$419$	1.14576	+	1.98451i	0.0559739	+	0.0969496i	−0.836681	+	0.547691i	$0.815507\pi$
$420$	7.35384	−	12.7372i	0.358831	−	0.621513i
$421$	7.61292			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$421$	7.61292			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$422$	−23.2926	+	40.3439i	−1.13386	+	1.96391i
$423$	6.06193	−	10.4996i	0.294741	−	0.510507i
$424$	−30.4359			−1.47810
$425$	2.11746	−	3.66755i	0.102712	−	0.177902i
$426$	−4.74519	−	8.21892i	−0.229905	−	0.398208i
$427$	3.87720	+	6.71551i	0.187631	+	0.324986i
$428$	−45.2936			−2.18935
$429$	−11.3821	−	3.12819i	−0.549535	−	0.151030i
$430$	−82.8435			−3.99507
$431$	−10.4314	−	18.0677i	−0.502462	−	0.870290i	−0.999996	−	0.00284520i	$-0.999094\pi$
$431$	−10.4314	−	18.0677i	−0.502462	−	0.870290i	0.497534	−	0.867444i	$-0.334239\pi$
$432$	1.01415	+	1.75656i	0.0487932	+	0.0845123i
$433$	11.6882	−	20.2446i	0.561699	−	0.972891i	−0.435649	−	0.900116i	$-0.643481\pi$
$433$	11.6882	−	20.2446i	0.561699	−	0.972891i	0.997348	−	0.0727749i	$-0.0231855\pi$
$434$	15.0488			0.722368
$435$	17.4816	−	30.2790i	0.838177	−	1.45177i
$436$	22.1468	−	38.3594i	1.06064	−	1.83708i
$437$	−6.72903			−0.321893
$438$	−8.91577	+	15.4426i	−0.426012	+	0.737875i
$439$	−4.57754	−	7.92853i	−0.218474	−	0.378408i	0.735868	−	0.677125i	$-0.236775\pi$
$439$	−4.57754	−	7.92853i	−0.218474	−	0.378408i	−0.954342	+	0.298717i	$0.903441\pi$
$440$	25.8817	+	44.8285i	1.23386	+	2.13711i
$441$	1.00000			0.0476190
$442$	0.816735	+	3.12819i	0.0388481	+	0.148793i
$443$	11.2632			0.535132			0.267566	−	0.963540i	$-0.413781\pi$
$443$	11.2632			0.535132			0.267566	+	0.963540i	$0.413781\pi$
$444$	7.35384	+	12.7372i	0.348998	+	0.604482i
$445$	12.8075	+	22.1833i	0.607135	+	1.05159i
$446$	−33.1235	+	57.3715i	−1.56844	+	2.71662i
$447$	10.0283			0.474322
$448$	−5.62773	+	9.74752i	−0.265885	+	0.460527i
$449$	16.8924	−	29.2585i	0.797202	−	1.38079i	−0.124229	−	0.992254i	$-0.539646\pi$
$449$	16.8924	−	29.2585i	0.797202	−	1.38079i	0.921431	−	0.388541i	$-0.127021\pi$
$450$	−26.6893			−1.25814
$451$	12.2915	−	21.2895i	0.578785	−	1.00248i
$452$	19.4816	+	33.7431i	0.916336	+	1.58714i
$453$	−4.85772	−	8.41381i	−0.228236	−	0.395315i
$454$	−28.5987			−1.34221
$455$	−14.0049	−	3.84902i	−0.656562	−	0.180445i
$456$	−13.9250			−0.652097
$457$	−17.1472	−	29.6999i	−0.802113	−	1.38930i	−0.918223	−	0.396064i	$-0.870376\pi$
$457$	−17.1472	−	29.6999i	−0.802113	−	1.38930i	0.116110	−	0.993236i	$-0.462958\pi$
$458$	−10.9338	−	18.9379i	−0.510903	−	0.884909i
$459$	−0.188601	+	0.326667i	−0.00880316	+	0.0152475i
$460$	−27.8959			−1.30065
$461$	−9.66630	+	16.7425i	−0.450205	+	0.779777i	−0.998398	−	0.0565741i	$-0.981982\pi$
$461$	−9.66630	+	16.7425i	−0.450205	+	0.779777i	0.548194	+	0.836351i	$0.315316\pi$
$462$	−3.89135	+	6.74002i	−0.181042	+	0.313574i
$463$	6.29444			0.292527			0.146264	−	0.989246i	$-0.453275\pi$
$463$	6.29444			0.292527			0.146264	+	0.989246i	$0.453275\pi$
$464$	8.80219	−	15.2458i	0.408631	−	0.707770i
$465$	−12.7505	−	22.0846i	−0.591292	−	1.02415i
$466$	−14.8007	−	25.6356i	−0.685630	−	1.18755i
$467$	24.2293			1.12120			0.560599	−	0.828087i	$-0.310571\pi$
$467$	24.2293			1.12120			0.560599	+	0.828087i	$0.310571\pi$
$468$	9.36799	−	9.24862i	0.433036	−	0.427518i
$469$	−5.58383			−0.257837
$470$	58.0495	+	100.545i	2.67762	+	4.63778i
$471$	8.78804	+	15.2213i	0.404931	+	0.701362i
$472$	−4.12773	+	7.14944i	−0.189994	+	0.329080i
$473$	28.3227			1.30228
$474$	1.38214	−	2.39394i	0.0634838	−	0.109957i
$475$	19.9158	−	34.4951i	0.913798	−	1.58275i
$476$	1.37720			0.0631240
$477$	−3.87720	+	6.71551i	−0.177525	+	0.307482i
$478$	−3.85772	−	6.68176i	−0.176448	−	0.305617i
$479$	16.8149	+	29.1242i	0.768291	+	1.33072i	0.938489	+	0.345309i	$0.112226\pi$
$479$	16.8149	+	29.1242i	0.768291	+	1.33072i	−0.170198	+	0.985410i	$0.554441\pi$
$480$	12.1989			0.556800
$481$	10.3358	−	10.2041i	0.471273	−	0.465268i
$482$	−22.4076			−1.02064
$483$	−0.948344	−	1.64258i	−0.0431511	−	0.0747400i
$484$	0.514148	+	0.890531i	0.0233704	+	0.0404787i
$485$	10.0137	−	17.3443i	0.454701	−	0.787565i
$486$	2.37720			0.107832
$487$	3.96249	−	6.86324i	0.179558	−	0.311003i	−0.762171	−	0.647375i	$-0.775867\pi$
$487$	3.96249	−	6.86324i	0.179558	−	0.311003i	0.941729	+	0.336372i	$0.109200\pi$
$488$	15.2180	−	26.3583i	0.688885	−	1.19318i
$489$	5.49119			0.248320
$490$	−4.78804	+	8.29313i	−0.216302	+	0.374645i
$491$	−1.21584	−	2.10589i	−0.0548699	−	0.0950375i	0.837286	−	0.546766i	$-0.184141\pi$
$491$	−1.21584	−	2.10589i	−0.0548699	−	0.0950375i	−0.892156	+	0.451728i	$0.850808\pi$
$492$	13.7077	+	23.7424i	0.617990	+	1.07039i
$493$	3.27389			0.147449
$494$	7.68180	+	29.4222i	0.345621	+	1.32377i
$495$	13.1882			0.592766
$496$	−6.42005	−	11.1198i	−0.288269	−	0.499296i
$497$	1.99612	+	3.45739i	0.0895384	+	0.155085i
$498$	−18.0435	+	31.2523i	−0.808549	+	1.40045i
$499$	−18.5838			−0.831926			−0.415963	−	0.909381i	$-0.636555\pi$
$499$	−18.5838			−0.831926			−0.415963	+	0.909381i	$0.636555\pi$
$500$	45.7936	−	79.3169i	2.04795	−	3.54716i
$501$	2.21836	−	3.84231i	0.0991090	−	0.171662i
$502$	28.5011			1.27206
$503$	8.72717	−	15.1159i	0.389125	−	0.673985i	−0.603207	−	0.797585i	$-0.706111\pi$
$503$	8.72717	−	15.1159i	0.389125	−	0.673985i	0.992332	+	0.123600i	$0.0394440\pi$
$504$	−1.96249	−	3.39914i	−0.0874163	−	0.151410i
$505$	11.8768	+	20.5712i	0.528511	+	0.915408i
$506$	14.7614			0.656222
$507$	−11.1741	−	6.64383i	−0.496257	−	0.295063i
$508$	26.7643			1.18747
$509$	−1.38495	−	2.39881i	−0.0613870	−	0.106325i	0.833699	−	0.552220i	$-0.186219\pi$
$509$	−1.38495	−	2.39881i	−0.0613870	−	0.106325i	−0.895086	+	0.445894i	$0.852886\pi$
$510$	−1.80606	−	3.12819i	−0.0799738	−	0.138519i
$511$	3.75053	−	6.49611i	0.165914	−	0.287371i
$512$	22.0643			0.975115
$513$	−1.77389	+	3.07247i	−0.0783192	+	0.135653i
$514$	17.3496	−	30.0503i	0.765257	−	1.32546i
$515$	−42.5606			−1.87544
$516$	−15.7930	+	27.3542i	−0.695247	+	1.20420i
$517$	−19.8461	−	34.3744i	−0.872830	−	1.51179i
$518$	−4.78804	−	8.29313i	−0.210374	−	0.364379i
$519$	−22.1599			−0.972712
$520$	14.4012	+	55.1584i	0.631535	+	2.41885i
$521$	−26.2816			−1.15142			−0.575710	−	0.817654i	$-0.695274\pi$
$521$	−26.2816			−1.15142			−0.575710	+	0.817654i	$0.695274\pi$
$522$	−10.3163	−	17.8684i	−0.451534	−	0.782079i
$523$	−2.62521	−	4.54700i	−0.114792	−	0.198826i	0.802904	−	0.596108i	$-0.203287\pi$
$523$	−2.62521	−	4.54700i	−0.114792	−	0.198826i	−0.917697	+	0.397282i	$0.869954\pi$
$524$	−20.8549	+	36.1218i	−0.911051	+	1.57799i
$525$	11.2272			0.489994
$526$	26.9256	−	46.6366i	1.17401	−	2.03345i
$527$	1.19394	−	2.06796i	0.0520088	−	0.0900818i
$528$	6.64042			0.288987
$529$	9.70129	−	16.8031i	0.421795	−	0.730571i
$530$	−37.1284	−	64.3083i	−1.61275	−	2.79337i
$531$	1.05166	+	1.82152i	0.0456380	+	0.0790473i
$532$	12.9533			0.561596
$533$	19.2661	−	19.0206i	0.834509	−	0.823876i
$534$	15.1161			0.654138
$535$	−24.9865	−	43.2779i	−1.08026	−	1.87107i
$536$	10.9582	+	18.9802i	0.473323	+	0.819819i
$537$	−0.970242	+	1.68051i	−0.0418690	+	0.0725193i
$538$	66.5363			2.86858
$539$	1.63695	−	2.83527i	0.0705082	−	0.122124i
$540$	−7.35384	+	12.7372i	−0.316459	+	0.548123i
$541$	−0.111863			−0.00480937			−0.00240468	−	0.999997i	$-0.500765\pi$
$541$	−0.111863			−0.00480937			−0.00240468	+	0.999997i	$0.500765\pi$
$542$	−9.04204	+	15.6613i	−0.388389	+	0.672710i
$543$	−4.25053	−	7.36214i	−0.182408	−	0.315939i
$544$	0.571141	+	0.989245i	0.0244875	+	0.0424135i
$545$	48.8697			2.09335
$546$	−6.09944	+	6.02172i	−0.261032	+	0.257706i
$547$	−33.7515			−1.44311			−0.721555	−	0.692358i	$-0.756572\pi$
$547$	−33.7515			−1.44311			−0.721555	+	0.692358i	$0.756572\pi$
$548$	5.82555	+	10.0901i	0.248855	+	0.431030i
$549$	−3.87720	−	6.71551i	−0.165475	−	0.286611i
$550$	−43.6889	+	75.6713i	−1.86290	+	3.22664i
$551$	30.7926			1.31181
$552$	−3.72223	+	6.44710i	−0.158429	+	0.274407i
$553$	−0.581414	+	1.00704i	−0.0247242	+	0.0428236i
$554$	16.3764			0.695767
$555$	−8.11359	+	14.0531i	−0.344403	+	0.596523i
$556$	−9.81633	−	17.0024i	−0.416305	−	0.721062i
$557$	−14.5073	−	25.1275i	−0.614696	−	1.06468i	−0.990438	−	0.137960i	$-0.955945\pi$
$557$	−14.5073	−	25.1275i	−0.614696	−	1.06468i	0.375742	−	0.926724i	$-0.377388\pi$
$558$	−15.0488			−0.637068
$559$	30.0767	+	8.26609i	1.27211	+	0.349618i
$560$	8.17058			0.345270
$561$	0.617460	+	1.06947i	0.0260692	+	0.0451532i
$562$	12.8442	+	22.2469i	0.541801	+	0.938427i
$563$	−0.715836	+	1.23986i	−0.0301689	+	0.0522541i	−0.880716	−	0.473645i	$-0.842938\pi$
$563$	−0.715836	+	1.23986i	−0.0301689	+	0.0522541i	0.850547	+	0.525899i	$0.176271\pi$
$564$	44.2653			1.86391
$565$	−21.4943	+	37.2292i	−0.904270	+	1.56624i
$566$	−9.06299	+	15.6976i	−0.380946	+	0.659818i
$567$	−1.00000			−0.0419961
$568$	7.83476	−	13.5702i	0.328739	−	0.569393i
$569$	12.2505	+	21.2185i	0.513569	+	0.889528i	0.999876	+	0.0157396i	$0.00501028\pi$
$569$	12.2505	+	21.2185i	0.513569	+	0.889528i	−0.486307	+	0.873788i	$0.661656\pi$
$570$	−16.9869	−	29.4222i	−0.711503	−	1.23236i
$571$	−47.3735			−1.98252			−0.991259	−	0.131929i	$-0.957883\pi$
$571$	−47.3735			−1.98252			−0.991259	+	0.131929i	$0.957883\pi$
$572$	−10.8875	−	41.7003i	−0.455228	−	1.74358i
$573$	−0.651093			−0.0271998
$574$	−8.92498	−	15.4585i	−0.372522	−	0.645226i
$575$	−10.6472	−	18.4415i	−0.444020	−	0.769065i
$576$	5.62773	−	9.74752i	0.234489	−	0.406147i
$577$	27.4055			1.14091			0.570453	−	0.821330i	$-0.306768\pi$
$577$	27.4055			1.14091			0.570453	+	0.821330i	$0.306768\pi$
$578$	−20.0371	+	34.7053i	−0.833434	+	1.44355i
$579$	9.53217	−	16.5102i	0.396144	−	0.686141i
$580$	127.654			5.30053
$581$	7.59023	−	13.1467i	0.314896	−	0.545415i
$582$	−5.90937	−	10.2353i	−0.244951	−	0.424268i
$583$	12.6935	+	21.9859i	0.525713	+	0.910561i
$584$	−29.4415			−1.21830
$585$	14.0049	+	3.84902i	0.579033	+	0.159138i
$586$	52.9914			2.18906
$587$	−13.9479	−	24.1585i	−0.575693	−	0.997130i	−0.995966	−	0.0897321i	$-0.971399\pi$
$587$	−13.9479	−	24.1585i	−0.575693	−	0.997130i	0.420273	−	0.907398i	$-0.361934\pi$
$588$	1.82555	+	3.16194i	0.0752843	+	0.130396i
$589$	11.2296	−	19.4502i	0.462707	−	0.801432i
$590$	−20.1415			−0.829212
$591$	12.3549	−	21.3993i	0.508213	−	0.880250i
$592$	−4.08529	+	7.07593i	−0.167904	+	0.290819i
$593$	−16.6015			−0.681740			−0.340870	−	0.940110i	$-0.610722\pi$
$593$	−16.6015			−0.681740			−0.340870	+	0.940110i	$0.610722\pi$
$594$	3.89135	−	6.74002i	0.159664	−	0.276546i
$595$	0.759742	+	1.31591i	0.0311464	+	0.0539472i
$596$	18.3071	+	31.7089i	0.749889	+	1.29885i
$597$	−13.1444			−0.537965
$598$	15.6755	+	4.30815i	0.641019	+	0.176173i
$599$	11.7913			0.481778			0.240889	−	0.970553i	$-0.422561\pi$
$599$	11.7913			0.481778			0.240889	+	0.970553i	$0.422561\pi$
$600$	−22.0332	−	38.1627i	−0.899503	−	1.55798i
$601$	−6.91084	−	11.9699i	−0.281899	−	0.488263i	0.689954	−	0.723854i	$-0.257631\pi$
$601$	−6.91084	−	11.9699i	−0.281899	−	0.488263i	−0.971852	+	0.235590i	$0.924298\pi$
$602$	10.2827	−	17.8102i	0.419092	−	0.725888i
$603$	5.58383			0.227391
$604$	17.7360	−	30.7196i	0.721667	−	1.24996i
$605$	−0.567266	+	0.982533i	−0.0230626	+	0.0399457i
$606$	14.0176			0.569427
$607$	10.5474	−	18.2686i	0.428105	−	0.741500i	−0.568600	−	0.822614i	$-0.692515\pi$
$607$	10.5474	−	18.2686i	0.428105	−	0.741500i	0.996705	+	0.0811147i	$0.0258480\pi$
$608$	5.37187	+	9.30435i	0.217858	+	0.377341i
$609$	4.33969	+	7.51657i	0.175853	+	0.304587i
$610$	74.2568			3.00657
$611$	−11.0428	−	42.2954i	−0.446746	−	1.71109i
$612$	−1.37720			−0.0556701
$613$	−1.09691	−	1.89991i	−0.0443039	−	0.0767367i	0.843023	−	0.537877i	$-0.180774\pi$
$613$	−1.09691	−	1.89991i	−0.0443039	−	0.0767367i	−0.887327	+	0.461141i	$0.847440\pi$
$614$	−33.5718	−	58.1481i	−1.35485	−	2.34666i
$615$	−15.1239	+	26.1953i	−0.609853	+	1.05630i
$616$	−12.8500			−0.517740
$617$	3.17405	−	5.49762i	0.127783	−	0.221326i	−0.795035	−	0.606564i	$-0.792547\pi$
$617$	3.17405	−	5.49762i	0.127783	−	0.221326i	0.922817	+	0.385238i	$0.125881\pi$
$618$	−12.5581	+	21.7512i	−0.505159	+	0.874961i
$619$	−7.77203			−0.312384			−0.156192	−	0.987727i	$-0.549922\pi$
$619$	−7.77203			−0.312384			−0.156192	+	0.987727i	$0.549922\pi$
$620$	46.5534	−	80.6328i	1.86963	−	3.23829i
$621$	0.948344	+	1.64258i	0.0380557	+	0.0659145i
$622$	−3.16378	−	5.47983i	−0.126856	−	0.219721i
$623$	−6.35878			−0.254759
$624$	7.05166	+	1.93803i	0.282292	+	0.0775833i
$625$	44.9135			1.79654
$626$	−26.7229	−	46.2854i	−1.06806	−	1.84994i
$627$	5.80752	+	10.0589i	0.231930	+	0.401715i
$628$	−32.0860	+	55.5745i	−1.28037	+	2.21766i
$629$	−1.51948			−0.0605858
$630$	4.78804	−	8.29313i	0.190760	−	0.330406i
$631$	−17.1312	+	29.6721i	−0.681983	+	1.18123i	0.292392	+	0.956298i	$0.405549\pi$
$631$	−17.1312	+	29.6721i	−0.681983	+	1.18123i	−0.974375	+	0.224930i	$0.927785\pi$
$632$	4.56408			0.181549
$633$	−9.79831	+	16.9712i	−0.389448	+	0.674544i
$634$	22.3832	+	38.7688i	0.888950	+	1.53971i
$635$	14.7647	+	25.5732i	0.585918	+	1.01484i
$636$	−28.3121			−1.12265
$637$	2.56580	−	2.53311i	0.101661	−	0.100365i
$638$	−67.5491			−2.67429
$639$	−1.99612	−	3.45739i	−0.0789655	−	0.136772i
$640$	41.6927	+	72.2139i	1.64805	+	2.85451i
$641$	11.6093	−	20.1079i	0.458540	−	0.794215i	−0.540344	−	0.841444i	$-0.681706\pi$
$641$	11.6093	−	20.1079i	0.458540	−	0.794215i	0.998884	+	0.0472294i	$0.0150392\pi$
$642$	−29.4904			−1.16389
$643$	−10.0400	+	17.3898i	−0.395940	+	0.685788i	−0.993221	−	0.116244i	$-0.962915\pi$
$643$	−10.0400	+	17.3898i	−0.395940	+	0.685788i	0.597281	+	0.802032i	$0.296248\pi$
$644$	3.46249	−	5.99721i	0.136441	−	0.236323i
$645$	−34.8492			−1.37218
$646$	1.59063	−	2.75504i	0.0625823	−	0.108396i
$647$	8.26468	+	14.3148i	0.324918	+	0.562775i	0.981496	−	0.191484i	$-0.0613299\pi$
$647$	8.26468	+	14.3148i	0.324918	+	0.562775i	−0.656578	+	0.754258i	$0.727997\pi$
$648$	1.96249	+	3.39914i	0.0770940	+	0.133531i
$649$	6.88601			0.270300
$650$	−68.4794	+	67.6068i	−2.68598	+	2.65176i
$651$	6.33048			0.248111
$652$	10.0244	+	17.3628i	0.392587	+	0.679980i
$653$	0.463954	+	0.803591i	0.0181559	+	0.0314470i	0.874961	−	0.484194i	$-0.160887\pi$
$653$	0.463954	+	0.803591i	0.0181559	+	0.0314470i	−0.856805	+	0.515641i	$0.827554\pi$
$654$	14.4196	−	24.9756i	0.563853	−	0.976622i
$655$	−46.0189			−1.79811
$656$	−7.61505	+	13.1896i	−0.297318	+	0.514969i
$657$	−3.75053	+	6.49611i	−0.146322	+	0.253437i
$658$	−28.8209			−1.12355
$659$	−16.1284	+	27.9352i	−0.628273	+	1.08820i	0.359625	+	0.933097i	$0.382905\pi$
$659$	−16.1284	+	27.9352i	−0.628273	+	1.08820i	−0.987898	+	0.155104i	$0.950429\pi$
$660$	24.0757	+	41.7003i	0.937144	+	1.62318i
$661$	11.4285	+	19.7947i	0.444516	+	0.769923i	0.998018	−	0.0629238i	$-0.0200425\pi$
$661$	11.4285	+	19.7947i	0.444516	+	0.769923i	−0.553503	+	0.832847i	$0.686709\pi$
$662$	42.3892			1.64750
$663$	0.343570	+	1.31591i	0.0133431	+	0.0511058i
$664$	−59.5830			−2.31227
$665$	7.14576	+	12.3768i	0.277101	+	0.479952i
$666$	4.78804	+	8.29313i	0.185533	+	0.321352i
$667$	8.23105	−	14.2566i	0.318707	−	0.552017i
$668$	16.1989			0.626753
$669$	−13.9338	+	24.1340i	−0.538712	+	0.933076i
$670$	−26.7356	+	46.3074i	−1.03289	+	1.78901i
$671$	−25.3871			−0.980057
$672$	−1.51415	+	2.62258i	−0.0584095	+	0.101168i
$673$	−0.542845	−	0.940235i	−0.0209251	−	0.0362434i	0.855373	−	0.518012i	$-0.173328\pi$
$673$	−0.542845	−	0.940235i	−0.0209251	−	0.0362434i	−0.876298	+	0.481769i	$0.839994\pi$
$674$	9.00494	+	15.5970i	0.346857	+	0.600774i
$675$	−11.2272			−0.432134
$676$	0.608649	−	47.4603i	0.0234096	−	1.82540i
$677$	−8.60730			−0.330805			−0.165403	−	0.986226i	$-0.552892\pi$
$677$	−8.60730			−0.330805			−0.165403	+	0.986226i	$0.552892\pi$
$678$	12.6843	+	21.9699i	0.487139	+	0.843749i
$679$	2.48585	+	4.30562i	0.0953982	+	0.165235i
$680$	2.98198	−	5.16494i	0.114354	−	0.198066i
$681$	−12.0304			−0.461007
$682$	−24.6341	+	42.6676i	−0.943290	+	1.63383i
$683$	−16.7310	+	28.9790i	−0.640196	+	1.10885i	0.345193	+	0.938532i	$0.387813\pi$
$683$	−16.7310	+	28.9790i	−0.640196	+	1.10885i	−0.985389	+	0.170320i	$0.945520\pi$
$684$	−12.9533			−0.495281
$685$	−6.42740	+	11.1326i	−0.245578	+	0.425354i
$686$	−1.18860	−	2.05872i	−0.0453810	−	0.0786022i
$687$	−4.59944	−	7.96646i	−0.175479	−	0.303939i
$688$	−17.5470			−0.668972
$689$	7.06299	+	27.0521i	0.269079	+	1.03060i
$690$	−18.1628			−0.691447
$691$	2.34609	+	4.06355i	0.0892496	+	0.154585i	0.907194	−	0.420712i	$-0.138220\pi$
$691$	2.34609	+	4.06355i	0.0892496	+	0.154585i	−0.817945	+	0.575297i	$0.804886\pi$
$692$	−40.4539	−	70.0683i	−1.53783	−	2.66360i
$693$	−1.63695	+	2.83527i	−0.0621824	+	0.107703i
$694$	−18.7517			−0.711805
$695$	10.8305	−	18.7589i	0.410824	−	0.711567i
$696$	17.0332	−	29.5024i	0.645643	−	1.11829i
$697$	−2.83235			−0.107283
$698$	−13.9469	+	24.1567i	−0.527897	+	0.914345i
$699$	−6.22611	−	10.7839i	−0.235493	−	0.407886i
$700$	20.4957	+	35.4996i	0.774666	+	1.34176i
$701$	41.4535			1.56568			0.782839	−	0.622224i	$-0.213771\pi$
$701$	41.4535			1.56568			0.782839	+	0.622224i	$0.213771\pi$
$702$	6.09944	−	6.02172i	0.230208	−	0.227275i
$703$	−14.2915			−0.539015
$704$	−18.4246	−	31.9123i	−0.694403	−	1.20274i
$705$	24.4192	+	42.2954i	0.919682	+	1.59294i
$706$	−14.9016	+	25.8104i	−0.560830	+	0.971386i
$707$	−5.89669			−0.221768
$708$	−3.83969	+	6.65055i	−0.144305	+	0.249943i
$709$	−1.92111	+	3.32746i	−0.0721488	+	0.124965i	−0.899843	−	0.436214i	$-0.856319\pi$
$709$	−1.92111	+	3.32746i	−0.0721488	+	0.124965i	0.827694	+	0.561180i	$0.189652\pi$
$710$	38.2301			1.43475
$711$	0.581414	−	1.00704i	0.0218047	−	0.0377669i
$712$	12.4791	+	21.6144i	0.467672	+	0.810032i
$713$	−6.00347	−	10.3983i	−0.224832	−	0.389420i
$714$	0.896688			0.0335577
$715$	33.8383	−	33.4072i	1.26548	−	1.24936i
$716$	−7.08489			−0.264775
$717$	−1.62280	−	2.81077i	−0.0606045	−	0.104970i
$718$	−5.96395	−	10.3299i	−0.222573	−	0.385507i
$719$	−4.45609	+	7.71818i	−0.166184	+	0.287840i	−0.937075	−	0.349128i	$-0.886478\pi$
$719$	−4.45609	+	7.71818i	−0.166184	+	0.287840i	0.770891	+	0.636967i	$0.219811\pi$
$720$	−8.17058			−0.304499
$721$	5.28270	−	9.14991i	0.196738	−	0.340760i
$722$	−7.62280	+	13.2031i	−0.283691	+	0.491367i
$723$	−9.42605			−0.350558
$724$	15.5191	−	26.8798i	0.576762	−	0.998981i
$725$	48.7225	+	84.3898i	1.80951	+	3.13416i
$726$	0.334758	+	0.579819i	0.0124241	+	0.0215191i
$727$	29.6815			1.10083			0.550413	−	0.834892i	$-0.314470\pi$
$727$	29.6815			1.10083			0.550413	+	0.834892i	$0.314470\pi$
$728$	−13.6458	−	3.75031i	−0.505745	−	0.138996i
$729$	1.00000			0.0370370
$730$	−35.9154	−	62.2072i	−1.32929	−	2.30239i
$731$	−1.63161	−	2.82603i	−0.0603472	−	0.104524i
$732$	14.1560	−	24.5190i	0.523222	−	0.906247i
$733$	5.30299			0.195870			0.0979352	−	0.995193i	$-0.468776\pi$
$733$	5.30299			0.195870			0.0979352	+	0.995193i	$0.468776\pi$
$734$	28.1815	−	48.8118i	1.04020	−	1.80168i
$735$	−2.01415	+	3.48861i	−0.0742930	+	0.128679i
$736$	5.74373			0.211717
$737$	9.14042	−	15.8317i	0.336692	−	0.583167i
$738$	8.92498	+	15.4585i	0.328533	+	0.569036i
$739$	10.4572	+	18.1123i	0.384673	+	0.666273i	0.991724	−	0.128390i	$-0.0409810\pi$
$739$	10.4572	+	18.1123i	0.384673	+	0.666273i	−0.607051	+	0.794663i	$0.707648\pi$
$740$	−59.2469			−2.17796
$741$	3.23145	+	12.3768i	0.118710	+	0.454674i
$742$	18.4338			0.676726
$743$	0.159244	+	0.275818i	0.00584209	+	0.0101188i	0.868932	−	0.494932i	$-0.164807\pi$
$743$	0.159244	+	0.275818i	0.00584209	+	0.0101188i	−0.863090	+	0.505051i	$0.831474\pi$
$744$	−12.4235	−	21.5182i	−0.455468	−	0.788894i
$745$	−20.1985	+	34.9848i	−0.740015	+	1.28174i
$746$	23.6610			0.866290
$747$	−7.59023	+	13.1467i	−0.277712	+	0.481011i
$748$	−2.25441	+	3.90475i	−0.0824292	+	0.142772i
$749$	12.4055			0.453287
$750$	29.8159	−	51.6427i	1.08872	−	1.88573i
$751$	−19.7940	−	34.2843i	−0.722295	−	1.25105i	−0.960078	−	0.279733i	$-0.909754\pi$
$751$	−19.7940	−	34.2843i	−0.722295	−	1.25105i	0.237783	−	0.971318i	$-0.423579\pi$
$752$	12.2954	+	21.2962i	0.448367	+	0.776594i
$753$	11.9893			0.436915
$754$	−71.7324	−	19.7144i	−2.61234	−	0.717958i
$755$	39.1367			1.42433
$756$	−1.82555	−	3.16194i	−0.0663945	−	0.114999i
$757$	5.12667	+	8.87966i	0.186332	+	0.322737i	0.944025	−	0.329875i	$-0.107007\pi$
$757$	5.12667	+	8.87966i	0.186332	+	0.322737i	−0.757693	+	0.652612i	$0.773673\pi$
$758$	−33.1025	+	57.3352i	−1.20234	+	2.08251i
$759$	6.20955			0.225392
$760$	28.0470	−	48.5788i	1.01737	−	1.76214i
$761$	8.73920	−	15.1367i	0.316796	−	0.548706i	−0.663022	−	0.748600i	$-0.730726\pi$
$761$	8.73920	−	15.1367i	0.316796	−	0.548706i	0.979818	+	0.199894i	$0.0640597\pi$
$762$	17.4260			0.631279
$763$	−6.06580	+	10.5063i	−0.219597	+	0.380353i
$764$	−1.18860	−	2.05872i	−0.0430021	−	0.0744818i
$765$	−0.759742	−	1.31591i	−0.0274685	−	0.0475769i
$766$	16.4132			0.593035
$767$	7.31246	+	2.00971i	0.264038	+	0.0725663i
$768$	26.6970			0.963345
$769$	−18.0283	−	31.2259i	−0.650117	−	1.12604i	−0.983094	−	0.183101i	$-0.941387\pi$
$769$	−18.0283	−	31.2259i	−0.650117	−	1.12604i	0.332977	−	0.942935i	$-0.391947\pi$
$770$	−15.6755	−	27.1508i	−0.564906	−	0.978446i
$771$	7.29831	−	12.6410i	0.262842	−	0.455256i
$772$	69.6057			2.50516
$773$

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)

\(f(q)\)	\(=\)	\(q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.78804 - 8.29313i) q^{10} +(1.63695 + 2.83527i) q^{11} -3.65109 q^{12} +(0.910836 + 3.48861i) q^{13} +2.37720 q^{14} +(-2.01415 - 3.48861i) q^{15} +(-1.01415 - 1.75656i) q^{16} +(0.188601 - 0.326667i) q^{17} -2.37720 q^{18} +(1.77389 - 3.07247i) q^{19} +(7.35384 - 12.7372i) q^{20} +1.00000 q^{21} +(-3.89135 + 6.74002i) q^{22} +(-0.948344 - 1.64258i) q^{23} +(-1.96249 - 3.39914i) q^{24} +11.2272 q^{25} +(-6.09944 + 6.02172i) q^{26} -1.00000 q^{27} +(1.82555 + 3.16194i) q^{28} +(4.33969 + 7.51657i) q^{29} +(4.78804 - 8.29313i) q^{30} +6.33048 q^{31} +(-1.51415 + 2.62258i) q^{32} +(-1.63695 + 2.83527i) q^{33} +0.896688 q^{34} +(-2.01415 + 3.48861i) q^{35} +(-1.82555 - 3.16194i) q^{36} +(-2.01415 - 3.48861i) q^{37} +8.43380 q^{38} +(-2.56580 + 2.53311i) q^{39} +15.8110 q^{40} +(-3.75441 - 6.50282i) q^{41} +(1.18860 + 2.05872i) q^{42} +(4.32555 - 7.49207i) q^{43} -11.9533 q^{44} +(2.01415 - 3.48861i) q^{45} +(2.25441 - 3.90475i) q^{46} -12.1239 q^{47} +(1.01415 - 1.75656i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(13.3446 + 23.1136i) q^{50} +0.377203 q^{51} +(-12.6935 - 3.48861i) q^{52} +7.75441 q^{53} +(-1.18860 - 2.05872i) q^{54} +(-6.59410 - 11.4213i) q^{55} +(-1.96249 + 3.39914i) q^{56} +3.54778 q^{57} +(-10.3163 + 17.8684i) q^{58} +(1.05166 - 1.82152i) q^{59} +14.7077 q^{60} +(-3.87720 + 6.71551i) q^{61} +(7.52442 + 13.0327i) q^{62} +(0.500000 + 0.866025i) q^{63} -11.2555 q^{64} +(-3.66912 - 14.0531i) q^{65} -7.78270 q^{66} +(-2.79191 - 4.83574i) q^{67} +(0.688601 + 1.19269i) q^{68} +(0.948344 - 1.64258i) q^{69} -9.57608 q^{70} +(-1.99612 + 3.45739i) q^{71} +(1.96249 - 3.39914i) q^{72} +7.50106 q^{73} +(4.78804 - 8.29313i) q^{74} +(5.61359 + 9.72302i) q^{75} +(6.47664 + 11.2179i) q^{76} +3.27389 q^{77} +(-8.26468 - 2.27141i) q^{78} -1.16283 q^{79} +(4.08529 + 7.07593i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.92498 - 15.4585i) q^{82} +15.1805 q^{83} +(-1.82555 + 3.16194i) q^{84} +(-0.759742 + 1.31591i) q^{85} +20.5654 q^{86} +(-4.33969 + 7.51657i) q^{87} +(-6.42498 - 11.1284i) q^{88} +(-3.17939 - 5.50686i) q^{89} +9.57608 q^{90} +(3.47664 + 0.955496i) q^{91} +6.92498 q^{92} +(3.16524 + 5.48236i) q^{93} +(-14.4104 - 24.9596i) q^{94} +(-7.14576 + 12.3768i) q^{95} -3.02830 q^{96} +(-2.48585 + 4.30562i) q^{97} +(1.18860 - 2.05872i) q^{98} -3.27389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

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