LMFDB - Embedded newform 273.2.k.d.211.1

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			211.1
Root			$-0.136945 - 0.237196i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.d.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.41471 - 4.18240i) q^{10} +(2.18860 + 3.79077i) q^{11} -0.726109 q^{12} +(2.56580 - 2.53311i) q^{13} -1.65109 q^{14} +(1.46249 + 2.53311i) q^{15} +(2.46249 + 4.26516i) q^{16} +(-1.82555 + 3.16194i) q^{17} +1.65109 q^{18} +(2.87720 - 4.98346i) q^{19} +(-1.06193 + 1.83932i) q^{20} +1.00000 q^{21} +(3.61359 - 6.25891i) q^{22} +(-3.51415 - 6.08668i) q^{23} +(-1.05166 - 1.82152i) q^{24} +3.55553 q^{25} +(-5.74026 - 1.57761i) q^{26} -1.00000 q^{27} +(0.363055 + 0.628829i) q^{28} +(-0.599437 - 1.03826i) q^{29} +(2.41471 - 4.18240i) q^{30} -6.47277 q^{31} +(1.96249 - 3.39914i) q^{32} +(-2.18860 + 3.79077i) q^{33} +6.02830 q^{34} +(1.46249 - 2.53311i) q^{35} +(-0.363055 - 0.628829i) q^{36} +(1.46249 + 2.53311i) q^{37} -9.50106 q^{38} +(3.47664 + 0.955496i) q^{39} -6.15215 q^{40} +(4.30219 + 7.45161i) q^{41} +(-0.825547 - 1.42989i) q^{42} +(2.86305 - 4.95896i) q^{43} -3.17833 q^{44} +(-1.46249 + 2.53311i) q^{45} +(-5.80219 + 10.0497i) q^{46} -9.58383 q^{47} +(-2.46249 + 4.26516i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.93526 - 5.08401i) q^{50} -3.65109 q^{51} +(0.661367 + 2.53311i) q^{52} -0.302187 q^{53} +(0.825547 + 1.42989i) q^{54} +(6.40162 + 11.0879i) q^{55} +(-1.05166 + 1.82152i) q^{56} +5.75441 q^{57} +(-0.989727 + 1.71426i) q^{58} +(-1.51415 + 2.62258i) q^{59} -2.12386 q^{60} +(0.151093 - 0.261701i) q^{61} +(5.34357 + 9.25533i) q^{62} +(0.500000 + 0.866025i) q^{63} +3.36945 q^{64} +(7.50494 - 7.40931i) q^{65} +7.22717 q^{66} +(4.35384 + 7.54108i) q^{67} +(-1.32555 - 2.29591i) q^{68} +(3.51415 - 6.08668i) q^{69} -4.82942 q^{70} +(-6.76855 + 11.7235i) q^{71} +(1.05166 - 1.82152i) q^{72} +0.932734 q^{73} +(2.41471 - 4.18240i) q^{74} +(1.77777 + 3.07918i) q^{75} +(2.08916 + 3.61854i) q^{76} +4.37720 q^{77} +(-1.50388 - 5.76002i) q^{78} -16.9426 q^{79} +(7.20275 + 12.4755i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.10331 - 12.3033i) q^{82} -1.26614 q^{83} +(-0.363055 + 0.628829i) q^{84} +(-5.33969 + 9.24862i) q^{85} -9.45434 q^{86} +(0.599437 - 1.03826i) q^{87} +(-4.60331 - 7.97317i) q^{88} +(6.69887 + 11.6028i) q^{89} +4.82942 q^{90} +(-0.910836 - 3.48861i) q^{91} +5.10331 q^{92} +(-3.23638 - 5.60558i) q^{93} +(7.91190 + 13.7038i) q^{94} +(8.41577 - 14.5765i) q^{95} +3.92498 q^{96} +(-5.96249 + 10.3273i) q^{97} +(-0.825547 + 1.42989i) q^{98} -4.37720 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 $

$2$	−0.825547	−	1.42989i	−0.583750	−	1.01108i	−0.995030	−	0.0995752i	$-0.968252\pi$
$2$	−0.825547	−	1.42989i	−0.583750	−	1.01108i	0.411280	−	0.911509i	$-0.365082\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.363055	+	0.628829i	−0.181527	+	0.314415i
$5$	2.92498			1.30809			0.654046	−	0.756455i	$-0.273070\pi$
$5$	2.92498			1.30809			0.654046	+	0.756455i	$0.273070\pi$
$6$	0.825547	−	1.42989i	0.337028	−	0.583750i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−2.10331			−0.743633
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.41471	−	4.18240i	−0.763599	−	1.32259i
$11$	2.18860	+	3.79077i	0.659888	+	1.14296i	0.980644	+	0.195798i	$0.0627297\pi$
$11$	2.18860	+	3.79077i	0.659888	+	1.14296i	−0.320756	+	0.947162i	$0.603937\pi$
$12$	−0.726109			−0.209610
$13$	2.56580	−	2.53311i	0.711626	−	0.702558i
$13$	2.56580	−	2.53311i	0.711626	−	0.702558i
$14$	−1.65109			−0.441273
$15$	1.46249	+	2.53311i	0.377614	+	0.654046i
$16$	2.46249	+	4.26516i	0.615623	+	1.06629i
$17$	−1.82555	+	3.16194i	−0.442760	+	0.766883i	−0.997893	−	0.0648786i	$-0.979334\pi$
$17$	−1.82555	+	3.16194i	−0.442760	+	0.766883i	0.555133	+	0.831762i	$0.312667\pi$
$18$	1.65109			0.389166
$19$	2.87720	−	4.98346i	0.660076	−	1.14328i	−0.320520	−	0.947242i	$-0.603858\pi$
$19$	2.87720	−	4.98346i	0.660076	−	1.14328i	0.980595	−	0.196043i	$-0.0628091\pi$
$20$	−1.06193	+	1.83932i	−0.237455	+	0.411283i
$21$	1.00000			0.218218
$22$	3.61359	−	6.25891i	0.770419	−	1.33440i
$23$	−3.51415	−	6.08668i	−0.732751	−	1.26916i	−0.955703	−	0.294332i	$-0.904903\pi$
$23$	−3.51415	−	6.08668i	−0.732751	−	1.26916i	0.222953	−	0.974829i	$-0.428430\pi$
$24$	−1.05166	−	1.82152i	−0.214668	−	0.371817i
$25$	3.55553			0.711106
$26$	−5.74026	−	1.57761i	−1.12576	−	0.309396i
$27$	−1.00000			−0.192450
$28$	0.363055	+	0.628829i	0.0686109	+	0.118838i
$29$	−0.599437	−	1.03826i	−0.111313	−	0.192799i	0.804987	−	0.593292i	$-0.202172\pi$
$29$	−0.599437	−	1.03826i	−0.111313	−	0.192799i	−0.916300	+	0.400493i	$0.868839\pi$
$30$	2.41471	−	4.18240i	0.440864	−	0.763599i
$31$	−6.47277			−1.16254			−0.581271	−	0.813710i	$-0.697445\pi$
$31$	−6.47277			−1.16254			−0.581271	+	0.813710i	$0.697445\pi$
$32$	1.96249	−	3.39914i	0.346923	−	0.600888i
$33$	−2.18860	+	3.79077i	−0.380987	+	0.659888i
$34$	6.02830			1.03384
$35$	1.46249	−	2.53311i	0.247206	−	0.428174i
$36$	−0.363055	−	0.628829i	−0.0605091	−	0.104805i
$37$	1.46249	+	2.53311i	0.240432	+	0.416441i	0.960837	−	0.277113i	$-0.0893775\pi$
$37$	1.46249	+	2.53311i	0.240432	+	0.416441i	−0.720405	+	0.693553i	$0.756044\pi$
$38$	−9.50106			−1.54128
$39$	3.47664	+	0.955496i	0.556708	+	0.153002i
$40$	−6.15215			−0.972741
$41$	4.30219	+	7.45161i	0.671889	+	1.16375i	0.977368	+	0.211547i	$0.0678500\pi$
$41$	4.30219	+	7.45161i	0.671889	+	1.16375i	−0.305479	+	0.952199i	$0.598817\pi$
$42$	−0.825547	−	1.42989i	−0.127385	−	0.220637i
$43$	2.86305	−	4.95896i	0.436612	−	0.756234i	−0.560814	−	0.827942i	$-0.689512\pi$
$43$	2.86305	−	4.95896i	0.436612	−	0.756234i	0.997426	+	0.0717081i	$0.0228450\pi$
$44$	−3.17833			−0.479151
$45$	−1.46249	+	2.53311i	−0.218015	+	0.377614i
$46$	−5.80219	+	10.0497i	−0.855486	+	1.48174i
$47$	−9.58383			−1.39794			−0.698972	−	0.715149i	$-0.746359\pi$
$47$	−9.58383			−1.39794			−0.698972	+	0.715149i	$0.746359\pi$
$48$	−2.46249	+	4.26516i	−0.355430	+	0.615623i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.93526	−	5.08401i	−0.415108	−	0.718988i
$51$	−3.65109			−0.511255
$52$	0.661367	+	2.53311i	0.0917150	+	0.351279i
$53$	−0.302187			−0.0415086			−0.0207543	−	0.999785i	$-0.506607\pi$
$53$	−0.302187			−0.0415086			−0.0207543	+	0.999785i	$0.506607\pi$
$54$	0.825547	+	1.42989i	0.112343	+	0.194583i
$55$	6.40162	+	11.0879i	0.863195	+	1.49510i
$56$	−1.05166	+	1.82152i	−0.140533	+	0.243411i
$57$	5.75441			0.762190
$58$	−0.989727	+	1.71426i	−0.129958	+	0.225093i
$59$	−1.51415	+	2.62258i	−0.197125	+	0.341431i	−0.947595	−	0.319474i	$-0.896494\pi$
$59$	−1.51415	+	2.62258i	−0.197125	+	0.341431i	0.750470	+	0.660905i	$0.229827\pi$
$60$	−2.12386			−0.274189
$61$	0.151093	−	0.261701i	0.0193455	−	0.0335074i	−0.856191	−	0.516660i	$-0.827175\pi$
$61$	0.151093	−	0.261701i	0.0193455	−	0.0335074i	0.875536	+	0.483153i	$0.160508\pi$
$62$	5.34357	+	9.25533i	0.678634	+	1.17543i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	3.36945			0.421182
$65$	7.50494	−	7.40931i	0.930873	−	0.919011i
$66$	7.22717			0.889603
$67$	4.35384	+	7.54108i	0.531907	+	0.921289i	0.999306	+	0.0372431i	$0.0118576\pi$
$67$	4.35384	+	7.54108i	0.531907	+	0.921289i	−0.467400	+	0.884046i	$0.654809\pi$
$68$	−1.32555	−	2.29591i	−0.160746	−	0.278420i
$69$	3.51415	−	6.08668i	0.423054	−	0.732751i
$70$	−4.82942			−0.577226
$71$	−6.76855	+	11.7235i	−0.803280	+	1.39132i	0.114167	+	0.993462i	$0.463580\pi$
$71$	−6.76855	+	11.7235i	−0.803280	+	1.39132i	−0.917446	+	0.397859i	$0.869753\pi$
$72$	1.05166	−	1.82152i	0.123939	−	0.214668i
$73$	0.932734			0.109168			0.0545841	−	0.998509i	$-0.482617\pi$
$73$	0.932734			0.109168			0.0545841	+	0.998509i	$0.482617\pi$
$74$	2.41471	−	4.18240i	0.280704	−	0.486194i
$75$	1.77777	+	3.07918i	0.205279	+	0.355553i
$76$	2.08916	+	3.61854i	0.239644	+	0.415075i
$77$	4.37720			0.498829
$78$	−1.50388	−	5.76002i	−0.170280	−	0.652193i
$79$	−16.9426			−1.90619			−0.953096	−	0.302668i	$-0.902123\pi$
$79$	−16.9426			−1.90619			−0.953096	+	0.302668i	$0.902123\pi$
$80$	7.20275	+	12.4755i	0.805292	+	1.39481i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.10331	−	12.3033i	0.784430	−	1.35867i
$83$	−1.26614			−0.138977			−0.0694885	−	0.997583i	$-0.522137\pi$
$83$	−1.26614			−0.138977			−0.0694885	+	0.997583i	$0.522137\pi$
$84$	−0.363055	+	0.628829i	−0.0396125	+	0.0686109i
$85$	−5.33969	+	9.24862i	−0.579171	+	1.00315i
$86$	−9.45434			−1.01949
$87$	0.599437	−	1.03826i	0.0642664	−	0.111313i
$88$	−4.60331	−	7.97317i	−0.490715	−	0.849943i
$89$	6.69887	+	11.6028i	0.710079	+	1.22989i	0.964827	+	0.262886i	$0.0846743\pi$
$89$	6.69887	+	11.6028i	0.710079	+	1.22989i	−0.254748	+	0.967008i	$0.581992\pi$
$90$	4.82942			0.509066
$91$	−0.910836	−	3.48861i	−0.0954815	−	0.365705i
$92$	5.10331			0.532057
$93$	−3.23638	−	5.60558i	−0.335597	−	0.581271i
$94$	7.91190	+	13.7038i	0.816050	+	1.41344i
$95$	8.41577	−	14.5765i	0.863440	−	1.49552i
$96$	3.92498			0.400592
$97$	−5.96249	+	10.3273i	−0.605399	+	1.04858i	0.386589	+	0.922252i	$0.373653\pi$
$97$	−5.96249	+	10.3273i	−0.605399	+	1.04858i	−0.991988	+	0.126330i	$0.959680\pi$
$98$	−0.825547	+	1.42989i	−0.0833928	+	0.144441i
$99$	−4.37720			−0.439925
$100$	−1.29085	+	2.23582i	−0.129085	+	0.223582i
$101$	−5.51415	−	9.55078i	−0.548678	−	0.950339i	−0.998365	−	0.0571525i	$-0.981798\pi$
$101$	−5.51415	−	9.55078i	−0.548678	−	0.950339i	0.449687	−	0.893186i	$-0.351535\pi$
$102$	3.01415	+	5.22066i	0.298445	+	0.516922i
$103$	−19.4543			−1.91689			−0.958447	−	0.285272i	$-0.907916\pi$
$103$	−19.4543			−1.91689			−0.958447	+	0.285272i	$0.907916\pi$
$104$	−5.39669	+	5.32792i	−0.529189	+	0.522446i
$105$	2.92498			0.285449
$106$	0.249469	+	0.432094i	0.0242306	+	0.0419686i
$107$	0.711961	+	1.23315i	0.0688279	+	0.119213i	0.898386	−	0.439208i	$-0.144741\pi$
$107$	0.711961	+	1.23315i	0.0688279	+	0.119213i	−0.829558	+	0.558421i	$0.811407\pi$
$108$	0.363055	−	0.628829i	0.0349350	−	0.0605091i
$109$	−0.0467198			−0.00447494			−0.00223747	−	0.999997i	$-0.500712\pi$
$109$	−0.0467198			−0.00447494			−0.00223747	+	0.999997i	$0.500712\pi$
$110$	10.5697	−	18.3072i	1.00778	−	1.74553i
$111$	−1.46249	+	2.53311i	−0.138814	+	0.240432i
$112$	4.92498			0.465367
$113$	5.16912	−	8.95317i	0.486270	−	0.842244i	−0.513606	−	0.858026i	$-0.671691\pi$
$113$	5.16912	−	8.95317i	0.486270	−	0.842244i	0.999875	+	0.0157826i	$0.00502397\pi$
$114$	−4.75053	−	8.22816i	−0.444928	−	0.770638i
$115$	−10.2788	−	17.8035i	−0.958506	−	1.66018i
$116$	0.870514			0.0808252
$117$	0.910836	+	3.48861i	0.0842068	+	0.322522i
$118$	5.00000			0.460287
$119$	1.82555	+	3.16194i	0.167348	+	0.289855i
$120$	−3.07608	−	5.32792i	−0.280806	−	0.486371i
$121$	−4.07995	+	7.06668i	−0.370905	+	0.642426i
$122$	−0.498939			−0.0451718
$123$	−4.30219	+	7.45161i	−0.387915	+	0.671889i
$124$	2.34997	−	4.07026i	0.211033	−	0.365520i
$125$	−4.22505			−0.377900
$126$	0.825547	−	1.42989i	0.0735455	−	0.127385i
$127$	2.73638	+	4.73955i	0.242815	+	0.420567i	0.961515	−	0.274753i	$-0.0885960\pi$
$127$	2.73638	+	4.73955i	0.242815	+	0.420567i	−0.718700	+	0.695320i	$0.755263\pi$
$128$	−6.70662	−	11.6162i	−0.592787	−	1.02674i
$129$	5.72611			0.504156
$130$	−16.7902	−	4.61450i	−1.47259	−	0.404718i
$131$	16.1706			1.41283			0.706415	−	0.707798i	$-0.250311\pi$
$131$	16.1706			1.41283			0.706415	+	0.707798i	$0.250311\pi$
$132$	−1.58916	−	2.75251i	−0.138319	−	0.239576i
$133$	−2.87720	−	4.98346i	−0.249485	−	0.432121i
$134$	7.18860	−	12.4510i	0.621001	−	1.07560i
$135$	−2.92498			−0.251743
$136$	3.83969	−	6.65055i	0.329251	−	0.570280i
$137$	6.00881	−	10.4076i	0.513367	−	0.889178i	−0.486512	−	0.873674i	$-0.661731\pi$
$137$	6.00881	−	10.4076i	0.513367	−	0.889178i	0.999880	−	0.0155048i	$-0.00493551\pi$
$138$	−11.6044			−0.987830
$139$	−0.674453	+	1.16819i	−0.0572064	+	0.0990844i	−0.893210	−	0.449639i	$-0.851553\pi$
$139$	−0.674453	+	1.16819i	−0.0572064	+	0.0990844i	0.836004	+	0.548723i	$0.184886\pi$
$140$	1.06193	+	1.83932i	0.0897494	+	0.155451i
$141$	−4.79191	−	8.29984i	−0.403552	−	0.698972i
$142$	22.3510			1.87566
$143$	15.2180	+	4.18240i	1.27259	+	0.349750i
$144$	−4.92498			−0.410415
$145$	−1.75334	−	3.03688i	−0.145607	−	0.252199i
$146$	−0.770016	−	1.33371i	−0.0637269	−	0.110378i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	−2.12386			−0.174580
$149$	1.53751	−	2.66304i	0.125958	−	0.218165i	−0.796149	−	0.605100i	$-0.793133\pi$
$149$	1.53751	−	2.66304i	0.125958	−	0.218165i	0.922107	+	0.386935i	$0.126466\pi$
$150$	2.93526	−	5.08401i	0.239663	−	0.415108i
$151$	16.6610			1.35585			0.677925	−	0.735131i	$-0.262879\pi$
$151$	16.6610			1.35585			0.677925	+	0.735131i	$0.262879\pi$
$152$	−6.05166	+	10.4818i	−0.490854	+	0.850184i
$153$	−1.82555	−	3.16194i	−0.147587	−	0.255628i
$154$	−3.61359	−	6.25891i	−0.291191	−	0.504358i
$155$	−18.9327			−1.52071
$156$	−1.86305	+	1.83932i	−0.149164	+	0.147263i
$157$	12.8294			1.02390			0.511950	−	0.859015i	$-0.328923\pi$
$157$	12.8294			1.02390			0.511950	+	0.859015i	$0.328923\pi$
$158$	13.9869	+	24.2260i	1.11274	+	1.92732i
$159$	−0.151093	−	0.261701i	−0.0119825	−	0.0207543i
$160$	5.74026	−	9.94242i	0.453807	−	0.786017i
$161$	−7.02830			−0.553907
$162$	−0.825547	+	1.42989i	−0.0648611	+	0.112343i
$163$	10.8022	−	18.7099i	0.846093	−	1.46548i	−0.0385764	−	0.999256i	$-0.512282\pi$
$163$	10.8022	−	18.7099i	0.846093	−	1.46548i	0.884669	−	0.466220i	$-0.154384\pi$
$164$	−6.24772			−0.487865
$165$	−6.40162	+	11.0879i	−0.498366	+	0.863195i
$166$	1.04526	+	1.81044i	0.0811278	+	0.140517i
$167$	−10.6599	−	18.4635i	−0.824888	−	1.42875i	−0.902005	−	0.431726i	$-0.857905\pi$
$167$	−10.6599	−	18.4635i	−0.824888	−	1.42875i	0.0771165	−	0.997022i	$-0.475429\pi$
$168$	−2.10331			−0.162274
$169$	0.166703	−	12.9989i	0.0128233	−	0.999918i
$170$	17.6327			1.35236
$171$	2.87720	+	4.98346i	0.220025	+	0.381095i
$172$	2.07889	+	3.60074i	0.158514	+	0.274554i
$173$	−1.56087	+	2.70350i	−0.118671	+	0.205543i	−0.919241	−	0.393695i	$-0.871197\pi$
$173$	−1.56087	+	2.70350i	−0.118671	+	0.205543i	0.800570	+	0.599239i	$0.204530\pi$
$174$	−1.97945			−0.150062
$175$	1.77777	−	3.07918i	0.134386	−	0.232764i
$176$	−10.7788	+	18.6695i	−0.812485	+	1.40726i
$177$	−3.02830			−0.227621
$178$	11.0605	−	19.1573i	0.829017	−	1.43590i
$179$	−9.48545	−	16.4293i	−0.708976	−	1.22798i	−0.965237	−	0.261375i	$-0.915824\pi$
$179$	−9.48545	−	16.4293i	−0.708976	−	1.22798i	0.256261	−	0.966608i	$-0.417509\pi$
$180$	−1.06193	−	1.83932i	−0.0791515	−	0.137094i
$181$	−1.93273			−0.143659			−0.0718295	−	0.997417i	$-0.522884\pi$
$181$	−1.93273			−0.143659			−0.0718295	+	0.997417i	$0.522884\pi$
$182$	−4.23638	+	4.18240i	−0.314022	+	0.310020i
$183$	0.302187			0.0223383
$184$	7.39135	+	12.8022i	0.544898	+	0.943790i
$185$	4.27777	+	7.40931i	0.314508	+	0.544743i
$186$	−5.34357	+	9.25533i	−0.391810	+	0.678634i
$187$	−15.9816			−1.16869
$188$	3.47945	−	6.02659i	0.253765	−	0.439534i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	−27.7905			−2.01613
$191$	1.13695	−	1.96925i	0.0822665	−	0.142490i	−0.821957	−	0.569550i	$-0.807117\pi$
$191$	1.13695	−	1.96925i	0.0822665	−	0.142490i	0.904223	+	0.427060i	$0.140451\pi$
$192$	1.68473	+	2.91803i	0.121585	+	0.210591i
$193$	2.19354	+	3.79932i	0.157894	+	0.273481i	0.934109	−	0.356988i	$-0.116196\pi$
$193$	2.19354	+	3.79932i	0.157894	+	0.273481i	−0.776215	+	0.630468i	$0.782863\pi$
$194$	19.6893			1.41361
$195$	10.1691	+	2.79481i	0.728226	+	0.200141i
$196$	0.726109			0.0518650
$197$	2.62920	+	4.55390i	0.187322	+	0.324452i	0.944357	−	0.328923i	$-0.106686\pi$
$197$	2.62920	+	4.55390i	0.187322	+	0.324452i	−0.757034	+	0.653375i	$0.773352\pi$
$198$	3.61359	+	6.25891i	0.256806	+	0.444802i
$199$	−6.59798	+	11.4280i	−0.467718	+	0.810111i	−0.999320	−	0.0368831i	$-0.988257\pi$
$199$	−6.59798	+	11.4280i	−0.467718	+	0.810111i	0.531601	+	0.846995i	$0.321590\pi$
$200$	−7.47839			−0.528802
$201$	−4.35384	+	7.54108i	−0.307096	+	0.531907i
$202$	−9.10437	+	15.7692i	−0.640581	+	1.10952i
$203$	−1.19887			−0.0841445
$204$	1.32555	−	2.29591i	0.0928068	−	0.160746i
$205$	12.5838	+	21.7958i	0.878893	+	1.52229i
$206$	16.0605	+	27.8175i	1.11899	+	1.93814i
$207$	7.02830			0.488500
$208$	17.1224	+	4.70580i	1.18722	+	0.326289i
$209$	25.1882			1.74230
$210$	−2.41471	−	4.18240i	−0.166631	−	0.288613i
$211$	8.72077	+	15.1048i	0.600363	+	1.03986i	0.992766	+	0.120065i	$0.0383105\pi$
$211$	8.72077	+	15.1048i	0.600363	+	1.03986i	−0.392403	+	0.919793i	$0.628356\pi$
$212$	0.109710	−	0.190024i	0.00753494	−	0.0130509i
$213$	−13.5371			−0.927547
$214$	1.17551	−	2.03605i	0.0803565	−	0.139182i
$215$	8.37439	−	14.5049i	0.571129	−	0.989224i
$216$	2.10331			0.143112
$217$	−3.23638	+	5.60558i	−0.219700	+	0.380531i
$218$	0.0385694	+	0.0668041i	0.00261225	+	0.00452454i
$219$	0.466367	+	0.807771i	0.0315142	+	0.0545841i
$220$	−9.29656			−0.626774
$221$	3.32555	+	12.7372i	0.223700	+	0.856799i
$222$	4.82942			0.324130
$223$	−4.00106	−	6.93004i	−0.267931	−	0.464070i	0.700396	−	0.713754i	$-0.253007\pi$
$223$	−4.00106	−	6.93004i	−0.267931	−	0.464070i	−0.968327	+	0.249684i	$0.919673\pi$
$224$	−1.96249	−	3.39914i	−0.131125	−	0.227114i
$225$	−1.77777	+	3.07918i	−0.118518	+	0.205279i
$226$	−17.0694			−1.13544
$227$	4.02976	−	6.97975i	0.267464	−	0.463262i	−0.700742	−	0.713415i	$-0.747148\pi$
$227$	4.02976	−	6.97975i	0.267464	−	0.463262i	0.968206	+	0.250153i	$0.0804809\pi$
$228$	−2.08916	+	3.61854i	−0.138358	+	0.239644i
$229$	−8.48052			−0.560408			−0.280204	−	0.959940i	$-0.590402\pi$
$229$	−8.48052			−0.560408			−0.280204	+	0.959940i	$0.590402\pi$
$230$	−16.9713	+	29.3952i	−1.11905	+	1.93826i
$231$	2.18860	+	3.79077i	0.143999	+	0.249414i
$232$	1.26080	+	2.18378i	0.0827758	+	0.143372i
$233$	−10.2456			−0.671211			−0.335606	−	0.942003i	$-0.608941\pi$
$233$	−10.2456			−0.671211			−0.335606	+	0.942003i	$0.608941\pi$
$234$	4.23638	−	4.18240i	0.276941	−	0.273412i
$235$	−28.0325			−1.82864
$236$	−1.09944	−	1.90428i	−0.0715673	−	0.123958i
$237$	−8.47130	−	14.6727i	−0.550270	−	0.953096i
$238$	3.01415	−	5.22066i	0.195378	−	0.338405i
$239$	−11.3022			−0.731078			−0.365539	−	0.930796i	$-0.619115\pi$
$239$	−11.3022			−0.731078			−0.365539	+	0.930796i	$0.619115\pi$
$240$	−7.20275	+	12.4755i	−0.464935	+	0.805292i
$241$	−0.518023	+	0.897242i	−0.0333688	+	0.0577965i	−0.882228	−	0.470823i	$-0.843957\pi$
$241$	−0.518023	+	0.897242i	−0.0333688	+	0.0577965i	0.848859	+	0.528620i	$0.177290\pi$
$242$	13.4728			0.866062
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.109710	+	0.190024i	0.00702349	+	0.0121650i
$245$	−1.46249	−	2.53311i	−0.0934352	−	0.161834i
$246$	14.2066			0.905781
$247$	−5.24132	−	20.0749i	−0.333497	−	1.27733i
$248$	13.6142			0.864506
$249$	−0.633070	−	1.09651i	−0.0401192	−	0.0694885i
$250$	3.48797	+	6.04135i	0.220599	+	0.382088i
$251$	−6.64188	+	11.5041i	−0.419232	+	0.726131i	−0.995862	−	0.0908742i	$-0.971034\pi$
$251$	−6.64188	+	11.5041i	−0.419232	+	0.726131i	0.576631	+	0.817005i	$0.304367\pi$
$252$	−0.726109			−0.0457406
$253$	15.3821	−	26.6426i	0.967067	−	1.67501i
$254$	4.51802	−	7.82545i	0.283486	−	0.491012i
$255$	−10.6794			−0.668769
$256$	−7.70381	+	13.3434i	−0.481488	+	0.833962i
$257$	−6.22077	−	10.7747i	−0.388041	−	0.672107i	0.604145	−	0.796875i	$-0.293515\pi$
$257$	−6.22077	−	10.7747i	−0.388041	−	0.672107i	−0.992186	+	0.124768i	$0.960181\pi$
$258$	−4.72717	−	8.18770i	−0.294301	−	0.509744i
$259$	2.92498			0.181750
$260$	1.93449	+	7.40931i	0.119972	+	0.459506i
$261$	1.19887			0.0742085
$262$	−13.3496	−	23.1221i	−0.824739	−	1.42849i
$263$	−3.29579	−	5.70847i	−0.203227	−	0.352000i	0.746339	−	0.665566i	$-0.231810\pi$
$263$	−3.29579	−	5.70847i	−0.203227	−	0.352000i	−0.949566	+	0.313566i	$0.898476\pi$
$264$	4.60331	−	7.97317i	0.283314	−	0.490715i
$265$	−0.883892			−0.0542970
$266$	−4.75053	+	8.22816i	−0.291274	+	0.504501i
$267$	−6.69887	+	11.6028i	−0.409964	+	0.710079i
$268$	−6.32273			−0.386222
$269$	1.35812	−	2.35233i	0.0828059	−	0.143424i	−0.821648	−	0.569995i	$-0.806945\pi$
$269$	1.35812	−	2.35233i	0.0828059	−	0.143424i	0.904454	+	0.426571i	$0.140279\pi$
$270$	2.41471	+	4.18240i	0.146955	+	0.254533i
$271$	15.3627	+	26.6089i	0.933215	+	1.61638i	0.777787	+	0.628528i	$0.216342\pi$
$271$	15.3627	+	26.6089i	0.933215	+	1.61638i	0.155428	+	0.987847i	$0.450324\pi$
$272$	−17.9816			−1.09029
$273$	2.56580	−	2.53311i	0.155290	−	0.153311i
$274$	−19.8422			−1.19871
$275$	7.78164	+	13.4782i	0.469251	+	0.812766i
$276$	2.55166	+	4.41960i	0.153592	+	0.266029i
$277$	10.7827	−	18.6762i	0.647870	−	1.12214i	−0.335761	−	0.941947i	$-0.608993\pi$
$277$	10.7827	−	18.6762i	0.647870	−	1.12214i	0.983631	−	0.180196i	$-0.0576732\pi$
$278$	2.22717			0.133577
$279$	3.23638	−	5.60558i	0.193757	−	0.335597i
$280$	−3.07608	+	5.32792i	−0.183831	+	0.318404i
$281$	33.2058			1.98089			0.990447	−	0.137896i	$-0.0440340\pi$
$281$	33.2058			1.98089			0.990447	+	0.137896i	$0.0440340\pi$
$282$	−7.91190	+	13.7038i	−0.471147	+	0.816050i
$283$	−0.741719	−	1.28470i	−0.0440906	−	0.0763672i	0.843138	−	0.537697i	$-0.180706\pi$
$283$	−0.741719	−	1.28470i	−0.0440906	−	0.0763672i	−0.887229	+	0.461330i	$0.847372\pi$
$284$	−4.91471	−	8.51253i	−0.291634	−	0.505126i
$285$	16.8315			0.997015
$286$	−6.58277	−	25.2128i	−0.389247	−	1.49086i
$287$	8.60437			0.507900
$288$	1.96249	+	3.39914i	0.115641	+	0.200296i
$289$	1.83476	+	3.17789i	0.107927	+	0.186935i
$290$	−2.89494	+	5.01418i	−0.169996	+	0.294442i
$291$	−11.9250			−0.699055
$292$	−0.338633	+	0.586530i	−0.0198170	+	0.0343241i
$293$	−4.41577	+	7.64834i	−0.257972	+	0.446821i	−0.965699	−	0.259666i	$-0.916388\pi$
$293$	−4.41577	+	7.64834i	−0.257972	+	0.446821i	0.707726	+	0.706487i	$0.249721\pi$
$294$	−1.65109			−0.0962937
$295$	−4.42886	+	7.67101i	−0.257858	+	0.446623i
$296$	−3.07608	−	5.32792i	−0.178793	−	0.309679i
$297$	−2.18860	−	3.79077i	−0.126996	−	0.219963i
$298$	−5.07714			−0.294111
$299$	−24.4349	−	6.71551i	−1.41310	−	0.388368i
$300$	−2.58170			−0.149055
$301$	−2.86305	−	4.95896i	−0.165024	−	0.285829i
$302$	−13.7544	−	23.8233i	−0.791477	−	1.37088i
$303$	5.51415	−	9.55078i	0.316780	−	0.548678i
$304$	28.3404			1.62543
$305$	0.441946	−	0.765473i	0.0253057	−	0.0438308i
$306$	−3.01415	+	5.22066i	−0.172307	+	0.298445i
$307$	11.6532			0.665084			0.332542	−	0.943088i	$-0.392094\pi$
$307$	11.6532			0.665084			0.332542	+	0.943088i	$0.392094\pi$
$308$	−1.58916	+	2.75251i	−0.0905510	+	0.156839i
$309$	−9.72717	−	16.8480i	−0.553359	−	0.958447i
$310$	15.6299	+	27.0717i	0.887716	+	1.53757i
$311$	−25.0099			−1.41818			−0.709090	−	0.705118i	$-0.750894\pi$
$311$	−25.0099			−1.41818			−0.709090	+	0.705118i	$0.750894\pi$
$312$	−7.31246	−	2.00971i	−0.413987	−	0.113777i
$313$	−0.186078			−0.0105178			−0.00525889	−	0.999986i	$-0.501674\pi$
$313$	−0.186078			−0.0105178			−0.00525889	+	0.999986i	$0.501674\pi$
$314$	−10.5913	−	18.3446i	−0.597701	−	1.03525i
$315$	1.46249	+	2.53311i	0.0824021	+	0.142725i
$316$	6.15109	−	10.6540i	0.346026	−	0.599335i
$317$	−0.540031			−0.0303312			−0.0151656	−	0.999885i	$-0.504828\pi$
$317$	−0.540031			−0.0303312			−0.0151656	+	0.999885i	$0.504828\pi$
$318$	−0.249469	+	0.432094i	−0.0139895	+	0.0242306i
$319$	2.62386	−	4.54466i	0.146908	−	0.254452i
$320$	9.85560			0.550945
$321$	−0.711961	+	1.23315i	−0.0397378	+	0.0688279i
$322$	5.80219	+	10.0497i	0.323343	+	0.560047i
$323$	10.5049	+	18.1951i	0.584510	+	1.01240i
$324$	0.726109			0.0403394
$325$	9.12280	−	9.00655i	0.506042	−	0.499594i
$326$	−35.6708			−1.97563
$327$	−0.0233599	−	0.0404605i	−0.00129180	−	0.00223747i
$328$	−9.04884	−	15.6731i	−0.499639	−	0.865400i
$329$	−4.79191	+	8.29984i	−0.264187	+	0.457585i
$330$	21.1394			1.16368
$331$	−0.770016	+	1.33371i	−0.0423239	+	0.0733071i	−0.886411	−	0.462898i	$-0.846809\pi$
$331$	−0.770016	+	1.33371i	−0.0423239	+	0.0733071i	0.844087	+	0.536206i	$0.180143\pi$
$332$	0.459678	−	0.796186i	0.0252281	−	0.0436964i
$333$	−2.92498			−0.160288
$334$	−17.6005	+	30.4850i	−0.963056	+	1.66806i
$335$	12.7349	+	22.0575i	0.695783	+	1.20513i
$336$	2.46249	+	4.26516i	0.134340	+	0.232684i
$337$	2.82942			0.154128			0.0770642	−	0.997026i	$-0.475445\pi$
$337$	2.82942			0.154128			0.0770642	+	0.997026i	$0.475445\pi$
$338$	−18.7246	+	10.4929i	−1.01849	+	0.570736i
$339$	10.3382			0.561496
$340$	−3.87720	−	6.71551i	−0.210271	−	0.364200i
$341$	−14.1663	−	24.5368i	−0.767148	−	1.32874i
$342$	4.75053	−	8.22816i	0.256879	−	0.444928i
$343$	−1.00000			−0.0539949
$344$	−6.02190	+	10.4302i	−0.324679	+	0.562361i
$345$	10.2788	−	17.8035i	0.553393	−	0.958506i
$346$	5.15428			0.277096
$347$	12.6950	−	21.9884i	0.681503	−	1.18040i	−0.293019	−	0.956107i	$-0.594660\pi$
$347$	12.6950	−	21.9884i	0.681503	−	1.18040i	0.974522	−	0.224292i	$-0.0720068\pi$
$348$	0.435257	+	0.753887i	0.0233322	+	0.0404126i
$349$	0.542845	+	0.940235i	0.0290578	+	0.0503296i	0.880189	−	0.474624i	$-0.157416\pi$
$349$	0.542845	+	0.940235i	0.0290578	+	0.0503296i	−0.851131	+	0.524954i	$0.824083\pi$
$350$	−5.87051			−0.313792
$351$	−2.56580	+	2.53311i	−0.136953	+	0.135207i
$352$	17.1805			0.915721
$353$	−5.26468	−	9.11869i	−0.280211	−	0.485339i	0.691226	−	0.722639i	$-0.257071\pi$
$353$	−5.26468	−	9.11869i	−0.280211	−	0.485339i	−0.971436	+	0.237300i	$0.923738\pi$
$354$	2.50000	+	4.33013i	0.132874	+	0.230144i
$355$	−19.7979	+	34.2910i	−1.05076	+	1.81998i
$356$	−9.72823			−0.515595
$357$	−1.82555	+	3.16194i	−0.0966182	+	0.167348i
$358$	−15.6614	+	27.1263i	−0.827729	+	1.43367i
$359$	27.2087			1.43602			0.718011	−	0.696031i	$-0.245053\pi$
$359$	27.2087			1.43602			0.718011	+	0.696031i	$0.245053\pi$
$360$	3.07608	−	5.32792i	0.162124	−	0.280806i
$361$	−7.05659	−	12.2224i	−0.371400	−	0.643283i
$362$	1.59556	+	2.76359i	0.0838609	+	0.145251i
$363$	−8.15990			−0.428284
$364$	2.52442	+	0.693795i	0.132316	+	0.0363647i
$365$	2.72823			0.142802
$366$	−0.249469	−	0.432094i	−0.0130400	−	0.0225859i
$367$	3.12920	+	5.41993i	0.163343	+	0.282918i	0.936065	−	0.351826i	$-0.114439\pi$
$367$	3.12920	+	5.41993i	0.163343	+	0.282918i	−0.772723	+	0.634744i	$0.781106\pi$
$368$	17.3071	−	29.9768i	0.902196	−	1.56265i
$369$	−8.60437			−0.447926
$370$	7.06299	−	12.2335i	0.367187	−	0.635987i
$371$	−0.151093	+	0.261701i	−0.00784438	+	0.0135869i
$372$	4.69994			0.243680
$373$	0.589164	−	1.02046i	0.0305058	−	0.0528375i	−0.850369	−	0.526186i	$-0.823622\pi$
$373$	0.589164	−	1.02046i	0.0305058	−	0.0528375i	0.880875	+	0.473349i	$0.156955\pi$
$374$	13.1935	+	22.8519i	0.682222	+	1.18164i
$375$	−2.11252	−	3.65900i	−0.109090	−	0.188950i
$376$	20.1578			1.03956
$377$	−4.16806	−	1.14552i	−0.214666	−	0.0589973i
$378$	1.65109			0.0849231
$379$	12.1033	+	20.9636i	0.621705	+	1.07683i	0.989168	+	0.146787i	$0.0468932\pi$
$379$	12.1033	+	20.9636i	0.621705	+	1.07683i	−0.367463	+	0.930038i	$0.619773\pi$
$380$	6.11077	+	10.5842i	0.313476	+	0.542956i
$381$	−2.73638	+	4.73955i	−0.140189	+	0.242815i
$382$	−3.75441			−0.192092
$383$	1.24559	−	2.15743i	0.0636469	−	0.110240i	−0.832446	−	0.554106i	$-0.813060\pi$
$383$	1.24559	−	2.15743i	0.0636469	−	0.110240i	0.896093	+	0.443866i	$0.146394\pi$
$384$	6.70662	−	11.6162i	0.342246	−	0.592787i
$385$	12.8032			0.652514
$386$	3.62174	−	6.27303i	0.184341	−	0.319289i
$387$	2.86305	+	4.95896i	0.145537	+	0.252078i
$388$	−4.32942	−	7.49878i	−0.219793	−	0.380693i
$389$	23.6065			1.19690			0.598448	−	0.801161i	$-0.295784\pi$
$389$	23.6065			1.19690			0.598448	+	0.801161i	$0.295784\pi$
$390$	−4.39881	−	16.8480i	−0.222742	−	0.853129i
$391$	25.6610			1.29773
$392$	1.05166	+	1.82152i	0.0531167	+	0.0920007i
$393$	8.08529	+	14.0041i	0.407849	+	0.706415i
$394$	4.34105	−	7.51891i	0.218699	−	0.378797i
$395$	−49.5569			−2.49348
$396$	1.58916	−	2.75251i	0.0798585	−	0.138319i
$397$	4.42352	−	7.66177i	0.222010	−	0.384533i	−0.733408	−	0.679789i	$-0.762071\pi$
$397$	4.42352	−	7.66177i	0.222010	−	0.384533i	0.955418	+	0.295256i	$0.0954048\pi$
$398$	21.7877			1.09212
$399$	2.87720	−	4.98346i	0.144040	−	0.249485i
$400$	8.75547	+	15.1649i	0.437773	+	0.758246i
$401$	9.45716	+	16.3803i	0.472268	+	0.817992i	0.999496	−	0.0317317i	$-0.0101022\pi$
$401$	9.45716	+	16.3803i	0.472268	+	0.817992i	−0.527229	+	0.849723i	$0.676769\pi$
$402$	14.3772			0.717070
$403$	−16.6078	+	16.3962i	−0.827296	+	0.816754i
$404$	8.00775			0.398400
$405$	−1.46249	−	2.53311i	−0.0726718	−	0.125871i
$406$	0.989727	+	1.71426i	0.0491193	+	0.0850772i
$407$	−6.40162	+	11.0879i	−0.317317	+	0.549609i
$408$	7.67939			0.380186
$409$	−1.74947	+	3.03017i	−0.0865057	+	0.149832i	−0.906032	−	0.423210i	$-0.860903\pi$
$409$	−1.74947	+	3.03017i	−0.0865057	+	0.149832i	0.819526	+	0.573042i	$0.194237\pi$
$410$	20.7771	−	35.9869i	1.02611	−	1.77727i
$411$	12.0176			0.592786
$412$	7.06299	−	12.2335i	0.347969	−	0.602699i
$413$	1.51415	+	2.62258i	0.0745064	+	0.129049i
$414$	−5.80219	−	10.0497i	−0.285162	−	0.493915i
$415$	−3.70344			−0.181795
$416$	−3.57502	−	13.6927i	−0.175280	−	0.671341i
$417$	−1.34891			−0.0660562
$418$	−20.7940	−	36.0163i	−1.01707	−	1.76162i
$419$	−14.4158	−	24.9688i	−0.704257	−	1.21981i	−0.966959	−	0.254931i	$-0.917947\pi$
$419$	−14.4158	−	24.9688i	−0.704257	−	1.21981i	0.262703	−	0.964877i	$-0.415386\pi$
$420$	−1.06193	+	1.83932i	−0.0518168	+	0.0897494i
$421$	34.3227			1.67279			0.836394	−	0.548129i	$-0.184660\pi$
$421$	34.3227			1.67279			0.836394	+	0.548129i	$0.184660\pi$
$422$	14.3988	−	24.9395i	0.700923	−	1.21403i
$423$	4.79191	−	8.29984i	0.232991	−	0.403552i
$424$	0.635593			0.0308671
$425$	−6.49079	+	11.2424i	−0.314849	+	0.545335i
$426$	11.1755	+	19.3566i	0.541455	+	0.937828i
$427$	−0.151093	−	0.261701i	−0.00731192	−	0.0126646i
$428$	−1.03392			−0.0499766
$429$	3.98691	+	15.2703i	0.192490	+	0.737259i
$430$	−27.6538			−1.33358
$431$	−14.6779	−	25.4229i	−0.707011	−	1.22458i	−0.965961	−	0.258688i	$-0.916710\pi$
$431$	−14.6779	−	25.4229i	−0.707011	−	1.22458i	0.258950	−	0.965891i	$-0.416624\pi$
$432$	−2.46249	−	4.26516i	−0.118477	−	0.205208i
$433$	−14.3032	+	24.7740i	−0.687370	+	1.19056i	0.285315	+	0.958434i	$0.407902\pi$
$433$	−14.3032	+	24.7740i	−0.687370	+	1.19056i	−0.972686	+	0.232126i	$0.925432\pi$
$434$	10.6871			0.512999
$435$	1.75334	−	3.03688i	0.0840664	−	0.145607i
$436$	0.0169618	−	0.0293788i	0.000812325	−	0.00140699i
$437$	−40.4437			−1.93468
$438$	0.770016	−	1.33371i	0.0367928	−	0.0637269i
$439$	−17.2399	−	29.8603i	−0.822813	−	1.42515i	−0.903579	−	0.428422i	$-0.859070\pi$
$439$	−17.2399	−	29.8603i	−0.822813	−	1.42515i	0.0807654	−	0.996733i	$-0.474264\pi$
$440$	−13.4646	−	23.3214i	−0.641900	−	1.11180i
$441$	1.00000			0.0476190
$442$	15.4674	−	15.2703i	0.735711	−	0.726336i
$443$	−12.9066			−0.613209			−0.306605	−	0.951837i	$-0.599193\pi$
$443$	−12.9066			−0.613209			−0.306605	+	0.951837i	$0.599193\pi$
$444$	−1.06193	−	1.83932i	−0.0503969	−	0.0872900i
$445$	19.5941	+	33.9380i	0.928849	+	1.60881i
$446$	−6.60613	+	11.4421i	−0.312809	+	0.541801i
$447$	3.07502			0.145443
$448$	1.68473	−	2.91803i	0.0795958	−	0.137864i
$449$	2.81915	−	4.88291i	0.133044	−	0.230439i	−0.791805	−	0.610774i	$-0.790858\pi$
$449$	2.81915	−	4.88291i	0.133044	−	0.230439i	0.924848	+	0.380336i	$0.124192\pi$
$450$	5.87051			0.276739
$451$	−18.8315	+	32.6172i	−0.886743	+	1.53588i
$452$	3.75334	+	6.50098i	0.176542	+	0.305781i
$453$	8.33048	+	14.4288i	0.391400	+	0.677925i
$454$	−13.3070			−0.624529
$455$	−2.66418	−	10.2041i	−0.124899	−	0.478376i
$456$	−12.1033			−0.566790
$457$	−18.9947	−	32.8997i	−0.888533	−	1.53898i	−0.841610	−	0.540086i	$-0.818392\pi$
$457$	−18.9947	−	32.8997i	−0.888533	−	1.53898i	−0.0469228	−	0.998899i	$-0.514941\pi$
$458$	7.00106	+	12.1262i	0.327138	+	0.566620i
$459$	1.82555	−	3.16194i	0.0852092	−	0.147587i
$460$	14.9271			0.695980
$461$	3.30365	−	5.72209i	0.153866	−	0.266504i	−0.778779	−	0.627298i	$-0.784161\pi$
$461$	3.30365	−	5.72209i	0.153866	−	0.266504i	0.932646	+	0.360794i	$0.117494\pi$
$462$	3.61359	−	6.25891i	0.168119	−	0.291191i
$463$	9.98933			0.464243			0.232122	−	0.972687i	$-0.425433\pi$
$463$	9.98933			0.464243			0.232122	+	0.972687i	$0.425433\pi$
$464$	2.95222	−	5.11339i	0.137053	−	0.237383i
$465$	−9.46637	−	16.3962i	−0.438992	−	0.760357i
$466$	8.45822	+	14.6501i	0.391819	+	0.678651i
$467$	3.42100			0.158305			0.0791525	−	0.996863i	$-0.474779\pi$
$467$	3.42100			0.158305			0.0791525	+	0.996863i	$0.474779\pi$
$468$	−2.52442	−	0.693795i	−0.116691	−	0.0320707i
$469$	8.70769			0.402084
$470$	23.1422	+	40.0834i	1.06747	+	1.84891i
$471$	6.41471	+	11.1106i	0.295574	+	0.511950i
$472$	3.18473	−	5.51611i	0.146589	−	0.253899i
$473$	25.0643			1.15246
$474$	−13.9869	+	24.2260i	−0.642440	+	1.11274i
$475$	10.2300	−	17.7189i	0.469384	−	0.812997i
$476$	−2.65109			−0.121513
$477$	0.151093	−	0.261701i	0.00691809	−	0.0119825i
$478$	9.33048	+	16.1609i	0.426766	+	0.739181i
$479$	−9.92071	−	17.1832i	−0.453289	−	0.785119i	0.545299	−	0.838241i	$-0.316416\pi$
$479$	−9.92071	−	17.1832i	−0.453289	−	0.785119i	−0.998588	+	0.0531223i	$0.983083\pi$
$480$	11.4805			0.524011
$481$	10.1691	+	2.79481i	0.463672	+	0.127432i
$482$	1.71061			0.0779161
$483$	−3.51415	−	6.08668i	−0.159899	−	0.276954i
$484$	−2.96249	−	5.13119i	−0.134659	−	0.233236i
$485$	−17.4402	+	30.2073i	−0.791918	+	1.37164i
$486$	−1.65109			−0.0748951
$487$	3.05166	−	5.28562i	0.138284	−	0.239514i	−0.788563	−	0.614954i	$-0.789175\pi$
$487$	3.05166	−	5.28562i	0.138284	−	0.239514i	0.926847	+	0.375439i	$0.122508\pi$
$488$	−0.317797	+	0.550440i	−0.0143860	+	0.0249172i
$489$	21.6044			0.976984
$490$	−2.41471	+	4.18240i	−0.109086	+	0.188942i
$491$	1.18326	+	2.04947i	0.0534000	+	0.0924915i	0.891490	−	0.453041i	$-0.149661\pi$
$491$	1.18326	+	2.04947i	0.0534000	+	0.0924915i	−0.838090	+	0.545532i	$0.816328\pi$
$492$	−3.12386	−	5.41068i	−0.140834	−	0.243932i
$493$	4.37720			0.197139
$494$	−24.3779	+	24.0672i	−1.09681	+	1.08284i
$495$	−12.8032			−0.575463
$496$	−15.9391	−	27.6074i	−0.715688	−	1.23961i
$497$	6.76855	+	11.7235i	0.303611	+	0.525870i
$498$	−1.04526	+	1.81044i	−0.0468391	+	0.0811278i
$499$	−4.29231			−0.192150			−0.0960752	−	0.995374i	$-0.530629\pi$
$499$	−4.29231			−0.192150			−0.0960752	+	0.995374i	$0.530629\pi$
$500$	1.53392	−	2.65683i	0.0685992	−	0.118817i
$501$	10.6599	−	18.4635i	0.476249	−	0.824888i
$502$	21.9327			0.978906
$503$	1.05553	−	1.82823i	0.0470638	−	0.0815169i	−0.841534	−	0.540204i	$-0.818347\pi$
$503$	1.05553	−	1.82823i	0.0470638	−	0.0815169i	0.888598	+	0.458687i	$0.151680\pi$
$504$	−1.05166	−	1.82152i	−0.0468445	−	0.0811370i
$505$	−16.1288	−	27.9359i	−0.717722	−	1.24313i
$506$	−50.7947			−2.25810
$507$	11.3408	−	6.35510i	0.503661	−	0.282240i
$508$	−3.97383			−0.176310
$509$	12.1882	+	21.1106i	0.540233	+	0.935710i	0.998890	+	0.0470972i	$0.0149970\pi$
$509$	12.1882	+	21.1106i	0.540233	+	0.935710i	−0.458658	+	0.888613i	$0.651670\pi$
$510$	8.81633	+	15.2703i	0.390394	+	0.676182i
$511$	0.466367	−	0.807771i	0.0206309	−	0.0357337i
$512$	−1.38708			−0.0613007
$513$	−2.87720	+	4.98346i	−0.127032	+	0.220025i
$514$	−10.2711	+	17.7900i	−0.453038	+	0.784684i
$515$	−56.9036			−2.50747
$516$	−2.07889	+	3.60074i	−0.0915181	+	0.158514i
$517$	−20.9752	−	36.3301i	−0.922487	−	1.59779i
$518$	−2.41471	−	4.18240i	−0.106096	−	0.183764i
$519$	−3.12174			−0.137029
$520$	−15.7852	+	15.5841i	−0.692228	+	0.683407i
$521$	−17.8401			−0.781589			−0.390794	−	0.920478i	$-0.627800\pi$
$521$	−17.8401			−0.781589			−0.390794	+	0.920478i	$0.627800\pi$
$522$	−0.989727	−	1.71426i	−0.0433192	−	0.0750310i
$523$	15.5279	+	26.8951i	0.678987	+	1.17604i	0.975286	+	0.220945i	$0.0709143\pi$
$523$	15.5279	+	26.8951i	0.678987	+	1.17604i	−0.296299	+	0.955095i	$0.595752\pi$
$524$	−5.87080	+	10.1685i	−0.256467	+	0.444214i
$525$	3.55553			0.155176
$526$	−5.44166	+	9.42522i	−0.237267	+	0.410959i
$527$	11.8163	−	20.4665i	0.514728	−	0.891534i
$528$	−21.5577			−0.938176
$529$	−13.1985	+	22.8604i	−0.573847	+	0.993932i
$530$	0.729694	+	1.26387i	0.0316959	+	0.0548989i
$531$	−1.51415	−	2.62258i	−0.0657084	−	0.113810i
$532$	4.17833			0.181154
$533$	29.9143	+	8.22145i	1.29573	+	0.356110i
$534$	22.1209			0.957266
$535$	2.08248	+	3.60695i	0.0900333	+	0.155942i
$536$	−9.15749	−	15.8612i	−0.395543	−	0.685101i
$537$	9.48545	−	16.4293i	0.409327	−	0.708976i
$538$	−4.48476			−0.193352
$539$	2.18860	−	3.79077i	0.0942697	−	0.163280i
$540$	1.06193	−	1.83932i	0.0456982	−	0.0791515i
$541$	−33.3900			−1.43555			−0.717774	−	0.696276i	$-0.754839\pi$
$541$	−33.3900			−1.43555			−0.717774	+	0.696276i	$0.754839\pi$
$542$	25.3652	−	43.9338i	1.08953	−	1.88712i
$543$	−0.966367	−	1.67380i	−0.0414708	−	0.0718295i
$544$	7.16524	+	12.4106i	0.307207	+	0.532098i
$545$	−0.136655			−0.00585364
$546$	−5.74026	−	1.57761i	−0.245660	−	0.0675156i
$547$	9.12306			0.390074			0.195037	−	0.980796i	$-0.437517\pi$
$547$	9.12306			0.390074			0.195037	+	0.980796i	$0.437517\pi$
$548$	4.36305	+	7.55703i	0.186380	+	0.322820i
$549$	0.151093	+	0.261701i	0.00644851	+	0.0111691i
$550$	12.8482	−	22.2538i	0.547850	−	0.948904i
$551$	−6.89881			−0.293899
$552$	−7.39135	+	12.8022i	−0.314597	+	0.544898i
$553$	−8.47130	+	14.6727i	−0.360236	+	0.623948i
$554$	−35.6065			−1.51278
$555$	−4.27777	+	7.40931i	−0.181581	+	0.314508i
$556$	−0.489727	−	0.848232i	−0.0207690	−	0.0359730i
$557$	19.0148	+	32.9346i	0.805683	+	1.39548i	0.915829	+	0.401569i	$0.131535\pi$
$557$	19.0148	+	32.9346i	0.805683	+	1.39548i	−0.110145	+	0.993915i	$0.535132\pi$
$558$	−10.6871			−0.452423
$559$	−5.21555	−	19.9761i	−0.220594	−	0.844901i
$560$	14.4055			0.608743
$561$	−7.99079	−	13.8405i	−0.337371	−	0.584344i
$562$	−27.4130	−	47.4806i	−1.15635	−	2.00285i
$563$	1.68326	−	2.91550i	0.0709411	−	0.122874i	−0.828373	−	0.560177i	$-0.810733\pi$
$563$	1.68326	−	2.91550i	0.0709411	−	0.122874i	0.899314	+	0.437303i	$0.144066\pi$
$564$	6.95891			0.293023
$565$	15.1196	−	26.1879i	0.636086	−	1.10173i
$566$	−1.22465	+	2.12115i	−0.0514758	+	0.0891587i
$567$	−1.00000			−0.0419961
$568$	14.2364	−	24.6581i	0.597345	−	1.03463i
$569$	8.96637	+	15.5302i	0.375890	+	0.651060i	0.990460	−	0.137802i	$-0.0440038\pi$
$569$	8.96637	+	15.5302i	0.375890	+	0.651060i	−0.614570	+	0.788862i	$0.710671\pi$
$570$	−13.8952	−	24.0672i	−0.582007	−	1.00807i
$571$	39.4274			1.64998			0.824992	−	0.565144i	$-0.191180\pi$
$571$	39.4274			1.64998			0.824992	+	0.565144i	$0.191180\pi$
$572$	−8.15497	+	8.05106i	−0.340976	+	0.336632i
$573$	2.27389			0.0949931
$574$	−7.10331	−	12.3033i	−0.296487	−	0.513530i
$575$	−12.4947	−	21.6414i	−0.521063	−	0.902508i
$576$	−1.68473	+	2.91803i	−0.0701969	+	0.121585i
$577$	16.4239			0.683737			0.341868	−	0.939748i	$-0.388940\pi$
$577$	16.4239			0.683737			0.341868	+	0.939748i	$0.388940\pi$
$578$	3.02936	−	5.24700i	0.126005	−	0.218246i
$579$	−2.19354	+	3.79932i	−0.0911603	+	0.157894i
$580$	2.54624			0.105727
$581$	−0.633070	+	1.09651i	−0.0262642	+	0.0454909i
$582$	9.84463	+	17.0514i	0.408073	+	0.706803i
$583$	−0.661367	−	1.14552i	−0.0273910	−	0.0474426i
$584$	−1.96183			−0.0811811
$585$	2.66418	+	10.2041i	0.110150	+	0.421888i
$586$	14.5817			0.602365
$587$	7.46355	+	12.9273i	0.308054	+	0.533565i	0.977937	−	0.208902i	$-0.0669890\pi$
$587$	7.46355	+	12.9273i	0.308054	+	0.533565i	−0.669883	+	0.742467i	$0.733656\pi$
$588$	0.363055	+	0.628829i	0.0149721	+	0.0259325i
$589$	−18.6235	+	32.2568i	−0.767366	+	1.32912i
$590$	14.6249			0.602098
$591$	−2.62920	+	4.55390i	−0.108151	+	0.187322i
$592$	−7.20275	+	12.4755i	−0.296031	+	0.512741i
$593$	29.9164			1.22852			0.614260	−	0.789103i	$-0.289454\pi$
$593$	29.9164			1.22852			0.614260	+	0.789103i	$0.289454\pi$
$594$	−3.61359	+	6.25891i	−0.148267	+	0.256806i
$595$	5.33969	+	9.24862i	0.218906	+	0.379157i
$596$	1.11640	+	1.93366i	0.0457295	+	0.0792058i
$597$	−13.1960			−0.540074
$598$	10.5697	+	40.4831i	0.432226	+	1.65548i
$599$	35.1911			1.43787			0.718935	−	0.695077i	$-0.244630\pi$
$599$	35.1911			1.43787			0.718935	+	0.695077i	$0.244630\pi$
$600$	−3.73920	−	6.47648i	−0.152652	−	0.264401i
$601$	−8.56580	−	14.8364i	−0.349406	−	0.605190i	0.636738	−	0.771080i	$-0.280283\pi$
$601$	−8.56580	−	14.8364i	−0.349406	−	0.605190i	−0.986144	+	0.165891i	$0.946950\pi$
$602$	−4.72717	+	8.18770i	−0.192665	+	0.333706i
$603$	−8.70769			−0.354604
$604$	−6.04884	+	10.4769i	−0.246124	+	0.426299i
$605$	−11.9338	+	20.6699i	−0.485178	+	0.840353i
$606$	−18.2087			−0.739680
$607$	−11.2233	+	19.4393i	−0.455540	+	0.789018i	−0.998719	−	0.0505990i	$-0.983887\pi$
$607$	−11.2233	+	19.4393i	−0.455540	+	0.789018i	0.543180	+	0.839617i	$0.317220\pi$
$608$	−11.2930	−	19.5600i	−0.457991	−	0.793263i
$609$	−0.599437	−	1.03826i	−0.0242904	−	0.0420722i
$610$	−1.45939			−0.0590889
$611$	−24.5902	+	24.2769i	−0.994814	+	0.982138i
$612$	2.65109			0.107164
$613$	10.1029	+	17.4988i	0.408053	+	0.706768i	0.994672	−	0.103095i	$-0.0328746\pi$
$613$	10.1029	+	17.4988i	0.408053	+	0.706768i	−0.586619	+	0.809863i	$0.699541\pi$
$614$	−9.62027	−	16.6628i	−0.388243	−	0.672456i
$615$	−12.5838	+	21.7958i	−0.507429	+	0.878893i
$616$	−9.20662			−0.370945
$617$	−19.3408	+	33.4992i	−0.778630	+	1.34863i	0.154102	+	0.988055i	$0.450751\pi$
$617$	−19.3408	+	33.4992i	−0.778630	+	1.34863i	−0.932732	+	0.360571i	$0.882582\pi$
$618$	−16.0605	+	27.8175i	−0.646047	+	1.11899i
$619$	32.5109			1.30672			0.653362	−	0.757045i	$-0.273358\pi$
$619$	32.5109			1.30672			0.653362	+	0.757045i	$0.273358\pi$
$620$	6.87362	−	11.9055i	0.276051	−	0.478135i
$621$	3.51415	+	6.08668i	0.141018	+	0.244250i
$622$	20.6468	+	35.7613i	0.827862	+	1.43390i
$623$	13.3977			0.536769
$624$	4.48585	+	17.1813i	0.179578	+	0.687804i
$625$	−30.1359			−1.20543
$626$	0.153616	+	0.266071i	0.00613975	+	0.0106344i
$627$	12.5941	+	21.8136i	0.502960	+	0.871152i
$628$	−4.65778	+	8.06752i	−0.185866	+	0.321929i
$629$	−10.6794			−0.425815
$630$	2.41471	−	4.18240i	0.0962044	−	0.166631i
$631$	18.9310	−	32.7894i	0.753630	−	1.30533i	−0.192422	−	0.981312i	$-0.561634\pi$
$631$	18.9310	−	32.7894i	0.753630	−	1.30533i	0.946052	−	0.324014i	$-0.105032\pi$
$632$	35.6356			1.41751
$633$	−8.72077	+	15.1048i	−0.346620	+	0.600363i
$634$	0.445821	+	0.772184i	0.0177058	+	0.0306674i
$635$	8.00388	+	13.8631i	0.317624	+	0.550141i
$636$	0.219421			0.00870060
$637$	−3.47664	−	0.955496i	−0.137749	−	0.0378581i
$638$	−8.66447			−0.343030
$639$	−6.76855	−	11.7235i	−0.267760	−	0.463774i
$640$	−19.6168	−	33.9772i	−0.775421	−	1.34307i
$641$	−11.4314	+	19.7997i	−0.451512	+	0.782042i	−0.998480	−	0.0551112i	$-0.982449\pi$
$641$	−11.4314	+	19.7997i	−0.451512	+	0.782042i	0.546968	+	0.837154i	$0.315782\pi$
$642$	2.35103			0.0927877
$643$	−21.7915	+	37.7440i	−0.859373	+	1.48848i	0.0131542	+	0.999913i	$0.495813\pi$
$643$	−21.7915	+	37.7440i	−0.859373	+	1.48848i	−0.872528	+	0.488565i	$0.837521\pi$
$644$	2.55166	−	4.41960i	0.100549	−	0.174157i
$645$	16.7488			0.659483
$646$	17.3446	−	30.0418i	0.682415	−	1.18198i
$647$	1.50388	+	2.60479i	0.0591234	+	0.102405i	0.894072	−	0.447923i	$-0.147836\pi$
$647$	1.50388	+	2.60479i	0.0591234	+	0.102405i	−0.834949	+	0.550328i	$0.814503\pi$
$648$	1.05166	+	1.82152i	0.0413130	+	0.0715561i
$649$	−13.2555			−0.520323
$650$	−20.4097	−	5.60926i	−0.800533	−	0.220013i
$651$	−6.47277			−0.253688
$652$	7.84357	+	13.5855i	0.307178	+	0.532048i
$653$	16.9621	+	29.3792i	0.663778	+	1.14970i	0.979615	+	0.200884i	$0.0643813\pi$
$653$	16.9621	+	29.3792i	0.663778	+	1.14970i	−0.315837	+	0.948813i	$0.602285\pi$
$654$	−0.0385694	+	0.0668041i	−0.00150818	+	0.00261225i
$655$	47.2987			1.84811
$656$	−21.1882	+	36.6990i	−0.827260	+	1.43286i
$657$	−0.466367	+	0.807771i	−0.0181947	+	0.0315142i
$658$	15.8238			0.616876
$659$	21.7297	−	37.6369i	0.846469	−	1.46613i	−0.0378709	−	0.999283i	$-0.512058\pi$
$659$	21.7297	−	37.6369i	0.846469	−	1.46613i	0.884340	−	0.466844i	$-0.154609\pi$
$660$	−4.64828	−	8.05106i	−0.180934	−	0.313387i
$661$	−19.1429	−	33.1565i	−0.744574	−	1.28964i	−0.950393	−	0.311050i	$-0.899319\pi$
$661$	−19.1429	−	33.1565i	−0.744574	−	1.28964i	0.205819	−	0.978590i	$-0.434014\pi$
$662$	2.54274			0.0988262
$663$	−9.36799	+	9.24862i	−0.363823	+	0.359187i
$664$	2.66309			0.103348
$665$	−8.41577	−	14.5765i	−0.326350	−	0.565254i
$666$	2.41471	+	4.18240i	0.0935681	+	0.162065i
$667$	−4.21302	+	7.29717i	−0.163129	+	0.282548i
$668$	15.4805			0.598959
$669$	4.00106	−	6.93004i	0.154690	−	0.267931i
$670$	21.0265	−	36.4190i	0.812326	−	1.40699i
$671$	1.32273			0.0510635
$672$	1.96249	−	3.39914i	0.0757048	−	0.131125i
$673$	−14.0902	−	24.4050i	−0.543138	−	0.940743i	−0.998722	−	0.0505499i	$-0.983903\pi$
$673$	−14.0902	−	24.4050i	−0.543138	−	0.940743i	0.455583	−	0.890193i	$-0.349431\pi$
$674$	−2.33582	−	4.04576i	−0.0899724	−	0.155837i
$675$	−3.55553			−0.136852
$676$	8.11359	+	4.82415i	0.312061	+	0.185544i
$677$	−31.7253			−1.21930			−0.609651	−	0.792670i	$-0.708691\pi$
$677$	−31.7253			−1.21930			−0.609651	+	0.792670i	$0.708691\pi$
$678$	−8.53469	−	14.7825i	−0.327773	−	0.567719i
$679$	5.96249	+	10.3273i	0.228819	+	0.396327i
$680$	11.2310	−	19.4527i	0.430691	−	0.745979i
$681$	8.05952			0.308841
$682$	−23.3899	+	40.5125i	−0.895645	+	1.55130i
$683$	−4.28698	+	7.42526i	−0.164037	+	0.284120i	−0.936313	−	0.351167i	$-0.885785\pi$
$683$	−4.28698	+	7.42526i	−0.164037	+	0.284120i	0.772276	+	0.635287i	$0.219118\pi$
$684$	−4.17833			−0.159762
$685$	17.5757	−	30.4420i	0.671532	−	1.16313i
$686$	0.825547	+	1.42989i	0.0315195	+	0.0545934i
$687$	−4.24026	−	7.34434i	−0.161776	−	0.280204i
$688$	28.2010			1.07515
$689$	−0.775352	+	0.765473i	−0.0295386	+	0.0291622i
$690$	−33.9426			−1.29217
$691$	3.47518	+	6.01919i	0.132202	+	0.228981i	0.924525	−	0.381121i	$-0.124462\pi$
$691$	3.47518	+	6.01919i	0.132202	+	0.228981i	−0.792323	+	0.610102i	$0.791129\pi$
$692$	−1.13336	−	1.96304i	−0.0430839	−	0.0746235i
$693$	−2.18860	+	3.79077i	−0.0831381	+	0.143999i
$694$	−41.9213			−1.59131
$695$	−1.97277	+	3.41693i	−0.0748312	+	0.129612i
$696$	−1.26080	+	2.18378i	−0.0477906	+	0.0827758i
$697$	−31.4154			−1.18994
$698$	0.896287	−	1.55242i	0.0339250	−	0.0587598i
$699$	−5.12280	−	8.87294i	−0.193762	−	0.335606i
$700$	1.29085	+	2.23582i	0.0487896	+	0.0845061i
$701$	−21.8443			−0.825049			−0.412525	−	0.910946i	$-0.635353\pi$
$701$	−21.8443			−0.825049			−0.412525	+	0.910946i	$0.635353\pi$
$702$	5.74026	+	1.57761i	0.216652	+	0.0595432i
$703$	16.8315			0.634814
$704$	7.37439	+	12.7728i	0.277933	+	0.481394i
$705$	−14.0163	−	24.2769i	−0.527883	−	0.914321i
$706$	−8.69248	+	15.0558i	−0.327146	+	0.566633i
$707$	−11.0283			−0.414762
$708$	1.09944	−	1.90428i	0.0413194	−	0.0715673i
$709$	−4.87187	+	8.43832i	−0.182967	+	0.316908i	−0.942890	−	0.333106i	$-0.891903\pi$
$709$	−4.87187	+	8.43832i	−0.182967	+	0.316908i	0.759923	+	0.650013i	$0.225237\pi$
$710$	65.3764			2.45353
$711$	8.47130	−	14.6727i	0.317699	−	0.550270i
$712$	−14.0898	−	24.4043i	−0.528039	−	0.914590i
$713$	22.7463	+	39.3977i	0.851854	+	1.47545i
$714$	6.02830			0.225603
$715$	44.5123	+	12.2335i	1.66467	+	0.457505i
$716$	13.7750			0.514794
$717$	−5.65109	−	9.78798i	−0.211044	−	0.365539i
$718$	−22.4621	−	38.9055i	−0.838278	−	1.45194i
$719$	2.52296	−	4.36989i	0.0940905	−	0.162970i	−0.815138	−	0.579267i	$-0.803339\pi$
$719$	2.52296	−	4.36989i	0.0940905	−	0.162970i	0.909229	+	0.416297i	$0.136672\pi$
$720$	−14.4055			−0.536861
$721$	−9.72717	+	16.8480i	−0.362259	+	0.627451i
$722$	−11.6511	+	20.1803i	−0.433609	+	0.751032i
$723$	−1.03605			−0.0385310
$724$	0.701688	−	1.21536i	0.0260780	−	0.0451685i
$725$	−2.13132	−	3.69155i	−0.0791552	−	0.137101i
$726$	6.73638	+	11.6678i	0.250011	+	0.433031i
$727$	6.66659			0.247250			0.123625	−	0.992329i	$-0.460548\pi$
$727$	6.66659			0.247250			0.123625	+	0.992329i	$0.460548\pi$
$728$	1.91577	+	7.33763i	0.0710032	+	0.271951i
$729$	1.00000			0.0370370
$730$	−2.25228	−	3.90107i	−0.0833607	−	0.144385i
$731$	10.4533	+	18.1056i	0.386629	+	0.669660i
$732$	−0.109710	+	0.190024i	−0.00405501	+	0.00702349i
$733$	47.4076			1.75104			0.875520	−	0.483181i	$-0.160519\pi$
$733$	47.4076			1.75104			0.875520	+	0.483181i	$0.160519\pi$
$734$	5.16659	−	8.94880i	0.190702	−	0.330306i
$735$	1.46249	−	2.53311i	0.0539448	−	0.0934352i
$736$	−27.5860			−1.01683
$737$	−19.0577	+	33.0088i	−0.701998	+	1.21590i
$738$	7.10331	+	12.3033i	0.261477	+	0.452891i
$739$	−3.09023	−	5.35243i	−0.113676	−	0.196892i	0.803574	−	0.595205i	$-0.202929\pi$
$739$	−3.09023	−	5.35243i	−0.113676	−	0.196892i	−0.917250	+	0.398313i	$0.869596\pi$
$740$	−6.21225			−0.228367
$741$	14.7647	−	14.5765i	0.542394	−	0.535483i
$742$	0.498939			0.0183166
$743$	11.6667	+	20.2073i	0.428010	+	0.741335i	0.996696	−	0.0812197i	$-0.0258815\pi$
$743$	11.6667	+	20.2073i	0.428010	+	0.741335i	−0.568686	+	0.822554i	$0.692548\pi$
$744$	6.80712	+	11.7903i	0.249561	+	0.432253i
$745$	4.49719	−	7.78936i	0.164764	−	0.285380i
$746$	−1.94553			−0.0712309
$747$	0.633070	−	1.09651i	0.0231628	−	0.0401192i
$748$	5.80219	−	10.0497i	0.212149	−	0.367453i
$749$	1.42392			0.0520290
$750$	−3.48797	+	6.04135i	−0.127363	+	0.220599i
$751$	0.488375	+	0.845890i	0.0178211	+	0.0308670i	0.874798	−	0.484487i	$-0.160994\pi$
$751$	0.488375	+	0.845890i	0.0178211	+	0.0308670i	−0.856977	+	0.515354i	$0.827660\pi$
$752$	−23.6001	−	40.8766i	−0.860607	−	1.49062i
$753$	−13.2838			−0.484087
$754$	1.80296	+	6.90554i	0.0656598	+	0.251485i
$755$	48.7331			1.77358
$756$	−0.363055	−	0.628829i	−0.0132042	−	0.0228703i
$757$	4.38254	+	7.59078i	0.159286	+	0.275892i	0.934611	−	0.355670i	$-0.115747\pi$
$757$	4.38254	+	7.59078i	0.159286	+	0.275892i	−0.775325	+	0.631562i	$0.782414\pi$
$758$	19.9837	−	34.6128i	0.725841	−	1.25719i
$759$	30.7643			1.11667
$760$	−17.7010	+	30.6590i	−0.642083	+	1.11212i
$761$	10.7276	−	18.5807i	0.388874	−	0.673550i	−0.603424	−	0.797420i	$-0.706197\pi$
$761$	10.7276	−	18.5807i	0.388874	−	0.673550i	0.992298	+	0.123871i	$0.0395308\pi$
$762$	9.03605			0.327341
$763$	−0.0233599	+	0.0404605i	−0.000845685	+	0.00146477i
$764$	0.825547	+	1.42989i	0.0298672	+	0.0517316i
$765$	−5.33969	−	9.24862i	−0.193057	−	0.334385i
$766$	−4.11319			−0.148615
$767$	2.75828	+	10.5645i	0.0995957	+	0.381463i
$768$	−15.4076			−0.555975
$769$	−11.0750	−	19.1825i	−0.399375	−	0.691738i	0.594274	−	0.804263i	$-0.297440\pi$
$769$	−11.0750	−	19.1825i	−0.399375	−	0.691738i	−0.993649	+	0.112525i	$0.964106\pi$
$770$	−10.5697	−	18.3072i	−0.380905	−	0.659746i
$771$	6.22077	−	10.7747i	0.224036	−	0.388041i
$772$	−3.18550			−0.114649

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)

\(f(q)\)	\(=\)	\(q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.41471 - 4.18240i) q^{10} +(2.18860 + 3.79077i) q^{11} -0.726109 q^{12} +(2.56580 - 2.53311i) q^{13} -1.65109 q^{14} +(1.46249 + 2.53311i) q^{15} +(2.46249 + 4.26516i) q^{16} +(-1.82555 + 3.16194i) q^{17} +1.65109 q^{18} +(2.87720 - 4.98346i) q^{19} +(-1.06193 + 1.83932i) q^{20} +1.00000 q^{21} +(3.61359 - 6.25891i) q^{22} +(-3.51415 - 6.08668i) q^{23} +(-1.05166 - 1.82152i) q^{24} +3.55553 q^{25} +(-5.74026 - 1.57761i) q^{26} -1.00000 q^{27} +(0.363055 + 0.628829i) q^{28} +(-0.599437 - 1.03826i) q^{29} +(2.41471 - 4.18240i) q^{30} -6.47277 q^{31} +(1.96249 - 3.39914i) q^{32} +(-2.18860 + 3.79077i) q^{33} +6.02830 q^{34} +(1.46249 - 2.53311i) q^{35} +(-0.363055 - 0.628829i) q^{36} +(1.46249 + 2.53311i) q^{37} -9.50106 q^{38} +(3.47664 + 0.955496i) q^{39} -6.15215 q^{40} +(4.30219 + 7.45161i) q^{41} +(-0.825547 - 1.42989i) q^{42} +(2.86305 - 4.95896i) q^{43} -3.17833 q^{44} +(-1.46249 + 2.53311i) q^{45} +(-5.80219 + 10.0497i) q^{46} -9.58383 q^{47} +(-2.46249 + 4.26516i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.93526 - 5.08401i) q^{50} -3.65109 q^{51} +(0.661367 + 2.53311i) q^{52} -0.302187 q^{53} +(0.825547 + 1.42989i) q^{54} +(6.40162 + 11.0879i) q^{55} +(-1.05166 + 1.82152i) q^{56} +5.75441 q^{57} +(-0.989727 + 1.71426i) q^{58} +(-1.51415 + 2.62258i) q^{59} -2.12386 q^{60} +(0.151093 - 0.261701i) q^{61} +(5.34357 + 9.25533i) q^{62} +(0.500000 + 0.866025i) q^{63} +3.36945 q^{64} +(7.50494 - 7.40931i) q^{65} +7.22717 q^{66} +(4.35384 + 7.54108i) q^{67} +(-1.32555 - 2.29591i) q^{68} +(3.51415 - 6.08668i) q^{69} -4.82942 q^{70} +(-6.76855 + 11.7235i) q^{71} +(1.05166 - 1.82152i) q^{72} +0.932734 q^{73} +(2.41471 - 4.18240i) q^{74} +(1.77777 + 3.07918i) q^{75} +(2.08916 + 3.61854i) q^{76} +4.37720 q^{77} +(-1.50388 - 5.76002i) q^{78} -16.9426 q^{79} +(7.20275 + 12.4755i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.10331 - 12.3033i) q^{82} -1.26614 q^{83} +(-0.363055 + 0.628829i) q^{84} +(-5.33969 + 9.24862i) q^{85} -9.45434 q^{86} +(0.599437 - 1.03826i) q^{87} +(-4.60331 - 7.97317i) q^{88} +(6.69887 + 11.6028i) q^{89} +4.82942 q^{90} +(-0.910836 - 3.48861i) q^{91} +5.10331 q^{92} +(-3.23638 - 5.60558i) q^{93} +(7.91190 + 13.7038i) q^{94} +(8.41577 - 14.5765i) q^{95} +3.92498 q^{96} +(-5.96249 + 10.3273i) q^{97} +(-0.825547 + 1.42989i) q^{98} -4.37720 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

Introduction

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