LMFDB - Embedded newform 273.2.k.d.22.1

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			22.1
Root			$-0.136945 + 0.237196i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.d.211.1

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.411280	+	0.911509i	$0.365082\pi$
$2$	−0.825547	+	1.42989i	−0.583750	+	1.01108i	−0.995030	+	0.0995752i	$0.968252\pi$
$3$	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	−0.320756	−	0.947162i	$-0.603937\pi$
$11$	2.18860	−	3.79077i	0.659888	−	1.14296i	0.980644	−	0.195798i	$-0.0627297\pi$
$12$	−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	0.555133	−	0.831762i	$-0.312667\pi$
$17$	−1.82555	−	3.16194i	−0.442760	−	0.766883i	−0.997893	+	0.0648786i	$0.979334\pi$
$18$	1.65109			0.389166
$19$	2.87720	+	4.98346i	0.660076	+	1.14328i	0.980595	+	0.196043i	$0.0628091\pi$
$19$	2.87720	+	4.98346i	0.660076	+	1.14328i	−0.320520	+	0.947242i	$0.603858\pi$
$20$	−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	0.222953	+	0.974829i	$0.428430\pi$
$23$	−3.51415	+	6.08668i	−0.732751	+	1.26916i	−0.955703	+	0.294332i	$0.904903\pi$
$24$	−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	−0.916300	−	0.400493i	$-0.868839\pi$
$29$	−0.599437	+	1.03826i	−0.111313	+	0.192799i	0.804987	+	0.593292i	$0.202172\pi$
$30$	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	−0.720405	−	0.693553i	$-0.756044\pi$
$37$	1.46249	−	2.53311i	0.240432	−	0.416441i	0.960837	+	0.277113i	$0.0893775\pi$
$38$	−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	−0.305479	−	0.952199i	$-0.598817\pi$
$41$	4.30219	−	7.45161i	0.671889	−	1.16375i	0.977368	−	0.211547i	$-0.0678500\pi$
$42$	−0.825547	+	1.42989i	−0.127385	+	0.220637i
$43$	2.86305	+	4.95896i	0.436612	+	0.756234i	0.997426	−	0.0717081i	$-0.0228450\pi$
$43$	2.86305	+	4.95896i	0.436612	+	0.756234i	−0.560814	+	0.827942i	$0.689512\pi$
$44$	−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	0.750470	−	0.660905i	$-0.229827\pi$
$59$	−1.51415	−	2.62258i	−0.197125	−	0.341431i	−0.947595	+	0.319474i	$0.896494\pi$
$60$	−2.12386			−0.274189
$61$	0.151093	+	0.261701i	0.0193455	+	0.0335074i	0.875536	−	0.483153i	$-0.160508\pi$
$61$	0.151093	+	0.261701i	0.0193455	+	0.0335074i	−0.856191	+	0.516660i	$0.827175\pi$
$62$	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	−0.467400	−	0.884046i	$-0.654809\pi$
$67$	4.35384	−	7.54108i	0.531907	−	0.921289i	0.999306	−	0.0372431i	$-0.0118576\pi$
$68$	−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	−0.917446	−	0.397859i	$-0.869753\pi$
$71$	−6.76855	−	11.7235i	−0.803280	−	1.39132i	0.114167	−	0.993462i	$-0.463580\pi$
$72$	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	−0.254748	−	0.967008i	$-0.581992\pi$
$89$	6.69887	−	11.6028i	0.710079	−	1.22989i	0.964827	−	0.262886i	$-0.0846743\pi$
$90$	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	−0.991988	−	0.126330i	$-0.959680\pi$
$97$	−5.96249	−	10.3273i	−0.605399	−	1.04858i	0.386589	−	0.922252i	$-0.373653\pi$
$98$	−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	0.449687	+	0.893186i	$0.351535\pi$
$101$	−5.51415	+	9.55078i	−0.548678	+	0.950339i	−0.998365	+	0.0571525i	$0.981798\pi$
$102$	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	−0.829558	−	0.558421i	$-0.811407\pi$
$107$	0.711961	−	1.23315i	0.0688279	−	0.119213i	0.898386	+	0.439208i	$0.144741\pi$
$108$	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	0.999875	−	0.0157826i	$-0.00502397\pi$
$113$	5.16912	+	8.95317i	0.486270	+	0.842244i	−0.513606	+	0.858026i	$0.671691\pi$
$114$	−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	−0.718700	−	0.695320i	$-0.755263\pi$
$127$	2.73638	−	4.73955i	0.242815	−	0.420567i	0.961515	+	0.274753i	$0.0885960\pi$
$128$	−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	0.999880	+	0.0155048i	$0.00493551\pi$
$137$	6.00881	+	10.4076i	0.513367	+	0.889178i	−0.486512	+	0.873674i	$0.661731\pi$
$138$	−11.6044			−0.987830
$139$	−0.674453	−	1.16819i	−0.0572064	−	0.0990844i	0.836004	−	0.548723i	$-0.184886\pi$
$139$	−0.674453	−	1.16819i	−0.0572064	−	0.0990844i	−0.893210	+	0.449639i	$0.851553\pi$
$140$	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	0.922107	−	0.386935i	$-0.126466\pi$
$149$	1.53751	+	2.66304i	0.125958	+	0.218165i	−0.796149	+	0.605100i	$0.793133\pi$
$150$	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	0.884669	+	0.466220i	$0.154384\pi$
$163$	10.8022	+	18.7099i	0.846093	+	1.46548i	−0.0385764	+	0.999256i	$0.512282\pi$
$164$	−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	0.0771165	+	0.997022i	$0.475429\pi$
$167$	−10.6599	+	18.4635i	−0.824888	+	1.42875i	−0.902005	+	0.431726i	$0.857905\pi$
$168$	−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	0.800570	−	0.599239i	$-0.204530\pi$
$173$	−1.56087	−	2.70350i	−0.118671	−	0.205543i	−0.919241	+	0.393695i	$0.871197\pi$
$174$	−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	0.256261	+	0.966608i	$0.417509\pi$
$179$	−9.48545	+	16.4293i	−0.708976	+	1.22798i	−0.965237	+	0.261375i	$0.915824\pi$
$180$	−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	0.904223	−	0.427060i	$-0.140451\pi$
$191$	1.13695	+	1.96925i	0.0822665	+	0.142490i	−0.821957	+	0.569550i	$0.807117\pi$
$192$	1.68473	−	2.91803i	0.121585	−	0.210591i
$193$	2.19354	−	3.79932i	0.157894	−	0.273481i	−0.776215	−	0.630468i	$-0.782863\pi$
$193$	2.19354	−	3.79932i	0.157894	−	0.273481i	0.934109	+	0.356988i	$0.116196\pi$
$194$	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	−0.757034	−	0.653375i	$-0.773352\pi$
$197$	2.62920	−	4.55390i	0.187322	−	0.324452i	0.944357	+	0.328923i	$0.106686\pi$
$198$	3.61359	−	6.25891i	0.256806	−	0.444802i
$199$	−6.59798	−	11.4280i	−0.467718	−	0.810111i	0.531601	−	0.846995i	$-0.321590\pi$
$199$	−6.59798	−	11.4280i	−0.467718	−	0.810111i	−0.999320	+	0.0368831i	$0.988257\pi$
$200$	−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	−0.392403	−	0.919793i	$-0.628356\pi$
$211$	8.72077	−	15.1048i	0.600363	−	1.03986i	0.992766	−	0.120065i	$-0.0383105\pi$
$212$	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	−0.968327	−	0.249684i	$-0.919673\pi$
$223$	−4.00106	+	6.93004i	−0.267931	+	0.464070i	0.700396	+	0.713754i	$0.253007\pi$
$224$	−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	0.968206	−	0.250153i	$-0.0804809\pi$
$227$	4.02976	+	6.97975i	0.267464	+	0.463262i	−0.700742	+	0.713415i	$0.747148\pi$
$228$	−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	0.848859	−	0.528620i	$-0.177290\pi$
$241$	−0.518023	−	0.897242i	−0.0333688	−	0.0577965i	−0.882228	+	0.470823i	$0.843957\pi$
$242$	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	0.576631	−	0.817005i	$-0.304367\pi$
$251$	−6.64188	−	11.5041i	−0.419232	−	0.726131i	−0.995862	+	0.0908742i	$0.971034\pi$
$252$	−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	−0.992186	−	0.124768i	$-0.960181\pi$
$257$	−6.22077	+	10.7747i	−0.388041	+	0.672107i	0.604145	+	0.796875i	$0.293515\pi$
$258$	−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	−0.949566	−	0.313566i	$-0.898476\pi$
$263$	−3.29579	+	5.70847i	−0.203227	+	0.352000i	0.746339	+	0.665566i	$0.231810\pi$
$264$	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	0.904454	−	0.426571i	$-0.140279\pi$
$269$	1.35812	+	2.35233i	0.0828059	+	0.143424i	−0.821648	+	0.569995i	$0.806945\pi$
$270$	2.41471	−	4.18240i	0.146955	−	0.254533i
$271$	15.3627	−	26.6089i	0.933215	−	1.61638i	0.155428	−	0.987847i	$-0.450324\pi$
$271$	15.3627	−	26.6089i	0.933215	−	1.61638i	0.777787	−	0.628528i	$-0.216342\pi$
$272$	−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	0.983631	+	0.180196i	$0.0576732\pi$
$277$	10.7827	+	18.6762i	0.647870	+	1.12214i	−0.335761	+	0.941947i	$0.608993\pi$
$278$	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	−0.887229	−	0.461330i	$-0.847372\pi$
$283$	−0.741719	+	1.28470i	−0.0440906	+	0.0763672i	0.843138	+	0.537697i	$0.180706\pi$
$284$	−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	0.707726	−	0.706487i	$-0.249721\pi$
$293$	−4.41577	−	7.64834i	−0.257972	−	0.446821i	−0.965699	+	0.259666i	$0.916388\pi$
$294$	−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	0.844087	−	0.536206i	$-0.180143\pi$
$331$	−0.770016	−	1.33371i	−0.0423239	−	0.0733071i	−0.886411	+	0.462898i	$0.846809\pi$
$332$	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	0.974522	+	0.224292i	$0.0720068\pi$
$347$	12.6950	+	21.9884i	0.681503	+	1.18040i	−0.293019	+	0.956107i	$0.594660\pi$
$348$	0.435257	−	0.753887i	0.0233322	−	0.0404126i
$349$	0.542845	−	0.940235i	0.0290578	−	0.0503296i	−0.851131	−	0.524954i	$-0.824083\pi$
$349$	0.542845	−	0.940235i	0.0290578	−	0.0503296i	0.880189	+	0.474624i	$0.157416\pi$
$350$	−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	−0.971436	−	0.237300i	$-0.923738\pi$
$353$	−5.26468	+	9.11869i	−0.280211	+	0.485339i	0.691226	+	0.722639i	$0.257071\pi$
$354$	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	−0.772723	−	0.634744i	$-0.781106\pi$
$367$	3.12920	−	5.41993i	0.163343	−	0.282918i	0.936065	+	0.351826i	$0.114439\pi$
$368$	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	0.880875	−	0.473349i	$-0.156955\pi$
$373$	0.589164	+	1.02046i	0.0305058	+	0.0528375i	−0.850369	+	0.526186i	$0.823622\pi$
$374$	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	−0.367463	−	0.930038i	$-0.619773\pi$
$379$	12.1033	−	20.9636i	0.621705	−	1.07683i	0.989168	−	0.146787i	$-0.0468932\pi$
$380$	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	0.896093	−	0.443866i	$-0.146394\pi$
$383$	1.24559	+	2.15743i	0.0636469	+	0.110240i	−0.832446	+	0.554106i	$0.813060\pi$
$384$	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	0.955418	−	0.295256i	$-0.0954048\pi$
$397$	4.42352	+	7.66177i	0.222010	+	0.384533i	−0.733408	+	0.679789i	$0.762071\pi$
$398$	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	−0.527229	−	0.849723i	$-0.676769\pi$
$401$	9.45716	−	16.3803i	0.472268	−	0.817992i	0.999496	+	0.0317317i	$0.0101022\pi$
$402$	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	0.819526	−	0.573042i	$-0.194237\pi$
$409$	−1.74947	−	3.03017i	−0.0865057	−	0.149832i	−0.906032	+	0.423210i	$0.860903\pi$
$410$	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	0.262703	+	0.964877i	$0.415386\pi$
$419$	−14.4158	+	24.9688i	−0.704257	+	1.21981i	−0.966959	+	0.254931i	$0.917947\pi$
$420$	−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	0.258950	+	0.965891i	$0.416624\pi$
$431$	−14.6779	+	25.4229i	−0.707011	+	1.22458i	−0.965961	+	0.258688i	$0.916710\pi$
$432$	−2.46249	+	4.26516i	−0.118477	+	0.205208i
$433$	−14.3032	−	24.7740i	−0.687370	−	1.19056i	−0.972686	−	0.232126i	$-0.925432\pi$
$433$	−14.3032	−	24.7740i	−0.687370	−	1.19056i	0.285315	−	0.958434i	$-0.407902\pi$
$434$	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	0.0807654	+	0.996733i	$0.474264\pi$
$439$	−17.2399	+	29.8603i	−0.822813	+	1.42515i	−0.903579	+	0.428422i	$0.859070\pi$
$440$	−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	0.924848	−	0.380336i	$-0.124192\pi$
$449$	2.81915	+	4.88291i	0.133044	+	0.230439i	−0.791805	+	0.610774i	$0.790858\pi$
$450$	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	−0.0469228	+	0.998899i	$0.514941\pi$
$457$	−18.9947	+	32.8997i	−0.888533	+	1.53898i	−0.841610	+	0.540086i	$0.818392\pi$
$458$	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	0.932646	−	0.360794i	$-0.117494\pi$
$461$	3.30365	+	5.72209i	0.153866	+	0.266504i	−0.778779	+	0.627298i	$0.784161\pi$
$462$	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	−0.998588	−	0.0531223i	$-0.983083\pi$
$479$	−9.92071	+	17.1832i	−0.453289	+	0.785119i	0.545299	+	0.838241i	$0.316416\pi$
$480$	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	0.926847	−	0.375439i	$-0.122508\pi$
$487$	3.05166	+	5.28562i	0.138284	+	0.239514i	−0.788563	+	0.614954i	$0.789175\pi$
$488$	−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	−0.838090	−	0.545532i	$-0.816328\pi$
$491$	1.18326	−	2.04947i	0.0534000	−	0.0924915i	0.891490	+	0.453041i	$0.149661\pi$
$492$	−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	0.888598	−	0.458687i	$-0.151680\pi$
$503$	1.05553	+	1.82823i	0.0470638	+	0.0815169i	−0.841534	+	0.540204i	$0.818347\pi$
$504$	−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	−0.458658	−	0.888613i	$-0.651670\pi$
$509$	12.1882	−	21.1106i	0.540233	−	0.935710i	0.998890	−	0.0470972i	$-0.0149970\pi$
$510$	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	−0.296299	−	0.955095i	$-0.595752\pi$
$523$	15.5279	−	26.8951i	0.678987	−	1.17604i	0.975286	−	0.220945i	$-0.0709143\pi$
$524$	−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	−0.110145	−	0.993915i	$-0.535132\pi$
$557$	19.0148	−	32.9346i	0.805683	−	1.39548i	0.915829	−	0.401569i	$-0.131535\pi$
$558$	−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	0.899314	−	0.437303i	$-0.144066\pi$
$563$	1.68326	+	2.91550i	0.0709411	+	0.122874i	−0.828373	+	0.560177i	$0.810733\pi$
$564$	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	−0.614570	−	0.788862i	$-0.710671\pi$
$569$	8.96637	−	15.5302i	0.375890	−	0.651060i	0.990460	+	0.137802i	$0.0440038\pi$
$570$	−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	−0.669883	−	0.742467i	$-0.733656\pi$
$587$	7.46355	−	12.9273i	0.308054	−	0.533565i	0.977937	+	0.208902i	$0.0669890\pi$
$588$	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	−0.986144	−	0.165891i	$-0.946950\pi$
$601$	−8.56580	+	14.8364i	−0.349406	+	0.605190i	0.636738	+	0.771080i	$0.280283\pi$
$602$	−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	0.543180	−	0.839617i	$-0.317220\pi$
$607$	−11.2233	−	19.4393i	−0.455540	−	0.789018i	−0.998719	+	0.0505990i	$0.983887\pi$
$608$	−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	−0.586619	−	0.809863i	$-0.699541\pi$
$613$	10.1029	−	17.4988i	0.408053	−	0.706768i	0.994672	+	0.103095i	$0.0328746\pi$
$614$	−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	−0.932732	−	0.360571i	$-0.882582\pi$
$617$	−19.3408	−	33.4992i	−0.778630	−	1.34863i	0.154102	−	0.988055i	$-0.450751\pi$
$618$	−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	0.946052	+	0.324014i	$0.105032\pi$
$631$	18.9310	+	32.7894i	0.753630	+	1.30533i	−0.192422	+	0.981312i	$0.561634\pi$
$632$	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	0.546968	−	0.837154i	$-0.315782\pi$
$641$	−11.4314	−	19.7997i	−0.451512	−	0.782042i	−0.998480	+	0.0551112i	$0.982449\pi$
$642$	2.35103			0.0927877
$643$	−21.7915	−	37.7440i	−0.859373	−	1.48848i	−0.872528	−	0.488565i	$-0.837521\pi$
$643$	−21.7915	−	37.7440i	−0.859373	−	1.48848i	0.0131542	−	0.999913i	$-0.495813\pi$
$644$	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	−0.834949	−	0.550328i	$-0.814503\pi$
$647$	1.50388	−	2.60479i	0.0591234	−	0.102405i	0.894072	+	0.447923i	$0.147836\pi$
$648$	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	−0.315837	−	0.948813i	$-0.602285\pi$
$653$	16.9621	−	29.3792i	0.663778	−	1.14970i	0.979615	−	0.200884i	$-0.0643813\pi$
$654$	−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	0.884340	+	0.466844i	$0.154609\pi$
$659$	21.7297	+	37.6369i	0.846469	+	1.46613i	−0.0378709	+	0.999283i	$0.512058\pi$
$660$	−4.64828	+	8.05106i	−0.180934	+	0.313387i
$661$	−19.1429	+	33.1565i	−0.744574	+	1.28964i	0.205819	+	0.978590i	$0.434014\pi$
$661$	−19.1429	+	33.1565i	−0.744574	+	1.28964i	−0.950393	+	0.311050i	$0.899319\pi$
$662$	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	0.455583	+	0.890193i	$0.349431\pi$
$673$	−14.0902	+	24.4050i	−0.543138	+	0.940743i	−0.998722	+	0.0505499i	$0.983903\pi$
$674$	−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	0.772276	−	0.635287i	$-0.219118\pi$
$683$	−4.28698	−	7.42526i	−0.164037	−	0.284120i	−0.936313	+	0.351167i	$0.885785\pi$
$684$	−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	−0.792323	−	0.610102i	$-0.791129\pi$
$691$	3.47518	−	6.01919i	0.132202	−	0.228981i	0.924525	+	0.381121i	$0.124462\pi$
$692$	−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	0.759923	−	0.650013i	$-0.225237\pi$
$709$	−4.87187	−	8.43832i	−0.182967	−	0.316908i	−0.942890	+	0.333106i	$0.891903\pi$
$710$	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	0.909229	−	0.416297i	$-0.136672\pi$
$719$	2.52296	+	4.36989i	0.0940905	+	0.162970i	−0.815138	+	0.579267i	$0.803339\pi$
$720$	−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	−0.917250	−	0.398313i	$-0.869596\pi$
$739$	−3.09023	+	5.35243i	−0.113676	+	0.196892i	0.803574	+	0.595205i	$0.202929\pi$
$740$	−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	−0.568686	−	0.822554i	$-0.692548\pi$
$743$	11.6667	−	20.2073i	0.428010	−	0.741335i	0.996696	+	0.0812197i	$0.0258815\pi$
$744$	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	−0.856977	−	0.515354i	$-0.827660\pi$
$751$	0.488375	−	0.845890i	0.0178211	−	0.0308670i	0.874798	+	0.484487i	$0.160994\pi$
$752$	−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	−0.775325	−	0.631562i	$-0.782414\pi$
$757$	4.38254	−	7.59078i	0.159286	−	0.275892i	0.934611	+	0.355670i	$0.115747\pi$
$758$	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	0.992298	−	0.123871i	$-0.0395308\pi$
$761$	10.7276	+	18.5807i	0.388874	+	0.673550i	−0.603424	+	0.797420i	$0.706197\pi$
$762$	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	−0.993649	−	0.112525i	$-0.964106\pi$
$769$	−11.0750	+	19.1825i	−0.399375	+	0.691738i	0.594274	+	0.804263i	$0.297440\pi$
$770$	−10.5697	+	18.3072i	−0.380905	+	0.659746i
$771$	6.22077	+	10.7747i	0.224036	+	0.388041i
$772$	−3.18550			−0.114649
$773$	9.57995	+	16.5930i	0.344567	+	0.596807i	0.985275	−	0.170977i	$-0.0546924\pi$
$773$	9.57995	+	16.5930i	0.344567	+	0.596807i	−0.640708	+	0.767785i	$0.721359\pi$
$774$	4.72717	+	8.18770i	0.169915	+	0.294301i
$775$	−23.0141			−0.826692
$776$	12.5410	+	21.7216i	0.450195	+	0.779761i
$777$	1.46249	−	2.53311i	0.0524666	−	0.0908748i
$778$	−19.4883	+	33.7547i	−0.698688	+	1.21016i
$779$	49.5131			1.77399
$780$	−5.44941	−	5.37997i	−0.195120	−	0.192634i
$781$	−59.2547			−2.12030
$782$	−21.1843	+	36.6923i	−0.757550	+	1.31212i
$783$	0.599437	−	1.03826i	0.0214221	−	0.0371042i
$784$	2.46249	+	4.26516i	0.0879461	+	0.152327i
$785$	37.5259			1.33936
$786$	13.3496	+	23.1221i	0.476163	+	0.824739i
$787$	−22.0898	−	38.2607i	−0.787417	−	1.36385i	−0.927544	−	0.373713i	$-0.878084\pi$
$787$	−22.0898	−	38.2607i	−0.787417	−	1.36385i	0.140127	−	0.990134i	$-0.455249\pi$
$788$	−3.81817			−0.136017
$789$	3.29579	+	5.70847i	0.117333	+	0.203227i
$790$	40.9115	−	70.8608i	1.45557	−	2.52111i
$791$	−5.16912	+	8.95317i	−0.183793	+	0.318338i
$792$	9.20662			0.327143
$793$	−0.275243	+	1.05421i	−0.00977415	+	0.0374361i
$794$	−14.6073			−0.518394
$795$	−0.441946	+	0.765473i	−0.0156742	+	0.0271485i
$796$	−4.79085	+	8.29800i	−0.169807	+	0.294115i
$797$	−6.82807	−	11.8266i	−0.241863	−	0.418918i	0.719382	−	0.694614i	$-0.244425\pi$
$797$	−6.82807	−	11.8266i	−0.241863	−	0.418918i	−0.961245	+	0.275696i	$0.911092\pi$
$798$	−9.50106			−0.336334
$799$	17.4957	+	30.3035i	0.618954	+	1.07206i
$800$	6.97770	+	12.0857i	0.246699	+	0.427295i
$801$	−13.3977			−0.473386
$802$	15.6146	+	27.0454i	0.551372	+	0.955005i
$803$	2.04138	−	3.53578i	0.0720388	−	0.124775i
$804$	−3.16137	+	5.47565i	−0.111493	+	0.193111i
$805$	−20.5577			−0.724562
$806$	37.1553	−	10.2115i	1.30874	−	0.359686i
$807$	2.71624			0.0956161
$808$	11.5980	−	20.0883i	0.408015	−	0.706703i
$809$	−17.0039	+	29.4516i	−0.597824	+	1.03546i	0.395317	+	0.918545i	$0.370635\pi$
$809$	−17.0039	+	29.4516i	−0.597824	+	1.03546i	−0.993142	+	0.116918i	$0.962699\pi$
$810$	−2.41471	−	4.18240i	−0.0848443	−	0.146955i
$811$	−21.4084			−0.751751			−0.375876	−	0.926670i	$-0.622658\pi$
$811$	−21.4084			−0.751751			−0.375876	+	0.926670i	$0.622658\pi$
$812$	0.435257	+	0.753887i	0.0152745	+	0.0264563i
$813$	−15.3627	−	26.6089i	−0.538792	−	0.933215i
$814$	21.1394			0.740934
$815$	31.5962	+	54.7263i	1.10677	+	1.91698i
$816$	−8.99079	+	15.5725i	−0.314741	+	0.545147i
$817$	−16.4752	+	28.5358i	−0.576394	+	0.998343i
$818$	5.77707			0.201991
$819$	3.47664	−	0.955496i	0.121484	−	0.0333877i
$820$	−18.2745			−0.638172
$821$	−13.5683	+	23.5010i	−0.473538	+	0.820192i	−0.999541	−	0.0302909i	$-0.990357\pi$
$821$	−13.5683	+	23.5010i	−0.473538	+	0.820192i	0.526003	+	0.850483i	$0.323690\pi$
$822$	−9.92111	+	17.1839i	−0.346038	+	0.599356i
$823$	23.3209	+	40.3929i	0.812914	+	1.40801i	0.910816	+	0.412813i	$0.135454\pi$
$823$	23.3209	+	40.3929i	0.812914	+	1.40801i	−0.0979013	+	0.995196i	$0.531213\pi$
$824$	40.9186			1.42547
$825$	−7.78164	−	13.4782i	−0.270922	−	0.469251i
$826$	2.50000	+	4.33013i	0.0869861	+	0.150664i
$827$	−27.2789			−0.948582			−0.474291	−	0.880368i	$-0.657295\pi$
$827$	−27.2789			−0.948582			−0.474291	+	0.880368i	$0.657295\pi$
$828$	−2.55166	−	4.41960i	−0.0886762	−	0.153592i
$829$	12.6610	−	21.9294i	0.439734	−	0.761641i	−0.557935	−	0.829885i	$-0.688406\pi$
$829$	12.6610	−	21.9294i	0.439734	−	0.761641i	0.997669	+	0.0682437i	$0.0217396\pi$
$830$	3.05736	−	5.29551i	0.106123	−	0.183810i
$831$	21.5654			0.748096
$832$	8.64536	+	8.53520i	0.299724	+	0.295905i
$833$	3.65109			0.126503
$834$	1.11359	−	1.92879i	0.0385603	−	0.0667884i
$835$	−31.1801	+	54.0054i	−1.07903	+	1.86894i
$836$	−9.14470	−	15.8391i	−0.316276	−	0.547806i
$837$	6.47277			0.223731
$838$	−23.8018	−	41.2259i	−0.822219	−	1.42413i
$839$	−0.183265	−	0.317424i	−0.00632700	−	0.0109587i	0.862845	−	0.505469i	$-0.168681\pi$
$839$	−0.183265	−	0.317424i	−0.00632700	−	0.0109587i	−0.869172	+	0.494511i	$0.835347\pi$
$840$	−6.15215			−0.212270
$841$	13.7813	+	23.8700i	0.475219	+	0.823103i
$842$	−28.3350	+	49.0777i	−0.976489	+	1.69133i
$843$	16.6029	−	28.7571i	0.571835	−	0.990447i
$844$	−12.6645			−0.435929
$845$	0.487604	+	38.0217i	0.0167741	+	1.30799i
$846$	−15.8238			−0.544033
$847$	4.07995	−	7.06668i	0.140189	−	0.242814i
$848$	−0.744133	+	1.28888i	−0.0255536	+	0.0442602i
$849$	0.741719	+	1.28470i	0.0254557	+	0.0440906i
$850$	21.4338			0.735173
$851$	10.2788	+	17.8035i	0.352354	+	0.610294i
$852$	4.91471	+	8.51253i	0.168375	+	0.291634i
$853$	−49.3134			−1.68846			−0.844229	−	0.535983i	$-0.819941\pi$
$853$	−49.3134			−1.68846			−0.844229	+	0.535983i	$0.819941\pi$
$854$	−0.249469	−	0.432094i	−0.00853666	−	0.0147859i
$855$	8.41577	−	14.5765i	0.287813	−	0.498507i
$856$	−1.49748	+	2.59371i	−0.0511827	+	0.0886511i
$857$	26.0878			0.891143			0.445571	−	0.895246i	$-0.353001\pi$
$857$	26.0878			0.891143			0.445571	+	0.895246i	$0.353001\pi$
$858$	18.5435	+	18.3072i	0.633065	+	0.624998i
$859$	29.6815			1.01272			0.506360	−	0.862322i	$-0.330991\pi$
$859$	29.6815			1.01272			0.506360	+	0.862322i	$0.330991\pi$
$860$	6.08072	−	10.5321i	0.207351	−	0.359142i
$861$	4.30219	−	7.45161i	0.146618	−	0.253950i
$862$	−24.2346	−	41.9756i	−0.825435	−	1.42969i
$863$	17.8804			0.608655			0.304328	−	0.952567i	$-0.401568\pi$
$863$	17.8804			0.608655			0.304328	+	0.952567i	$0.401568\pi$
$864$	−1.96249	−	3.39914i	−0.0667653	−	0.115641i
$865$	−4.56551	−	7.90770i	−0.155232	−	0.268870i
$866$	47.2320			1.60501
$867$	−1.83476	−	3.17789i	−0.0623117	−	0.107927i
$868$	−2.34997	+	4.07026i	−0.0797631	+	0.138154i
$869$	−37.0806	+	64.2255i	−1.25787	+	2.17870i
$870$	−5.78987			−0.196295
$871$	30.2735	−	8.32016i	1.02578	−	0.281918i
$872$	0.0982663			0.00332772
$873$	−5.96249	+	10.3273i	−0.201800	+	0.349527i
$874$	33.3881	−	57.8299i	1.12937	−	1.95613i
$875$	−2.11252	−	3.65900i	−0.0714163	−	0.123697i
$876$	−0.677267			−0.0228827
$877$	−12.8061	−	22.1807i	−0.432430	−	0.748991i	0.564652	−	0.825329i	$-0.309010\pi$
$877$	−12.8061	−	22.1807i	−0.432430	−	0.748991i	−0.997082	+	0.0763384i	$0.975677\pi$
$878$	−28.4646	−	49.3022i	−0.960634	−	1.66387i
$879$	−8.83154			−0.297881
$880$	−31.5279	−	54.6079i	−1.06281	−	1.84083i
$881$	21.0821	−	36.5152i	0.710273	−	1.23023i	−0.254481	−	0.967078i	$-0.581905\pi$
$881$	21.0821	−	36.5152i	0.710273	−	1.23023i	0.964755	−	0.263152i	$-0.0847619\pi$
$882$	−0.825547	+	1.42989i	−0.0277976	+	0.0481469i
$883$	−32.9992			−1.11051			−0.555256	−	0.831680i	$-0.687380\pi$
$883$	−32.9992			−1.11051			−0.555256	+	0.831680i	$0.687380\pi$
$884$	−9.21690	+	2.53311i	−0.309998	+	0.0851977i
$885$	−8.85772			−0.297749
$886$	10.6550	−	18.4549i	0.357961	−	0.620006i
$887$	−4.64334	+	8.04251i	−0.155908	+	0.270041i	−0.933389	−	0.358865i	$-0.883164\pi$
$887$	−4.64334	+	8.04251i	−0.155908	+	0.270041i	0.777481	+	0.628906i	$0.216497\pi$
$888$	3.07608	+	5.32792i	0.103226	+	0.178793i
$889$	5.47277			0.183551
$890$	32.3517	+	56.0348i	1.08443	+	1.87829i
$891$	2.18860	+	3.79077i	0.0733209	+	0.126996i
$892$	5.81042			0.194547
$893$	−27.5746	−	47.7606i	−0.922749	−	1.59825i
$894$	−2.53857	+	4.39693i	−0.0849025	+	0.147055i
$895$	−27.7448	+	48.0554i	−0.927406	+	1.60631i
$896$	−13.4132			−0.448105
$897$	−6.40162	+	24.5190i	−0.213744	+	0.818664i
$898$	−9.30936			−0.310657
$899$	3.88002	−	6.72039i	0.129406	−	0.224137i
$900$	−1.29085	+	2.23582i	−0.0430284	+	0.0745274i
$901$	0.551656	+	0.955496i	0.0183783	+	0.0318322i
$902$	62.1853			2.07054
$903$	2.86305	+	4.95896i	0.0952765	+	0.165024i
$904$	−10.8723	−	18.8313i	−0.361606	−	0.626320i
$905$	−5.65322			−0.187919
$906$	13.7544	+	23.8233i	0.456960	+	0.791477i
$907$	−10.6224	+	18.3985i	−0.352711	+	0.610913i	−0.986723	−	0.162410i	$-0.948073\pi$
$907$	−10.6224	+	18.3985i	−0.352711	+	0.610913i	0.634013	+	0.773323i	$0.281407\pi$
$908$	2.92605	−	5.06806i	0.0971042	−	0.168189i
$909$	11.0283			0.365785
$910$	−12.3914	−	12.2335i	−0.410769	−	0.405535i
$911$	−54.0785			−1.79170			−0.895850	−	0.444357i	$-0.853432\pi$
$911$	−54.0785			−1.79170			−0.895850	+	0.444357i	$0.853432\pi$
$912$	14.1702	−	24.5435i	0.469221	−	0.812715i
$913$	−2.77108	+	4.79965i	−0.0917093	+	0.158845i
$914$	−31.3620	−	54.3205i	−1.03736	−	1.79676i
$915$	0.883892			0.0292206
$916$	3.07889	+	5.33280i	0.101729	+	0.176201i
$917$	8.08529	+	14.0041i	0.267000	+	0.462457i
$918$	−6.02830			−0.198963
$919$	9.47130	+	16.4048i	0.312429	+	0.541144i	0.978888	−	0.204399i	$-0.0655239\pi$
$919$	9.47130	+	16.4048i	0.312429	+	0.541144i	−0.666458	+	0.745542i	$0.732191\pi$
$920$	21.6196	−	37.4462i	0.712777	−	1.23457i
$921$	5.82661	−	10.0920i	0.191993	−	0.332542i
$922$	−10.9093			−0.359277
$923$	12.3301	−	47.2256i	0.405850	−	1.55445i
$924$	−3.17833			−0.104559
$925$	5.19994	−	9.00655i	0.170973	−	0.296134i
$926$	−8.24666	+	14.2836i	−0.271002	+	0.469389i
$927$	9.72717	+	16.8480i	0.319482	+	0.553359i
$928$	−4.70556			−0.154468
$929$	22.6674	+	39.2610i	0.743692	+	1.28811i	0.950803	+	0.309795i	$0.100260\pi$
$929$	22.6674	+	39.2610i	0.743692	+	1.28811i	−0.207111	+	0.978317i	$0.566406\pi$
$930$	−15.6299	−	27.0717i	−0.512523	−	0.887716i
$931$	−5.75441			−0.188593
$932$	3.71971	+	6.44273i	0.121843	+	0.211039i
$933$	−12.5049	+	21.6592i	−0.409393	+	0.709090i
$934$	−2.82419	+	4.89165i	−0.0924105	+	0.160060i
$935$	−46.7459			−1.52875
$936$	−1.91577	+	7.33763i	−0.0626190	+	0.239838i
$937$	3.71544			0.121378			0.0606890	−	0.998157i	$-0.480670\pi$
$937$	3.71544			0.121378			0.0606890	+	0.998157i	$0.480670\pi$
$938$	−7.18860	+	12.4510i	−0.234716	+	0.406540i
$939$	−0.0930392	+	0.161149i	−0.00303622	+	0.00525889i
$940$	10.1773	+	17.6277i	0.331948	+	0.574952i
$941$	−4.28376			−0.139647			−0.0698233	−	0.997559i	$-0.522244\pi$
$941$	−4.28376			−0.139647			−0.0698233	+	0.997559i	$0.522244\pi$
$942$	10.5913	+	18.3446i	0.345083	+	0.597701i
$943$	30.2370	+	52.3721i	0.984654	+	1.70547i
$944$	−14.9143			−0.485419
$945$	−1.46249	−	2.53311i	−0.0475749	−	0.0824021i
$946$	−20.6918	+	35.8392i	−0.672748	+	1.16523i
$947$	12.5103	−	21.6684i	0.406529	−	0.704129i	−0.587969	−	0.808884i	$-0.700072\pi$
$947$	12.5103	−	21.6684i	0.406529	−	0.704129i	0.994498	+	0.104754i	$0.0334056\pi$
$948$	12.3022			0.399556
$949$	2.39321	+	2.36272i	0.0776870	+	0.0766971i
$950$	−33.7813			−1.09601
$951$	−0.270016	+	0.467681i	−0.00875585	+	0.0151656i
$952$	−3.83969	+	6.65055i	−0.124445	+	0.215545i
$953$	1.42217	+	2.46327i	0.0460686	+	0.0797932i	0.888140	−	0.459573i	$-0.151997\pi$
$953$	1.42217	+	2.46327i	0.0460686	+	0.0797932i	−0.842072	+	0.539366i	$0.818664\pi$
$954$	−0.498939			−0.0161537
$955$	3.32555	+	5.76002i	0.107612	+	0.186390i
$956$	4.10331	+	7.10715i	0.132711	+	0.229862i
$957$	5.24772			0.169635
$958$	−16.3800	−	28.3710i	−0.529214	−	0.916626i
$959$	−6.00881	+	10.4076i	−0.194035	+	0.336078i
$960$	4.92780	−	8.53520i	0.159044	−	0.275472i
$961$	10.8967			0.351506
$962$	−4.39881	+	16.8480i	−0.141823	+	0.543200i
$963$	−1.42392			−0.0458853
$964$	−0.376142	+	0.651496i	−0.0121147	+	0.0209833i
$965$	6.41606	−	11.1129i	0.206540	−	0.357738i
$966$	−5.80219	−	10.0497i	−0.186682	−	0.323343i
$967$	−6.68444			−0.214957			−0.107478	−	0.994207i	$-0.534278\pi$
$967$	−6.68444			−0.214957			−0.107478	+	0.994207i	$0.534278\pi$
$968$	8.58141	+	14.8634i	0.275817	+	0.477729i
$969$	−10.5049	−	18.1951i	−0.337467	−	0.584510i
$970$	57.5908			1.84913
$971$	13.3139	+	23.0604i	0.427264	+	0.740043i	0.996629	−	0.0820419i	$-0.0261441\pi$
$971$	13.3139	+	23.0604i	0.427264	+	0.740043i	−0.569365	+	0.822085i	$0.692811\pi$
$972$	0.363055	−	0.628829i	0.0116450	−	0.0201697i
$973$	0.674453	−	1.16819i	0.0216220	−	0.0374504i
$974$	−10.0771			−0.322892
$975$	12.3613	−	3.39730i	0.395879	−	0.108801i
$976$	1.48827			0.0476382
$977$	13.9090	−	24.0910i	0.444987	−	0.770741i	−0.553064	−	0.833139i	$-0.686541\pi$
$977$	13.9090	−	24.0910i	0.444987	−	0.770741i	0.998051	+	0.0623979i	$0.0198748\pi$
$978$	−17.8354	+	30.8919i	−0.570314	+	0.987813i
$979$	−29.3223	−	50.7878i	−0.937146	−	1.62318i
$980$	2.12386			0.0678442
$981$	0.0233599	+	0.0404605i	0.000745824	+	0.00129180i
$982$	1.95368	+	3.38387i	0.0623445	+	0.107984i
$983$	51.3454			1.63766			0.818832	−	0.574033i	$-0.194622\pi$
$983$	51.3454			1.63766			0.818832	+	0.574033i	$0.194622\pi$
$984$	9.04884	+	15.6731i	0.288467	+	0.499639i
$985$	7.69035	−	13.3201i	0.245035	−	0.424413i
$986$	−3.61359	+	6.25891i	−0.115080	+	0.199324i
$987$	−9.58383			−0.305057
$988$	14.5265	−	3.99238i	0.462151	−	0.127014i
$989$	−40.2448			−1.27971
$990$	10.5697	−	18.3072i	0.335926	−	0.581842i
$991$	11.6872	−	20.2429i	0.371258	−	0.643037i	−0.618502	−	0.785784i	$-0.712260\pi$
$991$	11.6872	−	20.2429i	0.371258	−	0.643037i	0.989759	+	0.142746i	$0.0455933\pi$
$992$	−12.7027	−	22.0018i	−0.403313	−	0.698558i
$993$	−1.54003			−0.0488714
$994$	11.1755	+	19.3566i	0.354466	+	0.613953i
$995$	−19.2990	−	33.4268i	−0.611819	−	1.05970i
$996$	0.919357			0.0291309
$997$	14.3977	+	24.9376i	0.455981	+	0.789783i	0.998744	−	0.0501033i	$-0.0159551\pi$
$997$	14.3977	+	24.9376i	0.455981	+	0.789783i	−0.542763	+	0.839886i	$0.682622\pi$
$998$	3.54351	−	6.13753i	0.112168	−	0.194280i
$999$	−1.46249	+	2.53311i	−0.0462712	+	0.0801441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.d.22.1	✓	6
3.2	odd	2		819.2.o.d.568.3		6
13.3	even	3	inner	273.2.k.d.211.1	yes	6
13.4	even	6		3549.2.a.s.1.1		3
13.9	even	3		3549.2.a.h.1.3		3
39.29	odd	6		819.2.o.d.757.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.1	✓	6	1.1	even	1	trivial
273.2.k.d.211.1	yes	6	13.3	even	3	inner
819.2.o.d.568.3		6	3.2	odd	2
819.2.o.d.757.3		6	39.29	odd	6
3549.2.a.h.1.3		3	13.9	even	3
3549.2.a.s.1.1		3	13.4	even	6

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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