LMFDB - Embedded newform 91.2.g.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(9,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.g (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$0.217953 - 0.377506i$ of defining polynomial
Character	$\chi$	$=$	91.9
Dual form			91.2.g.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929081 - 1.60921i) q^{2} +2.29407 q^{3} +(-0.726381 + 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 - 3.69165i) q^{6} +(1.58836 + 2.11592i) q^{7} -1.01686 q^{8} +2.26275 q^{9} +O(q^{10})$	\(q+(-0.929081 - 1.60921i) q^{2} +2.29407 q^{3} +(-0.726381 + 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 - 3.69165i) q^{6} +(1.58836 + 2.11592i) q^{7} -1.01686 q^{8} +2.26275 q^{9} -0.366731 q^{10} -4.18274 q^{11} +(-1.66637 + 2.88623i) q^{12} +(-2.72221 - 2.36423i) q^{13} +(1.92926 - 4.52187i) q^{14} +(0.226381 - 0.392104i) q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +(-2.10227 - 3.64125i) q^{18} +1.35175 q^{19} +(0.143360 + 0.248307i) q^{20} +(3.64380 + 4.85406i) q^{21} +(3.88610 + 6.73092i) q^{22} +(2.05760 + 3.56386i) q^{23} -2.33274 q^{24} +(2.48052 + 4.29639i) q^{25} +(-1.27540 + 6.57718i) q^{26} -1.69131 q^{27} +(-3.81585 + 0.461395i) q^{28} +(4.11931 - 7.13485i) q^{29} -0.841305 q^{30} +(0.640350 + 1.10912i) q^{31} +(3.43809 - 5.95495i) q^{32} -9.59548 q^{33} +1.56328 q^{34} +(0.518396 - 0.0626819i) q^{35} +(-1.64362 + 2.84683i) q^{36} +(-1.52242 - 2.63692i) q^{37} +(-1.25589 - 2.17526i) q^{38} +(-6.24494 - 5.42370i) q^{39} +(-0.100344 + 0.173802i) q^{40} +(-2.69848 + 4.67390i) q^{41} +(4.42585 - 10.3735i) q^{42} +(-2.66389 - 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} +(0.223290 - 0.386750i) q^{45} +(3.82334 - 6.62223i) q^{46} +(5.83204 - 10.1014i) q^{47} +(5.50003 + 9.52634i) q^{48} +(-1.95424 + 6.72168i) q^{49} +(4.60921 - 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(4.95187 - 1.70756i) q^{52} +(-2.32398 - 4.02525i) q^{53} +(1.57136 + 2.72168i) q^{54} +(-0.412757 + 0.714916i) q^{55} +(-1.61513 - 2.15159i) q^{56} +3.10101 q^{57} -15.3087 q^{58} +(-3.02905 + 5.24648i) q^{59} +(0.328878 + 0.569634i) q^{60} -11.3657 q^{61} +(1.18987 - 2.06092i) q^{62} +(3.59405 + 4.78779i) q^{63} -3.18704 q^{64} +(-0.672726 + 0.231978i) q^{65} +(8.91498 + 15.4412i) q^{66} +13.3970 q^{67} +(-0.611109 - 1.05847i) q^{68} +(4.72026 + 8.17574i) q^{69} +(-0.582500 - 0.775973i) q^{70} +(2.98520 + 5.17051i) q^{71} -2.30089 q^{72} +(-1.94273 - 3.36491i) q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} +(-0.981887 + 1.70068i) q^{76} +(-6.64368 - 8.85034i) q^{77} +(-2.92585 + 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +0.946353 q^{80} -10.6682 q^{81} +10.0284 q^{82} +3.07390 q^{83} +(-8.75383 + 1.05847i) q^{84} +(0.0830210 + 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} +(9.44997 - 16.3678i) q^{87} +4.25324 q^{88} +(5.99207 + 10.3786i) q^{89} -0.829819 q^{90} +(0.678673 - 9.51522i) q^{91} -5.97840 q^{92} +(1.46901 + 2.54439i) q^{93} -21.6737 q^{94} +(0.133392 - 0.231042i) q^{95} +(7.88721 - 13.6611i) q^{96} +(-9.73637 - 16.8639i) q^{97} +(12.6323 - 3.10019i) q^{98} -9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.929081	−	1.60921i	−0.656959	−	1.13789i	−0.981399	−	0.191980i	$-0.938509\pi$
$2$	−0.929081	−	1.60921i	−0.656959	−	1.13789i	0.324440	−	0.945906i	$-0.394824\pi$
$3$	2.29407			1.32448			0.662240	−	0.749291i	$-0.269606\pi$
$3$	2.29407			1.32448			0.662240	+	0.749291i	$0.269606\pi$
$4$	−0.726381	+	1.25813i	−0.363191	+	0.629065i
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	−0.843116	−	0.537732i	$-0.819281\pi$
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	0.887247	+	0.461294i	$0.152615\pi$
$6$	−2.13137	−	3.69165i	−0.870130	−	1.50711i
$7$	1.58836	+	2.11592i	0.600343	+	0.799743i
$7$	1.58836	+	2.11592i	0.600343	+	0.799743i
$8$	−1.01686			−0.359513
$9$	2.26275			0.754249
$10$	−0.366731			−0.115970
$11$	−4.18274			−1.26114			−0.630571	−	0.776131i	$-0.717179\pi$
$11$	−4.18274			−1.26114			−0.630571	+	0.776131i	$0.717179\pi$
$12$	−1.66637	+	2.88623i	−0.481039	+	0.833184i
$13$	−2.72221	−	2.36423i	−0.755005	−	0.655719i
$13$	−2.72221	−	2.36423i	−0.755005	−	0.655719i
$14$	1.92926	−	4.52187i	0.515616	−	1.20852i
$15$	0.226381	−	0.392104i	0.0584514	−	0.101241i
$16$	2.39750	+	4.15260i	0.599376	+	1.03815i
$17$	−0.420653	+	0.728592i	−0.102023	+	0.176709i	−0.912518	−	0.409036i	$-0.865865\pi$
$17$	−0.420653	+	0.728592i	−0.102023	+	0.176709i	0.810495	+	0.585746i	$0.199198\pi$
$18$	−2.10227	−	3.64125i	−0.495511	−	0.858250i
$19$	1.35175			0.310113			0.155057	−	0.987906i	$-0.450444\pi$
$19$	1.35175			0.310113			0.155057	+	0.987906i	$0.450444\pi$
$20$	0.143360	+	0.248307i	0.0320563	+	0.0555232i
$21$	3.64380	+	4.85406i	0.795143	+	1.05924i
$22$	3.88610	+	6.73092i	0.828519	+	1.43504i
$23$	2.05760	+	3.56386i	0.429038	+	0.743116i	0.996788	−	0.0800850i	$-0.0255192\pi$
$23$	2.05760	+	3.56386i	0.429038	+	0.743116i	−0.567750	+	0.823201i	$0.692186\pi$
$24$	−2.33274			−0.476168
$25$	2.48052	+	4.29639i	0.496105	+	0.859279i
$26$	−1.27540	+	6.57718i	−0.250126	+	1.28989i
$27$	−1.69131			−0.325492
$28$	−3.81585	+	0.461395i	−0.721129	+	0.0871954i
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	−0.175344	−	0.984507i	$-0.556104\pi$
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	0.940280	−	0.340401i	$-0.110563\pi$
$30$	−0.841305			−0.153601
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	0.917784	−	0.397080i	$-0.129977\pi$
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	−0.802774	+	0.596284i	$0.796643\pi$
$32$	3.43809	−	5.95495i	0.607774	−	1.05270i
$33$	−9.59548			−1.67036
$34$	1.56328			0.268100
$35$	0.518396	−	0.0626819i	0.0876249	−	0.0105952i
$36$	−1.64362	+	2.84683i	−0.273936	+	0.474471i
$37$	−1.52242	−	2.63692i	−0.250285	−	0.433506i	0.713319	−	0.700839i	$-0.247191\pi$
$37$	−1.52242	−	2.63692i	−0.250285	−	0.433506i	−0.963604	+	0.267333i	$0.913858\pi$
$38$	−1.25589	−	2.17526i	−0.203732	−	0.352874i
$39$	−6.24494	−	5.42370i	−0.999990	−	0.868487i
$40$	−0.100344	+	0.173802i	−0.0158659	+	0.0274805i
$41$	−2.69848	+	4.67390i	−0.421431	+	0.729941i	−0.996080	−	0.0884599i	$-0.971805\pi$
$41$	−2.69848	+	4.67390i	−0.421431	+	0.729941i	0.574648	+	0.818400i	$0.305139\pi$
$42$	4.42585	−	10.3735i	0.682923	−	1.60066i
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	0.588226	−	0.808697i	$-0.299827\pi$
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	−0.994465	+	0.105070i	$0.966493\pi$
$44$	3.03826	−	5.26242i	0.458035	−	0.793340i
$45$	0.223290	−	0.386750i	0.0332862	−	0.0576534i
$46$	3.82334	−	6.62223i	0.563721	−	0.976394i
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	−0.0298969	−	0.999553i	$-0.509518\pi$
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	0.880587	−	0.473885i	$-0.157149\pi$
$48$	5.50003	+	9.52634i	0.793862	+	1.37501i
$49$	−1.95424	+	6.72168i	−0.279177	+	0.960240i
$50$	4.60921	−	7.98339i	0.651841	−	1.12902i
$51$	−0.965006	+	1.67144i	−0.135128	+	0.234048i
$52$	4.95187	−	1.70756i	0.686700	−	0.236796i
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	0.661103	−	0.750295i	$-0.270089\pi$
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	−0.980326	+	0.197384i	$0.936755\pi$
$54$	1.57136	+	2.72168i	0.213835	+	0.370373i
$55$	−0.412757	+	0.714916i	−0.0556562	+	0.0963993i
$56$	−1.61513	−	2.15159i	−0.215831	−	0.287518i
$57$	3.10101			0.410739
$58$	−15.3087			−2.01013
$59$	−3.02905	+	5.24648i	−0.394349	+	0.683033i	−0.993018	−	0.117964i	$-0.962363\pi$
$59$	−3.02905	+	5.24648i	−0.394349	+	0.683033i	0.598669	+	0.800997i	$0.295697\pi$
$60$	0.328878	+	0.569634i	0.0424580	+	0.0735394i
$61$	−11.3657			−1.45523			−0.727614	−	0.685986i	$-0.759371\pi$
$61$	−11.3657			−1.45523			−0.727614	+	0.685986i	$0.759371\pi$
$62$	1.18987	−	2.06092i	0.151114	−	0.261737i
$63$	3.59405	+	4.78779i	0.452808	+	0.603205i
$64$	−3.18704			−0.398380
$65$	−0.672726	+	0.231978i	−0.0834414	+	0.0287733i
$66$	8.91498	+	15.4412i	1.09736	+	1.90068i
$67$	13.3970			1.63671			0.818354	−	0.574715i	$-0.194887\pi$
$67$	13.3970			1.63671			0.818354	+	0.574715i	$0.194887\pi$
$68$	−0.611109	−	1.05847i	−0.0741078	−	0.128358i
$69$	4.72026	+	8.17574i	0.568253	+	0.984243i
$70$	−0.582500	−	0.775973i	−0.0696221	−	0.0927465i
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	0.986994	−	0.160757i	$-0.0513934\pi$
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	−0.632716	+	0.774384i	$0.718060\pi$
$72$	−2.30089			−0.271162
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	0.729651	−	0.683820i	$-0.239683\pi$
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	−0.957031	+	0.289986i	$0.906349\pi$
$74$	−2.82891	+	4.89982i	−0.328854	+	0.569592i
$75$	5.69049	+	9.85622i	0.657081	+	1.13810i
$76$	−0.981887	+	1.70068i	−0.112630	+	0.195081i
$77$	−6.64368	−	8.85034i	−0.757118	−	1.00859i
$78$	−2.92585	+	15.0885i	−0.331287	+	1.70844i
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	0.946353			0.105806
$81$	−10.6682			−1.18536
$82$	10.0284			1.10745
$83$	3.07390			0.337404			0.168702	−	0.985667i	$-0.446042\pi$
$83$	3.07390			0.337404			0.168702	+	0.985667i	$0.446042\pi$
$84$	−8.75383	+	1.05847i	−0.955121	+	0.115489i
$85$	0.0830210	+	0.143797i	0.00900489	+	0.0155969i
$86$	−4.94994	+	8.57354i	−0.533765	+	0.924509i
$87$	9.44997	−	16.3678i	1.01314	−	1.75482i
$88$	4.25324			0.453397
$89$	5.99207	+	10.3786i	0.635159	+	1.10013i	0.986482	+	0.163873i	$0.0523986\pi$
$89$	5.99207	+	10.3786i	0.635159	+	1.10013i	−0.351323	+	0.936254i	$0.614268\pi$
$90$	−0.829819			−0.0874706
$91$	0.678673	−	9.51522i	0.0711442	−	0.997466i
$92$	−5.97840			−0.623291
$93$	1.46901	+	2.54439i	0.152329	+	0.263841i
$94$	−21.6737			−2.23547
$95$	0.133392	−	0.231042i	0.0136858	−	0.0237045i
$96$	7.88721	−	13.6611i	0.804986	−	1.39428i
$97$	−9.73637	−	16.8639i	−0.988578	−	1.71227i	−0.624807	−	0.780779i	$-0.714822\pi$
$97$	−9.73637	−	16.8639i	−0.988578	−	1.71227i	−0.363771	−	0.931488i	$-0.618511\pi$
$98$	12.6323	−	3.10019i	1.27605	−	0.313167i
$99$	−9.46448			−0.951216
$100$	−7.20722			−0.720722
$101$	−16.9339			−1.68499			−0.842495	−	0.538704i	$-0.818914\pi$
$101$	−16.9339			−1.68499			−0.842495	+	0.538704i	$0.818914\pi$
$102$	3.58627			0.355094
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	−0.630952	−	0.775822i	$-0.717335\pi$
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	0.987357	+	0.158509i	$0.0506688\pi$
$104$	2.76809	+	2.40408i	0.271434	+	0.235739i
$105$	1.18923	−	0.143797i	0.116057	−	0.0140331i
$106$	−4.31833	+	7.47957i	−0.419434	+	0.726480i
$107$	4.92625	+	8.53251i	0.476238	+	0.824869i	0.999629	−	0.0272237i	$-0.00866664\pi$
$107$	4.92625	+	8.53251i	0.476238	+	0.824869i	−0.523391	+	0.852093i	$0.675333\pi$
$108$	1.22853	−	2.12788i	0.118216	−	0.204756i
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	1.53394			0.146255
$111$	−3.49255	−	6.04927i	−0.331498	−	0.574171i
$112$	−4.97847	+	11.6687i	−0.470421	+	1.10259i
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	0.948780	−	0.315938i	$-0.102319\pi$
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	−0.748000	+	0.663699i	$0.768986\pi$
$114$	−2.88109	−	4.99019i	−0.269839	−	0.467374i
$115$	0.812183			0.0757365
$116$	5.98437	+	10.3652i	0.555635	+	0.962388i
$117$	−6.15967	−	5.34965i	−0.569462	−	0.494575i
$118$	11.2569			1.03629
$119$	−2.20979	+	0.267197i	−0.202571	+	0.0244939i
$120$	−0.230197	+	0.398713i	−0.0210140	+	0.0363973i
$121$	6.49529			0.590481
$122$	10.5596	+	18.2898i	0.956026	+	1.65589i
$123$	−6.19049	+	10.7222i	−0.558178	+	0.966792i
$124$	−1.86055			−0.167082
$125$	1.96593			0.175839
$126$	4.36542	−	10.2318i	0.388903	−	0.911526i
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	−0.813339	−	0.581791i	$-0.802352\pi$
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	0.910515	+	0.413477i	$0.135686\pi$
$128$	−3.91516	−	6.78126i	−0.346055	−	0.599385i
$129$	−6.11114	−	10.5848i	−0.538056	−	0.931941i
$130$	0.998318	+	0.867035i	0.0875583	+	0.0760440i
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	−0.911450	−	0.411411i	$-0.865036\pi$
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	0.812017	+	0.583633i	$0.198369\pi$
$132$	6.96998	−	12.0724i	0.606659	−	1.05076i
$133$	2.14707	+	2.86020i	0.186174	+	0.248011i
$134$	−12.4469	−	21.5587i	−1.07525	−	1.86239i
$135$	−0.166900	+	0.289079i	−0.0143645	+	0.0248800i
$136$	0.427743	−	0.740873i	0.0366787	−	0.0635293i
$137$	−6.72399	+	11.6463i	−0.574469	+	0.995010i	0.421630	+	0.906768i	$0.361458\pi$
$137$	−6.72399	+	11.6463i	−0.574469	+	0.995010i	−0.996099	+	0.0882417i	$0.971875\pi$
$138$	8.77101	−	15.1918i	0.746638	−	1.29321i
$139$	−2.02270	−	3.50342i	−0.171563	−	0.297156i	0.767403	−	0.641165i	$-0.221548\pi$
$139$	−2.02270	−	3.50342i	−0.171563	−	0.297156i	−0.938966	+	0.344009i	$0.888215\pi$
$140$	−0.297691	+	0.697740i	−0.0251595	+	0.0589698i
$141$	13.3791	−	23.1733i	1.12672	−	1.95154i
$142$	5.54698	−	9.60765i	0.465492	−	0.806256i
$143$	11.3863	+	9.88894i	0.952169	+	0.826955i
$144$	5.42494	+	9.39628i	0.452079	+	0.783023i
$145$	−0.812996	−	1.40815i	−0.0675156	−	0.116940i
$146$	−3.60991	+	6.25255i	−0.298758	+	0.517465i
$147$	−4.48315	+	15.4200i	−0.369764	+	1.27182i
$148$	4.42344			0.363605
$149$	15.3519			1.25768			0.628840	−	0.777535i	$-0.283530\pi$
$149$	15.3519			1.25768			0.628840	+	0.777535i	$0.283530\pi$
$150$	10.5738	−	18.3144i	0.863351	−	1.49537i
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	−1.37454			−0.111490
$153$	−0.951831	+	1.64862i	−0.0769510	+	0.133283i
$154$	−8.06958	+	18.9138i	−0.650265	+	1.52412i
$155$	0.252762			0.0203023
$156$	11.3599	−	3.91726i	0.909521	−	0.313632i
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	0.761199	−	0.648518i	$-0.224611\pi$
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	−0.942233	+	0.334959i	$0.891278\pi$
$158$	−19.9443			−1.58669
$159$	−5.33137	−	9.23421i	−0.422805	−	0.732320i
$160$	−0.678549	−	1.17528i	−0.0536440	−	0.0929142i
$161$	−4.27265	+	10.0144i	−0.336732	+	0.789245i
$162$	9.91163	+	17.1674i	0.778731	+	1.34880i
$163$	1.82254			0.142752			0.0713762	−	0.997449i	$-0.477261\pi$
$163$	1.82254			0.142752			0.0713762	+	0.997449i	$0.477261\pi$
$164$	−3.92025	−	6.79007i	−0.306120	−	0.530215i
$165$	−0.946893	+	1.64007i	−0.0737155	+	0.127679i
$166$	−2.85590	−	4.94656i	−0.221661	−	0.383928i
$167$	5.35397	−	9.27336i	0.414303	−	0.717594i	−0.581052	−	0.813866i	$-0.697359\pi$
$167$	5.35397	−	9.27336i	0.414303	−	0.717594i	0.995355	+	0.0962726i	$0.0306921\pi$
$168$	−3.70522	−	4.93588i	−0.285864	−	0.380812i
$169$	1.82086	+	12.8718i	0.140066	+	0.990142i
$170$	0.154266	−	0.267197i	0.0118317	−	0.0204931i
$171$	3.05867			0.233903
$172$	7.74000			0.590169
$173$	−13.4927			−1.02583			−0.512915	−	0.858439i	$-0.671434\pi$
$173$	−13.4927			−1.02583			−0.512915	+	0.858439i	$0.671434\pi$
$174$	−35.1191			−2.66237
$175$	−5.15087	+	12.0728i	−0.389369	+	0.912618i
$176$	−10.0281	−	17.3692i	−0.755898	−	1.30925i
$177$	−6.94886	+	12.0358i	−0.522308	+	0.904664i
$178$	11.1342	−	19.2851i	0.834547	−	1.44548i
$179$	10.4692			0.782502			0.391251	−	0.920284i	$-0.372042\pi$
$179$	10.4692			0.782502			0.391251	+	0.920284i	$0.372042\pi$
$180$	0.324388	+	0.561857i	0.0241785	+	0.0418783i
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$	−15.9426	+	7.74828i	−1.18174	+	0.574340i
$183$	−26.0737			−1.92742
$184$	−2.09228	−	3.62393i	−0.154245	−	0.267160i
$185$	−0.600938			−0.0441819
$186$	2.72965	−	4.72789i	0.200148	−	0.346666i
$187$	1.75948	−	3.04751i	0.128666	−	0.222856i
$188$	8.47256	+	14.6749i	0.617925	+	1.07028i
$189$	−2.68640	−	3.57867i	−0.195407	−	0.260310i
$190$	−0.495729			−0.0359640
$191$	13.1137			0.948874			0.474437	−	0.880290i	$-0.342652\pi$
$191$	13.1137			0.948874			0.474437	+	0.880290i	$0.342652\pi$
$192$	−7.31129			−0.527647
$193$	1.04157			0.0749740			0.0374870	−	0.999297i	$-0.488065\pi$
$193$	1.04157			0.0749740			0.0374870	+	0.999297i	$0.488065\pi$
$194$	−18.0917	+	31.3358i	−1.29891	+	2.24978i
$195$	−1.54328	+	0.532172i	−0.110517	+	0.0381096i
$196$	−7.03722	−	7.34118i	−0.502658	−	0.524370i
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	−0.891155	−	0.453698i	$-0.850104\pi$
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	0.838492	+	0.544914i	$0.183438\pi$
$198$	8.79326	+	15.2304i	0.624910	+	1.08238i
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	−1.00000		0.000281618i	$-0.999910\pi$
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	0.500244	+	0.865885i	$0.333244\pi$
$200$	−2.52233	−	4.36881i	−0.178356	−	0.308922i
$201$	30.7337			2.16779
$202$	15.7330	+	27.2503i	1.10697	+	1.91733i
$203$	21.6397	−	2.61657i	1.51881	−	0.183647i
$204$	−1.40192	−	2.42820i	−0.0981543	−	0.170008i
$205$	0.532578	+	0.922451i	0.0371968	+	0.0644268i
$206$	−13.4424			−0.936576
$207$	4.65582	+	8.06412i	0.323602	+	0.560495i
$208$	3.29118	−	16.9725i	0.228202	−	1.17683i
$209$	−5.65402			−0.391097
$210$	−1.33629	−	1.78014i	−0.0922131	−	0.122841i
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.0986067	+	0.995126i	$0.531439\pi$
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.812501	+	0.582959i	$0.801895\pi$
$212$	6.75239			0.463756
$213$	6.84825	+	11.8615i	0.469234	+	0.812737i
$214$	9.15376	−	15.8548i	0.625738	−	1.08381i
$215$	−1.05150			−0.0717119
$216$	1.71981			0.117019
$217$	−1.32970	+	3.11661i	−0.0902660	+	0.211569i
$218$	12.8361	−	22.2328i	0.869370	−	1.50579i
$219$	−4.45676	−	7.71934i	−0.301160	−	0.521625i
$220$	−0.599638	−	1.03860i	−0.0404276	−	0.0700227i
$221$	2.86766	−	0.988862i	0.192900	−	0.0665180i
$222$	−6.48971	+	11.2405i	−0.435561	+	0.754414i
$223$	0.364024	−	0.630508i	0.0243769	−	0.0422219i	−0.853580	−	0.520962i	$-0.825573\pi$
$223$	0.364024	−	0.630508i	0.0243769	−	0.0422219i	0.877956	+	0.478740i	$0.158907\pi$
$224$	18.0611	−	2.18386i	1.20676	−	0.145916i
$225$	5.61280	+	9.72165i	0.374187	+	0.648110i
$226$	3.96591	−	6.86916i	0.263808	−	0.456929i
$227$	1.42598	−	2.46986i	0.0946454	−	0.163931i	−0.814815	−	0.579721i	$-0.803162\pi$
$227$	1.42598	−	2.46986i	0.0946454	−	0.163931i	0.909461	+	0.415790i	$0.136495\pi$
$228$	−2.25252	+	3.90147i	−0.149177	+	0.258381i
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	−0.913679	−	0.406436i	$-0.866772\pi$
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	0.808823	+	0.588052i	$0.200105\pi$
$230$	−0.754584	−	1.30698i	−0.0497558	−	0.0861795i
$231$	−15.2411	−	20.3033i	−1.00279	−	1.33586i
$232$	−4.18874	+	7.25511i	−0.275004	+	0.476321i
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	−0.997625	−	0.0688769i	$-0.978058\pi$
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	0.558462	+	0.829530i	$0.311392\pi$
$234$	−2.88590	+	14.8825i	−0.188657	+	0.972899i
$235$	−1.15102	−	1.99363i	−0.0750845	−	0.130050i
$236$	−4.40050	−	7.62188i	−0.286448	−	0.496142i
$237$	12.3115	−	21.3242i	0.799721	−	1.38516i
$238$	2.48305	+	3.30778i	0.160952	+	0.214411i
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	2.17100			0.140137
$241$	3.78787	−	6.56078i	0.243998	−	0.422617i	−0.717851	−	0.696196i	$-0.754874\pi$
$241$	3.78787	−	6.56078i	0.243998	−	0.422617i	0.961849	+	0.273579i	$0.0882076\pi$
$242$	−6.03465	−	10.4523i	−0.387922	−	0.671900i
$243$	−19.3997			−1.24449
$244$	8.25583	−	14.2995i	0.528525	−	0.915433i
$245$	0.956028	+	0.997322i	0.0610784	+	0.0637166i
$246$	23.0059			1.46680
$247$	−3.67975	−	3.19585i	−0.234137	−	0.203347i
$248$	−0.651143	−	1.12781i	−0.0413476	−	0.0716162i
$249$	7.05173			0.446885
$250$	−1.82651	−	3.16361i	−0.115519	−	0.200084i
$251$	−0.637382	−	1.10398i	−0.0402312	−	0.0696825i	0.845209	−	0.534436i	$-0.179476\pi$
$251$	−0.637382	−	1.10398i	−0.0402312	−	0.0696825i	−0.885440	+	0.464754i	$0.846143\pi$
$252$	−8.63432	+	1.04402i	−0.543911	+	0.0657671i
$253$	−8.60638	−	14.9067i	−0.541079	−	0.937176i
$254$	−4.06982			−0.255363
$255$	0.190456	+	0.329879i	0.0119268	+	0.0206578i
$256$	−10.4620	+	18.1208i	−0.653878	+	1.13255i
$257$	4.24010	+	7.34406i	0.264490	+	0.458110i	0.967430	−	0.253139i	$-0.0814631\pi$
$257$	4.24010	+	7.34406i	0.264490	+	0.458110i	−0.702940	+	0.711249i	$0.748130\pi$
$258$	−11.3555	+	19.6683i	−0.706962	+	1.22449i
$259$	3.16135	−	7.40970i	0.196437	−	0.460416i
$260$	0.196798	−	1.01488i	0.0122049	−	0.0629402i
$261$	9.32095	−	16.1444i	0.576952	−	0.999311i
$262$	4.22939			0.261293
$263$	12.7883			0.788560			0.394280	−	0.918990i	$-0.370994\pi$
$263$	12.7883			0.788560			0.394280	+	0.918990i	$0.370994\pi$
$264$	9.75722			0.600515
$265$	−0.917333			−0.0563513
$266$	2.60788	−	6.11245i	0.159899	−	0.374778i
$267$	13.7462	+	23.8092i	0.841255	+	1.45710i
$268$	−9.73135	+	16.8552i	−0.594437	+	1.02959i
$269$	2.35586	−	4.08047i	0.143639	−	0.248790i	−0.785225	−	0.619210i	$-0.787453\pi$
$269$	2.35586	−	4.08047i	0.143639	−	0.248790i	0.928864	+	0.370420i	$0.120786\pi$
$270$	0.620254			0.0377475
$271$	9.00562	+	15.5982i	0.547052	+	0.947522i	0.998475	+	0.0552119i	$0.0175834\pi$
$271$	9.00562	+	15.5982i	0.547052	+	0.947522i	−0.451422	+	0.892310i	$0.649083\pi$
$272$	−4.03407			−0.244601
$273$	1.55692	−	21.8286i	0.0942292	−	1.32112i
$274$	24.9885			1.50961
$275$	−10.3754	−	17.9707i	−0.625659	−	1.08367i
$276$	−13.7148			−0.825537
$277$	13.0604	−	22.6213i	0.784725	−	1.35918i	−0.144438	−	0.989514i	$-0.546137\pi$
$277$	13.0604	−	22.6213i	0.784725	−	1.35918i	0.929163	−	0.369670i	$-0.120529\pi$
$278$	−3.75850	+	6.50991i	−0.225420	+	0.390439i
$279$	1.44895	+	2.50965i	0.0867463	+	0.150249i
$280$	−0.527133	+	0.0637384i	−0.0315022	+	0.00380910i
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	−49.7210			−2.96084
$283$	7.64527			0.454464			0.227232	−	0.973841i	$-0.427032\pi$
$283$	7.64527			0.454464			0.227232	+	0.973841i	$0.427032\pi$
$284$	−8.67357			−0.514682
$285$	0.306011	−	0.530027i	0.0181265	−	0.0313961i
$286$	5.33465	−	27.5106i	0.315445	−	1.62674i
$287$	−14.1757	+	1.71406i	−0.836768	+	0.101178i
$288$	7.77953	−	13.4745i	0.458413	−	0.793995i
$289$	8.14610	+	14.1095i	0.479183	+	0.829968i
$290$	−1.51068	+	2.61657i	−0.0887100	+	0.153650i
$291$	−22.3359	−	38.6869i	−1.30935	−	2.26787i
$292$	5.64466			0.330329
$293$	8.57670	+	14.8553i	0.501056	+	0.867855i	0.999999	+	0.00122001i	$0.000388343\pi$
$293$	8.57670	+	14.8553i	0.501056	+	0.867855i	−0.498943	+	0.866635i	$0.666278\pi$
$294$	28.9793	−	7.11205i	1.69011	−	0.414783i
$295$	0.597821	+	1.03546i	0.0348065	+	0.0602866i
$296$	1.54809	+	2.68136i	0.0899807	+	0.155851i
$297$	7.07429			0.410492
$298$	−14.2632	−	24.7045i	−0.826244	−	1.43110i
$299$	2.82457	−	14.5662i	0.163349	−	0.842385i
$300$	−16.5339			−0.954583
$301$	5.53163	−	12.9652i	0.318838	−	0.747305i
$302$	−5.68698	+	9.85014i	−0.327249	+	0.566812i
$303$	−38.8476			−2.23174
$304$	3.24083	+	5.61328i	0.185874	+	0.321944i
$305$	−1.12158	+	1.94263i	−0.0642215	+	0.111235i
$306$	3.53731			0.202215
$307$	−28.0696			−1.60201			−0.801007	−	0.598655i	$-0.795702\pi$
$307$	−28.0696			−1.60201			−0.801007	+	0.598655i	$0.795702\pi$
$308$	15.9607	−	1.92989i	0.909446	−	0.109966i
$309$	8.29793	−	14.3724i	0.472052	−	0.817619i
$310$	−0.234836	−	0.406748i	−0.0133378	−	0.0231017i
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	0.978671	+	0.205436i	$0.0658611\pi$
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	−0.311423	+	0.950271i	$0.600806\pi$
$312$	6.35020	+	5.51512i	0.359509	+	0.312232i
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	−0.814820	−	0.579714i	$-0.803164\pi$
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	0.909457	+	0.415798i	$0.136498\pi$
$314$	−4.21494	+	7.30050i	−0.237863	+	0.411991i
$315$	1.17300	−	0.141833i	0.0660910	−	0.00799140i
$316$	7.79652	+	13.5040i	0.438588	+	0.759658i
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	−0.745544	−	0.666456i	$-0.767810\pi$
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	0.949940	+	0.312432i	$0.101144\pi$
$318$	−9.90655	+	17.1586i	−0.555532	+	0.962209i
$319$	−17.2300	+	29.8432i	−0.964694	+	1.67090i
$320$	−0.314501	+	0.544732i	−0.0175811	+	0.0304514i
$321$	11.3011	+	19.5742i	0.630768	+	1.09252i
$322$	20.0849	−	2.42857i	1.11929	−	0.135339i
$323$	−0.568618	+	0.984875i	−0.0316388	+	0.0547999i
$324$	7.74919	−	13.4220i	0.430511	−	0.745666i
$325$	3.40514	−	17.5602i	0.188883	−	0.974065i
$326$	−1.69329	−	2.93286i	−0.0937826	−	0.162436i
$327$	15.8473	+	27.4484i	0.876359	+	1.51790i
$328$	2.74396	−	4.75268i	0.151510	−	0.262423i
$329$	30.6371	−	3.70449i	1.68908	−	0.204235i
$330$	3.51896			0.193712
$331$	−14.3234			−0.787283			−0.393642	−	0.919264i	$-0.628785\pi$
$331$	−14.3234			−0.787283			−0.393642	+	0.919264i	$0.628785\pi$
$332$	−2.23282	+	3.86736i	−0.122542	+	0.212249i
$333$	−3.44486	−	5.96668i	−0.188777	−	0.326972i
$334$	−19.8971			−1.08872
$335$	1.32203	−	2.28983i	0.0722304	−	0.125107i
$336$	−11.4210	+	26.7689i	−0.623064	+	1.46036i
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	19.0218	−	14.8891i	1.03465	−	0.809862i
$339$	4.89627	+	8.48060i	0.265929	+	0.460603i
$340$	−0.241220			−0.0130820
$341$	−2.67841	−	4.63915i	−0.145044	−	0.251224i
$342$	−2.84175	−	4.92206i	−0.153664	−	0.266155i
$343$	−17.3266	+	6.54142i	−0.935547	+	0.353203i
$344$	2.70879	+	4.69176i	0.146048	+	0.252963i
$345$	1.86320			0.100312
$346$	12.5358	+	21.7126i	0.673928	+	1.16728i
$347$	3.85139	−	6.67080i	0.206753	−	0.358107i	−0.743937	−	0.668250i	$-0.767044\pi$
$347$	3.85139	−	6.67080i	0.206753	−	0.358107i	0.950690	+	0.310143i	$0.100377\pi$
$348$	13.7286	+	23.7786i	0.735928	+	1.27466i
$349$	−11.1850	+	19.3730i	−0.598721	+	1.03702i	0.394289	+	0.918986i	$0.370991\pi$
$349$	−11.1850	+	19.3730i	−0.598721	+	1.03702i	−0.993010	+	0.118029i	$0.962343\pi$
$350$	24.2133	−	2.92776i	1.29426	−	0.156495i
$351$	4.60409	+	3.99863i	0.245748	+	0.213431i
$352$	−14.3806	+	24.9080i	−0.766490	+	1.32760i
$353$	−22.2623			−1.18490			−0.592451	−	0.805606i	$-0.701840\pi$
$353$	−22.2623			−1.18490			−0.592451	+	0.805606i	$0.701840\pi$
$354$	25.8242			1.37254
$355$	1.17833			0.0625393
$356$	−17.4101			−0.922735
$357$	−5.06941	+	0.612968i	−0.268301	+	0.0324417i
$358$	−9.72670	−	16.8471i	−0.514072	−	0.890399i
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	−0.827332	−	0.561713i	$-0.810142\pi$
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	0.900124	+	0.435634i	$0.143476\pi$
$360$	−0.227054	+	0.393269i	−0.0119668	+	0.0207271i
$361$	−17.1728			−0.903830
$362$	−11.6330	−	20.1489i	−0.611415	−	1.05900i
$363$	14.9006			0.782081
$364$	11.4784	+	7.76553i	0.601632	+	0.407025i
$365$	−0.766844			−0.0401385
$366$	24.2246	+	41.9582i	1.26624	+	2.19319i
$367$	−14.1497			−0.738609			−0.369304	−	0.929308i	$-0.620404\pi$
$367$	−14.1497			−0.738609			−0.369304	+	0.929308i	$0.620404\pi$
$368$	−9.86618	+	17.0887i	−0.514310	+	0.890812i
$369$	−6.10597	+	10.5759i	−0.317864	+	0.550557i
$370$	0.558320	+	0.967039i	0.0290257	+	0.0502740i
$371$	4.82580	−	11.3109i	0.250543	−	0.587233i
$372$	−4.26823			−0.221298
$373$	−5.04284			−0.261109			−0.130554	−	0.991441i	$-0.541676\pi$
$373$	−5.04284			−0.261109			−0.130554	+	0.991441i	$0.541676\pi$
$374$	−6.53879			−0.338113
$375$	4.50999			0.232895
$376$	−5.93034	+	10.2716i	−0.305834	+	0.529720i
$377$	−28.0820	+	9.68358i	−1.44630	+	0.498730i
$378$	−3.26297	+	7.64787i	−0.167829	+	0.393364i
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	−0.777657	−	0.628688i	$-0.783592\pi$
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	0.933289	+	0.359127i	$0.116925\pi$
$380$	0.193787	+	0.335650i	0.00994109	+	0.0172185i
$381$	2.51228	−	4.35139i	0.128708	−	0.222929i
$382$	−12.1837	−	21.1028i	−0.623371	−	1.07971i
$383$	−4.54105			−0.232037			−0.116018	−	0.993247i	$-0.537013\pi$
$383$	−4.54105			−0.232037			−0.116018	+	0.993247i	$0.537013\pi$
$384$	−8.98165	−	15.5567i	−0.458343	−	0.793873i
$385$	−2.16831	+	0.262182i	−0.110507	+	0.0133620i
$386$	−0.967705	−	1.67611i	−0.0492549	−	0.0853120i
$387$	−6.02771	−	10.4403i	−0.306406	−	0.530710i
$388$	28.2893			1.43617
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	0.803216	−	0.595688i	$-0.203121\pi$
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	−0.917489	+	0.397761i	$0.869787\pi$
$390$	2.29021	+	1.98904i	0.115969	+	0.100719i
$391$	−3.46213			−0.175088
$392$	1.98718	−	6.83498i	0.100368	−	0.345218i
$393$	−2.61078	+	4.52201i	−0.131697	+	0.228105i
$394$	2.74698			0.138391
$395$	−1.05918	−	1.83456i	−0.0532932	−	0.0923065i
$396$	6.87482	−	11.9075i	0.345473	−	0.598376i
$397$	4.00349			0.200929			0.100465	−	0.994941i	$-0.467967\pi$
$397$	4.00349			0.200929			0.100465	+	0.994941i	$0.467967\pi$
$398$	26.1998			1.31328
$399$	4.92552	+	6.56149i	0.246584	+	0.328485i
$400$	−11.8941	+	20.6012i	−0.594706	+	1.03006i
$401$	−6.30674	−	10.9236i	−0.314944	−	0.545498i	0.664482	−	0.747304i	$-0.268652\pi$
$401$	−6.30674	−	10.9236i	−0.314944	−	0.545498i	−0.979426	+	0.201806i	$0.935319\pi$
$402$	−28.5541	−	49.4571i	−1.42415	−	2.46670i
$403$	0.879041	−	4.53318i	0.0437882	−	0.225814i
$404$	12.3005	−	21.3051i	0.611972	−	1.05997i
$405$	−1.05275	+	1.82342i	−0.0523116	+	0.0906064i
$406$	−24.3157	−	32.3919i	−1.20677	−	1.60758i
$407$	6.36790	+	11.0295i	0.315645	+	0.546713i
$408$	0.981272	−	1.69961i	0.0485802	−	0.0841434i
$409$	−10.3476	+	17.9226i	−0.511657	+	0.886216i	0.488252	+	0.872703i	$0.337635\pi$
$409$	−10.3476	+	17.9226i	−0.511657	+	0.886216i	−0.999909	+	0.0135128i	$0.995699\pi$
$410$	0.989615	−	1.71406i	0.0488736	−	0.0846516i
$411$	−15.4253	+	26.7174i	−0.760873	+	1.31787i
$412$	5.25482	+	9.10162i	0.258886	+	0.448404i
$413$	−15.9123	+	1.92404i	−0.782995	+	0.0946760i
$414$	8.65126	−	14.9844i	0.425186	−	0.736444i
$415$	0.303336	−	0.525393i	0.0148902	−	0.0257905i
$416$	−23.4381	+	8.08219i	−1.14915	+	0.396262i
$417$	−4.64021	−	8.03708i	−0.227232	−	0.393577i
$418$	5.25304	+	9.09854i	0.256935	+	0.445024i
$419$	10.9088	−	18.8945i	0.532928	−	0.923058i	−0.466333	−	0.884609i	$-0.654425\pi$
$419$	10.9088	−	18.8945i	0.532928	−	0.923058i	0.999261	−	0.0384484i	$-0.0122415\pi$
$420$	−0.682923	+	1.60066i	−0.0333232	+	0.0781043i
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	49.1841			2.39424
$423$	13.1964	−	22.8569i	0.641632	−	1.11134i
$424$	2.36315	+	4.09310i	0.114765	+	0.198779i
$425$	−4.17376			−0.202457
$426$	12.7251	−	22.0406i	0.616535	−	1.06787i
$427$	−18.0528	−	24.0489i	−0.873636	−	1.16381i
$428$	−14.3133			−0.691861
$429$	26.1209	+	22.6859i	1.26113	+	1.09529i
$430$	0.976930	+	1.69209i	0.0471118	+	0.0816000i
$431$	20.4275			0.983960			0.491980	−	0.870607i	$-0.336273\pi$
$431$	20.4275			0.983960			0.491980	+	0.870607i	$0.336273\pi$
$432$	−4.05491	−	7.02332i	−0.195092	−	0.337909i
$433$	−13.1743	−	22.8186i	−0.633117	−	1.09659i	−0.986911	−	0.161267i	$-0.948442\pi$
$433$	−13.1743	−	22.8186i	−0.633117	−	1.09659i	0.353794	−	0.935323i	$-0.384891\pi$
$434$	6.25069	−	0.755803i	0.300043	−	0.0362797i
$435$	−1.86507	−	3.23039i	−0.0894231	−	0.154885i
$436$	−20.0712			−0.961238
$437$	2.78136	+	4.81745i	0.133050	+	0.230450i
$438$	−8.28138	+	14.3438i	−0.395700	+	0.685372i
$439$	−12.5655	−	21.7641i	−0.599720	−	1.03875i	−0.992862	−	0.119267i	$-0.961945\pi$
$439$	−12.5655	−	21.7641i	−0.599720	−	1.03875i	0.393142	−	0.919478i	$-0.371388\pi$
$440$	0.419714	−	0.726967i	0.0200091	−	0.0346568i
$441$	−4.42195	+	15.2095i	−0.210569	+	0.724260i
$442$	−4.25558	−	3.69595i	−0.202417	−	0.175799i
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	−0.997685	−	0.0679994i	$-0.978338\pi$
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	0.557732	+	0.830021i	$0.311672\pi$
$444$	10.1477			0.481587
$445$	2.36522			0.112122
$446$	−1.35283			−0.0640584
$447$	35.2184			1.66577
$448$	−5.06216	−	6.74353i	−0.239165	−	0.318602i
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	0.695333	−	0.718688i	$-0.255257\pi$
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	−0.970068	+	0.242832i	$0.921924\pi$
$450$	10.4295	−	18.0644i	0.491651	−	0.851564i
$451$	11.2870	−	19.5497i	0.531485	−	0.920559i
$452$	−6.20132			−0.291685
$453$	−7.02109	−	12.1609i	−0.329880	−	0.571368i
$454$	−5.29939			−0.248713
$455$	−1.55938	−	1.05497i	−0.0731047	−	0.0494578i
$456$	−3.15328			−0.147666
$457$	−10.2592	−	17.7695i	−0.479906	−	0.831222i	0.519828	−	0.854271i	$-0.325996\pi$
$457$	−10.2592	−	17.7695i	−0.479906	−	0.831222i	−0.999734	+	0.0230490i	$0.992663\pi$
$458$	5.89691			0.275544
$459$	0.711453	−	1.23227i	0.0332078	−	0.0575176i
$460$	−0.589955	+	1.02183i	−0.0275068	+	0.0476431i
$461$	−1.02038	−	1.76734i	−0.0475236	−	0.0823134i	0.841285	−	0.540592i	$-0.181800\pi$
$461$	−1.02038	−	1.76734i	−0.0475236	−	0.0823134i	−0.888809	+	0.458278i	$0.848466\pi$
$462$	−18.5122	+	43.3895i	−0.861264	+	2.01866i
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	39.5042			1.83394
$465$	0.579853			0.0268900
$466$	24.9125			1.15405
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	−0.676827	−	0.736142i	$-0.736645\pi$
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	0.975931	+	0.218078i	$0.0699787\pi$
$468$	11.2048	−	3.86378i	0.517943	−	0.178603i
$469$	21.2793	+	28.3470i	0.982585	+	1.30894i
$470$	−2.13879	+	3.70449i	−0.0986549	+	0.170875i
$471$	−5.20373	−	9.01312i	−0.239775	−	0.415303i
$472$	3.08011	−	5.33491i	0.141774	−	0.245559i
$473$	11.1423	+	19.2991i	0.512326	+	0.887374i
$474$	−45.7537			−2.10153
$475$	3.35305	+	5.80766i	0.153849	+	0.266474i
$476$	1.26898	−	2.97429i	0.0581637	−	0.136326i
$477$	−5.25858	−	9.10814i	−0.240774	−	0.417033i
$478$	14.4507	+	25.0294i	0.660962	+	1.14482i
$479$	36.5821			1.67148			0.835740	−	0.549126i	$-0.185039\pi$
$479$	36.5821			1.67148			0.835740	+	0.549126i	$0.185039\pi$
$480$	−1.55664	−	2.69618i	−0.0710505	−	0.123063i
$481$	−2.08991	+	10.7776i	−0.0952918	+	0.491416i
$482$	−14.0769			−0.641187
$483$	−9.80174	+	22.9737i	−0.445995	+	1.04534i
$484$	−4.71806	+	8.17191i	−0.214457	+	0.371451i
$485$	−3.84318			−0.174510
$486$	18.0239	+	31.2183i	0.817580	+	1.41609i
$487$	−18.3748	+	31.8261i	−0.832642	+	1.44218i	0.0632939	+	0.997995i	$0.479839\pi$
$487$	−18.3748	+	31.8261i	−0.832642	+	1.44218i	−0.895936	+	0.444183i	$0.853494\pi$
$488$	11.5573			0.523173
$489$	4.18103			0.189073
$490$	0.716679	−	2.46505i	0.0323763	−	0.111359i
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	−0.758587	−	0.651572i	$-0.774110\pi$
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$492$	−8.99331	−	15.5769i	−0.405450	−	0.702260i
$493$	3.46560	+	6.00259i	0.156083	+	0.270343i
$494$	−1.72402	+	8.89071i	−0.0775673	+	0.400012i
$495$	−0.933965	+	1.61768i	−0.0419786	+	0.0727091i
$496$	−3.07048	+	5.31823i	−0.137869	+	0.238795i
$497$	−6.19883	+	14.5291i	−0.278056	+	0.651718i
$498$	−6.55163	−	11.3478i	−0.293585	−	0.508505i
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	−1.42802	+	2.47340i	−0.0638629	+	0.110614i
$501$	12.2824	−	21.2737i	0.548736	−	0.950439i
$502$	−1.18436	+	2.05137i	−0.0528605	+	0.0915571i
$503$	−0.00909609	−	0.0157549i	−0.000405575	−	0.000702476i	0.865823	−	0.500351i	$-0.166796\pi$
$503$	−0.00909609	−	0.0157549i	−0.000405575	−	0.000702476i	−0.866228	+	0.499649i	$0.833462\pi$
$504$	−3.65463	−	4.86849i	−0.162790	−	0.216860i
$505$	−1.67106	+	2.89436i	−0.0743612	+	0.128797i
$506$	−15.9920	+	27.6990i	−0.710933	+	1.23137i
$507$	4.17717	+	29.5289i	0.185515	+	1.31142i
$508$	1.59095	+	2.75560i	0.0705869	+	0.122260i
$509$	−21.5503	−	37.3262i	−0.955200	−	1.65446i	−0.733909	−	0.679248i	$-0.762306\pi$
$509$	−21.5503	−	37.3262i	−0.955200	−	1.65446i	−0.221292	−	0.975208i	$-0.571027\pi$
$510$	0.353897	−	0.612968i	0.0156708	−	0.0271427i
$511$	4.03413	−	9.45535i	0.178459	−	0.418280i
$512$	23.2197			1.02617
$513$	−2.28623			−0.100939
$514$	7.87878	−	13.6464i	0.347518	−	0.601919i
$515$	−0.713884	−	1.23648i	−0.0314575	−	0.0544859i
$516$	17.7561			0.781668
$517$	−24.3939	+	42.2514i	−1.07284	+	1.85822i
$518$	−14.8609	+	1.79691i	−0.652952	+	0.0789519i
$519$	−30.9531			−1.35869
$520$	0.684065	−	0.235888i	0.0299983	−	0.0103444i
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	0.539903	−	0.841727i	$-0.318461\pi$
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	−0.998909	+	0.0467056i	$0.985128\pi$
$522$	−34.6397			−1.51614
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	0.943084	+	0.332555i	$0.107911\pi$
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	−0.183541	+	0.983012i	$0.558756\pi$
$524$	−1.65333	−	2.86365i	−0.0722260	−	0.125099i
$525$	−11.8164	+	27.6958i	−0.515712	+	1.20875i
$526$	−11.8814	−	20.5791i	−0.518052	−	0.897292i
$527$	−1.07746			−0.0469349
$528$	−23.0052	−	39.8462i	−1.00117	−	1.73408i
$529$	3.03260	−	5.25262i	0.131852	−	0.228375i
$530$	0.852276	+	1.47619i	0.0370205	+	0.0641214i
$531$	−6.85398	+	11.8714i	−0.297438	+	0.515177i
$532$	−5.15809	+	0.623691i	−0.223631	+	0.0270404i
$533$	18.3960	−	6.34352i	0.796819	−	0.274769i
$534$	25.5427	−	44.2413i	1.10534	−	1.91451i
$535$	1.94451			0.0840685
$536$	−13.6228			−0.588417
$537$	24.0170			1.03641
$538$	−8.75513			−0.377460
$539$	8.17406	−	28.1150i	0.352082	−	1.21100i
$540$	−0.242466	−	0.419964i	−0.0104341	−	0.0180724i
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	16.7339	−	28.9839i	0.718782	−	1.24497i
$543$	28.7239			1.23266
$544$	2.89249	+	5.00993i	0.124014	+	0.214799i
$545$	2.72674			0.116801
$546$	−36.5733	+	17.7751i	−1.56519	+	0.760703i
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	−9.76836	−	16.9193i	−0.417284	−	0.722756i
$549$	−25.7177			−1.09761
$550$	−19.2791	+	33.3924i	−0.822065	+	1.42386i
$551$	5.56828	−	9.64455i	0.237217	−	0.410871i
$552$	−4.79983	−	8.31354i	−0.204294	−	0.353848i
$553$	28.1925	−	3.40890i	1.19887	−	0.144961i
$554$	−48.5368			−2.06213
$555$	−1.37859			−0.0585180
$556$	5.87700			0.249240
$557$	−14.2866			−0.605342			−0.302671	−	0.953095i	$-0.597878\pi$
$557$	−14.2866			−0.605342			−0.302671	+	0.953095i	$0.597878\pi$
$558$	2.69238	−	4.66334i	0.113978	−	0.197415i
$559$	−3.65686	+	18.8583i	−0.154669	+	0.797621i
$560$	1.50315	+	2.00241i	0.0635196	+	0.0846172i
$561$	4.03637	−	6.99119i	0.170416	−	0.295168i
$562$	3.40226	+	5.89289i	0.143516	+	0.248577i
$563$	−3.39392	+	5.87844i	−0.143037	+	0.247747i	−0.928639	−	0.370985i	$-0.879020\pi$
$563$	−3.39392	+	5.87844i	−0.143037	+	0.247747i	0.785602	+	0.618732i	$0.212353\pi$
$564$	19.4366	+	33.6652i	0.818430	+	1.41756i
$565$	0.842468			0.0354429
$566$	−7.10307	−	12.3029i	−0.298564	−	0.517128i
$567$	−16.9449	−	22.5731i	−0.711621	−	0.947981i
$568$	−3.03552	−	5.25767i	−0.127367	−	0.220607i
$569$	8.66061	+	15.0006i	0.363072	+	0.628859i	0.988465	−	0.151451i	$-0.0483947\pi$
$569$	8.66061	+	15.0006i	0.363072	+	0.628859i	−0.625393	+	0.780310i	$0.715061\pi$
$570$	−1.13724			−0.0476336
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$	−20.7124	+	7.14228i	−0.866027	+	0.298634i
$573$	30.0837			1.25676
$574$	15.9287	+	21.2193i	0.664851	+	0.885677i
$575$	−10.2078	+	17.6805i	−0.425696	+	0.737327i
$576$	−7.21147			−0.300478
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	0.873539	−	0.486755i	$-0.161820\pi$
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	−0.858311	+	0.513129i	$0.828486\pi$
$578$	15.1368	−	26.2177i	0.629607	−	1.09051i
$579$	2.38944			0.0993017
$580$	2.36218			0.0980842
$581$	4.88245	+	6.50412i	0.202558	+	0.269837i
$582$	−41.5037	+	71.8865i	−1.72038	+	2.97979i
$583$	9.72061	+	16.8366i	0.402586	+	0.697300i
$584$	1.97548	+	3.42163i	0.0817459	+	0.141588i
$585$	−1.52221	+	0.524907i	−0.0629356	+	0.0217022i
$586$	15.9369	−	27.6035i	0.658347	−	1.14029i
$587$	4.26142	−	7.38099i	0.175888	−	0.304646i	−0.764581	−	0.644528i	$-0.777054\pi$
$587$	4.26142	−	7.38099i	0.175888	−	0.304646i	0.940468	+	0.339882i	$0.110387\pi$
$588$	−16.1439	−	16.8412i	−0.665761	−	0.694518i
$589$	0.865594	+	1.49925i	0.0356662	+	0.0617756i
$590$	1.11085	−	1.92404i	0.0457329	−	0.0792117i
$591$	−1.69570	+	2.93704i	−0.0697517	+	0.120814i
$592$	7.30004	−	12.6440i	0.300030	−	0.519667i
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	−0.341932	−	0.939725i	$-0.611081\pi$
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	0.984791	−	0.173741i	$-0.0555854\pi$
$594$	−6.57259	−	11.3841i	−0.269677	−	0.467093i
$595$	−0.172395	+	0.404066i	−0.00706751	+	0.0165651i
$596$	−11.1514	+	19.3147i	−0.456777	+	0.791161i
$597$	−16.1730	+	28.0125i	−0.661917	+	1.14647i
$598$	−26.0644	+	8.98784i	−1.06585	+	0.367540i
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	0.873587	−	0.486668i	$-0.161788\pi$
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	−0.858260	+	0.513215i	$0.828454\pi$
$600$	−5.78641	−	10.0224i	−0.236229	−	0.409161i
$601$	4.77652	−	8.27318i	0.194838	−	0.337470i	−0.752009	−	0.659153i	$-0.770915\pi$
$601$	4.77652	−	8.27318i	0.194838	−	0.337470i	0.946848	+	0.321683i	$0.104248\pi$
$602$	−26.0032	+	3.14418i	−1.05981	+	0.128147i
$603$	30.3141			1.23449
$604$	8.89248			0.361830
$605$	0.640963	−	1.11018i	0.0260588	−	0.0451352i
$606$	36.0925	+	62.5141i	1.46616	+	2.53946i
$607$	22.2395			0.902672			0.451336	−	0.892354i	$-0.350948\pi$
$607$	22.2395			0.902672			0.451336	+	0.892354i	$0.350948\pi$
$608$	4.64745	−	8.04961i	0.188479	−	0.326455i
$609$	49.6430	−	6.00259i	2.01163	−	0.243237i
$610$	4.16815			0.168764
$611$	−39.7580	+	13.7098i	−1.60844	+	0.554640i
$612$	−1.38278	−	2.39505i	−0.0558957	−	0.0968143i
$613$	−8.27987			−0.334421			−0.167210	−	0.985921i	$-0.553476\pi$
$613$	−8.27987			−0.334421			−0.167210	+	0.985921i	$0.553476\pi$
$614$	26.0789	+	45.1699i	1.05246	+	1.82291i
$615$	1.22177	+	2.11617i	0.0492665	+	0.0853321i
$616$	6.75567	+	8.99952i	0.272194	+	0.362601i
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	0.585554	−	0.810633i	$-0.300877\pi$
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	−0.994806	+	0.101789i	$0.967543\pi$
$618$	−30.8378			−1.24048
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	0.807354	−	0.590067i	$-0.200899\pi$
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	−0.914690	+	0.404156i	$0.867565\pi$
$620$	−0.183601	+	0.318007i	−0.00737361	+	0.0127715i
$621$	−3.48003	−	6.02758i	−0.139649	−	0.241879i
$622$	21.8651	−	37.8714i	0.876709	−	1.51850i
$623$	−12.4427	+	29.1636i	−0.498506	+	1.16842i
$624$	7.55018	−	38.9360i	0.302249	−	1.55869i
$625$	−12.2086	+	21.1459i	−0.488345	+	0.845838i
$626$	−6.22224			−0.248691
$627$	−12.9707			−0.518000
$628$	6.59072			0.262998
$629$	2.56165			0.102140
$630$	−1.31805	−	1.75583i	−0.0525124	−	0.0699540i
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	0.794463	−	0.607312i	$-0.207752\pi$
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	−0.923179	+	0.384369i	$0.874419\pi$
$632$	−5.45714	+	9.45205i	−0.217074	+	0.375982i
$633$	−30.3611	+	52.5870i	−1.20675	+	2.09014i
$634$	−13.5243			−0.537120
$635$	−0.216135	−	0.374357i	−0.00857707	−	0.0148559i
$636$	15.4904			0.614236
$637$	21.2114	−	13.6776i	0.840427	−	0.541925i
$638$	64.0322			2.53506
$639$	6.75475	+	11.6996i	0.267214	+	0.462828i
$640$	−1.54541			−0.0610877
$641$	−11.6644	+	20.2034i	−0.460717	+	0.797985i	−0.998997	−	0.0447808i	$-0.985741\pi$
$641$	−11.6644	+	20.2034i	−0.460717	+	0.797985i	0.538280	+	0.842766i	$0.319074\pi$
$642$	20.9993	−	36.3719i	0.828778	−	1.43549i
$643$	1.79439	+	3.10797i	0.0707637	+	0.122566i	0.899236	−	0.437463i	$-0.144123\pi$
$643$	1.79439	+	3.10797i	0.0707637	+	0.122566i	−0.828472	+	0.560030i	$0.810790\pi$
$644$	−9.49583	−	12.6498i	−0.374188	−	0.498472i
$645$	−2.41222			−0.0949810
$646$	2.11317			0.0831415
$647$	−39.6524			−1.55890			−0.779448	−	0.626467i	$-0.784500\pi$
$647$	−39.6524			−1.55890			−0.779448	+	0.626467i	$0.784500\pi$
$648$	10.8480			0.426151
$649$	12.6697	−	21.9446i	0.497331	−	0.861402i
$650$	−31.4218	+	10.8352i	−1.23246	+	0.424993i
$651$	−3.05042	+	7.14970i	−0.119556	+	0.280219i
$652$	−1.32386	+	2.29299i	−0.0518464	+	0.0898005i
$653$	−9.06777	−	15.7058i	−0.354849	−	0.614617i	0.632243	−	0.774770i	$-0.282135\pi$
$653$	−9.06777	−	15.7058i	−0.354849	−	0.614617i	−0.987092	+	0.160153i	$0.948801\pi$
$654$	29.4469	−	51.0035i	1.15146	−	1.99439i
$655$	0.224610	+	0.389035i	0.00877623	+	0.0152009i
$656$	−25.8784			−1.01038
$657$	−4.39592	−	7.61395i	−0.171501	−	0.297048i
$658$	−34.4256	−	45.8599i	−1.34205	−	1.78780i
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	0.704352	−	0.709851i	$-0.251238\pi$
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	−0.966925	+	0.255061i	$0.917905\pi$
$660$	−1.37561	−	2.38263i	−0.0535456	−	0.0927437i
$661$	10.3122			0.401099			0.200549	−	0.979684i	$-0.435727\pi$
$661$	10.3122			0.401099			0.200549	+	0.979684i	$0.435727\pi$
$662$	13.3076	+	23.0494i	0.517213	+	0.895839i
$663$	6.57861	−	2.26852i	0.255492	−	0.0881018i
$664$	−3.12571			−0.121301
$665$	0.700742	−	0.0847304i	0.0271736	−	0.00328570i
$666$	−6.40111	+	11.0870i	−0.248038	+	0.429614i
$667$	33.9035			1.31275
$668$	7.77805	+	13.4720i	0.300942	+	0.521247i
$669$	0.835096	−	1.44643i	0.0322867	−	0.0559222i
$670$	−4.91310			−0.189810
$671$	47.5397			1.83525
$672$	41.4334	−	5.00993i	1.59833	−	0.193262i
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	−0.763257	−	0.646095i	$-0.776401\pi$
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	0.941163	+	0.337953i	$0.109734\pi$
$674$	−15.9618	−	27.6467i	−0.614827	−	1.06491i
$675$	−4.19533	−	7.26652i	−0.161478	−	0.279689i
$676$	−17.5171	−	7.05900i	−0.673734	−	0.271500i
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	−0.589018	−	0.808120i	$-0.700485\pi$
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	0.994361	+	0.106045i	$0.0338187\pi$
$678$	9.09807	−	15.7583i	0.349409	−	0.605194i
$679$	20.2178	−	47.3873i	0.775888	−	1.81856i
$680$	−0.0844203	−	0.146220i	−0.00323737	−	0.00560729i
$681$	3.27129	−	5.66604i	0.125356	−	0.217123i
$682$	−4.97693	+	8.62029i	−0.190576	+	0.330088i
$683$	19.1106	−	33.1005i	0.731246	−	1.26656i	−0.225104	−	0.974335i	$-0.572272\pi$
$683$	19.1106	−	33.1005i	0.731246	−	1.26656i	0.956351	−	0.292221i	$-0.0943944\pi$
$684$	−2.22176	+	3.84821i	−0.0849512	+	0.147140i
$685$	1.32706	+	2.29854i	0.0507044	+	0.0878226i
$686$	26.6243	+	21.8047i	1.01652	+	0.832506i
$687$	−3.64013	+	6.30490i	−0.138880	+	0.240547i
$688$	12.7734	−	22.1241i	0.486980	−	0.843474i
$689$	−3.19025	+	16.4520i	−0.121539	+	0.626772i
$690$	−1.73107	−	2.99830i	−0.0659006	−	0.114143i
$691$	13.1161	+	22.7178i	0.498960	+	0.864224i	0.999999	−	0.00120019i	$-0.000382034\pi$
$691$	13.1161	+	22.7178i	0.498960	+	0.864224i	−0.501039	+	0.865425i	$0.667049\pi$
$692$	9.80084	−	16.9755i	0.372572	−	0.645313i
$693$	−15.0330	−	20.0261i	−0.571056	−	0.760728i
$694$	−14.3130			−0.543314
$695$	−0.798409			−0.0302854
$696$	−9.60925	+	16.6437i	−0.364238	+	0.630878i
$697$	−2.27024	−	3.93218i	−0.0859916	−	0.148942i
$698$	41.5672			1.57334
$699$	−15.3784	+	26.6361i	−0.581664	+	1.00747i
$700$	−11.4477	−	15.2499i	−0.432681	−	0.576393i
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$	2.15709	−	11.1240i	0.0814140	−	0.419849i
$703$	−2.05794	−	3.56446i	−0.0776167	−	0.134436i
$704$	13.3306			0.502414
$705$	−2.64053	−	4.57353i	−0.0994480	−	0.172249i
$706$	20.6835	+	35.8248i	0.778433	+	1.34828i
$707$	−26.8972	−	35.8309i	−1.01157	−	1.34756i
$708$	−10.0950	−	17.4851i	−0.379395	−	0.657131i
$709$	−47.4464			−1.78189			−0.890944	−	0.454113i	$-0.849956\pi$
$709$	−47.4464			−1.78189			−0.890944	+	0.454113i	$0.849956\pi$
$710$	−1.09476	−	1.89619i	−0.0410858	−	0.0711626i
$711$	12.1435	−	21.0331i	0.455415	−	0.788802i
$712$	−6.09307	−	10.5535i	−0.228348	−	0.395510i
$713$	−2.63516	+	4.56423i	−0.0986876	+	0.170932i
$714$	5.69629	+	7.58827i	0.213178	+	0.283984i
$715$	2.81384	−	0.970301i	0.105232	−	0.0362872i
$716$	−7.60461	+	13.1716i	−0.284197	+	0.492244i
$717$	−35.6815			−1.33255
$718$	−5.12560			−0.191286
$719$	−49.2380			−1.83627			−0.918133	−	0.396273i	$-0.870304\pi$
$719$	−49.2380			−1.83627			−0.918133	+	0.396273i	$0.870304\pi$
$720$	2.14136			0.0798037
$721$	19.0016	−	2.29758i	0.707657	−	0.0855665i
$722$	15.9549	+	27.6347i	0.593779	+	1.02846i
$723$	8.68963	−	15.0509i	0.323171	−	0.559748i
$724$	−9.09498	+	15.7530i	−0.338012	+	0.585454i
$725$	40.8722			1.51795
$726$	−13.8439	−	23.9783i	−0.513795	−	0.889919i
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$	−0.690112	+	9.67560i	−0.0255773	+	0.358602i
$729$	−12.4996			−0.462947
$730$	0.712460	+	1.23402i	0.0263693	+	0.0456730i
$731$	4.48229			0.165783
$732$	18.9394	−	32.8041i	0.700022	−	1.21247i
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	0.478894	+	0.877873i	$0.341038\pi$
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	−0.999707	+	0.0242025i	$0.992295\pi$
$734$	13.1462	+	22.7699i	0.485236	+	0.840453i
$735$	2.19319	+	2.28793i	0.0808971	+	0.0843914i
$736$	28.2968			1.04303
$737$	−56.0362			−2.06412
$738$	22.6918			0.835295
$739$	−42.5370			−1.56475			−0.782375	−	0.622808i	$-0.785992\pi$
$739$	−42.5370			−1.56475			−0.782375	+	0.622808i	$0.785992\pi$
$740$	0.436510	−	0.756058i	0.0160464	−	0.0277932i
$741$	−8.44160	−	7.33149i	−0.310110	−	0.269329i
$742$	−22.6852	+	2.74299i	−0.832801	+	0.100698i
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	−0.974263	−	0.225413i	$-0.927627\pi$
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	0.682345	+	0.731030i	$0.260960\pi$
$744$	−1.49377	−	2.58728i	−0.0547641	−	0.0948543i
$745$	1.51495	−	2.62396i	0.0555033	−	0.0961346i
$746$	4.68521	+	8.11502i	0.171538	+	0.297112i
$747$	6.95546			0.254487
$748$	2.55611	+	4.42731i	0.0934605	+	0.161878i
$749$	−10.2295	+	23.9762i	−0.373777	+	0.876072i
$750$	−4.19014	−	7.25754i	−0.153002	−	0.265008i
$751$	−9.09981	−	15.7613i	−0.332057	−	0.575139i	0.650858	−	0.759199i	$-0.274409\pi$
$751$	−9.09981	−	15.7613i	−0.332057	−	0.575139i	−0.982915	+	0.184060i	$0.941076\pi$
$752$	55.9293			2.03953
$753$	−1.46220	−	2.53260i	−0.0532855	−	0.0922931i
$754$	41.6734	+	36.1932i	1.51766	+	1.31808i
$755$	−1.20807			−0.0439662
$756$	6.45378	−	0.780360i	0.234722	−	0.0283814i
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	−0.0926649	−	0.995697i	$-0.529539\pi$
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	0.908632	−	0.417598i	$-0.137128\pi$
$758$	−11.2598			−0.408974
$759$	−19.7436	−	34.1970i	−0.716648	−	1.24127i
$760$	−0.135641	+	0.234937i	−0.00492021	+	0.00852205i
$761$	−26.4888			−0.960217			−0.480108	−	0.877209i	$-0.659403\pi$
$761$	−26.4888			−0.960217			−0.480108	+	0.877209i	$0.659403\pi$
$762$	−9.33644			−0.338223
$763$	−14.3445	+	33.6213i	−0.519307	+	1.21717i
$764$	−9.52554	+	16.4987i	−0.344622	+	0.596903i
$765$	0.187856	+	0.325375i	0.00679193	+	0.0117640i
$766$	4.21900	+	7.30752i	0.152439	+	0.264031i
$767$	20.6496	−	7.12064i	0.745613	−	0.257111i
$768$	−24.0006	+	41.5703i	−0.866049	+	1.50004i
$769$	−6.98127	+	12.0919i	−0.251751	+	0.436045i	−0.964008	−	0.265873i	$-0.914340\pi$
$769$	−6.98127	+	12.0919i	−0.251751	+	0.436045i	0.712257	+	0.701919i	$0.247673\pi$
$770$	2.43644	+	3.24569i	0.0878033	+	0.116967i
$771$	9.72707	+	16.8478i	0.350312	+	0.606758i
$772$	−0.756579	+	1.31043i	−0.0272299	+	0.0471635i
$773$	−6.40564	+	11.0949i	−0.230395	+	0.399056i	−0.957924	−	0.287021i	$-0.907335\pi$
$773$	−6.40564	+	11.0949i	−0.230395	+	0.399056i	0.727529	+	0.686077i	$0.240668\pi$
$774$	−11.2005	+	19.3998i	−0.402592	+	0.697310i
$775$	−3.17681	+	5.50239i	−0.114114	+	0.197652i
$776$	9.90048	+	17.1481i	0.355406	+	0.615582i
$777$	7.25235	−	16.9983i	0.260177	−	0.609812i
$778$	−4.18797	+	7.25378i	−0.150146	+	0.260061i
$779$	−3.64767	+	6.31795i	−0.130691	+	0.226364i
$780$	0.451468	−	2.32821i	0.0161652	−	0.0833631i
$781$	−12.4863	−	21.6269i	−0.446795	−	0.773871i
$782$	3.21660	+	5.57132i	0.115025	+	0.199230i
$783$	−6.96701	+	12.0672i	−0.248981	+	0.431247i
$784$	−32.5977	+	8.00008i	−1.16420	+	0.285717i
$785$	−0.895370			−0.0319571
$786$	9.70251			0.346077
$787$	13.6599	−	23.6597i	0.486924	−	0.843377i	−0.512963	−	0.858411i	$-0.671452\pi$
$787$	13.6599	−	23.6597i	0.486924	−	0.843377i	0.999887	+	0.0150334i	$0.00478545\pi$
$788$	−1.07383	−	1.85993i	−0.0382537	−	0.0662574i
$789$	29.3372			1.04443
$790$	−1.96813	+	3.40890i	−0.0700229	+	0.121283i
$791$	−4.43196	+	10.3878i	−0.157583	+	0.369348i
$792$	9.62401			0.341974
$793$	30.9398	+	26.8711i	1.09871	+	0.954221i
$794$	−3.71956	−	6.44247i	−0.132002	−	0.228635i
$795$	−2.10442			−0.0746362
$796$	−10.2419	−	17.7394i	−0.363013	−	0.628758i
$797$	14.7002	+	25.4614i	0.520707	+	0.901891i	0.999710	+	0.0240775i	$0.00766483\pi$
$797$	14.7002	+	25.4614i	0.520707	+	0.901891i	−0.479003	+	0.877813i	$0.659002\pi$
$798$	5.98265	−	14.0224i	0.211783	−	0.496386i
$799$	4.90652	+	8.49835i	0.173580	+	0.300650i
$800$	34.1131			1.20608
$801$	13.5586	+	23.4841i	0.479068	+	0.829770i
$802$	−11.7189	+	20.2978i	−0.413810	+	0.716740i
$803$	8.12594	+	14.0745i	0.286758	+	0.496680i
$804$	−22.3244	+	38.6669i	−0.787320	+	1.36368i
$805$	1.29004	+	1.71852i	0.0454679	+	0.0605697i
$806$	−8.11157	+	2.79713i	−0.285718	+	0.0985246i
$807$	5.40450	−	9.36087i	0.190247	−	0.329518i
$808$	17.2194			0.605775
$809$	−6.01233			−0.211382			−0.105691	−	0.994399i	$-0.533706\pi$
$809$	−6.01233			−0.211382			−0.105691	+	0.994399i	$0.533706\pi$
$810$	3.91236			0.137466
$811$	8.44807			0.296652			0.148326	−	0.988939i	$-0.452612\pi$
$811$	8.44807			0.296652			0.148326	+	0.988939i	$0.452612\pi$
$812$	−12.4267	+	29.1262i	−0.436091	+	1.02213i
$813$	20.6595	+	35.7833i	0.724560	+	1.25497i
$814$	11.8326	−	20.4946i	0.414732	−	0.718337i
$815$	0.179850	−	0.311510i	0.00629989	−	0.0109117i
$816$	−9.25442			−0.323969
$817$	−3.60092	−	6.23697i	−0.125980	−	0.218204i
$818$	38.4551			1.34455
$819$	1.53567	−	21.5305i	0.0536605	−	0.752338i
$820$	−1.54742			−0.0540382
$821$	17.1318	+	29.6731i	0.597903	+	1.03560i	0.993130	+	0.117014i	$0.0373324\pi$
$821$	17.1318	+	29.6731i	0.597903	+	1.03560i	−0.395228	+	0.918583i	$0.629334\pi$
$822$	57.3253			1.99945
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	−0.806538	−	0.591182i	$-0.798661\pi$
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	0.915248	+	0.402891i	$0.131995\pi$
$824$	−3.67809	+	6.37064i	−0.128132	+	0.221932i
$825$	−23.8018	−	41.2260i	−0.828673	−	1.43530i
$826$	17.8801	+	23.8188i	0.622127	+	0.828762i
$827$	19.5232			0.678889			0.339445	−	0.940626i	$-0.389761\pi$
$827$	19.5232			0.678889			0.339445	+	0.940626i	$0.389761\pi$
$828$	−13.5276			−0.470117
$829$	32.6766			1.13491			0.567453	−	0.823406i	$-0.307929\pi$
$829$	32.6766			1.13491			0.567453	+	0.823406i	$0.307929\pi$
$830$	−1.12729			−0.0391289
$831$	29.9615	−	51.8949i	1.03935	−	1.80021i
$832$	8.67580	+	7.53489i	0.300779	+	0.261225i
$833$	−4.07530	−	4.25133i	−0.141201	−	0.147300i
$834$	−8.62225	+	14.9342i	−0.298564	+	0.517128i
$835$	−1.05667	−	1.83021i	−0.0365677	−	0.0633370i
$836$	4.10698	−	7.11349i	0.142043	−	0.246025i
$837$	−1.08303	−	1.87586i	−0.0374349	−	0.0648392i
$838$	−40.5405			−1.40045
$839$	−12.3713	−	21.4278i	−0.427106	−	0.739769i	0.569508	−	0.821985i	$-0.307134\pi$
$839$	−12.3713	−	21.4278i	−0.427106	−	0.739769i	−0.996615	+	0.0822161i	$0.973800\pi$
$840$	−1.20928	+	0.146220i	−0.0417241	+	0.00504508i
$841$	−19.4374	−	33.6665i	−0.670255	−	1.16092i
$842$	−8.75869	−	15.1705i	−0.301844	−	0.522810i
$843$	−8.40080			−0.289339
$844$	−19.2267	−	33.3017i	−0.661812	−	1.14629i
$845$	2.37975	+	0.958986i	0.0818659	+	0.0329901i
$846$	−49.0422			−1.68610
$847$	10.3168	+	13.7435i	0.354491	+	0.472233i
$848$	11.1435	−	19.3011i	0.382670	−	0.662803i
$849$	17.5388			0.601929
$850$	3.87776	+	6.71647i	0.133006	+	0.230373i
$851$	6.26507	−	10.8514i	0.214764	−	0.371982i
$852$	−19.8978			−0.681686
$853$	18.2245			0.623994			0.311997	−	0.950083i	$-0.399002\pi$
$853$	18.2245			0.623994			0.311997	+	0.950083i	$0.399002\pi$
$854$	−21.9274	+	51.3942i	−0.750339	+	1.75867i
$855$	0.301833	−	0.522791i	0.0103225	−	0.0178791i
$856$	−5.00928	−	8.67633i	−0.171214	−	0.296551i
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	0.843457	−	0.537197i	$-0.180517\pi$
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	−0.886955	+	0.461856i	$0.847184\pi$
$858$	12.2381	−	63.1112i	0.417800	−	2.15458i
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.124104	+	0.992269i	$0.539606\pi$
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.797278	+	0.603612i	$0.793728\pi$
$860$	0.763792	−	1.32293i	0.0260451	−	0.0451114i
$861$	−32.5201	+	3.93218i	−1.10828	+	0.134008i
$862$	−18.9788	−	32.8723i	−0.646421	−	1.11963i
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	−0.876410	−	0.481565i	$-0.840069\pi$
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	0.855253	+	0.518211i	$0.173402\pi$
$864$	−5.81487	+	10.0716i	−0.197826	+	0.342644i
$865$	−1.33147	+	2.30618i	−0.0452715	+	0.0784125i
$866$	−24.4800	+	42.4006i	−0.831864	+	1.44083i
$867$	18.6877	+	32.3681i	0.634668	+	1.09928i
$868$	−2.95522	−	3.93678i	−0.100307	−	0.133623i
$869$	−22.4474	+	38.8801i	−0.761477	+	1.31892i
$870$	−3.46560	+	6.00259i	−0.117495	+	0.203507i
$871$	−36.4695	−	31.6736i	−1.23572	−	1.07322i
$872$	−7.02440	−	12.1666i	−0.237876	−	0.412013i
$873$	−22.0309	−	38.1587i	−0.745634	−	1.29148i
$874$	5.16821	−	8.95161i	0.174817	−	0.302793i
$875$	3.12261	+	4.15976i	0.105563	+	0.140626i
$876$	12.9492			0.437514
$877$	0.802661			0.0271039			0.0135520	−	0.999908i	$-0.495686\pi$
$877$	0.802661			0.0271039			0.0135520	+	0.999908i	$0.495686\pi$
$878$	−23.3488	+	40.4412i	−0.787983	+	1.36483i
$879$	19.6755	+	34.0790i	0.663639	+	1.14946i
$880$	−3.95835			−0.133436
$881$	18.5318	−	32.0980i	0.624352	−	1.08141i	−0.364314	−	0.931276i	$-0.618696\pi$
$881$	18.5318	−	32.0980i	0.624352	−	1.08141i	0.988666	−	0.150133i	$-0.0479703\pi$
$882$	28.5836	−	7.01495i	0.962461	−	0.236206i
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	−0.838900	+	4.32618i	−0.0282153	+	0.145505i
$885$	1.37144	+	2.37541i	0.0461005	+	0.0798484i
$886$	34.4130			1.15613
$887$	24.6287	+	42.6581i	0.826950	+	1.43232i	0.900420	+	0.435022i	$0.143259\pi$
$887$	24.6287	+	42.6581i	0.826950	+	1.43232i	−0.0734699	+	0.997297i	$0.523407\pi$
$888$	3.55141	+	6.15123i	0.119178	+	0.206422i
$889$	5.75292	−	0.695616i	0.192947	−	0.0233302i
$890$	−2.19748	−	3.80614i	−0.0736597	−	0.127582i
$891$	44.6223			1.49490
$892$	0.528840	+	0.915978i	0.0177069	+	0.0306692i
$893$	7.88347	−	13.6546i	0.263810	−	0.456932i
$894$	−32.7207	−	56.6739i	−1.09434	−	1.89546i
$895$	1.03311	−	1.78940i	0.0345330	−	0.0598130i
$896$	8.12993	−	19.0552i	0.271602	−	0.636591i
$897$	6.47975	−	33.4159i	0.216353	−	1.11572i
$898$	−10.8174	+	18.7362i	−0.360980	+	0.625236i
$899$	10.5512			0.351902
$900$	−16.3081			−0.543604
$901$	3.91036			0.130273
$902$	−41.9462			−1.39666
$903$	12.6899	−	29.7432i	0.422295	−	0.989790i
$904$	−2.17029	−	3.75906i	−0.0721829	−	0.125024i
$905$	1.23558	−	2.14009i	0.0410721	−	0.0711390i
$906$	−13.0463	+	22.5969i	−0.433435	+	0.750731i
$907$	−5.00455			−0.166173			−0.0830867	−	0.996542i	$-0.526478\pi$
$907$	−5.00455			−0.166173			−0.0830867	+	0.996542i	$0.526478\pi$
$908$	2.07161	+	3.58813i	0.0687487	+	0.119076i
$909$	−38.3172			−1.27090
$910$	−0.248890	+	3.48952i	−0.00825063	+	0.115677i
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	7.43468	+	12.8772i	0.246187	+	0.426408i
$913$	−12.8573			−0.425515
$914$	−19.0633	+	33.0186i	−0.630557	+	1.09216i
$915$	−2.57298	+	4.45653i	−0.0850601	+	0.147328i
$916$	−2.30518	−	3.99270i	−0.0761654	−	0.131922i
$917$	−5.97849	+	0.722891i	−0.197427	+	0.0238719i
$918$	−2.64399			−0.0872646
$919$	29.6056			0.976598			0.488299	−	0.872676i	$-0.337618\pi$
$919$	29.6056			0.976598			0.488299	+	0.872676i	$0.337618\pi$
$920$	−0.825873			−0.0272282
$921$	−64.3935			−2.12184
$922$	−1.89602	+	3.28401i	−0.0624422	+	0.108153i
$923$	4.09794	−	21.1329i	0.134885	−	0.695598i
$924$	36.6150	−	4.42731i	1.20454	−	0.145648i
$925$	7.55282	−	13.0819i	0.248335	−	0.430129i
$926$	−2.81656	−	4.87842i	−0.0925578	−	0.160315i
$927$	8.18464	−	14.1762i	0.268819	−	0.465608i
$928$	−28.3251	−	49.0605i	−0.929817	−	1.61049i
$929$	16.8305			0.552191			0.276095	−	0.961130i	$-0.410959\pi$
$929$	16.8305			0.552191			0.276095	+	0.961130i	$0.410959\pi$
$930$	−0.538730	−	0.933107i	−0.0176656	−	0.0305978i
$931$	−2.64164	+	9.08604i	−0.0865764	+	0.297783i
$932$	−9.73865	−	16.8678i	−0.319000	−	0.552524i
$933$	26.9944	+	46.7557i	0.883757	+	1.53071i
$934$	−24.0212			−0.785998
$935$	−0.347255	−	0.601463i	−0.0113565	−	0.0196699i
$936$	6.26350	+	5.43982i	0.204729	+	0.177806i
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	25.8463	−	60.5796i	0.843912	−	1.97799i
$939$	3.84096	−	6.65273i	0.125345	−	0.217104i
$940$	3.34433			0.109080
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	−0.867071	−	0.498184i	$-0.834000\pi$
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	0.00209573	−	0.999998i	$-0.499333\pi$
$942$	−9.66937	+	16.7478i	−0.315045	+	0.545674i
$943$	−22.2095			−0.723241
$944$	−29.0487			−0.945453
$945$	−0.876766	+	0.106014i	−0.0285212	+	0.00344865i
$946$	20.7043	−	35.8609i	0.673154	−	1.16594i
$947$	13.9409	+	24.1463i	0.453017	+	0.784649i	0.998572	−	0.0534265i	$-0.0170143\pi$
$947$	13.9409	+	24.1463i	0.453017	+	0.784649i	−0.545555	+	0.838075i	$0.683681\pi$
$948$	17.8857	+	30.9790i	0.580902	+	1.00615i
$949$	−2.66689	+	13.7531i	−0.0865709	+	0.446443i
$950$	6.23051	−	10.7916i	0.202145	−	0.350125i
$951$	8.34851	−	14.4600i	0.270719	−	0.468899i
$952$	2.24704	−	0.271701i	0.0728269	−	0.00880588i
$953$	18.1784	+	31.4859i	0.588856	+	1.01993i	0.994383	+	0.105845i	$0.0337548\pi$
$953$	18.1784	+	31.4859i	0.588856	+	1.01993i	−0.405527	+	0.914083i	$0.632912\pi$
$954$	−9.77130	+	16.9244i	−0.316357	+	0.547947i
$955$	1.29407	−	2.24140i	0.0418753	−	0.0725301i
$956$	11.2980	−	19.5687i	0.365403	−	0.632897i
$957$	−39.5267	+	68.4623i	−1.27772	+	2.21307i
$958$	−33.9877	−	58.8685i	−1.09809	−	1.90195i
$959$	−35.3227	+	4.27105i	−1.14063	+	0.137920i
$960$	−0.721486	+	1.24965i	−0.0232859	+	0.0403323i
$961$	14.6799	−	25.4263i	0.473545	−	0.820205i
$962$	19.2852	−	6.65014i	0.621779	−	0.214409i
$963$	11.1469	+	19.3069i	0.359202	+	0.622157i
$964$	5.50287	+	9.53126i	0.177236	+	0.306981i
$965$	0.102784	−	0.178026i	0.00330872	−	0.00573087i
$966$	46.0762	−	5.57132i	1.48248	−	0.179254i
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	−6.60477			−0.212285
$969$	−1.30445	+	2.25937i	−0.0419049	+	0.0725815i
$970$	3.57063	+	6.18450i	0.114646	+	0.198572i
$971$	−36.8920			−1.18392			−0.591961	−	0.805967i	$-0.701646\pi$
$971$	−36.8920			−1.18392			−0.591961	+	0.805967i	$0.701646\pi$
$972$	14.0916	−	24.4073i	0.451987	−	0.782865i
$973$	4.20018	−	9.84455i	0.134652	−	0.315602i
$974$	68.2867			2.18805
$975$	7.81163	−	40.2843i	0.250172	−	1.29013i
$976$	−27.2493	−	47.1972i	−0.872229	−	1.51074i
$977$	−0.443914			−0.0142021			−0.00710104	−	0.999975i	$-0.502260\pi$
$977$	−0.443914			−0.0142021			−0.00710104	+	0.999975i	$0.502260\pi$
$978$	−3.88452	−	6.72818i	−0.124213	−	0.215144i
$979$	−25.0633	−	43.4109i	−0.801026	−	1.38742i
$980$	−1.94920	+	0.478370i	−0.0622649	+	0.0152810i
$981$	15.6310	+	27.0736i	0.499058	+	0.864394i
$982$	−15.2332			−0.486109
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	−0.958323	−	0.285688i	$-0.907778\pi$
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	0.231748	−	0.972776i	$-0.425556\pi$
$984$	6.29483	−	10.9030i	0.200672	−	0.347574i
$985$	0.145884	+	0.252678i	0.00464824	+	0.00805099i
$986$	6.43964	−	11.1538i	0.205080	−	0.355209i
$987$	70.2835	−	8.49835i	2.23715	−	0.270505i
$988$	6.69369	−	2.30820i	0.212955	−	0.0734336i
$989$	10.9624	−	18.9875i	0.348585	−	0.603766i
$990$	3.47092			0.110313
$991$	53.6295			1.70360			0.851799	−	0.523869i	$-0.175512\pi$
$991$	53.6295			1.70360			0.851799	+	0.523869i	$0.175512\pi$
$992$	8.80632			0.279601
$993$	−32.8588			−1.04274
$994$	29.1396	−	3.52342i	0.924252	−	0.111756i
$995$	1.39139	+	2.40996i	0.0441100	+	0.0764008i
$996$	−5.12225	+	8.87199i	−0.162305	+	0.281120i
$997$	−14.5426	+	25.1886i	−0.460569	+	0.797730i	−0.998989	−	0.0449470i	$-0.985688\pi$
$997$	−14.5426	+	25.1886i	−0.460569	+	0.797730i	0.538420	+	0.842677i	$0.319021\pi$
$998$	−80.3715			−2.54412
$999$	2.57489	+	4.45984i	0.0814658	+	0.141103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.g.b.9.1	✓	12
3.2	odd	2		819.2.n.d.100.6		12
7.2	even	3		637.2.f.k.295.1		12
7.3	odd	6		637.2.h.l.165.6		12
7.4	even	3		91.2.h.b.74.6	yes	12
7.5	odd	6		637.2.f.j.295.1		12
7.6	odd	2		637.2.g.l.373.1		12
13.3	even	3		91.2.h.b.16.6	yes	12
13.4	even	6		1183.2.e.g.170.6		12
13.9	even	3		1183.2.e.h.170.1		12
21.11	odd	6		819.2.s.d.802.1		12
39.29	odd	6		819.2.s.d.289.1		12
91.3	odd	6		637.2.g.l.263.1		12
91.4	even	6		1183.2.e.g.508.6		12
91.9	even	3		8281.2.a.bz.1.6		6
91.16	even	3		637.2.f.k.393.1		12
91.30	even	6		8281.2.a.ce.1.1		6
91.55	odd	6		637.2.h.l.471.6		12
91.61	odd	6		8281.2.a.ca.1.6		6
91.68	odd	6		637.2.f.j.393.1		12
91.74	even	3		1183.2.e.h.508.1		12
91.81	even	3	inner	91.2.g.b.81.1	yes	12
91.82	odd	6		8281.2.a.cf.1.1		6
273.263	odd	6		819.2.n.d.172.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	1.1	even	1	trivial
91.2.g.b.81.1	yes	12	91.81	even	3	inner
91.2.h.b.16.6	yes	12	13.3	even	3
91.2.h.b.74.6	yes	12	7.4	even	3
637.2.f.j.295.1		12	7.5	odd	6
637.2.f.j.393.1		12	91.68	odd	6
637.2.f.k.295.1		12	7.2	even	3
637.2.f.k.393.1		12	91.16	even	3
637.2.g.l.263.1		12	91.3	odd	6
637.2.g.l.373.1		12	7.6	odd	2
637.2.h.l.165.6		12	7.3	odd	6
637.2.h.l.471.6		12	91.55	odd	6
819.2.n.d.100.6		12	3.2	odd	2
819.2.n.d.172.6		12	273.263	odd	6
819.2.s.d.289.1		12	39.29	odd	6
819.2.s.d.802.1		12	21.11	odd	6
1183.2.e.g.170.6		12	13.4	even	6
1183.2.e.g.508.6		12	91.4	even	6
1183.2.e.h.170.1		12	13.9	even	3
1183.2.e.h.508.1		12	91.74	even	3
8281.2.a.bz.1.6		6	91.9	even	3
8281.2.a.ca.1.6		6	91.61	odd	6
8281.2.a.ce.1.1		6	91.30	even	6
8281.2.a.cf.1.1		6	91.82	odd	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929081 - 1.60921i) q^{2} +2.29407 q^{3} +(-0.726381 + 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 - 3.69165i) q^{6} +(1.58836 + 2.11592i) q^{7} -1.01686 q^{8} +2.26275 q^{9} +O(q^{10})\)	\(q+(-0.929081 - 1.60921i) q^{2} +2.29407 q^{3} +(-0.726381 + 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 - 3.69165i) q^{6} +(1.58836 + 2.11592i) q^{7} -1.01686 q^{8} +2.26275 q^{9} -0.366731 q^{10} -4.18274 q^{11} +(-1.66637 + 2.88623i) q^{12} +(-2.72221 - 2.36423i) q^{13} +(1.92926 - 4.52187i) q^{14} +(0.226381 - 0.392104i) q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +(-2.10227 - 3.64125i) q^{18} +1.35175 q^{19} +(0.143360 + 0.248307i) q^{20} +(3.64380 + 4.85406i) q^{21} +(3.88610 + 6.73092i) q^{22} +(2.05760 + 3.56386i) q^{23} -2.33274 q^{24} +(2.48052 + 4.29639i) q^{25} +(-1.27540 + 6.57718i) q^{26} -1.69131 q^{27} +(-3.81585 + 0.461395i) q^{28} +(4.11931 - 7.13485i) q^{29} -0.841305 q^{30} +(0.640350 + 1.10912i) q^{31} +(3.43809 - 5.95495i) q^{32} -9.59548 q^{33} +1.56328 q^{34} +(0.518396 - 0.0626819i) q^{35} +(-1.64362 + 2.84683i) q^{36} +(-1.52242 - 2.63692i) q^{37} +(-1.25589 - 2.17526i) q^{38} +(-6.24494 - 5.42370i) q^{39} +(-0.100344 + 0.173802i) q^{40} +(-2.69848 + 4.67390i) q^{41} +(4.42585 - 10.3735i) q^{42} +(-2.66389 - 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} +(0.223290 - 0.386750i) q^{45} +(3.82334 - 6.62223i) q^{46} +(5.83204 - 10.1014i) q^{47} +(5.50003 + 9.52634i) q^{48} +(-1.95424 + 6.72168i) q^{49} +(4.60921 - 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(4.95187 - 1.70756i) q^{52} +(-2.32398 - 4.02525i) q^{53} +(1.57136 + 2.72168i) q^{54} +(-0.412757 + 0.714916i) q^{55} +(-1.61513 - 2.15159i) q^{56} +3.10101 q^{57} -15.3087 q^{58} +(-3.02905 + 5.24648i) q^{59} +(0.328878 + 0.569634i) q^{60} -11.3657 q^{61} +(1.18987 - 2.06092i) q^{62} +(3.59405 + 4.78779i) q^{63} -3.18704 q^{64} +(-0.672726 + 0.231978i) q^{65} +(8.91498 + 15.4412i) q^{66} +13.3970 q^{67} +(-0.611109 - 1.05847i) q^{68} +(4.72026 + 8.17574i) q^{69} +(-0.582500 - 0.775973i) q^{70} +(2.98520 + 5.17051i) q^{71} -2.30089 q^{72} +(-1.94273 - 3.36491i) q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} +(-0.981887 + 1.70068i) q^{76} +(-6.64368 - 8.85034i) q^{77} +(-2.92585 + 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +0.946353 q^{80} -10.6682 q^{81} +10.0284 q^{82} +3.07390 q^{83} +(-8.75383 + 1.05847i) q^{84} +(0.0830210 + 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} +(9.44997 - 16.3678i) q^{87} +4.25324 q^{88} +(5.99207 + 10.3786i) q^{89} -0.829819 q^{90} +(0.678673 - 9.51522i) q^{91} -5.97840 q^{92} +(1.46901 + 2.54439i) q^{93} -21.6737 q^{94} +(0.133392 - 0.231042i) q^{95} +(7.88721 - 13.6611i) q^{96} +(-9.73637 - 16.8639i) q^{97} +(12.6323 - 3.10019i) q^{98} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

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