LMFDB - Embedded newform 1110.2.d.j.889.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(889,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1110.889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.d (of order $2$, degree $1$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.57815240704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 $ x^8 - 2x^7 + 2x^6 + 89x^4 - 170x^3 + 162x^2 - 72x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			889.5
Root			$0.353624 + 0.353624i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.j.889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.20793 + 0.353624i) q^{5} -1.00000 q^{6} +4.51003i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.20793 + 0.353624i) q^{5} -1.00000 q^{6} +4.51003i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-0.353624 - 2.20793i) q^{10} -6.51003 q^{11} -1.00000i q^{12} +0.854305i q^{13} -4.51003 q^{14} +(-0.353624 - 2.20793i) q^{15} +1.00000 q^{16} +1.38693i q^{17} -1.00000i q^{18} +7.74990 q^{19} +(2.20793 - 0.353624i) q^{20} -4.51003 q^{21} -6.51003i q^{22} -4.68466i q^{23} +1.00000 q^{24} +(4.74990 - 1.56155i) q^{25} -0.854305 q^{26} -1.00000i q^{27} -4.51003i q^{28} +2.36297 q^{29} +(2.20793 - 0.353624i) q^{30} -9.17599 q^{31} +1.00000i q^{32} -6.51003i q^{33} -1.38693 q^{34} +(-1.59485 - 9.95783i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +7.74990i q^{38} -0.854305 q^{39} +(0.353624 + 2.20793i) q^{40} +4.17463 q^{41} -4.51003i q^{42} +3.65573i q^{43} +6.51003 q^{44} +(2.20793 - 0.353624i) q^{45} +4.68466 q^{46} -10.4159i q^{47} +1.00000i q^{48} -13.3404 q^{49} +(1.56155 + 4.74990i) q^{50} -1.38693 q^{51} -0.854305i q^{52} +9.61444i q^{53} +1.00000 q^{54} +(14.3737 - 2.30210i) q^{55} +4.51003 q^{56} +7.74990i q^{57} +2.36297i q^{58} -6.41586 q^{59} +(0.353624 + 2.20793i) q^{60} -10.9672 q^{61} -9.17599i q^{62} -4.51003i q^{63} -1.00000 q^{64} +(-0.302103 - 1.88624i) q^{65} +6.51003 q^{66} -12.9143i q^{67} -1.38693i q^{68} +4.68466 q^{69} +(9.95783 - 1.59485i) q^{70} -0.0391629 q^{71} +1.00000i q^{72} +7.16440i q^{73} +1.00000 q^{74} +(1.56155 + 4.74990i) q^{75} -7.74990 q^{76} -29.3604i q^{77} -0.854305i q^{78} +7.35062 q^{79} +(-2.20793 + 0.353624i) q^{80} +1.00000 q^{81} +4.17463i q^{82} -10.9975i q^{83} +4.51003 q^{84} +(-0.490450 - 3.06223i) q^{85} -3.65573 q^{86} +2.36297i q^{87} +6.51003i q^{88} -5.73120 q^{89} +(0.353624 + 2.20793i) q^{90} -3.85294 q^{91} +4.68466i q^{92} -9.17599i q^{93} +10.4159 q^{94} +(-17.1112 + 2.74055i) q^{95} -1.00000 q^{96} +11.6744i q^{97} -13.3404i q^{98} +6.51003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} - 2 q^{10} - 10 q^{11} + 6 q^{14} - 2 q^{15} + 8 q^{16} + 24 q^{19} + 2 q^{20} + 6 q^{21} + 8 q^{24} + 8 q^{26} - 10 q^{29} + 2 q^{30} - 38 q^{31} - 2 q^{34} + 12 q^{35} + 8 q^{36} + 8 q^{39} + 2 q^{40} + 26 q^{41} + 10 q^{44} + 2 q^{45} - 12 q^{46} - 30 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{54} + 30 q^{55} - 6 q^{56} - 20 q^{59} + 2 q^{60} - 6 q^{61} - 8 q^{64} + 24 q^{65} + 10 q^{66} - 12 q^{69} + 26 q^{70} - 12 q^{71} + 8 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 2 q^{80} + 8 q^{81} - 6 q^{84} + 44 q^{85} - 2 q^{86} - 64 q^{89} + 2 q^{90} - 44 q^{91} + 52 q^{94} - 8 q^{96} + 10 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 - 2 * q^10 - 10 * q^11 + 6 * q^14 - 2 * q^15 + 8 * q^16 + 24 * q^19 + 2 * q^20 + 6 * q^21 + 8 * q^24 + 8 * q^26 - 10 * q^29 + 2 * q^30 - 38 * q^31 - 2 * q^34 + 12 * q^35 + 8 * q^36 + 8 * q^39 + 2 * q^40 + 26 * q^41 + 10 * q^44 + 2 * q^45 - 12 * q^46 - 30 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^54 + 30 * q^55 - 6 * q^56 - 20 * q^59 + 2 * q^60 - 6 * q^61 - 8 * q^64 + 24 * q^65 + 10 * q^66 - 12 * q^69 + 26 * q^70 - 12 * q^71 + 8 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 2 * q^80 + 8 * q^81 - 6 * q^84 + 44 * q^85 - 2 * q^86 - 64 * q^89 + 2 * q^90 - 44 * q^91 + 52 * q^94 - 8 * q^96 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	−2.20793	+	0.353624i	−0.987416	+	0.158145i
$5$	−2.20793	+	0.353624i	−0.987416	+	0.158145i
$6$	−1.00000			−0.408248
$7$			4.51003i			1.70463i	0.523027	+	0.852316i	$0.324803\pi$
$7$			4.51003i			1.70463i	−0.523027	+	0.852316i	$0.675197\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−0.353624	−	2.20793i	−0.111826	−	0.698208i
$11$	−6.51003			−1.96285			−0.981424	−	0.191850i	$-0.938551\pi$
$11$	−6.51003			−1.96285			−0.981424	+	0.191850i	$0.938551\pi$
$12$		−	1.00000i		−	0.288675i
$13$			0.854305i			0.236942i	0.992958	+	0.118471i	$0.0377992\pi$
$13$			0.854305i			0.236942i	−0.992958	+	0.118471i	$0.962201\pi$
$14$	−4.51003			−1.20536
$15$	−0.353624	−	2.20793i	−0.0913053	−	0.570085i
$16$	1.00000			0.250000
$17$			1.38693i			0.336379i	0.985755	+	0.168189i	$0.0537920\pi$
$17$			1.38693i			0.336379i	−0.985755	+	0.168189i	$0.946208\pi$
$18$		−	1.00000i		−	0.235702i
$19$	7.74990			1.77795			0.888975	−	0.457957i	$-0.151419\pi$
$19$	7.74990			1.77795			0.888975	+	0.457957i	$0.151419\pi$
$20$	2.20793	−	0.353624i	0.493708	−	0.0790727i
$21$	−4.51003			−0.984170
$22$		−	6.51003i		−	1.38794i
$23$		−	4.68466i		−	0.976819i	−0.872615	−	0.488409i	$-0.837577\pi$
$23$		−	4.68466i		−	0.976819i	0.872615	−	0.488409i	$-0.162423\pi$
$24$	1.00000			0.204124
$25$	4.74990	−	1.56155i	0.949980	−	0.312311i
$26$	−0.854305			−0.167543
$27$		−	1.00000i		−	0.192450i
$28$		−	4.51003i		−	0.852316i
$29$	2.36297			0.438793			0.219397	−	0.975636i	$-0.429591\pi$
$29$	2.36297			0.438793			0.219397	+	0.975636i	$0.429591\pi$
$30$	2.20793	−	0.353624i	0.403111	−	0.0645626i
$31$	−9.17599			−1.64806			−0.824028	−	0.566549i	$-0.808278\pi$
$31$	−9.17599			−1.64806			−0.824028	+	0.566549i	$0.808278\pi$
$32$			1.00000i			0.176777i
$33$		−	6.51003i		−	1.13325i
$34$	−1.38693			−0.237856
$35$	−1.59485	−	9.95783i	−0.269580	−	1.68318i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			7.74990i			1.25720i
$39$	−0.854305			−0.136798
$40$	0.353624	+	2.20793i	0.0559128	+	0.349104i
$41$	4.17463			0.651967			0.325984	−	0.945375i	$-0.394305\pi$
$41$	4.17463			0.651967			0.325984	+	0.945375i	$0.394305\pi$
$42$		−	4.51003i		−	0.695913i
$43$			3.65573i			0.557493i	0.960365	+	0.278747i	$0.0899189\pi$
$43$			3.65573i			0.557493i	−0.960365	+	0.278747i	$0.910081\pi$
$44$	6.51003			0.981424
$45$	2.20793	−	0.353624i	0.329139	−	0.0527151i
$46$	4.68466			0.690715
$47$		−	10.4159i		−	1.51931i	−0.650327	−	0.759655i	$-0.725368\pi$
$47$		−	10.4159i		−	1.51931i	0.650327	−	0.759655i	$-0.274632\pi$
$48$			1.00000i			0.144338i
$49$	−13.3404			−1.90577
$50$	1.56155	+	4.74990i	0.220837	+	0.671737i
$51$	−1.38693			−0.194208
$52$		−	0.854305i		−	0.118471i
$53$			9.61444i			1.32064i	0.750982	+	0.660322i	$0.229580\pi$
$53$			9.61444i			1.32064i	−0.750982	+	0.660322i	$0.770420\pi$
$54$	1.00000			0.136083
$55$	14.3737	−	2.30210i	1.93815	−	0.310415i
$56$	4.51003			0.602678
$57$			7.74990i			1.02650i
$58$			2.36297i			0.310274i
$59$	−6.41586			−0.835274			−0.417637	−	0.908614i	$-0.637142\pi$
$59$	−6.41586			−0.835274			−0.417637	+	0.908614i	$0.637142\pi$
$60$	0.353624	+	2.20793i	0.0456526	+	0.285042i
$61$	−10.9672			−1.40420			−0.702102	−	0.712077i	$-0.747755\pi$
$61$	−10.9672			−1.40420			−0.702102	+	0.712077i	$0.747755\pi$
$62$		−	9.17599i		−	1.16535i
$63$		−	4.51003i		−	0.568211i
$64$	−1.00000			−0.125000
$65$	−0.302103	−	1.88624i	−0.0374712	−	0.233960i
$66$	6.51003			0.801329
$67$		−	12.9143i		−	1.57773i	−0.614565	−	0.788866i	$-0.710668\pi$
$67$		−	12.9143i		−	1.57773i	0.614565	−	0.788866i	$-0.289332\pi$
$68$		−	1.38693i		−	0.168189i
$69$	4.68466			0.563967
$70$	9.95783	−	1.59485i	1.19019	−	0.190622i
$71$	−0.0391629			−0.00464778			−0.00232389	−	0.999997i	$-0.500740\pi$
$71$	−0.0391629			−0.00464778			−0.00232389	+	0.999997i	$0.500740\pi$
$72$			1.00000i			0.117851i
$73$			7.16440i			0.838529i	0.907864	+	0.419265i	$0.137712\pi$
$73$			7.16440i			0.838529i	−0.907864	+	0.419265i	$0.862288\pi$
$74$	1.00000			0.116248
$75$	1.56155	+	4.74990i	0.180313	+	0.548471i
$76$	−7.74990			−0.888975
$77$		−	29.3604i		−	3.34593i
$78$		−	0.854305i		−	0.0967310i
$79$	7.35062			0.827009			0.413504	−	0.910502i	$-0.364305\pi$
$79$	7.35062			0.827009			0.413504	+	0.910502i	$0.364305\pi$
$80$	−2.20793	+	0.353624i	−0.246854	+	0.0395364i
$81$	1.00000			0.111111
$82$			4.17463i			0.461010i
$83$		−	10.9975i		−	1.20713i	−0.797314	−	0.603565i	$-0.793746\pi$
$83$		−	10.9975i		−	1.20713i	0.797314	−	0.603565i	$-0.206254\pi$
$84$	4.51003			0.492085
$85$	−0.490450	−	3.06223i	−0.0531968	−	0.332146i
$86$	−3.65573			−0.394207
$87$			2.36297i			0.253337i
$88$			6.51003i			0.693972i
$89$	−5.73120			−0.607506			−0.303753	−	0.952751i	$-0.598240\pi$
$89$	−5.73120			−0.607506			−0.303753	+	0.952751i	$0.598240\pi$
$90$	0.353624	+	2.20793i	0.0372752	+	0.232736i
$91$	−3.85294			−0.403898
$92$			4.68466i			0.488409i
$93$		−	9.17599i		−	0.951506i
$94$	10.4159			1.07431
$95$	−17.1112	+	2.74055i	−1.75558	+	0.281174i
$96$	−1.00000			−0.102062
$97$			11.6744i			1.18536i	0.805439	+	0.592679i	$0.201930\pi$
$97$			11.6744i			1.18536i	−0.805439	+	0.592679i	$0.798070\pi$
$98$		−	13.3404i		−	1.34758i
$99$	6.51003			0.654283
$100$	−4.74990	+	1.56155i	−0.474990	+	0.156155i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$		−	1.38693i		−	0.137326i
$103$		−	0.310091i		−	0.0305542i	−0.999883	−	0.0152771i	$-0.995137\pi$
$103$		−	0.310091i		−	0.0305542i	0.999883	−	0.0152771i	$-0.00486303\pi$
$104$	0.854305			0.0837715
$105$	9.95783	−	1.59485i	0.971785	−	0.155642i
$106$	−9.61444			−0.933837
$107$			5.10052i			0.493086i	0.969132	+	0.246543i	$0.0792946\pi$
$107$			5.10052i			0.493086i	−0.969132	+	0.246543i	$0.920705\pi$
$108$			1.00000i			0.0962250i
$109$	−6.40426			−0.613417			−0.306709	−	0.951803i	$-0.599228\pi$
$109$	−6.40426			−0.613417			−0.306709	+	0.951803i	$0.599228\pi$
$110$	2.30210	+	14.3737i	0.219497	+	1.37048i
$111$	1.00000			0.0949158
$112$			4.51003i			0.426158i
$113$			6.72097i			0.632256i	0.948717	+	0.316128i	$0.102383\pi$
$113$			6.72097i			0.632256i	−0.948717	+	0.316128i	$0.897617\pi$
$114$	−7.74990			−0.725845
$115$	1.65661	+	10.3434i	0.154479	+	0.964526i
$116$	−2.36297			−0.219397
$117$		−	0.854305i		−	0.0789805i
$118$		−	6.41586i		−	0.590628i
$119$	−6.25508			−0.573402
$120$	−2.20793	+	0.353624i	−0.201555	+	0.0322813i
$121$	31.3805			2.85277
$122$		−	10.9672i		−	0.992922i
$123$			4.17463i			0.376413i
$124$	9.17599			0.824028
$125$	−9.93524	+	5.12748i	−0.888635	+	0.458615i
$126$	4.51003			0.401786
$127$		−	16.8543i		−	1.49558i	−0.663937	−	0.747789i	$-0.731116\pi$
$127$		−	16.8543i		−	1.49558i	0.663937	−	0.747789i	$-0.268884\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.65573			−0.321869
$130$	1.88624	−	0.302103i	0.165435	−	0.0264962i
$131$	1.05650			0.0923070			0.0461535	−	0.998934i	$-0.485304\pi$
$131$	1.05650			0.0923070			0.0461535	+	0.998934i	$0.485304\pi$
$132$			6.51003i			0.566626i
$133$			34.9523i			3.03075i
$134$	12.9143			1.11563
$135$	0.353624	+	2.20793i	0.0304351	+	0.190028i
$136$	1.38693			0.118928
$137$			19.3329i			1.65172i	0.563876	+	0.825860i	$0.309310\pi$
$137$			19.3329i			1.65172i	−0.563876	+	0.825860i	$0.690690\pi$
$138$			4.68466i			0.398785i
$139$	−6.69625			−0.567969			−0.283984	−	0.958829i	$-0.591656\pi$
$139$	−6.69625			−0.567969			−0.283984	+	0.958829i	$0.591656\pi$
$140$	1.59485	+	9.95783i	0.134790	+	0.841590i
$141$	10.4159			0.877173
$142$		−	0.0391629i		−	0.00328648i
$143$		−	5.56155i		−	0.465080i
$144$	−1.00000			−0.0833333
$145$	−5.21728	+	0.835604i	−0.433271	+	0.0693931i
$146$	−7.16440			−0.592930
$147$		−	13.3404i		−	1.10030i
$148$			1.00000i			0.0821995i
$149$	−15.3968			−1.26135			−0.630676	−	0.776046i	$-0.717222\pi$
$149$	−15.3968			−1.26135			−0.630676	+	0.776046i	$0.717222\pi$
$150$	−4.74990	+	1.56155i	−0.387828	+	0.127500i
$151$	−13.9774			−1.13747			−0.568733	−	0.822522i	$-0.692566\pi$
$151$	−13.9774			−1.13747			−0.568733	+	0.822522i	$0.692566\pi$
$152$		−	7.74990i		−	0.628600i
$153$		−	1.38693i		−	0.112126i
$154$	29.3604			2.36593
$155$	20.2599	−	3.24485i	1.62732	−	0.260633i
$156$	0.854305			0.0683991
$157$			3.07022i			0.245030i	0.992467	+	0.122515i	$0.0390960\pi$
$157$			3.07022i			0.245030i	−0.992467	+	0.122515i	$0.960904\pi$
$158$			7.35062i			0.584784i
$159$	−9.61444			−0.762474
$160$	−0.353624	−	2.20793i	−0.0279564	−	0.174552i
$161$	21.1280			1.66512
$162$			1.00000i			0.0785674i
$163$			15.3026i			1.19859i	0.800528	+	0.599295i	$0.204553\pi$
$163$			15.3026i			1.19859i	−0.800528	+	0.599295i	$0.795447\pi$
$164$	−4.17463			−0.325984
$165$	2.30210	+	14.3737i	0.179218	+	1.11899i
$166$	10.9975			0.853570
$167$			5.16712i			0.399844i	0.979812	+	0.199922i	$0.0640688\pi$
$167$			5.16712i			0.399844i	−0.979812	+	0.199922i	$0.935931\pi$
$168$			4.51003i			0.347956i
$169$	12.2702			0.943859
$170$	3.06223	−	0.490450i	0.234863	−	0.0376158i
$171$	−7.74990			−0.592650
$172$		−	3.65573i		−	0.278747i
$173$		−	7.59397i		−	0.577359i	−0.957426	−	0.288680i	$-0.906784\pi$
$173$		−	7.59397i		−	0.577359i	0.957426	−	0.288680i	$-0.0932162\pi$
$174$	−2.36297			−0.179137
$175$	7.04265	+	21.4222i	0.532374	+	1.61937i
$176$	−6.51003			−0.490712
$177$		−	6.41586i		−	0.482245i
$178$		−	5.73120i		−	0.429572i
$179$	−15.1258			−1.13056			−0.565279	−	0.824900i	$-0.691231\pi$
$179$	−15.1258			−1.13056			−0.565279	+	0.824900i	$0.691231\pi$
$180$	−2.20793	+	0.353624i	−0.164569	+	0.0263576i
$181$	−23.0360			−1.71226			−0.856128	−	0.516764i	$-0.827136\pi$
$181$	−23.0360			−1.71226			−0.856128	+	0.516764i	$0.827136\pi$
$182$		−	3.85294i		−	0.285599i
$183$		−	10.9672i		−	0.810717i
$184$	−4.68466			−0.345358
$185$	0.353624	+	2.20793i	0.0259989	+	0.162330i
$186$	9.17599			0.672816
$187$		−	9.02893i		−	0.660261i
$188$			10.4159i			0.759655i
$189$	4.51003			0.328057
$190$	−2.74055	−	17.1112i	−0.198820	−	1.24138i
$191$	3.99113			0.288788			0.144394	−	0.989520i	$-0.453877\pi$
$191$	3.99113			0.288788			0.144394	+	0.989520i	$0.453877\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	14.3767i		−	1.03486i	−0.855726	−	0.517429i	$-0.826889\pi$
$193$		−	14.3767i		−	1.03486i	0.855726	−	0.517429i	$-0.173111\pi$
$194$	−11.6744			−0.838175
$195$	1.88624	−	0.302103i	0.135077	−	0.0216340i
$196$	13.3404			0.952885
$197$		−	19.0614i		−	1.35807i	−0.734108	−	0.679033i	$-0.762399\pi$
$197$		−	19.0614i		−	1.35807i	0.734108	−	0.679033i	$-0.237601\pi$
$198$			6.51003i			0.462648i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−1.56155	−	4.74990i	−0.110418	−	0.335869i
$201$	12.9143			0.910904
$202$			2.00000i			0.140720i
$203$			10.6571i			0.747981i
$204$	1.38693			0.0971042
$205$	−9.21728	+	1.47625i	−0.643763	+	0.103106i
$206$	0.310091			0.0216050
$207$			4.68466i			0.325606i
$208$			0.854305i			0.0592354i
$209$	−50.4521			−3.48984
$210$	1.59485	+	9.95783i	0.110055	+	0.687155i
$211$	−21.0916			−1.45201			−0.726004	−	0.687690i	$-0.758625\pi$
$211$	−21.0916			−1.45201			−0.726004	+	0.687690i	$0.758625\pi$
$212$		−	9.61444i		−	0.660322i
$213$		−	0.0391629i		−	0.00268340i
$214$	−5.10052			−0.348664
$215$	−1.29275	−	8.07158i	−0.0881650	−	0.550477i
$216$	−1.00000			−0.0680414
$217$		−	41.3840i		−	2.80933i
$218$		−	6.40426i		−	0.433752i
$219$	−7.16440			−0.484125
$220$	−14.3737	+	2.30210i	−0.969074	+	0.155208i
$221$	−1.18486			−0.0797022
$222$			1.00000i			0.0671156i
$223$		−	2.48744i		−	0.166571i	−0.996526	−	0.0832857i	$-0.973459\pi$
$223$		−	2.48744i		−	0.166571i	0.996526	−	0.0832857i	$-0.0265414\pi$
$224$	−4.51003			−0.301339
$225$	−4.74990	+	1.56155i	−0.316660	+	0.104104i
$226$	−6.72097			−0.447072
$227$			21.1583i			1.40432i	0.712018	+	0.702161i	$0.247781\pi$
$227$			21.1583i			1.40432i	−0.712018	+	0.702161i	$0.752219\pi$
$228$		−	7.74990i		−	0.513250i
$229$	−1.58414			−0.104683			−0.0523415	−	0.998629i	$-0.516668\pi$
$229$	−1.58414			−0.104683			−0.0523415	+	0.998629i	$0.516668\pi$
$230$	−10.3434	+	1.65661i	−0.682023	+	0.109233i
$231$	29.3604			1.93178
$232$		−	2.36297i		−	0.155137i
$233$			19.8491i			1.30035i	0.759782	+	0.650177i	$0.225305\pi$
$233$			19.8491i			1.30035i	−0.759782	+	0.650177i	$0.774695\pi$
$234$	0.854305			0.0558477
$235$	3.68330	+	22.9975i	0.240272	+	1.50019i
$236$	6.41586			0.417637
$237$			7.35062i			0.477474i
$238$		−	6.25508i		−	0.405457i
$239$	9.86454			0.638084			0.319042	−	0.947741i	$-0.396639\pi$
$239$	9.86454			0.638084			0.319042	+	0.947741i	$0.396639\pi$
$240$	−0.353624	−	2.20793i	−0.0228263	−	0.142521i
$241$	−4.35799			−0.280723			−0.140362	−	0.990100i	$-0.544826\pi$
$241$	−4.35799			−0.280723			−0.140362	+	0.990100i	$0.544826\pi$
$242$			31.3805i			2.01722i
$243$			1.00000i			0.0641500i
$244$	10.9672			0.702102
$245$	29.4546	−	4.71748i	1.88179	−	0.301389i
$246$	−4.17463			−0.266164
$247$			6.62078i			0.421270i
$248$			9.17599i			0.582676i
$249$	10.9975			0.696937
$250$	−5.12748	−	9.93524i	−0.324290	−	0.628360i
$251$	−29.5604			−1.86584			−0.932918	−	0.360090i	$-0.882746\pi$
$251$	−29.5604			−1.86584			−0.932918	+	0.360090i	$0.882746\pi$
$252$			4.51003i			0.284105i
$253$			30.4973i			1.91735i
$254$	16.8543			1.05753
$255$	3.06223	−	0.490450i	0.191765	−	0.0307132i
$256$	1.00000			0.0625000
$257$		−	14.2511i		−	0.888957i	−0.895790	−	0.444478i	$-0.853389\pi$
$257$		−	14.2511i		−	0.888957i	0.895790	−	0.444478i	$-0.146611\pi$
$258$		−	3.65573i		−	0.227596i
$259$	4.51003			0.280240
$260$	0.302103	+	1.88624i	0.0187356	+	0.116980i
$261$	−2.36297			−0.146264
$262$			1.05650i			0.0652709i
$263$			9.53398i			0.587891i	0.955822	+	0.293945i	$0.0949684\pi$
$263$			9.53398i			0.587891i	−0.955822	+	0.293945i	$0.905032\pi$
$264$	−6.51003			−0.400665
$265$	−3.39989	−	21.2280i	−0.208854	−	1.30403i
$266$	−34.9523			−2.14306
$267$		−	5.73120i		−	0.350744i
$268$			12.9143i			0.788866i
$269$	−12.2049			−0.744147			−0.372074	−	0.928203i	$-0.621353\pi$
$269$	−12.2049			−0.744147			−0.372074	+	0.928203i	$0.621353\pi$
$270$	−2.20793	+	0.353624i	−0.134370	+	0.0215209i
$271$	−1.30873			−0.0794996			−0.0397498	−	0.999210i	$-0.512656\pi$
$271$	−1.30873			−0.0794996			−0.0397498	+	0.999210i	$0.512656\pi$
$272$			1.38693i			0.0840947i
$273$		−	3.85294i		−	0.233191i
$274$	−19.3329			−1.16794
$275$	−30.9220	+	10.1658i	−1.86467	+	0.613018i
$276$	−4.68466			−0.281983
$277$			0.854305i			0.0513302i	0.999671	+	0.0256651i	$0.00817035\pi$
$277$			0.854305i			0.0513302i	−0.999671	+	0.0256651i	$0.991830\pi$
$278$		−	6.69625i		−	0.401614i
$279$	9.17599			0.549352
$280$	−9.95783	+	1.59485i	−0.595094	+	0.0953108i
$281$	−14.5397			−0.867367			−0.433684	−	0.901065i	$-0.642786\pi$
$281$	−14.5397			−0.867367			−0.433684	+	0.901065i	$0.642786\pi$
$282$			10.4159i			0.620255i
$283$		−	25.5538i		−	1.51901i	−0.650499	−	0.759507i	$-0.725440\pi$
$283$		−	25.5538i		−	1.51901i	0.650499	−	0.759507i	$-0.274560\pi$
$284$	0.0391629			0.00232389
$285$	−2.74055	−	17.1112i	−0.162336	−	1.01358i
$286$	5.56155			0.328862
$287$			18.8277i			1.11136i
$288$		−	1.00000i		−	0.0589256i
$289$	15.0764			0.886849
$290$	−0.835604	−	5.21728i	−0.0490684	−	0.306369i
$291$	−11.6744			−0.684367
$292$		−	7.16440i		−	0.419265i
$293$			7.80551i			0.456003i	0.973661	+	0.228001i	$0.0732191\pi$
$293$			7.80551i			0.456003i	−0.973661	+	0.228001i	$0.926781\pi$
$294$	13.3404			0.778027
$295$	14.1658	−	2.26880i	0.824762	−	0.132095i
$296$	−1.00000			−0.0581238
$297$			6.51003i			0.377750i
$298$		−	15.3968i		−	0.891910i
$299$	4.00213			0.231449
$300$	−1.56155	−	4.74990i	−0.0901563	−	0.274236i
$301$	−16.4874			−0.950320
$302$		−	13.9774i		−	0.804310i
$303$			2.00000i			0.114897i
$304$	7.74990			0.444487
$305$	24.2148	−	3.87826i	1.38653	−	0.222068i
$306$	1.38693			0.0792853
$307$			12.6868i			0.724073i	0.932164	+	0.362037i	$0.117918\pi$
$307$			12.6868i			0.724073i	−0.932164	+	0.362037i	$0.882082\pi$
$308$			29.3604i			1.67297i
$309$	0.310091			0.0176404
$310$	3.24485	+	20.2599i	0.184295	+	1.15069i
$311$	6.09806			0.345789			0.172895	−	0.984940i	$-0.444688\pi$
$311$	6.09806			0.345789			0.172895	+	0.984940i	$0.444688\pi$
$312$			0.854305i			0.0483655i
$313$			13.0113i			0.735443i	0.929936	+	0.367722i	$0.119862\pi$
$313$			13.0113i			0.735443i	−0.929936	+	0.367722i	$0.880138\pi$
$314$	−3.07022			−0.173263
$315$	1.59485	+	9.95783i	0.0898599	+	0.561060i
$316$	−7.35062			−0.413504
$317$		−	3.89198i		−	0.218595i	−0.994009	−	0.109298i	$-0.965140\pi$
$317$		−	3.89198i		−	0.218595i	0.994009	−	0.109298i	$-0.0348602\pi$
$318$		−	9.61444i		−	0.539151i
$319$	−15.3830			−0.861285
$320$	2.20793	−	0.353624i	0.123427	−	0.0197682i
$321$	−5.10052			−0.284683
$322$			21.1280i			1.17742i
$323$			10.7485i			0.598065i
$324$	−1.00000			−0.0555556
$325$	1.33404	+	4.05786i	0.0739994	+	0.225090i
$326$	−15.3026			−0.847532
$327$		−	6.40426i		−	0.354157i
$328$		−	4.17463i		−	0.230505i
$329$	46.9758			2.58986
$330$	−14.3737	+	2.30210i	−0.791245	+	0.126727i
$331$	18.0374			0.991425			0.495713	−	0.868487i	$-0.334907\pi$
$331$	18.0374			0.991425			0.495713	+	0.868487i	$0.334907\pi$
$332$			10.9975i			0.603565i
$333$			1.00000i			0.0547997i
$334$	−5.16712			−0.282732
$335$	4.56680	+	28.5138i	0.249511	+	1.55788i
$336$	−4.51003			−0.246042
$337$			15.6843i			0.854376i	0.904163	+	0.427188i	$0.140496\pi$
$337$			15.6843i			0.854376i	−0.904163	+	0.427188i	$0.859504\pi$
$338$			12.2702i			0.667409i
$339$	−6.72097			−0.365033
$340$	0.490450	+	3.06223i	0.0265984	+	0.166073i
$341$	59.7360			3.23488
$342$		−	7.74990i		−	0.419067i
$343$		−	28.5953i		−	1.54400i
$344$	3.65573			0.197104
$345$	−10.3434	+	1.65661i	−0.556870	+	0.0891887i
$346$	7.59397			0.408255
$347$		−	18.8052i		−	1.00952i	−0.863260	−	0.504759i	$-0.831581\pi$
$347$		−	18.8052i		−	1.00952i	0.863260	−	0.504759i	$-0.168419\pi$
$348$		−	2.36297i		−	0.126669i
$349$	18.3981			0.984829			0.492414	−	0.870361i	$-0.336114\pi$
$349$	18.3981			0.984829			0.492414	+	0.870361i	$0.336114\pi$
$350$	−21.4222	+	7.04265i	−1.14506	+	0.376446i
$351$	0.854305			0.0455994
$352$		−	6.51003i		−	0.346986i
$353$			15.6078i			0.830721i	0.909657	+	0.415360i	$0.136344\pi$
$353$			15.6078i			0.830721i	−0.909657	+	0.415360i	$0.863656\pi$
$354$	6.41586			0.340999
$355$	0.0864689	−	0.0138489i	0.00458929	−	0.000735025i
$356$	5.73120			0.303753
$357$		−	6.25508i		−	0.331054i
$358$		−	15.1258i		−	0.799425i
$359$	−16.4984			−0.870754			−0.435377	−	0.900248i	$-0.643385\pi$
$359$	−16.4984			−0.870754			−0.435377	+	0.900248i	$0.643385\pi$
$360$	−0.353624	−	2.20793i	−0.0186376	−	0.116368i
$361$	41.0610			2.16110
$362$		−	23.0360i		−	1.21075i
$363$			31.3805i			1.64705i
$364$	3.85294			0.201949
$365$	−2.53350	−	15.8185i	−0.132610	−	0.827977i
$366$	10.9672			0.573264
$367$		−	6.69565i		−	0.349510i	−0.984612	−	0.174755i	$-0.944087\pi$
$367$		−	6.69565i		−	0.349510i	0.984612	−	0.174755i	$-0.0559134\pi$
$368$		−	4.68466i		−	0.244205i
$369$	−4.17463			−0.217322
$370$	−2.20793	+	0.353624i	−0.114785	+	0.0183840i
$371$	−43.3614			−2.25121
$372$			9.17599i			0.475753i
$373$		−	0.179607i		−	0.00929970i	−0.999989	−	0.00464985i	$-0.998520\pi$
$373$		−	0.179607i		−	0.00929970i	0.999989	−	0.00464985i	$-0.00148010\pi$
$374$	9.02893			0.466875
$375$	−5.12748	−	9.93524i	−0.264782	−	0.513054i
$376$	−10.4159			−0.537157
$377$			2.01870i			0.103968i
$378$			4.51003i			0.231971i
$379$	−11.0288			−0.566512			−0.283256	−	0.959044i	$-0.591415\pi$
$379$	−11.0288			−0.566512			−0.283256	+	0.959044i	$0.591415\pi$
$380$	17.1112	−	2.74055i	0.877788	−	0.140587i
$381$	16.8543			0.863472
$382$			3.99113i			0.204204i
$383$		−	9.47897i		−	0.484353i	−0.970232	−	0.242176i	$-0.922139\pi$
$383$		−	9.47897i		−	0.484353i	0.970232	−	0.242176i	$-0.0778613\pi$
$384$	1.00000			0.0510310
$385$	10.3826	+	64.8258i	0.529144	+	3.30383i
$386$	14.3767			0.731755
$387$		−	3.65573i		−	0.185831i
$388$		−	11.6744i		−	0.592679i
$389$	7.73405			0.392132			0.196066	−	0.980591i	$-0.437183\pi$
$389$	7.73405			0.392132			0.196066	+	0.980591i	$0.437183\pi$
$390$	0.302103	+	1.88624i	0.0152976	+	0.0955137i
$391$	6.49727			0.328581
$392$			13.3404i			0.673791i
$393$			1.05650i			0.0532934i
$394$	19.0614			0.960297
$395$	−16.2296	+	2.59935i	−0.816602	+	0.130788i
$396$	−6.51003			−0.327141
$397$			23.0300i			1.15584i	0.816092	+	0.577922i	$0.196136\pi$
$397$			23.0300i			1.15584i	−0.816092	+	0.577922i	$0.803864\pi$
$398$			8.00000i			0.401004i
$399$	−34.9523			−1.74980
$400$	4.74990	−	1.56155i	0.237495	−	0.0780776i
$401$	10.5355			0.526116			0.263058	−	0.964780i	$-0.415269\pi$
$401$	10.5355			0.526116			0.263058	+	0.964780i	$0.415269\pi$
$402$			12.9143i			0.644107i
$403$		−	7.83909i		−	0.390493i
$404$	−2.00000			−0.0995037
$405$	−2.20793	+	0.353624i	−0.109713	+	0.0175717i
$406$	−10.6571			−0.528902
$407$			6.51003i			0.322690i
$408$			1.38693i			0.0686631i
$409$	16.4186			0.811847			0.405923	−	0.913907i	$-0.366950\pi$
$409$	16.4186			0.811847			0.405923	+	0.913907i	$0.366950\pi$
$410$	−1.47625	−	9.21728i	−0.0729067	−	0.455209i
$411$	−19.3329			−0.953621
$412$			0.310091i			0.0152771i
$413$		−	28.9357i		−	1.42383i
$414$	−4.68466			−0.230238
$415$	3.88897	+	24.2816i	0.190902	+	1.19194i
$416$	−0.854305			−0.0418858
$417$		−	6.69625i		−	0.327917i
$418$		−	50.4521i		−	2.46769i
$419$	−6.45442			−0.315319			−0.157660	−	0.987494i	$-0.550395\pi$
$419$	−6.45442			−0.315319			−0.157660	+	0.987494i	$0.550395\pi$
$420$	−9.95783	+	1.59485i	−0.485892	+	0.0778210i
$421$	−32.8966			−1.60328			−0.801640	−	0.597807i	$-0.796039\pi$
$421$	−32.8966			−1.60328			−0.801640	+	0.597807i	$0.796039\pi$
$422$		−	21.0916i		−	1.02673i
$423$			10.4159i			0.506436i
$424$	9.61444			0.466918
$425$	2.16576	+	6.58776i	0.105055	+	0.319553i
$426$	0.0391629			0.00189745
$427$		−	49.4623i		−	2.39365i
$428$		−	5.10052i		−	0.246543i
$429$	5.56155			0.268514
$430$	8.07158	−	1.29275i	0.389246	−	0.0623420i
$431$	−25.3879			−1.22289			−0.611446	−	0.791286i	$-0.709412\pi$
$431$	−25.3879			−1.22289			−0.611446	+	0.791286i	$0.709412\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			0.147057i			0.00706712i	0.999994	+	0.00353356i	$0.00112477\pi$
$433$			0.147057i			0.00706712i	−0.999994	+	0.00353356i	$0.998875\pi$
$434$	41.3840			1.98650
$435$	−0.835604	−	5.21728i	−0.0400642	−	0.250149i
$436$	6.40426			0.306709
$437$		−	36.3056i		−	1.73673i
$438$		−	7.16440i		−	0.342328i
$439$	−7.91068			−0.377556			−0.188778	−	0.982020i	$-0.560453\pi$
$439$	−7.91068			−0.377556			−0.188778	+	0.982020i	$0.560453\pi$
$440$	−2.30210	−	14.3737i	−0.109748	−	0.685239i
$441$	13.3404			0.635256
$442$		−	1.18486i		−	0.0563579i
$443$		−	2.31883i		−	0.110171i	−0.998482	−	0.0550855i	$-0.982457\pi$
$443$		−	2.31883i		−	0.110171i	0.998482	−	0.0550855i	$-0.0175431\pi$
$444$	−1.00000			−0.0474579
$445$	12.6541	−	2.02669i	0.599861	−	0.0960743i
$446$	2.48744			0.117784
$447$		−	15.3968i		−	0.728242i
$448$		−	4.51003i		−	0.213079i
$449$	5.97256			0.281862			0.140931	−	0.990019i	$-0.454990\pi$
$449$	5.97256			0.281862			0.140931	+	0.990019i	$0.454990\pi$
$450$	−1.56155	−	4.74990i	−0.0736123	−	0.223912i
$451$	−27.1770			−1.27971
$452$		−	6.72097i		−	0.316128i
$453$		−	13.9774i		−	0.656716i
$454$	−21.1583			−0.993006
$455$	8.50702	−	1.36249i	0.398815	−	0.0638746i
$456$	7.74990			0.362922
$457$		−	25.5928i		−	1.19718i	−0.801055	−	0.598591i	$-0.795728\pi$
$457$		−	25.5928i		−	1.19718i	0.801055	−	0.598591i	$-0.204272\pi$
$458$		−	1.58414i		−	0.0740221i
$459$	1.38693			0.0647362
$460$	−1.65661	−	10.3434i	−0.0772397	−	0.482263i
$461$	−7.65573			−0.356563			−0.178281	−	0.983980i	$-0.557054\pi$
$461$	−7.65573			−0.356563			−0.178281	+	0.983980i	$0.557054\pi$
$462$			29.3604i			1.36597i
$463$		−	9.76744i		−	0.453931i	−0.973903	−	0.226966i	$-0.927119\pi$
$463$		−	9.76744i		−	0.453931i	0.973903	−	0.226966i	$-0.0728805\pi$
$464$	2.36297			0.109698
$465$	3.24485	+	20.2599i	0.150476	+	0.939532i
$466$	−19.8491			−0.919490
$467$		−	20.8856i		−	0.966469i	−0.875491	−	0.483234i	$-0.839462\pi$
$467$		−	20.8856i		−	0.966469i	0.875491	−	0.483234i	$-0.160538\pi$
$468$			0.854305i			0.0394903i
$469$	58.2439			2.68945
$470$	−22.9975	+	3.68330i	−1.06079	+	0.169898i
$471$	−3.07022			−0.141468
$472$			6.41586i			0.295314i
$473$		−	23.7989i		−	1.09427i
$474$	−7.35062			−0.337625
$475$	36.8113	−	12.1019i	1.68902	−	0.555272i
$476$	6.25508			0.286701
$477$		−	9.61444i		−	0.440215i
$478$			9.86454i			0.451193i
$479$	−12.4357			−0.568203			−0.284101	−	0.958794i	$-0.591695\pi$
$479$	−12.4357			−0.568203			−0.284101	+	0.958794i	$0.591695\pi$
$480$	2.20793	−	0.353624i	0.100778	−	0.0161406i
$481$	0.854305			0.0389530
$482$		−	4.35799i		−	0.198501i
$483$			21.1280i			0.961355i
$484$	−31.3805			−1.42639
$485$	−4.12836	−	25.7763i	−0.187459	−	1.17044i
$486$	−1.00000			−0.0453609
$487$			15.7113i			0.711949i	0.934496	+	0.355974i	$0.115851\pi$
$487$			15.7113i			0.711949i	−0.934496	+	0.355974i	$0.884149\pi$
$488$			10.9672i			0.496461i
$489$	−15.3026			−0.692007
$490$	4.71748	+	29.4546i	0.213114	+	1.33062i
$491$	25.6656			1.15827			0.579135	−	0.815231i	$-0.303390\pi$
$491$	25.6656			1.15827			0.579135	+	0.815231i	$0.303390\pi$
$492$		−	4.17463i		−	0.188207i
$493$			3.27727i			0.147601i
$494$	−6.62078			−0.297883
$495$	−14.3737	+	2.30210i	−0.646049	+	0.103472i
$496$	−9.17599			−0.412014
$497$		−	0.176626i		−	0.00792275i
$498$			10.9975i			0.492809i
$499$	−28.4361			−1.27298			−0.636488	−	0.771287i	$-0.719613\pi$
$499$	−28.4361			−1.27298			−0.636488	+	0.771287i	$0.719613\pi$
$500$	9.93524	−	5.12748i	0.444317	−	0.229308i
$501$	−5.16712			−0.230850
$502$		−	29.5604i		−	1.31934i
$503$			36.0980i			1.60953i	0.593594	+	0.804765i	$0.297709\pi$
$503$			36.0980i			1.60953i	−0.593594	+	0.804765i	$0.702291\pi$
$504$	−4.51003			−0.200893
$505$	−4.41586	+	0.707248i	−0.196503	+	0.0314721i
$506$	−30.4973			−1.35577
$507$			12.2702i			0.544937i
$508$			16.8543i			0.747789i
$509$	6.31222			0.279784			0.139892	−	0.990167i	$-0.455324\pi$
$509$	6.31222			0.279784			0.139892	+	0.990167i	$0.455324\pi$
$510$	0.490450	+	3.06223i	0.0217175	+	0.135598i
$511$	−32.3117			−1.42938
$512$			1.00000i			0.0441942i
$513$		−	7.74990i		−	0.342166i
$514$	14.2511			0.628587
$515$	0.109656	+	0.684658i	0.00483200	+	0.0301697i
$516$	3.65573			0.160934
$517$			67.8076i			2.98217i
$518$			4.51003i			0.198159i
$519$	7.59397			0.333338
$520$	−1.88624	+	0.302103i	−0.0827173	+	0.0132481i
$521$	43.5235			1.90680			0.953399	−	0.301712i	$-0.0975580\pi$
$521$	43.5235			1.90680			0.953399	+	0.301712i	$0.0975580\pi$
$522$		−	2.36297i		−	0.103425i
$523$		−	19.1286i		−	0.836433i	−0.908347	−	0.418217i	$-0.862655\pi$
$523$		−	19.1286i		−	0.836433i	0.908347	−	0.418217i	$-0.137345\pi$
$524$	−1.05650			−0.0461535
$525$	−21.4222	+	7.04265i	−0.934941	+	0.307367i
$526$	−9.53398			−0.415701
$527$		−	12.7264i		−	0.554371i
$528$		−	6.51003i		−	0.283313i
$529$	1.05398			0.0458250
$530$	21.2280	−	3.39989i	0.922085	−	0.147682i
$531$	6.41586			0.278425
$532$		−	34.9523i		−	1.51537i
$533$			3.56640i			0.154478i
$534$	5.73120			0.248013
$535$	−1.80366	−	11.2616i	−0.0779792	−	0.486880i
$536$	−12.9143			−0.557813
$537$		−	15.1258i		−	0.652728i
$538$		−	12.2049i		−	0.526192i
$539$	86.8463			3.74074
$540$	−0.353624	−	2.20793i	−0.0152175	−	0.0950141i
$541$	−0.447188			−0.0192261			−0.00961305	−	0.999954i	$-0.503060\pi$
$541$	−0.447188			−0.0192261			−0.00961305	+	0.999954i	$0.503060\pi$
$542$		−	1.30873i		−	0.0562147i
$543$		−	23.0360i		−	0.988571i
$544$	−1.38693			−0.0594640
$545$	14.1402	−	2.26470i	0.605698	−	0.0970091i
$546$	3.85294			0.164891
$547$		−	12.3404i		−	0.527637i	−0.964572	−	0.263818i	$-0.915018\pi$
$547$		−	12.3404i		−	0.527637i	0.964572	−	0.263818i	$-0.0849820\pi$
$548$		−	19.3329i		−	0.825860i
$549$	10.9672			0.468068
$550$	−10.1658	−	30.9220i	−0.433469	−	1.31852i
$551$	18.3128			0.780152
$552$		−	4.68466i		−	0.199392i
$553$			33.1515i			1.40975i
$554$	−0.854305			−0.0362959
$555$	−2.20793	+	0.353624i	−0.0937214	+	0.0150105i
$556$	6.69625			0.283984
$557$			3.48110i			0.147499i	0.997277	+	0.0737495i	$0.0234965\pi$
$557$			3.48110i			0.147499i	−0.997277	+	0.0737495i	$0.976503\pi$
$558$			9.17599i			0.388451i
$559$	−3.12311			−0.132093
$560$	−1.59485	−	9.95783i	−0.0673949	−	0.420795i
$561$	9.02893			0.381202
$562$		−	14.5397i		−	0.613321i
$563$			34.3606i			1.44813i	0.689732	+	0.724064i	$0.257728\pi$
$563$			34.3606i			1.44813i	−0.689732	+	0.724064i	$0.742272\pi$
$564$	−10.4159			−0.438587
$565$	−2.37669	−	14.8394i	−0.0999883	−	0.624299i
$566$	25.5538			1.07411
$567$			4.51003i			0.189404i
$568$			0.0391629i			0.00164324i
$569$	−9.38195			−0.393312			−0.196656	−	0.980473i	$-0.563008\pi$
$569$	−9.38195			−0.393312			−0.196656	+	0.980473i	$0.563008\pi$
$570$	17.1112	−	2.74055i	0.716711	−	0.114789i
$571$	−13.7528			−0.575535			−0.287767	−	0.957700i	$-0.592913\pi$
$571$	−13.7528			−0.575535			−0.287767	+	0.957700i	$0.592913\pi$
$572$			5.56155i			0.232540i
$573$			3.99113i			0.166732i
$574$	−18.8277			−0.785853
$575$	−7.31534	−	22.2517i	−0.305071	−	0.927958i
$576$	1.00000			0.0416667
$577$			32.8718i			1.36847i	0.729260	+	0.684236i	$0.239864\pi$
$577$			32.8718i			1.36847i	−0.729260	+	0.684236i	$0.760136\pi$
$578$			15.0764i			0.627097i
$579$	14.3767			0.597475
$580$	5.21728	−	0.835604i	0.216636	−	0.0346966i
$581$	49.5990			2.05771
$582$		−	11.6744i		−	0.483921i
$583$		−	62.5903i		−	2.59222i
$584$	7.16440			0.296465
$585$	0.302103	+	1.88624i	0.0124904	+	0.0779866i
$586$	−7.80551			−0.322443
$587$			4.80355i			0.198264i	0.995074	+	0.0991318i	$0.0316066\pi$
$587$			4.80355i			0.198264i	−0.995074	+	0.0991318i	$0.968393\pi$
$588$			13.3404i			0.550148i
$589$	−71.1130			−2.93016
$590$	2.26880	+	14.1658i	0.0934050	+	0.583195i
$591$	19.0614			0.784079
$592$		−	1.00000i		−	0.0410997i
$593$			3.78847i			0.155574i	0.996970	+	0.0777868i	$0.0247854\pi$
$593$			3.78847i			0.155574i	−0.996970	+	0.0777868i	$0.975215\pi$
$594$	−6.51003			−0.267110
$595$	13.8108	−	2.21195i	0.566186	−	0.0906809i
$596$	15.3968			0.630676
$597$			8.00000i			0.327418i
$598$			4.00213i			0.163659i
$599$	−9.85354			−0.402605			−0.201302	−	0.979529i	$-0.564517\pi$
$599$	−9.85354			−0.402605			−0.201302	+	0.979529i	$0.564517\pi$
$600$	4.74990	−	1.56155i	0.193914	−	0.0637501i
$601$	43.6546			1.78071			0.890353	−	0.455270i	$-0.150457\pi$
$601$	43.6546			1.78071			0.890353	+	0.455270i	$0.150457\pi$
$602$		−	16.4874i		−	0.671978i
$603$			12.9143i			0.525911i
$604$	13.9774			0.568733
$605$	−69.2859	+	11.0969i	−2.81687	+	0.451153i
$606$	−2.00000			−0.0812444
$607$		−	27.9648i		−	1.13506i	−0.823354	−	0.567528i	$-0.807900\pi$
$607$		−	27.9648i		−	1.13506i	0.823354	−	0.567528i	$-0.192100\pi$
$608$			7.74990i			0.314300i
$609$	−10.6571			−0.431847
$610$	3.87826	+	24.2148i	0.157026	+	0.980427i
$611$	8.89832			0.359987
$612$			1.38693i			0.0560632i
$613$		−	18.0930i		−	0.730770i	−0.930857	−	0.365385i	$-0.880937\pi$
$613$		−	18.0930i		−	0.730770i	0.930857	−	0.365385i	$-0.119063\pi$
$614$	−12.6868			−0.511997
$615$	−1.47625	−	9.21728i	−0.0595281	−	0.371677i
$616$	−29.3604			−1.18297
$617$		−	17.5417i		−	0.706202i	−0.935585	−	0.353101i	$-0.885127\pi$
$617$		−	17.5417i		−	0.706202i	0.935585	−	0.353101i	$-0.114873\pi$
$618$			0.310091i			0.0124737i
$619$	32.1144			1.29079			0.645394	−	0.763850i	$-0.276693\pi$
$619$	32.1144			1.29079			0.645394	+	0.763850i	$0.276693\pi$
$620$	−20.2599	+	3.24485i	−0.813658	+	0.130316i
$621$	−4.68466			−0.187989
$622$			6.09806i			0.244510i
$623$		−	25.8479i		−	1.03557i
$624$	−0.854305			−0.0341996
$625$	20.1231	−	14.8344i	0.804924	−	0.593378i
$626$	−13.0113			−0.520037
$627$		−	50.4521i		−	2.01486i
$628$		−	3.07022i		−	0.122515i
$629$	1.38693			0.0553004
$630$	−9.95783	+	1.59485i	−0.396729	+	0.0635405i
$631$	−23.8441			−0.949218			−0.474609	−	0.880197i	$-0.657410\pi$
$631$	−23.8441			−0.949218			−0.474609	+	0.880197i	$0.657410\pi$
$632$		−	7.35062i		−	0.292392i
$633$		−	21.0916i		−	0.838318i
$634$	3.89198			0.154570
$635$	5.96008	+	37.2131i	0.236519	+	1.47676i
$636$	9.61444			0.381237
$637$		−	11.3968i		−	0.451556i
$638$		−	15.3830i		−	0.609020i
$639$	0.0391629			0.00154926
$640$	0.353624	+	2.20793i	0.0139782	+	0.0872761i
$641$	25.0729			0.990322			0.495161	−	0.868801i	$-0.335109\pi$
$641$	25.0729			0.990322			0.495161	+	0.868801i	$0.335109\pi$
$642$		−	5.10052i		−	0.201301i
$643$			32.8834i			1.29680i	0.761301	+	0.648398i	$0.224561\pi$
$643$			32.8834i			1.29680i	−0.761301	+	0.648398i	$0.775439\pi$
$644$	−21.1280			−0.832558
$645$	8.07158	−	1.29275i	0.317818	−	0.0509021i
$646$	−10.7485			−0.422896
$647$			7.99611i			0.314360i	0.987570	+	0.157180i	$0.0502402\pi$
$647$			7.99611i			0.314360i	−0.987570	+	0.157180i	$0.949760\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	41.7674			1.63952
$650$	−4.05786	+	1.33404i	−0.159163	+	0.0523254i
$651$	41.3840			1.62197
$652$		−	15.3026i		−	0.599295i
$653$			6.04518i			0.236566i	0.992980	+	0.118283i	$0.0377390\pi$
$653$			6.04518i			0.236566i	−0.992980	+	0.118283i	$0.962261\pi$
$654$	6.40426			0.250427
$655$	−2.33268	+	0.373604i	−0.0911454	+	0.0145979i
$656$	4.17463			0.162992
$657$		−	7.16440i		−	0.279510i
$658$			46.9758i			1.83131i
$659$	7.77643			0.302927			0.151463	−	0.988463i	$-0.451601\pi$
$659$	7.77643			0.302927			0.151463	+	0.988463i	$0.451601\pi$
$660$	−2.30210	−	14.3737i	−0.0896092	−	0.559495i
$661$	−19.4023			−0.754663			−0.377332	−	0.926078i	$-0.623158\pi$
$661$	−19.4023			−0.754663			−0.377332	+	0.926078i	$0.623158\pi$
$662$			18.0374i			0.701044i
$663$		−	1.18486i		−	0.0460161i
$664$	−10.9975			−0.426785
$665$	−12.3600	−	77.1722i	−0.479299	−	2.99261i
$666$	−1.00000			−0.0387492
$667$		−	11.0697i		−	0.428622i
$668$		−	5.16712i		−	0.199922i
$669$	2.48744			0.0961701
$670$	−28.5138	+	4.56680i	−1.10159	+	0.176431i
$671$	71.3967			2.75624
$672$		−	4.51003i		−	0.173978i
$673$		−	27.9784i		−	1.07849i	−0.842150	−	0.539244i	$-0.818710\pi$
$673$		−	27.9784i		−	1.07849i	0.842150	−	0.539244i	$-0.181290\pi$
$674$	−15.6843			−0.604135
$675$	−1.56155	−	4.74990i	−0.0601042	−	0.182824i
$676$	−12.2702			−0.471929
$677$			10.9733i			0.421739i	0.977514	+	0.210870i	$0.0676295\pi$
$677$			10.9733i			0.421739i	−0.977514	+	0.210870i	$0.932370\pi$
$678$		−	6.72097i		−	0.258117i
$679$	−52.6520			−2.02060
$680$	−3.06223	+	0.490450i	−0.117431	+	0.0188079i
$681$	−21.1583			−0.810786
$682$			59.7360i			2.28741i
$683$		−	20.2973i		−	0.776656i	−0.921521	−	0.388328i	$-0.873053\pi$
$683$		−	20.2973i		−	0.776656i	0.921521	−	0.388328i	$-0.126947\pi$
$684$	7.74990			0.296325
$685$	−6.83657	−	42.6856i	−0.261212	−	1.63093i
$686$	28.5953			1.09178
$687$		−	1.58414i		−	0.0604388i
$688$			3.65573i			0.139373i
$689$	−8.21366			−0.312916
$690$	−1.65661	−	10.3434i	−0.0630660	−	0.393766i
$691$	45.4838			1.73028			0.865142	−	0.501527i	$-0.167228\pi$
$691$	45.4838			1.73028			0.865142	+	0.501527i	$0.167228\pi$
$692$			7.59397i			0.288680i
$693$			29.3604i			1.11531i
$694$	18.8052			0.713837
$695$	14.7848	−	2.36795i	0.560821	−	0.0898216i
$696$	2.36297			0.0895683
$697$			5.78990i			0.219308i
$698$			18.3981i			0.696379i
$699$	−19.8491			−0.750760
$700$	−7.04265	−	21.4222i	−0.266187	−	0.809683i
$701$	30.3520			1.14638			0.573189	−	0.819423i	$-0.305706\pi$
$701$	30.3520			1.14638			0.573189	+	0.819423i	$0.305706\pi$
$702$			0.854305i			0.0322437i
$703$		−	7.74990i		−	0.292293i
$704$	6.51003			0.245356
$705$	−22.9975	+	3.68330i	−0.866135	+	0.138721i
$706$	−15.6078			−0.587408
$707$			9.02006i			0.339234i
$708$			6.41586i			0.241123i
$709$	−39.1082			−1.46874			−0.734370	−	0.678749i	$-0.762522\pi$
$709$	−39.1082			−1.46874			−0.734370	+	0.678749i	$0.762522\pi$
$710$	0.0138489	+	0.0864689i	0.000519741	+	0.00324512i
$711$	−7.35062			−0.275670
$712$			5.73120i			0.214786i
$713$			42.9864i			1.60985i
$714$	6.25508			0.234090
$715$	1.96670	+	12.2795i	0.0735503	+	0.459228i
$716$	15.1258			0.565279
$717$			9.86454i			0.368398i
$718$		−	16.4984i		−	0.615716i
$719$	−11.9883			−0.447087			−0.223544	−	0.974694i	$-0.571763\pi$
$719$	−11.9883			−0.447087			−0.223544	+	0.974694i	$0.571763\pi$
$720$	2.20793	−	0.353624i	0.0822847	−	0.0131788i
$721$	1.39852			0.0520836
$722$			41.0610i			1.52813i
$723$		−	4.35799i		−	0.162076i
$724$	23.0360			0.856128
$725$	11.2239	−	3.68991i	0.416845	−	0.137040i
$726$	−31.3805			−1.16464
$727$			19.2051i			0.712278i	0.934433	+	0.356139i	$0.115907\pi$
$727$			19.2051i			0.712278i	−0.934433	+	0.356139i	$0.884093\pi$
$728$			3.85294i			0.142800i
$729$	−1.00000			−0.0370370
$730$	15.8185	−	2.53350i	0.585468	−	0.0937691i
$731$	−5.07022			−0.187529
$732$			10.9672i			0.405359i
$733$		−	24.9166i		−	0.920314i	−0.887838	−	0.460157i	$-0.847793\pi$
$733$		−	24.9166i		−	0.920314i	0.887838	−	0.460157i	$-0.152207\pi$
$734$	6.69565			0.247141
$735$	4.71748	+	29.4546i	0.174007	+	1.08645i
$736$	4.68466			0.172679
$737$			84.0725i			3.09685i
$738$		−	4.17463i		−	0.153670i
$739$	−23.9047			−0.879347			−0.439674	−	0.898158i	$-0.644906\pi$
$739$	−23.9047			−0.879347			−0.439674	+	0.898158i	$0.644906\pi$
$740$	−0.353624	−	2.20793i	−0.0129995	−	0.0811651i
$741$	−6.62078			−0.243220
$742$		−	43.3614i		−	1.59185i
$743$			27.0739i			0.993245i	0.867967	+	0.496623i	$0.165427\pi$
$743$			27.0739i			0.993245i	−0.867967	+	0.496623i	$0.834573\pi$
$744$	−9.17599			−0.336408
$745$	33.9949	−	5.44466i	1.24548	−	0.199477i
$746$	0.179607			0.00657588
$747$			10.9975i			0.402377i
$748$			9.02893i			0.330130i
$749$	−23.0035			−0.840529
$750$	9.93524	−	5.12748i	0.362784	−	0.187229i
$751$	39.8313			1.45347			0.726733	−	0.686920i	$-0.241038\pi$
$751$	39.8313			1.45347			0.726733	+	0.686920i	$0.241038\pi$
$752$		−	10.4159i		−	0.379827i
$753$		−	29.5604i		−	1.07724i
$754$	−2.01870			−0.0735167
$755$	30.8611	−	4.94275i	1.12315	−	0.179885i
$756$	−4.51003			−0.164028
$757$		−	51.2182i		−	1.86156i	−0.365585	−	0.930778i	$-0.619131\pi$
$757$		−	51.2182i		−	1.86156i	0.365585	−	0.930778i	$-0.380869\pi$
$758$		−	11.0288i		−	0.400584i
$759$	−30.4973			−1.10698
$760$	2.74055	+	17.1112i	0.0994102	+	0.620690i
$761$	−20.8063			−0.754227			−0.377113	−	0.926167i	$-0.623083\pi$
$761$	−20.8063			−0.754227			−0.377113	+	0.926167i	$0.623083\pi$
$762$			16.8543i			0.610567i
$763$		−	28.8834i		−	1.04565i
$764$	−3.99113			−0.144394
$765$	0.490450	+	3.06223i	0.0177323	+	0.110715i
$766$	9.47897			0.342489
$767$		−	5.48110i		−	0.197911i
$768$			1.00000i			0.0360844i
$769$	−49.3329			−1.77899			−0.889495	−	0.456946i	$-0.848943\pi$
$769$	−49.3329			−1.77899			−0.889495	+	0.456946i	$0.848943\pi$
$770$	−64.8258	+	10.3826i	−2.33616	+	0.374161i
$771$	14.2511			0.513240
$772$			14.3767i			0.517429i
$773$			3.38244i			0.121658i	0.998148	+	0.0608290i	$0.0193744\pi$
$773$			3.38244i			0.121658i	−0.998148	+	0.0608290i	$0.980626\pi$
$774$	3.65573			0.131402
$775$	−43.5850	+	14.3288i	−1.56562	+	0.514705i
$776$	11.6744			0.419088
$777$			4.51003i			0.161796i
$778$			7.73405i			0.277279i
$779$	32.3529			1.15916
$780$	−1.88624	+	0.302103i	−0.0675384	+	0.0108170i
$781$	0.254952			0.00912289
$782$			6.49727i			0.232342i
$783$		−	2.36297i		−	0.0844458i
$784$	−13.3404			−0.476442
$785$	−1.08570	−	6.77883i	−0.0387504	−	0.241947i
$786$	−1.05650			−0.0376842
$787$		−	9.39676i		−	0.334958i	−0.985876	−	0.167479i	$-0.946437\pi$
$787$		−	9.39676i		−	0.334958i	0.985876	−	0.167479i	$-0.0535627\pi$
$788$			19.0614i			0.679033i
$789$	−9.53398			−0.339419
$790$	−2.59935	−	16.2296i	−0.0924808	−	0.577425i
$791$	−30.3118			−1.07776
$792$		−	6.51003i		−	0.231324i
$793$		−	9.36932i		−	0.332714i
$794$	−23.0300			−0.817305
$795$	21.2280	−	3.39989i	0.752879	−	0.120582i
$796$	−8.00000			−0.283552
$797$			36.9562i			1.30906i	0.756038	+	0.654528i	$0.227132\pi$
$797$			36.9562i			1.30906i	−0.756038	+	0.654528i	$0.772868\pi$
$798$		−	34.9523i		−	1.23730i
$799$	14.4460			0.511064
$800$	1.56155	+	4.74990i	0.0552092	+	0.167934i
$801$	5.73120			0.202502
$802$			10.5355i			0.372021i
$803$		−	46.6404i		−	1.64591i
$804$	−12.9143			−0.455452
$805$	−46.6490	+	7.47135i	−1.64416	+	0.263331i
$806$	7.83909			0.276120
$807$		−	12.2049i		−	0.429634i
$808$		−	2.00000i		−	0.0703598i
$809$	12.4367			0.437251			0.218625	−	0.975809i	$-0.429843\pi$
$809$	12.4367			0.437251			0.218625	+	0.975809i	$0.429843\pi$
$810$	−0.353624	−	2.20793i	−0.0124251	−	0.0775787i
$811$	−9.95987			−0.349738			−0.174869	−	0.984592i	$-0.555950\pi$
$811$	−9.95987			−0.349738			−0.174869	+	0.984592i	$0.555950\pi$
$812$		−	10.6571i		−	0.373991i
$813$		−	1.30873i		−	0.0458991i
$814$	−6.51003			−0.228176
$815$	−5.41136	−	33.7870i	−0.189552	−	1.18351i
$816$	−1.38693			−0.0485521
$817$			28.3315i			0.991194i
$818$			16.4186i			0.574062i
$819$	3.85294			0.134633
$820$	9.21728	−	1.47625i	0.321881	−	0.0515528i
$821$	17.1744			0.599389			0.299695	−	0.954035i	$-0.403115\pi$
$821$	17.1744			0.599389			0.299695	+	0.954035i	$0.403115\pi$
$822$		−	19.3329i		−	0.674312i
$823$			27.1379i			0.945968i	0.881071	+	0.472984i	$0.156823\pi$
$823$			27.1379i			0.945968i	−0.881071	+	0.472984i	$0.843177\pi$
$824$	−0.310091			−0.0108025
$825$	−10.1658	−	30.9220i	−0.353926	−	1.07657i
$826$	28.9357			1.00680
$827$		−	15.4931i		−	0.538746i	−0.963036	−	0.269373i	$-0.913183\pi$
$827$		−	15.4931i		−	0.538746i	0.963036	−	0.269373i	$-0.0868165\pi$
$828$		−	4.68466i		−	0.162803i
$829$	−50.4296			−1.75149			−0.875747	−	0.482771i	$-0.839630\pi$
$829$	−50.4296			−1.75149			−0.875747	+	0.482771i	$0.839630\pi$
$830$	−24.2816	+	3.88897i	−0.842828	+	0.134988i
$831$	−0.854305			−0.0296355
$832$		−	0.854305i		−	0.0296177i
$833$		−	18.5021i		−	0.641061i
$834$	6.69625			0.231872
$835$	−1.82722	−	11.4086i	−0.0632335	−	0.394812i
$836$	50.4521			1.74492
$837$			9.17599i			0.317169i
$838$		−	6.45442i		−	0.222964i
$839$	−18.6346			−0.643339			−0.321669	−	0.946852i	$-0.604244\pi$
$839$	−18.6346			−0.643339			−0.321669	+	0.946852i	$0.604244\pi$
$840$	−1.59485	−	9.95783i	−0.0550277	−	0.343578i
$841$	−23.4164			−0.807460
$842$		−	32.8966i		−	1.13369i
$843$		−	14.5397i		−	0.500775i
$844$	21.0916			0.726004
$845$	−27.0916	+	4.33902i	−0.931981	+	0.149267i
$846$	−10.4159			−0.358105
$847$			141.527i			4.86293i
$848$			9.61444i			0.330161i
$849$	25.5538			0.877003
$850$	−6.58776	+	2.16576i	−0.225958	+	0.0742849i
$851$	−4.68466			−0.160588
$852$			0.0391629i			0.00134170i
$853$			4.78169i			0.163722i	0.996644	+	0.0818609i	$0.0260863\pi$
$853$			4.78169i			0.163722i	−0.996644	+	0.0818609i	$0.973914\pi$
$854$	49.4623			1.69257
$855$	17.1112	−	2.74055i	0.585192	−	0.0937248i
$856$	5.10052			0.174332
$857$		−	11.2938i		−	0.385790i	−0.981219	−	0.192895i	$-0.938212\pi$
$857$		−	11.2938i		−	0.385790i	0.981219	−	0.192895i	$-0.0617877\pi$
$858$			5.56155i			0.189868i
$859$	10.1196			0.345277			0.172638	−	0.984985i	$-0.444771\pi$
$859$	10.1196			0.345277			0.172638	+	0.984985i	$0.444771\pi$
$860$	1.29275	+	8.07158i	0.0440825	+	0.275239i
$861$	−18.8277			−0.641646
$862$		−	25.3879i		−	0.864715i
$863$		−	6.87015i		−	0.233863i	−0.993140	−	0.116931i	$-0.962694\pi$
$863$		−	6.87015i		−	0.233863i	0.993140	−	0.116931i	$-0.0373058\pi$
$864$	1.00000			0.0340207
$865$	2.68541	+	16.7670i	0.0913067	+	0.570094i
$866$	−0.147057			−0.00499721
$867$			15.0764i			0.512023i
$868$			41.3840i			1.40466i
$869$	−47.8527			−1.62329
$870$	5.21728	−	0.835604i	0.176882	−	0.0283296i
$871$	11.0327			0.373830
$872$			6.40426i			0.216876i
$873$		−	11.6744i		−	0.395120i
$874$	36.3056			1.22806
$875$	−23.1251	−	44.8082i	−0.781770	−	1.51480i
$876$	7.16440			0.242063
$877$			18.2202i			0.615253i	0.951507	+	0.307626i	$0.0995346\pi$
$877$			18.2202i			0.615253i	−0.951507	+	0.307626i	$0.900465\pi$
$878$		−	7.91068i		−	0.266972i
$879$	−7.80551			−0.263273
$880$	14.3737	−	2.30210i	0.484537	−	0.0776039i
$881$	−36.3314			−1.22404			−0.612019	−	0.790843i	$-0.709642\pi$
$881$	−36.3314			−1.22404			−0.612019	+	0.790843i	$0.709642\pi$
$882$			13.3404i			0.449194i
$883$			14.7550i			0.496546i	0.968690	+	0.248273i	$0.0798630\pi$
$883$			14.7550i			0.496546i	−0.968690	+	0.248273i	$0.920137\pi$
$884$	1.18486			0.0398511
$885$	2.26880	+	14.1658i	0.0762649	+	0.476177i
$886$	2.31883			0.0779027
$887$			44.7843i			1.50371i	0.659329	+	0.751855i	$0.270840\pi$
$887$			44.7843i			1.50371i	−0.659329	+	0.751855i	$0.729160\pi$
$888$		−	1.00000i		−	0.0335578i
$889$	76.0134			2.54941
$890$	2.02669	+	12.6541i	0.0679348	+	0.424166i
$891$	−6.51003			−0.218094
$892$			2.48744i			0.0832857i
$893$		−	80.7219i		−	2.70125i
$894$	15.3968			0.514945
$895$	33.3968	−	5.34885i	1.11633	−	0.178792i
$896$	4.51003			0.150670
$897$			4.00213i			0.133627i
$898$			5.97256i			0.199307i
$899$	−21.6826			−0.723156
$900$	4.74990	−	1.56155i	0.158330	−	0.0520518i
$901$	−13.3345			−0.444237
$902$		−	27.1770i		−	0.904894i
$903$		−	16.4874i		−	0.548668i
$904$	6.72097			0.223536
$905$	50.8619	−	8.14609i	1.69071	−	0.270785i
$906$	13.9774			0.464368
$907$		−	5.82252i		−	0.193334i	−0.995317	−	0.0966668i	$-0.969182\pi$
$907$		−	5.82252i		−	0.193334i	0.995317	−	0.0966668i	$-0.0308181\pi$
$908$		−	21.1583i		−	0.702161i
$909$	−2.00000			−0.0663358
$910$	1.36249	+	8.50702i	0.0451662	+	0.282005i
$911$	18.2462			0.604524			0.302262	−	0.953225i	$-0.402258\pi$
$911$	18.2462			0.604524			0.302262	+	0.953225i	$0.402258\pi$
$912$			7.74990i			0.256625i
$913$			71.5939i			2.36941i
$914$	25.5928			0.846535
$915$	3.87826	+	24.2148i	0.128211	+	0.800515i
$916$	1.58414			0.0523415
$917$			4.76485i			0.157349i
$918$			1.38693i			0.0457754i
$919$	−23.5996			−0.778477			−0.389239	−	0.921137i	$-0.627262\pi$
$919$	−23.5996			−0.778477			−0.389239	+	0.921137i	$0.627262\pi$
$920$	10.3434	−	1.65661i	0.341012	−	0.0546167i
$921$	−12.6868			−0.418044
$922$		−	7.65573i		−	0.252128i
$923$		−	0.0334571i		−	0.00110125i
$924$	−29.3604			−0.965888
$925$	−1.56155	−	4.74990i	−0.0513435	−	0.156176i
$926$	9.76744			0.320978
$927$			0.310091i			0.0101847i
$928$			2.36297i			0.0775684i
$929$	−4.67307			−0.153318			−0.0766591	−	0.997057i	$-0.524425\pi$
$929$	−4.67307			−0.153318			−0.0766591	+	0.997057i	$0.524425\pi$
$930$	−20.2599	+	3.24485i	−0.664349	+	0.106403i
$931$	−103.387			−3.38836
$932$		−	19.8491i		−	0.650177i
$933$			6.09806i			0.199642i
$934$	20.8856			0.683396
$935$	3.19285	+	19.9352i	0.104417	+	0.651952i
$936$	−0.854305			−0.0279238
$937$			26.4577i			0.864337i	0.901793	+	0.432168i	$0.142251\pi$
$937$			26.4577i			0.864337i	−0.901793	+	0.432168i	$0.857749\pi$
$938$			58.2439i			1.90173i
$939$	−13.0113			−0.424608
$940$	−3.68330	−	22.9975i	−0.120136	−	0.750095i
$941$	−7.74056			−0.252335			−0.126168	−	0.992009i	$-0.540268\pi$
$941$	−7.74056			−0.252335			−0.126168	+	0.992009i	$0.540268\pi$
$942$		−	3.07022i		−	0.100033i
$943$		−	19.5567i		−	0.636854i
$944$	−6.41586			−0.208818
$945$	−9.95783	+	1.59485i	−0.323928	+	0.0518806i
$946$	23.7989			0.773769
$947$		−	13.7393i		−	0.446466i	−0.974765	−	0.223233i	$-0.928339\pi$
$947$		−	13.7393i		−	0.446466i	0.974765	−	0.223233i	$-0.0716611\pi$
$948$		−	7.35062i		−	0.238737i
$949$	−6.12058			−0.198682
$950$	12.1019	+	36.8113i	0.392637	+	1.19431i
$951$	3.89198			0.126206
$952$			6.25508i			0.202728i
$953$		−	28.6516i		−	0.928115i	−0.885805	−	0.464058i	$-0.846393\pi$
$953$		−	28.6516i		−	0.928115i	0.885805	−	0.464058i	$-0.153607\pi$
$954$	9.61444			0.311279
$955$	−8.81213	+	1.41136i	−0.285154	+	0.0456705i
$956$	−9.86454			−0.319042
$957$		−	15.3830i		−	0.497263i
$958$		−	12.4357i		−	0.401780i
$959$	−87.1919			−2.81557
$960$	0.353624	+	2.20793i	0.0114132	+	0.0712606i
$961$	53.1988			1.71609
$962$			0.854305i			0.0275439i
$963$		−	5.10052i		−	0.164362i
$964$	4.35799			0.140362
$965$	5.08394	+	31.7427i	0.163658	+	1.02183i
$966$	−21.1280			−0.679781
$967$		−	2.16539i		−	0.0696343i	−0.999394	−	0.0348172i	$-0.988915\pi$
$967$		−	2.16539i		−	0.0696343i	0.999394	−	0.0348172i	$-0.0110849\pi$
$968$		−	31.3805i		−	1.00861i
$969$	−10.7485			−0.345293
$970$	25.7763	−	4.12836i	0.827627	−	0.132554i
$971$	53.3720			1.71279			0.856394	−	0.516323i	$-0.172700\pi$
$971$	53.3720			1.71279			0.856394	+	0.516323i	$0.172700\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	30.2003i		−	0.968177i
$974$	−15.7113			−0.503424
$975$	−4.05786	+	1.33404i	−0.129956	+	0.0427236i
$976$	−10.9672			−0.351051
$977$			4.38460i			0.140276i	0.997537	+	0.0701379i	$0.0223439\pi$
$977$			4.38460i			0.140276i	−0.997537	+	0.0701379i	$0.977656\pi$
$978$		−	15.3026i		−	0.489323i
$979$	37.3103			1.19244
$980$	−29.4546	+	4.71748i	−0.940893	+	0.150694i
$981$	6.40426			0.204472
$982$			25.6656i			0.819021i
$983$			57.7282i			1.84124i	0.390455	+	0.920622i	$0.372318\pi$
$983$			57.7282i			1.84124i	−0.390455	+	0.920622i	$0.627682\pi$
$984$	4.17463			0.133082
$985$	6.74055	+	42.0861i	0.214772	+	1.34098i
$986$	−3.27727			−0.104370
$987$			46.9758i			1.49526i
$988$		−	6.62078i		−	0.210635i
$989$	17.1258			0.544570
$990$	−2.30210	−	14.3737i	−0.0731656	−	0.456826i
$991$	−35.0278			−1.11269			−0.556347	−	0.830950i	$-0.687797\pi$
$991$	−35.0278			−1.11269			−0.556347	+	0.830950i	$0.687797\pi$
$992$		−	9.17599i		−	0.291338i
$993$			18.0374i			0.572400i
$994$	0.176626			0.00560223
$995$	−17.6634	+	2.82899i	−0.559968	+	0.0896850i
$996$	−10.9975			−0.348468
$997$			19.8165i			0.627595i	0.949490	+	0.313797i	$0.101601\pi$
$997$			19.8165i			0.627595i	−0.949490	+	0.313797i	$0.898399\pi$
$998$		−	28.4361i		−	0.900130i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.d.j.889.5	yes	8
3.2	odd	2		3330.2.d.o.1999.4		8
5.2	odd	4		5550.2.a.cl.1.1		4
5.3	odd	4		5550.2.a.cm.1.4		4
5.4	even	2	inner	1110.2.d.j.889.1	✓	8
15.14	odd	2		3330.2.d.o.1999.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.j.889.1	✓	8	5.4	even	2	inner
1110.2.d.j.889.5	yes	8	1.1	even	1	trivial
3330.2.d.o.1999.4		8	3.2	odd	2
3330.2.d.o.1999.8		8	15.14	odd	2
5550.2.a.cl.1.1		4	5.2	odd	4
5550.2.a.cm.1.4		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.20793 + 0.353624i) q^{5} -1.00000 q^{6} +4.51003i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.20793 + 0.353624i) q^{5} -1.00000 q^{6} +4.51003i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-0.353624 - 2.20793i) q^{10} -6.51003 q^{11} -1.00000i q^{12} +0.854305i q^{13} -4.51003 q^{14} +(-0.353624 - 2.20793i) q^{15} +1.00000 q^{16} +1.38693i q^{17} -1.00000i q^{18} +7.74990 q^{19} +(2.20793 - 0.353624i) q^{20} -4.51003 q^{21} -6.51003i q^{22} -4.68466i q^{23} +1.00000 q^{24} +(4.74990 - 1.56155i) q^{25} -0.854305 q^{26} -1.00000i q^{27} -4.51003i q^{28} +2.36297 q^{29} +(2.20793 - 0.353624i) q^{30} -9.17599 q^{31} +1.00000i q^{32} -6.51003i q^{33} -1.38693 q^{34} +(-1.59485 - 9.95783i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +7.74990i q^{38} -0.854305 q^{39} +(0.353624 + 2.20793i) q^{40} +4.17463 q^{41} -4.51003i q^{42} +3.65573i q^{43} +6.51003 q^{44} +(2.20793 - 0.353624i) q^{45} +4.68466 q^{46} -10.4159i q^{47} +1.00000i q^{48} -13.3404 q^{49} +(1.56155 + 4.74990i) q^{50} -1.38693 q^{51} -0.854305i q^{52} +9.61444i q^{53} +1.00000 q^{54} +(14.3737 - 2.30210i) q^{55} +4.51003 q^{56} +7.74990i q^{57} +2.36297i q^{58} -6.41586 q^{59} +(0.353624 + 2.20793i) q^{60} -10.9672 q^{61} -9.17599i q^{62} -4.51003i q^{63} -1.00000 q^{64} +(-0.302103 - 1.88624i) q^{65} +6.51003 q^{66} -12.9143i q^{67} -1.38693i q^{68} +4.68466 q^{69} +(9.95783 - 1.59485i) q^{70} -0.0391629 q^{71} +1.00000i q^{72} +7.16440i q^{73} +1.00000 q^{74} +(1.56155 + 4.74990i) q^{75} -7.74990 q^{76} -29.3604i q^{77} -0.854305i q^{78} +7.35062 q^{79} +(-2.20793 + 0.353624i) q^{80} +1.00000 q^{81} +4.17463i q^{82} -10.9975i q^{83} +4.51003 q^{84} +(-0.490450 - 3.06223i) q^{85} -3.65573 q^{86} +2.36297i q^{87} +6.51003i q^{88} -5.73120 q^{89} +(0.353624 + 2.20793i) q^{90} -3.85294 q^{91} +4.68466i q^{92} -9.17599i q^{93} +10.4159 q^{94} +(-17.1112 + 2.74055i) q^{95} -1.00000 q^{96} +11.6744i q^{97} -13.3404i q^{98} +6.51003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} - 2 q^{10} - 10 q^{11} + 6 q^{14} - 2 q^{15} + 8 q^{16} + 24 q^{19} + 2 q^{20} + 6 q^{21} + 8 q^{24} + 8 q^{26} - 10 q^{29} + 2 q^{30} - 38 q^{31} - 2 q^{34} + 12 q^{35} + 8 q^{36} + 8 q^{39} + 2 q^{40} + 26 q^{41} + 10 q^{44} + 2 q^{45} - 12 q^{46} - 30 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{54} + 30 q^{55} - 6 q^{56} - 20 q^{59} + 2 q^{60} - 6 q^{61} - 8 q^{64} + 24 q^{65} + 10 q^{66} - 12 q^{69} + 26 q^{70} - 12 q^{71} + 8 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 2 q^{80} + 8 q^{81} - 6 q^{84} + 44 q^{85} - 2 q^{86} - 64 q^{89} + 2 q^{90} - 44 q^{91} + 52 q^{94} - 8 q^{96} + 10 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 - 2 * q^10 - 10 * q^11 + 6 * q^14 - 2 * q^15 + 8 * q^16 + 24 * q^19 + 2 * q^20 + 6 * q^21 + 8 * q^24 + 8 * q^26 - 10 * q^29 + 2 * q^30 - 38 * q^31 - 2 * q^34 + 12 * q^35 + 8 * q^36 + 8 * q^39 + 2 * q^40 + 26 * q^41 + 10 * q^44 + 2 * q^45 - 12 * q^46 - 30 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^54 + 30 * q^55 - 6 * q^56 - 20 * q^59 + 2 * q^60 - 6 * q^61 - 8 * q^64 + 24 * q^65 + 10 * q^66 - 12 * q^69 + 26 * q^70 - 12 * q^71 + 8 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 2 * q^80 + 8 * q^81 - 6 * q^84 + 44 * q^85 - 2 * q^86 - 64 * q^89 + 2 * q^90 - 44 * q^91 + 52 * q^94 - 8 * q^96 + 10 * q^99

Introduction

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