LMFDB - Embedded newform 1110.2.x.d.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.1
Root			$4.75759i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.d.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.37879 - 4.12019i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.37879 - 4.12019i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.36873 q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.67740 + 0.968450i) q^{13} +4.75759i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.25417 + 1.87879i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.63763 - 0.945484i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.37879 + 4.12019i) q^{21} +(4.64945 + 2.68436i) q^{22} -0.204849i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.93690 q^{26} +1.00000 q^{27} +(2.37879 - 4.12019i) q^{28} +2.07147i q^{29} +(-0.500000 - 0.866025i) q^{30} +1.95056i q^{31} +(0.866025 - 0.500000i) q^{32} +(2.68436 + 4.64945i) q^{33} +(-1.87879 - 3.25417i) q^{34} +(4.12019 + 2.37879i) q^{35} -1.00000 q^{36} +(2.60554 - 5.49647i) q^{37} -1.89097 q^{38} +(1.67740 + 0.968450i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.63525 + 6.29644i) q^{41} +(4.12019 - 2.37879i) q^{42} -1.74571i q^{43} +(-2.68436 - 4.64945i) q^{44} -1.00000i q^{45} +(-0.102424 + 0.177404i) q^{46} +8.35130 q^{47} +1.00000 q^{48} +(-7.81733 + 13.5400i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.75759i q^{51} +(-1.67740 - 0.968450i) q^{52} +(-6.35084 + 11.0000i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(4.64945 - 2.68436i) q^{55} +(-4.12019 + 2.37879i) q^{56} +(-1.63763 - 0.945484i) q^{57} +(1.03573 - 1.79395i) q^{58} +(-8.23050 - 4.75188i) q^{59} +1.00000i q^{60} +(-3.60010 + 2.07852i) q^{61} +(0.975279 - 1.68923i) q^{62} +4.75759 q^{63} -1.00000 q^{64} +(0.968450 - 1.67740i) q^{65} -5.36873i q^{66} +(-2.26454 - 3.92230i) q^{67} +3.75759i q^{68} +(-0.177404 + 0.102424i) q^{69} +(-2.37879 - 4.12019i) q^{70} +(4.89062 + 8.47081i) q^{71} +(0.866025 + 0.500000i) q^{72} +15.0985 q^{73} +(-5.00470 + 3.45731i) q^{74} -1.00000 q^{75} +(1.63763 + 0.945484i) q^{76} +(12.7711 + 22.1202i) q^{77} +(-0.968450 - 1.67740i) q^{78} +(-10.1927 + 5.88473i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -7.27050i q^{82} +(-2.10501 + 3.64598i) q^{83} -4.75759 q^{84} -3.75759 q^{85} +(-0.872855 + 1.51183i) q^{86} +(1.79395 - 1.03573i) q^{87} +5.36873i q^{88} +(5.32602 + 3.07498i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(7.98040 + 4.60749i) q^{91} +(0.177404 - 0.102424i) q^{92} +(1.68923 - 0.975279i) q^{93} +(-7.23244 - 4.17565i) q^{94} +(-0.945484 + 1.63763i) q^{95} +(-0.866025 - 0.500000i) q^{96} -2.30537i q^{97} +(13.5400 - 7.81733i) q^{98} +(2.68436 - 4.64945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	−2.37879	−	4.12019i	−0.899100	−	1.55729i	−0.828647	−	0.559771i	$-0.810889\pi$
$7$	−2.37879	−	4.12019i	−0.899100	−	1.55729i	−0.0704527	−	0.997515i	$-0.522444\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−5.36873			−1.61873			−0.809366	−	0.587304i	$-0.800189\pi$
$11$	−5.36873			−1.61873			−0.809366	+	0.587304i	$0.800189\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.67740	+	0.968450i	−0.465228	+	0.268600i	−0.714240	−	0.699901i	$-0.753228\pi$
$13$	−1.67740	+	0.968450i	−0.465228	+	0.268600i	0.249012	+	0.968500i	$0.419894\pi$
$14$			4.75759i			1.27152i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.25417	+	1.87879i	0.789252	+	0.455675i	0.839699	−	0.543052i	$-0.182731\pi$
$17$	3.25417	+	1.87879i	0.789252	+	0.455675i	−0.0504475	+	0.998727i	$0.516065\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	1.63763	−	0.945484i	0.375697	−	0.216909i	−0.300247	−	0.953861i	$-0.597069\pi$
$19$	1.63763	−	0.945484i	0.375697	−	0.216909i	0.675945	+	0.736952i	$0.263736\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−2.37879	+	4.12019i	−0.519095	+	0.899100i
$22$	4.64945	+	2.68436i	0.991267	+	0.572308i
$23$		−	0.204849i		−	0.0427139i	−0.999772	−	0.0213570i	$-0.993201\pi$
$23$		−	0.204849i		−	0.0427139i	0.999772	−	0.0213570i	$-0.00679865\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.93690			0.379857
$27$	1.00000			0.192450
$28$	2.37879	−	4.12019i	0.449550	−	0.778643i
$29$			2.07147i			0.384662i	0.981330	+	0.192331i	$0.0616048\pi$
$29$			2.07147i			0.384662i	−0.981330	+	0.192331i	$0.938395\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			1.95056i			0.350331i	0.984539	+	0.175165i	$0.0560460\pi$
$31$			1.95056i			0.350331i	−0.984539	+	0.175165i	$0.943954\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.68436	+	4.64945i	0.467288	+	0.809366i
$34$	−1.87879	−	3.25417i	−0.322211	−	0.558085i
$35$	4.12019	+	2.37879i	0.696440	+	0.402090i
$36$	−1.00000			−0.166667
$37$	2.60554	−	5.49647i	0.428348	−	0.903614i
$37$	2.60554	−	5.49647i	0.428348	−	0.903614i
$38$	−1.89097			−0.306756
$39$	1.67740	+	0.968450i	0.268600	+	0.155076i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.63525	+	6.29644i	0.567731	+	0.983338i	0.996790	+	0.0800620i	$0.0255118\pi$
$41$	3.63525	+	6.29644i	0.567731	+	0.983338i	−0.429059	+	0.903276i	$0.641155\pi$
$42$	4.12019	−	2.37879i	0.635760	−	0.367056i
$43$		−	1.74571i		−	0.266218i	−0.991101	−	0.133109i	$-0.957504\pi$
$43$		−	1.74571i		−	0.266218i	0.991101	−	0.133109i	$-0.0424961\pi$
$44$	−2.68436	−	4.64945i	−0.404683	−	0.700932i
$45$		−	1.00000i		−	0.149071i
$46$	−0.102424	+	0.177404i	−0.0151017	+	0.0261568i
$47$	8.35130			1.21816			0.609081	−	0.793108i	$-0.291538\pi$
$47$	8.35130			1.21816			0.609081	+	0.793108i	$0.291538\pi$
$48$	1.00000			0.144338
$49$	−7.81733	+	13.5400i	−1.11676	+	1.93429i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		−	3.75759i		−	0.526168i
$52$	−1.67740	−	0.968450i	−0.232614	−	0.134300i
$53$	−6.35084	+	11.0000i	−0.872356	+	1.51096i	−0.0128024	+	0.999918i	$0.504075\pi$
$53$	−6.35084	+	11.0000i	−0.872356	+	1.51096i	−0.859553	+	0.511046i	$0.829258\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	4.64945	−	2.68436i	0.626932	−	0.361960i
$56$	−4.12019	+	2.37879i	−0.550584	+	0.317880i
$57$	−1.63763	−	0.945484i	−0.216909	−	0.125232i
$58$	1.03573	−	1.79395i	0.135999	−	0.235557i
$59$	−8.23050	−	4.75188i	−1.07152	−	0.618642i	−0.142923	−	0.989734i	$-0.545650\pi$
$59$	−8.23050	−	4.75188i	−1.07152	−	0.618642i	−0.928596	+	0.371092i	$0.878984\pi$
$60$			1.00000i			0.129099i
$61$	−3.60010	+	2.07852i	−0.460945	+	0.266127i	−0.712442	−	0.701731i	$-0.752411\pi$
$61$	−3.60010	+	2.07852i	−0.460945	+	0.266127i	0.251496	+	0.967858i	$0.419077\pi$
$62$	0.975279	−	1.68923i	0.123861	−	0.214533i
$63$	4.75759			0.599400
$64$	−1.00000			−0.125000
$65$	0.968450	−	1.67740i	0.120121	−	0.208056i
$66$		−	5.36873i		−	0.660845i
$67$	−2.26454	−	3.92230i	−0.276658	−	0.479185i	0.693894	−	0.720077i	$-0.255894\pi$
$67$	−2.26454	−	3.92230i	−0.276658	−	0.479185i	−0.970552	+	0.240892i	$0.922560\pi$
$68$			3.75759i			0.455675i
$69$	−0.177404	+	0.102424i	−0.0213570	+	0.0123305i
$70$	−2.37879	−	4.12019i	−0.284320	−	0.492457i
$71$	4.89062	+	8.47081i	0.580410	+	1.00530i	0.995431	+	0.0954878i	$0.0304411\pi$
$71$	4.89062	+	8.47081i	0.580410	+	1.00530i	−0.415020	+	0.909812i	$0.636226\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	15.0985			1.76714			0.883572	−	0.468295i	$-0.155131\pi$
$73$	15.0985			1.76714			0.883572	+	0.468295i	$0.155131\pi$
$74$	−5.00470	+	3.45731i	−0.581784	+	0.401904i
$75$	−1.00000			−0.115470
$76$	1.63763	+	0.945484i	0.187849	+	0.108454i
$77$	12.7711	+	22.1202i	1.45540	+	2.52083i
$78$	−0.968450	−	1.67740i	−0.109655	−	0.189929i
$79$	−10.1927	+	5.88473i	−1.14676	+	0.662084i	−0.948097	−	0.317983i	$-0.896995\pi$
$79$	−10.1927	+	5.88473i	−1.14676	+	0.662084i	−0.198667	+	0.980067i	$0.563661\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	7.27050i		−	0.802892i
$83$	−2.10501	+	3.64598i	−0.231054	+	0.400198i	−0.958119	−	0.286371i	$-0.907551\pi$
$83$	−2.10501	+	3.64598i	−0.231054	+	0.400198i	0.727064	+	0.686569i	$0.240884\pi$
$84$	−4.75759			−0.519095
$85$	−3.75759			−0.407568
$86$	−0.872855	+	1.51183i	−0.0941223	+	0.163025i
$87$	1.79395	−	1.03573i	0.192331	−	0.111042i
$88$			5.36873i			0.572308i
$89$	5.32602	+	3.07498i	0.564557	+	0.325947i	0.754973	−	0.655756i	$-0.227650\pi$
$89$	5.32602	+	3.07498i	0.564557	+	0.325947i	−0.190415	+	0.981704i	$0.560983\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	7.98040	+	4.60749i	0.836573	+	0.482996i
$92$	0.177404	−	0.102424i	0.0184957	−	0.0106785i
$93$	1.68923	−	0.975279i	0.175165	−	0.101132i
$94$	−7.23244	−	4.17565i	−0.745969	−	0.430685i
$95$	−0.945484	+	1.63763i	−0.0970046	+	0.168017i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$		−	2.30537i		−	0.234075i	−0.993128	−	0.117037i	$-0.962660\pi$
$97$		−	2.30537i		−	0.234075i	0.993128	−	0.117037i	$-0.0373397\pi$
$98$	13.5400	−	7.81733i	1.36775	−	0.789669i
$99$	2.68436	−	4.64945i	0.269789	−	0.467288i
$100$	1.00000			0.100000
$101$	3.28606			0.326975			0.163487	−	0.986545i	$-0.447726\pi$
$101$	3.28606			0.326975			0.163487	+	0.986545i	$0.447726\pi$
$102$	−1.87879	+	3.25417i	−0.186028	+	0.322211i
$103$		−	11.9300i		−	1.17550i	−0.809042	−	0.587751i	$-0.800014\pi$
$103$		−	11.9300i		−	1.17550i	0.809042	−	0.587751i	$-0.199986\pi$
$104$	0.968450	+	1.67740i	0.0949643	+	0.164483i
$105$		−	4.75759i		−	0.464293i
$106$	11.0000	−	6.35084i	1.06841	−	0.616849i
$107$	7.21086	+	12.4896i	0.697100	+	1.20741i	0.969468	+	0.245219i	$0.0788600\pi$
$107$	7.21086	+	12.4896i	0.697100	+	1.20741i	−0.272368	+	0.962193i	$0.587807\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.91578	−	1.68342i	−0.279281	−	0.161243i	0.353817	−	0.935315i	$-0.384884\pi$
$109$	−2.91578	−	1.68342i	−0.279281	−	0.161243i	−0.633098	+	0.774072i	$0.718217\pi$
$110$	−5.36873			−0.511888
$111$	−6.06285	+	0.491772i	−0.575460	+	0.0466769i
$112$	4.75759			0.449550
$113$	5.48942	+	3.16932i	0.516401	+	0.298144i	0.735461	−	0.677567i	$-0.236966\pi$
$113$	5.48942	+	3.16932i	0.516401	+	0.298144i	−0.219060	+	0.975711i	$0.570299\pi$
$114$	0.945484	+	1.63763i	0.0885527	+	0.153378i
$115$	0.102424	+	0.177404i	0.00955113	+	0.0165430i
$116$	−1.79395	+	1.03573i	−0.166564	+	0.0961656i
$117$		−	1.93690i		−	0.179066i
$118$	4.75188	+	8.23050i	0.437446	+	0.757679i
$119$		−	17.8771i		−	1.63879i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	17.8232			1.62029
$122$	4.15704			0.376360
$123$	3.63525	−	6.29644i	0.327779	−	0.567731i
$124$	−1.68923	+	0.975279i	−0.151698	+	0.0875826i
$125$			1.00000i			0.0894427i
$126$	−4.12019	−	2.37879i	−0.367056	−	0.211920i
$127$	−6.26976	+	10.8595i	−0.556351	+	0.963629i	0.441446	+	0.897288i	$0.354466\pi$
$127$	−6.26976	+	10.8595i	−0.556351	+	0.963629i	−0.997797	+	0.0663409i	$0.978868\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.51183	+	0.872855i	−0.133109	+	0.0768506i
$130$	−1.67740	+	0.968450i	−0.147118	+	0.0849387i
$131$	3.17214	+	1.83144i	0.277151	+	0.160013i	0.632133	−	0.774860i	$-0.282180\pi$
$131$	3.17214	+	1.83144i	0.277151	+	0.160013i	−0.354982	+	0.934873i	$0.615513\pi$
$132$	−2.68436	+	4.64945i	−0.233644	+	0.404683i
$133$	−7.79115	−	4.49822i	−0.675579	−	0.390045i
$134$			4.52908i			0.391253i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	1.87879	−	3.25417i	0.161105	−	0.279043i
$137$	−10.1933			−0.870871			−0.435436	−	0.900220i	$-0.643406\pi$
$137$	−10.1933			−0.870871			−0.435436	+	0.900220i	$0.643406\pi$
$138$	0.204849			0.0174379
$139$	6.53350	−	11.3164i	0.554164	−	0.959841i	−0.443804	−	0.896124i	$-0.646371\pi$
$139$	6.53350	−	11.3164i	0.554164	−	0.959841i	0.997968	−	0.0637169i	$-0.0202955\pi$
$140$			4.75759i			0.402090i
$141$	−4.17565	−	7.23244i	−0.351653	−	0.609081i
$142$		−	9.78125i		−	0.820824i
$143$	9.00553	−	5.19934i	0.753080	−	0.434791i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.03573	−	1.79395i	−0.0860131	−	0.148979i
$146$	−13.0757	−	7.54925i	−1.08215	−	0.624780i
$147$	15.6347			1.28952
$148$	6.06285	−	0.491772i	0.498363	−	0.0404234i
$149$	−11.9826			−0.981652			−0.490826	−	0.871258i	$-0.663305\pi$
$149$	−11.9826			−0.981652			−0.490826	+	0.871258i	$0.663305\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	6.34419	+	10.9885i	0.516283	+	0.894229i	0.999821	+	0.0189053i	$0.00601809\pi$
$151$	6.34419	+	10.9885i	0.516283	+	0.894229i	−0.483538	+	0.875323i	$0.660649\pi$
$152$	−0.945484	−	1.63763i	−0.0766889	−	0.132829i
$153$	−3.25417	+	1.87879i	−0.263084	+	0.151892i
$154$		−	25.5422i		−	2.05825i
$155$	−0.975279	−	1.68923i	−0.0783363	−	0.135682i
$156$			1.93690i			0.155076i
$157$	3.39699	−	5.88376i	0.271109	−	0.469575i	−0.698037	−	0.716062i	$-0.745943\pi$
$157$	3.39699	−	5.88376i	0.271109	−	0.469575i	0.969146	+	0.246487i	$0.0792761\pi$
$158$	11.7695			0.936329
$159$	12.7017			1.00731
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−0.844017	+	0.487293i	−0.0665179	+	0.0384041i
$162$			1.00000i			0.0785674i
$163$	−0.157804	−	0.0911079i	−0.0123601	−	0.00713613i	0.493807	−	0.869571i	$-0.335605\pi$
$163$	−0.157804	−	0.0911079i	−0.0123601	−	0.00713613i	−0.506167	+	0.862435i	$0.668938\pi$
$164$	−3.63525	+	6.29644i	−0.283865	+	0.491669i
$165$	−4.64945	−	2.68436i	−0.361960	−	0.208977i
$166$	3.64598	−	2.10501i	0.282983	−	0.163380i
$167$	−22.0553	+	12.7336i	−1.70669	+	0.985359i	−0.768101	+	0.640329i	$0.778798\pi$
$167$	−22.0553	+	12.7336i	−1.70669	+	0.985359i	−0.938591	+	0.345031i	$0.887868\pi$
$168$	4.12019	+	2.37879i	0.317880	+	0.183528i
$169$	−4.62421	+	8.00937i	−0.355708	+	0.616105i
$170$	3.25417	+	1.87879i	0.249583	+	0.144097i
$171$			1.89097i			0.144606i
$172$	1.51183	−	0.872855i	0.115276	−	0.0665545i
$173$	−2.64127	+	4.57482i	−0.200812	+	0.347817i	−0.948790	−	0.315906i	$-0.897691\pi$
$173$	−2.64127	+	4.57482i	−0.200812	+	0.347817i	0.747978	+	0.663723i	$0.231025\pi$
$174$	−2.07147			−0.157038
$175$	−4.75759			−0.359640
$176$	2.68436	−	4.64945i	0.202342	−	0.350466i
$177$			9.50376i			0.714346i
$178$	−3.07498	−	5.32602i	−0.230479	−	0.399202i
$179$		−	14.1350i		−	1.05650i	−0.849090	−	0.528248i	$-0.822849\pi$
$179$		−	14.1350i		−	1.05650i	0.849090	−	0.528248i	$-0.177151\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−5.33735	−	9.24456i	−0.396722	−	0.687143i	0.596597	−	0.802541i	$-0.296519\pi$
$181$	−5.33735	−	9.24456i	−0.396722	−	0.687143i	−0.993319	+	0.115398i	$0.963186\pi$
$182$	−4.60749	−	7.98040i	−0.341530	−	0.591547i
$183$	3.60010	+	2.07852i	0.266127	+	0.153648i
$184$	−0.204849			−0.0151017
$185$	0.491772	+	6.06285i	0.0361558	+	0.445750i
$186$	−1.95056			−0.143022
$187$	−17.4707	−	10.0867i	−1.27759	−	0.737615i
$188$	4.17565	+	7.23244i	0.304541	+	0.527480i
$189$	−2.37879	−	4.12019i	−0.173032	−	0.299700i
$190$	1.63763	−	0.945484i	0.118806	−	0.0685926i
$191$			16.1575i			1.16912i	0.811352	+	0.584558i	$0.198732\pi$
$191$			16.1575i			1.16912i	−0.811352	+	0.584558i	$0.801268\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$			14.4537i			1.04040i	0.854045	+	0.520199i	$0.174142\pi$
$193$			14.4537i			1.04040i	−0.854045	+	0.520199i	$0.825858\pi$
$194$	−1.15268	+	1.99651i	−0.0827578	+	0.143341i
$195$	−1.93690			−0.138704
$196$	−15.6347			−1.11676
$197$	2.12901	−	3.68755i	0.151685	−	0.262727i	−0.780162	−	0.625578i	$-0.784863\pi$
$197$	2.12901	−	3.68755i	0.151685	−	0.262727i	0.931847	+	0.362851i	$0.118197\pi$
$198$	−4.64945	+	2.68436i	−0.330422	+	0.190769i
$199$			25.8669i			1.83366i	0.399279	+	0.916829i	$0.369260\pi$
$199$			25.8669i			1.83366i	−0.399279	+	0.916829i	$0.630740\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−2.26454	+	3.92230i	−0.159728	+	0.276658i
$202$	−2.84581	−	1.64303i	−0.200230	−	0.115603i
$203$	8.53486	−	4.92760i	0.599029	−	0.345850i
$204$	3.25417	−	1.87879i	0.227837	−	0.131542i
$205$	−6.29644	−	3.63525i	−0.439762	−	0.253897i
$206$	−5.96502	+	10.3317i	−0.415603	+	0.719845i
$207$	0.177404	+	0.102424i	0.0123305	+	0.00711899i
$208$		−	1.93690i		−	0.134300i
$209$	−8.79197	+	5.07605i	−0.608153	+	0.351117i
$210$	−2.37879	+	4.12019i	−0.164152	+	0.284320i
$211$	15.0540			1.03636			0.518180	−	0.855271i	$-0.326610\pi$
$211$	15.0540			1.03636			0.518180	+	0.855271i	$0.326610\pi$
$212$	−12.7017			−0.872356
$213$	4.89062	−	8.47081i	0.335100	−	0.580410i
$214$		−	14.4217i		−	0.985848i
$215$	0.872855	+	1.51183i	0.0595282	+	0.103106i
$216$		−	1.00000i		−	0.0680414i
$217$	8.03668	−	4.63998i	0.545565	−	0.314982i
$218$	1.68342	+	2.91578i	0.114016	+	0.197481i
$219$	−7.54925	−	13.0757i	−0.510131	−	0.883572i
$220$	4.64945	+	2.68436i	0.313466	+	0.180980i
$221$	−7.27807			−0.489576
$222$	5.49647	+	2.60554i	0.368899	+	0.174872i
$223$	−18.2023			−1.21892			−0.609459	−	0.792817i	$-0.708613\pi$
$223$	−18.2023			−1.21892			−0.609459	+	0.792817i	$0.708613\pi$
$224$	−4.12019	−	2.37879i	−0.275292	−	0.158940i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−3.16932	−	5.48942i	−0.210820	−	0.365151i
$227$	−3.03976	+	1.75501i	−0.201756	+	0.116484i	−0.597474	−	0.801888i	$-0.703829\pi$
$227$	−3.03976	+	1.75501i	−0.201756	+	0.116484i	0.395718	+	0.918372i	$0.370496\pi$
$228$		−	1.89097i		−	0.125232i
$229$	0.950846	+	1.64691i	0.0628337	+	0.108831i	0.895731	−	0.444596i	$-0.146653\pi$
$229$	0.950846	+	1.64691i	0.0628337	+	0.108831i	−0.832897	+	0.553428i	$0.813320\pi$
$230$		−	0.204849i		−	0.0135073i
$231$	12.7711	−	22.1202i	0.840277	−	1.45540i
$232$	2.07147			0.135999
$233$	−15.8822			−1.04048			−0.520240	−	0.854020i	$-0.674157\pi$
$233$	−15.8822			−1.04048			−0.520240	+	0.854020i	$0.674157\pi$
$234$	−0.968450	+	1.67740i	−0.0633095	+	0.109655i
$235$	−7.23244	+	4.17565i	−0.471792	+	0.272389i
$236$		−	9.50376i		−	0.618642i
$237$	10.1927	+	5.88473i	0.662084	+	0.382255i
$238$	−8.93853	+	15.4820i	−0.579399	+	1.00355i
$239$	−21.4695	−	12.3954i	−1.38875	−	0.801793i	−0.395572	−	0.918435i	$-0.629454\pi$
$239$	−21.4695	−	12.3954i	−1.38875	−	0.801793i	−0.993174	+	0.116642i	$0.962787\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−3.96591	+	2.28972i	−0.255467	+	0.147494i	−0.622265	−	0.782807i	$-0.713787\pi$
$241$	−3.96591	+	2.28972i	−0.255467	+	0.147494i	0.366798	+	0.930301i	$0.380454\pi$
$242$	−15.4354	−	8.91162i	−0.992224	−	0.572861i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.60010	−	2.07852i	−0.230473	−	0.133063i
$245$		−	15.6347i		−	0.998861i
$246$	−6.29644	+	3.63525i	−0.401446	+	0.231775i
$247$	−1.83131	+	3.17192i	−0.116523	+	0.201824i
$248$	1.95056			0.123861
$249$	4.21001			0.266799
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			2.61798i			0.165246i	0.996581	+	0.0826228i	$0.0263297\pi$
$251$			2.61798i			0.165246i	−0.996581	+	0.0826228i	$0.973670\pi$
$252$	2.37879	+	4.12019i	0.149850	+	0.259548i
$253$			1.09978i			0.0691424i
$254$	10.8595	−	6.26976i	0.681389	−	0.393400i
$255$	1.87879	+	3.25417i	0.117655	+	0.203784i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.30900	−	3.64250i	−0.393545	−	0.227213i	0.290150	−	0.956981i	$-0.406295\pi$
$257$	−6.30900	−	3.64250i	−0.393545	−	0.227213i	−0.683695	+	0.729768i	$0.739628\pi$
$258$	1.74571			0.108683
$259$	−28.8446	+	2.33965i	−1.79231	+	0.145379i
$260$	1.93690			0.120121
$261$	−1.79395	−	1.03573i	−0.111042	−	0.0641104i
$262$	−1.83144	−	3.17214i	−0.113146	−	0.195975i
$263$	−7.84447	−	13.5870i	−0.483711	−	0.837812i	0.516114	−	0.856520i	$-0.327378\pi$
$263$	−7.84447	−	13.5870i	−0.483711	−	0.837812i	−0.999825	+	0.0187079i	$0.994045\pi$
$264$	4.64945	−	2.68436i	0.286154	−	0.165211i
$265$		−	12.7017i		−	0.780259i
$266$	4.49822	+	7.79115i	0.275804	+	0.477706i
$267$		−	6.14996i		−	0.376371i
$268$	2.26454	−	3.92230i	0.138329	−	0.239593i
$269$	−10.8924			−0.664120			−0.332060	−	0.943258i	$-0.607744\pi$
$269$	−10.8924			−0.664120			−0.332060	+	0.943258i	$0.607744\pi$
$270$	1.00000			0.0608581
$271$	6.68920	−	11.5860i	0.406340	−	0.703801i	−0.588136	−	0.808762i	$-0.700138\pi$
$271$	6.68920	−	11.5860i	0.406340	−	0.703801i	0.994476	+	0.104960i	$0.0334715\pi$
$272$	−3.25417	+	1.87879i	−0.197313	+	0.113919i
$273$		−	9.21497i		−	0.557716i
$274$	8.82764	+	5.09664i	0.533297	+	0.307899i
$275$	−2.68436	+	4.64945i	−0.161873	+	0.280373i
$276$	−0.177404	−	0.102424i	−0.0106785	−	0.00616523i
$277$	6.82382	−	3.93974i	0.410004	−	0.236716i	−0.280788	−	0.959770i	$-0.590596\pi$
$277$	6.82382	−	3.93974i	0.410004	−	0.236716i	0.690791	+	0.723054i	$0.257262\pi$
$278$	−11.3164	+	6.53350i	−0.678710	+	0.391853i
$279$	−1.68923	−	0.975279i	−0.101132	−	0.0583884i
$280$	2.37879	−	4.12019i	0.142160	−	0.246229i
$281$	−9.54036	−	5.50813i	−0.569130	−	0.328588i	0.187672	−	0.982232i	$-0.439906\pi$
$281$	−9.54036	−	5.50813i	−0.569130	−	0.328588i	−0.756802	+	0.653644i	$0.773239\pi$
$282$			8.35130i			0.497313i
$283$	−22.5402	+	13.0136i	−1.33988	+	0.773579i	−0.986789	−	0.162010i	$-0.948202\pi$
$283$	−22.5402	+	13.0136i	−1.33988	+	0.773579i	−0.353090	+	0.935590i	$0.614869\pi$
$284$	−4.89062	+	8.47081i	−0.290205	+	0.502650i
$285$	1.89097			0.112011
$286$	−10.3987			−0.614887
$287$	17.2950	−	29.9559i	1.02089	−	1.76824i
$288$			1.00000i			0.0589256i
$289$	−1.44026	−	2.49461i	−0.0847214	−	0.146742i
$290$			2.07147i			0.121641i
$291$	−1.99651	+	1.15268i	−0.117037	+	0.0675715i
$292$	7.54925	+	13.0757i	0.441786	+	0.765196i
$293$	−13.3314	−	23.0906i	−0.778827	−	1.34897i	−0.932618	−	0.360865i	$-0.882482\pi$
$293$	−13.3314	−	23.0906i	−0.778827	−	1.34897i	0.153791	−	0.988103i	$-0.450852\pi$
$294$	−13.5400	−	7.81733i	−0.789669	−	0.455916i
$295$	9.50376			0.553330
$296$	−5.49647	−	2.60554i	−0.319476	−	0.151444i
$297$	−5.36873			−0.311525
$298$	10.3772	+	5.99129i	0.601136	+	0.347066i
$299$	0.198386	+	0.343614i	0.0114730	+	0.0198717i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−7.19266	+	4.15268i	−0.414578	+	0.239357i
$302$		−	12.6884i		−	0.730135i
$303$	−1.64303	−	2.84581i	−0.0943895	−	0.163487i
$304$			1.89097i			0.108454i
$305$	2.07852	−	3.60010i	0.119016	−	0.206141i
$306$	3.75759			0.214807
$307$	−14.8746			−0.848937			−0.424468	−	0.905443i	$-0.639539\pi$
$307$	−14.8746			−0.848937			−0.424468	+	0.905443i	$0.639539\pi$
$308$	−12.7711	+	22.1202i	−0.727701	+	1.26042i
$309$	−10.3317	+	5.96502i	−0.587751	+	0.339338i
$310$			1.95056i			0.110784i
$311$	25.1237	+	14.5052i	1.42464	+	0.822514i	0.996690	−	0.0812907i	$-0.0259042\pi$
$311$	25.1237	+	14.5052i	1.42464	+	0.822514i	0.427945	+	0.903805i	$0.359238\pi$
$312$	0.968450	−	1.67740i	0.0548277	−	0.0949643i
$313$	19.3094	+	11.1483i	1.09143	+	0.630140i	0.933958	−	0.357383i	$-0.116331\pi$
$313$	19.3094	+	11.1483i	1.09143	+	0.630140i	0.157476	+	0.987523i	$0.449664\pi$
$314$	−5.88376	+	3.39699i	−0.332040	+	0.191703i
$315$	−4.12019	+	2.37879i	−0.232147	+	0.134030i
$316$	−10.1927	−	5.88473i	−0.573382	−	0.331042i
$317$	3.90714	−	6.76736i	0.219447	−	0.380093i	−0.735192	−	0.677859i	$-0.762908\pi$
$317$	3.90714	−	6.76736i	0.219447	−	0.380093i	0.954639	+	0.297766i	$0.0962415\pi$
$318$	−11.0000	−	6.35084i	−0.616849	−	0.356138i
$319$		−	11.1212i		−	0.622665i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	7.21086	−	12.4896i	0.402471	−	0.697100i
$322$	0.974587			0.0543116
$323$	7.10548			0.395359
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			1.93690i			0.107440i
$326$	0.0911079	+	0.157804i	0.00504600	+	0.00873993i
$327$			3.36685i			0.186187i
$328$	6.29644	−	3.63525i	0.347663	−	0.200723i
$329$	−19.8660	−	34.4090i	−1.09525	−	1.89703i
$330$	2.68436	+	4.64945i	0.147769	+	0.255944i
$331$	21.6889	+	12.5221i	1.19213	+	0.688277i	0.958790	−	0.284117i	$-0.0917005\pi$
$331$	21.6889	+	12.5221i	1.19213	+	0.688277i	0.233342	+	0.972395i	$0.425034\pi$
$332$	−4.21001			−0.231054
$333$	3.45731	+	5.00470i	0.189460	+	0.274256i
$334$	25.4673			1.39351
$335$	3.92230	+	2.26454i	0.214298	+	0.123725i
$336$	−2.37879	−	4.12019i	−0.129774	−	0.224775i
$337$	12.0335	+	20.8426i	0.655505	+	1.13537i	0.981767	+	0.190088i	$0.0608775\pi$
$337$	12.0335	+	20.8426i	0.655505	+	1.13537i	−0.326262	+	0.945279i	$0.605789\pi$
$338$	8.00937	−	4.62421i	0.435652	−	0.251524i
$339$		−	6.33864i		−	0.344268i
$340$	−1.87879	−	3.25417i	−0.101892	−	0.176482i
$341$		−	10.4720i		−	0.567091i
$342$	0.945484	−	1.63763i	0.0511259	−	0.0885527i
$343$	41.0801			2.21812
$344$	−1.74571			−0.0941223
$345$	0.102424	−	0.177404i	0.00551435	−	0.00955113i
$346$	4.57482	−	2.64127i	0.245944	−	0.141996i
$347$		−	32.7869i		−	1.76009i	−0.474887	−	0.880047i	$-0.657511\pi$
$347$		−	32.7869i		−	1.76009i	0.474887	−	0.880047i	$-0.342489\pi$
$348$	1.79395	+	1.03573i	0.0961656	+	0.0555212i
$349$	−14.3818	+	24.9100i	−0.769840	+	1.33340i	0.167809	+	0.985819i	$0.446331\pi$
$349$	−14.3818	+	24.9100i	−0.769840	+	1.33340i	−0.937649	+	0.347583i	$0.887003\pi$
$350$	4.12019	+	2.37879i	0.220234	+	0.127152i
$351$	−1.67740	+	0.968450i	−0.0895332	+	0.0516920i
$352$	−4.64945	+	2.68436i	−0.247817	+	0.143077i
$353$	8.80262	+	5.08220i	0.468516	+	0.270498i	0.715618	−	0.698491i	$-0.246145\pi$
$353$	8.80262	+	5.08220i	0.468516	+	0.270498i	−0.247102	+	0.968989i	$0.579478\pi$
$354$	4.75188	−	8.23050i	0.252560	−	0.437446i
$355$	−8.47081	−	4.89062i	−0.449584	−	0.259567i
$356$			6.14996i			0.325947i
$357$	−15.4820	+	8.93853i	−0.819394	+	0.473077i
$358$	−7.06748	+	12.2412i	−0.373528	+	0.646969i
$359$	26.4697			1.39702			0.698509	−	0.715601i	$-0.253847\pi$
$359$	26.4697			1.39702			0.698509	+	0.715601i	$0.253847\pi$
$360$	−1.00000			−0.0527046
$361$	−7.71212	+	13.3578i	−0.405901	+	0.703041i
$362$			10.6747i			0.561050i
$363$	−8.91162	−	15.4354i	−0.467739	−	0.810147i
$364$			9.21497i			0.482996i
$365$	−13.0757	+	7.54925i	−0.684412	+	0.395146i
$366$	−2.07852	−	3.60010i	−0.108646	−	0.188180i
$367$	−3.31961	−	5.74973i	−0.173282	−	0.300134i	0.766283	−	0.642503i	$-0.222104\pi$
$367$	−3.31961	−	5.74973i	−0.173282	−	0.300134i	−0.939565	+	0.342369i	$0.888771\pi$
$368$	0.177404	+	0.102424i	0.00924784	+	0.00533924i
$369$	−7.27050			−0.378487
$370$	2.60554	−	5.49647i	0.135455	−	0.285748i
$371$	60.4294			3.13734
$372$	1.68923	+	0.975279i	0.0875826	+	0.0505659i
$373$	−14.8306	−	25.6874i	−0.767900	−	1.33004i	−0.938700	−	0.344736i	$-0.887968\pi$
$373$	−14.8306	−	25.6874i	−0.767900	−	1.33004i	0.170799	−	0.985306i	$-0.445365\pi$
$374$	10.0867	+	17.4707i	0.521573	+	0.903390i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		−	8.35130i		−	0.430685i
$377$	−2.00611	−	3.47469i	−0.103320	−	0.178956i
$378$			4.75759i			0.244704i
$379$	11.9535	−	20.7040i	0.614009	−	1.06349i	−0.376549	−	0.926397i	$-0.622889\pi$
$379$	11.9535	−	20.7040i	0.614009	−	1.06349i	0.990558	−	0.137097i	$-0.0437773\pi$
$380$	−1.89097			−0.0970046
$381$	12.5395			0.642419
$382$	8.07875	−	13.9928i	0.413345	−	0.715935i
$383$	31.7499	−	18.3308i	1.62234	−	0.936660i	0.636052	−	0.771646i	$-0.280566\pi$
$383$	31.7499	−	18.3308i	1.62234	−	0.936660i	0.986291	−	0.165014i	$-0.0527670\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−22.1202	−	12.7711i	−1.12735	−	0.650876i
$386$	7.22683	−	12.5172i	0.367836	−	0.637111i
$387$	1.51183	+	0.872855i	0.0768506	+	0.0443697i
$388$	1.99651	−	1.15268i	0.101357	−	0.0585186i
$389$	−30.0362	+	17.3414i	−1.52290	+	0.879244i	−0.523262	+	0.852172i	$0.675285\pi$
$389$	−30.0362	+	17.3414i	−1.52290	+	0.879244i	−0.999633	+	0.0270719i	$0.991382\pi$
$390$	1.67740	+	0.968450i	0.0849387	+	0.0490394i
$391$	0.384869	−	0.666613i	0.0194637	−	0.0337120i
$392$	13.5400	+	7.81733i	0.683874	+	0.394835i
$393$		−	3.66287i		−	0.184767i
$394$	−3.68755	+	2.12901i	−0.185776	+	0.107258i
$395$	5.88473	−	10.1927i	0.296093	−	0.512848i
$396$	5.36873			0.269789
$397$	25.0721			1.25833			0.629166	−	0.777271i	$-0.283397\pi$
$397$	25.0721			1.25833			0.629166	+	0.777271i	$0.283397\pi$
$398$	12.9335	−	22.4014i	0.648296	−	1.12288i
$399$			8.99645i			0.450386i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	12.1747i		−	0.607974i	−0.952676	−	0.303987i	$-0.901682\pi$
$401$		−	12.1747i		−	0.607974i	0.952676	−	0.303987i	$-0.0983180\pi$
$402$	3.92230	−	2.26454i	0.195627	−	0.112945i
$403$	−1.88902	−	3.27187i	−0.0940987	−	0.162984i
$404$	1.64303	+	2.84581i	0.0817437	+	0.141584i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−9.85520			−0.489105
$407$	−13.9884	+	29.5090i	−0.693381	+	1.46271i
$408$	−3.75759			−0.186028
$409$	17.4322	+	10.0645i	0.861965	+	0.497656i	0.864670	−	0.502340i	$-0.167528\pi$
$409$	17.4322	+	10.0645i	0.861965	+	0.497656i	−0.00270462	+	0.999996i	$0.500861\pi$
$410$	3.63525	+	6.29644i	0.179532	+	0.310959i
$411$	5.09664	+	8.82764i	0.251399	+	0.435436i
$412$	10.3317	−	5.96502i	0.509007	−	0.293875i
$413$			45.2150i			2.22488i
$414$	−0.102424	−	0.177404i	−0.00503389	−	0.00871895i
$415$		−	4.21001i		−	0.206661i
$416$	−0.968450	+	1.67740i	−0.0474822	+	0.0822415i
$417$	−13.0670			−0.639894
$418$	10.1521			0.496555
$419$	−11.8802	+	20.5772i	−0.580388	+	1.00526i	0.415046	+	0.909801i	$0.363766\pi$
$419$	−11.8802	+	20.5772i	−0.580388	+	1.00526i	−0.995433	+	0.0954604i	$0.969568\pi$
$420$	4.12019	−	2.37879i	0.201045	−	0.116073i
$421$		−	2.63292i		−	0.128321i	−0.997940	−	0.0641603i	$-0.979563\pi$
$421$		−	2.63292i		−	0.128321i	0.997940	−	0.0641603i	$-0.0204369\pi$
$422$	−13.0372	−	7.52700i	−0.634639	−	0.366409i
$423$	−4.17565	+	7.23244i	−0.203027	+	0.351653i
$424$	11.0000	+	6.35084i	0.534207	+	0.308424i
$425$	3.25417	−	1.87879i	0.157850	−	0.0911349i
$426$	−8.47081	+	4.89062i	−0.410412	+	0.236951i
$427$	17.1278	+	9.88873i	0.828872	+	0.478549i
$428$	−7.21086	+	12.4896i	−0.348550	+	0.603706i
$429$	−9.00553	−	5.19934i	−0.434791	−	0.251027i
$430$		−	1.74571i		−	0.0841856i
$431$	−20.3340	+	11.7398i	−0.979454	+	0.565488i	−0.902105	−	0.431516i	$-0.857979\pi$
$431$	−20.3340	+	11.7398i	−0.979454	+	0.565488i	−0.0773485	+	0.997004i	$0.524645\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−23.3059			−1.12001			−0.560006	−	0.828489i	$-0.689201\pi$
$433$	−23.3059			−1.12001			−0.560006	+	0.828489i	$0.689201\pi$
$434$	−9.27995			−0.445452
$435$	−1.03573	+	1.79395i	−0.0496597	+	0.0860131i
$436$		−	3.36685i		−	0.161243i
$437$	−0.193681	−	0.335466i	−0.00926503	−	0.0160475i
$438$			15.0985i			0.721434i
$439$	−34.7240	+	20.0479i	−1.65729	+	0.956834i	−0.683326	+	0.730114i	$0.739467\pi$
$439$	−34.7240	+	20.0479i	−1.65729	+	0.956834i	−0.973960	+	0.226721i	$0.927200\pi$
$440$	−2.68436	−	4.64945i	−0.127972	−	0.221654i
$441$	−7.81733	−	13.5400i	−0.372254	−	0.644762i
$442$	6.30300	+	3.63904i	0.299803	+	0.173091i
$443$	8.21144			0.390137			0.195069	−	0.980790i	$-0.437507\pi$
$443$	8.21144			0.390137			0.195069	+	0.980790i	$0.437507\pi$
$444$	−3.45731	−	5.00470i	−0.164077	−	0.237512i
$445$	−6.14996			−0.291536
$446$	15.7637	+	9.10117i	0.746432	+	0.430953i
$447$	5.99129	+	10.3772i	0.283378	+	0.490826i
$448$	2.37879	+	4.12019i	0.112387	+	0.194661i
$449$	−16.5471	+	9.55346i	−0.780905	+	0.450856i	−0.836751	−	0.547584i	$-0.815548\pi$
$449$	−16.5471	+	9.55346i	−0.780905	+	0.450856i	0.0558459	+	0.998439i	$0.482214\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−19.5167	−	33.8039i	−0.919004	−	1.59176i
$452$			6.33864i			0.298144i
$453$	6.34419	−	10.9885i	0.298076	−	0.516283i
$454$	3.51002			0.164733
$455$	−9.21497			−0.432005
$456$	−0.945484	+	1.63763i	−0.0442763	+	0.0766889i
$457$	23.4540	−	13.5412i	1.09713	−	0.633430i	0.161666	−	0.986846i	$-0.448313\pi$
$457$	23.4540	−	13.5412i	1.09713	−	0.633430i	0.935466	+	0.353416i	$0.114980\pi$
$458$		−	1.90169i		−	0.0888602i
$459$	3.25417	+	1.87879i	0.151892	+	0.0876946i
$460$	−0.102424	+	0.177404i	−0.00477556	+	0.00827152i
$461$	8.89789	+	5.13720i	0.414416	+	0.239263i	0.692685	−	0.721240i	$-0.256427\pi$
$461$	8.89789	+	5.13720i	0.414416	+	0.239263i	−0.278269	+	0.960503i	$0.589761\pi$
$462$	−22.1202	+	12.7711i	−1.02912	+	0.594165i
$463$	−3.16157	+	1.82533i	−0.146931	+	0.0848305i	−0.571663	−	0.820488i	$-0.693702\pi$
$463$	−3.16157	+	1.82533i	−0.146931	+	0.0848305i	0.424732	+	0.905319i	$0.360368\pi$
$464$	−1.79395	−	1.03573i	−0.0832818	−	0.0480828i
$465$	−0.975279	+	1.68923i	−0.0452275	+	0.0783363i
$466$	13.7544	+	7.94111i	0.637161	+	0.367865i
$467$			41.2635i			1.90945i	0.297496	+	0.954723i	$0.403849\pi$
$467$			41.2635i			1.90945i	−0.297496	+	0.954723i	$0.596151\pi$
$468$	1.67740	−	0.968450i	0.0775380	−	0.0447666i
$469$	−10.7738	+	18.6607i	−0.497486	+	0.861671i
$470$	8.35130			0.385217
$471$	−6.79398			−0.313050
$472$	−4.75188	+	8.23050i	−0.218723	+	0.378839i
$473$			9.37224i			0.430936i
$474$	−5.88473	−	10.1927i	−0.270295	−	0.468164i
$475$		−	1.89097i		−	0.0867636i
$476$	15.4820	−	8.93853i	0.709616	−	0.409697i
$477$	−6.35084	−	11.0000i	−0.290785	−	0.503655i
$478$	12.3954	+	21.4695i	0.566953	+	0.981992i
$479$	0.245953	+	0.142001i	0.0112379	+	0.00648818i	0.505608	−	0.862763i	$-0.331268\pi$
$479$	0.245953	+	0.142001i	0.0112379	+	0.00648818i	−0.494371	+	0.869251i	$0.664601\pi$
$480$	1.00000			0.0456435
$481$	0.952513	+	11.7431i	0.0434309	+	0.535441i
$482$	4.57944			0.208588
$483$	0.844017	+	0.487293i	0.0384041	+	0.0221726i
$484$	8.91162	+	15.4354i	0.405074	+	0.701608i
$485$	1.15268	+	1.99651i	0.0523407	+	0.0906567i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	31.2302i		−	1.41518i	−0.706626	−	0.707588i	$-0.749783\pi$
$487$		−	31.2302i		−	1.41518i	0.706626	−	0.707588i	$-0.250217\pi$
$488$	2.07852	+	3.60010i	0.0940901	+	0.162969i
$489$			0.182216i			0.00824009i
$490$	−7.81733	+	13.5400i	−0.353151	+	0.611675i
$491$	10.1615			0.458582			0.229291	−	0.973358i	$-0.426359\pi$
$491$	10.1615			0.458582			0.229291	+	0.973358i	$0.426359\pi$
$492$	7.27050			0.327779
$493$	−3.89187	+	6.74091i	−0.175281	+	0.303595i
$494$	3.17192	−	1.83131i	0.142711	−	0.0823944i
$495$			5.36873i			0.241306i
$496$	−1.68923	−	0.975279i	−0.0758488	−	0.0437913i
$497$	23.2676	−	40.3006i	1.04369	−	1.80773i
$498$	−3.64598	−	2.10501i	−0.163380	−	0.0943275i
$499$	10.6809	−	6.16661i	0.478142	−	0.276055i	−0.241500	−	0.970401i	$-0.577639\pi$
$499$	10.6809	−	6.16661i	0.478142	−	0.276055i	0.719642	+	0.694346i	$0.244306\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	22.0553	+	12.7336i	0.985359	+	0.568898i
$502$	1.30899	−	2.26724i	0.0584231	−	0.101192i
$503$	7.02334	+	4.05493i	0.313155	+	0.180800i	0.648337	−	0.761353i	$-0.275465\pi$
$503$	7.02334	+	4.05493i	0.313155	+	0.180800i	−0.335182	+	0.942153i	$0.608798\pi$
$504$		−	4.75759i		−	0.211920i
$505$	−2.84581	+	1.64303i	−0.126637	+	0.0731138i
$506$	0.549889	−	0.952436i	0.0244455	−	0.0423409i
$507$	9.24842			0.410737
$508$	−12.5395			−0.556351
$509$	−6.20749	+	10.7517i	−0.275142	+	0.476560i	−0.970171	−	0.242422i	$-0.922058\pi$
$509$	−6.20749	+	10.7517i	−0.275142	+	0.476560i	0.695029	+	0.718982i	$0.255392\pi$
$510$		−	3.75759i		−	0.166389i
$511$	−35.9162	−	62.2087i	−1.58884	−	2.75195i
$512$			1.00000i			0.0441942i
$513$	1.63763	−	0.945484i	0.0723030	−	0.0417441i
$514$	3.64250	+	6.30900i	0.160664	+	0.278278i
$515$	5.96502	+	10.3317i	0.262850	+	0.455270i
$516$	−1.51183	−	0.872855i	−0.0665545	−	0.0384253i
$517$	−44.8359			−1.97188
$518$	26.1499	+	12.3961i	1.14896	+	0.544652i
$519$	5.28255			0.231878
$520$	−1.67740	−	0.968450i	−0.0735590	−	0.0424693i
$521$	13.8998	+	24.0752i	0.608962	+	1.05475i	0.991412	+	0.130777i	$0.0417471\pi$
$521$	13.8998	+	24.0752i	0.608962	+	1.05475i	−0.382450	+	0.923976i	$0.624920\pi$
$522$	1.03573	+	1.79395i	0.0453329	+	0.0785189i
$523$	−25.2169	+	14.5590i	−1.10266	+	0.636619i	−0.936918	−	0.349550i	$-0.886334\pi$
$523$	−25.2169	+	14.5590i	−1.10266	+	0.636619i	−0.165740	+	0.986170i	$0.553001\pi$
$524$			3.66287i			0.160013i
$525$	2.37879	+	4.12019i	0.103819	+	0.179820i
$526$			15.6889i			0.684071i
$527$	−3.66470	+	6.34744i	−0.159637	+	0.276499i
$528$	−5.36873			−0.233644
$529$	22.9580			0.998176
$530$	−6.35084	+	11.0000i	−0.275863	+	0.477809i
$531$	8.23050	−	4.75188i	0.357173	−	0.206214i
$532$		−	8.99645i		−	0.390045i
$533$	−12.1956	−	7.04111i	−0.528249	−	0.304985i
$534$	−3.07498	+	5.32602i	−0.133067	+	0.230479i
$535$	−12.4896	−	7.21086i	−0.539971	−	0.311753i
$536$	−3.92230	+	2.26454i	−0.169418	+	0.0978133i
$537$	−12.2412	+	7.06748i	−0.528248	+	0.304984i
$538$	9.43308	+	5.44619i	0.406689	+	0.234802i
$539$	41.9691	−	72.6926i	1.80774	−	3.13109i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$			37.6109i			1.61702i	0.588482	+	0.808510i	$0.299726\pi$
$541$			37.6109i			1.61702i	−0.588482	+	0.808510i	$0.700274\pi$
$542$	−11.5860	+	6.68920i	−0.497663	+	0.287326i
$543$	−5.33735	+	9.24456i	−0.229048	+	0.396722i
$544$	3.75759			0.161105
$545$	3.36685			0.144220
$546$	−4.60749	+	7.98040i	−0.197182	+	0.341530i
$547$			6.12219i			0.261766i	0.991398	+	0.130883i	$0.0417812\pi$
$547$			6.12219i			0.261766i	−0.991398	+	0.130883i	$0.958219\pi$
$548$	−5.09664	−	8.82764i	−0.217718	−	0.377098i
$549$		−	4.15704i		−	0.177418i
$550$	4.64945	−	2.68436i	0.198253	−	0.114462i
$551$	1.95854	+	3.39229i	0.0834367	+	0.144517i
$552$	0.102424	+	0.177404i	0.00435947	+	0.00755083i
$553$	48.4925	+	27.9971i	2.06211	+	1.19056i
$554$	−7.87947			−0.334767
$555$	5.00470	−	3.45731i	0.212438	−	0.146755i
$556$	13.0670			0.554164
$557$	13.0000	+	7.50554i	0.550826	+	0.318020i	0.749455	−	0.662055i	$-0.230315\pi$
$557$	13.0000	+	7.50554i	0.550826	+	0.318020i	−0.198629	+	0.980075i	$0.563649\pi$
$558$	0.975279	+	1.68923i	0.0412869	+	0.0715109i
$559$	1.69063	+	2.92826i	0.0715061	+	0.123852i
$560$	−4.12019	+	2.37879i	−0.174110	+	0.100522i
$561$			20.1735i			0.851725i
$562$	5.50813	+	9.54036i	0.232346	+	0.402436i
$563$		−	12.6975i		−	0.535135i	−0.963539	−	0.267567i	$-0.913780\pi$
$563$		−	12.6975i		−	0.535135i	0.963539	−	0.267567i	$-0.0862198\pi$
$564$	4.17565	−	7.23244i	0.175827	−	0.304541i
$565$	−6.33864			−0.266668
$566$	26.0272			1.09401
$567$	−2.37879	+	4.12019i	−0.0999000	+	0.173032i
$568$	8.47081	−	4.89062i	0.355427	−	0.205206i
$569$		−	37.5046i		−	1.57227i	−0.618053	−	0.786137i	$-0.712078\pi$
$569$		−	37.5046i		−	1.57227i	0.618053	−	0.786137i	$-0.287922\pi$
$570$	−1.63763	−	0.945484i	−0.0685926	−	0.0396020i
$571$	−19.6205	+	33.9837i	−0.821091	+	1.42217i	0.0837786	+	0.996484i	$0.473301\pi$
$571$	−19.6205	+	33.9837i	−0.821091	+	1.42217i	−0.904870	+	0.425688i	$0.860032\pi$
$572$	9.00553	+	5.19934i	0.376540	+	0.217395i
$573$	13.9928	−	8.07875i	0.584558	−	0.337495i
$574$	−29.9559	+	17.2950i	−1.25033	+	0.721880i
$575$	−0.177404	−	0.102424i	−0.00739827	−	0.00427139i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−4.09848	−	2.36626i	−0.170622	−	0.0985085i	0.412257	−	0.911067i	$-0.364741\pi$
$577$	−4.09848	−	2.36626i	−0.170622	−	0.0985085i	−0.582879	+	0.812559i	$0.698074\pi$
$578$			2.88053i			0.119814i
$579$	12.5172	−	7.22683i	0.520199	−	0.300337i
$580$	1.03573	−	1.79395i	0.0430066	−	0.0744895i
$581$	20.0295			0.830964
$582$	2.30537			0.0955605
$583$	34.0960	−	59.0559i	1.41211	−	2.44585i
$584$		−	15.0985i		−	0.624780i
$585$	0.968450	+	1.67740i	0.0400405	+	0.0693521i
$586$			26.6627i			1.10143i
$587$	14.5676	−	8.41058i	0.601267	−	0.347142i	−0.168273	−	0.985740i	$-0.553819\pi$
$587$	14.5676	−	8.41058i	0.601267	−	0.347142i	0.769540	+	0.638599i	$0.220486\pi$
$588$	7.81733	+	13.5400i	0.322381	+	0.558380i
$589$	1.84422	+	3.19429i	0.0759898	+	0.131618i
$590$	−8.23050	−	4.75188i	−0.338844	−	0.195632i
$591$	−4.25801			−0.175151
$592$	3.45731	+	5.00470i	0.142095	+	0.205692i
$593$	−29.3265			−1.20429			−0.602147	−	0.798385i	$-0.705688\pi$
$593$	−29.3265			−1.20429			−0.602147	+	0.798385i	$0.705688\pi$
$594$	4.64945	+	2.68436i	0.190769	+	0.110141i
$595$	8.93853	+	15.4820i	0.366444	+	0.634700i
$596$	−5.99129	−	10.3772i	−0.245413	−	0.425068i
$597$	22.4014	−	12.9335i	0.916829	−	0.529332i
$598$		−	0.396772i		−	0.0162252i
$599$	7.12556	+	12.3418i	0.291143	+	0.504274i	0.974080	−	0.226203i	$-0.0726313\pi$
$599$	7.12556	+	12.3418i	0.291143	+	0.504274i	−0.682938	+	0.730477i	$0.739298\pi$
$600$			1.00000i			0.0408248i
$601$	−0.461616	+	0.799543i	−0.0188297	+	0.0326140i	−0.875287	−	0.483604i	$-0.839327\pi$
$601$	−0.461616	+	0.799543i	−0.0188297	+	0.0326140i	0.856457	+	0.516218i	$0.172661\pi$
$602$	8.30537			0.338501
$603$	4.52908			0.184439
$604$	−6.34419	+	10.9885i	−0.258142	+	0.447114i
$605$	−15.4354	+	8.91162i	−0.627537	+	0.362309i
$606$			3.28606i			0.133487i
$607$	21.3290	+	12.3143i	0.865718	+	0.499823i	0.865923	−	0.500177i	$-0.166732\pi$
$607$	21.3290	+	12.3143i	0.865718	+	0.499823i	−0.000204616		1.00000i	$0.500065\pi$
$608$	0.945484	−	1.63763i	0.0383444	−	0.0664145i
$609$	−8.53486	−	4.92760i	−0.345850	−	0.199676i
$610$	−3.60010	+	2.07852i	−0.145764	+	0.0841567i
$611$	−14.0085	+	8.08781i	−0.566723	+	0.327198i
$612$	−3.25417	−	1.87879i	−0.131542	−	0.0759458i
$613$	−9.14393	+	15.8378i	−0.369320	+	0.639681i	−0.989459	−	0.144811i	$-0.953743\pi$
$613$	−9.14393	+	15.8378i	−0.369320	+	0.639681i	0.620139	+	0.784492i	$0.287076\pi$
$614$	12.8818	+	7.43729i	0.519866	+	0.300145i
$615$			7.27050i			0.293175i
$616$	22.1202	−	12.7711i	0.891248	−	0.514562i
$617$	−2.88264	+	4.99288i	−0.116051	+	0.201006i	−0.918199	−	0.396119i	$-0.870357\pi$
$617$	−2.88264	+	4.99288i	−0.116051	+	0.201006i	0.802149	+	0.597125i	$0.203690\pi$
$618$	11.9300			0.479896
$619$	22.5666			0.907030			0.453515	−	0.891249i	$-0.350170\pi$
$619$	22.5666			0.907030			0.453515	+	0.891249i	$0.350170\pi$
$620$	0.975279	−	1.68923i	0.0391681	−	0.0678412i
$621$		−	0.204849i		−	0.00822030i
$622$	−14.5052	−	25.1237i	−0.581605	−	1.00737i
$623$		−	29.2590i		−	1.17224i
$624$	−1.67740	+	0.968450i	−0.0671499	+	0.0387690i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.1483	−	19.3094i	−0.445576	−	0.771761i
$627$	8.79197	+	5.07605i	0.351117	+	0.202718i
$628$	6.79398			0.271109
$629$	18.8056	−	12.9912i	0.749828	−	0.517991i
$630$	4.75759			0.189547
$631$	8.15056	+	4.70573i	0.324469	+	0.187332i	0.653383	−	0.757028i	$-0.273349\pi$
$631$	8.15056	+	4.70573i	0.324469	+	0.187332i	−0.328914	+	0.944360i	$0.606683\pi$
$632$	5.88473	+	10.1927i	0.234082	+	0.405442i
$633$	−7.52700	−	13.0372i	−0.299172	−	0.518180i
$634$	−6.76736	+	3.90714i	−0.268766	+	0.155172i
$635$		−	12.5395i		−	0.497616i
$636$	6.35084	+	11.0000i	0.251827	+	0.436178i
$637$		−	30.2828i		−	1.19985i
$638$	−5.56058	+	9.63121i	−0.220145	+	0.381303i
$639$	−9.78125			−0.386940
$640$	−1.00000			−0.0395285
$641$	−5.14868	+	8.91778i	−0.203361	+	0.352231i	−0.949609	−	0.313436i	$-0.898520\pi$
$641$	−5.14868	+	8.91778i	−0.203361	+	0.352231i	0.746248	+	0.665667i	$0.231853\pi$
$642$	−12.4896	+	7.21086i	−0.492924	+	0.284590i
$643$			22.3349i			0.880802i	0.897801	+	0.440401i	$0.145164\pi$
$643$			22.3349i			0.880802i	−0.897801	+	0.440401i	$0.854836\pi$
$644$	−0.844017	−	0.487293i	−0.0332589	−	0.0192020i
$645$	0.872855	−	1.51183i	0.0343686	−	0.0595282i
$646$	−6.15353	−	3.55274i	−0.242107	−	0.139781i
$647$	−22.5961	+	13.0459i	−0.888344	+	0.512886i	−0.873401	−	0.487003i	$-0.838090\pi$
$647$	−22.5961	+	13.0459i	−0.888344	+	0.512886i	−0.0149437	+	0.999888i	$0.504757\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	44.1873	+	25.5115i	1.73450	+	1.00142i
$650$	0.968450	−	1.67740i	0.0379857	−	0.0657932i
$651$	−8.03668	−	4.63998i	−0.314982	−	0.181855i
$652$		−	0.182216i		−	0.00713613i
$653$	31.7581	−	18.3355i	1.24279	−	0.717525i	0.273128	−	0.961978i	$-0.411942\pi$
$653$	31.7581	−	18.3355i	1.24279	−	0.717525i	0.969661	+	0.244453i	$0.0786084\pi$
$654$	1.68342	−	2.91578i	0.0658271	−	0.114016i
$655$	−3.66287			−0.143120
$656$	−7.27050			−0.283865
$657$	−7.54925	+	13.0757i	−0.294524	+	0.510131i
$658$			39.7320i			1.54892i
$659$	24.9009	+	43.1297i	0.970003	+	1.68009i	0.695527	+	0.718500i	$0.255171\pi$
$659$	24.9009	+	43.1297i	0.970003	+	1.68009i	0.274475	+	0.961594i	$0.411496\pi$
$660$		−	5.36873i		−	0.208977i
$661$	10.7505	−	6.20682i	0.418147	−	0.241417i	−0.276137	−	0.961118i	$-0.589054\pi$
$661$	10.7505	−	6.20682i	0.418147	−	0.241417i	0.694284	+	0.719701i	$0.255721\pi$
$662$	−12.5221	−	21.6889i	−0.486686	−	0.842964i
$663$	3.63904	+	6.30300i	0.141328	+	0.244788i
$664$	3.64598	+	2.10501i	0.141491	+	0.0816900i
$665$	8.99645			0.348867
$666$	−0.491772	−	6.06285i	−0.0190558	−	0.234931i
$667$	0.424338			0.0164304
$668$	−22.0553	−	12.7336i	−0.853346	−	0.492680i
$669$	9.10117	+	15.7637i	0.351871	+	0.609459i
$670$	−2.26454	−	3.92230i	−0.0874869	−	0.151532i
$671$	19.3280	−	11.1590i	0.746147	−	0.430788i
$672$			4.75759i			0.183528i
$673$	24.9387	+	43.1950i	0.961315	+	1.66505i	0.719205	+	0.694798i	$0.244506\pi$
$673$	24.9387	+	43.1950i	0.961315	+	1.66505i	0.242110	+	0.970249i	$0.422161\pi$
$674$		−	24.0669i		−	0.927024i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−9.24842			−0.355708
$677$	−39.4514			−1.51624			−0.758120	−	0.652115i	$-0.773882\pi$
$677$	−39.4514			−1.51624			−0.758120	+	0.652115i	$0.773882\pi$
$678$	−3.16932	+	5.48942i	−0.121717	+	0.210820i
$679$	−9.49856	+	5.48399i	−0.364521	+	0.210456i
$680$			3.75759i			0.144097i
$681$	3.03976	+	1.75501i	0.116484	+	0.0672521i
$682$	−5.23601	+	9.06903i	−0.200497	+	0.347271i
$683$	−16.1531	−	9.32598i	−0.618080	−	0.356849i	0.158041	−	0.987433i	$-0.449482\pi$
$683$	−16.1531	−	9.32598i	−0.618080	−	0.356849i	−0.776121	+	0.630584i	$0.782815\pi$
$684$	−1.63763	+	0.945484i	−0.0626162	+	0.0361515i
$685$	8.82764	−	5.09664i	0.337287	−	0.194733i
$686$	−35.5764	−	20.5401i	−1.35831	−	0.784223i
$687$	0.950846	−	1.64691i	0.0362770	−	0.0628337i
$688$	1.51183	+	0.872855i	0.0576379	+	0.0332773i
$689$		−	24.6019i		−	0.937258i
$690$	−0.177404	+	0.102424i	−0.00675367	+	0.00389923i
$691$	−10.9603	+	18.9839i	−0.416951	+	0.722181i	−0.995631	−	0.0933739i	$-0.970235\pi$
$691$	−10.9603	+	18.9839i	−0.416951	+	0.722181i	0.578680	+	0.815555i	$0.303568\pi$
$692$	−5.28255			−0.200812
$693$	−25.5422			−0.970268
$694$	−16.3935	+	28.3943i	−0.622287	+	1.07783i
$695$			13.0670i			0.495660i
$696$	−1.03573	−	1.79395i	−0.0392594	−	0.0679993i
$697$			27.3195i			1.03480i
$698$	24.9100	−	14.3818i	0.942858	−	0.544359i
$699$	7.94111	+	13.7544i	0.300360	+	0.520240i
$700$	−2.37879	−	4.12019i	−0.0899100	−	0.155729i
$701$	−24.8824	−	14.3659i	−0.939797	−	0.542592i	−0.0499001	−	0.998754i	$-0.515890\pi$
$701$	−24.8824	−	14.3659i	−0.939797	−	0.542592i	−0.889897	+	0.456162i	$0.849224\pi$
$702$	1.93690			0.0731036
$703$	−0.929925	−	11.4647i	−0.0350728	−	0.432398i
$704$	5.36873			0.202342
$705$	7.23244	+	4.17565i	0.272389	+	0.157264i
$706$	−5.08220	−	8.80262i	−0.191271	−	0.331291i
$707$	−7.81685	−	13.5392i	−0.293983	−	0.509194i
$708$	−8.23050	+	4.75188i	−0.309321	+	0.178587i
$709$		−	4.43747i		−	0.166653i	−0.996522	−	0.0833263i	$-0.973446\pi$
$709$		−	4.43747i		−	0.166653i	0.996522	−	0.0833263i	$-0.0265544\pi$
$710$	4.89062	+	8.47081i	0.183542	+	0.317904i
$711$		−	11.7695i		−	0.441390i
$712$	3.07498	−	5.32602i	0.115240	−	0.199601i
$713$	0.399570			0.0149640
$714$	17.8771			0.669032
$715$	−5.19934	+	9.00553i	−0.194444	+	0.336788i
$716$	12.2412	−	7.06748i	0.457476	−	0.264124i
$717$			24.7908i			0.925831i
$718$	−22.9235	−	13.2349i	−0.855496	−	0.493921i
$719$	22.3711	−	38.7479i	0.834302	−	1.44505i	−0.0602957	−	0.998181i	$-0.519204\pi$
$719$	22.3711	−	38.7479i	0.834302	−	1.44505i	0.894598	−	0.446873i	$-0.147462\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	−49.1541	+	28.3791i	−1.83059	+	1.05689i
$722$	13.3578	−	7.71212i	0.497125	−	0.287015i
$723$	3.96591	+	2.28972i	0.147494	+	0.0851556i
$724$	5.33735	−	9.24456i	0.198361	−	0.343571i
$725$	1.79395	+	1.03573i	0.0666255	+	0.0384662i
$726$			17.8232i			0.661482i
$727$	−37.3973	+	21.5914i	−1.38699	+	0.800779i	−0.992975	−	0.118325i	$-0.962248\pi$
$727$	−37.3973	+	21.5914i	−1.38699	+	0.800779i	−0.394015	+	0.919104i	$0.628914\pi$
$728$	4.60749	−	7.98040i	0.170765	−	0.295773i
$729$	1.00000			0.0370370
$730$	15.0985			0.558820
$731$	3.27983	−	5.68083i	0.121309	−	0.210113i
$732$			4.15704i			0.153648i
$733$	−14.5314	−	25.1691i	−0.536729	−	0.929641i	−0.999078	−	0.0429432i	$-0.986327\pi$
$733$	−14.5314	−	25.1691i	−0.536729	−	0.929641i	0.462349	−	0.886698i	$-0.347007\pi$
$734$			6.63922i			0.245058i
$735$	−13.5400	+	7.81733i	−0.499431	+	0.288346i
$736$	−0.102424	−	0.177404i	−0.00377542	−	0.00653921i
$737$	12.1577	+	21.0578i	0.447835	+	0.775673i
$738$	6.29644	+	3.63525i	0.231775	+	0.133815i
$739$	44.2733			1.62862			0.814309	−	0.580431i	$-0.197116\pi$
$739$	44.2733			1.62862			0.814309	+	0.580431i	$0.197116\pi$
$740$	−5.00470	+	3.45731i	−0.183976	+	0.127093i
$741$	3.66262			0.134550
$742$	−52.3334	−	30.2147i	−1.92122	−	1.10922i
$743$	−20.8251	−	36.0701i	−0.763997	−	1.32328i	−0.940775	−	0.339031i	$-0.889901\pi$
$743$	−20.8251	−	36.0701i	−0.763997	−	1.32328i	0.176778	−	0.984251i	$-0.443433\pi$
$744$	−0.975279	−	1.68923i	−0.0357555	−	0.0619303i
$745$	10.3772	−	5.99129i	0.380192	−	0.219504i
$746$			29.6612i			1.08597i
$747$	−2.10501	−	3.64598i	−0.0770181	−	0.133399i
$748$		−	20.1735i		−	0.737615i
$749$	34.3063	−	59.4203i	1.25352	−	2.17117i
$750$	−1.00000			−0.0365148
$751$	15.8097			0.576905			0.288452	−	0.957494i	$-0.406859\pi$
$751$	15.8097			0.576905			0.288452	+	0.957494i	$0.406859\pi$
$752$	−4.17565	+	7.23244i	−0.152270	+	0.263740i
$753$	2.26724	−	1.30899i	0.0826228	−	0.0477023i
$754$			4.01223i			0.146117i
$755$	−10.9885	−	6.34419i	−0.399911	−	0.230889i
$756$	2.37879	−	4.12019i	0.0865159	−	0.149850i
$757$	−17.1132	−	9.88032i	−0.621991	−	0.359107i	0.155653	−	0.987812i	$-0.450252\pi$
$757$	−17.1132	−	9.88032i	−0.621991	−	0.359107i	−0.777644	+	0.628705i	$0.783585\pi$
$758$	−20.7040	+	11.9535i	−0.752004	+	0.434170i
$759$	0.952436	−	0.549889i	0.0345712	−	0.0199597i
$760$	1.63763	+	0.945484i	0.0594029	+	0.0342963i
$761$	15.1511	−	26.2424i	0.549225	−	0.951286i	−0.449102	−	0.893480i	$-0.648256\pi$
$761$	15.1511	−	26.2424i	0.549225	−	0.951286i	0.998328	−	0.0578061i	$-0.0184105\pi$
$762$	−10.8595	−	6.26976i	−0.393400	−	0.227130i
$763$			16.0181i			0.579893i
$764$	−13.9928	+	8.07875i	−0.506242	+	0.292279i
$765$	1.87879	−	3.25417i	0.0679280	−	0.117655i
$766$	−36.6616			−1.32464
$767$	18.4078			0.664668
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$			10.9287i			0.394097i	0.980394	+	0.197049i	$0.0631357\pi$
$769$			10.9287i			0.394097i	−0.980394	+	0.197049i	$0.936864\pi$
$770$	12.7711	+	22.1202i	0.460239	+	0.797156i
$771$			7.28500i			0.262363i
$772$	−12.5172	+	7.22683i	−0.450505	+	0.260099i
$773$	13.6280	+	23.6044i	0.490165	+	0.848991i	0.999936	−	0.0113194i	$-0.00360314\pi$
$773$	13.6280	+	23.6044i	0.490165	+	0.848991i	−0.509771	+	0.860310i	$0.670270\pi$
$774$	−0.872855	−	1.51183i	−0.0313741	−	0.0543416i
$775$	1.68923	+	0.975279i	0.0606790	+	0.0350331i
$776$	−2.30537			−0.0827578
$777$	16.4485	+	23.8103i	0.590086	+	0.854189i
$778$	34.6828			1.24344
$779$	11.9064	+	6.87414i	0.426590	+	0.246292i
$780$	−0.968450	−	1.67740i	−0.0346761	−	0.0600607i
$781$	−26.2564	−	45.4775i	−0.939529	−	1.62731i
$782$	−0.666613	+	0.384869i	−0.0238380	+	0.0137629i
$783$			2.07147i			0.0740283i
$784$	−7.81733	−	13.5400i	−0.279190	−	0.483572i
$785$			6.79398i			0.242488i
$786$	−1.83144	+	3.17214i	−0.0653251	+	0.113146i
$787$	8.98924			0.320432			0.160216	−	0.987082i	$-0.448781\pi$
$787$	8.98924			0.320432			0.160216	+	0.987082i	$0.448781\pi$
$788$	4.25801			0.151685
$789$	−7.84447	+	13.5870i	−0.279271	+	0.483711i
$790$	−10.1927	+	5.88473i	−0.362639	+	0.209369i
$791$		−	30.1566i		−	1.07225i
$792$	−4.64945	−	2.68436i	−0.165211	−	0.0953847i
$793$	4.02588	−	6.97303i	0.142963	−	0.247620i
$794$	−21.7130	−	12.5360i	−0.770567	−	0.444887i
$795$	−11.0000	+	6.35084i	−0.390129	+	0.225241i
$796$	−22.4014	+	12.9335i	−0.793997	+	0.458415i
$797$	−14.4534	−	8.34466i	−0.511965	−	0.295583i	0.221676	−	0.975120i	$-0.428847\pi$
$797$	−14.4534	−	8.34466i	−0.511965	−	0.295583i	−0.733641	+	0.679537i	$0.762181\pi$
$798$	4.49822	−	7.79115i	0.159235	−	0.275804i
$799$	27.1765	+	15.6904i	0.961436	+	0.555086i
$800$		−	1.00000i		−	0.0353553i
$801$	−5.32602	+	3.07498i	−0.188186	+	0.108649i
$802$	−6.08734	+	10.5436i	−0.214951	+	0.372307i
$803$	−81.0597			−2.86053
$804$	−4.52908			−0.159728
$805$	0.487293	−	0.844017i	0.0171748	−	0.0297477i
$806$			3.77804i			0.133076i
$807$	5.44619	+	9.43308i	0.191715	+	0.332060i
$808$		−	3.28606i		−	0.115603i
$809$	7.61668	−	4.39749i	0.267788	−	0.154608i	−0.360094	−	0.932916i	$-0.617255\pi$
$809$	7.61668	−	4.39749i	0.267788	−	0.154608i	0.627882	+	0.778309i	$0.283922\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−1.81337	−	3.14084i	−0.0636759	−	0.110290i	0.832430	−	0.554130i	$-0.186949\pi$
$811$	−1.81337	−	3.14084i	−0.0636759	−	0.110290i	−0.896106	+	0.443840i	$0.853616\pi$
$812$	8.53486	+	4.92760i	0.299515	+	0.172925i
$813$	−13.3784			−0.469201
$814$	26.8689	−	18.5614i	0.941753	−	0.650576i
$815$	0.182216			0.00638274
$816$	3.25417	+	1.87879i	0.113919	+	0.0657710i
$817$	−1.65054	−	2.85882i	−0.0577451	−	0.100017i
$818$	−10.0645	−	17.4322i	−0.351896	−	0.609502i
$819$	−7.98040	+	4.60749i	−0.278858	+	0.160999i
$820$		−	7.27050i		−	0.253897i
$821$	19.4137	+	33.6255i	0.677542	+	1.17354i	0.975719	+	0.219026i	$0.0702881\pi$
$821$	19.4137	+	33.6255i	0.677542	+	1.17354i	−0.298177	+	0.954511i	$0.596379\pi$
$822$		−	10.1933i		−	0.355532i
$823$	0.468746	−	0.811891i	0.0163394	−	0.0283008i	−0.857740	−	0.514084i	$-0.828132\pi$
$823$	0.468746	−	0.811891i	0.0163394	−	0.0283008i	0.874080	+	0.485783i	$0.161465\pi$
$824$	−11.9300			−0.415603
$825$	5.36873			0.186915
$826$	22.6075	−	39.1573i	0.786615	−	1.36246i
$827$	−36.6349	+	21.1512i	−1.27392	+	0.735499i	−0.975724	−	0.219005i	$-0.929719\pi$
$827$	−36.6349	+	21.1512i	−1.27392	+	0.735499i	−0.298198	+	0.954504i	$0.596385\pi$
$828$			0.204849i			0.00711899i
$829$	12.2197	+	7.05505i	0.424408	+	0.245032i	0.696961	−	0.717109i	$-0.254535\pi$
$829$	12.2197	+	7.05505i	0.424408	+	0.245032i	−0.272554	+	0.962141i	$0.587868\pi$
$830$	−2.10501	+	3.64598i	−0.0730658	+	0.126554i
$831$	−6.82382	−	3.93974i	−0.236716	−	0.136668i
$832$	1.67740	−	0.968450i	0.0581535	−	0.0335750i
$833$	−50.8778	+	29.3743i	−1.76281	+	1.01776i
$834$	11.3164	+	6.53350i	0.391853	+	0.226237i
$835$	12.7336	−	22.0553i	0.440666	−	0.763256i
$836$	−8.79197	−	5.07605i	−0.304077	−	0.175559i
$837$			1.95056i			0.0674212i
$838$	20.5772	−	11.8802i	0.710827	−	0.410396i
$839$	−4.88886	+	8.46775i	−0.168782	+	0.292339i	−0.937992	−	0.346657i	$-0.887317\pi$
$839$	−4.88886	+	8.46775i	−0.168782	+	0.292339i	0.769210	+	0.638996i	$0.220650\pi$
$840$	−4.75759			−0.164152
$841$	24.7090			0.852035
$842$	−1.31646	+	2.28018i	−0.0453682	+	0.0785800i
$843$			11.0163i			0.379420i
$844$	7.52700	+	13.0372i	0.259090	+	0.448757i
$845$		−	9.24842i		−	0.318155i
$846$	7.23244	−	4.17565i	0.248656	−	0.143562i
$847$	−42.3978	−	73.4352i	−1.45681	−	2.52326i
$848$	−6.35084	−	11.0000i	−0.218089	−	0.377741i
$849$	22.5402	+	13.0136i	0.773579	+	0.446626i
$850$	−3.75759			−0.128884
$851$	−1.12595	−	0.533742i	−0.0385969	−	0.0182964i
$852$	9.78125			0.335100
$853$	−38.0577	−	21.9726i	−1.30307	−	0.752328i	−0.322140	−	0.946692i	$-0.604402\pi$
$853$	−38.0577	−	21.9726i	−1.30307	−	0.752328i	−0.980929	+	0.194364i	$0.937736\pi$
$854$	−9.88873	−	17.1278i	−0.338386	−	0.586101i
$855$	−0.945484	−	1.63763i	−0.0323349	−	0.0560056i
$856$	12.4896	−	7.21086i	0.426885	−	0.246462i
$857$			33.1293i			1.13167i	0.824517	+	0.565837i	$0.191447\pi$
$857$			33.1293i			1.13167i	−0.824517	+	0.565837i	$0.808553\pi$
$858$	5.19934	+	9.00553i	0.177503	+	0.307444i
$859$			27.5354i			0.939496i	0.882800	+	0.469748i	$0.155655\pi$
$859$			27.5354i			0.939496i	−0.882800	+	0.469748i	$0.844345\pi$
$860$	−0.872855	+	1.51183i	−0.0297641	+	0.0515529i
$861$	−34.5900			−1.17883
$862$	23.4797			0.799721
$863$	9.94846	−	17.2312i	0.338650	−	0.586558i	−0.645529	−	0.763735i	$-0.723363\pi$
$863$	9.94846	−	17.2312i	0.338650	−	0.586558i	0.984179	+	0.177177i	$0.0566966\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		−	5.28255i		−	0.179612i
$866$	20.1835	+	11.6530i	0.685864	+	0.395984i
$867$	−1.44026	+	2.49461i	−0.0489139	+	0.0847214i
$868$	8.03668	+	4.63998i	0.272783	+	0.157491i
$869$	54.7216	−	31.5935i	1.85630	−	1.07174i
$870$	1.79395	−	1.03573i	0.0608204	−	0.0351147i
$871$	7.59710	+	4.38619i	0.257418	+	0.148620i
$872$	−1.68342	+	2.91578i	−0.0570079	+	0.0987406i
$873$	1.99651	+	1.15268i	0.0675715	+	0.0390124i
$874$			0.387363i			0.0131027i
$875$	4.12019	−	2.37879i	0.139288	−	0.0804179i
$876$	7.54925	−	13.0757i	0.255065	−	0.441786i
$877$	22.8746			0.772422			0.386211	−	0.922411i	$-0.373784\pi$
$877$	22.8746			0.772422			0.386211	+	0.922411i	$0.373784\pi$
$878$	40.0958			1.35317
$879$	−13.3314	+	23.0906i	−0.449656	+	0.778827i
$880$			5.36873i			0.180980i
$881$	−4.80574	−	8.32378i	−0.161909	−	0.280435i	0.773644	−	0.633620i	$-0.218432\pi$
$881$	−4.80574	−	8.32378i	−0.161909	−	0.280435i	−0.935553	+	0.353185i	$0.885099\pi$
$882$			15.6347i			0.526446i
$883$	−33.4794	+	19.3294i	−1.12667	+	0.650484i	−0.943096	−	0.332521i	$-0.892101\pi$
$883$	−33.4794	+	19.3294i	−1.12667	+	0.650484i	−0.183576	+	0.983005i	$0.558767\pi$
$884$	−3.63904	−	6.30300i	−0.122394	−	0.211993i
$885$	−4.75188	−	8.23050i	−0.159733	−	0.276665i
$886$	−7.11131	−	4.10572i	−0.238909	−	0.137934i
$887$	15.9836			0.536678			0.268339	−	0.963325i	$-0.413525\pi$
$887$	15.9836			0.536678			0.268339	+	0.963325i	$0.413525\pi$
$888$	0.491772	+	6.06285i	0.0165028	+	0.203456i
$889$	59.6579			2.00086
$890$	5.32602	+	3.07498i	0.178529	+	0.103074i
$891$	2.68436	+	4.64945i	0.0899296	+	0.155763i
$892$	−9.10117	−	15.7637i	−0.304730	−	0.527807i
$893$	13.6763	−	7.89602i	0.457660	−	0.264230i
$894$		−	11.9826i		−	0.400758i
$895$	7.06748	+	12.2412i	0.236240	+	0.409179i
$896$		−	4.75759i		−	0.158940i
$897$	0.198386	−	0.343614i	0.00662391	−	0.0114730i
$898$	19.1069			0.637606
$899$	−4.04052			−0.134759
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−41.3334	+	23.8639i	−1.37702	+	0.795021i
$902$			39.0333i			1.29967i
$903$	7.19266	+	4.15268i	0.239357	+	0.138193i
$904$	3.16932	−	5.48942i	0.105410	−	0.182575i
$905$	9.24456	+	5.33735i	0.307300	+	0.177420i
$906$	−10.9885	+	6.34419i	−0.365067	+	0.210772i
$907$	35.7145	−	20.6198i	1.18588	−	0.684669i	0.228513	−	0.973541i	$-0.426614\pi$
$907$	35.7145	−	20.6198i	1.18588	−	0.684669i	0.957368	+	0.288872i	$0.0932803\pi$
$908$	−3.03976	−	1.75501i	−0.100878	−	0.0582420i
$909$	−1.64303	+	2.84581i	−0.0544958	+	0.0943895i
$910$	7.98040	+	4.60749i	0.264548	+	0.152737i
$911$			8.29023i			0.274667i	0.990525	+	0.137334i	$0.0438533\pi$
$911$			8.29023i			0.274667i	−0.990525	+	0.137334i	$0.956147\pi$
$912$	1.63763	−	0.945484i	0.0542272	−	0.0313081i
$913$	11.3012	−	19.5743i	0.374015	−	0.647813i
$914$	−27.0824			−0.895805
$915$	−4.15704			−0.137427
$916$	−0.950846	+	1.64691i	−0.0314168	+	0.0544155i
$917$		−	17.4264i		−	0.575472i
$918$	−1.87879	−	3.25417i	−0.0620095	−	0.107404i
$919$		−	27.5582i		−	0.909062i	−0.890731	−	0.454531i	$-0.849807\pi$
$919$		−	27.5582i		−	0.909062i	0.890731	−	0.454531i	$-0.150193\pi$
$920$	0.177404	−	0.102424i	0.00584885	−	0.00337683i
$921$	7.43729	+	12.8818i	0.245067	+	0.424468i
$922$	−5.13720	−	8.89789i	−0.169185	−	0.293036i
$923$	−16.4071	−	9.47265i	−0.540046	−	0.311796i
$924$	25.5422			0.840277
$925$	−3.45731	−	5.00470i	−0.113676	−	0.164553i
$926$	3.65067			0.119968
$927$	10.3317	+	5.96502i	0.339338	+	0.195917i
$928$	1.03573	+	1.79395i	0.0339997	+	0.0588891i
$929$	−7.33293	−	12.7010i	−0.240586	−	0.416707i	0.720296	−	0.693667i	$-0.244006\pi$
$929$	−7.33293	−	12.7010i	−0.240586	−	0.416707i	−0.960881	+	0.276961i	$0.910673\pi$
$930$	1.68923	−	0.975279i	0.0553921	−	0.0319807i
$931$			29.5646i			0.968941i
$932$	−7.94111	−	13.7544i	−0.260120	−	0.450541i
$933$		−	29.0104i		−	0.949757i
$934$	20.6317	−	35.7352i	0.675091	−	1.16929i
$935$	20.1735			0.659743
$936$	−1.93690			−0.0633095
$937$	−9.78069	+	16.9407i	−0.319521	+	0.553427i	−0.980388	−	0.197076i	$-0.936855\pi$
$937$	−9.78069	+	16.9407i	−0.319521	+	0.553427i	0.660867	+	0.750503i	$0.270189\pi$
$938$	18.6607	−	10.7738i	0.609293	−	0.351776i
$939$		−	22.2966i		−	0.727623i
$940$	−7.23244	−	4.17565i	−0.235896	−	0.136195i
$941$	−4.62175	+	8.00511i	−0.150665	+	0.260959i	−0.931472	−	0.363813i	$-0.881475\pi$
$941$	−4.62175	+	8.00511i	−0.150665	+	0.260959i	0.780807	+	0.624772i	$0.214808\pi$
$942$	5.88376	+	3.39699i	0.191703	+	0.110680i
$943$	1.28982	−	0.744677i	0.0420023	−	0.0242500i
$944$	8.23050	−	4.75188i	0.267880	−	0.154660i
$945$	4.12019	+	2.37879i	0.134030	+	0.0773822i
$946$	4.68612	−	8.11660i	0.152359	−	0.263893i
$947$	15.7312	+	9.08242i	0.511196	+	0.295139i	0.733325	−	0.679878i	$-0.237967\pi$
$947$	15.7312	+	9.08242i	0.511196	+	0.295139i	−0.222129	+	0.975017i	$0.571301\pi$
$948$			11.7695i			0.382255i
$949$	−25.3263	+	14.6221i	−0.822126	+	0.474655i
$950$	−0.945484	+	1.63763i	−0.0306756	+	0.0531316i
$951$	−7.81427			−0.253395
$952$	−17.8771			−0.579399
$953$	23.7999	−	41.2227i	0.770956	−	1.33533i	−0.166084	−	0.986112i	$-0.553112\pi$
$953$	23.7999	−	41.2227i	0.770956	−	1.33533i	0.937040	−	0.349223i	$-0.113554\pi$
$954$			12.7017i			0.411232i
$955$	−8.07875	−	13.9928i	−0.261422	−	0.452797i
$956$		−	24.7908i		−	0.801793i
$957$	−9.63121	+	5.56058i	−0.311333	+	0.179748i
$958$	−0.142001	−	0.245953i	−0.00458784	−	0.00794637i
$959$	24.2477	+	41.9983i	0.783000	+	1.35620i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	27.1953			0.877268
$962$	5.04667	−	10.6461i	0.162711	−	0.343244i
$963$	−14.4217			−0.464733
$964$	−3.96591	−	2.28972i	−0.127733	−	0.0737469i
$965$	−7.22683	−	12.5172i	−0.232640	−	0.402944i
$966$	−0.487293	−	0.844017i	−0.0156784	−	0.0271558i
$967$	−29.5379	+	17.0537i	−0.949874	+	0.548410i	−0.893042	−	0.449973i	$-0.851433\pi$
$967$	−29.5379	+	17.0537i	−0.949874	+	0.548410i	−0.0568325	+	0.998384i	$0.518100\pi$
$968$		−	17.8232i		−	0.572861i
$969$	−3.55274	−	6.15353i	−0.114130	−	0.197680i
$970$		−	2.30537i		−	0.0740209i
$971$	−27.7388	+	48.0451i	−0.890182	+	1.54184i	−0.0505244	+	0.998723i	$0.516089\pi$
$971$	−27.7388	+	48.0451i	−0.890182	+	1.54184i	−0.839657	+	0.543117i	$0.817244\pi$
$972$	−1.00000			−0.0320750
$973$	−62.1674			−1.99300
$974$	−15.6151	+	27.0461i	−0.500340	+	0.866614i
$975$	1.67740	−	0.968450i	0.0537199	−	0.0310152i
$976$		−	4.15704i		−	0.133063i
$977$	−8.80063	−	5.08105i	−0.281557	−	0.162557i	0.352571	−	0.935785i	$-0.385308\pi$
$977$	−8.80063	−	5.08105i	−0.281557	−	0.162557i	−0.634128	+	0.773228i	$0.718641\pi$
$978$	0.0911079	−	0.157804i	0.00291331	−	0.00504600i
$979$	−28.5940	−	16.5087i	−0.913867	−	0.527621i
$980$	13.5400	−	7.81733i	0.432520	−	0.249715i
$981$	2.91578	−	1.68342i	0.0930935	−	0.0537476i
$982$	−8.80012	−	5.08075i	−0.280823	−	0.162133i
$983$	23.2606	−	40.2885i	0.741898	−	1.28500i	−0.209732	−	0.977759i	$-0.567259\pi$
$983$	23.2606	−	40.2885i	0.741898	−	1.28500i	0.951630	−	0.307246i	$-0.0994074\pi$
$984$	−6.29644	−	3.63525i	−0.200723	−	0.115888i
$985$			4.25801i			0.135672i
$986$	6.74091	−	3.89187i	0.214674	−	0.123942i
$987$	−19.8660	+	34.4090i	−0.632342	+	1.09525i
$988$	−3.66262			−0.116523
$989$	−0.357607			−0.0113712
$990$	2.68436	−	4.64945i	0.0853147	−	0.147769i
$991$		−	26.6949i		−	0.847991i	−0.905664	−	0.423995i	$-0.860627\pi$
$991$		−	26.6949i		−	0.847991i	0.905664	−	0.423995i	$-0.139373\pi$
$992$	0.975279	+	1.68923i	0.0309651	+	0.0536332i
$993$		−	25.0442i		−	0.794754i
$994$	−40.3006	+	23.2676i	−1.27826	+	0.738003i
$995$	−12.9335	−	22.4014i	−0.410019	−	0.710173i
$996$	2.10501	+	3.64598i	0.0666996	+	0.115527i
$997$	−10.5442	−	6.08769i	−0.333938	−	0.192799i	0.323650	−	0.946177i	$-0.395090\pi$
$997$	−10.5442	−	6.08769i	−0.333938	−	0.192799i	−0.657588	+	0.753378i	$0.728423\pi$
$998$	−12.3332			−0.390401
$999$	2.60554	−	5.49647i	0.0824356	−	0.173901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.841.1	yes	16
37.11	even	6	inner	1110.2.x.d.751.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.1	✓	16	37.11	even	6	inner
1110.2.x.d.841.1	yes	16	1.1	even	1	trivial

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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.37879 - 4.12019i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.37879 - 4.12019i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.36873 q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.67740 + 0.968450i) q^{13} +4.75759i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.25417 + 1.87879i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.63763 - 0.945484i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.37879 + 4.12019i) q^{21} +(4.64945 + 2.68436i) q^{22} -0.204849i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.93690 q^{26} +1.00000 q^{27} +(2.37879 - 4.12019i) q^{28} +2.07147i q^{29} +(-0.500000 - 0.866025i) q^{30} +1.95056i q^{31} +(0.866025 - 0.500000i) q^{32} +(2.68436 + 4.64945i) q^{33} +(-1.87879 - 3.25417i) q^{34} +(4.12019 + 2.37879i) q^{35} -1.00000 q^{36} +(2.60554 - 5.49647i) q^{37} -1.89097 q^{38} +(1.67740 + 0.968450i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.63525 + 6.29644i) q^{41} +(4.12019 - 2.37879i) q^{42} -1.74571i q^{43} +(-2.68436 - 4.64945i) q^{44} -1.00000i q^{45} +(-0.102424 + 0.177404i) q^{46} +8.35130 q^{47} +1.00000 q^{48} +(-7.81733 + 13.5400i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.75759i q^{51} +(-1.67740 - 0.968450i) q^{52} +(-6.35084 + 11.0000i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(4.64945 - 2.68436i) q^{55} +(-4.12019 + 2.37879i) q^{56} +(-1.63763 - 0.945484i) q^{57} +(1.03573 - 1.79395i) q^{58} +(-8.23050 - 4.75188i) q^{59} +1.00000i q^{60} +(-3.60010 + 2.07852i) q^{61} +(0.975279 - 1.68923i) q^{62} +4.75759 q^{63} -1.00000 q^{64} +(0.968450 - 1.67740i) q^{65} -5.36873i q^{66} +(-2.26454 - 3.92230i) q^{67} +3.75759i q^{68} +(-0.177404 + 0.102424i) q^{69} +(-2.37879 - 4.12019i) q^{70} +(4.89062 + 8.47081i) q^{71} +(0.866025 + 0.500000i) q^{72} +15.0985 q^{73} +(-5.00470 + 3.45731i) q^{74} -1.00000 q^{75} +(1.63763 + 0.945484i) q^{76} +(12.7711 + 22.1202i) q^{77} +(-0.968450 - 1.67740i) q^{78} +(-10.1927 + 5.88473i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -7.27050i q^{82} +(-2.10501 + 3.64598i) q^{83} -4.75759 q^{84} -3.75759 q^{85} +(-0.872855 + 1.51183i) q^{86} +(1.79395 - 1.03573i) q^{87} +5.36873i q^{88} +(5.32602 + 3.07498i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(7.98040 + 4.60749i) q^{91} +(0.177404 - 0.102424i) q^{92} +(1.68923 - 0.975279i) q^{93} +(-7.23244 - 4.17565i) q^{94} +(-0.945484 + 1.63763i) q^{95} +(-0.866025 - 0.500000i) q^{96} -2.30537i q^{97} +(13.5400 - 7.81733i) q^{98} +(2.68436 - 4.64945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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