LMFDB - Embedded newform 1110.2.bb.d.1009.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.3
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.16486 + 0.559786i) q^{5} +1.00000 q^{6} +(-2.76595 + 1.59692i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.16486 + 0.559786i) q^{5} +1.00000 q^{6} +(-2.76595 + 1.59692i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.15472 + 0.597644i) q^{10} -4.26721 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-2.86606 + 1.65472i) q^{13} +3.19385 q^{14} +(1.59494 - 1.56722i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.167875 + 0.0969230i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.557077 + 0.964886i) q^{19} +(-1.56722 - 1.59494i) q^{20} +(1.59692 - 2.76595i) q^{21} +(3.69551 + 2.13361i) q^{22} -3.44373i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.37328 - 2.42372i) q^{25} +3.30944 q^{26} +1.00000i q^{27} +(-2.76595 - 1.59692i) q^{28} -4.19385 q^{29} +(-2.16486 + 0.559786i) q^{30} +1.04223 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.69551 - 2.13361i) q^{33} +(-0.0969230 - 0.167875i) q^{34} +(5.09398 - 5.00546i) q^{35} +1.00000 q^{36} +(1.46220 + 5.90440i) q^{37} -1.11415i q^{38} +(1.65472 - 2.86606i) q^{39} +(0.559786 + 2.16486i) q^{40} +(2.83824 + 4.91597i) q^{41} +(-2.76595 + 1.59692i) q^{42} +0.530223i q^{43} +(-2.13361 - 3.69551i) q^{44} +(-0.597644 + 2.15472i) q^{45} +(-1.72186 + 2.98235i) q^{46} -12.6135i q^{47} -1.00000i q^{48} +(1.60033 - 2.77185i) q^{49} +(-4.99923 - 0.0876353i) q^{50} -0.193846 q^{51} +(-2.86606 - 1.65472i) q^{52} +(6.53942 + 3.77554i) q^{53} +(0.500000 - 0.866025i) q^{54} +(9.23794 - 2.38872i) q^{55} +(1.59692 + 2.76595i) q^{56} +(-0.964886 - 0.557077i) q^{57} +(3.63198 + 2.09692i) q^{58} +(3.27626 - 5.67465i) q^{59} +(2.15472 + 0.597644i) q^{60} +(2.65132 + 4.59222i) q^{61} +(-0.902598 - 0.521115i) q^{62} +3.19385i q^{63} -1.00000 q^{64} +(5.27834 - 5.18663i) q^{65} -4.26721 q^{66} +(4.40816 - 2.54505i) q^{67} +0.193846i q^{68} +(1.72186 + 2.98235i) q^{69} +(-6.91424 + 1.78787i) q^{70} +(1.82817 + 3.16649i) q^{71} +(-0.866025 - 0.500000i) q^{72} +1.24307i q^{73} +(1.68590 - 5.84446i) q^{74} +(-2.57551 + 4.28564i) q^{75} +(-0.557077 + 0.964886i) q^{76} +(11.8029 - 6.81441i) q^{77} +(-2.86606 + 1.65472i) q^{78} +(2.12738 + 3.68473i) q^{79} +(0.597644 - 2.15472i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.67647i q^{82} +(-14.4122 - 8.32089i) q^{83} +3.19385 q^{84} +(-0.417684 - 0.115851i) q^{85} +(0.265111 - 0.459186i) q^{86} +(3.63198 - 2.09692i) q^{87} +4.26721i q^{88} +(6.09036 - 10.5488i) q^{89} +(1.59494 - 1.56722i) q^{90} +(5.28492 - 9.15376i) q^{91} +(2.98235 - 1.72186i) q^{92} +(-0.902598 + 0.521115i) q^{93} +(-6.30676 + 10.9236i) q^{94} +(-1.74613 - 1.77700i) q^{95} +(-0.500000 + 0.866025i) q^{96} -17.1015i q^{97} +(-2.77185 + 1.60033i) q^{98} +(-2.13361 + 3.69551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.16486	+	0.559786i	−0.968157	+	0.250344i
$5$	−2.16486	+	0.559786i	−0.968157	+	0.250344i
$6$	1.00000			0.408248
$7$	−2.76595	+	1.59692i	−1.04543	+	0.603580i	−0.921367	−	0.388694i	$-0.872926\pi$
$7$	−2.76595	+	1.59692i	−1.04543	+	0.603580i	−0.124065	+	0.992274i	$0.539593\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.15472	+	0.597644i	0.681383	+	0.188992i
$11$	−4.26721			−1.28661			−0.643306	−	0.765609i	$-0.722438\pi$
$11$	−4.26721			−1.28661			−0.643306	+	0.765609i	$0.722438\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−2.86606	+	1.65472i	−0.794902	+	0.458937i	−0.841686	−	0.539968i	$-0.818436\pi$
$13$	−2.86606	+	1.65472i	−0.794902	+	0.458937i	0.0467833	+	0.998905i	$0.485103\pi$
$14$	3.19385			0.853591
$15$	1.59494	−	1.56722i	0.411810	−	0.404655i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.167875	+	0.0969230i	0.0407158	+	0.0235073i	0.520220	−	0.854032i	$-0.325850\pi$
$17$	0.167875	+	0.0969230i	0.0407158	+	0.0235073i	−0.479504	+	0.877540i	$0.659183\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	0.557077	+	0.964886i	0.127802	+	0.221360i	0.922825	−	0.385220i	$-0.125874\pi$
$19$	0.557077	+	0.964886i	0.127802	+	0.221360i	−0.795023	+	0.606580i	$0.792541\pi$
$20$	−1.56722	−	1.59494i	−0.350441	−	0.356638i
$21$	1.59692	−	2.76595i	0.348477	−	0.603580i
$22$	3.69551	+	2.13361i	0.787886	+	0.454886i
$23$		−	3.44373i		−	0.718066i	−0.933325	−	0.359033i	$-0.883106\pi$
$23$		−	3.44373i		−	0.718066i	0.933325	−	0.359033i	$-0.116894\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.37328	−	2.42372i	0.874656	−	0.484744i
$26$	3.30944			0.649035
$27$			1.00000i			0.192450i
$28$	−2.76595	−	1.59692i	−0.522716	−	0.301790i
$29$	−4.19385			−0.778778			−0.389389	−	0.921073i	$-0.627314\pi$
$29$	−4.19385			−0.778778			−0.389389	+	0.921073i	$0.627314\pi$
$30$	−2.16486	+	0.559786i	−0.395248	+	0.102202i
$31$	1.04223			0.187190			0.0935951	−	0.995610i	$-0.470164\pi$
$31$	1.04223			0.187190			0.0935951	+	0.995610i	$0.470164\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.69551	−	2.13361i	0.643306	−	0.371413i
$34$	−0.0969230	−	0.167875i	−0.0166221	−	0.0287904i
$35$	5.09398	−	5.00546i	0.861039	−	0.846078i
$36$	1.00000			0.166667
$37$	1.46220	+	5.90440i	0.240384	+	0.970678i
$37$	1.46220	+	5.90440i	0.240384	+	0.970678i
$38$		−	1.11415i		−	0.180740i
$39$	1.65472	−	2.86606i	0.264967	−	0.458937i
$40$	0.559786	+	2.16486i	0.0885099	+	0.342295i
$41$	2.83824	+	4.91597i	0.443258	+	0.767746i	0.997929	−	0.0643242i	$-0.0204892\pi$
$41$	2.83824	+	4.91597i	0.443258	+	0.767746i	−0.554671	+	0.832070i	$0.687156\pi$
$42$	−2.76595	+	1.59692i	−0.426796	+	0.246411i
$43$			0.530223i			0.0808582i	0.999182	+	0.0404291i	$0.0128725\pi$
$43$			0.530223i			0.0808582i	−0.999182	+	0.0404291i	$0.987128\pi$
$44$	−2.13361	−	3.69551i	−0.321653	−	0.557120i
$45$	−0.597644	+	2.15472i	−0.0890915	+	0.321207i
$46$	−1.72186	+	2.98235i	−0.253875	+	0.439724i
$47$		−	12.6135i		−	1.83987i	−0.392070	−	0.919935i	$-0.628241\pi$
$47$		−	12.6135i		−	1.83987i	0.392070	−	0.919935i	$-0.371759\pi$
$48$		−	1.00000i		−	0.144338i
$49$	1.60033	−	2.77185i	0.228618	−	0.395978i
$50$	−4.99923	−	0.0876353i	−0.706998	−	0.0123935i
$51$	−0.193846			−0.0271439
$52$	−2.86606	−	1.65472i	−0.397451	−	0.229469i
$53$	6.53942	+	3.77554i	0.898259	+	0.518610i	0.876635	−	0.481156i	$-0.159783\pi$
$53$	6.53942	+	3.77554i	0.898259	+	0.518610i	0.0216239	+	0.999766i	$0.493116\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	9.23794	−	2.38872i	1.24564	−	0.322096i
$56$	1.59692	+	2.76595i	0.213398	+	0.369616i
$57$	−0.964886	−	0.557077i	−0.127802	−	0.0737867i
$58$	3.63198	+	2.09692i	0.476902	+	0.275339i
$59$	3.27626	−	5.67465i	0.426532	−	0.738776i	−0.570030	−	0.821624i	$-0.693068\pi$
$59$	3.27626	−	5.67465i	0.426532	−	0.738776i	0.996562	+	0.0828482i	$0.0264017\pi$
$60$	2.15472	+	0.597644i	0.278173	+	0.0771555i
$61$	2.65132	+	4.59222i	0.339466	+	0.587973i	0.984332	−	0.176322i	$-0.0564202\pi$
$61$	2.65132	+	4.59222i	0.339466	+	0.587973i	−0.644866	+	0.764296i	$0.723087\pi$
$62$	−0.902598	−	0.521115i	−0.114630	−	0.0661817i
$63$			3.19385i			0.402387i
$64$	−1.00000			−0.125000
$65$	5.27834	−	5.18663i	0.654698	−	0.643322i
$66$	−4.26721			−0.525257
$67$	4.40816	−	2.54505i	0.538542	−	0.310927i	−0.205946	−	0.978563i	$-0.566027\pi$
$67$	4.40816	−	2.54505i	0.538542	−	0.310927i	0.744488	+	0.667636i	$0.232694\pi$
$68$			0.193846i			0.0235073i
$69$	1.72186	+	2.98235i	0.207288	+	0.359033i
$70$	−6.91424	+	1.78787i	−0.826410	+	0.213691i
$71$	1.82817	+	3.16649i	0.216964	+	0.375793i	0.953878	−	0.300193i	$-0.0970512\pi$
$71$	1.82817	+	3.16649i	0.216964	+	0.375793i	−0.736914	+	0.675986i	$0.763718\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			1.24307i			0.145491i	0.997351	+	0.0727454i	$0.0231761\pi$
$73$			1.24307i			0.145491i	−0.997351	+	0.0727454i	$0.976824\pi$
$74$	1.68590	−	5.84446i	0.195982	−	0.679405i
$75$	−2.57551	+	4.28564i	−0.297394	+	0.494864i
$76$	−0.557077	+	0.964886i	−0.0639011	+	0.110680i
$77$	11.8029	−	6.81441i	1.34507	−	0.776574i
$78$	−2.86606	+	1.65472i	−0.324517	+	0.187360i
$79$	2.12738	+	3.68473i	0.239349	+	0.414565i	0.960528	−	0.278184i	$-0.0897326\pi$
$79$	2.12738	+	3.68473i	0.239349	+	0.414565i	−0.721179	+	0.692749i	$0.756399\pi$
$80$	0.597644	−	2.15472i	0.0668186	−	0.240905i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	5.67647i		−	0.626862i
$83$	−14.4122	−	8.32089i	−1.58194	−	0.913336i	−0.994576	−	0.104016i	$-0.966831\pi$
$83$	−14.4122	−	8.32089i	−1.58194	−	0.913336i	−0.587368	−	0.809320i	$-0.699836\pi$
$84$	3.19385			0.348477
$85$	−0.417684	−	0.115851i	−0.0453042	−	0.0125658i
$86$	0.265111	−	0.459186i	0.0285877	−	0.0495153i
$87$	3.63198	−	2.09692i	0.389389	−	0.224814i
$88$			4.26721i			0.454886i
$89$	6.09036	−	10.5488i	0.645577	−	1.11817i	−0.338591	−	0.940933i	$-0.609950\pi$
$89$	6.09036	−	10.5488i	0.645577	−	1.11817i	0.984168	−	0.177238i	$-0.0567162\pi$
$90$	1.59494	−	1.56722i	0.168121	−	0.165200i
$91$	5.28492	−	9.15376i	0.554011	−	0.959574i
$92$	2.98235	−	1.72186i	0.310932	−	0.179517i
$93$	−0.902598	+	0.521115i	−0.0935951	+	0.0540371i
$94$	−6.30676	+	10.9236i	−0.650493	+	1.12669i
$95$	−1.74613	−	1.77700i	−0.179149	−	0.182317i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	17.1015i		−	1.73640i	−0.496218	−	0.868198i	$-0.665278\pi$
$97$		−	17.1015i		−	1.73640i	0.496218	−	0.868198i	$-0.334722\pi$
$98$	−2.77185	+	1.60033i	−0.279999	+	0.161657i
$99$	−2.13361	+	3.69551i	−0.214435	+	0.371413i
$100$	4.28564	+	2.57551i	0.428564	+	0.257551i
$101$	5.59331			0.556555			0.278277	−	0.960501i	$-0.410237\pi$
$101$	5.59331			0.556555			0.278277	+	0.960501i	$0.410237\pi$
$102$	0.167875	+	0.0969230i	0.0166221	+	0.00959680i
$103$			6.48119i			0.638610i	0.947652	+	0.319305i	$0.103449\pi$
$103$			6.48119i			0.638610i	−0.947652	+	0.319305i	$0.896551\pi$
$104$	1.65472	+	2.86606i	0.162259	+	0.281040i
$105$	−1.90878	+	6.88185i	−0.186278	+	0.671599i
$106$	−3.77554	−	6.53942i	−0.366713	−	0.635165i
$107$	2.59468	−	1.49804i	0.250837	−	0.144821i	−0.369310	−	0.929306i	$-0.620406\pi$
$107$	2.59468	−	1.49804i	0.250837	−	0.144821i	0.620147	+	0.784485i	$0.287073\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−2.49564	+	4.32258i	−0.239039	+	0.414028i	−0.960439	−	0.278491i	$-0.910166\pi$
$109$	−2.49564	+	4.32258i	−0.239039	+	0.414028i	0.721400	+	0.692519i	$0.243499\pi$
$110$	−9.19465	−	2.55027i	−0.876675	−	0.243159i
$111$	−4.21850	−	4.38226i	−0.400403	−	0.415946i
$112$		−	3.19385i		−	0.301790i
$113$	−1.57329	−	0.908340i	−0.148003	−	0.0854494i	0.424170	−	0.905583i	$-0.360566\pi$
$113$	−1.57329	−	0.908340i	−0.148003	−	0.0854494i	−0.572173	+	0.820133i	$0.693899\pi$
$114$	0.557077	+	0.964886i	0.0521751	+	0.0903699i
$115$	1.92775	+	7.45520i	0.179764	+	0.695201i
$116$	−2.09692	−	3.63198i	−0.194694	−	0.337221i
$117$			3.30944i			0.305958i
$118$	−5.67465	+	3.27626i	−0.522393	+	0.301604i
$119$	−0.619114			−0.0567541
$120$	−1.56722	−	1.59494i	−0.143067	−	0.145597i
$121$	7.20909			0.655372
$122$		−	5.30264i		−	0.480078i
$123$	−4.91597	−	2.83824i	−0.443258	−	0.255915i
$124$	0.521115	+	0.902598i	0.0467975	+	0.0810557i
$125$	−8.11079	+	7.69513i	−0.725451	+	0.688273i
$126$	1.59692	−	2.76595i	0.142265	−	0.246411i
$127$	0.0665183	+	0.0384044i	0.00590254	+	0.00340784i	0.502948	−	0.864316i	$-0.332249\pi$
$127$	0.0665183	+	0.0384044i	0.00590254	+	0.00340784i	−0.497046	+	0.867724i	$0.665582\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.265111	−	0.459186i	−0.0233418	−	0.0404291i
$130$	−7.16449	+	1.85258i	−0.628368	+	0.162482i
$131$	−7.40018	+	12.8175i	−0.646557	+	1.11987i	0.337382	+	0.941368i	$0.390458\pi$
$131$	−7.40018	+	12.8175i	−0.646557	+	1.11987i	−0.983940	+	0.178502i	$0.942875\pi$
$132$	3.69551	+	2.13361i	0.321653	+	0.185707i
$133$	−3.08170	−	1.77922i	−0.267217	−	0.154278i
$134$	−5.09010			−0.439718
$135$	−0.559786	−	2.16486i	−0.0481787	−	0.186322i
$136$	0.0969230	−	0.167875i	0.00831107	−	0.0143952i
$137$		−	17.5496i		−	1.49936i	−0.661798	−	0.749682i	$-0.730206\pi$
$137$		−	17.5496i		−	1.49936i	0.661798	−	0.749682i	$-0.269794\pi$
$138$		−	3.44373i		−	0.293149i
$139$	7.79525	−	13.5018i	0.661185	−	1.14521i	−0.319120	−	0.947714i	$-0.603387\pi$
$139$	7.79525	−	13.5018i	0.661185	−	1.14521i	0.980305	−	0.197491i	$-0.0632794\pi$
$140$	6.88185	+	1.90878i	0.581622	+	0.161321i
$141$	6.30676	+	10.9236i	0.531125	+	0.919935i
$142$		−	3.65634i		−	0.306834i
$143$	12.2301	−	7.06104i	1.02273	−	0.590474i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	9.07911	−	2.34766i	0.753979	−	0.194962i
$146$	0.621537	−	1.07653i	0.0514388	−	0.0890946i
$147$			3.20065i			0.263985i
$148$	−4.38226	+	4.21850i	−0.360220	+	0.346759i
$149$	−18.2871			−1.49814			−0.749069	−	0.662492i	$-0.769499\pi$
$149$	−18.2871			−1.49814			−0.749069	+	0.662492i	$0.769499\pi$
$150$	4.37328	−	2.42372i	0.357077	−	0.197896i
$151$	−8.03136	−	13.9107i	−0.653583	−	1.13204i	−0.982247	−	0.187592i	$-0.939932\pi$
$151$	−8.03136	−	13.9107i	−0.653583	−	1.13204i	0.328664	−	0.944447i	$-0.393402\pi$
$152$	0.964886	−	0.557077i	0.0782626	−	0.0451849i
$153$	0.167875	−	0.0969230i	0.0135719	−	0.00783576i
$154$	−13.6288			−1.09824
$155$	−2.25629	+	0.583426i	−0.181229	+	0.0468619i
$156$	3.30944			0.264967
$157$	9.03871	+	5.21850i	0.721368	+	0.416482i	0.815256	−	0.579101i	$-0.196596\pi$
$157$	9.03871	+	5.21850i	0.721368	+	0.416482i	−0.0938882	+	0.995583i	$0.529930\pi$
$158$		−	4.25476i		−	0.338491i
$159$	−7.55107			−0.598839
$160$	−1.59494	+	1.56722i	−0.126091	+	0.123900i
$161$	5.49936	+	9.52518i	0.433411	+	0.750689i
$162$			1.00000i			0.0785674i
$163$	−3.23228	−	1.86616i	−0.253172	−	0.146169i	0.368044	−	0.929808i	$-0.380028\pi$
$163$	−3.23228	−	1.86616i	−0.253172	−	0.146169i	−0.621216	+	0.783640i	$0.713361\pi$
$164$	−2.83824	+	4.91597i	−0.221629	+	0.383873i
$165$	−6.80592	+	6.68766i	−0.529840	+	0.520634i
$166$	8.32089	+	14.4122i	0.645826	+	1.11860i
$167$	15.9918	−	9.23287i	1.23748	−	0.714461i	0.268904	−	0.963167i	$-0.413339\pi$
$167$	15.9918	−	9.23287i	1.23748	−	0.714461i	0.968579	+	0.248706i	$0.0800053\pi$
$168$	−2.76595	−	1.59692i	−0.213398	−	0.123205i
$169$	−1.02380	+	1.77327i	−0.0787537	+	0.136405i
$170$	0.303799	+	0.309172i	0.0233004	+	0.0237124i
$171$	1.11415			0.0852015
$172$	−0.459186	+	0.265111i	−0.0350126	+	0.0202146i
$173$	20.4312	+	11.7960i	1.55336	+	0.896831i	0.997865	+	0.0653097i	$0.0208035\pi$
$173$	20.4312	+	11.7960i	1.55336	+	0.896831i	0.555492	+	0.831522i	$0.312530\pi$
$174$	−4.19385			−0.317935
$175$	−8.22578	+	13.6877i	−0.621811	+	1.03469i
$176$	2.13361	−	3.69551i	0.160827	−	0.278560i
$177$			6.55252i			0.492517i
$178$	−10.5488	+	6.09036i	−0.790667	+	0.456492i
$179$	1.79411			0.134098			0.0670489	−	0.997750i	$-0.478642\pi$
$179$	1.79411			0.134098			0.0670489	+	0.997750i	$0.478642\pi$
$180$	−2.16486	+	0.559786i	−0.161359	+	0.0417240i
$181$	0.774014	+	1.34063i	0.0575320	+	0.0996483i	0.893357	−	0.449348i	$-0.148344\pi$
$181$	0.774014	+	1.34063i	0.0575320	+	0.0996483i	−0.835825	+	0.548996i	$0.815010\pi$
$182$	−9.15376	+	5.28492i	−0.678522	+	0.391745i
$183$	−4.59222	−	2.65132i	−0.339466	−	0.195991i
$184$	−3.44373			−0.253875
$185$	−6.47066	−	11.9637i	−0.475733	−	0.879590i
$186$	1.04223			0.0764201
$187$	−0.716360	−	0.413591i	−0.0523854	−	0.0302447i
$188$	10.9236	−	6.30676i	0.796687	−	0.459968i
$189$	−1.59692	−	2.76595i	−0.116159	−	0.201193i
$190$	0.623688	+	2.41199i	0.0452471	+	0.174984i
$191$	−16.9881			−1.22921			−0.614607	−	0.788833i	$-0.710685\pi$
$191$	−16.9881			−1.22921			−0.614607	+	0.788833i	$0.710685\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$			20.3587i			1.46545i	0.680523	+	0.732726i	$0.261752\pi$
$193$			20.3587i			1.46545i	−0.680523	+	0.732726i	$0.738248\pi$
$194$	−8.55076	+	14.8103i	−0.613908	+	1.06332i
$195$	−1.97787	+	7.13092i	−0.141638	+	0.510656i
$196$	3.20065			0.228618
$197$	−12.0297	−	6.94535i	−0.857080	−	0.494836i	0.00595307	−	0.999982i	$-0.498105\pi$
$197$	−12.0297	−	6.94535i	−0.857080	−	0.494836i	−0.863034	+	0.505147i	$0.831438\pi$
$198$	3.69551	−	2.13361i	0.262629	−	0.151629i
$199$	4.57809			0.324532			0.162266	−	0.986747i	$-0.448120\pi$
$199$	4.57809			0.324532			0.162266	+	0.986747i	$0.448120\pi$
$200$	−2.42372	−	4.37328i	−0.171383	−	0.309238i
$201$	−2.54505	+	4.40816i	−0.179514	+	0.310927i
$202$	−4.84394	−	2.79665i	−0.340819	−	0.196772i
$203$	11.6000	−	6.69725i	0.814159	−	0.470055i
$204$	−0.0969230	−	0.167875i	−0.00678596	−	0.0117536i
$205$	−8.89629	−	9.05361i	−0.621344	−	0.632331i
$206$	3.24059	−	5.61287i	0.225783	−	0.391067i
$207$	−2.98235	−	1.72186i	−0.207288	−	0.119678i
$208$		−	3.30944i		−	0.229469i
$209$	−2.37717	−	4.11737i	−0.164432	−	0.284805i
$210$	5.09398	−	5.00546i	0.351518	−	0.345410i
$211$	15.6806			1.07950			0.539750	−	0.841825i	$-0.318519\pi$
$211$	15.6806			1.07950			0.539750	+	0.841825i	$0.318519\pi$
$212$			7.55107i			0.518610i
$213$	−3.16649	−	1.82817i	−0.216964	−	0.125264i
$214$	−2.99608			−0.204808
$215$	−0.296811	−	1.14786i	−0.0202424	−	0.0782835i
$216$	1.00000			0.0680414
$217$	−2.88276	+	1.66436i	−0.195694	+	0.112984i
$218$	4.32258	−	2.49564i	0.292762	−	0.169026i
$219$	−0.621537	−	1.07653i	−0.0419996	−	0.0727454i
$220$	6.68766	+	6.80592i	0.450882	+	0.458855i
$221$	−0.641522			−0.0431534
$222$	1.46220	+	5.90440i	0.0981363	+	0.396278i
$223$		−	18.1317i		−	1.21419i	−0.794631	−	0.607093i	$-0.792336\pi$
$223$		−	18.1317i		−	1.21419i	0.794631	−	0.607093i	$-0.207664\pi$
$224$	−1.59692	+	2.76595i	−0.106699	+	0.184808i
$225$	0.0876353	−	4.99923i	0.00584235	−	0.333282i
$226$	0.908340	+	1.57329i	0.0604219	+	0.104654i
$227$	0.866099	−	0.500042i	0.0574850	−	0.0331890i	−0.470982	−	0.882143i	$-0.656100\pi$
$227$	0.866099	−	0.500042i	0.0574850	−	0.0331890i	0.528467	+	0.848954i	$0.322767\pi$
$228$		−	1.11415i		−	0.0737867i
$229$	6.09970	+	10.5650i	0.403080	+	0.698154i	0.994096	−	0.108505i	$-0.0346064\pi$
$229$	6.09970	+	10.5650i	0.403080	+	0.698154i	−0.591016	+	0.806660i	$0.701273\pi$
$230$	2.05812	−	7.42027i	0.135708	−	0.489278i
$231$	−6.81441	+	11.8029i	−0.448355	+	0.776574i
$232$			4.19385i			0.275339i
$233$			20.3003i			1.32992i	0.746880	+	0.664959i	$0.231551\pi$
$233$			20.3003i			1.32992i	−0.746880	+	0.664959i	$0.768449\pi$
$234$	1.65472	−	2.86606i	0.108172	−	0.187360i
$235$	7.06087	+	27.3066i	0.460600	+	1.78128i
$236$	6.55252			0.426532
$237$	−3.68473	−	2.12738i	−0.239349	−	0.138188i
$238$	0.536168	+	0.309557i	0.0347546	+	0.0200656i
$239$	−5.66979	+	9.82037i	−0.366748	+	0.635227i	−0.989055	−	0.147547i	$-0.952862\pi$
$239$	−5.66979	+	9.82037i	−0.366748	+	0.635227i	0.622307	+	0.782773i	$0.286196\pi$
$240$	0.559786	+	2.16486i	0.0361340	+	0.139741i
$241$	−6.90124	−	11.9533i	−0.444548	−	0.769980i	0.553473	−	0.832867i	$-0.313302\pi$
$241$	−6.90124	−	11.9533i	−0.444548	−	0.769980i	−0.998021	+	0.0628877i	$0.979969\pi$
$242$	−6.24326	−	3.60455i	−0.401332	−	0.231709i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.65132	+	4.59222i	−0.169733	+	0.293987i
$245$	−1.91285	+	6.89651i	−0.122207	+	0.440602i
$246$	2.83824	+	4.91597i	0.180959	+	0.313431i
$247$	−3.19323	−	1.84361i	−0.203181	−	0.117306i
$248$		−	1.04223i		−	0.0661817i
$249$	16.6418			1.05463
$250$	10.8717	−	2.60878i	0.687588	−	0.164994i
$251$	−20.4047			−1.28793			−0.643966	−	0.765054i	$-0.722712\pi$
$251$	−20.4047			−1.28793			−0.643966	+	0.765054i	$0.722712\pi$
$252$	−2.76595	+	1.59692i	−0.174239	+	0.100597i
$253$			14.6951i			0.923873i
$254$	−0.0384044	−	0.0665183i	−0.00240970	−	0.00417373i
$255$	0.419650	−	0.108512i	0.0262795	−	0.00679530i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0465	+	6.95507i	0.751443	+	0.433846i	0.826215	−	0.563355i	$-0.190490\pi$
$257$	12.0465	+	6.95507i	0.751443	+	0.433846i	−0.0747723	+	0.997201i	$0.523823\pi$
$258$			0.530223i			0.0330102i
$259$	−13.4732	−	13.9963i	−0.837187	−	0.869686i
$260$	7.13092	+	1.97787i	0.442241	+	0.122662i
$261$	−2.09692	+	3.63198i	−0.129796	+	0.224814i
$262$	12.8175	−	7.40018i	0.791867	−	0.457185i
$263$	−19.5696	+	11.2985i	−1.20671	+	0.696696i	−0.962040	−	0.272909i	$-0.912014\pi$
$263$	−19.5696	+	11.2985i	−1.20671	+	0.696696i	−0.244674	+	0.969605i	$0.578681\pi$
$264$	−2.13361	−	3.69551i	−0.131314	−	0.227443i
$265$	−16.2705	−	4.51285i	−0.999486	−	0.277222i
$266$	1.77922	+	3.08170i	0.109091	+	0.188951i
$267$			12.1807i			0.745448i
$268$	4.40816	+	2.54505i	0.269271	+	0.155464i
$269$	12.3810			0.754881			0.377441	−	0.926034i	$-0.376804\pi$
$269$	12.3810			0.754881			0.377441	+	0.926034i	$0.376804\pi$
$270$	−0.597644	+	2.15472i	−0.0363714	+	0.131132i
$271$	−7.61718	+	13.1933i	−0.462711	+	0.801438i	−0.999095	−	0.0425356i	$-0.986456\pi$
$271$	−7.61718	+	13.1933i	−0.462711	+	0.801438i	0.536384	+	0.843974i	$0.319790\pi$
$272$	−0.167875	+	0.0969230i	−0.0101789	+	0.00587682i
$273$			10.5698i			0.639716i
$274$	−8.77481	+	15.1984i	−0.530105	+	0.918170i
$275$	−18.6617	+	10.3425i	−1.12534	+	0.623678i
$276$	−1.72186	+	2.98235i	−0.103644	+	0.179517i
$277$	−6.70591	+	3.87166i	−0.402919	+	0.232625i	−0.687743	−	0.725955i	$-0.741398\pi$
$277$	−6.70591	+	3.87166i	−0.402919	+	0.232625i	0.284824	+	0.958580i	$0.408065\pi$
$278$	−13.5018	+	7.79525i	−0.809783	+	0.467528i
$279$	0.521115	−	0.902598i	0.0311984	−	0.0540371i
$280$	−5.00546	−	5.09398i	−0.299134	−	0.304423i
$281$	−7.79373	+	13.4991i	−0.464935	+	0.805291i	−0.999199	−	0.0400267i	$-0.987256\pi$
$281$	−7.79373	+	13.4991i	−0.464935	+	0.805291i	0.534263	+	0.845318i	$0.320589\pi$
$282$		−	12.6135i		−	0.751124i
$283$	−2.34418	+	1.35341i	−0.139347	+	0.0804519i	−0.568053	−	0.822992i	$-0.692303\pi$
$283$	−2.34418	+	1.35341i	−0.139347	+	0.0804519i	0.428706	+	0.903444i	$0.358970\pi$
$284$	−1.82817	+	3.16649i	−0.108482	+	0.187896i
$285$	2.40069	+	0.665867i	0.142205	+	0.0394426i
$286$	−14.1221			−0.835056
$287$	−15.7009	−	9.06489i	−0.926792	−	0.535084i
$288$		−	1.00000i		−	0.0589256i
$289$	−8.48121	−	14.6899i	−0.498895	−	0.864111i
$290$	−9.03657	−	2.50643i	−0.530646	−	0.147182i
$291$	8.55076	+	14.8103i	0.501254	+	0.868198i
$292$	−1.07653	+	0.621537i	−0.0629994	+	0.0363727i
$293$	2.03490	−	1.17485i	0.118880	−	0.0686355i	−0.439381	−	0.898301i	$-0.644802\pi$
$293$	2.03490	−	1.17485i	0.118880	−	0.0686355i	0.558261	+	0.829665i	$0.311469\pi$
$294$	1.60033	−	2.77185i	0.0933329	−	0.161657i
$295$	−3.91607	+	14.1188i	−0.228002	+	0.822031i
$296$	5.90440	−	1.46220i	0.343186	−	0.0849885i
$297$		−	4.26721i		−	0.247609i
$298$	15.8371	+	9.14356i	0.917419	+	0.529672i
$299$	5.69840	+	9.86993i	0.329547	+	0.570793i
$300$	−4.99923	−	0.0876353i	−0.288631	−	0.00505963i
$301$	−0.846725	−	1.46657i	−0.0488044	−	0.0845317i
$302$			16.0627i			0.924306i
$303$	−4.84394	+	2.79665i	−0.278277	+	0.160663i
$304$	−1.11415			−0.0639011
$305$	−8.31040	−	8.45736i	−0.475852	−	0.484267i
$306$	−0.193846			−0.0110814
$307$			5.06023i			0.288803i	0.989519	+	0.144401i	$0.0461256\pi$
$307$			5.06023i			0.288803i	−0.989519	+	0.144401i	$0.953874\pi$
$308$	11.8029	+	6.81441i	0.672533	+	0.388287i
$309$	−3.24059	−	5.61287i	−0.184351	−	0.319305i
$310$	2.24572	+	0.622883i	0.127548	+	0.0353774i
$311$	−1.77350	+	3.07179i	−0.100566	+	0.174185i	−0.911918	−	0.410373i	$-0.865399\pi$
$311$	−1.77350	+	3.07179i	−0.100566	+	0.174185i	0.811352	+	0.584558i	$0.198732\pi$
$312$	−2.86606	−	1.65472i	−0.162259	−	0.0936801i
$313$	−12.4632	−	7.19561i	−0.704459	−	0.406720i	0.104547	−	0.994520i	$-0.466661\pi$
$313$	−12.4632	−	7.19561i	−0.704459	−	0.406720i	−0.809006	+	0.587800i	$0.799994\pi$
$314$	−5.21850	−	9.03871i	−0.294497	−	0.510084i
$315$	−1.78787	−	6.91424i	−0.100735	−	0.389574i
$316$	−2.12738	+	3.68473i	−0.119675	+	0.207282i
$317$	21.2706	+	12.2806i	1.19468	+	0.689748i	0.959364	−	0.282172i	$-0.0910548\pi$
$317$	21.2706	+	12.2806i	1.19468	+	0.689748i	0.235314	+	0.971919i	$0.424388\pi$
$318$	6.53942	+	3.77554i	0.366713	+	0.211722i
$319$	17.8960			1.00199
$320$	2.16486	−	0.559786i	0.121020	−	0.0312930i
$321$	−1.49804	+	2.59468i	−0.0836124	+	0.144821i
$322$		−	10.9987i		−	0.612935i
$323$			0.215974i			0.0120171i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−8.52350	+	14.1831i	−0.472799	+	0.786736i
$326$	1.86616	+	3.23228i	0.103357	+	0.179019i
$327$		−	4.99128i		−	0.276018i
$328$	4.91597	−	2.83824i	0.271439	−	0.156715i
$329$	20.1428	+	34.8884i	1.11051	+	1.92346i
$330$	9.23794	−	2.38872i	0.508532	−	0.131495i
$331$	3.34593	−	5.79532i	0.183909	−	0.318539i	−0.759299	−	0.650741i	$-0.774458\pi$
$331$	3.34593	−	5.79532i	0.183909	−	0.318539i	0.943208	+	0.332202i	$0.107792\pi$
$332$		−	16.6418i		−	0.913336i
$333$	5.84446	+	1.68590i	0.320275	+	0.0923868i
$334$	−18.4657			−1.01040
$335$	−8.11838	+	7.97732i	−0.443555	+	0.435847i
$336$	1.59692	+	2.76595i	0.0871193	+	0.150895i
$337$	28.1935	−	16.2775i	1.53580	−	0.886694i	0.536722	−	0.843759i	$-0.319663\pi$
$337$	28.1935	−	16.2775i	1.53580	−	0.886694i	0.999078	−	0.0429349i	$-0.0136708\pi$
$338$	1.77327	−	1.02380i	0.0964531	−	0.0556872i
$339$	1.81668			0.0986685
$340$	−0.108512	−	0.419650i	−0.00588490	−	0.0227587i
$341$	−4.44742			−0.240841
$342$	−0.964886	−	0.557077i	−0.0521751	−	0.0301233i
$343$		−	12.1345i		−	0.655203i
$344$	0.530223			0.0285877
$345$	−5.39708	−	5.49252i	−0.290569	−	0.295707i
$346$	−11.7960	−	20.4312i	−0.634156	−	1.09839i
$347$		−	15.1246i		−	0.811930i	−0.913889	−	0.405965i	$-0.866936\pi$
$347$		−	15.1246i		−	0.811930i	0.913889	−	0.405965i	$-0.133064\pi$
$348$	3.63198	+	2.09692i	0.194694	+	0.112407i
$349$	8.37294	−	14.5024i	0.448193	−	0.776294i	−0.550075	−	0.835115i	$-0.685401\pi$
$349$	8.37294	−	14.5024i	0.448193	−	0.776294i	0.998269	+	0.0588214i	$0.0187342\pi$
$350$	13.9676	−	7.74099i	0.746599	−	0.413773i
$351$	−1.65472	−	2.86606i	−0.0883225	−	0.152979i
$352$	−3.69551	+	2.13361i	−0.196972	+	0.113722i
$353$	25.7954	+	14.8930i	1.37295	+	0.792674i	0.991299	−	0.131631i	$-0.0420214\pi$
$353$	25.7954	+	14.8930i	1.37295	+	0.792674i	0.381654	+	0.924305i	$0.375355\pi$
$354$	3.27626	−	5.67465i	0.174131	−	0.301604i
$355$	−5.73030	−	5.83163i	−0.304133	−	0.309511i
$356$	12.1807			0.645577
$357$	0.536168	−	0.309557i	0.0283770	−	0.0163835i
$358$	−1.55374	−	0.897053i	−0.0821177	−	0.0474107i
$359$	17.0677			0.900796			0.450398	−	0.892828i	$-0.351282\pi$
$359$	17.0677			0.900796			0.450398	+	0.892828i	$0.351282\pi$
$360$	2.15472	+	0.597644i	0.113564	+	0.0314986i
$361$	8.87933	−	15.3795i	0.467333	−	0.809445i
$362$		−	1.54803i		−	0.0813625i
$363$	−6.24326	+	3.60455i	−0.327686	+	0.189190i
$364$	10.5698			0.554011
$365$	−0.695855	−	2.69109i	−0.0364227	−	0.140858i
$366$	2.65132	+	4.59222i	0.138587	+	0.240039i
$367$	2.69960	−	1.55861i	0.140918	−	0.0813590i	−0.427883	−	0.903834i	$-0.640741\pi$
$367$	2.69960	−	1.55861i	0.140918	−	0.0813590i	0.568801	+	0.822475i	$0.307407\pi$
$368$	2.98235	+	1.72186i	0.155466	+	0.0897583i
$369$	5.67647			0.295505
$370$	−0.378100	+	13.5962i	−0.0196565	+	0.706834i
$371$	−24.1170			−1.25209
$372$	−0.902598	−	0.521115i	−0.0467975	−	0.0270186i
$373$	−13.1227	+	7.57637i	−0.679466	+	0.392290i	−0.799654	−	0.600462i	$-0.794984\pi$
$373$	−13.1227	+	7.57637i	−0.679466	+	0.392290i	0.120188	+	0.992751i	$0.461650\pi$
$374$	0.413591	+	0.716360i	0.0213863	+	0.0370421i
$375$	3.17659	−	10.7196i	0.164038	−	0.553556i
$376$	−12.6135			−0.650493
$377$	12.0198	−	6.93964i	0.619052	−	0.357410i
$378$			3.19385i			0.164274i
$379$	−1.85010	+	3.20447i	−0.0950334	+	0.164603i	−0.909623	−	0.415436i	$-0.863629\pi$
$379$	−1.85010	+	3.20447i	−0.0950334	+	0.164603i	0.814589	+	0.580038i	$0.196962\pi$
$380$	0.665867	−	2.40069i	0.0341583	−	0.123153i
$381$	−0.0768087			−0.00393503
$382$	14.7121	+	8.49404i	0.752737	+	0.434593i
$383$	−27.2734	+	15.7463i	−1.39360	+	0.804597i	−0.993712	−	0.111965i	$-0.964285\pi$
$383$	−27.2734	+	15.7463i	−1.39360	+	0.804597i	−0.399891	+	0.916563i	$0.630952\pi$
$384$	−1.00000			−0.0510310
$385$	−21.7371	+	21.3594i	−1.10782	+	1.08857i
$386$	10.1794	−	17.6312i	0.518116	−	0.897403i
$387$	0.459186	+	0.265111i	0.0233418	+	0.0134764i
$388$	14.8103	−	8.55076i	0.751881	−	0.434099i
$389$	−7.99233	−	13.8431i	−0.405227	−	0.701874i	0.589121	−	0.808045i	$-0.299474\pi$
$389$	−7.99233	−	13.8431i	−0.405227	−	0.701874i	−0.994348	+	0.106171i	$0.966141\pi$
$390$	5.27834	−	5.18663i	0.267279	−	0.262635i
$391$	0.333776	−	0.578117i	0.0168798	−	0.0292366i
$392$	−2.77185	−	1.60033i	−0.139999	−	0.0808287i
$393$		−	14.8004i		−	0.746580i
$394$	6.94535	+	12.0297i	0.349902	+	0.606047i
$395$	−6.66816	−	6.78607i	−0.335511	−	0.341444i
$396$	−4.26721			−0.214435
$397$		−	2.23054i		−	0.111947i	−0.998432	−	0.0559737i	$-0.982174\pi$
$397$		−	2.23054i		−	0.111947i	0.998432	−	0.0559737i	$-0.0178263\pi$
$398$	−3.96475	−	2.28905i	−0.198735	−	0.114740i
$399$	3.55844			0.178145
$400$	−0.0876353	+	4.99923i	−0.00438177	+	0.249962i
$401$	14.1146			0.704852			0.352426	−	0.935840i	$-0.385357\pi$
$401$	14.1146			0.704852			0.352426	+	0.935840i	$0.385357\pi$
$402$	4.40816	−	2.54505i	0.219859	−	0.126936i
$403$	−2.98710	+	1.72460i	−0.148798	+	0.0859085i
$404$	2.79665	+	4.84394i	0.139139	+	0.240995i
$405$	1.56722	+	1.59494i	0.0778758	+	0.0792530i
$406$	−13.3945			−0.664758
$407$	−6.23951	−	25.1953i	−0.309281	−	1.24889i
$408$			0.193846i			0.00959680i
$409$	16.3841	−	28.3780i	0.810140	−	1.40320i	−0.102626	−	0.994720i	$-0.532725\pi$
$409$	16.3841	−	28.3780i	0.810140	−	1.40320i	0.912766	−	0.408483i	$-0.133942\pi$
$410$	3.17761	+	12.2888i	0.156931	+	0.606900i
$411$	8.77481	+	15.1984i	0.432829	+	0.749682i
$412$	−5.61287	+	3.24059i	−0.276526	+	0.159653i
$413$			20.9277i			1.02979i
$414$	1.72186	+	2.98235i	0.0846249	+	0.146575i
$415$	35.8584	+	9.94585i	1.76022	+	0.488222i
$416$	−1.65472	+	2.86606i	−0.0811294	+	0.140520i
$417$			15.5905i			0.763470i
$418$			4.75433i			0.232542i
$419$	18.9817	−	32.8773i	0.927317	−	1.60616i	0.139526	−	0.990218i	$-0.455442\pi$
$419$	18.9817	−	32.8773i	0.927317	−	1.60616i	0.787791	−	0.615943i	$-0.211225\pi$
$420$	−6.91424	+	1.78787i	−0.337381	+	0.0872391i
$421$	−20.4242			−0.995413			−0.497706	−	0.867346i	$-0.665824\pi$
$421$	−20.4242			−0.995413			−0.497706	+	0.867346i	$0.665824\pi$
$422$	−13.5798	−	7.84032i	−0.661056	−	0.381661i
$423$	−10.9236	−	6.30676i	−0.531125	−	0.306645i
$424$	3.77554	−	6.53942i	0.183356	−	0.317582i
$425$	0.969081	+	0.0169877i	0.0470073	+	0.000824027i
$426$	1.82817	+	3.16649i	0.0885752	+	0.153417i
$427$	−14.6668	−	8.46790i	−0.709778	−	0.409790i
$428$	2.59468	+	1.49804i	0.125419	+	0.0724104i
$429$	−7.06104	+	12.2301i	−0.340910	+	0.590474i
$430$	−0.316884	+	1.14248i	−0.0152815	+	0.0550954i
$431$	−6.60347	−	11.4376i	−0.318078	−	0.550927i	0.662009	−	0.749496i	$-0.269704\pi$
$431$	−6.60347	−	11.4376i	−0.318078	−	0.550927i	−0.980087	+	0.198569i	$0.936371\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	20.4183i		−	0.981242i	−0.871373	−	0.490621i	$-0.836770\pi$
$433$		−	20.4183i		−	0.981242i	0.871373	−	0.490621i	$-0.163230\pi$
$434$	3.32872			0.159784
$435$	−6.68891	+	6.57268i	−0.320709	+	0.315136i
$436$	−4.99128			−0.239039
$437$	3.32280	−	1.91842i	0.158951	−	0.0917705i
$438$			1.24307i			0.0593964i
$439$	9.05730	+	15.6877i	0.432281	+	0.748733i	0.997069	−	0.0765027i	$-0.0243754\pi$
$439$	9.05730	+	15.6877i	0.432281	+	0.748733i	−0.564788	+	0.825236i	$0.691042\pi$
$440$	−2.38872	−	9.23794i	−0.113878	−	0.440401i
$441$	−1.60033	−	2.77185i	−0.0762060	−	0.131993i
$442$	0.555574	+	0.320761i	0.0264260	+	0.0152570i
$443$			17.1304i			0.813891i	0.913452	+	0.406945i	$0.133406\pi$
$443$			17.1304i			0.813891i	−0.913452	+	0.406945i	$0.866594\pi$
$444$	1.68590	−	5.84446i	0.0800093	−	0.277366i
$445$	−7.27973	+	26.2460i	−0.345092	+	1.24418i
$446$	−9.06583	+	15.7025i	−0.429279	+	0.743533i
$447$	15.8371	−	9.14356i	0.749069	−	0.432475i
$448$	2.76595	−	1.59692i	0.130679	−	0.0754475i
$449$	−10.8011	−	18.7080i	−0.509734	−	0.882885i	−0.999936	−	0.0112766i	$-0.996410\pi$
$449$	−10.8011	−	18.7080i	−0.509734	−	0.882885i	0.490202	−	0.871609i	$-0.336923\pi$
$450$	−2.57551	+	4.28564i	−0.121411	+	0.202027i
$451$	−12.1114	−	20.9775i	−0.570301	−	0.987791i
$452$		−	1.81668i		−	0.0854494i
$453$	13.9107	+	8.03136i	0.653583	+	0.377346i
$454$	−1.00008			−0.0469363
$455$	−6.31700	+	22.7751i	−0.296146	+	1.06771i
$456$	−0.557077	+	0.964886i	−0.0260875	+	0.0451849i
$457$	1.91953	−	1.10824i	0.0897919	−	0.0518414i	−0.454432	−	0.890782i	$-0.650158\pi$
$457$	1.91953	−	1.10824i	0.0897919	−	0.0518414i	0.544224	+	0.838940i	$0.316824\pi$
$458$		−	12.1994i		−	0.570041i
$459$	−0.0969230	+	0.167875i	−0.00452398	+	0.00783576i
$460$	−5.49252	+	5.39708i	−0.256090	+	0.251640i
$461$	11.2124	−	19.4205i	0.522215	−	0.904502i	−0.477451	−	0.878658i	$-0.658439\pi$
$461$	11.2124	−	19.4205i	0.522215	−	0.904502i	0.999666	−	0.0258440i	$-0.00822732\pi$
$462$	11.8029	−	6.81441i	0.549121	−	0.317035i
$463$	−11.6407	+	6.72077i	−0.540990	+	0.312341i	−0.745480	−	0.666528i	$-0.767780\pi$
$463$	−11.6407	+	6.72077i	−0.540990	+	0.312341i	0.204490	+	0.978869i	$0.434446\pi$
$464$	2.09692	−	3.63198i	0.0973472	−	0.168610i
$465$	1.66229	−	1.63341i	0.0770869	−	0.0757474i
$466$	10.1502	−	17.5806i	0.470197	−	0.814405i
$467$		−	36.1934i		−	1.67483i	−0.546569	−	0.837414i	$-0.684066\pi$
$467$		−	36.1934i		−	1.67483i	0.546569	−	0.837414i	$-0.315934\pi$
$468$	−2.86606	+	1.65472i	−0.132484	+	0.0764895i
$469$	−8.12850	+	14.0790i	−0.375339	+	0.650107i
$470$	7.53839	−	27.1786i	0.347720	−	1.25366i
$471$	−10.4370			−0.480912
$472$	−5.67465	−	3.27626i	−0.261197	−	0.150802i
$473$		−	2.26257i		−	0.104033i
$474$	2.12738	+	3.68473i	0.0977139	+	0.169245i
$475$	4.77487	+	2.86952i	0.219086	+	0.131662i
$476$	−0.309557	−	0.536168i	−0.0141885	−	0.0245752i
$477$	6.53942	−	3.77554i	0.299420	−	0.172870i
$478$	9.82037	−	5.66979i	0.449173	−	0.259330i
$479$	2.55176	−	4.41978i	0.116593	−	0.201945i	−0.801822	−	0.597562i	$-0.796136\pi$
$479$	2.55176	−	4.41978i	0.116593	−	0.201945i	0.918415	+	0.395617i	$0.129469\pi$
$480$	0.597644	−	2.15472i	0.0272786	−	0.0983491i
$481$	−13.9609	−	14.5028i	−0.636562	−	0.661273i
$482$			13.8025i			0.628686i
$483$	−9.52518	−	5.49936i	−0.433411	−	0.250230i
$484$	3.60455	+	6.24326i	0.163843	+	0.283784i
$485$	9.57318	+	37.0225i	0.434696	+	1.68110i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$		−	18.9209i		−	0.857389i	−0.903450	−	0.428694i	$-0.858974\pi$
$487$		−	18.9209i		−	0.857389i	0.903450	−	0.428694i	$-0.141026\pi$
$488$	4.59222	−	2.65132i	0.207880	−	0.120020i
$489$	3.73232			0.168781
$490$	5.10483	−	5.01613i	0.230613	−	0.226606i
$491$	−27.2584			−1.23015			−0.615077	−	0.788467i	$-0.710875\pi$
$491$	−27.2584			−1.23015			−0.615077	+	0.788467i	$0.710875\pi$
$492$		−	5.67647i		−	0.255915i
$493$	−0.704044	−	0.406480i	−0.0317085	−	0.0183069i
$494$	1.84361	+	3.19323i	0.0829482	+	0.143670i
$495$	2.55027	−	9.19465i	0.114626	−	0.413269i
$496$	−0.521115	+	0.902598i	−0.0233988	+	0.0405279i
$497$	−10.1133	−	5.83890i	−0.453642	−	0.261910i
$498$	−14.4122	−	8.32089i	−0.645826	−	0.372868i
$499$	−0.594301	−	1.02936i	−0.0266046	−	0.0460805i	0.852417	−	0.522863i	$-0.175136\pi$
$499$	−0.594301	−	1.02936i	−0.0266046	−	0.0460805i	−0.879021	+	0.476783i	$0.841803\pi$
$500$	−10.7196	−	3.17659i	−0.479394	−	0.142061i
$501$	−9.23287	+	15.9918i	−0.412494	+	0.714461i
$502$	17.6710	+	10.2023i	0.788694	+	0.455353i
$503$	−9.98003	−	5.76197i	−0.444988	−	0.256914i	0.260723	−	0.965414i	$-0.416039\pi$
$503$	−9.98003	−	5.76197i	−0.444988	−	0.256914i	−0.705711	+	0.708500i	$0.749372\pi$
$504$	3.19385			0.142265
$505$	−12.1087	+	3.13105i	−0.538832	+	0.139330i
$506$	7.34755	−	12.7263i	0.326639	−	0.565755i
$507$		−	2.04760i		−	0.0909369i
$508$			0.0768087i			0.00340784i
$509$	16.7089	−	28.9406i	0.740608	−	1.28277i	−0.211610	−	0.977354i	$-0.567871\pi$
$509$	16.7089	−	28.9406i	0.740608	−	1.28277i	0.952219	−	0.305417i	$-0.0987960\pi$
$510$	−0.417684	−	0.115851i	−0.0184954	−	0.00512996i
$511$	−1.98509	−	3.43828i	−0.0878154	−	0.152101i
$512$			1.00000i			0.0441942i
$513$	−0.964886	+	0.557077i	−0.0426008	+	0.0245956i
$514$	−6.95507	−	12.0465i	−0.306775	−	0.531350i
$515$	−3.62808	−	14.0309i	−0.159872	−	0.618275i
$516$	0.265111	−	0.459186i	0.0116709	−	0.0202146i
$517$			53.8245i			2.36720i
$518$	4.67004	+	18.8578i	0.205190	+	0.828562i
$519$	−23.5919			−1.03557
$520$	−5.18663	−	5.27834i	−0.227449	−	0.231471i
$521$	21.6358	+	37.4743i	0.947882	+	1.64178i	0.749875	+	0.661580i	$0.230114\pi$
$521$	21.6358	+	37.4743i	0.947882	+	1.64178i	0.198008	+	0.980200i	$0.436553\pi$
$522$	3.63198	−	2.09692i	0.158967	−	0.0917798i
$523$	26.1999	−	15.1265i	1.14564	−	0.661436i	0.197820	−	0.980238i	$-0.436614\pi$
$523$	26.1999	−	15.1265i	1.14564	−	0.661436i	0.947821	+	0.318802i	$0.103281\pi$
$524$	−14.8004			−0.646557
$525$	0.279894	−	15.9668i	0.0122156	−	0.696847i
$526$	22.5970			0.985277
$527$	0.174965	+	0.101016i	0.00762159	+	0.00440033i
$528$			4.26721i			0.185707i
$529$	11.1408			0.484381
$530$	11.8342	+	12.0435i	0.514045	+	0.523135i
$531$	−3.27626	−	5.67465i	−0.142177	−	0.246259i
$532$		−	3.55844i		−	0.154278i
$533$	−16.2691	−	9.39298i	−0.704694	−	0.406855i
$534$	6.09036	−	10.5488i	0.263556	−	0.456492i
$535$	−4.77855	+	4.69552i	−0.206595	+	0.203005i
$536$	−2.54505	−	4.40816i	−0.109929	−	0.190403i
$537$	−1.55374	+	0.897053i	−0.0670489	+	0.0387107i
$538$	−10.7222	−	6.19049i	−0.462268	−	0.266891i
$539$	−6.82893	+	11.8281i	−0.294143	+	0.509470i
$540$	1.59494	−	1.56722i	0.0686351	−	0.0674425i
$541$	22.5497			0.969488			0.484744	−	0.874656i	$-0.338913\pi$
$541$	22.5497			0.969488			0.484744	+	0.874656i	$0.338913\pi$
$542$	13.1933	−	7.61718i	0.566702	−	0.327186i
$543$	−1.34063	−	0.774014i	−0.0575320	−	0.0332161i
$544$	0.193846			0.00831107
$545$	2.98301	−	10.7548i	0.127778	−	0.460686i
$546$	5.28492	−	9.15376i	0.226174	−	0.391745i
$547$		−	43.7821i		−	1.87199i	−0.352017	−	0.935993i	$-0.614504\pi$
$547$		−	43.7821i		−	1.87199i	0.352017	−	0.935993i	$-0.385496\pi$
$548$	15.1984	−	8.77481i	0.649244	−	0.374841i
$549$	5.30264			0.226311
$550$	21.3328	+	0.373958i	0.909633	+	0.0159456i
$551$	−2.33630	−	4.04658i	−0.0995296	−	0.172390i
$552$	2.98235	−	1.72186i	0.126937	−	0.0732873i
$553$	−11.7685	−	6.79453i	−0.500446	−	0.288933i
$554$	7.74331			0.328982
$555$	11.5856	+	7.12555i	0.491782	+	0.302463i
$556$	15.5905			0.661185
$557$	−22.6846	−	13.0970i	−0.961178	−	0.554936i	−0.0646424	−	0.997908i	$-0.520591\pi$
$557$	−22.6846	−	13.0970i	−0.961178	−	0.554936i	−0.896535	+	0.442972i	$0.853924\pi$
$558$	−0.902598	+	0.521115i	−0.0382100	+	0.0220606i
$559$	−0.877371	−	1.51965i	−0.0371088	−	0.0642744i
$560$	1.78787	+	6.91424i	0.0755513	+	0.292180i
$561$	0.827181			0.0349236
$562$	13.4991	−	7.79373i	0.569427	−	0.328759i
$563$		−	26.6763i		−	1.12427i	−0.827045	−	0.562135i	$-0.809980\pi$
$563$		−	26.6763i		−	1.12427i	0.827045	−	0.562135i	$-0.190020\pi$
$564$	−6.30676	+	10.9236i	−0.265562	+	0.459968i
$565$	3.91444	+	1.08573i	0.164682	+	0.0456769i
$566$	2.70682			0.113776
$567$	2.76595	+	1.59692i	0.116159	+	0.0670645i
$568$	3.16649	−	1.82817i	0.132863	−	0.0767084i
$569$	25.5075			1.06933			0.534665	−	0.845064i	$-0.320438\pi$
$569$	25.5075			1.06933			0.534665	+	0.845064i	$0.320438\pi$
$570$	−1.74613	−	1.77700i	−0.0731372	−	0.0744305i
$571$	9.79873	−	16.9719i	0.410064	−	0.710252i	−0.584832	−	0.811154i	$-0.698840\pi$
$571$	9.79873	−	16.9719i	0.410064	−	0.710252i	0.994896	+	0.100902i	$0.0321730\pi$
$572$	12.2301	+	7.06104i	0.511366	+	0.295237i
$573$	14.7121	−	8.49404i	0.614607	−	0.354844i
$574$	9.06489	+	15.7009i	0.378361	+	0.655341i
$575$	−8.34663	−	15.0604i	−0.348079	−	0.628061i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−25.3021	−	14.6082i	−1.05334	−	0.608147i	−0.129759	−	0.991546i	$-0.541420\pi$
$577$	−25.3021	−	14.6082i	−1.05334	−	0.608147i	−0.923583	+	0.383399i	$0.874754\pi$
$578$			16.9624i			0.705544i
$579$	−10.1794	−	17.6312i	−0.423040	−	0.732726i
$580$	6.57268	+	6.68891i	0.272916	+	0.277742i
$581$	53.1513			2.20509
$582$		−	17.1015i		−	0.708880i
$583$	−27.9051	−	16.1110i	−1.15571	−	0.667250i
$584$	1.24307			0.0514388
$585$	−1.85258	−	7.16449i	−0.0765947	−	0.296215i
$586$	−2.34970			−0.0970652
$587$	−38.9840	+	22.5074i	−1.60904	+	0.928981i	−0.619457	+	0.785031i	$0.712647\pi$
$587$	−38.9840	+	22.5074i	−1.60904	+	0.928981i	−0.989585	+	0.143950i	$0.954020\pi$
$588$	−2.77185	+	1.60033i	−0.114309	+	0.0659963i
$589$	0.580603	+	1.00563i	0.0239233	+	0.0414364i
$590$	10.4508	−	10.2692i	0.430254	−	0.422778i
$591$	13.8907			0.571387
$592$	−5.84446	−	1.68590i	−0.240206	−	0.0692901i
$593$			3.44657i			0.141534i	0.997493	+	0.0707669i	$0.0225447\pi$
$593$			3.44657i			0.141534i	−0.997493	+	0.0707669i	$0.977455\pi$
$594$	−2.13361	+	3.69551i	−0.0875429	+	0.151629i
$595$	1.34030	−	0.346571i	0.0549469	−	0.0142080i
$596$	−9.14356	−	15.8371i	−0.374535	−	0.648713i
$597$	−3.96475	+	2.28905i	−0.162266	+	0.0936845i
$598$		−	11.3968i		−	0.466050i
$599$	−4.13216	−	7.15712i	−0.168836	−	0.292432i	0.769175	−	0.639038i	$-0.220667\pi$
$599$	−4.13216	−	7.15712i	−0.168836	−	0.292432i	−0.938011	+	0.346606i	$0.887334\pi$
$600$	4.28564	+	2.57551i	0.174961	+	0.105145i
$601$	18.1366	−	31.4135i	0.739806	−	1.28138i	−0.212776	−	0.977101i	$-0.568250\pi$
$601$	18.1366	−	31.4135i	0.739806	−	1.28138i	0.952582	−	0.304281i	$-0.0984163\pi$
$602$			1.69345i			0.0690199i
$603$		−	5.09010i		−	0.207285i
$604$	8.03136	−	13.9107i	0.326791	−	0.566019i
$605$	−15.6067	+	4.03555i	−0.634503	+	0.164068i
$606$	5.59331			0.227212
$607$	−19.5670	−	11.2970i	−0.794202	−	0.458533i	0.0472380	−	0.998884i	$-0.484958\pi$
$607$	−19.5670	−	11.2970i	−0.794202	−	0.458533i	−0.841440	+	0.540351i	$0.818291\pi$
$608$	0.964886	+	0.557077i	0.0391313	+	0.0225925i
$609$	−6.69725	+	11.6000i	−0.271386	+	0.470055i
$610$	2.96834	+	11.4795i	0.120185	+	0.464791i
$611$	20.8719	+	36.1511i	0.844385	+	1.46252i
$612$	0.167875	+	0.0969230i	0.00678596	+	0.00391788i
$613$	−0.835756	−	0.482524i	−0.0337559	−	0.0194890i	0.483027	−	0.875605i	$-0.339537\pi$
$613$	−0.835756	−	0.482524i	−0.0337559	−	0.0194890i	−0.516783	+	0.856116i	$0.672871\pi$
$614$	2.53012	−	4.38229i	0.102107	−	0.176855i
$615$	12.2312	+	3.39251i	0.493210	+	0.136799i
$616$	−6.81441	−	11.8029i	−0.274560	−	0.475552i
$617$	32.4902	+	18.7582i	1.30801	+	0.755177i	0.981763	−	0.190109i	$-0.0608841\pi$
$617$	32.4902	+	18.7582i	1.30801	+	0.755177i	0.326243	+	0.945286i	$0.394217\pi$
$618$			6.48119i			0.260712i
$619$	17.9959			0.723315			0.361658	−	0.932311i	$-0.382211\pi$
$619$	17.9959			0.723315			0.361658	+	0.932311i	$0.382211\pi$
$620$	−1.63341	−	1.66229i	−0.0655992	−	0.0667592i
$621$	3.44373			0.138192
$622$	3.07179	−	1.77350i	0.123167	−	0.0711107i
$623$			38.9033i			1.55863i
$624$	1.65472	+	2.86606i	0.0662419	+	0.114734i
$625$	13.2511	−	21.1992i	0.530046	−	0.847969i
$626$	7.19561	+	12.4632i	0.287594	+	0.498128i
$627$	4.11737	+	2.37717i	0.164432	+	0.0949349i
$628$			10.4370i			0.416482i
$629$	−0.326805	+	1.13293i	−0.0130306	+	0.0451727i
$630$	−1.90878	+	6.88185i	−0.0760477	+	0.274179i
$631$	15.6815	−	27.1611i	0.624269	−	1.08127i	−0.364412	−	0.931238i	$-0.618730\pi$
$631$	15.6815	−	27.1611i	0.624269	−	1.08127i	0.988682	−	0.150028i	$-0.0479365\pi$
$632$	3.68473	−	2.12738i	0.146571	−	0.0846227i
$633$	−13.5798	+	7.84032i	−0.539750	+	0.311625i
$634$	−12.2806	−	21.2706i	−0.487725	−	0.844765i
$635$	−0.165501	−	0.0459042i	−0.00656772	−	0.00182165i
$636$	−3.77554	−	6.53942i	−0.149710	−	0.259305i
$637$			10.5924i			0.419685i
$638$	−15.4984	−	8.94801i	−0.613588	−	0.354255i
$639$	3.65634			0.144643
$640$	−2.15472	−	0.597644i	−0.0851728	−	0.0236239i
$641$	−11.3794	+	19.7098i	−0.449461	+	0.778489i	−0.998351	−	0.0574058i	$-0.981717\pi$
$641$	−11.3794	+	19.7098i	−0.449461	+	0.778489i	0.548890	+	0.835894i	$0.315050\pi$
$642$	2.59468	−	1.49804i	0.102404	−	0.0591229i
$643$		−	26.7296i		−	1.05411i	−0.849831	−	0.527055i	$-0.823296\pi$
$643$		−	26.7296i		−	1.05411i	0.849831	−	0.527055i	$-0.176704\pi$
$644$	−5.49936	+	9.52518i	−0.216705	+	0.375345i
$645$	0.830976	+	0.845671i	0.0327197	+	0.0332983i
$646$	0.107987	−	0.187039i	0.00424870	−	0.00735896i
$647$	−6.72466	+	3.88249i	−0.264374	+	0.152636i	−0.626328	−	0.779560i	$-0.715443\pi$
$647$	−6.72466	+	3.88249i	−0.264374	+	0.152636i	0.361954	+	0.932196i	$0.382110\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−13.9805	+	24.2149i	−0.548782	+	0.950518i
$650$	14.4731	−	8.02117i	0.567682	−	0.314616i
$651$	1.66436	−	2.88276i	0.0652315	−	0.112984i
$652$		−	3.73232i		−	0.146169i
$653$	−14.3288	+	8.27272i	−0.560728	+	0.323737i	−0.753438	−	0.657519i	$-0.771606\pi$
$653$	−14.3288	+	8.27272i	−0.560728	+	0.323737i	0.192710	+	0.981256i	$0.438272\pi$
$654$	−2.49564	+	4.32258i	−0.0975872	+	0.169026i
$655$	8.84535	−	31.8907i	0.345616	−	1.24607i
$656$	−5.67647			−0.221629
$657$	1.07653	+	0.621537i	0.0419996	+	0.0242485i
$658$		−	40.2856i		−	1.57050i
$659$	1.40114	+	2.42684i	0.0545805	+	0.0945362i	0.892025	−	0.451987i	$-0.149285\pi$
$659$	1.40114	+	2.42684i	0.0545805	+	0.0945362i	−0.837444	+	0.546523i	$0.815951\pi$
$660$	−9.19465	−	2.55027i	−0.357901	−	0.0992692i
$661$	−21.3281	−	36.9414i	−0.829569	−	1.43686i	−0.898377	−	0.439225i	$-0.855253\pi$
$661$	−21.3281	−	36.9414i	−0.829569	−	1.43686i	0.0688084	−	0.997630i	$-0.478080\pi$
$662$	−5.79532	+	3.34593i	−0.225241	+	0.130043i
$663$	0.555574	−	0.320761i	0.0215767	−	0.0124573i
$664$	−8.32089	+	14.4122i	−0.322913	+	0.559302i
$665$	7.66744	+	2.12668i	0.297331	+	0.0824690i
$666$	−4.21850	−	4.38226i	−0.163464	−	0.169809i
$667$			14.4425i			0.559214i
$668$	15.9918	+	9.23287i	0.618741	+	0.357231i
$669$	9.06583	+	15.7025i	0.350505	+	0.607093i
$670$	11.0194	−	2.84937i	0.425716	−	0.110081i
$671$	−11.3137	−	19.5960i	−0.436762	−	0.756494i
$672$		−	3.19385i		−	0.123205i
$673$	21.8380	−	12.6082i	0.841794	−	0.486010i	−0.0160794	−	0.999871i	$-0.505118\pi$
$673$	21.8380	−	12.6082i	0.841794	−	0.486010i	0.857874	+	0.513861i	$0.171785\pi$
$674$	−32.5551			−1.25398
$675$	2.42372	+	4.37328i	0.0932891	+	0.168328i
$676$	−2.04760			−0.0787537
$677$			51.5166i			1.97994i	0.141269	+	0.989971i	$0.454882\pi$
$677$			51.5166i			1.97994i	−0.141269	+	0.989971i	$0.545118\pi$
$678$	−1.57329	−	0.908340i	−0.0604219	−	0.0348846i
$679$	27.3098	+	47.3020i	1.04805	+	1.81528i
$680$	−0.115851	+	0.417684i	−0.00444267	+	0.0160174i
$681$	−0.500042	+	0.866099i	−0.0191617	+	0.0331890i
$682$	3.85158	+	2.22371i	0.147485	+	0.0851502i
$683$	33.6241	+	19.4129i	1.28659	+	0.742814i	0.978045	−	0.208395i	$-0.0668239\pi$
$683$	33.6241	+	19.4129i	1.28659	+	0.742814i	0.308547	+	0.951209i	$0.400157\pi$
$684$	0.557077	+	0.964886i	0.0213004	+	0.0368933i
$685$	9.82403	+	37.9925i	0.375357	+	1.45162i
$686$	−6.06727	+	10.5088i	−0.231649	+	0.401228i
$687$	−10.5650	−	6.09970i	−0.403080	−	0.232718i
$688$	−0.459186	−	0.265111i	−0.0175063	−	0.0101073i
$689$	−24.9898			−0.952037
$690$	1.92775	+	7.45520i	0.0733882	+	0.283815i
$691$	−10.4387	+	18.0804i	−0.397109	+	0.687812i	−0.993368	−	0.114980i	$-0.963320\pi$
$691$	−10.4387	+	18.0804i	−0.397109	+	0.687812i	0.596259	+	0.802792i	$0.296653\pi$
$692$			23.5919i			0.896831i
$693$		−	13.6288i		−	0.517716i
$694$	−7.56229	+	13.0983i	−0.287060	+	0.497203i
$695$	−9.31757	+	33.5932i	−0.353435	+	1.27426i
$696$	−2.09692	−	3.63198i	−0.0794837	−	0.137670i
$697$			1.10036i			0.0416792i
$698$	−14.5024	+	8.37294i	−0.548923	+	0.316921i
$699$	−10.1502	−	17.5806i	−0.383914	−	0.664959i
$700$	−15.9668	−	0.279894i	−0.603487	−	0.0105790i
$701$	−8.57769	+	14.8570i	−0.323975	+	0.561141i	−0.981304	−	0.192462i	$-0.938353\pi$
$701$	−8.57769	+	14.8570i	−0.323975	+	0.561141i	0.657330	+	0.753603i	$0.271686\pi$
$702$			3.30944i			0.124907i
$703$	−4.88252	+	4.70006i	−0.184148	+	0.177266i
$704$	4.26721			0.160827
$705$	−19.7682	−	20.1177i	−0.744513	−	0.757678i
$706$	−14.8930	−	25.7954i	−0.560505	−	0.970824i
$707$	−15.4708	+	8.93208i	−0.581840	+	0.335925i
$708$	−5.67465	+	3.27626i	−0.213266	+	0.123129i
$709$	13.4264			0.504239			0.252120	−	0.967696i	$-0.418872\pi$
$709$	13.4264			0.504239			0.252120	+	0.967696i	$0.418872\pi$
$710$	2.04677	+	7.91549i	0.0768139	+	0.297063i
$711$	4.25476			0.159566
$712$	−10.5488	−	6.09036i	−0.395333	−	0.228246i
$713$		−	3.58916i		−	0.134415i
$714$	−0.619114			−0.0231698
$715$	−22.5238	+	22.1324i	−0.842343	+	0.827706i
$716$	0.897053	+	1.55374i	0.0335244	+	0.0580660i
$717$		−	11.3396i		−	0.423484i
$718$	−14.7810	−	8.53383i	−0.551623	−	0.318480i
$719$	1.99668	−	3.45835i	0.0744636	−	0.128975i	−0.826389	−	0.563099i	$-0.809609\pi$
$719$	1.99668	−	3.45835i	0.0744636	−	0.128975i	0.900853	+	0.434125i	$0.142942\pi$
$720$	−1.56722	−	1.59494i	−0.0584069	−	0.0594397i
$721$	−10.3500	−	17.9266i	−0.385452	−	0.667623i
$722$	−15.3795	+	8.87933i	−0.572364	+	0.330454i
$723$	11.9533	+	6.90124i	0.444548	+	0.256660i
$724$	−0.774014	+	1.34063i	−0.0287660	+	0.0498242i
$725$	−18.3409	+	10.1647i	−0.681162	+	0.377508i
$726$	7.20909			0.267554
$727$	14.5632	−	8.40804i	0.540117	−	0.311837i	−0.205009	−	0.978760i	$-0.565722\pi$
$727$	14.5632	−	8.40804i	0.540117	−	0.311837i	0.745127	+	0.666923i	$0.232389\pi$
$728$	−9.15376	−	5.28492i	−0.339261	−	0.195872i
$729$	−1.00000			−0.0370370
$730$	−0.742915	+	2.67848i	−0.0274965	+	0.0991349i
$731$	−0.0513908	+	0.0890114i	−0.00190076	+	0.00329221i
$732$		−	5.30264i		−	0.195991i
$733$	36.5875	−	21.1238i	1.35139	−	0.780225i	0.362945	−	0.931810i	$-0.381771\pi$
$733$	36.5875	−	21.1238i	1.35139	−	0.780225i	0.988444	+	0.151585i	$0.0484378\pi$
$734$	−3.11723			−0.115059
$735$	−1.79168	−	6.92898i	−0.0660871	−	0.255579i
$736$	−1.72186	−	2.98235i	−0.0634687	−	0.109931i
$737$	−18.8105	+	10.8603i	−0.692895	+	0.400043i
$738$	−4.91597	−	2.83824i	−0.180959	−	0.104477i
$739$	34.5965			1.27265			0.636326	−	0.771420i	$-0.280453\pi$
$739$	34.5965			1.27265			0.636326	+	0.771420i	$0.280453\pi$
$740$	7.12555	−	11.5856i	0.261940	−	0.425896i
$741$	3.68723			0.135454
$742$	20.8859	+	12.0585i	0.766746	+	0.442681i
$743$	−7.63173	+	4.40618i	−0.279981	+	0.161647i	−0.633415	−	0.773812i	$-0.718347\pi$
$743$	−7.63173	+	4.40618i	−0.279981	+	0.161647i	0.353434	+	0.935460i	$0.385014\pi$
$744$	0.521115	+	0.902598i	0.0191050	+	0.0330909i
$745$	39.5891	−	10.2369i	1.45043	−	0.375050i
$746$	15.1527			0.554781
$747$	−14.4122	+	8.32089i	−0.527315	+	0.304445i
$748$		−	0.827181i		−	0.0302447i
$749$	−4.78450	+	8.28700i	−0.174822	+	0.302801i
$750$	−8.11079	+	7.69513i	−0.296164	+	0.280986i
$751$	31.7368			1.15809			0.579045	−	0.815295i	$-0.303425\pi$
$751$	31.7368			1.15809			0.579045	+	0.815295i	$0.303425\pi$
$752$	10.9236	+	6.30676i	0.398344	+	0.229984i
$753$	17.6710	−	10.2023i	0.643966	−	0.371794i
$754$	−13.8793			−0.505454
$755$	25.1738	+	25.6190i	0.916170	+	0.932371i
$756$	1.59692	−	2.76595i	0.0580795	−	0.100597i
$757$	21.2066	+	12.2436i	0.770767	+	0.445003i	0.833148	−	0.553050i	$-0.186536\pi$
$757$	21.2066	+	12.2436i	0.770767	+	0.445003i	−0.0623810	+	0.998052i	$0.519869\pi$
$758$	3.20447	−	1.85010i	0.116392	−	0.0671988i
$759$	−7.34755	−	12.7263i	−0.266699	−	0.461937i
$760$	−1.77700	+	1.74613i	−0.0644587	+	0.0633387i
$761$	16.7286	−	28.9747i	0.606410	−	1.05033i	−0.385417	−	0.922743i	$-0.625942\pi$
$761$	16.7286	−	28.9747i	0.606410	−	1.05033i	0.991827	−	0.127591i	$-0.0407244\pi$
$762$	0.0665183	+	0.0384044i	0.00240970	+	0.00139124i
$763$		−	15.9414i		−	0.577117i
$764$	−8.49404	−	14.7121i	−0.307304	−	0.532265i
$765$	−0.309172	+	0.303799i	−0.0111781	+	0.0109839i
$766$	31.4926			1.13787
$767$			21.6852i			0.783006i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−13.2958			−0.479458			−0.239729	−	0.970840i	$-0.577059\pi$
$769$	−13.2958			−0.479458			−0.239729	+	0.970840i	$0.577059\pi$
$770$	29.5045	−	7.62922i	1.06327	−	0.274938i
$771$	−13.9101			−0.500962
$772$	−17.6312	+	10.1794i	−0.634560	+	0.366363i
$773$	−38.3025	+	22.1139i	−1.37764	+	0.795383i	−0.991876	−	0.127212i	$-0.959397\pi$
$773$	−38.3025	+	22.1139i	−1.37764	+	0.795383i	−0.385769	+	0.922596i	$0.626064\pi$
$774$	−0.265111	−	0.459186i	−0.00952923	−	0.0165051i
$775$	4.55797	−	2.52608i	0.163727	−	0.0907394i
$776$	−17.1015			−0.613908
$777$	18.6663	+	5.38451i	0.669650	+	0.193168i
$778$			15.9847i			0.573078i
$779$	−3.16223	+	5.47715i	−0.113299	+	0.196239i
$780$	−7.16449	+	1.85258i	−0.256530	+	0.0663330i
$781$	−7.80120	−	13.5121i	−0.279149	−	0.483500i
$782$	−0.578117	+	0.333776i	−0.0206734	+	0.0119358i
$783$		−	4.19385i		−	0.149876i
$784$	1.60033	+	2.77185i	0.0571545	+	0.0989945i
$785$	−22.4888	−	6.23761i	−0.802661	−	0.222630i
$786$	−7.40018	+	12.8175i	−0.263956	+	0.457185i
$787$			42.7114i			1.52250i	0.648460	+	0.761249i	$0.275413\pi$
$787$			42.7114i			1.52250i	−0.648460	+	0.761249i	$0.724587\pi$
$788$		−	13.8907i		−	0.494836i
$789$	11.2985	−	19.5696i	0.402238	−	0.696696i
$790$	2.38176	+	9.21099i	0.0847391	+	0.327712i
$791$	5.80219			0.206302
$792$	3.69551	+	2.13361i	0.131314	+	0.0758144i
$793$	−15.1977	−	8.77438i	−0.539685	−	0.311587i
$794$	−1.11527	+	1.93170i	−0.0395794	+	0.0685535i
$795$	16.3471	−	4.22698i	0.579770	−	0.149916i
$796$	2.28905	+	3.96475i	0.0811331	+	0.140527i
$797$	−2.42031	−	1.39737i	−0.0857320	−	0.0494974i	0.456521	−	0.889713i	$-0.349095\pi$
$797$	−2.42031	−	1.39737i	−0.0857320	−	0.0494974i	−0.542253	+	0.840215i	$0.682429\pi$
$798$	−3.08170	−	1.77922i	−0.109091	−	0.0629837i
$799$	1.22254	−	2.11750i	0.0432503	−	0.0749118i
$800$	2.57551	−	4.28564i	0.0910580	−	0.151520i
$801$	−6.09036	−	10.5488i	−0.215192	−	0.372724i
$802$	−12.2236	−	7.05732i	−0.431632	−	0.249203i
$803$		−	5.30446i		−	0.187190i
$804$	−5.09010			−0.179514
$805$	−17.2374	−	17.5423i	−0.607540	−	0.618283i
$806$	3.44920			0.121493
$807$	−10.7222	+	6.19049i	−0.377441	+	0.217915i
$808$		−	5.59331i		−	0.196772i
$809$	−4.71582	−	8.16805i	−0.165800	−	0.287173i	0.771139	−	0.636666i	$-0.219687\pi$
$809$	−4.71582	−	8.16805i	−0.165800	−	0.287173i	−0.936939	+	0.349493i	$0.886354\pi$
$810$	−0.559786	−	2.16486i	−0.0196689	−	0.0760656i
$811$	−18.4860	−	32.0187i	−0.649131	−	1.12433i	−0.983331	−	0.181826i	$-0.941799\pi$
$811$	−18.4860	−	32.0187i	−0.649131	−	1.12433i	0.334200	−	0.942502i	$-0.391534\pi$
$812$	11.6000	+	6.69725i	0.407079	+	0.235027i
$813$		−	15.2344i		−	0.534292i
$814$	−7.19410	+	24.9396i	−0.252153	+	0.874131i
$815$	8.04210	+	2.23059i	0.281702	+	0.0781343i
$816$	0.0969230	−	0.167875i	0.00339298	−	0.00587682i
$817$	−0.511605	+	0.295375i	−0.0178988	+	0.0103339i
$818$	−28.3780	+	16.3841i	−0.992214	+	0.572855i
$819$	−5.28492	−	9.15376i	−0.184670	−	0.319858i
$820$	3.39251	−	12.2312i	0.118472	−	0.427133i
$821$	10.9750	+	19.0092i	0.383030	+	0.663427i	0.991494	−	0.130155i	$-0.0415474\pi$
$821$	10.9750	+	19.0092i	0.383030	+	0.663427i	−0.608464	+	0.793581i	$0.708214\pi$
$822$		−	17.5496i		−	0.612113i
$823$	37.5282	+	21.6669i	1.30815	+	0.755262i	0.981788	−	0.189982i	$-0.0608430\pi$
$823$	37.5282	+	21.6669i	1.30815	+	0.755262i	0.326365	+	0.945244i	$0.394176\pi$
$824$	6.48119			0.225783
$825$	10.9902	−	18.2877i	0.382631	−	0.636698i
$826$	10.4639	−	18.1239i	0.364084	−	0.630613i
$827$	−2.93855	+	1.69657i	−0.102183	+	0.0589956i	−0.550221	−	0.835019i	$-0.685456\pi$
$827$	−2.93855	+	1.69657i	−0.102183	+	0.0589956i	0.448037	+	0.894015i	$0.352123\pi$
$828$		−	3.44373i		−	0.119678i
$829$	0.574295	−	0.994707i	0.0199461	−	0.0345476i	−0.855880	−	0.517174i	$-0.826984\pi$
$829$	0.574295	−	0.994707i	0.0199461	−	0.0345476i	0.875826	+	0.482627i	$0.160317\pi$
$830$	−26.0813	−	26.5425i	−0.905296	−	0.921305i
$831$	3.87166	−	6.70591i	0.134306	−	0.232625i
$832$	2.86606	−	1.65472i	0.0993628	−	0.0573671i
$833$	0.537311	−	0.310217i	0.0186167	−	0.0107484i
$834$	7.79525	−	13.5018i	0.269928	−	0.467528i
$835$	−29.4517	+	28.9399i	−1.01922	+	1.00151i
$836$	2.37717	−	4.11737i	0.0822160	−	0.142402i
$837$			1.04223i			0.0360248i
$838$	−32.8773	+	18.9817i	−1.13573	+	0.655712i
$839$	10.9710	−	19.0024i	0.378762	−	0.656035i	−0.612120	−	0.790765i	$-0.709683\pi$
$839$	10.9710	−	19.0024i	0.378762	−	0.656035i	0.990882	+	0.134730i	$0.0430166\pi$
$840$	6.88185	+	1.90878i	0.237446	+	0.0658592i
$841$	−11.4117			−0.393505
$842$	17.6878	+	10.2121i	0.609563	+	0.351932i
$843$		−	15.5875i		−	0.536861i
$844$	7.84032	+	13.5798i	0.269875	+	0.467437i
$845$	1.22373	−	4.41200i	0.0420977	−	0.151777i
$846$	6.30676	+	10.9236i	0.216831	+	0.375562i
$847$	−19.9400	+	11.5124i	−0.685146	+	0.395569i
$848$	−6.53942	+	3.77554i	−0.224565	+	0.129652i
$849$	1.35341	−	2.34418i	0.0464489	−	0.0804519i
$850$	−0.830755	−	0.499252i	−0.0284946	−	0.0171242i
$851$	20.3331	−	5.03541i	0.697011	−	0.172612i
$852$		−	3.65634i		−	0.125264i
$853$	−23.0982	−	13.3358i	−0.790868	−	0.456608i	0.0494001	−	0.998779i	$-0.484269\pi$
$853$	−23.0982	−	13.3358i	−0.790868	−	0.456608i	−0.840268	+	0.542171i	$0.817602\pi$
$854$	8.46790	+	14.6668i	0.289766	+	0.501889i
$855$	−2.41199	+	0.623688i	−0.0824885	+	0.0213297i
$856$	−1.49804	−	2.59468i	−0.0512019	−	0.0886843i
$857$			24.3978i			0.833413i	0.909041	+	0.416707i	$0.136816\pi$
$857$			24.3978i			0.833413i	−0.909041	+	0.416707i	$0.863184\pi$
$858$	12.2301	−	7.06104i	0.417528	−	0.241060i
$859$	−11.6036			−0.395910			−0.197955	−	0.980211i	$-0.563430\pi$
$859$	−11.6036			−0.395910			−0.197955	+	0.980211i	$0.563430\pi$
$860$	0.845671	−	0.830976i	0.0288371	−	0.0283361i
$861$	18.1298			0.617861
$862$			13.2069i			0.449830i
$863$	36.6233	+	21.1445i	1.24667	+	0.719766i	0.970444	−	0.241327i	$-0.0775825\pi$
$863$	36.6233	+	21.1445i	1.24667	+	0.719766i	0.276227	+	0.961092i	$0.410916\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−50.8341	−	14.0996i	−1.72841	−	0.479400i
$866$	−10.2092	+	17.6828i	−0.346921	+	0.600885i
$867$	14.6899	+	8.48121i	0.498895	+	0.288037i
$868$	−2.88276	−	1.66436i	−0.0978472	−	0.0564921i
$869$	−9.07799	−	15.7235i	−0.307950	−	0.533385i
$870$	9.07911	−	2.34766i	0.307811	−	0.0795930i
$871$	−8.42270	+	14.5885i	−0.285392	+	0.494314i
$872$	4.32258	+	2.49564i	0.146381	+	0.0845130i
$873$	−14.8103	−	8.55076i	−0.501254	−	0.289399i
$874$	−3.83684			−0.129783
$875$	10.1455	−	34.2367i	0.342982	−	1.15741i
$876$	0.621537	−	1.07653i	0.0209998	−	0.0363727i
$877$			39.8426i			1.34539i	0.739920	+	0.672695i	$0.234863\pi$
$877$			39.8426i			1.34539i	−0.739920	+	0.672695i	$0.765137\pi$
$878$		−	18.1146i		−	0.611338i
$879$	−1.17485	+	2.03490i	−0.0396267	+	0.0686355i
$880$	−2.55027	+	9.19465i	−0.0859696	+	0.309952i
$881$	8.23513	+	14.2637i	0.277449	+	0.480555i	0.970750	−	0.240093i	$-0.0771778\pi$
$881$	8.23513	+	14.2637i	0.277449	+	0.480555i	−0.693301	+	0.720648i	$0.743844\pi$
$882$			3.20065i			0.107772i
$883$	17.5060	−	10.1071i	0.589123	−	0.340130i	−0.175628	−	0.984457i	$-0.556196\pi$
$883$	17.5060	−	10.1071i	0.589123	−	0.340130i	0.764750	+	0.644327i	$0.222862\pi$
$884$	−0.320761	−	0.555574i	−0.0107884	−	0.0186860i
$885$	−3.66801	−	14.1853i	−0.123299	−	0.476834i
$886$	8.56521	−	14.8354i	0.287754	−	0.498404i
$887$		−	8.99895i		−	0.302155i	−0.988522	−	0.151078i	$-0.951726\pi$
$887$		−	8.99895i		−	0.302155i	0.988522	−	0.151078i	$-0.0482743\pi$
$888$	−4.38226	+	4.21850i	−0.147059	+	0.141564i
$889$	−0.245315			−0.00822761
$890$	19.4274	−	19.0899i	0.651210	−	0.639894i
$891$	2.13361	+	3.69551i	0.0714785	+	0.123804i
$892$	15.7025	−	9.06583i	0.525758	−	0.303546i
$893$	12.1706	−	7.02670i	0.407274	−	0.235140i
$894$	−18.2871			−0.611612
$895$	−3.88400	+	1.00431i	−0.129828	+	0.0335705i
$896$	−3.19385			−0.106699
$897$	−9.86993	−	5.69840i	−0.329547	−	0.190264i
$898$			21.6021i			0.720873i
$899$	−4.37095			−0.145780
$900$	4.37328	−	2.42372i	0.145776	−	0.0807907i
$901$	0.731872	+	1.26764i	0.0243822	+	0.0422312i
$902$			24.2227i			0.806528i
$903$	1.46657	+	0.846725i	0.0488044	+	0.0281772i
$904$	−0.908340	+	1.57329i	−0.0302109	+	0.0523269i
$905$	−2.42610	−	2.46900i	−0.0806463	−	0.0820724i
$906$	−8.03136	−	13.9107i	−0.266824	−	0.462153i
$907$	−40.9198	+	23.6251i	−1.35872	+	0.784458i	−0.989451	−	0.144865i	$-0.953725\pi$
$907$	−40.9198	+	23.6251i	−1.35872	+	0.784458i	−0.369269	+	0.929322i	$0.620392\pi$
$908$	0.866099	+	0.500042i	0.0287425	+	0.0165945i
$909$	2.79665	−	4.84394i	0.0927591	−	0.160663i
$910$	16.8582	−	16.5653i	0.558845	−	0.549134i
$911$	25.1612			0.833626			0.416813	−	0.908992i	$-0.363147\pi$
$911$	25.1612			0.833626			0.416813	+	0.908992i	$0.363147\pi$
$912$	0.964886	−	0.557077i	0.0319506	−	0.0184467i
$913$	61.4999	+	35.5070i	2.03535	+	1.17511i
$914$	−2.21648			−0.0733148
$915$	11.4257	+	3.16909i	0.377722	+	0.104767i
$916$	−6.09970	+	10.5650i	−0.201540	+	0.349077i
$917$		−	47.2701i		−	1.56100i
$918$	0.167875	−	0.0969230i	0.00554072	−	0.00319893i
$919$	1.70721			0.0563158			0.0281579	−	0.999603i	$-0.491036\pi$
$919$	1.70721			0.0563158			0.0281579	+	0.999603i	$0.491036\pi$
$920$	7.45520	−	1.92775i	0.245791	−	0.0635560i
$921$	−2.53012	−	4.38229i	−0.0833702	−	0.144401i
$922$	−19.4205	+	11.2124i	−0.639580	+	0.369261i
$923$	−10.4793	−	6.05023i	−0.344931	−	0.199146i
$924$	−13.6288			−0.448355
$925$	20.7052	+	22.2776i	0.680784	+	0.732484i
$926$	13.4415			0.441717
$927$	5.61287	+	3.24059i	0.184351	+	0.106435i
$928$	−3.63198	+	2.09692i	−0.119225	+	0.0688349i
$929$	−17.8239	−	30.8719i	−0.584782	−	1.01287i	−0.994903	−	0.100841i	$-0.967847\pi$
$929$	−17.8239	−	30.8719i	−0.584782	−	1.01287i	0.410120	−	0.912031i	$-0.365487\pi$
$930$	−2.25629	+	0.583426i	−0.0739866	+	0.0191313i
$931$	3.56602			0.116872
$932$	−17.5806	+	10.1502i	−0.575871	+	0.332480i
$933$		−	3.54699i		−	0.116123i
$934$	−18.0967	+	31.3444i	−0.592141	+	1.02562i
$935$	1.78235	+	0.494360i	0.0582889	+	0.0161673i
$936$	3.30944			0.108172
$937$	−11.9641	−	6.90746i	−0.390849	−	0.225657i	0.291679	−	0.956516i	$-0.405786\pi$
$937$	−11.9641	−	6.90746i	−0.390849	−	0.225657i	−0.682528	+	0.730859i	$0.739120\pi$
$938$	14.0790	−	8.12850i	0.459695	−	0.265405i
$939$	14.3912			0.469639
$940$	−20.1177	+	19.7682i	−0.656168	+	0.644767i
$941$	6.76832	−	11.7231i	0.220641	−	0.382161i	−0.734362	−	0.678758i	$-0.762518\pi$
$941$	6.76832	−	11.7231i	0.220641	−	0.382161i	0.955003	+	0.296597i	$0.0958518\pi$
$942$	9.03871	+	5.21850i	0.294497	+	0.170028i
$943$	16.9293	−	9.77411i	0.551292	−	0.318289i
$944$	3.27626	+	5.67465i	0.106633	+	0.184694i
$945$	5.00546	+	5.09398i	0.162828	+	0.165707i
$946$	−1.13129	+	1.95945i	−0.0367813	+	0.0637071i
$947$	22.4801	+	12.9789i	0.730507	+	0.421758i	0.818607	−	0.574353i	$-0.194746\pi$
$947$	22.4801	+	12.9789i	0.730507	+	0.421758i	−0.0881009	+	0.996112i	$0.528080\pi$
$948$		−	4.25476i		−	0.138188i
$949$	−2.05694	−	3.56273i	−0.0667711	−	0.115651i
$950$	−2.70040	−	4.87251i	−0.0876126	−	0.158085i
$951$	−24.5612			−0.796452
$952$			0.619114i			0.0200656i
$953$	−5.09358	−	2.94078i	−0.164997	−	0.0952611i	0.415228	−	0.909718i	$-0.363702\pi$
$953$	−5.09358	−	2.94078i	−0.164997	−	0.0952611i	−0.580225	+	0.814456i	$0.697035\pi$
$954$	−7.55107			−0.244475
$955$	36.7769	−	9.50969i	1.19007	−	0.307726i
$956$	−11.3396			−0.366748
$957$	−15.4984	+	8.94801i	−0.500993	+	0.289248i
$958$	−4.41978	+	2.55176i	−0.142797	+	0.0824437i
$959$	28.0254	+	48.5414i	0.904987	+	1.56748i
$960$	−1.59494	+	1.56722i	−0.0514763	+	0.0505818i
$961$	−29.9138			−0.964960
$962$	4.83906	+	19.5403i	0.156018	+	0.630004i
$963$		−	2.99608i		−	0.0965472i
$964$	6.90124	−	11.9533i	0.222274	−	0.384990i
$965$	−11.3965	−	44.0739i	−0.366867	−	1.41879i
$966$	5.49936	+	9.52518i	0.176939	+	0.306468i
$967$	46.1224	−	26.6288i	1.48319	−	0.856323i	0.483377	−	0.875412i	$-0.339410\pi$
$967$	46.1224	−	26.6288i	1.48319	−	0.856323i	0.999818	+	0.0190892i	$0.00607664\pi$
$968$		−	7.20909i		−	0.231709i
$969$	−0.107987	−	0.187039i	−0.00346905	−	0.00600857i
$970$	10.2206	−	36.8490i	0.328164	−	1.18315i
$971$	−4.84667	+	8.39467i	−0.155537	+	0.269398i	−0.933254	−	0.359216i	$-0.883044\pi$
$971$	−4.84667	+	8.39467i	−0.155537	+	0.269398i	0.777717	+	0.628614i	$0.216377\pi$
$972$			1.00000i			0.0320750i
$973$			49.7937i			1.59631i
$974$	−9.46046	+	16.3860i	−0.303133	+	0.525041i
$975$	0.290024	−	16.5447i	0.00928820	−	0.529853i
$976$	−5.30264			−0.169733
$977$	−45.4867	−	26.2618i	−1.45525	−	0.840189i	−0.456478	−	0.889735i	$-0.650889\pi$
$977$	−45.4867	−	26.2618i	−1.45525	−	0.840189i	−0.998772	+	0.0495457i	$0.984223\pi$
$978$	−3.23228	−	1.86616i	−0.103357	−	0.0596732i
$979$	−25.9888	+	45.0140i	−0.830607	+	1.43865i
$980$	−6.92898	+	1.79168i	−0.221338	+	0.0572331i
$981$	2.49564	+	4.32258i	0.0796797	+	0.138009i
$982$	23.6065	+	13.6292i	0.753313	+	0.434925i
$983$	12.2999	+	7.10136i	0.392306	+	0.226498i	0.683159	−	0.730270i	$-0.260606\pi$
$983$	12.2999	+	7.10136i	0.392306	+	0.226498i	−0.290853	+	0.956768i	$0.593939\pi$
$984$	−2.83824	+	4.91597i	−0.0904797	+	0.156715i
$985$	29.9306	+	8.30169i	0.953667	+	0.264514i
$986$	0.406480	+	0.704044i	0.0129450	+	0.0224213i
$987$	−34.8884	−	20.1428i	−1.11051	−	0.641153i
$988$		−	3.68723i		−	0.117306i
$989$	1.82594			0.0580616
$990$	−6.80592	+	6.68766i	−0.216306	+	0.212548i
$991$	−16.6891			−0.530146			−0.265073	−	0.964228i	$-0.585396\pi$
$991$	−16.6891			−0.530146			−0.265073	+	0.964228i	$0.585396\pi$
$992$	0.902598	−	0.521115i	0.0286575	−	0.0165454i
$993$			6.69185i			0.212360i
$994$	5.83890	+	10.1133i	0.185199	+	0.320773i
$995$	−9.91096	+	2.56275i	−0.314198	+	0.0812447i
$996$	8.32089	+	14.4122i	0.263657	+	0.456668i
$997$	15.6927	+	9.06016i	0.496991	+	0.286938i	0.727470	−	0.686139i	$-0.240696\pi$
$997$	15.6927	+	9.06016i	0.496991	+	0.286938i	−0.230479	+	0.973077i	$0.574029\pi$
$998$			1.18860i			0.0376246i
$999$	−5.90440	+	1.46220i	−0.186807	+	0.0462619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1009.3	✓	28
5.4	even	2	inner	1110.2.bb.d.1009.12	yes	28
37.26	even	3	inner	1110.2.bb.d.1099.12	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.3	✓	28	1.1	even	1	trivial
1110.2.bb.d.1009.12	yes	28	5.4	even	2	inner
1110.2.bb.d.1099.3	yes	28	185.174	even	6	inner
1110.2.bb.d.1099.12	yes	28	37.26	even	3	inner

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.16486 + 0.559786i) q^{5} +1.00000 q^{6} +(-2.76595 + 1.59692i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.16486 + 0.559786i) q^{5} +1.00000 q^{6} +(-2.76595 + 1.59692i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.15472 + 0.597644i) q^{10} -4.26721 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-2.86606 + 1.65472i) q^{13} +3.19385 q^{14} +(1.59494 - 1.56722i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.167875 + 0.0969230i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.557077 + 0.964886i) q^{19} +(-1.56722 - 1.59494i) q^{20} +(1.59692 - 2.76595i) q^{21} +(3.69551 + 2.13361i) q^{22} -3.44373i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.37328 - 2.42372i) q^{25} +3.30944 q^{26} +1.00000i q^{27} +(-2.76595 - 1.59692i) q^{28} -4.19385 q^{29} +(-2.16486 + 0.559786i) q^{30} +1.04223 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.69551 - 2.13361i) q^{33} +(-0.0969230 - 0.167875i) q^{34} +(5.09398 - 5.00546i) q^{35} +1.00000 q^{36} +(1.46220 + 5.90440i) q^{37} -1.11415i q^{38} +(1.65472 - 2.86606i) q^{39} +(0.559786 + 2.16486i) q^{40} +(2.83824 + 4.91597i) q^{41} +(-2.76595 + 1.59692i) q^{42} +0.530223i q^{43} +(-2.13361 - 3.69551i) q^{44} +(-0.597644 + 2.15472i) q^{45} +(-1.72186 + 2.98235i) q^{46} -12.6135i q^{47} -1.00000i q^{48} +(1.60033 - 2.77185i) q^{49} +(-4.99923 - 0.0876353i) q^{50} -0.193846 q^{51} +(-2.86606 - 1.65472i) q^{52} +(6.53942 + 3.77554i) q^{53} +(0.500000 - 0.866025i) q^{54} +(9.23794 - 2.38872i) q^{55} +(1.59692 + 2.76595i) q^{56} +(-0.964886 - 0.557077i) q^{57} +(3.63198 + 2.09692i) q^{58} +(3.27626 - 5.67465i) q^{59} +(2.15472 + 0.597644i) q^{60} +(2.65132 + 4.59222i) q^{61} +(-0.902598 - 0.521115i) q^{62} +3.19385i q^{63} -1.00000 q^{64} +(5.27834 - 5.18663i) q^{65} -4.26721 q^{66} +(4.40816 - 2.54505i) q^{67} +0.193846i q^{68} +(1.72186 + 2.98235i) q^{69} +(-6.91424 + 1.78787i) q^{70} +(1.82817 + 3.16649i) q^{71} +(-0.866025 - 0.500000i) q^{72} +1.24307i q^{73} +(1.68590 - 5.84446i) q^{74} +(-2.57551 + 4.28564i) q^{75} +(-0.557077 + 0.964886i) q^{76} +(11.8029 - 6.81441i) q^{77} +(-2.86606 + 1.65472i) q^{78} +(2.12738 + 3.68473i) q^{79} +(0.597644 - 2.15472i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.67647i q^{82} +(-14.4122 - 8.32089i) q^{83} +3.19385 q^{84} +(-0.417684 - 0.115851i) q^{85} +(0.265111 - 0.459186i) q^{86} +(3.63198 - 2.09692i) q^{87} +4.26721i q^{88} +(6.09036 - 10.5488i) q^{89} +(1.59494 - 1.56722i) q^{90} +(5.28492 - 9.15376i) q^{91} +(2.98235 - 1.72186i) q^{92} +(-0.902598 + 0.521115i) q^{93} +(-6.30676 + 10.9236i) q^{94} +(-1.74613 - 1.77700i) q^{95} +(-0.500000 + 0.866025i) q^{96} -17.1015i q^{97} +(-2.77185 + 1.60033i) q^{98} +(-2.13361 + 3.69551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more