LMFDB - Embedded newform 770.2.o.a.439.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.12
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.0752187 - 0.130283i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.125277 - 2.23256i) q^{5} +0.150437 q^{6} +(-2.53943 - 0.742498i) q^{7} +1.00000 q^{8} +(1.48868 - 2.57848i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0752187 - 0.130283i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.125277 - 2.23256i) q^{5} +0.150437 q^{6} +(-2.53943 - 0.742498i) q^{7} +1.00000 q^{8} +(1.48868 - 2.57848i) q^{9} +(1.87081 + 1.22477i) q^{10} +(0.899444 + 3.19233i) q^{11} +(-0.0752187 + 0.130283i) q^{12} -2.51463i q^{13} +(1.91274 - 1.82796i) q^{14} +(-0.300286 + 0.151609i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.99073 + 1.14935i) q^{17} +(1.48868 + 2.57848i) q^{18} +(-3.16071 + 5.47452i) q^{19} +(-1.99609 + 1.00778i) q^{20} +(0.0942780 + 0.386693i) q^{21} +(-3.21436 - 0.817226i) q^{22} +(-4.94308 - 2.85389i) q^{23} +(-0.0752187 - 0.130283i) q^{24} +(-4.96861 - 0.559376i) q^{25} +(2.17773 + 1.25732i) q^{26} -0.899220 q^{27} +(0.626692 + 2.57046i) q^{28} -6.85099i q^{29} +(0.0188464 - 0.335860i) q^{30} +(1.82057 - 1.05111i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.348251 - 0.357305i) q^{33} -2.29870i q^{34} +(-1.97580 + 5.57640i) q^{35} -2.97737 q^{36} +(-9.79562 - 5.65550i) q^{37} +(-3.16071 - 5.47452i) q^{38} +(-0.327613 + 0.189147i) q^{39} +(0.125277 - 2.23256i) q^{40} +0.710102 q^{41} +(-0.382025 - 0.111699i) q^{42} -2.99747 q^{43} +(2.31492 - 2.37511i) q^{44} +(-5.57010 - 3.64659i) q^{45} +(4.94308 - 2.85389i) q^{46} +(-3.34066 + 5.78618i) q^{47} +0.150437 q^{48} +(5.89739 + 3.77104i) q^{49} +(2.96874 - 4.02326i) q^{50} +(0.299480 + 0.172905i) q^{51} +(-2.17773 + 1.25732i) q^{52} +(-3.78207 + 2.18358i) q^{53} +(0.449610 - 0.778747i) q^{54} +(7.23975 - 1.60813i) q^{55} +(-2.53943 - 0.742498i) q^{56} +0.950979 q^{57} +(5.93313 + 3.42550i) q^{58} +(7.75012 - 4.47453i) q^{59} +(0.281440 + 0.184251i) q^{60} +(-5.17631 + 8.96564i) q^{61} +2.10222i q^{62} +(-5.69492 + 5.44251i) q^{63} +1.00000 q^{64} +(-5.61405 - 0.315026i) q^{65} +(0.135310 + 0.480247i) q^{66} +(6.84041 - 3.94931i) q^{67} +(1.99073 + 1.14935i) q^{68} +0.858663i q^{69} +(-3.84140 - 4.49929i) q^{70} -11.7961 q^{71} +(1.48868 - 2.57848i) q^{72} +(11.5308 - 6.65729i) q^{73} +(9.79562 - 5.65550i) q^{74} +(0.300856 + 0.689399i) q^{75} +6.32143 q^{76} +(0.0862272 - 8.77454i) q^{77} -0.378295i q^{78} +(-7.29423 - 4.21133i) q^{79} +(1.87081 + 1.22477i) q^{80} +(-4.39841 - 7.61828i) q^{81} +(-0.355051 + 0.614966i) q^{82} -8.40993i q^{83} +(0.287747 - 0.274994i) q^{84} +(2.31659 + 4.58841i) q^{85} +(1.49873 - 2.59588i) q^{86} +(-0.892565 + 0.515323i) q^{87} +(0.899444 + 3.19233i) q^{88} +(3.02422 + 1.74604i) q^{89} +(5.94309 - 3.00055i) q^{90} +(-1.86711 + 6.38573i) q^{91} +5.70778i q^{92} +(-0.273882 - 0.158126i) q^{93} +(-3.34066 - 5.78618i) q^{94} +(11.8262 + 7.74230i) q^{95} +(-0.0752187 + 0.130283i) q^{96} +9.73846 q^{97} +(-6.21451 + 3.22177i) q^{98} +(9.57035 + 2.43318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.0752187	−	0.130283i	−0.0434275	−	0.0752187i	0.843495	−	0.537138i	$-0.180494\pi$
$3$	−0.0752187	−	0.130283i	−0.0434275	−	0.0752187i	−0.886922	+	0.461919i	$0.847161\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.125277	−	2.23256i	0.0560256	−	0.998429i
$5$	0.125277	−	2.23256i	0.0560256	−	0.998429i
$6$	0.150437			0.0614158
$7$	−2.53943	−	0.742498i	−0.959814	−	0.280638i
$7$	−2.53943	−	0.742498i	−0.959814	−	0.280638i
$8$	1.00000			0.353553
$9$	1.48868	−	2.57848i	0.496228	−	0.859492i
$10$	1.87081	+	1.22477i	0.591603	+	0.387307i
$11$	0.899444	+	3.19233i	0.271193	+	0.962525i
$11$	0.899444	+	3.19233i	0.271193	+	0.962525i
$12$	−0.0752187	+	0.130283i	−0.0217138	+	0.0376094i
$13$		−	2.51463i		−	0.697433i	−0.937228	−	0.348717i	$-0.886618\pi$
$13$		−	2.51463i		−	0.697433i	0.937228	−	0.348717i	$-0.113382\pi$
$14$	1.91274	−	1.82796i	0.511200	−	0.488543i
$15$	−0.300286	+	0.151609i	−0.0775336	+	0.0391452i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.99073	+	1.14935i	−0.482823	+	0.278758i	−0.721592	−	0.692318i	$-0.756589\pi$
$17$	−1.99073	+	1.14935i	−0.482823	+	0.278758i	0.238769	+	0.971076i	$0.423256\pi$
$18$	1.48868	+	2.57848i	0.350886	+	0.607753i
$19$	−3.16071	+	5.47452i	−0.725118	+	1.25594i	0.233808	+	0.972283i	$0.424881\pi$
$19$	−3.16071	+	5.47452i	−0.725118	+	1.25594i	−0.958926	+	0.283658i	$0.908452\pi$
$20$	−1.99609	+	1.00778i	−0.446339	+	0.225348i
$21$	0.0942780	+	0.386693i	0.0205731	+	0.0843834i
$22$	−3.21436	−	0.817226i	−0.685305	−	0.174233i
$23$	−4.94308	−	2.85389i	−1.03070	−	0.595077i	−0.113517	−	0.993536i	$-0.536212\pi$
$23$	−4.94308	−	2.85389i	−1.03070	−	0.595077i	−0.917186	+	0.398459i	$0.869545\pi$
$24$	−0.0752187	−	0.130283i	−0.0153540	−	0.0265938i
$25$	−4.96861	−	0.559376i	−0.993722	−	0.111875i
$26$	2.17773	+	1.25732i	0.427089	+	0.246580i
$27$	−0.899220			−0.173055
$28$	0.626692	+	2.57046i	0.118434	+	0.485771i
$29$		−	6.85099i		−	1.27220i	−0.771608	−	0.636099i	$-0.780547\pi$
$29$		−	6.85099i		−	1.27220i	0.771608	−	0.636099i	$-0.219453\pi$
$30$	0.0188464	−	0.335860i	0.00344086	−	0.0613194i
$31$	1.82057	−	1.05111i	0.326985	−	0.188785i	−0.327517	−	0.944845i	$-0.606212\pi$
$31$	1.82057	−	1.05111i	0.326985	−	0.188785i	0.654502	+	0.756061i	$0.272879\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.348251	−	0.357305i	0.0606227	−	0.0621989i
$34$		−	2.29870i		−	0.394224i
$35$	−1.97580	+	5.57640i	−0.333971	+	0.942583i
$36$	−2.97737			−0.496228
$37$	−9.79562	−	5.65550i	−1.61039	−	0.929759i	−0.989279	−	0.146036i	$-0.953349\pi$
$37$	−9.79562	−	5.65550i	−1.61039	−	0.929759i	−0.621110	−	0.783723i	$-0.713318\pi$
$38$	−3.16071	−	5.47452i	−0.512736	−	0.888084i
$39$	−0.327613	+	0.189147i	−0.0524600	+	0.0302878i
$40$	0.125277	−	2.23256i	0.0198080	−	0.352998i
$41$	0.710102			0.110899			0.0554496	−	0.998461i	$-0.482341\pi$
$41$	0.710102			0.110899			0.0554496	+	0.998461i	$0.482341\pi$
$42$	−0.382025	−	0.111699i	−0.0589477	−	0.0172356i
$43$	−2.99747			−0.457109			−0.228555	−	0.973531i	$-0.573400\pi$
$43$	−2.99747			−0.457109			−0.228555	+	0.973531i	$0.573400\pi$
$44$	2.31492	−	2.37511i	0.348987	−	0.358061i
$45$	−5.57010	−	3.64659i	−0.830341	−	0.543602i
$46$	4.94308	−	2.85389i	0.728818	−	0.420783i
$47$	−3.34066	+	5.78618i	−0.487285	+	0.844002i	−0.999893	−	0.0146208i	$-0.995346\pi$
$47$	−3.34066	+	5.78618i	−0.487285	+	0.844002i	0.512608	+	0.858622i	$0.328679\pi$
$48$	0.150437			0.0217138
$49$	5.89739	+	3.77104i	0.842485	+	0.538720i
$50$	2.96874	−	4.02326i	0.419843	−	0.568974i
$51$	0.299480	+	0.172905i	0.0419357	+	0.0242116i
$52$	−2.17773	+	1.25732i	−0.301997	+	0.174358i
$53$	−3.78207	+	2.18358i	−0.519507	+	0.299938i	−0.736733	−	0.676184i	$-0.763633\pi$
$53$	−3.78207	+	2.18358i	−0.519507	+	0.299938i	0.217226	+	0.976121i	$0.430299\pi$
$54$	0.449610	−	0.778747i	0.0611842	−	0.105974i
$55$	7.23975	−	1.60813i	0.976207	−	0.216841i
$56$	−2.53943	−	0.742498i	−0.339345	−	0.0992204i
$57$	0.950979			0.125960
$58$	5.93313	+	3.42550i	0.779059	+	0.449790i
$59$	7.75012	−	4.47453i	1.00898	−	0.582535i	0.0980868	−	0.995178i	$-0.468728\pi$
$59$	7.75012	−	4.47453i	1.00898	−	0.582535i	0.910893	+	0.412643i	$0.135394\pi$
$60$	0.281440	+	0.184251i	0.0363338	+	0.0237868i
$61$	−5.17631	+	8.96564i	−0.662759	+	1.14793i	0.317129	+	0.948382i	$0.397281\pi$
$61$	−5.17631	+	8.96564i	−0.662759	+	1.14793i	−0.979888	+	0.199550i	$0.936052\pi$
$62$			2.10222i			0.266982i
$63$	−5.69492	+	5.44251i	−0.717493	+	0.685692i
$64$	1.00000			0.125000
$65$	−5.61405	−	0.315026i	−0.696338	−	0.0390741i
$66$	0.135310	+	0.480247i	0.0166555	+	0.0591143i
$67$	6.84041	−	3.94931i	0.835689	−	0.482485i	−0.0201077	−	0.999798i	$-0.506401\pi$
$67$	6.84041	−	3.94931i	0.835689	−	0.482485i	0.855796	+	0.517313i	$0.173068\pi$
$68$	1.99073	+	1.14935i	0.241412	+	0.139379i
$69$			0.858663i			0.103371i
$70$	−3.84140	−	4.49929i	−0.459135	−	0.537768i
$71$	−11.7961			−1.39994			−0.699969	−	0.714173i	$-0.746803\pi$
$71$	−11.7961			−1.39994			−0.699969	+	0.714173i	$0.746803\pi$
$72$	1.48868	−	2.57848i	0.175443	−	0.303876i
$73$	11.5308	−	6.65729i	1.34957	−	0.779177i	0.361385	−	0.932417i	$-0.382304\pi$
$73$	11.5308	−	6.65729i	1.34957	−	0.779177i	0.988189	+	0.153240i	$0.0489706\pi$
$74$	9.79562	−	5.65550i	1.13872	−	0.657439i
$75$	0.300856	+	0.689399i	0.0347398	+	0.0796050i
$76$	6.32143			0.725118
$77$	0.0862272	−	8.77454i	0.00982650	−	0.999952i
$78$		−	0.378295i		−	0.0428334i
$79$	−7.29423	−	4.21133i	−0.820665	−	0.473811i	0.0299808	−	0.999550i	$-0.490455\pi$
$79$	−7.29423	−	4.21133i	−0.820665	−	0.473811i	−0.850646	+	0.525739i	$0.823789\pi$
$80$	1.87081	+	1.22477i	0.209163	+	0.136934i
$81$	−4.39841	−	7.61828i	−0.488713	−	0.846475i
$82$	−0.355051	+	0.614966i	−0.0392088	+	0.0679116i
$83$		−	8.40993i		−	0.923110i	−0.887112	−	0.461555i	$-0.847292\pi$
$83$		−	8.40993i		−	0.923110i	0.887112	−	0.461555i	$-0.152708\pi$
$84$	0.287747	−	0.274994i	0.0313958	−	0.0300043i
$85$	2.31659	+	4.58841i	0.251270	+	0.497683i
$86$	1.49873	−	2.59588i	0.161613	−	0.279921i
$87$	−0.892565	+	0.515323i	−0.0956931	+	0.0552484i
$88$	0.899444	+	3.19233i	0.0958811	+	0.340304i
$89$	3.02422	+	1.74604i	0.320567	+	0.185080i	0.651645	−	0.758524i	$-0.274079\pi$
$89$	3.02422	+	1.74604i	0.320567	+	0.185080i	−0.331078	+	0.943603i	$0.607412\pi$
$90$	5.94309	−	3.00055i	0.626457	−	0.316285i
$91$	−1.86711	+	6.38573i	−0.195726	+	0.669406i
$92$			5.70778i			0.595077i
$93$	−0.273882	−	0.158126i	−0.0284003	−	0.0163969i
$94$	−3.34066	−	5.78618i	−0.344562	−	0.596799i
$95$	11.8262	+	7.74230i	1.21334	+	0.794344i
$96$	−0.0752187	+	0.130283i	−0.00767698	+	0.0132969i
$97$	9.73846			0.988791			0.494395	−	0.869237i	$-0.335390\pi$
$97$	9.73846			0.988791			0.494395	+	0.869237i	$0.335390\pi$
$98$	−6.21451	+	3.22177i	−0.627761	+	0.325448i
$99$	9.57035	+	2.43318i	0.961856	+	0.244544i
$100$	1.99987	+	4.58263i	0.199987	+	0.458263i
$101$	−9.39320	−	16.2695i	−0.934658	−	1.61888i	−0.775243	−	0.631664i	$-0.782372\pi$
$101$	−9.39320	−	16.2695i	−0.934658	−	1.61888i	−0.159416	−	0.987212i	$-0.550961\pi$
$102$	−0.299480	+	0.172905i	−0.0296530	+	0.0171202i
$103$	2.31245	−	4.00529i	0.227853	−	0.394653i	−0.729319	−	0.684174i	$-0.760163\pi$
$103$	2.31245	−	4.00529i	0.227853	−	0.394653i	0.957172	+	0.289521i	$0.0934961\pi$
$104$		−	2.51463i		−	0.246580i
$105$	0.875125	−	0.162037i	0.0854034	−	0.0158132i
$106$		−	4.36716i		−	0.424176i
$107$	3.71349	−	6.43195i	0.358996	−	0.621800i	−0.628797	−	0.777569i	$-0.716452\pi$
$107$	3.71349	−	6.43195i	0.358996	−	0.621800i	0.987793	+	0.155770i	$0.0497858\pi$
$108$	0.449610	+	0.778747i	0.0432637	+	0.0749350i
$109$	−0.976031	+	0.563512i	−0.0934868	+	0.0539746i	−0.546015	−	0.837776i	$-0.683856\pi$
$109$	−0.976031	+	0.563512i	−0.0934868	+	0.0539746i	0.452528	+	0.891750i	$0.350522\pi$
$110$	−2.22719	+	7.07387i	−0.212354	+	0.674467i
$111$			1.70160i			0.161509i
$112$	1.91274	−	1.82796i	0.180737	−	0.172726i
$113$			13.0798i			1.23045i	0.788353	+	0.615223i	$0.210934\pi$
$113$			13.0798i			1.23045i	−0.788353	+	0.615223i	$0.789066\pi$
$114$	−0.475490	+	0.823572i	−0.0445337	+	0.0771346i
$115$	−6.99072	+	10.6782i	−0.651888	+	0.995745i
$116$	−5.93313	+	3.42550i	−0.550878	+	0.318049i
$117$	−6.48392	−	3.74349i	−0.599438	−	0.346086i
$118$			8.94907i			0.823828i
$119$	5.90871	−	1.44058i	0.541651	−	0.132057i
$120$	−0.300286	+	0.151609i	−0.0274123	+	0.0138399i
$121$	−9.38200	+	5.74265i	−0.852909	+	0.522059i
$122$	−5.17631	−	8.96564i	−0.468641	−	0.811711i
$123$	−0.0534129	−	0.0925139i	−0.00481608	−	0.00834170i
$124$	−1.82057	−	1.05111i	−0.163492	−	0.0943923i
$125$	−1.87129	+	11.0226i	−0.167373	+	0.985894i
$126$	−1.86589	−	7.65320i	−0.166227	−	0.681801i
$127$	−5.56609			−0.493911			−0.246955	−	0.969027i	$-0.579430\pi$
$127$	−5.56609			−0.493911			−0.246955	+	0.969027i	$0.579430\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.225466	+	0.390518i	0.0198511	+	0.0343832i
$130$	3.07985	−	4.70440i	0.270121	−	0.412603i
$131$	−4.48765	+	7.77284i	−0.392088	+	0.679117i	−0.992725	−	0.120406i	$-0.961581\pi$
$131$	−4.48765	+	7.77284i	−0.392088	+	0.679117i	0.600637	+	0.799522i	$0.294914\pi$
$132$	−0.483561	−	0.122941i	−0.0420886	−	0.0107007i
$133$	12.0912	−	11.5553i	1.04844	−	1.00197i
$134$			7.89862i			0.682337i
$135$	−0.112652	+	2.00756i	−0.00969551	+	0.172783i
$136$	−1.99073	+	1.14935i	−0.170704	+	0.0985559i
$137$	−5.60178	+	3.23419i	−0.478593	+	0.276316i	−0.719830	−	0.694151i	$-0.755780\pi$
$137$	−5.60178	+	3.23419i	−0.478593	+	0.276316i	0.241237	+	0.970466i	$0.422447\pi$
$138$	−0.743624	−	0.429332i	−0.0633015	−	0.0365471i
$139$	15.0603			1.27740			0.638698	−	0.769457i	$-0.279473\pi$
$139$	15.0603			1.27740			0.638698	+	0.769457i	$0.279473\pi$
$140$	5.81720	−	1.07711i	0.491643	−	0.0910321i
$141$	1.00512			0.0846463
$142$	5.89804	−	10.2157i	0.494953	−	0.857283i
$143$	8.02754	−	2.26177i	0.671297	−	0.189139i
$144$	1.48868	+	2.57848i	0.124057	+	0.214873i
$145$	−15.2952	−	0.858272i	−1.27020	−	0.0712756i
$146$			13.3146i			1.10192i
$147$	0.0477067	−	1.05198i	0.00393478	−	0.0867659i
$148$			11.3110i			0.929759i
$149$	−10.8989	−	6.29248i	−0.892872	−	0.515500i	−0.0179911	−	0.999838i	$-0.505727\pi$
$149$	−10.8989	−	6.29248i	−0.892872	−	0.515500i	−0.874881	+	0.484338i	$0.839060\pi$
$150$	−0.747465	−	0.0841511i	−0.0610303	−	0.00687091i
$151$	15.4680	−	8.93044i	1.25877	−	0.726749i	0.285932	−	0.958250i	$-0.407697\pi$
$151$	15.4680	−	8.93044i	1.25877	−	0.726749i	0.972835	+	0.231501i	$0.0743637\pi$
$152$	−3.16071	+	5.47452i	−0.256368	+	0.444042i
$153$			6.84407i			0.553311i
$154$	7.55586	+	4.46195i	0.608869	+	0.359554i
$155$	−2.11858	−	4.19621i	−0.170169	−	0.337048i
$156$	0.327613	+	0.189147i	0.0262300	+	0.0151439i
$157$	10.7967	+	18.7004i	0.861670	+	1.49246i	0.870316	+	0.492494i	$0.163915\pi$
$157$	10.7967	+	18.7004i	0.861670	+	1.49246i	−0.00864568	+	0.999963i	$0.502752\pi$
$158$	7.29423	−	4.21133i	0.580298	−	0.335035i
$159$	0.568965	+	0.328492i	0.0451218	+	0.0260511i
$160$	−1.99609	+	1.00778i	−0.157805	+	0.0796724i
$161$	10.4336	+	10.9175i	0.822282	+	0.860417i
$162$	8.79683			0.691144
$163$	−1.09053	−	0.629619i	−0.0854170	−	0.0493155i	0.456683	−	0.889629i	$-0.349037\pi$
$163$	−1.09053	−	0.629619i	−0.0854170	−	0.0493155i	−0.542100	+	0.840314i	$0.682371\pi$
$164$	−0.355051	−	0.614966i	−0.0277248	−	0.0480208i
$165$	−0.754076	−	0.822251i	−0.0587047	−	0.0640122i
$166$	7.28322	+	4.20497i	0.565287	+	0.326369i
$167$			5.74722i			0.444733i	0.974963	+	0.222366i	$0.0713781\pi$
$167$			5.74722i			0.444733i	−0.974963	+	0.222366i	$0.928622\pi$
$168$	0.0942780	+	0.386693i	0.00727370	+	0.0298340i
$169$	6.67663			0.513587
$170$	−5.13197	−	0.287974i	−0.393604	−	0.0220866i
$171$	9.41061	+	16.2997i	0.719648	+	1.24647i
$172$	1.49873	+	2.59588i	0.114277	+	0.197934i
$173$	−1.41797	−	0.818664i	−0.107806	−	0.0622418i	0.445128	−	0.895467i	$-0.353158\pi$
$173$	−1.41797	−	0.818664i	−0.107806	−	0.0622418i	−0.552934	+	0.833225i	$0.686492\pi$
$174$		−	1.03065i		−	0.0781330i
$175$	12.2021	+	5.10968i	0.922392	+	0.386255i
$176$	−3.21436	−	0.817226i	−0.242292	−	0.0616007i
$177$	−1.16591	−	0.673137i	−0.0876350	−	0.0505961i
$178$	−3.02422	+	1.74604i	−0.226675	+	0.130871i
$179$	−9.81605	−	17.0019i	−0.733686	−	1.27078i	−0.955297	−	0.295646i	$-0.904465\pi$
$179$	−9.81605	−	17.0019i	−0.733686	−	1.27078i	0.221612	−	0.975135i	$-0.428868\pi$
$180$	−0.372996	+	6.64714i	−0.0278015	+	0.495449i
$181$		−	3.38062i		−	0.251279i	−0.992076	−	0.125640i	$-0.959902\pi$
$181$		−	3.38062i		−	0.251279i	0.992076	−	0.125640i	$-0.0400983\pi$
$182$	−4.59665	−	4.80983i	−0.340726	−	0.356528i
$183$	1.55742			0.115128
$184$	−4.94308	−	2.85389i	−0.364409	−	0.210391i
$185$	−13.8534	+	21.1608i	−1.01852	+	1.55577i
$186$	0.273882	−	0.158126i	0.0200820	−	0.0115944i
$187$	−5.45966	−	5.32131i	−0.399250	−	0.389132i
$188$	6.68131			0.487285
$189$	2.28350	+	0.667669i	0.166101	+	0.0485658i
$190$	−12.6181	+	6.37064i	−0.915416	+	0.462175i
$191$	−2.09173	+	3.62298i	−0.151352	+	0.262150i	−0.931725	−	0.363165i	$-0.881696\pi$
$191$	−2.09173	+	3.62298i	−0.151352	+	0.262150i	0.780373	+	0.625315i	$0.215029\pi$
$192$	−0.0752187	−	0.130283i	−0.00542844	−	0.00940234i
$193$	−4.48341	−	7.76550i	−0.322723	−	0.558973i	0.658326	−	0.752733i	$-0.271265\pi$
$193$	−4.48341	−	7.76550i	−0.322723	−	0.558973i	−0.981049	+	0.193760i	$0.937932\pi$
$194$	−4.86923	+	8.43375i	−0.349590	+	0.605508i
$195$	0.381240	+	0.755110i	0.0273011	+	0.0540745i
$196$	0.317120	−	6.99281i	0.0226514	−	0.499487i
$197$	19.3704			1.38009			0.690044	−	0.723768i	$-0.257591\pi$
$197$	19.3704			1.38009			0.690044	+	0.723768i	$0.257591\pi$
$198$	−6.89237	+	7.07157i	−0.489820	+	0.502555i
$199$	14.4670	−	8.35255i	1.02554	−	0.592097i	0.109837	−	0.993950i	$-0.464967\pi$
$199$	14.4670	−	8.35255i	1.02554	−	0.592097i	0.915704	+	0.401853i	$0.131634\pi$
$200$	−4.96861	−	0.559376i	−0.351334	−	0.0395539i
$201$	−1.02905	−	0.594124i	−0.0725838	−	0.0419063i
$202$	18.7864			1.32181
$203$	−5.08685	+	17.3976i	−0.357027	+	1.22107i
$204$		−	0.345810i		−	0.0242116i
$205$	0.0889594	−	1.58534i	0.00621320	−	0.110725i
$206$	2.31245	+	4.00529i	0.161116	+	0.279062i
$207$	−14.7174	+	8.49708i	−1.02293	+	0.590588i
$208$	2.17773	+	1.25732i	0.150999	+	0.0871792i
$209$	−20.3194	−	5.16603i	−1.40552	−	0.357342i
$210$	−0.297234	+	0.838899i	−0.0205111	+	0.0578895i
$211$			18.4793i			1.27217i	0.771620	+	0.636083i	$0.219447\pi$
$211$			18.4793i			1.27217i	−0.771620	+	0.636083i	$0.780553\pi$
$212$	3.78207	+	2.18358i	0.259754	+	0.149969i
$213$	0.887286	+	1.53682i	0.0607958	+	0.105301i
$214$	3.71349	+	6.43195i	0.253849	+	0.439679i
$215$	−0.375514	+	6.69201i	−0.0256098	+	0.456391i
$216$	−0.899220			−0.0611842
$217$	−5.40366	+	1.31744i	−0.366824	+	0.0894339i
$218$		−	1.12702i		−	0.0763316i
$219$	−1.73466	−	1.00151i	−0.117217	−	0.0676755i
$220$	−5.01256	−	5.46574i	−0.337947	−	0.368500i
$221$	2.89019	+	5.00596i	0.194415	+	0.336737i
$222$	−1.47363	−	0.850799i	−0.0989034	−	0.0571019i
$223$	8.16431			0.546723			0.273361	−	0.961911i	$-0.411865\pi$
$223$	8.16431			0.546723			0.273361	+	0.961911i	$0.411865\pi$
$224$	0.626692	+	2.57046i	0.0418726	+	0.171746i
$225$	−8.83903	+	11.9787i	−0.589269	+	0.798581i
$226$	−11.3275	−	6.53991i	−0.753491	−	0.435028i
$227$	−25.3374	+	14.6286i	−1.68171	+	0.970933i	−0.721177	+	0.692751i	$0.756398\pi$
$227$	−25.3374	+	14.6286i	−1.68171	+	0.970933i	−0.960528	+	0.278182i	$0.910268\pi$
$228$	−0.475490	−	0.823572i	−0.0314901	−	0.0545424i
$229$	6.32273	+	3.65043i	0.417818	+	0.241227i	0.694143	−	0.719837i	$-0.255783\pi$
$229$	6.32273	+	3.65043i	0.417818	+	0.241227i	−0.276325	+	0.961064i	$0.589117\pi$
$230$	−5.75221	−	11.3932i	−0.379290	−	0.751247i
$231$	−1.14966	+	0.648776i	−0.0756418	+	0.0426863i
$232$		−	6.85099i		−	0.449790i
$233$	9.93050	−	17.2001i	0.650569	−	1.12682i	−0.332416	−	0.943133i	$-0.607864\pi$
$233$	9.93050	−	17.2001i	0.650569	−	1.12682i	0.982985	−	0.183685i	$-0.0588027\pi$
$234$	6.48392	−	3.74349i	0.423867	−	0.244720i
$235$	12.4995	+	8.18308i	0.815376	+	0.533805i
$236$	−7.75012	−	4.47453i	−0.504490	−	0.291267i
$237$			1.26708i			0.0823058i
$238$	−1.70678	+	5.83738i	−0.110634	+	0.378381i
$239$		−	21.5398i		−	1.39329i	−0.717414	−	0.696647i	$-0.754674\pi$
$239$		−	21.5398i		−	1.39329i	0.717414	−	0.696647i	$-0.245326\pi$
$240$	0.0188464	−	0.335860i	0.00121653	−	0.0216797i
$241$	0.352616	+	0.610749i	0.0227140	+	0.0393418i	0.877159	−	0.480200i	$-0.159436\pi$
$241$	0.352616	+	0.610749i	0.0227140	+	0.0393418i	−0.854445	+	0.519542i	$0.826103\pi$
$242$	−0.282284	−	10.9964i	−0.0181459	−	0.706874i
$243$	−2.01052	+	3.48232i	−0.128975	+	0.223391i
$244$	10.3526			0.662759
$245$	9.15787	−	12.6938i	0.585075	−	0.810979i
$246$	0.106826			0.00681097
$247$	13.7664	+	7.94803i	0.875935	+	0.505721i
$248$	1.82057	−	1.05111i	0.115607	−	0.0667455i
$249$	−1.09567	+	0.632584i	−0.0694351	+	0.0400884i
$250$	−8.61023	−	7.13190i	−0.544559	−	0.451061i
$251$		−	3.87831i		−	0.244796i	−0.992481	−	0.122398i	$-0.960941\pi$
$251$		−	3.87831i		−	0.244796i	0.992481	−	0.122398i	$-0.0390585\pi$
$252$	7.56081	+	2.21069i	0.476287	+	0.139260i
$253$	4.66454	−	18.3469i	0.293257	−	1.15346i
$254$	2.78304	−	4.82037i	0.174624	−	0.302457i
$255$	0.423538	−	0.646946i	0.0265230	−	0.0405133i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.94552	−	17.2261i	0.620384	−	1.07454i	−0.369030	−	0.929418i	$-0.620310\pi$
$257$	9.94552	−	17.2261i	0.620384	−	1.07454i	0.989414	−	0.145120i	$-0.0463567\pi$
$258$	−0.450931			−0.0280737
$259$	20.6761	+	21.6350i	1.28475	+	1.34433i
$260$	2.53421	+	5.01943i	0.157165	+	0.311292i
$261$	−17.6651	−	10.1990i	−1.09344	−	0.631300i
$262$	−4.48765	−	7.77284i	−0.277248	−	0.480208i
$263$	−8.95455	−	15.5097i	−0.552161	−	0.956371i	−0.998118	−	0.0613168i	$-0.980470\pi$
$263$	−8.95455	−	15.5097i	−0.552161	−	0.956371i	0.445957	−	0.895054i	$-0.352863\pi$
$264$	0.348251	−	0.357305i	0.0214333	−	0.0219906i
$265$	4.40116	+	8.71723i	0.270361	+	0.535495i
$266$	3.96159	+	16.2490i	0.242901	+	0.996288i
$267$		−	0.525339i		−	0.0321502i
$268$	−6.84041	−	3.94931i	−0.417844	−	0.241243i
$269$	8.49686	−	4.90567i	0.518063	−	0.299104i	−0.218079	−	0.975931i	$-0.569979\pi$
$269$	8.49686	−	4.90567i	0.518063	−	0.299104i	0.736142	+	0.676827i	$0.236646\pi$
$270$	−1.68227	−	1.10134i	−0.102380	−	0.0670253i
$271$	7.77154	−	13.4607i	0.472087	−	0.817680i	−0.527402	−	0.849616i	$-0.676834\pi$
$271$	7.77154	−	13.4607i	0.472087	−	0.817680i	0.999490	+	0.0319361i	$0.0101673\pi$
$272$		−	2.29870i		−	0.139379i
$273$	0.972391	−	0.237074i	0.0588518	−	0.0143484i
$274$		−	6.46838i		−	0.390769i
$275$	−2.68327	−	16.3646i	−0.161807	−	0.986822i
$276$	0.743624	−	0.429332i	0.0447609	−	0.0258427i
$277$	14.3031	+	24.7737i	0.859388	+	1.48850i	0.872513	+	0.488591i	$0.162489\pi$
$277$	14.3031	+	24.7737i	0.859388	+	1.48850i	−0.0131248	+	0.999914i	$0.504178\pi$
$278$	−7.53014	+	13.0426i	−0.451628	+	0.782242i
$279$		−	6.25908i		−	0.374721i
$280$	−1.97580	+	5.57640i	−0.118077	+	0.333254i
$281$		−	28.9870i		−	1.72922i	−0.502445	−	0.864609i	$-0.667566\pi$
$281$		−	28.9870i		−	1.72922i	0.502445	−	0.864609i	$-0.332434\pi$
$282$	−0.502559	+	0.870459i	−0.0299270	+	0.0518351i
$283$	15.1298	−	8.73518i	0.899372	−	0.519252i	0.0223753	−	0.999750i	$-0.492877\pi$
$283$	15.1298	−	8.73518i	0.899372	−	0.519252i	0.876996	+	0.480497i	$0.159544\pi$
$284$	5.89804	+	10.2157i	0.349984	+	0.606191i
$285$	0.119136	−	2.12311i	0.00705700	−	0.125762i
$286$	−2.05502	+	8.08294i	−0.121516	+	0.477954i
$287$	−1.80325	−	0.527249i	−0.106443	−	0.0311225i
$288$	−2.97737			−0.175443
$289$	−5.85799	+	10.1463i	−0.344588	+	0.596844i
$290$	8.39090	−	12.8169i	0.492731	−	0.752635i
$291$	−0.732514	−	1.26875i	−0.0429407	−	0.0743755i
$292$	−11.5308	−	6.65729i	−0.674787	−	0.389588i
$293$		−	0.637578i		−	0.0372477i	−0.999827	−	0.0186239i	$-0.994071\pi$
$293$		−	0.637578i		−	0.0372477i	0.999827	−	0.0186239i	$-0.00592850\pi$
$294$	0.887189	+	0.567306i	0.0517419	+	0.0330859i
$295$	−9.01873	−	17.8631i	−0.525091	−	1.04003i
$296$	−9.79562	−	5.65550i	−0.569359	−	0.328719i
$297$	−0.808798	−	2.87061i	−0.0469312	−	0.166570i
$298$	10.8989	−	6.29248i	0.631356	−	0.364513i
$299$	−7.17648	+	12.4300i	−0.415026	+	0.718847i
$300$	0.446609	−	0.605248i	0.0257850	−	0.0349440i
$301$	7.61185	+	2.22561i	0.438740	+	0.128282i
$302$			17.8609i			1.02778i
$303$	−1.41309	+	2.44754i	−0.0811798	+	0.140608i
$304$	−3.16071	−	5.47452i	−0.181279	−	0.313985i
$305$	19.3678	+	12.6796i	1.10900	+	0.726032i
$306$	−5.92714	−	3.42204i	−0.338832	−	0.195625i
$307$			17.8871i			1.02087i	0.859917	+	0.510434i	$0.170515\pi$
$307$			17.8871i			1.02087i	−0.859917	+	0.510434i	$0.829485\pi$
$308$	−7.64209	+	4.31260i	−0.435448	+	0.245733i
$309$	−0.695759			−0.0395804
$310$	4.69332	+	0.263360i	0.266563	+	0.0149578i
$311$	−19.0018	+	10.9707i	−1.07749	+	0.622091i	−0.930219	−	0.367005i	$-0.880383\pi$
$311$	−19.0018	+	10.9707i	−1.07749	+	0.622091i	−0.147274	+	0.989096i	$0.547050\pi$
$312$	−0.327613	+	0.189147i	−0.0185474	+	0.0107084i
$313$	0.686648	−	1.18931i	0.0388117	−	0.0672238i	−0.845967	−	0.533235i	$-0.820976\pi$
$313$	0.686648	−	1.18931i	0.0388117	−	0.0672238i	0.884779	+	0.466011i	$0.154309\pi$
$314$	−21.5934			−1.21859
$315$	11.4373	+	13.3961i	0.644417	+	0.754782i
$316$			8.42265i			0.473811i
$317$	−3.93592	−	2.27240i	−0.221063	−	0.127631i	0.385379	−	0.922758i	$-0.374071\pi$
$317$	−3.93592	−	2.27240i	−0.221063	−	0.127631i	−0.606442	+	0.795127i	$0.707404\pi$
$318$	−0.568965	+	0.328492i	−0.0319060	+	0.0184209i
$319$	21.8707	−	6.16209i	1.22452	−	0.345011i
$320$	0.125277	−	2.23256i	0.00700320	−	0.124804i
$321$	−1.11729			−0.0623613
$322$	−14.6716	+	3.57702i	−0.817617	+	0.199340i
$323$		−	14.5311i		−	0.808530i
$324$	−4.39841	+	7.61828i	−0.244356	+	0.423238i
$325$	−1.40662	+	12.4942i	−0.0780255	+	0.693055i
$326$	1.09053	−	0.629619i	0.0603990	−	0.0348714i
$327$	0.146832	+	0.0847732i	0.00811980	+	0.00468797i
$328$	0.710102			0.0392088
$329$	12.7796	−	12.2132i	0.704561	−	0.673334i
$330$	1.08913	−	0.241923i	0.0599545	−	0.0133174i
$331$	8.20177	−	14.2059i	0.450810	−	0.780826i	−0.547627	−	0.836723i	$-0.684469\pi$
$331$	8.20177	−	14.2059i	0.450810	−	0.780826i	0.998437	+	0.0558972i	$0.0178019\pi$
$332$	−7.28322	+	4.20497i	−0.399718	+	0.230778i
$333$	−29.1652	+	16.8385i	−1.59824	+	0.922745i
$334$	−4.97724	−	2.87361i	−0.272342	−	0.157237i
$335$	−7.96011	−	15.7664i	−0.434907	−	0.861408i
$336$	−0.382025	−	0.111699i	−0.0208412	−	0.00609370i
$337$	10.0052			0.545019			0.272509	−	0.962153i	$-0.412146\pi$
$337$	10.0052			0.545019			0.272509	+	0.962153i	$0.412146\pi$
$338$	−3.33831	+	5.78213i	−0.181580	+	0.314506i
$339$	1.70407	−	0.983847i	0.0925525	−	0.0534352i
$340$	2.81538	−	4.30043i	0.152685	−	0.233224i
$341$	4.99299	+	4.86647i	0.270386	+	0.263534i
$342$	−18.8212			−1.01774
$343$	−12.1760	−	13.9551i	−0.657443	−	0.753504i
$344$	−2.99747			−0.161613
$345$	1.91701	+	0.107571i	0.103209	+	0.00579142i
$346$	1.41797	−	0.818664i	0.0762304	−	0.0440116i
$347$	11.3115	+	19.5921i	0.607234	+	1.05176i	0.991694	+	0.128619i	$0.0410545\pi$
$347$	11.3115	+	19.5921i	0.607234	+	1.05176i	−0.384460	+	0.923142i	$0.625612\pi$
$348$	0.892565	+	0.515323i	0.0478465	+	0.0276242i
$349$	5.52218			0.295596			0.147798	−	0.989018i	$-0.452782\pi$
$349$	5.52218			0.295596			0.147798	+	0.989018i	$0.452782\pi$
$350$	−10.5262	+	8.01249i	−0.562647	+	0.428285i
$351$			2.26121i			0.120694i
$352$	2.31492	−	2.37511i	0.123386	−	0.126594i
$353$	−15.4786	−	26.8097i	−0.823843	−	1.42694i	−0.902800	−	0.430060i	$-0.858492\pi$
$353$	−15.4786	−	26.8097i	−0.823843	−	1.42694i	0.0789574	−	0.996878i	$-0.474841\pi$
$354$	1.16591	−	0.673137i	0.0619673	−	0.0357768i
$355$	−1.47778	+	26.3354i	−0.0784323	+	1.39774i
$356$		−	3.49207i		−	0.185080i
$357$	−0.632128	−	0.661444i	−0.0334557	−	0.0350073i
$358$	19.6321			1.03759
$359$	10.3087	+	5.95171i	0.544070	+	0.314119i	0.746727	−	0.665131i	$-0.231624\pi$
$359$	10.3087	+	5.95171i	0.544070	+	0.314119i	−0.202657	+	0.979250i	$0.564958\pi$
$360$	−5.57010	−	3.64659i	−0.293570	−	0.192192i
$361$	−10.4802	−	18.1523i	−0.551591	−	0.955384i
$362$	2.92770	+	1.69031i	0.153877	+	0.0888407i
$363$	1.45387	+	0.790357i	0.0763084	+	0.0414830i
$364$	6.46376	−	1.57590i	0.338793	−	0.0825996i
$365$	−13.4182	−	26.5771i	−0.702342	−	1.39111i
$366$	−0.778711	+	1.34877i	−0.0407039	+	0.0705012i
$367$	1.17584	+	2.03662i	0.0613785	+	0.106311i	0.895082	−	0.445902i	$-0.147117\pi$
$367$	1.17584	+	2.03662i	0.0613785	+	0.106311i	−0.833703	+	0.552213i	$0.813784\pi$
$368$	4.94308	−	2.85389i	0.257676	−	0.148769i
$369$	1.05712	−	1.83098i	0.0550313	−	0.0953170i
$370$	−11.3991	−	22.5778i	−0.592609	−	1.17376i
$371$	11.2256	−	2.73686i	0.582804	−	0.142091i
$372$			0.316252i			0.0163969i
$373$	−1.20762	+	2.09166i	−0.0625284	+	0.108302i	−0.895595	−	0.444870i	$-0.853250\pi$
$373$	−1.20762	+	2.09166i	−0.0625284	+	0.108302i	0.833067	+	0.553173i	$0.186583\pi$
$374$	7.33822	−	2.06755i	0.379450	−	0.106911i
$375$	1.57681	−	0.585311i	0.0814263	−	0.0302253i
$376$	−3.34066	+	5.78618i	−0.172281	+	0.298400i
$377$	−17.2277			−0.887273
$378$	−1.71997	+	1.64374i	−0.0884657	+	0.0845448i
$379$	21.8665			1.12321			0.561604	−	0.827406i	$-0.310184\pi$
$379$	21.8665			1.12321			0.561604	+	0.827406i	$0.310184\pi$
$380$	0.791930	−	14.1129i	0.0406252	−	0.723979i
$381$	0.418674	+	0.725165i	0.0214493	+	0.0371513i
$382$	−2.09173	−	3.62298i	−0.107022	−	0.185368i
$383$	−0.897916	+	1.55524i	−0.0458814	+	0.0794688i	−0.888054	−	0.459739i	$-0.847943\pi$
$383$	−0.897916	+	1.55524i	−0.0458814	+	0.0794688i	0.842173	+	0.539208i	$0.181276\pi$
$384$	0.150437			0.00767698
$385$	−19.5788	−	1.29176i	−0.997831	−	0.0658340i
$386$	8.96683			0.456399
$387$	−4.46228	+	7.72890i	−0.226830	+	0.392882i
$388$	−4.86923	−	8.43375i	−0.247198	−	0.428159i
$389$	−11.6237	−	20.1329i	−0.589346	−	1.02078i	−0.994318	−	0.106448i	$-0.966052\pi$
$389$	−11.6237	−	20.1329i	−0.589346	−	1.02078i	0.404972	−	0.914329i	$-0.367281\pi$
$390$	−0.844564	−	0.0473916i	−0.0427662	−	0.00239977i
$391$	13.1205			0.663530
$392$	5.89739	+	3.77104i	0.297863	+	0.190466i
$393$	1.35022			0.0681097
$394$	−9.68522	+	16.7753i	−0.487934	+	0.845127i
$395$	−10.3158	+	15.7572i	−0.519045	+	0.792830i
$396$	−2.67798	−	9.50476i	−0.134573	−	0.477632i
$397$	9.25277	−	16.0263i	0.464383	−	0.804335i	−0.534790	−	0.844985i	$-0.679609\pi$
$397$	9.25277	−	16.0263i	0.464383	−	0.804335i	0.999173	+	0.0406495i	$0.0129427\pi$
$398$			16.7051i			0.837351i
$399$	−2.41494	−	0.706100i	−0.120898	−	0.0353492i
$400$	2.96874	−	4.02326i	0.148437	−	0.201163i
$401$	−0.501146	+	0.868010i	−0.0250260	+	0.0433463i	−0.878267	−	0.478170i	$-0.841300\pi$
$401$	−0.501146	+	0.868010i	−0.0250260	+	0.0433463i	0.853241	+	0.521517i	$0.174634\pi$
$402$	1.02905	−	0.594124i	0.0513245	−	0.0296322i
$403$	−2.64315	−	4.57807i	−0.131665	−	0.228050i
$404$	−9.39320	+	16.2695i	−0.467329	+	0.809438i
$405$	−17.5593	+	8.86531i	−0.872526	+	0.440521i
$406$	−12.5233	−	13.1041i	−0.621523	−	0.650348i
$407$	9.24364	−	36.3577i	0.458190	−	1.80218i
$408$	0.299480	+	0.172905i	0.0148265	+	0.00856008i
$409$	−19.4357	−	33.6637i	−0.961035	−	1.66456i	−0.719911	−	0.694066i	$-0.755818\pi$
$409$	−19.4357	−	33.6637i	−0.961035	−	1.66456i	−0.241123	−	0.970494i	$-0.577516\pi$
$410$	1.32847	+	0.869712i	0.0656083	+	0.0429520i
$411$	0.842718	+	0.486543i	0.0415682	+	0.0239994i
$412$	−4.62491			−0.227853
$413$	−23.0032	+	5.60831i	−1.13191	+	0.275967i
$414$		−	16.9942i		−	0.835217i
$415$	−18.7756	−	1.05357i	−0.921660	−	0.0517178i
$416$	−2.17773	+	1.25732i	−0.106772	+	0.0616450i
$417$	−1.13281	−	1.96209i	−0.0554742	−	0.0960841i
$418$	14.6336	−	15.0141i	0.715753	−	0.734363i
$419$		−	3.06449i		−	0.149710i	−0.997194	−	0.0748551i	$-0.976151\pi$
$419$		−	3.06449i		−	0.149710i	0.997194	−	0.0748551i	$-0.0238494\pi$
$420$	−0.577891	−	0.676862i	−0.0281982	−	0.0330275i
$421$	1.36943			0.0667418			0.0333709	−	0.999443i	$-0.489376\pi$
$421$	1.36943			0.0667418			0.0333709	+	0.999443i	$0.489376\pi$
$422$	−16.0035	−	9.23964i	−0.779040	−	0.449779i
$423$	9.94636	+	17.2276i	0.483609	+	0.837635i
$424$	−3.78207	+	2.18358i	−0.183674	+	0.106044i
$425$	10.5341	−	4.59710i	0.510978	−	0.222992i
$426$	−1.77457			−0.0859783
$427$	19.8018	−	18.9242i	0.958278	−	0.915806i
$428$	−7.42697			−0.358996
$429$	−0.898491	−	0.875722i	−0.0433795	−	0.0422803i
$430$	−5.60769	−	3.67121i	−0.270427	−	0.177041i
$431$	−4.27542	+	2.46842i	−0.205940	+	0.118899i	−0.599423	−	0.800432i	$-0.704603\pi$
$431$	−4.27542	+	2.46842i	−0.205940	+	0.118899i	0.393483	+	0.919332i	$0.371270\pi$
$432$	0.449610	−	0.778747i	0.0216319	−	0.0374675i
$433$	−21.0664			−1.01239			−0.506194	−	0.862420i	$-0.668948\pi$
$433$	−21.0664			−1.01239			−0.506194	+	0.862420i	$0.668948\pi$
$434$	1.56089	−	5.33843i	0.0749252	−	0.256253i
$435$	1.03867	+	2.05726i	0.0498004	+	0.0986381i
$436$	0.976031	+	0.563512i	0.0467434	+	0.0269873i
$437$	31.2473	−	18.0407i	1.49476	−	0.863002i
$438$	1.73466	−	1.00151i	0.0828852	−	0.0478538i
$439$	−0.332519	+	0.575940i	−0.0158703	+	0.0274881i	−0.873851	−	0.486193i	$-0.838385\pi$
$439$	−0.332519	+	0.575940i	−0.0158703	+	0.0274881i	0.857981	+	0.513681i	$0.171719\pi$
$440$	7.23975	−	1.60813i	0.345141	−	0.0766647i
$441$	18.5029	−	9.59241i	0.881090	−	0.456781i
$442$	−5.78038			−0.274945
$443$	−11.1850	−	6.45766i	−0.531415	−	0.306813i	0.210177	−	0.977663i	$-0.432596\pi$
$443$	−11.1850	−	6.45766i	−0.531415	−	0.306813i	−0.741592	+	0.670851i	$0.765929\pi$
$444$	1.47363	−	0.850799i	0.0699353	−	0.0403771i
$445$	4.27699	−	6.53301i	0.202749	−	0.309694i
$446$	−4.08216	+	7.07050i	−0.193296	+	0.334798i
$447$			1.89325i			0.0895476i
$448$	−2.53943	−	0.742498i	−0.119977	−	0.0350797i
$449$	5.67095			0.267629			0.133814	−	0.991006i	$-0.457277\pi$
$449$	5.67095			0.267629			0.133814	+	0.991006i	$0.457277\pi$
$450$	−5.95436	−	13.6442i	−0.280691	−	0.643193i
$451$	0.638697	+	2.26688i	0.0300751	+	0.106743i
$452$	11.3275	−	6.53991i	0.532799	−	0.307611i
$453$	−2.32696	−	1.34347i	−0.109330	−	0.0631218i
$454$		−	29.2572i		−	1.37311i
$455$	14.0226	+	4.96841i	0.657389	+	0.232923i
$456$	0.950979			0.0445337
$457$	7.46931	−	12.9372i	0.349400	−	0.605178i	−0.636743	−	0.771076i	$-0.719719\pi$
$457$	7.46931	−	12.9372i	0.349400	−	0.605178i	0.986143	+	0.165898i	$0.0530523\pi$
$458$	−6.32273	+	3.65043i	−0.295442	+	0.170573i
$459$	1.79011	−	1.03352i	0.0835550	−	0.0482405i
$460$	12.7429	+	0.715054i	0.594142	+	0.0333395i
$461$	25.3833			1.18222			0.591108	−	0.806592i	$-0.298691\pi$
$461$	25.3833			1.18222			0.591108	+	0.806592i	$0.298691\pi$
$462$	0.0129718	−	1.32002i	0.000603503	−	0.0614128i
$463$		−	1.50092i		−	0.0697538i	−0.999392	−	0.0348769i	$-0.988896\pi$
$463$		−	1.50092i		−	0.0697538i	0.999392	−	0.0348769i	$-0.0111039\pi$
$464$	5.93313	+	3.42550i	0.275439	+	0.159025i
$465$	−0.387336	+	0.591648i	−0.0179623	+	0.0274370i
$466$	9.93050	+	17.2001i	0.460022	+	0.796781i
$467$	−19.9490	+	34.5527i	−0.923130	+	1.59891i	−0.128588	+	0.991698i	$0.541045\pi$
$467$	−19.9490	+	34.5527i	−0.923130	+	1.59891i	−0.794541	+	0.607210i	$0.792289\pi$
$468$			7.48698i			0.346086i
$469$	−20.3031	+	4.95001i	−0.937509	+	0.228570i
$470$	−13.3365	+	6.73332i	−0.615166	+	0.310585i
$471$	1.62423	−	2.81324i	0.0748404	−	0.129627i
$472$	7.75012	−	4.47453i	0.356728	−	0.205957i
$473$	−2.69605	−	9.56892i	−0.123965	−	0.439979i
$474$	−1.09732	−	0.633541i	−0.0504018	−	0.0290995i
$475$	18.7667	−	25.4327i	0.861074	−	1.16693i
$476$	−4.20193	−	4.39680i	−0.192595	−	0.201527i
$477$			13.0026i			0.595350i
$478$	18.6540	+	10.7699i	0.853215	+	0.492604i
$479$	−0.799999	−	1.38564i	−0.0365529	−	0.0633114i	0.847170	−	0.531322i	$-0.178304\pi$
$479$	−0.799999	−	1.38564i	−0.0365529	−	0.0633114i	−0.883723	+	0.468010i	$0.844971\pi$
$480$	0.281440	+	0.184251i	0.0128459	+	0.00840989i
$481$	−14.2215	+	24.6324i	−0.648445	+	1.12314i
$482$	−0.705232			−0.0321224
$483$	0.637556	−	2.18051i	0.0290098	−	0.0992168i
$484$	9.66428	+	5.25372i	0.439286	+	0.238806i
$485$	1.22001	−	21.7416i	0.0553976	−	0.987237i
$486$	−2.01052	−	3.48232i	−0.0911989	−	0.157961i
$487$	1.38080	−	0.797207i	0.0625702	−	0.0361249i	−0.468389	−	0.883523i	$-0.655165\pi$
$487$	1.38080	−	0.797207i	0.0625702	−	0.0361249i	0.530959	+	0.847398i	$0.321832\pi$
$488$	−5.17631	+	8.96564i	−0.234321	+	0.405855i
$489$			0.189436i			0.00856661i
$490$	6.41425	+	14.2779i	0.289766	+	0.645008i
$491$		−	12.5303i		−	0.565484i	−0.959196	−	0.282742i	$-0.908756\pi$
$491$		−	12.5303i		−	0.565484i	0.959196	−	0.282742i	$-0.0912441\pi$
$492$	−0.0534129	+	0.0925139i	−0.00240804	+	0.00417085i
$493$	7.87418	+	13.6385i	0.354635	+	0.614247i
$494$	−13.7664	+	7.94803i	−0.619379	+	0.357599i
$495$	6.63116	−	21.0615i	0.298049	−	0.946645i
$496$			2.10222i			0.0943923i
$497$	29.9553	+	8.75857i	1.34368	+	0.392875i
$498$		−	1.26517i		−	0.0566936i
$499$	−1.40578	+	2.43488i	−0.0629314	+	0.109000i	−0.895775	−	0.444509i	$-0.853378\pi$
$499$	−1.40578	+	2.43488i	−0.0629314	+	0.109000i	0.832843	+	0.553509i	$0.186712\pi$
$500$	10.4815	−	3.89073i	0.468748	−	0.173999i
$501$	0.748762	−	0.432298i	0.0334522	−	0.0193137i
$502$	3.35871	+	1.93915i	0.149907	+	0.0865486i
$503$			33.6599i			1.50082i	0.660971	+	0.750411i	$0.270145\pi$
$503$			33.6599i			1.50082i	−0.660971	+	0.750411i	$0.729855\pi$
$504$	−5.69492	+	5.44251i	−0.253672	+	0.242429i
$505$	−37.4993	+	18.9326i	−1.66870	+	0.842492i
$506$	13.5566	+	13.2131i	0.602664	+	0.587392i
$507$	−0.502207	−	0.869849i	−0.0223038	−	0.0386313i
$508$	2.78304	+	4.82037i	0.123478	+	0.213870i
$509$	−37.2991	−	21.5346i	−1.65325	−	0.954505i	−0.975723	−	0.219008i	$-0.929718\pi$
$509$	−37.2991	−	21.5346i	−1.65325	−	0.954505i	−0.677528	−	0.735497i	$-0.736949\pi$
$510$	0.348502	+	0.690268i	0.0154319	+	0.0305656i
$511$	−34.2246	+	8.34415i	−1.51401	+	0.369123i
$512$	1.00000			0.0441942
$513$	2.84218	−	4.92280i	0.125485	−	0.217347i
$514$	9.94552	+	17.2261i	0.438678	+	0.759812i
$515$	−8.65233	−	5.66445i	−0.381267	−	0.249606i
$516$	0.225466	−	0.390518i	0.00992557	−	0.0171916i
$517$	−21.4762	−	5.46014i	−0.944521	−	0.240137i
$518$	−29.0745	+	7.08852i	−1.27746	+	0.311452i
$519$			0.246315i			0.0108120i
$520$	−5.61405	−	0.315026i	−0.246193	−	0.0138148i
$521$	−11.7930	+	6.80870i	−0.516661	+	0.298295i	−0.735568	−	0.677451i	$-0.763084\pi$
$521$	−11.7930	+	6.80870i	−0.516661	+	0.298295i	0.218906	+	0.975746i	$0.429751\pi$
$522$	17.6651	−	10.1990i	0.773182	−	0.446397i
$523$	−8.25059	−	4.76348i	−0.360773	−	0.208293i	0.308647	−	0.951177i	$-0.400124\pi$
$523$	−8.25059	−	4.76348i	−0.360773	−	0.208293i	−0.669420	+	0.742884i	$0.733457\pi$
$524$	8.97531			0.392088
$525$	−0.252124	−	1.97406i	−0.0110036	−	0.0861552i
$526$	17.9091			0.780874
$527$	−2.41618	+	4.18495i	−0.105251	+	0.182299i
$528$	0.135310	+	0.480247i	0.00588861	+	0.0209000i
$529$	4.78937	+	8.29543i	0.208233	+	0.360671i
$530$	−9.74992	−	0.547105i	−0.423510	−	0.0237647i
$531$		−	26.6447i		−	1.15628i
$532$	−16.0528	−	4.69365i	−0.695978	−	0.203495i
$533$		−	1.78564i		−	0.0773448i
$534$	0.454957	+	0.262669i	0.0196879	+	0.0113668i
$535$	−13.8945	−	9.09634i	−0.600710	−	0.393269i
$536$	6.84041	−	3.94931i	0.295461	−	0.170584i
$537$	−1.47670	+	2.55772i	−0.0637243	+	0.110374i
$538$			9.81133i			0.422997i
$539$	−6.73405	+	22.2183i	−0.290056	+	0.957010i
$540$	1.79492	−	0.906220i	0.0772412	−	0.0389975i
$541$	−12.8688	−	7.42981i	−0.553273	−	0.319433i	0.197168	−	0.980370i	$-0.436826\pi$
$541$	−12.8688	−	7.42981i	−0.553273	−	0.319433i	−0.750441	+	0.660937i	$0.770159\pi$
$542$	7.77154	+	13.4607i	0.333816	+	0.578187i
$543$	−0.440436	+	0.254286i	−0.0189009	+	0.0109124i
$544$	1.99073	+	1.14935i	0.0853519	+	0.0492779i
$545$	1.13580	+	2.24964i	0.0486522	+	0.0963639i
$546$	−0.280883	+	0.960652i	−0.0120207	+	0.0411121i
$547$	−26.3597			−1.12706			−0.563530	−	0.826096i	$-0.690557\pi$
$547$	−26.3597			−1.12706			−0.563530	+	0.826096i	$0.690557\pi$
$548$	5.60178	+	3.23419i	0.239296	+	0.138158i
$549$	15.4118	+	26.6940i	0.657759	+	1.13927i
$550$	15.5138	+	5.85852i	0.661510	+	0.249808i
$551$	37.5059	+	21.6540i	1.59780	+	0.922493i
$552$			0.858663i			0.0365471i
$553$	15.3963	+	16.1103i	0.654716	+	0.685080i
$554$	−28.6061			−1.21536
$555$	3.79891	+	0.213171i	0.161255	+	0.00904861i
$556$	−7.53014	−	13.0426i	−0.319349	−	0.553129i
$557$	0.427951	+	0.741233i	0.0181329	+	0.0314070i	0.874949	−	0.484214i	$-0.160894\pi$
$557$	0.427951	+	0.741233i	0.0181329	+	0.0314070i	−0.856817	+	0.515621i	$0.827561\pi$
$558$	5.42052	+	3.12954i	0.229469	+	0.132484i
$559$			7.53752i			0.318803i
$560$	−3.84140	−	4.49929i	−0.162329	−	0.190130i
$561$	−0.282605	+	1.11156i	−0.0119316	+	0.0469301i
$562$	25.1035	+	14.4935i	1.05893	+	0.611371i
$563$	13.2721	−	7.66263i	0.559351	−	0.322941i	−0.193534	−	0.981094i	$-0.561995\pi$
$563$	13.2721	−	7.66263i	0.559351	−	0.322941i	0.752885	+	0.658152i	$0.228662\pi$
$564$	−0.502559	−	0.870459i	−0.0211616	−	0.0366529i
$565$	29.2014	+	1.63860i	1.22851	+	0.0689365i
$566$			17.4704i			0.734334i
$567$	5.51290	+	22.6119i	0.231520	+	0.949610i
$568$	−11.7961			−0.494953
$569$	5.29602	+	3.05766i	0.222021	+	0.128184i	0.606886	−	0.794789i	$-0.292419\pi$
$569$	5.29602	+	3.05766i	0.222021	+	0.128184i	−0.384865	+	0.922973i	$0.625752\pi$
$570$	1.77910	+	1.16473i	0.0745184	+	0.0487853i
$571$	−0.258367	+	0.149168i	−0.0108123	+	0.00624250i	−0.505396	−	0.862887i	$-0.668654\pi$
$571$	−0.258367	+	0.149168i	−0.0108123	+	0.00624250i	0.494584	+	0.869130i	$0.335320\pi$
$572$	−5.97252	−	5.82117i	−0.249724	−	0.243395i
$573$	0.629348			0.0262914
$574$	1.35824	−	1.29804i	0.0566917	−	0.0541790i
$575$	22.9639	+	16.9449i	0.957659	+	0.706651i
$576$	1.48868	−	2.57848i	0.0620285	−	0.107437i
$577$	−6.51423	−	11.2830i	−0.271191	−	0.469716i	0.697976	−	0.716121i	$-0.254084\pi$
$577$	−6.51423	−	11.2830i	−0.271191	−	0.469716i	−0.969167	+	0.246405i	$0.920751\pi$
$578$	−5.85799	−	10.1463i	−0.243660	−	0.422032i
$579$	−0.674473	+	1.16822i	−0.0280301	+	0.0485496i
$580$	6.90433	+	13.6752i	0.286687	+	0.567831i
$581$	−6.24436	+	21.3564i	−0.259060	+	0.886014i
$582$	1.46503			0.0607274
$583$	−10.3725	−	10.1096i	−0.429584	−	0.418698i
$584$	11.5308	−	6.65729i	0.477147	−	0.275481i
$585$	−9.16984	+	14.0067i	−0.379126	+	0.579107i
$586$	0.552159	+	0.318789i	0.0228095	+	0.0131691i
$587$	12.5469			0.517865			0.258933	−	0.965895i	$-0.416629\pi$
$587$	12.5469			0.517865			0.258933	+	0.965895i	$0.416629\pi$
$588$	−0.934895	+	0.484675i	−0.0385544	+	0.0199877i
$589$			13.2890i			0.547564i
$590$	19.9793	+	1.12111i	0.822534	+	0.0461555i
$591$	−1.45702	−	2.52363i	−0.0599338	−	0.103808i
$592$	9.79562	−	5.65550i	0.402597	−	0.232440i
$593$	−3.60727	−	2.08266i	−0.148133	−	0.0855244i	0.424102	−	0.905615i	$-0.360590\pi$
$593$	−3.60727	−	2.08266i	−0.148133	−	0.0855244i	−0.572234	+	0.820090i	$0.693923\pi$
$594$	2.89042	+	0.734866i	0.118595	+	0.0301519i
$595$	−2.47594	−	13.3720i	−0.101504	−	0.548198i
$596$			12.5850i			0.515500i
$597$	−2.17638	−	1.25654i	−0.0890735	−	0.0514266i
$598$	−7.17648	−	12.4300i	−0.293468	−	0.508302i
$599$	1.73769	+	3.00977i	0.0710001	+	0.122976i	0.899340	−	0.437250i	$-0.144048\pi$
$599$	1.73769	+	3.00977i	0.0710001	+	0.122976i	−0.828340	+	0.560226i	$0.810714\pi$
$600$	0.300856	+	0.689399i	0.0122824	+	0.0281446i
$601$	−16.4938			−0.672798			−0.336399	−	0.941720i	$-0.609209\pi$
$601$	−16.4938			−0.672798			−0.336399	+	0.941720i	$0.609209\pi$
$602$	−5.73336	+	5.47925i	−0.233674	+	0.223318i
$603$		−	23.5171i		−	0.957691i
$604$	−15.4680	−	8.93044i	−0.629383	−	0.363374i
$605$	11.6454	+	21.6653i	0.473455	+	0.880818i
$606$	−1.41309	−	2.44754i	−0.0574028	−	0.0994245i
$607$	−2.49553	−	1.44079i	−0.101290	−	0.0584800i	0.448499	−	0.893783i	$-0.351959\pi$
$607$	−2.49553	−	1.44079i	−0.101290	−	0.0584800i	−0.549789	+	0.835303i	$0.685292\pi$
$608$	6.32143			0.256368
$609$	2.64923	−	0.645898i	0.107352	−	0.0261731i
$610$	−20.6648	+	10.4332i	−0.836692	+	0.422429i
$611$	14.5501	+	8.40052i	0.588635	+	0.339848i
$612$	5.92714	−	3.42204i	0.239590	−	0.138328i
$613$	−18.5685	−	32.1616i	−0.749974	−	1.29899i	−0.947835	−	0.318763i	$-0.896733\pi$
$613$	−18.5685	−	32.1616i	−0.749974	−	1.29899i	0.197861	−	0.980230i	$-0.436601\pi$
$614$	−15.4906	−	8.94353i	−0.625152	−	0.360931i
$615$	−0.213234	+	0.107657i	−0.00859842	+	0.00434117i
$616$	0.0862272	−	8.77454i	0.00347419	−	0.353536i
$617$		−	26.7017i		−	1.07497i	−0.843274	−	0.537484i	$-0.819375\pi$
$617$		−	26.7017i		−	1.07497i	0.843274	−	0.537484i	$-0.180625\pi$
$618$	0.347880	−	0.602545i	0.0139938	−	0.0242379i
$619$	−27.9452	+	16.1342i	−1.12321	+	0.648488i	−0.942219	−	0.334996i	$-0.891265\pi$
$619$	−27.9452	+	16.1342i	−1.12321	+	0.648488i	−0.180994	+	0.983484i	$0.557932\pi$
$620$	−2.57473	+	3.93285i	−0.103404	+	0.157947i
$621$	4.44492	+	2.56627i	0.178368	+	0.102981i
$622$		−	21.9414i		−	0.879770i
$623$	−6.38337	−	6.67942i	−0.255744	−	0.267605i
$624$		−	0.378295i		−	0.0151439i
$625$	24.3742	+	5.55864i	0.974968	+	0.222346i
$626$	0.686648	+	1.18931i	0.0274440	+	0.0475344i
$627$	0.855353	+	3.03584i	0.0341595	+	0.121240i
$628$	10.7967	−	18.7004i	0.430835	−	0.746228i
$629$	26.0006			1.03671
$630$	−17.3200	+	3.20694i	−0.690044	+	0.127768i
$631$	−3.18917			−0.126959			−0.0634793	−	0.997983i	$-0.520220\pi$
$631$	−3.18917			−0.126959			−0.0634793	+	0.997983i	$0.520220\pi$
$632$	−7.29423	−	4.21133i	−0.290149	−	0.167518i
$633$	2.40753	−	1.38999i	0.0956907	−	0.0552471i
$634$	3.93592	−	2.27240i	0.156315	−	0.0902487i
$635$	−0.697303	+	12.4266i	−0.0276716	+	0.493135i
$636$		−	0.656984i		−	0.0260511i
$637$	9.48278	−	14.8298i	0.375721	−	0.587577i
$638$	−5.59881	+	22.0216i	−0.221659	+	0.871843i
$639$	−17.5606	+	30.4159i	−0.694688	+	1.20324i
$640$	1.87081	+	1.22477i	0.0739503	+	0.0484133i
$641$	19.0098	+	32.9259i	0.750842	+	1.30050i	0.947415	+	0.320007i	$0.103685\pi$
$641$	19.0098	+	32.9259i	0.750842	+	1.30050i	−0.196573	+	0.980489i	$0.562981\pi$
$642$	0.558647	−	0.967605i	0.0220480	−	0.0381883i
$643$	12.9770			0.511762			0.255881	−	0.966708i	$-0.417635\pi$
$643$	12.9770			0.511762			0.255881	+	0.966708i	$0.417635\pi$
$644$	4.23801	−	14.4945i	0.167001	−	0.571163i
$645$	0.900098	−	0.454441i	0.0354413	−	0.0178936i
$646$	12.5843	+	7.26553i	0.495121	+	0.285858i
$647$	13.7688	+	23.8482i	0.541307	+	0.937571i	0.998829	+	0.0483728i	$0.0154035\pi$
$647$	13.7688	+	23.8482i	0.541307	+	0.937571i	−0.457523	+	0.889198i	$0.651263\pi$
$648$	−4.39841	−	7.61828i	−0.172786	−	0.299274i
$649$	21.2550	+	20.7164i	0.834332	+	0.813189i
$650$	−10.1170	−	7.46529i	−0.396822	−	0.292813i
$651$	0.578096	+	0.604907i	0.0226574	+	0.0237082i
$652$			1.25924i			0.0493155i
$653$	29.3260	+	16.9314i	1.14762	+	0.662577i	0.948305	−	0.317359i	$-0.102796\pi$
$653$	29.3260	+	16.9314i	1.14762	+	0.662577i	0.199312	+	0.979936i	$0.436129\pi$
$654$	−0.146832	+	0.0847732i	−0.00574157	+	0.00331490i
$655$	16.7911	+	10.9927i	0.656083	+	0.429520i
$656$	−0.355051	+	0.614966i	−0.0138624	+	0.0240104i
$657$		−	39.6424i		−	1.54660i
$658$	4.18713	+	17.1740i	0.163231	+	0.669513i
$659$			34.5640i			1.34642i	0.739450	+	0.673211i	$0.235086\pi$
$659$			34.5640i			1.34642i	−0.739450	+	0.673211i	$0.764914\pi$
$660$	−0.335052	+	1.06417i	−0.0130419	+	0.0414229i
$661$	−1.63580	+	0.944428i	−0.0636252	+	0.0367340i	−0.531475	−	0.847074i	$-0.678362\pi$
$661$	−1.63580	+	0.944428i	−0.0636252	+	0.0367340i	0.467850	+	0.883808i	$0.345029\pi$
$662$	8.20177	+	14.2059i	0.318771	+	0.552127i
$663$	0.434793	−	0.753083i	0.0168859	−	0.0292473i
$664$		−	8.40993i		−	0.326369i
$665$	−24.2832	−	28.4420i	−0.941660	−	1.10293i
$666$		−	33.6770i		−	1.30496i
$667$	−19.5520	+	33.8650i	−0.757056	+	1.31126i
$668$	4.97724	−	2.87361i	0.192575	−	0.111183i
$669$	−0.614109	−	1.06367i	−0.0237428	−	0.0411238i
$670$	17.6341	+	0.989516i	0.681265	+	0.0382283i
$671$	−33.2771	−	8.46043i	−1.28465	−	0.326611i
$672$	0.287747	−	0.274994i	0.0111001	−	0.0106081i
$673$	5.08760			0.196113			0.0980563	−	0.995181i	$-0.468737\pi$
$673$	5.08760			0.196113			0.0980563	+	0.995181i	$0.468737\pi$
$674$	−5.00261	+	8.66477i	−0.192693	+	0.333754i
$675$	4.46787	+	0.503002i	0.171969	+	0.0193606i
$676$	−3.33831	−	5.78213i	−0.128397	−	0.222390i
$677$	3.07608	+	1.77597i	0.118223	+	0.0682562i	0.557946	−	0.829878i	$-0.311590\pi$
$677$	3.07608	+	1.77597i	0.118223	+	0.0682562i	−0.439722	+	0.898134i	$0.644923\pi$
$678$			1.96769i			0.0755688i
$679$	−24.7301	−	7.23078i	−0.949055	−	0.277492i
$680$	2.31659	+	4.58841i	0.0888373	+	0.175957i
$681$	3.81170	+	2.20069i	0.146065	+	0.0843305i
$682$	−6.71098	+	1.89083i	−0.256977	+	0.0724035i
$683$	7.34303	−	4.23950i	0.280973	−	0.162220i	−0.352891	−	0.935665i	$-0.614801\pi$
$683$	7.34303	−	4.23950i	0.280973	−	0.162220i	0.633864	+	0.773445i	$0.281468\pi$
$684$	9.41061	−	16.2997i	0.359824	−	0.623233i
$685$	6.51874	+	12.9115i	0.249068	+	0.493322i
$686$	18.1735	−	3.56720i	0.693866	−	0.136196i
$687$		−	1.09832i		−	0.0419036i
$688$	1.49873	−	2.59588i	0.0571387	−	0.0989671i
$689$	5.49090	+	9.51051i	0.209186	+	0.362322i
$690$	−1.05167	+	1.60640i	−0.0400362	+	0.0611545i
$691$	12.5036	+	7.21898i	0.475661	+	0.274623i	0.718607	−	0.695417i	$-0.244780\pi$
$691$	12.5036	+	7.21898i	0.475661	+	0.274623i	−0.242945	+	0.970040i	$0.578114\pi$
$692$			1.63733i			0.0622418i
$693$	−22.4966	−	13.2849i	−0.854575	−	0.504650i
$694$	−22.6230			−0.858759
$695$	1.88671	−	33.6229i	0.0715669	−	1.27539i
$696$	−0.892565	+	0.515323i	−0.0338326	+	0.0195333i
$697$	−1.41362	+	0.816155i	−0.0535447	+	0.0309141i
$698$	−2.76109	+	4.78235i	−0.104509	+	0.181015i
$699$	−2.98784			−0.113010
$700$	−1.67594	−	13.1222i	−0.0633445	−	0.495971i
$701$			17.2789i			0.652617i	0.945263	+	0.326308i	$0.105805\pi$
$701$			17.2789i			0.652617i	−0.945263	+	0.326308i	$0.894195\pi$
$702$	−1.95826	−	1.13060i	−0.0739098	−	0.0426719i
$703$	61.9223	−	35.7509i	2.33544	−	1.34837i
$704$	0.899444	+	3.19233i	0.0338991	+	0.120316i
$705$	0.125918	−	2.24398i	0.00474236	−	0.0845133i
$706$	30.9572			1.16509
$707$	11.7733	+	48.2896i	0.442780	+	1.81612i
$708$			1.34627i			0.0505961i
$709$	−21.2909	+	36.8769i	−0.799597	+	1.38494i	0.120282	+	0.992740i	$0.461620\pi$
$709$	−21.2909	+	36.8769i	−0.799597	+	1.38494i	−0.919879	+	0.392202i	$0.871713\pi$
$710$	−22.0683	−	14.4475i	−0.828207	−	0.542205i
$711$	−21.7176	+	12.5387i	−0.814474	+	0.470237i
$712$	3.02422	+	1.74604i	0.113338	+	0.0654355i
$713$	−11.9990			−0.449366
$714$	0.888891	−	0.216717i	0.0332659	−	0.00811042i
$715$	−4.04386	−	18.2053i	−0.151232	−	0.680839i
$716$	−9.81605	+	17.0019i	−0.366843	+	0.635391i
$717$	−2.80626	+	1.62020i	−0.104802	+	0.0605073i
$718$	−10.3087	+	5.95171i	−0.384716	+	0.222116i
$719$	−42.3616	−	24.4575i	−1.57982	−	0.912109i	−0.994883	−	0.101030i	$-0.967786\pi$
$719$	−42.3616	−	24.4575i	−1.57982	−	0.912109i	−0.584937	−	0.811079i	$-0.698881\pi$
$720$	5.94309	−	3.00055i	0.221486	−	0.111824i
$721$	−8.84623	+	8.45415i	−0.329451	+	0.314849i
$722$	20.9605			0.780068
$723$	0.0530466	−	0.0918795i	0.00197283	−	0.00341703i
$724$	−2.92770	+	1.69031i	−0.108807	+	0.0628199i
$725$	−3.83228	+	34.0399i	−0.142327	+	1.26421i
$726$	−1.41140	+	0.863910i	−0.0523821	+	0.0320627i
$727$	15.2692			0.566303			0.283151	−	0.959075i	$-0.408620\pi$
$727$	15.2692			0.566303			0.283151	+	0.959075i	$0.408620\pi$
$728$	−1.86711	+	6.38573i	−0.0691996	+	0.236671i
$729$	−25.7856			−0.955021
$730$	29.7255	+	1.66801i	1.10019	+	0.0617359i
$731$	5.96715	−	3.44514i	0.220703	−	0.127423i
$732$	−0.778711	−	1.34877i	−0.0287820	−	0.0498519i
$733$	19.4734	+	11.2430i	0.719266	+	0.415269i	0.814483	−	0.580188i	$-0.197021\pi$
$733$	19.4734	+	11.2430i	0.719266	+	0.415269i	−0.0952162	+	0.995457i	$0.530354\pi$
$734$	−2.35169			−0.0868024
$735$	−2.34263	−	0.238297i	−0.0864092	−	0.00878971i
$736$			5.70778i			0.210391i
$737$	18.7601	+	18.2847i	0.691037	+	0.673525i
$738$	1.05712	+	1.83098i	0.0389130	+	0.0673993i
$739$	−29.6892	+	17.1411i	−1.09213	+	0.630544i	−0.934144	−	0.356897i	$-0.883835\pi$
$739$	−29.6892	+	17.1411i	−1.09213	+	0.630544i	−0.157990	+	0.987441i	$0.550501\pi$
$740$	25.2525	+	1.41701i	0.928299	+	0.0520903i
$741$		−	2.39136i		−	0.0878489i
$742$	−3.24261	+	11.0901i	−0.119040	+	0.407130i
$743$	15.1161			0.554555			0.277277	−	0.960790i	$-0.410568\pi$
$743$	15.1161			0.554555			0.277277	+	0.960790i	$0.410568\pi$
$744$	−0.273882	−	0.158126i	−0.0100410	−	0.00579718i
$745$	−15.4137	+	23.5441i	−0.564714	+	0.862588i
$746$	−1.20762	−	2.09166i	−0.0442142	−	0.0765813i
$747$	−21.6848	−	12.5197i	−0.793406	−	0.458073i
$748$	−1.87856	+	7.38886i	−0.0686868	+	0.270163i
$749$	−14.2058	+	13.5762i	−0.519070	+	0.496064i
$750$	−0.281512	+	1.65822i	−0.0102794	+	0.0605495i
$751$	26.8014	−	46.4215i	0.977998	−	1.69394i	0.308336	−	0.951278i	$-0.400228\pi$
$751$	26.8014	−	46.4215i	0.977998	−	1.69394i	0.669663	−	0.742665i	$-0.266439\pi$
$752$	−3.34066	−	5.78618i	−0.121821	−	0.211000i
$753$	−0.505276	+	0.291721i	−0.0184133	+	0.0106309i
$754$	8.61386	−	14.9196i	0.313698	−	0.543341i
$755$	−17.9999	−	35.6519i	−0.655084	−	1.29751i
$756$	−0.563534	−	2.31141i	−0.0204955	−	0.0840651i
$757$			24.8459i			0.903038i	0.892261	+	0.451519i	$0.149118\pi$
$757$			24.8459i			0.903038i	−0.892261	+	0.451519i	$0.850882\pi$
$758$	−10.9333	+	18.9370i	−0.397114	+	0.687822i
$759$	−2.74114	+	0.772320i	−0.0994971	+	0.0280334i
$760$	11.8262	+	7.74230i	0.428981	+	0.280843i
$761$	18.1534	−	31.4425i	0.658059	−	1.13979i	−0.323059	−	0.946379i	$-0.604711\pi$
$761$	18.1534	−	31.4425i	0.658059	−	1.13979i	0.981118	−	0.193413i	$-0.0619556\pi$
$762$	−0.837348			−0.0303339
$763$	2.89697	−	0.706297i	0.104877	−	0.0255697i
$764$	4.18346			0.151352
$765$	15.2798	+	0.857405i	0.552441	+	0.0309996i
$766$	−0.897916	−	1.55524i	−0.0324430	−	0.0561930i
$767$	−11.2518	−	19.4887i	−0.406279	−	0.703696i
$768$	−0.0752187	+	0.130283i	−0.00271422	+	0.00470117i
$769$	4.82841			0.174117			0.0870584	−	0.996203i	$-0.472253\pi$
$769$	4.82841			0.174117			0.0870584	+	0.996203i	$0.472253\pi$
$770$	10.9081	−	16.3099i	0.393101	−	0.587768i
$771$	−2.99236			−0.107767
$772$	−4.48341	+	7.76550i	−0.161362	+	0.279486i
$773$	19.2709	+	33.3781i	0.693125	+	1.20053i	0.970809	+	0.239855i	$0.0770998\pi$
$773$	19.2709	+	33.3781i	0.693125	+	1.20053i	−0.277684	+	0.960672i	$0.589567\pi$
$774$	−4.46228	−	7.72890i	−0.160393	−	0.277809i
$775$	−9.63369	+	4.20416i	−0.346052	+	0.151018i
$776$	9.73846			0.349590
$777$	1.26343	−	4.32109i	0.0453254	−	0.155018i
$778$	23.2474			0.833461
$779$	−2.24443	+	3.88746i	−0.0804150	+	0.139283i
$780$	0.463324	−	0.707718i	0.0165897	−	0.0253404i
$781$	−10.6099	−	37.6570i	−0.379653	−	1.34748i
$782$	−6.56023	+	11.3627i	−0.234593	+	0.406328i
$783$			6.16055i			0.220160i
$784$	−6.21451	+	3.22177i	−0.221947	+	0.115063i
$785$	43.1023	−	21.7615i	1.53839	−	0.776701i
$786$	−0.675111	+	1.16933i	−0.0240804	+	0.0417085i
$787$	−33.0637	+	19.0893i	−1.17859	+	0.680461i	−0.955689	−	0.294379i	$-0.904887\pi$
$787$	−33.0637	+	19.0893i	−1.17859	+	0.680461i	−0.222905	+	0.974840i	$0.571554\pi$
$788$	−9.68522	−	16.7753i	−0.345022	−	0.597595i
$789$	−1.34710	+	2.33324i	−0.0479580	+	0.0830657i
$790$	−8.48822	−	16.8124i	−0.301997	−	0.598157i
$791$	9.71174	−	33.2153i	0.345310	−	1.18100i
$792$	9.57035	+	2.43318i	0.340068	+	0.0864594i
$793$	22.5453	+	13.0165i	0.800606	+	0.462230i
$794$	9.25277	+	16.0263i	0.328369	+	0.568751i
$795$	0.804655	−	1.22909i	0.0285382	−	0.0435914i
$796$	−14.4670	−	8.35255i	−0.512771	−	0.296048i
$797$	−4.95216			−0.175415			−0.0877073	−	0.996146i	$-0.527954\pi$
$797$	−4.95216			−0.175415			−0.0877073	+	0.996146i	$0.527954\pi$
$798$	1.81897	−	1.73835i	0.0643909	−	0.0615370i
$799$		−	15.3583i		−	0.543338i
$800$	1.99987	+	4.58263i	0.0707061	+	0.162020i
$801$	9.00423	−	5.19860i	0.318149	−	0.183683i
$802$	−0.501146	−	0.868010i	−0.0176961	−	0.0306505i
$803$	31.6236	+	30.8222i	1.11597	+	1.08769i
$804$			1.18825i			0.0419063i
$805$	25.6810	−	21.9259i	0.905135	−	0.772785i
$806$	5.28630			0.186202
$807$	−1.27825	−	0.737996i	−0.0449964	−	0.0259787i
$808$	−9.39320	−	16.2695i	−0.330452	−	0.572359i
$809$	27.1876	−	15.6968i	0.955865	−	0.551869i	0.0609670	−	0.998140i	$-0.480582\pi$
$809$	27.1876	−	15.6968i	0.955865	−	0.551869i	0.894898	+	0.446271i	$0.147248\pi$
$810$	1.10204	−	19.6394i	0.0387218	−	0.690059i
$811$	−31.0236			−1.08938			−0.544692	−	0.838636i	$-0.683353\pi$
$811$	−31.0236			−1.08938			−0.544692	+	0.838636i	$0.683353\pi$
$812$	17.6102	−	4.29346i	0.617997	−	0.150671i
$813$	−2.33826			−0.0820064
$814$	26.8649	+	26.1841i	0.941613	+	0.917752i
$815$	−1.54228	+	2.35580i	−0.0540236	+	0.0825199i
$816$	−0.299480	+	0.172905i	−0.0104839	+	0.00605289i
$817$	9.47414	−	16.4097i	0.331458	−	0.574102i
$818$	38.8714			1.35911
$819$	13.6859	+	14.3206i	0.478224	+	0.500403i
$820$	−1.41743	+	0.715630i	−0.0494986	+	0.0249909i
$821$	17.5276	+	10.1196i	0.611719	+	0.353176i	0.773638	−	0.633628i	$-0.218435\pi$
$821$	17.5276	+	10.1196i	0.611719	+	0.353176i	−0.161919	+	0.986804i	$0.551768\pi$
$822$	−0.842718	+	0.486543i	−0.0293932	+	0.0169701i
$823$	−31.6000	+	18.2443i	−1.10151	+	0.635955i	−0.936616	−	0.350357i	$-0.886060\pi$
$823$	−31.6000	+	18.2443i	−1.10151	+	0.635955i	−0.164890	+	0.986312i	$0.552727\pi$
$824$	2.31245	−	4.00529i	0.0805581	−	0.139531i
$825$	−1.93019	+	1.58051i	−0.0672006	+	0.0550262i
$826$	6.64466	−	22.7255i	0.231197	−	0.790722i
$827$	−32.3840			−1.12610			−0.563051	−	0.826422i	$-0.690373\pi$
$827$	−32.3840			−1.12610			−0.563051	+	0.826422i	$0.690373\pi$
$828$	14.7174	+	8.49708i	0.511464	+	0.295294i
$829$	−36.0031	+	20.7864i	−1.25044	+	0.721941i	−0.971197	−	0.238280i	$-0.923417\pi$
$829$	−36.0031	+	20.7864i	−1.25044	+	0.721941i	−0.279242	+	0.960221i	$0.590083\pi$
$830$	10.3002	−	15.7334i	0.357527	−	0.546114i
$831$	2.15172	−	3.72688i	0.0746423	−	0.129284i
$832$		−	2.51463i		−	0.0871792i
$833$	−16.0744	−	0.728963i	−0.556944	−	0.0252571i
$834$	2.26563			0.0784523
$835$	12.8310	+	0.719994i	0.444034	+	0.0249164i
$836$	5.68577	+	20.1801i	0.196647	+	0.697944i
$837$	−1.63710	+	0.945178i	−0.0565863	+	0.0326701i
$838$	2.65393	+	1.53224i	0.0916784	+	0.0529305i
$839$			34.7899i			1.20108i	0.799595	+	0.600540i	$0.205048\pi$
$839$			34.7899i			1.20108i	−0.799595	+	0.600540i	$0.794952\pi$
$840$	0.875125	−	0.162037i	0.0301947	−	0.00559081i
$841$	−17.9361			−0.618487
$842$	−0.684714	+	1.18596i	−0.0235968	+	0.0408708i
$843$	−3.77650	+	2.18036i	−0.130070	+	0.0750957i
$844$	16.0035	−	9.23964i	0.550864	−	0.318042i
$845$	0.836428	−	14.9059i	0.0287740	−	0.512780i
$846$	−19.8927			−0.683926
$847$	28.0888	−	7.61694i	0.965143	−	0.261721i
$848$		−	4.36716i		−	0.149969i
$849$	−2.27608	−	1.31410i	−0.0781150	−	0.0450997i
$850$	−1.28584	+	11.4213i	−0.0441038	+	0.391749i
$851$	32.2804	+	55.9112i	1.10656	+	1.91661i
$852$	0.887286	−	1.53682i	0.0303979	−	0.0526507i
$853$			45.0615i			1.54288i	0.636305	+	0.771438i	$0.280462\pi$
$853$			45.0615i			1.54288i	−0.636305	+	0.771438i	$0.719538\pi$
$854$	6.48791	+	26.6110i	0.222012	+	0.910609i
$855$	37.5688	−	18.9677i	1.28483	−	0.648683i
$856$	3.71349	−	6.43195i	0.126924	−	0.219839i
$857$	−17.5391	+	10.1262i	−0.599126	+	0.345905i	−0.768698	−	0.639612i	$-0.779095\pi$
$857$	−17.5391	+	10.1262i	−0.599126	+	0.345905i	0.169572	+	0.985518i	$0.445762\pi$
$858$	1.20764	−	0.340255i	0.0412283	−	0.0116161i
$859$	−49.0561	−	28.3226i	−1.67377	−	0.966354i	−0.965495	−	0.260421i	$-0.916139\pi$
$859$	−49.0561	−	28.3226i	−1.67377	−	0.966354i	−0.708279	−	0.705933i	$-0.750528\pi$
$860$	5.98321	−	3.02080i	0.204026	−	0.103008i
$861$	0.0669469	+	0.274591i	0.00228155	+	0.00935805i
$862$		−	4.93683i		−	0.168149i
$863$	−17.7679	−	10.2583i	−0.604828	−	0.349198i	0.166111	−	0.986107i	$-0.446879\pi$
$863$	−17.7679	−	10.2583i	−0.604828	−	0.349198i	−0.770939	+	0.636910i	$0.780212\pi$
$864$	0.449610	+	0.778747i	0.0152960	+	0.0264935i
$865$	−2.00535	+	3.06313i	−0.0681840	+	0.104150i
$866$	10.5332	−	18.2441i	0.357933	−	0.619959i
$867$	1.76252			0.0598584
$868$	3.84277	+	4.02099i	0.130432	+	0.136481i
$869$	6.88321	−	27.0735i	0.233497	−	0.918405i
$870$	−2.30097	−	0.129116i	−0.0780103	−	0.00437745i
$871$	−9.93106	−	17.2011i	−0.336501	−	0.582837i
$872$	−0.976031	+	0.563512i	−0.0330526	+	0.0190829i
$873$	14.4975	−	25.1104i	0.490666	−	0.849858i
$874$			36.0813i			1.22047i
$875$	12.9363	−	26.6017i	0.437326	−	0.899303i
$876$			2.00301i			0.0676755i
$877$	12.2237	−	21.1721i	0.412765	−	0.714930i	−0.582426	−	0.812884i	$-0.697896\pi$
$877$	12.2237	−	21.1721i	0.412765	−	0.714930i	0.995191	+	0.0979537i	$0.0312297\pi$
$878$	−0.332519	−	0.575940i	−0.0112220	−	0.0194370i
$879$	−0.0830654	+	0.0479578i	−0.00280173	+	0.00161758i
$880$	−2.22719	+	7.07387i	−0.0750785	+	0.238460i
$881$		−	14.8378i		−	0.499900i	−0.968259	−	0.249950i	$-0.919586\pi$
$881$		−	14.8378i		−	0.499900i	0.968259	−	0.249950i	$-0.0804141\pi$
$882$	−0.944182	+	20.8202i	−0.0317923	+	0.701052i
$883$		−	10.1754i		−	0.342430i	−0.985234	−	0.171215i	$-0.945231\pi$
$883$		−	10.1754i		−	0.342430i	0.985234	−	0.171215i	$-0.0547693\pi$
$884$	2.89019	−	5.00596i	0.0972076	−	0.168369i
$885$	−1.64888	+	2.51863i	−0.0554264	+	0.0846627i
$886$	11.1850	−	6.45766i	0.375767	−	0.216949i
$887$	−13.4692	−	7.77646i	−0.452252	−	0.261108i	0.256529	−	0.966537i	$-0.417421\pi$
$887$	−13.4692	−	7.77646i	−0.452252	−	0.261108i	−0.708781	+	0.705429i	$0.750755\pi$
$888$			1.70160i			0.0571019i
$889$	14.1347	+	4.13281i	0.474062	+	0.138610i
$890$	3.51926	+	6.97049i	0.117966	+	0.233651i
$891$	20.3640	−	20.8934i	0.682218	−	0.699956i
$892$	−4.08216	−	7.07050i	−0.136681	−	0.236738i
$893$	−21.1177	−	36.5770i	−0.706677	−	1.22400i
$894$	−1.63960	−	0.946624i	−0.0548365	−	0.0316598i
$895$	−39.1874	+	19.7849i	−1.30989	+	0.661337i
$896$	1.91274	−	1.82796i	0.0639000	−	0.0610679i
$897$	2.15922			0.0720943
$898$	−2.83548	+	4.91119i	−0.0946211	+	0.163888i
$899$	−7.20114	−	12.4727i	−0.240171	−	0.415989i
$900$	14.7934	+	1.66547i	0.493113	+	0.0555156i
$901$	5.01939	−	8.69384i	0.167220	−	0.289634i
$902$	−2.28253	−	0.580313i	−0.0759998	−	0.0193223i
$903$	−0.282595	−	1.15910i	−0.00940417	−	0.0385724i
$904$			13.0798i			0.435028i
$905$	−7.54742	−	0.423514i	−0.250885	−	0.0140781i
$906$	2.32696	−	1.34347i	0.0773082	−	0.0446339i
$907$	17.8776	−	10.3216i	0.593616	−	0.342725i	−0.172910	−	0.984938i	$-0.555317\pi$
$907$	17.8776	−	10.3216i	0.593616	−	0.342725i	0.766526	+	0.642213i	$0.221984\pi$
$908$	25.3374	+	14.6286i	0.840853	+	0.485466i
$909$	−55.9340			−1.85521
$910$	−11.3141	+	9.65971i	−0.375057	+	0.320216i
$911$	−2.08440			−0.0690591			−0.0345296	−	0.999404i	$-0.510993\pi$
$911$	−2.08440			−0.0690591			−0.0345296	+	0.999404i	$0.510993\pi$
$912$	−0.475490	+	0.823572i	−0.0157450	+	0.0272712i
$913$	26.8473	−	7.56427i	0.888517	−	0.250341i
$914$	7.46931	+	12.9372i	0.247063	+	0.427925i
$915$	0.195109	−	3.47703i	0.00645011	−	0.114947i
$916$		−	7.30086i		−	0.241227i
$917$	17.1674	−	16.4065i	0.566917	−	0.541791i
$918$			2.06704i			0.0682223i
$919$	36.7923	+	21.2420i	1.21367	+	0.700710i	0.963556	−	0.267507i	$-0.0861999\pi$
$919$	36.7923	+	21.2420i	1.21367	+	0.700710i	0.250110	+	0.968217i	$0.419533\pi$
$920$	−6.99072	+	10.6782i	−0.230477	+	0.352049i
$921$	2.33037	−	1.34544i	0.0767884	−	0.0443338i
$922$	−12.6916	+	21.9826i	−0.417977	+	0.723957i
$923$			29.6628i			0.976363i
$924$	1.13668	+	0.671243i	0.0373942	+	0.0220823i
$925$	45.5071	+	33.5794i	1.49626	+	1.10408i
$926$	1.29984	+	0.750461i	0.0427153	+	0.0246617i
$927$	−6.88503	−	11.9252i	−0.226134	−	0.391676i
$928$	−5.93313	+	3.42550i	−0.194765	+	0.112447i
$929$	−1.28969	−	0.744603i	−0.0423134	−	0.0244296i	0.478694	−	0.877982i	$-0.341110\pi$
$929$	−1.28969	−	0.744603i	−0.0423134	−	0.0244296i	−0.521007	+	0.853552i	$0.674444\pi$
$930$	−0.318714	−	0.631267i	−0.0104510	−	0.0207001i
$931$	−39.2846	+	20.3662i	−1.28750	+	0.667476i
$932$	−19.8610			−0.650569
$933$	2.85858	+	1.65040i	0.0935858	+	0.0540318i
$934$	−19.9490	−	34.5527i	−0.652751	−	1.13060i
$935$	−12.5641	+	11.5224i	−0.410889	+	0.376821i
$936$	−6.48392	−	3.74349i	−0.211934	−	0.122360i
$937$			6.06069i			0.197994i	0.995088	+	0.0989970i	$0.0315634\pi$
$937$			6.06069i			0.197994i	−0.995088	+	0.0989970i	$0.968437\pi$
$938$	5.86471	−	20.0580i	0.191490	−	0.654916i
$939$	−0.206595			−0.00674198
$940$	0.837015	−	14.9164i	0.0273004	−	0.486519i
$941$	8.92371	+	15.4563i	0.290905	+	0.503861i	0.974024	−	0.226445i	$-0.0727105\pi$
$941$	8.92371	+	15.4563i	0.290905	+	0.503861i	−0.683119	+	0.730307i	$0.739377\pi$
$942$	1.62423	+	2.81324i	0.0529202	+	0.0916604i
$943$	−3.51009	−	2.02655i	−0.114304	−	0.0659936i
$944$			8.94907i			0.291267i
$945$	1.77668	−	5.01441i	0.0577954	−	0.163119i
$946$	9.63495	+	2.44961i	0.313259	+	0.0796436i
$947$	−41.8092	−	24.1385i	−1.35862	−	0.784397i	−0.369179	−	0.929358i	$-0.620361\pi$
$947$	−41.8092	−	24.1385i	−1.35862	−	0.784397i	−0.989437	+	0.144961i	$0.953694\pi$
$948$	1.09732	−	0.633541i	0.0356395	−	0.0205764i
$949$	−16.7406	−	28.9956i	−0.543424	−	0.941238i
$950$	12.6420	+	28.9688i	0.410162	+	0.939871i
$951$			0.683709i			0.0221708i
$952$	5.90871	−	1.44058i	0.191502	−	0.0466894i
$953$	2.66449			0.0863114			0.0431557	−	0.999068i	$-0.486259\pi$
$953$	2.66449			0.0863114			0.0431557	+	0.999068i	$0.486259\pi$
$954$	−11.2606	−	6.50132i	−0.364576	−	0.210488i
$955$	7.82646	+	5.12378i	0.253258	+	0.165801i
$956$	−18.6540	+	10.7699i	−0.603314	+	0.348323i
$957$	−2.44790	−	2.38586i	−0.0791292	−	0.0771240i
$958$	1.60000			0.0516936
$959$	16.6267	−	4.05369i	0.536904	−	0.130900i
$960$	−0.300286	+	0.151609i	−0.00969170	+	0.00489314i
$961$	−13.2903	+	23.0195i	−0.428721	+	0.742566i
$962$	−14.2215	−	24.6324i	−0.458520	−	0.794179i
$963$	−11.0564	−	19.1503i	−0.356288	−	0.617109i
$964$	0.352616	−	0.610749i	0.0113570	−	0.0196709i
$965$	−17.8986	+	9.03663i	−0.576176	+	0.290899i
$966$	1.56960	+	1.64240i	0.0505011	+	0.0528432i
$967$	−34.3843			−1.10572			−0.552862	−	0.833273i	$-0.686464\pi$
$967$	−34.3843			−1.10572			−0.552862	+	0.833273i	$0.686464\pi$
$968$	−9.38200	+	5.74265i	−0.301549	+	0.184576i
$969$	−1.89314	+	1.09301i	−0.0608166	+	0.0351125i
$970$	18.2188	+	11.9274i	0.584971	+	0.382965i
$971$	−4.41826	−	2.55088i	−0.141789	−	0.0818617i	0.427428	−	0.904050i	$-0.359420\pi$
$971$	−4.41826	−	2.55088i	−0.141789	−	0.0818617i	−0.569216	+	0.822188i	$0.692753\pi$
$972$	4.02103			0.128975
$973$	−38.2445	−	11.1822i	−1.22606	−	0.358486i
$974$			1.59441i			0.0510883i
$975$	1.73358	−	0.756541i	0.0555191	−	0.0242287i
$976$	−5.17631	−	8.96564i	−0.165690	−	0.286983i
$977$	−29.4505	+	17.0032i	−0.942203	+	0.543981i	−0.890650	−	0.454689i	$-0.849750\pi$
$977$	−29.4505	+	17.0032i	−0.942203	+	0.543981i	−0.0515531	+	0.998670i	$0.516417\pi$
$978$	−0.164057	−	0.0947182i	−0.00524596	−	0.00302875i
$979$	−2.85381	+	11.2248i	−0.0912082	+	0.358746i
$980$	−15.5721	−	1.58403i	−0.497433	−	0.0505999i
$981$			3.35556i			0.107135i
$982$	10.8516	+	6.26515i	0.346287	+	0.199929i
$983$	−17.6465	−	30.5646i	−0.562835	−	0.974858i	−0.997248	−	0.0741445i	$-0.976377\pi$
$983$	−17.6465	−	30.5646i	−0.562835	−	0.974858i	0.434413	−	0.900714i	$-0.356956\pi$
$984$	−0.0534129	−	0.0925139i	−0.00170274	−	0.00294924i
$985$	2.42667	−	43.2456i	0.0773202	−	1.37792i
$986$	−15.7484			−0.501530
$987$	−2.55243	−	0.746299i	−0.0812447	−	0.0237549i
$988$		−	15.8961i		−	0.505721i
$989$	14.8167	+	8.55444i	0.471144	+	0.272015i
$990$	14.9242	+	16.2735i	0.474323	+	0.517206i
$991$	−5.37871	−	9.31619i	−0.170860	−	0.295939i	0.767861	−	0.640617i	$-0.221321\pi$
$991$	−5.37871	−	9.31619i	−0.170860	−	0.295939i	−0.938721	+	0.344678i	$0.887988\pi$
$992$	−1.82057	−	1.05111i	−0.0578033	−	0.0333727i
$993$	−2.46771			−0.0783103
$994$	−22.5628	+	21.5628i	−0.715648	+	0.683930i
$995$	−16.8351	−	33.3449i	−0.533710	−	1.05710i
$996$	1.09567	+	0.632584i	0.0347176	+	0.0200442i
$997$	17.5630	−	10.1400i	0.556225	−	0.321137i	−0.195404	−	0.980723i	$-0.562602\pi$
$997$	17.5630	−	10.1400i	0.556225	−	0.321137i	0.751629	+	0.659586i	$0.229268\pi$
$998$	−1.40578	−	2.43488i	−0.0444992	−	0.0770749i
$999$	8.80841	+	5.08554i	0.278686	+	0.160899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.439.12	✓	48
5.4	even	2		770.2.o.b.439.13	yes	48
7.3	odd	6	inner	770.2.o.a.549.13	yes	48
11.10	odd	2		770.2.o.b.439.12	yes	48
35.24	odd	6		770.2.o.b.549.12	yes	48
55.54	odd	2	inner	770.2.o.a.439.13	yes	48
77.10	even	6		770.2.o.b.549.13	yes	48
385.164	even	6	inner	770.2.o.a.549.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.12	✓	48	1.1	even	1	trivial
770.2.o.a.439.13	yes	48	55.54	odd	2	inner
770.2.o.a.549.12	yes	48	385.164	even	6	inner
770.2.o.a.549.13	yes	48	7.3	odd	6	inner
770.2.o.b.439.12	yes	48	11.10	odd	2
770.2.o.b.439.13	yes	48	5.4	even	2
770.2.o.b.549.12	yes	48	35.24	odd	6
770.2.o.b.549.13	yes	48	77.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0752187 - 0.130283i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.125277 - 2.23256i) q^{5} +0.150437 q^{6} +(-2.53943 - 0.742498i) q^{7} +1.00000 q^{8} +(1.48868 - 2.57848i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.0752187 - 0.130283i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.125277 - 2.23256i) q^{5} +0.150437 q^{6} +(-2.53943 - 0.742498i) q^{7} +1.00000 q^{8} +(1.48868 - 2.57848i) q^{9} +(1.87081 + 1.22477i) q^{10} +(0.899444 + 3.19233i) q^{11} +(-0.0752187 + 0.130283i) q^{12} -2.51463i q^{13} +(1.91274 - 1.82796i) q^{14} +(-0.300286 + 0.151609i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.99073 + 1.14935i) q^{17} +(1.48868 + 2.57848i) q^{18} +(-3.16071 + 5.47452i) q^{19} +(-1.99609 + 1.00778i) q^{20} +(0.0942780 + 0.386693i) q^{21} +(-3.21436 - 0.817226i) q^{22} +(-4.94308 - 2.85389i) q^{23} +(-0.0752187 - 0.130283i) q^{24} +(-4.96861 - 0.559376i) q^{25} +(2.17773 + 1.25732i) q^{26} -0.899220 q^{27} +(0.626692 + 2.57046i) q^{28} -6.85099i q^{29} +(0.0188464 - 0.335860i) q^{30} +(1.82057 - 1.05111i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.348251 - 0.357305i) q^{33} -2.29870i q^{34} +(-1.97580 + 5.57640i) q^{35} -2.97737 q^{36} +(-9.79562 - 5.65550i) q^{37} +(-3.16071 - 5.47452i) q^{38} +(-0.327613 + 0.189147i) q^{39} +(0.125277 - 2.23256i) q^{40} +0.710102 q^{41} +(-0.382025 - 0.111699i) q^{42} -2.99747 q^{43} +(2.31492 - 2.37511i) q^{44} +(-5.57010 - 3.64659i) q^{45} +(4.94308 - 2.85389i) q^{46} +(-3.34066 + 5.78618i) q^{47} +0.150437 q^{48} +(5.89739 + 3.77104i) q^{49} +(2.96874 - 4.02326i) q^{50} +(0.299480 + 0.172905i) q^{51} +(-2.17773 + 1.25732i) q^{52} +(-3.78207 + 2.18358i) q^{53} +(0.449610 - 0.778747i) q^{54} +(7.23975 - 1.60813i) q^{55} +(-2.53943 - 0.742498i) q^{56} +0.950979 q^{57} +(5.93313 + 3.42550i) q^{58} +(7.75012 - 4.47453i) q^{59} +(0.281440 + 0.184251i) q^{60} +(-5.17631 + 8.96564i) q^{61} +2.10222i q^{62} +(-5.69492 + 5.44251i) q^{63} +1.00000 q^{64} +(-5.61405 - 0.315026i) q^{65} +(0.135310 + 0.480247i) q^{66} +(6.84041 - 3.94931i) q^{67} +(1.99073 + 1.14935i) q^{68} +0.858663i q^{69} +(-3.84140 - 4.49929i) q^{70} -11.7961 q^{71} +(1.48868 - 2.57848i) q^{72} +(11.5308 - 6.65729i) q^{73} +(9.79562 - 5.65550i) q^{74} +(0.300856 + 0.689399i) q^{75} +6.32143 q^{76} +(0.0862272 - 8.77454i) q^{77} -0.378295i q^{78} +(-7.29423 - 4.21133i) q^{79} +(1.87081 + 1.22477i) q^{80} +(-4.39841 - 7.61828i) q^{81} +(-0.355051 + 0.614966i) q^{82} -8.40993i q^{83} +(0.287747 - 0.274994i) q^{84} +(2.31659 + 4.58841i) q^{85} +(1.49873 - 2.59588i) q^{86} +(-0.892565 + 0.515323i) q^{87} +(0.899444 + 3.19233i) q^{88} +(3.02422 + 1.74604i) q^{89} +(5.94309 - 3.00055i) q^{90} +(-1.86711 + 6.38573i) q^{91} +5.70778i q^{92} +(-0.273882 - 0.158126i) q^{93} +(-3.34066 - 5.78618i) q^{94} +(11.8262 + 7.74230i) q^{95} +(-0.0752187 + 0.130283i) q^{96} +9.73846 q^{97} +(-6.21451 + 3.22177i) q^{98} +(9.57035 + 2.43318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

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