LMFDB - Embedded newform 600.2.bk.a.59.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(59,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bk (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.8
Character	$\chi$	$=$	600.59
Dual form			600.2.bk.a.539.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38243 - 0.298125i) q^{2} +(-1.70754 + 0.290346i) q^{3} +(1.82224 + 0.824276i) q^{4} +(-0.232683 - 2.22393i) q^{5} +(2.44712 + 0.107677i) q^{6} +1.95460 q^{7} +(-2.27339 - 1.68276i) q^{8} +(2.83140 - 0.991555i) q^{9} +(-0.341340 + 3.14380i) q^{10} +(2.21748 - 3.05211i) q^{11} +(-3.35088 - 0.878405i) q^{12} +(-1.72354 + 1.25222i) q^{13} +(-2.70210 - 0.582714i) q^{14} +(1.04302 + 3.72989i) q^{15} +(2.64114 + 3.00406i) q^{16} +(-2.17748 + 6.70160i) q^{17} +(-4.20983 + 0.526647i) q^{18} +(0.402962 - 1.24019i) q^{19} +(1.40912 - 4.24433i) q^{20} +(-3.33755 + 0.567508i) q^{21} +(-3.97543 + 3.55824i) q^{22} +(4.91902 - 6.77045i) q^{23} +(4.37049 + 2.21332i) q^{24} +(-4.89172 + 1.03494i) q^{25} +(2.75600 - 1.21729i) q^{26} +(-4.54684 + 2.51521i) q^{27} +(3.56175 + 1.61113i) q^{28} +(-0.629917 - 1.93868i) q^{29} +(-0.329938 - 5.46728i) q^{30} +(4.09280 + 1.32983i) q^{31} +(-2.75561 - 4.94030i) q^{32} +(-2.90028 + 5.85544i) q^{33} +(5.00814 - 8.61535i) q^{34} +(-0.454802 - 4.34688i) q^{35} +(5.97681 + 0.527000i) q^{36} +(3.71150 - 2.69656i) q^{37} +(-0.926798 + 1.59434i) q^{38} +(2.57944 - 2.63865i) q^{39} +(-3.21336 + 5.44741i) q^{40} +(-3.23510 - 4.45273i) q^{41} +(4.78313 + 0.210466i) q^{42} -8.41043i q^{43} +(6.55657 - 3.73386i) q^{44} +(-2.86397 - 6.06611i) q^{45} +(-8.81866 + 7.89321i) q^{46} +(1.45527 - 0.472847i) q^{47} +(-5.38207 - 4.36272i) q^{48} -3.17955 q^{49} +(7.07101 + 0.0276044i) q^{50} +(1.77236 - 12.0755i) q^{51} +(-4.17288 + 0.861185i) q^{52} +(-0.906474 + 0.294531i) q^{53} +(7.03555 - 2.12158i) q^{54} +(-7.30364 - 4.22135i) q^{55} +(-4.44356 - 3.28912i) q^{56} +(-0.327990 + 2.23467i) q^{57} +(0.292847 + 2.86790i) q^{58} +(-0.361751 - 0.497907i) q^{59} +(-1.17382 + 7.65651i) q^{60} +(7.41094 - 10.2003i) q^{61} +(-5.26157 - 3.05857i) q^{62} +(5.53424 - 1.93809i) q^{63} +(2.33662 + 7.65116i) q^{64} +(3.18589 + 3.54165i) q^{65} +(5.75510 - 7.23010i) q^{66} +(-10.9221 - 3.54880i) q^{67} +(-9.49186 + 10.4171i) q^{68} +(-6.43366 + 12.9890i) q^{69} +(-0.667181 + 6.14486i) q^{70} +(-2.33603 - 7.18955i) q^{71} +(-8.10543 - 2.51038i) q^{72} +(8.16865 - 11.2432i) q^{73} +(-5.93482 + 2.62133i) q^{74} +(8.05232 - 3.18750i) q^{75} +(1.75655 - 1.92777i) q^{76} +(4.33429 - 5.96563i) q^{77} +(-4.35254 + 2.87876i) q^{78} +(10.3991 - 3.37889i) q^{79} +(6.06627 - 6.57270i) q^{80} +(7.03364 - 5.61497i) q^{81} +(3.14484 + 7.12007i) q^{82} +(-0.864776 + 2.66151i) q^{83} +(-6.54962 - 1.71693i) q^{84} +(15.4105 + 3.28321i) q^{85} +(-2.50736 + 11.6269i) q^{86} +(1.63850 + 3.12749i) q^{87} +(-10.1772 + 3.20713i) q^{88} +(-8.87863 + 12.2204i) q^{89} +(2.15078 + 9.23981i) q^{90} +(-3.36882 + 2.44759i) q^{91} +(14.5444 - 8.28278i) q^{92} +(-7.37474 - 1.08242i) q^{93} +(-2.15278 + 0.219826i) q^{94} +(-2.85185 - 0.607586i) q^{95} +(6.13972 + 7.63570i) q^{96} +(-3.15132 + 1.02393i) q^{97} +(4.39552 + 0.947905i) q^{98} +(3.25225 - 10.8405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} - 16 q^{10} - 5 q^{12} - 18 q^{16} - 12 q^{19} - 10 q^{22} + 12 q^{24} - 16 q^{25} - 10 q^{27} - 50 q^{28} - 21 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 32 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) $ 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9 - 16 * q^10 - 5 * q^12 - 18 * q^16 - 12 * q^19 - 10 * q^22 + 12 * q^24 - 16 * q^25 - 10 * q^27 - 50 * q^28 - 21 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 32 * q^40 + 15 * q^42 - 34 * q^46 - 70 * q^48 + 336 * q^49 - 4 * q^51 - 60 * q^52 + 40 * q^54 - 70 * q^58 - 50 * q^60 - 30 * q^64 + 28 * q^66 - 20 * q^67 - 16 * q^70 - 5 * q^72 - 20 * q^73 - 42 * q^75 - 48 * q^76 + 75 * q^78 - 6 * q^81 - 76 * q^84 - 70 * q^88 + 66 * q^90 - 96 * q^91 - 108 * q^94 - 50 * q^96 - 60 * q^97 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.38243	−	0.298125i	−0.977528	−	0.210806i
$2$	−1.38243	−	0.298125i	−0.977528	−	0.210806i
$3$	−1.70754	+	0.290346i	−0.985850	+	0.167631i
$3$	−1.70754	+	0.290346i	−0.985850	+	0.167631i
$4$	1.82224	+	0.824276i	0.911121	+	0.412138i
$5$	−0.232683	−	2.22393i	−0.104059	−	0.994571i
$5$	−0.232683	−	2.22393i	−0.104059	−	0.994571i
$6$	2.44712	+	0.107677i	0.999033	+	0.0439591i
$7$	1.95460			0.738768			0.369384	−	0.929277i	$-0.379569\pi$
$7$	1.95460			0.738768			0.369384	+	0.929277i	$0.379569\pi$
$8$	−2.27339	−	1.68276i	−0.803765	−	0.594946i
$9$	2.83140	−	0.991555i	0.943800	−	0.330518i
$10$	−0.341340	+	3.14380i	−0.107941	+	0.994157i
$11$	2.21748	−	3.05211i	0.668597	−	0.920245i	−0.331131	−	0.943585i	$-0.607430\pi$
$11$	2.21748	−	3.05211i	0.668597	−	0.920245i	0.999728	+	0.0233403i	$0.00743012\pi$
$12$	−3.35088	−	0.878405i	−0.967316	−	0.253574i
$13$	−1.72354	+	1.25222i	−0.478023	+	0.347304i	−0.800560	−	0.599253i	$-0.795464\pi$
$13$	−1.72354	+	1.25222i	−0.478023	+	0.347304i	0.322537	+	0.946557i	$0.395464\pi$
$14$	−2.70210	−	0.582714i	−0.722166	−	0.155737i
$15$	1.04302	+	3.72989i	0.269308	+	0.963054i
$16$	2.64114	+	3.00406i	0.660285	+	0.751015i
$17$	−2.17748	+	6.70160i	−0.528117	+	1.62538i	0.229953	+	0.973202i	$0.426143\pi$
$17$	−2.17748	+	6.70160i	−0.528117	+	1.62538i	−0.758069	+	0.652174i	$0.773857\pi$
$18$	−4.20983	+	0.526647i	−0.992266	+	0.124132i
$19$	0.402962	−	1.24019i	0.0924457	−	0.284519i	−0.894134	−	0.447800i	$-0.852208\pi$
$19$	0.402962	−	1.24019i	0.0924457	−	0.284519i	0.986580	+	0.163281i	$0.0522077\pi$
$20$	1.40912	−	4.24433i	0.315090	−	0.949062i
$21$	−3.33755	+	0.567508i	−0.728314	+	0.123841i
$22$	−3.97543	+	3.55824i	−0.847565	+	0.758620i
$23$	4.91902	−	6.77045i	1.02569	−	1.41174i	0.117548	−	0.993067i	$-0.462497\pi$
$23$	4.91902	−	6.77045i	1.02569	−	1.41174i	0.908139	−	0.418670i	$-0.137503\pi$
$24$	4.37049	+	2.21332i	0.892123	+	0.451792i
$25$	−4.89172	+	1.03494i	−0.978343	+	0.206989i
$26$	2.75600	−	1.21729i	0.540495	−	0.238729i
$27$	−4.54684	+	2.51521i	−0.875039	+	0.484052i
$28$	3.56175	+	1.61113i	0.673107	+	0.304474i
$29$	−0.629917	−	1.93868i	−0.116973	−	0.360005i	0.875381	−	0.483434i	$-0.160611\pi$
$29$	−0.629917	−	1.93868i	−0.116973	−	0.360005i	−0.992353	+	0.123429i	$0.960611\pi$
$30$	−0.329938	−	5.46728i	−0.0602381	−	0.998184i
$31$	4.09280	+	1.32983i	0.735089	+	0.238845i	0.652553	−	0.757743i	$-0.273698\pi$
$31$	4.09280	+	1.32983i	0.735089	+	0.238845i	0.0825359	+	0.996588i	$0.473698\pi$
$32$	−2.75561	−	4.94030i	−0.487128	−	0.873331i
$33$	−2.90028	+	5.85544i	−0.504874	+	1.01930i
$34$	5.00814	−	8.61535i	0.858888	−	1.47752i
$35$	−0.454802	−	4.34688i	−0.0768756	−	0.734757i
$36$	5.97681	+	0.527000i	0.996135	+	0.0878333i
$37$	3.71150	−	2.69656i	0.610167	−	0.443313i	−0.239306	−	0.970944i	$-0.576920\pi$
$37$	3.71150	−	2.69656i	0.610167	−	0.443313i	0.849473	+	0.527632i	$0.176920\pi$
$38$	−0.926798	+	1.59434i	−0.150347	+	0.258637i
$39$	2.57944	−	2.63865i	0.413040	−	0.422522i
$40$	−3.21336	+	5.44741i	−0.508077	+	0.861311i
$41$	−3.23510	−	4.45273i	−0.505237	−	0.695400i	0.477870	−	0.878431i	$-0.341409\pi$
$41$	−3.23510	−	4.45273i	−0.505237	−	0.695400i	−0.983107	+	0.183031i	$0.941409\pi$
$42$	4.78313	+	0.210466i	0.738054	+	0.0324756i
$43$		−	8.41043i		−	1.28258i	−0.767299	−	0.641290i	$-0.778400\pi$
$43$		−	8.41043i		−	1.28258i	0.767299	−	0.641290i	$-0.221600\pi$
$44$	6.55657	−	3.73386i	0.988441	−	0.562900i
$45$	−2.86397	−	6.06611i	−0.426935	−	0.904282i
$46$	−8.81866	+	7.89321i	−1.30024	+	1.16379i
$47$	1.45527	−	0.472847i	0.212273	−	0.0689718i	−0.200950	−	0.979601i	$-0.564403\pi$
$47$	1.45527	−	0.472847i	0.212273	−	0.0689718i	0.413223	+	0.910630i	$0.364403\pi$
$48$	−5.38207	−	4.36272i	−0.776835	−	0.629704i
$49$	−3.17955			−0.454222
$50$	7.07101	+	0.0276044i	0.999992	+	0.00390385i
$51$	1.77236	−	12.0755i	0.248180	−	1.69091i
$52$	−4.17288	+	0.861185i	−0.578675	+	0.119425i
$53$	−0.906474	+	0.294531i	−0.124514	+	0.0404570i	−0.370611	−	0.928788i	$-0.620852\pi$
$53$	−0.906474	+	0.294531i	−0.124514	+	0.0404570i	0.246097	+	0.969245i	$0.420852\pi$
$54$	7.03555	−	2.12158i	0.957417	−	0.288710i
$55$	−7.30364	−	4.22135i	−0.984822	−	0.569207i
$56$	−4.44356	−	3.28912i	−0.593796	−	0.439527i
$57$	−0.327990	+	2.23467i	−0.0434434	+	0.295989i
$58$	0.292847	+	2.86790i	0.0384528	+	0.376573i
$59$	−0.361751	−	0.497907i	−0.0470960	−	0.0648220i	0.784820	−	0.619724i	$-0.212756\pi$
$59$	−0.361751	−	0.497907i	−0.0470960	−	0.0648220i	−0.831915	+	0.554902i	$0.812756\pi$
$60$	−1.17382	+	7.65651i	−0.151539	+	0.988451i
$61$	7.41094	−	10.2003i	0.948873	−	1.30601i	−0.00315249	−	0.999995i	$-0.501003\pi$
$61$	7.41094	−	10.2003i	0.948873	−	1.30601i	0.952026	−	0.306017i	$-0.0989965\pi$
$62$	−5.26157	−	3.05857i	−0.668220	−	0.388439i
$63$	5.53424	−	1.93809i	0.697249	−	0.244176i
$64$	2.33662	+	7.65116i	0.292078	+	0.956395i
$65$	3.18589	+	3.54165i	0.395162	+	0.439288i
$66$	5.75510	−	7.23010i	0.708404	−	0.889964i
$67$	−10.9221	−	3.54880i	−1.33434	−	0.433554i	−0.446946	−	0.894561i	$-0.647488\pi$
$67$	−10.9221	−	3.54880i	−1.33434	−	0.433554i	−0.887397	+	0.461006i	$0.847488\pi$
$68$	−9.49186	+	10.4171i	−1.15106	+	1.26326i
$69$	−6.43366	+	12.9890i	−0.774522	+	1.56370i
$70$	−0.667181	+	6.14486i	−0.0797434	+	0.734451i
$71$	−2.33603	−	7.18955i	−0.277235	−	0.853242i	−0.988619	−	0.150439i	$-0.951931\pi$
$71$	−2.33603	−	7.18955i	−0.277235	−	0.853242i	0.711384	−	0.702803i	$-0.248069\pi$
$72$	−8.10543	−	2.51038i	−0.955234	−	0.295851i
$73$	8.16865	−	11.2432i	0.956068	−	1.31592i	0.00728981	−	0.999973i	$-0.497680\pi$
$73$	8.16865	−	11.2432i	0.956068	−	1.31592i	0.948779	−	0.315942i	$-0.102320\pi$
$74$	−5.93482	+	2.62133i	−0.689909	+	0.304723i
$75$	8.05232	−	3.18750i	0.929802	−	0.368060i
$76$	1.75655	−	1.92777i	0.201490	−	0.221131i
$77$	4.33429	−	5.96563i	0.493938	−	0.679847i
$78$	−4.35254	+	2.87876i	−0.492829	+	0.325955i
$79$	10.3991	−	3.37889i	1.17000	−	0.380155i	0.341354	−	0.939935i	$-0.389114\pi$
$79$	10.3991	−	3.37889i	1.17000	−	0.380155i	0.828641	+	0.559780i	$0.189114\pi$
$80$	6.06627	−	6.57270i	0.678230	−	0.734850i
$81$	7.03364	−	5.61497i	0.781515	−	0.623886i
$82$	3.14484	+	7.12007i	0.347289	+	0.786280i
$83$	−0.864776	+	2.66151i	−0.0949215	+	0.292138i	−0.987233	−	0.159281i	$-0.949082\pi$
$83$	−0.864776	+	2.66151i	−0.0949215	+	0.292138i	0.892312	+	0.451420i	$0.149082\pi$
$84$	−6.54962	−	1.71693i	−0.714622	−	0.187332i
$85$	15.4105	+	3.28321i	1.67151	+	0.356114i
$86$	−2.50736	+	11.6269i	−0.270376	+	1.25376i
$87$	1.63850	+	3.12749i	0.175665	+	0.335302i
$88$	−10.1772	+	3.20713i	−1.08489	+	0.341881i
$89$	−8.87863	+	12.2204i	−0.941133	+	1.29536i	0.0142226	+	0.999899i	$0.495473\pi$
$89$	−8.87863	+	12.2204i	−0.941133	+	1.29536i	−0.955355	+	0.295459i	$0.904527\pi$
$90$	2.15078	+	9.23981i	0.226712	+	0.973962i
$91$	−3.36882	+	2.44759i	−0.353148	+	0.256577i
$92$	14.5444	−	8.28278i	1.51636	−	0.863539i
$93$	−7.37474	−	1.08242i	−0.764725	−	0.112241i
$94$	−2.15278	+	0.219826i	−0.222043	+	0.0226733i
$95$	−2.85185	−	0.607586i	−0.292594	−	0.0623371i
$96$	6.13972	+	7.63570i	0.626632	+	0.779315i
$97$	−3.15132	+	1.02393i	−0.319968	+	0.103964i	−0.464597	−	0.885522i	$-0.653801\pi$
$97$	−3.15132	+	1.02393i	−0.319968	+	0.103964i	0.144630	+	0.989486i	$0.453801\pi$
$98$	4.39552	+	0.947905i	0.444015	+	0.0957528i
$99$	3.25225	−	10.8405i	0.326864	−	1.08951i
$100$	−9.76697	−	2.14621i	−0.976697	−	0.214621i
$101$	−16.6923			−1.66094			−0.830472	−	0.557061i	$-0.811929\pi$
$101$	−16.6923			−1.66094			−0.830472	+	0.557061i	$0.811929\pi$
$102$	−6.05017	+	16.1652i	−0.599056	+	1.60059i
$103$	−2.40026	−	7.38723i	−0.236504	−	0.727886i	−0.996918	−	0.0784470i	$-0.975004\pi$
$103$	−2.40026	−	7.38723i	−0.236504	−	0.727886i	0.760414	−	0.649439i	$-0.224996\pi$
$104$	6.02547	+	0.0535101i	0.590846	+	0.00524710i
$105$	2.03869	+	7.29043i	0.198956	+	0.711473i
$106$	1.34095	−	0.136927i	0.130244	−	0.0132996i
$107$	−0.182459			−0.0176389			−0.00881947	−	0.999961i	$-0.502807\pi$
$107$	−0.182459			−0.0176389			−0.00881947	+	0.999961i	$0.502807\pi$
$108$	−10.3587	+	0.835467i	−0.996763	+	0.0803929i
$109$	5.23045	+	7.19910i	0.500986	+	0.689549i	0.982367	−	0.186963i	$-0.0598645\pi$
$109$	5.23045	+	7.19910i	0.500986	+	0.689549i	−0.481381	+	0.876512i	$0.659864\pi$
$110$	8.83830	+	8.01314i	0.842699	+	0.764023i
$111$	−5.55461	+	5.68212i	−0.527220	+	0.539323i
$112$	5.16236	+	5.87173i	0.487797	+	0.554826i
$113$	−2.77605	+	2.01692i	−0.261149	+	0.189736i	−0.710653	−	0.703542i	$-0.751600\pi$
$113$	−2.77605	+	2.01692i	−0.261149	+	0.189736i	0.449505	+	0.893278i	$0.351600\pi$
$114$	1.11964	−	2.99150i	0.104864	−	0.280180i
$115$	−16.2016	−	9.36418i	−1.51080	−	0.873214i
$116$	0.450149	−	4.05198i	0.0417953	−	0.376217i
$117$	−3.63837	+	5.25453i	−0.336368	+	0.485781i
$118$	0.351658	+	0.796171i	0.0323727	+	0.0732935i
$119$	−4.25609	+	13.0989i	−0.390156	+	1.20078i
$120$	3.90532	−	10.2347i	0.356505	−	0.934293i
$121$	−0.998925	−	3.07438i	−0.0908114	−	0.279489i
$122$	−13.2861	+	11.8918i	−1.20287	+	1.07663i
$123$	6.81690	+	6.66393i	0.614659	+	0.600866i
$124$	6.36193	+	5.79687i	0.571318	+	0.520575i
$125$	3.43986	+	10.6380i	0.307670	+	0.951493i
$126$	−8.22851	+	1.02938i	−0.733054	+	0.0917047i
$127$	−2.47665	−	1.79939i	−0.219767	−	0.159670i	0.472455	−	0.881355i	$-0.343368\pi$
$127$	−2.47665	−	1.79939i	−0.219767	−	0.159670i	−0.692222	+	0.721685i	$0.743368\pi$
$128$	−0.949221	−	11.2738i	−0.0839000	−	0.996474i
$129$	2.44193	+	14.3612i	0.215000	+	1.26443i
$130$	−3.34843	−	5.84589i	−0.293677	−	0.512719i
$131$	4.84277	+	1.57351i	0.423115	+	0.137478i	0.512832	−	0.858489i	$-0.328596\pi$
$131$	4.84277	+	1.57351i	0.423115	+	0.137478i	−0.0897174	+	0.995967i	$0.528596\pi$
$132$	−10.1115	+	8.27939i	−0.880094	+	0.720629i
$133$	0.787627	−	2.42407i	0.0682959	−	0.210193i
$134$	14.0410	+	8.16211i	1.21296	+	0.705099i
$135$	6.65161	+	9.52660i	0.572480	+	0.819919i
$136$	16.2275	−	11.5712i	1.39149	−	0.992220i
$137$	5.87482	−	4.26831i	0.501920	−	0.364666i	−0.307830	−	0.951441i	$-0.599603\pi$
$137$	5.87482	−	4.26831i	0.501920	−	0.364666i	0.809750	+	0.586775i	$0.199603\pi$
$138$	12.7665	−	16.0385i	1.08675	−	1.36528i
$139$	14.2006	+	10.3174i	1.20448	+	0.875107i	0.994718	−	0.102645i	$-0.0327306\pi$
$139$	14.2006	+	10.3174i	1.20448	+	0.875107i	0.209763	+	0.977752i	$0.432731\pi$
$140$	2.75427	−	8.29596i	0.232778	−	0.701136i
$141$	−2.34765	+	1.22994i	−0.197708	+	0.103579i
$142$	1.08602	+	10.6355i	0.0911364	+	0.892511i
$143$			8.03721i			0.672105i
$144$	10.4568	+	5.88686i	0.871401	+	0.490572i
$145$	−4.16492	+	1.85199i	−0.345878	+	0.153799i
$146$	−14.6445	+	13.1077i	−1.21199	+	1.08480i
$147$	5.42922	−	0.923170i	0.447795	−	0.0761418i
$148$	8.98597	−	1.85449i	0.738642	−	0.152438i
$149$	15.0202			1.23050			0.615250	−	0.788332i	$-0.289055\pi$
$149$	15.0202			1.23050			0.615250	+	0.788332i	$0.289055\pi$
$150$	−12.0821	+	2.00590i	−0.986497	+	0.163781i
$151$			9.00360i			0.732702i	0.930477	+	0.366351i	$0.119393\pi$
$151$			9.00360i			0.732702i	−0.930477	+	0.366351i	$0.880607\pi$
$152$	−3.00303	+	2.14134i	−0.243578	+	0.173686i
$153$	0.479684	+	21.1340i	0.0387802	+	1.70858i
$154$	−7.77037	+	6.95493i	−0.626154	+	0.560444i
$155$	2.00512	−	9.41153i	0.161055	−	0.755952i
$156$	6.87533	−	2.68209i	0.550467	−	0.214739i
$157$	4.26928			0.340726			0.170363	−	0.985381i	$-0.445506\pi$
$157$	4.26928			0.340726			0.170363	+	0.985381i	$0.445506\pi$
$158$	−15.3835	+	1.57084i	−1.22384	+	0.124969i
$159$	1.46233	−	0.766116i	0.115970	−	0.0607569i
$160$	−10.3457	+	7.27781i	−0.817899	+	0.575361i
$161$	9.61470	−	13.2335i	0.757744	−	1.04295i
$162$	−11.3975	+	5.66542i	−0.895472	+	0.445118i
$163$	−4.25673	−	5.85888i	−0.333413	−	0.458903i	0.609090	−	0.793101i	$-0.291535\pi$
$163$	−4.25673	−	5.85888i	−0.333413	−	0.458903i	−0.942503	+	0.334198i	$0.891535\pi$
$164$	−2.22486	−	10.7806i	−0.173732	−	0.841821i
$165$	13.6969	+	5.08756i	1.06630	+	0.396066i
$166$	1.98896	−	3.42155i	0.154373	−	0.265563i
$167$	12.1290	+	3.94096i	0.938572	+	0.304961i	0.738064	−	0.674731i	$-0.235740\pi$
$167$	12.1290	+	3.94096i	0.938572	+	0.304961i	0.200509	+	0.979692i	$0.435740\pi$
$168$	8.54255	+	4.32614i	0.659072	+	0.333769i
$169$	−2.61470	+	8.04723i	−0.201131	+	0.619017i
$170$	−20.3252	−	9.13309i	−1.55887	−	0.700476i
$171$	−0.0887697	−	3.91103i	−0.00678839	−	0.299084i
$172$	6.93252	−	15.3259i	0.528599	−	1.16859i
$173$	7.10790	−	9.78318i	0.540403	−	0.743802i	−0.448268	−	0.893899i	$-0.647959\pi$
$173$	7.10790	−	9.78318i	0.540403	−	0.743802i	0.988671	+	0.150098i	$0.0479589\pi$
$174$	−1.33273	−	4.81203i	−0.101034	−	0.364799i
$175$	−9.56133	+	2.02289i	−0.722769	+	0.152916i
$176$	15.0254	−	1.39957i	1.13258	−	0.105497i
$177$	0.762270	+	0.745165i	0.0572957	+	0.0560100i
$178$	15.9173	−	14.2469i	1.19305	−	1.06785i
$179$	−18.0831	+	5.87556i	−1.35159	+	0.439160i	−0.893228	−	0.449604i	$-0.851565\pi$
$179$	−18.0831	+	5.87556i	−1.35159	+	0.439160i	−0.458366	+	0.888763i	$0.651565\pi$
$180$	−0.218695	−	13.4146i	−0.0163005	−	0.999867i
$181$	−20.4803	−	6.65445i	−1.52229	−	0.494621i	−0.575863	−	0.817546i	$-0.695334\pi$
$181$	−20.4803	−	6.65445i	−1.52229	−	0.494621i	−0.946425	+	0.322925i	$0.895334\pi$
$182$	5.38686	−	2.37930i	0.399300	−	0.176366i
$183$	−9.69288	+	19.5691i	−0.716518	+	1.44659i
$184$	−22.5759	+	7.11435i	−1.66432	+	0.524477i
$185$	−6.86057	−	7.62667i	−0.504399	−	0.560724i
$186$	9.87239	+	3.69496i	0.723879	+	0.270928i
$187$	15.6255	+	21.5066i	1.14265	+	1.57272i
$188$	3.04162	+	0.337904i	0.221833	+	0.0246442i
$189$	−8.88723	+	4.91621i	−0.646451	+	0.357602i
$190$	3.76136	+	1.69016i	0.272878	+	0.122617i
$191$	2.36511	−	1.71835i	0.171133	−	0.124336i	−0.498922	−	0.866647i	$-0.666270\pi$
$191$	2.36511	−	1.71835i	0.171133	−	0.124336i	0.670055	+	0.742311i	$0.266270\pi$
$192$	−6.21136	−	12.3862i	−0.448266	−	0.893900i
$193$		−	5.32811i		−	0.383526i	−0.981441	−	0.191763i	$-0.938580\pi$
$193$		−	5.32811i		−	0.383526i	0.981441	−	0.191763i	$-0.0614205\pi$
$194$	4.66174	−	0.476022i	0.334694	−	0.0341764i
$195$	−6.46835	−	5.12251i	−0.463208	−	0.366831i
$196$	−5.79392	−	2.62083i	−0.413852	−	0.187202i
$197$	−12.8302	+	4.16880i	−0.914116	+	0.297014i	−0.728051	−	0.685523i	$-0.759574\pi$
$197$	−12.8302	+	4.16880i	−0.914116	+	0.297014i	−0.186065	+	0.982537i	$0.559574\pi$
$198$	−7.72784	+	14.0167i	−0.549194	+	0.996121i
$199$		−	23.6410i		−	1.67587i	−0.545774	−	0.837933i	$-0.683764\pi$
$199$		−	23.6410i		−	1.67587i	0.545774	−	0.837933i	$-0.316236\pi$
$200$	12.8624	+	5.87877i	0.909506	+	0.415692i
$201$	19.6803	+	2.88854i	1.38814	+	0.203742i
$202$	23.0760	+	4.97638i	1.62362	+	0.350137i
$203$	−1.23123	−	3.78935i	−0.0864156	−	0.265960i
$204$	13.1832	−	20.5435i	0.923008	−	1.43834i
$205$	−9.14980	+	8.23070i	−0.639050	+	0.574857i
$206$	1.11588	+	10.9279i	0.0777468	+	0.761385i
$207$	7.21444	−	24.0473i	0.501438	−	1.67140i
$208$	−8.31386	−	1.87032i	−0.576462	−	0.129683i
$209$	−2.89162	−	3.97998i	−0.200018	−	0.275301i
$210$	−0.644895	−	10.6863i	−0.0445020	−	0.737426i
$211$	−0.585199	−	0.425172i	−0.0402868	−	0.0292701i	0.567460	−	0.823401i	$-0.307926\pi$
$211$	−0.585199	−	0.425172i	−0.0402868	−	0.0292701i	−0.607746	+	0.794131i	$0.707926\pi$
$212$	−1.89459	−	0.210477i	−0.130121	−	0.0144556i
$213$	6.07632	+	11.5982i	0.416342	+	0.794695i
$214$	0.252237	+	0.0543955i	0.0172426	+	0.00371840i
$215$	−18.7042	+	1.95697i	−1.27562	+	0.133464i
$216$	14.5692	+	1.93320i	0.991311	+	0.131538i
$217$	7.99977	+	2.59928i	0.543060	+	0.176451i
$218$	−5.08452	−	11.5116i	−0.344367	−	0.779664i
$219$	−10.6839	+	21.5699i	−0.721951	+	1.45756i
$220$	−9.82944	−	13.7125i	−0.662701	−	0.924500i
$221$	−4.63893	−	14.2771i	−0.312048	−	0.960385i
$222$	9.37286	−	6.19918i	0.629065	−	0.416062i
$223$	17.8306	+	12.9547i	1.19402	+	0.867509i	0.993684	−	0.112217i	$-0.0357952\pi$
$223$	17.8306	+	12.9547i	1.19402	+	0.867509i	0.200340	+	0.979726i	$0.435795\pi$
$224$	−5.38611	−	9.65630i	−0.359874	−	0.645189i
$225$	−12.8242	+	7.78074i	−0.854947	+	0.518716i
$226$	4.43899	−	1.96064i	0.295277	−	0.130420i
$227$	20.6726	+	15.0195i	1.37209	+	0.996880i	0.997571	+	0.0696596i	$0.0221913\pi$
$227$	20.6726	+	15.0195i	1.37209	+	0.996880i	0.374517	+	0.927220i	$0.377809\pi$
$228$	−2.43966	+	3.80176i	−0.161571	+	0.251778i
$229$	−21.6697	+	7.04090i	−1.43197	+	0.465276i	−0.919385	−	0.393359i	$-0.871313\pi$
$229$	−21.6697	+	7.04090i	−1.43197	+	0.465276i	−0.512587	+	0.858635i	$0.671313\pi$
$230$	19.6059	+	17.7754i	1.29277	+	1.17208i
$231$	−5.66888	+	11.4450i	−0.372985	+	0.753026i
$232$	−1.83030	+	5.46739i	−0.120165	+	0.358952i
$233$	5.70002	−	17.5428i	0.373420	−	1.14927i	−0.571118	−	0.820868i	$-0.693490\pi$
$233$	5.70002	−	17.5428i	0.373420	−	1.14927i	0.944538	−	0.328402i	$-0.106510\pi$
$234$	6.59632	−	6.17934i	0.431215	−	0.403956i
$235$	−1.39019	−	3.12640i	−0.0906863	−	0.203944i
$236$	−0.248785	−	1.20549i	−0.0161945	−	0.0784708i
$237$	−16.7759	+	8.78894i	−1.08971	+	0.570903i
$238$	9.78888	−	16.8395i	0.634519	−	1.09154i
$239$	−2.04007	−	1.48220i	−0.131961	−	0.0958754i	0.519847	−	0.854260i	$-0.325989\pi$
$239$	−2.04007	−	1.48220i	−0.131961	−	0.0958754i	−0.651808	+	0.758384i	$0.725989\pi$
$240$	−8.45005	+	12.9845i	−0.545449	+	0.838144i
$241$	1.42155	−	1.03282i	0.0915702	−	0.0665296i	−0.541058	−	0.840985i	$-0.681976\pi$
$241$	1.42155	−	1.03282i	0.0915702	−	0.0665296i	0.632628	+	0.774456i	$0.281976\pi$
$242$	0.464399	+	4.54792i	0.0298527	+	0.292352i
$243$	−10.3799	+	11.6300i	−0.665874	+	0.746064i
$244$	21.9124	−	12.4787i	1.40280	−	0.798869i
$245$	0.739830	+	7.07110i	0.0472660	+	0.451756i
$246$	−7.43722	−	11.2447i	−0.474180	−	0.716937i
$247$	0.858473	+	2.64211i	0.0546233	+	0.168113i
$248$	−7.06675	−	9.91044i	−0.448739	−	0.629314i
$249$	0.703885	−	4.79572i	0.0446069	−	0.303916i
$250$	−1.58392	−	15.7319i	−0.100176	−	0.994970i
$251$		−	3.88280i		−	0.245080i	−0.992464	−	0.122540i	$-0.960896\pi$
$251$		−	3.88280i		−	0.245080i	0.992464	−	0.122540i	$-0.0391040\pi$
$252$	11.6823	+	1.03007i	0.735913	+	0.0648884i
$253$	−9.75628	−	30.0267i	−0.613372	−	1.88777i
$254$	2.88736	+	3.22589i	0.181169	+	0.202410i
$255$	−27.2674	−	1.13184i	−1.70755	−	0.0708785i
$256$	−2.04877	+	15.8683i	−0.128048	+	0.991768i
$257$	12.5720			0.784218			0.392109	−	0.919919i	$-0.371746\pi$
$257$	12.5720			0.784218			0.392109	+	0.919919i	$0.371746\pi$
$258$	0.905614	−	20.5814i	0.0563811	−	1.28134i
$259$	7.25449	−	5.27069i	0.450772	−	0.327505i
$260$	2.88617	+	9.07981i	0.178993	+	0.563106i
$261$	−3.70586	−	4.86459i	−0.229387	−	0.301111i
$262$	−6.22570	−	3.61902i	−0.384625	−	0.223584i
$263$	−0.383515	−	0.527862i	−0.0236485	−	0.0325494i	0.797029	−	0.603941i	$-0.206404\pi$
$263$	−0.383515	−	0.527862i	−0.0236485	−	0.0325494i	−0.820678	+	0.571392i	$0.806404\pi$
$264$	16.4468	−	8.43121i	1.01223	−	0.518905i
$265$	0.865938	+	1.94740i	0.0531942	+	0.119628i
$266$	−1.81152	+	3.11630i	−0.111071	+	0.191073i
$267$	11.6125	−	23.4447i	0.710673	−	1.43479i
$268$	−16.9775	−	15.4696i	−1.03706	−	0.944954i
$269$	−1.42503	+	4.38579i	−0.0868855	+	0.267406i	−0.985054	−	0.172245i	$-0.944898\pi$
$269$	−1.42503	+	4.38579i	−0.0868855	+	0.267406i	0.898169	+	0.439651i	$0.144898\pi$
$270$	−6.35529	−	15.1529i	−0.386771	−	0.922176i
$271$	−3.90022	+	1.26726i	−0.236921	+	0.0769804i	−0.425071	−	0.905160i	$-0.639751\pi$
$271$	−3.90022	+	1.26726i	−0.236921	+	0.0769804i	0.188150	+	0.982140i	$0.439751\pi$
$272$	−25.8830	+	11.1586i	−1.56939	+	0.676587i
$273$	5.04175	−	5.15749i	0.305141	−	0.312145i
$274$	−9.39404	+	4.14922i	−0.567515	+	0.250664i
$275$	−7.68855	+	17.2250i	−0.463637	+	1.03871i
$276$	−22.4303	+	18.3661i	−1.35014	+	1.10551i
$277$	−4.70931	−	3.42151i	−0.282955	−	0.205579i	0.437250	−	0.899340i	$-0.355952\pi$
$277$	−4.70931	−	3.42151i	−0.282955	−	0.205579i	−0.720205	+	0.693761i	$0.755952\pi$
$278$	−16.5556	−	18.4966i	−0.992936	−	1.10935i
$279$	12.9070	−	0.292953i	0.772719	−	0.0175386i
$280$	−6.28083	+	10.6475i	−0.375351	+	0.636309i
$281$	−4.43477	−	1.44094i	−0.264556	−	0.0859595i	0.173735	−	0.984792i	$-0.444416\pi$
$281$	−4.43477	−	1.44094i	−0.264556	−	0.0859595i	−0.438292	+	0.898833i	$0.644416\pi$
$282$	3.61214	−	1.00041i	0.215100	−	0.0595737i
$283$	6.41212	+	2.08342i	0.381161	+	0.123847i	0.493330	−	0.869843i	$-0.335780\pi$
$283$	6.41212	+	2.08342i	0.381161	+	0.123847i	−0.112169	+	0.993689i	$0.535780\pi$
$284$	1.66936	−	15.0266i	0.0990585	−	0.891666i
$285$	5.04607	+	0.209456i	0.298903	+	0.0124071i
$286$	2.39609	−	11.1109i	0.141684	−	0.657001i
$287$	−6.32331	−	8.70329i	−0.373253	−	0.513739i
$288$	−12.7008	−	11.2556i	−0.748403	−	0.663244i
$289$	−26.4167	−	19.1928i	−1.55392	−	1.12899i
$290$	6.30985	−	1.31858i	0.370527	−	0.0774299i
$291$	5.08372	−	2.66337i	0.298013	−	0.156129i
$292$	24.1528	−	13.7546i	1.41343	−	0.804927i
$293$			5.81207i			0.339545i	0.985483	+	0.169772i	$0.0543032\pi$
$293$			5.81207i			0.339545i	−0.985483	+	0.169772i	$0.945697\pi$
$294$	−7.78076	−	0.342366i	−0.453783	−	0.0199672i
$295$	−1.02314	+	0.920363i	−0.0595694	+	0.0535856i
$296$	−12.9754	−	0.115230i	−0.754179	−	0.00669760i
$297$	−2.40587	+	19.4549i	−0.139603	+	1.12889i
$298$	−20.7644	−	4.47789i	−1.20285	−	0.259397i
$299$			17.8288i			1.03107i
$300$	17.3007	+	0.828940i	0.998854	+	0.0478589i
$301$		−	16.4390i		−	0.947528i
$302$	2.68420	−	12.4469i	0.154458	−	0.716237i
$303$	28.5028	−	4.84653i	1.63744	−	0.278426i
$304$	4.78988	−	2.06499i	0.274718	−	0.118435i
$305$	−24.4091	−	14.1080i	−1.39766	−	0.807820i
$306$	5.63744	−	29.3593i	0.322271	−	1.67836i
$307$			0.799007i			0.0456017i	0.999740	+	0.0228009i	$0.00725837\pi$
$307$			0.799007i			0.0456017i	−0.999740	+	0.0228009i	$0.992742\pi$
$308$	12.8155	−	7.29819i	0.730228	−	0.415853i
$309$	6.24339	+	11.9171i	0.355174	+	0.677941i
$310$	−5.57776	+	12.4130i	−0.316796	+	0.705013i
$311$	−9.63444	−	6.99983i	−0.546319	−	0.396924i	0.280108	−	0.959969i	$-0.409630\pi$
$311$	−9.63444	−	6.99983i	−0.546319	−	0.396924i	−0.826426	+	0.563045i	$0.809630\pi$
$312$	−10.3043	+	1.65810i	−0.583365	+	0.0938714i
$313$	18.2960	+	25.1823i	1.03415	+	1.42339i	0.901783	+	0.432189i	$0.142259\pi$
$313$	18.2960	+	25.1823i	1.03415	+	1.42339i	0.132370	+	0.991200i	$0.457741\pi$
$314$	−5.90199	−	1.27278i	−0.333069	−	0.0718271i
$315$	−5.59790	−	11.8568i	−0.315406	−	0.668055i
$316$	21.7349	+	2.41461i	1.22268	+	0.135833i
$317$	30.3014	+	9.84551i	1.70189	+	0.552979i	0.988951	−	0.148242i	$-0.0473616\pi$
$317$	30.3014	+	9.84551i	1.70189	+	0.552979i	0.712943	+	0.701221i	$0.247362\pi$
$318$	−2.24997	+	0.623147i	−0.126172	+	0.0349444i
$319$	−7.31390	−	2.37643i	−0.409500	−	0.133055i
$320$	16.4719	−	6.97677i	0.920809	−	0.390014i
$321$	0.311556	−	0.0529761i	0.0173893	−	0.00295684i
$322$	−17.2369	+	15.4280i	−0.960576	+	0.859771i
$323$	7.43380	+	5.40097i	0.413628	+	0.300518i
$324$	17.4453	−	4.43419i	0.969182	−	0.246344i
$325$	7.13508	−	7.90929i	0.395783	−	0.438728i
$326$	4.13796	+	9.36855i	0.229181	+	0.518876i
$327$	−11.0214	−	10.7741i	−0.609487	−	0.595810i
$328$	−0.138242	+	15.5667i	−0.00763316	+	0.859527i
$329$	2.84447	−	0.924224i	0.156821	−	0.0509541i
$330$	−17.4183	−	11.1166i	−0.958848	−	0.611949i
$331$	−1.03336	+	3.18036i	−0.0567987	+	0.174808i	−0.975431	−	0.220305i	$-0.929295\pi$
$331$	−1.03336	+	3.18036i	−0.0567987	+	0.174808i	0.918632	+	0.395113i	$0.129295\pi$
$332$	−3.76965	+	4.13710i	−0.206886	+	0.227053i
$333$	7.83495	−	11.3152i	0.429353	−	0.620070i
$334$	−15.5927	−	9.06408i	−0.853193	−	0.495964i
$335$	−5.35088	+	25.1156i	−0.292350	+	1.37221i
$336$	−10.5198	−	8.52735i	−0.573901	−	0.465205i
$337$	−0.775653	−	1.06759i	−0.0422525	−	0.0581556i	0.787368	−	0.616483i	$-0.211443\pi$
$337$	−0.775653	−	1.06759i	−0.0422525	−	0.0581556i	−0.829621	+	0.558328i	$0.811443\pi$
$338$	6.01373	−	10.3452i	0.327104	−	0.562707i
$339$	4.15461	−	4.24998i	0.225648	−	0.230827i
$340$	25.3755	+	18.6853i	1.37618	+	1.01335i
$341$	13.1345	−	9.54278i	0.711274	−	0.516771i
$342$	−1.04326	+	5.43320i	−0.0564128	+	0.293794i
$343$	−19.8969			−1.07433
$344$	−14.1528	+	19.1202i	−0.763066	+	1.03089i
$345$	30.3837	+	11.2857i	1.63580	+	0.607600i
$346$	−12.7428	+	11.4056i	−0.685057	+	0.613166i
$347$	6.37016	+	19.6053i	0.341968	+	1.05247i	0.963187	+	0.268832i	$0.0866377\pi$
$347$	6.37016	+	19.6053i	0.341968	+	1.05247i	−0.621219	+	0.783637i	$0.713362\pi$
$348$	0.407826	+	7.04962i	0.0218618	+	0.377900i
$349$			30.5926i			1.63759i	0.574088	+	0.818793i	$0.305357\pi$
$349$			30.5926i			1.63759i	−0.574088	+	0.818793i	$0.694643\pi$
$350$	13.8210	+	0.0539554i	0.738762	+	0.00288404i
$351$	4.68705	−	10.0287i	0.250176	−	0.535293i
$352$	−21.1889	−	2.54463i	−1.12937	−	0.135629i
$353$	4.07690	+	12.5474i	0.216991	+	0.667831i	0.999006	+	0.0445709i	$0.0141921\pi$
$353$	4.07690	+	12.5474i	0.216991	+	0.667831i	−0.782015	+	0.623260i	$0.785808\pi$
$354$	−0.831635	−	1.25739i	−0.0442009	−	0.0668297i
$355$	−15.4455	+	6.86804i	−0.819761	+	0.364518i
$356$	−26.2520	+	14.9501i	−1.39135	+	0.792352i
$357$	3.46425	−	23.6027i	0.183347	−	1.24919i
$358$	26.7503	−	2.73154i	1.41380	−	0.144366i
$359$	19.7313	−	14.3357i	1.04138	−	0.756607i	0.0708261	−	0.997489i	$-0.477436\pi$
$359$	19.7313	−	14.3357i	1.04138	−	0.756607i	0.970555	+	0.240881i	$0.0774365\pi$
$360$	−3.69690	+	18.6100i	−0.194844	+	0.980834i
$361$	13.9956	+	10.1684i	0.736612	+	0.535180i
$362$	26.3288	+	15.3050i	1.38381	+	0.804414i
$363$	2.59834	+	4.95959i	0.136377	+	0.260311i
$364$	−8.15630	+	1.68327i	−0.427506	+	0.0882272i
$365$	−26.9047	−	15.5504i	−1.40826	−	0.813945i
$366$	19.2338	−	24.1633i	1.00537	−	1.26304i
$367$	8.99721	−	27.6906i	0.469651	−	1.44544i	−0.383388	−	0.923587i	$-0.625243\pi$
$367$	8.99721	−	27.6906i	0.469651	−	1.44544i	0.853038	−	0.521848i	$-0.174757\pi$
$368$	33.3307	−	3.10466i	1.73748	−	0.161842i
$369$	−13.5750	−	9.39968i	−0.706685	−	0.489328i
$370$	7.21058	+	12.5887i	0.374860	+	0.654454i
$371$	−1.77179	+	0.575690i	−0.0919868	+	0.0298883i
$372$	−12.5464	−	8.05124i	−0.650498	−	0.417438i
$373$	15.4533	+	11.2275i	0.800141	+	0.581337i	0.910956	−	0.412504i	$-0.135346\pi$
$373$	15.4533	+	11.2275i	0.800141	+	0.581337i	−0.110814	+	0.993841i	$0.535346\pi$
$374$	−15.1895	−	34.3898i	−0.785430	−	1.77825i
$375$	−8.96241	−	17.1661i	−0.462817	−	0.886454i
$376$	−4.10409	−	1.37391i	−0.211652	−	0.0708541i
$377$	3.51335	+	2.55260i	0.180947	+	0.131466i
$378$	13.7516	−	4.14683i	0.707309	−	0.213290i
$379$	−1.56278	−	4.80975i	−0.0802747	−	0.247060i	0.902863	−	0.429929i	$-0.141462\pi$
$379$	−1.56278	−	4.80975i	−0.0802747	−	0.247060i	−0.983137	+	0.182869i	$0.941462\pi$
$380$	−4.69595	−	3.45788i	−0.240897	−	0.177386i
$381$	4.75142	+	2.35345i	0.243423	+	0.120571i
$382$	−3.78189	+	1.67041i	−0.193498	+	0.0854656i
$383$	9.42206	+	3.06141i	0.481445	+	0.156431i	0.539677	−	0.841872i	$-0.318546\pi$
$383$	9.42206	+	3.06141i	0.481445	+	0.156431i	−0.0582323	+	0.998303i	$0.518546\pi$
$384$	4.89414	+	18.9749i	0.249753	+	0.968310i
$385$	−14.2757	−	8.25104i	−0.727555	−	0.420512i
$386$	−1.58844	+	7.36576i	−0.0808496	+	0.374907i
$387$	−8.33941	−	23.8133i	−0.423916	−	1.21050i
$388$	−6.58646	−	0.731715i	−0.334377	−	0.0371472i
$389$	16.5807	+	12.0466i	0.840677	+	0.610788i	0.922560	−	0.385854i	$-0.126093\pi$
$389$	16.5807	+	12.0466i	0.840677	+	0.610788i	−0.0818828	+	0.996642i	$0.526093\pi$
$390$	7.41492	+	9.00991i	0.375469	+	0.456234i
$391$	34.6618	+	47.7078i	1.75292	+	2.41269i
$392$	7.22837	+	5.35044i	0.365088	+	0.270238i
$393$	−8.72609	−	1.28076i	−0.440173	−	0.0646057i
$394$	18.9798	−	1.93807i	0.956187	−	0.0976384i
$395$	−9.93411	−	22.3407i	−0.499839	−	1.12409i
$396$	14.8619	−	17.0732i	0.746841	−	0.857963i
$397$	7.43601	+	22.8857i	0.373203	+	1.14860i	0.944683	+	0.327984i	$0.106369\pi$
$397$	7.43601	+	22.8857i	0.373203	+	1.14860i	−0.571481	+	0.820616i	$0.693631\pi$
$398$	−7.04797	+	32.6821i	−0.353283	+	1.63820i
$399$	−0.641089	+	4.36788i	−0.0320946	+	0.218667i
$400$	−16.0287	−	11.9616i	−0.801437	−	0.598080i
$401$			17.0229i			0.850084i	0.905174	+	0.425042i	$0.139741\pi$
$401$			17.0229i			0.850084i	−0.905174	+	0.425042i	$0.860259\pi$
$402$	−26.3455	−	9.86040i	−1.31399	−	0.491792i
$403$	−8.71934	+	2.83309i	−0.434341	+	0.141126i
$404$	−30.4174	−	13.7590i	−1.51332	−	0.684538i
$405$	−14.1239	−	14.3358i	−0.701823	−	0.712351i
$406$	0.572399	+	5.60558i	0.0284077	+	0.278200i
$407$		−	17.3075i		−	0.857901i
$408$	−24.3494	+	24.4698i	−1.20548	+	1.21144i
$409$	15.9374	−	11.5792i	0.788054	−	0.572554i	−0.119332	−	0.992854i	$-0.538075\pi$
$409$	15.9374	−	11.5792i	0.788054	−	0.572554i	0.907385	+	0.420300i	$0.138075\pi$
$410$	15.1028	−	8.65061i	0.745873	−	0.427223i
$411$	−8.79222	+	8.99405i	−0.433688	+	0.443644i
$412$	1.71527	−	15.4398i	0.0845051	−	0.760665i
$413$	−0.707077	−	0.973208i	−0.0347930	−	0.0478884i
$414$	−17.1426	+	31.0930i	−0.842512	+	1.52814i
$415$	6.12022	+	1.30391i	0.300430	+	0.0640065i
$416$	10.9358	+	5.06416i	0.536170	+	0.248291i
$417$	−27.2438	−	13.4942i	−1.33413	−	0.660815i
$418$	2.81095	+	6.36412i	0.137488	+	0.311279i
$419$	24.3199	+	7.90200i	1.18810	+	0.386038i	0.835371	−	0.549686i	$-0.185253\pi$
$419$	24.3199	+	7.90200i	1.18810	+	0.386038i	0.352732	+	0.935724i	$0.385253\pi$
$420$	−2.29434	+	14.9654i	−0.111952	+	0.730236i
$421$	−14.1777	+	4.60661i	−0.690979	+	0.224513i	−0.633396	−	0.773828i	$-0.718339\pi$
$421$	−14.1777	+	4.60661i	−0.690979	+	0.224513i	−0.0575831	+	0.998341i	$0.518339\pi$
$422$	0.682245	+	0.762235i	0.0332111	+	0.0371050i
$423$	3.65160	−	2.78180i	0.177547	−	0.135256i
$424$	2.55640	+	0.855796i	0.124150	+	0.0415611i
$425$	3.71585	−	35.0359i	0.180245	−	1.69949i
$426$	−4.94239	−	17.8452i	−0.239459	−	0.864604i
$427$	14.4854	−	19.9374i	0.700997	−	0.964840i
$428$	−0.332484	−	0.150396i	−0.0160712	−	0.00726967i
$429$	−2.33357	−	13.7239i	−0.112666	−	0.662595i
$430$	26.4407	+	2.87081i	1.27509	+	0.138443i
$431$	−0.811271	+	2.49684i	−0.0390776	+	0.120268i	−0.968692	−	0.248264i	$-0.920140\pi$
$431$	−0.811271	+	2.49684i	−0.0390776	+	0.120268i	0.929615	+	0.368533i	$0.120140\pi$
$432$	−19.5647	−	7.01598i	−0.941305	−	0.337556i
$433$	−15.6818	−	5.09534i	−0.753621	−	0.244866i	−0.0930824	−	0.995658i	$-0.529672\pi$
$433$	−15.6818	−	5.09534i	−0.753621	−	0.244866i	−0.660539	+	0.750792i	$0.729672\pi$
$434$	−10.2842	−	5.97827i	−0.493659	−	0.286966i
$435$	6.57407	−	4.37162i	0.315202	−	0.209603i
$436$	3.59711	+	17.4298i	0.172270	+	0.834738i
$437$	−6.41446	−	8.82874i	−0.306845	−	0.422336i
$438$	21.2003	−	26.6339i	1.01299	−	1.27262i
$439$	19.6962	−	27.1095i	0.940050	−	1.29387i	−0.0157575	−	0.999876i	$-0.505016\pi$
$439$	19.6962	−	27.1095i	0.940050	−	1.29387i	0.955808	−	0.293992i	$-0.0949840\pi$
$440$	9.50049	+	21.8871i	0.452918	+	1.04343i
$441$	−9.00259	+	3.15270i	−0.428695	+	0.150129i
$442$	2.15663	+	21.1202i	0.102580	+	1.00458i
$443$	15.7775			0.749611			0.374805	−	0.927104i	$-0.377710\pi$
$443$	15.7775			0.749611			0.374805	+	0.927104i	$0.377710\pi$
$444$	−14.8055	+	5.77566i	−0.702637	+	0.274101i
$445$	29.2432	+	16.9020i	1.38626	+	0.801230i
$446$	−20.7875	−	23.2247i	−0.984316	−	1.09972i
$447$	−25.6476	+	4.36104i	−1.21309	+	0.206270i
$448$	4.56715	+	14.9549i	0.215778	+	0.706554i
$449$			5.58581i			0.263611i	0.991276	+	0.131805i	$0.0420774\pi$
$449$			5.58581i			0.263611i	−0.991276	+	0.131805i	$0.957923\pi$
$450$	20.0482	−	6.93314i	0.945083	−	0.326831i
$451$	−20.7640			−0.977738
$452$	−6.72113	+	1.38708i	−0.316135	+	0.0652429i
$453$	−2.61416	−	15.3740i	−0.122824	−	0.722334i
$454$	−24.1008	−	26.9265i	−1.13111	−	1.26372i
$455$	6.22714	+	6.92250i	0.291933	+	0.324532i
$456$	4.50607	−	4.52835i	0.211016	−	0.212060i
$457$		−	1.19627i		−	0.0559590i	−0.999608	−	0.0279795i	$-0.991093\pi$
$457$		−	1.19627i		−	0.0559590i	0.999608	−	0.0279795i	$-0.00890731\pi$
$458$	32.0559	−	3.27331i	1.49788	−	0.152952i
$459$	−6.95524	−	35.9479i	−0.324643	−	1.67790i
$460$	−21.8045	−	30.4184i	−1.01664	−	1.41826i
$461$	23.1772	+	16.8392i	1.07947	+	0.784279i	0.977590	−	0.210518i	$-0.0675149\pi$
$461$	23.1772	+	16.8392i	1.07947	+	0.784279i	0.101878	+	0.994797i	$0.467515\pi$
$462$	11.2489	−	14.1319i	0.523346	−	0.657477i
$463$	−31.6013	+	22.9597i	−1.46864	+	1.06703i	−0.487631	+	0.873050i	$0.662139\pi$
$463$	−31.6013	+	22.9597i	−1.46864	+	1.06703i	−0.981006	+	0.193977i	$0.937861\pi$
$464$	4.16023	−	7.01264i	0.193134	−	0.325554i
$465$	−0.691237	+	16.6528i	−0.0320553	+	0.772253i
$466$	−13.1099	+	22.5525i	−0.607302	+	1.04472i
$467$	−0.932042	+	2.86853i	−0.0431297	+	0.132740i	−0.970303	−	0.241894i	$-0.922231\pi$
$467$	−0.932042	+	2.86853i	−0.0431297	+	0.132740i	0.927173	+	0.374633i	$0.122231\pi$
$468$	−10.9612	+	6.57600i	−0.506681	+	0.303976i
$469$	−21.3482	−	6.93646i	−0.985770	−	0.320296i
$470$	0.989794	+	4.73649i	0.0456558	+	0.218478i
$471$	−7.28997	+	1.23957i	−0.335904	+	0.0571162i
$472$	−0.0154584	+	1.74068i	−0.000711529	+	0.0801213i
$473$	−25.6695	−	18.6500i	−1.18029	−	0.857528i
$474$	25.8118	−	7.14880i	1.18558	−	0.328355i
$475$	−0.687650	+	6.48369i	−0.0315516	+	0.297492i
$476$	−18.5528	+	20.3612i	−0.850364	+	0.933254i
$477$	−2.27455	+	1.73275i	−0.104144	+	0.0793374i
$478$	2.37838	+	2.65724i	0.108785	+	0.121539i
$479$	3.50930	+	10.8005i	0.160344	+	0.493489i	0.998663	−	0.0516915i	$-0.0164613\pi$
$479$	3.50930	+	10.8005i	0.160344	+	0.493489i	−0.838319	+	0.545180i	$0.816461\pi$
$480$	15.5526	−	15.4310i	0.709877	−	0.704325i
$481$	−3.02021	+	9.29526i	−0.137710	+	0.423828i
$482$	−2.27311	+	1.00400i	−0.103537	+	0.0457310i
$483$	−12.5752	+	25.3883i	−0.572192	+	1.15521i
$484$	0.713849	−	6.42565i	0.0324477	−	0.292075i
$485$	3.01040	+	6.77006i	0.136695	+	0.307412i
$486$	17.8168	−	12.9832i	0.808185	−	0.588928i
$487$	−14.1265	+	10.2635i	−0.640131	+	0.465083i	−0.859895	−	0.510470i	$-0.829471\pi$
$487$	−14.1265	+	10.2635i	−0.640131	+	0.465083i	0.219764	+	0.975553i	$0.429471\pi$
$488$	−34.0126	+	10.7184i	−1.53968	+	0.485199i
$489$	8.96964	+	8.76837i	0.405621	+	0.396519i
$490$	1.08531	−	9.99589i	0.0490292	−	0.451568i
$491$	13.2612	+	18.2525i	0.598471	+	0.823725i	0.995567	−	0.0940519i	$-0.0299820\pi$
$491$	13.2612	+	18.2525i	0.598471	+	0.823725i	−0.397096	+	0.917777i	$0.629982\pi$
$492$	6.92913	+	17.7623i	0.312389	+	0.800786i
$493$	14.3639			0.646918
$494$	−0.399103	−	3.90847i	−0.0179565	−	0.175850i
$495$	−24.8652	−	4.71038i	−1.11761	−	0.211716i
$496$	6.81476	+	15.8073i	0.305992	+	0.709769i
$497$	−4.56599	−	14.0527i	−0.204812	−	0.630348i
$498$	−2.40280	+	6.41992i	−0.107672	+	0.287683i
$499$	−5.20170			−0.232860			−0.116430	−	0.993199i	$-0.537145\pi$
$499$	−5.20170			−0.232860			−0.116430	+	0.993199i	$0.537145\pi$
$500$	−2.50040	+	22.2204i	−0.111821	+	0.993728i
$501$	−21.8551	−	3.20774i	−0.976412	−	0.143311i
$502$	−1.15756	+	5.36771i	−0.0516644	+	0.239573i
$503$	−16.6063	+	5.39572i	−0.740439	+	0.240583i	−0.654862	−	0.755748i	$-0.727273\pi$
$503$	−16.6063	+	5.39572i	−0.740439	+	0.240583i	−0.0855770	+	0.996332i	$0.527273\pi$
$504$	−15.8428	−	4.90678i	−0.705696	−	0.218565i
$505$	3.88401	+	37.1224i	0.172836	+	1.65193i
$506$	4.53568	+	44.4186i	0.201636	+	1.97465i
$507$	2.12824	−	14.5001i	0.0945183	−	0.643974i
$508$	−3.02986	−	5.32037i	−0.134428	−	0.236053i
$509$	0.795868	−	0.578232i	0.0352762	−	0.0256297i	−0.570007	−	0.821640i	$-0.693060\pi$
$509$	0.795868	−	0.578232i	0.0352762	−	0.0256297i	0.605284	+	0.796010i	$0.293060\pi$
$510$	37.3579	+	9.69379i	1.65424	+	0.429248i
$511$	15.9664	−	21.9759i	0.706313	−	0.972156i
$512$	7.56303	−	21.3261i	0.334242	−	0.942487i
$513$	1.28713	+	6.65247i	0.0568281	+	0.293714i
$514$	−17.3799	−	3.74802i	−0.766595	−	0.165318i
$515$	−15.8702	+	7.05689i	−0.699324	+	0.310964i
$516$	−7.38777	+	28.1824i	−0.325228	+	1.24066i
$517$	1.78387	−	5.49018i	0.0784543	−	0.241458i
$518$	−11.6002	+	5.12364i	−0.509682	+	0.225120i
$519$	−9.29653	+	18.7689i	−0.408072	+	0.823865i
$520$	−1.28302	−	13.4127i	−0.0562643	−	0.588184i
$521$	28.5657	−	9.28156i	1.25149	−	0.406632i	0.393033	−	0.919525i	$-0.371426\pi$
$521$	28.5657	−	9.28156i	1.25149	−	0.406632i	0.858453	+	0.512892i	$0.171426\pi$
$522$	3.67284	+	7.82978i	0.160756	+	0.342700i
$523$	4.88625	−	6.72535i	0.213661	−	0.294079i	−0.688712	−	0.725035i	$-0.741824\pi$
$523$	4.88625	−	6.72535i	0.213661	−	0.294079i	0.902373	+	0.430956i	$0.141824\pi$
$524$	7.52769	+	6.85910i	0.328849	+	0.299641i
$525$	15.7390	−	6.23027i	0.686908	−	0.271911i
$526$	0.372814	+	0.844070i	0.0162555	+	0.0368032i
$527$	−17.8240	+	24.5326i	−0.776425	+	1.06866i
$528$	−25.2501	+	6.75239i	−1.09887	+	0.293860i
$529$	−14.5349	−	44.7337i	−0.631950	−	1.94494i
$530$	−0.616533	−	2.95031i	−0.0267805	−	0.128153i
$531$	−1.51796	−	1.05108i	−0.0658740	−	0.0456129i
$532$	3.43335	−	3.76802i	0.148854	−	0.163364i
$533$	11.1516	+	3.62338i	0.483031	+	0.156946i
$534$	−23.0429	+	28.9487i	−0.997166	+	1.25273i
$535$	0.0424551	+	0.405775i	0.00183549	+	0.0175432i
$536$	18.8584	+	26.4471i	0.814557	+	1.14234i
$537$	29.1717	−	15.2831i	1.25885	−	0.659515i
$538$	3.27752	−	5.63822i	0.141304	−	0.243081i
$539$	−7.05061	+	9.70434i	−0.303691	+	0.417995i
$540$	4.26831	+	22.8425i	0.183679	+	0.982986i
$541$	−8.88022	−	12.2226i	−0.381790	−	0.525489i	0.574267	−	0.818668i	$-0.305287\pi$
$541$	−8.88022	−	12.2226i	−0.381790	−	0.525489i	−0.956058	+	0.293179i	$0.905287\pi$
$542$	5.76959	−	0.589146i	0.247825	−	0.0253060i
$543$	36.9030	+	5.41639i	1.58366	+	0.232439i
$544$	39.1082	−	7.70958i	1.67675	−	0.330546i
$545$	14.7932	−	13.3073i	0.633673	−	0.570020i
$546$	−8.50746	+	5.62681i	−0.364086	+	0.240805i
$547$	29.4636	−	9.57330i	1.25977	−	0.409325i	0.398359	−	0.917230i	$-0.369580\pi$
$547$	29.4636	−	9.57330i	1.25977	−	0.409325i	0.861413	+	0.507905i	$0.169580\pi$
$548$	14.2236	−	2.93542i	0.607603	−	0.125395i
$549$	10.8692	−	36.2294i	0.463885	−	1.54623i
$550$	15.7641	−	21.5203i	0.672184	−	0.917627i
$551$	−2.65817			−0.113242
$552$	36.4837	−	18.7029i	1.55285	−	0.796047i
$553$	20.3261	−	6.60436i	0.864355	−	0.280846i
$554$	5.49026	+	6.13397i	0.233259	+	0.260608i
$555$	13.9291	+	11.0309i	0.591257	+	0.468237i
$556$	17.3726	+	30.5060i	0.736764	+	1.29374i
$557$		−	2.58456i		−	0.109511i	−0.998500	−	0.0547556i	$-0.982562\pi$
$557$		−	2.58456i		−	0.109511i	0.998500	−	0.0547556i	$-0.0174380\pi$
$558$	−17.9303	−	3.44290i	−0.759052	−	0.145749i
$559$	10.5317	+	14.4957i	0.445445	+	0.613103i
$560$	11.8571	−	12.8470i	0.501054	−	0.542884i
$561$	−32.9255	−	32.1866i	−1.39011	−	1.35892i
$562$	5.70119	+	3.31413i	0.240490	+	0.139798i
$563$	−15.3614	+	11.1607i	−0.647406	+	0.470368i	−0.862387	−	0.506250i	$-0.831031\pi$
$563$	−15.3614	+	11.1607i	−0.647406	+	0.470368i	0.214980	+	0.976618i	$0.431031\pi$
$564$	−5.29180	+	0.306134i	−0.222825	+	0.0128906i
$565$	5.13142	+	5.70443i	0.215880	+	0.239987i
$566$	−8.24321	−	4.79181i	−0.346488	−	0.201415i
$567$	13.7479	−	10.9750i	0.577358	−	0.460907i
$568$	−6.78760	+	20.2756i	−0.284801	+	0.850747i
$569$	−6.04883	−	1.96538i	−0.253580	−	0.0823931i	0.179469	−	0.983764i	$-0.442562\pi$
$569$	−6.04883	−	1.96538i	−0.253580	−	0.0823931i	−0.433049	+	0.901371i	$0.642562\pi$
$570$	−6.91341	−	1.79392i	−0.289571	−	0.0751390i
$571$	8.36734	+	25.7520i	0.350162	+	1.07769i	0.958762	+	0.284211i	$0.0917316\pi$
$571$	8.36734	+	25.7520i	0.350162	+	1.07769i	−0.608600	+	0.793478i	$0.708268\pi$
$572$	−6.62488	+	14.6457i	−0.277000	+	0.612369i
$573$	−3.53961	+	3.62086i	−0.147869	+	0.151264i
$574$	6.14689	+	13.9169i	0.256566	+	0.580878i
$575$	−17.0554	+	38.2100i	−0.711261	+	1.59347i
$576$	14.2024	+	19.3466i	0.591769	+	0.806108i
$577$	−16.2330	+	22.3428i	−0.675789	+	0.930144i	−0.999874	−	0.0158844i	$-0.994944\pi$
$577$	−16.2330	+	22.3428i	−0.675789	+	0.930144i	0.324085	+	0.946028i	$0.394944\pi$
$578$	30.7974	+	34.4083i	1.28100	+	1.43120i
$579$	1.54699	+	9.09797i	0.0642909	+	0.378099i
$580$	−9.11606	−	0.0582719i	−0.378524	−	0.00241961i
$581$	−1.69029	+	5.20217i	−0.0701250	+	0.215822i
$582$	−7.82191	+	2.16634i	−0.324229	+	0.0897979i
$583$	−1.11115	+	3.41977i	−0.0460192	+	0.141633i
$584$	−37.4902	+	11.8143i	−1.55135	+	0.488878i
$585$	12.5323	+	6.86884i	0.518146	+	0.283992i
$586$	1.73272	−	8.03480i	0.0715781	−	0.331914i
$587$	−9.00492	+	6.54246i	−0.371673	+	0.270036i	−0.757904	−	0.652366i	$-0.773777\pi$
$587$	−9.00492	+	6.54246i	−0.371673	+	0.270036i	0.386231	+	0.922402i	$0.373777\pi$
$588$	10.6543	+	2.79294i	0.439376	+	0.115179i
$589$	3.29848	−	4.53997i	0.135912	−	0.187066i
$590$	1.68880	−	0.967318i	0.0695269	−	0.0398238i
$591$	20.6978	−	10.8436i	0.851393	−	0.446046i
$592$	17.9032	+	4.02758i	0.735819	+	0.165533i
$593$	1.51420			0.0621808			0.0310904	−	0.999517i	$-0.490102\pi$
$593$	1.51420			0.0621808			0.0310904	+	0.999517i	$0.490102\pi$
$594$	9.12594	−	26.1778i	0.374442	−	1.07409i
$595$	30.1214	+	6.41735i	1.23486	+	0.263086i
$596$	27.3704	+	12.3808i	1.12114	+	0.507136i
$597$	6.86406	+	40.3680i	0.280927	+	1.65215i
$598$	5.31522	−	24.6472i	0.217356	−	1.00790i
$599$	−34.9331			−1.42733			−0.713663	−	0.700489i	$-0.752965\pi$
$599$	−34.9331			−1.42733			−0.713663	+	0.700489i	$0.752965\pi$
$600$	−23.6699	−	6.30371i	−0.966319	−	0.257348i
$601$	−9.21481			−0.375880			−0.187940	−	0.982181i	$-0.560181\pi$
$601$	−9.21481			−0.375880			−0.187940	+	0.982181i	$0.560181\pi$
$602$	−4.90088	+	22.7258i	−0.199745	+	0.926235i
$603$	−34.4436	+	0.781776i	−1.40265	+	0.0318364i
$604$	−7.42145	+	16.4067i	−0.301974	+	0.667581i
$605$	−6.60476	+	2.93689i	−0.268522	+	0.119402i
$606$	−40.8480	−	1.79738i	−1.65934	−	0.0730136i
$607$	−41.1452			−1.67003			−0.835015	−	0.550227i	$-0.814541\pi$
$607$	−41.1452			−1.67003			−0.835015	+	0.550227i	$0.814541\pi$
$608$	−7.23731	+	1.42672i	−0.293512	+	0.0578613i
$609$	3.20260	+	6.11298i	0.129776	+	0.247711i
$610$	29.5380	+	26.7803i	1.19596	+	1.08430i
$611$	−1.91611	+	2.63730i	−0.0775174	+	0.106694i
$612$	−16.5461	+	38.9066i	−0.668838	+	1.57271i
$613$	22.2142	−	16.1396i	0.897225	−	0.651872i	−0.0405268	−	0.999178i	$-0.512904\pi$
$613$	22.2142	−	16.1396i	0.897225	−	0.651872i	0.937752	+	0.347306i	$0.112904\pi$
$614$	0.238204	−	1.10457i	0.00961313	−	0.0445769i
$615$	13.2339	−	16.7109i	0.533643	−	0.673848i
$616$	−19.8923	+	6.26865i	−0.801483	+	0.252571i
$617$	3.55281	−	10.9344i	0.143031	−	0.440204i	−0.853722	−	0.520730i	$-0.825660\pi$
$617$	3.55281	−	10.9344i	0.143031	−	0.440204i	0.996753	+	0.0805258i	$0.0256599\pi$
$618$	−5.07829	−	18.3359i	−0.204279	−	0.737579i
$619$	−2.17366	+	6.68985i	−0.0873669	+	0.268888i	−0.985189	−	0.171470i	$-0.945148\pi$
$619$	−2.17366	+	6.68985i	−0.0873669	+	0.268888i	0.897822	+	0.440358i	$0.145148\pi$
$620$	11.4115	−	15.4973i	0.458298	−	0.622387i
$621$	−5.33691	+	43.1565i	−0.214163	+	1.73181i
$622$	11.2321	+	12.5491i	0.450368	+	0.503172i
$623$	−17.3541	+	23.8859i	−0.695279	+	0.956969i
$624$	14.7393	+	0.779753i	0.590044	+	0.0312151i
$625$	22.8578	−	10.1253i	0.914312	−	0.405012i
$626$	−17.7856	−	40.2674i	−0.710854	−	1.60941i
$627$	6.09314	+	5.95641i	0.243337	+	0.237876i
$628$	7.77967	+	3.51906i	0.310442	+	0.140426i
$629$	9.98956	+	30.7447i	0.398310	+	1.22587i
$630$	4.20391	+	18.0601i	0.167488	+	0.719532i
$631$	27.2526	+	8.85492i	1.08491	+	0.352509i	0.796278	−	0.604931i	$-0.206799\pi$
$631$	27.2526	+	8.85492i	1.08491	+	0.352509i	0.288633	+	0.957440i	$0.406799\pi$
$632$	−29.3272	−	9.81776i	−1.16657	−	0.390529i
$633$	1.12270	+	0.556089i	0.0446233	+	0.0221026i
$634$	−38.9544	−	22.6444i	−1.54708	−	0.899322i
$635$	−3.42544	+	5.92658i	−0.135934	+	0.235189i
$636$	3.29621	−	0.190688i	0.130703	−	0.00756127i
$637$	5.48008	−	3.98151i	0.217129	−	0.157753i
$638$	9.40251	+	5.46571i	0.372249	+	0.216390i
$639$	−13.7430	−	18.0402i	−0.543667	−	0.713658i
$640$	−24.8513	+	4.73423i	−0.982334	+	0.187137i
$641$	−16.9336	−	23.3071i	−0.668837	−	0.920575i	0.330897	−	0.943667i	$-0.392649\pi$
$641$	−16.9336	−	23.3071i	−0.668837	−	0.920575i	−0.999733	+	0.0230923i	$0.992649\pi$
$642$	−0.446498	−	0.0196467i	−0.0176219	−	0.000775393i
$643$		−	19.4561i		−	0.767275i	−0.923484	−	0.383637i	$-0.874671\pi$
$643$		−	19.4561i		−	0.767275i	0.923484	−	0.383637i	$-0.125329\pi$
$644$	28.4284	−	16.1895i	1.12023	−	0.637955i
$645$	31.3700	−	8.77229i	1.23519	−	0.345409i
$646$	−8.66657	−	9.68268i	−0.340981	−	0.380960i
$647$	−3.15086	+	1.02378i	−0.123873	+	0.0402488i	−0.370298	−	0.928913i	$-0.620744\pi$
$647$	−3.15086	+	1.02378i	−0.123873	+	0.0402488i	0.246424	+	0.969162i	$0.420744\pi$
$648$	−25.4389	+	0.929095i	−0.999334	+	0.0364983i
$649$	−2.32184			−0.0911403
$650$	−12.2217	+	8.80691i	−0.479376	+	0.345436i
$651$	−14.4146	−	2.11569i	−0.564954	−	0.0829203i
$652$	−2.92746	−	14.1850i	−0.114648	−	0.555529i
$653$	−34.5021	+	11.2104i	−1.35017	+	0.438697i	−0.892750	−	0.450553i	$-0.851227\pi$
$653$	−34.5021	+	11.2104i	−1.35017	+	0.438697i	−0.457421	+	0.889250i	$0.651227\pi$
$654$	12.0244	+	18.1803i	0.470190	+	0.710905i
$655$	2.37254	−	11.1361i	0.0927030	−	0.435123i
$656$	4.83194	−	21.4787i	0.188655	−	0.838603i
$657$	11.9805	−	39.9336i	0.467403	−	1.55796i
$658$	−4.20782	+	0.429671i	−0.164038	+	0.0167503i
$659$	17.8381	+	24.5521i	0.694875	+	0.956414i	0.999992	+	0.00409890i	$0.00130473\pi$
$659$	17.8381	+	24.5521i	0.694875	+	0.956414i	−0.305116	+	0.952315i	$0.598695\pi$
$660$	20.7656	+	20.5608i	0.808298	+	0.800328i
$661$	−10.8050	+	14.8717i	−0.420264	+	0.578444i	−0.965684	−	0.259719i	$-0.916370\pi$
$661$	−10.8050	+	14.8717i	−0.420264	+	0.578444i	0.545420	+	0.838163i	$0.316370\pi$
$662$	2.37670	−	4.08856i	0.0923730	−	0.158907i
$663$	12.0665	+	23.0319i	0.468623	+	0.894486i
$664$	6.44466	−	4.59544i	0.250101	−	0.178338i
$665$	−5.57422	−	1.18759i	−0.216159	−	0.0460526i
$666$	−14.2046	+	13.3067i	−0.550419	+	0.515625i
$667$	−16.2243	−	5.27161i	−0.628209	−	0.204118i
$668$	18.8536	+	17.1791i	0.729468	+	0.664677i
$669$	−34.2078	−	16.9436i	−1.32255	−	0.655078i
$670$	14.8848	−	33.1255i	0.575052	−	1.27975i
$671$	−14.6987	−	45.2379i	−0.567437	−	1.74639i
$672$	12.0007	+	14.9247i	0.462936	+	0.575733i
$673$	−13.1398	+	18.0854i	−0.506502	+	0.697140i	−0.983325	−	0.181859i	$-0.941788\pi$
$673$	−13.1398	+	18.0854i	−0.506502	+	0.697140i	0.476822	+	0.879000i	$0.341788\pi$
$674$	0.754011	+	1.70712i	0.0290434	+	0.0657558i
$675$	19.6388	−	17.0094i	0.755896	−	0.654692i
$676$	−11.3978	+	12.5088i	−0.438375	+	0.481106i
$677$	13.2599	−	18.2506i	0.509618	−	0.701429i	−0.474237	−	0.880397i	$-0.657276\pi$
$677$	13.2599	−	18.2506i	0.509618	−	0.701429i	0.983855	+	0.178969i	$0.0572760\pi$
$678$	−7.01050	+	4.63672i	−0.269237	+	0.178072i
$679$	−6.15955	+	2.00136i	−0.236382	+	0.0768052i
$680$	−29.5093	−	33.3963i	−1.13163	−	1.28069i
$681$	−39.6601	−	19.6442i	−1.51978	−	0.752769i
$682$	−21.0025	+	9.27653i	−0.804228	+	0.355217i
$683$	−11.1525	+	34.3237i	−0.426737	+	1.31336i	0.474585	+	0.880210i	$0.342598\pi$
$683$	−11.1525	+	34.3237i	−0.426737	+	1.31336i	−0.901321	+	0.433151i	$0.857402\pi$
$684$	3.06200	−	7.20001i	0.117079	−	0.275299i
$685$	−10.8594	−	12.0720i	−0.414916	−	0.461248i
$686$	27.5062	+	5.93177i	1.05019	+	0.226476i
$687$	34.9576	−	18.3143i	1.33371	−	0.698735i
$688$	25.2655	−	22.2131i	0.963237	−	0.846867i
$689$	1.19352	−	1.64274i	0.0454696	−	0.0625836i
$690$	−38.6389	−	24.6598i	−1.47096	−	0.938784i
$691$	−32.1574	+	23.3637i	−1.22333	+	0.888798i	−0.996372	−	0.0851070i	$-0.972877\pi$
$691$	−32.1574	+	23.3637i	−1.22333	+	0.888798i	−0.226954	+	0.973905i	$0.572877\pi$
$692$	21.0164	−	11.9685i	0.798922	−	0.454973i
$693$	6.35684	−	21.1888i	0.241476	−	0.804895i
$694$	−2.96148	−	29.0022i	−0.112416	−	1.10091i
$695$	19.6408	−	33.9819i	0.745019	−	1.28901i
$696$	1.53788	−	9.86722i	0.0582931	−	0.374016i
$697$	36.8848	−	11.9846i	1.39711	−	0.453949i
$698$	9.12043	−	42.2923i	0.345213	−	1.60079i
$699$	−4.63953	+	31.6101i	−0.175483	+	1.19560i
$700$	−19.0905	−	4.19497i	−0.721553	−	0.158555i
$701$	−5.49557			−0.207565			−0.103782	−	0.994600i	$-0.533095\pi$
$701$	−5.49557			−0.207565			−0.103782	+	0.994600i	$0.533095\pi$
$702$	−9.46934	+	12.4667i	−0.357397	+	0.470525i
$703$	−1.84865	−	5.68957i	−0.0697233	−	0.214586i
$704$	28.5336	+	9.83471i	1.07540	+	0.370660i
$705$	3.28155	+	4.93482i	0.123590	+	0.185856i
$706$	−1.89534	−	18.5614i	−0.0713322	−	0.698566i
$707$	−32.6266			−1.22705
$708$	0.774820	+	1.98619i	0.0291195	+	0.0746457i
$709$	10.2196	+	14.0661i	0.383806	+	0.528263i	0.956588	−	0.291445i	$-0.0941359\pi$
$709$	10.2196	+	14.0661i	0.383806	+	0.528263i	−0.572782	+	0.819708i	$0.694136\pi$
$710$	23.3999	−	4.88992i	0.878182	−	0.183516i
$711$	26.0938	−	19.8783i	0.978593	−	0.745495i
$712$	40.7486	−	12.8411i	1.52712	−	0.481240i
$713$	29.1361	−	21.1686i	1.09116	−	0.792772i
$714$	−11.8256	+	31.5964i	−0.442563	+	1.18246i
$715$	17.8742	−	1.87012i	0.668456	−	0.0699387i
$716$	−37.7949	−	4.19877i	−1.41246	−	0.156916i
$717$	3.91386	+	1.93859i	0.146166	+	0.0723980i
$718$	−31.5511	+	13.9357i	−1.17748	+	0.520075i
$719$	15.2512	−	46.9383i	0.568773	−	1.75050i	−0.0876942	−	0.996147i	$-0.527950\pi$
$719$	15.2512	−	46.9383i	0.568773	−	1.75050i	0.656467	−	0.754355i	$-0.272050\pi$
$720$	10.6588	−	24.6250i	0.397231	−	0.917718i
$721$	−4.69153	−	14.4391i	−0.174722	−	0.537739i
$722$	−16.3166	−	18.2296i	−0.607240	−	0.678436i
$723$	−2.12748	+	2.17632i	−0.0791220	+	0.0809382i
$724$	−31.8350	−	29.0074i	−1.18314	−	1.07805i
$725$	5.08780	+	8.83157i	0.188956	+	0.327996i
$726$	−2.11345	−	7.63093i	−0.0784375	−	0.283210i
$727$	−22.4667	−	16.3230i	−0.833244	−	0.605387i	0.0872313	−	0.996188i	$-0.472198\pi$
$727$	−22.4667	−	16.3230i	−0.833244	−	0.605387i	−0.920475	+	0.390801i	$0.872198\pi$
$728$	11.7774	+	0.104591i	0.436498	+	0.00387639i
$729$	14.3475	−	22.8725i	0.531388	−	0.847128i
$730$	32.5581	+	29.5184i	1.20503	+	1.09252i
$731$	56.3633	+	18.3136i	2.08467	+	0.677351i
$732$	−33.7932	+	27.6701i	−1.24903	+	1.02272i
$733$	8.65749	−	26.6450i	0.319772	−	0.984156i	−0.653974	−	0.756517i	$-0.726900\pi$
$733$	8.65749	−	26.6450i	0.319772	−	0.984156i	0.973746	−	0.227639i	$-0.0731005\pi$
$734$	−20.6933	+	35.5981i	−0.763803	+	1.31395i
$735$	−3.31635	−	11.8594i	−0.122326	−	0.437440i
$736$	−47.0030	−	5.64472i	−1.73255	−	0.208067i
$737$	−35.0508	+	25.4659i	−1.29111	+	0.938049i
$738$	15.9642	+	17.0415i	0.587651	+	0.627305i
$739$	−39.8731	−	28.9695i	−1.46675	−	1.06566i	−0.981539	−	0.191264i	$-0.938741\pi$
$739$	−39.8731	−	28.9695i	−1.46675	−	1.06566i	−0.485215	−	0.874395i	$-0.661259\pi$
$740$	−6.21515	−	19.5527i	−0.228473	−	0.718770i
$741$	−2.23300	−	4.26226i	−0.0820314	−	0.156578i
$742$	2.62101	−	0.267637i	0.0962203	−	0.00982528i
$743$		−	37.5780i		−	1.37860i	−0.724475	−	0.689301i	$-0.757918\pi$
$743$		−	37.5780i		−	1.37860i	0.724475	−	0.689301i	$-0.242082\pi$
$744$	14.9442	+	14.8707i	0.547882	+	0.545186i
$745$	−3.49494	−	33.4038i	−0.128045	−	1.22382i
$746$	−18.0160	−	20.1283i	−0.659611	−	0.736948i
$747$	0.190504	+	8.39326i	0.00697019	+	0.307093i
$748$	10.7460	+	52.0699i	0.392913	+	1.90386i
$749$	−0.356633			−0.0130311
$750$	7.27228	+	26.4029i	0.265546	+	0.964098i
$751$			15.7378i			0.574280i	0.957889	+	0.287140i	$0.0927044\pi$
$751$			15.7378i			0.574280i	−0.957889	+	0.287140i	$0.907296\pi$
$752$	5.26404	+	3.12287i	0.191960	+	0.113880i
$753$	1.12735	+	6.63005i	0.0410831	+	0.241612i
$754$	−4.09598	−	4.57622i	−0.149167	−	0.166656i
$755$	20.0234	−	2.09499i	0.728724	−	0.0762444i
$756$	−20.2470	+	1.63300i	−0.736377	+	0.0593917i
$757$	21.6497			0.786872			0.393436	−	0.919352i	$-0.371286\pi$
$757$	21.6497			0.786872			0.393436	+	0.919352i	$0.371286\pi$
$758$	0.726535	+	7.11506i	0.0263889	+	0.258430i
$759$	25.3774	+	48.4392i	0.921141	+	1.75823i
$760$	5.46095	+	6.18027i	0.198090	+	0.224182i
$761$	11.8538	−	16.3153i	0.429699	−	0.591430i	−0.538185	−	0.842827i	$-0.680890\pi$
$761$	11.8538	−	16.3153i	0.429699	−	0.591430i	0.967884	+	0.251396i	$0.0808898\pi$
$762$	−5.86690	−	4.67000i	−0.212536	−	0.169176i
$763$	10.2234	+	14.0713i	0.370113	+	0.509416i
$764$	5.72621	−	1.18175i	0.207167	−	0.0427544i
$765$	46.8889	−	5.98431i	1.69527	−	0.216363i
$766$	−12.1127	−	7.04115i	−0.437649	−	0.254407i
$767$	1.24698	+	0.405169i	0.0450259	+	0.0146298i
$768$	−1.10892	−	27.6906i	−0.0400148	−	0.999199i
$769$	−10.8012	+	33.2425i	−0.389499	+	1.19876i	0.543664	+	0.839303i	$0.317037\pi$
$769$	−10.8012	+	33.2425i	−0.389499	+	1.19876i	−0.933163	+	0.359453i	$0.882963\pi$
$770$	17.2753	+	15.6624i	0.622559	+	0.564435i
$771$	−21.4672	+	3.65022i	−0.773121	+	0.131459i
$772$	4.39183	−	9.70911i	0.158066	−	0.349439i
$773$	10.0362	−	13.8136i	0.360977	−	0.496842i	−0.589444	−	0.807809i	$-0.700653\pi$
$773$	10.0362	−	13.8136i	0.360977	−	0.496842i	0.950420	+	0.310968i	$0.100653\pi$
$774$	4.42933	+	35.4065i	0.159209	+	1.27266i
$775$	−21.3971	−	2.26935i	−0.768607	−	0.0815173i
$776$	8.88720	+	2.97514i	0.319032	+	0.106801i
$777$	−10.8570	+	11.1062i	−0.389493	+	0.398434i
$778$	−19.3304	−	21.5968i	−0.693027	−	0.774282i
$779$	−6.82584	+	2.21785i	−0.244561	+	0.0794628i
$780$	−7.56455	−	14.6662i	−0.270854	−	0.525133i
$781$	−27.1234	−	8.81291i	−0.970550	−	0.315351i
$782$	−33.6947	−	76.2864i	−1.20492	−	2.72800i
$783$	7.74032	+	7.23052i	0.276617	+	0.258398i
$784$	−8.39764	−	9.55158i	−0.299916	−	0.341128i
$785$	−0.993391	−	9.49457i	−0.0354556	−	0.338876i
$786$	11.6814	+	4.37203i	0.416662	+	0.155945i
$787$	7.23882	+	9.96338i	0.258036	+	0.355156i	0.918305	−	0.395873i	$-0.129558\pi$
$787$	7.23882	+	9.96338i	0.258036	+	0.355156i	−0.660269	+	0.751029i	$0.729558\pi$
$788$	−26.8160	−	2.97909i	−0.955282	−	0.106126i
$789$	0.808130	+	0.789995i	0.0287702	+	0.0281246i
$790$	7.07291	+	33.8462i	0.251643	+	1.20419i
$791$	−5.42605	+	3.94226i	−0.192928	+	0.140170i
$792$	−25.6356	+	19.1719i	−0.910922	+	0.681244i
$793$			26.8607i			0.953852i
$794$	−3.45699	−	33.8548i	−0.122684	−	1.20146i
$795$	−2.04405	−	3.07385i	−0.0724948	−	0.109018i
$796$	19.4867	−	43.0796i	0.690688	−	1.52692i
$797$	−7.02914	+	2.28391i	−0.248985	+	0.0809001i	−0.430851	−	0.902423i	$-0.641786\pi$
$797$	−7.02914	+	2.28391i	−0.248985	+	0.0809001i	0.181866	+	0.983323i	$0.441786\pi$
$798$	2.18844	−	5.84718i	0.0774698	−	0.206988i
$799$			10.7823i			0.381449i
$800$	18.5926	+	21.3147i	0.657348	+	0.753587i
$801$	−13.0218	+	43.4044i	−0.460101	+	1.53362i
$802$	5.07496	−	23.5331i	0.179203	−	0.830981i
$803$	−16.2015	−	49.8632i	−0.571740	−	1.75963i
$804$	33.4813	+	21.4856i	1.18079	+	0.757738i
$805$	−31.6675	−	18.3032i	−1.11613	−	0.645103i
$806$	12.8985	−	1.31710i	0.454331	−	0.0463928i
$807$	1.15990	−	7.90267i	0.0408305	−	0.278187i
$808$	37.9481	+	28.0891i	1.33501	+	0.988172i
$809$	3.61895	+	4.98106i	0.127236	+	0.175125i	0.867882	−	0.496770i	$-0.165481\pi$
$809$	3.61895	+	4.98106i	0.127236	+	0.175125i	−0.740647	+	0.671895i	$0.765481\pi$
$810$	15.2515	+	24.0290i	0.535883	+	0.844292i
$811$	20.1386	+	14.6316i	0.707163	+	0.513784i	0.882257	−	0.470768i	$-0.156023\pi$
$811$	20.1386	+	14.6316i	0.707163	+	0.513784i	−0.175094	+	0.984552i	$0.556023\pi$
$812$	0.879860	−	7.91998i	0.0308770	−	0.277937i
$813$	6.29184	−	3.29631i	0.220665	−	0.115607i
$814$	−5.15980	+	23.9265i	−0.180851	+	0.838622i
$815$	−12.0393	+	10.8299i	−0.421717	+	0.379356i
$816$	40.9565	−	26.5687i	1.43377	−	0.930092i
$817$	−10.4305	−	3.38908i	−0.364918	−	0.118569i
$818$	−25.4844	+	11.2561i	−0.891042	+	0.393561i
$819$	−7.11155	+	10.2705i	−0.248498	+	0.358879i
$820$	−23.4575	+	7.45638i	−0.819173	+	0.260388i
$821$	−11.6523	−	35.8621i	−0.406668	−	1.25160i	−0.919494	−	0.393103i	$-0.871402\pi$
$821$	−11.6523	−	35.8621i	−0.406668	−	1.25160i	0.512826	−	0.858492i	$-0.328598\pi$
$822$	14.8360	−	9.81249i	0.517465	−	0.342250i
$823$	4.98406	+	3.62113i	0.173734	+	0.126225i	0.671254	−	0.741227i	$-0.265756\pi$
$823$	4.98406	+	3.62113i	0.173734	+	0.126225i	−0.497520	+	0.867452i	$0.665756\pi$
$824$	−6.97423	+	20.8331i	−0.242959	+	0.725757i
$825$	8.12732	−	31.6448i	0.282957	−	1.10173i
$826$	0.687349	+	1.55619i	0.0239159	+	0.0541469i
$827$	−41.0660	−	29.8362i	−1.42800	−	1.03751i	−0.990384	−	0.138347i	$-0.955821\pi$
$827$	−41.0660	−	29.8362i	−1.42800	−	1.03751i	−0.437621	−	0.899160i	$-0.644179\pi$
$828$	32.9681	−	37.8734i	1.14572	−	1.31619i
$829$	−26.9557	+	8.75844i	−0.936210	+	0.304193i	−0.737100	−	0.675784i	$-0.763805\pi$
$829$	−26.9557	+	8.75844i	−0.936210	+	0.304193i	−0.199111	+	0.979977i	$0.563805\pi$
$830$	−8.07207	−	3.62716i	−0.280186	−	0.125901i
$831$	9.03476	+	4.47505i	0.313412	+	0.155238i
$832$	−13.6082	−	10.2611i	−0.471780	−	0.355739i
$833$	6.92342	−	21.3081i	0.239882	−	0.738282i
$834$	33.6397	+	26.7769i	1.16485	+	0.927209i
$835$	5.94219	−	27.8911i	0.205638	−	0.965211i
$836$	−1.98864	−	9.63598i	−0.0687786	−	0.333268i
$837$	−21.9541	+	4.24771i	−0.758845	+	0.146822i
$838$	−31.2648	−	18.1744i	−1.08002	−	0.627823i
$839$	38.3587	+	27.8692i	1.32429	+	0.962153i	0.999868	+	0.0162409i	$0.00516988\pi$
$839$	38.3587	+	27.8692i	1.32429	+	0.962153i	0.324422	+	0.945912i	$0.394830\pi$
$840$	7.63332	−	20.0046i	0.263375	−	0.690226i
$841$	20.0998	−	14.6034i	0.693096	−	0.503564i
$842$	20.9731	−	2.14161i	0.722780	−	0.0738047i
$843$	7.99093	+	1.17286i	0.275222	+	0.0403953i
$844$	−0.715916	−	1.25713i	−0.0246429	−	0.0432723i
$845$	18.5049	+	3.94245i	0.636586	+	0.135625i
$846$	−5.87742	+	2.75702i	−0.202070	+	0.0947882i
$847$	−1.95249	−	6.00916i	−0.0670885	−	0.206477i
$848$	−3.27892	−	1.94521i	−0.112598	−	0.0667987i
$849$	−11.5539	−	1.69580i	−0.396528	−	0.0581998i
$850$	−15.5820	+	47.3270i	−0.534458	+	1.62330i
$851$		−	38.3930i		−	1.31610i
$852$	1.51241	+	26.1433i	0.0518142	+	0.895654i
$853$	−0.565413	−	1.74016i	−0.0193594	−	0.0595820i	0.940910	−	0.338656i	$-0.109972\pi$
$853$	−0.565413	−	1.74016i	−0.0193594	−	0.0595820i	−0.960269	+	0.279074i	$0.909972\pi$
$854$	−25.9689	+	23.2437i	−0.888639	+	0.795383i
$855$	−8.67719	+	1.10745i	−0.296753	+	0.0378739i
$856$	0.414800	+	0.307034i	0.0141776	+	0.0104942i
$857$	−53.4248			−1.82496			−0.912478	−	0.409126i	$-0.865834\pi$
$857$	−53.4248			−1.82496			−0.912478	+	0.409126i	$0.865834\pi$
$858$	−0.865426	+	19.6680i	−0.0295452	+	0.671455i
$859$	32.0923	−	23.3164i	1.09498	−	0.795547i	0.114743	−	0.993395i	$-0.463395\pi$
$859$	32.0923	−	23.3164i	1.09498	−	0.795547i	0.980233	+	0.197849i	$0.0633955\pi$
$860$	−35.6967	−	11.8514i	−1.21725	−	0.404128i
$861$	13.3243	+	13.0253i	0.454090	+	0.443901i
$862$	1.86590	−	3.20985i	0.0635527	−	0.109328i
$863$	−15.7111	−	21.6244i	−0.534811	−	0.736104i	0.453043	−	0.891489i	$-0.350338\pi$
$863$	−15.7111	−	21.6244i	−0.534811	−	0.736104i	−0.987854	+	0.155384i	$0.950338\pi$
$864$	24.9552	+	15.5318i	0.848993	+	0.528404i
$865$	−23.4110	−	13.5311i	−0.795998	−	0.460070i
$866$	20.1600	+	11.7191i	0.685066	+	0.398232i
$867$	50.6802	+	25.1026i	1.72119	+	0.852529i
$868$	12.4350	+	11.3305i	0.422071	+	0.384584i
$869$	12.7472	−	39.2319i	0.432420	−	1.33085i
$870$	−10.3915	+	4.08358i	−0.352305	+	0.138446i
$871$	23.2685	−	7.56039i	0.788423	−	0.256174i
$872$	0.223508	−	25.1680i	0.00756894	−	0.852295i
$873$	−7.90736	+	6.02385i	−0.267624	+	0.203876i
$874$	6.23549	+	14.1175i	0.210919	+	0.477530i
$875$	6.72354	+	20.7930i	0.227297	+	0.702932i
$876$	−37.2483	+	30.4992i	−1.25850	+	1.03047i
$877$	32.6557	+	23.7257i	1.10270	+	0.801161i	0.981499	−	0.191466i	$-0.0613243\pi$
$877$	32.6557	+	23.7257i	1.10270	+	0.801161i	0.121205	+	0.992628i	$0.461324\pi$
$878$	−35.3108	+	31.6052i	−1.19168	+	1.06662i
$879$	−1.68751	−	9.92435i	−0.0569183	−	0.334740i
$880$	−6.60871	−	33.0898i	−0.222780	−	1.11546i
$881$	7.70864	+	2.50469i	0.259711	+	0.0843851i	0.435978	−	0.899957i	$-0.356402\pi$
$881$	7.70864	+	2.50469i	0.259711	+	0.0843851i	−0.176268	+	0.984342i	$0.556402\pi$
$882$	13.3854	−	1.67450i	0.450709	−	0.0563835i
$883$	−7.69313	−	2.49965i	−0.258894	−	0.0841199i	0.176694	−	0.984266i	$-0.443460\pi$
$883$	−7.69313	−	2.49965i	−0.258894	−	0.0841199i	−0.435588	+	0.900146i	$0.643460\pi$
$884$	3.31506	−	29.8402i	0.111497	−	1.00363i
$885$	1.47983	−	1.86862i	0.0497438	−	0.0628130i
$886$	−21.8113	−	4.70366i	−0.732765	−	0.158023i
$887$	19.9642	+	27.4783i	0.670331	+	0.922632i	0.999768	−	0.0215457i	$-0.00685873\pi$
$887$	19.9642	+	27.4783i	0.670331	+	0.922632i	−0.329436	+	0.944178i	$0.606859\pi$
$888$	22.1895	−	3.57059i	0.744630	−	0.119821i
$889$	−4.84084	−	3.51708i	−0.162357	−	0.117959i
$890$	−35.3878	−	32.0839i	−1.18620	−	1.07546i
$891$	−1.54051	−	33.9185i	−0.0516091	−	1.13631i
$892$	21.8134	+	38.3039i	0.730368	+	1.28251i
$893$		−	1.99535i		−	0.0667719i
$894$	36.7562	+	1.61733i	1.22931	+	0.0540917i
$895$	17.2745	+	38.8484i	0.577421	+	1.29856i
$896$	−1.85534	−	22.0358i	−0.0619826	−	0.736163i
$897$	−5.17653	−	30.4435i	−0.172839	−	1.01648i
$898$	1.66527	−	7.72201i	0.0555708	−	0.257687i
$899$		−	8.77233i		−	0.292574i
$900$	−29.7823	+	3.60772i	−0.992743	+	0.120257i
$901$		−	6.71616i		−	0.223748i
$902$	28.7048	+	6.19026i	0.955766	+	0.206113i
$903$	4.77299	+	28.0703i	0.158835	+	0.934120i
$904$	9.70503	+	0.0861870i	0.322785	+	0.00286654i
$905$	−10.0336	+	47.0951i	−0.333528	+	1.56549i
$906$	−0.969484	+	22.0329i	−0.0322090	+	0.731994i
$907$		−	20.2111i		−	0.671100i	−0.942022	−	0.335550i	$-0.891078\pi$
$907$		−	20.2111i		−	0.671100i	0.942022	−	0.335550i	$-0.108922\pi$
$908$	25.2902	+	44.4091i	0.839286	+	1.47377i
$909$	−47.2625	+	16.5513i	−1.56760	+	0.548972i
$910$	−6.54483	−	11.4264i	−0.216959	−	0.378780i
$911$	24.6417	+	17.9032i	0.816415	+	0.593161i	0.915683	−	0.401900i	$-0.131650\pi$
$911$	24.6417	+	17.9032i	0.816415	+	0.593161i	−0.0992680	+	0.995061i	$0.531650\pi$
$912$	−7.57936	+	4.91677i	−0.250978	+	0.162811i
$913$	6.20558	+	8.54124i	0.205375	+	0.282674i
$914$	−0.356637	+	1.65376i	−0.0117965	+	0.0547015i
$915$	45.7757	+	17.0029i	1.51330	+	0.562097i
$916$	−45.2911	−	5.03155i	−1.49646	−	0.166247i
$917$	9.46566	+	3.07558i	0.312583	+	0.101565i
$918$	−1.10181	+	51.7691i	−0.0363651	+	1.70863i
$919$	−2.30142	−	0.747778i	−0.0759169	−	0.0246669i	0.270812	−	0.962632i	$-0.412708\pi$
$919$	−2.30142	−	0.747778i	−0.0759169	−	0.0246669i	−0.346729	+	0.937965i	$0.612708\pi$
$920$	21.0748	+	48.5519i	0.694817	+	1.60071i
$921$	−0.231988	−	1.36434i	−0.00764427	−	0.0449564i
$922$	−27.0207	−	30.1887i	−0.889879	−	0.994213i
$923$	13.0291	+	9.46623i	0.428860	+	0.311585i
$924$	−19.7639	+	16.1829i	−0.650185	+	0.532377i
$925$	−15.3648	+	17.0320i	−0.505193	+	0.560009i
$926$	50.5315	−	22.3191i	1.66057	−	0.733451i
$927$	−14.1209	−	18.5362i	−0.463792	−	0.608809i
$928$	−7.84189	+	8.45424i	−0.257422	+	0.277524i
$929$	17.5980	−	5.71793i	0.577371	−	0.187599i	−0.00575160	−	0.999983i	$-0.501831\pi$
$929$	17.5980	−	5.71793i	0.577371	−	0.187599i	0.583122	+	0.812384i	$0.301831\pi$
$930$	5.92019	−	22.8152i	0.194131	−	0.748141i
$931$	−1.28124	+	3.94325i	−0.0419909	+	0.129235i
$932$	24.8470	−	27.2689i	0.813889	−	0.893224i
$933$	18.4836	+	9.15518i	0.605125	+	0.299727i
$934$	2.14367	−	3.68769i	0.0701429	−	0.120665i
$935$	44.1933	−	39.7541i	1.44528	−	1.30010i
$936$	17.1136	−	5.82308i	0.559375	−	0.190333i
$937$	12.4116	+	17.0831i	0.405469	+	0.558080i	0.962106	−	0.272676i	$-0.0879086\pi$
$937$	12.4116	+	17.0831i	0.405469	+	0.558080i	−0.556637	+	0.830756i	$0.687909\pi$
$938$	27.4446	+	15.9536i	0.896097	+	0.520905i
$939$	−38.5528	−	37.6877i	−1.25812	−	1.22989i
$940$	0.0437417	−	6.84296i	0.00142670	−	0.223193i
$941$	20.7745	−	15.0936i	0.677230	−	0.492037i	−0.195207	−	0.980762i	$-0.562538\pi$
$941$	20.7745	−	15.0936i	0.677230	−	0.492037i	0.872438	+	0.488725i	$0.162538\pi$
$942$	10.4474	+	0.459705i	0.340396	+	0.0149780i
$943$	−46.0605			−1.49994
$944$	0.540310	−	2.40176i	0.0175856	−	0.0781708i
$945$	13.0012	+	18.6206i	0.422930	+	0.605730i
$946$	29.9264	+	33.4351i	0.972991	+	1.08707i
$947$	−9.35634	−	28.7958i	−0.304040	−	0.935739i	−0.980034	−	0.198832i	$-0.936285\pi$
$947$	−9.35634	−	28.7958i	−0.304040	−	0.935739i	0.675994	−	0.736907i	$-0.263715\pi$
$948$	−37.8143	+	2.18759i	−1.22815	+	0.0710495i
$949$			29.6070i			0.961085i
$950$	2.88358	−	8.75826i	0.0935557	−	0.284156i
$951$	−54.5995	−	8.01375i	−1.77051	−	0.259864i
$952$	31.7181	−	22.6170i	1.02799	−	0.733020i
$953$	18.6354	+	57.3539i	0.603660	+	1.85787i	0.505752	+	0.862679i	$0.331215\pi$
$953$	18.6354	+	57.3539i	0.603660	+	1.85787i	0.0979077	+	0.995196i	$0.468785\pi$
$954$	3.66099	−	1.71732i	0.118529	−	0.0556002i
$955$	−4.37182	−	4.86001i	−0.141469	−	0.157266i
$956$	−2.49576	−	4.38251i	−0.0807188	−	0.141740i
$957$	13.1788	+	1.93430i	0.426009	+	0.0625269i
$958$	−1.63147	−	15.9772i	−0.0527104	−	0.516200i
$959$	11.4829	−	8.34282i	0.370802	−	0.269404i
$960$	−26.1008	+	16.6957i	−0.842401	+	0.538851i
$961$	−10.0970	−	7.33587i	−0.325708	−	0.236641i
$962$	6.94639	−	11.9497i	0.223961	−	0.385273i
$963$	−0.516613	+	0.180918i	−0.0166476	+	0.00582999i
$964$	3.44174	−	0.710294i	0.110851	−	0.0228770i
$965$	−11.8493	+	1.23976i	−0.381444	+	0.0399094i
$966$	24.9533	−	31.3487i	0.802859	−	1.00863i
$967$	6.53088	−	20.1000i	0.210019	−	0.646371i	−0.789451	−	0.613814i	$-0.789635\pi$
$967$	6.53088	−	20.1000i	0.210019	−	0.646371i	0.999470	−	0.0325579i	$-0.0103653\pi$
$968$	−2.90250	+	8.67021i	−0.0932897	+	0.278671i
$969$	−14.2617	−	7.06401i	−0.458151	−	0.226929i
$970$	−2.14335	−	10.2566i	−0.0688188	−	0.329320i
$971$	−51.2347	+	16.6472i	−1.64420	+	0.534233i	−0.977472	−	0.211067i	$-0.932306\pi$
$971$	−51.2347	+	16.6472i	−1.64420	+	0.534233i	−0.666729	+	0.745300i	$0.732306\pi$
$972$	−28.5011	+	12.6367i	−0.914173	+	0.405323i
$973$	27.7565	+	20.1663i	0.889832	+	0.646501i
$974$	22.5887	−	9.97712i	0.723788	−	0.319688i
$975$	−9.88702	+	15.5771i	−0.316638	+	0.498866i
$976$	50.2156	−	4.67744i	1.60736	−	0.149721i
$977$	−4.26137	−	3.09607i	−0.136333	−	0.0990519i	0.517528	−	0.855666i	$-0.326852\pi$
$977$	−4.26137	−	3.09607i	−0.136333	−	0.0990519i	−0.653862	+	0.756614i	$0.726852\pi$
$978$	−9.78586	−	14.7958i	−0.312917	−	0.473116i
$979$	17.6097	+	54.1970i	0.562808	+	1.73214i
$980$	−4.48039	+	13.4951i	−0.143121	+	0.431085i
$981$	21.9478	+	15.1972i	0.700739	+	0.485210i
$982$	−12.8912	−	29.1864i	−0.411376	−	0.931376i
$983$	−34.7321	−	11.2851i	−1.10778	−	0.359940i	−0.302689	−	0.953089i	$-0.597884\pi$
$983$	−34.7321	−	11.2851i	−1.10778	−	0.359940i	−0.805093	+	0.593149i	$0.797884\pi$
$984$	−4.28367	−	26.6209i	−0.136558	−	0.848645i
$985$	12.2565	+	27.5635i	0.390524	+	0.878247i
$986$	−19.8572	−	4.28224i	−0.632380	−	0.136374i
$987$	−4.58871	+	2.40403i	−0.146060	+	0.0765211i
$988$	−0.613480	+	5.52218i	−0.0195174	+	0.175684i
$989$	−56.9424	−	41.3711i	−1.81066	−	1.31552i
$990$	32.9702	+	13.9247i	1.04786	+	0.442557i
$991$	−11.8015	−	16.2433i	−0.374886	−	0.515986i	0.579335	−	0.815090i	$-0.303312\pi$
$991$	−11.8015	−	16.2433i	−0.374886	−	0.515986i	−0.954221	+	0.299104i	$0.903312\pi$
$992$	−4.70840	−	23.8842i	−0.149492	−	0.758323i
$993$	0.841104	−	5.73063i	0.0266916	−	0.181856i
$994$	2.12272	+	20.7881i	0.0673286	+	0.659358i
$995$	−52.5759	+	5.50087i	−1.66677	+	0.174389i
$996$	5.23565	−	8.15877i	0.165898	−	0.258521i
$997$	5.68273	+	17.4897i	0.179974	+	0.553903i	0.999826	−	0.0186731i	$-0.00594418\pi$
$997$	5.68273	+	17.4897i	0.179974	+	0.553903i	−0.819852	+	0.572576i	$0.805944\pi$
$998$	7.19101	+	1.55076i	0.227627	+	0.0490884i
$999$	−10.0932	+	21.5960i	−0.319334	+	0.683268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bk.a.59.8	✓	464
3.2	odd	2	inner	600.2.bk.a.59.109	yes	464
8.3	odd	2	inner	600.2.bk.a.59.38	yes	464
24.11	even	2	inner	600.2.bk.a.59.79	yes	464
25.14	even	10	inner	600.2.bk.a.539.79	yes	464
75.14	odd	10	inner	600.2.bk.a.539.38	yes	464
200.139	odd	10	inner	600.2.bk.a.539.109	yes	464
600.539	even	10	inner	600.2.bk.a.539.8	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bk.a.59.8	✓	464	1.1	even	1	trivial
600.2.bk.a.59.38	yes	464	8.3	odd	2	inner
600.2.bk.a.59.79	yes	464	24.11	even	2	inner
600.2.bk.a.59.109	yes	464	3.2	odd	2	inner
600.2.bk.a.539.8	yes	464	600.539	even	10	inner
600.2.bk.a.539.38	yes	464	75.14	odd	10	inner
600.2.bk.a.539.79	yes	464	25.14	even	10	inner
600.2.bk.a.539.109	yes	464	200.139	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bk (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38243 - 0.298125i) q^{2} +(-1.70754 + 0.290346i) q^{3} +(1.82224 + 0.824276i) q^{4} +(-0.232683 - 2.22393i) q^{5} +(2.44712 + 0.107677i) q^{6} +1.95460 q^{7} +(-2.27339 - 1.68276i) q^{8} +(2.83140 - 0.991555i) q^{9} +(-0.341340 + 3.14380i) q^{10} +(2.21748 - 3.05211i) q^{11} +(-3.35088 - 0.878405i) q^{12} +(-1.72354 + 1.25222i) q^{13} +(-2.70210 - 0.582714i) q^{14} +(1.04302 + 3.72989i) q^{15} +(2.64114 + 3.00406i) q^{16} +(-2.17748 + 6.70160i) q^{17} +(-4.20983 + 0.526647i) q^{18} +(0.402962 - 1.24019i) q^{19} +(1.40912 - 4.24433i) q^{20} +(-3.33755 + 0.567508i) q^{21} +(-3.97543 + 3.55824i) q^{22} +(4.91902 - 6.77045i) q^{23} +(4.37049 + 2.21332i) q^{24} +(-4.89172 + 1.03494i) q^{25} +(2.75600 - 1.21729i) q^{26} +(-4.54684 + 2.51521i) q^{27} +(3.56175 + 1.61113i) q^{28} +(-0.629917 - 1.93868i) q^{29} +(-0.329938 - 5.46728i) q^{30} +(4.09280 + 1.32983i) q^{31} +(-2.75561 - 4.94030i) q^{32} +(-2.90028 + 5.85544i) q^{33} +(5.00814 - 8.61535i) q^{34} +(-0.454802 - 4.34688i) q^{35} +(5.97681 + 0.527000i) q^{36} +(3.71150 - 2.69656i) q^{37} +(-0.926798 + 1.59434i) q^{38} +(2.57944 - 2.63865i) q^{39} +(-3.21336 + 5.44741i) q^{40} +(-3.23510 - 4.45273i) q^{41} +(4.78313 + 0.210466i) q^{42} -8.41043i q^{43} +(6.55657 - 3.73386i) q^{44} +(-2.86397 - 6.06611i) q^{45} +(-8.81866 + 7.89321i) q^{46} +(1.45527 - 0.472847i) q^{47} +(-5.38207 - 4.36272i) q^{48} -3.17955 q^{49} +(7.07101 + 0.0276044i) q^{50} +(1.77236 - 12.0755i) q^{51} +(-4.17288 + 0.861185i) q^{52} +(-0.906474 + 0.294531i) q^{53} +(7.03555 - 2.12158i) q^{54} +(-7.30364 - 4.22135i) q^{55} +(-4.44356 - 3.28912i) q^{56} +(-0.327990 + 2.23467i) q^{57} +(0.292847 + 2.86790i) q^{58} +(-0.361751 - 0.497907i) q^{59} +(-1.17382 + 7.65651i) q^{60} +(7.41094 - 10.2003i) q^{61} +(-5.26157 - 3.05857i) q^{62} +(5.53424 - 1.93809i) q^{63} +(2.33662 + 7.65116i) q^{64} +(3.18589 + 3.54165i) q^{65} +(5.75510 - 7.23010i) q^{66} +(-10.9221 - 3.54880i) q^{67} +(-9.49186 + 10.4171i) q^{68} +(-6.43366 + 12.9890i) q^{69} +(-0.667181 + 6.14486i) q^{70} +(-2.33603 - 7.18955i) q^{71} +(-8.10543 - 2.51038i) q^{72} +(8.16865 - 11.2432i) q^{73} +(-5.93482 + 2.62133i) q^{74} +(8.05232 - 3.18750i) q^{75} +(1.75655 - 1.92777i) q^{76} +(4.33429 - 5.96563i) q^{77} +(-4.35254 + 2.87876i) q^{78} +(10.3991 - 3.37889i) q^{79} +(6.06627 - 6.57270i) q^{80} +(7.03364 - 5.61497i) q^{81} +(3.14484 + 7.12007i) q^{82} +(-0.864776 + 2.66151i) q^{83} +(-6.54962 - 1.71693i) q^{84} +(15.4105 + 3.28321i) q^{85} +(-2.50736 + 11.6269i) q^{86} +(1.63850 + 3.12749i) q^{87} +(-10.1772 + 3.20713i) q^{88} +(-8.87863 + 12.2204i) q^{89} +(2.15078 + 9.23981i) q^{90} +(-3.36882 + 2.44759i) q^{91} +(14.5444 - 8.28278i) q^{92} +(-7.37474 - 1.08242i) q^{93} +(-2.15278 + 0.219826i) q^{94} +(-2.85185 - 0.607586i) q^{95} +(6.13972 + 7.63570i) q^{96} +(-3.15132 + 1.02393i) q^{97} +(4.39552 + 0.947905i) q^{98} +(3.25225 - 10.8405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 10 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} - 16 q^{10} - 5 q^{12} - 18 q^{16} - 12 q^{19} - 10 q^{22} + 12 q^{24} - 16 q^{25} - 10 q^{27} - 50 q^{28} - 21 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 32 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) \) 464 * q - 10 * q^3 - 6 * q^4 + q^6 - 6 * q^9 - 16 * q^10 - 5 * q^12 - 18 * q^16 - 12 * q^19 - 10 * q^22 + 12 * q^24 - 16 * q^25 - 10 * q^27 - 50 * q^28 - 21 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 32 * q^40 + 15 * q^42 - 34 * q^46 - 70 * q^48 + 336 * q^49 - 4 * q^51 - 60 * q^52 + 40 * q^54 - 70 * q^58 - 50 * q^60 - 30 * q^64 + 28 * q^66 - 20 * q^67 - 16 * q^70 - 5 * q^72 - 20 * q^73 - 42 * q^75 - 48 * q^76 + 75 * q^78 - 6 * q^81 - 76 * q^84 - 70 * q^88 + 66 * q^90 - 96 * q^91 - 108 * q^94 - 50 * q^96 - 60 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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