LMFDB - Embedded newform 585.2.bt.b.571.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.9
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71224 + 0.988562i) q^{2} +(-1.13208 + 1.31087i) q^{3} +(0.954509 - 1.65326i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.642514 - 3.36366i) q^{6} +(-3.18919 + 1.84128i) q^{7} -0.179881i q^{8} +(-0.436783 - 2.96803i) q^{9} +O(q^{10})$	\(q+(-1.71224 + 0.988562i) q^{2} +(-1.13208 + 1.31087i) q^{3} +(0.954509 - 1.65326i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.642514 - 3.36366i) q^{6} +(-3.18919 + 1.84128i) q^{7} -0.179881i q^{8} +(-0.436783 - 2.96803i) q^{9} +1.97712 q^{10} +(1.59587 - 0.921379i) q^{11} +(1.08663 + 3.12287i) q^{12} +(-3.58458 - 0.388332i) q^{13} +(3.64043 - 6.30542i) q^{14} +(1.63585 - 0.569210i) q^{15} +(2.08684 + 3.61452i) q^{16} +0.179874 q^{17} +(3.68196 + 4.65020i) q^{18} -0.475894i q^{19} +(-1.65326 + 0.954509i) q^{20} +(1.19674 - 6.26510i) q^{21} +(-1.82168 + 3.15524i) q^{22} +(3.15723 - 5.46848i) q^{23} +(0.235801 + 0.203640i) q^{24} +(0.500000 + 0.866025i) q^{25} +(6.52155 - 2.87866i) q^{26} +(4.38519 + 2.78749i) q^{27} +7.03007i q^{28} +(-0.00188512 - 0.00326513i) q^{29} +(-2.23827 + 2.59176i) q^{30} +(-1.31356 - 0.758387i) q^{31} +(-6.83478 - 3.94606i) q^{32} +(-0.598848 + 3.13507i) q^{33} +(-0.307988 + 0.177817i) q^{34} +3.68256 q^{35} +(-5.32384 - 2.11090i) q^{36} +5.39633i q^{37} +(0.470451 + 0.814844i) q^{38} +(4.56709 - 4.25931i) q^{39} +(-0.0899405 + 0.155782i) q^{40} +(1.53334 + 0.885273i) q^{41} +(4.14434 + 11.9104i) q^{42} +(1.10082 + 1.90667i) q^{43} -3.51786i q^{44} +(-1.10575 + 2.78878i) q^{45} +12.4845i q^{46} +(7.86397 - 4.54027i) q^{47} +(-7.10065 - 1.35634i) q^{48} +(3.28061 - 5.68218i) q^{49} +(-1.71224 - 0.988562i) q^{50} +(-0.203632 + 0.235792i) q^{51} +(-4.06353 + 5.55557i) q^{52} -9.08755 q^{53} +(-10.2641 - 0.437811i) q^{54} -1.84276 q^{55} +(0.331211 + 0.573674i) q^{56} +(0.623837 + 0.538751i) q^{57} +(0.00645557 + 0.00372713i) q^{58} +(3.80390 + 2.19618i) q^{59} +(0.620382 - 3.24780i) q^{60} +(3.04023 + 5.26583i) q^{61} +2.99885 q^{62} +(6.85796 + 8.66137i) q^{63} +7.25635 q^{64} +(2.91017 + 2.12859i) q^{65} +(-2.07384 - 5.95998i) q^{66} +(10.1270 + 5.84681i) q^{67} +(0.171692 - 0.297378i) q^{68} +(3.59425 + 10.3295i) q^{69} +(-6.30542 + 3.64043i) q^{70} +12.0988i q^{71} +(-0.533893 + 0.0785690i) q^{72} +4.31020i q^{73} +(-5.33460 - 9.23980i) q^{74} +(-1.70129 - 0.324974i) q^{75} +(-0.786776 - 0.454245i) q^{76} +(-3.39303 + 5.87690i) q^{77} +(-3.60936 + 11.8078i) q^{78} +(-5.42831 - 9.40211i) q^{79} -4.17368i q^{80} +(-8.61844 + 2.59277i) q^{81} -3.50059 q^{82} +(15.1698 - 8.75827i) q^{83} +(-9.21554 - 7.95861i) q^{84} +(-0.155776 - 0.0899371i) q^{85} +(-3.76973 - 2.17645i) q^{86} +(0.00641429 + 0.00122523i) q^{87} +(-0.165739 - 0.287068i) q^{88} -2.06569i q^{89} +(-0.863575 - 5.86817i) q^{90} +(12.1469 - 5.36174i) q^{91} +(-6.02721 - 10.4394i) q^{92} +(2.48121 - 0.863362i) q^{93} +(-8.97667 + 15.5480i) q^{94} +(-0.237947 + 0.412136i) q^{95} +(12.9103 - 4.49228i) q^{96} +(9.54063 - 5.50829i) q^{97} +12.9723i q^{98} +(-3.43173 - 4.33417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.71224	+	0.988562i	−1.21074	+	0.699019i	−0.962920	−	0.269788i	$-0.913046\pi$
$2$	−1.71224	+	0.988562i	−1.21074	+	0.699019i	−0.247816	+	0.968807i	$0.579713\pi$
$3$	−1.13208	+	1.31087i	−0.653608	+	0.756834i
$3$	−1.13208	+	1.31087i	−0.653608	+	0.756834i
$4$	0.954509	−	1.65326i	0.477255	−	0.826629i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.642514	−	3.36366i	0.262305	−	1.37321i
$7$	−3.18919	+	1.84128i	−1.20540	+	0.695938i	−0.961751	−	0.273926i	$-0.911678\pi$
$7$	−3.18919	+	1.84128i	−1.20540	+	0.695938i	−0.243648	+	0.969864i	$0.578344\pi$
$8$		−	0.179881i		−	0.0635976i
$9$	−0.436783	−	2.96803i	−0.145594	−	0.989344i
$10$	1.97712			0.625221
$11$	1.59587	−	0.921379i	0.481174	−	0.277806i	−0.239731	−	0.970839i	$-0.577059\pi$
$11$	1.59587	−	0.921379i	0.481174	−	0.277806i	0.720906	+	0.693033i	$0.243726\pi$
$12$	1.08663	+	3.12287i	0.313684	+	0.901494i
$13$	−3.58458	−	0.388332i	−0.994183	−	0.107704i
$13$	−3.58458	−	0.388332i	−0.994183	−	0.107704i
$14$	3.64043	−	6.30542i	0.972947	−	1.68519i
$15$	1.63585	−	0.569210i	0.422374	−	0.146969i
$16$	2.08684	+	3.61452i	0.521711	+	0.903629i
$17$	0.179874			0.0436259			0.0218129	−	0.999762i	$-0.493056\pi$
$17$	0.179874			0.0436259			0.0218129	+	0.999762i	$0.493056\pi$
$18$	3.68196	+	4.65020i	0.867847	+	1.09606i
$19$		−	0.475894i		−	0.109178i	−0.998509	−	0.0545888i	$-0.982615\pi$
$19$		−	0.475894i		−	0.109178i	0.998509	−	0.0545888i	$-0.0173848\pi$
$20$	−1.65326	+	0.954509i	−0.369680	+	0.213435i
$21$	1.19674	−	6.26510i	0.261149	−	1.36716i
$22$	−1.82168	+	3.15524i	−0.388383	+	0.672700i
$23$	3.15723	−	5.46848i	0.658328	−	1.14026i	−0.322720	−	0.946494i	$-0.604597\pi$
$23$	3.15723	−	5.46848i	0.658328	−	1.14026i	0.981048	−	0.193763i	$-0.0620694\pi$
$24$	0.235801	+	0.203640i	0.0481328	+	0.0415678i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	6.52155	−	2.87866i	1.27898	−	0.564552i
$27$	4.38519	+	2.78749i	0.843931	+	0.536452i
$28$			7.03007i			1.32856i
$29$	−0.00188512	−	0.00326513i	−0.000350059	−	0.000606320i	0.865850	−	0.500303i	$-0.166778\pi$
$29$	−0.00188512	−	0.00326513i	−0.000350059	−	0.000606320i	−0.866200	+	0.499697i	$0.833445\pi$
$30$	−2.23827	+	2.59176i	−0.408649	+	0.473189i
$31$	−1.31356	−	0.758387i	−0.235923	−	0.136210i	0.377378	−	0.926059i	$-0.376826\pi$
$31$	−1.31356	−	0.758387i	−0.235923	−	0.136210i	−0.613302	+	0.789849i	$0.710159\pi$
$32$	−6.83478	−	3.94606i	−1.20823	−	0.697572i
$33$	−0.598848	+	3.13507i	−0.104246	+	0.545745i
$34$	−0.307988	+	0.177817i	−0.0528194	+	0.0304953i
$35$	3.68256			0.622465
$36$	−5.32384	−	2.11090i	−0.887307	−	0.351817i
$37$			5.39633i			0.887151i	0.896237	+	0.443575i	$0.146290\pi$
$37$			5.39633i			0.887151i	−0.896237	+	0.443575i	$0.853710\pi$
$38$	0.470451	+	0.814844i	0.0763172	+	0.132185i
$39$	4.56709	−	4.25931i	0.731319	−	0.682035i
$40$	−0.0899405	+	0.155782i	−0.0142208	+	0.0246312i
$41$	1.53334	+	0.885273i	0.239467	+	0.138256i	0.614932	−	0.788580i	$-0.289184\pi$
$41$	1.53334	+	0.885273i	0.239467	+	0.138256i	−0.375465	+	0.926837i	$0.622517\pi$
$42$	4.14434	+	11.9104i	0.639486	+	1.83781i
$43$	1.10082	+	1.90667i	0.167873	+	0.290765i	0.937672	−	0.347522i	$-0.112977\pi$
$43$	1.10082	+	1.90667i	0.167873	+	0.290765i	−0.769799	+	0.638287i	$0.779643\pi$
$44$		−	3.51786i		−	0.530337i
$45$	−1.10575	+	2.78878i	−0.164836	+	0.415727i
$46$			12.4845i			1.84074i
$47$	7.86397	−	4.54027i	1.14708	−	0.662266i	0.198904	−	0.980019i	$-0.436262\pi$
$47$	7.86397	−	4.54027i	1.14708	−	0.662266i	0.948173	+	0.317753i	$0.102928\pi$
$48$	−7.10065	−	1.35634i	−1.02489	−	0.195771i
$49$	3.28061	−	5.68218i	0.468658	−	0.811740i
$50$	−1.71224	−	0.988562i	−0.242147	−	0.139804i
$51$	−0.203632	+	0.235792i	−0.0285142	+	0.0330175i
$52$	−4.06353	+	5.55557i	−0.563510	+	0.770419i
$53$	−9.08755			−1.24827			−0.624135	−	0.781316i	$-0.714549\pi$
$53$	−9.08755			−1.24827			−0.624135	+	0.781316i	$0.714549\pi$
$54$	−10.2641	−	0.437811i	−1.39677	−	0.0595785i
$55$	−1.84276			−0.248477
$56$	0.331211	+	0.573674i	0.0442599	+	0.0766605i
$57$	0.623837	+	0.538751i	0.0826292	+	0.0713593i
$58$	0.00645557	+	0.00372713i	0.000847658	+	0.000489396i
$59$	3.80390	+	2.19618i	0.495226	+	0.285919i	0.726740	−	0.686913i	$-0.241035\pi$
$59$	3.80390	+	2.19618i	0.495226	+	0.285919i	−0.231514	+	0.972832i	$0.574368\pi$
$60$	0.620382	−	3.24780i	0.0800909	−	0.419289i
$61$	3.04023	+	5.26583i	0.389262	+	0.674221i	0.992350	−	0.123453i	$-0.0393968\pi$
$61$	3.04023	+	5.26583i	0.389262	+	0.674221i	−0.603089	+	0.797674i	$0.706064\pi$
$62$	2.99885			0.380854
$63$	6.85796	+	8.66137i	0.864021	+	1.09123i
$64$	7.25635			0.907044
$65$	2.91017	+	2.12859i	0.360962	+	0.264020i
$66$	−2.07384	−	5.95998i	−0.255272	−	0.733623i
$67$	10.1270	+	5.84681i	1.23721	+	0.714301i	0.968522	−	0.248927i	$-0.0800780\pi$
$67$	10.1270	+	5.84681i	1.23721	+	0.714301i	0.268684	+	0.963228i	$0.413411\pi$
$68$	0.171692	−	0.297378i	0.0208207	−	0.0360624i
$69$	3.59425	+	10.3295i	0.432697	+	1.24353i
$70$	−6.30542	+	3.64043i	−0.753641	+	0.435115i
$71$			12.0988i			1.43586i	0.696115	+	0.717930i	$0.254910\pi$
$71$			12.0988i			1.43586i	−0.696115	+	0.717930i	$0.745090\pi$
$72$	−0.533893	+	0.0785690i	−0.0629199	+	0.00925945i
$73$			4.31020i			0.504471i	0.967666	+	0.252235i	$0.0811657\pi$
$73$			4.31020i			0.504471i	−0.967666	+	0.252235i	$0.918834\pi$
$74$	−5.33460	−	9.23980i	−0.620135	−	1.07411i
$75$	−1.70129	−	0.324974i	−0.196448	−	0.0375248i
$76$	−0.786776	−	0.454245i	−0.0902494	−	0.0521055i
$77$	−3.39303	+	5.87690i	−0.386671	+	0.669735i
$78$	−3.60936	+	11.8078i	−0.408680	+	1.33697i
$79$	−5.42831	−	9.40211i	−0.610732	−	1.05782i	−0.991117	−	0.132991i	$-0.957542\pi$
$79$	−5.42831	−	9.40211i	−0.610732	−	1.05782i	0.380385	−	0.924828i	$-0.375792\pi$
$80$		−	4.17368i		−	0.466632i
$81$	−8.61844	+	2.59277i	−0.957605	+	0.288086i
$82$	−3.50059			−0.386575
$83$	15.1698	−	8.75827i	1.66510	−	0.961345i	0.694877	−	0.719129i	$-0.255459\pi$
$83$	15.1698	−	8.75827i	1.66510	−	0.961345i	0.970222	−	0.242216i	$-0.0778744\pi$
$84$	−9.21554	−	7.95861i	−1.00550	−	0.868355i
$85$	−0.155776	−	0.0899371i	−0.0168962	−	0.00975504i
$86$	−3.76973	−	2.17645i	−0.406500	−	0.234693i
$87$	0.00641429	+	0.00122523i	0.000687684	+	0.000131359i
$88$	−0.165739	−	0.287068i	−0.0176678	−	0.0306015i
$89$		−	2.06569i		−	0.218963i	−0.993989	−	0.109481i	$-0.965081\pi$
$89$		−	2.06569i		−	0.218963i	0.993989	−	0.109481i	$-0.0349190\pi$
$90$	−0.863575	−	5.86817i	−0.0910288	−	0.618559i
$91$	12.1469	−	5.36174i	1.27334	−	0.562063i
$92$	−6.02721	−	10.4394i	−0.628380	−	1.08839i
$93$	2.48121	−	0.863362i	0.257290	−	0.0895265i
$94$	−8.97667	+	15.5480i	−0.925872	+	1.60366i
$95$	−0.237947	+	0.412136i	−0.0244128	+	0.0422843i
$96$	12.9103	−	4.49228i	1.31765	−	0.458491i
$97$	9.54063	−	5.50829i	0.968705	−	0.559282i	0.0698636	−	0.997557i	$-0.477744\pi$
$97$	9.54063	−	5.50829i	0.968705	−	0.559282i	0.898841	+	0.438275i	$0.144410\pi$
$98$			12.9723i			1.31040i
$99$	−3.43173	−	4.33417i	−0.344902	−	0.435600i
$100$	1.90902			0.190902
$101$	−2.14975	−	3.72348i	−0.213908	−	0.370500i	0.739026	−	0.673677i	$-0.235286\pi$
$101$	−2.14975	−	3.72348i	−0.213908	−	0.370500i	−0.952934	+	0.303177i	$0.901953\pi$
$102$	0.115572	−	0.605036i	0.0114433	−	0.0599075i
$103$	8.61522	−	14.9220i	0.848883	−	1.47031i	−0.0333232	−	0.999445i	$-0.510609\pi$
$103$	8.61522	−	14.9220i	0.848883	−	1.47031i	0.882206	−	0.470864i	$-0.156058\pi$
$104$	−0.0698536	+	0.644798i	−0.00684971	+	0.0632276i
$105$	−4.16895	+	4.82737i	−0.406848	+	0.471103i
$106$	15.5601	−	8.98361i	1.51133	−	0.872565i
$107$	−8.40204			−0.812256			−0.406128	−	0.913816i	$-0.633121\pi$
$107$	−8.40204			−0.812256			−0.406128	+	0.913816i	$0.633121\pi$
$108$	8.79415	−	4.58918i	0.846217	−	0.441594i
$109$		−	17.0795i		−	1.63592i	−0.575278	−	0.817958i	$-0.695106\pi$
$109$		−	17.0795i		−	1.63592i	0.575278	−	0.817958i	$-0.304894\pi$
$110$	3.15524	−	1.82168i	0.300841	−	0.173690i
$111$	−7.07391	−	6.10908i	−0.671426	−	0.579848i
$112$	−13.3107	−	7.68491i	−1.25774	−	0.726156i
$113$	2.24214	−	3.88350i	0.210923	−	0.365329i	−0.741081	−	0.671416i	$-0.765687\pi$
$113$	2.24214	−	3.88350i	0.210923	−	0.365329i	0.952004	+	0.306087i	$0.0990199\pi$
$114$	−1.60075	−	0.305768i	−0.149924	−	0.0286378i
$115$	−5.46848	+	3.15723i	−0.509939	+	0.294413i
$116$	−0.00719748			−0.000668269
$117$	0.413101	+	10.8088i	0.0381912	+	0.999270i
$118$	−8.68426			−0.799451
$119$	−0.573652	+	0.331198i	−0.0525866	+	0.0303609i
$120$	−0.102390	−	0.294258i	−0.00934689	−	0.0268620i
$121$	−3.80212	+	6.58547i	−0.345647	+	0.598679i
$122$	−10.4112	−	6.01091i	−0.942586	−	0.544203i
$123$	−2.89634	+	1.00781i	−0.261155	+	0.0908714i
$124$	−2.50762	+	1.44777i	−0.225191	+	0.130014i
$125$		−	1.00000i		−	0.0894427i
$126$	−20.3048	−	8.05083i	−1.80889	−	0.717225i
$127$	6.28102			0.557350			0.278675	−	0.960385i	$-0.410105\pi$
$127$	6.28102			0.557350			0.278675	+	0.960385i	$0.410105\pi$
$128$	1.24496	−	0.718780i	0.110040	−	0.0635318i
$129$	−3.74563	−	0.715475i	−0.329784	−	0.0629941i
$130$	−7.08715	−	0.767781i	−0.621585	−	0.0673388i
$131$	10.3974	−	18.0088i	0.908423	−	1.57343i	0.0921678	−	0.995743i	$-0.470620\pi$
$131$	10.3974	−	18.0088i	0.908423	−	1.57343i	0.816255	−	0.577691i	$-0.196046\pi$
$132$	4.61147	+	3.98250i	0.401377	+	0.346632i
$133$	0.876253	+	1.51771i	0.0759808	+	0.131603i
$134$	−23.1197			−1.99724
$135$	−2.40394	−	4.60663i	−0.206899	−	0.396476i
$136$		−	0.0323559i		−	0.00277450i
$137$	6.19634	−	3.57746i	0.529389	−	0.305643i	−0.211379	−	0.977404i	$-0.567795\pi$
$137$	6.19634	−	3.57746i	0.529389	−	0.305643i	0.740768	+	0.671761i	$0.234462\pi$
$138$	−16.3656	−	14.1334i	−1.39313	−	1.20312i
$139$	8.25510	−	14.2982i	0.700188	−	1.21276i	−0.268212	−	0.963360i	$-0.586433\pi$
$139$	8.25510	−	14.2982i	0.700188	−	1.21276i	0.968400	−	0.249402i	$-0.0802340\pi$
$140$	3.51503	−	6.08822i	0.297075	−	0.514548i
$141$	−2.95094	+	15.4486i	−0.248514	+	1.30101i
$142$	−11.9604	−	20.7160i	−1.00369	−	1.73845i
$143$	−6.07834	+	2.68302i	−0.508296	+	0.224366i
$144$	9.81651	−	7.77258i	0.818042	−	0.647715i
$145$			0.00377025i			0.000313102i
$146$	−4.26090	−	7.38010i	−0.352635	−	0.610781i
$147$	3.73471	+	10.7332i	0.308034	+	0.885256i
$148$	8.92153	+	5.15085i	0.733345	+	0.423397i
$149$	−14.4350	−	8.33407i	−1.18256	−	0.682753i	−0.225957	−	0.974137i	$-0.572551\pi$
$149$	−14.4350	−	8.33407i	−1.18256	−	0.682753i	−0.956606	+	0.291384i	$0.905884\pi$
$150$	3.23428	−	1.12540i	0.264077	−	0.0918884i
$151$	−8.26158	+	4.76983i	−0.672318	+	0.388163i	−0.796954	−	0.604040i	$-0.793557\pi$
$151$	−8.26158	+	4.76983i	−0.672318	+	0.388163i	0.124636	+	0.992202i	$0.460224\pi$
$152$	−0.0856043			−0.00694343
$153$	−0.0785660	−	0.533872i	−0.00635169	−	0.0431610i
$154$		−	13.4169i		−	1.08116i
$155$	0.758387	+	1.31356i	0.0609151	+	0.105508i
$156$	−2.68241	−	11.6161i	−0.214765	−	0.930035i
$157$	4.32832	−	7.49686i	0.345437	−	0.598315i	−0.639996	−	0.768378i	$-0.721064\pi$
$157$	4.32832	−	7.49686i	0.345437	−	0.598315i	0.985433	+	0.170064i	$0.0543973\pi$
$158$	18.5891	+	10.7324i	1.47887	+	0.853827i
$159$	10.2878	−	11.9126i	0.815879	−	0.944733i
$160$	3.94606	+	6.83478i	0.311964	+	0.540337i
$161$			23.2534i			1.83262i
$162$	12.1937	−	12.9593i	0.958029	−	1.01818i
$163$		−	3.30102i		−	0.258555i	−0.991608	−	0.129278i	$-0.958734\pi$
$163$		−	3.30102i		−	0.258555i	0.991608	−	0.129278i	$-0.0412659\pi$
$164$	2.92717	−	1.69000i	0.228574	−	0.131967i
$165$	2.08615	−	2.41562i	0.162407	−	0.188056i
$166$	−17.3162	+	29.9925i	−1.34400	+	2.32787i
$167$	−8.05426	−	4.65013i	−0.623257	−	0.359838i	0.154879	−	0.987933i	$-0.450501\pi$
$167$	−8.05426	−	4.65013i	−0.623257	−	0.359838i	−0.778136	+	0.628096i	$0.783835\pi$
$168$	−1.12697	−	0.215270i	−0.0869478	−	0.0166084i
$169$	12.6984	+	2.78401i	0.976800	+	0.214155i
$170$	0.355633			0.0272758
$171$	−1.41247	+	0.207863i	−0.108014	+	0.0158956i
$172$	4.20297			0.320473
$173$	7.33343	+	12.7019i	0.557550	+	0.965705i	0.997700	+	0.0677809i	$0.0215919\pi$
$173$	7.33343	+	12.7019i	0.557550	+	0.965705i	−0.440150	+	0.897924i	$0.645075\pi$
$174$	−0.0121940	+	0.00424303i	−0.000924427	+	0.000321663i
$175$	−3.18919	−	1.84128i	−0.241080	−	0.139188i
$176$	6.66068	+	3.84554i	0.502068	+	0.289869i
$177$	−7.18525	+	2.50018i	−0.540076	+	0.187925i
$178$	2.04206	+	3.53696i	0.153059	+	0.265106i
$179$	−3.91870			−0.292897			−0.146449	−	0.989218i	$-0.546784\pi$
$179$	−3.91870			−0.292897			−0.146449	+	0.989218i	$0.546784\pi$
$180$	3.55513	+	4.49001i	0.264984	+	0.334666i
$181$	18.4224			1.36933			0.684664	−	0.728858i	$-0.259949\pi$
$181$	18.4224			1.36933			0.684664	+	0.728858i	$0.259949\pi$
$182$	−15.4980	+	21.1886i	−1.14879	+	1.57060i
$183$	−10.3446	−	1.97599i	−0.764698	−	0.146070i
$184$	−0.983677	−	0.567926i	−0.0725176	−	0.0418681i
$185$	2.69816	−	4.67336i	0.198373	−	0.343592i
$186$	−3.39494	+	3.93111i	−0.248929	+	0.288243i
$187$	0.287057	−	0.165732i	0.0209917	−	0.0121195i
$188$		−	17.3349i		−	1.26428i
$189$	−19.1177	−	0.815458i	−1.39061	−	0.0593159i
$190$		−	0.940901i		−	0.0682601i
$191$	0.300236	+	0.520024i	0.0217243	+	0.0376276i	0.876683	−	0.481068i	$-0.159751\pi$
$191$	0.300236	+	0.520024i	0.0217243	+	0.0376276i	−0.854959	+	0.518696i	$0.826418\pi$
$192$	−8.21478	+	9.51216i	−0.592850	+	0.686481i
$193$	0.779254	+	0.449902i	0.0560919	+	0.0323847i	0.527784	−	0.849379i	$-0.323023\pi$
$193$	0.779254	+	0.449902i	0.0560919	+	0.0323847i	−0.471692	+	0.881763i	$0.656356\pi$
$194$	−10.8906	+	18.8630i	−0.781897	+	1.35429i
$195$	−6.08487	+	1.40512i	−0.435746	+	0.100623i
$196$	−6.26274	−	10.8474i	−0.447339	−	0.774813i
$197$		−	1.36267i		−	0.0970863i	−0.998821	−	0.0485432i	$-0.984542\pi$
$197$		−	1.36267i		−	0.0970863i	0.998821	−	0.0485432i	$-0.0154578\pi$
$198$	10.1605	+	4.02865i	0.722078	+	0.286304i
$199$	25.1448			1.78247			0.891235	−	0.453542i	$-0.149840\pi$
$199$	25.1448			1.78247			0.891235	+	0.453542i	$0.149840\pi$
$200$	0.155782	−	0.0899405i	0.0110154	−	0.00635976i
$201$	−19.1290	+	6.65612i	−1.34925	+	0.469486i
$202$	7.36179	+	4.25033i	0.517973	+	0.299052i
$203$	0.0120240	+	0.00694208i	0.000843921	+	0.000487238i
$204$	0.195457	+	0.561723i	0.0136847	+	0.0393285i
$205$	−0.885273	−	1.53334i	−0.0618301	−	0.107093i
$206$			34.0667i			2.37354i
$207$	−17.6097	−	6.98222i	−1.22396	−	0.485298i
$208$	−6.07682	−	13.7669i	−0.421351	−	0.954563i
$209$	−0.438479	−	0.759467i	−0.0303302	−	0.0525334i
$210$	2.36609	−	12.3869i	0.163276	−	0.854776i
$211$	−11.5692	+	20.0385i	−0.796458	+	1.37951i	0.125452	+	0.992100i	$0.459962\pi$
$211$	−11.5692	+	20.0385i	−0.796458	+	1.37951i	−0.921909	+	0.387405i	$0.873371\pi$
$212$	−8.67415	+	15.0241i	−0.595743	+	1.03186i
$213$	−15.8600	−	13.6968i	−1.08671	−	0.938490i
$214$	14.3863	−	8.30594i	0.983428	−	0.567782i
$215$		−	2.20164i		−	0.150150i
$216$	0.501416	−	0.788813i	0.0341170	−	0.0536719i
$217$	5.58560			0.379175
$218$	16.8841	+	29.2441i	1.14354	+	1.98066i
$219$	−5.65013	−	4.87950i	−0.381801	−	0.329726i
$220$	−1.75893	+	3.04656i	−0.118587	+	0.205399i
$221$	−0.644773	−	0.0698509i	−0.0433721	−	0.00469868i
$222$	18.1514	+	3.46722i	1.21824	+	0.232704i
$223$	−3.91964	+	2.26301i	−0.262479	+	0.151542i	−0.625465	−	0.780252i	$-0.715091\pi$
$223$	−3.91964	+	2.26301i	−0.262479	+	0.151542i	0.362986	+	0.931795i	$0.381757\pi$
$224$	29.0632			1.94187
$225$	2.35200	−	1.86228i	0.156800	−	0.124152i
$226$			8.86597i			0.589756i
$227$	20.0281	−	11.5632i	1.32931	−	0.767478i	0.344118	−	0.938926i	$-0.388178\pi$
$227$	20.0281	−	11.5632i	1.32931	−	0.767478i	0.985193	+	0.171448i	$0.0548446\pi$
$228$	1.48615	−	0.517122i	0.0984229	−	0.0342472i
$229$	−6.05063	−	3.49333i	−0.399837	−	0.230846i	0.286577	−	0.958057i	$-0.407483\pi$
$229$	−6.05063	−	3.49333i	−0.399837	−	0.230846i	−0.686413	+	0.727211i	$0.740816\pi$
$230$	6.24224	−	10.8119i	0.411601	−	0.712914i
$231$	−3.86269	−	11.1010i	−0.254146	−	0.730390i
$232$	−0.000587335	0	0.000339098i	−3.85605e−5	0	2.22629e-5i
$233$	−22.6754			−1.48552			−0.742758	−	0.669559i	$-0.766483\pi$
$233$	−22.6754			−1.48552			−0.742758	+	0.669559i	$0.766483\pi$
$234$	−11.3925	−	18.0988i	−0.744748	−	1.18316i
$235$	−9.08053			−0.592348
$236$	7.26172	−	4.19256i	0.472698	−	0.272912i
$237$	18.4703	+	3.52812i	1.19977	+	0.229176i
$238$	0.654820	−	1.13418i	0.0424457	−	0.0735181i
$239$	22.3254	+	12.8896i	1.44411	+	0.833756i	0.998120	−	0.0612833i	$-0.0195193\pi$
$239$	22.3254	+	12.8896i	1.44411	+	0.833756i	0.445987	+	0.895039i	$0.352853\pi$
$240$	5.47118	+	4.72495i	0.353163	+	0.304994i
$241$	−5.14460	+	2.97024i	−0.331393	+	0.191330i	−0.656459	−	0.754361i	$-0.727947\pi$
$241$	−5.14460	+	2.97024i	−0.331393	+	0.191330i	0.325067	+	0.945691i	$0.394613\pi$
$242$		−	15.0345i		−	0.966456i
$243$	6.35797	−	14.2329i	0.407864	−	0.913043i
$244$	11.6077			0.743108
$245$	−5.68218	+	3.28061i	−0.363021	+	0.209590i
$246$	3.96295	−	4.58883i	0.252669	−	0.292573i
$247$	−0.184805	+	1.70588i	−0.0117589	+	0.108542i
$248$	−0.136419	+	0.236285i	−0.00866264	+	0.0150041i
$249$	−5.69242	+	29.8007i	−0.360743	+	1.88855i
$250$	0.988562	+	1.71224i	0.0625221	+	0.108292i
$251$	20.7925			1.31241			0.656206	−	0.754582i	$-0.272160\pi$
$251$	20.7925			1.31241			0.656206	+	0.754582i	$0.272160\pi$
$252$	20.8655	−	3.07062i	1.31440	−	0.193431i
$253$		−	11.6360i		−	0.731551i
$254$	−10.7546	+	6.20918i	−0.674804	+	0.389598i
$255$	0.294247	−	0.102386i	0.0184264	−	0.00641167i
$256$	−8.67747	+	15.0298i	−0.542342	+	0.939363i
$257$	2.10977	−	3.65423i	0.131604	−	0.227945i	−0.792691	−	0.609624i	$-0.791321\pi$
$257$	2.10977	−	3.65423i	0.131604	−	0.227945i	0.924295	+	0.381679i	$0.124654\pi$
$258$	7.12070	−	2.47772i	0.443315	−	0.154256i
$259$	−9.93614	−	17.2099i	−0.617402	−	1.06937i
$260$	6.29690	−	2.77950i	0.390517	−	0.172377i
$261$	−0.00886763	+	0.00702127i	−0.000548892	+	0.000434606i
$262$			41.1138i			2.54002i
$263$	−15.4548	−	26.7685i	−0.952985	−	1.65062i	−0.738913	−	0.673801i	$-0.764661\pi$
$263$	−15.4548	−	26.7685i	−0.952985	−	1.65062i	−0.214072	−	0.976818i	$-0.568673\pi$
$264$	0.563939	+	0.107721i	0.0347081	+	0.00662980i
$265$	7.87005	+	4.54377i	0.483453	+	0.279122i
$266$	−3.00071	−	1.73246i	−0.183985	−	0.106224i
$267$	2.70786	+	2.33853i	0.165718	+	0.143116i
$268$	19.3326	−	11.1617i	1.18092	−	0.681807i
$269$	1.86363			0.113628			0.0568138	−	0.998385i	$-0.481906\pi$
$269$	1.86363			0.113628			0.0568138	+	0.998385i	$0.481906\pi$
$270$	8.67007	+	5.51121i	0.527644	+	0.335401i
$271$		−	5.61519i		−	0.341098i	−0.985349	−	0.170549i	$-0.945446\pi$
$271$		−	5.61519i		−	0.341098i	0.985349	−	0.170549i	$-0.0545542\pi$
$272$	0.375369	+	0.650158i	0.0227601	+	0.0394216i
$273$	−6.72273	+	21.9930i	−0.406878	+	1.33108i
$274$	−7.07308	+	12.2509i	−0.427300	+	0.740106i
$275$	1.59587	+	0.921379i	0.0962349	+	0.0555612i
$276$	20.5081	+	3.91738i	1.23444	+	0.235798i
$277$	0.341185	+	0.590950i	0.0204998	+	0.0355067i	0.876093	−	0.482142i	$-0.160141\pi$
$277$	0.341185	+	0.590950i	0.0204998	+	0.0355067i	−0.855593	+	0.517648i	$0.826808\pi$
$278$			32.6427i			1.95778i
$279$	−1.67717	+	4.22995i	−0.100410	+	0.253241i
$280$		−	0.662422i		−	0.0395873i
$281$	22.9981	−	13.2780i	1.37195	−	0.792097i	0.380778	−	0.924666i	$-0.375656\pi$
$281$	22.9981	−	13.2780i	1.37195	−	0.792097i	0.991174	+	0.132569i	$0.0423227\pi$
$282$	−10.2192	−	29.3689i	−0.608545	−	1.74889i
$283$	−13.9923	+	24.2353i	−0.831755	+	1.44064i	0.0648907	+	0.997892i	$0.479330\pi$
$283$	−13.9923	+	24.2353i	−0.831755	+	1.44064i	−0.896646	+	0.442749i	$0.854003\pi$
$284$	20.0024	+	11.5484i	1.18692	+	0.685271i
$285$	−0.270883	−	0.778490i	−0.0160458	−	0.0461138i
$286$	7.75524	−	10.6028i	0.458577	−	0.626956i
$287$	−6.52013			−0.384871
$288$	−8.72673	+	22.0094i	−0.514228	+	1.29692i
$289$	−16.9676			−0.998097
$290$	−0.00372713	−	0.00645557i	−0.000218864	−	0.000379084i
$291$	−3.58010	+	18.7424i	−0.209869	+	1.09870i
$292$	7.12588	+	4.11413i	0.417010	+	0.240761i
$293$	−3.52118	−	2.03295i	−0.205710	−	0.118766i	0.393606	−	0.919279i	$-0.371227\pi$
$293$	−3.52118	−	2.03295i	−0.205710	−	0.118766i	−0.599316	+	0.800513i	$0.704561\pi$
$294$	−17.0051	−	14.6857i	−0.991758	−	0.856490i
$295$	−2.19618	−	3.80390i	−0.127867	−	0.221472i
$296$	0.970697			0.0564206
$297$	9.56655	+	0.408057i	0.555108	+	0.0236779i
$298$	32.9550			1.90903
$299$	−13.4409	+	18.3762i	−0.777309	+	1.06272i
$300$	−2.16116	+	2.50248i	−0.124775	+	0.144481i
$301$	−7.02143	−	4.05383i	−0.404709	−	0.233659i
$302$	9.43054	−	16.3342i	0.542666	−	0.939926i
$303$	7.31471	+	1.39723i	0.420219	+	0.0802687i
$304$	1.72013	−	0.993116i	0.0986560	−	0.0569591i
$305$		−	6.08046i		−	0.348166i
$306$	0.662290	+	0.836450i	0.0378606	+	0.0478167i
$307$			17.1314i			0.977739i	0.872357	+	0.488870i	$0.162591\pi$
$307$			17.1314i			0.977739i	−0.872357	+	0.488870i	$0.837409\pi$
$308$	6.47736	+	11.2191i	0.369082	+	0.639268i
$309$	9.80774	+	28.1864i	0.557943	+	1.60347i
$310$	−2.59708	−	1.49942i	−0.147504	−	0.0851616i
$311$	1.95051	−	3.37838i	0.110603	−	0.191570i	−0.805410	−	0.592717i	$-0.798055\pi$
$311$	1.95051	−	3.37838i	0.110603	−	0.191570i	0.916014	+	0.401147i	$0.131388\pi$
$312$	−0.766169	−	0.821533i	−0.0433758	−	0.0465101i
$313$	5.78100	+	10.0130i	0.326762	+	0.565968i	0.981867	−	0.189569i	$-0.0607092\pi$
$313$	5.78100	+	10.0130i	0.326762	+	0.565968i	−0.655106	+	0.755537i	$0.727376\pi$
$314$			17.1152i			0.965868i
$315$	−1.60848	−	10.9299i	−0.0906275	−	0.615833i
$316$	−20.7255			−1.16590
$317$	−10.1371	+	5.85264i	−0.569354	+	0.328717i	−0.756891	−	0.653541i	$-0.773283\pi$
$317$	−10.1371	+	5.85264i	−0.569354	+	0.328717i	0.187537	+	0.982258i	$0.439950\pi$
$318$	−5.83888	+	30.5675i	−0.327428	+	1.71414i
$319$	−0.00601685	−	0.00347383i	−0.000336879	−	0.000194497i
$320$	−6.28418	−	3.62817i	−0.351296	−	0.202821i
$321$	9.51180	−	11.0140i	0.530897	−	0.614743i
$322$	−22.9874	−	39.8153i	−1.28104	−	2.21882i
$323$		−	0.0856010i		−	0.00476297i
$324$	−3.93986	+	16.7233i	−0.218881	+	0.929074i
$325$	−1.45598	−	3.29850i	−0.0807634	−	0.182968i
$326$	3.26326	+	5.65213i	0.180735	+	0.313042i
$327$	22.3890	+	19.3353i	1.23812	+	1.06925i
$328$	0.159244	−	0.275818i	0.00879277	−	0.0152295i
$329$	−16.7198	+	28.9595i	−0.921791	+	1.59659i
$330$	−1.18400	+	6.19842i	−0.0651769	+	0.341212i
$331$	−14.8937	+	8.59889i	−0.818633	+	0.472638i	−0.849945	−	0.526872i	$-0.823365\pi$
$331$	−14.8937	+	8.59889i	−0.818633	+	0.472638i	0.0313119	+	0.999510i	$0.490031\pi$
$332$		−	33.4394i		−	1.83523i
$333$	16.0165	−	2.35703i	0.877698	−	0.129164i
$334$	18.3878			1.00613
$335$	−5.84681	−	10.1270i	−0.319445	−	0.553295i
$336$	25.1427	−	8.74866i	1.37165	−	0.477278i
$337$	9.49177	−	16.4402i	0.517050	−	0.895557i	−0.482754	−	0.875756i	$-0.660363\pi$
$337$	9.49177	−	16.4402i	0.517050	−	0.895557i	0.999804	−	0.0198007i	$-0.00630319\pi$
$338$	−24.4949	+	7.78625i	−1.33235	+	0.423516i
$339$	2.55249	+	7.33560i	0.138632	+	0.398415i
$340$	−0.297378	+	0.171692i	−0.0161276	+	0.00931128i
$341$	−2.79505			−0.151360
$342$	2.21300	−	1.75222i	0.119665	−	0.0947494i
$343$		−	1.61585i		−	0.0872477i
$344$	0.342975	−	0.198016i	0.0184919	−	0.0106763i
$345$	2.05204	−	10.7427i	0.110478	−	0.578370i
$346$	−25.1132	−	14.4991i	−1.35009	−	0.779476i
$347$	−11.9344	+	20.6711i	−0.640674	+	1.10968i	0.344608	+	0.938747i	$0.388012\pi$
$347$	−11.9344	+	20.6711i	−0.640674	+	1.10968i	−0.985282	+	0.170934i	$0.945322\pi$
$348$	0.00814813	−	0.00943499i	0.000436786	−	0.000505768i
$349$	25.2213	−	14.5615i	1.35006	−	0.779460i	0.361806	−	0.932253i	$-0.382160\pi$
$349$	25.2213	−	14.5615i	1.35006	−	0.779460i	0.988258	+	0.152794i	$0.0488270\pi$
$350$	7.28087			0.389179
$351$	−14.6366	−	11.6949i	−0.781244	−	0.624226i
$352$	−14.5433			−0.775160
$353$	1.85874	−	1.07314i	0.0989308	−	0.0571177i	−0.449718	−	0.893170i	$-0.648476\pi$
$353$	1.85874	−	1.07314i	0.0989308	−	0.0571177i	0.548649	+	0.836053i	$0.315142\pi$
$354$	9.83128	−	11.3840i	0.522527	−	0.605051i
$355$	6.04939	−	10.4779i	0.321068	−	0.556107i
$356$	−3.41512	−	1.97172i	−0.181001	−	0.104501i
$357$	0.215262	−	1.12693i	0.0113929	−	0.0596434i
$358$	6.70975	−	3.87388i	0.354621	−	0.204741i
$359$			2.98854i			0.157729i	0.996885	+	0.0788646i	$0.0251295\pi$
$359$			2.98854i			0.157729i	−0.996885	+	0.0788646i	$0.974871\pi$
$360$	0.501649	+	0.198904i	0.0264392	+	0.0104831i
$361$	18.7735			0.988080
$362$	−31.5436	+	18.2117i	−1.65790	+	0.957187i
$363$	−4.32841	−	12.4394i	−0.227183	−	0.652899i
$364$	2.73000	−	25.1998i	0.143091	−	1.32083i
$365$	2.15510	−	3.73274i	0.112803	−	0.195381i
$366$	19.6659	−	6.84294i	1.02795	−	0.357686i
$367$	−15.8370	−	27.4306i	−0.826687	−	1.43186i	−0.900623	−	0.434601i	$-0.856889\pi$
$367$	−15.8370	−	27.4306i	−0.826687	−	1.43186i	0.0739360	−	0.997263i	$-0.476444\pi$
$368$	26.3546			1.37383
$369$	1.95778	−	4.93767i	0.101918	−	0.257045i
$370$			10.6692i			0.554666i
$371$	28.9819	−	16.7327i	1.50466	−	0.868719i
$372$	0.940978	−	4.92617i	0.0487875	−	0.255410i
$373$	9.20545	−	15.9443i	0.476640	−	0.825565i	−0.523002	−	0.852332i	$-0.675188\pi$
$373$	9.20545	−	15.9443i	0.476640	−	0.825565i	0.999642	+	0.0267670i	$0.00852122\pi$
$374$	−0.327673	+	0.567546i	−0.0169436	+	0.0293471i
$375$	1.31087	+	1.13208i	0.0676933	+	0.0584604i
$376$	−0.816708	−	1.41458i	−0.0421185	−	0.0729514i
$377$	0.00548942	+	0.0124362i	0.000282720	+	0.000640496i
$378$	33.5403	−	17.5028i	1.72513	−	0.900247i
$379$			21.6000i			1.10952i	0.832011	+	0.554760i	$0.187190\pi$
$379$			21.6000i			1.10952i	−0.832011	+	0.554760i	$0.812810\pi$
$380$	0.454245	+	0.786776i	0.0233023	+	0.0403607i
$381$	−7.11062	+	8.23363i	−0.364288	+	0.421821i
$382$	−1.02815	−	0.593604i	−0.0526049	−	0.0303714i
$383$	−22.9806	−	13.2679i	−1.17426	−	0.677957i	−0.219577	−	0.975595i	$-0.570468\pi$
$383$	−22.9806	−	13.2679i	−1.17426	−	0.677957i	−0.954679	+	0.297638i	$0.903801\pi$
$384$	−0.467170	+	2.44571i	−0.0238401	+	0.124807i
$385$	5.87690	−	3.39303i	0.299514	−	0.172925i
$386$	−1.77903			−0.0905500
$387$	5.17825	−	4.10007i	0.263225	−	0.208418i
$388$		−	21.0309i		−	1.06768i
$389$	17.9599	+	31.1075i	0.910605	+	1.57721i	0.813212	+	0.581968i	$0.197717\pi$
$389$	17.9599	+	31.1075i	0.910605	+	1.57721i	0.0973928	+	0.995246i	$0.468950\pi$
$390$	9.02970	−	8.42118i	0.457237	−	0.426423i
$391$	0.567904	−	0.983639i	0.0287201	−	0.0497448i
$392$	−1.02212	−	0.590119i	−0.0516247	−	0.0298055i
$393$	11.8366	+	34.0171i	0.597076	+	1.71593i
$394$	1.34709	+	2.33322i	0.0678652	+	0.117546i
$395$			10.8566i			0.546256i
$396$	−10.4411	+	1.53654i	−0.524686	+	0.0772141i
$397$			14.4262i			0.724031i	0.932172	+	0.362016i	$0.117911\pi$
$397$			14.4262i			0.724031i	−0.932172	+	0.362016i	$0.882089\pi$
$398$	−43.0540	+	24.8572i	−2.15810	+	1.24598i
$399$	−2.98152	−	0.569519i	−0.149263	−	0.0285116i
$400$	−2.08684	+	3.61452i	−0.104342	+	0.180726i
$401$	−32.5154	−	18.7728i	−1.62374	−	0.937469i	−0.985906	−	0.167298i	$-0.946496\pi$
$401$	−32.5154	−	18.7728i	−1.62374	−	0.937469i	−0.637838	−	0.770171i	$-0.720171\pi$
$402$	26.1734	−	30.3071i	1.30541	−	1.51158i
$403$	4.41407	+	3.22860i	0.219880	+	0.160828i
$404$	−8.20784			−0.408355
$405$	8.76018	+	2.06381i	0.435297	+	0.102552i
$406$	−0.0274507			−0.00136235
$407$	4.97206	+	8.61186i	0.246456	+	0.426874i
$408$	0.0424146	+	0.0366296i	0.00209983	+	0.00181343i
$409$	−21.8998	−	12.6439i	−1.08288	−	0.625199i	−0.151205	−	0.988502i	$-0.548315\pi$
$409$	−21.8998	−	12.6439i	−1.08288	−	0.625199i	−0.931671	+	0.363304i	$0.881649\pi$
$410$	3.03160	+	1.75029i	0.149720	+	0.0864409i
$411$	−2.32516	+	12.1726i	−0.114692	+	0.600430i
$412$	−16.4466	−	28.4864i	−0.810267	−	1.40342i
$413$	−16.1751			−0.795927
$414$	37.0543	−	5.45301i	1.82112	−	0.268001i
$415$	−17.5165			−0.859853
$416$	22.9674	+	16.7991i	1.12607	+	0.823646i
$417$	9.39777	+	27.0082i	0.460211	+	1.32260i
$418$	1.50156	+	0.866926i	0.0734437	+	0.0424028i
$419$	−17.4957	+	30.3034i	−0.854721	+	1.48042i	0.0221830	+	0.999754i	$0.492938\pi$
$419$	−17.4957	+	30.3034i	−0.854721	+	1.48042i	−0.876904	+	0.480666i	$0.840395\pi$
$420$	4.00158	+	11.5001i	0.195257	+	0.561149i
$421$	−23.1033	+	13.3387i	−1.12599	+	0.650088i	−0.942922	−	0.333013i	$-0.891935\pi$
$421$	−23.1033	+	13.3387i	−1.12599	+	0.650088i	−0.183064	+	0.983101i	$0.558601\pi$
$422$		−	45.7475i		−	2.22696i
$423$	−16.9105	−	21.3574i	−0.822217	−	1.03843i
$424$			1.63468i			0.0793870i
$425$	0.0899371	+	0.155776i	0.00436259	+	0.00755622i
$426$	40.6962	+	7.77364i	1.97174	+	0.376634i
$427$	−19.3917	−	11.1958i	−0.938432	−	0.541804i
$428$	−8.01983	+	13.8908i	−0.387653	+	0.671435i
$429$	3.36407	−	11.0053i	0.162419	−	0.531343i
$430$	2.17645	+	3.76973i	0.104958	+	0.181793i
$431$		−	26.5012i		−	1.27652i	−0.769821	−	0.638260i	$-0.779654\pi$
$431$		−	26.5012i		−	1.27652i	0.769821	−	0.638260i	$-0.220346\pi$
$432$	−0.924213	+	21.6674i	−0.0444662	+	1.04247i
$433$	−10.2308			−0.491659			−0.245829	−	0.969313i	$-0.579060\pi$
$433$	−10.2308			−0.491659			−0.245829	+	0.969313i	$0.579060\pi$
$434$	−9.56389	+	5.52171i	−0.459081	+	0.265051i
$435$	−0.00494232	−	0.00426823i	−0.000236966	−	0.000204646i
$436$	−28.2368	−	16.3025i	−1.35230	−	0.780748i
$437$	−2.60242	−	1.50251i	−0.124491	−	0.0718747i
$438$	14.4981	+	2.76936i	0.692744	+	0.132325i
$439$	7.70352	+	13.3429i	0.367669	+	0.636821i	0.989201	−	0.146568i	$-0.0468226\pi$
$439$	7.70352	+	13.3429i	0.367669	+	0.636821i	−0.621532	+	0.783389i	$0.713489\pi$
$440$			0.331477i			0.0158026i
$441$	−18.2978	−	7.25507i	−0.871324	−	0.345480i
$442$	1.17306	−	0.517796i	0.0557966	−	0.0246291i
$443$	−12.0434	−	20.8597i	−0.572198	−	0.991076i	−0.996340	−	0.0854802i	$-0.972758\pi$
$443$	−12.0434	−	20.8597i	−0.572198	−	0.991076i	0.424142	−	0.905596i	$-0.360576\pi$
$444$	−16.8520	+	5.86382i	−0.799761	+	0.278285i
$445$	−1.03285	+	1.78894i	−0.0489616	+	0.0848039i
$446$	4.47424	−	7.74962i	0.211862	−	0.366955i
$447$	27.2665	−	9.48766i	1.28966	−	0.448751i
$448$	−23.1418	+	13.3610i	−1.09335	+	0.631246i
$449$		−	21.2128i		−	1.00109i	−0.865710	−	0.500546i	$-0.833132\pi$
$449$		−	21.2128i		−	1.00109i	0.865710	−	0.500546i	$-0.166868\pi$
$450$	−2.18621	+	5.51377i	−0.103059	+	0.259922i
$451$	3.26269			0.153634
$452$	−4.28028	−	7.41367i	−0.201328	−	0.348710i
$453$	3.10014	−	16.2297i	0.145657	−	0.762539i
$454$	−22.8619	+	39.5980i	−1.07296	+	1.85843i
$455$	−13.2004	−	1.43005i	−0.618845	−	0.0670420i
$456$	0.0969110	−	0.112216i	0.00453828	−	0.00525502i
$457$	4.57485	−	2.64129i	0.214002	−	0.123554i	−0.389168	−	0.921167i	$-0.627237\pi$
$457$	4.57485	−	2.64129i	0.214002	−	0.123554i	0.603170	+	0.797613i	$0.293904\pi$
$458$	13.8135			0.645462
$459$	0.788783	+	0.501397i	0.0368172	+	0.0234032i
$460$			12.0544i			0.562041i
$461$	−19.7917	+	11.4268i	−0.921793	+	0.532197i	−0.884206	−	0.467096i	$-0.845300\pi$
$461$	−19.7917	+	11.4268i	−0.921793	+	0.532197i	−0.0375860	+	0.999293i	$0.511967\pi$
$462$	17.5878	+	15.1890i	0.818260	+	0.706656i
$463$	12.7675	+	7.37130i	0.593355	+	0.342574i	0.766423	−	0.642336i	$-0.222035\pi$
$463$	12.7675	+	7.37130i	0.593355	+	0.342574i	−0.173068	+	0.984910i	$0.555368\pi$
$464$	0.00786792	−	0.0136276i	0.000365259	−	0.000632647i
$465$	−2.58047	−	0.492912i	−0.119667	−	0.0228582i
$466$	38.8258	−	22.4161i	1.79857	−	1.03840i
$467$	30.2235			1.39858			0.699288	−	0.714840i	$-0.253501\pi$
$467$	30.2235			1.39858			0.699288	+	0.714840i	$0.253501\pi$
$468$	18.2640	+	9.63410i	0.844253	+	0.445337i
$469$	−43.0624			−1.98844
$470$	15.5480	−	8.97667i	0.717178	−	0.414063i
$471$	4.92744	+	14.1609i	0.227044	+	0.652501i
$472$	0.395052	−	0.684250i	0.0181837	−	0.0314952i
$473$	3.51354	+	2.02854i	0.161553	+	0.0932725i
$474$	−35.1133	+	12.2180i	−1.61281	+	0.561192i
$475$	0.412136	−	0.237947i	0.0189101	−	0.0109178i
$476$			1.26453i			0.0579595i
$477$	3.96929	+	26.9721i	0.181741	+	1.23497i
$478$	−50.9685			−2.33124
$479$	−11.6401	+	6.72044i	−0.531852	+	0.307065i	−0.741770	−	0.670654i	$-0.766013\pi$
$479$	−11.6401	+	6.72044i	−0.531852	+	0.307065i	0.209918	+	0.977719i	$0.432680\pi$
$480$	−13.4268	−	2.56474i	−0.612847	−	0.117064i
$481$	2.09557	−	19.3436i	0.0955496	−	0.881990i
$482$	5.87252	−	10.1715i	0.267486	−	0.463300i
$483$	−30.4822	−	26.3247i	−1.38699	−	1.19782i
$484$	7.25832	+	12.5718i	0.329924	+	0.571445i
$485$	−11.0166			−0.500237
$486$	3.18375	+	30.6554i	0.144418	+	1.39056i
$487$		−	14.5660i		−	0.660048i	−0.943973	−	0.330024i	$-0.892943\pi$
$487$		−	14.5660i		−	0.660048i	0.943973	−	0.330024i	$-0.107057\pi$
$488$	0.947224	−	0.546880i	0.0428788	−	0.0247561i
$489$	4.32722	+	3.73702i	0.195684	+	0.168994i
$490$	6.48617	−	11.2344i	0.293015	−	0.507517i
$491$	18.7197	−	32.4236i	0.844810	−	1.46325i	−0.0409752	−	0.999160i	$-0.513046\pi$
$491$	18.7197	−	32.4236i	0.844810	−	1.46325i	0.885786	−	0.464094i	$-0.153620\pi$
$492$	−1.09841	+	5.75037i	−0.0495203	+	0.259247i
$493$	−0.000339085	0	0.000587313i	−1.52716e−5	0	2.64512e-5i
$494$	−1.36994	−	3.10356i	−0.0616364	−	0.139636i
$495$	0.804886	+	5.46937i	0.0361769	+	0.245830i
$496$		−	6.33053i		−	0.284249i
$497$	−22.2772	−	38.5853i	−0.999270	−	1.73079i
$498$	−19.7131	−	56.6533i	−0.883365	−	2.53870i
$499$	30.8555	+	17.8144i	1.38128	+	0.797483i	0.992311	−	0.123768i	$-0.0394979\pi$
$499$	30.8555	+	17.8144i	1.38128	+	0.797483i	0.388969	+	0.921251i	$0.372831\pi$
$500$	−1.65326	−	0.954509i	−0.0739360	−	0.0426870i
$501$	15.2138	−	5.29380i	0.679703	−	0.236509i
$502$	−35.6018	+	20.5547i	−1.58898	+	0.917401i
$503$	−4.68505			−0.208896			−0.104448	−	0.994530i	$-0.533308\pi$
$503$	−4.68505			−0.208896			−0.104448	+	0.994530i	$0.533308\pi$
$504$	1.55802	−	1.23362i	0.0693996	−	0.0549496i
$505$			4.29951i			0.191326i
$506$	11.5029	+	19.9237i	0.511368	+	0.885715i
$507$	−18.0251	+	13.4943i	−0.800523	+	0.599302i
$508$	5.99529	−	10.3841i	0.265998	−	0.460722i
$509$	17.9569	+	10.3674i	0.795926	+	0.459528i	0.842045	−	0.539408i	$-0.181352\pi$
$509$	17.9569	+	10.3674i	0.795926	+	0.459528i	−0.0461186	+	0.998936i	$0.514685\pi$
$510$	−0.402606	+	0.466191i	−0.0178277	+	0.0206433i
$511$	−7.93628	−	13.7460i	−0.351080	−	0.608089i
$512$		−	31.4377i		−	1.38936i
$513$	1.32655	−	2.08689i	0.0585685	−	0.0921383i
$514$			8.34256i			0.367975i
$515$	−14.9220	+	8.61522i	−0.657542	+	0.379632i
$516$	−4.75810	+	5.50956i	−0.209464	+	0.242545i
$517$	8.36661	−	14.4914i	0.367963	−	0.637331i
$518$	34.0261	+	19.6450i	1.49502	+	0.863151i
$519$	−24.9526	−	4.76635i	−1.09530	−	0.209219i
$520$	0.382894	−	0.523484i	0.0167910	−	0.0229563i
$521$	3.45022			0.151157			0.0755784	−	0.997140i	$-0.475920\pi$
$521$	3.45022			0.151157			0.0755784	+	0.997140i	$0.475920\pi$
$522$	0.00824255	−	0.0207883i	0.000360766	−	0.000909879i
$523$	−19.4273			−0.849494			−0.424747	−	0.905312i	$-0.639637\pi$
$523$	−19.4273			−0.849494			−0.424747	+	0.905312i	$0.639637\pi$
$524$	−19.8488	−	34.3791i	−0.867098	−	1.50186i
$525$	6.02410	−	2.09615i	0.262913	−	0.0914833i
$526$	52.9247	+	30.5561i	2.30763	+	1.33231i
$527$	−0.236276	−	0.136414i	−0.0102924	−	0.00594229i
$528$	−12.5815	+	4.37784i	−0.547538	+	0.190521i
$529$	−8.43622	−	14.6120i	−0.366792	−	0.635302i
$530$	−17.9672			−0.780446
$531$	4.85687	−	12.2494i	0.210770	−	0.531577i
$532$	3.34557			0.145049
$533$	−5.15259	−	3.76877i	−0.223183	−	0.163244i
$534$	−6.94829	−	1.32724i	−0.300682	−	0.0574351i
$535$	7.27638	+	4.20102i	0.314586	+	0.181626i
$536$	1.05173	−	1.82165i	0.0454278	−	0.0786833i
$537$	4.43629	−	5.13692i	0.191440	−	0.221675i
$538$	−3.19098	+	1.84231i	−0.137573	+	0.0794278i
$539$		−	12.0907i		−	0.520785i
$540$	−9.91054	−	0.422730i	−0.426482	−	0.0181914i
$541$			10.9817i			0.472139i	0.971736	+	0.236069i	$0.0758592\pi$
$541$			10.9817i			0.472139i	−0.971736	+	0.236069i	$0.924141\pi$
$542$	5.55096	+	9.61454i	0.238434	+	0.412980i
$543$	−20.8557	+	24.1495i	−0.895004	+	1.03635i
$544$	−1.22940	−	0.709795i	−0.0527101	−	0.0304322i
$545$	−8.53973	+	14.7912i	−0.365802	+	0.633587i
$546$	−10.2305	−	44.3031i	−0.437826	−	1.89600i
$547$	17.6658	+	30.5981i	0.755335	+	1.30828i	0.945208	+	0.326470i	$0.105859\pi$
$547$	17.6658	+	30.5981i	0.755335	+	1.30828i	−0.189872	+	0.981809i	$0.560807\pi$
$548$		−	13.6589i		−	0.583478i
$549$	14.3012	−	11.3235i	0.610362	−	0.483277i
$550$	−3.64336			−0.155353
$551$	−0.00155386		0.000897119i	−6.61965e−5		3.82186e-5i
$552$	1.85808	−	0.646538i	0.0790852	−	0.0275185i
$553$	34.6238	+	19.9900i	1.47235	+	0.850063i
$554$	−1.16838	−	0.674565i	−0.0496398	−	0.0286595i
$555$	3.07164	+	8.82757i	0.130384	+	0.374710i
$556$	−15.7591	−	27.2956i	−0.668336	−	1.15759i
$557$		−	10.1075i		−	0.428267i	−0.976804	−	0.214134i	$-0.931307\pi$
$557$		−	10.1075i		−	0.428267i	0.976804	−	0.214134i	$-0.0686928\pi$
$558$	−1.30985	−	8.90068i	−0.0554503	−	0.376796i
$559$	−3.20555	−	7.26210i	−0.135580	−	0.307154i
$560$	7.68491	+	13.3107i	0.324747	+	0.562478i
$561$	−0.107717	+	0.563917i	−0.00454783	+	0.0238086i
$562$	−26.2522	+	45.4701i	−1.10738	+	1.91804i
$563$	18.2497	−	31.6093i	0.769131	−	1.33217i	−0.168903	−	0.985633i	$-0.554023\pi$
$563$	18.2497	−	31.6093i	0.769131	−	1.33217i	0.938034	−	0.346542i	$-0.112644\pi$
$564$	22.7239	+	19.6245i	0.956848	+	0.826341i
$565$	−3.88350	+	2.24214i	−0.163380	+	0.0943275i
$566$		−	55.3289i		−	2.32565i
$567$	22.7118	−	24.1378i	0.953806	−	1.01369i
$568$	2.17634			0.0913173
$569$	−4.37142	−	7.57152i	−0.183259	−	0.317415i	0.759729	−	0.650240i	$-0.225331\pi$
$569$	−4.37142	−	7.57152i	−0.183259	−	0.317415i	−0.942989	+	0.332825i	$0.891998\pi$
$570$	1.23340	+	1.06518i	0.0516616	+	0.0446153i
$571$	10.5346	−	18.2464i	0.440859	−	0.763590i	−0.556894	−	0.830583i	$-0.688007\pi$
$571$	10.5346	−	18.2464i	0.440859	−	0.763590i	0.997753	+	0.0669932i	$0.0213406\pi$
$572$	−1.36610	+	12.6100i	−0.0571194	+	0.527252i
$573$	−1.02158	−	0.195138i	−0.0426770	−	0.00815200i
$574$	11.1640	−	6.44556i	0.465978	−	0.269032i
$575$	6.31446			0.263331
$576$	−3.16945	−	21.5371i	−0.132061	−	0.897378i
$577$		−	23.6128i		−	0.983014i	−0.870874	−	0.491507i	$-0.836446\pi$
$577$		−	23.6128i		−	0.983014i	0.870874	−	0.491507i	$-0.163554\pi$
$578$	29.0527	−	16.7736i	1.20843	−	0.697688i
$579$	−1.47194	+	0.512178i	−0.0611719	+	0.0212854i
$580$	0.00623320	+	0.00359874i	0.000258819	+	0.000149429i
$581$	−32.2528	+	55.8635i	−1.33807	+	2.31761i
$582$	−12.3980	−	35.6306i	−0.513915	−	1.47694i
$583$	−14.5026	+	8.37308i	−0.600636	+	0.346777i
$584$	0.775323			0.0320831
$585$	5.04663	−	9.56721i	0.208652	−	0.395556i
$586$	8.03880			0.332080
$587$	1.83805	−	1.06120i	0.0758643	−	0.0438003i	−0.461588	−	0.887094i	$-0.652720\pi$
$587$	1.83805	−	1.06120i	0.0758643	−	0.0438003i	0.537452	+	0.843294i	$0.319387\pi$
$588$	21.3095	+	4.07046i	0.878789	+	0.167863i
$589$	−0.360912	+	0.625117i	−0.0148711	+	0.0257575i
$590$	7.52079	+	4.34213i	0.309626	+	0.178763i
$591$	1.78629	+	1.54266i	0.0734782	+	0.0634564i
$592$	−19.5051	+	11.2613i	−0.801655	+	0.462836i
$593$			11.5522i			0.474391i	0.971462	+	0.237196i	$0.0762282\pi$
$593$			11.5522i			0.474391i	−0.971462	+	0.237196i	$0.923772\pi$
$594$	−16.7836	+	8.75844i	−0.688640	+	0.359363i
$595$	0.662396			0.0271556
$596$	−27.5567	+	15.9099i	−1.12877	+	0.651694i
$597$	−28.4660	+	32.9617i	−1.16504	+	1.34903i
$598$	4.84812	−	44.7516i	0.198254	−	1.83003i
$599$	20.3446	−	35.2379i	0.831258	−	1.43978i	−0.0657834	−	0.997834i	$-0.520955\pi$
$599$	20.3446	−	35.2379i	0.831258	−	1.43978i	0.897041	−	0.441947i	$-0.145712\pi$
$600$	−0.0584567	+	0.306030i	−0.00238648	+	0.0124936i
$601$	−5.12863	−	8.88304i	−0.209201	−	0.362347i	0.742262	−	0.670110i	$-0.233753\pi$
$601$	−5.12863	−	8.88304i	−0.209201	−	0.362347i	−0.951463	+	0.307763i	$0.900420\pi$
$602$	16.0298			0.653327
$603$	12.9302	−	32.6110i	0.526559	−	1.32802i
$604$			18.2114i			0.741010i
$605$	6.58547	−	3.80212i	0.267737	−	0.154578i
$606$	−13.9058	+	4.83866i	−0.564884	+	0.196557i
$607$	−17.1143	+	29.6428i	−0.694648	+	1.20317i	0.275651	+	0.961258i	$0.411106\pi$
$607$	−17.1143	+	29.6428i	−0.694648	+	1.20317i	−0.970299	+	0.241908i	$0.922227\pi$
$608$	−1.87791	+	3.25263i	−0.0761592	+	0.131912i
$609$	−0.0227124	+	0.00790300i	−0.000920352	+	0.000320246i
$610$	6.01091	+	10.4112i	0.243375	+	0.421537i
$611$	−29.9521	+	13.2211i	−1.21173	+	0.534869i
$612$	−0.957621	−	0.379696i	−0.0387095	−	0.0153483i
$613$			48.3073i			1.95111i	0.219752	+	0.975556i	$0.429475\pi$
$613$			48.3073i			1.95111i	−0.219752	+	0.975556i	$0.570525\pi$
$614$	−16.9354	−	29.3330i	−0.683458	−	1.18378i
$615$	3.01221	+	0.575382i	0.121464	+	0.0232016i
$616$	1.05714	+	0.610342i	0.0425935	+	0.0245914i
$617$	1.19929	+	0.692413i	0.0482818	+	0.0278755i	0.523947	−	0.851751i	$-0.324459\pi$
$617$	1.19929	+	0.692413i	0.0482818	+	0.0278755i	−0.475665	+	0.879627i	$0.657792\pi$
$618$	−44.6572	−	38.5663i	−1.79638	−	1.55136i
$619$	11.0458	−	6.37731i	0.443969	−	0.256326i	−0.261311	−	0.965255i	$-0.584155\pi$
$619$	11.0458	−	6.37731i	0.443969	−	0.256326i	0.705280	+	0.708929i	$0.250821\pi$
$620$	2.89555			0.116288
$621$	29.0884	−	15.1796i	1.16728	−	0.609137i
$622$			7.71279i			0.309255i
$623$	3.80351	+	6.58788i	0.152384	+	0.263938i
$624$	24.9261	+	7.61932i	0.997844	+	0.305017i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−19.7969	−	11.4298i	−0.791244	−	0.456825i
$627$	1.49196	+	0.284988i	0.0595831	+	0.0113813i
$628$	−8.26284	−	14.3117i	−0.329723	−	0.571097i
$629$			0.970660i			0.0387027i
$630$	13.5590	+	17.1246i	0.540205	+	0.682261i
$631$		−	36.8152i		−	1.46559i	−0.680449	−	0.732796i	$-0.738215\pi$
$631$		−	36.8152i		−	1.46559i	0.680449	−	0.732796i	$-0.261785\pi$
$632$	−1.69126	+	0.976450i	−0.0672747	+	0.0388411i
$633$	−13.1706	−	37.8510i	−0.523485	−	1.50444i
$634$	11.5714	−	20.0422i	0.459559	−	0.795979i
$635$	−5.43952	−	3.14051i	−0.215861	−	0.124627i
$636$	−9.87482	−	28.3792i	−0.391562	−	1.12531i
$637$	−13.9662	+	19.0942i	−0.553360	+	0.756542i
$638$	0.0137364			0.000543828
$639$	35.9096	−	5.28455i	1.42056	−	0.209053i
$640$	−1.43756			−0.0568245
$641$	−3.25193	−	5.63250i	−0.128443	−	0.222470i	0.794630	−	0.607094i	$-0.207665\pi$
$641$	−3.25193	−	5.63250i	−0.128443	−	0.222470i	−0.923074	+	0.384623i	$0.874331\pi$
$642$	−5.39843	+	28.2616i	−0.213059	+	1.11540i
$643$	18.8197	+	10.8655i	0.742175	+	0.428495i	0.822860	−	0.568245i	$-0.192377\pi$
$643$	18.8197	+	10.8655i	0.742175	+	0.428495i	−0.0806847	+	0.996740i	$0.525711\pi$
$644$	38.4438	+	22.1955i	1.51490	+	0.874627i
$645$	2.88607	+	2.49243i	0.113639	+	0.0981394i
$646$	0.0846219	+	0.146569i	0.00332940	+	0.00576670i
$647$	2.31013			0.0908207			0.0454104	−	0.998968i	$-0.485540\pi$
$647$	2.31013			0.0908207			0.0454104	+	0.998968i	$0.485540\pi$
$648$	0.466391	+	1.55029i	0.0183216	+	0.0609013i
$649$	8.09407			0.317720
$650$	5.75377	+	4.20849i	0.225681	+	0.165071i
$651$	−6.32336	+	7.32202i	−0.247832	+	0.286973i
$652$	−5.45743	−	3.15085i	−0.213730	−	0.123397i
$653$	6.74124	−	11.6762i	0.263805	−	0.456924i	−0.703445	−	0.710750i	$-0.748356\pi$
$653$	6.74124	−	11.6762i	0.263805	−	0.456924i	0.967250	+	0.253826i	$0.0816890\pi$
$654$	−57.4496	−	10.9738i	−2.24646	−	0.429109i
$655$	−18.0088	+	10.3974i	−0.703661	+	0.406259i
$656$			7.38970i			0.288519i
$657$	12.7928	−	1.88262i	0.499095	−	0.0734481i
$658$		−	66.1141i		−	2.57740i
$659$	4.46412	+	7.73208i	0.173897	+	0.301199i	0.939779	−	0.341782i	$-0.111031\pi$
$659$	4.46412	+	7.73208i	0.173897	+	0.301199i	−0.765882	+	0.642981i	$0.777697\pi$
$660$	−2.00240	−	5.75468i	−0.0779433	−	0.224001i
$661$	−28.3029	−	16.3407i	−1.10085	−	0.635579i	−0.164409	−	0.986392i	$-0.552572\pi$
$661$	−28.3029	−	16.3407i	−1.10085	−	0.635579i	−0.936445	+	0.350813i	$0.885905\pi$
$662$	17.0011	−	29.4467i	0.660766	−	1.14448i
$663$	0.821501	−	0.766139i	0.0319045	−	0.0297544i
$664$	−1.57545	−	2.72876i	−0.0611392	−	0.105896i
$665$		−	1.75251i		−	0.0679593i
$666$	−25.0940	+	19.8691i	−0.972372	+	0.769911i
$667$	−0.0238071			−0.000921815
$668$	−15.3757	+	8.87718i	−0.594905	+	0.343469i
$669$	1.47084	−	7.70007i	0.0568658	−	0.297702i
$670$	20.0223	+	11.5599i	0.773528	+	0.446596i
$671$	9.70366	+	5.60241i	0.374606	+	0.216279i
$672$	−32.9019	+	38.0982i	−1.26922	+	1.46967i
$673$	20.0752	+	34.7712i	0.773842	+	1.34033i	0.935443	+	0.353477i	$0.115001\pi$
$673$	20.0752	+	34.7712i	0.773842	+	1.34033i	−0.161602	+	0.986856i	$0.551666\pi$
$674$			37.5328i			1.44571i
$675$	−0.221438	+	5.19143i	−0.00852316	+	0.199818i
$676$	16.7234	−	18.3364i	0.643209	−	0.705245i
$677$	19.1300	+	33.1342i	0.735227	+	1.27345i	0.954624	+	0.297814i	$0.0962577\pi$
$677$	19.1300	+	33.1342i	0.735227	+	1.27345i	−0.219397	+	0.975636i	$0.570409\pi$
$678$	−11.6222	−	10.0370i	−0.446347	−	0.385469i
$679$	−20.2846	+	35.1339i	−0.778451	+	1.34832i
$680$	−0.0161780	+	0.0280211i	−0.000620397	+	0.00107456i
$681$	−7.51550	+	39.3448i	−0.287994	+	1.50770i
$682$	4.78579	−	2.76308i	0.183257	−	0.105804i
$683$			18.5501i			0.709801i	0.934904	+	0.354901i	$0.115485\pi$
$683$			18.5501i			0.709801i	−0.934904	+	0.354901i	$0.884515\pi$
$684$	−1.00456	+	2.53358i	−0.0384105	+	0.0968740i
$685$	−7.15492			−0.273375
$686$	1.59737	+	2.76672i	0.0609878	+	0.105634i
$687$	11.4291	−	3.97688i	0.436048	−	0.151727i
$688$	−4.59447	+	7.95786i	−0.175163	+	0.303390i
$689$	32.5750	+	3.52899i	1.24101	+	0.134444i
$690$	7.10629	+	20.4227i	0.270532	+	0.777479i
$691$	38.8399	−	22.4242i	1.47754	−	0.853058i	0.477862	−	0.878435i	$-0.341412\pi$
$691$	38.8399	−	22.4242i	1.47754	−	0.853058i	0.999678	+	0.0253767i	$0.00807852\pi$
$692$	27.9993			1.06437
$693$	18.9248	+	7.50369i	0.718895	+	0.285042i
$694$		−	47.1917i		−	1.79137i
$695$	−14.2982	+	8.25510i	−0.542364	+	0.313134i
$696$	0.000220396	−	0.00115381i	8.35410e−6	−	4.37350e-5i
$697$	0.275808	+	0.159238i	0.0104470	+	0.00603156i
$698$	−28.7899	+	49.8656i	−1.08971	+	1.88744i
$699$	25.6704	−	29.7246i	0.970945	−	1.12429i
$700$	−6.08822	+	3.51503i	−0.230113	+	0.132856i
$701$	−32.7223			−1.23591			−0.617953	−	0.786215i	$-0.712038\pi$
$701$	−32.7223			−1.23591			−0.617953	+	0.786215i	$0.712038\pi$
$702$	36.6225	+	5.55525i	1.38223	+	0.209669i
$703$	2.56808			0.0968569
$704$	11.5802	−	6.68585i	0.436446	−	0.251982i
$705$	10.2799	−	11.9034i	0.387163	−	0.448309i
$706$	−2.12174	+	3.67496i	−0.0798528	+	0.138309i
$707$	13.7119	+	7.91659i	0.515690	+	0.297734i
$708$	−2.72494	+	14.2655i	−0.102410	+	0.536131i
$709$	9.06616	−	5.23435i	0.340487	−	0.196580i	−0.320001	−	0.947417i	$-0.603683\pi$
$709$	9.06616	−	5.23435i	0.340487	−	0.196580i	0.660487	+	0.750837i	$0.270350\pi$
$710$			23.9208i			0.897731i
$711$	−25.5348	+	20.2181i	−0.957629	+	0.758237i
$712$	−0.371579			−0.0139255
$713$	−8.29445	+	4.78880i	−0.310630	+	0.179342i
$714$	0.745460	+	2.14237i	0.0278981	+	0.0801763i
$715$	6.60551	+	0.715602i	0.247032	+	0.0267620i
$716$	−3.74043	+	6.47862i	−0.139787	+	0.242118i
$717$	−42.1707	+	14.6737i	−1.57489	+	0.548000i
$718$	−2.95436	−	5.11710i	−0.110256	−	0.190969i
$719$	−10.0212			−0.373727			−0.186864	−	0.982386i	$-0.559832\pi$
$719$	−10.0212			−0.373727			−0.186864	+	0.982386i	$0.559832\pi$
$720$	−12.3876	+	1.82300i	−0.461660	+	0.0679390i
$721$			63.4520i			2.36308i
$722$	−32.1448	+	18.5588i	−1.19630	+	0.690687i
$723$	1.93050	−	10.1065i	0.0717960	−	0.375864i
$724$	17.5844	−	30.4571i	0.653519	−	1.13193i
$725$	0.00188512	−	0.00326513i	7.00118e−5	−	0.000121264i
$726$	19.7084	+	17.0203i	0.731447	+	0.631683i
$727$	22.6535	+	39.2370i	0.840171	+	1.45522i	0.889750	+	0.456448i	$0.150879\pi$
$727$	22.6535	+	39.2370i	0.840171	+	1.45522i	−0.0495795	+	0.998770i	$0.515788\pi$
$728$	−0.964475	−	2.18500i	−0.0357458	−	0.0809815i
$729$	11.4598	+	24.4473i	0.424438	+	0.905457i
$730$			8.52180i			0.315406i
$731$	0.198009	+	0.342961i	0.00732362	+	0.0126849i
$732$	−13.1409	+	15.2163i	−0.485701	+	0.562409i
$733$	−0.358019	−	0.206702i	−0.0132237	−	0.00763473i	0.493374	−	0.869818i	$-0.335764\pi$
$733$	−0.358019	−	0.206702i	−0.0132237	−	0.00763473i	−0.506597	+	0.862183i	$0.669097\pi$
$734$	54.2336	+	31.3118i	2.00180	+	1.15574i
$735$	2.13222	−	11.1625i	0.0786483	−	0.411736i
$736$	−43.1580	+	24.9173i	−1.59082	+	0.918463i
$737$	21.5485			0.793749
$738$	1.52900	+	10.3899i	0.0562832	+	0.382456i
$739$		−	8.98933i		−	0.330678i	−0.986237	−	0.165339i	$-0.947128\pi$
$739$		−	8.98933i		−	0.330678i	0.986237	−	0.165339i	$-0.0528718\pi$
$740$	−5.15085	−	8.92153i	−0.189349	−	0.327962i
$741$	−2.02698	−	2.17345i	−0.0744629	−	0.0798437i
$742$	−33.0826	+	57.3008i	−1.21450	+	2.10358i
$743$	6.96651	+	4.02211i	0.255576	+	0.147557i	0.622315	−	0.782767i	$-0.286192\pi$
$743$	6.96651	+	4.02211i	0.255576	+	0.147557i	−0.366739	+	0.930324i	$0.619526\pi$
$744$	−0.155303	−	0.446323i	−0.00569367	−	0.0163630i
$745$	8.33407	+	14.4350i	0.305337	+	0.528858i
$746$			36.4006i			1.33272i
$747$	−32.6207	−	41.1989i	−1.19353	−	1.50739i
$748$		−	0.632772i		−	0.0231364i
$749$	26.7957	−	15.4705i	0.979093	−	0.565280i
$750$	−3.36366	−	0.642514i	−0.122824	−	0.0234613i
$751$	−3.76057	+	6.51349i	−0.137225	+	0.237681i	−0.926445	−	0.376430i	$-0.877152\pi$
$751$	−3.76057	+	6.51349i	−0.137225	+	0.237681i	0.789220	+	0.614110i	$0.210485\pi$
$752$	32.8217	+	18.9496i	1.19689	+	0.691022i
$753$	−23.5388	+	27.2564i	−0.857802	+	0.993277i
$754$	−0.0216931	−	0.0158671i	−0.000790017	−	0.000577845i
$755$	9.53965			0.347183
$756$	−19.5962	+	30.8282i	−0.712708	+	1.12121i
$757$	−38.3328			−1.39323			−0.696614	−	0.717446i	$-0.745311\pi$
$757$	−38.3328			−1.39323			−0.696614	+	0.717446i	$0.745311\pi$
$758$	−21.3530	−	36.9844i	−0.775575	−	1.34334i
$759$	15.2534	+	13.1729i	0.553662	+	0.478147i
$760$	0.0741355	+	0.0428021i	0.00268918	+	0.00155260i
$761$	−11.3676	−	6.56308i	−0.412075	−	0.237912i	0.279606	−	0.960115i	$-0.409796\pi$
$761$	−11.3676	−	6.56308i	−0.412075	−	0.237912i	−0.691681	+	0.722203i	$0.743129\pi$
$762$	4.03564	−	21.1272i	0.146196	−	0.765359i
$763$	31.4480	+	54.4696i	1.13850	+	1.97193i
$764$	1.14631			0.0414721
$765$	−0.198896	+	0.501630i	−0.00719110	+	0.0181365i
$766$	52.4645			1.89562
$767$	−12.7825	−	9.34957i	−0.461551	−	0.337593i
$768$	−9.87860	−	28.3900i	−0.356463	−	1.02444i
$769$	36.5074	+	21.0776i	1.31649	+	0.760077i	0.983162	−	0.182734i	$-0.0584947\pi$
$769$	36.5074	+	21.0776i	1.31649	+	0.760077i	0.333329	+	0.942811i	$0.391828\pi$
$770$	−6.70844	+	11.6194i	−0.241755	+	0.418732i
$771$	2.40181	+	6.90254i	0.0864989	+	0.248589i
$772$	1.48761	−	0.858872i	0.0535403	−	0.0309115i
$773$		−	2.91191i		−	0.104734i	−0.998628	−	0.0523671i	$-0.983323\pi$
$773$		−	2.91191i		−	0.104734i	0.998628	−	0.0523671i	$-0.0166766\pi$
$774$	−4.81323	+	12.1393i	−0.173008	+	0.436339i
$775$		−	1.51677i		−	0.0544841i
$776$	−0.990837	−	1.71618i	−0.0355690	−	0.0616073i
$777$	33.8085	+	6.45797i	1.21287	+	0.231679i
$778$	−61.5034	−	35.5090i	−2.20500	−	1.27306i
$779$	0.421296	−	0.729706i	0.0150945	−	0.0261444i
$780$	−3.48503	+	11.4011i	−0.124784	+	0.408224i
$781$	11.1476	+	19.3081i	0.398891	+	0.690900i
$782$			2.24563i			0.0803037i
$783$	0.000834877	−	0.0195730i	2.98361e−5	−	0.000699482i
$784$	27.3844			0.978016
$785$	−7.49686	+	4.32832i	−0.267574	+	0.154484i
$786$	−53.8950	−	46.5442i	−1.92237	−	1.66018i
$787$	−18.7041	−	10.7988i	−0.666730	−	0.384937i	0.128107	−	0.991760i	$-0.459110\pi$
$787$	−18.7041	−	10.7988i	−0.666730	−	0.384937i	−0.794836	+	0.606824i	$0.792443\pi$
$788$	−2.25285	−	1.30068i	−0.0802544	−	0.0463349i
$789$	52.5863	+	10.0448i	1.87212	+	0.357606i
$790$	−10.7324	−	18.5891i	−0.381843	−	0.661371i
$791$			16.5136i			0.587156i
$792$	−0.779634	+	0.617304i	−0.0277031	+	0.0219349i
$793$	−8.85305	−	20.0564i	−0.314381	−	0.712224i
$794$	−14.2612	−	24.7012i	−0.506112	−	0.876611i
$795$	−14.8659	+	5.17272i	−0.527237	+	0.183458i
$796$	24.0010	−	41.5709i	0.850692	−	1.47344i
$797$	2.33705	−	4.04788i	0.0827824	−	0.143383i	−0.821662	−	0.569976i	$-0.806953\pi$
$797$	2.33705	−	4.04788i	0.0827824	−	0.143383i	0.904444	+	0.426592i	$0.140286\pi$
$798$	5.66809	−	1.97227i	0.200648	−	0.0698175i
$799$	1.41452	−	0.816676i	0.0500423	−	0.0288919i
$800$		−	7.89213i		−	0.279029i
$801$	−6.13104	+	0.902260i	−0.216630	+	0.0318798i
$802$	74.2323			2.62123
$803$	3.97133	+	6.87854i	0.140145	+	0.242738i
$804$	−7.25450	+	37.9785i	−0.255847	+	1.33940i
$805$	11.6267	−	20.1380i	0.409787	−	0.709771i
$806$	−10.7496	−	1.16455i	−0.378639	−	0.0410195i
$807$	−2.10978	+	2.44299i	−0.0742679	+	0.0859972i
$808$	−0.669784	+	0.386700i	−0.0235629	+	0.0136041i
$809$	−18.0978			−0.636284			−0.318142	−	0.948043i	$-0.603059\pi$
$809$	−18.0978			−0.636284			−0.318142	+	0.948043i	$0.603059\pi$
$810$	−17.0397	+	5.12624i	−0.598715	+	0.180118i
$811$			2.20322i			0.0773655i	0.999252	+	0.0386828i	$0.0123162\pi$
$811$			2.20322i			0.0773655i	−0.999252	+	0.0386828i	$0.987684\pi$
$812$	0.0229541	−	0.0132526i	0.000805531	−	0.000465074i
$813$	7.36080	+	6.35685i	0.258155	+	0.222944i
$814$	−17.0267	−	9.83038i	−0.596786	−	0.344555i
$815$	−1.65051	+	2.85876i	−0.0578148	+	0.100138i
$816$	−1.27722	−	0.243970i	−0.0447118	−	0.00854067i
$817$	0.907374	−	0.523873i	0.0317450	−	0.0183280i
$818$	49.9970			1.74810
$819$	−21.2194	−	33.7105i	−0.741466	−	1.17794i
$820$	−3.38001			−0.118035
$821$	−19.9180	+	11.4997i	−0.695145	+	0.401342i	−0.805536	−	0.592546i	$-0.798123\pi$
$821$	−19.9180	+	11.4997i	−0.695145	+	0.401342i	0.110392	+	0.993888i	$0.464789\pi$
$822$	−8.05213	−	23.1410i	−0.280850	−	0.807134i
$823$	17.9342	−	31.0629i	0.625146	−	1.08278i	−0.363367	−	0.931646i	$-0.618373\pi$
$823$	17.9342	−	31.0629i	0.625146	−	1.08278i	0.988513	−	0.151138i	$-0.0482939\pi$
$824$	−2.68418	−	1.54971i	−0.0935080	−	0.0539869i
$825$	−3.01447	+	1.04892i	−0.104950	+	0.0365186i
$826$	27.6957	−	15.9901i	0.963657	−	0.556368i
$827$		−	40.7759i		−	1.41792i	−0.705250	−	0.708959i	$-0.749165\pi$
$827$		−	40.7759i		−	1.41792i	0.705250	−	0.708959i	$-0.250835\pi$
$828$	−28.3520	+	22.4487i	−0.985301	+	0.780148i
$829$	19.0813			0.662720			0.331360	−	0.943504i	$-0.392492\pi$
$829$	19.0813			0.662720			0.331360	+	0.943504i	$0.392492\pi$
$830$	29.9925	−	17.3162i	1.04106	−	0.601054i
$831$	−1.16091	−	0.221753i	−0.0402715	−	0.00769251i
$832$	−26.0109	−	2.81787i	−0.901767	−	0.0976922i
$833$	0.590096	−	1.02208i	0.0204456	−	0.0354129i
$834$	−42.7905	−	36.9542i	−1.48171	−	1.27962i
$835$	4.65013	+	8.05426i	0.160924	+	0.278729i
$836$	−1.67413			−0.0579009
$837$	−3.64624	−	6.98722i	−0.126032	−	0.241513i
$838$		−	69.1823i		−	2.38986i
$839$	−14.2583	+	8.23204i	−0.492252	+	0.284202i	−0.725508	−	0.688214i	$-0.758395\pi$
$839$	−14.2583	+	8.23204i	−0.492252	+	0.284202i	0.233257	+	0.972415i	$0.425062\pi$
$840$	0.868352	+	0.749916i	0.0299610	+	0.0258745i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	26.3723	−	45.6781i	0.908848	−	1.57417i
$843$	−8.62999	+	45.1794i	−0.297233	+	1.55606i
$844$	22.0858	+	38.2538i	0.760226	+	1.31675i
$845$	−9.60513	−	8.76022i	−0.330426	−	0.301361i
$846$	50.0680	+	19.8519i	1.72137	+	0.682523i
$847$		−	28.0031i		−	0.962196i
$848$	−18.9643	−	32.8471i	−0.651236	−	1.12797i
$849$	−15.9291	−	45.7785i	−0.546685	−	1.57111i
$850$	−0.307988	−	0.177817i	−0.0105639	−	0.00609906i
$851$	29.5097	+	17.0375i	1.01158	+	0.584036i
$852$	−37.7829	+	13.1469i	−1.29442	+	0.450406i
$853$	45.0815	−	26.0278i	1.54356	−	0.891176i	0.544953	−	0.838467i	$-0.316548\pi$
$853$	45.0815	−	26.0278i	1.54356	−	0.891176i	0.998610	−	0.0527094i	$-0.0167857\pi$
$854$	44.2710			1.51492
$855$	1.32717	+	0.526220i	0.0453881	+	0.0179964i
$856$			1.51137i			0.0516575i
$857$	−3.08305	−	5.34000i	−0.105315	−	0.182411i	0.808552	−	0.588425i	$-0.200252\pi$
$857$	−3.08305	−	5.34000i	−0.105315	−	0.182411i	−0.913867	+	0.406014i	$0.866918\pi$
$858$	5.11937	+	22.1694i	0.174773	+	0.756850i
$859$	3.61022	−	6.25308i	0.123179	−	0.213352i	−0.797841	−	0.602868i	$-0.794024\pi$
$859$	3.61022	−	6.25308i	0.123179	−	0.213352i	0.921020	+	0.389516i	$0.127358\pi$
$860$	−3.63988	−	2.10148i	−0.124119	−	0.0716600i
$861$	7.38132	−	8.54708i	0.251555	−	0.291284i
$862$	26.1981	+	45.3765i	0.892312	+	1.54553i
$863$		−	4.07628i		−	0.138758i	−0.997590	−	0.0693791i	$-0.977898\pi$
$863$		−	4.07628i		−	0.138758i	0.997590	−	0.0693791i	$-0.0221018\pi$
$864$	−18.9722	−	36.3561i	−0.645449	−	1.23686i
$865$		−	14.6669i		−	0.498688i
$866$	17.5175	−	10.1137i	0.595269	−	0.343679i
$867$	19.2088	−	22.2425i	0.652364	−	0.755393i
$868$	5.33151	−	9.23445i	0.180963	−	0.313438i
$869$	−17.3258	−	10.0031i	−0.587738	−	0.339330i
$870$	0.0126819	+	0.00242244i	0.000429955	+	8.21283e-5i
$871$	−34.0304	−	24.8910i	−1.15308	−	0.843398i
$872$	−3.07227			−0.104040
$873$	−20.5160	−	25.9110i	−0.694360	−	0.876954i
$874$	5.94128			0.200967
$875$	1.84128	+	3.18919i	0.0622465	+	0.107814i
$876$	−13.4602	+	4.68360i	−0.454777	+	0.158244i
$877$	43.7145	+	25.2386i	1.47613	+	0.852246i	0.999637	−	0.0269308i	$-0.00857338\pi$
$877$	43.7145	+	25.2386i	1.47613	+	0.852246i	0.476496	+	0.879177i	$0.341907\pi$
$878$	−26.3805	−	15.2308i	−0.890300	−	0.514015i
$879$	6.65121	−	2.31435i	0.224340	−	0.0780612i
$880$	−3.84554	−	6.66068i	−0.129633	−	0.224531i
$881$	−23.9632			−0.807340			−0.403670	−	0.914905i	$-0.632266\pi$
$881$	−23.9632			−0.807340			−0.403670	+	0.914905i	$0.632266\pi$
$882$	38.5023	−	5.66610i	1.29644	−	0.190787i
$883$	23.2839			0.783564			0.391782	−	0.920058i	$-0.371859\pi$
$883$	23.2839			0.783564			0.391782	+	0.920058i	$0.371859\pi$
$884$	−0.730923	+	0.999303i	−0.0245836	+	0.0336102i
$885$	7.47270	+	1.42741i	0.251192	+	0.0479817i
$886$	41.2423	+	23.8112i	1.38556	+	0.799954i
$887$	8.34180	−	14.4484i	0.280090	−	0.485130i	−0.691316	−	0.722552i	$-0.742969\pi$
$887$	8.34180	−	14.4484i	0.280090	−	0.485130i	0.971407	+	0.237422i	$0.0763023\pi$
$888$	−1.09891	+	1.27246i	−0.0368769	+	0.0427010i
$889$	−20.0313	+	11.5651i	−0.671830	+	0.387881i
$890$		−	4.08413i		−	0.136900i
$891$	−11.3650	+	12.0786i	−0.380743	+	0.404648i
$892$			8.64024i			0.289297i
$893$	−2.16068	−	3.74242i	−0.0723045	−	0.125235i
$894$	−37.3077	+	43.1998i	−1.24776	+	1.44482i
$895$	3.39369	+	1.95935i	0.113439	+	0.0654938i
$896$	−2.64695	+	4.58465i	−0.0884283	+	0.153162i
$897$	−8.87260	−	38.4227i	−0.296248	−	1.28290i
$898$	20.9701	+	36.3214i	0.699783	+	1.21206i
$899$			0.00571861i			0.000190726i
$900$	−0.833828	−	5.66603i	−0.0277943	−	0.188868i
$901$	−1.63461			−0.0544569
$902$	−5.58650	+	3.22537i	−0.186010	+	0.107393i
$903$	13.2629	−	4.61495i	0.441361	−	0.153576i
$904$	−0.698568	−	0.403318i	−0.0232340	−	0.0134142i
$905$	−15.9543	−	9.21122i	−0.530339	−	0.306191i
$906$	10.7359	+	30.8539i	0.356677	+	1.02505i
$907$	9.26718	+	16.0512i	0.307712	+	0.532972i	0.977861	−	0.209254i	$-0.0671035\pi$
$907$	9.26718	+	16.0512i	0.307712	+	0.532972i	−0.670150	+	0.742226i	$0.733770\pi$
$908$		−	44.1488i		−	1.46513i
$909$	−10.1124	+	8.00689i	−0.335409	+	0.265572i
$910$	24.0160	−	10.6008i	0.796121	−	0.351414i
$911$	1.92222	+	3.32938i	0.0636859	+	0.110307i	0.896110	−	0.443831i	$-0.146381\pi$
$911$	1.92222	+	3.32938i	0.0636859	+	0.110307i	−0.832424	+	0.554139i	$0.813048\pi$
$912$	−0.645474	+	3.37916i	−0.0213738	+	0.111895i
$913$	16.1394	−	27.9542i	0.534135	−	0.925149i
$914$	−5.22215	+	9.04504i	−0.172733	+	0.299183i
$915$	7.97072	+	6.88358i	0.263504	+	0.227564i
$916$	−11.5508	+	6.66883i	−0.381648	+	0.220344i
$917$			76.5778i			2.52882i
$918$	−1.84625	−	0.0787508i	−0.0609352	−	0.00259916i
$919$	−37.5628			−1.23908			−0.619541	−	0.784964i	$-0.712681\pi$
$919$	−37.5628			−1.23908			−0.619541	+	0.784964i	$0.712681\pi$
$920$	0.567926	+	0.983677i	0.0187240	+	0.0324309i
$921$	−22.4571	−	19.3941i	−0.739986	−	0.639058i
$922$	22.5921	−	39.1307i	0.744032	−	1.28870i
$923$	4.69834	−	43.3690i	0.154648	−	1.42751i
$924$	−22.0397	−	4.20995i	−0.725054	−	0.138497i
$925$	−4.67336	+	2.69816i	−0.153659	+	0.0887151i
$926$	−29.1480			−0.957862
$927$	−48.0520	−	19.0526i	−1.57823	−	0.625769i
$928$			0.0297553i			0.000976766i
$929$	15.6563	−	9.03915i	0.513666	−	0.296565i	−0.220674	−	0.975348i	$-0.570826\pi$
$929$	15.6563	−	9.03915i	0.513666	−	0.296565i	0.734339	+	0.678783i	$0.237492\pi$
$930$	4.90566	−	1.70697i	0.160863	−	0.0559739i
$931$	−2.70411	−	1.56122i	−0.0886238	−	0.0511670i
$932$	−21.6439	+	37.4884i	−0.708970	+	1.22797i
$933$	2.22050	+	6.38147i	0.0726957	+	0.208920i
$934$	−51.7498	+	29.8778i	−1.69331	+	0.977630i
$935$	−0.331464			−0.0108400
$936$	1.94429	−	0.0743091i	0.0635512	−	0.00242887i
$937$	−22.7662			−0.743741			−0.371870	−	0.928285i	$-0.621283\pi$
$937$	−22.7662			−0.743741			−0.371870	+	0.928285i	$0.621283\pi$
$938$	73.7331	−	42.5698i	2.40747	−	1.38995i
$939$	−19.6703	−	3.75735i	−0.641917	−	0.122617i
$940$	−8.66745	+	15.0125i	−0.282701	+	0.489653i
$941$	−17.5655	−	10.1414i	−0.572619	−	0.330602i	0.185576	−	0.982630i	$-0.440585\pi$
$941$	−17.5655	−	10.1414i	−0.572619	−	0.330602i	−0.758195	+	0.652028i	$0.773918\pi$
$942$	−22.4359	−	19.3758i	−0.731002	−	0.631299i
$943$	9.68220	−	5.59002i	0.315296	−	0.182036i
$944$			18.3324i			0.596667i
$945$	16.1487	+	10.2651i	0.525318	+	0.333923i
$946$	−8.02136			−0.260797
$947$	−1.68376	+	0.972120i	−0.0547149	+	0.0315896i	−0.527108	−	0.849798i	$-0.676724\pi$
$947$	−1.68376	+	0.972120i	−0.0547149	+	0.0315896i	0.472393	+	0.881388i	$0.343390\pi$
$948$	23.4629	−	27.1685i	0.762041	−	0.882392i
$949$	1.67379	−	15.4502i	0.0543335	−	0.501536i
$950$	−0.470451	+	0.814844i	−0.0152634	+	0.0264370i
$951$	3.80391	−	19.9141i	0.123350	−	0.645758i
$952$	0.0595763	+	0.103189i	0.00193088	+	0.00334438i
$953$	50.6834			1.64180			0.820898	−	0.571075i	$-0.193474\pi$
$953$	50.6834			1.64180			0.820898	+	0.571075i	$0.193474\pi$
$954$	−33.4600	−	42.2589i	−1.08331	−	1.36818i
$955$		−	0.600472i		−	0.0194308i
$956$	42.6195	−	24.6064i	1.37841	−	0.795828i
$957$	0.0113653	−	0.00395467i	0.000367388	−	0.000127836i
$958$	13.2871	−	23.0140i	0.429288	−	0.743549i
$959$	−13.1742	+	22.8184i	−0.425417	+	0.736843i
$960$	11.8703	−	4.13038i	0.383112	−	0.133308i
$961$	−14.3497	−	24.8544i	−0.462894	−	0.801755i
$962$	15.5342	+	35.1924i	0.500842	+	1.13465i
$963$	3.66987	+	24.9375i	0.118260	+	0.803601i
$964$			11.3405i			0.365252i
$965$	−0.449902	−	0.779254i	−0.0144829	−	0.0250851i
$966$	78.2165	+	14.9406i	2.51657	+	0.480706i
$967$	−19.0701	−	11.0101i	−0.613253	−	0.354062i	0.160985	−	0.986957i	$-0.448533\pi$
$967$	−19.0701	−	11.0101i	−0.613253	−	0.354062i	−0.774237	+	0.632895i	$0.781866\pi$
$968$	1.18460	+	0.683930i	0.0380745	+	0.0219823i
$969$	0.112212	+	0.0969073i	0.00360477	+	0.00311311i
$970$	18.8630	−	10.8906i	0.605655	−	0.349675i
$971$	−12.2478			−0.393050			−0.196525	−	0.980499i	$-0.562966\pi$
$971$	−12.2478			−0.393050			−0.196525	+	0.980499i	$0.562966\pi$
$972$	−17.4620	−	24.0968i	−0.560093	−	0.772906i
$973$			60.7997i			1.94915i
$974$	14.3994	+	24.9405i	0.461386	+	0.799144i
$975$	5.97221	+	1.82556i	0.191264	+	0.0584647i
$976$	−12.6890	+	21.9779i	−0.406164	+	0.703497i
$977$	6.16072	+	3.55689i	0.197099	+	0.113795i	0.595302	−	0.803502i	$-0.297033\pi$
$977$	6.16072	+	3.55689i	0.197099	+	0.113795i	−0.398203	+	0.917297i	$0.630366\pi$
$978$	−11.1035	−	2.12095i	−0.355051	−	0.0678205i
$979$	−1.90328	−	3.29659i	−0.0608292	−	0.105359i
$980$			12.5255i			0.400112i
$981$	−50.6924	+	7.46002i	−1.61848	+	0.238180i
$982$			74.0225i			2.36215i
$983$	−40.8515	+	23.5856i	−1.30296	+	0.752264i	−0.980911	−	0.194459i	$-0.937705\pi$
$983$	−40.8515	+	23.5856i	−1.30296	+	0.752264i	−0.322049	+	0.946723i	$0.604371\pi$
$984$	0.181286	+	0.520998i	0.00577920	+	0.0166088i
$985$	−0.681336	+	1.18011i	−0.0217092	+	0.0376014i
$986$	0.00116119		0.000670413i	3.69798e−5		2.13503e-5i
$987$	−19.0341	−	54.7020i	−0.605863	−	1.74119i
$988$	2.64386	+	1.93381i	0.0841124	+	0.0615226i
$989$	13.9022			0.442063
$990$	−6.78496	−	8.56918i	−0.215640	−	0.272347i
$991$	−4.32831			−0.137493			−0.0687467	−	0.997634i	$-0.521900\pi$
$991$	−4.32831			−0.137493			−0.0687467	+	0.997634i	$0.521900\pi$
$992$	5.98529	+	10.3668i	0.190033	+	0.329147i
$993$	5.58883	−	29.2584i	0.177356	−	0.928489i
$994$	76.2879	+	44.0448i	2.41970	+	1.39702i
$995$	−21.7761	−	12.5724i	−0.690348	−	0.398572i
$996$	43.8349	+	37.8561i	1.38896	+	1.19952i
$997$	5.02697	+	8.70698i	0.159206	+	0.275753i	0.934583	−	0.355746i	$-0.115773\pi$
$997$	5.02697	+	8.70698i	0.159206	+	0.275753i	−0.775377	+	0.631499i	$0.782440\pi$
$998$	−70.4426			−2.22982
$999$	−15.0422	+	23.6639i	−0.475914	+	0.748694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.9	yes	108
9.7	even	3	inner	585.2.bt.b.376.46	yes	108
13.12	even	2	inner	585.2.bt.b.571.46	yes	108
117.25	even	6	inner	585.2.bt.b.376.9	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.9	✓	108	117.25	even	6	inner
585.2.bt.b.376.46	yes	108	9.7	even	3	inner
585.2.bt.b.571.9	yes	108	1.1	even	1	trivial
585.2.bt.b.571.46	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71224 + 0.988562i) q^{2} +(-1.13208 + 1.31087i) q^{3} +(0.954509 - 1.65326i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.642514 - 3.36366i) q^{6} +(-3.18919 + 1.84128i) q^{7} -0.179881i q^{8} +(-0.436783 - 2.96803i) q^{9} +O(q^{10})\)	\(q+(-1.71224 + 0.988562i) q^{2} +(-1.13208 + 1.31087i) q^{3} +(0.954509 - 1.65326i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.642514 - 3.36366i) q^{6} +(-3.18919 + 1.84128i) q^{7} -0.179881i q^{8} +(-0.436783 - 2.96803i) q^{9} +1.97712 q^{10} +(1.59587 - 0.921379i) q^{11} +(1.08663 + 3.12287i) q^{12} +(-3.58458 - 0.388332i) q^{13} +(3.64043 - 6.30542i) q^{14} +(1.63585 - 0.569210i) q^{15} +(2.08684 + 3.61452i) q^{16} +0.179874 q^{17} +(3.68196 + 4.65020i) q^{18} -0.475894i q^{19} +(-1.65326 + 0.954509i) q^{20} +(1.19674 - 6.26510i) q^{21} +(-1.82168 + 3.15524i) q^{22} +(3.15723 - 5.46848i) q^{23} +(0.235801 + 0.203640i) q^{24} +(0.500000 + 0.866025i) q^{25} +(6.52155 - 2.87866i) q^{26} +(4.38519 + 2.78749i) q^{27} +7.03007i q^{28} +(-0.00188512 - 0.00326513i) q^{29} +(-2.23827 + 2.59176i) q^{30} +(-1.31356 - 0.758387i) q^{31} +(-6.83478 - 3.94606i) q^{32} +(-0.598848 + 3.13507i) q^{33} +(-0.307988 + 0.177817i) q^{34} +3.68256 q^{35} +(-5.32384 - 2.11090i) q^{36} +5.39633i q^{37} +(0.470451 + 0.814844i) q^{38} +(4.56709 - 4.25931i) q^{39} +(-0.0899405 + 0.155782i) q^{40} +(1.53334 + 0.885273i) q^{41} +(4.14434 + 11.9104i) q^{42} +(1.10082 + 1.90667i) q^{43} -3.51786i q^{44} +(-1.10575 + 2.78878i) q^{45} +12.4845i q^{46} +(7.86397 - 4.54027i) q^{47} +(-7.10065 - 1.35634i) q^{48} +(3.28061 - 5.68218i) q^{49} +(-1.71224 - 0.988562i) q^{50} +(-0.203632 + 0.235792i) q^{51} +(-4.06353 + 5.55557i) q^{52} -9.08755 q^{53} +(-10.2641 - 0.437811i) q^{54} -1.84276 q^{55} +(0.331211 + 0.573674i) q^{56} +(0.623837 + 0.538751i) q^{57} +(0.00645557 + 0.00372713i) q^{58} +(3.80390 + 2.19618i) q^{59} +(0.620382 - 3.24780i) q^{60} +(3.04023 + 5.26583i) q^{61} +2.99885 q^{62} +(6.85796 + 8.66137i) q^{63} +7.25635 q^{64} +(2.91017 + 2.12859i) q^{65} +(-2.07384 - 5.95998i) q^{66} +(10.1270 + 5.84681i) q^{67} +(0.171692 - 0.297378i) q^{68} +(3.59425 + 10.3295i) q^{69} +(-6.30542 + 3.64043i) q^{70} +12.0988i q^{71} +(-0.533893 + 0.0785690i) q^{72} +4.31020i q^{73} +(-5.33460 - 9.23980i) q^{74} +(-1.70129 - 0.324974i) q^{75} +(-0.786776 - 0.454245i) q^{76} +(-3.39303 + 5.87690i) q^{77} +(-3.60936 + 11.8078i) q^{78} +(-5.42831 - 9.40211i) q^{79} -4.17368i q^{80} +(-8.61844 + 2.59277i) q^{81} -3.50059 q^{82} +(15.1698 - 8.75827i) q^{83} +(-9.21554 - 7.95861i) q^{84} +(-0.155776 - 0.0899371i) q^{85} +(-3.76973 - 2.17645i) q^{86} +(0.00641429 + 0.00122523i) q^{87} +(-0.165739 - 0.287068i) q^{88} -2.06569i q^{89} +(-0.863575 - 5.86817i) q^{90} +(12.1469 - 5.36174i) q^{91} +(-6.02721 - 10.4394i) q^{92} +(2.48121 - 0.863362i) q^{93} +(-8.97667 + 15.5480i) q^{94} +(-0.237947 + 0.412136i) q^{95} +(12.9103 - 4.49228i) q^{96} +(9.54063 - 5.50829i) q^{97} +12.9723i q^{98} +(-3.43173 - 4.33417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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