LMFDB - Embedded newform 731.2.m.c.689.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.13
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.286708 + 0.286708i) q^{2} +(-2.99617 - 1.24105i) q^{3} +1.83560i q^{4} +(-0.918391 + 2.21719i) q^{5} +(1.21484 - 0.503205i) q^{6} +(-1.74237 - 4.20646i) q^{7} +(-1.09970 - 1.09970i) q^{8} +(5.31549 + 5.31549i) q^{9} +O(q^{10})$	\(q+(-0.286708 + 0.286708i) q^{2} +(-2.99617 - 1.24105i) q^{3} +1.83560i q^{4} +(-0.918391 + 2.21719i) q^{5} +(1.21484 - 0.503205i) q^{6} +(-1.74237 - 4.20646i) q^{7} +(-1.09970 - 1.09970i) q^{8} +(5.31549 + 5.31549i) q^{9} +(-0.372376 - 0.898996i) q^{10} +(-5.16669 + 2.14011i) q^{11} +(2.27808 - 5.49976i) q^{12} +4.32837i q^{13} +(1.70558 + 0.706474i) q^{14} +(5.50331 - 5.50331i) q^{15} -3.04061 q^{16} +(-3.09361 - 2.72572i) q^{17} -3.04799 q^{18} +(-1.17381 + 1.17381i) q^{19} +(-4.06987 - 1.68580i) q^{20} +14.7657i q^{21} +(0.867743 - 2.09492i) q^{22} +(-0.709798 + 0.294008i) q^{23} +(1.93009 + 4.65966i) q^{24} +(-0.536960 - 0.536960i) q^{25} +(-1.24098 - 1.24098i) q^{26} +(-5.60614 - 13.5344i) q^{27} +(7.72137 - 3.19830i) q^{28} +(2.37185 - 5.72615i) q^{29} +3.15568i q^{30} +(4.72161 + 1.95575i) q^{31} +(3.07116 - 3.07116i) q^{32} +18.1363 q^{33} +(1.66845 - 0.105478i) q^{34} +10.9267 q^{35} +(-9.75711 + 9.75711i) q^{36} +(8.39726 + 3.47826i) q^{37} -0.673082i q^{38} +(5.37174 - 12.9685i) q^{39} +(3.44819 - 1.42829i) q^{40} +(-1.29038 - 3.11525i) q^{41} +(-4.23343 - 4.23343i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-3.92839 - 9.48396i) q^{44} +(-16.6672 + 6.90377i) q^{45} +(0.119210 - 0.287799i) q^{46} -8.64397i q^{47} +(9.11019 + 3.77356i) q^{48} +(-9.70872 + 9.70872i) q^{49} +0.307902 q^{50} +(5.88623 + 12.0061i) q^{51} -7.94515 q^{52} +(3.96634 - 3.96634i) q^{53} +(5.48775 + 2.27310i) q^{54} -13.4210i q^{55} +(-2.70975 + 6.54191i) q^{56} +(4.97370 - 2.06018i) q^{57} +(0.961704 + 2.32176i) q^{58} +(2.40335 + 2.40335i) q^{59} +(10.1019 + 10.1019i) q^{60} +(-1.81077 - 4.37160i) q^{61} +(-1.91445 + 0.792992i) q^{62} +(13.0979 - 31.6210i) q^{63} -4.32017i q^{64} +(-9.59683 - 3.97514i) q^{65} +(-5.19981 + 5.19981i) q^{66} +9.52146 q^{67} +(5.00332 - 5.67863i) q^{68} +2.49155 q^{69} +(-3.13277 + 3.13277i) q^{70} +(-0.661153 - 0.273859i) q^{71} -11.6909i q^{72} +(-4.23025 + 10.2127i) q^{73} +(-3.40480 + 1.41032i) q^{74} +(0.942428 + 2.27522i) q^{75} +(-2.15465 - 2.15465i) q^{76} +(18.0046 + 18.0046i) q^{77} +(2.17806 + 5.25830i) q^{78} +(0.123367 - 0.0511002i) q^{79} +(2.79247 - 6.74162i) q^{80} +24.9572i q^{81} +(1.26313 + 0.523205i) q^{82} +(-2.68247 + 2.68247i) q^{83} -27.1038 q^{84} +(8.88459 - 4.35586i) q^{85} +0.405466 q^{86} +(-14.2129 + 14.2129i) q^{87} +(8.03526 + 3.32831i) q^{88} -8.46370i q^{89} +(2.79924 - 6.75797i) q^{90} +(18.2071 - 7.54164i) q^{91} +(-0.539680 - 1.30290i) q^{92} +(-11.7195 - 11.7195i) q^{93} +(2.47829 + 2.47829i) q^{94} +(-1.52455 - 3.68058i) q^{95} +(-13.0132 + 5.39024i) q^{96} +(4.92448 - 11.8887i) q^{97} -5.56713i q^{98} +(-38.8393 - 16.0878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.286708	+	0.286708i	−0.202733	+	0.202733i	−0.801170	−	0.598437i	$-0.795789\pi$
$2$	−0.286708	+	0.286708i	−0.202733	+	0.202733i	0.598437	+	0.801170i	$0.295789\pi$
$3$	−2.99617	−	1.24105i	−1.72984	−	0.716523i	−0.999439	−	0.0335036i	$-0.989333\pi$
$3$	−2.99617	−	1.24105i	−1.72984	−	0.716523i	−0.730400	−	0.683019i	$-0.760667\pi$
$4$			1.83560i			0.917799i
$5$	−0.918391	+	2.21719i	−0.410717	+	0.991558i	0.574229	+	0.818695i	$0.305302\pi$
$5$	−0.918391	+	2.21719i	−0.410717	+	0.991558i	−0.984946	+	0.172863i	$0.944698\pi$
$6$	1.21484	−	0.503205i	0.495958	−	0.205433i
$7$	−1.74237	−	4.20646i	−0.658556	−	1.58989i	−0.800036	−	0.599953i	$-0.795186\pi$
$7$	−1.74237	−	4.20646i	−0.658556	−	1.58989i	0.141480	−	0.989941i	$-0.454814\pi$
$8$	−1.09970	−	1.09970i	−0.388801	−	0.388801i
$9$	5.31549	+	5.31549i	1.77183	+	1.77183i
$10$	−0.372376	−	0.898996i	−0.117756	−	0.284287i
$11$	−5.16669	+	2.14011i	−1.55782	+	0.645268i	−0.984708	−	0.174212i	$-0.944262\pi$
$11$	−5.16669	+	2.14011i	−1.55782	+	0.645268i	−0.573107	+	0.819480i	$0.694262\pi$
$12$	2.27808	−	5.49976i	0.657624	−	1.58764i
$13$			4.32837i			1.20047i	0.799822	+	0.600237i	$0.204927\pi$
$13$			4.32837i			1.20047i	−0.799822	+	0.600237i	$0.795073\pi$
$14$	1.70558	+	0.706474i	0.455835	+	0.188813i
$15$	5.50331	−	5.50331i	1.42095	−	1.42095i
$16$	−3.04061			−0.760153
$17$	−3.09361	−	2.72572i	−0.750312	−	0.661084i
$17$	−3.09361	−	2.72572i	−0.750312	−	0.661084i
$18$	−3.04799			−0.718417
$19$	−1.17381	+	1.17381i	−0.269291	+	0.269291i	−0.828814	−	0.559523i	$-0.810984\pi$
$19$	−1.17381	+	1.17381i	−0.269291	+	0.269291i	0.559523	+	0.828814i	$0.310984\pi$
$20$	−4.06987	−	1.68580i	−0.910051	−	0.376955i
$21$			14.7657i			3.22213i
$22$	0.867743	−	2.09492i	0.185003	−	0.446638i
$23$	−0.709798	+	0.294008i	−0.148003	+	0.0613049i	−0.455455	−	0.890259i	$-0.650524\pi$
$23$	−0.709798	+	0.294008i	−0.148003	+	0.0613049i	0.307452	+	0.951563i	$0.400524\pi$
$24$	1.93009	+	4.65966i	0.393978	+	0.951148i
$25$	−0.536960	−	0.536960i	−0.107392	−	0.107392i
$26$	−1.24098	−	1.24098i	−0.243376	−	0.243376i
$27$	−5.60614	−	13.5344i	−1.07890	−	2.60470i
$28$	7.72137	−	3.19830i	1.45920	−	0.604421i
$29$	2.37185	−	5.72615i	0.440441	−	1.06332i	−0.535353	−	0.844629i	$-0.679821\pi$
$29$	2.37185	−	5.72615i	0.440441	−	1.06332i	0.975794	−	0.218691i	$-0.0701786\pi$
$30$			3.15568i			0.576146i
$31$	4.72161	+	1.95575i	0.848026	+	0.351264i	0.764013	−	0.645201i	$-0.223226\pi$
$31$	4.72161	+	1.95575i	0.848026	+	0.351264i	0.0840130	+	0.996465i	$0.473226\pi$
$32$	3.07116	−	3.07116i	0.542909	−	0.542909i
$33$	18.1363			3.15712
$34$	1.66845	−	0.105478i	0.286137	−	0.0180893i
$35$	10.9267			1.84695
$36$	−9.75711	+	9.75711i	−1.62618	+	1.62618i
$37$	8.39726	+	3.47826i	1.38050	+	0.571822i	0.944615	−	0.328180i	$-0.106435\pi$
$37$	8.39726	+	3.47826i	1.38050	+	0.571822i	0.435886	+	0.900002i	$0.356435\pi$
$38$		−	0.673082i		−	0.109188i
$39$	5.37174	−	12.9685i	0.860167	−	2.07663i
$40$	3.44819	−	1.42829i	0.545206	−	0.225832i
$41$	−1.29038	−	3.11525i	−0.201523	−	0.486521i	0.790517	−	0.612440i	$-0.209812\pi$
$41$	−1.29038	−	3.11525i	−0.201523	−	0.486521i	−0.992040	+	0.125919i	$0.959812\pi$
$42$	−4.23343	−	4.23343i	−0.653232	−	0.653232i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	−3.92839	−	9.48396i	−0.592226	−	1.42976i
$45$	−16.6672	+	6.90377i	−2.48459	+	1.02915i
$46$	0.119210	−	0.287799i	0.0175766	−	0.0424336i
$47$		−	8.64397i		−	1.26085i	−0.776249	−	0.630426i	$-0.782880\pi$
$47$		−	8.64397i		−	1.26085i	0.776249	−	0.630426i	$-0.217120\pi$
$48$	9.11019	+	3.77356i	1.31494	+	0.544667i
$49$	−9.70872	+	9.70872i	−1.38696	+	1.38696i
$50$	0.307902			0.0435438
$51$	5.88623	+	12.0061i	0.824236	+	1.68118i
$52$	−7.94515			−1.10179
$53$	3.96634	−	3.96634i	0.544819	−	0.544819i	−0.380119	−	0.924938i	$-0.624117\pi$
$53$	3.96634	−	3.96634i	0.544819	−	0.544819i	0.924938	+	0.380119i	$0.124117\pi$
$54$	5.48775	+	2.27310i	0.746788	+	0.309330i
$55$		−	13.4210i		−	1.80969i
$56$	−2.70975	+	6.54191i	−0.362105	+	0.874200i
$57$	4.97370	−	2.06018i	0.658783	−	0.272877i
$58$	0.961704	+	2.32176i	0.126278	+	0.304862i
$59$	2.40335	+	2.40335i	0.312890	+	0.312890i	0.846028	−	0.533138i	$-0.178988\pi$
$59$	2.40335	+	2.40335i	0.312890	+	0.312890i	−0.533138	+	0.846028i	$0.678988\pi$
$60$	10.1019	+	10.1019i	1.30414	+	1.30414i
$61$	−1.81077	−	4.37160i	−0.231846	−	0.559725i	0.764549	−	0.644566i	$-0.222962\pi$
$61$	−1.81077	−	4.37160i	−0.231846	−	0.559725i	−0.996395	+	0.0848406i	$0.972962\pi$
$62$	−1.91445	+	0.792992i	−0.243136	+	0.100710i
$63$	13.0979	−	31.6210i	1.65017	−	3.98387i
$64$		−	4.32017i		−	0.540022i
$65$	−9.59683	−	3.97514i	−1.19034	−	0.493055i
$66$	−5.19981	+	5.19981i	−0.640052	+	0.640052i
$67$	9.52146			1.16323			0.581616	−	0.813464i	$-0.302421\pi$
$67$	9.52146			1.16323			0.581616	+	0.813464i	$0.302421\pi$
$68$	5.00332	−	5.67863i	0.606742	−	0.688635i
$69$	2.49155			0.299948
$70$	−3.13277	+	3.13277i	−0.374438	+	0.374438i
$71$	−0.661153	−	0.273859i	−0.0784644	−	0.0325010i	0.343106	−	0.939297i	$-0.388521\pi$
$71$	−0.661153	−	0.273859i	−0.0784644	−	0.0325010i	−0.421570	+	0.906796i	$0.638521\pi$
$72$		−	11.6909i		−	1.37778i
$73$	−4.23025	+	10.2127i	−0.495114	+	1.19531i	0.456973	+	0.889481i	$0.348934\pi$
$73$	−4.23025	+	10.2127i	−0.495114	+	1.19531i	−0.952086	+	0.305829i	$0.901066\pi$
$74$	−3.40480	+	1.41032i	−0.395800	+	0.163946i
$75$	0.942428	+	2.27522i	0.108822	+	0.262720i
$76$	−2.15465	−	2.15465i	−0.247155	−	0.247155i
$77$	18.0046	+	18.0046i	2.05182	+	2.05182i
$78$	2.17806	+	5.25830i	0.246617	+	0.595385i
$79$	0.123367	−	0.0511002i	0.0138799	−	0.00574922i	−0.375733	−	0.926728i	$-0.622609\pi$
$79$	0.123367	−	0.0511002i	0.0138799	−	0.00574922i	0.389613	+	0.920979i	$0.372609\pi$
$80$	2.79247	−	6.74162i	0.312208	−	0.753736i
$81$			24.9572i			2.77302i
$82$	1.26313	+	0.523205i	0.139489	+	0.0577783i
$83$	−2.68247	+	2.68247i	−0.294440	+	0.294440i	−0.838831	−	0.544391i	$-0.816761\pi$
$83$	−2.68247	+	2.68247i	−0.294440	+	0.294440i	0.544391	+	0.838831i	$0.316761\pi$
$84$	−27.1038			−2.95727
$85$	8.88459	−	4.35586i	0.963669	−	0.472459i
$86$	0.405466			0.0437225
$87$	−14.2129	+	14.2129i	−1.52379	+	1.52379i
$88$	8.03526	+	3.32831i	0.856561	+	0.354799i
$89$		−	8.46370i		−	0.897150i	−0.893745	−	0.448575i	$-0.851932\pi$
$89$		−	8.46370i		−	0.897150i	0.893745	−	0.448575i	$-0.148068\pi$
$90$	2.79924	−	6.75797i	0.295066	−	0.712353i
$91$	18.2071	−	7.54164i	1.90863	−	0.790579i
$92$	−0.539680	−	1.30290i	−0.0562655	−	0.135837i
$93$	−11.7195	−	11.7195i	−1.21526	−	1.21526i
$94$	2.47829	+	2.47829i	0.255617	+	0.255617i
$95$	−1.52455	−	3.68058i	−0.156415	−	0.377620i
$96$	−13.0132	+	5.39024i	−1.32815	+	0.550139i
$97$	4.92448	−	11.8887i	0.500005	−	1.20712i	−0.449476	−	0.893292i	$-0.648389\pi$
$97$	4.92448	−	11.8887i	0.500005	−	1.20712i	0.949481	−	0.313826i	$-0.101611\pi$
$98$		−	5.56713i		−	0.562365i
$99$	−38.8393	−	16.0878i	−3.90349	−	1.61688i
$100$	0.985643	−	0.985643i	0.0985643	−	0.0985643i
$101$	−5.15020			−0.512464			−0.256232	−	0.966615i	$-0.582481\pi$
$101$	−5.15020			−0.512464			−0.256232	+	0.966615i	$0.582481\pi$
$102$	−5.12986	−	1.75460i	−0.507932	−	0.173732i
$103$	−4.67620			−0.460759			−0.230380	−	0.973101i	$-0.573997\pi$
$103$	−4.67620			−0.460759			−0.230380	+	0.973101i	$0.573997\pi$
$104$	4.75989	−	4.75989i	0.466746	−	0.466746i
$105$	−32.7383	−	13.5606i	−3.19493	−	1.32338i
$106$			2.27436i			0.220905i
$107$	−3.16715	+	7.64618i	−0.306180	+	0.739184i	0.693642	+	0.720320i	$0.256005\pi$
$107$	−3.16715	+	7.64618i	−0.306180	+	0.739184i	−0.999822	+	0.0188644i	$0.993995\pi$
$108$	24.8438	−	10.2906i	2.39059	−	0.990215i
$109$	5.34114	+	12.8947i	0.511589	+	1.23508i	0.942959	+	0.332910i	$0.108030\pi$
$109$	5.34114	+	12.8947i	0.511589	+	1.23508i	−0.431370	+	0.902175i	$0.641970\pi$
$110$	3.84790	+	3.84790i	0.366883	+	0.366883i
$111$	−20.8429	−	20.8429i	−1.97832	−	1.97832i
$112$	5.29788	+	12.7902i	0.500603	+	1.20856i
$113$	7.44737	−	3.08480i	0.700590	−	0.290194i	−0.00381456	−	0.999993i	$-0.501214\pi$
$113$	7.44737	−	3.08480i	0.700590	−	0.290194i	0.704404	+	0.709799i	$0.251214\pi$
$114$	−0.835331	+	2.01667i	−0.0782359	+	0.188878i
$115$		−	1.84377i		−	0.171932i
$116$	10.5109	+	4.35376i	0.975913	+	0.404236i
$117$	−23.0074	+	23.0074i	−2.12704	+	2.12704i
$118$	−1.37812			−0.126866
$119$	−6.07541	+	17.7624i	−0.556932	+	1.62828i
$120$	−12.1039			−1.10493
$121$	14.3364	−	14.3364i	1.30331	−	1.30331i
$122$	1.77253	+	0.734207i	0.160478	+	0.0664720i
$123$			10.9353i			0.985998i
$124$	−3.58998	+	8.66697i	−0.322390	+	0.778317i
$125$	−9.40227	+	3.89455i	−0.840965	+	0.348339i
$126$	5.31073	+	12.8212i	0.473118	+	1.14221i
$127$	−6.22170	−	6.22170i	−0.552087	−	0.552087i	0.374956	−	0.927043i	$-0.377658\pi$
$127$	−6.22170	−	6.22170i	−0.552087	−	0.552087i	−0.927043	+	0.374956i	$0.877658\pi$
$128$	7.38094	+	7.38094i	0.652389	+	0.652389i
$129$	1.24105	+	2.99617i	0.109269	+	0.263798i
$130$	3.89119	−	1.61178i	0.341280	−	0.141363i
$131$	−3.21824	+	7.76952i	−0.281179	+	0.678826i	−0.999864	−	0.0165102i	$-0.994744\pi$
$131$	−3.21824	+	7.76952i	−0.281179	+	0.678826i	0.718685	+	0.695336i	$0.244744\pi$
$132$			33.2909i			2.89760i
$133$	6.98282	+	2.89238i	0.605487	+	0.250801i
$134$	−2.72988	+	2.72988i	−0.235825	+	0.235825i
$135$	35.1570			3.02584
$136$	0.404571	+	6.39950i	0.0346917	+	0.548752i
$137$	−6.39736			−0.546563			−0.273282	−	0.961934i	$-0.588109\pi$
$137$	−6.39736			−0.546563			−0.273282	+	0.961934i	$0.588109\pi$
$138$	−0.714348	+	0.714348i	−0.0608093	+	0.0608093i
$139$	8.13029	+	3.36768i	0.689602	+	0.285643i	0.699834	−	0.714305i	$-0.253257\pi$
$139$	8.13029	+	3.36768i	0.689602	+	0.285643i	−0.0102324	+	0.999948i	$0.503257\pi$
$140$			20.0570i			1.69513i
$141$	−10.7276	+	25.8988i	−0.903430	+	2.18107i
$142$	0.268075	−	0.111040i	0.0224964	−	0.00931830i
$143$	−9.26320	−	22.3634i	−0.774628	−	1.87012i
$144$	−16.1624	−	16.1624i	−1.34686	−	1.34686i
$145$	10.5177	+	10.5177i	0.873446	+	0.873446i
$146$	−1.71522	−	4.14092i	−0.141953	−	0.342705i
$147$	41.1380	−	17.0399i	3.39301	−	1.40543i
$148$	−6.38468	+	15.4140i	−0.524818	+	1.26702i
$149$		−	14.2238i		−	1.16526i	−0.812737	−	0.582631i	$-0.802023\pi$
$149$		−	14.2238i		−	1.16526i	0.812737	−	0.582631i	$-0.197977\pi$
$150$	−0.922525	−	0.382122i	−0.0753238	−	0.0312002i
$151$	−5.17973	+	5.17973i	−0.421520	+	0.421520i	−0.885727	−	0.464207i	$-0.846339\pi$
$151$	−5.17973	+	5.17973i	−0.421520	+	0.421520i	0.464207	+	0.885727i	$0.346339\pi$
$152$	2.58167			0.209401
$153$	−1.95554	−	30.9326i	−0.158096	−	2.50076i
$154$	−10.3241			−0.831942
$155$	−8.67256	+	8.67256i	−0.696597	+	0.696597i
$156$	23.8050	+	9.86036i	1.90593	+	0.789460i
$157$		−	3.29791i		−	0.263202i	−0.991303	−	0.131601i	$-0.957988\pi$
$157$		−	3.29791i		−	0.263202i	0.991303	−	0.131601i	$-0.0420117\pi$
$158$	−0.0207194	+	0.0500211i	−0.00164835	+	0.00397946i
$159$	−16.8063	+	6.96138i	−1.33282	+	0.552073i
$160$	3.98882	+	9.62987i	0.315344	+	0.761308i
$161$	2.47347	+	2.47347i	0.194936	+	0.194936i
$162$	−7.15543	−	7.15543i	−0.562184	−	0.562184i
$163$	−4.14963	−	10.0181i	−0.325024	−	0.784677i	−0.998947	−	0.0458759i	$-0.985392\pi$
$163$	−4.14963	−	10.0181i	−0.325024	−	0.784677i	0.673923	−	0.738801i	$-0.264608\pi$
$164$	5.71835	−	2.36862i	0.446528	−	0.184958i
$165$	−16.6562	+	40.2116i	−1.29668	+	3.13047i
$166$		−	1.53817i		−	0.119385i
$167$	−3.21329	−	1.33099i	−0.248652	−	0.102995i	0.254877	−	0.966974i	$-0.417965\pi$
$167$	−3.21329	−	1.33099i	−0.248652	−	0.102995i	−0.503529	+	0.863979i	$0.667965\pi$
$168$	16.2377	−	16.2377i	1.25277	−	1.25277i
$169$	−5.73480			−0.441139
$170$	−1.29842	+	3.79614i	−0.0995845	+	0.291151i
$171$	−12.4788			−0.954276
$172$	1.29796	−	1.29796i	0.0989688	−	0.0989688i
$173$	−4.49102	−	1.86024i	−0.341446	−	0.141431i	0.205370	−	0.978684i	$-0.434160\pi$
$173$	−4.49102	−	1.86024i	−0.341446	−	0.141431i	−0.546816	+	0.837253i	$0.684160\pi$
$174$		−	8.14991i		−	0.617843i
$175$	−1.32312	+	3.19429i	−0.100018	+	0.241466i
$176$	15.7099	−	6.50725i	1.18418	−	0.490503i
$177$	−4.21816	−	10.1835i	−0.317056	−	0.765441i
$178$	2.42661	+	2.42661i	0.181882	+	0.181882i
$179$	13.2994	+	13.2994i	0.994045	+	0.994045i	0.999982	−	0.00593736i	$-0.00188993\pi$
$179$	13.2994	+	13.2994i	0.994045	+	0.994045i	−0.00593736	+	0.999982i	$0.501890\pi$
$180$	−12.6725	−	30.5942i	−0.944555	−	2.28036i
$181$	7.70684	−	3.19228i	0.572845	−	0.237280i	−0.0774060	−	0.997000i	$-0.524664\pi$
$181$	7.70684	−	3.19228i	0.572845	−	0.237280i	0.650251	+	0.759720i	$0.274664\pi$
$182$	−3.05788	+	7.38238i	−0.226665	+	0.547218i
$183$			15.3453i			1.13436i
$184$	1.10388	+	0.457242i	0.0813791	+	0.0337083i
$185$	−15.4239	+	15.4239i	−1.13399	+	1.13399i
$186$	6.72017			0.492747
$187$	21.8171	+	7.46227i	1.59542	+	0.545695i
$188$	15.8669			1.15721
$189$	−47.1641	+	47.1641i	−3.43068	+	3.43068i
$190$	1.49235	+	0.618152i	0.108267	+	0.0448455i
$191$		−	0.0822586i		−	0.00595202i	−0.999996	−	0.00297601i	$-0.999053\pi$
$191$		−	0.0822586i		−	0.00595202i	0.999996	−	0.00297601i	$-0.000947296\pi$
$192$	−5.36157	+	12.9440i	−0.386938	+	0.934151i
$193$	−6.84388	+	2.83483i	−0.492634	+	0.204055i	−0.615149	−	0.788411i	$-0.710904\pi$
$193$	−6.84388	+	2.83483i	−0.492634	+	0.204055i	0.122515	+	0.992467i	$0.460904\pi$
$194$	1.99671	+	4.82048i	0.143355	+	0.346090i
$195$	23.8204	+	23.8204i	1.70581	+	1.70581i
$196$	−17.8213	−	17.8213i	−1.27295	−	1.27295i
$197$	−0.815526	−	1.96885i	−0.0581038	−	0.140275i	0.892161	−	0.451717i	$-0.149188\pi$
$197$	−0.815526	−	1.96885i	−0.0581038	−	0.140275i	−0.950265	+	0.311442i	$0.899188\pi$
$198$	15.7480	−	6.52304i	1.11916	−	0.463572i
$199$	4.04060	−	9.75487i	0.286430	−	0.691504i	−0.713528	−	0.700627i	$-0.752904\pi$
$199$	4.04060	−	9.75487i	0.286430	−	0.691504i	0.999958	+	0.00912244i	$0.00290380\pi$
$200$			1.18099i			0.0835083i
$201$	−28.5279	−	11.8166i	−2.01220	−	0.833482i
$202$	1.47660	−	1.47660i	0.103893	−	0.103893i
$203$	−28.2195			−1.98062
$204$	−22.0383	+	10.8047i	−1.54299	+	0.756483i
$205$	8.09218			0.565182
$206$	1.34070	−	1.34070i	0.0934112	−	0.0934112i
$207$	−5.33572	−	2.21013i	−0.370858	−	0.153615i
$208$		−	13.1609i		−	0.912544i
$209$	3.55263	−	8.57681i	0.245741	−	0.593271i
$210$	13.2743	−	5.49838i	0.916011	−	0.379424i
$211$	−6.27317	−	15.1448i	−0.431863	−	1.04261i	−0.978686	−	0.205361i	$-0.934163\pi$
$211$	−6.27317	−	15.1448i	−0.431863	−	1.04261i	0.546823	−	0.837248i	$-0.315837\pi$
$212$	7.28060	+	7.28060i	0.500034	+	0.500034i
$213$	1.64105	+	1.64105i	0.112443	+	0.112443i
$214$	−1.28417	−	3.10027i	−0.0877843	−	0.211930i
$215$	2.21719	−	0.918391i	0.151211	−	0.0626337i
$216$	−8.71870	+	21.0488i	−0.593232	+	1.43219i
$217$		−	23.2689i		−	1.57960i
$218$	−5.22835	−	2.16565i	−0.354108	−	0.146677i
$219$	25.3491	−	25.3491i	1.71293	−	1.71293i
$220$	24.6355			1.66093
$221$	11.7979	−	13.3903i	0.793615	−	0.900730i
$222$	11.9516			0.802142
$223$	7.08170	−	7.08170i	0.474226	−	0.474226i	−0.429054	−	0.903279i	$-0.641153\pi$
$223$	7.08170	−	7.08170i	0.474226	−	0.474226i	0.903279	+	0.429054i	$0.141153\pi$
$224$	−18.2698	−	7.56761i	−1.22070	−	0.505632i
$225$		−	5.70842i		−	0.380561i
$226$	−1.25078	+	3.01966i	−0.0832008	+	0.200865i
$227$	−22.0414	+	9.12986i	−1.46294	+	0.605970i	−0.965237	−	0.261377i	$-0.915823\pi$
$227$	−22.0414	+	9.12986i	−1.46294	+	0.605970i	−0.497704	+	0.867347i	$0.665823\pi$
$228$	3.78165	+	9.12972i	0.250446	+	0.604630i
$229$	−11.1342	−	11.1342i	−0.735767	−	0.735767i	0.235989	−	0.971756i	$-0.424167\pi$
$229$	−11.1342	−	11.1342i	−0.735767	−	0.735767i	−0.971756	+	0.235989i	$0.924167\pi$
$230$	0.528623	+	0.528623i	0.0348564	+	0.0348564i
$231$	−31.6002	−	76.2896i	−2.07914	−	5.01948i
$232$	−8.90533	+	3.68871i	−0.584664	+	0.242176i
$233$	−8.58988	+	20.7378i	−0.562742	+	1.35858i	0.344823	+	0.938668i	$0.387939\pi$
$233$	−8.58988	+	20.7378i	−0.562742	+	1.35858i	−0.907565	+	0.419912i	$0.862061\pi$
$234$		−	13.1928i		−	0.862442i
$235$	19.1653	+	7.93854i	1.25021	+	0.517853i
$236$	−4.41158	+	4.41158i	−0.287170	+	0.287170i
$237$	−0.433046			−0.0281294
$238$	−3.35075	−	6.83449i	−0.217197	−	0.443014i
$239$	24.9203			1.61196			0.805979	−	0.591944i	$-0.201639\pi$
$239$	24.9203			1.61196			0.805979	+	0.591944i	$0.201639\pi$
$240$	−16.7334	+	16.7334i	−1.08014	+	1.08014i
$241$	−2.68104	−	1.11053i	−0.172701	−	0.0715352i	0.294658	−	0.955603i	$-0.404794\pi$
$241$	−2.68104	−	1.11053i	−0.172701	−	0.0715352i	−0.467359	+	0.884068i	$0.654794\pi$
$242$			8.22073i			0.528448i
$243$	14.1548	−	34.1728i	0.908033	−	2.19218i
$244$	8.02449	−	3.32385i	0.513715	−	0.212788i
$245$	−12.6097	−	30.4425i	−0.805603	−	1.94490i
$246$	−3.13522	−	3.13522i	−0.199894	−	0.199894i
$247$	−5.08070	−	5.08070i	−0.323277	−	0.323277i
$248$	−3.04160	−	7.34307i	−0.193142	−	0.466285i
$249$	11.3662	−	4.70805i	0.720306	−	0.298361i
$250$	1.57911	−	3.81230i	0.0998715	−	0.241111i
$251$		−	0.831872i		−	0.0525073i	−0.999655	−	0.0262536i	$-0.991642\pi$
$251$		−	0.831872i		−	0.0525073i	0.999655	−	0.0262536i	$-0.00835775\pi$
$252$	58.0434	+	24.0424i	3.65639	+	1.51453i
$253$	3.03809	−	3.03809i	0.191003	−	0.191003i
$254$	3.56762			0.223852
$255$	−32.0256	+	2.02463i	−2.00552	+	0.126787i
$256$	4.40800			0.275500
$257$	21.5934	−	21.5934i	1.34696	−	1.34696i	0.458011	−	0.888947i	$-0.348562\pi$
$257$	21.5934	−	21.5934i	1.34696	−	1.34696i	0.888947	−	0.458011i	$-0.151438\pi$
$258$	−1.21484	−	0.503205i	−0.0756329	−	0.0313282i
$259$		−	41.3832i		−	2.57143i
$260$	7.29675	−	17.6159i	0.452525	−	1.09249i
$261$	43.0449	−	17.8298i	2.66441	−	1.10363i
$262$	−1.30489	−	3.15028i	−0.0806162	−	0.194625i
$263$	−6.32219	−	6.32219i	−0.389843	−	0.389843i	0.484789	−	0.874631i	$-0.338897\pi$
$263$	−6.32219	−	6.32219i	−0.389843	−	0.389843i	−0.874631	+	0.484789i	$0.838897\pi$
$264$	−19.9444	−	19.9444i	−1.22749	−	1.22749i
$265$	5.15148	+	12.4368i	0.316453	+	0.763985i
$266$	−2.83130	+	1.17276i	−0.173598	+	0.0719066i
$267$	−10.5039	+	25.3587i	−0.642828	+	1.55193i
$268$			17.4776i			1.06761i
$269$	−7.15121	−	2.96213i	−0.436017	−	0.180604i	0.153868	−	0.988091i	$-0.450827\pi$
$269$	−7.15121	−	2.96213i	−0.436017	−	0.180604i	−0.589885	+	0.807487i	$0.700827\pi$
$270$	−10.0798	+	10.0798i	−0.613437	+	0.613437i
$271$	21.0463			1.27847			0.639235	−	0.769011i	$-0.279251\pi$
$271$	21.0463			1.27847			0.639235	+	0.769011i	$0.279251\pi$
$272$	9.40648	+	8.28786i	0.570352	+	0.502525i
$273$	−63.9112			−3.86808
$274$	1.83417	−	1.83417i	0.110806	−	0.110806i
$275$	3.92346	+	1.62515i	0.236594	+	0.0980004i
$276$			4.57349i			0.275292i
$277$	9.72643	−	23.4817i	0.584405	−	1.41088i	−0.304379	−	0.952551i	$-0.598449\pi$
$277$	9.72643	−	23.4817i	0.584405	−	1.41088i	0.888784	−	0.458327i	$-0.151551\pi$
$278$	−3.29656	+	1.36548i	−0.197714	+	0.0818959i
$279$	14.7019	+	35.4935i	0.880179	+	2.12494i
$280$	−12.0161	−	12.0161i	−0.718097	−	0.718097i
$281$	0.806536	+	0.806536i	0.0481139	+	0.0481139i	0.730754	−	0.682640i	$-0.239168\pi$
$281$	0.806536	+	0.806536i	0.0481139	+	0.0481139i	−0.682640	+	0.730754i	$0.739168\pi$
$282$	−4.34969	−	10.5011i	−0.259020	−	0.625330i
$283$	−15.0631	+	6.23936i	−0.895411	+	0.370891i	−0.782454	−	0.622708i	$-0.786032\pi$
$283$	−15.0631	+	6.23936i	−0.895411	+	0.370891i	−0.112957	+	0.993600i	$0.536032\pi$
$284$	0.502694	−	1.21361i	0.0298294	−	0.0720145i
$285$			12.9197i			0.765297i
$286$	9.06758	+	3.75591i	0.536177	+	0.222092i
$287$	−10.8559	+	10.8559i	−0.640802	+	0.640802i
$288$	32.6494			1.92389
$289$	2.14090	+	16.8647i	0.125935	+	0.992038i
$290$	−6.03100			−0.354153
$291$	−29.5091	+	29.5091i	−1.72986	+	1.72986i
$292$	−18.7465	−	7.76504i	−1.09705	−	0.454415i
$293$		−	31.4338i		−	1.83638i	−0.396139	−	0.918191i	$-0.629650\pi$
$293$		−	31.4338i		−	1.83638i	0.396139	−	0.918191i	$-0.370350\pi$
$294$	−6.90911	+	16.6801i	−0.402947	+	0.972801i
$295$	−7.53590	+	3.12147i	−0.438757	+	0.181739i
$296$	−5.40940	−	13.0595i	−0.314415	−	0.759066i
$297$	57.9304	+	57.9304i	3.36146	+	3.36146i
$298$	4.07808	+	4.07808i	0.236237	+	0.236237i
$299$	−1.27257	−	3.07227i	−0.0735949	−	0.177674i
$300$	−4.17639	+	1.72992i	−0.241124	+	0.0998768i
$301$	−1.74237	+	4.20646i	−0.100429	+	0.242457i
$302$		−	2.97014i		−	0.170912i
$303$	15.4309	+	6.39168i	0.886480	+	0.367192i
$304$	3.56911	−	3.56911i	0.204702	−	0.204702i
$305$	11.3557			0.650223
$306$	9.42930	+	8.30796i	0.539037	+	0.474934i
$307$	11.2028			0.639379			0.319689	−	0.947522i	$-0.396421\pi$
$307$	11.2028			0.639379			0.319689	+	0.947522i	$0.396421\pi$
$308$	−33.0492	+	33.0492i	−1.88315	+	1.88315i
$309$	14.0107	+	5.80341i	0.797040	+	0.330145i
$310$		−	4.97298i		−	0.282446i
$311$	1.63471	−	3.94655i	0.0926962	−	0.223788i	−0.870730	−	0.491761i	$-0.836354\pi$
$311$	1.63471	−	3.94655i	0.0926962	−	0.223788i	0.963427	+	0.267972i	$0.0863535\pi$
$312$	−20.1687	+	8.35416i	−1.14183	+	0.472961i
$313$	−8.85433	−	21.3763i	−0.500477	−	1.20826i	−0.949225	−	0.314599i	$-0.898130\pi$
$313$	−8.85433	−	21.3763i	−0.500477	−	1.20826i	0.448748	−	0.893658i	$-0.351870\pi$
$314$	0.945535	+	0.945535i	0.0533596	+	0.0533596i
$315$	58.0809	+	58.0809i	3.27249	+	3.27249i
$316$	0.0937994	+	0.226452i	0.00527663	+	0.0127389i
$317$	16.8901	−	6.99609i	0.948640	−	0.392940i	0.145921	−	0.989296i	$-0.453386\pi$
$317$	16.8901	−	6.99609i	0.948640	−	0.392940i	0.802720	+	0.596357i	$0.203386\pi$
$318$	2.82260	−	6.81437i	0.158284	−	0.382131i
$319$			34.6613i			1.94066i
$320$	9.57865	+	3.96761i	0.535463	+	0.221796i
$321$	18.9787	−	18.9787i	1.05928	−	1.05928i
$322$	−1.41832			−0.0790401
$323$	6.83081	−	0.431838i	0.380076	−	0.0240281i
$324$	−45.8114			−2.54508
$325$	2.32416	−	2.32416i	0.128921	−	0.128921i
$326$	4.06200	+	1.68253i	0.224973	+	0.0931869i
$327$		−	45.2632i		−	2.50306i
$328$	−2.00680	+	4.84485i	−0.110807	+	0.267512i
$329$	−36.3606	+	15.0610i	−2.00462	+	0.830342i
$330$	−6.75352	−	16.3044i	−0.371769	−	0.897529i
$331$	21.3978	+	21.3978i	1.17613	+	1.17613i	0.980722	+	0.195408i	$0.0626031\pi$
$331$	21.3978	+	21.3978i	1.17613	+	1.17613i	0.195408	+	0.980722i	$0.437397\pi$
$332$	−4.92394	−	4.92394i	−0.270236	−	0.270236i
$333$	26.1469	+	63.1243i	1.43284	+	3.45919i
$334$	1.30288	−	0.539671i	0.0712904	−	0.0295295i
$335$	−8.74442	+	21.1109i	−0.477759	+	1.15341i
$336$		−	44.8966i		−	2.44931i
$337$	0.389486	+	0.161331i	0.0212167	+	0.00878824i	0.393267	−	0.919425i	$-0.371345\pi$
$337$	0.389486	+	0.161331i	0.0212167	+	0.00878824i	−0.372050	+	0.928213i	$0.621345\pi$
$338$	1.64421	−	1.64421i	0.0894334	−	0.0894334i
$339$	−26.1420			−1.41984
$340$	7.99560	+	16.3085i	0.433622	+	0.884454i
$341$	−28.5806			−1.54773
$342$	3.57776	−	3.57776i	0.193463	−	0.193463i
$343$	28.3104	+	11.7265i	1.52862	+	0.633173i
$344$			1.55520i			0.0838510i
$345$	−2.28822	+	5.52425i	−0.123194	+	0.297416i
$346$	1.82095	−	0.754264i	0.0978951	−	0.0405495i
$347$	1.22276	+	2.95200i	0.0656411	+	0.158472i	0.953296	−	0.302038i	$-0.0976668\pi$
$347$	1.22276	+	2.95200i	0.0656411	+	0.158472i	−0.887655	+	0.460509i	$0.847667\pi$
$348$	−26.0892	−	26.0892i	−1.39853	−	1.39853i
$349$	−9.05965	−	9.05965i	−0.484952	−	0.484952i	0.421757	−	0.906709i	$-0.361414\pi$
$349$	−9.05965	−	9.05965i	−0.484952	−	0.484952i	−0.906709	+	0.421757i	$0.861414\pi$
$350$	−0.536480	−	1.29518i	−0.0286760	−	0.0692301i
$351$	58.5820	−	24.2655i	3.12688	−	1.29519i
$352$	−9.29510	+	22.4403i	−0.495430	+	1.19607i
$353$		−	1.44106i		−	0.0766999i	−0.999264	−	0.0383499i	$-0.987790\pi$
$353$		−	1.44106i		−	0.0766999i	0.999264	−	0.0383499i	$-0.0122102\pi$
$354$	4.12908	+	1.71032i	0.219458	+	0.0909024i
$355$	1.21439	−	1.21439i	0.0644533	−	0.0644533i
$356$	15.5359			0.823403
$357$	40.2470	−	45.6792i	2.13010	−	2.41760i
$358$	−7.62609			−0.403052
$359$	−6.06951	+	6.06951i	−0.320337	+	0.320337i	−0.848896	−	0.528560i	$-0.822732\pi$
$359$	−6.06951	+	6.06951i	−0.320337	+	0.320337i	0.528560	+	0.848896i	$0.322732\pi$
$360$	25.9208	+	10.7368i	1.36615	+	0.565877i
$361$			16.2443i			0.854965i
$362$	−1.29436	+	3.12486i	−0.0680301	+	0.164239i
$363$	−60.7466	+	25.1621i	−3.18837	+	1.32067i
$364$	13.8434	+	33.4210i	0.725592	+	1.75173i
$365$	−18.7586	−	18.7586i	−0.981868	−	0.981868i
$366$	−4.39962	−	4.39962i	−0.229972	−	0.229972i
$367$	−3.06051	−	7.38874i	−0.159758	−	0.385689i	0.823650	−	0.567098i	$-0.191934\pi$
$367$	−3.06051	−	7.38874i	−0.159758	−	0.385689i	−0.983408	+	0.181409i	$0.941934\pi$
$368$	2.15822	−	0.893964i	0.112505	−	0.0466011i
$369$	9.70010	−	23.4181i	0.504967	−	1.21910i
$370$		−	8.84432i		−	0.459794i
$371$	−23.5951	−	9.77341i	−1.22500	−	0.507410i
$372$	21.5124	−	21.5124i	1.11536	−	1.11536i
$373$	16.8403			0.871959			0.435979	−	0.899957i	$-0.356402\pi$
$373$	16.8403			0.871959			0.435979	+	0.899957i	$0.356402\pi$
$374$	−8.39462	+	4.11564i	−0.434076	+	0.212815i
$375$	33.0041			1.70433
$376$	−9.50574	+	9.50574i	−0.490221	+	0.490221i
$377$	24.7849	+	10.2662i	1.27649	+	0.528739i
$378$		−	27.0446i		−	1.39102i
$379$	−12.8898	+	31.1187i	−0.662103	+	1.59846i	0.132399	+	0.991197i	$0.457732\pi$
$379$	−12.8898	+	31.1187i	−0.662103	+	1.59846i	−0.794502	+	0.607262i	$0.792268\pi$
$380$	6.75607	−	2.79846i	0.346579	−	0.143558i
$381$	10.9198	+	26.3627i	0.559438	+	1.35060i
$382$	0.0235842	+	0.0235842i	0.00120667	+	0.00120667i
$383$	9.38111	+	9.38111i	0.479352	+	0.479352i	0.904924	−	0.425572i	$-0.139927\pi$
$383$	9.38111	+	9.38111i	0.479352	+	0.479352i	−0.425572	+	0.904924i	$0.639927\pi$
$384$	−12.9544	−	31.2747i	−0.661077	−	1.59598i
$385$	−56.4549	+	23.3844i	−2.87721	+	1.19178i
$386$	1.14943	−	2.77496i	0.0585043	−	0.141242i
$387$		−	7.51724i		−	0.382123i
$388$	21.8229	+	9.03935i	1.10789	+	0.458904i
$389$	−2.18588	+	2.18588i	−0.110829	+	0.110829i	−0.760346	−	0.649518i	$-0.774971\pi$
$389$	−2.18588	+	2.18588i	−0.110829	+	0.110829i	0.649518	+	0.760346i	$0.274971\pi$
$390$	−13.6590			−0.691649
$391$	2.99722	+	1.02516i	0.151576	+	0.0518447i
$392$	21.3533			1.07850
$393$	19.2848	−	19.2848i	0.972788	−	0.972788i
$394$	0.798303	+	0.330668i	0.0402179	+	0.0166588i
$395$			0.320458i			0.0161240i
$396$	29.5306	−	71.2932i	1.48397	−	3.58262i
$397$	10.8523	−	4.49517i	0.544662	−	0.225606i	−0.0933495	−	0.995633i	$-0.529757\pi$
$397$	10.8523	−	4.49517i	0.544662	−	0.225606i	0.638011	+	0.770027i	$0.279757\pi$
$398$	1.63833	+	3.95527i	0.0821219	+	0.198260i
$399$	−17.3321	−	17.3321i	−0.867691	−	0.867691i
$400$	1.63269	+	1.63269i	0.0816344	+	0.0816344i
$401$	1.05178	+	2.53922i	0.0525234	+	0.126803i	0.947963	−	0.318380i	$-0.103139\pi$
$401$	1.05178	+	2.53922i	0.0525234	+	0.126803i	−0.895440	+	0.445183i	$0.853139\pi$
$402$	11.5671	−	4.79125i	0.576914	−	0.238966i
$403$	−8.46523	+	20.4369i	−0.421683	+	1.01803i
$404$		−	9.45369i		−	0.470339i
$405$	−55.3349	−	22.9205i	−2.74961	−	1.13893i
$406$	8.09075	−	8.09075i	0.401537	−	0.401537i
$407$	−50.8299			−2.51954
$408$	6.72996	−	19.6761i	0.333182	−	0.974111i
$409$	18.1659			0.898248			0.449124	−	0.893470i	$-0.351736\pi$
$409$	18.1659			0.898248			0.449124	+	0.893470i	$0.351736\pi$
$410$	−2.32009	+	2.32009i	−0.114581	+	0.114581i
$411$	19.1676	+	7.93946i	0.945466	+	0.391625i
$412$		−	8.58362i		−	0.422884i
$413$	5.92207	−	14.2971i	0.291406	−	0.703516i
$414$	2.16345	−	0.896132i	0.106328	−	0.0440425i
$415$	−3.48400	−	8.41112i	−0.171023	−	0.412885i
$416$	13.2931	+	13.2931i	0.651749	+	0.651749i
$417$	−20.1803	−	20.1803i	−0.988231	−	0.988231i
$418$	1.44047	+	3.47761i	0.0704558	+	0.170095i
$419$	26.9899	−	11.1796i	1.31855	−	0.546159i	0.391179	−	0.920315i	$-0.372067\pi$
$419$	26.9899	−	11.1796i	1.31855	−	0.546159i	0.927366	+	0.374155i	$0.122067\pi$
$420$	24.8919	−	60.0943i	1.21460	−	2.93230i
$421$		−	8.73908i		−	0.425917i	−0.977061	−	0.212958i	$-0.931690\pi$
$421$		−	8.73908i		−	0.425917i	0.977061	−	0.212958i	$-0.0683099\pi$
$422$	6.14069	+	2.54356i	0.298924	+	0.123818i
$423$	45.9470	−	45.9470i	2.23402	−	2.23402i
$424$	−8.72353			−0.423652
$425$	0.197544	+	3.12475i	0.00958231	+	0.151573i
$426$	−0.941005			−0.0455919
$427$	−15.2339	+	15.2339i	−0.737221	+	0.737221i
$428$	−14.0353	−	5.81362i	−0.678422	−	0.281012i
$429$			78.5005i			3.79004i
$430$	−0.372376	+	0.898996i	−0.0179576	+	0.0433534i
$431$	13.5438	−	5.61001i	0.652380	−	0.270225i	−0.0318482	−	0.999493i	$-0.510139\pi$
$431$	13.5438	−	5.61001i	0.652380	−	0.270225i	0.684228	+	0.729268i	$0.260139\pi$
$432$	17.0461	+	41.1529i	0.820131	+	1.97997i
$433$	−9.96613	−	9.96613i	−0.478942	−	0.478942i	0.425852	−	0.904793i	$-0.359975\pi$
$433$	−9.96613	−	9.96613i	−0.478942	−	0.478942i	−0.904793	+	0.425852i	$0.859975\pi$
$434$	6.67139	+	6.67139i	0.320237	+	0.320237i
$435$	−18.4597	−	44.5658i	−0.885077	−	2.13677i
$436$	−23.6694	+	9.80419i	−1.13356	+	0.469536i
$437$	0.488059	−	1.17828i	0.0233470	−	0.0563647i
$438$			14.5356i			0.694536i
$439$	−0.610895	−	0.253041i	−0.0291564	−	0.0120770i	0.368058	−	0.929803i	$-0.380023\pi$
$439$	−0.610895	−	0.253041i	−0.0291564	−	0.0120770i	−0.397214	+	0.917726i	$0.630023\pi$
$440$	−14.7590	+	14.7590i	−0.703608	+	0.703608i
$441$	−103.213			−4.91492
$442$	0.456548	+	7.22167i	0.0217158	+	0.343500i
$443$	−12.1011			−0.574939			−0.287470	−	0.957790i	$-0.592814\pi$
$443$	−12.1011			−0.574939			−0.287470	+	0.957790i	$0.592814\pi$
$444$	38.2592	−	38.2592i	1.81570	−	1.81570i
$445$	18.7656	+	7.77298i	0.889576	+	0.368475i
$446$			4.06076i			0.192282i
$447$	−17.6525	+	42.6170i	−0.834937	+	2.01572i
$448$	−18.1727	+	7.52736i	−0.858577	+	0.355634i
$449$	−9.44546	−	22.8034i	−0.445759	−	1.07616i	−0.973895	−	0.226998i	$-0.927109\pi$
$449$	−9.44546	−	22.8034i	−0.445759	−	1.07616i	0.528136	−	0.849160i	$-0.322891\pi$
$450$	1.63665	+	1.63665i	0.0771524	+	0.0771524i
$451$	13.3340	+	13.3340i	0.627873	+	0.627873i
$452$	5.66245	+	13.6704i	0.266339	+	0.643000i
$453$	21.9477	−	9.09102i	1.03119	−	0.427133i
$454$	3.70185	−	8.93705i	0.173736	−	0.419436i
$455$			47.2949i			2.21722i
$456$	−7.73513	−	3.20399i	−0.362231	−	0.150041i
$457$	6.21464	−	6.21464i	0.290709	−	0.290709i	−0.546651	−	0.837360i	$-0.684098\pi$
$457$	6.21464	−	6.21464i	0.290709	−	0.290709i	0.837360	+	0.546651i	$0.184098\pi$
$458$	6.38451			0.298328
$459$	−19.5478	+	57.1511i	−0.912414	+	2.66758i
$460$	3.38442			0.157799
$461$	4.60808	−	4.60808i	0.214619	−	0.214619i	−0.591607	−	0.806226i	$-0.701506\pi$
$461$	4.60808	−	4.60808i	0.214619	−	0.214619i	0.806226	+	0.591607i	$0.201506\pi$
$462$	30.9328	+	12.8128i	1.43913	+	0.596105i
$463$		−	8.11992i		−	0.377365i	−0.982038	−	0.188682i	$-0.939578\pi$
$463$		−	8.11992i		−	0.377365i	0.982038	−	0.188682i	$-0.0604217\pi$
$464$	−7.21187	+	17.4110i	−0.334803	+	0.808285i
$465$	36.7476	−	15.2213i	1.70413	−	0.705873i
$466$	−3.48291	−	8.40848i	−0.161343	−	0.389515i
$467$	0.912506	+	0.912506i	0.0422258	+	0.0422258i	0.727904	−	0.685679i	$-0.240494\pi$
$467$	0.912506	+	0.912506i	0.0422258	+	0.0422258i	−0.685679	+	0.727904i	$0.740494\pi$
$468$	−42.2324	−	42.2324i	−1.95219	−	1.95219i
$469$	−16.5899	−	40.0517i	−0.766052	−	1.84941i
$470$	−7.77089	+	3.21881i	−0.358445	+	0.148473i
$471$	−4.09288	+	9.88108i	−0.188590	+	0.455296i
$472$		−	5.28591i		−	0.243304i
$473$	5.16669	+	2.14011i	0.237565	+	0.0984025i
$474$	0.124158	−	0.124158i	0.00570275	−	0.00570275i
$475$	1.26058			0.0578395
$476$	−32.6046	−	11.1520i	−1.49443	−	0.511151i
$477$	42.1661			1.93065
$478$	−7.14484	+	7.14484i	−0.326797	+	0.326797i
$479$	−26.8502	−	11.1217i	−1.22682	−	0.508165i	−0.327247	−	0.944939i	$-0.606121\pi$
$479$	−26.8502	−	11.1217i	−1.22682	−	0.508165i	−0.899571	+	0.436774i	$0.856121\pi$
$480$		−	33.8031i		−	1.54289i
$481$	−15.0552	+	36.3465i	−0.686458	+	1.65726i
$482$	1.08707	−	0.450280i	0.0495148	−	0.0205097i
$483$	−4.34122	−	10.4806i	−0.197532	−	0.476885i
$484$	26.3159	+	26.3159i	1.19618	+	1.19618i
$485$	21.8370	+	21.8370i	0.991567	+	0.991567i
$486$	5.73930	+	13.8559i	0.260340	+	0.628516i
$487$	31.0084	−	12.8441i	1.40513	−	0.582022i	0.454049	−	0.890976i	$-0.349979\pi$
$487$	31.0084	−	12.8441i	1.40513	−	0.582022i	0.951077	+	0.308954i	$0.0999789\pi$
$488$	−2.81612	+	6.79872i	−0.127480	+	0.307764i
$489$			35.1658i			1.59025i
$490$	12.3434	+	5.11280i	0.557618	+	0.230973i
$491$	13.4107	−	13.4107i	0.605216	−	0.605216i	−0.336476	−	0.941692i	$-0.609235\pi$
$491$	13.4107	−	13.4107i	0.605216	−	0.605216i	0.941692	+	0.336476i	$0.109235\pi$
$492$	−20.0727			−0.904948
$493$	−22.9455	+	11.2495i	−1.03341	+	0.506652i
$494$	2.91335			0.131078
$495$	71.3392	−	71.3392i	3.20646	−	3.20646i
$496$	−14.3566	−	5.94669i	−0.644630	−	0.267014i
$497$			3.25828i			0.146154i
$498$	−1.90895	+	4.60862i	−0.0855423	+	0.206517i
$499$	−17.3379	+	7.18159i	−0.776151	+	0.321492i	−0.735361	−	0.677676i	$-0.762987\pi$
$499$	−17.3379	+	7.18159i	−0.776151	+	0.321492i	−0.0407897	+	0.999168i	$0.512987\pi$
$500$	−7.14882	−	17.2588i	−0.319705	−	0.771836i
$501$	7.97573	+	7.97573i	0.356329	+	0.356329i
$502$	0.238504	+	0.238504i	0.0106450	+	0.0106450i
$503$	7.59224	+	18.3293i	0.338521	+	0.817263i	0.997858	+	0.0654153i	$0.0208372\pi$
$503$	7.59224	+	18.3293i	0.338521	+	0.817263i	−0.659337	+	0.751848i	$0.729163\pi$
$504$	−49.1771	+	20.3698i	−2.19052	+	0.907345i
$505$	4.72990	−	11.4190i	0.210478	−	0.508138i
$506$			1.74209i			0.0774454i
$507$	17.1824	+	7.11720i	0.763099	+	0.316086i
$508$	11.4205	−	11.4205i	0.506704	−	0.506704i
$509$	−36.9100			−1.63600			−0.818002	−	0.575215i	$-0.804918\pi$
$509$	−36.9100			−1.63600			−0.818002	+	0.575215i	$0.804918\pi$
$510$	8.60151	−	9.76246i	0.380881	−	0.432289i
$511$	50.3302			2.22648
$512$	−16.0257	+	16.0257i	−0.708242	+	0.708242i
$513$	22.4674	+	9.30632i	0.991961	+	0.410884i
$514$			12.3820i			0.546145i
$515$	4.29458	−	10.3680i	0.189242	−	0.456870i
$516$	−5.49976	+	2.27808i	−0.242113	+	0.100287i
$517$	18.4991	+	44.6607i	0.813588	+	1.96418i
$518$	11.8649	+	11.8649i	0.521313	+	0.521313i
$519$	11.1472	+	11.1472i	0.489307	+	0.489307i
$520$	6.18215	+	14.9250i	0.271105	+	0.654506i
$521$	12.7631	−	5.28666i	0.559163	−	0.231613i	−0.0851590	−	0.996367i	$-0.527140\pi$
$521$	12.7631	−	5.28666i	0.559163	−	0.231613i	0.644322	+	0.764755i	$0.277140\pi$
$522$	−7.22937	+	17.4532i	−0.316421	+	0.763907i
$523$		−	8.74761i		−	0.382506i	−0.981541	−	0.191253i	$-0.938745\pi$
$523$		−	8.74761i		−	0.382506i	0.981541	−	0.191253i	$-0.0612552\pi$
$524$	−14.2617	−	5.90739i	−0.623025	−	0.258066i
$525$	7.92857	−	7.92857i	0.346031	−	0.346031i
$526$	3.62524			0.158068
$527$	−9.27600	−	18.9201i	−0.404069	−	0.824174i
$528$	−55.1454			−2.39989
$529$	−15.8461	+	15.8461i	−0.688960	+	0.688960i
$530$	−5.04269	−	2.08875i	−0.219041	−	0.0907295i
$531$			25.5500i			1.10877i
$532$	−5.30924	+	12.8176i	−0.230185	+	0.555715i
$533$	13.4840	−	5.58524i	0.584055	−	0.241924i
$534$	−4.25898	−	10.2821i	−0.184304	−	0.444949i
$535$	−14.0444	−	14.0444i	−0.607191	−	0.607191i
$536$	−10.4707	−	10.4707i	−0.452266	−	0.452266i
$537$	−23.3420	−	56.3526i	−1.00728	−	2.43179i
$538$	2.89957	−	1.20104i	0.125010	−	0.0517806i
$539$	29.3842	−	70.9397i	1.26567	−	3.05559i
$540$			64.5342i			2.77711i
$541$	15.5904	+	6.45777i	0.670285	+	0.277641i	0.691759	−	0.722128i	$-0.256836\pi$
$541$	15.5904	+	6.45777i	0.670285	+	0.277641i	−0.0214742	+	0.999769i	$0.506836\pi$
$542$	−6.03413	+	6.03413i	−0.259188	+	0.259188i
$543$	−27.0528			−1.16095
$544$	−17.8721	+	1.12986i	−0.766260	+	0.0484424i
$545$	−33.4952			−1.43478
$546$	18.3239	−	18.3239i	0.784189	−	0.784189i
$547$	−1.38472	−	0.573570i	−0.0592063	−	0.0245241i	0.352884	−	0.935667i	$-0.385201\pi$
$547$	−1.38472	−	0.573570i	−0.0592063	−	0.0245241i	−0.412090	+	0.911143i	$0.635201\pi$
$548$		−	11.7430i		−	0.501635i
$549$	13.6120	−	32.8623i	0.580947	−	1.40253i
$550$	−1.59083	+	0.658944i	−0.0678333	+	0.0280975i
$551$	3.93732	+	9.50553i	0.167735	+	0.404949i
$552$	−2.73995	−	2.73995i	−0.116620	−	0.116620i
$553$	−0.429902	−	0.429902i	−0.0182813	−	0.0182813i
$554$	3.94374	+	9.52103i	0.167553	+	0.404510i
$555$	65.3546	−	27.0708i	2.77415	−	1.14909i
$556$	−6.18170	+	14.9239i	−0.262162	+	0.632916i
$557$		−	4.01932i		−	0.170304i	−0.996368	−	0.0851520i	$-0.972862\pi$
$557$		−	4.01932i		−	0.170304i	0.996368	−	0.0851520i	$-0.0271376\pi$
$558$	−14.3914	−	5.96112i	−0.609237	−	0.252354i
$559$	3.06062	−	3.06062i	0.129450	−	0.129450i
$560$	−33.2239			−1.40397
$561$	−56.1066	−	49.4344i	−2.36882	−	2.08712i
$562$	−0.462480			−0.0195085
$563$	−0.295624	+	0.295624i	−0.0124590	+	0.0124590i	−0.713309	−	0.700850i	$-0.752804\pi$
$563$	−0.295624	+	0.295624i	−0.0124590	+	0.0124590i	0.700850	+	0.713309i	$0.252804\pi$
$564$	−47.5398	−	19.6916i	−2.00179	−	0.829167i
$565$			19.3453i			0.813863i
$566$	2.52985	−	6.10759i	0.106337	−	0.256721i
$567$	104.982	−	43.4848i	4.40881	−	1.82619i
$568$	0.425906	+	1.02823i	0.0178706	+	0.0431435i
$569$	1.37231	+	1.37231i	0.0575303	+	0.0575303i	0.735287	−	0.677756i	$-0.237048\pi$
$569$	1.37231	+	1.37231i	0.0575303	+	0.0575303i	−0.677756	+	0.735287i	$0.737048\pi$
$570$	−3.70418	−	3.70418i	−0.155151	−	0.155151i
$571$	−12.0521	−	29.0964i	−0.504366	−	1.21765i	−0.947084	−	0.320987i	$-0.895985\pi$
$571$	−12.0521	−	29.0964i	−0.504366	−	1.21765i	0.442717	−	0.896661i	$-0.354015\pi$
$572$	41.0501	−	17.0035i	1.71639	−	0.710953i
$573$	−0.102087	+	0.246461i	−0.00426476	+	0.0102960i
$574$		−	6.22492i		−	0.259823i
$575$	0.539004	+	0.223263i	0.0224780	+	0.00931070i
$576$	22.9639	−	22.9639i	0.956827	−	0.956827i
$577$	−46.3934			−1.93138			−0.965690	−	0.259696i	$-0.916378\pi$
$577$	−46.3934			−1.93138			−0.965690	+	0.259696i	$0.916378\pi$
$578$	−5.44904	−	4.22142i	−0.226650	−	0.175588i
$579$	24.0236			0.998387
$580$	−19.3062	+	19.3062i	−0.801648	+	0.801648i
$581$	15.9576	+	6.60986i	0.662033	+	0.274223i
$582$		−	16.9210i		−	0.701398i
$583$	−12.0044	+	28.9813i	−0.497173	+	1.20028i
$584$	15.8829	−	6.57891i	0.657238	−	0.272237i
$585$	−29.8821	−	72.1417i	−1.23547	−	2.98269i
$586$	9.01231	+	9.01231i	0.372295	+	0.372295i
$587$	15.4552	+	15.4552i	0.637904	+	0.637904i	0.950038	−	0.312134i	$-0.101044\pi$
$587$	15.4552	+	15.4552i	0.637904	+	0.637904i	−0.312134	+	0.950038i	$0.601044\pi$
$588$	31.2784	+	75.5128i	1.28990	+	3.11410i
$589$	−7.83797	+	3.24659i	−0.322958	+	0.133774i
$590$	1.26565	−	3.05555i	0.0521060	−	0.125795i
$591$			6.91113i			0.284286i
$592$	−25.5328	−	10.5760i	−1.04939	−	0.434672i
$593$	−13.1313	+	13.1313i	−0.539237	+	0.539237i	−0.923305	−	0.384068i	$-0.874523\pi$
$593$	−13.1313	+	13.1313i	−0.539237	+	0.539237i	0.384068	+	0.923305i	$0.374523\pi$
$594$	−33.2182			−1.36296
$595$	−33.8030	−	29.7832i	−1.38579	−	1.22099i
$596$	26.1092			1.06948
$597$	−24.2126	+	24.2126i	−0.990957	+	0.990957i
$598$	1.24570	+	0.515986i	0.0509405	+	0.0211002i
$599$			4.75635i			0.194339i	0.995268	+	0.0971696i	$0.0309789\pi$
$599$			4.75635i			0.194339i	−0.995268	+	0.0971696i	$0.969021\pi$
$600$	1.46567	−	3.53843i	0.0598356	−	0.144456i
$601$	28.0904	−	11.6354i	1.14583	−	0.474618i	0.272696	−	0.962100i	$-0.412085\pi$
$601$	28.0904	−	11.6354i	1.14583	−	0.474618i	0.873133	+	0.487482i	$0.162085\pi$
$602$	−0.706474	−	1.70558i	−0.0287937	−	0.0695142i
$603$	50.6113	+	50.6113i	2.06105	+	2.06105i
$604$	−9.50789	−	9.50789i	−0.386871	−	0.386871i
$605$	18.6202	+	44.9530i	0.757017	+	1.82760i
$606$	−6.25669	+	2.59161i	−0.254161	+	0.105277i
$607$	1.05182	−	2.53933i	0.0426922	−	0.103068i	−0.901095	−	0.433622i	$-0.857235\pi$
$607$	1.05182	−	2.53933i	0.0426922	−	0.103068i	0.943787	+	0.330554i	$0.107235\pi$
$608$			7.20993i			0.292401i
$609$	84.5504	+	35.0219i	3.42615	+	1.41916i
$610$	−3.25576	+	3.25576i	−0.131822	+	0.131822i
$611$	37.4143			1.51362
$612$	56.7799	−	3.58958i	2.29519	−	0.145100i
$613$	18.6755			0.754295			0.377147	−	0.926153i	$-0.376905\pi$
$613$	18.6755			0.754295			0.377147	+	0.926153i	$0.376905\pi$
$614$	−3.21193	+	3.21193i	−0.129623	+	0.129623i
$615$	−24.2455	−	10.0428i	−0.977674	−	0.404966i
$616$		−	39.5992i		−	1.59550i
$617$	16.8537	−	40.6885i	0.678506	−	1.63806i	−0.0882345	−	0.996100i	$-0.528122\pi$
$617$	16.8537	−	40.6885i	0.678506	−	1.63806i	0.766740	−	0.641958i	$-0.221878\pi$
$618$	−5.68085	+	2.35309i	−0.228517	+	0.0946550i
$619$	−4.44398	−	10.7287i	−0.178619	−	0.431223i	0.809059	−	0.587728i	$-0.199977\pi$
$619$	−4.44398	−	10.7287i	−0.178619	−	0.431223i	−0.987677	+	0.156505i	$0.949977\pi$
$620$	−15.9193	−	15.9193i	−0.639336	−	0.639336i
$621$	7.95845	+	7.95845i	0.319362	+	0.319362i
$622$	0.662821	+	1.60019i	0.0265767	+	0.0641619i
$623$	−35.6022	+	14.7469i	−1.42637	+	0.590823i
$624$	−16.3334	+	39.4323i	−0.653859	+	1.57855i
$625$		−	28.2202i		−	1.12881i
$626$	8.66734	+	3.59013i	0.346417	+	0.143491i
$627$	−21.2886	+	21.2886i	−0.850184	+	0.850184i
$628$	6.05363			0.241566
$629$	−16.4971	−	33.6490i	−0.657783	−	1.34167i
$630$	−33.3045			−1.32688
$631$	24.0194	−	24.0194i	0.956198	−	0.956198i	−0.0428817	−	0.999080i	$-0.513654\pi$
$631$	24.0194	−	24.0194i	0.956198	−	0.956198i	0.999080	+	0.0428817i	$0.0136539\pi$
$632$	−0.191861	−	0.0794713i	−0.00763181	−	0.00316120i
$633$			53.1617i			2.11299i
$634$	−2.83668	+	6.84835i	−0.112659	+	0.271983i
$635$	19.5086	−	8.08075i	0.774177	−	0.320675i
$636$	−12.7783	−	30.8495i	−0.506692	−	1.22326i
$637$	−42.0229	−	42.0229i	−1.66501	−	1.66501i
$638$	−9.93765	−	9.93765i	−0.393436	−	0.393436i
$639$	−2.05866	−	4.97005i	−0.0814394	−	0.196612i
$640$	−23.1436	+	9.58637i	−0.914829	+	0.378935i
$641$	−2.44130	+	5.89381i	−0.0964254	+	0.232791i	−0.964731	−	0.263238i	$-0.915209\pi$
$641$	−2.44130	+	5.89381i	−0.0964254	+	0.232791i	0.868305	+	0.496030i	$0.165209\pi$
$642$			10.8827i			0.429504i
$643$	−28.9428	−	11.9885i	−1.14139	−	0.472780i	−0.269754	−	0.962929i	$-0.586942\pi$
$643$	−28.9428	−	11.9885i	−1.14139	−	0.472780i	−0.871639	+	0.490149i	$0.836942\pi$
$644$	−4.54029	+	4.54029i	−0.178912	+	0.178912i
$645$	−7.78285			−0.306449
$646$	−1.83463	+	2.08226i	−0.0721827	+	0.0819253i
$647$	0.962636			0.0378451			0.0189226	−	0.999821i	$-0.493976\pi$
$647$	0.962636			0.0378451			0.0189226	+	0.999821i	$0.493976\pi$
$648$	27.4453	−	27.4453i	1.07816	−	1.07816i
$649$	−17.5608	−	7.27392i	−0.689322	−	0.285526i
$650$			1.33271i			0.0522733i
$651$	−28.8780	+	69.7177i	−1.13182	+	2.73245i
$652$	18.3892	−	7.61705i	0.720176	−	0.298307i
$653$	0.0448775	+	0.108344i	0.00175619	+	0.00423982i	0.924755	−	0.380563i	$-0.124270\pi$
$653$	0.0448775	+	0.108344i	0.00175619	+	0.00423982i	−0.922999	+	0.384802i	$0.874270\pi$
$654$	12.9773	+	12.9773i	0.507454	+	0.507454i
$655$	−14.2709	−	14.2709i	−0.557610	−	0.557610i
$656$	3.92354	+	9.47227i	0.153189	+	0.369830i
$657$	−76.7716	+	31.7998i	−2.99515	+	1.24063i
$658$	6.10674	−	14.7430i	0.238065	−	0.574741i
$659$		−	21.7602i		−	0.847657i	−0.905742	−	0.423828i	$-0.860686\pi$
$659$		−	21.7602i		−	0.847657i	0.905742	−	0.423828i	$-0.139314\pi$
$660$	−73.8123	−	30.5740i	−2.87314	−	1.19009i
$661$	−7.94582	+	7.94582i	−0.309057	+	0.309057i	−0.844544	−	0.535487i	$-0.820128\pi$
$661$	−7.94582	+	7.94582i	−0.309057	+	0.309057i	0.535487	+	0.844544i	$0.320128\pi$
$662$	−12.2698			−0.476881
$663$	−51.9667	+	25.4778i	−2.01822	+	0.989475i
$664$	5.89981			0.228957
$665$	−12.8259	+	12.8259i	−0.497367	+	0.497367i
$666$	−25.5947	−	10.6017i	−0.991776	−	0.410807i
$667$			4.76175i			0.184376i
$668$	2.44316	−	5.89831i	0.0945287	−	0.228212i
$669$	−30.0067	+	12.4292i	−1.16013	+	0.480540i
$670$	−3.54556	−	8.55975i	−0.136977	−	0.330692i
$671$	18.7114	+	18.7114i	0.722346	+	0.722346i
$672$	45.3477	+	45.3477i	1.74932	+	1.74932i
$673$	9.52856	+	23.0040i	0.367299	+	0.886739i	0.994191	+	0.107632i	$0.0343269\pi$
$673$	9.52856	+	23.0040i	0.367299	+	0.886739i	−0.626892	+	0.779106i	$0.715673\pi$
$674$	−0.157924	+	0.0654141i	−0.00608299	+	0.00251966i
$675$	−4.25717	+	10.2777i	−0.163859	+	0.395590i
$676$		−	10.5268i		−	0.404876i
$677$	−3.69983	−	1.53252i	−0.142196	−	0.0588995i	0.310451	−	0.950590i	$-0.399520\pi$
$677$	−3.69983	−	1.53252i	−0.142196	−	0.0588995i	−0.452647	+	0.891690i	$0.649520\pi$
$678$	7.49511	−	7.49511i	0.287848	−	0.287848i
$679$	−58.5898			−2.24847
$680$	−14.5605	−	4.98023i	−0.558368	−	0.190983i
$681$	77.3705			2.96484
$682$	8.19429	−	8.19429i	0.313776	−	0.313776i
$683$	31.5247	+	13.0580i	1.20626	+	0.499649i	0.893016	−	0.450024i	$-0.148585\pi$
$683$	31.5247	+	13.0580i	1.20626	+	0.499649i	0.313243	+	0.949673i	$0.398585\pi$
$684$		−	22.9060i		−	0.875834i
$685$	5.87527	−	14.1842i	0.224483	−	0.541949i
$686$	−11.4789	+	4.75471i	−0.438266	+	0.181536i
$687$	19.5418	+	47.1780i	0.745564	+	1.79995i
$688$	2.15004	+	2.15004i	0.0819694	+	0.0819694i
$689$	17.1678	+	17.1678i	0.654041	+	0.654041i
$690$	−0.927795	−	2.23990i	−0.0353205	−	0.0852713i
$691$	36.6646	−	15.1870i	1.39479	−	0.577740i	0.446394	−	0.894837i	$-0.352708\pi$
$691$	36.6646	−	15.1870i	1.39479	−	0.577740i	0.948393	+	0.317097i	$0.102708\pi$
$692$	3.41465	−	8.24370i	0.129806	−	0.313378i
$693$			191.407i			7.27094i
$694$	−1.19694	−	0.495787i	−0.0454350	−	0.0188198i
$695$	−14.9336	+	14.9336i	−0.566462	+	0.566462i
$696$	31.2598			1.18490
$697$	−4.49937	+	13.1546i	−0.170426	+	0.498266i
$698$	5.19494			0.196632
$699$	51.4735	−	51.4735i	1.94691	−	1.94691i
$700$	−5.86343	−	2.42871i	−0.221617	−	0.0917967i
$701$			45.7695i			1.72869i	0.502899	+	0.864345i	$0.332267\pi$
$701$			45.7695i			1.72869i	−0.502899	+	0.864345i	$0.667733\pi$
$702$	−9.83882	+	23.7530i	−0.371342	+	0.896500i
$703$	−13.9396	+	5.77398i	−0.525743	+	0.217770i
$704$	9.24566	+	22.3210i	0.348459	+	0.841254i
$705$	−47.5704	−	47.5704i	−1.79161	−	1.79161i
$706$	0.413163	+	0.413163i	0.0155496	+	0.0155496i
$707$	8.97358	+	21.6641i	0.337486	+	0.814763i
$708$	18.6929	−	7.74284i	0.702521	−	0.290994i
$709$	−2.39392	+	5.77943i	−0.0899054	+	0.217051i	−0.962436	−	0.271509i	$-0.912477\pi$
$709$	−2.39392	+	5.77943i	−0.0899054	+	0.217051i	0.872531	+	0.488559i	$0.162477\pi$
$710$			0.696352i			0.0261336i
$711$	0.927378	+	0.384133i	0.0347794	+	0.0144061i
$712$	−9.30749	+	9.30749i	−0.348813	+	0.348813i
$713$	−3.92639			−0.147045
$714$	1.55745	+	24.6357i	0.0582862	+	0.921969i
$715$	58.0911			2.17248
$716$	−24.4124	+	24.4124i	−0.912333	+	0.912333i
$717$	−74.6653	−	30.9274i	−2.78843	−	1.15500i
$718$		−	3.48035i		−	0.129886i
$719$	15.4347	−	37.2628i	0.575619	−	1.38967i	−0.321091	−	0.947048i	$-0.604050\pi$
$719$	15.4347	−	37.2628i	0.575619	−	1.38967i	0.896710	−	0.442618i	$-0.145950\pi$
$720$	50.6784	−	20.9917i	1.88867	−	0.782313i
$721$	8.14769	+	19.6703i	0.303436	+	0.732559i
$722$	−4.65738	−	4.65738i	−0.173330	−	0.173330i
$723$	6.65464	+	6.65464i	0.247489	+	0.247489i
$724$	5.85974	+	14.1467i	0.217775	+	0.525756i
$725$	−4.34831	+	1.80113i	−0.161492	+	0.0668922i
$726$	10.2024	−	24.6307i	0.378645	−	0.914131i
$727$			18.0827i			0.670651i	0.942102	+	0.335325i	$0.108846\pi$
$727$			18.0827i			0.670651i	−0.942102	+	0.335325i	$0.891154\pi$
$728$	−28.3158	−	11.7288i	−1.04945	−	0.434698i
$729$	−31.8783	+	31.8783i	−1.18068	+	1.18068i
$730$	10.7564			0.398114
$731$	0.260140	+	4.11489i	0.00962163	+	0.152195i
$732$	−28.1678			−1.04111
$733$	3.16884	−	3.16884i	0.117044	−	0.117044i	−0.646159	−	0.763203i	$-0.723626\pi$
$733$	3.16884	−	3.16884i	0.117044	−	0.117044i	0.763203	+	0.646159i	$0.223626\pi$
$734$	2.99588	+	1.24093i	0.110580	+	0.0458037i
$735$			106.860i			3.94159i
$736$	−1.27696	+	3.08284i	−0.0470692	+	0.113635i
$737$	−49.1944	+	20.3770i	−1.81210	+	0.750596i
$738$	3.93306	+	9.49525i	0.144778	+	0.349525i
$739$	−33.2526	−	33.2526i	−1.22322	−	1.22322i	−0.966482	−	0.256733i	$-0.917354\pi$
$739$	−33.2526	−	33.2526i	−1.22322	−	1.22322i	−0.256733	−	0.966482i	$-0.582646\pi$
$740$	−28.3121	−	28.3121i	−1.04077	−	1.04077i
$741$	8.91721	+	21.5280i	0.327582	+	0.790852i
$742$	9.56701	−	3.96279i	0.351216	−	0.145478i
$743$	−5.20311	+	12.5614i	−0.190883	+	0.460833i	−0.990127	−	0.140174i	$-0.955234\pi$
$743$	−5.20311	+	12.5614i	−0.190883	+	0.460833i	0.799243	+	0.601007i	$0.205234\pi$
$744$			25.7759i			0.944989i
$745$	31.5370	+	13.0630i	1.15542	+	0.478593i
$746$	−4.82825	+	4.82825i	−0.176775	+	0.176775i
$747$	−28.5173			−1.04340
$748$	−13.6977	+	40.0474i	−0.500838	+	1.46428i
$749$	37.6818			1.37686
$750$	−9.46254	+	9.46254i	−0.345523	+	0.345523i
$751$	−25.2323	−	10.4516i	−0.920739	−	0.381383i	−0.128581	−	0.991699i	$-0.541042\pi$
$751$	−25.2323	−	10.4516i	−0.920739	−	0.381383i	−0.792158	+	0.610316i	$0.791042\pi$
$752$			26.2830i			0.958441i
$753$	−1.03240	+	2.49243i	−0.0376227	+	0.0908291i
$754$	−10.0494	+	4.16261i	−0.365979	+	0.151593i
$755$	−6.72743	−	16.2415i	−0.244836	−	0.591087i
$756$	−86.5742	−	86.5742i	−3.14867	−	3.14867i
$757$	32.4574	+	32.4574i	1.17969	+	1.17969i	0.979824	+	0.199861i	$0.0640492\pi$
$757$	32.4574	+	32.4574i	1.17969	+	1.17969i	0.199861	+	0.979824i	$0.435951\pi$
$758$	−5.22637	−	12.6176i	−0.189830	−	0.458290i
$759$	−12.8731	+	5.33220i	−0.467263	+	0.193547i
$760$	−2.37098	+	5.72406i	−0.0860046	+	0.207634i
$761$		−	5.50581i		−	0.199585i	−0.995008	−	0.0997926i	$-0.968182\pi$
$761$		−	5.50581i		−	0.199585i	0.995008	−	0.0997926i	$-0.0318179\pi$
$762$	−10.6892	−	4.42761i	−0.387229	−	0.160395i
$763$	44.9347	−	44.9347i	1.62674	−	1.62674i
$764$	0.150994			0.00546276
$765$	70.3795	+	24.0724i	2.54458	+	0.870341i
$766$	−5.37927			−0.194361
$767$	−10.4026	+	10.4026i	−0.375616	+	0.375616i
$768$	−13.2071	−	5.47056i	−0.476571	−	0.197402i
$769$		−	39.7341i		−	1.43285i	−0.697666	−	0.716423i	$-0.745778\pi$
$769$		−	39.7341i		−	1.43285i	0.697666	−	0.716423i	$-0.254222\pi$
$770$	9.48158	−	22.8906i	0.341692	−	0.824918i
$771$	−91.4959	+	37.8988i	−3.29514	+	1.36489i
$772$	−5.20361	−	12.5626i	−0.187282	−	0.452138i
$773$	−13.7933	−	13.7933i	−0.496112	−	0.496112i	0.414113	−	0.910225i	$-0.364092\pi$
$773$	−13.7933	−	13.7933i	−0.496112	−	0.496112i	−0.910225	+	0.414113i	$0.864092\pi$
$774$	2.15525	+	2.15525i	0.0774689	+	0.0774689i
$775$	−1.48515	−	3.58548i	−0.0533483	−	0.128794i
$776$	−18.4894	+	7.65857i	−0.663731	+	0.274926i
$777$	−51.3588	+	123.991i	−1.84249	+	4.44815i
$778$		−	1.25342i		−	0.0449372i
$779$	5.17138	+	2.14206i	0.185284	+	0.0767472i
$780$	−43.7246	+	43.7246i	−1.56559	+	1.56559i
$781$	4.00206			0.143205
$782$	−1.15325	+	0.565405i	−0.0412401	+	0.0202188i
$783$	−90.7971			−3.24482
$784$	29.5204	−	29.5204i	1.05430	−	1.05430i
$785$	7.31209	+	3.02877i	0.260980	+	0.108101i
$786$			11.0582i			0.394433i
$787$	20.3017	−	49.0127i	0.723678	−	1.74711i	0.0610847	−	0.998133i	$-0.480544\pi$
$787$	20.3017	−	49.0127i	0.723678	−	1.74711i	0.662593	−	0.748980i	$-0.269456\pi$
$788$	3.61402	−	1.49698i	0.128744	−	0.0533276i
$789$	11.0962	+	26.7885i	0.395034	+	0.953697i
$790$	−0.0918777	−	0.0918777i	−0.00326886	−	0.00326886i
$791$	−25.9522	−	25.9522i	−0.922755	−	0.922755i
$792$	25.0197	+	60.4030i	0.889038	+	2.14633i
$793$	18.9219	−	7.83770i	0.671936	−	0.278325i
$794$	−1.82264	+	4.40024i	−0.0646831	+	0.156159i
$795$		−	43.6560i		−	1.54832i
$796$	17.9060	+	7.41691i	0.634662	+	0.262886i
$797$	7.61799	−	7.61799i	0.269843	−	0.269843i	−0.559194	−	0.829037i	$-0.688889\pi$
$797$	7.61799	−	7.61799i	0.269843	−	0.269843i	0.829037	+	0.559194i	$0.188889\pi$
$798$	9.93850			0.351819
$799$	−23.5610	+	26.7411i	−0.833530	+	0.946033i
$800$	−3.29818			−0.116608
$801$	44.9887	−	44.9887i	1.58960	−	1.58960i
$802$	−1.02957	−	0.426461i	−0.0363553	−	0.0150589i
$803$		−	61.8192i		−	2.18155i
$804$	21.6906	−	52.3657i	0.764968	−	1.84680i
$805$	−7.75575	+	3.21254i	−0.273354	+	0.113227i
$806$	−3.43236	−	8.28646i	−0.120900	−	0.291878i
$807$	17.7501	+	17.7501i	0.624833	+	0.624833i
$808$	5.66365	+	5.66365i	0.199247	+	0.199247i
$809$	−2.92670	−	7.06569i	−0.102897	−	0.248416i	0.864043	−	0.503417i	$-0.167924\pi$
$809$	−2.92670	−	7.06569i	−0.102897	−	0.248416i	−0.966941	+	0.255001i	$0.917924\pi$
$810$	22.4364	−	9.29348i	0.788336	−	0.326539i
$811$	11.7192	−	28.2926i	0.411515	−	0.993486i	−0.573216	−	0.819404i	$-0.694304\pi$
$811$	11.7192	−	28.2926i	0.411515	−	0.993486i	0.984731	−	0.174082i	$-0.0556957\pi$
$812$		−	51.7996i		−	1.81781i
$813$	−63.0582	−	26.1196i	−2.21155	−	0.916053i
$814$	14.5733	−	14.5733i	0.510795	−	0.510795i
$815$	26.0230			0.911546
$816$	−17.8977	−	36.5058i	−0.626546	−	1.27796i
$817$	1.66002			0.0580768
$818$	−5.20832	+	5.20832i	−0.182104	+	0.182104i
$819$	136.867	+	56.6924i	4.78254	+	1.98099i
$820$			14.8540i			0.518724i
$821$	−9.88961	+	23.8756i	−0.345150	+	0.833265i	0.652029	+	0.758194i	$0.273918\pi$
$821$	−9.88961	+	23.8756i	−0.345150	+	0.833265i	−0.997178	+	0.0750706i	$0.976082\pi$
$822$	−7.77180	+	3.21918i	−0.271072	+	0.112282i
$823$	10.3232	+	24.9225i	0.359845	+	0.868744i	0.995321	+	0.0966228i	$0.0308040\pi$
$823$	10.3232	+	24.9225i	0.359845	+	0.868744i	−0.635476	+	0.772121i	$0.719196\pi$
$824$	5.14239	+	5.14239i	0.179144	+	0.179144i
$825$	−9.73846	−	9.73846i	−0.339050	−	0.339050i
$826$	2.40120	+	5.79700i	0.0835484	+	0.201704i
$827$	−34.8761	+	14.4461i	−1.21276	+	0.502342i	−0.895101	−	0.445863i	$-0.852897\pi$
$827$	−34.8761	+	14.4461i	−1.21276	+	0.502342i	−0.317659	+	0.948205i	$0.602897\pi$
$828$	4.05690	−	9.79423i	0.140987	−	0.340373i
$829$		−	41.8188i		−	1.45243i	−0.687469	−	0.726213i	$-0.741278\pi$
$829$		−	41.8188i		−	1.45243i	0.687469	−	0.726213i	$-0.258722\pi$
$830$	3.41042	+	1.41264i	0.118377	+	0.0490336i
$831$	−58.2841	+	58.2841i	−2.02185	+	2.02185i
$832$	18.6993			0.648282
$833$	56.4983	−	3.57178i	1.95755	−	0.123755i
$834$	11.5717			0.400694
$835$	5.90211	−	5.90211i	0.204251	−	0.204251i
$836$	15.7436	+	6.52120i	0.544503	+	0.225541i
$837$		−	74.8685i		−	2.58783i
$838$	−4.53295	+	10.9435i	−0.156588	+	0.378037i
$839$	33.7780	−	13.9913i	1.16615	−	0.483033i	0.286229	−	0.958161i	$-0.407598\pi$
$839$	33.7780	−	13.9913i	1.16615	−	0.483033i	0.879917	+	0.475128i	$0.157598\pi$
$840$	21.0896	+	50.9147i	0.727659	+	1.75672i
$841$	−6.65703	−	6.65703i	−0.229553	−	0.229553i
$842$	2.50556	+	2.50556i	0.0863474	+	0.0863474i
$843$	−1.41556	−	3.41747i	−0.0487546	−	0.117704i
$844$	27.7997	−	11.5150i	0.956906	−	0.396363i
$845$	5.26679	−	12.7152i	0.181183	−	0.437415i
$846$			26.3467i			0.905819i
$847$	−85.2851	−	35.3262i	−2.93043	−	1.21382i
$848$	−12.0601	+	12.0601i	−0.414145	+	0.414145i
$849$	52.8751			1.81467
$850$	−0.952528	−	0.839253i	−0.0326715	−	0.0287862i
$851$	−6.98299			−0.239374
$852$	−3.01231	+	3.01231i	−0.103200	+	0.103200i
$853$	50.1708	+	20.7814i	1.71782	+	0.711543i	0.999881	+	0.0154336i	$0.00491286\pi$
$853$	50.1708	+	20.7814i	1.71782	+	0.711543i	0.717936	+	0.696109i	$0.245087\pi$
$854$		−	8.73536i		−	0.298918i
$855$	11.4604	−	27.6678i	0.391937	−	0.946220i
$856$	11.8914	−	4.92557i	0.406439	−	0.168353i
$857$	5.65143	+	13.6438i	0.193049	+	0.466062i	0.990532	−	0.137279i	$-0.0438357\pi$
$857$	5.65143	+	13.6438i	0.193049	+	0.466062i	−0.797483	+	0.603341i	$0.793836\pi$
$858$	−22.5067	−	22.5067i	−0.768366	−	0.768366i
$859$	11.4162	+	11.4162i	0.389515	+	0.389515i	0.874514	−	0.485000i	$-0.161180\pi$
$859$	11.4162	+	11.4162i	0.389515	+	0.389515i	−0.485000	+	0.874514i	$0.661180\pi$
$860$	1.68580	+	4.06987i	0.0574851	+	0.138781i
$861$	45.9987	−	19.0533i	1.56763	−	0.649335i
$862$	−2.27467	+	5.49153i	−0.0774755	+	0.187042i
$863$		−	52.1297i		−	1.77452i	−0.461274	−	0.887258i	$-0.652608\pi$
$863$		−	52.1297i		−	1.77452i	0.461274	−	0.887258i	$-0.347392\pi$
$864$	−58.7837	−	24.3490i	−1.99986	−	0.828370i
$865$	8.24901	−	8.24901i	0.280475	−	0.280475i
$866$	5.71473			0.194195
$867$	14.5155	−	53.1863i	0.492971	−	1.80630i
$868$	42.7124			1.44975
$869$	−0.528038	+	0.528038i	−0.0179125	+	0.0179125i
$870$	18.0699	+	7.48480i	0.612627	+	0.253759i
$871$			41.2124i			1.39643i
$872$	8.30657	−	20.0538i	0.281296	−	0.679109i
$873$	89.3705	−	37.0185i	3.02473	−	1.25289i
$874$	0.197891	+	0.477752i	0.00669378	+	0.0161602i
$875$	32.7645	+	32.7645i	1.10764	+	1.10764i
$876$	46.5307	+	46.5307i	1.57213	+	1.57213i
$877$	−16.5992	−	40.0739i	−0.560514	−	1.35320i	−0.909356	−	0.416018i	$-0.863425\pi$
$877$	−16.5992	−	40.0739i	−0.560514	−	1.35320i	0.348843	−	0.937181i	$-0.386575\pi$
$878$	0.247697	−	0.102600i	0.00835938	−	0.00346257i
$879$	−39.0110	+	94.1809i	−1.31581	+	3.17664i
$880$			40.8080i			1.37564i
$881$	40.6078	+	16.8203i	1.36811	+	0.566690i	0.941276	−	0.337639i	$-0.109628\pi$
$881$	40.6078	+	16.8203i	1.36811	+	0.566690i	0.426835	+	0.904329i	$0.359628\pi$
$882$	29.5921	−	29.5921i	0.996416	−	0.996416i
$883$	0.409414			0.0137779			0.00688894	−	0.999976i	$-0.497807\pi$
$883$	0.409414			0.0137779			0.00688894	+	0.999976i	$0.497807\pi$
$884$	24.5792	+	21.6563i	0.826689	+	0.728379i
$885$	26.4527			0.889199
$886$	3.46947	−	3.46947i	0.116559	−	0.116559i
$887$	−38.5201	−	15.9556i	−1.29338	−	0.535735i	−0.373389	−	0.927675i	$-0.621804\pi$
$887$	−38.5201	−	15.9556i	−1.29338	−	0.535735i	−0.919991	+	0.391940i	$0.871804\pi$
$888$			45.8417i			1.53835i
$889$	−15.3308	+	37.0119i	−0.514179	+	1.24134i
$890$	−7.60883	+	3.15168i	−0.255048	+	0.105645i
$891$	−53.4113	−	128.946i	−1.78934	−	4.31986i
$892$	12.9991	+	12.9991i	0.435244	+	0.435244i
$893$	10.1464	+	10.1464i	0.339536	+	0.339536i
$894$	−7.15751	−	17.2798i	−0.239383	−	0.577921i
$895$	−41.7014	+	17.2733i	−1.39392	+	0.577382i
$896$	18.1873	−	43.9080i	0.607595	−	1.46686i
$897$			10.7844i			0.360080i
$898$	9.24599	+	3.82981i	0.308543	+	0.127803i
$899$	22.3979	−	22.3979i	0.747012	−	0.747012i
$900$	10.4784			0.349279
$901$	−23.0815	+	1.45919i	−0.768955	+	0.0486127i
$902$	−7.64591			−0.254581
$903$	10.4409	−	10.4409i	0.347451	−	0.347451i
$904$	−11.5822	−	4.79750i	−0.385218	−	0.159562i
$905$			20.0193i			0.665464i
$906$	−3.68610	+	8.89903i	−0.122462	+	0.295650i
$907$	−5.62594	+	2.33034i	−0.186806	+	0.0773776i	−0.474126	−	0.880457i	$-0.657236\pi$
$907$	−5.62594	+	2.33034i	−0.186806	+	0.0773776i	0.287320	+	0.957835i	$0.407236\pi$
$908$	−16.7587	−	40.4592i	−0.556158	−	1.34268i
$909$	−27.3759	−	27.3759i	−0.908000	−	0.908000i
$910$	−13.5598	−	13.5598i	−0.449503	−	0.449503i
$911$	10.1213	+	24.4350i	0.335334	+	0.809567i	0.998151	+	0.0607858i	$0.0193607\pi$
$911$	10.1213	+	24.4350i	0.335334	+	0.809567i	−0.662817	+	0.748781i	$0.730639\pi$
$912$	−15.1231	+	6.26420i	−0.500776	+	0.207428i
$913$	8.11871	−	19.6003i	0.268690	−	0.648676i
$914$			3.56357i			0.117873i
$915$	−34.0235	−	14.0930i	−1.12478	−	0.465900i
$916$	20.4379	−	20.4379i	0.675286	−	0.675286i
$917$	38.2896			1.26443
$918$	−10.7811	−	21.9902i	−0.355831	−	0.725784i
$919$	−46.5868			−1.53676			−0.768379	−	0.639995i	$-0.778936\pi$
$919$	−46.5868			−1.53676			−0.768379	+	0.639995i	$0.778936\pi$
$920$	−2.02759	+	2.02759i	−0.0668475	+	0.0668475i
$921$	−33.5655	−	13.9033i	−1.10602	−	0.458129i
$922$			2.64234i			0.0870209i
$923$	1.18536	−	2.86172i	0.0390167	−	0.0941945i
$924$	140.037	−	58.0052i	4.60688	−	1.90823i
$925$	−2.64131	−	6.37668i	−0.0868457	−	0.209664i
$926$	2.32805	+	2.32805i	0.0765043	+	0.0765043i
$927$	−24.8563	−	24.8563i	−0.816388	−	0.816388i
$928$	−10.3016	−	24.8702i	−0.338166	−	0.816406i
$929$	15.0874	−	6.24942i	0.495002	−	0.205037i	−0.121195	−	0.992629i	$-0.538673\pi$
$929$	15.0874	−	6.24942i	0.495002	−	0.205037i	0.616197	+	0.787592i	$0.288673\pi$
$930$	−6.17174	+	14.8999i	−0.202379	+	0.488587i
$931$		−	22.7924i		−	0.746992i
$932$	−38.0663	−	15.7676i	−1.24690	−	0.516484i
$933$	−9.79576	+	9.79576i	−0.320699	+	0.320699i
$934$	−0.523245			−0.0171211
$935$	−36.5819	+	41.5194i	−1.19636	+	1.35783i
$936$	50.6023			1.65399
$937$	−41.0522	+	41.0522i	−1.34112	+	1.34112i	−0.446169	+	0.894949i	$0.647212\pi$
$937$	−41.0522	+	41.0522i	−1.34112	+	1.34112i	−0.894949	+	0.446169i	$0.852788\pi$
$938$	16.2396	+	6.72666i	0.530241	+	0.219633i
$939$			75.0356i			2.44869i
$940$	−14.5720	+	35.1798i	−0.475285	+	1.14744i
$941$	5.11552	−	2.11892i	0.166761	−	0.0690747i	−0.297741	−	0.954647i	$-0.596233\pi$
$941$	5.11552	−	2.11892i	0.166761	−	0.0690747i	0.464502	+	0.885572i	$0.346233\pi$
$942$	−1.65952	−	4.00644i	−0.0540702	−	0.130537i
$943$	1.83182	+	1.83182i	0.0596521	+	0.0596521i
$944$	−7.30766	−	7.30766i	−0.237844	−	0.237844i
$945$	−61.2567	−	147.887i	−1.99268	−	4.81076i
$946$	−2.09492	+	0.867743i	−0.0681116	+	0.0282128i
$947$	19.2971	−	46.5874i	0.627072	−	1.51389i	−0.216171	−	0.976355i	$-0.569357\pi$
$947$	19.2971	−	46.5874i	0.627072	−	1.51389i	0.843244	−	0.537531i	$-0.180643\pi$
$948$		−	0.794898i		−	0.0258171i
$949$	−44.2045	−	18.3101i	−1.43494	−	0.594371i
$950$	−0.361419	+	0.361419i	−0.0117260	+	0.0117260i
$951$	−59.2880			−1.92255
$952$	26.2143	−	12.8521i	0.849611	−	0.416540i
$953$	−60.5097			−1.96010			−0.980051	−	0.198748i	$-0.936313\pi$
$953$	−60.5097			−1.96010			−0.980051	+	0.198748i	$0.936313\pi$
$954$	−12.0893	+	12.0893i	−0.391407	+	0.391407i
$955$	0.182383	+	0.0755455i	0.00590178	+	0.00244460i
$956$			45.7436i			1.47945i
$957$	43.0165	−	103.851i	1.39053	−	3.35703i
$958$	10.8869	−	4.50948i	0.351738	−	0.145695i
$959$	11.1466	+	26.9102i	0.359942	+	0.868977i
$960$	−23.7752	−	23.7752i	−0.767343	−	0.767343i
$961$	−3.45169	−	3.45169i	−0.111345	−	0.111345i
$962$	−6.10437	−	14.7373i	−0.196813	−	0.475148i
$963$	−57.4782	+	23.8083i	−1.85221	+	0.767210i
$964$	2.03848	−	4.92132i	0.0656549	−	0.158505i
$965$		−	17.7777i		−	0.572284i
$966$	4.24954	+	1.76022i	0.136727	+	0.0566340i
$967$	19.5949	−	19.5949i	0.630130	−	0.630130i	−0.317970	−	0.948101i	$-0.603001\pi$
$967$	19.5949	−	19.5949i	0.630130	−	0.630130i	0.948101	+	0.317970i	$0.103001\pi$
$968$	−31.5314			−1.01346
$969$	−21.0022	−	7.18354i	−0.674687	−	0.230768i
$970$	−12.5217			−0.402047
$971$	−37.4426	+	37.4426i	−1.20159	+	1.20159i	−0.227906	+	0.973683i	$0.573188\pi$
$971$	−37.4426	+	37.4426i	−1.20159	+	1.20159i	−0.973683	+	0.227906i	$0.926812\pi$
$972$	62.7275	+	25.9826i	2.01198	+	0.833391i
$973$		−	40.0675i		−	1.28451i
$974$	−5.20785	+	12.5729i	−0.166870	+	0.402861i
$975$	−9.84800	+	4.07918i	−0.315389	+	0.130638i
$976$	5.50586	+	13.2923i	0.176238	+	0.425477i
$977$	14.0031	+	14.0031i	0.448000	+	0.448000i	0.894689	−	0.446689i	$-0.147397\pi$
$977$	14.0031	+	14.0031i	0.448000	+	0.448000i	−0.446689	+	0.894689i	$0.647397\pi$
$978$	−10.0823	−	10.0823i	−0.322397	−	0.322397i
$979$	18.1133	+	43.7293i	0.578902	+	1.39759i
$980$	55.8801	−	23.1463i	1.78503	−	0.739382i
$981$	−40.1507	+	96.9323i	−1.28191	+	3.09481i
$982$			7.68990i			0.245395i
$983$	−5.23391	−	2.16796i	−0.166936	−	0.0691471i	0.297651	−	0.954675i	$-0.403797\pi$
$983$	−5.23391	−	2.16796i	−0.166936	−	0.0691471i	−0.464586	+	0.885528i	$0.653797\pi$
$984$	12.0254	−	12.0254i	0.383357	−	0.383357i
$985$	5.11430			0.162955
$986$	3.35333	−	9.80397i	0.106792	−	0.312222i
$987$	127.634			4.06263
$988$	9.32611	−	9.32611i	0.296703	−	0.296703i
$989$	0.709798	+	0.294008i	0.0225702	+	0.00934890i
$990$			40.9070i			1.30011i
$991$	13.2281	−	31.9355i	0.420205	−	1.01447i	−0.562081	−	0.827082i	$-0.689999\pi$
$991$	13.2281	−	31.9355i	0.420205	−	1.01447i	0.982287	−	0.187384i	$-0.0600007\pi$
$992$	20.5072	−	8.49438i	0.651106	−	0.269697i
$993$	−37.5556	−	90.6673i	−1.19179	−	2.87724i
$994$	−0.934174	−	0.934174i	−0.0296302	−	0.0296302i
$995$	17.9176	+	17.9176i	0.568025	+	0.568025i
$996$	8.64209	+	20.8638i	0.273835	+	0.661096i
$997$	−47.6629	+	19.7426i	−1.50950	+	0.625255i	−0.975455	−	0.220201i	$-0.929329\pi$
$997$	−47.6629	+	19.7426i	−1.50950	+	0.625255i	−0.534045	+	0.845456i	$0.679329\pi$
$998$	2.91189	−	7.02993i	0.0921743	−	0.222528i
$999$		−	133.152i		−	4.21273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.13	yes	128
17.2	even	8	inner	731.2.m.c.87.13	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.13	✓	128	17.2	even	8	inner
731.2.m.c.689.13	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.286708 + 0.286708i) q^{2} +(-2.99617 - 1.24105i) q^{3} +1.83560i q^{4} +(-0.918391 + 2.21719i) q^{5} +(1.21484 - 0.503205i) q^{6} +(-1.74237 - 4.20646i) q^{7} +(-1.09970 - 1.09970i) q^{8} +(5.31549 + 5.31549i) q^{9} +O(q^{10})\)	\(q+(-0.286708 + 0.286708i) q^{2} +(-2.99617 - 1.24105i) q^{3} +1.83560i q^{4} +(-0.918391 + 2.21719i) q^{5} +(1.21484 - 0.503205i) q^{6} +(-1.74237 - 4.20646i) q^{7} +(-1.09970 - 1.09970i) q^{8} +(5.31549 + 5.31549i) q^{9} +(-0.372376 - 0.898996i) q^{10} +(-5.16669 + 2.14011i) q^{11} +(2.27808 - 5.49976i) q^{12} +4.32837i q^{13} +(1.70558 + 0.706474i) q^{14} +(5.50331 - 5.50331i) q^{15} -3.04061 q^{16} +(-3.09361 - 2.72572i) q^{17} -3.04799 q^{18} +(-1.17381 + 1.17381i) q^{19} +(-4.06987 - 1.68580i) q^{20} +14.7657i q^{21} +(0.867743 - 2.09492i) q^{22} +(-0.709798 + 0.294008i) q^{23} +(1.93009 + 4.65966i) q^{24} +(-0.536960 - 0.536960i) q^{25} +(-1.24098 - 1.24098i) q^{26} +(-5.60614 - 13.5344i) q^{27} +(7.72137 - 3.19830i) q^{28} +(2.37185 - 5.72615i) q^{29} +3.15568i q^{30} +(4.72161 + 1.95575i) q^{31} +(3.07116 - 3.07116i) q^{32} +18.1363 q^{33} +(1.66845 - 0.105478i) q^{34} +10.9267 q^{35} +(-9.75711 + 9.75711i) q^{36} +(8.39726 + 3.47826i) q^{37} -0.673082i q^{38} +(5.37174 - 12.9685i) q^{39} +(3.44819 - 1.42829i) q^{40} +(-1.29038 - 3.11525i) q^{41} +(-4.23343 - 4.23343i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-3.92839 - 9.48396i) q^{44} +(-16.6672 + 6.90377i) q^{45} +(0.119210 - 0.287799i) q^{46} -8.64397i q^{47} +(9.11019 + 3.77356i) q^{48} +(-9.70872 + 9.70872i) q^{49} +0.307902 q^{50} +(5.88623 + 12.0061i) q^{51} -7.94515 q^{52} +(3.96634 - 3.96634i) q^{53} +(5.48775 + 2.27310i) q^{54} -13.4210i q^{55} +(-2.70975 + 6.54191i) q^{56} +(4.97370 - 2.06018i) q^{57} +(0.961704 + 2.32176i) q^{58} +(2.40335 + 2.40335i) q^{59} +(10.1019 + 10.1019i) q^{60} +(-1.81077 - 4.37160i) q^{61} +(-1.91445 + 0.792992i) q^{62} +(13.0979 - 31.6210i) q^{63} -4.32017i q^{64} +(-9.59683 - 3.97514i) q^{65} +(-5.19981 + 5.19981i) q^{66} +9.52146 q^{67} +(5.00332 - 5.67863i) q^{68} +2.49155 q^{69} +(-3.13277 + 3.13277i) q^{70} +(-0.661153 - 0.273859i) q^{71} -11.6909i q^{72} +(-4.23025 + 10.2127i) q^{73} +(-3.40480 + 1.41032i) q^{74} +(0.942428 + 2.27522i) q^{75} +(-2.15465 - 2.15465i) q^{76} +(18.0046 + 18.0046i) q^{77} +(2.17806 + 5.25830i) q^{78} +(0.123367 - 0.0511002i) q^{79} +(2.79247 - 6.74162i) q^{80} +24.9572i q^{81} +(1.26313 + 0.523205i) q^{82} +(-2.68247 + 2.68247i) q^{83} -27.1038 q^{84} +(8.88459 - 4.35586i) q^{85} +0.405466 q^{86} +(-14.2129 + 14.2129i) q^{87} +(8.03526 + 3.32831i) q^{88} -8.46370i q^{89} +(2.79924 - 6.75797i) q^{90} +(18.2071 - 7.54164i) q^{91} +(-0.539680 - 1.30290i) q^{92} +(-11.7195 - 11.7195i) q^{93} +(2.47829 + 2.47829i) q^{94} +(-1.52455 - 3.68058i) q^{95} +(-13.0132 + 5.39024i) q^{96} +(4.92448 - 11.8887i) q^{97} -5.56713i q^{98} +(-38.8393 - 16.0878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more