LMFDB - Embedded newform 572.2.t.a.87.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(87,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("572.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.t (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			87.10
Character	$\chi$	$=$	572.87
Dual form			572.2.t.a.263.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33912 + 0.454709i) q^{2} +(0.665321 + 0.384123i) q^{3} +(1.58648 - 1.21782i) q^{4} +2.62826 q^{5} +(-1.06561 - 0.211859i) q^{6} +(-0.983531 - 1.70353i) q^{7} +(-1.57073 + 2.35219i) q^{8} +(-1.20490 - 2.08695i) q^{9} +O(q^{10})$	\(q+(-1.33912 + 0.454709i) q^{2} +(0.665321 + 0.384123i) q^{3} +(1.58648 - 1.21782i) q^{4} +2.62826 q^{5} +(-1.06561 - 0.211859i) q^{6} +(-0.983531 - 1.70353i) q^{7} +(-1.57073 + 2.35219i) q^{8} +(-1.20490 - 2.08695i) q^{9} +(-3.51955 + 1.19509i) q^{10} +(1.82723 - 2.76789i) q^{11} +(1.52331 - 0.200837i) q^{12} +(2.52266 + 2.57608i) q^{13} +(2.09167 + 1.83400i) q^{14} +(1.74864 + 1.00958i) q^{15} +(1.03383 - 3.86409i) q^{16} +(2.89638 - 1.67223i) q^{17} +(2.56246 + 2.24679i) q^{18} +(-2.73174 - 4.73151i) q^{19} +(4.16968 - 3.20074i) q^{20} -1.51119i q^{21} +(-1.18829 + 4.53740i) q^{22} +(-5.13652 - 2.96557i) q^{23} +(-1.94857 + 0.961608i) q^{24} +1.90775 q^{25} +(-4.54951 - 2.30260i) q^{26} -4.15606i q^{27} +(-3.63494 - 1.50484i) q^{28} +(2.41927 + 1.39676i) q^{29} +(-2.80069 - 0.556821i) q^{30} +7.98457i q^{31} +(0.372613 + 5.64457i) q^{32} +(2.27890 - 1.13966i) q^{33} +(-3.11822 + 3.55632i) q^{34} +(-2.58497 - 4.47731i) q^{35} +(-4.45307 - 1.84355i) q^{36} +(0.00572710 - 0.00991962i) q^{37} +(5.80958 + 5.09390i) q^{38} +(0.688846 + 2.68293i) q^{39} +(-4.12829 + 6.18217i) q^{40} +(-5.65382 - 3.26423i) q^{41} +(0.687151 + 2.02366i) q^{42} +(4.33729 + 7.51240i) q^{43} +(-0.471935 - 6.61644i) q^{44} +(-3.16679 - 5.48504i) q^{45} +(8.22688 + 1.63563i) q^{46} -3.61145i q^{47} +(2.17212 - 2.17374i) q^{48} +(1.56533 - 2.71124i) q^{49} +(-2.55470 + 0.867470i) q^{50} +2.56936 q^{51} +(7.13935 + 1.01475i) q^{52} +12.4169 q^{53} +(1.88980 + 5.56545i) q^{54} +(4.80243 - 7.27474i) q^{55} +(5.55188 + 0.362326i) q^{56} -4.19729i q^{57} +(-3.87481 - 0.770370i) q^{58} +(-0.129956 + 0.0750302i) q^{59} +(4.00365 - 0.527852i) q^{60} +(6.56619 - 3.79099i) q^{61} +(-3.63066 - 10.6923i) q^{62} +(-2.37011 + 4.10515i) q^{63} +(-3.06561 - 7.38932i) q^{64} +(6.63020 + 6.77060i) q^{65} +(-2.53351 + 2.56237i) q^{66} +(8.37159 + 4.83334i) q^{67} +(2.55858 - 6.18022i) q^{68} +(-2.27829 - 3.94611i) q^{69} +(5.49746 + 4.82023i) q^{70} +(-3.21751 + 1.85763i) q^{71} +(6.80147 + 0.443877i) q^{72} +12.5532i q^{73} +(-0.00315872 + 0.0158877i) q^{74} +(1.26926 + 0.732809i) q^{75} +(-10.0960 - 4.17967i) q^{76} +(-6.51231 - 0.390421i) q^{77} +(-2.14240 - 3.27954i) q^{78} +2.12366 q^{79} +(2.71718 - 10.1558i) q^{80} +(-2.01826 + 3.49573i) q^{81} +(9.05541 + 1.80035i) q^{82} +1.17064 q^{83} +(-1.84035 - 2.39747i) q^{84} +(7.61244 - 4.39504i) q^{85} +(-9.22410 - 8.08779i) q^{86} +(1.07306 + 1.85859i) q^{87} +(3.64053 + 8.64561i) q^{88} +(-8.38748 + 14.5275i) q^{89} +(6.73480 + 5.90515i) q^{90} +(1.90730 - 6.83107i) q^{91} +(-11.7605 + 1.55054i) q^{92} +(-3.06706 + 5.31230i) q^{93} +(1.64216 + 4.83616i) q^{94} +(-7.17971 - 12.4356i) q^{95} +(-1.92030 + 3.89858i) q^{96} +(6.41179 + 11.1055i) q^{97} +(-0.863344 + 4.34244i) q^{98} +(-7.97807 - 0.478295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) $ 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9	$ 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) $ 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9 - 4 * q^12 + 8 * q^14 - 14 * q^16 - 26 * q^20 + 112 * q^25 - 14 * q^33 + 12 * q^34 - 6 * q^36 - 4 * q^37 + 40 * q^38 + 54 * q^42 - 16 * q^44 - 48 * q^45 - 40 * q^48 - 52 * q^49 - 32 * q^53 - 18 * q^56 - 6 * q^58 - 52 * q^60 + 16 * q^64 - 84 * q^66 - 12 * q^69 - 68 * q^70 - 4 * q^77 + 28 * q^78 - 44 * q^80 - 40 * q^81 - 38 * q^82 + 120 * q^86 - 14 * q^88 - 64 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.33912	+	0.454709i	−0.946900	+	0.321528i
$2$	−1.33912	+	0.454709i	−0.946900	+	0.321528i
$3$	0.665321	+	0.384123i	0.384123	+	0.221774i	0.679611	−	0.733573i	$-0.262149\pi$
$3$	0.665321	+	0.384123i	0.384123	+	0.221774i	−0.295488	+	0.955347i	$0.595482\pi$
$4$	1.58648	−	1.21782i	0.793240	−	0.608910i
$5$	2.62826			1.17539			0.587697	−	0.809081i	$-0.300035\pi$
$5$	2.62826			1.17539			0.587697	+	0.809081i	$0.300035\pi$
$6$	−1.06561	−	0.211859i	−0.435033	−	0.0864911i
$7$	−0.983531	−	1.70353i	−0.371740	−	0.643872i	0.618094	−	0.786105i	$-0.287905\pi$
$7$	−0.983531	−	1.70353i	−0.371740	−	0.643872i	−0.989833	+	0.142233i	$0.954572\pi$
$8$	−1.57073	+	2.35219i	−0.555337	+	0.831625i
$9$	−1.20490	−	2.08695i	−0.401633	−	0.695649i
$10$	−3.51955	+	1.19509i	−1.11298	+	0.377922i
$11$	1.82723	−	2.76789i	0.550930	−	0.834551i
$11$	1.82723	−	2.76789i	0.550930	−	0.834551i
$12$	1.52331	−	0.200837i	0.439742	−	0.0579767i
$13$	2.52266	+	2.57608i	0.699660	+	0.714476i
$13$	2.52266	+	2.57608i	0.699660	+	0.714476i
$14$	2.09167	+	1.83400i	0.559023	+	0.490158i
$15$	1.74864	+	1.00958i	0.451496	+	0.260671i
$16$	1.03383	−	3.86409i	0.258458	−	0.966022i
$17$	2.89638	−	1.67223i	0.702475	−	0.405574i	−0.105793	−	0.994388i	$-0.533738\pi$
$17$	2.89638	−	1.67223i	0.702475	−	0.405574i	0.808269	+	0.588814i	$0.200405\pi$
$18$	2.56246	+	2.24679i	0.603977	+	0.529574i
$19$	−2.73174	−	4.73151i	−0.626703	−	1.08548i	−0.988209	−	0.153112i	$-0.951070\pi$
$19$	−2.73174	−	4.73151i	−0.626703	−	1.08548i	0.361506	−	0.932370i	$-0.382263\pi$
$20$	4.16968	−	3.20074i	0.932368	−	0.715708i
$21$		−	1.51119i		−	0.329768i
$22$	−1.18829	+	4.53740i	−0.253344	+	0.967376i
$23$	−5.13652	−	2.96557i	−1.07104	−	0.618364i	−0.142573	−	0.989784i	$-0.545538\pi$
$23$	−5.13652	−	2.96557i	−1.07104	−	0.618364i	−0.928465	+	0.371420i	$0.878871\pi$
$24$	−1.94857	+	0.961608i	−0.397750	+	0.196287i
$25$	1.90775			0.381549
$26$	−4.54951	−	2.30260i	−0.892232	−	0.451577i
$27$		−	4.15606i		−	0.799833i
$28$	−3.63494	−	1.50484i	−0.686938	−	0.284389i
$29$	2.41927	+	1.39676i	0.449246	+	0.259372i	0.707512	−	0.706701i	$-0.249818\pi$
$29$	2.41927	+	1.39676i	0.449246	+	0.259372i	−0.258266	+	0.966074i	$0.583151\pi$
$30$	−2.80069	−	0.556821i	−0.511334	−	0.101661i
$31$			7.98457i			1.43407i	0.697037	+	0.717036i	$0.254501\pi$
$31$			7.98457i			1.43407i	−0.697037	+	0.717036i	$0.745499\pi$
$32$	0.372613	+	5.64457i	0.0658693	+	0.997828i
$33$	2.27890	−	1.13966i	0.396706	−	0.198389i
$34$	−3.11822	+	3.55632i	−0.534771	+	0.609904i
$35$	−2.58497	−	4.47731i	−0.436940	−	0.756803i
$36$	−4.45307	−	1.84355i	−0.742178	−	0.307258i
$37$	0.00572710	−	0.00991962i	0.000941529	−	0.00163078i	−0.865554	−	0.500815i	$-0.833034\pi$
$37$	0.00572710	−	0.00991962i	0.000941529	−	0.00163078i	0.866496	+	0.499184i	$0.166367\pi$
$38$	5.80958	+	5.09390i	0.942438	+	0.826340i
$39$	0.688846	+	2.68293i	0.110304	+	0.429613i
$40$	−4.12829	+	6.18217i	−0.652740	+	0.977487i
$41$	−5.65382	−	3.26423i	−0.882978	−	0.509788i	−0.0113390	−	0.999936i	$-0.503609\pi$
$41$	−5.65382	−	3.26423i	−0.882978	−	0.509788i	−0.871639	+	0.490148i	$0.836943\pi$
$42$	0.687151	+	2.02366i	0.106030	+	0.312257i
$43$	4.33729	+	7.51240i	0.661430	+	1.14563i	0.980240	+	0.197812i	$0.0633835\pi$
$43$	4.33729	+	7.51240i	0.661430	+	1.14563i	−0.318810	+	0.947819i	$0.603283\pi$
$44$	−0.471935	−	6.61644i	−0.0711469	−	0.997466i
$45$	−3.16679	−	5.48504i	−0.472077	−	0.817661i
$46$	8.22688	+	1.63563i	1.21299	+	0.241160i
$47$		−	3.61145i		−	0.526784i	−0.964689	−	0.263392i	$-0.915159\pi$
$47$		−	3.61145i		−	0.526784i	0.964689	−	0.263392i	$-0.0848413\pi$
$48$	2.17212	−	2.17374i	0.313518	−	0.313752i
$49$	1.56533	−	2.71124i	0.223619	−	0.387320i
$50$	−2.55470	+	0.867470i	−0.361289	+	0.122679i
$51$	2.56936			0.359783
$52$	7.13935	+	1.01475i	0.990049	+	0.140721i
$53$	12.4169			1.70560			0.852798	−	0.522241i	$-0.174904\pi$
$53$	12.4169			1.70560			0.852798	+	0.522241i	$0.174904\pi$
$54$	1.88980	+	5.56545i	0.257169	+	0.757362i
$55$	4.80243	−	7.27474i	0.647559	−	0.980926i
$56$	5.55188	+	0.362326i	0.741901	+	0.0484179i
$57$		−	4.19729i		−	0.555945i
$58$	−3.87481	−	0.770370i	−0.508787	−	0.101155i
$59$	−0.129956	+	0.0750302i	−0.0169188	+	0.00976810i	−0.508436	−	0.861100i	$-0.669776\pi$
$59$	−0.129956	+	0.0750302i	−0.0169188	+	0.00976810i	0.491517	+	0.870868i	$0.336443\pi$
$60$	4.00365	−	0.527852i	0.516869	−	0.0681454i
$61$	6.56619	−	3.79099i	0.840714	−	0.485387i	−0.0167926	−	0.999859i	$-0.505346\pi$
$61$	6.56619	−	3.79099i	0.840714	−	0.485387i	0.857507	+	0.514472i	$0.172012\pi$
$62$	−3.63066	−	10.6923i	−0.461094	−	1.35792i
$63$	−2.37011	+	4.10515i	−0.298606	+	0.517200i
$64$	−3.06561	−	7.38932i	−0.383201	−	0.923665i
$65$	6.63020	+	6.77060i	0.822376	+	0.839790i
$66$	−2.53351	+	2.56237i	−0.311854	+	0.315407i
$67$	8.37159	+	4.83334i	1.02275	+	0.590487i	0.914900	−	0.403680i	$-0.132269\pi$
$67$	8.37159	+	4.83334i	1.02275	+	0.590487i	0.107853	+	0.994167i	$0.465602\pi$
$68$	2.55858	−	6.18022i	0.310273	−	0.749462i
$69$	−2.27829	−	3.94611i	−0.274274	−	0.475056i
$70$	5.49746	+	4.82023i	0.657072	+	0.576128i
$71$	−3.21751	+	1.85763i	−0.381848	+	0.220460i	−0.678622	−	0.734488i	$-0.737423\pi$
$71$	−3.21751	+	1.85763i	−0.381848	+	0.220460i	0.296774	+	0.954948i	$0.404089\pi$
$72$	6.80147	+	0.443877i	0.801561	+	0.0523114i
$73$			12.5532i			1.46924i	0.678478	+	0.734621i	$0.262640\pi$
$73$			12.5532i			1.46924i	−0.678478	+	0.734621i	$0.737360\pi$
$74$	−0.00315872	+	0.0158877i	−0.000367194	+	0.00184691i
$75$	1.26926	+	0.732809i	0.146562	+	0.0846175i
$76$	−10.0960	−	4.17967i	−1.15809	−	0.479442i
$77$	−6.51231	−	0.390421i	−0.742147	−	0.0444926i
$78$	−2.14240	−	3.27954i	−0.242579	−	0.371335i
$79$	2.12366			0.238931			0.119465	−	0.992838i	$-0.461882\pi$
$79$	2.12366			0.238931			0.119465	+	0.992838i	$0.461882\pi$
$80$	2.71718	−	10.1558i	0.303790	−	1.13546i
$81$	−2.01826	+	3.49573i	−0.224251	+	0.388414i
$82$	9.05541	+	1.80035i	1.00000	+	0.198816i
$83$	1.17064			0.128494			0.0642471	−	0.997934i	$-0.479535\pi$
$83$	1.17064			0.128494			0.0642471	+	0.997934i	$0.479535\pi$
$84$	−1.84035	−	2.39747i	−0.200799	−	0.261585i
$85$	7.61244	−	4.39504i	0.825685	−	0.476709i
$86$	−9.22410	−	8.08779i	−0.994660	−	0.872129i
$87$	1.07306	+	1.85859i	0.115044	+	0.199262i
$88$	3.64053	+	8.64561i	0.388082	+	0.921625i
$89$	−8.38748	+	14.5275i	−0.889071	+	1.53992i	−0.0480964	+	0.998843i	$0.515315\pi$
$89$	−8.38748	+	14.5275i	−0.889071	+	1.53992i	−0.840975	+	0.541074i	$0.818018\pi$
$90$	6.73480	+	5.90515i	0.709910	+	0.622457i
$91$	1.90730	−	6.83107i	0.199940	−	0.716091i
$92$	−11.7605	+	1.55054i	−1.22612	+	0.161655i
$93$	−3.06706	+	5.31230i	−0.318039	+	0.550860i
$94$	1.64216	+	4.83616i	0.169376	+	0.498812i
$95$	−7.17971	−	12.4356i	−0.736623	−	1.27587i
$96$	−1.92030	+	3.89858i	−0.195990	+	0.397897i
$97$	6.41179	+	11.1055i	0.651018	+	1.12760i	0.982876	+	0.184267i	$0.0589912\pi$
$97$	6.41179	+	11.1055i	0.651018	+	1.12760i	−0.331858	+	0.943329i	$0.607675\pi$
$98$	−0.863344	+	4.34244i	−0.0872109	+	0.438653i
$99$	−7.97807	−	0.478295i	−0.801826	−	0.0480704i
$100$	3.02660	−	2.32329i	0.302660	−	0.232329i
$101$	2.07597	+	1.19856i	0.206567	+	0.119261i	0.599715	−	0.800214i	$-0.295281\pi$
$101$	2.07597	+	1.19856i	0.206567	+	0.119261i	−0.393148	+	0.919475i	$0.628614\pi$
$102$	−3.44068	+	1.16831i	−0.340678	+	0.115680i
$103$			4.48270i			0.441694i	0.975308	+	0.220847i	$0.0708821\pi$
$103$			4.48270i			0.441694i	−0.975308	+	0.220847i	$0.929118\pi$
$104$	−10.0219	+	1.88745i	−0.982723	+	0.185080i
$105$		−	3.97179i		−	0.387607i
$106$	−16.6277	+	5.64609i	−1.61503	+	0.548397i
$107$	4.81748	−	8.34412i	0.465723	−	0.806657i	−0.533510	−	0.845793i	$-0.679128\pi$
$107$	4.81748	−	8.34412i	0.465723	−	0.806657i	0.999234	+	0.0391369i	$0.0124608\pi$
$108$	−5.06133	−	6.59350i	−0.487026	−	0.634460i
$109$		−	0.709194i		−	0.0679285i	−0.999423	−	0.0339642i	$-0.989187\pi$
$109$		−	0.709194i		−	0.0679285i	0.999423	−	0.0339642i	$-0.0108132\pi$
$110$	−3.12313	+	11.9255i	−0.297779	+	1.13705i
$111$	0.00762071	−	0.00439982i	0.000723326	−	0.000417612i
$112$	−7.59938	+	2.03929i	−0.718074	+	0.192695i
$113$	−3.39246	−	5.87592i	−0.319136	−	0.552760i	0.661172	−	0.750234i	$-0.270059\pi$
$113$	−3.39246	−	5.87592i	−0.319136	−	0.552760i	−0.980308	+	0.197474i	$0.936726\pi$
$114$	1.90855	+	5.62067i	0.178752	+	0.526424i
$115$	−13.5001	−	7.79429i	−1.25889	−	0.726821i
$116$	5.53912	−	0.730292i	0.514294	−	0.0678059i
$117$	2.33659	−	8.36857i	0.216018	−	0.773675i
$118$	0.139910	−	0.159567i	0.0128797	−	0.0146893i
$119$	−5.69736	−	3.28937i	−0.522276	−	0.301536i
$120$	−5.12135	+	2.52735i	−0.467513	+	0.230715i
$121$	−4.32247	−	10.1151i	−0.392952	−	0.919559i
$122$	−7.06911	+	8.06229i	−0.640007	+	0.729926i
$123$	−2.50774	−	4.34352i	−0.226115	−	0.391642i
$124$	9.72376	+	12.6674i	0.873220	+	1.13756i
$125$	−8.12724			−0.726923
$126$	1.30721	−	6.57500i	0.116455	−	0.585747i
$127$	−5.12402	+	8.87506i	−0.454683	+	0.787534i	−0.998670	−	0.0515598i	$-0.983581\pi$
$127$	−5.12402	+	8.87506i	−0.454683	+	0.787534i	0.543987	+	0.839094i	$0.316914\pi$
$128$	7.46521	+	8.50122i	0.659837	+	0.751408i
$129$			6.66421i			0.586751i
$130$	−11.9573	−	6.05183i	−1.04872	−	0.530781i
$131$	−2.21738			−0.193733			−0.0968667	−	0.995297i	$-0.530882\pi$
$131$	−2.21738			−0.193733			−0.0968667	+	0.995297i	$0.530882\pi$
$132$	2.22754	−	4.58334i	0.193882	−	0.398928i
$133$	−5.37349	+	9.30716i	−0.465941	+	0.807033i
$134$	−13.4083	−	2.66578i	−1.15830	−	0.230288i
$135$		−	10.9232i		−	0.940119i
$136$	−0.616037	+	9.43946i	−0.0528248	+	0.809427i
$137$	−8.94887	−	15.4999i	−0.764554	−	1.32425i	−0.940482	−	0.339843i	$-0.889626\pi$
$137$	−8.94887	−	15.4999i	−0.764554	−	1.32425i	0.175929	−	0.984403i	$-0.443707\pi$
$138$	4.84523	+	4.24835i	0.412453	+	0.361644i
$139$	3.31185	+	5.73629i	0.280907	+	0.486546i	0.971608	−	0.236595i	$-0.0760313\pi$
$139$	3.31185	+	5.73629i	0.280907	+	0.486546i	−0.690701	+	0.723140i	$0.742698\pi$
$140$	−9.55356	−	3.95512i	−0.807423	−	0.334269i
$141$	1.38724	−	2.40277i	0.116827	−	0.202350i
$142$	3.46395	−	3.95062i	0.290688	−	0.331529i
$143$	11.7398	−	2.27537i	0.981731	−	0.190276i
$144$	−9.30981	+	2.49829i	−0.775818	+	0.208191i
$145$	6.35846	+	3.67106i	0.528041	+	0.304865i
$146$	−5.70806	−	16.8102i	−0.472402	−	1.39122i
$147$	2.08290	−	1.20256i	0.171795	−	0.0991857i
$148$	−0.00299439	−	0.0227118i	−0.000246137	−	0.00186690i
$149$	−10.3386	+	5.96898i	−0.846969	+	0.488998i	−0.859627	−	0.510922i	$-0.829304\pi$
$149$	−10.3386	+	5.96898i	−0.846969	+	0.488998i	0.0126580	+	0.999920i	$0.495971\pi$
$150$	−2.03291	−	0.404173i	−0.165986	−	0.0330006i
$151$	−5.85664			−0.476606			−0.238303	−	0.971191i	$-0.576591\pi$
$151$	−5.85664			−0.476606			−0.238303	+	0.971191i	$0.576591\pi$
$152$	15.4202	+	1.00635i	1.25075	+	0.0816261i
$153$	−6.97969	−	4.02973i	−0.564275	−	0.325784i
$154$	8.89829	−	2.43839i	0.717045	−	0.196491i
$155$			20.9855i			1.68560i
$156$	4.36017	+	3.41752i	0.349093	+	0.273621i
$157$	13.3026			1.06167			0.530833	−	0.847477i	$-0.321879\pi$
$157$	13.3026			1.06167			0.530833	+	0.847477i	$0.321879\pi$
$158$	−2.84384	+	0.965649i	−0.226244	+	0.0768229i
$159$	8.26124	+	4.76963i	0.655159	+	0.378256i
$160$	0.979324	+	14.8354i	0.0774223	+	1.17284i
$161$			11.6669i			0.919482i
$162$	1.11315	−	5.59892i	0.0874573	−	0.439892i
$163$	−19.4392	+	11.2232i	−1.52260	+	0.879073i	−0.522955	+	0.852360i	$0.675170\pi$
$163$	−19.4392	+	11.2232i	−1.52260	+	0.879073i	−0.999643	+	0.0267123i	$0.991496\pi$
$164$	−12.9449	+	1.70669i	−1.01083	+	0.133270i
$165$	5.98955	−	2.99531i	0.466286	−	0.233185i
$166$	−1.56762	+	0.532299i	−0.121671	+	0.0413145i
$167$	7.81219	−	13.5311i	0.604525	−	1.04707i	−0.387601	−	0.921827i	$-0.626696\pi$
$167$	7.81219	−	13.5311i	0.604525	−	1.04707i	0.992126	−	0.125241i	$-0.0399705\pi$
$168$	3.55460	+	2.37367i	0.274244	+	0.183132i
$169$	−0.272372	+	12.9971i	−0.0209517	+	0.999780i
$170$	−8.19549	+	9.34693i	−0.628566	+	0.716877i
$171$	−6.58293	+	11.4020i	−0.503409	+	0.871931i
$172$	16.0298	+	6.63624i	1.22226	+	0.506008i
$173$	−19.1684	+	11.0669i	−1.45735	+	0.841399i	−0.998880	−	0.0473125i	$-0.984934\pi$
$173$	−19.1684	+	11.0669i	−1.45735	+	0.841399i	−0.458466	+	0.888712i	$0.651601\pi$
$174$	−2.28207	−	2.00095i	−0.173003	−	0.151691i
$175$	−1.87633	−	3.24989i	−0.141837	−	0.245669i
$176$	−8.80634	−	9.92211i	−0.663803	−	0.747907i
$177$	−0.115283			−0.00866522
$178$	4.62603	−	23.2680i	0.346735	−	1.74401i
$179$	−2.60826	−	1.50588i	−0.194951	−	0.112555i	0.399347	−	0.916800i	$-0.369237\pi$
$179$	−2.60826	−	1.50588i	−0.194951	−	0.112555i	−0.594298	+	0.804245i	$0.702570\pi$
$180$	−11.7038	−	4.84532i	−0.872351	−	0.361149i
$181$	9.15088			0.680180			0.340090	−	0.940393i	$-0.389542\pi$
$181$	9.15088			0.680180			0.340090	+	0.940393i	$0.389542\pi$
$182$	0.552044	+	10.0149i	0.0409202	+	0.742352i
$183$	5.82483			0.430584
$184$	15.0437	−	7.42396i	1.10903	−	0.547302i
$185$	0.0150523	−	0.0260713i	0.00110667	−	0.00191680i
$186$	1.69160	−	8.50842i	0.124034	−	0.623868i
$187$	0.663804	−	11.0724i	0.0485422	−	0.809695i
$188$	−4.39809	−	5.72949i	−0.320764	−	0.417866i
$189$	−7.07995	+	4.08761i	−0.514990	+	0.297330i
$190$	15.2691	+	13.3881i	1.10774	+	0.971275i
$191$	9.49924	−	5.48439i	0.687341	−	0.396836i	−0.115274	−	0.993334i	$-0.536775\pi$
$191$	9.49924	−	5.48439i	0.687341	−	0.396836i	0.802615	+	0.596497i	$0.203441\pi$
$192$	0.798794	−	6.09384i	0.0576480	−	0.439785i
$193$	−20.5207	−	11.8476i	−1.47711	−	0.852811i	−0.477446	−	0.878661i	$-0.658438\pi$
$193$	−20.5207	−	11.8476i	−1.47711	−	0.852811i	−0.999666	+	0.0258498i	$0.991771\pi$
$194$	−13.6359	−	11.9561i	−0.979003	−	0.858401i
$195$	1.81047	+	7.05144i	0.129650	+	0.504964i
$196$	−0.818429	−	6.20762i	−0.0584592	−	0.443401i
$197$	−2.91394	−	1.68237i	−0.207610	−	0.119864i	0.392590	−	0.919714i	$-0.371579\pi$
$197$	−2.91394	−	1.68237i	−0.207610	−	0.119864i	−0.600200	+	0.799850i	$0.704912\pi$
$198$	10.9011	−	2.98721i	0.774705	−	0.212292i
$199$	9.08952	−	5.24784i	0.644339	−	0.372009i	−0.141945	−	0.989875i	$-0.545336\pi$
$199$	9.08952	−	5.24784i	0.644339	−	0.372009i	0.786284	+	0.617865i	$0.212002\pi$
$200$	−2.99656	+	4.48738i	−0.211888	+	0.317306i
$201$	3.71320	+	6.43145i	0.261909	+	0.453639i
$202$	−3.32497	−	0.661054i	−0.233944	−	0.0465116i
$203$		−	5.49504i		−	0.385676i
$204$	4.07624	−	3.12902i	0.285394	−	0.219075i
$205$	−14.8597	−	8.57925i	−1.03785	−	0.599201i
$206$	−2.03833	−	6.00287i	−0.142017	−	0.418240i
$207$			14.2928i			0.993422i
$208$	12.5622	−	7.08455i	0.871033	−	0.491225i
$209$	−18.0878	−	1.08439i	−1.25116	−	0.0750085i
$210$	1.80601	+	5.31870i	0.124627	+	0.367025i
$211$	−3.05789	+	5.29642i	−0.210514	+	0.364620i	−0.951875	−	0.306485i	$-0.900847\pi$
$211$	−3.05789	+	5.29642i	−0.210514	+	0.364620i	0.741362	+	0.671106i	$0.234180\pi$
$212$	19.6992	−	15.1216i	1.35295	−	1.03855i
$213$	−2.85423			−0.195569
$214$	−2.65703	+	13.3643i	−0.181631	+	0.913566i
$215$	11.3995	+	19.7445i	0.777440	+	1.34657i
$216$	9.77584	+	6.52805i	0.665162	+	0.444177i
$217$	13.6019	−	7.85307i	0.923358	−	0.533101i
$218$	0.322477	+	0.949695i	0.0218409	+	0.0643215i
$219$	−4.82198	+	8.35191i	−0.325839	+	0.564370i
$220$	−1.24037	−	17.3897i	−0.0836256	−	1.17241i
$221$	11.6144	+	3.24285i	0.781267	+	0.218138i
$222$	−0.00820440	+	0.00935709i	−0.000550643	+	0.000628007i
$223$	16.6720	+	9.62560i	1.11644	+	0.644578i	0.940490	−	0.339821i	$-0.110366\pi$
$223$	16.6720	+	9.62560i	1.11644	+	0.644578i	0.175952	+	0.984399i	$0.443700\pi$
$224$	9.24919	−	6.18636i	0.617987	−	0.413344i
$225$	−2.29864	−	3.98136i	−0.153243	−	0.265424i
$226$	7.21475	+	6.32597i	0.479918	+	0.420797i
$227$	10.5657	+	18.3004i	0.701273	+	1.21464i	0.968020	+	0.250874i	$0.0807180\pi$
$227$	10.5657	+	18.3004i	0.701273	+	1.21464i	−0.266746	+	0.963767i	$0.585949\pi$
$228$	−5.11154	−	6.65892i	−0.338520	−	0.440998i
$229$	−1.89921			−0.125503			−0.0627516	−	0.998029i	$-0.519988\pi$
$229$	−1.89921			−0.125503			−0.0627516	+	0.998029i	$0.519988\pi$
$230$	21.6224	+	4.29886i	1.42574	+	0.283458i
$231$	−4.18281	−	2.76128i	−0.275208	−	0.181679i
$232$	−7.08547	+	3.49664i	−0.465184	+	0.229565i
$233$		−	19.5170i		−	1.27860i	−0.768956	−	0.639302i	$-0.779223\pi$
$233$		−	19.5170i		−	1.27860i	0.768956	−	0.639302i	$-0.220777\pi$
$234$	0.676296	+	12.2690i	0.0442108	+	0.802048i
$235$		−	9.49183i		−	0.619179i
$236$	−0.114799	+	0.277297i	−0.00747281	+	0.0180505i
$237$	1.41292	+	0.815748i	0.0917788	+	0.0529885i
$238$	9.12515	+	1.81422i	0.591495	+	0.117598i
$239$	9.06814			0.586569			0.293284	−	0.956025i	$-0.405252\pi$
$239$	9.06814			0.586569			0.293284	+	0.956025i	$0.405252\pi$
$240$	5.70888	−	5.71315i	0.368507	−	0.368782i
$241$	−13.0339	+	7.52514i	−0.839588	+	0.484737i	−0.857124	−	0.515110i	$-0.827751\pi$
$241$	−13.0339	+	7.52514i	−0.839588	+	0.484737i	0.0175359	+	0.999846i	$0.494418\pi$
$242$	10.3878	+	11.5799i	0.667750	+	0.744385i
$243$	−13.4833	+	7.78460i	−0.864956	+	0.499383i
$244$	5.80038	−	14.0108i	0.371331	−	0.896947i
$245$	4.11411	−	7.12584i	0.262841	−	0.455253i
$246$	5.33320	+	4.67621i	0.340032	+	0.298144i
$247$	5.29749	−	18.9732i	0.337071	−	1.20723i
$248$	−18.7812	−	12.5416i	−1.19261	−	0.796393i
$249$	0.778849	+	0.449669i	0.0493576	+	0.0284966i
$250$	10.8833	−	3.69553i	0.688323	−	0.233726i
$251$	−11.0650	+	6.38838i	−0.698417	+	0.403231i	−0.806758	−	0.590883i	$-0.798780\pi$
$251$	−11.0650	+	6.38838i	−0.698417	+	0.403231i	0.108341	+	0.994114i	$0.465446\pi$
$252$	1.23920	+	9.39910i	0.0780624	+	0.592088i
$253$	−17.5940	+	8.79856i	−1.10612	+	0.553161i
$254$	2.82610	−	14.2147i	0.177325	−	0.891909i
$255$	6.75295			0.422886
$256$	−13.8624	−	7.98964i	−0.866399	−	0.499352i
$257$	−2.91607	+	5.05079i	−0.181900	+	0.315059i	−0.942527	−	0.334129i	$-0.891558\pi$
$257$	−2.91607	+	5.05079i	−0.181900	+	0.315059i	0.760628	+	0.649188i	$0.224891\pi$
$258$	−3.03028	−	8.92417i	−0.188657	−	0.555594i
$259$	−0.0225311			−0.00140001
$260$	18.7641	+	2.66703i	1.16370	+	0.165402i
$261$		−	6.73184i		−	0.416690i
$262$	2.96934	−	1.00826i	0.183446	−	0.0622907i
$263$	−8.13518	+	14.0905i	−0.501636	+	0.868860i	0.498362	+	0.866969i	$0.333935\pi$
$263$	−8.13518	+	14.0905i	−0.501636	+	0.868860i	−0.999998	+	0.00189068i	$0.999398\pi$
$264$	−0.898855	+	7.15051i	−0.0553207	+	0.440084i
$265$	32.6349			2.00475
$266$	2.96369	−	14.9068i	0.181716	−	0.913993i
$267$	−11.1607	+	6.44365i	−0.683026	+	0.394345i
$268$	19.1675	−	2.52709i	1.17084	−	0.154367i
$269$	−7.89014	−	13.6661i	−0.481070	−	0.833238i	0.518694	−	0.854960i	$-0.326418\pi$
$269$	−7.89014	−	13.6661i	−0.481070	−	0.833238i	−0.999764	+	0.0217221i	$0.993085\pi$
$270$	4.96688	+	14.6275i	0.302274	+	0.890199i
$271$	−8.09981	+	14.0293i	−0.492028	+	0.852218i	−0.999958	−	0.00918065i	$-0.997078\pi$
$271$	−8.09981	+	14.0293i	−0.492028	+	0.852218i	0.507930	+	0.861399i	$0.330411\pi$
$272$	−3.46726	−	12.9207i	−0.210234	−	0.783431i
$273$	3.89294	−	3.81221i	0.235611	−	0.230726i
$274$	19.0315	+	16.6871i	1.14974	+	1.00810i
$275$	3.48589	−	5.28044i	0.210207	−	0.318422i
$276$	−8.42011	−	3.48588i	−0.506831	−	0.209825i
$277$	−5.93496	+	3.42655i	−0.356597	+	0.205881i	−0.667587	−	0.744532i	$-0.732673\pi$
$277$	−5.93496	+	3.42655i	−0.356597	+	0.205881i	0.310990	+	0.950413i	$0.399339\pi$
$278$	−7.04330	−	6.17564i	−0.422429	−	0.370391i
$279$	16.6634	−	9.62060i	0.997610	−	0.575970i
$280$	14.5918	+	0.952288i	0.872026	+	0.0569101i
$281$			25.4766i			1.51981i	0.650037	+	0.759903i	$0.274753\pi$
$281$			25.4766i			1.51981i	−0.650037	+	0.759903i	$0.725247\pi$
$282$	−0.765119	+	3.84839i	−0.0455621	+	0.229168i
$283$	3.17740	−	5.50342i	0.188877	−	0.327144i	−0.755999	−	0.654572i	$-0.772849\pi$
$283$	3.17740	−	5.50342i	0.188877	−	0.327144i	0.944876	+	0.327428i	$0.106182\pi$
$284$	−2.84225	+	6.86544i	−0.168657	+	0.407389i
$285$		−	11.0316i		−	0.653454i
$286$	−14.6863	+	8.38518i	−0.868422	+	0.495826i
$287$			12.8419i			0.758033i
$288$	11.3310	−	7.57876i	0.667683	−	0.446583i
$289$	−2.90732	+	5.03563i	−0.171019	+	0.296213i
$290$	−10.1840	−	2.02473i	−0.598025	−	0.118896i
$291$			9.85166i			0.577515i
$292$	15.2875	+	19.9154i	0.894635	+	1.16546i
$293$	6.65732	−	3.84361i	0.388925	−	0.224546i	−0.292769	−	0.956183i	$-0.594577\pi$
$293$	6.65732	−	3.84361i	0.388925	−	0.224546i	0.681694	+	0.731637i	$0.261243\pi$
$294$	−2.24243	+	2.55749i	−0.130781	+	0.149156i
$295$	−0.341558	+	0.197199i	−0.0198863	+	0.0114814i
$296$	0.0143371	+	0.0290523i	0.000833329	+	0.00168863i
$297$	−11.5035	−	7.59406i	−0.667502	−	0.440652i
$298$	11.1304	−	12.6942i	0.644769	−	0.735356i
$299$	−5.31814	−	20.7132i	−0.307556	−	1.19788i
$300$	2.90609	−	0.383146i	0.167783	−	0.0221210i
$301$	8.53171	−	14.7774i	0.491760	−	0.851752i
$302$	7.84273	−	2.66307i	0.451299	−	0.153242i
$303$	0.920790	+	1.59485i	0.0528980	+	0.0916220i
$304$	−21.1071	+	5.66409i	−1.21058	+	0.324858i
$305$	17.2576	−	9.96371i	0.988170	−	0.570520i
$306$	11.1790	+	2.22255i	0.639060	+	0.127055i
$307$	6.72549			0.383844			0.191922	−	0.981410i	$-0.438528\pi$
$307$	6.72549			0.383844			0.191922	+	0.981410i	$0.438528\pi$
$308$	−10.8071	+	7.31143i	−0.615792	+	0.416607i
$309$	−1.72191	+	2.98244i	−0.0979560	+	0.169665i
$310$	−9.54231	−	28.1021i	−0.541967	−	1.59609i
$311$		−	11.9153i		−	0.675652i	−0.941209	−	0.337826i	$-0.890308\pi$
$311$		−	11.9153i		−	0.675652i	0.941209	−	0.337826i	$-0.109692\pi$
$312$	−7.39276	−	2.59386i	−0.418533	−	0.146849i
$313$	24.4836			1.38390			0.691948	−	0.721947i	$-0.256753\pi$
$313$	24.4836			1.38390			0.691948	+	0.721947i	$0.256753\pi$
$314$	−17.8138	+	6.04883i	−1.00529	+	0.341355i
$315$	−6.22926	+	10.7894i	−0.350979	+	0.607914i
$316$	3.36915	−	2.58624i	0.189529	−	0.145487i
$317$	13.1864			0.740621			0.370311	−	0.928908i	$-0.379251\pi$
$317$	13.1864			0.740621			0.370311	+	0.928908i	$0.379251\pi$
$318$	−13.2316	−	2.63064i	−0.741990	−	0.147519i
$319$	8.28664	−	4.14406i	0.463963	−	0.232023i
$320$	−8.05722	−	19.4210i	−0.450412	−	1.08567i
$321$	6.41034	−	3.70101i	0.357790	−	0.206570i
$322$	−5.30505	−	15.6234i	−0.295639	−	0.870658i
$323$	−15.8243	−	9.13616i	−0.880487	−	0.508350i
$324$	1.05524	+	8.00377i	0.0586244	+	0.444654i
$325$	4.81260	+	4.91451i	0.266955	+	0.272608i
$326$	20.9281	−	23.8685i	1.15910	−	1.32195i
$327$	0.272418	−	0.471842i	0.0150647	−	0.0260929i
$328$	16.5587	−	8.17163i	0.914303	−	0.451203i
$329$	−6.15220	+	3.55197i	−0.339182	+	0.195827i
$330$	−6.65873	+	6.73458i	−0.366551	+	0.370727i
$331$	−21.9733	+	12.6863i	−1.20776	+	0.697303i	−0.962270	−	0.272096i	$-0.912283\pi$
$331$	−21.9733	+	12.6863i	−1.20776	+	0.697303i	−0.245493	+	0.969398i	$0.578950\pi$
$332$	1.85719	−	1.42562i	0.101927	−	0.0782413i
$333$	−0.0276023			−0.00151260
$334$	−4.30873	+	21.6720i	−0.235763	+	1.18584i
$335$	22.0027	+	12.7033i	1.20214	+	0.694054i
$336$	−5.83936	−	1.56231i	−0.318563	−	0.0852312i
$337$		−	34.2467i		−	1.86554i	−0.360474	−	0.932769i	$-0.617385\pi$
$337$		−	34.2467i		−	1.86554i	0.360474	−	0.932769i	$-0.382615\pi$
$338$	−5.54518	−	17.5286i	−0.301618	−	0.953429i
$339$		−	5.21249i		−	0.283104i
$340$	6.72461	−	16.2432i	0.364693	−	0.880912i
$341$	22.1004	+	14.5896i	1.19681	+	0.790073i
$342$	3.63075	−	18.2619i	0.196328	−	0.987491i
$343$	−19.9276			−1.07599
$344$	−24.4833	−	1.59783i	−1.32005	−	0.0861491i
$345$	−5.98793	−	10.3714i	−0.322379	−	0.558377i
$346$	20.6366	−	23.5359i	1.10943	−	1.26530i
$347$	10.4971	+	18.1815i	0.563513	+	0.976033i	0.997186	+	0.0749628i	$0.0238838\pi$
$347$	10.4971	+	18.1815i	0.563513	+	0.976033i	−0.433674	+	0.901070i	$0.642783\pi$
$348$	3.96581	+	1.64183i	0.212590	+	0.0880111i
$349$	−8.72799	−	5.03911i	−0.467198	−	0.269737i	0.247868	−	0.968794i	$-0.420270\pi$
$349$	−8.72799	−	5.03911i	−0.467198	−	0.269737i	−0.715066	+	0.699057i	$0.753603\pi$
$350$	3.99038	+	3.49881i	0.213295	+	0.187019i
$351$	10.7063	−	10.4843i	0.571462	−	0.559611i
$352$	16.3044	+	9.28256i	0.869028	+	0.494762i
$353$	12.6725	−	21.9494i	0.674488	−	1.16825i	−0.302130	−	0.953267i	$-0.597698\pi$
$353$	12.6725	−	21.9494i	0.674488	−	1.16825i	0.976618	−	0.214981i	$-0.0689690\pi$
$354$	0.154378	−	0.0524204i	0.00820510	−	0.00278611i
$355$	−8.45645	+	4.88233i	−0.448822	+	0.259127i
$356$	4.38536	+	33.2621i	0.232424	+	1.76289i
$357$	−2.52705	−	4.37697i	−0.133745	−	0.231654i
$358$	4.17751	+	0.830553i	0.220788	+	0.0438961i
$359$	3.77885			0.199440			0.0997199	−	0.995016i	$-0.468205\pi$
$359$	3.77885			0.199440			0.0997199	+	0.995016i	$0.468205\pi$
$360$	17.8760	+	1.16662i	0.942149	+	0.0614865i
$361$	−5.42477	+	9.39597i	−0.285514	+	0.494525i
$362$	−12.2541	+	4.16099i	−0.644062	+	0.218697i
$363$	1.00963	−	8.39018i	0.0529919	−	0.440370i
$364$	−5.29311	−	13.1601i	−0.277434	−	0.689777i
$365$			32.9931i			1.72694i
$366$	−7.80014	+	2.64860i	−0.407720	+	0.138445i
$367$	31.5814	+	18.2335i	1.64853	+	0.951781i	0.977656	+	0.210213i	$0.0674157\pi$
$367$	31.5814	+	18.2335i	1.64853	+	0.951781i	0.670877	+	0.741568i	$0.265918\pi$
$368$	−16.7695	+	16.7821i	−0.874172	+	0.874826i
$369$			15.7323i			0.818990i
$370$	−0.00830194	+	0.0417570i	−0.000431597	+	0.00217085i
$371$	−12.2124	−	21.1525i	−0.634038	−	1.09819i
$372$	1.60360	+	12.1630i	0.0831427	+	0.630621i
$373$	0.973095	−	0.561817i	0.0503849	−	0.0290898i	−0.474596	−	0.880204i	$-0.657406\pi$
$373$	0.973095	−	0.561817i	0.0503849	−	0.0290898i	0.524981	+	0.851114i	$0.324072\pi$
$374$	4.14581	+	15.1291i	0.214375	+	0.782308i
$375$	−5.40722	−	3.12186i	−0.279228	−	0.161212i
$376$	8.49482	+	5.67262i	0.438087	+	0.292543i
$377$	2.50481	+	9.75578i	0.129004	+	0.502448i
$378$	7.62222	−	8.69311i	0.392045	−	0.447125i
$379$	−16.3496	−	9.43942i	−0.839820	−	0.484871i	0.0173827	−	0.999849i	$-0.494467\pi$
$379$	−16.3496	−	9.43942i	−0.839820	−	0.484871i	−0.857203	+	0.514978i	$0.827800\pi$
$380$	−26.5348	−	10.9853i	−1.36121	−	0.563532i
$381$	−6.81823	+	3.93651i	−0.349308	+	0.201673i
$382$	−10.2268	+	11.6636i	−0.523249	+	0.596764i
$383$	32.6348	−	18.8417i	1.66756	−	0.962767i	0.698613	−	0.715499i	$-0.253801\pi$
$383$	32.6348	−	18.8417i	1.66756	−	0.962767i	0.968947	−	0.247267i	$-0.0795326\pi$
$384$	1.70124	+	8.52359i	0.0868163	+	0.434968i
$385$	−17.1160	−	1.02613i	−0.872314	−	0.0522963i
$386$	32.8669	+	6.53444i	1.67288	+	0.332594i
$387$	10.4520	−	18.1034i	0.531304	−	0.920246i
$388$	23.6967	+	9.81031i	1.20302	+	0.498043i
$389$	−26.9244			−1.36512			−0.682560	−	0.730830i	$-0.739133\pi$
$389$	−26.9244			−1.36512			−0.682560	+	0.730830i	$0.739133\pi$
$390$	−5.63078	−	8.61948i	−0.285126	−	0.436464i
$391$	−19.8364			−1.00317
$392$	3.91863	+	7.94059i	0.197921	+	0.401061i
$393$	−1.47527	−	0.851747i	−0.0744175	−	0.0429650i
$394$	4.66711	+	0.927892i	0.235125	+	0.0467465i
$395$	5.58154			0.280838
$396$	−13.2395	+	8.95704i	−0.665311	+	0.450108i
$397$	4.51938	+	7.82779i	0.226821	+	0.392866i	0.956864	−	0.290535i	$-0.0938334\pi$
$397$	4.51938	+	7.82779i	0.226821	+	0.392866i	−0.730043	+	0.683401i	$0.760500\pi$
$398$	−9.78571	+	11.1606i	−0.490513	+	0.559429i
$399$	−7.15019	+	4.12817i	−0.357957	+	0.206667i
$400$	1.97229	−	7.37170i	0.0986145	−	0.368585i
$401$	8.04611	−	13.9363i	0.401804	−	0.695945i	−0.592140	−	0.805835i	$-0.701717\pi$
$401$	8.04611	−	13.9363i	0.401804	−	0.695945i	0.993944	+	0.109891i	$0.0350501\pi$
$402$	−7.89685	−	6.92405i	−0.393859	−	0.345340i
$403$	−20.5689	+	20.1424i	−1.02461	+	1.00336i
$404$	4.75311	−	0.626663i	0.236476	−	0.0311776i
$405$	−5.30451	+	9.18768i	−0.263583	+	0.456539i
$406$	2.49865	+	7.35851i	0.124006	+	0.365197i
$407$	−0.0169918	−	0.0339774i	−0.000842250	−	0.00168420i
$408$	−4.03578	+	6.04363i	−0.199801	+	0.299204i
$409$	−7.35146	+	4.24437i	−0.363506	+	0.209870i	−0.670618	−	0.741803i	$-0.733971\pi$
$409$	−7.35146	+	4.24437i	−0.363506	+	0.209870i	0.307111	+	0.951674i	$0.400638\pi$
$410$	23.8000	+	4.73180i	1.17540	+	0.233687i
$411$		−	13.7499i		−	0.678231i
$412$	5.45912	+	7.11172i	0.268952	+	0.350369i
$413$	0.255632	+	0.147589i	0.0125788	+	0.00726238i
$414$	−6.49909	−	19.1398i	−0.319413	−	0.940671i
$415$	3.07674			0.151031
$416$	−13.6009	+	15.1992i	−0.666838	+	0.745203i
$417$			5.08863i			0.249191i
$418$	24.7148	−	6.77257i	1.20884	−	0.331257i
$419$	−2.04882	−	1.18289i	−0.100092	−	0.0577879i	0.449119	−	0.893472i	$-0.351738\pi$
$419$	−2.04882	−	1.18289i	−0.100092	−	0.0577879i	−0.549210	+	0.835684i	$0.685071\pi$
$420$	−4.83693	−	6.30117i	−0.236018	−	0.307465i
$421$	4.00418			0.195152			0.0975759	−	0.995228i	$-0.468891\pi$
$421$	4.00418			0.195152			0.0975759	+	0.995228i	$0.468891\pi$
$422$	1.68655	−	8.48298i	0.0820998	−	0.412945i
$423$	−7.53690	+	4.35143i	−0.366457	+	0.211574i
$424$	−19.5036	+	29.2070i	−0.947181	+	1.41842i
$425$	5.52556	−	3.19018i	0.268029	−	0.154747i
$426$	3.82216	−	1.29785i	0.185184	−	0.0628809i
$427$	−12.9161	−	7.45711i	−0.625054	−	0.360875i
$428$	−2.51880	−	19.1046i	−0.121751	−	0.923455i
$429$	8.68475	+	2.99567i	0.419304	+	0.144633i
$430$	−24.2433	−	21.2568i	−1.16912	−	1.02509i
$431$	10.7452	−	18.6112i	0.517578	−	0.896471i	−0.482214	−	0.876053i	$-0.660167\pi$
$431$	10.7452	−	18.6112i	0.517578	−	0.896471i	0.999792	−	0.0204171i	$-0.00649942\pi$
$432$	−16.0594	−	4.29666i	−0.772657	−	0.206723i
$433$	−4.59574	−	7.96006i	−0.220857	−	0.382536i	0.734211	−	0.678921i	$-0.237552\pi$
$433$	−4.59574	−	7.96006i	−0.220857	−	0.382536i	−0.955069	+	0.296385i	$0.904219\pi$
$434$	−14.6437	+	16.7011i	−0.702921	+	0.801679i
$435$	2.82028	+	4.88486i	0.135222	+	0.234211i
$436$	−0.863670	−	1.12512i	−0.0413623	−	0.0538836i
$437$			32.4046i			1.55012i
$438$	2.65951	−	13.3768i	0.127076	−	0.639168i
$439$	−13.0411	+	22.5879i	−0.622418	+	1.07806i	0.366616	+	0.930372i	$0.380516\pi$
$439$	−13.0411	+	22.5879i	−0.622418	+	1.07806i	−0.989034	+	0.147688i	$0.952817\pi$
$440$	9.56826	+	22.7229i	0.456149	+	1.08327i
$441$	−7.54428			−0.359251
$442$	−17.0276	+	0.938601i	−0.809919	+	0.0446447i
$443$			23.5366i			1.11826i	0.829081	+	0.559128i	$0.188864\pi$
$443$			23.5366i			1.11826i	−0.829081	+	0.559128i	$0.811136\pi$
$444$	0.00673192	−	0.0162609i	0.000319483	−	0.000771707i
$445$	−22.0445	+	38.1822i	−1.04501	+	1.81001i
$446$	−26.7027	−	5.30890i	−1.26441	−	0.251384i
$447$	−9.17129			−0.433787
$448$	−9.57277	+	12.4900i	−0.452271	+	0.590095i
$449$	−1.50734	−	2.61079i	−0.0711357	−	0.123211i	0.828264	−	0.560339i	$-0.189329\pi$
$449$	−1.50734	−	2.61079i	−0.0711357	−	0.123211i	−0.899399	+	0.437128i	$0.855996\pi$
$450$	4.88852	+	4.28631i	0.230447	+	0.202058i
$451$	−19.3659	+	9.68467i	−0.911903	+	0.456033i
$452$	−12.5379	−	5.19062i	−0.589732	−	0.244146i
$453$	−3.89654	−	2.24967i	−0.183076	−	0.105699i
$454$	−22.4702	−	19.7021i	−1.05458	−	0.924665i
$455$	5.01289	−	17.9538i	0.235008	−	0.841688i
$456$	9.87284	+	6.59282i	0.462338	+	0.308737i
$457$	−7.18672	−	4.14926i	−0.336181	−	0.194094i	0.322401	−	0.946603i	$-0.395510\pi$
$457$	−7.18672	−	4.14926i	−0.336181	−	0.194094i	−0.658582	+	0.752509i	$0.728843\pi$
$458$	2.54326	−	0.863587i	0.118839	−	0.0403528i
$459$	−6.94987	−	12.0375i	−0.324392	−	0.561863i
$460$	−30.9097	+	4.07521i	−1.44117	+	0.190008i
$461$	31.8937	−	18.4138i	1.48544	−	0.857618i	0.485575	−	0.874195i	$-0.338610\pi$
$461$	31.8937	−	18.4138i	1.48544	−	0.857618i	0.999863	+	0.0165777i	$0.00527709\pi$
$462$	6.85686	+	1.79573i	0.319010	+	0.0835448i
$463$			41.2929i			1.91904i	0.281635	+	0.959522i	$0.409123\pi$
$463$			41.2929i			1.91904i	−0.281635	+	0.959522i	$0.590877\pi$
$464$	7.89833	−	7.90424i	0.366671	−	0.366945i
$465$	−8.06102	+	13.9621i	−0.373821	+	0.647477i
$466$	8.87458	+	26.1356i	0.411107	+	1.21071i
$467$		−	2.28069i		−	0.105538i	−0.998607	−	0.0527689i	$-0.983195\pi$
$467$		−	2.28069i		−	0.105538i	0.998607	−	0.0527689i	$-0.0168047\pi$
$468$	−6.48446	−	16.1221i	−0.299744	−	0.745245i
$469$		−	19.0150i		−	0.878029i
$470$	4.31602	+	12.7107i	0.199083	+	0.586300i
$471$	8.85051	+	5.10985i	0.407810	+	0.235449i
$472$	0.0276406	−	0.423534i	0.00127226	−	0.0194947i
$473$	28.7187	+	1.72172i	1.32049	+	0.0791649i
$474$	−2.26299	−	0.449917i	−0.103943	−	0.0206654i
$475$	−5.21146	−	9.02651i	−0.239118	−	0.414165i
$476$	−13.0446	+	1.71983i	−0.597898	+	0.0788285i
$477$	−14.9611	−	25.9135i	−0.685024	−	1.18650i
$478$	−12.1433	+	4.12336i	−0.555422	+	0.188598i
$479$	10.9848	−	19.0262i	0.501909	−	0.869331i	−0.498089	−	0.867126i	$-0.665965\pi$
$479$	10.9848	−	19.0262i	0.501909	−	0.869331i	0.999998	−	0.00220537i	$-0.000701991\pi$
$480$	−5.04705	+	10.2465i	−0.230365	+	0.467685i
$481$	0.0400013	−	0.0102704i	0.00182390	−	0.000468289i
$482$	14.0322	−	16.0037i	0.639150	−	0.728948i
$483$	−4.48153	+	7.76224i	−0.203917	+	0.353194i
$484$	−19.1759	−	10.7835i	−0.871633	−	0.490158i
$485$	16.8518	+	29.1882i	0.765202	+	1.32537i
$486$	14.5161	−	16.5555i	0.658462	−	0.750973i
$487$	−2.58957	+	1.49509i	−0.117344	+	0.0677489i	−0.557523	−	0.830161i	$-0.688248\pi$
$487$	−2.58957	+	1.49509i	−0.117344	+	0.0677489i	0.440179	+	0.897910i	$0.354915\pi$
$488$	−1.39658	+	21.3996i	−0.0632201	+	0.968713i
$489$	−17.2444			−0.779820
$490$	−2.26909	+	11.4131i	−0.102507	+	0.515590i
$491$	19.2756	−	33.3863i	0.869895	−	1.50670i	0.00779278	−	0.999970i	$-0.497519\pi$
$491$	19.2756	−	33.3863i	0.869895	−	1.50670i	0.862103	−	0.506734i	$-0.169147\pi$
$492$	−9.26810	−	3.83694i	−0.417838	−	0.172983i
$493$	9.34282			0.420779
$494$	1.53329	+	27.8161i	0.0689861	+	1.25151i
$495$	−20.9684	−	1.25708i	−0.942461	−	0.0565017i
$496$	30.8531	+	8.25470i	1.38534	+	0.370647i
$497$	6.32904	+	3.65407i	0.283896	+	0.163908i
$498$	−1.24744	−	0.248010i	−0.0558991	−	0.0111136i
$499$		−	41.5422i		−	1.85968i	−0.367961	−	0.929841i	$-0.619944\pi$
$499$		−	41.5422i		−	1.85968i	0.367961	−	0.929841i	$-0.380056\pi$
$500$	−12.8937	+	9.89752i	−0.576624	+	0.442630i
$501$	10.3952	−	6.00168i	0.464424	−	0.268135i
$502$	11.9125	−	13.5862i	0.531681	−	0.606380i
$503$	−1.52538	−	2.64203i	−0.0680132	−	0.117802i	0.830013	−	0.557743i	$-0.188333\pi$
$503$	−1.52538	−	2.64203i	−0.0680132	−	0.117802i	−0.898027	+	0.439941i	$0.854999\pi$
$504$	−5.93330	−	12.0230i	−0.264290	−	0.535549i
$505$	5.45618	+	3.15013i	0.242797	+	0.140179i
$506$	19.5596	−	19.7825i	0.869532	−	0.879438i
$507$	−5.17372	+	8.54265i	−0.229773	+	0.379392i
$508$	2.67907	+	20.3202i	0.118865	+	0.901564i
$509$	−12.7112	+	22.0164i	−0.563414	+	0.975861i	0.433781	+	0.901018i	$0.357179\pi$
$509$	−12.7112	+	22.0164i	−0.563414	+	0.975861i	−0.997195	+	0.0748433i	$0.976154\pi$
$510$	−9.04300	+	3.07063i	−0.400431	+	0.135970i
$511$	21.3847	−	12.3465i	0.946003	−	0.546175i
$512$	22.1963	+	4.39573i	0.980949	+	0.194265i
$513$	−19.6644	+	11.3533i	−0.868205	+	0.501258i
$514$	1.60833	−	8.08957i	0.0709404	−	0.356816i
$515$			11.7817i			0.519164i
$516$	8.11580	+	10.5726i	0.357278	+	0.465434i
$517$	−9.99611	−	6.59894i	−0.439628	−	0.290221i
$518$	0.0301718	−	0.0102451i	0.00132567	−	0.000450144i
$519$	−17.0042			−0.746401
$520$	−26.3400	+	4.96072i	−1.15509	+	0.217542i
$521$	−15.5093			−0.679476			−0.339738	−	0.940520i	$-0.610338\pi$
$521$	−15.5093			−0.679476			−0.339738	+	0.940520i	$0.610338\pi$
$522$	3.06103	+	9.01473i	0.133978	+	0.394564i
$523$	−11.7125	+	20.2867i	−0.512152	+	0.887073i	0.487749	+	0.872984i	$0.337818\pi$
$523$	−11.7125	+	20.2867i	−0.512152	+	0.887073i	−0.999901	+	0.0140893i	$0.995515\pi$
$524$	−3.51783	+	2.70037i	−0.153677	+	0.117966i
$525$		−	2.88296i		−	0.125823i
$526$	4.48687	−	22.5680i	0.195637	−	0.984014i
$527$	13.3520	+	23.1264i	0.581622	+	1.00740i
$528$	−2.04773	−	9.98411i	−0.0891160	−	0.434502i
$529$	6.08921	+	10.5468i	0.264748	+	0.458558i
$530$	−43.7020	+	14.8394i	−1.89829	+	0.644582i
$531$	0.313168	+	0.180808i	0.0135903	+	0.00784638i
$532$	2.80951	+	21.3096i	0.121808	+	0.923887i
$533$	−5.85374	−	22.7992i	−0.253554	−	0.987545i
$534$	12.0156	−	13.7037i	0.519964	−	0.593017i
$535$	12.6616	−	21.9305i	0.547408	−	0.948139i
$536$	−24.5185	+	12.0997i	−1.05904	+	0.522628i
$537$	−1.15689	−	2.00379i	−0.0499234	−	0.0864698i
$538$	16.7799	+	14.7128i	0.723435	+	0.634316i
$539$	−4.64420	−	9.28673i	−0.200040	−	0.400008i
$540$	−13.3025	−	17.3294i	−0.572447	−	0.745739i
$541$		−	22.6410i		−	0.973414i	−0.873565	−	0.486707i	$-0.838198\pi$
$541$		−	22.6410i		−	0.973414i	0.873565	−	0.486707i	$-0.161802\pi$
$542$	4.46736	−	22.4699i	0.191890	−	0.965166i
$543$	6.08827	+	3.51507i	0.261273	+	0.150846i
$544$	10.5182	+	15.7257i	0.450965	+	0.674235i
$545$		−	1.86395i		−	0.0798427i
$546$	−3.47966	+	6.87516i	−0.148916	+	0.294230i
$547$	38.3434			1.63945			0.819723	−	0.572761i	$-0.194128\pi$
$547$	38.3434			1.63945			0.819723	+	0.572761i	$0.194128\pi$
$548$	−33.0733	−	13.6922i	−1.41282	−	0.584900i
$549$	−15.8232	−	9.13552i	−0.675317	−	0.389895i
$550$	−2.26695	+	8.65620i	−0.0966633	+	0.369102i
$551$		−	15.2624i		−	0.650198i
$552$	12.8606	+	0.839307i	0.547383	+	0.0357233i
$553$	−2.08869	−	3.61771i	−0.0888200	−	0.153841i
$554$	6.38953	−	7.28724i	0.271465	−	0.309605i
$555$	0.0200292	−	0.0115639i	0.000850193	−	0.000490859i
$556$	12.2399	+	5.06727i	0.519089	+	0.214900i
$557$	17.6919	+	10.2144i	0.749630	+	0.432799i	0.825560	−	0.564314i	$-0.190859\pi$
$557$	17.6919	+	10.2144i	0.749630	+	0.432799i	−0.0759305	+	0.997113i	$0.524193\pi$
$558$	−17.9397	+	20.4601i	−0.759446	+	0.866146i
$559$	−8.41104	+	30.1244i	−0.355749	+	1.27413i
$560$	−19.9731	+	5.35979i	−0.844019	+	0.226492i
$561$	4.69481	−	7.11172i	0.198215	−	0.300257i
$562$	−11.5844	−	34.1162i	−0.488660	−	1.43910i
$563$	19.1797	+	33.2202i	0.808326	+	1.40006i	0.914022	+	0.405664i	$0.132960\pi$
$563$	19.1797	+	33.2202i	0.808326	+	1.40006i	−0.105696	+	0.994399i	$0.533707\pi$
$564$	−0.725313	−	5.50136i	−0.0305412	−	0.231649i
$565$	−8.91627	−	15.4434i	−0.375110	−	0.649710i
$566$	−1.75246	+	8.81452i	−0.0736614	+	0.370502i
$567$	7.94008			0.333452
$568$	0.684339	−	10.4860i	0.0287142	−	0.439984i
$569$	13.6509	+	7.88136i	0.572276	+	0.330404i	0.758058	−	0.652187i	$-0.226148\pi$
$569$	13.6509	+	7.88136i	0.572276	+	0.330404i	−0.185782	+	0.982591i	$0.559482\pi$
$570$	5.01616	+	14.7726i	0.210104	+	0.618756i
$571$	−9.48300			−0.396851			−0.198426	−	0.980116i	$-0.563583\pi$
$571$	−9.48300			−0.396851			−0.198426	+	0.980116i	$0.563583\pi$
$572$	15.8539	−	17.9068i	0.662887	−	0.748720i
$573$	8.42672			0.352031
$574$	−5.83933	−	17.1968i	−0.243729	−	0.717782i
$575$	−9.79917	−	5.65756i	−0.408654	−	0.235936i
$576$	−11.7274	+	15.3011i	−0.488640	+	0.637548i
$577$	−21.1328			−0.879772			−0.439886	−	0.898054i	$-0.644981\pi$
$577$	−21.1328			−0.879772			−0.439886	+	0.898054i	$0.644981\pi$
$578$	1.60350	−	8.06529i	0.0666969	−	0.335472i
$579$	−9.10190	−	15.7649i	−0.378262	−	0.655169i
$580$	14.5582	−	1.91940i	0.604498	−	0.0796986i
$581$	−1.15136	−	1.99421i	−0.0477664	−	0.0827338i
$582$	−4.47964	−	13.1925i	−0.185687	−	0.546849i
$583$	22.6886	−	34.3687i	0.939664	−	1.42341i
$584$	−29.5275	−	19.7177i	−1.22186	−	0.815924i
$585$	6.14116	−	21.9948i	0.253906	−	0.909372i
$586$	−7.16723	+	8.17419i	−0.296075	+	0.337673i
$587$	−23.9062	−	13.8022i	−0.986714	−	0.569679i	−0.0824233	−	0.996597i	$-0.526266\pi$
$587$	−23.9062	−	13.8022i	−0.986714	−	0.569679i	−0.904290	+	0.426918i	$0.859599\pi$
$588$	1.83997	−	4.44443i	0.0758792	−	0.183285i
$589$	37.7790	−	21.8117i	1.55666	−	0.898737i
$590$	0.367719	−	0.419382i	0.0151388	−	0.0172657i
$591$	−1.29247	−	2.23863i	−0.0531652	−	0.0920848i
$592$	−0.0324095	−	0.0323852i	−0.00133202	−	0.00133103i
$593$			5.61933i			0.230758i	0.993322	+	0.115379i	$0.0368083\pi$
$593$			5.61933i			0.230758i	−0.993322	+	0.115379i	$0.963192\pi$
$594$	18.8577	+	4.93860i	0.773740	+	0.202633i
$595$	−14.9741	−	8.64532i	−0.613880	−	0.354424i
$596$	−9.13279	+	22.0602i	−0.374094	+	0.903620i
$597$	8.06326			0.330007
$598$	16.5401	+	25.3192i	0.676376	+	1.03538i
$599$		−	12.3252i		−	0.503596i	−0.967780	−	0.251798i	$-0.918978\pi$
$599$		−	12.3252i		−	0.503596i	0.967780	−	0.251798i	$-0.0810218\pi$
$600$	−3.71738	+	1.83450i	−0.151761	+	0.0748933i
$601$	20.9801	+	12.1129i	0.855798	+	0.494095i	0.862603	−	0.505882i	$-0.168833\pi$
$601$	20.9801	+	12.1129i	0.855798	+	0.494095i	−0.00680514	+	0.999977i	$0.502166\pi$
$602$	−4.70557	+	23.6681i	−0.191785	+	0.964639i
$603$		−	23.2948i		−	0.948636i
$604$	−9.29143	+	7.13233i	−0.378063	+	0.290210i
$605$	−11.3606	−	26.5852i	−0.461873	−	1.08084i
$606$	−1.95824	−	1.71701i	−0.0795481	−	0.0697487i
$607$	−9.93301	−	17.2045i	−0.403169	−	0.698308i	0.590938	−	0.806717i	$-0.298758\pi$
$607$	−9.93301	−	17.2045i	−0.403169	−	0.698308i	−0.994106	+	0.108409i	$0.965425\pi$
$608$	25.6894	−	17.1825i	1.04184	−	0.696842i
$609$	2.11077	−	3.65596i	0.0855328	−	0.148147i
$610$	−18.5795	+	21.1898i	−0.752260	+	0.857950i
$611$	9.30338	−	9.11046i	0.376375	−	0.368570i
$612$	−15.9806	+	2.10693i	−0.645978	+	0.0851674i
$613$	15.0183	+	8.67081i	0.606583	+	0.350211i	0.771627	−	0.636076i	$-0.219443\pi$
$613$	15.0183	+	8.67081i	0.606583	+	0.350211i	−0.165044	+	0.986286i	$0.552777\pi$
$614$	−9.00624	+	3.05814i	−0.363462	+	0.123417i
$615$	−6.59098	−	11.4159i	−0.265774	−	0.460334i
$616$	11.1474	−	14.7050i	0.449143	−	0.592480i
$617$	16.4324	+	28.4617i	0.661542	+	1.14582i	0.980211	+	0.197958i	$0.0634309\pi$
$617$	16.4324	+	28.4617i	0.661542	+	1.14582i	−0.318669	+	0.947866i	$0.603236\pi$
$618$	0.949702	−	4.77680i	0.0382026	−	0.192151i
$619$			42.5883i			1.71177i	0.517169	+	0.855883i	$0.326986\pi$
$619$			42.5883i			1.71177i	−0.517169	+	0.855883i	$0.673014\pi$
$620$	25.5566	+	33.2931i	1.02638	+	1.33708i
$621$	−12.3251	+	21.3477i	−0.494588	+	0.856652i
$622$	5.41798	+	15.9560i	0.217241	+	0.639775i
$623$	32.9974			1.32201
$624$	11.0792	+	0.111936i	0.443524	+	0.00448102i
$625$	−30.8992			−1.23597
$626$	−32.7865	+	11.1329i	−1.31041	+	0.444961i
$627$	−11.6177	−	7.66941i	−0.463965	−	0.306287i
$628$	21.1043	−	16.2002i	0.842155	−	0.646458i
$629$		−	0.0383080i		−	0.00152744i
$630$	3.43569	−	17.2808i	0.136881	−	0.688483i
$631$	24.8716	−	14.3596i	0.990123	−	0.571648i	0.0848119	−	0.996397i	$-0.472971\pi$
$631$	24.8716	−	14.3596i	0.990123	−	0.571648i	0.905311	+	0.424749i	$0.139638\pi$
$632$	−3.33570	+	4.99526i	−0.132687	+	0.198701i
$633$	−4.06895	+	2.34921i	−0.161726	+	0.0933728i
$634$	−17.6581	+	5.99597i	−0.701294	+	0.238130i
$635$	−13.4672	+	23.3259i	−0.534431	+	0.925662i
$636$	18.9148	−	2.49378i	0.750022	−	0.0988848i
$637$	10.9332	−	2.80711i	0.433188	−	0.111222i
$638$	−9.21246	+	9.31741i	−0.364725	+	0.368880i
$639$	7.75355	+	4.47651i	0.306726	+	0.177088i
$640$	19.6205	+	22.3434i	0.775568	+	0.883200i
$641$	12.0307	+	20.8377i	0.475182	+	0.823040i	0.999596	−	0.0284237i	$-0.00904876\pi$
$641$	12.0307	+	20.8377i	0.475182	+	0.823040i	−0.524414	+	0.851464i	$0.675715\pi$
$642$	−6.90132	+	7.87093i	−0.272373	+	0.310641i
$643$	10.9049	−	6.29593i	0.430046	−	0.248287i	−0.269320	−	0.963051i	$-0.586799\pi$
$643$	10.9049	−	6.29593i	0.430046	−	0.248287i	0.699366	+	0.714763i	$0.253466\pi$
$644$	14.2082	+	18.5093i	0.559881	+	0.729369i
$645$			17.5153i			0.689663i
$646$	25.3449	+	5.03895i	0.997182	+	0.198255i
$647$	5.89790	+	3.40515i	0.231870	+	0.133870i	0.611435	−	0.791295i	$-0.290593\pi$
$647$	5.89790	+	3.40515i	0.231870	+	0.133870i	−0.379564	+	0.925165i	$0.623926\pi$
$648$	−5.05248	−	10.2382i	−0.198480	−	0.402194i
$649$	−0.0297839	+	0.496802i	−0.00116912	+	0.0195012i
$650$	−8.67931	−	4.39278i	−0.340430	−	0.172299i
$651$	12.0662			0.472911
$652$	−17.1721	+	41.4789i	−0.672509	+	1.62444i
$653$	−7.17164	+	12.4217i	−0.280648	+	0.486097i	−0.971545	−	0.236857i	$-0.923883\pi$
$653$	−7.17164	+	12.4217i	−0.280648	+	0.486097i	0.690896	+	0.722954i	$0.257216\pi$
$654$	−0.150249	+	0.755723i	−0.00587521	+	0.0295511i
$655$	−5.82785			−0.227713
$656$	−18.4584	+	18.4722i	−0.720679	+	0.721218i
$657$	26.1979	−	15.1253i	1.02208	−	0.590096i
$658$	6.62341	−	7.55397i	0.258207	−	0.294485i
$659$	−6.09921	−	10.5641i	−0.237592	−	0.411521i	0.722431	−	0.691443i	$-0.243025\pi$
$659$	−6.09921	−	10.5641i	−0.237592	−	0.411521i	−0.960023	+	0.279922i	$0.909691\pi$
$660$	5.85455	−	12.0462i	0.227888	−	0.468897i
$661$	21.9802	−	38.0708i	0.854930	−	1.48078i	−0.0217808	−	0.999763i	$-0.506934\pi$
$661$	21.9802	−	38.0708i	0.854930	−	1.48078i	0.876710	−	0.481019i	$-0.159733\pi$
$662$	23.6563	−	26.9800i	0.919429	−	1.04861i
$663$	6.48163	+	6.61888i	0.251726	+	0.257056i
$664$	−1.83876	+	2.75356i	−0.0713576	+	0.106859i
$665$	−14.1229	+	24.4616i	−0.547664	+	0.948582i
$666$	0.0369628	−	0.0125510i	0.00143228	−	0.000486342i
$667$	−8.28440	−	14.3490i	−0.320773	−	0.555596i
$668$	−4.08457	−	30.9806i	−0.158037	−	1.19868i
$669$	7.39483	+	12.8082i	0.285901	+	0.495195i
$670$	−35.2406	−	7.00636i	−1.36146	−	0.270679i
$671$	1.50487	−	25.1015i	0.0580947	−	0.969033i
$672$	8.53000	−	0.563088i	0.329052	−	0.0217216i
$673$	−23.1305	−	13.3544i	−0.891615	−	0.514774i	−0.0171445	−	0.999853i	$-0.505458\pi$
$673$	−23.1305	−	13.3544i	−0.891615	−	0.514774i	−0.874470	+	0.485079i	$0.838791\pi$
$674$	15.5723	+	45.8605i	0.599823	+	1.76648i
$675$		−	7.92870i		−	0.305176i
$676$	15.3961	+	20.9514i	0.592156	+	0.805823i
$677$		−	6.89476i		−	0.264987i	−0.991184	−	0.132493i	$-0.957702\pi$
$677$		−	6.89476i		−	0.264987i	0.991184	−	0.132493i	$-0.0422984\pi$
$678$	2.37017	+	6.98015i	0.0910258	+	0.268071i
$679$	12.6124	−	21.8453i	0.484019	−	0.838345i
$680$	−1.61911	+	24.8093i	−0.0620899	+	0.951395i
$681$			16.2342i			0.622096i
$682$	−36.2292	−	9.48798i	−1.38729	−	0.363314i
$683$	−14.9920	+	8.65564i	−0.573653	+	0.331199i	−0.758607	−	0.651548i	$-0.774120\pi$
$683$	−14.9920	+	8.65564i	−0.573653	+	0.331199i	0.184954	+	0.982747i	$0.440786\pi$
$684$	3.44186	+	26.1058i	0.131603	+	0.998181i
$685$	−23.5200	−	40.7377i	−0.898651	−	1.55651i
$686$	26.6855	−	9.06128i	1.01886	−	0.345961i
$687$	−1.26358	−	0.729529i	−0.0482087	−	0.0278333i
$688$	33.5126	−	8.99310i	1.27766	−	0.342859i
$689$	31.3237	+	31.9870i	1.19334	+	1.21861i
$690$	12.7345	+	11.1658i	0.484795	+	0.425074i
$691$	−16.0964	−	9.29326i	−0.612336	−	0.353532i	0.161543	−	0.986866i	$-0.448353\pi$
$691$	−16.0964	−	9.29326i	−0.612336	−	0.353532i	−0.773879	+	0.633333i	$0.781686\pi$
$692$	−16.9328	+	40.9010i	−0.643689	+	1.55482i
$693$	7.03189	+	14.0613i	0.267119	+	0.534143i
$694$	−22.3241	−	19.5740i	−0.847412	−	0.743020i
$695$	8.70439	+	15.0765i	0.330176	+	0.571882i
$696$	−6.05725	−	0.395308i	−0.229599	−	0.0149841i
$697$	−21.8341			−0.827027
$698$	13.9791	+	2.77927i	0.529118	+	0.105197i
$699$	7.49695	−	12.9851i	0.283561	−	0.491141i
$700$	−6.93454	−	2.87086i	−0.262101	−	0.108508i
$701$			1.69846i			0.0641498i	0.999485	+	0.0320749i	$0.0102115\pi$
$701$			1.69846i			0.0641498i	−0.999485	+	0.0320749i	$0.989788\pi$
$702$	−9.56974	+	18.9080i	−0.361186	+	0.713637i
$703$	−0.0625797			−0.00236024
$704$	−26.0544	−	5.01669i	−0.981963	−	0.189074i
$705$	3.64603	−	6.31511i	0.137317	−	0.237841i
$706$	−6.98938	+	35.1551i	−0.263049	+	1.32308i
$707$		−	4.71529i		−	0.177337i
$708$	−0.182895	+	0.140394i	−0.00687360	+	0.00527634i
$709$	15.7441	+	27.2696i	0.591282	+	1.02413i	0.994060	+	0.108832i	$0.0347111\pi$
$709$	15.7441	+	27.2696i	0.591282	+	1.02413i	−0.402779	+	0.915297i	$0.631956\pi$
$710$	9.10415	−	10.3833i	0.341673	−	0.389676i
$711$	−2.55880	−	4.43197i	−0.0959625	−	0.166212i
$712$	−20.9971	−	42.5478i	−0.786899	−	1.59455i
$713$	23.6788	−	41.0129i	0.886778	−	1.53594i
$714$	5.37427	+	4.71222i	0.201127	+	0.176350i
$715$	30.8552	−	5.98026i	1.15392	−	0.223649i
$716$	−5.97184	+	0.787344i	−0.223178	+	0.0294244i
$717$	6.03322	+	3.48328i	0.225315	+	0.130085i
$718$	−5.06032	+	1.71828i	−0.188850	+	0.0641255i
$719$	−25.9715	+	14.9947i	−0.968574	+	0.559207i	−0.898801	−	0.438356i	$-0.855561\pi$
$719$	−25.9715	+	14.9947i	−0.968574	+	0.559207i	−0.0697730	+	0.997563i	$0.522227\pi$
$720$	−24.4686	+	6.56614i	−0.911891	+	0.244706i
$721$	7.63640	−	4.40888i	0.284394	−	0.164195i
$722$	2.99197	−	15.0490i	0.111350	−	0.560067i
$723$	−11.5623			−0.430007
$724$	14.5177	−	11.1441i	0.539546	−	0.414168i
$725$	4.61534	+	2.66467i	0.171410	+	0.0989634i
$726$	2.46308	+	11.6945i	0.0914133	+	0.434025i
$727$		−	13.2491i		−	0.491380i	−0.969348	−	0.245690i	$-0.920985\pi$
$727$		−	13.2491i		−	0.491380i	0.969348	−	0.245690i	$-0.0790146\pi$
$728$	13.0721	+	15.2161i	0.484485	+	0.563947i
$729$	0.148571			0.00550264
$730$	−15.0023	−	44.1817i	−0.555258	−	1.63524i
$731$	25.1249	+	14.5058i	0.929277	+	0.536518i
$732$	9.24097	−	7.09359i	0.341556	−	0.262187i
$733$		−	29.5258i		−	1.09056i	−0.838254	−	0.545280i	$-0.816423\pi$
$733$		−	29.5258i		−	1.09056i	0.838254	−	0.545280i	$-0.183577\pi$
$734$	−50.5821	−	10.0565i	−1.86702	−	0.371192i
$735$	5.47440	−	3.16065i	0.201926	−	0.116582i
$736$	14.8254	−	30.0984i	0.546473	−	1.10944i
$737$	28.6750	−	14.3401i	1.05626	−	0.528223i
$738$	−7.15362	−	21.0674i	−0.263328	−	0.775502i
$739$	−9.31583	+	16.1355i	−0.342688	+	0.593554i	−0.984931	−	0.172948i	$-0.944671\pi$
$739$	−9.31583	+	16.1355i	−0.342688	+	0.593554i	0.642243	+	0.766501i	$0.278004\pi$
$740$	−0.00787003	−	0.0596926i	−0.000289308	−	0.00219434i
$741$	10.8126	−	10.5883i	0.397209	−	0.388972i
$742$	25.9722	+	22.7727i	0.953468	+	0.836011i
$743$	4.69544	−	8.13273i	0.172259	−	0.298361i	−0.766950	−	0.641706i	$-0.778227\pi$
$743$	4.69544	−	8.13273i	0.172259	−	0.298361i	0.939209	+	0.343345i	$0.111560\pi$
$744$	−7.67803	−	15.5585i	−0.281490	−	0.570402i
$745$	−27.1725	+	15.6880i	−0.995522	+	0.574765i
$746$	−1.04763	+	1.19481i	−0.0383563	+	0.0437453i
$747$	−1.41050	−	2.44306i	−0.0516075	−	0.0893868i
$748$	−12.4311	−	18.3745i	−0.454526	−	0.671840i
$749$	−18.9526			−0.692511
$750$	8.66046	+	1.72183i	0.316235	+	0.0628724i
$751$	26.2784	+	15.1718i	0.958912	+	0.553628i	0.895838	−	0.444381i	$-0.146576\pi$
$751$	26.2784	+	15.1718i	0.958912	+	0.553628i	0.0630741	+	0.998009i	$0.479910\pi$
$752$	−13.9550	−	3.73363i	−0.508885	−	0.136152i
$753$	−9.81570			−0.357704
$754$	−7.79028	−	11.9252i	−0.283705	−	0.434290i
$755$	−15.3928			−0.560200
$756$	−6.25422	+	15.1070i	−0.227464	+	0.549436i
$757$	−11.1387	+	19.2928i	−0.404844	+	0.701210i	−0.994303	−	0.106588i	$-0.966007\pi$
$757$	−11.1387	+	19.2928i	−0.404844	+	0.701210i	0.589460	+	0.807798i	$0.299341\pi$
$758$	26.1862	+	5.20622i	0.951126	+	0.189098i
$759$	−15.0854	−	0.904386i	−0.547564	−	0.0328271i
$760$	40.5284	+	2.64496i	1.47012	+	0.0959428i
$761$	35.6382	−	20.5757i	1.29188	−	0.745870i	0.312896	−	0.949787i	$-0.398701\pi$
$761$	35.6382	−	20.5757i	1.29188	−	0.745870i	0.978988	+	0.203917i	$0.0653674\pi$
$762$	7.34045	−	8.37176i	0.265917	−	0.303277i
$763$	−1.20813	+	0.697514i	−0.0437373	+	0.0252517i
$764$	8.39135	−	20.2692i	0.303588	−	0.733315i
$765$	−18.3444	−	10.5912i	−0.663245	−	0.382924i
$766$	−35.1344	+	40.0706i	−1.26946	+	1.44781i
$767$	−0.521119	−	0.145502i	−0.0188165	−	0.00525376i
$768$	−6.15393	−	10.6405i	−0.222061	−	0.383957i
$769$	−10.3020	−	5.94785i	−0.371499	−	0.214485i	0.302614	−	0.953113i	$-0.402141\pi$
$769$	−10.3020	−	5.94785i	−0.371499	−	0.214485i	−0.674113	+	0.738628i	$0.735474\pi$
$770$	23.3870	−	6.40872i	0.842809	−	0.230954i
$771$	−3.88025	+	2.24026i	−0.139744	+	0.0806811i
$772$	−46.9839	+	6.19448i	−1.69099	+	0.222944i
$773$	9.55790	+	16.5548i	0.343774	+	0.595433i	0.985130	−	0.171810i	$-0.0549614\pi$
$773$	9.55790	+	16.5548i	0.343774	+	0.595433i	−0.641357	+	0.767243i	$0.721628\pi$
$774$	−5.76468	+	28.9952i	−0.207207	+	1.04221i
$775$			15.2325i			0.547169i
$776$	−36.1935	−	2.36206i	−1.29927	−	0.0847931i
$777$	−0.0149904	−	0.00865472i	−0.000537778	−	0.000310486i
$778$	36.0549	−	12.2428i	1.29263	−	0.438924i
$779$			35.6681i			1.27794i
$780$	11.4596	+	8.98214i	0.410321	+	0.321612i
$781$	−0.737402	+	12.3000i	−0.0263863	+	0.440130i
$782$	26.5633	−	9.01980i	0.949902	−	0.322547i
$783$	5.80503	−	10.0546i	0.207455	−	0.359322i
$784$	−8.85818	−	8.85156i	−0.316364	−	0.316127i
$785$	34.9627			1.24787
$786$	2.36286	+	0.469772i	0.0842804	+	0.0167562i
$787$	−11.3236	−	19.6131i	−0.403643	−	0.699131i	0.590519	−	0.807024i	$-0.298923\pi$
$787$	−11.3236	−	19.6131i	−0.403643	−	0.699131i	−0.994163	+	0.107893i	$0.965590\pi$
$788$	−6.67173	+	0.879619i	−0.237671	+	0.0313351i
$789$	−10.8250	+	6.24982i	−0.385380	+	0.222499i
$790$	−7.47434	+	2.53798i	−0.265925	+	0.0902971i
$791$	−6.67318	+	11.5583i	−0.237271	+	0.410966i
$792$	13.6564	−	18.0147i	0.485261	−	0.640124i
$793$	26.3302	+	7.35164i	0.935011	+	0.261065i
$794$	−9.61135	−	8.42734i	−0.341094	−	0.299075i
$795$	21.7127	+	12.5358i	0.770069	+	0.444600i
$796$	8.02942	−	19.3950i	0.284595	−	0.687437i
$797$	−19.6846	−	34.0947i	−0.697263	−	1.20769i	−0.969412	−	0.245440i	$-0.921068\pi$
$797$	−19.6846	−	34.0947i	−0.697263	−	1.20769i	0.272149	−	0.962255i	$-0.412266\pi$
$798$	7.69784	−	8.77936i	0.272501	−	0.310786i
$799$	−6.03916	−	10.4601i	−0.213650	−	0.370053i
$800$	0.710851	+	10.7684i	0.0251324	+	0.380721i
$801$	40.4243			1.42832
$802$	−4.43775	+	22.3210i	−0.156702	+	0.788181i
$803$	34.7459	+	22.9376i	1.22616	+	0.809449i
$804$	13.7232	+	5.68135i	0.483982	+	0.200366i
$805$			30.6637i			1.08075i
$806$	18.3853	−	36.3259i	0.647594	−	1.27952i
$807$		−	12.1231i		−	0.426755i
$808$	−6.08003	+	3.00046i	−0.213895	+	0.105556i
$809$	−13.4971	−	7.79258i	−0.474534	−	0.273973i	0.243602	−	0.969875i	$-0.421671\pi$
$809$	−13.4971	−	7.79258i	−0.474534	−	0.273973i	−0.718136	+	0.695903i	$0.755004\pi$
$810$	2.92565	−	14.7154i	0.102797	−	0.517047i
$811$	−21.2017			−0.744491			−0.372245	−	0.928134i	$-0.621412\pi$
$811$	−21.2017			−0.744491			−0.372245	+	0.928134i	$0.621412\pi$
$812$	−6.69197	−	8.71777i	−0.234842	−	0.305934i
$813$	−10.7779	+	6.22265i	−0.377999	+	0.218238i
$814$	0.0382038	+	0.0377735i	0.00133904	+	0.00132396i
$815$	−51.0913	+	29.4976i	−1.78965	+	1.03326i
$816$	2.65629	−	9.92825i	0.0929887	−	0.347558i
$817$	23.6966	−	41.0438i	0.829041	−	1.43594i
$818$	7.91453	−	9.02649i	0.276725	−	0.315604i
$819$	−16.5542	+	4.25031i	−0.578450	+	0.148518i
$820$	−34.0226	+	4.48563i	−1.18812	+	0.156645i
$821$	−28.5066	−	16.4583i	−0.994886	−	0.574398i	−0.0881550	−	0.996107i	$-0.528097\pi$
$821$	−28.5066	−	16.4583i	−0.994886	−	0.574398i	−0.906731	+	0.421709i	$0.861430\pi$
$822$	6.25219	+	18.4127i	0.218070	+	0.642217i
$823$	−22.4763	+	12.9767i	−0.783476	+	0.452340i	−0.837661	−	0.546191i	$-0.816077\pi$
$823$	−22.4763	+	12.9767i	−0.783476	+	0.452340i	0.0541849	+	0.998531i	$0.482744\pi$
$824$	−10.5442	−	7.04112i	−0.367324	−	0.245289i
$825$	4.34757	−	2.17418i	0.151363	−	0.0756951i
$826$	−0.409431	−	0.0814012i	−0.0142459	−	0.00283231i
$827$	−12.8658			−0.447388			−0.223694	−	0.974659i	$-0.571812\pi$
$827$	−12.8658			−0.447388			−0.223694	+	0.974659i	$0.571812\pi$
$828$	17.4061	+	22.6753i	0.604904	+	0.788021i
$829$	2.65696	−	4.60199i	0.0922801	−	0.159834i	−0.816190	−	0.577783i	$-0.803918\pi$
$829$	2.65696	−	4.60199i	0.0922801	−	0.159834i	0.908470	+	0.417950i	$0.137251\pi$
$830$	−4.12012	+	1.39902i	−0.143011	+	0.0485607i
$831$	−5.26487			−0.182636
$832$	11.3020	−	26.5380i	0.391826	−	0.920039i
$833$		−	10.4704i		−	0.362777i
$834$	−2.31385	−	6.81428i	−0.0801219	−	0.235959i
$835$	20.5325	−	35.5632i	0.710555	−	1.23072i
$836$	−30.0165	+	20.3073i	−1.03814	+	0.702344i
$837$	33.1843			1.14702
$838$	3.28149	+	0.652410i	0.113357	+	0.0225371i
$839$	−33.4498	+	19.3122i	−1.15481	+	0.666733i	−0.950056	−	0.312080i	$-0.898974\pi$
$839$	−33.4498	+	19.3122i	−1.15481	+	0.666733i	−0.204759	+	0.978812i	$0.565641\pi$
$840$	9.34242	+	6.23862i	0.322344	+	0.215253i
$841$	−10.5981	−	18.3565i	−0.365452	−	0.632981i
$842$	−5.36207	+	1.82074i	−0.184789	+	0.0627468i
$843$	−9.78614	+	16.9501i	−0.337053	+	0.583792i
$844$	1.59880	+	12.1266i	0.0550331	+	0.417415i
$845$	−0.715864	+	34.1599i	−0.0246265	+	1.17514i
$846$	8.11417	−	9.25418i	0.278971	−	0.318165i
$847$	−12.9801	+	17.3120i	−0.446002	+	0.594847i
$848$	12.8370	−	47.9801i	0.440825	−	1.64764i
$849$	4.22798	−	2.44102i	0.145104	−	0.0837758i
$850$	−5.94877	+	6.78456i	−0.204041	+	0.232708i
$851$	−0.0588347	+	0.0339682i	−0.00201683	+	0.00116442i
$852$	−4.52818	+	3.47594i	−0.155133	+	0.119084i
$853$			1.98553i			0.0679833i	0.999422	+	0.0339916i	$0.0108220\pi$
$853$			1.98553i			0.0679833i	−0.999422	+	0.0339916i	$0.989178\pi$
$854$	20.6870	+	4.11289i	0.707895	+	0.140740i
$855$	−17.3017	+	29.9673i	−0.591704	+	1.02486i
$856$	12.0600	+	24.4380i	0.412203	+	0.835274i
$857$			57.0085i			1.94737i	0.227890	+	0.973687i	$0.426817\pi$
$857$			57.0085i			1.94737i	−0.227890	+	0.973687i	$0.573183\pi$
$858$	−12.9921	−	0.0625294i	−0.443542	−	0.00213472i
$859$		−	20.3043i		−	0.692773i	−0.938092	−	0.346387i	$-0.887409\pi$
$859$		−	20.3043i		−	0.692773i	0.938092	−	0.346387i	$-0.112591\pi$
$860$	42.1304	+	17.4417i	1.43663	+	0.594759i
$861$	−4.93287	+	8.54398i	−0.168112	+	0.291178i
$862$	−5.92640	+	29.8086i	−0.201854	+	1.01528i
$863$		−	41.0714i		−	1.39809i	−0.715079	−	0.699043i	$-0.753609\pi$
$863$		−	41.0714i		−	1.39809i	0.715079	−	0.699043i	$-0.246391\pi$
$864$	23.4591	−	1.54860i	0.798096	−	0.0526845i
$865$	−50.3795	+	29.0866i	−1.71296	+	0.988975i
$866$	9.77376	+	8.56974i	0.332126	+	0.291212i
$867$	−3.86860	+	2.23354i	−0.131385	+	0.0758549i
$868$	12.0155	−	29.0234i	0.407834	−	0.985119i
$869$	3.88042	−	5.87807i	0.131634	−	0.199400i
$870$	−5.99787	−	5.25900i	−0.203347	−	0.178297i
$871$	8.66761	+	33.7588i	0.293691	+	1.14387i
$872$	1.66816	+	1.11395i	0.0564911	+	0.0377232i
$873$	15.4511	−	26.7621i	0.522941	−	0.905760i
$874$	−14.7347	−	43.3936i	−0.498408	−	1.46781i
$875$	7.99339	+	13.8450i	0.270226	+	0.468045i
$876$	2.52115	+	19.1224i	0.0851818	+	0.646087i
$877$	−22.8207	+	13.1755i	−0.770601	+	0.444907i	−0.833089	−	0.553139i	$-0.813430\pi$
$877$	−22.8207	+	13.1755i	−0.770601	+	0.444907i	0.0624881	+	0.998046i	$0.480096\pi$
$878$	7.19269	−	36.1778i	0.242742	−	1.22094i
$879$	5.90567			0.199193
$880$	−23.1454	−	26.0779i	−0.780230	−	0.879085i
$881$	7.52191	−	13.0283i	0.253420	−	0.438936i	−0.711045	−	0.703146i	$-0.751778\pi$
$881$	7.52191	−	13.0283i	0.253420	−	0.438936i	0.964465	+	0.264210i	$0.0851113\pi$
$882$	10.1027	−	3.43045i	0.340175	−	0.115509i
$883$		−	34.9951i		−	1.17768i	−0.808250	−	0.588840i	$-0.799585\pi$
$883$		−	34.9951i		−	1.17768i	0.808250	−	0.588840i	$-0.200415\pi$
$884$	22.3752	−	8.99949i	0.752558	−	0.302686i
$885$	−0.302994			−0.0101850
$886$	−10.7023	−	31.5183i	−0.359551	−	1.05888i
$887$	−0.282929	+	0.490048i	−0.00949984	+	0.0164542i	−0.870736	−	0.491750i	$-0.836357\pi$
$887$	−0.282929	+	0.490048i	−0.00949984	+	0.0164542i	0.861236	+	0.508205i	$0.169691\pi$
$888$	−0.00162087	+	0.0248363i	−5.43927e−5	+	0.000833452i
$889$	20.1585			0.676095
$890$	12.1584	−	61.1543i	0.407551	−	2.04990i
$891$	5.98798	+	11.9738i	0.200605	+	0.401138i
$892$	38.1721	−	5.03271i	1.27810	−	0.168507i
$893$	−17.0876	+	9.86553i	−0.571815	+	0.330137i
$894$	12.2814	−	4.17027i	0.410753	−	0.139475i
$895$	−6.85519	−	3.95785i	−0.229144	−	0.132296i
$896$	7.13977	−	21.0784i	0.238523	−	0.704179i
$897$	4.41815	−	15.8237i	0.147518	−	0.528340i
$898$	3.20565	+	2.81075i	0.106974	+	0.0937960i
$899$	−11.1526	+	19.3168i	−0.371959	+	0.644251i
$900$	−8.49533	−	3.51702i	−0.283178	−	0.117234i
$901$	35.9641	−	20.7639i	1.19814	−	0.691746i
$902$	21.5295	−	21.7748i	0.716854	−	0.725020i
$903$	11.3526	−	6.55445i	0.377792	−	0.218119i
$904$	19.1499	+	1.24976i	0.636917	+	0.0415665i
$905$	24.0509			0.799479
$906$	6.24088	+	1.24078i	0.207339	+	0.0412222i
$907$	−5.03813	−	2.90877i	−0.167289	−	0.0965841i	0.414018	−	0.910269i	$-0.364125\pi$
$907$	−5.03813	−	2.90877i	−0.167289	−	0.0965841i	−0.581307	+	0.813685i	$0.697458\pi$
$908$	39.0489	+	16.1660i	1.29588	+	0.536489i
$909$		−	5.77658i		−	0.191597i
$910$	1.45092	+	26.3217i	0.0480974	+	0.872556i
$911$			9.42644i			0.312312i	0.987732	+	0.156156i	$0.0499103\pi$
$911$			9.42644i			0.312312i	−0.987732	+	0.156156i	$0.950090\pi$
$912$	−16.2187	−	4.33930i	−0.537055	−	0.143688i
$913$	2.13902	−	3.24020i	0.0707913	−	0.107235i
$914$	11.5106	+	2.28848i	0.380736	+	0.0756962i
$915$	15.3092			0.506105
$916$	−3.01305	+	2.31289i	−0.0995541	+	0.0764201i
$917$	2.18086	+	3.77736i	0.0720184	+	0.124740i
$918$	14.7803	+	12.9595i	0.487822	+	0.427727i
$919$	4.41310	+	7.64371i	0.145575	+	0.252143i	0.929587	−	0.368602i	$-0.120164\pi$
$919$	4.41310	+	7.64371i	0.145575	+	0.252143i	−0.784013	+	0.620745i	$0.786830\pi$
$920$	39.5387	−	19.5121i	1.30355	−	0.643295i
$921$	4.47461	+	2.58342i	0.147443	+	0.0851265i
$922$	−34.3365	+	39.1607i	−1.13081	+	1.28969i
$923$	−12.9021	−	3.60239i	−0.424677	−	0.118574i
$924$	−9.99868	+	0.713182i	−0.328932	+	0.0234620i
$925$	0.0109258	−	0.0189241i	0.000359240	−	0.000622221i
$926$	−18.7763	−	55.2961i	−0.617026	−	1.81714i
$927$	9.35516	−	5.40121i	0.307264	−	0.177399i
$928$	−6.98268	+	14.1762i	−0.229218	+	0.465355i
$929$	−2.66345	−	4.61324i	−0.0873851	−	0.151355i	0.819020	−	0.573765i	$-0.194518\pi$
$929$	−2.66345	−	4.61324i	−0.0873851	−	0.151355i	−0.906405	+	0.422410i	$0.861184\pi$
$930$	4.44597	−	22.3623i	0.145789	−	0.733290i
$931$	−17.1043			−0.560572
$932$	−23.7682	−	30.9634i	−0.778555	−	1.01424i
$933$	4.57693	−	7.92747i	0.149842	−	0.259534i
$934$	1.03705	+	3.05411i	0.0339333	+	0.0999337i
$935$	1.74465	−	29.1012i	0.0570561	−	0.951710i
$936$	16.0143	+	18.6409i	0.523445	+	0.609296i
$937$			14.9499i			0.488392i	0.969726	+	0.244196i	$0.0785240\pi$
$937$			14.9499i			0.488392i	−0.969726	+	0.244196i	$0.921476\pi$
$938$	8.64628	+	25.4633i	0.282311	+	0.831406i
$939$	16.2895	+	9.40473i	0.531587	+	0.306912i
$940$	−11.5593	−	15.0586i	−0.377024	−	0.491157i
$941$			31.6646i			1.03224i	0.856517	+	0.516118i	$0.172624\pi$
$941$			31.6646i			1.03224i	−0.856517	+	0.516118i	$0.827376\pi$
$942$	−14.1754	−	2.81828i	−0.461859	−	0.0918246i
$943$	19.3606	+	33.5336i	0.630469	+	1.09200i
$944$	0.155571	+	0.579731i	0.00506339	+	0.0188686i
$945$	−18.6079	+	10.7433i	−0.605316	+	0.349479i
$946$	−39.2407	+	10.7531i	−1.27582	+	0.349613i
$947$	−7.32411	−	4.22857i	−0.238001	−	0.137410i	0.376256	−	0.926516i	$-0.377211\pi$
$947$	−7.32411	−	4.22857i	−0.238001	−	0.137410i	−0.614258	+	0.789105i	$0.710545\pi$
$948$	3.23500	−	0.426510i	0.105068	−	0.0138524i
$949$	−32.3381	+	31.6675i	−1.04974	+	1.02797i
$950$	11.0832	+	9.71788i	0.359587	+	0.315290i
$951$	8.77318	+	5.06520i	0.284490	+	0.164250i
$952$	16.6862	−	8.23456i	0.540804	−	0.266884i
$953$	−26.4742	+	15.2849i	−0.857583	+	0.495126i	−0.863202	−	0.504858i	$-0.831545\pi$
$953$	−26.4742	+	15.2849i	−0.857583	+	0.495126i	0.00561887	+	0.999984i	$0.498211\pi$
$954$	31.8178	+	27.8982i	1.03014	+	0.903239i
$955$	24.9665	−	14.4144i	0.807896	−	0.466439i
$956$	14.3864	−	11.0434i	0.465290	−	0.357168i
$957$	7.10511	+	0.425960i	0.229675	+	0.0137693i
$958$	−6.05856	+	30.4733i	−0.195743	+	0.984548i
$959$	−17.6030	+	30.4893i	−0.568430	+	0.984549i
$960$	2.09944	−	16.0162i	0.0677590	−	0.516920i
$961$	−32.7534			−1.05656
$962$	−0.0488964	+	0.0319422i	−0.00157648	+	0.00102986i
$963$	−23.2183			−0.748200
$964$	−11.5138	+	27.8114i	−0.370834	+	0.895746i
$965$	−53.9337	−	31.1386i	−1.73619	−	1.00239i
$966$	2.47174	−	12.4324i	0.0795270	−	0.400005i
$967$	32.0750			1.03146			0.515731	−	0.856751i	$-0.327520\pi$
$967$	32.0750			1.03146			0.515731	+	0.856751i	$0.327520\pi$
$968$	30.5822	+	5.72089i	0.982949	+	0.183876i
$969$	−7.01882	−	12.1570i	−0.225477	−	0.390538i
$970$	−35.8388	−	31.4238i	−1.15071	−	1.00896i
$971$	−37.8267	+	21.8392i	−1.21392	+	0.700854i	−0.963610	−	0.267313i	$-0.913864\pi$
$971$	−37.8267	+	21.8392i	−1.21392	+	0.700854i	−0.250305	+	0.968167i	$0.580531\pi$
$972$	−11.9108	+	28.7704i	−0.382038	+	0.922810i
$973$	6.51461	−	11.2836i	0.208849	−	0.361737i
$974$	2.78791	−	3.17960i	0.0893303	−	0.101881i
$975$	1.31414	+	5.11835i	0.0420863	+	0.163918i
$976$	−7.86039	−	29.2916i	−0.251605	−	0.937601i
$977$	−14.4850	+	25.0888i	−0.463417	+	0.802661i	−0.999129	−	0.0417395i	$-0.986710\pi$
$977$	−14.4850	+	25.0888i	−0.463417	+	0.802661i	0.535712	+	0.844401i	$0.320043\pi$
$978$	23.0923	−	7.84120i	0.738412	−	0.250734i
$979$	24.8849	+	49.7608i	0.795324	+	1.59036i
$980$	−2.15104	−	16.3152i	−0.0687125	−	0.521171i
$981$	−1.48005	+	0.854507i	−0.0472544	+	0.0272823i
$982$	−10.6313	+	53.4730i	−0.339257	+	1.70639i
$983$		−	56.5089i		−	1.80235i	−0.433452	−	0.901177i	$-0.642705\pi$
$983$		−	56.5089i		−	1.80235i	0.433452	−	0.901177i	$-0.357295\pi$
$984$	14.1558	+	0.923834i	0.451270	+	0.0294507i
$985$	−7.65860	−	4.42170i	−0.244023	−	0.140887i
$986$	−12.5111	+	4.24826i	−0.398436	+	0.135292i
$987$	−5.45758			−0.173717
$988$	−14.7015	−	36.5519i	−0.467717	−	1.16287i
$989$		−	51.4501i		−	1.63602i
$990$	28.6508	−	7.85116i	0.910583	−	0.249526i
$991$	23.4354	+	13.5304i	0.744450	+	0.429808i	0.823685	−	0.567048i	$-0.191915\pi$
$991$	23.4354	+	13.5304i	0.744450	+	0.429808i	−0.0792354	+	0.996856i	$0.525248\pi$
$992$	−45.0695	+	2.97516i	−1.43096	+	0.0944613i
$993$	−19.4924			−0.618573
$994$	−10.1369	−	2.01537i	−0.321522	−	0.0639235i
$995$	23.8896	−	13.7927i	0.757352	−	0.437257i
$996$	1.78324	−	0.235107i	0.0565042	−	0.00744967i
$997$	2.69408	−	1.55543i	0.0853222	−	0.0492608i	−0.456732	−	0.889604i	$-0.650980\pi$
$997$	2.69408	−	1.55543i	0.0853222	−	0.0492608i	0.542054	+	0.840344i	$0.317647\pi$
$998$	18.8896	+	55.6299i	0.597940	+	1.76093i
$999$	−0.0412265	−	0.0238021i	−0.00130435	−	0.000753066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.t.a.87.10	✓	160
4.3	odd	2	inner	572.2.t.a.87.38	yes	160
11.10	odd	2	inner	572.2.t.a.87.71	yes	160
13.3	even	3	inner	572.2.t.a.263.43	yes	160
44.43	even	2	inner	572.2.t.a.87.43	yes	160
52.3	odd	6	inner	572.2.t.a.263.71	yes	160
143.120	odd	6	inner	572.2.t.a.263.38	yes	160
572.263	even	6	inner	572.2.t.a.263.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.t.a.87.10	✓	160	1.1	even	1	trivial
572.2.t.a.87.38	yes	160	4.3	odd	2	inner
572.2.t.a.87.43	yes	160	44.43	even	2	inner
572.2.t.a.87.71	yes	160	11.10	odd	2	inner
572.2.t.a.263.10	yes	160	572.263	even	6	inner
572.2.t.a.263.38	yes	160	143.120	odd	6	inner
572.2.t.a.263.43	yes	160	13.3	even	3	inner
572.2.t.a.263.71	yes	160	52.3	odd	6	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33912 + 0.454709i) q^{2} +(0.665321 + 0.384123i) q^{3} +(1.58648 - 1.21782i) q^{4} +2.62826 q^{5} +(-1.06561 - 0.211859i) q^{6} +(-0.983531 - 1.70353i) q^{7} +(-1.57073 + 2.35219i) q^{8} +(-1.20490 - 2.08695i) q^{9} +O(q^{10})\)	\(q+(-1.33912 + 0.454709i) q^{2} +(0.665321 + 0.384123i) q^{3} +(1.58648 - 1.21782i) q^{4} +2.62826 q^{5} +(-1.06561 - 0.211859i) q^{6} +(-0.983531 - 1.70353i) q^{7} +(-1.57073 + 2.35219i) q^{8} +(-1.20490 - 2.08695i) q^{9} +(-3.51955 + 1.19509i) q^{10} +(1.82723 - 2.76789i) q^{11} +(1.52331 - 0.200837i) q^{12} +(2.52266 + 2.57608i) q^{13} +(2.09167 + 1.83400i) q^{14} +(1.74864 + 1.00958i) q^{15} +(1.03383 - 3.86409i) q^{16} +(2.89638 - 1.67223i) q^{17} +(2.56246 + 2.24679i) q^{18} +(-2.73174 - 4.73151i) q^{19} +(4.16968 - 3.20074i) q^{20} -1.51119i q^{21} +(-1.18829 + 4.53740i) q^{22} +(-5.13652 - 2.96557i) q^{23} +(-1.94857 + 0.961608i) q^{24} +1.90775 q^{25} +(-4.54951 - 2.30260i) q^{26} -4.15606i q^{27} +(-3.63494 - 1.50484i) q^{28} +(2.41927 + 1.39676i) q^{29} +(-2.80069 - 0.556821i) q^{30} +7.98457i q^{31} +(0.372613 + 5.64457i) q^{32} +(2.27890 - 1.13966i) q^{33} +(-3.11822 + 3.55632i) q^{34} +(-2.58497 - 4.47731i) q^{35} +(-4.45307 - 1.84355i) q^{36} +(0.00572710 - 0.00991962i) q^{37} +(5.80958 + 5.09390i) q^{38} +(0.688846 + 2.68293i) q^{39} +(-4.12829 + 6.18217i) q^{40} +(-5.65382 - 3.26423i) q^{41} +(0.687151 + 2.02366i) q^{42} +(4.33729 + 7.51240i) q^{43} +(-0.471935 - 6.61644i) q^{44} +(-3.16679 - 5.48504i) q^{45} +(8.22688 + 1.63563i) q^{46} -3.61145i q^{47} +(2.17212 - 2.17374i) q^{48} +(1.56533 - 2.71124i) q^{49} +(-2.55470 + 0.867470i) q^{50} +2.56936 q^{51} +(7.13935 + 1.01475i) q^{52} +12.4169 q^{53} +(1.88980 + 5.56545i) q^{54} +(4.80243 - 7.27474i) q^{55} +(5.55188 + 0.362326i) q^{56} -4.19729i q^{57} +(-3.87481 - 0.770370i) q^{58} +(-0.129956 + 0.0750302i) q^{59} +(4.00365 - 0.527852i) q^{60} +(6.56619 - 3.79099i) q^{61} +(-3.63066 - 10.6923i) q^{62} +(-2.37011 + 4.10515i) q^{63} +(-3.06561 - 7.38932i) q^{64} +(6.63020 + 6.77060i) q^{65} +(-2.53351 + 2.56237i) q^{66} +(8.37159 + 4.83334i) q^{67} +(2.55858 - 6.18022i) q^{68} +(-2.27829 - 3.94611i) q^{69} +(5.49746 + 4.82023i) q^{70} +(-3.21751 + 1.85763i) q^{71} +(6.80147 + 0.443877i) q^{72} +12.5532i q^{73} +(-0.00315872 + 0.0158877i) q^{74} +(1.26926 + 0.732809i) q^{75} +(-10.0960 - 4.17967i) q^{76} +(-6.51231 - 0.390421i) q^{77} +(-2.14240 - 3.27954i) q^{78} +2.12366 q^{79} +(2.71718 - 10.1558i) q^{80} +(-2.01826 + 3.49573i) q^{81} +(9.05541 + 1.80035i) q^{82} +1.17064 q^{83} +(-1.84035 - 2.39747i) q^{84} +(7.61244 - 4.39504i) q^{85} +(-9.22410 - 8.08779i) q^{86} +(1.07306 + 1.85859i) q^{87} +(3.64053 + 8.64561i) q^{88} +(-8.38748 + 14.5275i) q^{89} +(6.73480 + 5.90515i) q^{90} +(1.90730 - 6.83107i) q^{91} +(-11.7605 + 1.55054i) q^{92} +(-3.06706 + 5.31230i) q^{93} +(1.64216 + 4.83616i) q^{94} +(-7.17971 - 12.4356i) q^{95} +(-1.92030 + 3.89858i) q^{96} +(6.41179 + 11.1055i) q^{97} +(-0.863344 + 4.34244i) q^{98} +(-7.97807 - 0.478295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) \) 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9	\( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) \) 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9 - 4 * q^12 + 8 * q^14 - 14 * q^16 - 26 * q^20 + 112 * q^25 - 14 * q^33 + 12 * q^34 - 6 * q^36 - 4 * q^37 + 40 * q^38 + 54 * q^42 - 16 * q^44 - 48 * q^45 - 40 * q^48 - 52 * q^49 - 32 * q^53 - 18 * q^56 - 6 * q^58 - 52 * q^60 + 16 * q^64 - 84 * q^66 - 12 * q^69 - 68 * q^70 - 4 * q^77 + 28 * q^78 - 44 * q^80 - 40 * q^81 - 38 * q^82 + 120 * q^86 - 14 * q^88 - 64 * q^92 - 8 * q^93

Introduction

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