LMFDB - Embedded newform 627.2.j.c.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(58,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("627.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.j (of order $5$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.2
Character	$\chi$	$=$	627.58
Dual form			627.2.j.c.400.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82006 + 1.32235i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.945976 - 2.91141i) q^{4} +(-1.97134 - 1.43226i) q^{5} +(1.82006 + 1.32235i) q^{6} +(-1.36214 + 4.19225i) q^{7} +(0.737778 + 2.27065i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.48193 q^{10} +(2.60100 - 2.05786i) q^{11} -3.06124 q^{12} +(-3.94848 + 2.86874i) q^{13} +(-3.06444 - 9.43138i) q^{14} +(-0.752986 + 2.31745i) q^{15} +(0.607798 + 0.441591i) q^{16} +(4.90417 + 3.56309i) q^{17} +(0.695202 - 2.13961i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-6.03476 + 4.38451i) q^{20} +4.40799 q^{21} +(-2.01278 + 7.18487i) q^{22} -6.29746 q^{23} +(1.93153 - 1.40334i) q^{24} +(0.289728 + 0.891690i) q^{25} +(3.39299 - 10.4426i) q^{26} +(0.809017 + 0.587785i) q^{27} +(10.9168 + 7.93153i) q^{28} +(2.66237 - 8.19392i) q^{29} +(-1.69401 - 5.21362i) q^{30} +(3.45973 - 2.51364i) q^{31} -6.46517 q^{32} +(-2.76089 - 1.83779i) q^{33} -13.6375 q^{34} +(8.68966 - 6.31341i) q^{35} +(0.945976 + 2.91141i) q^{36} +(1.70180 - 5.23759i) q^{37} +(1.82006 + 1.32235i) q^{38} +(3.94848 + 2.86874i) q^{39} +(1.79775 - 5.53292i) q^{40} +(-2.23778 - 6.88717i) q^{41} +(-8.02281 + 5.82892i) q^{42} +5.31450 q^{43} +(-3.53079 - 9.51928i) q^{44} +2.43671 q^{45} +(11.4618 - 8.32746i) q^{46} +(-3.56419 - 10.9695i) q^{47} +(0.232158 - 0.714509i) q^{48} +(-10.0564 - 7.30639i) q^{49} +(-1.70645 - 1.23981i) q^{50} +(1.87323 - 5.76519i) q^{51} +(4.61692 + 14.2094i) q^{52} +(2.38477 - 1.73264i) q^{53} -2.24972 q^{54} +(-8.07487 + 0.331418i) q^{55} -10.5241 q^{56} +(-0.809017 + 0.587785i) q^{57} +(5.98958 + 18.4340i) q^{58} +(-1.40230 + 4.31583i) q^{59} +(6.03476 + 4.38451i) q^{60} +(2.81427 + 2.04469i) q^{61} +(-2.97300 + 9.14997i) q^{62} +(-1.36214 - 4.19225i) q^{63} +(10.5514 - 7.66605i) q^{64} +11.8926 q^{65} +(7.45520 - 0.305985i) q^{66} +4.41626 q^{67} +(15.0128 - 10.9075i) q^{68} +(1.94602 + 5.98924i) q^{69} +(-7.46717 + 22.9816i) q^{70} +(10.4825 + 7.61598i) q^{71} +(-1.93153 - 1.40334i) q^{72} +(0.0627017 - 0.192976i) q^{73} +(3.82856 + 11.7831i) q^{74} +(0.758517 - 0.551095i) q^{75} -3.06124 q^{76} +(5.08411 + 13.7071i) q^{77} -10.9800 q^{78} +(-0.0135983 + 0.00987976i) q^{79} +(-0.565703 - 1.74106i) q^{80} +(0.309017 - 0.951057i) q^{81} +(13.1802 + 9.57594i) q^{82} +(1.21330 + 0.881516i) q^{83} +(4.16985 - 12.8335i) q^{84} +(-4.56452 - 14.0481i) q^{85} +(-9.67272 + 7.02764i) q^{86} -8.61560 q^{87} +(6.59163 + 4.38772i) q^{88} -11.2119 q^{89} +(-4.43497 + 3.22220i) q^{90} +(-6.64806 - 20.4606i) q^{91} +(-5.95724 + 18.3345i) q^{92} +(-3.45973 - 2.51364i) q^{93} +(20.9926 + 15.2520i) q^{94} +(-0.752986 + 2.31745i) q^{95} +(1.99785 + 6.14874i) q^{96} +(11.0636 - 8.03816i) q^{97} +27.9648 q^{98} +(-0.894678 + 3.19367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{2} + 10 q^{3} - 3 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 13 q^{8} - 10 q^{9} + 10 q^{10} + 7 q^{11} - 42 q^{12} - 12 q^{13} - 2 q^{14} - 7 q^{15} - 27 q^{16} + 11 q^{17} - 4 q^{18} + 10 q^{19}+ \cdots - 13 q^{99}+O(q^{100}) $ 40 * q + q^2 + 10 * q^3 - 3 * q^4 + 2 * q^5 - q^6 + 4 * q^7 - 13 * q^8 - 10 * q^9 + 10 * q^10 + 7 * q^11 - 42 * q^12 - 12 * q^13 - 2 * q^14 - 7 * q^15 - 27 * q^16 + 11 * q^17 - 4 * q^18 + 10 * q^19 - 11 * q^20 + 6 * q^21 - 2 * q^22 - 60 * q^23 - 7 * q^24 - 18 * q^25 - 35 * q^26 + 10 * q^27 + 20 * q^28 + 25 * q^29 - 5 * q^30 - 12 * q^31 + 40 * q^32 + 3 * q^33 - 10 * q^34 + 24 * q^35 - 3 * q^36 - 23 * q^37 - q^38 + 12 * q^39 + 80 * q^40 + 18 * q^41 - 28 * q^42 - 6 * q^43 + 14 * q^44 - 18 * q^45 - 15 * q^46 - 9 * q^47 - 8 * q^48 - 4 * q^49 + 90 * q^50 + 4 * q^51 + 15 * q^52 - 26 * q^53 - 6 * q^54 + 38 * q^55 - 124 * q^56 - 10 * q^57 + 10 * q^58 + 7 * q^59 + 11 * q^60 + 18 * q^61 + 105 * q^62 + 4 * q^63 - 85 * q^64 + 36 * q^65 - 8 * q^66 - 88 * q^67 + 40 * q^68 - 103 * q^70 + 30 * q^71 + 7 * q^72 - 2 * q^73 - 4 * q^74 + 13 * q^75 - 42 * q^76 + 57 * q^77 + 20 * q^78 + 59 * q^79 + 11 * q^80 - 10 * q^81 + 40 * q^82 - 54 * q^83 - 15 * q^84 + 21 * q^85 - 108 * q^86 - 30 * q^87 + 83 * q^88 - 74 * q^89 - 10 * q^90 + q^91 - 125 * q^92 + 12 * q^93 - 10 * q^94 - 7 * q^95 + 55 * q^96 - 17 * q^97 + 78 * q^98 - 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.82006	+	1.32235i	−1.28698	+	0.935044i	−0.999740	−	0.0228146i	$-0.992737\pi$
$2$	−1.82006	+	1.32235i	−1.28698	+	0.935044i	−0.287239	+	0.957859i	$0.592737\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.945976	−	2.91141i	0.472988	−	1.45571i
$5$	−1.97134	−	1.43226i	−0.881612	−	0.640528i	0.0520657	−	0.998644i	$-0.483419\pi$
$5$	−1.97134	−	1.43226i	−0.881612	−	0.640528i	−0.933677	+	0.358115i	$0.883419\pi$
$6$	1.82006	+	1.32235i	0.743037	+	0.539848i
$7$	−1.36214	+	4.19225i	−0.514842	+	1.58452i	0.268728	+	0.963216i	$0.413397\pi$
$7$	−1.36214	+	4.19225i	−0.514842	+	1.58452i	−0.783570	+	0.621304i	$0.786603\pi$
$8$	0.737778	+	2.27065i	0.260844	+	0.802795i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	5.48193			1.73354
$11$	2.60100	−	2.05786i	0.784232	−	0.620467i
$11$	2.60100	−	2.05786i	0.784232	−	0.620467i
$12$	−3.06124			−0.883705
$13$	−3.94848	+	2.86874i	−1.09511	+	0.795645i	−0.980255	−	0.197737i	$-0.936641\pi$
$13$	−3.94848	+	2.86874i	−1.09511	+	0.795645i	−0.114856	+	0.993382i	$0.536641\pi$
$14$	−3.06444	−	9.43138i	−0.819007	−	2.52064i
$15$	−0.752986	+	2.31745i	−0.194420	+	0.598364i
$16$	0.607798	+	0.441591i	0.151950	+	0.110398i
$17$	4.90417	+	3.56309i	1.18944	+	0.864175i	0.993204	−	0.116382i	$-0.0371298\pi$
$17$	4.90417	+	3.56309i	1.18944	+	0.864175i	0.196231	+	0.980558i	$0.437130\pi$
$18$	0.695202	−	2.13961i	0.163861	−	0.504311i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−6.03476	+	4.38451i	−1.34941	+	0.980406i
$21$	4.40799			0.961902
$22$	−2.01278	+	7.18487i	−0.429125	+	1.53182i
$23$	−6.29746			−1.31311			−0.656555	−	0.754278i	$-0.727987\pi$
$23$	−6.29746			−1.31311			−0.656555	+	0.754278i	$0.727987\pi$
$24$	1.93153	−	1.40334i	0.394271	−	0.286455i
$25$	0.289728	+	0.891690i	0.0579455	+	0.178338i
$26$	3.39299	−	10.4426i	0.665421	−	2.04796i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	10.9168	+	7.93153i	2.06308	+	1.49892i
$29$	2.66237	−	8.19392i	0.494389	−	1.52157i	−0.323518	−	0.946222i	$-0.604866\pi$
$29$	2.66237	−	8.19392i	0.494389	−	1.52157i	0.817907	−	0.575351i	$-0.195134\pi$
$30$	−1.69401	−	5.21362i	−0.309282	−	0.951873i
$31$	3.45973	−	2.51364i	0.621386	−	0.451463i	−0.232019	−	0.972711i	$-0.574533\pi$
$31$	3.45973	−	2.51364i	0.621386	−	0.451463i	0.853405	+	0.521248i	$0.174533\pi$
$32$	−6.46517			−1.14289
$33$	−2.76089	−	1.83779i	−0.480610	−	0.319918i
$34$	−13.6375			−2.33882
$35$	8.68966	−	6.31341i	1.46882	−	1.06716i
$36$	0.945976	+	2.91141i	0.157663	+	0.485236i
$37$	1.70180	−	5.23759i	0.279773	−	0.861054i	−0.708143	−	0.706069i	$-0.750467\pi$
$37$	1.70180	−	5.23759i	0.279773	−	0.861054i	0.987917	−	0.154985i	$-0.0495330\pi$
$38$	1.82006	+	1.32235i	0.295253	+	0.214514i
$39$	3.94848	+	2.86874i	0.632263	+	0.459366i
$40$	1.79775	−	5.53292i	0.284250	−	0.874831i
$41$	−2.23778	−	6.88717i	−0.349482	−	1.07559i	−0.959140	−	0.282931i	$-0.908693\pi$
$41$	−2.23778	−	6.88717i	−0.349482	−	1.07559i	0.609658	−	0.792664i	$-0.291307\pi$
$42$	−8.02281	+	5.82892i	−1.23795	+	0.899421i
$43$	5.31450			0.810454			0.405227	−	0.914216i	$-0.367193\pi$
$43$	5.31450			0.810454			0.405227	+	0.914216i	$0.367193\pi$
$44$	−3.53079	−	9.51928i	−0.532287	−	1.43509i
$45$	2.43671			0.363244
$46$	11.4618	−	8.32746i	1.68994	−	1.22782i
$47$	−3.56419	−	10.9695i	−0.519891	−	1.60006i	−0.774202	−	0.632938i	$-0.781849\pi$
$47$	−3.56419	−	10.9695i	−0.519891	−	1.60006i	0.254311	−	0.967122i	$-0.418151\pi$
$48$	0.232158	−	0.714509i	0.0335092	−	0.103131i
$49$	−10.0564	−	7.30639i	−1.43663	−	1.04377i
$50$	−1.70645	−	1.23981i	−0.241329	−	0.175335i
$51$	1.87323	−	5.76519i	0.262304	−	0.807289i
$52$	4.61692	+	14.2094i	0.640252	+	1.97049i
$53$	2.38477	−	1.73264i	0.327574	−	0.237996i	−0.411827	−	0.911262i	$-0.635109\pi$
$53$	2.38477	−	1.73264i	0.327574	−	0.237996i	0.739400	+	0.673266i	$0.235109\pi$
$54$	−2.24972			−0.306148
$55$	−8.07487	+	0.331418i	−1.08882	+	0.0446884i
$56$	−10.5241			−1.40634
$57$	−0.809017	+	0.587785i	−0.107157	+	0.0778541i
$58$	5.98958	+	18.4340i	0.786470	+	2.42051i
$59$	−1.40230	+	4.31583i	−0.182564	+	0.561873i	−0.999898	−	0.0142905i	$-0.995451\pi$
$59$	−1.40230	+	4.31583i	−0.182564	+	0.561873i	0.817334	+	0.576164i	$0.195451\pi$
$60$	6.03476	+	4.38451i	0.779084	+	0.566038i
$61$	2.81427	+	2.04469i	0.360330	+	0.261795i	0.753190	−	0.657803i	$-0.228514\pi$
$61$	2.81427	+	2.04469i	0.360330	+	0.261795i	−0.392860	+	0.919598i	$0.628514\pi$
$62$	−2.97300	+	9.14997i	−0.377572	+	1.16205i
$63$	−1.36214	−	4.19225i	−0.171614	−	0.528173i
$64$	10.5514	−	7.66605i	1.31893	−	0.958256i
$65$	11.8926			1.47510
$66$	7.45520	−	0.305985i	0.917672	−	0.0376641i
$67$	4.41626			0.539532			0.269766	−	0.962926i	$-0.413054\pi$
$67$	4.41626			0.539532			0.269766	+	0.962926i	$0.413054\pi$
$68$	15.0128	−	10.9075i	1.82057	−	1.32273i
$69$	1.94602	+	5.98924i	0.234273	+	0.721019i
$70$	−7.46717	+	22.9816i	−0.892498	+	2.74683i
$71$	10.4825	+	7.61598i	1.24404	+	0.903850i	0.997861	−	0.0653737i	$-0.0208239\pi$
$71$	10.4825	+	7.61598i	1.24404	+	0.903850i	0.246182	+	0.969224i	$0.420824\pi$
$72$	−1.93153	−	1.40334i	−0.227633	−	0.165385i
$73$	0.0627017	−	0.192976i	0.00733868	−	0.0225861i	−0.947320	−	0.320288i	$-0.896220\pi$
$73$	0.0627017	−	0.192976i	0.00733868	−	0.0225861i	0.954659	+	0.297702i	$0.0962202\pi$
$74$	3.82856	+	11.7831i	0.445061	+	1.36976i
$75$	0.758517	−	0.551095i	0.0875860	−	0.0636349i
$76$	−3.06124			−0.351149
$77$	5.08411	+	13.7071i	0.579388	+	1.56207i
$78$	−10.9800			−1.24324
$79$	−0.0135983	+	0.00987976i	−0.00152993	+	0.00111156i	−0.588550	−	0.808461i	$-0.700301\pi$
$79$	−0.0135983	+	0.00987976i	−0.00152993	+	0.00111156i	0.587020	+	0.809572i	$0.300301\pi$
$80$	−0.565703	−	1.74106i	−0.0632476	−	0.194656i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	13.1802	+	9.57594i	1.45550	+	1.05749i
$83$	1.21330	+	0.881516i	0.133177	+	0.0967589i	0.652379	−	0.757892i	$-0.273771\pi$
$83$	1.21330	+	0.881516i	0.133177	+	0.0967589i	−0.519202	+	0.854651i	$0.673771\pi$
$84$	4.16985	−	12.8335i	0.454968	−	1.40025i
$85$	−4.56452	−	14.0481i	−0.495091	−	1.52373i
$86$	−9.67272	+	7.02764i	−1.04304	+	0.757810i
$87$	−8.61560			−0.923689
$88$	6.59163	+	4.38772i	0.702670	+	0.467732i
$89$	−11.2119			−1.18846			−0.594229	−	0.804296i	$-0.702543\pi$
$89$	−11.2119			−1.18846			−0.594229	+	0.804296i	$0.702543\pi$
$90$	−4.43497	+	3.22220i	−0.467487	+	0.339649i
$91$	−6.64806	−	20.4606i	−0.696906	−	2.14486i
$92$	−5.95724	+	18.3345i	−0.621085	+	1.91150i
$93$	−3.45973	−	2.51364i	−0.358757	−	0.260652i
$94$	20.9926	+	15.2520i	2.16522	+	1.57312i
$95$	−0.752986	+	2.31745i	−0.0772548	+	0.237766i
$96$	1.99785	+	6.14874i	0.203904	+	0.627553i
$97$	11.0636	−	8.03816i	1.12334	−	0.816152i	0.138625	−	0.990345i	$-0.455732\pi$
$97$	11.0636	−	8.03816i	1.12334	−	0.816152i	0.984712	+	0.174193i	$0.0557317\pi$
$98$	27.9648			2.82488
$99$	−0.894678	+	3.19367i	−0.0899185	+	0.320976i
$100$	2.87015			0.287015
$101$	−2.01357	+	1.46295i	−0.200358	+	0.145569i	−0.683441	−	0.730006i	$-0.739517\pi$
$101$	−2.01357	+	1.46295i	−0.200358	+	0.145569i	0.483082	+	0.875575i	$0.339517\pi$
$102$	4.21423	+	12.9701i	0.417271	+	1.28423i
$103$	2.42932	−	7.47668i	0.239368	−	0.736699i	−0.757144	−	0.653248i	$-0.773406\pi$
$103$	2.42932	−	7.47668i	0.239368	−	0.736699i	0.996512	−	0.0834507i	$-0.0265941\pi$
$104$	−9.42699	−	6.84911i	−0.924392	−	0.671610i
$105$	−8.68966	−	6.31341i	−0.848024	−	0.616126i
$106$	−2.04928	+	6.30702i	−0.199043	+	0.612592i
$107$	−1.19958	−	3.69193i	−0.115968	−	0.356912i	0.876180	−	0.481984i	$-0.160084\pi$
$107$	−1.19958	−	3.69193i	−0.115968	−	0.356912i	−0.992148	+	0.125072i	$0.960084\pi$
$108$	2.47660	−	1.79935i	0.238311	−	0.173143i
$109$	8.70618			0.833901			0.416950	−	0.908929i	$-0.363099\pi$
$109$	8.70618			0.833901			0.416950	+	0.908929i	$0.363099\pi$
$110$	14.2585	−	11.2810i	1.35950	−	1.07560i
$111$	−5.50712			−0.522713
$112$	−2.67917	+	1.94653i	−0.253158	+	0.183930i
$113$	−5.36806	−	16.5212i	−0.504984	−	1.55418i	−0.800797	−	0.598936i	$-0.795590\pi$
$113$	−5.36806	−	16.5212i	−0.504984	−	1.55418i	0.295812	−	0.955246i	$-0.404410\pi$
$114$	0.695202	−	2.13961i	0.0651116	−	0.200393i
$115$	12.4145	+	9.01963i	1.15765	+	0.841084i
$116$	−21.3374	−	15.5025i	−1.98112	−	1.43937i
$117$	1.50818	−	4.64172i	0.139432	−	0.429127i
$118$	−3.15478	−	9.70941i	−0.290421	−	0.893824i
$119$	−21.6175	+	15.7060i	−1.98167	+	1.43977i
$120$	−5.81765			−0.531077
$121$	2.53044	−	10.7050i	0.230040	−	0.973181i
$122$	−7.82594			−0.708528
$123$	−5.85857	+	4.25650i	−0.528250	+	0.383796i
$124$	−4.04543	−	12.4506i	−0.363290	−	1.11809i
$125$	−3.05895	+	9.41447i	−0.273601	+	0.842056i
$126$	8.02281	+	5.82892i	0.714729	+	0.519281i
$127$	−13.7262	−	9.97267i	−1.21800	−	0.884932i	−0.222071	−	0.975031i	$-0.571282\pi$
$127$	−13.7262	−	9.97267i	−1.21800	−	0.884932i	−0.995933	+	0.0900990i	$0.971282\pi$
$128$	−5.07131	+	15.6079i	−0.448245	+	1.37956i
$129$	−1.64227	−	5.05439i	−0.144594	−	0.445014i
$130$	−21.6453	+	15.7262i	−1.89842	+	1.37928i
$131$	16.1486			1.41091			0.705454	−	0.708755i	$-0.250743\pi$
$131$	16.1486			1.41091			0.705454	+	0.708755i	$0.250743\pi$
$132$	−7.96230	+	6.29960i	−0.693030	+	0.548310i
$133$	4.40799			0.382221
$134$	−8.03786	+	5.83985i	−0.694365	+	0.504486i
$135$	−0.752986	−	2.31745i	−0.0648067	−	0.199455i
$136$	−4.47232	+	13.7644i	−0.383499	+	1.18029i
$137$	10.3629	+	7.52908i	0.885361	+	0.643252i	0.934664	−	0.355531i	$-0.115700\pi$
$137$	10.3629	+	7.52908i	0.885361	+	0.643252i	−0.0493033	+	0.998784i	$0.515700\pi$
$138$	−11.4618	−	8.32746i	−0.975690	−	0.708880i
$139$	−0.845086	+	2.60091i	−0.0716793	+	0.220606i	−0.980478	−	0.196629i	$-0.937001\pi$
$139$	−0.845086	+	2.60091i	−0.0716793	+	0.220606i	0.908799	+	0.417235i	$0.137001\pi$
$140$	−10.1607	−	31.2715i	−0.858739	−	2.64293i
$141$	−9.33118	+	6.77950i	−0.785827	+	0.570937i
$142$	−29.1498			−2.44620
$143$	−4.36656	+	15.5870i	−0.365150	+	1.30345i
$144$	−0.751280			−0.0626066
$145$	−16.9843	+	12.3398i	−1.41047	+	1.02477i
$146$	0.141061	+	0.434142i	0.0116743	+	0.0359299i
$147$	−3.84119	+	11.8220i	−0.316816	+	0.975061i
$148$	−13.6389	−	9.90926i	−1.12111	−	0.814536i
$149$	−12.4469	−	9.04318i	−1.01969	−	0.740846i	−0.0534688	−	0.998570i	$-0.517028\pi$
$149$	−12.4469	−	9.04318i	−1.01969	−	0.740846i	−0.966219	+	0.257723i	$0.917028\pi$
$150$	−0.651806	+	2.00605i	−0.0532198	+	0.163794i
$151$	−0.178053	−	0.547992i	−0.0144898	−	0.0445950i	0.943550	−	0.331230i	$-0.107463\pi$
$151$	−0.178053	−	0.547992i	−0.0144898	−	0.0445950i	−0.958040	+	0.286635i	$0.907463\pi$
$152$	1.93153	−	1.40334i	0.156668	−	0.113826i
$153$	−6.06188			−0.490074
$154$	−27.3791	−	18.2249i	−2.20627	−	1.46860i
$155$	−10.4205			−0.836996
$156$	12.0873	−	8.78190i	0.967755	−	0.703115i
$157$	4.65198	+	14.3173i	0.371269	+	1.14265i	0.945962	+	0.324278i	$0.105121\pi$
$157$	4.65198	+	14.3173i	0.371269	+	1.14265i	−0.574693	+	0.818369i	$0.694879\pi$
$158$	0.0116853	−	0.0359636i	0.000929630	−	0.00286111i
$159$	−2.38477	−	1.73264i	−0.189125	−	0.137407i
$160$	12.7451	+	9.25983i	1.00759	+	0.732054i
$161$	8.57804	−	26.4005i	0.676044	−	2.08065i
$162$	0.695202	+	2.13961i	0.0546202	+	0.168104i
$163$	3.03262	−	2.20333i	0.237533	−	0.172578i	−0.462650	−	0.886541i	$-0.653101\pi$
$163$	3.03262	−	2.20333i	0.237533	−	0.172578i	0.700184	+	0.713963i	$0.253101\pi$
$164$	−22.1683			−1.73105
$165$	2.81047	+	7.57724i	0.218795	+	0.589888i
$166$	−3.37396			−0.261870
$167$	4.16190	−	3.02379i	0.322057	−	0.233988i	−0.414996	−	0.909823i	$-0.636217\pi$
$167$	4.16190	−	3.02379i	0.322057	−	0.233988i	0.737053	+	0.675835i	$0.236217\pi$
$168$	3.25212	+	10.0090i	0.250906	+	0.772210i
$169$	3.34361	−	10.2906i	0.257201	−	0.791583i
$170$	26.8843	+	19.5326i	2.06193	+	1.49808i
$171$	0.809017	+	0.587785i	0.0618671	+	0.0449491i
$172$	5.02739	−	15.4727i	0.383335	−	1.17978i
$173$	0.882306	+	2.71546i	0.0670805	+	0.206452i	0.978978	−	0.203965i	$-0.0653829\pi$
$173$	0.882306	+	2.71546i	0.0670805	+	0.206452i	−0.911898	+	0.410418i	$0.865383\pi$
$174$	15.6809	−	11.3929i	1.18877	−	0.863690i
$175$	−4.13284			−0.312413
$176$	2.48962	−	0.102182i	0.187662	−	0.00770224i
$177$	4.53793			0.341092
$178$	20.4063	−	14.8261i	1.52952	−	1.11126i
$179$	−1.83911	−	5.66019i	−0.137461	−	0.423063i	0.858503	−	0.512808i	$-0.171395\pi$
$179$	−1.83911	−	5.66019i	−0.137461	−	0.423063i	−0.995965	+	0.0897453i	$0.971395\pi$
$180$	2.30507	−	7.09429i	0.171810	−	0.528777i
$181$	−2.01813	−	1.46626i	−0.150006	−	0.108986i	0.510251	−	0.860026i	$-0.329553\pi$
$181$	−2.01813	−	1.46626i	−0.150006	−	0.108986i	−0.660257	+	0.751040i	$0.729553\pi$
$182$	39.1561	+	28.4485i	2.90244	+	2.10875i
$183$	1.07496	−	3.30837i	0.0794630	−	0.244562i
$184$	−4.64612	−	14.2993i	−0.342517	−	1.05416i
$185$	−10.8564	+	7.88766i	−0.798181	+	0.579912i
$186$	9.62084			0.705434
$187$	20.0881	−	0.824478i	1.46899	−	0.0602918i
$188$	−35.3083			−2.57512
$189$	−3.56614	+	2.59095i	−0.259398	+	0.188464i
$190$	−1.69401	−	5.21362i	−0.122896	−	0.378236i
$191$	−5.37076	+	16.5295i	−0.388614	+	1.19603i	0.545210	+	0.838299i	$0.316450\pi$
$191$	−5.37076	+	16.5295i	−0.388614	+	1.19603i	−0.933824	+	0.357732i	$0.883550\pi$
$192$	−10.5514	−	7.66605i	−0.761482	−	0.553249i
$193$	−4.90362	−	3.56269i	−0.352970	−	0.256448i	0.397144	−	0.917756i	$-0.370001\pi$
$193$	−4.90362	−	3.56269i	−0.352970	−	0.256448i	−0.750114	+	0.661308i	$0.770001\pi$
$194$	−9.50712	+	29.2599i	−0.682572	+	2.10074i
$195$	−3.67502	−	11.3105i	−0.263173	−	0.809964i
$196$	−30.7850	+	22.3666i	−2.19893	+	1.59762i
$197$	−12.2008			−0.869274			−0.434637	−	0.900606i	$-0.643123\pi$
$197$	−12.2008			−0.869274			−0.434637	+	0.900606i	$0.643123\pi$
$198$	−2.59479	−	6.99576i	−0.184404	−	0.497167i
$199$	13.1851			0.934664			0.467332	−	0.884082i	$-0.345215\pi$
$199$	13.1851			0.934664			0.467332	+	0.884082i	$0.345215\pi$
$200$	−1.81096	+	1.31574i	−0.128054	+	0.0930367i
$201$	−1.36470	−	4.20011i	−0.0962584	−	0.296253i
$202$	1.73030	−	5.32531i	0.121743	−	0.374687i
$203$	30.7244	+	22.3226i	2.15643	+	1.56674i
$204$	−15.0128	−	10.9075i	−1.05111	−	0.763676i
$205$	−5.45282	+	16.7821i	−0.380842	+	1.17211i
$206$	5.46529	+	16.8204i	0.380785	+	1.17193i
$207$	5.09475	−	3.70155i	0.354110	−	0.257276i
$208$	−3.66669			−0.254239
$209$	−2.76089	−	1.83779i	−0.190975	−	0.127122i
$210$	24.1643			1.66749
$211$	18.7850	−	13.6481i	1.29321	−	0.939575i	0.293349	−	0.956005i	$-0.405230\pi$
$211$	18.7850	−	13.6481i	1.29321	−	0.939575i	0.999865	+	0.0164301i	$0.00523010\pi$
$212$	−2.78849	−	8.58210i	−0.191515	−	0.589421i
$213$	4.00396	−	12.3229i	0.274346	−	0.844352i
$214$	7.06535	+	5.13328i	0.482977	+	0.350903i
$215$	−10.4767	−	7.61177i	−0.714506	−	0.519119i
$216$	−0.737778	+	2.27065i	−0.0501994	+	0.154498i
$217$	5.82515	+	17.9280i	0.395437	+	1.21703i
$218$	−15.8458	+	11.5126i	−1.07321	+	0.779734i
$219$	−0.202907			−0.0137112
$220$	−6.67374	+	23.8228i	−0.449943	+	1.60613i
$221$	−29.5856			−1.99014
$222$	10.0233	−	7.28236i	0.672720	−	0.488760i
$223$	−7.49961	−	23.0814i	−0.502211	−	1.54565i	−0.805409	−	0.592719i	$-0.798055\pi$
$223$	−7.49961	−	23.0814i	−0.502211	−	1.54565i	0.303199	−	0.952927i	$-0.401945\pi$
$224$	8.80649	−	27.1036i	0.588408	−	1.81093i
$225$	−0.758517	−	0.551095i	−0.0505678	−	0.0367397i
$226$	31.6170	+	22.9711i	2.10313	+	1.52802i
$227$	−2.25681	+	6.94574i	−0.149790	+	0.461005i	−0.997596	−	0.0693013i	$-0.977923\pi$
$227$	−2.25681	+	6.94574i	−0.149790	+	0.461005i	0.847806	+	0.530306i	$0.177923\pi$
$228$	0.945976	+	2.91141i	0.0626488	+	0.192813i
$229$	−19.9785	+	14.5152i	−1.32022	+	0.959194i	−0.320288	+	0.947320i	$0.603780\pi$
$229$	−19.9785	+	14.5152i	−1.32022	+	0.959194i	−0.999930	+	0.0118740i	$0.996220\pi$
$230$	−34.5222			−2.27633
$231$	11.4652	−	9.07101i	0.754355	−	0.596829i
$232$	20.5697			1.35047
$233$	−1.05702	+	0.767968i	−0.0692475	+	0.0503113i	−0.621870	−	0.783120i	$-0.713627\pi$
$233$	−1.05702	+	0.767968i	−0.0692475	+	0.0503113i	0.552623	+	0.833431i	$0.313627\pi$
$234$	3.39299	+	10.4426i	0.221807	+	0.682652i
$235$	−8.68492	+	26.7294i	−0.566542	+	1.74364i
$236$	11.2386	+	8.16535i	0.731573	+	0.531519i
$237$	0.0135983	+	0.00987976i	0.000883306	+	0.000641759i
$238$	18.5763	−	57.1720i	1.20412	−	3.70591i
$239$	−1.82903	−	5.62917i	−0.118310	−	0.364121i	0.874313	−	0.485363i	$-0.161312\pi$
$239$	−1.82903	−	5.62917i	−0.118310	−	0.364121i	−0.992623	+	0.121242i	$0.961312\pi$
$240$	−1.48103	+	1.07603i	−0.0956001	+	0.0694575i
$241$	−25.4459			−1.63912			−0.819558	−	0.572996i	$-0.805781\pi$
$241$	−25.4459			−1.63912			−0.819558	+	0.572996i	$0.805781\pi$
$242$	9.55021	+	22.8299i	0.613911	+	1.46756i
$243$	−1.00000			−0.0641500
$244$	8.61516	−	6.25928i	0.551529	−	0.400709i
$245$	9.35989	+	28.8068i	0.597982	+	1.84040i
$246$	5.03437	−	15.4942i	0.320980	−	0.987874i
$247$	3.94848	+	2.86874i	0.251236	+	0.182533i
$248$	8.26010	+	6.00131i	0.524517	+	0.381084i
$249$	0.463440	−	1.42632i	0.0293693	−	0.0903895i
$250$	−6.88178	−	21.1799i	−0.435242	−	1.33954i
$251$	22.6679	−	16.4692i	1.43079	−	1.03953i	0.440918	−	0.897547i	$-0.354653\pi$
$251$	22.6679	−	16.4692i	1.43079	−	1.03953i	0.989869	−	0.141981i	$-0.0453472\pi$
$252$	−13.4939			−0.850037
$253$	−16.3797	+	12.9593i	−1.02978	+	0.814742i
$254$	38.1699			2.39499
$255$	−11.9501	+	8.68222i	−0.748342	+	0.543702i
$256$	−3.34847	−	10.3055i	−0.209279	−	0.644096i
$257$	8.74840	−	26.9248i	0.545710	−	1.67952i	−0.173585	−	0.984819i	$-0.555535\pi$
$257$	8.74840	−	26.9248i	0.545710	−	1.67952i	0.719295	−	0.694704i	$-0.244465\pi$
$258$	9.67272	+	7.02764i	0.602197	+	0.437522i
$259$	19.6392	+	14.2687i	1.22032	+	0.886613i
$260$	11.2501	−	34.6243i	0.697703	−	2.14731i
$261$	2.66237	+	8.19392i	0.164796	+	0.507191i
$262$	−29.3914	+	21.3541i	−1.81581	+	1.31926i
$263$	10.1010			0.622854			0.311427	−	0.950270i	$-0.399193\pi$
$263$	10.1010			0.622854			0.311427	+	0.950270i	$0.399193\pi$
$264$	2.13604	−	7.62489i	0.131464	−	0.469280i
$265$	−7.18281			−0.441236
$266$	−8.02281	+	5.82892i	−0.491910	+	0.357394i
$267$	3.46466	+	10.6631i	0.212034	+	0.652574i
$268$	4.17767	−	12.8576i	0.255192	−	0.785400i
$269$	−3.64386	−	2.64742i	−0.222170	−	0.161416i	0.471133	−	0.882062i	$-0.343845\pi$
$269$	−3.64386	−	2.64742i	−0.222170	−	0.161416i	−0.693303	+	0.720646i	$0.743845\pi$
$270$	4.43497	+	3.22220i	0.269904	+	0.196097i
$271$	−1.79120	+	5.51274i	−0.108808	+	0.334875i	−0.990605	−	0.136753i	$-0.956333\pi$
$271$	−1.79120	+	5.51274i	−0.108808	+	0.334875i	0.881798	+	0.471628i	$0.156333\pi$
$272$	1.40732	+	4.33127i	0.0853311	+	0.262622i
$273$	−17.4049	+	12.6454i	−1.05339	+	0.765332i
$274$	−28.8172			−1.74091
$275$	2.58855	+	1.72307i	0.156096	+	0.103905i
$276$	19.2780			1.16040
$277$	6.60065	−	4.79565i	0.396594	−	0.288143i	−0.371558	−	0.928410i	$-0.621176\pi$
$277$	6.60065	−	4.79565i	0.396594	−	0.288143i	0.768152	+	0.640267i	$0.221176\pi$
$278$	−1.90121	−	5.85132i	−0.114027	−	0.350939i
$279$	−1.32150	+	4.06716i	−0.0791161	+	0.243494i
$280$	20.7466	+	15.0733i	1.23984	+	0.900799i
$281$	−10.3326	−	7.50709i	−0.616392	−	0.447835i	0.235267	−	0.971931i	$-0.424404\pi$
$281$	−10.3326	−	7.50709i	−0.616392	−	0.447835i	−0.851660	+	0.524095i	$0.824404\pi$
$282$	8.01844	−	24.6782i	0.477491	−	1.46957i
$283$	−2.10885	−	6.49038i	−0.125358	−	0.385813i	0.868608	−	0.495500i	$-0.165015\pi$
$283$	−2.10885	−	6.49038i	−0.125358	−	0.385813i	−0.993966	+	0.109687i	$0.965015\pi$
$284$	32.0894	−	23.3143i	1.90416	−	1.38345i
$285$	2.43671			0.144339
$286$	−12.6641	−	34.1434i	−0.748845	−	2.01894i
$287$	31.9209			1.88423
$288$	5.23043	−	3.80013i	0.308206	−	0.223925i
$289$	6.10199	+	18.7800i	0.358940	+	1.10470i
$290$	14.5949	−	44.9185i	0.857042	−	2.63770i
$291$	−11.0636	−	8.03816i	−0.648559	−	0.471205i
$292$	−0.502519	−	0.365102i	−0.0294077	−	0.0213659i
$293$	−3.64562	+	11.2201i	−0.212980	+	0.655484i	0.786311	+	0.617831i	$0.211988\pi$
$293$	−3.64562	+	11.2201i	−0.212980	+	0.655484i	−0.999291	+	0.0376532i	$0.988012\pi$
$294$	−8.64161	−	26.5962i	−0.503989	−	1.55112i
$295$	8.94583	−	6.49952i	0.520846	−	0.378417i
$296$	13.1483			0.764227
$297$	3.31383	−	0.136010i	0.192288	−	0.00789211i
$298$	34.6124			2.00504
$299$	24.8654	−	18.0658i	1.43800	−	1.04477i
$300$	−0.886927	−	2.72968i	−0.0512067	−	0.157598i
$301$	−7.23911	+	22.2797i	−0.417256	+	1.28418i
$302$	1.04871	+	0.761930i	0.0603463	+	0.0438442i
$303$	2.01357	+	1.46295i	0.115677	+	0.0840441i
$304$	0.232158	−	0.714509i	0.0133152	−	0.0409799i
$305$	−2.61936	−	8.06156i	−0.149984	−	0.461604i
$306$	11.0330	−	8.01595i	0.630715	−	0.458241i
$307$	19.5015			1.11301			0.556503	−	0.830845i	$-0.312143\pi$
$307$	19.5015			1.11301			0.556503	+	0.830845i	$0.312143\pi$
$308$	44.7166	−	1.83531i	2.54797	−	0.104577i
$309$	−7.86144			−0.447222
$310$	18.9660	−	13.7796i	1.07720	−	0.782628i
$311$	4.99842	+	15.3836i	0.283435	+	0.872322i	0.986864	+	0.161556i	$0.0516513\pi$
$311$	4.99842	+	15.3836i	0.283435	+	0.872322i	−0.703429	+	0.710766i	$0.748349\pi$
$312$	−3.60079	+	11.0821i	−0.203855	+	0.627400i
$313$	10.8710	+	7.89825i	0.614466	+	0.446436i	0.850984	−	0.525191i	$-0.176006\pi$
$313$	10.8710	+	7.89825i	0.614466	+	0.446436i	−0.236518	+	0.971627i	$0.576006\pi$
$314$	−27.3994	−	19.9069i	−1.54624	−	1.12341i
$315$	−3.31915	+	10.2153i	−0.187013	+	0.575567i
$316$	0.0159004	+	0.0489364i	0.000894467	+	0.00275289i
$317$	−12.2813	+	8.92285i	−0.689784	+	0.501157i	−0.876589	−	0.481240i	$-0.840187\pi$
$317$	−12.2813	+	8.92285i	−0.689784	+	0.501157i	0.186805	+	0.982397i	$0.440187\pi$
$318$	6.63160			0.371881
$319$	−9.93710	−	26.7912i	−0.556371	−	1.50002i
$320$	−31.7803			−1.77657
$321$	−3.14054	+	2.28174i	−0.175288	+	0.127354i
$322$	19.2982	+	59.3937i	1.07545	+	3.30988i
$323$	1.87323	−	5.76519i	0.104229	−	0.320784i
$324$	−2.47660	−	1.79935i	−0.137589	−	0.0999641i
$325$	−3.70201	−	2.68967i	−0.205351	−	0.149196i
$326$	−2.60598	+	8.02038i	−0.144332	+	0.444208i
$327$	−2.69036	−	8.28007i	−0.148777	−	0.457889i
$328$	13.9873	−	10.1624i	0.772322	−	0.561124i
$329$	50.8416			2.80299
$330$	−15.1350	−	10.0746i	−0.833155	−	0.554590i
$331$	8.85968			0.486972			0.243486	−	0.969904i	$-0.421709\pi$
$331$	8.85968			0.486972			0.243486	+	0.969904i	$0.421709\pi$
$332$	3.71421	−	2.69853i	0.203844	−	0.148101i
$333$	1.70180	+	5.23759i	0.0932578	+	0.287018i
$334$	−3.57639	+	11.0070i	−0.195691	+	0.602276i
$335$	−8.70596	−	6.32525i	−0.475657	−	0.345585i
$336$	2.67917	+	1.94653i	0.146161	+	0.106192i
$337$	−5.29100	+	16.2840i	−0.288219	+	0.887048i	0.697196	+	0.716881i	$0.254431\pi$
$337$	−5.29100	+	16.2840i	−0.288219	+	0.887048i	−0.985415	+	0.170167i	$0.945569\pi$
$338$	7.52219	+	23.1509i	0.409153	+	1.25924i
$339$	−14.0538	+	10.2107i	−0.763295	+	0.554567i
$340$	−45.2179			−2.45228
$341$	3.82606	−	13.6576i	0.207193	−	0.739602i
$342$	−2.24972			−0.121651
$343$	19.3654	−	14.0698i	1.04564	−	0.759698i
$344$	3.92092	+	12.0674i	0.211402	+	0.650628i
$345$	4.74190	−	14.5941i	0.255295	−	0.785718i
$346$	−5.19665	−	3.77558i	−0.279373	−	0.202977i
$347$	−1.07500	−	0.781030i	−0.0577088	−	0.0419279i	0.558557	−	0.829466i	$-0.311355\pi$
$347$	−1.07500	−	0.781030i	−0.0577088	−	0.0419279i	−0.616266	+	0.787538i	$0.711355\pi$
$348$	−8.15015	+	25.0836i	−0.436894	+	1.34462i
$349$	4.20500	+	12.9417i	0.225089	+	0.692751i	0.998283	+	0.0585819i	$0.0186579\pi$
$349$	4.20500	+	12.9417i	0.225089	+	0.692751i	−0.773194	+	0.634170i	$0.781342\pi$
$350$	7.52202	−	5.46507i	0.402069	−	0.292120i
$351$	−4.88059			−0.260507
$352$	−16.8159	+	13.3044i	−0.896292	+	0.709127i
$353$	−1.14372			−0.0608738			−0.0304369	−	0.999537i	$-0.509690\pi$
$353$	−1.14372			−0.0608738			−0.0304369	+	0.999537i	$0.509690\pi$
$354$	−8.25932	+	6.00075i	−0.438978	+	0.318936i
$355$	−9.75650	−	30.0274i	−0.517821	−	1.59369i
$356$	−10.6062	+	32.6425i	−0.562126	+	1.73005i
$357$	21.6175	+	15.7060i	1.14412	+	0.831252i
$358$	10.8321	+	7.86995i	0.572492	+	0.415940i
$359$	−0.749761	+	2.30753i	−0.0395708	+	0.121787i	−0.968891	−	0.247490i	$-0.920394\pi$
$359$	−0.749761	+	2.30753i	−0.0395708	+	0.121787i	0.929320	+	0.369276i	$0.120394\pi$
$360$	1.79775	+	5.53292i	0.0947499	+	0.291610i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	5.61202			0.294961
$363$	−10.9630	+	0.901431i	−0.575408	+	0.0473128i
$364$	−65.8583			−3.45191
$365$	−0.400000	+	0.290617i	−0.0209369	+	0.0152116i
$366$	2.41835	+	7.44291i	0.126409	+	0.389047i
$367$	3.32651	−	10.2379i	0.173642	−	0.534416i	−0.825927	−	0.563778i	$-0.809347\pi$
$367$	3.32651	−	10.2379i	0.173642	−	0.534416i	0.999569	+	0.0293616i	$0.00934744\pi$
$368$	−3.82758	−	2.78090i	−0.199527	−	0.144964i
$369$	5.85857	+	4.25650i	0.304985	+	0.221585i
$370$	9.32912	−	28.7121i	0.484998	−	1.49267i
$371$	4.01525	+	12.3577i	0.208461	+	0.641578i
$372$	−10.5911	+	7.69486i	−0.549122	+	0.398960i
$373$	31.5232			1.63221			0.816105	−	0.577903i	$-0.196129\pi$
$373$	31.5232			1.63221			0.816105	+	0.577903i	$0.196129\pi$
$374$	−35.4713	+	28.0641i	−1.83418	+	1.45116i
$375$	9.89896			0.511180
$376$	22.2782	−	16.1860i	1.14891	−	0.834732i
$377$	12.9939	+	39.9912i	0.669221	+	2.05965i
$378$	3.06444	−	9.43138i	0.157618	−	0.485098i
$379$	6.03806	+	4.38690i	0.310154	+	0.225340i	0.731963	−	0.681345i	$-0.238605\pi$
$379$	6.03806	+	4.38690i	0.310154	+	0.225340i	−0.421809	+	0.906685i	$0.638605\pi$
$380$	6.03476	+	4.38451i	0.309577	+	0.224921i
$381$	−5.24294	+	16.1361i	−0.268604	+	0.826679i
$382$	−12.0827	−	37.1867i	−0.618205	−	1.90264i
$383$	−9.79006	+	7.11290i	−0.500249	+	0.363452i	−0.809112	−	0.587654i	$-0.800051\pi$
$383$	−9.79006	+	7.11290i	−0.500249	+	0.363452i	0.308863	+	0.951106i	$0.400051\pi$
$384$	16.4111			0.837476
$385$	9.60975	−	34.3033i	0.489758	−	1.74826i
$386$	13.6360			0.694056
$387$	−4.29952	+	3.12379i	−0.218557	+	0.158791i
$388$	−12.9365	−	39.8146i	−0.656753	−	2.02128i
$389$	7.21941	−	22.2191i	0.366039	−	1.12655i	−0.583289	−	0.812264i	$-0.698235\pi$
$389$	7.21941	−	22.2191i	0.366039	−	1.12655i	0.949328	−	0.314287i	$-0.101765\pi$
$390$	21.6453	+	15.7262i	1.09605	+	0.796328i
$391$	−30.8838	−	22.4384i	−1.56186	−	1.13476i
$392$	9.17085	−	28.2250i	0.463198	−	1.42558i
$393$	−4.99019	−	15.3582i	−0.251722	−	0.774720i
$394$	22.2063	−	16.1338i	1.11874	−	0.812810i
$395$	0.0409574			0.00206079
$396$	8.45176	+	5.62592i	0.424717	+	0.282713i
$397$	−27.9019			−1.40036			−0.700178	−	0.713968i	$-0.746896\pi$
$397$	−27.9019			−1.40036			−0.700178	+	0.713968i	$0.746896\pi$
$398$	−23.9976	+	17.4353i	−1.20289	+	0.873953i
$399$	−1.36214	−	4.19225i	−0.0681925	−	0.209875i
$400$	−0.217667	+	0.669909i	−0.0108833	+	0.0334954i
$401$	−18.8557	−	13.6995i	−0.941610	−	0.684119i	0.00719798	−	0.999974i	$-0.497709\pi$
$401$	−18.8557	−	13.6995i	−0.941610	−	0.684119i	−0.948808	+	0.315855i	$0.897709\pi$
$402$	8.03786	+	5.83985i	0.400892	+	0.291265i
$403$	−6.44970	+	19.8501i	−0.321282	+	0.988805i
$404$	2.35445	+	7.24626i	0.117138	+	0.360515i
$405$	−1.97134	+	1.43226i	−0.0979569	+	0.0711698i
$406$	−85.4387			−4.24025
$407$	−6.35183	−	17.1250i	−0.314849	−	0.848857i
$408$	14.4727			0.716507
$409$	−6.25479	+	4.54437i	−0.309279	+	0.224705i	−0.731587	−	0.681748i	$-0.761220\pi$
$409$	−6.25479	+	4.54437i	−0.309279	+	0.224705i	0.422308	+	0.906452i	$0.361220\pi$
$410$	−12.2673	−	37.7549i	−0.605840	−	1.86458i
$411$	3.95827	−	12.1823i	0.195247	−	0.600909i
$412$	−19.4696	−	14.1455i	−0.959200	−	0.696899i
$413$	−16.1829	−	11.7576i	−0.796308	−	0.578552i
$414$	−4.37800	+	13.4741i	−0.215167	+	0.662216i
$415$	−1.12927	−	3.47554i	−0.0554338	−	0.170608i
$416$	25.5276	−	18.5469i	1.25159	−	0.909335i
$417$	2.73476			0.133922
$418$	7.45520	−	0.305985i	0.364646	−	0.0149662i
$419$	29.1950			1.42627			0.713133	−	0.701028i	$-0.247275\pi$
$419$	29.1950			1.42627			0.713133	+	0.701028i	$0.247275\pi$
$420$	−26.6012	+	19.3269i	−1.29800	+	0.943055i
$421$	−2.48343	−	7.64321i	−0.121035	−	0.372507i	0.872123	−	0.489287i	$-0.162743\pi$
$421$	−2.48343	−	7.64321i	−0.121035	−	0.372507i	−0.993158	+	0.116780i	$0.962743\pi$
$422$	−16.1423	+	49.6808i	−0.785794	+	2.41843i
$423$	9.33118	+	6.77950i	0.453698	+	0.329631i
$424$	5.69364	+	4.13667i	0.276508	+	0.200895i
$425$	−1.75630	+	5.40532i	−0.0851928	+	0.262197i
$426$	9.00778	+	27.7231i	0.436428	+	1.34319i
$427$	−12.4053	+	9.01296i	−0.600333	+	0.436168i
$428$	−11.8835			−0.574412
$429$	16.1735	−	0.663810i	0.780862	−	0.0320490i
$430$	29.1337			1.40495
$431$	−18.5797	+	13.4989i	−0.894953	+	0.650221i	−0.937165	−	0.348887i	$-0.886560\pi$
$431$	−18.5797	+	13.4989i	−0.894953	+	0.650221i	0.0422117	+	0.999109i	$0.486560\pi$
$432$	0.232158	+	0.714509i	0.0111697	+	0.0343769i
$433$	−8.44425	+	25.9887i	−0.405805	+	1.24894i	0.514417	+	0.857540i	$0.328008\pi$
$433$	−8.44425	+	25.9887i	−0.405805	+	1.24894i	−0.920222	+	0.391398i	$0.871992\pi$
$434$	−34.3093	−	24.9271i	−1.64690	−	1.19654i
$435$	16.9843	+	12.3398i	0.814335	+	0.591649i
$436$	8.23584	−	25.3473i	0.394425	−	1.21392i
$437$	1.94602	+	5.98924i	0.0930908	+	0.286504i
$438$	0.369304	−	0.268315i	0.0176460	−	0.0128206i
$439$	8.45006			0.403300			0.201650	−	0.979458i	$-0.435370\pi$
$439$	8.45006			0.403300			0.201650	+	0.979458i	$0.435370\pi$
$440$	−6.70999	−	18.0907i	−0.319886	−	0.862438i
$441$	12.4304			0.591922
$442$	53.8476	−	39.1225i	2.56127	−	1.86087i
$443$	−4.52081	−	13.9136i	−0.214790	−	0.661056i	−0.999168	−	0.0407733i	$-0.987018\pi$
$443$	−4.52081	−	13.9136i	−0.214790	−	0.661056i	0.784378	−	0.620283i	$-0.212982\pi$
$444$	−5.20961	+	16.0335i	−0.247237	+	0.760917i
$445$	22.1025	+	16.0584i	1.04776	+	0.761241i
$446$	44.1715	+	32.0925i	2.09158	+	1.51962i
$447$	−4.75428	+	14.6322i	−0.224870	+	0.692078i
$448$	17.7654	+	54.6764i	0.839338	+	2.58322i
$449$	4.41630	−	3.20863i	0.208418	−	0.151425i	−0.478680	−	0.877990i	$-0.658884\pi$
$449$	4.41630	−	3.20863i	0.208418	−	0.151425i	0.687098	+	0.726565i	$0.258884\pi$
$450$	2.10929			0.0994329
$451$	−19.9933	−	13.3085i	−0.941447	−	0.626674i
$452$	−53.1781			−2.50129
$453$	−0.466150	+	0.338678i	−0.0219016	+	0.0159125i
$454$	−5.07719	−	15.6260i	−0.238284	−	0.733363i
$455$	−16.1994	+	49.8567i	−0.759441	+	2.33732i
$456$	−1.93153	−	1.40334i	−0.0904520	−	0.0657173i
$457$	−6.04266	−	4.39025i	−0.282664	−	0.205367i	0.437415	−	0.899260i	$-0.355894\pi$
$457$	−6.04266	−	4.39025i	−0.282664	−	0.205367i	−0.720078	+	0.693893i	$0.755894\pi$
$458$	17.1679	−	52.8373i	0.802202	−	2.46892i
$459$	1.87323	+	5.76519i	0.0874347	+	0.269096i
$460$	38.0036	−	27.6113i	1.77193	−	1.28738i
$461$	−30.6838			−1.42909			−0.714544	−	0.699591i	$-0.753366\pi$
$461$	−30.6838			−1.42909			−0.714544	+	0.699591i	$0.753366\pi$
$462$	−8.87229	+	31.6708i	−0.412776	+	1.47346i
$463$	−7.54486			−0.350640			−0.175320	−	0.984512i	$-0.556096\pi$
$463$	−7.54486			−0.350640			−0.175320	+	0.984512i	$0.556096\pi$
$464$	5.23654	−	3.80457i	0.243100	−	0.176623i
$465$	3.22012	+	9.91050i	0.149329	+	0.459588i
$466$	0.908313	−	2.79550i	0.0420768	−	0.129499i
$467$	−6.05623	−	4.40011i	−0.280249	−	0.203613i	0.438777	−	0.898596i	$-0.355412\pi$
$467$	−6.05623	−	4.40011i	−0.280249	−	0.203613i	−0.719026	+	0.694983i	$0.755412\pi$
$468$	−12.0873	−	8.78190i	−0.558733	−	0.405944i
$469$	−6.01557	+	18.5140i	−0.277773	+	0.854899i
$470$	−19.5387	−	60.1338i	−0.901251	−	2.77376i
$471$	12.1790	−	8.84859i	0.561181	−	0.407722i
$472$	−10.8343			−0.498690
$473$	13.8230	−	10.9365i	0.635584	−	0.502860i
$474$	−0.0378143			−0.00173687
$475$	0.758517	−	0.551095i	0.0348031	−	0.0252860i
$476$	25.2772	+	77.7951i	1.15858	+	3.56573i
$477$	−0.910903	+	2.80347i	−0.0417074	+	0.128362i
$478$	10.7727	+	7.82682i	0.492732	+	0.357991i
$479$	10.4601	+	7.59972i	0.477935	+	0.347240i	0.800526	−	0.599299i	$-0.204554\pi$
$479$	10.4601	+	7.59972i	0.477935	+	0.347240i	−0.322591	+	0.946539i	$0.604554\pi$
$480$	4.86818	−	14.9827i	0.222201	−	0.683865i
$481$	8.30576	+	25.5625i	0.378710	+	1.16555i
$482$	46.3132	−	33.6485i	2.10951	−	1.53265i
$483$	−27.7591			−1.26308
$484$	−28.7729	−	17.4938i	−1.30786	−	0.795174i
$485$	−33.3229			−1.51312
$486$	1.82006	−	1.32235i	0.0825597	−	0.0599831i
$487$	−2.95371	−	9.09060i	−0.133846	−	0.411934i	0.861563	−	0.507651i	$-0.169486\pi$
$487$	−2.95371	−	9.09060i	−0.133846	−	0.411934i	−0.995409	+	0.0957162i	$0.969486\pi$
$488$	−2.56645	+	7.89874i	−0.116178	+	0.357559i
$489$	−3.03262	−	2.20333i	−0.137140	−	0.0996379i
$490$	−55.1283	−	40.0531i	−2.49044	−	1.80941i
$491$	3.70108	−	11.3907i	0.167027	−	0.514057i	−0.832153	−	0.554547i	$-0.812892\pi$
$491$	3.70108	−	11.3907i	0.167027	−	0.514057i	0.999180	+	0.0404894i	$0.0128917\pi$
$492$	6.85038	+	21.0833i	0.308839	+	0.950508i
$493$	42.2523	−	30.6981i	1.90295	−	1.38257i
$494$	−10.9800			−0.494012
$495$	6.33790	−	5.01441i	0.284868	−	0.225381i
$496$	3.21282			0.144260
$497$	−46.2067	+	33.5711i	−2.07265	+	1.50587i
$498$	1.04261	+	3.20883i	0.0467205	+	0.143791i
$499$	11.6956	−	35.9954i	0.523568	−	1.61138i	−0.243562	−	0.969885i	$-0.578316\pi$
$499$	11.6956	−	35.9954i	0.523568	−	1.61138i	0.767130	−	0.641491i	$-0.221684\pi$
$500$	24.5157	+	17.8117i	1.09638	+	0.796565i
$501$	−4.16190	−	3.02379i	−0.185940	−	0.135093i
$502$	−19.4789	+	59.9500i	−0.869388	+	2.67570i
$503$	10.1672	+	31.2913i	0.453332	+	1.39521i	0.873083	+	0.487572i	$0.162117\pi$
$503$	10.1672	+	31.2913i	0.453332	+	1.39521i	−0.419751	+	0.907639i	$0.637883\pi$
$504$	8.51415	−	6.18589i	0.379250	−	0.275542i
$505$	6.06477			0.269879
$506$	12.6754	−	45.2464i	0.563489	−	2.01145i
$507$	−10.8201			−0.480540
$508$	−42.0192	+	30.5288i	−1.86430	+	1.35449i
$509$	−10.9431	−	33.6794i	−0.485045	−	1.49281i	−0.831916	−	0.554901i	$-0.812756\pi$
$509$	−10.9431	−	33.6794i	−0.485045	−	1.49281i	0.346872	−	0.937913i	$-0.387244\pi$
$510$	10.2689	−	31.6044i	0.454714	−	1.39947i
$511$	0.723595	+	0.525722i	0.0320099	+	0.0232566i
$512$	−6.83175	−	4.96356i	−0.301924	−	0.219360i
$513$	0.309017	−	0.951057i	0.0136434	−	0.0419902i
$514$	19.6815	+	60.5733i	0.868112	+	2.67177i
$515$	−15.4976	+	11.2597i	−0.682906	+	0.496160i
$516$	−16.2690			−0.716202
$517$	−31.8441	−	21.1970i	−1.40050	−	0.932243i
$518$	−54.6127			−2.39955
$519$	2.30991	−	1.67825i	0.101394	−	0.0736668i
$520$	8.77410	+	27.0039i	0.384770	+	1.18420i
$521$	0.0989920	−	0.304666i	0.00433692	−	0.0133477i	−0.948865	−	0.315683i	$-0.897766\pi$
$521$	0.0989920	−	0.304666i	0.00433692	−	0.0133477i	0.953202	+	0.302336i	$0.0977663\pi$
$522$	−15.6809	−	11.3929i	−0.686335	−	0.498652i
$523$	0.749999	+	0.544906i	0.0327952	+	0.0238271i	0.604062	−	0.796937i	$-0.293548\pi$
$523$	0.749999	+	0.544906i	0.0327952	+	0.0238271i	−0.571267	+	0.820764i	$0.693548\pi$
$524$	15.2762	−	47.0152i	0.667343	−	2.05387i
$525$	1.27712	+	3.93056i	0.0557379	+	0.171544i
$526$	−18.3844	+	13.3571i	−0.801599	+	0.582396i
$527$	25.9234			1.12924
$528$	−0.866515	−	2.33619i	−0.0377102	−	0.101670i
$529$	16.6580			0.724259
$530$	13.0732	−	9.49820i	0.567862	−	0.412576i
$531$	−1.40230	−	4.31583i	−0.0608546	−	0.187291i
$532$	4.16985	−	12.8335i	0.180786	−	0.556402i
$533$	28.5933	+	20.7742i	1.23851	+	0.899832i
$534$	−20.4063	−	14.8261i	−0.883069	−	0.641587i
$535$	−2.92304	+	8.99618i	−0.126374	+	0.388939i
$536$	3.25822	+	10.0278i	0.140733	+	0.433133i
$537$	−4.81485	+	3.49819i	−0.207776	+	0.150958i
$538$	10.1329			0.436860
$539$	−41.1922	+	1.69066i	−1.77427	+	0.0728217i
$540$	−7.45937			−0.321000
$541$	10.1376	−	7.36539i	0.435849	−	0.316663i	−0.348134	−	0.937445i	$-0.613185\pi$
$541$	10.1376	−	7.36539i	0.435849	−	0.316663i	0.783983	+	0.620782i	$0.213185\pi$
$542$	−4.02970	−	12.4021i	−0.173090	−	0.532717i
$543$	−0.770856	+	2.37245i	−0.0330806	+	0.101812i
$544$	−31.7063	−	23.0359i	−1.35939	−	0.987658i
$545$	−17.1629	−	12.4696i	−0.735177	−	0.534137i
$546$	14.9563	−	46.0307i	0.640070	−	1.96993i
$547$	−1.98500	−	6.10919i	−0.0848723	−	0.261210i	0.899610	−	0.436694i	$-0.143851\pi$
$547$	−1.98500	−	6.10919i	−0.0848723	−	0.261210i	−0.984482	+	0.175484i	$0.943851\pi$
$548$	31.7233	−	23.0483i	1.35515	−	0.984576i
$549$	−3.47863			−0.148464
$550$	−6.98984	+	0.286885i	−0.298048	+	0.0122328i
$551$	−8.61560			−0.367037
$552$	−12.1637	+	8.83745i	−0.517722	+	0.376147i
$553$	−0.0228955	−	0.0704652i	−0.000973617	−	0.00299648i
$554$	−5.67205	+	17.4568i	−0.240982	+	0.741667i
$555$	10.8564	+	7.88766i	0.460830	+	0.334813i
$556$	6.77289	+	4.92079i	0.287235	+	0.208688i
$557$	−1.36997	+	4.21635i	−0.0580477	+	0.178652i	−0.975876	−	0.218325i	$-0.929941\pi$
$557$	−1.36997	+	4.21635i	−0.0580477	+	0.178652i	0.917828	+	0.396977i	$0.129941\pi$
$558$	−2.97300	−	9.14997i	−0.125857	−	0.387349i
$559$	−20.9842	+	15.2459i	−0.887537	+	0.644833i
$560$	8.06950			0.340999
$561$	−6.99168	−	18.8501i	−0.295189	−	0.795853i
$562$	28.7330			1.21203
$563$	3.77493	−	2.74264i	0.159094	−	0.115589i	−0.505390	−	0.862891i	$-0.668651\pi$
$563$	3.77493	−	2.74264i	0.159094	−	0.115589i	0.664484	+	0.747302i	$0.268651\pi$
$564$	10.9109	+	33.5802i	0.459430	+	1.41398i
$565$	−13.0804	+	40.2574i	−0.550298	+	1.69364i
$566$	12.4208	+	9.02425i	0.522086	+	0.379318i
$567$	3.56614	+	2.59095i	0.149764	+	0.108810i
$568$	−9.55944	+	29.4209i	−0.401105	+	1.23447i
$569$	0.903824	+	2.78168i	0.0378903	+	0.116614i	0.968213	−	0.250129i	$-0.0804729\pi$
$569$	0.903824	+	2.78168i	0.0378903	+	0.116614i	−0.930322	+	0.366743i	$0.880473\pi$
$570$	−4.43497	+	3.22220i	−0.185761	+	0.134963i
$571$	8.35249			0.349541			0.174770	−	0.984609i	$-0.444082\pi$
$571$	8.35249			0.349541			0.174770	+	0.984609i	$0.444082\pi$
$572$	41.2496	+	27.4578i	1.72473	+	1.14807i
$573$	17.3801			0.726065
$574$	−58.0980	+	42.2106i	−2.42496	+	1.76184i
$575$	−1.82455	−	5.61538i	−0.0760889	−	0.234178i
$576$	−4.03028	+	12.4039i	−0.167928	+	0.516830i
$577$	−32.9636	−	23.9494i	−1.37229	−	0.997028i	−0.997554	−	0.0698961i	$-0.977733\pi$
$577$	−32.9636	−	23.9494i	−1.37229	−	0.997028i	−0.374736	−	0.927131i	$-0.622267\pi$
$578$	−35.9398	−	26.1118i	−1.49490	−	1.08611i
$579$	−1.87302	+	5.76455i	−0.0778399	+	0.239567i
$580$	19.8596	+	61.1215i	0.824624	+	2.53793i
$581$	−5.34822	+	3.88571i	−0.221882	+	0.161206i
$582$	30.7657			1.27528
$583$	2.63728	−	9.41413i	0.109225	−	0.389893i
$584$	0.484440			0.0200463
$585$	−9.62132	+	6.99030i	−0.397793	+	0.289013i
$586$	−8.20163	−	25.2420i	−0.338806	−	1.04274i
$587$	7.10896	−	21.8791i	0.293418	−	0.903049i	−0.690330	−	0.723495i	$-0.742535\pi$
$587$	7.10896	−	21.8791i	0.293418	−	0.903049i	0.983748	−	0.179554i	$-0.0574655\pi$
$588$	30.7850	+	22.3666i	1.26955	+	0.922384i
$589$	−3.45973	−	2.51364i	−0.142556	−	0.103573i
$590$	−7.68730	+	23.6591i	−0.316481	+	0.974029i
$591$	3.77027	+	11.6037i	0.155088	+	0.477312i
$592$	3.34722	−	2.43190i	0.137570	−	0.0999504i
$593$	−6.91461			−0.283949			−0.141974	−	0.989870i	$-0.545345\pi$
$593$	−6.91461			−0.283949			−0.141974	+	0.989870i	$0.545345\pi$
$594$	−5.85153	+	4.62960i	−0.240091	+	0.189955i
$595$	65.1108			2.66928
$596$	−38.1029	+	27.6834i	−1.56076	+	1.13396i
$597$	−4.07441	−	12.5397i	−0.166754	−	0.513217i
$598$	−21.3672	+	65.7616i	−0.873771	+	2.68919i
$599$	−28.4628	−	20.6795i	−1.16296	−	0.844940i	−0.172811	−	0.984955i	$-0.555285\pi$
$599$	−28.4628	−	20.6795i	−1.16296	−	0.844940i	−0.990149	+	0.140015i	$0.955285\pi$
$600$	1.81096	+	1.31574i	0.0739321	+	0.0537148i
$601$	−4.00042	+	12.3120i	−0.163181	+	0.502218i	−0.998898	−	0.0469421i	$-0.985052\pi$
$601$	−4.00042	+	12.3120i	−0.163181	+	0.502218i	0.835717	+	0.549160i	$0.185052\pi$
$602$	−16.2860	−	50.1231i	−0.663767	−	2.04287i
$603$	−3.57283	+	2.59581i	−0.145497	+	0.105710i
$604$	−1.76387			−0.0717707
$605$	−20.3208	+	17.4790i	−0.826156	+	0.710621i
$606$	−5.59936			−0.227459
$607$	28.6323	−	20.8026i	1.16215	−	0.844352i	0.172102	−	0.985079i	$-0.444944\pi$
$607$	28.6323	−	20.8026i	1.16215	−	0.844352i	0.990048	+	0.140728i	$0.0449441\pi$
$608$	1.99785	+	6.14874i	0.0810234	+	0.249364i
$609$	11.7357	−	36.1187i	0.475554	−	1.46360i
$610$	15.4276	+	11.2088i	0.624646	+	0.453832i
$611$	45.5417	+	33.0880i	1.84242	+	1.33860i
$612$	−5.73440	+	17.6487i	−0.231799	+	0.713405i
$613$	−3.41676	−	10.5157i	−0.138002	−	0.424725i	0.858043	−	0.513578i	$-0.171680\pi$
$613$	−3.41676	−	10.5157i	−0.138002	−	0.424725i	−0.996045	+	0.0888522i	$0.971680\pi$
$614$	−35.4939	+	25.7878i	−1.43242	+	1.04071i
$615$	17.6457			0.711543
$616$	−27.3731	+	21.6570i	−1.10290	+	0.872587i
$617$	−32.0120			−1.28876			−0.644378	−	0.764707i	$-0.722884\pi$
$617$	−32.0120			−1.28876			−0.644378	+	0.764707i	$0.722884\pi$
$618$	14.3083	−	10.3956i	0.575565	−	0.418172i
$619$	8.48710	+	26.1206i	0.341125	+	1.04988i	0.963625	+	0.267256i	$0.0861171\pi$
$619$	8.48710	+	26.1206i	0.341125	+	1.04988i	−0.622500	+	0.782620i	$0.713883\pi$
$620$	−9.85756	+	30.3384i	−0.395889	+	1.21842i
$621$	−5.09475	−	3.70155i	−0.204445	−	0.148538i
$622$	−29.4399	−	21.3894i	−1.18043	−	0.857635i
$623$	15.2722	−	47.0030i	0.611868	−	1.88314i
$624$	1.13307	+	3.48723i	0.0453591	+	0.139601i
$625$	23.3068	−	16.9334i	0.932274	−	0.677336i
$626$	−30.2302			−1.20824
$627$	−0.894678	+	3.19367i	−0.0357300	+	0.127543i
$628$	46.0843			1.83897
$629$	27.0079	−	19.6224i	1.07687	−	0.782395i
$630$	−7.46717	−	22.9816i	−0.297499	−	0.915608i
$631$	−2.26952	+	6.98487i	−0.0903482	+	0.278063i	−0.986013	−	0.166666i	$-0.946700\pi$
$631$	−2.26952	+	6.98487i	−0.0903482	+	0.278063i	0.895665	+	0.444729i	$0.146700\pi$
$632$	−0.0324660	−	0.0235879i	−0.00129143	−	0.000938277i
$633$	−18.7850	−	13.6481i	−0.746638	−	0.542464i
$634$	10.5535	−	32.4803i	0.419133	−	1.28996i
$635$	12.7756	+	39.3191i	0.506983	+	1.56033i
$636$	−7.30037	+	5.30403i	−0.289479	+	0.210318i
$637$	60.6675			2.40373
$638$	53.5135	+	35.6213i	2.11862	+	1.41026i
$639$	−12.9571			−0.512574
$640$	32.3519	−	23.5051i	1.27882	−	0.929119i
$641$	−8.20044	−	25.2384i	−0.323898	−	0.996855i	−0.971936	−	0.235247i	$-0.924410\pi$
$641$	−8.20044	−	25.2384i	−0.323898	−	0.996855i	0.648038	−	0.761608i	$-0.275590\pi$
$642$	2.69872	−	8.30581i	0.106510	−	0.327804i
$643$	−8.81408	−	6.40381i	−0.347593	−	0.252541i	0.400265	−	0.916399i	$-0.368918\pi$
$643$	−8.81408	−	6.40381i	−0.347593	−	0.252541i	−0.747859	+	0.663858i	$0.768918\pi$
$644$	−68.7482	−	49.9485i	−2.70906	−	1.96824i
$645$	−4.00175	+	12.3161i	−0.157569	+	0.484946i
$646$	4.21423	+	12.9701i	0.165807	+	0.510301i
$647$	32.8384	−	23.8585i	1.29101	−	0.937973i	0.291184	−	0.956667i	$-0.405951\pi$
$647$	32.8384	−	23.8585i	1.29101	−	0.937973i	0.999825	+	0.0186943i	$0.00595094\pi$
$648$	2.38750			0.0937898
$649$	5.23398	+	14.1112i	0.205452	+	0.553914i
$650$	10.2946			0.403786
$651$	15.2505	−	11.0801i	0.597712	−	0.434263i
$652$	−3.54601	−	10.9135i	−0.138873	−	0.427406i
$653$	1.16988	−	3.60053i	0.0457811	−	0.140900i	−0.925553	−	0.378618i	$-0.876399\pi$
$653$	1.16988	−	3.60053i	0.0457811	−	0.140900i	0.971334	+	0.237718i	$0.0763995\pi$
$654$	15.8458	+	11.5126i	0.619619	+	0.450180i
$655$	−31.8344	−	23.1291i	−1.24387	−	0.903727i
$656$	1.68120	−	5.17419i	0.0656397	−	0.202018i
$657$	0.0627017	+	0.192976i	0.00244623	+	0.00752872i
$658$	−92.5349	+	67.2306i	−3.60739	+	2.62092i
$659$	17.9238			0.698211			0.349106	−	0.937083i	$-0.386485\pi$
$659$	17.9238			0.698211			0.349106	+	0.937083i	$0.386485\pi$
$660$	24.7191	−	1.01455i	0.962191	−	0.0394913i
$661$	21.9029			0.851923			0.425961	−	0.904741i	$-0.359936\pi$
$661$	21.9029			0.851923			0.425961	+	0.904741i	$0.359936\pi$
$662$	−16.1252	+	11.7156i	−0.626722	+	0.455340i
$663$	9.14244	+	28.1375i	0.355063	+	1.09277i
$664$	−1.10646	+	3.40534i	−0.0429391	+	0.132153i
$665$	−8.68966	−	6.31341i	−0.336971	−	0.244823i
$666$	−10.0233	−	7.28236i	−0.388395	−	0.282186i
$667$	−16.7661	+	51.6009i	−0.649187	+	1.99799i
$668$	−4.86647	−	14.9774i	−0.188289	−	0.579495i
$669$	−19.6342	+	14.2651i	−0.759103	+	0.551521i
$670$	24.2096			0.935298
$671$	11.5276	−	0.473129i	0.445018	−	0.0182649i
$672$	−28.4984			−1.09935
$673$	−0.708175	+	0.514519i	−0.0272982	+	0.0198333i	−0.601351	−	0.798985i	$-0.705371\pi$
$673$	−0.708175	+	0.514519i	−0.0272982	+	0.0198333i	0.574053	+	0.818818i	$0.305371\pi$
$674$	−11.9033	−	36.6345i	−0.458497	−	1.41111i
$675$	−0.289728	+	0.891690i	−0.0111516	+	0.0343212i
$676$	−26.7972	−	19.4693i	−1.03066	−	0.748818i
$677$	9.39439	+	6.82543i	0.361056	+	0.262322i	0.753492	−	0.657457i	$-0.228368\pi$
$677$	9.39439	+	6.82543i	0.361056	+	0.262322i	−0.392437	+	0.919779i	$0.628368\pi$
$678$	12.0766	−	37.1680i	0.463800	−	1.42743i
$679$	18.6278	+	57.3304i	0.714868	+	2.20014i
$680$	28.5307	−	20.7288i	1.09410	−	0.794913i
$681$	7.30318			0.279859
$682$	11.0965	+	29.9171i	0.424908	+	1.14559i
$683$	−28.6518			−1.09633			−0.548166	−	0.836370i	$-0.684674\pi$
$683$	−28.6518			−1.09633			−0.548166	+	0.836370i	$0.684674\pi$
$684$	2.47660	−	1.79935i	0.0946951	−	0.0688000i
$685$	−9.64517	−	29.6848i	−0.368523	−	1.13420i
$686$	−16.6410	+	51.2159i	−0.635358	+	1.95543i
$687$	19.9785	+	14.5152i	0.762228	+	0.553791i
$688$	3.23014	+	2.34684i	0.123148	+	0.0894723i
$689$	−4.44574	+	13.6826i	−0.169369	+	0.521265i
$690$	10.6679	+	32.8326i	0.406122	+	1.24991i
$691$	−6.16680	+	4.48044i	−0.234596	+	0.170444i	−0.698872	−	0.715246i	$-0.746314\pi$
$691$	−6.16680	+	4.48044i	−0.234596	+	0.170444i	0.464276	+	0.885690i	$0.346314\pi$
$692$	8.74047			0.332263
$693$	−12.1700	−	8.10095i	−0.462300	−	0.307730i
$694$	2.98936			0.113474
$695$	5.39115	−	3.91690i	0.204498	−	0.148576i
$696$	−6.35640	−	19.5630i	−0.240939	−	0.741533i
$697$	13.5651	−	41.7492i	0.513816	−	1.58136i
$698$	−24.7668	−	17.9941i	−0.937437	−	0.681088i
$699$	1.05702	+	0.767968i	0.0399801	+	0.0290472i
$700$	−3.90956	+	12.0324i	−0.147768	+	0.454782i
$701$	0.512257	+	1.57657i	0.0193477	+	0.0595460i	0.960264	−	0.279093i	$-0.0900336\pi$
$701$	0.512257	+	1.57657i	0.0193477	+	0.0595460i	−0.940917	+	0.338639i	$0.890034\pi$
$702$	8.88298	−	6.45386i	0.335266	−	0.243585i
$703$	−5.50712			−0.207705
$704$	11.6686	−	41.6527i	0.439778	−	1.56985i
$705$	28.1050			1.05850
$706$	2.08163	−	1.51240i	0.0783433	−	0.0569198i
$707$	−3.39026	−	10.4341i	−0.127504	−	0.392416i
$708$	4.29278	−	13.2118i	0.161332	−	0.496530i
$709$	−33.1914	−	24.1149i	−1.24653	−	0.905656i	−0.248513	−	0.968629i	$-0.579942\pi$
$709$	−33.1914	−	24.1149i	−1.24653	−	0.905656i	−0.998015	+	0.0629728i	$0.979942\pi$
$710$	57.4642	+	41.7502i	2.15659	+	1.56686i
$711$	0.00519410	−	0.0159858i	0.000194794	−	0.000599514i
$712$	−8.27188	−	25.4582i	−0.310002	−	0.954088i
$713$	−21.7875	+	15.8295i	−0.815948	+	0.592821i
$714$	−60.1141			−2.24972
$715$	30.9327	−	24.4733i	1.15682	−	0.915249i
$716$	−18.2189			−0.680873
$717$	−4.78846	+	3.47902i	−0.178828	+	0.129926i
$718$	−1.68675	−	5.19129i	−0.0629490	−	0.193737i
$719$	−1.80785	+	5.56398i	−0.0674213	+	0.207501i	−0.979091	−	0.203422i	$-0.934794\pi$
$719$	−1.80785	+	5.56398i	−0.0674213	+	0.207501i	0.911670	+	0.410923i	$0.134794\pi$
$720$	1.48103	+	1.07603i	0.0551947	+	0.0401013i
$721$	28.0350	+	20.3686i	1.04408	+	0.758567i
$722$	0.695202	−	2.13961i	0.0258727	−	0.0796281i
$723$	7.86322	+	24.2005i	0.292436	+	0.900027i
$724$	−6.17798	+	4.48856i	−0.229603	+	0.166816i
$725$	8.07780			0.300002
$726$	18.7613	−	16.1376i	0.696298	−	0.598923i
$727$	−32.9359			−1.22153			−0.610763	−	0.791814i	$-0.709137\pi$
$727$	−32.9359			−1.22153			−0.610763	+	0.791814i	$0.709137\pi$
$728$	41.5541	−	30.1908i	1.54010	−	1.11895i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.343726	−	1.05788i	0.0127219	−	0.0391539i
$731$	26.0632	+	18.9360i	0.963982	+	0.700374i
$732$	−8.61516	−	6.25928i	−0.318426	−	0.231350i
$733$	4.39585	−	13.5290i	0.162364	−	0.499706i	−0.836468	−	0.548016i	$-0.815383\pi$
$733$	4.39585	−	13.5290i	0.162364	−	0.499706i	0.998832	+	0.0483097i	$0.0153834\pi$
$734$	7.48371	+	23.0325i	0.276229	+	0.850145i
$735$	24.5045	−	17.8036i	0.903863	−	0.656695i
$736$	40.7141			1.50074
$737$	11.4867	−	9.08803i	0.423118	−	0.334762i
$738$	−16.2916			−0.599701
$739$	22.9209	−	16.6530i	0.843160	−	0.612592i	−0.0800914	−	0.996788i	$-0.525521\pi$
$739$	22.9209	−	16.6530i	0.843160	−	0.612592i	0.923252	+	0.384196i	$0.125521\pi$
$740$	12.6943	+	39.0691i	0.466653	+	1.43621i
$741$	1.50818	−	4.64172i	0.0554046	−	0.170518i
$742$	−23.6492	−	17.1821i	−0.868189	−	0.630776i
$743$	−10.2043	−	7.41389i	−0.374361	−	0.271989i	0.384656	−	0.923060i	$-0.374320\pi$
$743$	−10.2043	−	7.41389i	−0.374361	−	0.271989i	−0.759017	+	0.651071i	$0.774320\pi$
$744$	3.15508	−	9.71033i	0.115671	−	0.355998i
$745$	11.5848	+	35.6544i	0.424435	+	1.30628i
$746$	−57.3742	+	41.6848i	−2.10062	+	1.52619i
$747$	−1.49972			−0.0548720
$748$	16.6024	−	59.2647i	0.607046	−	2.16693i
$749$	17.1115			0.625240
$750$	−18.0167	+	13.0899i	−0.657878	+	0.477976i
$751$	−0.551201	−	1.69642i	−0.0201136	−	0.0619034i	0.940496	−	0.339805i	$-0.110361\pi$
$751$	−0.551201	−	1.69642i	−0.0201136	−	0.0619034i	−0.960610	+	0.277902i	$0.910361\pi$
$752$	2.67771	−	8.24113i	0.0976459	−	0.300523i
$753$	−22.6679	−	16.4692i	−0.826066	−	0.600172i
$754$	−76.5321	−	55.6039i	−2.78714	−	2.02497i
$755$	−0.433865	+	1.33530i	−0.0157900	+	0.0485966i
$756$	4.16985	+	12.8335i	0.151656	+	0.466749i
$757$	3.96196	−	2.87853i	0.144000	−	0.104622i	−0.513453	−	0.858118i	$-0.671634\pi$
$757$	3.96196	−	2.87853i	0.144000	−	0.104622i	0.657453	+	0.753496i	$0.271634\pi$
$758$	−16.7907			−0.609865
$759$	17.3866	+	11.5734i	0.631094	+	0.420088i
$760$	−5.81765			−0.211028
$761$	−28.5988	+	20.7783i	−1.03671	+	0.753211i	−0.969640	−	0.244537i	$-0.921364\pi$
$761$	−28.5988	+	20.7783i	−1.03671	+	0.753211i	−0.0670664	+	0.997749i	$0.521364\pi$
$762$	−11.7952	−	36.3018i	−0.427294	−	1.31507i
$763$	−11.8591	+	36.4985i	−0.429327	+	1.32133i
$764$	43.0436	+	31.2730i	1.55726	+	1.13142i
$765$	11.9501	+	8.68222i	0.432055	+	0.313906i
$766$	8.41276	−	25.8918i	0.303966	−	0.935510i
$767$	−6.84404	−	21.0638i	−0.247124	−	0.760570i
$768$	−8.76641	+	6.36917i	−0.316331	+	0.229828i
$769$	−25.1401			−0.906575			−0.453287	−	0.891364i	$-0.649749\pi$
$769$	−25.1401			−0.906575			−0.453287	+	0.891364i	$0.649749\pi$
$770$	27.8707	+	75.1416i	1.00439	+	2.70791i
$771$	−28.3104			−1.01957
$772$	−15.0112	+	10.9063i	−0.540264	+	0.392525i
$773$	13.6638	+	42.0528i	0.491452	+	1.51253i	0.822414	+	0.568890i	$0.192627\pi$
$773$	13.6638	+	42.0528i	0.491452	+	1.51253i	−0.330961	+	0.943644i	$0.607373\pi$
$774$	3.69465	−	11.3710i	0.132802	−	0.408721i
$775$	3.24377	+	2.35674i	0.116520	+	0.0846564i
$776$	26.4143	+	19.1911i	0.948218	+	0.688921i
$777$	7.50149	−	23.0872i	0.269115	−	0.828250i
$778$	16.2417	+	49.9867i	0.582292	+	1.79211i
$779$	−5.85857	+	4.25650i	−0.209905	+	0.152505i
$780$	−36.4061			−1.30355
$781$	42.9376	−	1.76229i	1.53643	−	0.0630598i
$782$	85.8819			3.07113
$783$	6.97016	−	5.06412i	0.249093	−	0.180977i
$784$	−2.88581	−	8.88161i	−0.103065	−	0.317201i
$785$	11.3356	−	34.8872i	0.404583	−	1.24518i
$786$	29.3914	+	21.3541i	1.04836	+	0.761676i
$787$	40.1918	+	29.2011i	1.43268	+	1.04091i	0.989509	+	0.144470i	$0.0461476\pi$
$787$	40.1918	+	29.2011i	1.43268	+	1.04091i	0.443174	+	0.896436i	$0.353852\pi$
$788$	−11.5417	+	35.5217i	−0.411156	+	1.26541i
$789$	−3.12138	−	9.60661i	−0.111124	−	0.342004i
$790$	−0.0745450	+	0.0541601i	−0.00265219	+	0.00192693i
$791$	76.5729			2.72262
$792$	−7.91178	+	0.324724i	−0.281133	+	0.0115386i
$793$	−16.9778			−0.602898
$794$	50.7832	−	36.8962i	1.80223	−	1.30940i
$795$	2.21961	+	6.83126i	0.0787214	+	0.242280i
$796$	12.4728	−	38.3872i	0.442085	−	1.36060i
$797$	4.48721	+	3.26015i	0.158945	+	0.115480i	0.664415	−	0.747364i	$-0.268681\pi$
$797$	4.48721	+	3.26015i	0.158945	+	0.115480i	−0.505470	+	0.862844i	$0.668681\pi$
$798$	8.02281	+	5.82892i	0.284005	+	0.206341i
$799$	21.6057	−	66.4956i	0.764356	−	2.35245i
$800$	−1.87314	−	5.76493i	−0.0662254	−	0.203821i
$801$	9.07061	−	6.59018i	0.320494	−	0.232853i
$802$	52.4341			1.85151
$803$	−0.234030	−	0.630963i	−0.00825874	−	0.0222662i
$804$	−13.5192			−0.476787
$805$	−54.7228	+	39.7584i	−1.92872	+	1.40130i
$806$	−14.5100	−	44.6572i	−0.511093	−	1.57298i
$807$	−1.39183	+	4.28362i	−0.0489948	+	0.150791i
$808$	−4.80741	−	3.49278i	−0.169124	−	0.122876i
$809$	4.02915	+	2.92735i	0.141657	+	0.102920i	0.656357	−	0.754451i	$-0.272097\pi$
$809$	4.02915	+	2.92735i	0.141657	+	0.102920i	−0.514700	+	0.857371i	$0.672097\pi$
$810$	1.69401	−	5.21362i	0.0595214	−	0.183188i
$811$	−3.87399	−	11.9229i	−0.136034	−	0.418670i	0.859715	−	0.510773i	$-0.170641\pi$
$811$	−3.87399	−	11.9229i	−0.136034	−	0.418670i	−0.995749	+	0.0921036i	$0.970641\pi$
$812$	94.0549	−	68.3349i	3.30068	−	2.39808i
$813$	5.79644			0.203290
$814$	34.2061	+	22.7693i	1.19892	+	0.798062i
$815$	−9.13408			−0.319953
$816$	3.68440	−	2.67687i	0.128980	−	0.0937094i
$817$	−1.64227	−	5.05439i	−0.0574558	−	0.176831i
$818$	5.37484	−	16.5421i	0.187927	−	0.578380i
$819$	17.4049	+	12.6454i	0.608175	+	0.441865i
$820$	43.7013	+	31.7508i	1.52612	+	1.10879i
$821$	1.33915	−	4.12148i	0.0467367	−	0.143841i	−0.924965	−	0.380052i	$-0.875906\pi$
$821$	1.33915	−	4.12148i	0.0467367	−	0.143841i	0.971702	+	0.236212i	$0.0759059\pi$
$822$	8.90500	+	27.4068i	0.310598	+	0.955921i
$823$	3.87675	−	2.81663i	0.135135	−	0.0981814i	−0.518164	−	0.855281i	$-0.673384\pi$
$823$	3.87675	−	2.81663i	0.135135	−	0.0981814i	0.653299	+	0.757100i	$0.273384\pi$
$824$	18.7692			0.653855
$825$	0.838831	−	2.99432i	0.0292043	−	0.104249i
$826$	45.0015			1.56580
$827$	−9.11259	+	6.62069i	−0.316876	+	0.230224i	−0.734841	−	0.678239i	$-0.762743\pi$
$827$	−9.11259	+	6.62069i	−0.316876	+	0.230224i	0.417965	+	0.908463i	$0.362743\pi$
$828$	−5.95724	−	18.3345i	−0.207028	−	0.637168i
$829$	4.54152	−	13.9774i	0.157733	−	0.485453i	−0.840694	−	0.541510i	$-0.817853\pi$
$829$	4.54152	−	13.9774i	0.157733	−	0.485453i	0.998428	+	0.0560567i	$0.0178528\pi$
$830$	6.65123	+	4.83240i	0.230868	+	0.167735i
$831$	−6.60065	−	4.79565i	−0.228974	−	0.166359i
$832$	−19.6701	+	60.5385i	−0.681939	+	2.09879i
$833$	−23.2849	−	71.6635i	−0.806773	−	2.48299i
$834$	−4.97743	+	3.61631i	−0.172354	+	0.125223i
$835$	−12.5354			−0.433805
$836$	−7.96230	+	6.29960i	−0.275382	+	0.217876i
$837$	4.27646			0.147816
$838$	−53.1366	+	38.6060i	−1.83557	+	1.33362i
$839$	1.61454	+	4.96904i	0.0557401	+	0.171550i	0.975051	−	0.221982i	$-0.0712528\pi$
$839$	1.61454	+	4.96904i	0.0557401	+	0.171550i	−0.919311	+	0.393533i	$0.871253\pi$
$840$	7.92448	−	24.3890i	0.273420	−	0.841502i
$841$	−36.5906	−	26.5847i	−1.26175	−	0.916712i
$842$	14.6270	+	10.6271i	0.504080	+	0.366236i
$843$	−3.94671	+	12.1467i	−0.135932	+	0.418355i
$844$	−21.9652	−	67.6018i	−0.756072	−	2.32695i
$845$	−21.3302	+	15.4973i	−0.733782	+	0.533124i
$846$	−25.9482			−0.892118
$847$	41.4311	+	25.1900i	1.42359	+	0.865538i
$848$	2.21458			0.0760490
$849$	−5.52105	+	4.01128i	−0.189482	+	0.137667i
$850$	−3.95117	−	12.1605i	−0.135524	−	0.417100i
$851$	−10.7170	+	32.9835i	−0.367373	+	1.13066i
$852$	−32.0894	−	23.3143i	−1.09937	−	0.798736i
$853$	−26.4214	−	19.1963i	−0.904652	−	0.657268i	0.0350045	−	0.999387i	$-0.488855\pi$
$853$	−26.4214	−	19.1963i	−0.904652	−	0.657268i	−0.939657	+	0.342119i	$0.888855\pi$
$854$	10.6601	−	32.8083i	0.364780	−	1.12268i
$855$	−0.752986	−	2.31745i	−0.0257516	−	0.0792552i
$856$	7.49805	−	5.44765i	0.256278	−	0.186197i
$857$	−18.8398			−0.643555			−0.321777	−	0.946815i	$-0.604280\pi$
$857$	−18.8398			−0.643555			−0.321777	+	0.946815i	$0.604280\pi$
$858$	−28.5589	+	22.5952i	−0.974986	+	0.771387i
$859$	−36.0989			−1.23168			−0.615839	−	0.787872i	$-0.711183\pi$
$859$	−36.0989			−1.23168			−0.615839	+	0.787872i	$0.711183\pi$
$860$	−32.0717	+	23.3015i	−1.09364	+	0.794574i
$861$	−9.86409	−	30.3586i	−0.336167	−	1.03462i
$862$	15.9659	−	49.1378i	0.543799	−	1.67364i
$863$	13.8729	+	10.0793i	0.472240	+	0.343102i	0.798313	−	0.602242i	$-0.205726\pi$
$863$	13.8729	+	10.0793i	0.472240	+	0.343102i	−0.326074	+	0.945344i	$0.605726\pi$
$864$	−5.23043	−	3.80013i	−0.177943	−	0.129283i
$865$	2.14993	−	6.61680i	0.0730997	−	0.224978i
$866$	−18.9972	−	58.4673i	−0.645551	−	1.98680i
$867$	15.9752	−	11.6067i	0.542546	−	0.394183i
$868$	57.7062			1.95868
$869$	−0.0150381	+	0.0536807i	−0.000510134	+	0.00182099i
$870$	−47.2301			−1.60125
$871$	−17.4375	+	12.6691i	−0.590847	+	0.429276i
$872$	6.42323	+	19.7687i	0.217518	+	0.669451i
$873$	−4.22591	+	13.0060i	−0.143025	+	0.440187i
$874$	−11.4618	−	8.32746i	−0.387700	−	0.281680i
$875$	−35.3011	−	25.6477i	−1.19339	−	0.867051i
$876$	−0.191945	+	0.590747i	−0.00648523	+	0.0199595i
$877$	−5.19832	−	15.9988i	−0.175535	−	0.540241i	0.824123	−	0.566412i	$-0.191669\pi$
$877$	−5.19832	−	15.9988i	−0.175535	−	0.540241i	−0.999657	+	0.0261705i	$0.991669\pi$
$878$	−15.3796	+	11.1740i	−0.519038	+	0.377103i
$879$	11.7975			0.397919
$880$	−5.05424	−	3.36436i	−0.170378	−	0.113412i
$881$	29.3383			0.988431			0.494215	−	0.869339i	$-0.335455\pi$
$881$	29.3383			0.988431			0.494215	+	0.869339i	$0.335455\pi$
$882$	−22.6240	+	16.4373i	−0.761791	+	0.553474i
$883$	7.20334	+	22.1696i	0.242412	+	0.746067i	0.996051	+	0.0887788i	$0.0282964\pi$
$883$	7.20334	+	22.1696i	0.242412	+	0.746067i	−0.753640	+	0.657288i	$0.771704\pi$
$884$	−27.9872	+	86.1358i	−0.941313	+	2.89706i
$885$	−8.94583	−	6.49952i	−0.300711	−	0.218479i
$886$	26.6269	+	19.3456i	0.894547	+	0.649927i
$887$	−4.64963	+	14.3101i	−0.156119	+	0.480486i	−0.998273	−	0.0587522i	$-0.981288\pi$
$887$	−4.64963	+	14.3101i	−0.156119	+	0.480486i	0.842153	+	0.539238i	$0.181288\pi$
$888$	−4.06303	−	12.5047i	−0.136346	−	0.419631i
$889$	60.5050	−	43.9594i	2.02927	−	1.47435i
$890$	−61.4628			−2.06024
$891$	−1.15338	−	3.10961i	−0.0386398	−	0.104176i
$892$	−74.2940			−2.48755
$893$	−9.33118	+	6.77950i	−0.312256	+	0.226867i
$894$	−10.6958	−	32.9183i	−0.357721	−	1.10095i
$895$	−4.48138	+	13.7923i	−0.149796	+	0.461025i
$896$	−58.5243	−	42.5204i	−1.95516	−	1.42051i
$897$	−24.8654	−	18.0658i	−0.830231	−	0.603198i
$898$	−3.79500	+	11.6798i	−0.126641	+	0.389760i
$899$	−11.3855	−	35.0410i	−0.379728	−	1.16868i
$900$	−2.32200	+	1.68703i	−0.0774001	+	0.0562345i
$901$	17.8689			0.595299
$902$	53.9876	−	2.21582i	1.79759	−	0.0737787i
$903$	23.4263			0.779577
$904$	33.5533	−	24.3779i	1.11597	−	0.810798i
$905$	1.87836	+	5.78099i	0.0624387	+	0.192166i
$906$	0.400571	−	1.23283i	0.0133081	−	0.0409580i
$907$	−40.7993	−	29.6424i	−1.35472	−	0.984260i	−0.998761	−	0.0497572i	$-0.984155\pi$
$907$	−40.7993	−	29.6424i	−1.35472	−	0.984260i	−0.355956	−	0.934503i	$-0.615845\pi$
$908$	18.0870	+	13.1410i	0.600239	+	0.436099i
$909$	0.769117	−	2.36710i	0.0255100	−	0.0785117i
$910$	−36.4442	−	112.164i	−1.20811	−	3.71819i
$911$	−41.5187	+	30.1651i	−1.37558	+	0.999414i	−0.378298	+	0.925684i	$0.623490\pi$
$911$	−41.5187	+	30.1651i	−1.37558	+	0.999414i	−0.997278	+	0.0737305i	$0.976510\pi$
$912$	−0.751280			−0.0248774
$913$	4.96984	−	0.203978i	0.164478	−	0.00675068i
$914$	16.8035			0.555810
$915$	−6.85757	+	4.98232i	−0.226704	+	0.164710i
$916$	23.3607	+	71.8968i	0.771859	+	2.37554i
$917$	−21.9967	+	67.6989i	−0.726395	+	2.23561i
$918$	−11.0330	−	8.01595i	−0.364143	−	0.264566i
$919$	17.9010	+	13.0058i	0.590500	+	0.429023i	0.842494	−	0.538706i	$-0.181086\pi$
$919$	17.9010	+	13.0058i	0.590500	+	0.429023i	−0.251995	+	0.967729i	$0.581086\pi$
$920$	−11.3213	+	34.8433i	−0.373251	+	1.14875i
$921$	−6.02628	−	18.5470i	−0.198573	−	0.611144i
$922$	55.8464	−	40.5748i	1.83920	−	1.33626i
$923$	−63.2381			−2.08151
$924$	−15.5637	−	41.9609i	−0.512008	−	1.38041i
$925$	5.16336			0.169770
$926$	13.7321	−	9.97697i	0.451265	−	0.327864i
$927$	2.42932	+	7.47668i	0.0797893	+	0.245566i
$928$	−17.2126	+	52.9751i	−0.565033	+	1.73899i
$929$	−37.3481	−	27.1350i	−1.22535	−	0.890271i	−0.228819	−	0.973469i	$-0.573487\pi$
$929$	−37.3481	−	27.1350i	−1.22535	−	0.890271i	−0.996533	+	0.0831982i	$0.973487\pi$
$930$	−18.9660	−	13.7796i	−0.621919	−	0.451851i
$931$	−3.84119	+	11.8220i	−0.125890	+	0.387450i
$932$	1.23596	+	3.80390i	0.0404852	+	0.124601i
$933$	13.0860	−	9.50756i	0.428418	−	0.311264i
$934$	16.8412			0.551061
$935$	−40.7814	−	27.1461i	−1.33369	−	0.887773i
$936$	11.6524			0.380871
$937$	−10.5340	+	7.65342i	−0.344132	+	0.250026i	−0.746403	−	0.665494i	$-0.768221\pi$
$937$	−10.5340	+	7.65342i	−0.344132	+	0.250026i	0.402271	+	0.915520i	$0.368221\pi$
$938$	−13.5334	−	41.6514i	−0.441880	−	1.35997i
$939$	4.15236	−	12.7796i	0.135507	−	0.417048i
$940$	69.6048	+	50.5708i	2.27026	+	1.64944i
$941$	34.2919	+	24.9145i	1.11788	+	0.812191i	0.983887	−	0.178791i	$-0.0572186\pi$
$941$	34.2919	+	24.9145i	1.11788	+	0.812191i	0.133997	+	0.990982i	$0.457219\pi$
$942$	−10.4657	+	32.2100i	−0.340990	+	1.04946i
$943$	14.0923	+	43.3716i	0.458908	+	1.41237i
$944$	−2.75815	+	2.00391i	−0.0897701	+	0.0652218i
$945$	10.7410			0.349405
$946$	−10.6969	+	38.1840i	−0.347786	+	1.24147i
$947$	−15.3494			−0.498787			−0.249394	−	0.968402i	$-0.580231\pi$
$947$	−15.3494			−0.498787			−0.249394	+	0.968402i	$0.580231\pi$
$948$	0.0416278	−	0.0302443i	0.00135201	−	0.000982290i
$949$	0.306021	+	0.941837i	0.00993388	+	0.0305733i
$950$	−0.651806	+	2.00605i	−0.0211474	+	0.0650850i
$951$	12.2813	+	8.92285i	0.398247	+	0.289343i
$952$	−51.6118	−	37.4982i	−1.67275	−	1.21532i
$953$	−11.8067	+	36.3372i	−0.382456	+	1.17708i	0.555853	+	0.831281i	$0.312392\pi$
$953$	−11.8067	+	36.3372i	−0.382456	+	1.17708i	−0.938309	+	0.345798i	$0.887608\pi$
$954$	−2.04928	−	6.30702i	−0.0663478	−	0.204197i
$955$	34.2622	−	24.8929i	1.10870	−	0.805517i
$956$	−18.1191			−0.586013
$957$	−22.4092	+	17.7297i	−0.724387	+	0.573119i
$958$	−29.0876			−0.939776
$959$	−45.6795	+	33.1881i	−1.47507	+	1.07170i
$960$	9.82064	+	30.2248i	0.316960	+	0.975502i
$961$	−3.92819	+	12.0897i	−0.126716	+	0.389991i
$962$	−48.9197	−	35.5422i	−1.57723	−	1.14593i
$963$	3.14054	+	2.28174i	0.101203	+	0.0735280i
$964$	−24.0712	+	74.0836i	−0.775282	+	2.38607i
$965$	4.56401	+	14.0466i	0.146921	+	0.452175i
$966$	50.5233	−	36.7073i	1.62556	−	1.18104i
$967$	−29.4003			−0.945450			−0.472725	−	0.881210i	$-0.656730\pi$
$967$	−29.4003			−0.945450			−0.472725	+	0.881210i	$0.656730\pi$
$968$	26.1742	−	2.15216i	0.841269	−	0.0691732i
$969$	−6.06188			−0.194736
$970$	60.6498	−	44.0646i	1.94735	−	1.41483i
$971$	5.13102	+	15.7917i	0.164662	+	0.506778i	0.999011	−	0.0444583i	$-0.0141562\pi$
$971$	5.13102	+	15.7917i	0.164662	+	0.506778i	−0.834349	+	0.551237i	$0.814156\pi$
$972$	−0.945976	+	2.91141i	−0.0303422	+	0.0933837i
$973$	−9.75252	−	7.08562i	−0.312651	−	0.227155i
$974$	17.3969	+	12.6396i	0.557433	+	0.404999i
$975$	−1.41404	+	4.35197i	−0.0452856	+	0.139375i
$976$	0.807592	+	2.48551i	0.0258504	+	0.0795593i
$977$	46.5281	−	33.8047i	1.48857	−	1.08151i	0.513898	−	0.857851i	$-0.328201\pi$
$977$	46.5281	−	33.8047i	1.48857	−	1.08151i	0.974668	−	0.223655i	$-0.0717990\pi$
$978$	8.43313			0.269662
$979$	−29.1622	+	23.0725i	−0.932027	+	0.737400i
$980$	92.7228			2.96192
$981$	−7.04345	+	5.11736i	−0.224880	+	0.163385i
$982$	8.32639	+	25.6260i	0.265706	+	0.817758i
$983$	−6.85495	+	21.0974i	−0.218639	+	0.672901i	0.780236	+	0.625485i	$0.215099\pi$
$983$	−6.85495	+	21.0974i	−0.218639	+	0.672901i	−0.998875	+	0.0474164i	$0.984901\pi$
$984$	−13.9873	−	10.1624i	−0.445900	−	0.323965i
$985$	24.0521	+	17.4748i	0.766362	+	0.556795i
$986$	−36.3081	+	111.745i	−1.15629	+	3.55868i
$987$	−15.7109	−	48.3533i	−0.500084	−	1.53910i
$988$	12.0873	−	8.78190i	0.384547	−	0.279390i
$989$	−33.4678			−1.06422
$990$	−4.90456	+	17.5075i	−0.155877	+	0.556424i
$991$	−9.61045			−0.305286			−0.152643	−	0.988281i	$-0.548778\pi$
$991$	−9.61045			−0.305286			−0.152643	+	0.988281i	$0.548778\pi$
$992$	−22.3677	+	16.2511i	−0.710176	+	0.515973i
$993$	−2.73779	−	8.42606i	−0.0868812	−	0.267393i
$994$	39.7062	−	122.203i	1.25940	−	3.87605i
$995$	−25.9923	−	18.8845i	−0.824011	−	0.598679i
$996$	−3.71421	−	2.69853i	−0.117689	−	0.0855063i
$997$	13.5782	−	41.7896i	0.430027	−	1.32349i	−0.468070	−	0.883691i	$-0.655050\pi$
$997$	13.5782	−	41.7896i	0.430027	−	1.32349i	0.898097	−	0.439797i	$-0.144950\pi$
$998$	26.3119	+	80.9797i	0.832888	+	2.56337i
$999$	4.45536	−	3.23701i	0.140961	−	0.102414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.j.c.58.2	✓	40
11.2	odd	10		6897.2.a.bn.1.3		20
11.4	even	5	inner	627.2.j.c.400.2	yes	40
11.9	even	5		6897.2.a.bo.1.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.c.58.2	✓	40	1.1	even	1	trivial
627.2.j.c.400.2	yes	40	11.4	even	5	inner
6897.2.a.bn.1.3		20	11.2	odd	10
6897.2.a.bo.1.18		20	11.9	even	5

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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82006 + 1.32235i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.945976 - 2.91141i) q^{4} +(-1.97134 - 1.43226i) q^{5} +(1.82006 + 1.32235i) q^{6} +(-1.36214 + 4.19225i) q^{7} +(0.737778 + 2.27065i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.48193 q^{10} +(2.60100 - 2.05786i) q^{11} -3.06124 q^{12} +(-3.94848 + 2.86874i) q^{13} +(-3.06444 - 9.43138i) q^{14} +(-0.752986 + 2.31745i) q^{15} +(0.607798 + 0.441591i) q^{16} +(4.90417 + 3.56309i) q^{17} +(0.695202 - 2.13961i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-6.03476 + 4.38451i) q^{20} +4.40799 q^{21} +(-2.01278 + 7.18487i) q^{22} -6.29746 q^{23} +(1.93153 - 1.40334i) q^{24} +(0.289728 + 0.891690i) q^{25} +(3.39299 - 10.4426i) q^{26} +(0.809017 + 0.587785i) q^{27} +(10.9168 + 7.93153i) q^{28} +(2.66237 - 8.19392i) q^{29} +(-1.69401 - 5.21362i) q^{30} +(3.45973 - 2.51364i) q^{31} -6.46517 q^{32} +(-2.76089 - 1.83779i) q^{33} -13.6375 q^{34} +(8.68966 - 6.31341i) q^{35} +(0.945976 + 2.91141i) q^{36} +(1.70180 - 5.23759i) q^{37} +(1.82006 + 1.32235i) q^{38} +(3.94848 + 2.86874i) q^{39} +(1.79775 - 5.53292i) q^{40} +(-2.23778 - 6.88717i) q^{41} +(-8.02281 + 5.82892i) q^{42} +5.31450 q^{43} +(-3.53079 - 9.51928i) q^{44} +2.43671 q^{45} +(11.4618 - 8.32746i) q^{46} +(-3.56419 - 10.9695i) q^{47} +(0.232158 - 0.714509i) q^{48} +(-10.0564 - 7.30639i) q^{49} +(-1.70645 - 1.23981i) q^{50} +(1.87323 - 5.76519i) q^{51} +(4.61692 + 14.2094i) q^{52} +(2.38477 - 1.73264i) q^{53} -2.24972 q^{54} +(-8.07487 + 0.331418i) q^{55} -10.5241 q^{56} +(-0.809017 + 0.587785i) q^{57} +(5.98958 + 18.4340i) q^{58} +(-1.40230 + 4.31583i) q^{59} +(6.03476 + 4.38451i) q^{60} +(2.81427 + 2.04469i) q^{61} +(-2.97300 + 9.14997i) q^{62} +(-1.36214 - 4.19225i) q^{63} +(10.5514 - 7.66605i) q^{64} +11.8926 q^{65} +(7.45520 - 0.305985i) q^{66} +4.41626 q^{67} +(15.0128 - 10.9075i) q^{68} +(1.94602 + 5.98924i) q^{69} +(-7.46717 + 22.9816i) q^{70} +(10.4825 + 7.61598i) q^{71} +(-1.93153 - 1.40334i) q^{72} +(0.0627017 - 0.192976i) q^{73} +(3.82856 + 11.7831i) q^{74} +(0.758517 - 0.551095i) q^{75} -3.06124 q^{76} +(5.08411 + 13.7071i) q^{77} -10.9800 q^{78} +(-0.0135983 + 0.00987976i) q^{79} +(-0.565703 - 1.74106i) q^{80} +(0.309017 - 0.951057i) q^{81} +(13.1802 + 9.57594i) q^{82} +(1.21330 + 0.881516i) q^{83} +(4.16985 - 12.8335i) q^{84} +(-4.56452 - 14.0481i) q^{85} +(-9.67272 + 7.02764i) q^{86} -8.61560 q^{87} +(6.59163 + 4.38772i) q^{88} -11.2119 q^{89} +(-4.43497 + 3.22220i) q^{90} +(-6.64806 - 20.4606i) q^{91} +(-5.95724 + 18.3345i) q^{92} +(-3.45973 - 2.51364i) q^{93} +(20.9926 + 15.2520i) q^{94} +(-0.752986 + 2.31745i) q^{95} +(1.99785 + 6.14874i) q^{96} +(11.0636 - 8.03816i) q^{97} +27.9648 q^{98} +(-0.894678 + 3.19367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{2} + 10 q^{3} - 3 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 13 q^{8} - 10 q^{9} + 10 q^{10} + 7 q^{11} - 42 q^{12} - 12 q^{13} - 2 q^{14} - 7 q^{15} - 27 q^{16} + 11 q^{17} - 4 q^{18} + 10 q^{19}+ \cdots - 13 q^{99}+O(q^{100}) \) 40 * q + q^2 + 10 * q^3 - 3 * q^4 + 2 * q^5 - q^6 + 4 * q^7 - 13 * q^8 - 10 * q^9 + 10 * q^10 + 7 * q^11 - 42 * q^12 - 12 * q^13 - 2 * q^14 - 7 * q^15 - 27 * q^16 + 11 * q^17 - 4 * q^18 + 10 * q^19 - 11 * q^20 + 6 * q^21 - 2 * q^22 - 60 * q^23 - 7 * q^24 - 18 * q^25 - 35 * q^26 + 10 * q^27 + 20 * q^28 + 25 * q^29 - 5 * q^30 - 12 * q^31 + 40 * q^32 + 3 * q^33 - 10 * q^34 + 24 * q^35 - 3 * q^36 - 23 * q^37 - q^38 + 12 * q^39 + 80 * q^40 + 18 * q^41 - 28 * q^42 - 6 * q^43 + 14 * q^44 - 18 * q^45 - 15 * q^46 - 9 * q^47 - 8 * q^48 - 4 * q^49 + 90 * q^50 + 4 * q^51 + 15 * q^52 - 26 * q^53 - 6 * q^54 + 38 * q^55 - 124 * q^56 - 10 * q^57 + 10 * q^58 + 7 * q^59 + 11 * q^60 + 18 * q^61 + 105 * q^62 + 4 * q^63 - 85 * q^64 + 36 * q^65 - 8 * q^66 - 88 * q^67 + 40 * q^68 - 103 * q^70 + 30 * q^71 + 7 * q^72 - 2 * q^73 - 4 * q^74 + 13 * q^75 - 42 * q^76 + 57 * q^77 + 20 * q^78 + 59 * q^79 + 11 * q^80 - 10 * q^81 + 40 * q^82 - 54 * q^83 - 15 * q^84 + 21 * q^85 - 108 * q^86 - 30 * q^87 + 83 * q^88 - 74 * q^89 - 10 * q^90 + q^91 - 125 * q^92 + 12 * q^93 - 10 * q^94 - 7 * q^95 + 55 * q^96 - 17 * q^97 + 78 * q^98 - 13 * q^99

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