LMFDB - Embedded newform 637.2.bd.b.440.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			440.6
Character	$\chi$	$=$	637.440
Dual form			637.2.bd.b.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.419805 - 1.56673i) q^{2} +(0.445073 - 0.256963i) q^{3} +(-0.546366 - 0.315445i) q^{4} +(1.07946 - 1.07946i) q^{5} +(-0.215749 - 0.805186i) q^{6} +(1.57027 - 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +O(q^{10})$	\(q+(0.419805 - 1.56673i) q^{2} +(0.445073 - 0.256963i) q^{3} +(-0.546366 - 0.315445i) q^{4} +(1.07946 - 1.07946i) q^{5} +(-0.215749 - 0.805186i) q^{6} +(1.57027 - 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +(-1.23806 - 2.14439i) q^{10} +(2.78252 + 0.745574i) q^{11} -0.324231 q^{12} +(-2.94467 - 2.08061i) q^{13} +(0.203057 - 0.757819i) q^{15} +(-2.43188 - 4.21214i) q^{16} +(3.10787 - 5.38299i) q^{17} +(3.13786 + 3.13786i) q^{18} +(-0.598564 - 2.23387i) q^{19} +(-0.930289 + 0.249270i) q^{20} +(2.33623 - 4.04647i) q^{22} +(4.86913 - 2.81119i) q^{23} +(0.295384 - 1.10239i) q^{24} +2.66954i q^{25} +(-4.49595 + 3.74006i) q^{26} +2.94782i q^{27} +(0.379237 + 0.656858i) q^{29} +(-1.10206 - 0.636273i) q^{30} +(-6.12208 + 6.12208i) q^{31} +(-3.33015 + 0.892311i) q^{32} +(1.43001 - 0.383170i) q^{33} +(-7.12901 - 7.12901i) q^{34} +(1.49479 - 0.863019i) q^{36} +(5.82334 + 1.56036i) q^{37} -3.75116 q^{38} +(-1.84523 - 0.169352i) q^{39} -3.39009i q^{40} +(-1.94919 - 0.522283i) q^{41} +(-2.24252 - 1.29472i) q^{43} +(-1.28509 - 1.28509i) q^{44} +(1.08097 + 4.03424i) q^{45} +(-2.36030 - 8.80878i) q^{46} +(1.56216 + 1.56216i) q^{47} +(-2.16473 - 1.24981i) q^{48} +(4.18246 + 1.12069i) q^{50} -3.19443i q^{51} +(0.952550 + 2.06565i) q^{52} -4.94657 q^{53} +(4.61845 + 1.23751i) q^{54} +(3.80843 - 2.19880i) q^{55} +(-0.840427 - 0.840427i) q^{57} +(1.18833 - 0.318411i) q^{58} +(0.851400 - 0.228132i) q^{59} +(-0.349994 + 0.349994i) q^{60} +(-4.48249 - 2.58797i) q^{61} +(7.02159 + 12.1617i) q^{62} -4.13546i q^{64} +(-5.42458 + 0.932716i) q^{65} -2.40130i q^{66} +(-4.06383 + 15.1664i) q^{67} +(-3.39607 + 1.96072i) q^{68} +(1.44475 - 2.50237i) q^{69} +(-10.3040 + 2.76095i) q^{71} +(1.57247 + 5.86855i) q^{72} +(4.91976 + 4.91976i) q^{73} +(4.88933 - 8.46857i) q^{74} +(0.685973 + 1.18814i) q^{75} +(-0.377628 + 1.40933i) q^{76} +(-1.03997 + 2.81989i) q^{78} +8.49528 q^{79} +(-7.17194 - 1.92172i) q^{80} +(-3.34634 - 5.79603i) q^{81} +(-1.63656 + 2.83460i) q^{82} +(-1.51432 + 1.51432i) q^{83} +(-2.45590 - 9.16553i) q^{85} +(-2.96990 + 2.96990i) q^{86} +(0.337576 + 0.194900i) q^{87} +(5.54006 - 3.19856i) q^{88} +(-2.16531 + 8.08103i) q^{89} +6.77438 q^{90} -3.54710 q^{92} +(-1.15162 + 4.29792i) q^{93} +(3.10329 - 1.79169i) q^{94} +(-3.05750 - 1.76525i) q^{95} +(-1.25287 + 1.25287i) q^{96} +(-0.933928 - 3.48547i) q^{97} +(-5.57284 + 5.57284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.419805	−	1.56673i	0.296847	−	1.10785i	−0.642893	−	0.765956i	$-0.722266\pi$
$2$	0.419805	−	1.56673i	0.296847	−	1.10785i	0.939739	−	0.341891i	$-0.111068\pi$
$3$	0.445073	−	0.256963i	0.256963	−	0.148358i	−0.365985	−	0.930621i	$-0.619268\pi$
$3$	0.445073	−	0.256963i	0.256963	−	0.148358i	0.622948	+	0.782263i	$0.285935\pi$
$4$	−0.546366	−	0.315445i	−0.273183	−	0.157722i
$5$	1.07946	−	1.07946i	0.482749	−	0.482749i	−0.423260	−	0.906008i	$-0.639114\pi$
$5$	1.07946	−	1.07946i	0.482749	−	0.482749i	0.906008	+	0.423260i	$0.139114\pi$
$6$	−0.215749	−	0.805186i	−0.0880791	−	0.328716i
$7$		0			0
$7$		0			0
$8$	1.57027	−	1.57027i	0.555175	−	0.555175i
$9$	−1.36794	+	2.36934i	−0.455980	+	0.789780i
$10$	−1.23806	−	2.14439i	−0.391509	−	0.678114i
$11$	2.78252	+	0.745574i	0.838961	+	0.224799i	0.652619	−	0.757686i	$-0.273670\pi$
$11$	2.78252	+	0.745574i	0.838961	+	0.224799i	0.186342	+	0.982485i	$0.440337\pi$
$12$	−0.324231			−0.0935974
$13$	−2.94467	−	2.08061i	−0.816704	−	0.577057i
$13$	−2.94467	−	2.08061i	−0.816704	−	0.577057i
$14$		0			0
$15$	0.203057	−	0.757819i	0.0524291	−	0.195668i
$16$	−2.43188	−	4.21214i	−0.607970	−	1.05303i
$17$	3.10787	−	5.38299i	0.753769	−	1.30557i	−0.192215	−	0.981353i	$-0.561567\pi$
$17$	3.10787	−	5.38299i	0.753769	−	1.30557i	0.945984	−	0.324213i	$-0.105100\pi$
$18$	3.13786	+	3.13786i	0.739600	+	0.739600i
$19$	−0.598564	−	2.23387i	−0.137320	−	0.512485i	−0.999978	−	0.00669672i	$-0.997868\pi$
$19$	−0.598564	−	2.23387i	−0.137320	−	0.512485i	0.862658	−	0.505788i	$-0.168798\pi$
$20$	−0.930289	+	0.249270i	−0.208019	+	0.0557385i
$21$		0			0
$22$	2.33623	−	4.04647i	0.498086	−	0.862710i
$23$	4.86913	−	2.81119i	1.01528	−	0.586174i	0.102549	−	0.994728i	$-0.467300\pi$
$23$	4.86913	−	2.81119i	1.01528	−	0.586174i	0.912734	+	0.408554i	$0.133967\pi$
$24$	0.295384	−	1.10239i	0.0602950	−	0.225024i
$25$			2.66954i			0.533908i
$26$	−4.49595	+	3.74006i	−0.881727	+	0.733486i
$27$			2.94782i			0.567308i
$28$		0			0
$29$	0.379237	+	0.656858i	0.0704225	+	0.121975i	0.899087	−	0.437771i	$-0.144232\pi$
$29$	0.379237	+	0.656858i	0.0704225	+	0.121975i	−0.828664	+	0.559746i	$0.810899\pi$
$30$	−1.10206	−	0.636273i	−0.201207	−	0.116167i
$31$	−6.12208	+	6.12208i	−1.09956	+	1.09956i	−0.105096	+	0.994462i	$0.533515\pi$
$31$	−6.12208	+	6.12208i	−1.09956	+	1.09956i	−0.994462	+	0.105096i	$0.966485\pi$
$32$	−3.33015	+	0.892311i	−0.588693	+	0.157740i
$33$	1.43001	−	0.383170i	0.248933	−	0.0667013i
$34$	−7.12901	−	7.12901i	−1.22261	−	1.22261i
$35$		0			0
$36$	1.49479	−	0.863019i	0.249132	−	0.143837i
$37$	5.82334	+	1.56036i	0.957351	+	0.256521i	0.703479	−	0.710716i	$-0.251629\pi$
$37$	5.82334	+	1.56036i	0.957351	+	0.256521i	0.253872	+	0.967238i	$0.418296\pi$
$38$	−3.75116			−0.608518
$39$	−1.84523	−	0.169352i	−0.295474	−	0.0271181i
$40$		−	3.39009i		−	0.536020i
$41$	−1.94919	−	0.522283i	−0.304412	−	0.0815669i	0.103380	−	0.994642i	$-0.467034\pi$
$41$	−1.94919	−	0.522283i	−0.304412	−	0.0815669i	−0.407792	+	0.913075i	$0.633701\pi$
$42$		0			0
$43$	−2.24252	−	1.29472i	−0.341981	−	0.197443i	0.319167	−	0.947699i	$-0.396597\pi$
$43$	−2.24252	−	1.29472i	−0.341981	−	0.197443i	−0.661148	+	0.750256i	$0.729930\pi$
$44$	−1.28509	−	1.28509i	−0.193734	−	0.193734i
$45$	1.08097	+	4.03424i	0.161142	+	0.601389i
$46$	−2.36030	−	8.80878i	−0.348008	−	1.29878i
$47$	1.56216	+	1.56216i	0.227865	+	0.227865i	0.811800	−	0.583935i	$-0.198488\pi$
$47$	1.56216	+	1.56216i	0.227865	+	0.227865i	−0.583935	+	0.811800i	$0.698488\pi$
$48$	−2.16473	−	1.24981i	−0.312452	−	0.180394i
$49$		0			0
$50$	4.18246	+	1.12069i	0.591488	+	0.158489i
$51$		−	3.19443i		−	0.447310i
$52$	0.952550	+	2.06565i	0.132095	+	0.286455i
$53$	−4.94657			−0.679463			−0.339732	−	0.940522i	$-0.610336\pi$
$53$	−4.94657			−0.679463			−0.339732	+	0.940522i	$0.610336\pi$
$54$	4.61845	+	1.23751i	0.628491	+	0.168404i
$55$	3.80843	−	2.19880i	0.513529	−	0.296486i
$56$		0			0
$57$	−0.840427	−	0.840427i	−0.111317	−	0.111317i
$58$	1.18833	−	0.318411i	0.156035	−	0.0418094i
$59$	0.851400	−	0.228132i	0.110843	−	0.0297003i	−0.202971	−	0.979185i	$-0.565060\pi$
$59$	0.851400	−	0.228132i	0.110843	−	0.0297003i	0.313814	+	0.949484i	$0.398393\pi$
$60$	−0.349994	+	0.349994i	−0.0451840	+	0.0451840i
$61$	−4.48249	−	2.58797i	−0.573924	−	0.331355i	0.184791	−	0.982778i	$-0.440839\pi$
$61$	−4.48249	−	2.58797i	−0.573924	−	0.331355i	−0.758715	+	0.651423i	$0.774172\pi$
$62$	7.02159	+	12.1617i	0.891742	+	1.54454i
$63$		0			0
$64$		−	4.13546i		−	0.516933i
$65$	−5.42458	+	0.932716i	−0.672836	+	0.115689i
$66$		−	2.40130i		−	0.295580i
$67$	−4.06383	+	15.1664i	−0.496476	+	1.85287i	0.0251264	+	0.999684i	$0.492001\pi$
$67$	−4.06383	+	15.1664i	−0.496476	+	1.85287i	−0.521602	+	0.853189i	$0.674665\pi$
$68$	−3.39607	+	1.96072i	−0.411834	+	0.237773i
$69$	1.44475	−	2.50237i	0.173927	−	0.301250i
$70$		0			0
$71$	−10.3040	+	2.76095i	−1.22286	+	0.327665i	−0.811796	−	0.583941i	$-0.801510\pi$
$71$	−10.3040	+	2.76095i	−1.22286	+	0.327665i	−0.411066	+	0.911606i	$0.634843\pi$
$72$	1.57247	+	5.86855i	0.185318	+	0.691615i
$73$	4.91976	+	4.91976i	0.575815	+	0.575815i	0.933747	−	0.357933i	$-0.116518\pi$
$73$	4.91976	+	4.91976i	0.575815	+	0.575815i	−0.357933	+	0.933747i	$0.616518\pi$
$74$	4.88933	−	8.46857i	0.568373	−	0.984452i
$75$	0.685973	+	1.18814i	0.0792094	+	0.137195i
$76$	−0.377628	+	1.40933i	−0.0433169	+	0.161661i
$77$		0			0
$78$	−1.03997	+	2.81989i	−0.117753	+	0.319290i
$79$	8.49528			0.955794			0.477897	−	0.878416i	$-0.341399\pi$
$79$	8.49528			0.955794			0.477897	+	0.878416i	$0.341399\pi$
$80$	−7.17194	−	1.92172i	−0.801847	−	0.214854i
$81$	−3.34634	−	5.79603i	−0.371815	−	0.644003i
$82$	−1.63656	+	2.83460i	−0.180727	+	0.313029i
$83$	−1.51432	+	1.51432i	−0.166218	+	0.166218i	−0.785315	−	0.619096i	$-0.787499\pi$
$83$	−1.51432	+	1.51432i	−0.166218	+	0.166218i	0.619096	+	0.785315i	$0.287499\pi$
$84$		0			0
$85$	−2.45590	−	9.16553i	−0.266379	−	0.994141i
$86$	−2.96990	+	2.96990i	−0.320253	+	0.320253i
$87$	0.337576	+	0.194900i	0.0361920	+	0.0208955i
$88$	5.54006	−	3.19856i	0.590573	−	0.340967i
$89$	−2.16531	+	8.08103i	−0.229522	+	0.856588i	0.751020	+	0.660279i	$0.229562\pi$
$89$	−2.16531	+	8.08103i	−0.229522	+	0.856588i	−0.980542	+	0.196308i	$0.937105\pi$
$90$	6.77438			0.714082
$91$		0			0
$92$	−3.54710			−0.369811
$93$	−1.15162	+	4.29792i	−0.119418	+	0.445674i
$94$	3.10329	−	1.79169i	0.320080	−	0.184798i
$95$	−3.05750	−	1.76525i	−0.313692	−	0.181110i
$96$	−1.25287	+	1.25287i	−0.127870	+	0.127870i
$97$	−0.933928	−	3.48547i	−0.0948260	−	0.353896i	0.902167	−	0.431387i	$-0.141976\pi$
$97$	−0.933928	−	3.48547i	−0.0948260	−	0.353896i	−0.996993	+	0.0774914i	$0.975309\pi$
$98$		0			0
$99$	−5.57284	+	5.57284i	−0.560091	+	0.560091i
$100$	0.842092	−	1.45855i	0.0842092	−	0.145855i
$101$	9.84474	+	17.0516i	0.979589	+	1.69670i	0.663876	+	0.747843i	$0.268910\pi$
$101$	9.84474	+	17.0516i	0.979589	+	1.69670i	0.315713	+	0.948855i	$0.397756\pi$
$102$	−5.00482	−	1.34104i	−0.495551	−	0.132783i
$103$	9.40261			0.926467			0.463233	−	0.886236i	$-0.346689\pi$
$103$	9.40261			0.926467			0.463233	+	0.886236i	$0.346689\pi$
$104$	−7.89105	+	1.35681i	−0.773781	+	0.133046i
$105$		0			0
$106$	−2.07659	+	7.74995i	−0.201697	+	0.752742i
$107$	−0.0359206	−	0.0622163i	−0.00347258	−	0.00601468i	0.864284	−	0.503004i	$-0.167772\pi$
$107$	−0.0359206	−	0.0622163i	−0.00347258	−	0.00601468i	−0.867756	+	0.496990i	$0.834439\pi$
$108$	0.929874	−	1.61059i	0.0894772	−	0.154979i
$109$	5.17943	+	5.17943i	0.496099	+	0.496099i	0.910221	−	0.414122i	$-0.135911\pi$
$109$	5.17943	+	5.17943i	0.496099	+	0.496099i	−0.414122	+	0.910221i	$0.635911\pi$
$110$	−1.84613	−	6.88986i	−0.176022	−	0.656922i
$111$	2.99277	−	0.801910i	0.284061	−	0.0761139i
$112$		0			0
$113$	−8.15754	+	14.1293i	−0.767396	+	1.32917i	0.171574	+	0.985171i	$0.445115\pi$
$113$	−8.15754	+	14.1293i	−0.767396	+	1.32917i	−0.938970	+	0.343998i	$0.888219\pi$
$114$	−1.66954	+	0.963910i	−0.156367	+	0.0902784i
$115$	2.22146	−	8.29059i	0.207152	−	0.773101i
$116$		−	0.478513i		−	0.0444288i
$117$	8.95780	−	4.13077i	0.828149	−	0.381890i
$118$		−	1.42969i		−	0.131613i
$119$		0			0
$120$	−0.871127	−	1.50884i	−0.0795227	−	0.137737i
$121$	−2.33975	−	1.35085i	−0.212704	−	0.122805i
$122$	−5.93642	+	5.93642i	−0.537459	+	0.537459i
$123$	−1.00174	+	0.268415i	−0.0903238	+	0.0242022i
$124$	5.27608	−	1.41372i	0.473806	−	0.126956i
$125$	8.27895	+	8.27895i	0.740492	+	0.740492i
$126$		0			0
$127$	14.9037	−	8.60464i	1.32249	−	0.763538i	0.338362	−	0.941016i	$-0.390127\pi$
$127$	14.9037	−	8.60464i	1.32249	−	0.763538i	0.984125	+	0.177478i	$0.0567937\pi$
$128$	−13.1395	−	3.52071i	−1.16138	−	0.311190i
$129$	−1.33078			−0.117169
$130$	−0.815948	+	8.89042i	−0.0715633	+	0.779742i
$131$		−	5.47021i		−	0.477935i	−0.971028	−	0.238967i	$-0.923191\pi$
$131$		−	5.47021i		−	0.477935i	0.971028	−	0.238967i	$-0.0768089\pi$
$132$	−0.902178	−	0.241738i	−0.0785245	−	0.0210406i
$133$		0			0
$134$	22.0557	+	12.7339i	1.90532	+	1.10004i
$135$	3.18205	+	3.18205i	0.273867	+	0.273867i
$136$	−3.57255	−	13.3330i	−0.306344	−	1.14329i
$137$	−0.454089	−	1.69468i	−0.0387955	−	0.144787i	0.943811	−	0.330484i	$-0.107212\pi$
$137$	−0.454089	−	1.69468i	−0.0387955	−	0.144787i	−0.982607	+	0.185698i	$0.940545\pi$
$138$	−3.31404	−	3.31404i	−0.282110	−	0.282110i
$139$	7.13953	+	4.12201i	0.605567	+	0.349624i	0.771228	−	0.636559i	$-0.219643\pi$
$139$	7.13953	+	4.12201i	0.605567	+	0.349624i	−0.165662	+	0.986183i	$0.552976\pi$
$140$		0			0
$141$	1.09669	+	0.293858i	0.0923583	+	0.0247473i
$142$			17.3027i			1.45201i
$143$	−6.64235	−	7.98480i	−0.555461	−	0.667722i
$144$	13.3067			1.10889
$145$	1.11842	+	0.299680i	0.0928798	+	0.0248871i
$146$	9.77330	−	5.64262i	0.808844	−	0.466986i
$147$		0			0
$148$	−2.68947	−	2.68947i	−0.221073	−	0.221073i
$149$	−4.29875	+	1.15185i	−0.352167	+	0.0943628i	−0.430566	−	0.902559i	$-0.641686\pi$
$149$	−4.29875	+	1.15185i	−0.352167	+	0.0943628i	0.0783988	+	0.996922i	$0.475019\pi$
$150$	2.14947	−	0.575950i	0.175504	−	0.0470261i
$151$	6.36476	−	6.36476i	0.517957	−	0.517957i	−0.398996	−	0.916953i	$-0.630641\pi$
$151$	6.36476	−	6.36476i	0.517957	−	0.517957i	0.916953	+	0.398996i	$0.130641\pi$
$152$	−4.44769	−	2.56788i	−0.360755	−	0.208282i
$153$	8.50276	+	14.7272i	0.687407	+	1.19062i
$154$		0			0
$155$			13.2171i			1.06162i
$156$	0.954752	+	0.674597i	0.0764413	+	0.0540110i
$157$		−	4.86250i		−	0.388070i	−0.980995	−	0.194035i	$-0.937842\pi$
$157$		−	4.86250i		−	0.388070i	0.980995	−	0.194035i	$-0.0621575\pi$
$158$	3.56636	−	13.3098i	0.283724	−	1.05887i
$159$	−2.20159	+	1.27109i	−0.174597	+	0.100804i
$160$	−2.63155	+	4.55797i	−0.208042	+	0.360339i
$161$		0			0
$162$	−10.4856	+	2.80962i	−0.823830	+	0.220744i
$163$	−1.65351	−	6.17099i	−0.129513	−	0.483349i	0.870447	−	0.492262i	$-0.163830\pi$
$163$	−1.65351	−	6.17099i	−0.129513	−	0.483349i	−0.999960	+	0.00891239i	$0.997163\pi$
$164$	0.900219	+	0.900219i	0.0702953	+	0.0702953i
$165$	1.13002	−	1.95725i	0.0879719	−	0.152372i
$166$	1.73682	+	3.00826i	0.134803	+	0.233486i
$167$	2.62064	−	9.78037i	0.202791	−	0.756828i	−0.787320	−	0.616544i	$-0.788532\pi$
$167$	2.62064	−	9.78037i	0.202791	−	0.756828i	0.990111	−	0.140283i	$-0.0448013\pi$
$168$		0			0
$169$	4.34213	+	12.2534i	0.334010	+	0.942569i
$170$	−15.3909			−1.18043
$171$	6.11160	+	1.63760i	0.467366	+	0.125230i
$172$	0.816825	+	1.41478i	0.0622823	+	0.107876i
$173$	−8.82380	+	15.2833i	−0.670861	+	1.16197i	0.306799	+	0.951774i	$0.400742\pi$
$173$	−8.82380	+	15.2833i	−0.670861	+	1.16197i	−0.977660	+	0.210192i	$0.932591\pi$
$174$	0.447072	−	0.447072i	0.0338925	−	0.0338925i
$175$		0			0
$176$	−3.62629	−	13.5335i	−0.273342	−	1.02013i
$177$	0.320314	−	0.320314i	0.0240763	−	0.0240763i
$178$	11.7518	+	6.78491i	0.880836	+	0.508551i
$179$	17.5138	−	10.1116i	1.30904	−	0.755775i	0.327105	−	0.944988i	$-0.393927\pi$
$179$	17.5138	−	10.1116i	1.30904	−	0.755775i	0.981936	+	0.189213i	$0.0605936\pi$
$180$	0.681974	−	2.54516i	0.0508313	−	0.189705i
$181$	−17.4649			−1.29815			−0.649077	−	0.760722i	$-0.724845\pi$
$181$	−17.4649			−1.29815			−0.649077	+	0.760722i	$0.724845\pi$
$182$		0			0
$183$	−2.66005			−0.196636
$184$	3.23152	−	12.0602i	0.238231	−	0.889089i
$185$	7.97040	−	4.60171i	0.585995	−	0.338324i
$186$	6.25024	+	3.60858i	0.458290	+	0.264594i
$187$	12.6611	−	12.6611i	0.925873	−	0.925873i
$188$	−0.360737	−	1.34629i	−0.0263094	−	0.0981882i
$189$		0			0
$190$	−4.04922	+	4.04922i	−0.293761	+	0.293761i
$191$	−0.0207944	+	0.0360170i	−0.00150463	+	0.00260610i	−0.866777	−	0.498696i	$-0.833812\pi$
$191$	−0.0207944	+	0.0360170i	−0.00150463	+	0.00260610i	0.865272	+	0.501302i	$0.167146\pi$
$192$	−1.06266	−	1.84058i	−0.0766910	−	0.132833i
$193$	−12.0647	−	3.23272i	−0.868434	−	0.232696i	−0.203024	−	0.979174i	$-0.565077\pi$
$193$	−12.0647	−	3.23272i	−0.868434	−	0.232696i	−0.665411	+	0.746478i	$0.731744\pi$
$194$	−5.85286			−0.420211
$195$	−2.17466	+	1.80904i	−0.155731	+	0.129548i
$196$		0			0
$197$	0.962573	−	3.59237i	0.0685805	−	0.255946i	−0.923121	−	0.384510i	$-0.874370\pi$
$197$	0.962573	−	3.59237i	0.0685805	−	0.255946i	0.991701	+	0.128565i	$0.0410369\pi$
$198$	6.39164	+	11.0707i	0.454234	+	0.786757i
$199$	4.38853	−	7.60116i	0.311095	−	0.538832i	−0.667505	−	0.744606i	$-0.732638\pi$
$199$	4.38853	−	7.60116i	0.311095	−	0.538832i	0.978600	+	0.205773i	$0.0659710\pi$
$200$	4.19190	+	4.19190i	0.296412	+	0.296412i
$201$	2.08851	+	7.79442i	0.147312	+	0.549776i
$202$	30.8482	−	8.26575i	2.17047	−	0.581576i
$203$		0			0
$204$	−1.00767	+	1.74533i	−0.0705508	+	0.122198i
$205$	−2.66785	+	1.54028i	−0.186331	+	0.107578i
$206$	3.94726	−	14.7314i	0.275019	−	1.02638i
$207$			15.3822i			1.06913i
$208$	−1.60274	+	17.4631i	−0.111130	+	1.21085i
$209$		−	6.66206i		−	0.460824i
$210$		0			0
$211$	−3.33665	−	5.77924i	−0.229704	−	0.397859i	0.728016	−	0.685560i	$-0.240443\pi$
$211$	−3.33665	−	5.77924i	−0.229704	−	0.397859i	−0.957720	+	0.287701i	$0.907109\pi$
$212$	2.70264	+	1.56037i	0.185618	+	0.107167i
$213$	−3.87658	+	3.87658i	−0.265619	+	0.265619i
$214$	−0.112556	+	0.0301593i	−0.00769417	+	0.00206165i
$215$	−3.81830	+	1.02311i	−0.260406	+	0.0697756i
$216$	4.62888	+	4.62888i	0.314955	+	0.314955i
$217$		0			0
$218$	10.2891	−	5.94043i	0.696868	−	0.402337i
$219$	3.45385	+	0.925457i	0.233390	+	0.0625366i
$220$	−2.77440			−0.187050
$221$	−20.3515	+	9.38485i	−1.36899	+	0.631293i
$222$		−	5.02551i		−	0.337290i
$223$	−6.10027	−	1.63456i	−0.408505	−	0.109458i	0.0487142	−	0.998813i	$-0.484488\pi$
$223$	−6.10027	−	1.63456i	−0.408505	−	0.109458i	−0.457219	+	0.889354i	$0.651154\pi$
$224$		0			0
$225$	−6.32505	−	3.65177i	−0.421670	−	0.243451i
$226$	18.7122	+	18.7122i	1.24472	+	1.24472i
$227$	6.09476	+	22.7459i	0.404523	+	1.50970i	0.804933	+	0.593365i	$0.202201\pi$
$227$	6.09476	+	22.7459i	0.404523	+	1.50970i	−0.400410	+	0.916336i	$0.631132\pi$
$228$	0.194073	+	0.724290i	0.0128528	+	0.0479673i
$229$	−13.3812	−	13.3812i	−0.884252	−	0.884252i	0.109711	−	0.993963i	$-0.465007\pi$
$229$	−13.3812	−	13.3812i	−0.884252	−	0.884252i	−0.993963	+	0.109711i	$0.965007\pi$
$230$	−12.0566	−	6.96086i	−0.794986	−	0.458985i
$231$		0			0
$232$	1.62695	+	0.435940i	0.106814	+	0.0286209i
$233$		−	7.35252i		−	0.481680i	−0.970565	−	0.240840i	$-0.922577\pi$
$233$		−	7.35252i		−	0.481680i	0.970565	−	0.240840i	$-0.0774229\pi$
$234$	−2.71129	−	15.7686i	−0.177243	−	1.03083i
$235$	3.37258			0.220003
$236$	−0.537140	−	0.143926i	−0.0349648	−	0.00936879i
$237$	3.78102	−	2.18297i	0.245604	−	0.141799i
$238$		0			0
$239$	−4.08646	−	4.08646i	−0.264331	−	0.264331i	0.562480	−	0.826811i	$-0.309847\pi$
$239$	−4.08646	−	4.08646i	−0.264331	−	0.264331i	−0.826811	+	0.562480i	$0.809847\pi$
$240$	−3.68585	+	0.987620i	−0.237921	+	0.0637506i
$241$	−27.7607	+	7.43847i	−1.78823	+	0.479154i	−0.992043	−	0.125900i	$-0.959818\pi$
$241$	−27.7607	+	7.43847i	−1.78823	+	0.479154i	−0.796184	+	0.605054i	$0.793151\pi$
$242$	−3.09867	+	3.09867i	−0.199190	+	0.199190i
$243$	−10.6374	−	6.14150i	−0.682389	−	0.393977i
$244$	1.63272	+	2.82796i	0.104524	+	0.181041i
$245$		0			0
$246$			1.68214i			0.107249i
$247$	−2.88524	+	7.82338i	−0.183583	+	0.497790i
$248$			19.2267i			1.22089i
$249$	−0.284859	+	1.06311i	−0.0180522	+	0.0673718i
$250$	16.4464	−	9.49536i	1.04016	−	0.600539i
$251$	−9.72695	+	16.8476i	−0.613960	+	1.06341i	0.376606	+	0.926373i	$0.377091\pi$
$251$	−9.72695	+	16.8476i	−0.613960	+	1.06341i	−0.990566	+	0.137036i	$0.956242\pi$
$252$		0			0
$253$	15.6444	−	4.19190i	0.983554	−	0.263543i
$254$	−7.22454	−	26.9624i	−0.453308	−	1.69177i
$255$	−3.44826	−	3.44826i	−0.215938	−	0.215938i
$256$	−6.89656	+	11.9452i	−0.431035	+	0.746575i
$257$	12.6024	+	21.8280i	0.786116	+	1.36159i	0.928330	+	0.371756i	$0.121244\pi$
$257$	12.6024	+	21.8280i	0.786116	+	1.36159i	−0.142215	+	0.989836i	$0.545422\pi$
$258$	−0.558668	+	2.08498i	−0.0347812	+	0.129805i
$259$		0			0
$260$	3.25803	+	1.20155i	0.202054	+	0.0745170i
$261$	−2.07509			−0.128445
$262$	−8.57036	−	2.29642i	−0.529479	−	0.141873i
$263$	−15.6393	−	27.0881i	−0.964362	−	1.67032i	−0.711320	−	0.702868i	$-0.751902\pi$
$263$	−15.6393	−	27.0881i	−0.964362	−	1.67032i	−0.253041	−	0.967455i	$-0.581431\pi$
$264$	1.64382	−	2.84718i	0.101170	−	0.175232i
$265$	−5.33961	+	5.33961i	−0.328010	+	0.328010i
$266$		0			0
$267$	1.11281	+	4.15306i	0.0681027	+	0.254163i
$268$	7.00451	−	7.00451i	0.427868	−	0.427868i
$269$	7.80980	+	4.50899i	0.476172	+	0.274918i	0.718820	−	0.695196i	$-0.244683\pi$
$269$	7.80980	+	4.50899i	0.476172	+	0.274918i	−0.242648	+	0.970114i	$0.578016\pi$
$270$	6.32126	−	3.64958i	0.384700	−	0.222107i
$271$	0.881552	−	3.29000i	0.0535505	−	0.199853i	−0.933968	−	0.357357i	$-0.883678\pi$
$271$	0.881552	−	3.29000i	0.0535505	−	0.199853i	0.987518	+	0.157504i	$0.0503446\pi$
$272$	−30.2318			−1.83308
$273$		0			0
$274$	−2.84575			−0.171918
$275$	−1.99034	+	7.42804i	−0.120022	+	0.447928i
$276$	−1.57872	+	0.911475i	−0.0950279	+	0.0548644i
$277$	−3.48926	−	2.01452i	−0.209649	−	0.121041i	0.391499	−	0.920178i	$-0.371957\pi$
$277$	−3.48926	−	2.01452i	−0.209649	−	0.121041i	−0.601148	+	0.799137i	$0.705290\pi$
$278$	9.45529	−	9.45529i	0.567091	−	0.567091i
$279$	−6.13066	−	22.8799i	−0.367033	−	1.36979i
$280$		0			0
$281$	−3.28511	+	3.28511i	−0.195973	+	0.195973i	−0.798271	−	0.602298i	$-0.794252\pi$
$281$	−3.28511	+	3.28511i	−0.195973	+	0.195973i	0.602298	+	0.798271i	$0.294252\pi$
$282$	0.920795	−	1.59486i	0.0548326	−	0.0949728i
$283$	0.514830	+	0.891711i	0.0306035	+	0.0530067i	0.880921	−	0.473262i	$-0.156924\pi$
$283$	0.514830	+	0.891711i	0.0306035	+	0.0530067i	−0.850318	+	0.526269i	$0.823590\pi$
$284$	6.50070	+	1.74186i	0.385745	+	0.103360i
$285$	−1.81441			−0.107477
$286$	−15.2985	+	7.05473i	−0.904622	+	0.417155i
$287$		0			0
$288$	2.44126	−	9.11089i	0.143852	−	0.536864i
$289$	−10.8177	−	18.7368i	−0.636336	−	1.10217i
$290$	0.939037	−	1.62646i	0.0551422	−	0.0955090i
$291$	−1.31130	−	1.31130i	−0.0768699	−	0.0768699i
$292$	−1.13608	−	4.23991i	−0.0664840	−	0.248122i
$293$	24.6989	−	6.61806i	1.44293	−	0.386631i	0.549369	−	0.835580i	$-0.314868\pi$
$293$	24.6989	−	6.61806i	1.44293	−	0.386631i	0.893558	+	0.448948i	$0.148201\pi$
$294$		0			0
$295$	0.672792	−	1.16531i	0.0391715	−	0.0678470i
$296$	11.5944	−	6.69404i	0.673912	−	0.389083i
$297$	−2.19782	+	8.20236i	−0.127530	+	0.475949i
$298$			7.21854i			0.418159i
$299$	−20.1870	−	1.85272i	−1.16744	−	0.107146i
$300$		−	0.865547i		−	0.0499724i
$301$		0			0
$302$	−7.29993	−	12.6438i	−0.420064	−	0.727571i
$303$	8.76327	+	5.05947i	0.503436	+	0.290659i
$304$	−7.95374	+	7.95374i	−0.456178	+	0.456178i
$305$	−7.63226	+	2.04506i	−0.437022	+	0.117100i
$306$	26.6431	−	7.13900i	1.52309	−	0.408109i
$307$	−14.0195	−	14.0195i	−0.800136	−	0.800136i	0.182981	−	0.983117i	$-0.441425\pi$
$307$	−14.0195	−	14.0195i	−0.800136	−	0.800136i	−0.983117	+	0.182981i	$0.941425\pi$
$308$		0			0
$309$	4.18485	−	2.41612i	0.238068	−	0.137449i
$310$	20.7076	+	5.54859i	1.17611	+	0.315139i
$311$	−6.41705			−0.363878			−0.181939	−	0.983310i	$-0.558237\pi$
$311$	−6.41705			−0.363878			−0.181939	+	0.983310i	$0.558237\pi$
$312$	−3.16345	+	2.63159i	−0.179095	+	0.148984i
$313$			25.1734i			1.42288i	0.702746	+	0.711441i	$0.251957\pi$
$313$			25.1734i			1.42288i	−0.702746	+	0.711441i	$0.748043\pi$
$314$	−7.61824	−	2.04130i	−0.429922	−	0.115197i
$315$		0			0
$316$	−4.64154	−	2.67979i	−0.261107	−	0.150750i
$317$	−17.0381	−	17.0381i	−0.956957	−	0.956957i	0.0421542	−	0.999111i	$-0.486578\pi$
$317$	−17.0381	−	17.0381i	−0.956957	−	0.956957i	−0.999111	+	0.0421542i	$0.986578\pi$
$318$	1.06722	+	3.98291i	0.0598465	+	0.223350i
$319$	0.565498	+	2.11047i	0.0316618	+	0.118163i
$320$	−4.46406	−	4.46406i	−0.249549	−	0.249549i
$321$	−0.0319746	−	0.0184606i	−0.00178465	−	0.00103037i
$322$		0			0
$323$	−13.8852	−	3.72052i	−0.772591	−	0.207015i
$324$			4.22234i			0.234574i
$325$	5.55427	−	7.86090i	0.308095	−	0.436044i
$326$	−10.3625			−0.573923
$327$	3.63615	+	0.974303i	0.201079	+	0.0538791i
$328$	−3.88088	+	2.24063i	−0.214286	+	0.123718i
$329$		0			0
$330$	−2.59210	−	2.59210i	−0.142691	−	0.142691i
$331$	5.70964	−	1.52989i	0.313830	−	0.0840905i	−0.0984660	−	0.995140i	$-0.531394\pi$
$331$	5.70964	−	1.52989i	0.313830	−	0.0840905i	0.412296	+	0.911050i	$0.364727\pi$
$332$	1.30506	−	0.349690i	0.0716245	−	0.0191917i
$333$	−11.6630	+	11.6630i	−0.639129	+	0.639129i
$334$	−14.2231	−	8.21169i	−0.778252	−	0.449324i
$335$	11.9848	+	20.7583i	0.654799	+	1.13414i
$336$		0			0
$337$		−	11.5318i		−	0.628179i	−0.949393	−	0.314089i	$-0.898301\pi$
$337$		−	11.5318i		−	0.628179i	0.949393	−	0.314089i	$-0.101699\pi$
$338$	21.0207	−	1.65893i	1.14337	−	0.0902338i
$339$			8.38475i			0.455397i
$340$	−1.54940	+	5.78244i	−0.0840280	+	0.313597i
$341$	−21.5993	+	12.4703i	−1.16967	+	0.675307i
$342$	5.13136	−	8.88778i	0.277472	−	0.480596i
$343$		0			0
$344$	−5.55442	+	1.48830i	−0.299474	+	0.0802439i
$345$	−1.14166	−	4.26075i	−0.0614652	−	0.229391i
$346$	20.2405	+	20.2405i	1.08814	+	1.08814i
$347$	−4.53652	+	7.85749i	−0.243533	+	0.421812i	−0.961718	−	0.274040i	$-0.911640\pi$
$347$	−4.53652	+	7.85749i	−0.243533	+	0.421812i	0.718185	+	0.695852i	$0.244973\pi$
$348$	−0.122960	−	0.212973i	−0.00659136	−	0.0114166i
$349$	−7.77792	+	29.0276i	−0.416342	+	1.55381i	0.365789	+	0.930698i	$0.380799\pi$
$349$	−7.77792	+	29.0276i	−0.416342	+	1.55381i	−0.782132	+	0.623113i	$0.785868\pi$
$350$		0			0
$351$	6.13326	−	8.68035i	0.327369	−	0.463323i
$352$	−9.93149			−0.529350
$353$	−27.9907	−	7.50007i	−1.48979	−	0.399189i	−0.580125	−	0.814527i	$-0.696996\pi$
$353$	−27.9907	−	7.50007i	−1.48979	−	0.399189i	−0.909667	+	0.415338i	$0.863663\pi$
$354$	−0.367377	−	0.636316i	−0.0195259	−	0.0338198i
$355$	−8.14242	+	14.1031i	−0.432155	+	0.748514i
$356$	3.73217	−	3.73217i	0.197805	−	0.197805i
$357$		0			0
$358$	−8.48978	−	31.6843i	−0.448699	−	1.67457i
$359$	6.24225	−	6.24225i	0.329454	−	0.329454i	−0.522925	−	0.852379i	$-0.675159\pi$
$359$	6.24225	−	6.24225i	0.329454	−	0.329454i	0.852379	+	0.522925i	$0.175159\pi$
$360$	8.03227	+	4.63743i	0.423338	+	0.244414i
$361$	11.8226	−	6.82577i	0.622241	−	0.359251i
$362$	−7.33185	+	27.3628i	−0.385353	+	1.43816i
$363$	−1.38848			−0.0728763
$364$		0			0
$365$	10.6214			0.555947
$366$	−1.11670	+	4.16759i	−0.0583709	+	0.217843i
$367$	11.5082	−	6.64427i	0.600724	−	0.346828i	−0.168602	−	0.985684i	$-0.553925\pi$
$367$	11.5082	−	6.64427i	0.600724	−	0.346828i	0.769326	+	0.638856i	$0.220592\pi$
$368$	−23.6823	−	13.6730i	−1.23452	−	0.712752i
$369$	3.90384	−	3.90384i	0.203226	−	0.203226i
$370$	−3.86364	−	14.4193i	−0.200861	−	0.749624i
$371$		0			0
$372$	1.98497	−	1.98497i	0.102916	−	0.102916i
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	−0.739251	−	0.673430i	$-0.764820\pi$
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	0.952833	+	0.303495i	$0.0981535\pi$
$374$	−14.5214	−	25.1518i	−0.750884	−	1.30057i
$375$	5.81212	+	1.55735i	0.300137	+	0.0804214i
$376$	4.90604			0.253009
$377$	0.249937	−	2.72327i	0.0128724	−	0.140256i
$378$		0			0
$379$	0.896568	−	3.34604i	0.0460536	−	0.171874i	−0.939069	−	0.343730i	$-0.888310\pi$
$379$	0.896568	−	3.34604i	0.0460536	−	0.171874i	0.985122	+	0.171855i	$0.0549762\pi$
$380$	1.11368	+	1.92894i	0.0571303	+	0.0989526i
$381$	4.42215	−	7.65939i	0.226554	−	0.392402i
$382$	0.0476994	+	0.0476994i	0.00244052	+	0.00244052i
$383$	−8.91088	−	33.2559i	−0.455325	−	1.69930i	−0.687131	−	0.726534i	$-0.741130\pi$
$383$	−8.91088	−	33.2559i	−0.455325	−	1.69930i	0.231806	−	0.972762i	$-0.425537\pi$
$384$	−6.75272	+	1.80939i	−0.344598	+	0.0923348i
$385$		0			0
$386$	−10.1296	+	17.5450i	−0.515584	+	0.893018i
$387$	6.13526	−	3.54220i	0.311873	−	0.180060i
$388$	−0.589205	+	2.19894i	−0.0299124	+	0.111635i
$389$		−	9.32537i		−	0.472815i	−0.971654	−	0.236408i	$-0.924030\pi$
$389$		−	9.32537i		−	0.472815i	0.971654	−	0.236408i	$-0.0759701\pi$
$390$	1.92136	+	4.16656i	0.0972916	+	0.210982i
$391$		−	34.9473i		−	1.76736i
$392$		0			0
$393$	−1.40564	−	2.43465i	−0.0709053	−	0.122812i
$394$	−5.22420	−	3.01619i	−0.263191	−	0.151954i
$395$	9.17030	−	9.17030i	0.461408	−	0.461408i
$396$	4.80273	−	1.28689i	0.241346	−	0.0646686i
$397$	19.1089	−	5.12022i	0.959049	−	0.256977i	0.254852	−	0.966980i	$-0.417973\pi$
$397$	19.1089	−	5.12022i	0.959049	−	0.256977i	0.704198	+	0.710004i	$0.251307\pi$
$398$	−10.0667	−	10.0667i	−0.504596	−	0.504596i
$399$		0			0
$400$	11.2445	−	6.49199i	0.562223	−	0.324600i
$401$	−11.6317	−	3.11669i	−0.580857	−	0.155640i	−0.0435858	−	0.999050i	$-0.513878\pi$
$401$	−11.6317	−	3.11669i	−0.580857	−	0.155640i	−0.537271	+	0.843409i	$0.680545\pi$
$402$	13.0885			0.652798
$403$	30.7651	−	5.28984i	1.53252	−	0.263506i
$404$		−	12.4219i		−	0.618012i
$405$	−9.86881	−	2.64434i	−0.490385	−	0.131398i
$406$		0			0
$407$	15.0402	+	8.68346i	0.745514	+	0.430423i
$408$	−5.01613	−	5.01613i	−0.248335	−	0.248335i
$409$	−5.04619	−	18.8327i	−0.249518	−	0.931215i	−0.971058	−	0.238842i	$-0.923232\pi$
$409$	−5.04619	−	18.8327i	−0.249518	−	0.931215i	0.721540	−	0.692373i	$-0.243435\pi$
$410$	1.29324	+	4.82643i	0.0638685	+	0.238360i
$411$	−0.637575	−	0.637575i	−0.0314492	−	0.0314492i
$412$	−5.13727	−	2.96600i	−0.253095	−	0.146125i
$413$		0			0
$414$	24.0998	+	6.45751i	1.18444	+	0.317369i
$415$			3.26930i			0.160483i
$416$	11.6627	+	4.30118i	0.571813	+	0.210883i
$417$	4.23682			0.207478
$418$	−10.4377	−	2.79677i	−0.510523	−	0.136794i
$419$	−3.34749	+	1.93268i	−0.163536	+	0.0944174i	−0.579534	−	0.814948i	$-0.696765\pi$
$419$	−3.34749	+	1.93268i	−0.163536	+	0.0944174i	0.415999	+	0.909365i	$0.363432\pi$
$420$		0			0
$421$	3.65782	+	3.65782i	0.178271	+	0.178271i	0.790602	−	0.612331i	$-0.209768\pi$
$421$	3.65782	+	3.65782i	0.178271	+	0.178271i	−0.612331	+	0.790602i	$0.709768\pi$
$422$	−10.4553	+	2.80148i	−0.508955	+	0.136374i
$423$	−5.83824	+	1.56435i	−0.283865	+	0.0760613i
$424$	−7.76746	+	7.76746i	−0.377221	+	0.377221i
$425$	14.3701	+	8.29658i	0.697052	+	0.402443i
$426$	4.44616	+	7.70097i	0.215417	+	0.373113i
$427$		0			0
$428$			0.0453239i			0.00219081i
$429$	−5.00813	−	1.84698i	−0.241795	−	0.0891732i
$430$			6.41177i			0.309203i
$431$	−2.60423	+	9.71910i	−0.125441	+	0.468153i	−0.999855	−	0.0170280i	$-0.994580\pi$
$431$	−2.60423	+	9.71910i	−0.125441	+	0.468153i	0.874414	+	0.485181i	$0.161246\pi$
$432$	12.4166	−	7.16874i	0.597395	−	0.344906i
$433$	−3.80951	+	6.59826i	−0.183073	+	0.317092i	−0.942926	−	0.333004i	$-0.891938\pi$
$433$	−3.80951	+	6.59826i	−0.183073	+	0.317092i	0.759852	+	0.650096i	$0.225271\pi$
$434$		0			0
$435$	0.574786	−	0.154013i	0.0275589	−	0.00738438i
$436$	−1.19604	−	4.46369i	−0.0572800	−	0.213772i
$437$	−9.19432	−	9.19432i	−0.439824	−	0.439824i
$438$	2.89989	−	5.02276i	0.138562	−	0.239997i
$439$	−11.1814	−	19.3667i	−0.533658	−	0.924323i	−0.999227	−	0.0393115i	$-0.987484\pi$
$439$	−11.1814	−	19.3667i	−0.533658	−	0.924323i	0.465569	−	0.885012i	$-0.345850\pi$
$440$	2.52756	−	9.43298i	0.120497	−	0.449700i
$441$		0			0
$442$	6.15988	+	35.8252i	0.292996	+	1.70403i
$443$	25.6918			1.22065			0.610326	−	0.792150i	$-0.291038\pi$
$443$	25.6918			1.22065			0.610326	+	0.792150i	$0.291038\pi$
$444$	−1.88811	−	0.505917i	−0.0896056	−	0.0240097i
$445$	6.38578	+	11.0605i	0.302715	+	0.524318i
$446$	−5.12185	+	8.87130i	−0.242527	+	0.420068i
$447$	−1.61727	+	1.61727i	−0.0764945	+	0.0764945i
$448$		0			0
$449$	−0.821652	−	3.06645i	−0.0387761	−	0.144715i	0.943824	−	0.330449i	$-0.107200\pi$
$449$	−0.821652	−	3.06645i	−0.0387761	−	0.144715i	−0.982600	+	0.185735i	$0.940534\pi$
$450$	−8.37663	+	8.37663i	−0.394878	+	0.394878i
$451$	−5.03425	−	2.90653i	−0.237054	−	0.136863i
$452$	8.91401	−	5.14650i	0.419280	−	0.242071i
$453$	1.19728	−	4.46829i	0.0562529	−	0.209939i
$454$	38.1954			1.79260
$455$		0			0
$456$	−2.63940			−0.123601
$457$	−8.49782	+	31.7143i	−0.397511	+	1.48353i	0.419949	+	0.907548i	$0.362048\pi$
$457$	−8.49782	+	31.7143i	−0.397511	+	1.48353i	−0.817460	+	0.575985i	$0.804619\pi$
$458$	−26.5822	+	15.3472i	−1.24210	+	0.717129i
$459$	15.8681	+	9.16144i	0.740658	+	0.427619i
$460$	−3.82895	+	3.82895i	−0.178526	+	0.178526i
$461$	−1.38662	−	5.17492i	−0.0645811	−	0.241020i	0.926088	−	0.377307i	$-0.123150\pi$
$461$	−1.38662	−	5.17492i	−0.0645811	−	0.241020i	−0.990669	+	0.136287i	$0.956483\pi$
$462$		0			0
$463$	−17.0182	+	17.0182i	−0.790903	+	0.790903i	−0.981641	−	0.190738i	$-0.938912\pi$
$463$	−17.0182	+	17.0182i	−0.790903	+	0.790903i	0.190738	+	0.981641i	$0.438912\pi$
$464$	1.84452	−	3.19480i	0.0856295	−	0.148315i
$465$	3.39630	+	5.88256i	0.157500	+	0.272797i
$466$	−11.5194	−	3.08663i	−0.533628	−	0.142985i
$467$	7.46893			0.345621			0.172811	−	0.984955i	$-0.444715\pi$
$467$	7.46893			0.345621			0.172811	+	0.984955i	$0.444715\pi$
$468$	−6.19727	−	0.568775i	−0.286469	−	0.0262916i
$469$		0			0
$470$	1.41582	−	5.28393i	0.0653071	−	0.243729i
$471$	−1.24948	−	2.16417i	−0.0575732	−	0.0997197i
$472$	0.978701	−	1.69516i	0.0450483	−	0.0780260i
$473$	−5.27454	−	5.27454i	−0.242524	−	0.242524i
$474$	−1.83285	−	6.84028i	−0.0841854	−	0.314184i
$475$	5.96340	−	1.59789i	0.273620	−	0.0733162i
$476$		0			0
$477$	6.76661	−	11.7201i	0.309822	−	0.536627i
$478$	−8.11792	+	4.68688i	−0.371305	+	0.214373i
$479$	5.39566	−	20.1369i	0.246534	−	0.920078i	−0.726072	−	0.687619i	$-0.758656\pi$
$479$	5.39566	−	20.1369i	0.246534	−	0.920078i	0.972606	−	0.232459i	$-0.0746773\pi$
$480$			2.70484i			0.123459i
$481$	−13.9013	−	16.7108i	−0.633845	−	0.761948i
$482$			46.6164i			2.12332i
$483$		0			0
$484$	0.852240	+	1.47612i	0.0387382	+	0.0670965i
$485$	−4.77055	−	2.75428i	−0.216620	−	0.125065i
$486$	−14.0877	+	14.0877i	−0.639032	+	0.639032i
$487$	18.0347	−	4.83239i	0.817232	−	0.218977i	0.174096	−	0.984729i	$-0.444300\pi$
$487$	18.0347	−	4.83239i	0.817232	−	0.218977i	0.643136	+	0.765752i	$0.277633\pi$
$488$	−11.1025	+	2.97492i	−0.502588	+	0.134668i
$489$	−2.32165	−	2.32165i	−0.104989	−	0.104989i
$490$		0			0
$491$	26.9636	−	15.5675i	1.21685	−	0.702550i	0.252609	−	0.967569i	$-0.418711\pi$
$491$	26.9636	−	15.5675i	1.21685	−	0.702550i	0.964243	+	0.265019i	$0.0853781\pi$
$492$	0.631987	+	0.169340i	0.0284922	+	0.00763445i
$493$	4.71447			0.212329
$494$	11.0459	+	7.80470i	0.496979	+	0.351150i
$495$			12.0313i			0.540766i
$496$	40.6752	+	10.8989i	1.82637	+	0.489374i
$497$		0			0
$498$	1.54602	+	0.892597i	0.0692790	+	0.0399982i
$499$	−13.1039	−	13.1039i	−0.586611	−	0.586611i	0.350101	−	0.936712i	$-0.386147\pi$
$499$	−13.1039	−	13.1039i	−0.586611	−	0.586611i	−0.936712	+	0.350101i	$0.886147\pi$
$500$	−1.91179	−	7.13489i	−0.0854978	−	0.319082i
$501$	−1.34682	−	5.02639i	−0.0601713	−	0.224563i
$502$	22.3122	+	22.3122i	0.995844	+	0.995844i
$503$	−22.0368	−	12.7230i	−0.982573	−	0.567289i	−0.0795268	−	0.996833i	$-0.525341\pi$
$503$	−22.0368	−	12.7230i	−0.982573	−	0.567289i	−0.903046	+	0.429544i	$0.858674\pi$
$504$		0			0
$505$	29.0335	+	7.77950i	1.29197	+	0.346183i
$506$		−	26.2704i		−	1.16786i
$507$	5.08124	+	4.33789i	0.225666	+	0.192653i
$508$	−10.8572			−0.481708
$509$	23.9551	+	6.41875i	1.06179	+	0.284506i	0.747116	−	0.664694i	$-0.231438\pi$
$509$	23.9551	+	6.41875i	1.06179	+	0.284506i	0.314674	+	0.949200i	$0.398105\pi$
$510$	−6.85009	+	3.95490i	−0.303327	+	0.175126i
$511$		0			0
$512$	−3.41779	−	3.41779i	−0.151046	−	0.151046i
$513$	6.58505	−	1.76446i	0.290737	−	0.0779027i
$514$	39.4892	−	10.5811i	1.74179	−	0.466712i
$515$	10.1497	−	10.1497i	0.447250	−	0.447250i
$516$	0.727094	+	0.419788i	0.0320085	+	0.0184801i
$517$	3.18204	+	5.51145i	0.139946	+	0.242393i
$518$		0			0
$519$			9.06957i			0.398110i
$520$	−7.05344	+	9.98268i	−0.309314	+	0.437769i
$521$		−	4.07940i		−	0.178722i	−0.995999	−	0.0893610i	$-0.971518\pi$
$521$		−	4.07940i		−	0.178722i	0.995999	−	0.0893610i	$-0.0284825\pi$
$522$	−0.871134	+	3.25112i	−0.0381285	+	0.142298i
$523$	25.5006	−	14.7228i	1.11506	−	0.643781i	0.174926	−	0.984582i	$-0.444031\pi$
$523$	25.5006	−	14.7228i	1.11506	−	0.643781i	0.940136	+	0.340800i	$0.110698\pi$
$524$	−1.72555	+	2.98874i	−0.0753810	+	0.130564i
$525$		0			0
$526$	−49.0053	+	13.1309i	−2.13673	+	0.572536i
$527$	13.9285	+	51.9817i	0.606733	+	2.26436i
$528$	−5.09157	−	5.09157i	−0.221582	−	0.221582i
$529$	4.30560	−	7.45752i	0.187200	−	0.324240i
$530$	6.12416	+	10.6073i	0.266016	+	0.460754i
$531$	−0.624142	+	2.32933i	−0.0270854	+	0.101084i
$532$		0			0
$533$	4.65304	+	5.59345i	0.201546	+	0.242279i
$534$	6.97389			0.301790
$535$	−0.105935	−	0.0283851i	−0.00457996	−	0.00122720i
$536$	17.4341	+	30.1967i	0.753038	+	1.30430i
$537$	5.19661	−	9.00079i	0.224250	−	0.388413i
$538$	10.3430	−	10.3430i	0.445917	−	0.445917i
$539$		0			0
$540$	−0.734804	−	2.74233i	−0.0316209	−	0.118011i
$541$	−26.6129	+	26.6129i	−1.14418	+	1.14418i	−0.156499	+	0.987678i	$0.550021\pi$
$541$	−26.6129	+	26.6129i	−1.14418	+	1.14418i	−0.987678	+	0.156499i	$0.949979\pi$
$542$	−4.78447	−	2.76232i	−0.205511	−	0.118652i
$543$	−7.77315	+	4.48783i	−0.333578	+	0.192591i
$544$	−5.54637	+	20.6993i	−0.237799	+	0.887477i
$545$	11.1820			0.478982
$546$		0			0
$547$	−36.7251			−1.57025			−0.785125	−	0.619337i	$-0.787401\pi$
$547$	−36.7251			−1.57025			−0.785125	+	0.619337i	$0.787401\pi$
$548$	−0.286480	+	1.06916i	−0.0122378	+	0.0456722i
$549$	12.2636	−	7.08037i	0.523396	−	0.302183i
$550$	10.8022	+	6.23666i	0.460608	+	0.265932i
$551$	1.24034	−	1.24034i	0.0528401	−	0.0528401i
$552$	−1.66076	−	6.19805i	−0.0706867	−	0.263806i
$553$		0			0
$554$	−4.62103	+	4.62103i	−0.196329	+	0.196329i
$555$	2.36494	−	4.09620i	0.100386	−	0.173874i
$556$	−2.60053	−	4.50425i	−0.110287	−	0.191023i
$557$	19.3262	+	5.17843i	0.818876	+	0.219417i	0.643855	−	0.765148i	$-0.277334\pi$
$557$	19.3262	+	5.17843i	0.818876	+	0.219417i	0.175021	+	0.984565i	$0.444001\pi$
$558$	−38.4204			−1.62647
$559$	3.90967	+	8.47832i	0.165361	+	0.358595i
$560$		0			0
$561$	2.38168	−	8.88857i	0.100555	−	0.375276i
$562$	3.76778	+	6.52599i	0.158934	+	0.275282i
$563$	−7.84601	+	13.5897i	−0.330670	+	0.572737i	−0.982643	−	0.185505i	$-0.940608\pi$
$563$	−7.84601	+	13.5897i	−0.330670	+	0.572737i	0.651973	+	0.758242i	$0.273941\pi$
$564$	−0.506501	−	0.506501i	−0.0213275	−	0.0213275i
$565$	6.44624	+	24.0577i	0.271195	+	1.01211i
$566$	1.61320	−	0.432256i	0.0678079	−	0.0181691i
$567$		0			0
$568$	−11.8447	+	20.5155i	−0.496991	+	0.860813i
$569$	−4.39537	+	2.53767i	−0.184263	+	0.106385i	−0.589294	−	0.807918i	$-0.700594\pi$
$569$	−4.39537	+	2.53767i	−0.184263	+	0.106385i	0.405031	+	0.914303i	$0.367261\pi$
$570$	−0.761699	+	2.84270i	−0.0319041	+	0.119068i
$571$		−	20.2814i		−	0.848748i	−0.905487	−	0.424374i	$-0.860494\pi$
$571$		−	20.2814i		−	0.848748i	0.905487	−	0.424374i	$-0.139506\pi$
$572$	1.11039	+	6.45792i	0.0464278	+	0.270019i
$573$			0.0213736i			0.000892895i
$574$		0			0
$575$	7.50459	+	12.9983i	0.312963	+	0.542068i
$576$	9.79832	+	5.65706i	0.408263	+	0.235711i
$577$	18.5181	−	18.5181i	0.770920	−	0.770920i	−0.207347	−	0.978267i	$-0.566483\pi$
$577$	18.5181	−	18.5181i	0.770920	−	0.770920i	0.978267	+	0.207347i	$0.0664831\pi$
$578$	−33.8969	+	9.08265i	−1.40993	+	0.377789i
$579$	−6.20036	+	1.66138i	−0.257678	+	0.0690446i
$580$	−0.516535	−	0.516535i	−0.0214480	−	0.0214480i
$581$		0			0
$582$	−2.60495	+	1.50397i	−0.107979	+	0.0623416i
$583$	−13.7639	−	3.68803i	−0.570043	−	0.152743i
$584$	15.4507			0.639356
$585$	5.21057	−	14.1286i	0.215431	−	0.584145i
$586$		−	41.4749i		−	1.71331i
$587$	1.75410	+	0.470009i	0.0723994	+	0.0193994i	0.294837	−	0.955548i	$-0.404735\pi$
$587$	1.75410	+	0.470009i	0.0723994	+	0.0193994i	−0.222438	+	0.974947i	$0.571401\pi$
$588$		0			0
$589$	17.3404	+	10.0115i	0.714498	+	0.412516i
$590$	−1.54329	−	1.54329i	−0.0635362	−	0.0635362i
$591$	−0.494692	−	1.84621i	−0.0203489	−	0.0759431i
$592$	−7.58921	−	28.3233i	−0.311915	−	1.16408i
$593$	−22.6574	−	22.6574i	−0.930429	−	0.930429i	0.0673034	−	0.997733i	$-0.478560\pi$
$593$	−22.6574	−	22.6574i	−0.930429	−	0.930429i	−0.997733	+	0.0673034i	$0.978560\pi$
$594$	11.9283	+	6.88679i	0.489423	+	0.282568i
$595$		0			0
$596$	2.71203	+	0.726687i	0.111089	+	0.0297663i
$597$		−	4.51077i		−	0.184613i
$598$	−11.3773	+	30.8498i	−0.465253	+	1.26154i
$599$	−3.62697			−0.148194			−0.0740970	−	0.997251i	$-0.523607\pi$
$599$	−3.62697			−0.148194			−0.0740970	+	0.997251i	$0.523607\pi$
$600$	2.94287	+	0.788539i	0.120142	+	0.0321920i
$601$	22.0032	−	12.7035i	0.897529	−	0.518189i	0.0211313	−	0.999777i	$-0.493273\pi$
$601$	22.0032	−	12.7035i	0.897529	−	0.518189i	0.876398	+	0.481588i	$0.159940\pi$
$602$		0			0
$603$	−30.3753	−	30.3753i	−1.23698	−	1.23698i
$604$	−5.48522	+	1.46976i	−0.223191	+	0.0598037i
$605$	−3.98385	+	1.06747i	−0.161967	+	0.0433988i
$606$	11.6057	−	11.6057i	0.471450	−	0.471450i
$607$	−3.52942	−	2.03771i	−0.143255	−	0.0827081i	0.426660	−	0.904412i	$-0.359690\pi$
$607$	−3.52942	−	2.03771i	−0.143255	−	0.0827081i	−0.569914	+	0.821704i	$0.693024\pi$
$608$	3.98661	+	6.90502i	0.161679	+	0.280035i
$609$		0			0
$610$			12.8162i			0.518915i
$611$	−1.34980	−	7.85029i	−0.0546070	−	0.317589i
$612$		−	10.7286i		−	0.433678i
$613$	6.00524	−	22.4119i	0.242550	−	0.905207i	−0.732050	−	0.681251i	$-0.761436\pi$
$613$	6.00524	−	22.4119i	0.242550	−	0.905207i	0.974599	−	0.223956i	$-0.0718972\pi$
$614$	−27.8503	+	16.0794i	−1.12395	+	0.648911i
$615$	−0.791593	+	1.37108i	−0.0319201	+	0.0552872i
$616$		0			0
$617$	0.685439	−	0.183663i	0.0275948	−	0.00739399i	−0.244995	−	0.969524i	$-0.578786\pi$
$617$	0.685439	−	0.183663i	0.0275948	−	0.00739399i	0.272590	+	0.962130i	$0.412120\pi$
$618$	−2.02860	−	7.57085i	−0.0816023	−	0.304544i
$619$	−9.68489	−	9.68489i	−0.389268	−	0.389268i	0.485158	−	0.874426i	$-0.338762\pi$
$619$	−9.68489	−	9.68489i	−0.389268	−	0.389268i	−0.874426	+	0.485158i	$0.838762\pi$
$620$	4.16925	−	7.22136i	0.167441	−	0.290017i
$621$	8.28689	+	14.3533i	0.332541	+	0.575979i
$622$	−2.69391	+	10.0538i	−0.108016	+	0.403121i
$623$		0			0
$624$	3.77405	+	8.18422i	0.151083	+	0.327631i
$625$	4.52587			0.181035
$626$	39.4399	+	10.5679i	1.57634	+	0.422378i
$627$	−1.71190	−	2.96510i	−0.0683669	−	0.118415i
$628$	−1.53385	+	2.65671i	−0.0612073	+	0.106014i
$629$	26.4976	−	26.4976i	1.05653	−	1.05653i
$630$		0			0
$631$	−0.371814	−	1.38763i	−0.0148017	−	0.0552407i	0.958130	−	0.286334i	$-0.0924365\pi$
$631$	−0.371814	−	1.38763i	−0.0148017	−	0.0552407i	−0.972932	+	0.231093i	$0.925770\pi$
$632$	13.3399	−	13.3399i	0.530633	−	0.530633i
$633$	−2.97011	−	1.71479i	−0.118051	−	0.0681568i
$634$	−33.8469	+	19.5415i	−1.34423	+	0.776093i
$635$	6.79955	−	25.3762i	0.269832	−	1.00703i
$636$	1.60383			0.0635960
$637$		0			0
$638$	3.54394			0.140306
$639$	7.55363	−	28.1905i	0.298817	−	1.11520i
$640$	−17.9840	+	10.3830i	−0.710879	+	0.410426i
$641$	−9.56157	−	5.52037i	−0.377659	−	0.218042i	0.299140	−	0.954209i	$-0.403300\pi$
$641$	−9.56157	−	5.52037i	−0.377659	−	0.218042i	−0.676799	+	0.736168i	$0.736634\pi$
$642$	−0.0423459	+	0.0423459i	−0.00167126	+	0.00167126i
$643$	11.5604	+	43.1441i	0.455899	+	1.70144i	0.685431	+	0.728138i	$0.259614\pi$
$643$	11.5604	+	43.1441i	0.455899	+	1.70144i	−0.229532	+	0.973301i	$0.573719\pi$
$644$		0			0
$645$	−1.43652	+	1.43652i	−0.0565630	+	0.0565630i
$646$	−11.6581	+	20.1924i	−0.458682	+	0.794461i
$647$	−5.20304	−	9.01192i	−0.204552	−	0.354295i	0.745438	−	0.666575i	$-0.232241\pi$
$647$	−5.20304	−	9.01192i	−0.204552	−	0.354295i	−0.949990	+	0.312280i	$0.898907\pi$
$648$	−14.3560	−	3.84668i	−0.563957	−	0.151112i
$649$	2.53913			0.0996694
$650$	−9.98423	−	12.0021i	−0.391614	−	0.470761i
$651$		0			0
$652$	−1.04318	+	3.89321i	−0.0408542	+	0.152470i
$653$	5.21928	+	9.04007i	0.204246	+	0.353765i	0.949892	−	0.312577i	$-0.101192\pi$
$653$	5.21928	+	9.04007i	0.204246	+	0.353765i	−0.745646	+	0.666342i	$0.767859\pi$
$654$	3.05295	−	5.28786i	0.119380	−	0.206772i
$655$	−5.90487	−	5.90487i	−0.230722	−	0.230722i
$656$	2.54026	+	9.48038i	0.0991804	+	0.370146i
$657$	−18.3865	+	4.92666i	−0.717327	+	0.192207i
$658$		0			0
$659$	−3.86557	+	6.69537i	−0.150581	+	0.260815i	−0.931441	−	0.363892i	$-0.881448\pi$
$659$	−3.86557	+	6.69537i	−0.150581	+	0.260815i	0.780860	+	0.624706i	$0.214781\pi$
$660$	−1.23481	+	0.712918i	−0.0480649	+	0.0277503i
$661$	−11.5938	+	43.2687i	−0.450947	+	1.68296i	0.248790	+	0.968558i	$0.419967\pi$
$661$	−11.5938	+	43.2687i	−0.450947	+	1.68296i	−0.699737	+	0.714401i	$0.746699\pi$
$662$		−	9.58774i		−	0.372638i
$663$	−6.64636	+	9.40654i	−0.258123	+	0.365320i
$664$			4.75580i			0.184561i
$665$		0			0
$666$	13.3766	+	23.1690i	0.518334	+	0.897780i
$667$	3.69311	+	2.13222i	0.142998	+	0.0825597i
$668$	−4.51700	+	4.51700i	−0.174768	+	0.174768i
$669$	−3.13509	+	0.840045i	−0.121210	+	0.0324780i
$670$	37.5539	−	10.0625i	1.45083	−	0.388750i
$671$	−10.5431	−	10.5431i	−0.407012	−	0.407012i
$672$		0			0
$673$	−19.6804	+	11.3625i	−0.758625	+	0.437992i	−0.828802	−	0.559542i	$-0.810977\pi$
$673$	−19.6804	+	11.3625i	−0.758625	+	0.437992i	0.0701768	+	0.997535i	$0.477644\pi$
$674$	−18.0673	−	4.84112i	−0.695927	−	0.186473i
$675$	−7.86932			−0.302890
$676$	1.49288	−	8.06455i	0.0574183	−	0.310175i
$677$			8.74056i			0.335927i	0.985793	+	0.167964i	$0.0537191\pi$
$677$			8.74056i			0.335927i	−0.985793	+	0.167964i	$0.946281\pi$
$678$	13.1367	+	3.51996i	0.504510	+	0.135183i
$679$		0			0
$680$	−18.2488	−	10.5359i	−0.699809	−	0.404035i
$681$	8.55748	+	8.55748i	0.327923	+	0.327923i
$682$	10.4702	+	39.0754i	0.400925	+	1.49627i
$683$	0.577561	+	2.15549i	0.0220998	+	0.0824774i	0.976095	−	0.217344i	$-0.0697395\pi$
$683$	0.577561	+	2.15549i	0.0220998	+	0.0824774i	−0.953995	+	0.299822i	$0.903073\pi$
$684$	−2.82260	−	2.82260i	−0.107925	−	0.107925i
$685$	−2.31951	−	1.33917i	−0.0886240	−	0.0511671i
$686$		0			0
$687$	−9.39407	−	2.51713i	−0.358406	−	0.0960346i
$688$			12.5944i			0.480157i
$689$	14.5660	+	10.2919i	0.554920	+	0.392089i
$690$	−7.15474			−0.272376
$691$	4.45128	+	1.19272i	0.169335	+	0.0453731i	0.342490	−	0.939521i	$-0.388730\pi$
$691$	4.45128	+	1.19272i	0.169335	+	0.0453731i	−0.173155	+	0.984895i	$0.555396\pi$
$692$	9.64206	−	5.56685i	0.366536	−	0.211620i
$693$		0			0
$694$	10.4061	+	10.4061i	0.395012	+	0.395012i
$695$	12.1564	−	3.25729i	0.461117	−	0.123556i
$696$	0.836132	−	0.224041i	0.0316935	−	0.00849225i
$697$	−8.86926	+	8.86926i	−0.335947	+	0.335947i
$698$	42.2133	+	24.3718i	1.59780	+	0.922488i
$699$	−1.88933	−	3.27241i	−0.0714609	−	0.123774i
$700$		0			0
$701$			10.7910i			0.407569i	0.979016	+	0.203784i	$0.0653242\pi$
$701$			10.7910i			0.407569i	−0.979016	+	0.203784i	$0.934676\pi$
$702$	−11.0250	−	13.2532i	−0.416113	−	0.500211i
$703$		−	13.9426i		−	0.525854i
$704$	3.08329	−	11.5070i	0.116206	−	0.433686i
$705$	1.50104	−	0.866628i	0.0565326	−	0.0326391i
$706$	−23.5012	+	40.7053i	−0.884481	+	1.53197i
$707$		0			0
$708$	−0.276050	+	0.0739674i	−0.0103746	+	0.00277987i
$709$	5.99502	+	22.3737i	0.225148	+	0.840262i	0.982345	+	0.187076i	$0.0599012\pi$
$709$	5.99502	+	22.3737i	0.225148	+	0.840262i	−0.757198	+	0.653186i	$0.773432\pi$
$710$	18.6776	+	18.6776i	0.700956	+	0.700956i
$711$	−11.6210	+	20.1282i	−0.435823	+	0.754867i
$712$	9.28930	+	16.0895i	0.348131	+	0.602981i
$713$	−12.5988	+	47.0195i	−0.471830	+	1.76090i
$714$		0			0
$715$	−15.7894	−	1.44912i	−0.590490	−	0.0541941i
$716$	−12.7586			−0.476811
$717$	−2.86885	−	0.768705i	−0.107139	−	0.0287078i
$718$	−7.15942	−	12.4005i	−0.267187	−	0.462782i
$719$	17.9493	−	31.0890i	0.669394	−	1.15942i	−0.308679	−	0.951166i	$-0.599887\pi$
$719$	17.9493	−	31.0890i	0.669394	−	1.15942i	0.978074	−	0.208259i	$-0.0667796\pi$
$720$	14.3640	−	14.3640i	0.535314	−	0.535314i
$721$		0			0
$722$	−5.73099	−	21.3883i	−0.213285	−	0.795991i
$723$	−10.4442	+	10.4442i	−0.388422	+	0.388422i
$724$	9.54223	+	5.50921i	0.354634	+	0.204748i
$725$	−1.75351	+	1.01239i	−0.0651236	+	0.0375991i
$726$	−0.582891	+	2.17538i	−0.0216331	+	0.0807358i
$727$	40.7770			1.51234			0.756168	−	0.654377i	$-0.227069\pi$
$727$	40.7770			1.51234			0.756168	+	0.654377i	$0.227069\pi$
$728$		0			0
$729$	13.7655			0.509832
$730$	4.45890	−	16.6408i	0.165031	−	0.615905i
$731$	−13.9389	+	8.04764i	−0.515549	+	0.297653i
$732$	1.45336	+	0.839099i	0.0537178	+	0.0310140i
$733$	−17.5698	+	17.5698i	−0.648954	+	0.648954i	−0.952740	−	0.303787i	$-0.901749\pi$
$733$	−17.5698	+	17.5698i	−0.648954	+	0.648954i	0.303787	+	0.952740i	$0.401749\pi$
$734$	−5.57860	−	20.8196i	−0.205910	−	0.768466i
$735$		0			0
$736$	−13.7065	+	13.7065i	−0.505227	+	0.505227i
$737$	−22.6154	+	39.1710i	−0.833048	+	1.44288i
$738$	−4.47742	−	7.75512i	−0.164816	−	0.285470i
$739$	41.0071	+	10.9878i	1.50847	+	0.404194i	0.915927	−	0.401344i	$-0.131457\pi$
$739$	41.0071	+	10.9878i	1.50847	+	0.404194i	0.592544	+	0.805538i	$0.298124\pi$
$740$	−5.80634			−0.213445
$741$	0.726179	+	4.22338i	0.0266768	+	0.155150i
$742$		0			0
$743$	−6.30753	+	23.5400i	−0.231401	+	0.863600i	0.748337	+	0.663318i	$0.230852\pi$
$743$	−6.30753	+	23.5400i	−0.231401	+	0.863600i	−0.979738	+	0.200282i	$0.935814\pi$
$744$	4.94054	+	8.55727i	0.181129	+	0.313725i
$745$	−3.39695	+	5.88369i	−0.124455	+	0.215562i
$746$	−9.46206	−	9.46206i	−0.346431	−	0.346431i
$747$	−1.51644	−	5.65945i	−0.0554838	−	0.207068i
$748$	−10.9115	+	2.92373i	−0.398964	+	0.106902i
$749$		0			0
$750$	4.87992	−	8.45226i	0.178189	−	0.308633i
$751$	24.6348	−	14.2229i	0.898936	−	0.519001i	0.0220813	−	0.999756i	$-0.492971\pi$
$751$	24.6348	−	14.2229i	0.898936	−	0.519001i	0.876855	+	0.480755i	$0.159637\pi$
$752$	2.78105	−	10.3790i	0.101415	−	0.378484i
$753$			9.99787i			0.364343i
$754$	−4.16171	−	1.53483i	−0.151561	−	0.0558951i
$755$		−	13.7410i		−	0.500086i
$756$		0			0
$757$	−26.0081	−	45.0474i	−0.945282	−	1.63728i	−0.755187	−	0.655510i	$-0.772454\pi$
$757$	−26.0081	−	45.0474i	−0.945282	−	1.63728i	−0.190095	−	0.981766i	$-0.560880\pi$
$758$	−4.86597	−	2.80937i	−0.176740	−	0.102041i
$759$	5.88574	−	5.88574i	0.213639	−	0.213639i
$760$	−7.57301	+	2.02918i	−0.274702	+	0.0736062i
$761$	−5.72561	+	1.53417i	−0.207553	+	0.0556137i	−0.361098	−	0.932528i	$-0.617598\pi$
$761$	−5.72561	+	1.53417i	−0.207553	+	0.0556137i	0.153544	+	0.988142i	$0.450931\pi$
$762$	−10.1438	−	10.1438i	−0.367470	−	0.367470i
$763$		0			0
$764$	0.0227228	−	0.0131190i	0.000822080	−	0.000474628i
$765$	25.0758	+	6.71904i	0.906617	+	0.242927i
$766$	−55.8439			−2.01772
$767$	−2.98174	−	1.09966i	−0.107665	−	0.0397064i
$768$			7.08865i			0.255790i
$769$	0.310861	+	0.0832949i	0.0112099	+	0.00300369i	0.264420	−	0.964408i	$-0.414820\pi$
$769$	0.310861	+	0.0832949i	0.0112099	+	0.00300369i	−0.253210	+	0.967411i	$0.581486\pi$
$770$		0			0
$771$	11.2180	+	6.47670i	0.404005	+	0.233253i
$772$	5.57199	+	5.57199i	0.200540	+	0.200540i
$773$	8.22900	+	30.7110i	0.295977	+	1.10460i	0.940439	+	0.339963i	$0.110415\pi$
$773$	8.22900	+	30.7110i	0.295977	+	1.10460i	−0.644462	+	0.764636i	$0.722919\pi$
$774$	−2.97406	−	11.0994i	−0.106900	−	0.398958i
$775$	−16.3431	−	16.3431i	−0.587062	−	0.587062i
$776$	−6.93965	−	4.00661i	−0.249119	−	0.143829i
$777$		0			0
$778$	−14.6104	−	3.91484i	−0.523807	−	0.140354i
$779$			4.66685i			0.167207i
$780$	1.75882	−	0.302415i	0.0629757	−	0.0108282i
$781$	−30.7296			−1.09959
$782$	−54.7531	−	14.6710i	−1.95797	−	0.524635i
$783$	−1.93630	+	1.11792i	−0.0691976	+	0.0399513i
$784$		0			0
$785$	−5.24887	−	5.24887i	−0.187340	−	0.187340i
$786$	−4.40454	+	1.18019i	−0.157105	+	0.0420960i
$787$	−32.4294	+	8.68944i	−1.15598	+	0.309745i	−0.785361	−	0.619038i	$-0.787523\pi$
$787$	−32.4294	+	8.68944i	−1.15598	+	0.309745i	−0.370623	+	0.928783i	$0.620856\pi$
$788$	−1.65911	+	1.65911i	−0.0591034	+	0.0591034i
$789$	−13.9213	−	8.03746i	−0.495611	−	0.286141i
$790$	−10.5177	−	18.2172i	−0.374202	−	0.648137i
$791$		0			0
$792$			17.5017i			0.621897i
$793$	7.81490	+	16.9470i	0.277515	+	0.601806i
$794$		−	32.0881i		−	1.13876i
$795$	−1.00444	+	3.74860i	−0.0356237	+	0.132949i
$796$	−4.79549	+	2.76868i	−0.169972	+	0.0981333i
$797$	6.34434	−	10.9887i	0.224728	−	0.389240i	−0.731510	−	0.681831i	$-0.761184\pi$
$797$	6.34434	−	10.9887i	0.224728	−	0.389240i	0.956238	+	0.292591i	$0.0945173\pi$
$798$		0			0
$799$	13.2641	−	3.55410i	0.469250	−	0.125735i
$800$	−2.38206	−	8.88996i	−0.0842185	−	0.314308i
$801$	−16.1847	−	16.1847i	−0.571859	−	0.571859i
$802$	−9.76605	+	16.9153i	−0.344851	+	0.597300i
$803$	10.0213	+	17.3574i	0.353644	+	0.612529i
$804$	1.31762	−	4.91742i	0.0464688	−	0.173424i
$805$		0			0
$806$	4.62759	−	50.4215i	0.163000	−	1.77602i
$807$	4.63458			0.163145
$808$	42.2346	+	11.3167i	1.48581	+	0.398121i
$809$	21.4022	+	37.0698i	0.752463	+	1.30330i	0.946626	+	0.322334i	$0.104467\pi$
$809$	21.4022	+	37.0698i	0.752463	+	1.30330i	−0.194163	+	0.980969i	$0.562199\pi$
$810$	−8.28595	+	14.3517i	−0.291138	+	0.504267i
$811$	1.51360	−	1.51360i	0.0531496	−	0.0531496i	−0.680032	−	0.733182i	$-0.738034\pi$
$811$	1.51360	−	1.51360i	0.0531496	−	0.0531496i	0.733182	+	0.680032i	$0.238034\pi$
$812$		0			0
$813$	−0.453053	−	1.69082i	−0.0158893	−	0.0592995i
$814$	19.9186	−	19.9186i	0.698147	−	0.698147i
$815$	−8.44623	−	4.87643i	−0.295858	−	0.170814i
$816$	−13.4554	+	7.76847i	−0.471033	+	0.271951i
$817$	−1.54994	+	5.78447i	−0.0542257	+	0.202373i
$818$	−31.6242			−1.10571
$819$		0			0
$820$	1.94350			0.0678699
$821$	9.73769	−	36.3415i	0.339848	−	1.26833i	−0.558670	−	0.829390i	$-0.688688\pi$
$821$	9.73769	−	36.3415i	0.339848	−	1.26833i	0.898517	−	0.438938i	$-0.144645\pi$
$822$	−1.26657	+	0.731252i	−0.0441766	+	0.0255054i
$823$	38.5355	+	22.2485i	1.34326	+	0.775533i	0.987285	−	0.158962i	$-0.0508148\pi$
$823$	38.5355	+	22.2485i	1.34326	+	0.775533i	0.355977	+	0.934495i	$0.384148\pi$
$824$	14.7646	−	14.7646i	0.514351	−	0.514351i
$825$	1.02289	+	3.81747i	0.0356124	+	0.132907i
$826$		0			0
$827$	12.3898	−	12.3898i	0.430835	−	0.430835i	−0.458077	−	0.888912i	$-0.651462\pi$
$827$	12.3898	−	12.3898i	0.430835	−	0.430835i	0.888912	+	0.458077i	$0.151462\pi$
$828$	4.85222	−	8.40430i	0.168626	−	0.292070i
$829$	−21.1381	−	36.6122i	−0.734155	−	1.27159i	−0.955093	−	0.296306i	$-0.904245\pi$
$829$	−21.1381	−	36.6122i	−0.734155	−	1.27159i	0.220938	−	0.975288i	$-0.429088\pi$
$830$	5.12212	+	1.37247i	0.177791	+	0.0476390i
$831$	−2.07063			−0.0718295
$832$	−8.60428	+	12.1776i	−0.298300	+	0.422181i
$833$		0			0
$834$	1.77864	−	6.63796i	0.0615891	−	0.229854i
$835$	−7.72863	−	13.3864i	−0.267460	−	0.463255i
$836$	−2.10151	+	3.63993i	−0.0726823	+	0.125889i
$837$	−18.0468	−	18.0468i	−0.623788	−	0.623788i
$838$	1.62269	+	6.05597i	0.0560550	+	0.209200i
$839$	25.6907	−	6.88379i	0.886940	−	0.237655i	0.213541	−	0.976934i	$-0.431500\pi$
$839$	25.6907	−	6.88379i	0.886940	−	0.237655i	0.673399	+	0.739279i	$0.264834\pi$
$840$		0			0
$841$	14.2124	−	24.6165i	0.490081	−	0.848846i
$842$	7.26640	−	4.19526i	0.250417	−	0.144578i
$843$	−0.617962	+	2.30626i	−0.0212837	+	0.0794320i
$844$			4.21011i			0.144918i
$845$	17.9142	+	8.53989i	0.616267	+	0.293781i
$846$			9.80368i			0.337058i
$847$		0			0
$848$	12.0295	+	20.8356i	0.413093	+	0.715498i
$849$	0.458274	+	0.264585i	0.0157279	+	0.00908052i
$850$	19.0312	−	19.0312i	0.652763	−	0.652763i
$851$	32.7411	−	8.77294i	1.12235	−	0.300732i
$852$	3.34088	−	0.895186i	0.114457	−	0.0306686i
$853$	−0.950856	−	0.950856i	−0.0325567	−	0.0325567i	0.690641	−	0.723198i	$-0.257328\pi$
$853$	−0.950856	−	0.950856i	−0.0325567	−	0.0325567i	−0.723198	+	0.690641i	$0.757328\pi$
$854$		0			0
$855$	8.36494	−	4.82950i	0.286075	−	0.165165i
$856$	−0.154102	−	0.0412914i	−0.00526709	−	0.00141131i
$857$	42.3805			1.44769			0.723845	−	0.689962i	$-0.242373\pi$
$857$	42.3805			1.44769			0.723845	+	0.689962i	$0.242373\pi$
$858$	−4.99617	+	7.07103i	−0.170566	+	0.241401i
$859$			6.73225i			0.229701i	0.993383	+	0.114851i	$0.0366390\pi$
$859$			6.73225i			0.229701i	−0.993383	+	0.114851i	$0.963361\pi$
$860$	2.40893	+	0.645470i	0.0821437	+	0.0220103i
$861$		0			0
$862$	14.1340	+	8.16026i	0.481405	+	0.277939i
$863$	−13.0451	−	13.0451i	−0.444061	−	0.444061i	0.449313	−	0.893374i	$-0.351669\pi$
$863$	−13.0451	−	13.0451i	−0.444061	−	0.444061i	−0.893374	+	0.449313i	$0.851669\pi$
$864$	−2.63037	−	9.81668i	−0.0894871	−	0.333970i
$865$	6.97273	+	26.0226i	0.237080	+	0.884795i
$866$	8.73846	+	8.73846i	0.296945	+	0.296945i
$867$	−9.62934	−	5.55950i	−0.327030	−	0.188811i
$868$		0			0
$869$	23.6383	+	6.33386i	0.801874	+	0.214861i
$870$		−	0.965192i		−	0.0327231i
$871$	43.5220	−	36.2048i	1.47469	−	1.22675i
$872$	16.2662			0.550844
$873$	9.53582	+	2.55511i	0.322739	+	0.0864775i
$874$	−18.2649	+	10.5452i	−0.617819	+	0.356698i
$875$		0			0
$876$	−1.59514	−	1.59514i	−0.0538948	−	0.0538948i
$877$	−14.5547	+	3.89991i	−0.491476	+	0.131691i	−0.496041	−	0.868299i	$-0.665213\pi$
$877$	−14.5547	+	3.89991i	−0.491476	+	0.131691i	0.00456529	+	0.999990i	$0.498547\pi$
$878$	−35.0365	+	9.38800i	−1.18242	+	0.316830i
$879$	9.29224	−	9.29224i	0.313419	−	0.313419i
$880$	−18.5233	−	10.6944i	−0.624420	−	0.360509i
$881$	−22.3633	−	38.7344i	−0.753439	−	1.30500i	−0.946146	−	0.323739i	$-0.895060\pi$
$881$	−22.3633	−	38.7344i	−0.753439	−	1.30500i	0.192707	−	0.981256i	$-0.438273\pi$
$882$		0			0
$883$		−	46.5076i		−	1.56510i	−0.622585	−	0.782552i	$-0.713917\pi$
$883$		−	46.5076i		−	1.56510i	0.622585	−	0.782552i	$-0.286083\pi$
$884$	14.0798	+	1.29222i	0.473555	+	0.0434620i
$885$		−	0.691531i		−	0.0232456i
$886$	10.7855	−	40.2522i	0.362347	−	1.35230i
$887$	39.8820	−	23.0259i	1.33911	−	0.773133i	0.352431	−	0.935838i	$-0.385355\pi$
$887$	39.8820	−	23.0259i	1.33911	−	0.773133i	0.986675	+	0.162704i	$0.0520217\pi$
$888$	3.44024	−	5.95867i	0.115447	−	0.199960i
$889$		0			0
$890$	20.0096	−	5.36156i	0.670724	−	0.179720i
$891$	−4.98988	−	18.6225i	−0.167167	−	0.623877i
$892$	2.81737	+	2.81737i	0.0943325	+	0.0943325i
$893$	2.55461	−	4.42472i	0.0854869	−	0.148068i
$894$	1.85490	+	3.21278i	0.0620371	+	0.107451i
$895$	7.99036	−	29.8204i	0.267088	−	0.996787i
$896$		0			0
$897$	−9.46076	+	4.36271i	−0.315885	+	0.145667i
$898$	−5.14924			−0.171832
$899$	−6.34305	−	1.69962i	−0.211553	−	0.0566854i
$900$	2.30386	+	3.99041i	0.0767954	+	0.133014i
$901$	−15.3733	+	26.6273i	−0.512158	+	0.887085i
$902$	−6.66715	+	6.66715i	−0.221992	+	0.221992i
$903$		0			0
$904$	9.37724	+	34.9963i	0.311882	+	1.16396i
$905$	−18.8526	+	18.8526i	−0.626682	+	0.626682i
$906$	−6.49800	−	3.75162i	−0.215882	−	0.124639i
$907$	−27.6067	+	15.9387i	−0.916666	+	0.529237i	−0.882570	−	0.470181i	$-0.844189\pi$
$907$	−27.6067	+	15.9387i	−0.916666	+	0.529237i	−0.0340961	+	0.999419i	$0.510855\pi$
$908$	3.84512	−	14.3502i	0.127605	−	0.476227i
$909$	−53.8681			−1.78669
$910$		0			0
$911$	34.8516			1.15469			0.577343	−	0.816502i	$-0.304090\pi$
$911$	34.8516			1.15469			0.577343	+	0.816502i	$0.304090\pi$
$912$	−1.49618	+	5.58381i	−0.0495434	+	0.184899i
$913$	−5.34267	+	3.08459i	−0.176817	+	0.102085i
$914$	46.1204	+	26.6276i	1.52553	+	0.880764i
$915$	−2.87141	+	2.87141i	−0.0949260	+	0.0949260i
$916$	3.09000	+	11.5320i	0.102096	+	0.381029i
$917$		0			0
$918$	21.0150	−	21.0150i	0.693599	−	0.693599i
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	−0.832892	−	0.553436i	$-0.813316\pi$
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	0.895736	+	0.444587i	$0.146650\pi$
$920$	−9.53018	−	16.5068i	−0.314201	−	0.544212i
$921$	−9.84221	−	2.63721i	−0.324312	−	0.0868991i
$922$	−8.68983			−0.286184
$923$	36.0864	+	13.3085i	1.18780	+	0.438056i
$924$		0			0
$925$	−4.16544	+	15.5456i	−0.136959	+	0.511137i
$926$	19.5187	+	33.8073i	0.641423	+	1.11098i
$927$	−12.8622	+	22.2780i	−0.422450	+	0.731705i
$928$	−1.84904	−	1.84904i	−0.0606976	−	0.0606976i
$929$	−9.73846	−	36.3444i	−0.319509	−	1.19242i	−0.919718	−	0.392579i	$-0.871583\pi$
$929$	−9.73846	−	36.3444i	−0.319509	−	1.19242i	0.600210	−	0.799843i	$-0.295084\pi$
$930$	10.6422	−	2.85157i	0.348971	−	0.0935065i
$931$		0			0
$932$	−2.31931	+	4.01717i	−0.0759717	+	0.131587i
$933$	−2.85606	+	1.64895i	−0.0935032	+	0.0539841i
$934$	3.13550	−	11.7018i	0.102597	−	0.382895i
$935$		−	27.3343i		−	0.893927i
$936$	7.57974	−	20.5526i	0.247752	−	0.671783i
$937$		−	38.0350i		−	1.24255i	−0.783593	−	0.621275i	$-0.786615\pi$
$937$		−	38.0350i		−	1.24255i	0.783593	−	0.621275i	$-0.213385\pi$
$938$		0			0
$939$	6.46863	+	11.2040i	0.211096	+	0.365628i
$940$	−1.84266	−	1.06386i	−0.0601010	−	0.0346993i
$941$	18.5706	−	18.5706i	0.605385	−	0.605385i	−0.336352	−	0.941736i	$-0.609193\pi$
$941$	18.5706	−	18.5706i	0.605385	−	0.605385i	0.941736	+	0.336352i	$0.109193\pi$
$942$	−3.91522	+	1.04908i	−0.127565	+	0.0341808i
$943$	−10.9591	+	2.93648i	−0.356877	+	0.0956248i
$944$	−3.03143	−	3.03143i	−0.0986645	−	0.0986645i
$945$		0			0
$946$	−10.4781	+	6.04952i	−0.340672	+	0.196687i
$947$	7.52805	+	2.01713i	0.244629	+	0.0655480i	0.379050	−	0.925376i	$-0.376251\pi$
$947$	7.52805	+	2.01713i	0.244629	+	0.0655480i	−0.134421	+	0.990924i	$0.542918\pi$
$948$	−2.75443			−0.0894598
$949$	−4.25097	−	24.7232i	−0.137992	−	0.802548i
$950$		−	10.0139i		−	0.324893i
$951$	−11.9614	−	3.20505i	−0.387875	−	0.103931i
$952$		0			0
$953$	−7.95143	−	4.59076i	−0.257572	−	0.148709i	0.365654	−	0.930751i	$-0.380845\pi$
$953$	−7.95143	−	4.59076i	−0.257572	−	0.148709i	−0.623227	+	0.782041i	$0.714179\pi$
$954$	−15.5216	−	15.5216i	−0.502531	−	0.502531i
$955$	0.0164321	+	0.0613256i	0.000531732	+	0.00198445i
$956$	0.943653	+	3.52176i	0.0305199	+	0.113902i
$957$	0.794000	+	0.794000i	0.0256664	+	0.0256664i
$958$	−29.2840	−	16.9071i	−0.946124	−	0.546245i
$959$		0			0
$960$	−3.13393	−	0.839735i	−0.101147	−	0.0271023i
$961$		−	43.9597i		−	1.41805i
$962$	−32.0173	+	14.7643i	−1.03228	+	0.476022i
$963$	0.196549			0.00633370
$964$	17.5140	+	4.69285i	0.564087	+	0.151147i
$965$	−16.5129	+	9.53373i	−0.531569	+	0.306902i
$966$		0			0
$967$	29.3315	+	29.3315i	0.943237	+	0.943237i	0.998473	−	0.0552359i	$-0.0175911\pi$
$967$	29.3315	+	29.3315i	0.943237	+	0.943237i	−0.0552359	+	0.998473i	$0.517591\pi$
$968$	−5.79525	+	1.55283i	−0.186266	+	0.0499099i
$969$	−7.13595	+	1.91207i	−0.229240	+	0.0614246i
$970$	−6.31792	+	6.31792i	−0.202856	+	0.202856i
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.122665	−	0.992448i	$-0.539144\pi$
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.920818	+	0.389993i	$0.872478\pi$
$972$	3.87461	+	6.71102i	0.124278	+	0.215256i
$973$		0			0
$974$		−	30.2843i		−	0.970371i
$975$	0.452092	−	4.92592i	0.0144785	−	0.157756i
$976$			25.1745i			0.805816i
$977$	−7.45485	+	27.8219i	−0.238502	+	0.890101i	0.738037	+	0.674760i	$0.235753\pi$
$977$	−7.45485	+	27.8219i	−0.238502	+	0.890101i	−0.976539	+	0.215341i	$0.930914\pi$
$978$	−4.61205	+	2.66277i	−0.147477	+	0.0851460i
$979$	−12.0500	+	20.8712i	−0.385120	+	0.667047i
$980$		0			0
$981$	−19.3570	+	5.18669i	−0.618021	+	0.165598i
$982$	−13.0706	−	48.7801i	−0.417099	−	1.55664i
$983$	13.9263	+	13.9263i	0.444180	+	0.444180i	0.893414	−	0.449234i	$-0.148303\pi$
$983$	13.9263	+	13.9263i	0.444180	+	0.444180i	−0.449234	+	0.893414i	$0.648303\pi$
$984$	−1.15152	+	1.99449i	−0.0367090	+	0.0635819i
$985$	−2.83876	−	4.91687i	−0.0904504	−	0.156665i
$986$	1.97916	−	7.38633i	0.0630293	−	0.235229i
$987$		0			0
$988$	4.04424	−	3.36430i	0.128665	−	0.107033i
$989$	−14.5588			−0.462943
$990$	18.8498	+	5.05080i	0.599087	+	0.160525i
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	−0.997546	−	0.0700140i	$-0.977696\pi$
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	0.438139	−	0.898907i	$-0.355638\pi$
$992$	14.9246	−	25.8502i	0.473858	−	0.820746i
$993$	2.14808	−	2.14808i	0.0681673	−	0.0681673i
$994$		0			0
$995$	−3.46790	−	12.9424i	−0.109940	−	0.410301i
$996$	0.490990	−	0.490990i	0.0155576	−	0.0155576i
$997$	−31.7101	−	18.3078i	−1.00427	−	0.579814i	−0.0947594	−	0.995500i	$-0.530208\pi$
$997$	−31.7101	−	18.3078i	−1.00427	−	0.579814i	−0.909508	+	0.415686i	$0.863541\pi$
$998$	−26.0314	+	15.0292i	−0.824009	+	0.475742i
$999$	−4.59966	+	17.1662i	−0.145527	+	0.543113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.440.6		28
7.2	even	3		637.2.x.a.570.2		28
7.3	odd	6		637.2.bb.a.362.6		28
7.4	even	3		91.2.ba.a.89.6	yes	28
7.5	odd	6		91.2.w.a.24.2	yes	28
7.6	odd	2		637.2.bd.a.440.6		28
13.6	odd	12		637.2.bd.a.97.6		28
21.5	even	6		819.2.gh.b.388.6		28
21.11	odd	6		819.2.et.b.271.2		28
91.6	even	12	inner	637.2.bd.b.97.6		28
91.19	even	12		91.2.ba.a.45.6	yes	28
91.32	odd	12		91.2.w.a.19.2	✓	28
91.45	even	12		637.2.x.a.19.2		28
91.58	odd	12		637.2.bb.a.227.6		28
273.32	even	12		819.2.gh.b.19.6		28
273.110	odd	12		819.2.et.b.136.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.2	✓	28	91.32	odd	12
91.2.w.a.24.2	yes	28	7.5	odd	6
91.2.ba.a.45.6	yes	28	91.19	even	12
91.2.ba.a.89.6	yes	28	7.4	even	3
637.2.x.a.19.2		28	91.45	even	12
637.2.x.a.570.2		28	7.2	even	3
637.2.bb.a.227.6		28	91.58	odd	12
637.2.bb.a.362.6		28	7.3	odd	6
637.2.bd.a.97.6		28	13.6	odd	12
637.2.bd.a.440.6		28	7.6	odd	2
637.2.bd.b.97.6		28	91.6	even	12	inner
637.2.bd.b.440.6		28	1.1	even	1	trivial
819.2.et.b.136.2		28	273.110	odd	12
819.2.et.b.271.2		28	21.11	odd	6
819.2.gh.b.19.6		28	273.32	even	12
819.2.gh.b.388.6		28	21.5	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.419805 - 1.56673i) q^{2} +(0.445073 - 0.256963i) q^{3} +(-0.546366 - 0.315445i) q^{4} +(1.07946 - 1.07946i) q^{5} +(-0.215749 - 0.805186i) q^{6} +(1.57027 - 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +O(q^{10})\)	\(q+(0.419805 - 1.56673i) q^{2} +(0.445073 - 0.256963i) q^{3} +(-0.546366 - 0.315445i) q^{4} +(1.07946 - 1.07946i) q^{5} +(-0.215749 - 0.805186i) q^{6} +(1.57027 - 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +(-1.23806 - 2.14439i) q^{10} +(2.78252 + 0.745574i) q^{11} -0.324231 q^{12} +(-2.94467 - 2.08061i) q^{13} +(0.203057 - 0.757819i) q^{15} +(-2.43188 - 4.21214i) q^{16} +(3.10787 - 5.38299i) q^{17} +(3.13786 + 3.13786i) q^{18} +(-0.598564 - 2.23387i) q^{19} +(-0.930289 + 0.249270i) q^{20} +(2.33623 - 4.04647i) q^{22} +(4.86913 - 2.81119i) q^{23} +(0.295384 - 1.10239i) q^{24} +2.66954i q^{25} +(-4.49595 + 3.74006i) q^{26} +2.94782i q^{27} +(0.379237 + 0.656858i) q^{29} +(-1.10206 - 0.636273i) q^{30} +(-6.12208 + 6.12208i) q^{31} +(-3.33015 + 0.892311i) q^{32} +(1.43001 - 0.383170i) q^{33} +(-7.12901 - 7.12901i) q^{34} +(1.49479 - 0.863019i) q^{36} +(5.82334 + 1.56036i) q^{37} -3.75116 q^{38} +(-1.84523 - 0.169352i) q^{39} -3.39009i q^{40} +(-1.94919 - 0.522283i) q^{41} +(-2.24252 - 1.29472i) q^{43} +(-1.28509 - 1.28509i) q^{44} +(1.08097 + 4.03424i) q^{45} +(-2.36030 - 8.80878i) q^{46} +(1.56216 + 1.56216i) q^{47} +(-2.16473 - 1.24981i) q^{48} +(4.18246 + 1.12069i) q^{50} -3.19443i q^{51} +(0.952550 + 2.06565i) q^{52} -4.94657 q^{53} +(4.61845 + 1.23751i) q^{54} +(3.80843 - 2.19880i) q^{55} +(-0.840427 - 0.840427i) q^{57} +(1.18833 - 0.318411i) q^{58} +(0.851400 - 0.228132i) q^{59} +(-0.349994 + 0.349994i) q^{60} +(-4.48249 - 2.58797i) q^{61} +(7.02159 + 12.1617i) q^{62} -4.13546i q^{64} +(-5.42458 + 0.932716i) q^{65} -2.40130i q^{66} +(-4.06383 + 15.1664i) q^{67} +(-3.39607 + 1.96072i) q^{68} +(1.44475 - 2.50237i) q^{69} +(-10.3040 + 2.76095i) q^{71} +(1.57247 + 5.86855i) q^{72} +(4.91976 + 4.91976i) q^{73} +(4.88933 - 8.46857i) q^{74} +(0.685973 + 1.18814i) q^{75} +(-0.377628 + 1.40933i) q^{76} +(-1.03997 + 2.81989i) q^{78} +8.49528 q^{79} +(-7.17194 - 1.92172i) q^{80} +(-3.34634 - 5.79603i) q^{81} +(-1.63656 + 2.83460i) q^{82} +(-1.51432 + 1.51432i) q^{83} +(-2.45590 - 9.16553i) q^{85} +(-2.96990 + 2.96990i) q^{86} +(0.337576 + 0.194900i) q^{87} +(5.54006 - 3.19856i) q^{88} +(-2.16531 + 8.08103i) q^{89} +6.77438 q^{90} -3.54710 q^{92} +(-1.15162 + 4.29792i) q^{93} +(3.10329 - 1.79169i) q^{94} +(-3.05750 - 1.76525i) q^{95} +(-1.25287 + 1.25287i) q^{96} +(-0.933928 - 3.48547i) q^{97} +(-5.57284 + 5.57284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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