LMFDB - Embedded newform 475.2.l.f.226.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.4
Character	$\chi$	$=$	475.226
Dual form			475.2.l.f.351.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0424530 + 0.240763i) q^{2} +(-2.09771 - 1.76019i) q^{3} +(1.82322 + 0.663598i) q^{4} +(0.512843 - 0.430326i) q^{6} +(0.970136 + 1.68032i) q^{7} +(-0.481648 + 0.834240i) q^{8} +(0.781184 + 4.43031i) q^{9} +O(q^{10})$	\(q+(-0.0424530 + 0.240763i) q^{2} +(-2.09771 - 1.76019i) q^{3} +(1.82322 + 0.663598i) q^{4} +(0.512843 - 0.430326i) q^{6} +(0.970136 + 1.68032i) q^{7} +(-0.481648 + 0.834240i) q^{8} +(0.781184 + 4.43031i) q^{9} +(-2.11666 + 3.66617i) q^{11} +(-2.65653 - 4.60125i) q^{12} +(-0.972742 + 0.816227i) q^{13} +(-0.445745 + 0.162238i) q^{14} +(2.79220 + 2.34293i) q^{16} +(-0.427212 + 2.42284i) q^{17} -1.09982 q^{18} +(1.64247 - 4.03761i) q^{19} +(0.922623 - 5.23246i) q^{21} +(-0.792820 - 0.665255i) q^{22} +(4.82735 + 1.75701i) q^{23} +(2.47878 - 0.902202i) q^{24} +(-0.155222 - 0.268852i) q^{26} +(2.05194 - 3.55406i) q^{27} +(0.653712 + 3.70738i) q^{28} +(1.50053 + 8.50995i) q^{29} +(-2.55042 - 4.41746i) q^{31} +(-2.15849 + 1.81118i) q^{32} +(10.8933 - 3.96484i) q^{33} +(-0.565193 - 0.205714i) q^{34} +(-1.51568 + 8.59583i) q^{36} +11.0305 q^{37} +(0.902380 + 0.566855i) q^{38} +3.47724 q^{39} +(1.91387 + 1.60593i) q^{41} +(1.22061 + 0.444267i) q^{42} +(-4.19929 + 1.52842i) q^{43} +(-6.29201 + 5.27962i) q^{44} +(-0.627959 + 1.08766i) q^{46} +(1.17543 + 6.66617i) q^{47} +(-1.73322 - 9.82960i) q^{48} +(1.61767 - 2.80189i) q^{49} +(5.16082 - 4.33044i) q^{51} +(-2.31517 + 0.842653i) q^{52} +(-0.648201 - 0.235926i) q^{53} +(0.768575 + 0.644911i) q^{54} -1.86906 q^{56} +(-10.5524 + 5.57868i) q^{57} -2.11258 q^{58} +(0.901817 - 5.11446i) q^{59} +(-2.63378 - 0.958619i) q^{61} +(1.17183 - 0.426513i) q^{62} +(-6.68651 + 5.61065i) q^{63} +(3.30053 + 5.71668i) q^{64} +(0.492133 + 2.79103i) q^{66} +(-0.905101 - 5.13308i) q^{67} +(-2.38669 + 4.13387i) q^{68} +(-7.03371 - 12.1828i) q^{69} +(-0.744158 + 0.270851i) q^{71} +(-4.07220 - 1.48216i) q^{72} +(1.08454 + 0.910034i) q^{73} +(-0.468279 + 2.65574i) q^{74} +(5.67394 - 6.27151i) q^{76} -8.21381 q^{77} +(-0.147620 + 0.837192i) q^{78} +(-4.64448 - 3.89718i) q^{79} +(2.12188 - 0.772300i) q^{81} +(-0.467899 + 0.392614i) q^{82} +(-5.92611 - 10.2643i) q^{83} +(5.15439 - 8.92767i) q^{84} +(-0.189714 - 1.07592i) q^{86} +(11.8314 - 20.4926i) q^{87} +(-2.03898 - 3.53161i) q^{88} +(-1.71051 + 1.43529i) q^{89} +(-2.31522 - 0.842670i) q^{91} +(7.63537 + 6.40684i) q^{92} +(-2.42551 + 13.7558i) q^{93} -1.65487 q^{94} +7.71591 q^{96} +(-1.49508 + 8.47901i) q^{97} +(0.605917 + 0.508425i) q^{98} +(-17.8958 - 6.51353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.0424530	+	0.240763i	−0.0300188	+	0.170245i	−0.996131	−	0.0878757i	$-0.971992\pi$
$2$	−0.0424530	+	0.240763i	−0.0300188	+	0.170245i	0.966113	+	0.258121i	$0.0831033\pi$
$3$	−2.09771	−	1.76019i	−1.21111	−	1.01625i	−0.999241	−	0.0389482i	$-0.987599\pi$
$3$	−2.09771	−	1.76019i	−1.21111	−	1.01625i	−0.211873	−	0.977297i	$-0.567956\pi$
$4$	1.82322	+	0.663598i	0.911610	+	0.331799i
$5$		0			0
$5$		0			0
$6$	0.512843	−	0.430326i	0.209367	−	0.175680i
$7$	0.970136	+	1.68032i	0.366677	+	0.635103i	0.989044	−	0.147623i	$-0.0471621\pi$
$7$	0.970136	+	1.68032i	0.366677	+	0.635103i	−0.622367	+	0.782726i	$0.713829\pi$
$8$	−0.481648	+	0.834240i	−0.170288	+	0.294948i
$9$	0.781184	+	4.43031i	0.260395	+	1.47677i
$10$		0			0
$11$	−2.11666	+	3.66617i	−0.638198	+	1.10539i	0.347630	+	0.937632i	$0.386987\pi$
$11$	−2.11666	+	3.66617i	−0.638198	+	1.10539i	−0.985828	+	0.167760i	$0.946347\pi$
$12$	−2.65653	−	4.60125i	−0.766875	−	1.32827i
$13$	−0.972742	+	0.816227i	−0.269790	+	0.226381i	−0.767638	−	0.640884i	$-0.778568\pi$
$13$	−0.972742	+	0.816227i	−0.269790	+	0.226381i	0.497848	+	0.867264i	$0.334124\pi$
$14$	−0.445745	+	0.162238i	−0.119130	+	0.0433599i
$15$		0			0
$16$	2.79220	+	2.34293i	0.698050	+	0.585733i
$17$	−0.427212	+	2.42284i	−0.103614	+	0.587624i	0.888151	+	0.459552i	$0.151990\pi$
$17$	−0.427212	+	2.42284i	−0.103614	+	0.587624i	−0.991765	+	0.128072i	$0.959121\pi$
$18$	−1.09982			−0.259230
$19$	1.64247	−	4.03761i	0.376809	−	0.926291i
$19$	1.64247	−	4.03761i	0.376809	−	0.926291i
$20$		0			0
$21$	0.922623	−	5.23246i	0.201333	−	1.14182i
$22$	−0.792820	−	0.665255i	−0.169030	−	0.141833i
$23$	4.82735	+	1.75701i	1.00657	+	0.366362i	0.792115	−	0.610371i	$-0.208980\pi$
$23$	4.82735	+	1.75701i	1.00657	+	0.366362i	0.214457	+	0.976734i	$0.431202\pi$
$24$	2.47878	−	0.902202i	0.505979	−	0.184161i
$25$		0			0
$26$	−0.155222	−	0.268852i	−0.0304415	−	0.0527261i
$27$	2.05194	−	3.55406i	0.394895	−	0.683979i
$28$	0.653712	+	3.70738i	0.123540	+	0.700629i
$29$	1.50053	+	8.50995i	0.278642	+	1.58026i	0.727150	+	0.686479i	$0.240845\pi$
$29$	1.50053	+	8.50995i	0.278642	+	1.58026i	−0.448508	+	0.893779i	$0.648044\pi$
$30$		0			0
$31$	−2.55042	−	4.41746i	−0.458069	−	0.793399i	0.540790	−	0.841158i	$-0.318125\pi$
$31$	−2.55042	−	4.41746i	−0.458069	−	0.793399i	−0.998859	+	0.0477591i	$0.984792\pi$
$32$	−2.15849	+	1.81118i	−0.381570	+	0.320175i
$33$	10.8933	−	3.96484i	1.89628	−	0.690190i
$34$	−0.565193	−	0.205714i	−0.0969299	−	0.0352796i
$35$		0			0
$36$	−1.51568	+	8.59583i	−0.252613	+	1.43264i
$37$	11.0305			1.81341			0.906703	−	0.421770i	$-0.138591\pi$
$37$	11.0305			1.81341			0.906703	+	0.421770i	$0.138591\pi$
$38$	0.902380	+	0.566855i	0.146385	+	0.0919561i
$39$	3.47724			0.556805
$40$		0			0
$41$	1.91387	+	1.60593i	0.298897	+	0.250804i	0.779885	−	0.625923i	$-0.215278\pi$
$41$	1.91387	+	1.60593i	0.298897	+	0.250804i	−0.480988	+	0.876727i	$0.659722\pi$
$42$	1.22061	+	0.444267i	0.188345	+	0.0685519i
$43$	−4.19929	+	1.52842i	−0.640386	+	0.233081i	−0.641745	−	0.766918i	$-0.721789\pi$
$43$	−4.19929	+	1.52842i	−0.640386	+	0.233081i	0.00135976	+	0.999999i	$0.499567\pi$
$44$	−6.29201	+	5.27962i	−0.948556	+	0.795933i
$45$		0			0
$46$	−0.627959	+	1.08766i	−0.0925876	+	0.160366i
$47$	1.17543	+	6.66617i	0.171454	+	0.972362i	0.942158	+	0.335169i	$0.108793\pi$
$47$	1.17543	+	6.66617i	0.171454	+	0.972362i	−0.770705	+	0.637193i	$0.780096\pi$
$48$	−1.73322	−	9.82960i	−0.250169	−	1.41878i
$49$	1.61767	−	2.80189i	0.231096	−	0.400270i
$50$		0			0
$51$	5.16082	−	4.33044i	0.722659	−	0.606383i
$52$	−2.31517	+	0.842653i	−0.321056	+	0.116855i
$53$	−0.648201	−	0.235926i	−0.0890373	−	0.0324069i	0.297117	−	0.954841i	$-0.403975\pi$
$53$	−0.648201	−	0.235926i	−0.0890373	−	0.0324069i	−0.386155	+	0.922434i	$0.626197\pi$
$54$	0.768575	+	0.644911i	0.104590	+	0.0877613i
$55$		0			0
$56$	−1.86906			−0.249763
$57$	−10.5524	+	5.57868i	−1.39770	+	0.738914i
$58$	−2.11258			−0.277396
$59$	0.901817	−	5.11446i	0.117407	−	0.665846i	−0.868124	−	0.496348i	$-0.834674\pi$
$59$	0.901817	−	5.11446i	0.117407	−	0.665846i	0.985530	−	0.169498i	$-0.0542147\pi$
$60$		0			0
$61$	−2.63378	−	0.958619i	−0.337221	−	0.122739i	0.167859	−	0.985811i	$-0.446315\pi$
$61$	−2.63378	−	0.958619i	−0.337221	−	0.122739i	−0.505080	+	0.863073i	$0.668537\pi$
$62$	1.17183	−	0.426513i	0.148823	−	0.0541672i
$63$	−6.68651	+	5.61065i	−0.842421	+	0.706875i
$64$	3.30053	+	5.71668i	0.412566	+	0.714585i
$65$		0			0
$66$	0.492133	+	2.79103i	0.0605774	+	0.343551i
$67$	−0.905101	−	5.13308i	−0.110576	−	0.627106i	−0.988846	−	0.148941i	$-0.952413\pi$
$67$	−0.905101	−	5.13308i	−0.110576	−	0.627106i	0.878270	−	0.478164i	$-0.158698\pi$
$68$	−2.38669	+	4.13387i	−0.289429	+	0.501305i
$69$	−7.03371	−	12.1828i	−0.846760	−	1.46663i
$70$		0			0
$71$	−0.744158	+	0.270851i	−0.0883153	+	0.0321441i	−0.385800	−	0.922582i	$-0.626075\pi$
$71$	−0.744158	+	0.270851i	−0.0883153	+	0.0321441i	0.297485	+	0.954727i	$0.403852\pi$
$72$	−4.07220	−	1.48216i	−0.479913	−	0.174674i
$73$	1.08454	+	0.910034i	0.126935	+	0.106511i	0.704045	−	0.710155i	$-0.251375\pi$
$73$	1.08454	+	0.910034i	0.126935	+	0.106511i	−0.577110	+	0.816666i	$0.695820\pi$
$74$	−0.468279	+	2.65574i	−0.0544363	+	0.308724i
$75$		0			0
$76$	5.67394	−	6.27151i	0.650845	−	0.719392i
$77$	−8.21381			−0.936050
$78$	−0.147620	+	0.837192i	−0.0167146	+	0.0947934i
$79$	−4.64448	−	3.89718i	−0.522545	−	0.438467i	0.342973	−	0.939345i	$-0.388566\pi$
$79$	−4.64448	−	3.89718i	−0.522545	−	0.438467i	−0.865518	+	0.500878i	$0.833011\pi$
$80$		0			0
$81$	2.12188	−	0.772300i	0.235764	−	0.0858112i
$82$	−0.467899	+	0.392614i	−0.0516708	+	0.0433569i
$83$	−5.92611	−	10.2643i	−0.650476	−	1.12666i	−0.983008	−	0.183565i	$-0.941236\pi$
$83$	−5.92611	−	10.2643i	−0.650476	−	1.12666i	0.332532	−	0.943092i	$-0.392097\pi$
$84$	5.15439	−	8.92767i	0.562391	−	0.974089i
$85$		0			0
$86$	−0.189714	−	1.07592i	−0.0204574	−	0.116019i
$87$	11.8314	−	20.4926i	1.26846	−	2.19704i
$88$	−2.03898	−	3.53161i	−0.217356	−	0.376471i
$89$	−1.71051	+	1.43529i	−0.181314	+	0.152140i	−0.728927	−	0.684591i	$-0.759981\pi$
$89$	−1.71051	+	1.43529i	−0.181314	+	0.152140i	0.547614	+	0.836731i	$0.315536\pi$
$90$		0			0
$91$	−2.31522	−	0.842670i	−0.242701	−	0.0883358i
$92$	7.63537	+	6.40684i	0.796043	+	0.667959i
$93$	−2.42551	+	13.7558i	−0.251514	+	1.42641i
$94$	−1.65487			−0.170687
$95$		0			0
$96$	7.71591			0.787501
$97$	−1.49508	+	8.47901i	−0.151802	+	0.860913i	0.809849	+	0.586638i	$0.199549\pi$
$97$	−1.49508	+	8.47901i	−0.151802	+	0.860913i	−0.961651	+	0.274275i	$0.911562\pi$
$98$	0.605917	+	0.508425i	0.0612069	+	0.0513587i
$99$	−17.8958	−	6.51353i	−1.79859	−	0.654635i
$100$		0			0
$101$	−10.3041	+	8.64614i	−1.02529	+	0.860323i	−0.990283	−	0.139064i	$-0.955591\pi$
$101$	−10.3041	+	8.64614i	−1.02529	+	0.860323i	−0.0350095	+	0.999387i	$0.511146\pi$
$102$	0.823518	+	1.42637i	0.0815404	+	0.141232i
$103$	−2.01789	+	3.49510i	−0.198829	+	0.344382i	−0.948149	−	0.317826i	$-0.897047\pi$
$103$	−2.01789	+	3.49510i	−0.198829	+	0.344382i	0.749320	+	0.662208i	$0.230381\pi$
$104$	−0.212409	−	1.20463i	−0.0208285	−	0.118124i
$105$		0			0
$106$	0.0843204	−	0.146047i	0.00818992	−	0.0141854i
$107$	−8.47947	−	14.6869i	−0.819741	−	1.41983i	−0.905873	−	0.423550i	$-0.860784\pi$
$107$	−8.47947	−	14.6869i	−0.819741	−	1.41983i	0.0861313	−	0.996284i	$-0.472550\pi$
$108$	6.09960	−	5.11817i	0.586934	−	0.492496i
$109$	−6.42343	+	2.33794i	−0.615253	+	0.223934i	−0.630800	−	0.775945i	$-0.717273\pi$
$109$	−6.42343	+	2.33794i	−0.615253	+	0.223934i	0.0155471	+	0.999879i	$0.495051\pi$
$110$		0			0
$111$	−23.1388	−	19.4158i	−2.19624	−	1.84287i
$112$	−1.22808	+	6.96476i	−0.116042	+	0.658108i
$113$	5.92416			0.557298			0.278649	−	0.960393i	$-0.410113\pi$
$113$	5.92416			0.557298			0.278649	+	0.960393i	$0.410113\pi$
$114$	−0.895159	−	2.77746i	−0.0838394	−	0.260133i
$115$		0			0
$116$	−2.91138	+	16.5113i	−0.270315	+	1.53303i
$117$	−4.37603	−	3.67193i	−0.404564	−	0.339470i
$118$	1.19309	+	0.434249i	0.109833	+	0.0399758i
$119$	−4.48561	+	1.63263i	−0.411195	+	0.149663i
$120$		0			0
$121$	−3.46054	−	5.99383i	−0.314594	−	0.544893i
$122$	0.342612	−	0.593422i	0.0310186	−	0.0537259i
$123$	−1.18801	−	6.73756i	−0.107120	−	0.607505i
$124$	−1.71856	−	9.74645i	−0.154331	−	0.875257i
$125$		0			0
$126$	−1.06697	−	1.84805i	−0.0950536	−	0.164638i
$127$	−14.6929	+	12.3288i	−1.30378	+	1.09400i	−0.314303	+	0.949323i	$0.601771\pi$
$127$	−14.6929	+	12.3288i	−1.30378	+	1.09400i	−0.989479	+	0.144680i	$0.953785\pi$
$128$	−6.81203	+	2.47938i	−0.602104	+	0.219148i
$129$	11.4992	+	4.18537i	1.01245	+	0.368501i
$130$		0			0
$131$	−0.0534819	+	0.303311i	−0.00467273	+	0.0265004i	−0.987055	−	0.160382i	$-0.948727\pi$
$131$	−0.0534819	+	0.303311i	−0.00467273	+	0.0265004i	0.982382	+	0.186883i	$0.0598384\pi$
$132$	22.4920			1.95767
$133$	8.37791	−	1.15714i	0.726457	−	0.100337i
$134$	1.27428			0.110081
$135$		0			0
$136$	−1.81546	−	1.52335i	−0.155674	−	0.130626i
$137$	13.6249	+	4.95907i	1.16406	+	0.423682i	0.850545	−	0.525902i	$-0.176272\pi$
$137$	13.6249	+	4.95907i	1.16406	+	0.423682i	0.313512	+	0.949584i	$0.398494\pi$
$138$	3.23176	−	1.17626i	0.275106	−	0.100130i
$139$	12.1014	−	10.1543i	1.02643	−	0.861278i	0.0360091	−	0.999351i	$-0.488535\pi$
$139$	12.1014	−	10.1543i	1.02643	−	0.861278i	0.990422	+	0.138074i	$0.0440910\pi$
$140$		0			0
$141$	9.26802	−	16.0527i	0.780508	−	1.35188i
$142$	−0.0336192	−	0.190664i	−0.00282126	−	0.0160002i
$143$	−0.933460	−	5.29391i	−0.0780598	−	0.442699i
$144$	−8.19871	+	14.2006i	−0.683226	+	1.18338i
$145$		0			0
$146$	−0.265144	+	0.222483i	−0.0219435	+	0.0184128i
$147$	−8.32527	+	3.03015i	−0.686657	+	0.249923i
$148$	20.1111	+	7.31983i	1.65312	+	0.601686i
$149$	−9.54872	−	8.01233i	−0.782262	−	0.656396i	0.161555	−	0.986864i	$-0.448349\pi$
$149$	−9.54872	−	8.01233i	−0.782262	−	0.656396i	−0.943817	+	0.330468i	$0.892793\pi$
$150$		0			0
$151$	13.8400			1.12629			0.563143	−	0.826360i	$-0.309592\pi$
$151$	13.8400			1.12629			0.563143	+	0.826360i	$0.309592\pi$
$152$	2.57724	+	3.31492i	0.209042	+	0.268876i
$153$	−11.0677			−0.894767
$154$	0.348701	−	1.97758i	0.0280991	−	0.159358i
$155$		0			0
$156$	6.33978	+	2.30749i	0.507589	+	0.184747i
$157$	17.0996	−	6.22373i	1.36469	−	0.496708i	0.447191	−	0.894438i	$-0.352424\pi$
$157$	17.0996	−	6.22373i	1.36469	−	0.496708i	0.917502	+	0.397731i	$0.130202\pi$
$158$	1.13547	−	0.952772i	0.0903331	−	0.0757985i
$159$	0.944465	+	1.63586i	0.0749010	+	0.129732i
$160$		0			0
$161$	1.73084	+	9.81605i	0.136409	+	0.773613i
$162$	0.0958613	+	0.543656i	0.00753158	+	0.0427137i
$163$	7.66687	−	13.2794i	0.600516	−	1.04012i	−0.392227	−	0.919868i	$-0.628295\pi$
$163$	7.66687	−	13.2794i	0.600516	−	1.04012i	0.992743	−	0.120256i	$-0.0383714\pi$
$164$	2.42372	+	4.19801i	0.189261	+	0.327809i
$165$		0			0
$166$	2.72285	−	0.991038i	0.211334	−	0.0769195i
$167$	5.84198	+	2.12631i	0.452066	+	0.164539i	0.558011	−	0.829833i	$-0.311565\pi$
$167$	5.84198	+	2.12631i	0.452066	+	0.164539i	−0.105945	+	0.994372i	$0.533787\pi$
$168$	3.92074	+	3.28989i	0.302492	+	0.253821i
$169$	−1.97743	+	11.2145i	−0.152110	+	0.862657i
$170$		0			0
$171$	19.1709	+	4.12255i	1.46604	+	0.315259i
$172$	−8.67048			−0.661118
$173$	0.480317	−	2.72401i	0.0365178	−	0.207103i	−0.961090	−	0.276237i	$-0.910913\pi$
$173$	0.480317	−	2.72401i	0.0365178	−	0.207103i	0.997607	+	0.0691341i	$0.0220236\pi$
$174$	4.43159	+	3.71855i	0.335958	+	0.281902i
$175$		0			0
$176$	−14.4997	+	5.27747i	−1.09296	+	0.397805i
$177$	−10.8942	+	9.14129i	−0.818856	+	0.687102i
$178$	−0.272948	−	0.472760i	−0.0204583	−	0.0354349i
$179$	5.68916	−	9.85392i	0.425228	−	0.736516i	−0.571214	−	0.820801i	$-0.693527\pi$
$179$	5.68916	−	9.85392i	0.425228	−	0.736516i	0.996442	+	0.0842849i	$0.0268606\pi$
$180$		0			0
$181$	0.619323	+	3.51236i	0.0460339	+	0.261071i	0.999135	−	0.0415803i	$-0.0132392\pi$
$181$	0.619323	+	3.51236i	0.0460339	+	0.261071i	−0.953101	+	0.302652i	$0.902128\pi$
$182$	0.301172	−	0.521645i	0.0223243	−	0.0386669i
$183$	3.83757	+	6.64686i	0.283681	+	0.491350i
$184$	−3.79085	+	3.18090i	−0.279466	+	0.234499i
$185$		0			0
$186$	−3.20891	−	1.16795i	−0.235289	−	0.0856381i
$187$	−7.97827	−	6.69456i	−0.583429	−	0.489555i
$188$	−2.28060	+	12.9339i	−0.166330	+	0.943303i
$189$	7.96263			0.579196
$190$		0			0
$191$	−8.67323			−0.627573			−0.313786	−	0.949494i	$-0.601598\pi$
$191$	−8.67323			−0.627573			−0.313786	+	0.949494i	$0.601598\pi$
$192$	3.13888	−	17.8015i	0.226529	−	1.28471i
$193$	−0.323355	−	0.271327i	−0.0232756	−	0.0195306i	0.631076	−	0.775721i	$-0.282614\pi$
$193$	−0.323355	−	0.271327i	−0.0232756	−	0.0195306i	−0.654351	+	0.756191i	$0.727058\pi$
$194$	−1.97796	−	0.719919i	−0.142009	−	0.0516872i
$195$		0			0
$196$	4.80871	−	4.03498i	0.343479	−	0.288213i
$197$	−7.62075	−	13.1995i	−0.542956	−	0.940427i	−0.998732	−	0.0503329i	$-0.983972\pi$
$197$	−7.62075	−	13.1995i	−0.542956	−	0.940427i	0.455777	−	0.890094i	$-0.349362\pi$
$198$	2.32795	−	4.03213i	0.165440	−	0.286551i
$199$	2.24465	+	12.7301i	0.159119	+	0.902410i	0.954923	+	0.296855i	$0.0959378\pi$
$199$	2.24465	+	12.7301i	0.159119	+	0.902410i	−0.795803	+	0.605555i	$0.792951\pi$
$200$		0			0
$201$	−7.13656	+	12.3609i	−0.503374	+	0.871869i
$202$	−1.64423	−	2.84789i	−0.115688	−	0.200377i
$203$	−12.8438	+	10.7772i	−0.901455	+	0.756410i
$204$	12.2830	−	4.47064i	0.859981	−	0.313007i
$205$		0			0
$206$	−0.755824	−	0.634212i	−0.0526608	−	0.0441876i
$207$	−4.01306	+	22.7592i	−0.278927	+	1.58188i
$208$	−4.62845			−0.320926
$209$	11.3260	+	14.5678i	0.783436	+	1.00768i
$210$		0			0
$211$	−0.772073	+	4.37864i	−0.0531517	+	0.301438i	−0.999782	−	0.0208833i	$-0.993352\pi$
$211$	−0.772073	+	4.37864i	−0.0531517	+	0.301438i	0.946630	+	0.322322i	$0.104463\pi$
$212$	−1.02525	−	0.860290i	−0.0704148	−	0.0590850i
$213$	2.03778	+	0.741690i	0.139626	+	0.0508198i
$214$	3.89604	−	1.41804i	0.266328	−	0.0969353i
$215$		0			0
$216$	1.97662	+	3.42361i	0.134492	+	0.232947i
$217$	4.94851	−	8.57106i	0.335926	−	0.581842i
$218$	−0.290195	−	1.64578i	−0.0196545	−	0.111466i
$219$	−0.673212	−	3.81798i	−0.0454915	−	0.257995i
$220$		0			0
$221$	−1.56202	−	2.70550i	−0.105073	−	0.181991i
$222$	5.65692	−	4.74672i	0.379668	−	0.318579i
$223$	−8.64417	+	3.14622i	−0.578856	+	0.210687i	−0.614821	−	0.788667i	$-0.710772\pi$
$223$	−8.64417	+	3.14622i	−0.578856	+	0.210687i	0.0359647	+	0.999353i	$0.488550\pi$
$224$	−5.13740	−	1.86986i	−0.343257	−	0.124935i
$225$		0			0
$226$	−0.251499	+	1.42632i	−0.0167294	+	0.0948774i
$227$	0.600308			0.0398438			0.0199219	−	0.999802i	$-0.493658\pi$
$227$	0.600308			0.0398438			0.0199219	+	0.999802i	$0.493658\pi$
$228$	−22.9413	+	3.16862i	−1.51933	+	0.209847i
$229$	−7.11499			−0.470172			−0.235086	−	0.971975i	$-0.575537\pi$
$229$	−7.11499			−0.470172			−0.235086	+	0.971975i	$0.575537\pi$
$230$		0			0
$231$	17.2302	+	14.4579i	1.13366	+	0.951257i
$232$	−7.82207	−	2.84700i	−0.513544	−	0.186915i
$233$	18.9501	−	6.89726i	1.24146	−	0.451854i	0.363952	−	0.931418i	$-0.381427\pi$
$233$	18.9501	−	6.89726i	1.24146	−	0.451854i	0.877507	+	0.479563i	$0.159205\pi$
$234$	1.06984	−	0.897702i	0.0699376	−	0.0586846i
$235$		0			0
$236$	5.03816	−	8.72635i	0.327956	−	0.568037i
$237$	2.88300	+	16.3503i	0.187271	+	1.06207i
$238$	−0.202649	−	1.14928i	−0.0131358	−	0.0744967i
$239$	5.81710	−	10.0755i	0.376277	−	0.651731i	−0.614240	−	0.789119i	$-0.710537\pi$
$239$	5.81710	−	10.0755i	0.376277	−	0.651731i	0.990517	+	0.137388i	$0.0438707\pi$
$240$		0			0
$241$	19.5572	−	16.4104i	1.25979	−	1.05709i	0.264084	−	0.964500i	$-0.414930\pi$
$241$	19.5572	−	16.4104i	1.25979	−	1.05709i	0.995704	−	0.0925884i	$-0.0295141\pi$
$242$	1.59000	−	0.578714i	0.102209	−	0.0372011i
$243$	−17.3796	−	6.32567i	−1.11490	−	0.405792i
$244$	−4.16583	−	3.49555i	−0.266690	−	0.223779i
$245$		0			0
$246$	1.67259			0.106640
$247$	1.69791	+	5.26818i	0.108035	+	0.335206i
$248$	4.91362			0.312015
$249$	−5.63588	+	31.9627i	−0.357160	+	2.02555i
$250$		0			0
$251$	−14.4509	−	5.25969i	−0.912131	−	0.331988i	−0.157027	−	0.987594i	$-0.550191\pi$
$251$	−14.4509	−	5.25969i	−0.912131	−	0.331988i	−0.755103	+	0.655606i	$0.772413\pi$
$252$	−15.9142	+	5.79229i	−1.00250	+	0.364880i
$253$	−16.6594	+	13.9789i	−1.04737	+	0.878845i
$254$	−2.34456	−	4.06090i	−0.147111	−	0.254803i
$255$		0			0
$256$	1.98477	+	11.2562i	0.124048	+	0.703512i
$257$	−2.78765	−	15.8096i	−0.173889	−	0.986173i	−0.939419	−	0.342772i	$-0.888634\pi$
$257$	−2.78765	−	15.8096i	−0.173889	−	0.986173i	0.765530	−	0.643401i	$-0.222477\pi$
$258$	−1.49586	+	2.59090i	−0.0931280	+	0.161302i
$259$	10.7011	+	18.5348i	0.664934	+	1.15170i
$260$		0			0
$261$	−36.5295	+	13.2957i	−2.26112	+	0.822981i
$262$	−0.0707556	−	0.0257529i	−0.00437129	−	0.00159102i
$263$	−10.9082	−	9.15308i	−0.672629	−	0.564403i	0.241213	−	0.970472i	$-0.422455\pi$
$263$	−10.9082	−	9.15308i	−0.672629	−	0.564403i	−0.913842	+	0.406069i	$0.866899\pi$
$264$	−1.93912	+	10.9973i	−0.119344	+	0.676836i
$265$		0			0
$266$	−0.0770701	+	2.06622i	−0.00472547	+	0.126688i
$267$	6.11453			0.374203
$268$	1.75611	−	9.95937i	0.107271	−	0.608365i
$269$	12.4416	+	10.4398i	0.758579	+	0.636523i	0.937756	−	0.347294i	$-0.112899\pi$
$269$	12.4416	+	10.4398i	0.758579	+	0.636523i	−0.179178	+	0.983817i	$0.557344\pi$
$270$		0			0
$271$	5.56796	−	2.02657i	0.338230	−	0.123106i	−0.167321	−	0.985902i	$-0.553512\pi$
$271$	5.56796	−	2.02657i	0.338230	−	0.123106i	0.505551	+	0.862797i	$0.331289\pi$
$272$	−6.86941	+	5.76412i	−0.416519	+	0.349501i
$273$	3.37340	+	5.84290i	0.204167	+	0.353628i
$274$	−1.77238	+	3.06985i	−0.107073	+	0.185457i
$275$		0			0
$276$	−4.73956	−	26.8794i	−0.285288	−	1.61795i
$277$	−3.15468	+	5.46407i	−0.189546	+	0.328304i	−0.945099	−	0.326784i	$-0.894035\pi$
$277$	−3.15468	+	5.46407i	−0.189546	+	0.328304i	0.755553	+	0.655088i	$0.227368\pi$
$278$	1.93104	+	3.34466i	0.115816	+	0.200600i
$279$	17.5784	−	14.7500i	1.05239	−	0.883059i
$280$		0			0
$281$	2.51801	+	0.916481i	0.150212	+	0.0546727i	0.416032	−	0.909350i	$-0.363420\pi$
$281$	2.51801	+	0.916481i	0.150212	+	0.0546727i	−0.265820	+	0.964023i	$0.585643\pi$
$282$	3.47144	+	2.91288i	0.206721	+	0.173460i
$283$	5.39425	−	30.5923i	0.320655	−	1.81853i	−0.217942	−	0.975962i	$-0.569934\pi$
$283$	5.39425	−	30.5923i	0.320655	−	1.81853i	0.538597	−	0.842564i	$-0.318955\pi$
$284$	−1.53650			−0.0911745
$285$		0			0
$286$	1.31421			0.0777107
$287$	−0.841767	+	4.77390i	−0.0496880	+	0.281794i
$288$	−9.71029	−	8.14790i	−0.572184	−	0.480120i
$289$	10.2871	+	3.74421i	0.605126	+	0.220248i
$290$		0			0
$291$	18.0609	−	15.1549i	1.05875	−	0.888396i
$292$	1.37345	+	2.37889i	0.0803752	+	0.139214i
$293$	−0.432825	+	0.749675i	−0.0252859	+	0.0437965i	−0.878391	−	0.477942i	$-0.841383\pi$
$293$	−0.432825	+	0.749675i	−0.0252859	+	0.0437965i	0.853106	+	0.521738i	$0.174716\pi$
$294$	−0.376116	−	2.13306i	−0.0219355	−	0.124402i
$295$		0			0
$296$	−5.31283	+	9.20209i	−0.308802	+	0.534861i
$297$	8.68652	+	15.0455i	0.504043	+	0.873029i
$298$	2.33445	−	1.95883i	0.135231	−	0.113472i
$299$	−6.12988	+	2.23110i	−0.354500	+	0.129028i
$300$		0			0
$301$	−6.64212	−	5.57340i	−0.382845	−	0.321245i
$302$	−0.587551	+	3.33217i	−0.0338098	+	0.191745i
$303$	36.8338			2.11605
$304$	14.0460	−	7.42561i	0.805591	−	0.425888i
$305$		0			0
$306$	0.469856	−	2.66468i	0.0268599	−	0.152330i
$307$	−6.88828	−	5.77995i	−0.393135	−	0.329879i	0.424698	−	0.905335i	$-0.360380\pi$
$307$	−6.88828	−	5.77995i	−0.393135	−	0.329879i	−0.817833	+	0.575456i	$0.804825\pi$
$308$	−14.9756	−	5.45067i	−0.853313	−	0.310581i
$309$	10.3850	−	3.77983i	0.590781	−	0.215027i
$310$		0			0
$311$	5.72035	+	9.90793i	0.324371	+	0.561827i	0.981385	−	0.192051i	$-0.0615140\pi$
$311$	5.72035	+	9.90793i	0.324371	+	0.561827i	−0.657014	+	0.753879i	$0.728181\pi$
$312$	−1.67481	+	2.90086i	−0.0948174	+	0.164229i
$313$	1.36578	+	7.74572i	0.0771984	+	0.437814i	0.998769	+	0.0496032i	$0.0157957\pi$
$313$	1.36578	+	7.74572i	0.0771984	+	0.437814i	−0.921571	+	0.388211i	$0.873093\pi$
$314$	0.772517	+	4.38116i	0.0435956	+	0.247243i
$315$		0			0
$316$	−5.88175	−	10.1875i	−0.330874	−	0.573091i
$317$	12.6600	−	10.6230i	0.711056	−	0.596647i	−0.213839	−	0.976869i	$-0.568597\pi$
$317$	12.6600	−	10.6230i	0.711056	−	0.596647i	0.924895	+	0.380222i	$0.124152\pi$
$318$	−0.433951	+	0.157945i	−0.0243347	+	0.00885712i
$319$	−34.3750	−	12.5115i	−1.92463	−	0.700509i
$320$		0			0
$321$	−8.06419	+	45.7343i	−0.450099	+	2.55264i
$322$	−2.43682			−0.135799
$323$	9.08079	+	5.70435i	0.505269	+	0.317399i
$324$	4.38115			0.243397
$325$		0			0
$326$	2.87171	+	2.40965i	0.159049	+	0.133458i
$327$	17.5897	+	6.40213i	0.972713	+	0.354039i
$328$	−2.26155	+	0.823135i	−0.124873	+	0.0454500i
$329$	−10.0610	+	8.44219i	−0.554682	+	0.465433i
$330$		0			0
$331$	−3.95723	+	6.85412i	−0.217509	+	0.376736i	−0.954046	−	0.299661i	$-0.903126\pi$
$331$	−3.95723	+	6.85412i	−0.217509	+	0.376736i	0.736537	+	0.676397i	$0.236460\pi$
$332$	−3.99322	−	22.6467i	−0.219157	−	1.24290i
$333$	8.61686	+	48.8686i	0.472201	+	2.67798i
$334$	−0.759946	+	1.31627i	−0.0415824	+	0.0720228i
$335$		0			0
$336$	14.8354	−	12.4484i	0.809340	−	0.679117i
$337$	17.8880	−	6.51071i	0.974423	−	0.354661i	0.194754	−	0.980852i	$-0.437609\pi$
$337$	17.8880	−	6.51071i	0.974423	−	0.354661i	0.779670	+	0.626191i	$0.215387\pi$
$338$	−2.61610	−	0.952183i	−0.142297	−	0.0517919i
$339$	−12.4272	−	10.4276i	−0.674952	−	0.566352i
$340$		0			0
$341$	21.5935			1.16936
$342$	−1.80642	+	4.44064i	−0.0976801	+	0.240122i
$343$	19.8594			1.07230
$344$	0.747516	−	4.23937i	0.0403034	−	0.228572i
$345$		0			0
$346$	0.635451	+	0.231285i	0.0341621	+	0.0124340i
$347$	5.13467	−	1.86887i	0.275644	−	0.100326i	−0.200500	−	0.979694i	$-0.564257\pi$
$347$	5.13467	−	1.86887i	0.275644	−	0.100326i	0.476143	+	0.879368i	$0.342034\pi$
$348$	35.1702	−	29.5113i	1.88532	−	1.58197i
$349$	3.13218	+	5.42509i	0.167662	+	0.290398i	0.937597	−	0.347723i	$-0.113045\pi$
$349$	3.13218	+	5.42509i	0.167662	+	0.290398i	−0.769936	+	0.638121i	$0.779712\pi$
$350$		0			0
$351$	0.904915	+	5.13203i	0.0483008	+	0.273927i
$352$	−2.07132	−	11.7470i	−0.110402	−	0.626120i
$353$	4.14699	−	7.18280i	0.220722	−	0.382302i	−0.734305	−	0.678819i	$-0.762492\pi$
$353$	4.14699	−	7.18280i	0.220722	−	0.382302i	0.955027	+	0.296517i	$0.0958253\pi$
$354$	−1.73840	−	3.01099i	−0.0923947	−	0.160032i
$355$		0			0
$356$	−4.07109	+	1.48176i	−0.215767	+	0.0785329i
$357$	12.2832	+	4.47073i	0.650098	+	0.236616i
$358$	2.13094	+	1.78807i	0.112624	+	0.0945024i
$359$	2.27231	−	12.8869i	0.119928	−	0.680145i	−0.864264	−	0.503039i	$-0.832215\pi$
$359$	2.27231	−	12.8869i	0.119928	−	0.680145i	0.984192	−	0.177106i	$-0.0566735\pi$
$360$		0			0
$361$	−13.6046	−	13.2633i	−0.716030	−	0.698069i
$362$	−0.871938			−0.0458281
$363$	−3.29106	+	18.6645i	−0.172736	+	0.979633i
$364$	−3.66196	−	3.07275i	−0.191939	−	0.161056i
$365$		0			0
$366$	−1.76324	+	0.641765i	−0.0921658	+	0.0335456i
$367$	19.9893	−	16.7730i	1.04343	−	0.875545i	0.0510458	−	0.998696i	$-0.483745\pi$
$367$	19.9893	−	16.7730i	1.04343	−	0.875545i	0.992388	+	0.123151i	$0.0393001\pi$
$368$	9.36236	+	16.2161i	0.488047	+	0.845322i
$369$	−5.61969	+	9.73359i	−0.292549	+	0.506710i
$370$		0			0
$371$	−0.232411	−	1.31807i	−0.0120662	−	0.0684307i
$372$	−13.5505	+	23.4702i	−0.702563	+	1.21687i
$373$	−13.5984	−	23.5532i	−0.704100	−	1.21954i	−0.967015	−	0.254718i	$-0.918017\pi$
$373$	−13.5984	−	23.5532i	−0.704100	−	1.21954i	0.262915	−	0.964819i	$-0.415316\pi$
$374$	1.95051	−	1.63667i	0.100858	−	0.0846301i
$375$		0			0
$376$	−6.12733	−	2.23017i	−0.315993	−	0.115012i
$377$	−8.40568	−	7.05320i	−0.432915	−	0.363258i
$378$	−0.338038	+	1.91711i	−0.0173868	+	0.0986054i
$379$	13.6999			0.703714			0.351857	−	0.936054i	$-0.385550\pi$
$379$	13.6999			0.703714			0.351857	+	0.936054i	$0.385550\pi$
$380$		0			0
$381$	52.5224			2.69080
$382$	0.368205	−	2.08819i	0.0188390	−	0.106841i
$383$	7.85310	+	6.58953i	0.401275	+	0.336709i	0.820986	−	0.570948i	$-0.193424\pi$
$383$	7.85310	+	6.58953i	0.401275	+	0.336709i	−0.419711	+	0.907658i	$0.637869\pi$
$384$	18.6538	+	6.78945i	0.951925	+	0.346472i
$385$		0			0
$386$	0.0790530	−	0.0663333i	0.00402369	−	0.00337628i
$387$	−10.0518	−	17.4102i	−0.510961	−	0.885010i
$388$	−8.35251	+	14.4670i	−0.424035	+	0.734449i
$389$	−0.878089	−	4.97989i	−0.0445209	−	0.252490i	0.954422	−	0.298461i	$-0.0964732\pi$
$389$	−0.878089	−	4.97989i	−0.0445209	−	0.252490i	−0.998943	+	0.0459703i	$0.985362\pi$
$390$		0			0
$391$	−6.31925	+	10.9453i	−0.319578	+	0.553526i
$392$	1.55830	+	2.69905i	0.0787060	+	0.136323i
$393$	0.646074	−	0.542120i	0.0325901	−	0.0273463i
$394$	3.50148	−	1.27444i	0.176402	−	0.0642051i
$395$		0			0
$396$	−28.3056	−	23.7512i	−1.42241	−	1.19354i
$397$	4.14599	−	23.5131i	0.208081	−	1.18009i	−0.684435	−	0.729073i	$-0.739951\pi$
$397$	4.14599	−	23.5131i	0.208081	−	1.18009i	0.892517	−	0.451014i	$-0.148938\pi$
$398$	−3.16022			−0.158408
$399$	−19.6112	−	12.3194i	−0.981790	−	0.616739i
$400$		0			0
$401$	−4.30049	+	24.3893i	−0.214756	+	1.21794i	0.666573	+	0.745440i	$0.267760\pi$
$401$	−4.30049	+	24.3893i	−0.214756	+	1.21794i	−0.881329	+	0.472503i	$0.843351\pi$
$402$	−2.67307	−	2.24298i	−0.133321	−	0.111869i
$403$	6.08655	+	2.21532i	0.303192	+	0.110353i
$404$	−24.5241	+	8.92606i	−1.22012	+	0.444088i
$405$		0			0
$406$	−2.04949	−	3.54983i	−0.101715	−	0.176175i
$407$	−23.3479	+	40.4398i	−1.15731	+	2.00452i
$408$	1.12692	+	6.39111i	0.0557911	+	0.316407i
$409$	−1.71911	−	9.74958i	−0.0850047	−	0.482086i	−0.997356	−	0.0726764i	$-0.976846\pi$
$409$	−1.71911	−	9.74958i	−0.0850047	−	0.482086i	0.912351	−	0.409409i	$-0.134265\pi$
$410$		0			0
$411$	−19.8523	−	34.3852i	−0.979241	−	1.69609i
$412$	−5.99841	+	5.03326i	−0.295520	+	0.247971i
$413$	9.46884	−	3.44637i	0.465931	−	0.169585i
$414$	−5.30921	−	1.93240i	−0.260934	−	0.0949721i
$415$		0			0
$416$	0.621311	−	3.52363i	0.0304623	−	0.172760i
$417$	−43.2588			−2.11839
$418$	−3.98822	+	2.10843i	−0.195070	+	0.103127i
$419$	4.00810			0.195808			0.0979042	−	0.995196i	$-0.468786\pi$
$419$	4.00810			0.195808			0.0979042	+	0.995196i	$0.468786\pi$
$420$		0			0
$421$	15.5339	+	13.0345i	0.757077	+	0.635263i	0.937364	−	0.348351i	$-0.113258\pi$
$421$	15.5339	+	13.0345i	0.757077	+	0.635263i	−0.180287	+	0.983614i	$0.557703\pi$
$422$	−1.02144	−	0.371774i	−0.0497229	−	0.0180977i
$423$	−28.6150	+	10.4150i	−1.39131	+	0.506395i
$424$	0.509024	−	0.427122i	0.0247204	−	0.0207429i
$425$		0			0
$426$	−0.265082	+	0.459135i	−0.0128432	+	0.0222451i
$427$	−0.944337	−	5.35560i	−0.0456997	−	0.259176i
$428$	−5.71377	−	32.4044i	−0.276185	−	1.56632i
$429$	−7.36016	+	12.7482i	−0.355352	+	0.615487i
$430$		0			0
$431$	10.3250	−	8.66371i	0.497338	−	0.417316i	−0.359309	−	0.933219i	$-0.616988\pi$
$431$	10.3250	−	8.66371i	0.497338	−	0.417316i	0.856648	+	0.515902i	$0.172543\pi$
$432$	14.0563	−	5.11609i	0.676286	−	0.246148i
$433$	−32.3043	−	11.7578i	−1.55245	−	0.565045i	−0.583458	−	0.812144i	$-0.698301\pi$
$433$	−32.3043	−	11.7578i	−1.55245	−	0.565045i	−0.968990	+	0.247099i	$0.920523\pi$
$434$	1.85352	+	1.55529i	0.0889717	+	0.0746561i
$435$		0			0
$436$	−13.2628			−0.635172
$437$	15.0229	−	16.6051i	0.718643	−	0.794330i
$438$	0.947808			0.0452880
$439$	4.06648	−	23.0621i	0.194082	−	1.10070i	−0.719637	−	0.694350i	$-0.755692\pi$
$439$	4.06648	−	23.0621i	0.194082	−	1.10070i	0.913720	−	0.406345i	$-0.133197\pi$
$440$		0			0
$441$	13.6770	+	4.97801i	0.651284	+	0.237048i
$442$	0.717696	−	0.261220i	0.0341373	−	0.0124250i
$443$	−1.83765	+	1.54197i	−0.0873093	+	0.0732612i	−0.685398	−	0.728169i	$-0.740372\pi$
$443$	−1.83765	+	1.54197i	−0.0873093	+	0.0732612i	0.598088	+	0.801430i	$0.295927\pi$
$444$	−29.3029	−	50.7542i	−1.39066	−	2.40869i
$445$		0			0
$446$	−0.390523	−	2.21476i	−0.0184918	−	0.104872i
$447$	5.92725	+	33.6151i	0.280349	+	1.58994i
$448$	−6.40391	+	11.0919i	−0.302557	+	0.524043i
$449$	−19.1010	−	33.0838i	−0.901430	−	1.56132i	−0.825638	−	0.564200i	$-0.809185\pi$
$449$	−19.1010	−	33.0838i	−0.901430	−	1.56132i	−0.0757922	−	0.997124i	$-0.524149\pi$
$450$		0			0
$451$	−9.93864	+	3.61737i	−0.467992	+	0.170335i
$452$	10.8011	+	3.93126i	0.508039	+	0.184911i
$453$	−29.0324	−	24.3611i	−1.36406	−	1.14458i
$454$	−0.0254849	+	0.144532i	−0.00119606	+	0.00678322i
$455$		0			0
$456$	0.428585	−	11.4902i	0.0200703	−	0.538077i
$457$	1.87605			0.0877581			0.0438790	−	0.999037i	$-0.486028\pi$
$457$	1.87605			0.0877581			0.0438790	+	0.999037i	$0.486028\pi$
$458$	0.302053	−	1.71303i	0.0141140	−	0.0800445i
$459$	7.73430	+	6.48984i	0.361006	+	0.302920i
$460$		0			0
$461$	−15.8060	+	5.75290i	−0.736157	+	0.267939i	−0.682769	−	0.730634i	$-0.739224\pi$
$461$	−15.8060	+	5.75290i	−0.736157	+	0.267939i	−0.0533885	+	0.998574i	$0.517002\pi$
$462$	−4.21239	+	3.53462i	−0.195978	+	0.164445i
$463$	12.1821	+	21.0999i	0.566148	+	0.980598i	0.996942	+	0.0781471i	$0.0249004\pi$
$463$	12.1821	+	21.0999i	0.566148	+	0.980598i	−0.430794	+	0.902450i	$0.641766\pi$
$464$	−15.7485	+	27.2771i	−0.731104	+	1.26631i
$465$		0			0
$466$	0.856118	+	4.85529i	0.0396589	+	0.224917i
$467$	−6.82553	+	11.8222i	−0.315848	+	0.547065i	−0.979617	−	0.200873i	$-0.935622\pi$
$467$	−6.82553	+	11.8222i	−0.315848	+	0.547065i	0.663770	+	0.747937i	$0.268956\pi$
$468$	−5.54179	−	9.59866i	−0.256169	−	0.443698i
$469$	7.74717	−	6.50065i	0.357731	−	0.300172i
$470$		0			0
$471$	−46.8249	−	17.0429i	−2.15758	−	0.785293i
$472$	3.83233	+	3.21570i	0.176397	+	0.148015i
$473$	3.28505	−	18.6305i	0.151047	−	0.856629i
$474$	−4.05895			−0.186434
$475$		0			0
$476$	−9.26166			−0.424507
$477$	0.538862	−	3.05604i	0.0246728	−	0.139926i
$478$	2.17886	+	1.82828i	0.0996587	+	0.0836236i
$479$	20.4294	+	7.43570i	0.933444	+	0.339746i	0.763574	−	0.645720i	$-0.223443\pi$
$479$	20.4294	+	7.43570i	0.933444	+	0.339746i	0.169870	+	0.985466i	$0.445665\pi$
$480$		0			0
$481$	−10.7298	+	9.00341i	−0.489239	+	0.410520i
$482$	3.12076	+	5.40532i	0.142147	+	0.246206i
$483$	13.6473	−	23.6378i	0.620974	−	1.07556i
$484$	−2.33183	−	13.2245i	−0.105992	−	0.601112i
$485$		0			0
$486$	2.26080	−	3.91583i	0.102552	−	0.177626i
$487$	14.6227	+	25.3273i	0.662618	+	1.14769i	0.979925	+	0.199366i	$0.0638882\pi$
$487$	14.6227	+	25.3273i	0.662618	+	1.14769i	−0.317307	+	0.948323i	$0.602778\pi$
$488$	2.06828	−	1.73549i	0.0936264	−	0.0785619i
$489$	−39.4572	+	14.3612i	−1.78431	+	0.649437i
$490$		0			0
$491$	−14.0612	−	11.7987i	−0.634572	−	0.532469i	0.267774	−	0.963482i	$-0.413712\pi$
$491$	−14.0612	−	11.7987i	−0.634572	−	0.532469i	−0.902346	+	0.431012i	$0.858157\pi$
$492$	2.30502	−	13.0724i	0.103918	−	0.589350i
$493$	−21.2593			−0.957469
$494$	−1.34046	+	0.185143i	−0.0603104	+	0.00832997i
$495$		0			0
$496$	3.22853	−	18.3099i	0.144965	−	0.822138i
$497$	−1.17705	−	0.987664i	−0.0527980	−	0.0443028i
$498$	−7.45618	−	2.71383i	−0.334119	−	0.121609i
$499$	−9.78774	+	3.56245i	−0.438159	+	0.159477i	−0.551675	−	0.834059i	$-0.686011\pi$
$499$	−9.78774	+	3.56245i	−0.438159	+	0.159477i	0.113516	+	0.993536i	$0.463789\pi$
$500$		0			0
$501$	−8.51208	−	14.7434i	−0.380292	−	0.658685i
$502$	1.87982	−	3.25595i	0.0839006	−	0.145320i
$503$	0.756638	+	4.29111i	0.0337368	+	0.191331i	0.997019	−	0.0771614i	$-0.0245857\pi$
$503$	0.756638	+	4.29111i	0.0337368	+	0.191331i	−0.963282	+	0.268492i	$0.913475\pi$
$504$	−1.46008	−	8.28051i	−0.0650370	−	0.368843i
$505$		0			0
$506$	−2.65836	−	4.60441i	−0.118178	−	0.204691i
$507$	23.8878	−	20.0442i	1.06089	−	0.890196i
$508$	−34.9697	+	12.7279i	−1.55153	+	0.564711i
$509$	35.9534	+	13.0860i	1.59361	+	0.580026i	0.978106	−	0.208109i	$-0.0667310\pi$
$509$	35.9534	+	13.0860i	1.59361	+	0.580026i	0.615502	+	0.788135i	$0.288953\pi$
$510$		0			0
$511$	−0.477005	+	2.70523i	−0.0211015	+	0.119672i
$512$	−17.2928			−0.764239
$513$	−10.9797	−	14.1224i	−0.484764	−	0.623517i
$514$	3.92470			0.173111
$515$		0			0
$516$	18.1882	+	15.2617i	0.800690	+	0.671858i
$517$	−26.9273	−	9.80074i	−1.18426	−	0.431036i
$518$	−4.91680	+	1.78957i	−0.216032	+	0.0786292i
$519$	−5.80235	+	4.86875i	−0.254695	+	0.213714i
$520$		0			0
$521$	1.24406	−	2.15478i	0.0545033	−	0.0944025i	−0.837486	−	0.546458i	$-0.815976\pi$
$521$	1.24406	−	2.15478i	0.0545033	−	0.0944025i	0.891990	+	0.452056i	$0.149309\pi$
$522$	−1.65032	−	9.35941i	−0.0722324	−	0.409650i
$523$	3.37803	+	19.1578i	0.147711	+	0.837712i	0.965150	+	0.261696i	$0.0842819\pi$
$523$	3.37803	+	19.1578i	0.147711	+	0.837712i	−0.817439	+	0.576015i	$0.804607\pi$
$524$	−0.298786	+	0.517512i	−0.0130525	+	0.0226076i
$525$		0			0
$526$	2.66681	−	2.23772i	0.116278	−	0.0975692i
$527$	11.7923	−	4.29206i	0.513683	−	0.186965i
$528$	39.7056	+	14.4517i	1.72797	+	0.628928i
$529$	2.59720	+	2.17931i	0.112922	+	0.0947525i
$530$		0			0
$531$	23.3631			1.01387
$532$	16.0427	+	3.44984i	0.695538	+	0.149569i
$533$	−3.17251			−0.137417
$534$	−0.259581	+	1.47215i	−0.0112332	+	0.0637064i
$535$		0			0
$536$	4.71816	+	1.71727i	0.203794	+	0.0741748i
$537$	−29.2790	+	10.6567i	−1.26348	+	0.459869i
$538$	−3.04169	+	2.55228i	−0.131137	+	0.110037i
$539$	6.84814	+	11.8613i	0.294970	+	0.510904i
$540$		0			0
$541$	2.51035	+	14.2369i	0.107928	+	0.612093i	0.990010	+	0.140996i	$0.0450305\pi$
$541$	2.51035	+	14.2369i	0.107928	+	0.612093i	−0.882082	+	0.471097i	$0.843858\pi$
$542$	0.251547	+	1.42659i	0.0108049	+	0.0612775i
$543$	4.88325	−	8.45804i	0.209560	−	0.362969i
$544$	−3.46608	−	6.00342i	−0.148607	−	0.257394i
$545$		0			0
$546$	−1.54997	+	0.564141i	−0.0663324	+	0.0241430i
$547$	−29.5027	−	10.7381i	−1.26144	−	0.459128i	−0.377191	−	0.926136i	$-0.623110\pi$
$547$	−29.5027	−	10.7381i	−1.26144	−	0.459128i	−0.884253	+	0.467007i	$0.845332\pi$
$548$	21.5504	+	18.0830i	0.920589	+	0.772466i
$549$	2.18951	−	12.4173i	0.0934461	−	0.529959i
$550$		0			0
$551$	36.8244	+	7.91878i	1.56877	+	0.337351i
$552$	13.5511			0.576774
$553$	2.04275	−	11.5850i	0.0868667	−	0.492646i
$554$	−1.18162	−	0.991497i	−0.0502022	−	0.0421247i
$555$		0			0
$556$	28.8020	−	10.4831i	1.22148	−	0.444581i
$557$	−23.3248	+	19.5718i	−0.988304	+	0.829286i	−0.985321	−	0.170710i	$-0.945394\pi$
$557$	−23.3248	+	19.5718i	−0.988304	+	0.829286i	−0.00298303	+	0.999996i	$0.500950\pi$
$558$	2.80500	+	4.85840i	0.118745	+	0.205673i
$559$	2.83729	−	4.91433i	0.120005	−	0.207854i
$560$		0			0
$561$	4.95241	+	28.0865i	0.209091	+	1.18581i
$562$	−0.327552	+	0.567337i	−0.0138169	+	0.0239317i
$563$	13.3506	+	23.1239i	0.562661	+	0.974558i	0.997263	+	0.0739355i	$0.0235559\pi$
$563$	13.3506	+	23.1239i	0.562661	+	0.974558i	−0.434602	+	0.900623i	$0.643111\pi$
$564$	27.5502	−	23.1173i	1.16007	−	0.973416i
$565$		0			0
$566$	7.13650	+	2.59747i	0.299970	+	0.109180i
$567$	3.35622	+	2.81621i	0.140948	+	0.118270i
$568$	0.132468	−	0.751261i	0.00555822	−	0.0315222i
$569$	−25.6513			−1.07536			−0.537679	−	0.843150i	$-0.680699\pi$
$569$	−25.6513			−1.07536			−0.537679	+	0.843150i	$0.680699\pi$
$570$		0			0
$571$	2.93559			0.122851			0.0614253	−	0.998112i	$-0.480435\pi$
$571$	2.93559			0.122851			0.0614253	+	0.998112i	$0.480435\pi$
$572$	1.81113	−	10.2714i	0.0757271	−	0.429470i
$573$	18.1939	+	15.2665i	0.760062	+	0.637768i
$574$	−1.11364	−	0.405333i	−0.0464826	−	0.0169183i
$575$		0			0
$576$	−22.7484	+	19.0881i	−0.947848	+	0.795339i
$577$	8.88661	+	15.3921i	0.369954	+	0.640780i	0.989558	−	0.144135i	$-0.0460400\pi$
$577$	8.88661	+	15.3921i	0.369954	+	0.640780i	−0.619604	+	0.784915i	$0.712707\pi$
$578$	−1.33819	+	2.31781i	−0.0556613	+	0.0964083i
$579$	0.200719	+	1.13833i	0.00834158	+	0.0473075i
$580$		0			0
$581$	11.4983	−	19.9156i	0.477029	−	0.826238i
$582$	2.88200	+	4.99177i	0.119463	+	0.206916i
$583$	2.23697	−	1.87704i	0.0926458	−	0.0777391i
$584$	−1.28155	+	0.466447i	−0.0530310	+	0.0193017i
$585$		0			0
$586$	−0.162119	−	0.136034i	−0.00669709	−	0.00561952i
$587$	4.01538	−	22.7723i	0.165732	−	0.939915i	−0.782574	−	0.622558i	$-0.786094\pi$
$587$	4.01538	−	22.7723i	0.165732	−	0.939915i	0.948306	−	0.317357i	$-0.102795\pi$
$588$	−17.1896			−0.708887
$589$	−22.0250	+	3.04205i	−0.907522	+	0.125346i
$590$		0			0
$591$	−7.24752	+	41.1027i	−0.298123	+	1.69074i
$592$	30.7994	+	25.8438i	1.26585	+	1.06217i
$593$	−16.1227	−	5.86817i	−0.662078	−	0.240977i	−0.0109447	−	0.999940i	$-0.503484\pi$
$593$	−16.1227	−	5.86817i	−0.662078	−	0.240977i	−0.651133	+	0.758963i	$0.725706\pi$
$594$	−3.99117	+	1.45267i	−0.163760	+	0.0596037i
$595$		0			0
$596$	−12.0925	−	20.9448i	−0.495327	−	0.857931i
$597$	17.6987	−	30.6550i	0.724358	−	1.25463i
$598$	−0.276933	−	1.57057i	−0.0113246	−	0.0642253i
$599$	−2.32632	−	13.1932i	−0.0950508	−	0.539060i	−0.994732	−	0.102512i	$-0.967312\pi$
$599$	−2.32632	−	13.1932i	−0.0950508	−	0.539060i	0.899681	−	0.436548i	$-0.143799\pi$
$600$		0			0
$601$	−4.13126	−	7.15554i	−0.168517	−	0.291881i	0.769381	−	0.638790i	$-0.220565\pi$
$601$	−4.13126	−	7.15554i	−0.168517	−	0.291881i	−0.937899	+	0.346909i	$0.887231\pi$
$602$	1.62385	−	1.36257i	0.0661830	−	0.0555342i
$603$	22.0341	−	8.01976i	0.897298	−	0.326590i
$604$	25.2334	+	9.18421i	1.02673	+	0.373700i
$605$		0			0
$606$	−1.56371	+	8.86822i	−0.0635212	+	0.360247i
$607$	−23.5191			−0.954612			−0.477306	−	0.878737i	$-0.658387\pi$
$607$	−23.5191			−0.954612			−0.477306	+	0.878737i	$0.658387\pi$
$608$	3.76761	+	11.6899i	0.152797	+	0.474090i
$609$	45.9124			1.86046
$610$		0			0
$611$	−6.58450	−	5.52505i	−0.266380	−	0.223520i
$612$	−20.1788	−	7.34447i	−0.815679	−	0.296883i
$613$	28.0323	−	10.2029i	1.13221	−	0.412092i	0.293118	−	0.956076i	$-0.405307\pi$
$613$	28.0323	−	10.2029i	1.13221	−	0.412092i	0.839095	+	0.543984i	$0.183085\pi$
$614$	1.68403	−	1.41307i	0.0679619	−	0.0570268i
$615$		0			0
$616$	3.95617	−	6.85228i	0.159399	−	0.276086i
$617$	2.01262	+	11.4142i	0.0810251	+	0.459516i	0.998144	+	0.0609020i	$0.0193977\pi$
$617$	2.01262	+	11.4142i	0.0810251	+	0.459516i	−0.917119	+	0.398614i	$0.869491\pi$
$618$	0.469169	+	2.66079i	0.0188727	+	0.107033i
$619$	−14.8349	+	25.6947i	−0.596264	+	1.03276i	0.397104	+	0.917774i	$0.370015\pi$
$619$	−14.8349	+	25.6947i	−0.596264	+	1.03276i	−0.993367	+	0.114985i	$0.963318\pi$
$620$		0			0
$621$	16.1499	−	13.5514i	0.648075	−	0.543799i
$622$	−2.62831	+	0.956627i	−0.105386	+	0.0383573i
$623$	−4.07118	−	1.48179i	−0.163108	−	0.0593666i
$624$	9.70916	+	8.14695i	0.388677	+	0.326139i
$625$		0			0
$626$	−1.92287			−0.0768532
$627$	1.88347	−	50.4950i	0.0752185	−	2.01658i
$628$	35.3063			1.40888
$629$	−4.71236	+	26.7251i	−0.187894	+	1.06560i
$630$		0			0
$631$	23.0191	+	8.37827i	0.916376	+	0.333534i	0.756796	−	0.653651i	$-0.226764\pi$
$631$	23.0191	+	8.37827i	0.916376	+	0.333534i	0.159580	+	0.987185i	$0.448986\pi$
$632$	5.48819	−	1.99754i	0.218308	−	0.0794578i
$633$	9.32683	−	7.82614i	0.370708	−	0.311061i
$634$	2.02017	+	3.49904i	0.0802313	+	0.138965i
$635$		0			0
$636$	0.636414	+	3.60928i	0.0252354	+	0.143117i
$637$	0.713402	+	4.04591i	0.0282660	+	0.160305i
$638$	4.47163	−	7.74509i	0.177034	−	0.306631i
$639$	−1.78128	−	3.08527i	−0.0704663	−	0.122051i
$640$		0			0
$641$	−11.6336	+	4.23428i	−0.459499	+	0.167244i	−0.561390	−	0.827552i	$-0.689733\pi$
$641$	−11.6336	+	4.23428i	−0.459499	+	0.167244i	0.101890	+	0.994796i	$0.467511\pi$
$642$	−10.6688	−	3.88312i	−0.421063	−	0.153254i
$643$	35.1685	+	29.5099i	1.38691	+	1.16376i	0.966574	+	0.256387i	$0.0825323\pi$
$643$	35.1685	+	29.5099i	1.38691	+	1.16376i	0.420336	+	0.907369i	$0.361912\pi$
$644$	−3.35822	+	19.0454i	−0.132332	+	0.750494i
$645$		0			0
$646$	−1.75891	+	1.94415i	−0.0692032	+	0.0764916i
$647$	33.6773			1.32399			0.661996	−	0.749508i	$-0.269710\pi$
$647$	33.6773			1.32399			0.661996	+	0.749508i	$0.269710\pi$
$648$	−0.377716	+	2.14213i	−0.0148381	+	0.0841509i
$649$	16.8416	+	14.1318i	0.661092	+	0.554722i
$650$		0			0
$651$	−25.4672	+	9.26931i	−0.998139	+	0.363293i
$652$	22.7906	−	19.1236i	0.892549	−	0.748937i
$653$	−9.81827	−	17.0057i	−0.384219	−	0.665486i	0.607442	−	0.794364i	$-0.292196\pi$
$653$	−9.81827	−	17.0057i	−0.384219	−	0.665486i	−0.991660	+	0.128878i	$0.958862\pi$
$654$	−2.28813	+	3.96316i	−0.0894731	+	0.154972i
$655$		0			0
$656$	1.58133	+	8.96816i	0.0617405	+	0.350148i
$657$	−3.18451	+	5.51574i	−0.124240	+	0.215189i
$658$	−1.60545	−	2.78072i	−0.0625869	−	0.108404i
$659$	15.9102	−	13.3503i	0.619775	−	0.520053i	−0.277958	−	0.960593i	$-0.589658\pi$
$659$	15.9102	−	13.3503i	0.619775	−	0.520053i	0.897733	+	0.440540i	$0.145213\pi$
$660$		0			0
$661$	−12.4567	−	4.53386i	−0.484508	−	0.176347i	0.0882049	−	0.996102i	$-0.471887\pi$
$661$	−12.4567	−	4.53386i	−0.484508	−	0.176347i	−0.572713	+	0.819756i	$0.694109\pi$
$662$	−1.48222	−	1.24373i	−0.0576082	−	0.0483390i
$663$	−1.48552	+	8.42480i	−0.0576928	+	0.327192i
$664$	11.4172			0.443074
$665$		0			0
$666$	−12.1316			−0.470089
$667$	−7.70848	+	43.7170i	−0.298473	+	1.69273i
$668$	9.24020	+	7.75345i	0.357514	+	0.299990i
$669$	23.6709	+	8.61551i	0.915171	+	0.333095i
$670$		0			0
$671$	9.08930	−	7.62682i	0.350888	−	0.294430i
$672$	7.48548	+	12.9652i	0.288759	+	0.500144i
$673$	−6.42879	+	11.1350i	−0.247812	+	0.429223i	−0.962918	−	0.269793i	$-0.913045\pi$
$673$	−6.42879	+	11.1350i	−0.247812	+	0.429223i	0.715107	+	0.699015i	$0.246378\pi$
$674$	0.808138	+	4.58318i	0.0311283	+	0.176537i
$675$		0			0
$676$	−11.0472	+	19.1344i	−0.424894	+	0.735937i
$677$	12.7786	+	22.1332i	0.491122	+	0.850649i	0.999948	−	0.0102207i	$-0.00325342\pi$
$677$	12.7786	+	22.1332i	0.491122	+	0.850649i	−0.508825	+	0.860870i	$0.669920\pi$
$678$	3.03816	−	2.54932i	0.116680	−	0.0979062i
$679$	−15.6979	+	5.71357i	−0.602431	+	0.219267i
$680$		0			0
$681$	−1.25927	−	1.05665i	−0.0482554	−	0.0404911i
$682$	−0.916711	+	5.19893i	−0.0351027	+	0.199077i
$683$	−22.8692			−0.875064			−0.437532	−	0.899203i	$-0.644147\pi$
$683$	−22.8692			−0.875064			−0.437532	+	0.899203i	$0.644147\pi$
$684$	32.2171	+	20.2381i	1.23185	+	0.773824i
$685$		0			0
$686$	−0.843090	+	4.78140i	−0.0321893	+	0.182555i
$687$	14.9252	+	12.5237i	0.569432	+	0.477810i
$688$	−15.3062	−	5.57101i	−0.583545	−	0.212393i
$689$	0.823102	−	0.299585i	0.0313577	−	0.0114133i
$690$		0			0
$691$	16.1574	+	27.9854i	0.614657	+	1.06462i	0.990445	+	0.137911i	$0.0440388\pi$
$691$	16.1574	+	27.9854i	0.614657	+	1.06462i	−0.375788	+	0.926706i	$0.622628\pi$
$692$	2.68337	−	4.64774i	0.102007	−	0.176681i
$693$	−6.41649	−	36.3897i	−0.243742	−	1.38233i
$694$	0.231972	+	1.31558i	0.00880554	+	0.0499387i
$695$		0			0
$696$	11.3972	+	19.7405i	0.432009	+	0.748262i
$697$	−4.70854	+	3.95093i	−0.178349	+	0.149652i
$698$	−1.43913	+	0.523801i	−0.0544719	+	0.0198262i
$699$	−51.8922	−	18.8872i	−1.96274	−	0.714381i
$700$		0			0
$701$	6.03353	−	34.2179i	0.227883	−	1.29239i	−0.629212	−	0.777233i	$-0.716622\pi$
$701$	6.03353	−	34.2179i	0.227883	−	1.29239i	0.857096	−	0.515157i	$-0.172266\pi$
$702$	−1.27402			−0.0480848
$703$	18.1173	−	44.5369i	0.683307	−	1.67974i
$704$	−27.9444			−1.05319
$705$		0			0
$706$	1.55330	+	1.30337i	0.0584593	+	0.0490531i
$707$	−24.5247	−	8.92625i	−0.922345	−	0.335706i
$708$	−25.9286	+	9.43724i	−0.974457	+	0.354673i
$709$	6.13431	−	5.14730i	0.230379	−	0.193311i	−0.520290	−	0.853990i	$-0.674176\pi$
$709$	6.13431	−	5.14730i	0.230379	−	0.193311i	0.750669	+	0.660679i	$0.229732\pi$
$710$		0			0
$711$	13.6375	−	23.6209i	0.511448	−	0.885853i
$712$	−0.373510	−	2.11828i	−0.0139979	−	0.0793859i
$713$	−4.55025	−	25.8057i	−0.170408	−	0.966432i
$714$	−1.59785	+	2.76755i	−0.0597980	+	0.103573i
$715$		0			0
$716$	16.9116	−	14.1905i	0.632018	−	0.530326i
$717$	−29.9374	+	10.8963i	−1.11803	+	0.406931i
$718$	3.00622	+	1.09418i	0.112191	+	0.0408343i
$719$	10.9307	+	9.17191i	0.407645	+	0.342055i	0.823440	−	0.567404i	$-0.192052\pi$
$719$	10.9307	+	9.17191i	0.407645	+	0.342055i	−0.415795	+	0.909458i	$0.636497\pi$
$720$		0			0
$721$	−7.83053			−0.291624
$722$	3.77087	−	2.71241i	0.140337	−	0.100946i
$723$	−69.9107			−2.60001
$724$	−1.20163	+	6.81478i	−0.0446582	+	0.253269i
$725$		0			0
$726$	−4.35401	−	1.58473i	−0.161593	−	0.0588149i
$727$	−2.94724	+	1.07271i	−0.109307	+	0.0397846i	−0.396095	−	0.918210i	$-0.629635\pi$
$727$	−2.94724	+	1.07271i	−0.109307	+	0.0397846i	0.286788	+	0.957994i	$0.407413\pi$
$728$	1.81811	−	1.52558i	0.0673836	−	0.0565416i
$729$	21.9360	+	37.9942i	0.812444	+	1.40719i
$730$		0			0
$731$	−1.90912	−	10.8272i	−0.0706113	−	0.400457i
$732$	2.58589	+	14.6653i	0.0955772	+	0.542045i
$733$	−6.20021	+	10.7391i	−0.229010	+	0.396657i	−0.957515	−	0.288384i	$-0.906882\pi$
$733$	−6.20021	+	10.7391i	−0.229010	+	0.396657i	0.728505	+	0.685041i	$0.240216\pi$
$734$	3.18972	+	5.52476i	0.117735	+	0.203922i
$735$		0			0
$736$	−13.6020	+	4.95074i	−0.501378	+	0.182487i
$737$	20.7346	+	7.54676i	0.763767	+	0.277988i
$738$	−2.10492	−	1.76623i	−0.0774830	−	0.0650160i
$739$	−1.62242	+	9.20119i	−0.0596816	+	0.338471i	−0.999998	−	0.00182926i	$-0.999418\pi$
$739$	−1.62242	+	9.20119i	−0.0596816	+	0.338471i	0.940317	+	0.340301i	$0.110529\pi$
$740$		0			0
$741$	5.71127	−	14.0398i	0.209809	−	0.515763i
$742$	0.327209			0.0120122
$743$	−6.65396	+	37.7365i	−0.244110	+	1.38442i	0.578441	+	0.815725i	$0.303661\pi$
$743$	−6.65396	+	37.7365i	−0.244110	+	1.38442i	−0.822551	+	0.568692i	$0.807450\pi$
$744$	−10.3074	−	8.64890i	−0.377886	−	0.317084i
$745$		0			0
$746$	6.24803	−	2.27410i	0.228757	−	0.0832606i
$747$	40.8448	−	34.2729i	1.49443	−	1.25398i
$748$	−10.1036	−	17.5000i	−0.369426	−	0.639864i
$749$	16.4525	−	28.4965i	0.601160	−	1.04124i
$750$		0			0
$751$	−8.51519	−	48.2921i	−0.310724	−	1.76220i	−0.595257	−	0.803536i	$-0.702950\pi$
$751$	−8.51519	−	48.2921i	−0.310724	−	1.76220i	0.284533	−	0.958666i	$-0.408162\pi$
$752$	−12.3364	+	21.3672i	−0.449861	+	0.779183i
$753$	21.0557	+	36.4696i	0.767313	+	1.32902i
$754$	2.05500	−	1.72435i	0.0748386	−	0.0627971i
$755$		0			0
$756$	14.5176	+	5.28399i	0.528001	+	0.192177i
$757$	−28.1855	−	23.6504i	−1.02442	−	0.859590i	−0.0342429	−	0.999414i	$-0.510902\pi$
$757$	−28.1855	−	23.6504i	−1.02442	−	0.859590i	−0.990176	+	0.139824i	$0.955346\pi$
$758$	−0.581600	+	3.29842i	−0.0211247	+	0.119804i
$759$	59.5521			2.16160
$760$		0			0
$761$	−0.255560			−0.00926406			−0.00463203	−	0.999989i	$-0.501474\pi$
$761$	−0.255560			−0.00926406			−0.00463203	+	0.999989i	$0.501474\pi$
$762$	−2.22973	+	12.6455i	−0.0807748	+	0.458096i
$763$	−10.1601	−	8.52533i	−0.367820	−	0.308638i
$764$	−15.8132	−	5.75554i	−0.572102	−	0.208228i
$765$		0			0
$766$	−1.91990	+	1.61099i	−0.0693690	+	0.0582075i
$767$	3.29733	+	5.71114i	0.119060	+	0.206217i
$768$	15.6495	−	27.1058i	0.564704	−	0.978096i
$769$	−1.64209	−	9.31277i	−0.0592154	−	0.335827i	0.940780	−	0.339019i	$-0.110095\pi$
$769$	−1.64209	−	9.31277i	−0.0592154	−	0.335827i	−0.999995	+	0.00319194i	$0.998984\pi$
$770$		0			0
$771$	−21.9801	+	38.0707i	−0.791594	+	1.37108i
$772$	−0.409495	−	0.709267i	−0.0147381	−	0.0255271i
$773$	−23.1544	+	19.4288i	−0.832806	+	0.698807i	−0.955933	−	0.293584i	$-0.905152\pi$
$773$	−23.1544	+	19.4288i	−0.832806	+	0.698807i	0.123128	+	0.992391i	$0.460708\pi$
$774$	4.61846	−	1.68098i	0.166007	−	0.0604217i
$775$		0			0
$776$	−6.35342	−	5.33116i	−0.228075	−	0.191377i
$777$	10.1770	−	57.7167i	0.365098	−	2.07058i
$778$	1.23625			0.0443217
$779$	9.62760	−	5.08978i	0.344945	−	0.182360i
$780$		0			0
$781$	0.582145	−	3.30151i	0.0208308	−	0.118137i
$782$	−2.36695	−	1.98610i	−0.0846418	−	0.0710229i
$783$	33.3239	+	12.1289i	1.19090	+	0.433451i
$784$	11.0815	−	4.03334i	0.395768	−	0.144048i
$785$		0			0
$786$	0.103095	+	0.178565i	0.00367727	+	0.00636922i
$787$	−18.1988	+	31.5212i	−0.648717	+	1.12361i	0.334712	+	0.942320i	$0.391361\pi$
$787$	−18.1988	+	31.5212i	−0.648717	+	1.12361i	−0.983430	+	0.181291i	$0.941973\pi$
$788$	−5.13513	−	29.1228i	−0.182931	−	1.03746i
$789$	6.77114	+	38.4010i	0.241059	+	1.36711i
$790$		0			0
$791$	5.74724	+	9.95452i	0.204348	+	0.353942i
$792$	14.0533	−	11.7921i	0.499363	−	0.419015i
$793$	3.34444	−	1.21728i	0.118765	−	0.0432268i
$794$	5.48507	+	1.99640i	0.194658	+	0.0708497i
$795$		0			0
$796$	−4.35514	+	24.6993i	−0.154364	+	0.875442i
$797$	−19.2118			−0.680517			−0.340258	−	0.940332i	$-0.610515\pi$
$797$	−19.2118			−0.680517			−0.340258	+	0.940332i	$0.610515\pi$
$798$	3.79860	−	4.19867i	0.134469	−	0.148631i
$799$	−16.6532			−0.589148
$800$		0			0
$801$	−7.69500	−	6.45687i	−0.271889	−	0.228142i
$802$	−5.68947	−	2.07080i	−0.200902	−	0.0731224i
$803$	−5.63194	+	2.04986i	−0.198747	+	0.0723379i
$804$	−21.2142	+	17.8008i	−0.748166	+	0.627786i
$805$		0			0
$806$	−0.791760	+	1.37137i	−0.0278886	+	0.0483044i
$807$	−7.72298	−	43.7992i	−0.271862	−	1.54180i
$808$	−2.25001	−	12.7605i	−0.0791552	−	0.448911i
$809$	21.5251	−	37.2825i	0.756781	−	1.31078i	−0.187703	−	0.982226i	$-0.560104\pi$
$809$	21.5251	−	37.2825i	0.756781	−	1.31078i	0.944484	−	0.328557i	$-0.106562\pi$
$810$		0			0
$811$	−23.9988	+	20.1373i	−0.842710	+	0.707118i	−0.958172	−	0.286194i	$-0.907610\pi$
$811$	−23.9988	+	20.1373i	−0.842710	+	0.707118i	0.115461	+	0.993312i	$0.463165\pi$
$812$	−30.5687	+	11.1261i	−1.07275	+	0.390450i
$813$	−15.2471	−	5.54950i	−0.534740	−	0.194629i
$814$	−8.74521	−	7.33810i	−0.306520	−	0.257200i
$815$		0			0
$816$	24.5560			0.859631
$817$	−0.726064	+	19.4655i	−0.0254018	+	0.681011i
$818$	2.42032			0.0846245
$819$	1.92468	−	10.9154i	0.0672539	−	0.381416i
$820$		0			0
$821$	−16.0413	−	5.83857i	−0.559847	−	0.203768i	0.0465693	−	0.998915i	$-0.485171\pi$
$821$	−16.0413	−	5.83857i	−0.559847	−	0.203768i	−0.606416	+	0.795148i	$0.707393\pi$
$822$	9.12147	−	3.31994i	0.318148	−	0.115796i
$823$	−27.8179	+	23.3420i	−0.969670	+	0.813650i	−0.982499	−	0.186268i	$-0.940361\pi$
$823$	−27.8179	+	23.3420i	−0.969670	+	0.813650i	0.0128292	+	0.999918i	$0.495916\pi$
$824$	−1.94383	−	3.36682i	−0.0677166	−	0.117289i
$825$		0			0
$826$	0.427779	+	2.42606i	0.0148843	+	0.0844133i
$827$	3.35888	+	19.0492i	0.116800	+	0.662404i	0.985843	+	0.167669i	$0.0536239\pi$
$827$	3.35888	+	19.0492i	0.116800	+	0.662404i	−0.869044	+	0.494735i	$0.835265\pi$
$828$	−22.4197	+	38.8320i	−0.779138	+	1.34951i
$829$	10.0921	+	17.4801i	0.350514	+	0.607109i	0.986340	−	0.164724i	$-0.0526734\pi$
$829$	10.0921	+	17.4801i	0.350514	+	0.607109i	−0.635825	+	0.771833i	$0.719340\pi$
$830$		0			0
$831$	16.2354	−	5.90920i	0.563200	−	0.204988i
$832$	−7.87666	−	2.86687i	−0.273074	−	0.0993909i
$833$	6.09744	+	5.11636i	0.211264	+	0.177271i
$834$	1.83647	−	10.4151i	0.0635917	−	0.360647i
$835$		0			0
$836$	10.9826	+	34.0763i	0.379841	+	1.17855i
$837$	−20.9332			−0.723557
$838$	−0.170156	+	0.965002i	−0.00587794	+	0.0333355i
$839$	19.7800	+	16.5974i	0.682880	+	0.573005i	0.916846	−	0.399240i	$-0.130726\pi$
$839$	19.7800	+	16.5974i	0.682880	+	0.573005i	−0.233966	+	0.972245i	$0.575170\pi$
$840$		0			0
$841$	−42.9165	+	15.6203i	−1.47988	+	0.538632i
$842$	−3.79769	+	3.18664i	−0.130877	+	0.109819i
$843$	−3.66888	−	6.35469i	−0.126363	−	0.218867i
$844$	−4.31332	+	7.47089i	−0.148471	+	0.257159i
$845$		0			0
$846$	−1.29276	−	7.33159i	−0.0444459	−	0.252065i
$847$	6.71438	−	11.6296i	0.230709	−	0.399599i
$848$	−1.25715	−	2.17745i	−0.0431707	−	0.0747738i
$849$	−65.1639	+	54.6790i	−2.23642	+	1.87658i
$850$		0			0
$851$	53.2482	+	19.3807i	1.82532	+	0.664363i
$852$	3.22313	+	2.70453i	0.110423	+	0.0926557i
$853$	2.48724	−	14.1058i	0.0851613	−	0.482974i	−0.912160	−	0.409834i	$-0.865587\pi$
$853$	2.48724	−	14.1058i	0.0851613	−	0.482974i	0.997322	−	0.0731404i	$-0.0233021\pi$
$854$	1.32952			0.0454953
$855$		0			0
$856$	16.3365			0.558370
$857$	4.21356	−	23.8963i	0.143932	−	0.816281i	−0.824286	−	0.566174i	$-0.808423\pi$
$857$	4.21356	−	23.8963i	0.143932	−	0.816281i	0.968218	−	0.250107i	$-0.0804659\pi$
$858$	−2.75683	−	2.31325i	−0.0941166	−	0.0789732i
$859$	−38.0794	−	13.8598i	−1.29925	−	0.472889i	−0.402499	−	0.915421i	$-0.631858\pi$
$859$	−38.0794	−	13.8598i	−1.29925	−	0.472889i	−0.896753	+	0.442532i	$0.854080\pi$
$860$		0			0
$861$	10.1687	−	8.53259i	0.346550	−	0.290790i
$862$	1.64757	+	2.85368i	0.0561166	+	0.0971968i
$863$	−11.4580	+	19.8458i	−0.390035	+	0.675560i	−0.992454	−	0.122620i	$-0.960870\pi$
$863$	−11.4580	+	19.8458i	−0.390035	+	0.675560i	0.602419	+	0.798180i	$0.294204\pi$
$864$	2.00798	+	11.3878i	0.0683129	+	0.387422i
$865$		0			0
$866$	4.20227	−	7.27854i	0.142799	−	0.247335i
$867$	−14.9889	−	25.9616i	−0.509051	−	0.881702i
$868$	14.7100	−	12.3431i	0.499289	−	0.418953i
$869$	24.1185	−	8.77843i	0.818165	−	0.297788i
$870$		0			0
$871$	5.07019	+	4.25440i	0.171797	+	0.144155i
$872$	1.14344	−	6.48474i	0.0387216	−	0.219601i
$873$	−38.7326			−1.31090
$874$	3.36013	+	4.32190i	0.113658	+	0.146190i
$875$		0			0
$876$	1.30619	−	7.40776i	0.0441320	−	0.250285i
$877$	38.0686	+	31.9434i	1.28549	+	1.07865i	0.992463	+	0.122546i	$0.0391059\pi$
$877$	38.0686	+	31.9434i	1.28549	+	1.07865i	0.293024	+	0.956105i	$0.405338\pi$
$878$	5.37988	+	1.95812i	0.181562	+	0.0660832i
$879$	2.22751	−	0.810748i	0.0751321	−	0.0273458i
$880$		0			0
$881$	5.51788	+	9.55725i	0.185902	+	0.321992i	0.943880	−	0.330288i	$-0.107146\pi$
$881$	5.51788	+	9.55725i	0.185902	+	0.321992i	−0.757978	+	0.652280i	$0.773813\pi$
$882$	−1.77915	+	3.08158i	−0.0599071	+	0.103762i
$883$	3.84187	+	21.7883i	0.129289	+	0.733235i	0.978667	+	0.205451i	$0.0658661\pi$
$883$	3.84187	+	21.7883i	0.129289	+	0.733235i	−0.849378	+	0.527785i	$0.823023\pi$
$884$	−1.05254	−	5.96927i	−0.0354009	−	0.200768i
$885$		0			0
$886$	−0.293236	−	0.507899i	−0.00985145	−	0.0170632i
$887$	−15.3461	+	12.8769i	−0.515272	+	0.432365i	−0.862980	−	0.505238i	$-0.831405\pi$
$887$	−15.3461	+	12.8769i	−0.515272	+	0.432365i	0.347708	+	0.937603i	$0.386960\pi$
$888$	27.3422	−	9.95175i	0.917544	−	0.333959i
$889$	−34.9704	−	12.7282i	−1.17287	−	0.426890i
$890$		0			0
$891$	−1.65992	+	9.41387i	−0.0556094	+	0.315376i
$892$	−17.8481			−0.597597
$893$	28.8460	+	6.20309i	0.965295	+	0.207578i
$894$	−8.34491			−0.279095
$895$		0			0
$896$	−10.7748	−	9.04109i	−0.359959	−	0.302042i
$897$	16.7859	+	6.10956i	0.560464	+	0.203992i
$898$	8.77627	−	3.19430i	0.292868	−	0.106595i
$899$	33.7653	−	28.3325i	1.12614	−	0.944941i
$900$		0			0
$901$	0.848530	−	1.46970i	0.0282686	−	0.0489627i
$902$	−0.449004	−	2.54643i	−0.0149502	−	0.0847868i
$903$	4.12301	+	23.3828i	0.137205	+	0.778129i
$904$	−2.85336	+	4.94217i	−0.0949015	+	0.164374i
$905$		0			0
$906$	7.09776	−	5.95572i	0.235807	−	0.197866i
$907$	−0.640274	+	0.233041i	−0.0212600	+	0.00773799i	−0.352628	−	0.935763i	$-0.614712\pi$
$907$	−0.640274	+	0.233041i	−0.0212600	+	0.00773799i	0.331368	+	0.943501i	$0.392490\pi$
$908$	1.09449	+	0.398363i	0.0363220	+	0.0132201i
$909$	−46.3545	−	38.8960i	−1.53748	−	1.29010i
$910$		0			0
$911$	28.7169			0.951433			0.475716	−	0.879599i	$-0.342189\pi$
$911$	28.7169			0.951433			0.475716	+	0.879599i	$0.342189\pi$
$912$	−42.5348	−	9.14675i	−1.40847	−	0.302879i
$913$	50.1744			1.66053
$914$	−0.0796442	+	0.451684i	−0.00263439	+	0.0149404i
$915$		0			0
$916$	−12.9722	−	4.72149i	−0.428613	−	0.156002i
$917$	−0.561545	+	0.204386i	−0.0185439	+	0.00674941i
$918$	−1.89086	+	1.58662i	−0.0624077	+	0.0523663i
$919$	−3.45629	−	5.98648i	−0.114013	−	0.197476i	0.803372	−	0.595477i	$-0.203037\pi$
$919$	−3.45629	−	5.98648i	−0.114013	−	0.197476i	−0.917385	+	0.398002i	$0.869704\pi$
$920$		0			0
$921$	4.27581	+	24.2494i	0.140893	+	0.799043i
$922$	−0.714075	−	4.04972i	−0.0235168	−	0.133371i
$923$	0.502797	−	0.870870i	0.0165498	−	0.0286650i
$924$	21.8202	+	37.7938i	0.717833	+	1.24332i
$925$		0			0
$926$	−5.59725	+	2.03723i	−0.183937	+	0.0669477i
$927$	−17.0607	−	6.20959i	−0.560347	−	0.203950i
$928$	−18.6520	−	15.6509i	−0.612281	−	0.513765i
$929$	7.09009	−	40.2099i	0.232618	−	1.31924i	−0.614953	−	0.788563i	$-0.710825\pi$
$929$	7.09009	−	40.2099i	0.232618	−	1.31924i	0.847572	−	0.530681i	$-0.178064\pi$
$930$		0			0
$931$	−8.65596	−	11.1336i	−0.283688	−	0.364888i
$932$	39.1272			1.28165
$933$	5.44020	−	30.8529i	0.178104	−	1.01008i
$934$	−2.55658	−	2.14522i	−0.0836538	−	0.0701938i
$935$		0			0
$936$	5.17097	−	1.88208i	0.169019	−	0.0615177i
$937$	11.2945	−	9.47723i	0.368976	−	0.309608i	−0.439380	−	0.898301i	$-0.644802\pi$
$937$	11.2945	−	9.47723i	0.368976	−	0.309608i	0.808356	+	0.588694i	$0.200358\pi$
$938$	1.23623	+	2.14121i	0.0403642	+	0.0699129i
$939$	10.7689	−	18.6523i	0.351430	−	0.608695i
$940$		0			0
$941$	−9.06681	−	51.4204i	−0.295570	−	1.67626i	−0.664878	−	0.746952i	$-0.731517\pi$
$941$	−9.06681	−	51.4204i	−0.295570	−	1.67626i	0.369309	−	0.929307i	$-0.379594\pi$
$942$	6.09115	−	10.5502i	0.198460	−	0.343743i
$943$	6.41730	+	11.1151i	0.208976	+	0.361957i
$944$	14.5009	−	12.1677i	0.471964	−	0.396025i
$945$		0			0
$946$	4.34607	+	1.58184i	0.141303	+	0.0514300i
$947$	43.9252	+	36.8577i	1.42738	+	1.19771i	0.947242	+	0.320519i	$0.103857\pi$
$947$	43.9252	+	36.8577i	1.42738	+	1.19771i	0.480137	+	0.877194i	$0.340587\pi$
$948$	−5.59369	+	31.7234i	−0.181675	+	1.03033i
$949$	−1.79777			−0.0583580
$950$		0			0
$951$	−45.2555			−1.46751
$952$	0.798483	−	4.52842i	0.0258790	−	0.146767i
$953$	7.13773	+	5.98927i	0.231214	+	0.194011i	0.751033	−	0.660265i	$-0.229556\pi$
$953$	7.13773	+	5.98927i	0.231214	+	0.194011i	−0.519819	+	0.854277i	$0.674001\pi$
$954$	0.712905	+	0.259476i	0.0230811	+	0.00840085i
$955$		0			0
$956$	17.2920	−	14.5097i	0.559262	−	0.469277i
$957$	50.0863	+	86.7521i	1.61906	+	2.80430i
$958$	−2.65753	+	4.60298i	−0.0858610	+	0.148716i
$959$	4.88519	+	27.7053i	0.157751	+	0.894650i
$960$		0			0
$961$	2.49072	−	4.31405i	0.0803458	−	0.139163i
$962$	−1.71217	−	2.96557i	−0.0552027	−	0.0956139i
$963$	58.4434	−	49.0399i	1.88331	−	1.58029i
$964$	46.5470	−	16.9417i	1.49918	−	0.545656i
$965$		0			0
$966$	5.11175	+	4.28927i	0.164468	+	0.138005i
$967$	−1.53279	+	8.69287i	−0.0492911	+	0.279544i	−0.999484	−	0.0321185i	$-0.989775\pi$
$967$	−1.53279	+	8.69287i	−0.0492911	+	0.279544i	0.950193	+	0.311662i	$0.100886\pi$
$968$	6.66705			0.214287
$969$	−9.00813	−	27.9500i	−0.289383	−	0.897883i
$970$		0			0
$971$	9.72287	−	55.1412i	0.312022	−	1.76956i	−0.276432	−	0.961033i	$-0.589152\pi$
$971$	9.72287	−	55.1412i	0.312022	−	1.76956i	0.588454	−	0.808531i	$-0.299737\pi$
$972$	−27.4892	−	23.0662i	−0.881716	−	0.739848i
$973$	28.8026	+	10.4833i	0.923369	+	0.336079i
$974$	−6.71866	+	2.44539i	−0.215280	+	0.0783554i
$975$		0			0
$976$	−5.10807	−	8.84743i	−0.163505	−	0.283199i
$977$	20.5517	−	35.5965i	0.657506	−	1.13883i	−0.323753	−	0.946142i	$-0.604945\pi$
$977$	20.5517	−	35.5965i	0.657506	−	1.13883i	0.981259	−	0.192693i	$-0.0617220\pi$
$978$	−1.78258	−	10.1095i	−0.0570006	−	0.323266i
$979$	−1.64144	−	9.30905i	−0.0524605	−	0.297518i
$980$		0			0
$981$	−15.3757	−	26.6314i	−0.490907	−	0.850277i
$982$	3.43764	−	2.88452i	0.109700	−	0.0920488i
$983$	−2.34795	+	0.854584i	−0.0748880	+	0.0272570i	−0.379193	−	0.925318i	$-0.623798\pi$
$983$	−2.34795	+	0.854584i	−0.0748880	+	0.0272570i	0.304305	+	0.952575i	$0.401576\pi$
$984$	6.19294	+	2.25405i	0.197424	+	0.0718564i
$985$		0			0
$986$	0.902520	−	5.11845i	0.0287421	−	0.163005i
$987$	35.9650			1.14478
$988$	−0.400297	+	10.7318i	−0.0127351	+	0.341423i
$989$	−22.9569			−0.729986
$990$		0			0
$991$	13.3471	+	11.1995i	0.423983	+	0.355764i	0.829676	−	0.558245i	$-0.188525\pi$
$991$	13.3471	+	11.1995i	0.423983	+	0.355764i	−0.405693	+	0.914010i	$0.632970\pi$
$992$	13.5059	+	4.91574i	0.428812	+	0.156075i
$993$	20.3657	−	7.41250i	0.646285	−	0.235228i
$994$	0.287762	−	0.241461i	0.00912727	−	0.00765869i
$995$		0			0
$996$	−31.4858	+	54.5351i	−0.997667	+	1.72801i
$997$	2.22287	+	12.6065i	0.0703990	+	0.399253i	0.999562	+	0.0295832i	$0.00941800\pi$
$997$	2.22287	+	12.6065i	0.0703990	+	0.399253i	−0.929163	+	0.369670i	$0.879471\pi$
$998$	−0.442186	−	2.50776i	−0.0139972	−	0.0793819i
$999$	22.6339	−	39.2031i	0.716106	−	1.24033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.226.4		48
5.2	odd	4		95.2.p.a.74.4	yes	48
5.3	odd	4		95.2.p.a.74.5	yes	48
5.4	even	2	inner	475.2.l.f.226.5		48
15.2	even	4		855.2.da.b.739.5		48
15.8	even	4		855.2.da.b.739.4		48
19.3	odd	18		9025.2.a.ct.1.13		24
19.9	even	9	inner	475.2.l.f.351.4		48
19.16	even	9		9025.2.a.cu.1.12		24
95.3	even	36		1805.2.b.l.1084.12		24
95.9	even	18	inner	475.2.l.f.351.5		48
95.22	even	36		1805.2.b.l.1084.13		24
95.28	odd	36		95.2.p.a.9.4	✓	48
95.47	odd	36		95.2.p.a.9.5	yes	48
95.54	even	18		9025.2.a.cu.1.13		24
95.73	odd	36		1805.2.b.k.1084.13		24
95.79	odd	18		9025.2.a.ct.1.12		24
95.92	odd	36		1805.2.b.k.1084.12		24
285.47	even	36		855.2.da.b.199.4		48
285.218	even	36		855.2.da.b.199.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.4	✓	48	95.28	odd	36
95.2.p.a.9.5	yes	48	95.47	odd	36
95.2.p.a.74.4	yes	48	5.2	odd	4
95.2.p.a.74.5	yes	48	5.3	odd	4
475.2.l.f.226.4		48	1.1	even	1	trivial
475.2.l.f.226.5		48	5.4	even	2	inner
475.2.l.f.351.4		48	19.9	even	9	inner
475.2.l.f.351.5		48	95.9	even	18	inner
855.2.da.b.199.4		48	285.47	even	36
855.2.da.b.199.5		48	285.218	even	36
855.2.da.b.739.4		48	15.8	even	4
855.2.da.b.739.5		48	15.2	even	4
1805.2.b.k.1084.12		24	95.92	odd	36
1805.2.b.k.1084.13		24	95.73	odd	36
1805.2.b.l.1084.12		24	95.3	even	36
1805.2.b.l.1084.13		24	95.22	even	36
9025.2.a.ct.1.12		24	95.79	odd	18
9025.2.a.ct.1.13		24	19.3	odd	18
9025.2.a.cu.1.12		24	19.16	even	9
9025.2.a.cu.1.13		24	95.54	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0424530 + 0.240763i) q^{2} +(-2.09771 - 1.76019i) q^{3} +(1.82322 + 0.663598i) q^{4} +(0.512843 - 0.430326i) q^{6} +(0.970136 + 1.68032i) q^{7} +(-0.481648 + 0.834240i) q^{8} +(0.781184 + 4.43031i) q^{9} +O(q^{10})\)	\(q+(-0.0424530 + 0.240763i) q^{2} +(-2.09771 - 1.76019i) q^{3} +(1.82322 + 0.663598i) q^{4} +(0.512843 - 0.430326i) q^{6} +(0.970136 + 1.68032i) q^{7} +(-0.481648 + 0.834240i) q^{8} +(0.781184 + 4.43031i) q^{9} +(-2.11666 + 3.66617i) q^{11} +(-2.65653 - 4.60125i) q^{12} +(-0.972742 + 0.816227i) q^{13} +(-0.445745 + 0.162238i) q^{14} +(2.79220 + 2.34293i) q^{16} +(-0.427212 + 2.42284i) q^{17} -1.09982 q^{18} +(1.64247 - 4.03761i) q^{19} +(0.922623 - 5.23246i) q^{21} +(-0.792820 - 0.665255i) q^{22} +(4.82735 + 1.75701i) q^{23} +(2.47878 - 0.902202i) q^{24} +(-0.155222 - 0.268852i) q^{26} +(2.05194 - 3.55406i) q^{27} +(0.653712 + 3.70738i) q^{28} +(1.50053 + 8.50995i) q^{29} +(-2.55042 - 4.41746i) q^{31} +(-2.15849 + 1.81118i) q^{32} +(10.8933 - 3.96484i) q^{33} +(-0.565193 - 0.205714i) q^{34} +(-1.51568 + 8.59583i) q^{36} +11.0305 q^{37} +(0.902380 + 0.566855i) q^{38} +3.47724 q^{39} +(1.91387 + 1.60593i) q^{41} +(1.22061 + 0.444267i) q^{42} +(-4.19929 + 1.52842i) q^{43} +(-6.29201 + 5.27962i) q^{44} +(-0.627959 + 1.08766i) q^{46} +(1.17543 + 6.66617i) q^{47} +(-1.73322 - 9.82960i) q^{48} +(1.61767 - 2.80189i) q^{49} +(5.16082 - 4.33044i) q^{51} +(-2.31517 + 0.842653i) q^{52} +(-0.648201 - 0.235926i) q^{53} +(0.768575 + 0.644911i) q^{54} -1.86906 q^{56} +(-10.5524 + 5.57868i) q^{57} -2.11258 q^{58} +(0.901817 - 5.11446i) q^{59} +(-2.63378 - 0.958619i) q^{61} +(1.17183 - 0.426513i) q^{62} +(-6.68651 + 5.61065i) q^{63} +(3.30053 + 5.71668i) q^{64} +(0.492133 + 2.79103i) q^{66} +(-0.905101 - 5.13308i) q^{67} +(-2.38669 + 4.13387i) q^{68} +(-7.03371 - 12.1828i) q^{69} +(-0.744158 + 0.270851i) q^{71} +(-4.07220 - 1.48216i) q^{72} +(1.08454 + 0.910034i) q^{73} +(-0.468279 + 2.65574i) q^{74} +(5.67394 - 6.27151i) q^{76} -8.21381 q^{77} +(-0.147620 + 0.837192i) q^{78} +(-4.64448 - 3.89718i) q^{79} +(2.12188 - 0.772300i) q^{81} +(-0.467899 + 0.392614i) q^{82} +(-5.92611 - 10.2643i) q^{83} +(5.15439 - 8.92767i) q^{84} +(-0.189714 - 1.07592i) q^{86} +(11.8314 - 20.4926i) q^{87} +(-2.03898 - 3.53161i) q^{88} +(-1.71051 + 1.43529i) q^{89} +(-2.31522 - 0.842670i) q^{91} +(7.63537 + 6.40684i) q^{92} +(-2.42551 + 13.7558i) q^{93} -1.65487 q^{94} +7.71591 q^{96} +(-1.49508 + 8.47901i) q^{97} +(0.605917 + 0.508425i) q^{98} +(-17.8958 - 6.51353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

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