LMFDB - Embedded newform 867.2.i.g.503.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

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

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

chi := DirichletCharacter("867.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			503.3
Character	$\chi$	$=$	867.503
Dual form			867.2.i.g.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21437 + 0.503008i) q^{2} +(1.72523 - 0.153573i) q^{3} +(-0.192538 - 0.192538i) q^{4} +(-0.0274494 - 0.137998i) q^{5} +(2.17231 + 0.681311i) q^{6} +(-1.73519 - 0.345150i) q^{7} +(-1.14298 - 2.75940i) q^{8} +(2.95283 - 0.529896i) q^{9} +(0.0360802 - 0.181387i) q^{10} +(3.02807 - 2.02329i) q^{11} +(-0.361741 - 0.302603i) q^{12} +(0.0825311 - 0.0825311i) q^{13} +(-1.93354 - 1.29195i) q^{14} +(-0.0685492 - 0.233862i) q^{15} -3.38128i q^{16} +(3.85237 + 0.841809i) q^{18} +(2.56928 - 6.20278i) q^{19} +(-0.0212847 + 0.0318548i) q^{20} +(-3.04660 - 0.328986i) q^{21} +(4.69492 - 0.933878i) q^{22} +(3.48870 + 5.22121i) q^{23} +(-2.39567 - 4.58506i) q^{24} +(4.60111 - 1.90584i) q^{25} +(0.141737 - 0.0587094i) q^{26} +(5.01293 - 1.36767i) q^{27} +(0.267635 + 0.400544i) q^{28} +(-3.86068 + 0.767936i) q^{29} +(0.0343905 - 0.318476i) q^{30} +(-4.97452 + 7.44489i) q^{31} +(-0.585150 + 1.41268i) q^{32} +(4.91339 - 3.95567i) q^{33} +0.248926i q^{35} +(-0.670557 - 0.466507i) q^{36} +(-0.309641 - 0.206896i) q^{37} +(6.24010 - 6.24010i) q^{38} +(0.129711 - 0.155060i) q^{39} +(-0.349416 + 0.233473i) q^{40} +(-0.857920 + 4.31306i) q^{41} +(-3.53422 - 1.93198i) q^{42} +(-0.806985 - 1.94823i) q^{43} +(-0.972578 - 0.193458i) q^{44} +(-0.154178 - 0.392938i) q^{45} +(1.61026 + 8.09532i) q^{46} +(-2.11141 - 2.11141i) q^{47} +(-0.519272 - 5.83348i) q^{48} +(-3.57541 - 1.48098i) q^{49} +6.54610 q^{50} -0.0317807 q^{52} +(5.91755 + 2.45113i) q^{53} +(6.77550 + 0.860694i) q^{54} +(-0.362328 - 0.362328i) q^{55} +(1.03088 + 5.18257i) q^{56} +(3.48001 - 11.0958i) q^{57} +(-5.07456 - 1.00939i) q^{58} +(3.65974 + 8.83540i) q^{59} +(-0.0318290 + 0.0582256i) q^{60} +(0.775290 - 3.89765i) q^{61} +(-9.78574 + 6.53863i) q^{62} +(-5.30661 - 0.0997012i) q^{63} +(-6.20303 + 6.20303i) q^{64} +(-0.0136545 - 0.00912367i) q^{65} +(7.95640 - 2.33217i) q^{66} -5.81844i q^{67} +(6.82064 + 8.47201i) q^{69} +(-0.125212 + 0.302288i) q^{70} +(-7.22012 + 10.8057i) q^{71} +(-4.83722 - 7.54238i) q^{72} +(-4.38175 + 0.871585i) q^{73} +(-0.271949 - 0.407000i) q^{74} +(7.64528 - 3.99462i) q^{75} +(-1.68895 + 0.699588i) q^{76} +(-5.95260 + 2.46565i) q^{77} +(0.235513 - 0.123054i) q^{78} +(-1.35888 - 2.03371i) q^{79} +(-0.466609 + 0.0928142i) q^{80} +(8.43842 - 3.12939i) q^{81} +(-3.21133 + 4.80610i) q^{82} +(-2.12000 + 5.11813i) q^{83} +(0.523244 + 0.649928i) q^{84} -2.77180i q^{86} +(-6.54262 + 1.91776i) q^{87} +(-9.04408 - 6.04306i) q^{88} +(-2.89760 + 2.89760i) q^{89} +(0.0104222 - 0.554725i) q^{90} +(-0.171693 + 0.114721i) q^{91} +(0.333574 - 1.67699i) q^{92} +(-7.43885 + 13.6081i) q^{93} +(-1.50197 - 3.62608i) q^{94} +(-0.926494 - 0.184291i) q^{95} +(-0.792569 + 2.52705i) q^{96} +(0.894911 + 4.49902i) q^{97} +(-3.59692 - 3.59692i) q^{98} +(7.86924 - 7.57899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 8 q^{6} + 24 q^{9} + 16 q^{10} + 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} - 16 q^{22} - 24 q^{24} - 24 q^{27} + 8 q^{30} - 32 q^{31} - 24 q^{36} - 16 q^{37}+ \cdots + 96 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 8 * q^6 + 24 * q^9 + 16 * q^10 + 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 - 16 * q^22 - 24 * q^24 - 24 * q^27 + 8 * q^30 - 32 * q^31 - 24 * q^36 - 16 * q^37 + 64 * q^39 - 16 * q^40 - 24 * q^42 - 32 * q^43 - 40 * q^45 + 40 * q^48 - 64 * q^49 - 96 * q^52 + 88 * q^54 + 48 * q^55 + 24 * q^57 + 64 * q^58 + 48 * q^60 + 32 * q^61 + 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 - 48 * q^73 - 16 * q^75 + 32 * q^76 - 88 * q^78 + 32 * q^79 - 48 * q^81 - 96 * q^82 - 56 * q^87 - 128 * q^88 - 8 * q^90 - 64 * q^91 - 56 * q^93 - 48 * q^94 - 16 * q^96 - 128 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	1.21437	+	0.503008i	0.858689	+	0.355681i	0.768195	−	0.640216i	$-0.221155\pi$
$2$	1.21437	+	0.503008i	0.858689	+	0.355681i	0.0904942	+	0.995897i	$0.471155\pi$
$3$	1.72523	−	0.153573i	0.996061	−	0.0886652i
$3$	1.72523	−	0.153573i	0.996061	−	0.0886652i
$4$	−0.192538	−	0.192538i	−0.0962690	−	0.0962690i
$5$	−0.0274494	−	0.137998i	−0.0122758	−	0.0617144i	0.974162	−	0.225851i	$-0.0725162\pi$
$5$	−0.0274494	−	0.137998i	−0.0122758	−	0.0617144i	−0.986438	+	0.164137i	$0.947516\pi$
$6$	2.17231	+	0.681311i	0.886843	+	0.278144i
$7$	−1.73519	−	0.345150i	−0.655839	−	0.130455i	−0.144056	−	0.989569i	$-0.546015\pi$
$7$	−1.73519	−	0.345150i	−0.655839	−	0.130455i	−0.511783	+	0.859115i	$0.671015\pi$
$8$	−1.14298	−	2.75940i	−0.404105	−	0.975595i
$9$	2.95283	−	0.529896i	0.984277	−	0.176632i
$10$	0.0360802	−	0.181387i	0.0114096	−	0.0573597i
$11$	3.02807	−	2.02329i	0.912997	−	0.610045i	−0.00785036	−	0.999969i	$-0.502499\pi$
$11$	3.02807	−	2.02329i	0.912997	−	0.610045i	0.920847	+	0.389924i	$0.127499\pi$
$12$	−0.361741	−	0.302603i	−0.104426	−	0.0873541i
$13$	0.0825311	−	0.0825311i	0.0228900	−	0.0228900i	−0.695569	−	0.718459i	$-0.744848\pi$
$13$	0.0825311	−	0.0825311i	0.0228900	−	0.0228900i	0.718459	+	0.695569i	$0.244848\pi$
$14$	−1.93354	−	1.29195i	−0.516762	−	0.345289i
$15$	−0.0685492	−	0.233862i	−0.0176993	−	0.0603829i
$16$		−	3.38128i		−	0.845320i
$17$		0			0
$17$		0			0
$18$	3.85237	+	0.841809i	0.908012	+	0.198416i
$19$	2.56928	−	6.20278i	0.589432	−	1.42302i	−0.294614	−	0.955616i	$-0.595191\pi$
$19$	2.56928	−	6.20278i	0.589432	−	1.42302i	0.884046	−	0.467399i	$-0.154809\pi$
$20$	−0.0212847	+	0.0318548i	−0.00475941	+	0.00712296i
$21$	−3.04660	−	0.328986i	−0.664823	−	0.0717906i
$22$	4.69492	−	0.933878i	1.00096	−	0.199104i
$23$	3.48870	+	5.22121i	0.727444	+	1.08870i	0.992233	+	0.124391i	$0.0396977\pi$
$23$	3.48870	+	5.22121i	0.727444	+	1.08870i	−0.264789	+	0.964306i	$0.585302\pi$
$24$	−2.39567	−	4.58506i	−0.489014	−	0.935922i
$25$	4.60111	−	1.90584i	0.920222	−	0.381168i
$26$	0.141737	−	0.0587094i	0.0277969	−	0.0115139i
$27$	5.01293	−	1.36767i	0.964739	−	0.263208i
$28$	0.267635	+	0.400544i	0.0505782	+	0.0756957i
$29$	−3.86068	+	0.767936i	−0.716909	+	0.142602i	−0.540049	−	0.841634i	$-0.681594\pi$
$29$	−3.86068	+	0.767936i	−0.716909	+	0.142602i	−0.176861	+	0.984236i	$0.556594\pi$
$30$	0.0343905	−	0.318476i	0.00627881	−	0.0581455i
$31$	−4.97452	+	7.44489i	−0.893450	+	1.33714i	0.0475974	+	0.998867i	$0.484844\pi$
$31$	−4.97452	+	7.44489i	−0.893450	+	1.33714i	−0.941047	+	0.338275i	$0.890156\pi$
$32$	−0.585150	+	1.41268i	−0.103441	+	0.249728i
$33$	4.91339	−	3.95567i	0.855311	−	0.688593i
$34$		0			0
$35$			0.248926i			0.0420762i
$36$	−0.670557	−	0.466507i	−0.111760	−	0.0777511i
$37$	−0.309641	−	0.206896i	−0.0509047	−	0.0340135i	0.529858	−	0.848087i	$-0.322245\pi$
$37$	−0.309641	−	0.206896i	−0.0509047	−	0.0340135i	−0.580762	+	0.814073i	$0.697245\pi$
$38$	6.24010	−	6.24010i	1.01228	−	1.01228i
$39$	0.129711	−	0.155060i	0.0207703	−	0.0248294i
$40$	−0.349416	+	0.233473i	−0.0552476	+	0.0369153i
$41$	−0.857920	+	4.31306i	−0.133985	+	0.673586i	0.854154	+	0.520020i	$0.174076\pi$
$41$	−0.857920	+	4.31306i	−0.133985	+	0.673586i	−0.988138	+	0.153566i	$0.950924\pi$
$42$	−3.53422	−	1.93198i	−0.545341	−	0.298110i
$43$	−0.806985	−	1.94823i	−0.123064	−	0.297103i	0.850326	−	0.526256i	$-0.176404\pi$
$43$	−0.806985	−	1.94823i	−0.123064	−	0.297103i	−0.973390	+	0.229153i	$0.926404\pi$
$44$	−0.972578	−	0.193458i	−0.146622	−	0.0291648i
$45$	−0.154178	−	0.392938i	−0.0229835	−	0.0585758i
$46$	1.61026	+	8.09532i	0.237420	+	1.19359i
$47$	−2.11141	−	2.11141i	−0.307980	−	0.307980i	0.536145	−	0.844126i	$-0.319880\pi$
$47$	−2.11141	−	2.11141i	−0.307980	−	0.307980i	−0.844126	+	0.536145i	$0.819880\pi$
$48$	−0.519272	−	5.83348i	−0.0749505	−	0.841990i
$49$	−3.57541	−	1.48098i	−0.510773	−	0.211569i
$50$	6.54610			0.925758
$51$		0			0
$52$	−0.0317807			−0.00440720
$53$	5.91755	+	2.45113i	0.812837	+	0.336688i	0.750085	−	0.661341i	$-0.230012\pi$
$53$	5.91755	+	2.45113i	0.812837	+	0.336688i	0.0627519	+	0.998029i	$0.480012\pi$
$54$	6.77550	+	0.860694i	0.922029	+	0.117126i
$55$	−0.362328	−	0.362328i	−0.0488563	−	0.0488563i
$56$	1.03088	+	5.18257i	0.137757	+	0.692551i
$57$	3.48001	−	11.0958i	0.460939	−	1.46967i
$58$	−5.07456	−	1.00939i	−0.666323	−	0.132540i
$59$	3.65974	+	8.83540i	0.476458	+	1.15027i	0.961259	+	0.275647i	$0.0888919\pi$
$59$	3.65974	+	8.83540i	0.476458	+	1.15027i	−0.484801	+	0.874624i	$0.661108\pi$
$60$	−0.0318290	+	0.0582256i	−0.00410910	+	0.00751690i
$61$	0.775290	−	3.89765i	0.0992658	−	0.499043i	−0.898881	−	0.438193i	$-0.855619\pi$
$61$	0.775290	−	3.89765i	0.0992658	−	0.499043i	0.998147	−	0.0608502i	$-0.0193812\pi$
$62$	−9.78574	+	6.53863i	−1.24279	+	0.830406i
$63$	−5.30661	−	0.0997012i	−0.668570	−	0.0125612i
$64$	−6.20303	+	6.20303i	−0.775378	+	0.775378i
$65$	−0.0136545	−	0.00912367i	−0.00169364	−	0.00113165i
$66$	7.95640	−	2.33217i	0.979365	−	0.287070i
$67$		−	5.81844i		−	0.710836i	−0.934707	−	0.355418i	$-0.884339\pi$
$67$		−	5.81844i		−	0.710836i	0.934707	−	0.355418i	$-0.115661\pi$
$68$		0			0
$69$	6.82064	+	8.47201i	0.821109	+	1.01991i
$70$	−0.125212	+	0.302288i	−0.0149657	+	0.0361303i
$71$	−7.22012	+	10.8057i	−0.856870	+	1.28240i	0.100910	+	0.994896i	$0.467825\pi$
$71$	−7.22012	+	10.8057i	−0.856870	+	1.28240i	−0.957780	+	0.287502i	$0.907175\pi$
$72$	−4.83722	−	7.54238i	−0.570072	−	0.888878i
$73$	−4.38175	+	0.871585i	−0.512845	+	0.102011i	−0.444727	−	0.895666i	$-0.646699\pi$
$73$	−4.38175	+	0.871585i	−0.512845	+	0.102011i	−0.0681180	+	0.997677i	$0.521699\pi$
$74$	−0.271949	−	0.407000i	−0.0316134	−	0.0473128i
$75$	7.64528	−	3.99462i	0.882801	−	0.461259i
$76$	−1.68895	+	0.699588i	−0.193736	+	0.0802482i
$77$	−5.95260	+	2.46565i	−0.678362	+	0.280987i
$78$	0.235513	−	0.123054i	0.0266666	−	0.0139331i
$79$	−1.35888	−	2.03371i	−0.152886	−	0.228811i	0.747118	−	0.664691i	$-0.231437\pi$
$79$	−1.35888	−	2.03371i	−0.152886	−	0.228811i	−0.900004	+	0.435881i	$0.856437\pi$
$80$	−0.466609	+	0.0928142i	−0.0521684	+	0.0103769i
$81$	8.43842	−	3.12939i	0.937602	−	0.347710i
$82$	−3.21133	+	4.80610i	−0.354633	+	0.530745i
$83$	−2.12000	+	5.11813i	−0.232700	+	0.561788i	−0.996493	−	0.0836731i	$-0.973335\pi$
$83$	−2.12000	+	5.11813i	−0.232700	+	0.561788i	0.763793	+	0.645461i	$0.223335\pi$
$84$	0.523244	+	0.649928i	0.0570906	+	0.0709130i
$85$		0			0
$86$		−	2.77180i		−	0.298890i
$87$	−6.54262	+	1.91776i	−0.701442	+	0.205605i
$88$	−9.04408	−	6.04306i	−0.964103	−	0.644193i
$89$	−2.89760	+	2.89760i	−0.307145	+	0.307145i	−0.843801	−	0.536656i	$-0.819687\pi$
$89$	−2.89760	+	2.89760i	−0.307145	+	0.307145i	0.536656	+	0.843801i	$0.319687\pi$
$90$	0.0104222	−	0.554725i	0.00109860	−	0.0584732i
$91$	−0.171693	+	0.114721i	−0.0179983	+	0.0120261i
$92$	0.333574	−	1.67699i	0.0347775	−	0.174838i
$93$	−7.43885	+	13.6081i	−0.771373	+	1.41109i
$94$	−1.50197	−	3.62608i	−0.154917	−	0.374002i
$95$	−0.926494	−	0.184291i	−0.0950563	−	0.0189079i
$96$	−0.792569	+	2.52705i	−0.0808912	+	0.257916i
$97$	0.894911	+	4.49902i	0.0908645	+	0.456807i	0.999252	+	0.0386768i	$0.0123143\pi$
$97$	0.894911	+	4.49902i	0.0908645	+	0.456807i	−0.908387	+	0.418130i	$0.862686\pi$
$98$	−3.59692	−	3.59692i	−0.363344	−	0.363344i
$99$	7.86924	−	7.57899i	0.790888	−	0.761717i
$100$	−1.25283	−	0.518941i	−0.125283	−	0.0518941i
$101$	−5.06729			−0.504214			−0.252107	−	0.967699i	$-0.581123\pi$
$101$	−5.06729			−0.504214			−0.252107	+	0.967699i	$0.581123\pi$
$102$		0			0
$103$	−15.9760			−1.57416			−0.787080	−	0.616851i	$-0.788408\pi$
$103$	−15.9760			−1.57416			−0.787080	+	0.616851i	$0.788408\pi$
$104$	−0.322068	−	0.133405i	−0.0315813	−	0.0130814i
$105$	0.0382282	+	0.429454i	0.00373069	+	0.0419104i
$106$	5.95315	+	5.95315i	0.578221	+	0.578221i
$107$	0.265818	+	1.33636i	0.0256976	+	0.129191i	0.991505	−	0.130071i	$-0.0415207\pi$
$107$	0.265818	+	1.33636i	0.0256976	+	0.129191i	−0.965807	+	0.259262i	$0.916521\pi$
$108$	−1.22851	−	0.701852i	−0.118213	−	0.0675357i
$109$	11.2577	+	2.23930i	1.07829	+	0.214486i	0.702116	−	0.712062i	$-0.252239\pi$
$109$	11.2577	+	2.23930i	1.07829	+	0.214486i	0.376176	+	0.926548i	$0.377239\pi$
$110$	−0.257746	−	0.622254i	−0.0245751	−	0.0593296i
$111$	−0.565976	−	0.309390i	−0.0537201	−	0.0293660i
$112$	−1.16705	+	5.86715i	−0.110276	+	0.554394i
$113$	11.2676	−	7.52875i	1.05996	−	0.708245i	0.101899	−	0.994795i	$-0.467508\pi$
$113$	11.2676	−	7.52875i	1.05996	−	0.708245i	0.958066	+	0.286549i	$0.0925082\pi$
$114$	9.80729	−	11.7239i	0.918537	−	1.09805i
$115$	0.624752	−	0.624752i	0.0582584	−	0.0582584i
$116$	0.891183	+	0.595470i	0.0827443	+	0.0552880i
$117$	0.199968	−	0.287433i	0.0184870	−	0.0265732i
$118$			12.5703i			1.15719i
$119$		0			0
$120$	−0.566968	+	0.456454i	−0.0517569	+	0.0416684i
$121$	0.865970	−	2.09064i	0.0787246	−	0.190058i
$122$	2.90204	−	4.34321i	0.262738	−	0.393215i
$123$	−0.817741	+	7.57276i	−0.0737332	+	0.682813i
$124$	2.39121	−	0.475641i	0.214737	−	0.0427138i
$125$	−0.780146	−	1.16757i	−0.0697784	−	0.104431i
$126$	−6.39403	−	2.79034i	−0.569626	−	0.248583i
$127$	9.13631	−	3.78439i	0.810717	−	0.335810i	0.0614768	−	0.998109i	$-0.480419\pi$
$127$	9.13631	−	3.78439i	0.810717	−	0.335810i	0.749240	+	0.662299i	$0.230419\pi$
$128$	−7.82759	+	3.24229i	−0.691867	+	0.286581i
$129$	−1.69143	−	3.23722i	−0.148922	−	0.285021i
$130$	−0.0119924	−	0.0179478i	−0.00105180	−	0.00157413i
$131$	12.7789	−	2.54189i	1.11650	−	0.222086i	0.397845	−	0.917453i	$-0.369758\pi$
$131$	12.7789	−	2.54189i	1.11650	−	0.222086i	0.718655	+	0.695367i	$0.244758\pi$
$132$	−1.70763	−	0.184398i	−0.148630	−	0.0160497i
$133$	−6.59907	+	9.87620i	−0.572212	+	0.856375i
$134$	2.92672	−	7.06574i	0.252830	−	0.610387i
$135$	−0.326337	−	0.654231i	−0.0280866	−	0.0563073i
$136$		0			0
$137$			3.20492i			0.273815i	0.990584	+	0.136907i	$0.0437163\pi$
$137$			3.20492i			0.273815i	−0.990584	+	0.136907i	$0.956284\pi$
$138$	4.02129	+	13.7190i	0.342315	+	1.16784i
$139$	−4.23589	−	2.83033i	−0.359283	−	0.240065i	0.362807	−	0.931864i	$-0.381818\pi$
$139$	−4.23589	−	2.83033i	−0.359283	−	0.240065i	−0.722090	+	0.691799i	$0.756818\pi$
$140$	0.0479277	−	0.0479277i	0.00405063	−	0.00405063i
$141$	−3.96691	−	3.31840i	−0.334074	−	0.279460i
$142$	−14.2032	+	9.49030i	−1.19191	+	0.796408i
$143$	0.0829254	−	0.416894i	0.00693457	−	0.0348624i
$144$	−1.79173	−	9.98434i	−0.149311	−	0.832029i
$145$	0.211947	+	0.511685i	0.0176012	+	0.0424931i
$146$	−5.75948	−	1.14563i	−0.476658	−	0.0948132i
$147$	−6.39584	−	2.00595i	−0.527520	−	0.165448i
$148$	0.0197824	+	0.0994530i	0.00162611	+	0.00817499i
$149$	15.7137	+	15.7137i	1.28731	+	1.28731i	0.936412	+	0.350902i	$0.114125\pi$
$149$	15.7137	+	15.7137i	1.28731	+	1.28731i	0.350902	+	0.936412i	$0.385875\pi$
$150$	11.2935	−	1.00530i	0.922112	−	0.0820826i
$151$	−3.81101	−	1.57857i	−0.310135	−	0.128462i	0.222187	−	0.975004i	$-0.428681\pi$
$151$	−3.81101	−	1.57857i	−0.310135	−	0.128462i	−0.532322	+	0.846542i	$0.678681\pi$
$152$	−20.0526			−1.62648
$153$		0			0
$154$	−8.46890			−0.682443
$155$	1.16393	+	0.482114i	0.0934887	+	0.0387243i
$156$	−0.0548291	+	0.00488065i	−0.00438984	+	0.000390765i
$157$	9.87094	+	9.87094i	0.787787	+	0.787787i	0.981131	−	0.193344i	$-0.0619335\pi$
$157$	9.87094	+	9.87094i	0.787787	+	0.787787i	−0.193344	+	0.981131i	$0.561933\pi$
$158$	−0.627212	−	3.15321i	−0.0498983	−	0.250856i
$159$	10.5855	+	3.31998i	0.839489	+	0.263292i
$160$	0.211008	+	0.0419721i	0.0166817	+	0.00331819i
$161$	−4.25145	−	10.2639i	−0.335061	−	0.808909i
$162$	11.8215	+	0.444363i	0.928782	+	0.0349125i
$163$	−2.17609	+	10.9399i	−0.170444	+	0.856881i	0.797035	+	0.603933i	$0.206400\pi$
$163$	−2.17609	+	10.9399i	−0.170444	+	0.856881i	−0.967480	+	0.252949i	$0.918600\pi$
$164$	0.995609	−	0.665245i	0.0777440	−	0.0519469i
$165$	−0.680742	−	0.569455i	−0.0529957	−	0.0443320i
$166$	−5.14893	+	5.14893i	−0.399634	+	0.399634i
$167$	1.74605	+	1.16668i	0.135114	+	0.0902801i	0.621290	−	0.783581i	$-0.286609\pi$
$167$	1.74605	+	1.16668i	0.135114	+	0.0902801i	−0.486177	+	0.873861i	$0.661609\pi$
$168$	2.57440	+	8.78281i	0.198619	+	0.677609i
$169$			12.9864i			0.998952i
$170$		0			0
$171$	4.29981	−	19.6772i	0.328815	−	1.50475i
$172$	−0.219734	+	0.530484i	−0.0167545	+	0.0404490i
$173$	6.84154	−	10.2391i	0.520153	−	0.778463i	−0.474662	−	0.880168i	$-0.657430\pi$
$173$	6.84154	−	10.2391i	0.520153	−	0.778463i	0.994815	+	0.101705i	$0.0324297\pi$
$174$	−8.90980	−	0.962121i	−0.675450	−	0.0729382i
$175$	−8.64158	+	1.71892i	−0.653242	+	0.129938i
$176$	−6.84131	−	10.2387i	−0.515683	−	0.771774i
$177$	7.67077	+	14.6811i	0.576570	+	1.10350i
$178$	−4.97628	+	2.06124i	−0.372988	+	0.154497i
$179$	17.0796	−	7.07462i	1.27659	−	0.528782i	0.361630	−	0.932322i	$-0.382220\pi$
$179$	17.0796	−	7.07462i	1.27659	−	0.528782i	0.914962	+	0.403540i	$0.132220\pi$
$180$	−0.0459704	+	0.105341i	−0.00342643	+	0.00785163i
$181$	1.18265	+	1.76995i	0.0879054	+	0.131560i	0.872816	−	0.488049i	$-0.162291\pi$
$181$	1.18265	+	1.76995i	0.0879054	+	0.131560i	−0.784911	+	0.619609i	$0.787291\pi$
$182$	−0.266204	+	0.0529513i	−0.0197324	+	0.00392501i
$183$	0.738981	−	6.84340i	0.0546271	−	0.505879i
$184$	10.4199	−	15.5945i	0.768164	−	1.14964i
$185$	−0.0200517	+	0.0484090i	−0.00147423	+	0.00355910i
$186$	−15.8785	+	12.7834i	−1.16427	+	0.937328i
$187$		0			0
$188$			0.813051i			0.0592979i
$189$	−9.17043	+	0.642943i	−0.667050	+	0.0467672i
$190$	−1.03241	−	0.689832i	−0.0748986	−	0.0500457i
$191$	−12.2604	+	12.2604i	−0.887130	+	0.887130i	−0.994247	−	0.107116i	$-0.965838\pi$
$191$	−12.2604	+	12.2604i	−0.887130	+	0.887130i	0.107116	+	0.994247i	$0.465838\pi$
$192$	−9.74903	+	11.6543i	−0.703575	+	0.841074i
$193$	−13.5001	+	9.02046i	−0.971757	+	0.649307i	−0.936720	−	0.350079i	$-0.886155\pi$
$193$	−13.5001	+	9.02046i	−0.971757	+	0.649307i	−0.0350364	+	0.999386i	$0.511155\pi$
$194$	−1.17629	+	5.91362i	−0.0844529	+	0.424573i
$195$	−0.0249583	−	0.0136435i	−0.00178730	−	0.000977028i
$196$	0.403257	+	0.973548i	0.0288040	+	0.0695391i
$197$	−7.70009	−	1.53164i	−0.548609	−	0.109125i	−0.0869994	−	0.996208i	$-0.527728\pi$
$197$	−7.70009	−	1.53164i	−0.548609	−	0.109125i	−0.461609	+	0.887083i	$0.652728\pi$
$198$	13.3685	−	5.24541i	0.950055	−	0.372775i
$199$	−2.49706	−	12.5536i	−0.177012	−	0.889898i	−0.962554	−	0.271090i	$-0.912616\pi$
$199$	−2.49706	−	12.5536i	−0.177012	−	0.889898i	0.785542	−	0.618808i	$-0.212384\pi$
$200$	−10.5180	−	10.5180i	−0.743732	−	0.743732i
$201$	−0.893554	−	10.0381i	−0.0630264	−	0.708036i
$202$	−6.15356	−	2.54889i	−0.432963	−	0.179339i
$203$	6.96405			0.488780
$204$		0			0
$205$	0.618741			0.0432147
$206$	−19.4007	−	8.03605i	−1.35171	−	0.559898i
$207$	13.0682	+	13.5687i	0.908305	+	0.943090i
$208$	−0.279061	−	0.279061i	−0.0193494	−	0.0193494i
$209$	−4.77008	−	23.9808i	−0.329954	−	1.65879i
$210$	−0.169596	+	0.540745i	−0.0117032	+	0.0373150i
$211$	−5.02173	−	0.998885i	−0.345710	−	0.0687661i	0.0191813	−	0.999816i	$-0.493894\pi$
$211$	−5.02173	−	0.998885i	−0.345710	−	0.0687661i	−0.364892	+	0.931050i	$0.618894\pi$
$212$	−0.667417	−	1.61129i	−0.0458384	−	0.110664i
$213$	−10.7969	+	19.7511i	−0.739792	+	1.35332i
$214$	−0.349398	+	1.75654i	−0.0238843	+	0.120075i
$215$	−0.246700	+	0.164840i	−0.0168248	+	0.0112420i
$216$	−9.50362	−	12.2695i	−0.646640	−	0.834831i
$217$	11.2013	−	11.2013i	0.760395	−	0.760395i
$218$	12.5446	+	8.38205i	0.849630	+	0.567704i
$219$	−7.42568	+	2.17660i	−0.501781	+	0.147081i
$220$			0.139524i			0.00940669i
$221$		0			0
$222$	−0.531678	−	0.660405i	−0.0356839	−	0.0443235i
$223$	−0.0722764	+	0.174491i	−0.00483999	+	0.0116848i	−0.926281	−	0.376833i	$-0.877013\pi$
$223$	−0.0722764	+	0.174491i	−0.00483999	+	0.0116848i	0.921441	+	0.388518i	$0.127013\pi$
$224$	1.50293	−	2.24929i	0.100419	−	0.150287i
$225$	12.5764	−	8.06574i	0.838426	−	0.537716i
$226$	17.4700	−	3.47500i	1.16209	−	0.231154i
$227$	−1.18348	−	1.77120i	−0.0785504	−	0.117559i	0.790114	−	0.612960i	$-0.210021\pi$
$227$	−1.18348	−	1.77120i	−0.0785504	−	0.117559i	−0.868665	+	0.495401i	$0.835021\pi$
$228$	−2.80639	+	1.46633i	−0.185858	+	0.0971098i
$229$	15.9683	−	6.61427i	1.05521	−	0.437084i	0.213463	−	0.976951i	$-0.431526\pi$
$229$	15.9683	−	6.61427i	1.05521	−	0.437084i	0.841750	+	0.539868i	$0.181526\pi$
$230$	1.07293	−	0.444424i	0.0707472	−	0.0293045i
$231$	−9.89094	+	5.16796i	−0.650776	+	0.340027i
$232$	6.53172	+	9.77541i	0.428828	+	0.641787i
$233$	−9.60397	+	1.91035i	−0.629177	+	0.125151i	−0.499371	−	0.866388i	$-0.666435\pi$
$233$	−9.60397	+	1.91035i	−0.629177	+	0.125151i	−0.129806	+	0.991539i	$0.541435\pi$
$234$	0.387416	−	0.248465i	0.0253262	−	0.0162427i
$235$	−0.233412	+	0.349326i	−0.0152261	+	0.0227875i
$236$	0.996510	−	2.40579i	0.0648673	−	0.156603i
$237$	−2.65671	−	3.29993i	−0.172572	−	0.214354i
$238$		0			0
$239$		−	22.4367i		−	1.45131i	−0.688059	−	0.725654i	$-0.741537\pi$
$239$		−	22.4367i		−	1.45131i	0.688059	−	0.725654i	$-0.258463\pi$
$240$	−0.790753	+	0.231784i	−0.0510429	+	0.0149616i
$241$	−0.337157	−	0.225281i	−0.0217182	−	0.0145116i	0.544664	−	0.838655i	$-0.316657\pi$
$241$	−0.337157	−	0.225281i	−0.0217182	−	0.0145116i	−0.566382	+	0.824143i	$0.691657\pi$
$242$	2.10322	−	2.10322i	0.135200	−	0.135200i
$243$	14.0776	−	6.69482i	0.903080	−	0.429473i
$244$	−0.899718	+	0.601172i	−0.0575985	+	0.0384861i
$245$	−0.106229	+	0.534050i	−0.00678674	+	0.0341192i
$246$	−4.80220	+	8.78480i	−0.306177	+	0.560098i
$247$	−0.299877	−	0.723968i	−0.0190807	−	0.0460650i
$248$	26.2292	+	5.21731i	1.66556	+	0.331300i
$249$	−2.87148	+	9.15553i	−0.181973	+	0.580208i
$250$	−0.360088	−	1.81028i	−0.0227739	−	0.114492i
$251$	0.749951	+	0.749951i	0.0473365	+	0.0473365i	0.730379	−	0.683042i	$-0.239344\pi$
$251$	0.749951	+	0.749951i	0.0473365	+	0.0473365i	−0.683042	+	0.730379i	$0.739344\pi$
$252$	1.00253	+	1.04092i	0.0631533	+	0.0655718i
$253$	21.1280	+	8.75152i	1.32831	+	0.550203i
$254$	12.9984			0.815594
$255$		0			0
$256$	6.40833			0.400521
$257$	−18.5997	−	7.70425i	−1.16022	−	0.480578i	−0.282270	−	0.959335i	$-0.591087\pi$
$257$	−18.5997	−	7.70425i	−1.16022	−	0.480578i	−0.877947	+	0.478757i	$0.841087\pi$
$258$	−0.425672	−	4.78198i	−0.0265012	−	0.297713i
$259$	0.465876	+	0.465876i	0.0289481	+	0.0289481i
$260$	0.000872364		0.00438567i	5.41017e−5		0.000271988i
$261$	−10.9930	+	4.31334i	−0.680449	+	0.266989i
$262$	16.7969	+	3.34111i	1.03772	+	0.206415i
$263$	−2.11297	−	5.10116i	−0.130291	−	0.314551i	0.845249	−	0.534373i	$-0.179452\pi$
$263$	−2.11297	−	5.10116i	−0.130291	−	0.314551i	−0.975540	+	0.219822i	$0.929452\pi$
$264$	−16.5312	−	9.03675i	−1.01742	−	0.556173i
$265$	0.175817	−	0.883889i	0.0108003	−	0.0542969i
$266$	−12.9815	+	8.67397i	−0.795948	+	0.531835i
$267$	−4.55404	+	5.44402i	−0.278702	+	0.333169i
$268$	−1.12027	+	1.12027i	−0.0684314	+	0.0684314i
$269$	−7.59932	−	5.07770i	−0.463339	−	0.309593i	0.301900	−	0.953340i	$-0.402379\pi$
$269$	−7.59932	−	5.07770i	−0.463339	−	0.309593i	−0.765239	+	0.643747i	$0.777379\pi$
$270$	−0.0672099	−	0.958628i	−0.00409026	−	0.0583403i
$271$			2.64822i			0.160868i	0.996760	+	0.0804339i	$0.0256306\pi$
$271$			2.64822i			0.160868i	−0.996760	+	0.0804339i	$0.974369\pi$
$272$		0			0
$273$	−0.278591	+	0.224288i	−0.0168611	+	0.0135745i
$274$	−1.61210	+	3.89196i	−0.0973906	+	0.235122i
$275$	10.0764	−	15.0804i	0.607629	−	0.909382i
$276$	0.317951	−	2.94442i	0.0191384	−	0.177233i
$277$	−20.2921	+	4.03634i	−1.21923	+	0.242520i	−0.762444	−	0.647055i	$-0.776001\pi$
$277$	−20.2921	+	4.03634i	−1.21923	+	0.242520i	−0.456789	+	0.889575i	$0.651001\pi$
$278$	−3.72025	−	5.56775i	−0.223126	−	0.333931i
$279$	−10.7439	+	24.6195i	−0.643220	+	1.47393i
$280$	0.686886	−	0.284517i	0.0410493	−	0.0170032i
$281$	9.50546	−	3.93729i	0.567048	−	0.234879i	−0.0806938	−	0.996739i	$-0.525714\pi$
$281$	9.50546	−	3.93729i	0.567048	−	0.234879i	0.647742	+	0.761860i	$0.275714\pi$
$282$	−3.14811	−	6.02516i	−0.187467	−	0.358793i
$283$	−7.13505	−	10.6783i	−0.424134	−	0.634762i	0.556445	−	0.830884i	$-0.312165\pi$
$283$	−7.13505	−	10.6783i	−0.424134	−	0.634762i	−0.980579	+	0.196122i	$0.937165\pi$
$284$	3.47065	−	0.690355i	0.205945	−	0.0409650i
$285$	−1.62672	−	0.175660i	−0.0963584	−	0.0104052i
$286$	0.310403	−	0.464551i	0.0183545	−	0.0274695i
$287$	2.97730	−	7.18785i	0.175745	−	0.424285i
$288$	−0.979277	+	4.48146i	−0.0577044	+	0.264073i
$289$		0			0
$290$			0.727985i			0.0427488i
$291$	2.23485	+	7.62441i	0.131009	+	0.446951i
$292$	1.01147	+	0.675840i	0.0591916	+	0.0395506i
$293$	0.797696	−	0.797696i	0.0466019	−	0.0466019i	−0.683422	−	0.730024i	$-0.739509\pi$
$293$	0.797696	−	0.797696i	0.0466019	−	0.0466019i	0.730024	+	0.683422i	$0.239509\pi$
$294$	−6.75790	−	5.65313i	−0.394129	−	0.329697i
$295$	1.11881	−	0.747562i	0.0651394	−	0.0435248i
$296$	−0.216994	+	1.09090i	−0.0126125	+	0.0634074i
$297$	12.4123	−	14.2840i	0.720235	−	0.828842i
$298$	11.1781	+	26.9863i	0.647530	+	1.56327i
$299$	0.718839	+	0.142986i	0.0415715	+	0.00826909i
$300$	−2.24112	−	0.702891i	−0.129391	−	0.0405814i
$301$	0.727837	+	3.65908i	0.0419518	+	0.210906i
$302$	−3.83394	−	3.83394i	−0.220618	−	0.220618i
$303$	−8.74223	+	0.778197i	−0.502228	+	0.0447062i
$304$	−20.9733	−	8.68744i	−1.20290	−	0.498259i
$305$	−0.559148			−0.0320167
$306$		0			0
$307$	−19.5814			−1.11757			−0.558785	−	0.829312i	$-0.688732\pi$
$307$	−19.5814			−1.11757			−0.558785	+	0.829312i	$0.688732\pi$
$308$	1.62083	+	0.671371i	0.0923555	+	0.0382549i
$309$	−27.5622	+	2.45347i	−1.56796	+	0.139573i
$310$	1.17093	+	1.17093i	0.0665042	+	0.0665042i
$311$	5.73078	+	28.8106i	0.324963	+	1.63370i	0.705342	+	0.708867i	$0.250793\pi$
$311$	5.73078	+	28.8106i	0.324963	+	1.63370i	−0.380380	+	0.924830i	$0.624207\pi$
$312$	−0.576128	−	0.180693i	−0.0326168	−	0.0102297i
$313$	−17.4779	−	3.47657i	−0.987910	−	0.196507i	−0.325413	−	0.945572i	$-0.605503\pi$
$313$	−17.4779	−	3.47657i	−0.987910	−	0.196507i	−0.662497	+	0.749065i	$0.730503\pi$
$314$	7.02180	+	16.9521i	0.396263	+	0.956664i
$315$	0.131905	+	0.735036i	0.00743200	+	0.0414146i
$316$	−0.129930	+	0.653204i	−0.00730915	+	0.0367456i
$317$	−11.7412	+	7.84523i	−0.659452	+	0.440632i	−0.839745	−	0.542981i	$-0.817296\pi$
$317$	−11.7412	+	7.84523i	−0.659452	+	0.440632i	0.180293	+	0.983613i	$0.442296\pi$
$318$	11.1848	+	9.35630i	0.627212	+	0.524675i
$319$	−10.1366	+	10.1366i	−0.567542	+	0.567542i
$320$	1.02627	+	0.685733i	0.0573704	+	0.0383337i
$321$	0.663825	+	2.26470i	0.0370511	+	0.126403i
$322$		−	14.6027i		−	0.813775i
$323$		0			0
$324$	−2.22724	−	1.02219i	−0.123736	−	0.0567883i
$325$	0.222443	−	0.537026i	0.0123389	−	0.0297888i
$326$	−8.14545	+	12.1905i	−0.451135	+	0.675171i
$327$	19.7660	+	2.13442i	1.09306	+	0.118034i
$328$	12.8820	−	2.56239i	0.711291	−	0.141485i
$329$	2.93493	+	4.39244i	0.161808	+	0.242163i
$330$	−0.540232	−	1.03395i	−0.0297388	−	0.0569169i
$331$	−6.68245	+	2.76796i	−0.367301	+	0.152141i	−0.558697	−	0.829372i	$-0.688698\pi$
$331$	−6.68245	+	2.76796i	−0.367301	+	0.152141i	0.191396	+	0.981513i	$0.438698\pi$
$332$	1.39362	−	0.577254i	0.0764846	−	0.0316810i
$333$	−1.02395	−	0.446851i	−0.0561122	−	0.0244873i
$334$	1.53351	+	2.29505i	0.0839097	+	0.125580i
$335$	−0.802931	+	0.159713i	−0.0438688	+	0.00872605i
$336$	−1.11239	+	10.3014i	−0.0606860	+	0.561988i
$337$	−7.42687	+	11.1151i	−0.404568	+	0.605478i	−0.976681	−	0.214696i	$-0.931124\pi$
$337$	−7.42687	+	11.1151i	−0.404568	+	0.605478i	0.572113	+	0.820175i	$0.306124\pi$
$338$	−6.53226	+	15.7703i	−0.355308	+	0.857789i
$339$	18.2829	−	14.7192i	0.992993	−	0.799438i
$340$		0			0
$341$			32.6085i			1.76585i
$342$	15.1194	−	21.7326i	0.817561	−	1.17516i
$343$	15.9900	+	10.6842i	0.863378	+	0.576891i
$344$	−4.45359	+	4.45359i	−0.240121	+	0.240121i
$345$	0.981895	−	1.17378i	0.0528634	−	0.0631944i
$346$	13.4585	−	8.99268i	0.723534	−	0.483450i
$347$	6.53027	−	32.8299i	0.350563	−	1.76240i	−0.255329	−	0.966854i	$-0.582184\pi$
$347$	6.53027	−	32.8299i	0.350563	−	1.76240i	0.605893	−	0.795546i	$-0.292816\pi$
$348$	1.62894	+	0.890460i	0.0873205	+	0.0477337i
$349$	−10.6503	−	25.7122i	−0.570099	−	1.37634i	−0.901471	−	0.432840i	$-0.857511\pi$
$349$	−10.6503	−	25.7122i	−0.570099	−	1.37634i	0.331372	−	0.943500i	$-0.392489\pi$
$350$	−11.3587	−	2.25939i	−0.607148	−	0.120769i
$351$	0.300848	−	0.526598i	0.0160581	−	0.0281077i
$352$	1.08638	+	5.46161i	0.0579043	+	0.291105i
$353$	5.10785	+	5.10785i	0.271864	+	0.271864i	0.829850	−	0.557986i	$-0.188426\pi$
$353$	5.10785	+	5.10785i	0.271864	+	0.271864i	−0.557986	+	0.829850i	$0.688426\pi$
$354$	1.93046	+	21.6867i	0.102603	+	1.15263i
$355$	1.68935	+	0.699750i	0.0896611	+	0.0371389i
$356$	1.11580			0.0591371
$357$		0			0
$358$	24.2996			1.28427
$359$	25.4579	+	10.5450i	1.34362	+	0.556544i	0.934508	−	0.355942i	$-0.115840\pi$
$359$	25.4579	+	10.5450i	1.34362	+	0.556544i	0.409108	+	0.912486i	$0.365840\pi$
$360$	−0.908051	+	0.874559i	−0.0478585	+	0.0460933i
$361$	−18.4383	−	18.4383i	−0.970437	−	0.970437i
$362$	0.545867	+	2.74426i	0.0286901	+	0.144235i
$363$	1.17293	−	3.73982i	0.0615630	−	0.196290i
$364$	0.0551455	+	0.0109691i	0.00289041	+	0.000574939i
$365$	0.240553	+	0.580747i	0.0125911	+	0.0303977i
$366$	4.33968	−	7.93870i	0.226839	−	0.414963i
$367$	2.19159	−	11.0178i	0.114400	−	0.575127i	−0.880482	−	0.474080i	$-0.842781\pi$
$367$	2.19159	−	11.0178i	0.114400	−	0.575127i	0.994882	−	0.101047i	$-0.0322192\pi$
$368$	17.6544	−	11.7963i	0.920297	−	0.614923i
$369$	−0.247822	+	13.1903i	−0.0129011	+	0.686661i
$370$	−0.0487002	+	0.0487002i	−0.00253180	+	0.00253180i
$371$	−9.42204	−	6.29561i	−0.489168	−	0.326852i
$372$	4.05234	−	1.18781i	0.210104	−	0.0615853i
$373$			5.50325i			0.284948i	0.989799	+	0.142474i	$0.0455057\pi$
$373$			5.50325i			0.284948i	−0.989799	+	0.142474i	$0.954494\pi$
$374$		0			0
$375$	−1.52524	−	1.89452i	−0.0787630	−	0.0978326i
$376$	−3.41292	+	8.23951i	−0.176008	+	0.424920i
$377$	−0.255247	+	0.382005i	−0.0131459	+	0.0196742i
$378$	−11.4597	−	3.83203i	−0.589423	−	0.197098i
$379$	−5.16575	+	1.02753i	−0.265347	+	0.0527808i	−0.325971	−	0.945380i	$-0.605691\pi$
$379$	−5.16575	+	1.02753i	−0.265347	+	0.0527808i	0.0606237	+	0.998161i	$0.480691\pi$
$380$	0.142902	+	0.213868i	0.00733073	+	0.0109712i
$381$	15.1811	−	7.93202i	0.777749	−	0.406370i
$382$	−21.0557	+	8.72156i	−1.07730	+	0.446234i
$383$	−19.5477	+	8.09691i	−0.998840	+	0.413733i	−0.821372	−	0.570394i	$-0.806791\pi$
$383$	−19.5477	+	8.09691i	−0.998840	+	0.413733i	−0.177468	+	0.984127i	$0.556791\pi$
$384$	−13.0065	+	6.79580i	−0.663733	+	0.346797i
$385$	0.503649	+	0.753764i	0.0256683	+	0.0384154i
$386$	−20.9314	+	4.16352i	−1.06538	+	0.211918i
$387$	−3.41525	−	5.32519i	−0.173607	−	0.270694i
$388$	0.693928	−	1.03854i	0.0352289	−	0.0527237i
$389$	4.78245	−	11.5459i	0.242480	−	0.585398i	−0.755048	−	0.655669i	$-0.772387\pi$
$389$	4.78245	−	11.5459i	0.242480	−	0.585398i	0.997528	+	0.0702713i	$0.0223865\pi$
$390$	−0.0234459	−	0.0291224i	−0.00118723	−	0.00147467i
$391$		0			0
$392$			11.5587i			0.583804i
$393$	21.6562	−	6.34783i	1.09241	−	0.320206i
$394$	−8.58033	−	5.73319i	−0.432271	−	0.288834i
$395$	−0.243347	+	0.243347i	−0.0122441	+	0.0122441i
$396$	−2.97437	−	0.0558828i	−0.149468	−	0.00280822i
$397$	32.3438	−	21.6114i	1.62329	−	1.08465i	0.691049	−	0.722808i	$-0.257149\pi$
$397$	32.3438	−	21.6114i	1.62329	−	1.08465i	0.932240	−	0.361839i	$-0.117851\pi$
$398$	3.28219	−	16.5007i	0.164521	−	0.827105i
$399$	−9.86819	+	18.0521i	−0.494027	+	0.903738i
$400$	−6.44418	−	15.5576i	−0.322209	−	0.777881i
$401$	26.7045	+	5.31186i	1.33356	+	0.265262i	0.809851	−	0.586635i	$-0.199548\pi$
$401$	26.7045	+	5.31186i	1.33356	+	0.265262i	0.523709	+	0.851897i	$0.324548\pi$
$402$	3.96417	−	12.6395i	0.197715	−	0.630400i
$403$	0.203883	+	1.02499i	0.0101561	+	0.0510583i
$404$	0.975645	+	0.975645i	0.0485401	+	0.0485401i
$405$	−0.663478	−	1.07858i	−0.0329685	−	0.0535952i
$406$	8.45693	+	3.50297i	0.419710	+	0.173850i
$407$	−1.35623			−0.0672256
$408$		0			0
$409$	28.2231			1.39554			0.697770	−	0.716322i	$-0.254176\pi$
$409$	28.2231			1.39554			0.697770	+	0.716322i	$0.254176\pi$
$410$	0.751380	+	0.311232i	0.0371080	+	0.0153706i
$411$	0.492188	+	5.52922i	0.0242778	+	0.272736i
$412$	3.07598	+	3.07598i	0.151543	+	0.151543i
$413$	−3.30080	−	16.5942i	−0.162422	−	0.816549i
$414$	9.04450	+	23.0508i	0.444513	+	1.13289i
$415$	0.764483	+	0.152065i	0.0375270	+	0.00746459i
$416$	0.0682967	+	0.164883i	0.00334852	+	0.00808405i
$417$	−7.74253	−	4.23245i	−0.379154	−	0.207264i
$418$	6.26991	−	31.5210i	0.306671	−	1.54174i
$419$	7.76628	−	5.18926i	0.379408	−	0.253512i	−0.351213	−	0.936295i	$-0.614231\pi$
$419$	7.76628	−	5.18926i	0.379408	−	0.253512i	0.730621	+	0.682784i	$0.239231\pi$
$420$	0.0753258	−	0.0900466i	0.00367552	−	0.00439382i
$421$	9.40617	−	9.40617i	0.458429	−	0.458429i	−0.439711	−	0.898139i	$-0.644919\pi$
$421$	9.40617	−	9.40617i	0.458429	−	0.458429i	0.898139	+	0.439711i	$0.144919\pi$
$422$	−5.59579	−	3.73899i	−0.272399	−	0.182011i
$423$	−7.35345	−	5.11580i	−0.357537	−	0.248739i
$424$		−	19.1305i		−	0.929057i
$425$		0			0
$426$	−23.0464	+	18.5542i	−1.11660	+	0.898952i
$427$	−2.69055	+	6.49556i	−0.130205	+	0.314342i
$428$	0.206119	−	0.308480i	0.00996316	−	0.0149109i
$429$	0.0790418	−	0.731973i	0.00381617	−	0.0353400i
$430$	−0.382501	+	0.0760842i	−0.0184459	+	0.00366911i
$431$	8.11718	+	12.1482i	0.390991	+	0.585159i	0.973788	−	0.227459i	$-0.0730416\pi$
$431$	8.11718	+	12.1482i	0.390991	+	0.585159i	−0.582797	+	0.812618i	$0.698042\pi$
$432$	−4.62446	−	16.9501i	−0.222494	−	0.815513i
$433$	−16.4827	+	6.82738i	−0.792110	+	0.328103i	−0.741792	−	0.670631i	$-0.766024\pi$
$433$	−16.4827	+	6.82738i	−0.792110	+	0.328103i	−0.0503185	+	0.998733i	$0.516024\pi$
$434$	19.2369	−	7.96819i	0.923401	−	0.382485i
$435$	0.444237	+	0.850224i	0.0212996	+	0.0407651i
$436$	−1.73639	−	2.59869i	−0.0831578	−	0.124454i
$437$	41.3495	−	8.22492i	1.97801	−	0.393451i
$438$	−10.1124	−	1.09198i	−0.483187	−	0.0521768i
$439$	14.6447	−	21.9174i	0.698955	−	1.04606i	−0.296882	−	0.954914i	$-0.595947\pi$
$439$	14.6447	−	21.9174i	0.698955	−	1.04606i	0.995838	−	0.0911464i	$-0.0290531\pi$
$440$	−0.585674	+	1.41394i	−0.0279209	+	0.0674070i
$441$	−11.3424	−	2.47850i	−0.540112	−	0.118024i
$442$		0			0
$443$			9.67036i			0.459453i	0.973255	+	0.229726i	$0.0737831\pi$
$443$			9.67036i			0.459453i	−0.973255	+	0.229726i	$0.926217\pi$
$444$	0.0494025	+	0.168541i	0.00234454	+	0.00799861i
$445$	0.479400	+	0.320325i	0.0227257	+	0.0151848i
$446$	−0.175541	+	0.175541i	−0.00831208	+	0.00831208i
$447$	29.5229	+	24.6965i	1.39638	+	1.16810i
$448$	12.9044	−	8.62244i	0.609675	−	0.407372i
$449$	−0.206155	+	1.03641i	−0.00972906	+	0.0489113i	−0.985345	−	0.170574i	$-0.945438\pi$
$449$	−0.206155	+	1.03641i	−0.00972906	+	0.0489113i	0.975616	+	0.219485i	$0.0704378\pi$
$450$	19.3295	−	3.46875i	0.911202	−	0.163519i
$451$	6.12872	+	14.7960i	0.288590	+	0.696718i
$452$	−3.61901	−	0.719865i	−0.170224	−	0.0338596i
$453$	−6.81729	−	2.13813i	−0.320304	−	0.100458i
$454$	−0.546252	−	2.74620i	−0.0256369	−	0.128885i
$455$	0.0205441	+	0.0205441i	0.000963124	+	0.000963124i
$456$	−34.5953	+	3.07953i	−1.62007	+	0.144212i
$457$	19.7952	+	8.19942i	0.925978	+	0.383553i	0.794151	−	0.607720i	$-0.207916\pi$
$457$	19.7952	+	8.19942i	0.925978	+	0.383553i	0.131827	+	0.991273i	$0.457916\pi$
$458$	22.7184			1.06156
$459$		0			0
$460$	−0.240577			−0.0112169
$461$	22.7649	+	9.42954i	1.06027	+	0.439177i	0.843547	−	0.537056i	$-0.180464\pi$
$461$	22.7649	+	9.42954i	1.06027	+	0.439177i	0.216721	+	0.976233i	$0.430464\pi$
$462$	−14.6108	+	1.30059i	−0.679755	+	0.0605090i
$463$	−13.6466	−	13.6466i	−0.634213	−	0.634213i	0.314909	−	0.949122i	$-0.398026\pi$
$463$	−13.6466	−	13.6466i	−0.634213	−	0.634213i	−0.949122	+	0.314909i	$0.898026\pi$
$464$	2.59661	+	13.0540i	0.120544	+	0.606018i
$465$	2.08208	+	0.653009i	0.0965540	+	0.0302826i
$466$	−12.6237	−	2.51101i	−0.584781	−	0.116320i
$467$	−4.76264	−	11.4980i	−0.220389	−	0.532066i	0.774554	−	0.632508i	$-0.217974\pi$
$467$	−4.76264	−	11.4980i	−0.220389	−	0.532066i	−0.994943	+	0.100442i	$0.967974\pi$
$468$	−0.0938432	+	0.0168405i	−0.00433790	+	0.000778452i
$469$	−2.00824	+	10.0961i	−0.0927317	+	0.466194i
$470$	−0.459162	+	0.306802i	−0.0211796	+	0.0141517i
$471$	18.5455	+	15.5137i	0.854533	+	0.714835i
$472$	20.1974	−	20.1974i	0.929660	−	0.929660i
$473$	−6.38545	−	4.26662i	−0.293603	−	0.196179i
$474$	−1.56633	−	5.34369i	−0.0719440	−	0.245444i
$475$		−	33.4363i		−	1.53416i
$476$		0			0
$477$	18.7724	+	4.10208i	0.859527	+	0.187821i
$478$	11.2858	−	27.2464i	0.516202	−	1.24622i
$479$	−12.6109	+	18.8736i	−0.576208	+	0.862357i	−0.999038	−	0.0438524i	$-0.986037\pi$
$479$	−12.6109	+	18.8736i	−0.576208	+	0.862357i	0.422830	+	0.906209i	$0.361037\pi$
$480$	0.370483	+	0.0400064i	0.0169102	+	0.00182604i
$481$	−0.0426304	+	0.00847972i	−0.00194378	+	0.000386642i
$482$	−0.296115	−	0.443167i	−0.0134877	−	0.0201857i
$483$	−8.91097	−	17.0547i	−0.405463	−	0.776014i
$484$	−0.569259	+	0.235795i	−0.0258754	+	0.0107179i
$485$	0.596290	−	0.246991i	0.0270761	−	0.0112153i
$486$	20.4630	−	1.04883i	0.928220	−	0.0475757i
$487$	−12.7700	−	19.1116i	−0.578662	−	0.866028i	0.420486	−	0.907299i	$-0.361859\pi$
$487$	−12.7700	−	19.1116i	−0.578662	−	0.866028i	−0.999148	+	0.0412704i	$0.986859\pi$
$488$	−11.6413	+	2.31560i	−0.526977	+	0.104822i
$489$	−2.07417	+	19.2081i	−0.0937974	+	0.868619i
$490$	−0.397633	+	0.595100i	−0.0179632	+	0.0268839i
$491$	7.79649	−	18.8224i	0.351851	−	0.849443i	−0.644541	−	0.764570i	$-0.722951\pi$
$491$	7.79649	−	18.8224i	0.351851	−	0.849443i	0.996392	−	0.0848732i	$-0.0270485\pi$
$492$	1.61549	−	1.30060i	0.0728319	−	0.0586355i
$493$		0			0
$494$		−	1.03001i		−	0.0463421i
$495$	−1.26189	−	0.877897i	−0.0567177	−	0.0394585i
$496$	25.1733	+	16.8202i	1.13031	+	0.755251i
$497$	16.2578	−	16.2578i	0.729264	−	0.729264i
$498$	−8.09235	+	9.67381i	−0.362627	+	0.433494i
$499$	0.897288	−	0.599548i	0.0401681	−	0.0268395i	−0.535324	−	0.844647i	$-0.679811\pi$
$499$	0.897288	−	0.599548i	0.0401681	−	0.0268395i	0.575492	+	0.817807i	$0.304811\pi$
$500$	−0.0745940	+	0.375010i	−0.00333595	+	0.0167709i
$501$	3.19151	+	1.74464i	0.142586	+	0.0779446i
$502$	0.533486	+	1.28795i	0.0238106	+	0.0574840i
$503$	−9.20449	−	1.83089i	−0.410408	−	0.0816353i	−0.0144315	−	0.999896i	$-0.504594\pi$
$503$	−9.20449	−	1.83089i	−0.410408	−	0.0816353i	−0.395977	+	0.918261i	$0.629594\pi$
$504$	5.79023	+	14.7570i	0.257918	+	0.657329i
$505$	0.139094	+	0.699273i	0.00618961	+	0.0311173i
$506$	21.2552	+	21.2552i	0.944907	+	0.944907i
$507$	1.99435	+	22.4045i	0.0885723	+	0.995018i
$508$	−2.48772	−	1.03045i	−0.110375	−	0.0457188i
$509$	7.99190			0.354235			0.177117	−	0.984190i	$-0.443323\pi$
$509$	7.99190			0.354235			0.177117	+	0.984190i	$0.443323\pi$
$510$		0			0
$511$	7.90399			0.349652
$512$	23.4372	+	9.70803i	1.03579	+	0.429038i
$513$	4.39627	−	34.6080i	0.194100	−	1.52798i
$514$	−18.7116	−	18.7116i	−0.825334	−	0.825334i
$515$	0.438531	+	2.20465i	0.0193240	+	0.0971483i
$516$	−0.297623	+	0.948952i	−0.0131021	+	0.0417753i
$517$	−10.6655	−	2.12149i	−0.469066	−	0.0933031i
$518$	0.331406	+	0.800085i	0.0145611	+	0.0351537i
$519$	10.2308	−	18.7154i	0.449081	−	0.821517i
$520$	−0.00956898	+	0.0481065i	−0.000419627	+	0.00210961i
$521$	−1.31074	+	0.875810i	−0.0574246	+	0.0383699i	−0.583951	−	0.811789i	$-0.698494\pi$
$521$	−1.31074	+	0.875810i	−0.0574246	+	0.0383699i	0.526527	+	0.850159i	$0.323494\pi$
$522$	−15.5192	−	0.291577i	−0.679257	−	0.0127620i
$523$	−24.2095	+	24.2095i	−1.05861	+	1.05861i	−0.0604341	+	0.998172i	$0.519249\pi$
$523$	−24.2095	+	24.2095i	−1.05861	+	1.05861i	−0.998172	+	0.0604341i	$0.980751\pi$
$524$	−2.94984	−	1.97102i	−0.128864	−	0.0861043i
$525$	−14.6447	+	4.29264i	−0.639149	+	0.187346i
$526$		−	7.25753i		−	0.316443i
$527$		0			0
$528$	−13.3752	−	16.6135i	−0.582081	−	0.723011i
$529$	−6.28827	+	15.1812i	−0.273403	+	0.660054i
$530$	0.658110	−	0.984931i	0.0285865	−	0.0427827i
$531$	15.4884	+	24.1502i	0.672141	+	1.04803i
$532$	3.17211	−	0.630973i	0.137529	−	0.0273561i
$533$	0.285156	+	0.426766i	0.0123515	+	0.0184853i
$534$	−8.26867	+	4.32033i	−0.357820	+	0.186959i
$535$	0.177118	−	0.0733645i	0.00765746	−	0.00317183i
$536$	−16.0554	+	6.65037i	−0.693488	+	0.287252i
$537$	28.3798	−	14.8283i	1.22468	−	0.639889i
$538$	−6.67425	−	9.98873i	−0.287747	−	0.430645i
$539$	−13.8230	+	2.74957i	−0.595401	+	0.118433i
$540$	−0.0631321	+	0.188797i	−0.00271677	+	0.00812451i
$541$	1.68432	−	2.52076i	0.0724146	−	0.108376i	−0.793495	−	0.608577i	$-0.791741\pi$
$541$	1.68432	−	2.52076i	0.0724146	−	0.108376i	0.865909	+	0.500201i	$0.166741\pi$
$542$	−1.33208	+	3.21592i	−0.0572176	+	0.138135i
$543$	2.31215	+	2.87196i	0.0992239	+	0.123247i
$544$		0			0
$545$		−	1.61500i		−	0.0691792i
$546$	−0.451131	+	0.132235i	−0.0193066	+	0.00565912i
$547$	−1.44506	−	0.965555i	−0.0617861	−	0.0412842i	0.524294	−	0.851538i	$-0.324329\pi$
$547$	−1.44506	−	0.965555i	−0.0617861	−	0.0412842i	−0.586080	+	0.810253i	$0.699329\pi$
$548$	0.617069	−	0.617069i	0.0263599	−	0.0263599i
$549$	0.223953	−	11.9199i	0.00955807	−	0.508730i
$550$	19.8220	−	13.2447i	0.845214	−	0.564754i
$551$	−5.15580	+	25.9200i	−0.219645	+	1.10423i
$552$	15.5818	−	28.5042i	0.663206	−	1.21322i
$553$	1.65598	+	3.99789i	0.0704195	+	0.170008i
$554$	−26.6724	−	5.30547i	−1.13320	−	0.225408i
$555$	−0.0271594	+	0.0865959i	−0.00115285	+	0.00367579i
$556$	0.270623	+	1.36051i	0.0114770	+	0.0576986i
$557$	−29.9311	−	29.9311i	−1.26822	−	1.26822i	−0.947006	−	0.321217i	$-0.895908\pi$
$557$	−29.9311	−	29.9311i	−1.26822	−	1.26822i	−0.321217	−	0.947006i	$-0.604092\pi$
$558$	−25.4309	+	24.4929i	−1.07657	+	1.03687i
$559$	−0.227391	−	0.0941886i	−0.00961763	−	0.00398375i
$560$	0.841688			0.0355678
$561$		0			0
$562$	13.5236			0.570460
$563$	−26.2627	−	10.8784i	−1.10684	−	0.458468i	−0.246991	−	0.969018i	$-0.579442\pi$
$563$	−26.2627	−	10.8784i	−1.10684	−	0.458468i	−0.859848	+	0.510550i	$0.829442\pi$
$564$	0.124862	+	1.40270i	0.00525766	+	0.0590643i
$565$	−1.34824	−	1.34824i	−0.0567208	−	0.0567208i
$566$	−3.29328	−	16.5564i	−0.138427	−	0.695919i
$567$	−15.7223	+	2.51755i	−0.660276	+	0.105727i
$568$	38.0696	+	7.57252i	1.59737	+	0.317736i
$569$	7.98685	+	19.2820i	0.334826	+	0.808342i	0.998195	+	0.0600499i	$0.0191260\pi$
$569$	7.98685	+	19.2820i	0.334826	+	0.808342i	−0.663369	+	0.748292i	$0.730874\pi$
$570$	−1.88708	−	1.03157i	−0.0790410	−	0.0432077i
$571$	1.22502	−	6.15858i	0.0512654	−	0.257728i	−0.946650	−	0.322263i	$-0.895556\pi$
$571$	1.22502	−	6.15858i	0.0512654	−	0.257728i	0.997915	+	0.0645348i	$0.0205564\pi$
$572$	−0.0962342	+	0.0643017i	−0.00402376	+	0.00268859i
$573$	−19.2691	+	23.0348i	−0.804979	+	0.962294i
$574$	7.23109	−	7.23109i	0.301820	−	0.301820i
$575$	26.0027	+	17.3744i	1.08439	+	0.724564i
$576$	−15.0295	+	21.6034i	−0.626230	+	0.900144i
$577$			36.1978i			1.50693i	0.657485	+	0.753467i	$0.271620\pi$
$577$			36.1978i			1.50693i	−0.657485	+	0.753467i	$0.728380\pi$
$578$		0			0
$579$	−21.9054	+	17.6356i	−0.910358	+	0.732911i
$580$	0.0577109	−	0.139326i	0.00239632	−	0.00578522i
$581$	5.44512	−	8.14920i	0.225902	−	0.338086i
$582$	−1.12120	+	10.3830i	−0.0464754	+	0.430389i
$583$	22.8781	−	4.55073i	0.947513	−	0.188472i
$584$	7.41331	+	11.0948i	0.306765	+	0.459106i
$585$	−0.0451541	−	0.0197052i	−0.00186689	−	0.000814708i
$586$	1.36995	−	0.567450i	0.0565919	−	0.0234412i
$587$	7.20502	−	2.98442i	0.297383	−	0.123180i	−0.229003	−	0.973426i	$-0.573547\pi$
$587$	7.20502	−	2.98442i	0.297383	−	0.123180i	0.526386	+	0.850246i	$0.323547\pi$
$588$	0.845221	+	1.61766i	0.0348563	+	0.0667113i
$589$	33.3981	+	49.9838i	1.37615	+	2.05955i
$590$	1.73467	−	0.345048i	0.0714154	−	0.0142054i
$591$	−13.5196	−	1.45991i	−0.556124	−	0.0600528i
$592$	−0.699572	+	1.04698i	−0.0287523	+	0.0430308i
$593$	−11.6027	+	28.0114i	−0.476465	+	1.15029i	0.484790	+	0.874630i	$0.338896\pi$
$593$	−11.6027	+	28.0114i	−0.476465	+	1.15029i	−0.961256	+	0.275659i	$0.911104\pi$
$594$	22.2581	−	11.1026i	0.913261	−	0.455543i
$595$		0			0
$596$		−	6.05095i		−	0.247857i
$597$	−6.23588	−	21.2743i	−0.255218	−	0.870698i
$598$	0.801013	+	0.535220i	0.0327558	+	0.0218868i
$599$	17.7610	−	17.7610i	0.725695	−	0.725695i	−0.244064	−	0.969759i	$-0.578481\pi$
$599$	17.7610	−	17.7610i	0.725695	−	0.725695i	0.969759	+	0.244064i	$0.0784808\pi$
$600$	−19.7611	−	16.5306i	−0.806746	−	0.674859i
$601$	−25.3288	+	16.9242i	−1.03318	+	0.690351i	−0.951922	−	0.306341i	$-0.900895\pi$
$601$	−25.3288	+	16.9242i	−1.03318	+	0.690351i	−0.0812623	+	0.996693i	$0.525895\pi$
$602$	−0.956686	+	4.80958i	−0.0389916	+	0.196024i
$603$	−3.08317	−	17.1809i	−0.125556	−	0.699659i
$604$	0.429829	+	1.03770i	0.0174895	+	0.0422233i
$605$	−0.312273	−	0.0621150i	−0.0126957	−	0.00252534i
$606$	−11.0077	−	3.45240i	−0.447159	−	0.140244i
$607$	−4.25153	−	21.3739i	−0.172564	−	0.867539i	−0.965932	−	0.258796i	$-0.916674\pi$
$607$	−4.25153	−	21.3739i	−0.172564	−	0.867539i	0.793368	−	0.608743i	$-0.208326\pi$
$608$	7.25911	+	7.25911i	0.294396	+	0.294396i
$609$	12.0146	−	1.06949i	0.486855	−	0.0433378i
$610$	−0.679012	−	0.281256i	−0.0274924	−	0.0113877i
$611$	−0.348513			−0.0140993
$612$		0			0
$613$	17.5623			0.709337			0.354668	−	0.934992i	$-0.384594\pi$
$613$	17.5623			0.709337			0.354668	+	0.934992i	$0.384594\pi$
$614$	−23.7791	−	9.84962i	−0.959646	−	0.397498i
$615$	1.06747	−	0.0950217i	0.0430445	−	0.00383164i
$616$	13.6074	+	13.6074i	0.548258	+	0.548258i
$617$	4.61012	+	23.1766i	0.185596	+	0.933056i	0.955521	+	0.294922i	$0.0952935\pi$
$617$	4.61012	+	23.1766i	0.185596	+	0.933056i	−0.769925	+	0.638134i	$0.779706\pi$
$618$	−34.7048	−	10.8846i	−1.39603	−	0.437843i
$619$	−39.1709	−	7.79157i	−1.57441	−	0.313170i	−0.670837	−	0.741605i	$-0.734065\pi$
$619$	−39.1709	−	7.79157i	−1.57441	−	0.313170i	−0.903572	+	0.428435i	$0.859065\pi$
$620$	−0.131275	−	0.316925i	−0.00527211	−	0.0127280i
$621$	24.6295	+	21.4022i	0.988347	+	0.858840i
$622$	−7.53267	+	37.8693i	−0.302033	+	1.51842i
$623$	6.02799	−	4.02777i	0.241506	−	0.161369i
$624$	−0.524300	−	0.438588i	−0.0209888	−	0.0175576i
$625$	17.4680	−	17.4680i	0.698719	−	0.698719i
$626$	−19.4759	−	13.0134i	−0.778413	−	0.520119i
$627$	−11.9123	−	40.6399i	−0.475731	−	1.62300i
$628$		−	3.80106i		−	0.151679i
$629$		0			0
$630$	−0.209548	+	0.958955i	−0.00834859	+	0.0382057i
$631$	10.2510	−	24.7481i	0.408085	−	0.985205i	−0.577556	−	0.816351i	$-0.695993\pi$
$631$	10.2510	−	24.7481i	0.408085	−	0.985205i	0.985641	−	0.168854i	$-0.0540067\pi$
$632$	−4.05865	+	6.07420i	−0.161444	+	0.241619i
$633$	−8.81704	−	0.952104i	−0.350446	−	0.0378428i
$634$	−18.2044	+	3.62108i	−0.722988	+	0.143811i
$635$	−0.773023	−	1.15691i	−0.0306765	−	0.0459106i
$636$	−1.39890	−	2.67734i	−0.0554699	−	0.106164i
$637$	−0.417310	+	0.172855i	−0.0165344	+	0.00684878i
$638$	−17.4084	+	7.21080i	−0.689206	+	0.285478i
$639$	−15.5939	+	35.7332i	−0.616885	+	1.41358i
$640$	0.662291	+	0.991189i	0.0261794	+	0.0391802i
$641$	−41.7612	+	8.30682i	−1.64947	+	0.328100i	−0.930318	−	0.366754i	$-0.880469\pi$
$641$	−41.7612	+	8.30682i	−1.64947	+	0.328100i	−0.719151	+	0.694854i	$0.755469\pi$
$642$	−0.333034	+	3.08409i	−0.0131438	+	0.121719i
$643$	14.3260	−	21.4404i	0.564962	−	0.845525i	−0.433490	−	0.901159i	$-0.642718\pi$
$643$	14.3260	−	21.4404i	0.564962	−	0.845525i	0.998451	+	0.0556337i	$0.0177179\pi$
$644$	−1.15763	+	2.79475i	−0.0456168	+	0.110129i
$645$	−0.400300	+	0.322273i	−0.0157618	+	0.0126895i
$646$		0			0
$647$		−	38.1903i		−	1.50142i	−0.660634	−	0.750709i	$-0.729712\pi$
$647$		−	38.1903i		−	1.50142i	0.660634	−	0.750709i	$-0.270288\pi$
$648$	−18.2802	−	19.7081i	−0.718113	−	0.774209i
$649$	28.9585	+	19.3495i	1.13672	+	0.759533i
$650$	0.540257	−	0.540257i	0.0211906	−	0.0211906i
$651$	17.6046	−	21.0451i	0.689980	−	0.824821i
$652$	2.52533	−	1.68737i	0.0988996	−	0.0660826i
$653$	−6.69257	+	33.6458i	−0.261901	+	1.31666i	0.596057	+	0.802942i	$0.296733\pi$
$653$	−6.69257	+	33.6458i	−0.261901	+	1.31666i	−0.857957	+	0.513721i	$0.828267\pi$
$654$	22.9296	+	12.5345i	0.896619	+	0.490136i
$655$	−0.701548	−	1.69369i	−0.0274118	−	0.0661778i
$656$	14.5836	+	2.90087i	0.569396	+	0.113260i
$657$	−12.4767	+	4.89552i	−0.486763	+	0.190992i
$658$	1.35466	+	6.81033i	0.0528101	+	0.265494i
$659$	−24.7106	−	24.7106i	−0.962589	−	0.962589i	0.0367361	−	0.999325i	$-0.488304\pi$
$659$	−24.7106	−	24.7106i	−0.962589	−	0.962589i	−0.999325	+	0.0367361i	$0.988304\pi$
$660$	0.0214270	+	0.240710i	0.000834046	+	0.00936964i
$661$	11.2271	+	4.65040i	0.436682	+	0.180880i	0.590184	−	0.807269i	$-0.299055\pi$
$661$	11.2271	+	4.65040i	0.436682	+	0.180880i	−0.153502	+	0.988148i	$0.549055\pi$
$662$	−9.50727			−0.369510
$663$		0			0
$664$	16.5461			0.642113
$665$	1.54403	+	0.639559i	0.0598750	+	0.0248011i
$666$	−1.01869	−	1.05770i	−0.0394733	−	0.0409850i
$667$	−17.4783	−	17.4783i	−0.676762	−	0.676762i
$668$	−0.111552	−	0.560811i	−0.00431608	−	0.0216984i
$669$	−0.0978964	+	0.312136i	−0.00378489	+	0.0120679i
$670$	−1.05539	−	0.209931i	−0.0407734	−	0.00811032i
$671$	−5.53844	−	13.3710i	−0.213809	−	0.516181i
$672$	2.24747	−	4.11136i	0.0866980	−	0.158599i
$673$	7.90952	−	39.7638i	0.304890	−	1.53278i	−0.459587	−	0.888133i	$-0.652003\pi$
$673$	7.90952	−	39.7638i	0.304890	−	1.53278i	0.764477	−	0.644651i	$-0.222997\pi$
$674$	−14.6100	+	9.76206i	−0.562755	+	0.376021i
$675$	20.4585	−	15.8466i	0.787447	−	0.609937i
$676$	2.50037	−	2.50037i	0.0961681	−	0.0961681i
$677$	−5.69882	−	3.80783i	−0.219024	−	0.146347i	0.441219	−	0.897400i	$-0.354546\pi$
$677$	−5.69882	−	3.80783i	−0.219024	−	0.146347i	−0.660242	+	0.751053i	$0.729546\pi$
$678$	29.6061	−	8.67810i	1.13702	−	0.333280i
$679$		−	8.11552i		−	0.311445i
$680$		0			0
$681$	−2.31378	−	2.87398i	−0.0886644	−	0.110131i
$682$	−16.4024	+	39.5988i	−0.628079	+	1.51632i
$683$	−5.48609	+	8.21052i	−0.209919	+	0.314167i	−0.921456	−	0.388482i	$-0.872999\pi$
$683$	−5.48609	+	8.21052i	−0.209919	+	0.314167i	0.711537	+	0.702649i	$0.247999\pi$
$684$	−4.61649	+	2.96073i	−0.176516	+	0.113206i
$685$	0.442271	−	0.0879732i	0.0168983	−	0.00336128i
$686$	14.0435	+	21.0176i	0.536184	+	0.802457i
$687$	26.5332	−	13.8634i	1.01230	−	0.528923i
$688$	−6.58752	+	2.72864i	−0.251147	+	0.104028i
$689$	0.690676	−	0.286087i	0.0263127	−	0.0108991i
$690$	1.78281	−	0.931507i	0.0678703	−	0.0354619i
$691$	−7.70668	−	11.5339i	−0.293176	−	0.438769i	0.655417	−	0.755267i	$-0.272493\pi$
$691$	−7.70668	−	11.5339i	−0.293176	−	0.438769i	−0.948593	+	0.316498i	$0.897493\pi$
$692$	−3.28867	+	0.654157i	−0.125016	+	0.0248673i
$693$	−16.2705	+	10.4349i	−0.618065	+	0.396389i
$694$	24.4439	−	36.5828i	0.927876	−	1.38867i
$695$	−0.274306	+	0.662233i	−0.0104050	+	0.0251199i
$696$	12.7699	+	15.8617i	0.484044	+	0.601237i
$697$		0			0
$698$		−	36.5813i		−	1.38462i
$699$	−16.2757	+	4.77070i	−0.615602	+	0.180444i
$700$	1.99479	+	1.33288i	0.0753960	+	0.0503780i
$701$	−7.15325	+	7.15325i	−0.270175	+	0.270175i	−0.829170	−	0.558996i	$-0.811187\pi$
$701$	−7.15325	+	7.15325i	−0.270175	+	0.270175i	0.558996	+	0.829170i	$0.311187\pi$
$702$	0.630224	−	0.488156i	0.0237863	−	0.0184242i
$703$	−2.07888	+	1.38907i	−0.0784066	+	0.0523896i
$704$	−6.23266	+	31.3337i	−0.234902	+	1.18093i
$705$	−0.349042	+	0.638513i	−0.0131457	+	0.0240478i
$706$	3.63353	+	8.77211i	0.136750	+	0.330143i
$707$	8.79269	+	1.74897i	0.330683	+	0.0657770i
$708$	1.34974	−	4.30357i	0.0507265	−	0.161738i
$709$	−8.78850	−	44.1828i	−0.330059	−	1.65932i	−0.688102	−	0.725614i	$-0.741556\pi$
$709$	−8.78850	−	44.1828i	−0.330059	−	1.65932i	0.358043	−	0.933705i	$-0.383444\pi$
$710$	1.69951	+	1.69951i	0.0637814	+	0.0637814i
$711$	−5.09021	−	5.28514i	−0.190898	−	0.198208i
$712$	11.3075	+	4.68374i	0.423768	+	0.175531i
$713$	−56.2259			−2.10568
$714$		0			0
$715$	−0.0598067			−0.00223664
$716$	−4.65061	−	1.92635i	−0.173801	−	0.0719909i
$717$	−3.44566	−	38.7084i	−0.128681	−	1.44559i
$718$	25.6111	+	25.6111i	0.955796	+	0.955796i
$719$	−5.61120	−	28.2094i	−0.209263	−	1.05203i	−0.932427	−	0.361358i	$-0.882313\pi$
$719$	−5.61120	−	28.2094i	−0.209263	−	1.05203i	0.723165	−	0.690676i	$-0.242687\pi$
$720$	−1.32863	+	0.521319i	−0.0495153	+	0.0194284i
$721$	27.7213	+	5.51411i	1.03240	+	0.205356i
$722$	−13.1163	−	31.6655i	−0.488138	−	1.17847i
$723$	−0.616270	−	0.336883i	−0.0229193	−	0.0125288i
$724$	0.113079	−	0.568488i	0.00420256	−	0.0211277i
$725$	−16.2998	+	10.8912i	−0.605360	+	0.404489i
$726$	3.30553	−	3.95153i	0.122680	−	0.146655i
$727$	1.86673	−	1.86673i	0.0692331	−	0.0692331i	−0.671642	−	0.740876i	$-0.734411\pi$
$727$	1.86673	−	1.86673i	0.0692331	−	0.0692331i	0.740876	+	0.671642i	$0.234411\pi$
$728$	0.512803	+	0.342644i	0.0190058	+	0.0126992i
$729$	23.2590	−	13.7120i	0.861444	−	0.507853i
$730$			0.826242i			0.0305806i
$731$		0			0
$732$	−1.45990	+	1.17533i	−0.0539593	+	0.0434415i
$733$	−11.9956	+	28.9600i	−0.443068	+	1.06966i	0.531798	+	0.846871i	$0.321516\pi$
$733$	−11.9956	+	28.9600i	−0.443068	+	1.06966i	−0.974866	+	0.222790i	$0.928484\pi$
$734$	8.20346	−	12.2773i	0.302795	−	0.453165i
$735$	−0.101254	+	0.937673i	−0.00373482	+	0.0345866i
$736$	−9.41729	+	1.87322i	−0.347126	+	0.0690477i
$737$	−11.7724	−	17.6186i	−0.433642	−	0.648991i
$738$	−6.93579	+	15.8933i	−0.255310	+	0.585040i
$739$	4.41201	−	1.82751i	0.162298	−	0.0672262i	−0.300055	−	0.953922i	$-0.597005\pi$
$739$	4.41201	−	1.82751i	0.162298	−	0.0672262i	0.462354	+	0.886696i	$0.347005\pi$
$740$	0.0131813	−	0.00545986i	0.000484553	−	0.000200708i
$741$	−0.628539	−	1.20296i	−0.0230900	−	0.0441918i
$742$	−8.27510	−	12.3846i	−0.303788	−	0.454651i
$743$	20.6527	−	4.10808i	0.757674	−	0.150711i	0.198888	−	0.980022i	$-0.436267\pi$
$743$	20.6527	−	4.10808i	0.757674	−	0.150711i	0.558787	+	0.829312i	$0.311267\pi$
$744$	46.0526	+	4.97297i	1.68837	+	0.182318i
$745$	1.73712	−	2.59978i	0.0636431	−	0.0952486i
$746$	−2.76818	+	6.68298i	−0.101350	+	0.244681i
$747$	−3.54792	+	16.2364i	−0.129812	+	0.594058i
$748$		0			0
$749$		−	2.41058i		−	0.0880806i
$750$	−0.899244	−	3.06785i	−0.0328357	−	0.112022i
$751$	−19.2693	−	12.8753i	−0.703145	−	0.469827i	0.151889	−	0.988397i	$-0.451464\pi$
$751$	−19.2693	−	12.8753i	−0.703145	−	0.469827i	−0.855035	+	0.518571i	$0.826464\pi$
$752$	−7.13925	+	7.13925i	−0.260342	+	0.260342i
$753$	1.40901	+	1.17866i	0.0513471	+	0.0429529i
$754$	−0.502116	+	0.335503i	−0.0182860	+	0.0122183i
$755$	−0.113229	+	0.569241i	−0.00412083	+	0.0207168i
$756$	1.88945	+	1.64186i	0.0687185	+	0.0597140i
$757$	9.85760	+	23.7983i	0.358280	+	0.864965i	0.995542	+	0.0943180i	$0.0300670\pi$
$757$	9.85760	+	23.7983i	0.358280	+	0.864965i	−0.637262	+	0.770647i	$0.719933\pi$
$758$	−6.78999	−	1.35061i	−0.246623	−	0.0490564i
$759$	37.7947	+	11.8537i	1.37186	+	0.430262i
$760$	0.550432	+	2.76721i	0.0199663	+	0.100377i
$761$	15.9336	+	15.9336i	0.577594	+	0.577594i	0.934240	−	0.356646i	$-0.116080\pi$
$761$	15.9336	+	15.9336i	0.577594	+	0.577594i	−0.356646	+	0.934240i	$0.616080\pi$
$762$	22.4253	−	1.99620i	0.812382	−	0.0723149i
$763$	−18.7613	−	7.77120i	−0.679206	−	0.281336i
$764$	4.72118			0.170806
$765$		0			0
$766$	−27.8109			−1.00485
$767$	1.03124	+	0.427153i	0.0372359	+	0.0154236i
$768$	11.0558	−	0.984144i	0.398943	−	0.0355122i
$769$	−10.2112	−	10.2112i	−0.368226	−	0.368226i	0.498604	−	0.866830i	$-0.333846\pi$
$769$	−10.2112	−	10.2112i	−0.368226	−	0.368226i	−0.866830	+	0.498604i	$0.833846\pi$
$770$	0.232466	+	1.16869i	0.00837751	+	0.0421166i
$771$	−33.2719	−	10.4352i	−1.19826	−	0.375814i
$772$	4.33606	+	0.862495i	0.156058	+	0.0310419i
$773$	−0.930920	−	2.24744i	−0.0334829	−	0.0808348i	0.906254	−	0.422734i	$-0.138930\pi$
$773$	−0.930920	−	2.24744i	−0.0334829	−	0.0808348i	−0.939736	+	0.341900i	$0.888930\pi$
$774$	−1.46876	−	8.18464i	−0.0527936	−	0.294191i
$775$	−8.69951	+	43.7354i	−0.312496	+	1.57102i
$776$	11.3917	−	7.61171i	0.408939	−	0.273245i
$777$	0.875288	+	0.732197i	0.0314008	+	0.0262674i
$778$	11.6153	−	11.6153i	0.416429	−	0.416429i
$779$	24.5487	+	16.4029i	0.879549	+	0.587696i
$780$	0.00217855	+	0.00743231i	7.80045e−5	+	0.000266119i
$781$			47.3287i			1.69355i
$782$		0			0
$783$	−18.3030	+	9.12973i	−0.654097	+	0.326270i
$784$	−5.00762	+	12.0895i	−0.178844	+	0.431766i
$785$	1.09121	−	1.63312i	0.0389471	−	0.0582885i
$786$	29.4916	+	3.18464i	1.05193	+	0.113592i
$787$	−31.1021	+	6.18658i	−1.10867	+	0.220528i	−0.715276	−	0.698843i	$-0.753699\pi$
$787$	−31.1021	+	6.18658i	−1.10867	+	0.220528i	−0.393393	+	0.919370i	$0.628699\pi$
$788$	1.18766	+	1.77746i	0.0423086	+	0.0633194i
$789$	−4.42876	−	8.47617i	−0.157668	−	0.301760i
$790$	−0.417919	+	0.173108i	−0.0148689	+	0.00615889i
$791$	−22.1499	+	9.17479i	−0.787560	+	0.326218i
$792$	−29.9078	−	13.0517i	−1.06273	−	0.463773i
$793$	−0.257692	−	0.385663i	−0.00915090	−	0.0136953i
$794$	50.1481	−	9.97507i	1.77969	−	0.354002i
$795$	0.167583	−	1.55191i	0.00594354	−	0.0550407i
$796$	−1.93626	+	2.89781i	−0.0686288	+	0.102710i
$797$	−17.3442	+	41.8726i	−0.614363	+	1.48320i	0.243800	+	0.969825i	$0.421606\pi$
$797$	−17.3442	+	41.8726i	−0.614363	+	1.48320i	−0.858163	+	0.513377i	$0.828394\pi$
$798$	−21.0640	+	16.9582i	−0.745658	+	0.600314i
$799$		0			0
$800$			7.61508i			0.269234i
$801$	−7.02070	+	10.0916i	−0.248064	+	0.356568i
$802$	29.7572	+	19.8832i	1.05076	+	0.702099i
$803$	−11.5048	+	11.5048i	−0.405995	+	0.405995i
$804$	−1.76068	+	2.10477i	−0.0620944	+	0.0742294i
$805$	−1.29969	+	0.868428i	−0.0458082	+	0.0306081i
$806$	−0.267988	+	1.34727i	−0.00943949	+	0.0474555i
$807$	−13.8904	−	7.59315i	−0.488964	−	0.267292i
$808$	5.79181	+	13.9827i	0.203755	+	0.491908i
$809$	−24.6676	−	4.90669i	−0.867266	−	0.172510i	−0.258646	−	0.965972i	$-0.583276\pi$
$809$	−24.6676	−	4.90669i	−0.867266	−	0.172510i	−0.608620	+	0.793462i	$0.708276\pi$
$810$	−0.263172	−	1.64353i	−0.00924691	−	0.0577478i
$811$	−4.54032	−	22.8258i	−0.159432	−	0.801521i	−0.974887	−	0.222700i	$-0.928513\pi$
$811$	−4.54032	−	22.8258i	−0.159432	−	0.801521i	0.815455	−	0.578821i	$-0.196487\pi$
$812$	−1.34084	−	1.34084i	−0.0470544	−	0.0470544i
$813$	0.406694	+	4.56878i	0.0142634	+	0.160234i
$814$	−1.64696	−	0.682192i	−0.0577259	−	0.0239108i
$815$	1.56942			0.0549743
$816$		0			0
$817$	−14.1578			−0.495320
$818$	34.2732	+	14.1964i	1.19834	+	0.496367i
$819$	−0.446189	+	0.429732i	−0.0155911	+	0.0150160i
$820$	−0.119131	−	0.119131i	−0.00416024	−	0.00416024i
$821$	8.43190	+	42.3900i	0.294275	+	1.47942i	0.791162	+	0.611607i	$0.209476\pi$
$821$	8.43190	+	42.3900i	0.294275	+	1.47942i	−0.496887	+	0.867815i	$0.665524\pi$
$822$	−2.18355	+	6.96209i	−0.0761599	+	0.242831i
$823$	−16.5420	−	3.29041i	−0.576617	−	0.114696i	−0.101838	−	0.994801i	$-0.532472\pi$
$823$	−16.5420	−	3.29041i	−0.576617	−	0.114696i	−0.474780	+	0.880105i	$0.657472\pi$
$824$	18.2602	+	44.0841i	0.636125	+	1.53574i
$825$	15.0682	−	27.5646i	0.524606	−	0.959676i
$826$	4.33865	−	21.8119i	0.150961	−	0.758931i
$827$	18.4337	−	12.3170i	0.641002	−	0.428304i	−0.192136	−	0.981368i	$-0.561542\pi$
$827$	18.4337	−	12.3170i	0.641002	−	0.428304i	0.833139	+	0.553064i	$0.186542\pi$
$828$	0.0963571	−	5.12862i	0.00334864	−	0.178232i
$829$	−19.3451	+	19.3451i	−0.671883	+	0.671883i	−0.958150	−	0.286267i	$-0.907585\pi$
$829$	−19.3451	+	19.3451i	−0.671883	+	0.671883i	0.286267	+	0.958150i	$0.407585\pi$
$830$	0.851875	+	0.569205i	0.0295690	+	0.0197574i
$831$	−34.3886	+	10.0799i	−1.19293	+	0.349669i
$832$			1.02389i			0.0354968i
$833$		0			0
$834$	−7.27334	−	9.03431i	−0.251855	−	0.312833i
$835$	0.113070	−	0.272976i	0.00391296	−	0.00944672i
$836$	−3.69880	+	5.53564i	−0.127926	+	0.191454i
$837$	−14.7548	+	44.1242i	−0.510000	+	1.52516i
$838$	12.0414	−	2.39518i	0.415962	−	0.0827400i
$839$	−13.7956	−	20.6465i	−0.476276	−	0.712798i	0.513075	−	0.858344i	$-0.328506\pi$
$839$	−13.7956	−	20.6465i	−0.476276	−	0.712798i	−0.989352	+	0.145546i	$0.953506\pi$
$840$	1.14134	−	0.596345i	0.0393800	−	0.0205758i
$841$	−12.4774	+	5.16832i	−0.430256	+	0.178218i
$842$	16.1539	−	6.69119i	0.556702	−	0.230593i
$843$	15.7944	−	8.25250i	0.543989	−	0.284231i
$844$	0.774551	+	1.15920i	0.0266611	+	0.0399012i
$845$	1.79209	−	0.356469i	0.0616498	−	0.0122629i
$846$	−6.35651	−	9.91131i	−0.218541	−	0.340758i
$847$	−2.22420	+	3.32876i	−0.0764246	+	0.114377i
$848$	8.28795	−	20.0089i	0.284609	−	0.687107i
$849$	−13.9495	−	17.3269i	−0.478745	−	0.594656i
$850$		0			0
$851$		−	2.33850i		−	0.0801628i
$852$	5.88164	−	1.72402i	0.201502	−	0.0590638i
$853$	−24.8055	−	16.5745i	−0.849323	−	0.567499i	0.0529834	−	0.998595i	$-0.483127\pi$
$853$	−24.8055	−	16.5745i	−0.849323	−	0.567499i	−0.902306	+	0.431096i	$0.858127\pi$
$854$	−6.53464	+	6.53464i	−0.223611	+	0.223611i
$855$	−2.83344	−	0.0532349i	−0.0969015	−	0.00182060i
$856$	3.38372	−	2.26093i	0.115653	−	0.0772770i
$857$	6.63871	−	33.3750i	0.226774	−	1.14007i	−0.684736	−	0.728791i	$-0.740082\pi$
$857$	6.63871	−	33.3750i	0.226774	−	1.14007i	0.911510	−	0.411279i	$-0.134918\pi$
$858$	0.464174	−	0.849127i	0.0158467	−	0.0289887i
$859$	−7.54327	−	18.2111i	−0.257373	−	0.621354i	0.741390	−	0.671074i	$-0.234167\pi$
$859$	−7.54327	−	18.2111i	−0.257373	−	0.621354i	−0.998763	+	0.0497206i	$0.984167\pi$
$860$	0.0792371	+	0.0157612i	0.00270196	+	0.000537454i
$861$	4.03267	−	12.8579i	0.137433	−	0.438197i
$862$	3.74660	+	18.8354i	0.127610	+	0.641538i
$863$	4.36492	+	4.36492i	0.148584	+	0.148584i	0.777485	−	0.628901i	$-0.216495\pi$
$863$	4.36492	+	4.36492i	0.148584	+	0.148584i	−0.628901	+	0.777485i	$0.716495\pi$
$864$	−1.00125	+	7.88194i	−0.0340631	+	0.268149i
$865$	−1.60077	−	0.663059i	−0.0544277	−	0.0225447i
$866$	−23.4504			−0.796876
$867$		0			0
$868$	−4.31336			−0.146405
$869$	−8.22958	−	3.40880i	−0.279169	−	0.115636i
$870$	0.111799	+	1.25594i	0.00379033	+	0.0425804i
$871$	−0.480203	−	0.480203i	−0.0162710	−	0.0162710i
$872$	−6.68823	−	33.6240i	−0.226492	−	1.13865i
$873$	5.02654	+	12.8106i	0.170122	+	0.433575i
$874$	54.3507	+	10.8110i	1.83844	+	0.365689i
$875$	0.950712	+	2.29522i	0.0321399	+	0.0775927i
$876$	1.84880	+	1.01065i	0.0624652	+	0.0341466i
$877$	−1.85986	+	9.35016i	−0.0628031	+	0.315732i	−0.999398	−	0.0346804i	$-0.988959\pi$
$877$	−1.85986	+	9.35016i	−0.0628031	+	0.315732i	0.936595	+	0.350413i	$0.113959\pi$
$878$	28.8088	−	19.2494i	0.972248	−	0.649636i
$879$	1.25370	−	1.49871i	0.0422864	−	0.0505503i
$880$	−1.22513	+	1.22513i	−0.0412992	+	0.0412992i
$881$	35.7652	+	23.8975i	1.20496	+	0.805128i	0.985364	−	0.170464i	$-0.0545265\pi$
$881$	35.7652	+	23.8975i	1.20496	+	0.805128i	0.219595	+	0.975591i	$0.429527\pi$
$882$	−12.5271	−	8.71511i	−0.421809	−	0.293453i
$883$			41.3162i			1.39040i	0.718816	+	0.695200i	$0.244684\pi$
$883$			41.3162i			1.39040i	−0.718816	+	0.695200i	$0.755316\pi$
$884$		0			0
$885$	1.81539	−	1.46153i	0.0610237	−	0.0491289i
$886$	−4.86427	+	11.7434i	−0.163418	+	0.394527i
$887$	−8.24630	+	12.3415i	−0.276884	+	0.414386i	−0.943683	−	0.330852i	$-0.892664\pi$
$887$	−8.24630	+	12.3415i	−0.276884	+	0.414386i	0.666799	+	0.745238i	$0.267664\pi$
$888$	−0.206831	+	1.91538i	−0.00694081	+	0.0642760i
$889$	−17.1594	+	3.41322i	−0.575508	+	0.114476i
$890$	0.421042	+	0.630135i	0.0141134	+	0.0211222i
$891$	19.2204	−	26.5494i	0.643909	−	0.889437i
$892$	0.0475120	−	0.0196801i	0.00159082	−	0.000658939i
$893$	−18.5214	+	7.67180i	−0.619794	+	0.256727i
$894$	23.4291	+	44.8409i	0.783587	+	1.49970i
$895$	−1.44511	−	2.16276i	−0.0483046	−	0.0722930i
$896$	14.7014	−	2.92429i	0.491139	−	0.0976937i
$897$	1.26212	+	0.136289i	0.0421410	+	0.00455057i
$898$	−0.771672	+	1.15489i	−0.0257510	+	0.0385391i
$899$	13.4878	−	32.5624i	0.449843	−	1.08602i
$900$	−3.97439	−	0.868473i	−0.132480	−	0.0289491i
$901$		0			0
$902$			21.0507i			0.700910i
$903$	1.81762	+	6.20098i	0.0604866	+	0.206356i
$904$	−33.6535	−	22.4865i	−1.11930	−	0.747890i
$905$	0.211787	−	0.211787i	0.00704002	−	0.00704002i
$906$	−7.20321	−	6.02563i	−0.239310	−	0.200188i
$907$	−14.2246	+	9.50457i	−0.472320	+	0.315594i	−0.768850	−	0.639429i	$-0.779171\pi$
$907$	−14.2246	+	9.50457i	−0.472320	+	0.315594i	0.296530	+	0.955024i	$0.404171\pi$
$908$	−0.113159	+	0.568889i	−0.00375531	+	0.0188792i
$909$	−14.9628	+	2.68514i	−0.496286	+	0.0890603i
$910$	0.0146143	+	0.0352820i	0.000484459	+	0.00116959i
$911$	−54.2580	−	10.7926i	−1.79765	−	0.357574i	−0.820751	−	0.571286i	$-0.806445\pi$
$911$	−54.2580	−	10.7926i	−1.79765	−	0.357574i	−0.976897	+	0.213712i	$0.931445\pi$
$912$	−37.5180	−	11.7669i	−1.24234	−	0.389641i
$913$	3.93596	+	19.7874i	0.130261	+	0.654868i
$914$	19.9143	+	19.9143i	0.658705	+	0.658705i
$915$	−0.964658	+	0.0858698i	−0.0318906	+	0.00283877i
$916$	−4.34800	−	1.80100i	−0.143662	−	0.0595067i
$917$	−23.0511			−0.761216
$918$		0			0
$919$	−57.0283			−1.88119			−0.940595	−	0.339530i	$-0.889732\pi$
$919$	−57.0283			−1.88119			−0.940595	+	0.339530i	$0.889732\pi$
$920$	−2.43802	−	1.00986i	−0.0803791	−	0.0332941i
$921$	−33.7824	+	3.00717i	−1.11317	+	0.0990897i
$922$	22.9019	+	22.9019i	0.754233	+	0.754233i
$923$	0.295920	+	1.48769i	0.00974032	+	0.0489679i
$924$	2.89941	+	0.909353i	0.0953836	+	0.0299155i
$925$	−1.81900	−	0.361822i	−0.0598085	−	0.0118966i
$926$	−9.70769	−	23.4364i	−0.319014	−	0.770169i
$927$	−47.1743	+	8.46561i	−1.54941	+	0.278047i
$928$	1.17423	−	5.90324i	0.0385459	−	0.193783i
$929$	−29.7790	+	19.8977i	−0.977016	+	0.652822i	−0.938079	−	0.346420i	$-0.887397\pi$
$929$	−29.7790	+	19.8977i	−0.977016	+	0.652822i	−0.0389370	+	0.999242i	$0.512397\pi$
$930$	2.19994	+	1.84030i	0.0721389	+	0.0603457i
$931$	−18.3724	+	18.3724i	−0.602132	+	0.602132i
$932$	2.21694	+	1.48131i	0.0726184	+	0.0485220i
$933$	14.3114	+	48.8247i	0.468535	+	1.59845i
$934$		−	16.3585i		−	0.535267i
$935$		0			0
$936$	−1.02170	−	0.223259i	−0.0333954	−	0.00729746i
$937$	7.73785	−	18.6808i	0.252785	−	0.610276i	−0.745642	−	0.666347i	$-0.767857\pi$
$937$	7.73785	−	18.6808i	0.252785	−	0.610276i	0.998427	+	0.0560704i	$0.0178571\pi$
$938$	−7.51715	+	11.2502i	−0.245444	+	0.367333i
$939$	−30.6873	−	3.31375i	−1.00144	−	0.108140i
$940$	0.112199	−	0.0223178i	0.00365953	−	0.000727926i
$941$	4.31354	+	6.45567i	0.140618	+	0.210449i	0.895093	−	0.445879i	$-0.147109\pi$
$941$	4.31354	+	6.45567i	0.140618	+	0.210449i	−0.754476	+	0.656328i	$0.772109\pi$
$942$	14.7176	+	28.1679i	0.479525	+	0.917761i
$943$	−25.5124	+	10.5676i	−0.830798	+	0.344128i
$944$	29.8749	−	12.3746i	0.972347	−	0.402759i
$945$	0.340448	+	1.24785i	0.0110748	+	0.0405925i
$946$	−5.60815	−	8.39318i	−0.182337	−	0.272886i
$947$	3.53370	−	0.702897i	0.114830	−	0.0228411i	−0.137341	−	0.990524i	$-0.543856\pi$
$947$	3.53370	−	0.702897i	0.114830	−	0.0228411i	0.252171	+	0.967683i	$0.418856\pi$
$948$	−0.123845	+	1.14688i	−0.00402231	+	0.0372489i
$949$	−0.289698	+	0.433564i	−0.00940400	+	0.0140741i
$950$	16.8187	−	40.6040i	0.545672	−	1.31737i
$951$	−19.0515	+	15.3379i	−0.617786	+	0.497367i
$952$		0			0
$953$			22.5397i			0.730132i	0.930982	+	0.365066i	$0.118954\pi$
$953$			22.5397i			0.730132i	−0.930982	+	0.365066i	$0.881046\pi$
$954$	20.7332	+	14.4241i	0.671262	+	0.466997i
$955$	2.02845	+	1.35536i	0.0656389	+	0.0438585i
$956$	−4.31991	+	4.31991i	−0.139716	+	0.139716i
$957$	−15.9313	+	19.0447i	−0.514986	+	0.615628i
$958$	−24.8079	+	16.5761i	−0.801507	+	0.535550i
$959$	1.10618	−	5.56114i	0.0357204	−	0.179578i
$960$	1.87587	+	1.02544i	0.0605433	+	0.0330959i
$961$	−18.8174	−	45.4292i	−0.607013	−	1.46546i
$962$	−0.0560344	−	0.0111459i	−0.00180662	−	0.000359360i
$963$	1.49305	+	3.80518i	0.0481128	+	0.122620i
$964$	0.0215404	+	0.108291i	0.000693768	+	0.00348781i
$965$	1.61537	+	1.61537i	0.0520007	+	0.0520007i
$966$	−2.24257	−	25.1930i	−0.0721536	−	0.810570i
$967$	20.7527	+	8.59605i	0.667362	+	0.276430i	0.690533	−	0.723301i	$-0.257376\pi$
$967$	20.7527	+	8.59605i	0.667362	+	0.276430i	−0.0231709	+	0.999732i	$0.507376\pi$
$968$	−6.75869			−0.217233
$969$		0			0
$970$	0.848355			0.0272390
$971$	−31.6660	−	13.1165i	−1.01621	−	0.420928i	−0.188493	−	0.982075i	$-0.560360\pi$
$971$	−31.6660	−	13.1165i	−1.01621	−	0.420928i	−0.827716	+	0.561147i	$0.810360\pi$
$972$	−3.99948	−	1.42147i	−0.128283	−	0.0455936i
$973$	6.37317	+	6.37317i	0.204314	+	0.204314i
$974$	−5.89415	−	29.6319i	−0.188861	−	0.949468i
$975$	0.301293	−	0.960654i	0.00964911	−	0.0307655i
$976$	−13.1790	−	2.62147i	−0.421851	−	0.0839113i
$977$	10.7764	+	26.0166i	0.344769	+	0.832345i	0.997220	+	0.0745143i	$0.0237406\pi$
$977$	10.7764	+	26.0166i	0.344769	+	0.832345i	−0.652451	+	0.757831i	$0.726259\pi$
$978$	−12.1806	+	22.2824i	−0.389494	+	0.712512i
$979$	−2.91144	+	14.6368i	−0.0930502	+	0.467795i
$980$	0.123278	−	0.0823718i	0.00393798	−	0.00263127i
$981$	34.4287	+	0.646850i	1.09922	+	0.0206523i
$982$	18.9356	−	18.9356i	0.604261	−	0.604261i
$983$	−34.6933	−	23.1813i	−1.10654	−	0.739370i	−0.138554	−	0.990355i	$-0.544245\pi$
$983$	−34.6933	−	23.1813i	−1.10654	−	0.739370i	−0.967991	+	0.250985i	$0.919245\pi$
$984$	21.8309	−	6.39905i	0.695945	−	0.203994i
$985$			1.10464i			0.0351967i
$986$		0			0
$987$	5.73799	+	7.12723i	0.182642	+	0.226862i
$988$	−0.0816535	+	0.197129i	−0.00259774	+	0.00627151i
$989$	7.35681	−	11.0102i	0.233933	−	0.350105i
$990$	−1.09081	−	1.70083i	−0.0346682	−	0.0540560i
$991$	9.95379	−	1.97993i	0.316193	−	0.0628946i	−0.0344428	−	0.999407i	$-0.510966\pi$
$991$	9.95379	−	1.97993i	0.316193	−	0.0628946i	0.350635	+	0.936512i	$0.385966\pi$
$992$	−7.60639	−	11.3838i	−0.241503	−	0.361435i
$993$	−11.1037	+	5.80161i	−0.352364	+	0.184108i
$994$	27.9208	−	11.5652i	0.885595	−	0.366826i
$995$	−1.66382	+	0.689176i	−0.0527466	+	0.0218483i
$996$	2.31566	−	1.20992i	0.0733743	−	0.0383377i
$997$	22.1815	+	33.1970i	0.702496	+	1.05136i	0.995455	+	0.0952350i	$0.0303602\pi$
$997$	22.1815	+	33.1970i	0.702496	+	1.05136i	−0.292958	+	0.956125i	$0.594640\pi$
$998$	1.39122	−	0.276730i	0.0440382	−	0.00875974i
$999$	−1.83518	−	0.613668i	−0.0580624	−	0.0194156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.g.503.3		32
3.2	odd	2	inner	867.2.i.g.503.2		32
17.2	even	8		867.2.i.d.329.2		32
17.3	odd	16		867.2.i.b.158.3		32
17.4	even	4		867.2.i.b.653.2		32
17.5	odd	16		867.2.i.f.131.2		32
17.6	odd	16		867.2.i.d.224.3		32
17.7	odd	16		867.2.i.h.65.2		32
17.8	even	8		51.2.i.a.11.3	yes	32
17.9	even	8		867.2.i.h.827.3		32
17.10	odd	16		51.2.i.a.14.2	yes	32
17.11	odd	16		867.2.i.c.224.3		32
17.12	odd	16	inner	867.2.i.g.131.2		32
17.13	even	4		867.2.i.i.653.2		32
17.14	odd	16		867.2.i.i.158.3		32
17.15	even	8		867.2.i.c.329.2		32
17.16	even	2		867.2.i.f.503.3		32
51.2	odd	8		867.2.i.d.329.3		32
51.5	even	16		867.2.i.f.131.3		32
51.8	odd	8		51.2.i.a.11.2	✓	32
51.11	even	16		867.2.i.c.224.2		32
51.14	even	16		867.2.i.i.158.2		32
51.20	even	16		867.2.i.b.158.2		32
51.23	even	16		867.2.i.d.224.2		32
51.26	odd	8		867.2.i.h.827.2		32
51.29	even	16	inner	867.2.i.g.131.3		32
51.32	odd	8		867.2.i.c.329.3		32
51.38	odd	4		867.2.i.b.653.3		32
51.41	even	16		867.2.i.h.65.3		32
51.44	even	16		51.2.i.a.14.3	yes	32
51.47	odd	4		867.2.i.i.653.3		32
51.50	odd	2		867.2.i.f.503.2		32
68.27	even	16		816.2.cj.c.65.1		32
68.59	odd	8		816.2.cj.c.113.4		32
204.59	even	8		816.2.cj.c.113.1		32
204.95	odd	16		816.2.cj.c.65.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	51.8	odd	8
51.2.i.a.11.3	yes	32	17.8	even	8
51.2.i.a.14.2	yes	32	17.10	odd	16
51.2.i.a.14.3	yes	32	51.44	even	16
816.2.cj.c.65.1		32	68.27	even	16
816.2.cj.c.65.4		32	204.95	odd	16
816.2.cj.c.113.1		32	204.59	even	8
816.2.cj.c.113.4		32	68.59	odd	8
867.2.i.b.158.2		32	51.20	even	16
867.2.i.b.158.3		32	17.3	odd	16
867.2.i.b.653.2		32	17.4	even	4
867.2.i.b.653.3		32	51.38	odd	4
867.2.i.c.224.2		32	51.11	even	16
867.2.i.c.224.3		32	17.11	odd	16
867.2.i.c.329.2		32	17.15	even	8
867.2.i.c.329.3		32	51.32	odd	8
867.2.i.d.224.2		32	51.23	even	16
867.2.i.d.224.3		32	17.6	odd	16
867.2.i.d.329.2		32	17.2	even	8
867.2.i.d.329.3		32	51.2	odd	8
867.2.i.f.131.2		32	17.5	odd	16
867.2.i.f.131.3		32	51.5	even	16
867.2.i.f.503.2		32	51.50	odd	2
867.2.i.f.503.3		32	17.16	even	2
867.2.i.g.131.2		32	17.12	odd	16	inner
867.2.i.g.131.3		32	51.29	even	16	inner
867.2.i.g.503.2		32	3.2	odd	2	inner
867.2.i.g.503.3		32	1.1	even	1	trivial
867.2.i.h.65.2		32	17.7	odd	16
867.2.i.h.65.3		32	51.41	even	16
867.2.i.h.827.2		32	51.26	odd	8
867.2.i.h.827.3		32	17.9	even	8
867.2.i.i.158.2		32	51.14	even	16
867.2.i.i.158.3		32	17.14	odd	16
867.2.i.i.653.2		32	17.13	even	4
867.2.i.i.653.3		32	51.47	odd	4

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21437 + 0.503008i) q^{2} +(1.72523 - 0.153573i) q^{3} +(-0.192538 - 0.192538i) q^{4} +(-0.0274494 - 0.137998i) q^{5} +(2.17231 + 0.681311i) q^{6} +(-1.73519 - 0.345150i) q^{7} +(-1.14298 - 2.75940i) q^{8} +(2.95283 - 0.529896i) q^{9} +(0.0360802 - 0.181387i) q^{10} +(3.02807 - 2.02329i) q^{11} +(-0.361741 - 0.302603i) q^{12} +(0.0825311 - 0.0825311i) q^{13} +(-1.93354 - 1.29195i) q^{14} +(-0.0685492 - 0.233862i) q^{15} -3.38128i q^{16} +(3.85237 + 0.841809i) q^{18} +(2.56928 - 6.20278i) q^{19} +(-0.0212847 + 0.0318548i) q^{20} +(-3.04660 - 0.328986i) q^{21} +(4.69492 - 0.933878i) q^{22} +(3.48870 + 5.22121i) q^{23} +(-2.39567 - 4.58506i) q^{24} +(4.60111 - 1.90584i) q^{25} +(0.141737 - 0.0587094i) q^{26} +(5.01293 - 1.36767i) q^{27} +(0.267635 + 0.400544i) q^{28} +(-3.86068 + 0.767936i) q^{29} +(0.0343905 - 0.318476i) q^{30} +(-4.97452 + 7.44489i) q^{31} +(-0.585150 + 1.41268i) q^{32} +(4.91339 - 3.95567i) q^{33} +0.248926i q^{35} +(-0.670557 - 0.466507i) q^{36} +(-0.309641 - 0.206896i) q^{37} +(6.24010 - 6.24010i) q^{38} +(0.129711 - 0.155060i) q^{39} +(-0.349416 + 0.233473i) q^{40} +(-0.857920 + 4.31306i) q^{41} +(-3.53422 - 1.93198i) q^{42} +(-0.806985 - 1.94823i) q^{43} +(-0.972578 - 0.193458i) q^{44} +(-0.154178 - 0.392938i) q^{45} +(1.61026 + 8.09532i) q^{46} +(-2.11141 - 2.11141i) q^{47} +(-0.519272 - 5.83348i) q^{48} +(-3.57541 - 1.48098i) q^{49} +6.54610 q^{50} -0.0317807 q^{52} +(5.91755 + 2.45113i) q^{53} +(6.77550 + 0.860694i) q^{54} +(-0.362328 - 0.362328i) q^{55} +(1.03088 + 5.18257i) q^{56} +(3.48001 - 11.0958i) q^{57} +(-5.07456 - 1.00939i) q^{58} +(3.65974 + 8.83540i) q^{59} +(-0.0318290 + 0.0582256i) q^{60} +(0.775290 - 3.89765i) q^{61} +(-9.78574 + 6.53863i) q^{62} +(-5.30661 - 0.0997012i) q^{63} +(-6.20303 + 6.20303i) q^{64} +(-0.0136545 - 0.00912367i) q^{65} +(7.95640 - 2.33217i) q^{66} -5.81844i q^{67} +(6.82064 + 8.47201i) q^{69} +(-0.125212 + 0.302288i) q^{70} +(-7.22012 + 10.8057i) q^{71} +(-4.83722 - 7.54238i) q^{72} +(-4.38175 + 0.871585i) q^{73} +(-0.271949 - 0.407000i) q^{74} +(7.64528 - 3.99462i) q^{75} +(-1.68895 + 0.699588i) q^{76} +(-5.95260 + 2.46565i) q^{77} +(0.235513 - 0.123054i) q^{78} +(-1.35888 - 2.03371i) q^{79} +(-0.466609 + 0.0928142i) q^{80} +(8.43842 - 3.12939i) q^{81} +(-3.21133 + 4.80610i) q^{82} +(-2.12000 + 5.11813i) q^{83} +(0.523244 + 0.649928i) q^{84} -2.77180i q^{86} +(-6.54262 + 1.91776i) q^{87} +(-9.04408 - 6.04306i) q^{88} +(-2.89760 + 2.89760i) q^{89} +(0.0104222 - 0.554725i) q^{90} +(-0.171693 + 0.114721i) q^{91} +(0.333574 - 1.67699i) q^{92} +(-7.43885 + 13.6081i) q^{93} +(-1.50197 - 3.62608i) q^{94} +(-0.926494 - 0.184291i) q^{95} +(-0.792569 + 2.52705i) q^{96} +(0.894911 + 4.49902i) q^{97} +(-3.59692 - 3.59692i) q^{98} +(7.86924 - 7.57899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 8 q^{6} + 24 q^{9} + 16 q^{10} + 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} - 16 q^{22} - 24 q^{24} - 24 q^{27} + 8 q^{30} - 32 q^{31} - 24 q^{36} - 16 q^{37}+ \cdots + 96 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 8 * q^6 + 24 * q^9 + 16 * q^10 + 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 - 16 * q^22 - 24 * q^24 - 24 * q^27 + 8 * q^30 - 32 * q^31 - 24 * q^36 - 16 * q^37 + 64 * q^39 - 16 * q^40 - 24 * q^42 - 32 * q^43 - 40 * q^45 + 40 * q^48 - 64 * q^49 - 96 * q^52 + 88 * q^54 + 48 * q^55 + 24 * q^57 + 64 * q^58 + 48 * q^60 + 32 * q^61 + 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 - 48 * q^73 - 16 * q^75 + 32 * q^76 - 88 * q^78 + 32 * q^79 - 48 * q^81 - 96 * q^82 - 56 * q^87 - 128 * q^88 - 8 * q^90 - 64 * q^91 - 56 * q^93 - 48 * q^94 - 16 * q^96 - 128 * q^97 + 96 * q^99

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