LMFDB - Embedded newform 867.2.i.g.131.2

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			131.2
Character	$\chi$	$=$	867.131
Dual form			867.2.i.g.503.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21437 + 0.503008i) q^{2} +(0.518334 - 1.65267i) q^{3} +(-0.192538 + 0.192538i) q^{4} +(0.0274494 - 0.137998i) q^{5} +(0.201860 + 2.26768i) q^{6} +(-1.73519 + 0.345150i) q^{7} +(1.14298 - 2.75940i) q^{8} +(-2.46266 - 1.71327i) q^{9} +(0.0360802 + 0.181387i) q^{10} +(-3.02807 - 2.02329i) q^{11} +(0.218403 + 0.418001i) q^{12} +(0.0825311 + 0.0825311i) q^{13} +(1.93354 - 1.29195i) q^{14} +(-0.213837 - 0.116894i) q^{15} +3.38128i q^{16} +(3.85237 + 0.841809i) q^{18} +(2.56928 + 6.20278i) q^{19} +(0.0212847 + 0.0318548i) q^{20} +(-0.328986 + 3.04660i) q^{21} +(4.69492 + 0.933878i) q^{22} +(-3.48870 + 5.22121i) q^{23} +(-3.96794 - 3.31926i) q^{24} +(4.60111 + 1.90584i) q^{25} +(-0.141737 - 0.0587094i) q^{26} +(-4.10796 + 3.18193i) q^{27} +(0.267635 - 0.400544i) q^{28} +(3.86068 + 0.767936i) q^{29} +(0.318476 + 0.0343905i) q^{30} +(-4.97452 - 7.44489i) q^{31} +(0.585150 + 1.41268i) q^{32} +(-4.91339 + 3.95567i) q^{33} +0.248926i q^{35} +(0.804026 - 0.144285i) q^{36} +(-0.309641 + 0.206896i) q^{37} +(-6.24010 - 6.24010i) q^{38} +(0.179176 - 0.0936183i) q^{39} +(-0.349416 - 0.233473i) q^{40} +(0.857920 + 4.31306i) q^{41} +(-1.13296 - 3.86518i) q^{42} +(-0.806985 + 1.94823i) q^{43} +(0.972578 - 0.193458i) q^{44} +(-0.304026 + 0.292813i) q^{45} +(1.61026 - 8.09532i) q^{46} +(2.11141 - 2.11141i) q^{47} +(5.58815 + 1.75263i) q^{48} +(-3.57541 + 1.48098i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(-5.91755 + 2.45113i) q^{53} +(3.38805 - 5.93037i) q^{54} +(-0.362328 + 0.362328i) q^{55} +(-1.03088 + 5.18257i) q^{56} +(11.5829 - 1.03106i) q^{57} +(-5.07456 + 1.00939i) q^{58} +(-3.65974 + 8.83540i) q^{59} +(0.0636782 - 0.0186653i) q^{60} +(0.775290 + 3.89765i) q^{61} +(9.78574 + 6.53863i) q^{62} +(4.86451 + 2.12286i) q^{63} +(-6.20303 - 6.20303i) q^{64} +(0.0136545 - 0.00912367i) q^{65} +(3.97693 - 7.27511i) q^{66} +5.81844i q^{67} +(6.82064 + 8.47201i) q^{69} +(-0.125212 - 0.302288i) q^{70} +(7.22012 + 10.8057i) q^{71} +(-7.54238 + 4.83722i) q^{72} +(-4.38175 - 0.871585i) q^{73} +(0.271949 - 0.407000i) q^{74} +(5.53464 - 6.61627i) q^{75} +(-1.68895 - 0.699588i) q^{76} +(5.95260 + 2.46565i) q^{77} +(-0.170495 + 0.203814i) q^{78} +(-1.35888 + 2.03371i) q^{79} +(0.466609 + 0.0928142i) q^{80} +(3.12939 + 8.43842i) q^{81} +(-3.21133 - 4.80610i) q^{82} +(2.12000 + 5.11813i) q^{83} +(-0.523244 - 0.649928i) q^{84} -2.77180i q^{86} +(3.27027 - 5.98239i) q^{87} +(-9.04408 + 6.04306i) q^{88} +(2.89760 + 2.89760i) q^{89} +(0.221913 - 0.508511i) q^{90} +(-0.171693 - 0.114721i) q^{91} +(-0.333574 - 1.67699i) q^{92} +(-14.8824 + 4.36231i) q^{93} +(-1.50197 + 3.62608i) q^{94} +(0.926494 - 0.184291i) q^{95} +(2.63800 - 0.234823i) q^{96} +(0.894911 - 4.49902i) q^{97} +(3.59692 - 3.59692i) q^{98} +(3.99065 + 10.1706i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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	$-0.778845\pi$
$2$	−1.21437	+	0.503008i	−0.858689	+	0.355681i	−0.0904942	+	0.995897i	$0.528845\pi$
$3$	0.518334	−	1.65267i	0.299260	−	0.954172i
$3$	0.518334	−	1.65267i	0.299260	−	0.954172i
$4$	−0.192538	+	0.192538i	−0.0962690	+	0.0962690i
$5$	0.0274494	−	0.137998i	0.0122758	−	0.0617144i	−0.974162	−	0.225851i	$-0.927484\pi$
$5$	0.0274494	−	0.137998i	0.0122758	−	0.0617144i	0.986438	+	0.164137i	$0.0524838\pi$
$6$	0.201860	+	2.26768i	0.0824088	+	0.925777i
$7$	−1.73519	+	0.345150i	−0.655839	+	0.130455i	−0.511783	−	0.859115i	$-0.671015\pi$
$7$	−1.73519	+	0.345150i	−0.655839	+	0.130455i	−0.144056	+	0.989569i	$0.546015\pi$
$8$	1.14298	−	2.75940i	0.404105	−	0.975595i
$9$	−2.46266	−	1.71327i	−0.820887	−	0.571091i
$10$	0.0360802	+	0.181387i	0.0114096	+	0.0573597i
$11$	−3.02807	−	2.02329i	−0.912997	−	0.610045i	0.00785036	−	0.999969i	$-0.497501\pi$
$11$	−3.02807	−	2.02329i	−0.912997	−	0.610045i	−0.920847	+	0.389924i	$0.872501\pi$
$12$	0.218403	+	0.418001i	0.0630476	+	0.120667i
$13$	0.0825311	+	0.0825311i	0.0228900	+	0.0228900i	0.718459	−	0.695569i	$-0.244848\pi$
$13$	0.0825311	+	0.0825311i	0.0228900	+	0.0228900i	−0.695569	+	0.718459i	$0.744848\pi$
$14$	1.93354	−	1.29195i	0.516762	−	0.345289i
$15$	−0.213837	−	0.116894i	−0.0552125	−	0.0301819i
$16$			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	0.884046	+	0.467399i	$0.154809\pi$
$19$	2.56928	+	6.20278i	0.589432	+	1.42302i	−0.294614	+	0.955616i	$0.595191\pi$
$20$	0.0212847	+	0.0318548i	0.00475941	+	0.00712296i
$21$	−0.328986	+	3.04660i	−0.0717906	+	0.664823i
$22$	4.69492	+	0.933878i	1.00096	+	0.199104i
$23$	−3.48870	+	5.22121i	−0.727444	+	1.08870i	0.264789	+	0.964306i	$0.414698\pi$
$23$	−3.48870	+	5.22121i	−0.727444	+	1.08870i	−0.992233	+	0.124391i	$0.960302\pi$
$24$	−3.96794	−	3.31926i	−0.809952	−	0.677542i
$25$	4.60111	+	1.90584i	0.920222	+	0.381168i
$26$	−0.141737	−	0.0587094i	−0.0277969	−	0.0115139i
$27$	−4.10796	+	3.18193i	−0.790578	+	0.612362i
$28$	0.267635	−	0.400544i	0.0505782	−	0.0756957i
$29$	3.86068	+	0.767936i	0.716909	+	0.142602i	0.540049	−	0.841634i	$-0.318406\pi$
$29$	3.86068	+	0.767936i	0.716909	+	0.142602i	0.176861	+	0.984236i	$0.443406\pi$
$30$	0.318476	+	0.0343905i	0.0581455	+	0.00627881i
$31$	−4.97452	−	7.44489i	−0.893450	−	1.33714i	−0.941047	−	0.338275i	$-0.890156\pi$
$31$	−4.97452	−	7.44489i	−0.893450	−	1.33714i	0.0475974	−	0.998867i	$-0.484844\pi$
$32$	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
$36$	0.804026	−	0.144285i	0.134004	−	0.0240475i
$37$	−0.309641	+	0.206896i	−0.0509047	+	0.0340135i	−0.580762	−	0.814073i	$-0.697245\pi$
$37$	−0.309641	+	0.206896i	−0.0509047	+	0.0340135i	0.529858	+	0.848087i	$0.322245\pi$
$38$	−6.24010	−	6.24010i	−1.01228	−	1.01228i
$39$	0.179176	−	0.0936183i	0.0286911	−	0.0149909i
$40$	−0.349416	−	0.233473i	−0.0552476	−	0.0369153i
$41$	0.857920	+	4.31306i	0.133985	+	0.673586i	0.988138	+	0.153566i	$0.0490757\pi$
$41$	0.857920	+	4.31306i	0.133985	+	0.673586i	−0.854154	+	0.520020i	$0.825924\pi$
$42$	−1.13296	−	3.86518i	−0.174819	−	0.596410i
$43$	−0.806985	+	1.94823i	−0.123064	+	0.297103i	−0.973390	−	0.229153i	$-0.926404\pi$
$43$	−0.806985	+	1.94823i	−0.123064	+	0.297103i	0.850326	+	0.526256i	$0.176404\pi$
$44$	0.972578	−	0.193458i	0.146622	−	0.0291648i
$45$	−0.304026	+	0.292813i	−0.0453216	+	0.0436500i
$46$	1.61026	−	8.09532i	0.237420	−	1.19359i
$47$	2.11141	−	2.11141i	0.307980	−	0.307980i	−0.536145	−	0.844126i	$-0.680120\pi$
$47$	2.11141	−	2.11141i	0.307980	−	0.307980i	0.844126	+	0.536145i	$0.180120\pi$
$48$	5.58815	+	1.75263i	0.806580	+	0.252971i
$49$	−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	$-0.769988\pi$
$53$	−5.91755	+	2.45113i	−0.812837	+	0.336688i	−0.0627519	+	0.998029i	$0.519988\pi$
$54$	3.38805	−	5.93037i	0.461055	−	0.807021i
$55$	−0.362328	+	0.362328i	−0.0488563	+	0.0488563i
$56$	−1.03088	+	5.18257i	−0.137757	+	0.692551i
$57$	11.5829	−	1.03106i	1.53419	−	0.136568i
$58$	−5.07456	+	1.00939i	−0.666323	+	0.132540i
$59$	−3.65974	+	8.83540i	−0.476458	+	1.15027i	0.484801	+	0.874624i	$0.338892\pi$
$59$	−3.65974	+	8.83540i	−0.476458	+	1.15027i	−0.961259	+	0.275647i	$0.911108\pi$
$60$	0.0636782	−	0.0186653i	0.00822083	−	0.00240967i
$61$	0.775290	+	3.89765i	0.0992658	+	0.499043i	0.998147	+	0.0608502i	$0.0193812\pi$
$61$	0.775290	+	3.89765i	0.0992658	+	0.499043i	−0.898881	+	0.438193i	$0.855619\pi$
$62$	9.78574	+	6.53863i	1.24279	+	0.830406i
$63$	4.86451	+	2.12286i	0.612871	+	0.267456i
$64$	−6.20303	−	6.20303i	−0.775378	−	0.775378i
$65$	0.0136545	−	0.00912367i	0.00169364	−	0.00113165i
$66$	3.97693	−	7.27511i	0.489527	−	0.895505i
$67$			5.81844i			0.710836i	0.934707	+	0.355418i	$0.115661\pi$
$67$			5.81844i			0.710836i	−0.934707	+	0.355418i	$0.884339\pi$
$68$		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	0.957780	+	0.287502i	$0.0928246\pi$
$71$	7.22012	+	10.8057i	0.856870	+	1.28240i	−0.100910	+	0.994896i	$0.532175\pi$
$72$	−7.54238	+	4.83722i	−0.888878	+	0.570072i
$73$	−4.38175	−	0.871585i	−0.512845	−	0.102011i	−0.0681180	−	0.997677i	$-0.521699\pi$
$73$	−4.38175	−	0.871585i	−0.512845	−	0.102011i	−0.444727	+	0.895666i	$0.646699\pi$
$74$	0.271949	−	0.407000i	0.0316134	−	0.0473128i
$75$	5.53464	−	6.61627i	0.639086	−	0.763981i
$76$	−1.68895	−	0.699588i	−0.193736	−	0.0802482i
$77$	5.95260	+	2.46565i	0.678362	+	0.280987i
$78$	−0.170495	+	0.203814i	−0.0193047	+	0.0230774i
$79$	−1.35888	+	2.03371i	−0.152886	+	0.228811i	−0.900004	−	0.435881i	$-0.856437\pi$
$79$	−1.35888	+	2.03371i	−0.152886	+	0.228811i	0.747118	+	0.664691i	$0.231437\pi$
$80$	0.466609	+	0.0928142i	0.0521684	+	0.0103769i
$81$	3.12939	+	8.43842i	0.347710	+	0.937602i
$82$	−3.21133	−	4.80610i	−0.354633	−	0.530745i
$83$	2.12000	+	5.11813i	0.232700	+	0.561788i	0.996493	−	0.0836731i	$-0.0266652\pi$
$83$	2.12000	+	5.11813i	0.232700	+	0.561788i	−0.763793	+	0.645461i	$0.776665\pi$
$84$	−0.523244	−	0.649928i	−0.0570906	−	0.0709130i
$85$		0			0
$86$		−	2.77180i		−	0.298890i
$87$	3.27027	−	5.98239i	0.350609	−	0.641379i
$88$	−9.04408	+	6.04306i	−0.964103	+	0.644193i
$89$	2.89760	+	2.89760i	0.307145	+	0.307145i	0.843801	−	0.536656i	$-0.180313\pi$
$89$	2.89760	+	2.89760i	0.307145	+	0.307145i	−0.536656	+	0.843801i	$0.680313\pi$
$90$	0.221913	−	0.508511i	0.0233917	−	0.0536017i
$91$	−0.171693	−	0.114721i	−0.0179983	−	0.0120261i
$92$	−0.333574	−	1.67699i	−0.0347775	−	0.174838i
$93$	−14.8824	+	4.36231i	−1.54324	+	0.452351i
$94$	−1.50197	+	3.62608i	−0.154917	+	0.374002i
$95$	0.926494	−	0.184291i	0.0950563	−	0.0189079i
$96$	2.63800	−	0.234823i	0.269239	−	0.0239666i
$97$	0.894911	−	4.49902i	0.0908645	−	0.456807i	−0.908387	−	0.418130i	$-0.862686\pi$
$97$	0.894911	−	4.49902i	0.0908645	−	0.456807i	0.999252	−	0.0386768i	$-0.0123143\pi$
$98$	3.59692	−	3.59692i	0.363344	−	0.363344i
$99$	3.99065	+	10.1706i	0.401075	+	1.02218i
$100$	−1.25283	+	0.518941i	−0.125283	+	0.0518941i
$101$	5.06729			0.504214			0.252107	−	0.967699i	$-0.418877\pi$
$101$	5.06729			0.504214			0.252107	+	0.967699i	$0.418877\pi$
$102$		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
$105$	0.411393	+	0.129027i	0.0401479	+	0.0125917i
$106$	5.95315	−	5.95315i	0.578221	−	0.578221i
$107$	−0.265818	+	1.33636i	−0.0256976	+	0.129191i	−0.991505	−	0.130071i	$-0.958479\pi$
$107$	−0.265818	+	1.33636i	−0.0256976	+	0.129191i	0.965807	+	0.259262i	$0.0834793\pi$
$108$	0.178297	−	1.40358i	0.0171567	−	0.135060i
$109$	11.2577	−	2.23930i	1.07829	−	0.214486i	0.376176	−	0.926548i	$-0.377239\pi$
$109$	11.2577	−	2.23930i	1.07829	−	0.214486i	0.702116	+	0.712062i	$0.252239\pi$
$110$	0.257746	−	0.622254i	0.0245751	−	0.0593296i
$111$	0.181434	+	0.618977i	0.0172209	+	0.0587507i
$112$	−1.16705	−	5.86715i	−0.110276	−	0.554394i
$113$	−11.2676	−	7.52875i	−1.05996	−	0.708245i	−0.101899	−	0.994795i	$-0.532492\pi$
$113$	−11.2676	−	7.52875i	−1.05996	−	0.708245i	−0.958066	+	0.286549i	$0.907492\pi$
$114$	−13.5473	+	7.07839i	−1.26882	+	0.662952i
$115$	0.624752	+	0.624752i	0.0582584	+	0.0582584i
$116$	−0.891183	+	0.595470i	−0.0827443	+	0.0552880i
$117$	−0.0618477	−	0.344645i	−0.00571782	−	0.0318624i
$118$		−	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
$123$	7.57276	+	0.817741i	0.682813	+	0.0737332i
$124$	2.39121	+	0.475641i	0.214737	+	0.0427138i
$125$	0.780146	−	1.16757i	0.0697784	−	0.104431i
$126$	−6.97513	−	0.131050i	−0.621394	−	0.0116748i
$127$	9.13631	+	3.78439i	0.810717	+	0.335810i	0.749240	−	0.662299i	$-0.230419\pi$
$127$	9.13631	+	3.78439i	0.810717	+	0.335810i	0.0614768	+	0.998109i	$0.480419\pi$
$128$	7.82759	+	3.24229i	0.691867	+	0.286581i
$129$	2.80151	+	2.34352i	0.246659	+	0.206335i
$130$	−0.0119924	+	0.0179478i	−0.00105180	+	0.00157413i
$131$	−12.7789	−	2.54189i	−1.11650	−	0.222086i	−0.397845	−	0.917453i	$-0.630242\pi$
$131$	−12.7789	−	2.54189i	−1.11650	−	0.222086i	−0.718655	+	0.695367i	$0.755242\pi$
$132$	0.184398	−	1.70763i	0.0160497	−	0.148630i
$133$	−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	$0.956284\pi$
$138$	−12.5443	−	6.85731i	−1.06784	−	0.583733i
$139$	−4.23589	+	2.83033i	−0.359283	+	0.240065i	−0.722090	−	0.691799i	$-0.756818\pi$
$139$	−4.23589	+	2.83033i	−0.359283	+	0.240065i	0.362807	+	0.931864i	$0.381818\pi$
$140$	−0.0479277	−	0.0479277i	−0.00405063	−	0.00405063i
$141$	−2.39505	−	4.58388i	−0.201700	−	0.386032i
$142$	−14.2032	−	9.49030i	−1.19191	−	0.796408i
$143$	−0.0829254	−	0.416894i	−0.00693457	−	0.0348624i
$144$	5.79306	−	8.32694i	0.482755	−	0.693912i
$145$	0.211947	−	0.511685i	0.0176012	−	0.0424931i
$146$	5.75948	−	1.14563i	0.476658	−	0.0948132i
$147$	0.594326	+	6.67663i	0.0490192	+	0.550679i
$148$	0.0197824	−	0.0994530i	0.00162611	−	0.00817499i
$149$	−15.7137	+	15.7137i	−1.28731	+	1.28731i	−0.350902	+	0.936412i	$0.614125\pi$
$149$	−15.7137	+	15.7137i	−1.28731	+	1.28731i	−0.936412	+	0.350902i	$0.885875\pi$
$150$	−3.39306	+	10.8186i	−0.277043	+	0.883332i
$151$	−3.81101	+	1.57857i	−0.310135	+	0.128462i	−0.532322	−	0.846542i	$-0.678681\pi$
$151$	−3.81101	+	1.57857i	−0.310135	+	0.128462i	0.222187	+	0.975004i	$0.428681\pi$
$152$	20.0526			1.62648
$153$		0			0
$154$	−8.46890			−0.682443
$155$	−1.16393	+	0.482114i	−0.0934887	+	0.0387243i
$156$	−0.0164730	+	0.0525232i	−0.00131890	+	0.00420522i
$157$	9.87094	−	9.87094i	0.787787	−	0.787787i	−0.193344	−	0.981131i	$-0.561933\pi$
$157$	9.87094	−	9.87094i	0.787787	−	0.787787i	0.981131	+	0.193344i	$0.0619335\pi$
$158$	0.627212	−	3.15321i	0.0498983	−	0.250856i
$159$	0.983649	+	11.0503i	0.0780085	+	0.876344i
$160$	0.211008	−	0.0419721i	0.0166817	−	0.00331819i
$161$	4.25145	−	10.2639i	0.335061	−	0.808909i
$162$	−8.04483	−	8.67325i	−0.632061	−	0.681435i
$163$	−2.17609	−	10.9399i	−0.170444	−	0.856881i	−0.967480	−	0.252949i	$-0.918600\pi$
$163$	−2.17609	−	10.9399i	−0.170444	−	0.856881i	0.797035	−	0.603933i	$-0.206400\pi$
$164$	−0.995609	−	0.665245i	−0.0777440	−	0.0519469i
$165$	0.411003	+	0.786617i	0.0319965	+	0.0612380i
$166$	−5.14893	−	5.14893i	−0.399634	−	0.399634i
$167$	−1.74605	+	1.16668i	−0.135114	+	0.0902801i	−0.621290	−	0.783581i	$-0.713391\pi$
$167$	−1.74605	+	1.16668i	−0.135114	+	0.0902801i	0.486177	+	0.873861i	$0.338391\pi$
$168$	8.03076	+	4.39001i	0.619587	+	0.338697i
$169$		−	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	$-0.342570\pi$
$173$	−6.84154	−	10.2391i	−0.520153	−	0.778463i	−0.994815	+	0.101705i	$0.967570\pi$
$174$	−0.962121	+	8.90980i	−0.0729382	+	0.675450i
$175$	−8.64158	−	1.71892i	−0.653242	−	0.129938i
$176$	6.84131	−	10.2387i	0.515683	−	0.771774i
$177$	12.7051	+	10.6280i	0.954971	+	0.798853i
$178$	−4.97628	−	2.06124i	−0.372988	−	0.154497i
$179$	−17.0796	−	7.07462i	−1.27659	−	0.528782i	−0.361630	−	0.932322i	$-0.617780\pi$
$179$	−17.0796	−	7.07462i	−1.27659	−	0.528782i	−0.914962	+	0.403540i	$0.867780\pi$
$180$	0.00215902	−	0.114914i	0.000160924	−	0.00856520i
$181$	1.18265	−	1.76995i	0.0879054	−	0.131560i	−0.784911	−	0.619609i	$-0.787291\pi$
$181$	1.18265	−	1.76995i	0.0879054	−	0.131560i	0.872816	+	0.488049i	$0.162291\pi$
$182$	0.266204	+	0.0529513i	0.0197324	+	0.00392501i
$183$	6.84340	+	0.738981i	0.505879	+	0.0546271i
$184$	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
$189$	6.02984	−	6.93910i	0.438606	−	0.504745i
$190$	−1.03241	+	0.689832i	−0.0748986	+	0.0500457i
$191$	12.2604	+	12.2604i	0.887130	+	0.887130i	0.994247	−	0.107116i	$-0.0341617\pi$
$191$	12.2604	+	12.2604i	0.887130	+	0.887130i	−0.107116	+	0.994247i	$0.534162\pi$
$192$	−13.4668	+	7.03634i	−0.971884	+	0.507804i
$193$	−13.5001	−	9.02046i	−0.971757	−	0.649307i	−0.0350364	−	0.999386i	$-0.511155\pi$
$193$	−13.5001	−	9.02046i	−0.971757	−	0.649307i	−0.936720	+	0.350079i	$0.886155\pi$
$194$	1.17629	+	5.91362i	0.0844529	+	0.424573i
$195$	−0.00800084	−	0.0272956i	−0.000572952	−	0.00195468i
$196$	0.403257	−	0.973548i	0.0288040	−	0.0695391i
$197$	7.70009	−	1.53164i	0.548609	−	0.109125i	0.0869994	−	0.996208i	$-0.472272\pi$
$197$	7.70009	−	1.53164i	0.548609	−	0.109125i	0.461609	+	0.887083i	$0.347272\pi$
$198$	−9.96201	−	10.3435i	−0.707969	−	0.735081i
$199$	−2.49706	+	12.5536i	−0.177012	+	0.889898i	0.785542	+	0.618808i	$0.212384\pi$
$199$	−2.49706	+	12.5536i	−0.177012	+	0.889898i	−0.962554	+	0.271090i	$0.912616\pi$
$200$	10.5180	−	10.5180i	0.743732	−	0.743732i
$201$	9.61599	+	3.01590i	0.678259	+	0.212725i
$202$	−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
$207$	17.5368	−	6.88096i	1.21889	−	0.478260i
$208$	−0.279061	+	0.279061i	−0.0193494	+	0.0193494i
$209$	4.77008	−	23.9808i	0.329954	−	1.65879i
$210$	−0.564485	+	0.0502481i	−0.0389532	+	0.00346745i
$211$	−5.02173	+	0.998885i	−0.345710	+	0.0687661i	−0.364892	−	0.931050i	$-0.618894\pi$
$211$	−5.02173	+	0.998885i	−0.345710	+	0.0687661i	0.0191813	+	0.999816i	$0.493894\pi$
$212$	0.667417	−	1.61129i	0.0458384	−	0.110664i
$213$	21.6007	−	6.33155i	1.48005	−	0.433831i
$214$	−0.349398	−	1.75654i	−0.0238843	−	0.120075i
$215$	0.246700	+	0.164840i	0.0168248	+	0.0112420i
$216$	4.08488	+	14.9724i	0.277941	+	1.01874i
$217$	11.2013	+	11.2013i	0.760395	+	0.760395i
$218$	−12.5446	+	8.38205i	−0.849630	+	0.567704i
$219$	−3.71166	+	6.78984i	−0.250810	+	0.458815i
$220$		−	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	0.921441	−	0.388518i	$-0.127013\pi$
$223$	−0.0722764	−	0.174491i	−0.00483999	−	0.0116848i	−0.926281	+	0.376833i	$0.877013\pi$
$224$	−1.50293	−	2.24929i	−0.100419	−	0.150287i
$225$	−8.06574	−	12.5764i	−0.537716	−	0.838426i
$226$	17.4700	+	3.47500i	1.16209	+	0.231154i
$227$	1.18348	−	1.77120i	0.0785504	−	0.117559i	−0.790114	−	0.612960i	$-0.789979\pi$
$227$	1.18348	−	1.77120i	0.0785504	−	0.117559i	0.868665	+	0.495401i	$0.164979\pi$
$228$	−2.03163	+	2.42867i	−0.134548	+	0.160843i
$229$	15.9683	+	6.61427i	1.05521	+	0.437084i	0.841750	−	0.539868i	$-0.181526\pi$
$229$	15.9683	+	6.61427i	1.05521	+	0.437084i	0.213463	+	0.976951i	$0.431526\pi$
$230$	−1.07293	−	0.444424i	−0.0707472	−	0.0293045i
$231$	7.16035	−	8.55968i	0.471116	−	0.563185i
$232$	6.53172	−	9.77541i	0.428828	−	0.641787i
$233$	9.60397	+	1.91035i	0.629177	+	0.125151i	0.499371	−	0.866388i	$-0.333565\pi$
$233$	9.60397	+	1.91035i	0.629177	+	0.125151i	0.129806	+	0.991539i	$0.458565\pi$
$234$	0.248465	+	0.387416i	0.0162427	+	0.0253262i
$235$	−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	$-0.258463\pi$
$240$	0.395251	−	0.723043i	0.0255133	−	0.0466722i
$241$	−0.337157	+	0.225281i	−0.0217182	+	0.0145116i	−0.566382	−	0.824143i	$-0.691657\pi$
$241$	−0.337157	+	0.225281i	−0.0217182	+	0.0145116i	0.544664	+	0.838655i	$0.316657\pi$
$242$	−2.10322	−	2.10322i	−0.135200	−	0.135200i
$243$	15.5680	−	0.797936i	0.998689	−	0.0511876i
$244$	−0.899718	−	0.601172i	−0.0575985	−	0.0384861i
$245$	0.106229	+	0.534050i	0.00678674	+	0.0341192i
$246$	−9.60746	+	2.81612i	−0.612549	+	0.179549i
$247$	−0.299877	+	0.723968i	−0.0190807	+	0.0460650i
$248$	−26.2292	+	5.21731i	−1.66556	+	0.331300i
$249$	9.55747	−	0.850766i	0.605680	−	0.0539151i
$250$	−0.360088	+	1.81028i	−0.0227739	+	0.114492i
$251$	−0.749951	+	0.749951i	−0.0473365	+	0.0473365i	−0.730379	−	0.683042i	$-0.760656\pi$
$251$	−0.749951	+	0.749951i	−0.0473365	+	0.0473365i	0.683042	+	0.730379i	$0.260656\pi$
$252$	−1.34533	+	0.527872i	−0.0847481	+	0.0332528i
$253$	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	$-0.408913\pi$
$257$	18.5997	−	7.70425i	1.16022	−	0.480578i	0.877947	+	0.478757i	$0.158913\pi$
$258$	−4.58087	−	1.43672i	−0.285193	−	0.0894460i
$259$	0.465876	−	0.465876i	0.0289481	−	0.0289481i
$260$	−0.000872364		0.00438567i	−5.41017e−5		0.000271988i
$261$	−8.19185	−	8.50556i	−0.507063	−	0.526481i
$262$	16.7969	−	3.34111i	1.03772	−	0.206415i
$263$	2.11297	−	5.10116i	0.130291	−	0.314551i	−0.845249	−	0.534373i	$-0.820548\pi$
$263$	2.11297	−	5.10116i	0.130291	−	0.314551i	0.975540	+	0.219822i	$0.0705477\pi$
$264$	5.29936	+	18.0792i	0.326153	+	1.11270i
$265$	0.175817	+	0.883889i	0.0108003	+	0.0542969i
$266$	12.9815	+	8.67397i	0.795948	+	0.531835i
$267$	6.29072	−	3.28687i	0.384986	−	0.201153i
$268$	−1.12027	−	1.12027i	−0.0684314	−	0.0684314i
$269$	7.59932	−	5.07770i	0.463339	−	0.309593i	−0.301900	−	0.953340i	$-0.597621\pi$
$269$	7.59932	−	5.07770i	0.463339	−	0.309593i	0.765239	+	0.643747i	$0.222621\pi$
$270$	−0.725377	−	0.630328i	−0.0441451	−	0.0383605i
$271$		−	2.64822i		−	0.160868i	−0.996760	−	0.0804339i	$-0.974369\pi$
$271$		−	2.64822i		−	0.160868i	0.996760	−	0.0804339i	$-0.0256306\pi$
$272$		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
$276$	−2.94442	−	0.317951i	−0.177233	−	0.0191384i
$277$	−20.2921	−	4.03634i	−1.21923	−	0.242520i	−0.456789	−	0.889575i	$-0.651001\pi$
$277$	−20.2921	−	4.03634i	−1.21923	−	0.242520i	−0.762444	+	0.647055i	$0.776001\pi$
$278$	3.72025	−	5.56775i	0.223126	−	0.333931i
$279$	−0.504591	+	26.8569i	−0.0302091	+	1.60788i
$280$	0.686886	+	0.284517i	0.0410493	+	0.0170032i
$281$	−9.50546	−	3.93729i	−0.567048	−	0.234879i	0.0806938	−	0.996739i	$-0.474286\pi$
$281$	−9.50546	−	3.93729i	−0.567048	−	0.234879i	−0.647742	+	0.761860i	$0.724286\pi$
$282$	5.21420	+	4.36179i	0.310501	+	0.259741i
$283$	−7.13505	+	10.6783i	−0.424134	+	0.634762i	−0.980579	−	0.196122i	$-0.937165\pi$
$283$	−7.13505	+	10.6783i	−0.424134	+	0.634762i	0.556445	+	0.830884i	$0.312165\pi$
$284$	−3.47065	−	0.690355i	−0.205945	−	0.0409650i
$285$	0.175660	−	1.62672i	0.0104052	−	0.0963584i
$286$	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
$291$	−6.97155	−	3.81099i	−0.408680	−	0.223404i
$292$	1.01147	−	0.675840i	0.0591916	−	0.0395506i
$293$	−0.797696	−	0.797696i	−0.0466019	−	0.0466019i	0.683422	−	0.730024i	$-0.260491\pi$
$293$	−0.797696	−	0.797696i	−0.0466019	−	0.0466019i	−0.730024	+	0.683422i	$0.760491\pi$
$294$	−4.08013	−	7.80895i	−0.237958	−	0.455427i
$295$	1.11881	+	0.747562i	0.0651394	+	0.0435248i
$296$	0.216994	+	1.09090i	0.0126125	+	0.0634074i
$297$	18.8771	−	1.32348i	1.09536	−	0.0767964i
$298$	11.1781	−	26.9863i	0.647530	−	1.56327i
$299$	−0.718839	+	0.142986i	−0.0415715	+	0.00826909i
$300$	0.208254	+	2.33951i	0.0120235	+	0.135072i
$301$	0.727837	−	3.65908i	0.0419518	−	0.210906i
$302$	3.83394	−	3.83394i	0.220618	−	0.220618i
$303$	2.62655	−	8.37457i	0.150891	−	0.481106i
$304$	−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
$309$	−8.28089	+	26.4031i	−0.471083	+	1.50202i
$310$	1.17093	−	1.17093i	0.0665042	−	0.0665042i
$311$	−5.73078	+	28.8106i	−0.324963	+	1.63370i	0.380380	+	0.924830i	$0.375793\pi$
$311$	−5.73078	+	28.8106i	−0.324963	+	1.63370i	−0.705342	+	0.708867i	$0.749207\pi$
$312$	−0.0535360	−	0.601421i	−0.00303088	−	0.0340488i
$313$	−17.4779	+	3.47657i	−0.987910	+	0.196507i	−0.662497	−	0.749065i	$-0.730503\pi$
$313$	−17.4779	+	3.47657i	−0.987910	+	0.196507i	−0.325413	+	0.945572i	$0.605503\pi$
$314$	−7.02180	+	16.9521i	−0.396263	+	0.956664i
$315$	0.426478	−	0.613020i	0.0240293	−	0.0345398i
$316$	−0.129930	−	0.653204i	−0.00730915	−	0.0367456i
$317$	11.7412	+	7.84523i	0.659452	+	0.440632i	0.839745	−	0.542981i	$-0.182704\pi$
$317$	11.7412	+	7.84523i	0.659452	+	0.440632i	−0.180293	+	0.983613i	$0.557704\pi$
$318$	−6.75289	−	12.9243i	−0.378683	−	0.724760i
$319$	−10.1366	−	10.1366i	−0.567542	−	0.567542i
$320$	−1.02627	+	0.685733i	−0.0573704	+	0.0383337i
$321$	2.07078	+	1.13199i	0.115580	+	0.0631815i
$322$			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
$327$	2.13442	−	19.7660i	0.118034	−	1.09306i
$328$	12.8820	+	2.56239i	0.711291	+	0.141485i
$329$	−2.93493	+	4.39244i	−0.161808	+	0.242163i
$330$	−0.894784	−	0.748505i	−0.0492562	−	0.0412039i
$331$	−6.68245	−	2.76796i	−0.367301	−	0.152141i	0.191396	−	0.981513i	$-0.438698\pi$
$331$	−6.68245	−	2.76796i	−0.367301	−	0.152141i	−0.558697	+	0.829372i	$0.688698\pi$
$332$	−1.39362	−	0.577254i	−0.0764846	−	0.0316810i
$333$	1.11701	+	0.0209865i	0.0612118	+	0.00115005i
$334$	1.53351	−	2.29505i	0.0839097	−	0.125580i
$335$	0.802931	+	0.159713i	0.0438688	+	0.00872605i
$336$	−10.3014	−	1.11239i	−0.561988	−	0.0606860i
$337$	−7.42687	−	11.1151i	−0.404568	−	0.605478i	0.572113	−	0.820175i	$-0.306124\pi$
$337$	−7.42687	−	11.1151i	−0.404568	−	0.605478i	−0.976681	+	0.214696i	$0.931124\pi$
$338$	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
$342$	4.67625	+	26.0582i	0.252862	+	1.40907i
$343$	15.9900	−	10.6842i	0.863378	−	0.576891i
$344$	4.45359	+	4.45359i	0.240121	+	0.240121i
$345$	1.35634	−	0.708681i	0.0730229	−	0.0381541i
$346$	13.4585	+	8.99268i	0.723534	+	0.483450i
$347$	−6.53027	−	32.8299i	−0.350563	−	1.76240i	−0.605893	−	0.795546i	$-0.707184\pi$
$347$	−6.53027	−	32.8299i	−0.350563	−	1.76240i	0.255329	−	0.966854i	$-0.417816\pi$
$348$	0.522186	+	1.78149i	0.0279921	+	0.0954977i
$349$	−10.6503	+	25.7122i	−0.570099	+	1.37634i	0.331372	+	0.943500i	$0.392489\pi$
$349$	−10.6503	+	25.7122i	−0.570099	+	1.37634i	−0.901471	+	0.432840i	$0.857511\pi$
$350$	11.3587	−	2.25939i	0.607148	−	0.120769i
$351$	−0.601643	−	0.0764269i	−0.0321133	−	0.00407937i
$352$	1.08638	−	5.46161i	0.0579043	−	0.291105i
$353$	−5.10785	+	5.10785i	−0.271864	+	0.271864i	−0.829850	−	0.557986i	$-0.811574\pi$
$353$	−5.10785	+	5.10785i	−0.271864	+	0.271864i	0.557986	+	0.829850i	$0.311574\pi$
$354$	−20.7746	−	6.51562i	−1.10416	−	0.346301i
$355$	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	$-0.884160\pi$
$359$	−25.4579	+	10.5450i	−1.34362	+	0.556544i	−0.409108	+	0.912486i	$0.634160\pi$
$360$	0.460491	+	1.17361i	0.0242700	+	0.0618546i
$361$	−18.4383	+	18.4383i	−0.970437	+	0.970437i
$362$	−0.545867	+	2.74426i	−0.0286901	+	0.144235i
$363$	3.90400	−	0.347518i	0.204907	−	0.0182400i
$364$	0.0551455	−	0.0109691i	0.00289041	−	0.000574939i
$365$	−0.240553	+	0.580747i	−0.0125911	+	0.0303977i
$366$	−8.68213	+	2.54489i	−0.453822	+	0.133024i
$367$	2.19159	+	11.0178i	0.114400	+	0.575127i	0.994882	+	0.101047i	$0.0322192\pi$
$367$	2.19159	+	11.0178i	0.114400	+	0.575127i	−0.880482	+	0.474080i	$0.842781\pi$
$368$	−17.6544	−	11.7963i	−0.920297	−	0.614923i
$369$	5.27668	−	12.0914i	0.274693	−	0.629455i
$370$	−0.0487002	−	0.0487002i	−0.00253180	−	0.00253180i
$371$	9.42204	−	6.29561i	0.489168	−	0.326852i
$372$	2.02552	−	3.70534i	0.105018	−	0.192113i
$373$		−	5.50325i		−	0.284948i	−0.989799	−	0.142474i	$-0.954494\pi$
$373$		−	5.50325i		−	0.284948i	0.989799	−	0.142474i	$-0.0455057\pi$
$374$		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
$378$	−3.83203	+	11.4597i	−0.197098	+	0.589423i
$379$	−5.16575	−	1.02753i	−0.265347	−	0.0527808i	0.0606237	−	0.998161i	$-0.480691\pi$
$379$	−5.16575	−	1.02753i	−0.265347	−	0.0527808i	−0.325971	+	0.945380i	$0.605691\pi$
$380$	−0.142902	+	0.213868i	−0.00733073	+	0.0109712i
$381$	10.9900	−	13.1378i	0.563036	−	0.673068i
$382$	−21.0557	−	8.72156i	−1.07730	−	0.446234i
$383$	19.5477	+	8.09691i	0.998840	+	0.413733i	0.821372	−	0.570394i	$-0.193209\pi$
$383$	19.5477	+	8.09691i	0.998840	+	0.413733i	0.177468	+	0.984127i	$0.443209\pi$
$384$	9.41575	−	11.2559i	0.480496	−	0.574398i
$385$	0.503649	−	0.753764i	0.0256683	−	0.0384154i
$386$	20.9314	+	4.16352i	1.06538	+	0.211918i
$387$	5.32519	−	3.41525i	0.270694	−	0.173607i
$388$	0.693928	+	1.03854i	0.0352289	+	0.0527237i
$389$	−4.78245	−	11.5459i	−0.242480	−	0.585398i	0.755048	−	0.655669i	$-0.227613\pi$
$389$	−4.78245	−	11.5459i	−0.242480	−	0.585398i	−0.997528	+	0.0702713i	$0.977613\pi$
$390$	0.0234459	+	0.0291224i	0.00118723	+	0.00147467i
$391$		0			0
$392$			11.5587i			0.583804i
$393$	−10.8247	+	19.8018i	−0.546032	+	0.998871i
$394$	−8.58033	+	5.73319i	−0.432271	+	0.288834i
$395$	0.243347	+	0.243347i	0.0122441	+	0.0122441i
$396$	−2.72657	−	1.18987i	−0.137015	−	0.0597933i
$397$	32.3438	+	21.6114i	1.62329	+	1.08465i	0.932240	+	0.361839i	$0.117851\pi$
$397$	32.3438	+	21.6114i	1.62329	+	1.08465i	0.691049	+	0.722808i	$0.257149\pi$
$398$	−3.28219	−	16.5007i	−0.164521	−	0.827105i
$399$	−19.7427	+	5.78693i	−0.988369	+	0.289709i
$400$	−6.44418	+	15.5576i	−0.322209	+	0.777881i
$401$	−26.7045	+	5.31186i	−1.33356	+	0.265262i	−0.809851	−	0.586635i	$-0.800452\pi$
$401$	−26.7045	+	5.31186i	−1.33356	+	0.265262i	−0.523709	+	0.851897i	$0.675452\pi$
$402$	−13.1944	+	1.17451i	−0.658076	+	0.0585792i
$403$	0.203883	−	1.02499i	0.0101561	−	0.0510583i
$404$	−0.975645	+	0.975645i	−0.0485401	+	0.0485401i
$405$	1.25038	−	0.200218i	0.0621320	−	0.00994892i
$406$	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
$411$	5.29669	+	1.66122i	0.261266	+	0.0819419i
$412$	3.07598	−	3.07598i	0.151543	−	0.151543i
$413$	3.30080	−	16.5942i	0.162422	−	0.816549i
$414$	−17.8350	+	17.1772i	−0.876543	+	0.844214i
$415$	0.764483	−	0.152065i	0.0375270	−	0.00746459i
$416$	−0.0682967	+	0.164883i	−0.00334852	+	0.00808405i
$417$	2.48201	+	8.46759i	0.121544	+	0.414660i
$418$	6.26991	+	31.5210i	0.306671	+	1.54174i
$419$	−7.76628	−	5.18926i	−0.379408	−	0.253512i	0.351213	−	0.936295i	$-0.385769\pi$
$419$	−7.76628	−	5.18926i	−0.379408	−	0.253512i	−0.730621	+	0.682784i	$0.760769\pi$
$420$	−0.104051	+	0.0543663i	−0.00507719	+	0.00265280i
$421$	9.40617	+	9.40617i	0.458429	+	0.458429i	0.898139	−	0.439711i	$-0.144919\pi$
$421$	9.40617	+	9.40617i	0.458429	+	0.458429i	−0.439711	+	0.898139i	$0.644919\pi$
$422$	5.59579	−	3.73899i	0.272399	−	0.182011i
$423$	−8.81709	+	1.58226i	−0.428702	+	0.0769320i
$424$			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
$429$	−0.731973	−	0.0790418i	−0.0353400	−	0.00381617i
$430$	−0.382501	−	0.0760842i	−0.0184459	−	0.00366911i
$431$	−8.11718	+	12.1482i	−0.390991	+	0.585159i	−0.973788	−	0.227459i	$-0.926958\pi$
$431$	−8.11718	+	12.1482i	−0.390991	+	0.585159i	0.582797	+	0.812618i	$0.301958\pi$
$432$	−10.7590	−	13.8902i	−0.517641	−	0.668291i
$433$	−16.4827	−	6.82738i	−0.792110	−	0.328103i	−0.0503185	−	0.998733i	$-0.516024\pi$
$433$	−16.4827	−	6.82738i	−0.792110	−	0.328103i	−0.741792	+	0.670631i	$0.766024\pi$
$434$	−19.2369	−	7.96819i	−0.923401	−	0.382485i
$435$	−0.735789	−	0.615502i	−0.0352784	−	0.0295111i
$436$	−1.73639	+	2.59869i	−0.0831578	+	0.124454i
$437$	−41.3495	−	8.22492i	−1.97801	−	0.393451i
$438$	1.09198	−	10.1124i	0.0521768	−	0.483187i
$439$	14.6447	+	21.9174i	0.698955	+	1.04606i	0.995838	+	0.0911464i	$0.0290531\pi$
$439$	14.6447	+	21.9174i	0.698955	+	1.04606i	−0.296882	+	0.954914i	$0.595947\pi$
$440$	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	$0.926217\pi$
$444$	−0.154109	−	0.0842438i	−0.00731371	−	0.00399803i
$445$	0.479400	−	0.320325i	0.0227257	−	0.0151848i
$446$	0.175541	+	0.175541i	0.00831208	+	0.00831208i
$447$	17.8246	+	34.1145i	0.843076	+	1.61356i
$448$	12.9044	+	8.62244i	0.609675	+	0.407372i
$449$	0.206155	+	1.03641i	0.00972906	+	0.0489113i	0.985345	−	0.170574i	$-0.0545622\pi$
$449$	0.206155	+	1.03641i	0.00972906	+	0.0489113i	−0.975616	+	0.219485i	$0.929562\pi$
$450$	16.1208	+	11.2153i	0.759942	+	0.528692i
$451$	6.12872	−	14.7960i	0.288590	−	0.696718i
$452$	3.61901	−	0.719865i	0.170224	−	0.0338596i
$453$	0.633488	+	7.11658i	0.0297639	+	0.334366i
$454$	−0.546252	+	2.74620i	−0.0256369	+	0.128885i
$455$	−0.0205441	+	0.0205441i	−0.000963124	+	0.000963124i
$456$	10.3939	−	33.1404i	0.486741	−	1.55194i
$457$	19.7952	−	8.19942i	0.925978	−	0.383553i	0.131827	−	0.991273i	$-0.457916\pi$
$457$	19.7952	−	8.19942i	0.925978	−	0.383553i	0.794151	+	0.607720i	$0.207916\pi$
$458$	−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	$-0.819536\pi$
$461$	−22.7649	+	9.42954i	−1.06027	+	0.439177i	−0.216721	+	0.976233i	$0.569536\pi$
$462$	−4.38972	+	13.9963i	−0.204228	+	0.651168i
$463$	−13.6466	+	13.6466i	−0.634213	+	0.634213i	−0.949122	−	0.314909i	$-0.898026\pi$
$463$	−13.6466	+	13.6466i	−0.634213	+	0.634213i	0.314909	+	0.949122i	$0.398026\pi$
$464$	−2.59661	+	13.0540i	−0.120544	+	0.606018i
$465$	0.193474	+	2.17348i	0.00897216	+	0.100793i
$466$	−12.6237	+	2.51101i	−0.584781	+	0.116320i
$467$	4.76264	−	11.4980i	0.220389	−	0.532066i	−0.774554	−	0.632508i	$-0.782026\pi$
$467$	4.76264	−	11.4980i	0.220389	−	0.532066i	0.994943	+	0.100442i	$0.0320257\pi$
$468$	0.0782652	+	0.0544491i	0.00361781	+	0.00251691i
$469$	−2.00824	−	10.0961i	−0.0927317	−	0.466194i
$470$	0.459162	+	0.306802i	0.0211796	+	0.0141517i
$471$	−11.1970	−	21.4299i	−0.515930	−	0.987437i
$472$	20.1974	+	20.1974i	0.929660	+	0.929660i
$473$	6.38545	−	4.26662i	0.293603	−	0.196179i
$474$	−4.88612	−	2.67099i	−0.224427	−	0.122683i
$475$			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	$-0.0139631\pi$
$479$	12.6109	+	18.8736i	0.576208	+	0.862357i	−0.422830	+	0.906209i	$0.638963\pi$
$480$	0.0400064	−	0.370483i	0.00182604	−	0.0169102i
$481$	−0.0426304	−	0.00847972i	−0.00194378	−	0.000386642i
$482$	0.296115	−	0.443167i	0.0134877	−	0.0201857i
$483$	−14.7592	−	12.3464i	−0.671567	−	0.561780i
$484$	−0.569259	−	0.235795i	−0.0258754	−	0.0107179i
$485$	−0.596290	−	0.246991i	−0.0270761	−	0.0112153i
$486$	−18.5040	+	8.79983i	−0.839357	+	0.399169i
$487$	−12.7700	+	19.1116i	−0.578662	+	0.866028i	−0.999148	−	0.0412704i	$-0.986859\pi$
$487$	−12.7700	+	19.1116i	−0.578662	+	0.866028i	0.420486	+	0.907299i	$0.361859\pi$
$488$	11.6413	+	2.31560i	0.526977	+	0.104822i
$489$	−19.2081	−	2.07417i	−0.868619	−	0.0937974i
$490$	−0.397633	−	0.595100i	−0.0179632	−	0.0268839i
$491$	−7.79649	−	18.8224i	−0.351851	−	0.849443i	−0.996392	−	0.0848732i	$-0.972951\pi$
$491$	−7.79649	−	18.8224i	−0.351851	−	0.849443i	0.644541	−	0.764570i	$-0.277049\pi$
$492$	−1.61549	+	1.30060i	−0.0728319	+	0.0586355i
$493$		0			0
$494$		−	1.03001i		−	0.0463421i
$495$	1.51306	−	0.271524i	0.0680069	−	0.0122041i
$496$	25.1733	−	16.8202i	1.13031	−	0.755251i
$497$	−16.2578	−	16.2578i	−0.729264	−	0.729264i
$498$	−11.1784	+	5.84063i	−0.500914	+	0.261725i
$499$	0.897288	+	0.599548i	0.0401681	+	0.0268395i	0.575492	−	0.817807i	$-0.304811\pi$
$499$	0.897288	+	0.599548i	0.0401681	+	0.0268395i	−0.535324	+	0.844647i	$0.679811\pi$
$500$	0.0745940	+	0.375010i	0.00333595	+	0.0167709i
$501$	1.02309	+	3.49038i	0.0457085	+	0.155939i
$502$	0.533486	−	1.28795i	0.0238106	−	0.0574840i
$503$	9.20449	−	1.83089i	0.410408	−	0.0816353i	0.0144315	−	0.999896i	$-0.495406\pi$
$503$	9.20449	−	1.83089i	0.410408	−	0.0816353i	0.395977	+	0.918261i	$0.370406\pi$
$504$	11.4179	−	10.9967i	0.508592	−	0.489834i
$505$	0.139094	−	0.699273i	0.00618961	−	0.0311173i
$506$	−21.2552	+	21.2552i	−0.944907	+	0.944907i
$507$	−21.4622	−	6.73128i	−0.953172	−	0.298947i
$508$	−2.48772	+	1.03045i	−0.110375	+	0.0457188i
$509$	−7.99190			−0.354235			−0.177117	−	0.984190i	$-0.556677\pi$
$509$	−7.99190			−0.354235			−0.177117	+	0.984190i	$0.556677\pi$
$510$		0			0
$511$	7.90399			0.349652
$512$	−23.4372	+	9.70803i	−1.03579	+	0.429038i
$513$	−30.2913	−	17.3055i	−1.33739	−	0.764059i
$514$	−18.7116	+	18.7116i	−0.825334	+	0.825334i
$515$	−0.438531	+	2.20465i	−0.0193240	+	0.0971483i
$516$	−0.990613	+	0.0881802i	−0.0436093	+	0.00388192i
$517$	−10.6655	+	2.12149i	−0.469066	+	0.0933031i
$518$	−0.331406	+	0.800085i	−0.0145611	+	0.0351537i
$519$	−20.4681	+	5.99957i	−0.898449	+	0.263352i
$520$	−0.00956898	−	0.0481065i	−0.000419627	−	0.00210961i
$521$	1.31074	+	0.875810i	0.0574246	+	0.0383699i	0.583951	−	0.811789i	$-0.301506\pi$
$521$	1.31074	+	0.875810i	0.0574246	+	0.0383699i	−0.526527	+	0.850159i	$0.676506\pi$
$522$	14.2263	+	6.20832i	0.622668	+	0.271731i
$523$	−24.2095	−	24.2095i	−1.05861	−	1.05861i	−0.998172	−	0.0604341i	$-0.980751\pi$
$523$	−24.2095	−	24.2095i	−1.05861	−	1.05861i	−0.0604341	−	0.998172i	$-0.519249\pi$
$524$	2.94984	−	1.97102i	0.128864	−	0.0861043i
$525$	−7.32004	+	13.3907i	−0.319473	+	0.584420i
$526$			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
$531$	24.1502	−	15.4884i	1.04803	−	0.672141i
$532$	3.17211	+	0.630973i	0.137529	+	0.0273561i
$533$	−0.285156	+	0.426766i	−0.0123515	+	0.0184853i
$534$	−5.98593	+	7.15575i	−0.259037	+	0.309660i
$535$	0.177118	+	0.0733645i	0.00765746	+	0.00317183i
$536$	16.0554	+	6.65037i	0.693488	+	0.287252i
$537$	−20.5450	+	24.5601i	−0.886582	+	1.05984i
$538$	−6.67425	+	9.98873i	−0.287747	+	0.430645i
$539$	13.8230	+	2.74957i	0.595401	+	0.118433i
$540$	−0.188797	−	0.0631321i	−0.00812451	−	0.00271677i
$541$	1.68432	+	2.52076i	0.0724146	+	0.108376i	0.865909	−	0.500201i	$-0.166741\pi$
$541$	1.68432	+	2.52076i	0.0724146	+	0.108376i	−0.793495	+	0.608577i	$0.791741\pi$
$542$	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
$546$	0.225494	−	0.412502i	0.00965024	−	0.0176535i
$547$	−1.44506	+	0.965555i	−0.0617861	+	0.0412842i	−0.586080	−	0.810253i	$-0.699329\pi$
$547$	−1.44506	+	0.965555i	−0.0617861	+	0.0412842i	0.524294	+	0.851538i	$0.324329\pi$
$548$	−0.617069	−	0.617069i	−0.0263599	−	0.0263599i
$549$	4.76846	−	10.9269i	0.203513	−	0.466347i
$550$	19.8220	+	13.2447i	0.845214	+	0.564754i
$551$	5.15580	+	25.9200i	0.219645	+	1.10423i
$552$	31.1735	−	9.13753i	1.32683	−	0.388919i
$553$	1.65598	−	3.99789i	0.0704195	−	0.170008i
$554$	26.6724	−	5.30547i	1.13320	−	0.225408i
$555$	0.0903977	−	0.00804682i	0.00383717	−	0.000341569i
$556$	0.270623	−	1.36051i	0.0114770	−	0.0576986i
$557$	29.9311	−	29.9311i	1.26822	−	1.26822i	0.321217	−	0.947006i	$-0.395908\pi$
$557$	29.9311	−	29.9311i	1.26822	−	1.26822i	0.947006	−	0.321217i	$-0.104092\pi$
$558$	−12.8965	−	32.8681i	−0.545953	−	1.39142i
$559$	−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	$-0.420558\pi$
$563$	26.2627	−	10.8784i	1.10684	−	0.458468i	0.859848	+	0.510550i	$0.170558\pi$
$564$	1.34371	+	0.421432i	0.0565803	+	0.0177455i
$565$	−1.34824	+	1.34824i	−0.0567208	+	0.0567208i
$566$	3.29328	−	16.5564i	0.138427	−	0.695919i
$567$	−8.34259	−	13.5621i	−0.350356	−	0.569556i
$568$	38.0696	−	7.57252i	1.59737	−	0.317736i
$569$	−7.98685	+	19.2820i	−0.334826	+	0.808342i	0.663369	+	0.748292i	$0.269126\pi$
$569$	−7.98685	+	19.2820i	−0.334826	+	0.808342i	−0.998195	+	0.0600499i	$0.980874\pi$
$570$	0.604936	+	2.06379i	0.0253380	+	0.0864428i
$571$	1.22502	+	6.15858i	0.0512654	+	0.257728i	0.997915	−	0.0645348i	$-0.0205564\pi$
$571$	1.22502	+	6.15858i	0.0512654	+	0.257728i	−0.946650	+	0.322263i	$0.895556\pi$
$572$	0.0962342	+	0.0643017i	0.00402376	+	0.00268859i
$573$	26.6174	−	13.9074i	1.11196	−	0.580992i
$574$	7.23109	+	7.23109i	0.301820	+	0.301820i
$575$	−26.0027	+	17.3744i	−1.08439	+	0.724564i
$576$	4.64846	+	25.9034i	0.193686	+	1.07931i
$577$		−	36.1978i		−	1.50693i	−0.657485	−	0.753467i	$-0.728380\pi$
$577$		−	36.1978i		−	1.50693i	0.657485	−	0.753467i	$-0.271620\pi$
$578$		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
$582$	10.3830	+	1.12120i	0.430389	+	0.0464754i
$583$	22.8781	+	4.55073i	0.947513	+	0.188472i
$584$	−7.41331	+	11.0948i	−0.306765	+	0.459106i
$585$	−0.0492578		0.000925462i	−0.00203656		3.82631e-5i
$586$	1.36995	+	0.567450i	0.0565919	+	0.0234412i
$587$	−7.20502	−	2.98442i	−0.297383	−	0.123180i	0.229003	−	0.973426i	$-0.426453\pi$
$587$	−7.20502	−	2.98442i	−0.297383	−	0.123180i	−0.526386	+	0.850246i	$0.676453\pi$
$588$	−1.39994	−	1.17107i	−0.0577323	−	0.0482943i
$589$	33.3981	−	49.9838i	1.37615	−	2.05955i
$590$	−1.73467	−	0.345048i	−0.0714154	−	0.0142054i
$591$	1.45991	−	13.5196i	0.0600528	−	0.556124i
$592$	−0.699572	−	1.04698i	−0.0287523	−	0.0430308i
$593$	11.6027	+	28.0114i	0.476465	+	1.15029i	0.961256	+	0.275659i	$0.0888960\pi$
$593$	11.6027	+	28.0114i	0.476465	+	1.15029i	−0.484790	+	0.874630i	$0.661104\pi$
$594$	−22.2581	+	11.1026i	−0.913261	+	0.455543i
$595$		0			0
$596$		−	6.05095i		−	0.247857i
$597$	19.4526	+	10.6338i	0.796143	+	0.435211i
$598$	0.801013	−	0.535220i	0.0327558	−	0.0218868i
$599$	−17.7610	−	17.7610i	−0.725695	−	0.725695i	0.244064	−	0.969759i	$-0.421519\pi$
$599$	−17.7610	−	17.7610i	−0.725695	−	0.725695i	−0.969759	+	0.244064i	$0.921519\pi$
$600$	−11.9309	−	22.8346i	−0.487078	−	0.932217i
$601$	−25.3288	−	16.9242i	−1.03318	−	0.690351i	−0.0812623	−	0.996693i	$-0.525895\pi$
$601$	−25.3288	−	16.9242i	−1.03318	−	0.690351i	−0.951922	+	0.306341i	$0.900895\pi$
$602$	0.956686	+	4.80958i	0.0389916	+	0.196024i
$603$	9.96858	−	14.3288i	0.405952	−	0.583516i
$604$	0.429829	−	1.03770i	0.0174895	−	0.0422233i
$605$	0.312273	−	0.0621150i	0.0126957	−	0.00252534i
$606$	1.02288	+	11.4910i	0.0415517	+	0.466790i
$607$	−4.25153	+	21.3739i	−0.172564	+	0.867539i	0.793368	+	0.608743i	$0.208326\pi$
$607$	−4.25153	+	21.3739i	−0.172564	+	0.867539i	−0.965932	+	0.258796i	$0.916674\pi$
$608$	−7.25911	+	7.25911i	−0.294396	+	0.294396i
$609$	−3.60970	+	11.5093i	−0.146273	+	0.466380i
$610$	−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
$615$	0.320714	−	1.02258i	0.0129325	−	0.0412343i
$616$	13.6074	−	13.6074i	0.548258	−	0.548258i
$617$	−4.61012	+	23.1766i	−0.185596	+	0.933056i	0.769925	+	0.638134i	$0.220294\pi$
$617$	−4.61012	+	23.1766i	−0.185596	+	0.933056i	−0.955521	+	0.294922i	$0.904706\pi$
$618$	−3.22490	−	36.2284i	−0.129725	−	1.45732i
$619$	−39.1709	+	7.79157i	−1.57441	+	0.313170i	−0.903572	−	0.428435i	$-0.859065\pi$
$619$	−39.1709	+	7.79157i	−1.57441	+	0.313170i	−0.670837	+	0.741605i	$0.734065\pi$
$620$	0.131275	−	0.316925i	0.00527211	−	0.0127280i
$621$	−2.28205	−	32.5493i	−0.0915754	−	1.30616i
$622$	−7.53267	−	37.8693i	−0.302033	−	1.51842i
$623$	−6.02799	−	4.02777i	−0.241506	−	0.161369i
$624$	0.316550	+	0.605843i	0.0126721	+	0.0242531i
$625$	17.4680	+	17.4680i	0.698719	+	0.698719i
$626$	19.4759	−	13.0134i	0.778413	−	0.520119i
$627$	−37.1600	−	20.3135i	−1.48403	−	0.811242i
$628$			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	0.985641	+	0.168854i	$0.0540067\pi$
$631$	10.2510	+	24.7481i	0.408085	+	0.985205i	−0.577556	+	0.816351i	$0.695993\pi$
$632$	4.05865	+	6.07420i	0.161444	+	0.241619i
$633$	−0.952104	+	8.81704i	−0.0378428	+	0.350446i
$634$	−18.2044	−	3.62108i	−0.722988	−	0.143811i
$635$	0.773023	−	1.15691i	0.0306765	−	0.0459106i
$636$	−2.31699	−	1.93821i	−0.0918745	−	0.0768549i
$637$	−0.417310	−	0.172855i	−0.0165344	−	0.00684878i
$638$	17.4084	+	7.21080i	0.689206	+	0.285478i
$639$	0.732374	−	38.9807i	0.0289723	−	1.54205i
$640$	0.662291	−	0.991189i	0.0261794	−	0.0391802i
$641$	41.7612	+	8.30682i	1.64947	+	0.328100i	0.930318	−	0.366754i	$-0.119531\pi$
$641$	41.7612	+	8.30682i	1.64947	+	0.328100i	0.719151	+	0.694854i	$0.244531\pi$
$642$	−3.08409	−	0.333034i	−0.121719	−	0.0131438i
$643$	14.3260	+	21.4404i	0.564962	+	0.845525i	0.998451	−	0.0556337i	$-0.0177179\pi$
$643$	14.3260	+	21.4404i	0.564962	+	0.845525i	−0.433490	+	0.901159i	$0.642718\pi$
$644$	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	$-0.270288\pi$
$648$	26.8618	+	1.00972i	1.05523	+	0.0396656i
$649$	28.9585	−	19.3495i	1.13672	−	0.759533i
$650$	−0.540257	−	0.540257i	−0.0211906	−	0.0211906i
$651$	24.3182	−	12.7061i	0.953104	−	0.497992i
$652$	2.52533	+	1.68737i	0.0988996	+	0.0660826i
$653$	6.69257	+	33.6458i	0.261901	+	1.31666i	0.857957	+	0.513721i	$0.171733\pi$
$653$	6.69257	+	33.6458i	0.261901	+	1.31666i	−0.596057	+	0.802942i	$0.703267\pi$
$654$	7.35049	+	25.0769i	0.287427	+	0.980584i
$655$	−0.701548	+	1.69369i	−0.0274118	+	0.0661778i
$656$	−14.5836	+	2.90087i	−0.569396	+	0.113260i
$657$	9.29750	+	9.65356i	0.362730	+	0.376621i
$658$	1.35466	−	6.81033i	0.0528101	−	0.265494i
$659$	24.7106	−	24.7106i	0.962589	−	0.962589i	−0.0367361	−	0.999325i	$-0.511696\pi$
$659$	24.7106	−	24.7106i	0.962589	−	0.962589i	0.999325	+	0.0367361i	$0.0116961\pi$
$660$	−0.230587	−	0.0723199i	−0.00897559	−	0.00281505i
$661$	11.2271	−	4.65040i	0.436682	−	0.180880i	−0.153502	−	0.988148i	$-0.549055\pi$
$661$	11.2271	−	4.65040i	0.436682	−	0.180880i	0.590184	+	0.807269i	$0.299055\pi$
$662$	9.50727			0.369510
$663$		0			0
$664$	16.5461			0.642113
$665$	−1.54403	+	0.639559i	−0.0598750	+	0.0248011i
$666$	−1.36702	+	0.536380i	−0.0529710	+	0.0207843i
$667$	−17.4783	+	17.4783i	−0.676762	+	0.676762i
$668$	0.111552	−	0.560811i	0.00431608	−	0.0216984i
$669$	−0.325839	+	0.0290049i	−0.0125977	+	0.00112139i
$670$	−1.05539	+	0.209931i	−0.0407734	+	0.00811032i
$671$	5.53844	−	13.3710i	0.213809	−	0.516181i
$672$	−4.49637	+	1.31797i	−0.173451	+	0.0508417i
$673$	7.90952	+	39.7638i	0.304890	+	1.53278i	0.764477	+	0.644651i	$0.222997\pi$
$673$	7.90952	+	39.7638i	0.304890	+	1.53278i	−0.459587	+	0.888133i	$0.652003\pi$
$674$	14.6100	+	9.76206i	0.562755	+	0.376021i
$675$	−24.9654	+	6.81126i	−0.960919	+	0.262165i
$676$	2.50037	+	2.50037i	0.0961681	+	0.0961681i
$677$	5.69882	−	3.80783i	0.219024	−	0.146347i	−0.441219	−	0.897400i	$-0.645454\pi$
$677$	5.69882	−	3.80783i	0.219024	−	0.146347i	0.660242	+	0.751053i	$0.270454\pi$
$678$	14.7984	−	27.0710i	0.568327	−	1.03966i
$679$			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	$-0.127001\pi$
$683$	5.48609	+	8.21052i	0.209919	+	0.314167i	−0.711537	+	0.702649i	$0.752001\pi$
$684$	2.96073	+	4.61649i	0.113206	+	0.176516i
$685$	0.442271	+	0.0879732i	0.0168983	+	0.00336128i
$686$	−14.0435	+	21.0176i	−0.536184	+	0.802457i
$687$	19.2081	−	22.9619i	0.732836	−	0.876052i
$688$	−6.58752	−	2.72864i	−0.251147	−	0.104028i
$689$	−0.690676	−	0.286087i	−0.0263127	−	0.0108991i
$690$	−1.29063	+	1.54285i	−0.0491333	+	0.0587353i
$691$	−7.70668	+	11.5339i	−0.293176	+	0.438769i	−0.948593	−	0.316498i	$-0.897493\pi$
$691$	−7.70668	+	11.5339i	−0.293176	+	0.438769i	0.655417	+	0.755267i	$0.272493\pi$
$692$	3.28867	+	0.654157i	0.125016	+	0.0248673i
$693$	−10.4349	−	16.2705i	−0.396389	−	0.618065i
$694$	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
$699$	8.13525	−	14.8820i	0.307703	−	0.562890i
$700$	1.99479	−	1.33288i	0.0753960	−	0.0503780i
$701$	7.15325	+	7.15325i	0.270175	+	0.270175i	0.829170	−	0.558996i	$-0.188813\pi$
$701$	7.15325	+	7.15325i	0.270175	+	0.270175i	−0.558996	+	0.829170i	$0.688813\pi$
$702$	0.769060	−	0.209821i	0.0290263	−	0.00791917i
$703$	−2.07888	−	1.38907i	−0.0784066	−	0.0523896i
$704$	6.23266	+	31.3337i	0.234902	+	1.18093i
$705$	−0.698307	+	0.204687i	−0.0262998	+	0.00770894i
$706$	3.63353	−	8.77211i	0.136750	−	0.330143i
$707$	−8.79269	+	1.74897i	−0.330683	+	0.0657770i
$708$	−4.49251	+	0.399904i	−0.168839	+	0.0150293i
$709$	−8.78850	+	44.1828i	−0.330059	+	1.65932i	0.358043	+	0.933705i	$0.383444\pi$
$709$	−8.78850	+	44.1828i	−0.330059	+	1.65932i	−0.688102	+	0.725614i	$0.741556\pi$
$710$	−1.69951	+	1.69951i	−0.0637814	+	0.0637814i
$711$	6.83078	−	2.68020i	0.256174	−	0.100516i
$712$	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
$717$	−37.0805	−	11.6297i	−1.38480	−	0.434319i
$718$	25.6111	−	25.6111i	0.955796	−	0.955796i
$719$	5.61120	−	28.2094i	0.209263	−	1.05203i	−0.723165	−	0.690676i	$-0.757313\pi$
$719$	5.61120	−	28.2094i	0.209263	−	1.05203i	0.932427	−	0.361358i	$-0.117687\pi$
$720$	−0.990082	−	1.02800i	−0.0368982	−	0.0383112i
$721$	27.7213	−	5.51411i	1.03240	−	0.205356i
$722$	13.1163	−	31.6655i	0.488138	−	1.17847i
$723$	0.197556	+	0.673981i	0.00734719	+	0.0250656i
$724$	0.113079	+	0.568488i	0.00420256	+	0.0211277i
$725$	16.2998	+	10.8912i	0.605360	+	0.404489i
$726$	−4.56610	+	2.38576i	−0.169464	+	0.0885439i
$727$	1.86673	+	1.86673i	0.0692331	+	0.0692331i	0.740876	−	0.671642i	$-0.234411\pi$
$727$	1.86673	+	1.86673i	0.0692331	+	0.0692331i	−0.671642	+	0.740876i	$0.734411\pi$
$728$	−0.512803	+	0.342644i	−0.0190058	+	0.0126992i
$729$	6.75071	−	26.1425i	0.250026	−	0.968239i
$730$		−	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	−0.974866	−	0.222790i	$-0.928484\pi$
$733$	−11.9956	−	28.9600i	−0.443068	−	1.06966i	0.531798	−	0.846871i	$-0.321516\pi$
$734$	−8.20346	−	12.2773i	−0.302795	−	0.453165i
$735$	0.937673	+	0.101254i	0.0345866	+	0.00373482i
$736$	−9.41729	−	1.87322i	−0.347126	−	0.0690477i
$737$	11.7724	−	17.6186i	0.433642	−	0.648991i
$738$	−0.325743	+	17.3377i	−0.0119907	+	0.638209i
$739$	4.41201	+	1.82751i	0.162298	+	0.0672262i	0.462354	−	0.886696i	$-0.347005\pi$
$739$	4.41201	+	1.82751i	0.162298	+	0.0672262i	−0.300055	+	0.953922i	$0.597005\pi$
$740$	−0.0131813	−	0.00545986i	−0.000484553	−	0.000200708i
$741$	1.04105	+	0.870857i	0.0382438	+	0.0319917i
$742$	−8.27510	+	12.3846i	−0.303788	+	0.454651i
$743$	−20.6527	−	4.10808i	−0.757674	−	0.150711i	−0.198888	−	0.980022i	$-0.563733\pi$
$743$	−20.6527	−	4.10808i	−0.757674	−	0.150711i	−0.558787	+	0.829312i	$0.688733\pi$
$744$	−4.97297	+	46.0526i	−0.182318	+	1.68837i
$745$	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
$750$	2.80516	+	1.53344i	0.102430	+	0.0559933i
$751$	−19.2693	+	12.8753i	−0.703145	+	0.469827i	−0.855035	−	0.518571i	$-0.826464\pi$
$751$	−19.2693	+	12.8753i	−0.703145	+	0.469827i	0.151889	+	0.988397i	$0.451464\pi$
$752$	7.13925	+	7.13925i	0.260342	+	0.260342i
$753$	0.850699	+	1.62815i	0.0310012	+	0.0593330i
$754$	−0.502116	−	0.335503i	−0.0182860	−	0.0122183i
$755$	0.113229	+	0.569241i	0.00412083	+	0.0207168i
$756$	0.175067	+	2.49701i	0.00636711	+	0.0908155i
$757$	9.85760	−	23.7983i	0.358280	−	0.864965i	−0.637262	−	0.770647i	$-0.719933\pi$
$757$	9.85760	−	23.7983i	0.358280	−	0.864965i	0.995542	−	0.0943180i	$-0.0300670\pi$
$758$	6.78999	−	1.35061i	0.246623	−	0.0490564i
$759$	−3.51203	−	39.4540i	−0.127478	−	1.43209i
$760$	0.550432	−	2.76721i	0.0199663	−	0.100377i
$761$	−15.9336	+	15.9336i	−0.577594	+	0.577594i	−0.934240	−	0.356646i	$-0.883920\pi$
$761$	−15.9336	+	15.9336i	−0.577594	+	0.577594i	0.356646	+	0.934240i	$0.383920\pi$
$762$	−6.73753	+	21.4822i	−0.244075	+	0.778217i
$763$	−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
$768$	3.32165	−	10.5909i	0.119860	−	0.382165i
$769$	−10.2112	+	10.2112i	−0.368226	+	0.368226i	−0.866830	−	0.498604i	$-0.833846\pi$
$769$	−10.2112	+	10.2112i	−0.368226	+	0.368226i	0.498604	+	0.866830i	$0.333846\pi$
$770$	−0.232466	+	1.16869i	−0.00837751	+	0.0421166i
$771$	−3.09175	−	34.7326i	−0.111347	−	1.25086i
$772$	4.33606	−	0.862495i	0.156058	−	0.0310419i
$773$	0.930920	−	2.24744i	0.0334829	−	0.0808348i	−0.906254	−	0.422734i	$-0.861070\pi$
$773$	0.930920	−	2.24744i	0.0334829	−	0.0808348i	0.939736	+	0.341900i	$0.111070\pi$
$774$	−4.74884	+	6.82599i	−0.170694	+	0.245355i
$775$	−8.69951	−	43.7354i	−0.312496	−	1.57102i
$776$	−11.3917	−	7.61171i	−0.408939	−	0.273245i
$777$	−0.528461	−	1.01142i	−0.0189584	−	0.0362845i
$778$	11.6153	+	11.6153i	0.416429	+	0.416429i
$779$	−24.5487	+	16.4029i	−0.879549	+	0.587696i
$780$	0.00679590	+	0.00371497i	0.000243332	+	0.000133017i
$781$		−	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
$786$	3.18464	−	29.4916i	0.113592	−	1.05193i
$787$	−31.1021	−	6.18658i	−1.10867	−	0.220528i	−0.393393	−	0.919370i	$-0.628699\pi$
$787$	−31.1021	−	6.18658i	−1.10867	−	0.220528i	−0.715276	+	0.698843i	$0.753699\pi$
$788$	−1.18766	+	1.77746i	−0.0423086	+	0.0633194i
$789$	−7.33533	−	6.13615i	−0.261145	−	0.218453i
$790$	−0.417919	−	0.173108i	−0.0148689	−	0.00615889i
$791$	22.1499	+	9.17479i	0.787560	+	0.326218i
$792$	32.6259	+	0.612980i	1.15931	+	0.0217813i
$793$	−0.257692	+	0.385663i	−0.00915090	+	0.0136953i
$794$	−50.1481	−	9.97507i	−1.77969	−	0.354002i
$795$	1.55191	+	0.167583i	0.0550407	+	0.00594354i
$796$	−1.93626	−	2.89781i	−0.0686288	−	0.102710i
$797$	17.3442	+	41.8726i	0.614363	+	1.48320i	0.858163	+	0.513377i	$0.171606\pi$
$797$	17.3442	+	41.8726i	0.614363	+	1.48320i	−0.243800	+	0.969825i	$0.578394\pi$
$798$	21.0640	−	16.9582i	0.745658	−	0.600314i
$799$		0			0
$800$			7.61508i			0.269234i
$801$	−2.17142	−	12.1002i	−0.0767235	−	0.427539i
$802$	29.7572	−	19.8832i	1.05076	−	0.702099i
$803$	11.5048	+	11.5048i	0.405995	+	0.405995i
$804$	−2.43212	+	1.27077i	−0.0857741	+	0.0448165i
$805$	−1.29969	−	0.868428i	−0.0458082	−	0.0306081i
$806$	0.267988	+	1.34727i	0.00943949	+	0.0474555i
$807$	−4.45280	−	15.1911i	−0.156746	−	0.534753i
$808$	5.79181	−	13.9827i	0.203755	−	0.491908i
$809$	24.6676	−	4.90669i	0.867266	−	0.172510i	0.258646	−	0.965972i	$-0.416724\pi$
$809$	24.6676	−	4.90669i	0.867266	−	0.172510i	0.608620	+	0.793462i	$0.291724\pi$
$810$	−1.41771	+	0.872091i	−0.0498134	+	0.0306422i
$811$	−4.54032	+	22.8258i	−0.159432	+	0.801521i	0.815455	+	0.578821i	$0.196487\pi$
$811$	−4.54032	+	22.8258i	−0.159432	+	0.801521i	−0.974887	+	0.222700i	$0.928513\pi$
$812$	1.34084	−	1.34084i	0.0470544	−	0.0470544i
$813$	−4.37664	−	1.37266i	−0.153496	−	0.0481413i
$814$	−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
$819$	0.226271	+	0.576676i	0.00790656	+	0.0201507i
$820$	−0.119131	+	0.119131i	−0.00416024	+	0.00416024i
$821$	−8.43190	+	42.3900i	−0.294275	+	1.47942i	0.496887	+	0.867815i	$0.334476\pi$
$821$	−8.43190	+	42.3900i	−0.294275	+	1.47942i	−0.791162	+	0.611607i	$0.790524\pi$
$822$	−7.26774	+	0.646944i	−0.253492	+	0.0225648i
$823$	−16.5420	+	3.29041i	−0.576617	+	0.114696i	−0.474780	−	0.880105i	$-0.657472\pi$
$823$	−16.5420	+	3.29041i	−0.576617	+	0.114696i	−0.101838	+	0.994801i	$0.532472\pi$
$824$	−18.2602	+	44.0841i	−0.636125	+	1.53574i
$825$	−30.1459	+	8.83631i	−1.04955	+	0.307641i
$826$	4.33865	+	21.8119i	0.150961	+	0.758931i
$827$	−18.4337	−	12.3170i	−0.641002	−	0.428304i	0.192136	−	0.981368i	$-0.438458\pi$
$827$	−18.4337	−	12.3170i	−0.641002	−	0.428304i	−0.833139	+	0.553064i	$0.813458\pi$
$828$	−2.05166	+	4.70135i	−0.0713001	+	0.163383i
$829$	−19.3451	−	19.3451i	−0.671883	−	0.671883i	0.286267	−	0.958150i	$-0.407585\pi$
$829$	−19.3451	−	19.3451i	−0.671883	−	0.671883i	−0.958150	+	0.286267i	$0.907585\pi$
$830$	−0.851875	+	0.569205i	−0.0295690	+	0.0197574i
$831$	−17.1888	+	31.4440i	−0.596274	+	1.09078i
$832$		−	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
$837$	44.1242	+	14.7548i	1.52516	+	0.510000i
$838$	12.0414	+	2.39518i	0.415962	+	0.0827400i
$839$	13.7956	−	20.6465i	0.476276	−	0.712798i	−0.513075	−	0.858344i	$-0.671494\pi$
$839$	13.7956	−	20.6465i	0.476276	−	0.712798i	0.989352	+	0.145546i	$0.0464938\pi$
$840$	0.826251	−	0.987723i	0.0285084	−	0.0340797i
$841$	−12.4774	−	5.16832i	−0.430256	−	0.178218i
$842$	−16.1539	−	6.69119i	−0.556702	−	0.230593i
$843$	−11.4341	+	13.6686i	−0.393810	+	0.470771i
$844$	0.774551	−	1.15920i	0.0266611	−	0.0399012i
$845$	−1.79209	−	0.356469i	−0.0616498	−	0.0122629i
$846$	9.91131	−	6.35651i	0.340758	−	0.218541i
$847$	−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
$852$	−2.93989	+	5.37801i	−0.100719	+	0.184248i
$853$	−24.8055	+	16.5745i	−0.849323	+	0.567499i	−0.902306	−	0.431096i	$-0.858127\pi$
$853$	−24.8055	+	16.5745i	−0.849323	+	0.567499i	0.0529834	+	0.998595i	$0.483127\pi$
$854$	6.53464	+	6.53464i	0.223611	+	0.223611i
$855$	−2.59738	−	1.13349i	−0.0888286	−	0.0387646i
$856$	3.38372	+	2.26093i	0.115653	+	0.0772770i
$857$	−6.63871	−	33.3750i	−0.226774	−	1.14007i	−0.911510	−	0.411279i	$-0.865082\pi$
$857$	−6.63871	−	33.3750i	−0.226774	−	1.14007i	0.684736	−	0.728791i	$-0.259918\pi$
$858$	0.928644	−	0.272203i	0.0317034	−	0.00929284i
$859$	−7.54327	+	18.2111i	−0.257373	+	0.621354i	−0.998763	−	0.0497206i	$-0.984167\pi$
$859$	−7.54327	+	18.2111i	−0.257373	+	0.621354i	0.741390	+	0.671074i	$0.234167\pi$
$860$	−0.0792371	+	0.0157612i	−0.00270196	+	0.000537454i
$861$	−13.4224	+	1.19481i	−0.457434	+	0.0407189i
$862$	3.74660	−	18.8354i	0.127610	−	0.641538i
$863$	−4.36492	+	4.36492i	−0.148584	+	0.148584i	−0.777485	−	0.628901i	$-0.783505\pi$
$863$	−4.36492	+	4.36492i	−0.148584	+	0.148584i	0.628901	+	0.777485i	$0.283505\pi$
$864$	−6.89880	−	3.94132i	−0.234702	−	0.134086i
$865$	−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
$870$	1.20312	+	0.377339i	0.0407897	+	0.0127930i
$871$	−0.480203	+	0.480203i	−0.0162710	+	0.0162710i
$872$	6.68823	−	33.6240i	0.226492	−	1.13865i
$873$	−9.91192	+	9.54633i	−0.335468	+	0.323094i
$874$	54.3507	−	10.8110i	1.83844	−	0.365689i
$875$	−0.950712	+	2.29522i	−0.0321399	+	0.0775927i
$876$	−0.592666	−	2.02194i	−0.0200243	−	0.0683149i
$877$	−1.85986	−	9.35016i	−0.0628031	−	0.315732i	0.936595	−	0.350413i	$-0.113959\pi$
$877$	−1.85986	−	9.35016i	−0.0628031	−	0.315732i	−0.999398	+	0.0346804i	$0.988959\pi$
$878$	−28.8088	−	19.2494i	−0.972248	−	0.649636i
$879$	−1.73180	+	0.904859i	−0.0584123	+	0.0305201i
$880$	−1.22513	−	1.22513i	−0.0412992	−	0.0412992i
$881$	−35.7652	+	23.8975i	−1.20496	+	0.805128i	−0.985364	−	0.170464i	$-0.945473\pi$
$881$	−35.7652	+	23.8975i	−1.20496	+	0.805128i	−0.219595	+	0.975591i	$0.570473\pi$
$882$	−15.0205	+	2.69548i	−0.505767	+	0.0907617i
$883$		−	41.3162i		−	1.39040i	−0.718816	−	0.695200i	$-0.755316\pi$
$883$		−	41.3162i		−	1.39040i	0.718816	−	0.695200i	$-0.244684\pi$
$884$		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	$-0.107336\pi$
$887$	8.24630	+	12.3415i	0.276884	+	0.414386i	−0.666799	+	0.745238i	$0.732336\pi$
$888$	1.91538	+	0.206831i	0.0642760	+	0.00694081i
$889$	−17.1594	−	3.41322i	−0.575508	−	0.114476i
$890$	−0.421042	+	0.630135i	−0.0141134	+	0.0211222i
$891$	7.59737	−	31.8838i	0.254522	−	1.06815i
$892$	0.0475120	+	0.0196801i	0.00159082	+	0.000658939i
$893$	18.5214	+	7.67180i	0.619794	+	0.256727i
$894$	−38.8056	−	32.4617i	−1.29785	−	1.08568i
$895$	−1.44511	+	2.16276i	−0.0483046	+	0.0722930i
$896$	−14.7014	−	2.92429i	−0.491139	−	0.0976937i
$897$	−0.136289	+	1.26212i	−0.00455057	+	0.0421410i
$898$	−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
$903$	−5.67001	−	3.09950i	−0.188686	−	0.103145i
$904$	−33.6535	+	22.4865i	−1.11930	+	0.747890i
$905$	−0.211787	−	0.211787i	−0.00704002	−	0.00704002i
$906$	−4.34899	−	8.32350i	−0.144485	−	0.276530i
$907$	−14.2246	−	9.50457i	−0.472320	−	0.315594i	0.296530	−	0.955024i	$-0.404171\pi$
$907$	−14.2246	−	9.50457i	−0.472320	−	0.315594i	−0.768850	+	0.639429i	$0.779171\pi$
$908$	0.113159	+	0.568889i	0.00375531	+	0.0188792i
$909$	−12.4790	−	8.68165i	−0.413902	−	0.287952i
$910$	0.0146143	−	0.0352820i	0.000484459	−	0.00116959i
$911$	54.2580	−	10.7926i	1.79765	−	0.357574i	0.820751	−	0.571286i	$-0.193555\pi$
$911$	54.2580	−	10.7926i	1.79765	−	0.357574i	0.976897	+	0.213712i	$0.0685554\pi$
$912$	3.48631	+	39.1651i	0.115443	+	1.29689i
$913$	3.93596	−	19.7874i	0.130261	−	0.654868i
$914$	−19.9143	+	19.9143i	−0.658705	+	0.658705i
$915$	0.289825	−	0.924088i	0.00958132	−	0.0305494i
$916$	−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
$921$	−10.1497	+	32.3617i	−0.334445	+	1.06635i
$922$	22.9019	−	22.9019i	0.754233	−	0.754233i
$923$	−0.295920	+	1.48769i	−0.00974032	+	0.0489679i
$924$	0.269424	+	3.02670i	0.00886341	+	0.0995711i
$925$	−1.81900	+	0.361822i	−0.0598085	+	0.0118966i
$926$	9.70769	−	23.4364i	0.319014	−	0.770169i
$927$	39.3434	+	27.3712i	1.29221	+	0.898989i
$928$	1.17423	+	5.90324i	0.0385459	+	0.193783i
$929$	29.7790	+	19.8977i	0.977016	+	0.652822i	0.938079	−	0.346420i	$-0.112603\pi$
$929$	29.7790	+	19.8977i	0.977016	+	0.652822i	0.0389370	+	0.999242i	$0.487603\pi$
$930$	−1.32823	−	2.54209i	−0.0435544	−	0.0833585i
$931$	−18.3724	−	18.3724i	−0.602132	−	0.602132i
$932$	−2.21694	+	1.48131i	−0.0726184	+	0.0485220i
$933$	44.6440	+	24.4046i	1.46158	+	0.798971i
$934$			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	0.998427	−	0.0560704i	$-0.0178571\pi$
$937$	7.73785	+	18.6808i	0.252785	+	0.610276i	−0.745642	+	0.666347i	$0.767857\pi$
$938$	7.51715	+	11.2502i	0.245444	+	0.367333i
$939$	−3.31375	+	30.6873i	−0.108140	+	1.00144i
$940$	0.112199	+	0.0223178i	0.00365953	+	0.000727926i
$941$	−4.31354	+	6.45567i	−0.140618	+	0.210449i	−0.895093	−	0.445879i	$-0.852891\pi$
$941$	−4.31354	+	6.45567i	−0.140618	+	0.210449i	0.754476	+	0.656328i	$0.227891\pi$
$942$	24.3767	+	20.3916i	0.794236	+	0.664394i
$943$	−25.5124	−	10.5676i	−0.830798	−	0.344128i
$944$	−29.8749	−	12.3746i	−0.972347	−	0.402759i
$945$	−0.792064	−	1.02258i	−0.0257658	−	0.0332645i
$946$	−5.60815	+	8.39318i	−0.182337	+	0.272886i
$947$	−3.53370	−	0.702897i	−0.114830	−	0.0228411i	0.137341	−	0.990524i	$-0.456144\pi$
$947$	−3.53370	−	0.702897i	−0.114830	−	0.0228411i	−0.252171	+	0.967683i	$0.581144\pi$
$948$	−1.14688	−	0.123845i	−0.0372489	−	0.00402231i
$949$	−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	$0.881046\pi$
$954$	−24.8600	+	4.46121i	−0.804871	+	0.144437i
$955$	2.02845	−	1.35536i	0.0656389	−	0.0438585i
$956$	4.31991	+	4.31991i	0.139716	+	0.139716i
$957$	−22.0067	+	11.4984i	−0.711375	+	0.371690i
$958$	−24.8079	−	16.5761i	−0.801507	−	0.535550i
$959$	−1.10618	−	5.56114i	−0.0357204	−	0.179578i
$960$	0.601342	+	2.05153i	0.0194082	+	0.0662129i
$961$	−18.8174	+	45.4292i	−0.607013	+	1.46546i
$962$	0.0560344	−	0.0111459i	0.00180662	−	0.000359360i
$963$	2.94417	−	2.83558i	0.0948744	−	0.0913751i
$964$	0.0215404	−	0.108291i	0.000693768	−	0.00348781i
$965$	−1.61537	+	1.61537i	−0.0520007	+	0.0520007i
$966$	24.1335	+	7.56906i	0.776481	+	0.243531i
$967$	20.7527	−	8.59605i	0.667362	−	0.276430i	−0.0231709	−	0.999732i	$-0.507376\pi$
$967$	20.7527	−	8.59605i	0.667362	−	0.276430i	0.690533	+	0.723301i	$0.257376\pi$
$968$	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	$-0.439640\pi$
$971$	31.6660	−	13.1165i	1.01621	−	0.420928i	0.827716	+	0.561147i	$0.189640\pi$
$972$	−2.84380	+	3.15107i	−0.0912150	+	0.101071i
$973$	6.37317	−	6.37317i	0.204314	−	0.204314i
$974$	5.89415	−	29.6319i	0.188861	−	0.949468i
$975$	1.00283	−	0.0892676i	0.0321162	−	0.00285885i
$976$	−13.1790	+	2.62147i	−0.421851	+	0.0839113i
$977$	−10.7764	+	26.0166i	−0.344769	+	0.832345i	0.652451	+	0.757831i	$0.273741\pi$
$977$	−10.7764	+	26.0166i	−0.344769	+	0.832345i	−0.997220	+	0.0745143i	$0.976259\pi$
$978$	24.3690	−	7.14301i	0.779235	−	0.228408i
$979$	−2.91144	−	14.6368i	−0.0930502	−	0.467795i
$980$	−0.123278	−	0.0823718i	−0.00393798	−	0.00263127i
$981$	−31.5604	−	13.7729i	−1.00765	−	0.439735i
$982$	18.9356	+	18.9356i	0.604261	+	0.604261i
$983$	34.6933	−	23.1813i	1.10654	−	0.739370i	0.138554	−	0.990355i	$-0.455755\pi$
$983$	34.6933	−	23.1813i	1.10654	−	0.739370i	0.967991	+	0.250985i	$0.0807546\pi$
$984$	10.9120	−	19.9616i	0.347862	−	0.636353i
$985$		−	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
$990$	−1.70083	+	1.09081i	−0.0540560	+	0.0346682i
$991$	9.95379	+	1.97993i	0.316193	+	0.0628946i	0.350635	−	0.936512i	$-0.385966\pi$
$991$	9.95379	+	1.97993i	0.316193	+	0.0628946i	−0.0344428	+	0.999407i	$0.510966\pi$
$992$	7.60639	−	11.3838i	0.241503	−	0.361435i
$993$	−8.03828	+	9.60918i	−0.255087	+	0.304938i
$994$	27.9208	+	11.5652i	0.885595	+	0.366826i
$995$	1.66382	+	0.689176i	0.0527466	+	0.0218483i
$996$	−1.67637	+	2.00398i	−0.0531179	+	0.0634986i
$997$	22.1815	−	33.1970i	0.702496	−	1.05136i	−0.292958	−	0.956125i	$-0.594640\pi$
$997$	22.1815	−	33.1970i	0.702496	−	1.05136i	0.995455	−	0.0952350i	$-0.0303602\pi$
$998$	−1.39122	−	0.276730i	−0.0440382	−	0.00875974i
$999$	0.613668	−	1.83518i	0.0194156	−	0.0580624i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	51.29	even	16
51.2.i.a.11.3	yes	32	17.12	odd	16
51.2.i.a.14.2	yes	32	17.15	even	8
51.2.i.a.14.3	yes	32	51.32	odd	8
816.2.cj.c.65.1		32	68.15	odd	8
816.2.cj.c.65.4		32	204.83	even	8
816.2.cj.c.113.1		32	204.131	odd	16
816.2.cj.c.113.4		32	68.63	even	16
867.2.i.b.158.2		32	51.47	odd	4
867.2.i.b.158.3		32	17.13	even	4
867.2.i.b.653.2		32	17.6	odd	16
867.2.i.b.653.3		32	51.23	even	16
867.2.i.c.224.2		32	51.8	odd	8
867.2.i.c.224.3		32	17.8	even	8
867.2.i.c.329.2		32	17.14	odd	16
867.2.i.c.329.3		32	51.14	even	16
867.2.i.d.224.2		32	51.26	odd	8
867.2.i.d.224.3		32	17.9	even	8
867.2.i.d.329.2		32	17.3	odd	16
867.2.i.d.329.3		32	51.20	even	16
867.2.i.f.131.2		32	17.16	even	2
867.2.i.f.131.3		32	51.50	odd	2
867.2.i.f.503.2		32	51.41	even	16
867.2.i.f.503.3		32	17.7	odd	16
867.2.i.g.131.2		32	1.1	even	1	trivial
867.2.i.g.131.3		32	3.2	odd	2	inner
867.2.i.g.503.2		32	51.44	even	16	inner
867.2.i.g.503.3		32	17.10	odd	16	inner
867.2.i.h.65.2		32	17.2	even	8
867.2.i.h.65.3		32	51.2	odd	8
867.2.i.h.827.2		32	51.5	even	16
867.2.i.h.827.3		32	17.5	odd	16
867.2.i.i.158.2		32	51.38	odd	4
867.2.i.i.158.3		32	17.4	even	4
867.2.i.i.653.2		32	17.11	odd	16
867.2.i.i.653.3		32	51.11	even	16

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} +(0.518334 - 1.65267i) q^{3} +(-0.192538 + 0.192538i) q^{4} +(0.0274494 - 0.137998i) q^{5} +(0.201860 + 2.26768i) q^{6} +(-1.73519 + 0.345150i) q^{7} +(1.14298 - 2.75940i) q^{8} +(-2.46266 - 1.71327i) q^{9} +(0.0360802 + 0.181387i) q^{10} +(-3.02807 - 2.02329i) q^{11} +(0.218403 + 0.418001i) q^{12} +(0.0825311 + 0.0825311i) q^{13} +(1.93354 - 1.29195i) q^{14} +(-0.213837 - 0.116894i) q^{15} +3.38128i q^{16} +(3.85237 + 0.841809i) q^{18} +(2.56928 + 6.20278i) q^{19} +(0.0212847 + 0.0318548i) q^{20} +(-0.328986 + 3.04660i) q^{21} +(4.69492 + 0.933878i) q^{22} +(-3.48870 + 5.22121i) q^{23} +(-3.96794 - 3.31926i) q^{24} +(4.60111 + 1.90584i) q^{25} +(-0.141737 - 0.0587094i) q^{26} +(-4.10796 + 3.18193i) q^{27} +(0.267635 - 0.400544i) q^{28} +(3.86068 + 0.767936i) q^{29} +(0.318476 + 0.0343905i) q^{30} +(-4.97452 - 7.44489i) q^{31} +(0.585150 + 1.41268i) q^{32} +(-4.91339 + 3.95567i) q^{33} +0.248926i q^{35} +(0.804026 - 0.144285i) q^{36} +(-0.309641 + 0.206896i) q^{37} +(-6.24010 - 6.24010i) q^{38} +(0.179176 - 0.0936183i) q^{39} +(-0.349416 - 0.233473i) q^{40} +(0.857920 + 4.31306i) q^{41} +(-1.13296 - 3.86518i) q^{42} +(-0.806985 + 1.94823i) q^{43} +(0.972578 - 0.193458i) q^{44} +(-0.304026 + 0.292813i) q^{45} +(1.61026 - 8.09532i) q^{46} +(2.11141 - 2.11141i) q^{47} +(5.58815 + 1.75263i) q^{48} +(-3.57541 + 1.48098i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(-5.91755 + 2.45113i) q^{53} +(3.38805 - 5.93037i) q^{54} +(-0.362328 + 0.362328i) q^{55} +(-1.03088 + 5.18257i) q^{56} +(11.5829 - 1.03106i) q^{57} +(-5.07456 + 1.00939i) q^{58} +(-3.65974 + 8.83540i) q^{59} +(0.0636782 - 0.0186653i) q^{60} +(0.775290 + 3.89765i) q^{61} +(9.78574 + 6.53863i) q^{62} +(4.86451 + 2.12286i) q^{63} +(-6.20303 - 6.20303i) q^{64} +(0.0136545 - 0.00912367i) q^{65} +(3.97693 - 7.27511i) q^{66} +5.81844i q^{67} +(6.82064 + 8.47201i) q^{69} +(-0.125212 - 0.302288i) q^{70} +(7.22012 + 10.8057i) q^{71} +(-7.54238 + 4.83722i) q^{72} +(-4.38175 - 0.871585i) q^{73} +(0.271949 - 0.407000i) q^{74} +(5.53464 - 6.61627i) q^{75} +(-1.68895 - 0.699588i) q^{76} +(5.95260 + 2.46565i) q^{77} +(-0.170495 + 0.203814i) q^{78} +(-1.35888 + 2.03371i) q^{79} +(0.466609 + 0.0928142i) q^{80} +(3.12939 + 8.43842i) q^{81} +(-3.21133 - 4.80610i) q^{82} +(2.12000 + 5.11813i) q^{83} +(-0.523244 - 0.649928i) q^{84} -2.77180i q^{86} +(3.27027 - 5.98239i) q^{87} +(-9.04408 + 6.04306i) q^{88} +(2.89760 + 2.89760i) q^{89} +(0.221913 - 0.508511i) q^{90} +(-0.171693 - 0.114721i) q^{91} +(-0.333574 - 1.67699i) q^{92} +(-14.8824 + 4.36231i) q^{93} +(-1.50197 + 3.62608i) q^{94} +(0.926494 - 0.184291i) q^{95} +(2.63800 - 0.234823i) q^{96} +(0.894911 - 4.49902i) q^{97} +(3.59692 - 3.59692i) q^{98} +(3.99065 + 10.1706i) 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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