LMFDB - Embedded newform 867.2.i.i.653.3

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			653.3
Character	$\chi$	$=$	867.653
Dual form			867.2.i.i.158.3

$q$-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} +(-1.65267 + 0.518334i) q^{3} +(-0.192538 - 0.192538i) q^{4} +(-0.137998 + 0.0274494i) q^{5} +(-2.26768 - 0.201860i) q^{6} +(-0.345150 + 1.73519i) q^{7} +(-1.14298 - 2.75940i) q^{8} +(2.46266 - 1.71327i) q^{9} +(-0.181387 - 0.0360802i) q^{10} +(2.02329 + 3.02807i) q^{11} +(0.418001 + 0.218403i) q^{12} +(0.0825311 - 0.0825311i) q^{13} +(-1.29195 + 1.93354i) q^{14} +(0.213837 - 0.116894i) q^{15} -3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(-2.56928 + 6.20278i) q^{19} +(0.0318548 + 0.0212847i) q^{20} +(-0.328986 - 3.04660i) q^{21} +(0.933878 + 4.69492i) q^{22} +(-5.22121 + 3.48870i) q^{23} +(3.31926 + 3.96794i) q^{24} +(-4.60111 + 1.90584i) q^{25} +(0.141737 - 0.0587094i) q^{26} +(-3.18193 + 4.10796i) q^{27} +(0.400544 - 0.267635i) q^{28} +(0.767936 + 3.86068i) q^{29} +(0.318476 - 0.0343905i) q^{30} +(-7.44489 - 4.97452i) q^{31} +(-0.585150 + 1.41268i) q^{32} +(-4.91339 - 3.95567i) q^{33} -0.248926i q^{35} +(-0.804026 - 0.144285i) q^{36} +(0.206896 - 0.309641i) q^{37} +(-6.24010 + 6.24010i) q^{38} +(-0.0936183 + 0.179176i) q^{39} +(0.233473 + 0.349416i) q^{40} +(-4.31306 - 0.857920i) q^{41} +(1.13296 - 3.86518i) q^{42} +(0.806985 + 1.94823i) q^{43} +(0.193458 - 0.972578i) q^{44} +(-0.292813 + 0.304026i) q^{45} +(-8.09532 + 1.61026i) q^{46} +(2.11141 + 2.11141i) q^{47} +(1.75263 + 5.58815i) q^{48} +(3.57541 + 1.48098i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(5.91755 + 2.45113i) q^{53} +(-5.93037 + 3.38805i) q^{54} +(-0.362328 - 0.362328i) q^{55} +(5.18257 - 1.03088i) q^{56} +(1.03106 - 11.5829i) q^{57} +(-1.00939 + 5.07456i) q^{58} +(3.65974 + 8.83540i) q^{59} +(-0.0636782 - 0.0186653i) q^{60} +(-3.89765 - 0.775290i) q^{61} +(-6.53863 - 9.78574i) q^{62} +(2.12286 + 4.86451i) q^{63} +(-6.20303 + 6.20303i) q^{64} +(-0.00912367 + 0.0136545i) q^{65} +(-3.97693 - 7.27511i) q^{66} -5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(0.125212 - 0.302288i) q^{70} +(10.8057 + 7.22012i) q^{71} +(-7.54238 - 4.83722i) q^{72} +(-0.871585 - 4.38175i) q^{73} +(0.407000 - 0.271949i) q^{74} +(6.61627 - 5.53464i) q^{75} +(1.68895 - 0.699588i) q^{76} +(-5.95260 + 2.46565i) q^{77} +(-0.203814 + 0.170495i) q^{78} +(-2.03371 + 1.35888i) q^{79} +(0.0928142 + 0.466609i) q^{80} +(3.12939 - 8.43842i) q^{81} +(-4.80610 - 3.21133i) q^{82} +(-2.12000 + 5.11813i) q^{83} +(-0.523244 + 0.649928i) q^{84} +2.77180i q^{86} +(-3.27027 - 5.98239i) q^{87} +(6.04306 - 9.04408i) q^{88} +(2.89760 - 2.89760i) q^{89} +(-0.508511 + 0.221913i) q^{90} +(0.114721 + 0.171693i) q^{91} +(1.67699 + 0.333574i) q^{92} +(14.8824 + 4.36231i) q^{93} +(1.50197 + 3.62608i) q^{94} +(0.184291 - 0.926494i) q^{95} +(0.234823 - 2.63800i) q^{96} +(-4.49902 + 0.894911i) q^{97} +(3.59692 + 3.59692i) q^{98} +(10.1706 + 3.99065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 16 q^{4} - 16 q^{6} - 24 q^{9} + 32 q^{10} + 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} + 16 q^{24} - 16 q^{27} + 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 + 16 * q^4 - 16 * q^6 - 24 * q^9 + 32 * q^10 + 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 + 16 * q^24 - 16 * q^27 + 32 * q^28 + 8 * q^30 + 24 * q^36 - 96 * q^37 + 48 * q^39 + 80 * q^40 + 24 * q^42 + 32 * q^43 - 40 * q^45 - 64 * q^46 + 48 * q^48 + 64 * q^49 - 96 * q^52 + 48 * q^54 + 48 * q^55 - 8 * q^57 - 48 * q^60 - 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 - 144 * q^73 + 8 * q^75 - 32 * q^76 - 40 * q^78 + 64 * q^79 - 48 * q^81 - 32 * q^82 + 56 * q^87 + 32 * q^88 + 24 * q^90 + 48 * q^91 + 56 * q^93 + 48 * q^94 - 72 * q^96 - 32 * q^97 - 16 * q^99

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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	$0.471155\pi$
$3$	−1.65267	+	0.518334i	−0.954172	+	0.299260i
$3$	−1.65267	+	0.518334i	−0.954172	+	0.299260i
$4$	−0.192538	−	0.192538i	−0.0962690	−	0.0962690i
$5$	−0.137998	+	0.0274494i	−0.0617144	+	0.0122758i	−0.225851	−	0.974162i	$-0.572516\pi$
$5$	−0.137998	+	0.0274494i	−0.0617144	+	0.0122758i	0.164137	+	0.986438i	$0.447516\pi$
$6$	−2.26768	−	0.201860i	−0.925777	−	0.0824088i
$7$	−0.345150	+	1.73519i	−0.130455	+	0.655839i	0.859115	+	0.511783i	$0.171015\pi$
$7$	−0.345150	+	1.73519i	−0.130455	+	0.655839i	−0.989569	+	0.144056i	$0.953985\pi$
$8$	−1.14298	−	2.75940i	−0.404105	−	0.975595i
$9$	2.46266	−	1.71327i	0.820887	−	0.571091i
$10$	−0.181387	−	0.0360802i	−0.0573597	−	0.0114096i
$11$	2.02329	+	3.02807i	0.610045	+	0.912997i	0.999969	−	0.00785036i	$-0.00249887\pi$
$11$	2.02329	+	3.02807i	0.610045	+	0.912997i	−0.389924	+	0.920847i	$0.627499\pi$
$12$	0.418001	+	0.218403i	0.120667	+	0.0630476i
$13$	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	$0.244848\pi$
$14$	−1.29195	+	1.93354i	−0.345289	+	0.516762i
$15$	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	0.294614	+	0.955616i	$0.404809\pi$
$19$	−2.56928	+	6.20278i	−0.589432	+	1.42302i	−0.884046	+	0.467399i	$0.845191\pi$
$20$	0.0318548	+	0.0212847i	0.00712296	+	0.00475941i
$21$	−0.328986	−	3.04660i	−0.0717906	−	0.664823i
$22$	0.933878	+	4.69492i	0.199104	+	1.00096i
$23$	−5.22121	+	3.48870i	−1.08870	+	0.727444i	−0.964306	−	0.264789i	$-0.914698\pi$
$23$	−5.22121	+	3.48870i	−1.08870	+	0.727444i	−0.124391	+	0.992233i	$0.539698\pi$
$24$	3.31926	+	3.96794i	0.677542	+	0.809952i
$25$	−4.60111	+	1.90584i	−0.920222	+	0.381168i
$26$	0.141737	−	0.0587094i	0.0277969	−	0.0115139i
$27$	−3.18193	+	4.10796i	−0.612362	+	0.790578i
$28$	0.400544	−	0.267635i	0.0756957	−	0.0505782i
$29$	0.767936	+	3.86068i	0.142602	+	0.716909i	0.984236	+	0.176861i	$0.0565942\pi$
$29$	0.767936	+	3.86068i	0.142602	+	0.716909i	−0.841634	+	0.540049i	$0.818406\pi$
$30$	0.318476	−	0.0343905i	0.0581455	−	0.00627881i
$31$	−7.44489	−	4.97452i	−1.33714	−	0.893450i	−0.338275	−	0.941047i	$-0.609844\pi$
$31$	−7.44489	−	4.97452i	−1.33714	−	0.893450i	−0.998867	+	0.0475974i	$0.984844\pi$
$32$	−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
$37$	0.206896	−	0.309641i	0.0340135	−	0.0509047i	−0.814073	−	0.580762i	$-0.802755\pi$
$37$	0.206896	−	0.309641i	0.0340135	−	0.0509047i	0.848087	+	0.529858i	$0.177755\pi$
$38$	−6.24010	+	6.24010i	−1.01228	+	1.01228i
$39$	−0.0936183	+	0.179176i	−0.0149909	+	0.0286911i
$40$	0.233473	+	0.349416i	0.0369153	+	0.0552476i
$41$	−4.31306	−	0.857920i	−0.673586	−	0.133985i	−0.153566	−	0.988138i	$-0.549076\pi$
$41$	−4.31306	−	0.857920i	−0.673586	−	0.133985i	−0.520020	+	0.854154i	$0.674076\pi$
$42$	1.13296	−	3.86518i	0.174819	−	0.596410i
$43$	0.806985	+	1.94823i	0.123064	+	0.297103i	0.973390	−	0.229153i	$-0.0735955\pi$
$43$	0.806985	+	1.94823i	0.123064	+	0.297103i	−0.850326	+	0.526256i	$0.823596\pi$
$44$	0.193458	−	0.972578i	0.0291648	−	0.146622i
$45$	−0.292813	+	0.304026i	−0.0436500	+	0.0453216i
$46$	−8.09532	+	1.61026i	−1.19359	+	0.237420i
$47$	2.11141	+	2.11141i	0.307980	+	0.307980i	0.844126	−	0.536145i	$-0.180120\pi$
$47$	2.11141	+	2.11141i	0.307980	+	0.307980i	−0.536145	+	0.844126i	$0.680120\pi$
$48$	1.75263	+	5.58815i	0.252971	+	0.806580i
$49$	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	$0.480012\pi$
$54$	−5.93037	+	3.38805i	−0.807021	+	0.461055i
$55$	−0.362328	−	0.362328i	−0.0488563	−	0.0488563i
$56$	5.18257	−	1.03088i	0.692551	−	0.137757i
$57$	1.03106	−	11.5829i	0.136568	−	1.53419i
$58$	−1.00939	+	5.07456i	−0.132540	+	0.666323i
$59$	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	$0.661108\pi$
$60$	−0.0636782	−	0.0186653i	−0.00822083	−	0.00240967i
$61$	−3.89765	−	0.775290i	−0.499043	−	0.0992658i	−0.0608502	−	0.998147i	$-0.519381\pi$
$61$	−3.89765	−	0.775290i	−0.499043	−	0.0992658i	−0.438193	+	0.898881i	$0.644381\pi$
$62$	−6.53863	−	9.78574i	−0.830406	−	1.24279i
$63$	2.12286	+	4.86451i	0.267456	+	0.612871i
$64$	−6.20303	+	6.20303i	−0.775378	+	0.775378i
$65$	−0.00912367	+	0.0136545i	−0.00113165	+	0.00169364i
$66$	−3.97693	−	7.27511i	−0.489527	−	0.895505i
$67$		−	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
$71$	10.8057	+	7.22012i	1.28240	+	0.856870i	0.994896	−	0.100910i	$-0.0321754\pi$
$71$	10.8057	+	7.22012i	1.28240	+	0.856870i	0.287502	+	0.957780i	$0.407175\pi$
$72$	−7.54238	−	4.83722i	−0.888878	−	0.570072i
$73$	−0.871585	−	4.38175i	−0.102011	−	0.512845i	−0.997677	−	0.0681180i	$-0.978301\pi$
$73$	−0.871585	−	4.38175i	−0.102011	−	0.512845i	0.895666	−	0.444727i	$-0.146699\pi$
$74$	0.407000	−	0.271949i	0.0473128	−	0.0316134i
$75$	6.61627	−	5.53464i	0.763981	−	0.639086i
$76$	1.68895	−	0.699588i	0.193736	−	0.0802482i
$77$	−5.95260	+	2.46565i	−0.678362	+	0.280987i
$78$	−0.203814	+	0.170495i	−0.0230774	+	0.0193047i
$79$	−2.03371	+	1.35888i	−0.228811	+	0.152886i	−0.664691	−	0.747118i	$-0.731437\pi$
$79$	−2.03371	+	1.35888i	−0.228811	+	0.152886i	0.435881	+	0.900004i	$0.356437\pi$
$80$	0.0928142	+	0.466609i	0.0103769	+	0.0521684i
$81$	3.12939	−	8.43842i	0.347710	−	0.937602i
$82$	−4.80610	−	3.21133i	−0.530745	−	0.354633i
$83$	−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
$87$	−3.27027	−	5.98239i	−0.350609	−	0.641379i
$88$	6.04306	−	9.04408i	0.644193	−	0.964103i
$89$	2.89760	−	2.89760i	0.307145	−	0.307145i	−0.536656	−	0.843801i	$-0.680313\pi$
$89$	2.89760	−	2.89760i	0.307145	−	0.307145i	0.843801	+	0.536656i	$0.180313\pi$
$90$	−0.508511	+	0.221913i	−0.0536017	+	0.0233917i
$91$	0.114721	+	0.171693i	0.0120261	+	0.0179983i
$92$	1.67699	+	0.333574i	0.174838	+	0.0347775i
$93$	14.8824	+	4.36231i	1.54324	+	0.452351i
$94$	1.50197	+	3.62608i	0.154917	+	0.374002i
$95$	0.184291	−	0.926494i	0.0189079	−	0.0950563i
$96$	0.234823	−	2.63800i	0.0239666	−	0.269239i
$97$	−4.49902	+	0.894911i	−0.456807	+	0.0908645i	−0.418130	−	0.908387i	$-0.637314\pi$
$97$	−4.49902	+	0.894911i	−0.456807	+	0.0908645i	−0.0386768	+	0.999252i	$0.512314\pi$
$98$	3.59692	+	3.59692i	0.363344	+	0.363344i
$99$	10.1706	+	3.99065i	1.02218	+	0.401075i
$100$	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
$105$	0.129027	+	0.411393i	0.0125917	+	0.0401479i
$106$	5.95315	+	5.95315i	0.578221	+	0.578221i
$107$	1.33636	−	0.265818i	0.129191	−	0.0256976i	−0.130071	−	0.991505i	$-0.541521\pi$
$107$	1.33636	−	0.265818i	0.129191	−	0.0256976i	0.259262	+	0.965807i	$0.416521\pi$
$108$	1.40358	−	0.178297i	0.135060	−	0.0171567i
$109$	2.23930	−	11.2577i	0.214486	−	1.07829i	−0.712062	−	0.702116i	$-0.752239\pi$
$109$	2.23930	−	11.2577i	0.214486	−	1.07829i	0.926548	−	0.376176i	$-0.122761\pi$
$110$	−0.257746	−	0.622254i	−0.0245751	−	0.0593296i
$111$	−0.181434	+	0.618977i	−0.0172209	+	0.0587507i
$112$	5.86715	+	1.16705i	0.554394	+	0.110276i
$113$	7.52875	+	11.2676i	0.708245	+	1.05996i	0.994795	+	0.101899i	$0.0324918\pi$
$113$	7.52875	+	11.2676i	0.708245	+	1.05996i	−0.286549	+	0.958066i	$0.592508\pi$
$114$	7.07839	−	13.5473i	0.662952	−	1.26882i
$115$	0.624752	−	0.624752i	0.0582584	−	0.0582584i
$116$	0.595470	−	0.891183i	0.0552880	−	0.0827443i
$117$	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
$122$	−4.34321	−	2.90204i	−0.393215	−	0.262738i
$123$	7.57276	−	0.817741i	0.682813	−	0.0737332i
$124$	0.475641	+	2.39121i	0.0427138	+	0.214737i
$125$	1.16757	−	0.780146i	0.104431	−	0.0697784i
$126$	0.131050	+	6.97513i	0.0116748	+	0.621394i
$127$	−9.13631	+	3.78439i	−0.810717	+	0.335810i	−0.749240	−	0.662299i	$-0.769581\pi$
$127$	−9.13631	+	3.78439i	−0.810717	+	0.335810i	−0.0614768	+	0.998109i	$0.519581\pi$
$128$	−7.82759	+	3.24229i	−0.691867	+	0.286581i
$129$	−2.34352	−	2.80151i	−0.206335	−	0.246659i
$130$	−0.0179478	+	0.0119924i	−0.00157413	+	0.00105180i
$131$	−2.54189	−	12.7789i	−0.222086	−	1.11650i	−0.917453	−	0.397845i	$-0.869758\pi$
$131$	−2.54189	−	12.7789i	−0.222086	−	1.11650i	0.695367	−	0.718655i	$-0.255242\pi$
$132$	0.184398	+	1.70763i	0.0160497	+	0.148630i
$133$	−9.87620	−	6.59907i	−0.856375	−	0.572212i
$134$	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	$-0.956284\pi$
$137$		−	3.20492i		−	0.273815i	0.990584	−	0.136907i	$-0.0437163\pi$
$138$	12.5443	−	6.85731i	1.06784	−	0.583733i
$139$	2.83033	−	4.23589i	0.240065	−	0.359283i	−0.691799	−	0.722090i	$-0.743182\pi$
$139$	2.83033	−	4.23589i	0.240065	−	0.359283i	0.931864	+	0.362807i	$0.118182\pi$
$140$	−0.0479277	+	0.0479277i	−0.00405063	+	0.00405063i
$141$	−4.58388	−	2.39505i	−0.386032	−	0.201700i
$142$	9.49030	+	14.2032i	0.796408	+	1.19191i
$143$	0.416894	+	0.0829254i	0.0348624	+	0.00693457i
$144$	−5.79306	−	8.32694i	−0.482755	−	0.693912i
$145$	−0.211947	−	0.511685i	−0.0176012	−	0.0424931i
$146$	1.14563	−	5.75948i	0.0948132	−	0.476658i
$147$	−6.67663	−	0.594326i	−0.550679	−	0.0490192i
$148$	−0.0994530	+	0.0197824i	−0.00817499	+	0.00162611i
$149$	−15.7137	−	15.7137i	−1.28731	−	1.28731i	−0.936412	−	0.350902i	$-0.885875\pi$
$149$	−15.7137	−	15.7137i	−1.28731	−	1.28731i	−0.350902	−	0.936412i	$-0.614125\pi$
$150$	10.8186	−	3.39306i	0.883332	−	0.277043i
$151$	3.81101	+	1.57857i	0.310135	+	0.128462i	0.532322	−	0.846542i	$-0.321319\pi$
$151$	3.81101	+	1.57857i	0.310135	+	0.128462i	−0.222187	+	0.975004i	$0.571319\pi$
$152$	20.0526			1.62648
$153$		0			0
$154$	−8.46890			−0.682443
$155$	1.16393	+	0.482114i	0.0934887	+	0.0387243i
$156$	0.0525232	−	0.0164730i	0.00420522	−	0.00131890i
$157$	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	$0.561933\pi$
$158$	−3.15321	+	0.627212i	−0.250856	+	0.0498983i
$159$	−11.0503	−	0.983649i	−0.876344	−	0.0780085i
$160$	0.0419721	−	0.211008i	0.00331819	−	0.0166817i
$161$	−4.25145	−	10.2639i	−0.335061	−	0.808909i
$162$	8.04483	−	8.67325i	0.632061	−	0.681435i
$163$	10.9399	+	2.17609i	0.856881	+	0.170444i	0.603933	−	0.797035i	$-0.293600\pi$
$163$	10.9399	+	2.17609i	0.856881	+	0.170444i	0.252949	+	0.967480i	$0.418600\pi$
$164$	0.665245	+	0.995609i	0.0519469	+	0.0777440i
$165$	0.786617	+	0.411003i	0.0612380	+	0.0319965i
$166$	−5.14893	+	5.14893i	−0.399634	+	0.399634i
$167$	1.16668	−	1.74605i	0.0902801	−	0.135114i	−0.783581	−	0.621290i	$-0.786609\pi$
$167$	1.16668	−	1.74605i	0.0902801	−	0.135114i	0.873861	+	0.486177i	$0.161609\pi$
$168$	−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
$173$	−10.2391	−	6.84154i	−0.778463	−	0.520153i	0.101705	−	0.994815i	$-0.467570\pi$
$173$	−10.2391	−	6.84154i	−0.778463	−	0.520153i	−0.880168	+	0.474662i	$0.842570\pi$
$174$	−0.962121	−	8.90980i	−0.0729382	−	0.675450i
$175$	−1.71892	−	8.64158i	−0.129938	−	0.653242i
$176$	10.2387	−	6.84131i	0.771774	−	0.515683i
$177$	−10.6280	−	12.7051i	−0.798853	−	0.954971i
$178$	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	$0.132220\pi$
$180$	0.114914	−	0.00215902i	0.00856520	−	0.000160924i
$181$	1.76995	−	1.18265i	0.131560	−	0.0879054i	−0.488049	−	0.872816i	$-0.662291\pi$
$181$	1.76995	−	1.18265i	0.131560	−	0.0879054i	0.619609	+	0.784911i	$0.287291\pi$
$182$	0.0529513	+	0.266204i	0.00392501	+	0.0197324i
$183$	6.84340	−	0.738981i	0.505879	−	0.0546271i
$184$	15.5945	+	10.4199i	1.14964	+	0.768164i
$185$	−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
$190$	0.689832	−	1.03241i	0.0500457	−	0.0748986i
$191$	12.2604	−	12.2604i	0.887130	−	0.887130i	−0.107116	−	0.994247i	$-0.534162\pi$
$191$	12.2604	−	12.2604i	0.887130	−	0.887130i	0.994247	+	0.107116i	$0.0341617\pi$
$192$	7.03634	−	13.4668i	0.507804	−	0.971884i
$193$	9.02046	+	13.5001i	0.649307	+	0.971757i	0.999386	+	0.0350364i	$0.0111547\pi$
$193$	9.02046	+	13.5001i	0.649307	+	0.971757i	−0.350079	+	0.936720i	$0.613845\pi$
$194$	−5.91362	−	1.17629i	−0.424573	−	0.0844529i
$195$	0.00800084	−	0.0272956i	0.000572952	−	0.00195468i
$196$	−0.403257	−	0.973548i	−0.0288040	−	0.0695391i
$197$	1.53164	−	7.70009i	0.109125	−	0.548609i	−0.887083	−	0.461609i	$-0.847272\pi$
$197$	1.53164	−	7.70009i	0.109125	−	0.548609i	0.996208	−	0.0869994i	$-0.0277278\pi$
$198$	10.3435	+	9.96201i	0.735081	+	0.707969i
$199$	12.5536	−	2.49706i	0.889898	−	0.177012i	0.271090	−	0.962554i	$-0.412616\pi$
$199$	12.5536	−	2.49706i	0.889898	−	0.177012i	0.618808	+	0.785542i	$0.287616\pi$
$200$	10.5180	+	10.5180i	0.743732	+	0.743732i
$201$	3.01590	+	9.61599i	0.212725	+	0.678259i
$202$	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
$207$	−6.88096	+	17.5368i	−0.478260	+	1.21889i
$208$	−0.279061	−	0.279061i	−0.0193494	−	0.0193494i
$209$	−23.9808	+	4.77008i	−1.65879	+	0.329954i
$210$	−0.0502481	+	0.564485i	−0.00346745	+	0.0389532i
$211$	−0.998885	+	5.02173i	−0.0687661	+	0.345710i	−0.999816	−	0.0191813i	$-0.993894\pi$
$211$	−0.998885	+	5.02173i	−0.0687661	+	0.345710i	0.931050	+	0.364892i	$0.118894\pi$
$212$	−0.667417	−	1.61129i	−0.0458384	−	0.110664i
$213$	−21.6007	−	6.33155i	−1.48005	−	0.433831i
$214$	1.75654	+	0.349398i	0.120075	+	0.0238843i
$215$	−0.164840	−	0.246700i	−0.0112420	−	0.0168248i
$216$	14.9724	+	4.08488i	1.01874	+	0.277941i
$217$	11.2013	−	11.2013i	0.760395	−	0.760395i
$218$	8.38205	−	12.5446i	0.567704	−	0.849630i
$219$	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	$-0.872987\pi$
$223$	0.0722764	−	0.174491i	0.00483999	−	0.0116848i	0.926281	+	0.376833i	$0.122987\pi$
$224$	−2.24929	−	1.50293i	−0.150287	−	0.100419i
$225$	−8.06574	+	12.5764i	−0.537716	+	0.838426i
$226$	3.47500	+	17.4700i	0.231154	+	1.16209i
$227$	1.77120	−	1.18348i	0.117559	−	0.0785504i	−0.495401	−	0.868665i	$-0.664979\pi$
$227$	1.77120	−	1.18348i	0.117559	−	0.0785504i	0.612960	+	0.790114i	$0.289979\pi$
$228$	−2.42867	+	2.03163i	−0.160843	+	0.134548i
$229$	−15.9683	+	6.61427i	−1.05521	+	0.437084i	−0.841750	−	0.539868i	$-0.818474\pi$
$229$	−15.9683	+	6.61427i	−1.05521	+	0.437084i	−0.213463	+	0.976951i	$0.568474\pi$
$230$	1.07293	−	0.444424i	0.0707472	−	0.0293045i
$231$	8.55968	−	7.16035i	0.563185	−	0.471116i
$232$	9.77541	−	6.53172i	0.641787	−	0.428828i
$233$	1.91035	+	9.60397i	0.125151	+	0.629177i	0.991539	+	0.129806i	$0.0414355\pi$
$233$	1.91035	+	9.60397i	0.125151	+	0.629177i	−0.866388	+	0.499371i	$0.833565\pi$
$234$	0.248465	−	0.387416i	0.0162427	−	0.0253262i
$235$	−0.349326	−	0.233412i	−0.0227875	−	0.0152261i
$236$	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	$0.258463\pi$
$239$			22.4367i			1.45131i	−0.688059	+	0.725654i	$0.741537\pi$
$240$	−0.395251	−	0.723043i	−0.0255133	−	0.0466722i
$241$	0.225281	−	0.337157i	0.0145116	−	0.0217182i	−0.824143	−	0.566382i	$-0.808343\pi$
$241$	0.225281	−	0.337157i	0.0145116	−	0.0217182i	0.838655	+	0.544664i	$0.183343\pi$
$242$	−2.10322	+	2.10322i	−0.135200	+	0.135200i
$243$	−0.797936	+	15.5680i	−0.0511876	+	0.998689i
$244$	0.601172	+	0.899718i	0.0384861	+	0.0575985i
$245$	−0.534050	−	0.106229i	−0.0341192	−	0.00678674i
$246$	9.60746	+	2.81612i	0.612549	+	0.179549i
$247$	0.299877	+	0.723968i	0.0190807	+	0.0460650i
$248$	−5.21731	+	26.2292i	−0.331300	+	1.66556i
$249$	0.850766	−	9.55747i	0.0539151	−	0.605680i
$250$	1.81028	−	0.360088i	0.114492	−	0.0227739i
$251$	−0.749951	−	0.749951i	−0.0473365	−	0.0473365i	0.683042	−	0.730379i	$-0.260656\pi$
$251$	−0.749951	−	0.749951i	−0.0473365	−	0.0473365i	−0.730379	+	0.683042i	$0.760656\pi$
$252$	0.527872	−	1.34533i	0.0332528	−	0.0847481i
$253$	−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	$0.841087\pi$
$258$	−1.43672	−	4.58087i	−0.0894460	−	0.285193i
$259$	0.465876	+	0.465876i	0.0289481	+	0.0289481i
$260$	0.00438567		0.000872364i	0.000271988		5.41017e-5i
$261$	8.50556	+	8.19185i	0.526481	+	0.507063i
$262$	3.34111	−	16.7969i	0.206415	−	1.03772i
$263$	−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	$0.929452\pi$
$264$	−5.29936	+	18.0792i	−0.326153	+	1.11270i
$265$	−0.883889	−	0.175817i	−0.0542969	−	0.0108003i
$266$	−8.67397	−	12.9815i	−0.531835	−	0.795948i
$267$	−3.28687	+	6.29072i	−0.201153	+	0.384986i
$268$	−1.12027	+	1.12027i	−0.0684314	+	0.0684314i
$269$	−5.07770	+	7.59932i	−0.309593	+	0.463339i	−0.953340	−	0.301900i	$-0.902379\pi$
$269$	−5.07770	+	7.59932i	−0.309593	+	0.463339i	0.643747	+	0.765239i	$0.277379\pi$
$270$	0.725377	−	0.630328i	0.0441451	−	0.0383605i
$271$			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
$275$	−15.0804	−	10.0764i	−0.909382	−	0.607629i
$276$	−2.94442	+	0.317951i	−0.177233	+	0.0191384i
$277$	−4.03634	−	20.2921i	−0.242520	−	1.21923i	−0.889575	−	0.456789i	$-0.848999\pi$
$277$	−4.03634	−	20.2921i	−0.242520	−	1.21923i	0.647055	−	0.762444i	$-0.276001\pi$
$278$	5.56775	−	3.72025i	0.333931	−	0.223126i
$279$	−26.8569	+	0.504591i	−1.60788	+	0.0302091i
$280$	−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	$0.275714\pi$
$282$	−4.36179	−	5.21420i	−0.259741	−	0.310501i
$283$	−10.6783	+	7.13505i	−0.634762	+	0.424134i	−0.830884	−	0.556445i	$-0.812165\pi$
$283$	−10.6783	+	7.13505i	−0.634762	+	0.424134i	0.196122	+	0.980579i	$0.437165\pi$
$284$	−0.690355	−	3.47065i	−0.0409650	−	0.205945i
$285$	0.175660	+	1.62672i	0.0104052	+	0.0963584i
$286$	0.464551	+	0.310403i	0.0274695	+	0.0183545i
$287$	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
$292$	−0.675840	+	1.01147i	−0.0395506	+	0.0591916i
$293$	−0.797696	+	0.797696i	−0.0466019	+	0.0466019i	−0.730024	−	0.683422i	$-0.760491\pi$
$293$	−0.797696	+	0.797696i	−0.0466019	+	0.0466019i	0.683422	+	0.730024i	$0.260491\pi$
$294$	−7.80895	−	4.08013i	−0.455427	−	0.237958i
$295$	−0.747562	−	1.11881i	−0.0435248	−	0.0651394i
$296$	−1.09090	−	0.216994i	−0.0634074	−	0.0126125i
$297$	−18.8771	−	1.32348i	−1.09536	−	0.0767964i
$298$	−11.1781	−	26.9863i	−0.647530	−	1.56327i
$299$	−0.142986	+	0.718839i	−0.00826909	+	0.0415715i
$300$	−2.33951	−	0.208254i	−0.135072	−	0.0120235i
$301$	−3.65908	+	0.727837i	−0.210906	+	0.0419518i
$302$	3.83394	+	3.83394i	0.220618	+	0.220618i
$303$	−8.37457	+	2.62655i	−0.481106	+	0.150891i
$304$	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
$309$	26.4031	−	8.28089i	1.50202	−	0.471083i
$310$	1.17093	+	1.17093i	0.0665042	+	0.0665042i
$311$	28.8106	−	5.73078i	1.63370	−	0.324963i	0.708867	−	0.705342i	$-0.249207\pi$
$311$	28.8106	−	5.73078i	1.63370	−	0.324963i	0.924830	+	0.380380i	$0.124207\pi$
$312$	0.601421	+	0.0535360i	0.0340488	+	0.00303088i
$313$	−3.47657	+	17.4779i	−0.196507	+	0.987910i	0.749065	+	0.662497i	$0.230503\pi$
$313$	−3.47657	+	17.4779i	−0.196507	+	0.987910i	−0.945572	+	0.325413i	$0.894497\pi$
$314$	7.02180	+	16.9521i	0.396263	+	0.956664i
$315$	−0.426478	−	0.613020i	−0.0240293	−	0.0345398i
$316$	0.653204	+	0.129930i	0.0367456	+	0.00730915i
$317$	−7.84523	−	11.7412i	−0.440632	−	0.659452i	0.542981	−	0.839745i	$-0.317296\pi$
$317$	−7.84523	−	11.7412i	−0.440632	−	0.659452i	−0.983613	+	0.180293i	$0.942296\pi$
$318$	−12.9243	−	6.75289i	−0.724760	−	0.378683i
$319$	−10.1366	+	10.1366i	−0.567542	+	0.567542i
$320$	0.685733	−	1.02627i	0.0383337	−	0.0573704i
$321$	−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
$326$	12.1905	+	8.14545i	0.675171	+	0.451135i
$327$	2.13442	+	19.7660i	0.118034	+	1.09306i
$328$	2.56239	+	12.8820i	0.141485	+	0.711291i
$329$	−4.39244	+	2.93493i	−0.242163	+	0.161808i
$330$	0.748505	+	0.894784i	0.0412039	+	0.0492562i
$331$	6.68245	−	2.76796i	0.367301	−	0.152141i	−0.191396	−	0.981513i	$-0.561302\pi$
$331$	6.68245	−	2.76796i	0.367301	−	0.152141i	0.558697	+	0.829372i	$0.311302\pi$
$332$	1.39362	−	0.577254i	0.0764846	−	0.0316810i
$333$	−0.0209865	−	1.11701i	−0.00115005	−	0.0612118i
$334$	2.29505	−	1.53351i	0.125580	−	0.0839097i
$335$	0.159713	+	0.802931i	0.00872605	+	0.0438688i
$336$	−10.3014	+	1.11239i	−0.561988	+	0.0606860i
$337$	−11.1151	−	7.42687i	−0.605478	−	0.404568i	0.214696	−	0.976681i	$-0.431124\pi$
$337$	−11.1151	−	7.42687i	−0.605478	−	0.404568i	−0.820175	+	0.572113i	$0.806124\pi$
$338$	−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
$343$	−10.6842	+	15.9900i	−0.576891	+	0.863378i
$344$	4.45359	−	4.45359i	0.240121	−	0.240121i
$345$	−0.708681	+	1.35634i	−0.0381541	+	0.0730229i
$346$	−8.99268	−	13.4585i	−0.483450	−	0.723534i
$347$	32.8299	+	6.53027i	1.76240	+	0.350563i	0.966854	−	0.255329i	$-0.0821839\pi$
$347$	32.8299	+	6.53027i	1.76240	+	0.350563i	0.795546	+	0.605893i	$0.207184\pi$
$348$	−0.522186	+	1.78149i	−0.0279921	+	0.0954977i
$349$	10.6503	+	25.7122i	0.570099	+	1.37634i	0.901471	+	0.432840i	$0.142489\pi$
$349$	10.6503	+	25.7122i	0.570099	+	1.37634i	−0.331372	+	0.943500i	$0.607511\pi$
$350$	2.25939	−	11.3587i	0.120769	−	0.607148i
$351$	0.0764269	+	0.601643i	0.00407937	+	0.0321133i
$352$	−5.46161	+	1.08638i	−0.291105	+	0.0579043i
$353$	−5.10785	−	5.10785i	−0.271864	−	0.271864i	0.557986	−	0.829850i	$-0.311574\pi$
$353$	−5.10785	−	5.10785i	−0.271864	−	0.271864i	−0.829850	+	0.557986i	$0.811574\pi$
$354$	−6.51562	−	20.7746i	−0.346301	−	1.10416i
$355$	−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	$0.365840\pi$
$360$	1.17361	+	0.460491i	0.0618546	+	0.0242700i
$361$	−18.4383	−	18.4383i	−0.970437	−	0.970437i
$362$	2.74426	−	0.545867i	0.144235	−	0.0286901i
$363$	0.347518	−	3.90400i	0.0182400	−	0.204907i
$364$	0.0109691	−	0.0551455i	0.000574939	−	0.00289041i
$365$	0.240553	+	0.580747i	0.0125911	+	0.0303977i
$366$	8.68213	+	2.54489i	0.453822	+	0.133024i
$367$	−11.0178	−	2.19159i	−0.575127	−	0.114400i	−0.101047	−	0.994882i	$-0.532219\pi$
$367$	−11.0178	−	2.19159i	−0.575127	−	0.114400i	−0.474080	+	0.880482i	$0.657219\pi$
$368$	11.7963	+	17.6544i	0.614923	+	0.920297i
$369$	−12.0914	+	5.27668i	−0.629455	+	0.274693i
$370$	−0.0487002	+	0.0487002i	−0.00253180	+	0.00253180i
$371$	−6.29561	+	9.42204i	−0.326852	+	0.489168i
$372$	−2.02552	−	3.70534i	−0.105018	−	0.192113i
$373$			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
$377$	0.382005	+	0.255247i	0.0196742	+	0.0131459i
$378$	−3.83203	−	11.4597i	−0.197098	−	0.589423i
$379$	−1.02753	−	5.16575i	−0.0527808	−	0.265347i	0.945380	−	0.325971i	$-0.105691\pi$
$379$	−1.02753	−	5.16575i	−0.0527808	−	0.265347i	−0.998161	+	0.0606237i	$0.980691\pi$
$380$	−0.213868	+	0.142902i	−0.0109712	+	0.00733073i
$381$	13.1378	−	10.9900i	0.673068	−	0.563036i
$382$	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	$0.556791\pi$
$384$	11.2559	−	9.41575i	0.574398	−	0.480496i
$385$	0.753764	−	0.503649i	0.0384154	−	0.0256683i
$386$	4.16352	+	20.9314i	0.211918	+	1.06538i
$387$	5.32519	+	3.41525i	0.270694	+	0.173607i
$388$	1.03854	+	0.693928i	0.0527237	+	0.0352289i
$389$	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
$393$	10.8247	+	19.8018i	0.546032	+	0.998871i
$394$	5.73319	−	8.58033i	0.288834	−	0.432271i
$395$	0.243347	−	0.243347i	0.0122441	−	0.0122441i
$396$	−1.18987	−	2.72657i	−0.0597933	−	0.137015i
$397$	−21.6114	−	32.3438i	−1.08465	−	1.62329i	−0.722808	−	0.691049i	$-0.757149\pi$
$397$	−21.6114	−	32.3438i	−1.08465	−	1.62329i	−0.361839	−	0.932240i	$-0.617851\pi$
$398$	16.5007	+	3.28219i	0.827105	+	0.164521i
$399$	19.7427	+	5.78693i	0.988369	+	0.289709i
$400$	6.44418	+	15.5576i	0.322209	+	0.777881i
$401$	−5.31186	+	26.7045i	−0.265262	+	1.33356i	0.586635	+	0.809851i	$0.300452\pi$
$401$	−5.31186	+	26.7045i	−0.265262	+	1.33356i	−0.851897	+	0.523709i	$0.824548\pi$
$402$	−1.17451	+	13.1944i	−0.0585792	+	0.658076i
$403$	−1.02499	+	0.203883i	−0.0510583	+	0.0101561i
$404$	−0.975645	−	0.975645i	−0.0485401	−	0.0485401i
$405$	−0.200218	+	1.25038i	−0.00994892	+	0.0621320i
$406$	−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
$411$	1.66122	+	5.29669i	0.0819419	+	0.261266i
$412$	3.07598	+	3.07598i	0.151543	+	0.151543i
$413$	−16.5942	+	3.30080i	−0.816549	+	0.162422i
$414$	−17.1772	+	17.8350i	−0.844214	+	0.876543i
$415$	0.152065	−	0.764483i	0.00746459	−	0.0375270i
$416$	0.0682967	+	0.164883i	0.00334852	+	0.00808405i
$417$	−2.48201	+	8.46759i	−0.121544	+	0.414660i
$418$	−31.5210	−	6.26991i	−1.54174	−	0.306671i
$419$	5.18926	+	7.76628i	0.253512	+	0.379408i	0.936295	−	0.351213i	$-0.114231\pi$
$419$	5.18926	+	7.76628i	0.253512	+	0.379408i	−0.682784	+	0.730621i	$0.739231\pi$
$420$	0.0543663	−	0.104051i	0.00265280	−	0.00507719i
$421$	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	$0.144919\pi$
$422$	−3.73899	+	5.59579i	−0.182011	+	0.272399i
$423$	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
$428$	−0.308480	−	0.206119i	−0.0149109	−	0.00996316i
$429$	−0.731973	+	0.0790418i	−0.0353400	+	0.00381617i
$430$	−0.0760842	−	0.382501i	−0.00366911	−	0.0184459i
$431$	−12.1482	+	8.11718i	−0.585159	+	0.390991i	−0.812618	−	0.582797i	$-0.801958\pi$
$431$	−12.1482	+	8.11718i	−0.585159	+	0.390991i	0.227459	+	0.973788i	$0.426958\pi$
$432$	13.8902	+	10.7590i	0.668291	+	0.517641i
$433$	16.4827	−	6.82738i	0.792110	−	0.328103i	0.0503185	−	0.998733i	$-0.483976\pi$
$433$	16.4827	−	6.82738i	0.792110	−	0.328103i	0.741792	+	0.670631i	$0.233976\pi$
$434$	19.2369	−	7.96819i	0.923401	−	0.382485i
$435$	0.615502	+	0.735789i	0.0295111	+	0.0352784i
$436$	−2.59869	+	1.73639i	−0.124454	+	0.0831578i
$437$	−8.22492	−	41.3495i	−0.393451	−	1.97801i
$438$	1.09198	+	10.1124i	0.0521768	+	0.483187i
$439$	21.9174	+	14.6447i	1.04606	+	0.698955i	0.954914	−	0.296882i	$-0.0959469\pi$
$439$	21.9174	+	14.6447i	1.04606	+	0.698955i	0.0911464	+	0.995838i	$0.470947\pi$
$440$	−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	$-0.926217\pi$
$443$		−	9.67036i		−	0.459453i	0.973255	−	0.229726i	$-0.0737831\pi$
$444$	0.154109	−	0.0842438i	0.00731371	−	0.00399803i
$445$	−0.320325	+	0.479400i	−0.0151848	+	0.0227257i
$446$	0.175541	−	0.175541i	0.00831208	−	0.00831208i
$447$	34.1145	+	17.8246i	1.61356	+	0.843076i
$448$	−8.62244	−	12.9044i	−0.407372	−	0.609675i
$449$	−1.03641	−	0.206155i	−0.0489113	−	0.00972906i	0.170574	−	0.985345i	$-0.445438\pi$
$449$	−1.03641	−	0.206155i	−0.0489113	−	0.00972906i	−0.219485	+	0.975616i	$0.570438\pi$
$450$	−16.1208	+	11.2153i	−0.759942	+	0.528692i
$451$	−6.12872	−	14.7960i	−0.288590	−	0.696718i
$452$	0.719865	−	3.61901i	0.0338596	−	0.170224i
$453$	−7.11658	−	0.633488i	−0.334366	−	0.0297639i
$454$	2.74620	−	0.546252i	0.128885	−	0.0256369i
$455$	−0.0205441	−	0.0205441i	−0.000963124	−	0.000963124i
$456$	−33.1404	+	10.3939i	−1.55194	+	0.486741i
$457$	−19.7952	−	8.19942i	−0.925978	−	0.383553i	−0.131827	−	0.991273i	$-0.542084\pi$
$457$	−19.7952	−	8.19942i	−0.925978	−	0.383553i	−0.794151	+	0.607720i	$0.792084\pi$
$458$	−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	$0.430464\pi$
$462$	13.9963	−	4.38972i	0.651168	−	0.204228i
$463$	−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	$0.898026\pi$
$464$	13.0540	−	2.59661i	0.606018	−	0.120544i
$465$	−2.17348	−	0.193474i	−0.100793	−	0.00897216i
$466$	−2.51101	+	12.6237i	−0.116320	+	0.584781i
$467$	−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	$0.967974\pi$
$468$	−0.0782652	+	0.0544491i	−0.00361781	+	0.00251691i
$469$	10.0961	+	2.00824i	0.466194	+	0.0927317i
$470$	−0.306802	−	0.459162i	−0.0141517	−	0.0211796i
$471$	−21.4299	−	11.1970i	−0.987437	−	0.515930i
$472$	20.1974	−	20.1974i	0.929660	−	0.929660i
$473$	−4.26662	+	6.38545i	−0.196179	+	0.293603i
$474$	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
$479$	18.8736	+	12.6109i	0.862357	+	0.576208i	0.906209	−	0.422830i	$-0.138963\pi$
$479$	18.8736	+	12.6109i	0.862357	+	0.576208i	−0.0438524	+	0.999038i	$0.513963\pi$
$480$	0.0400064	+	0.370483i	0.00182604	+	0.0169102i
$481$	−0.00847972	−	0.0426304i	−0.000386642	−	0.00194378i
$482$	0.443167	−	0.296115i	0.0201857	−	0.0134877i
$483$	12.3464	+	14.7592i	0.561780	+	0.671567i
$484$	0.569259	−	0.235795i	0.0258754	−	0.0107179i
$485$	0.596290	−	0.246991i	0.0270761	−	0.0112153i
$486$	−8.79983	+	18.5040i	−0.399169	+	0.839357i
$487$	−19.1116	+	12.7700i	−0.866028	+	0.578662i	−0.907299	−	0.420486i	$-0.861859\pi$
$487$	−19.1116	+	12.7700i	−0.866028	+	0.578662i	0.0412704	+	0.999148i	$0.486859\pi$
$488$	2.31560	+	11.6413i	0.104822	+	0.526977i
$489$	−19.2081	+	2.07417i	−0.868619	+	0.0937974i
$490$	−0.595100	−	0.397633i	−0.0268839	−	0.0179632i
$491$	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
$495$	−1.51306	−	0.271524i	−0.0680069	−	0.0122041i
$496$	−16.8202	+	25.1733i	−0.755251	+	1.13031i
$497$	−16.2578	+	16.2578i	−0.729264	+	0.729264i
$498$	5.84063	−	11.1784i	0.261725	−	0.500914i
$499$	−0.599548	−	0.897288i	−0.0268395	−	0.0401681i	0.817807	−	0.575492i	$-0.195189\pi$
$499$	−0.599548	−	0.897288i	−0.0268395	−	0.0401681i	−0.844647	+	0.535324i	$0.820189\pi$
$500$	−0.375010	−	0.0745940i	−0.0167709	−	0.00333595i
$501$	−1.02309	+	3.49038i	−0.0457085	+	0.155939i
$502$	−0.533486	−	1.28795i	−0.0238106	−	0.0574840i
$503$	1.83089	−	9.20449i	0.0816353	−	0.410408i	−0.918261	−	0.395977i	$-0.870406\pi$
$503$	1.83089	−	9.20449i	0.0816353	−	0.410408i	0.999896	−	0.0144315i	$-0.00459386\pi$
$504$	10.9967	−	11.4179i	0.489834	−	0.508592i
$505$	−0.699273	+	0.139094i	−0.0311173	+	0.00618961i
$506$	−21.2552	−	21.2552i	−0.944907	−	0.944907i
$507$	−6.73128	−	21.4622i	−0.298947	−	0.953172i
$508$	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
$513$	−17.3055	−	30.2913i	−0.764059	−	1.33739i
$514$	−18.7116	−	18.7116i	−0.825334	−	0.825334i
$515$	2.20465	−	0.438531i	0.0971483	−	0.0193240i
$516$	−0.0881802	+	0.990613i	−0.00388192	+	0.0436093i
$517$	−2.12149	+	10.6655i	−0.0933031	+	0.469066i
$518$	0.331406	+	0.800085i	0.0145611	+	0.0351537i
$519$	20.4681	+	5.99957i	0.898449	+	0.263352i
$520$	0.0481065	+	0.00956898i	0.00210961	+	0.000419627i
$521$	−0.875810	−	1.31074i	−0.0383699	−	0.0574246i	0.811789	−	0.583951i	$-0.198494\pi$
$521$	−0.875810	−	1.31074i	−0.0383699	−	0.0574246i	−0.850159	+	0.526527i	$0.823494\pi$
$522$	6.20832	+	14.2263i	0.271731	+	0.622668i
$523$	−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	$0.980751\pi$
$524$	−1.97102	+	2.94984i	−0.0861043	+	0.128864i
$525$	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
$530$	−0.984931	−	0.658110i	−0.0427827	−	0.0285865i
$531$	24.1502	+	15.4884i	1.04803	+	0.672141i
$532$	0.630973	+	3.17211i	0.0273561	+	0.137529i
$533$	−0.426766	+	0.285156i	−0.0184853	+	0.0123515i
$534$	−7.15575	+	5.98593i	−0.309660	+	0.259037i
$535$	−0.177118	+	0.0733645i	−0.00765746	+	0.00317183i
$536$	−16.0554	+	6.65037i	−0.693488	+	0.287252i
$537$	−24.5601	+	20.5450i	−1.05984	+	0.886582i
$538$	−9.98873	+	6.67425i	−0.430645	+	0.287747i
$539$	2.74957	+	13.8230i	0.118433	+	0.595401i
$540$	−0.188797	+	0.0631321i	−0.00812451	+	0.00271677i
$541$	2.52076	+	1.68432i	0.108376	+	0.0724146i	0.608577	−	0.793495i	$-0.291741\pi$
$541$	2.52076	+	1.68432i	0.108376	+	0.0724146i	−0.500201	+	0.865909i	$0.666741\pi$
$542$	−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
$547$	0.965555	−	1.44506i	0.0412842	−	0.0617861i	−0.810253	−	0.586080i	$-0.800671\pi$
$547$	0.965555	−	1.44506i	0.0412842	−	0.0617861i	0.851538	+	0.524294i	$0.175671\pi$
$548$	−0.617069	+	0.617069i	−0.0263599	+	0.0263599i
$549$	−10.9269	+	4.76846i	−0.466347	+	0.203513i
$550$	−13.2447	−	19.8220i	−0.564754	−	0.845214i
$551$	−25.9200	−	5.15580i	−1.10423	−	0.219645i
$552$	−31.1735	−	9.13753i	−1.32683	−	0.388919i
$553$	−1.65598	−	3.99789i	−0.0704195	−	0.170008i
$554$	5.30547	−	26.6724i	0.225408	−	1.13320i
$555$	0.00804682	−	0.0903977i	0.000341569	−	0.00383717i
$556$	−1.36051	+	0.270623i	−0.0576986	+	0.0114770i
$557$	29.9311	+	29.9311i	1.26822	+	1.26822i	0.947006	+	0.321217i	$0.104092\pi$
$557$	29.9311	+	29.9311i	1.26822	+	1.26822i	0.321217	+	0.947006i	$0.395908\pi$
$558$	−32.8681	−	12.8965i	−1.39142	−	0.545953i
$559$	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	$0.829442\pi$
$564$	0.421432	+	1.34371i	0.0177455	+	0.0565803i
$565$	−1.34824	−	1.34824i	−0.0567208	−	0.0567208i
$566$	−16.5564	+	3.29328i	−0.695919	+	0.138427i
$567$	13.5621	+	8.34259i	0.569556	+	0.350356i
$568$	7.57252	−	38.0696i	0.317736	−	1.59737i
$569$	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	$0.730874\pi$
$570$	−0.604936	+	2.06379i	−0.0253380	+	0.0864428i
$571$	−6.15858	−	1.22502i	−0.257728	−	0.0512654i	0.0645348	−	0.997915i	$-0.479444\pi$
$571$	−6.15858	−	1.22502i	−0.257728	−	0.0512654i	−0.322263	+	0.946650i	$0.604444\pi$
$572$	−0.0643017	−	0.0962342i	−0.00268859	−	0.00402376i
$573$	−13.9074	+	26.6174i	−0.580992	+	1.11196i
$574$	7.23109	−	7.23109i	0.301820	−	0.301820i
$575$	17.3744	−	26.0027i	0.724564	−	1.08439i
$576$	−4.64846	+	25.9034i	−0.193686	+	1.07931i
$577$			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
$581$	−8.14920	−	5.44512i	−0.338086	−	0.225902i
$582$	10.3830	−	1.12120i	0.430389	−	0.0464754i
$583$	4.55073	+	22.8781i	0.188472	+	0.947513i
$584$	−11.0948	+	7.41331i	−0.459106	+	0.306765i
$585$	0.000925462		0.0492578i	3.82631e−5		0.00203656i
$586$	−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	$0.323547\pi$
$588$	1.17107	+	1.39994i	0.0482943	+	0.0577323i
$589$	49.9838	−	33.3981i	2.05955	−	1.37615i
$590$	−0.345048	−	1.73467i	−0.0142054	−	0.0714154i
$591$	1.45991	+	13.5196i	0.0600528	+	0.556124i
$592$	−1.04698	−	0.699572i	−0.0430308	−	0.0287523i
$593$	−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
$597$	−19.4526	+	10.6338i	−0.796143	+	0.435211i
$598$	−0.535220	+	0.801013i	−0.0218868	+	0.0327558i
$599$	−17.7610	+	17.7610i	−0.725695	+	0.725695i	−0.969759	−	0.244064i	$-0.921519\pi$
$599$	−17.7610	+	17.7610i	−0.725695	+	0.725695i	0.244064	+	0.969759i	$0.421519\pi$
$600$	−22.8346	−	11.9309i	−0.932217	−	0.487078i
$601$	16.9242	+	25.3288i	0.690351	+	1.03318i	0.996693	+	0.0812623i	$0.0258951\pi$
$601$	16.9242	+	25.3288i	0.690351	+	1.03318i	−0.306341	+	0.951922i	$0.599105\pi$
$602$	−4.80958	−	0.956686i	−0.196024	−	0.0389916i
$603$	−9.96858	−	14.3288i	−0.405952	−	0.583516i
$604$	−0.429829	−	1.03770i	−0.0174895	−	0.0422233i
$605$	0.0621150	−	0.312273i	0.00252534	−	0.0126957i
$606$	−11.4910	−	1.02288i	−0.466790	−	0.0415517i
$607$	21.3739	−	4.25153i	0.867539	−	0.172564i	0.258796	−	0.965932i	$-0.416674\pi$
$607$	21.3739	−	4.25153i	0.867539	−	0.172564i	0.608743	+	0.793368i	$0.291674\pi$
$608$	−7.25911	−	7.25911i	−0.294396	−	0.294396i
$609$	11.5093	−	3.60970i	0.466380	−	0.146273i
$610$	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
$615$	−1.02258	+	0.320714i	−0.0412343	+	0.0129325i
$616$	13.6074	+	13.6074i	0.548258	+	0.548258i
$617$	23.1766	−	4.61012i	0.933056	−	0.185596i	0.294922	−	0.955521i	$-0.404706\pi$
$617$	23.1766	−	4.61012i	0.933056	−	0.185596i	0.638134	+	0.769925i	$0.279706\pi$
$618$	36.2284	+	3.22490i	1.45732	+	0.129725i
$619$	−7.79157	+	39.1709i	−0.313170	+	1.57441i	0.428435	+	0.903572i	$0.359065\pi$
$619$	−7.79157	+	39.1709i	−0.313170	+	1.57441i	−0.741605	+	0.670837i	$0.765935\pi$
$620$	−0.131275	−	0.316925i	−0.00527211	−	0.0127280i
$621$	2.28205	−	32.5493i	0.0915754	−	1.30616i
$622$	37.8693	+	7.53267i	1.51842	+	0.302033i
$623$	4.02777	+	6.02799i	0.161369	+	0.241506i
$624$	0.605843	+	0.316550i	0.0242531	+	0.0126721i
$625$	17.4680	−	17.4680i	0.698719	−	0.698719i
$626$	−13.0134	+	19.4759i	−0.520119	+	0.778413i
$627$	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	0.577556	+	0.816351i	$0.304007\pi$
$631$	−10.2510	+	24.7481i	−0.408085	+	0.985205i	−0.985641	+	0.168854i	$0.945993\pi$
$632$	6.07420	+	4.05865i	0.241619	+	0.161444i
$633$	−0.952104	−	8.81704i	−0.0378428	−	0.350446i
$634$	−3.62108	−	18.2044i	−0.143811	−	0.722988i
$635$	1.15691	−	0.773023i	0.0459106	−	0.0306765i
$636$	1.93821	+	2.31699i	0.0768549	+	0.0918745i
$637$	0.417310	−	0.172855i	0.0165344	−	0.00684878i
$638$	−17.4084	+	7.21080i	−0.689206	+	0.285478i
$639$	38.9807	−	0.732374i	1.54205	−	0.0289723i
$640$	0.991189	−	0.662291i	0.0391802	−	0.0261794i
$641$	8.30682	+	41.7612i	0.328100	+	1.64947i	0.694854	+	0.719151i	$0.255469\pi$
$641$	8.30682	+	41.7612i	0.328100	+	1.64947i	−0.366754	+	0.930318i	$0.619531\pi$
$642$	−3.08409	+	0.333034i	−0.121719	+	0.0131438i
$643$	21.4404	+	14.3260i	0.845525	+	0.564962i	0.901159	−	0.433490i	$-0.142718\pi$
$643$	21.4404	+	14.3260i	0.845525	+	0.564962i	−0.0556337	+	0.998451i	$0.517718\pi$
$644$	−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	$0.270288\pi$
$647$			38.1903i			1.50142i	−0.660634	+	0.750709i	$0.729712\pi$
$648$	−26.8618	+	1.00972i	−1.05523	+	0.0396656i
$649$	−19.3495	+	28.9585i	−0.759533	+	1.13672i
$650$	−0.540257	+	0.540257i	−0.0211906	+	0.0211906i
$651$	−12.7061	+	24.3182i	−0.497992	+	0.953104i
$652$	−1.68737	−	2.52533i	−0.0660826	−	0.0988996i
$653$	−33.6458	−	6.69257i	−1.31666	−	0.261901i	−0.513721	−	0.857957i	$-0.671733\pi$
$653$	−33.6458	−	6.69257i	−1.31666	−	0.261901i	−0.802942	+	0.596057i	$0.796733\pi$
$654$	−7.35049	+	25.0769i	−0.287427	+	0.980584i
$655$	0.701548	+	1.69369i	0.0274118	+	0.0661778i
$656$	−2.90087	+	14.5836i	−0.113260	+	0.569396i
$657$	−9.65356	−	9.29750i	−0.376621	−	0.362730i
$658$	−6.81033	+	1.35466i	−0.265494	+	0.0528101i
$659$	24.7106	+	24.7106i	0.962589	+	0.962589i	0.999325	−	0.0367361i	$-0.0116961\pi$
$659$	24.7106	+	24.7106i	0.962589	+	0.962589i	−0.0367361	+	0.999325i	$0.511696\pi$
$660$	−0.0723199	−	0.230587i	−0.00281505	−	0.00897559i
$661$	−11.2271	−	4.65040i	−0.436682	−	0.180880i	0.153502	−	0.988148i	$-0.450945\pi$
$661$	−11.2271	−	4.65040i	−0.436682	−	0.180880i	−0.590184	+	0.807269i	$0.700945\pi$
$662$	9.50727			0.369510
$663$		0			0
$664$	16.5461			0.642113
$665$	1.54403	+	0.639559i	0.0598750	+	0.0248011i
$666$	0.536380	−	1.36702i	0.0207843	−	0.0529710i
$667$	−17.4783	−	17.4783i	−0.676762	−	0.676762i
$668$	−0.560811	+	0.111552i	−0.0216984	+	0.00431608i
$669$	−0.0290049	+	0.325839i	−0.00112139	+	0.0125977i
$670$	−0.209931	+	1.05539i	−0.00811032	+	0.0407734i
$671$	−5.53844	−	13.3710i	−0.213809	−	0.516181i
$672$	4.49637	+	1.31797i	0.173451	+	0.0508417i
$673$	−39.7638	−	7.90952i	−1.53278	−	0.304890i	−0.644651	−	0.764477i	$-0.722997\pi$
$673$	−39.7638	−	7.90952i	−1.53278	−	0.304890i	−0.888133	+	0.459587i	$0.847997\pi$
$674$	−9.76206	−	14.6100i	−0.376021	−	0.562755i
$675$	6.81126	−	24.9654i	0.262165	−	0.960919i
$676$	2.50037	−	2.50037i	0.0961681	−	0.0961681i
$677$	−3.80783	+	5.69882i	−0.146347	+	0.219024i	−0.897400	−	0.441219i	$-0.854546\pi$
$677$	−3.80783	+	5.69882i	−0.146347	+	0.219024i	0.751053	+	0.660242i	$0.229546\pi$
$678$	−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
$683$	8.21052	+	5.48609i	0.314167	+	0.209919i	0.702649	−	0.711537i	$-0.252001\pi$
$683$	8.21052	+	5.48609i	0.314167	+	0.209919i	−0.388482	+	0.921456i	$0.627001\pi$
$684$	2.96073	−	4.61649i	0.113206	−	0.176516i
$685$	0.0879732	+	0.442271i	0.00336128	+	0.0168983i
$686$	−21.0176	+	14.0435i	−0.802457	+	0.536184i
$687$	22.9619	−	19.2081i	0.876052	−	0.732836i
$688$	6.58752	−	2.72864i	0.251147	−	0.104028i
$689$	0.690676	−	0.286087i	0.0263127	−	0.0108991i
$690$	−1.54285	+	1.29063i	−0.0587353	+	0.0491333i
$691$	−11.5339	+	7.70668i	−0.438769	+	0.293176i	−0.755267	−	0.655417i	$-0.772493\pi$
$691$	−11.5339	+	7.70668i	−0.438769	+	0.293176i	0.316498	+	0.948593i	$0.397493\pi$
$692$	0.654157	+	3.28867i	0.0248673	+	0.125016i
$693$	−10.4349	+	16.2705i	−0.396389	+	0.618065i
$694$	36.5828	+	24.4439i	1.38867	+	0.927876i
$695$	−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
$700$	−1.33288	+	1.99479i	−0.0503780	+	0.0753960i
$701$	7.15325	−	7.15325i	0.270175	−	0.270175i	−0.558996	−	0.829170i	$-0.688813\pi$
$701$	7.15325	−	7.15325i	0.270175	−	0.270175i	0.829170	+	0.558996i	$0.188813\pi$
$702$	−0.209821	+	0.769060i	−0.00791917	+	0.0290263i
$703$	1.38907	+	2.07888i	0.0523896	+	0.0784066i
$704$	−31.3337	−	6.23266i	−1.18093	−	0.234902i
$705$	0.698307	+	0.204687i	0.0262998	+	0.00770894i
$706$	−3.63353	−	8.77211i	−0.136750	−	0.330143i
$707$	−1.74897	+	8.79269i	−0.0657770	+	0.330683i
$708$	−0.399904	+	4.49251i	−0.0150293	+	0.168839i
$709$	44.1828	−	8.78850i	1.65932	−	0.330059i	0.725614	−	0.688102i	$-0.241556\pi$
$709$	44.1828	−	8.78850i	1.65932	−	0.330059i	0.933705	+	0.358043i	$0.116556\pi$
$710$	−1.69951	−	1.69951i	−0.0637814	−	0.0637814i
$711$	−2.68020	+	6.83078i	−0.100516	+	0.256174i
$712$	−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
$717$	−11.6297	−	37.0805i	−0.434319	−	1.38480i
$718$	25.6111	+	25.6111i	0.955796	+	0.955796i
$719$	−28.2094	+	5.61120i	−1.05203	+	0.209263i	−0.690676	−	0.723165i	$-0.742687\pi$
$719$	−28.2094	+	5.61120i	−1.05203	+	0.209263i	−0.361358	+	0.932427i	$0.617687\pi$
$720$	1.02800	+	0.990082i	0.0383112	+	0.0368982i
$721$	5.51411	−	27.7213i	0.205356	−	1.03240i
$722$	−13.1163	−	31.6655i	−0.488138	−	1.17847i
$723$	−0.197556	+	0.673981i	−0.00734719	+	0.0250656i
$724$	−0.568488	−	0.113079i	−0.0211277	−	0.00420256i
$725$	−10.8912	−	16.2998i	−0.404489	−	0.605360i
$726$	2.38576	−	4.56610i	0.0885439	−	0.169464i
$727$	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	$0.234411\pi$
$728$	0.342644	−	0.512803i	0.0126992	−	0.0190058i
$729$	−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	−0.531798	−	0.846871i	$-0.678484\pi$
$733$	11.9956	−	28.9600i	0.443068	−	1.06966i	0.974866	−	0.222790i	$-0.0715164\pi$
$734$	−12.2773	−	8.20346i	−0.453165	−	0.302795i
$735$	0.937673	−	0.101254i	0.0345866	−	0.00373482i
$736$	−1.87322	−	9.41729i	−0.0690477	−	0.347126i
$737$	17.6186	−	11.7724i	0.648991	−	0.433642i
$738$	−17.3377	+	0.325743i	−0.638209	+	0.0119907i
$739$	−4.41201	+	1.82751i	−0.162298	+	0.0672262i	−0.462354	−	0.886696i	$-0.652995\pi$
$739$	−4.41201	+	1.82751i	−0.162298	+	0.0672262i	0.300055	+	0.953922i	$0.402995\pi$
$740$	0.0131813	−	0.00545986i	0.000484553	−	0.000200708i
$741$	−0.870857	−	1.04105i	−0.0319917	−	0.0382438i
$742$	−12.3846	+	8.27510i	−0.454651	+	0.303788i
$743$	−4.10808	−	20.6527i	−0.150711	−	0.757674i	−0.980022	−	0.198888i	$-0.936267\pi$
$743$	−4.10808	−	20.6527i	−0.150711	−	0.757674i	0.829312	−	0.558787i	$-0.188733\pi$
$744$	−4.97297	−	46.0526i	−0.182318	−	1.68837i
$745$	2.59978	+	1.73712i	0.0952486	+	0.0636431i
$746$	−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
$751$	12.8753	−	19.2693i	0.469827	−	0.703145i	−0.518571	−	0.855035i	$-0.673536\pi$
$751$	12.8753	−	19.2693i	0.469827	−	0.703145i	0.988397	+	0.151889i	$0.0485358\pi$
$752$	7.13925	−	7.13925i	0.260342	−	0.260342i
$753$	1.62815	+	0.850699i	0.0593330	+	0.0310012i
$754$	0.335503	+	0.502116i	0.0122183	+	0.0182860i
$755$	−0.569241	−	0.113229i	−0.0207168	−	0.00412083i
$756$	−0.175067	+	2.49701i	−0.00636711	+	0.0908155i
$757$	−9.85760	−	23.7983i	−0.358280	−	0.864965i	−0.995542	−	0.0943180i	$-0.969933\pi$
$757$	−9.85760	−	23.7983i	−0.358280	−	0.864965i	0.637262	−	0.770647i	$-0.280067\pi$
$758$	1.35061	−	6.78999i	0.0490564	−	0.246623i
$759$	39.4540	+	3.51203i	1.43209	+	0.127478i
$760$	−2.76721	+	0.550432i	−0.100377	+	0.0199663i
$761$	−15.9336	−	15.9336i	−0.577594	−	0.577594i	0.356646	−	0.934240i	$-0.383920\pi$
$761$	−15.9336	−	15.9336i	−0.577594	−	0.577594i	−0.934240	+	0.356646i	$0.883920\pi$
$762$	21.4822	−	6.73753i	0.778217	−	0.244075i
$763$	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
$768$	−10.5909	+	3.32165i	−0.382165	+	0.119860i
$769$	−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	$0.833846\pi$
$770$	1.16869	−	0.232466i	0.0421166	−	0.00837751i
$771$	34.7326	+	3.09175i	1.25086	+	0.111347i
$772$	0.862495	−	4.33606i	0.0310419	−	0.156058i
$773$	−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	$0.888930\pi$
$774$	4.74884	+	6.82599i	0.170694	+	0.245355i
$775$	43.7354	+	8.69951i	1.57102	+	0.312496i
$776$	7.61171	+	11.3917i	0.273245	+	0.408939i
$777$	−1.01142	−	0.528461i	−0.0362845	−	0.0189584i
$778$	11.6153	−	11.6153i	0.416429	−	0.416429i
$779$	16.4029	−	24.5487i	0.587696	−	0.879549i
$780$	−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
$785$	−1.63312	−	1.09121i	−0.0582885	−	0.0389471i
$786$	3.18464	+	29.4916i	0.113592	+	1.05193i
$787$	−6.18658	−	31.1021i	−0.220528	−	1.10867i	−0.919370	−	0.393393i	$-0.871301\pi$
$787$	−6.18658	−	31.1021i	−0.220528	−	1.10867i	0.698843	−	0.715276i	$-0.253699\pi$
$788$	−1.77746	+	1.18766i	−0.0633194	+	0.0423086i
$789$	6.13615	+	7.33533i	0.218453	+	0.261145i
$790$	0.417919	−	0.173108i	0.0148689	−	0.00615889i
$791$	−22.1499	+	9.17479i	−0.787560	+	0.326218i
$792$	−0.612980	−	32.6259i	−0.0217813	−	1.15931i
$793$	−0.385663	+	0.257692i	−0.0136953	+	0.00915090i
$794$	−9.97507	−	50.1481i	−0.354002	−	1.77969i
$795$	1.55191	−	0.167583i	0.0550407	−	0.00594354i
$796$	−2.89781	−	1.93626i	−0.102710	−	0.0686288i
$797$	−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
$801$	2.17142	−	12.1002i	0.0767235	−	0.427539i
$802$	−19.8832	+	29.7572i	−0.702099	+	1.05076i
$803$	11.5048	−	11.5048i	0.405995	−	0.405995i
$804$	1.27077	−	2.43212i	0.0448165	−	0.0857741i
$805$	0.868428	+	1.29969i	0.0306081	+	0.0458082i
$806$	−1.34727	−	0.267988i	−0.0474555	−	0.00943949i
$807$	4.45280	−	15.1911i	0.156746	−	0.534753i
$808$	−5.79181	−	13.9827i	−0.203755	−	0.491908i
$809$	4.90669	−	24.6676i	0.172510	−	0.867266i	−0.793462	−	0.608620i	$-0.791724\pi$
$809$	4.90669	−	24.6676i	0.172510	−	0.867266i	0.965972	−	0.258646i	$-0.0832764\pi$
$810$	−0.872091	+	1.41771i	−0.0306422	+	0.0498134i
$811$	22.8258	−	4.54032i	0.801521	−	0.159432i	0.222700	−	0.974887i	$-0.428513\pi$
$811$	22.8258	−	4.54032i	0.801521	−	0.159432i	0.578821	+	0.815455i	$0.303513\pi$
$812$	1.34084	+	1.34084i	0.0470544	+	0.0470544i
$813$	−1.37266	−	4.37664i	−0.0481413	−	0.153496i
$814$	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
$819$	0.576676	+	0.226271i	0.0201507	+	0.00790656i
$820$	−0.119131	−	0.119131i	−0.00416024	−	0.00416024i
$821$	42.3900	−	8.43190i	1.47942	−	0.294275i	0.611607	−	0.791162i	$-0.290524\pi$
$821$	42.3900	−	8.43190i	1.47942	−	0.294275i	0.867815	+	0.496887i	$0.165524\pi$
$822$	−0.646944	+	7.26774i	−0.0225648	+	0.253492i
$823$	−3.29041	+	16.5420i	−0.114696	+	0.576617i	0.880105	+	0.474780i	$0.157472\pi$
$823$	−3.29041	+	16.5420i	−0.114696	+	0.576617i	−0.994801	+	0.101838i	$0.967528\pi$
$824$	18.2602	+	44.0841i	0.636125	+	1.53574i
$825$	30.1459	+	8.83631i	1.04955	+	0.307641i
$826$	−21.8119	−	4.33865i	−0.758931	−	0.150961i
$827$	12.3170	+	18.4337i	0.428304	+	0.641002i	0.981368	−	0.192136i	$-0.0615416\pi$
$827$	12.3170	+	18.4337i	0.428304	+	0.641002i	−0.553064	+	0.833139i	$0.686542\pi$
$828$	4.70135	−	2.05166i	0.163383	−	0.0713001i
$829$	−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	$0.407585\pi$
$830$	0.569205	−	0.851875i	0.0197574	−	0.0295690i
$831$	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
$836$	5.53564	+	3.69880i	0.191454	+	0.127926i
$837$	44.1242	−	14.7548i	1.52516	−	0.510000i
$838$	2.39518	+	12.0414i	0.0827400	+	0.415962i
$839$	20.6465	−	13.7956i	0.712798	−	0.476276i	−0.145546	−	0.989352i	$-0.546494\pi$
$839$	20.6465	−	13.7956i	0.712798	−	0.476276i	0.858344	+	0.513075i	$0.171494\pi$
$840$	0.987723	−	0.826251i	0.0340797	−	0.0285084i
$841$	12.4774	−	5.16832i	0.430256	−	0.178218i
$842$	16.1539	−	6.69119i	0.556702	−	0.230593i
$843$	−13.6686	+	11.4341i	−0.470771	+	0.393810i
$844$	1.15920	−	0.774551i	0.0399012	−	0.0266611i
$845$	−0.356469	−	1.79209i	−0.0122629	−	0.0616498i
$846$	9.91131	+	6.35651i	0.340758	+	0.218541i
$847$	−3.32876	−	2.22420i	−0.114377	−	0.0764246i
$848$	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
$853$	16.5745	−	24.8055i	0.567499	−	0.849323i	−0.431096	−	0.902306i	$-0.641873\pi$
$853$	16.5745	−	24.8055i	0.567499	−	0.849323i	0.998595	+	0.0529834i	$0.0168730\pi$
$854$	6.53464	−	6.53464i	0.223611	−	0.223611i
$855$	−1.13349	−	2.59738i	−0.0387646	−	0.0888286i
$856$	−2.26093	−	3.38372i	−0.0772770	−	0.115653i
$857$	33.3750	+	6.63871i	1.14007	+	0.226774i	0.728791	−	0.684736i	$-0.240082\pi$
$857$	33.3750	+	6.63871i	1.14007	+	0.226774i	0.411279	+	0.911510i	$0.365082\pi$
$858$	−0.928644	−	0.272203i	−0.0317034	−	0.00929284i
$859$	7.54327	+	18.2111i	0.257373	+	0.621354i	0.998763	−	0.0497206i	$-0.0158331\pi$
$859$	7.54327	+	18.2111i	0.257373	+	0.621354i	−0.741390	+	0.671074i	$0.765833\pi$
$860$	−0.0157612	+	0.0792371i	−0.000537454	+	0.00270196i
$861$	−1.19481	+	13.4224i	−0.0407189	+	0.457434i
$862$	−18.8354	+	3.74660i	−0.641538	+	0.127610i
$863$	−4.36492	−	4.36492i	−0.148584	−	0.148584i	0.628901	−	0.777485i	$-0.283505\pi$
$863$	−4.36492	−	4.36492i	−0.148584	−	0.148584i	−0.777485	+	0.628901i	$0.783505\pi$
$864$	−3.94132	−	6.89880i	−0.134086	−	0.234702i
$865$	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
$870$	0.377339	+	1.20312i	0.0127930	+	0.0407897i
$871$	−0.480203	−	0.480203i	−0.0162710	−	0.0162710i
$872$	−33.6240	+	6.68823i	−1.13865	+	0.226492i
$873$	−9.54633	+	9.91192i	−0.323094	+	0.335468i
$874$	10.8110	−	54.3507i	0.365689	−	1.83844i
$875$	0.950712	+	2.29522i	0.0321399	+	0.0775927i
$876$	0.592666	−	2.02194i	0.0200243	−	0.0683149i
$877$	9.35016	+	1.85986i	0.315732	+	0.0628031i	0.350413	−	0.936595i	$-0.386041\pi$
$877$	9.35016	+	1.85986i	0.315732	+	0.0628031i	−0.0346804	+	0.999398i	$0.511041\pi$
$878$	19.2494	+	28.8088i	0.649636	+	0.972248i
$879$	0.904859	−	1.73180i	0.0305201	−	0.0584123i
$880$	−1.22513	+	1.22513i	−0.0412992	+	0.0412992i
$881$	23.8975	−	35.7652i	0.805128	−	1.20496i	−0.170464	−	0.985364i	$-0.554527\pi$
$881$	23.8975	−	35.7652i	0.805128	−	1.20496i	0.975591	−	0.219595i	$-0.0704735\pi$
$882$	15.0205	+	2.69548i	0.505767	+	0.0907617i
$883$			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
$887$	12.3415	+	8.24630i	0.414386	+	0.276884i	0.745238	−	0.666799i	$-0.232336\pi$
$887$	12.3415	+	8.24630i	0.414386	+	0.276884i	−0.330852	+	0.943683i	$0.607336\pi$
$888$	1.91538	−	0.206831i	0.0642760	−	0.00694081i
$889$	−3.41322	−	17.1594i	−0.114476	−	0.575508i
$890$	−0.630135	+	0.421042i	−0.0211222	+	0.0141134i
$891$	31.8838	−	7.59737i	1.06815	−	0.254522i
$892$	−0.0475120	+	0.0196801i	−0.00159082	+	0.000658939i
$893$	−18.5214	+	7.67180i	−0.619794	+	0.256727i
$894$	32.4617	+	38.8056i	1.08568	+	1.29785i
$895$	−2.16276	+	1.44511i	−0.0722930	+	0.0483046i
$896$	−2.92429	−	14.7014i	−0.0976937	−	0.491139i
$897$	−0.136289	−	1.26212i	−0.00455057	−	0.0421410i
$898$	−1.15489	−	0.771672i	−0.0385391	−	0.0257510i
$899$	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
$904$	22.4865	−	33.6535i	0.747890	−	1.11930i
$905$	−0.211787	+	0.211787i	−0.00704002	+	0.00704002i
$906$	−8.32350	−	4.34899i	−0.276530	−	0.144485i
$907$	9.50457	+	14.2246i	0.315594	+	0.472320i	0.955024	−	0.296530i	$-0.0958294\pi$
$907$	9.50457	+	14.2246i	0.315594	+	0.472320i	−0.639429	+	0.768850i	$0.720829\pi$
$908$	−0.568889	−	0.113159i	−0.0188792	−	0.00375531i
$909$	12.4790	−	8.68165i	0.413902	−	0.287952i
$910$	−0.0146143	−	0.0352820i	−0.000484459	−	0.00116959i
$911$	10.7926	−	54.2580i	0.357574	−	1.79765i	−0.213712	−	0.976897i	$-0.568555\pi$
$911$	10.7926	−	54.2580i	0.357574	−	1.79765i	0.571286	−	0.820751i	$-0.306445\pi$
$912$	−39.1651	−	3.48631i	−1.29689	−	0.115443i
$913$	−19.7874	+	3.93596i	−0.654868	+	0.130261i
$914$	−19.9143	−	19.9143i	−0.658705	−	0.658705i
$915$	−0.924088	+	0.289825i	−0.0305494	+	0.00958132i
$916$	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
$921$	32.3617	−	10.1497i	1.06635	−	0.334445i
$922$	22.9019	+	22.9019i	0.754233	+	0.754233i
$923$	1.48769	−	0.295920i	0.0489679	−	0.00974032i
$924$	−3.02670	−	0.269424i	−0.0995711	−	0.00886341i
$925$	−0.361822	+	1.81900i	−0.0118966	+	0.0598085i
$926$	−9.70769	−	23.4364i	−0.319014	−	0.770169i
$927$	−39.3434	+	27.3712i	−1.29221	+	0.898989i
$928$	−5.90324	−	1.17423i	−0.193783	−	0.0385459i
$929$	−19.8977	−	29.7790i	−0.652822	−	0.977016i	−0.999242	−	0.0389370i	$-0.987603\pi$
$929$	−19.8977	−	29.7790i	−0.652822	−	0.977016i	0.346420	−	0.938079i	$-0.387397\pi$
$930$	−2.54209	−	1.32823i	−0.0833585	−	0.0435544i
$931$	−18.3724	+	18.3724i	−0.602132	+	0.602132i
$932$	1.48131	−	2.21694i	0.0485220	−	0.0726184i
$933$	−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	$-0.982143\pi$
$937$	−7.73785	+	18.6808i	−0.252785	+	0.610276i	0.745642	+	0.666347i	$0.232143\pi$
$938$	11.2502	+	7.51715i	0.367333	+	0.245444i
$939$	−3.31375	−	30.6873i	−0.108140	−	1.00144i
$940$	0.0223178	+	0.112199i	0.000727926	+	0.00365953i
$941$	−6.45567	+	4.31354i	−0.210449	+	0.140618i	−0.656328	−	0.754476i	$-0.727891\pi$
$941$	−6.45567	+	4.31354i	−0.210449	+	0.140618i	0.445879	+	0.895093i	$0.352891\pi$
$942$	−20.3916	−	24.3767i	−0.664394	−	0.794236i
$943$	25.5124	−	10.5676i	0.830798	−	0.344128i
$944$	29.8749	−	12.3746i	0.972347	−	0.402759i
$945$	1.02258	+	0.792064i	0.0332645	+	0.0257658i
$946$	−8.39318	+	5.60815i	−0.272886	+	0.182337i
$947$	−0.702897	−	3.53370i	−0.0228411	−	0.114830i	0.967683	−	0.252171i	$-0.0811444\pi$
$947$	−0.702897	−	3.53370i	−0.0228411	−	0.114830i	−0.990524	+	0.137341i	$0.956144\pi$
$948$	−1.14688	+	0.123845i	−0.0372489	+	0.00402231i
$949$	−0.433564	−	0.289698i	−0.0140741	−	0.00940400i
$950$	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	$-0.881046\pi$
$953$		−	22.5397i		−	0.730132i	0.930982	−	0.365066i	$-0.118954\pi$
$954$	24.8600	+	4.46121i	0.804871	+	0.144437i
$955$	−1.35536	+	2.02845i	−0.0438585	+	0.0656389i
$956$	4.31991	−	4.31991i	0.139716	−	0.139716i
$957$	11.4984	−	22.0067i	0.371690	−	0.711375i
$958$	16.5761	+	24.8079i	0.535550	+	0.801507i
$959$	5.56114	+	1.10618i	0.179578	+	0.0357204i
$960$	−0.601342	+	2.05153i	−0.0194082	+	0.0662129i
$961$	18.8174	+	45.4292i	0.607013	+	1.46546i
$962$	0.0111459	−	0.0560344i	0.000359360	−	0.00180662i
$963$	2.83558	−	2.94417i	0.0913751	−	0.0948744i
$964$	−0.108291	+	0.0215404i	−0.00348781	+	0.000693768i
$965$	−1.61537	−	1.61537i	−0.0520007	−	0.0520007i
$966$	7.56906	+	24.1335i	0.243531	+	0.776481i
$967$	−20.7527	−	8.59605i	−0.667362	−	0.276430i	0.0231709	−	0.999732i	$-0.492624\pi$
$967$	−20.7527	−	8.59605i	−0.667362	−	0.276430i	−0.690533	+	0.723301i	$0.742624\pi$
$968$	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	$0.810360\pi$
$972$	3.15107	−	2.84380i	0.101071	−	0.0912150i
$973$	6.37317	+	6.37317i	0.204314	+	0.204314i
$974$	−29.6319	+	5.89415i	−0.949468	+	0.188861i
$975$	0.0892676	−	1.00283i	0.00285885	−	0.0321162i
$976$	−2.62147	+	13.1790i	−0.0839113	+	0.421851i
$977$	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	$0.726259\pi$
$978$	−24.3690	−	7.14301i	−0.779235	−	0.228408i
$979$	14.6368	+	2.91144i	0.467795	+	0.0930502i
$980$	0.0823718	+	0.123278i	0.00263127	+	0.00393798i
$981$	−13.7729	−	31.5604i	−0.439735	−	1.00765i
$982$	18.9356	−	18.9356i	0.604261	−	0.604261i
$983$	−23.1813	+	34.6933i	−0.739370	+	1.10654i	0.250985	+	0.967991i	$0.419245\pi$
$983$	−23.1813	+	34.6933i	−0.739370	+	1.10654i	−0.990355	+	0.138554i	$0.955755\pi$
$984$	−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
$989$	−11.0102	−	7.35681i	−0.350105	−	0.233933i
$990$	−1.70083	−	1.09081i	−0.0540560	−	0.0346682i
$991$	1.97993	+	9.95379i	0.0628946	+	0.316193i	0.999407	−	0.0344428i	$-0.0109656\pi$
$991$	1.97993	+	9.95379i	0.0628946	+	0.316193i	−0.936512	+	0.350635i	$0.885966\pi$
$992$	11.3838	−	7.60639i	0.361435	−	0.241503i
$993$	−9.60918	+	8.03828i	−0.304938	+	0.255087i
$994$	−27.9208	+	11.5652i	−0.885595	+	0.366826i
$995$	−1.66382	+	0.689176i	−0.0527466	+	0.0218483i
$996$	−2.00398	+	1.67637i	−0.0634986	+	0.0531179i
$997$	33.1970	−	22.1815i	1.05136	−	0.702496i	0.0952350	−	0.995455i	$-0.469640\pi$
$997$	33.1970	−	22.1815i	1.05136	−	0.702496i	0.956125	+	0.292958i	$0.0946398\pi$
$998$	−0.276730	−	1.39122i	−0.00875974	−	0.0440382i
$999$	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.i.653.3		32
3.2	odd	2	inner	867.2.i.i.653.2		32
17.2	even	8		867.2.i.h.827.2		32
17.3	odd	16		867.2.i.f.131.3		32
17.4	even	4		867.2.i.g.503.2		32
17.5	odd	16	inner	867.2.i.i.158.2		32
17.6	odd	16		51.2.i.a.14.3	yes	32
17.7	odd	16		867.2.i.d.224.2		32
17.8	even	8		867.2.i.d.329.3		32
17.9	even	8		867.2.i.c.329.3		32
17.10	odd	16		867.2.i.c.224.2		32
17.11	odd	16		867.2.i.h.65.3		32
17.12	odd	16		867.2.i.b.158.2		32
17.13	even	4		867.2.i.f.503.2		32
17.14	odd	16		867.2.i.g.131.3		32
17.15	even	8		51.2.i.a.11.2	✓	32
17.16	even	2		867.2.i.b.653.3		32
51.2	odd	8		867.2.i.h.827.3		32
51.5	even	16	inner	867.2.i.i.158.3		32
51.8	odd	8		867.2.i.d.329.2		32
51.11	even	16		867.2.i.h.65.2		32
51.14	even	16		867.2.i.g.131.2		32
51.20	even	16		867.2.i.f.131.2		32
51.23	even	16		51.2.i.a.14.2	yes	32
51.26	odd	8		867.2.i.c.329.2		32
51.29	even	16		867.2.i.b.158.3		32
51.32	odd	8		51.2.i.a.11.3	yes	32
51.38	odd	4		867.2.i.g.503.3		32
51.41	even	16		867.2.i.d.224.3		32
51.44	even	16		867.2.i.c.224.3		32
51.47	odd	4		867.2.i.f.503.3		32
51.50	odd	2		867.2.i.b.653.2		32
68.15	odd	8		816.2.cj.c.113.1		32
68.23	even	16		816.2.cj.c.65.4		32
204.23	odd	16		816.2.cj.c.65.1		32
204.83	even	8		816.2.cj.c.113.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	17.15	even	8
51.2.i.a.11.3	yes	32	51.32	odd	8
51.2.i.a.14.2	yes	32	51.23	even	16
51.2.i.a.14.3	yes	32	17.6	odd	16
816.2.cj.c.65.1		32	204.23	odd	16
816.2.cj.c.65.4		32	68.23	even	16
816.2.cj.c.113.1		32	68.15	odd	8
816.2.cj.c.113.4		32	204.83	even	8
867.2.i.b.158.2		32	17.12	odd	16
867.2.i.b.158.3		32	51.29	even	16
867.2.i.b.653.2		32	51.50	odd	2
867.2.i.b.653.3		32	17.16	even	2
867.2.i.c.224.2		32	17.10	odd	16
867.2.i.c.224.3		32	51.44	even	16
867.2.i.c.329.2		32	51.26	odd	8
867.2.i.c.329.3		32	17.9	even	8
867.2.i.d.224.2		32	17.7	odd	16
867.2.i.d.224.3		32	51.41	even	16
867.2.i.d.329.2		32	51.8	odd	8
867.2.i.d.329.3		32	17.8	even	8
867.2.i.f.131.2		32	51.20	even	16
867.2.i.f.131.3		32	17.3	odd	16
867.2.i.f.503.2		32	17.13	even	4
867.2.i.f.503.3		32	51.47	odd	4
867.2.i.g.131.2		32	51.14	even	16
867.2.i.g.131.3		32	17.14	odd	16
867.2.i.g.503.2		32	17.4	even	4
867.2.i.g.503.3		32	51.38	odd	4
867.2.i.h.65.2		32	51.11	even	16
867.2.i.h.65.3		32	17.11	odd	16
867.2.i.h.827.2		32	17.2	even	8
867.2.i.h.827.3		32	51.2	odd	8
867.2.i.i.158.2		32	17.5	odd	16	inner
867.2.i.i.158.3		32	51.5	even	16	inner
867.2.i.i.653.2		32	3.2	odd	2	inner
867.2.i.i.653.3		32	1.1	even	1	trivial

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} +(-1.65267 + 0.518334i) q^{3} +(-0.192538 - 0.192538i) q^{4} +(-0.137998 + 0.0274494i) q^{5} +(-2.26768 - 0.201860i) q^{6} +(-0.345150 + 1.73519i) q^{7} +(-1.14298 - 2.75940i) q^{8} +(2.46266 - 1.71327i) q^{9} +(-0.181387 - 0.0360802i) q^{10} +(2.02329 + 3.02807i) q^{11} +(0.418001 + 0.218403i) q^{12} +(0.0825311 - 0.0825311i) q^{13} +(-1.29195 + 1.93354i) q^{14} +(0.213837 - 0.116894i) q^{15} -3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(-2.56928 + 6.20278i) q^{19} +(0.0318548 + 0.0212847i) q^{20} +(-0.328986 - 3.04660i) q^{21} +(0.933878 + 4.69492i) q^{22} +(-5.22121 + 3.48870i) q^{23} +(3.31926 + 3.96794i) q^{24} +(-4.60111 + 1.90584i) q^{25} +(0.141737 - 0.0587094i) q^{26} +(-3.18193 + 4.10796i) q^{27} +(0.400544 - 0.267635i) q^{28} +(0.767936 + 3.86068i) q^{29} +(0.318476 - 0.0343905i) q^{30} +(-7.44489 - 4.97452i) q^{31} +(-0.585150 + 1.41268i) q^{32} +(-4.91339 - 3.95567i) q^{33} -0.248926i q^{35} +(-0.804026 - 0.144285i) q^{36} +(0.206896 - 0.309641i) q^{37} +(-6.24010 + 6.24010i) q^{38} +(-0.0936183 + 0.179176i) q^{39} +(0.233473 + 0.349416i) q^{40} +(-4.31306 - 0.857920i) q^{41} +(1.13296 - 3.86518i) q^{42} +(0.806985 + 1.94823i) q^{43} +(0.193458 - 0.972578i) q^{44} +(-0.292813 + 0.304026i) q^{45} +(-8.09532 + 1.61026i) q^{46} +(2.11141 + 2.11141i) q^{47} +(1.75263 + 5.58815i) q^{48} +(3.57541 + 1.48098i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(5.91755 + 2.45113i) q^{53} +(-5.93037 + 3.38805i) q^{54} +(-0.362328 - 0.362328i) q^{55} +(5.18257 - 1.03088i) q^{56} +(1.03106 - 11.5829i) q^{57} +(-1.00939 + 5.07456i) q^{58} +(3.65974 + 8.83540i) q^{59} +(-0.0636782 - 0.0186653i) q^{60} +(-3.89765 - 0.775290i) q^{61} +(-6.53863 - 9.78574i) q^{62} +(2.12286 + 4.86451i) q^{63} +(-6.20303 + 6.20303i) q^{64} +(-0.00912367 + 0.0136545i) q^{65} +(-3.97693 - 7.27511i) q^{66} -5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(0.125212 - 0.302288i) q^{70} +(10.8057 + 7.22012i) q^{71} +(-7.54238 - 4.83722i) q^{72} +(-0.871585 - 4.38175i) q^{73} +(0.407000 - 0.271949i) q^{74} +(6.61627 - 5.53464i) q^{75} +(1.68895 - 0.699588i) q^{76} +(-5.95260 + 2.46565i) q^{77} +(-0.203814 + 0.170495i) q^{78} +(-2.03371 + 1.35888i) q^{79} +(0.0928142 + 0.466609i) q^{80} +(3.12939 - 8.43842i) q^{81} +(-4.80610 - 3.21133i) q^{82} +(-2.12000 + 5.11813i) q^{83} +(-0.523244 + 0.649928i) q^{84} +2.77180i q^{86} +(-3.27027 - 5.98239i) q^{87} +(6.04306 - 9.04408i) q^{88} +(2.89760 - 2.89760i) q^{89} +(-0.508511 + 0.221913i) q^{90} +(0.114721 + 0.171693i) q^{91} +(1.67699 + 0.333574i) q^{92} +(14.8824 + 4.36231i) q^{93} +(1.50197 + 3.62608i) q^{94} +(0.184291 - 0.926494i) q^{95} +(0.234823 - 2.63800i) q^{96} +(-4.49902 + 0.894911i) q^{97} +(3.59692 + 3.59692i) q^{98} +(10.1706 + 3.99065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 16 q^{4} - 16 q^{6} - 24 q^{9} + 32 q^{10} + 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} + 16 q^{24} - 16 q^{27} + 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 + 16 * q^4 - 16 * q^6 - 24 * q^9 + 32 * q^10 + 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 + 16 * q^24 - 16 * q^27 + 32 * q^28 + 8 * q^30 + 24 * q^36 - 96 * q^37 + 48 * q^39 + 80 * q^40 + 24 * q^42 + 32 * q^43 - 40 * q^45 - 64 * q^46 + 48 * q^48 + 64 * q^49 - 96 * q^52 + 48 * q^54 + 48 * q^55 - 8 * q^57 - 48 * q^60 - 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 - 144 * q^73 + 8 * q^75 - 32 * q^76 - 40 * q^78 + 64 * q^79 - 48 * q^81 - 32 * q^82 + 56 * q^87 + 32 * q^88 + 24 * q^90 + 48 * q^91 + 56 * q^93 + 48 * q^94 - 72 * q^96 - 32 * q^97 - 16 * q^99

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