LMFDB - Embedded newform 1000.2.o.a.949.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(149,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			949.11
Character	$\chi$	$=$	1000.949
Dual form			1000.2.o.a.549.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.345564 + 1.37134i) q^{2} +(-0.615546 + 1.89446i) q^{3} +(-1.76117 - 0.947775i) q^{4} +(-2.38524 - 1.49878i) q^{6} -1.38088i q^{7} +(1.90832 - 2.08765i) q^{8} +(-0.783019 - 0.568896i) q^{9} +(3.04233 + 4.18740i) q^{11} +(2.87960 - 2.75306i) q^{12} +(2.49716 + 1.81429i) q^{13} +(1.89366 + 0.477183i) q^{14} +(2.20344 + 3.33839i) q^{16} +(3.63061 - 1.17966i) q^{17} +(1.05074 - 0.877198i) q^{18} +(6.09071 - 1.97899i) q^{19} +(2.61602 + 0.849997i) q^{21} +(-6.79369 + 2.72506i) q^{22} +(0.168832 + 0.232378i) q^{23} +(2.78031 + 4.90029i) q^{24} +(-3.35095 + 2.79751i) q^{26} +(-3.27483 + 2.37930i) q^{27} +(-1.30877 + 2.43197i) q^{28} +(-8.75018 - 2.84311i) q^{29} +(1.38826 + 4.27263i) q^{31} +(-5.33951 + 1.86805i) q^{32} +(-9.80555 + 3.18602i) q^{33} +(0.363107 + 5.38647i) q^{34} +(0.839843 + 1.74405i) q^{36} +(-4.07603 - 2.96141i) q^{37} +(0.609147 + 9.03633i) q^{38} +(-4.97421 + 3.61398i) q^{39} +(3.28522 + 2.38685i) q^{41} +(-2.06964 + 3.29374i) q^{42} +7.54302 q^{43} +(-1.38934 - 10.2582i) q^{44} +(-0.377013 + 0.151226i) q^{46} +(-0.954360 - 0.310090i) q^{47} +(-7.68075 + 2.11940i) q^{48} +5.09317 q^{49} +7.60418i q^{51} +(-2.67838 - 5.56202i) q^{52} +(-1.02485 + 3.15418i) q^{53} +(-2.13118 - 5.31312i) q^{54} +(-2.88280 - 2.63517i) q^{56} +12.7567i q^{57} +(6.92263 - 11.0170i) q^{58} +(-1.05228 + 1.44834i) q^{59} +(-1.30861 - 1.80115i) q^{61} +(-6.33899 + 0.427317i) q^{62} +(-0.785578 + 1.08126i) q^{63} +(-0.716599 - 7.96784i) q^{64} +(-0.980677 - 14.5478i) q^{66} +(-0.552275 - 1.69973i) q^{67} +(-7.51218 - 1.36343i) q^{68} +(-0.544154 + 0.176806i) q^{69} +(-4.68658 + 14.4238i) q^{71} +(-2.68191 + 0.549033i) q^{72} +(-6.88021 - 9.46979i) q^{73} +(5.46964 - 4.56628i) q^{74} +(-12.6024 - 2.28728i) q^{76} +(5.78231 - 4.20109i) q^{77} +(-3.23710 - 8.07022i) q^{78} +(-0.381800 + 1.17506i) q^{79} +(-3.38894 - 10.4301i) q^{81} +(-4.40845 + 3.68036i) q^{82} +(1.29836 + 3.99593i) q^{83} +(-3.80165 - 3.97639i) q^{84} +(-2.60660 + 10.3441i) q^{86} +(10.7723 - 14.8268i) q^{87} +(14.5476 + 1.63960i) q^{88} +(-9.13763 + 6.63888i) q^{89} +(2.50532 - 3.44828i) q^{91} +(-0.0771007 - 0.569272i) q^{92} -8.94886 q^{93} +(0.755034 - 1.20160i) q^{94} +(-0.252228 - 11.2653i) q^{96} +(4.65397 + 1.51217i) q^{97} +(-1.76002 + 6.98448i) q^{98} -5.00958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.345564	+	1.37134i	−0.244351	+	0.969687i
$2$	−0.345564	+	1.37134i	−0.244351	+	0.969687i
$3$	−0.615546	+	1.89446i	−0.355386	+	1.09377i	0.600400	+	0.799700i	$0.295008\pi$
$3$	−0.615546	+	1.89446i	−0.355386	+	1.09377i	−0.955785	+	0.294065i	$0.904992\pi$
$4$	−1.76117	−	0.947775i	−0.880585	−	0.473888i
$5$		0			0
$5$		0			0
$6$	−2.38524	−	1.49878i	−0.973771	−	0.611875i
$7$		−	1.38088i		−	0.521924i	−0.965349	−	0.260962i	$-0.915960\pi$
$7$		−	1.38088i		−	0.521924i	0.965349	−	0.260962i	$-0.0840398\pi$
$8$	1.90832	−	2.08765i	0.674694	−	0.738097i
$9$	−0.783019	−	0.568896i	−0.261006	−	0.189632i
$10$		0			0
$11$	3.04233	+	4.18740i	0.917296	+	1.26255i	0.964613	+	0.263670i	$0.0849330\pi$
$11$	3.04233	+	4.18740i	0.917296	+	1.26255i	−0.0473169	+	0.998880i	$0.515067\pi$
$12$	2.87960	−	2.75306i	0.831269	−	0.794741i
$13$	2.49716	+	1.81429i	0.692587	+	0.503194i	0.877510	−	0.479559i	$-0.159203\pi$
$13$	2.49716	+	1.81429i	0.692587	+	0.503194i	−0.184923	+	0.982753i	$0.559203\pi$
$14$	1.89366	+	0.477183i	0.506103	+	0.127533i
$15$		0			0
$16$	2.20344	+	3.33839i	0.550861	+	0.834597i
$17$	3.63061	−	1.17966i	0.880553	−	0.286109i	0.166366	−	0.986064i	$-0.446797\pi$
$17$	3.63061	−	1.17966i	0.880553	−	0.286109i	0.714187	+	0.699955i	$0.246797\pi$
$18$	1.05074	−	0.877198i	0.247661	−	0.206758i
$19$	6.09071	−	1.97899i	1.39730	−	0.454012i	0.488986	−	0.872292i	$-0.337367\pi$
$19$	6.09071	−	1.97899i	1.39730	−	0.454012i	0.908318	+	0.418280i	$0.137367\pi$
$20$		0			0
$21$	2.61602	+	0.849997i	0.570863	+	0.185484i
$22$	−6.79369	+	2.72506i	−1.44842	+	0.580985i
$23$	0.168832	+	0.232378i	0.0352040	+	0.0484541i	0.826256	−	0.563295i	$-0.190466\pi$
$23$	0.168832	+	0.232378i	0.0352040	+	0.0484541i	−0.791052	+	0.611749i	$0.790466\pi$
$24$	2.78031	+	4.90029i	0.567528	+	1.00027i
$25$		0			0
$26$	−3.35095	+	2.79751i	−0.657175	+	0.548637i
$27$	−3.27483	+	2.37930i	−0.630241	+	0.457897i
$28$	−1.30877	+	2.43197i	−0.247333	+	0.459599i
$29$	−8.75018	−	2.84311i	−1.62487	−	0.527952i	−0.651785	−	0.758404i	$-0.725979\pi$
$29$	−8.75018	−	2.84311i	−1.62487	−	0.527952i	−0.973084	+	0.230452i	$0.925979\pi$
$30$		0			0
$31$	1.38826	+	4.27263i	0.249339	+	0.767388i	0.994892	+	0.100941i	$0.0321855\pi$
$31$	1.38826	+	4.27263i	0.249339	+	0.767388i	−0.745553	+	0.666446i	$0.767815\pi$
$32$	−5.33951	+	1.86805i	−0.943901	+	0.330228i
$33$	−9.80555	+	3.18602i	−1.70693	+	0.554614i
$34$	0.363107	+	5.38647i	0.0622723	+	0.923772i
$35$		0			0
$36$	0.839843	+	1.74405i	0.139974	+	0.290675i
$37$	−4.07603	−	2.96141i	−0.670095	−	0.486853i	0.199962	−	0.979804i	$-0.435918\pi$
$37$	−4.07603	−	2.96141i	−0.670095	−	0.486853i	−0.870057	+	0.492951i	$0.835918\pi$
$38$	0.609147	+	9.03633i	0.0988166	+	1.46589i
$39$	−4.97421	+	3.61398i	−0.796512	+	0.578700i
$40$		0			0
$41$	3.28522	+	2.38685i	0.513065	+	0.372764i	0.813985	−	0.580886i	$-0.197294\pi$
$41$	3.28522	+	2.38685i	0.513065	+	0.372764i	−0.300920	+	0.953649i	$0.597294\pi$
$42$	−2.06964	+	3.29374i	−0.319353	+	0.508235i
$43$	7.54302			1.15030			0.575150	−	0.818048i	$-0.304944\pi$
$43$	7.54302			1.15030			0.575150	+	0.818048i	$0.304944\pi$
$44$	−1.38934	−	10.2582i	−0.209451	−	1.54648i
$45$		0			0
$46$	−0.377013	+	0.151226i	−0.0555875	+	0.0222970i
$47$	−0.954360	−	0.310090i	−0.139208	−	0.0452313i	0.238584	−	0.971122i	$-0.423317\pi$
$47$	−0.954360	−	0.310090i	−0.139208	−	0.0452313i	−0.377792	+	0.925890i	$0.623317\pi$
$48$	−7.68075	+	2.11940i	−1.10862	+	0.305909i
$49$	5.09317			0.727595
$50$		0			0
$51$			7.60418i			1.06480i
$52$	−2.67838	−	5.56202i	−0.371425	−	0.771314i
$53$	−1.02485	+	3.15418i	−0.140775	+	0.433260i	−0.996443	−	0.0842641i	$-0.973146\pi$
$53$	−1.02485	+	3.15418i	−0.140775	+	0.433260i	0.855669	+	0.517524i	$0.173146\pi$
$54$	−2.13118	−	5.31312i	−0.290017	−	0.723024i
$55$		0			0
$56$	−2.88280	−	2.63517i	−0.385231	−	0.352139i
$57$			12.7567i			1.68967i
$58$	6.92263	−	11.0170i	0.908986	−	1.44661i
$59$	−1.05228	+	1.44834i	−0.136996	+	0.188558i	−0.872003	−	0.489501i	$-0.837179\pi$
$59$	−1.05228	+	1.44834i	−0.136996	+	0.188558i	0.735007	+	0.678060i	$0.237179\pi$
$60$		0			0
$61$	−1.30861	−	1.80115i	−0.167550	−	0.230613i	0.716983	−	0.697091i	$-0.245523\pi$
$61$	−1.30861	−	1.80115i	−0.167550	−	0.230613i	−0.884533	+	0.466478i	$0.845523\pi$
$62$	−6.33899	+	0.427317i	−0.805052	+	0.0542693i
$63$	−0.785578	+	1.08126i	−0.0989736	+	0.136225i
$64$	−0.716599	−	7.96784i	−0.0895748	−	0.995980i
$65$		0			0
$66$	−0.980677	−	14.5478i	−0.120713	−	1.79071i
$67$	−0.552275	−	1.69973i	−0.0674711	−	0.207655i	0.911637	−	0.410997i	$-0.134819\pi$
$67$	−0.552275	−	1.69973i	−0.0674711	−	0.207655i	−0.979108	+	0.203343i	$0.934819\pi$
$68$	−7.51218	−	1.36343i	−0.910986	−	0.165340i
$69$	−0.544154	+	0.176806i	−0.0655085	+	0.0212850i
$70$		0			0
$71$	−4.68658	+	14.4238i	−0.556194	+	1.71179i	0.136574	+	0.990630i	$0.456391\pi$
$71$	−4.68658	+	14.4238i	−0.556194	+	1.71179i	−0.692768	+	0.721161i	$0.743609\pi$
$72$	−2.68191	+	0.549033i	−0.316066	+	0.0647042i
$73$	−6.88021	−	9.46979i	−0.805267	−	1.10836i	−0.992036	−	0.125951i	$-0.959802\pi$
$73$	−6.88021	−	9.46979i	−0.805267	−	1.10836i	0.186769	−	0.982404i	$-0.440198\pi$
$74$	5.46964	−	4.56628i	0.635833	−	0.530820i
$75$		0			0
$76$	−12.6024	−	2.28728i	−1.44560	−	0.262369i
$77$	5.78231	−	4.20109i	0.658955	−	0.478759i
$78$	−3.23710	−	8.07022i	−0.366529	−	0.913773i
$79$	−0.381800	+	1.17506i	−0.0429559	+	0.132205i	−0.970234	−	0.242167i	$-0.922142\pi$
$79$	−0.381800	+	1.17506i	−0.0429559	+	0.132205i	0.927279	+	0.374372i	$0.122142\pi$
$80$		0			0
$81$	−3.38894	−	10.4301i	−0.376549	−	1.15890i
$82$	−4.40845	+	3.68036i	−0.486832	+	0.406428i
$83$	1.29836	+	3.99593i	0.142513	+	0.438610i	0.996683	−	0.0813841i	$-0.0259341\pi$
$83$	1.29836	+	3.99593i	0.142513	+	0.438610i	−0.854170	+	0.519994i	$0.825934\pi$
$84$	−3.80165	−	3.97639i	−0.414794	−	0.433860i
$85$		0			0
$86$	−2.60660	+	10.3441i	−0.281077	+	1.11543i
$87$	10.7723	−	14.8268i	1.15491	−	1.58960i
$88$	14.5476	+	1.63960i	1.55078	+	0.174782i
$89$	−9.13763	+	6.63888i	−0.968587	+	0.703720i	−0.955129	−	0.296190i	$-0.904284\pi$
$89$	−9.13763	+	6.63888i	−0.968587	+	0.703720i	−0.0134580	+	0.999909i	$0.504284\pi$
$90$		0			0
$91$	2.50532	−	3.44828i	0.262629	−	0.361478i
$92$	−0.0771007	−	0.569272i	−0.00803830	−	0.0593508i
$93$	−8.94886			−0.927954
$94$	0.755034	−	1.20160i	0.0778758	−	0.123936i
$95$		0			0
$96$	−0.252228	−	11.2653i	−0.0257429	−	1.14976i
$97$	4.65397	+	1.51217i	0.472539	+	0.153537i	0.535599	−	0.844473i	$-0.320086\pi$
$97$	4.65397	+	1.51217i	0.472539	+	0.153537i	−0.0630600	+	0.998010i	$0.520086\pi$
$98$	−1.76002	+	6.98448i	−0.177788	+	0.705539i
$99$		−	5.00958i		−	0.503482i
$100$		0			0
$101$		−	16.5698i		−	1.64876i	−0.566039	−	0.824378i	$-0.691525\pi$
$101$		−	16.5698i		−	1.64876i	0.566039	−	0.824378i	$-0.308475\pi$
$102$	−10.4279	−	2.62773i	−1.03252	−	0.260184i
$103$	3.86872	+	1.25702i	0.381196	+	0.123858i	0.493346	−	0.869833i	$-0.335774\pi$
$103$	3.86872	+	1.25702i	0.381196	+	0.123858i	−0.112150	+	0.993691i	$0.535774\pi$
$104$	8.55300	−	1.75095i	0.838691	−	0.171694i
$105$		0			0
$106$	−3.97131	−	2.49540i	−0.385728	−	0.242375i
$107$	13.5206			1.30709			0.653545	−	0.756888i	$-0.273281\pi$
$107$	13.5206			1.30709			0.653545	+	0.756888i	$0.273281\pi$
$108$	8.02258	−	1.08656i	0.771973	−	0.104554i
$109$	−5.89818	+	8.11815i	−0.564944	+	0.777578i	−0.991945	−	0.126673i	$-0.959570\pi$
$109$	−5.89818	+	8.11815i	−0.564944	+	0.777578i	0.427001	+	0.904251i	$0.359570\pi$
$110$		0			0
$111$	8.11925	−	5.89898i	0.770645	−	0.559906i
$112$	4.60992	−	3.04270i	0.435596	−	0.287508i
$113$	−5.59149	+	7.69603i	−0.526004	+	0.723982i	−0.986515	−	0.163672i	$-0.947666\pi$
$113$	−5.59149	+	7.69603i	−0.526004	+	0.723982i	0.460511	+	0.887654i	$0.347666\pi$
$114$	−17.4939	−	4.40828i	−1.63845	−	0.412873i
$115$		0			0
$116$	12.7159	+	13.3004i	1.18065	+	1.23491i
$117$	−0.923177	−	2.84125i	−0.0853478	−	0.262673i
$118$	−1.62255	−	1.94354i	−0.149367	−	0.178917i
$119$	−1.62897	−	5.01345i	−0.149327	−	0.459582i
$120$		0			0
$121$	−4.87941	+	15.0173i	−0.443583	+	1.36521i
$122$	2.92220	−	1.17214i	0.264564	−	0.106121i
$123$	−6.54400	+	4.75449i	−0.590052	+	0.428698i
$124$	1.60453	−	8.84060i	0.144091	−	0.793909i
$125$		0			0
$126$	−1.21131	−	1.45094i	−0.107912	−	0.129260i
$127$	4.92287	+	6.77575i	0.436834	+	0.601251i	0.969505	−	0.245072i	$-0.0788116\pi$
$127$	4.92287	+	6.77575i	0.436834	+	0.601251i	−0.532671	+	0.846323i	$0.678812\pi$
$128$	11.1743	+	1.77070i	0.987677	+	0.156509i
$129$	−4.64308	+	14.2899i	−0.408800	+	1.25816i
$130$		0			0
$131$	−8.61583	+	2.79945i	−0.752769	+	0.244589i	−0.660172	−	0.751114i	$-0.729517\pi$
$131$	−8.61583	+	2.79945i	−0.752769	+	0.244589i	−0.0925967	+	0.995704i	$0.529517\pi$
$132$	20.2889	+	3.68234i	1.76592	+	0.320507i
$133$	−2.73275	−	8.41055i	−0.236960	−	0.729287i
$134$	2.52176	−	0.169994i	0.217847	−	0.0146852i
$135$		0			0
$136$	4.46567	−	9.83064i	0.382928	−	0.842970i
$137$	0.409034	−	0.562988i	0.0349462	−	0.0480993i	−0.791186	−	0.611575i	$-0.790536\pi$
$137$	0.409034	−	0.562988i	0.0349462	−	0.0480993i	0.826133	+	0.563476i	$0.190536\pi$
$138$	−0.0544222	−	0.807321i	−0.00463273	−	0.0687237i
$139$	6.25490	+	8.60913i	0.530533	+	0.730217i	0.987212	−	0.159415i	$-0.0509609\pi$
$139$	6.25490	+	8.60913i	0.530533	+	0.730217i	−0.456678	+	0.889632i	$0.650961\pi$
$140$		0			0
$141$	1.17491	−	1.61712i	0.0989449	−	0.136186i
$142$	−18.1605	−	11.4113i	−1.52399	−	0.957612i
$143$			15.9763i			1.33600i
$144$	0.173859	−	3.86755i	0.0144883	−	0.322296i
$145$		0			0
$146$	15.3639	−	6.16271i	1.27153	−	0.510029i
$147$	−3.13508	+	9.64878i	−0.258577	+	0.795818i
$148$	4.37183	+	9.07871i	0.359363	+	0.746265i
$149$			3.22211i			0.263966i	0.991252	+	0.131983i	$0.0421344\pi$
$149$			3.22211i			0.263966i	−0.991252	+	0.131983i	$0.957866\pi$
$150$		0			0
$151$	20.1976			1.64366			0.821828	−	0.569736i	$-0.192955\pi$
$151$	20.1976			1.64366			0.821828	+	0.569736i	$0.192955\pi$
$152$	7.49160	−	16.4918i	0.607649	−	1.33767i
$153$	−3.51394	−	1.14175i	−0.284085	−	0.0923049i
$154$	3.76299	+	9.38129i	0.303230	+	0.755966i
$155$		0			0
$156$	12.1857	−	1.65039i	0.975635	−	0.132137i
$157$	−21.3717			−1.70565			−0.852824	−	0.522198i	$-0.825112\pi$
$157$	−21.3717			−1.70565			−0.852824	+	0.522198i	$0.825112\pi$
$158$	−1.47948	−	0.929638i	−0.117701	−	0.0739581i
$159$	−5.34461	−	3.88309i	−0.423855	−	0.307949i
$160$		0			0
$161$	0.320886	−	0.233138i	0.0252894	−	0.0183738i
$162$	15.4743	−	1.04314i	1.21578	−	0.0819566i
$163$	−10.2617	−	7.45556i	−0.803759	−	0.583965i	0.108256	−	0.994123i	$-0.465473\pi$
$163$	−10.2617	−	7.45556i	−0.803759	−	0.583965i	−0.912014	+	0.410158i	$0.865473\pi$
$164$	−3.52363	−	7.31731i	−0.275150	−	0.571386i
$165$		0			0
$166$	−5.92846	+	0.399643i	−0.460138	+	0.0310183i
$167$	−8.75032	+	2.84315i	−0.677120	+	0.220010i	−0.627334	−	0.778750i	$-0.715854\pi$
$167$	−8.75032	+	2.84315i	−0.677120	+	0.220010i	−0.0497860	+	0.998760i	$0.515854\pi$
$168$	6.76671	−	3.83928i	0.522063	−	0.296207i
$169$	−1.07308	−	3.30259i	−0.0825444	−	0.254045i
$170$		0			0
$171$	−5.89498	−	1.91539i	−0.450800	−	0.146474i
$172$	−13.2845	−	7.14909i	−1.01294	−	0.545113i
$173$	15.7758	−	11.4618i	1.19941	−	0.871423i	0.205184	−	0.978723i	$-0.434221\pi$
$173$	15.7758	−	11.4618i	1.19941	−	0.871423i	0.994227	+	0.107301i	$0.0342208\pi$
$174$	16.6101	+	19.8961i	1.25921	+	1.50832i
$175$		0			0
$176$	−7.27558	+	19.3832i	−0.548418	+	1.46106i
$177$	−2.09609	−	2.88503i	−0.157552	−	0.216852i
$178$	−5.94655	−	14.8250i	−0.445713	−	1.11118i
$179$	−3.15544	−	1.02527i	−0.235849	−	0.0766320i	0.188708	−	0.982033i	$-0.439570\pi$
$179$	−3.15544	−	1.02527i	−0.235849	−	0.0766320i	−0.424557	+	0.905401i	$0.639570\pi$
$180$		0			0
$181$	4.68953	−	1.52372i	0.348570	−	0.113257i	−0.129499	−	0.991580i	$-0.541337\pi$
$181$	4.68953	−	1.52372i	0.348570	−	0.113257i	0.478069	+	0.878322i	$0.341337\pi$
$182$	3.86303	+	4.62726i	0.286347	+	0.342995i
$183$	4.21771	−	1.37042i	0.311782	−	0.101304i
$184$	0.807312	+	0.0909887i	0.0595158	+	0.00670777i
$185$		0			0
$186$	3.09241	−	12.2720i	0.226746	−	0.899825i
$187$	15.9852	+	11.6139i	1.16896	+	0.849296i
$188$	1.38690	+	1.45064i	0.101150	+	0.105799i
$189$	3.28554	+	4.52215i	0.238988	+	0.328938i
$190$		0			0
$191$	−0.543712	−	0.395030i	−0.0393416	−	0.0285833i	0.567941	−	0.823069i	$-0.307740\pi$
$191$	−0.543712	−	0.395030i	−0.0393416	−	0.0285833i	−0.607282	+	0.794486i	$0.707740\pi$
$192$	15.5358	+	3.54701i	1.12120	+	0.255983i
$193$			4.75497i			0.342270i	0.985248	+	0.171135i	$0.0547434\pi$
$193$			4.75497i			0.342270i	−0.985248	+	0.171135i	$0.945257\pi$
$194$	−3.68194	+	5.85964i	−0.264348	+	0.420698i
$195$		0			0
$196$	−8.96993	−	4.82718i	−0.640710	−	0.344798i
$197$	−1.73569	+	5.34192i	−0.123663	+	0.380596i	−0.993655	−	0.112470i	$-0.964124\pi$
$197$	−1.73569	+	5.34192i	−0.123663	+	0.380596i	0.869992	+	0.493066i	$0.164124\pi$
$198$	6.86986	+	1.73113i	0.488220	+	0.123026i
$199$	3.56353			0.252612			0.126306	−	0.991991i	$-0.459688\pi$
$199$	3.56353			0.252612			0.126306	+	0.991991i	$0.459688\pi$
$200$		0			0
$201$	3.56001			0.251104
$202$	22.7229	+	5.72593i	1.59878	+	0.402875i
$203$	−3.92599	+	12.0830i	−0.275551	+	0.848058i
$204$	7.20705	−	13.3923i	0.504595	−	0.937645i
$205$		0			0
$206$	−3.06070	+	4.87096i	−0.213249	+	0.339376i
$207$		−	0.278004i		−	0.0193226i
$208$	−0.554462	+	12.3342i	−0.0384450	+	0.855221i
$209$	26.8168	+	19.4835i	1.85495	+	1.34770i
$210$		0			0
$211$	−16.5725	−	22.8101i	−1.14090	−	1.57031i	−0.765487	−	0.643452i	$-0.777502\pi$
$211$	−16.5725	−	22.8101i	−1.14090	−	1.57031i	−0.375411	−	0.926859i	$-0.622498\pi$
$212$	4.79440	−	4.58371i	0.329280	−	0.314811i
$213$	−24.4405	−	17.7570i	−1.67463	−	1.21669i
$214$	−4.67225	+	18.5415i	−0.319389	+	1.26747i
$215$		0			0
$216$	−1.28227	+	11.3772i	−0.0872478	+	0.774120i
$217$	5.90000	−	1.91703i	0.400518	−	0.130136i
$218$	−9.09458	−	10.8938i	−0.615963	−	0.737820i
$219$	22.1752	−	7.20516i	1.49846	−	0.486879i
$220$		0			0
$221$	11.2065	+	3.64120i	0.753828	+	0.244934i
$222$	5.28381	+	13.1728i	0.354626	+	0.884098i
$223$	−9.72513	−	13.3855i	−0.651243	−	0.896359i	0.347909	−	0.937528i	$-0.386892\pi$
$223$	−9.72513	−	13.3855i	−0.651243	−	0.896359i	−0.999152	+	0.0411689i	$0.986892\pi$
$224$	2.57956	+	7.37323i	0.172354	+	0.492645i
$225$		0			0
$226$	−8.62169	−	10.3273i	−0.573506	−	0.686964i
$227$	9.97209	−	7.24515i	0.661871	−	0.480878i	−0.205423	−	0.978673i	$-0.565857\pi$
$227$	9.97209	−	7.24515i	0.661871	−	0.480878i	0.867294	+	0.497796i	$0.165857\pi$
$228$	12.0905	−	22.4668i	0.800715	−	1.48790i
$229$	10.7797	+	3.50252i	0.712340	+	0.231453i	0.642699	−	0.766119i	$-0.277815\pi$
$229$	10.7797	+	3.50252i	0.712340	+	0.231453i	0.0696410	+	0.997572i	$0.477815\pi$
$230$		0			0
$231$	4.39951	+	13.5403i	0.289467	+	0.890887i
$232$	−22.6336	+	12.8418i	−1.48597	+	0.843105i
$233$	6.12514	−	1.99018i	0.401271	−	0.130381i	−0.101427	−	0.994843i	$-0.532341\pi$
$233$	6.12514	−	1.99018i	0.401271	−	0.130381i	0.502698	+	0.864462i	$0.332341\pi$
$234$	4.21535	−	0.284160i	0.275566	−	0.0185761i
$235$		0			0
$236$	3.22595	−	1.55345i	0.209992	−	0.101121i
$237$	−1.99109	−	1.44661i	−0.129335	−	0.0939673i
$238$	7.43808	−	0.501407i	0.482139	−	0.0325014i
$239$	1.70418	−	1.23816i	0.110234	−	0.0800897i	−0.531303	−	0.847182i	$-0.678297\pi$
$239$	1.70418	−	1.23816i	0.110234	−	0.0800897i	0.641537	+	0.767092i	$0.278297\pi$
$240$		0			0
$241$	−17.2054	−	12.5005i	−1.10830	−	0.805227i	−0.125904	−	0.992042i	$-0.540183\pi$
$241$	−17.2054	−	12.5005i	−1.10830	−	0.805227i	−0.982395	+	0.186816i	$0.940183\pi$
$242$	−18.9077	−	11.8808i	−1.21543	−	0.763726i
$243$	9.70164			0.622360
$244$	0.597603	+	4.41240i	0.0382576	+	0.282475i
$245$		0			0
$246$	−4.25867	−	10.6171i	−0.271523	−	0.676919i
$247$	18.7999	+	6.10847i	1.19621	+	0.388672i
$248$	11.5690	+	5.25536i	0.734635	+	0.333716i
$249$	−8.36931			−0.530384
$250$		0			0
$251$			17.4979i			1.10446i	0.833693	+	0.552229i	$0.186222\pi$
$251$			17.4979i			1.10446i	−0.833693	+	0.552229i	$0.813778\pi$
$252$	2.40833	−	1.15972i	0.151710	−	0.0730558i
$253$	−0.459417	+	1.41394i	−0.0288833	+	0.0888936i
$254$	−10.9931	+	4.40949i	−0.689766	+	0.276676i
$255$		0			0
$256$	−6.28967	+	14.7119i	−0.393104	+	0.919494i
$257$			28.7486i			1.79329i	0.442753	+	0.896644i	$0.354002\pi$
$257$			28.7486i			1.79329i	−0.442753	+	0.896644i	$0.645998\pi$
$258$	−17.9919	−	11.3053i	−1.12013	−	0.703840i
$259$	−4.08936	+	5.62852i	−0.254100	+	0.349739i
$260$		0			0
$261$	5.23412	+	7.20415i	0.323984	+	0.445926i
$262$	−0.861691	−	12.7827i	−0.0532354	−	0.789716i
$263$	12.3479	−	16.9955i	0.761407	−	1.04799i	−0.235689	−	0.971829i	$-0.575735\pi$
$263$	12.3479	−	16.9955i	0.761407	−	1.04799i	0.997096	−	0.0761580i	$-0.0242653\pi$
$264$	−12.0609	+	26.5505i	−0.742295	+	1.63407i
$265$		0			0
$266$	12.4781	−	0.841160i	0.765081	−	0.0515748i
$267$	−6.95243	−	21.3974i	−0.425482	−	1.30950i
$268$	−0.638309	+	3.51694i	−0.0389910	+	0.214831i
$269$	15.0792	−	4.89953i	0.919396	−	0.298730i	0.189177	−	0.981943i	$-0.439418\pi$
$269$	15.0792	−	4.89953i	0.919396	−	0.298730i	0.730219	+	0.683213i	$0.239418\pi$
$270$		0			0
$271$	9.17886	−	28.2496i	0.557576	−	1.71604i	−0.131465	−	0.991321i	$-0.541968\pi$
$271$	9.17886	−	28.2496i	0.557576	−	1.71604i	0.689041	−	0.724722i	$-0.258032\pi$
$272$	11.9380	+	9.52109i	0.723848	+	0.577301i
$273$	4.99048	+	6.86880i	0.302037	+	0.415719i
$274$	0.630702	+	0.755475i	0.0381021	+	0.0456399i
$275$		0			0
$276$	1.12592	+	0.204350i	0.0677725	+	0.0123004i
$277$	0.881062	−	0.640129i	0.0529379	−	0.0384616i	−0.561002	−	0.827815i	$-0.689584\pi$
$277$	0.881062	−	0.640129i	0.0529379	−	0.0384616i	0.613940	+	0.789353i	$0.289584\pi$
$278$	−13.9675	+	5.60261i	−0.837718	+	0.336022i
$279$	1.34365	−	4.13533i	0.0804422	−	0.247576i
$280$		0			0
$281$	−7.85909	−	24.1878i	−0.468834	−	1.44292i	−0.854096	−	0.520116i	$-0.825889\pi$
$281$	−7.85909	−	24.1878i	−0.468834	−	1.44292i	0.385261	−	0.922808i	$-0.374111\pi$
$282$	1.81162	+	2.17002i	0.107881	+	0.129223i
$283$	7.75392	+	23.8641i	0.460923	+	1.41857i	0.864039	+	0.503425i	$0.167927\pi$
$283$	7.75392	+	23.8641i	0.460923	+	1.41857i	−0.403116	+	0.915149i	$0.632073\pi$
$284$	21.9244	−	20.9610i	1.30097	−	1.24380i
$285$		0			0
$286$	−21.9090	−	5.52083i	−1.29550	−	0.326454i
$287$	3.29596	−	4.53650i	0.194554	−	0.267781i
$288$	5.24366	+	1.57491i	0.308986	+	0.0928024i
$289$	−1.96352	+	1.42658i	−0.115501	+	0.0839166i
$290$		0			0
$291$	−5.72946	+	7.88593i	−0.335867	+	0.462281i
$292$	3.14198	+	23.1988i	0.183871	+	1.35761i
$293$	31.6461			1.84879			0.924393	−	0.381440i	$-0.124572\pi$
$293$	31.6461			1.84879			0.924393	+	0.381440i	$0.124572\pi$
$294$	−12.1484	−	7.63355i	−0.708511	−	0.445198i
$295$		0			0
$296$	−13.9608	+	2.85801i	−0.811454	+	0.166119i
$297$	−19.9262	−	6.47442i	−1.15624	−	0.375684i
$298$	−4.41863	−	1.11345i	−0.255964	−	0.0645003i
$299$			0.886596i			0.0512731i
$300$		0			0
$301$		−	10.4160i		−	0.600369i
$302$	−6.97956	+	27.6978i	−0.401629	+	1.59383i
$303$	31.3908	+	10.1995i	1.80335	+	0.585945i
$304$	20.0272	+	15.9726i	1.14864	+	0.916089i
$305$		0			0
$306$	2.78002	−	4.42428i	0.158923	−	0.252919i
$307$	−3.74062			−0.213488			−0.106744	−	0.994287i	$-0.534043\pi$
$307$	−3.74062			−0.213488			−0.106744	+	0.994287i	$0.534043\pi$
$308$	−14.1653	+	1.91851i	−0.807144	+	0.109317i
$309$	−4.76275	+	6.55536i	−0.270943	+	0.372921i
$310$		0			0
$311$	−9.08998	+	6.60426i	−0.515446	+	0.374493i	−0.814885	−	0.579622i	$-0.803200\pi$
$311$	−9.08998	+	6.60426i	−0.515446	+	0.374493i	0.299440	+	0.954115i	$0.403200\pi$
$312$	−1.94768	+	17.2811i	−0.110265	+	0.978348i
$313$	3.87093	−	5.32787i	0.218798	−	0.301149i	−0.685482	−	0.728089i	$-0.740409\pi$
$313$	3.87093	−	5.32787i	0.218798	−	0.301149i	0.904280	+	0.426940i	$0.140409\pi$
$314$	7.38530	−	29.3080i	0.416777	−	1.65394i
$315$		0			0
$316$	1.78611	−	1.70762i	0.100476	−	0.0960612i
$317$	6.24885	+	19.2320i	0.350970	+	1.08018i	0.958309	+	0.285733i	$0.0922370\pi$
$317$	6.24885	+	19.2320i	0.350970	+	1.08018i	−0.607339	+	0.794443i	$0.707763\pi$
$318$	7.17195	−	5.98744i	0.402183	−	0.335759i
$319$	−14.7157	−	45.2902i	−0.823920	−	2.53577i
$320$		0			0
$321$	−8.32258	+	25.6143i	−0.464521	+	1.42965i
$322$	0.208825	+	0.520610i	0.0116374	+	0.0290125i
$323$	19.7785	−	14.3699i	1.10050	−	0.799563i
$324$	−3.91687	+	21.5811i	−0.217604	+	1.19895i
$325$		0			0
$326$	13.7702	−	11.4960i	0.762662	−	0.636702i
$327$	−11.7489	−	16.1710i	−0.649715	−	0.894256i
$328$	11.2522	−	2.30352i	0.621298	−	0.127190i
$329$	−0.428198	+	1.31786i	−0.0236073	+	0.0726559i
$330$		0			0
$331$	20.2986	−	6.59541i	1.11571	−	0.362517i	0.307582	−	0.951522i	$-0.400480\pi$
$331$	20.2986	−	6.59541i	1.11571	−	0.362517i	0.808129	+	0.589005i	$0.200480\pi$
$332$	1.50062	−	8.26806i	0.0823570	−	0.453769i
$333$	1.50687	+	4.63768i	0.0825761	+	0.254143i
$334$	−0.875141	−	12.9822i	−0.0478856	−	0.710354i
$335$		0			0
$336$	2.92664	+	10.6062i	0.159661	+	0.578616i
$337$	−9.78712	+	13.4708i	−0.533139	+	0.733802i	−0.987605	−	0.156962i	$-0.949830\pi$
$337$	−9.78712	+	13.4708i	−0.533139	+	0.733802i	0.454466	+	0.890764i	$0.349830\pi$
$338$	4.89981	−	0.330300i	0.266514	−	0.0179660i
$339$	−11.1380	−	15.3301i	−0.604932	−	0.832617i
$340$		0			0
$341$	−13.6677	+	18.8120i	−0.740147	+	1.01873i
$342$	4.66376	−	7.42215i	0.252187	−	0.401344i
$343$		−	16.6992i		−	0.901674i
$344$	14.3945	−	15.7472i	0.776101	−	0.849033i
$345$		0			0
$346$	10.2665	+	25.5948i	0.551930	+	1.37599i
$347$	4.90149	−	15.0852i	0.263126	−	0.809818i	−0.728993	−	0.684521i	$-0.760012\pi$
$347$	4.90149	−	15.0852i	0.263126	−	0.809818i	0.992119	−	0.125297i	$-0.0399884\pi$
$348$	−33.0243	+	15.9028i	−1.77029	+	0.852479i
$349$		−	11.9445i		−	0.639375i	−0.947523	−	0.319688i	$-0.896422\pi$
$349$		−	11.9445i		−	0.639375i	0.947523	−	0.319688i	$-0.103578\pi$
$350$		0			0
$351$	−12.4945			−0.666908
$352$	−24.0668	−	16.6755i	−1.28277	−	0.888805i
$353$	−4.78471	−	1.55465i	−0.254665	−	0.0827456i	0.178903	−	0.983867i	$-0.442745\pi$
$353$	−4.78471	−	1.55465i	−0.254665	−	0.0827456i	−0.433567	+	0.901121i	$0.642745\pi$
$354$	4.68070	−	1.87751i	0.248776	−	0.0997883i
$355$		0			0
$356$	22.3851	−	3.03178i	1.18641	−	0.160684i
$357$	10.5005			0.555744
$358$	2.49640	−	3.97291i	0.131939	−	0.209975i
$359$	4.41690	+	3.20906i	0.233115	+	0.169368i	0.698210	−	0.715893i	$-0.253980\pi$
$359$	4.41690	+	3.20906i	0.233115	+	0.169368i	−0.465096	+	0.885260i	$0.653980\pi$
$360$		0			0
$361$	17.8090	−	12.9390i	0.937315	−	0.681000i
$362$	0.469011	+	6.95750i	0.0246507	+	0.365678i
$363$	−25.4461	−	18.4877i	−1.33557	−	0.970351i
$364$	−7.68049	+	3.69853i	−0.402567	+	0.193855i
$365$		0			0
$366$	0.421823	+	6.25749i	0.0220491	+	0.327084i
$367$	−14.3846	+	4.67384i	−0.750871	+	0.243973i	−0.659356	−	0.751831i	$-0.729171\pi$
$367$	−14.3846	+	4.67384i	−0.750871	+	0.243973i	−0.0915149	+	0.995804i	$0.529171\pi$
$368$	−0.403755	+	1.07566i	−0.0210472	+	0.0560727i
$369$	−1.21452	−	3.73790i	−0.0632253	−	0.194587i
$370$		0			0
$371$	4.35555	+	1.41520i	0.226129	+	0.0734737i
$372$	15.7605	+	8.48151i	0.817142	+	0.439746i
$373$	26.1912	−	19.0290i	1.35613	−	0.985284i	0.357447	−	0.933933i	$-0.383647\pi$
$373$	26.1912	−	19.0290i	1.35613	−	0.985284i	0.998681	−	0.0513509i	$-0.0163527\pi$
$374$	−21.4506	+	17.9079i	−1.10919	+	0.925994i
$375$		0			0
$376$	−2.46859	+	1.40062i	−0.127308	+	0.0722315i
$377$	−16.6924	−	22.9751i	−0.859701	−	1.18328i
$378$	−7.33679	+	2.94291i	−0.377364	+	0.151367i
$379$	−12.3752	−	4.02096i	−0.635674	−	0.206543i	−0.0265869	−	0.999647i	$-0.508464\pi$
$379$	−12.3752	−	4.02096i	−0.635674	−	0.206543i	−0.609087	+	0.793104i	$0.708464\pi$
$380$		0			0
$381$	−15.8666	+	5.15538i	−0.812872	+	0.264118i
$382$	0.729609	−	0.609108i	0.0373300	−	0.0311647i
$383$	−13.4131	+	4.35817i	−0.685376	+	0.222692i	−0.630948	−	0.775825i	$-0.717334\pi$
$383$	−13.4131	+	4.35817i	−0.685376	+	0.222692i	−0.0544287	+	0.998518i	$0.517334\pi$
$384$	−10.2328	+	20.0793i	−0.522190	+	1.02467i
$385$		0			0
$386$	−6.52070	−	1.64315i	−0.331895	−	0.0836340i
$387$	−5.90632	−	4.29119i	−0.300235	−	0.218134i
$388$	−6.76324	−	7.07410i	−0.343351	−	0.359133i
$389$	−11.6423	−	16.0243i	−0.590290	−	0.812465i	0.404486	−	0.914544i	$-0.367450\pi$
$389$	−11.6423	−	16.0243i	−0.590290	−	0.812465i	−0.994776	+	0.102080i	$0.967450\pi$
$390$		0			0
$391$	0.887092	+	0.644510i	0.0448622	+	0.0325943i
$392$	9.71941	−	10.6328i	0.490904	−	0.537036i
$393$		−	18.0455i		−	0.910276i
$394$	−6.72582	−	4.22621i	−0.338842	−	0.212913i
$395$		0			0
$396$	−4.74796	+	8.82273i	−0.238594	+	0.443359i
$397$	3.25515	−	10.0183i	0.163371	−	0.502805i	−0.835541	−	0.549428i	$-0.814846\pi$
$397$	3.25515	−	10.0183i	0.163371	−	0.502805i	0.998913	+	0.0466224i	$0.0148457\pi$
$398$	−1.23143	+	4.88682i	−0.0617259	+	0.244954i
$399$	17.6156			0.881881
$400$		0			0
$401$	−14.5328			−0.725732			−0.362866	−	0.931841i	$-0.618202\pi$
$401$	−14.5328			−0.725732			−0.362866	+	0.931841i	$0.618202\pi$
$402$	−1.23021	+	4.88200i	−0.0613574	+	0.243492i
$403$	−4.28509	+	13.1882i	−0.213456	+	0.656949i
$404$	−15.7044	+	29.1822i	−0.781325	+	1.45187i
$405$		0			0
$406$	−15.2132	−	9.55933i	−0.755020	−	0.474422i
$407$		−	26.0776i		−	1.29262i
$408$	15.8749	+	14.5112i	0.785924	+	0.718413i
$409$	−20.3026	−	14.7507i	−1.00390	−	0.729375i	−0.0409776	−	0.999160i	$-0.513047\pi$
$409$	−20.3026	−	14.7507i	−1.00390	−	0.729375i	−0.962920	+	0.269785i	$0.913047\pi$
$410$		0			0
$411$	0.814776	+	1.12144i	0.0401899	+	0.0553167i
$412$	−5.62209	−	5.88050i	−0.276981	−	0.289712i
$413$	1.99999	+	1.45308i	0.0984131	+	0.0715013i
$414$	0.381240	+	0.0960684i	0.0187369	+	0.00472150i
$415$		0			0
$416$	−16.7228	−	5.02261i	−0.819902	−	0.246254i
$417$	−20.1598	+	6.55032i	−0.987230	+	0.320770i
$418$	−35.9855	+	30.0422i	−1.76011	+	1.46941i
$419$	0.728039	−	0.236554i	0.0355671	−	0.0115564i	−0.291179	−	0.956668i	$-0.594048\pi$
$419$	0.728039	−	0.236554i	0.0355671	−	0.0115564i	0.326746	+	0.945112i	$0.394048\pi$
$420$		0			0
$421$	−11.1284	−	3.61584i	−0.542366	−	0.176225i	0.0250056	−	0.999687i	$-0.492040\pi$
$421$	−11.1284	−	3.61584i	−0.542366	−	0.176225i	−0.567371	+	0.823462i	$0.692040\pi$
$422$	37.0073	−	14.8442i	1.80149	−	0.722606i
$423$	0.570872	+	0.785739i	0.0277568	+	0.0382039i
$424$	4.62908	+	8.15874i	0.224808	+	0.396223i
$425$		0			0
$426$	32.7968	−	27.3801i	1.58901	−	1.32657i
$427$	−2.48717	+	1.80704i	−0.120363	+	0.0874486i
$428$	−23.8122	−	12.8145i	−1.15100	−	0.619414i
$429$	−30.2664	−	9.83414i	−1.46127	−	0.474797i
$430$		0			0
$431$	6.71966	+	20.6810i	0.323675	+	0.996169i	0.972035	+	0.234835i	$0.0754550\pi$
$431$	6.71966	+	20.6810i	0.323675	+	0.996169i	−0.648360	+	0.761334i	$0.724545\pi$
$432$	−15.1589	−	5.68999i	−0.729335	−	0.273760i
$433$	3.49647	−	1.13607i	0.168030	−	0.0545962i	−0.223794	−	0.974636i	$-0.571844\pi$
$433$	3.49647	−	1.13607i	0.168030	−	0.0545962i	0.391824	+	0.920040i	$0.371844\pi$
$434$	0.590074	+	8.75339i	0.0283245	+	0.420176i
$435$		0			0
$436$	18.0819	−	8.70730i	0.865966	−	0.417004i
$437$	1.48818	+	1.08123i	0.0711894	+	0.0517222i
$438$	2.21780	+	32.8997i	0.105970	+	1.57201i
$439$	−1.89736	+	1.37851i	−0.0905559	+	0.0657927i	−0.632142	−	0.774853i	$-0.717824\pi$
$439$	−1.89736	+	1.37851i	−0.0905559	+	0.0657927i	0.541586	+	0.840645i	$0.317824\pi$
$440$		0			0
$441$	−3.98804	−	2.89748i	−0.189907	−	0.137975i
$442$	−8.86589	+	14.1096i	−0.421707	+	0.671127i
$443$	−0.969245			−0.0460502			−0.0230251	−	0.999735i	$-0.507330\pi$
$443$	−0.969245			−0.0460502			−0.0230251	+	0.999735i	$0.507330\pi$
$444$	−19.8903	+	2.69389i	−0.943951	+	0.127846i
$445$		0			0
$446$	21.7168	−	8.71096i	1.02832	−	0.412476i
$447$	−6.10416	−	1.98336i	−0.288717	−	0.0938098i
$448$	−11.0026	+	0.989538i	−0.519826	+	0.0467513i
$449$	34.3240			1.61985			0.809925	−	0.586533i	$-0.199508\pi$
$449$	34.3240			1.61985			0.809925	+	0.586533i	$0.199508\pi$
$450$		0			0
$451$			21.0181i			0.989705i
$452$	17.1417	−	8.25455i	0.806277	−	0.388261i
$453$	−12.4325	+	38.2634i	−0.584132	+	1.79777i
$454$	6.48960	+	16.1788i	0.304572	+	0.759311i
$455$		0			0
$456$	26.6317	+	24.3440i	1.24714	+	1.14001i
$457$		−	34.4324i		−	1.61068i	−0.592812	−	0.805341i	$-0.701982\pi$
$457$		−	34.4324i		−	1.61068i	0.592812	−	0.805341i	$-0.298018\pi$
$458$	−8.52823	+	13.5723i	−0.398498	+	0.634191i
$459$	−9.08288	+	12.5015i	−0.423953	+	0.583521i
$460$		0			0
$461$	21.8458	+	30.0682i	1.01746	+	1.40041i	0.913969	+	0.405783i	$0.133001\pi$
$461$	21.8458	+	30.0682i	1.01746	+	1.40041i	0.103491	+	0.994630i	$0.466999\pi$
$462$	−20.0887	+	1.35420i	−0.934612	+	0.0630031i
$463$	8.48120	−	11.6734i	0.394155	−	0.542507i	−0.565110	−	0.825015i	$-0.691166\pi$
$463$	8.48120	−	11.6734i	0.394155	−	0.542507i	0.959265	+	0.282508i	$0.0911664\pi$
$464$	−9.78914	−	35.4761i	−0.454450	−	1.64694i
$465$		0			0
$466$	0.612591	+	9.08741i	0.0283777	+	0.420966i
$467$	3.46409	+	10.6614i	0.160299	+	0.493349i	0.998659	−	0.0517673i	$-0.0164854\pi$
$467$	3.46409	+	10.6614i	0.160299	+	0.493349i	−0.838360	+	0.545116i	$0.816485\pi$
$468$	−1.06699	+	5.87889i	−0.0493217	+	0.271752i
$469$	−2.34712	+	0.762626i	−0.108380	+	0.0352148i
$470$		0			0
$471$	13.1553	−	40.4878i	0.606163	−	1.86558i
$472$	1.01554	+	4.96071i	0.0467441	+	0.228335i
$473$	22.9483	+	31.5857i	1.05517	+	1.45231i
$474$	2.67185	−	2.23057i	0.122722	−	0.102453i
$475$		0			0
$476$	−1.88273	+	10.3734i	−0.0862949	+	0.475466i
$477$	2.59688	−	1.88674i	0.118903	−	0.0863881i
$478$	1.10904	+	2.76488i	0.0507262	+	0.126462i
$479$	1.46974	−	4.52340i	0.0671543	−	0.206680i	−0.911848	−	0.410527i	$-0.865345\pi$
$479$	1.46974	−	4.52340i	0.0671543	−	0.206680i	0.979003	+	0.203848i	$0.0653447\pi$
$480$		0			0
$481$	−4.80563	−	14.7902i	−0.219118	−	0.674376i
$482$	23.0880	−	19.2749i	1.05163	−	0.877946i
$483$	0.244149	+	0.751413i	0.0111092	+	0.0341905i
$484$	22.8265	−	21.8234i	1.03757	−	0.991973i
$485$		0			0
$486$	−3.35254	+	13.3043i	−0.152074	+	0.603495i
$487$	−7.81977	+	10.7630i	−0.354348	+	0.487718i	−0.948563	−	0.316588i	$-0.897463\pi$
$487$	−7.81977	+	10.7630i	−0.354348	+	0.487718i	0.594215	+	0.804306i	$0.297463\pi$
$488$	−6.25742	−	0.705248i	−0.283260	−	0.0319251i
$489$	20.4408	−	14.8511i	0.924365	−	0.671590i
$490$		0			0
$491$	10.4364	−	14.3645i	0.470990	−	0.648262i	−0.505752	−	0.862679i	$-0.668785\pi$
$491$	10.4364	−	14.3645i	0.470990	−	0.648262i	0.976742	+	0.214417i	$0.0687851\pi$
$492$	16.0313	−	2.17123i	0.722746	−	0.0978867i
$493$	−35.1224			−1.58184
$494$	−14.8734	+	23.6703i	−0.669186	+	1.06498i
$495$		0			0
$496$	−11.2048	+	14.0491i	−0.503108	+	0.630822i
$497$	19.9176	+	6.47161i	0.893425	+	0.290291i
$498$	2.89214	−	11.4772i	0.129600	−	0.514306i
$499$		−	15.6179i		−	0.699151i	−0.936908	−	0.349576i	$-0.886326\pi$
$499$		−	15.6179i		−	0.699151i	0.936908	−	0.349576i	$-0.113674\pi$
$500$		0			0
$501$		−	18.3272i		−	0.818799i
$502$	−23.9956	−	6.04665i	−1.07098	−	0.269875i
$503$	−0.0298452	−	0.00969730i	−0.00133073	−	0.000432381i	0.308352	−	0.951272i	$-0.400223\pi$
$503$	−0.0298452	−	0.00969730i	−0.00133073	−	0.000432381i	−0.309682	+	0.950840i	$0.600223\pi$
$504$	0.758150	+	3.70340i	0.0337707	+	0.164963i
$505$		0			0
$506$	−1.78024	−	1.11863i	−0.0791413	−	0.0497290i
$507$	6.91715			0.307201
$508$	−2.24813	−	16.5990i	−0.0997445	−	0.736463i
$509$	−6.00479	+	8.26488i	−0.266157	+	0.366334i	−0.921088	−	0.389355i	$-0.872698\pi$
$509$	−6.00479	+	8.26488i	−0.266157	+	0.366334i	0.654930	+	0.755689i	$0.272698\pi$
$510$		0			0
$511$	−13.0767	+	9.50075i	−0.578477	+	0.420288i
$512$	−18.0016	−	13.7092i	−0.795566	−	0.605867i
$513$	−15.2374	+	20.9725i	−0.672748	+	0.925959i
$514$	−39.4242	−	9.93448i	−1.73893	−	0.438191i
$515$		0			0
$516$	21.7209	−	20.7664i	0.956209	−	0.914189i
$517$	−1.60500	−	4.93969i	−0.0705879	−	0.217247i
$518$	−6.30550	−	7.55293i	−0.277048	−	0.331857i
$519$	12.0031	+	36.9418i	0.526878	+	1.62156i
$520$		0			0
$521$	6.03139	−	18.5627i	0.264240	−	0.813248i	−0.727627	−	0.685973i	$-0.759377\pi$
$521$	6.03139	−	18.5627i	0.264240	−	0.813248i	0.991867	−	0.127275i	$-0.0406231\pi$
$522$	−11.6881	+	4.68829i	−0.511574	+	0.205201i
$523$	−7.08464	+	5.14729i	−0.309789	+	0.225075i	−0.731806	−	0.681513i	$-0.761322\pi$
$523$	−7.08464	+	5.14729i	−0.309789	+	0.225075i	0.422017	+	0.906588i	$0.361322\pi$
$524$	17.8272	+	3.23556i	0.778785	+	0.141346i
$525$		0			0
$526$	19.0397	+	22.8063i	0.830168	+	0.994403i
$527$	10.0805	+	13.8746i	0.439113	+	0.604388i
$528$	−32.2421	−	25.7145i	−1.40316	−	1.11908i
$529$	7.08190	−	21.7958i	0.307909	−	0.947645i
$530$		0			0
$531$	1.64791	−	0.535440i	0.0715134	−	0.0232361i
$532$	−3.15847	+	17.4024i	−0.136937	+	0.754492i
$533$	3.87327	+	11.9207i	0.167770	+	0.516343i
$534$	31.7457	−	2.14001i	1.37377	−	0.0926071i
$535$		0			0
$536$	−4.60236	−	2.09067i	−0.198792	−	0.0903033i
$537$	3.88464	−	5.34675i	0.167635	−	0.230729i
$538$	1.50811	+	22.3719i	0.0650192	+	0.964521i
$539$	15.4951	+	21.3271i	0.667420	+	0.918625i
$540$		0			0
$541$	15.5336	−	21.3802i	0.667843	−	0.919208i	−0.331866	−	0.943327i	$-0.607678\pi$
$541$	15.5336	−	21.3802i	0.667843	−	0.919208i	0.999709	+	0.0241190i	$0.00767806\pi$
$542$	35.5681	+	22.3494i	1.52778	+	0.959991i
$543$			9.82203i			0.421504i
$544$	−17.1820	+	13.0810i	−0.736674	+	0.560842i
$545$		0			0
$546$	−11.1440	+	4.47005i	−0.476920	+	0.191300i
$547$	−8.93390	+	27.4957i	−0.381986	+	1.17563i	0.556657	+	0.830742i	$0.312084\pi$
$547$	−8.93390	+	27.4957i	−0.381986	+	1.17563i	−0.938643	+	0.344890i	$0.887916\pi$
$548$	−1.25397	+	0.603844i	−0.0535667	+	0.0257950i
$549$			2.15480i			0.0919644i
$550$		0			0
$551$	−58.9213			−2.51013
$552$	−0.669312	+	1.47341i	−0.0284878	+	0.0627125i
$553$	1.62262	+	0.527221i	0.0690008	+	0.0224197i
$554$	0.573374	+	1.42944i	0.0243603	+	0.0607313i
$555$		0			0
$556$	−2.85642	−	21.0904i	−0.121139	−	0.894431i
$557$	−33.1381			−1.40411			−0.702053	−	0.712125i	$-0.747733\pi$
$557$	−33.1381			−1.40411			−0.702053	+	0.712125i	$0.747733\pi$
$558$	5.20664	+	3.27163i	0.220415	+	0.138499i
$559$	18.8361	+	13.6852i	0.796682	+	0.578824i
$560$		0			0
$561$	−31.8418	+	23.1344i	−1.34436	+	0.976735i
$562$	35.8856	−	2.41908i	1.51374	−	0.102043i
$563$	−25.4540	−	18.4934i	−1.07276	−	0.779404i	−0.0963518	−	0.995347i	$-0.530717\pi$
$563$	−25.4540	−	18.4934i	−1.07276	−	0.779404i	−0.976406	+	0.215943i	$0.930717\pi$
$564$	−3.60188	+	1.73448i	−0.151666	+	0.0730346i
$565$		0			0
$566$	−35.4054	+	2.38671i	−1.48820	+	0.100321i
$567$	−14.4027	+	4.67972i	−0.604857	+	0.196530i
$568$	21.1684	+	37.3092i	0.888206	+	1.56546i
$569$	−5.66167	−	17.4248i	−0.237350	−	0.730487i	−0.996801	−	0.0799229i	$-0.974533\pi$
$569$	−5.66167	−	17.4248i	−0.237350	−	0.730487i	0.759451	−	0.650564i	$-0.225467\pi$
$570$		0			0
$571$	−4.90965	−	1.59524i	−0.205462	−	0.0667588i	0.204478	−	0.978871i	$-0.434450\pi$
$571$	−4.90965	−	1.59524i	−0.205462	−	0.0667588i	−0.409940	+	0.912112i	$0.634450\pi$
$572$	15.1419	−	28.1369i	0.633115	−	1.17646i
$573$	1.08305	−	0.786879i	0.0452449	−	0.0328723i
$574$	5.08214	+	6.08755i	0.212124	+	0.254089i
$575$		0			0
$576$	−3.97176	+	6.64664i	−0.165490	+	0.276943i
$577$	−0.868662	−	1.19561i	−0.0361629	−	0.0497739i	0.790553	−	0.612394i	$-0.209793\pi$
$577$	−0.868662	−	1.19561i	−0.0361629	−	0.0497739i	−0.826716	+	0.562620i	$0.809793\pi$
$578$	−1.27781	−	3.18564i	−0.0531500	−	0.132505i
$579$	−9.00808	−	2.92690i	−0.374363	−	0.121638i
$580$		0			0
$581$	5.51790	−	1.79288i	0.228921	−	0.0743810i
$582$	−8.83443	−	10.5822i	−0.366199	−	0.438645i
$583$	−16.3258	+	5.30456i	−0.676144	+	0.219692i
$584$	−32.8993	−	3.70794i	−1.36138	−	0.153436i
$585$		0			0
$586$	−10.9358	+	43.3977i	−0.451753	+	1.79274i
$587$	−6.19025	−	4.49748i	−0.255499	−	0.185631i	0.452662	−	0.891682i	$-0.350475\pi$
$587$	−6.19025	−	4.49748i	−0.255499	−	0.185631i	−0.708160	+	0.706052i	$0.750475\pi$
$588$	14.6663	−	14.0218i	0.604828	−	0.578249i
$589$	16.9110	+	23.2760i	0.696806	+	0.959071i
$590$		0			0
$591$	−9.05163	−	6.57640i	−0.372334	−	0.270517i
$592$	0.905030	−	20.1327i	0.0371965	−	0.827448i
$593$		−	31.1703i		−	1.28001i	−0.768370	−	0.640006i	$-0.778932\pi$
$593$		−	31.1703i		−	1.28001i	0.768370	−	0.640006i	$-0.221068\pi$
$594$	15.7644	−	25.0884i	0.646823	−	1.02939i
$595$		0			0
$596$	3.05384	−	5.67469i	0.125090	−	0.232445i
$597$	−2.19352	+	6.75095i	−0.0897747	+	0.276298i
$598$	−1.21583	−	0.306376i	−0.0497189	−	0.0125286i
$599$	−30.2376			−1.23547			−0.617737	−	0.786385i	$-0.711950\pi$
$599$	−30.2376			−1.23547			−0.617737	+	0.786385i	$0.711950\pi$
$600$		0			0
$601$	47.2925			1.92910			0.964551	−	0.263895i	$-0.0850073\pi$
$601$	47.2925			1.92910			0.964551	+	0.263895i	$0.0850073\pi$
$602$	14.2839	+	3.59940i	0.582170	+	0.146701i
$603$	−0.534527	+	1.64511i	−0.0217676	+	0.0669939i
$604$	−35.5714	−	19.1428i	−1.44738	−	0.778908i
$605$		0			0
$606$	−24.8345	+	39.5230i	−1.00883	+	1.60551i
$607$		−	13.6800i		−	0.555252i	−0.960689	−	0.277626i	$-0.910452\pi$
$607$		−	13.6800i		−	0.555252i	0.960689	−	0.277626i	$-0.0895477\pi$
$608$	−28.8245	+	21.9446i	−1.16899	+	0.889971i
$609$	−20.4740	−	14.8753i	−0.829650	−	0.602776i
$610$		0			0
$611$	−1.82059	−	2.50583i	−0.0736533	−	0.101375i
$612$	5.10653	+	5.34124i	0.206419	+	0.215907i
$613$	−12.8625	−	9.34518i	−0.519513	−	0.377448i	0.296907	−	0.954906i	$-0.404045\pi$
$613$	−12.8625	−	9.34518i	−0.519513	−	0.377448i	−0.816420	+	0.577458i	$0.804045\pi$
$614$	1.29262	−	5.12968i	0.0521661	−	0.207017i
$615$		0			0
$616$	2.26409	−	20.0885i	0.0912228	−	0.809389i
$617$	10.0312	−	3.25933i	0.403840	−	0.131216i	−0.100052	−	0.994982i	$-0.531901\pi$
$617$	10.0312	−	3.25933i	0.403840	−	0.131216i	0.503892	+	0.863767i	$0.331901\pi$
$618$	−7.34382	−	8.79667i	−0.295412	−	0.353854i
$619$	−25.5938	+	8.31591i	−1.02870	+	0.334245i	−0.774276	−	0.632848i	$-0.781886\pi$
$619$	−25.5938	+	8.31591i	−1.02870	+	0.334245i	−0.254424	+	0.967093i	$0.581886\pi$
$620$		0			0
$621$	−1.10580	−	0.359295i	−0.0443740	−	0.0144180i
$622$	−5.91554	−	14.7477i	−0.237192	−	0.591329i
$623$	9.16751	+	12.6180i	0.367288	+	0.505529i
$624$	−23.0253	−	8.64266i	−0.921748	−	0.345983i
$625$		0			0
$626$	5.96869	+	7.14949i	0.238557	+	0.285751i
$627$	−53.4176	+	38.8102i	−2.13330	+	1.54993i
$628$	37.6392	+	20.2556i	1.50197	+	0.808286i
$629$	−18.2919	−	5.94341i	−0.729348	−	0.236979i
$630$		0			0
$631$	0.0360428	+	0.110928i	0.00143484	+	0.00441599i	0.951771	−	0.306808i	$-0.0992610\pi$
$631$	0.0360428	+	0.110928i	0.00143484	+	0.00441599i	−0.950337	+	0.311224i	$0.899261\pi$
$632$	1.72452	+	3.03946i	0.0685978	+	0.120903i
$633$	53.4138	−	17.3552i	2.12301	−	0.689808i
$634$	−28.5330	+	1.92344i	−1.13319	+	0.0763895i
$635$		0			0
$636$	5.73247	+	11.9043i	0.227307	+	0.472035i
$637$	12.7184	+	9.24049i	0.503923	+	0.366121i
$638$	67.1937	−	4.52959i	2.66022	−	0.179328i
$639$	11.8753	−	8.62793i	0.469781	−	0.341316i
$640$		0			0
$641$	8.56388	+	6.22202i	0.338253	+	0.245755i	0.743924	−	0.668264i	$-0.232962\pi$
$641$	8.56388	+	6.22202i	0.338253	+	0.245755i	−0.405672	+	0.914019i	$0.632962\pi$
$642$	−32.2500	−	20.2645i	−1.27281	−	0.799776i
$643$	7.74220			0.305323			0.152661	−	0.988279i	$-0.451216\pi$
$643$	7.74220			0.305323			0.152661	+	0.988279i	$0.451216\pi$
$644$	−0.786098	+	0.106467i	−0.0309766	+	0.00419538i
$645$		0			0
$646$	12.8714	+	32.0888i	0.506417	+	1.26252i
$647$	−21.5750	−	7.01014i	−0.848200	−	0.275597i	−0.147508	−	0.989061i	$-0.547125\pi$
$647$	−21.5750	−	7.01014i	−0.848200	−	0.275597i	−0.700692	+	0.713464i	$0.747125\pi$
$648$	−28.2416	−	12.8290i	−1.10943	−	0.503972i
$649$	−9.26619			−0.363730
$650$		0			0
$651$			12.3573i			0.484322i
$652$	11.0064	+	22.8563i	0.431044	+	0.895122i
$653$	−9.55959	+	29.4214i	−0.374096	+	1.15135i	0.569991	+	0.821651i	$0.306947\pi$
$653$	−9.55959	+	29.4214i	−0.374096	+	1.15135i	−0.944087	+	0.329697i	$0.893053\pi$
$654$	26.2359	−	10.5237i	1.02591	−	0.411508i
$655$		0			0
$656$	−0.729441	+	16.2266i	−0.0284799	+	0.633544i
$657$			11.3291i			0.441992i
$658$	−1.65927	−	1.04261i	−0.0646850	−	0.0406453i
$659$	13.3643	−	18.3944i	0.520601	−	0.716545i	−0.465061	−	0.885279i	$-0.653968\pi$
$659$	13.3643	−	18.3944i	0.520601	−	0.716545i	0.985662	+	0.168733i	$0.0539676\pi$
$660$		0			0
$661$	−9.06815	−	12.4812i	−0.352710	−	0.485464i	0.595389	−	0.803437i	$-0.296998\pi$
$661$	−9.06815	−	12.4812i	−0.352710	−	0.485464i	−0.948100	+	0.317973i	$0.896998\pi$
$662$	2.03011	+	30.1155i	0.0789025	+	1.17047i
$663$	−13.7962	+	18.9888i	−0.535800	+	0.737465i
$664$	10.8198	+	4.91501i	0.419890	+	0.190739i
$665$		0			0
$666$	−6.88057	+	0.463826i	−0.266617	+	0.0179729i
$667$	−0.816640	−	2.51336i	−0.0316204	−	0.0973176i
$668$	18.1055	+	3.28606i	0.700522	+	0.127142i
$669$	31.3445	−	10.1845i	1.21185	−	0.393754i
$670$		0			0
$671$	3.56091	−	10.9594i	0.137467	−	0.423081i
$672$	−15.5561	+	0.348297i	−0.600090	+	0.0134359i
$673$	−13.5949	−	18.7118i	−0.524046	−	0.721288i	0.462162	−	0.886795i	$-0.347074\pi$
$673$	−13.5949	−	18.7118i	−0.524046	−	0.721288i	−0.986209	+	0.165507i	$0.947074\pi$
$674$	−15.0910	−	18.0765i	−0.581286	−	0.696283i
$675$		0			0
$676$	−1.24024	+	6.83346i	−0.0477017	+	0.262825i
$677$	2.66645	−	1.93729i	0.102480	−	0.0744561i	−0.535365	−	0.844621i	$-0.679826\pi$
$677$	2.66645	−	1.93729i	0.102480	−	0.0744561i	0.637845	+	0.770165i	$0.279826\pi$
$678$	24.8717	−	9.97646i	0.955194	−	0.383144i
$679$	2.08812	−	6.42658i	0.0801348	−	0.246629i
$680$		0			0
$681$	7.58734	+	23.3514i	0.290747	+	0.894829i
$682$	−21.0746	−	25.2439i	−0.806989	−	0.966637i
$683$	4.53666	+	13.9624i	0.173591	+	0.534257i	0.999566	−	0.0294489i	$-0.00937522\pi$
$683$	4.53666	+	13.9624i	0.173591	+	0.534257i	−0.825976	+	0.563706i	$0.809375\pi$
$684$	8.56670	+	8.96045i	0.327556	+	0.342611i
$685$		0			0
$686$	22.9004	+	5.77066i	0.874341	+	0.220325i
$687$	−13.2708	+	18.2656i	−0.506311	+	0.696877i
$688$	16.6206	+	25.1815i	0.633655	+	0.960036i
$689$	−8.28182	+	6.01710i	−0.315512	+	0.229233i
$690$		0			0
$691$	−0.529926	+	0.729380i	−0.0201593	+	0.0277469i	−0.818978	−	0.573825i	$-0.805459\pi$
$691$	−0.529926	+	0.729380i	−0.0201593	+	0.0277469i	0.798818	+	0.601572i	$0.205459\pi$
$692$	−38.6470	+	5.23425i	−1.46914	+	0.198976i
$693$	−6.91764			−0.262779
$694$	18.9933	+	11.9346i	0.720975	+	0.453029i
$695$		0			0
$696$	−10.3962	−	50.7831i	−0.394066	−	1.92493i
$697$	14.7430	+	4.79030i	0.558433	+	0.181446i
$698$	16.3800	+	4.12760i	0.619994	+	0.156232i
$699$			12.8289i			0.485232i
$700$		0			0
$701$		−	25.3479i		−	0.957379i	−0.877984	−	0.478689i	$-0.841112\pi$
$701$		−	25.3479i		−	0.957379i	0.877984	−	0.478689i	$-0.158888\pi$
$702$	4.31766	−	17.1343i	0.162960	−	0.646692i
$703$	−30.6865	−	9.97065i	−1.15736	−	0.376050i
$704$	31.1844	−	27.2415i	1.17531	−	1.02670i
$705$		0			0
$706$	3.78538	−	6.02426i	0.142465	−	0.226726i
$707$	−22.8809			−0.860526
$708$	0.957223	+	7.06765i	0.0359746	+	0.265619i
$709$	3.03019	−	4.17070i	0.113801	−	0.156634i	−0.748317	−	0.663342i	$-0.769138\pi$
$709$	3.03019	−	4.17070i	0.113801	−	0.156634i	0.862118	+	0.506708i	$0.169138\pi$
$710$		0			0
$711$	0.967444	−	0.702889i	0.0362820	−	0.0263604i
$712$	−3.57788	+	31.7453i	−0.134087	+	1.18971i
$713$	−0.758482	+	1.04396i	−0.0284054	+	0.0390966i
$714$	−3.62859	+	14.3998i	−0.135796	+	0.538897i
$715$		0			0
$716$	4.58555	+	4.79632i	0.171370	+	0.179247i
$717$	1.29663	+	3.99063i	0.0484237	+	0.149033i
$718$	−5.92705	+	4.94815i	−0.221196	+	0.184663i
$719$	5.09933	+	15.6941i	0.190173	+	0.585292i	0.999999	−	0.00137806i	$-0.000438650\pi$
$719$	5.09933	+	15.6941i	0.190173	+	0.585292i	−0.809826	+	0.586670i	$0.800439\pi$
$720$		0			0
$721$	1.73580	−	5.34224i	0.0646445	−	0.198955i
$722$	11.5897	+	28.8935i	0.431322	+	1.07531i
$723$	34.2724	−	24.9003i	1.27460	−	0.926053i
$724$	−9.70320	−	1.76109i	−0.360617	−	0.0654503i
$725$		0			0
$726$	34.1462	−	28.5067i	1.26729	−	1.05798i
$727$	13.5429	+	18.6402i	0.502278	+	0.691326i	0.982593	−	0.185770i	$-0.0594778\pi$
$727$	13.5429	+	18.6402i	0.502278	+	0.691326i	−0.480315	+	0.877096i	$0.659478\pi$
$728$	−2.41785	−	11.8107i	−0.0896114	−	0.437733i
$729$	4.19500	−	12.9109i	0.155370	−	0.478181i
$730$		0			0
$731$	27.3858	−	8.89818i	1.01290	−	0.329111i
$732$	−8.72695	−	1.58390i	−0.322557	−	0.0585427i
$733$	−11.8423	−	36.4467i	−0.437404	−	1.34619i	−0.890603	−	0.454781i	$-0.849718\pi$
$733$	−11.8423	−	36.4467i	−0.437404	−	1.34619i	0.453200	−	0.891409i	$-0.350282\pi$
$734$	−1.43864	−	21.3414i	−0.0531012	−	0.787724i
$735$		0			0
$736$	−1.33558	−	0.925397i	−0.0492300	−	0.0341106i
$737$	5.43724	−	7.48373i	0.200283	−	0.275667i
$738$	5.54564	−	0.373837i	0.204138	−	0.0137611i
$739$	5.15085	+	7.08954i	0.189477	+	0.260793i	0.893178	−	0.449704i	$-0.148470\pi$
$739$	5.15085	+	7.08954i	0.189477	+	0.260793i	−0.703701	+	0.710497i	$0.748470\pi$
$740$		0			0
$741$	−23.1444	+	31.8556i	−0.850233	+	1.17024i
$742$	−3.44585	+	5.48391i	−0.126501	+	0.201321i
$743$			7.97007i			0.292393i	0.989256	+	0.146197i	$0.0467032\pi$
$743$			7.97007i			0.292393i	−0.989256	+	0.146197i	$0.953297\pi$
$744$	−17.0773	+	18.6821i	−0.626085	+	0.684920i
$745$		0			0
$746$	17.0446	+	42.4929i	0.624046	+	1.55577i
$747$	1.25663	−	3.86752i	0.0459778	−	0.141505i
$748$	−17.1453	−	35.6045i	−0.626894	−	1.30183i
$749$		−	18.6704i		−	0.682202i
$750$		0			0
$751$	1.54105			0.0562339			0.0281169	−	0.999605i	$-0.491049\pi$
$751$	1.54105			0.0562339			0.0281169	+	0.999605i	$0.491049\pi$
$752$	−1.06768	−	3.86929i	−0.0389342	−	0.141099i
$753$	−33.1490	−	10.7708i	−1.20802	−	0.392508i
$754$	37.2750	−	14.9516i	1.35748	−	0.544506i
$755$		0			0
$756$	−1.50041	−	11.0782i	−0.0545692	−	0.402911i
$757$	20.8270			0.756971			0.378485	−	0.925607i	$-0.376445\pi$
$757$	20.8270			0.756971			0.378485	+	0.925607i	$0.376445\pi$
$758$	9.79056	−	15.5812i	0.355609	−	0.565935i
$759$	−2.39585	−	1.74069i	−0.0869640	−	0.0631831i
$760$		0			0
$761$	−7.81874	+	5.68064i	−0.283429	+	0.205923i	−0.720412	−	0.693547i	$-0.756047\pi$
$761$	−7.81874	+	5.68064i	−0.283429	+	0.205923i	0.436983	+	0.899470i	$0.356047\pi$
$762$	−1.58686	−	23.5401i	−0.0574859	−	0.852768i
$763$	11.2102	+	8.14469i	0.405837	+	0.294858i
$764$	0.583170	+	1.21103i	0.0210983	+	0.0438136i
$765$		0			0
$766$	−1.34148	−	19.9000i	−0.0484695	−	0.719015i
$767$	−5.25543	+	1.70759i	−0.189763	+	0.0616576i
$768$	−23.9995	−	20.9714i	−0.866007	−	0.756739i
$769$	−1.06128	−	3.26628i	−0.0382706	−	0.117785i	0.930096	−	0.367316i	$-0.119723\pi$
$769$	−1.06128	−	3.26628i	−0.0382706	−	0.117785i	−0.968367	+	0.249532i	$0.919723\pi$
$770$		0			0
$771$	−54.4630	−	17.6961i	−1.96144	−	0.637309i
$772$	4.50664	−	8.37431i	0.162198	−	0.301398i
$773$	−5.52497	+	4.01412i	−0.198719	+	0.144378i	−0.682695	−	0.730703i	$-0.739192\pi$
$773$	−5.52497	+	4.01412i	−0.198719	+	0.144378i	0.483976	+	0.875081i	$0.339192\pi$
$774$	7.92572	−	6.61672i	0.284884	−	0.237833i
$775$		0			0
$776$	12.0382	−	6.83017i	0.432145	−	0.245189i
$777$	−8.14579	−	11.2117i	−0.292229	−	0.402218i
$778$	25.9980	−	10.4282i	0.932074	−	0.373870i
$779$	24.7329	+	8.03620i	0.886147	+	0.287927i
$780$		0			0
$781$	−74.6564	+	24.2573i	−2.67142	+	0.867996i
$782$	−1.19039	+	0.993789i	−0.0425684	+	0.0355378i
$783$	35.4200	−	11.5086i	1.26581	−	0.411286i
$784$	11.2225	+	17.0030i	0.400804	+	0.607249i
$785$		0			0
$786$	24.7466	+	6.23589i	0.882683	+	0.222427i
$787$	3.59275	+	2.61029i	0.128068	+	0.0930467i	0.649975	−	0.759956i	$-0.274779\pi$
$787$	3.59275	+	2.61029i	0.128068	+	0.0930467i	−0.521907	+	0.853002i	$0.674779\pi$
$788$	8.11979	−	7.76298i	0.289256	−	0.276545i
$789$	24.5965	+	33.8542i	0.875658	+	1.20524i
$790$		0			0
$791$	10.6273	+	7.72119i	0.377864	+	0.274534i
$792$	−10.4583	−	9.55991i	−0.371619	−	0.339697i
$793$		−	6.87195i		−	0.244030i
$794$	12.6137	+	7.92591i	0.447644	+	0.281280i
$795$		0			0
$796$	−6.27598	−	3.37742i	−0.222446	−	0.119710i
$797$	4.56123	−	14.0380i	0.161567	−	0.497252i	−0.837200	−	0.546897i	$-0.815809\pi$
$797$	4.56123	−	14.0380i	0.161567	−	0.497252i	0.998767	+	0.0496450i	$0.0158090\pi$
$798$	−6.08731	+	24.1570i	−0.215488	+	0.855148i
$799$	−3.83071			−0.135521
$800$		0			0
$801$	10.9318			0.386255
$802$	5.02201	−	19.9294i	0.177333	−	0.703733i
$803$	18.7220	−	57.6204i	0.660685	−	2.03338i
$804$	−6.26979	−	3.37409i	−0.221118	−	0.118995i
$805$		0			0
$806$	−16.6047	−	10.4337i	−0.584877	−	0.367511i
$807$			31.5828i			1.11177i
$808$	−34.5920	−	31.6205i	−1.21694	−	1.11241i
$809$	14.9496	+	10.8616i	0.525601	+	0.381872i	0.818710	−	0.574207i	$-0.194690\pi$
$809$	14.9496	+	10.8616i	0.525601	+	0.381872i	−0.293108	+	0.956079i	$0.594690\pi$
$810$		0			0
$811$	15.6070	+	21.4812i	0.548036	+	0.754307i	0.989744	−	0.142852i	$-0.0456274\pi$
$811$	15.6070	+	21.4812i	0.548036	+	0.754307i	−0.441708	+	0.897159i	$0.645627\pi$
$812$	18.3663	−	17.5592i	0.644530	−	0.616207i
$813$	47.8677	+	34.7779i	1.67879	+	1.21971i
$814$	35.7613	+	9.01148i	1.25343	+	0.315852i
$815$		0			0
$816$	−25.3857	+	16.7554i	−0.888677	+	0.586555i
$817$	45.9423	−	14.9276i	1.60732	−	0.522249i
$818$	27.2441	−	22.7445i	0.952568	−	0.795243i
$819$	−3.92343	+	1.27480i	−0.137096	+	0.0445451i
$820$		0			0
$821$	41.8393	+	13.5944i	1.46020	+	0.474448i	0.928132	−	0.372252i	$-0.121414\pi$
$821$	41.8393	+	13.5944i	1.46020	+	0.474448i	0.532070	+	0.846700i	$0.321414\pi$
$822$	−1.81944	+	0.729808i	−0.0634603	+	0.0254550i
$823$	−14.3603	−	19.7653i	−0.500569	−	0.688975i	0.481724	−	0.876323i	$-0.340011\pi$
$823$	−14.3603	−	19.7653i	−0.500569	−	0.688975i	−0.982294	+	0.187348i	$0.940011\pi$
$824$	10.0070	−	5.67774i	0.348610	−	0.197793i
$825$		0			0
$826$	−2.68380	+	2.24054i	−0.0933812	+	0.0779585i
$827$	38.6082	−	28.0505i	1.34254	−	0.975412i	0.343192	−	0.939265i	$-0.388492\pi$
$827$	38.6082	−	28.0505i	1.34254	−	0.975412i	0.999347	−	0.0361465i	$-0.0115083\pi$
$828$	−0.263486	+	0.489613i	−0.00915676	+	0.0170152i
$829$	22.8468	+	7.42337i	0.793502	+	0.257824i	0.677595	−	0.735436i	$-0.263022\pi$
$829$	22.8468	+	7.42337i	0.793502	+	0.257824i	0.115907	+	0.993260i	$0.463022\pi$
$830$		0			0
$831$	0.670362	+	2.06316i	0.0232546	+	0.0715703i
$832$	12.6665	−	21.1971i	0.439133	−	0.734876i
$833$	18.4913	−	6.00819i	0.640686	−	0.208172i
$834$	−2.01623	−	29.9096i	−0.0698164	−	1.03568i
$835$		0			0
$836$	−28.7629	−	59.7301i	−0.994785	−	2.06581i
$837$	−14.7122	−	10.6891i	−0.508529	−	0.369468i
$838$	0.0728130	+	1.08014i	0.00251528	+	0.0373127i
$839$	13.1474	−	9.55211i	0.453897	−	0.329776i	−0.337235	−	0.941420i	$-0.609492\pi$
$839$	13.1474	−	9.55211i	0.453897	−	0.329776i	0.791132	+	0.611645i	$0.209492\pi$
$840$		0			0
$841$	45.0210	+	32.7096i	1.55245	+	1.12792i
$842$	8.80415	−	14.0114i	0.303411	−	0.482864i
$843$	50.6604			1.74484
$844$	7.56816	+	55.8794i	0.260507	+	1.92345i
$845$		0			0
$846$	−1.27479	+	0.511340i	−0.0438282	+	0.0175802i
$847$	20.7371	+	6.73789i	0.712535	+	0.231517i
$848$	−12.7881	+	3.52869i	−0.439144	+	0.121176i
$849$	−49.9824			−1.71539
$850$		0			0
$851$		−	1.44716i		−	0.0496081i
$852$	26.2141	+	54.4372i	0.898082	+	1.86499i
$853$	−14.3719	+	44.2323i	−0.492086	+	1.51449i	0.329363	+	0.944203i	$0.393166\pi$
$853$	−14.3719	+	44.2323i	−0.492086	+	1.51449i	−0.821449	+	0.570282i	$0.806834\pi$
$854$	−1.61859	−	4.03522i	−0.0553870	−	0.138082i
$855$		0			0
$856$	25.8018	−	28.2264i	0.881886	−	0.964759i
$857$		−	34.8114i		−	1.18913i	−0.804046	−	0.594567i	$-0.797323\pi$
$857$		−	34.8114i		−	1.18913i	0.804046	−	0.594567i	$-0.202677\pi$
$858$	23.9450	−	38.1073i	0.817468	−	1.30096i
$859$	−23.5563	+	32.4224i	−0.803730	+	1.10624i	0.188531	+	0.982067i	$0.439627\pi$
$859$	−23.5563	+	32.4224i	−0.803730	+	1.10624i	−0.992261	+	0.124172i	$0.960373\pi$
$860$		0			0
$861$	6.56539	+	9.03648i	0.223748	+	0.307963i
$862$	−30.6828	+	2.06836i	−1.04506	+	0.0704485i
$863$	−30.0211	+	41.3205i	−1.02193	+	1.40657i	−0.111087	+	0.993811i	$0.535433\pi$
$863$	−30.0211	+	41.3205i	−1.02193	+	1.40657i	−0.910842	+	0.412755i	$0.864567\pi$
$864$	13.0413	−	18.8219i	0.443675	−	0.640333i
$865$		0			0
$866$	0.349691	+	5.18745i	0.0118830	+	0.176277i
$867$	−1.49396	−	4.59793i	−0.0507375	−	0.156154i
$868$	−12.2078	−	2.21567i	−0.414360	−	0.0752046i
$869$	−6.08201	+	1.97617i	−0.206318	+	0.0670368i
$870$		0			0
$871$	1.70468	−	5.24648i	0.0577610	−	0.177770i
$872$	5.69225	+	27.8054i	0.192764	+	0.941611i
$873$	−2.78388	−	3.83168i	−0.0942200	−	0.129683i
$874$	−1.99700	+	1.66718i	−0.0675495	+	0.0563931i
$875$		0			0
$876$	−45.8832	−	8.32759i	−1.55025	−	0.281363i
$877$	14.2117	−	10.3254i	0.479894	−	0.348664i	−0.321390	−	0.946947i	$-0.604150\pi$
$877$	14.2117	−	10.3254i	0.479894	−	0.348664i	0.801285	+	0.598283i	$0.204150\pi$
$878$	−1.23475	−	3.07829i	−0.0416709	−	0.103887i
$879$	−19.4797	+	59.9522i	−0.657033	+	2.02214i
$880$		0			0
$881$	2.27227	+	6.99332i	0.0765546	+	0.235611i	0.982009	−	0.188832i	$-0.0604701\pi$
$881$	2.27227	+	6.99332i	0.0765546	+	0.235611i	−0.905455	+	0.424443i	$0.860470\pi$
$882$	5.35157	−	4.46771i	0.180197	−	0.150436i
$883$	−13.8280	−	42.5583i	−0.465350	−	1.43220i	−0.858541	−	0.512745i	$-0.828629\pi$
$883$	−13.8280	−	42.5583i	−0.465350	−	1.43220i	0.393191	−	0.919457i	$-0.371371\pi$
$884$	−16.2854	−	17.0340i	−0.547739	−	0.572915i
$885$		0			0
$886$	0.334936	−	1.32917i	0.0112524	−	0.0446543i
$887$	−22.0394	+	30.3347i	−0.740012	+	1.01854i	0.258606	+	0.965983i	$0.416737\pi$
$887$	−22.0394	+	30.3347i	−0.740012	+	1.01854i	−0.998618	+	0.0525565i	$0.983263\pi$
$888$	3.17913	−	28.2073i	0.106685	−	0.946577i
$889$	9.35651	−	6.79790i	0.313807	−	0.227994i
$890$		0			0
$891$	33.3647	−	45.9226i	1.11776	−	1.53846i
$892$	4.44118	+	32.7914i	0.148702	+	1.09794i
$893$	−6.42640			−0.215051
$894$	4.82925	−	7.68552i	0.161514	−	0.257042i
$895$		0			0
$896$	2.44512	−	15.4304i	0.0816859	−	0.515492i
$897$	−1.67962	−	0.545741i	−0.0560808	−	0.0182218i
$898$	−11.8612	+	47.0700i	−0.395812	+	1.57075i
$899$		−	41.3333i		−	1.37854i
$900$		0			0
$901$			12.6606i			0.421785i
$902$	−28.8231	−	7.26312i	−0.959704	−	0.241835i
$903$	19.7327	+	6.41154i	0.656663	+	0.213363i
$904$	5.39627	+	26.3596i	0.179477	+	0.876708i
$905$		0			0
$906$	−48.1761	−	30.2718i	−1.60054	−	1.00571i
$907$	9.10715			0.302398			0.151199	−	0.988503i	$-0.451687\pi$
$907$	9.10715			0.302398			0.151199	+	0.988503i	$0.451687\pi$
$908$	−24.4293	+	3.30864i	−0.810716	+	0.109801i
$909$	−9.42650	+	12.9745i	−0.312657	+	0.430336i
$910$		0			0
$911$	4.83681	−	3.51415i	0.160251	−	0.116429i	−0.504770	−	0.863254i	$-0.668423\pi$
$911$	4.83681	−	3.51415i	0.160251	−	0.116429i	0.665021	+	0.746825i	$0.268423\pi$
$912$	−42.5870	+	28.1088i	−1.41020	+	0.930774i
$913$	−12.7825	+	17.5937i	−0.423040	+	0.582265i
$914$	47.2187	+	11.8986i	1.56186	+	0.393571i
$915$		0			0
$916$	−15.6652	−	16.3852i	−0.517593	−	0.541384i
$917$	3.86572	+	11.8974i	0.127657	+	0.392888i
$918$	−14.0052	−	16.7758i	−0.462239	−	0.553685i
$919$	5.41966	+	16.6800i	0.178778	+	0.550222i	0.999786	−	0.0206948i	$-0.00658785\pi$
$919$	5.41966	+	16.6800i	0.178778	+	0.550222i	−0.821008	+	0.570917i	$0.806588\pi$
$920$		0			0
$921$	2.30252	−	7.08644i	0.0758708	−	0.233506i
$922$	−48.7829	+	19.5676i	−1.60658	+	0.644425i
$923$	−37.8721	+	27.5157i	−1.24658	+	0.905690i
$924$	5.08488	−	28.0165i	0.167280	−	0.921676i
$925$		0			0
$926$	13.0774	+	15.6645i	0.429750	+	0.514769i
$927$	−2.31416	−	3.18517i	−0.0760070	−	0.104615i
$928$	52.0328	−	1.16500i	1.70806	−	0.0382430i
$929$	−8.23207	+	25.3357i	−0.270085	+	0.831237i	0.720393	+	0.693566i	$0.243962\pi$
$929$	−8.23207	+	25.3357i	−0.270085	+	0.831237i	−0.990478	+	0.137671i	$0.956038\pi$
$930$		0			0
$931$	31.0210	−	10.0793i	1.01667	−	0.330337i
$932$	−12.6737	−	2.30021i	−0.415140	−	0.0753460i
$933$	−6.91618	−	21.2858i	−0.226425	−	0.696866i
$934$	−15.8175	+	1.06627i	−0.517563	+	0.0348894i
$935$		0			0
$936$	−7.69326	−	3.49475i	−0.251462	−	0.114229i
$937$	−5.75045	+	7.91482i	−0.187859	+	0.258566i	−0.892550	−	0.450949i	$-0.851086\pi$
$937$	−5.75045	+	7.91482i	−0.187859	+	0.258566i	0.704691	+	0.709515i	$0.251086\pi$
$938$	−0.234742	−	3.48225i	−0.00766458	−	0.113699i
$939$	7.71069	+	10.6129i	0.251629	+	0.346337i
$940$		0			0
$941$	0.184526	−	0.253979i	0.00601539	−	0.00827947i	−0.805999	−	0.591917i	$-0.798371\pi$
$941$	0.184526	−	0.253979i	0.00601539	−	0.00827947i	0.812014	+	0.583638i	$0.198371\pi$
$942$	50.9767	+	32.0316i	1.66091	+	1.04364i
$943$			1.16639i			0.0379829i
$944$	−7.15378	−	0.321586i	−0.232836	−	0.0104667i
$945$		0			0
$946$	−51.2449	+	20.5552i	−1.66612	+	0.668306i
$947$	14.4398	−	44.4410i	0.469229	−	1.44414i	−0.384356	−	0.923185i	$-0.625576\pi$
$947$	14.4398	−	44.4410i	0.469229	−	1.44414i	0.853585	−	0.520954i	$-0.174424\pi$
$948$	2.13558	+	4.43483i	0.0693605	+	0.144036i
$949$		−	36.1303i		−	1.17284i
$950$		0			0
$951$	−40.2806			−1.30619
$952$	−13.5749	−	6.16656i	−0.439967	−	0.199859i
$953$	31.6721	+	10.2909i	1.02596	+	0.333354i	0.773191	−	0.634173i	$-0.218659\pi$
$953$	31.6721	+	10.2909i	1.02596	+	0.333354i	0.252768	+	0.967527i	$0.418659\pi$
$954$	1.68999	+	4.21321i	0.0547153	+	0.136408i
$955$		0			0
$956$	−4.17484	+	0.565429i	−0.135024	+	0.0182873i
$957$	94.8585			3.06634
$958$	5.69525	+	3.57865i	0.184005	+	0.115621i
$959$	−0.777419	−	0.564828i	−0.0251042	−	0.0182393i
$960$		0			0
$961$	8.75140	−	6.35826i	0.282303	−	0.205105i
$962$	21.9431	−	1.47921i	0.707475	−	0.0476915i
$963$	−10.5869	−	7.69184i	−0.341159	−	0.247866i
$964$	18.4541	+	38.3224i	0.594365	+	1.23428i
$965$		0			0
$966$	−1.11481	+	0.0751506i	−0.0358686	+	0.00241793i
$967$	28.5494	−	9.27626i	0.918087	−	0.298304i	0.188405	−	0.982091i	$-0.439668\pi$
$967$	28.5494	−	9.27626i	0.918087	−	0.298304i	0.729682	+	0.683787i	$0.239668\pi$
$968$	22.0394	+	38.8444i	0.708373	+	1.24851i
$969$	15.0486	+	46.3148i	0.483431	+	1.48785i
$970$		0			0
$971$	−12.0721	−	3.92245i	−0.387411	−	0.125878i	0.108834	−	0.994060i	$-0.465288\pi$
$971$	−12.0721	−	3.92245i	−0.387411	−	0.125878i	−0.496245	+	0.868182i	$0.665288\pi$
$972$	−17.0862	−	9.19498i	−0.548042	−	0.294929i
$973$	11.8882	−	8.63727i	0.381118	−	0.276898i
$974$	−12.0575	−	14.4429i	−0.386348	−	0.462781i
$975$		0			0
$976$	3.12948	−	8.33737i	0.100172	−	0.266873i
$977$	29.7939	+	41.0078i	0.953191	+	1.31196i	0.950095	+	0.311960i	$0.100986\pi$
$977$	29.7939	+	41.0078i	0.953191	+	1.31196i	0.00309631	+	0.999995i	$0.499014\pi$
$978$	13.3024	+	33.1634i	0.425363	+	1.06045i
$979$	−55.5993	−	18.0653i	−1.77696	−	0.577370i
$980$		0			0
$981$	9.23677	−	3.00121i	0.294907	−	0.0958213i
$982$	16.0922	+	19.2758i	0.513524	+	0.615116i
$983$	−50.4346	+	16.3872i	−1.60862	+	0.522671i	−0.969218	−	0.246206i	$-0.920816\pi$
$983$	−50.4346	+	16.3872i	−1.60862	+	0.522671i	−0.639397	+	0.768876i	$0.720816\pi$
$984$	−2.56233	+	22.7347i	−0.0816842	+	0.724756i
$985$		0			0
$986$	12.1371	−	48.1650i	0.386523	−	1.53388i
$987$	−2.23305	−	1.62241i	−0.0710788	−	0.0516418i
$988$	−27.3204	−	28.5762i	−0.869178	−	0.909129i
$989$	1.27351	+	1.75283i	0.0404951	+	0.0557368i
$990$		0			0
$991$	1.47581	+	1.07224i	0.0468808	+	0.0340609i	0.610979	−	0.791647i	$-0.290776\pi$
$991$	1.47581	+	1.07224i	0.0468808	+	0.0340609i	−0.564098	+	0.825708i	$0.690776\pi$
$992$	−15.3942	−	20.2204i	−0.488765	−	0.641999i
$993$			42.5146i			1.34916i
$994$	−15.7576	+	25.0775i	−0.499801	+	0.795409i
$995$		0			0
$996$	14.7398	+	7.93223i	0.467048	+	0.251342i
$997$	5.04048	−	15.5130i	0.159634	−	0.491302i	−0.838967	−	0.544182i	$-0.816840\pi$
$997$	5.04048	−	15.5130i	0.159634	−	0.491302i	0.998601	+	0.0528802i	$0.0168401\pi$
$998$	21.4175	+	5.39697i	0.677958	+	0.170838i
$999$	20.3944			0.645250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.949.11		112
5.2	odd	4		1000.2.t.b.301.5		224
5.3	odd	4		1000.2.t.b.301.52		224
5.4	even	2		200.2.o.a.189.18	yes	112
8.5	even	2	inner	1000.2.o.a.949.28		112
20.19	odd	2		800.2.be.a.689.7		112
25.9	even	10	inner	1000.2.o.a.549.28		112
25.12	odd	20		1000.2.t.b.701.27		224
25.13	odd	20		1000.2.t.b.701.30		224
25.16	even	5		200.2.o.a.109.1	✓	112
40.13	odd	4		1000.2.t.b.301.30		224
40.19	odd	2		800.2.be.a.689.22		112
40.29	even	2		200.2.o.a.189.1	yes	112
40.37	odd	4		1000.2.t.b.301.27		224
100.91	odd	10		800.2.be.a.209.22		112
200.13	odd	20		1000.2.t.b.701.52		224
200.37	odd	20		1000.2.t.b.701.5		224
200.91	odd	10		800.2.be.a.209.7		112
200.109	even	10	inner	1000.2.o.a.549.11		112
200.141	even	10		200.2.o.a.109.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.1	✓	112	25.16	even	5
200.2.o.a.109.18	yes	112	200.141	even	10
200.2.o.a.189.1	yes	112	40.29	even	2
200.2.o.a.189.18	yes	112	5.4	even	2
800.2.be.a.209.7		112	200.91	odd	10
800.2.be.a.209.22		112	100.91	odd	10
800.2.be.a.689.7		112	20.19	odd	2
800.2.be.a.689.22		112	40.19	odd	2
1000.2.o.a.549.11		112	200.109	even	10	inner
1000.2.o.a.549.28		112	25.9	even	10	inner
1000.2.o.a.949.11		112	1.1	even	1	trivial
1000.2.o.a.949.28		112	8.5	even	2	inner
1000.2.t.b.301.5		224	5.2	odd	4
1000.2.t.b.301.27		224	40.37	odd	4
1000.2.t.b.301.30		224	40.13	odd	4
1000.2.t.b.301.52		224	5.3	odd	4
1000.2.t.b.701.5		224	200.37	odd	20
1000.2.t.b.701.27		224	25.12	odd	20
1000.2.t.b.701.30		224	25.13	odd	20
1000.2.t.b.701.52		224	200.13	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.345564 + 1.37134i) q^{2} +(-0.615546 + 1.89446i) q^{3} +(-1.76117 - 0.947775i) q^{4} +(-2.38524 - 1.49878i) q^{6} -1.38088i q^{7} +(1.90832 - 2.08765i) q^{8} +(-0.783019 - 0.568896i) q^{9} +(3.04233 + 4.18740i) q^{11} +(2.87960 - 2.75306i) q^{12} +(2.49716 + 1.81429i) q^{13} +(1.89366 + 0.477183i) q^{14} +(2.20344 + 3.33839i) q^{16} +(3.63061 - 1.17966i) q^{17} +(1.05074 - 0.877198i) q^{18} +(6.09071 - 1.97899i) q^{19} +(2.61602 + 0.849997i) q^{21} +(-6.79369 + 2.72506i) q^{22} +(0.168832 + 0.232378i) q^{23} +(2.78031 + 4.90029i) q^{24} +(-3.35095 + 2.79751i) q^{26} +(-3.27483 + 2.37930i) q^{27} +(-1.30877 + 2.43197i) q^{28} +(-8.75018 - 2.84311i) q^{29} +(1.38826 + 4.27263i) q^{31} +(-5.33951 + 1.86805i) q^{32} +(-9.80555 + 3.18602i) q^{33} +(0.363107 + 5.38647i) q^{34} +(0.839843 + 1.74405i) q^{36} +(-4.07603 - 2.96141i) q^{37} +(0.609147 + 9.03633i) q^{38} +(-4.97421 + 3.61398i) q^{39} +(3.28522 + 2.38685i) q^{41} +(-2.06964 + 3.29374i) q^{42} +7.54302 q^{43} +(-1.38934 - 10.2582i) q^{44} +(-0.377013 + 0.151226i) q^{46} +(-0.954360 - 0.310090i) q^{47} +(-7.68075 + 2.11940i) q^{48} +5.09317 q^{49} +7.60418i q^{51} +(-2.67838 - 5.56202i) q^{52} +(-1.02485 + 3.15418i) q^{53} +(-2.13118 - 5.31312i) q^{54} +(-2.88280 - 2.63517i) q^{56} +12.7567i q^{57} +(6.92263 - 11.0170i) q^{58} +(-1.05228 + 1.44834i) q^{59} +(-1.30861 - 1.80115i) q^{61} +(-6.33899 + 0.427317i) q^{62} +(-0.785578 + 1.08126i) q^{63} +(-0.716599 - 7.96784i) q^{64} +(-0.980677 - 14.5478i) q^{66} +(-0.552275 - 1.69973i) q^{67} +(-7.51218 - 1.36343i) q^{68} +(-0.544154 + 0.176806i) q^{69} +(-4.68658 + 14.4238i) q^{71} +(-2.68191 + 0.549033i) q^{72} +(-6.88021 - 9.46979i) q^{73} +(5.46964 - 4.56628i) q^{74} +(-12.6024 - 2.28728i) q^{76} +(5.78231 - 4.20109i) q^{77} +(-3.23710 - 8.07022i) q^{78} +(-0.381800 + 1.17506i) q^{79} +(-3.38894 - 10.4301i) q^{81} +(-4.40845 + 3.68036i) q^{82} +(1.29836 + 3.99593i) q^{83} +(-3.80165 - 3.97639i) q^{84} +(-2.60660 + 10.3441i) q^{86} +(10.7723 - 14.8268i) q^{87} +(14.5476 + 1.63960i) q^{88} +(-9.13763 + 6.63888i) q^{89} +(2.50532 - 3.44828i) q^{91} +(-0.0771007 - 0.569272i) q^{92} -8.94886 q^{93} +(0.755034 - 1.20160i) q^{94} +(-0.252228 - 11.2653i) q^{96} +(4.65397 + 1.51217i) q^{97} +(-1.76002 + 6.98448i) q^{98} -5.00958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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