LMFDB - Embedded newform 1000.2.t.b.301.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(101,1000)] 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("1000.101"); 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, 6])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [224] 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:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			301.5
Character	$\chi$	$=$	1000.301
Dual form			1000.2.t.b.701.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37134 - 0.345564i) q^{2} +(1.89446 + 0.615546i) q^{3} +(1.76117 + 0.947775i) q^{4} +(-2.38524 - 1.49878i) q^{6} +1.38088 q^{7} +(-2.08765 - 1.90832i) q^{8} +(0.783019 + 0.568896i) q^{9} +(3.04233 + 4.18740i) q^{11} +(2.75306 + 2.87960i) q^{12} +(1.81429 - 2.49716i) q^{13} +(-1.89366 - 0.477183i) q^{14} +(2.20344 + 3.33839i) q^{16} +(1.17966 + 3.63061i) q^{17} +(-0.877198 - 1.05074i) q^{18} +(-6.09071 + 1.97899i) q^{19} +(2.61602 + 0.849997i) q^{21} +(-2.72506 - 6.79369i) q^{22} +(0.232378 - 0.168832i) q^{23} +(-2.78031 - 4.90029i) q^{24} +(-3.35095 + 2.79751i) q^{26} +(-2.37930 - 3.27483i) q^{27} +(2.43197 + 1.30877i) q^{28} +(8.75018 + 2.84311i) q^{29} +(1.38826 + 4.27263i) q^{31} +(-1.86805 - 5.33951i) q^{32} +(3.18602 + 9.80555i) q^{33} +(-0.363107 - 5.38647i) q^{34} +(0.839843 + 1.74405i) q^{36} +(2.96141 - 4.07603i) q^{37} +(9.03633 - 0.609147i) q^{38} +(4.97421 - 3.61398i) q^{39} +(3.28522 + 2.38685i) q^{41} +(-3.29374 - 2.06964i) q^{42} -7.54302i q^{43} +(1.38934 + 10.2582i) q^{44} +(-0.377013 + 0.151226i) q^{46} +(0.310090 - 0.954360i) q^{47} +(2.11940 + 7.68075i) q^{48} -5.09317 q^{49} +7.60418i q^{51} +(5.56202 - 2.67838i) q^{52} +(3.15418 + 1.02485i) q^{53} +(2.13118 + 5.31312i) q^{54} +(-2.88280 - 2.63517i) q^{56} -12.7567 q^{57} +(-11.0170 - 6.92263i) q^{58} +(1.05228 - 1.44834i) q^{59} +(-1.30861 - 1.80115i) q^{61} +(-0.427317 - 6.33899i) q^{62} +(1.08126 + 0.785578i) q^{63} +(0.716599 + 7.96784i) q^{64} +(-0.980677 - 14.5478i) q^{66} +(1.69973 - 0.552275i) q^{67} +(-1.36343 + 7.51218i) q^{68} +(0.544154 - 0.176806i) q^{69} +(-4.68658 + 14.4238i) q^{71} +(-0.549033 - 2.68191i) q^{72} +(-9.46979 + 6.88021i) q^{73} +(-5.46964 + 4.56628i) q^{74} +(-12.6024 - 2.28728i) q^{76} +(4.20109 + 5.78231i) q^{77} +(-8.07022 + 3.23710i) q^{78} +(0.381800 - 1.17506i) q^{79} +(-3.38894 - 10.4301i) q^{81} +(-3.68036 - 4.40845i) q^{82} +(3.99593 - 1.29836i) q^{83} +(3.80165 + 3.97639i) q^{84} +(-2.60660 + 10.3441i) q^{86} +(14.8268 + 10.7723i) q^{87} +(1.63960 - 14.5476i) q^{88} +(9.13763 - 6.63888i) q^{89} +(2.50532 - 3.44828i) q^{91} +(0.569272 - 0.0771007i) q^{92} +8.94886i q^{93} +(-0.755034 + 1.20160i) q^{94} +(-0.252228 - 11.2653i) q^{96} +(-1.51217 + 4.65397i) q^{97} +(6.98448 + 1.76002i) q^{98} +5.00958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$

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 $

$2$	−1.37134	−	0.345564i	−0.969687	−	0.244351i
$2$	−1.37134	−	0.345564i	−0.969687	−	0.244351i
$3$	1.89446	+	0.615546i	1.09377	+	0.355386i	0.799700	−	0.600400i	$-0.204992\pi$
$3$	1.89446	+	0.615546i	1.09377	+	0.355386i	0.294065	+	0.955785i	$0.404992\pi$
$4$	1.76117	+	0.947775i	0.880585	+	0.473888i
$5$		0			0
$5$		0			0
$6$	−2.38524	−	1.49878i	−0.973771	−	0.611875i
$7$	1.38088			0.521924			0.260962	−	0.965349i	$-0.415960\pi$
$7$	1.38088			0.521924			0.260962	+	0.965349i	$0.415960\pi$
$8$	−2.08765	−	1.90832i	−0.738097	−	0.674694i
$9$	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	$0.515067\pi$
$12$	2.75306	+	2.87960i	0.794741	+	0.831269i
$13$	1.81429	−	2.49716i	0.503194	−	0.692587i	−0.479559	−	0.877510i	$-0.659203\pi$
$13$	1.81429	−	2.49716i	0.503194	−	0.692587i	0.982753	+	0.184923i	$0.0592034\pi$
$14$	−1.89366	−	0.477183i	−0.506103	−	0.127533i
$15$		0			0
$16$	2.20344	+	3.33839i	0.550861	+	0.834597i
$17$	1.17966	+	3.63061i	0.286109	+	0.880553i	0.986064	+	0.166366i	$0.0532034\pi$
$17$	1.17966	+	3.63061i	0.286109	+	0.880553i	−0.699955	+	0.714187i	$0.746797\pi$
$18$	−0.877198	−	1.05074i	−0.206758	−	0.247661i
$19$	−6.09071	+	1.97899i	−1.39730	+	0.454012i	−0.908318	−	0.418280i	$-0.862633\pi$
$19$	−6.09071	+	1.97899i	−1.39730	+	0.454012i	−0.488986	+	0.872292i	$0.662633\pi$
$20$		0			0
$21$	2.61602	+	0.849997i	0.570863	+	0.185484i
$22$	−2.72506	−	6.79369i	−0.580985	−	1.44842i
$23$	0.232378	−	0.168832i	0.0484541	−	0.0352040i	−0.563295	−	0.826256i	$-0.690466\pi$
$23$	0.232378	−	0.168832i	0.0484541	−	0.0352040i	0.611749	+	0.791052i	$0.290466\pi$
$24$	−2.78031	−	4.90029i	−0.567528	−	1.00027i
$25$		0			0
$26$	−3.35095	+	2.79751i	−0.657175	+	0.548637i
$27$	−2.37930	−	3.27483i	−0.457897	−	0.630241i
$28$	2.43197	+	1.30877i	0.459599	+	0.247333i
$29$	8.75018	+	2.84311i	1.62487	+	0.527952i	0.973084	−	0.230452i	$-0.0740206\pi$
$29$	8.75018	+	2.84311i	1.62487	+	0.527952i	0.651785	+	0.758404i	$0.274021\pi$
$30$		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	$0.767815\pi$
$32$	−1.86805	−	5.33951i	−0.330228	−	0.943901i
$33$	3.18602	+	9.80555i	0.554614	+	1.70693i
$34$	−0.363107	−	5.38647i	−0.0622723	−	0.923772i
$35$		0			0
$36$	0.839843	+	1.74405i	0.139974	+	0.290675i
$37$	2.96141	−	4.07603i	0.486853	−	0.670095i	−0.492951	−	0.870057i	$-0.664082\pi$
$37$	2.96141	−	4.07603i	0.486853	−	0.670095i	0.979804	+	0.199962i	$0.0640818\pi$
$38$	9.03633	−	0.609147i	1.46589	−	0.0988166i
$39$	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	$0.597294\pi$
$42$	−3.29374	−	2.06964i	−0.508235	−	0.319353i
$43$		−	7.54302i		−	1.15030i	−0.818048	−	0.575150i	$-0.804944\pi$
$43$		−	7.54302i		−	1.15030i	0.818048	−	0.575150i	$-0.195056\pi$
$44$	1.38934	+	10.2582i	0.209451	+	1.54648i
$45$		0			0
$46$	−0.377013	+	0.151226i	−0.0555875	+	0.0222970i
$47$	0.310090	−	0.954360i	0.0452313	−	0.139208i	−0.925890	−	0.377792i	$-0.876683\pi$
$47$	0.310090	−	0.954360i	0.0452313	−	0.139208i	0.971122	+	0.238584i	$0.0766834\pi$
$48$	2.11940	+	7.68075i	0.305909	+	1.10862i
$49$	−5.09317			−0.727595
$50$		0			0
$51$			7.60418i			1.06480i
$52$	5.56202	−	2.67838i	0.771314	−	0.371425i
$53$	3.15418	+	1.02485i	0.433260	+	0.140775i	0.517524	−	0.855669i	$-0.326854\pi$
$53$	3.15418	+	1.02485i	0.433260	+	0.140775i	−0.0842641	+	0.996443i	$0.526854\pi$
$54$	2.13118	+	5.31312i	0.290017	+	0.723024i
$55$		0			0
$56$	−2.88280	−	2.63517i	−0.385231	−	0.352139i
$57$	−12.7567			−1.68967
$58$	−11.0170	−	6.92263i	−1.44661	−	0.908986i
$59$	1.05228	−	1.44834i	0.136996	−	0.188558i	−0.735007	−	0.678060i	$-0.762821\pi$
$59$	1.05228	−	1.44834i	0.136996	−	0.188558i	0.872003	+	0.489501i	$0.162821\pi$
$60$		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	$0.845523\pi$
$62$	−0.427317	−	6.33899i	−0.0542693	−	0.805052i
$63$	1.08126	+	0.785578i	0.136225	+	0.0989736i
$64$	0.716599	+	7.96784i	0.0895748	+	0.995980i
$65$		0			0
$66$	−0.980677	−	14.5478i	−0.120713	−	1.79071i
$67$	1.69973	−	0.552275i	0.207655	−	0.0674711i	−0.203343	−	0.979108i	$-0.565181\pi$
$67$	1.69973	−	0.552275i	0.207655	−	0.0674711i	0.410997	+	0.911637i	$0.365181\pi$
$68$	−1.36343	+	7.51218i	−0.165340	+	0.910986i
$69$	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	$0.743609\pi$
$72$	−0.549033	−	2.68191i	−0.0647042	−	0.316066i
$73$	−9.46979	+	6.88021i	−1.10836	+	0.805267i	−0.982404	−	0.186769i	$-0.940198\pi$
$73$	−9.46979	+	6.88021i	−1.10836	+	0.805267i	−0.125951	+	0.992036i	$0.540198\pi$
$74$	−5.46964	+	4.56628i	−0.635833	+	0.530820i
$75$		0			0
$76$	−12.6024	−	2.28728i	−1.44560	−	0.262369i
$77$	4.20109	+	5.78231i	0.478759	+	0.658955i
$78$	−8.07022	+	3.23710i	−0.913773	+	0.366529i
$79$	0.381800	−	1.17506i	0.0429559	−	0.132205i	−0.927279	−	0.374372i	$-0.877858\pi$
$79$	0.381800	−	1.17506i	0.0429559	−	0.132205i	0.970234	+	0.242167i	$0.0778583\pi$
$80$		0			0
$81$	−3.38894	−	10.4301i	−0.376549	−	1.15890i
$82$	−3.68036	−	4.40845i	−0.406428	−	0.486832i
$83$	3.99593	−	1.29836i	0.438610	−	0.142513i	−0.0813841	−	0.996683i	$-0.525934\pi$
$83$	3.99593	−	1.29836i	0.438610	−	0.142513i	0.519994	+	0.854170i	$0.325934\pi$
$84$	3.80165	+	3.97639i	0.414794	+	0.433860i
$85$		0			0
$86$	−2.60660	+	10.3441i	−0.281077	+	1.11543i
$87$	14.8268	+	10.7723i	1.58960	+	1.15491i
$88$	1.63960	−	14.5476i	0.174782	−	1.55078i
$89$	9.13763	−	6.63888i	0.968587	−	0.703720i	0.0134580	−	0.999909i	$-0.495716\pi$
$89$	9.13763	−	6.63888i	0.968587	−	0.703720i	0.955129	+	0.296190i	$0.0957160\pi$
$90$		0			0
$91$	2.50532	−	3.44828i	0.262629	−	0.361478i
$92$	0.569272	−	0.0771007i	0.0593508	−	0.00803830i
$93$			8.94886i			0.927954i
$94$	−0.755034	+	1.20160i	−0.0778758	+	0.123936i
$95$		0			0
$96$	−0.252228	−	11.2653i	−0.0257429	−	1.14976i
$97$	−1.51217	+	4.65397i	−0.153537	+	0.472539i	−0.998010	−	0.0630600i	$-0.979914\pi$
$97$	−1.51217	+	4.65397i	−0.153537	+	0.472539i	0.844473	+	0.535599i	$0.179914\pi$
$98$	6.98448	+	1.76002i	0.705539	+	0.177788i
$99$			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	$-0.308475\pi$
$102$	2.62773	−	10.4279i	0.260184	−	1.03252i
$103$	1.25702	−	3.86872i	0.123858	−	0.381196i	−0.869833	−	0.493346i	$-0.835774\pi$
$103$	1.25702	−	3.86872i	0.123858	−	0.381196i	0.993691	+	0.112150i	$0.0357737\pi$
$104$	−8.55300	+	1.75095i	−0.838691	+	0.171694i
$105$		0			0
$106$	−3.97131	−	2.49540i	−0.385728	−	0.242375i
$107$			13.5206i			1.30709i	0.756888	+	0.653545i	$0.226719\pi$
$107$			13.5206i			1.30709i	−0.756888	+	0.653545i	$0.773281\pi$
$108$	−1.08656	−	8.02258i	−0.104554	−	0.771973i
$109$	5.89818	−	8.11815i	0.564944	−	0.777578i	−0.427001	−	0.904251i	$-0.640430\pi$
$109$	5.89818	−	8.11815i	0.564944	−	0.777578i	0.991945	+	0.126673i	$0.0404299\pi$
$110$		0			0
$111$	8.11925	−	5.89898i	0.770645	−	0.559906i
$112$	3.04270	+	4.60992i	0.287508	+	0.435596i
$113$	7.69603	+	5.59149i	0.723982	+	0.526004i	0.887654	−	0.460511i	$-0.152334\pi$
$113$	7.69603	+	5.59149i	0.723982	+	0.526004i	−0.163672	+	0.986515i	$0.552334\pi$
$114$	17.4939	+	4.40828i	1.63845	+	0.412873i
$115$		0			0
$116$	12.7159	+	13.3004i	1.18065	+	1.23491i
$117$	2.84125	−	0.923177i	0.262673	−	0.0853478i
$118$	−1.94354	+	1.62255i	−0.178917	+	0.149367i
$119$	1.62897	+	5.01345i	0.149327	+	0.459582i
$120$		0			0
$121$	−4.87941	+	15.0173i	−0.443583	+	1.36521i
$122$	1.17214	+	2.92220i	0.106121	+	0.264564i
$123$	4.75449	+	6.54400i	0.428698	+	0.590052i
$124$	−1.60453	+	8.84060i	−0.144091	+	0.793909i
$125$		0			0
$126$	−1.21131	−	1.45094i	−0.107912	−	0.129260i
$127$	−6.77575	+	4.92287i	−0.601251	+	0.436834i	−0.846323	−	0.532671i	$-0.821188\pi$
$127$	−6.77575	+	4.92287i	−0.601251	+	0.436834i	0.245072	+	0.969505i	$0.421188\pi$
$128$	1.77070	−	11.1743i	0.156509	−	0.987677i
$129$	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	$0.529517\pi$
$132$	−3.68234	+	20.2889i	−0.320507	+	1.76592i
$133$	−8.41055	+	2.73275i	−0.729287	+	0.236960i
$134$	−2.52176	+	0.169994i	−0.217847	+	0.0146852i
$135$		0			0
$136$	4.46567	−	9.83064i	0.382928	−	0.842970i
$137$	0.562988	+	0.409034i	0.0480993	+	0.0349462i	0.611575	−	0.791186i	$-0.290536\pi$
$137$	0.562988	+	0.409034i	0.0480993	+	0.0349462i	−0.563476	+	0.826133i	$0.690536\pi$
$138$	−0.807321	+	0.0544222i	−0.0687237	+	0.00463273i
$139$	−6.25490	−	8.60913i	−0.530533	−	0.730217i	0.456678	−	0.889632i	$-0.349039\pi$
$139$	−6.25490	−	8.60913i	−0.530533	−	0.730217i	−0.987212	+	0.159415i	$0.949039\pi$
$140$		0			0
$141$	1.17491	−	1.61712i	0.0989449	−	0.136186i
$142$	11.4113	−	18.1605i	0.957612	−	1.52399i
$143$	15.9763			1.33600
$144$	−0.173859	+	3.86755i	−0.0144883	+	0.322296i
$145$		0			0
$146$	15.3639	−	6.16271i	1.27153	−	0.510029i
$147$	−9.64878	−	3.13508i	−0.795818	−	0.258577i
$148$	9.07871	−	4.37183i	0.746265	−	0.359363i
$149$		−	3.22211i		−	0.263966i	−0.991252	−	0.131983i	$-0.957866\pi$
$149$		−	3.22211i		−	0.263966i	0.991252	−	0.131983i	$-0.0421344\pi$
$150$		0			0
$151$	20.1976			1.64366			0.821828	−	0.569736i	$-0.192955\pi$
$151$	20.1976			1.64366			0.821828	+	0.569736i	$0.192955\pi$
$152$	16.4918	+	7.49160i	1.33767	+	0.607649i
$153$	−1.14175	+	3.51394i	−0.0923049	+	0.284085i
$154$	−3.76299	−	9.38129i	−0.303230	−	0.755966i
$155$		0			0
$156$	12.1857	−	1.65039i	0.975635	−	0.132137i
$157$		−	21.3717i		−	1.70565i	−0.522198	−	0.852824i	$-0.674888\pi$
$157$		−	21.3717i		−	1.70565i	0.522198	−	0.852824i	$-0.325112\pi$
$158$	−0.929638	+	1.47948i	−0.0739581	+	0.117701i
$159$	5.34461	+	3.88309i	0.423855	+	0.307949i
$160$		0			0
$161$	0.320886	−	0.233138i	0.0252894	−	0.0183738i
$162$	1.04314	+	15.4743i	0.0819566	+	1.21578i
$163$	−7.45556	+	10.2617i	−0.583965	+	0.803759i	−0.994123	−	0.108256i	$-0.965473\pi$
$163$	−7.45556	+	10.2617i	−0.583965	+	0.803759i	0.410158	+	0.912014i	$0.365473\pi$
$164$	3.52363	+	7.31731i	0.275150	+	0.571386i
$165$		0			0
$166$	−5.92846	+	0.399643i	−0.460138	+	0.0310183i
$167$	−2.84315	−	8.75032i	−0.220010	−	0.677120i	−0.998760	−	0.0497860i	$-0.984146\pi$
$167$	−2.84315	−	8.75032i	−0.220010	−	0.677120i	0.778750	−	0.627334i	$-0.215854\pi$
$168$	−3.83928	−	6.76671i	−0.296207	−	0.522063i
$169$	1.07308	+	3.30259i	0.0825444	+	0.254045i
$170$		0			0
$171$	−5.89498	−	1.91539i	−0.450800	−	0.146474i
$172$	7.14909	−	13.2845i	0.545113	−	1.01294i
$173$	−11.4618	−	15.7758i	−0.871423	−	1.19941i	−0.978723	−	0.205184i	$-0.934221\pi$
$173$	−11.4618	−	15.7758i	−0.871423	−	1.19941i	0.107301	−	0.994227i	$-0.465779\pi$
$174$	−16.6101	−	19.8961i	−1.25921	−	1.50832i
$175$		0			0
$176$	−7.27558	+	19.3832i	−0.548418	+	1.46106i
$177$	2.88503	−	2.09609i	0.216852	−	0.157552i
$178$	−14.8250	+	5.94655i	−1.11118	+	0.445713i
$179$	3.15544	+	1.02527i	0.235849	+	0.0766320i	0.424557	−	0.905401i	$-0.360430\pi$
$179$	3.15544	+	1.02527i	0.235849	+	0.0766320i	−0.188708	+	0.982033i	$0.560430\pi$
$180$		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	$0.341337\pi$
$182$	−4.62726	+	3.86303i	−0.342995	+	0.286347i
$183$	−1.37042	−	4.21771i	−0.101304	−	0.311782i
$184$	−0.807312	−	0.0909887i	−0.0595158	−	0.00670777i
$185$		0			0
$186$	3.09241	−	12.2720i	0.226746	−	0.899825i
$187$	−11.6139	+	15.9852i	−0.849296	+	1.16896i
$188$	1.45064	−	1.38690i	0.105799	−	0.101150i
$189$	−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	$0.707740\pi$
$192$	−3.54701	+	15.5358i	−0.255983	+	1.12120i
$193$	4.75497			0.342270			0.171135	−	0.985248i	$-0.445257\pi$
$193$	4.75497			0.342270			0.171135	+	0.985248i	$0.445257\pi$
$194$	3.68194	−	5.85964i	0.264348	−	0.420698i
$195$		0			0
$196$	−8.96993	−	4.82718i	−0.640710	−	0.344798i
$197$	−5.34192	−	1.73569i	−0.380596	−	0.123663i	0.112470	−	0.993655i	$-0.464124\pi$
$197$	−5.34192	−	1.73569i	−0.380596	−	0.123663i	−0.493066	+	0.869992i	$0.664124\pi$
$198$	1.73113	−	6.86986i	0.123026	−	0.488220i
$199$	−3.56353			−0.252612			−0.126306	−	0.991991i	$-0.540312\pi$
$199$	−3.56353			−0.252612			−0.126306	+	0.991991i	$0.540312\pi$
$200$		0			0
$201$	3.56001			0.251104
$202$	−5.72593	+	22.7229i	−0.402875	+	1.59878i
$203$	12.0830	+	3.92599i	0.848058	+	0.275551i
$204$	−7.20705	+	13.3923i	−0.504595	+	0.937645i
$205$		0			0
$206$	−3.06070	+	4.87096i	−0.213249	+	0.339376i
$207$	0.278004			0.0193226
$208$	12.3342	+	0.554462i	0.855221	+	0.0384450i
$209$	−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	$-0.622498\pi$
$212$	4.58371	+	4.79440i	0.314811	+	0.329280i
$213$	−17.7570	+	24.4405i	−1.21669	+	1.67463i
$214$	4.67225	−	18.5415i	0.319389	−	1.26747i
$215$		0			0
$216$	−1.28227	+	11.3772i	−0.0872478	+	0.774120i
$217$	1.91703	+	5.90000i	0.130136	+	0.400518i
$218$	−10.8938	+	9.09458i	−0.737820	+	0.615963i
$219$	−22.1752	+	7.20516i	−1.49846	+	0.486879i
$220$		0			0
$221$	11.2065	+	3.64120i	0.753828	+	0.244934i
$222$	−13.1728	+	5.28381i	−0.884098	+	0.354626i
$223$	−13.3855	+	9.72513i	−0.896359	+	0.651243i	−0.937528	−	0.347909i	$-0.886892\pi$
$223$	−13.3855	+	9.72513i	−0.896359	+	0.651243i	0.0411689	+	0.999152i	$0.486892\pi$
$224$	−2.57956	−	7.37323i	−0.172354	−	0.492645i
$225$		0			0
$226$	−8.62169	−	10.3273i	−0.573506	−	0.686964i
$227$	7.24515	+	9.97209i	0.480878	+	0.661871i	0.978673	−	0.205423i	$-0.0658571\pi$
$227$	7.24515	+	9.97209i	0.480878	+	0.661871i	−0.497796	+	0.867294i	$0.665857\pi$
$228$	−22.4668	−	12.0905i	−1.48790	−	0.800715i
$229$	−10.7797	−	3.50252i	−0.712340	−	0.231453i	−0.0696410	−	0.997572i	$-0.522185\pi$
$229$	−10.7797	−	3.50252i	−0.712340	−	0.231453i	−0.642699	+	0.766119i	$0.722185\pi$
$230$		0			0
$231$	4.39951	+	13.5403i	0.289467	+	0.890887i
$232$	−12.8418	−	22.6336i	−0.843105	−	1.48597i
$233$	−1.99018	−	6.12514i	−0.130381	−	0.401271i	0.864462	−	0.502698i	$-0.167659\pi$
$233$	−1.99018	−	6.12514i	−0.130381	−	0.401271i	−0.994843	+	0.101427i	$0.967659\pi$
$234$	−4.21535	+	0.284160i	−0.275566	+	0.0185761i
$235$		0			0
$236$	3.22595	−	1.55345i	0.209992	−	0.101121i
$237$	1.44661	−	1.99109i	0.0939673	−	0.129335i
$238$	−0.501407	−	7.43808i	−0.0325014	−	0.482139i
$239$	−1.70418	+	1.23816i	−0.110234	+	0.0800897i	−0.641537	−	0.767092i	$-0.721703\pi$
$239$	−1.70418	+	1.23816i	−0.110234	+	0.0800897i	0.531303	+	0.847182i	$0.321703\pi$
$240$		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	$0.940183\pi$
$242$	11.8808	−	18.9077i	0.763726	−	1.21543i
$243$		−	9.70164i		−	0.622360i
$244$	−0.597603	−	4.41240i	−0.0382576	−	0.282475i
$245$		0			0
$246$	−4.25867	−	10.6171i	−0.271523	−	0.676919i
$247$	−6.10847	+	18.7999i	−0.388672	+	1.19621i
$248$	5.25536	−	11.5690i	0.333716	−	0.734635i
$249$	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	$0.813778\pi$
$252$	1.15972	+	2.40833i	0.0730558	+	0.151710i
$253$	1.41394	+	0.459417i	0.0888936	+	0.0288833i
$254$	10.9931	−	4.40949i	0.689766	−	0.276676i
$255$		0			0
$256$	−6.28967	+	14.7119i	−0.393104	+	0.919494i
$257$	−28.7486			−1.79329			−0.896644	−	0.442753i	$-0.854002\pi$
$257$	−28.7486			−1.79329			−0.896644	+	0.442753i	$0.854002\pi$
$258$	−11.3053	+	17.9919i	−0.703840	+	1.12013i
$259$	4.08936	−	5.62852i	0.254100	−	0.349739i
$260$		0			0
$261$	5.23412	+	7.20415i	0.323984	+	0.445926i
$262$	12.7827	−	0.861691i	0.789716	−	0.0532354i
$263$	−16.9955	−	12.3479i	−1.04799	−	0.761407i	−0.0761580	−	0.997096i	$-0.524265\pi$
$263$	−16.9955	−	12.3479i	−1.04799	−	0.761407i	−0.971829	+	0.235689i	$0.924265\pi$
$264$	12.0609	−	26.5505i	0.742295	−	1.63407i
$265$		0			0
$266$	12.4781	−	0.841160i	0.765081	−	0.0515748i
$267$	21.3974	−	6.95243i	1.30950	−	0.425482i
$268$	3.51694	+	0.638309i	0.214831	+	0.0389910i
$269$	−15.0792	+	4.89953i	−0.919396	+	0.298730i	−0.730219	−	0.683213i	$-0.760582\pi$
$269$	−15.0792	+	4.89953i	−0.919396	+	0.298730i	−0.189177	+	0.981943i	$0.560582\pi$
$270$		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	$-0.258032\pi$
$272$	−9.52109	+	11.9380i	−0.577301	+	0.723848i
$273$	6.86880	−	4.99048i	0.415719	−	0.302037i
$274$	−0.630702	−	0.755475i	−0.0381021	−	0.0456399i
$275$		0			0
$276$	1.12592	+	0.204350i	0.0677725	+	0.0123004i
$277$	0.640129	+	0.881062i	0.0384616	+	0.0529379i	0.827815	−	0.561002i	$-0.189584\pi$
$277$	0.640129	+	0.881062i	0.0384616	+	0.0529379i	−0.789353	+	0.613940i	$0.789584\pi$
$278$	5.60261	+	13.9675i	0.336022	+	0.837718i
$279$	−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	$-0.374111\pi$
$282$	−2.17002	+	1.81162i	−0.129223	+	0.107881i
$283$	23.8641	−	7.75392i	1.41857	−	0.460923i	0.503425	−	0.864039i	$-0.332073\pi$
$283$	23.8641	−	7.75392i	1.41857	−	0.460923i	0.915149	+	0.403116i	$0.132073\pi$
$284$	−21.9244	+	20.9610i	−1.30097	+	1.24380i
$285$		0			0
$286$	−21.9090	−	5.52083i	−1.29550	−	0.326454i
$287$	4.53650	+	3.29596i	0.267781	+	0.194554i
$288$	1.57491	−	5.24366i	0.0928024	−	0.308986i
$289$	1.96352	−	1.42658i	0.115501	−	0.0839166i
$290$		0			0
$291$	−5.72946	+	7.88593i	−0.335867	+	0.462281i
$292$	−23.1988	+	3.14198i	−1.35761	+	0.183871i
$293$		−	31.6461i		−	1.84879i	−0.381440	−	0.924393i	$-0.624572\pi$
$293$		−	31.6461i		−	1.84879i	0.381440	−	0.924393i	$-0.375428\pi$
$294$	12.1484	+	7.63355i	0.708511	+	0.445198i
$295$		0			0
$296$	−13.9608	+	2.85801i	−0.811454	+	0.166119i
$297$	6.47442	−	19.9262i	0.375684	−	1.15624i
$298$	−1.11345	+	4.41863i	−0.0645003	+	0.255964i
$299$		−	0.886596i		−	0.0512731i
$300$		0			0
$301$		−	10.4160i		−	0.600369i
$302$	−27.6978	−	6.97956i	−1.59383	−	0.401629i
$303$	10.1995	−	31.3908i	0.585945	−	1.80335i
$304$	−20.0272	−	15.9726i	−1.14864	−	0.916089i
$305$		0			0
$306$	2.78002	−	4.42428i	0.158923	−	0.252919i
$307$		−	3.74062i		−	0.213488i	−0.994287	−	0.106744i	$-0.965957\pi$
$307$		−	3.74062i		−	0.213488i	0.994287	−	0.106744i	$-0.0340426\pi$
$308$	1.91851	+	14.1653i	0.109317	+	0.807144i
$309$	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	$0.403200\pi$
$312$	−17.2811	−	1.94768i	−0.978348	−	0.110265i
$313$	−5.32787	−	3.87093i	−0.301149	−	0.218798i	0.426940	−	0.904280i	$-0.359591\pi$
$313$	−5.32787	−	3.87093i	−0.301149	−	0.218798i	−0.728089	+	0.685482i	$0.759591\pi$
$314$	−7.38530	+	29.3080i	−0.416777	+	1.65394i
$315$		0			0
$316$	1.78611	−	1.70762i	0.100476	−	0.0960612i
$317$	−19.2320	+	6.24885i	−1.08018	+	0.350970i	−0.794443	−	0.607339i	$-0.792237\pi$
$317$	−19.2320	+	6.24885i	−1.08018	+	0.350970i	−0.285733	+	0.958309i	$0.592237\pi$
$318$	−5.98744	−	7.17195i	−0.335759	−	0.402183i
$319$	14.7157	+	45.2902i	0.823920	+	2.53577i
$320$		0			0
$321$	−8.32258	+	25.6143i	−0.464521	+	1.42965i
$322$	−0.520610	+	0.208825i	−0.0290125	+	0.0116374i
$323$	−14.3699	−	19.7785i	−0.799563	−	1.10050i
$324$	3.91687	−	21.5811i	0.217604	−	1.19895i
$325$		0			0
$326$	13.7702	−	11.4960i	0.762662	−	0.636702i
$327$	16.1710	−	11.7489i	0.894256	−	0.649715i
$328$	−2.30352	−	11.2522i	−0.127190	−	0.621298i
$329$	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	$0.200480\pi$
$332$	8.26806	+	1.50062i	0.453769	+	0.0823570i
$333$	4.63768	−	1.50687i	0.254143	−	0.0825761i
$334$	0.875141	+	12.9822i	0.0478856	+	0.710354i
$335$		0			0
$336$	2.92664	+	10.6062i	0.159661	+	0.578616i
$337$	−13.4708	−	9.78712i	−0.733802	−	0.533139i	0.156962	−	0.987605i	$-0.449830\pi$
$337$	−13.4708	−	9.78712i	−0.733802	−	0.533139i	−0.890764	+	0.454466i	$0.849830\pi$
$338$	−0.330300	−	4.89981i	−0.0179660	−	0.266514i
$339$	11.1380	+	15.3301i	0.604932	+	0.832617i
$340$		0			0
$341$	−13.6677	+	18.8120i	−0.740147	+	1.01873i
$342$	7.42215	+	4.66376i	0.401344	+	0.252187i
$343$	−16.6992			−0.901674
$344$	−14.3945	+	15.7472i	−0.776101	+	0.849033i
$345$		0			0
$346$	10.2665	+	25.5948i	0.551930	+	1.37599i
$347$	15.0852	+	4.90149i	0.809818	+	0.263126i	0.684521	−	0.728993i	$-0.260012\pi$
$347$	15.0852	+	4.90149i	0.809818	+	0.263126i	0.125297	+	0.992119i	$0.460012\pi$
$348$	15.9028	+	33.0243i	0.852479	+	1.77029i
$349$			11.9445i			0.639375i	0.947523	+	0.319688i	$0.103578\pi$
$349$			11.9445i			0.639375i	−0.947523	+	0.319688i	$0.896422\pi$
$350$		0			0
$351$	−12.4945			−0.666908
$352$	16.6755	−	24.0668i	0.888805	−	1.28277i
$353$	−1.55465	+	4.78471i	−0.0827456	+	0.254665i	−0.983867	−	0.178903i	$-0.942745\pi$
$353$	−1.55465	+	4.78471i	−0.0827456	+	0.254665i	0.901121	+	0.433567i	$0.142745\pi$
$354$	−4.68070	+	1.87751i	−0.248776	+	0.0997883i
$355$		0			0
$356$	22.3851	−	3.03178i	1.18641	−	0.160684i
$357$			10.5005i			0.555744i
$358$	−3.97291	−	2.49640i	−0.209975	−	0.131939i
$359$	−4.41690	−	3.20906i	−0.233115	−	0.169368i	0.465096	−	0.885260i	$-0.346020\pi$
$359$	−4.41690	−	3.20906i	−0.233115	−	0.169368i	−0.698210	+	0.715893i	$0.746020\pi$
$360$		0			0
$361$	17.8090	−	12.9390i	0.937315	−	0.681000i
$362$	−6.95750	+	0.469011i	−0.365678	+	0.0246507i
$363$	−18.4877	+	25.4461i	−0.970351	+	1.33557i
$364$	7.68049	−	3.69853i	0.402567	−	0.193855i
$365$		0			0
$366$	0.421823	+	6.25749i	0.0220491	+	0.327084i
$367$	−4.67384	−	14.3846i	−0.243973	−	0.750871i	−0.995804	−	0.0915149i	$-0.970829\pi$
$367$	−4.67384	−	14.3846i	−0.243973	−	0.750871i	0.751831	−	0.659356i	$-0.229171\pi$
$368$	1.07566	+	0.403755i	0.0560727	+	0.0210472i
$369$	1.21452	+	3.73790i	0.0632253	+	0.194587i
$370$		0			0
$371$	4.35555	+	1.41520i	0.226129	+	0.0734737i
$372$	−8.48151	+	15.7605i	−0.439746	+	0.817142i
$373$	−19.0290	−	26.1912i	−0.985284	−	1.35613i	−0.933933	−	0.357447i	$-0.883647\pi$
$373$	−19.0290	−	26.1912i	−0.985284	−	1.35613i	−0.0513509	−	0.998681i	$-0.516353\pi$
$374$	21.4506	−	17.9079i	1.10919	−	0.925994i
$375$		0			0
$376$	−2.46859	+	1.40062i	−0.127308	+	0.0722315i
$377$	22.9751	−	16.6924i	1.18328	−	0.859701i
$378$	2.94291	+	7.33679i	0.151367	+	0.377364i
$379$	12.3752	+	4.02096i	0.635674	+	0.206543i	0.609087	−	0.793104i	$-0.291536\pi$
$379$	12.3752	+	4.02096i	0.635674	+	0.206543i	0.0265869	+	0.999647i	$0.491536\pi$
$380$		0			0
$381$	−15.8666	+	5.15538i	−0.812872	+	0.264118i
$382$	0.609108	+	0.729609i	0.0311647	+	0.0373300i
$383$	4.35817	+	13.4131i	0.222692	+	0.685376i	0.998518	+	0.0544287i	$0.0173337\pi$
$383$	4.35817	+	13.4131i	0.222692	+	0.685376i	−0.775825	+	0.630948i	$0.782666\pi$
$384$	10.2328	−	20.0793i	0.522190	−	1.02467i
$385$		0			0
$386$	−6.52070	−	1.64315i	−0.331895	−	0.0836340i
$387$	4.29119	−	5.90632i	0.218134	−	0.300235i
$388$	−7.07410	+	6.76324i	−0.359133	+	0.343351i
$389$	11.6423	+	16.0243i	0.590290	+	0.812465i	0.994776	−	0.102080i	$-0.0325496\pi$
$389$	11.6423	+	16.0243i	0.590290	+	0.812465i	−0.404486	+	0.914544i	$0.632550\pi$
$390$		0			0
$391$	0.887092	+	0.644510i	0.0448622	+	0.0325943i
$392$	10.6328	+	9.71941i	0.537036	+	0.490904i
$393$	−18.0455			−0.910276
$394$	6.72582	+	4.22621i	0.338842	+	0.212913i
$395$		0			0
$396$	−4.74796	+	8.82273i	−0.238594	+	0.443359i
$397$	10.0183	+	3.25515i	0.502805	+	0.163371i	0.549428	−	0.835541i	$-0.314846\pi$
$397$	10.0183	+	3.25515i	0.502805	+	0.163371i	−0.0466224	+	0.998913i	$0.514846\pi$
$398$	4.88682	+	1.23143i	0.244954	+	0.0617259i
$399$	−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	$0.618202\pi$
$402$	−4.88200	−	1.23021i	−0.243492	−	0.0613574i
$403$	13.1882	+	4.28509i	0.656949	+	0.213456i
$404$	15.7044	−	29.1822i	0.781325	−	1.45187i
$405$		0			0
$406$	−15.2132	−	9.55933i	−0.755020	−	0.474422i
$407$	26.0776			1.29262
$408$	14.5112	−	15.8749i	0.718413	−	0.785924i
$409$	20.3026	+	14.7507i	1.00390	+	0.729375i	0.962920	−	0.269785i	$-0.0869528\pi$
$409$	20.3026	+	14.7507i	1.00390	+	0.729375i	0.0409776	+	0.999160i	$0.486953\pi$
$410$		0			0
$411$	0.814776	+	1.12144i	0.0401899	+	0.0553167i
$412$	5.88050	−	5.62209i	0.289712	−	0.276981i
$413$	1.45308	−	1.99999i	0.0715013	−	0.0984131i
$414$	−0.381240	−	0.0960684i	−0.0187369	−	0.00472150i
$415$		0			0
$416$	−16.7228	−	5.02261i	−0.819902	−	0.246254i
$417$	−6.55032	−	20.1598i	−0.320770	−	0.987230i
$418$	30.0422	+	35.9855i	1.46941	+	1.76011i
$419$	−0.728039	+	0.236554i	−0.0355671	+	0.0115564i	−0.326746	−	0.945112i	$-0.605952\pi$
$419$	−0.728039	+	0.236554i	−0.0355671	+	0.0115564i	0.291179	+	0.956668i	$0.405952\pi$
$420$		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	$0.692040\pi$
$422$	14.8442	+	37.0073i	0.722606	+	1.80149i
$423$	0.785739	−	0.570872i	0.0382039	−	0.0277568i
$424$	−4.62908	−	8.15874i	−0.224808	−	0.396223i
$425$		0			0
$426$	32.7968	−	27.3801i	1.58901	−	1.32657i
$427$	−1.80704	−	2.48717i	−0.0874486	−	0.120363i
$428$	−12.8145	+	23.8122i	−0.619414	+	1.15100i
$429$	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	$0.724545\pi$
$432$	5.68999	−	15.1589i	0.273760	−	0.729335i
$433$	−1.13607	−	3.49647i	−0.0545962	−	0.168030i	0.920040	−	0.391824i	$-0.128156\pi$
$433$	−1.13607	−	3.49647i	−0.0545962	−	0.168030i	−0.974636	+	0.223794i	$0.928156\pi$
$434$	−0.590074	−	8.75339i	−0.0283245	−	0.420176i
$435$		0			0
$436$	18.0819	−	8.70730i	0.865966	−	0.417004i
$437$	−1.08123	+	1.48818i	−0.0517222	+	0.0711894i
$438$	32.8997	−	2.21780i	1.57201	−	0.105970i
$439$	1.89736	−	1.37851i	0.0905559	−	0.0657927i	−0.541586	−	0.840645i	$-0.682176\pi$
$439$	1.89736	−	1.37851i	0.0905559	−	0.0657927i	0.632142	+	0.774853i	$0.282176\pi$
$440$		0			0
$441$	−3.98804	−	2.89748i	−0.189907	−	0.137975i
$442$	−14.1096	−	8.86589i	−0.671127	−	0.421707i
$443$			0.969245i			0.0460502i	0.999735	+	0.0230251i	$0.00732977\pi$
$443$			0.969245i			0.0460502i	−0.999735	+	0.0230251i	$0.992670\pi$
$444$	19.8903	−	2.69389i	0.943951	−	0.127846i
$445$		0			0
$446$	21.7168	−	8.71096i	1.02832	−	0.412476i
$447$	1.98336	−	6.10416i	0.0938098	−	0.288717i
$448$	0.989538	+	11.0026i	0.0467513	+	0.519826i
$449$	−34.3240			−1.61985			−0.809925	−	0.586533i	$-0.800492\pi$
$449$	−34.3240			−1.61985			−0.809925	+	0.586533i	$0.800492\pi$
$450$		0			0
$451$			21.0181i			0.989705i
$452$	8.25455	+	17.1417i	0.388261	+	0.806277i
$453$	38.2634	+	12.4325i	1.79777	+	0.584132i
$454$	−6.48960	−	16.1788i	−0.304572	−	0.759311i
$455$		0			0
$456$	26.6317	+	24.3440i	1.24714	+	1.14001i
$457$	34.4324			1.61068			0.805341	−	0.592812i	$-0.201982\pi$
$457$	34.4324			1.61068			0.805341	+	0.592812i	$0.201982\pi$
$458$	13.5723	+	8.52823i	0.634191	+	0.398498i
$459$	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	$0.466999\pi$
$462$	−1.35420	−	20.0887i	−0.0630031	−	0.934612i
$463$	−11.6734	−	8.48120i	−0.542507	−	0.394155i	0.282508	−	0.959265i	$-0.408834\pi$
$463$	−11.6734	−	8.48120i	−0.542507	−	0.394155i	−0.825015	+	0.565110i	$0.808834\pi$
$464$	9.78914	+	35.4761i	0.454450	+	1.64694i
$465$		0			0
$466$	0.612591	+	9.08741i	0.0283777	+	0.420966i
$467$	−10.6614	+	3.46409i	−0.493349	+	0.160299i	−0.545116	−	0.838360i	$-0.683515\pi$
$467$	−10.6614	+	3.46409i	−0.493349	+	0.160299i	0.0517673	+	0.998659i	$0.483515\pi$
$468$	5.87889	+	1.06699i	0.271752	+	0.0493217i
$469$	2.34712	−	0.762626i	0.108380	−	0.0352148i
$470$		0			0
$471$	13.1553	−	40.4878i	0.606163	−	1.86558i
$472$	−4.96071	+	1.01554i	−0.228335	+	0.0467441i
$473$	31.5857	−	22.9483i	1.45231	−	1.05517i
$474$	−2.67185	+	2.23057i	−0.122722	+	0.102453i
$475$		0			0
$476$	−1.88273	+	10.3734i	−0.0862949	+	0.475466i
$477$	1.88674	+	2.59688i	0.0863881	+	0.118903i
$478$	2.76488	−	1.10904i	0.126462	−	0.0507262i
$479$	−1.46974	+	4.52340i	−0.0671543	+	0.206680i	−0.979003	−	0.203848i	$-0.934655\pi$
$479$	−1.46974	+	4.52340i	−0.0671543	+	0.206680i	0.911848	+	0.410527i	$0.134655\pi$
$480$		0			0
$481$	−4.80563	−	14.7902i	−0.219118	−	0.674376i
$482$	19.2749	+	23.0880i	0.877946	+	1.05163i
$483$	0.751413	−	0.244149i	0.0341905	−	0.0111092i
$484$	−22.8265	+	21.8234i	−1.03757	+	0.991973i
$485$		0			0
$486$	−3.35254	+	13.3043i	−0.152074	+	0.603495i
$487$	−10.7630	−	7.81977i	−0.487718	−	0.354348i	0.316588	−	0.948563i	$-0.397463\pi$
$487$	−10.7630	−	7.81977i	−0.487718	−	0.354348i	−0.804306	+	0.594215i	$0.797463\pi$
$488$	−0.705248	+	6.25742i	−0.0319251	+	0.283260i
$489$	−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	$0.0687851\pi$
$492$	2.17123	+	16.0313i	0.0978867	+	0.722746i
$493$			35.1224i			1.58184i
$494$	14.8734	−	23.6703i	0.669186	−	1.06498i
$495$		0			0
$496$	−11.2048	+	14.0491i	−0.503108	+	0.630822i
$497$	−6.47161	+	19.9176i	−0.290291	+	0.893425i
$498$	−11.4772	−	2.89214i	−0.514306	−	0.129600i
$499$			15.6179i			0.699151i	0.936908	+	0.349576i	$0.113674\pi$
$499$			15.6179i			0.699151i	−0.936908	+	0.349576i	$0.886326\pi$
$500$		0			0
$501$		−	18.3272i		−	0.818799i
$502$	6.04665	−	23.9956i	0.269875	−	1.07098i
$503$	−0.00969730	+	0.0298452i	−0.000432381	+	0.00133073i	−0.951272	−	0.308352i	$-0.900223\pi$
$503$	−0.00969730	+	0.0298452i	−0.000432381	+	0.00133073i	0.950840	+	0.309682i	$0.100223\pi$
$504$	−0.758150	−	3.70340i	−0.0337707	−	0.164963i
$505$		0			0
$506$	−1.78024	−	1.11863i	−0.0791413	−	0.0497290i
$507$			6.91715i			0.307201i
$508$	−16.5990	+	2.24813i	−0.736463	+	0.0997445i
$509$	6.00479	−	8.26488i	0.266157	−	0.366334i	−0.654930	−	0.755689i	$-0.727302\pi$
$509$	6.00479	−	8.26488i	0.266157	−	0.366334i	0.921088	+	0.389355i	$0.127302\pi$
$510$		0			0
$511$	−13.0767	+	9.50075i	−0.578477	+	0.420288i
$512$	13.7092	−	18.0016i	0.605867	−	0.795566i
$513$	20.9725	+	15.2374i	0.925959	+	0.672748i
$514$	39.4242	+	9.93448i	1.73893	+	0.438191i
$515$		0			0
$516$	21.7209	−	20.7664i	0.956209	−	0.914189i
$517$	4.93969	−	1.60500i	0.217247	−	0.0705879i
$518$	−7.55293	+	6.30550i	−0.331857	+	0.277048i
$519$	−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	$-0.0406231\pi$
$522$	−4.68829	−	11.6881i	−0.205201	−	0.511574i
$523$	5.14729	+	7.08464i	0.225075	+	0.309789i	0.906588	−	0.422017i	$-0.138678\pi$
$523$	5.14729	+	7.08464i	0.225075	+	0.309789i	−0.681513	+	0.731806i	$0.738678\pi$
$524$	−17.8272	−	3.23556i	−0.778785	−	0.141346i
$525$		0			0
$526$	19.0397	+	22.8063i	0.830168	+	0.994403i
$527$	−13.8746	+	10.0805i	−0.604388	+	0.439113i
$528$	−25.7145	+	32.2421i	−1.11908	+	1.40316i
$529$	−7.08190	+	21.7958i	−0.307909	+	0.947645i
$530$		0			0
$531$	1.64791	−	0.535440i	0.0715134	−	0.0232361i
$532$	−17.4024	−	3.15847i	−0.754492	−	0.136937i
$533$	11.9207	−	3.87327i	0.516343	−	0.167770i
$534$	−31.7457	+	2.14001i	−1.37377	+	0.0926071i
$535$		0			0
$536$	−4.60236	−	2.09067i	−0.198792	−	0.0903033i
$537$	5.34675	+	3.88464i	0.230729	+	0.167635i
$538$	22.3719	−	1.50811i	0.964521	−	0.0650192i
$539$	−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	$0.00767806\pi$
$542$	−22.3494	+	35.5681i	−0.959991	+	1.52778i
$543$	9.82203			0.421504
$544$	17.1820	−	13.0810i	0.736674	−	0.560842i
$545$		0			0
$546$	−11.1440	+	4.47005i	−0.476920	+	0.191300i
$547$	−27.4957	−	8.93390i	−1.17563	−	0.381986i	−0.344890	−	0.938643i	$-0.612084\pi$
$547$	−27.4957	−	8.93390i	−1.17563	−	0.381986i	−0.830742	+	0.556657i	$0.812084\pi$
$548$	0.603844	+	1.25397i	0.0257950	+	0.0535667i
$549$		−	2.15480i		−	0.0919644i
$550$		0			0
$551$	−58.9213			−2.51013
$552$	−1.47341	−	0.669312i	−0.0627125	−	0.0284878i
$553$	0.527221	−	1.62262i	0.0224197	−	0.0690008i
$554$	−0.573374	−	1.42944i	−0.0243603	−	0.0607313i
$555$		0			0
$556$	−2.85642	−	21.0904i	−0.121139	−	0.894431i
$557$		−	33.1381i		−	1.40411i	−0.712125	−	0.702053i	$-0.752267\pi$
$557$		−	33.1381i		−	1.40411i	0.712125	−	0.702053i	$-0.247733\pi$
$558$	3.27163	−	5.20664i	0.138499	−	0.220415i
$559$	−18.8361	−	13.6852i	−0.796682	−	0.578824i
$560$		0			0
$561$	−31.8418	+	23.1344i	−1.34436	+	0.976735i
$562$	2.41908	+	35.8856i	0.102043	+	1.51374i
$563$	−18.4934	+	25.4540i	−0.779404	+	1.07276i	0.215943	+	0.976406i	$0.430717\pi$
$563$	−18.4934	+	25.4540i	−0.779404	+	1.07276i	−0.995347	+	0.0963518i	$0.969283\pi$
$564$	3.60188	−	1.73448i	0.151666	−	0.0730346i
$565$		0			0
$566$	−35.4054	+	2.38671i	−1.48820	+	0.100321i
$567$	−4.67972	−	14.4027i	−0.196530	−	0.604857i
$568$	37.3092	−	21.1684i	1.56546	−	0.888206i
$569$	5.66167	+	17.4248i	0.237350	+	0.730487i	0.996801	+	0.0799229i	$0.0254674\pi$
$569$	5.66167	+	17.4248i	0.237350	+	0.730487i	−0.759451	+	0.650564i	$0.774533\pi$
$570$		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	$0.634450\pi$
$572$	28.1369	+	15.1419i	1.17646	+	0.633115i
$573$	−0.786879	−	1.08305i	−0.0328723	−	0.0452449i
$574$	−5.08214	−	6.08755i	−0.212124	−	0.254089i
$575$		0			0
$576$	−3.97176	+	6.64664i	−0.165490	+	0.276943i
$577$	1.19561	−	0.868662i	0.0497739	−	0.0361629i	−0.562620	−	0.826716i	$-0.690207\pi$
$577$	1.19561	−	0.868662i	0.0497739	−	0.0361629i	0.612394	+	0.790553i	$0.290207\pi$
$578$	−3.18564	+	1.27781i	−0.132505	+	0.0531500i
$579$	9.00808	+	2.92690i	0.374363	+	0.121638i
$580$		0			0
$581$	5.51790	−	1.79288i	0.228921	−	0.0743810i
$582$	10.5822	−	8.83443i	0.438645	−	0.366199i
$583$	5.30456	+	16.3258i	0.219692	+	0.676144i
$584$	32.8993	+	3.70794i	1.36138	+	0.153436i
$585$		0			0
$586$	−10.9358	+	43.3977i	−0.451753	+	1.79274i
$587$	4.49748	−	6.19025i	0.185631	−	0.255499i	−0.706052	−	0.708160i	$-0.749525\pi$
$587$	4.49748	−	6.19025i	0.185631	−	0.255499i	0.891682	+	0.452662i	$0.149525\pi$
$588$	−14.0218	−	14.6663i	−0.578249	−	0.604828i
$589$	−16.9110	−	23.2760i	−0.696806	−	0.959071i
$590$		0			0
$591$	−9.05163	−	6.57640i	−0.372334	−	0.270517i
$592$	20.1327	+	0.905030i	0.827448	+	0.0371965i
$593$	−31.1703			−1.28001			−0.640006	−	0.768370i	$-0.721068\pi$
$593$	−31.1703			−1.28001			−0.640006	+	0.768370i	$0.721068\pi$
$594$	−15.7644	+	25.0884i	−0.646823	+	1.02939i
$595$		0			0
$596$	3.05384	−	5.67469i	0.125090	−	0.232445i
$597$	−6.75095	−	2.19352i	−0.276298	−	0.0897747i
$598$	−0.306376	+	1.21583i	−0.0125286	+	0.0497189i
$599$	30.2376			1.23547			0.617737	−	0.786385i	$-0.288050\pi$
$599$	30.2376			1.23547			0.617737	+	0.786385i	$0.288050\pi$
$600$		0			0
$601$	47.2925			1.92910			0.964551	−	0.263895i	$-0.0850073\pi$
$601$	47.2925			1.92910			0.964551	+	0.263895i	$0.0850073\pi$
$602$	−3.59940	+	14.2839i	−0.146701	+	0.582170i
$603$	1.64511	+	0.534527i	0.0669939	+	0.0217676i
$604$	35.5714	+	19.1428i	1.44738	+	0.778908i
$605$		0			0
$606$	−24.8345	+	39.5230i	−1.00883	+	1.60551i
$607$	13.6800			0.555252			0.277626	−	0.960689i	$-0.410452\pi$
$607$	13.6800			0.555252			0.277626	+	0.960689i	$0.410452\pi$
$608$	21.9446	+	28.8245i	0.889971	+	1.16899i
$609$	20.4740	+	14.8753i	0.829650	+	0.602776i
$610$		0			0
$611$	−1.82059	−	2.50583i	−0.0736533	−	0.101375i
$612$	−5.34124	+	5.10653i	−0.215907	+	0.206419i
$613$	−9.34518	+	12.8625i	−0.377448	+	0.519513i	−0.954906	−	0.296907i	$-0.904045\pi$
$613$	−9.34518	+	12.8625i	−0.377448	+	0.519513i	0.577458	+	0.816420i	$0.304045\pi$
$614$	−1.29262	+	5.12968i	−0.0521661	+	0.207017i
$615$		0			0
$616$	2.26409	−	20.0885i	0.0912228	−	0.809389i
$617$	3.25933	+	10.0312i	0.131216	+	0.403840i	0.994982	−	0.100052i	$-0.0319009\pi$
$617$	3.25933	+	10.0312i	0.131216	+	0.403840i	−0.863767	+	0.503892i	$0.831901\pi$
$618$	−8.79667	+	7.34382i	−0.353854	+	0.295412i
$619$	25.5938	−	8.31591i	1.02870	−	0.334245i	0.254424	−	0.967093i	$-0.418114\pi$
$619$	25.5938	−	8.31591i	1.02870	−	0.334245i	0.774276	+	0.632848i	$0.218114\pi$
$620$		0			0
$621$	−1.10580	−	0.359295i	−0.0443740	−	0.0144180i
$622$	14.7477	−	5.91554i	0.591329	−	0.237192i
$623$	12.6180	−	9.16751i	0.505529	−	0.367288i
$624$	23.0253	+	8.64266i	0.921748	+	0.345983i
$625$		0			0
$626$	5.96869	+	7.14949i	0.238557	+	0.285751i
$627$	−38.8102	−	53.4176i	−1.54993	−	2.13330i
$628$	20.2556	−	37.6392i	0.808286	−	1.50197i
$629$	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	$0.899261\pi$
$632$	−3.03946	+	1.72452i	−0.120903	+	0.0685978i
$633$	−17.3552	−	53.4138i	−0.689808	−	2.12301i
$634$	28.5330	−	1.92344i	1.13319	−	0.0763895i
$635$		0			0
$636$	5.73247	+	11.9043i	0.227307	+	0.472035i
$637$	−9.24049	+	12.7184i	−0.366121	+	0.503923i
$638$	−4.52959	−	67.1937i	−0.179328	−	2.66022i
$639$	−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	$0.632962\pi$
$642$	20.2645	−	32.2500i	0.799776	−	1.27281i
$643$		−	7.74220i		−	0.305323i	−0.988279	−	0.152661i	$-0.951216\pi$
$643$		−	7.74220i		−	0.305323i	0.988279	−	0.152661i	$-0.0487844\pi$
$644$	0.786098	−	0.106467i	0.0309766	−	0.00419538i
$645$		0			0
$646$	12.8714	+	32.0888i	0.506417	+	1.26252i
$647$	7.01014	−	21.5750i	0.275597	−	0.848200i	−0.713464	−	0.700692i	$-0.752875\pi$
$647$	7.01014	−	21.5750i	0.275597	−	0.848200i	0.989061	−	0.147508i	$-0.0471253\pi$
$648$	−12.8290	+	28.2416i	−0.503972	+	1.10943i
$649$	9.26619			0.363730
$650$		0			0
$651$			12.3573i			0.484322i
$652$	−22.8563	+	11.0064i	−0.895122	+	0.431044i
$653$	29.4214	+	9.55959i	1.15135	+	0.374096i	0.821651	−	0.569991i	$-0.193053\pi$
$653$	29.4214	+	9.55959i	1.15135	+	0.374096i	0.329697	+	0.944087i	$0.393053\pi$
$654$	−26.2359	+	10.5237i	−1.02591	+	0.411508i
$655$		0			0
$656$	−0.729441	+	16.2266i	−0.0284799	+	0.633544i
$657$	−11.3291			−0.441992
$658$	−1.04261	+	1.65927i	−0.0406453	+	0.0646850i
$659$	−13.3643	+	18.3944i	−0.520601	+	0.716545i	−0.985662	−	0.168733i	$-0.946032\pi$
$659$	−13.3643	+	18.3944i	−0.520601	+	0.716545i	0.465061	+	0.885279i	$0.346032\pi$
$660$		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	$0.896998\pi$
$662$	−30.1155	+	2.03011i	−1.17047	+	0.0789025i
$663$	18.9888	+	13.7962i	0.737465	+	0.535800i
$664$	−10.8198	−	4.91501i	−0.419890	−	0.190739i
$665$		0			0
$666$	−6.88057	+	0.463826i	−0.266617	+	0.0179729i
$667$	2.51336	−	0.816640i	0.0973176	−	0.0316204i
$668$	3.28606	−	18.1055i	0.127142	−	0.700522i
$669$	−31.3445	+	10.1845i	−1.21185	+	0.393754i
$670$		0			0
$671$	3.56091	−	10.9594i	0.137467	−	0.423081i
$672$	−0.348297	−	15.5561i	−0.0134359	−	0.600090i
$673$	−18.7118	+	13.5949i	−0.721288	+	0.524046i	−0.886795	−	0.462162i	$-0.847074\pi$
$673$	−18.7118	+	13.5949i	−0.721288	+	0.524046i	0.165507	+	0.986209i	$0.447074\pi$
$674$	15.0910	+	18.0765i	0.581286	+	0.696283i
$675$		0			0
$676$	−1.24024	+	6.83346i	−0.0477017	+	0.262825i
$677$	1.93729	+	2.66645i	0.0744561	+	0.102480i	0.844621	−	0.535365i	$-0.179826\pi$
$677$	1.93729	+	2.66645i	0.0744561	+	0.102480i	−0.770165	+	0.637845i	$0.779826\pi$
$678$	−9.97646	−	24.8717i	−0.383144	−	0.955194i
$679$	−2.08812	+	6.42658i	−0.0801348	+	0.246629i
$680$		0			0
$681$	7.58734	+	23.3514i	0.290747	+	0.894829i
$682$	25.2439	−	21.0746i	0.966637	−	0.806989i
$683$	13.9624	−	4.53666i	0.534257	−	0.173591i	−0.0294489	−	0.999566i	$-0.509375\pi$
$683$	13.9624	−	4.53666i	0.534257	−	0.173591i	0.563706	+	0.825976i	$0.309375\pi$
$684$	−8.56670	−	8.96045i	−0.327556	−	0.342611i
$685$		0			0
$686$	22.9004	+	5.77066i	0.874341	+	0.220325i
$687$	−18.2656	−	13.2708i	−0.696877	−	0.506311i
$688$	25.1815	−	16.6206i	0.960036	−	0.633655i
$689$	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	$0.205459\pi$
$692$	−5.23425	−	38.6470i	−0.198976	−	1.46914i
$693$			6.91764i			0.262779i
$694$	−18.9933	−	11.9346i	−0.720975	−	0.453029i
$695$		0			0
$696$	−10.3962	−	50.7831i	−0.394066	−	1.92493i
$697$	−4.79030	+	14.7430i	−0.181446	+	0.558433i
$698$	4.12760	−	16.3800i	0.156232	−	0.619994i
$699$		−	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	$-0.158888\pi$
$702$	17.1343	+	4.31766i	0.646692	+	0.162960i
$703$	−9.97065	+	30.6865i	−0.376050	+	1.15736i
$704$	−31.1844	+	27.2415i	−1.17531	+	1.02670i
$705$		0			0
$706$	3.78538	−	6.02426i	0.142465	−	0.226726i
$707$		−	22.8809i		−	0.860526i
$708$	7.06765	−	0.957223i	0.265619	−	0.0359746i
$709$	−3.03019	+	4.17070i	−0.113801	+	0.156634i	−0.862118	−	0.506708i	$-0.830862\pi$
$709$	−3.03019	+	4.17070i	−0.113801	+	0.156634i	0.748317	+	0.663342i	$0.230862\pi$
$710$		0			0
$711$	0.967444	−	0.702889i	0.0362820	−	0.0263604i
$712$	−31.7453	−	3.57788i	−1.18971	−	0.134087i
$713$	1.04396	+	0.758482i	0.0390966	+	0.0284054i
$714$	3.62859	−	14.3998i	0.135796	−	0.538897i
$715$		0			0
$716$	4.58555	+	4.79632i	0.171370	+	0.179247i
$717$	−3.99063	+	1.29663i	−0.149033	+	0.0484237i
$718$	4.94815	+	5.92705i	0.184663	+	0.221196i
$719$	−5.09933	−	15.6941i	−0.190173	−	0.585292i	0.809826	−	0.586670i	$-0.199561\pi$
$719$	−5.09933	−	15.6941i	−0.190173	−	0.585292i	−0.999999	+	0.00137806i	$0.999561\pi$
$720$		0			0
$721$	1.73580	−	5.34224i	0.0646445	−	0.198955i
$722$	−28.8935	+	11.5897i	−1.07531	+	0.431322i
$723$	−24.9003	−	34.2724i	−0.926053	−	1.27460i
$724$	9.70320	+	1.76109i	0.360617	+	0.0654503i
$725$		0			0
$726$	34.1462	−	28.5067i	1.26729	−	1.05798i
$727$	−18.6402	+	13.5429i	−0.691326	+	0.502278i	−0.877096	−	0.480315i	$-0.840522\pi$
$727$	−18.6402	+	13.5429i	−0.691326	+	0.502278i	0.185770	+	0.982593i	$0.440522\pi$
$728$	−11.8107	+	2.41785i	−0.437733	+	0.0896114i
$729$	−4.19500	+	12.9109i	−0.155370	+	0.478181i
$730$		0			0
$731$	27.3858	−	8.89818i	1.01290	−	0.329111i
$732$	1.58390	−	8.72695i	0.0585427	−	0.322557i
$733$	−36.4467	+	11.8423i	−1.34619	+	0.437404i	−0.891409	−	0.453200i	$-0.850282\pi$
$733$	−36.4467	+	11.8423i	−1.34619	+	0.437404i	−0.454781	+	0.890603i	$0.650282\pi$
$734$	1.43864	+	21.3414i	0.0531012	+	0.787724i
$735$		0			0
$736$	−1.33558	−	0.925397i	−0.0492300	−	0.0341106i
$737$	7.48373	+	5.43724i	0.275667	+	0.200283i
$738$	−0.373837	−	5.54564i	−0.0137611	−	0.204138i
$739$	−5.15085	−	7.08954i	−0.189477	−	0.260793i	0.703701	−	0.710497i	$-0.251530\pi$
$739$	−5.15085	−	7.08954i	−0.189477	−	0.260793i	−0.893178	+	0.449704i	$0.851530\pi$
$740$		0			0
$741$	−23.1444	+	31.8556i	−0.850233	+	1.17024i
$742$	−5.48391	−	3.44585i	−0.201321	−	0.126501i
$743$	7.97007			0.292393			0.146197	−	0.989256i	$-0.453297\pi$
$743$	7.97007			0.292393			0.146197	+	0.989256i	$0.453297\pi$
$744$	17.0773	−	18.6821i	0.626085	−	0.684920i
$745$		0			0
$746$	17.0446	+	42.4929i	0.624046	+	1.55577i
$747$	3.86752	+	1.25663i	0.141505	+	0.0459778i
$748$	−35.6045	+	17.1453i	−1.30183	+	0.626894i
$749$			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	$0.491049\pi$
$752$	3.86929	−	1.06768i	0.141099	−	0.0389342i
$753$	−10.7708	+	33.1490i	−0.392508	+	1.20802i
$754$	−37.2750	+	14.9516i	−1.35748	+	0.544506i
$755$		0			0
$756$	−1.50041	−	11.0782i	−0.0545692	−	0.402911i
$757$			20.8270i			0.756971i	0.925607	+	0.378485i	$0.123555\pi$
$757$			20.8270i			0.756971i	−0.925607	+	0.378485i	$0.876445\pi$
$758$	−15.5812	−	9.79056i	−0.565935	−	0.355609i
$759$	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	$0.356047\pi$
$762$	23.5401	−	1.58686i	0.852768	−	0.0574859i
$763$	8.14469	−	11.2102i	0.294858	−	0.405837i
$764$	−0.583170	−	1.21103i	−0.0210983	−	0.0438136i
$765$		0			0
$766$	−1.34148	−	19.9000i	−0.0484695	−	0.719015i
$767$	−1.70759	−	5.25543i	−0.0616576	−	0.189763i
$768$	−20.9714	+	23.9995i	−0.756739	+	0.866007i
$769$	1.06128	+	3.26628i	0.0382706	+	0.117785i	0.968367	−	0.249532i	$-0.0802766\pi$
$769$	1.06128	+	3.26628i	0.0382706	+	0.117785i	−0.930096	+	0.367316i	$0.880277\pi$
$770$		0			0
$771$	−54.4630	−	17.6961i	−1.96144	−	0.637309i
$772$	8.37431	+	4.50664i	0.301398	+	0.162198i
$773$	4.01412	+	5.52497i	0.144378	+	0.198719i	0.875081	−	0.483976i	$-0.160808\pi$
$773$	4.01412	+	5.52497i	0.144378	+	0.198719i	−0.730703	+	0.682695i	$0.760808\pi$
$774$	−7.92572	+	6.61672i	−0.284884	+	0.237833i
$775$		0			0
$776$	12.0382	−	6.83017i	0.432145	−	0.245189i
$777$	11.2117	−	8.14579i	0.402218	−	0.292229i
$778$	−10.4282	−	25.9980i	−0.373870	−	0.932074i
$779$	−24.7329	−	8.03620i	−0.886147	−	0.287927i
$780$		0			0
$781$	−74.6564	+	24.2573i	−2.67142	+	0.867996i
$782$	−0.993789	−	1.19039i	−0.0355378	−	0.0425684i
$783$	−11.5086	−	35.4200i	−0.411286	−	1.26581i
$784$	−11.2225	−	17.0030i	−0.400804	−	0.607249i
$785$		0			0
$786$	24.7466	+	6.23589i	0.882683	+	0.222427i
$787$	−2.61029	+	3.59275i	−0.0930467	+	0.128068i	−0.853002	−	0.521907i	$-0.825221\pi$
$787$	−2.61029	+	3.59275i	−0.0930467	+	0.128068i	0.759956	+	0.649975i	$0.225221\pi$
$788$	−7.76298	−	8.11979i	−0.276545	−	0.289256i
$789$	−24.5965	−	33.8542i	−0.875658	−	1.20524i
$790$		0			0
$791$	10.6273	+	7.72119i	0.377864	+	0.274534i
$792$	9.55991	−	10.4583i	0.339697	−	0.371619i
$793$	−6.87195			−0.244030
$794$	−12.6137	−	7.92591i	−0.447644	−	0.281280i
$795$		0			0
$796$	−6.27598	−	3.37742i	−0.222446	−	0.119710i
$797$	14.0380	+	4.56123i	0.497252	+	0.161567i	0.546897	−	0.837200i	$-0.315809\pi$
$797$	14.0380	+	4.56123i	0.497252	+	0.161567i	−0.0496450	+	0.998767i	$0.515809\pi$
$798$	24.1570	+	6.08731i	0.855148	+	0.215488i
$799$	3.83071			0.135521
$800$		0			0
$801$	10.9318			0.386255
$802$	19.9294	+	5.02201i	0.703733	+	0.177333i
$803$	−57.6204	−	18.7220i	−2.03338	−	0.660685i
$804$	6.26979	+	3.37409i	0.221118	+	0.118995i
$805$		0			0
$806$	−16.6047	−	10.4337i	−0.584877	−	0.367511i
$807$	−31.5828			−1.11177
$808$	−31.6205	+	34.5920i	−1.11241	+	1.21694i
$809$	−14.9496	−	10.8616i	−0.525601	−	0.381872i	0.293108	−	0.956079i	$-0.405310\pi$
$809$	−14.9496	−	10.8616i	−0.525601	−	0.381872i	−0.818710	+	0.574207i	$0.805310\pi$
$810$		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	$0.645627\pi$
$812$	17.5592	+	18.3663i	0.616207	+	0.644530i
$813$	34.7779	−	47.8677i	1.21971	−	1.67879i
$814$	−35.7613	−	9.01148i	−1.25343	−	0.315852i
$815$		0			0
$816$	−25.3857	+	16.7554i	−0.888677	+	0.586555i
$817$	14.9276	+	45.9423i	0.522249	+	1.60732i
$818$	−22.7445	−	27.2441i	−0.795243	−	0.952568i
$819$	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	$0.321414\pi$
$822$	−0.729808	−	1.81944i	−0.0254550	−	0.0634603i
$823$	−19.7653	+	14.3603i	−0.688975	+	0.500569i	−0.876323	−	0.481724i	$-0.840011\pi$
$823$	−19.7653	+	14.3603i	−0.688975	+	0.500569i	0.187348	+	0.982294i	$0.440011\pi$
$824$	−10.0070	+	5.67774i	−0.348610	+	0.197793i
$825$		0			0
$826$	−2.68380	+	2.24054i	−0.0933812	+	0.0779585i
$827$	28.0505	+	38.6082i	0.975412	+	1.34254i	0.939265	+	0.343192i	$0.111508\pi$
$827$	28.0505	+	38.6082i	0.975412	+	1.34254i	0.0361465	+	0.999347i	$0.488492\pi$
$828$	0.489613	+	0.263486i	0.0170152	+	0.00915676i
$829$	−22.8468	−	7.42337i	−0.793502	−	0.257824i	−0.115907	−	0.993260i	$-0.536978\pi$
$829$	−22.8468	−	7.42337i	−0.793502	−	0.257824i	−0.677595	+	0.735436i	$0.736978\pi$
$830$		0			0
$831$	0.670362	+	2.06316i	0.0232546	+	0.0715703i
$832$	21.1971	+	12.6665i	0.734876	+	0.439133i
$833$	−6.00819	−	18.4913i	−0.208172	−	0.640686i
$834$	2.01623	+	29.9096i	0.0698164	+	1.03568i
$835$		0			0
$836$	−28.7629	−	59.7301i	−0.994785	−	2.06581i
$837$	10.6891	−	14.7122i	0.369468	−	0.508529i
$838$	1.08014	−	0.0728130i	0.0373127	−	0.00251528i
$839$	−13.1474	+	9.55211i	−0.453897	+	0.329776i	−0.791132	−	0.611645i	$-0.790508\pi$
$839$	−13.1474	+	9.55211i	−0.453897	+	0.329776i	0.337235	+	0.941420i	$0.390508\pi$
$840$		0			0
$841$	45.0210	+	32.7096i	1.55245	+	1.12792i
$842$	14.0114	+	8.80415i	0.482864	+	0.303411i
$843$		−	50.6604i		−	1.74484i
$844$	−7.56816	−	55.8794i	−0.260507	−	1.92345i
$845$		0			0
$846$	−1.27479	+	0.511340i	−0.0438282	+	0.0175802i
$847$	−6.73789	+	20.7371i	−0.231517	+	0.712535i
$848$	3.52869	+	12.7881i	0.121176	+	0.439144i
$849$	49.9824			1.71539
$850$		0			0
$851$		−	1.44716i		−	0.0496081i
$852$	−54.4372	+	26.2141i	−1.86499	+	0.898082i
$853$	44.2323	+	14.3719i	1.51449	+	0.492086i	0.944203	−	0.329363i	$-0.106834\pi$
$853$	44.2323	+	14.3719i	1.51449	+	0.492086i	0.570282	+	0.821449i	$0.306834\pi$
$854$	1.61859	+	4.03522i	0.0553870	+	0.138082i
$855$		0			0
$856$	25.8018	−	28.2264i	0.881886	−	0.964759i
$857$	34.8114			1.18913			0.594567	−	0.804046i	$-0.297323\pi$
$857$	34.8114			1.18913			0.594567	+	0.804046i	$0.297323\pi$
$858$	−38.1073	−	23.9450i	−1.30096	−	0.817468i
$859$	23.5563	−	32.4224i	0.803730	−	1.10624i	−0.188531	−	0.982067i	$-0.560373\pi$
$859$	23.5563	−	32.4224i	0.803730	−	1.10624i	0.992261	−	0.124172i	$-0.0396275\pi$
$860$		0			0
$861$	6.56539	+	9.03648i	0.223748	+	0.307963i
$862$	−2.06836	−	30.6828i	−0.0704485	−	1.04506i
$863$	41.3205	+	30.0211i	1.40657	+	1.02193i	0.993811	+	0.111087i	$0.0354334\pi$
$863$	41.3205	+	30.0211i	1.40657	+	1.02193i	0.412755	+	0.910842i	$0.364567\pi$
$864$	−13.0413	+	18.8219i	−0.443675	+	0.640333i
$865$		0			0
$866$	0.349691	+	5.18745i	0.0118830	+	0.176277i
$867$	4.59793	−	1.49396i	0.156154	−	0.0507375i
$868$	−2.21567	+	12.2078i	−0.0752046	+	0.414360i
$869$	6.08201	−	1.97617i	0.206318	−	0.0670368i
$870$		0			0
$871$	1.70468	−	5.24648i	0.0577610	−	0.177770i
$872$	−27.8054	+	5.69225i	−0.941611	+	0.192764i
$873$	−3.83168	+	2.78388i	−0.129683	+	0.0942200i
$874$	1.99700	−	1.66718i	0.0675495	−	0.0563931i
$875$		0			0
$876$	−45.8832	−	8.32759i	−1.55025	−	0.281363i
$877$	10.3254	+	14.2117i	0.348664	+	0.479894i	0.946947	−	0.321390i	$-0.104150\pi$
$877$	10.3254	+	14.2117i	0.348664	+	0.479894i	−0.598283	+	0.801285i	$0.704150\pi$
$878$	−3.07829	+	1.23475i	−0.103887	+	0.0416709i
$879$	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	$0.860470\pi$
$882$	4.46771	+	5.35157i	0.150436	+	0.180197i
$883$	−42.5583	+	13.8280i	−1.43220	+	0.465350i	−0.919457	−	0.393191i	$-0.871371\pi$
$883$	−42.5583	+	13.8280i	−1.43220	+	0.465350i	−0.512745	+	0.858541i	$0.671371\pi$
$884$	16.2854	+	17.0340i	0.547739	+	0.572915i
$885$		0			0
$886$	0.334936	−	1.32917i	0.0112524	−	0.0446543i
$887$	−30.3347	−	22.0394i	−1.01854	−	0.740012i	−0.0525565	−	0.998618i	$-0.516737\pi$
$887$	−30.3347	−	22.0394i	−1.01854	−	0.740012i	−0.965983	+	0.258606i	$0.916737\pi$
$888$	−28.2073	−	3.17913i	−0.946577	−	0.106685i
$889$	−9.35651	+	6.79790i	−0.313807	+	0.227994i
$890$		0			0
$891$	33.3647	−	45.9226i	1.11776	−	1.53846i
$892$	−32.7914	+	4.44118i	−1.09794	+	0.148702i
$893$			6.42640i			0.215051i
$894$	−4.82925	+	7.68552i	−0.161514	+	0.257042i
$895$		0			0
$896$	2.44512	−	15.4304i	0.0816859	−	0.515492i
$897$	0.545741	−	1.67962i	0.0182218	−	0.0560808i
$898$	47.0700	+	11.8612i	1.57075	+	0.395812i
$899$			41.3333i			1.37854i
$900$		0			0
$901$			12.6606i			0.421785i
$902$	7.26312	−	28.8231i	0.241835	−	0.959704i
$903$	6.41154	−	19.7327i	0.213363	−	0.656663i
$904$	−5.39627	−	26.3596i	−0.179477	−	0.876708i
$905$		0			0
$906$	−48.1761	−	30.2718i	−1.60054	−	1.00571i
$907$			9.10715i			0.302398i	0.988503	+	0.151199i	$0.0483134\pi$
$907$			9.10715i			0.302398i	−0.988503	+	0.151199i	$0.951687\pi$
$908$	3.30864	+	24.4293i	0.109801	+	0.810716i
$909$	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	$0.268423\pi$
$912$	−28.1088	−	42.5870i	−0.930774	−	1.41020i
$913$	17.5937	+	12.7825i	0.582265	+	0.423040i
$914$	−47.2187	−	11.8986i	−1.56186	−	0.393571i
$915$		0			0
$916$	−15.6652	−	16.3852i	−0.517593	−	0.541384i
$917$	−11.8974	+	3.86572i	−0.392888	+	0.127657i
$918$	−16.7758	+	14.0052i	−0.553685	+	0.462239i
$919$	−5.41966	−	16.6800i	−0.178778	−	0.550222i	0.821008	−	0.570917i	$-0.193412\pi$
$919$	−5.41966	−	16.6800i	−0.178778	−	0.550222i	−0.999786	+	0.0206948i	$0.993412\pi$
$920$		0			0
$921$	2.30252	−	7.08644i	0.0758708	−	0.233506i
$922$	−19.5676	−	48.7829i	−0.644425	−	1.60658i
$923$	27.5157	+	37.8721i	0.905690	+	1.24658i
$924$	−5.08488	+	28.0165i	−0.167280	+	0.921676i
$925$		0			0
$926$	13.0774	+	15.6645i	0.429750	+	0.514769i
$927$	3.18517	−	2.31416i	0.104615	−	0.0760070i
$928$	−1.16500	−	52.0328i	−0.0382430	−	1.70806i
$929$	8.23207	−	25.3357i	0.270085	−	0.831237i	−0.720393	−	0.693566i	$-0.756038\pi$
$929$	8.23207	−	25.3357i	0.270085	−	0.831237i	0.990478	−	0.137671i	$-0.0439616\pi$
$930$		0			0
$931$	31.0210	−	10.0793i	1.01667	−	0.330337i
$932$	2.30021	−	12.6737i	0.0753460	−	0.415140i
$933$	−21.2858	+	6.91618i	−0.696866	+	0.226425i
$934$	15.8175	−	1.06627i	0.517563	−	0.0348894i
$935$		0			0
$936$	−7.69326	−	3.49475i	−0.251462	−	0.114229i
$937$	−7.91482	−	5.75045i	−0.258566	−	0.187859i	0.450949	−	0.892550i	$-0.351086\pi$
$937$	−7.91482	−	5.75045i	−0.258566	−	0.187859i	−0.709515	+	0.704691i	$0.751086\pi$
$938$	−3.48225	+	0.234742i	−0.113699	+	0.00766458i
$939$	−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	$0.198371\pi$
$942$	−32.0316	+	50.9767i	−1.04364	+	1.66091i
$943$	1.16639			0.0379829
$944$	7.15378	+	0.321586i	0.232836	+	0.0104667i
$945$		0			0
$946$	−51.2449	+	20.5552i	−1.66612	+	0.668306i
$947$	44.4410	+	14.4398i	1.44414	+	0.469229i	0.923185	−	0.384356i	$-0.125576\pi$
$947$	44.4410	+	14.4398i	1.44414	+	0.469229i	0.520954	+	0.853585i	$0.325576\pi$
$948$	4.43483	−	2.13558i	0.144036	−	0.0693605i
$949$			36.1303i			1.17284i
$950$		0			0
$951$	−40.2806			−1.30619
$952$	6.16656	−	13.5749i	0.199859	−	0.439967i
$953$	10.2909	−	31.6721i	0.333354	−	1.02596i	−0.634173	−	0.773191i	$-0.718659\pi$
$953$	10.2909	−	31.6721i	0.333354	−	1.02596i	0.967527	−	0.252768i	$-0.0813408\pi$
$954$	−1.68999	−	4.21321i	−0.0547153	−	0.136408i
$955$		0			0
$956$	−4.17484	+	0.565429i	−0.135024	+	0.0182873i
$957$			94.8585i			3.06634i
$958$	3.57865	−	5.69525i	0.115621	−	0.184005i
$959$	0.777419	+	0.564828i	0.0251042	+	0.0182393i
$960$		0			0
$961$	8.75140	−	6.35826i	0.282303	−	0.205105i
$962$	1.47921	+	21.9431i	0.0476915	+	0.707475i
$963$	−7.69184	+	10.5869i	−0.247866	+	0.341159i
$964$	−18.4541	−	38.3224i	−0.594365	−	1.23428i
$965$		0			0
$966$	−1.11481	+	0.0751506i	−0.0358686	+	0.00241793i
$967$	9.27626	+	28.5494i	0.298304	+	0.918087i	0.982091	+	0.188405i	$0.0603318\pi$
$967$	9.27626	+	28.5494i	0.298304	+	0.918087i	−0.683787	+	0.729682i	$0.739668\pi$
$968$	38.8444	−	22.0394i	1.24851	−	0.708373i
$969$	−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	$0.665288\pi$
$972$	9.19498	−	17.0862i	0.294929	−	0.548042i
$973$	−8.63727	−	11.8882i	−0.276898	−	0.381118i
$974$	12.0575	+	14.4429i	0.386348	+	0.462781i
$975$		0			0
$976$	3.12948	−	8.33737i	0.100172	−	0.266873i
$977$	−41.0078	+	29.7939i	−1.31196	+	0.953191i	−0.311960	+	0.950095i	$0.600986\pi$
$977$	−41.0078	+	29.7939i	−1.31196	+	0.953191i	−0.999995	+	0.00309631i	$0.999014\pi$
$978$	33.1634	−	13.3024i	1.06045	−	0.425363i
$979$	55.5993	+	18.0653i	1.77696	+	0.577370i
$980$		0			0
$981$	9.23677	−	3.00121i	0.294907	−	0.0958213i
$982$	−19.2758	+	16.0922i	−0.615116	+	0.513524i
$983$	16.3872	+	50.4346i	0.522671	+	1.60862i	0.768876	+	0.639397i	$0.220816\pi$
$983$	16.3872	+	50.4346i	0.522671	+	1.60862i	−0.246206	+	0.969218i	$0.579184\pi$
$984$	2.56233	−	22.7347i	0.0816842	−	0.724756i
$985$		0			0
$986$	12.1371	−	48.1650i	0.386523	−	1.53388i
$987$	1.62241	−	2.23305i	0.0516418	−	0.0710788i
$988$	−28.5762	+	27.3204i	−0.909129	+	0.869178i
$989$	−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	$0.690776\pi$
$992$	20.2204	−	15.3942i	0.641999	−	0.488765i
$993$	42.5146			1.34916
$994$	15.7576	−	25.0775i	0.499801	−	0.795409i
$995$		0			0
$996$	14.7398	+	7.93223i	0.467048	+	0.251342i
$997$	15.5130	+	5.04048i	0.491302	+	0.159634i	0.544182	−	0.838967i	$-0.316840\pi$
$997$	15.5130	+	5.04048i	0.491302	+	0.159634i	−0.0528802	+	0.998601i	$0.516840\pi$
$998$	5.39697	−	21.4175i	0.170838	−	0.677958i
$999$	−20.3944			−0.645250

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.1	✓	112	25.13	odd	20
200.2.o.a.109.18	yes	112	200.13	odd	20
200.2.o.a.189.1	yes	112	40.37	odd	4
200.2.o.a.189.18	yes	112	5.2	odd	4
800.2.be.a.209.7		112	200.163	even	20
800.2.be.a.209.22		112	100.63	even	20
800.2.be.a.689.7		112	20.7	even	4
800.2.be.a.689.22		112	40.27	even	4
1000.2.o.a.549.11		112	200.37	odd	20
1000.2.o.a.549.28		112	25.12	odd	20
1000.2.o.a.949.11		112	5.3	odd	4
1000.2.o.a.949.28		112	40.13	odd	4
1000.2.t.b.301.5		224	1.1	even	1	trivial
1000.2.t.b.301.27		224	8.5	even	2	inner
1000.2.t.b.301.30		224	40.29	even	2	inner
1000.2.t.b.301.52		224	5.4	even	2	inner
1000.2.t.b.701.5		224	200.141	even	10	inner
1000.2.t.b.701.27		224	25.16	even	5	inner
1000.2.t.b.701.30		224	25.9	even	10	inner
1000.2.t.b.701.52		224	200.109	even	10	inner

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.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37134 - 0.345564i) q^{2} +(1.89446 + 0.615546i) q^{3} +(1.76117 + 0.947775i) q^{4} +(-2.38524 - 1.49878i) q^{6} +1.38088 q^{7} +(-2.08765 - 1.90832i) q^{8} +(0.783019 + 0.568896i) q^{9} +(3.04233 + 4.18740i) q^{11} +(2.75306 + 2.87960i) q^{12} +(1.81429 - 2.49716i) q^{13} +(-1.89366 - 0.477183i) q^{14} +(2.20344 + 3.33839i) q^{16} +(1.17966 + 3.63061i) q^{17} +(-0.877198 - 1.05074i) q^{18} +(-6.09071 + 1.97899i) q^{19} +(2.61602 + 0.849997i) q^{21} +(-2.72506 - 6.79369i) q^{22} +(0.232378 - 0.168832i) q^{23} +(-2.78031 - 4.90029i) q^{24} +(-3.35095 + 2.79751i) q^{26} +(-2.37930 - 3.27483i) q^{27} +(2.43197 + 1.30877i) q^{28} +(8.75018 + 2.84311i) q^{29} +(1.38826 + 4.27263i) q^{31} +(-1.86805 - 5.33951i) q^{32} +(3.18602 + 9.80555i) q^{33} +(-0.363107 - 5.38647i) q^{34} +(0.839843 + 1.74405i) q^{36} +(2.96141 - 4.07603i) q^{37} +(9.03633 - 0.609147i) q^{38} +(4.97421 - 3.61398i) q^{39} +(3.28522 + 2.38685i) q^{41} +(-3.29374 - 2.06964i) q^{42} -7.54302i q^{43} +(1.38934 + 10.2582i) q^{44} +(-0.377013 + 0.151226i) q^{46} +(0.310090 - 0.954360i) q^{47} +(2.11940 + 7.68075i) q^{48} -5.09317 q^{49} +7.60418i q^{51} +(5.56202 - 2.67838i) q^{52} +(3.15418 + 1.02485i) q^{53} +(2.13118 + 5.31312i) q^{54} +(-2.88280 - 2.63517i) q^{56} -12.7567 q^{57} +(-11.0170 - 6.92263i) q^{58} +(1.05228 - 1.44834i) q^{59} +(-1.30861 - 1.80115i) q^{61} +(-0.427317 - 6.33899i) q^{62} +(1.08126 + 0.785578i) q^{63} +(0.716599 + 7.96784i) q^{64} +(-0.980677 - 14.5478i) q^{66} +(1.69973 - 0.552275i) q^{67} +(-1.36343 + 7.51218i) q^{68} +(0.544154 - 0.176806i) q^{69} +(-4.68658 + 14.4238i) q^{71} +(-0.549033 - 2.68191i) q^{72} +(-9.46979 + 6.88021i) q^{73} +(-5.46964 + 4.56628i) q^{74} +(-12.6024 - 2.28728i) q^{76} +(4.20109 + 5.78231i) q^{77} +(-8.07022 + 3.23710i) q^{78} +(0.381800 - 1.17506i) q^{79} +(-3.38894 - 10.4301i) q^{81} +(-3.68036 - 4.40845i) q^{82} +(3.99593 - 1.29836i) q^{83} +(3.80165 + 3.97639i) q^{84} +(-2.60660 + 10.3441i) q^{86} +(14.8268 + 10.7723i) q^{87} +(1.63960 - 14.5476i) q^{88} +(9.13763 - 6.63888i) q^{89} +(2.50532 - 3.44828i) q^{91} +(0.569272 - 0.0771007i) q^{92} +8.94886i q^{93} +(-0.755034 + 1.20160i) q^{94} +(-0.252228 - 11.2653i) q^{96} +(-1.51217 + 4.65397i) q^{97} +(6.98448 + 1.76002i) q^{98} +5.00958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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