LMFDB - Embedded newform 200.3.u.a.17.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,3,Mod(17,200)] 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("200.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.u (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	200.17
Dual form			200.3.u.a.153.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.706680 - 4.46180i) q^{3} +(-4.37575 - 2.41926i) q^{5} +(-0.0526437 - 0.0526437i) q^{7} +(-10.8488 - 3.52499i) q^{9} +(0.687682 + 2.11647i) q^{11} +(-6.99352 - 13.7256i) q^{13} +(-13.8865 + 17.8141i) q^{15} +(0.370977 + 2.34226i) q^{17} +(-13.0079 + 17.9039i) q^{19} +(-0.272088 + 0.197684i) q^{21} +(-5.97894 - 3.04642i) q^{23} +(13.2943 + 21.1722i) q^{25} +(-4.93664 + 9.68871i) q^{27} +(-27.6101 - 38.0021i) q^{29} +(3.69691 + 2.68596i) q^{31} +(9.92924 - 1.57264i) q^{33} +(0.102997 + 0.357714i) q^{35} +(59.9395 - 30.5407i) q^{37} +(-66.1829 + 21.5041i) q^{39} +(-0.779270 + 2.39835i) q^{41} +(46.3634 - 46.3634i) q^{43} +(38.9437 + 41.6705i) q^{45} +(-61.7008 - 9.77245i) q^{47} -48.9945i q^{49} +10.7129 q^{51} +(7.85019 - 49.5641i) q^{53} +(2.11117 - 10.9248i) q^{55} +(70.6911 + 70.6911i) q^{57} +(14.3158 + 4.65148i) q^{59} +(-19.4521 - 59.8674i) q^{61} +(0.385552 + 0.756689i) q^{63} +(-2.60384 + 76.9787i) q^{65} +(15.8246 + 99.9126i) q^{67} +(-17.8178 + 24.5240i) q^{69} +(81.7241 - 59.3761i) q^{71} +(91.3922 + 46.5667i) q^{73} +(103.861 - 44.3548i) q^{75} +(0.0752166 - 0.147621i) q^{77} +(74.6124 + 102.695i) q^{79} +(-43.3164 - 31.4712i) q^{81} +(63.0041 - 9.97887i) q^{83} +(4.04324 - 11.1466i) q^{85} +(-189.069 + 96.3357i) q^{87} +(-36.9068 + 11.9918i) q^{89} +(-0.354399 + 1.09073i) q^{91} +(14.5968 - 14.5968i) q^{93} +(100.234 - 46.8732i) q^{95} +(-138.512 - 21.9382i) q^{97} -25.3852i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 10 q^{5} - 4 q^{7} + 40 q^{9} - 16 q^{11} + 14 q^{13} - 10 q^{15} + 22 q^{17} + 50 q^{19} + 100 q^{21} - 48 q^{23} + 150 q^{25} - 210 q^{27} - 108 q^{31} - 140 q^{33} + 70 q^{35} + 236 q^{37} + 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) $ 56 * q - 10 * q^5 - 4 * q^7 + 40 * q^9 - 16 * q^11 + 14 * q^13 - 10 * q^15 + 22 * q^17 + 50 * q^19 + 100 * q^21 - 48 * q^23 + 150 * q^25 - 210 * q^27 - 108 * q^31 - 140 * q^33 + 70 * q^35 + 236 * q^37 + 80 * q^39 + 104 * q^41 + 96 * q^43 + 20 * q^45 + 104 * q^47 - 200 * q^51 + 88 * q^53 - 140 * q^55 - 280 * q^57 + 200 * q^59 + 108 * q^61 - 654 * q^63 - 510 * q^65 - 282 * q^67 + 40 * q^69 + 470 * q^71 + 62 * q^73 + 350 * q^75 - 396 * q^77 - 560 * q^79 - 586 * q^81 - 468 * q^83 + 50 * q^85 - 280 * q^87 + 230 * q^89 - 62 * q^91 - 300 * q^93 - 360 * q^95 + 386 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.706680	−	4.46180i	0.235560	−	1.48727i	−0.532248	−	0.846588i	$-0.678653\pi$
$3$	0.706680	−	4.46180i	0.235560	−	1.48727i	0.767808	−	0.640680i	$-0.221347\pi$
$4$		0			0
$5$	−4.37575	−	2.41926i	−0.875150	−	0.483852i
$5$	−4.37575	−	2.41926i	−0.875150	−	0.483852i
$6$		0			0
$7$	−0.0526437	−	0.0526437i	−0.00752053	−	0.00752053i	0.703337	−	0.710857i	$-0.251693\pi$
$7$	−0.0526437	−	0.0526437i	−0.00752053	−	0.00752053i	−0.710857	+	0.703337i	$0.751693\pi$
$8$		0			0
$9$	−10.8488	−	3.52499i	−1.20542	−	0.391665i
$10$		0			0
$11$	0.687682	+	2.11647i	0.0625166	+	0.192406i	0.977437	−	0.211229i	$-0.0677465\pi$
$11$	0.687682	+	2.11647i	0.0625166	+	0.192406i	−0.914920	+	0.403635i	$0.867747\pi$
$12$		0			0
$13$	−6.99352	−	13.7256i	−0.537963	−	1.05581i	−0.986761	−	0.162179i	$-0.948148\pi$
$13$	−6.99352	−	13.7256i	−0.537963	−	1.05581i	0.448798	−	0.893633i	$-0.351852\pi$
$14$		0			0
$15$	−13.8865	+	17.8141i	−0.925769	+	1.18761i
$16$		0			0
$17$	0.370977	+	2.34226i	0.0218222	+	0.137780i	0.996194	−	0.0871635i	$-0.0277803\pi$
$17$	0.370977	+	2.34226i	0.0218222	+	0.137780i	−0.974372	+	0.224943i	$0.927780\pi$
$18$		0			0
$19$	−13.0079	+	17.9039i	−0.684627	+	0.942309i	−0.999978	−	0.00666661i	$-0.997878\pi$
$19$	−13.0079	+	17.9039i	−0.684627	+	0.942309i	0.315350	+	0.948975i	$0.397878\pi$
$20$		0			0
$21$	−0.272088	+	0.197684i	−0.0129566	+	0.00941350i
$22$		0			0
$23$	−5.97894	−	3.04642i	−0.259954	−	0.132453i	0.319157	−	0.947702i	$-0.396600\pi$
$23$	−5.97894	−	3.04642i	−0.259954	−	0.132453i	−0.579111	+	0.815249i	$0.696600\pi$
$24$		0			0
$25$	13.2943	+	21.1722i	0.531774	+	0.846887i
$26$		0			0
$27$	−4.93664	+	9.68871i	−0.182839	+	0.358841i
$28$		0			0
$29$	−27.6101	−	38.0021i	−0.952074	−	1.31042i	−0.950600	−	0.310418i	$-0.899531\pi$
$29$	−27.6101	−	38.0021i	−0.952074	−	1.31042i	−0.00147357	−	0.999999i	$-0.500469\pi$
$30$		0			0
$31$	3.69691	+	2.68596i	0.119255	+	0.0866439i	0.645814	−	0.763495i	$-0.276518\pi$
$31$	3.69691	+	2.68596i	0.119255	+	0.0866439i	−0.526559	+	0.850139i	$0.676518\pi$
$32$		0			0
$33$	9.92924	−	1.57264i	0.300886	−	0.0476557i
$34$		0			0
$35$	0.102997	+	0.357714i	0.00294276	+	0.0102204i
$36$		0			0
$37$	59.9395	−	30.5407i	1.61999	−	0.825424i	0.620846	−	0.783932i	$-0.286789\pi$
$37$	59.9395	−	30.5407i	1.61999	−	0.825424i	0.999139	−	0.0414916i	$-0.0132110\pi$
$38$		0			0
$39$	−66.1829	+	21.5041i	−1.69700	+	0.551388i
$40$		0			0
$41$	−0.779270	+	2.39835i	−0.0190066	+	0.0584963i	−0.960110	−	0.279623i	$-0.909791\pi$
$41$	−0.779270	+	2.39835i	−0.0190066	+	0.0584963i	0.941103	+	0.338119i	$0.109791\pi$
$42$		0			0
$43$	46.3634	−	46.3634i	1.07822	−	1.07822i	0.0815493	−	0.996669i	$-0.474013\pi$
$43$	46.3634	−	46.3634i	1.07822	−	1.07822i	0.996669	−	0.0815493i	$-0.0259868\pi$
$44$		0			0
$45$	38.9437	+	41.6705i	0.865416	+	0.926012i
$46$		0			0
$47$	−61.7008	−	9.77245i	−1.31278	−	0.207925i	−0.539500	−	0.841985i	$-0.681387\pi$
$47$	−61.7008	−	9.77245i	−1.31278	−	0.207925i	−0.773283	+	0.634061i	$0.781387\pi$
$48$		0			0
$49$		−	48.9945i		−	0.999887i
$50$		0			0
$51$	10.7129			0.210056
$52$		0			0
$53$	7.85019	−	49.5641i	0.148117	−	0.935172i	−0.795937	−	0.605380i	$-0.793021\pi$
$53$	7.85019	−	49.5641i	0.148117	−	0.935172i	0.944053	−	0.329792i	$-0.106979\pi$
$54$		0			0
$55$	2.11117	−	10.9248i	0.0383849	−	0.198633i
$56$		0			0
$57$	70.6911	+	70.6911i	1.24019	+	1.24019i
$58$		0			0
$59$	14.3158	+	4.65148i	0.242641	+	0.0788387i	0.427813	−	0.903867i	$-0.359284\pi$
$59$	14.3158	+	4.65148i	0.242641	+	0.0788387i	−0.185172	+	0.982706i	$0.559284\pi$
$60$		0			0
$61$	−19.4521	−	59.8674i	−0.318887	−	0.981433i	−0.974125	−	0.226011i	$-0.927432\pi$
$61$	−19.4521	−	59.8674i	−0.318887	−	0.981433i	0.655238	−	0.755423i	$-0.272568\pi$
$62$		0			0
$63$	0.385552	+	0.756689i	0.00611988	+	0.0120109i
$64$		0			0
$65$	−2.60384	+	76.9787i	−0.0400591	+	1.18429i
$66$		0			0
$67$	15.8246	+	99.9126i	0.236188	+	1.49123i	0.765848	+	0.643022i	$0.222320\pi$
$67$	15.8246	+	99.9126i	0.236188	+	1.49123i	−0.529660	+	0.848210i	$0.677680\pi$
$68$		0			0
$69$	−17.8178	+	24.5240i	−0.258228	+	0.355421i
$70$		0			0
$71$	81.7241	−	59.3761i	1.15104	−	0.836283i	0.162425	−	0.986721i	$-0.448068\pi$
$71$	81.7241	−	59.3761i	1.15104	−	0.836283i	0.988619	+	0.150438i	$0.0480685\pi$
$72$		0			0
$73$	91.3922	+	46.5667i	1.25195	+	0.637899i	0.949051	−	0.315124i	$-0.102046\pi$
$73$	91.3922	+	46.5667i	1.25195	+	0.637899i	0.302898	+	0.953023i	$0.402046\pi$
$74$		0			0
$75$	103.861	−	44.3548i	1.38481	−	0.591397i
$76$		0			0
$77$	0.0752166	−	0.147621i	0.000976839	−	0.00191715i
$78$		0			0
$79$	74.6124	+	102.695i	0.944461	+	1.29994i	0.953944	+	0.299984i	$0.0969815\pi$
$79$	74.6124	+	102.695i	0.944461	+	1.29994i	−0.00948284	+	0.999955i	$0.503019\pi$
$80$		0			0
$81$	−43.3164	−	31.4712i	−0.534770	−	0.388533i
$82$		0			0
$83$	63.0041	−	9.97887i	0.759085	−	0.120227i	0.235119	−	0.971967i	$-0.424452\pi$
$83$	63.0041	−	9.97887i	0.759085	−	0.120227i	0.523966	+	0.851739i	$0.324452\pi$
$84$		0			0
$85$	4.04324	−	11.1466i	0.0475675	−	0.131137i
$86$		0			0
$87$	−189.069	+	96.3357i	−2.17321	+	1.10731i
$88$		0			0
$89$	−36.9068	+	11.9918i	−0.414684	+	0.134739i	−0.508926	−	0.860810i	$-0.669957\pi$
$89$	−36.9068	+	11.9918i	−0.414684	+	0.134739i	0.0942421	+	0.995549i	$0.469957\pi$
$90$		0			0
$91$	−0.354399	+	1.09073i	−0.00389450	+	0.0119860i
$92$		0			0
$93$	14.5968	−	14.5968i	0.156954	−	0.156954i
$94$		0			0
$95$	100.234	−	46.8732i	1.05509	−	0.493402i
$96$		0			0
$97$	−138.512	−	21.9382i	−1.42796	−	0.226167i	−0.605889	−	0.795549i	$-0.707182\pi$
$97$	−138.512	−	21.9382i	−1.42796	−	0.226167i	−0.822073	+	0.569382i	$0.807182\pi$
$98$		0			0
$99$		−	25.3852i		−	0.256416i
$100$		0			0
$101$	−141.716			−1.40313			−0.701563	−	0.712608i	$-0.747514\pi$
$101$	−141.716			−1.40313			−0.701563	+	0.712608i	$0.747514\pi$
$102$		0			0
$103$	−18.0581	+	114.014i	−0.175321	+	1.10693i	0.730388	+	0.683033i	$0.239339\pi$
$103$	−18.0581	+	114.014i	−0.175321	+	1.10693i	−0.905709	+	0.423900i	$0.860661\pi$
$104$		0			0
$105$	1.66884	−	0.206761i	0.0158937	−	0.00196915i
$106$		0			0
$107$	9.07821	+	9.07821i	0.0848431	+	0.0848431i	0.748255	−	0.663412i	$-0.230892\pi$
$107$	9.07821	+	9.07821i	0.0848431	+	0.0848431i	−0.663412	+	0.748255i	$0.730892\pi$
$108$		0			0
$109$	−10.6751	−	3.46855i	−0.0979366	−	0.0318215i	0.259639	−	0.965706i	$-0.416396\pi$
$109$	−10.6751	−	3.46855i	−0.0979366	−	0.0318215i	−0.357575	+	0.933884i	$0.616396\pi$
$110$		0			0
$111$	−93.9085	−	289.021i	−0.846023	−	2.60379i
$112$		0			0
$113$	−10.0041	−	19.6342i	−0.0885322	−	0.173754i	0.842495	−	0.538704i	$-0.181086\pi$
$113$	−10.0041	−	19.6342i	−0.0885322	−	0.173754i	−0.931027	+	0.364950i	$0.881086\pi$
$114$		0			0
$115$	18.7923	+	27.7950i	0.163411	+	0.241696i
$116$		0			0
$117$	27.4889	+	173.558i	0.234947	+	1.48340i
$118$		0			0
$119$	0.103776	−	0.142835i	0.000872063	−	0.00120029i
$120$		0			0
$121$	93.8845	−	68.2111i	0.775905	−	0.563728i
$122$		0			0
$123$	10.1503	+	5.17182i	0.0825224	+	0.0420473i
$124$		0			0
$125$	−6.95165	−	124.807i	−0.0556132	−	0.998452i
$126$		0			0
$127$	85.7277	−	168.250i	0.675021	−	1.32480i	−0.258406	−	0.966036i	$-0.583197\pi$
$127$	85.7277	−	168.250i	0.675021	−	1.32480i	0.933427	−	0.358767i	$-0.116803\pi$
$128$		0			0
$129$	−174.100	−	239.629i	−1.34962	−	1.85759i
$130$		0			0
$131$	−108.739	−	79.0037i	−0.830071	−	0.603082i	0.0895088	−	0.995986i	$-0.471470\pi$
$131$	−108.739	−	79.0037i	−0.830071	−	0.603082i	−0.919579	+	0.392905i	$0.871470\pi$
$132$		0			0
$133$	1.62731	−	0.257741i	0.0122354	−	0.00193790i
$134$		0			0
$135$	45.0410	−	30.4523i	0.333637	−	0.225573i
$136$		0			0
$137$	−67.2226	+	34.2516i	−0.490676	+	0.250012i	−0.681779	−	0.731558i	$-0.738794\pi$
$137$	−67.2226	+	34.2516i	−0.490676	+	0.250012i	0.191103	+	0.981570i	$0.438794\pi$
$138$		0			0
$139$	99.7167	−	32.3999i	0.717386	−	0.233093i	0.0724967	−	0.997369i	$-0.476903\pi$
$139$	99.7167	−	32.3999i	0.717386	−	0.233093i	0.644890	+	0.764276i	$0.276903\pi$
$140$		0			0
$141$	−87.2055	+	268.391i	−0.618479	+	1.90348i
$142$		0			0
$143$	24.2404	−	24.2404i	0.169513	−	0.169513i
$144$		0			0
$145$	28.8780	+	233.084i	0.199158	+	1.60747i
$146$		0			0
$147$	−218.604	−	34.6234i	−1.48710	−	0.235534i
$148$		0			0
$149$			179.838i			1.20697i	0.797374	+	0.603485i	$0.206222\pi$
$149$			179.838i			1.20697i	−0.797374	+	0.603485i	$0.793778\pi$
$150$		0			0
$151$	−196.687			−1.30256			−0.651282	−	0.758836i	$-0.725768\pi$
$151$	−196.687			−1.30256			−0.651282	+	0.758836i	$0.725768\pi$
$152$		0			0
$153$	4.23178	−	26.7184i	0.0276587	−	0.174630i
$154$		0			0
$155$	−9.67869	−	20.6969i	−0.0624432	−	0.133528i
$156$		0			0
$157$	140.697	+	140.697i	0.896159	+	0.896159i	0.995094	−	0.0989345i	$-0.0315434\pi$
$157$	140.697	+	140.697i	0.896159	+	0.896159i	−0.0989345	+	0.995094i	$0.531543\pi$
$158$		0			0
$159$	−215.598	−	70.0520i	−1.35596	−	0.440579i
$160$		0			0
$161$	0.154379	+	0.475129i	0.000958874	+	0.00295111i
$162$		0			0
$163$	33.8077	+	66.3513i	0.207409	+	0.407063i	0.971153	−	0.238456i	$-0.0766411\pi$
$163$	33.8077	+	66.3513i	0.207409	+	0.407063i	−0.763744	+	0.645519i	$0.776641\pi$
$164$		0			0
$165$	−47.2525	−	17.1400i	−0.286379	−	0.103879i
$166$		0			0
$167$	5.49549	+	34.6972i	0.0329071	+	0.207768i	0.998664	−	0.0516830i	$-0.0164585\pi$
$167$	5.49549	+	34.6972i	0.0329071	+	0.207768i	−0.965756	+	0.259451i	$0.916459\pi$
$168$		0			0
$169$	−40.1458	+	55.2559i	−0.237549	+	0.326958i
$170$		0			0
$171$	204.231	−	148.383i	1.19433	−	0.867735i
$172$		0			0
$173$	13.2636	+	6.75816i	0.0766684	+	0.0390645i	0.491904	−	0.870649i	$-0.336301\pi$
$173$	13.2636	+	6.75816i	0.0766684	+	0.0390645i	−0.415236	+	0.909714i	$0.636301\pi$
$174$		0			0
$175$	0.414718	−	1.81444i	0.00236982	−	0.0103682i
$176$		0			0
$177$	30.8707	−	60.5872i	0.174411	−	0.342300i
$178$		0			0
$179$	125.985	+	173.403i	0.703825	+	0.968733i	0.999908	+	0.0135702i	$0.00431965\pi$
$179$	125.985	+	173.403i	0.703825	+	0.968733i	−0.296083	+	0.955162i	$0.595680\pi$
$180$		0			0
$181$	95.9822	+	69.7351i	0.530288	+	0.385277i	0.820466	−	0.571696i	$-0.193714\pi$
$181$	95.9822	+	69.7351i	0.530288	+	0.385277i	−0.290177	+	0.956973i	$0.593714\pi$
$182$		0			0
$183$	−280.863	+	44.4844i	−1.53477	+	0.243084i
$184$		0			0
$185$	−336.166	−	11.3710i	−1.81711	−	0.0614647i
$186$		0			0
$187$	−4.70220	+	2.39589i	−0.0251455	+	0.0128123i
$188$		0			0
$189$	0.769932	−	0.250166i	0.00407372	−	0.00132363i
$190$		0			0
$191$	−50.9394	+	156.775i	−0.266699	+	0.820814i	0.724599	+	0.689171i	$0.242025\pi$
$191$	−50.9394	+	156.775i	−0.266699	+	0.820814i	−0.991297	+	0.131643i	$0.957975\pi$
$192$		0			0
$193$	209.063	−	209.063i	1.08323	−	1.08323i	0.0870203	−	0.996207i	$-0.472265\pi$
$193$	209.063	−	209.063i	1.08323	−	1.08323i	0.996207	−	0.0870203i	$-0.0277345\pi$
$194$		0			0
$195$	341.624	+	66.0172i	1.75192	+	0.338550i
$196$		0			0
$197$	−52.3675	−	8.29420i	−0.265825	−	0.0421025i	0.0220991	−	0.999756i	$-0.492965\pi$
$197$	−52.3675	−	8.29420i	−0.265825	−	0.0421025i	−0.287924	+	0.957653i	$0.592965\pi$
$198$		0			0
$199$			174.355i			0.876158i	0.898936	+	0.438079i	$0.144341\pi$
$199$			174.355i			0.876158i	−0.898936	+	0.438079i	$0.855659\pi$
$200$		0			0
$201$	456.973			2.27350
$202$		0			0
$203$	−0.547071	+	3.45407i	−0.00269493	+	0.0170151i
$204$		0			0
$205$	9.21212	−	8.60930i	0.0449372	−	0.0419966i
$206$		0			0
$207$	54.1257	+	54.1257i	0.261477	+	0.261477i
$208$		0			0
$209$	−46.8383	−	15.2187i	−0.224107	−	0.0728167i
$210$		0			0
$211$	17.0119	+	52.3573i	0.0806251	+	0.248139i	0.983242	−	0.182307i	$-0.0583564\pi$
$211$	17.0119	+	52.3573i	0.0806251	+	0.248139i	−0.902617	+	0.430446i	$0.858356\pi$
$212$		0			0
$213$	−207.172	−	406.597i	−0.972636	−	1.90891i
$214$		0			0
$215$	−315.040	+	90.7093i	−1.46530	+	0.421904i
$216$		0			0
$217$	−0.0532200	−	0.336018i	−0.000245253	−	0.00154847i
$218$		0			0
$219$	272.356	−	374.866i	1.24364	−	1.71172i
$220$		0			0
$221$	29.5544	−	21.4725i	0.133730	−	0.0971606i
$222$		0			0
$223$	135.136	+	68.8553i	0.605991	+	0.308768i	0.729930	−	0.683522i	$-0.239553\pi$
$223$	135.136	+	68.8553i	0.605991	+	0.308768i	−0.123939	+	0.992290i	$0.539553\pi$
$224$		0			0
$225$	−69.5960	−	276.555i	−0.309315	−	1.22913i
$226$		0			0
$227$	195.862	−	384.400i	0.862826	−	1.69339i	0.153926	−	0.988082i	$-0.450808\pi$
$227$	195.862	−	384.400i	0.862826	−	1.69339i	0.708900	−	0.705309i	$-0.249192\pi$
$228$		0			0
$229$	0.300534	+	0.413649i	0.00131237	+	0.00180633i	0.809673	−	0.586882i	$-0.199645\pi$
$229$	0.300534	+	0.413649i	0.00131237	+	0.00180633i	−0.808360	+	0.588688i	$0.799645\pi$
$230$		0			0
$231$	−0.605501	−	0.439922i	−0.00262122	−	0.00190443i
$232$		0			0
$233$	225.714	−	35.7496i	0.968729	−	0.153432i	0.348033	−	0.937482i	$-0.386850\pi$
$233$	225.714	−	35.7496i	0.968729	−	0.153432i	0.620697	+	0.784051i	$0.286850\pi$
$234$		0			0
$235$	246.345	+	192.032i	1.04828	+	0.817159i
$236$		0			0
$237$	510.933	−	260.333i	2.15584	−	1.09845i
$238$		0			0
$239$	−57.7501	+	18.7641i	−0.241632	+	0.0785111i	−0.427330	−	0.904096i	$-0.640546\pi$
$239$	−57.7501	+	18.7641i	−0.241632	+	0.0785111i	0.185697	+	0.982607i	$0.440546\pi$
$240$		0			0
$241$	−73.7937	+	227.114i	−0.306198	+	0.942381i	0.673029	+	0.739616i	$0.264993\pi$
$241$	−73.7937	+	227.114i	−0.306198	+	0.942381i	−0.979227	+	0.202765i	$0.935007\pi$
$242$		0			0
$243$	−240.230	+	240.230i	−0.988601	+	0.988601i
$244$		0			0
$245$	−118.530	+	214.387i	−0.483798	+	0.875051i
$246$		0			0
$247$	336.712	+	53.3299i	1.36320	+	0.215910i
$248$		0			0
$249$		−	288.164i		−	1.15728i
$250$		0			0
$251$	207.257			0.825727			0.412864	−	0.910793i	$-0.364529\pi$
$251$	207.257			0.825727			0.412864	+	0.910793i	$0.364529\pi$
$252$		0			0
$253$	2.33605	−	14.7492i	0.00923339	−	0.0582973i
$254$		0			0
$255$	−46.8768	−	25.9172i	−0.183831	−	0.101636i
$256$		0			0
$257$	−172.275	−	172.275i	−0.670332	−	0.670332i	0.287461	−	0.957792i	$-0.407189\pi$
$257$	−172.275	−	172.275i	−0.670332	−	0.670332i	−0.957792	+	0.287461i	$0.907189\pi$
$258$		0			0
$259$	−4.76321	−	1.54766i	−0.0183908	−	0.00597552i
$260$		0			0
$261$	165.580	+	509.602i	0.634406	+	1.95250i
$262$		0			0
$263$	−43.8680	−	86.0959i	−0.166799	−	0.327361i	0.792444	−	0.609945i	$-0.208808\pi$
$263$	−43.8680	−	86.0959i	−0.166799	−	0.327361i	−0.959243	+	0.282584i	$0.908808\pi$
$264$		0			0
$265$	−154.259	+	197.888i	−0.582110	+	0.746749i
$266$		0			0
$267$	27.4235	+	173.145i	0.102710	+	0.648485i
$268$		0			0
$269$	−253.452	+	348.846i	−0.942200	+	1.29683i	0.0127068	+	0.999919i	$0.495955\pi$
$269$	−253.452	+	348.846i	−0.942200	+	1.29683i	−0.954906	+	0.296907i	$0.904045\pi$
$270$		0			0
$271$	25.0842	−	18.2248i	0.0925618	−	0.0672501i	−0.540542	−	0.841317i	$-0.681781\pi$
$271$	25.0842	−	18.2248i	0.0925618	−	0.0672501i	0.633104	+	0.774067i	$0.281781\pi$
$272$		0			0
$273$	4.61617	+	2.35206i	0.0169090	+	0.00861559i
$274$		0			0
$275$	−35.6679	+	42.6968i	−0.129702	+	0.155261i
$276$		0			0
$277$	63.5139	−	124.653i	0.229292	−	0.450011i	−0.747482	−	0.664282i	$-0.768737\pi$
$277$	63.5139	−	124.653i	0.229292	−	0.450011i	0.976774	+	0.214271i	$0.0687375\pi$
$278$		0			0
$279$	−30.6390	−	42.1710i	−0.109817	−	0.151151i
$280$		0			0
$281$	−30.4919	−	22.1536i	−0.108512	−	0.0788386i	0.532206	−	0.846615i	$-0.321363\pi$
$281$	−30.4919	−	22.1536i	−0.108512	−	0.0788386i	−0.640718	+	0.767776i	$0.721363\pi$
$282$		0			0
$283$	−420.731	+	66.6373i	−1.48668	+	0.235467i	−0.846349	−	0.532630i	$-0.821204\pi$
$283$	−420.731	+	66.6373i	−1.48668	+	0.235467i	−0.640334	+	0.768097i	$0.721204\pi$
$284$		0			0
$285$	−138.306	−	480.347i	−0.485285	−	1.68543i
$286$		0			0
$287$	0.167281	−	0.0852341i	0.000582862	−	0.000296983i
$288$		0			0
$289$	269.507	−	87.5681i	0.932549	−	0.303004i
$290$		0			0
$291$	−195.768	+	602.512i	−0.672742	+	2.07049i
$292$		0			0
$293$	240.569	−	240.569i	0.821054	−	0.821054i	−0.165205	−	0.986259i	$-0.552829\pi$
$293$	240.569	−	240.569i	0.821054	−	0.821054i	0.986259	+	0.165205i	$0.0528286\pi$
$294$		0			0
$295$	−51.3891	−	54.9874i	−0.174200	−	0.186398i
$296$		0			0
$297$	−23.9007	−	3.78550i	−0.0804737	−	0.0127458i
$298$		0			0
$299$			103.370i			0.345718i
$300$		0			0
$301$	−4.88148			−0.0162175
$302$		0			0
$303$	−100.148	+	632.308i	−0.330520	+	2.08682i
$304$		0			0
$305$	−59.7175	+	309.024i	−0.195795	+	1.01320i
$306$		0			0
$307$	−206.372	−	206.372i	−0.672222	−	0.672222i	0.286006	−	0.958228i	$-0.407672\pi$
$307$	−206.372	−	206.372i	−0.672222	−	0.672222i	−0.958228	+	0.286006i	$0.907672\pi$
$308$		0			0
$309$	495.947	+	161.143i	1.60501	+	0.521499i
$310$		0			0
$311$	−55.1913	−	169.861i	−0.177464	−	0.546178i	0.822273	−	0.569093i	$-0.192705\pi$
$311$	−55.1913	−	169.861i	−0.177464	−	0.546178i	−0.999737	+	0.0229146i	$0.992705\pi$
$312$		0			0
$313$	167.138	+	328.027i	0.533987	+	1.04801i	0.987627	+	0.156824i	$0.0501255\pi$
$313$	167.138	+	328.027i	0.533987	+	1.04801i	−0.453639	+	0.891185i	$0.649875\pi$
$314$		0			0
$315$	0.143550	−	4.24383i	0.000455713	−	0.0134725i
$316$		0			0
$317$	−29.4856	−	186.165i	−0.0930145	−	0.587270i	−0.989538	−	0.144274i	$-0.953915\pi$
$317$	−29.4856	−	186.165i	−0.0930145	−	0.587270i	0.896523	−	0.442997i	$-0.146085\pi$
$318$		0			0
$319$	61.4432	−	84.5694i	0.192612	−	0.265108i
$320$		0			0
$321$	46.9206	−	34.0898i	0.146170	−	0.106199i
$322$		0			0
$323$	−46.7611	−	23.8260i	−0.144771	−	0.0737647i
$324$		0			0
$325$	197.625	−	330.540i	0.608078	−	1.01705i
$326$		0			0
$327$	−23.0199	+	45.1790i	−0.0703971	+	0.138162i
$328$		0			0
$329$	2.73370	+	3.76262i	0.00830912	+	0.0114365i
$330$		0			0
$331$	−302.888	−	220.061i	−0.915069	−	0.664836i	0.0272230	−	0.999629i	$-0.491334\pi$
$331$	−302.888	−	220.061i	−0.915069	−	0.664836i	−0.942292	+	0.334793i	$0.891334\pi$
$332$		0			0
$333$	−757.927	+	120.044i	−2.27606	+	0.360492i
$334$		0			0
$335$	172.470	−	475.476i	0.514837	−	1.41933i
$336$		0			0
$337$	170.539	−	86.8941i	0.506051	−	0.257846i	−0.182275	−	0.983248i	$-0.558346\pi$
$337$	170.539	−	86.8941i	0.506051	−	0.257846i	0.688326	+	0.725402i	$0.258346\pi$
$338$		0			0
$339$	−94.6738	+	30.7614i	−0.279274	+	0.0907416i
$340$		0			0
$341$	−3.14245	+	9.67148i	−0.00921541	+	0.0283621i
$342$		0			0
$343$	−5.15879	+	5.15879i	−0.0150402	+	0.0150402i
$344$		0			0
$345$	137.296	−	64.2052i	0.397960	−	0.186102i
$346$		0			0
$347$	−405.251	−	64.1855i	−1.16787	−	0.184973i	−0.457769	−	0.889071i	$-0.651351\pi$
$347$	−405.251	−	64.1855i	−1.16787	−	0.184973i	−0.710102	+	0.704098i	$0.751351\pi$
$348$		0			0
$349$		−	391.257i		−	1.12108i	−0.828127	−	0.560541i	$-0.810593\pi$
$349$		−	391.257i		−	1.12108i	0.828127	−	0.560541i	$-0.189407\pi$
$350$		0			0
$351$	167.507			0.477229
$352$		0			0
$353$	−51.9440	+	327.962i	−0.147150	+	0.929070i	0.798053	+	0.602587i	$0.205863\pi$
$353$	−51.9440	+	327.962i	−0.147150	+	0.929070i	−0.945203	+	0.326483i	$0.894137\pi$
$354$		0			0
$355$	−501.251	+	62.1025i	−1.41197	+	0.174937i
$356$		0			0
$357$	−0.563965	−	0.563965i	−0.00157973	−	0.00157973i
$358$		0			0
$359$	529.753	+	172.127i	1.47563	+	0.479463i	0.932806	−	0.360380i	$-0.117353\pi$
$359$	529.753	+	172.127i	1.47563	+	0.479463i	0.542829	+	0.839843i	$0.317353\pi$
$360$		0			0
$361$	−39.7873	−	122.453i	−0.110214	−	0.339204i
$362$		0			0
$363$	−237.998	−	467.098i	−0.655643	−	1.28677i
$364$		0			0
$365$	−287.252	−	424.866i	−0.786993	−	1.16402i
$366$		0			0
$367$	−97.4605	−	615.342i	−0.265560	−	1.67668i	−0.655001	−	0.755628i	$-0.727332\pi$
$367$	−97.4605	−	615.342i	−0.265560	−	1.67668i	0.389441	−	0.921052i	$-0.372668\pi$
$368$		0			0
$369$	16.9083	−	23.2723i	0.0458219	−	0.0630685i
$370$		0			0
$371$	−3.02250	+	2.19598i	−0.00814690	+	0.00591907i
$372$		0			0
$373$	−16.7670	−	8.54321i	−0.0449518	−	0.0229041i	0.431370	−	0.902175i	$-0.358030\pi$
$373$	−16.7670	−	8.54321i	−0.0449518	−	0.0229041i	−0.476322	+	0.879271i	$0.658030\pi$
$374$		0			0
$375$	−561.775	−	57.1814i	−1.49807	−	0.152484i
$376$		0			0
$377$	−328.508	+	644.733i	−0.871373	+	1.71017i
$378$		0			0
$379$	372.648	+	512.906i	0.983241	+	1.35331i	0.935065	+	0.354476i	$0.115341\pi$
$379$	372.648	+	512.906i	0.983241	+	1.35331i	0.0481753	+	0.998839i	$0.484659\pi$
$380$		0			0
$381$	−690.117	−	501.399i	−1.81133	−	1.31601i
$382$		0			0
$383$	237.795	−	37.6630i	0.620874	−	0.0983367i	0.161930	−	0.986802i	$-0.448228\pi$
$383$	237.795	−	37.6630i	0.620874	−	0.0983367i	0.458943	+	0.888465i	$0.348228\pi$
$384$		0			0
$385$	−0.686262	+	0.463983i	−0.00178250	+	0.00120515i
$386$		0			0
$387$	−666.418	+	339.557i	−1.72201	+	0.877408i
$388$		0			0
$389$	307.741	−	99.9913i	0.791109	−	0.257047i	0.114533	−	0.993419i	$-0.463463\pi$
$389$	307.741	−	99.9913i	0.791109	−	0.257047i	0.676576	+	0.736373i	$0.263463\pi$
$390$		0			0
$391$	4.91746	−	15.1344i	0.0125766	−	0.0387069i
$392$		0			0
$393$	−429.343	+	429.343i	−1.09248	+	1.09248i
$394$		0			0
$395$	−78.0386	−	629.875i	−0.197566	−	1.59462i
$396$		0			0
$397$	53.6156	+	8.49188i	0.135052	+	0.0213901i	0.223594	−	0.974682i	$-0.428221\pi$
$397$	53.6156	+	8.49188i	0.135052	+	0.0213901i	−0.0885425	+	0.996072i	$0.528221\pi$
$398$		0			0
$399$		−	7.44288i		−	0.0186538i
$400$		0			0
$401$	511.874			1.27649			0.638247	−	0.769832i	$-0.279660\pi$
$401$	511.874			1.27649			0.638247	+	0.769832i	$0.279660\pi$
$402$		0			0
$403$	11.0119	−	69.5264i	0.0273248	−	0.172522i
$404$		0			0
$405$	113.404	+	242.504i	0.280011	+	0.598774i
$406$		0			0
$407$	105.858	+	105.858i	0.260093	+	0.260093i
$408$		0			0
$409$	121.365	+	39.4338i	0.296735	+	0.0964152i	0.453601	−	0.891205i	$-0.350139\pi$
$409$	121.365	+	39.4338i	0.296735	+	0.0964152i	−0.156866	+	0.987620i	$0.550139\pi$
$410$		0			0
$411$	105.319	+	324.139i	0.256251	+	0.788660i
$412$		0			0
$413$	−0.508765	−	0.998507i	−0.00123188	−	0.00241769i
$414$		0			0
$415$	−299.831	−	108.758i	−0.722485	−	0.262068i
$416$		0			0
$417$	−74.0943	−	467.813i	−0.177684	−	1.12185i
$418$		0			0
$419$	136.283	−	187.577i	0.325258	−	0.447679i	−0.614806	−	0.788679i	$-0.710766\pi$
$419$	136.283	−	187.577i	0.325258	−	0.447679i	0.940063	+	0.341000i	$0.110766\pi$
$420$		0			0
$421$	−295.953	+	215.023i	−0.702977	+	0.510742i	−0.880900	−	0.473302i	$-0.843062\pi$
$421$	−295.953	+	215.023i	−0.702977	+	0.510742i	0.177924	+	0.984044i	$0.443062\pi$
$422$		0			0
$423$	634.932	+	323.514i	1.50102	+	0.764809i
$424$		0			0
$425$	−44.6588	+	38.9932i	−0.105080	+	0.0917486i
$426$		0			0
$427$	−2.12761	+	4.17567i	−0.00498270	+	0.00977909i
$428$		0			0
$429$	−91.0257	−	125.286i	−0.212181	−	0.292042i
$430$		0			0
$431$	165.792	+	120.455i	0.384668	+	0.279478i	0.763267	−	0.646083i	$-0.223594\pi$
$431$	165.792	+	120.455i	0.384668	+	0.279478i	−0.378599	+	0.925561i	$0.623594\pi$
$432$		0			0
$433$	−354.920	+	56.2139i	−0.819677	+	0.129824i	−0.552170	−	0.833732i	$-0.686200\pi$
$433$	−354.920	+	56.2139i	−0.819677	+	0.129824i	−0.267507	+	0.963556i	$0.586200\pi$
$434$		0			0
$435$	1060.38	+	35.8679i	2.43766	+	0.0824550i
$436$		0			0
$437$	132.316	−	67.4186i	0.302784	−	0.154276i
$438$		0			0
$439$	−338.042	+	109.837i	−0.770028	+	0.250197i	−0.667577	−	0.744541i	$-0.732668\pi$
$439$	−338.042	+	109.837i	−0.770028	+	0.250197i	−0.102451	+	0.994738i	$0.532668\pi$
$440$		0			0
$441$	−172.705	+	531.531i	−0.391621	+	1.20529i
$442$		0			0
$443$	375.972	−	375.972i	0.848696	−	0.848696i	−0.141274	−	0.989970i	$-0.545120\pi$
$443$	375.972	−	375.972i	0.848696	−	0.848696i	0.989970	+	0.141274i	$0.0451199\pi$
$444$		0			0
$445$	190.506	+	36.8144i	0.428104	+	0.0827290i
$446$		0			0
$447$	802.404	+	127.088i	1.79509	+	0.284314i
$448$		0			0
$449$			197.943i			0.440853i	0.975404	+	0.220426i	$0.0707449\pi$
$449$			197.943i			0.440853i	−0.975404	+	0.220426i	$0.929255\pi$
$450$		0			0
$451$	−5.61192			−0.0124433
$452$		0			0
$453$	−138.995	+	877.580i	−0.306832	+	1.93726i
$454$		0			0
$455$	4.18952	−	3.91537i	0.00920773	−	0.00860520i
$456$		0			0
$457$	−56.7642	−	56.7642i	−0.124210	−	0.124210i	0.642269	−	0.766479i	$-0.277993\pi$
$457$	−56.7642	−	56.7642i	−0.124210	−	0.124210i	−0.766479	+	0.642269i	$0.777993\pi$
$458$		0			0
$459$	−24.5248	−	7.96861i	−0.0534310	−	0.0173608i
$460$		0			0
$461$	18.9770	+	58.4051i	0.0411648	+	0.126692i	0.969527	−	0.244985i	$-0.0787829\pi$
$461$	18.9770	+	58.4051i	0.0411648	+	0.126692i	−0.928362	+	0.371677i	$0.878783\pi$
$462$		0			0
$463$	108.886	+	213.700i	0.235174	+	0.461555i	0.978188	−	0.207721i	$-0.0666046\pi$
$463$	108.886	+	213.700i	0.235174	+	0.461555i	−0.743014	+	0.669276i	$0.766605\pi$
$464$		0			0
$465$	−99.1852	+	28.5584i	−0.213301	+	0.0614158i
$466$		0			0
$467$	−30.4472	−	192.236i	−0.0651974	−	0.411640i	−0.998604	−	0.0528199i	$-0.983179\pi$
$467$	−30.4472	−	192.236i	−0.0651974	−	0.411640i	0.933407	−	0.358820i	$-0.116821\pi$
$468$		0			0
$469$	4.42670	−	6.09283i	0.00943859	−	0.0129911i
$470$		0			0
$471$	727.191	−	528.335i	1.54393	−	1.12173i
$472$		0			0
$473$	130.010	+	66.2434i	0.274863	+	0.140049i
$474$		0			0
$475$	−551.995	−	37.3858i	−1.16210	−	0.0787069i
$476$		0			0
$477$	−259.878	+	510.039i	−0.544818	+	1.06926i
$478$		0			0
$479$	224.113	+	308.465i	0.467876	+	0.643977i	0.976119	−	0.217237i	$-0.0697046\pi$
$479$	224.113	+	308.465i	0.467876	+	0.643977i	−0.508242	+	0.861214i	$0.669705\pi$
$480$		0			0
$481$	−838.375	−	609.115i	−1.74298	−	1.26635i
$482$		0			0
$483$	2.22903	−	0.353043i	0.00461496	−	0.000730938i
$484$		0			0
$485$	553.021	+	431.094i	1.14025	+	0.888853i
$486$		0			0
$487$	95.6879	−	48.7554i	0.196484	−	0.100114i	−0.352980	−	0.935631i	$-0.614832\pi$
$487$	95.6879	−	48.7554i	0.196484	−	0.100114i	0.549465	+	0.835517i	$0.314832\pi$
$488$		0			0
$489$	319.938	−	103.954i	0.654270	−	0.212585i
$490$		0			0
$491$	−187.535	+	577.172i	−0.381944	+	1.17550i	0.556728	+	0.830695i	$0.312056\pi$
$491$	−187.535	+	577.172i	−0.381944	+	1.17550i	−0.938673	+	0.344809i	$0.887944\pi$
$492$		0			0
$493$	78.7680	−	78.7680i	0.159773	−	0.159773i
$494$		0			0
$495$	−61.4135	+	111.079i	−0.124068	+	0.224403i
$496$		0			0
$497$	−7.42803	−	1.17649i	−0.0149457	−	0.00236717i
$498$		0			0
$499$		−	497.932i		−	0.997860i	−0.866642	−	0.498930i	$-0.833726\pi$
$499$		−	497.932i		−	0.997860i	0.866642	−	0.498930i	$-0.166274\pi$
$500$		0			0
$501$	158.696			0.316758
$502$		0			0
$503$	63.6808	−	402.065i	0.126602	−	0.799334i	−0.839912	−	0.542722i	$-0.817394\pi$
$503$	63.6808	−	402.065i	0.126602	−	0.799334i	0.966515	−	0.256612i	$-0.0826062\pi$
$504$		0			0
$505$	620.112	+	342.847i	1.22794	+	0.678906i
$506$		0			0
$507$	218.171	+	218.171i	0.430318	+	0.430318i
$508$		0			0
$509$	−91.1612	−	29.6201i	−0.179099	−	0.0581927i	0.218095	−	0.975928i	$-0.430016\pi$
$509$	−91.1612	−	29.6201i	−0.179099	−	0.0581927i	−0.397193	+	0.917735i	$0.630016\pi$
$510$		0			0
$511$	−2.35978	−	7.26266i	−0.00461797	−	0.0142126i
$512$		0			0
$513$	−109.250	−	214.415i	−0.212963	−	0.417963i
$514$		0			0
$515$	354.847	−	455.210i	0.689024	−	0.883902i
$516$		0			0
$517$	−21.7475	−	137.308i	−0.0420648	−	0.265587i
$518$		0			0
$519$	39.5267	−	54.4039i	0.0761594	−	0.104824i
$520$		0			0
$521$	17.2061	−	12.5009i	0.0330250	−	0.0239941i	−0.571150	−	0.820846i	$-0.693503\pi$
$521$	17.2061	−	12.5009i	0.0330250	−	0.0239941i	0.604175	+	0.796851i	$0.293503\pi$
$522$		0			0
$523$	−212.904	−	108.480i	−0.407082	−	0.207418i	0.238445	−	0.971156i	$-0.423362\pi$
$523$	−212.904	−	108.480i	−0.407082	−	0.207418i	−0.645527	+	0.763737i	$0.723362\pi$
$524$		0			0
$525$	−7.80262	−	3.13262i	−0.0148621	−	0.00596690i
$526$		0			0
$527$	−4.91975	+	9.65555i	−0.00933538	+	0.0183217i
$528$		0			0
$529$	−284.471	−	391.541i	−0.537753	−	0.740153i
$530$		0			0
$531$	−138.913	−	100.926i	−0.261606	−	0.190068i
$532$		0			0
$533$	38.3685	−	6.07697i	0.0719859	−	0.0114014i
$534$		0			0
$535$	−17.7614	−	61.6865i	−0.0331989	−	0.115302i
$536$		0			0
$537$	862.722	−	439.579i	1.60656	−	0.818582i
$538$		0			0
$539$	103.695	−	33.6926i	0.192384	−	0.0625095i
$540$		0			0
$541$	247.358	−	761.290i	0.457224	−	1.40719i	−0.411280	−	0.911509i	$-0.634918\pi$
$541$	247.358	−	761.290i	0.457224	−	1.40719i	0.868504	−	0.495682i	$-0.165082\pi$
$542$		0			0
$543$	378.973	−	378.973i	0.697925	−	0.697925i
$544$		0			0
$545$	38.3202	+	41.0033i	0.0703123	+	0.0752355i
$546$		0			0
$547$	521.386	+	82.5795i	0.953174	+	0.150968i	0.613605	−	0.789613i	$-0.289719\pi$
$547$	521.386	+	82.5795i	0.953174	+	0.150968i	0.339569	+	0.940581i	$0.389719\pi$
$548$		0			0
$549$			718.058i			1.30794i
$550$		0			0
$551$	1039.53			1.88663
$552$		0			0
$553$	1.47838	−	9.33413i	0.00267338	−	0.0168791i
$554$		0			0
$555$	−288.297	+	1491.87i	−0.519454	+	2.68806i
$556$		0			0
$557$	−545.295	−	545.295i	−0.978985	−	0.978985i	0.0207984	−	0.999784i	$-0.493379\pi$
$557$	−545.295	−	545.295i	−0.978985	−	0.978985i	−0.999784	+	0.0207984i	$0.993379\pi$
$558$		0			0
$559$	−960.607	−	312.120i	−1.71844	−	0.558354i
$560$		0			0
$561$	7.36705	+	22.6734i	0.0131320	+	0.0404161i
$562$		0			0
$563$	−363.431	−	713.274i	−0.645526	−	1.26692i	−0.949360	−	0.314192i	$-0.898267\pi$
$563$	−363.431	−	713.274i	−0.645526	−	1.26692i	0.303833	−	0.952725i	$-0.401733\pi$
$564$		0			0
$565$	−3.72476	+	110.117i	−0.00659250	+	0.194897i
$566$		0			0
$567$	0.623574	+	3.93709i	0.00109978	+	0.00694372i
$568$		0			0
$569$	−447.082	+	615.356i	−0.785733	+	1.08147i	0.208893	+	0.977938i	$0.433014\pi$
$569$	−447.082	+	615.356i	−0.785733	+	1.08147i	−0.994626	+	0.103530i	$0.966986\pi$
$570$		0			0
$571$	−281.200	+	204.304i	−0.492469	+	0.357800i	−0.806133	−	0.591734i	$-0.798443\pi$
$571$	−281.200	+	204.304i	−0.492469	+	0.357800i	0.313664	+	0.949534i	$0.398443\pi$
$572$		0			0
$573$	663.503	+	338.072i	1.15795	+	0.590003i
$574$		0			0
$575$	−14.9867	−	167.087i	−0.0260638	−	0.290587i
$576$		0			0
$577$	−176.411	+	346.227i	−0.305739	+	0.600047i	−0.991844	−	0.127456i	$-0.959319\pi$
$577$	−176.411	+	346.227i	−0.305739	+	0.600047i	0.686105	+	0.727502i	$0.259319\pi$
$578$		0			0
$579$	−785.057	−	1080.54i	−1.35588	−	1.86621i
$580$		0			0
$581$	−3.84209	−	2.79144i	−0.00661289	−	0.00480455i
$582$		0			0
$583$	110.299	−	17.4697i	0.189193	−	0.0299652i
$584$		0			0
$585$	299.598	−	825.948i	0.512133	−	1.41188i
$586$		0			0
$587$	−806.067	+	410.711i	−1.37320	+	0.699679i	−0.975942	−	0.218030i	$-0.930037\pi$
$587$	−806.067	+	410.711i	−1.37320	+	0.699679i	−0.397255	+	0.917708i	$0.630037\pi$
$588$		0			0
$589$	−96.1782	+	31.2502i	−0.163291	+	0.0530563i
$590$		0			0
$591$	−74.0142	+	227.792i	−0.125236	+	0.385435i
$592$		0			0
$593$	512.766	−	512.766i	0.864699	−	0.864699i	−0.127181	−	0.991880i	$-0.540593\pi$
$593$	512.766	−	512.766i	0.864699	−	0.864699i	0.991880	+	0.127181i	$0.0405928\pi$
$594$		0			0
$595$	−0.799650	+	0.373949i	−0.00134395	+	0.000628485i
$596$		0			0
$597$	777.940	+	123.214i	1.30308	+	0.206388i
$598$		0			0
$599$			597.049i			0.996742i	0.866964	+	0.498371i	$0.166068\pi$
$599$			597.049i			0.996742i	−0.866964	+	0.498371i	$0.833932\pi$
$600$		0			0
$601$	808.063			1.34453			0.672266	−	0.740310i	$-0.265321\pi$
$601$	808.063			1.34453			0.672266	+	0.740310i	$0.265321\pi$
$602$		0			0
$603$	180.513	−	1139.71i	0.299358	−	1.89007i
$604$		0			0
$605$	−575.836	+	71.3433i	−0.951794	+	0.117923i
$606$		0			0
$607$	154.240	+	154.240i	0.254102	+	0.254102i	0.822650	−	0.568548i	$-0.192495\pi$
$607$	154.240	+	154.240i	0.254102	+	0.254102i	−0.568548	+	0.822650i	$0.692495\pi$
$608$		0			0
$609$	15.0248	+	4.88185i	0.0246712	+	0.00801617i
$610$		0			0
$611$	297.374	+	915.222i	0.486700	+	1.49791i
$612$		0			0
$613$	−153.517	−	301.295i	−0.250436	−	0.491509i	0.731227	−	0.682135i	$-0.238948\pi$
$613$	−153.517	−	301.295i	−0.250436	−	0.491509i	−0.981663	+	0.190626i	$0.938948\pi$
$614$		0			0
$615$	−31.9030	−	47.1867i	−0.0518748	−	0.0767263i
$616$		0			0
$617$	93.4789	+	590.203i	0.151506	+	0.956568i	0.939913	+	0.341415i	$0.110906\pi$
$617$	93.4789	+	590.203i	0.151506	+	0.956568i	−0.788407	+	0.615154i	$0.789094\pi$
$618$		0			0
$619$	−55.1535	+	75.9123i	−0.0891009	+	0.122637i	−0.851240	−	0.524776i	$-0.824149\pi$
$619$	−55.1535	+	75.9123i	−0.0891009	+	0.122637i	0.762139	+	0.647413i	$0.224149\pi$
$620$		0			0
$621$	59.0318	−	42.8891i	0.0950593	−	0.0690646i
$622$		0			0
$623$	2.57420	+	1.31162i	0.00413195	+	0.00210533i
$624$		0			0
$625$	−271.521	+	562.940i	−0.434434	+	0.900704i
$626$		0			0
$627$	−101.002	+	198.229i	−0.161089	+	0.316154i
$628$		0			0
$629$	93.7704	+	129.064i	0.149078	+	0.205189i
$630$		0			0
$631$	−592.798	−	430.693i	−0.939458	−	0.682556i	0.00883183	−	0.999961i	$-0.497189\pi$
$631$	−592.798	−	430.693i	−0.939458	−	0.682556i	−0.948290	+	0.317405i	$0.897189\pi$
$632$		0			0
$633$	245.630	−	38.9039i	0.388041	−	0.0614596i
$634$		0			0
$635$	−782.164	+	528.822i	−1.23175	+	0.832791i
$636$		0			0
$637$	−672.476	+	342.644i	−1.05569	+	0.537902i
$638$		0			0
$639$	−1095.91	+	356.082i	−1.71504	+	0.557249i
$640$		0			0
$641$	96.4586	−	296.869i	0.150481	−	0.463134i	−0.847194	−	0.531284i	$-0.821710\pi$
$641$	96.4586	−	296.869i	0.150481	−	0.463134i	0.997675	+	0.0681501i	$0.0217097\pi$
$642$		0			0
$643$	409.912	−	409.912i	0.637500	−	0.637500i	−0.312438	−	0.949938i	$-0.601146\pi$
$643$	409.912	−	409.912i	0.637500	−	0.637500i	0.949938	+	0.312438i	$0.101146\pi$
$644$		0			0
$645$	182.095	+	1469.75i	0.282318	+	2.27868i
$646$		0			0
$647$	1249.34	+	197.876i	1.93098	+	0.305837i	0.998469	−	0.0553121i	$-0.0176154\pi$
$647$	1249.34	+	197.876i	1.93098	+	0.305837i	0.932508	+	0.361149i	$0.117615\pi$
$648$		0			0
$649$			33.4977i			0.0516143i
$650$		0			0
$651$	−1.53685			−0.00236076
$652$		0			0
$653$	1.48768	−	9.39285i	0.00227822	−	0.0143841i	−0.986523	−	0.163622i	$-0.947682\pi$
$653$	1.48768	−	9.39285i	0.00227822	−	0.0143841i	0.988801	+	0.149238i	$0.0476821\pi$
$654$		0			0
$655$	284.685	+	608.769i	0.434633	+	0.929418i
$656$		0			0
$657$	−827.349	−	827.349i	−1.25928	−	1.25928i
$658$		0			0
$659$	−824.113	−	267.770i	−1.25055	−	0.406328i	−0.392432	−	0.919781i	$-0.628366\pi$
$659$	−824.113	−	267.770i	−1.25055	−	0.406328i	−0.858118	+	0.513453i	$0.828366\pi$
$660$		0			0
$661$	108.522	+	333.995i	0.164178	+	0.505288i	0.998975	−	0.0452705i	$-0.0144150\pi$
$661$	108.522	+	333.995i	0.164178	+	0.505288i	−0.834797	+	0.550558i	$0.814415\pi$
$662$		0			0
$663$	−74.9206	−	147.040i	−0.113002	−	0.221780i
$664$		0			0
$665$	−7.74424	−	2.80908i	−0.0116455	−	0.00422418i
$666$		0			0
$667$	49.3090	+	311.325i	0.0739265	+	0.466754i
$668$		0			0
$669$	402.717	−	554.292i	0.601968	−	0.828538i
$670$		0			0
$671$	113.331	−	82.3395i	0.168898	−	0.122712i
$672$		0			0
$673$	−1130.82	−	576.182i	−1.68027	−	0.856140i	−0.991341	−	0.131310i	$-0.958082\pi$
$673$	−1130.82	−	576.182i	−1.68027	−	0.856140i	−0.688928	−	0.724830i	$-0.741918\pi$
$674$		0			0
$675$	−270.760	+	24.2855i	−0.401126	+	0.0359786i
$676$		0			0
$677$	−498.902	+	979.151i	−0.736931	+	1.44631i	0.152054	+	0.988372i	$0.451411\pi$
$677$	−498.902	+	979.151i	−0.736931	+	1.44631i	−0.888985	+	0.457936i	$0.848589\pi$
$678$		0			0
$679$	6.13689	+	8.44670i	0.00903813	+	0.0124399i
$680$		0			0
$681$	−1576.71	−	1145.54i	−2.31528	−	1.68215i
$682$		0			0
$683$	−430.626	+	68.2045i	−0.630493	+	0.0998602i	−0.463499	−	0.886098i	$-0.653406\pi$
$683$	−430.626	+	68.2045i	−0.630493	+	0.0998602i	−0.166994	+	0.985958i	$0.553406\pi$
$684$		0			0
$685$	377.013	+	12.7526i	0.550384	+	0.0186170i
$686$		0			0
$687$	2.05800	−	1.04861i	0.00299564	−	0.00152635i
$688$		0			0
$689$	−735.195	+	238.879i	−1.06705	+	0.346705i
$690$		0			0
$691$	−192.465	+	592.345i	−0.278531	+	0.857229i	0.709733	+	0.704471i	$0.248816\pi$
$691$	−192.465	+	592.345i	−0.278531	+	0.857229i	−0.988264	+	0.152758i	$0.951184\pi$
$692$		0			0
$693$	−1.33637	+	1.33637i	−0.00192839	+	0.00192839i
$694$		0			0
$695$	−514.719	−	99.4670i	−0.740603	−	0.143118i
$696$		0			0
$697$	−5.90664	−	0.935520i	−0.00847438	−	0.00134221i
$698$		0			0
$699$		−	1032.35i		−	1.47690i
$700$		0			0
$701$	302.170			0.431055			0.215528	−	0.976498i	$-0.430853\pi$
$701$	302.170			0.431055			0.215528	+	0.976498i	$0.430853\pi$
$702$		0			0
$703$	−232.891	+	1470.42i	−0.331282	+	2.09163i
$704$		0			0
$705$	1030.90	−	963.439i	1.46227	−	1.36658i
$706$		0			0
$707$	7.46043	+	7.46043i	0.0105522	+	0.0105522i
$708$		0			0
$709$	−1123.00	−	364.885i	−1.58392	−	0.514647i	−0.620857	−	0.783923i	$-0.713215\pi$
$709$	−1123.00	−	364.885i	−1.58392	−	0.514647i	−0.963063	+	0.269277i	$0.913215\pi$
$710$		0			0
$711$	−447.456	−	1377.13i	−0.629333	−	1.93689i
$712$		0			0
$713$	−13.9210	−	27.3216i	−0.0195246	−	0.0383192i
$714$		0			0
$715$	−164.714	+	47.4260i	−0.230369	+	0.0663300i
$716$		0			0
$717$	42.9111	+	270.930i	0.0598481	+	0.377866i
$718$		0			0
$719$	−514.227	+	707.773i	−0.715198	+	0.984385i	0.284472	+	0.958684i	$0.408182\pi$
$719$	−514.227	+	707.773i	−0.715198	+	0.984385i	−0.999670	+	0.0257010i	$0.991818\pi$
$720$		0			0
$721$	6.95276	−	5.05148i	0.00964322	−	0.00700621i
$722$		0			0
$723$	961.189	+	489.750i	1.32945	+	0.677386i
$724$		0			0
$725$	437.528	−	1089.78i	0.603487	−	1.50314i
$726$		0			0
$727$	194.758	−	382.234i	0.267893	−	0.525769i	−0.717396	−	0.696665i	$-0.754666\pi$
$727$	194.758	−	382.234i	0.267893	−	0.525769i	0.985289	+	0.170896i	$0.0546663\pi$
$728$		0			0
$729$	618.853	+	851.778i	0.848907	+	1.16842i
$730$		0			0
$731$	125.795	+	91.3953i	0.172086	+	0.125028i
$732$		0			0
$733$	188.540	−	29.8618i	0.257217	−	0.0407392i	−0.0264940	−	0.999649i	$-0.508434\pi$
$733$	188.540	−	29.8618i	0.257217	−	0.0407392i	0.283711	+	0.958910i	$0.408434\pi$
$734$		0			0
$735$	872.792	+	680.363i	1.18747	+	0.925664i
$736$		0			0
$737$	−200.580	+	102.200i	−0.272157	+	0.138671i
$738$		0			0
$739$	642.483	−	208.755i	0.869395	−	0.282484i	0.159848	−	0.987142i	$-0.448900\pi$
$739$	642.483	−	208.755i	0.869395	−	0.282484i	0.709547	+	0.704658i	$0.248900\pi$
$740$		0			0
$741$	475.895	−	1464.65i	0.642233	−	1.97659i
$742$		0			0
$743$	365.561	−	365.561i	0.492006	−	0.492006i	−0.416932	−	0.908938i	$-0.636895\pi$
$743$	365.561	−	365.561i	0.492006	−	0.492006i	0.908938	+	0.416932i	$0.136895\pi$
$744$		0			0
$745$	435.076	−	786.928i	0.583995	−	1.05628i
$746$		0			0
$747$	−718.694	−	113.830i	−0.962107	−	0.152383i
$748$		0			0
$749$		−	0.955821i		−	0.00127613i
$750$		0			0
$751$	−1191.63			−1.58673			−0.793363	−	0.608749i	$-0.791672\pi$
$751$	−1191.63			−1.58673			−0.793363	+	0.608749i	$0.791672\pi$
$752$		0			0
$753$	146.465	−	924.742i	0.194508	−	1.22808i
$754$		0			0
$755$	860.653	+	475.838i	1.13994	+	0.630249i
$756$		0			0
$757$	−932.823	−	932.823i	−1.23226	−	1.23226i	−0.963093	−	0.269170i	$-0.913251\pi$
$757$	−932.823	−	932.823i	−1.23226	−	1.23226i	−0.269170	−	0.963093i	$-0.586749\pi$
$758$		0			0
$759$	−64.1573	−	20.8460i	−0.0845287	−	0.0274651i
$760$		0			0
$761$	−94.1031	−	289.620i	−0.123657	−	0.380578i	0.869997	−	0.493057i	$-0.164121\pi$
$761$	−94.1031	−	289.620i	−0.123657	−	0.380578i	−0.993654	+	0.112480i	$0.964121\pi$
$762$		0			0
$763$	0.379379	+	0.744573i	0.000497220	+	0.000975850i
$764$		0			0
$765$	−83.1560	+	106.675i	−0.108701	+	0.139445i
$766$		0			0
$767$	−36.2736	−	229.022i	−0.0472928	−	0.298595i
$768$		0			0
$769$	547.076	−	752.985i	0.711412	−	0.979175i	−0.288353	−	0.957524i	$-0.593108\pi$
$769$	547.076	−	752.985i	0.711412	−	0.979175i	0.999766	−	0.0216508i	$-0.00689220\pi$
$770$		0			0
$771$	−890.402	+	646.915i	−1.15487	+	0.839060i
$772$		0			0
$773$	1314.34	+	669.690i	1.70031	+	0.866352i	0.986045	+	0.166480i	$0.0532400\pi$
$773$	1314.34	+	669.690i	1.70031	+	0.866352i	0.714267	+	0.699873i	$0.246760\pi$
$774$		0			0
$775$	−7.71966	+	113.980i	−0.00996085	+	0.147070i
$776$		0			0
$777$	−10.2714	+	20.1588i	−0.0132193	+	0.0259444i
$778$		0			0
$779$	−32.8030	−	45.1494i	−0.0421091	−	0.0579582i
$780$		0			0
$781$	181.868	+	132.135i	0.232865	+	0.169187i
$782$		0			0
$783$	504.493	−	79.9038i	0.644307	−	0.102048i
$784$		0			0
$785$	−275.272	−	956.038i	−0.350665	−	1.21788i
$786$		0			0
$787$	497.627	−	253.554i	0.632309	−	0.322178i	−0.108295	−	0.994119i	$-0.534539\pi$
$787$	497.627	−	253.554i	0.632309	−	0.322178i	0.740604	+	0.671941i	$0.234539\pi$
$788$		0			0
$789$	−415.144	+	134.888i	−0.526164	+	0.170961i
$790$		0			0
$791$	−0.506963	+	1.56027i	−0.000640914	+	0.00197253i
$792$		0			0
$793$	−685.675	+	685.675i	−0.864659	+	0.864659i
$794$		0			0
$795$	773.928	+	828.118i	0.973494	+	1.04166i
$796$		0			0
$797$	−1409.78	−	223.288i	−1.76886	−	0.280160i	−0.814795	−	0.579750i	$-0.803150\pi$
$797$	−1409.78	−	223.288i	−1.76886	−	0.280160i	−0.954068	+	0.299589i	$0.903150\pi$
$798$		0			0
$799$		−	148.145i		−	0.185413i
$800$		0			0
$801$	442.666			0.552641
$802$		0			0
$803$	−35.7081	+	225.452i	−0.0444683	+	0.280762i
$804$		0			0
$805$	0.473939	−	2.45253i	0.000588744	−	0.00304662i
$806$		0			0
$807$	1377.37	+	1377.37i	1.70678	+	1.70678i
$808$		0			0
$809$	867.364	+	281.824i	1.07214	+	0.348361i	0.791322	−	0.611399i	$-0.209393\pi$
$809$	867.364	+	281.824i	1.07214	+	0.348361i	0.280821	+	0.959760i	$0.409393\pi$
$810$		0			0
$811$	−263.642	−	811.406i	−0.325082	−	1.00050i	−0.971403	−	0.237435i	$-0.923693\pi$
$811$	−263.642	−	811.406i	−0.325082	−	1.00050i	0.646321	−	0.763066i	$-0.276307\pi$
$812$		0			0
$813$	−63.5888	−	124.800i	−0.0782150	−	0.153506i
$814$		0			0
$815$	12.5873	−	372.126i	0.0154446	−	0.456597i
$816$		0			0
$817$	226.993	+	1433.18i	0.277837	+	1.75419i
$818$		0			0
$819$	7.68961	−	10.5838i	0.00938902	−	0.0129229i
$820$		0			0
$821$	868.835	−	631.245i	1.05826	−	0.768874i	0.0844975	−	0.996424i	$-0.473071\pi$
$821$	868.835	−	631.245i	1.05826	−	0.768874i	0.973766	+	0.227550i	$0.0730715\pi$
$822$		0			0
$823$	−749.888	−	382.087i	−0.911164	−	0.464261i	−0.0654248	−	0.997858i	$-0.520840\pi$
$823$	−749.888	−	382.087i	−0.911164	−	0.464261i	−0.845739	+	0.533596i	$0.820840\pi$
$824$		0			0
$825$	165.299	+	189.316i	0.200362	+	0.229474i
$826$		0			0
$827$	−597.962	+	1173.57i	−0.723049	+	1.41906i	0.177416	+	0.984136i	$0.443226\pi$
$827$	−597.962	+	1173.57i	−0.723049	+	1.41906i	−0.900465	+	0.434928i	$0.856774\pi$
$828$		0			0
$829$	−80.9286	−	111.389i	−0.0976219	−	0.134365i	0.757412	−	0.652938i	$-0.226464\pi$
$829$	−80.9286	−	111.389i	−0.0976219	−	0.134365i	−0.855034	+	0.518573i	$0.826464\pi$
$830$		0			0
$831$	−511.294	−	371.477i	−0.615275	−	0.447024i
$832$		0			0
$833$	114.758	−	18.1758i	0.137764	−	0.0218197i
$834$		0			0
$835$	59.8947	−	165.121i	0.0717302	−	0.197750i
$836$		0			0
$837$	−44.2738	+	22.5586i	−0.0528958	+	0.0269518i
$838$		0			0
$839$	1054.29	−	342.560i	1.25661	−	0.408296i	0.396322	−	0.918112i	$-0.370287\pi$
$839$	1054.29	−	342.560i	1.25661	−	0.408296i	0.860283	+	0.509816i	$0.170287\pi$
$840$		0			0
$841$	−421.956	+	1298.65i	−0.501731	+	1.54417i
$842$		0			0
$843$	−120.393	+	120.393i	−0.142815	+	0.142815i
$844$		0			0
$845$	309.346	−	144.663i	0.366090	−	0.171199i
$846$		0			0
$847$	−8.53331	−	1.35154i	−0.0100747	−	0.00159568i
$848$		0			0
$849$			1924.31i			2.26656i
$850$		0			0
$851$	−451.415			−0.530452
$852$		0			0
$853$	−103.591	+	654.045i	−0.121443	+	0.766759i	0.849525	+	0.527548i	$0.176889\pi$
$853$	−103.591	+	654.045i	−0.121443	+	0.766759i	−0.970968	+	0.239210i	$0.923111\pi$
$854$		0			0
$855$	−1252.64	+	155.196i	−1.46508	+	0.181516i
$856$		0			0
$857$	187.455	+	187.455i	0.218734	+	0.218734i	0.807965	−	0.589231i	$-0.200569\pi$
$857$	187.455	+	187.455i	0.218734	+	0.218734i	−0.589231	+	0.807965i	$0.700569\pi$
$858$		0			0
$859$	784.404	+	254.868i	0.913160	+	0.296704i	0.727658	−	0.685940i	$-0.240609\pi$
$859$	784.404	+	254.868i	0.913160	+	0.296704i	0.185502	+	0.982644i	$0.440609\pi$
$860$		0			0
$861$	−0.262084	−	0.806610i	−0.000304394	−	0.000936830i
$862$		0			0
$863$	660.998	+	1297.28i	0.765930	+	1.50322i	0.861477	+	0.507797i	$0.169540\pi$
$863$	660.998	+	1297.28i	0.765930	+	1.50322i	−0.0955465	+	0.995425i	$0.530460\pi$
$864$		0			0
$865$	−41.6885	−	61.6602i	−0.0481948	−	0.0712835i
$866$		0			0
$867$	−200.256	−	1264.37i	−0.230976	−	1.45833i
$868$		0			0
$869$	−166.042	+	228.537i	−0.191072	+	0.262988i
$870$		0			0
$871$	1260.69	−	915.942i	1.44740	−	1.05160i
$872$		0			0
$873$	1425.36	+	726.257i	1.63271	+	0.831910i
$874$		0			0
$875$	−6.20432	+	6.93624i	−0.00709065	+	0.00792713i
$876$		0			0
$877$	−328.289	+	644.303i	−0.374332	+	0.734667i	−0.998929	−	0.0462800i	$-0.985263\pi$
$877$	−328.289	+	644.303i	−0.374332	+	0.734667i	0.624597	+	0.780947i	$0.285263\pi$
$878$		0			0
$879$	−903.366	−	1243.38i	−1.02772	−	1.41454i
$880$		0			0
$881$	470.154	+	341.587i	0.533659	+	0.387726i	0.821725	−	0.569885i	$-0.193012\pi$
$881$	470.154	+	341.587i	0.533659	+	0.387726i	−0.288065	+	0.957611i	$0.593012\pi$
$882$		0			0
$883$	−90.9085	+	14.3985i	−0.102954	+	0.0163063i	−0.207699	−	0.978193i	$-0.566597\pi$
$883$	−90.9085	+	14.3985i	−0.102954	+	0.0163063i	0.104745	+	0.994499i	$0.466597\pi$
$884$		0			0
$885$	−281.659	+	190.430i	−0.318258	+	0.215175i
$886$		0			0
$887$	−647.447	+	329.891i	−0.729929	+	0.371917i	−0.779122	−	0.626872i	$-0.784335\pi$
$887$	−647.447	+	329.891i	−0.729929	+	0.371917i	0.0491934	+	0.998789i	$0.484335\pi$
$888$		0			0
$889$	−13.3703	+	4.34428i	−0.0150397	+	0.00488671i
$890$		0			0
$891$	36.8199	−	113.320i	0.0413242	−	0.127183i
$892$		0			0
$893$	977.564	−	977.564i	1.09470	−	1.09470i
$894$		0			0
$895$	−131.770	−	1063.56i	−0.147229	−	1.18833i
$896$		0			0
$897$	461.215	+	73.0492i	0.514175	+	0.0814373i
$898$		0			0
$899$		−	214.650i		−	0.238765i
$900$		0			0
$901$	119.004			0.132080
$902$		0			0
$903$	−3.44965	+	21.7802i	−0.00382021	+	0.0241198i
$904$		0			0
$905$	−251.286	−	537.349i	−0.277664	−	0.593756i
$906$		0			0
$907$	1038.51	+	1038.51i	1.14500	+	1.14500i	0.987523	+	0.157473i	$0.0503347\pi$
$907$	1038.51	+	1038.51i	1.14500	+	1.14500i	0.157473	+	0.987523i	$0.449665\pi$
$908$		0			0
$909$	1537.44	+	499.546i	1.69136	+	0.549556i
$910$		0			0
$911$	225.644	+	694.462i	0.247689	+	0.762307i	0.995183	+	0.0980385i	$0.0312568\pi$
$911$	225.644	+	694.462i	0.247689	+	0.762307i	−0.747494	+	0.664268i	$0.768743\pi$
$912$		0			0
$913$	64.4468	+	126.484i	0.0705879	+	0.138537i
$914$		0			0
$915$	1336.61	+	484.829i	1.46077	+	0.529868i
$916$		0			0
$917$	1.56539	+	9.88348i	0.00170708	+	0.0107781i
$918$		0			0
$919$	−205.383	+	282.686i	−0.223486	+	0.307602i	−0.906006	−	0.423265i	$-0.860884\pi$
$919$	−205.383	+	282.686i	−0.223486	+	0.307602i	0.682520	+	0.730867i	$0.260884\pi$
$920$		0			0
$921$	−1066.63	+	774.953i	−1.15812	+	0.841426i
$922$		0			0
$923$	−1386.51	−	706.461i	−1.50218	−	0.765397i
$924$		0			0
$925$	1443.47	+	863.030i	1.56051	+	0.933005i
$926$		0			0
$927$	597.806	−	1173.26i	0.644883	−	1.26565i
$928$		0			0
$929$	940.726	+	1294.80i	1.01262	+	1.39375i	0.917250	+	0.398313i	$0.130404\pi$
$929$	940.726	+	1294.80i	1.01262	+	1.39375i	0.0953723	+	0.995442i	$0.469596\pi$
$930$		0			0
$931$	877.190	+	637.316i	0.942202	+	0.684550i
$932$		0			0
$933$	−796.891	+	126.215i	−0.854117	+	0.135279i
$934$		0			0
$935$	26.3719	+	0.892044i	0.0282053	+	0.000954057i
$936$		0			0
$937$	−225.510	+	114.903i	−0.240673	+	0.122629i	−0.570167	−	0.821529i	$-0.693122\pi$
$937$	−225.510	+	114.903i	−0.240673	+	0.122629i	0.329495	+	0.944157i	$0.393122\pi$
$938$		0			0
$939$	1581.71	−	513.927i	1.68446	−	0.547313i
$940$		0			0
$941$	425.229	−	1308.72i	0.451891	−	1.39078i	−0.422856	−	0.906197i	$-0.638972\pi$
$941$	425.229	−	1308.72i	0.451891	−	1.39078i	0.874747	−	0.484580i	$-0.161028\pi$
$942$		0			0
$943$	11.9656	−	11.9656i	0.0126889	−	0.0126889i
$944$		0			0
$945$	−3.97425	−	0.768004i	−0.00420555	−	0.000812703i
$946$		0			0
$947$	−1665.28	−	263.755i	−1.75848	−	0.278516i	−0.807975	−	0.589217i	$-0.799436\pi$
$947$	−1665.28	−	263.755i	−1.75848	−	0.278516i	−0.950508	+	0.310701i	$0.899436\pi$
$948$		0			0
$949$		−	1580.07i		−	1.66499i
$950$		0			0
$951$	−851.468			−0.895339
$952$		0			0
$953$	102.884	−	649.585i	0.107958	−	0.681621i	−0.873047	−	0.487637i	$-0.837859\pi$
$953$	102.884	−	649.585i	0.107958	−	0.681621i	0.981005	−	0.193984i	$-0.0621410\pi$
$954$		0			0
$955$	602.179	−	562.774i	0.630554	−	0.589292i
$956$		0			0
$957$	−333.911	−	333.911i	−0.348915	−	0.348915i
$958$		0			0
$959$	5.34198	+	1.73571i	0.00557036	+	0.00180992i
$960$		0			0
$961$	−290.513	−	894.106i	−0.302302	−	0.930391i
$962$		0			0
$963$	−66.4871	−	130.488i	−0.0690416	−	0.135502i
$964$		0			0
$965$	−1420.58	+	409.028i	−1.47211	+	0.423864i
$966$		0			0
$967$	−42.0019	−	265.190i	−0.0434353	−	0.274240i	0.956406	−	0.292039i	$-0.0943338\pi$
$967$	−42.0019	−	265.190i	−0.0434353	−	0.274240i	−0.999842	+	0.0177999i	$0.994334\pi$
$968$		0			0
$969$	−139.352	+	191.802i	−0.143810	+	0.197938i
$970$		0			0
$971$	974.410	−	707.950i	1.00351	−	0.729094i	0.0406734	−	0.999172i	$-0.487050\pi$
$971$	974.410	−	707.950i	1.00351	−	0.729094i	0.962838	+	0.270079i	$0.0870497\pi$
$972$		0			0
$973$	−6.95511	−	3.54380i	−0.00714810	−	0.00364214i
$974$		0			0
$975$	−1335.15	−	1115.35i	−1.36938	−	1.14395i
$976$		0			0
$977$	706.688	−	1386.95i	0.723324	−	1.41960i	−0.176923	−	0.984225i	$-0.556614\pi$
$977$	706.688	−	1386.95i	0.723324	−	1.41960i	0.900247	−	0.435379i	$-0.143386\pi$
$978$		0			0
$979$	−50.7604	−	69.8657i	−0.0518492	−	0.0713643i
$980$		0			0
$981$	103.585	+	75.2592i	0.105592	+	0.0767168i
$982$		0			0
$983$	683.311	−	108.226i	0.695128	−	0.110097i	0.201135	−	0.979563i	$-0.435537\pi$
$983$	683.311	−	108.226i	0.695128	−	0.110097i	0.493993	+	0.869466i	$0.335537\pi$
$984$		0			0
$985$	209.081	+	162.984i	0.212265	+	0.165466i
$986$		0			0
$987$	18.7199	−	9.53827i	0.0189665	−	0.00966390i
$988$		0			0
$989$	−418.447	+	135.962i	−0.423101	+	0.137474i
$990$		0			0
$991$	−231.005	+	710.961i	−0.233103	+	0.717418i	0.764264	+	0.644903i	$0.223102\pi$
$991$	−231.005	+	710.961i	−0.233103	+	0.717418i	−0.997367	+	0.0725146i	$0.976898\pi$
$992$		0			0
$993$	−1195.91	+	1195.91i	−1.20434	+	1.20434i
$994$		0			0
$995$	421.812	−	762.935i	0.423931	−	0.766769i
$996$		0			0
$997$	−131.033	−	20.7536i	−0.131427	−	0.0208160i	0.0903743	−	0.995908i	$-0.471194\pi$
$997$	−131.033	−	20.7536i	−0.131427	−	0.0208160i	−0.221801	+	0.975092i	$0.571194\pi$
$998$		0			0
$999$			731.504i			0.732237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.u.a.17.7	✓	56
4.3	odd	2		400.3.bg.e.17.1		56
25.3	odd	20	inner	200.3.u.a.153.7	yes	56
100.3	even	20		400.3.bg.e.353.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.17.7	✓	56	1.1	even	1	trivial
200.3.u.a.153.7	yes	56	25.3	odd	20	inner
400.3.bg.e.17.1		56	4.3	odd	2
400.3.bg.e.353.1		56	100.3	even	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.706680 - 4.46180i) q^{3} +(-4.37575 - 2.41926i) q^{5} +(-0.0526437 - 0.0526437i) q^{7} +(-10.8488 - 3.52499i) q^{9} +(0.687682 + 2.11647i) q^{11} +(-6.99352 - 13.7256i) q^{13} +(-13.8865 + 17.8141i) q^{15} +(0.370977 + 2.34226i) q^{17} +(-13.0079 + 17.9039i) q^{19} +(-0.272088 + 0.197684i) q^{21} +(-5.97894 - 3.04642i) q^{23} +(13.2943 + 21.1722i) q^{25} +(-4.93664 + 9.68871i) q^{27} +(-27.6101 - 38.0021i) q^{29} +(3.69691 + 2.68596i) q^{31} +(9.92924 - 1.57264i) q^{33} +(0.102997 + 0.357714i) q^{35} +(59.9395 - 30.5407i) q^{37} +(-66.1829 + 21.5041i) q^{39} +(-0.779270 + 2.39835i) q^{41} +(46.3634 - 46.3634i) q^{43} +(38.9437 + 41.6705i) q^{45} +(-61.7008 - 9.77245i) q^{47} -48.9945i q^{49} +10.7129 q^{51} +(7.85019 - 49.5641i) q^{53} +(2.11117 - 10.9248i) q^{55} +(70.6911 + 70.6911i) q^{57} +(14.3158 + 4.65148i) q^{59} +(-19.4521 - 59.8674i) q^{61} +(0.385552 + 0.756689i) q^{63} +(-2.60384 + 76.9787i) q^{65} +(15.8246 + 99.9126i) q^{67} +(-17.8178 + 24.5240i) q^{69} +(81.7241 - 59.3761i) q^{71} +(91.3922 + 46.5667i) q^{73} +(103.861 - 44.3548i) q^{75} +(0.0752166 - 0.147621i) q^{77} +(74.6124 + 102.695i) q^{79} +(-43.3164 - 31.4712i) q^{81} +(63.0041 - 9.97887i) q^{83} +(4.04324 - 11.1466i) q^{85} +(-189.069 + 96.3357i) q^{87} +(-36.9068 + 11.9918i) q^{89} +(-0.354399 + 1.09073i) q^{91} +(14.5968 - 14.5968i) q^{93} +(100.234 - 46.8732i) q^{95} +(-138.512 - 21.9382i) q^{97} -25.3852i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 10 q^{5} - 4 q^{7} + 40 q^{9} - 16 q^{11} + 14 q^{13} - 10 q^{15} + 22 q^{17} + 50 q^{19} + 100 q^{21} - 48 q^{23} + 150 q^{25} - 210 q^{27} - 108 q^{31} - 140 q^{33} + 70 q^{35} + 236 q^{37} + 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) \) 56 * q - 10 * q^5 - 4 * q^7 + 40 * q^9 - 16 * q^11 + 14 * q^13 - 10 * q^15 + 22 * q^17 + 50 * q^19 + 100 * q^21 - 48 * q^23 + 150 * q^25 - 210 * q^27 - 108 * q^31 - 140 * q^33 + 70 * q^35 + 236 * q^37 + 80 * q^39 + 104 * q^41 + 96 * q^43 + 20 * q^45 + 104 * q^47 - 200 * q^51 + 88 * q^53 - 140 * q^55 - 280 * q^57 + 200 * q^59 + 108 * q^61 - 654 * q^63 - 510 * q^65 - 282 * q^67 + 40 * q^69 + 470 * q^71 + 62 * q^73 + 350 * q^75 - 396 * q^77 - 560 * q^79 - 586 * q^81 - 468 * q^83 + 50 * q^85 - 280 * q^87 + 230 * q^89 - 62 * q^91 - 300 * q^93 - 360 * q^95 + 386 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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