LMFDB - Embedded newform 200.3.g.f.51.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,3,Mod(51,200)] 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("200.51"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.189974000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 8x^{4} - 8x^{3} + 23x^{2} + 3x + 40 $ x^6 - 3x^5 + 8x^4 - 8x^3 + 23x^2 + 3*x + 40
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Root			$0.198648 + 1.83244i$ of defining polynomial
Character	$\chi$	$=$	200.51
Dual form			200.3.g.f.51.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.801352 - 1.83244i) q^{2} -4.03404 q^{3} +(-2.71567 - 2.93686i) q^{4} +(-3.23269 + 7.39214i) q^{6} +11.1194i q^{7} +(-7.55783 + 2.62284i) q^{8} +7.27349 q^{9} +17.3075 q^{11} +(10.9551 + 11.8474i) q^{12} -6.70171i q^{13} +(20.3756 + 8.91056i) q^{14} +(-1.25029 + 15.9511i) q^{16} -3.45185 q^{17} +(5.82863 - 13.3282i) q^{18} +0.787598 q^{19} -44.8561i q^{21} +(13.8694 - 31.7150i) q^{22} +38.1544i q^{23} +(30.4886 - 10.5806i) q^{24} +(-12.2805 - 5.37044i) q^{26} +6.96480 q^{27} +(32.6561 - 30.1966i) q^{28} +37.7759i q^{29} +42.7225i q^{31} +(28.2275 + 15.0735i) q^{32} -69.8193 q^{33} +(-2.76615 + 6.32531i) q^{34} +(-19.7524 - 21.3612i) q^{36} +0.378525i q^{37} +(0.631143 - 1.44322i) q^{38} +27.0350i q^{39} -8.91793 q^{41} +(-82.1961 - 35.9456i) q^{42} -9.21939 q^{43} +(-47.0015 - 50.8298i) q^{44} +(69.9156 + 30.5751i) q^{46} -31.6031i q^{47} +(5.04372 - 64.3473i) q^{48} -74.6410 q^{49} +13.9249 q^{51} +(-19.6820 + 18.1996i) q^{52} +23.9939i q^{53} +(5.58126 - 12.7626i) q^{54} +(-29.1644 - 84.0384i) q^{56} -3.17720 q^{57} +(69.2220 + 30.2718i) q^{58} -47.9566 q^{59} -59.0166i q^{61} +(78.2863 + 34.2357i) q^{62} +80.8769i q^{63} +(50.2414 - 39.6459i) q^{64} +(-55.9499 + 127.940i) q^{66} -96.3852 q^{67} +(9.37409 + 10.1376i) q^{68} -153.916i q^{69} +41.1955i q^{71} +(-54.9718 + 19.0772i) q^{72} +112.816 q^{73} +(0.693623 + 0.303332i) q^{74} +(-2.13885 - 2.31306i) q^{76} +192.449i q^{77} +(49.5400 + 21.6646i) q^{78} +69.7575i q^{79} -93.5577 q^{81} +(-7.14641 + 16.3416i) q^{82} +58.6785 q^{83} +(-131.736 + 121.814i) q^{84} +(-7.38798 + 16.8940i) q^{86} -152.389i q^{87} +(-130.807 + 45.3949i) q^{88} +44.9025 q^{89} +74.5190 q^{91} +(112.054 - 103.615i) q^{92} -172.344i q^{93} +(-57.9107 - 25.3252i) q^{94} +(-113.871 - 60.8072i) q^{96} +126.268 q^{97} +(-59.8137 + 136.775i) q^{98} +125.886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + q^{6} - 3 q^{8} - 8 q^{9} + 30 q^{11} + 27 q^{12} + 4 q^{14} - 39 q^{16} + 2 q^{17} + 20 q^{18} - 2 q^{19} + 37 q^{22} + 59 q^{24} - 36 q^{26} - 62 q^{27} + 40 q^{28}+ \cdots + 304 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + q^6 - 3 * q^8 - 8 * q^9 + 30 * q^11 + 27 * q^12 + 4 * q^14 - 39 * q^16 + 2 * q^17 + 20 * q^18 - 2 * q^19 + 37 * q^22 + 59 * q^24 - 36 * q^26 - 62 * q^27 + 40 * q^28 - 47 * q^32 - 138 * q^33 + 89 * q^34 - 8 * q^36 + 113 * q^38 - 70 * q^41 - 220 * q^42 - 76 * q^43 - 77 * q^44 + 184 * q^46 - 57 * q^48 - 138 * q^49 + 114 * q^51 + 200 * q^52 - 69 * q^54 - 176 * q^56 + 78 * q^57 - 20 * q^58 - 44 * q^59 + 320 * q^62 + 113 * q^64 - 101 * q^66 - 18 * q^67 + 143 * q^68 - 240 * q^72 + 18 * q^73 + 204 * q^74 + 155 * q^76 + 180 * q^78 - 142 * q^81 - 323 * q^82 + 398 * q^83 - 400 * q^84 + 218 * q^86 - 317 * q^88 + 98 * q^89 + 288 * q^91 + 600 * q^92 - 316 * q^94 - 409 * q^96 + 76 * q^97 - 213 * q^98 + 304 * q^99

Character values

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

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.801352	−	1.83244i	0.400676	−	0.916220i
$2$	0.801352	−	1.83244i	0.400676	−	0.916220i
$3$	−4.03404			−1.34468			−0.672340	−	0.740242i	$-0.734711\pi$
$3$	−4.03404			−1.34468			−0.672340	+	0.740242i	$0.734711\pi$
$4$	−2.71567	−	2.93686i	−0.678917	−	0.734215i
$5$		0			0
$5$		0			0
$6$	−3.23269	+	7.39214i	−0.538782	+	1.23202i
$7$			11.1194i			1.58849i	0.607601	+	0.794243i	$0.292132\pi$
$7$			11.1194i			1.58849i	−0.607601	+	0.794243i	$0.707868\pi$
$8$	−7.55783	+	2.62284i	−0.944728	+	0.327855i
$9$	7.27349			0.808166
$10$		0			0
$11$	17.3075			1.57341			0.786706	−	0.617328i	$-0.211785\pi$
$11$	17.3075			1.57341			0.786706	+	0.617328i	$0.211785\pi$
$12$	10.9551	+	11.8474i	0.912927	+	0.987285i
$13$		−	6.70171i		−	0.515517i	−0.966209	−	0.257758i	$-0.917016\pi$
$13$		−	6.70171i		−	0.515517i	0.966209	−	0.257758i	$-0.0829838\pi$
$14$	20.3756	+	8.91056i	1.45540	+	0.636468i
$15$		0			0
$16$	−1.25029	+	15.9511i	−0.0781431	+	0.996942i
$17$	−3.45185			−0.203050			−0.101525	−	0.994833i	$-0.532372\pi$
$17$	−3.45185			−0.203050			−0.101525	+	0.994833i	$0.532372\pi$
$18$	5.82863	−	13.3282i	0.323813	−	0.740458i
$19$	0.787598			0.0414525			0.0207263	−	0.999785i	$-0.493402\pi$
$19$	0.787598			0.0414525			0.0207263	+	0.999785i	$0.493402\pi$
$20$		0			0
$21$		−	44.8561i		−	2.13601i
$22$	13.8694	−	31.7150i	0.630429	−	1.44159i
$23$			38.1544i			1.65889i	0.558591	+	0.829443i	$0.311342\pi$
$23$			38.1544i			1.65889i	−0.558591	+	0.829443i	$0.688658\pi$
$24$	30.4886	−	10.5806i	1.27036	−	0.440860i
$25$		0			0
$26$	−12.2805	−	5.37044i	−0.472326	−	0.206555i
$27$	6.96480			0.257956
$28$	32.6561	−	30.1966i	1.16629	−	1.07845i
$29$			37.7759i			1.30262i	0.758813	+	0.651308i	$0.225779\pi$
$29$			37.7759i			1.30262i	−0.758813	+	0.651308i	$0.774221\pi$
$30$		0			0
$31$			42.7225i			1.37814i	0.724693	+	0.689072i	$0.241982\pi$
$31$			42.7225i			1.37814i	−0.724693	+	0.689072i	$0.758018\pi$
$32$	28.2275	+	15.0735i	0.882108	+	0.471047i
$33$	−69.8193			−2.11574
$34$	−2.76615	+	6.32531i	−0.0813574	+	0.186039i
$35$		0			0
$36$	−19.7524	−	21.3612i	−0.548678	−	0.593367i
$37$			0.378525i			0.0102304i	0.999987	+	0.00511520i	$0.00162823\pi$
$37$			0.378525i			0.0102304i	−0.999987	+	0.00511520i	$0.998372\pi$
$38$	0.631143	−	1.44322i	0.0166090	−	0.0379796i
$39$			27.0350i			0.693205i
$40$		0			0
$41$	−8.91793			−0.217511			−0.108755	−	0.994069i	$-0.534686\pi$
$41$	−8.91793			−0.217511			−0.108755	+	0.994069i	$0.534686\pi$
$42$	−82.1961	−	35.9456i	−1.95705	−	0.855846i
$43$	−9.21939			−0.214405			−0.107202	−	0.994237i	$-0.534189\pi$
$43$	−9.21939			−0.214405			−0.107202	+	0.994237i	$0.534189\pi$
$44$	−47.0015	−	50.8298i	−1.06822	−	1.15522i
$45$		0			0
$46$	69.9156	+	30.5751i	1.51990	+	0.664676i
$47$		−	31.6031i		−	0.672406i	−0.941790	−	0.336203i	$-0.890857\pi$
$47$		−	31.6031i		−	0.672406i	0.941790	−	0.336203i	$-0.109143\pi$
$48$	5.04372	−	64.3473i	0.105078	−	1.34057i
$49$	−74.6410			−1.52328
$50$		0			0
$51$	13.9249			0.273038
$52$	−19.6820	+	18.1996i	−0.378500	+	0.349993i
$53$			23.9939i			0.452715i	0.974044	+	0.226358i	$0.0726818\pi$
$53$			23.9939i			0.452715i	−0.974044	+	0.226358i	$0.927318\pi$
$54$	5.58126	−	12.7626i	0.103357	−	0.236344i
$55$		0			0
$56$	−29.1644	−	84.0384i	−0.520792	−	1.50069i
$57$	−3.17720			−0.0557404
$58$	69.2220	+	30.2718i	1.19348	+	0.521927i
$59$	−47.9566			−0.812825			−0.406412	−	0.913690i	$-0.633220\pi$
$59$	−47.9566			−0.812825			−0.406412	+	0.913690i	$0.633220\pi$
$60$		0			0
$61$		−	59.0166i		−	0.967485i	−0.875210	−	0.483743i	$-0.839277\pi$
$61$		−	59.0166i		−	0.967485i	0.875210	−	0.483743i	$-0.160723\pi$
$62$	78.2863	+	34.2357i	1.26268	+	0.552189i
$63$			80.8769i			1.28376i
$64$	50.2414	−	39.6459i	0.785022	−	0.619467i
$65$		0			0
$66$	−55.9499	+	127.940i	−0.847726	+	1.93848i
$67$	−96.3852			−1.43859			−0.719293	−	0.694707i	$-0.755534\pi$
$67$	−96.3852			−1.43859			−0.719293	+	0.694707i	$0.755534\pi$
$68$	9.37409	+	10.1376i	0.137854	+	0.149083i
$69$		−	153.916i		−	2.23067i
$70$		0			0
$71$			41.1955i			0.580218i	0.956994	+	0.290109i	$0.0936916\pi$
$71$			41.1955i			0.580218i	−0.956994	+	0.290109i	$0.906308\pi$
$72$	−54.9718	+	19.0772i	−0.763497	+	0.264961i
$73$	112.816			1.54542			0.772711	−	0.634758i	$-0.218900\pi$
$73$	112.816			1.54542			0.772711	+	0.634758i	$0.218900\pi$
$74$	0.693623	+	0.303332i	0.00937329	+	0.00409908i
$75$		0			0
$76$	−2.13885	−	2.31306i	−0.0281428	−	0.0304350i
$77$			192.449i			2.49934i
$78$	49.5400	+	21.6646i	0.635128	+	0.277751i
$79$			69.7575i			0.883006i	0.897260	+	0.441503i	$0.145555\pi$
$79$			69.7575i			0.883006i	−0.897260	+	0.441503i	$0.854445\pi$
$80$		0			0
$81$	−93.5577			−1.15503
$82$	−7.14641	+	16.3416i	−0.0871513	+	0.199287i
$83$	58.6785			0.706970			0.353485	−	0.935440i	$-0.384997\pi$
$83$	58.6785			0.706970			0.353485	+	0.935440i	$0.384997\pi$
$84$	−131.736	+	121.814i	−1.56829	+	1.45017i
$85$		0			0
$86$	−7.38798	+	16.8940i	−0.0859068	+	0.196442i
$87$		−	152.389i		−	1.75160i
$88$	−130.807	+	45.3949i	−1.48645	+	0.515851i
$89$	44.9025			0.504523			0.252262	−	0.967659i	$-0.418826\pi$
$89$	44.9025			0.504523			0.252262	+	0.967659i	$0.418826\pi$
$90$		0			0
$91$	74.5190			0.818890
$92$	112.054	−	103.615i	1.21798	−	1.12625i
$93$		−	172.344i		−	1.85316i
$94$	−57.9107	−	25.3252i	−0.616071	−	0.269417i
$95$		0			0
$96$	−113.871	−	60.8072i	−1.18615	−	0.633408i
$97$	126.268			1.30173			0.650864	−	0.759194i	$-0.274407\pi$
$97$	126.268			1.30173			0.650864	+	0.759194i	$0.274407\pi$
$98$	−59.8137	+	136.775i	−0.610344	+	1.39566i
$99$	125.886			1.27158
$100$		0			0
$101$		−	40.5888i		−	0.401869i	−0.979605	−	0.200935i	$-0.935602\pi$
$101$		−	40.5888i		−	0.401869i	0.979605	−	0.200935i	$-0.0643979\pi$
$102$	11.1588	−	25.5166i	0.109400	−	0.250163i
$103$		−	111.422i		−	1.08177i	−0.841097	−	0.540884i	$-0.818090\pi$
$103$		−	111.422i		−	1.08177i	0.841097	−	0.540884i	$-0.181910\pi$
$104$	17.5775	+	50.6504i	0.169015	+	0.487023i
$105$		0			0
$106$	43.9674	+	19.2276i	0.414787	+	0.181392i
$107$	−28.2816			−0.264314			−0.132157	−	0.991229i	$-0.542190\pi$
$107$	−28.2816			−0.264314			−0.132157	+	0.991229i	$0.542190\pi$
$108$	−18.9141	−	20.4546i	−0.175130	−	0.189395i
$109$			12.2679i			0.112549i	0.998415	+	0.0562746i	$0.0179222\pi$
$109$			12.2679i			0.112549i	−0.998415	+	0.0562746i	$0.982078\pi$
$110$		0			0
$111$		−	1.52698i		−	0.0137566i
$112$	−177.366	−	13.9025i	−1.58363	−	0.124129i
$113$	−73.6529			−0.651795			−0.325898	−	0.945405i	$-0.605666\pi$
$113$	−73.6529			−0.651795			−0.325898	+	0.945405i	$0.605666\pi$
$114$	−2.54606	+	5.82203i	−0.0223338	+	0.0510704i
$115$		0			0
$116$	110.942	−	102.587i	0.956400	−	0.884368i
$117$		−	48.7449i		−	0.416623i
$118$	−38.4302	+	87.8777i	−0.325679	+	0.744726i
$119$		−	38.3825i		−	0.322542i
$120$		0			0
$121$	178.551			1.47563
$122$	−108.144	−	47.2931i	−0.886429	−	0.387648i
$123$	35.9753			0.292482
$124$	125.470	−	116.020i	1.01185	−	0.935645i
$125$		0			0
$126$	148.202	+	64.8109i	1.17621	+	0.514372i
$127$		−	55.8251i		−	0.439568i	−0.975549	−	0.219784i	$-0.929465\pi$
$127$		−	55.8251i		−	0.439568i	0.975549	−	0.219784i	$-0.0705352\pi$
$128$	−32.3876	−	123.835i	−0.253028	−	0.967459i
$129$	37.1914			0.288306
$130$		0			0
$131$	−160.997			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$131$	−160.997			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$132$	189.606	+	205.050i	1.43641	+	1.55341i
$133$			8.75761i			0.0658467i
$134$	−77.2385	+	176.620i	−0.576407	+	1.31806i
$135$		0			0
$136$	26.0885	−	9.05365i	0.191827	−	0.0665710i
$137$	−93.0774			−0.679397			−0.339699	−	0.940534i	$-0.610325\pi$
$137$	−93.0774			−0.679397			−0.339699	+	0.940534i	$0.610325\pi$
$138$	−282.043	−	123.341i	−2.04379	−	0.893778i
$139$	98.2327			0.706710			0.353355	−	0.935489i	$-0.385041\pi$
$139$	98.2327			0.706710			0.353355	+	0.935489i	$0.385041\pi$
$140$		0			0
$141$			127.488i			0.904171i
$142$	75.4882	+	33.0121i	0.531607	+	0.232480i
$143$		−	115.990i		−	0.811120i
$144$	−9.09397	+	116.020i	−0.0631526	+	0.805695i
$145$		0			0
$146$	90.4053	−	206.728i	0.619214	−	1.41595i
$147$	301.105			2.04833
$148$	1.11167	−	1.02795i	0.00751131	−	0.00694559i
$149$			29.2413i			0.196250i	0.995174	+	0.0981251i	$0.0312845\pi$
$149$			29.2413i			0.196250i	−0.995174	+	0.0981251i	$0.968715\pi$
$150$		0			0
$151$			238.075i			1.57666i	0.615254	+	0.788329i	$0.289054\pi$
$151$			238.075i			1.57666i	−0.615254	+	0.788329i	$0.710946\pi$
$152$	−5.95252	+	2.06574i	−0.0391613	+	0.0135904i
$153$	−25.1070			−0.164098
$154$	352.652	+	154.220i	2.28995	+	1.00143i
$155$		0			0
$156$	79.3980	−	73.4181i	0.508961	−	0.470629i
$157$		−	230.982i		−	1.47122i	−0.677403	−	0.735612i	$-0.736895\pi$
$157$		−	230.982i		−	1.47122i	0.677403	−	0.735612i	$-0.263105\pi$
$158$	127.826	+	55.9003i	0.809027	+	0.353799i
$159$		−	96.7925i		−	0.608758i
$160$		0			0
$161$	−424.254			−2.63512
$162$	−74.9727	+	171.439i	−0.462795	+	1.05826i
$163$	139.882			0.858175			0.429087	−	0.903263i	$-0.358835\pi$
$163$	139.882			0.858175			0.429087	+	0.903263i	$0.358835\pi$
$164$	24.2181	+	26.1907i	0.147672	+	0.159699i
$165$		0			0
$166$	47.0221	−	107.525i	0.283266	−	0.647740i
$167$			259.015i			1.55099i	0.631354	+	0.775495i	$0.282500\pi$
$167$			259.015i			1.55099i	−0.631354	+	0.775495i	$0.717500\pi$
$168$	117.650	+	339.015i	0.700299	+	2.01794i
$169$	124.087			0.734243
$170$		0			0
$171$	5.72859			0.0335005
$172$	25.0368	+	27.0761i	0.145563	+	0.157419i
$173$			45.2346i			0.261472i	0.991417	+	0.130736i	$0.0417340\pi$
$173$			45.2346i			0.261472i	−0.991417	+	0.130736i	$0.958266\pi$
$174$	−279.244	−	122.118i	−1.60485	−	0.701826i
$175$		0			0
$176$	−21.6394	+	276.074i	−0.122951	+	1.56860i
$177$	193.459			1.09299
$178$	35.9828	−	82.2812i	0.202150	−	0.462254i
$179$	−39.3701			−0.219944			−0.109972	−	0.993935i	$-0.535076\pi$
$179$	−39.3701			−0.219944			−0.109972	+	0.993935i	$0.535076\pi$
$180$		0			0
$181$			2.81294i			0.0155411i	0.999970	+	0.00777056i	$0.00247347\pi$
$181$			2.81294i			0.0155411i	−0.999970	+	0.00777056i	$0.997527\pi$
$182$	59.7160	−	136.552i	0.328110	−	0.750283i
$183$			238.075i			1.30096i
$184$	−100.073	−	288.364i	−0.543874	−	1.56720i
$185$		0			0
$186$	−315.810	−	138.108i	−1.69790	−	0.742519i
$187$	−59.7431			−0.319482
$188$	−92.8138	+	85.8234i	−0.493690	+	0.456508i
$189$			77.4444i			0.409759i
$190$		0			0
$191$			22.9361i			0.120084i	0.998196	+	0.0600421i	$0.0191235\pi$
$191$			22.9361i			0.120084i	−0.998196	+	0.0600421i	$0.980876\pi$
$192$	−202.676	+	159.933i	−1.05560	+	0.832986i
$193$	152.406			0.789666			0.394833	−	0.918753i	$-0.370802\pi$
$193$	152.406			0.789666			0.394833	+	0.918753i	$0.370802\pi$
$194$	101.185	−	231.378i	0.521572	−	1.19267i
$195$		0			0
$196$	202.700	+	219.210i	1.03418	+	1.11842i
$197$		−	43.0232i		−	0.218392i	−0.994020	−	0.109196i	$-0.965172\pi$
$197$		−	43.0232i		−	0.218392i	0.994020	−	0.109196i	$-0.0348276\pi$
$198$	100.879	−	230.679i	0.509491	−	1.16505i
$199$		−	57.1240i		−	0.287055i	−0.989646	−	0.143528i	$-0.954155\pi$
$199$		−	57.1240i		−	0.287055i	0.989646	−	0.143528i	$-0.0458446\pi$
$200$		0			0
$201$	388.822			1.93444
$202$	−74.3765	−	32.5259i	−0.368201	−	0.161020i
$203$	−420.045			−2.06919
$204$	−37.8155	−	40.8955i	−0.185370	−	0.200468i
$205$		0			0
$206$	−204.174	−	89.2884i	−0.991137	−	0.433439i
$207$			277.516i			1.34066i
$208$	106.900	+	8.37908i	0.513940	+	0.0402841i
$209$	13.6314			0.0652219
$210$		0			0
$211$	149.294			0.707553			0.353776	−	0.935330i	$-0.384897\pi$
$211$	149.294			0.707553			0.353776	+	0.935330i	$0.384897\pi$
$212$	70.4668	−	65.1595i	0.332390	−	0.307356i
$213$		−	166.184i		−	0.780208i
$214$	−22.6636	+	51.8244i	−0.105905	+	0.242170i
$215$		0			0
$216$	−52.6387	+	18.2675i	−0.243698	+	0.0845720i
$217$	−475.048			−2.18916
$218$	22.4801	+	9.83088i	0.103120	+	0.0450958i
$219$	−455.104			−2.07810
$220$		0			0
$221$			23.1333i			0.104676i
$222$	−2.79811	−	1.22365i	−0.0126041	−	0.00551195i
$223$		−	172.404i		−	0.773112i	−0.922266	−	0.386556i	$-0.873665\pi$
$223$		−	172.404i		−	0.773112i	0.922266	−	0.386556i	$-0.126335\pi$
$224$	−167.608	+	313.872i	−0.748252	+	1.40122i
$225$		0			0
$226$	−59.0219	+	134.964i	−0.261159	+	0.597188i
$227$	−159.295			−0.701738			−0.350869	−	0.936425i	$-0.614114\pi$
$227$	−159.295			−0.701738			−0.350869	+	0.936425i	$0.614114\pi$
$228$	8.62823	+	9.33100i	0.0378431	+	0.0409254i
$229$			249.350i			1.08887i	0.838804	+	0.544433i	$0.183255\pi$
$229$			249.350i			1.08887i	−0.838804	+	0.544433i	$0.816745\pi$
$230$		0			0
$231$		−	776.349i		−	3.36082i
$232$	−99.0800	−	285.503i	−0.427069	−	1.23062i
$233$	149.303			0.640787			0.320394	−	0.947285i	$-0.396185\pi$
$233$	149.303			0.640787			0.320394	+	0.947285i	$0.396185\pi$
$234$	−89.3220	−	39.0618i	−0.381718	−	0.166931i
$235$		0			0
$236$	130.234	+	140.842i	0.551840	+	0.596788i
$237$		−	281.405i		−	1.18736i
$238$	−70.3337	−	30.7579i	−0.295520	−	0.129235i
$239$		−	309.119i		−	1.29338i	−0.762751	−	0.646692i	$-0.776152\pi$
$239$		−	309.119i		−	1.29338i	0.762751	−	0.646692i	$-0.223848\pi$
$240$		0			0
$241$	3.56700			0.0148008			0.00740042	−	0.999973i	$-0.497644\pi$
$241$	3.56700			0.0148008			0.00740042	+	0.999973i	$0.497644\pi$
$242$	143.082	−	327.183i	0.591248	−	1.35200i
$243$	314.733			1.29520
$244$	−173.323	+	160.269i	−0.710342	+	0.656842i
$245$		0			0
$246$	28.8289	−	65.9226i	0.117191	−	0.267978i
$247$		−	5.27825i		−	0.0213695i
$248$	−112.054	−	322.889i	−0.451831	−	1.30197i
$249$	−236.711			−0.950648
$250$		0			0
$251$	−67.0372			−0.267080			−0.133540	−	0.991043i	$-0.542635\pi$
$251$	−67.0372			−0.267080			−0.133540	+	0.991043i	$0.542635\pi$
$252$	237.524	−	219.635i	0.942555	−	0.871566i
$253$			660.359i			2.61011i
$254$	−102.296	−	44.7356i	−0.402741	−	0.176124i
$255$		0			0
$256$	−252.874	−	39.8869i	−0.987787	−	0.155808i
$257$	−115.730			−0.450311			−0.225156	−	0.974323i	$-0.572289\pi$
$257$	−115.730			−0.450311			−0.225156	+	0.974323i	$0.572289\pi$
$258$	29.8034	−	68.1510i	0.115517	−	0.264151i
$259$	−4.20897			−0.0162508
$260$		0			0
$261$			274.763i			1.05273i
$262$	−129.015	+	295.016i	−0.492424	+	1.12602i
$263$		−	207.074i		−	0.787353i	−0.919249	−	0.393677i	$-0.871203\pi$
$263$		−	207.074i		−	0.787353i	0.919249	−	0.393677i	$-0.128797\pi$
$264$	527.682	−	183.125i	1.99880	−	0.693654i
$265$		0			0
$266$	16.0478	+	7.01793i	0.0603300	+	0.0263832i
$267$	−181.139			−0.678422
$268$	261.750	+	283.070i	0.976680	+	1.05623i
$269$		−	179.906i		−	0.668797i	−0.942432	−	0.334399i	$-0.891467\pi$
$269$		−	179.906i		−	0.668797i	0.942432	−	0.334399i	$-0.108533\pi$
$270$		0			0
$271$		−	410.106i		−	1.51331i	−0.653817	−	0.756653i	$-0.726833\pi$
$271$		−	410.106i		−	1.51331i	0.653817	−	0.756653i	$-0.273167\pi$
$272$	4.31582	−	55.0608i	0.0158670	−	0.202429i
$273$	−300.613			−1.10115
$274$	−74.5878	+	170.559i	−0.272218	+	0.622477i
$275$		0			0
$276$	−452.031	+	417.986i	−1.63779	+	1.51444i
$277$			168.937i			0.609883i	0.952371	+	0.304941i	$0.0986368\pi$
$277$			168.937i			0.609883i	−0.952371	+	0.304941i	$0.901363\pi$
$278$	78.7190	−	180.006i	0.283162	−	0.647502i
$279$			310.742i			1.11377i
$280$		0			0
$281$	419.569			1.49313			0.746564	−	0.665314i	$-0.231702\pi$
$281$	419.569			1.49313			0.746564	+	0.665314i	$0.231702\pi$
$282$	233.614	+	102.163i	0.828419	+	0.362280i
$283$	−326.668			−1.15430			−0.577151	−	0.816637i	$-0.695836\pi$
$283$	−326.668			−1.15430			−0.577151	+	0.816637i	$0.695836\pi$
$284$	120.985	−	111.873i	0.426005	−	0.393920i
$285$		0			0
$286$	−212.545	−	92.9490i	−0.743164	−	0.324997i
$287$		−	99.1620i		−	0.345512i
$288$	205.312	+	109.637i	0.712890	+	0.380684i
$289$	−277.085			−0.958771
$290$		0			0
$291$	−509.369			−1.75041
$292$	−306.370	−	331.324i	−1.04921	−	1.13467i
$293$			363.495i			1.24060i	0.784366	+	0.620298i	$0.212988\pi$
$293$			363.495i			1.24060i	−0.784366	+	0.620298i	$0.787012\pi$
$294$	241.291	−	551.756i	0.820718	−	1.87672i
$295$		0			0
$296$	−0.992809	−	2.86082i	−0.00335408	−	0.00966494i
$297$	120.544			0.405870
$298$	53.5829	+	23.4326i	0.179808	+	0.0786328i
$299$	255.700			0.855183
$300$		0			0
$301$		−	102.514i		−	0.340578i
$302$	436.259	+	190.782i	1.44457	+	0.631729i
$303$			163.737i			0.540386i
$304$	−0.984725	+	12.5630i	−0.00323923	+	0.0413258i
$305$		0			0
$306$	−20.1196	+	46.0071i	−0.0657503	+	0.150350i
$307$	566.800			1.84626			0.923128	−	0.384494i	$-0.125624\pi$
$307$	566.800			1.84626			0.923128	+	0.384494i	$0.125624\pi$
$308$	565.197	−	522.629i	1.83505	−	1.69685i
$309$			449.481i			1.45463i
$310$		0			0
$311$			258.199i			0.830220i	0.909771	+	0.415110i	$0.136257\pi$
$311$			258.199i			0.830220i	−0.909771	+	0.415110i	$0.863743\pi$
$312$	−70.9084	−	204.326i	−0.227271	−	0.654890i
$313$	−24.2700			−0.0775400			−0.0387700	−	0.999248i	$-0.512344\pi$
$313$	−24.2700			−0.0775400			−0.0387700	+	0.999248i	$0.512344\pi$
$314$	−423.261	−	185.098i	−1.34796	−	0.589485i
$315$		0			0
$316$	204.868	−	189.438i	0.648316	−	0.599488i
$317$			398.458i			1.25696i	0.777824	+	0.628482i	$0.216323\pi$
$317$			398.458i			1.25696i	−0.777824	+	0.628482i	$0.783677\pi$
$318$	−177.366	−	77.5649i	−0.557756	−	0.243915i
$319$			653.807i			2.04955i
$320$		0			0
$321$	114.089			0.355419
$322$	−339.977	+	777.419i	−1.05583	+	2.41435i
$323$	−2.71867			−0.00841694
$324$	254.072	+	274.766i	0.784172	+	0.848043i
$325$		0			0
$326$	112.095	−	256.326i	0.343850	−	0.786277i
$327$		−	49.4890i		−	0.151343i
$328$	67.4002	−	23.3903i	0.205488	−	0.0713119i
$329$	351.407			1.06811
$330$		0			0
$331$	412.040			1.24483			0.622417	−	0.782686i	$-0.286151\pi$
$331$	412.040			1.24483			0.622417	+	0.782686i	$0.286151\pi$
$332$	−159.351	−	172.330i	−0.479974	−	0.519068i
$333$			2.75320i			0.00826786i
$334$	474.630	+	207.563i	1.42105	+	0.621445i
$335$		0			0
$336$	715.503	+	56.0831i	2.12947	+	0.166914i
$337$	312.690			0.927863			0.463932	−	0.885871i	$-0.346438\pi$
$337$	312.690			0.927863			0.463932	+	0.885871i	$0.346438\pi$
$338$	99.4374	−	227.382i	0.294194	−	0.672728i
$339$	297.119			0.876456
$340$		0			0
$341$			739.420i			2.16839i
$342$	4.59062	−	10.4973i	0.0134229	−	0.0306938i
$343$		−	285.112i		−	0.831230i
$344$	69.6786	−	24.1810i	0.202554	−	0.0702935i
$345$		0			0
$346$	82.8897	+	36.2489i	0.239566	+	0.104766i
$347$	−429.418			−1.23751			−0.618757	−	0.785582i	$-0.712364\pi$
$347$	−429.418			−1.23751			−0.618757	+	0.785582i	$0.712364\pi$
$348$	−447.546	+	413.839i	−1.28605	+	1.18919i
$349$		−	650.147i		−	1.86288i	−0.363890	−	0.931442i	$-0.618551\pi$
$349$		−	650.147i		−	1.86288i	0.363890	−	0.931442i	$-0.381449\pi$
$350$		0			0
$351$		−	46.6761i		−	0.132980i
$352$	488.548	+	260.885i	1.38792	+	0.741152i
$353$	−383.224			−1.08562			−0.542810	−	0.839856i	$-0.682640\pi$
$353$	−383.224			−1.08562			−0.542810	+	0.839856i	$0.682640\pi$
$354$	155.029	−	354.502i	0.437935	−	1.00142i
$355$		0			0
$356$	−121.940	−	131.872i	−0.342529	−	0.370428i
$357$			154.837i			0.433716i
$358$	−31.5493	+	72.1433i	−0.0881265	+	0.201517i
$359$		−	656.475i		−	1.82862i	−0.405014	−	0.914310i	$-0.632733\pi$
$359$		−	656.475i		−	1.82862i	0.405014	−	0.914310i	$-0.367267\pi$
$360$		0			0
$361$	−360.380			−0.998282
$362$	5.15455	+	2.25416i	0.0142391	+	0.00622696i
$363$	−720.281			−1.98425
$364$	−202.369	−	218.852i	−0.555959	−	0.601241i
$365$		0			0
$366$	436.259	+	190.782i	1.19196	+	0.521263i
$367$			1.05782i			0.00288235i	0.999999	+	0.00144117i	$0.000458740\pi$
$367$			1.05782i			0.00288235i	−0.999999	+	0.00144117i	$0.999541\pi$
$368$	−608.604	−	47.7040i	−1.65381	−	0.129631i
$369$	−64.8645			−0.175785
$370$		0			0
$371$	−266.798			−0.719132
$372$	−506.151	+	468.030i	−1.36062	+	1.25814i
$373$			0.816797i			0.00218980i	0.999999	+	0.00109490i	$0.000348518\pi$
$373$			0.816797i			0.00218980i	−0.999999	+	0.00109490i	$0.999651\pi$
$374$	−47.8753	+	109.476i	−0.128009	+	0.292715i
$375$		0			0
$376$	82.8897	+	238.850i	0.220451	+	0.635241i
$377$	253.163			0.671520
$378$	141.912	+	62.0602i	0.375429	+	0.164180i
$379$	−630.860			−1.66454			−0.832269	−	0.554372i	$-0.812959\pi$
$379$	−630.860			−1.66454			−0.832269	+	0.554372i	$0.812959\pi$
$380$		0			0
$381$			225.201i			0.591078i
$382$	42.0290	+	18.3799i	0.110024	+	0.0481149i
$383$			392.809i			1.02561i	0.858505	+	0.512805i	$0.171394\pi$
$383$			392.809i			1.02561i	−0.858505	+	0.512805i	$0.828606\pi$
$384$	130.653	+	499.555i	0.340242	+	1.30092i
$385$		0			0
$386$	122.131	−	279.274i	0.316400	−	0.723507i
$387$	−67.0572			−0.173274
$388$	−342.901	−	370.831i	−0.883766	−	0.955749i
$389$			292.218i			0.751203i	0.926781	+	0.375602i	$0.122564\pi$
$389$			292.218i			0.751203i	−0.926781	+	0.375602i	$0.877436\pi$
$390$		0			0
$391$		−	131.703i		−	0.336837i
$392$	564.123	−	195.771i	1.43909	−	0.499416i
$393$	649.467			1.65259
$394$	−78.8375	−	34.4768i	−0.200095	−	0.0875045i
$395$		0			0
$396$	−341.865	−	369.710i	−0.863296	−	0.933612i
$397$		−	676.730i		−	1.70461i	−0.523045	−	0.852305i	$-0.675204\pi$
$397$		−	676.730i		−	1.70461i	0.523045	−	0.852305i	$-0.324796\pi$
$398$	−104.676	−	45.7764i	−0.263006	−	0.115016i
$399$		−	35.3286i		−	0.0885428i
$400$		0			0
$401$	195.666			0.487945			0.243972	−	0.969782i	$-0.421549\pi$
$401$	195.666			0.487945			0.243972	+	0.969782i	$0.421549\pi$
$402$	311.583	−	712.493i	0.775083	−	1.77237i
$403$	286.314			0.710456
$404$	−119.204	+	110.226i	−0.295059	+	0.272836i
$405$		0			0
$406$	−336.604	+	769.707i	−0.829074	+	1.89583i
$407$			6.55133i			0.0160966i
$408$	−105.242	+	36.5228i	−0.257946	+	0.0895167i
$409$	424.927			1.03894			0.519471	−	0.854488i	$-0.326129\pi$
$409$	424.927			1.03894			0.519471	+	0.854488i	$0.326129\pi$
$410$		0			0
$411$	375.478			0.913572
$412$	−327.231	+	302.585i	−0.794250	+	0.734431i
$413$		−	533.249i		−	1.29116i
$414$	508.531	+	222.388i	1.22834	+	0.537169i
$415$		0			0
$416$	101.018	−	189.172i	0.242833	−	0.454741i
$417$	−396.275			−0.950300
$418$	10.9235	−	24.9787i	0.0261329	−	0.0597576i
$419$	448.621			1.07069			0.535347	−	0.844632i	$-0.320181\pi$
$419$	448.621			1.07069			0.535347	+	0.844632i	$0.320181\pi$
$420$		0			0
$421$		−	762.020i		−	1.81002i	−0.425387	−	0.905012i	$-0.639862\pi$
$421$		−	762.020i		−	1.81002i	0.425387	−	0.905012i	$-0.360138\pi$
$422$	119.637	−	273.572i	0.283500	−	0.648274i
$423$		−	229.865i		−	0.543415i
$424$	−62.9322	−	181.342i	−0.148425	−	0.427693i
$425$		0			0
$426$	−304.523	−	133.172i	−0.714842	−	0.312611i
$427$	656.229			1.53684
$428$	76.8036	+	83.0592i	0.179448	+	0.194064i
$429$			467.909i			1.09070i
$430$		0			0
$431$			103.559i			0.240276i	0.992757	+	0.120138i	$0.0383337\pi$
$431$			103.559i			0.240276i	−0.992757	+	0.120138i	$0.961666\pi$
$432$	−8.70802	+	111.096i	−0.0201574	+	0.257167i
$433$	290.705			0.671375			0.335687	−	0.941973i	$-0.391031\pi$
$433$	290.705			0.671375			0.335687	+	0.941973i	$0.391031\pi$
$434$	−380.681	+	870.497i	−0.877145	+	2.00575i
$435$		0			0
$436$	36.0290	−	33.3154i	0.0826353	−	0.0764115i
$437$			30.0503i			0.0687650i
$438$	−364.699	+	833.950i	−0.832645	+	1.90400i
$439$			331.332i			0.754742i	0.926062	+	0.377371i	$0.123172\pi$
$439$			331.332i			0.754742i	−0.926062	+	0.377371i	$0.876828\pi$
$440$		0			0
$441$	−542.901			−1.23107
$442$	42.3904	+	18.5380i	0.0959060	+	0.0419411i
$443$	533.782			1.20493			0.602463	−	0.798147i	$-0.294186\pi$
$443$	533.782			1.20493			0.602463	+	0.798147i	$0.294186\pi$
$444$	−4.48454	+	4.14678i	−0.0101003	+	0.00933960i
$445$		0			0
$446$	−315.920	−	138.156i	−0.708340	−	0.309768i
$447$		−	117.961i		−	0.263894i
$448$	440.838	+	558.654i	0.984015	+	1.24700i
$449$	431.419			0.960844			0.480422	−	0.877038i	$-0.340484\pi$
$449$	431.419			0.960844			0.480422	+	0.877038i	$0.340484\pi$
$450$		0			0
$451$	−154.347			−0.342234
$452$	200.017	+	216.308i	0.442515	+	0.478558i
$453$		−	960.406i		−	2.12010i
$454$	−127.651	+	291.898i	−0.281170	+	0.642946i
$455$		0			0
$456$	24.0127	−	8.33329i	0.0526595	−	0.0182747i
$457$	142.066			0.310865			0.155433	−	0.987846i	$-0.450323\pi$
$457$	142.066			0.310865			0.155433	+	0.987846i	$0.450323\pi$
$458$	456.919	+	199.817i	0.997640	+	0.436283i
$459$	−24.0415			−0.0523779
$460$		0			0
$461$		−	594.329i		−	1.28922i	−0.764513	−	0.644609i	$-0.777020\pi$
$461$		−	594.329i		−	1.28922i	0.764513	−	0.644609i	$-0.222980\pi$
$462$	−1422.61	−	622.129i	−3.07925	−	1.34660i
$463$		−	594.339i		−	1.28367i	−0.766843	−	0.641835i	$-0.778173\pi$
$463$		−	594.339i		−	1.28367i	0.766843	−	0.641835i	$-0.221827\pi$
$464$	−602.566	−	47.2308i	−1.29863	−	0.101790i
$465$		0			0
$466$	119.645	−	273.589i	0.256748	−	0.587102i
$467$	−305.531			−0.654242			−0.327121	−	0.944982i	$-0.606078\pi$
$467$	−305.531			−0.654242			−0.327121	+	0.944982i	$0.606078\pi$
$468$	−143.157	+	132.375i	−0.305891	+	0.282852i
$469$		−	1071.75i		−	2.28517i
$470$		0			0
$471$			931.792i			1.97833i
$472$	362.448	−	125.783i	0.767898	−	0.266488i
$473$	−159.565			−0.337347
$474$	−515.657	−	225.504i	−1.08788	−	0.475747i
$475$		0			0
$476$	−112.724	+	104.234i	−0.236815	+	0.218979i
$477$			174.520i			0.365869i
$478$	−566.441	−	247.713i	−1.18502	−	0.518228i
$479$		−	726.619i		−	1.51695i	−0.651703	−	0.758475i	$-0.725945\pi$
$479$		−	726.619i		−	1.51695i	0.651703	−	0.758475i	$-0.274055\pi$
$480$		0			0
$481$	2.53676			0.00527394
$482$	2.85843	−	6.53632i	0.00593035	−	0.0135608i
$483$	1711.46			3.54339
$484$	−484.885	−	524.379i	−1.00183	−	1.08343i
$485$		0			0
$486$	252.212	−	576.728i	0.518954	−	1.18668i
$487$			331.827i			0.681369i	0.940178	+	0.340685i	$0.110659\pi$
$487$			331.827i			0.681369i	−0.940178	+	0.340685i	$0.889341\pi$
$488$	154.791	+	446.037i	0.317195	+	0.914010i
$489$	−564.292			−1.15397
$490$		0			0
$491$	431.486			0.878790			0.439395	−	0.898294i	$-0.355193\pi$
$491$	431.486			0.878790			0.439395	+	0.898294i	$0.355193\pi$
$492$	−97.6970	−	105.654i	−0.198571	−	0.214745i
$493$		−	130.397i		−	0.264497i
$494$	−9.67208	−	4.22974i	−0.0195791	−	0.00856223i
$495$		0			0
$496$	−681.469	−	53.4155i	−1.37393	−	0.107692i
$497$	−458.069			−0.921668
$498$	−189.689	+	433.759i	−0.380902	+	0.871003i
$499$	992.291			1.98856			0.994279	−	0.106812i	$-0.0340643\pi$
$499$	992.291			1.98856			0.994279	+	0.106812i	$0.0340643\pi$
$500$		0			0
$501$		−	1044.88i		−	2.08559i
$502$	−53.7204	+	122.842i	−0.107013	+	0.244704i
$503$			949.823i			1.88832i	0.329492	+	0.944158i	$0.393123\pi$
$503$			949.823i			1.88832i	−0.329492	+	0.944158i	$0.606877\pi$
$504$	−212.127	−	611.253i	−0.420887	−	1.21280i
$505$		0			0
$506$	1210.07	+	529.180i	2.39144	+	1.04581i
$507$	−500.572			−0.987322
$508$	−163.951	+	151.603i	−0.322737	+	0.298430i
$509$			283.683i			0.557335i	0.960388	+	0.278667i	$0.0898927\pi$
$509$			283.683i			0.557335i	−0.960388	+	0.278667i	$0.910107\pi$
$510$		0			0
$511$			1254.44i			2.45488i
$512$	−275.731	+	431.412i	−0.538538	+	0.842602i
$513$	5.48546			0.0106929
$514$	−92.7405	+	212.068i	−0.180429	+	0.412584i
$515$		0			0
$516$	−101.000	−	109.226i	−0.195736	−	0.211678i
$517$		−	546.971i		−	1.05797i
$518$	−3.37286	+	7.71267i	−0.00651132	+	0.0148893i
$519$		−	182.478i		−	0.351596i
$520$		0			0
$521$	−605.738			−1.16264			−0.581322	−	0.813673i	$-0.697464\pi$
$521$	−605.738			−1.16264			−0.581322	+	0.813673i	$0.697464\pi$
$522$	503.486	+	220.182i	0.964532	+	0.421804i
$523$	−681.592			−1.30324			−0.651618	−	0.758548i	$-0.725909\pi$
$523$	−681.592			−1.30324			−0.651618	+	0.758548i	$0.725909\pi$
$524$	437.213	+	472.824i	0.834376	+	0.902336i
$525$		0			0
$526$	−379.450	−	165.939i	−0.721388	−	0.315474i
$527$		−	147.472i		−	0.279832i
$528$	87.2944	−	1113.69i	0.165330	−	2.10927i
$529$	−926.758			−1.75190
$530$		0			0
$531$	−348.812			−0.656897
$532$	25.7199	−	23.7828i	0.0483456	−	0.0447044i
$533$			59.7654i			0.112130i
$534$	−145.156	+	331.926i	−0.271828	+	0.621584i
$535$		0			0
$536$	728.463	−	252.803i	1.35907	−	0.471647i
$537$	158.820			0.295755
$538$	−329.668	−	144.169i	−0.612765	−	0.267971i
$539$	−1291.85			−2.39676
$540$		0			0
$541$			244.206i			0.451398i	0.974197	+	0.225699i	$0.0724666\pi$
$541$			244.206i			0.451398i	−0.974197	+	0.225699i	$0.927533\pi$
$542$	−751.494	−	328.639i	−1.38652	−	0.606346i
$543$		−	11.3475i		−	0.0208979i
$544$	−97.4371	−	52.0316i	−0.179112	−	0.0956463i
$545$		0			0
$546$	−240.897	+	550.855i	−0.441203	+	1.00889i
$547$	377.177			0.689538			0.344769	−	0.938688i	$-0.387957\pi$
$547$	377.177			0.689538			0.344769	+	0.938688i	$0.387957\pi$
$548$	252.767	+	273.355i	0.461254	+	0.498824i
$549$		−	429.257i		−	0.781888i
$550$		0			0
$551$			29.7522i			0.0539967i
$552$	403.698	+	1163.27i	0.731337	+	2.10738i
$553$	−775.661			−1.40264
$554$	309.568	+	135.378i	0.558786	+	0.244365i
$555$		0			0
$556$	−266.768	−	288.496i	−0.479798	−	0.518877i
$557$			729.906i			1.31042i	0.755445	+	0.655212i	$0.227421\pi$
$557$			729.906i			1.31042i	−0.755445	+	0.655212i	$0.772579\pi$
$558$	569.415	+	249.013i	1.02046	+	0.446261i
$559$			61.7858i			0.110529i
$560$		0			0
$561$	241.006			0.429601
$562$	336.222	−	768.834i	0.598261	−	1.36803i
$563$	93.4375			0.165964			0.0829818	−	0.996551i	$-0.473556\pi$
$563$	93.4375			0.165964			0.0829818	+	0.996551i	$0.473556\pi$
$564$	374.415	−	346.215i	0.663856	−	0.613857i
$565$		0			0
$566$	−261.776	+	598.599i	−0.462502	+	1.05760i
$567$		−	1040.31i		−	1.83475i
$568$	−108.049	−	311.348i	−0.190227	−	0.548148i
$569$	−152.601			−0.268191			−0.134096	−	0.990968i	$-0.542813\pi$
$569$	−152.601			−0.268191			−0.134096	+	0.990968i	$0.542813\pi$
$570$		0			0
$571$	−197.023			−0.345049			−0.172524	−	0.985005i	$-0.555192\pi$
$571$	−197.023			−0.345049			−0.172524	+	0.985005i	$0.555192\pi$
$572$	−340.647	+	314.991i	−0.595536	+	0.550683i
$573$		−	92.5252i		−	0.161475i
$574$	−181.708	−	79.4637i	−0.316565	−	0.138439i
$575$		0			0
$576$	365.431	−	288.364i	0.634428	−	0.500632i
$577$	105.556			0.182939			0.0914693	−	0.995808i	$-0.470844\pi$
$577$	105.556			0.182939			0.0914693	+	0.995808i	$0.470844\pi$
$578$	−222.043	+	507.741i	−0.384157	+	0.878445i
$579$	−614.810			−1.06185
$580$		0			0
$581$			652.469i			1.12301i
$582$	−408.184	+	933.388i	−0.701348	+	1.60376i
$583$			415.276i			0.712308i
$584$	−852.642	+	295.898i	−1.46000	+	0.506674i
$585$		0			0
$586$	666.082	+	291.287i	1.13666	+	0.497077i
$587$	140.879			0.239998			0.119999	−	0.992774i	$-0.461711\pi$
$587$	140.879			0.239998			0.119999	+	0.992774i	$0.461711\pi$
$588$	−817.701	−	884.302i	−1.39065	−	1.50392i
$589$			33.6481i			0.0571275i
$590$		0			0
$591$			173.558i			0.293668i
$592$	−6.03787	−	0.473265i	−0.0101991	−	0.000799435i
$593$	830.224			1.40004			0.700020	−	0.714123i	$-0.253174\pi$
$593$	830.224			1.40004			0.700020	+	0.714123i	$0.253174\pi$
$594$	96.5978	−	220.889i	0.162623	−	0.371866i
$595$		0			0
$596$	85.8775	−	79.4096i	0.144090	−	0.133238i
$597$			230.440i			0.385997i
$598$	204.906	−	468.554i	0.342652	−	0.783536i
$599$			708.746i			1.18321i	0.806226	+	0.591607i	$0.201506\pi$
$599$			708.746i			1.18321i	−0.806226	+	0.591607i	$0.798494\pi$
$600$		0			0
$601$	−877.605			−1.46024			−0.730120	−	0.683319i	$-0.760536\pi$
$601$	−877.605			−1.46024			−0.730120	+	0.683319i	$0.760536\pi$
$602$	−187.851	−	82.1499i	−0.312045	−	0.136462i
$603$	−701.057			−1.16262
$604$	699.194	−	646.534i	1.15761	−	1.07042i
$605$		0			0
$606$	300.038	+	131.211i	0.495112	+	0.216520i
$607$			177.574i			0.292543i	0.989244	+	0.146271i	$0.0467273\pi$
$607$			177.574i			0.292543i	−0.989244	+	0.146271i	$0.953273\pi$
$608$	22.2319	+	11.8719i	0.0365656	+	0.0195261i
$609$	1694.48			2.78239
$610$		0			0
$611$	−211.795			−0.346636
$612$	68.1824	+	73.7358i	0.111409	+	0.120483i
$613$			332.413i			0.542272i	0.962541	+	0.271136i	$0.0873993\pi$
$613$			332.413i			0.542272i	−0.962541	+	0.271136i	$0.912601\pi$
$614$	454.207	−	1038.63i	0.739751	−	1.69158i
$615$		0			0
$616$	−504.763	−	1454.50i	−0.819421	−	2.36120i
$617$	726.357			1.17724			0.588620	−	0.808410i	$-0.299671\pi$
$617$	726.357			1.17724			0.588620	+	0.808410i	$0.299671\pi$
$618$	823.647	+	360.193i	1.33276	+	0.582837i
$619$	944.637			1.52607			0.763035	−	0.646358i	$-0.223709\pi$
$619$	944.637			1.52607			0.763035	+	0.646358i	$0.223709\pi$
$620$		0			0
$621$			265.738i			0.427919i
$622$	473.133	+	206.908i	0.760664	+	0.332650i
$623$			499.289i			0.801427i
$624$	−431.237	−	33.8016i	−0.691085	−	0.0541692i
$625$		0			0
$626$	−19.4488	+	44.4733i	−0.0310684	+	0.0710437i
$627$	−54.9895			−0.0877026
$628$	−678.362	+	627.271i	−1.08020	+	0.998840i
$629$		−	1.30661i		−	0.00207728i
$630$		0			0
$631$		−	373.587i		−	0.592056i	−0.955179	−	0.296028i	$-0.904338\pi$
$631$		−	373.587i		−	0.592056i	0.955179	−	0.296028i	$-0.0956621\pi$
$632$	−182.963	−	527.215i	−0.289498	−	0.834200i
$633$	−602.257			−0.951432
$634$	730.149	+	319.305i	1.15166	+	0.503636i
$635$		0			0
$636$	−284.266	+	262.856i	−0.446959	+	0.413296i
$637$			500.222i			0.785279i
$638$	1198.06	+	523.930i	1.87784	+	0.821207i
$639$			299.635i			0.468912i
$640$		0			0
$641$	218.071			0.340205			0.170102	−	0.985426i	$-0.445590\pi$
$641$	218.071			0.340205			0.170102	+	0.985426i	$0.445590\pi$
$642$	91.4258	−	209.062i	0.142408	−	0.325641i
$643$	−180.700			−0.281027			−0.140513	−	0.990079i	$-0.544875\pi$
$643$	−180.700			−0.281027			−0.140513	+	0.990079i	$0.544875\pi$
$644$	1152.13	+	1245.97i	1.78903	+	1.93474i
$645$		0			0
$646$	−2.17861	+	4.98180i	−0.00337247	+	0.00771177i
$647$		−	286.652i		−	0.443048i	−0.975155	−	0.221524i	$-0.928897\pi$
$647$		−	286.652i		−	0.443048i	0.975155	−	0.221524i	$-0.0711031\pi$
$648$	707.093	−	245.387i	1.09119	−	0.378683i
$649$	−830.011			−1.27891
$650$		0			0
$651$	1916.36			2.94372
$652$	−379.874	−	410.815i	−0.582630	−	0.630085i
$653$		−	863.087i		−	1.32173i	−0.750506	−	0.660863i	$-0.770190\pi$
$653$		−	863.087i		−	1.32173i	0.750506	−	0.660863i	$-0.229810\pi$
$654$	−90.6857	−	39.6582i	−0.138663	−	0.0606394i
$655$		0			0
$656$	11.1500	−	142.251i	0.0169969	−	0.216845i
$657$	820.565			1.24896
$658$	281.601	−	643.932i	0.427965	−	0.978620i
$659$	1119.80			1.69924			0.849618	−	0.527398i	$-0.176832\pi$
$659$	1119.80			1.69924			0.849618	+	0.527398i	$0.176832\pi$
$660$		0			0
$661$		−	805.904i		−	1.21922i	−0.792702	−	0.609609i	$-0.791326\pi$
$661$		−	805.904i		−	1.21922i	0.792702	−	0.609609i	$-0.208674\pi$
$662$	330.189	−	755.039i	0.498776	−	1.14054i
$663$		−	93.3209i		−	0.140755i
$664$	−443.482	+	153.904i	−0.667894	+	0.231783i
$665$		0			0
$666$	5.04507	+	2.20628i	0.00757517	+	0.00331273i
$667$	−1441.32			−2.16089
$668$	760.692	−	703.400i	1.13876	−	1.05299i
$669$			695.485i			1.03959i
$670$		0			0
$671$		−	1021.43i		−	1.52225i
$672$	676.139	−	1266.17i	1.00616	−	1.88419i
$673$	531.504			0.789753			0.394876	−	0.918734i	$-0.370787\pi$
$673$	531.504			0.789753			0.394876	+	0.918734i	$0.370787\pi$
$674$	250.575	−	572.985i	0.371773	−	0.850127i
$675$		0			0
$676$	−336.979	−	364.426i	−0.498490	−	0.539092i
$677$			520.567i			0.768931i	0.923139	+	0.384466i	$0.125614\pi$
$677$			520.567i			0.768931i	−0.923139	+	0.384466i	$0.874386\pi$
$678$	238.097	−	544.452i	0.351175	−	0.803027i
$679$			1404.02i			2.06778i
$680$		0			0
$681$	642.601			0.943613
$682$	1354.94	+	592.536i	1.98672	+	0.868822i
$683$	−870.065			−1.27389			−0.636944	−	0.770910i	$-0.719802\pi$
$683$	−870.065			−1.27389			−0.636944	+	0.770910i	$0.719802\pi$
$684$	−15.5569	−	16.8241i	−0.0227441	−	0.0245966i
$685$		0			0
$686$	−522.450	−	228.475i	−0.761590	−	0.333054i
$687$		−	1005.89i		−	1.46418i
$688$	11.5269	−	147.059i	0.0167542	−	0.213749i
$689$	160.800			0.233382
$690$		0			0
$691$	−713.215			−1.03215			−0.516074	−	0.856544i	$-0.672607\pi$
$691$	−713.215			−1.03215			−0.516074	+	0.856544i	$0.672607\pi$
$692$	132.848	−	122.842i	0.191977	−	0.177518i
$693$			1399.78i			2.01988i
$694$	−344.115	+	786.882i	−0.495843	+	1.13384i
$695$		0			0
$696$	399.693	+	1151.73i	0.574271	+	1.65479i
$697$	30.7834			0.0441656
$698$	−1191.35	−	520.997i	−1.70681	−	0.746413i
$699$	−602.296			−0.861654
$700$		0			0
$701$		−	1002.11i		−	1.42954i	−0.699360	−	0.714769i	$-0.746532\pi$
$701$		−	1002.11i		−	1.42954i	0.699360	−	0.714769i	$-0.253468\pi$
$702$	−85.5311	−	37.4040i	−0.121839	−	0.0532821i
$703$			0.298125i			0.000424076i
$704$	869.555	−	686.173i	1.23516	−	0.974677i
$705$		0			0
$706$	−307.097	+	702.234i	−0.434982	+	0.994666i
$707$	451.323			0.638364
$708$	−525.371	−	568.162i	−0.742049	−	0.802489i
$709$		−	1003.90i		−	1.41594i	−0.706241	−	0.707971i	$-0.749611\pi$
$709$		−	1003.90i		−	1.41594i	0.706241	−	0.707971i	$-0.250389\pi$
$710$		0			0
$711$			507.380i			0.713615i
$712$	−339.366	+	117.772i	−0.476637	+	0.165410i
$713$	−1630.05			−2.28618
$714$	283.729	+	124.079i	0.397379	+	0.173780i
$715$		0			0
$716$	106.916	+	115.624i	0.149324	+	0.161487i
$717$			1247.00i			1.73919i
$718$	−1202.95	−	526.068i	−1.67542	−	0.732685i
$719$			1207.30i			1.67914i	0.543252	+	0.839569i	$0.317193\pi$
$719$			1207.30i			1.67914i	−0.543252	+	0.839569i	$0.682807\pi$
$720$		0			0
$721$	1238.95			1.71837
$722$	−288.791	+	660.374i	−0.399988	+	0.914645i
$723$	−14.3894			−0.0199024
$724$	8.26122	−	7.63902i	0.0114105	−	0.0105511i
$725$		0			0
$726$	−577.199	+	1319.87i	−0.795040	+	1.81801i
$727$			587.117i			0.807588i	0.914850	+	0.403794i	$0.132309\pi$
$727$			587.117i			0.807588i	−0.914850	+	0.403794i	$0.867691\pi$
$728$	−563.202	+	195.451i	−0.773629	+	0.268477i
$729$	−427.625			−0.586591
$730$		0			0
$731$	31.8240			0.0435349
$732$	699.194	−	646.534i	0.955183	−	0.883243i
$733$		−	434.408i		−	0.592644i	−0.955088	−	0.296322i	$-0.904240\pi$
$733$		−	434.408i		−	0.592644i	0.955088	−	0.296322i	$-0.0957602\pi$
$734$	1.93839	+	0.847688i	0.00264086	+	0.00115489i
$735$		0			0
$736$	−575.121	+	1077.00i	−0.781414	+	1.46332i
$737$	−1668.19			−2.26349
$738$	−51.9793	+	118.860i	−0.0704327	+	0.161057i
$739$	−310.341			−0.419948			−0.209974	−	0.977707i	$-0.567338\pi$
$739$	−310.341			−0.419948			−0.209974	+	0.977707i	$0.567338\pi$
$740$		0			0
$741$			21.2927i			0.0287351i
$742$	−213.799	+	488.891i	−0.288139	+	0.658883i
$743$		−	610.976i		−	0.822310i	−0.911566	−	0.411155i	$-0.865126\pi$
$743$		−	610.976i		−	0.822310i	0.911566	−	0.411155i	$-0.134874\pi$
$744$	452.031	+	1302.55i	0.607568	+	1.75074i
$745$		0			0
$746$	1.49673	+	0.654542i	0.00200634	+	0.000877402i
$747$	426.798			0.571349
$748$	162.242	+	175.457i	0.216902	+	0.234568i
$749$		−	314.475i		−	0.419860i
$750$		0			0
$751$		−	622.287i		−	0.828611i	−0.910138	−	0.414306i	$-0.864024\pi$
$751$		−	622.287i		−	0.828611i	0.910138	−	0.414306i	$-0.135976\pi$
$752$	504.103	+	39.5130i	0.670350	+	0.0525439i
$753$	270.431			0.359138
$754$	202.873	−	463.906i	0.269062	−	0.615260i
$755$		0			0
$756$	227.443	−	210.313i	0.300851	−	0.278192i
$757$		−	796.999i		−	1.05284i	−0.850225	−	0.526419i	$-0.823534\pi$
$757$		−	796.999i		−	1.05284i	0.850225	−	0.526419i	$-0.176466\pi$
$758$	−505.541	+	1156.01i	−0.666941	+	1.52508i
$759$		−	2663.91i		−	3.50977i
$760$		0			0
$761$	129.738			0.170484			0.0852419	−	0.996360i	$-0.472834\pi$
$761$	129.738			0.170484			0.0852419	+	0.996360i	$0.472834\pi$
$762$	412.667	+	180.465i	0.541558	+	0.236831i
$763$	−136.411			−0.178783
$764$	67.3601	−	62.2868i	0.0881677	−	0.0815273i
$765$		0			0
$766$	719.798	+	314.778i	0.939684	+	0.410938i
$767$			321.392i			0.419024i
$768$	1020.10	+	160.906i	1.32826	+	0.209512i
$769$	−814.433			−1.05908			−0.529540	−	0.848285i	$-0.677636\pi$
$769$	−814.433			−1.05908			−0.529540	+	0.848285i	$0.677636\pi$
$770$		0			0
$771$	466.860			0.605525
$772$	−413.883	−	447.594i	−0.536118	−	0.579784i
$773$			650.087i			0.840992i	0.907294	+	0.420496i	$0.138144\pi$
$773$			650.087i			0.840992i	−0.907294	+	0.420496i	$0.861856\pi$
$774$	−53.7365	+	122.878i	−0.0694270	+	0.158757i
$775$		0			0
$776$	−954.309	+	331.180i	−1.22978	+	0.426778i
$777$	16.9791			0.0218522
$778$	535.472	+	234.170i	0.688267	+	0.300989i
$779$	−7.02374			−0.00901636
$780$		0			0
$781$			712.992i			0.912922i
$782$	−241.338	−	105.541i	−0.308617	−	0.134963i
$783$			263.101i			0.336017i
$784$	93.3228	−	1190.60i	0.119034	−	1.51863i
$785$		0			0
$786$	520.452	−	1190.11i	0.662152	−	1.51413i
$787$	−20.6114			−0.0261898			−0.0130949	−	0.999914i	$-0.504168\pi$
$787$	−20.6114			−0.0261898			−0.0130949	+	0.999914i	$0.504168\pi$
$788$	−126.353	+	116.837i	−0.160347	+	0.148270i
$789$			835.345i			1.05874i
$790$		0			0
$791$		−	818.975i		−	1.03537i
$792$	−951.426	+	330.179i	−1.20130	+	0.416893i
$793$	−395.512			−0.498754
$794$	−1240.07	−	542.300i	−1.56180	−	0.682997i
$795$		0			0
$796$	−167.765	+	155.130i	−0.210760	+	0.194887i
$797$		−	805.629i		−	1.01083i	−0.862877	−	0.505413i	$-0.831340\pi$
$797$		−	805.629i		−	1.01083i	0.862877	−	0.505413i	$-0.168660\pi$
$798$	−64.7375	−	28.3106i	−0.0811246	−	0.0354770i
$799$			109.089i			0.136532i
$800$		0			0
$801$	326.598			0.407738
$802$	156.797	−	358.546i	0.195508	−	0.447065i
$803$	1952.56			2.43159
$804$	−1055.91	−	1141.92i	−1.31332	−	1.42029i
$805$		0			0
$806$	229.438	−	524.653i	0.284663	−	0.650934i
$807$			725.750i			0.899319i
$808$	106.458	+	306.763i	0.131755	+	0.379657i
$809$	−292.924			−0.362081			−0.181041	−	0.983476i	$-0.557947\pi$
$809$	−292.924			−0.362081			−0.181041	+	0.983476i	$0.557947\pi$
$810$		0			0
$811$	−827.255			−1.02004			−0.510021	−	0.860162i	$-0.670363\pi$
$811$	−827.255			−1.02004			−0.510021	+	0.860162i	$0.670363\pi$
$812$	1140.70	+	1233.61i	1.40481	+	1.51923i
$813$			1654.38i			2.03491i
$814$	12.0049	+	5.24992i	0.0147481	+	0.00644954i
$815$		0			0
$816$	−17.4102	+	222.117i	−0.0213360	+	0.272203i
$817$	−7.26117			−0.00888761
$818$	340.516	−	778.653i	0.416279	−	0.951898i
$819$	542.014			0.661799
$820$		0			0
$821$			1205.34i			1.46814i	0.679075	+	0.734069i	$0.262381\pi$
$821$			1205.34i			1.46814i	−0.679075	+	0.734069i	$0.737619\pi$
$822$	300.890	−	688.041i	0.366047	−	0.837033i
$823$		−	667.377i		−	0.810908i	−0.914116	−	0.405454i	$-0.867114\pi$
$823$		−	667.377i		−	0.810908i	0.914116	−	0.405454i	$-0.132886\pi$
$824$	292.242	+	842.109i	0.354663	+	1.02198i
$825$		0			0
$826$	−977.146	−	427.320i	−1.18299	−	0.517337i
$827$	−513.257			−0.620625			−0.310313	−	0.950635i	$-0.600434\pi$
$827$	−513.257			−0.620625			−0.310313	+	0.950635i	$0.600434\pi$
$828$	815.025	−	753.641i	0.984329	−	0.910194i
$829$			749.848i			0.904521i	0.891886	+	0.452260i	$0.149382\pi$
$829$			749.848i			0.904521i	−0.891886	+	0.452260i	$0.850618\pi$
$830$		0			0
$831$		−	681.501i		−	0.820097i
$832$	−265.696	−	336.704i	−0.319346	−	0.404692i
$833$	257.650			0.309303
$834$	−317.556	+	726.150i	−0.380762	+	0.870683i
$835$		0			0
$836$	−37.0183	−	40.0334i	−0.0442803	−	0.0478869i
$837$			297.553i			0.355500i
$838$	359.503	−	822.070i	0.429002	−	0.980991i
$839$			48.2988i			0.0575672i	0.999586	+	0.0287836i	$0.00916336\pi$
$839$			48.2988i			0.0575672i	−0.999586	+	0.0287836i	$0.990837\pi$
$840$		0			0
$841$	−586.016			−0.696809
$842$	−1396.36	−	610.646i	−1.65838	−	0.725233i
$843$	−1692.56			−2.00778
$844$	−405.432	−	438.454i	−0.480370	−	0.519496i
$845$		0			0
$846$	−421.213	−	184.203i	−0.497888	−	0.217734i
$847$			1985.38i			2.34401i
$848$	−382.729	−	29.9993i	−0.451331	−	0.0353766i
$849$	1317.79			1.55217
$850$		0			0
$851$	−14.4424			−0.0169711
$852$	−488.060	+	451.301i	−0.572840	+	0.529696i
$853$		−	925.590i		−	1.08510i	−0.840023	−	0.542550i	$-0.817459\pi$
$853$		−	925.590i		−	1.08510i	0.840023	−	0.542550i	$-0.182541\pi$
$854$	525.871	−	1202.50i	0.615773	−	1.40808i
$855$		0			0
$856$	213.748	−	74.1782i	0.249705	−	0.0866567i
$857$	23.8375			0.0278151			0.0139076	−	0.999903i	$-0.495573\pi$
$857$	23.8375			0.0278151			0.0139076	+	0.999903i	$0.495573\pi$
$858$	857.415	+	374.960i	0.999318	+	0.437017i
$859$	−1227.62			−1.42913			−0.714563	−	0.699571i	$-0.753374\pi$
$859$	−1227.62			−1.42913			−0.714563	+	0.699571i	$0.753374\pi$
$860$		0			0
$861$			400.024i			0.464604i
$862$	189.766	+	82.9873i	0.220146	+	0.0962730i
$863$			698.456i			0.809335i	0.914464	+	0.404667i	$0.132613\pi$
$863$			698.456i			0.809335i	−0.914464	+	0.404667i	$0.867387\pi$
$864$	196.599	+	104.984i	0.227545	+	0.121509i
$865$		0			0
$866$	232.957	−	532.700i	0.269004	−	0.615127i
$867$	1117.77			1.28924
$868$	1290.07	+	1395.15i	1.48626	+	1.60731i
$869$			1207.33i			1.38933i
$870$		0			0
$871$			645.946i			0.741614i
$872$	−32.1766	−	92.7183i	−0.0368998	−	0.106328i
$873$	918.407			1.05201
$874$	55.0654	+	24.0809i	0.0630039	+	0.0275525i
$875$		0			0
$876$	1235.91	+	1336.58i	1.41086	+	1.52577i
$877$		−	1098.23i		−	1.25225i	−0.779722	−	0.626126i	$-0.784640\pi$
$877$		−	1098.23i		−	1.25225i	0.779722	−	0.626126i	$-0.215360\pi$
$878$	607.145	+	265.514i	0.691510	+	0.302407i
$879$		−	1466.35i		−	1.66821i
$880$		0			0
$881$	435.466			0.494286			0.247143	−	0.968979i	$-0.420508\pi$
$881$	435.466			0.494286			0.247143	+	0.968979i	$0.420508\pi$
$882$	−435.055	+	994.832i	−0.493259	+	1.12793i
$883$	146.771			0.166219			0.0831094	−	0.996540i	$-0.473515\pi$
$883$	146.771			0.166219			0.0831094	+	0.996540i	$0.473515\pi$
$884$	67.9394	−	62.8225i	0.0768545	−	0.0710662i
$885$		0			0
$886$	427.748	−	978.123i	0.482785	−	1.10398i
$887$		−	95.2031i		−	0.107332i	−0.998559	−	0.0536658i	$-0.982909\pi$
$887$		−	95.2031i		−	0.107332i	0.998559	−	0.0536658i	$-0.0170906\pi$
$888$	4.00503	+	11.5407i	0.00451017	+	0.0129963i
$889$	620.742			0.698247
$890$		0			0
$891$	−1619.25			−1.81734
$892$	−506.326	+	468.192i	−0.567630	+	0.524879i
$893$		−	24.8905i		−	0.0278729i
$894$	−216.156	−	94.5280i	−0.241785	−	0.105736i
$895$		0			0
$896$	1376.97	−	360.131i	1.53679	−	0.401932i
$897$	−1031.50			−1.14995
$898$	345.718	−	790.549i	0.384987	−	0.880344i
$899$	−1613.88			−1.79519
$900$		0			0
$901$		−	82.8235i		−	0.0919240i
$902$	−123.687	+	282.832i	−0.137125	+	0.313561i
$903$			413.546i			0.457969i
$904$	556.655	−	193.180i	0.615769	−	0.213694i
$905$		0			0
$906$	−1759.89	−	769.624i	−1.94248	−	0.849474i
$907$	496.182			0.547058			0.273529	−	0.961864i	$-0.411809\pi$
$907$	496.182			0.547058			0.273529	+	0.961864i	$0.411809\pi$
$908$	432.591	+	467.826i	0.476422	+	0.515226i
$909$		−	295.222i		−	0.324777i
$910$		0			0
$911$			1431.36i			1.57120i	0.618736	+	0.785599i	$0.287645\pi$
$911$			1431.36i			1.57120i	−0.618736	+	0.785599i	$0.712355\pi$
$912$	3.97242	−	50.6798i	0.00435573	−	0.0555699i
$913$	1015.58			1.11235
$914$	113.845	−	260.326i	0.124556	−	0.284821i
$915$		0			0
$916$	732.307	−	677.153i	0.799462	−	0.739250i
$917$		−	1790.18i		−	1.95222i
$918$	−19.2657	+	44.0545i	−0.0209866	+	0.0479897i
$919$			496.178i			0.539911i	0.962873	+	0.269955i	$0.0870090\pi$
$919$			496.178i			0.539911i	−0.962873	+	0.269955i	$0.912991\pi$
$920$		0			0
$921$	−2286.50			−2.48262
$922$	−1089.07	−	476.267i	−1.18121	−	0.516559i
$923$	276.080			0.299112
$924$	−2280.03	+	2108.31i	−2.46756	+	2.28172i
$925$		0			0
$926$	−1089.09	−	476.275i	−1.17612	−	0.514336i
$927$		−	810.428i		−	0.874248i
$928$	−569.415	+	1066.32i	−0.613594	+	1.14905i
$929$	−832.634			−0.896269			−0.448135	−	0.893966i	$-0.647911\pi$
$929$	−832.634			−0.896269			−0.448135	+	0.893966i	$0.647911\pi$
$930$		0			0
$931$	−58.7870			−0.0631440
$932$	−405.459	−	438.483i	−0.435041	−	0.470476i
$933$		−	1041.58i		−	1.11638i
$934$	−244.838	+	559.867i	−0.262139	+	0.599429i
$935$		0			0
$936$	127.850	+	368.405i	0.136592	+	0.393595i
$937$	146.334			0.156173			0.0780865	−	0.996947i	$-0.475119\pi$
$937$	146.334			0.156173			0.0780865	+	0.996947i	$0.475119\pi$
$938$	−1963.91	−	858.846i	−2.09372	−	0.915614i
$939$	97.9063			0.104267
$940$		0			0
$941$			672.850i			0.715037i	0.933906	+	0.357519i	$0.116377\pi$
$941$			672.850i			0.715037i	−0.933906	+	0.357519i	$0.883623\pi$
$942$	1707.45	+	746.694i	1.81258	+	0.792669i
$943$		−	340.258i		−	0.360825i
$944$	59.9597	−	764.960i	0.0635166	−	0.810339i
$945$		0			0
$946$	−127.868	+	292.393i	−0.135167	+	0.309084i
$947$	445.927			0.470883			0.235442	−	0.971888i	$-0.424346\pi$
$947$	445.927			0.470883			0.235442	+	0.971888i	$0.424346\pi$
$948$	−826.446	+	764.201i	−0.871778	+	0.806120i
$949$		−	756.060i		−	0.796691i
$950$		0			0
$951$		−	1607.39i		−	1.69022i
$952$	100.671	+	290.088i	0.105747	+	0.304715i
$953$	1490.29			1.56379			0.781894	−	0.623411i	$-0.214254\pi$
$953$	1490.29			1.56379			0.781894	+	0.623411i	$0.214254\pi$
$954$	319.797	+	139.852i	0.335217	+	0.146595i
$955$		0			0
$956$	−907.839	+	839.464i	−0.949622	+	0.878101i
$957$		−	2637.49i		−	2.75599i
$958$	−1331.48	−	582.278i	−1.38986	−	0.607805i
$959$		−	1034.96i		−	1.07921i
$960$		0			0
$961$	−864.209			−0.899281
$962$	2.03284	−	4.64847i	0.00211314	−	0.00483209i
$963$	−205.706			−0.213610
$964$	−9.68680	−	10.4758i	−0.0100485	−	0.0108670i
$965$		0			0
$966$	1371.48	−	3136.14i	1.41975	−	3.24652i
$967$		−	165.170i		−	0.170807i	−0.996346	−	0.0854034i	$-0.972782\pi$
$967$		−	165.170i		−	0.170807i	0.996346	−	0.0854034i	$-0.0272179\pi$
$968$	−1349.46	+	468.310i	−1.39407	+	0.483791i
$969$	10.9672			0.0113181
$970$		0			0
$971$	1252.88			1.29030			0.645151	−	0.764055i	$-0.276795\pi$
$971$	1252.88			1.29030			0.645151	+	0.764055i	$0.276795\pi$
$972$	−854.709	−	924.326i	−0.879331	−	0.950952i
$973$			1092.29i			1.12260i
$974$	608.052	+	265.910i	0.624284	+	0.273008i
$975$		0			0
$976$	941.378	+	73.7878i	0.964527	+	0.0756023i
$977$	1446.44			1.48049			0.740246	−	0.672336i	$-0.234709\pi$
$977$	1446.44			1.48049			0.740246	+	0.672336i	$0.234709\pi$
$978$	−452.197	+	1034.03i	−0.462369	+	1.05729i
$979$	777.152			0.793823
$980$		0			0
$981$			89.2302i			0.0909584i
$982$	345.772	−	790.671i	0.352110	−	0.805164i
$983$		−	762.431i		−	0.775617i	−0.921740	−	0.387808i	$-0.873232\pi$
$983$		−	762.431i		−	0.775617i	0.921740	−	0.387808i	$-0.126768\pi$
$984$	−271.895	+	94.3574i	−0.276316	+	0.0958917i
$985$		0			0
$986$	−238.944	−	104.494i	−0.242337	−	0.105977i
$987$	−1417.59			−1.43626
$988$	−15.5015	+	14.3340i	−0.0156898	+	0.0145081i
$989$		−	351.760i		−	0.355673i
$990$		0			0
$991$			191.767i			0.193509i	0.995308	+	0.0967545i	$0.0308462\pi$
$991$			191.767i			0.193509i	−0.995308	+	0.0967545i	$0.969154\pi$
$992$	−643.978	+	1205.95i	−0.649171	+	1.21567i
$993$	−1662.19			−1.67390
$994$	−367.075	+	839.383i	−0.369290	+	0.844450i
$995$		0			0
$996$	642.830	+	695.188i	0.645411	+	0.697980i
$997$			409.797i			0.411030i	0.978654	+	0.205515i	$0.0658869\pi$
$997$			409.797i			0.411030i	−0.978654	+	0.205515i	$0.934113\pi$
$998$	795.175	−	1818.31i	0.796768	−	1.82196i
$999$			2.63635i			0.00263899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.g.f.51.3	yes	6
4.3	odd	2		800.3.g.f.751.5		6
5.2	odd	4		200.3.e.c.99.12		12
5.3	odd	4		200.3.e.c.99.1		12
5.4	even	2		200.3.g.e.51.4	yes	6
8.3	odd	2	inner	200.3.g.f.51.4	yes	6
8.5	even	2		800.3.g.f.751.6		6
20.3	even	4		800.3.e.c.399.11		12
20.7	even	4		800.3.e.c.399.2		12
20.19	odd	2		800.3.g.e.751.2		6
40.3	even	4		200.3.e.c.99.11		12
40.13	odd	4		800.3.e.c.399.12		12
40.19	odd	2		200.3.g.e.51.3	✓	6
40.27	even	4		200.3.e.c.99.2		12
40.29	even	2		800.3.g.e.751.1		6
40.37	odd	4		800.3.e.c.399.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.e.c.99.1		12	5.3	odd	4
200.3.e.c.99.2		12	40.27	even	4
200.3.e.c.99.11		12	40.3	even	4
200.3.e.c.99.12		12	5.2	odd	4
200.3.g.e.51.3	✓	6	40.19	odd	2
200.3.g.e.51.4	yes	6	5.4	even	2
200.3.g.f.51.3	yes	6	1.1	even	1	trivial
200.3.g.f.51.4	yes	6	8.3	odd	2	inner
800.3.e.c.399.1		12	40.37	odd	4
800.3.e.c.399.2		12	20.7	even	4
800.3.e.c.399.11		12	20.3	even	4
800.3.e.c.399.12		12	40.13	odd	4
800.3.g.e.751.1		6	40.29	even	2
800.3.g.e.751.2		6	20.19	odd	2
800.3.g.f.751.5		6	4.3	odd	2
800.3.g.f.751.6		6	8.5	even	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.801352 - 1.83244i) q^{2} -4.03404 q^{3} +(-2.71567 - 2.93686i) q^{4} +(-3.23269 + 7.39214i) q^{6} +11.1194i q^{7} +(-7.55783 + 2.62284i) q^{8} +7.27349 q^{9} +17.3075 q^{11} +(10.9551 + 11.8474i) q^{12} -6.70171i q^{13} +(20.3756 + 8.91056i) q^{14} +(-1.25029 + 15.9511i) q^{16} -3.45185 q^{17} +(5.82863 - 13.3282i) q^{18} +0.787598 q^{19} -44.8561i q^{21} +(13.8694 - 31.7150i) q^{22} +38.1544i q^{23} +(30.4886 - 10.5806i) q^{24} +(-12.2805 - 5.37044i) q^{26} +6.96480 q^{27} +(32.6561 - 30.1966i) q^{28} +37.7759i q^{29} +42.7225i q^{31} +(28.2275 + 15.0735i) q^{32} -69.8193 q^{33} +(-2.76615 + 6.32531i) q^{34} +(-19.7524 - 21.3612i) q^{36} +0.378525i q^{37} +(0.631143 - 1.44322i) q^{38} +27.0350i q^{39} -8.91793 q^{41} +(-82.1961 - 35.9456i) q^{42} -9.21939 q^{43} +(-47.0015 - 50.8298i) q^{44} +(69.9156 + 30.5751i) q^{46} -31.6031i q^{47} +(5.04372 - 64.3473i) q^{48} -74.6410 q^{49} +13.9249 q^{51} +(-19.6820 + 18.1996i) q^{52} +23.9939i q^{53} +(5.58126 - 12.7626i) q^{54} +(-29.1644 - 84.0384i) q^{56} -3.17720 q^{57} +(69.2220 + 30.2718i) q^{58} -47.9566 q^{59} -59.0166i q^{61} +(78.2863 + 34.2357i) q^{62} +80.8769i q^{63} +(50.2414 - 39.6459i) q^{64} +(-55.9499 + 127.940i) q^{66} -96.3852 q^{67} +(9.37409 + 10.1376i) q^{68} -153.916i q^{69} +41.1955i q^{71} +(-54.9718 + 19.0772i) q^{72} +112.816 q^{73} +(0.693623 + 0.303332i) q^{74} +(-2.13885 - 2.31306i) q^{76} +192.449i q^{77} +(49.5400 + 21.6646i) q^{78} +69.7575i q^{79} -93.5577 q^{81} +(-7.14641 + 16.3416i) q^{82} +58.6785 q^{83} +(-131.736 + 121.814i) q^{84} +(-7.38798 + 16.8940i) q^{86} -152.389i q^{87} +(-130.807 + 45.3949i) q^{88} +44.9025 q^{89} +74.5190 q^{91} +(112.054 - 103.615i) q^{92} -172.344i q^{93} +(-57.9107 - 25.3252i) q^{94} +(-113.871 - 60.8072i) q^{96} +126.268 q^{97} +(-59.8137 + 136.775i) q^{98} +125.886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + q^{6} - 3 q^{8} - 8 q^{9} + 30 q^{11} + 27 q^{12} + 4 q^{14} - 39 q^{16} + 2 q^{17} + 20 q^{18} - 2 q^{19} + 37 q^{22} + 59 q^{24} - 36 q^{26} - 62 q^{27} + 40 q^{28}+ \cdots + 304 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + q^6 - 3 * q^8 - 8 * q^9 + 30 * q^11 + 27 * q^12 + 4 * q^14 - 39 * q^16 + 2 * q^17 + 20 * q^18 - 2 * q^19 + 37 * q^22 + 59 * q^24 - 36 * q^26 - 62 * q^27 + 40 * q^28 - 47 * q^32 - 138 * q^33 + 89 * q^34 - 8 * q^36 + 113 * q^38 - 70 * q^41 - 220 * q^42 - 76 * q^43 - 77 * q^44 + 184 * q^46 - 57 * q^48 - 138 * q^49 + 114 * q^51 + 200 * q^52 - 69 * q^54 - 176 * q^56 + 78 * q^57 - 20 * q^58 - 44 * q^59 + 320 * q^62 + 113 * q^64 - 101 * q^66 - 18 * q^67 + 143 * q^68 - 240 * q^72 + 18 * q^73 + 204 * q^74 + 155 * q^76 + 180 * q^78 - 142 * q^81 - 323 * q^82 + 398 * q^83 - 400 * q^84 + 218 * q^86 - 317 * q^88 + 98 * q^89 + 288 * q^91 + 600 * q^92 - 316 * q^94 - 409 * q^96 + 76 * q^97 - 213 * q^98 + 304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more