LMFDB - Embedded newform 200.3.e.c.99.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,3,Mod(99,200)] 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("200.99"); 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, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.83244 - 0.801352i$ of defining polynomial
Character	$\chi$	$=$	200.99
Dual form			200.3.e.c.99.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83244 - 0.801352i) q^{2} -4.03404i q^{3} +(2.71567 + 2.93686i) q^{4} +(-3.23269 + 7.39214i) q^{6} +11.1194 q^{7} +(-2.62284 - 7.55783i) q^{8} -7.27349 q^{9} +17.3075 q^{11} +(11.8474 - 10.9551i) q^{12} +6.70171 q^{13} +(-20.3756 - 8.91056i) q^{14} +(-1.25029 + 15.9511i) q^{16} +3.45185i q^{17} +(13.3282 + 5.82863i) q^{18} -0.787598 q^{19} -44.8561i q^{21} +(-31.7150 - 13.8694i) q^{22} -38.1544 q^{23} +(-30.4886 + 10.5806i) q^{24} +(-12.2805 - 5.37044i) q^{26} -6.96480i q^{27} +(30.1966 + 32.6561i) q^{28} -37.7759i q^{29} +42.7225i q^{31} +(15.0735 - 28.2275i) q^{32} -69.8193i q^{33} +(2.76615 - 6.32531i) q^{34} +(-19.7524 - 21.3612i) q^{36} +0.378525 q^{37} +(1.44322 + 0.631143i) q^{38} -27.0350i q^{39} -8.91793 q^{41} +(-35.9456 + 82.1961i) q^{42} -9.21939i q^{43} +(47.0015 + 50.8298i) q^{44} +(69.9156 + 30.5751i) q^{46} -31.6031 q^{47} +(64.3473 + 5.04372i) q^{48} +74.6410 q^{49} +13.9249 q^{51} +(18.1996 + 19.6820i) q^{52} -23.9939 q^{53} +(-5.58126 + 12.7626i) q^{54} +(-29.1644 - 84.0384i) q^{56} +3.17720i q^{57} +(-30.2718 + 69.2220i) q^{58} +47.9566 q^{59} -59.0166i q^{61} +(34.2357 - 78.2863i) q^{62} -80.8769 q^{63} +(-50.2414 + 39.6459i) q^{64} +(-55.9499 + 127.940i) q^{66} +96.3852i q^{67} +(-10.1376 + 9.37409i) q^{68} +153.916i q^{69} +41.1955i q^{71} +(19.0772 + 54.9718i) q^{72} +112.816i q^{73} +(-0.693623 - 0.303332i) q^{74} +(-2.13885 - 2.31306i) q^{76} +192.449 q^{77} +(-21.6646 + 49.5400i) q^{78} -69.7575i q^{79} -93.5577 q^{81} +(16.3416 + 7.14641i) q^{82} +58.6785i q^{83} +(131.736 - 121.814i) q^{84} +(-7.38798 + 16.8940i) q^{86} -152.389 q^{87} +(-45.3949 - 130.807i) q^{88} -44.9025 q^{89} +74.5190 q^{91} +(-103.615 - 112.054i) q^{92} +172.344 q^{93} +(57.9107 + 25.3252i) q^{94} +(-113.871 - 60.8072i) q^{96} -126.268i q^{97} +(-136.775 - 59.8137i) q^{98} -125.886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 14 q^{4} + 2 q^{6} + 16 q^{9} + 60 q^{11} - 8 q^{14} - 78 q^{16} + 4 q^{19} - 118 q^{24} - 72 q^{26} - 178 q^{34} - 16 q^{36} - 140 q^{41} + 154 q^{44} + 368 q^{46} + 276 q^{49} + 228 q^{51} + 138 q^{54}+ \cdots - 608 q^{99}+O(q^{100}) $ 12 * q + 14 * q^4 + 2 * q^6 + 16 * q^9 + 60 * q^11 - 8 * q^14 - 78 * q^16 + 4 * q^19 - 118 * q^24 - 72 * q^26 - 178 * q^34 - 16 * q^36 - 140 * q^41 + 154 * q^44 + 368 * q^46 + 276 * q^49 + 228 * q^51 + 138 * q^54 - 352 * q^56 + 88 * q^59 - 226 * q^64 - 202 * q^66 - 408 * q^74 + 310 * q^76 - 284 * q^81 + 800 * q^84 + 436 * q^86 - 196 * q^89 + 576 * q^91 + 632 * q^94 - 818 * q^96 - 608 * 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 $

$2$	−1.83244	−	0.801352i	−0.916220	−	0.400676i
$2$	−1.83244	−	0.801352i	−0.916220	−	0.400676i
$3$		−	4.03404i		−	1.34468i	−0.740242	−	0.672340i	$-0.765289\pi$
$3$		−	4.03404i		−	1.34468i	0.740242	−	0.672340i	$-0.234711\pi$
$4$	2.71567	+	2.93686i	0.678917	+	0.734215i
$5$		0			0
$5$		0			0
$6$	−3.23269	+	7.39214i	−0.538782	+	1.23202i
$7$	11.1194			1.58849			0.794243	−	0.607601i	$-0.207868\pi$
$7$	11.1194			1.58849			0.794243	+	0.607601i	$0.207868\pi$
$8$	−2.62284	−	7.55783i	−0.327855	−	0.944728i
$9$	−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	$0.211785\pi$
$12$	11.8474	−	10.9551i	0.987285	−	0.912927i
$13$	6.70171			0.515517			0.257758	−	0.966209i	$-0.417016\pi$
$13$	6.70171			0.515517			0.257758	+	0.966209i	$0.417016\pi$
$14$	−20.3756	−	8.91056i	−1.45540	−	0.636468i
$15$		0			0
$16$	−1.25029	+	15.9511i	−0.0781431	+	0.996942i
$17$			3.45185i			0.203050i	0.994833	+	0.101525i	$0.0323722\pi$
$17$			3.45185i			0.203050i	−0.994833	+	0.101525i	$0.967628\pi$
$18$	13.3282	+	5.82863i	0.740458	+	0.323813i
$19$	−0.787598			−0.0414525			−0.0207263	−	0.999785i	$-0.506598\pi$
$19$	−0.787598			−0.0414525			−0.0207263	+	0.999785i	$0.506598\pi$
$20$		0			0
$21$		−	44.8561i		−	2.13601i
$22$	−31.7150	−	13.8694i	−1.44159	−	0.630429i
$23$	−38.1544			−1.65889			−0.829443	−	0.558591i	$-0.811342\pi$
$23$	−38.1544			−1.65889			−0.829443	+	0.558591i	$0.811342\pi$
$24$	−30.4886	+	10.5806i	−1.27036	+	0.440860i
$25$		0			0
$26$	−12.2805	−	5.37044i	−0.472326	−	0.206555i
$27$		−	6.96480i		−	0.257956i
$28$	30.1966	+	32.6561i	1.07845	+	1.16629i
$29$		−	37.7759i		−	1.30262i	−0.758813	−	0.651308i	$-0.774221\pi$
$29$		−	37.7759i		−	1.30262i	0.758813	−	0.651308i	$-0.225779\pi$
$30$		0			0
$31$			42.7225i			1.37814i	0.724693	+	0.689072i	$0.241982\pi$
$31$			42.7225i			1.37814i	−0.724693	+	0.689072i	$0.758018\pi$
$32$	15.0735	−	28.2275i	0.471047	−	0.882108i
$33$		−	69.8193i		−	2.11574i
$34$	2.76615	−	6.32531i	0.0813574	−	0.186039i
$35$		0			0
$36$	−19.7524	−	21.3612i	−0.548678	−	0.593367i
$37$	0.378525			0.0102304			0.00511520	−	0.999987i	$-0.498372\pi$
$37$	0.378525			0.0102304			0.00511520	+	0.999987i	$0.498372\pi$
$38$	1.44322	+	0.631143i	0.0379796	+	0.0166090i
$39$		−	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	$0.534686\pi$
$42$	−35.9456	+	82.1961i	−0.855846	+	1.95705i
$43$		−	9.21939i		−	0.214405i	−0.994237	−	0.107202i	$-0.965811\pi$
$43$		−	9.21939i		−	0.214405i	0.994237	−	0.107202i	$-0.0341892\pi$
$44$	47.0015	+	50.8298i	1.06822	+	1.15522i
$45$		0			0
$46$	69.9156	+	30.5751i	1.51990	+	0.664676i
$47$	−31.6031			−0.672406			−0.336203	−	0.941790i	$-0.609143\pi$
$47$	−31.6031			−0.672406			−0.336203	+	0.941790i	$0.609143\pi$
$48$	64.3473	+	5.04372i	1.34057	+	0.105078i
$49$	74.6410			1.52328
$50$		0			0
$51$	13.9249			0.273038
$52$	18.1996	+	19.6820i	0.349993	+	0.378500i
$53$	−23.9939			−0.452715			−0.226358	−	0.974044i	$-0.572682\pi$
$53$	−23.9939			−0.452715			−0.226358	+	0.974044i	$0.572682\pi$
$54$	−5.58126	+	12.7626i	−0.103357	+	0.236344i
$55$		0			0
$56$	−29.1644	−	84.0384i	−0.520792	−	1.50069i
$57$			3.17720i			0.0557404i
$58$	−30.2718	+	69.2220i	−0.521927	+	1.19348i
$59$	47.9566			0.812825			0.406412	−	0.913690i	$-0.366780\pi$
$59$	47.9566			0.812825			0.406412	+	0.913690i	$0.366780\pi$
$60$		0			0
$61$		−	59.0166i		−	0.967485i	−0.875210	−	0.483743i	$-0.839277\pi$
$61$		−	59.0166i		−	0.967485i	0.875210	−	0.483743i	$-0.160723\pi$
$62$	34.2357	−	78.2863i	0.552189	−	1.26268i
$63$	−80.8769			−1.28376
$64$	−50.2414	+	39.6459i	−0.785022	+	0.619467i
$65$		0			0
$66$	−55.9499	+	127.940i	−0.847726	+	1.93848i
$67$			96.3852i			1.43859i	0.694707	+	0.719293i	$0.255534\pi$
$67$			96.3852i			1.43859i	−0.694707	+	0.719293i	$0.744466\pi$
$68$	−10.1376	+	9.37409i	−0.149083	+	0.137854i
$69$			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	$0.906308\pi$
$72$	19.0772	+	54.9718i	0.264961	+	0.763497i
$73$			112.816i			1.54542i	0.634758	+	0.772711i	$0.281100\pi$
$73$			112.816i			1.54542i	−0.634758	+	0.772711i	$0.718900\pi$
$74$	−0.693623	−	0.303332i	−0.00937329	−	0.00409908i
$75$		0			0
$76$	−2.13885	−	2.31306i	−0.0281428	−	0.0304350i
$77$	192.449			2.49934
$78$	−21.6646	+	49.5400i	−0.277751	+	0.635128i
$79$		−	69.7575i		−	0.883006i	−0.897260	−	0.441503i	$-0.854445\pi$
$79$		−	69.7575i		−	0.883006i	0.897260	−	0.441503i	$-0.145555\pi$
$80$		0			0
$81$	−93.5577			−1.15503
$82$	16.3416	+	7.14641i	0.199287	+	0.0871513i
$83$			58.6785i			0.706970i	0.935440	+	0.353485i	$0.115003\pi$
$83$			58.6785i			0.706970i	−0.935440	+	0.353485i	$0.884997\pi$
$84$	131.736	−	121.814i	1.56829	−	1.45017i
$85$		0			0
$86$	−7.38798	+	16.8940i	−0.0859068	+	0.196442i
$87$	−152.389			−1.75160
$88$	−45.3949	−	130.807i	−0.515851	−	1.48645i
$89$	−44.9025			−0.504523			−0.252262	−	0.967659i	$-0.581174\pi$
$89$	−44.9025			−0.504523			−0.252262	+	0.967659i	$0.581174\pi$
$90$		0			0
$91$	74.5190			0.818890
$92$	−103.615	−	112.054i	−1.12625	−	1.21798i
$93$	172.344			1.85316
$94$	57.9107	+	25.3252i	0.616071	+	0.269417i
$95$		0			0
$96$	−113.871	−	60.8072i	−1.18615	−	0.633408i
$97$		−	126.268i		−	1.30173i	−0.759194	−	0.650864i	$-0.774407\pi$
$97$		−	126.268i		−	1.30173i	0.759194	−	0.650864i	$-0.225593\pi$
$98$	−136.775	−	59.8137i	−1.39566	−	0.610344i
$99$	−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	$-0.0643979\pi$
$102$	−25.5166	−	11.1588i	−0.250163	−	0.109400i
$103$	111.422			1.08177			0.540884	−	0.841097i	$-0.318090\pi$
$103$	111.422			1.08177			0.540884	+	0.841097i	$0.318090\pi$
$104$	−17.5775	−	50.6504i	−0.169015	−	0.487023i
$105$		0			0
$106$	43.9674	+	19.2276i	0.414787	+	0.181392i
$107$			28.2816i			0.264314i	0.991229	+	0.132157i	$0.0421904\pi$
$107$			28.2816i			0.264314i	−0.991229	+	0.132157i	$0.957810\pi$
$108$	20.4546	−	18.9141i	0.189395	−	0.175130i
$109$		−	12.2679i		−	0.112549i	−0.998415	−	0.0562746i	$-0.982078\pi$
$109$		−	12.2679i		−	0.112549i	0.998415	−	0.0562746i	$-0.0179222\pi$
$110$		0			0
$111$		−	1.52698i		−	0.0137566i
$112$	−13.9025	+	177.366i	−0.124129	+	1.58363i
$113$		−	73.6529i		−	0.651795i	−0.945405	−	0.325898i	$-0.894334\pi$
$113$		−	73.6529i		−	0.651795i	0.945405	−	0.325898i	$-0.105666\pi$
$114$	2.54606	−	5.82203i	0.0223338	−	0.0510704i
$115$		0			0
$116$	110.942	−	102.587i	0.956400	−	0.884368i
$117$	−48.7449			−0.416623
$118$	−87.8777	−	38.4302i	−0.744726	−	0.325679i
$119$			38.3825i			0.322542i
$120$		0			0
$121$	178.551			1.47563
$122$	−47.2931	+	108.144i	−0.387648	+	0.886429i
$123$			35.9753i			0.292482i
$124$	−125.470	+	116.020i	−1.01185	+	0.935645i
$125$		0			0
$126$	148.202	+	64.8109i	1.17621	+	0.514372i
$127$	−55.8251			−0.439568			−0.219784	−	0.975549i	$-0.570535\pi$
$127$	−55.8251			−0.439568			−0.219784	+	0.975549i	$0.570535\pi$
$128$	123.835	−	32.3876i	0.967459	−	0.253028i
$129$	−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	$0.710638\pi$
$132$	205.050	−	189.606i	1.55341	−	1.43641i
$133$	−8.75761			−0.0658467
$134$	77.2385	−	176.620i	0.576407	−	1.31806i
$135$		0			0
$136$	26.0885	−	9.05365i	0.191827	−	0.0665710i
$137$			93.0774i			0.679397i	0.940534	+	0.339699i	$0.110325\pi$
$137$			93.0774i			0.679397i	−0.940534	+	0.339699i	$0.889675\pi$
$138$	123.341	−	282.043i	0.893778	−	2.04379i
$139$	−98.2327			−0.706710			−0.353355	−	0.935489i	$-0.614959\pi$
$139$	−98.2327			−0.706710			−0.353355	+	0.935489i	$0.614959\pi$
$140$		0			0
$141$			127.488i			0.904171i
$142$	33.0121	−	75.4882i	0.232480	−	0.531607i
$143$	115.990			0.811120
$144$	9.09397	−	116.020i	0.0631526	−	0.805695i
$145$		0			0
$146$	90.4053	−	206.728i	0.619214	−	1.41595i
$147$		−	301.105i		−	2.04833i
$148$	1.02795	+	1.11167i	0.00694559	+	0.00751131i
$149$		−	29.2413i		−	0.196250i	−0.995174	−	0.0981251i	$-0.968715\pi$
$149$		−	29.2413i		−	0.196250i	0.995174	−	0.0981251i	$-0.0312845\pi$
$150$		0			0
$151$			238.075i			1.57666i	0.615254	+	0.788329i	$0.289054\pi$
$151$			238.075i			1.57666i	−0.615254	+	0.788329i	$0.710946\pi$
$152$	2.06574	+	5.95252i	0.0135904	+	0.0391613i
$153$		−	25.1070i		−	0.164098i
$154$	−352.652	−	154.220i	−2.28995	−	1.00143i
$155$		0			0
$156$	79.3980	−	73.4181i	0.508961	−	0.470629i
$157$	−230.982			−1.47122			−0.735612	−	0.677403i	$-0.763105\pi$
$157$	−230.982			−1.47122			−0.735612	+	0.677403i	$0.763105\pi$
$158$	−55.9003	+	127.826i	−0.353799	+	0.809027i
$159$			96.7925i			0.608758i
$160$		0			0
$161$	−424.254			−2.63512
$162$	171.439	+	74.9727i	1.05826	+	0.462795i
$163$			139.882i			0.858175i	0.903263	+	0.429087i	$0.141165\pi$
$163$			139.882i			0.858175i	−0.903263	+	0.429087i	$0.858835\pi$
$164$	−24.2181	−	26.1907i	−0.147672	−	0.159699i
$165$		0			0
$166$	47.0221	−	107.525i	0.283266	−	0.647740i
$167$	259.015			1.55099			0.775495	−	0.631354i	$-0.217500\pi$
$167$	259.015			1.55099			0.775495	+	0.631354i	$0.217500\pi$
$168$	−339.015	+	117.650i	−2.01794	+	0.700299i
$169$	−124.087			−0.734243
$170$		0			0
$171$	5.72859			0.0335005
$172$	27.0761	−	25.0368i	0.157419	−	0.145563i
$173$	−45.2346			−0.261472			−0.130736	−	0.991417i	$-0.541734\pi$
$173$	−45.2346			−0.261472			−0.130736	+	0.991417i	$0.541734\pi$
$174$	279.244	+	122.118i	1.60485	+	0.701826i
$175$		0			0
$176$	−21.6394	+	276.074i	−0.122951	+	1.56860i
$177$		−	193.459i		−	1.09299i
$178$	82.2812	+	35.9828i	0.462254	+	0.202150i
$179$	39.3701			0.219944			0.109972	−	0.993935i	$-0.464924\pi$
$179$	39.3701			0.219944			0.109972	+	0.993935i	$0.464924\pi$
$180$		0			0
$181$			2.81294i			0.0155411i	0.999970	+	0.00777056i	$0.00247347\pi$
$181$			2.81294i			0.0155411i	−0.999970	+	0.00777056i	$0.997527\pi$
$182$	−136.552	−	59.7160i	−0.750283	−	0.328110i
$183$	−238.075			−1.30096
$184$	100.073	+	288.364i	0.543874	+	1.56720i
$185$		0			0
$186$	−315.810	−	138.108i	−1.69790	−	0.742519i
$187$			59.7431i			0.319482i
$188$	−85.8234	−	92.8138i	−0.456508	−	0.493690i
$189$		−	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	$0.980876\pi$
$192$	159.933	+	202.676i	0.832986	+	1.05560i
$193$			152.406i			0.789666i	0.918753	+	0.394833i	$0.129198\pi$
$193$			152.406i			0.789666i	−0.918753	+	0.394833i	$0.870802\pi$
$194$	−101.185	+	231.378i	−0.521572	+	1.19267i
$195$		0			0
$196$	202.700	+	219.210i	1.03418	+	1.11842i
$197$	−43.0232			−0.218392			−0.109196	−	0.994020i	$-0.534828\pi$
$197$	−43.0232			−0.218392			−0.109196	+	0.994020i	$0.534828\pi$
$198$	230.679	+	100.879i	1.16505	+	0.509491i
$199$			57.1240i			0.287055i	0.989646	+	0.143528i	$0.0458446\pi$
$199$			57.1240i			0.287055i	−0.989646	+	0.143528i	$0.954155\pi$
$200$		0			0
$201$	388.822			1.93444
$202$	−32.5259	+	74.3765i	−0.161020	+	0.368201i
$203$		−	420.045i		−	2.06919i
$204$	37.8155	+	40.8955i	0.185370	+	0.200468i
$205$		0			0
$206$	−204.174	−	89.2884i	−0.991137	−	0.433439i
$207$	277.516			1.34066
$208$	−8.37908	+	106.900i	−0.0402841	+	0.513940i
$209$	−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	$0.384897\pi$
$212$	−65.1595	−	70.4668i	−0.307356	−	0.332390i
$213$	166.184			0.780208
$214$	22.6636	−	51.8244i	0.105905	−	0.242170i
$215$		0			0
$216$	−52.6387	+	18.2675i	−0.243698	+	0.0845720i
$217$			475.048i			2.18916i
$218$	−9.83088	+	22.4801i	−0.0450958	+	0.103120i
$219$	455.104			2.07810
$220$		0			0
$221$			23.1333i			0.104676i
$222$	−1.22365	+	2.79811i	−0.00551195	+	0.0126041i
$223$	172.404			0.773112			0.386556	−	0.922266i	$-0.373665\pi$
$223$	172.404			0.773112			0.386556	+	0.922266i	$0.373665\pi$
$224$	167.608	−	313.872i	0.748252	−	1.40122i
$225$		0			0
$226$	−59.0219	+	134.964i	−0.261159	+	0.597188i
$227$			159.295i			0.701738i	0.936425	+	0.350869i	$0.114114\pi$
$227$			159.295i			0.701738i	−0.936425	+	0.350869i	$0.885886\pi$
$228$	−9.33100	+	8.62823i	−0.0409254	+	0.0378431i
$229$		−	249.350i		−	1.08887i	−0.838804	−	0.544433i	$-0.816745\pi$
$229$		−	249.350i		−	1.08887i	0.838804	−	0.544433i	$-0.183255\pi$
$230$		0			0
$231$		−	776.349i		−	3.36082i
$232$	−285.503	+	99.0800i	−1.23062	+	0.427069i
$233$			149.303i			0.640787i	0.947285	+	0.320394i	$0.103815\pi$
$233$			149.303i			0.640787i	−0.947285	+	0.320394i	$0.896185\pi$
$234$	89.3220	+	39.0618i	0.381718	+	0.166931i
$235$		0			0
$236$	130.234	+	140.842i	0.551840	+	0.596788i
$237$	−281.405			−1.18736
$238$	30.7579	−	70.3337i	0.129235	−	0.295520i
$239$			309.119i			1.29338i	0.762751	+	0.646692i	$0.223848\pi$
$239$			309.119i			1.29338i	−0.762751	+	0.646692i	$0.776152\pi$
$240$		0			0
$241$	3.56700			0.0148008			0.00740042	−	0.999973i	$-0.497644\pi$
$241$	3.56700			0.0148008			0.00740042	+	0.999973i	$0.497644\pi$
$242$	−327.183	−	143.082i	−1.35200	−	0.591248i
$243$			314.733i			1.29520i
$244$	173.323	−	160.269i	0.710342	−	0.656842i
$245$		0			0
$246$	28.8289	−	65.9226i	0.117191	−	0.267978i
$247$	−5.27825			−0.0213695
$248$	322.889	−	112.054i	1.30197	−	0.451831i
$249$	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	$0.542635\pi$
$252$	−219.635	−	237.524i	−0.871566	−	0.942555i
$253$	−660.359			−2.61011
$254$	102.296	+	44.7356i	0.402741	+	0.176124i
$255$		0			0
$256$	−252.874	−	39.8869i	−0.987787	−	0.155808i
$257$			115.730i			0.450311i	0.974323	+	0.225156i	$0.0722890\pi$
$257$			115.730i			0.450311i	−0.974323	+	0.225156i	$0.927711\pi$
$258$	68.1510	+	29.8034i	0.264151	+	0.115517i
$259$	4.20897			0.0162508
$260$		0			0
$261$			274.763i			1.05273i
$262$	295.016	+	129.015i	1.12602	+	0.492424i
$263$	207.074			0.787353			0.393677	−	0.919249i	$-0.371203\pi$
$263$	207.074			0.787353			0.393677	+	0.919249i	$0.371203\pi$
$264$	−527.682	+	183.125i	−1.99880	+	0.693654i
$265$		0			0
$266$	16.0478	+	7.01793i	0.0603300	+	0.0263832i
$267$			181.139i			0.678422i
$268$	−283.070	+	261.750i	−1.05623	+	0.976680i
$269$			179.906i			0.668797i	0.942432	+	0.334399i	$0.108533\pi$
$269$			179.906i			0.668797i	−0.942432	+	0.334399i	$0.891467\pi$
$270$		0			0
$271$		−	410.106i		−	1.51331i	−0.653817	−	0.756653i	$-0.726833\pi$
$271$		−	410.106i		−	1.51331i	0.653817	−	0.756653i	$-0.273167\pi$
$272$	−55.0608	−	4.31582i	−0.202429	−	0.0158670i
$273$		−	300.613i		−	1.10115i
$274$	74.5878	−	170.559i	0.272218	−	0.622477i
$275$		0			0
$276$	−452.031	+	417.986i	−1.63779	+	1.51444i
$277$	168.937			0.609883			0.304941	−	0.952371i	$-0.401363\pi$
$277$	168.937			0.609883			0.304941	+	0.952371i	$0.401363\pi$
$278$	180.006	+	78.7190i	0.647502	+	0.283162i
$279$		−	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	$0.231702\pi$
$282$	102.163	−	233.614i	0.362280	−	0.828419i
$283$		−	326.668i		−	1.15430i	−0.816637	−	0.577151i	$-0.804164\pi$
$283$		−	326.668i		−	1.15430i	0.816637	−	0.577151i	$-0.195836\pi$
$284$	−120.985	+	111.873i	−0.426005	+	0.393920i
$285$		0			0
$286$	−212.545	−	92.9490i	−0.743164	−	0.324997i
$287$	−99.1620			−0.345512
$288$	−109.637	+	205.312i	−0.380684	+	0.712890i
$289$	277.085			0.958771
$290$		0			0
$291$	−509.369			−1.75041
$292$	−331.324	+	306.370i	−1.13467	+	1.04921i
$293$	−363.495			−1.24060			−0.620298	−	0.784366i	$-0.712988\pi$
$293$	−363.495			−1.24060			−0.620298	+	0.784366i	$0.712988\pi$
$294$	−241.291	+	551.756i	−0.820718	+	1.87672i
$295$		0			0
$296$	−0.992809	−	2.86082i	−0.00335408	−	0.00966494i
$297$		−	120.544i		−	0.405870i
$298$	−23.4326	+	53.5829i	−0.0786328	+	0.179808i
$299$	−255.700			−0.855183
$300$		0			0
$301$		−	102.514i		−	0.340578i
$302$	190.782	−	436.259i	0.631729	−	1.44457i
$303$	−163.737			−0.540386
$304$	0.984725	−	12.5630i	0.00323923	−	0.0413258i
$305$		0			0
$306$	−20.1196	+	46.0071i	−0.0657503	+	0.150350i
$307$		−	566.800i		−	1.84626i	−0.384494	−	0.923128i	$-0.625624\pi$
$307$		−	566.800i		−	1.84626i	0.384494	−	0.923128i	$-0.374376\pi$
$308$	522.629	+	565.197i	1.69685	+	1.83505i
$309$		−	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	$0.863743\pi$
$312$	−204.326	+	70.9084i	−0.654890	+	0.227271i
$313$		−	24.2700i		−	0.0775400i	−0.999248	−	0.0387700i	$-0.987656\pi$
$313$		−	24.2700i		−	0.0775400i	0.999248	−	0.0387700i	$-0.0123440\pi$
$314$	423.261	+	185.098i	1.34796	+	0.589485i
$315$		0			0
$316$	204.868	−	189.438i	0.648316	−	0.599488i
$317$	398.458			1.25696			0.628482	−	0.777824i	$-0.283677\pi$
$317$	398.458			1.25696			0.628482	+	0.777824i	$0.283677\pi$
$318$	77.5649	−	177.366i	0.243915	−	0.557756i
$319$		−	653.807i		−	2.04955i
$320$		0			0
$321$	114.089			0.355419
$322$	777.419	+	339.977i	2.41435	+	1.05583i
$323$		−	2.71867i		−	0.00841694i
$324$	−254.072	−	274.766i	−0.784172	−	0.848043i
$325$		0			0
$326$	112.095	−	256.326i	0.343850	−	0.786277i
$327$	−49.4890			−0.151343
$328$	23.3903	+	67.4002i	0.0713119	+	0.205488i
$329$	−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	$0.286151\pi$
$332$	−172.330	+	159.351i	−0.519068	+	0.479974i
$333$	−2.75320			−0.00826786
$334$	−474.630	−	207.563i	−1.42105	−	0.621445i
$335$		0			0
$336$	715.503	+	56.0831i	2.12947	+	0.166914i
$337$		−	312.690i		−	0.927863i	−0.885871	−	0.463932i	$-0.846438\pi$
$337$		−	312.690i		−	0.927863i	0.885871	−	0.463932i	$-0.153562\pi$
$338$	227.382	+	99.4374i	0.672728	+	0.294194i
$339$	−297.119			−0.876456
$340$		0			0
$341$			739.420i			2.16839i
$342$	−10.4973	−	4.59062i	−0.0306938	−	0.0134229i
$343$	285.112			0.831230
$344$	−69.6786	+	24.1810i	−0.202554	+	0.0702935i
$345$		0			0
$346$	82.8897	+	36.2489i	0.239566	+	0.104766i
$347$			429.418i			1.23751i	0.785582	+	0.618757i	$0.212364\pi$
$347$			429.418i			1.23751i	−0.785582	+	0.618757i	$0.787636\pi$
$348$	−413.839	−	447.546i	−1.18919	−	1.28605i
$349$			650.147i			1.86288i	0.363890	+	0.931442i	$0.381449\pi$
$349$			650.147i			1.86288i	−0.363890	+	0.931442i	$0.618551\pi$
$350$		0			0
$351$		−	46.6761i		−	0.132980i
$352$	260.885	−	488.548i	0.741152	−	1.38792i
$353$		−	383.224i		−	1.08562i	−0.839856	−	0.542810i	$-0.817360\pi$
$353$		−	383.224i		−	1.08562i	0.839856	−	0.542810i	$-0.182640\pi$
$354$	−155.029	+	354.502i	−0.437935	+	1.00142i
$355$		0			0
$356$	−121.940	−	131.872i	−0.342529	−	0.370428i
$357$	154.837			0.433716
$358$	−72.1433	−	31.5493i	−0.201517	−	0.0881265i
$359$			656.475i			1.82862i	0.405014	+	0.914310i	$0.367267\pi$
$359$			656.475i			1.82862i	−0.405014	+	0.914310i	$0.632733\pi$
$360$		0			0
$361$	−360.380			−0.998282
$362$	2.25416	−	5.15455i	0.00622696	−	0.0142391i
$363$		−	720.281i		−	1.98425i
$364$	202.369	+	218.852i	0.555959	+	0.601241i
$365$		0			0
$366$	436.259	+	190.782i	1.19196	+	0.521263i
$367$	1.05782			0.00288235			0.00144117	−	0.999999i	$-0.499541\pi$
$367$	1.05782			0.00288235			0.00144117	+	0.999999i	$0.499541\pi$
$368$	47.7040	−	608.604i	0.129631	−	1.65381i
$369$	64.8645			0.175785
$370$		0			0
$371$	−266.798			−0.719132
$372$	468.030	+	506.151i	1.25814	+	1.36062i
$373$	−0.816797			−0.00218980			−0.00109490	−	0.999999i	$-0.500349\pi$
$373$	−0.816797			−0.00218980			−0.00109490	+	0.999999i	$0.500349\pi$
$374$	47.8753	−	109.476i	0.128009	−	0.292715i
$375$		0			0
$376$	82.8897	+	238.850i	0.220451	+	0.635241i
$377$		−	253.163i		−	0.671520i
$378$	−62.0602	+	141.912i	−0.164180	+	0.375429i
$379$	630.860			1.66454			0.832269	−	0.554372i	$-0.187041\pi$
$379$	630.860			1.66454			0.832269	+	0.554372i	$0.187041\pi$
$380$		0			0
$381$			225.201i			0.591078i
$382$	18.3799	−	42.0290i	0.0481149	−	0.110024i
$383$	−392.809			−1.02561			−0.512805	−	0.858505i	$-0.671394\pi$
$383$	−392.809			−1.02561			−0.512805	+	0.858505i	$0.671394\pi$
$384$	−130.653	−	499.555i	−0.340242	−	1.30092i
$385$		0			0
$386$	122.131	−	279.274i	0.316400	−	0.723507i
$387$			67.0572i			0.173274i
$388$	370.831	−	342.901i	0.955749	−	0.883766i
$389$		−	292.218i		−	0.751203i	−0.926781	−	0.375602i	$-0.877436\pi$
$389$		−	292.218i		−	0.751203i	0.926781	−	0.375602i	$-0.122564\pi$
$390$		0			0
$391$		−	131.703i		−	0.336837i
$392$	−195.771	−	564.123i	−0.499416	−	1.43909i
$393$			649.467i			1.65259i
$394$	78.8375	+	34.4768i	0.200095	+	0.0875045i
$395$		0			0
$396$	−341.865	−	369.710i	−0.863296	−	0.933612i
$397$	−676.730			−1.70461			−0.852305	−	0.523045i	$-0.824796\pi$
$397$	−676.730			−1.70461			−0.852305	+	0.523045i	$0.824796\pi$
$398$	45.7764	−	104.676i	0.115016	−	0.263006i
$399$			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	$0.421549\pi$
$402$	−712.493	−	311.583i	−1.77237	−	0.775083i
$403$			286.314i			0.710456i
$404$	119.204	−	110.226i	0.295059	−	0.272836i
$405$		0			0
$406$	−336.604	+	769.707i	−0.829074	+	1.89583i
$407$	6.55133			0.0160966
$408$	−36.5228	−	105.242i	−0.0895167	−	0.257946i
$409$	−424.927			−1.03894			−0.519471	−	0.854488i	$-0.673871\pi$
$409$	−424.927			−1.03894			−0.519471	+	0.854488i	$0.673871\pi$
$410$		0			0
$411$	375.478			0.913572
$412$	302.585	+	327.231i	0.734431	+	0.794250i
$413$	533.249			1.29116
$414$	−508.531	−	222.388i	−1.22834	−	0.537169i
$415$		0			0
$416$	101.018	−	189.172i	0.242833	−	0.454741i
$417$			396.275i			0.950300i
$418$	24.9787	+	10.9235i	0.0597576	+	0.0261329i
$419$	−448.621			−1.07069			−0.535347	−	0.844632i	$-0.679819\pi$
$419$	−448.621			−1.07069			−0.535347	+	0.844632i	$0.679819\pi$
$420$		0			0
$421$		−	762.020i		−	1.81002i	−0.425387	−	0.905012i	$-0.639862\pi$
$421$		−	762.020i		−	1.81002i	0.425387	−	0.905012i	$-0.360138\pi$
$422$	−273.572	−	119.637i	−0.648274	−	0.283500i
$423$	229.865			0.543415
$424$	62.9322	+	181.342i	0.148425	+	0.427693i
$425$		0			0
$426$	−304.523	−	133.172i	−0.714842	−	0.312611i
$427$		−	656.229i		−	1.53684i
$428$	−83.0592	+	76.8036i	−0.194064	+	0.179448i
$429$		−	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	$0.961666\pi$
$432$	111.096	+	8.70802i	0.257167	+	0.0201574i
$433$			290.705i			0.671375i	0.941973	+	0.335687i	$0.108969\pi$
$433$			290.705i			0.671375i	−0.941973	+	0.335687i	$0.891031\pi$
$434$	380.681	−	870.497i	0.877145	−	2.00575i
$435$		0			0
$436$	36.0290	−	33.3154i	0.0826353	−	0.0764115i
$437$	30.0503			0.0687650
$438$	−833.950	−	364.699i	−1.90400	−	0.832645i
$439$		−	331.332i		−	0.754742i	−0.926062	−	0.377371i	$-0.876828\pi$
$439$		−	331.332i		−	0.754742i	0.926062	−	0.377371i	$-0.123172\pi$
$440$		0			0
$441$	−542.901			−1.23107
$442$	18.5380	−	42.3904i	0.0419411	−	0.0959060i
$443$			533.782i			1.20493i	0.798147	+	0.602463i	$0.205814\pi$
$443$			533.782i			1.20493i	−0.798147	+	0.602463i	$0.794186\pi$
$444$	4.48454	−	4.14678i	0.0101003	−	0.00933960i
$445$		0			0
$446$	−315.920	−	138.156i	−0.708340	−	0.309768i
$447$	−117.961			−0.263894
$448$	−558.654	+	440.838i	−1.24700	+	0.984015i
$449$	−431.419			−0.960844			−0.480422	−	0.877038i	$-0.659516\pi$
$449$	−431.419			−0.960844			−0.480422	+	0.877038i	$0.659516\pi$
$450$		0			0
$451$	−154.347			−0.342234
$452$	216.308	−	200.017i	0.478558	−	0.442515i
$453$	960.406			2.12010
$454$	127.651	−	291.898i	0.281170	−	0.642946i
$455$		0			0
$456$	24.0127	−	8.33329i	0.0526595	−	0.0182747i
$457$		−	142.066i		−	0.310865i	−0.987846	−	0.155433i	$-0.950323\pi$
$457$		−	142.066i		−	0.310865i	0.987846	−	0.155433i	$-0.0496772\pi$
$458$	−199.817	+	456.919i	−0.436283	+	0.997640i
$459$	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	$-0.222980\pi$
$462$	−622.129	+	1422.61i	−1.34660	+	3.07925i
$463$	594.339			1.28367			0.641835	−	0.766843i	$-0.278173\pi$
$463$	594.339			1.28367			0.641835	+	0.766843i	$0.278173\pi$
$464$	602.566	+	47.2308i	1.29863	+	0.101790i
$465$		0			0
$466$	119.645	−	273.589i	0.256748	−	0.587102i
$467$			305.531i			0.654242i	0.944982	+	0.327121i	$0.106078\pi$
$467$			305.531i			0.654242i	−0.944982	+	0.327121i	$0.893922\pi$
$468$	−132.375	−	143.157i	−0.282852	−	0.305891i
$469$			1071.75i			2.28517i
$470$		0			0
$471$			931.792i			1.97833i
$472$	−125.783	−	362.448i	−0.266488	−	0.767898i
$473$		−	159.565i		−	0.337347i
$474$	515.657	+	225.504i	1.08788	+	0.475747i
$475$		0			0
$476$	−112.724	+	104.234i	−0.236815	+	0.218979i
$477$	174.520			0.365869
$478$	247.713	−	566.441i	0.518228	−	1.18502i
$479$			726.619i			1.51695i	0.651703	+	0.758475i	$0.274055\pi$
$479$			726.619i			1.51695i	−0.651703	+	0.758475i	$0.725945\pi$
$480$		0			0
$481$	2.53676			0.00527394
$482$	−6.53632	−	2.85843i	−0.0135608	−	0.00593035i
$483$			1711.46i			3.54339i
$484$	484.885	+	524.379i	1.00183	+	1.08343i
$485$		0			0
$486$	252.212	−	576.728i	0.518954	−	1.18668i
$487$	331.827			0.681369			0.340685	−	0.940178i	$-0.389341\pi$
$487$	331.827			0.681369			0.340685	+	0.940178i	$0.389341\pi$
$488$	−446.037	+	154.791i	−0.914010	+	0.317195i
$489$	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	$0.355193\pi$
$492$	−105.654	+	97.6970i	−0.214745	+	0.198571i
$493$	130.397			0.264497
$494$	9.67208	+	4.22974i	0.0195791	+	0.00856223i
$495$		0			0
$496$	−681.469	−	53.4155i	−1.37393	−	0.107692i
$497$			458.069i			0.921668i
$498$	−433.759	−	189.689i	−0.871003	−	0.380902i
$499$	−992.291			−1.98856			−0.994279	−	0.106812i	$-0.965936\pi$
$499$	−992.291			−1.98856			−0.994279	+	0.106812i	$0.965936\pi$
$500$		0			0
$501$		−	1044.88i		−	2.08559i
$502$	122.842	+	53.7204i	0.244704	+	0.107013i
$503$	−949.823			−1.88832			−0.944158	−	0.329492i	$-0.893123\pi$
$503$	−949.823			−1.88832			−0.944158	+	0.329492i	$0.893123\pi$
$504$	212.127	+	611.253i	0.420887	+	1.21280i
$505$		0			0
$506$	1210.07	+	529.180i	2.39144	+	1.04581i
$507$			500.572i			0.987322i
$508$	−151.603	−	163.951i	−0.298430	−	0.322737i
$509$		−	283.683i		−	0.557335i	−0.960388	−	0.278667i	$-0.910107\pi$
$509$		−	283.683i		−	0.557335i	0.960388	−	0.278667i	$-0.0898927\pi$
$510$		0			0
$511$			1254.44i			2.45488i
$512$	431.412	+	275.731i	0.842602	+	0.538538i
$513$			5.48546i			0.0106929i
$514$	92.7405	−	212.068i	0.180429	−	0.412584i
$515$		0			0
$516$	−101.000	−	109.226i	−0.195736	−	0.211678i
$517$	−546.971			−1.05797
$518$	−7.71267	−	3.37286i	−0.0148893	−	0.00651132i
$519$			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	$0.697464\pi$
$522$	220.182	−	503.486i	0.421804	−	0.964532i
$523$		−	681.592i		−	1.30324i	−0.758548	−	0.651618i	$-0.774091\pi$
$523$		−	681.592i		−	1.30324i	0.758548	−	0.651618i	$-0.225909\pi$
$524$	−437.213	−	472.824i	−0.834376	−	0.902336i
$525$		0			0
$526$	−379.450	−	165.939i	−0.721388	−	0.315474i
$527$	−147.472			−0.279832
$528$	1113.69	+	87.2944i	2.10927	+	0.165330i
$529$	926.758			1.75190
$530$		0			0
$531$	−348.812			−0.656897
$532$	−23.7828	−	25.7199i	−0.0447044	−	0.0483456i
$533$	−59.7654			−0.112130
$534$	145.156	−	331.926i	0.271828	−	0.621584i
$535$		0			0
$536$	728.463	−	252.803i	1.35907	−	0.471647i
$537$		−	158.820i		−	0.295755i
$538$	144.169	−	329.668i	0.267971	−	0.612765i
$539$	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	$0.927533\pi$
$542$	−328.639	+	751.494i	−0.606346	+	1.38652i
$543$	11.3475			0.0208979
$544$	97.4371	+	52.0316i	0.179112	+	0.0956463i
$545$		0			0
$546$	−240.897	+	550.855i	−0.441203	+	1.00889i
$547$		−	377.177i		−	0.689538i	−0.938688	−	0.344769i	$-0.887957\pi$
$547$		−	377.177i		−	0.689538i	0.938688	−	0.344769i	$-0.112043\pi$
$548$	−273.355	+	252.767i	−0.498824	+	0.461254i
$549$			429.257i			0.781888i
$550$		0			0
$551$			29.7522i			0.0539967i
$552$	1163.27	−	403.698i	2.10738	−	0.731337i
$553$		−	775.661i		−	1.40264i
$554$	−309.568	−	135.378i	−0.558786	−	0.244365i
$555$		0			0
$556$	−266.768	−	288.496i	−0.479798	−	0.518877i
$557$	729.906			1.31042			0.655212	−	0.755445i	$-0.272579\pi$
$557$	729.906			1.31042			0.655212	+	0.755445i	$0.272579\pi$
$558$	−249.013	+	569.415i	−0.446261	+	1.02046i
$559$		−	61.7858i		−	0.110529i
$560$		0			0
$561$	241.006			0.429601
$562$	−768.834	−	336.222i	−1.36803	−	0.598261i
$563$			93.4375i			0.165964i	0.996551	+	0.0829818i	$0.0264443\pi$
$563$			93.4375i			0.165964i	−0.996551	+	0.0829818i	$0.973556\pi$
$564$	−374.415	+	346.215i	−0.663856	+	0.613857i
$565$		0			0
$566$	−261.776	+	598.599i	−0.462502	+	1.05760i
$567$	−1040.31			−1.83475
$568$	311.348	−	108.049i	0.548148	−	0.190227i
$569$	152.601			0.268191			0.134096	−	0.990968i	$-0.457187\pi$
$569$	152.601			0.268191			0.134096	+	0.990968i	$0.457187\pi$
$570$		0			0
$571$	−197.023			−0.345049			−0.172524	−	0.985005i	$-0.555192\pi$
$571$	−197.023			−0.345049			−0.172524	+	0.985005i	$0.555192\pi$
$572$	314.991	+	340.647i	0.550683	+	0.595536i
$573$	92.5252			0.161475
$574$	181.708	+	79.4637i	0.316565	+	0.138439i
$575$		0			0
$576$	365.431	−	288.364i	0.634428	−	0.500632i
$577$		−	105.556i		−	0.182939i	−0.995808	−	0.0914693i	$-0.970844\pi$
$577$		−	105.556i		−	0.182939i	0.995808	−	0.0914693i	$-0.0291563\pi$
$578$	−507.741	−	222.043i	−0.878445	−	0.384157i
$579$	614.810			1.06185
$580$		0			0
$581$			652.469i			1.12301i
$582$	933.388	+	408.184i	1.60376	+	0.701348i
$583$	−415.276			−0.712308
$584$	852.642	−	295.898i	1.46000	−	0.506674i
$585$		0			0
$586$	666.082	+	291.287i	1.13666	+	0.497077i
$587$		−	140.879i		−	0.239998i	−0.992774	−	0.119999i	$-0.961711\pi$
$587$		−	140.879i		−	0.239998i	0.992774	−	0.119999i	$-0.0382892\pi$
$588$	884.302	−	817.701i	1.50392	−	1.39065i
$589$		−	33.6481i		−	0.0571275i
$590$		0			0
$591$			173.558i			0.293668i
$592$	−0.473265	+	6.03787i	−0.000799435	+	0.0101991i
$593$			830.224i			1.40004i	0.714123	+	0.700020i	$0.246826\pi$
$593$			830.224i			1.40004i	−0.714123	+	0.700020i	$0.753174\pi$
$594$	−96.5978	+	220.889i	−0.162623	+	0.371866i
$595$		0			0
$596$	85.8775	−	79.4096i	0.144090	−	0.133238i
$597$	230.440			0.385997
$598$	468.554	+	204.906i	0.783536	+	0.342652i
$599$		−	708.746i		−	1.18321i	−0.806226	−	0.591607i	$-0.798494\pi$
$599$		−	708.746i		−	1.18321i	0.806226	−	0.591607i	$-0.201506\pi$
$600$		0			0
$601$	−877.605			−1.46024			−0.730120	−	0.683319i	$-0.760536\pi$
$601$	−877.605			−1.46024			−0.730120	+	0.683319i	$0.760536\pi$
$602$	−82.1499	+	187.851i	−0.136462	+	0.312045i
$603$		−	701.057i		−	1.16262i
$604$	−699.194	+	646.534i	−1.15761	+	1.07042i
$605$		0			0
$606$	300.038	+	131.211i	0.495112	+	0.216520i
$607$	177.574			0.292543			0.146271	−	0.989244i	$-0.453273\pi$
$607$	177.574			0.292543			0.146271	+	0.989244i	$0.453273\pi$
$608$	−11.8719	+	22.2319i	−0.0195261	+	0.0365656i
$609$	−1694.48			−2.78239
$610$		0			0
$611$	−211.795			−0.346636
$612$	73.7358	−	68.1824i	0.120483	−	0.111409i
$613$	−332.413			−0.542272			−0.271136	−	0.962541i	$-0.587399\pi$
$613$	−332.413			−0.542272			−0.271136	+	0.962541i	$0.587399\pi$
$614$	−454.207	+	1038.63i	−0.739751	+	1.69158i
$615$		0			0
$616$	−504.763	−	1454.50i	−0.819421	−	2.36120i
$617$		−	726.357i		−	1.17724i	−0.808410	−	0.588620i	$-0.799671\pi$
$617$		−	726.357i		−	1.17724i	0.808410	−	0.588620i	$-0.200329\pi$
$618$	−360.193	+	823.647i	−0.582837	+	1.33276i
$619$	−944.637			−1.52607			−0.763035	−	0.646358i	$-0.776291\pi$
$619$	−944.637			−1.52607			−0.763035	+	0.646358i	$0.776291\pi$
$620$		0			0
$621$			265.738i			0.427919i
$622$	206.908	−	473.133i	0.332650	−	0.760664i
$623$	−499.289			−0.801427
$624$	431.237	+	33.8016i	0.691085	+	0.0541692i
$625$		0			0
$626$	−19.4488	+	44.4733i	−0.0310684	+	0.0710437i
$627$			54.9895i			0.0877026i
$628$	−627.271	−	678.362i	−0.998840	−	1.08020i
$629$			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	$-0.0956621\pi$
$632$	−527.215	+	182.963i	−0.834200	+	0.289498i
$633$		−	602.257i		−	0.951432i
$634$	−730.149	−	319.305i	−1.15166	−	0.503636i
$635$		0			0
$636$	−284.266	+	262.856i	−0.446959	+	0.413296i
$637$	500.222			0.785279
$638$	−523.930	+	1198.06i	−0.821207	+	1.87784i
$639$		−	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	$0.445590\pi$
$642$	−209.062	−	91.4258i	−0.325641	−	0.142408i
$643$		−	180.700i		−	0.281027i	−0.990079	−	0.140513i	$-0.955125\pi$
$643$		−	180.700i		−	0.281027i	0.990079	−	0.140513i	$-0.0448753\pi$
$644$	−1152.13	−	1245.97i	−1.78903	−	1.93474i
$645$		0			0
$646$	−2.17861	+	4.98180i	−0.00337247	+	0.00771177i
$647$	−286.652			−0.443048			−0.221524	−	0.975155i	$-0.571103\pi$
$647$	−286.652			−0.443048			−0.221524	+	0.975155i	$0.571103\pi$
$648$	245.387	+	707.093i	0.378683	+	1.09119i
$649$	830.011			1.27891
$650$		0			0
$651$	1916.36			2.94372
$652$	−410.815	+	379.874i	−0.630085	+	0.582630i
$653$	863.087			1.32173			0.660863	−	0.750506i	$-0.270190\pi$
$653$	863.087			1.32173			0.660863	+	0.750506i	$0.270190\pi$
$654$	90.6857	+	39.6582i	0.138663	+	0.0606394i
$655$		0			0
$656$	11.1500	−	142.251i	0.0169969	−	0.216845i
$657$		−	820.565i		−	1.24896i
$658$	643.932	+	281.601i	0.978620	+	0.427965i
$659$	−1119.80			−1.69924			−0.849618	−	0.527398i	$-0.823168\pi$
$659$	−1119.80			−1.69924			−0.849618	+	0.527398i	$0.823168\pi$
$660$		0			0
$661$		−	805.904i		−	1.21922i	−0.792702	−	0.609609i	$-0.791326\pi$
$661$		−	805.904i		−	1.21922i	0.792702	−	0.609609i	$-0.208674\pi$
$662$	−755.039	−	330.189i	−1.14054	−	0.498776i
$663$	93.3209			0.140755
$664$	443.482	−	153.904i	0.667894	−	0.231783i
$665$		0			0
$666$	5.04507	+	2.20628i	0.00757517	+	0.00331273i
$667$			1441.32i			2.16089i
$668$	703.400	+	760.692i	1.05299	+	1.13876i
$669$		−	695.485i		−	1.03959i
$670$		0			0
$671$		−	1021.43i		−	1.52225i
$672$	−1266.17	−	676.139i	−1.88419	−	1.00616i
$673$			531.504i			0.789753i	0.918734	+	0.394876i	$0.129213\pi$
$673$			531.504i			0.789753i	−0.918734	+	0.394876i	$0.870787\pi$
$674$	−250.575	+	572.985i	−0.371773	+	0.850127i
$675$		0			0
$676$	−336.979	−	364.426i	−0.498490	−	0.539092i
$677$	520.567			0.768931			0.384466	−	0.923139i	$-0.374386\pi$
$677$	520.567			0.768931			0.384466	+	0.923139i	$0.374386\pi$
$678$	544.452	+	238.097i	0.803027	+	0.351175i
$679$		−	1404.02i		−	2.06778i
$680$		0			0
$681$	642.601			0.943613
$682$	592.536	−	1354.94i	0.868822	−	1.98672i
$683$		−	870.065i		−	1.27389i	−0.770910	−	0.636944i	$-0.780198\pi$
$683$		−	870.065i		−	1.27389i	0.770910	−	0.636944i	$-0.219802\pi$
$684$	15.5569	+	16.8241i	0.0227441	+	0.0245966i
$685$		0			0
$686$	−522.450	−	228.475i	−0.761590	−	0.333054i
$687$	−1005.89			−1.46418
$688$	147.059	+	11.5269i	0.213749	+	0.0167542i
$689$	−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	$0.672607\pi$
$692$	−122.842	−	132.848i	−0.177518	−	0.191977i
$693$	−1399.78			−2.01988
$694$	344.115	−	786.882i	0.495843	−	1.13384i
$695$		0			0
$696$	399.693	+	1151.73i	0.574271	+	1.65479i
$697$		−	30.7834i		−	0.0441656i
$698$	520.997	−	1191.35i	0.746413	−	1.70681i
$699$	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	$-0.253468\pi$
$702$	−37.4040	+	85.5311i	−0.0532821	+	0.121839i
$703$	−0.298125			−0.000424076
$704$	−869.555	+	686.173i	−1.23516	+	0.974677i
$705$		0			0
$706$	−307.097	+	702.234i	−0.434982	+	0.994666i
$707$		−	451.323i		−	0.638364i
$708$	568.162	−	525.371i	0.802489	−	0.742049i
$709$			1003.90i			1.41594i	0.706241	+	0.707971i	$0.250389\pi$
$709$			1003.90i			1.41594i	−0.706241	+	0.707971i	$0.749611\pi$
$710$		0			0
$711$			507.380i			0.713615i
$712$	117.772	+	339.366i	0.165410	+	0.476637i
$713$		−	1630.05i		−	2.28618i
$714$	−283.729	−	124.079i	−0.397379	−	0.173780i
$715$		0			0
$716$	106.916	+	115.624i	0.149324	+	0.161487i
$717$	1247.00			1.73919
$718$	526.068	−	1202.95i	0.732685	−	1.67542i
$719$		−	1207.30i		−	1.67914i	−0.543252	−	0.839569i	$-0.682807\pi$
$719$		−	1207.30i		−	1.67914i	0.543252	−	0.839569i	$-0.317193\pi$
$720$		0			0
$721$	1238.95			1.71837
$722$	660.374	+	288.791i	0.914645	+	0.399988i
$723$		−	14.3894i		−	0.0199024i
$724$	−8.26122	+	7.63902i	−0.0114105	+	0.0105511i
$725$		0			0
$726$	−577.199	+	1319.87i	−0.795040	+	1.81801i
$727$	587.117			0.807588			0.403794	−	0.914850i	$-0.367691\pi$
$727$	587.117			0.807588			0.403794	+	0.914850i	$0.367691\pi$
$728$	−195.451	−	563.202i	−0.268477	−	0.773629i
$729$	427.625			0.586591
$730$		0			0
$731$	31.8240			0.0435349
$732$	−646.534	−	699.194i	−0.883243	−	0.955183i
$733$	434.408			0.592644			0.296322	−	0.955088i	$-0.404240\pi$
$733$	434.408			0.592644			0.296322	+	0.955088i	$0.404240\pi$
$734$	−1.93839	−	0.847688i	−0.00264086	−	0.00115489i
$735$		0			0
$736$	−575.121	+	1077.00i	−0.781414	+	1.46332i
$737$			1668.19i			2.26349i
$738$	−118.860	−	51.9793i	−0.161057	−	0.0704327i
$739$	310.341			0.419948			0.209974	−	0.977707i	$-0.432662\pi$
$739$	310.341			0.419948			0.209974	+	0.977707i	$0.432662\pi$
$740$		0			0
$741$			21.2927i			0.0287351i
$742$	488.891	+	213.799i	0.658883	+	0.288139i
$743$	610.976			0.822310			0.411155	−	0.911566i	$-0.365126\pi$
$743$	610.976			0.822310			0.411155	+	0.911566i	$0.365126\pi$
$744$	−452.031	−	1302.55i	−0.607568	−	1.75074i
$745$		0			0
$746$	1.49673	+	0.654542i	0.00200634	+	0.000877402i
$747$		−	426.798i		−	0.571349i
$748$	−175.457	+	162.242i	−0.234568	+	0.216902i
$749$			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	$-0.135976\pi$
$752$	39.5130	−	504.103i	0.0525439	−	0.670350i
$753$			270.431i			0.359138i
$754$	−202.873	+	463.906i	−0.269062	+	0.615260i
$755$		0			0
$756$	227.443	−	210.313i	0.300851	−	0.278192i
$757$	−796.999			−1.05284			−0.526419	−	0.850225i	$-0.676466\pi$
$757$	−796.999			−1.05284			−0.526419	+	0.850225i	$0.676466\pi$
$758$	−1156.01	−	505.541i	−1.52508	−	0.666941i
$759$			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	$0.472834\pi$
$762$	180.465	−	412.667i	0.236831	−	0.541558i
$763$		−	136.411i		−	0.178783i
$764$	−67.3601	+	62.2868i	−0.0881677	+	0.0815273i
$765$		0			0
$766$	719.798	+	314.778i	0.939684	+	0.410938i
$767$	321.392			0.419024
$768$	−160.906	+	1020.10i	−0.209512	+	1.32826i
$769$	814.433			1.05908			0.529540	−	0.848285i	$-0.322364\pi$
$769$	814.433			1.05908			0.529540	+	0.848285i	$0.322364\pi$
$770$		0			0
$771$	466.860			0.605525
$772$	−447.594	+	413.883i	−0.579784	+	0.536118i
$773$	−650.087			−0.840992			−0.420496	−	0.907294i	$-0.638144\pi$
$773$	−650.087			−0.840992			−0.420496	+	0.907294i	$0.638144\pi$
$774$	53.7365	−	122.878i	0.0694270	−	0.158757i
$775$		0			0
$776$	−954.309	+	331.180i	−1.22978	+	0.426778i
$777$		−	16.9791i		−	0.0218522i
$778$	−234.170	+	535.472i	−0.300989	+	0.688267i
$779$	7.02374			0.00901636
$780$		0			0
$781$			712.992i			0.912922i
$782$	−105.541	+	241.338i	−0.134963	+	0.308617i
$783$	−263.101			−0.336017
$784$	−93.3228	+	1190.60i	−0.119034	+	1.51863i
$785$		0			0
$786$	520.452	−	1190.11i	0.662152	−	1.51413i
$787$			20.6114i			0.0261898i	0.999914	+	0.0130949i	$0.00416835\pi$
$787$			20.6114i			0.0261898i	−0.999914	+	0.0130949i	$0.995832\pi$
$788$	−116.837	−	126.353i	−0.148270	−	0.160347i
$789$		−	835.345i		−	1.05874i
$790$		0			0
$791$		−	818.975i		−	1.03537i
$792$	330.179	+	951.426i	0.416893	+	1.20130i
$793$		−	395.512i		−	0.498754i
$794$	1240.07	+	542.300i	1.56180	+	0.682997i
$795$		0			0
$796$	−167.765	+	155.130i	−0.210760	+	0.194887i
$797$	−805.629			−1.01083			−0.505413	−	0.862877i	$-0.668660\pi$
$797$	−805.629			−1.01083			−0.505413	+	0.862877i	$0.668660\pi$
$798$	28.3106	−	64.7375i	0.0354770	−	0.0811246i
$799$		−	109.089i		−	0.136532i
$800$		0			0
$801$	326.598			0.407738
$802$	−358.546	−	156.797i	−0.447065	−	0.195508i
$803$			1952.56i			2.43159i
$804$	1055.91	+	1141.92i	1.31332	+	1.42029i
$805$		0			0
$806$	229.438	−	524.653i	0.284663	−	0.650934i
$807$	725.750			0.899319
$808$	−306.763	+	106.458i	−0.379657	+	0.131755i
$809$	292.924			0.362081			0.181041	−	0.983476i	$-0.442053\pi$
$809$	292.924			0.362081			0.181041	+	0.983476i	$0.442053\pi$
$810$		0			0
$811$	−827.255			−1.02004			−0.510021	−	0.860162i	$-0.670363\pi$
$811$	−827.255			−1.02004			−0.510021	+	0.860162i	$0.670363\pi$
$812$	1233.61	−	1140.70i	1.51923	−	1.40481i
$813$	−1654.38			−2.03491
$814$	−12.0049	−	5.24992i	−0.0147481	−	0.00644954i
$815$		0			0
$816$	−17.4102	+	222.117i	−0.0213360	+	0.272203i
$817$			7.26117i			0.00888761i
$818$	778.653	+	340.516i	0.951898	+	0.416279i
$819$	−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	$0.737619\pi$
$822$	−688.041	−	300.890i	−0.837033	−	0.366047i
$823$	667.377			0.810908			0.405454	−	0.914116i	$-0.367114\pi$
$823$	667.377			0.810908			0.405454	+	0.914116i	$0.367114\pi$
$824$	−292.242	−	842.109i	−0.354663	−	1.02198i
$825$		0			0
$826$	−977.146	−	427.320i	−1.18299	−	0.517337i
$827$			513.257i			0.620625i	0.950635	+	0.310313i	$0.100434\pi$
$827$			513.257i			0.620625i	−0.950635	+	0.310313i	$0.899566\pi$
$828$	753.641	+	815.025i	0.910194	+	0.984329i
$829$		−	749.848i		−	0.904521i	−0.891886	−	0.452260i	$-0.850618\pi$
$829$		−	749.848i		−	0.904521i	0.891886	−	0.452260i	$-0.149382\pi$
$830$		0			0
$831$		−	681.501i		−	0.820097i
$832$	−336.704	+	265.696i	−0.404692	+	0.319346i
$833$			257.650i			0.309303i
$834$	317.556	−	726.150i	0.380762	−	0.870683i
$835$		0			0
$836$	−37.0183	−	40.0334i	−0.0442803	−	0.0478869i
$837$	297.553			0.355500
$838$	822.070	+	359.503i	0.980991	+	0.429002i
$839$		−	48.2988i		−	0.0575672i	−0.999586	−	0.0287836i	$-0.990837\pi$
$839$		−	48.2988i		−	0.0575672i	0.999586	−	0.0287836i	$-0.00916336\pi$
$840$		0			0
$841$	−586.016			−0.696809
$842$	−610.646	+	1396.36i	−0.725233	+	1.65838i
$843$		−	1692.56i		−	2.00778i
$844$	405.432	+	438.454i	0.480370	+	0.519496i
$845$		0			0
$846$	−421.213	−	184.203i	−0.497888	−	0.217734i
$847$	1985.38			2.34401
$848$	29.9993	−	382.729i	0.0353766	−	0.451331i
$849$	−1317.79			−1.55217
$850$		0			0
$851$	−14.4424			−0.0169711
$852$	451.301	+	488.060i	0.529696	+	0.572840i
$853$	925.590			1.08510			0.542550	−	0.840023i	$-0.317459\pi$
$853$	925.590			1.08510			0.542550	+	0.840023i	$0.317459\pi$
$854$	−525.871	+	1202.50i	−0.615773	+	1.40808i
$855$		0			0
$856$	213.748	−	74.1782i	0.249705	−	0.0866567i
$857$		−	23.8375i		−	0.0278151i	−0.999903	−	0.0139076i	$-0.995573\pi$
$857$		−	23.8375i		−	0.0278151i	0.999903	−	0.0139076i	$-0.00442705\pi$
$858$	−374.960	+	857.415i	−0.437017	+	0.999318i
$859$	1227.62			1.42913			0.714563	−	0.699571i	$-0.246626\pi$
$859$	1227.62			1.42913			0.714563	+	0.699571i	$0.246626\pi$
$860$		0			0
$861$			400.024i			0.464604i
$862$	82.9873	−	189.766i	0.0962730	−	0.220146i
$863$	−698.456			−0.809335			−0.404667	−	0.914464i	$-0.632613\pi$
$863$	−698.456			−0.809335			−0.404667	+	0.914464i	$0.632613\pi$
$864$	−196.599	−	104.984i	−0.227545	−	0.121509i
$865$		0			0
$866$	232.957	−	532.700i	0.269004	−	0.615127i
$867$		−	1117.77i		−	1.28924i
$868$	−1395.15	+	1290.07i	−1.60731	+	1.48626i
$869$		−	1207.33i		−	1.38933i
$870$		0			0
$871$			645.946i			0.741614i
$872$	−92.7183	+	32.1766i	−0.106328	+	0.0368998i
$873$			918.407i			1.05201i
$874$	−55.0654	−	24.0809i	−0.0630039	−	0.0275525i
$875$		0			0
$876$	1235.91	+	1336.58i	1.41086	+	1.52577i
$877$	−1098.23			−1.25225			−0.626126	−	0.779722i	$-0.715360\pi$
$877$	−1098.23			−1.25225			−0.626126	+	0.779722i	$0.715360\pi$
$878$	−265.514	+	607.145i	−0.302407	+	0.691510i
$879$			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	$0.420508\pi$
$882$	994.832	+	435.055i	1.12793	+	0.493259i
$883$			146.771i			0.166219i	0.996540	+	0.0831094i	$0.0264851\pi$
$883$			146.771i			0.166219i	−0.996540	+	0.0831094i	$0.973515\pi$
$884$	−67.9394	+	62.8225i	−0.0768545	+	0.0710662i
$885$		0			0
$886$	427.748	−	978.123i	0.482785	−	1.10398i
$887$	−95.2031			−0.107332			−0.0536658	−	0.998559i	$-0.517091\pi$
$887$	−95.2031			−0.107332			−0.0536658	+	0.998559i	$0.517091\pi$
$888$	−11.5407	+	4.00503i	−0.0129963	+	0.00451017i
$889$	−620.742			−0.698247
$890$		0			0
$891$	−1619.25			−1.81734
$892$	468.192	+	506.326i	0.524879	+	0.567630i
$893$	24.8905			0.0278729
$894$	216.156	+	94.5280i	0.241785	+	0.105736i
$895$		0			0
$896$	1376.97	−	360.131i	1.53679	−	0.401932i
$897$			1031.50i			1.14995i
$898$	790.549	+	345.718i	0.880344	+	0.384987i
$899$	1613.88			1.79519
$900$		0			0
$901$		−	82.8235i		−	0.0919240i
$902$	282.832	+	123.687i	0.313561	+	0.137125i
$903$	−413.546			−0.457969
$904$	−556.655	+	193.180i	−0.615769	+	0.213694i
$905$		0			0
$906$	−1759.89	−	769.624i	−1.94248	−	0.849474i
$907$		−	496.182i		−	0.547058i	−0.961864	−	0.273529i	$-0.911809\pi$
$907$		−	496.182i		−	0.547058i	0.961864	−	0.273529i	$-0.0881909\pi$
$908$	−467.826	+	432.591i	−0.515226	+	0.476422i
$909$			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	$0.712355\pi$
$912$	−50.6798	−	3.97242i	−0.0555699	−	0.00435573i
$913$			1015.58i			1.11235i
$914$	−113.845	+	260.326i	−0.124556	+	0.284821i
$915$		0			0
$916$	732.307	−	677.153i	0.799462	−	0.739250i
$917$	−1790.18			−1.95222
$918$	−44.0545	−	19.2657i	−0.0479897	−	0.0209866i
$919$		−	496.178i		−	0.539911i	−0.962873	−	0.269955i	$-0.912991\pi$
$919$		−	496.178i		−	0.539911i	0.962873	−	0.269955i	$-0.0870090\pi$
$920$		0			0
$921$	−2286.50			−2.48262
$922$	−476.267	+	1089.07i	−0.516559	+	1.18121i
$923$			276.080i			0.299112i
$924$	2280.03	−	2108.31i	2.46756	−	2.28172i
$925$		0			0
$926$	−1089.09	−	476.275i	−1.17612	−	0.514336i
$927$	−810.428			−0.874248
$928$	−1066.32	−	569.415i	−1.14905	−	0.613594i
$929$	832.634			0.896269			0.448135	−	0.893966i	$-0.352089\pi$
$929$	832.634			0.896269			0.448135	+	0.893966i	$0.352089\pi$
$930$		0			0
$931$	−58.7870			−0.0631440
$932$	−438.483	+	405.459i	−0.470476	+	0.435041i
$933$	1041.58			1.11638
$934$	244.838	−	559.867i	0.262139	−	0.599429i
$935$		0			0
$936$	127.850	+	368.405i	0.136592	+	0.393595i
$937$		−	146.334i		−	0.156173i	−0.996947	−	0.0780865i	$-0.975119\pi$
$937$		−	146.334i		−	0.156173i	0.996947	−	0.0780865i	$-0.0248810\pi$
$938$	858.846	−	1963.91i	0.915614	−	2.09372i
$939$	−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	$0.883623\pi$
$942$	746.694	−	1707.45i	0.792669	−	1.81258i
$943$	340.258			0.360825
$944$	−59.9597	+	764.960i	−0.0635166	+	0.810339i
$945$		0			0
$946$	−127.868	+	292.393i	−0.135167	+	0.309084i
$947$		−	445.927i		−	0.470883i	−0.971888	−	0.235442i	$-0.924346\pi$
$947$		−	445.927i		−	0.470883i	0.971888	−	0.235442i	$-0.0756537\pi$
$948$	−764.201	−	826.446i	−0.806120	−	0.871778i
$949$			756.060i			0.796691i
$950$		0			0
$951$		−	1607.39i		−	1.69022i
$952$	290.088	−	100.671i	0.304715	−	0.105747i
$953$			1490.29i			1.56379i	0.623411	+	0.781894i	$0.285746\pi$
$953$			1490.29i			1.56379i	−0.623411	+	0.781894i	$0.714254\pi$
$954$	−319.797	−	139.852i	−0.335217	−	0.146595i
$955$		0			0
$956$	−907.839	+	839.464i	−0.949622	+	0.878101i
$957$	−2637.49			−2.75599
$958$	582.278	−	1331.48i	0.607805	−	1.38986i
$959$			1034.96i			1.07921i
$960$		0			0
$961$	−864.209			−0.899281
$962$	−4.64847	−	2.03284i	−0.00483209	−	0.00211314i
$963$		−	205.706i		−	0.213610i
$964$	9.68680	+	10.4758i	0.0100485	+	0.0108670i
$965$		0			0
$966$	1371.48	−	3136.14i	1.41975	−	3.24652i
$967$	−165.170			−0.170807			−0.0854034	−	0.996346i	$-0.527218\pi$
$967$	−165.170			−0.170807			−0.0854034	+	0.996346i	$0.527218\pi$
$968$	−468.310	−	1349.46i	−0.483791	−	1.39407i
$969$	−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	$0.276795\pi$
$972$	−924.326	+	854.709i	−0.950952	+	0.879331i
$973$	−1092.29			−1.12260
$974$	−608.052	−	265.910i	−0.624284	−	0.273008i
$975$		0			0
$976$	941.378	+	73.7878i	0.964527	+	0.0756023i
$977$		−	1446.44i		−	1.48049i	−0.672336	−	0.740246i	$-0.734709\pi$
$977$		−	1446.44i		−	1.48049i	0.672336	−	0.740246i	$-0.265291\pi$
$978$	−1034.03	−	452.197i	−1.05729	−	0.462369i
$979$	−777.152			−0.793823
$980$		0			0
$981$			89.2302i			0.0909584i
$982$	−790.671	−	345.772i	−0.805164	−	0.352110i
$983$	762.431			0.775617			0.387808	−	0.921740i	$-0.373232\pi$
$983$	762.431			0.775617			0.387808	+	0.921740i	$0.373232\pi$
$984$	271.895	−	94.3574i	0.276316	−	0.0958917i
$985$		0			0
$986$	−238.944	−	104.494i	−0.242337	−	0.105977i
$987$			1417.59i			1.43626i
$988$	−14.3340	−	15.5015i	−0.0145081	−	0.0156898i
$989$			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	$0.969154\pi$
$992$	1205.95	+	643.978i	1.21567	+	0.649171i
$993$		−	1662.19i		−	1.67390i
$994$	367.075	−	839.383i	0.369290	−	0.844450i
$995$		0			0
$996$	642.830	+	695.188i	0.645411	+	0.697980i
$997$	409.797			0.411030			0.205515	−	0.978654i	$-0.434113\pi$
$997$	409.797			0.411030			0.205515	+	0.978654i	$0.434113\pi$
$998$	1818.31	+	795.175i	1.82196	+	0.796768i
$999$		−	2.63635i		−	0.00263899i

Twists

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

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

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.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.83244 - 0.801352i) q^{2} -4.03404i q^{3} +(2.71567 + 2.93686i) q^{4} +(-3.23269 + 7.39214i) q^{6} +11.1194 q^{7} +(-2.62284 - 7.55783i) q^{8} -7.27349 q^{9} +17.3075 q^{11} +(11.8474 - 10.9551i) q^{12} +6.70171 q^{13} +(-20.3756 - 8.91056i) q^{14} +(-1.25029 + 15.9511i) q^{16} +3.45185i q^{17} +(13.3282 + 5.82863i) q^{18} -0.787598 q^{19} -44.8561i q^{21} +(-31.7150 - 13.8694i) q^{22} -38.1544 q^{23} +(-30.4886 + 10.5806i) q^{24} +(-12.2805 - 5.37044i) q^{26} -6.96480i q^{27} +(30.1966 + 32.6561i) q^{28} -37.7759i q^{29} +42.7225i q^{31} +(15.0735 - 28.2275i) q^{32} -69.8193i q^{33} +(2.76615 - 6.32531i) q^{34} +(-19.7524 - 21.3612i) q^{36} +0.378525 q^{37} +(1.44322 + 0.631143i) q^{38} -27.0350i q^{39} -8.91793 q^{41} +(-35.9456 + 82.1961i) q^{42} -9.21939i q^{43} +(47.0015 + 50.8298i) q^{44} +(69.9156 + 30.5751i) q^{46} -31.6031 q^{47} +(64.3473 + 5.04372i) q^{48} +74.6410 q^{49} +13.9249 q^{51} +(18.1996 + 19.6820i) q^{52} -23.9939 q^{53} +(-5.58126 + 12.7626i) q^{54} +(-29.1644 - 84.0384i) q^{56} +3.17720i q^{57} +(-30.2718 + 69.2220i) q^{58} +47.9566 q^{59} -59.0166i q^{61} +(34.2357 - 78.2863i) q^{62} -80.8769 q^{63} +(-50.2414 + 39.6459i) q^{64} +(-55.9499 + 127.940i) q^{66} +96.3852i q^{67} +(-10.1376 + 9.37409i) q^{68} +153.916i q^{69} +41.1955i q^{71} +(19.0772 + 54.9718i) q^{72} +112.816i q^{73} +(-0.693623 - 0.303332i) q^{74} +(-2.13885 - 2.31306i) q^{76} +192.449 q^{77} +(-21.6646 + 49.5400i) q^{78} -69.7575i q^{79} -93.5577 q^{81} +(16.3416 + 7.14641i) q^{82} +58.6785i q^{83} +(131.736 - 121.814i) q^{84} +(-7.38798 + 16.8940i) q^{86} -152.389 q^{87} +(-45.3949 - 130.807i) q^{88} -44.9025 q^{89} +74.5190 q^{91} +(-103.615 - 112.054i) q^{92} +172.344 q^{93} +(57.9107 + 25.3252i) q^{94} +(-113.871 - 60.8072i) q^{96} -126.268i q^{97} +(-136.775 - 59.8137i) q^{98} -125.886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 14 q^{4} + 2 q^{6} + 16 q^{9} + 60 q^{11} - 8 q^{14} - 78 q^{16} + 4 q^{19} - 118 q^{24} - 72 q^{26} - 178 q^{34} - 16 q^{36} - 140 q^{41} + 154 q^{44} + 368 q^{46} + 276 q^{49} + 228 q^{51} + 138 q^{54}+ \cdots - 608 q^{99}+O(q^{100}) \) 12 * q + 14 * q^4 + 2 * q^6 + 16 * q^9 + 60 * q^11 - 8 * q^14 - 78 * q^16 + 4 * q^19 - 118 * q^24 - 72 * q^26 - 178 * q^34 - 16 * q^36 - 140 * q^41 + 154 * q^44 + 368 * q^46 + 276 * q^49 + 228 * q^51 + 138 * q^54 - 352 * q^56 + 88 * q^59 - 226 * q^64 - 202 * q^66 - 408 * q^74 + 310 * q^76 - 284 * q^81 + 800 * q^84 + 436 * q^86 - 196 * q^89 + 576 * q^91 + 632 * q^94 - 818 * q^96 - 608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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