LMFDB - Embedded newform 51.7.f.a.38.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.14
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.73857 q^{2} +(-13.3008 + 23.4965i) q^{3} -50.0231 q^{4} +(94.5565 + 94.5565i) q^{5} +(49.7261 - 87.8435i) q^{6} +(434.343 + 434.343i) q^{7} +426.283 q^{8} +(-375.175 - 625.048i) q^{9} +(-353.506 - 353.506i) q^{10} +(-1770.84 + 1770.84i) q^{11} +(665.349 - 1175.37i) q^{12} -413.246 q^{13} +(-1623.82 - 1623.82i) q^{14} +(-3479.43 + 964.070i) q^{15} +1607.79 q^{16} +(-71.7642 - 4912.48i) q^{17} +(1402.62 + 2336.78i) q^{18} -2602.41i q^{19} +(-4730.01 - 4730.01i) q^{20} +(-15982.7 + 4428.44i) q^{21} +(6620.40 - 6620.40i) q^{22} +(-12070.1 + 12070.1i) q^{23} +(-5669.93 + 10016.2i) q^{24} +2256.88i q^{25} +1544.95 q^{26} +(19676.6 - 501.662i) q^{27} +(-21727.2 - 21727.2i) q^{28} +(2530.60 + 2530.60i) q^{29} +(13008.1 - 3604.24i) q^{30} +(-13399.8 + 13399.8i) q^{31} -33293.0 q^{32} +(-18054.9 - 65162.2i) q^{33} +(268.295 + 18365.6i) q^{34} +82140.0i q^{35} +(18767.4 + 31266.8i) q^{36} +(57080.5 - 57080.5i) q^{37} +9729.29i q^{38} +(5496.52 - 9709.86i) q^{39} +(40307.9 + 40307.9i) q^{40} +(-2173.23 + 2173.23i) q^{41} +(59752.5 - 16556.0i) q^{42} -51379.6i q^{43} +(88582.8 - 88582.8i) q^{44} +(23627.1 - 94577.6i) q^{45} +(45124.9 - 45124.9i) q^{46} +30383.5i q^{47} +(-21384.9 + 37777.5i) q^{48} +259659. i q^{49} -8437.49i q^{50} +(116381. + 63653.9i) q^{51} +20671.9 q^{52} -34296.0 q^{53} +(-73562.4 + 1875.50i) q^{54} -334889. q^{55} +(185153. + 185153. i) q^{56} +(61147.6 + 34614.2i) q^{57} +(-9460.83 - 9460.83i) q^{58} -281320. q^{59} +(174052. - 48225.8i) q^{60} +(4102.23 + 4102.23i) q^{61} +(50096.1 - 50096.1i) q^{62} +(108530. - 434440. i) q^{63} +21569.6 q^{64} +(-39075.1 - 39075.1i) q^{65} +(67499.6 + 243613. i) q^{66} +94048.0 q^{67} +(3589.87 + 245737. i) q^{68} +(-123063. - 444148. i) q^{69} -307086. i q^{70} +(159726. + 159726. i) q^{71} +(-159931. - 266447. i) q^{72} +(150763. - 150763. i) q^{73} +(-213399. + 213399. i) q^{74} +(-53028.8 - 30018.4i) q^{75} +130181. i q^{76} -1.53830e6 q^{77} +(-20549.1 + 36301.0i) q^{78} +(48317.1 + 48317.1i) q^{79} +(152027. + 152027. i) q^{80} +(-249928. + 469005. i) q^{81} +(8124.77 - 8124.77i) q^{82} -307361. q^{83} +(799504. - 221524. i) q^{84} +(457721. - 471292. i) q^{85} +192086. i q^{86} +(-93119.5 + 25801.3i) q^{87} +(-754879. + 754879. i) q^{88} +461255. i q^{89} +(-88331.5 + 353585. i) q^{90} +(-179491. - 179491. i) q^{91} +(603784. - 603784. i) q^{92} +(-136620. - 493078. i) q^{93} -113591. i q^{94} +(246075. - 246075. i) q^{95} +(442824. - 782270. i) q^{96} +(-808124. + 808124. i) q^{97} -970755. i q^{98} +(1.77123e6 + 442483. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−3.73857			−0.467321			−0.233661	−	0.972318i	$-0.575070\pi$
$2$	−3.73857			−0.467321			−0.233661	+	0.972318i	$0.575070\pi$
$3$	−13.3008	+	23.4965i	−0.492624	+	0.870242i
$3$	−13.3008	+	23.4965i	−0.492624	+	0.870242i
$4$	−50.0231			−0.781611
$5$	94.5565	+	94.5565i	0.756452	+	0.756452i	0.975675	−	0.219223i	$-0.0703521\pi$
$5$	94.5565	+	94.5565i	0.756452	+	0.756452i	−0.219223	+	0.975675i	$0.570352\pi$
$6$	49.7261	−	87.8435i	0.230214	−	0.406683i
$7$	434.343	+	434.343i	1.26631	+	1.26631i	0.947981	+	0.318326i	$0.103121\pi$
$7$	434.343	+	434.343i	1.26631	+	1.26631i	0.318326	+	0.947981i	$0.396879\pi$
$8$	426.283			0.832585
$9$	−375.175	−	625.048i	−0.514644	−	0.857404i
$10$	−353.506	−	353.506i	−0.353506	−	0.353506i
$11$	−1770.84	+	1770.84i	−1.33046	+	1.33046i	−0.425497	+	0.904960i	$0.639901\pi$
$11$	−1770.84	+	1770.84i	−1.33046	+	1.33046i	−0.904960	+	0.425497i	$0.860099\pi$
$12$	665.349	−	1175.37i	0.385040	−	0.680191i
$13$	−413.246			−0.188096			−0.0940479	−	0.995568i	$-0.529981\pi$
$13$	−413.246			−0.188096			−0.0940479	+	0.995568i	$0.529981\pi$
$14$	−1623.82	−	1623.82i	−0.591772	−	0.591772i
$15$	−3479.43	+	964.070i	−1.03094	+	0.285650i
$16$	1607.79			0.392526
$17$	−71.7642	−	4912.48i	−0.0146070	−	0.999893i
$17$	−71.7642	−	4912.48i	−0.0146070	−	0.999893i
$18$	1402.62	+	2336.78i	0.240504	+	0.400683i
$19$		−	2602.41i		−	0.379415i	−0.981841	−	0.189708i	$-0.939246\pi$
$19$		−	2602.41i		−	0.379415i	0.981841	−	0.189708i	$-0.0607540\pi$
$20$	−4730.01	−	4730.01i	−0.591251	−	0.591251i
$21$	−15982.7	+	4428.44i	−1.72581	+	0.478181i
$22$	6620.40	−	6620.40i	0.621751	−	0.621751i
$23$	−12070.1	+	12070.1i	−0.992036	+	0.992036i	−0.999969	−	0.00793243i	$-0.997475\pi$
$23$	−12070.1	+	12070.1i	−0.992036	+	0.992036i	0.00793243	+	0.999969i	$0.497475\pi$
$24$	−5669.93	+	10016.2i	−0.410151	+	0.724550i
$25$			2256.88i			0.144440i
$26$	1544.95			0.0879011
$27$	19676.6	−	501.662i	0.999675	−	0.0254871i
$28$	−21727.2	−	21727.2i	−0.989760	−	0.989760i
$29$	2530.60	+	2530.60i	0.103760	+	0.103760i	0.757081	−	0.653321i	$-0.226625\pi$
$29$	2530.60	+	2530.60i	0.103760	+	0.103760i	−0.653321	+	0.757081i	$0.726625\pi$
$30$	13008.1	−	3604.24i	0.481782	−	0.133491i
$31$	−13399.8	+	13399.8i	−0.449794	+	0.449794i	−0.895286	−	0.445492i	$-0.853029\pi$
$31$	−13399.8	+	13399.8i	−0.449794	+	0.449794i	0.445492	+	0.895286i	$0.353029\pi$
$32$	−33293.0			−1.01602
$33$	−18054.9	−	65162.2i	−0.502405	−	1.81323i
$34$	268.295	+	18365.6i	0.00682616	+	0.467271i
$35$			82140.0i			1.91580i
$36$	18767.4	+	31266.8i	0.402251	+	0.670156i
$37$	57080.5	−	57080.5i	1.12689	−	1.12689i	0.136213	−	0.990680i	$-0.456507\pi$
$37$	57080.5	−	57080.5i	1.12689	−	1.12689i	0.990680	−	0.136213i	$-0.0434933\pi$
$38$			9729.29i			0.177309i
$39$	5496.52	−	9709.86i	0.0926604	−	0.163689i
$40$	40307.9	+	40307.9i	0.629811	+	0.629811i
$41$	−2173.23	+	2173.23i	−0.0315322	+	0.0315322i	−0.722697	−	0.691165i	$-0.757098\pi$
$41$	−2173.23	+	2173.23i	−0.0315322	+	0.0315322i	0.691165	+	0.722697i	$0.257098\pi$
$42$	59752.5	−	16556.0i	0.806507	−	0.223464i
$43$		−	51379.6i		−	0.646227i	−0.946360	−	0.323114i	$-0.895270\pi$
$43$		−	51379.6i		−	0.646227i	0.946360	−	0.323114i	$-0.104730\pi$
$44$	88582.8	−	88582.8i	1.03990	−	1.03990i
$45$	23627.1	−	94577.6i	0.259282	−	1.03789i
$46$	45124.9	−	45124.9i	0.463600	−	0.463600i
$47$			30383.5i			0.292647i	0.989237	+	0.146323i	$0.0467440\pi$
$47$			30383.5i			0.292647i	−0.989237	+	0.146323i	$0.953256\pi$
$48$	−21384.9	+	37777.5i	−0.193368	+	0.341593i
$49$			259659.i			2.20707i
$50$		−	8437.49i		−	0.0675000i
$51$	116381.	+	63653.9i	0.877345	+	0.479860i
$52$	20671.9			0.147018
$53$	−34296.0			−0.230365			−0.115182	−	0.993344i	$-0.536745\pi$
$53$	−34296.0			−0.230365			−0.115182	+	0.993344i	$0.536745\pi$
$54$	−73562.4	+	1875.50i	−0.467169	+	0.0119107i
$55$	−334889.			−2.01285
$56$	185153.	+	185153.i	1.05431	+	1.05431i
$57$	61147.6	+	34614.2i	0.330183	+	0.186909i
$58$	−9460.83	−	9460.83i	−0.0484892	−	0.0484892i
$59$	−281320.			−1.36976			−0.684881	−	0.728655i	$-0.740146\pi$
$59$	−281320.			−1.36976			−0.684881	+	0.728655i	$0.740146\pi$
$60$	174052.	−	48225.8i	0.805796	−	0.223268i
$61$	4102.23	+	4102.23i	0.0180730	+	0.0180730i	0.716086	−	0.698013i	$-0.245932\pi$
$61$	4102.23	+	4102.23i	0.0180730	+	0.0180730i	−0.698013	+	0.716086i	$0.745932\pi$
$62$	50096.1	−	50096.1i	0.210198	−	0.210198i
$63$	108530.	−	434440.i	0.434040	−	1.73743i
$64$	21569.6			0.0822817
$65$	−39075.1	−	39075.1i	−0.142285	−	0.142285i
$66$	67499.6	+	243613.i	0.234785	+	0.847363i
$67$	94048.0			0.312698			0.156349	−	0.987702i	$-0.450028\pi$
$67$	94048.0			0.312698			0.156349	+	0.987702i	$0.450028\pi$
$68$	3589.87	+	245737.i	0.0114170	+	0.781527i
$69$	−123063.	−	444148.i	−0.374611	−	1.35201i
$70$		−	307086.i		−	0.895295i
$71$	159726.	+	159726.i	0.446273	+	0.446273i	0.894114	−	0.447840i	$-0.147807\pi$
$71$	159726.	+	159726.i	0.446273	+	0.446273i	−0.447840	+	0.894114i	$0.647807\pi$
$72$	−159931.	−	266447.i	−0.428484	−	0.713862i
$73$	150763.	−	150763.i	0.387549	−	0.387549i	−0.486263	−	0.873812i	$-0.661640\pi$
$73$	150763.	−	150763.i	0.387549	−	0.387549i	0.873812	+	0.486263i	$0.161640\pi$
$74$	−213399.	+	213399.i	−0.526621	+	0.526621i
$75$	−53028.8	−	30018.4i	−0.125698	−	0.0711546i
$76$			130181.i			0.296555i
$77$	−1.53830e6			−3.36953
$78$	−20549.1	+	36301.0i	−0.0433022	+	0.0764953i
$79$	48317.1	+	48317.1i	0.0979985	+	0.0979985i	0.754406	−	0.656408i	$-0.227925\pi$
$79$	48317.1	+	48317.1i	0.0979985	+	0.0979985i	−0.656408	+	0.754406i	$0.727925\pi$
$80$	152027.	+	152027.i	0.296927	+	0.296927i
$81$	−249928.	+	469005.i	−0.470284	+	0.882515i
$82$	8124.77	−	8124.77i	0.0147357	−	0.0147357i
$83$	−307361.			−0.537544			−0.268772	−	0.963204i	$-0.586618\pi$
$83$	−307361.			−0.537544			−0.268772	+	0.963204i	$0.586618\pi$
$84$	799504.	−	221524.i	1.34891	−	0.373752i
$85$	457721.	−	471292.i	0.745322	−	0.767421i
$86$			192086.i			0.301996i
$87$	−93119.5	+	25801.3i	−0.141411	+	0.0391817i
$88$	−754879.	+	754879.i	−1.10772	+	1.10772i
$89$			461255.i			0.654292i	0.944974	+	0.327146i	$0.106087\pi$
$89$			461255.i			0.654292i	−0.944974	+	0.327146i	$0.893913\pi$
$90$	−88331.5	+	353585.i	−0.121168	+	0.485027i
$91$	−179491.	−	179491.i	−0.238187	−	0.238187i
$92$	603784.	−	603784.i	0.775386	−	0.775386i
$93$	−136620.	−	493078.i	−0.169850	−	0.613009i
$94$		−	113591.i		−	0.136760i
$95$	246075.	−	246075.i	0.287010	−	0.287010i
$96$	442824.	−	782270.i	0.500516	−	0.884184i
$97$	−808124.	+	808124.i	−0.885447	+	0.885447i	−0.994082	−	0.108635i	$-0.965352\pi$
$97$	−808124.	+	808124.i	−0.885447	+	0.885447i	0.108635	+	0.994082i	$0.465352\pi$
$98$		−	970755.i		−	1.03141i
$99$	1.77123e6	+	442483.i	1.82545	+	0.456028i
$100$		−	112896.i		−	0.112896i
$101$			1.33633e6i			1.29703i	0.761202	+	0.648514i	$0.224609\pi$
$101$			1.33633e6i			1.29703i	−0.761202	+	0.648514i	$0.775391\pi$
$102$	−435098.	−	237974.i	−0.410002	−	0.224249i
$103$	1.41816e6			1.29782			0.648909	−	0.760866i	$-0.275226\pi$
$103$	1.41816e6			1.29782			0.648909	+	0.760866i	$0.275226\pi$
$104$	−176160.			−0.156606
$105$	−1.93001e6	−	1.09253e6i	−1.66721	−	0.943770i
$106$	128218.			0.107654
$107$	−70561.2	−	70561.2i	−0.0575990	−	0.0575990i	0.677721	−	0.735320i	$-0.262968\pi$
$107$	−70561.2	−	70561.2i	−0.0575990	−	0.0575990i	−0.735320	+	0.677721i	$0.762968\pi$
$108$	−984285.	+	25094.7i	−0.781357	+	0.0199210i
$109$	194594.	+	194594.i	0.150263	+	0.150263i	0.778235	−	0.627973i	$-0.216115\pi$
$109$	194594.	+	194594.i	0.150263	+	0.150263i	−0.627973	+	0.778235i	$0.716115\pi$
$110$	1.25200e6			0.940649
$111$	581976.	+	2.10041e6i	0.425536	+	1.53580i
$112$	698332.	+	698332.i	0.497059	+	0.497059i
$113$	41296.5	−	41296.5i	0.0286206	−	0.0286206i	−0.692652	−	0.721272i	$-0.743558\pi$
$113$	41296.5	−	41296.5i	0.0286206	−	0.0286206i	0.721272	+	0.692652i	$0.243558\pi$
$114$	−228605.	−	129408.i	−0.154302	−	0.0873465i
$115$	−2.28261e6			−1.50086
$116$	−126588.	−	126588.i	−0.0810999	−	0.0810999i
$117$	155040.	+	258299.i	0.0968023	+	0.161274i
$118$	1.05174e6			0.640119
$119$	2.10253e6	−	2.16487e6i	1.24768	−	1.28467i
$120$	−1.48322e6	+	410967.i	−0.858347	+	0.237828i
$121$		−	4.50017e6i		−	2.54023i
$122$	−15336.5	−	15336.5i	−0.00844591	−	0.00844591i
$123$	−22157.6	−	79969.2i	−0.0119071	−	0.0429742i
$124$	670300.	−	670300.i	0.351564	−	0.351564i
$125$	1.26404e6	−	1.26404e6i	0.647190	−	0.647190i
$126$	−405749.	+	1.62419e6i	−0.202836	+	0.811940i
$127$			3.69525e6i			1.80398i	0.431754	+	0.901991i	$0.357895\pi$
$127$			3.69525e6i			1.80398i	−0.431754	+	0.901991i	$0.642105\pi$
$128$	2.05011e6			0.977569
$129$	1.20724e6	+	683392.i	0.562375	+	0.318347i
$130$	146085.	+	146085.i	0.0664930	+	0.0664930i
$131$	406547.	+	406547.i	0.180841	+	0.180841i	0.791722	−	0.610881i	$-0.209185\pi$
$131$	406547.	+	406547.i	0.180841	+	0.180841i	−0.610881	+	0.791722i	$0.709185\pi$
$132$	903164.	+	3.25961e6i	0.392685	+	1.41724i
$133$	1.13034e6	−	1.13034e6i	0.480456	−	0.480456i
$134$	−351605.			−0.146130
$135$	1.90799e6	+	1.81312e6i	0.775486	+	0.736927i
$136$	−30591.9	−	2.09411e6i	−0.0121616	−	0.832496i
$137$			3.74405e6i			1.45606i	0.685544	+	0.728031i	$0.259564\pi$
$137$			3.74405e6i			1.45606i	−0.685544	+	0.728031i	$0.740436\pi$
$138$	460080.	+	1.66048e6i	0.175064	+	0.631824i
$139$	−1.24433e6	+	1.24433e6i	−0.463330	+	0.463330i	−0.899745	−	0.436415i	$-0.856248\pi$
$139$	−1.24433e6	+	1.24433e6i	−0.463330	+	0.463330i	0.436415	+	0.899745i	$0.356248\pi$
$140$		−	4.10890e6i		−	1.49741i
$141$	−713906.	−	404125.i	−0.254674	−	0.144165i
$142$	−597148.	−	597148.i	−0.208553	−	0.208553i
$143$	731792.	−	731792.i	0.250253	−	0.250253i
$144$	−603202.	−	1.00494e6i	−0.202011	−	0.336554i
$145$			478570.i			0.156979i
$146$	−563639.	+	563639.i	−0.181110	+	0.181110i
$147$	−6.10110e6	−	3.45369e6i	−1.92068	−	1.08725i
$148$	−2.85534e6	+	2.85534e6i	−0.880792	+	0.880792i
$149$		−	4.03044e6i		−	1.21841i	−0.793013	−	0.609205i	$-0.791489\pi$
$149$		−	4.03044e6i		−	1.21841i	0.793013	−	0.609205i	$-0.208511\pi$
$150$	198252.	+	112226.i	0.0587413	+	0.0332521i
$151$			2.81889e6i			0.818743i	0.912368	+	0.409372i	$0.134252\pi$
$151$			2.81889e6i			0.818743i	−0.912368	+	0.409372i	$0.865748\pi$
$152$		−	1.10936e6i		−	0.315895i
$153$	−3.04361e6	+	1.88790e6i	−0.849795	+	0.527113i
$154$	5.75106e6			1.57465
$155$	−2.53408e6			−0.680495
$156$	−274953.	+	485717.i	−0.0724244	+	0.127941i
$157$	4.30703e6			1.11296			0.556479	−	0.830862i	$-0.312152\pi$
$157$	4.30703e6			1.11296			0.556479	+	0.830862i	$0.312152\pi$
$158$	−180637.	−	180637.i	−0.0457968	−	0.0457968i
$159$	456166.	−	805838.i	0.113483	−	0.200473i
$160$	−3.14807e6	−	3.14807e6i	−0.768571	−	0.768571i
$161$	−1.04851e7			−2.51245
$162$	934374.	−	1.75341e6i	0.219774	−	0.412418i
$163$	−3.84393e6	−	3.84393e6i	−0.887591	−	0.887591i	0.106700	−	0.994291i	$-0.465971\pi$
$163$	−3.84393e6	−	3.84393e6i	−0.887591	−	0.887591i	−0.994291	+	0.106700i	$0.965971\pi$
$164$	108712.	−	108712.i	0.0246459	−	0.0246459i
$165$	4.45430e6	−	7.86872e6i	0.991580	−	1.75167i
$166$	1.14909e6			0.251206
$167$	3.01245e6	+	3.01245e6i	0.646801	+	0.646801i	0.952219	−	0.305418i	$-0.0987961\pi$
$167$	3.01245e6	+	3.01245e6i	0.646801	+	0.646801i	−0.305418	+	0.952219i	$0.598796\pi$
$168$	−6.81316e6	+	1.88777e6i	−1.43688	+	0.398126i
$169$	−4.65604e6			−0.964620
$170$	−1.71122e6	+	1.76196e6i	−0.348305	+	0.358632i
$171$	−1.62663e6	+	976359.i	−0.325312	+	0.195264i
$172$			2.57017e6i			0.505098i
$173$	1.38731e6	+	1.38731e6i	0.267939	+	0.267939i	0.828269	−	0.560330i	$-0.189326\pi$
$173$	1.38731e6	+	1.38731e6i	0.267939	+	0.267939i	−0.560330	+	0.828269i	$0.689326\pi$
$174$	348134.	−	96459.8i	0.0660843	−	0.0183104i
$175$	−980260.	+	980260.i	−0.182906	+	0.182906i
$176$	−2.84713e6	+	2.84713e6i	−0.522239	+	0.522239i
$177$	3.74180e6	−	6.61006e6i	0.674777	−	1.19202i
$178$		−	1.72444e6i		−	0.305764i
$179$	2.44325e6			0.426000			0.213000	−	0.977052i	$-0.431677\pi$
$179$	2.44325e6			0.426000			0.213000	+	0.977052i	$0.431677\pi$
$180$	−1.18190e6	+	4.73106e6i	−0.202658	+	0.811225i
$181$	−2.75239e6	−	2.75239e6i	−0.464166	−	0.464166i	0.435852	−	0.900018i	$-0.356447\pi$
$181$	−2.75239e6	−	2.75239e6i	−0.464166	−	0.464166i	−0.900018	+	0.435852i	$0.856447\pi$
$182$	671039.	+	671039.i	0.111310	+	0.111310i
$183$	−150952.	+	41825.2i	−0.0246311	+	0.00682471i
$184$	−5.14528e6	+	5.14528e6i	−0.825954	+	0.825954i
$185$	1.07947e7			1.70488
$186$	510765.	+	1.84341e6i	0.0793748	+	0.286472i
$187$	8.82628e6	+	8.57211e6i	1.34975	+	1.31088i
$188$		−	1.51987e6i		−	0.228736i
$189$	8.76430e6	+	8.32851e6i	1.29817	+	1.23362i
$190$	−919968.	+	919968.i	−0.134126	+	0.134126i
$191$		−	6.66473e6i		−	0.956494i	−0.878225	−	0.478247i	$-0.841272\pi$
$191$		−	6.66473e6i		−	0.956494i	0.878225	−	0.478247i	$-0.158728\pi$
$192$	−286894.	+	506812.i	−0.0405339	+	0.0716050i
$193$	4.53124e6	+	4.53124e6i	0.630297	+	0.630297i	0.948142	−	0.317846i	$-0.102959\pi$
$193$	4.53124e6	+	4.53124e6i	0.630297	+	0.630297i	−0.317846	+	0.948142i	$0.602959\pi$
$194$	3.02123e6	−	3.02123e6i	0.413788	−	0.413788i
$195$	1.43786e6	−	398399.i	0.193916	−	0.0537296i
$196$		−	1.29890e7i		−	1.72507i
$197$	−1.18145e6	+	1.18145e6i	−0.154531	+	0.154531i	−0.780138	−	0.625607i	$-0.784851\pi$
$197$	−1.18145e6	+	1.18145e6i	−0.154531	+	0.154531i	0.625607	+	0.780138i	$0.284851\pi$
$198$	−6.62188e6	−	1.65426e6i	−0.853072	−	0.213112i
$199$	1.16528e6	−	1.16528e6i	0.147867	−	0.147867i	−0.629297	−	0.777165i	$-0.716657\pi$
$199$	1.16528e6	−	1.16528e6i	0.147867	−	0.147867i	0.777165	+	0.629297i	$0.216657\pi$
$200$			962069.i			0.120259i
$201$	−1.25092e6	+	2.20980e6i	−0.154043	+	0.272123i
$202$		−	4.99596e6i		−	0.606129i
$203$			2.19830e6i			0.262784i
$204$	−5.82172e6	−	3.18416e6i	−0.685743	−	0.375063i
$205$	−410986.			−0.0477052
$206$	−5.30189e6			−0.606498
$207$	1.20728e7	+	3.01599e6i	1.36112	+	0.340031i
$208$	−664412.			−0.0738325
$209$	4.60844e6	+	4.60844e6i	0.504795	+	0.504795i
$210$	7.21547e6	+	4.08451e6i	0.779124	+	0.441044i
$211$	2.02370e6	+	2.02370e6i	0.215426	+	0.215426i	0.806568	−	0.591141i	$-0.201323\pi$
$211$	2.02370e6	+	2.02370e6i	0.215426	+	0.215426i	−0.591141	+	0.806568i	$0.701323\pi$
$212$	1.71559e6			0.180056
$213$	−5.87751e6	+	1.62852e6i	−0.608211	+	0.168521i
$214$	263798.	+	263798.i	0.0269172	+	0.0269172i
$215$	4.85828e6	−	4.85828e6i	0.488840	−	0.488840i
$216$	8.38781e6	−	213850.i	0.832314	−	0.0212202i
$217$	−1.16402e7			−1.13915
$218$	−727505.	−	727505.i	−0.0702209	−	0.0702209i
$219$	1.53714e6	+	5.54770e6i	0.146346	+	0.528178i
$220$	1.67522e7			1.57327
$221$	29656.3	+	2.03006e6i	0.00274751	+	0.188076i
$222$	−2.17576e6	−	7.85254e6i	−0.198862	−	0.717714i
$223$		−	6.62397e6i		−	0.597315i	−0.954360	−	0.298658i	$-0.903461\pi$
$223$		−	6.62397e6i		−	0.597315i	0.954360	−	0.298658i	$-0.0965388\pi$
$224$	−1.44606e7	−	1.44606e7i	−1.28659	−	1.28659i
$225$	1.41066e6	−	846724.i	0.123844	−	0.0743352i
$226$	−154390.	+	154390.i	−0.0133750	+	0.0133750i
$227$	−8.62736e6	+	8.62736e6i	−0.737565	+	0.737565i	−0.972106	−	0.234541i	$-0.924641\pi$
$227$	−8.62736e6	+	8.62736e6i	−0.737565	+	0.737565i	0.234541	+	0.972106i	$0.424641\pi$
$228$	−3.05879e6	−	1.73151e6i	−0.258075	−	0.146090i
$229$			9.71423e6i			0.808914i	0.914557	+	0.404457i	$0.132539\pi$
$229$			9.71423e6i			0.808914i	−0.914557	+	0.404457i	$0.867461\pi$
$230$	8.53371e6			0.701382
$231$	2.04607e7	−	3.61448e7i	1.65991	−	2.93231i
$232$	1.07875e6	+	1.07875e6i	0.0863889	+	0.0863889i
$233$	8.46800e6	+	8.46800e6i	0.669442	+	0.669442i	0.957587	−	0.288145i	$-0.0930385\pi$
$233$	8.46800e6	+	8.46800e6i	0.669442	+	0.669442i	−0.288145	+	0.957587i	$0.593038\pi$
$234$	−579627.	−	965668.i	−0.0452378	−	0.0753668i
$235$	−2.87295e6	+	2.87295e6i	−0.221373	+	0.221373i
$236$	1.40725e7			1.07062
$237$	−1.77794e6	+	492627.i	−0.133559	+	0.0370061i
$238$	−7.86046e6	+	8.09353e6i	−0.583065	+	0.600353i
$239$			6.32735e6i			0.463477i	0.972778	+	0.231738i	$0.0744413\pi$
$239$			6.32735e6i			0.463477i	−0.972778	+	0.231738i	$0.925559\pi$
$240$	−5.59419e6	+	1.55002e6i	−0.404672	+	0.112125i
$241$	−1.11306e7	+	1.11306e7i	−0.795185	+	0.795185i	−0.982332	−	0.187147i	$-0.940076\pi$
$241$	−1.11306e7	+	1.11306e7i	−0.795185	+	0.795185i	0.187147	+	0.982332i	$0.440076\pi$
$242$			1.68242e7i			1.18710i
$243$	−7.69574e6	−	1.21106e7i	−0.536329	−	0.844009i
$244$	−205206.	−	205206.i	−0.0141261	−	0.0141261i
$245$	−2.45525e7	+	2.45525e7i	−1.66954	+	1.66954i
$246$	82837.8	+	298970.i	0.00556446	+	0.0200827i
$247$			1.07544e6i			0.0713664i
$248$	−5.71211e6	+	5.71211e6i	−0.374491	+	0.374491i
$249$	4.08816e6	−	7.22192e6i	0.264807	−	0.467794i
$250$	−4.72571e6	+	4.72571e6i	−0.302446	+	0.302446i
$251$			9.27808e6i			0.586728i	0.956001	+	0.293364i	$0.0947748\pi$
$251$			9.27808e6i			0.586728i	−0.956001	+	0.293364i	$0.905225\pi$
$252$	−5.42903e6	+	2.17320e7i	−0.339250	+	1.35800i
$253$		−	4.27484e7i		−	2.63972i
$254$		−	1.38149e7i		−	0.843040i
$255$	4.98567e6	+	1.70234e7i	0.300679	+	1.02666i
$256$	−9.04494e6			−0.539120
$257$	−3.06611e7			−1.80629			−0.903146	−	0.429334i	$-0.858748\pi$
$257$	−3.06611e7			−1.80629			−0.903146	+	0.429334i	$0.858748\pi$
$258$	−4.51336e6	−	2.55491e6i	−0.262810	−	0.148770i
$259$	4.95851e7			2.85399
$260$	1.95466e6	+	1.95466e6i	0.111212	+	0.111212i
$261$	632327.	−	2.53116e6i	0.0355648	−	0.142364i
$262$	−1.51990e6	−	1.51990e6i	−0.0845108	−	0.0845108i
$263$	9.26023e6			0.509043			0.254522	−	0.967067i	$-0.418082\pi$
$263$	9.26023e6			0.509043			0.254522	+	0.967067i	$0.418082\pi$
$264$	−7.69652e6	−	2.77776e7i	−0.418295	−	1.50967i
$265$	−3.24291e6	−	3.24291e6i	−0.174260	−	0.174260i
$266$	−4.22585e6	+	4.22585e6i	−0.224527	+	0.224527i
$267$	−1.08379e7	−	6.13508e6i	−0.569392	−	0.322320i
$268$	−4.70457e6			−0.244408
$269$	−1.56822e7	−	1.56822e7i	−0.805656	−	0.805656i	0.178317	−	0.983973i	$-0.442935\pi$
$269$	−1.56822e7	−	1.56822e7i	−0.805656	−	0.805656i	−0.983973	+	0.178317i	$0.942935\pi$
$270$	−7.13314e6	−	6.77846e6i	−0.362401	−	0.344382i
$271$	1.35828e7			0.682465			0.341232	−	0.939979i	$-0.389156\pi$
$271$	1.35828e7			0.682465			0.341232	+	0.939979i	$0.389156\pi$
$272$	−115382.	−	7.89822e6i	−0.00573363	−	0.392484i
$273$	6.60479e6	−	1.83004e6i	0.324617	−	0.0899439i
$274$		−	1.39974e7i		−	0.680449i
$275$	−3.99656e6	−	3.99656e6i	−0.192171	−	0.192171i
$276$	6.15600e6	+	2.22177e7i	0.292800	+	1.05675i
$277$	5.10052e6	−	5.10052e6i	0.239980	−	0.239980i	−0.576862	−	0.816842i	$-0.695723\pi$
$277$	5.10052e6	−	5.10052e6i	0.239980	−	0.239980i	0.816842	+	0.576862i	$0.195723\pi$
$278$	4.65201e6	−	4.65201e6i	0.216524	−	0.216524i
$279$	1.34028e7	+	3.34824e6i	0.617139	+	0.154172i
$280$			3.50149e7i			1.59507i
$281$	−3.32388e7			−1.49805			−0.749026	−	0.662541i	$-0.769478\pi$
$281$	−3.32388e7			−1.49805			−0.749026	+	0.662541i	$0.769478\pi$
$282$	2.66899e6	+	1.51085e6i	0.119014	+	0.0673712i
$283$	−7.17873e6	−	7.17873e6i	−0.316729	−	0.316729i	0.530780	−	0.847510i	$-0.321899\pi$
$283$	−7.17873e6	−	7.17873e6i	−0.316729	−	0.316729i	−0.847510	+	0.530780i	$0.821899\pi$
$284$	−7.99000e6	−	7.99000e6i	−0.348812	−	0.348812i
$285$	2.50891e6	+	9.05491e6i	0.108380	+	0.391156i
$286$	−2.73586e6	+	2.73586e6i	−0.116949	+	0.116949i
$287$	−1.88786e6			−0.0798589
$288$	1.24907e7	+	2.08097e7i	0.522889	+	0.871140i
$289$	−2.41273e7	+	705080.i	−0.999573	+	0.0292109i
$290$		−	1.78917e6i		−	0.0733596i
$291$	−8.23939e6	−	2.97368e7i	−0.334361	−	1.20675i
$292$	−7.54165e6	+	7.54165e6i	−0.302913	+	0.302913i
$293$			1.57011e7i			0.624206i	0.950048	+	0.312103i	$0.101033\pi$
$293$			1.57011e7i			0.624206i	−0.950048	+	0.312103i	$0.898967\pi$
$294$	2.28094e7	+	1.29119e7i	0.897577	+	0.508097i
$295$	−2.66007e7	−	2.66007e7i	−1.03616	−	1.03616i
$296$	2.43325e7	−	2.43325e7i	0.938234	−	0.938234i
$297$	−3.39557e7	+	3.57324e7i	−1.29611	+	1.36393i
$298$			1.50681e7i			0.569389i
$299$	4.98793e6	−	4.98793e6i	0.186598	−	0.186598i
$300$	2.65267e6	+	1.50161e6i	0.0982469	+	0.0556152i
$301$	2.23164e7	−	2.23164e7i	0.818323	−	0.818323i
$302$		−	1.05386e7i		−	0.382616i
$303$	−3.13991e7	−	1.77743e7i	−1.12873	−	0.638947i
$304$		−	4.18412e6i		−	0.148930i
$305$			775786.i			0.0273428i
$306$	1.13787e7	−	7.05803e6i	0.397127	−	0.246331i
$307$	−2.95551e7			−1.02145			−0.510725	−	0.859744i	$-0.670623\pi$
$307$	−2.95551e7			−1.02145			−0.510725	+	0.859744i	$0.670623\pi$
$308$	7.69507e7			2.63366
$309$	−1.88627e7	+	3.33219e7i	−0.639336	+	1.12942i
$310$	9.47383e6			0.318010
$311$	3.01432e7	+	3.01432e7i	1.00209	+	1.00209i	0.999998	+	0.00209668i	$0.000667395\pi$
$311$	3.01432e7	+	3.01432e7i	1.00209	+	1.00209i	0.00209668	+	0.999998i	$0.499333\pi$
$312$	2.34308e6	−	4.13915e6i	0.0771476	−	0.136285i
$313$	3.91734e7	+	3.91734e7i	1.27749	+	1.27749i	0.942067	+	0.335426i	$0.108880\pi$
$313$	3.91734e7	+	3.91734e7i	1.27749	+	1.27749i	0.335426	+	0.942067i	$0.391120\pi$
$314$	−1.61021e7			−0.520109
$315$	5.13414e7	−	3.08169e7i	1.64262	−	0.985956i
$316$	−2.41697e6	−	2.41697e6i	−0.0765967	−	0.0765967i
$317$	1.51946e7	−	1.51946e7i	0.476994	−	0.476994i	−0.427175	−	0.904169i	$-0.640491\pi$
$317$	1.51946e7	−	1.51946e7i	0.476994	−	0.476994i	0.904169	+	0.427175i	$0.140491\pi$
$318$	−1.70541e6	+	3.01268e6i	−0.0530331	+	0.0936854i
$319$	−8.96257e6			−0.276096
$320$	2.03955e6	+	2.03955e6i	0.0622422	+	0.0622422i
$321$	2.59647e6	−	719421.i	0.0784997	−	0.0217504i
$322$	3.91994e7			1.17412
$323$	−1.27843e7	+	186760.i	−0.379375	+	0.00554212i
$324$	1.25022e7	−	2.34611e7i	0.367579	−	0.689783i
$325$		−	932646.i		−	0.0271686i
$326$	1.43708e7	+	1.43708e7i	0.414790	+	0.414790i
$327$	−7.16056e6	+	1.98403e6i	−0.204788	+	0.0567419i
$328$	−926412.	+	926412.i	−0.0262532	+	0.0262532i
$329$	−1.31969e7	+	1.31969e7i	−0.370581	+	0.370581i
$330$	−1.66527e7	+	2.94178e7i	−0.463386	+	0.818593i
$331$			2.46685e7i			0.680234i	0.940383	+	0.340117i	$0.110467\pi$
$331$			2.46685e7i			0.680234i	−0.940383	+	0.340117i	$0.889533\pi$
$332$	1.53751e7			0.420150
$333$	−5.70932e7	−	1.42628e7i	−1.54615	−	0.386254i
$334$	−1.12623e7	−	1.12623e7i	−0.302264	−	0.302264i
$335$	8.89285e6	+	8.89285e6i	0.236541	+	0.236541i
$336$	−2.56968e7	+	7.11999e6i	−0.677425	+	0.187699i
$337$	−1.72576e7	+	1.72576e7i	−0.450912	+	0.450912i	−0.895657	−	0.444745i	$-0.853294\pi$
$337$	−1.72576e7	+	1.72576e7i	−0.450912	+	0.450912i	0.444745	+	0.895657i	$0.353294\pi$
$338$	1.74069e7			0.450787
$339$	421047.	+	1.51960e6i	0.0108077	+	0.0390060i
$340$	−2.28966e7	+	2.35755e7i	−0.582552	+	0.599825i
$341$		−	4.74578e7i		−	1.19686i
$342$	6.08127e6	−	3.65019e6i	0.152025	−	0.0912508i
$343$	−6.16813e7	+	6.16813e7i	−1.52852	+	1.52852i
$344$		−	2.19023e7i		−	0.538039i
$345$	3.03607e7	−	5.36336e7i	0.739357	−	1.30611i
$346$	−5.18657e6	−	5.18657e6i	−0.125214	−	0.125214i
$347$	1.33344e7	−	1.33344e7i	0.319142	−	0.319142i	−0.529295	−	0.848438i	$-0.677544\pi$
$347$	1.33344e7	−	1.33344e7i	0.319142	−	0.319142i	0.848438	+	0.529295i	$0.177544\pi$
$348$	4.65812e6	−	1.29066e6i	0.110528	−	0.0306248i
$349$		−	1.68578e7i		−	0.396574i	−0.980144	−	0.198287i	$-0.936462\pi$
$349$		−	1.68578e7i		−	0.396574i	0.980144	−	0.198287i	$-0.0635378\pi$
$350$	3.66477e6	−	3.66477e6i	0.0854757	−	0.0854757i
$351$	−8.13128e6	+	207310.i	−0.188035	+	0.00479401i
$352$	5.89564e7	−	5.89564e7i	1.35177	−	1.35177i
$353$		−	5.22157e7i		−	1.18707i	−0.804808	−	0.593536i	$-0.797732\pi$
$353$		−	5.22157e7i		−	1.18707i	0.804808	−	0.593536i	$-0.202268\pi$
$354$	−1.39890e7	+	2.47122e7i	−0.315338	+	0.557059i
$355$			3.02063e7i			0.675169i
$356$		−	2.30734e7i		−	0.511401i
$357$	2.29016e7	+	7.81968e7i	0.503339	+	1.71864i
$358$	−9.13427e6			−0.199079
$359$	3.93998e6			0.0851551			0.0425775	−	0.999093i	$-0.486443\pi$
$359$	3.93998e6			0.0851551			0.0425775	+	0.999093i	$0.486443\pi$
$360$	1.00718e7	−	4.03169e7i	0.215874	−	0.864130i
$361$	4.02733e7			0.856044
$362$	1.02900e7	+	1.02900e7i	0.216915	+	0.216915i
$363$	1.05738e8	+	5.98561e7i	2.21062	+	1.25138i
$364$	8.97869e6	+	8.97869e6i	0.186170	+	0.186170i
$365$	2.85113e7			0.586325
$366$	564343.	−	156366.i	0.0115106	−	0.00318933i
$367$	−3.37221e7	−	3.37221e7i	−0.682207	−	0.682207i	0.278290	−	0.960497i	$-0.410232\pi$
$367$	−3.37221e7	−	3.37221e7i	−0.682207	−	0.682207i	−0.960497	+	0.278290i	$0.910232\pi$
$368$	−1.94062e7	+	1.94062e7i	−0.389400	+	0.389400i
$369$	2.17371e6	+	543030.i	0.0432637	+	0.0108080i
$370$	−4.03566e7			−0.796727
$371$	−1.48963e7	−	1.48963e7i	−0.291713	−	0.291713i
$372$	6.83418e6	+	2.46653e7i	0.132757	+	0.479134i
$373$	8.96619e7			1.72775			0.863876	−	0.503705i	$-0.168030\pi$
$373$	8.96619e7			1.72775			0.863876	+	0.503705i	$0.168030\pi$
$374$	−3.29977e7	−	3.20475e7i	−0.630766	−	0.612602i
$375$	1.28878e7	+	4.65135e7i	0.244391	+	0.882034i
$376$			1.29520e7i			0.243653i
$377$	−1.04576e6	−	1.04576e6i	−0.0195168	−	0.0195168i
$378$	−3.27659e7	−	3.11367e7i	−0.606663	−	0.576498i
$379$	4.16362e7	−	4.16362e7i	0.764811	−	0.764811i	−0.212377	−	0.977188i	$-0.568121\pi$
$379$	4.16362e7	−	4.16362e7i	0.764811	−	0.764811i	0.977188	+	0.212377i	$0.0681205\pi$
$380$	−1.23094e7	+	1.23094e7i	−0.224330	+	0.224330i
$381$	−8.68256e7	−	4.91499e7i	−1.56990	−	0.888685i
$382$			2.49165e7i			0.446990i
$383$	4.24873e7			0.756246			0.378123	−	0.925755i	$-0.376570\pi$
$383$	4.24873e7			0.756246			0.378123	+	0.925755i	$0.376570\pi$
$384$	−2.72682e7	+	4.81705e7i	−0.481573	+	0.850722i
$385$	−1.45457e8	−	1.45457e8i	−2.54889	−	2.54889i
$386$	−1.69404e7	−	1.69404e7i	−0.294551	−	0.294551i
$387$	−3.21147e7	+	1.92764e7i	−0.554078	+	0.332577i
$388$	4.04248e7	−	4.04248e7i	0.692075	−	0.692075i
$389$	−6.16591e7			−1.04749			−0.523743	−	0.851876i	$-0.675465\pi$
$389$	−6.16591e7			−1.04749			−0.523743	+	0.851876i	$0.675465\pi$
$390$	−5.37555e6	+	1.48944e6i	−0.0906211	+	0.0251090i
$391$	6.01603e7	+	5.84279e7i	1.00642	+	0.977440i
$392$			1.10688e8i			1.83757i
$393$	−1.49599e7	+	4.14503e6i	−0.246462	+	0.0682889i
$394$	4.41693e6	−	4.41693e6i	0.0722157	−	0.0722157i
$395$			9.13739e6i			0.148262i
$396$	−8.86025e7	−	2.21344e7i	−1.42679	−	0.356436i
$397$	4.82582e7	+	4.82582e7i	0.771257	+	0.771257i	0.978326	−	0.207069i	$-0.0663924\pi$
$397$	4.82582e7	+	4.82582e7i	0.771257	+	0.771257i	−0.207069	+	0.978326i	$0.566392\pi$
$398$	−4.35649e6	+	4.35649e6i	−0.0691016	+	0.0691016i
$399$	1.15246e7	+	4.15935e7i	0.181429	+	0.654798i
$400$			3.62858e6i			0.0566966i
$401$	4.34201e6	−	4.34201e6i	0.0673376	−	0.0673376i	−0.672636	−	0.739974i	$-0.734838\pi$
$401$	4.34201e6	−	4.34201e6i	0.0673376	−	0.0673376i	0.739974	+	0.672636i	$0.234838\pi$
$402$	4.67664e6	−	8.26150e6i	0.0719873	−	0.127169i
$403$	5.53742e6	−	5.53742e6i	0.0846043	−	0.0846043i
$404$		−	6.68474e7i		−	1.01377i
$405$	−6.79798e7	+	2.07151e7i	−1.02333	+	0.311833i
$406$		−	8.21850e6i		−	0.122805i
$407$			2.02161e8i			2.99856i
$408$	4.96112e7	+	2.71346e7i	0.730464	+	0.399524i
$409$	5.54868e6			0.0810998			0.0405499	−	0.999178i	$-0.487089\pi$
$409$	5.54868e6			0.0810998			0.0405499	+	0.999178i	$0.487089\pi$
$410$	1.53650e6			0.0222937
$411$	−8.79722e7	−	4.97990e7i	−1.26713	−	0.717291i
$412$	−7.09408e7			−1.01439
$413$	−1.22190e8	−	1.22190e8i	−1.73454	−	1.73454i
$414$	−4.51350e7	−	1.12755e7i	−0.636081	−	0.158904i
$415$	−2.90630e7	−	2.90630e7i	−0.406627	−	0.406627i
$416$	1.37582e7			0.191109
$417$	−1.26868e7	−	4.57880e7i	−0.174962	−	0.631457i
$418$	−1.72290e7	−	1.72290e7i	−0.235902	−	0.235902i
$419$	6.67093e7	−	6.67093e7i	0.906869	−	0.906869i	−0.0891491	−	0.996018i	$-0.528415\pi$
$419$	6.67093e7	−	6.67093e7i	0.906869	−	0.906869i	0.996018	+	0.0891491i	$0.0284148\pi$
$420$	9.65449e7	+	5.46518e7i	1.30311	+	0.737661i
$421$	4.50138e7			0.603253			0.301626	−	0.953426i	$-0.402470\pi$
$421$	4.50138e7			0.603253			0.301626	+	0.953426i	$0.402470\pi$
$422$	−7.56575e6	−	7.56575e6i	−0.100673	−	0.100673i
$423$	1.89911e7	−	1.13991e7i	0.250916	−	0.150609i
$424$	−1.46198e7			−0.191798
$425$	1.10869e7	−	161963.i	0.144425	−	0.00210984i
$426$	2.19735e7	−	6.08834e6i	0.284230	−	0.0787535i
$427$			3.56356e6i			0.0457720i
$428$	3.52969e6	+	3.52969e6i	0.0450200	+	0.0450200i
$429$	7.46114e6	+	2.69280e7i	0.0945003	+	0.341062i
$430$	−1.81630e7	+	1.81630e7i	−0.228445	+	0.228445i
$431$	1.52947e7	−	1.52947e7i	0.191033	−	0.191033i	−0.605109	−	0.796143i	$-0.706871\pi$
$431$	1.52947e7	−	1.52947e7i	0.191033	−	0.191033i	0.796143	+	0.605109i	$0.206871\pi$
$432$	3.16358e7	−	806567.i	0.392399	−	0.0100044i
$433$			4.79572e6i			0.0590732i	0.999564	+	0.0295366i	$0.00940315\pi$
$433$			4.79572e6i			0.0590732i	−0.999564	+	0.0295366i	$0.990597\pi$
$434$	4.35178e7			0.532351
$435$	−1.12447e7	−	6.36538e6i	−0.136610	−	0.0773315i
$436$	−9.73421e6	−	9.73421e6i	−0.117447	−	0.117447i
$437$	3.14113e7	+	3.14113e7i	0.376394	+	0.376394i
$438$	−5.74670e6	−	2.07404e7i	−0.0683905	−	0.246829i
$439$	−2.93142e7	+	2.93142e7i	−0.346486	+	0.346486i	−0.858799	−	0.512313i	$-0.828789\pi$
$439$	−2.93142e7	+	2.93142e7i	−0.346486	+	0.346486i	0.512313	+	0.858799i	$0.328789\pi$
$440$	−1.42757e8			−1.67587
$441$	1.62300e8	−	9.74178e7i	1.89235	−	1.13585i
$442$	−110872.	−	7.58953e6i	−0.00128397	−	0.0878918i
$443$		−	6.73801e7i		−	0.775033i	−0.921863	−	0.387517i	$-0.873333\pi$
$443$		−	6.73801e7i		−	0.775033i	0.921863	−	0.387517i	$-0.126667\pi$
$444$	−2.91122e7	−	1.05069e8i	−0.332603	−	1.20040i
$445$	−4.36147e7	+	4.36147e7i	−0.494940	+	0.494940i
$446$			2.47642e7i			0.279138i
$447$	9.47014e7	+	5.36082e7i	1.06031	+	0.600218i
$448$	9.36863e6	+	9.36863e6i	0.104194	+	0.104194i
$449$	−8.77274e7	+	8.77274e7i	−0.969162	+	0.969162i	−0.999539	−	0.0303764i	$-0.990329\pi$
$449$	−8.77274e7	+	8.77274e7i	−0.969162	+	0.969162i	0.0303764	+	0.999539i	$0.490329\pi$
$450$	−5.27384e6	+	3.16554e6i	−0.0578747	+	0.0347384i
$451$		−	7.69688e6i		−	0.0839044i
$452$	−2.06578e6	+	2.06578e6i	−0.0223701	+	0.0223701i
$453$	−6.62342e7	−	3.74936e7i	−0.712505	−	0.403332i
$454$	3.22540e7	−	3.22540e7i	0.344680	−	0.344680i
$455$		−	3.39441e7i		−	0.360354i
$456$	2.60662e7	+	1.47555e7i	0.274905	+	0.155618i
$457$			9.92793e7i			1.04018i	0.854110	+	0.520092i	$0.174102\pi$
$457$			9.92793e7i			1.04018i	−0.854110	+	0.520092i	$0.825898\pi$
$458$		−	3.63173e7i		−	0.378022i
$459$	−3.87648e6	−	9.66249e7i	−0.0400866	−	0.999196i
$460$	1.14183e8			1.17309
$461$	1.04281e8			1.06439			0.532197	−	0.846621i	$-0.321367\pi$
$461$	1.04281e8			1.06439			0.532197	+	0.846621i	$0.321367\pi$
$462$	−7.64939e7	+	1.35130e8i	−0.775712	+	1.37033i
$463$	1.00577e8			1.01335			0.506673	−	0.862138i	$-0.330875\pi$
$463$	1.00577e8			1.01335			0.506673	+	0.862138i	$0.330875\pi$
$464$	4.06867e6	+	4.06867e6i	0.0407285	+	0.0407285i
$465$	3.37054e7	−	5.95421e7i	0.335228	−	0.592196i
$466$	−3.16582e7	−	3.16582e7i	−0.312844	−	0.312844i
$467$	8.24342e7			0.809388			0.404694	−	0.914452i	$-0.367378\pi$
$467$	8.24342e7			0.809388			0.404694	+	0.914452i	$0.367378\pi$
$468$	−7.75557e6	−	1.29209e7i	−0.0756617	−	0.126054i
$469$	4.08491e7	+	4.08491e7i	0.395972	+	0.395972i
$470$	1.07407e7	−	1.07407e7i	0.103452	−	0.103452i
$471$	−5.72871e7	+	1.01200e8i	−0.548270	+	0.968544i
$472$	−1.19922e8			−1.14044
$473$	9.09849e7	+	9.09849e7i	0.859778	+	0.859778i
$474$	6.64696e6	−	1.84172e6i	0.0624149	−	0.0172937i
$475$	5.87332e6			0.0548028
$476$	−1.05175e8	+	1.08294e8i	−0.975197	+	1.00411i
$477$	1.28670e7	+	2.14366e7i	0.118556	+	0.197516i
$478$		−	2.36552e7i		−	0.216593i
$479$	2.70772e7	+	2.70772e7i	0.246375	+	0.246375i	0.819481	−	0.573106i	$-0.194262\pi$
$479$	2.70772e7	+	2.70772e7i	0.246375	+	0.246375i	−0.573106	+	0.819481i	$0.694262\pi$
$480$	1.15841e8	−	3.20968e7i	1.04746	−	0.290227i
$481$	−2.35883e7	+	2.35883e7i	−0.211964	+	0.211964i
$482$	4.16126e7	−	4.16126e7i	0.371607	−	0.371607i
$483$	1.39461e8	−	2.46365e8i	1.23769	−	2.18644i
$484$			2.25113e8i			1.98547i
$485$	−1.52827e8			−1.33960
$486$	2.87711e7	+	4.52763e7i	0.250638	+	0.394423i
$487$	−3.19465e7	−	3.19465e7i	−0.276590	−	0.276590i	0.555156	−	0.831746i	$-0.312658\pi$
$487$	−3.19465e7	−	3.19465e7i	−0.276590	−	0.276590i	−0.831746	+	0.555156i	$0.812658\pi$
$488$	1.74871e6	+	1.74871e6i	0.0150473	+	0.0150473i
$489$	1.41447e8	−	3.91916e7i	1.20967	−	0.335171i
$490$	9.17912e7	−	9.17912e7i	0.780213	−	0.780213i
$491$	1.67930e8			1.41868			0.709338	−	0.704869i	$-0.248994\pi$
$491$	1.67930e8			1.41868			0.709338	+	0.704869i	$0.248994\pi$
$492$	1.10839e6	+	4.00031e6i	0.00930675	+	0.0335891i
$493$	1.22499e7	−	1.26131e7i	0.102233	−	0.105264i
$494$		−	4.02059e6i		−	0.0333510i
$495$	1.25642e8	+	2.09321e8i	1.03590	+	1.72583i
$496$	−2.15440e7	+	2.15440e7i	−0.176556	+	0.176556i
$497$			1.38752e8i			1.13024i
$498$	−1.52839e7	+	2.69996e7i	−0.123750	+	0.218610i
$499$	−7.49897e7	−	7.49897e7i	−0.603532	−	0.603532i	0.337716	−	0.941248i	$-0.390346\pi$
$499$	−7.49897e7	−	7.49897e7i	−0.603532	−	0.603532i	−0.941248	+	0.337716i	$0.890346\pi$
$500$	−6.32314e7	+	6.32314e7i	−0.505851	+	0.505851i
$501$	−1.10850e8	+	3.07141e7i	−0.881503	+	0.244244i
$502$		−	3.46867e7i		−	0.274190i
$503$	−2.26382e7	+	2.26382e7i	−0.177884	+	0.177884i	−0.790433	−	0.612549i	$-0.790144\pi$
$503$	−2.26382e7	+	2.26382e7i	−0.177884	+	0.177884i	0.612549	+	0.790433i	$0.290144\pi$
$504$	4.62647e7	−	1.85195e8i	0.361375	−	1.44656i
$505$	−1.26359e8	+	1.26359e8i	−0.981140	+	0.981140i
$506$			1.59818e8i			1.23360i
$507$	6.19292e7	−	1.09401e8i	0.475195	−	0.839453i
$508$		−	1.84848e8i		−	1.41001i
$509$		−	5.96157e7i		−	0.452072i	−0.974119	−	0.226036i	$-0.927423\pi$
$509$		−	5.96157e7i		−	0.452072i	0.974119	−	0.226036i	$-0.0725767\pi$
$510$	−1.86393e7	−	6.36433e7i	−0.140514	−	0.479780i
$511$	1.30966e8			0.981513
$512$	−9.73919e7			−0.725626
$513$	−1.30553e6	−	5.12066e7i	−0.00967019	−	0.379292i
$514$	1.14629e8			0.844119
$515$	1.34096e8	+	1.34096e8i	0.981737	+	0.981737i
$516$	−6.03900e7	−	3.41854e7i	−0.439558	−	0.248823i
$517$	−5.38042e7	−	5.38042e7i	−0.389354	−	0.389354i
$518$	−1.85377e8			−1.33373
$519$	−5.10495e7	+	1.41446e7i	−0.365166	+	0.101179i
$520$	−1.66571e7	−	1.66571e7i	−0.118465	−	0.118465i
$521$	1.25127e8	−	1.25127e8i	0.884784	−	0.884784i	−0.109232	−	0.994016i	$-0.534839\pi$
$521$	1.25127e8	−	1.25127e8i	0.884784	−	0.884784i	0.994016	+	0.109232i	$0.0348392\pi$
$522$	−2.36400e6	+	9.46294e6i	−0.0166202	+	0.0665295i
$523$	−1.45328e8			−1.01589			−0.507943	−	0.861391i	$-0.669594\pi$
$523$	−1.45328e8			−1.01589			−0.507943	+	0.861391i	$0.669594\pi$
$524$	−2.03367e7	−	2.03367e7i	−0.141347	−	0.141347i
$525$	−9.99444e6	−	3.60710e7i	−0.0690686	−	0.249276i
$526$	−3.46200e7			−0.237887
$527$	6.67878e7	+	6.48646e7i	0.456316	+	0.443176i
$528$	−2.90285e7	−	1.04767e8i	−0.197207	−	0.711742i
$529$		−	1.43339e8i		−	0.968271i
$530$	1.21239e7	+	1.21239e7i	0.0814354	+	0.0814354i
$531$	1.05544e8	+	1.75839e8i	0.704939	+	1.17444i
$532$	−5.65431e7	+	5.65431e7i	−0.375530	+	0.375530i
$533$	898079.	−	898079.i	0.00593107	−	0.00593107i
$534$	4.05183e7	+	2.29364e7i	0.266089	+	0.150627i
$535$		−	1.33440e7i		−	0.0871418i
$536$	4.00911e7			0.260348
$537$	−3.24973e7	+	5.74080e7i	−0.209858	+	0.370723i
$538$	5.86289e7	+	5.86289e7i	0.376500	+	0.376500i
$539$	−4.59815e8	−	4.59815e8i	−2.93641	−	2.93641i
$540$	−9.54434e7	−	9.06977e7i	−0.606129	−	0.575990i
$541$	−7.70914e7	+	7.70914e7i	−0.486871	+	0.486871i	−0.907317	−	0.420446i	$-0.861873\pi$
$541$	−7.70914e7	+	7.70914e7i	−0.486871	+	0.486871i	0.420446	+	0.907317i	$0.361873\pi$
$542$	−5.07801e7			−0.318930
$543$	1.01281e8	−	2.80625e7i	0.632597	−	0.175278i
$544$	2.38924e6	+	1.63551e8i	0.0148410	+	1.01591i
$545$			3.68003e7i			0.227333i
$546$	−2.46925e7	+	6.84171e6i	−0.151700	+	0.0420327i
$547$	1.95487e7	−	1.95487e7i	0.119442	−	0.119442i	−0.644859	−	0.764301i	$-0.723084\pi$
$547$	1.95487e7	−	1.95487e7i	0.119442	−	0.119442i	0.764301	+	0.644859i	$0.223084\pi$
$548$		−	1.87289e8i		−	1.13807i
$549$	1.02504e6	−	4.10315e6i	0.00619472	−	0.0247971i
$550$	1.49414e7	+	1.49414e7i	0.0898058	+	0.0898058i
$551$	6.58566e6	−	6.58566e6i	0.0393681	−	0.0393681i
$552$	−5.24598e7	−	1.89333e8i	−0.311896	−	1.12566i
$553$			4.19724e7i			0.248193i
$554$	−1.90686e7	+	1.90686e7i	−0.112148	+	0.112148i
$555$	−1.43578e8	+	2.53637e8i	−0.839865	+	1.48366i
$556$	6.22452e7	−	6.22452e7i	0.362144	−	0.362144i
$557$			1.22629e8i			0.709626i	0.934937	+	0.354813i	$0.115455\pi$
$557$			1.22629e8i			0.709626i	−0.934937	+	0.354813i	$0.884545\pi$
$558$	−5.01073e7	−	1.25176e7i	−0.288402	−	0.0720476i
$559$			2.12324e7i			0.121553i
$560$			1.32064e8i			0.752003i
$561$	−3.18812e8	+	9.33708e7i	−1.80570	+	0.528838i
$562$	1.24266e8			0.700071
$563$	−2.67613e8			−1.49963			−0.749813	−	0.661650i	$-0.769856\pi$
$563$	−2.67613e8			−1.49963			−0.749813	+	0.661650i	$0.769856\pi$
$564$	3.57118e7	+	2.02156e7i	0.199056	+	0.112681i
$565$	7.80971e6			0.0433002
$566$	2.68382e7	+	2.68382e7i	0.148014	+	0.148014i
$567$	−3.12264e8	+	9.51545e7i	−1.71306	+	0.522012i
$568$	6.80886e7	+	6.80886e7i	0.371560	+	0.371560i
$569$	2.55185e8			1.38522			0.692609	−	0.721314i	$-0.256461\pi$
$569$	2.55185e8			1.38522			0.692609	+	0.721314i	$0.256461\pi$
$570$	−9.37972e6	−	3.38524e7i	−0.0506483	−	0.182795i
$571$	−1.21282e8	−	1.21282e8i	−0.651458	−	0.651458i	0.301886	−	0.953344i	$-0.402384\pi$
$571$	−1.21282e8	−	1.21282e8i	−0.651458	−	0.651458i	−0.953344	+	0.301886i	$0.902384\pi$
$572$	−3.66065e7	+	3.66065e7i	−0.195601	+	0.195601i
$573$	1.56598e8	+	8.86465e7i	0.832382	+	0.471192i
$574$	7.05789e6			0.0373198
$575$	−2.72407e7	−	2.72407e7i	−0.143290	−	0.143290i
$576$	−8.09240e6	−	1.34821e7i	−0.0423457	−	0.0705486i
$577$	−1.98952e8			−1.03567			−0.517835	−	0.855481i	$-0.673262\pi$
$577$	−1.98952e8			−1.03567			−0.517835	+	0.855481i	$0.673262\pi$
$578$	9.02015e7	−	2.63599e6i	0.467122	−	0.0136509i
$579$	−1.66738e8	+	4.61992e7i	−0.859010	+	0.238012i
$580$		−	2.39395e7i		−	0.122696i
$581$	−1.33500e8	−	1.33500e8i	−0.680696	−	0.680696i
$582$	3.08035e7	+	1.11173e8i	0.156254	+	0.563938i
$583$	6.07327e7	−	6.07327e7i	0.306490	−	0.306490i
$584$	6.42679e7	−	6.42679e7i	0.322668	−	0.322668i
$585$	−9.76380e6	+	3.90838e7i	−0.0487698	+	0.195222i
$586$		−	5.86998e7i		−	0.291705i
$587$	1.38474e8			0.684628			0.342314	−	0.939586i	$-0.388789\pi$
$587$	1.38474e8			0.684628			0.342314	+	0.939586i	$0.388789\pi$
$588$	3.05196e8	+	1.72764e8i	1.50123	+	0.849810i
$589$	3.48718e7	+	3.48718e7i	0.170659	+	0.170659i
$590$	9.94485e7	+	9.94485e7i	0.484219	+	0.484219i
$591$	−1.20457e7	−	4.34742e7i	−0.0583539	−	0.210605i
$592$	9.17733e7	−	9.17733e7i	0.442335	−	0.442335i
$593$	1.40542e7			0.0673972			0.0336986	−	0.999432i	$-0.489271\pi$
$593$	1.40542e7			0.0673972			0.0336986	+	0.999432i	$0.489271\pi$
$594$	1.26946e8	−	1.33588e8i	0.605702	−	0.637395i
$595$	4.03511e8	−	5.89471e6i	1.91560	−	0.0279841i
$596$			2.01615e8i			0.952322i
$597$	1.18809e7	+	4.28794e7i	0.0558375	+	0.201523i
$598$	−1.86477e7	+	1.86477e7i	−0.0872011	+	0.0872011i
$599$		−	2.04983e8i		−	0.953758i	−0.878969	−	0.476879i	$-0.841768\pi$
$599$		−	2.04983e8i		−	0.953758i	0.878969	−	0.476879i	$-0.158232\pi$
$600$	−2.26053e7	−	1.27963e7i	−0.104654	−	0.0592423i
$601$	1.72208e8	+	1.72208e8i	0.793285	+	0.793285i	0.982027	−	0.188742i	$-0.0604408\pi$
$601$	1.72208e8	+	1.72208e8i	0.793285	+	0.793285i	−0.188742	+	0.982027i	$0.560441\pi$
$602$	−8.34314e7	+	8.34314e7i	−0.382420	+	0.382420i
$603$	−3.52845e7	−	5.87845e7i	−0.160928	−	0.268109i
$604$		−	1.41010e8i		−	0.639938i
$605$	4.25521e8	−	4.25521e8i	1.92156	−	1.92156i
$606$	1.17388e8	+	6.64505e7i	0.527479	+	0.298594i
$607$	1.10496e8	−	1.10496e8i	0.494059	−	0.494059i	−0.415523	−	0.909582i	$-0.636402\pi$
$607$	1.10496e8	−	1.10496e8i	0.494059	−	0.494059i	0.909582	+	0.415523i	$0.136402\pi$
$608$			8.66419e7i			0.385494i
$609$	−5.16524e7	−	2.92392e7i	−0.228686	−	0.129454i
$610$		−	2.90033e6i		−	0.0127779i
$611$		−	1.25558e7i		−	0.0550456i
$612$	1.52251e8	−	9.44384e7i	0.664209	−	0.411997i
$613$	−2.94589e8			−1.27890			−0.639449	−	0.768834i	$-0.720837\pi$
$613$	−2.94589e8			−1.27890			−0.639449	+	0.768834i	$0.720837\pi$
$614$	1.10494e8			0.477346
$615$	5.46646e6	−	9.65676e6i	0.0235007	−	0.0415151i
$616$	−6.55753e8			−2.80542
$617$	4.10098e7	+	4.10098e7i	0.174595	+	0.174595i	0.788995	−	0.614400i	$-0.210602\pi$
$617$	4.10098e7	+	4.10098e7i	0.174595	+	0.174595i	−0.614400	+	0.788995i	$0.710602\pi$
$618$	7.05196e7	−	1.24576e8i	0.298775	−	0.527800i
$619$	1.93318e8	+	1.93318e8i	0.815082	+	0.815082i	0.985391	−	0.170309i	$-0.0544766\pi$
$619$	1.93318e8	+	1.93318e8i	0.815082	+	0.815082i	−0.170309	+	0.985391i	$0.554477\pi$
$620$	1.26762e8			0.531882
$621$	−2.31444e8	+	2.43554e8i	−0.966430	+	1.01700i
$622$	−1.12693e8	−	1.12693e8i	−0.468300	−	0.468300i
$623$	−2.00343e8	+	2.00343e8i	−0.828534	+	0.828534i
$624$	8.83724e6	−	1.56114e7i	0.0363717	−	0.0642522i
$625$	2.74311e8			1.12358
$626$	−1.46453e8	−	1.46453e8i	−0.596999	−	0.596999i
$627$	−1.69579e8	+	4.69863e7i	−0.687969	+	0.190620i
$628$	−2.15451e8			−0.869900
$629$	−2.84503e8	−	2.76310e8i	−1.14323	−	1.11031i
$630$	−1.91944e8	+	1.15211e8i	−0.767630	+	0.460758i
$631$		−	1.11713e8i		−	0.444646i	−0.974973	−	0.222323i	$-0.928636\pi$
$631$		−	1.11713e8i		−	0.444646i	0.974973	−	0.222323i	$-0.0713640\pi$
$632$	2.05968e7	+	2.05968e7i	0.0815921	+	0.0815921i
$633$	−7.44669e7	+	2.06331e7i	−0.293597	+	0.0813490i
$634$	−5.68062e7	+	5.68062e7i	−0.222909	+	0.222909i
$635$	−3.49410e8	+	3.49410e8i	−1.36463	+	1.36463i
$636$	−2.28188e7	+	4.03105e7i	−0.0886997	+	0.156692i
$637$		−	1.07303e8i		−	0.415140i
$638$	3.35072e7			0.129026
$639$	3.99112e7	−	1.59762e8i	0.152965	−	0.612309i
$640$	1.93851e8	+	1.93851e8i	0.739484	+	0.739484i
$641$	3.61008e8	+	3.61008e8i	1.37070	+	1.37070i	0.859405	+	0.511295i	$0.170834\pi$
$641$	3.61008e8	+	3.61008e8i	1.37070	+	1.37070i	0.511295	+	0.859405i	$0.329166\pi$
$642$	−9.70708e6	+	2.68961e6i	−0.0366846	+	0.0101644i
$643$	−1.78383e8	+	1.78383e8i	−0.670998	+	0.670998i	−0.957946	−	0.286948i	$-0.907359\pi$
$643$	−1.78383e8	+	1.78383e8i	−0.670998	+	0.670998i	0.286948	+	0.957946i	$0.407359\pi$
$644$	5.24499e8			1.96375
$645$	4.95336e7	+	1.78772e8i	0.184595	+	0.666224i
$646$	4.77949e7	−	698215.i	0.177290	−	0.00258995i
$647$		−	3.51917e8i		−	1.29935i	−0.760211	−	0.649676i	$-0.774904\pi$
$647$		−	3.51917e8i		−	1.29935i	0.760211	−	0.649676i	$-0.225096\pi$
$648$	−1.06540e8	+	1.99929e8i	−0.391551	+	0.734769i
$649$	4.98173e8	−	4.98173e8i	1.82241	−	1.82241i
$650$			3.48676e6i			0.0126965i
$651$	1.54825e8	−	2.73505e8i	0.561174	−	0.991340i
$652$	1.92285e8	+	1.92285e8i	0.693751	+	0.693751i
$653$	2.30141e8	−	2.30141e8i	0.826524	−	0.826524i	−0.160510	−	0.987034i	$-0.551314\pi$
$653$	2.30141e8	−	2.30141e8i	0.826524	−	0.826524i	0.987034	+	0.160510i	$0.0513140\pi$
$654$	2.67703e7	−	7.41742e6i	0.0957017	−	0.0265167i
$655$			7.68833e7i			0.273595i
$656$	−3.49409e6	+	3.49409e6i	−0.0123772	+	0.0123772i
$657$	−1.50797e8	−	3.76716e7i	−0.531736	−	0.132837i
$658$	4.93374e7	−	4.93374e7i	0.173180	−	0.173180i
$659$		−	2.81518e8i		−	0.983671i	−0.870688	−	0.491835i	$-0.836326\pi$
$659$		−	2.81518e8i		−	0.983671i	0.870688	−	0.491835i	$-0.163674\pi$
$660$	−2.22818e8	+	3.93618e8i	−0.775029	+	1.36912i
$661$			3.19794e7i			0.110730i	0.998466	+	0.0553651i	$0.0176323\pi$
$661$			3.19794e7i			0.110730i	−0.998466	+	0.0553651i	$0.982368\pi$
$662$		−	9.22249e7i		−	0.317888i
$663$	−4.80939e7	−	2.63047e7i	−0.165025	−	0.0902595i
$664$	−1.31023e8			−0.447551
$665$	2.13762e8			0.726885
$666$	2.13447e8	+	5.33226e7i	0.722549	+	0.180505i
$667$	−6.10892e7			−0.205867
$668$	−1.50692e8	−	1.50692e8i	−0.505547	−	0.505547i
$669$	1.55640e8	+	8.81043e7i	0.519809	+	0.294252i
$670$	−3.32466e7	−	3.32466e7i	−0.110541	−	0.110541i
$671$	−1.45288e7			−0.0480908
$672$	5.32112e8	−	1.47436e8i	1.75346	−	0.485842i
$673$	−1.72400e8	−	1.72400e8i	−0.565576	−	0.565576i	0.365310	−	0.930886i	$-0.380963\pi$
$673$	−1.72400e8	−	1.72400e8i	−0.565576	−	0.565576i	−0.930886	+	0.365310i	$0.880963\pi$
$674$	6.45188e7	−	6.45188e7i	0.210721	−	0.210721i
$675$	1.13219e6	+	4.44077e7i	0.00368136	+	0.144393i
$676$	2.32909e8			0.753957
$677$	3.47029e8	+	3.47029e8i	1.11841	+	1.11841i	0.991975	+	0.126433i	$0.0403528\pi$
$677$	3.47029e8	+	3.47029e8i	1.11841	+	1.11841i	0.126433	+	0.991975i	$0.459647\pi$
$678$	−1.57411e6	−	5.68115e6i	−0.00505065	−	0.0182283i
$679$	−7.02006e8			−2.24250
$680$	1.95119e8	−	2.00904e8i	0.620544	−	0.638943i
$681$	−8.79620e7	−	3.17464e8i	−0.278518	−	1.00520i
$682$			1.77424e8i			0.559319i
$683$	1.40780e8	+	1.40780e8i	0.441853	+	0.441853i	0.892634	−	0.450782i	$-0.148855\pi$
$683$	1.40780e8	+	1.40780e8i	0.441853	+	0.441853i	−0.450782	+	0.892634i	$0.648855\pi$
$684$	8.13690e7	−	4.88405e7i	0.254268	−	0.152620i
$685$	−3.54024e8	+	3.54024e8i	−1.10144	+	1.10144i
$686$	2.30600e8	−	2.30600e8i	0.714310	−	0.714310i
$687$	−2.28251e8	−	1.29207e8i	−0.703951	−	0.398490i
$688$		−	8.26075e7i		−	0.253661i
$689$	1.41727e7			0.0433306
$690$	−1.13506e8	+	2.00513e8i	−0.345517	+	0.610372i
$691$	2.26697e8	+	2.26697e8i	0.687088	+	0.687088i	0.961587	−	0.274499i	$-0.0885120\pi$
$691$	2.26697e8	+	2.26697e8i	0.687088	+	0.687088i	−0.274499	+	0.961587i	$0.588512\pi$
$692$	−6.93978e7	−	6.93978e7i	−0.209424	−	0.209424i
$693$	5.77133e8	+	9.61513e8i	1.73411	+	2.88905i
$694$	−4.98515e7	+	4.98515e7i	−0.149142	+	0.149142i
$695$	−2.35319e8			−0.700975
$696$	−3.96953e7	+	1.09986e7i	−0.117737	+	0.0326221i
$697$	1.08319e7	+	1.05200e7i	0.0319894	+	0.0310682i
$698$			6.30240e7i			0.185328i
$699$	−3.11600e8	+	8.63372e7i	−0.912360	+	0.252794i
$700$	4.90356e7	−	4.90356e7i	0.142961	−	0.142961i
$701$		−	2.54046e8i		−	0.737494i	−0.929530	−	0.368747i	$-0.879787\pi$
$701$		−	2.54046e8i		−	0.737494i	0.929530	−	0.368747i	$-0.120213\pi$
$702$	3.03994e7	−	775044.i	0.0878726	−	0.00224034i
$703$	−1.48547e8	−	1.48547e8i	−0.427560	−	0.427560i
$704$	−3.81963e7	+	3.81963e7i	−0.109472	+	0.109472i
$705$	−2.92918e7	−	1.05717e8i	−0.0835947	−	0.301702i
$706$			1.95212e8i			0.554744i
$707$	−5.80426e8	+	5.80426e8i	−1.64244	+	1.64244i
$708$	−1.87176e8	+	3.30655e8i	−0.527413	+	0.931700i
$709$	2.03054e8	−	2.03054e8i	0.569736	−	0.569736i	−0.362319	−	0.932054i	$-0.618015\pi$
$709$	2.03054e8	−	2.03054e8i	0.569736	−	0.569736i	0.932054	+	0.362319i	$0.118015\pi$
$710$		−	1.12928e8i		−	0.315521i
$711$	1.20731e7	−	4.83279e7i	0.0335900	−	0.134459i
$712$			1.96625e8i			0.544753i
$713$		−	3.23474e8i		−	0.892423i
$714$	−8.56191e7	−	2.92344e8i	−0.235221	−	0.803156i
$715$	1.38391e8			0.378609
$716$	−1.22219e8			−0.332966
$717$	−1.48671e8	−	8.41590e7i	−0.403337	−	0.228320i
$718$	−1.47299e7			−0.0397948
$719$	2.22342e7	+	2.22342e7i	0.0598184	+	0.0598184i	0.736383	−	0.676565i	$-0.236532\pi$
$719$	2.22342e7	+	2.22342e7i	0.0598184	+	0.0598184i	−0.676565	+	0.736383i	$0.736532\pi$
$720$	3.79873e7	−	1.52061e8i	0.101775	−	0.407399i
$721$	6.15969e8	+	6.15969e8i	1.64344	+	1.64344i
$722$	−1.50565e8			−0.400048
$723$	−1.13484e8	−	4.09578e8i	−0.300277	−	1.08373i
$724$	1.37683e8	+	1.37683e8i	0.362797	+	0.362797i
$725$	−5.71126e6	+	5.71126e6i	−0.0149871	+	0.0149871i
$726$	−3.95311e8	−	2.23776e8i	−1.03307	−	0.584795i
$727$	−5.89785e8			−1.53494			−0.767469	−	0.641086i	$-0.778484\pi$
$727$	−5.89785e8			−1.53494			−0.767469	+	0.641086i	$0.778484\pi$
$728$	−7.65139e7	−	7.65139e7i	−0.198311	−	0.198311i
$729$	3.86917e8	−	1.97420e7i	0.998701	−	0.0509576i
$730$	−1.06592e8			−0.274002
$731$	−2.52401e8	+	3.68722e6i	−0.646159	+	0.00943945i
$732$	7.55106e6	−	2.09222e6i	0.0192520	−	0.00533427i
$733$		−	4.42030e8i		−	1.12238i	−0.827687	−	0.561190i	$-0.810344\pi$
$733$		−	4.42030e8i		−	1.12238i	0.827687	−	0.561190i	$-0.189656\pi$
$734$	1.26072e8	+	1.26072e8i	0.318810	+	0.318810i
$735$	−2.50330e8	−	9.03468e8i	−0.630450	−	2.27536i
$736$	4.01849e8	−	4.01849e8i	1.00793	−	1.00793i
$737$	−1.66544e8	+	1.66544e8i	−0.416031	+	0.416031i
$738$	−8.12659e6	−	2.03016e6i	−0.0202180	−	0.00505080i
$739$		−	3.03662e8i		−	0.752414i	−0.926536	−	0.376207i	$-0.877228\pi$
$739$		−	3.03662e8i		−	0.752414i	0.926536	−	0.376207i	$-0.122772\pi$
$740$	−5.39983e8			−1.33255
$741$	−2.52690e7	−	1.43042e7i	−0.0621060	−	0.0351568i
$742$	5.56907e7	+	5.56907e7i	0.136324	+	0.136324i
$743$	2.57282e8	+	2.57282e8i	0.627253	+	0.627253i	0.947376	−	0.320123i	$-0.103724\pi$
$743$	2.57282e8	+	2.57282e8i	0.627253	+	0.627253i	−0.320123	+	0.947376i	$0.603724\pi$
$744$	−5.82390e7	−	2.10191e8i	−0.141415	−	0.510382i
$745$	3.81104e8	−	3.81104e8i	0.921669	−	0.921669i
$746$	−3.35207e8			−0.807415
$747$	1.15314e8	+	1.92115e8i	0.276644	+	0.460893i
$748$	−4.41518e8	−	4.28804e8i	−1.05498	−	1.02460i
$749$		−	6.12956e7i		−	0.145876i
$750$	−4.81820e7	−	1.73894e8i	−0.114209	−	0.412193i
$751$	8.01211e7	−	8.01211e7i	0.189159	−	0.189159i	−0.606173	−	0.795332i	$-0.707296\pi$
$751$	8.01211e7	−	8.01211e7i	0.189159	−	0.189159i	0.795332	+	0.606173i	$0.207296\pi$
$752$			4.88501e7i			0.114872i
$753$	−2.18003e8	−	1.23406e8i	−0.510596	−	0.289036i
$754$	3.90965e6	+	3.90965e6i	0.00912061	+	0.00912061i
$755$	−2.66545e8	+	2.66545e8i	−0.619340	+	0.619340i
$756$	−4.38417e8	−	4.16618e8i	−1.01466	−	0.964212i
$757$			8.18543e8i			1.88692i	0.331486	+	0.943460i	$0.392450\pi$
$757$			8.18543e8i			1.88692i	−0.331486	+	0.943460i	$0.607550\pi$
$758$	−1.55660e8	+	1.55660e8i	−0.357412	+	0.357412i
$759$	1.00444e9	+	5.68590e8i	2.29720	+	1.30039i
$760$	1.04898e8	−	1.04898e8i	0.238960	−	0.238960i
$761$		−	3.96114e8i		−	0.898807i	−0.893329	−	0.449403i	$-0.851637\pi$
$761$		−	3.96114e8i		−	0.898807i	0.893329	−	0.449403i	$-0.148363\pi$
$762$	3.24603e8	+	1.83750e8i	0.733649	+	0.415301i
$763$			1.69042e8i			0.380557i
$764$			3.33390e8i			0.747606i
$765$	−4.66306e8	−	1.09280e8i	−1.04157	−	0.244094i
$766$	−1.58842e8			−0.353410
$767$	1.16255e8			0.257646
$768$	1.20305e8	−	2.12525e8i	0.265583	−	0.469165i
$769$	8.14130e7			0.179026			0.0895128	−	0.995986i	$-0.471469\pi$
$769$	8.14130e7			0.179026			0.0895128	+	0.995986i	$0.471469\pi$
$770$	5.43800e8	+	5.43800e8i	1.19115	+	1.19115i
$771$	4.07818e8	−	7.20429e8i	0.889822	−	1.57191i
$772$	−2.26667e8	−	2.26667e8i	−0.492647	−	0.492647i
$773$	−6.41676e8			−1.38924			−0.694620	−	0.719377i	$-0.744428\pi$
$773$	−6.41676e8			−1.38924			−0.694620	+	0.719377i	$0.744428\pi$
$774$	1.20063e8	−	7.20660e7i	0.258932	−	0.155420i
$775$	−3.02417e7	−	3.02417e7i	−0.0649683	−	0.0649683i
$776$	−3.44490e8	+	3.44490e8i	−0.737210	+	0.737210i
$777$	−6.59523e8	+	1.16508e9i	−1.40594	+	2.48366i
$778$	2.30517e8			0.489513
$779$	5.65563e6	+	5.65563e6i	0.0119638	+	0.0119638i
$780$	−7.19264e7	+	1.99291e7i	−0.151567	+	0.0419957i
$781$	−5.65698e8			−1.18750
$782$	−2.24913e8	−	2.18437e8i	−0.470322	−	0.456778i
$783$	5.10631e7	+	4.85241e7i	0.106371	+	0.101082i
$784$			4.17477e8i			0.866333i
$785$	4.07258e8	+	4.07258e8i	0.841900	+	0.841900i
$786$	5.59285e7	−	1.54965e7i	0.115177	−	0.0319129i
$787$	1.47490e7	−	1.47490e7i	0.0302579	−	0.0302579i	−0.691816	−	0.722074i	$-0.743189\pi$
$787$	1.47490e7	−	1.47490e7i	0.0302579	−	0.0302579i	0.722074	+	0.691816i	$0.243189\pi$
$788$	5.90997e7	−	5.90997e7i	0.120783	−	0.120783i
$789$	−1.23169e8	+	2.17583e8i	−0.250767	+	0.442991i
$790$		−	3.41608e7i		−	0.0692862i
$791$	3.58738e7			0.0724849
$792$	7.55047e8	+	1.88623e8i	1.51984	+	0.379682i
$793$	−1.69523e6	−	1.69523e6i	−0.00339946	−	0.00339946i
$794$	−1.80417e8	−	1.80417e8i	−0.360425	−	0.360425i
$795$	1.19331e8	−	3.30638e7i	0.237493	−	0.0658038i
$796$	−5.82911e7	+	5.82911e7i	−0.115575	+	0.115575i
$797$	3.64801e8			0.720579			0.360289	−	0.932841i	$-0.382678\pi$
$797$	3.64801e8			0.720579			0.360289	+	0.932841i	$0.382678\pi$
$798$	−4.30855e7	−	1.55500e8i	−0.0847857	−	0.306001i
$799$	1.49258e8	−	2.18044e6i	0.292615	−	0.00427469i
$800$		−	7.51381e7i		−	0.146754i
$801$	2.88307e8	−	1.73052e8i	0.560992	−	0.336727i
$802$	−1.62329e7	+	1.62329e7i	−0.0314683	+	0.0314683i
$803$			5.33955e8i			1.03124i
$804$	6.25748e7	−	1.10541e8i	0.120401	−	0.212694i
$805$	−9.91439e8	−	9.91439e8i	−1.90055	−	1.90055i
$806$	−2.07020e7	+	2.07020e7i	−0.0395374	+	0.0395374i
$807$	5.77063e8	−	1.59891e8i	1.09800	−	0.304231i
$808$			5.69655e8i			1.07989i
$809$	1.37557e8	−	1.37557e8i	0.259799	−	0.259799i	−0.565173	−	0.824972i	$-0.691191\pi$
$809$	1.37557e8	−	1.37557e8i	0.259799	−	0.259799i	0.824972	+	0.565173i	$0.191191\pi$
$810$	2.54147e8	−	7.74450e7i	0.478223	−	0.145726i
$811$	−4.12103e8	+	4.12103e8i	−0.772580	+	0.772580i	−0.978557	−	0.205977i	$-0.933963\pi$
$811$	−4.12103e8	+	4.12103e8i	−0.772580	+	0.772580i	0.205977	+	0.978557i	$0.433963\pi$
$812$		−	1.09966e8i		−	0.205395i
$813$	−1.80662e8	+	3.19148e8i	−0.336198	+	0.593910i
$814$		−	7.55792e8i		−	1.40129i
$815$		−	7.26938e8i		−	1.34284i
$816$	1.87116e8	+	1.02342e8i	0.344381	+	0.188358i
$817$	−1.33711e8			−0.245189
$818$	−2.07441e7			−0.0378996
$819$	−4.48498e7	+	1.79531e8i	−0.0816411	+	0.326804i
$820$	2.05588e7			0.0372869
$821$	−5.21314e8	−	5.21314e8i	−0.942041	−	0.942041i	0.0563686	−	0.998410i	$-0.482048\pi$
$821$	−5.21314e8	−	5.21314e8i	−0.942041	−	0.942041i	−0.998410	+	0.0563686i	$0.982048\pi$
$822$	3.28890e8	+	1.86177e8i	0.592155	+	0.335205i
$823$	3.71480e8	+	3.71480e8i	0.666401	+	0.666401i	0.956881	−	0.290480i	$-0.0938150\pi$
$823$	3.71480e8	+	3.71480e8i	0.666401	+	0.666401i	−0.290480	+	0.956881i	$0.593815\pi$
$824$	6.04538e8			1.08054
$825$	1.47063e8	−	4.07478e7i	0.261904	−	0.0725675i
$826$	4.56815e8	+	4.56815e8i	0.810587	+	0.810587i
$827$	−3.00427e8	+	3.00427e8i	−0.531156	+	0.531156i	−0.920916	−	0.389760i	$-0.872558\pi$
$827$	−3.00427e8	+	3.00427e8i	−0.531156	+	0.531156i	0.389760	+	0.920916i	$0.372558\pi$
$828$	−6.03918e8	−	1.50869e8i	−1.06387	−	0.265772i
$829$	6.07688e8			1.06664			0.533319	−	0.845914i	$-0.320944\pi$
$829$	6.07688e8			1.06664			0.533319	+	0.845914i	$0.320944\pi$
$830$	1.08654e8	+	1.08654e8i	0.190025	+	0.190025i
$831$	5.20034e7	+	1.87686e8i	0.0906209	+	0.327061i
$832$	−8.91358e6			−0.0154768
$833$	1.27557e9	−	1.86343e7i	2.20683	−	0.0322387i
$834$	4.74305e7	+	1.71182e8i	0.0817635	+	0.295093i
$835$			5.69694e8i			0.978548i
$836$	−2.30529e8	−	2.30529e8i	−0.394554	−	0.394554i
$837$	−2.56941e8	+	2.70385e8i	−0.438184	+	0.461112i
$838$	−2.49398e8	+	2.49398e8i	−0.423799	+	0.423799i
$839$	−7.59700e8	+	7.59700e8i	−1.28634	+	1.28634i	−0.349349	+	0.936993i	$0.613597\pi$
$839$	−7.59700e8	+	7.59700e8i	−1.28634	+	1.28634i	−0.936993	+	0.349349i	$0.886403\pi$
$840$	−8.22730e8	−	4.65728e8i	−1.38810	−	0.785768i
$841$		−	5.82015e8i		−	0.978468i
$842$	−1.68287e8			−0.281913
$843$	4.42104e8	−	7.80997e8i	0.737976	−	1.30367i
$844$	−1.01232e8	−	1.01232e8i	−0.168380	−	0.168380i
$845$	−4.40259e8	−	4.40259e8i	−0.729689	−	0.729689i
$846$	−7.09996e7	+	4.26164e7i	−0.117259	+	0.0703827i
$847$	1.95462e9	−	1.95462e9i	3.21671	−	3.21671i
$848$	−5.51407e7			−0.0904243
$849$	2.64159e8	−	7.31922e7i	0.431660	−	0.119603i
$850$	−4.14490e7	+	605510.i	−0.0674928	+	0.000985972i
$851$			1.37794e9i			2.23584i
$852$	2.94011e8	−	8.14637e7i	0.475384	−	0.131718i
$853$	2.94965e8	−	2.94965e8i	0.475251	−	0.475251i	−0.428358	−	0.903609i	$-0.640908\pi$
$853$	2.94965e8	−	2.94965e8i	0.475251	−	0.475251i	0.903609	+	0.428358i	$0.140908\pi$
$854$		−	1.33226e7i		−	0.0213902i
$855$	−2.46130e8	−	6.14873e7i	−0.393791	−	0.0983755i
$856$	−3.00791e7	−	3.00791e7i	−0.0479560	−	0.0479560i
$857$	7.62445e8	−	7.62445e8i	1.21134	−	1.21134i	0.240753	−	0.970586i	$-0.422606\pi$
$857$	7.62445e8	−	7.62445e8i	1.21134	−	1.21134i	0.970586	−	0.240753i	$-0.0773943\pi$
$858$	−2.78940e7	−	1.00672e8i	−0.0441620	−	0.159385i
$859$			8.38303e8i			1.32258i	0.750131	+	0.661289i	$0.229990\pi$
$859$			8.38303e8i			1.32258i	−0.750131	+	0.661289i	$0.770010\pi$
$860$	−2.43026e8	+	2.43026e8i	−0.382083	+	0.382083i
$861$	2.51101e7	−	4.43581e7i	0.0393404	−	0.0694966i
$862$	−5.71803e7	+	5.71803e7i	−0.0892740	+	0.0892740i
$863$			4.57354e8i			0.711573i	0.934567	+	0.355787i	$0.115787\pi$
$863$			4.57354e8i			0.711573i	−0.934567	+	0.355787i	$0.884213\pi$
$864$	−6.55092e8	+	1.67018e7i	−1.01569	+	0.0258954i
$865$			2.62359e8i			0.405367i
$866$		−	1.79291e7i		−	0.0276061i
$867$	3.04346e8	−	5.76286e8i	0.466993	−	0.884261i
$868$	5.82281e8			0.890375
$869$	−1.71123e8			−0.260766
$870$	4.20392e7	+	2.37974e7i	0.0638406	+	0.0361387i
$871$	−3.88650e7			−0.0588172
$872$	8.29523e7	+	8.29523e7i	0.125106	+	0.125106i
$873$	8.08304e8	+	2.01928e8i	1.21488	+	0.303496i
$874$	−1.17434e8	−	1.17434e8i	−0.175897	−	0.175897i
$875$	1.09806e9			1.63908
$876$	−7.68924e7	−	2.77513e8i	−0.114386	−	0.412830i
$877$	5.30844e8	+	5.30844e8i	0.786989	+	0.786989i	0.980999	−	0.194011i	$-0.0621496\pi$
$877$	5.30844e8	+	5.30844e8i	0.786989	+	0.786989i	−0.194011	+	0.980999i	$0.562150\pi$
$878$	1.09593e8	−	1.09593e8i	0.161920	−	0.161920i
$879$	−3.68922e8	−	2.08838e8i	−0.543211	−	0.307499i
$880$	−5.38430e8			−0.790098
$881$	2.64755e8	+	2.64755e8i	0.387184	+	0.387184i	0.873682	−	0.486498i	$-0.161726\pi$
$881$	2.64755e8	+	2.64755e8i	0.387184	+	0.387184i	−0.486498	+	0.873682i	$0.661726\pi$
$882$	−6.06768e8	+	3.64203e8i	−0.884335	+	0.530809i
$883$	−7.81689e8			−1.13541			−0.567704	−	0.823233i	$-0.692168\pi$
$883$	−7.81689e8			−1.13541			−0.567704	+	0.823233i	$0.692168\pi$
$884$	−1.48350e6	−	1.01550e8i	−0.00214749	−	0.147002i
$885$	9.78835e8	−	2.71213e8i	1.41215	−	0.391273i
$886$			2.51905e8i			0.362189i
$887$	−7.02089e8	−	7.02089e8i	−1.00605	−	1.00605i	−0.999982	−	0.00607193i	$-0.998067\pi$
$887$	−7.02089e8	−	7.02089e8i	−1.00605	−	1.00605i	−0.00607193	−	0.999982i	$-0.501933\pi$
$888$	2.48087e8	+	8.95371e8i	0.354295	+	1.27869i
$889$	−1.60501e9	+	1.60501e9i	−2.28440	+	2.28440i
$890$	1.63057e8	−	1.63057e8i	0.231296	−	0.231296i
$891$	−3.87949e8	−	1.27311e9i	−0.548456	−	1.79984i
$892$			3.31351e8i			0.466868i
$893$	7.90702e7			0.111035
$894$	−3.54048e8	−	2.00418e8i	−0.495506	−	0.280494i
$895$	2.31026e8	+	2.31026e8i	0.322248	+	0.322248i
$896$	8.90452e8	+	8.90452e8i	1.23790	+	1.23790i
$897$	5.08554e7	+	1.83543e8i	0.0704628	+	0.254308i
$898$	3.27975e8	−	3.27975e8i	0.452910	−	0.452910i
$899$	−6.78191e7			−0.0933411
$900$	−7.05654e7	+	4.23558e7i	−0.0967975	+	0.0581012i
$901$	2.46123e6	+	1.68478e8i	0.00336494	+	0.230340i
$902$			2.87753e7i			0.0392103i
$903$	2.27531e8	+	8.21185e8i	0.309014	+	1.11526i
$904$	1.76040e7	−	1.76040e7i	0.0238290	−	0.0238290i
$905$		−	5.20512e8i		−	0.702239i
$906$	2.47621e8	+	1.40173e8i	0.332969	+	0.188486i
$907$	−4.80540e8	−	4.80540e8i	−0.644032	−	0.644032i	0.307512	−	0.951544i	$-0.400504\pi$
$907$	−4.80540e8	−	4.80540e8i	−0.644032	−	0.644032i	−0.951544	+	0.307512i	$0.900504\pi$
$908$	4.31567e8	−	4.31567e8i	0.576489	−	0.576489i
$909$	8.35270e8	−	5.01358e8i	1.11208	−	0.667508i
$910$			1.26902e8i			0.168401i
$911$	1.56538e8	−	1.56538e8i	0.207044	−	0.207044i	−0.595966	−	0.803010i	$-0.703231\pi$
$911$	1.56538e8	−	1.56538e8i	0.207044	−	0.207044i	0.803010	+	0.595966i	$0.203231\pi$
$912$	9.83124e7	+	5.56523e7i	0.129606	+	0.0733667i
$913$	5.44286e8	−	5.44286e8i	0.715179	−	0.715179i
$914$		−	3.71163e8i		−	0.486100i
$915$	−1.82283e7	−	1.03186e7i	−0.0237948	−	0.0134697i
$916$		−	4.85936e8i		−	0.632256i
$917$			3.53162e8i			0.458000i
$918$	1.44925e7	+	3.61239e8i	0.0187333	+	0.466946i
$919$	−9.85848e8			−1.27018			−0.635088	−	0.772440i	$-0.719036\pi$
$919$	−9.85848e8			−1.27018			−0.635088	+	0.772440i	$0.719036\pi$
$920$	−9.73040e8			−1.24959
$921$	3.93108e8	−	6.94443e8i	0.503191	−	0.888910i
$922$	−3.89862e8			−0.497414
$923$	−6.60063e7	−	6.60063e7i	−0.0839421	−	0.0839421i
$924$	−1.02351e9	+	1.80808e9i	−1.29741	+	2.29193i
$925$	1.28824e8	+	1.28824e8i	0.162769	+	0.162769i
$926$	−3.76016e8			−0.473558
$927$	−5.32059e8	−	8.86418e8i	−0.667914	−	1.11275i
$928$	−8.42512e7	−	8.42512e7i	−0.105422	−	0.105422i
$929$	2.16871e8	−	2.16871e8i	0.270492	−	0.270492i	−0.558806	−	0.829298i	$-0.688741\pi$
$929$	2.16871e8	−	2.16871e8i	0.270492	−	0.270492i	0.829298	+	0.558806i	$0.188741\pi$
$930$	−1.26010e8	+	2.22602e8i	−0.156659	+	0.276746i
$931$	6.75740e8			0.837395
$932$	−4.23595e8	−	4.23595e8i	−0.523243	−	0.523243i
$933$	−1.10919e9	+	3.07331e8i	−1.36572	+	0.378410i
$934$	−3.08186e8			−0.378244
$935$	2.40330e7	+	1.64513e9i	0.0294018	+	2.01264i
$936$	6.60909e7	+	1.10108e8i	0.0805961	+	0.134274i
$937$		−	6.32539e8i		−	0.768897i	−0.923146	−	0.384449i	$-0.874392\pi$
$937$		−	6.32539e8i		−	0.768897i	0.923146	−	0.384449i	$-0.125608\pi$
$938$	−1.52717e8	−	1.52717e8i	−0.185046	−	0.185046i
$939$	−1.44148e9	+	3.99400e8i	−1.74105	+	0.482405i
$940$	1.43714e8	−	1.43714e8i	0.173028	−	0.173028i
$941$	4.74510e8	−	4.74510e8i	0.569477	−	0.569477i	−0.362505	−	0.931982i	$-0.618078\pi$
$941$	4.74510e8	−	4.74510e8i	0.569477	−	0.569477i	0.931982	+	0.362505i	$0.118078\pi$
$942$	2.14172e8	−	3.78345e8i	0.256218	−	0.452621i
$943$		−	5.24622e7i		−	0.0625622i
$944$	−4.52303e8			−0.537668
$945$	4.12066e7	+	1.61624e9i	0.0488282	+	1.91518i
$946$	−3.40154e8	−	3.40154e8i	−0.401792	−	0.401792i
$947$	−1.06534e9	−	1.06534e9i	−1.25441	−	1.25441i	−0.953724	−	0.300684i	$-0.902785\pi$
$947$	−1.06534e9	−	1.06534e9i	−1.25441	−	1.25441i	−0.300684	−	0.953724i	$-0.597215\pi$
$948$	8.89382e7	−	2.46427e7i	0.104391	−	0.0289243i
$949$	−6.23024e7	+	6.23024e7i	−0.0728964	+	0.0728964i
$950$	−2.19578e7			−0.0256105
$951$	1.54920e8	+	5.59123e8i	0.180122	+	0.650078i
$952$	8.96274e8	−	9.22849e8i	1.03880	−	1.06960i
$953$		−	1.30337e9i		−	1.50587i	−0.658094	−	0.752935i	$-0.728637\pi$
$953$		−	1.30337e9i		−	1.50587i	0.658094	−	0.752935i	$-0.271363\pi$
$954$	−4.81043e7	−	8.01424e7i	−0.0554036	−	0.0923033i
$955$	6.30193e8	−	6.30193e8i	0.723542	−	0.723542i
$956$		−	3.16513e8i		−	0.362258i
$957$	1.19210e8	−	2.10589e8i	0.136012	−	0.240271i
$958$	−1.01230e8	−	1.01230e8i	−0.115136	−	0.115136i
$959$	−1.62620e9	+	1.62620e9i	−1.84382	+	1.84382i
$960$	−7.50501e7	+	2.07947e7i	−0.0848277	+	0.0235038i
$961$			5.28394e8i			0.595371i
$962$	8.81865e7	−	8.81865e7i	0.0990552	−	0.0990552i
$963$	−1.76313e7	+	7.05769e7i	−0.0197427	+	0.0790285i
$964$	5.56788e8	−	5.56788e8i	0.621525	−	0.621525i
$965$			8.56917e8i			0.953579i
$966$	−5.21385e8	+	9.21051e8i	−0.578399	+	1.02177i
$967$			1.65992e9i			1.83573i	0.396898	+	0.917863i	$0.370087\pi$
$967$			1.65992e9i			1.83573i	−0.396898	+	0.917863i	$0.629913\pi$
$968$		−	1.91835e9i		−	2.11496i
$969$	1.65653e8	−	3.02870e8i	0.182066	−	0.332878i
$970$	5.71354e8			0.626022
$971$	6.12166e8			0.668670			0.334335	−	0.942454i	$-0.391488\pi$
$971$	6.12166e8			0.668670			0.334335	+	0.942454i	$0.391488\pi$
$972$	3.84965e8	+	6.05810e8i	0.419201	+	0.659686i
$973$	−1.08093e9			−1.17344
$974$	1.19434e8	+	1.19434e8i	0.129256	+	0.129256i
$975$	2.19140e7	+	1.24050e7i	0.0236432	+	0.0133839i
$976$	6.59552e6	+	6.59552e6i	0.00709414	+	0.00709414i
$977$	−1.17165e9			−1.25636			−0.628180	−	0.778068i	$-0.716200\pi$
$977$	−1.17165e9			−1.25636			−0.628180	+	0.778068i	$0.716200\pi$
$978$	−5.28808e8	+	1.46520e8i	−0.565303	+	0.156632i
$979$	−8.16808e8	−	8.16808e8i	−0.870507	−	0.870507i
$980$	1.22819e9	−	1.22819e9i	1.30493	−	1.30493i
$981$	4.86238e7	−	1.94638e8i	0.0515041	−	0.206167i
$982$	−6.27817e8			−0.662977
$983$	−4.99483e8	−	4.99483e8i	−0.525848	−	0.525848i	0.393484	−	0.919332i	$-0.371270\pi$
$983$	−4.99483e8	−	4.99483e8i	−0.525848	−	0.525848i	−0.919332	+	0.393484i	$0.871270\pi$
$984$	−9.44542e6	−	3.40895e7i	−0.00991371	−	0.0357796i
$985$	−2.23427e8			−0.233791
$986$	−4.57971e7	+	4.71550e7i	−0.0477758	+	0.0491923i
$987$	−1.34551e8	−	4.85610e8i	−0.139938	−	0.505052i
$988$		−	5.37966e7i		−	0.0557807i
$989$	6.20157e8	+	6.20157e8i	0.641081	+	0.641081i
$990$	−4.69721e8	−	7.82562e8i	−0.484099	−	0.806517i
$991$	3.69719e7	−	3.69719e7i	0.0379883	−	0.0379883i	−0.687857	−	0.725846i	$-0.741449\pi$
$991$	3.69719e7	−	3.69719e7i	0.0379883	−	0.0379883i	0.725846	+	0.687857i	$0.241449\pi$
$992$	4.46119e8	−	4.46119e8i	0.457000	−	0.457000i
$993$	−5.79624e8	−	3.28112e8i	−0.591969	−	0.335100i
$994$		−	5.18734e8i		−	0.528185i
$995$	2.20370e8			0.223709
$996$	−2.04502e8	+	3.61263e8i	−0.206976	+	0.365633i
$997$	−6.98660e8	−	6.98660e8i	−0.704986	−	0.704986i	0.260490	−	0.965476i	$-0.416116\pi$
$997$	−6.98660e8	−	6.98660e8i	−0.704986	−	0.704986i	−0.965476	+	0.260490i	$0.916116\pi$
$998$	2.80354e8	+	2.80354e8i	0.282043	+	0.282043i
$999$	1.09452e9	−	1.15179e9i	1.09781	−	1.15525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.14	✓	68
3.2	odd	2	inner	51.7.f.a.38.21	yes	68
17.13	even	4	inner	51.7.f.a.47.21	yes	68
51.47	odd	4	inner	51.7.f.a.47.14	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.14	✓	68	1.1	even	1	trivial
51.7.f.a.38.21	yes	68	3.2	odd	2	inner
51.7.f.a.47.14	yes	68	51.47	odd	4	inner
51.7.f.a.47.21	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.73857 q^{2} +(-13.3008 + 23.4965i) q^{3} -50.0231 q^{4} +(94.5565 + 94.5565i) q^{5} +(49.7261 - 87.8435i) q^{6} +(434.343 + 434.343i) q^{7} +426.283 q^{8} +(-375.175 - 625.048i) q^{9} +(-353.506 - 353.506i) q^{10} +(-1770.84 + 1770.84i) q^{11} +(665.349 - 1175.37i) q^{12} -413.246 q^{13} +(-1623.82 - 1623.82i) q^{14} +(-3479.43 + 964.070i) q^{15} +1607.79 q^{16} +(-71.7642 - 4912.48i) q^{17} +(1402.62 + 2336.78i) q^{18} -2602.41i q^{19} +(-4730.01 - 4730.01i) q^{20} +(-15982.7 + 4428.44i) q^{21} +(6620.40 - 6620.40i) q^{22} +(-12070.1 + 12070.1i) q^{23} +(-5669.93 + 10016.2i) q^{24} +2256.88i q^{25} +1544.95 q^{26} +(19676.6 - 501.662i) q^{27} +(-21727.2 - 21727.2i) q^{28} +(2530.60 + 2530.60i) q^{29} +(13008.1 - 3604.24i) q^{30} +(-13399.8 + 13399.8i) q^{31} -33293.0 q^{32} +(-18054.9 - 65162.2i) q^{33} +(268.295 + 18365.6i) q^{34} +82140.0i q^{35} +(18767.4 + 31266.8i) q^{36} +(57080.5 - 57080.5i) q^{37} +9729.29i q^{38} +(5496.52 - 9709.86i) q^{39} +(40307.9 + 40307.9i) q^{40} +(-2173.23 + 2173.23i) q^{41} +(59752.5 - 16556.0i) q^{42} -51379.6i q^{43} +(88582.8 - 88582.8i) q^{44} +(23627.1 - 94577.6i) q^{45} +(45124.9 - 45124.9i) q^{46} +30383.5i q^{47} +(-21384.9 + 37777.5i) q^{48} +259659. i q^{49} -8437.49i q^{50} +(116381. + 63653.9i) q^{51} +20671.9 q^{52} -34296.0 q^{53} +(-73562.4 + 1875.50i) q^{54} -334889. q^{55} +(185153. + 185153. i) q^{56} +(61147.6 + 34614.2i) q^{57} +(-9460.83 - 9460.83i) q^{58} -281320. q^{59} +(174052. - 48225.8i) q^{60} +(4102.23 + 4102.23i) q^{61} +(50096.1 - 50096.1i) q^{62} +(108530. - 434440. i) q^{63} +21569.6 q^{64} +(-39075.1 - 39075.1i) q^{65} +(67499.6 + 243613. i) q^{66} +94048.0 q^{67} +(3589.87 + 245737. i) q^{68} +(-123063. - 444148. i) q^{69} -307086. i q^{70} +(159726. + 159726. i) q^{71} +(-159931. - 266447. i) q^{72} +(150763. - 150763. i) q^{73} +(-213399. + 213399. i) q^{74} +(-53028.8 - 30018.4i) q^{75} +130181. i q^{76} -1.53830e6 q^{77} +(-20549.1 + 36301.0i) q^{78} +(48317.1 + 48317.1i) q^{79} +(152027. + 152027. i) q^{80} +(-249928. + 469005. i) q^{81} +(8124.77 - 8124.77i) q^{82} -307361. q^{83} +(799504. - 221524. i) q^{84} +(457721. - 471292. i) q^{85} +192086. i q^{86} +(-93119.5 + 25801.3i) q^{87} +(-754879. + 754879. i) q^{88} +461255. i q^{89} +(-88331.5 + 353585. i) q^{90} +(-179491. - 179491. i) q^{91} +(603784. - 603784. i) q^{92} +(-136620. - 493078. i) q^{93} -113591. i q^{94} +(246075. - 246075. i) q^{95} +(442824. - 782270. i) q^{96} +(-808124. + 808124. i) q^{97} -970755. i q^{98} +(1.77123e6 + 442483. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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