LMFDB - Embedded newform 20.7.d.d.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,7,Mod(19,20)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.60108167240$
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} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 $ x^12 + 16x^10 - 10x^8 - 1775x^6 - 1000x^4 + 160000*x^2 + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.8
Root			$-3.06674 + 0.771446i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.7.d.d.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.68788 + 7.09927i) q^{2} +31.7642 q^{3} +(-36.7991 + 52.3624i) q^{4} +(121.131 - 30.8579i) q^{5} +(117.142 + 225.502i) q^{6} -88.8045 q^{7} +(-507.445 - 68.1408i) q^{8} +279.961 q^{9} +O(q^{10})$	\(q+(3.68788 + 7.09927i) q^{2} +31.7642 q^{3} +(-36.7991 + 52.3624i) q^{4} +(121.131 - 30.8579i) q^{5} +(117.142 + 225.502i) q^{6} -88.8045 q^{7} +(-507.445 - 68.1408i) q^{8} +279.961 q^{9} +(665.785 + 746.143i) q^{10} +1790.06i q^{11} +(-1168.89 + 1663.25i) q^{12} -3328.41i q^{13} +(-327.500 - 630.447i) q^{14} +(3847.63 - 980.173i) q^{15} +(-1387.65 - 3853.78i) q^{16} -3001.09i q^{17} +(1032.46 + 1987.52i) q^{18} -6872.67i q^{19} +(-2841.74 + 7478.27i) q^{20} -2820.80 q^{21} +(-12708.1 + 6601.53i) q^{22} +5908.85 q^{23} +(-16118.6 - 2164.44i) q^{24} +(13720.6 - 7475.70i) q^{25} +(23629.3 - 12274.8i) q^{26} -14263.3 q^{27} +(3267.93 - 4650.02i) q^{28} -14040.2 q^{29} +(21148.1 + 23700.6i) q^{30} +51272.4i q^{31} +(22241.6 - 24063.5i) q^{32} +56859.8i q^{33} +(21305.5 - 11067.6i) q^{34} +(-10757.0 + 2740.32i) q^{35} +(-10302.3 + 14659.5i) q^{36} +18940.9i q^{37} +(48790.9 - 25345.6i) q^{38} -105724. i q^{39} +(-63570.2 + 7404.68i) q^{40} -11762.3 q^{41} +(-10402.8 - 20025.6i) q^{42} -100904. q^{43} +(-93732.0 - 65872.8i) q^{44} +(33912.1 - 8639.01i) q^{45} +(21791.1 + 41948.5i) q^{46} +129204. q^{47} +(-44077.4 - 122412. i) q^{48} -109763. q^{49} +(103672. + 69836.6i) q^{50} -95327.0i q^{51} +(174284. + 122483. i) q^{52} +47508.5i q^{53} +(-52601.4 - 101259. i) q^{54} +(55237.5 + 216833. i) q^{55} +(45063.4 + 6051.21i) q^{56} -218305. i q^{57} +(-51778.5 - 99675.1i) q^{58} +139889. i q^{59} +(-90265.4 + 237541. i) q^{60} +299920. q^{61} +(-363996. + 189086. i) q^{62} -24861.8 q^{63} +(252858. + 69155.5i) q^{64} +(-102708. - 403175. i) q^{65} +(-403663. + 209692. i) q^{66} -40858.7 q^{67} +(157144. + 110437. i) q^{68} +187690. q^{69} +(-59124.7 - 66260.9i) q^{70} -222756. i q^{71} +(-142065. - 19076.8i) q^{72} +633436. i q^{73} +(-134467. + 69851.8i) q^{74} +(435823. - 237459. i) q^{75} +(359870. + 252909. i) q^{76} -158966. i q^{77} +(750564. - 389897. i) q^{78} +166771. i q^{79} +(-287007. - 423994. i) q^{80} -657154. q^{81} +(-43378.0 - 83503.9i) q^{82} -328119. q^{83} +(103803. - 147704. i) q^{84} +(-92607.1 - 363526. i) q^{85} +(-372122. - 716345. i) q^{86} -445975. q^{87} +(121976. - 908359. i) q^{88} +27762.8 q^{89} +(186394. + 208891. i) q^{90} +295578. i q^{91} +(-217441. + 309402. i) q^{92} +1.62862e6i q^{93} +(476488. + 917254. i) q^{94} +(-212076. - 832496. i) q^{95} +(706485. - 764358. i) q^{96} +220750. i q^{97} +(-404791. - 779235. i) q^{98} +501148. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9}+O(q^{10}) $ 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9	$ 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9} + 2000 q^{10} + 512 q^{14} - 20928 q^{16} - 13760 q^{20} + 51216 q^{21} - 20928 q^{24} - 55700 q^{25} + 14496 q^{26} - 16072 q^{29} + 83520 q^{30} + 257216 q^{34} - 144960 q^{36} - 36800 q^{40} - 192136 q^{41} - 165120 q^{44} - 57180 q^{45} - 49472 q^{46} + 145796 q^{49} - 36000 q^{50} - 118656 q^{54} + 1078208 q^{56} - 902400 q^{60} + 215384 q^{61} - 6656 q^{64} + 710400 q^{65} - 1403520 q^{66} + 1015824 q^{69} + 530080 q^{70} - 1020384 q^{74} + 2515200 q^{76} - 127040 q^{80} - 2327652 q^{81} + 424704 q^{84} - 44800 q^{85} - 5268832 q^{86} - 4346152 q^{89} + 3582000 q^{90} + 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) $ 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9 + 2000 * q^10 + 512 * q^14 - 20928 * q^16 - 13760 * q^20 + 51216 * q^21 - 20928 * q^24 - 55700 * q^25 + 14496 * q^26 - 16072 * q^29 + 83520 * q^30 + 257216 * q^34 - 144960 * q^36 - 36800 * q^40 - 192136 * q^41 - 165120 * q^44 - 57180 * q^45 - 49472 * q^46 + 145796 * q^49 - 36000 * q^50 - 118656 * q^54 + 1078208 * q^56 - 902400 * q^60 + 215384 * q^61 - 6656 * q^64 + 710400 * q^65 - 1403520 * q^66 + 1015824 * q^69 + 530080 * q^70 - 1020384 * q^74 + 2515200 * q^76 - 127040 * q^80 - 2327652 * q^81 + 424704 * q^84 - 44800 * q^85 - 5268832 * q^86 - 4346152 * q^89 + 3582000 * q^90 + 4292992 * q^94 + 7673088 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	3.68788	+	7.09927i	0.460984	+	0.887408i
$2$	3.68788	+	7.09927i	0.460984	+	0.887408i
$3$	31.7642			1.17645			0.588225	−	0.808697i	$-0.299827\pi$
$3$	31.7642			1.17645			0.588225	+	0.808697i	$0.299827\pi$
$4$	−36.7991	+	52.3624i	−0.574987	+	0.818163i
$5$	121.131	−	30.8579i	0.969050	−	0.246863i
$5$	121.131	−	30.8579i	0.969050	−	0.246863i
$6$	117.142	+	225.502i	0.542325	+	1.04399i
$7$	−88.8045			−0.258905			−0.129453	−	0.991586i	$-0.541322\pi$
$7$	−88.8045			−0.258905			−0.129453	+	0.991586i	$0.541322\pi$
$8$	−507.445	−	68.1408i	−0.991104	−	0.133088i
$9$	279.961			0.384035
$10$	665.785	+	746.143i	0.665785	+	0.746143i
$11$			1790.06i			1.34490i	0.740142	+	0.672450i	$0.234758\pi$
$11$			1790.06i			1.34490i	−0.740142	+	0.672450i	$0.765242\pi$
$12$	−1168.89	+	1663.25i	−0.676443	+	0.962528i
$13$		−	3328.41i		−	1.51498i	−0.652847	−	0.757490i	$-0.726426\pi$
$13$		−	3328.41i		−	1.51498i	0.652847	−	0.757490i	$-0.273574\pi$
$14$	−327.500	−	630.447i	−0.119351	−	0.229755i
$15$	3847.63	−	980.173i	1.14004	−	0.290422i
$16$	−1387.65	−	3853.78i	−0.338781	−	0.940865i
$17$		−	3001.09i		−	0.610846i	−0.952217	−	0.305423i	$-0.901202\pi$
$17$		−	3001.09i		−	0.610846i	0.952217	−	0.305423i	$-0.0987979\pi$
$18$	1032.46	+	1987.52i	0.177034	+	0.340796i
$19$		−	6872.67i		−	1.00199i	−0.865449	−	0.500997i	$-0.832967\pi$
$19$		−	6872.67i		−	1.00199i	0.865449	−	0.500997i	$-0.167033\pi$
$20$	−2841.74	+	7478.27i	−0.355217	+	0.934784i
$21$	−2820.80			−0.304589
$22$	−12708.1	+	6601.53i	−1.19348	+	0.619978i
$23$	5908.85			0.485646			0.242823	−	0.970071i	$-0.421927\pi$
$23$	5908.85			0.485646			0.242823	+	0.970071i	$0.421927\pi$
$24$	−16118.6	−	2164.44i	−1.16598	−	0.156571i
$25$	13720.6	−	7475.70i	0.878118	−	0.478445i
$26$	23629.3	−	12274.8i	1.34441	−	0.698382i
$27$	−14263.3			−0.724652
$28$	3267.93	−	4650.02i	0.148867	−	0.211827i
$29$	−14040.2			−0.575677			−0.287839	−	0.957679i	$-0.592937\pi$
$29$	−14040.2			−0.575677			−0.287839	+	0.957679i	$0.592937\pi$
$30$	21148.1	+	23700.6i	0.783263	+	0.877801i
$31$			51272.4i			1.72107i	0.509392	+	0.860534i	$0.329870\pi$
$31$			51272.4i			1.72107i	−0.509392	+	0.860534i	$0.670130\pi$
$32$	22241.6	−	24063.5i	0.678759	−	0.734361i
$33$			56859.8i			1.58221i
$34$	21305.5	−	11067.6i	0.542070	−	0.281591i
$35$	−10757.0	+	2740.32i	−0.250892	+	0.0639141i
$36$	−10302.3	+	14659.5i	−0.220815	+	0.314203i
$37$			18940.9i			0.373935i	0.982366	+	0.186967i	$0.0598659\pi$
$37$			18940.9i			0.373935i	−0.982366	+	0.186967i	$0.940134\pi$
$38$	48790.9	−	25345.6i	0.889177	−	0.461903i
$39$		−	105724.i		−	1.78230i
$40$	−63570.2	+	7404.68i	−0.993284	+	0.115698i
$41$	−11762.3			−0.170664			−0.0853320	−	0.996353i	$-0.527195\pi$
$41$	−11762.3			−0.170664			−0.0853320	+	0.996353i	$0.527195\pi$
$42$	−10402.8	−	20025.6i	−0.140411	−	0.270295i
$43$	−100904.			−1.26912			−0.634561	−	0.772873i	$-0.718819\pi$
$43$	−100904.			−1.26912			−0.634561	+	0.772873i	$0.718819\pi$
$44$	−93732.0	−	65872.8i	−1.10035	−	0.773300i
$45$	33912.1	−	8639.01i	0.372149	−	0.0948039i
$46$	21791.1	+	41948.5i	0.223875	+	0.430966i
$47$	129204.			1.24446			0.622232	−	0.782833i	$-0.286226\pi$
$47$	129204.			1.24446			0.622232	+	0.782833i	$0.286226\pi$
$48$	−44077.4	−	122412.i	−0.398559	−	1.10688i
$49$	−109763.			−0.932968
$50$	103672.	+	69836.6i	0.829375	+	0.558693i
$51$		−	95327.0i		−	0.718630i
$52$	174284.	+	122483.i	1.23950	+	0.871093i
$53$			47508.5i			0.319112i	0.987189	+	0.159556i	$0.0510063\pi$
$53$			47508.5i			0.319112i	−0.987189	+	0.159556i	$0.948994\pi$
$54$	−52601.4	−	101259.i	−0.334053	−	0.643062i
$55$	55237.5	+	216833.i	0.332006	+	1.30328i
$56$	45063.4	+	6051.21i	0.256602	+	0.0344571i
$57$		−	218305.i		−	1.17880i
$58$	−51778.5	−	99675.1i	−0.265378	−	0.510861i
$59$			139889.i			0.681127i	0.940221	+	0.340564i	$0.110618\pi$
$59$			139889.i			0.681127i	−0.940221	+	0.340564i	$0.889382\pi$
$60$	−90265.4	+	237541.i	−0.417895	+	1.09973i
$61$	299920.			1.32134			0.660672	−	0.750675i	$-0.270271\pi$
$61$	299920.			1.32134			0.660672	+	0.750675i	$0.270271\pi$
$62$	−363996.	+	189086.i	−1.52729	+	0.793386i
$63$	−24861.8			−0.0994286
$64$	252858.	+	69155.5i	0.964575	+	0.263807i
$65$	−102708.	−	403175.i	−0.373992	−	1.46809i
$66$	−403663.	+	209692.i	−1.40406	+	0.729373i
$67$	−40858.7			−0.135850			−0.0679251	−	0.997690i	$-0.521638\pi$
$67$	−40858.7			−0.135850			−0.0679251	+	0.997690i	$0.521638\pi$
$68$	157144.	+	110437.i	0.499772	+	0.351229i
$69$	187690.			0.571338
$70$	−59124.7	−	66260.9i	−0.172375	−	0.193180i
$71$		−	222756.i		−	0.622378i	−0.950348	−	0.311189i	$-0.899273\pi$
$71$		−	222756.i		−	0.622378i	0.950348	−	0.311189i	$-0.100727\pi$
$72$	−142065.	−	19076.8i	−0.380619	−	0.0511103i
$73$			633436.i			1.62830i	0.580656	+	0.814149i	$0.302796\pi$
$73$			633436.i			1.62830i	−0.580656	+	0.814149i	$0.697204\pi$
$74$	−134467.	+	69851.8i	−0.331833	+	0.172378i
$75$	435823.	−	237459.i	1.03306	−	0.562867i
$76$	359870.	+	252909.i	0.819794	+	0.576133i
$77$		−	158966.i		−	0.348202i
$78$	750564.	−	389897.i	1.58163	−	0.821612i
$79$			166771.i			0.338251i	0.985594	+	0.169126i	$0.0540944\pi$
$79$			166771.i			0.338251i	−0.985594	+	0.169126i	$0.945906\pi$
$80$	−287007.	−	423994.i	−0.560560	−	0.828114i
$81$	−657154.			−1.23655
$82$	−43378.0	−	83503.9i	−0.0786734	−	0.151449i
$83$	−328119.			−0.573848			−0.286924	−	0.957953i	$-0.592633\pi$
$83$	−328119.			−0.573848			−0.286924	+	0.957953i	$0.592633\pi$
$84$	103803.	−	147704.i	0.175135	−	0.249203i
$85$	−92607.1	−	363526.i	−0.150795	−	0.591941i
$86$	−372122.	−	716345.i	−0.585046	−	1.12623i
$87$	−445975.			−0.677256
$88$	121976.	−	908359.i	0.178990	−	1.33294i
$89$	27762.8			0.0393816			0.0196908	−	0.999806i	$-0.493732\pi$
$89$	27762.8			0.0393816			0.0196908	+	0.999806i	$0.493732\pi$
$90$	186394.	+	208891.i	0.255685	+	0.286545i
$91$			295578.i			0.392236i
$92$	−217441.	+	309402.i	−0.279240	+	0.397337i
$93$			1.62862e6i			2.02475i
$94$	476488.	+	917254.i	0.573679	+	1.10435i
$95$	−212076.	−	832496.i	−0.247355	−	0.970982i
$96$	706485.	−	764358.i	0.798526	−	0.863939i
$97$			220750.i			0.241872i	0.992660	+	0.120936i	$0.0385895\pi$
$97$			220750.i			0.241872i	−0.992660	+	0.120936i	$0.961410\pi$
$98$	−404791.	−	779235.i	−0.430084	−	0.827924i
$99$			501148.i			0.516489i
$100$	−113460.	+	993543.i	−0.113460	+	0.993543i
$101$	186720.			0.181229			0.0906144	−	0.995886i	$-0.471117\pi$
$101$	186720.			0.181229			0.0906144	+	0.995886i	$0.471117\pi$
$102$	676752.	−	351554.i	0.637718	−	0.331277i
$103$	−1.15683e6			−1.05866			−0.529332	−	0.848415i	$-0.677557\pi$
$103$	−1.15683e6			−1.05866			−0.529332	+	0.848415i	$0.677557\pi$
$104$	−226801.	+	1.68899e6i	−0.201625	+	1.50150i
$105$	−341687.	+	87043.8i	−0.295162	+	0.0751917i
$106$	−337275.	+	175205.i	−0.283183	+	0.147106i
$107$	1.55229e6			1.26713			0.633566	−	0.773689i	$-0.281591\pi$
$107$	1.55229e6			1.26713			0.633566	+	0.773689i	$0.281591\pi$
$108$	524878.	−	746862.i	0.416665	−	0.592883i
$109$	1.76722e6			1.36462			0.682310	−	0.731063i	$-0.260975\pi$
$109$	1.76722e6			1.36462			0.682310	+	0.731063i	$0.260975\pi$
$110$	−1.33564e6	+	1.19180e6i	−1.00349	+	0.895415i
$111$			601642.i			0.439916i
$112$	123229.	+	342233.i	0.0877121	+	0.243595i
$113$		−	1.35571e6i		−	0.939572i	−0.882780	−	0.469786i	$-0.844331\pi$
$113$		−	1.35571e6i		−	0.939572i	0.882780	−	0.469786i	$-0.155669\pi$
$114$	1.54980e6	−	805080.i	1.04607	−	0.543406i
$115$	715747.	−	182335.i	0.470615	−	0.119888i
$116$	516667.	−	735178.i	0.331007	−	0.470998i
$117$		−	931827.i		−	0.581805i
$118$	−993111.	+	515894.i	−0.604438	+	0.313989i
$119$			266510.i			0.158151i
$120$	−2.01925e6	+	235204.i	−1.16855	+	0.136113i
$121$	−1.43276e6			−0.808757
$122$	1.10607e6	+	2.12921e6i	0.609119	+	1.17257i
$123$	−373620.			−0.200778
$124$	−2.68474e6	−	1.88678e6i	−1.40811	−	0.989592i
$125$	1.43131e6	−	1.32893e6i	0.732830	−	0.680412i
$126$	−91687.3	−	176501.i	−0.0458351	−	0.0882338i
$127$	933285.			0.455620			0.227810	−	0.973706i	$-0.426843\pi$
$127$	933285.			0.455620			0.227810	+	0.973706i	$0.426843\pi$
$128$	441554.	+	2.05014e6i	0.210549	+	0.977583i
$129$	−3.20513e6			−1.49306
$130$	2.48347e6	−	2.21601e6i	1.13039	−	1.00865i
$131$			10503.7i			0.00467227i	0.999997	+	0.00233614i	$0.000743616\pi$
$131$			10503.7i			0.00467227i	−0.999997	+	0.00233614i	$0.999256\pi$
$132$	−2.97732e6	−	2.09239e6i	−1.29450	−	0.909749i
$133$			610324.i			0.259421i
$134$	−150682.	−	290067.i	−0.0626248	−	0.120555i
$135$	−1.72774e6	+	440136.i	−0.702225	+	0.178890i
$136$	−204497.	+	1.52289e6i	−0.0812961	+	0.605412i
$137$		−	2.10446e6i		−	0.818425i	−0.912439	−	0.409213i	$-0.865803\pi$
$137$		−	2.10446e6i		−	0.818425i	0.912439	−	0.409213i	$-0.134197\pi$
$138$	692177.	+	1.33246e6i	0.263378	+	0.507010i
$139$		−	3.09139e6i		−	1.15109i	−0.817770	−	0.575545i	$-0.804790\pi$
$139$		−	3.09139e6i		−	1.15109i	0.817770	−	0.575545i	$-0.195210\pi$
$140$	252359.	−	664104.i	0.0919676	−	0.242020i
$141$	4.10406e6			1.46405
$142$	1.58140e6	−	821496.i	0.552303	−	0.286906i
$143$	5.95806e6			2.03750
$144$	−388487.	−	1.07891e6i	−0.130104	−	0.361325i
$145$	−1.70071e6	+	433250.i	−0.557860	+	0.142113i
$146$	−4.49693e6	+	2.33603e6i	−1.44497	+	0.750620i
$147$	−3.48652e6			−1.09759
$148$	−991792.	−	697010.i	−0.305940	−	0.215008i
$149$	1.54748e6			0.467806			0.233903	−	0.972260i	$-0.424850\pi$
$149$	1.54748e6			0.467806			0.233903	+	0.972260i	$0.424850\pi$
$150$	3.29305e6	+	2.21830e6i	0.975718	+	0.657274i
$151$		−	2.13696e6i		−	0.620677i	−0.950626	−	0.310339i	$-0.899558\pi$
$151$		−	2.13696e6i		−	0.620677i	0.950626	−	0.310339i	$-0.100442\pi$
$152$	−468310.	+	3.48751e6i	−0.133353	+	0.993080i
$153$		−	840189.i		−	0.234586i
$154$	1.12854e6	−	586245.i	0.308997	−	0.160516i
$155$	1.58215e6	+	6.21069e6i	0.424868	+	1.66780i
$156$	5.53597e6	+	3.89056e6i	1.45821	+	1.02480i
$157$			6.53669e6i			1.68911i	0.535467	+	0.844556i	$0.320136\pi$
$157$			6.53669e6i			1.68911i	−0.535467	+	0.844556i	$0.679864\pi$
$158$	−1.18395e6	+	615031.i	−0.300167	+	0.155929i
$159$			1.50907e6i			0.375420i
$160$	1.95160e6	−	3.60118e6i	0.476465	−	0.879193i
$161$	−524733.			−0.125736
$162$	−2.42350e6	−	4.66531e6i	−0.570031	−	1.09733i
$163$	−7.13681e6			−1.64794			−0.823970	−	0.566633i	$-0.808246\pi$
$163$	−7.13681e6			−1.64794			−0.823970	+	0.566633i	$0.808246\pi$
$164$	432844.	−	615904.i	0.0981295	−	0.139631i
$165$	1.75457e6	+	6.88750e6i	0.390588	+	1.53324i
$166$	−1.21006e6	−	2.32940e6i	−0.264535	−	0.509237i
$167$	−4.55070e6			−0.977078			−0.488539	−	0.872542i	$-0.662470\pi$
$167$	−4.55070e6			−0.977078			−0.488539	+	0.872542i	$0.662470\pi$
$168$	1.43140e6	+	192212.i	0.301880	+	0.0405370i
$169$	−6.25151e6			−1.29516
$170$	2.23924e6	−	1.99808e6i	0.455779	−	0.406692i
$171$		−	1.92408e6i		−	0.384801i
$172$	3.71319e6	−	5.28358e6i	0.729729	−	1.03835i
$173$		−	8.29944e6i		−	1.60292i	−0.598051	−	0.801458i	$-0.704058\pi$
$173$		−	8.29944e6i		−	1.60292i	0.598051	−	0.801458i	$-0.295942\pi$
$174$	−1.64470e6	−	3.16609e6i	−0.312204	−	0.601002i
$175$	−1.21845e6	+	663876.i	−0.227349	+	0.123872i
$176$	6.89852e6	−	2.48397e6i	1.26537	−	0.455626i
$177$			4.44346e6i			0.801312i
$178$	102386.	+	197096.i	0.0181543	+	0.0349476i
$179$		−	3.03619e6i		−	0.529384i	−0.964333	−	0.264692i	$-0.914730\pi$
$179$		−	3.03619e6i		−	0.529384i	0.964333	−	0.264692i	$-0.0852702\pi$
$180$	−795577.	+	2.09363e6i	−0.136416	+	0.358990i
$181$	−644931.			−0.108762			−0.0543811	−	0.998520i	$-0.517319\pi$
$181$	−644931.			−0.108762			−0.0543811	+	0.998520i	$0.517319\pi$
$182$	−2.09839e6	+	1.09005e6i	−0.348074	+	0.180815i
$183$	9.52670e6			1.55450
$184$	−2.99842e6	−	402634.i	−0.481326	−	0.0646335i
$185$	584476.	+	2.29434e6i	0.0923106	+	0.362362i
$186$	−1.15620e7	+	6.00616e6i	−1.79678	+	0.933379i
$187$	5.37214e6			0.821528
$188$	−4.75460e6	+	6.76543e6i	−0.715550	+	1.01817i
$189$	1.26665e6			0.187616
$190$	5.12800e6	−	4.57572e6i	0.747631	−	0.667113i
$191$			4.62842e6i			0.664252i	0.943235	+	0.332126i	$0.107766\pi$
$191$			4.62842e6i			0.664252i	−0.943235	+	0.332126i	$0.892234\pi$
$192$	8.03181e6	+	2.19667e6i	1.13477	+	0.310356i
$193$		−	5.13781e6i		−	0.714671i	−0.933976	−	0.357335i	$-0.883685\pi$
$193$		−	5.13781e6i		−	0.714671i	0.933976	−	0.357335i	$-0.116315\pi$
$194$	−1.56716e6	+	814098.i	−0.214639	+	0.111499i
$195$	−3.26242e6	−	1.28065e7i	−0.439983	−	1.72714i
$196$	4.03918e6	−	5.74744e6i	0.536444	−	0.763320i
$197$		−	5.52253e6i		−	0.722337i	−0.932501	−	0.361168i	$-0.882378\pi$
$197$		−	5.52253e6i		−	0.722337i	0.932501	−	0.361168i	$-0.117622\pi$
$198$	−3.55779e6	+	1.84817e6i	−0.458336	+	0.238093i
$199$		−	4.29058e6i		−	0.544449i	−0.962234	−	0.272224i	$-0.912241\pi$
$199$		−	4.29058e6i		−	0.544449i	0.962234	−	0.272224i	$-0.0877593\pi$
$200$	−7.47185e6	+	2.85858e6i	−0.933981	+	0.357322i
$201$	−1.29784e6			−0.159821
$202$	688601.	+	1.32558e6i	0.0835437	+	0.160824i
$203$	1.24683e6			0.149046
$204$	4.99155e6	+	3.50795e6i	0.587957	+	0.413203i
$205$	−1.42479e6	+	362960.i	−0.165382	+	0.0421306i
$206$	−4.26625e6	−	8.21265e6i	−0.488028	−	0.939467i
$207$	1.65425e6			0.186505
$208$	−1.28270e7	+	4.61865e6i	−1.42539	+	0.513246i
$209$	1.23025e7			1.34758
$210$	−1.87805e6	−	2.10472e6i	−0.202791	−	0.227267i
$211$			1.06723e7i			1.13608i	0.823000	+	0.568041i	$0.192298\pi$
$211$			1.06723e7i			1.13608i	−0.823000	+	0.568041i	$0.807702\pi$
$212$	−2.48766e6	−	1.74827e6i	−0.261086	−	0.183485i
$213$		−	7.07565e6i		−	0.732196i
$214$	5.72465e6	+	1.10201e7i	0.584128	+	1.12446i
$215$	−1.22226e7	+	3.11368e6i	−1.22984	+	0.313299i
$216$	7.23786e6	+	971915.i	0.718206	+	0.0964422i
$217$		−	4.55322e6i		−	0.445594i
$218$	6.51730e6	+	1.25460e7i	0.629069	+	1.21097i
$219$			2.01205e7i			1.91561i
$220$	−1.33866e7	−	5.08689e6i	−1.25719	−	0.477732i
$221$	−9.98885e6			−0.925420
$222$	−4.27122e6	+	2.21878e6i	−0.390385	+	0.202794i
$223$	6.50950e6			0.586993			0.293497	−	0.955960i	$-0.405181\pi$
$223$	6.50950e6			0.586993			0.293497	+	0.955960i	$0.405181\pi$
$224$	−1.97515e6	+	2.13695e6i	−0.175734	+	0.190130i
$225$	3.84124e6	−	2.09291e6i	0.337228	−	0.183740i
$226$	9.62451e6	−	4.99967e6i	0.833784	−	0.433128i
$227$	8.28329e6			0.708150			0.354075	−	0.935217i	$-0.384796\pi$
$227$	8.28329e6			0.708150			0.354075	+	0.935217i	$0.384796\pi$
$228$	1.14310e7	+	8.03343e6i	0.964447	+	0.677792i
$229$	5.99134e6			0.498904			0.249452	−	0.968387i	$-0.419749\pi$
$229$	5.99134e6			0.498904			0.249452	+	0.968387i	$0.419749\pi$
$230$	3.93403e6	+	4.40885e6i	0.323336	+	0.362362i
$231$		−	5.04941e6i		−	0.409642i
$232$	7.12463e6	+	956711.i	0.570556	+	0.0766155i
$233$			1.67538e6i			0.132448i	0.997805	+	0.0662239i	$0.0210952\pi$
$233$			1.67538e6i			0.132448i	−0.997805	+	0.0662239i	$0.978905\pi$
$234$	6.61528e6	−	3.43646e6i	0.516299	−	0.268203i
$235$	1.56506e7	−	3.98696e6i	1.20595	−	0.307212i
$236$	−7.32494e6	−	5.14780e6i	−0.557273	−	0.391639i
$237$			5.29734e6i			0.397936i
$238$	−1.89203e6	+	982856.i	−0.140345	+	0.0729053i
$239$		−	4.03994e6i		−	0.295925i	−0.988993	−	0.147962i	$-0.952729\pi$
$239$		−	4.03994e6i		−	0.295925i	0.988993	−	0.147962i	$-0.0472715\pi$
$240$	−9.11653e6	−	1.34678e7i	−0.659471	−	0.974234i
$241$	9.32032e6			0.665855			0.332928	−	0.942952i	$-0.391964\pi$
$241$	9.32032e6			0.665855			0.332928	+	0.942952i	$0.391964\pi$
$242$	−5.28385e6	−	1.01716e7i	−0.372824	−	0.717698i
$243$	−1.04760e7			−0.730090
$244$	−1.10368e7	+	1.57045e7i	−0.759755	+	1.08107i
$245$	−1.32957e7	+	3.38704e6i	−0.904093	+	0.230315i
$246$	−1.37787e6	−	2.65243e6i	−0.0925554	−	0.178172i
$247$	−2.28751e7			−1.51800
$248$	3.49374e6	−	2.60179e7i	0.229053	−	1.70576i
$249$	−1.04224e7			−0.675103
$250$	1.47129e7	+	5.26031e6i	0.941626	+	0.336660i
$251$		−	2.59353e7i		−	1.64010i	−0.572291	−	0.820051i	$-0.693945\pi$
$251$		−	2.59353e7i		−	1.64010i	0.572291	−	0.820051i	$-0.306055\pi$
$252$	914894.	−	1.30183e6i	0.0571701	−	0.0813488i
$253$			1.05772e7i			0.653146i
$254$	3.44184e6	+	6.62564e6i	0.210034	+	0.404321i
$255$	−2.94159e6	−	1.15471e7i	−0.177403	−	0.696389i
$256$	−1.29261e7	+	1.06954e7i	−0.770455	+	0.637494i
$257$			1.61283e7i			0.950146i	0.879946	+	0.475073i	$0.157578\pi$
$257$			1.61283e7i			0.950146i	−0.879946	+	0.475073i	$0.842422\pi$
$258$	−1.18201e7	−	2.27541e7i	−0.688277	−	1.32495i
$259$		−	1.68204e6i		−	0.0968137i
$260$	2.48908e7	+	9.45847e6i	1.41618	+	0.538147i
$261$	−3.93071e6			−0.221080
$262$	−74568.5	+	38736.3i	−0.00414621	+	0.00215385i
$263$	91845.2			0.00504881			0.00252441	−	0.999997i	$-0.499196\pi$
$263$	91845.2			0.00504881			0.00252441	+	0.999997i	$0.499196\pi$
$264$	3.87448e6	−	2.88533e7i	0.210572	−	1.56813i
$265$	1.46601e6	+	5.75476e6i	0.0787769	+	0.309236i
$266$	−4.33285e6	+	2.25080e6i	−0.230213	+	0.119589i
$267$	881862.			0.0463305
$268$	1.50357e6	−	2.13946e6i	0.0781121	−	0.111148i
$269$	−5.38438e6			−0.276617			−0.138308	−	0.990389i	$-0.544167\pi$
$269$	−5.38438e6			−0.276617			−0.138308	+	0.990389i	$0.544167\pi$
$270$	−9.49631e6	−	1.06425e7i	−0.482463	−	0.540694i
$271$			8.91843e6i			0.448106i	0.974577	+	0.224053i	$0.0719289\pi$
$271$			8.91843e6i			0.448106i	−0.974577	+	0.224053i	$0.928071\pi$
$272$	−1.15655e7	+	4.16445e6i	−0.574724	+	0.206943i
$273$			9.38878e6i			0.461446i
$274$	1.49401e7	−	7.76099e6i	0.726277	−	0.377281i
$275$	1.33820e7	+	2.45607e7i	0.643461	+	1.18098i
$276$	−6.90682e6	+	9.82789e6i	−0.328512	+	0.467448i
$277$		−	8.85192e6i		−	0.416484i	−0.978077	−	0.208242i	$-0.933226\pi$
$277$		−	8.85192e6i		−	0.416484i	0.978077	−	0.208242i	$-0.0667742\pi$
$278$	2.19466e7	−	1.14007e7i	1.02149	−	0.530635i
$279$			1.43543e7i			0.660951i
$280$	5.64532e6	−	657569.i	0.257167	−	0.0299549i
$281$	4.54352e6			0.204774			0.102387	−	0.994745i	$-0.467352\pi$
$281$	4.54352e6			0.204774			0.102387	+	0.994745i	$0.467352\pi$
$282$	1.51352e7	+	2.91358e7i	0.674904	+	1.29921i
$283$	−1.97987e7			−0.873528			−0.436764	−	0.899576i	$-0.643875\pi$
$283$	−1.97987e7			−0.873528			−0.436764	+	0.899576i	$0.643875\pi$
$284$	1.16640e7	+	8.19722e6i	0.509206	+	0.357859i
$285$	−6.73641e6	−	2.64435e7i	−0.291001	−	1.14231i
$286$	2.19726e7	+	4.22979e7i	0.939254	+	1.80809i
$287$	1.04455e6			0.0441858
$288$	6.22678e6	−	6.73686e6i	0.260667	−	0.282020i
$289$	1.51310e7			0.626867
$290$	−9.34775e6	−	1.04760e7i	−0.383277	−	0.429538i
$291$			7.01193e6i			0.284550i
$292$	−3.31682e7	−	2.33099e7i	−1.33221	−	0.936250i
$293$			3.44412e7i			1.36923i	0.728906	+	0.684614i	$0.240029\pi$
$293$			3.44412e7i			1.36923i	−0.728906	+	0.684614i	$0.759971\pi$
$294$	−1.28579e7	−	2.47517e7i	−0.505972	−	0.974011i
$295$	4.31668e6	+	1.69450e7i	0.168145	+	0.660047i
$296$	1.29065e6	−	9.61148e6i	0.0497661	−	0.370608i
$297$		−	2.55323e7i		−	0.974585i
$298$	5.70691e6	+	1.09860e7i	0.215651	+	0.415135i
$299$		−	1.96671e7i		−	0.735744i
$300$	−3.60396e6	+	3.15590e7i	−0.133480	+	1.16885i
$301$	8.96074e6			0.328582
$302$	1.51709e7	−	7.88085e6i	0.550794	−	0.286123i
$303$	5.93101e6			0.213207
$304$	−2.64858e7	+	9.53683e6i	−0.942741	+	0.339456i
$305$	3.63297e7	−	9.25489e6i	1.28045	−	0.326191i
$306$	5.96472e6	−	3.09851e6i	0.208174	−	0.108141i
$307$	1.94134e7			0.670944			0.335472	−	0.942050i	$-0.391104\pi$
$307$	1.94134e7			0.670944			0.335472	+	0.942050i	$0.391104\pi$
$308$	8.32382e6	+	5.84980e6i	0.284886	+	0.200211i
$309$	−3.67458e7			−1.24547
$310$	−3.82565e7	+	3.41364e7i	−1.28416	+	1.14586i
$311$		−	2.64127e7i		−	0.878075i	−0.898469	−	0.439038i	$-0.855319\pi$
$311$		−	2.64127e7i		−	0.878075i	0.898469	−	0.439038i	$-0.144681\pi$
$312$	−7.20413e6	+	5.36492e7i	−0.237202	+	1.76644i
$313$			4.96526e6i			0.161923i	0.996717	+	0.0809616i	$0.0257991\pi$
$313$			4.96526e6i			0.161923i	−0.996717	+	0.0809616i	$0.974201\pi$
$314$	−4.64057e7	+	2.41065e7i	−1.49893	+	0.778655i
$315$	−3.01155e6	+	767183.i	−0.0963514	+	0.0245452i
$316$	−8.73254e6	−	6.13704e6i	−0.276745	−	0.194490i
$317$		−	3.24542e7i		−	1.01881i	−0.860527	−	0.509405i	$-0.829865\pi$
$317$		−	3.24542e7i		−	1.01881i	0.860527	−	0.509405i	$-0.170135\pi$
$318$	−1.07133e7	+	5.56525e6i	−0.333150	+	0.173063i
$319$		−	2.51328e7i		−	0.774229i
$320$	3.27630e7	+	574255.i	0.999846	+	0.0175249i
$321$	4.93072e7			1.49072
$322$	−1.93515e6	−	3.72522e6i	−0.0579625	−	0.111579i
$323$	−2.06255e7			−0.612064
$324$	2.41827e7	−	3.44102e7i	0.711001	−	1.01170i
$325$	−2.48822e7	−	4.56677e7i	−0.724834	−	1.33033i
$326$	−2.63197e7	−	5.06661e7i	−0.759675	−	1.46240i
$327$	5.61343e7			1.60541
$328$	5.96874e6	+	801495.i	0.169146	+	0.0227133i
$329$	−1.14739e7			−0.322198
$330$	−4.24256e7	+	3.78564e7i	−1.18055	+	1.05341i
$331$			4.50251e7i			1.24157i	0.783981	+	0.620784i	$0.213186\pi$
$331$			4.50251e7i			1.24157i	−0.783981	+	0.620784i	$0.786814\pi$
$332$	1.20745e7	−	1.71811e7i	0.329955	−	0.469501i
$333$			5.30273e6i			0.143604i
$334$	−1.67824e7	−	3.23067e7i	−0.450418	−	0.867067i
$335$	−4.94927e6	+	1.26081e6i	−0.131646	+	0.0335364i
$336$	3.91427e6	+	1.08708e7i	0.103189	+	0.286577i
$337$			2.36631e6i			0.0618275i	0.999522	+	0.0309137i	$0.00984172\pi$
$337$			2.36631e6i			0.0618275i	−0.999522	+	0.0309137i	$0.990158\pi$
$338$	−2.30548e7	−	4.43811e7i	−0.597050	−	1.14934i
$339$		−	4.30628e7i		−	1.10536i
$340$	2.24429e7	+	8.52830e6i	0.571009	+	0.216983i
$341$	−9.17807e7			−2.31467
$342$	1.36596e7	−	7.09578e6i	0.341475	−	0.177387i
$343$	2.01952e7			0.500456
$344$	5.12033e7	+	6.87569e6i	1.25783	+	0.168904i
$345$	2.27351e7	−	5.79170e6i	0.553656	−	0.141042i
$346$	5.89200e7	−	3.06073e7i	1.42244	−	0.738919i
$347$	−3.57456e7			−0.855528			−0.427764	−	0.903890i	$-0.640699\pi$
$347$	−3.57456e7			−0.855528			−0.427764	+	0.903890i	$0.640699\pi$
$348$	1.64115e7	−	2.33523e7i	0.389413	−	0.554105i
$349$	2.95982e7			0.696288			0.348144	−	0.937441i	$-0.386812\pi$
$349$	2.95982e7			0.696288			0.348144	+	0.937441i	$0.386812\pi$
$350$	−9.20652e6	−	6.20181e6i	−0.214729	−	0.144649i
$351$			4.74742e7i			1.09783i
$352$	4.30752e7	+	3.98138e7i	0.987642	+	0.912863i
$353$			6.19569e7i			1.40853i	0.709938	+	0.704264i	$0.248723\pi$
$353$			6.19569e7i			1.40853i	−0.709938	+	0.704264i	$0.751277\pi$
$354$	−3.15453e7	+	1.63869e7i	−0.711091	+	0.369392i
$355$	−6.87376e6	−	2.69827e7i	−0.153642	−	0.603115i
$356$	−1.02165e6	+	1.45373e6i	−0.0226439	+	0.0322206i
$357$			8.46547e6i			0.186057i
$358$	2.15547e7	−	1.11971e7i	0.469779	−	0.244038i
$359$			4.08262e7i			0.882380i	0.897414	+	0.441190i	$0.145444\pi$
$359$			4.08262e7i			0.882380i	−0.897414	+	0.441190i	$0.854556\pi$
$360$	−1.77972e7	+	2.07303e6i	−0.381456	+	0.0444321i
$361$	−187766.			−0.00399111
$362$	−2.37843e6	−	4.57854e6i	−0.0501377	−	0.0965164i
$363$	−4.55105e7			−0.951463
$364$	−1.54772e7	−	1.08770e7i	−0.320913	−	0.225531i
$365$	1.95465e7	+	7.67289e7i	0.401966	+	1.57790i
$366$	3.51333e7	+	6.76326e7i	0.716598	+	1.37947i
$367$	−1.51049e7			−0.305577			−0.152788	−	0.988259i	$-0.548825\pi$
$367$	−1.51049e7			−0.305577			−0.152788	+	0.988259i	$0.548825\pi$
$368$	−8.19940e6	−	2.27715e7i	−0.164527	−	0.456928i
$369$	−3.29300e6			−0.0655409
$370$	−1.41326e7	+	1.26106e7i	−0.279009	+	0.248960i
$371$		−	4.21896e6i		−	0.0826198i
$372$	−8.52786e7	−	5.99319e7i	−1.65658	−	1.16421i
$373$		−	5.32493e7i		−	1.02610i	−0.858360	−	0.513048i	$-0.828516\pi$
$373$		−	5.32493e7i		−	1.02610i	0.858360	−	0.513048i	$-0.171484\pi$
$374$	1.98118e7	+	3.81382e7i	0.378711	+	0.729030i
$375$	4.54643e7	−	4.22123e7i	0.862138	−	0.800471i
$376$	−6.55640e7	−	8.80407e6i	−1.23339	−	0.165623i
$377$			4.67315e7i			0.872139i
$378$	4.67124e6	+	8.99227e6i	0.0864882	+	0.166492i
$379$		−	329020.i		−	0.00604373i	−0.999995	−	0.00302187i	$-0.999038\pi$
$379$		−	329020.i		−	0.00604373i	0.999995	−	0.00302187i	$-0.000961891\pi$
$380$	5.13957e7	+	1.95303e7i	0.936647	+	0.355925i
$381$	2.96450e7			0.536015
$382$	−3.28584e7	+	1.70691e7i	−0.589463	+	0.306210i
$383$	−8.05002e7			−1.43285			−0.716424	−	0.697665i	$-0.754223\pi$
$383$	−8.05002e7			−1.43285			−0.716424	+	0.697665i	$0.754223\pi$
$384$	1.40256e7	+	6.51210e7i	0.247701	+	1.15008i
$385$	−4.90534e6	−	1.92557e7i	−0.0859581	−	0.337425i
$386$	3.64747e7	−	1.89476e7i	0.634205	−	0.329452i
$387$	−2.82493e7			−0.487387
$388$	−1.15590e7	−	8.12340e6i	−0.197890	−	0.139073i
$389$	4.89579e7			0.831713			0.415857	−	0.909430i	$-0.363482\pi$
$389$	4.89579e7			0.831713			0.415857	+	0.909430i	$0.363482\pi$
$390$	7.88854e7	−	7.03896e7i	1.32985	−	1.18663i
$391$		−	1.77330e7i		−	0.296655i
$392$	5.56986e7	+	7.47933e6i	0.924669	+	0.124166i
$393$			333641.i			0.00549670i
$394$	3.92059e7	−	2.03664e7i	0.641008	−	0.332986i
$395$	5.14620e6	+	2.02012e7i	0.0835017	+	0.327783i
$396$	−2.62413e7	−	1.84418e7i	−0.422572	−	0.296974i
$397$			6.21417e7i			0.993142i	0.867996	+	0.496571i	$0.165408\pi$
$397$			6.21417e7i			0.993142i	−0.867996	+	0.496571i	$0.834592\pi$
$398$	3.04600e7	−	1.58231e7i	0.483148	−	0.250982i
$399$			1.93864e7i			0.305196i
$400$	−4.78491e7	−	4.25026e7i	−0.747642	−	0.664102i
$401$	382303.			0.00592891			0.00296445	−	0.999996i	$-0.499056\pi$
$401$	382303.			0.00592891			0.00296445	+	0.999996i	$0.499056\pi$
$402$	−4.78628e6	−	9.21373e6i	−0.0736750	−	0.141826i
$403$	1.70655e8			2.60738
$404$	−6.87115e6	+	9.77713e6i	−0.104204	+	0.148275i
$405$	−7.96020e7	+	2.02784e7i	−1.19828	+	0.305259i
$406$	4.59816e6	+	8.85159e6i	0.0687078	+	0.132265i
$407$	−3.39054e7			−0.502905
$408$	−6.49566e6	+	4.83733e7i	−0.0956408	+	0.712238i
$409$	−1.10847e8			−1.62015			−0.810074	−	0.586327i	$-0.800573\pi$
$409$	−1.10847e8			−1.62015			−0.810074	+	0.586327i	$0.800573\pi$
$410$	−7.83119e6	−	8.77639e6i	−0.113626	−	0.127340i
$411$		−	6.68464e7i		−	0.962836i
$412$	4.25704e7	−	6.05745e7i	0.608718	−	0.866159i
$413$		−	1.24228e7i		−	0.176347i
$414$	6.10067e6	+	1.17440e7i	0.0859759	+	0.165506i
$415$	−3.97454e7	+	1.01250e7i	−0.556087	+	0.141662i
$416$	−8.00933e7	−	7.40291e7i	−1.11254	−	1.02831i
$417$		−	9.81954e7i		−	1.35420i
$418$	4.53701e7	+	8.73388e7i	0.621214	+	1.19585i
$419$			1.21226e8i			1.64799i	0.566596	+	0.823995i	$0.308260\pi$
$419$			1.21226e8i			1.64799i	−0.566596	+	0.823995i	$0.691740\pi$
$420$	8.01597e6	−	2.10947e7i	0.108195	−	0.284725i
$421$	−826557.			−0.0110771			−0.00553856	−	0.999985i	$-0.501763\pi$
$421$	−826557.			−0.0110771			−0.00553856	+	0.999985i	$0.501763\pi$
$422$	−7.57653e7	+	3.93580e7i	−1.00817	+	0.523716i
$423$	3.61721e7			0.477918
$424$	3.23727e6	−	2.41080e7i	0.0424699	−	0.316273i
$425$	−2.24352e7	−	4.11767e7i	−0.292256	−	0.536395i
$426$	5.02319e7	−	2.60941e7i	0.649757	−	0.337531i
$427$	−2.66342e7			−0.342103
$428$	−5.71230e7	+	8.12817e7i	−0.728584	+	1.03672i
$429$	1.89253e8			2.39701
$430$	−6.71805e7	−	7.52890e7i	−0.844963	−	0.946948i
$431$		−	1.26492e8i		−	1.57990i	−0.613169	−	0.789952i	$-0.710106\pi$
$431$		−	1.26492e8i		−	1.57990i	0.613169	−	0.789952i	$-0.289894\pi$
$432$	1.97924e7	+	5.49678e7i	0.245498	+	0.681800i
$433$		−	1.05162e8i		−	1.29537i	−0.761907	−	0.647687i	$-0.775737\pi$
$433$		−	1.05162e8i		−	1.29537i	0.761907	−	0.647687i	$-0.224263\pi$
$434$	3.23245e7	−	1.67917e7i	0.395424	−	0.205412i
$435$	−5.40215e7	+	1.37618e7i	−0.656295	+	0.167189i
$436$	−6.50323e7	+	9.25360e7i	−0.784638	+	1.11648i
$437$		−	4.06096e7i		−	0.486614i
$438$	−1.42841e8	+	7.42021e7i	−1.69993	+	0.883067i
$439$		−	2.67453e7i		−	0.316122i	−0.987429	−	0.158061i	$-0.949476\pi$
$439$		−	2.67453e7i		−	0.316122i	0.987429	−	0.158061i	$-0.0505242\pi$
$440$	−1.32548e7	−	1.13795e8i	−0.155603	−	1.33587i
$441$	−3.07293e7			−0.358292
$442$	−3.68376e7	−	7.09135e7i	−0.426604	−	0.821225i
$443$	8.39480e7			0.965604			0.482802	−	0.875730i	$-0.339619\pi$
$443$	8.39480e7			0.965604			0.482802	+	0.875730i	$0.339619\pi$
$444$	−3.15034e7	−	2.21399e7i	−0.359923	−	0.252946i
$445$	3.36294e6	−	856700.i	0.0381628	−	0.00972185i
$446$	2.40062e7	+	4.62127e7i	0.270595	+	0.520903i
$447$	4.91543e7			0.550350
$448$	−2.24549e7	−	6.14132e6i	−0.249734	−	0.0683011i
$449$	−3.85437e7			−0.425808			−0.212904	−	0.977073i	$-0.568292\pi$
$449$	−3.85437e7			−0.425808			−0.212904	+	0.977073i	$0.568292\pi$
$450$	2.90241e7	+	1.95516e7i	0.318509	+	0.214558i
$451$		−	2.10553e7i		−	0.229526i
$452$	7.09880e7	+	4.98888e7i	0.768723	+	0.540241i
$453$		−	6.78788e7i		−	0.730196i
$454$	3.05477e7	+	5.88053e7i	0.326446	+	0.628418i
$455$	9.12089e6	+	3.58037e7i	0.0968285	+	0.380097i
$456$	−1.48755e7	+	1.10778e8i	−0.156883	+	1.16831i
$457$			1.01357e8i			1.06196i	0.847386	+	0.530978i	$0.178175\pi$
$457$			1.01357e8i			1.06196i	−0.847386	+	0.530978i	$0.821825\pi$
$458$	2.20953e7	+	4.25341e7i	0.229987	+	0.442732i
$459$			4.28055e7i			0.442651i
$460$	−1.67914e7	+	4.41880e7i	−0.172510	+	0.453974i
$461$	9.49132e7			0.968777			0.484388	−	0.874853i	$-0.339042\pi$
$461$	9.49132e7			0.968777			0.484388	+	0.874853i	$0.339042\pi$
$462$	3.58471e7	−	1.86216e7i	0.363520	−	0.188839i
$463$	−1.18102e8			−1.18991			−0.594955	−	0.803759i	$-0.702830\pi$
$463$	−1.18102e8			−1.18991			−0.594955	+	0.803759i	$0.702830\pi$
$464$	1.94828e7	+	5.41079e7i	0.195028	+	0.541635i
$465$	5.02558e7	+	1.97277e8i	0.499836	+	1.96209i
$466$	−1.18939e7	+	6.17858e6i	−0.117535	+	0.0610564i
$467$	1.86109e8			1.82733			0.913663	−	0.406473i	$-0.133241\pi$
$467$	1.86109e8			1.82733			0.913663	+	0.406473i	$0.133241\pi$
$468$	4.87927e7	+	3.42904e7i	0.476011	+	0.334530i
$469$	3.62844e6			0.0351723
$470$	8.60221e7	+	9.64047e7i	0.828546	+	0.928549i
$471$			2.07632e8i			1.98716i
$472$	9.53217e6	−	7.09861e7i	0.0906496	−	0.675068i
$473$		−	1.80625e8i		−	1.70684i
$474$	−3.76073e7	+	1.95359e7i	−0.353132	+	0.183442i
$475$	−5.13781e7	−	9.42971e7i	−0.479399	−	0.879868i
$476$	−1.39551e7	−	9.80734e6i	−0.129394	−	0.0909349i
$477$			1.33005e7i			0.122550i
$478$	2.86806e7	−	1.48988e7i	0.262606	−	0.136417i
$479$		−	5.01949e7i		−	0.456723i	−0.973576	−	0.228362i	$-0.926663\pi$
$479$		−	5.01949e7i		−	0.456723i	0.973576	−	0.228362i	$-0.0733368\pi$
$480$	6.19910e7	−	1.14388e8i	0.560538	−	1.03433i
$481$	6.30432e7			0.566504
$482$	3.43722e7	+	6.61674e7i	0.306949	+	0.590885i
$483$	−1.66677e7			−0.147922
$484$	5.27244e7	−	7.50229e7i	0.465025	−	0.661695i
$485$	6.81186e6	+	2.67397e7i	0.0597091	+	0.234386i
$486$	−3.86341e7	−	7.43718e7i	−0.336560	−	0.647888i
$487$	−1.08896e8			−0.942816			−0.471408	−	0.881915i	$-0.656254\pi$
$487$	−1.08896e8			−0.942816			−0.471408	+	0.881915i	$0.656254\pi$
$488$	−1.52193e8	−	2.04368e7i	−1.30959	−	0.175854i
$489$	−2.26695e8			−1.93872
$490$	−7.30784e7	−	8.18988e7i	−0.621156	−	0.696128i
$491$			1.71108e7i			0.144553i	0.997385	+	0.0722764i	$0.0230264\pi$
$491$			1.71108e7i			0.144553i	−0.997385	+	0.0722764i	$0.976974\pi$
$492$	1.37489e7	−	1.95637e7i	0.115444	−	0.164269i
$493$			4.21359e7i			0.351650i
$494$	−8.43604e7	−	1.62396e8i	−0.699774	−	1.34709i
$495$	1.54644e7	+	6.07048e7i	0.127502	+	0.500504i
$496$	1.97593e8	−	7.11479e7i	1.61929	−	0.583065i
$497$			1.97817e7i			0.161137i
$498$	−3.84366e7	−	7.39915e7i	−0.311212	−	0.599092i
$499$		−	2.08493e7i		−	0.167799i	−0.996474	−	0.0838994i	$-0.973263\pi$
$499$		−	2.08493e7i		−	0.167799i	0.996474	−	0.0838994i	$-0.0267374\pi$
$500$	1.69150e7	+	1.23850e8i	0.135320	+	0.990802i
$501$	−1.44549e8			−1.14948
$502$	1.84122e8	−	9.56463e7i	1.45544	−	0.756061i
$503$	−1.34897e7			−0.105998			−0.0529991	−	0.998595i	$-0.516878\pi$
$503$	−1.34897e7			−0.105998			−0.0529991	+	0.998595i	$0.516878\pi$
$504$	1.26160e7	+	1.69411e6i	0.0985442	+	0.0132327i
$505$	2.26177e7	−	5.76179e6i	0.175620	−	0.0447387i
$506$	−7.50905e7	+	3.90075e7i	−0.579607	+	0.301090i
$507$	−1.98574e8			−1.52369
$508$	−3.43441e7	+	4.88691e7i	−0.261976	+	0.372772i
$509$	1.73454e8			1.31531			0.657657	−	0.753317i	$-0.271547\pi$
$509$	1.73454e8			1.31531			0.657657	+	0.753317i	$0.271547\pi$
$510$	7.11276e7	−	6.34673e7i	0.536201	−	0.478453i
$511$		−	5.62519e7i		−	0.421575i
$512$	−1.23599e8	−	5.23226e7i	−0.920885	−	0.389834i
$513$			9.80272e7i			0.726097i
$514$	−1.14499e8	+	5.94793e7i	−0.843167	+	0.438002i
$515$	−1.40128e8	+	3.56973e7i	−1.02590	+	0.261345i
$516$	1.17946e8	−	1.67829e8i	0.858489	−	1.22157i
$517$			2.31283e8i			1.67368i
$518$	1.19412e7	−	6.20315e6i	0.0859133	−	0.0446296i
$519$		−	2.63625e8i		−	1.88575i
$520$	2.46458e7	+	2.11588e8i	0.175280	+	1.50481i
$521$	−1.78879e8			−1.26487			−0.632437	−	0.774612i	$-0.717945\pi$
$521$	−1.78879e8			−1.26487			−0.632437	+	0.774612i	$0.717945\pi$
$522$	−1.44960e7	−	2.79052e7i	−0.101915	−	0.196188i
$523$	1.77417e8			1.24020			0.620098	−	0.784525i	$-0.287093\pi$
$523$	1.77417e8			1.24020			0.620098	+	0.784525i	$0.287093\pi$
$524$	−549999.	−	386527.i	−0.00382268	−	0.00268649i
$525$	−3.87030e7	+	2.10875e7i	−0.267465	+	0.145729i
$526$	338714.	+	652034.i	0.00232742	+	0.00448036i
$527$	1.53873e8			1.05131
$528$	2.19126e8	−	7.89013e7i	1.48865	−	0.536022i
$529$	−1.13121e8			−0.764148
$530$	−3.54481e7	+	3.16304e7i	−0.238103	+	0.212460i
$531$			3.91636e7i			0.261577i
$532$	−3.19581e7	−	2.24594e7i	−0.212249	−	0.149164i
$533$			3.91499e7i			0.258552i
$534$	3.25220e6	+	6.26057e6i	0.0213576	+	0.0411141i
$535$	1.88031e8	−	4.79003e7i	1.22791	−	0.312808i
$536$	2.07336e7	+	2.78415e6i	0.134642	+	0.0180800i
$537$		−	9.64421e7i		−	0.622793i
$538$	−1.98569e7	−	3.82251e7i	−0.127516	−	0.245472i
$539$		−	1.96482e8i		−	1.25475i
$540$	4.05326e7	−	1.06665e8i	0.257409	−	0.677393i
$541$	1.34835e8			0.851553			0.425777	−	0.904828i	$-0.360001\pi$
$541$	1.34835e8			0.851553			0.425777	+	0.904828i	$0.360001\pi$
$542$	−6.33143e7	+	3.28901e7i	−0.397653	+	0.206570i
$543$	−2.04857e7			−0.127953
$544$	−7.22168e7	−	6.67489e7i	−0.448582	−	0.414617i
$545$	2.14066e8	−	5.45327e7i	1.32239	−	0.336874i
$546$	−6.66534e7	+	3.46246e7i	−0.409491	+	0.212720i
$547$	−2.22069e8			−1.35683			−0.678416	−	0.734678i	$-0.737333\pi$
$547$	−2.22069e8			−1.35683			−0.678416	+	0.734678i	$0.737333\pi$
$548$	1.10195e8	+	7.74423e7i	0.669605	+	0.470583i
$549$	8.39660e7			0.507442
$550$	−1.25012e8	+	1.85579e8i	−0.751386	+	1.11543i
$551$			9.64937e7i			0.576825i
$552$	−9.52423e7	−	1.27893e7i	−0.566256	−	0.0760380i
$553$		−	1.48100e7i		−	0.0875751i
$554$	6.28422e7	−	3.26448e7i	0.369591	−	0.191993i
$555$	1.85654e7	+	7.28777e7i	0.108599	+	0.426301i
$556$	1.61873e8	+	1.13760e8i	0.941779	+	0.661861i
$557$		−	2.84443e8i		−	1.64600i	−0.568042	−	0.823000i	$-0.692299\pi$
$557$		−	2.84443e8i		−	1.64600i	0.568042	−	0.823000i	$-0.307701\pi$
$558$	−1.01905e8	+	5.29368e7i	−0.586533	+	0.304688i
$559$			3.35850e8i			1.92269i
$560$	2.54875e7	+	3.76526e7i	0.145132	+	0.214403i
$561$	1.70641e8			0.966486
$562$	1.67560e7	+	3.22557e7i	0.0943974	+	0.181718i
$563$	−4.28842e7			−0.240310			−0.120155	−	0.992755i	$-0.538339\pi$
$563$	−4.28842e7			−0.240310			−0.120155	+	0.992755i	$0.538339\pi$
$564$	−1.51026e8	+	2.14898e8i	−0.841809	+	1.19783i
$565$	−4.18341e7	−	1.64218e8i	−0.231945	−	0.910492i
$566$	−7.30150e7	−	1.40556e8i	−0.402683	−	0.775176i
$567$	5.83583e7			0.320150
$568$	−1.51788e7	+	1.13036e8i	−0.0828307	+	0.616841i
$569$	−3.24019e8			−1.75887			−0.879435	−	0.476019i	$-0.842079\pi$
$569$	−3.24019e8			−1.75887			−0.879435	+	0.476019i	$0.842079\pi$
$570$	1.62887e8	−	1.45344e8i	0.879550	−	0.784825i
$571$			3.28824e8i			1.76626i	0.469126	+	0.883131i	$0.344569\pi$
$571$			3.28824e8i			1.76626i	−0.469126	+	0.883131i	$0.655431\pi$
$572$	−2.19252e8	+	3.11979e8i	−1.17153	+	1.66700i
$573$			1.47018e8i			0.781460i
$574$	3.85216e6	+	7.41552e6i	0.0203690	+	0.0392108i
$575$	8.10730e7	−	4.41728e7i	0.426454	−	0.232355i
$576$	7.07904e7	+	1.93609e7i	0.370431	+	0.101311i
$577$			9.48080e7i			0.493534i	0.969075	+	0.246767i	$0.0793683\pi$
$577$			9.48080e7i			0.493534i	−0.969075	+	0.246767i	$0.920632\pi$
$578$	5.58014e7	+	1.07419e8i	0.288976	+	0.556287i
$579$		−	1.63198e8i		−	0.840775i
$580$	3.98985e7	−	1.04996e8i	0.204490	−	0.538134i
$581$	2.91384e7			0.148572
$582$	−4.97796e7	+	2.58591e7i	−0.252512	+	0.131173i
$583$	−8.50431e7			−0.429174
$584$	4.31628e7	−	3.21434e8i	0.216706	−	1.61381i
$585$	−2.87542e7	−	1.12873e8i	−0.143626	−	0.563798i
$586$	−2.44507e8	+	1.27015e8i	−1.21506	+	0.631193i
$587$	5.12804e7			0.253534			0.126767	−	0.991932i	$-0.459540\pi$
$587$	5.12804e7			0.253534			0.126767	+	0.991932i	$0.459540\pi$
$588$	1.28301e8	−	1.82563e8i	0.631100	−	0.898008i
$589$	3.52378e8			1.72450
$590$	−1.04377e8	+	9.31362e7i	−0.508219	+	0.453484i
$591$		−	1.75419e8i		−	0.849793i
$592$	7.29942e7	−	2.62833e7i	0.351822	−	0.126682i
$593$		−	2.12368e7i		−	0.101842i	−0.998703	−	0.0509208i	$-0.983784\pi$
$593$		−	2.12368e7i		−	0.101842i	0.998703	−	0.0509208i	$-0.0162156\pi$
$594$	1.81260e8	−	9.41598e7i	0.864855	−	0.449269i
$595$	8.22393e6	+	3.22827e7i	0.0390417	+	0.153257i
$596$	−5.69459e7	+	8.10297e7i	−0.268982	+	0.382741i
$597$		−	1.36287e8i		−	0.640517i
$598$	1.39622e8	−	7.25298e7i	0.652905	−	0.339166i
$599$			2.38008e8i			1.10742i	0.832710	+	0.553709i	$0.186788\pi$
$599$			2.38008e8i			1.10742i	−0.832710	+	0.553709i	$0.813212\pi$
$600$	−2.37337e8	+	9.08003e7i	−1.09878	+	0.420372i
$601$	−1.59516e8			−0.734822			−0.367411	−	0.930059i	$-0.619756\pi$
$601$	−1.59516e8			−0.734822			−0.367411	+	0.930059i	$0.619756\pi$
$602$	3.30461e7	+	6.36147e7i	0.151471	+	0.291587i
$603$	−1.14389e7			−0.0521712
$604$	1.11896e8	+	7.86384e7i	0.507815	+	0.356881i
$605$	−1.73552e8	+	4.42120e7i	−0.783727	+	0.199652i
$606$	2.18728e7	+	4.21058e7i	0.0982850	+	0.189201i
$607$	1.87552e8			0.838602			0.419301	−	0.907847i	$-0.362275\pi$
$607$	1.87552e8			0.838602			0.419301	+	0.907847i	$0.362275\pi$
$608$	−1.65381e8	−	1.52859e8i	−0.735825	−	0.680112i
$609$	3.96046e7			0.175345
$610$	1.99682e8	+	2.23783e8i	0.879731	+	0.985912i
$611$		−	4.30044e8i		−	1.88534i
$612$	4.39943e7	+	3.09182e7i	0.191930	+	0.134884i
$613$		−	1.96888e7i		−	0.0854749i	−0.999086	−	0.0427374i	$-0.986392\pi$
$613$		−	1.96888e7i		−	0.0854749i	0.999086	−	0.0427374i	$-0.0136079\pi$
$614$	7.15942e7	+	1.37821e8i	0.309295	+	0.595401i
$615$	−4.52571e7	+	1.15291e7i	−0.194564	+	0.0495645i
$616$	−1.08320e7	+	8.06664e7i	−0.0463413	+	0.345104i
$617$		−	2.99111e8i		−	1.27344i	−0.771096	−	0.636719i	$-0.780291\pi$
$617$		−	2.99111e8i		−	1.27344i	0.771096	−	0.636719i	$-0.219709\pi$
$618$	−1.35514e8	−	2.60868e8i	−0.574140	−	1.10524i
$619$			6.73241e7i			0.283856i	0.989877	+	0.141928i	$0.0453302\pi$
$619$			6.73241e7i			0.283856i	−0.989877	+	0.141928i	$0.954670\pi$
$620$	−3.83429e8	−	1.45703e8i	−1.60883	−	0.611353i
$621$	−8.42799e7			−0.351924
$622$	1.87511e8	−	9.74068e7i	0.779211	−	0.404779i
$623$	−2.46546e6			−0.0101961
$624$	−4.07438e8	+	1.46708e8i	−1.67690	+	0.603808i
$625$	1.32368e8	−	2.05142e8i	0.542181	−	0.840262i
$626$	−3.52497e7	+	1.83113e7i	−0.143692	+	0.0746441i
$627$	3.90779e8			1.58536
$628$	−3.42277e8	−	2.40544e8i	−1.38197	−	0.971217i
$629$	5.68434e7			0.228417
$630$	−1.65526e7	−	1.85505e7i	−0.0661981	−	0.0741880i
$631$		−	3.74586e8i		−	1.49095i	−0.666533	−	0.745476i	$-0.732222\pi$
$631$		−	3.74586e8i		−	1.49095i	0.666533	−	0.745476i	$-0.267778\pi$
$632$	1.13639e7	−	8.46272e7i	0.0450171	−	0.335242i
$633$			3.38996e8i			1.33654i
$634$	2.30401e8	−	1.19687e8i	0.904101	−	0.469656i
$635$	1.13050e8	−	2.87992e7i	0.441519	−	0.112476i
$636$	−7.90183e7	−	5.55323e7i	−0.307154	−	0.215861i
$637$			3.65335e8i			1.41343i
$638$	1.78425e8	−	9.26867e7i	0.687057	−	0.356907i
$639$		−	6.23630e7i		−	0.239015i
$640$	1.16749e8	+	2.34711e8i	0.445362	+	0.895351i
$641$	3.70848e8			1.40806			0.704031	−	0.710169i	$-0.251382\pi$
$641$	3.70848e8			1.40806			0.704031	+	0.710169i	$0.251382\pi$
$642$	1.81839e8	+	3.50045e8i	0.687197	+	1.32287i
$643$	−4.50751e8			−1.69552			−0.847761	−	0.530378i	$-0.822050\pi$
$643$	−4.50751e8			−1.69552			−0.847761	+	0.530378i	$0.822050\pi$
$644$	1.93097e7	−	2.74763e7i	0.0722967	−	0.102873i
$645$	−3.88242e8	+	9.89036e7i	−1.44685	+	0.368581i
$646$	−7.60643e7	−	1.46426e8i	−0.282152	−	0.543151i
$647$	−3.12382e8			−1.15338			−0.576691	−	0.816962i	$-0.695656\pi$
$647$	−3.12382e8			−1.15338			−0.576691	+	0.816962i	$0.695656\pi$
$648$	3.33470e8	+	4.47791e7i	1.22555	+	0.164570i
$649$	−2.50410e8			−0.916048
$650$	2.32445e8	−	3.45062e8i	0.846408	−	1.25649i
$651$		−	1.44629e8i		−	0.524219i
$652$	2.62629e8	−	3.73701e8i	0.947544	−	1.34828i
$653$			1.75008e8i			0.628519i	0.949337	+	0.314260i	$0.101756\pi$
$653$			1.75008e8i			0.628519i	−0.949337	+	0.314260i	$0.898244\pi$
$654$	2.07016e8	+	3.98512e8i	0.740068	+	1.42465i
$655$	324121.	+	1.27233e6i	0.00115341	+	0.00452767i
$656$	1.63219e7	+	4.53295e7i	0.0578176	+	0.160572i
$657$			1.77338e8i			0.625323i
$658$	−4.23143e7	−	8.14562e7i	−0.148528	−	0.285921i
$659$			5.04270e8i			1.76200i	0.473113	+	0.881002i	$0.343130\pi$
$659$			5.04270e8i			1.76200i	−0.473113	+	0.881002i	$0.656870\pi$
$660$	−4.25213e8	−	1.61581e8i	−1.47902	−	0.562028i
$661$	−3.10890e8			−1.07647			−0.538236	−	0.842794i	$-0.680909\pi$
$661$	−3.10890e8			−1.07647			−0.538236	+	0.842794i	$0.680909\pi$
$662$	−3.19645e8	+	1.66047e8i	−1.10178	+	0.572344i
$663$	−3.17287e8			−1.08871
$664$	1.66502e8	+	2.23583e7i	0.568743	+	0.0763720i
$665$	1.88333e7	+	7.39294e7i	0.0640415	+	0.251392i
$666$	−3.76455e7	+	1.95558e7i	−0.127435	+	0.0661992i
$667$	−8.29615e7			−0.279575
$668$	1.67462e8	−	2.38286e8i	0.561807	−	0.799409i
$669$	2.06769e8			0.690569
$670$	−2.72031e7	−	3.04865e7i	−0.0904471	−	0.101364i
$671$			5.36875e8i			1.77708i
$672$	−6.27390e7	+	6.78784e7i	−0.206743	+	0.223678i
$673$			4.42525e8i			1.45175i	0.687826	+	0.725876i	$0.258565\pi$
$673$			4.42525e8i			1.45175i	−0.687826	+	0.725876i	$0.741435\pi$
$674$	−1.67990e7	+	8.72665e6i	−0.0548662	+	0.0285015i
$675$	−1.95701e8	+	1.06628e8i	−0.636330	+	0.346706i
$676$	2.30050e8	−	3.27344e8i	0.744702	−	1.05965i
$677$		−	3.01059e8i		−	0.970255i	−0.874443	−	0.485128i	$-0.838773\pi$
$677$		−	3.01059e8i		−	0.970255i	0.874443	−	0.485128i	$-0.161227\pi$
$678$	3.05714e8	−	1.58810e8i	0.980905	−	0.509553i
$679$		−	1.96036e7i		−	0.0626218i
$680$	2.22221e7	+	1.90780e8i	0.0706738	+	0.606744i
$681$	2.63112e8			0.833103
$682$	−3.38476e8	−	6.51576e8i	−1.06703	−	2.05405i
$683$	2.52236e8			0.791673			0.395836	−	0.918321i	$-0.370455\pi$
$683$	2.52236e8			0.791673			0.395836	+	0.918321i	$0.370455\pi$
$684$	1.00750e8	+	7.08046e7i	0.314829	+	0.221255i
$685$	−6.49391e7	−	2.54916e8i	−0.202039	−	0.793095i
$686$	7.44773e7	+	1.43371e8i	0.230702	+	0.444108i
$687$	1.90310e8			0.586936
$688$	1.40019e8	+	3.88863e8i	0.429954	+	1.19407i
$689$	1.58128e8			0.483448
$690$	1.24961e8	+	1.40043e8i	0.380389	+	0.426300i
$691$			6.69200e7i			0.202825i	0.994844	+	0.101413i	$0.0323362\pi$
$691$			6.69200e7i			0.202825i	−0.994844	+	0.101413i	$0.967664\pi$
$692$	4.34579e8	+	3.05413e8i	1.31145	+	0.921655i
$693$		−	4.45042e7i		−	0.133722i
$694$	−1.31825e8	−	2.53768e8i	−0.394385	−	0.759203i
$695$	−9.53936e7	−	3.74464e8i	−0.284161	−	1.11546i
$696$	2.26308e8	+	3.03891e7i	0.671231	+	0.0901343i
$697$			3.52998e7i			0.104249i
$698$	1.09154e8	+	2.10125e8i	0.320978	+	0.617892i
$699$			5.32169e7i			0.155818i
$700$	1.00758e7	−	8.82310e7i	0.0293754	−	0.257233i
$701$	−4.07068e8			−1.18171			−0.590857	−	0.806776i	$-0.701210\pi$
$701$	−4.07068e8			−1.18171			−0.590857	+	0.806776i	$0.701210\pi$
$702$	−3.37032e8	+	1.75079e8i	−0.974226	+	0.506084i
$703$	1.30175e8			0.374680
$704$	−1.23793e8	+	4.52631e8i	−0.354795	+	1.29726i
$705$	4.97130e8	−	1.26642e8i	1.41874	−	0.361420i
$706$	−4.39849e8	+	2.28489e8i	−1.24994	+	0.649310i
$707$	−1.65816e7			−0.0469211
$708$	−2.32670e8	−	1.63516e8i	−0.655604	−	0.460744i
$709$	2.14836e7			0.0602793			0.0301396	−	0.999546i	$-0.490405\pi$
$709$	2.14836e7			0.0602793			0.0301396	+	0.999546i	$0.490405\pi$
$710$	1.66208e8	−	1.48308e8i	0.464383	−	0.414370i
$711$			4.66895e7i			0.129900i
$712$	−1.40881e7	−	1.89178e6i	−0.0390313	−	0.00524120i
$713$			3.02961e8i			0.835830i
$714$	−6.00986e7	+	3.12196e7i	−0.165109	+	0.0857694i
$715$	7.21708e8	−	1.83853e8i	1.97444	−	0.502982i
$716$	1.58982e8	+	1.11729e8i	0.433122	+	0.304388i
$717$		−	1.28325e8i		−	0.348141i
$718$	−2.89836e8	+	1.50562e8i	−0.783031	+	0.406764i
$719$		−	4.75458e8i		−	1.27916i	−0.768724	−	0.639581i	$-0.779108\pi$
$719$		−	4.75458e8i		−	1.27916i	0.768724	−	0.639581i	$-0.220892\pi$
$720$	−8.03508e7	−	1.18702e8i	−0.215275	−	0.318025i
$721$	1.02732e8			0.274094
$722$	−692456.	−	1.33300e6i	−0.00183984	−	0.00354175i
$723$	2.96052e8			0.783345
$724$	2.37329e7	−	3.37702e7i	0.0625368	−	0.0889851i
$725$	−1.92640e8	+	1.04960e8i	−0.505512	+	0.275430i
$726$	−1.67837e8	−	3.23091e8i	−0.438609	−	0.844336i
$727$	−6.11316e8			−1.59097			−0.795486	−	0.605972i	$-0.792784\pi$
$727$	−6.11316e8			−1.59097			−0.795486	+	0.605972i	$0.792784\pi$
$728$	2.01409e7	−	1.49990e8i	0.0522018	−	0.388747i
$729$	1.46305e8			0.377638
$730$	−4.72634e8	+	4.21732e8i	−1.21494	+	1.08410i
$731$			3.02822e8i			0.775239i
$732$	−3.50575e8	+	4.98841e8i	−0.893814	+	1.27183i
$733$		−	5.86490e8i		−	1.48919i	−0.667519	−	0.744593i	$-0.732644\pi$
$733$		−	5.86490e8i		−	1.48919i	0.667519	−	0.744593i	$-0.267356\pi$
$734$	−5.57050e7	−	1.07234e8i	−0.140866	−	0.271171i
$735$	−4.22327e8	+	1.07587e8i	−1.06362	+	0.270954i
$736$	1.31422e8	−	1.42188e8i	0.329637	−	0.356639i
$737$		−	7.31397e7i		−	0.182705i
$738$	−1.21442e7	−	2.33779e7i	−0.0302133	−	0.0581615i
$739$		−	5.79830e8i		−	1.43671i	−0.695679	−	0.718353i	$-0.744896\pi$
$739$		−	5.79830e8i		−	1.43671i	0.695679	−	0.718353i	$-0.255104\pi$
$740$	−1.41645e8	−	5.38251e7i	−0.349548	−	0.132828i
$741$	−7.26607e8			−1.78585
$742$	2.99516e7	−	1.55590e7i	0.0733175	−	0.0380864i
$743$	3.73947e8			0.911681			0.455841	−	0.890061i	$-0.349339\pi$
$743$	3.73947e8			0.911681			0.455841	+	0.890061i	$0.349339\pi$
$744$	1.10976e8	−	8.26437e8i	0.269469	−	2.00674i
$745$	1.87448e8	−	4.77518e7i	0.453327	−	0.115484i
$746$	3.78031e8	−	1.96377e8i	0.910565	−	0.473014i
$747$	−9.18606e7			−0.220378
$748$	−1.97690e8	+	2.81298e8i	−0.472367	+	0.672143i
$749$	−1.37850e8			−0.328067
$750$	4.67343e8	+	1.67089e8i	1.10778	+	0.396064i
$751$		−	1.27510e8i		−	0.301041i	−0.988607	−	0.150521i	$-0.951905\pi$
$751$		−	1.27510e8i		−	0.301041i	0.988607	−	0.150521i	$-0.0480950\pi$
$752$	−1.79289e8	−	4.97924e8i	−0.421600	−	1.17087i
$753$		−	8.23814e8i		−	1.92950i
$754$	−3.31760e8	+	1.72340e8i	−0.773944	+	0.402043i
$755$	−6.59421e7	−	2.58853e8i	−0.153222	−	0.601468i
$756$	−4.66116e7	+	6.63247e7i	−0.107877	+	0.153501i
$757$			2.33748e7i			0.0538841i	0.999637	+	0.0269420i	$0.00857696\pi$
$757$			2.33748e7i			0.0538841i	−0.999637	+	0.0269420i	$0.991423\pi$
$758$	2.33580e6	−	1.21339e6i	0.00536326	−	0.00278607i
$759$			3.35976e8i			0.768393i
$760$	5.08900e7	+	4.36897e8i	0.115929	+	0.995265i
$761$	7.53332e8			1.70936			0.854678	−	0.519159i	$-0.173755\pi$
$761$	7.53332e8			1.70936			0.854678	+	0.519159i	$0.173755\pi$
$762$	1.09327e8	+	2.10458e8i	0.247094	+	0.475664i
$763$	−1.56937e8			−0.353307
$764$	−2.42355e8	−	1.70322e8i	−0.543467	−	0.381936i
$765$	−2.59264e7	−	1.01773e8i	−0.0579106	−	0.227326i
$766$	−2.96875e8	−	5.71492e8i	−0.660521	−	1.27152i
$767$	4.65609e8			1.03189
$768$	−4.10587e8	+	3.39729e8i	−0.906402	+	0.749980i
$769$	−6.33859e8			−1.39384			−0.696921	−	0.717148i	$-0.745447\pi$
$769$	−6.33859e8			−1.39384			−0.696921	+	0.717148i	$0.745447\pi$
$770$	1.18611e8	−	1.05837e8i	0.259808	−	0.231828i
$771$			5.12303e8i			1.11780i
$772$	2.69028e8	+	1.89067e8i	0.584717	+	0.410926i
$773$			1.08448e8i			0.234793i	0.993085	+	0.117396i	$0.0374548\pi$
$773$			1.08448e8i			0.234793i	−0.993085	+	0.117396i	$0.962545\pi$
$774$	−1.04180e8	−	2.00549e8i	−0.224678	−	0.432512i
$775$	3.83297e8	+	7.03487e8i	0.823437	+	1.51130i
$776$	1.50421e7	−	1.12018e8i	0.0321901	−	0.239720i
$777$		−	5.34285e7i		−	0.113896i
$778$	1.80551e8	+	3.47565e8i	0.383407	+	0.738069i
$779$			8.08387e7i			0.171004i
$780$	7.90634e8	+	3.00440e8i	1.66606	+	0.633103i
$781$	3.98747e8			0.837036
$782$	1.25891e8	−	6.53971e7i	0.263254	−	0.136753i
$783$	2.00260e8			0.417166
$784$	1.52312e8	+	4.23002e8i	0.316072	+	0.877797i
$785$	2.01708e8	+	7.91797e8i	0.416979	+	1.63684i
$786$	−2.36861e6	+	1.23043e6i	−0.00487781	+	0.00253389i
$787$	3.53415e8			0.725039			0.362519	−	0.931976i	$-0.381917\pi$
$787$	3.53415e8			0.725039			0.362519	+	0.931976i	$0.381917\pi$
$788$	2.89173e8	+	2.03225e8i	0.590989	+	0.415334i
$789$	2.91739e6			0.00593968
$790$	−1.24435e8	+	1.11034e8i	−0.252384	+	0.225203i
$791$			1.20393e8i			0.243260i
$792$	3.41487e7	−	2.54305e8i	0.0687382	−	0.511894i
$793$		−	9.98257e8i		−	2.00181i
$794$	−4.41160e8	+	2.29171e8i	−0.881322	+	0.457823i
$795$	4.65665e7	+	1.82795e8i	0.0926771	+	0.363800i
$796$	2.24665e8	+	1.57890e8i	0.445448	+	0.313051i
$797$			5.64122e8i			1.11429i	0.830415	+	0.557145i	$0.188103\pi$
$797$			5.64122e8i			1.11429i	−0.830415	+	0.557145i	$0.811897\pi$
$798$	−1.37629e8	+	7.14948e7i	−0.270834	+	0.140691i
$799$		−	3.87753e8i		−	0.760176i
$800$	1.25276e8	−	4.96437e8i	0.244679	−	0.969604i
$801$	7.77252e6			0.0151239
$802$	1.40989e6	+	2.71407e6i	0.00273313	+	0.00526136i
$803$	−1.13389e9			−2.18990
$804$	4.77595e7	−	6.79582e7i	0.0918949	−	0.130760i
$805$	−6.35616e7	+	1.61921e7i	−0.121845	+	0.0310396i
$806$	6.29356e8	+	1.21153e9i	1.20196	+	2.31381i
$807$	−1.71030e8			−0.325426
$808$	−9.47504e7	−	1.27233e7i	−0.179617	−	0.0241193i
$809$	−2.93587e8			−0.554487			−0.277243	−	0.960800i	$-0.589421\pi$
$809$	−2.93587e8			−0.554487			−0.277243	+	0.960800i	$0.589421\pi$
$810$	−4.37524e8	−	4.90331e8i	−0.823278	−	0.922645i
$811$		−	7.58312e8i		−	1.42163i	−0.703381	−	0.710813i	$-0.748327\pi$
$811$		−	7.58312e8i		−	1.42163i	0.703381	−	0.710813i	$-0.251673\pi$
$812$	−4.58824e7	+	6.52871e7i	−0.0856994	+	0.121944i
$813$			2.83286e8i			0.527174i
$814$	−1.25039e8	−	2.40704e8i	−0.231831	−	0.446282i
$815$	−8.64492e8	+	2.20227e8i	−1.59694	+	0.406815i
$816$	−3.67370e8	+	1.32280e8i	−0.676134	+	0.243458i
$817$			6.93481e8i			1.27165i
$818$	−4.08791e8	−	7.86934e8i	−0.746863	−	1.43773i
$819$			8.27504e7i			0.150632i
$820$	3.34255e7	−	8.79619e7i	0.0606228	−	0.159534i
$821$	−2.11510e7			−0.0382209			−0.0191104	−	0.999817i	$-0.506083\pi$
$821$	−2.11510e7			−0.0382209			−0.0191104	+	0.999817i	$0.506083\pi$
$822$	4.74560e8	−	2.46521e8i	0.854429	−	0.443853i
$823$	9.99192e8			1.79246			0.896230	−	0.443590i	$-0.146295\pi$
$823$	9.99192e8			1.79246			0.896230	+	0.443590i	$0.146295\pi$
$824$	5.87028e8	+	7.88274e7i	1.04925	+	0.140895i
$825$	4.25067e8	+	7.80150e8i	0.757000	+	1.38936i
$826$	8.81927e7	−	4.58137e7i	0.156492	−	0.0812934i
$827$	−5.08817e8			−0.899591			−0.449796	−	0.893131i	$-0.648503\pi$
$827$	−5.08817e8			−0.899591			−0.449796	+	0.893131i	$0.648503\pi$
$828$	−6.08750e7	+	8.66206e7i	−0.107238	+	0.152591i
$829$	9.05552e8			1.58946			0.794730	−	0.606963i	$-0.207612\pi$
$829$	9.05552e8			1.58946			0.794730	+	0.606963i	$0.207612\pi$
$830$	−2.18457e8	−	2.44824e8i	−0.382059	−	0.428173i
$831$		−	2.81174e8i		−	0.489973i
$832$	2.30178e8	−	8.41614e8i	0.399663	−	1.46131i
$833$			3.29408e8i			0.569900i
$834$	6.97115e8	−	3.62132e8i	1.20173	−	0.624265i
$835$	−5.51233e8	+	1.40425e8i	−0.946838	+	0.241204i
$836$	−4.52722e8	+	6.44189e8i	−0.774841	+	1.10254i
$837$		−	7.31315e8i		−	1.24718i
$838$	−8.60618e8	+	4.47068e8i	−1.46244	+	0.759698i
$839$		−	8.22611e8i		−	1.39286i	−0.717623	−	0.696432i	$-0.754770\pi$
$839$		−	8.22611e8i		−	1.39286i	0.717623	−	0.696432i	$-0.245230\pi$
$840$	1.79319e8	−	2.08871e7i	0.302544	−	0.0352404i
$841$	−3.97696e8			−0.668596
$842$	−3.04824e6	−	5.86795e6i	−0.00510638	−	0.00982992i
$843$	1.44321e8			0.240906
$844$	−5.58826e8	−	3.92730e8i	−0.929500	−	0.653232i
$845$	−7.57253e8	+	1.92908e8i	−1.25508	+	0.319728i
$846$	1.33398e8	+	2.56796e8i	0.220313	+	0.424108i
$847$	1.27236e8			0.209391
$848$	1.83087e8	−	6.59249e7i	0.300242	−	0.108109i
$849$	−6.28888e8			−1.02766
$850$	2.09586e8	−	3.11128e8i	0.341276	−	0.506620i
$851$			1.11919e8i			0.181600i
$852$	3.70498e8	+	2.60378e8i	0.599056	+	0.421003i
$853$			1.56058e8i			0.251443i	0.992066	+	0.125722i	$0.0401246\pi$
$853$			1.56058e8i			0.251443i	−0.992066	+	0.125722i	$0.959875\pi$
$854$	−9.82238e7	−	1.89084e8i	−0.157704	−	0.303585i
$855$	−5.93731e7	−	2.33067e8i	−0.0949929	−	0.372891i
$856$	−7.87703e8	−	1.05774e8i	−1.25586	−	0.168639i
$857$			3.39476e8i			0.539345i	0.962952	+	0.269672i	$0.0869154\pi$
$857$			3.39476e8i			0.539345i	−0.962952	+	0.269672i	$0.913085\pi$
$858$	6.97941e8	+	1.34356e9i	1.10499	+	2.12713i
$859$			6.27544e8i			0.990068i	0.868874	+	0.495034i	$0.164844\pi$
$859$			6.27544e8i			0.990068i	−0.868874	+	0.495034i	$0.835156\pi$
$860$	2.86743e8	−	7.54588e8i	0.450814	−	1.18636i
$861$	3.31792e7			0.0519824
$862$	8.97999e8	−	4.66486e8i	1.40202	−	0.728311i
$863$	5.09291e8			0.792381			0.396190	−	0.918168i	$-0.370332\pi$
$863$	5.09291e8			0.792381			0.396190	+	0.918168i	$0.370332\pi$
$864$	−3.17239e8	+	3.43226e8i	−0.491864	+	0.532156i
$865$	−2.56103e8	−	1.00532e9i	−0.395700	−	1.55331i
$866$	7.46573e8	−	3.87824e8i	1.14953	−	0.597147i
$867$	4.80625e8			0.737477
$868$	2.38417e8	+	1.67554e8i	0.364568	+	0.256210i
$869$	−2.98531e8			−0.454914
$870$	−2.96923e8	−	3.32761e8i	−0.450907	−	0.505330i
$871$			1.35995e8i			0.205810i
$872$	−8.96769e8	−	1.20420e8i	−1.35248	−	0.181614i
$873$			6.18014e7i			0.0928872i
$874$	2.88299e8	−	1.49763e8i	0.431825	−	0.224322i
$875$	−1.27107e8	+	1.18015e8i	−0.189733	+	0.176162i
$876$	−1.05356e9	−	7.40419e8i	−1.56728	−	1.10145i
$877$			6.30685e8i			0.935004i	0.883992	+	0.467502i	$0.154846\pi$
$877$			6.30685e8i			0.935004i	−0.883992	+	0.467502i	$0.845154\pi$
$878$	1.89872e8	−	9.86334e7i	0.280529	−	0.145727i
$879$			1.09400e9i			1.61083i
$880$	7.58976e8	−	5.13760e8i	1.11373	−	0.753898i
$881$	2.54533e8			0.372235			0.186117	−	0.982528i	$-0.440410\pi$
$881$	2.54533e8			0.372235			0.186117	+	0.982528i	$0.440410\pi$
$882$	−1.13326e8	−	2.18156e8i	−0.165167	−	0.317952i
$883$	3.28879e7			0.0477698			0.0238849	−	0.999715i	$-0.492396\pi$
$883$	3.28879e7			0.0477698			0.0238849	+	0.999715i	$0.492396\pi$
$884$	3.67581e8	−	5.23040e8i	0.532104	−	0.757144i
$885$	1.37116e8	+	5.38242e8i	0.197814	+	0.776512i
$886$	3.09590e8	+	5.95969e8i	0.445128	+	0.856885i
$887$	−2.38053e8			−0.341116			−0.170558	−	0.985348i	$-0.554557\pi$
$887$	−2.38053e8			−0.341116			−0.170558	+	0.985348i	$0.554557\pi$
$888$	4.09964e7	−	3.05301e8i	0.0585473	−	0.436002i
$889$	−8.28799e7			−0.117962
$890$	1.84841e7	+	2.07150e7i	0.0262197	+	0.0293843i
$891$		−	1.17635e9i		−	1.66304i
$892$	−2.39544e8	+	3.40853e8i	−0.337513	+	0.480256i
$893$		−	8.87977e8i		−	1.24695i
$894$	1.81275e8	+	3.48960e8i	0.253703	+	0.488385i
$895$	−9.36904e7	−	3.67778e8i	−0.130685	−	0.512999i
$896$	−3.92120e7	−	1.82062e8i	−0.0545123	−	0.253101i
$897$		−	6.24709e8i		−	0.865566i
$898$	−1.42144e8	−	2.73632e8i	−0.196291	−	0.377866i
$899$		−	7.19874e8i		−	0.990780i
$900$	−3.17644e7	+	2.78154e8i	−0.0435726	+	0.381555i
$901$	1.42577e8			0.194928
$902$	1.49477e8	−	7.76493e7i	0.203683	−	0.105808i
$903$	2.84630e8			0.386561
$904$	−9.23789e7	+	6.87946e8i	−0.125045	+	0.931213i
$905$	−7.81214e7	+	1.99012e7i	−0.105396	+	0.0268493i
$906$	4.81890e8	−	2.50329e8i	0.647982	−	0.336609i
$907$	−8.69796e8			−1.16572			−0.582861	−	0.812572i	$-0.698067\pi$
$907$	−8.69796e8			−1.16572			−0.582861	+	0.812572i	$0.698067\pi$
$908$	−3.04818e8	+	4.33733e8i	−0.407177	+	0.579382i
$909$	5.22745e7			0.0695982
$910$	−2.20543e8	+	1.96791e8i	−0.292664	+	0.261145i
$911$			3.98390e8i			0.526931i	0.964669	+	0.263466i	$0.0848655\pi$
$911$			3.98390e8i			0.526931i	−0.964669	+	0.263466i	$0.915134\pi$
$912$	−8.41299e8	+	3.02929e8i	−1.10909	+	0.399353i
$913$		−	5.87353e8i		−	0.771768i
$914$	−7.19563e8	+	3.73793e8i	−0.942388	+	0.489545i
$915$	1.15398e9	−	2.93974e8i	1.50638	−	0.383747i
$916$	−2.20476e8	+	3.13721e8i	−0.286863	+	0.408185i
$917$		−	932775.i		−	0.00120968i
$918$	−3.03888e8	+	1.57861e8i	−0.392812	+	0.204055i
$919$			1.03935e9i			1.33911i	0.742762	+	0.669555i	$0.233515\pi$
$919$			1.03935e9i			1.33911i	−0.742762	+	0.669555i	$0.766485\pi$
$920$	−3.75627e8	+	4.37532e7i	−0.482385	+	0.0561884i
$921$	6.16650e8			0.789332
$922$	3.50028e8	+	6.73814e8i	0.446591	+	0.859700i
$923$	−7.41423e8			−0.942889
$924$	2.64399e8	+	1.85814e8i	0.335154	+	0.235539i
$925$	1.41597e8	+	2.59881e8i	0.178907	+	0.328359i
$926$	−4.35545e8	−	8.38437e8i	−0.548530	−	1.05594i
$927$	−3.23868e8			−0.406564
$928$	−3.12276e8	+	3.37857e8i	−0.390746	+	0.422755i
$929$	9.01112e8			1.12391			0.561955	−	0.827168i	$-0.310049\pi$
$929$	9.01112e8			1.12391			0.561955	+	0.827168i	$0.310049\pi$
$930$	−1.21519e9	+	1.08431e9i	−1.51076	+	1.34805i
$931$			7.54364e8i			0.934828i
$932$	−8.77268e7	−	6.16525e7i	−0.108364	−	0.0761557i
$933$		−	8.38977e8i		−	1.03301i
$934$	6.86346e8	+	1.32123e9i	0.842369	+	1.62158i
$935$	6.50734e8	−	1.65773e8i	0.796102	−	0.202805i
$936$	−6.34955e7	+	4.72851e8i	−0.0774310	+	0.576629i
$937$			8.08145e7i			0.0982360i	0.998793	+	0.0491180i	$0.0156410\pi$
$937$			8.08145e7i			0.0982360i	−0.998793	+	0.0491180i	$0.984359\pi$
$938$	1.33812e7	+	2.57592e7i	0.0162139	+	0.0312122i
$939$			1.57717e8i			0.190495i
$940$	−3.67164e8	+	9.66223e8i	−0.442055	+	1.16330i
$941$	−5.21062e8			−0.625346			−0.312673	−	0.949861i	$-0.601224\pi$
$941$	−5.21062e8			−0.625346			−0.312673	+	0.949861i	$0.601224\pi$
$942$	−1.47404e9	+	7.65722e8i	−1.76342	+	0.916048i
$943$	−6.95019e7			−0.0828823
$944$	5.39103e8	−	1.94117e8i	0.640849	−	0.230753i
$945$	1.53431e8	−	3.90860e7i	0.181810	−	0.0463155i
$946$	1.28230e9	−	6.66121e8i	1.51467	−	0.786828i
$947$	1.67327e9			1.97023			0.985114	−	0.171902i	$-0.0549911\pi$
$947$	1.67327e9			1.97023			0.985114	+	0.171902i	$0.0549911\pi$
$948$	−2.77382e8	−	1.94938e8i	−0.325576	−	0.228808i
$949$	2.10833e9			2.46684
$950$	4.79964e8	−	7.12503e8i	0.559807	−	0.831028i
$951$		−	1.03088e9i		−	1.19858i
$952$	1.81602e7	−	1.35239e8i	0.0210480	−	0.156744i
$953$			5.89780e8i			0.681414i	0.940170	+	0.340707i	$0.110666\pi$
$953$			5.89780e8i			0.681414i	−0.940170	+	0.340707i	$0.889334\pi$
$954$	−9.44241e7	+	4.90507e7i	−0.108752	+	0.0564937i
$955$	1.42823e8	+	5.60647e8i	0.163979	+	0.643694i
$956$	2.11541e8	+	1.48666e8i	0.242115	+	0.170153i
$957$		−	7.98323e8i		−	0.910841i
$958$	3.56347e8	−	1.85112e8i	0.405300	−	0.210542i
$959$			1.86885e8i			0.211895i
$960$	1.04069e9	+	1.82407e7i	1.17627	+	0.0206171i
$961$	−1.74135e9			−1.96208
$962$	2.32495e8	+	4.47560e8i	0.261149	+	0.502720i
$963$	4.34581e8			0.486623
$964$	−3.42980e8	+	4.88035e8i	−0.382858	+	0.544778i
$965$	−1.58542e8	−	6.22350e8i	−0.176426	−	0.692552i
$966$	−6.14684e7	−	1.18328e8i	−0.0681900	−	0.131268i
$967$	−9.41406e8			−1.04111			−0.520556	−	0.853828i	$-0.674275\pi$
$967$	−9.41406e8			−1.04111			−0.520556	+	0.853828i	$0.674275\pi$
$968$	7.27049e8	+	9.76297e7i	0.801563	+	0.107636i
$969$	−6.55152e8			−0.720063
$970$	−1.64711e8	+	1.46972e8i	−0.180471	+	0.161035i
$971$			1.61734e9i			1.76662i	0.468787	+	0.883311i	$0.344691\pi$
$971$			1.61734e9i			1.76662i	−0.468787	+	0.883311i	$0.655309\pi$
$972$	3.85507e8	−	5.48548e8i	0.419792	−	0.597332i
$973$			2.74529e8i			0.298023i
$974$	−4.01597e8	−	7.73085e8i	−0.434623	−	0.836662i
$975$	−7.90362e8	−	1.45060e9i	−0.852732	−	1.56507i
$976$	−4.16183e8	−	1.15583e9i	−0.447646	−	1.24321i
$977$		−	6.67855e8i		−	0.716141i	−0.933695	−	0.358070i	$-0.883435\pi$
$977$		−	6.67855e8i		−	0.716141i	0.933695	−	0.358070i	$-0.116565\pi$
$978$	−8.36022e8	−	1.60937e9i	−0.893720	−	1.72044i
$979$			4.96972e7i			0.0529643i
$980$	3.11917e8	−	8.20836e8i	0.331406	−	0.872123i
$981$	4.94754e8			0.524062
$982$	−1.21474e8	+	6.31026e7i	−0.128277	+	0.0666366i
$983$	8.58744e7			0.0904073			0.0452036	−	0.998978i	$-0.485606\pi$
$983$	8.58744e7			0.0904073			0.0452036	+	0.998978i	$0.485606\pi$
$984$	1.89592e8	+	2.54588e7i	0.198992	+	0.0267210i
$985$	−1.70414e8	−	6.68952e8i	−0.178318	−	0.699981i
$986$	−2.99134e8	+	1.55392e8i	−0.312057	+	0.162105i
$987$	−3.64459e8			−0.379050
$988$	8.41783e8	−	1.19779e9i	0.872830	−	1.24197i
$989$	−5.96228e8			−0.616344
$990$	−3.73929e8	+	3.33657e8i	−0.385375	+	0.343871i
$991$			6.76605e8i			0.695208i	0.937642	+	0.347604i	$0.113005\pi$
$991$			6.76605e8i			0.695208i	−0.937642	+	0.347604i	$0.886995\pi$
$992$	1.23379e9	+	1.14038e9i	1.26389	+	1.16819i
$993$			1.43018e9i			1.46064i
$994$	−1.40436e8	+	7.29525e7i	−0.142994	+	0.0742816i
$995$	−1.32398e8	−	5.19724e8i	−0.134404	−	0.527598i
$996$	3.83536e8	−	5.45743e8i	0.388175	−	0.552344i
$997$			1.53009e9i			1.54394i	0.635659	+	0.771970i	$0.280728\pi$
$997$			1.53009e9i			1.54394i	−0.635659	+	0.771970i	$0.719272\pi$
$998$	1.48014e8	−	7.68895e7i	0.148906	−	0.0773526i
$999$		−	2.70161e8i		−	0.270973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.d.d.19.8	yes	12
3.2	odd	2		180.7.f.e.19.5		12
4.3	odd	2	inner	20.7.d.d.19.6	yes	12
5.2	odd	4		100.7.b.f.51.2		12
5.3	odd	4		100.7.b.f.51.11		12
5.4	even	2	inner	20.7.d.d.19.5	✓	12
8.3	odd	2		320.7.h.f.319.10		12
8.5	even	2		320.7.h.f.319.4		12
12.11	even	2		180.7.f.e.19.7		12
15.14	odd	2		180.7.f.e.19.8		12
20.3	even	4		100.7.b.f.51.12		12
20.7	even	4		100.7.b.f.51.1		12
20.19	odd	2	inner	20.7.d.d.19.7	yes	12
40.19	odd	2		320.7.h.f.319.3		12
40.29	even	2		320.7.h.f.319.9		12
60.59	even	2		180.7.f.e.19.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.5	✓	12	5.4	even	2	inner
20.7.d.d.19.6	yes	12	4.3	odd	2	inner
20.7.d.d.19.7	yes	12	20.19	odd	2	inner
20.7.d.d.19.8	yes	12	1.1	even	1	trivial
100.7.b.f.51.1		12	20.7	even	4
100.7.b.f.51.2		12	5.2	odd	4
100.7.b.f.51.11		12	5.3	odd	4
100.7.b.f.51.12		12	20.3	even	4
180.7.f.e.19.5		12	3.2	odd	2
180.7.f.e.19.6		12	60.59	even	2
180.7.f.e.19.7		12	12.11	even	2
180.7.f.e.19.8		12	15.14	odd	2
320.7.h.f.319.3		12	40.19	odd	2
320.7.h.f.319.4		12	8.5	even	2
320.7.h.f.319.9		12	40.29	even	2
320.7.h.f.319.10		12	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.68788 + 7.09927i) q^{2} +31.7642 q^{3} +(-36.7991 + 52.3624i) q^{4} +(121.131 - 30.8579i) q^{5} +(117.142 + 225.502i) q^{6} -88.8045 q^{7} +(-507.445 - 68.1408i) q^{8} +279.961 q^{9} +O(q^{10})\)	\(q+(3.68788 + 7.09927i) q^{2} +31.7642 q^{3} +(-36.7991 + 52.3624i) q^{4} +(121.131 - 30.8579i) q^{5} +(117.142 + 225.502i) q^{6} -88.8045 q^{7} +(-507.445 - 68.1408i) q^{8} +279.961 q^{9} +(665.785 + 746.143i) q^{10} +1790.06i q^{11} +(-1168.89 + 1663.25i) q^{12} -3328.41i q^{13} +(-327.500 - 630.447i) q^{14} +(3847.63 - 980.173i) q^{15} +(-1387.65 - 3853.78i) q^{16} -3001.09i q^{17} +(1032.46 + 1987.52i) q^{18} -6872.67i q^{19} +(-2841.74 + 7478.27i) q^{20} -2820.80 q^{21} +(-12708.1 + 6601.53i) q^{22} +5908.85 q^{23} +(-16118.6 - 2164.44i) q^{24} +(13720.6 - 7475.70i) q^{25} +(23629.3 - 12274.8i) q^{26} -14263.3 q^{27} +(3267.93 - 4650.02i) q^{28} -14040.2 q^{29} +(21148.1 + 23700.6i) q^{30} +51272.4i q^{31} +(22241.6 - 24063.5i) q^{32} +56859.8i q^{33} +(21305.5 - 11067.6i) q^{34} +(-10757.0 + 2740.32i) q^{35} +(-10302.3 + 14659.5i) q^{36} +18940.9i q^{37} +(48790.9 - 25345.6i) q^{38} -105724. i q^{39} +(-63570.2 + 7404.68i) q^{40} -11762.3 q^{41} +(-10402.8 - 20025.6i) q^{42} -100904. q^{43} +(-93732.0 - 65872.8i) q^{44} +(33912.1 - 8639.01i) q^{45} +(21791.1 + 41948.5i) q^{46} +129204. q^{47} +(-44077.4 - 122412. i) q^{48} -109763. q^{49} +(103672. + 69836.6i) q^{50} -95327.0i q^{51} +(174284. + 122483. i) q^{52} +47508.5i q^{53} +(-52601.4 - 101259. i) q^{54} +(55237.5 + 216833. i) q^{55} +(45063.4 + 6051.21i) q^{56} -218305. i q^{57} +(-51778.5 - 99675.1i) q^{58} +139889. i q^{59} +(-90265.4 + 237541. i) q^{60} +299920. q^{61} +(-363996. + 189086. i) q^{62} -24861.8 q^{63} +(252858. + 69155.5i) q^{64} +(-102708. - 403175. i) q^{65} +(-403663. + 209692. i) q^{66} -40858.7 q^{67} +(157144. + 110437. i) q^{68} +187690. q^{69} +(-59124.7 - 66260.9i) q^{70} -222756. i q^{71} +(-142065. - 19076.8i) q^{72} +633436. i q^{73} +(-134467. + 69851.8i) q^{74} +(435823. - 237459. i) q^{75} +(359870. + 252909. i) q^{76} -158966. i q^{77} +(750564. - 389897. i) q^{78} +166771. i q^{79} +(-287007. - 423994. i) q^{80} -657154. q^{81} +(-43378.0 - 83503.9i) q^{82} -328119. q^{83} +(103803. - 147704. i) q^{84} +(-92607.1 - 363526. i) q^{85} +(-372122. - 716345. i) q^{86} -445975. q^{87} +(121976. - 908359. i) q^{88} +27762.8 q^{89} +(186394. + 208891. i) q^{90} +295578. i q^{91} +(-217441. + 309402. i) q^{92} +1.62862e6i q^{93} +(476488. + 917254. i) q^{94} +(-212076. - 832496. i) q^{95} +(706485. - 764358. i) q^{96} +220750. i q^{97} +(-404791. - 779235. i) q^{98} +501148. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9}+O(q^{10}) \) 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9	\( 12 q + 64 q^{4} + 460 q^{5} - 672 q^{6} + 1956 q^{9} + 2000 q^{10} + 512 q^{14} - 20928 q^{16} - 13760 q^{20} + 51216 q^{21} - 20928 q^{24} - 55700 q^{25} + 14496 q^{26} - 16072 q^{29} + 83520 q^{30} + 257216 q^{34} - 144960 q^{36} - 36800 q^{40} - 192136 q^{41} - 165120 q^{44} - 57180 q^{45} - 49472 q^{46} + 145796 q^{49} - 36000 q^{50} - 118656 q^{54} + 1078208 q^{56} - 902400 q^{60} + 215384 q^{61} - 6656 q^{64} + 710400 q^{65} - 1403520 q^{66} + 1015824 q^{69} + 530080 q^{70} - 1020384 q^{74} + 2515200 q^{76} - 127040 q^{80} - 2327652 q^{81} + 424704 q^{84} - 44800 q^{85} - 5268832 q^{86} - 4346152 q^{89} + 3582000 q^{90} + 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) \) 12 * q + 64 * q^4 + 460 * q^5 - 672 * q^6 + 1956 * q^9 + 2000 * q^10 + 512 * q^14 - 20928 * q^16 - 13760 * q^20 + 51216 * q^21 - 20928 * q^24 - 55700 * q^25 + 14496 * q^26 - 16072 * q^29 + 83520 * q^30 + 257216 * q^34 - 144960 * q^36 - 36800 * q^40 - 192136 * q^41 - 165120 * q^44 - 57180 * q^45 - 49472 * q^46 + 145796 * q^49 - 36000 * q^50 - 118656 * q^54 + 1078208 * q^56 - 902400 * q^60 + 215384 * q^61 - 6656 * q^64 + 710400 * q^65 - 1403520 * q^66 + 1015824 * q^69 + 530080 * q^70 - 1020384 * q^74 + 2515200 * q^76 - 127040 * q^80 - 2327652 * q^81 + 424704 * q^84 - 44800 * q^85 - 5268832 * q^86 - 4346152 * q^89 + 3582000 * q^90 + 4292992 * q^94 + 7673088 * q^96

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