LMFDB - Embedded newform 100.7.b.f.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,7,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	100.b (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:	$23.0054083620$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.2
Root			$0.771446 + 3.06674i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.7.b.f.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.09927 + 3.68788i) q^{2} -31.7642i q^{3} +(36.7991 - 52.3624i) q^{4} +(117.142 + 225.502i) q^{6} -88.8045i q^{7} +(-68.1408 + 507.445i) q^{8} -279.961 q^{9} +O(q^{10})$	\(q+(-7.09927 + 3.68788i) q^{2} -31.7642i q^{3} +(36.7991 - 52.3624i) q^{4} +(117.142 + 225.502i) q^{6} -88.8045i q^{7} +(-68.1408 + 507.445i) q^{8} -279.961 q^{9} +1790.06i q^{11} +(-1663.25 - 1168.89i) q^{12} -3328.41 q^{13} +(327.500 + 630.447i) q^{14} +(-1387.65 - 3853.78i) q^{16} +3001.09 q^{17} +(1987.52 - 1032.46i) q^{18} +6872.67i q^{19} -2820.80 q^{21} +(-6601.53 - 12708.1i) q^{22} -5908.85i q^{23} +(16118.6 + 2164.44i) q^{24} +(23629.3 - 12274.8i) q^{26} -14263.3i q^{27} +(-4650.02 - 3267.93i) q^{28} +14040.2 q^{29} +51272.4i q^{31} +(24063.5 + 22241.6i) q^{32} +56859.8 q^{33} +(-21305.5 + 11067.6i) q^{34} +(-10302.3 + 14659.5i) q^{36} -18940.9 q^{37} +(-25345.6 - 48790.9i) q^{38} +105724. i q^{39} -11762.3 q^{41} +(20025.6 - 10402.8i) q^{42} +100904. i q^{43} +(93732.0 + 65872.8i) q^{44} +(21791.1 + 41948.5i) q^{46} +129204. i q^{47} +(-122412. + 44077.4i) q^{48} +109763. q^{49} -95327.0i q^{51} +(-122483. + 174284. i) q^{52} +47508.5 q^{53} +(52601.4 + 101259. i) q^{54} +(45063.4 + 6051.21i) q^{56} +218305. q^{57} +(-99675.1 + 51778.5i) q^{58} -139889. i q^{59} +299920. q^{61} +(-189086. - 363996. i) q^{62} +24861.8i q^{63} +(-252858. - 69155.5i) q^{64} +(-403663. + 209692. i) q^{66} -40858.7i q^{67} +(110437. - 157144. i) q^{68} -187690. q^{69} -222756. i q^{71} +(19076.8 - 142065. i) q^{72} +633436. q^{73} +(134467. - 69851.8i) q^{74} +(359870. + 252909. i) q^{76} +158966. q^{77} +(-389897. - 750564. i) q^{78} -166771. i q^{79} -657154. q^{81} +(83503.9 - 43378.0i) q^{82} +328119. i q^{83} +(-103803. + 147704. i) q^{84} +(-372122. - 716345. i) q^{86} -445975. i q^{87} +(-908359. - 121976. i) q^{88} -27762.8 q^{89} +295578. i q^{91} +(-309402. - 217441. i) q^{92} +1.62862e6 q^{93} +(-476488. - 917254. i) q^{94} +(706485. - 764358. i) q^{96} -220750. q^{97} +(-779235. + 404791. i) q^{98} -501148. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−7.09927	+	3.68788i	−0.887408	+	0.460984i
$2$	−7.09927	+	3.68788i	−0.887408	+	0.460984i
$3$		−	31.7642i		−	1.17645i	−0.808697	−	0.588225i	$-0.799827\pi$
$3$		−	31.7642i		−	1.17645i	0.808697	−	0.588225i	$-0.200173\pi$
$4$	36.7991	−	52.3624i	0.574987	−	0.818163i
$5$		0			0
$5$		0			0
$6$	117.142	+	225.502i	0.542325	+	1.04399i
$7$		−	88.8045i		−	0.258905i	−0.991586	−	0.129453i	$-0.958678\pi$
$7$		−	88.8045i		−	0.258905i	0.991586	−	0.129453i	$-0.0413220\pi$
$8$	−68.1408	+	507.445i	−0.133088	+	0.991104i
$9$	−279.961			−0.384035
$10$		0			0
$11$			1790.06i			1.34490i	0.740142	+	0.672450i	$0.234758\pi$
$11$			1790.06i			1.34490i	−0.740142	+	0.672450i	$0.765242\pi$
$12$	−1663.25	−	1168.89i	−0.962528	−	0.676443i
$13$	−3328.41			−1.51498			−0.757490	−	0.652847i	$-0.773574\pi$
$13$	−3328.41			−1.51498			−0.757490	+	0.652847i	$0.773574\pi$
$14$	327.500	+	630.447i	0.119351	+	0.229755i
$15$		0			0
$16$	−1387.65	−	3853.78i	−0.338781	−	0.940865i
$17$	3001.09			0.610846			0.305423	−	0.952217i	$-0.401202\pi$
$17$	3001.09			0.610846			0.305423	+	0.952217i	$0.401202\pi$
$18$	1987.52	−	1032.46i	0.340796	−	0.177034i
$19$			6872.67i			1.00199i	0.865449	+	0.500997i	$0.167033\pi$
$19$			6872.67i			1.00199i	−0.865449	+	0.500997i	$0.832967\pi$
$20$		0			0
$21$	−2820.80			−0.304589
$22$	−6601.53	−	12708.1i	−0.619978	−	1.19348i
$23$		−	5908.85i		−	0.485646i	−0.970071	−	0.242823i	$-0.921927\pi$
$23$		−	5908.85i		−	0.485646i	0.970071	−	0.242823i	$-0.0780734\pi$
$24$	16118.6	+	2164.44i	1.16598	+	0.156571i
$25$		0			0
$26$	23629.3	−	12274.8i	1.34441	−	0.698382i
$27$		−	14263.3i		−	0.724652i
$28$	−4650.02	−	3267.93i	−0.211827	−	0.148867i
$29$	14040.2			0.575677			0.287839	−	0.957679i	$-0.407063\pi$
$29$	14040.2			0.575677			0.287839	+	0.957679i	$0.407063\pi$
$30$		0			0
$31$			51272.4i			1.72107i	0.509392	+	0.860534i	$0.329870\pi$
$31$			51272.4i			1.72107i	−0.509392	+	0.860534i	$0.670130\pi$
$32$	24063.5	+	22241.6i	0.734361	+	0.678759i
$33$	56859.8			1.58221
$34$	−21305.5	+	11067.6i	−0.542070	+	0.281591i
$35$		0			0
$36$	−10302.3	+	14659.5i	−0.220815	+	0.314203i
$37$	−18940.9			−0.373935			−0.186967	−	0.982366i	$-0.559866\pi$
$37$	−18940.9			−0.373935			−0.186967	+	0.982366i	$0.559866\pi$
$38$	−25345.6	−	48790.9i	−0.461903	−	0.889177i
$39$			105724.i			1.78230i
$40$		0			0
$41$	−11762.3			−0.170664			−0.0853320	−	0.996353i	$-0.527195\pi$
$41$	−11762.3			−0.170664			−0.0853320	+	0.996353i	$0.527195\pi$
$42$	20025.6	−	10402.8i	0.270295	−	0.140411i
$43$			100904.i			1.26912i	0.772873	+	0.634561i	$0.218819\pi$
$43$			100904.i			1.26912i	−0.772873	+	0.634561i	$0.781181\pi$
$44$	93732.0	+	65872.8i	1.10035	+	0.773300i
$45$		0			0
$46$	21791.1	+	41948.5i	0.223875	+	0.430966i
$47$			129204.i			1.24446i	0.782833	+	0.622232i	$0.213774\pi$
$47$			129204.i			1.24446i	−0.782833	+	0.622232i	$0.786226\pi$
$48$	−122412.	+	44077.4i	−1.10688	+	0.398559i
$49$	109763.			0.932968
$50$		0			0
$51$		−	95327.0i		−	0.718630i
$52$	−122483.	+	174284.i	−0.871093	+	1.23950i
$53$	47508.5			0.319112			0.159556	−	0.987189i	$-0.448994\pi$
$53$	47508.5			0.319112			0.159556	+	0.987189i	$0.448994\pi$
$54$	52601.4	+	101259.i	0.334053	+	0.643062i
$55$		0			0
$56$	45063.4	+	6051.21i	0.256602	+	0.0344571i
$57$	218305.			1.17880
$58$	−99675.1	+	51778.5i	−0.510861	+	0.265378i
$59$		−	139889.i		−	0.681127i	−0.940221	−	0.340564i	$-0.889382\pi$
$59$		−	139889.i		−	0.681127i	0.940221	−	0.340564i	$-0.110618\pi$
$60$		0			0
$61$	299920.			1.32134			0.660672	−	0.750675i	$-0.270271\pi$
$61$	299920.			1.32134			0.660672	+	0.750675i	$0.270271\pi$
$62$	−189086.	−	363996.i	−0.793386	−	1.52729i
$63$			24861.8i			0.0994286i
$64$	−252858.	−	69155.5i	−0.964575	−	0.263807i
$65$		0			0
$66$	−403663.	+	209692.i	−1.40406	+	0.729373i
$67$		−	40858.7i		−	0.135850i	−0.997690	−	0.0679251i	$-0.978362\pi$
$67$		−	40858.7i		−	0.135850i	0.997690	−	0.0679251i	$-0.0216379\pi$
$68$	110437.	−	157144.i	0.351229	−	0.499772i
$69$	−187690.			−0.571338
$70$		0			0
$71$		−	222756.i		−	0.622378i	−0.950348	−	0.311189i	$-0.899273\pi$
$71$		−	222756.i		−	0.622378i	0.950348	−	0.311189i	$-0.100727\pi$
$72$	19076.8	−	142065.i	0.0511103	−	0.380619i
$73$	633436.			1.62830			0.814149	−	0.580656i	$-0.197204\pi$
$73$	633436.			1.62830			0.814149	+	0.580656i	$0.197204\pi$
$74$	134467.	−	69851.8i	0.331833	−	0.172378i
$75$		0			0
$76$	359870.	+	252909.i	0.819794	+	0.576133i
$77$	158966.			0.348202
$78$	−389897.	−	750564.i	−0.821612	−	1.58163i
$79$		−	166771.i		−	0.338251i	−0.985594	−	0.169126i	$-0.945906\pi$
$79$		−	166771.i		−	0.338251i	0.985594	−	0.169126i	$-0.0540944\pi$
$80$		0			0
$81$	−657154.			−1.23655
$82$	83503.9	−	43378.0i	0.151449	−	0.0786734i
$83$			328119.i			0.573848i	0.957953	+	0.286924i	$0.0926327\pi$
$83$			328119.i			0.573848i	−0.957953	+	0.286924i	$0.907367\pi$
$84$	−103803.	+	147704.i	−0.175135	+	0.249203i
$85$		0			0
$86$	−372122.	−	716345.i	−0.585046	−	1.12623i
$87$		−	445975.i		−	0.677256i
$88$	−908359.	−	121976.i	−1.33294	−	0.178990i
$89$	−27762.8			−0.0393816			−0.0196908	−	0.999806i	$-0.506268\pi$
$89$	−27762.8			−0.0393816			−0.0196908	+	0.999806i	$0.506268\pi$
$90$		0			0
$91$			295578.i			0.392236i
$92$	−309402.	−	217441.i	−0.397337	−	0.279240i
$93$	1.62862e6			2.02475
$94$	−476488.	−	917254.i	−0.573679	−	1.10435i
$95$		0			0
$96$	706485.	−	764358.i	0.798526	−	0.863939i
$97$	−220750.			−0.241872			−0.120936	−	0.992660i	$-0.538590\pi$
$97$	−220750.			−0.241872			−0.120936	+	0.992660i	$0.538590\pi$
$98$	−779235.	+	404791.i	−0.827924	+	0.430084i
$99$		−	501148.i		−	0.516489i
$100$		0			0
$101$	186720.			0.181229			0.0906144	−	0.995886i	$-0.471117\pi$
$101$	186720.			0.181229			0.0906144	+	0.995886i	$0.471117\pi$
$102$	351554.	+	676752.i	0.331277	+	0.637718i
$103$			1.15683e6i			1.05866i	0.848415	+	0.529332i	$0.177557\pi$
$103$			1.15683e6i			1.05866i	−0.848415	+	0.529332i	$0.822443\pi$
$104$	226801.	−	1.68899e6i	0.201625	−	1.50150i
$105$		0			0
$106$	−337275.	+	175205.i	−0.283183	+	0.147106i
$107$			1.55229e6i			1.26713i	0.773689	+	0.633566i	$0.218409\pi$
$107$			1.55229e6i			1.26713i	−0.773689	+	0.633566i	$0.781591\pi$
$108$	−746862.	−	524878.i	−0.592883	−	0.416665i
$109$	−1.76722e6			−1.36462			−0.682310	−	0.731063i	$-0.739025\pi$
$109$	−1.76722e6			−1.36462			−0.682310	+	0.731063i	$0.739025\pi$
$110$		0			0
$111$			601642.i			0.439916i
$112$	−342233.	+	123229.i	−0.243595	+	0.0877121i
$113$	−1.35571e6			−0.939572			−0.469786	−	0.882780i	$-0.655669\pi$
$113$	−1.35571e6			−0.939572			−0.469786	+	0.882780i	$0.655669\pi$
$114$	−1.54980e6	+	805080.i	−1.04607	+	0.543406i
$115$		0			0
$116$	516667.	−	735178.i	0.331007	−	0.470998i
$117$	931827.			0.581805
$118$	515894.	+	993111.i	0.313989	+	0.604438i
$119$		−	266510.i		−	0.158151i
$120$		0			0
$121$	−1.43276e6			−0.808757
$122$	−2.12921e6	+	1.10607e6i	−1.17257	+	0.609119i
$123$			373620.i			0.200778i
$124$	2.68474e6	+	1.88678e6i	1.40811	+	0.989592i
$125$		0			0
$126$	−91687.3	−	176501.i	−0.0458351	−	0.0882338i
$127$			933285.i			0.455620i	0.973706	+	0.227810i	$0.0731566\pi$
$127$			933285.i			0.455620i	−0.973706	+	0.227810i	$0.926843\pi$
$128$	2.05014e6	−	441554.i	0.977583	−	0.210549i
$129$	3.20513e6			1.49306
$130$		0			0
$131$			10503.7i			0.00467227i	0.999997	+	0.00233614i	$0.000743616\pi$
$131$			10503.7i			0.00467227i	−0.999997	+	0.00233614i	$0.999256\pi$
$132$	2.09239e6	−	2.97732e6i	0.909749	−	1.29450i
$133$	610324.			0.259421
$134$	150682.	+	290067.i	0.0626248	+	0.120555i
$135$		0			0
$136$	−204497.	+	1.52289e6i	−0.0812961	+	0.605412i
$137$	2.10446e6			0.818425			0.409213	−	0.912439i	$-0.365803\pi$
$137$	2.10446e6			0.818425			0.409213	+	0.912439i	$0.365803\pi$
$138$	1.33246e6	−	692177.i	0.507010	−	0.263378i
$139$			3.09139e6i			1.15109i	0.817770	+	0.575545i	$0.195210\pi$
$139$			3.09139e6i			1.15109i	−0.817770	+	0.575545i	$0.804790\pi$
$140$		0			0
$141$	4.10406e6			1.46405
$142$	821496.	+	1.58140e6i	0.286906	+	0.552303i
$143$		−	5.95806e6i		−	2.03750i
$144$	388487.	+	1.07891e6i	0.130104	+	0.361325i
$145$		0			0
$146$	−4.49693e6	+	2.33603e6i	−1.44497	+	0.750620i
$147$		−	3.48652e6i		−	1.09759i
$148$	−697010.	+	991792.i	−0.215008	+	0.305940i
$149$	−1.54748e6			−0.467806			−0.233903	−	0.972260i	$-0.575150\pi$
$149$	−1.54748e6			−0.467806			−0.233903	+	0.972260i	$0.575150\pi$
$150$		0			0
$151$		−	2.13696e6i		−	0.620677i	−0.950626	−	0.310339i	$-0.899558\pi$
$151$		−	2.13696e6i		−	0.620677i	0.950626	−	0.310339i	$-0.100442\pi$
$152$	−3.48751e6	−	468310.i	−0.993080	−	0.133353i
$153$	−840189.			−0.234586
$154$	−1.12854e6	+	586245.i	−0.308997	+	0.160516i
$155$		0			0
$156$	5.53597e6	+	3.89056e6i	1.45821	+	1.02480i
$157$	−6.53669e6			−1.68911			−0.844556	−	0.535467i	$-0.820136\pi$
$157$	−6.53669e6			−1.68911			−0.844556	+	0.535467i	$0.820136\pi$
$158$	615031.	+	1.18395e6i	0.155929	+	0.300167i
$159$		−	1.50907e6i		−	0.375420i
$160$		0			0
$161$	−524733.			−0.125736
$162$	4.66531e6	−	2.42350e6i	1.09733	−	0.570031i
$163$			7.13681e6i			1.64794i	0.566633	+	0.823970i	$0.308246\pi$
$163$			7.13681e6i			1.64794i	−0.566633	+	0.823970i	$0.691754\pi$
$164$	−432844.	+	615904.i	−0.0981295	+	0.139631i
$165$		0			0
$166$	−1.21006e6	−	2.32940e6i	−0.264535	−	0.509237i
$167$		−	4.55070e6i		−	0.977078i	−0.872542	−	0.488539i	$-0.837530\pi$
$167$		−	4.55070e6i		−	0.977078i	0.872542	−	0.488539i	$-0.162470\pi$
$168$	192212.	−	1.43140e6i	0.0405370	−	0.301880i
$169$	6.25151e6			1.29516
$170$		0			0
$171$		−	1.92408e6i		−	0.384801i
$172$	5.28358e6	+	3.71319e6i	1.03835	+	0.729729i
$173$	−8.29944e6			−1.60292			−0.801458	−	0.598051i	$-0.795942\pi$
$173$	−8.29944e6			−1.60292			−0.801458	+	0.598051i	$0.795942\pi$
$174$	1.64470e6	+	3.16609e6i	0.312204	+	0.601002i
$175$		0			0
$176$	6.89852e6	−	2.48397e6i	1.26537	−	0.455626i
$177$	−4.44346e6			−0.801312
$178$	197096.	−	102386.i	0.0349476	−	0.0181543i
$179$			3.03619e6i			0.529384i	0.964333	+	0.264692i	$0.0852702\pi$
$179$			3.03619e6i			0.529384i	−0.964333	+	0.264692i	$0.914730\pi$
$180$		0			0
$181$	−644931.			−0.108762			−0.0543811	−	0.998520i	$-0.517319\pi$
$181$	−644931.			−0.108762			−0.0543811	+	0.998520i	$0.517319\pi$
$182$	−1.09005e6	−	2.09839e6i	−0.180815	−	0.348074i
$183$		−	9.52670e6i		−	1.55450i
$184$	2.99842e6	+	402634.i	0.481326	+	0.0646335i
$185$		0			0
$186$	−1.15620e7	+	6.00616e6i	−1.79678	+	0.933379i
$187$			5.37214e6i			0.821528i
$188$	6.76543e6	+	4.75460e6i	1.01817	+	0.715550i
$189$	−1.26665e6			−0.187616
$190$		0			0
$191$			4.62842e6i			0.664252i	0.943235	+	0.332126i	$0.107766\pi$
$191$			4.62842e6i			0.664252i	−0.943235	+	0.332126i	$0.892234\pi$
$192$	−2.19667e6	+	8.03181e6i	−0.310356	+	1.13477i
$193$	−5.13781e6			−0.714671			−0.357335	−	0.933976i	$-0.616315\pi$
$193$	−5.13781e6			−0.714671			−0.357335	+	0.933976i	$0.616315\pi$
$194$	1.56716e6	−	814098.i	0.214639	−	0.111499i
$195$		0			0
$196$	4.03918e6	−	5.74744e6i	0.536444	−	0.763320i
$197$	5.52253e6			0.722337			0.361168	−	0.932501i	$-0.382378\pi$
$197$	5.52253e6			0.722337			0.361168	+	0.932501i	$0.382378\pi$
$198$	1.84817e6	+	3.55779e6i	0.238093	+	0.458336i
$199$			4.29058e6i			0.544449i	0.962234	+	0.272224i	$0.0877593\pi$
$199$			4.29058e6i			0.544449i	−0.962234	+	0.272224i	$0.912241\pi$
$200$		0			0
$201$	−1.29784e6			−0.159821
$202$	−1.32558e6	+	688601.i	−0.160824	+	0.0835437i
$203$		−	1.24683e6i		−	0.149046i
$204$	−4.99155e6	−	3.50795e6i	−0.587957	−	0.413203i
$205$		0			0
$206$	−4.26625e6	−	8.21265e6i	−0.488028	−	0.939467i
$207$			1.65425e6i			0.186505i
$208$	4.61865e6	+	1.28270e7i	0.513246	+	1.42539i
$209$	−1.23025e7			−1.34758
$210$		0			0
$211$			1.06723e7i			1.13608i	0.823000	+	0.568041i	$0.192298\pi$
$211$			1.06723e7i			1.13608i	−0.823000	+	0.568041i	$0.807702\pi$
$212$	1.74827e6	−	2.48766e6i	0.183485	−	0.261086i
$213$	−7.07565e6			−0.732196
$214$	−5.72465e6	−	1.10201e7i	−0.584128	−	1.12446i
$215$		0			0
$216$	7.23786e6	+	971915.i	0.718206	+	0.0964422i
$217$	4.55322e6			0.445594
$218$	1.25460e7	−	6.51730e6i	1.21097	−	0.629069i
$219$		−	2.01205e7i		−	1.91561i
$220$		0			0
$221$	−9.98885e6			−0.925420
$222$	−2.21878e6	−	4.27122e6i	−0.202794	−	0.390385i
$223$		−	6.50950e6i		−	0.586993i	−0.955960	−	0.293497i	$-0.905181\pi$
$223$		−	6.50950e6i		−	0.586993i	0.955960	−	0.293497i	$-0.0948190\pi$
$224$	1.97515e6	−	2.13695e6i	0.175734	−	0.190130i
$225$		0			0
$226$	9.62451e6	−	4.99967e6i	0.833784	−	0.433128i
$227$			8.28329e6i			0.708150i	0.935217	+	0.354075i	$0.115204\pi$
$227$			8.28329e6i			0.708150i	−0.935217	+	0.354075i	$0.884796\pi$
$228$	8.03343e6	−	1.14310e7i	0.677792	−	0.964447i
$229$	−5.99134e6			−0.498904			−0.249452	−	0.968387i	$-0.580251\pi$
$229$	−5.99134e6			−0.498904			−0.249452	+	0.968387i	$0.580251\pi$
$230$		0			0
$231$		−	5.04941e6i		−	0.409642i
$232$	−956711.	+	7.12463e6i	−0.0766155	+	0.570556i
$233$	1.67538e6			0.132448			0.0662239	−	0.997805i	$-0.478905\pi$
$233$	1.67538e6			0.132448			0.0662239	+	0.997805i	$0.478905\pi$
$234$	−6.61528e6	+	3.43646e6i	−0.516299	+	0.268203i
$235$		0			0
$236$	−7.32494e6	−	5.14780e6i	−0.557273	−	0.391639i
$237$	−5.29734e6			−0.397936
$238$	982856.	+	1.89203e6i	0.0729053	+	0.140345i
$239$			4.03994e6i			0.295925i	0.988993	+	0.147962i	$0.0472715\pi$
$239$			4.03994e6i			0.295925i	−0.988993	+	0.147962i	$0.952729\pi$
$240$		0			0
$241$	9.32032e6			0.665855			0.332928	−	0.942952i	$-0.391964\pi$
$241$	9.32032e6			0.665855			0.332928	+	0.942952i	$0.391964\pi$
$242$	1.01716e7	−	5.28385e6i	0.717698	−	0.372824i
$243$			1.04760e7i			0.730090i
$244$	1.10368e7	−	1.57045e7i	0.759755	−	1.08107i
$245$		0			0
$246$	−1.37787e6	−	2.65243e6i	−0.0925554	−	0.178172i
$247$		−	2.28751e7i		−	1.51800i
$248$	−2.60179e7	−	3.49374e6i	−1.70576	−	0.229053i
$249$	1.04224e7			0.675103
$250$		0			0
$251$		−	2.59353e7i		−	1.64010i	−0.572291	−	0.820051i	$-0.693945\pi$
$251$		−	2.59353e7i		−	1.64010i	0.572291	−	0.820051i	$-0.306055\pi$
$252$	1.30183e6	+	914894.i	0.0813488	+	0.0571701i
$253$	1.05772e7			0.653146
$254$	−3.44184e6	−	6.62564e6i	−0.210034	−	0.404321i
$255$		0			0
$256$	−1.29261e7	+	1.06954e7i	−0.770455	+	0.637494i
$257$	−1.61283e7			−0.950146			−0.475073	−	0.879946i	$-0.657578\pi$
$257$	−1.61283e7			−0.950146			−0.475073	+	0.879946i	$0.657578\pi$
$258$	−2.27541e7	+	1.18201e7i	−1.32495	+	0.688277i
$259$			1.68204e6i			0.0968137i
$260$		0			0
$261$	−3.93071e6			−0.221080
$262$	−38736.3	−	74568.5i	−0.00215385	−	0.00414621i
$263$		−	91845.2i		−	0.00504881i	−0.999997	−	0.00252441i	$-0.999196\pi$
$263$		−	91845.2i		−	0.00504881i	0.999997	−	0.00252441i	$-0.000803545\pi$
$264$	−3.87448e6	+	2.88533e7i	−0.210572	+	1.56813i
$265$		0			0
$266$	−4.33285e6	+	2.25080e6i	−0.230213	+	0.119589i
$267$			881862.i			0.0463305i
$268$	−2.13946e6	−	1.50357e6i	−0.111148	−	0.0781121i
$269$	5.38438e6			0.276617			0.138308	−	0.990389i	$-0.455833\pi$
$269$	5.38438e6			0.276617			0.138308	+	0.990389i	$0.455833\pi$
$270$		0			0
$271$			8.91843e6i			0.448106i	0.974577	+	0.224053i	$0.0719289\pi$
$271$			8.91843e6i			0.448106i	−0.974577	+	0.224053i	$0.928071\pi$
$272$	−4.16445e6	−	1.15655e7i	−0.206943	−	0.574724i
$273$	9.38878e6			0.461446
$274$	−1.49401e7	+	7.76099e6i	−0.726277	+	0.377281i
$275$		0			0
$276$	−6.90682e6	+	9.82789e6i	−0.328512	+	0.467448i
$277$	8.85192e6			0.416484			0.208242	−	0.978077i	$-0.433226\pi$
$277$	8.85192e6			0.416484			0.208242	+	0.978077i	$0.433226\pi$
$278$	−1.14007e7	−	2.19466e7i	−0.530635	−	1.02149i
$279$		−	1.43543e7i		−	0.660951i
$280$		0			0
$281$	4.54352e6			0.204774			0.102387	−	0.994745i	$-0.467352\pi$
$281$	4.54352e6			0.204774			0.102387	+	0.994745i	$0.467352\pi$
$282$	−2.91358e7	+	1.51352e7i	−1.29921	+	0.674904i
$283$			1.97987e7i			0.873528i	0.899576	+	0.436764i	$0.143875\pi$
$283$			1.97987e7i			0.873528i	−0.899576	+	0.436764i	$0.856125\pi$
$284$	−1.16640e7	−	8.19722e6i	−0.509206	−	0.357859i
$285$		0			0
$286$	2.19726e7	+	4.22979e7i	0.939254	+	1.80809i
$287$			1.04455e6i			0.0441858i
$288$	−6.73686e6	−	6.22678e6i	−0.282020	−	0.260667i
$289$	−1.51310e7			−0.626867
$290$		0			0
$291$			7.01193e6i			0.284550i
$292$	2.33099e7	−	3.31682e7i	0.936250	−	1.33221i
$293$	3.44412e7			1.36923			0.684614	−	0.728906i	$-0.259971\pi$
$293$	3.44412e7			1.36923			0.684614	+	0.728906i	$0.259971\pi$
$294$	1.28579e7	+	2.47517e7i	0.505972	+	0.974011i
$295$		0			0
$296$	1.29065e6	−	9.61148e6i	0.0497661	−	0.370608i
$297$	2.55323e7			0.974585
$298$	1.09860e7	−	5.70691e6i	0.415135	−	0.215651i
$299$			1.96671e7i			0.735744i
$300$		0			0
$301$	8.96074e6			0.328582
$302$	7.88085e6	+	1.51709e7i	0.286123	+	0.550794i
$303$		−	5.93101e6i		−	0.213207i
$304$	2.64858e7	−	9.53683e6i	0.942741	−	0.339456i
$305$		0			0
$306$	5.96472e6	−	3.09851e6i	0.208174	−	0.108141i
$307$			1.94134e7i			0.670944i	0.942050	+	0.335472i	$0.108896\pi$
$307$			1.94134e7i			0.670944i	−0.942050	+	0.335472i	$0.891104\pi$
$308$	5.84980e6	−	8.32382e6i	0.200211	−	0.284886i
$309$	3.67458e7			1.24547
$310$		0			0
$311$		−	2.64127e7i		−	0.878075i	−0.898469	−	0.439038i	$-0.855319\pi$
$311$		−	2.64127e7i		−	0.878075i	0.898469	−	0.439038i	$-0.144681\pi$
$312$	−5.36492e7	−	7.20413e6i	−1.76644	−	0.237202i
$313$	4.96526e6			0.161923			0.0809616	−	0.996717i	$-0.474201\pi$
$313$	4.96526e6			0.161923			0.0809616	+	0.996717i	$0.474201\pi$
$314$	4.64057e7	−	2.41065e7i	1.49893	−	0.778655i
$315$		0			0
$316$	−8.73254e6	−	6.13704e6i	−0.276745	−	0.194490i
$317$	3.24542e7			1.01881			0.509405	−	0.860527i	$-0.329865\pi$
$317$	3.24542e7			1.01881			0.509405	+	0.860527i	$0.329865\pi$
$318$	5.56525e6	+	1.07133e7i	0.173063	+	0.333150i
$319$			2.51328e7i			0.774229i
$320$		0			0
$321$	4.93072e7			1.49072
$322$	3.72522e6	−	1.93515e6i	0.111579	−	0.0579625i
$323$			2.06255e7i			0.612064i
$324$	−2.41827e7	+	3.44102e7i	−0.711001	+	1.01170i
$325$		0			0
$326$	−2.63197e7	−	5.06661e7i	−0.759675	−	1.46240i
$327$			5.61343e7i			1.60541i
$328$	801495.	−	5.96874e6i	0.0227133	−	0.169146i
$329$	1.14739e7			0.322198
$330$		0			0
$331$			4.50251e7i			1.24157i	0.783981	+	0.620784i	$0.213186\pi$
$331$			4.50251e7i			1.24157i	−0.783981	+	0.620784i	$0.786814\pi$
$332$	1.71811e7	+	1.20745e7i	0.469501	+	0.329955i
$333$	5.30273e6			0.143604
$334$	1.67824e7	+	3.23067e7i	0.450418	+	0.867067i
$335$		0			0
$336$	3.91427e6	+	1.08708e7i	0.103189	+	0.286577i
$337$	−2.36631e6			−0.0618275			−0.0309137	−	0.999522i	$-0.509842\pi$
$337$	−2.36631e6			−0.0618275			−0.0309137	+	0.999522i	$0.509842\pi$
$338$	−4.43811e7	+	2.30548e7i	−1.14934	+	0.597050i
$339$			4.30628e7i			1.10536i
$340$		0			0
$341$	−9.17807e7			−2.31467
$342$	7.09578e6	+	1.36596e7i	0.177387	+	0.341475i
$343$		−	2.01952e7i		−	0.500456i
$344$	−5.12033e7	−	6.87569e6i	−1.25783	−	0.168904i
$345$		0			0
$346$	5.89200e7	−	3.06073e7i	1.42244	−	0.738919i
$347$		−	3.57456e7i		−	0.855528i	−0.903890	−	0.427764i	$-0.859301\pi$
$347$		−	3.57456e7i		−	0.855528i	0.903890	−	0.427764i	$-0.140699\pi$
$348$	−2.33523e7	−	1.64115e7i	−0.554105	−	0.389413i
$349$	−2.95982e7			−0.696288			−0.348144	−	0.937441i	$-0.613188\pi$
$349$	−2.95982e7			−0.696288			−0.348144	+	0.937441i	$0.613188\pi$
$350$		0			0
$351$			4.74742e7i			1.09783i
$352$	−3.98138e7	+	4.30752e7i	−0.912863	+	0.987642i
$353$	6.19569e7			1.40853			0.704264	−	0.709938i	$-0.251277\pi$
$353$	6.19569e7			1.40853			0.704264	+	0.709938i	$0.251277\pi$
$354$	3.15453e7	−	1.63869e7i	0.711091	−	0.369392i
$355$		0			0
$356$	−1.02165e6	+	1.45373e6i	−0.0226439	+	0.0322206i
$357$	−8.46547e6			−0.186057
$358$	−1.11971e7	−	2.15547e7i	−0.244038	−	0.469779i
$359$		−	4.08262e7i		−	0.882380i	−0.897414	−	0.441190i	$-0.854556\pi$
$359$		−	4.08262e7i		−	0.882380i	0.897414	−	0.441190i	$-0.145444\pi$
$360$		0			0
$361$	−187766.			−0.00399111
$362$	4.57854e6	−	2.37843e6i	0.0965164	−	0.0501377i
$363$			4.55105e7i			0.951463i
$364$	1.54772e7	+	1.08770e7i	0.320913	+	0.225531i
$365$		0			0
$366$	3.51333e7	+	6.76326e7i	0.716598	+	1.37947i
$367$		−	1.51049e7i		−	0.305577i	−0.988259	−	0.152788i	$-0.951175\pi$
$367$		−	1.51049e7i		−	0.305577i	0.988259	−	0.152788i	$-0.0488253\pi$
$368$	−2.27715e7	+	8.19940e6i	−0.456928	+	0.164527i
$369$	3.29300e6			0.0655409
$370$		0			0
$371$		−	4.21896e6i		−	0.0826198i
$372$	5.99319e7	−	8.52786e7i	1.16421	−	1.65658i
$373$	−5.32493e7			−1.02610			−0.513048	−	0.858360i	$-0.671484\pi$
$373$	−5.32493e7			−1.02610			−0.513048	+	0.858360i	$0.671484\pi$
$374$	−1.98118e7	−	3.81382e7i	−0.378711	−	0.729030i
$375$		0			0
$376$	−6.55640e7	−	8.80407e6i	−1.23339	−	0.165623i
$377$	−4.67315e7			−0.872139
$378$	8.99227e6	−	4.67124e6i	0.166492	−	0.0864882i
$379$			329020.i			0.00604373i	0.999995	+	0.00302187i	$0.000961891\pi$
$379$			329020.i			0.00604373i	−0.999995	+	0.00302187i	$0.999038\pi$
$380$		0			0
$381$	2.96450e7			0.536015
$382$	−1.70691e7	−	3.28584e7i	−0.306210	−	0.589463i
$383$			8.05002e7i			1.43285i	0.697665	+	0.716424i	$0.254223\pi$
$383$			8.05002e7i			1.43285i	−0.697665	+	0.716424i	$0.745777\pi$
$384$	−1.40256e7	−	6.51210e7i	−0.247701	−	1.15008i
$385$		0			0
$386$	3.64747e7	−	1.89476e7i	0.634205	−	0.329452i
$387$		−	2.82493e7i		−	0.487387i
$388$	−8.12340e6	+	1.15590e7i	−0.139073	+	0.197890i
$389$	−4.89579e7			−0.831713			−0.415857	−	0.909430i	$-0.636518\pi$
$389$	−4.89579e7			−0.831713			−0.415857	+	0.909430i	$0.636518\pi$
$390$		0			0
$391$		−	1.77330e7i		−	0.296655i
$392$	−7.47933e6	+	5.56986e7i	−0.124166	+	0.924669i
$393$	333641.			0.00549670
$394$	−3.92059e7	+	2.03664e7i	−0.641008	+	0.332986i
$395$		0			0
$396$	−2.62413e7	−	1.84418e7i	−0.422572	−	0.296974i
$397$	−6.21417e7			−0.993142			−0.496571	−	0.867996i	$-0.665408\pi$
$397$	−6.21417e7			−0.993142			−0.496571	+	0.867996i	$0.665408\pi$
$398$	−1.58231e7	−	3.04600e7i	−0.250982	−	0.483148i
$399$		−	1.93864e7i		−	0.305196i
$400$		0			0
$401$	382303.			0.00592891			0.00296445	−	0.999996i	$-0.499056\pi$
$401$	382303.			0.00592891			0.00296445	+	0.999996i	$0.499056\pi$
$402$	9.21373e6	−	4.78628e6i	0.141826	−	0.0736750i
$403$		−	1.70655e8i		−	2.60738i
$404$	6.87115e6	−	9.77713e6i	0.104204	−	0.148275i
$405$		0			0
$406$	4.59816e6	+	8.85159e6i	0.0687078	+	0.132265i
$407$		−	3.39054e7i		−	0.502905i
$408$	4.83733e7	+	6.49566e6i	0.712238	+	0.0956408i
$409$	1.10847e8			1.62015			0.810074	−	0.586327i	$-0.199427\pi$
$409$	1.10847e8			1.62015			0.810074	+	0.586327i	$0.199427\pi$
$410$		0			0
$411$		−	6.68464e7i		−	0.962836i
$412$	6.05745e7	+	4.25704e7i	0.866159	+	0.608718i
$413$	−1.24228e7			−0.176347
$414$	−6.10067e6	−	1.17440e7i	−0.0859759	−	0.165506i
$415$		0			0
$416$	−8.00933e7	−	7.40291e7i	−1.11254	−	1.02831i
$417$	9.81954e7			1.35420
$418$	8.73388e7	−	4.53701e7i	1.19585	−	0.621214i
$419$		−	1.21226e8i		−	1.64799i	−0.566596	−	0.823995i	$-0.691740\pi$
$419$		−	1.21226e8i		−	1.64799i	0.566596	−	0.823995i	$-0.308260\pi$
$420$		0			0
$421$	−826557.			−0.0110771			−0.00553856	−	0.999985i	$-0.501763\pi$
$421$	−826557.			−0.0110771			−0.00553856	+	0.999985i	$0.501763\pi$
$422$	−3.93580e7	−	7.57653e7i	−0.523716	−	1.00817i
$423$		−	3.61721e7i		−	0.477918i
$424$	−3.23727e6	+	2.41080e7i	−0.0424699	+	0.316273i
$425$		0			0
$426$	5.02319e7	−	2.60941e7i	0.649757	−	0.337531i
$427$		−	2.66342e7i		−	0.342103i
$428$	8.12817e7	+	5.71230e7i	1.03672	+	0.728584i
$429$	−1.89253e8			−2.39701
$430$		0			0
$431$		−	1.26492e8i		−	1.57990i	−0.613169	−	0.789952i	$-0.710106\pi$
$431$		−	1.26492e8i		−	1.57990i	0.613169	−	0.789952i	$-0.289894\pi$
$432$	−5.49678e7	+	1.97924e7i	−0.681800	+	0.245498i
$433$	−1.05162e8			−1.29537			−0.647687	−	0.761907i	$-0.724263\pi$
$433$	−1.05162e8			−1.29537			−0.647687	+	0.761907i	$0.724263\pi$
$434$	−3.23245e7	+	1.67917e7i	−0.395424	+	0.205412i
$435$		0			0
$436$	−6.50323e7	+	9.25360e7i	−0.784638	+	1.11648i
$437$	4.06096e7			0.486614
$438$	7.42021e7	+	1.42841e8i	0.883067	+	1.69993i
$439$			2.67453e7i			0.316122i	0.987429	+	0.158061i	$0.0505242\pi$
$439$			2.67453e7i			0.316122i	−0.987429	+	0.158061i	$0.949476\pi$
$440$		0			0
$441$	−3.07293e7			−0.358292
$442$	7.09135e7	−	3.68376e7i	0.821225	−	0.426604i
$443$		−	8.39480e7i		−	0.965604i	−0.875730	−	0.482802i	$-0.839619\pi$
$443$		−	8.39480e7i		−	0.965604i	0.875730	−	0.482802i	$-0.160381\pi$
$444$	3.15034e7	+	2.21399e7i	0.359923	+	0.252946i
$445$		0			0
$446$	2.40062e7	+	4.62127e7i	0.270595	+	0.520903i
$447$			4.91543e7i			0.550350i
$448$	−6.14132e6	+	2.24549e7i	−0.0683011	+	0.249734i
$449$	3.85437e7			0.425808			0.212904	−	0.977073i	$-0.431708\pi$
$449$	3.85437e7			0.425808			0.212904	+	0.977073i	$0.431708\pi$
$450$		0			0
$451$		−	2.10553e7i		−	0.229526i
$452$	−4.98888e7	+	7.09880e7i	−0.540241	+	0.768723i
$453$	−6.78788e7			−0.730196
$454$	−3.05477e7	−	5.88053e7i	−0.326446	−	0.628418i
$455$		0			0
$456$	−1.48755e7	+	1.10778e8i	−0.156883	+	1.16831i
$457$	−1.01357e8			−1.06196			−0.530978	−	0.847386i	$-0.678175\pi$
$457$	−1.01357e8			−1.06196			−0.530978	+	0.847386i	$0.678175\pi$
$458$	4.25341e7	−	2.20953e7i	0.442732	−	0.229987i
$459$		−	4.28055e7i		−	0.442651i
$460$		0			0
$461$	9.49132e7			0.968777			0.484388	−	0.874853i	$-0.339042\pi$
$461$	9.49132e7			0.968777			0.484388	+	0.874853i	$0.339042\pi$
$462$	1.86216e7	+	3.58471e7i	0.188839	+	0.363520i
$463$			1.18102e8i			1.18991i	0.803759	+	0.594955i	$0.202830\pi$
$463$			1.18102e8i			1.18991i	−0.803759	+	0.594955i	$0.797170\pi$
$464$	−1.94828e7	−	5.41079e7i	−0.195028	−	0.541635i
$465$		0			0
$466$	−1.18939e7	+	6.17858e6i	−0.117535	+	0.0610564i
$467$			1.86109e8i			1.82733i	0.406473	+	0.913663i	$0.366759\pi$
$467$			1.86109e8i			1.82733i	−0.406473	+	0.913663i	$0.633241\pi$
$468$	3.42904e7	−	4.87927e7i	0.334530	−	0.476011i
$469$	−3.62844e6			−0.0351723
$470$		0			0
$471$			2.07632e8i			1.98716i
$472$	7.09861e7	+	9.53217e6i	0.675068	+	0.0906496i
$473$	−1.80625e8			−1.70684
$474$	3.76073e7	−	1.95359e7i	0.353132	−	0.183442i
$475$		0			0
$476$	−1.39551e7	−	9.80734e6i	−0.129394	−	0.0909349i
$477$	−1.33005e7			−0.122550
$478$	−1.48988e7	−	2.86806e7i	−0.136417	−	0.262606i
$479$			5.01949e7i			0.456723i	0.973576	+	0.228362i	$0.0733368\pi$
$479$			5.01949e7i			0.456723i	−0.973576	+	0.228362i	$0.926663\pi$
$480$		0			0
$481$	6.30432e7			0.566504
$482$	−6.61674e7	+	3.43722e7i	−0.590885	+	0.306949i
$483$			1.66677e7i			0.147922i
$484$	−5.27244e7	+	7.50229e7i	−0.465025	+	0.661695i
$485$		0			0
$486$	−3.86341e7	−	7.43718e7i	−0.336560	−	0.647888i
$487$		−	1.08896e8i		−	0.942816i	−0.881915	−	0.471408i	$-0.843746\pi$
$487$		−	1.08896e8i		−	0.942816i	0.881915	−	0.471408i	$-0.156254\pi$
$488$	−2.04368e7	+	1.52193e8i	−0.175854	+	1.30959i
$489$	2.26695e8			1.93872
$490$		0			0
$491$			1.71108e7i			0.144553i	0.997385	+	0.0722764i	$0.0230264\pi$
$491$			1.71108e7i			0.144553i	−0.997385	+	0.0722764i	$0.976974\pi$
$492$	1.95637e7	+	1.37489e7i	0.164269	+	0.115444i
$493$	4.21359e7			0.351650
$494$	8.43604e7	+	1.62396e8i	0.699774	+	1.34709i
$495$		0			0
$496$	1.97593e8	−	7.11479e7i	1.61929	−	0.583065i
$497$	−1.97817e7			−0.161137
$498$	−7.39915e7	+	3.84366e7i	−0.599092	+	0.311212i
$499$			2.08493e7i			0.167799i	0.996474	+	0.0838994i	$0.0267374\pi$
$499$			2.08493e7i			0.167799i	−0.996474	+	0.0838994i	$0.973263\pi$
$500$		0			0
$501$	−1.44549e8			−1.14948
$502$	9.56463e7	+	1.84122e8i	0.756061	+	1.45544i
$503$			1.34897e7i			0.105998i	0.998595	+	0.0529991i	$0.0168780\pi$
$503$			1.34897e7i			0.105998i	−0.998595	+	0.0529991i	$0.983122\pi$
$504$	−1.26160e7	−	1.69411e6i	−0.0985442	−	0.0132327i
$505$		0			0
$506$	−7.50905e7	+	3.90075e7i	−0.579607	+	0.301090i
$507$		−	1.98574e8i		−	1.52369i
$508$	4.88691e7	+	3.43441e7i	0.372772	+	0.261976i
$509$	−1.73454e8			−1.31531			−0.657657	−	0.753317i	$-0.728453\pi$
$509$	−1.73454e8			−1.31531			−0.657657	+	0.753317i	$0.728453\pi$
$510$		0			0
$511$		−	5.62519e7i		−	0.421575i
$512$	5.23226e7	−	1.23599e8i	0.389834	−	0.920885i
$513$	9.80272e7			0.726097
$514$	1.14499e8	−	5.94793e7i	0.843167	−	0.438002i
$515$		0			0
$516$	1.17946e8	−	1.67829e8i	0.858489	−	1.22157i
$517$	−2.31283e8			−1.67368
$518$	−6.20315e6	−	1.19412e7i	−0.0446296	−	0.0859133i
$519$			2.63625e8i			1.88575i
$520$		0			0
$521$	−1.78879e8			−1.26487			−0.632437	−	0.774612i	$-0.717945\pi$
$521$	−1.78879e8			−1.26487			−0.632437	+	0.774612i	$0.717945\pi$
$522$	2.79052e7	−	1.44960e7i	0.196188	−	0.101915i
$523$		−	1.77417e8i		−	1.24020i	−0.784525	−	0.620098i	$-0.787093\pi$
$523$		−	1.77417e8i		−	1.24020i	0.784525	−	0.620098i	$-0.212907\pi$
$524$	549999.	+	386527.i	0.00382268	+	0.00268649i
$525$		0			0
$526$	338714.	+	652034.i	0.00232742	+	0.00448036i
$527$			1.53873e8i			1.05131i
$528$	−7.89013e7	−	2.19126e8i	−0.536022	−	1.48865i
$529$	1.13121e8			0.764148
$530$		0			0
$531$			3.91636e7i			0.261577i
$532$	2.24594e7	−	3.19581e7i	0.149164	−	0.212249i
$533$	3.91499e7			0.258552
$534$	−3.25220e6	−	6.26057e6i	−0.0213576	−	0.0411141i
$535$		0			0
$536$	2.07336e7	+	2.78415e6i	0.134642	+	0.0180800i
$537$	9.64421e7			0.622793
$538$	−3.82251e7	+	1.98569e7i	−0.245472	+	0.127516i
$539$			1.96482e8i			1.25475i
$540$		0			0
$541$	1.34835e8			0.851553			0.425777	−	0.904828i	$-0.360001\pi$
$541$	1.34835e8			0.851553			0.425777	+	0.904828i	$0.360001\pi$
$542$	−3.28901e7	−	6.33143e7i	−0.206570	−	0.397653i
$543$			2.04857e7i			0.127953i
$544$	7.22168e7	+	6.67489e7i	0.448582	+	0.414617i
$545$		0			0
$546$	−6.66534e7	+	3.46246e7i	−0.409491	+	0.212720i
$547$		−	2.22069e8i		−	1.35683i	−0.734678	−	0.678416i	$-0.762667\pi$
$547$		−	2.22069e8i		−	1.35683i	0.734678	−	0.678416i	$-0.237333\pi$
$548$	7.74423e7	−	1.10195e8i	0.470583	−	0.669605i
$549$	−8.39660e7			−0.507442
$550$		0			0
$551$			9.64937e7i			0.576825i
$552$	1.27893e7	−	9.52423e7i	0.0760380	−	0.566256i
$553$	−1.48100e7			−0.0875751
$554$	−6.28422e7	+	3.26448e7i	−0.369591	+	0.191993i
$555$		0			0
$556$	1.61873e8	+	1.13760e8i	0.941779	+	0.661861i
$557$	2.84443e8			1.64600			0.823000	−	0.568042i	$-0.192299\pi$
$557$	2.84443e8			1.64600			0.823000	+	0.568042i	$0.192299\pi$
$558$	5.29368e7	+	1.01905e8i	0.304688	+	0.586533i
$559$		−	3.35850e8i		−	1.92269i
$560$		0			0
$561$	1.70641e8			0.966486
$562$	−3.22557e7	+	1.67560e7i	−0.181718	+	0.0943974i
$563$			4.28842e7i			0.240310i	0.992755	+	0.120155i	$0.0383392\pi$
$563$			4.28842e7i			0.240310i	−0.992755	+	0.120155i	$0.961661\pi$
$564$	1.51026e8	−	2.14898e8i	0.841809	−	1.19783i
$565$		0			0
$566$	−7.30150e7	−	1.40556e8i	−0.402683	−	0.775176i
$567$			5.83583e7i			0.320150i
$568$	1.13036e8	+	1.51788e7i	0.616841	+	0.0828307i
$569$	3.24019e8			1.75887			0.879435	−	0.476019i	$-0.157921\pi$
$569$	3.24019e8			1.75887			0.879435	+	0.476019i	$0.157921\pi$
$570$		0			0
$571$			3.28824e8i			1.76626i	0.469126	+	0.883131i	$0.344569\pi$
$571$			3.28824e8i			1.76626i	−0.469126	+	0.883131i	$0.655431\pi$
$572$	−3.11979e8	−	2.19252e8i	−1.66700	−	1.17153i
$573$	1.47018e8			0.781460
$574$	−3.85216e6	−	7.41552e6i	−0.0203690	−	0.0392108i
$575$		0			0
$576$	7.07904e7	+	1.93609e7i	0.370431	+	0.101311i
$577$	−9.48080e7			−0.493534			−0.246767	−	0.969075i	$-0.579368\pi$
$577$	−9.48080e7			−0.493534			−0.246767	+	0.969075i	$0.579368\pi$
$578$	1.07419e8	−	5.58014e7i	0.556287	−	0.288976i
$579$			1.63198e8i			0.840775i
$580$		0			0
$581$	2.91384e7			0.148572
$582$	−2.58591e7	−	4.97796e7i	−0.131173	−	0.252512i
$583$			8.50431e7i			0.429174i
$584$	−4.31628e7	+	3.21434e8i	−0.216706	+	1.61381i
$585$		0			0
$586$	−2.44507e8	+	1.27015e8i	−1.21506	+	0.631193i
$587$			5.12804e7i			0.253534i	0.991932	+	0.126767i	$0.0404601\pi$
$587$			5.12804e7i			0.253534i	−0.991932	+	0.126767i	$0.959540\pi$
$588$	−1.82563e8	−	1.28301e8i	−0.898008	−	0.631100i
$589$	−3.52378e8			−1.72450
$590$		0			0
$591$		−	1.75419e8i		−	0.849793i
$592$	2.62833e7	+	7.29942e7i	0.126682	+	0.351822i
$593$	−2.12368e7			−0.101842			−0.0509208	−	0.998703i	$-0.516216\pi$
$593$	−2.12368e7			−0.101842			−0.0509208	+	0.998703i	$0.516216\pi$
$594$	−1.81260e8	+	9.41598e7i	−0.864855	+	0.449269i
$595$		0			0
$596$	−5.69459e7	+	8.10297e7i	−0.268982	+	0.382741i
$597$	1.36287e8			0.640517
$598$	−7.25298e7	−	1.39622e8i	−0.339166	−	0.652905i
$599$		−	2.38008e8i		−	1.10742i	−0.832710	−	0.553709i	$-0.813212\pi$
$599$		−	2.38008e8i		−	1.10742i	0.832710	−	0.553709i	$-0.186788\pi$
$600$		0			0
$601$	−1.59516e8			−0.734822			−0.367411	−	0.930059i	$-0.619756\pi$
$601$	−1.59516e8			−0.734822			−0.367411	+	0.930059i	$0.619756\pi$
$602$	−6.36147e7	+	3.30461e7i	−0.291587	+	0.151471i
$603$			1.14389e7i			0.0521712i
$604$	−1.11896e8	−	7.86384e7i	−0.507815	−	0.356881i
$605$		0			0
$606$	2.18728e7	+	4.21058e7i	0.0982850	+	0.189201i
$607$			1.87552e8i			0.838602i	0.907847	+	0.419301i	$0.137725\pi$
$607$			1.87552e8i			0.838602i	−0.907847	+	0.419301i	$0.862275\pi$
$608$	−1.52859e8	+	1.65381e8i	−0.680112	+	0.735825i
$609$	−3.96046e7			−0.175345
$610$		0			0
$611$		−	4.30044e8i		−	1.88534i
$612$	−3.09182e7	+	4.39943e7i	−0.134884	+	0.191930i
$613$	−1.96888e7			−0.0854749			−0.0427374	−	0.999086i	$-0.513608\pi$
$613$	−1.96888e7			−0.0854749			−0.0427374	+	0.999086i	$0.513608\pi$
$614$	−7.15942e7	−	1.37821e8i	−0.309295	−	0.595401i
$615$		0			0
$616$	−1.08320e7	+	8.06664e7i	−0.0463413	+	0.345104i
$617$	2.99111e8			1.27344			0.636719	−	0.771096i	$-0.280291\pi$
$617$	2.99111e8			1.27344			0.636719	+	0.771096i	$0.280291\pi$
$618$	−2.60868e8	+	1.35514e8i	−1.10524	+	0.574140i
$619$		−	6.73241e7i		−	0.283856i	−0.989877	−	0.141928i	$-0.954670\pi$
$619$		−	6.73241e7i		−	0.283856i	0.989877	−	0.141928i	$-0.0453302\pi$
$620$		0			0
$621$	−8.42799e7			−0.351924
$622$	9.74068e7	+	1.87511e8i	0.404779	+	0.779211i
$623$			2.46546e6i			0.0101961i
$624$	4.07438e8	−	1.46708e8i	1.67690	−	0.603808i
$625$		0			0
$626$	−3.52497e7	+	1.83113e7i	−0.143692	+	0.0746441i
$627$			3.90779e8i			1.58536i
$628$	−2.40544e8	+	3.42277e8i	−0.971217	+	1.38197i
$629$	−5.68434e7			−0.228417
$630$		0			0
$631$		−	3.74586e8i		−	1.49095i	−0.666533	−	0.745476i	$-0.732222\pi$
$631$		−	3.74586e8i		−	1.49095i	0.666533	−	0.745476i	$-0.267778\pi$
$632$	8.46272e7	+	1.13639e7i	0.335242	+	0.0450171i
$633$	3.38996e8			1.33654
$634$	−2.30401e8	+	1.19687e8i	−0.904101	+	0.469656i
$635$		0			0
$636$	−7.90183e7	−	5.55323e7i	−0.307154	−	0.215861i
$637$	−3.65335e8			−1.41343
$638$	−9.26867e7	−	1.78425e8i	−0.356907	−	0.687057i
$639$			6.23630e7i			0.239015i
$640$		0			0
$641$	3.70848e8			1.40806			0.704031	−	0.710169i	$-0.251382\pi$
$641$	3.70848e8			1.40806			0.704031	+	0.710169i	$0.251382\pi$
$642$	−3.50045e8	+	1.81839e8i	−1.32287	+	0.687197i
$643$			4.50751e8i			1.69552i	0.530378	+	0.847761i	$0.322050\pi$
$643$			4.50751e8i			1.69552i	−0.530378	+	0.847761i	$0.677950\pi$
$644$	−1.93097e7	+	2.74763e7i	−0.0722967	+	0.102873i
$645$		0			0
$646$	−7.60643e7	−	1.46426e8i	−0.282152	−	0.543151i
$647$		−	3.12382e8i		−	1.15338i	−0.816962	−	0.576691i	$-0.804344\pi$
$647$		−	3.12382e8i		−	1.15338i	0.816962	−	0.576691i	$-0.195656\pi$
$648$	4.47791e7	−	3.33470e8i	0.164570	−	1.22555i
$649$	2.50410e8			0.916048
$650$		0			0
$651$		−	1.44629e8i		−	0.524219i
$652$	3.73701e8	+	2.62629e8i	1.34828	+	0.947544i
$653$	1.75008e8			0.628519			0.314260	−	0.949337i	$-0.398244\pi$
$653$	1.75008e8			0.628519			0.314260	+	0.949337i	$0.398244\pi$
$654$	−2.07016e8	−	3.98512e8i	−0.740068	−	1.42465i
$655$		0			0
$656$	1.63219e7	+	4.53295e7i	0.0578176	+	0.160572i
$657$	−1.77338e8			−0.625323
$658$	−8.14562e7	+	4.23143e7i	−0.285921	+	0.148528i
$659$		−	5.04270e8i		−	1.76200i	−0.473113	−	0.881002i	$-0.656870\pi$
$659$		−	5.04270e8i		−	1.76200i	0.473113	−	0.881002i	$-0.343130\pi$
$660$		0			0
$661$	−3.10890e8			−1.07647			−0.538236	−	0.842794i	$-0.680909\pi$
$661$	−3.10890e8			−1.07647			−0.538236	+	0.842794i	$0.680909\pi$
$662$	−1.66047e8	−	3.19645e8i	−0.572344	−	1.10178i
$663$			3.17287e8i			1.08871i
$664$	−1.66502e8	−	2.23583e7i	−0.568743	−	0.0763720i
$665$		0			0
$666$	−3.76455e7	+	1.95558e7i	−0.127435	+	0.0661992i
$667$		−	8.29615e7i		−	0.279575i
$668$	−2.38286e8	−	1.67462e8i	−0.799409	−	0.561807i
$669$	−2.06769e8			−0.690569
$670$		0			0
$671$			5.36875e8i			1.77708i
$672$	−6.78784e7	−	6.27390e7i	−0.223678	−	0.206743i
$673$	4.42525e8			1.45175			0.725876	−	0.687826i	$-0.241435\pi$
$673$	4.42525e8			1.45175			0.725876	+	0.687826i	$0.241435\pi$
$674$	1.67990e7	−	8.72665e6i	0.0548662	−	0.0285015i
$675$		0			0
$676$	2.30050e8	−	3.27344e8i	0.744702	−	1.05965i
$677$	3.01059e8			0.970255			0.485128	−	0.874443i	$-0.338773\pi$
$677$	3.01059e8			0.970255			0.485128	+	0.874443i	$0.338773\pi$
$678$	−1.58810e8	−	3.05714e8i	−0.509553	−	0.980905i
$679$			1.96036e7i			0.0626218i
$680$		0			0
$681$	2.63112e8			0.833103
$682$	6.51576e8	−	3.38476e8i	2.05405	−	1.06703i
$683$		−	2.52236e8i		−	0.791673i	−0.918321	−	0.395836i	$-0.870455\pi$
$683$		−	2.52236e8i		−	0.791673i	0.918321	−	0.395836i	$-0.129545\pi$
$684$	−1.00750e8	−	7.08046e7i	−0.314829	−	0.221255i
$685$		0			0
$686$	7.44773e7	+	1.43371e8i	0.230702	+	0.444108i
$687$			1.90310e8i			0.586936i
$688$	3.88863e8	−	1.40019e8i	1.19407	−	0.429954i
$689$	−1.58128e8			−0.483448
$690$		0			0
$691$			6.69200e7i			0.202825i	0.994844	+	0.101413i	$0.0323362\pi$
$691$			6.69200e7i			0.202825i	−0.994844	+	0.101413i	$0.967664\pi$
$692$	−3.05413e8	+	4.34579e8i	−0.921655	+	1.31145i
$693$	−4.45042e7			−0.133722
$694$	1.31825e8	+	2.53768e8i	0.394385	+	0.759203i
$695$		0			0
$696$	2.26308e8	+	3.03891e7i	0.671231	+	0.0901343i
$697$	−3.52998e7			−0.104249
$698$	2.10125e8	−	1.09154e8i	0.617892	−	0.320978i
$699$		−	5.32169e7i		−	0.155818i
$700$		0			0
$701$	−4.07068e8			−1.18171			−0.590857	−	0.806776i	$-0.701210\pi$
$701$	−4.07068e8			−1.18171			−0.590857	+	0.806776i	$0.701210\pi$
$702$	−1.75079e8	−	3.37032e8i	−0.506084	−	0.974226i
$703$		−	1.30175e8i		−	0.374680i
$704$	1.23793e8	−	4.52631e8i	0.354795	−	1.29726i
$705$		0			0
$706$	−4.39849e8	+	2.28489e8i	−1.24994	+	0.649310i
$707$		−	1.65816e7i		−	0.0469211i
$708$	−1.63516e8	+	2.32670e8i	−0.460744	+	0.655604i
$709$	−2.14836e7			−0.0602793			−0.0301396	−	0.999546i	$-0.509595\pi$
$709$	−2.14836e7			−0.0602793			−0.0301396	+	0.999546i	$0.509595\pi$
$710$		0			0
$711$			4.66895e7i			0.129900i
$712$	1.89178e6	−	1.40881e7i	0.00524120	−	0.0390313i
$713$	3.02961e8			0.835830
$714$	6.00986e7	−	3.12196e7i	0.165109	−	0.0857694i
$715$		0			0
$716$	1.58982e8	+	1.11729e8i	0.433122	+	0.304388i
$717$	1.28325e8			0.348141
$718$	1.50562e8	+	2.89836e8i	0.406764	+	0.783031i
$719$			4.75458e8i			1.27916i	0.768724	+	0.639581i	$0.220892\pi$
$719$			4.75458e8i			1.27916i	−0.768724	+	0.639581i	$0.779108\pi$
$720$		0			0
$721$	1.02732e8			0.274094
$722$	1.33300e6	−	692456.i	0.00354175	−	0.00183984i
$723$		−	2.96052e8i		−	0.783345i
$724$	−2.37329e7	+	3.37702e7i	−0.0625368	+	0.0889851i
$725$		0			0
$726$	−1.67837e8	−	3.23091e8i	−0.438609	−	0.844336i
$727$		−	6.11316e8i		−	1.59097i	−0.605972	−	0.795486i	$-0.707216\pi$
$727$		−	6.11316e8i		−	1.59097i	0.605972	−	0.795486i	$-0.292784\pi$
$728$	−1.49990e8	−	2.01409e7i	−0.388747	−	0.0522018i
$729$	−1.46305e8			−0.377638
$730$		0			0
$731$			3.02822e8i			0.775239i
$732$	−4.98841e8	−	3.50575e8i	−1.27183	−	0.893814i
$733$	−5.86490e8			−1.48919			−0.744593	−	0.667519i	$-0.767356\pi$
$733$	−5.86490e8			−1.48919			−0.744593	+	0.667519i	$0.767356\pi$
$734$	5.57050e7	+	1.07234e8i	0.140866	+	0.271171i
$735$		0			0
$736$	1.31422e8	−	1.42188e8i	0.329637	−	0.356639i
$737$	7.31397e7			0.182705
$738$	−2.33779e7	+	1.21442e7i	−0.0581615	+	0.0302133i
$739$			5.79830e8i			1.43671i	0.695679	+	0.718353i	$0.255104\pi$
$739$			5.79830e8i			1.43671i	−0.695679	+	0.718353i	$0.744896\pi$
$740$		0			0
$741$	−7.26607e8			−1.78585
$742$	1.55590e7	+	2.99516e7i	0.0380864	+	0.0733175i
$743$		−	3.73947e8i		−	0.911681i	−0.890061	−	0.455841i	$-0.849339\pi$
$743$		−	3.73947e8i		−	0.911681i	0.890061	−	0.455841i	$-0.150661\pi$
$744$	−1.10976e8	+	8.26437e8i	−0.269469	+	2.00674i
$745$		0			0
$746$	3.78031e8	−	1.96377e8i	0.910565	−	0.473014i
$747$		−	9.18606e7i		−	0.220378i
$748$	2.81298e8	+	1.97690e8i	0.672143	+	0.472367i
$749$	1.37850e8			0.328067
$750$		0			0
$751$		−	1.27510e8i		−	0.301041i	−0.988607	−	0.150521i	$-0.951905\pi$
$751$		−	1.27510e8i		−	0.301041i	0.988607	−	0.150521i	$-0.0480950\pi$
$752$	4.97924e8	−	1.79289e8i	1.17087	−	0.421600i
$753$	−8.23814e8			−1.92950
$754$	3.31760e8	−	1.72340e8i	0.773944	−	0.402043i
$755$		0			0
$756$	−4.66116e7	+	6.63247e7i	−0.107877	+	0.153501i
$757$	−2.33748e7			−0.0538841			−0.0269420	−	0.999637i	$-0.508577\pi$
$757$	−2.33748e7			−0.0538841			−0.0269420	+	0.999637i	$0.508577\pi$
$758$	−1.21339e6	−	2.33580e6i	−0.00278607	−	0.00536326i
$759$		−	3.35976e8i		−	0.768393i
$760$		0			0
$761$	7.53332e8			1.70936			0.854678	−	0.519159i	$-0.173755\pi$
$761$	7.53332e8			1.70936			0.854678	+	0.519159i	$0.173755\pi$
$762$	−2.10458e8	+	1.09327e8i	−0.475664	+	0.247094i
$763$			1.56937e8i			0.353307i
$764$	2.42355e8	+	1.70322e8i	0.543467	+	0.381936i
$765$		0			0
$766$	−2.96875e8	−	5.71492e8i	−0.660521	−	1.27152i
$767$			4.65609e8i			1.03189i
$768$	3.39729e8	+	4.10587e8i	0.749980	+	0.906402i
$769$	6.33859e8			1.39384			0.696921	−	0.717148i	$-0.254553\pi$
$769$	6.33859e8			1.39384			0.696921	+	0.717148i	$0.254553\pi$
$770$		0			0
$771$			5.12303e8i			1.11780i
$772$	−1.89067e8	+	2.69028e8i	−0.410926	+	0.584717i
$773$	1.08448e8			0.234793			0.117396	−	0.993085i	$-0.462545\pi$
$773$	1.08448e8			0.234793			0.117396	+	0.993085i	$0.462545\pi$
$774$	1.04180e8	+	2.00549e8i	0.224678	+	0.432512i
$775$		0			0
$776$	1.50421e7	−	1.12018e8i	0.0321901	−	0.239720i
$777$	5.34285e7			0.113896
$778$	3.47565e8	−	1.80551e8i	0.738069	−	0.383407i
$779$		−	8.08387e7i		−	0.171004i
$780$		0			0
$781$	3.98747e8			0.837036
$782$	6.53971e7	+	1.25891e8i	0.136753	+	0.263254i
$783$		−	2.00260e8i		−	0.417166i
$784$	−1.52312e8	−	4.23002e8i	−0.316072	−	0.877797i
$785$		0			0
$786$	−2.36861e6	+	1.23043e6i	−0.00487781	+	0.00253389i
$787$			3.53415e8i			0.725039i	0.931976	+	0.362519i	$0.118083\pi$
$787$			3.53415e8i			0.725039i	−0.931976	+	0.362519i	$0.881917\pi$
$788$	2.03225e8	−	2.89173e8i	0.415334	−	0.590989i
$789$	−2.91739e6			−0.00593968
$790$		0			0
$791$			1.20393e8i			0.243260i
$792$	2.54305e8	+	3.41487e7i	0.511894	+	0.0687382i
$793$	−9.98257e8			−2.00181
$794$	4.41160e8	−	2.29171e8i	0.881322	−	0.457823i
$795$		0			0
$796$	2.24665e8	+	1.57890e8i	0.445448	+	0.313051i
$797$	−5.64122e8			−1.11429			−0.557145	−	0.830415i	$-0.688103\pi$
$797$	−5.64122e8			−1.11429			−0.557145	+	0.830415i	$0.688103\pi$
$798$	7.14948e7	+	1.37629e8i	0.140691	+	0.270834i
$799$			3.87753e8i			0.760176i
$800$		0			0
$801$	7.77252e6			0.0151239
$802$	−2.71407e6	+	1.40989e6i	−0.00526136	+	0.00273313i
$803$			1.13389e9i			2.18990i
$804$	−4.77595e7	+	6.79582e7i	−0.0918949	+	0.130760i
$805$		0			0
$806$	6.29356e8	+	1.21153e9i	1.20196	+	2.31381i
$807$		−	1.71030e8i		−	0.325426i
$808$	−1.27233e7	+	9.47504e7i	−0.0241193	+	0.179617i
$809$	2.93587e8			0.554487			0.277243	−	0.960800i	$-0.410579\pi$
$809$	2.93587e8			0.554487			0.277243	+	0.960800i	$0.410579\pi$
$810$		0			0
$811$		−	7.58312e8i		−	1.42163i	−0.703381	−	0.710813i	$-0.748327\pi$
$811$		−	7.58312e8i		−	1.42163i	0.703381	−	0.710813i	$-0.251673\pi$
$812$	−6.52871e7	−	4.58824e7i	−0.121944	−	0.0856994i
$813$	2.83286e8			0.527174
$814$	1.25039e8	+	2.40704e8i	0.231831	+	0.446282i
$815$		0			0
$816$	−3.67370e8	+	1.32280e8i	−0.676134	+	0.243458i
$817$	−6.93481e8			−1.27165
$818$	−7.86934e8	+	4.08791e8i	−1.43773	+	0.746863i
$819$		−	8.27504e7i		−	0.150632i
$820$		0			0
$821$	−2.11510e7			−0.0382209			−0.0191104	−	0.999817i	$-0.506083\pi$
$821$	−2.11510e7			−0.0382209			−0.0191104	+	0.999817i	$0.506083\pi$
$822$	2.46521e8	+	4.74560e8i	0.443853	+	0.854429i
$823$		−	9.99192e8i		−	1.79246i	−0.443590	−	0.896230i	$-0.646295\pi$
$823$		−	9.99192e8i		−	1.79246i	0.443590	−	0.896230i	$-0.353705\pi$
$824$	−5.87028e8	−	7.88274e7i	−1.04925	−	0.140895i
$825$		0			0
$826$	8.81927e7	−	4.58137e7i	0.156492	−	0.0812934i
$827$		−	5.08817e8i		−	0.899591i	−0.893131	−	0.449796i	$-0.851497\pi$
$827$		−	5.08817e8i		−	0.899591i	0.893131	−	0.449796i	$-0.148503\pi$
$828$	8.66206e7	+	6.08750e7i	0.152591	+	0.107238i
$829$	−9.05552e8			−1.58946			−0.794730	−	0.606963i	$-0.792388\pi$
$829$	−9.05552e8			−1.58946			−0.794730	+	0.606963i	$0.792388\pi$
$830$		0			0
$831$		−	2.81174e8i		−	0.489973i
$832$	8.41614e8	+	2.30178e8i	1.46131	+	0.399663i
$833$	3.29408e8			0.569900
$834$	−6.97115e8	+	3.62132e8i	−1.20173	+	0.624265i
$835$		0			0
$836$	−4.52722e8	+	6.44189e8i	−0.774841	+	1.10254i
$837$	7.31315e8			1.24718
$838$	4.47068e8	+	8.60618e8i	0.759698	+	1.46244i
$839$			8.22611e8i			1.39286i	0.717623	+	0.696432i	$0.245230\pi$
$839$			8.22611e8i			1.39286i	−0.717623	+	0.696432i	$0.754770\pi$
$840$		0			0
$841$	−3.97696e8			−0.668596
$842$	5.86795e6	−	3.04824e6i	0.00982992	−	0.00510638i
$843$		−	1.44321e8i		−	0.240906i
$844$	5.58826e8	+	3.92730e8i	0.929500	+	0.653232i
$845$		0			0
$846$	1.33398e8	+	2.56796e8i	0.220313	+	0.424108i
$847$			1.27236e8i			0.209391i
$848$	−6.59249e7	−	1.83087e8i	−0.108109	−	0.300242i
$849$	6.28888e8			1.02766
$850$		0			0
$851$			1.11919e8i			0.181600i
$852$	−2.60378e8	+	3.70498e8i	−0.421003	+	0.599056i
$853$	1.56058e8			0.251443			0.125722	−	0.992066i	$-0.459875\pi$
$853$	1.56058e8			0.251443			0.125722	+	0.992066i	$0.459875\pi$
$854$	9.82238e7	+	1.89084e8i	0.157704	+	0.303585i
$855$		0			0
$856$	−7.87703e8	−	1.05774e8i	−1.25586	−	0.168639i
$857$	−3.39476e8			−0.539345			−0.269672	−	0.962952i	$-0.586915\pi$
$857$	−3.39476e8			−0.539345			−0.269672	+	0.962952i	$0.586915\pi$
$858$	1.34356e9	−	6.97941e8i	2.12713	−	1.10499i
$859$		−	6.27544e8i		−	0.990068i	−0.868874	−	0.495034i	$-0.835156\pi$
$859$		−	6.27544e8i		−	0.990068i	0.868874	−	0.495034i	$-0.164844\pi$
$860$		0			0
$861$	3.31792e7			0.0519824
$862$	4.66486e8	+	8.97999e8i	0.728311	+	1.40202i
$863$		−	5.09291e8i		−	0.792381i	−0.918168	−	0.396190i	$-0.870332\pi$
$863$		−	5.09291e8i		−	0.792381i	0.918168	−	0.396190i	$-0.129668\pi$
$864$	3.17239e8	−	3.43226e8i	0.491864	−	0.532156i
$865$		0			0
$866$	7.46573e8	−	3.87824e8i	1.14953	−	0.597147i
$867$			4.80625e8i			0.737477i
$868$	1.67554e8	−	2.38417e8i	0.256210	−	0.364568i
$869$	2.98531e8			0.454914
$870$		0			0
$871$			1.35995e8i			0.205810i
$872$	1.20420e8	−	8.96769e8i	0.181614	−	1.35248i
$873$	6.18014e7			0.0928872
$874$	−2.88299e8	+	1.49763e8i	−0.431825	+	0.224322i
$875$		0			0
$876$	−1.05356e9	−	7.40419e8i	−1.56728	−	1.10145i
$877$	−6.30685e8			−0.935004			−0.467502	−	0.883992i	$-0.654846\pi$
$877$	−6.30685e8			−0.935004			−0.467502	+	0.883992i	$0.654846\pi$
$878$	−9.86334e7	−	1.89872e8i	−0.145727	−	0.280529i
$879$		−	1.09400e9i		−	1.61083i
$880$		0			0
$881$	2.54533e8			0.372235			0.186117	−	0.982528i	$-0.440410\pi$
$881$	2.54533e8			0.372235			0.186117	+	0.982528i	$0.440410\pi$
$882$	2.18156e8	−	1.13326e8i	0.317952	−	0.165167i
$883$		−	3.28879e7i		−	0.0477698i	−0.999715	−	0.0238849i	$-0.992396\pi$
$883$		−	3.28879e7i		−	0.0477698i	0.999715	−	0.0238849i	$-0.00760352\pi$
$884$	−3.67581e8	+	5.23040e8i	−0.532104	+	0.757144i
$885$		0			0
$886$	3.09590e8	+	5.95969e8i	0.445128	+	0.856885i
$887$		−	2.38053e8i		−	0.341116i	−0.985348	−	0.170558i	$-0.945443\pi$
$887$		−	2.38053e8i		−	0.341116i	0.985348	−	0.170558i	$-0.0545571\pi$
$888$	−3.05301e8	−	4.09964e7i	−0.436002	−	0.0585473i
$889$	8.28799e7			0.117962
$890$		0			0
$891$		−	1.17635e9i		−	1.66304i
$892$	−3.40853e8	−	2.39544e8i	−0.480256	−	0.337513i
$893$	−8.87977e8			−1.24695
$894$	−1.81275e8	−	3.48960e8i	−0.253703	−	0.488385i
$895$		0			0
$896$	−3.92120e7	−	1.82062e8i	−0.0545123	−	0.253101i
$897$	6.24709e8			0.865566
$898$	−2.73632e8	+	1.42144e8i	−0.377866	+	0.196291i
$899$			7.19874e8i			0.990780i
$900$		0			0
$901$	1.42577e8			0.194928
$902$	7.76493e7	+	1.49477e8i	0.105808	+	0.203683i
$903$		−	2.84630e8i		−	0.386561i
$904$	9.23789e7	−	6.87946e8i	0.125045	−	0.931213i
$905$		0			0
$906$	4.81890e8	−	2.50329e8i	0.647982	−	0.336609i
$907$		−	8.69796e8i		−	1.16572i	−0.812572	−	0.582861i	$-0.801933\pi$
$907$		−	8.69796e8i		−	1.16572i	0.812572	−	0.582861i	$-0.198067\pi$
$908$	4.33733e8	+	3.04818e8i	0.579382	+	0.407177i
$909$	−5.22745e7			−0.0695982
$910$		0			0
$911$			3.98390e8i			0.526931i	0.964669	+	0.263466i	$0.0848655\pi$
$911$			3.98390e8i			0.526931i	−0.964669	+	0.263466i	$0.915134\pi$
$912$	−3.02929e8	−	8.41299e8i	−0.399353	−	1.10909i
$913$	−5.87353e8			−0.771768
$914$	7.19563e8	−	3.73793e8i	0.942388	−	0.489545i
$915$		0			0
$916$	−2.20476e8	+	3.13721e8i	−0.286863	+	0.408185i
$917$	932775.			0.00120968
$918$	1.57861e8	+	3.03888e8i	0.204055	+	0.392812i
$919$		−	1.03935e9i		−	1.33911i	−0.742762	−	0.669555i	$-0.766485\pi$
$919$		−	1.03935e9i		−	1.33911i	0.742762	−	0.669555i	$-0.233515\pi$
$920$		0			0
$921$	6.16650e8			0.789332
$922$	−6.73814e8	+	3.50028e8i	−0.859700	+	0.446591i
$923$			7.41423e8i			0.942889i
$924$	−2.64399e8	−	1.85814e8i	−0.335154	−	0.235539i
$925$		0			0
$926$	−4.35545e8	−	8.38437e8i	−0.548530	−	1.05594i
$927$		−	3.23868e8i		−	0.406564i
$928$	3.37857e8	+	3.12276e8i	0.422755	+	0.390746i
$929$	−9.01112e8			−1.12391			−0.561955	−	0.827168i	$-0.689951\pi$
$929$	−9.01112e8			−1.12391			−0.561955	+	0.827168i	$0.689951\pi$
$930$		0			0
$931$			7.54364e8i			0.934828i
$932$	6.16525e7	−	8.77268e7i	0.0761557	−	0.108364i
$933$	−8.38977e8			−1.03301
$934$	−6.86346e8	−	1.32123e9i	−0.842369	−	1.62158i
$935$		0			0
$936$	−6.34955e7	+	4.72851e8i	−0.0774310	+	0.576629i
$937$	−8.08145e7			−0.0982360			−0.0491180	−	0.998793i	$-0.515641\pi$
$937$	−8.08145e7			−0.0982360			−0.0491180	+	0.998793i	$0.515641\pi$
$938$	2.57592e7	−	1.33812e7i	0.0312122	−	0.0162139i
$939$		−	1.57717e8i		−	0.190495i
$940$		0			0
$941$	−5.21062e8			−0.625346			−0.312673	−	0.949861i	$-0.601224\pi$
$941$	−5.21062e8			−0.625346			−0.312673	+	0.949861i	$0.601224\pi$
$942$	−7.65722e8	−	1.47404e9i	−0.916048	−	1.76342i
$943$			6.95019e7i			0.0828823i
$944$	−5.39103e8	+	1.94117e8i	−0.640849	+	0.230753i
$945$		0			0
$946$	1.28230e9	−	6.66121e8i	1.51467	−	0.786828i
$947$			1.67327e9i			1.97023i	0.171902	+	0.985114i	$0.445009\pi$
$947$			1.67327e9i			1.97023i	−0.171902	+	0.985114i	$0.554991\pi$
$948$	−1.94938e8	+	2.77382e8i	−0.228808	+	0.325576i
$949$	−2.10833e9			−2.46684
$950$		0			0
$951$		−	1.03088e9i		−	1.19858i
$952$	1.35239e8	+	1.81602e7i	0.156744	+	0.0210480i
$953$	5.89780e8			0.681414			0.340707	−	0.940170i	$-0.389334\pi$
$953$	5.89780e8			0.681414			0.340707	+	0.940170i	$0.389334\pi$
$954$	9.44241e7	−	4.90507e7i	0.108752	−	0.0564937i
$955$		0			0
$956$	2.11541e8	+	1.48666e8i	0.242115	+	0.170153i
$957$	7.98323e8			0.910841
$958$	−1.85112e8	−	3.56347e8i	−0.210542	−	0.405300i
$959$		−	1.86885e8i		−	0.211895i
$960$		0			0
$961$	−1.74135e9			−1.96208
$962$	−4.47560e8	+	2.32495e8i	−0.502720	+	0.261149i
$963$		−	4.34581e8i		−	0.486623i
$964$	3.42980e8	−	4.88035e8i	0.382858	−	0.544778i
$965$		0			0
$966$	−6.14684e7	−	1.18328e8i	−0.0681900	−	0.131268i
$967$		−	9.41406e8i		−	1.04111i	−0.853828	−	0.520556i	$-0.825725\pi$
$967$		−	9.41406e8i		−	1.04111i	0.853828	−	0.520556i	$-0.174275\pi$
$968$	9.76297e7	−	7.27049e8i	0.107636	−	0.801563i
$969$	6.55152e8			0.720063
$970$		0			0
$971$			1.61734e9i			1.76662i	0.468787	+	0.883311i	$0.344691\pi$
$971$			1.61734e9i			1.76662i	−0.468787	+	0.883311i	$0.655309\pi$
$972$	5.48548e8	+	3.85507e8i	0.597332	+	0.419792i
$973$	2.74529e8			0.298023
$974$	4.01597e8	+	7.73085e8i	0.434623	+	0.836662i
$975$		0			0
$976$	−4.16183e8	−	1.15583e9i	−0.447646	−	1.24321i
$977$	6.67855e8			0.716141			0.358070	−	0.933695i	$-0.383435\pi$
$977$	6.67855e8			0.716141			0.358070	+	0.933695i	$0.383435\pi$
$978$	−1.60937e9	+	8.36022e8i	−1.72044	+	0.893720i
$979$		−	4.96972e7i		−	0.0529643i
$980$		0			0
$981$	4.94754e8			0.524062
$982$	−6.31026e7	−	1.21474e8i	−0.0666366	−	0.128277i
$983$		−	8.58744e7i		−	0.0904073i	−0.998978	−	0.0452036i	$-0.985606\pi$
$983$		−	8.58744e7i		−	0.0904073i	0.998978	−	0.0452036i	$-0.0143937\pi$
$984$	−1.89592e8	−	2.54588e7i	−0.198992	−	0.0267210i
$985$		0			0
$986$	−2.99134e8	+	1.55392e8i	−0.312057	+	0.162105i
$987$		−	3.64459e8i		−	0.379050i
$988$	−1.19779e9	−	8.41783e8i	−1.24197	−	0.872830i
$989$	5.96228e8			0.616344
$990$		0			0
$991$			6.76605e8i			0.695208i	0.937642	+	0.347604i	$0.113005\pi$
$991$			6.76605e8i			0.695208i	−0.937642	+	0.347604i	$0.886995\pi$
$992$	−1.14038e9	+	1.23379e9i	−1.16819	+	1.26389i
$993$	1.43018e9			1.46064
$994$	1.40436e8	−	7.29525e7i	0.142994	−	0.0742816i
$995$		0			0
$996$	3.83536e8	−	5.45743e8i	0.388175	−	0.552344i
$997$	−1.53009e9			−1.54394			−0.771970	−	0.635659i	$-0.780728\pi$
$997$	−1.53009e9			−1.54394			−0.771970	+	0.635659i	$0.780728\pi$
$998$	−7.68895e7	−	1.48014e8i	−0.0773526	−	0.148906i
$999$			2.70161e8i			0.270973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.7.b.f.51.2		12
4.3	odd	2	inner	100.7.b.f.51.1		12
5.2	odd	4		20.7.d.d.19.5	✓	12
5.3	odd	4		20.7.d.d.19.8	yes	12
5.4	even	2	inner	100.7.b.f.51.11		12
15.2	even	4		180.7.f.e.19.8		12
15.8	even	4		180.7.f.e.19.5		12
20.3	even	4		20.7.d.d.19.6	yes	12
20.7	even	4		20.7.d.d.19.7	yes	12
20.19	odd	2	inner	100.7.b.f.51.12		12
40.3	even	4		320.7.h.f.319.10		12
40.13	odd	4		320.7.h.f.319.4		12
40.27	even	4		320.7.h.f.319.3		12
40.37	odd	4		320.7.h.f.319.9		12
60.23	odd	4		180.7.f.e.19.7		12
60.47	odd	4		180.7.f.e.19.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.5	✓	12	5.2	odd	4
20.7.d.d.19.6	yes	12	20.3	even	4
20.7.d.d.19.7	yes	12	20.7	even	4
20.7.d.d.19.8	yes	12	5.3	odd	4
100.7.b.f.51.1		12	4.3	odd	2	inner
100.7.b.f.51.2		12	1.1	even	1	trivial
100.7.b.f.51.11		12	5.4	even	2	inner
100.7.b.f.51.12		12	20.19	odd	2	inner
180.7.f.e.19.5		12	15.8	even	4
180.7.f.e.19.6		12	60.47	odd	4
180.7.f.e.19.7		12	60.23	odd	4
180.7.f.e.19.8		12	15.2	even	4
320.7.h.f.319.3		12	40.27	even	4
320.7.h.f.319.4		12	40.13	odd	4
320.7.h.f.319.9		12	40.37	odd	4
320.7.h.f.319.10		12	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.09927 + 3.68788i) q^{2} -31.7642i q^{3} +(36.7991 - 52.3624i) q^{4} +(117.142 + 225.502i) q^{6} -88.8045i q^{7} +(-68.1408 + 507.445i) q^{8} -279.961 q^{9} +O(q^{10})\)	\(q+(-7.09927 + 3.68788i) q^{2} -31.7642i q^{3} +(36.7991 - 52.3624i) q^{4} +(117.142 + 225.502i) q^{6} -88.8045i q^{7} +(-68.1408 + 507.445i) q^{8} -279.961 q^{9} +1790.06i q^{11} +(-1663.25 - 1168.89i) q^{12} -3328.41 q^{13} +(327.500 + 630.447i) q^{14} +(-1387.65 - 3853.78i) q^{16} +3001.09 q^{17} +(1987.52 - 1032.46i) q^{18} +6872.67i q^{19} -2820.80 q^{21} +(-6601.53 - 12708.1i) q^{22} -5908.85i q^{23} +(16118.6 + 2164.44i) q^{24} +(23629.3 - 12274.8i) q^{26} -14263.3i q^{27} +(-4650.02 - 3267.93i) q^{28} +14040.2 q^{29} +51272.4i q^{31} +(24063.5 + 22241.6i) q^{32} +56859.8 q^{33} +(-21305.5 + 11067.6i) q^{34} +(-10302.3 + 14659.5i) q^{36} -18940.9 q^{37} +(-25345.6 - 48790.9i) q^{38} +105724. i q^{39} -11762.3 q^{41} +(20025.6 - 10402.8i) q^{42} +100904. i q^{43} +(93732.0 + 65872.8i) q^{44} +(21791.1 + 41948.5i) q^{46} +129204. i q^{47} +(-122412. + 44077.4i) q^{48} +109763. q^{49} -95327.0i q^{51} +(-122483. + 174284. i) q^{52} +47508.5 q^{53} +(52601.4 + 101259. i) q^{54} +(45063.4 + 6051.21i) q^{56} +218305. q^{57} +(-99675.1 + 51778.5i) q^{58} -139889. i q^{59} +299920. q^{61} +(-189086. - 363996. i) q^{62} +24861.8i q^{63} +(-252858. - 69155.5i) q^{64} +(-403663. + 209692. i) q^{66} -40858.7i q^{67} +(110437. - 157144. i) q^{68} -187690. q^{69} -222756. i q^{71} +(19076.8 - 142065. i) q^{72} +633436. q^{73} +(134467. - 69851.8i) q^{74} +(359870. + 252909. i) q^{76} +158966. q^{77} +(-389897. - 750564. i) q^{78} -166771. i q^{79} -657154. q^{81} +(83503.9 - 43378.0i) q^{82} +328119. i q^{83} +(-103803. + 147704. i) q^{84} +(-372122. - 716345. i) q^{86} -445975. i q^{87} +(-908359. - 121976. i) q^{88} -27762.8 q^{89} +295578. i q^{91} +(-309402. - 217441. i) q^{92} +1.62862e6 q^{93} +(-476488. - 917254. i) q^{94} +(706485. - 764358. i) q^{96} -220750. q^{97} +(-779235. + 404791. i) q^{98} -501148. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

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