LMFDB - Embedded newform 60.7.l.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.25131 - 4.99210i) q^{2} +(21.8589 + 15.8490i) q^{3} +(14.1578 + 62.4144i) q^{4} +(88.9335 + 87.8398i) q^{5} +(-57.5269 - 208.199i) q^{6} +(252.976 + 252.976i) q^{7} +(223.074 - 460.849i) q^{8} +(226.620 + 692.881i) q^{9} +O(q^{10})$	\(q+(-6.25131 - 4.99210i) q^{2} +(21.8589 + 15.8490i) q^{3} +(14.1578 + 62.4144i) q^{4} +(88.9335 + 87.8398i) q^{5} +(-57.5269 - 208.199i) q^{6} +(252.976 + 252.976i) q^{7} +(223.074 - 460.849i) q^{8} +(226.620 + 692.881i) q^{9} +(-117.447 - 993.079i) q^{10} -2238.23 q^{11} +(-679.730 + 1588.69i) q^{12} +(865.927 + 865.927i) q^{13} +(-318.550 - 2844.31i) q^{14} +(551.816 + 3329.58i) q^{15} +(-3695.11 + 1767.31i) q^{16} +(-5197.44 - 5197.44i) q^{17} +(2042.26 - 5462.73i) q^{18} +2187.89 q^{19} +(-4223.36 + 6794.35i) q^{20} +(1520.36 + 9539.18i) q^{21} +(13991.9 + 11173.5i) q^{22} +(8087.03 + 8087.03i) q^{23} +(12180.1 - 6538.15i) q^{24} +(193.352 + 15623.8i) q^{25} +(-1090.39 - 9735.98i) q^{26} +(-6027.80 + 18737.3i) q^{27} +(-12207.7 + 19370.9i) q^{28} +17442.0 q^{29} +(13172.0 - 23569.0i) q^{30} +24053.4i q^{31} +(31921.9 + 7398.38i) q^{32} +(-48925.1 - 35473.6i) q^{33} +(6544.68 + 58437.0i) q^{34} +(276.701 + 44719.4i) q^{35} +(-40037.3 + 23954.1i) q^{36} +(17936.3 - 17936.3i) q^{37} +(-13677.2 - 10922.2i) q^{38} +(5204.13 + 32652.2i) q^{39} +(60319.6 - 21390.2i) q^{40} -92866.9i q^{41} +(38116.3 - 67222.2i) q^{42} +(-15742.9 + 15742.9i) q^{43} +(-31688.5 - 139698. i) q^{44} +(-40708.4 + 81526.6i) q^{45} +(-10183.3 - 90925.8i) q^{46} +(-104251. + 104251. i) q^{47} +(-108781. - 19932.4i) q^{48} +10344.7i q^{49} +(76786.9 - 98634.5i) q^{50} +(-31236.0 - 195984. i) q^{51} +(-41786.6 + 66306.0i) q^{52} +(9294.84 - 9294.84i) q^{53} +(131220. - 87041.3i) q^{54} +(-199054. - 196605. i) q^{55} +(173016. - 60151.5i) q^{56} +(47824.9 + 34675.9i) q^{57} +(-109035. - 87072.1i) q^{58} +226501. i q^{59} +(-200001. + 81581.0i) q^{60} +159667. q^{61} +(120077. - 150366. i) q^{62} +(-117953. + 232612. i) q^{63} +(-162620. - 205607. i) q^{64} +(947.136 + 153073. i) q^{65} +(128758. + 465996. i) q^{66} +(79189.7 + 79189.7i) q^{67} +(250810. - 397979. i) q^{68} +(48602.1 + 304944. i) q^{69} +(221514. - 280936. i) q^{70} +570452. q^{71} +(369867. + 50126.0i) q^{72} +(43326.6 + 43326.6i) q^{73} +(-201665. + 22585.6i) q^{74} +(-243395. + 344583. i) q^{75} +(30975.9 + 136556. i) q^{76} +(-566218. - 566218. i) q^{77} +(130471. - 230099. i) q^{78} +415590. q^{79} +(-483859. - 167405. i) q^{80} +(-428728. + 314041. i) q^{81} +(-463601. + 580540. i) q^{82} +(-663468. - 663468. i) q^{83} +(-573857. + 229946. i) q^{84} +(-5684.87 - 918768. i) q^{85} +(177004. - 19823.6i) q^{86} +(381262. + 276437. i) q^{87} +(-499290. + 1.03149e6i) q^{88} +1.26073e6 q^{89} +(661470. - 306428. i) q^{90} +438117. i q^{91} +(-390252. + 619242. i) q^{92} +(-381222. + 525781. i) q^{93} +(1.17214e6 - 131275. i) q^{94} +(194577. + 192184. i) q^{95} +(580519. + 667649. i) q^{96} +(-7185.40 + 7185.40i) q^{97} +(51641.7 - 64667.9i) q^{98} +(-507227. - 1.55083e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−6.25131	−	4.99210i	−0.781414	−	0.624013i
$2$	−6.25131	−	4.99210i	−0.781414	−	0.624013i
$3$	21.8589	+	15.8490i	0.809588	+	0.586999i
$3$	21.8589	+	15.8490i	0.809588	+	0.586999i
$4$	14.1578	+	62.4144i	0.221216	+	0.975225i
$5$	88.9335	+	87.8398i	0.711468	+	0.702718i
$5$	88.9335	+	87.8398i	0.711468	+	0.702718i
$6$	−57.5269	−	208.199i	−0.266328	−	0.963882i
$7$	252.976	+	252.976i	0.737539	+	0.737539i	0.972101	−	0.234562i	$-0.0753656\pi$
$7$	252.976	+	252.976i	0.737539	+	0.737539i	−0.234562	+	0.972101i	$0.575366\pi$
$8$	223.074	−	460.849i	0.435691	−	0.900096i
$9$	226.620	+	692.881i	0.310864	+	0.950454i
$10$	−117.447	−	993.079i	−0.117447	−	0.993079i
$11$	−2238.23			−1.68161			−0.840807	−	0.541335i	$-0.817919\pi$
$11$	−2238.23			−1.68161			−0.840807	+	0.541335i	$0.817919\pi$
$12$	−679.730	+	1588.69i	−0.393362	+	0.919384i
$13$	865.927	+	865.927i	0.394141	+	0.394141i	0.876160	−	0.482020i	$-0.160097\pi$
$13$	865.927	+	865.927i	0.394141	+	0.394141i	−0.482020	+	0.876160i	$0.660097\pi$
$14$	−318.550	−	2844.31i	−0.116090	−	1.03656i
$15$	551.816	+	3329.58i	0.163501	+	0.986543i
$16$	−3695.11	+	1767.31i	−0.902127	+	0.431471i
$17$	−5197.44	−	5197.44i	−1.05790	−	1.05790i	−0.998218	−	0.0596773i	$-0.980993\pi$
$17$	−5197.44	−	5197.44i	−1.05790	−	1.05790i	−0.0596773	−	0.998218i	$-0.519007\pi$
$18$	2042.26	−	5462.73i	0.350182	−	0.936682i
$19$	2187.89			0.318981			0.159491	−	0.987199i	$-0.449015\pi$
$19$	2187.89			0.318981			0.159491	+	0.987199i	$0.449015\pi$
$20$	−4223.36	+	6794.35i	−0.527920	+	0.849294i
$21$	1520.36	+	9539.18i	0.164168	+	1.03004i
$22$	13991.9	+	11173.5i	1.31404	+	1.04935i
$23$	8087.03	+	8087.03i	0.664669	+	0.664669i	0.956477	−	0.291808i	$-0.0942568\pi$
$23$	8087.03	+	8087.03i	0.664669	+	0.664669i	−0.291808	+	0.956477i	$0.594257\pi$
$24$	12180.1	−	6538.15i	0.881086	−	0.472957i
$25$	193.352	+	15623.8i	0.0123745	+	0.999923i
$26$	−1090.39	−	9735.98i	−0.0620383	−	0.553936i
$27$	−6027.80	+	18737.3i	−0.306244	+	0.951953i
$28$	−12207.7	+	19370.9i	−0.556111	+	0.882422i
$29$	17442.0			0.715157			0.357579	−	0.933883i	$-0.383602\pi$
$29$	17442.0			0.715157			0.357579	+	0.933883i	$0.383602\pi$
$30$	13172.0	−	23569.0i	0.487853	−	0.872926i
$31$			24053.4i			0.807406i	0.914890	+	0.403703i	$0.132277\pi$
$31$			24053.4i			0.807406i	−0.914890	+	0.403703i	$0.867723\pi$
$32$	31921.9	+	7398.38i	0.974178	+	0.225781i
$33$	−48925.1	−	35473.6i	−1.36141	−	0.987106i
$34$	6544.68	+	58437.0i	0.166514	+	1.48679i
$35$	276.701	+	44719.4i	0.00645366	+	1.04302i
$36$	−40037.3	+	23954.1i	−0.858138	+	0.513418i
$37$	17936.3	−	17936.3i	0.354101	−	0.354101i	−0.507532	−	0.861633i	$-0.669442\pi$
$37$	17936.3	−	17936.3i	0.354101	−	0.354101i	0.861633	+	0.507532i	$0.169442\pi$
$38$	−13677.2	−	10922.2i	−0.249257	−	0.199048i
$39$	5204.13	+	32652.2i	0.0877312	+	0.550452i
$40$	60319.6	−	21390.2i	0.942494	−	0.334222i
$41$		−	92866.9i		−	1.34744i	−0.738987	−	0.673720i	$-0.764696\pi$
$41$		−	92866.9i		−	1.34744i	0.738987	−	0.673720i	$-0.235304\pi$
$42$	38116.3	−	67222.2i	0.514473	−	0.907329i
$43$	−15742.9	+	15742.9i	−0.198006	+	0.198006i	−0.799145	−	0.601139i	$-0.794714\pi$
$43$	−15742.9	+	15742.9i	−0.198006	+	0.198006i	0.601139	+	0.799145i	$0.294714\pi$
$44$	−31688.5	−	139698.i	−0.372001	−	1.63995i
$45$	−40708.4	+	81526.6i	−0.446731	+	0.894668i
$46$	−10183.3	−	90925.8i	−0.104620	−	0.934143i
$47$	−104251.	+	104251.i	−1.00413	+	1.00413i	−0.00413406	+	0.999991i	$0.501316\pi$
$47$	−104251.	+	104251.i	−1.00413	+	1.00413i	−0.999991	+	0.00413406i	$0.998684\pi$
$48$	−108781.	−	19932.4i	−0.983624	−	0.180234i
$49$			10344.7i			0.0879284i
$50$	76786.9	−	98634.5i	0.614295	−	0.789076i
$51$	−31236.0	−	195984.i	−0.235475	−	1.47744i
$52$	−41786.6	+	66306.0i	−0.297185	+	0.471566i
$53$	9294.84	−	9294.84i	0.0624330	−	0.0624330i	−0.675201	−	0.737634i	$-0.735943\pi$
$53$	9294.84	−	9294.84i	0.0624330	−	0.0624330i	0.737634	+	0.675201i	$0.235943\pi$
$54$	131220.	−	87041.3i	0.833334	−	0.552769i
$55$	−199054.	−	196605.i	−1.19642	−	1.18170i
$56$	173016.	−	60151.5i	0.985196	−	0.342517i
$57$	47824.9	+	34675.9i	0.258243	+	0.187242i
$58$	−109035.	−	87072.1i	−0.558834	−	0.446267i
$59$			226501.i			1.10285i	0.834226	+	0.551423i	$0.185915\pi$
$59$			226501.i			1.10285i	−0.834226	+	0.551423i	$0.814085\pi$
$60$	−200001.	+	81581.0i	−0.925932	+	0.377690i
$61$	159667.			0.703438			0.351719	−	0.936106i	$-0.385597\pi$
$61$	159667.			0.703438			0.351719	+	0.936106i	$0.385597\pi$
$62$	120077.	−	150366.i	0.503832	−	0.630919i
$63$	−117953.	+	232612.i	−0.471723	+	0.930272i
$64$	−162620.	−	205607.i	−0.620347	−	0.784328i
$65$	947.136	+	153073.i	0.00344883	+	0.557388i
$66$	128758.	+	465996.i	0.447862	+	1.62088i
$67$	79189.7	+	79189.7i	0.263296	+	0.263296i	0.826392	−	0.563096i	$-0.190390\pi$
$67$	79189.7	+	79189.7i	0.263296	+	0.263296i	−0.563096	+	0.826392i	$0.690390\pi$
$68$	250810.	−	397979.i	0.797662	−	1.26571i
$69$	48602.1	+	304944.i	0.147948	+	0.928268i
$70$	221514.	−	280936.i	0.645814	−	0.819056i
$71$	570452.			1.59384			0.796919	−	0.604086i	$-0.206462\pi$
$71$	570452.			1.59384			0.796919	+	0.604086i	$0.206462\pi$
$72$	369867.	+	50126.0i	0.990941	+	0.134297i
$73$	43326.6	+	43326.6i	0.111374	+	0.111374i	0.760598	−	0.649223i	$-0.224906\pi$
$73$	43326.6	+	43326.6i	0.111374	+	0.111374i	−0.649223	+	0.760598i	$0.724906\pi$
$74$	−201665.	+	22585.6i	−0.497664	+	0.0557361i
$75$	−243395.	+	344583.i	−0.576936	+	0.816789i
$76$	30975.9	+	136556.i	0.0705639	+	0.311078i
$77$	−566218.	−	566218.i	−1.24026	−	1.24026i
$78$	130471.	−	230099.i	0.274934	−	0.484876i
$79$	415590.			0.842914			0.421457	−	0.906848i	$-0.361519\pi$
$79$	415590.			0.842914			0.421457	+	0.906848i	$0.361519\pi$
$80$	−483859.	−	167405.i	−0.945037	−	0.326962i
$81$	−428728.	+	314041.i	−0.806727	+	0.590924i
$82$	−463601.	+	580540.i	−0.840819	+	1.05291i
$83$	−663468.	−	663468.i	−1.16034	−	1.16034i	−0.984401	−	0.175940i	$-0.943704\pi$
$83$	−663468.	−	663468.i	−1.16034	−	1.16034i	−0.175940	−	0.984401i	$-0.556296\pi$
$84$	−573857.	+	229946.i	−0.968201	+	0.387962i
$85$	−5684.87	−	918768.i	−0.00925686	−	1.49606i
$86$	177004.	−	19823.6i	0.278283	−	0.0311665i
$87$	381262.	+	276437.i	0.578982	+	0.419797i
$88$	−499290.	+	1.03149e6i	−0.732664	+	1.51361i
$89$	1.26073e6			1.78835			0.894174	−	0.447719i	$-0.147764\pi$
$89$	1.26073e6			1.78835			0.894174	+	0.447719i	$0.147764\pi$
$90$	661470.	−	306428.i	0.907367	−	0.420340i
$91$			438117.i			0.581388i
$92$	−390252.	+	619242.i	−0.501166	+	0.795237i
$93$	−381222.	+	525781.i	−0.473947	+	0.653666i
$94$	1.17214e6	−	131275.i	1.41123	−	0.158051i
$95$	194577.	+	192184.i	0.226945	+	0.224154i
$96$	580519.	+	667649.i	0.656150	+	0.754631i
$97$	−7185.40	+	7185.40i	−0.00787292	+	0.00787292i	−0.711032	−	0.703159i	$-0.751772\pi$
$97$	−7185.40	+	7185.40i	−0.00787292	+	0.00787292i	0.703159	+	0.711032i	$0.251772\pi$
$98$	51641.7	−	64667.9i	0.0548684	−	0.0687085i
$99$	−507227.	−	1.55083e6i	−0.522753	−	1.59830i
$100$	−972413.	+	233267.i	−0.972413	+	0.233267i
$101$		−	849410.i		−	0.824429i	−0.911087	−	0.412215i	$-0.864755\pi$
$101$		−	849410.i		−	0.824429i	0.911087	−	0.412215i	$-0.135245\pi$
$102$	−783107.	+	1.38109e6i	−0.737939	+	1.30143i
$103$	463161.	−	463161.i	0.423858	−	0.423858i	−0.462671	−	0.886530i	$-0.653109\pi$
$103$	463161.	−	463161.i	0.423858	−	0.423858i	0.886530	+	0.462671i	$0.153109\pi$
$104$	592227.	−	205896.i	0.526488	−	0.183041i
$105$	−702708.	+	981901.i	−0.607026	+	0.848203i
$106$	−104506.	+	11704.2i	−0.0877450	+	0.00982705i
$107$	61218.1	−	61218.1i	0.0499722	−	0.0499722i	−0.681679	−	0.731651i	$-0.738750\pi$
$107$	61218.1	−	61218.1i	0.0499722	−	0.0499722i	0.731651	+	0.681679i	$0.238750\pi$
$108$	−1.25482e6	−	110942.i	−0.996114	−	0.0880692i
$109$		−	474527.i		−	0.366422i	−0.983074	−	0.183211i	$-0.941351\pi$
$109$		−	474527.i		−	0.366422i	0.983074	−	0.183211i	$-0.0586491\pi$
$110$	262872.	+	2.22274e6i	0.197500	+	1.66998i
$111$	676339.	−	107795.i	0.494533	−	0.0788189i
$112$	−1.38186e6	−	487688.i	−0.983581	−	0.347127i
$113$	293449.	−	293449.i	0.203375	−	0.203375i	−0.598069	−	0.801444i	$-0.704065\pi$
$113$	293449.	−	293449.i	0.203375	−	0.203375i	0.801444	+	0.598069i	$0.204065\pi$
$114$	−125863.	−	455516.i	−0.0849538	−	0.307460i
$115$	8845.45	+	1.42957e6i	0.00581603	+	0.939966i
$116$	246941.	+	1.08863e6i	0.158204	+	0.697439i
$117$	−403748.	+	796221.i	−0.252088	+	0.497137i
$118$	1.13072e6	−	1.41593e6i	0.688189	−	0.861779i
$119$		−	2.62965e6i		−	1.56048i
$120$	1.65753e6	+	488439.i	0.959220	+	0.282661i
$121$	3.23810e6			1.82782
$122$	−998129.	−	797074.i	−0.549677	−	0.438954i
$123$	1.47184e6	−	2.02996e6i	0.790946	−	1.09087i
$124$	−1.50128e6	+	340545.i	−0.787402	+	0.178611i
$125$	−1.35520e6	+	1.40646e6i	−0.693860	+	0.720110i
$126$	1.89858e6	−	865296.i	0.949112	−	0.432567i
$127$	95290.2	+	95290.2i	0.0465197	+	0.0465197i	0.729984	−	0.683464i	$-0.239527\pi$
$127$	95290.2	+	95290.2i	0.0465197	+	0.0465197i	−0.683464	+	0.729984i	$0.739527\pi$
$128$	−9820.19	+	2.09713e6i	−0.00468263	+	0.999989i
$129$	−593630.	+	94613.0i	−0.276533	+	0.0440739i
$130$	758234.	−	961634.i	0.345122	−	0.437703i
$131$	3.45229e6			1.53566			0.767828	−	0.640656i	$-0.221338\pi$
$131$	3.45229e6			1.53566			0.767828	+	0.640656i	$0.221338\pi$
$132$	1.52139e6	−	3.55586e6i	0.661483	−	1.54605i
$133$	553484.	+	553484.i	0.235261	+	0.235261i
$134$	−99716.6	−	890362.i	−0.0414432	−	0.370043i
$135$	−2.18195e6	+	1.13689e6i	−0.886838	+	0.462081i
$136$	−3.55465e6	+	1.23582e6i	−1.41312	+	0.491292i
$137$	308268.	+	308268.i	0.119886	+	0.119886i	0.764504	−	0.644619i	$-0.222984\pi$
$137$	308268.	+	308268.i	0.119886	+	0.119886i	−0.644619	+	0.764504i	$0.722984\pi$
$138$	1.21849e6	−	2.14893e6i	0.463642	−	0.817683i
$139$	−2.63079e6			−0.979583			−0.489792	−	0.871839i	$-0.662927\pi$
$139$	−2.63079e6			−0.979583			−0.489792	+	0.871839i	$0.662927\pi$
$140$	−2.78722e6	+	650401.i	−1.01575	+	0.237026i
$141$	−3.93109e6	+	626539.i	−1.40235	+	0.223507i
$142$	−3.56608e6	−	2.84776e6i	−1.24545	−	0.994575i
$143$	−1.93814e6	−	1.93814e6i	−0.662792	−	0.662792i
$144$	−2.06192e6	−	2.15977e6i	−0.690533	−	0.723301i
$145$	1.55118e6	+	1.53210e6i	0.508812	+	0.502554i
$146$	−54557.4	−	487139.i	−0.0175305	−	0.156529i
$147$	−163953.	+	226123.i	−0.0516139	+	0.0711857i
$148$	1.37342e6	+	865544.i	0.423661	+	0.266995i
$149$	−281266.			−0.0850274			−0.0425137	−	0.999096i	$-0.513537\pi$
$149$	−281266.			−0.0850274			−0.0425137	+	0.999096i	$0.513537\pi$
$150$	3.24173e6	−	939045.i	0.960513	−	0.278236i
$151$		−	4.52950e6i		−	1.31559i	−0.753199	−	0.657793i	$-0.771490\pi$
$151$		−	4.52950e6i		−	1.31559i	0.753199	−	0.657793i	$-0.228510\pi$
$152$	488062.	−	1.00829e6i	0.138977	−	0.287114i
$153$	2.42336e6	−	4.77905e6i	0.676619	−	1.33434i
$154$	712989.	+	6.36622e6i	0.195218	+	1.74309i
$155$	−2.11285e6	+	2.13916e6i	−0.567379	+	0.574444i
$156$	−1.96429e6	+	787098.i	−0.517406	+	0.207327i
$157$	4.08873e6	−	4.08873e6i	1.05655	−	1.05655i	0.0582474	−	0.998302i	$-0.481449\pi$
$157$	4.08873e6	−	4.08873e6i	1.05655	−	1.05655i	0.998302	−	0.0582474i	$-0.0185512\pi$
$158$	−2.59798e6	−	2.07467e6i	−0.658665	−	0.525989i
$159$	350488.	−	55861.0i	0.0871931	−	0.0138969i
$160$	2.18905e6	+	3.46197e6i	0.534437	+	0.845208i
$161$			4.09165e6i			0.980439i
$162$	4.24784e6	+	177081.i	0.999132	+	0.0416511i
$163$	2.43778e6	−	2.43778e6i	0.562901	−	0.562901i	−0.367229	−	0.930130i	$-0.619694\pi$
$163$	2.43778e6	−	2.43778e6i	0.562901	−	0.562901i	0.930130	+	0.367229i	$0.119694\pi$
$164$	5.79623e6	−	1.31479e6i	1.31406	−	0.298076i
$165$	−1.23509e6	−	7.45237e6i	−0.274946	−	1.65898i
$166$	835447.	+	7.45964e6i	0.182639	+	1.63077i
$167$	−3.91467e6	+	3.91467e6i	−0.840515	+	0.840515i	−0.988926	−	0.148411i	$-0.952584\pi$
$167$	−3.91467e6	+	3.91467e6i	−0.840515	+	0.840515i	0.148411	+	0.988926i	$0.452584\pi$
$168$	4.73528e6	+	1.42728e6i	0.998659	+	0.301011i
$169$		−	3.32715e6i		−	0.689306i
$170$	−4.55105e6	+	5.77189e6i	−0.926327	+	1.17482i
$171$	495820.	+	1.51595e6i	0.0991599	+	0.303177i
$172$	−1.20547e6	−	759697.i	−0.236903	−	0.149298i
$173$	−3.82777e6	+	3.82777e6i	−0.739277	+	0.739277i	−0.972438	−	0.233161i	$-0.925093\pi$
$173$	−3.82777e6	+	3.82777e6i	−0.739277	+	0.739277i	0.233161	+	0.972438i	$0.425093\pi$
$174$	−1.00338e6	−	3.63139e6i	−0.190467	−	0.689327i
$175$	−3.90353e6	+	4.00136e6i	−0.728356	+	0.746609i
$176$	8.27050e6	−	3.95564e6i	1.51703	−	0.725568i
$177$	−3.58981e6	+	4.95106e6i	−0.647369	+	0.892850i
$178$	−7.88122e6	−	6.29369e6i	−1.39744	−	1.11595i
$179$			7.72419e6i			1.34677i	0.739291	+	0.673386i	$0.235161\pi$
$179$			7.72419e6i			1.34677i	−0.739291	+	0.673386i	$0.764839\pi$
$180$	−5.66478e6	−	1.38655e6i	−0.971327	−	0.237748i
$181$	−2.77977e6			−0.468784			−0.234392	−	0.972142i	$-0.575310\pi$
$181$	−2.77977e6			−0.468784			−0.234392	+	0.972142i	$0.575310\pi$
$182$	2.18713e6	−	2.73881e6i	0.362794	−	0.454305i
$183$	3.49014e6	+	2.53056e6i	0.569495	+	0.412917i
$184$	5.53090e6	−	1.92290e6i	0.887856	−	0.308676i
$185$	3.17066e6	−	19618.4i	0.500765	−	0.00309848i
$186$	5.00789e6	−	1.38372e6i	0.778244	−	0.215035i
$187$	1.16331e7	+	1.16331e7i	1.77897	+	1.77897i
$188$	−7.98276e6	−	5.03081e6i	−1.20138	−	0.757119i
$189$	−6.26497e6	+	3.21520e6i	−0.927970	+	0.476236i
$190$	−256960.	−	2.17275e6i	−0.0374632	−	0.316774i
$191$	−957077.			−0.137356			−0.0686778	−	0.997639i	$-0.521878\pi$
$191$	−957077.			−0.137356			−0.0686778	+	0.997639i	$0.521878\pi$
$192$	−296036.	−	7.07169e6i	−0.0418254	−	0.999125i
$193$	−453507.	−	453507.i	−0.0630829	−	0.0630829i	0.674861	−	0.737944i	$-0.264203\pi$
$193$	−453507.	−	453507.i	−0.0630829	−	0.0630829i	−0.737944	+	0.674861i	$0.764203\pi$
$194$	80788.4	−	9047.95i	0.0110648	−	0.00123921i
$195$	−2.40534e6	+	3.36101e6i	−0.324394	+	0.453279i
$196$	−645657.	+	146458.i	−0.0857499	+	0.0194512i
$197$	1.76469e6	+	1.76469e6i	0.230818	+	0.230818i	0.813034	−	0.582216i	$-0.197814\pi$
$197$	1.76469e6	+	1.76469e6i	0.230818	+	0.230818i	−0.582216	+	0.813034i	$0.697814\pi$
$198$	−4.57104e6	+	1.22268e7i	−0.588871	+	1.57514i
$199$	−7.31548e6			−0.928290			−0.464145	−	0.885759i	$-0.653638\pi$
$199$	−7.31548e6			−0.928290			−0.464145	+	0.885759i	$0.653638\pi$
$200$	7.24335e6	+	3.39615e6i	0.905419	+	0.424519i
$201$	475921.	+	2.98607e6i	0.0586067	+	0.367716i
$202$	−4.24034e6	+	5.30993e6i	−0.514454	+	0.644221i
$203$	4.41240e6	+	4.41240e6i	0.527457	+	0.527457i
$204$	1.17900e7	−	4.72429e6i	1.38875	−	0.556476i
$205$	8.15740e6	−	8.25898e6i	0.946870	−	0.958660i
$206$	−5.20752e6	+	583219.i	−0.595702	+	0.0667160i
$207$	−3.77067e6	+	7.43603e6i	−0.425116	+	0.838359i
$208$	−4.73005e6	−	1.66934e6i	−0.525625	−	0.185504i
$209$	−4.89700e6			−0.536403
$210$	9.29460e6	−	2.63018e6i	1.00363	−	0.284006i
$211$		−	4.55336e6i		−	0.484712i	−0.970187	−	0.242356i	$-0.922080\pi$
$211$		−	4.55336e6i		−	0.484712i	0.970187	−	0.242356i	$-0.0779203\pi$
$212$	711727.	+	448537.i	0.0746974	+	0.0470750i
$213$	1.24694e7	+	9.04108e6i	1.29035	+	0.935582i
$214$	−688300.	+	77086.6i	−0.0702323	+	0.00786570i
$215$	−2.78292e6	+	17219.3i	−0.280018	+	0.00173261i
$216$	7.29042e6	+	6.95771e6i	0.723422	+	0.690406i
$217$	−6.08494e6	+	6.08494e6i	−0.595494	+	0.595494i
$218$	−2.36888e6	+	2.96641e6i	−0.228652	+	0.286327i
$219$	260388.	+	1.63375e6i	0.0247907	+	0.155544i
$220$	9.45284e6	−	1.52073e7i	0.887757	−	1.42819i
$221$		−	9.00120e6i		−	0.833919i
$222$	−4.76613e6	−	2.70249e6i	−0.435619	−	0.247005i
$223$	6.94245e6	−	6.94245e6i	0.626035	−	0.626035i	−0.321033	−	0.947068i	$-0.604030\pi$
$223$	6.94245e6	−	6.94245e6i	0.626035	−	0.626035i	0.947068	+	0.321033i	$0.104030\pi$
$224$	6.20385e6	+	9.94708e6i	0.551973	+	0.885017i
$225$	−1.07816e7	+	3.67464e6i	−0.946535	+	0.322602i
$226$	−3.29937e6	+	369515.i	−0.285828	+	0.0320115i
$227$	4.95989e6	−	4.95989e6i	0.424028	−	0.424028i	−0.462560	−	0.886588i	$-0.653069\pi$
$227$	4.95989e6	−	4.95989e6i	0.424028	−	0.424028i	0.886588	+	0.462560i	$0.153069\pi$
$228$	−1.48718e6	+	3.47589e6i	−0.125475	+	0.293266i
$229$			7.34140e6i			0.611325i	0.952140	+	0.305663i	$0.0988779\pi$
$229$			7.34140e6i			0.611325i	−0.952140	+	0.305663i	$0.901122\pi$
$230$	7.08126e6	−	8.98085e6i	0.582006	−	0.738132i
$231$	−3.40291e6	−	2.13509e7i	−0.276067	−	1.73213i
$232$	3.89085e6	−	8.03812e6i	0.311588	−	0.643710i
$233$	3.75922e6	−	3.75922e6i	0.297187	−	0.297187i	−0.542724	−	0.839911i	$-0.682607\pi$
$233$	3.75922e6	−	3.75922e6i	0.297187	−	0.297187i	0.839911	+	0.542724i	$0.182607\pi$
$234$	6.49877e6	−	2.96187e6i	0.507205	−	0.231163i
$235$	−1.84289e7	+	114028.i	−1.42002	+	0.00878636i
$236$	−1.41369e7	+	3.20677e6i	−1.07552	+	0.243967i
$237$	9.08432e6	+	6.58667e6i	0.682413	+	0.494790i
$238$	−1.31275e7	+	1.64388e7i	−0.973758	+	1.21938i
$239$		−	1.37724e7i		−	1.00883i	−0.863462	−	0.504414i	$-0.831709\pi$
$239$		−	1.37724e7i		−	1.00883i	0.863462	−	0.504414i	$-0.168291\pi$
$240$	−7.92342e6	−	1.13279e7i	−0.573164	−	0.819441i
$241$	1.48455e7			1.06058			0.530289	−	0.847817i	$-0.322083\pi$
$241$	1.48455e7			1.06058			0.530289	+	0.847817i	$0.322083\pi$
$242$	−2.02424e7	−	1.61649e7i	−1.42829	−	1.14059i
$243$	−1.43487e7	+	69693.9i	−0.999988	+	0.00485709i
$244$	2.26054e6	+	9.96552e6i	0.155612	+	0.686010i
$245$	−908675.	+	919990.i	−0.0617889	+	0.0625583i
$246$	−1.93347e7	+	5.34235e6i	−1.29877	+	0.358861i
$247$	1.89456e6	+	1.89456e6i	0.125723	+	0.125723i
$248$	1.10850e7	+	5.36569e6i	0.726743	+	0.351780i
$249$	−3.98737e6	−	2.50179e7i	−0.258279	−	1.62052i
$250$	1.54930e7	−	2.02697e6i	0.991550	−	0.129726i
$251$	−1.30872e7			−0.827609			−0.413805	−	0.910366i	$-0.635800\pi$
$251$	−1.30872e7			−0.827609			−0.413805	+	0.910366i	$0.635800\pi$
$252$	−1.61883e7	−	4.06868e6i	−1.01158	−	0.254244i
$253$	−1.81006e7	−	1.81006e7i	−1.11772	−	1.11772i
$254$	−119991.	−	1.07139e6i	−0.00732227	−	0.0653801i
$255$	1.44373e7	−	2.01733e7i	0.870692	−	1.21663i
$256$	1.05305e7	−	1.30608e7i	0.627665	−	0.778484i
$257$	−1.35461e7	−	1.35461e7i	−0.798022	−	0.798022i	0.184762	−	0.982783i	$-0.440849\pi$
$257$	−1.35461e7	−	1.35461e7i	−0.798022	−	0.798022i	−0.982783	+	0.184762i	$0.940849\pi$
$258$	4.18329e6	+	2.37201e6i	0.243589	+	0.138120i
$259$	9.07490e6			0.522327
$260$	−9.54053e6	+	2.22630e6i	−0.542816	+	0.126667i
$261$	3.95270e6	+	1.20852e7i	0.222317	+	0.679724i
$262$	−2.15814e7	−	1.72342e7i	−1.19998	−	0.958269i
$263$	1.57037e7	+	1.57037e7i	0.863244	+	0.863244i	0.991713	−	0.128470i	$-0.0410065\pi$
$263$	1.57037e7	+	1.57037e7i	0.863244	+	0.863244i	−0.128470	+	0.991713i	$0.541006\pi$
$264$	−2.72619e7	+	1.46339e7i	−1.48165	+	0.795330i
$265$	1.64308e6	−	10166.5i	0.0882919	−	0.000546305i
$266$	−696954.	−	6.22305e6i	−0.0370305	−	0.330642i
$267$	2.75581e7	+	1.99813e7i	1.44782	+	1.04976i
$268$	−3.82142e6	+	6.06373e6i	−0.198527	+	0.315018i
$269$	3.29776e7			1.69419			0.847094	−	0.531443i	$-0.178350\pi$
$269$	3.29776e7			1.69419			0.847094	+	0.531443i	$0.178350\pi$
$270$	1.93156e7	+	3.78546e6i	0.981332	+	0.192321i
$271$		−	2.34144e7i		−	1.17645i	−0.808696	−	0.588227i	$-0.799826\pi$
$271$		−	2.34144e7i		−	1.17645i	0.808696	−	0.588227i	$-0.200174\pi$
$272$	2.83906e7	+	1.00196e7i	1.41081	+	0.497904i
$273$	−6.94371e6	+	9.57675e6i	−0.341274	+	0.470685i
$274$	−388175.	−	3.46599e6i	−0.0188702	−	0.168490i
$275$	−432765.	−	3.49696e7i	−0.0208091	−	1.68148i
$276$	−1.83448e7	+	7.35083e6i	−0.872541	+	0.349630i
$277$	−1.54820e7	+	1.54820e7i	−0.728428	+	0.728428i	−0.970307	−	0.241878i	$-0.922236\pi$
$277$	−1.54820e7	+	1.54820e7i	−0.728428	+	0.728428i	0.241878	+	0.970307i	$0.422236\pi$
$278$	1.64459e7	+	1.31332e7i	0.765460	+	0.611272i
$279$	−1.66662e7	+	5.45099e6i	−0.767403	+	0.250994i
$280$	2.06706e7	+	9.84821e6i	0.941629	+	0.448625i
$281$		−	1.57502e7i		−	0.709852i	−0.934894	−	0.354926i	$-0.884506\pi$
$281$		−	1.57502e7i		−	0.709852i	0.934894	−	0.354926i	$-0.115494\pi$
$282$	2.77022e7	+	1.57077e7i	1.23529	+	0.700432i
$283$	9.15143e6	−	9.15143e6i	0.403766	−	0.403766i	−0.475792	−	0.879558i	$-0.657838\pi$
$283$	9.15143e6	−	9.15143e6i	0.403766	−	0.403766i	0.879558	+	0.475792i	$0.157838\pi$
$284$	8.07638e6	+	3.56044e7i	0.352583	+	1.55435i
$285$	1.20731e6	+	7.28477e6i	0.0521538	+	0.314689i
$286$	2.44053e6	+	2.17913e7i	0.104325	+	0.931506i
$287$	2.34931e7	−	2.34931e7i	0.993789	−	0.993789i
$288$	2.10794e6	+	2.37947e7i	0.0882430	+	0.996099i
$289$			2.98892e7i			1.23828i
$290$	−2.04850e6	−	1.73213e7i	−0.0839927	−	0.710208i
$291$	−270946.	+	43183.5i	−0.0109952	+	0.00175242i
$292$	−2.09079e6	+	3.31761e6i	−0.0839773	+	0.133253i
$293$	−1.27308e7	+	1.27308e7i	−0.506119	+	0.506119i	−0.913333	−	0.407214i	$-0.866500\pi$
$293$	−1.27308e7	+	1.27308e7i	−0.506119	+	0.506119i	0.407214	+	0.913333i	$0.366500\pi$
$294$	2.15375e6	−	595098.i	0.0847526	−	0.0234178i
$295$	−1.98958e7	+	2.01436e7i	−0.774989	+	0.784640i
$296$	−4.26481e6	−	1.22670e7i	−0.164447	−	0.473004i
$297$	1.34916e7	−	4.19383e7i	0.514984	−	1.60082i
$298$	1.75828e6	+	1.40411e6i	0.0664416	+	0.0530582i
$299$			1.40055e7i			0.523946i
$300$	−2.49529e7	−	1.03128e7i	−0.924181	−	0.381955i
$301$	−7.96514e6			−0.292075
$302$	−2.26117e7	+	2.83153e7i	−0.820942	+	1.02802i
$303$	1.34623e7	−	1.85671e7i	0.483939	−	0.667448i
$304$	−8.08451e6	+	3.86668e6i	−0.287762	+	0.137631i
$305$	1.41998e7	+	1.40251e7i	0.500474	+	0.494319i
$306$	−3.90067e7	+	1.77777e7i	−1.36137	+	0.620455i
$307$	3.48830e7	+	3.48830e7i	1.20559	+	1.20559i	0.972442	+	0.233145i	$0.0749017\pi$
$307$	3.48830e7	+	3.48830e7i	1.20559	+	1.20559i	0.233145	+	0.972442i	$0.425098\pi$
$308$	2.73237e7	−	4.33566e7i	0.935164	−	1.48389i
$309$	1.74648e7	−	2.78355e6i	0.591955	−	0.0943460i
$310$	2.38870e7	−	2.82499e6i	0.801818	−	0.0948270i
$311$	−1.82720e6			−0.0607443			−0.0303722	−	0.999539i	$-0.509669\pi$
$311$	−1.82720e6			−0.0607443			−0.0303722	+	0.999539i	$0.509669\pi$
$312$	1.62087e7	+	4.88554e6i	0.533683	+	0.160860i
$313$	5.42997e6	+	5.42997e6i	0.177078	+	0.177078i	0.790081	−	0.613003i	$-0.210039\pi$
$313$	5.42997e6	+	5.42997e6i	0.177078	+	0.177078i	−0.613003	+	0.790081i	$0.710039\pi$
$314$	−4.59713e7	+	5.14858e6i	−1.48490	+	0.166303i
$315$	−3.09225e7	+	1.03260e7i	−0.989335	+	0.330371i
$316$	5.88385e6	+	2.59388e7i	0.186466	+	0.822031i
$317$	1.61184e7	+	1.61184e7i	0.505993	+	0.505993i	0.913294	−	0.407301i	$-0.133530\pi$
$317$	1.61184e7	+	1.61184e7i	0.505993	+	0.505993i	−0.407301	+	0.913294i	$0.633530\pi$
$318$	−2.46988e6	−	1.40047e6i	−0.0768058	−	0.0435504i
$319$	−3.90391e7			−1.20262
$320$	3.59806e6	−	3.25699e7i	0.109804	−	0.993953i
$321$	2.30840e6	−	367914.i	0.0697905	−	0.0111232i
$322$	2.04259e7	−	2.55782e7i	0.611806	−	0.766129i
$323$	−1.13714e7	−	1.13714e7i	−0.337449	−	0.337449i
$324$	−2.56706e7	−	2.23126e7i	−0.754745	−	0.656018i
$325$	−1.33616e7	+	1.36965e7i	−0.389233	+	0.398988i
$326$	−2.74090e7	+	3.06969e6i	−0.791116	+	0.0886015i
$327$	7.52076e6	−	1.03726e7i	0.215089	−	0.296650i
$328$	−4.27976e7	−	2.07162e7i	−1.21282	−	0.587067i
$329$	−5.27462e7			−1.48116
$330$	−2.94820e7	+	5.27528e7i	−0.820381	+	1.46792i
$331$			1.46410e7i			0.403727i	0.979414	+	0.201863i	$0.0646997\pi$
$331$			1.46410e7i			0.403727i	−0.979414	+	0.201863i	$0.935300\pi$
$332$	3.20167e7	−	5.08032e7i	0.874907	−	1.38828i
$333$	1.64924e7	+	8.36300e6i	0.446635	+	0.226480i
$334$	4.40142e7	−	4.92940e6i	1.18128	−	0.132298i
$335$	86616.3	+	1.39986e7i	0.00230391	+	0.372350i
$336$	−2.24765e7	−	3.25614e7i	−0.592532	−	0.858391i
$337$	−2.03563e7	+	2.03563e7i	−0.531874	+	0.531874i	−0.921130	−	0.389256i	$-0.872732\pi$
$337$	−2.03563e7	+	2.03563e7i	−0.531874	+	0.531874i	0.389256	+	0.921130i	$0.372732\pi$
$338$	−1.66095e7	+	2.07991e7i	−0.430136	+	0.538634i
$339$	1.10653e7	−	1.76360e6i	0.284031	−	0.0452689i
$340$	5.72639e7	−	1.33626e7i	1.45695	−	0.339981i
$341$		−	5.38371e7i		−	1.35775i
$342$	4.46825e6	−	1.19519e7i	0.111701	−	0.298784i
$343$	2.71454e7	−	2.71454e7i	0.672689	−	0.672689i
$344$	3.74327e6	+	1.07669e7i	0.0919552	+	0.264494i
$345$	−2.24639e7	+	3.13890e7i	−0.547050	+	0.764399i
$346$	4.30372e7	−	4.81997e6i	1.03900	−	0.116363i
$347$	−4.31558e7	+	4.31558e7i	−1.03288	+	1.03288i	−0.0334409	+	0.999441i	$0.510647\pi$
$347$	−4.31558e7	+	4.31558e7i	−1.03288	+	1.03288i	−0.999441	+	0.0334409i	$0.989353\pi$
$348$	−1.18558e7	+	2.77100e7i	−0.281316	+	0.657504i
$349$			7.82107e6i			0.183988i	0.995760	+	0.0919940i	$0.0293241\pi$
$349$			7.82107e6i			0.183988i	−0.995760	+	0.0919940i	$0.970676\pi$
$350$	4.43774e7	−	5.52692e6i	1.03504	−	0.128908i
$351$	−2.14448e7	+	1.10055e7i	−0.495907	+	0.254500i
$352$	−7.14484e7	−	1.65593e7i	−1.63819	−	0.379676i
$353$	9.86859e6	−	9.86859e6i	0.224352	−	0.224352i	−0.585976	−	0.810328i	$-0.699289\pi$
$353$	9.86859e6	−	9.86859e6i	0.224352	−	0.224352i	0.810328	+	0.585976i	$0.199289\pi$
$354$	4.71572e7	−	1.30299e7i	1.06301	−	0.293719i
$355$	5.07323e7	+	5.01084e7i	1.13397	+	1.12002i
$356$	1.78492e7	+	7.86877e7i	0.395612	+	1.74404i
$357$	4.16773e7	−	5.74813e7i	0.915999	−	1.26334i
$358$	3.85599e7	−	4.82863e7i	0.840403	−	1.05239i
$359$			2.42294e7i			0.523672i	0.965112	+	0.261836i	$0.0843279\pi$
$359$			2.42294e7i			0.523672i	−0.965112	+	0.261836i	$0.915672\pi$
$360$	2.84905e7	+	3.69469e7i	0.610651	+	0.791900i
$361$	−4.22590e7			−0.898251
$362$	1.73772e7	+	1.38769e7i	0.366315	+	0.292527i
$363$	7.07813e7	+	5.13206e7i	1.47978	+	1.07293i
$364$	−2.73448e7	+	6.20280e6i	−0.566984	+	0.128613i
$365$	47389.9	+	7.65898e6i	0.000974556	+	0.157504i
$366$	−9.18516e6	−	3.32425e7i	−0.187346	−	0.678032i
$367$	−6.01642e7	−	6.01642e7i	−1.21714	−	1.21714i	−0.968630	−	0.248508i	$-0.920060\pi$
$367$	−6.01642e7	−	6.01642e7i	−1.21714	−	1.21714i	−0.248508	−	0.968630i	$-0.579940\pi$
$368$	−4.41747e7	−	1.55902e7i	−0.886401	−	0.312830i
$369$	6.43457e7	−	2.10455e7i	1.28068	−	0.418871i
$370$	−1.99187e7	−	1.57056e7i	−0.393239	−	0.310063i
$371$	4.70274e6			0.0920936
$372$	−3.82136e7	−	1.63498e7i	−0.742316	−	0.317603i
$373$	−3.61958e7	−	3.61958e7i	−0.697480	−	0.697480i	0.266387	−	0.963866i	$-0.414170\pi$
$373$	−3.61958e7	−	3.61958e7i	−0.697480	−	0.697480i	−0.963866	+	0.266387i	$0.914170\pi$
$374$	−1.46485e7	−	1.30795e8i	−0.280013	−	2.50021i
$375$	−5.19141e7	+	9.26525e6i	−0.984444	+	0.175697i
$376$	2.47884e7	+	7.12999e7i	0.466321	+	1.34130i
$377$	1.51035e7	+	1.51035e7i	0.281873	+	0.281873i
$378$	5.52149e7	+	1.11762e7i	1.02231	+	0.206928i
$379$	−4.79460e7			−0.880715			−0.440357	−	0.897823i	$-0.645148\pi$
$379$	−4.79460e7			−0.880715			−0.440357	+	0.897823i	$0.645148\pi$
$380$	−9.24025e6	+	1.48653e7i	−0.168397	+	0.270909i
$381$	572684.	+	3.59319e6i	0.0103548	+	0.0649688i
$382$	5.98299e6	+	4.77782e6i	0.107332	+	0.0857117i
$383$	1.50168e7	+	1.50168e7i	0.267290	+	0.267290i	0.828007	−	0.560717i	$-0.189475\pi$
$383$	1.50168e7	+	1.50168e7i	0.267290	+	0.267290i	−0.560717	+	0.828007i	$0.689475\pi$
$384$	−3.34520e7	+	4.56852e7i	−0.590784	+	0.806830i
$385$	−619319.	−	1.00092e8i	−0.0108526	−	1.75395i
$386$	571061.	+	5.09897e6i	0.00992935	+	0.0886585i
$387$	−1.44756e7	−	7.34030e6i	−0.249749	−	0.126643i
$388$	−550202.	−	346743.i	−0.00941948	−	0.00593625i
$389$	−7.65148e6			−0.129986			−0.0649930	−	0.997886i	$-0.520703\pi$
$389$	−7.65148e6			−0.129986			−0.0649930	+	0.997886i	$0.520703\pi$
$390$	3.18150e7	−	9.00300e6i	0.536338	−	0.151773i
$391$		−	8.40636e7i		−	1.40630i
$392$	4.76734e6	+	2.30763e6i	0.0791440	+	0.0383096i
$393$	7.54632e7	+	5.47153e7i	1.24325	+	0.901429i
$394$	−2.22212e6	−	1.98412e7i	−0.0363312	−	0.324398i
$395$	3.69599e7	+	3.65053e7i	0.599707	+	0.592331i
$396$	8.96126e7	−	5.36146e7i	1.44306	−	0.863372i
$397$	−4.58644e7	+	4.58644e7i	−0.733000	+	0.733000i	−0.971213	−	0.238213i	$-0.923438\pi$
$397$	−4.58644e7	+	4.58644e7i	−0.733000	+	0.733000i	0.238213	+	0.971213i	$0.423438\pi$
$398$	4.57314e7	+	3.65196e7i	0.725379	+	0.579265i
$399$	3.32638e6	+	2.08707e7i	0.0523665	+	0.328563i
$400$	−2.83265e7	−	5.73900e7i	−0.442602	−	0.896718i
$401$			8.07968e7i			1.25303i	0.779410	+	0.626515i	$0.215519\pi$
$401$			8.07968e7i			1.25303i	−0.779410	+	0.626515i	$0.784481\pi$
$402$	1.19316e7	−	2.10427e7i	0.183663	−	0.323910i
$403$	−2.08285e7	+	2.08285e7i	−0.318232	+	0.318232i
$404$	5.30154e7	−	1.20258e7i	0.804004	−	0.182377i
$405$	−6.57136e7	−	9.73053e6i	−0.989214	−	0.146478i
$406$	−5.55615e6	−	4.96104e7i	−0.0830225	−	0.741302i
$407$	−4.01455e7	+	4.01455e7i	−0.595462	+	0.595462i
$408$	−9.72871e7	−	2.93238e7i	−1.43243	−	0.431758i
$409$			2.48258e7i			0.362855i	0.983404	+	0.181428i	$0.0580718\pi$
$409$			2.48258e7i			0.362855i	−0.983404	+	0.181428i	$0.941928\pi$
$410$	−9.22241e7	+	1.09069e7i	−1.33811	+	0.158252i
$411$	1.85266e6	+	1.16241e7i	0.0266851	+	0.167431i
$412$	3.54653e7	+	2.23506e7i	0.507122	+	0.319593i
$413$	−5.72994e7	+	5.72994e7i	−0.813392	+	0.813392i
$414$	6.06930e7	−	2.76614e7i	0.855338	−	0.389828i
$415$	−725690.	−	1.17283e8i	−0.0101533	−	1.64094i
$416$	2.12356e7	+	3.40485e7i	0.294974	+	0.472952i
$417$	−5.75060e7	−	4.16953e7i	−0.793059	−	0.575015i
$418$	3.06127e7	+	2.44463e7i	0.419153	+	0.334722i
$419$		−	2.14378e7i		−	0.291433i	−0.989326	−	0.145716i	$-0.953451\pi$
$419$		−	2.14378e7i		−	0.291433i	0.989326	−	0.145716i	$-0.0465487\pi$
$420$	−7.12336e7	−	2.99575e7i	−0.961472	−	0.404350i
$421$	9.82380e7			1.31654			0.658269	−	0.752783i	$-0.271289\pi$
$421$	9.82380e7			1.31654			0.658269	+	0.752783i	$0.271289\pi$
$422$	−2.27308e7	+	2.84645e7i	−0.302467	+	0.378761i
$423$	−9.58592e7	−	4.86084e7i	−1.26652	−	0.642229i
$424$	−2.21009e6	−	6.35696e6i	−0.0289942	−	0.0833972i
$425$	8.01988e7	−	8.22087e7i	1.04472	−	1.07090i
$426$	−3.28164e7	−	1.18767e8i	−0.424484	−	1.53627i
$427$	4.03919e7	+	4.03919e7i	0.518813	+	0.518813i
$428$	4.68760e6	+	2.95417e6i	0.0597888	+	0.0376794i
$429$	−1.16480e7	−	7.30831e7i	−0.147530	−	0.925647i
$430$	1.74829e7	+	1.37850e7i	0.219891	+	0.173381i
$431$	3.89181e7			0.486093			0.243047	−	0.970015i	$-0.421853\pi$
$431$	3.89181e7			0.486093			0.243047	+	0.970015i	$0.421853\pi$
$432$	−1.08411e7	−	7.98893e7i	−0.134470	−	0.990918i
$433$	−1.92688e7	−	1.92688e7i	−0.237350	−	0.237350i	0.578402	−	0.815752i	$-0.303677\pi$
$433$	−1.92688e7	−	1.92688e7i	−0.237350	−	0.237350i	−0.815752	+	0.578402i	$0.803677\pi$
$434$	6.84155e7	−	7.66223e6i	0.836923	−	0.0937316i
$435$	9.62476e6	+	5.80745e7i	0.116929	+	0.705533i
$436$	2.96173e7	−	6.71827e6i	0.357343	−	0.0810584i
$437$	1.76935e7	+	1.76935e7i	0.212017	+	0.212017i
$438$	6.52809e6	−	1.15130e7i	0.0776897	−	0.137014i
$439$	7.31057e7			0.864088			0.432044	−	0.901853i	$-0.357793\pi$
$439$	7.31057e7			0.864088			0.432044	+	0.901853i	$0.357793\pi$
$440$	−1.35009e8	+	4.78762e7i	−1.58491	+	0.562033i
$441$	−7.16764e6	+	2.34431e6i	−0.0835719	+	0.0273338i
$442$	−4.49349e7	+	5.62693e7i	−0.520376	+	0.651636i
$443$	−8.55227e7	−	8.55227e7i	−0.983717	−	0.983717i	0.0161525	−	0.999870i	$-0.494858\pi$
$443$	−8.55227e7	−	8.55227e7i	−0.983717	−	0.983717i	−0.999870	+	0.0161525i	$0.994858\pi$
$444$	1.63035e7	+	4.06871e7i	0.186265	+	0.464845i
$445$	1.12121e8	+	1.10742e8i	1.27235	+	1.25670i
$446$	−7.80569e7	+	8.74202e6i	−0.879846	+	0.0985388i
$447$	−6.14816e6	−	4.45778e6i	−0.0688371	−	0.0499110i
$448$	1.08746e7	−	9.31526e7i	0.120942	−	1.03600i
$449$	−1.13894e8			−1.25824			−0.629118	−	0.777310i	$-0.716584\pi$
$449$	−1.13894e8			−1.25824			−0.629118	+	0.777310i	$0.716584\pi$
$450$	8.57435e7	+	3.08517e7i	0.940943	+	0.338564i
$451$			2.07857e8i			2.26587i
$452$	2.24700e7	+	1.41608e7i	0.243326	+	0.153346i
$453$	7.17879e7	−	9.90097e7i	0.772248	−	1.06508i
$454$	−5.57661e7	+	6.24556e6i	−0.595941	+	0.0667427i
$455$	−3.84841e7	+	3.89633e7i	−0.408552	+	0.413639i
$456$	2.66488e7	−	1.43048e7i	0.281050	−	0.150864i
$457$	−6.66961e7	+	6.66961e7i	−0.698798	+	0.698798i	−0.964151	−	0.265353i	$-0.914512\pi$
$457$	−6.66961e7	+	6.66961e7i	−0.698798	+	0.698798i	0.265353	+	0.964151i	$0.414512\pi$
$458$	3.66490e7	−	4.58934e7i	0.381475	−	0.477698i
$459$	1.28715e8	−	6.60568e7i	1.33104	−	0.683092i
$460$	−8.91005e7	+	2.07917e7i	−0.915391	+	0.213608i
$461$			1.12888e8i			1.15224i	0.817365	+	0.576121i	$0.195434\pi$
$461$			1.12888e8i			1.15224i	−0.817365	+	0.576121i	$0.804566\pi$
$462$	−8.53130e7	+	1.50459e8i	−0.865146	+	1.52578i
$463$	−7.30973e7	+	7.30973e7i	−0.736476	+	0.736476i	−0.971894	−	0.235418i	$-0.924354\pi$
$463$	−7.30973e7	+	7.30973e7i	−0.736476	+	0.736476i	0.235418	+	0.971894i	$0.424354\pi$
$464$	−6.44500e7	+	3.08253e7i	−0.645162	+	0.308570i
$465$	−8.00879e7	+	1.32731e7i	−0.796541	+	0.132012i
$466$	−4.22664e7	+	4.73365e6i	−0.417675	+	0.0467777i
$467$	1.60114e7	−	1.60114e7i	0.157209	−	0.157209i	−0.624119	−	0.781329i	$-0.714542\pi$
$467$	1.60114e7	−	1.60114e7i	0.157209	−	0.157209i	0.781329	+	0.624119i	$0.214542\pi$
$468$	−5.54118e7	−	1.39269e7i	−0.540586	−	0.135868i
$469$			4.00662e7i			0.388382i
$470$	1.15774e8	+	9.12859e7i	1.11511	+	0.879245i
$471$	1.54177e8	−	2.45728e7i	1.47556	−	0.235176i
$472$	1.04383e8	+	5.05265e7i	0.992667	+	0.480500i
$473$	3.52362e7	−	3.52362e7i	0.332970	−	0.332970i
$474$	−2.39076e7	−	8.65252e7i	−0.224492	−	0.812470i
$475$	423033.	+	3.41832e7i	0.00394723	+	0.318957i
$476$	1.64128e8	−	3.72302e7i	1.52182	−	0.345203i
$477$	8.54662e6	+	4.33382e6i	0.0787479	+	0.0399315i
$478$	−6.87534e7	+	8.60958e7i	−0.629522	+	0.788313i
$479$		−	1.42888e8i		−	1.30014i	−0.759875	−	0.650069i	$-0.774740\pi$
$479$		−	1.42888e8i		−	1.30014i	0.759875	−	0.650069i	$-0.225260\pi$
$480$	−7.01851e6	+	1.10369e8i	−0.0634631	+	0.997984i
$481$	3.10630e7			0.279131
$482$	−9.28037e7	−	7.41101e7i	−0.828751	−	0.661815i
$483$	−6.48484e7	+	8.94387e7i	−0.575517	+	0.793751i
$484$	4.58446e7	+	2.02104e8i	0.404345	+	1.78254i
$485$	−1.27019e6	+	7859.27i	−0.0111338	+	6.88901e-5i
$486$	9.00464e7	+	7.11947e7i	0.784436	+	0.620210i
$487$	−6.87387e7	−	6.87387e7i	−0.595134	−	0.595134i	0.343880	−	0.939014i	$-0.388259\pi$
$487$	−6.87387e7	−	6.87387e7i	−0.595134	−	0.595134i	−0.939014	+	0.343880i	$0.888259\pi$
$488$	3.56175e7	−	7.35825e7i	0.306482	−	0.633162i
$489$	9.19235e7	−	1.46508e7i	0.786140	−	0.125295i
$490$	1.02731e7	−	1.21495e6i	0.0873198	−	0.0103269i
$491$	8.52359e7			0.720076			0.360038	−	0.932938i	$-0.382764\pi$
$491$	8.52359e7			0.720076			0.360038	+	0.932938i	$0.382764\pi$
$492$	1.47537e8	+	6.31243e7i	1.23881	+	0.530031i
$493$	−9.06536e7	−	9.06536e7i	−0.756561	−	0.756561i
$494$	−2.38565e6	−	2.13013e7i	−0.0197891	−	0.176695i
$495$	9.11147e7	−	1.82475e8i	0.751230	−	1.50449i
$496$	−4.25098e7	−	8.88801e7i	−0.348373	−	0.728382i
$497$	1.44311e8	+	1.44311e8i	1.17552	+	1.17552i
$498$	−9.99658e7	+	1.76300e8i	−0.809400	+	1.42746i
$499$	1.72119e8			1.38524			0.692622	−	0.721300i	$-0.256455\pi$
$499$	1.72119e8			1.38524			0.692622	+	0.721300i	$0.256455\pi$
$500$	−1.06970e8	−	6.46712e7i	−0.855762	−	0.517370i
$501$	−1.47614e8	+	2.35267e7i	−1.17385	+	0.187089i
$502$	8.18122e7	+	6.53326e7i	0.646706	+	0.516439i
$503$	−5.49552e7	−	5.49552e7i	−0.431822	−	0.431822i	0.457426	−	0.889248i	$-0.348771\pi$
$503$	−5.49552e7	−	5.49552e7i	−0.431822	−	0.431822i	−0.889248	+	0.457426i	$0.848771\pi$
$504$	8.08867e7	+	1.06248e8i	0.631809	+	0.829907i
$505$	7.46120e7	−	7.55411e7i	0.579341	−	0.586555i
$506$	2.27925e7	+	2.03513e8i	0.175930	+	1.57087i
$507$	5.27319e7	−	7.27277e7i	0.404622	−	0.558054i
$508$	−4.59837e6	+	7.29658e6i	−0.0350763	+	0.0556581i
$509$	−2.04084e8			−1.54759			−0.773794	−	0.633438i	$-0.781643\pi$
$509$	−2.04084e8			−1.54759			−0.773794	+	0.633438i	$0.781643\pi$
$510$	−1.90959e8	+	5.40375e7i	−1.43956	+	0.407366i
$511$			2.19212e7i			0.164286i
$512$	−1.31030e8	+	2.90779e7i	−0.976250	+	0.216647i
$513$	−1.31882e7	+	4.09952e7i	−0.0976861	+	0.303655i
$514$	1.70574e7	+	1.52304e8i	0.125610	+	1.12156i
$515$	8.18746e7	−	506598.i	0.599415	−	0.00370887i
$516$	−1.43097e7	−	3.57115e7i	−0.104156	−	0.259932i
$517$	2.33338e8	−	2.33338e8i	1.68855	−	1.68855i
$518$	−5.67301e7	−	4.53028e7i	−0.408154	−	0.325939i
$519$	−1.44337e8	+	2.30045e7i	−1.03246	+	0.164555i
$520$	7.07548e7	+	3.37100e7i	0.503206	+	0.239745i
$521$		−	2.66935e8i		−	1.88752i	−0.330630	−	0.943761i	$-0.607261\pi$
$521$		−	2.66935e8i		−	1.88752i	0.330630	−	0.943761i	$-0.392739\pi$
$522$	3.56211e7	−	9.52807e7i	0.250435	−	0.669875i
$523$	4.78537e7	−	4.78537e7i	0.334511	−	0.334511i	−0.519786	−	0.854297i	$-0.673988\pi$
$523$	4.78537e7	−	4.78537e7i	0.334511	−	0.334511i	0.854297	+	0.519786i	$0.173988\pi$
$524$	4.88771e7	+	2.15473e8i	0.339712	+	1.49761i
$525$	−1.48744e8	+	2.55982e7i	−1.02793	+	0.176901i
$526$	−1.97742e7	−	1.76563e8i	−0.135876	−	1.21323i
$527$	1.25016e8	−	1.25016e8i	0.854151	−	0.854151i
$528$	2.43477e8	+	4.46132e7i	1.65408	+	0.303083i
$529$		−	1.72359e7i		−	0.116431i
$530$	−1.03222e7	−	8.13887e6i	−0.0693335	−	0.0546684i
$531$	−1.56938e8	+	5.13297e7i	−1.04820	+	0.342835i
$532$	−2.67092e7	+	4.23815e7i	−0.177389	+	0.281476i
$533$	8.04159e7	−	8.04159e7i	0.531080	−	0.531080i
$534$	−7.25259e7	−	2.62482e8i	−0.476288	−	1.72376i
$535$	1.08217e7	−	66959.3i	0.0706700	−	0.000437270i
$536$	5.41596e7	−	1.88294e7i	0.351707	−	0.122276i
$537$	−1.22421e8	+	1.68842e8i	−0.790554	+	1.09033i
$538$	−2.06153e8	−	1.64627e8i	−1.32386	−	1.05720i
$539$		−	2.31538e7i		−	0.147862i
$540$	−1.01850e8	−	1.20089e8i	−0.646816	−	0.762646i
$541$	−1.64377e8			−1.03813			−0.519063	−	0.854736i	$-0.673719\pi$
$541$	−1.64377e8			−1.03813			−0.519063	+	0.854736i	$0.673719\pi$
$542$	−1.16887e8	+	1.46371e8i	−0.734123	+	0.919299i
$543$	−6.07626e7	−	4.40565e7i	−0.379522	−	0.275176i
$544$	−1.27459e8	−	2.04365e8i	−0.791726	−	1.26943i
$545$	4.16823e7	−	4.22013e7i	0.257491	−	0.260697i
$546$	9.12154e7	−	2.52036e7i	0.560390	−	0.154840i
$547$	−1.57185e8	−	1.57185e8i	−0.960392	−	0.960392i	0.0388525	−	0.999245i	$-0.487630\pi$
$547$	−1.57185e8	−	1.57185e8i	−0.960392	−	0.960392i	−0.999245	+	0.0388525i	$0.987630\pi$
$548$	−1.48759e7	+	2.36048e7i	−0.0903947	+	0.143436i
$549$	3.61837e7	+	1.10630e8i	0.218674	+	0.668586i
$550$	−1.71867e8	+	2.20767e8i	−1.03301	+	1.32692i
$551$	3.81612e7			0.228122
$552$	1.51375e8	+	4.56268e7i	0.899990	+	0.271271i
$553$	1.05134e8	+	1.05134e8i	0.621682	+	0.621682i
$554$	1.74070e8	−	1.94951e7i	1.02375	−	0.114656i
$555$	6.96179e7	+	4.98229e7i	0.407232	+	0.291440i
$556$	−3.72463e7	−	1.64199e8i	−0.216700	−	0.955314i
$557$	−7.19996e7	−	7.19996e7i	−0.416643	−	0.416643i	0.467402	−	0.884045i	$-0.345190\pi$
$557$	−7.19996e7	−	7.19996e7i	−0.416643	−	0.416643i	−0.884045	+	0.467402i	$0.845190\pi$
$558$	1.31397e8	+	4.91234e7i	0.756282	+	0.282739i
$559$	−2.72644e7			−0.156085
$560$	−8.00553e7	−	1.64754e8i	−0.455854	−	0.938150i
$561$	6.99134e7	+	4.38657e8i	0.395978	+	2.48449i
$562$	−7.86267e7	+	9.84596e7i	−0.442957	+	0.554688i
$563$	2.06264e7	+	2.06264e7i	0.115584	+	0.115584i	0.762533	−	0.646949i	$-0.223955\pi$
$563$	2.06264e7	+	2.06264e7i	0.115584	+	0.115584i	−0.646949	+	0.762533i	$0.723955\pi$
$564$	−9.47609e7	−	2.36486e8i	−0.528192	−	1.31816i
$565$	5.18739e7	−	320969.i	0.287610	−	0.00177958i
$566$	−1.02893e8	+	1.15236e7i	−0.567464	+	0.0635534i
$567$	−1.87903e8	−	2.90129e7i	−1.03082	−	0.159163i
$568$	1.27253e8	−	2.62893e8i	0.694421	−	1.43461i
$569$	3.44004e8			1.86736			0.933678	−	0.358114i	$-0.116580\pi$
$569$	3.44004e8			1.86736			0.933678	+	0.358114i	$0.116580\pi$
$570$	2.88190e7	−	5.15664e7i	0.155616	−	0.278447i
$571$			4.11554e7i			0.221064i	0.993873	+	0.110532i	$0.0352555\pi$
$571$			4.11554e7i			0.221064i	−0.993873	+	0.110532i	$0.964744\pi$
$572$	9.35280e7	−	1.48408e8i	0.499751	−	0.792992i
$573$	−2.09206e7	−	1.51687e7i	−0.111201	−	0.0806277i
$574$	−2.64142e8	+	2.95828e7i	−1.39670	+	0.156424i
$575$	−1.24786e8	+	1.27914e8i	−0.656393	+	0.672843i
$576$	1.05608e8	−	1.59271e8i	0.552624	−	0.833431i
$577$	1.44256e8	−	1.44256e8i	0.750940	−	0.750940i	−0.223715	−	0.974655i	$-0.571819\pi$
$577$	1.44256e8	−	1.44256e8i	0.750940	−	0.750940i	0.974655	+	0.223715i	$0.0718185\pi$
$578$	1.49210e8	−	1.86847e8i	0.772705	−	0.967613i
$579$	−2.72553e6	−	1.71008e7i	−0.0140415	−	0.0881008i
$580$	−7.36637e7	+	1.18507e8i	−0.377546	+	0.607379i
$581$		−	3.35683e8i		−	1.71159i
$582$	1.90934e6	+	1.08264e6i	0.00968535	+	0.00549179i
$583$	−2.08040e7	+	2.08040e7i	−0.104988	+	0.104988i
$584$	2.96320e7	−	1.03020e7i	0.148773	−	0.0517229i
$585$	−1.05847e8	+	3.53456e7i	−0.528700	+	0.176550i
$586$	1.43138e8	−	1.60308e7i	0.711313	−	0.0796639i
$587$	−1.66302e8	+	1.66302e8i	−0.822211	+	0.822211i	−0.986425	−	0.164214i	$-0.947491\pi$
$587$	−1.66302e8	+	1.66302e8i	−0.822211	+	0.822211i	0.164214	+	0.986425i	$0.447491\pi$
$588$	−1.64346e7	−	7.03159e6i	−0.0808399	−	0.0345877i
$589$			5.26263e7i			0.257547i
$590$	2.24934e8	−	2.66018e7i	1.09521	−	0.129525i
$591$	1.06056e7	+	6.65427e7i	0.0513775	+	0.322358i
$592$	−3.45777e7	+	9.79755e7i	−0.166660	+	0.472229i
$593$	−2.64518e8	+	2.64518e8i	−1.26850	+	1.26850i	−0.321641	+	0.946862i	$0.604234\pi$
$593$	−2.64518e8	+	2.64518e8i	−1.26850	+	1.26850i	−0.946862	+	0.321641i	$0.895766\pi$
$594$	−2.93701e8	+	1.94818e8i	−1.40135	+	0.929545i
$595$	2.30988e8	−	2.33864e8i	1.09658	−	1.11023i
$596$	−3.98212e6	−	1.75551e7i	−0.0188094	−	0.0829208i
$597$	−1.59908e8	−	1.15943e8i	−0.751532	−	0.544905i
$598$	6.99171e7	−	8.75531e7i	0.326949	−	0.409419i
$599$			3.63357e7i			0.169065i	0.996421	+	0.0845325i	$0.0269397\pi$
$599$			3.63357e7i			0.169065i	−0.996421	+	0.0845325i	$0.973060\pi$
$600$	1.04506e8	+	1.89036e8i	0.483823	+	0.875166i
$601$	2.26706e8			1.04434			0.522168	−	0.852843i	$-0.325124\pi$
$601$	2.26706e8			1.04434			0.522168	+	0.852843i	$0.325124\pi$
$602$	4.97926e7	+	3.97628e7i	0.228231	+	0.182258i
$603$	−3.69231e7	+	7.28150e7i	−0.168402	+	0.332100i
$604$	2.82706e8	−	6.41279e7i	1.28299	−	0.291029i
$605$	2.87976e8	+	2.84434e8i	1.30044	+	1.28445i
$606$	−1.76846e8	+	4.88640e7i	−0.794653	+	0.219569i
$607$	−1.75018e8	−	1.75018e8i	−0.782559	−	0.782559i	0.197703	−	0.980262i	$-0.436652\pi$
$607$	−1.75018e8	−	1.75018e8i	−0.782559	−	0.782559i	−0.980262	+	0.197703i	$0.936652\pi$
$608$	6.98416e7	+	1.61869e7i	0.310745	+	0.0720198i
$609$	2.65180e7	+	1.66382e8i	0.117406	+	0.736639i
$610$	−1.87523e7	−	1.58562e8i	−0.0826163	−	0.698570i
$611$	−1.80548e8			−0.791533
$612$	3.32591e8	+	8.35917e7i	1.45096	+	0.364677i
$613$	3.78952e7	+	3.78952e7i	0.164514	+	0.164514i	0.784563	−	0.620049i	$-0.212887\pi$
$613$	3.78952e7	+	3.78952e7i	0.164514	+	0.164514i	−0.620049	+	0.784563i	$0.712887\pi$
$614$	−4.39251e7	−	3.92204e8i	−0.189761	−	1.69436i
$615$	3.09208e8	−	5.12454e7i	1.32931	−	0.220308i
$616$	−3.87249e8	+	1.34633e8i	−1.65672	+	0.575982i
$617$	−2.32672e8	−	2.32672e8i	−0.990578	−	0.990578i	0.00937841	−	0.999956i	$-0.497015\pi$
$617$	−2.32672e8	−	2.32672e8i	−0.990578	−	0.990578i	−0.999956	+	0.00937841i	$0.997015\pi$
$618$	−1.23074e8	−	6.97853e7i	−0.521435	−	0.295664i
$619$	−3.50533e6			−0.0147794			−0.00738971	−	0.999973i	$-0.502352\pi$
$619$	−3.50533e6			−0.0147794			−0.00738971	+	0.999973i	$0.502352\pi$
$620$	−1.63428e8	−	1.01586e8i	−0.685725	−	0.426246i
$621$	−2.00276e8	+	1.02782e8i	−0.836284	+	0.429183i
$622$	1.14224e7	+	9.12159e6i	0.0474665	+	0.0379052i
$623$	3.18934e8	+	3.18934e8i	1.31898	+	1.31898i
$624$	−7.69363e7	−	1.11456e8i	−0.316649	−	0.458723i
$625$	−2.44066e8	+	6.04177e6i	−0.999694	+	0.0247471i
$626$	−6.83749e6	−	6.10515e7i	−0.0278724	−	0.248870i
$627$	−1.07043e8	−	7.76125e7i	−0.434266	−	0.314868i
$628$	3.13083e8	+	1.97308e8i	1.26410	+	0.796647i
$629$	−1.86446e8			−0.749204
$630$	2.44855e8	+	8.98171e7i	0.979236	+	0.359201i
$631$			3.28043e8i			1.30570i	0.757488	+	0.652849i	$0.226426\pi$
$631$			3.28043e8i			1.30570i	−0.757488	+	0.652849i	$0.773574\pi$
$632$	9.27071e7	−	1.91524e8i	0.367250	−	0.758704i
$633$	7.21660e7	−	9.95312e7i	0.284526	−	0.392417i
$634$	−2.02965e7	−	1.81226e8i	−0.0796440	−	0.711136i
$635$	104227.	+	1.68448e7i	0.000407060	+	0.0657875i
$636$	8.44869e6	+	2.10846e7i	0.0328411	+	0.0819587i
$637$	−8.95774e6	+	8.95774e6i	−0.0346561	+	0.0346561i
$638$	2.44046e8	+	1.94887e8i	0.939743	+	0.750449i
$639$	1.29276e8	+	3.95256e8i	0.495467	+	1.51487i
$640$	−1.85085e8	+	1.85643e8i	−0.706042	+	0.708170i
$641$		−	4.08321e8i		−	1.55034i	−0.631752	−	0.775170i	$-0.717664\pi$
$641$		−	4.08321e8i		−	1.55034i	0.631752	−	0.775170i	$-0.282336\pi$
$642$	−1.62672e7	−	9.22383e6i	−0.0614763	−	0.0348583i
$643$	−2.57851e8	+	2.57851e8i	−0.969920	+	0.969920i	−0.999561	−	0.0296405i	$-0.990564\pi$
$643$	−2.57851e8	+	2.57851e8i	−0.969920	+	0.969920i	0.0296405	+	0.999561i	$0.490564\pi$
$644$	−2.55378e8	+	5.79289e7i	−0.956148	+	0.216889i
$645$	−6.11044e7	−	4.37301e7i	−0.227716	−	0.162967i
$646$	1.43191e7	+	1.27854e8i	0.0531150	+	0.474260i
$647$	1.67261e8	−	1.67261e8i	0.617564	−	0.617564i	−0.327342	−	0.944906i	$-0.606153\pi$
$647$	1.67261e8	−	1.67261e8i	0.617564	−	0.617564i	0.944906	+	0.327342i	$0.106153\pi$
$648$	4.90879e7	+	2.67633e8i	0.180405	+	0.983592i
$649$		−	5.06961e8i		−	1.85456i
$650$	1.51902e8	−	1.89184e7i	0.553126	−	0.0688883i
$651$	−2.29450e8	+	3.65698e7i	−0.831659	+	0.132550i
$652$	1.86666e8	+	1.17639e8i	0.673478	+	0.424432i
$653$	−1.79441e8	+	1.79441e8i	−0.644439	+	0.644439i	−0.951643	−	0.307205i	$-0.900606\pi$
$653$	−1.79441e8	+	1.79441e8i	−0.644439	+	0.644439i	0.307205	+	0.951643i	$0.400606\pi$
$654$	−9.87958e7	+	2.72981e7i	−0.353187	+	0.0975885i
$655$	3.07025e8	+	3.03249e8i	1.09257	+	1.07913i
$656$	1.64124e8	+	3.43153e8i	0.581381	+	1.21556i
$657$	−2.02015e7	+	3.98388e7i	−0.0712340	+	0.140479i
$658$	3.29733e8	+	2.63314e8i	1.15740	+	0.924265i
$659$			4.79727e8i			1.67625i	0.545481	+	0.838123i	$0.316347\pi$
$659$			4.79727e8i			1.67625i	−0.545481	+	0.838123i	$0.683653\pi$
$660$	4.47649e8	−	1.82597e8i	1.55706	−	0.635128i
$661$	1.42041e8			0.491825			0.245913	−	0.969292i	$-0.420912\pi$
$661$	1.42041e8			0.491825			0.245913	+	0.969292i	$0.420912\pi$
$662$	7.30895e7	−	9.15257e7i	0.251931	−	0.315478i
$663$	1.42660e8	−	1.96756e8i	0.489510	−	0.675130i
$664$	−4.53761e8	+	1.57756e8i	−1.54997	+	0.538868i
$665$	605392.	+	9.78413e7i	0.00205860	+	0.332703i
$666$	−6.13505e7	−	1.34612e8i	−0.207680	−	0.455680i
$667$	1.41054e8	+	1.41054e8i	0.475343	+	0.475343i
$668$	−2.99755e8	−	1.88908e8i	−1.00563	−	0.633755i
$669$	2.61785e8	−	4.17234e7i	0.874312	−	0.139348i
$670$	6.93411e7	−	8.79422e7i	0.230551	−	0.292397i
$671$	−3.57371e8			−1.18291
$672$	−2.20418e7	+	3.15757e8i	−0.0726338	+	1.04051i
$673$	−1.35643e8	−	1.35643e8i	−0.444991	−	0.444991i	0.448694	−	0.893685i	$-0.351889\pi$
$673$	−1.35643e8	−	1.35643e8i	−0.444991	−	0.444991i	−0.893685	+	0.448694i	$0.851889\pi$
$674$	2.28874e8	−	2.56329e7i	0.747510	−	0.0837178i
$675$	−2.93913e8	−	9.05543e7i	−0.955670	−	0.294441i
$676$	2.07662e8	−	4.71053e7i	0.672229	−	0.152486i
$677$	3.82725e8	+	3.82725e8i	1.23345	+	1.23345i	0.962631	+	0.270817i	$0.0872940\pi$
$677$	3.82725e8	+	3.82725e8i	1.23345	+	1.23345i	0.270817	+	0.962631i	$0.412706\pi$
$678$	−7.79769e7	−	4.42144e7i	−0.250194	−	0.141865i
$679$	−3.63547e6			−0.0116132
$680$	−4.24682e8	−	2.02333e8i	−1.35063	−	0.643488i
$681$	1.87027e8	−	2.98084e7i	0.592192	−	0.0943838i
$682$	−2.68760e8	+	3.36552e8i	−0.847250	+	1.06096i
$683$	−4.39751e7	−	4.39751e7i	−0.138021	−	0.138021i	0.634721	−	0.772742i	$-0.281115\pi$
$683$	−4.39751e7	−	4.39751e7i	−0.138021	−	0.138021i	−0.772742	+	0.634721i	$0.781115\pi$
$684$	−8.75973e7	+	5.24089e7i	−0.273730	+	0.163771i
$685$	337178.	+	5.44936e7i	0.00104903	+	0.169540i
$686$	−3.05207e8	+	3.41818e7i	−0.945415	+	0.105882i
$687$	−1.16354e8	+	1.60475e8i	−0.358847	+	0.494921i
$688$	3.03492e7	−	8.59942e7i	0.0931927	−	0.264061i
$689$	1.60973e7			0.0492148
$690$	2.97126e8	−	8.40804e7i	0.904467	−	0.255946i
$691$		−	1.64739e8i		−	0.499300i	−0.968336	−	0.249650i	$-0.919684\pi$
$691$		−	1.64739e8i		−	0.499300i	0.968336	−	0.249650i	$-0.0803156\pi$
$692$	−2.93101e8	−	1.84715e8i	−0.884501	−	0.557421i
$693$	2.64005e8	−	5.20638e8i	0.793256	−	1.56436i
$694$	4.85218e8	−	5.43423e7i	1.45164	−	0.162577i
$695$	−2.33965e8	−	2.31088e8i	−0.696943	−	0.688371i
$696$	2.12445e8	−	1.14038e8i	0.630115	−	0.338238i
$697$	−4.82670e8	+	4.82670e8i	−1.42545	+	1.42545i
$698$	3.90436e7	−	4.88919e7i	0.114811	−	0.143771i
$699$	1.41752e8	−	2.25925e7i	0.415047	−	0.0661504i
$700$	−3.05008e8	−	1.86986e8i	−0.889236	−	0.545149i
$701$			1.02524e8i			0.297628i	0.988865	+	0.148814i	$0.0475455\pi$
$701$			1.02524e8i			0.297628i	−0.988865	+	0.148814i	$0.952454\pi$
$702$	1.88998e8	+	3.82557e7i	0.546320	+	0.110582i
$703$	3.92427e7	−	3.92427e7i	0.112952	−	0.112952i
$704$	3.63981e8	+	4.60195e8i	1.04318	+	1.31894i
$705$	−4.04641e8	−	2.89586e8i	−1.15479	−	0.826438i
$706$	−1.10957e8	+	1.24266e7i	−0.315311	+	0.0353134i
$707$	2.14880e8	−	2.14880e8i	0.608049	−	0.608049i
$708$	−3.59841e8	−	1.53960e8i	−1.01394	−	0.433817i
$709$			3.86424e8i			1.08424i	0.840301	+	0.542120i	$0.182378\pi$
$709$			3.86424e8i			1.08424i	−0.840301	+	0.542120i	$0.817622\pi$
$710$	−6.69976e7	−	5.66504e8i	−0.187191	−	1.58281i
$711$	9.41809e7	+	2.87954e8i	0.262032	+	0.801151i
$712$	2.81236e8	−	5.81007e8i	0.779167	−	1.60969i
$713$	−1.94521e8	+	1.94521e8i	−0.536658	+	0.536658i
$714$	−5.47490e8	+	1.51276e8i	−1.50412	+	0.415600i
$715$	−2.11991e6	−	3.42612e8i	−0.00579961	−	0.937312i
$716$	−4.82101e8	+	1.09358e8i	−1.31341	+	0.297928i
$717$	2.18279e8	−	3.01050e8i	0.592181	−	0.816735i
$718$	1.20956e8	−	1.51465e8i	0.326778	−	0.409204i
$719$		−	1.54874e7i		−	0.0416671i	−0.999783	−	0.0208335i	$-0.993368\pi$
$719$		−	1.54874e7i		−	0.0416671i	0.999783	−	0.0208335i	$-0.00663200\pi$
$720$	6.33950e6	−	3.73194e8i	0.0169847	−	0.999856i
$721$	2.34337e8			0.625224
$722$	2.64174e8	+	2.10961e8i	0.701906	+	0.560520i
$723$	3.24505e8	+	2.35286e8i	0.858631	+	0.622559i
$724$	−3.93556e7	−	1.73498e8i	−0.103703	−	0.457170i
$725$	3.37243e6	+	2.72510e8i	0.00884971	+	0.715102i
$726$	−1.86278e8	−	6.74169e8i	−0.486802	−	1.76181i
$727$	−5.11861e6	−	5.11861e6i	−0.0133214	−	0.0133214i	0.700415	−	0.713736i	$-0.252998\pi$
$727$	−5.11861e6	−	5.11861e6i	−0.0133214	−	0.0133214i	−0.713736	+	0.700415i	$0.752998\pi$
$728$	2.01906e8	+	9.77325e7i	0.523306	+	0.253306i
$729$	−3.14752e8	−	2.25889e8i	−0.812429	−	0.583060i
$730$	3.79382e7	−	4.81153e7i	0.0975232	−	0.123684i
$731$	1.63645e8			0.418940
$732$	−1.08530e8	+	2.53662e8i	−0.276706	+	0.646729i
$733$	4.35680e8	+	4.35680e8i	1.10626	+	1.10626i	0.993638	+	0.112617i	$0.0359233\pi$
$733$	4.35680e8	+	4.35680e8i	1.10626	+	1.10626i	0.112617	+	0.993638i	$0.464077\pi$
$734$	7.57595e7	+	6.76451e8i	0.191579	+	1.71060i
$735$	−3.44435e7	+	5.70837e6i	−0.0867451	+	0.0143764i
$736$	1.98322e8	+	3.17984e8i	0.497437	+	0.797575i
$737$	−1.77245e8	−	1.77245e8i	−0.442762	−	0.442762i
$738$	−5.07306e8	−	1.89658e8i	−1.26212	−	0.471849i
$739$	−6.07287e8			−1.50474			−0.752368	−	0.658743i	$-0.771088\pi$
$739$	−6.07287e8			−1.50474			−0.752368	+	0.658743i	$0.771088\pi$
$740$	4.61142e7	+	1.97617e8i	0.113799	+	0.487673i
$741$	1.13861e7	+	7.14396e7i	0.0279846	+	0.175584i
$742$	−2.93983e7	−	2.34766e7i	−0.0719633	−	0.0574676i
$743$	−2.65828e8	−	2.65828e8i	−0.648089	−	0.648089i	0.304442	−	0.952531i	$-0.401530\pi$
$743$	−2.65828e8	−	2.65828e8i	−0.648089	−	0.648089i	−0.952531	+	0.304442i	$0.901530\pi$
$744$	1.57265e8	+	2.92974e8i	0.381868	+	0.711394i
$745$	−2.50140e7	−	2.47064e7i	−0.0604943	−	0.0597503i
$746$	4.55782e7	+	4.06964e8i	0.109784	+	0.980257i
$747$	3.09349e8	−	6.10059e8i	0.742143	−	1.46356i
$748$	−5.61371e8	+	8.90769e8i	−1.34136	+	2.12843i
$749$	3.09734e7			0.0737129
$750$	3.70784e8	+	2.01240e8i	0.878896	+	0.477014i
$751$		−	4.46062e8i		−	1.05311i	−0.850140	−	0.526557i	$-0.823483\pi$
$751$		−	4.46062e8i		−	1.05311i	0.850140	−	0.526557i	$-0.176517\pi$
$752$	2.00976e8	−	5.69464e8i	0.472597	−	1.33910i
$753$	−2.86071e8	−	2.07419e8i	−0.670022	−	0.485806i
$754$	−1.90185e7	−	1.69815e8i	−0.0443672	−	0.396151i
$755$	3.97870e8	−	4.02824e8i	0.924486	−	0.935998i
$756$	−2.89373e8	−	3.45504e8i	−0.669719	−	0.799628i
$757$	4.01506e8	−	4.01506e8i	0.925560	−	0.925560i	−0.0718552	−	0.997415i	$-0.522892\pi$
$757$	4.01506e8	−	4.01506e8i	0.925560	−	0.925560i	0.997415	+	0.0718552i	$0.0228919\pi$
$758$	2.99726e8	+	2.39352e8i	0.688203	+	0.549577i
$759$	−1.08783e8	−	6.82535e8i	−0.248791	−	1.56099i
$760$	1.31973e8	−	4.67995e7i	0.300638	−	0.106611i
$761$		−	1.73669e8i		−	0.394064i	−0.980397	−	0.197032i	$-0.936870\pi$
$761$		−	1.73669e8i		−	0.394064i	0.980397	−	0.197032i	$-0.0631303\pi$
$762$	1.43575e7	−	2.53210e7i	0.0324500	−	0.0572290i
$763$	1.20044e8	−	1.20044e8i	0.270250	−	0.270250i
$764$	−1.35501e7	−	5.97354e7i	−0.0303853	−	0.133953i
$765$	6.35309e8	−	2.12150e8i	1.41906	−	0.473870i
$766$	−1.89094e7	−	1.68841e8i	−0.0420718	−	0.375656i
$767$	−1.96134e8	+	1.96134e8i	−0.434676	+	0.434676i
$768$	4.37184e8	−	1.18597e8i	0.965119	−	0.261812i
$769$			1.77705e8i			0.390771i	0.980727	+	0.195385i	$0.0625957\pi$
$769$			1.77705e8i			0.390771i	−0.980727	+	0.195385i	$0.937404\pi$
$770$	−4.95799e8	+	6.28800e8i	−1.08601	+	1.37734i
$771$	−8.14105e7	−	5.10794e8i	−0.177630	−	1.11451i
$772$	2.18847e7	−	3.47260e7i	0.0475651	−	0.0754750i
$773$	−1.76734e8	+	1.76734e8i	−0.382631	+	0.382631i	−0.872049	−	0.489418i	$-0.837209\pi$
$773$	−1.76734e8	+	1.76734e8i	−0.382631	+	0.382631i	0.489418	+	0.872049i	$0.337209\pi$
$774$	5.38480e7	+	1.18150e8i	0.116131	+	0.254807i
$775$	−3.75806e8	+	4.65077e6i	−0.807344	+	0.00999125i
$776$	1.70851e6	+	4.91426e6i	0.00365623	+	0.0105165i
$777$	1.98367e8	+	1.43828e8i	0.422870	+	0.306606i
$778$	4.78318e7	+	3.81970e7i	0.101573	+	0.0811130i
$779$		−	2.03183e8i		−	0.429808i
$780$	−2.43830e8	−	1.02543e8i	−0.513810	−	0.216085i
$781$	−1.27680e9			−2.68022
$782$	−4.19654e8	+	5.25508e8i	−0.877549	+	1.09890i
$783$	−1.05137e8	+	3.26815e8i	−0.219013	+	0.680796i
$784$	−1.82822e7	−	3.82248e7i	−0.0379386	−	0.0793225i
$785$	7.22779e8	−	4.47219e6i	1.49416	−	0.00924508i
$786$	−1.98600e8	−	7.18763e8i	−0.408989	−	1.48019i
$787$	6.66552e7	+	6.66552e7i	0.136745	+	0.136745i	0.772166	−	0.635421i	$-0.219173\pi$
$787$	6.66552e7	+	6.66552e7i	0.136745	+	0.136745i	−0.635421	+	0.772166i	$0.719173\pi$
$788$	−8.51579e7	+	1.35126e8i	−0.174039	+	0.276160i
$789$	9.43772e7	+	5.92151e8i	0.192148	+	1.20559i
$790$	−4.88095e7	−	4.12713e8i	−0.0989973	−	0.837081i
$791$	1.48471e8			0.299994
$792$	−8.27846e8	−	1.12193e8i	−1.66638	−	0.225835i
$793$	1.38260e8	+	1.38260e8i	0.277254	+	0.277254i
$794$	5.15672e8	−	5.77530e7i	1.03018	−	0.115375i
$795$	3.60770e7	+	2.58189e7i	0.0718007	+	0.0513850i
$796$	−1.03571e8	−	4.56591e8i	−0.205353	−	0.905291i
$797$	2.01411e8	+	2.01411e8i	0.397839	+	0.397839i	0.877470	−	0.479631i	$-0.159229\pi$
$797$	2.01411e8	+	2.01411e8i	0.397839	+	0.397839i	−0.479631	+	0.877470i	$0.659229\pi$
$798$	8.33944e7	−	1.47075e8i	0.164107	−	0.289421i
$799$	1.08368e9			2.12452
$800$	−1.09419e8	+	5.00172e8i	−0.213708	+	0.976898i
$801$	2.85707e8	+	8.73536e8i	0.555933	+	1.69974i
$802$	4.03346e8	−	5.05086e8i	0.781906	−	0.979135i
$803$	−9.69747e7	−	9.69747e7i	−0.187289	−	0.187289i
$804$	−1.79636e8	+	7.19807e7i	−0.345641	+	0.138499i
$805$	−3.59409e8	+	3.63885e8i	−0.688972	+	0.697551i
$806$	2.34184e8	−	2.62275e7i	0.447251	−	0.0500901i
$807$	7.20852e8	+	5.22661e8i	1.37159	+	0.994487i
$808$	−3.91450e8	−	1.89481e8i	−0.742066	−	0.359196i
$809$	−5.58607e8			−1.05502			−0.527511	−	0.849549i	$-0.676874\pi$
$809$	−5.58607e8			−1.05502			−0.527511	+	0.849549i	$0.676874\pi$
$810$	3.62221e8	+	3.88878e8i	0.681582	+	0.731742i
$811$		−	2.99089e8i		−	0.560709i	−0.959897	−	0.280354i	$-0.909548\pi$
$811$		−	2.99089e8i		−	0.560709i	0.959897	−	0.280354i	$-0.0904520\pi$
$812$	−2.12927e8	+	3.37867e8i	−0.397707	+	0.631071i
$813$	3.71094e8	−	5.11812e8i	0.690578	−	0.952443i
$814$	4.51373e8	−	5.05517e7i	0.836878	−	0.0937266i
$815$	4.30935e8	−	2.66640e6i	0.796047	−	0.00492553i
$816$	4.61785e8	+	6.68980e8i	0.849903	+	1.23124i
$817$	−3.44437e7	+	3.44437e7i	−0.0631603	+	0.0631603i
$818$	1.23933e8	−	1.55194e8i	0.226426	−	0.283540i
$819$	−3.03563e8	+	9.92862e7i	−0.552583	+	0.180733i
$820$	6.30970e8	+	3.92210e8i	1.14437	+	0.711340i
$821$		−	1.61243e8i		−	0.291375i	−0.989331	−	0.145687i	$-0.953461\pi$
$821$		−	1.61243e8i		−	0.291375i	0.989331	−	0.145687i	$-0.0465394\pi$
$822$	4.64472e7	−	8.19147e7i	0.0836266	−	0.147484i
$823$	−3.34968e8	+	3.34968e8i	−0.600902	+	0.600902i	−0.940552	−	0.339650i	$-0.889691\pi$
$823$	−3.34968e8	+	3.34968e8i	−0.600902	+	0.600902i	0.339650	+	0.940552i	$0.389691\pi$
$824$	−1.10128e8	−	3.16767e8i	−0.196842	−	0.566185i
$825$	5.44773e8	−	7.71255e8i	0.970183	−	1.37352i
$826$	6.44241e8	−	7.21521e7i	1.14316	−	0.128029i
$827$	1.07822e8	−	1.07822e8i	0.190631	−	0.190631i	−0.605338	−	0.795969i	$-0.706962\pi$
$827$	1.07822e8	−	1.07822e8i	0.190631	−	0.190631i	0.795969	+	0.605338i	$0.206962\pi$
$828$	−5.17500e8	−	1.30066e8i	−0.911631	−	0.229125i
$829$		−	7.46261e8i		−	1.30987i	−0.755686	−	0.654934i	$-0.772697\pi$
$829$		−	7.46261e8i		−	1.30987i	0.755686	−	0.654934i	$-0.227303\pi$
$830$	−5.80954e8	+	7.36798e8i	−1.01603	+	1.28859i
$831$	−5.83791e8	+	9.30449e7i	−1.01731	+	0.162140i
$832$	3.72233e7	−	3.18858e8i	0.0646315	−	0.553639i
$833$	5.37659e7	−	5.37659e7i	0.0930190	−	0.0930190i
$834$	1.51341e8	+	5.47726e8i	0.260891	+	0.944203i
$835$	−6.92008e8	+	4.28179e6i	−1.18864	+	0.00735472i
$836$	−6.93310e7	−	3.05643e8i	−0.118661	−	0.523114i
$837$	−4.50696e8	−	1.44989e8i	−0.768613	−	0.247263i
$838$	−1.07020e8	+	1.34014e8i	−0.181858	+	0.227730i
$839$		−	5.45946e8i		−	0.924408i	−0.886774	−	0.462204i	$-0.847059\pi$
$839$		−	5.45946e8i		−	0.924408i	0.886774	−	0.462204i	$-0.152941\pi$
$840$	2.95752e8	+	5.42879e8i	0.498989	+	0.915936i
$841$	−2.90601e8			−0.488550
$842$	−6.14117e8	−	4.90414e8i	−1.02876	−	0.821536i
$843$	2.49625e8	−	3.44282e8i	0.416682	−	0.574687i
$844$	2.84195e8	−	6.44657e7i	0.472704	−	0.107226i
$845$	2.92256e8	−	2.95895e8i	0.484388	−	0.490420i
$846$	3.56588e8	+	7.82405e8i	0.588919	+	1.29217i
$847$	8.19162e8	+	8.19162e8i	1.34809	+	1.34809i
$848$	−1.79186e7	+	5.07723e7i	−0.0293844	+	0.0832606i
$849$	3.45081e8	−	5.49991e7i	0.563894	−	0.0898737i
$850$	−9.11742e8	+	1.13552e8i	−1.48462	+	0.184900i
$851$	2.90103e8			0.470720
$852$	−3.87753e8	+	9.06275e8i	−0.626955	+	1.46535i
$853$	−6.14329e8	−	6.14329e8i	−0.989815	−	0.989815i	0.0101335	−	0.999949i	$-0.496774\pi$
$853$	−6.14329e8	−	6.14329e8i	−0.989815	−	0.989815i	−0.999949	+	0.0101335i	$0.996774\pi$
$854$	−5.08620e7	−	4.54143e8i	−0.0816620	−	0.729154i
$855$	−8.90656e7	+	1.78372e8i	−0.142499	+	0.285382i
$856$	−1.45562e7	−	4.18685e7i	−0.0232073	−	0.0667522i
$857$	1.95072e8	+	1.95072e8i	0.309922	+	0.309922i	0.844879	−	0.534957i	$-0.179672\pi$
$857$	1.95072e8	+	1.95072e8i	0.309922	+	0.309922i	−0.534957	+	0.844879i	$0.679672\pi$
$858$	−2.92023e8	+	5.15014e8i	−0.462333	+	0.815374i
$859$	8.40530e7			0.132609			0.0663046	−	0.997799i	$-0.478879\pi$
$859$	8.40530e7			0.132609			0.0663046	+	0.997799i	$0.478879\pi$
$860$	−4.04749e7	−	1.73451e8i	−0.0636342	−	0.272697i
$861$	8.85873e8	−	1.41191e8i	1.38791	−	0.221206i
$862$	−2.43289e8	−	1.94283e8i	−0.379840	−	0.303328i
$863$	−3.68625e8	−	3.68625e8i	−0.573525	−	0.573525i	0.359587	−	0.933112i	$-0.382918\pi$
$863$	−3.68625e8	−	3.68625e8i	−0.573525	−	0.573525i	−0.933112	+	0.359587i	$0.882918\pi$
$864$	−3.31044e8	+	5.53533e8i	−0.513269	+	0.858228i
$865$	−6.76647e8	+	4.18674e6i	−1.04548	+	0.00646887i
$866$	2.42635e7	+	2.16647e8i	0.0373593	+	0.333579i
$867$	−4.73713e8	+	6.53343e8i	−0.726871	+	1.00250i
$868$	−4.65937e8	−	2.93638e8i	−0.712473	−	0.449007i
$869$	−9.30184e8			−1.41746
$870$	2.29746e8	−	4.11090e8i	0.348892	−	0.624279i
$871$			1.37145e8i			0.207551i
$872$	−2.18685e8	−	1.05854e8i	−0.329815	−	0.159647i
$873$	−6.60698e6	−	3.35027e6i	−0.00993026	−	0.00503544i
$874$	−2.22799e7	−	1.98936e8i	−0.0333718	−	0.297974i
$875$	−6.98634e8	+	1.29697e7i	−1.04286	+	0.0193600i
$876$	−9.82831e7	+	3.93824e7i	−0.146206	+	0.0585854i
$877$	−2.82197e8	+	2.82197e8i	−0.418363	+	0.418363i	−0.884639	−	0.466276i	$-0.845595\pi$
$877$	−2.82197e8	+	2.82197e8i	−0.418363	+	0.418363i	0.466276	+	0.884639i	$0.345595\pi$
$878$	−4.57007e8	−	3.64951e8i	−0.675211	−	0.539202i
$879$	−4.80050e8	+	7.65106e7i	−0.706839	+	0.112656i
$880$	1.08299e9	+	3.74690e8i	1.58919	+	0.549825i
$881$		−	8.95804e8i		−	1.31004i	−0.755611	−	0.655021i	$-0.772660\pi$
$881$		−	8.95804e8i		−	1.31004i	0.755611	−	0.655021i	$-0.227340\pi$
$882$	5.65102e7	+	2.11265e7i	0.0823609	+	0.0307909i
$883$	5.14832e8	−	5.14832e8i	0.747797	−	0.747797i	−0.226268	−	0.974065i	$-0.572652\pi$
$883$	5.14832e8	−	5.14832e8i	0.747797	−	0.747797i	0.974065	+	0.226268i	$0.0726525\pi$
$884$	5.61805e8	−	1.27438e8i	0.813258	−	0.184476i
$885$	−7.54155e8	+	1.24987e8i	−1.08800	+	0.180316i
$886$	1.07691e8	+	9.61567e8i	0.154839	+	1.38254i
$887$	−8.33247e8	+	8.33247e8i	−1.19400	+	1.19400i	−0.218061	+	0.975935i	$0.569973\pi$
$887$	−8.33247e8	+	8.33247e8i	−1.19400	+	1.19400i	−0.975935	+	0.218061i	$0.930027\pi$
$888$	1.01196e8	−	3.35737e8i	0.144519	−	0.479468i
$889$			4.82123e7i			0.0686202i
$890$	−1.48068e8	−	1.25201e9i	−0.210035	−	1.77597i
$891$	9.59590e8	−	7.02896e8i	1.35660	−	0.993707i
$892$	5.31599e8	+	3.35019e8i	0.749014	+	0.472035i
$893$	−2.28091e8	+	2.28091e8i	−0.320297	+	0.320297i
$894$	1.61804e7	+	5.85592e7i	0.0226452	+	0.0819564i
$895$	−6.78491e8	+	6.86940e8i	−0.946401	+	0.958185i
$896$	−5.33008e8	+	5.28039e8i	−0.740985	+	0.734078i
$897$	−2.21974e8	+	3.06145e8i	−0.307556	+	0.424180i
$898$	7.11987e8	+	5.68571e8i	0.983203	+	0.785155i
$899$			4.19539e8i			0.577422i
$900$	−3.81995e8	−	6.20903e8i	−0.523998	−	0.851719i
$901$	−9.66187e7			−0.132095
$902$	1.03764e9	−	1.29938e9i	1.41393	−	1.77058i
$903$	−1.74109e8	−	1.26239e8i	−0.236460	−	0.171448i
$904$	−6.97750e7	−	2.00697e8i	−0.0944484	−	0.271666i
$905$	−2.47215e8	−	2.44174e8i	−0.333525	−	0.329423i
$906$	−9.43035e8	+	2.60568e8i	−1.26807	+	0.350378i
$907$	−2.07606e8	−	2.07606e8i	−0.278238	−	0.278238i	0.554167	−	0.832405i	$-0.313037\pi$
$907$	−2.07606e8	−	2.07606e8i	−0.278238	−	0.278238i	−0.832405	+	0.554167i	$0.813037\pi$
$908$	3.79790e8	+	2.39347e8i	0.507325	+	0.319721i
$909$	5.88540e8	−	1.92493e8i	0.783582	−	0.256285i
$910$	4.35085e8	−	5.14554e7i	0.577365	−	0.0682820i
$911$	9.38935e8			1.24188			0.620941	−	0.783857i	$-0.286751\pi$
$911$	9.38935e8			1.24188			0.620941	+	0.783857i	$0.286751\pi$
$912$	−2.38001e8	−	4.36099e7i	−0.313758	−	0.0574912i
$913$	1.48499e9	+	1.48499e9i	1.95125	+	1.95125i
$914$	7.49892e8	−	8.39846e7i	0.982110	−	0.109992i
$915$	8.81069e7	+	5.31625e8i	0.115013	+	0.693972i
$916$	−4.58209e8	+	1.03938e8i	−0.596179	+	0.135235i
$917$	8.73348e8	+	8.73348e8i	1.13261	+	1.13261i
$918$	−1.13440e9	−	2.29617e8i	−1.46635	−	0.296808i
$919$	−1.40696e8			−0.181274			−0.0906370	−	0.995884i	$-0.528890\pi$
$919$	−1.40696e8			−0.181274			−0.0906370	+	0.995884i	$0.528890\pi$
$920$	6.60790e8	+	3.14823e8i	0.848594	+	0.404300i
$921$	2.09643e8	+	1.31536e9i	0.268350	+	1.68371i
$922$	5.63546e8	−	7.05696e8i	0.719013	−	0.900378i
$923$	4.93970e8	+	4.93970e8i	0.628196	+	0.628196i
$924$	1.28442e9	−	5.14673e8i	1.62814	−	0.652402i
$925$	2.83701e8	+	2.76765e8i	0.358456	+	0.349692i
$926$	8.21864e8	−	9.20451e7i	1.03506	−	0.115922i
$927$	4.25877e8	+	2.15954e8i	0.534620	+	0.271096i
$928$	5.56780e8	+	1.29042e8i	0.696691	+	0.161469i
$929$	2.55592e8			0.318787			0.159393	−	0.987215i	$-0.449046\pi$
$929$	2.55592e8			0.318787			0.159393	+	0.987215i	$0.449046\pi$
$930$	5.66915e8	+	3.16833e8i	0.704805	+	0.393896i
$931$			2.26331e7i			0.0280475i
$932$	2.87852e8	+	1.81407e8i	0.355567	+	0.224081i
$933$	−3.99406e7	−	2.89593e7i	−0.0491779	−	0.0356569i
$934$	−1.80023e8	+	2.01618e7i	−0.220946	+	0.0247450i
$935$	1.27240e7	+	2.05641e9i	0.0155665	+	2.51580i
$936$	2.76872e8	+	3.63683e8i	0.337638	+	0.443502i
$937$	−1.54493e8	+	1.54493e8i	−0.187798	+	0.187798i	−0.794743	−	0.606946i	$-0.792395\pi$
$937$	−1.54493e8	+	1.54493e8i	−0.187798	+	0.187798i	0.606946	+	0.794743i	$0.292395\pi$
$938$	2.00014e8	−	2.50466e8i	0.242355	−	0.303487i
$939$	3.26335e7	+	2.04753e8i	0.0394155	+	0.247305i
$940$	−2.68030e8	−	1.14861e9i	−0.322701	−	1.38290i
$941$			6.51835e8i			0.782292i	0.920329	+	0.391146i	$0.127921\pi$
$941$			6.51835e8i			0.782292i	−0.920329	+	0.391146i	$0.872079\pi$
$942$	−1.08648e9	−	6.16056e8i	−1.29978	−	0.737000i
$943$	7.51017e8	−	7.51017e8i	0.895601	−	0.895601i
$944$	−4.00297e8	−	8.36947e8i	−0.475846	−	0.994906i
$945$	−8.39588e8	−	2.64375e8i	−0.994881	−	0.313275i
$946$	−3.96175e8	+	4.43698e7i	−0.467965	+	0.0524100i
$947$	−1.12697e7	+	1.12697e7i	−0.0132697	+	0.0132697i	−0.713711	−	0.700441i	$-0.752987\pi$
$947$	−1.12697e7	+	1.12697e7i	−0.0132697	+	0.0132697i	0.700441	+	0.713711i	$0.252987\pi$
$948$	−2.82489e8	+	6.60245e8i	−0.331570	+	0.774962i
$949$			7.50353e7i			0.0877944i
$950$	1.68002e8	−	2.15802e8i	0.195949	−	0.251701i
$951$	9.68698e7	+	6.07790e8i	0.112628	+	0.706663i
$952$	−1.21187e9	−	5.86607e8i	−1.40458	−	0.679886i
$953$	7.27640e8	−	7.27640e8i	0.840694	−	0.840694i	−0.148255	−	0.988949i	$-0.547366\pi$
$953$	7.27640e8	−	7.27640e8i	0.840694	−	0.840694i	0.988949	+	0.148255i	$0.0473657\pi$
$954$	−3.17927e7	−	6.97577e7i	−0.0366170	−	0.0803428i
$955$	−8.51162e7	−	8.40694e7i	−0.0977242	−	0.0965223i
$956$	8.59598e8	−	1.94988e8i	0.983834	−	0.223169i
$957$	−8.53351e8	−	6.18730e8i	−0.973625	−	0.705936i
$958$	−7.13312e8	+	8.93239e8i	−0.811303	+	1.01595i
$959$			1.55969e8i			0.176841i
$960$	5.94848e8	−	6.54915e8i	0.672346	−	0.740237i
$961$	3.08936e8			0.348095
$962$	−1.94185e8	−	1.55070e8i	−0.218117	−	0.174182i
$963$	5.62901e7	+	2.85436e7i	0.0630308	+	0.0319617i
$964$	2.10180e8	+	9.26571e8i	0.234617	+	1.03430i
$965$	−496038.	−	8.01679e7i	−0.000551992	−	0.0892110i
$966$	8.51875e8	−	2.35380e8i	0.945028	−	0.261119i
$967$	3.02595e8	+	3.02595e8i	0.334644	+	0.334644i	0.854347	−	0.519703i	$-0.173957\pi$
$967$	3.02595e8	+	3.02595e8i	0.334644	+	0.334644i	−0.519703	+	0.854347i	$0.673957\pi$
$968$	7.22336e8	−	1.49228e9i	0.796367	−	1.64522i
$969$	−6.83411e7	−	4.28792e8i	−0.0751122	−	0.471276i
$970$	7.97957e6	+	6.29177e6i	0.00874308	+	0.00689379i
$971$	−5.31982e8			−0.581084			−0.290542	−	0.956862i	$-0.593836\pi$
$971$	−5.31982e8			−0.581084			−0.290542	+	0.956862i	$0.593836\pi$
$972$	−2.07497e8	−	8.94581e8i	−0.225951	−	0.974139i
$973$	−6.65526e8	−	6.65526e8i	−0.722481	−	0.722481i
$974$	8.65567e7	+	7.72858e8i	0.0936750	+	0.836417i
$975$	−5.09146e8	+	8.76216e7i	−0.549324	+	0.0945360i
$976$	−5.89988e8	+	2.82181e8i	−0.634590	+	0.303513i
$977$	−9.63131e8	−	9.63131e8i	−1.03277	−	1.03277i	−0.999445	−	0.0333211i	$-0.989392\pi$
$977$	−9.63131e8	−	9.63131e8i	−1.03277	−	1.03277i	−0.0333211	−	0.999445i	$-0.510608\pi$
$978$	−6.47781e8	−	3.67305e8i	−0.692487	−	0.392654i
$979$	−2.82180e9			−3.00731
$980$	−7.02855e7	−	4.36893e7i	−0.0746771	−	0.0464191i
$981$	3.28791e8	−	1.07537e8i	0.348267	−	0.113907i
$982$	−5.32837e8	−	4.25506e8i	−0.562678	−	0.449337i
$983$	1.27322e6	+	1.27322e6i	0.00134043	+	0.00134043i	0.707777	−	0.706436i	$-0.249698\pi$
$983$	1.27322e6	+	1.27322e6i	0.00134043	+	0.00134043i	−0.706436	+	0.707777i	$0.749698\pi$
$984$	−6.07178e8	−	1.13113e9i	−0.637280	−	1.18721i
$985$	1.93019e6	+	3.11950e8i	0.00201972	+	0.326420i
$986$	1.14152e8	+	1.01926e9i	0.119084	+	1.06329i
$987$	−1.15297e9	−	8.35973e8i	−1.19913	−	0.869442i
$988$	−9.14247e7	+	1.45070e8i	−0.0947966	+	0.150421i
$989$	−2.54626e8			−0.263217
$990$	−1.48052e9	+	6.85856e8i	−1.52584	+	0.706850i
$991$		−	8.48500e8i		−	0.871829i	−0.899988	−	0.435914i	$-0.856425\pi$
$991$		−	8.48500e8i		−	0.871829i	0.899988	−	0.435914i	$-0.143575\pi$
$992$	−1.77956e8	+	7.67831e8i	−0.182297	+	0.786557i
$993$	−2.32045e8	+	3.20036e8i	−0.236987	+	0.326852i
$994$	−1.81718e8	−	1.62255e9i	−0.185028	−	1.65210i
$995$	−6.50592e8	−	6.42590e8i	−0.660449	−	0.652326i
$996$	1.50503e9	−	6.03069e8i	1.52323	−	0.610364i
$997$	3.48572e8	−	3.48572e8i	0.351728	−	0.351728i	−0.509024	−	0.860752i	$-0.669994\pi$
$997$	3.48572e8	−	3.48572e8i	0.351728	−	0.351728i	0.860752	+	0.509024i	$0.169994\pi$
$998$	−1.07597e9	−	8.59234e8i	−1.08245	−	0.864410i
$999$	2.27961e8	+	4.44194e8i	0.228646	+	0.445529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.16	✓	136
3.2	odd	2	inner	60.7.l.a.23.53	yes	136
4.3	odd	2	inner	60.7.l.a.23.19	yes	136
5.2	odd	4	inner	60.7.l.a.47.50	yes	136
12.11	even	2	inner	60.7.l.a.23.50	yes	136
15.2	even	4	inner	60.7.l.a.47.19	yes	136
20.7	even	4	inner	60.7.l.a.47.53	yes	136
60.47	odd	4	inner	60.7.l.a.47.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.16	✓	136	1.1	even	1	trivial
60.7.l.a.23.19	yes	136	4.3	odd	2	inner
60.7.l.a.23.50	yes	136	12.11	even	2	inner
60.7.l.a.23.53	yes	136	3.2	odd	2	inner
60.7.l.a.47.16	yes	136	60.47	odd	4	inner
60.7.l.a.47.19	yes	136	15.2	even	4	inner
60.7.l.a.47.50	yes	136	5.2	odd	4	inner
60.7.l.a.47.53	yes	136	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.25131 - 4.99210i) q^{2} +(21.8589 + 15.8490i) q^{3} +(14.1578 + 62.4144i) q^{4} +(88.9335 + 87.8398i) q^{5} +(-57.5269 - 208.199i) q^{6} +(252.976 + 252.976i) q^{7} +(223.074 - 460.849i) q^{8} +(226.620 + 692.881i) q^{9} +O(q^{10})\)	\(q+(-6.25131 - 4.99210i) q^{2} +(21.8589 + 15.8490i) q^{3} +(14.1578 + 62.4144i) q^{4} +(88.9335 + 87.8398i) q^{5} +(-57.5269 - 208.199i) q^{6} +(252.976 + 252.976i) q^{7} +(223.074 - 460.849i) q^{8} +(226.620 + 692.881i) q^{9} +(-117.447 - 993.079i) q^{10} -2238.23 q^{11} +(-679.730 + 1588.69i) q^{12} +(865.927 + 865.927i) q^{13} +(-318.550 - 2844.31i) q^{14} +(551.816 + 3329.58i) q^{15} +(-3695.11 + 1767.31i) q^{16} +(-5197.44 - 5197.44i) q^{17} +(2042.26 - 5462.73i) q^{18} +2187.89 q^{19} +(-4223.36 + 6794.35i) q^{20} +(1520.36 + 9539.18i) q^{21} +(13991.9 + 11173.5i) q^{22} +(8087.03 + 8087.03i) q^{23} +(12180.1 - 6538.15i) q^{24} +(193.352 + 15623.8i) q^{25} +(-1090.39 - 9735.98i) q^{26} +(-6027.80 + 18737.3i) q^{27} +(-12207.7 + 19370.9i) q^{28} +17442.0 q^{29} +(13172.0 - 23569.0i) q^{30} +24053.4i q^{31} +(31921.9 + 7398.38i) q^{32} +(-48925.1 - 35473.6i) q^{33} +(6544.68 + 58437.0i) q^{34} +(276.701 + 44719.4i) q^{35} +(-40037.3 + 23954.1i) q^{36} +(17936.3 - 17936.3i) q^{37} +(-13677.2 - 10922.2i) q^{38} +(5204.13 + 32652.2i) q^{39} +(60319.6 - 21390.2i) q^{40} -92866.9i q^{41} +(38116.3 - 67222.2i) q^{42} +(-15742.9 + 15742.9i) q^{43} +(-31688.5 - 139698. i) q^{44} +(-40708.4 + 81526.6i) q^{45} +(-10183.3 - 90925.8i) q^{46} +(-104251. + 104251. i) q^{47} +(-108781. - 19932.4i) q^{48} +10344.7i q^{49} +(76786.9 - 98634.5i) q^{50} +(-31236.0 - 195984. i) q^{51} +(-41786.6 + 66306.0i) q^{52} +(9294.84 - 9294.84i) q^{53} +(131220. - 87041.3i) q^{54} +(-199054. - 196605. i) q^{55} +(173016. - 60151.5i) q^{56} +(47824.9 + 34675.9i) q^{57} +(-109035. - 87072.1i) q^{58} +226501. i q^{59} +(-200001. + 81581.0i) q^{60} +159667. q^{61} +(120077. - 150366. i) q^{62} +(-117953. + 232612. i) q^{63} +(-162620. - 205607. i) q^{64} +(947.136 + 153073. i) q^{65} +(128758. + 465996. i) q^{66} +(79189.7 + 79189.7i) q^{67} +(250810. - 397979. i) q^{68} +(48602.1 + 304944. i) q^{69} +(221514. - 280936. i) q^{70} +570452. q^{71} +(369867. + 50126.0i) q^{72} +(43326.6 + 43326.6i) q^{73} +(-201665. + 22585.6i) q^{74} +(-243395. + 344583. i) q^{75} +(30975.9 + 136556. i) q^{76} +(-566218. - 566218. i) q^{77} +(130471. - 230099. i) q^{78} +415590. q^{79} +(-483859. - 167405. i) q^{80} +(-428728. + 314041. i) q^{81} +(-463601. + 580540. i) q^{82} +(-663468. - 663468. i) q^{83} +(-573857. + 229946. i) q^{84} +(-5684.87 - 918768. i) q^{85} +(177004. - 19823.6i) q^{86} +(381262. + 276437. i) q^{87} +(-499290. + 1.03149e6i) q^{88} +1.26073e6 q^{89} +(661470. - 306428. i) q^{90} +438117. i q^{91} +(-390252. + 619242. i) q^{92} +(-381222. + 525781. i) q^{93} +(1.17214e6 - 131275. i) q^{94} +(194577. + 192184. i) q^{95} +(580519. + 667649. i) q^{96} +(-7185.40 + 7185.40i) q^{97} +(51641.7 - 64667.9i) q^{98} +(-507227. - 1.55083e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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