LMFDB - Embedded newform 60.7.l.a.23.5

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			23.5
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.81252 - 1.72179i) q^{2} +(14.1892 - 22.9710i) q^{3} +(58.0709 + 26.9030i) q^{4} +(-24.8314 + 122.509i) q^{5} +(-150.404 + 155.031i) q^{6} +(-49.7637 - 49.7637i) q^{7} +(-407.358 - 310.166i) q^{8} +(-326.336 - 651.879i) q^{9} +O(q^{10})$	\(q+(-7.81252 - 1.72179i) q^{2} +(14.1892 - 22.9710i) q^{3} +(58.0709 + 26.9030i) q^{4} +(-24.8314 + 122.509i) q^{5} +(-150.404 + 155.031i) q^{6} +(-49.7637 - 49.7637i) q^{7} +(-407.358 - 310.166i) q^{8} +(-326.336 - 651.879i) q^{9} +(404.930 - 914.348i) q^{10} +258.225 q^{11} +(1441.97 - 952.216i) q^{12} +(-795.352 - 795.352i) q^{13} +(303.097 + 474.462i) q^{14} +(2461.82 + 2308.70i) q^{15} +(2648.45 + 3124.56i) q^{16} +(-3862.39 - 3862.39i) q^{17} +(1427.11 + 5654.70i) q^{18} -4588.60 q^{19} +(-4737.84 + 6446.15i) q^{20} +(-1849.23 + 437.018i) q^{21} +(-2017.39 - 444.609i) q^{22} +(-4613.38 - 4613.38i) q^{23} +(-12904.9 + 4956.44i) q^{24} +(-14391.8 - 6084.12i) q^{25} +(4844.27 + 7583.13i) q^{26} +(-19604.8 - 1753.35i) q^{27} +(-1551.03 - 4228.62i) q^{28} -33770.8 q^{29} +(-15257.9 - 22275.5i) q^{30} +49545.0i q^{31} +(-15311.3 - 28970.8i) q^{32} +(3663.99 - 5931.69i) q^{33} +(23524.7 + 36825.2i) q^{34} +(7332.19 - 4860.79i) q^{35} +(-1413.09 - 46634.6i) q^{36} +(16859.7 - 16859.7i) q^{37} +(35848.6 + 7900.61i) q^{38} +(-29555.4 + 6984.67i) q^{39} +(48113.4 - 42203.1i) q^{40} +44061.9i q^{41} +(15199.6 - 230.230i) q^{42} +(-93777.7 + 93777.7i) q^{43} +(14995.3 + 6947.03i) q^{44} +(87964.2 - 23791.9i) q^{45} +(28098.8 + 43985.4i) q^{46} +(43017.2 - 43017.2i) q^{47} +(109354. - 16502.8i) q^{48} -112696. i q^{49} +(101961. + 72312.0i) q^{50} +(-143527. + 33919.0i) q^{51} +(-24789.4 - 67584.1i) q^{52} +(157619. - 157619. i) q^{53} +(150144. + 47453.3i) q^{54} +(-6412.08 + 31634.8i) q^{55} +(4836.65 + 35706.7i) q^{56} +(-65108.4 + 105405. i) q^{57} +(263835. + 58146.1i) q^{58} -245373. i q^{59} +(80848.8 + 200298. i) q^{60} -342590. q^{61} +(85306.0 - 387071. i) q^{62} +(-16200.2 + 48679.6i) q^{63} +(69737.8 + 252698. i) q^{64} +(117187. - 77687.9i) q^{65} +(-38838.1 + 40032.8i) q^{66} +(-151420. - 151420. i) q^{67} +(-120382. - 328202. i) q^{68} +(-171434. + 40514.1i) q^{69} +(-65652.1 + 25350.5i) q^{70} +138995. q^{71} +(-69255.2 + 366767. i) q^{72} +(19031.6 + 19031.6i) q^{73} +(-160745. + 102688. i) q^{74} +(-343966. + 244266. i) q^{75} +(-266464. - 123447. i) q^{76} +(-12850.2 - 12850.2i) q^{77} +(242928. - 3679.67i) q^{78} +489634. q^{79} +(-448551. + 246872. i) q^{80} +(-318451. + 425463. i) q^{81} +(75865.4 - 344235. i) q^{82} +(325196. + 325196. i) q^{83} +(-119143. - 24371.8i) q^{84} +(569085. - 377268. i) q^{85} +(894105. - 571174. i) q^{86} +(-479179. + 775749. i) q^{87} +(-105190. - 80092.6i) q^{88} -1.07586e6 q^{89} +(-728187. + 34419.1i) q^{90} +79159.3i q^{91} +(-143789. - 392017. i) q^{92} +(1.13810e6 + 703001. i) q^{93} +(-410140. + 262006. i) q^{94} +(113941. - 562144. i) q^{95} +(-882743. - 59356.1i) q^{96} +(857855. - 857855. i) q^{97} +(-194039. + 880441. i) q^{98} +(-84268.0 - 168331. i) 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 $

$2$	−7.81252	−	1.72179i	−0.976565	−	0.215224i
$2$	−7.81252	−	1.72179i	−0.976565	−	0.215224i
$3$	14.1892	−	22.9710i	0.525524	−	0.850779i
$3$	14.1892	−	22.9710i	0.525524	−	0.850779i
$4$	58.0709	+	26.9030i	0.907358	+	0.420360i
$5$	−24.8314	+	122.509i	−0.198651	+	0.980070i
$5$	−24.8314	+	122.509i	−0.198651	+	0.980070i
$6$	−150.404	+	155.031i	−0.696316	+	0.717735i
$7$	−49.7637	−	49.7637i	−0.145084	−	0.145084i	0.630834	−	0.775918i	$-0.282713\pi$
$7$	−49.7637	−	49.7637i	−0.145084	−	0.145084i	−0.775918	+	0.630834i	$0.782713\pi$
$8$	−407.358	−	310.166i	−0.795622	−	0.605793i
$9$	−326.336	−	651.879i	−0.447648	−	0.894210i
$10$	404.930	−	914.348i	0.404930	−	0.914348i
$11$	258.225			0.194008			0.0970041	−	0.995284i	$-0.469074\pi$
$11$	258.225			0.194008			0.0970041	+	0.995284i	$0.469074\pi$
$12$	1441.97	−	952.216i	0.834472	−	0.551051i
$13$	−795.352	−	795.352i	−0.362017	−	0.362017i	0.502538	−	0.864555i	$-0.332400\pi$
$13$	−795.352	−	795.352i	−0.362017	−	0.362017i	−0.864555	+	0.502538i	$0.832400\pi$
$14$	303.097	+	474.462i	0.110458	+	0.172909i
$15$	2461.82	+	2308.70i	0.729427	+	0.684059i
$16$	2648.45	+	3124.56i	0.646595	+	0.762833i
$17$	−3862.39	−	3862.39i	−0.786156	−	0.786156i	0.194705	−	0.980862i	$-0.437625\pi$
$17$	−3862.39	−	3862.39i	−0.786156	−	0.786156i	−0.980862	+	0.194705i	$0.937625\pi$
$18$	1427.11	+	5654.70i	0.244703	+	0.969598i
$19$	−4588.60			−0.668990			−0.334495	−	0.942397i	$-0.608566\pi$
$19$	−4588.60			−0.668990			−0.334495	+	0.942397i	$0.608566\pi$
$20$	−4737.84	+	6446.15i	−0.592230	+	0.805769i
$21$	−1849.23	+	437.018i	−0.199679	+	0.0471891i
$22$	−2017.39	−	444.609i	−0.189462	−	0.0417552i
$23$	−4613.38	−	4613.38i	−0.379171	−	0.379171i	0.491632	−	0.870803i	$-0.336401\pi$
$23$	−4613.38	−	4613.38i	−0.379171	−	0.379171i	−0.870803	+	0.491632i	$0.836401\pi$
$24$	−12904.9	+	4956.44i	−0.933515	+	0.358539i
$25$	−14391.8	−	6084.12i	−0.921076	−	0.389384i
$26$	4844.27	+	7583.13i	0.275619	+	0.431448i
$27$	−19604.8	−	1753.35i	−0.996025	−	0.0890792i
$28$	−1551.03	−	4228.62i	−0.0706554	−	0.192630i
$29$	−33770.8			−1.38467			−0.692336	−	0.721575i	$-0.743418\pi$
$29$	−33770.8			−1.38467			−0.692336	+	0.721575i	$0.743418\pi$
$30$	−15257.9	−	22275.5i	−0.565107	−	0.825018i
$31$			49545.0i			1.66308i	0.555461	+	0.831542i	$0.312542\pi$
$31$			49545.0i			1.66308i	−0.555461	+	0.831542i	$0.687458\pi$
$32$	−15311.3	−	28970.8i	−0.467262	−	0.884119i
$33$	3663.99	−	5931.69i	0.101956	−	0.165058i
$34$	23524.7	+	36825.2i	0.598533	+	0.936932i
$35$	7332.19	−	4860.79i	0.171013	−	0.113371i
$36$	−1413.09	−	46634.6i	−0.0302874	−	0.999541i
$37$	16859.7	−	16859.7i	0.332846	−	0.332846i	−0.520820	−	0.853666i	$-0.674374\pi$
$37$	16859.7	−	16859.7i	0.332846	−	0.332846i	0.853666	+	0.520820i	$0.174374\pi$
$38$	35848.6	+	7900.61i	0.653312	+	0.143983i
$39$	−29555.4	+	6984.67i	−0.498245	+	0.117748i
$40$	48113.4	−	42203.1i	0.751771	−	0.659424i
$41$			44061.9i			0.639311i	0.947534	+	0.319655i	$0.103567\pi$
$41$			44061.9i			0.639311i	−0.947534	+	0.319655i	$0.896433\pi$
$42$	15199.6	−	230.230i	0.205156	−	0.00310753i
$43$	−93777.7	+	93777.7i	−1.17949	+	1.17949i	−0.199615	+	0.979874i	$0.563969\pi$
$43$	−93777.7	+	93777.7i	−1.17949	+	1.17949i	−0.979874	+	0.199615i	$0.936031\pi$
$44$	14995.3	+	6947.03i	0.176035	+	0.0815532i
$45$	87964.2	−	23791.9i	0.965314	−	0.261091i
$46$	28098.8	+	43985.4i	0.288679	+	0.451892i
$47$	43017.2	−	43017.2i	0.414333	−	0.414333i	−0.468912	−	0.883245i	$-0.655354\pi$
$47$	43017.2	−	43017.2i	0.414333	−	0.414333i	0.883245	+	0.468912i	$0.155354\pi$
$48$	109354.	−	16502.8i	0.988804	−	0.149222i
$49$		−	112696.i		−	0.957901i
$50$	101961.	+	72312.0i	0.815685	+	0.578496i
$51$	−143527.	+	33919.0i	−1.08199	+	0.255701i
$52$	−24789.4	−	67584.1i	−0.176302	−	0.480656i
$53$	157619.	−	157619.i	1.05872	−	1.05872i	0.0605514	−	0.998165i	$-0.480714\pi$
$53$	157619.	−	157619.i	1.05872	−	1.05872i	0.998165	−	0.0605514i	$-0.0192859\pi$
$54$	150144.	+	47453.3i	0.953511	+	0.301360i
$55$	−6412.08	+	31634.8i	−0.0385399	+	0.190142i
$56$	4836.65	+	35706.7i	0.0275410	+	0.203323i
$57$	−65108.4	+	105405.i	−0.351571	+	0.569163i
$58$	263835.	+	58146.1i	1.35222	+	0.298014i
$59$		−	245373.i		−	1.19473i	−0.801969	−	0.597366i	$-0.796214\pi$
$59$		−	245373.i		−	1.19473i	0.801969	−	0.597366i	$-0.203786\pi$
$60$	80848.8	+	200298.i	0.374300	+	0.927308i
$61$	−342590.			−1.50933			−0.754667	−	0.656108i	$-0.772201\pi$
$61$	−342590.			−1.50933			−0.754667	+	0.656108i	$0.772201\pi$
$62$	85306.0	−	387071.i	0.357935	−	1.62411i
$63$	−16200.2	+	48679.6i	−0.0647888	+	0.194682i
$64$	69737.8	+	252698.i	0.266029	+	0.963965i
$65$	117187.	−	77687.9i	0.426717	−	0.282887i
$66$	−38838.1	+	40032.8i	−0.135091	+	0.139246i
$67$	−151420.	−	151420.i	−0.503453	−	0.503453i	0.409056	−	0.912509i	$-0.365858\pi$
$67$	−151420.	−	151420.i	−0.503453	−	0.503453i	−0.912509	+	0.409056i	$0.865858\pi$
$68$	−120382.	−	328202.i	−0.382856	−	1.04379i
$69$	−171434.	+	40514.1i	−0.521855	+	0.123327i
$70$	−65652.1	+	25350.5i	−0.191406	+	0.0739082i
$71$	138995.			0.388350			0.194175	−	0.980967i	$-0.437797\pi$
$71$	138995.			0.388350			0.194175	+	0.980967i	$0.437797\pi$
$72$	−69255.2	+	366767.i	−0.185547	+	0.982635i
$73$	19031.6	+	19031.6i	0.0489222	+	0.0489222i	0.731145	−	0.682222i	$-0.238986\pi$
$73$	19031.6	+	19031.6i	0.0489222	+	0.0489222i	−0.682222	+	0.731145i	$0.738986\pi$
$74$	−160745.	+	102688.i	−0.396682	+	0.253410i
$75$	−343966.	+	244266.i	−0.815327	+	0.579001i
$76$	−266464.	−	123447.i	−0.607013	−	0.281217i
$77$	−12850.2	−	12850.2i	−0.0281474	−	0.0281474i
$78$	242928.	−	3679.67i	0.511911	−	0.00775399i
$79$	489634.			0.993094			0.496547	−	0.868010i	$-0.334601\pi$
$79$	489634.			0.993094			0.496547	+	0.868010i	$0.334601\pi$
$80$	−448551.	+	246872.i	−0.876077	+	0.482171i
$81$	−318451.	+	425463.i	−0.599222	+	0.800583i
$82$	75865.4	−	344235.i	0.137595	−	0.624328i
$83$	325196.	+	325196.i	0.568737	+	0.568737i	0.931774	−	0.363038i	$-0.118260\pi$
$83$	325196.	+	325196.i	0.568737	+	0.568737i	−0.363038	+	0.931774i	$0.618260\pi$
$84$	−119143.	−	24371.8i	−0.201017	−	0.0411197i
$85$	569085.	−	377268.i	0.926659	−	0.614318i
$86$	894105.	−	571174.i	1.40570	−	0.897994i
$87$	−479179.	+	775749.i	−0.727679	+	1.17805i
$88$	−105190.	−	80092.6i	−0.154357	−	0.117529i
$89$	−1.07586e6			−1.52611			−0.763053	−	0.646336i	$-0.776301\pi$
$89$	−1.07586e6			−1.52611			−0.763053	+	0.646336i	$0.776301\pi$
$90$	−728187.	+	34419.1i	−0.998885	+	0.0472141i
$91$			79159.3i			0.105046i
$92$	−143789.	−	392017.i	−0.184656	−	0.503432i
$93$	1.13810e6	+	703001.i	1.41492	+	0.873991i
$94$	−410140.	+	262006.i	−0.493797	+	0.315448i
$95$	113941.	−	562144.i	0.132896	−	0.655658i
$96$	−882743.	−	59356.1i	−0.997747	−	0.0670890i
$97$	857855.	−	857855.i	0.939937	−	0.939937i	−0.0583584	−	0.998296i	$-0.518587\pi$
$97$	857855.	−	857855.i	0.939937	−	0.939937i	0.998296	+	0.0583584i	$0.0185866\pi$
$98$	−194039.	+	880441.i	−0.206163	+	0.935453i
$99$	−84268.0	−	168331.i	−0.0868474	−	0.173484i
$100$	−672064.	−	740493.i	−0.672064	−	0.740493i
$101$			7248.69i			0.00703550i	0.999994	+	0.00351775i	$0.00111974\pi$
$101$			7248.69i			0.00703550i	−0.999994	+	0.00351775i	$0.998880\pi$
$102$	1.17971e6	−	17869.2i	1.11167	−	0.0168386i
$103$	1.34034e6	−	1.34034e6i	1.22660	−	1.22660i	0.261362	−	0.965241i	$-0.415828\pi$
$103$	1.34034e6	−	1.34034e6i	1.22660	−	1.22660i	0.965241	−	0.261362i	$-0.0841716\pi$
$104$	77302.0	+	570684.i	0.0687212	+	0.507336i
$105$	−7619.69	−	237398.i	−0.00658218	−	0.205074i
$106$	−1.50278e6	+	960012.i	−1.26177	+	0.806044i
$107$	−133697.	+	133697.i	−0.109137	+	0.109137i	−0.759567	−	0.650430i	$-0.774589\pi$
$107$	−133697.	+	133697.i	−0.109137	+	0.109137i	0.650430	+	0.759567i	$0.274589\pi$
$108$	−1.09129e6	−	629246.i	−0.866305	−	0.499515i
$109$			623379.i			0.481363i	0.970604	+	0.240682i	$0.0773709\pi$
$109$			623379.i			0.481363i	−0.970604	+	0.240682i	$0.922629\pi$
$110$	104563.	−	236107.i	0.0785597	−	0.177391i
$111$	−148059.	−	626508.i	−0.108260	−	0.458097i
$112$	23693.0	−	287287.i	0.0168642	−	0.204485i
$113$	−1.10892e6	+	1.10892e6i	−0.768535	+	0.768535i	−0.977849	−	0.209314i	$-0.932877\pi$
$113$	−1.10892e6	+	1.10892e6i	−0.768535	+	0.768535i	0.209314	+	0.977849i	$0.432877\pi$
$114$	690146.	−	711375.i	0.465829	−	0.480158i
$115$	679736.	−	450623.i	0.446937	−	0.296292i
$116$	−1.96110e6	−	908536.i	−1.25639	−	0.582060i
$117$	−258921.	+	778025.i	−0.161663	+	0.485776i
$118$	−422481.	+	1.91698e6i	−0.257135	+	1.16673i
$119$			384413.i			0.228117i
$120$	−286761.	−	1.70404e6i	−0.165950	−	0.986134i
$121$	−1.70488e6			−0.962361
$122$	2.67649e6	+	589868.i	1.47396	+	0.324844i
$123$	1.01215e6	+	625202.i	0.543912	+	0.335973i
$124$	−1.33291e6	+	2.87712e6i	−0.699094	+	1.50901i
$125$	1.10273e6	−	1.61205e6i	0.564596	−	0.825367i
$126$	210381.	−	352417.i	0.105171	−	0.176175i
$127$	−80798.8	−	80798.8i	−0.0394452	−	0.0394452i	0.687109	−	0.726554i	$-0.258879\pi$
$127$	−80798.8	−	80798.8i	−0.0394452	−	0.0394452i	−0.726554	+	0.687109i	$0.758879\pi$
$128$	−109736.	−	2.09428e6i	−0.0523261	−	0.998630i
$129$	823543.	+	3.48479e6i	0.383634	+	1.62333i
$130$	−1.04929e6	+	405166.i	−0.477601	+	0.184418i
$131$	1.46325e6			0.650887			0.325443	−	0.945562i	$-0.394486\pi$
$131$	1.46325e6			0.650887			0.325443	+	0.945562i	$0.394486\pi$
$132$	372352.	−	245886.i	0.161894	−	0.106908i
$133$	228346.	+	228346.i	0.0970596	+	0.0970596i
$134$	922259.	+	1.44369e6i	0.383300	+	0.600010i
$135$	701613.	−	2.35822e6i	0.285165	−	0.958478i
$136$	375394.	+	2.77136e6i	0.149235	+	1.10173i
$137$	561276.	+	561276.i	0.218280	+	0.218280i	0.807773	−	0.589493i	$-0.200672\pi$
$137$	561276.	+	561276.i	0.218280	+	0.218280i	−0.589493	+	0.807773i	$0.700672\pi$
$138$	1.40909e6	−	21343.7i	0.536168	−	0.00812142i
$139$	3.41339e6			1.27099			0.635493	−	0.772106i	$-0.280797\pi$
$139$	3.41339e6			1.27099			0.635493	+	0.772106i	$0.280797\pi$
$140$	556557.	−	85012.2i	0.202827	−	0.0309811i
$141$	−377772.	−	1.59853e6i	−0.134763	−	0.570247i
$142$	−1.08590e6	−	239320.i	−0.379249	−	0.0835821i
$143$	−205380.	−	205380.i	−0.0702343	−	0.0702343i
$144$	1.17255e6	−	2.74613e6i	0.392685	−	0.919673i
$145$	838574.	−	4.13721e6i	0.275066	−	1.35708i
$146$	−115916.	−	181453.i	−0.0372465	−	0.0583049i
$147$	−2.58875e6	−	1.59906e6i	−0.814962	−	0.503400i
$148$	1.43263e6	−	525480.i	0.441926	−	0.162095i
$149$	5.33373e6			1.61240			0.806199	−	0.591644i	$-0.201521\pi$
$149$	5.33373e6			1.61240			0.806199	+	0.591644i	$0.201521\pi$
$150$	3.10782e6	−	1.31609e6i	0.920834	−	0.389954i
$151$			4.51005e6i			1.30994i	0.755656	+	0.654969i	$0.227318\pi$
$151$			4.51005e6i			1.30994i	−0.755656	+	0.654969i	$0.772682\pi$
$152$	1.86921e6	+	1.42323e6i	0.532263	+	0.405270i
$153$	−1.25737e6	+	3.77824e6i	−0.351067	+	1.05491i
$154$	78267.2	+	122518.i	0.0214298	+	0.0335458i
$155$	−6.06969e6	−	1.23027e6i	−1.62994	−	0.330373i
$156$	−1.90422e6	−	389524.i	−0.501583	−	0.102603i
$157$	2.02662e6	−	2.02662e6i	0.523689	−	0.523689i	−0.394995	−	0.918683i	$-0.629254\pi$
$157$	2.02662e6	−	2.02662e6i	0.523689	−	0.523689i	0.918683	+	0.394995i	$0.129254\pi$
$158$	−3.82527e6	−	843047.i	−0.969820	−	0.213737i
$159$	−1.38418e6	−	5.85713e6i	−0.344352	−	1.45711i
$160$	3.92938e6	−	1.15638e6i	0.959321	−	0.282319i
$161$			459158.i			0.110023i
$162$	3.22046e6	−	2.77563e6i	0.757483	−	0.652854i
$163$	−1.30950e6	+	1.30950e6i	−0.302372	+	0.302372i	−0.841941	−	0.539569i	$-0.818587\pi$
$163$	−1.30950e6	+	1.30950e6i	−0.302372	+	0.302372i	0.539569	+	0.841941i	$0.318587\pi$
$164$	−1.18540e6	+	2.55872e6i	−0.268741	+	0.580084i
$165$	635702.	+	596163.i	0.141515	+	0.132713i
$166$	−1.98068e6	−	3.10052e6i	−0.433003	−	0.677814i
$167$	−2.08977e6	+	2.08977e6i	−0.448692	+	0.448692i	−0.894920	−	0.446227i	$-0.852767\pi$
$167$	−2.08977e6	+	2.08977e6i	−0.448692	+	0.448692i	0.446227	+	0.894920i	$0.352767\pi$
$168$	888847.	+	395545.i	0.187456	+	0.0834196i
$169$		−	3.56164e6i		−	0.737887i
$170$	−5.09556e6	+	1.96757e6i	−1.03716	+	0.400482i
$171$	1.49743e6	+	2.99121e6i	0.299472	+	0.598218i
$172$	−7.96865e6	+	2.92285e6i	−1.56603	+	0.574409i
$173$	−2.94550e6	+	2.94550e6i	−0.568880	+	0.568880i	−0.931815	−	0.362935i	$-0.881775\pi$
$173$	−2.94550e6	+	2.94550e6i	−0.568880	+	0.568880i	0.362935	+	0.931815i	$0.381775\pi$
$174$	5.07927e6	−	5.23551e6i	0.964169	−	0.993828i
$175$	413421.	+	1.01896e6i	0.0771398	+	0.190126i
$176$	683897.	+	806840.i	0.125445	+	0.147996i
$177$	−5.63647e6	−	3.48164e6i	−1.01645	−	0.627861i
$178$	8.40516e6	+	1.85240e6i	1.49034	+	0.328454i
$179$			8.31582e6i			1.44993i	0.688788	+	0.724963i	$0.258143\pi$
$179$			8.31582e6i			1.44993i	−0.688788	+	0.724963i	$0.741857\pi$
$180$	5.74824e6	+	984885.i	0.985637	+	0.168876i
$181$	−1.77516e6			−0.299366			−0.149683	−	0.988734i	$-0.547825\pi$
$181$	−1.77516e6			−0.299366			−0.149683	+	0.988734i	$0.547825\pi$
$182$	136296.	−	618433.i	0.0226083	−	0.102584i
$183$	−4.86106e6	+	7.86964e6i	−0.793192	+	1.28411i
$184$	448385.	+	3.31021e6i	0.0719776	+	0.531377i
$185$	1.64681e6	+	2.48411e6i	0.260093	+	0.392333i
$186$	−7.68099e6	−	7.45178e6i	−1.19365	−	1.15803i
$187$	−997364.	−	997364.i	−0.152521	−	0.152521i
$188$	3.65534e6	−	1.34076e6i	0.550116	−	0.201779i
$189$	888352.	+	1.06286e6i	0.131583	+	0.157431i
$190$	−1.85806e6	+	4.19558e6i	−0.270894	+	0.611690i
$191$	6.93164e6			0.994800			0.497400	−	0.867521i	$-0.334288\pi$
$191$	6.93164e6			0.994800			0.497400	+	0.867521i	$0.334288\pi$
$192$	6.79424e6	+	1.98362e6i	0.959925	+	0.280256i
$193$	−6.00848e6	−	6.00848e6i	−0.835782	−	0.835782i	0.152519	−	0.988301i	$-0.451262\pi$
$193$	−6.00848e6	−	6.00848e6i	−0.835782	−	0.835782i	−0.988301	+	0.152519i	$0.951262\pi$
$194$	−8.17906e6	+	5.22496e6i	−1.12021	+	0.715613i
$195$	−121782.	−	3.79424e6i	−0.0164240	−	0.511706i
$196$	3.03187e6	−	6.54436e6i	0.402663	−	0.869159i
$197$	−8.20017e6	−	8.20017e6i	−1.07257	−	1.07257i	−0.997152	−	0.0754143i	$-0.975972\pi$
$197$	−8.20017e6	−	8.20017e6i	−1.07257	−	1.07257i	−0.0754143	−	0.997152i	$-0.524028\pi$
$198$	368514.	+	1.46018e6i	0.0474743	+	0.188110i
$199$	−9.46207e6			−1.20068			−0.600340	−	0.799745i	$-0.704968\pi$
$199$	−9.46207e6			−1.20068			−0.600340	+	0.799745i	$0.704968\pi$
$200$	3.97553e6	+	6.94227e6i	0.496942	+	0.867784i
$201$	−5.62680e6	+	1.32975e6i	−0.692904	+	0.163750i
$202$	12480.7	−	56630.5i	0.00151421	−	0.00687063i
$203$	1.68056e6	+	1.68056e6i	0.200893	+	0.200893i
$204$	−9.24726e6	−	1.89161e6i	−1.08924	−	0.222813i
$205$	−5.39798e6	−	1.09412e6i	−0.626570	−	0.127000i
$206$	−1.27792e7	+	8.16366e6i	−1.46185	+	0.933863i
$207$	−1.50185e6	+	4.51287e6i	−0.169323	+	0.508794i
$208$	378675.	−	4.59158e6i	0.0420801	−	0.510237i
$209$	−1.18489e6			−0.129790
$210$	−349221.	+	1.86780e6i	−0.0377088	+	0.201684i
$211$		−	2.24929e6i		−	0.239441i	−0.992808	−	0.119721i	$-0.961800\pi$
$211$		−	2.24929e6i		−	0.239441i	0.992808	−	0.119721i	$-0.0381999\pi$
$212$	1.33935e7	−	4.91263e6i	1.40568	−	0.515593i
$213$	1.97222e6	−	3.19285e6i	0.204087	−	0.330400i
$214$	1.27471e6	−	814314.i	0.130068	−	0.0830904i
$215$	−9.15996e6	−	1.38172e7i	−0.921676	−	1.39029i
$216$	7.44233e6	+	6.79497e6i	0.738495	+	0.674258i
$217$	2.46554e6	−	2.46554e6i	0.241286	−	0.241286i
$218$	1.07333e6	−	4.87016e6i	0.103601	−	0.470082i
$219$	707217.	−	167133.i	0.0673318	−	0.0159122i
$220$	−1.22343e6	+	1.66456e6i	−0.114897	+	0.156326i
$221$			6.14391e6i			0.569204i
$222$	78000.8	+	5.14953e6i	0.00712919	+	0.470662i
$223$	1.02494e7	−	1.02494e7i	0.924234	−	0.924234i	−0.0730912	−	0.997325i	$-0.523286\pi$
$223$	1.02494e7	−	1.02494e7i	0.924234	−	0.924234i	0.997325	+	0.0730912i	$0.0232864\pi$
$224$	−679750.	+	2.20364e6i	−0.0604790	+	0.196063i
$225$	730449.	+	1.13672e7i	0.0641272	+	0.997942i
$226$	1.05728e7	−	6.75411e6i	0.915931	−	0.585117i
$227$	−9.87322e6	+	9.87322e6i	−0.844076	+	0.844076i	−0.989386	−	0.145311i	$-0.953582\pi$
$227$	−9.87322e6	+	9.87322e6i	−0.844076	+	0.844076i	0.145311	+	0.989386i	$0.453582\pi$
$228$	−6.61662e6	+	4.36934e6i	−0.558253	+	0.368648i
$229$			3.17820e6i			0.264651i	0.991206	+	0.132326i	$0.0422445\pi$
$229$			3.17820e6i			0.264651i	−0.991206	+	0.132326i	$0.957756\pi$
$230$	−6.08633e6	+	2.35014e6i	−0.500232	+	0.193157i
$231$	−477517.	+	112849.i	−0.0387394	+	0.00915507i
$232$	1.37568e7	+	1.04745e7i	1.10168	+	0.838825i
$233$	5.62144e6	−	5.62144e6i	0.444406	−	0.444406i	−0.449084	−	0.893490i	$-0.648249\pi$
$233$	5.62144e6	−	5.62144e6i	0.444406	−	0.444406i	0.893490	+	0.449084i	$0.148249\pi$
$234$	3.36242e6	−	5.63252e6i	0.262425	−	0.439598i
$235$	4.20181e6	+	6.33817e6i	0.323767	+	0.488383i
$236$	6.60127e6	−	1.42490e7i	0.502217	−	1.08405i
$237$	6.94749e6	−	1.12474e7i	0.521895	−	0.844903i
$238$	661879.	−	3.00324e6i	0.0490962	−	0.222771i
$239$		−	2.15010e7i		−	1.57494i	−0.616353	−	0.787470i	$-0.711390\pi$
$239$		−	2.15010e7i		−	1.57494i	0.616353	−	0.787470i	$-0.288610\pi$
$240$	−693671.	+	1.38066e7i	−0.0501787	+	0.998740i
$241$	1.81592e7			1.29732			0.648659	−	0.761079i	$-0.275330\pi$
$241$	1.81592e7			1.29732			0.648659	+	0.761079i	$0.275330\pi$
$242$	1.33194e7	+	2.93545e6i	0.939808	+	0.207123i
$243$	5.25476e6	+	1.33521e7i	0.366213	+	0.930531i
$244$	−1.98945e7	−	9.21671e6i	−1.36951	−	0.634463i
$245$	1.38063e7	+	2.79840e6i	0.938811	+	0.190288i
$246$	−6.83096e6	−	6.62711e6i	−0.458856	−	0.445163i
$247$	3.64955e6	+	3.64955e6i	0.242186	+	0.242186i
$248$	1.53672e7	−	2.01826e7i	1.00749	−	1.32319i
$249$	1.20843e7	−	2.85583e6i	0.782754	−	0.184984i
$250$	−1.13907e7	+	1.06955e7i	−0.729003	+	0.684510i
$251$	2.79925e7			1.77019			0.885097	−	0.465407i	$-0.154092\pi$
$251$	2.79925e7			1.77019			0.885097	+	0.465407i	$0.154092\pi$
$252$	−2.25039e6	+	2.39103e6i	−0.140623	+	0.149411i
$253$	−1.19129e6	−	1.19129e6i	−0.0735623	−	0.0735623i
$254$	492124.	+	770361.i	0.0300312	+	0.0470103i
$255$	−591399.	−	1.84256e7i	−0.0356665	−	1.11122i
$256$	−2.74859e6	+	1.65505e7i	−0.163829	+	0.986489i
$257$	−4.02745e6	−	4.02745e6i	−0.237264	−	0.237264i	0.578452	−	0.815716i	$-0.303657\pi$
$257$	−4.02745e6	−	4.02745e6i	−0.237264	−	0.237264i	−0.815716	+	0.578452i	$0.803657\pi$
$258$	−433860.	−	2.86430e7i	−0.0252633	−	1.66786i
$259$	−1.67800e6			−0.0965811
$260$	8.89521e6	−	1.35871e6i	0.506100	−	0.0773050i
$261$	1.10206e7	+	2.20144e7i	0.619846	+	1.23819i
$262$	−1.14317e7	−	2.51941e6i	−0.635633	−	0.140086i
$263$	6.99528e6	+	6.99528e6i	0.384537	+	0.384537i	0.872734	−	0.488197i	$-0.162345\pi$
$263$	6.99528e6	+	6.99528e6i	0.384537	+	0.384537i	−0.488197	+	0.872734i	$0.662345\pi$
$264$	−3.33237e6	+	1.27988e6i	−0.181109	+	0.0695595i
$265$	1.53958e7	+	2.32235e7i	0.827302	+	1.24793i
$266$	−1.39079e6	−	2.17712e6i	−0.0738954	−	0.115674i
$267$	−1.52655e7	+	2.47136e7i	−0.802006	+	1.29838i
$268$	−4.71944e6	−	1.28668e7i	−0.245181	−	0.668444i
$269$	−8.77891e6			−0.451007			−0.225504	−	0.974242i	$-0.572403\pi$
$269$	−8.77891e6			−0.451007			−0.225504	+	0.974242i	$0.572403\pi$
$270$	−9.54172e6	+	1.72156e7i	−0.484770	+	0.874642i
$271$		−	7.45528e6i		−	0.374590i	−0.982304	−	0.187295i	$-0.940028\pi$
$271$		−	7.45528e6i		−	0.374590i	0.982304	−	0.187295i	$-0.0599720\pi$
$272$	1.83892e6	−	2.22976e7i	0.0913811	−	1.10803i
$273$	1.81837e6	+	1.12320e6i	0.0893705	+	0.0552040i
$274$	−3.41858e6	−	5.35138e6i	−0.166186	−	0.260144i
$275$	−3.71632e6	−	1.57107e6i	−0.178696	−	0.0755436i
$276$	−1.10453e7	−	2.25940e6i	−0.525351	−	0.107465i
$277$	−2.52452e7	+	2.52452e7i	−1.18779	+	1.18779i	−0.210113	+	0.977677i	$0.567383\pi$
$277$	−2.52452e7	+	2.52452e7i	−1.18779	+	1.18779i	−0.977677	+	0.210113i	$0.932617\pi$
$278$	−2.66671e7	−	5.87713e6i	−1.24120	−	0.273547i
$279$	3.22973e7	−	1.61683e7i	1.48715	−	0.744477i
$280$	−4.49448e6	−	294114.i	−0.204741	−	0.0133981i
$281$			6.95963e6i			0.313666i	0.987625	+	0.156833i	$0.0501284\pi$
$281$			6.95963e6i			0.313666i	−0.987625	+	0.156833i	$0.949872\pi$
$282$	199018.	+	1.31390e7i	0.00887453	+	0.585887i
$283$	−5.08375e6	+	5.08375e6i	−0.224298	+	0.224298i	−0.810306	−	0.586008i	$-0.800699\pi$
$283$	−5.08375e6	+	5.08375e6i	−0.224298	+	0.224298i	0.586008	+	0.810306i	$0.300699\pi$
$284$	8.07154e6	+	3.73938e6i	0.352372	+	0.163247i
$285$	−1.12963e7	−	1.05937e7i	−0.487980	−	0.457629i
$286$	1.25091e6	+	1.95815e6i	0.0534722	+	0.0837044i
$287$	2.19269e6	−	2.19269e6i	0.0927536	−	0.0927536i
$288$	−1.38888e7	+	1.94353e7i	−0.581418	+	0.813605i
$289$			5.69848e6i			0.236083i
$290$	−1.36748e7	+	3.08782e7i	−0.560695	+	1.26607i
$291$	−7.53357e6	−	3.18781e7i	−0.305719	−	1.29364i
$292$	593173.	+	1.61719e6i	0.0238250	+	0.0649549i
$293$	−1.90585e7	+	1.90585e7i	−0.757680	+	0.757680i	−0.975900	−	0.218220i	$-0.929975\pi$
$293$	−1.90585e7	+	1.90585e7i	−0.757680	+	0.757680i	0.218220	+	0.975900i	$0.429975\pi$
$294$	1.74714e7	+	1.69500e7i	0.687519	+	0.667002i
$295$	3.00603e7	+	6.09295e6i	1.17092	+	0.237335i
$296$	−1.20972e7	+	1.63863e6i	−0.466456	+	0.0631837i
$297$	−5.06243e6	−	452758.i	−0.193237	−	0.0172821i
$298$	−4.16699e7	−	9.18356e6i	−1.57461	−	0.347026i
$299$			7.33852e6i			0.274533i
$300$	−2.65459e7	+	4.93101e6i	−0.983182	+	0.182630i
$301$	9.33345e6			0.342249
$302$	7.76536e6	−	3.52349e7i	0.281930	−	1.27924i
$303$	166510.	+	102853.i	0.00598566	+	0.00369733i
$304$	−1.21527e7	−	1.43374e7i	−0.432566	−	0.510328i
$305$	8.50698e6	−	4.19703e7i	0.299831	−	1.47925i
$306$	1.63286e7	−	2.73527e7i	0.569881	−	0.954630i
$307$	−3.88880e7	−	3.88880e7i	−1.34400	−	1.34400i	−0.892031	−	0.451973i	$-0.850720\pi$
$307$	−3.88880e7	−	3.88880e7i	−1.34400	−	1.34400i	−0.451973	−	0.892031i	$-0.649280\pi$
$308$	−400514.	−	1.09193e6i	−0.0137077	−	0.0373718i
$309$	−1.17707e7	−	4.98073e7i	−0.398958	−	1.68818i
$310$	4.53013e7	+	2.00622e7i	1.52064	+	0.673433i
$311$	5.05790e6			0.168147			0.0840735	−	0.996460i	$-0.473207\pi$
$311$	5.05790e6			0.168147			0.0840735	+	0.996460i	$0.473207\pi$
$312$	1.42061e7	+	6.32182e6i	0.467746	+	0.208151i
$313$	−5.69392e6	−	5.69392e6i	−0.185686	−	0.185686i	0.608142	−	0.793828i	$-0.291915\pi$
$313$	−5.69392e6	−	5.69392e6i	−0.185686	−	0.185686i	−0.793828	+	0.608142i	$0.791915\pi$
$314$	−1.93224e7	+	1.23436e7i	−0.624126	+	0.398706i
$315$	−5.56140e6	−	3.19345e6i	−0.177931	−	0.102171i
$316$	2.84335e7	+	1.31726e7i	0.901091	+	0.417457i
$317$	−7.10069e6	−	7.10069e6i	−0.222906	−	0.222906i	0.586815	−	0.809721i	$-0.300382\pi$
$317$	−7.10069e6	−	7.10069e6i	−0.222906	−	0.222906i	−0.809721	+	0.586815i	$0.800382\pi$
$318$	729218.	+	4.81422e7i	0.0226765	+	1.49708i
$319$	−8.72045e6			−0.268638
$320$	−3.26894e7	+	2.26867e6i	−0.997600	+	0.0692342i
$321$	1.17411e6	+	4.96822e6i	0.0354972	+	0.150205i
$322$	790573.	−	3.58718e6i	0.0236796	−	0.107445i
$323$	1.77230e7	+	1.77230e7i	0.525931	+	0.525931i
$324$	−2.99390e7	+	1.61397e7i	−0.880241	+	0.474526i
$325$	6.60753e6	+	1.62856e7i	0.192482	+	0.474409i
$326$	1.24851e7	−	7.97578e6i	0.360363	−	0.230208i
$327$	1.43197e7	+	8.84522e6i	0.409533	+	0.252968i
$328$	1.36665e7	−	1.79490e7i	0.387290	−	0.508650i
$329$	−4.28139e6			−0.120226
$330$	−3.93997e6	−	5.75208e6i	−0.109635	−	0.160060i
$331$			2.90568e7i			0.801242i	0.916244	+	0.400621i	$0.131206\pi$
$331$			2.90568e7i			0.801242i	−0.916244	+	0.400621i	$0.868794\pi$
$332$	1.01357e7	+	2.76332e7i	0.276973	+	0.755122i
$333$	−1.64924e7	−	5.48855e6i	−0.446632	−	0.148636i
$334$	1.99245e7	−	1.27282e7i	0.534746	−	0.341608i
$335$	2.23103e7	−	1.47903e7i	0.593431	−	0.393408i
$336$	−6.26309e6	−	4.62061e6i	−0.165109	−	0.121810i
$337$	488467.	−	488467.i	0.0127628	−	0.0127628i	−0.700697	−	0.713459i	$-0.747127\pi$
$337$	488467.	−	488467.i	0.0127628	−	0.0127628i	0.713459	+	0.700697i	$0.247127\pi$
$338$	−6.13240e6	+	2.78254e7i	−0.158811	+	0.720595i
$339$	9.73835e6	+	4.12075e7i	0.249969	+	1.05774i
$340$	4.31969e7	−	6.59818e6i	1.09905	−	0.167876i
$341$			1.27937e7i			0.322652i
$342$	−6.54842e6	−	2.59472e7i	−0.163704	−	0.648652i
$343$	−1.14628e7	+	1.14628e7i	−0.284060	+	0.284060i
$344$	6.72878e7	−	9.11446e6i	1.65295	−	0.223901i
$345$	−706389.	−	2.20082e7i	−0.0172023	−	0.535953i
$346$	2.80833e7	−	1.79402e7i	0.677984	−	0.433111i
$347$	−5.02130e7	+	5.02130e7i	−1.20179	+	1.20179i	−0.228167	+	0.973622i	$0.573273\pi$
$347$	−5.02130e7	+	5.02130e7i	−1.20179	+	1.20179i	−0.973622	+	0.228167i	$0.926727\pi$
$348$	−4.86963e7	+	3.21571e7i	−1.15547	+	0.763025i
$349$			1.11767e7i			0.262929i	0.991321	+	0.131464i	$0.0419679\pi$
$349$			1.11767e7i			0.262929i	−0.991321	+	0.131464i	$0.958032\pi$
$350$	−1.47543e6	−	8.67245e6i	−0.0344123	−	0.202273i
$351$	1.41981e7	+	1.69872e7i	0.328330	+	0.392826i
$352$	−3.95375e6	−	7.48098e6i	−0.0906527	−	0.171526i
$353$	−7.88598e6	+	7.88598e6i	−0.179280	+	0.179280i	−0.791042	−	0.611762i	$-0.790461\pi$
$353$	−7.88598e6	+	7.88598e6i	−0.179280	+	0.179280i	0.611762	+	0.791042i	$0.290461\pi$
$354$	3.80404e7	+	3.69051e7i	0.857501	+	0.831912i
$355$	−3.45143e6	+	1.70281e7i	−0.0771461	+	0.380610i
$356$	−6.24760e7	−	2.89438e7i	−1.38472	−	0.641514i
$357$	8.83036e6	+	5.45450e6i	0.194077	+	0.119881i
$358$	1.43181e7	−	6.49675e7i	0.312059	−	1.41595i
$359$		−	8.33602e7i		−	1.80167i	−0.434161	−	0.900835i	$-0.642955\pi$
$359$		−	8.33602e7i		−	1.80167i	0.434161	−	0.900835i	$-0.357045\pi$
$360$	−4.32124e7	−	1.75917e7i	−0.926193	−	0.377051i
$361$	−2.59906e7			−0.552452
$362$	1.38685e7	+	3.05646e6i	0.292350	+	0.0644307i
$363$	−2.41908e7	+	3.91629e7i	−0.505744	+	0.818756i
$364$	−2.12962e6	+	4.59685e6i	−0.0441569	+	0.0953139i
$365$	−2.80412e6	+	1.85895e6i	−0.0576657	+	0.0382288i
$366$	5.15270e7	−	5.31120e7i	1.05097	−	1.08330i
$367$	−2.57645e7	−	2.57645e7i	−0.521223	−	0.521223i	0.396718	−	0.917941i	$-0.370149\pi$
$367$	−2.57645e7	−	2.57645e7i	−0.521223	−	0.521223i	−0.917941	+	0.396718i	$0.870149\pi$
$368$	2.19648e6	−	2.66331e7i	0.0440741	−	0.534415i
$369$	2.87230e7	−	1.43790e7i	0.571678	−	0.286186i
$370$	−8.58861e6	−	2.22426e7i	−0.169558	−	0.439117i
$371$	−1.56874e7			−0.307205
$372$	4.71775e7	+	7.14422e7i	0.916445	+	1.38780i
$373$	−533218.	−	533218.i	−0.0102749	−	0.0102749i	0.701951	−	0.712226i	$-0.252313\pi$
$373$	−533218.	−	533218.i	−0.0102749	−	0.0102749i	−0.712226	+	0.701951i	$0.752313\pi$
$374$	6.07467e6	+	9.50918e6i	0.116120	+	0.181772i
$375$	−2.13836e7	−	4.82043e7i	−0.405496	−	0.914097i
$376$	−3.08659e7	+	4.18094e6i	−0.580652	+	0.0786522i
$377$	2.68596e7	+	2.68596e7i	0.501275	+	0.501275i
$378$	−5.11025e6	−	9.83315e6i	−0.0946164	−	0.182061i
$379$	−8.84426e7			−1.62459			−0.812295	−	0.583246i	$-0.801782\pi$
$379$	−8.84426e7			−1.62459			−0.812295	+	0.583246i	$0.801782\pi$
$380$	2.17401e7	−	2.95789e7i	0.396196	−	0.539052i
$381$	−3.00250e6	+	709565.i	−0.0542885	+	0.0128297i
$382$	−5.41535e7	−	1.19348e7i	−0.971487	−	0.214105i
$383$	−5.10191e7	−	5.10191e7i	−0.908106	−	0.908106i	0.0880133	−	0.996119i	$-0.471948\pi$
$383$	−5.10191e7	−	5.10191e7i	−0.908106	−	0.908106i	−0.996119	+	0.0880133i	$0.971948\pi$
$384$	−4.96648e7	−	2.71953e7i	−0.877112	−	0.480286i
$385$	1.89335e6	−	1.25518e6i	0.0331780	−	0.0219949i
$386$	3.65960e7	+	5.72867e7i	0.636315	+	0.996075i
$387$	9.17347e7	+	3.05287e7i	1.58271	+	0.526714i
$388$	7.28953e7	−	2.67375e7i	1.24797	−	0.457747i
$389$	5.95177e7			1.01111			0.505554	−	0.862795i	$-0.331288\pi$
$389$	5.95177e7			1.01111			0.505554	+	0.862795i	$0.331288\pi$
$390$	−5.58145e6	+	2.98522e7i	−0.0940921	+	0.503249i
$391$			3.56373e7i			0.596176i
$392$	−3.49545e7	+	4.59077e7i	−0.580290	+	0.762127i
$393$	2.07623e7	−	3.36124e7i	0.342057	−	0.553761i
$394$	4.99450e7	+	7.81830e7i	0.816589	+	1.27827i
$395$	−1.21583e7	+	5.99845e7i	−0.197279	+	0.973302i
$396$	−364894.	−	1.20422e7i	−0.00587600	−	0.193919i
$397$	−5.12286e6	+	5.12286e6i	−0.0818731	+	0.0818731i	−0.746857	−	0.664984i	$-0.768438\pi$
$397$	−5.12286e6	+	5.12286e6i	−0.0818731	+	0.0818731i	0.664984	+	0.746857i	$0.268438\pi$
$398$	7.39226e7	+	1.62917e7i	1.17254	+	0.258415i
$399$	8.48538e6	−	2.00530e6i	0.133583	−	0.0315690i
$400$	−1.91058e7	−	6.10817e7i	−0.298528	−	0.954401i
$401$		−	5.58473e7i		−	0.866102i	−0.901369	−	0.433051i	$-0.857437\pi$
$401$		−	5.58473e7i		−	0.866102i	0.901369	−	0.433051i	$-0.142563\pi$
$402$	4.62490e7	−	700541.i	0.711909	−	0.0107834i
$403$	3.94057e7	−	3.94057e7i	0.602065	−	0.602065i
$404$	−195012.	+	420938.i	−0.00295744	+	0.00638372i
$405$	−4.42153e7	−	4.95779e7i	−0.665592	−	0.746316i
$406$	−1.02358e7	−	1.60230e7i	−0.152948	−	0.239422i
$407$	4.35358e6	−	4.35358e6i	0.0645749	−	0.0645749i
$408$	6.89874e7	+	3.07000e7i	1.01576	+	0.452021i
$409$			9.53521e7i			1.39367i	0.717231	+	0.696836i	$0.245409\pi$
$409$			9.53521e7i			1.39367i	−0.717231	+	0.696836i	$0.754591\pi$
$410$	4.02879e7	+	1.78420e7i	0.584552	+	0.258876i
$411$	2.08571e7	−	4.92905e6i	0.300420	−	0.0709966i
$412$	1.13894e8	−	4.17756e7i	1.62858	−	0.597353i
$413$	−1.22107e7	+	1.22107e7i	−0.173336	+	0.173336i
$414$	1.95035e7	−	3.26710e7i	0.274860	−	0.460428i
$415$	−4.79145e7	+	3.17643e7i	−0.670382	+	0.444422i
$416$	−1.08641e7	+	3.52198e7i	−0.150909	+	0.489223i
$417$	4.84331e7	−	7.84090e7i	0.667935	−	1.08133i
$418$	9.25699e6	+	2.04013e6i	0.126748	+	0.0279338i
$419$			4.00561e7i			0.544536i	0.962221	+	0.272268i	$0.0877737\pi$
$419$			4.00561e7i			0.544536i	−0.962221	+	0.272268i	$0.912226\pi$
$420$	5.94425e6	−	1.39909e7i	0.0802323	−	0.188842i
$421$	−1.57212e7			−0.210687			−0.105344	−	0.994436i	$-0.533594\pi$
$421$	−1.57212e7			−0.210687			−0.105344	+	0.994436i	$0.533594\pi$
$422$	−3.87281e6	+	1.75726e7i	−0.0515334	+	0.233830i
$423$	−4.20801e7	−	1.40040e7i	−0.555975	−	0.185025i
$424$	−1.13095e8	+	1.53193e7i	−1.48370	+	0.200975i
$425$	3.20875e7	+	7.90859e7i	0.417993	+	1.03023i
$426$	−2.09054e7	+	2.15485e7i	−0.270414	+	0.278732i
$427$	1.70485e7	+	1.70485e7i	0.218980	+	0.218980i
$428$	−1.13608e7	+	4.16706e6i	−0.144903	+	0.0531494i
$429$	−7.63194e6	+	1.80362e6i	−0.0966636	+	0.0228440i
$430$	4.77720e7	+	1.23719e8i	0.600853	+	1.55607i
$431$	−2.34373e7			−0.292736			−0.146368	−	0.989230i	$-0.546758\pi$
$431$	−2.34373e7			−0.292736			−0.146368	+	0.989230i	$0.546758\pi$
$432$	−4.64438e7	−	6.59000e7i	−0.576072	−	0.817399i
$433$	−4.05054e7	−	4.05054e7i	−0.498941	−	0.498941i	0.412167	−	0.911108i	$-0.364772\pi$
$433$	−4.05054e7	−	4.05054e7i	−0.498941	−	0.498941i	−0.911108	+	0.412167i	$0.864772\pi$
$434$	−2.35072e7	+	1.50169e7i	−0.287562	+	0.183701i
$435$	−8.31374e7	−	7.79665e7i	−1.01002	−	0.947197i
$436$	−1.67708e7	+	3.62002e7i	−0.202346	+	0.436768i
$437$	2.11690e7	+	2.11690e7i	0.253662	+	0.253662i
$438$	−5.81291e6	+	88049.1i	−0.0691785	+	0.00104786i
$439$	1.96368e7			0.232101			0.116050	−	0.993243i	$-0.462977\pi$
$439$	1.96368e7			0.232101			0.116050	+	0.993243i	$0.462977\pi$
$440$	1.24241e7	−	1.08979e7i	0.145850	−	0.127934i
$441$	−7.34642e7	+	3.67768e7i	−0.856565	+	0.428803i
$442$	1.05785e7	−	4.79994e7i	0.122506	−	0.555865i
$443$	8.83057e7	+	8.83057e7i	1.01573	+	1.01573i	0.999874	+	0.0158545i	$0.00504687\pi$
$443$	8.83057e7	+	8.83057e7i	1.01573	+	1.01573i	0.0158545	+	0.999874i	$0.494953\pi$
$444$	8.25703e6	−	4.03651e7i	0.0943355	−	0.461166i
$445$	2.67150e7	−	1.31802e8i	0.303163	−	1.49569i
$446$	−9.77205e7	+	6.24260e7i	−1.10149	+	0.703657i
$447$	7.56811e7	−	1.22521e8i	0.847355	−	1.37179i
$448$	9.10476e6	−	1.60456e7i	0.101259	−	0.178452i
$449$	−1.18838e8			−1.31286			−0.656429	−	0.754388i	$-0.727934\pi$
$449$	−1.18838e8			−1.31286			−0.656429	+	0.754388i	$0.727934\pi$
$450$	1.38652e7	−	9.00640e7i	0.152156	−	0.988356i
$451$			1.13779e7i			0.124032i
$452$	−9.42290e7	+	3.45625e7i	−1.02040	+	0.374275i
$453$	1.03600e8	+	6.39938e7i	1.11447	+	0.688404i
$454$	9.41343e7	−	6.01351e7i	1.00596	−	0.642629i
$455$	−9.69771e6	−	1.96563e6i	−0.102952	−	0.0208674i
$456$	5.92155e7	−	2.27432e7i	0.624512	−	0.239859i
$457$	2.54472e7	−	2.54472e7i	0.266619	−	0.266619i	−0.561117	−	0.827736i	$-0.689628\pi$
$457$	2.54472e7	−	2.54472e7i	0.266619	−	0.266619i	0.827736	+	0.561117i	$0.189628\pi$
$458$	5.47219e6	−	2.48297e7i	0.0569593	−	0.258449i
$459$	6.89490e7	+	8.24932e7i	0.713001	+	0.853061i
$460$	5.15960e7	−	7.88111e6i	0.530081	−	0.0809681i
$461$		−	1.58579e8i		−	1.61861i	−0.587386	−	0.809307i	$-0.699843\pi$
$461$		−	1.58579e8i		−	1.61861i	0.587386	−	0.809307i	$-0.300157\pi$
$462$	3.92491e6	−	59451.2i	0.0398019	−	0.000602886i
$463$	8.40016e7	−	8.40016e7i	0.846340	−	0.846340i	−0.143335	−	0.989674i	$-0.545783\pi$
$463$	8.40016e7	−	8.40016e7i	0.846340	−	0.846340i	0.989674	+	0.143335i	$0.0457826\pi$
$464$	−8.94403e7	−	1.05519e8i	−0.895322	−	1.05627i
$465$	−1.14384e8	+	1.21971e8i	−1.13765	+	1.21310i
$466$	−5.35966e7	+	3.42387e7i	−0.529638	+	0.338345i
$467$	−8.23851e6	+	8.23851e6i	−0.0808906	+	0.0808906i	−0.746394	−	0.665504i	$-0.768217\pi$
$467$	−8.23851e6	+	8.23851e6i	−0.0808906	+	0.0808906i	0.665504	+	0.746394i	$0.268217\pi$
$468$	−3.59670e7	+	3.82148e7i	−0.350887	+	0.372816i
$469$			1.50705e7i			0.146086i
$470$	−2.19138e7	−	5.67517e7i	−0.211068	−	0.546620i
$471$	−1.77975e7	−	7.53095e7i	−0.170332	−	0.720754i
$472$	−7.61064e7	+	9.99547e7i	−0.723761	+	0.950555i
$473$	−2.42157e7	+	2.42157e7i	−0.228831	+	0.228831i
$474$	−7.36430e7	+	7.59083e7i	−0.691507	+	0.712778i
$475$	6.60383e7	+	2.79176e7i	0.616191	+	0.260494i
$476$	−1.03419e7	+	2.23232e7i	−0.0958912	+	0.206984i
$477$	−1.54185e8	−	5.13116e7i	−1.42065	−	0.472782i
$478$	−3.70201e7	+	1.67977e8i	−0.338965	+	1.53803i
$479$			5.21324e7i			0.474352i	0.971467	+	0.237176i	$0.0762219\pi$
$479$			5.21324e7i			0.474352i	−0.971467	+	0.237176i	$0.923778\pi$
$480$	2.91913e7	−	1.06670e8i	0.263955	−	0.964535i
$481$	−2.68187e7			−0.240992
$482$	−1.41869e8	−	3.12664e7i	−1.26692	−	0.279214i
$483$	1.05473e7	+	6.51506e6i	0.0936053	+	0.0578198i
$484$	−9.90039e7	−	4.58665e7i	−0.873205	−	0.404538i
$485$	8.37931e7	+	1.26397e8i	0.734485	+	1.10792i
$486$	−1.80634e7	−	1.13361e8i	−0.157359	−	0.987542i
$487$	2.57723e7	+	2.57723e7i	0.223134	+	0.223134i	0.809817	−	0.586683i	$-0.199566\pi$
$487$	2.57723e7	+	2.57723e7i	0.223134	+	0.223134i	−0.586683	+	0.809817i	$0.699566\pi$
$488$	1.39557e8	+	1.06260e8i	1.20086	+	0.914344i
$489$	1.14998e7	+	4.86611e7i	0.0983477	+	0.416155i
$490$	−1.03043e8	−	4.56340e7i	−0.875855	−	0.387883i
$491$	−7.35448e7			−0.621309			−0.310654	−	0.950523i	$-0.600548\pi$
$491$	−7.35448e7			−0.621309			−0.310654	+	0.950523i	$0.600548\pi$
$492$	4.19565e7	+	6.35359e7i	0.352293	+	0.533487i
$493$	1.30436e8	+	1.30436e8i	1.08857	+	1.08857i
$494$	−2.22284e7	−	3.47960e7i	−0.184386	−	0.288634i
$495$	2.27146e7	−	6.14367e6i	0.187279	−	0.0506538i
$496$	−1.54806e8	+	1.31218e8i	−1.26866	+	1.07534i
$497$	−6.91689e6	−	6.91689e6i	−0.0563432	−	0.0563432i
$498$	−9.93263e7	+	1.50451e6i	−0.804223	+	0.0121817i
$499$	3.39856e7			0.273523			0.136761	−	0.990604i	$-0.456331\pi$
$499$	3.39856e7			0.273523			0.136761	+	0.990604i	$0.456331\pi$
$500$	1.07405e8	−	6.39462e7i	0.859242	−	0.511570i
$501$	1.83521e7	+	7.76561e7i	0.145939	+	0.617536i
$502$	−2.18692e8	−	4.81972e7i	−1.72871	−	0.380988i
$503$	−1.50148e8	−	1.50148e8i	−1.17982	−	1.17982i	−0.979789	−	0.200033i	$-0.935895\pi$
$503$	−1.50148e8	−	1.50148e8i	−1.17982	−	1.17982i	−0.200033	−	0.979789i	$-0.564105\pi$
$504$	2.16981e7	−	1.48053e7i	0.169484	−	0.115644i
$505$	−888028.	−	179995.i	−0.00689529	−	0.00139761i
$506$	7.25582e6	+	1.13581e7i	0.0560060	+	0.0876707i
$507$	−8.18145e7	−	5.05367e7i	−0.627779	−	0.387778i
$508$	−2.51833e6	−	6.86579e6i	−0.0192097	−	0.0523721i
$509$	−5.21397e7			−0.395380			−0.197690	−	0.980265i	$-0.563344\pi$
$509$	−5.21397e7			−0.395380			−0.197690	+	0.980265i	$0.563344\pi$
$510$	−2.71046e7	+	1.44968e8i	−0.204330	+	1.09286i
$511$		−	1.89416e6i		−	0.0141956i
$512$	4.99700e7	−	1.24569e8i	0.372305	−	0.928110i
$513$	8.99585e7	+	8.04541e6i	0.666331	+	0.0595931i
$514$	2.45301e7	+	3.83990e7i	0.180639	+	0.282768i
$515$	1.30921e8	+	1.97486e8i	0.958491	+	1.44582i
$516$	−4.59277e7	+	2.24521e8i	−0.334291	+	1.63421i
$517$	1.11081e7	−	1.11081e7i	0.0803839	−	0.0803839i
$518$	1.31094e7	+	2.88916e6i	0.0943177	+	0.0207865i
$519$	2.58670e7	+	1.09455e8i	0.185031	+	0.782951i
$520$	−7.18334e7	−	4.70070e6i	−0.510877	−	0.0334313i
$521$		−	7.08068e7i		−	0.500682i	−0.968158	−	0.250341i	$-0.919457\pi$
$521$		−	7.08068e7i		−	0.500682i	0.968158	−	0.250341i	$-0.0805427\pi$
$522$	−4.81944e7	−	1.90963e8i	−0.338833	−	1.34258i
$523$	8.88846e7	−	8.88846e7i	0.621329	−	0.621329i	−0.324542	−	0.945871i	$-0.605210\pi$
$523$	8.88846e7	−	8.88846e7i	0.621329	−	0.621329i	0.945871	+	0.324542i	$0.105210\pi$
$524$	8.49724e7	+	3.93659e7i	0.590587	+	0.273607i
$525$	2.92726e7	+	4.96145e6i	0.202294	+	0.0342871i
$526$	−4.26063e7	−	6.66951e7i	−0.292764	−	0.458286i
$527$	1.91362e8	−	1.91362e8i	1.30744	−	1.30744i
$528$	2.82379e7	−	4.26142e6i	0.191836	−	0.0289503i
$529$		−	1.05469e8i		−	0.712458i
$530$	−8.02937e7	−	2.07943e8i	−0.539329	−	1.39674i
$531$	−1.59953e8	+	8.00740e7i	−1.06834	+	0.534820i
$532$	7.11705e6	+	1.94034e7i	0.0472678	+	0.128868i
$533$	3.50447e7	−	3.50447e7i	0.231441	−	0.231441i
$534$	1.61814e8	−	1.66791e8i	1.06265	−	1.09534i
$535$	−1.30592e7	−	1.96990e7i	−0.0852817	−	0.128642i
$536$	1.47169e7	+	1.08648e8i	0.0955699	+	0.705547i
$537$	1.91023e8	+	1.17994e8i	1.23357	+	0.761972i
$538$	6.85854e7	+	1.51154e7i	0.440438	+	0.0970675i
$539$		−	2.91009e7i		−	0.185841i
$540$	1.04186e8	−	1.18068e8i	0.661653	−	0.749811i
$541$	1.13550e8			0.717125			0.358563	−	0.933506i	$-0.383267\pi$
$541$	1.13550e8			0.717125			0.358563	+	0.933506i	$0.383267\pi$
$542$	−1.28364e7	+	5.82445e7i	−0.0806206	+	0.365811i
$543$	−2.51881e7	+	4.07773e7i	−0.157324	+	0.254694i
$544$	−5.27584e7	+	1.71034e8i	−0.327714	+	1.06240i
$545$	−7.63694e7	−	1.54794e7i	−0.471770	−	0.0956232i
$546$	−1.22721e7	−	1.19059e7i	−0.0753949	−	0.0731449i
$547$	394893.	+	394893.i	0.00241278	+	0.00241278i	0.708312	−	0.705899i	$-0.249457\pi$
$547$	394893.	+	394893.i	0.00241278	+	0.00241278i	−0.705899	+	0.708312i	$0.749457\pi$
$548$	1.74938e7	+	4.76938e7i	0.106302	+	0.289815i
$549$	1.11799e8	+	2.23327e8i	0.675651	+	1.34966i
$550$	2.63288e7	+	1.86728e7i	0.158250	+	0.112233i
$551$	1.54961e8			0.926332
$552$	8.24012e7	+	3.66693e7i	0.489910	+	0.218014i
$553$	−2.43660e7	−	2.43660e7i	−0.144082	−	0.144082i
$554$	2.40696e8	−	1.53762e8i	1.41559	−	0.904313i
$555$	8.04293e7	−	2.58151e6i	0.470473	−	0.0151006i
$556$	1.98218e8	+	9.18304e7i	1.15324	+	0.534272i
$557$	1.01097e8	+	1.01097e8i	0.585021	+	0.585021i	0.936279	−	0.351258i	$-0.114246\pi$
$557$	1.01097e8	+	1.01097e8i	0.585021	+	0.585021i	−0.351258	+	0.936279i	$0.614246\pi$
$558$	−2.80162e8	+	7.07059e7i	−1.61252	+	0.406961i
$559$	1.49172e8			0.853991
$560$	3.46068e7	+	1.00363e7i	0.197060	+	0.0571493i
$561$	−3.70622e7	+	8.75872e6i	−0.209915	+	0.0496080i
$562$	1.19830e7	−	5.43722e7i	0.0675083	−	0.306315i
$563$	−1.57528e8	−	1.57528e8i	−0.882739	−	0.882739i	0.111073	−	0.993812i	$-0.464571\pi$
$563$	−1.57528e8	−	1.57528e8i	−0.882739	−	0.882739i	−0.993812	+	0.111073i	$0.964571\pi$
$564$	2.10677e7	−	1.02991e8i	0.117430	−	0.574067i
$565$	−1.08316e8	−	1.63388e8i	−0.600548	−	0.905888i
$566$	4.84701e7	−	3.09638e7i	0.267316	−	0.170767i
$567$	3.70199e7	−	5.32529e6i	0.203089	−	0.0292142i
$568$	−5.66207e7	−	4.31115e7i	−0.308980	−	0.235260i
$569$	−1.04738e8			−0.568546			−0.284273	−	0.958743i	$-0.591752\pi$
$569$	−1.04738e8			−0.568546			−0.284273	+	0.958743i	$0.591752\pi$
$570$	7.00124e7	+	1.02213e8i	0.378051	+	0.551929i
$571$		−	7.02971e7i		−	0.377597i	−0.982016	−	0.188799i	$-0.939541\pi$
$571$		−	7.02971e7i		−	0.377597i	0.982016	−	0.188799i	$-0.0604594\pi$
$572$	−6.40124e6	−	1.74519e7i	−0.0342039	−	0.0932513i
$573$	9.83541e7	−	1.59227e8i	0.522792	−	0.846354i
$574$	−2.09057e7	+	1.33551e7i	−0.110543	+	0.0706171i
$575$	3.83265e7	+	9.44632e7i	0.201602	+	0.496889i
$576$	1.41970e8	−	1.27925e8i	0.742900	−	0.669403i
$577$	1.12054e7	−	1.12054e7i	0.0583311	−	0.0583311i	−0.677339	−	0.735671i	$-0.736867\pi$
$577$	1.12054e7	−	1.12054e7i	0.0583311	−	0.0583311i	0.735671	+	0.677339i	$0.236867\pi$
$578$	9.81158e6	−	4.45195e7i	0.0508107	−	0.230551i
$579$	−2.23276e8	+	5.27657e7i	−1.15029	+	0.271842i
$580$	1.60000e8	−	2.17692e8i	0.820044	−	1.11573i
$581$		−	3.23659e7i		−	0.165029i
$582$	3.96885e6	+	2.62019e8i	0.0201324	+	1.32912i
$583$	4.07010e7	−	4.07010e7i	0.205400	−	0.205400i
$584$	−1.84972e6	−	1.36556e7i	−0.00928684	−	0.0685603i
$585$	−8.88855e7	−	5.10395e7i	−0.443980	−	0.254941i
$586$	1.81710e8	−	1.16080e8i	0.902994	−	0.576853i
$587$	1.05573e8	−	1.05573e8i	0.521961	−	0.521961i	−0.396203	−	0.918163i	$-0.629672\pi$
$587$	1.05573e8	−	1.05573e8i	0.521961	−	0.521961i	0.918163	+	0.396203i	$0.129672\pi$
$588$	−1.07311e8	−	1.62504e8i	−0.527853	−	0.799341i
$589$		−	2.27342e8i		−	1.11259i
$590$	−2.24356e8	−	9.93588e7i	−1.09240	−	0.483783i
$591$	−3.04720e8	+	7.20128e7i	−1.47618	+	0.348857i
$592$	9.73312e7	+	8.02706e6i	0.469123	+	0.0386894i
$593$	−3.38052e7	+	3.38052e7i	−0.162114	+	0.162114i	−0.783502	−	0.621389i	$-0.786569\pi$
$593$	−3.38052e7	+	3.38052e7i	−0.162114	+	0.162114i	0.621389	+	0.783502i	$0.286569\pi$
$594$	3.87708e7	+	1.22536e7i	0.184989	+	0.0584662i
$595$	−4.70940e7	−	9.54551e6i	−0.223571	−	0.0453156i
$596$	3.09734e8	+	1.43494e8i	1.46302	+	0.677787i
$597$	−1.34259e8	+	2.17353e8i	−0.630986	+	1.02151i
$598$	1.26354e7	−	5.73323e7i	0.0590860	−	0.268099i
$599$		−	1.61215e8i		−	0.750112i	−0.927002	−	0.375056i	$-0.877623\pi$
$599$		−	1.61215e8i		−	0.750112i	0.927002	−	0.375056i	$-0.122377\pi$
$600$	2.15881e8	+	7.18287e6i	0.999447	+	0.0332540i
$601$	−1.53268e8			−0.706039			−0.353019	−	0.935616i	$-0.614845\pi$
$601$	−1.53268e8			−0.706039			−0.353019	+	0.935616i	$0.614845\pi$
$602$	−7.29177e7	−	1.60702e7i	−0.334229	−	0.0736602i
$603$	−4.92938e7	+	1.48121e8i	−0.224823	+	0.675563i
$604$	−1.21334e8	+	2.61903e8i	−0.550645	+	1.18858i
$605$	4.23345e7	−	2.08863e8i	0.191174	−	0.943181i
$606$	−1.12377e6	−	1.09023e6i	−0.00504963	−	0.00489894i
$607$	1.05002e8	+	1.05002e8i	0.469494	+	0.469494i	0.901751	−	0.432256i	$-0.142282\pi$
$607$	1.05002e8	+	1.05002e8i	0.469494	+	0.469494i	−0.432256	+	0.901751i	$0.642282\pi$
$608$	7.02573e7	+	1.32936e8i	0.312594	+	0.591467i
$609$	6.24498e7	−	1.47584e7i	0.276490	−	0.0653414i
$610$	−1.38725e8	+	3.13246e8i	−0.611174	+	1.38006i
$611$	−6.84277e7			−0.299991
$612$	−1.74663e8	+	1.85579e8i	−0.761985	+	0.809606i
$613$	−2.23117e8	−	2.23117e8i	−0.968614	−	0.968614i	0.0309085	−	0.999522i	$-0.490160\pi$
$613$	−2.23117e8	−	2.23117e8i	−0.968614	−	0.968614i	−0.999522	+	0.0309085i	$0.990160\pi$
$614$	2.36856e8	+	3.70770e8i	1.02325	+	1.60177i
$615$	−1.01726e8	+	1.08472e8i	−0.437326	+	0.466331i
$616$	1.24894e6	+	9.22035e6i	0.00534318	+	0.0394462i
$617$	1.72395e8	+	1.72395e8i	0.733955	+	0.733955i	0.971401	−	0.237446i	$-0.0763101\pi$
$617$	1.72395e8	+	1.72395e8i	0.733955	+	0.733955i	−0.237446	+	0.971401i	$0.576310\pi$
$618$	6.20106e6	+	4.09387e8i	0.0262724	+	1.73448i
$619$	−2.29120e8			−0.966033			−0.483016	−	0.875611i	$-0.660459\pi$
$619$	−2.29120e8			−0.966033			−0.483016	+	0.875611i	$0.660459\pi$
$620$	−3.19374e8	−	2.34736e8i	−1.34006	−	0.984928i
$621$	8.23553e7	+	9.85330e7i	0.343888	+	0.411440i
$622$	−3.95149e7	−	8.70864e6i	−0.164206	−	0.0361892i
$623$	5.35387e7	+	5.35387e7i	0.221413	+	0.221413i
$624$	−1.00100e8	−	7.38492e7i	−0.411985	−	0.303943i
$625$	1.70108e8	+	1.75123e8i	0.696760	+	0.717304i
$626$	3.46801e7	+	5.42876e7i	0.141370	+	0.221298i
$627$	−1.68126e7	+	2.72182e7i	−0.0682076	+	0.110422i
$628$	1.72210e8	−	6.31654e7i	0.695311	−	0.255035i
$629$	−1.30237e8			−0.523338
$630$	3.79501e7	+	3.45245e7i	0.151772	+	0.138072i
$631$		−	8.65685e7i		−	0.344565i	−0.985048	−	0.172283i	$-0.944886\pi$
$631$		−	8.65685e7i		−	0.344565i	0.985048	−	0.172283i	$-0.0551143\pi$
$632$	−1.99456e8	−	1.51868e8i	−0.790127	−	0.601610i
$633$	−5.16686e7	−	3.19156e7i	−0.203711	−	0.125832i
$634$	4.32484e7	+	6.77001e7i	0.169708	+	0.265657i
$635$	1.19049e7	−	7.89222e6i	0.0464949	−	0.0308232i
$636$	7.71938e7	−	3.77368e8i	0.300062	−	1.46688i
$637$	−8.96331e7	+	8.96331e7i	−0.346777	+	0.346777i
$638$	6.81287e7	+	1.50148e7i	0.262342	+	0.0578172i
$639$	−4.53589e7	−	9.06077e7i	−0.173844	−	0.347266i
$640$	2.59292e8	+	3.85602e7i	0.989122	+	0.147096i
$641$		−	4.83499e8i		−	1.83578i	−0.396830	−	0.917892i	$-0.629890\pi$
$641$		−	4.83499e8i		−	1.83578i	0.396830	−	0.917892i	$-0.370110\pi$
$642$	−618547.	−	4.08359e7i	−0.00233759	−	0.154325i
$643$	−3.16537e8	+	3.16537e8i	−1.19067	+	1.19067i	−0.213792	+	0.976879i	$0.568581\pi$
$643$	−3.16537e8	+	3.16537e8i	−1.19067	+	1.19067i	−0.976879	+	0.213792i	$0.931419\pi$
$644$	−1.23527e7	+	2.66637e7i	−0.0462493	+	0.0998303i
$645$	−4.47368e8	+	1.43590e7i	−1.66719	+	0.0535113i
$646$	−1.07946e8	−	1.68976e8i	−0.400413	−	0.626798i
$647$	−1.07934e8	+	1.07934e8i	−0.398516	+	0.398516i	−0.877709	−	0.479193i	$-0.840929\pi$
$647$	−1.07934e8	+	1.07934e8i	−0.398516	+	0.398516i	0.479193	+	0.877709i	$0.340929\pi$
$648$	2.61688e8	−	7.45431e7i	0.961742	−	0.273957i
$649$		−	6.33614e7i		−	0.231788i
$650$	−2.35811e7	−	1.38608e8i	−0.0858667	−	0.504717i
$651$	−2.16520e7	−	9.16199e7i	−0.0784795	−	0.332083i
$652$	−1.11273e8	+	4.08142e7i	−0.401464	+	0.147254i
$653$	−1.91561e8	+	1.91561e8i	−0.687966	+	0.687966i	−0.961782	−	0.273816i	$-0.911714\pi$
$653$	−1.91561e8	+	1.91561e8i	−0.687966	+	0.687966i	0.273816	+	0.961782i	$0.411714\pi$
$654$	−9.66430e7	−	9.37589e7i	−0.345491	−	0.335181i
$655$	−3.63346e7	+	1.79261e8i	−0.129299	+	0.637915i
$656$	−1.37674e8	+	1.16696e8i	−0.487688	+	0.413375i
$657$	6.19560e6	−	1.86170e7i	0.0218468	−	0.0656467i
$658$	3.34485e7	+	7.37166e6i	0.117408	+	0.0258754i
$659$			1.54849e8i			0.541070i	0.962710	+	0.270535i	$0.0872005\pi$
$659$			1.54849e8i			0.541070i	−0.962710	+	0.270535i	$0.912799\pi$
$660$	2.08772e7	+	5.17220e7i	0.0726173	+	0.179905i
$661$	3.36274e8			1.16436			0.582182	−	0.813059i	$-0.302199\pi$
$661$	3.36274e8			1.16436			0.582182	+	0.813059i	$0.302199\pi$
$662$	5.00297e7	−	2.27007e8i	0.172446	−	0.782465i
$663$	1.41132e8	+	8.71769e7i	0.484267	+	0.299131i
$664$	−3.16066e7	−	2.33336e8i	−0.107962	−	0.797036i
$665$	−3.36445e7	+	2.23042e7i	−0.114406	+	0.0758442i
$666$	1.19397e8	+	7.12758e7i	0.404175	+	0.241279i
$667$	1.55797e8	+	1.55797e8i	0.525028	+	0.525028i
$668$	−1.77576e8	+	6.51336e7i	−0.595736	+	0.218512i
$669$	−9.00085e7	−	3.80868e8i	−0.300611	−	1.27203i
$670$	−1.99765e8	+	7.71361e7i	−0.664195	+	0.256468i
$671$	−8.84653e7			−0.292823
$672$	4.09748e7	+	4.68823e7i	0.135023	+	0.154490i
$673$	−1.84324e8	−	1.84324e8i	−0.604694	−	0.604694i	0.336861	−	0.941555i	$-0.390635\pi$
$673$	−1.84324e8	−	1.84324e8i	−0.604694	−	0.604694i	−0.941555	+	0.336861i	$0.890635\pi$
$674$	−4.65720e6	+	2.97512e6i	−0.0152106	+	0.00971684i
$675$	2.71480e8	+	1.44512e8i	0.882728	+	0.469885i
$676$	9.58189e7	−	2.06828e8i	0.310178	−	0.669527i
$677$	2.18535e8	+	2.18535e8i	0.704297	+	0.704297i	0.965330	−	0.261033i	$-0.0840631\pi$
$677$	2.18535e8	+	2.18535e8i	0.704297	+	0.704297i	−0.261033	+	0.965330i	$0.584063\pi$
$678$	−5.13037e6	−	3.38702e8i	−0.0164611	−	1.08675i
$679$	−8.53801e7			−0.272739
$680$	−3.48837e8	−	2.28275e7i	−1.10942	−	0.0725993i
$681$	8.67053e7	+	3.66891e8i	0.274539	+	1.16170i
$682$	2.20281e7	−	9.99513e7i	0.0694424	−	0.315091i
$683$	−2.48635e8	−	2.48635e8i	−0.780370	−	0.780370i	0.199523	−	0.979893i	$-0.436061\pi$
$683$	−2.48635e8	−	2.48635e8i	−0.780370	−	0.780370i	−0.979893	+	0.199523i	$0.936061\pi$
$684$	6.48410e6	+	2.13988e8i	0.0202620	+	0.668683i
$685$	−8.26985e7	+	5.48240e7i	−0.257292	+	0.170569i
$686$	1.09290e8	−	6.98170e7i	0.338539	−	0.216266i
$687$	7.30064e7	+	4.50959e7i	0.225160	+	0.139081i
$688$	−5.41380e8	−	4.46485e7i	−1.66241	−	0.137101i
$689$	−2.50724e8			−0.766547
$690$	−3.23748e7	+	1.73156e8i	−0.0985507	+	0.527095i
$691$		−	9.38811e7i		−	0.284540i	−0.989828	−	0.142270i	$-0.954560\pi$
$691$		−	9.38811e7i		−	0.284540i	0.989828	−	0.142270i	$-0.0454402\pi$
$692$	−2.50290e8	+	9.18048e7i	−0.755311	+	0.277043i
$693$	−4.18330e6	+	1.25703e7i	−0.0125695	+	0.0377698i
$694$	4.78747e8	−	3.05834e8i	1.43228	−	0.914971i
$695$	−8.47591e7	+	4.18170e8i	−0.252483	+	1.24566i
$696$	4.35809e8	−	1.67383e8i	1.29261	−	0.496459i
$697$	1.70184e8	−	1.70184e8i	0.502598	−	0.502598i
$698$	1.92440e7	−	8.73183e7i	0.0565885	−	0.256767i
$699$	−4.93668e7	−	2.08894e8i	−0.144545	−	0.611638i
$700$	−3.40533e6	+	7.02941e7i	−0.00992806	+	0.204939i
$701$			2.73885e8i			0.795086i	0.917584	+	0.397543i	$0.130137\pi$
$701$			2.73885e8i			0.795086i	−0.917584	+	0.397543i	$0.869863\pi$
$702$	−8.16749e7	−	1.57159e8i	−0.236090	−	0.454285i
$703$	−7.73623e7	+	7.73623e7i	−0.222671	+	0.222671i
$704$	1.80080e7	+	6.52528e7i	0.0516117	+	0.187017i
$705$	2.05214e8	−	6.58669e6i	0.585653	−	0.0187975i
$706$	7.51874e7	−	4.80314e7i	0.213664	−	0.136493i
$707$	360722.	−	360722.i	0.00102074	−	0.00102074i
$708$	−2.33648e8	−	3.53820e8i	−0.658359	−	0.996970i
$709$		−	2.11125e8i		−	0.592382i	−0.955129	−	0.296191i	$-0.904284\pi$
$709$		−	2.11125e8i		−	0.592382i	0.955129	−	0.296191i	$-0.0957164\pi$
$710$	5.62831e7	−	1.27089e8i	0.157254	−	0.355087i
$711$	−1.59785e8	−	3.19182e8i	−0.444557	−	0.888034i
$712$	4.38260e8	+	3.33695e8i	1.21420	+	0.924505i
$713$	2.28570e8	−	2.28570e8i	0.630594	−	0.630594i
$714$	−5.95959e7	−	5.78174e7i	−0.163728	−	0.158842i
$715$	3.02607e7	−	2.00609e7i	0.0827866	−	0.0548824i
$716$	−2.23721e8	+	4.82907e8i	−0.609491	+	1.31560i
$717$	−4.93899e8	−	3.05080e8i	−1.33993	−	0.827669i
$718$	−1.43529e8	+	6.51253e8i	−0.387762	+	1.75945i
$719$			2.59772e8i			0.698885i	0.936958	+	0.349442i	$0.113629\pi$
$719$			2.59772e8i			0.698885i	−0.936958	+	0.349442i	$0.886371\pi$
$720$	3.07309e8	+	2.11838e8i	0.823337	+	0.567553i
$721$	−1.33401e8			−0.355920
$722$	2.03052e8	+	4.47503e7i	0.539505	+	0.118901i
$723$	2.57664e8	−	4.17136e8i	0.681772	−	1.10373i
$724$	−1.03085e8	−	4.77572e7i	−0.271632	−	0.125841i
$725$	4.86022e8	+	2.05465e8i	1.27539	+	0.539169i
$726$	2.56421e8	−	2.64309e8i	0.670107	−	0.690720i
$727$	−3.01758e8	−	3.01758e8i	−0.785337	−	0.785337i	0.195389	−	0.980726i	$-0.437403\pi$
$727$	−3.01758e8	−	3.01758e8i	−0.785337	−	0.785337i	−0.980726	+	0.195389i	$0.937403\pi$
$728$	2.45525e7	−	3.22462e7i	0.0636359	−	0.0835766i
$729$	3.81272e8	+	6.87478e7i	0.984130	+	0.177450i
$730$	2.51079e7	−	9.69502e6i	0.0645420	−	0.0249218i
$731$	7.24411e8			1.85453
$732$	−4.94003e8	+	3.26220e8i	−1.25950	+	0.831720i
$733$	3.13659e8	+	3.13659e8i	0.796426	+	0.796426i	0.982530	−	0.186104i	$-0.0595861\pi$
$733$	3.13659e8	+	3.13659e8i	0.796426	+	0.796426i	−0.186104	+	0.982530i	$0.559586\pi$
$734$	1.56925e8	+	2.45647e8i	0.396828	+	0.621188i
$735$	2.60181e8	−	2.77437e8i	0.655261	−	0.698719i
$736$	−6.30167e7	+	2.04290e8i	−0.158060	+	0.512405i
$737$	−3.91004e7	−	3.91004e7i	−0.0976741	−	0.0976741i
$738$	−2.49157e8	+	6.28810e7i	−0.619875	+	0.156441i
$739$	6.74457e8			1.67117			0.835586	−	0.549360i	$-0.185128\pi$
$739$	6.74457e8			1.67117			0.835586	+	0.549360i	$0.185128\pi$
$740$	2.88017e7	+	1.88558e8i	0.0710759	+	0.465319i
$741$	1.35618e8	−	3.20499e7i	0.333321	−	0.0787720i
$742$	1.22558e8	+	2.70103e7i	0.300006	+	0.0661178i
$743$	−7.69800e7	−	7.69800e7i	−0.187677	−	0.187677i	0.607014	−	0.794691i	$-0.292367\pi$
$743$	−7.69800e7	−	7.69800e7i	−0.187677	−	0.187677i	−0.794691	+	0.607014i	$0.792367\pi$
$744$	−2.45567e8	−	6.39373e8i	−0.596281	−	1.55251i
$745$	−1.32444e8	+	6.53429e8i	−0.320304	+	1.58026i
$746$	3.24768e6	+	5.08386e6i	0.00782271	+	0.0122455i
$747$	1.05865e8	−	3.18112e8i	0.253976	−	0.763164i
$748$	−3.10857e7	−	8.47499e7i	−0.0742773	−	0.202504i
$749$	1.33066e7			0.0316680
$750$	8.40618e7	+	4.13415e8i	0.199258	+	0.979947i
$751$			3.41689e8i			0.806699i	0.915046	+	0.403350i	$0.132154\pi$
$751$			3.41689e8i			0.806699i	−0.915046	+	0.403350i	$0.867846\pi$
$752$	2.48339e8	+	2.04810e7i	0.583972	+	0.0481611i
$753$	3.97190e8	−	6.43017e8i	0.930280	−	1.50604i
$754$	−1.63595e8	−	2.56088e8i	−0.381641	−	0.597414i
$755$	−5.52521e8	−	1.11991e8i	−1.28383	−	0.260220i
$756$	2.29933e7	+	8.56205e7i	0.0532152	+	0.198158i
$757$	−4.26121e8	+	4.26121e8i	−0.982303	+	0.982303i	−0.999846	−	0.0175436i	$-0.994415\pi$
$757$	−4.26121e8	+	4.26121e8i	−0.982303	+	0.982303i	0.0175436	+	0.999846i	$0.494415\pi$
$758$	6.90960e8	+	1.52280e8i	1.58652	+	0.349650i
$759$	−4.42685e7	+	1.04617e7i	−0.101244	+	0.0239265i
$760$	−2.20773e8	+	1.93654e8i	−0.502928	+	0.441148i
$761$		−	4.75251e8i		−	1.07837i	−0.842186	−	0.539187i	$-0.818732\pi$
$761$		−	4.75251e8i		−	1.07837i	0.842186	−	0.539187i	$-0.181268\pi$
$762$	2.46788e7	−	373814.i	0.0557775	−	0.000844871i
$763$	3.10217e7	−	3.10217e7i	0.0698379	−	0.0698379i
$764$	4.02526e8	+	1.86482e8i	0.902639	+	0.418174i
$765$	−4.31646e8	−	2.47858e8i	−0.964146	−	0.553629i
$766$	3.10744e8	+	4.86432e8i	0.691378	+	1.08227i
$767$	−1.95158e8	+	1.95158e8i	−0.432514	+	0.432514i
$768$	3.41182e8	+	2.97976e8i	0.753187	+	0.657806i
$769$			4.35445e8i			0.957534i	0.877942	+	0.478767i	$0.158916\pi$
$769$			4.35445e8i			0.957534i	−0.877942	+	0.478767i	$0.841084\pi$
$770$	−1.69530e7	+	6.54613e6i	−0.0371343	+	0.0143388i
$771$	−1.49661e8	+	3.53686e7i	−0.326547	+	0.0771710i
$772$	−1.87272e8	−	5.10564e8i	−0.407024	−	1.10968i
$773$	−2.48117e8	+	2.48117e8i	−0.537177	+	0.537177i	−0.922699	−	0.385522i	$-0.874021\pi$
$773$	−2.48117e8	+	2.48117e8i	−0.537177	+	0.537177i	0.385522	+	0.922699i	$0.374021\pi$
$774$	−6.64115e8	−	3.96454e8i	−1.43225	−	0.855007i
$775$	3.01438e8	−	7.13041e8i	0.647578	−	1.53183i
$776$	−6.15532e8	+	8.33769e7i	−1.31724	+	0.178427i
$777$	−2.38094e7	+	3.85453e7i	−0.0507557	+	0.0821692i
$778$	−4.64983e8	−	1.02477e8i	−0.987412	−	0.217614i
$779$		−	2.02183e8i		−	0.427693i
$780$	9.50044e7	−	2.23611e8i	0.200198	−	0.471204i
$781$	3.58919e7			0.0753430
$782$	6.13599e7	−	2.78417e8i	0.128311	−	0.582204i
$783$	6.62067e8	+	5.92118e7i	1.37917	+	0.123346i
$784$	3.52126e8	−	2.98471e8i	0.730719	−	0.619375i
$785$	1.97955e8	+	2.98602e8i	0.409220	+	0.617283i
$786$	−2.20080e8	+	2.26849e8i	−0.453223	+	0.467164i
$787$	8.34963e7	+	8.34963e7i	0.171294	+	0.171294i	0.787548	−	0.616254i	$-0.211350\pi$
$787$	8.34963e7	+	8.34963e7i	0.171294	+	0.171294i	−0.616254	+	0.787548i	$0.711350\pi$
$788$	−2.55582e8	−	6.96801e8i	−0.522337	−	1.42407i
$789$	2.59946e8	−	6.14316e7i	0.529239	−	0.125072i
$790$	1.98267e8	−	4.47696e8i	0.402133	−	0.908033i
$791$	1.10368e8			0.223004
$792$	−1.78834e7	+	9.47083e7i	−0.0359977	+	0.190639i
$793$	2.72480e8	+	2.72480e8i	0.546405	+	0.546405i
$794$	4.88429e7	−	3.12020e7i	0.0975754	−	0.0623333i
$795$	7.51921e8	−	2.41342e7i	1.49648	−	0.0480320i
$796$	−5.49471e8	−	2.54558e8i	−1.08945	−	0.504717i
$797$	−1.60585e8	−	1.60585e8i	−0.317198	−	0.317198i	0.530492	−	0.847690i	$-0.322007\pi$
$797$	−1.60585e8	−	1.60585e8i	−0.317198	−	0.317198i	−0.847690	+	0.530492i	$0.822007\pi$
$798$	−6.97449e7	+	1.05644e6i	−0.137247	+	0.00207891i
$799$	−3.32298e8			−0.651460
$800$	4.40947e7	+	5.10098e8i	0.0861225	+	0.996285i
$801$	3.51091e8	+	7.01329e8i	0.683159	+	1.36466i
$802$	−9.61573e7	+	4.36308e8i	−0.186406	+	0.845805i
$803$	4.91443e6	+	4.91443e6i	0.00949131	+	0.00949131i
$804$	−3.62528e8	−	7.41581e7i	−0.697546	−	0.142689i
$805$	−5.62508e7	−	1.14015e7i	−0.107830	−	0.0218562i
$806$	−3.75706e8	+	2.40009e8i	−0.717534	+	0.458377i
$807$	−1.24565e8	+	2.01660e8i	−0.237015	+	0.383707i
$808$	2.24830e6	−	2.95281e6i	0.00426206	−	0.00559760i
$809$	−6.13153e7			−0.115804			−0.0579020	−	0.998322i	$-0.518441\pi$
$809$	−6.13153e7			−0.115804			−0.0579020	+	0.998322i	$0.518441\pi$
$810$	2.60070e8	+	4.63458e8i	0.489368	+	0.872077i
$811$		−	8.80715e8i		−	1.65110i	−0.564331	−	0.825549i	$-0.690866\pi$
$811$		−	8.80715e8i		−	1.65110i	0.564331	−	0.825549i	$-0.309134\pi$
$812$	5.23794e7	+	1.42804e8i	0.0978346	+	0.266729i
$813$	−1.71255e8	−	1.05784e8i	−0.318693	−	0.196856i
$814$	−4.15084e7	+	2.65165e7i	−0.0769596	+	0.0491635i
$815$	−1.27908e8	−	1.92941e8i	−0.236279	−	0.356412i
$816$	−4.86107e8	−	3.58626e8i	−0.894666	−	0.660042i
$817$	4.30309e8	−	4.30309e8i	0.789067	−	0.789067i
$818$	1.64176e8	−	7.44940e8i	0.299951	−	1.36101i
$819$	5.16023e7	−	2.58325e7i	0.0939328	−	0.0470235i
$820$	−2.84030e8	−	2.08758e8i	−0.515137	−	0.378619i
$821$			3.77726e8i			0.682570i	0.939960	+	0.341285i	$0.110862\pi$
$821$			3.77726e8i			0.682570i	−0.939960	+	0.341285i	$0.889138\pi$
$822$	−1.71433e8	+	2.59673e6i	−0.308660	+	0.00467532i
$823$	−3.95663e8	+	3.95663e8i	−0.709783	+	0.709783i	−0.966490	−	0.256706i	$-0.917363\pi$
$823$	−3.95663e8	+	3.95663e8i	−0.709783	+	0.709783i	0.256706	+	0.966490i	$0.417363\pi$
$824$	−9.61728e8	+	1.30271e8i	−1.71898	+	0.232844i
$825$	−8.88206e7	+	6.30755e7i	−0.158180	+	0.112331i
$826$	1.16420e8	−	7.43719e7i	0.206580	−	0.131968i
$827$	1.57703e8	−	1.57703e8i	0.278821	−	0.278821i	−0.553818	−	0.832638i	$-0.686829\pi$
$827$	1.57703e8	−	1.57703e8i	0.278821	−	0.278821i	0.832638	+	0.553818i	$0.186829\pi$
$828$	−2.08624e8	+	2.21662e8i	−0.367513	+	0.390482i
$829$			5.33109e8i			0.935734i	0.883799	+	0.467867i	$0.154977\pi$
$829$			5.33109e8i			0.935734i	−0.883799	+	0.467867i	$0.845023\pi$
$830$	4.29024e8	−	1.65661e8i	0.750322	−	0.289725i
$831$	2.21700e8	+	9.38116e8i	0.386334	+	1.63476i
$832$	1.45517e8	−	2.56450e8i	0.252665	−	0.445279i
$833$	−4.35276e8	+	4.35276e8i	−0.753060	+	0.753060i
$834$	−5.13388e8	+	5.29180e8i	−0.885009	+	0.912232i
$835$	−2.04123e8	−	3.07907e8i	−0.350617	−	0.528883i
$836$	−6.88077e7	−	3.18772e7i	−0.117766	−	0.0545583i
$837$	8.68695e7	−	9.71317e8i	0.148146	−	1.65647i
$838$	6.89682e7	−	3.12939e8i	0.117197	−	0.531775i
$839$			4.04697e8i			0.685242i	0.939474	+	0.342621i	$0.111315\pi$
$839$			4.04697e8i			0.685242i	−0.939474	+	0.342621i	$0.888685\pi$
$840$	−7.05290e7	+	9.90696e7i	−0.118995	+	0.167149i
$841$	5.45641e8			0.917316
$842$	1.22822e8	+	2.70685e7i	0.205750	+	0.0453449i
$843$	1.59870e8	+	9.87513e7i	0.266860	+	0.164839i
$844$	6.05128e7	−	1.30618e8i	0.100651	−	0.217259i
$845$	4.36332e8	+	8.84404e7i	0.723181	+	0.146582i
$846$	3.04640e8	+	1.81859e8i	0.503124	+	0.300348i
$847$	8.48412e7	+	8.48412e7i	0.139623	+	0.139623i
$848$	9.09935e8	+	7.50438e7i	1.49219	+	0.123063i
$849$	4.46448e7	+	1.88913e8i	0.0729539	+	0.308702i
$850$	−1.14515e8	−	6.73108e8i	−0.186468	−	1.09604i
$851$	−1.55560e8			−0.252412
$852$	2.00426e8	−	1.32353e8i	0.324067	−	0.214001i
$853$	3.40431e8	+	3.40431e8i	0.548507	+	0.548507i	0.926009	−	0.377502i	$-0.123217\pi$
$853$	3.40431e8	+	3.40431e8i	0.548507	+	0.548507i	−0.377502	+	0.926009i	$0.623217\pi$
$854$	−1.03838e8	−	1.62546e8i	−0.166718	−	0.260977i
$855$	−4.03633e8	+	1.09172e8i	−0.645786	+	0.174668i
$856$	9.59311e7	−	1.29943e7i	0.152946	−	0.0207173i
$857$	−4.37634e8	−	4.37634e8i	−0.695294	−	0.695294i	0.268098	−	0.963392i	$-0.413605\pi$
$857$	−4.37634e8	−	4.37634e8i	−0.695294	−	0.695294i	−0.963392	+	0.268098i	$0.913605\pi$
$858$	6.27301e7	−	950183.i	0.0993149	−	0.00150434i
$859$	1.01487e8			0.160115			0.0800576	−	0.996790i	$-0.474490\pi$
$859$	1.01487e8			0.160115			0.0800576	+	0.996790i	$0.474490\pi$
$860$	−1.60202e8	−	1.04881e9i	−0.251868	−	1.64892i
$861$	−1.92559e7	−	8.14806e7i	−0.0301685	−	0.127657i
$862$	1.83104e8	+	4.03541e7i	0.285876	+	0.0630037i
$863$	4.62527e8	+	4.62527e8i	0.719623	+	0.719623i	0.968528	−	0.248905i	$-0.0800706\pi$
$863$	4.62527e8	+	4.62527e8i	0.719623	+	0.719623i	−0.248905	+	0.968528i	$0.580071\pi$
$864$	2.49377e8	+	5.94811e8i	0.386648	+	0.922227i
$865$	−2.87709e8	−	4.33990e8i	−0.444534	−	0.670550i
$866$	2.46707e8	+	3.86191e8i	0.379864	+	0.594632i
$867$	1.30900e8	+	8.08566e7i	0.200855	+	0.124068i
$868$	2.09507e8	−	7.68456e7i	0.320360	−	0.117506i
$869$	1.26436e8			0.192668
$870$	5.15270e8	+	7.52260e8i	0.782488	+	1.14238i
$871$			2.40865e8i			0.364518i
$872$	1.93351e8	−	2.53939e8i	0.291607	−	0.382983i
$873$	−8.39167e8	−	2.79269e8i	−1.26126	−	0.419740i
$874$	−1.28934e8	−	2.01831e8i	−0.193123	−	0.302311i
$875$	−1.35097e8	+	2.53456e7i	−0.201661	+	0.0378337i
$876$	4.55651e7	+	9.32072e6i	0.0677828	+	0.0138656i
$877$	−2.27548e6	+	2.27548e6i	−0.00337345	+	0.00337345i	−0.708791	−	0.705418i	$-0.750759\pi$
$877$	−2.27548e6	+	2.27548e6i	−0.00337345	+	0.00337345i	0.705418	+	0.708791i	$0.250759\pi$
$878$	−1.53413e8	−	3.38104e7i	−0.226661	−	0.0499536i
$879$	1.67369e8	+	7.08217e8i	0.246439	+	1.04280i
$880$	−1.15827e8	+	6.37484e7i	−0.169966	+	0.0935452i
$881$		−	9.63281e8i		−	1.40872i	−0.709842	−	0.704361i	$-0.751234\pi$
$881$		−	9.63281e8i		−	1.40872i	0.709842	−	0.704361i	$-0.248766\pi$
$882$	6.37263e8	−	1.60829e8i	0.928780	−	0.234401i
$883$	−2.37166e8	+	2.37166e8i	−0.344485	+	0.344485i	−0.858051	−	0.513565i	$-0.828324\pi$
$883$	−2.37166e8	+	2.37166e8i	−0.344485	+	0.344485i	0.513565	+	0.858051i	$0.328324\pi$
$884$	−1.65290e8	+	3.56782e8i	−0.239271	+	0.516472i
$885$	5.66492e8	−	6.04063e8i	0.817267	−	0.871470i
$886$	−5.37846e8	−	8.41934e8i	−0.773316	−	1.21053i
$887$	−7.04232e8	+	7.04232e8i	−1.00912	+	1.00912i	−0.00916630	+	0.999958i	$0.502918\pi$
$887$	−7.04232e8	+	7.04232e8i	−1.00912	+	1.00912i	−0.999958	+	0.00916630i	$0.997082\pi$
$888$	−1.34008e8	+	3.01136e8i	−0.191379	+	0.430055i
$889$			8.04170e6i			0.0114457i
$890$	−4.35647e8	+	9.83708e8i	−0.617966	+	1.39539i
$891$	−8.22320e7	+	1.09865e8i	−0.116254	+	0.155320i
$892$	8.70928e8	−	3.19450e8i	1.22712	−	0.450100i
$893$	−1.97389e8	+	1.97389e8i	−0.277184	+	0.277184i
$894$	−8.02216e8	+	8.26893e8i	−1.12274	+	1.15727i
$895$	−1.01876e9	−	2.06493e8i	−1.42103	−	0.288029i
$896$	−9.87582e7	+	1.09680e8i	−0.137293	+	0.152477i
$897$	1.68573e8	+	1.04127e8i	0.233567	+	0.144274i
$898$	9.28427e8	+	2.04615e8i	1.28209	+	0.282558i
$899$		−	1.67317e9i		−	2.30283i
$900$	−2.63394e8	+	6.79753e8i	−0.361308	+	0.932446i
$901$	−1.21757e9			−1.66463
$902$	1.95903e7	−	8.88900e7i	0.0266945	−	0.121125i
$903$	1.32434e8	−	2.14399e8i	0.179860	−	0.291178i
$904$	7.95675e8	−	1.07778e8i	1.07704	−	0.145890i
$905$	4.40797e7	−	2.17473e8i	0.0594693	−	0.293400i
$906$	−6.99197e8	−	6.78331e8i	−0.940188	−	0.912131i
$907$	1.10352e8	+	1.10352e8i	0.147897	+	0.147897i	0.777178	−	0.629281i	$-0.216651\pi$
$907$	1.10352e8	+	1.10352e8i	0.147897	+	0.147897i	−0.629281	+	0.777178i	$0.716651\pi$
$908$	−8.38966e8	+	3.07727e8i	−1.12069	+	0.411063i
$909$	4.72527e6	−	2.36551e6i	0.00629122	−	0.00314943i
$910$	7.23791e7	+	3.20540e7i	0.0960482	+	0.0425361i
$911$	1.15195e9			1.52363			0.761816	−	0.647794i	$-0.224308\pi$
$911$	1.15195e9			1.52363			0.761816	+	0.647794i	$0.224308\pi$
$912$	−5.01781e8	+	7.57247e7i	−0.661500	+	0.0998281i
$913$	8.39737e7	+	8.39737e7i	0.110340	+	0.110340i
$914$	−2.42621e8	+	1.54992e8i	−0.317753	+	0.202988i
$915$	−8.43394e8	−	7.90937e8i	−1.10095	−	1.03247i
$916$	−8.55031e7	+	1.84561e8i	−0.111249	+	0.240134i
$917$	−7.28169e7	−	7.28169e7i	−0.0944331	−	0.0944331i
$918$	−3.96629e8	−	7.63195e8i	−0.512692	−	0.986524i
$919$	−1.76125e8			−0.226921			−0.113461	−	0.993543i	$-0.536194\pi$
$919$	−1.76125e8			−0.226921			−0.113461	+	0.993543i	$0.536194\pi$
$920$	−4.16664e8	−	2.72661e7i	−0.535085	−	0.0350154i
$921$	−1.44509e9	+	3.41509e8i	−1.84976	+	0.437143i
$922$	−2.73040e8	+	1.23890e9i	−0.348364	+	1.58068i
$923$	−1.10550e8	−	1.10550e8i	−0.140589	−	0.140589i
$924$	−3.07658e7	−	6.29340e6i	−0.0389989	−	0.00797755i
$925$	−3.45217e8	+	1.40065e8i	−0.436182	+	0.176972i
$926$	−8.00897e8	+	5.11631e8i	−1.00866	+	0.644353i
$927$	−1.31114e9	−	4.36339e8i	−1.64593	−	0.547753i
$928$	5.17073e8	+	9.78366e8i	0.647005	+	1.22421i
$929$	7.13693e6			0.00890152			0.00445076	−	0.999990i	$-0.498583\pi$
$929$	7.13693e6			0.00890152			0.00445076	+	0.999990i	$0.498583\pi$
$930$	1.10364e9	−	7.55951e8i	1.37207	−	0.939821i
$931$			5.17118e8i			0.640827i
$932$	4.77676e8	−	1.75208e8i	0.590046	−	0.216425i
$933$	7.17673e7	−	1.16185e8i	0.0883653	−	0.143056i
$934$	7.85485e7	−	5.01785e7i	0.0964044	−	0.0615853i
$935$	1.46952e8	−	9.74199e7i	0.179779	−	0.119183i
$936$	3.46791e8	−	2.36626e8i	0.422902	−	0.288559i
$937$	1.16146e7	−	1.16146e7i	0.0141184	−	0.0141184i	−0.700012	−	0.714131i	$-0.746822\pi$
$937$	1.16146e7	−	1.16146e7i	0.0141184	−	0.0141184i	0.714131	+	0.700012i	$0.246822\pi$
$938$	2.59482e7	−	1.17738e8i	0.0314411	−	0.142662i
$939$	−2.11587e8	+	5.00033e7i	−0.255560	+	0.0603951i
$940$	7.34871e7	+	4.81104e8i	0.0884764	+	0.579236i
$941$			4.65318e7i			0.0558446i	0.999610	+	0.0279223i	$0.00888910\pi$
$941$			4.65318e7i			0.0558446i	−0.999610	+	0.0279223i	$0.991111\pi$
$942$	9.37610e6	+	6.19001e8i	0.0112168	+	0.740523i
$943$	2.03274e8	−	2.03274e8i	0.242408	−	0.242408i
$944$	7.66684e8	−	6.49859e8i	0.911382	−	0.772508i
$945$	−1.52268e8	+	8.24387e7i	−0.180432	+	0.0976868i
$946$	2.30880e8	−	1.47491e8i	0.272718	−	0.174218i
$947$	−3.42978e8	+	3.42978e8i	−0.403847	+	0.403847i	−0.879586	−	0.475739i	$-0.842181\pi$
$947$	−3.42978e8	+	3.42978e8i	−0.403847	+	0.403847i	0.475739	+	0.879586i	$0.342181\pi$
$948$	7.06036e8	−	4.66237e8i	0.828708	−	0.547245i
$949$		−	3.02736e7i		−	0.0354214i
$950$	−4.67857e8	−	3.31811e8i	−0.545686	−	0.387008i
$951$	−2.63863e8	+	6.23573e7i	−0.306787	+	0.0725013i
$952$	1.19232e8	−	1.56594e8i	0.138192	−	0.181495i
$953$	−5.14338e8	+	5.14338e8i	−0.594251	+	0.594251i	−0.938777	−	0.344526i	$-0.888040\pi$
$953$	−5.14338e8	+	5.14338e8i	−0.594251	+	0.594251i	0.344526	+	0.938777i	$0.388040\pi$
$954$	1.11622e9	+	6.66347e8i	1.28560	+	0.767459i
$955$	−1.72122e8	+	8.49186e8i	−0.197618	+	0.974974i
$956$	5.78441e8	−	1.24858e9i	0.662042	−	1.42903i
$957$	−1.23736e8	+	2.00318e8i	−0.141176	+	0.228551i
$958$	8.97610e7	−	4.07285e8i	0.102092	−	0.463236i
$959$		−	5.58623e7i		−	0.0633378i
$960$	−4.11721e8	+	7.83099e8i	−0.465360	+	0.885121i
$961$	−1.56720e9			−1.76585
$962$	2.09522e8	+	4.61762e7i	0.235344	+	0.0518672i
$963$	1.30785e8	+	4.35243e7i	0.146446	+	0.0487363i
$964$	1.05452e9	+	4.88538e8i	1.17713	+	0.545340i
$965$	8.85291e8	−	5.86893e8i	0.985154	−	0.653096i
$966$	−7.11836e7	−	6.90593e7i	−0.0789675	−	0.0766109i
$967$	2.27493e8	+	2.27493e8i	0.251587	+	0.251587i	0.821621	−	0.570034i	$-0.193070\pi$
$967$	2.27493e8	+	2.27493e8i	0.251587	+	0.251587i	−0.570034	+	0.821621i	$0.693070\pi$
$968$	6.94498e8	+	5.28796e8i	0.765675	+	0.582992i
$969$	6.58588e8	−	1.55641e8i	0.723840	−	0.171061i
$970$	−4.37007e8	−	1.13175e9i	−0.478821	−	1.24004i
$971$	1.63160e9			1.78220			0.891099	−	0.453809i	$-0.149935\pi$
$971$	1.63160e9			1.78220			0.891099	+	0.453809i	$0.149935\pi$
$972$	−5.40634e7	+	9.16737e8i	−0.0588714	+	0.998266i
$973$	−1.69863e8	−	1.69863e8i	−0.184399	−	0.184399i
$974$	−1.56972e8	−	2.45721e8i	−0.169881	−	0.265929i
$975$	4.67851e8	+	7.92967e7i	0.504771	+	0.0855542i
$976$	−9.07334e8	−	1.07044e9i	−0.975928	−	1.15137i
$977$	−5.38315e7	−	5.38315e7i	−0.0577235	−	0.0577235i	0.677656	−	0.735379i	$-0.262996\pi$
$977$	−5.38315e7	−	5.38315e7i	−0.0577235	−	0.0577235i	−0.735379	+	0.677656i	$0.762996\pi$
$978$	−6.05835e6	−	3.99966e8i	−0.00647646	−	0.427569i
$979$	−2.77813e8			−0.296077
$980$	7.26457e8	+	5.33936e8i	0.771848	+	0.567298i
$981$	4.06368e8	−	2.03431e8i	0.430440	−	0.215481i
$982$	5.74570e8	+	1.26629e8i	0.606748	+	0.133720i
$983$	1.19990e8	+	1.19990e8i	0.126324	+	0.126324i	0.767442	−	0.641118i	$-0.221529\pi$
$983$	1.19990e8	+	1.19990e8i	0.126324	+	0.126324i	−0.641118	+	0.767442i	$0.721529\pi$
$984$	−2.18391e8	−	5.68615e8i	−0.229218	−	0.596806i
$985$	1.20821e9	−	8.00972e8i	1.26426	−	0.838124i
$986$	−7.94448e8	−	1.24361e9i	−0.828772	−	1.29734i
$987$	−6.07494e7	+	9.83480e7i	−0.0631816	+	0.102286i
$988$	1.13749e8	+	3.10117e8i	0.117944	+	0.321554i
$989$	8.65264e8			0.894457
$990$	−1.88036e8	+	8.88786e6i	−0.193792	+	0.00915992i
$991$			6.24242e8i			0.641404i	0.947180	+	0.320702i	$0.103919\pi$
$991$			6.24242e8i			0.641404i	−0.947180	+	0.320702i	$0.896081\pi$
$992$	1.43536e9	−	7.58595e8i	1.47036	−	0.777097i
$993$	6.67464e8	+	4.12291e8i	0.681680	+	0.421072i
$994$	4.21289e7	+	6.59478e7i	0.0428964	+	0.0671492i
$995$	2.34956e8	−	1.15919e9i	0.238516	−	1.17675i
$996$	7.78579e8	+	1.59265e8i	0.787997	+	0.161192i
$997$	−3.09468e6	+	3.09468e6i	−0.00312270	+	0.00312270i	−0.708666	−	0.705544i	$-0.750703\pi$
$997$	−3.09468e6	+	3.09468e6i	−0.00312270	+	0.00312270i	0.705544	+	0.708666i	$0.250703\pi$
$998$	−2.65513e8	−	5.85161e7i	−0.267113	−	0.0588686i
$999$	−3.60090e8	+	3.00969e8i	−0.361173	+	0.301873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.5	✓	136
3.2	odd	2	inner	60.7.l.a.23.64	yes	136
4.3	odd	2	inner	60.7.l.a.23.30	yes	136
5.2	odd	4	inner	60.7.l.a.47.39	yes	136
12.11	even	2	inner	60.7.l.a.23.39	yes	136
15.2	even	4	inner	60.7.l.a.47.30	yes	136
20.7	even	4	inner	60.7.l.a.47.64	yes	136
60.47	odd	4	inner	60.7.l.a.47.5	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.5	✓	136	1.1	even	1	trivial
60.7.l.a.23.30	yes	136	4.3	odd	2	inner
60.7.l.a.23.39	yes	136	12.11	even	2	inner
60.7.l.a.23.64	yes	136	3.2	odd	2	inner
60.7.l.a.47.5	yes	136	60.47	odd	4	inner
60.7.l.a.47.30	yes	136	15.2	even	4	inner
60.7.l.a.47.39	yes	136	5.2	odd	4	inner
60.7.l.a.47.64	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)

\(f(q)\)	\(=\)	\(q+(-7.81252 - 1.72179i) q^{2} +(14.1892 - 22.9710i) q^{3} +(58.0709 + 26.9030i) q^{4} +(-24.8314 + 122.509i) q^{5} +(-150.404 + 155.031i) q^{6} +(-49.7637 - 49.7637i) q^{7} +(-407.358 - 310.166i) q^{8} +(-326.336 - 651.879i) q^{9} +O(q^{10})\)	\(q+(-7.81252 - 1.72179i) q^{2} +(14.1892 - 22.9710i) q^{3} +(58.0709 + 26.9030i) q^{4} +(-24.8314 + 122.509i) q^{5} +(-150.404 + 155.031i) q^{6} +(-49.7637 - 49.7637i) q^{7} +(-407.358 - 310.166i) q^{8} +(-326.336 - 651.879i) q^{9} +(404.930 - 914.348i) q^{10} +258.225 q^{11} +(1441.97 - 952.216i) q^{12} +(-795.352 - 795.352i) q^{13} +(303.097 + 474.462i) q^{14} +(2461.82 + 2308.70i) q^{15} +(2648.45 + 3124.56i) q^{16} +(-3862.39 - 3862.39i) q^{17} +(1427.11 + 5654.70i) q^{18} -4588.60 q^{19} +(-4737.84 + 6446.15i) q^{20} +(-1849.23 + 437.018i) q^{21} +(-2017.39 - 444.609i) q^{22} +(-4613.38 - 4613.38i) q^{23} +(-12904.9 + 4956.44i) q^{24} +(-14391.8 - 6084.12i) q^{25} +(4844.27 + 7583.13i) q^{26} +(-19604.8 - 1753.35i) q^{27} +(-1551.03 - 4228.62i) q^{28} -33770.8 q^{29} +(-15257.9 - 22275.5i) q^{30} +49545.0i q^{31} +(-15311.3 - 28970.8i) q^{32} +(3663.99 - 5931.69i) q^{33} +(23524.7 + 36825.2i) q^{34} +(7332.19 - 4860.79i) q^{35} +(-1413.09 - 46634.6i) q^{36} +(16859.7 - 16859.7i) q^{37} +(35848.6 + 7900.61i) q^{38} +(-29555.4 + 6984.67i) q^{39} +(48113.4 - 42203.1i) q^{40} +44061.9i q^{41} +(15199.6 - 230.230i) q^{42} +(-93777.7 + 93777.7i) q^{43} +(14995.3 + 6947.03i) q^{44} +(87964.2 - 23791.9i) q^{45} +(28098.8 + 43985.4i) q^{46} +(43017.2 - 43017.2i) q^{47} +(109354. - 16502.8i) q^{48} -112696. i q^{49} +(101961. + 72312.0i) q^{50} +(-143527. + 33919.0i) q^{51} +(-24789.4 - 67584.1i) q^{52} +(157619. - 157619. i) q^{53} +(150144. + 47453.3i) q^{54} +(-6412.08 + 31634.8i) q^{55} +(4836.65 + 35706.7i) q^{56} +(-65108.4 + 105405. i) q^{57} +(263835. + 58146.1i) q^{58} -245373. i q^{59} +(80848.8 + 200298. i) q^{60} -342590. q^{61} +(85306.0 - 387071. i) q^{62} +(-16200.2 + 48679.6i) q^{63} +(69737.8 + 252698. i) q^{64} +(117187. - 77687.9i) q^{65} +(-38838.1 + 40032.8i) q^{66} +(-151420. - 151420. i) q^{67} +(-120382. - 328202. i) q^{68} +(-171434. + 40514.1i) q^{69} +(-65652.1 + 25350.5i) q^{70} +138995. q^{71} +(-69255.2 + 366767. i) q^{72} +(19031.6 + 19031.6i) q^{73} +(-160745. + 102688. i) q^{74} +(-343966. + 244266. i) q^{75} +(-266464. - 123447. i) q^{76} +(-12850.2 - 12850.2i) q^{77} +(242928. - 3679.67i) q^{78} +489634. q^{79} +(-448551. + 246872. i) q^{80} +(-318451. + 425463. i) q^{81} +(75865.4 - 344235. i) q^{82} +(325196. + 325196. i) q^{83} +(-119143. - 24371.8i) q^{84} +(569085. - 377268. i) q^{85} +(894105. - 571174. i) q^{86} +(-479179. + 775749. i) q^{87} +(-105190. - 80092.6i) q^{88} -1.07586e6 q^{89} +(-728187. + 34419.1i) q^{90} +79159.3i q^{91} +(-143789. - 392017. i) q^{92} +(1.13810e6 + 703001. i) q^{93} +(-410140. + 262006. i) q^{94} +(113941. - 562144. i) q^{95} +(-882743. - 59356.1i) q^{96} +(857855. - 857855. i) q^{97} +(-194039. + 880441. i) q^{98} +(-84268.0 - 168331. i) 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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