LMFDB - Embedded newform 76.8.i.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	76.17
Dual form			76.8.i.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-62.6763 - 52.5916i) q^{3} +(458.247 - 166.788i) q^{5} +(128.407 + 222.408i) q^{7} +(782.666 + 4438.72i) q^{9} +O(q^{10})$	\(q+(-62.6763 - 52.5916i) q^{3} +(458.247 - 166.788i) q^{5} +(128.407 + 222.408i) q^{7} +(782.666 + 4438.72i) q^{9} +(-4007.98 + 6942.02i) q^{11} +(8230.60 - 6906.30i) q^{13} +(-37492.9 - 13646.3i) q^{15} +(-5073.41 + 28772.7i) q^{17} +(19198.8 + 22919.0i) q^{19} +(3648.71 - 20692.9i) q^{21} +(51083.4 + 18592.8i) q^{23} +(122325. - 102643. i) q^{25} +(94916.8 - 164401. i) q^{27} +(16138.4 + 91525.5i) q^{29} +(9058.57 + 15689.9i) q^{31} +(616297. - 224314. i) q^{33} +(95937.5 + 80501.1i) q^{35} +245181. q^{37} -879077. q^{39} +(-353308. - 296461. i) q^{41} +(-410553. + 149429. i) q^{43} +(1.09898e6 + 1.90349e6i) q^{45} +(-86855.1 - 492580. i) q^{47} +(378795. - 656091. i) q^{49} +(1.83119e6 - 1.53655e6i) q^{51} +(619908. + 225628. i) q^{53} +(-678797. + 3.84965e6i) q^{55} +(2037.27 - 2.44617e6i) q^{57} +(-17003.7 + 96432.8i) q^{59} +(-763548. - 277909. i) q^{61} +(-886708. + 744036. i) q^{63} +(2.61976e6 - 4.53756e6i) q^{65} +(401123. + 2.27488e6i) q^{67} +(-2.22389e6 - 3.85189e6i) q^{69} +(3.34948e6 - 1.21911e6i) q^{71} +(2.47576e6 + 2.07741e6i) q^{73} -1.30650e7 q^{75} -2.05862e6 q^{77} +(-1.34071e6 - 1.12499e6i) q^{79} +(-5.33237e6 + 1.94082e6i) q^{81} +(1.19432e6 + 2.06862e6i) q^{83} +(2.47408e6 + 1.40312e7i) q^{85} +(3.80198e6 - 6.58522e6i) q^{87} +(-9.40415e6 + 7.89102e6i) q^{89} +(2.59289e6 + 943734. i) q^{91} +(257400. - 1.45979e6i) q^{93} +(1.26204e7 + 7.30042e6i) q^{95} +(-60550.0 + 343396. i) q^{97} +(-3.39506e7 - 1.23570e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−62.6763	−	52.5916i	−1.34023	−	1.12458i	−0.981567	−	0.191117i	$-0.938789\pi$
$3$	−62.6763	−	52.5916i	−1.34023	−	1.12458i	−0.358661	−	0.933468i	$-0.616766\pi$
$4$		0			0
$5$	458.247	−	166.788i	1.63948	−	0.596720i	0.652529	−	0.757764i	$-0.273708\pi$
$5$	458.247	−	166.788i	1.63948	−	0.596720i	0.986947	+	0.161044i	$0.0514860\pi$
$6$		0			0
$7$	128.407	+	222.408i	0.141497	+	0.245080i	0.928061	−	0.372429i	$-0.121475\pi$
$7$	128.407	+	222.408i	0.141497	+	0.245080i	−0.786564	+	0.617509i	$0.788142\pi$
$8$		0			0
$9$	782.666	+	4438.72i	0.357872	+	2.02959i
$10$		0			0
$11$	−4007.98	+	6942.02i	−0.907927	+	1.57258i	−0.0909880	+	0.995852i	$0.529003\pi$
$11$	−4007.98	+	6942.02i	−0.907927	+	1.57258i	−0.816939	+	0.576724i	$0.804331\pi$
$12$		0			0
$13$	8230.60	−	6906.30i	1.03903	−	0.871853i	0.0471362	−	0.998888i	$-0.484991\pi$
$13$	8230.60	−	6906.30i	1.03903	−	0.871853i	0.991898	+	0.127035i	$0.0405461\pi$
$14$		0			0
$15$	−37492.9	−	13646.3i	−2.86833	−	1.04399i
$16$		0			0
$17$	−5073.41	+	28772.7i	−0.250454	+	1.42040i	0.557022	+	0.830498i	$0.311944\pi$
$17$	−5073.41	+	28772.7i	−0.250454	+	1.42040i	−0.807476	+	0.589900i	$0.799167\pi$
$18$		0			0
$19$	19198.8	+	22919.0i	0.642149	+	0.766580i
$19$	19198.8	+	22919.0i	0.642149	+	0.766580i
$20$		0			0
$21$	3648.71	−	20692.9i	0.0859750	−	0.487588i
$22$		0			0
$23$	51083.4	+	18592.8i	0.875452	+	0.318639i	0.740373	−	0.672196i	$-0.234649\pi$
$23$	51083.4	+	18592.8i	0.875452	+	0.318639i	0.135079	+	0.990835i	$0.456871\pi$
$24$		0			0
$25$	122325.	−	102643.i	1.56576	−	1.31383i
$26$		0			0
$27$	94916.8	−	164401.i	0.928047	−	1.60742i
$28$		0			0
$29$	16138.4	+	91525.5i	0.122876	+	0.696866i	0.982547	+	0.186016i	$0.0595578\pi$
$29$	16138.4	+	91525.5i	0.122876	+	0.696866i	−0.859670	+	0.510849i	$0.829331\pi$
$30$		0			0
$31$	9058.57	+	15689.9i	0.0546127	+	0.0945920i	0.892039	−	0.451958i	$-0.149274\pi$
$31$	9058.57	+	15689.9i	0.0546127	+	0.0945920i	−0.837427	+	0.546550i	$0.815941\pi$
$32$		0			0
$33$	616297.	−	224314.i	2.98532	−	1.08657i
$34$		0			0
$35$	95937.5	+	80501.1i	0.378225	+	0.317369i
$36$		0			0
$37$	245181.			0.795759			0.397879	−	0.917438i	$-0.369746\pi$
$37$	245181.			0.795759			0.397879	+	0.917438i	$0.369746\pi$
$38$		0			0
$39$	−879077.			−2.37302
$40$		0			0
$41$	−353308.	−	296461.i	−0.800591	−	0.671775i	0.147752	−	0.989025i	$-0.452796\pi$
$41$	−353308.	−	296461.i	−0.800591	−	0.671775i	−0.948342	+	0.317249i	$0.897241\pi$
$42$		0			0
$43$	−410553.	+	149429.i	−0.787463	+	0.286613i	−0.704281	−	0.709921i	$-0.748730\pi$
$43$	−410553.	+	149429.i	−0.787463	+	0.286613i	−0.0831818	+	0.996534i	$0.526508\pi$
$44$		0			0
$45$	1.09898e6	+	1.90349e6i	1.79782	+	3.11392i
$46$		0			0
$47$	−86855.1	−	492580.i	−0.122026	−	0.692045i	−0.983030	−	0.183446i	$-0.941275\pi$
$47$	−86855.1	−	492580.i	−0.122026	−	0.692045i	0.861004	−	0.508599i	$-0.169836\pi$
$48$		0			0
$49$	378795.	−	656091.i	0.459957	−	0.796669i
$50$		0			0
$51$	1.83119e6	−	1.53655e6i	1.93302	−	1.62200i
$52$		0			0
$53$	619908.	+	225628.i	0.571955	+	0.208174i	0.611774	−	0.791032i	$-0.290456\pi$
$53$	619908.	+	225628.i	0.571955	+	0.208174i	−0.0398196	+	0.999207i	$0.512678\pi$
$54$		0			0
$55$	−678797.	+	3.84965e6i	−0.550137	+	3.11998i
$56$		0			0
$57$	2037.27	−	2.44617e6i	0.00145709	−	1.74954i
$58$		0			0
$59$	−17003.7	+	96432.8i	−0.0107786	+	0.0611284i	−0.989723	−	0.143000i	$-0.954325\pi$
$59$	−17003.7	+	96432.8i	−0.0107786	+	0.0611284i	0.978944	+	0.204129i	$0.0654361\pi$
$60$		0			0
$61$	−763548.	−	277909.i	−0.430707	−	0.156764i	0.117564	−	0.993065i	$-0.462491\pi$
$61$	−763548.	−	277909.i	−0.430707	−	0.156764i	−0.548271	+	0.836301i	$0.684714\pi$
$62$		0			0
$63$	−886708.	+	744036.i	−0.446775	+	0.374888i
$64$		0			0
$65$	2.61976e6	−	4.53756e6i	1.18322	−	2.04940i
$66$		0			0
$67$	401123.	+	2.27488e6i	0.162936	+	0.924054i	0.951167	+	0.308675i	$0.0998857\pi$
$67$	401123.	+	2.27488e6i	0.162936	+	0.924054i	−0.788232	+	0.615378i	$0.789003\pi$
$68$		0			0
$69$	−2.22389e6	−	3.85189e6i	−0.814970	−	1.41157i
$70$		0			0
$71$	3.34948e6	−	1.21911e6i	1.11064	−	0.404240i	0.279412	−	0.960171i	$-0.409861\pi$
$71$	3.34948e6	−	1.21911e6i	1.11064	−	0.404240i	0.831228	+	0.555932i	$0.187638\pi$
$72$		0			0
$73$	2.47576e6	+	2.07741e6i	0.744867	+	0.625018i	0.934140	−	0.356907i	$-0.116169\pi$
$73$	2.47576e6	+	2.07741e6i	0.744867	+	0.625018i	−0.189273	+	0.981925i	$0.560613\pi$
$74$		0			0
$75$	−1.30650e7			−3.57599
$76$		0			0
$77$	−2.05862e6			−0.513876
$78$		0			0
$79$	−1.34071e6	−	1.12499e6i	−0.305944	−	0.256717i	0.476869	−	0.878974i	$-0.341771\pi$
$79$	−1.34071e6	−	1.12499e6i	−0.305944	−	0.256717i	−0.782813	+	0.622257i	$0.786216\pi$
$80$		0			0
$81$	−5.33237e6	+	1.94082e6i	−1.11487	+	0.405778i
$82$		0			0
$83$	1.19432e6	+	2.06862e6i	0.229270	+	0.397107i	0.957592	−	0.288128i	$-0.0930329\pi$
$83$	1.19432e6	+	2.06862e6i	0.229270	+	0.397107i	−0.728322	+	0.685235i	$0.759700\pi$
$84$		0			0
$85$	2.47408e6	+	1.40312e7i	0.436966	+	2.47816i
$86$		0			0
$87$	3.80198e6	−	6.58522e6i	0.619002	−	1.07214i
$88$		0			0
$89$	−9.40415e6	+	7.89102e6i	−1.41402	+	1.18650i	−0.459563	+	0.888145i	$0.651994\pi$
$89$	−9.40415e6	+	7.89102e6i	−1.41402	+	1.18650i	−0.954455	+	0.298356i	$0.903562\pi$
$90$		0			0
$91$	2.59289e6	+	943734.i	0.360694	+	0.131282i
$92$		0			0
$93$	257400.	−	1.45979e6i	0.0331832	−	0.188191i
$94$		0			0
$95$	1.26204e7	+	7.30042e6i	1.51022	+	0.873605i
$96$		0			0
$97$	−60550.0	+	343396.i	−0.00673617	+	0.0382027i	−0.987991	−	0.154514i	$-0.950619\pi$
$97$	−60550.0	+	343396.i	−0.00673617	+	0.0382027i	0.981254	+	0.192717i	$0.0617299\pi$
$98$		0			0
$99$	−3.39506e7	−	1.23570e7i	−3.51661	−	1.27994i
$100$		0			0
$101$	−8.66585e6	+	7.27151e6i	−0.836925	+	0.702263i	−0.956870	−	0.290517i	$-0.906173\pi$
$101$	−8.66585e6	+	7.27151e6i	−0.836925	+	0.702263i	0.119945	+	0.992781i	$0.461728\pi$
$102$		0			0
$103$	755548.	−	1.30865e6i	0.0681290	−	0.118003i	−0.829949	−	0.557840i	$-0.811630\pi$
$103$	755548.	−	1.30865e6i	0.0681290	−	0.118003i	0.898078	+	0.439837i	$0.144964\pi$
$104$		0			0
$105$	−1.77932e6	−	1.00910e7i	−0.150000	−	0.850692i
$106$		0			0
$107$	−3.94621e6	−	6.83503e6i	−0.311413	−	0.539383i	0.667256	−	0.744829i	$-0.267469\pi$
$107$	−3.94621e6	−	6.83503e6i	−0.311413	−	0.539383i	−0.978668	+	0.205446i	$0.934136\pi$
$108$		0			0
$109$	7.72282e6	−	2.81088e6i	0.571193	−	0.207897i	−0.0402446	−	0.999190i	$-0.512814\pi$
$109$	7.72282e6	−	2.81088e6i	0.571193	−	0.207897i	0.611438	+	0.791293i	$0.290591\pi$
$110$		0			0
$111$	−1.53671e7	−	1.28945e7i	−1.06650	−	0.894898i
$112$		0			0
$113$	2.10049e7			1.36945			0.684725	−	0.728801i	$-0.259922\pi$
$113$	2.10049e7			1.36945			0.684725	+	0.728801i	$0.259922\pi$
$114$		0			0
$115$	2.65099e7			1.62542
$116$		0			0
$117$	3.70969e7	+	3.11280e7i	2.14135	+	1.79680i
$118$		0			0
$119$	−7.05076e6	+	2.56627e6i	−0.383550	+	0.139601i
$120$		0			0
$121$	−2.23842e7	−	3.87706e7i	−1.14866	−	1.98954i
$122$		0			0
$123$	6.55269e6	+	3.71621e7i	0.317506	+	1.80066i
$124$		0			0
$125$	1.98864e7	−	3.44443e7i	0.910693	−	1.57737i
$126$		0			0
$127$	1.16150e7	−	9.74613e6i	0.503160	−	0.422201i	−0.355555	−	0.934655i	$-0.615708\pi$
$127$	1.16150e7	−	9.74613e6i	0.503160	−	0.422201i	0.858714	+	0.512454i	$0.171264\pi$
$128$		0			0
$129$	3.35907e7	+	1.22260e7i	1.37770	+	0.501442i
$130$		0			0
$131$	−645029.	+	3.65814e6i	−0.0250686	+	0.142171i	−0.994773	−	0.102110i	$-0.967441\pi$
$131$	−645029.	+	3.65814e6i	−0.0250686	+	0.142171i	0.969705	+	0.244281i	$0.0785518\pi$
$132$		0			0
$133$	−2.63210e6	+	7.21293e6i	−0.0970111	+	0.265847i
$134$		0			0
$135$	1.60752e7	−	9.11673e7i	0.562328	−	3.18912i
$136$		0			0
$137$	−2.79763e6	−	1.01825e6i	−0.0929539	−	0.0338325i	0.295125	−	0.955459i	$-0.404639\pi$
$137$	−2.79763e6	−	1.01825e6i	−0.0929539	−	0.0338325i	−0.388079	+	0.921626i	$0.626861\pi$
$138$		0			0
$139$	1.61819e7	−	1.35783e7i	0.511068	−	0.428837i	−0.350437	−	0.936586i	$-0.613967\pi$
$139$	1.61819e7	−	1.35783e7i	0.511068	−	0.428837i	0.861505	+	0.507749i	$0.169522\pi$
$140$		0			0
$141$	−2.04618e7	+	3.54409e7i	−0.614720	+	1.06473i
$142$		0			0
$143$	1.49556e7	+	8.48173e7i	0.427688	+	2.42554i
$144$		0			0
$145$	2.26608e7	+	3.92496e7i	0.617286	+	1.06917i
$146$		0			0
$147$	−5.82463e7	+	2.11999e7i	−1.51237	+	0.550458i
$148$		0			0
$149$	5.26189e7	+	4.41525e7i	1.30314	+	1.09346i	0.989594	+	0.143888i	$0.0459606\pi$
$149$	5.26189e7	+	4.41525e7i	1.30314	+	1.09346i	0.313544	+	0.949574i	$0.398484\pi$
$150$		0			0
$151$	−1.19734e6			−0.0283007			−0.0141504	−	0.999900i	$-0.504504\pi$
$151$	−1.19734e6			−0.0283007			−0.0141504	+	0.999900i	$0.504504\pi$
$152$		0			0
$153$	−1.31685e8			−2.97246
$154$		0			0
$155$	6.76796e6	+	5.67899e6i	0.145981	+	0.122493i
$156$		0			0
$157$	−4.43351e7	+	1.61367e7i	−0.914321	+	0.332786i	−0.755977	−	0.654598i	$-0.772838\pi$
$157$	−4.43351e7	+	1.61367e7i	−0.914321	+	0.332786i	−0.158344	+	0.987384i	$0.550616\pi$
$158$		0			0
$159$	−2.69874e7	−	4.67435e7i	−0.532440	−	0.922213i
$160$		0			0
$161$	2.42429e6	+	1.37488e7i	0.0457819	+	0.259642i
$162$		0			0
$163$	3.14302e7	−	5.44387e7i	0.568448	−	0.984580i	−0.428272	−	0.903650i	$-0.640877\pi$
$163$	3.14302e7	−	5.44387e7i	0.568448	−	0.984580i	0.996720	−	0.0809305i	$-0.0257892\pi$
$164$		0			0
$165$	2.45004e8	−	2.05583e8i	4.24599	−	3.56281i
$166$		0			0
$167$	−4.29135e7	−	1.56193e7i	−0.712995	−	0.259509i	−0.0400463	−	0.999198i	$-0.512751\pi$
$167$	−4.29135e7	−	1.56193e7i	−0.712995	−	0.259509i	−0.672949	+	0.739689i	$0.734973\pi$
$168$		0			0
$169$	9.14974e6	−	5.18907e7i	0.145816	−	0.826964i
$170$		0			0
$171$	−8.67046e7	+	1.03156e8i	−1.32604	+	1.57764i
$172$		0			0
$173$	−8.05461e6	+	4.56800e7i	−0.118272	+	0.670756i	0.866805	+	0.498647i	$0.166169\pi$
$173$	−8.05461e6	+	4.56800e7i	−0.118272	+	0.670756i	−0.985078	+	0.172110i	$0.944942\pi$
$174$		0			0
$175$	3.85361e7	+	1.40260e7i	0.543544	+	0.197834i
$176$		0			0
$177$	6.13729e6	−	5.14980e6i	0.0831898	−	0.0698045i
$178$		0			0
$179$	−2.35105e6	+	4.07213e6i	−0.0306391	+	0.0530684i	−0.880938	−	0.473231i	$-0.843088\pi$
$179$	−2.35105e6	+	4.07213e6i	−0.0306391	+	0.0530684i	0.850299	+	0.526299i	$0.176421\pi$
$180$		0			0
$181$	1.57150e7	+	8.91242e7i	0.196988	+	1.11717i	0.909559	+	0.415574i	$0.136419\pi$
$181$	1.57150e7	+	8.91242e7i	0.196988	+	1.11717i	−0.712571	+	0.701600i	$0.752470\pi$
$182$		0			0
$183$	3.32406e7	+	5.75745e7i	0.400950	+	0.694466i
$184$		0			0
$185$	1.12354e8	−	4.08934e7i	1.30463	−	0.474846i
$186$		0			0
$187$	−1.79407e8	−	1.50540e8i	−2.00629	−	1.68348i
$188$		0			0
$189$	4.87521e7			0.525263
$190$		0			0
$191$	9.29745e7			0.965489			0.482744	−	0.875761i	$-0.339640\pi$
$191$	9.29745e7			0.965489			0.482744	+	0.875761i	$0.339640\pi$
$192$		0			0
$193$	5.98868e7	+	5.02510e7i	0.599626	+	0.503146i	0.891325	−	0.453364i	$-0.149776\pi$
$193$	5.98868e7	+	5.02510e7i	0.599626	+	0.503146i	−0.291700	+	0.956510i	$0.594221\pi$
$194$		0			0
$195$	−4.02835e8	+	1.46620e8i	−3.89050	+	1.41603i
$196$		0			0
$197$	−1.61954e7	−	2.80513e7i	−0.150925	−	0.261409i	0.780643	−	0.624977i	$-0.214892\pi$
$197$	−1.61954e7	−	2.80513e7i	−0.150925	−	0.261409i	−0.931568	+	0.363568i	$0.881558\pi$
$198$		0			0
$199$	−6.22286e6	−	3.52916e7i	−0.0559763	−	0.317457i	0.943944	−	0.330107i	$-0.107085\pi$
$199$	−6.22286e6	−	3.52916e7i	−0.0559763	−	0.317457i	−0.999920	+	0.0126491i	$0.995974\pi$
$200$		0			0
$201$	9.44989e7	−	1.63677e8i	0.820806	−	1.42168i
$202$		0			0
$203$	−1.82837e7	+	1.53419e7i	−0.153401	+	0.128719i
$204$		0			0
$205$	−2.11349e8	−	7.69247e7i	−1.71341	−	0.623631i
$206$		0			0
$207$	−4.25472e7	+	2.41297e8i	−0.333407	+	1.89084i
$208$		0			0
$209$	−2.36052e8	+	4.14197e7i	−1.78853	+	0.313830i
$210$		0			0
$211$	1.84852e6	−	1.04835e7i	0.0135468	−	0.0768274i	−0.977285	−	0.211930i	$-0.932025\pi$
$211$	1.84852e6	−	1.04835e7i	0.0135468	−	0.0768274i	0.990832	+	0.135102i	$0.0431363\pi$
$212$		0			0
$213$	−2.74048e8	−	9.97453e7i	−1.94311	−	0.707235i
$214$		0			0
$215$	−1.63212e8	+	1.36951e8i	−1.12000	+	0.939790i
$216$		0			0
$217$	−2.32638e6	+	4.02940e6i	−0.0154551	+	0.0267690i
$218$		0			0
$219$	−4.59171e7	−	2.60409e8i	−0.295406	−	1.67533i
$220$		0			0
$221$	1.56956e8	+	2.71856e8i	0.978148	+	1.69420i
$222$		0			0
$223$	7.91141e7	−	2.87952e7i	0.477735	−	0.173881i	−0.0919182	−	0.995767i	$-0.529300\pi$
$223$	7.91141e7	−	2.87952e7i	0.477735	−	0.173881i	0.569653	+	0.821885i	$0.307078\pi$
$224$		0			0
$225$	5.51343e8	+	4.62632e8i	3.22688	+	2.70768i
$226$		0			0
$227$	−2.59452e8			−1.47220			−0.736099	−	0.676874i	$-0.763334\pi$
$227$	−2.59452e8			−1.47220			−0.736099	+	0.676874i	$0.763334\pi$
$228$		0			0
$229$	1.45575e8			0.801057			0.400529	−	0.916284i	$-0.368827\pi$
$229$	1.45575e8			0.801057			0.400529	+	0.916284i	$0.368827\pi$
$230$		0			0
$231$	1.29026e8	+	1.08266e8i	0.688711	+	0.577897i
$232$		0			0
$233$	−1.31700e7	+	4.79349e6i	−0.0682087	+	0.0248259i	−0.375899	−	0.926661i	$-0.622666\pi$
$233$	−1.31700e7	+	4.79349e6i	−0.0682087	+	0.0248259i	0.307690	+	0.951487i	$0.400444\pi$
$234$		0			0
$235$	−1.21958e8	−	2.11237e8i	−0.613016	−	1.06178i
$236$		0			0
$237$	2.48658e7	+	1.41021e8i	0.121334	+	0.688119i
$238$		0			0
$239$	1.76510e8	−	3.05724e8i	0.836326	−	1.44856i	−0.0566197	−	0.998396i	$-0.518032\pi$
$239$	1.76510e8	−	3.05724e8i	0.836326	−	1.44856i	0.892946	−	0.450164i	$-0.148634\pi$
$240$		0			0
$241$	−7.72439e7	+	6.48153e7i	−0.355471	+	0.298276i	−0.802983	−	0.596003i	$-0.796755\pi$
$241$	−7.72439e7	+	6.48153e7i	−0.355471	+	0.298276i	0.447511	+	0.894278i	$0.352310\pi$
$242$		0			0
$243$	4.61552e7	+	1.67991e7i	0.206347	+	0.0751043i
$244$		0			0
$245$	6.41532e7	−	3.63831e8i	0.278700	−	1.58059i
$246$		0			0
$247$	3.16303e8	+	5.60444e7i	1.33556	+	0.236642i
$248$		0			0
$249$	3.39367e7	−	1.92464e8i	0.139306	−	0.790046i
$250$		0			0
$251$	6.01423e7	+	2.18900e7i	0.240061	+	0.0873751i	0.459249	−	0.888308i	$-0.348119\pi$
$251$	6.01423e7	+	2.18900e7i	0.240061	+	0.0873751i	−0.219188	+	0.975683i	$0.570341\pi$
$252$		0			0
$253$	−3.33813e8	+	2.80103e8i	−1.29593	+	1.08741i
$254$		0			0
$255$	5.82859e8	−	1.00954e9i	2.20127	−	3.81270i
$256$		0			0
$257$	−3.64195e7	−	2.06545e8i	−0.133834	−	0.759012i	−0.975664	−	0.219269i	$-0.929633\pi$
$257$	−3.64195e7	−	2.06545e8i	−0.133834	−	0.759012i	0.841830	−	0.539743i	$-0.181478\pi$
$258$		0			0
$259$	3.14831e7	+	5.45304e7i	0.112597	+	0.195025i
$260$		0			0
$261$	−3.93625e8	+	1.43268e8i	−1.37038	+	0.498777i
$262$		0			0
$263$	8.07811e7	+	6.77834e7i	0.273820	+	0.229762i	0.769348	−	0.638830i	$-0.220581\pi$
$263$	8.07811e7	+	6.77834e7i	0.273820	+	0.229762i	−0.495528	+	0.868592i	$0.665026\pi$
$264$		0			0
$265$	3.21703e8			1.06193
$266$		0			0
$267$	1.00442e9			3.22943
$268$		0			0
$269$	−3.07308e8	−	2.57862e8i	−0.962589	−	0.807708i	0.0187832	−	0.999824i	$-0.494021\pi$
$269$	−3.07308e8	−	2.57862e8i	−0.962589	−	0.807708i	−0.981372	+	0.192115i	$0.938465\pi$
$270$		0			0
$271$	−3.32174e8	+	1.20901e8i	−1.01385	+	0.369010i	−0.794909	−	0.606728i	$-0.792482\pi$
$271$	−3.32174e8	+	1.20901e8i	−1.01385	+	0.369010i	−0.218938	+	0.975739i	$0.570259\pi$
$272$		0			0
$273$	−1.12880e8	−	1.95514e8i	−0.335775	−	0.581579i
$274$		0			0
$275$	2.22273e8	+	1.26057e9i	0.644500	+	3.65514i
$276$		0			0
$277$	−1.63249e8	+	2.82756e8i	−0.461500	+	0.799342i	−0.999036	−	0.0438993i	$-0.986022\pi$
$277$	−1.63249e8	+	2.82756e8i	−0.461500	+	0.799342i	0.537536	+	0.843241i	$0.319355\pi$
$278$		0			0
$279$	−6.25532e7	+	5.24884e7i	−0.172439	+	0.144693i
$280$		0			0
$281$	2.18981e8	+	7.97026e7i	0.588755	+	0.214289i	0.619182	−	0.785248i	$-0.287464\pi$
$281$	2.18981e8	+	7.97026e7i	0.588755	+	0.214289i	−0.0304267	+	0.999537i	$0.509687\pi$
$282$		0			0
$283$	−2.88319e7	+	1.63514e8i	−0.0756172	+	0.428846i	0.923372	+	0.383905i	$0.125421\pi$
$283$	−2.88319e7	+	1.63514e8i	−0.0756172	+	0.428846i	−0.998990	+	0.0449409i	$0.985690\pi$
$284$		0			0
$285$	−4.07059e8	−	1.12129e9i	−1.04160	−	2.86920i
$286$		0			0
$287$	2.05679e7	−	1.16647e8i	0.0513575	−	0.291263i
$288$		0			0
$289$	−4.16539e8	−	1.51608e8i	−1.01511	−	0.369470i
$290$		0			0
$291$	2.18548e7	−	1.83384e7i	0.0519902	−	0.0436250i
$292$		0			0
$293$	4.44648e7	−	7.70152e7i	0.103271	−	0.178871i	−0.809759	−	0.586762i	$-0.800402\pi$
$293$	4.44648e7	−	7.70152e7i	0.103271	−	0.178871i	0.913031	+	0.407891i	$0.133736\pi$
$294$		0			0
$295$	8.29197e6	+	4.70261e7i	0.0188053	+	0.106650i
$296$		0			0
$297$	7.60849e8	+	1.31783e9i	1.68520	+	2.91885i
$298$		0			0
$299$	5.48855e8	−	1.99767e8i	1.18743	−	0.432190i
$300$		0			0
$301$	−8.59524e7	−	7.21226e7i	−0.181667	−	0.152436i
$302$		0			0
$303$	9.25564e8			1.91142
$304$		0			0
$305$	−3.96246e8			−0.799678
$306$		0			0
$307$	−6.91787e8	−	5.80478e8i	−1.36455	−	1.14499i	−0.974549	−	0.224173i	$-0.928032\pi$
$307$	−6.91787e8	−	5.80478e8i	−1.36455	−	1.14499i	−0.389996	−	0.920816i	$-0.627524\pi$
$308$		0			0
$309$	−1.16179e8	+	4.22857e7i	−0.224013	+	0.0815339i
$310$		0			0
$311$	3.67035e8	+	6.35723e8i	0.691904	+	1.19841i	0.971213	+	0.238212i	$0.0765613\pi$
$311$	3.67035e8	+	6.35723e8i	0.691904	+	1.19841i	−0.279309	+	0.960201i	$0.590105\pi$
$312$		0			0
$313$	4.35450e6	+	2.46956e7i	0.00802663	+	0.0455213i	0.988558	−	0.150841i	$-0.0481982\pi$
$313$	4.35450e6	+	2.46956e7i	0.00802663	+	0.0455213i	−0.980531	+	0.196362i	$0.937087\pi$
$314$		0			0
$315$	−2.82235e8	+	4.88845e8i	−0.508773	+	0.881220i
$316$		0			0
$317$	−4.25113e8	+	3.56712e8i	−0.749544	+	0.628942i	−0.935382	−	0.353638i	$-0.884944\pi$
$317$	−4.25113e8	+	3.56712e8i	−0.749544	+	0.628942i	0.185838	+	0.982580i	$0.440500\pi$
$318$		0			0
$319$	−7.00054e8	−	2.54799e8i	−1.20744	−	0.439471i
$320$		0			0
$321$	−1.12132e8	+	6.35932e8i	−0.189218	+	1.07311i
$322$		0			0
$323$	−7.56845e8	+	4.36124e8i	−1.24968	+	0.720114i
$324$		0			0
$325$	2.97927e8	−	1.68963e9i	0.481413	−	2.73023i
$326$		0			0
$327$	−6.31866e8	−	2.29980e8i	−0.999327	−	0.363725i
$328$		0			0
$329$	9.84010e7	−	8.25683e7i	0.152340	−	0.127828i
$330$		0			0
$331$	4.87356e8	−	8.44126e8i	0.738667	−	1.27941i	−0.214429	−	0.976740i	$-0.568789\pi$
$331$	4.87356e8	−	8.44126e8i	0.738667	−	1.27941i	0.953096	−	0.302669i	$-0.0978776\pi$
$332$		0			0
$333$	1.91895e8	+	1.08829e9i	0.284780	+	1.61507i
$334$		0			0
$335$	5.63238e8	+	9.75557e8i	0.818531	+	1.41774i
$336$		0			0
$337$	3.08359e8	−	1.12234e8i	0.438887	−	0.159742i	−0.113120	−	0.993581i	$-0.536084\pi$
$337$	3.08359e8	−	1.12234e8i	0.438887	−	0.159742i	0.552007	+	0.833840i	$0.313862\pi$
$338$		0			0
$339$	−1.31651e9	−	1.10468e9i	−1.83538	−	1.54006i
$340$		0			0
$341$	−1.45226e8			−0.198337
$342$		0			0
$343$	4.06058e8			0.543324
$344$		0			0
$345$	−1.66154e9	−	1.39420e9i	−2.17844	−	1.82792i
$346$		0			0
$347$	1.33457e8	−	4.85744e7i	0.171470	−	0.0624100i	−0.254859	−	0.966978i	$-0.582029\pi$
$347$	1.33457e8	−	4.85744e7i	0.171470	−	0.0624100i	0.426329	+	0.904568i	$0.359807\pi$
$348$		0			0
$349$	−2.18521e8	−	3.78490e8i	−0.275172	−	0.476612i	0.695006	−	0.719004i	$-0.255402\pi$
$349$	−2.18521e8	−	3.78490e8i	−0.275172	−	0.476612i	−0.970179	+	0.242391i	$0.922068\pi$
$350$		0			0
$351$	−3.54178e8	−	2.00864e9i	−0.437166	−	2.47929i
$352$		0			0
$353$	−6.29442e8	+	1.09023e9i	−0.761631	+	1.31918i	0.180379	+	0.983597i	$0.442268\pi$
$353$	−6.29442e8	+	1.09023e9i	−0.761631	+	1.31918i	−0.942010	+	0.335586i	$0.891066\pi$
$354$		0			0
$355$	1.33156e9	−	1.11731e9i	1.57965	−	1.32548i
$356$		0			0
$357$	5.76879e8	+	2.09967e8i	0.671037	+	0.244237i
$358$		0			0
$359$	1.84596e7	−	1.04690e8i	0.0210568	−	0.119419i	−0.972468	−	0.233038i	$-0.925133\pi$
$359$	1.84596e7	−	1.04690e8i	0.0210568	−	0.119419i	0.993524	+	0.113619i	$0.0362444\pi$
$360$		0			0
$361$	−1.56685e8	+	8.80032e8i	−0.175288	+	0.984517i
$362$		0			0
$363$	−6.36049e8	+	3.60722e9i	−0.697939	+	3.95821i
$364$		0			0
$365$	1.48100e9	+	5.39040e8i	1.59415	+	0.580224i
$366$		0			0
$367$	−3.36651e8	+	2.82484e8i	−0.355508	+	0.298306i	−0.802997	−	0.595983i	$-0.796763\pi$
$367$	−3.36651e8	+	2.82484e8i	−0.355508	+	0.298306i	0.447489	+	0.894289i	$0.352318\pi$
$368$		0			0
$369$	1.03938e9	−	1.80027e9i	1.07692	−	1.86528i
$370$		0			0
$371$	2.94193e7	+	1.66845e8i	0.0299105	+	0.169631i
$372$		0			0
$373$	−1.94474e8	−	3.36839e8i	−0.194035	−	0.336079i	0.752549	−	0.658537i	$-0.228824\pi$
$373$	−1.94474e8	−	3.36839e8i	−0.194035	−	0.336079i	−0.946584	+	0.322458i	$0.895491\pi$
$374$		0			0
$375$	−3.05789e9	+	1.11298e9i	−2.99442	+	1.08988i
$376$		0			0
$377$	7.64931e8	+	6.41853e8i	0.735237	+	0.616937i
$378$		0			0
$379$	1.69500e9			1.59931			0.799653	−	0.600463i	$-0.205017\pi$
$379$	1.69500e9			1.59931			0.799653	+	0.600463i	$0.205017\pi$
$380$		0			0
$381$	−1.24055e9			−1.14915
$382$		0			0
$383$	1.57597e9	+	1.32240e9i	1.43335	+	1.20273i	0.943697	+	0.330812i	$0.107322\pi$
$383$	1.57597e9	+	1.32240e9i	1.43335	+	1.20273i	0.489657	+	0.871915i	$0.337122\pi$
$384$		0			0
$385$	−9.43356e8	+	3.43354e8i	−0.842487	+	0.306640i
$386$		0			0
$387$	−9.84600e8	−	1.70538e9i	−0.863518	−	1.49566i
$388$		0			0
$389$	−3.45147e7	−	1.95742e8i	−0.0297290	−	0.168602i	0.966328	−	0.257312i	$-0.0828367\pi$
$389$	−3.45147e7	−	1.95742e8i	−0.0297290	−	0.168602i	−0.996057	+	0.0887100i	$0.971726\pi$
$390$		0			0
$391$	−7.94134e8	+	1.37548e9i	−0.671855	+	1.16369i
$392$		0			0
$393$	2.32816e8	−	1.95356e8i	0.193481	−	0.162350i
$394$		0			0
$395$	−8.02015e8	−	2.91910e8i	−0.654776	−	0.238319i
$396$		0			0
$397$	2.18160e8	−	1.23724e9i	0.174988	−	0.992405i	−0.763170	−	0.646197i	$-0.776358\pi$
$397$	2.18160e8	−	1.23724e9i	0.174988	−	0.992405i	0.938158	−	0.346207i	$-0.112531\pi$
$398$		0			0
$399$	5.44310e8	−	3.13653e8i	0.428984	−	0.247198i
$400$		0			0
$401$	8.64265e7	−	4.90149e8i	0.0669332	−	0.379597i	−0.932878	−	0.360191i	$-0.882711\pi$
$401$	8.64265e7	−	4.90149e8i	0.0669332	−	0.379597i	0.999812	−	0.0194059i	$-0.00617748\pi$
$402$		0			0
$403$	1.82917e8	+	6.65762e7i	0.139215	+	0.0506701i
$404$		0			0
$405$	−2.11984e9	+	1.77875e9i	−1.58566	+	1.33053i
$406$		0			0
$407$	−9.82682e8	+	1.70206e9i	−0.722491	+	1.25139i
$408$		0			0
$409$	−3.50265e8	−	1.98645e9i	−0.253143	−	1.43564i	−0.800796	−	0.598938i	$-0.795590\pi$
$409$	−3.50265e8	−	1.98645e9i	−0.253143	−	1.43564i	0.547653	−	0.836706i	$-0.315521\pi$
$410$		0			0
$411$	1.21793e8	+	2.10952e8i	0.0865320	+	0.149878i
$412$		0			0
$413$	−2.36309e7	+	8.60093e6i	−0.0165065	+	0.00600787i
$414$		0			0
$415$	8.92315e8	+	7.48741e8i	0.612844	+	0.514237i
$416$		0			0
$417$	−1.72833e9			−1.16721
$418$		0			0
$419$	2.89629e9			1.92350			0.961752	−	0.273921i	$-0.0883207\pi$
$419$	2.89629e9			1.92350			0.961752	+	0.273921i	$0.0883207\pi$
$420$		0			0
$421$	−1.36313e9	−	1.14380e9i	−0.890326	−	0.747072i	0.0779495	−	0.996957i	$-0.475163\pi$
$421$	−1.36313e9	−	1.14380e9i	−0.890326	−	0.747072i	−0.968276	+	0.249885i	$0.919607\pi$
$422$		0			0
$423$	2.11845e9	−	7.71051e8i	1.36090	−	0.495327i
$424$		0			0
$425$	2.33271e9	+	4.04038e9i	1.47401	+	2.55306i
$426$		0			0
$427$	−3.62361e7	−	2.05505e8i	−0.0225239	−	0.127739i
$428$		0			0
$429$	3.52332e9	−	6.10257e9i	2.15453	−	3.73175i
$430$		0			0
$431$	−1.46189e8	+	1.22667e8i	−0.0879518	+	0.0738004i	−0.685704	−	0.727881i	$-0.740505\pi$
$431$	−1.46189e8	+	1.22667e8i	−0.0879518	+	0.0738004i	0.597752	+	0.801681i	$0.296061\pi$
$432$		0			0
$433$	4.23991e8	+	1.54320e8i	0.250986	+	0.0913514i	0.464449	−	0.885600i	$-0.346252\pi$
$433$	4.23991e8	+	1.54320e8i	0.250986	+	0.0913514i	−0.213464	+	0.976951i	$0.568474\pi$
$434$		0			0
$435$	6.43908e8	−	3.65179e9i	0.375069	−	2.12712i
$436$		0			0
$437$	5.54611e8	+	1.52774e9i	0.317909	+	0.875718i
$438$		0			0
$439$	−2.84078e8	+	1.61109e9i	−0.160255	+	0.908853i	0.793567	+	0.608482i	$0.208221\pi$
$439$	−2.84078e8	+	1.61109e9i	−0.160255	+	0.908853i	−0.953823	+	0.300370i	$0.902890\pi$
$440$		0			0
$441$	3.20867e9	+	1.16786e9i	1.78152	+	0.648420i
$442$		0			0
$443$	1.70234e9	−	1.42843e9i	0.930321	−	0.780632i	−0.0455541	−	0.998962i	$-0.514505\pi$
$443$	1.70234e9	−	1.42843e9i	0.930321	−	0.780632i	0.975875	+	0.218330i	$0.0700609\pi$
$444$		0			0
$445$	−2.99330e9	+	5.18455e9i	−1.61024	+	2.78901i
$446$		0			0
$447$	−9.75905e8	−	5.53463e9i	−0.516810	−	2.93098i
$448$		0			0
$449$	−1.57934e9	−	2.73551e9i	−0.823407	−	1.42618i	−0.903130	−	0.429366i	$-0.858737\pi$
$449$	−1.57934e9	−	2.73551e9i	−0.823407	−	1.42618i	0.0797230	−	0.996817i	$-0.474596\pi$
$450$		0			0
$451$	3.47409e9	−	1.26447e9i	1.78330	−	0.649067i
$452$		0			0
$453$	7.50447e7	+	6.29700e7i	0.0379294	+	0.0318266i
$454$		0			0
$455$	1.34559e9			0.669688
$456$		0			0
$457$	1.63587e9			0.801757			0.400878	−	0.916131i	$-0.368705\pi$
$457$	1.63587e9			0.801757			0.400878	+	0.916131i	$0.368705\pi$
$458$		0			0
$459$	4.24871e9	+	3.56509e9i	2.05075	+	1.72078i
$460$		0			0
$461$	−2.69781e9	+	9.81924e8i	−1.28250	+	0.466793i	−0.891260	−	0.453493i	$-0.850178\pi$
$461$	−2.69781e9	+	9.81924e8i	−1.28250	+	0.466793i	−0.391245	+	0.920287i	$0.627955\pi$
$462$		0			0
$463$	−8.62344e8	−	1.49362e9i	−0.403782	−	0.699371i	0.590397	−	0.807113i	$-0.298971\pi$
$463$	−8.62344e8	−	1.49362e9i	−0.403782	−	0.699371i	−0.994179	+	0.107742i	$0.965638\pi$
$464$		0			0
$465$	−1.25523e8	−	7.11876e8i	−0.0578946	−	0.328337i
$466$		0			0
$467$	−7.31692e8	+	1.26733e9i	−0.332445	+	0.575811i	−0.982991	−	0.183656i	$-0.941207\pi$
$467$	−7.31692e8	+	1.26733e9i	−0.332445	+	0.575811i	0.650546	+	0.759467i	$0.274540\pi$
$468$		0			0
$469$	−4.54446e8	+	3.81325e8i	−0.203412	+	0.170683i
$470$		0			0
$471$	3.62741e9	+	1.32027e9i	1.59964	+	0.582223i
$472$		0			0
$473$	6.08148e8	−	3.44898e9i	0.264238	−	1.49857i
$474$		0			0
$475$	4.70096e9	+	8.32944e8i	2.01261	+	0.356606i
$476$		0			0
$477$	−5.16318e8	+	2.92819e9i	−0.217823	+	1.23533i
$478$		0			0
$479$	−3.64286e9	−	1.32589e9i	−1.51450	−	0.551232i	−0.554731	−	0.832030i	$-0.687179\pi$
$479$	−3.64286e9	−	1.32589e9i	−1.51450	−	0.551232i	−0.959767	+	0.280798i	$0.909401\pi$
$480$		0			0
$481$	2.01799e9	−	1.69330e9i	0.826821	−	0.693785i
$482$		0			0
$483$	5.71128e8	−	9.89223e8i	0.230632	−	0.399465i
$484$		0			0
$485$	2.95276e7	+	1.67459e8i	0.0117526	+	0.0666521i
$486$		0			0
$487$	−7.86378e8	−	1.36205e9i	−0.308518	−	0.534368i	0.669521	−	0.742793i	$-0.266500\pi$
$487$	−7.86378e8	−	1.36205e9i	−0.308518	−	0.534368i	−0.978038	+	0.208425i	$0.933166\pi$
$488$		0			0
$489$	−4.83295e9	+	1.75905e9i	−1.86909	+	0.680295i
$490$		0			0
$491$	−2.29677e9	−	1.92722e9i	−0.875652	−	0.734760i	0.0896280	−	0.995975i	$-0.471432\pi$
$491$	−2.29677e9	−	1.92722e9i	−0.875652	−	0.734760i	−0.965280	+	0.261216i	$0.915877\pi$
$492$		0			0
$493$	−2.71532e9			−1.02060
$494$		0			0
$495$	−1.76188e10			−6.52916
$496$		0			0
$497$	7.01239e8	+	5.88409e8i	0.256223	+	0.214997i
$498$		0			0
$499$	−3.76473e9	+	1.37025e9i	−1.35638	+	0.493682i	−0.914933	−	0.403605i	$-0.867757\pi$
$499$	−3.76473e9	+	1.37025e9i	−1.35638	+	0.493682i	−0.441448	+	0.897287i	$0.645535\pi$
$500$		0			0
$501$	1.86822e9	+	3.23585e9i	0.663736	+	1.14963i
$502$		0			0
$503$	8.46742e8	+	4.80211e9i	0.296663	+	1.68246i	0.660367	+	0.750943i	$0.270401\pi$
$503$	8.46742e8	+	4.80211e9i	0.296663	+	1.68246i	−0.363704	+	0.931515i	$0.618488\pi$
$504$		0			0
$505$	−2.75830e9	+	4.77752e9i	−0.953063	+	1.65075i
$506$		0			0
$507$	−3.30249e9	+	2.77112e9i	−1.12542	+	0.944337i
$508$		0			0
$509$	4.45616e9	+	1.62191e9i	1.49778	+	0.545148i	0.955485	−	0.295039i	$-0.0953327\pi$
$509$	4.45616e9	+	1.62191e9i	1.49778	+	0.545148i	0.542297	+	0.840187i	$0.317555\pi$
$510$		0			0
$511$	−1.44127e8	+	8.17385e8i	−0.0477829	+	0.270990i
$512$		0			0
$513$	5.59018e9	−	9.80900e8i	1.82816	−	0.320785i
$514$		0			0
$515$	1.27961e8	−	7.25701e8i	0.0412811	−	0.234117i
$516$		0			0
$517$	3.76761e9	+	1.37130e9i	1.19908	+	0.436431i
$518$		0			0
$519$	2.90722e9	−	2.43945e9i	0.912834	−	0.765959i
$520$		0			0
$521$	2.47199e9	−	4.28162e9i	0.765799	−	1.32640i	−0.174023	−	0.984742i	$-0.555677\pi$
$521$	2.47199e9	−	4.28162e9i	0.765799	−	1.32640i	0.939823	−	0.341662i	$-0.110990\pi$
$522$		0			0
$523$	1.83556e8	+	1.04100e9i	0.0561065	+	0.318196i	0.999925	−	0.0122694i	$-0.00390556\pi$
$523$	1.83556e8	+	1.04100e9i	0.0561065	+	0.318196i	−0.943818	+	0.330465i	$0.892794\pi$
$524$		0			0
$525$	−1.67765e9	−	2.90577e9i	−0.505992	−	0.876404i
$526$		0			0
$527$	−4.97399e8	+	1.81039e8i	−0.148036	+	0.0538808i
$528$		0			0
$529$	−3.44425e8	−	2.89007e8i	−0.101158	−	0.0848817i
$530$		0			0
$531$	−4.41346e8			−0.127923
$532$		0			0
$533$	−4.95539e9			−1.41753
$534$		0			0
$535$	−2.94834e9	−	2.47395e9i	−0.832415	−	0.698479i
$536$		0			0
$537$	3.61515e8	−	1.31581e8i	0.100743	−	0.0366676i
$538$		0			0
$539$	3.03640e9	+	5.25920e9i	0.835215	+	1.44664i
$540$		0			0
$541$	−1.20709e9	−	6.84576e9i	−0.327756	−	1.85879i	−0.489558	−	0.871971i	$-0.662842\pi$
$541$	−1.20709e9	−	6.84576e9i	−0.327756	−	1.85879i	0.161802	−	0.986823i	$-0.448269\pi$
$542$		0			0
$543$	3.70223e9	−	6.41245e9i	0.992348	−	1.71880i
$544$		0			0
$545$	3.07014e9	−	2.57615e9i	0.812401	−	0.681685i
$546$		0			0
$547$	3.99221e9	+	1.45304e9i	1.04294	+	0.379597i	0.805992	−	0.591926i	$-0.201632\pi$
$547$	3.99221e9	+	1.45304e9i	1.04294	+	0.379597i	0.236943	+	0.971524i	$0.423855\pi$
$548$		0			0
$549$	6.35955e8	−	3.60668e9i	0.164030	−	0.930261i
$550$		0			0
$551$	−1.78783e9	+	2.12705e9i	−0.455298	+	0.541686i
$552$		0			0
$553$	7.80500e7	−	4.42644e8i	0.0196261	−	0.111305i
$554$		0			0
$555$	−9.19257e9	−	3.34582e9i	−2.28250	−	0.830763i
$556$		0			0
$557$	−4.76239e9	+	3.99612e9i	−1.16770	+	0.979819i	−0.999982	−	0.00601611i	$-0.998085\pi$
$557$	−4.76239e9	+	3.99612e9i	−1.16770	+	0.979819i	−0.167720	+	0.985835i	$0.553641\pi$
$558$		0			0
$559$	−2.34710e9	+	4.06530e9i	−0.568316	+	0.984353i
$560$		0			0
$561$	3.32740e9	+	1.88706e10i	0.795673	+	4.51248i
$562$		0			0
$563$	−3.49057e9	−	6.04584e9i	−0.824360	−	1.42783i	−0.902407	−	0.430884i	$-0.858202\pi$
$563$	−3.49057e9	−	6.04584e9i	−0.824360	−	1.42783i	0.0780476	−	0.996950i	$-0.475131\pi$
$564$		0			0
$565$	9.62545e9	−	3.50338e9i	2.24518	−	0.817179i
$566$		0			0
$567$	−1.11637e9	−	9.36746e8i	−0.257198	−	0.215815i
$568$		0			0
$569$	−1.72511e9			−0.392575			−0.196288	−	0.980546i	$-0.562889\pi$
$569$	−1.72511e9			−0.392575			−0.196288	+	0.980546i	$0.562889\pi$
$570$		0			0
$571$	−6.64239e9			−1.49313			−0.746565	−	0.665312i	$-0.768298\pi$
$571$	−6.64239e9			−1.49313			−0.746565	+	0.665312i	$0.768298\pi$
$572$		0			0
$573$	−5.82730e9	−	4.88968e9i	−1.29398	−	1.08577i
$574$		0			0
$575$	8.15721e9	−	2.96898e9i	1.78939	−	0.651284i
$576$		0			0
$577$	−2.67273e9	−	4.62930e9i	−0.579215	−	1.00323i	−0.995570	−	0.0940270i	$-0.970026\pi$
$577$	−2.67273e9	−	4.62930e9i	−0.579215	−	1.00323i	0.416355	−	0.909202i	$-0.363307\pi$
$578$		0			0
$579$	−1.11070e9	−	6.29908e9i	−0.237805	−	1.34866i
$580$		0			0
$581$	−3.06719e8	+	5.31252e8i	−0.0648819	+	0.112379i
$582$		0			0
$583$	−4.05089e9	+	3.39910e9i	−0.846663	+	0.710435i
$584$		0			0
$585$	2.21914e10	+	8.07699e9i	4.58288	+	1.66803i
$586$		0			0
$587$	−3.68197e8	+	2.08815e9i	−0.0751357	+	0.426116i	0.923917	+	0.382594i	$0.124969\pi$
$587$	−3.68197e8	+	2.08815e9i	−0.0751357	+	0.426116i	−0.999052	+	0.0435222i	$0.986142\pi$
$588$		0			0
$589$	−1.85683e8	+	5.08840e8i	−0.0374428	+	0.102607i
$590$		0			0
$591$	−4.60194e8	+	2.60989e9i	−0.0917033	+	0.520075i
$592$		0			0
$593$	4.02307e9	+	1.46428e9i	0.792257	+	0.288358i	0.706274	−	0.707939i	$-0.250375\pi$
$593$	4.02307e9	+	1.46428e9i	0.792257	+	0.288358i	0.0859828	+	0.996297i	$0.472597\pi$
$594$		0			0
$595$	−2.80297e9	+	2.35197e9i	−0.545518	+	0.457744i
$596$		0			0
$597$	−1.46602e9	+	2.53922e9i	−0.281987	+	0.488416i
$598$		0			0
$599$	−5.23106e8	−	2.96668e9i	−0.0994480	−	0.563998i	−0.993293	−	0.115622i	$-0.963114\pi$
$599$	−5.23106e8	−	2.96668e9i	−0.0994480	−	0.563998i	0.893845	−	0.448376i	$-0.147997\pi$
$600$		0			0
$601$	−3.86393e9	−	6.69252e9i	−0.726053	−	1.25756i	−0.958539	−	0.284961i	$-0.908020\pi$
$601$	−3.86393e9	−	6.69252e9i	−0.726053	−	1.25756i	0.232487	−	0.972600i	$-0.425314\pi$
$602$		0			0
$603$	−9.78362e9	+	3.56095e9i	−1.81714	+	0.661386i
$604$		0			0
$605$	−1.67240e10	−	1.40331e10i	−3.07041	−	2.57638i
$606$		0			0
$607$	−2.35532e9			−0.427454			−0.213727	−	0.976893i	$-0.568560\pi$
$607$	−2.35532e9			−0.427454			−0.213727	+	0.976893i	$0.568560\pi$
$608$		0			0
$609$	1.95281e9			0.350348
$610$		0			0
$611$	−4.11677e9	−	3.45438e9i	−0.730151	−	0.612669i
$612$		0			0
$613$	8.86473e8	−	3.22650e8i	0.155437	−	0.0565744i	−0.263130	−	0.964760i	$-0.584755\pi$
$613$	8.86473e8	−	3.22650e8i	0.155437	−	0.0565744i	0.418567	+	0.908186i	$0.362533\pi$
$614$		0			0
$615$	9.20097e9	+	1.59365e10i	1.59504	+	2.76268i
$616$		0			0
$617$	1.53183e9	+	8.68746e9i	0.262551	+	1.48900i	0.775920	+	0.630832i	$0.217286\pi$
$617$	1.53183e9	+	8.68746e9i	0.262551	+	1.48900i	−0.513369	+	0.858168i	$0.671603\pi$
$618$		0			0
$619$	6.40340e8	−	1.10910e9i	0.108516	−	0.187955i	−0.806653	−	0.591025i	$-0.798724\pi$
$619$	6.40340e8	−	1.10910e9i	0.108516	−	0.187955i	0.915169	+	0.403070i	$0.132057\pi$
$620$		0			0
$621$	7.90535e9	−	6.63338e9i	1.32465	−	1.11151i
$622$		0			0
$623$	−2.96259e9	−	1.07830e9i	−0.490867	−	0.178661i
$624$		0			0
$625$	1.20168e9	−	6.81505e9i	0.196883	−	1.11658i
$626$		0			0
$627$	1.69732e10	+	9.81834e9i	2.74997	+	1.59075i
$628$		0			0
$629$	−1.24391e9	+	7.05454e9i	−0.199301	+	1.13029i
$630$		0			0
$631$	1.78332e9	+	6.49074e8i	0.282570	+	0.102847i	0.479417	−	0.877587i	$-0.340848\pi$
$631$	1.78332e9	+	6.49074e8i	0.282570	+	0.102847i	−0.196847	+	0.980434i	$0.563070\pi$
$632$		0			0
$633$	−6.67201e8	+	5.59848e8i	−0.104555	+	0.0877318i
$634$		0			0
$635$	3.69700e9	−	6.40339e9i	0.572982	−	0.992434i
$636$		0			0
$637$	−1.41345e9	−	8.01609e9i	−0.216667	−	1.22878i
$638$		0			0
$639$	8.03281e9	+	1.39132e10i	1.21791	+	2.10948i
$640$		0			0
$641$	−3.16703e9	+	1.15270e9i	−0.474951	+	0.172868i	−0.568394	−	0.822757i	$-0.692435\pi$
$641$	−3.16703e9	+	1.15270e9i	−0.474951	+	0.172868i	0.0934427	+	0.995625i	$0.470213\pi$
$642$		0			0
$643$	4.43894e9	+	3.72471e9i	0.658477	+	0.552528i	0.909630	−	0.415420i	$-0.136365\pi$
$643$	4.43894e9	+	3.72471e9i	0.658477	+	0.552528i	−0.251153	+	0.967947i	$0.580810\pi$
$644$		0			0
$645$	1.74320e10			2.55793
$646$		0			0
$647$	6.25031e9			0.907270			0.453635	−	0.891188i	$-0.350127\pi$
$647$	6.25031e9			0.907270			0.453635	+	0.891188i	$0.350127\pi$
$648$		0			0
$649$	−6.01288e8	−	5.04541e8i	−0.0863428	−	0.0724502i
$650$		0			0
$651$	3.57721e8	−	1.30200e8i	0.0508173	−	0.0184960i
$652$		0			0
$653$	−7.92402e8	−	1.37248e9i	−0.111365	−	0.192890i	0.804956	−	0.593335i	$-0.202189\pi$
$653$	−7.92402e8	−	1.37248e9i	−0.111365	−	0.192890i	−0.916321	+	0.400445i	$0.868856\pi$
$654$		0			0
$655$	3.14553e8	+	1.78392e9i	0.0437370	+	0.248045i
$656$		0			0
$657$	−7.28335e9	+	1.26151e10i	−1.00196	+	1.73545i
$658$		0			0
$659$	−6.24698e9	+	5.24183e9i	−0.850297	+	0.713484i	−0.959855	−	0.280496i	$-0.909501\pi$
$659$	−6.24698e9	+	5.24183e9i	−0.850297	+	0.713484i	0.109558	+	0.993980i	$0.465057\pi$
$660$		0			0
$661$	−3.48746e9	−	1.26933e9i	−0.469683	−	0.170951i	0.0963259	−	0.995350i	$-0.469291\pi$
$661$	−3.48746e9	−	1.26933e9i	−0.469683	−	0.170951i	−0.566009	+	0.824399i	$0.691513\pi$
$662$		0			0
$663$	4.45992e9	−	2.52934e10i	0.594332	−	3.37063i
$664$		0			0
$665$	−3.11842e6	+	3.74431e9i	−0.000411205	+	0.493738i
$666$		0			0
$667$	−8.77314e8	+	4.97549e9i	−0.114476	+	0.649226i
$668$		0			0
$669$	−6.47296e9	−	2.35596e9i	−0.835818	−	0.304213i
$670$		0			0
$671$	4.98953e9	−	4.18671e9i	0.637574	−	0.534988i
$672$		0			0
$673$	2.77405e9	−	4.80480e9i	0.350802	−	0.607606i	−0.635589	−	0.772028i	$-0.719242\pi$
$673$	2.77405e9	−	4.80480e9i	0.350802	−	0.607606i	0.986390	+	0.164422i	$0.0525758\pi$
$674$		0			0
$675$	−5.26387e9	−	2.98529e10i	−0.658782	−	3.73614i
$676$		0			0
$677$	−3.60230e9	−	6.23936e9i	−0.446190	−	0.772823i	0.551945	−	0.833881i	$-0.313886\pi$
$677$	−3.60230e9	−	6.23936e9i	−0.446190	−	0.772823i	−0.998134	+	0.0610577i	$0.980553\pi$
$678$		0			0
$679$	−8.41492e7	+	3.06278e7i	−0.0103159	+	0.00375467i
$680$		0			0
$681$	1.62615e10	+	1.36450e10i	1.97308	+	1.65561i
$682$		0			0
$683$	−5.01842e9			−0.602691			−0.301346	−	0.953515i	$-0.597436\pi$
$683$	−5.01842e9			−0.602691			−0.301346	+	0.953515i	$0.597436\pi$
$684$		0			0
$685$	−1.45184e9			−0.172584
$686$		0			0
$687$	−9.12411e9	−	7.65604e9i	−1.07360	−	0.900857i
$688$		0			0
$689$	6.66047e9	−	2.42421e9i	0.775778	−	0.282360i
$690$		0			0
$691$	−3.90026e9	−	6.75544e9i	−0.449697	−	0.778898i	0.548669	−	0.836040i	$-0.315135\pi$
$691$	−3.90026e9	−	6.75544e9i	−0.449697	−	0.778898i	−0.998366	+	0.0571414i	$0.981801\pi$
$692$		0			0
$693$	−1.61121e9	−	9.13762e9i	−0.183902	−	1.04296i
$694$		0			0
$695$	5.15063e9	−	8.92116e9i	0.581988	−	1.00803i
$696$		0			0
$697$	1.03225e10	−	8.66158e9i	1.15470	−	0.968908i
$698$		0			0
$699$	1.07754e9	+	3.92194e8i	0.119334	+	0.0434341i
$700$		0			0
$701$	9.94024e8	−	5.63739e9i	0.108989	−	0.618109i	−0.880562	−	0.473930i	$-0.842835\pi$
$701$	9.94024e8	−	5.63739e9i	0.108989	−	0.618109i	0.989552	−	0.144179i	$-0.0460540\pi$
$702$		0			0
$703$	4.70719e9	+	5.61930e9i	0.510996	+	0.610013i
$704$		0			0
$705$	−3.46544e9	+	1.96535e10i	−0.372475	+	2.11241i
$706$		0			0
$707$	−2.73000e9	−	9.93640e8i	−0.290533	−	0.105745i
$708$		0			0
$709$	−9.25332e9	+	7.76446e9i	−0.975070	+	0.818181i	−0.983338	−	0.181785i	$-0.941812\pi$
$709$	−9.25332e9	+	7.76446e9i	−0.975070	+	0.818181i	0.00826855	+	0.999966i	$0.497368\pi$
$710$		0			0
$711$	3.94420e9	−	6.83155e9i	0.411543	−	0.712813i
$712$		0			0
$713$	1.71023e8	+	9.69919e8i	0.0176702	+	0.100213i
$714$		0			0
$715$	2.09999e10	+	3.63729e10i	2.14855	+	3.72140i
$716$		0			0
$717$	−2.71415e10	+	9.87869e9i	−2.74990	+	1.00088i
$718$		0			0
$719$	4.79349e9	+	4.02221e9i	0.480951	+	0.403566i	0.850770	−	0.525538i	$-0.176136\pi$
$719$	4.79349e9	+	4.02221e9i	0.480951	+	0.403566i	−0.369819	+	0.929104i	$0.620580\pi$
$720$		0			0
$721$	3.88072e8			0.0385602
$722$		0			0
$723$	8.25010e9			0.811849
$724$		0			0
$725$	1.13686e10	+	9.53937e9i	1.10796	+	0.929687i
$726$		0			0
$727$	−1.42631e10	+	5.19136e9i	−1.37672	+	0.501084i	−0.921181	−	0.389133i	$-0.872774\pi$
$727$	−1.42631e10	+	5.19136e9i	−1.37672	+	0.501084i	−0.455536	+	0.890218i	$0.650552\pi$
$728$		0			0
$729$	4.19582e9	+	7.26737e9i	0.401116	+	0.694753i
$730$		0			0
$731$	−2.21658e9	−	1.25709e10i	−0.209881	−	1.19029i
$732$		0			0
$733$	−1.63161e9	+	2.82602e9i	−0.153021	+	0.265040i	−0.932337	−	0.361591i	$-0.882234\pi$
$733$	−1.63161e9	+	2.82602e9i	−0.153021	+	0.265040i	0.779316	+	0.626632i	$0.215567\pi$
$734$		0			0
$735$	−2.31553e10	+	1.94296e10i	−2.15102	+	1.80492i
$736$		0			0
$737$	−1.74000e10	−	6.33308e9i	−1.60108	−	0.582745i
$738$		0			0
$739$	−1.24470e8	+	7.05906e8i	−0.0113451	+	0.0643415i	−0.989955	−	0.141385i	$-0.954845\pi$
$739$	−1.24470e8	+	7.05906e8i	−0.0113451	+	0.0643415i	0.978610	+	0.205726i	$0.0659557\pi$
$740$		0			0
$741$	−1.68772e10	−	2.01475e10i	−1.52383	−	1.81911i
$742$		0			0
$743$	2.77034e9	−	1.57114e10i	0.247784	−	1.40525i	−0.566154	−	0.824299i	$-0.691569\pi$
$743$	2.77034e9	−	1.57114e10i	0.247784	−	1.40525i	0.813938	−	0.580952i	$-0.197320\pi$
$744$		0			0
$745$	3.14766e10	+	1.14566e10i	2.78895	+	1.01510i
$746$		0			0
$747$	−8.24726e9	+	6.92027e9i	−0.723915	+	0.607437i
$748$		0			0
$749$	1.01344e9	−	1.75534e9i	0.0881280	−	0.152642i
$750$		0			0
$751$	−2.88566e9	−	1.63654e10i	−0.248602	−	1.40989i	−0.811976	−	0.583691i	$-0.801608\pi$
$751$	−2.88566e9	−	1.63654e10i	−0.248602	−	1.40989i	0.563373	−	0.826202i	$-0.309503\pi$
$752$		0			0
$753$	−2.61826e9	−	4.53496e9i	−0.223476	−	0.387072i
$754$		0			0
$755$	−5.48678e8	+	1.99702e8i	−0.0463984	+	0.0168876i
$756$		0			0
$757$	−1.02942e10	−	8.63786e9i	−0.862496	−	0.723720i	0.100008	−	0.994987i	$-0.468113\pi$
$757$	−1.02942e10	−	8.63786e9i	−0.862496	−	0.723720i	−0.962504	+	0.271266i	$0.912558\pi$
$758$		0			0
$759$	3.56532e10			2.95973
$760$		0			0
$761$	−2.30781e10			−1.89825			−0.949124	−	0.314903i	$-0.898028\pi$
$761$	−2.30781e10			−1.89825			−0.949124	+	0.314903i	$0.898028\pi$
$762$		0			0
$763$	1.61683e9	+	1.35668e9i	0.131774	+	0.110571i
$764$		0			0
$765$	−6.03443e10	+	2.19635e10i	−4.87328	+	1.77373i
$766$		0			0
$767$	5.26043e8	+	9.11133e8i	0.0420957	+	0.0729118i
$768$		0			0
$769$	1.45394e8	+	8.24568e8i	0.0115293	+	0.0653859i	0.990030	−	0.140859i	$-0.0449866\pi$
$769$	1.45394e8	+	8.24568e8i	0.0115293	+	0.0653859i	−0.978500	+	0.206245i	$0.933875\pi$
$770$		0			0
$771$	−8.57990e9	+	1.48608e10i	−0.674205	+	1.16776i
$772$		0			0
$773$	1.64406e10	−	1.37953e10i	1.28023	−	1.07424i	0.287019	−	0.957925i	$-0.407336\pi$
$773$	1.64406e10	−	1.37953e10i	1.28023	−	1.07424i	0.993212	−	0.116316i	$-0.0371087\pi$
$774$		0			0
$775$	2.71855e9	+	9.89471e8i	0.209788	+	0.0763567i
$776$		0			0
$777$	8.94597e8	−	5.07351e9i	0.0684154	−	0.388003i
$778$		0			0
$779$	1.14842e7	−	1.37891e10i	0.000870400	−	1.04510i
$780$		0			0
$781$	−4.96155e9	+	2.81383e10i	−0.372682	+	2.11359i
$782$		0			0
$783$	1.65787e10	+	6.03414e9i	1.23419	+	0.449210i
$784$		0			0
$785$	−1.76250e10	+	1.47892e10i	−1.30043	+	1.09119i
$786$		0			0
$787$	−7.11333e9	+	1.23207e10i	−0.520189	+	0.900994i	0.479535	+	0.877523i	$0.340805\pi$
$787$	−7.11333e9	+	1.23207e10i	−0.520189	+	0.900994i	−0.999725	+	0.0234717i	$0.992528\pi$
$788$		0			0
$789$	−1.49822e9	−	8.49682e9i	−0.108594	−	0.615867i
$790$		0			0
$791$	2.69719e9	+	4.67167e9i	0.193773	+	0.335625i
$792$		0			0
$793$	−8.20378e9	+	2.98593e9i	−0.584195	+	0.212630i
$794$		0			0
$795$	−2.01632e10	−	1.69189e10i	−1.42323	−	1.19423i
$796$		0			0
$797$	1.81565e10			1.27036			0.635181	−	0.772363i	$-0.280925\pi$
$797$	1.81565e10			1.27036			0.635181	+	0.772363i	$0.280925\pi$
$798$		0			0
$799$	1.46135e10			1.01354
$800$		0			0
$801$	−4.23863e10	−	3.55664e10i	−2.91415	−	2.44526i
$802$		0			0
$803$	−2.43442e10	+	8.86058e9i	−1.65917	+	0.603890i
$804$		0			0
$805$	3.40407e9	+	5.89603e9i	0.229992	+	0.398358i
$806$		0			0
$807$	5.69953e9	+	3.23237e10i	0.381753	+	2.16503i
$808$		0			0
$809$	−7.93831e7	+	1.37495e8i	−0.00527118	+	0.00912995i	−0.868649	−	0.495428i	$-0.835011\pi$
$809$	−7.93831e7	+	1.37495e8i	−0.00527118	+	0.00912995i	0.863378	+	0.504558i	$0.168345\pi$
$810$		0			0
$811$	1.85794e10	−	1.55900e10i	1.22309	−	1.02630i	0.224435	−	0.974489i	$-0.427946\pi$
$811$	1.85794e10	−	1.55900e10i	1.22309	−	1.02630i	0.998657	−	0.0518073i	$-0.0164982\pi$
$812$		0			0
$813$	2.71778e10	+	9.89191e9i	1.77377	+	0.645600i
$814$		0			0
$815$	5.32306e9	−	3.01886e10i	0.344437	−	1.95340i
$816$		0			0
$817$	−1.13069e10	−	6.54060e9i	−0.725380	−	0.419604i
$818$		0			0
$819$	−2.15961e9	+	1.22477e10i	−0.137366	+	0.779044i
$820$		0			0
$821$	−3.47189e9	−	1.26367e9i	−0.218960	−	0.0796950i	0.230211	−	0.973141i	$-0.426058\pi$
$821$	−3.47189e9	−	1.26367e9i	−0.218960	−	0.0796950i	−0.449171	+	0.893446i	$0.648281\pi$
$822$		0			0
$823$	8.72969e9	−	7.32508e9i	0.545882	−	0.458050i	−0.327661	−	0.944795i	$-0.606261\pi$
$823$	8.72969e9	−	7.32508e9i	0.545882	−	0.458050i	0.873544	+	0.486745i	$0.161816\pi$
$824$		0			0
$825$	5.23644e10	−	9.06978e10i	3.24674	−	5.62352i
$826$		0			0
$827$	3.33028e9	+	1.88870e10i	0.204744	+	1.16116i	0.897841	+	0.440319i	$0.145135\pi$
$827$	3.33028e9	+	1.88870e10i	0.204744	+	1.16116i	−0.693097	+	0.720844i	$0.743754\pi$
$828$		0			0
$829$	1.52231e10	+	2.63671e10i	0.928029	+	1.60739i	0.786616	+	0.617442i	$0.211831\pi$
$829$	1.52231e10	+	2.63671e10i	0.928029	+	1.60739i	0.141412	+	0.989951i	$0.454836\pi$
$830$		0			0
$831$	2.51024e10	−	9.13654e9i	1.51744	−	0.552304i
$832$		0			0
$833$	1.69558e10	+	1.42276e10i	1.01639	+	0.852852i
$834$		0			0
$835$	−2.22701e10			−1.32379
$836$		0			0
$837$	3.43924e9			0.202733
$838$		0			0
$839$	−1.02609e10	−	8.60992e9i	−0.599817	−	0.503306i	0.291570	−	0.956550i	$-0.405822\pi$
$839$	−1.02609e10	−	8.60992e9i	−0.599817	−	0.503306i	−0.891387	+	0.453243i	$0.850267\pi$
$840$		0			0
$841$	8.09312e9	−	2.94565e9i	0.469170	−	0.170764i
$842$		0			0
$843$	−9.53323e9	−	1.65120e10i	−0.548079	−	0.949301i
$844$		0			0
$845$	−4.46193e9	−	2.53049e10i	−0.254404	−	1.44280i
$846$		0			0
$847$	5.74860e9	−	9.95686e9i	0.325065	−	0.563029i
$848$		0			0
$849$	1.04065e10	−	8.73211e9i	0.583618	−	0.489714i
$850$		0			0
$851$	1.25247e10	+	4.55862e9i	0.696649	+	0.253560i
$852$		0			0
$853$	−5.42115e9	+	3.07449e10i	−0.299068	+	1.69610i	0.351124	+	0.936329i	$0.385799\pi$
$853$	−5.42115e9	+	3.07449e10i	−0.299068	+	1.69610i	−0.650192	+	0.759770i	$0.725312\pi$
$854$		0			0
$855$	−2.25269e10	+	6.17322e10i	−1.23260	+	3.37777i
$856$		0			0
$857$	2.88080e9	−	1.63378e10i	0.156344	−	0.886670i	−0.801203	−	0.598392i	$-0.795806\pi$
$857$	2.88080e9	−	1.63378e10i	0.156344	−	0.886670i	0.957547	−	0.288277i	$-0.0930825\pi$
$858$		0			0
$859$	−4.85906e9	−	1.76855e9i	−0.261563	−	0.0952012i	0.207910	−	0.978148i	$-0.433334\pi$
$859$	−4.85906e9	−	1.76855e9i	−0.261563	−	0.0952012i	−0.469473	+	0.882947i	$0.655556\pi$
$860$		0			0
$861$	−7.42375e9	+	6.22927e9i	−0.396381	+	0.332603i
$862$		0			0
$863$	1.65524e10	−	2.86697e10i	0.876646	−	1.51839i	0.0216464	−	0.999766i	$-0.493109\pi$
$863$	1.65524e10	−	2.86697e10i	0.876646	−	1.51839i	0.854999	−	0.518629i	$-0.173557\pi$
$864$		0			0
$865$	3.92789e9	+	2.22762e10i	0.206349	+	1.17026i
$866$		0			0
$867$	1.81338e10	+	3.14087e10i	0.944979	+	1.63675i
$868$		0			0
$869$	1.31833e10	−	4.79832e9i	0.681482	−	0.248039i
$870$		0			0
$871$	1.90125e10	+	1.59534e10i	0.974935	+	0.818068i
$872$		0			0
$873$	−1.57163e9			−0.0799467
$874$		0			0
$875$	1.02143e10			0.515441
$876$		0			0
$877$	−8.43669e9	−	7.07923e9i	−0.422351	−	0.354395i	0.406705	−	0.913559i	$-0.366678\pi$
$877$	−8.43669e9	−	7.07923e9i	−0.422351	−	0.354395i	−0.829057	+	0.559165i	$0.811122\pi$
$878$		0			0
$879$	−6.83724e9	+	2.48855e9i	−0.339563	+	0.123591i
$880$		0			0
$881$	1.09408e9	+	1.89501e9i	0.0539057	+	0.0933673i	0.891719	−	0.452589i	$-0.149500\pi$
$881$	1.09408e9	+	1.89501e9i	0.0539057	+	0.0933673i	−0.837813	+	0.545957i	$0.816166\pi$
$882$		0			0
$883$	2.20122e9	+	1.24837e10i	0.107597	+	0.610213i	0.990151	+	0.140002i	$0.0447110\pi$
$883$	2.20122e9	+	1.24837e10i	0.107597	+	0.610213i	−0.882554	+	0.470211i	$0.844178\pi$
$884$		0			0
$885$	1.95347e9	−	3.38351e9i	0.0947339	−	0.164084i
$886$		0			0
$887$	−2.07740e10	+	1.74315e10i	−0.999513	+	0.838691i	−0.986917	−	0.161230i	$-0.948454\pi$
$887$	−2.07740e10	+	1.74315e10i	−0.999513	+	0.838691i	−0.0125959	+	0.999921i	$0.504010\pi$
$888$		0			0
$889$	3.65907e9	+	1.33179e9i	0.174669	+	0.0635742i
$890$		0			0
$891$	7.89878e9	−	4.47962e10i	0.374100	−	2.12163i
$892$		0			0
$893$	9.62191e9	−	1.14476e10i	0.452148	−	0.537939i
$894$		0			0
$895$	−3.98177e8	+	2.25817e9i	−0.0185650	+	0.105287i
$896$		0			0
$897$	−4.49062e10	−	1.63445e10i	−2.07746	−	0.756135i
$898$		0			0
$899$	−1.28983e9	+	1.08230e9i	−0.0592073	+	0.0496808i
$900$		0			0
$901$	−9.63698e9	+	1.66917e10i	−0.438939	+	0.760265i
$902$		0			0
$903$	1.59413e9	+	9.04075e9i	0.0720471	+	0.408599i
$904$		0			0
$905$	2.20663e10	+	3.82199e10i	0.989597	+	1.71403i
$906$		0			0
$907$	−3.82429e10	+	1.39193e10i	−1.70187	+	0.619429i	−0.996036	−	0.0889524i	$-0.971648\pi$
$907$	−3.82429e10	+	1.39193e10i	−1.70187	+	0.619429i	−0.705830	+	0.708381i	$0.749426\pi$
$908$		0			0
$909$	−3.90587e10	−	3.27741e10i	−1.72482	−	1.44730i
$910$		0			0
$911$	2.23325e10			0.978639			0.489320	−	0.872105i	$-0.337245\pi$
$911$	2.23325e10			0.978639			0.489320	+	0.872105i	$0.337245\pi$
$912$		0			0
$913$	−1.91472e10			−0.832640
$914$		0			0
$915$	2.48352e10	+	2.08392e10i	1.07175	+	0.899306i
$916$		0			0
$917$	−8.96428e8	+	3.26273e8i	−0.0383904	+	0.0139730i
$918$		0			0
$919$	−1.53444e10	−	2.65773e10i	−0.652147	−	1.12955i	−0.982601	−	0.185729i	$-0.940535\pi$
$919$	−1.53444e10	−	2.65773e10i	−0.652147	−	1.12955i	0.330454	−	0.943822i	$-0.392798\pi$
$920$		0			0
$921$	1.28303e10	+	7.27644e10i	0.541164	+	3.06909i
$922$		0			0
$923$	1.91487e10	−	3.31665e10i	0.801555	−	1.38833i
$924$		0			0
$925$	2.99919e10	−	2.51662e10i	1.24597	−	1.04549i
$926$		0			0
$927$	6.40006e9	+	2.32943e9i	0.263879	+	0.0960442i
$928$		0			0
$929$	−7.08967e9	+	4.02075e10i	−0.290116	+	1.64533i	0.396302	+	0.918120i	$0.370293\pi$
$929$	−7.08967e9	+	4.02075e10i	−0.290116	+	1.64533i	−0.686418	+	0.727207i	$0.740818\pi$
$930$		0			0
$931$	2.23093e10	−	3.91458e9i	0.906072	−	0.158987i
$932$		0			0
$933$	1.04293e10	−	5.91477e10i	0.420408	−	2.38425i
$934$		0			0
$935$	−1.07321e11	−	3.90617e10i	−4.29383	−	1.56283i
$936$		0			0
$937$	1.14600e9	−	9.61606e8i	0.0455088	−	0.0381864i	−0.619750	−	0.784800i	$-0.712766\pi$
$937$	1.14600e9	−	9.61606e8i	0.0455088	−	0.0381864i	0.665258	+	0.746613i	$0.268321\pi$
$938$		0			0
$939$	1.02586e9	−	1.77684e9i	0.0404350	−	0.0700355i
$940$		0			0
$941$	1.66470e9	+	9.44097e9i	0.0651286	+	0.369363i	0.999900	+	0.0141138i	$0.00449272\pi$
$941$	1.66470e9	+	9.44097e9i	0.0651286	+	0.369363i	−0.934772	+	0.355249i	$0.884396\pi$
$942$		0			0
$943$	−1.25362e10	−	2.17132e10i	−0.486825	−	0.843206i
$944$		0			0
$945$	2.23405e10	−	8.13129e9i	0.861157	−	0.313435i
$946$		0			0
$947$	3.19016e10	+	2.67686e10i	1.22064	+	1.02424i	0.998791	+	0.0491563i	$0.0156532\pi$
$947$	3.19016e10	+	2.67686e10i	1.22064	+	1.02424i	0.221848	+	0.975081i	$0.428791\pi$
$948$		0			0
$949$	3.47242e10			1.31887
$950$		0			0
$951$	4.54046e10			1.71186
$952$		0			0
$953$	−2.38658e10	−	2.00258e10i	−0.893204	−	0.749487i	0.0756459	−	0.997135i	$-0.475898\pi$
$953$	−2.38658e10	−	2.00258e10i	−0.893204	−	0.749487i	−0.968850	+	0.247647i	$0.920343\pi$
$954$		0			0
$955$	4.26053e10	−	1.55071e10i	1.58290	−	0.576127i
$956$		0			0
$957$	3.04765e10	+	5.27868e10i	1.12402	+	1.94686i
$958$		0			0
$959$	−1.32768e8	−	7.52967e8i	−0.00486104	−	0.0275683i
$960$		0			0
$961$	1.35922e10	−	2.35424e10i	0.494035	−	0.855694i
$962$		0			0
$963$	2.72502e10	−	2.28656e10i	0.983282	−	0.825071i
$964$		0			0
$965$	3.58242e10	+	1.30390e10i	1.28331	+	0.467086i
$966$		0			0
$967$	2.11434e9	−	1.19910e10i	0.0751937	−	0.426444i	−0.923851	−	0.382751i	$-0.874977\pi$
$967$	2.11434e9	−	1.19910e10i	0.0751937	−	0.426444i	0.999045	−	0.0436930i	$-0.0139123\pi$
$968$		0			0
$969$	7.03727e10	+	1.24690e10i	2.48468	+	0.440250i
$970$		0			0
$971$	−2.79444e9	+	1.58480e10i	−0.0979551	+	0.555531i	0.895847	+	0.444364i	$0.146570\pi$
$971$	−2.79444e9	+	1.58480e10i	−0.0979551	+	0.555531i	−0.993802	+	0.111168i	$0.964541\pi$
$972$		0			0
$973$	5.09780e9	+	1.85545e9i	0.177414	+	0.0645734i
$974$		0			0
$975$	−1.07533e11	+	9.02311e10i	−3.71558	+	3.11774i
$976$		0			0
$977$	7.28410e8	−	1.26164e9i	0.0249888	−	0.0432818i	−0.853261	−	0.521485i	$-0.825378\pi$
$977$	7.28410e8	−	1.26164e9i	0.0249888	−	0.0432818i	0.878249	+	0.478203i	$0.158712\pi$
$978$		0			0
$979$	−1.70880e10	−	9.69109e10i	−0.582039	−	3.30091i
$980$		0			0
$981$	1.85211e10	+	3.20794e10i	0.626361	+	1.08489i
$982$		0			0
$983$	−4.64013e10	+	1.68887e10i	−1.55809	+	0.567098i	−0.970298	−	0.241914i	$-0.922225\pi$
$983$	−4.64013e10	+	1.68887e10i	−1.55809	+	0.567098i	−0.587792	+	0.809012i	$0.700003\pi$
$984$		0			0
$985$	−1.21001e10	−	1.01532e10i	−0.403425	−	0.338514i
$986$		0			0
$987$	−1.05098e10			−0.347924
$988$		0			0
$989$	−2.37508e10			−0.780712
$990$		0			0
$991$	1.38826e10	+	1.16489e10i	0.453121	+	0.380214i	0.840592	−	0.541668i	$-0.182207\pi$
$991$	1.38826e10	+	1.16489e10i	0.453121	+	0.380214i	−0.387472	+	0.921882i	$0.626651\pi$
$992$		0			0
$993$	−7.49396e10	+	2.72758e10i	−2.42878	+	0.884005i
$994$		0			0
$995$	−8.73784e9	−	1.51344e10i	−0.281205	−	0.487062i
$996$		0			0
$997$	−8.27282e9	−	4.69175e10i	−0.264375	−	1.49935i	−0.770809	−	0.637067i	$-0.780148\pi$
$997$	−8.27282e9	−	4.69175e10i	−0.264375	−	1.49935i	0.506434	−	0.862279i	$-0.330964\pi$
$998$		0			0
$999$	2.32718e10	−	4.03080e10i	0.738502	−	1.27912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.17.1	yes	72
19.9	even	9	inner	76.8.i.a.9.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.9.1	✓	72	19.9	even	9	inner
76.8.i.a.17.1	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-62.6763 - 52.5916i) q^{3} +(458.247 - 166.788i) q^{5} +(128.407 + 222.408i) q^{7} +(782.666 + 4438.72i) q^{9} +O(q^{10})\)	\(q+(-62.6763 - 52.5916i) q^{3} +(458.247 - 166.788i) q^{5} +(128.407 + 222.408i) q^{7} +(782.666 + 4438.72i) q^{9} +(-4007.98 + 6942.02i) q^{11} +(8230.60 - 6906.30i) q^{13} +(-37492.9 - 13646.3i) q^{15} +(-5073.41 + 28772.7i) q^{17} +(19198.8 + 22919.0i) q^{19} +(3648.71 - 20692.9i) q^{21} +(51083.4 + 18592.8i) q^{23} +(122325. - 102643. i) q^{25} +(94916.8 - 164401. i) q^{27} +(16138.4 + 91525.5i) q^{29} +(9058.57 + 15689.9i) q^{31} +(616297. - 224314. i) q^{33} +(95937.5 + 80501.1i) q^{35} +245181. q^{37} -879077. q^{39} +(-353308. - 296461. i) q^{41} +(-410553. + 149429. i) q^{43} +(1.09898e6 + 1.90349e6i) q^{45} +(-86855.1 - 492580. i) q^{47} +(378795. - 656091. i) q^{49} +(1.83119e6 - 1.53655e6i) q^{51} +(619908. + 225628. i) q^{53} +(-678797. + 3.84965e6i) q^{55} +(2037.27 - 2.44617e6i) q^{57} +(-17003.7 + 96432.8i) q^{59} +(-763548. - 277909. i) q^{61} +(-886708. + 744036. i) q^{63} +(2.61976e6 - 4.53756e6i) q^{65} +(401123. + 2.27488e6i) q^{67} +(-2.22389e6 - 3.85189e6i) q^{69} +(3.34948e6 - 1.21911e6i) q^{71} +(2.47576e6 + 2.07741e6i) q^{73} -1.30650e7 q^{75} -2.05862e6 q^{77} +(-1.34071e6 - 1.12499e6i) q^{79} +(-5.33237e6 + 1.94082e6i) q^{81} +(1.19432e6 + 2.06862e6i) q^{83} +(2.47408e6 + 1.40312e7i) q^{85} +(3.80198e6 - 6.58522e6i) q^{87} +(-9.40415e6 + 7.89102e6i) q^{89} +(2.59289e6 + 943734. i) q^{91} +(257400. - 1.45979e6i) q^{93} +(1.26204e7 + 7.30042e6i) q^{95} +(-60550.0 + 343396. i) q^{97} +(-3.39506e7 - 1.23570e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

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