LMFDB - Embedded newform 177.12.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

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:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-79.8853 q^{2} +243.000 q^{3} +4333.66 q^{4} -5377.20 q^{5} -19412.1 q^{6} -58607.4 q^{7} -182591. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-79.8853 q^{2} +243.000 q^{3} +4333.66 q^{4} -5377.20 q^{5} -19412.1 q^{6} -58607.4 q^{7} -182591. q^{8} +59049.0 q^{9} +429560. q^{10} -126129. q^{11} +1.05308e6 q^{12} +176292. q^{13} +4.68187e6 q^{14} -1.30666e6 q^{15} +5.71097e6 q^{16} +5.10282e6 q^{17} -4.71715e6 q^{18} -2.83908e6 q^{19} -2.33030e7 q^{20} -1.42416e7 q^{21} +1.00759e7 q^{22} -2.26275e7 q^{23} -4.43695e7 q^{24} -1.99138e7 q^{25} -1.40831e7 q^{26} +1.43489e7 q^{27} -2.53984e8 q^{28} -1.40162e8 q^{29} +1.04383e8 q^{30} -5.94487e7 q^{31} -8.22767e7 q^{32} -3.06495e7 q^{33} -4.07640e8 q^{34} +3.15144e8 q^{35} +2.55898e8 q^{36} +1.51143e8 q^{37} +2.26800e8 q^{38} +4.28390e7 q^{39} +9.81827e8 q^{40} +4.61623e6 q^{41} +1.13769e9 q^{42} -1.18990e9 q^{43} -5.46602e8 q^{44} -3.17519e8 q^{45} +1.80761e9 q^{46} +4.27766e8 q^{47} +1.38776e9 q^{48} +1.45750e9 q^{49} +1.59082e9 q^{50} +1.23999e9 q^{51} +7.63990e8 q^{52} -9.35982e7 q^{53} -1.14627e9 q^{54} +6.78224e8 q^{55} +1.07012e10 q^{56} -6.89896e8 q^{57} +1.11969e10 q^{58} +7.14924e8 q^{59} -5.66262e9 q^{60} -2.35775e8 q^{61} +4.74908e9 q^{62} -3.46071e9 q^{63} -5.12336e9 q^{64} -9.47959e8 q^{65} +2.44844e9 q^{66} -9.33033e9 q^{67} +2.21139e10 q^{68} -5.49849e9 q^{69} -2.51754e10 q^{70} +3.93536e9 q^{71} -1.07818e10 q^{72} -2.05323e10 q^{73} -1.20741e10 q^{74} -4.83905e9 q^{75} -1.23036e10 q^{76} +7.39212e9 q^{77} -3.42220e9 q^{78} -4.02922e10 q^{79} -3.07090e10 q^{80} +3.48678e9 q^{81} -3.68769e8 q^{82} -1.16799e10 q^{83} -6.17182e10 q^{84} -2.74389e10 q^{85} +9.50558e10 q^{86} -3.40594e10 q^{87} +2.30301e10 q^{88} -3.48789e9 q^{89} +2.53651e10 q^{90} -1.03320e10 q^{91} -9.80600e10 q^{92} -1.44460e10 q^{93} -3.41722e10 q^{94} +1.52663e10 q^{95} -1.99932e10 q^{96} -7.99476e10 q^{97} -1.16433e11 q^{98} -7.44782e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−79.8853	−1.76523	−0.882616	−	0.470094i	$-0.844220\pi$
$2$	−79.8853	−1.76523	−0.882616	+	0.470094i	$0.844220\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	4333.66	2.11604
$5$	−5377.20	−0.769523	−0.384761	−	0.923016i	$-0.625716\pi$
$5$	−5377.20	−0.769523	−0.384761	+	0.923016i	$0.625716\pi$
$6$	−19412.1	−1.01916
$7$	−58607.4	−1.31799	−0.658996	−	0.752146i	$-0.729019\pi$
$7$	−58607.4	−1.31799	−0.658996	+	0.752146i	$0.729019\pi$
$8$	−182591.	−1.97008
$9$	59049.0	0.333333
$10$	429560.	1.35839
$11$	−126129.	−0.236133	−0.118067	−	0.993006i	$-0.537670\pi$
$11$	−126129.	−0.236133	−0.118067	+	0.993006i	$0.537670\pi$
$12$	1.05308e6	1.22170
$13$	176292.	0.131687	0.0658437	−	0.997830i	$-0.479026\pi$
$13$	176292.	0.131687	0.0658437	+	0.997830i	$0.479026\pi$
$14$	4.68187e6	2.32656
$15$	−1.30666e6	−0.444284
$16$	5.71097e6	1.36160
$17$	5.10282e6	0.871648	0.435824	−	0.900032i	$-0.356457\pi$
$17$	5.10282e6	0.871648	0.435824	+	0.900032i	$0.356457\pi$
$18$	−4.71715e6	−0.588411
$19$	−2.83908e6	−0.263046	−0.131523	−	0.991313i	$-0.541987\pi$
$19$	−2.83908e6	−0.263046	−0.131523	+	0.991313i	$0.541987\pi$
$20$	−2.33030e7	−1.62834
$21$	−1.42416e7	−0.760943
$22$	1.00759e7	0.416830
$23$	−2.26275e7	−0.733051	−0.366526	−	0.930408i	$-0.619453\pi$
$23$	−2.26275e7	−0.733051	−0.366526	+	0.930408i	$0.619453\pi$
$24$	−4.43695e7	−1.13743
$25$	−1.99138e7	−0.407835
$26$	−1.40831e7	−0.232459
$27$	1.43489e7	0.192450
$28$	−2.53984e8	−2.78893
$29$	−1.40162e8	−1.26894	−0.634471	−	0.772947i	$-0.718782\pi$
$29$	−1.40162e8	−1.26894	−0.634471	+	0.772947i	$0.718782\pi$
$30$	1.04383e8	0.784265
$31$	−5.94487e7	−0.372952	−0.186476	−	0.982459i	$-0.559707\pi$
$31$	−5.94487e7	−0.372952	−0.186476	+	0.982459i	$0.559707\pi$
$32$	−8.22767e7	−0.433463
$33$	−3.06495e7	−0.136331
$34$	−4.07640e8	−1.53866
$35$	3.15144e8	1.01423
$36$	2.55898e8	0.705348
$37$	1.51143e8	0.358327	0.179163	−	0.983819i	$-0.442661\pi$
$37$	1.51143e8	0.358327	0.179163	+	0.983819i	$0.442661\pi$
$38$	2.26800e8	0.464338
$39$	4.28390e7	0.0760298
$40$	9.81827e8	1.51602
$41$	4.61623e6	0.00622266	0.00311133	−	0.999995i	$-0.499010\pi$
$41$	4.61623e6	0.00622266	0.00311133	+	0.999995i	$0.499010\pi$
$42$	1.13769e9	1.34324
$43$	−1.18990e9	−1.23434	−0.617170	−	0.786829i	$-0.711721\pi$
$43$	−1.18990e9	−1.23434	−0.617170	+	0.786829i	$0.711721\pi$
$44$	−5.46602e8	−0.499668
$45$	−3.17519e8	−0.256508
$46$	1.80761e9	1.29401
$47$	4.27766e8	0.272062	0.136031	−	0.990705i	$-0.456565\pi$
$47$	4.27766e8	0.272062	0.136031	+	0.990705i	$0.456565\pi$
$48$	1.38776e9	0.786120
$49$	1.45750e9	0.737104
$50$	1.59082e9	0.719923
$51$	1.23999e9	0.503246
$52$	7.63990e8	0.278657
$53$	−9.35982e7	−0.0307433	−0.0153716	−	0.999882i	$-0.504893\pi$
$53$	−9.35982e7	−0.0307433	−0.0153716	+	0.999882i	$0.504893\pi$
$54$	−1.14627e9	−0.339719
$55$	6.78224e8	0.181710
$56$	1.07012e10	2.59655
$57$	−6.89896e8	−0.151870
$58$	1.11969e10	2.23998
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−5.66262e9	−0.940125
$61$	−2.35775e8	−0.0357423	−0.0178712	−	0.999840i	$-0.505689\pi$
$61$	−2.35775e8	−0.0357423	−0.0178712	+	0.999840i	$0.505689\pi$
$62$	4.74908e9	0.658347
$63$	−3.46071e9	−0.439331
$64$	−5.12336e9	−0.596438
$65$	−9.47959e8	−0.101337
$66$	2.44844e9	0.240657
$67$	−9.33033e9	−0.844278	−0.422139	−	0.906531i	$-0.638721\pi$
$67$	−9.33033e9	−0.844278	−0.422139	+	0.906531i	$0.638721\pi$
$68$	2.21139e10	1.84445
$69$	−5.49849e9	−0.423227
$70$	−2.51754e10	−1.79034
$71$	3.93536e9	0.258859	0.129430	−	0.991589i	$-0.458685\pi$
$71$	3.93536e9	0.258859	0.129430	+	0.991589i	$0.458685\pi$
$72$	−1.07818e10	−0.656693
$73$	−2.05323e10	−1.15921	−0.579605	−	0.814898i	$-0.696793\pi$
$73$	−2.05323e10	−1.15921	−0.579605	+	0.814898i	$0.696793\pi$
$74$	−1.20741e10	−0.632530
$75$	−4.83905e9	−0.235463
$76$	−1.23036e10	−0.556618
$77$	7.39212e9	0.311222
$78$	−3.42220e9	−0.134210
$79$	−4.02922e10	−1.47323	−0.736617	−	0.676310i	$-0.763578\pi$
$79$	−4.02922e10	−1.47323	−0.736617	+	0.676310i	$0.763578\pi$
$80$	−3.07090e10	−1.04778
$81$	3.48678e9	0.111111
$82$	−3.68769e8	−0.0109844
$83$	−1.16799e10	−0.325470	−0.162735	−	0.986670i	$-0.552032\pi$
$83$	−1.16799e10	−0.325470	−0.162735	+	0.986670i	$0.552032\pi$
$84$	−6.17182e10	−1.61019
$85$	−2.74389e10	−0.670753
$86$	9.50558e10	2.17890
$87$	−3.40594e10	−0.732624
$88$	2.30301e10	0.465201
$89$	−3.48789e9	−0.0662091	−0.0331046	−	0.999452i	$-0.510539\pi$
$89$	−3.48789e9	−0.0662091	−0.0331046	+	0.999452i	$0.510539\pi$
$90$	2.53651e10	0.452795
$91$	−1.03320e10	−0.173563
$92$	−9.80600e10	−1.55117
$93$	−1.44460e10	−0.215324
$94$	−3.41722e10	−0.480253
$95$	1.52663e10	0.202420
$96$	−1.99932e10	−0.250260
$97$	−7.99476e10	−0.945281	−0.472640	−	0.881255i	$-0.656699\pi$
$97$	−7.99476e10	−0.945281	−0.472640	+	0.881255i	$0.656699\pi$
$98$	−1.16433e11	−1.30116
$99$	−7.44782e9	−0.0787110
$100$	−8.62996e10	−0.862996
$101$	−2.66255e10	−0.252076	−0.126038	−	0.992025i	$-0.540226\pi$
$101$	−2.66255e10	−0.252076	−0.126038	+	0.992025i	$0.540226\pi$
$102$	−9.90566e10	−0.888347
$103$	−3.83751e10	−0.326170	−0.163085	−	0.986612i	$-0.552145\pi$
$103$	−3.83751e10	−0.326170	−0.163085	+	0.986612i	$0.552145\pi$
$104$	−3.21893e10	−0.259435
$105$	7.65799e10	0.585563
$106$	7.47712e9	0.0542690
$107$	−2.47057e9	−0.0170289	−0.00851445	−	0.999964i	$-0.502710\pi$
$107$	−2.47057e9	−0.0170289	−0.00851445	+	0.999964i	$0.502710\pi$
$108$	6.21833e10	0.407233
$109$	1.54440e11	0.961419	0.480710	−	0.876880i	$-0.340379\pi$
$109$	1.54440e11	0.961419	0.480710	+	0.876880i	$0.340379\pi$
$110$	−5.41801e10	−0.320760
$111$	3.67278e10	0.206880
$112$	−3.34705e11	−1.79458
$113$	6.20470e10	0.316803	0.158401	−	0.987375i	$-0.449366\pi$
$113$	6.20470e10	0.316803	0.158401	+	0.987375i	$0.449366\pi$
$114$	5.51125e10	0.268086
$115$	1.21673e11	0.564099
$116$	−6.07415e11	−2.68514
$117$	1.04099e10	0.0438958
$118$	−5.71119e10	−0.229814
$119$	−2.99063e11	−1.14883
$120$	2.38584e11	0.875275
$121$	−2.69403e11	−0.944241
$122$	1.88349e10	0.0630935
$123$	1.12174e9	0.00359266
$124$	−2.57631e11	−0.789184
$125$	3.69639e11	1.08336
$126$	2.76460e11	0.775521
$127$	1.67974e10	0.0451151	0.0225576	−	0.999746i	$-0.492819\pi$
$127$	1.67974e10	0.0451151	0.0225576	+	0.999746i	$0.492819\pi$
$128$	5.77784e11	1.48631
$129$	−2.89146e11	−0.712647
$130$	7.57280e10	0.178882
$131$	2.57616e11	0.583420	0.291710	−	0.956507i	$-0.405776\pi$
$131$	2.57616e11	0.583420	0.291710	+	0.956507i	$0.405776\pi$
$132$	−1.32824e11	−0.288484
$133$	1.66391e11	0.346693
$134$	7.45356e11	1.49035
$135$	−7.71570e10	−0.148095
$136$	−9.31727e11	−1.71722
$137$	−3.64707e11	−0.645626	−0.322813	−	0.946463i	$-0.604628\pi$
$137$	−3.64707e11	−0.645626	−0.322813	+	0.946463i	$0.604628\pi$
$138$	4.39249e11	0.747094
$139$	−8.98927e10	−0.146941	−0.0734705	−	0.997297i	$-0.523407\pi$
$139$	−8.98927e10	−0.146941	−0.0734705	+	0.997297i	$0.523407\pi$
$140$	1.36573e12	2.14615
$141$	1.03947e11	0.157075
$142$	−3.14378e11	−0.456947
$143$	−2.22356e10	−0.0310958
$144$	3.37227e11	0.453867
$145$	7.53680e11	0.976479
$146$	1.64023e12	2.04627
$147$	3.54172e11	0.425567
$148$	6.55003e11	0.758235
$149$	2.74713e11	0.306446	0.153223	−	0.988192i	$-0.451035\pi$
$149$	2.74713e11	0.306446	0.153223	+	0.988192i	$0.451035\pi$
$150$	3.86569e11	0.415648
$151$	5.01401e11	0.519770	0.259885	−	0.965640i	$-0.416315\pi$
$151$	5.01401e11	0.519770	0.259885	+	0.965640i	$0.416315\pi$
$152$	5.18389e11	0.518222
$153$	3.01317e11	0.290549
$154$	−5.90521e11	−0.549378
$155$	3.19668e11	0.286995
$156$	1.85650e11	0.160882
$157$	−1.56386e12	−1.30843	−0.654215	−	0.756309i	$-0.727001\pi$
$157$	−1.56386e12	−1.30843	−0.654215	+	0.756309i	$0.727001\pi$
$158$	3.21875e12	2.60060
$159$	−2.27444e10	−0.0177496
$160$	4.42419e11	0.333560
$161$	1.32614e12	0.966156
$162$	−2.78543e11	−0.196137
$163$	−5.56452e11	−0.378788	−0.189394	−	0.981901i	$-0.560652\pi$
$163$	−5.56452e11	−0.378788	−0.189394	+	0.981901i	$0.560652\pi$
$164$	2.00052e10	0.0131674
$165$	1.64808e11	0.104910
$166$	9.33055e11	0.574530
$167$	1.46011e11	0.0869853	0.0434927	−	0.999054i	$-0.486151\pi$
$167$	1.46011e11	0.0869853	0.0434927	+	0.999054i	$0.486151\pi$
$168$	2.60038e12	1.49912
$169$	−1.76108e12	−0.982658
$170$	2.19197e12	1.18404
$171$	−1.67645e11	−0.0876821
$172$	−5.15664e12	−2.61192
$173$	−7.04663e11	−0.345723	−0.172861	−	0.984946i	$-0.555301\pi$
$173$	−7.04663e11	−0.345723	−0.172861	+	0.984946i	$0.555301\pi$
$174$	2.72084e12	1.29325
$175$	1.16710e12	0.537523
$176$	−7.20321e11	−0.321519
$177$	1.73727e11	0.0751646
$178$	2.78631e11	0.116874
$179$	−2.74310e11	−0.111571	−0.0557853	−	0.998443i	$-0.517766\pi$
$179$	−2.74310e11	−0.111571	−0.0557853	+	0.998443i	$0.517766\pi$
$180$	−1.37602e12	−0.542782
$181$	−5.00809e12	−1.91620	−0.958098	−	0.286442i	$-0.907528\pi$
$181$	−5.00809e12	−1.91620	−0.958098	+	0.286442i	$0.907528\pi$
$182$	8.25376e11	0.306379
$183$	−5.72932e10	−0.0206358
$184$	4.13157e12	1.44417
$185$	−8.12728e11	−0.275741
$186$	1.15403e12	0.380097
$187$	−6.43616e11	−0.205825
$188$	1.85379e12	0.575695
$189$	−8.40952e11	−0.253648
$190$	−1.21955e12	−0.357319
$191$	1.75218e12	0.498763	0.249381	−	0.968405i	$-0.419773\pi$
$191$	1.75218e12	0.498763	0.249381	+	0.968405i	$0.419773\pi$
$192$	−1.24498e12	−0.344354
$193$	−1.82880e12	−0.491589	−0.245794	−	0.969322i	$-0.579049\pi$
$193$	−1.82880e12	−0.491589	−0.245794	+	0.969322i	$0.579049\pi$
$194$	6.38663e12	1.66864
$195$	−2.30354e11	−0.0585067
$196$	6.31629e12	1.55975
$197$	6.33272e12	1.52064	0.760319	−	0.649550i	$-0.225042\pi$
$197$	6.33272e12	1.52064	0.760319	+	0.649550i	$0.225042\pi$
$198$	5.94971e11	0.138943
$199$	5.27508e12	1.19822	0.599110	−	0.800666i	$-0.295521\pi$
$199$	5.27508e12	1.19822	0.599110	+	0.800666i	$0.295521\pi$
$200$	3.63607e12	0.803466
$201$	−2.26727e12	−0.487444
$202$	2.12699e12	0.444972
$203$	8.21453e12	1.67246
$204$	5.37368e12	1.06489
$205$	−2.48224e10	−0.00478848
$206$	3.06560e12	0.575766
$207$	−1.33613e12	−0.244350
$208$	1.00680e12	0.179306
$209$	3.58091e11	0.0621139
$210$	−6.11761e12	−1.03366
$211$	6.90227e12	1.13616	0.568079	−	0.822974i	$-0.307687\pi$
$211$	6.90227e12	1.13616	0.568079	+	0.822974i	$0.307687\pi$
$212$	−4.05623e11	−0.0650541
$213$	9.56293e11	0.149453
$214$	1.97362e11	0.0300600
$215$	6.39835e12	0.949854
$216$	−2.61998e12	−0.379142
$217$	3.48413e12	0.491548
$218$	−1.23375e13	−1.69713
$219$	−4.98935e12	−0.669270
$220$	2.93919e12	0.384506
$221$	8.99587e11	0.114785
$222$	−2.93401e12	−0.365191
$223$	1.34382e13	1.63179	0.815893	−	0.578202i	$-0.196246\pi$
$223$	1.34382e13	1.63179	0.815893	+	0.578202i	$0.196246\pi$
$224$	4.82202e12	0.571301
$225$	−1.17589e12	−0.135945
$226$	−4.95664e12	−0.559231
$227$	−6.57119e11	−0.0723605	−0.0361803	−	0.999345i	$-0.511519\pi$
$227$	−6.57119e11	−0.0723605	−0.0361803	+	0.999345i	$0.511519\pi$
$228$	−2.98977e12	−0.321363
$229$	2.99837e12	0.314623	0.157312	−	0.987549i	$-0.449717\pi$
$229$	2.99837e12	0.314623	0.157312	+	0.987549i	$0.449717\pi$
$230$	−9.71987e12	−0.995767
$231$	1.79628e12	0.179684
$232$	2.55923e13	2.49991
$233$	1.19755e13	1.14245	0.571224	−	0.820794i	$-0.306469\pi$
$233$	1.19755e13	1.14245	0.571224	+	0.820794i	$0.306469\pi$
$234$	−8.31596e11	−0.0774863
$235$	−2.30018e12	−0.209358
$236$	3.09824e12	0.275486
$237$	−9.79100e12	−0.850572
$238$	2.38907e13	2.02795
$239$	−6.84363e12	−0.567673	−0.283836	−	0.958873i	$-0.591607\pi$
$239$	−6.84363e12	−0.567673	−0.283836	+	0.958873i	$0.591607\pi$
$240$	−7.46229e12	−0.604938
$241$	−1.27423e12	−0.100961	−0.0504807	−	0.998725i	$-0.516075\pi$
$241$	−1.27423e12	−0.100961	−0.0504807	+	0.998725i	$0.516075\pi$
$242$	2.15213e13	1.66680
$243$	8.47289e11	0.0641500
$244$	−1.02177e12	−0.0756324
$245$	−7.83726e12	−0.567219
$246$	−8.96109e10	−0.00634187
$247$	−5.00507e11	−0.0346399
$248$	1.08548e13	0.734745
$249$	−2.83822e12	−0.187910
$250$	−2.95287e13	−1.91238
$251$	−5.37908e12	−0.340802	−0.170401	−	0.985375i	$-0.554506\pi$
$251$	−5.37908e12	−0.340802	−0.170401	+	0.985375i	$0.554506\pi$
$252$	−1.49975e13	−0.929644
$253$	2.85400e12	0.173098
$254$	−1.34187e12	−0.0796387
$255$	−6.66766e12	−0.387260
$256$	−3.56638e13	−2.02725
$257$	−9.51524e12	−0.529404	−0.264702	−	0.964330i	$-0.585274\pi$
$257$	−9.51524e12	−0.529404	−0.264702	+	0.964330i	$0.585274\pi$
$258$	2.30986e13	1.25799
$259$	−8.85811e12	−0.472272
$260$	−4.10813e12	−0.214433
$261$	−8.27643e12	−0.422980
$262$	−2.05798e13	−1.02987
$263$	−1.31906e13	−0.646409	−0.323205	−	0.946329i	$-0.604760\pi$
$263$	−1.31906e13	−0.646409	−0.323205	+	0.946329i	$0.604760\pi$
$264$	5.59630e12	0.268584
$265$	5.03296e11	0.0236576
$266$	−1.32922e13	−0.611994
$267$	−8.47558e11	−0.0382259
$268$	−4.04345e13	−1.78653
$269$	2.67796e12	0.115922	0.0579612	−	0.998319i	$-0.481540\pi$
$269$	2.67796e12	0.115922	0.0579612	+	0.998319i	$0.481540\pi$
$270$	6.16371e12	0.261422
$271$	2.63328e13	1.09437	0.547187	−	0.837011i	$-0.315699\pi$
$271$	2.63328e13	1.09437	0.547187	+	0.837011i	$0.315699\pi$
$272$	2.91420e13	1.18684
$273$	−2.51068e12	−0.100207
$274$	2.91347e13	1.13968
$275$	2.51172e12	0.0963032
$276$	−2.38286e13	−0.895568
$277$	−3.57231e12	−0.131617	−0.0658083	−	0.997832i	$-0.520963\pi$
$277$	−3.57231e12	−0.131617	−0.0658083	+	0.997832i	$0.520963\pi$
$278$	7.18110e12	0.259385
$279$	−3.51039e12	−0.124317
$280$	−5.75423e13	−1.99810
$281$	1.76159e12	0.0599820	0.0299910	−	0.999550i	$-0.490452\pi$
$281$	1.76159e12	0.0599820	0.0299910	+	0.999550i	$0.490452\pi$
$282$	−8.30385e12	−0.277274
$283$	4.50842e13	1.47638	0.738192	−	0.674591i	$-0.235680\pi$
$283$	4.50842e13	1.47638	0.738192	+	0.674591i	$0.235680\pi$
$284$	1.70545e13	0.547758
$285$	3.70971e12	0.116867
$286$	1.77630e12	0.0548912
$287$	−2.70545e11	−0.00820143
$288$	−4.85836e12	−0.144488
$289$	−8.23310e12	−0.240229
$290$	−6.02080e13	−1.72371
$291$	−1.94273e13	−0.545758
$292$	−8.89800e13	−2.45294
$293$	−2.38021e12	−0.0643938	−0.0321969	−	0.999482i	$-0.510250\pi$
$293$	−2.38021e12	−0.0643938	−0.0321969	+	0.999482i	$0.510250\pi$
$294$	−2.82931e13	−0.751225
$295$	−3.84429e12	−0.100183
$296$	−2.75973e13	−0.705932
$297$	−1.80982e12	−0.0454438
$298$	−2.19455e13	−0.540948
$299$	−3.98906e12	−0.0965336
$300$	−2.09708e13	−0.498251
$301$	6.97371e13	1.62685
$302$	−4.00545e13	−0.917516
$303$	−6.47000e12	−0.145536
$304$	−1.62139e13	−0.358164
$305$	1.26781e12	0.0275045
$306$	−2.40708e13	−0.512887
$307$	7.90940e13	1.65532	0.827661	−	0.561228i	$-0.189671\pi$
$307$	7.90940e13	1.65532	0.827661	+	0.561228i	$0.189671\pi$
$308$	3.20349e13	0.658559
$309$	−9.32514e12	−0.188314
$310$	−2.55368e13	−0.506613
$311$	1.06285e12	0.0207152	0.0103576	−	0.999946i	$-0.496703\pi$
$311$	1.06285e12	0.0207152	0.0103576	+	0.999946i	$0.496703\pi$
$312$	−7.82199e12	−0.149785
$313$	3.83621e12	0.0721786	0.0360893	−	0.999349i	$-0.488510\pi$
$313$	3.83621e12	0.0721786	0.0360893	+	0.999349i	$0.488510\pi$
$314$	1.24930e14	2.30968
$315$	1.86089e13	0.338075
$316$	−1.74613e14	−3.11743
$317$	8.24316e13	1.44633	0.723166	−	0.690674i	$-0.242686\pi$
$317$	8.24316e13	1.44633	0.723166	+	0.690674i	$0.242686\pi$
$318$	1.81694e12	0.0313322
$319$	1.76786e13	0.299639
$320$	2.75494e13	0.458973
$321$	−6.00349e11	−0.00983164
$322$	−1.05939e14	−1.70549
$323$	−1.44873e13	−0.229284
$324$	1.51105e13	0.235116
$325$	−3.51065e12	−0.0537067
$326$	4.44523e13	0.668649
$327$	3.75288e13	0.555076
$328$	−8.42880e11	−0.0122591
$329$	−2.50702e13	−0.358576
$330$	−1.31658e13	−0.185191
$331$	−2.46273e13	−0.340693	−0.170346	−	0.985384i	$-0.554489\pi$
$331$	−2.46273e13	−0.340693	−0.170346	+	0.985384i	$0.554489\pi$
$332$	−5.06168e13	−0.688709
$333$	8.92486e12	0.119442
$334$	−1.16642e13	−0.153549
$335$	5.01711e13	0.649691
$336$	−8.13332e13	−1.03610
$337$	1.35539e14	1.69863	0.849315	−	0.527887i	$-0.177016\pi$
$337$	1.35539e14	1.69863	0.849315	+	0.527887i	$0.177016\pi$
$338$	1.40685e14	1.73462
$339$	1.50774e13	0.182906
$340$	−1.18911e14	−1.41934
$341$	7.49824e12	0.0880664
$342$	1.33923e13	0.154779
$343$	3.04659e13	0.346494
$344$	2.17265e14	2.43175
$345$	2.95665e13	0.325683
$346$	5.62922e13	0.610281
$347$	1.50378e13	0.160462	0.0802312	−	0.996776i	$-0.474434\pi$
$347$	1.50378e13	0.160462	0.0802312	+	0.996776i	$0.474434\pi$
$348$	−1.47602e14	−1.55026
$349$	−1.11845e14	−1.15631	−0.578156	−	0.815926i	$-0.696228\pi$
$349$	−1.11845e14	−1.15631	−0.578156	+	0.815926i	$0.696228\pi$
$350$	−9.32337e13	−0.948853
$351$	2.52960e12	0.0253433
$352$	1.03775e13	0.102355
$353$	9.34930e13	0.907858	0.453929	−	0.891038i	$-0.350022\pi$
$353$	9.34930e13	0.907858	0.453929	+	0.891038i	$0.350022\pi$
$354$	−1.38782e13	−0.132683
$355$	−2.11613e13	−0.199198
$356$	−1.51153e13	−0.140101
$357$	−7.26723e13	−0.663275
$358$	2.19133e13	0.196948
$359$	2.13254e14	1.88746	0.943731	−	0.330715i	$-0.107290\pi$
$359$	2.13254e14	1.88746	0.943731	+	0.330715i	$0.107290\pi$
$360$	5.79759e13	0.505340
$361$	−1.08430e14	−0.930807
$362$	4.00073e14	3.38253
$363$	−6.54649e13	−0.545158
$364$	−4.47754e13	−0.367267
$365$	1.10406e14	0.892039
$366$	4.57689e12	0.0364271
$367$	1.48764e14	1.16636	0.583181	−	0.812343i	$-0.301808\pi$
$367$	1.48764e14	1.16636	0.583181	+	0.812343i	$0.301808\pi$
$368$	−1.29225e14	−0.998123
$369$	2.72584e11	0.00207422
$370$	6.49250e13	0.486746
$371$	5.48554e12	0.0405194
$372$	−6.26042e13	−0.455635
$373$	2.19989e14	1.57762	0.788808	−	0.614639i	$-0.210698\pi$
$373$	2.19989e14	1.57762	0.788808	+	0.614639i	$0.210698\pi$
$374$	5.14155e13	0.363329
$375$	8.98224e13	0.625479
$376$	−7.81060e13	−0.535983
$377$	−2.47095e13	−0.167104
$378$	6.71797e13	0.447747
$379$	−2.90112e13	−0.190568	−0.0952840	−	0.995450i	$-0.530376\pi$
$379$	−2.90112e13	−0.190568	−0.0952840	+	0.995450i	$0.530376\pi$
$380$	6.61589e13	0.428330
$381$	4.08177e12	0.0260472
$382$	−1.39973e14	−0.880432
$383$	2.44855e14	1.51815	0.759076	−	0.651002i	$-0.225651\pi$
$383$	2.44855e14	1.51815	0.759076	+	0.651002i	$0.225651\pi$
$384$	1.40401e14	0.858124
$385$	−3.97489e13	−0.239492
$386$	1.46094e14	0.867768
$387$	−7.02626e13	−0.411447
$388$	−3.46466e14	−2.00026
$389$	−2.12542e14	−1.20982	−0.604911	−	0.796293i	$-0.706791\pi$
$389$	−2.12542e14	−1.20982	−0.604911	+	0.796293i	$0.706791\pi$
$390$	1.84019e13	0.103278
$391$	−1.15464e14	−0.638963
$392$	−2.66125e14	−1.45215
$393$	6.26008e13	0.336838
$394$	−5.05891e14	−2.68428
$395$	2.16659e14	1.13369
$396$	−3.22763e13	−0.166556
$397$	1.74540e14	0.888277	0.444138	−	0.895958i	$-0.353510\pi$
$397$	1.74540e14	0.888277	0.444138	+	0.895958i	$0.353510\pi$
$398$	−4.21401e14	−2.11514
$399$	4.04330e13	0.200163
$400$	−1.13727e14	−0.555308
$401$	6.36342e13	0.306476	0.153238	−	0.988189i	$-0.451030\pi$
$401$	6.36342e13	0.306476	0.153238	+	0.988189i	$0.451030\pi$
$402$	1.81121e14	0.860452
$403$	−1.04803e13	−0.0491131
$404$	−1.15386e14	−0.533403
$405$	−1.87492e13	−0.0855025
$406$	−6.56220e14	−2.95227
$407$	−1.90636e13	−0.0846128
$408$	−2.26410e14	−0.991435
$409$	−3.40083e14	−1.46929	−0.734643	−	0.678453i	$-0.762650\pi$
$409$	−3.40083e14	−1.46929	−0.734643	+	0.678453i	$0.762650\pi$
$410$	1.98295e12	0.00845278
$411$	−8.86238e13	−0.372752
$412$	−1.66304e14	−0.690191
$413$	−4.18998e13	−0.171588
$414$	1.06737e14	0.431335
$415$	6.28054e13	0.250456
$416$	−1.45047e13	−0.0570816
$417$	−2.18439e13	−0.0848364
$418$	−2.86062e13	−0.109646
$419$	−4.07914e13	−0.154309	−0.0771545	−	0.997019i	$-0.524583\pi$
$419$	−4.07914e13	−0.154309	−0.0771545	+	0.997019i	$0.524583\pi$
$420$	3.31871e14	1.23908
$421$	3.69687e14	1.36233	0.681165	−	0.732130i	$-0.261474\pi$
$421$	3.69687e14	1.36233	0.681165	+	0.732130i	$0.261474\pi$
$422$	−5.51390e14	−2.00558
$423$	2.52591e13	0.0906873
$424$	1.70901e13	0.0605666
$425$	−1.01617e14	−0.355488
$426$	−7.63938e13	−0.263818
$427$	1.38181e13	0.0471081
$428$	−1.07066e13	−0.0360339
$429$	−5.40326e12	−0.0179531
$430$	−5.11134e14	−1.67671
$431$	−3.53871e14	−1.14609	−0.573047	−	0.819523i	$-0.694239\pi$
$431$	−3.53871e14	−1.14609	−0.573047	+	0.819523i	$0.694239\pi$
$432$	8.19461e13	0.262040
$433$	4.32180e13	0.136452	0.0682261	−	0.997670i	$-0.478266\pi$
$433$	4.32180e13	0.136452	0.0682261	+	0.997670i	$0.478266\pi$
$434$	−2.78331e14	−0.867697
$435$	1.83144e14	0.563771
$436$	6.69289e14	2.03441
$437$	6.42413e13	0.192826
$438$	3.98576e14	1.18142
$439$	−1.72499e14	−0.504930	−0.252465	−	0.967606i	$-0.581241\pi$
$439$	−1.72499e14	−0.504930	−0.252465	+	0.967606i	$0.581241\pi$
$440$	−1.23837e14	−0.357982
$441$	8.60637e13	0.245701
$442$	−7.18638e13	−0.202622
$443$	1.12197e14	0.312435	0.156218	−	0.987723i	$-0.450070\pi$
$443$	1.12197e14	0.312435	0.156218	+	0.987723i	$0.450070\pi$
$444$	1.59166e14	0.437767
$445$	1.87551e13	0.0509494
$446$	−1.07351e15	−2.88048
$447$	6.67552e13	0.176927
$448$	3.00267e14	0.786101
$449$	1.93532e14	0.500492	0.250246	−	0.968182i	$-0.419488\pi$
$449$	1.93532e14	0.500492	0.250246	+	0.968182i	$0.419488\pi$
$450$	9.39363e13	0.239974
$451$	−5.82243e11	−0.00146938
$452$	2.68890e14	0.670369
$453$	1.21840e14	0.300090
$454$	5.24941e13	0.127733
$455$	5.55574e13	0.133561
$456$	1.25968e14	0.299196
$457$	−4.90137e14	−1.15021	−0.575107	−	0.818078i	$-0.695040\pi$
$457$	−4.90137e14	−1.15021	−0.575107	+	0.818078i	$0.695040\pi$
$458$	−2.39526e14	−0.555383
$459$	7.32199e13	0.167749
$460$	5.27289e14	1.19366
$461$	−1.03639e14	−0.231829	−0.115915	−	0.993259i	$-0.536980\pi$
$461$	−1.03639e14	−0.231829	−0.115915	+	0.993259i	$0.536980\pi$
$462$	−1.43497e14	−0.317184
$463$	−3.02702e14	−0.661180	−0.330590	−	0.943775i	$-0.607248\pi$
$463$	−3.02702e14	−0.661180	−0.330590	+	0.943775i	$0.607248\pi$
$464$	−8.00461e14	−1.72779
$465$	7.76793e13	0.165697
$466$	−9.56667e14	−2.01668
$467$	4.70737e14	0.980698	0.490349	−	0.871526i	$-0.336869\pi$
$467$	4.70737e14	0.980698	0.490349	+	0.871526i	$0.336869\pi$
$468$	4.51128e13	0.0928855
$469$	5.46826e14	1.11275
$470$	1.83751e14	0.369565
$471$	−3.80018e14	−0.755422
$472$	−1.30538e14	−0.256482
$473$	1.50082e14	0.291469
$474$	7.82157e14	1.50146
$475$	5.65368e13	0.107279
$476$	−1.29604e15	−2.43097
$477$	−5.52688e12	−0.0102478
$478$	5.46706e14	1.00207
$479$	9.34660e14	1.69359	0.846795	−	0.531919i	$-0.178529\pi$
$479$	9.34660e14	1.69359	0.846795	+	0.531919i	$0.178529\pi$
$480$	1.07508e14	0.192581
$481$	2.66454e13	0.0471871
$482$	1.01793e14	0.178220
$483$	3.22252e14	0.557810
$484$	−1.16750e15	−1.99806
$485$	4.29894e14	0.727415
$486$	−6.76859e13	−0.113240
$487$	−5.95529e13	−0.0985130	−0.0492565	−	0.998786i	$-0.515685\pi$
$487$	−5.95529e13	−0.0985130	−0.0492565	+	0.998786i	$0.515685\pi$
$488$	4.30502e13	0.0704152
$489$	−1.35218e14	−0.218693
$490$	6.26081e14	1.00127
$491$	−1.56801e14	−0.247971	−0.123985	−	0.992284i	$-0.539568\pi$
$491$	−1.56801e14	−0.247971	−0.123985	+	0.992284i	$0.539568\pi$
$492$	4.86126e12	0.00760222
$493$	−7.15222e14	−1.10607
$494$	3.99831e13	0.0611475
$495$	4.00484e13	0.0605699
$496$	−3.39510e14	−0.507812
$497$	−2.30641e14	−0.341175
$498$	2.26732e14	0.331705
$499$	−3.26747e14	−0.472779	−0.236389	−	0.971658i	$-0.575964\pi$
$499$	−3.26747e14	−0.472779	−0.236389	+	0.971658i	$0.575964\pi$
$500$	1.60189e15	2.29244
$501$	3.54808e13	0.0502210
$502$	4.29709e14	0.601595
$503$	8.02323e14	1.11103	0.555514	−	0.831507i	$-0.312521\pi$
$503$	8.02323e14	1.11103	0.555514	+	0.831507i	$0.312521\pi$
$504$	6.31892e14	0.865516
$505$	1.43171e14	0.193978
$506$	−2.27993e14	−0.305557
$507$	−4.27943e14	−0.567338
$508$	7.27943e13	0.0954656
$509$	5.48322e14	0.711358	0.355679	−	0.934608i	$-0.384250\pi$
$509$	5.48322e14	0.711358	0.355679	+	0.934608i	$0.384250\pi$
$510$	5.32648e14	0.683603
$511$	1.20334e15	1.52783
$512$	1.66571e15	2.09226
$513$	−4.07376e13	−0.0506233
$514$	7.60128e14	0.934522
$515$	2.06351e14	0.250995
$516$	−1.25306e15	−1.50799
$517$	−5.39539e13	−0.0642428
$518$	7.07632e14	0.833670
$519$	−1.71233e14	−0.199603
$520$	1.73088e14	0.199641
$521$	−1.28307e15	−1.46434	−0.732171	−	0.681121i	$-0.761493\pi$
$521$	−1.28307e15	−1.46434	−0.732171	+	0.681121i	$0.761493\pi$
$522$	6.61165e14	0.746659
$523$	1.03990e15	1.16207	0.581033	−	0.813880i	$-0.302649\pi$
$523$	1.03990e15	1.16207	0.581033	+	0.813880i	$0.302649\pi$
$524$	1.11642e15	1.23454
$525$	2.83604e14	0.310339
$526$	1.05373e15	1.14106
$527$	−3.03356e14	−0.325083
$528$	−1.75038e14	−0.185629
$529$	−4.40804e14	−0.462636
$530$	−4.02060e13	−0.0417612
$531$	4.22156e13	0.0433963
$532$	7.21081e14	0.733618
$533$	8.13805e11	0.000819447 0
$534$	6.77074e13	0.0674775
$535$	1.32848e13	0.0131041
$536$	1.70363e15	1.66329
$537$	−6.66573e13	−0.0644153
$538$	−2.13930e14	−0.204630
$539$	−1.83833e14	−0.174055
$540$	−3.34372e14	−0.313375
$541$	1.19638e14	0.110990	0.0554952	−	0.998459i	$-0.482326\pi$
$541$	1.19638e14	0.110990	0.0554952	+	0.998459i	$0.482326\pi$
$542$	−2.10360e15	−1.93182
$543$	−1.21697e15	−1.10632
$544$	−4.19843e14	−0.377827
$545$	−8.30453e14	−0.739834
$546$	2.00566e14	0.176888
$547$	−8.13071e14	−0.709901	−0.354951	−	0.934885i	$-0.615502\pi$
$547$	−8.13071e14	−0.709901	−0.354951	+	0.934885i	$0.615502\pi$
$548$	−1.58052e15	−1.36617
$549$	−1.39223e13	−0.0119141
$550$	−2.00649e14	−0.169998
$551$	3.97931e14	0.333790
$552$	1.00397e15	0.833791
$553$	2.36142e15	1.94171
$554$	2.85375e14	0.232334
$555$	−1.97493e14	−0.159199
$556$	−3.89564e14	−0.310934
$557$	−2.24978e15	−1.77802	−0.889011	−	0.457887i	$-0.848607\pi$
$557$	−2.24978e15	−1.77802	−0.889011	+	0.457887i	$0.848607\pi$
$558$	2.80428e14	0.219449
$559$	−2.09771e14	−0.162547
$560$	1.79978e15	1.38097
$561$	−1.56399e14	−0.118833
$562$	−1.40725e14	−0.105882
$563$	−1.70588e15	−1.27102	−0.635508	−	0.772094i	$-0.719209\pi$
$563$	−1.70588e15	−1.27102	−0.635508	+	0.772094i	$0.719209\pi$
$564$	4.50471e14	0.332378
$565$	−3.33639e14	−0.243787
$566$	−3.60157e15	−2.60616
$567$	−2.04351e14	−0.146444
$568$	−7.18560e14	−0.509973
$569$	−8.49138e14	−0.596844	−0.298422	−	0.954434i	$-0.596460\pi$
$569$	−8.49138e14	−0.596844	−0.298422	+	0.954434i	$0.596460\pi$
$570$	−2.96351e14	−0.206298
$571$	−2.05353e15	−1.41580	−0.707901	−	0.706312i	$-0.750358\pi$
$571$	−2.05353e15	−1.41580	−0.707901	+	0.706312i	$0.750358\pi$
$572$	−9.63616e13	−0.0658000
$573$	4.25779e14	0.287961
$574$	2.16126e13	0.0144774
$575$	4.50600e14	0.298964
$576$	−3.02529e14	−0.198813
$577$	1.13324e15	0.737659	0.368830	−	0.929497i	$-0.379759\pi$
$577$	1.13324e15	0.737659	0.368830	+	0.929497i	$0.379759\pi$
$578$	6.57704e14	0.424060
$579$	−4.44399e14	−0.283819
$580$	3.26619e15	2.06627
$581$	6.84530e14	0.428967
$582$	1.55195e15	0.963390
$583$	1.18055e13	0.00725950
$584$	3.74901e15	2.28373
$585$	−5.59760e13	−0.0337788
$586$	1.90144e14	0.113670
$587$	5.14998e13	0.0304998	0.0152499	−	0.999884i	$-0.495146\pi$
$587$	5.14998e13	0.0304998	0.0152499	+	0.999884i	$0.495146\pi$
$588$	1.53486e15	0.900520
$589$	1.68780e14	0.0981038
$590$	3.07103e14	0.176847
$591$	1.53885e15	0.877941
$592$	8.63174e14	0.487898
$593$	−5.81234e14	−0.325500	−0.162750	−	0.986667i	$-0.552036\pi$
$593$	−5.81234e14	−0.325500	−0.162750	+	0.986667i	$0.552036\pi$
$594$	1.44578e14	0.0802189
$595$	1.60812e15	0.884048
$596$	1.19051e15	0.648454
$597$	1.28184e15	0.691793
$598$	3.18667e14	0.170404
$599$	1.73245e15	0.917935	0.458968	−	0.888453i	$-0.348219\pi$
$599$	1.73245e15	0.917935	0.458968	+	0.888453i	$0.348219\pi$
$600$	8.83565e14	0.463881
$601$	−6.41826e14	−0.333893	−0.166947	−	0.985966i	$-0.553391\pi$
$601$	−6.41826e14	−0.333893	−0.166947	+	0.985966i	$0.553391\pi$
$602$	−5.57097e15	−2.87177
$603$	−5.50947e14	−0.281426
$604$	2.17290e15	1.09986
$605$	1.44864e15	0.726615
$606$	5.16858e14	0.256905
$607$	1.01087e15	0.497916	0.248958	−	0.968514i	$-0.419912\pi$
$607$	1.01087e15	0.497916	0.248958	+	0.968514i	$0.419912\pi$
$608$	2.33590e14	0.114021
$609$	1.99613e15	0.965592
$610$	−1.01279e14	−0.0485519
$611$	7.54118e13	0.0358272
$612$	1.30580e15	0.614816
$613$	2.84554e15	1.32780	0.663899	−	0.747823i	$-0.268901\pi$
$613$	2.84554e15	1.32780	0.663899	+	0.747823i	$0.268901\pi$
$614$	−6.31845e15	−2.92203
$615$	−6.03185e12	−0.00276463
$616$	−1.34973e15	−0.613131
$617$	2.05036e15	0.923128	0.461564	−	0.887107i	$-0.347288\pi$
$617$	2.05036e15	0.923128	0.461564	+	0.887107i	$0.347288\pi$
$618$	7.44942e14	0.332419
$619$	−1.26840e14	−0.0560991	−0.0280496	−	0.999607i	$-0.508930\pi$
$619$	−1.26840e14	−0.0560991	−0.0280496	+	0.999607i	$0.508930\pi$
$620$	1.38533e15	0.607295
$621$	−3.24680e14	−0.141076
$622$	−8.49060e13	−0.0365671
$623$	2.04416e14	0.0872631
$624$	2.44652e14	0.103522
$625$	−1.01527e15	−0.425836
$626$	−3.06457e14	−0.127412
$627$	8.70162e13	0.0358615
$628$	−6.77724e15	−2.76870
$629$	7.71257e14	0.312335
$630$	−1.48658e15	−0.596781
$631$	3.72069e15	1.48068	0.740342	−	0.672230i	$-0.234663\pi$
$631$	3.72069e15	1.48068	0.740342	+	0.672230i	$0.234663\pi$
$632$	7.35697e15	2.90239
$633$	1.67725e15	0.655961
$634$	−6.58508e15	−2.55311
$635$	−9.03232e13	−0.0347171
$636$	−9.85663e13	−0.0375590
$637$	2.56945e14	0.0970674
$638$	−1.41226e15	−0.528932
$639$	2.32379e14	0.0862865
$640$	−3.10686e15	−1.14375
$641$	2.79910e15	1.02164	0.510821	−	0.859687i	$-0.329341\pi$
$641$	2.79910e15	1.02164	0.510821	+	0.859687i	$0.329341\pi$
$642$	4.79591e13	0.0173551
$643$	−1.50932e15	−0.541527	−0.270763	−	0.962646i	$-0.587276\pi$
$643$	−1.50932e15	−0.541527	−0.270763	+	0.962646i	$0.587276\pi$
$644$	5.74704e15	2.04443
$645$	1.55480e15	0.548398
$646$	1.15732e15	0.404739
$647$	−3.98677e15	−1.38244	−0.691222	−	0.722643i	$-0.742927\pi$
$647$	−3.98677e15	−1.38244	−0.691222	+	0.722643i	$0.742927\pi$
$648$	−6.36654e14	−0.218898
$649$	−9.01730e13	−0.0307419
$650$	2.80449e14	0.0948048
$651$	8.46645e14	0.283796
$652$	−2.41147e15	−0.801532
$653$	2.85864e13	0.00942186	0.00471093	−	0.999989i	$-0.498500\pi$
$653$	2.85864e13	0.00942186	0.00471093	+	0.999989i	$0.498500\pi$
$654$	−2.99800e15	−0.979838
$655$	−1.38526e15	−0.448955
$656$	2.63631e13	0.00847278
$657$	−1.21241e15	−0.386403
$658$	2.00274e15	0.632969
$659$	−6.88757e14	−0.215872	−0.107936	−	0.994158i	$-0.534424\pi$
$659$	−6.88757e14	−0.215872	−0.107936	+	0.994158i	$0.534424\pi$
$660$	7.14224e14	0.221995
$661$	−2.13260e15	−0.657357	−0.328679	−	0.944442i	$-0.606603\pi$
$661$	−2.13260e15	−0.657357	−0.328679	+	0.944442i	$0.606603\pi$
$662$	1.96736e15	0.601402
$663$	2.18600e14	0.0662713
$664$	2.13264e15	0.641201
$665$	−8.94717e14	−0.266788
$666$	−7.12965e14	−0.210843
$667$	3.17152e15	0.930199
$668$	6.32763e14	0.184065
$669$	3.26548e15	0.942112
$670$	−4.00793e15	−1.14686
$671$	2.97381e13	0.00843995
$672$	1.17175e15	0.329841
$673$	2.04667e15	0.571432	0.285716	−	0.958314i	$-0.407769\pi$
$673$	2.04667e15	0.571432	0.285716	+	0.958314i	$0.407769\pi$
$674$	−1.08275e16	−2.99847
$675$	−2.85741e14	−0.0784878
$676$	−7.63193e15	−2.07935
$677$	−4.20708e15	−1.13695	−0.568477	−	0.822699i	$-0.692467\pi$
$677$	−4.20708e15	−1.13695	−0.568477	+	0.822699i	$0.692467\pi$
$678$	−1.20446e15	−0.322872
$679$	4.68552e15	1.24587
$680$	5.01009e15	1.32144
$681$	−1.59680e14	−0.0417774
$682$	−5.98999e14	−0.155458
$683$	−1.59000e15	−0.409340	−0.204670	−	0.978831i	$-0.565612\pi$
$683$	−1.59000e15	−0.409340	−0.204670	+	0.978831i	$0.565612\pi$
$684$	−7.26515e14	−0.185539
$685$	1.96110e15	0.496824
$686$	−2.43378e15	−0.611643
$687$	7.28605e14	0.181648
$688$	−6.79550e15	−1.68068
$689$	−1.65006e13	−0.00404850
$690$	−2.36193e15	−0.574906
$691$	−6.78840e15	−1.63922	−0.819612	−	0.572920i	$-0.805811\pi$
$691$	−6.78840e15	−1.63922	−0.819612	+	0.572920i	$0.805811\pi$
$692$	−3.05377e15	−0.731565
$693$	4.36497e14	0.103741
$694$	−1.20130e15	−0.283254
$695$	4.83371e14	0.113074
$696$	6.21892e15	1.44333
$697$	2.35558e13	0.00542398
$698$	8.93474e15	2.04116
$699$	2.91005e15	0.659592
$700$	5.05779e15	1.13742
$701$	5.58259e15	1.24562	0.622812	−	0.782372i	$-0.285990\pi$
$701$	5.58259e15	1.24562	0.622812	+	0.782372i	$0.285990\pi$
$702$	−2.02078e14	−0.0447367
$703$	−4.29107e14	−0.0942565
$704$	6.46207e14	0.140839
$705$	−5.58945e14	−0.120873
$706$	−7.46871e15	−1.60258
$707$	1.56045e15	0.332234
$708$	7.52872e14	0.159052
$709$	1.57903e15	0.331007	0.165504	−	0.986209i	$-0.447075\pi$
$709$	1.57903e15	0.331007	0.165504	+	0.986209i	$0.447075\pi$
$710$	1.69047e15	0.351631
$711$	−2.37921e15	−0.491078
$712$	6.36856e14	0.130437
$713$	1.34518e15	0.273393
$714$	5.80545e15	1.17083
$715$	1.19566e14	0.0239289
$716$	−1.18877e15	−0.236088
$717$	−1.66300e15	−0.327746
$718$	−1.70359e16	−3.33181
$719$	−6.92912e15	−1.34484	−0.672418	−	0.740172i	$-0.734744\pi$
$719$	−6.92912e15	−1.34484	−0.672418	+	0.740172i	$0.734744\pi$
$720$	−1.81334e15	−0.349261
$721$	2.24906e15	0.429890
$722$	8.66195e15	1.64309
$723$	−3.09639e14	−0.0582901
$724$	−2.17033e16	−4.05475
$725$	2.79116e15	0.517518
$726$	5.22969e15	0.962330
$727$	2.98687e15	0.545478	0.272739	−	0.962088i	$-0.412071\pi$
$727$	2.98687e15	0.545478	0.272739	+	0.962088i	$0.412071\pi$
$728$	1.88653e15	0.341933
$729$	2.05891e14	0.0370370
$730$	−8.81985e15	−1.57466
$731$	−6.07186e15	−1.07591
$732$	−2.48289e14	−0.0436664
$733$	−5.90090e15	−1.03002	−0.515011	−	0.857184i	$-0.672212\pi$
$733$	−5.90090e15	−1.03002	−0.515011	+	0.857184i	$0.672212\pi$
$734$	−1.18840e16	−2.05890
$735$	−1.90445e15	−0.327484
$736$	1.86172e15	0.317750
$737$	1.17683e15	0.199362
$738$	−2.17754e13	−0.00366148
$739$	−7.63713e15	−1.27464	−0.637318	−	0.770601i	$-0.719956\pi$
$739$	−7.63713e15	−1.27464	−0.637318	+	0.770601i	$0.719956\pi$
$740$	−3.52209e15	−0.583479
$741$	−1.21623e14	−0.0199994
$742$	−4.38214e14	−0.0715261
$743$	−3.21264e15	−0.520504	−0.260252	−	0.965541i	$-0.583806\pi$
$743$	−3.21264e15	−0.520504	−0.260252	+	0.965541i	$0.583806\pi$
$744$	2.63771e15	0.424205
$745$	−1.47719e15	−0.235817
$746$	−1.75739e16	−2.78486
$747$	−6.89688e14	−0.108490
$748$	−2.78921e15	−0.435535
$749$	1.44794e14	0.0224440
$750$	−7.17549e15	−1.10412
$751$	−1.15415e16	−1.76296	−0.881480	−	0.472221i	$-0.843452\pi$
$751$	−1.15415e16	−1.76296	−0.881480	+	0.472221i	$0.843452\pi$
$752$	2.44296e15	0.370440
$753$	−1.30712e15	−0.196762
$754$	1.97392e15	0.294977
$755$	−2.69613e15	−0.399975
$756$	−3.64440e15	−0.536730
$757$	2.06420e14	0.0301804	0.0150902	−	0.999886i	$-0.495196\pi$
$757$	2.06420e14	0.0301804	0.0150902	+	0.999886i	$0.495196\pi$
$758$	2.31757e15	0.336397
$759$	6.93522e14	0.0999379
$760$	−2.78748e15	−0.398784
$761$	−1.46112e15	−0.207525	−0.103763	−	0.994602i	$-0.533088\pi$
$761$	−1.46112e15	−0.207525	−0.103763	+	0.994602i	$0.533088\pi$
$762$	−3.26074e14	−0.0459794
$763$	−9.05130e15	−1.26714
$764$	7.59333e15	1.05540
$765$	−1.62024e15	−0.223584
$766$	−1.95603e16	−2.67989
$767$	1.26036e14	0.0171442
$768$	−8.66630e15	−1.17043
$769$	6.54282e14	0.0877345	0.0438672	−	0.999037i	$-0.486032\pi$
$769$	6.54282e14	0.0877345	0.0438672	+	0.999037i	$0.486032\pi$
$770$	3.17535e15	0.422759
$771$	−2.31220e15	−0.305652
$772$	−7.92541e15	−1.04022
$773$	−2.28734e15	−0.298087	−0.149044	−	0.988831i	$-0.547619\pi$
$773$	−2.28734e15	−0.298087	−0.149044	+	0.988831i	$0.547619\pi$
$774$	5.61295e15	0.726299
$775$	1.18385e15	0.152103
$776$	1.45977e16	1.86228
$777$	−2.15252e15	−0.272666
$778$	1.69790e16	2.13562
$779$	−1.31058e13	−0.00163685
$780$	−9.98276e14	−0.123803
$781$	−4.96365e14	−0.0611253
$782$	9.22390e15	1.12792
$783$	−2.01117e15	−0.244208
$784$	8.32371e15	1.00364
$785$	8.40920e15	1.00687
$786$	−5.00088e15	−0.594597
$787$	−4.31298e15	−0.509233	−0.254617	−	0.967042i	$-0.581949\pi$
$787$	−4.31298e15	−0.509233	−0.254617	+	0.967042i	$0.581949\pi$
$788$	2.74439e16	3.21774
$789$	−3.20531e15	−0.373205
$790$	−1.73079e16	−2.00122
$791$	−3.63641e15	−0.417544
$792$	1.35990e15	0.155067
$793$	−4.15652e13	−0.00470682
$794$	−1.39432e16	−1.56801
$795$	1.22301e14	0.0136587
$796$	2.28604e16	2.53549
$797$	5.27892e15	0.581466	0.290733	−	0.956804i	$-0.406101\pi$
$797$	5.27892e15	0.581466	0.290733	+	0.956804i	$0.406101\pi$
$798$	−3.23000e15	−0.353335
$799$	2.18281e15	0.237142
$800$	1.63844e15	0.176781
$801$	−2.05956e14	−0.0220697
$802$	−5.08344e15	−0.541002
$803$	2.58973e15	0.273728
$804$	−9.82557e15	−1.03145
$805$	−7.13093e15	−0.743479
$806$	8.37225e14	0.0866961
$807$	6.50745e14	0.0669278
$808$	4.86157e15	0.496608
$809$	3.78268e15	0.383781	0.191890	−	0.981416i	$-0.438538\pi$
$809$	3.78268e15	0.383781	0.191890	+	0.981416i	$0.438538\pi$
$810$	1.49778e15	0.150932
$811$	−7.41965e15	−0.742624	−0.371312	−	0.928508i	$-0.621092\pi$
$811$	−7.41965e15	−0.742624	−0.371312	+	0.928508i	$0.621092\pi$
$812$	3.55990e16	3.53899
$813$	6.39886e15	0.631837
$814$	1.52290e15	0.149361
$815$	2.99216e15	0.291486
$816$	7.08152e15	0.685221
$817$	3.37823e15	0.324689
$818$	2.71676e16	2.59363
$819$	−6.10095e14	−0.0578544
$820$	−1.07572e14	−0.0101326
$821$	−4.41256e15	−0.412861	−0.206430	−	0.978461i	$-0.566185\pi$
$821$	−4.41256e15	−0.412861	−0.206430	+	0.978461i	$0.566185\pi$
$822$	7.07974e15	0.657994
$823$	4.36342e15	0.402836	0.201418	−	0.979505i	$-0.435445\pi$
$823$	4.36342e15	0.402836	0.201418	+	0.979505i	$0.435445\pi$
$824$	7.00692e15	0.642581
$825$	6.10347e14	0.0556007
$826$	3.34718e15	0.302893
$827$	1.61404e16	1.45089	0.725445	−	0.688280i	$-0.241634\pi$
$827$	1.61404e16	1.45089	0.725445	+	0.688280i	$0.241634\pi$
$828$	−5.79035e15	−0.517056
$829$	7.10217e15	0.630001	0.315000	−	0.949092i	$-0.397995\pi$
$829$	7.10217e15	0.630001	0.315000	+	0.949092i	$0.397995\pi$
$830$	−5.01722e15	−0.442114
$831$	−8.68071e14	−0.0759888
$832$	−9.03208e14	−0.0785434
$833$	7.43734e15	0.642496
$834$	1.74501e15	0.149756
$835$	−7.85133e14	−0.0669372
$836$	1.55185e15	0.131436
$837$	−8.53024e14	−0.0717747
$838$	3.25863e15	0.272391
$839$	−5.77411e15	−0.479506	−0.239753	−	0.970834i	$-0.577067\pi$
$839$	−5.77411e15	−0.479506	−0.239753	+	0.970834i	$0.577067\pi$
$840$	−1.39828e16	−1.15361
$841$	7.44490e15	0.610212
$842$	−2.95325e16	−2.40483
$843$	4.28067e14	0.0346306
$844$	2.99121e16	2.40416
$845$	9.46969e15	0.756178
$846$	−2.01783e15	−0.160084
$847$	1.57890e16	1.24450
$848$	−5.34536e14	−0.0418600
$849$	1.09555e16	0.852391
$850$	8.11767e15	0.627520
$851$	−3.42000e15	−0.262672
$852$	4.14425e15	0.316248
$853$	3.94735e15	0.299286	0.149643	−	0.988740i	$-0.452188\pi$
$853$	3.94735e15	0.299286	0.149643	+	0.988740i	$0.452188\pi$
$854$	−1.10387e15	−0.0831568
$855$	9.01459e14	0.0674734
$856$	4.51103e14	0.0335483
$857$	−1.61729e16	−1.19507	−0.597536	−	0.801842i	$-0.703854\pi$
$857$	−1.61729e16	−1.19507	−0.597536	+	0.801842i	$0.703854\pi$
$858$	4.31641e14	0.0316915
$859$	1.41118e16	1.02949	0.514743	−	0.857345i	$-0.327888\pi$
$859$	1.41118e16	1.02949	0.514743	+	0.857345i	$0.327888\pi$
$860$	2.77283e16	2.00993
$861$	−6.57425e13	−0.00473510
$862$	2.82691e16	2.02312
$863$	9.26132e14	0.0658587	0.0329294	−	0.999458i	$-0.489516\pi$
$863$	9.26132e14	0.0658587	0.0329294	+	0.999458i	$0.489516\pi$
$864$	−1.18058e15	−0.0834200
$865$	3.78912e15	0.266041
$866$	−3.45248e15	−0.240870
$867$	−2.00064e15	−0.138696
$868$	1.50991e16	1.04014
$869$	5.08203e15	0.347879
$870$	−1.46305e16	−0.995186
$871$	−1.64486e15	−0.111181
$872$	−2.81992e16	−1.89407
$873$	−4.72082e15	−0.315094
$874$	−5.13194e15	−0.340383
$875$	−2.16636e16	−1.42786
$876$	−2.16222e16	−1.41621
$877$	2.38244e16	1.55069	0.775345	−	0.631538i	$-0.217576\pi$
$877$	2.38244e16	1.55069	0.775345	+	0.631538i	$0.217576\pi$
$878$	1.37801e16	0.891318
$879$	−5.78392e14	−0.0371778
$880$	3.87331e15	0.247416
$881$	1.15892e16	0.735676	0.367838	−	0.929890i	$-0.380098\pi$
$881$	1.15892e16	0.735676	0.367838	+	0.929890i	$0.380098\pi$
$882$	−6.87522e15	−0.433720
$883$	1.53134e16	0.960039	0.480019	−	0.877258i	$-0.340630\pi$
$883$	1.53134e16	0.960039	0.480019	+	0.877258i	$0.340630\pi$
$884$	3.89851e15	0.242891
$885$	−9.34163e14	−0.0578409
$886$	−8.96287e15	−0.551520
$887$	−2.03630e16	−1.24527	−0.622633	−	0.782514i	$-0.713937\pi$
$887$	−2.03630e16	−1.24527	−0.622633	+	0.782514i	$0.713937\pi$
$888$	−6.70615e15	−0.407570
$889$	−9.84453e14	−0.0594614
$890$	−1.49826e15	−0.0899376
$891$	−4.39786e14	−0.0262370
$892$	5.82365e16	3.45293
$893$	−1.21446e15	−0.0715649
$894$	−5.33275e15	−0.312317
$895$	1.47502e15	0.0858561
$896$	−3.38624e16	−1.95895
$897$	−9.69341e14	−0.0557337
$898$	−1.54603e16	−0.883485
$899$	8.33246e15	0.473255
$900$	−5.09591e15	−0.287665
$901$	−4.77615e14	−0.0267973
$902$	4.65126e13	0.00259379
$903$	1.69461e16	0.939264
$904$	−1.13292e16	−0.624126
$905$	2.69295e16	1.47456
$906$	−9.73325e15	−0.529728
$907$	2.90182e16	1.56975	0.784876	−	0.619653i	$-0.212727\pi$
$907$	2.90182e16	1.56975	0.784876	+	0.619653i	$0.212727\pi$
$908$	−2.84773e15	−0.153118
$909$	−1.57221e15	−0.0840252
$910$	−4.43822e15	−0.235766
$911$	−3.54949e16	−1.87420	−0.937098	−	0.349066i	$-0.886499\pi$
$911$	−3.54949e16	−1.87420	−0.937098	+	0.349066i	$0.886499\pi$
$912$	−3.93997e15	−0.206786
$913$	1.47318e15	0.0768542
$914$	3.91547e16	2.03039
$915$	3.08077e14	0.0158798
$916$	1.29939e16	0.665757
$917$	−1.50982e16	−0.768943
$918$	−5.84919e15	−0.296116
$919$	2.20469e16	1.10946	0.554730	−	0.832030i	$-0.312822\pi$
$919$	2.20469e16	1.10946	0.554730	+	0.832030i	$0.312822\pi$
$920$	−2.22163e16	−1.11132
$921$	1.92198e16	0.955701
$922$	8.27923e15	0.409232
$923$	6.93774e14	0.0340885
$924$	7.78448e15	0.380219
$925$	−3.00984e15	−0.146138
$926$	2.41814e16	1.16714
$927$	−2.26601e15	−0.108723
$928$	1.15321e16	0.550039
$929$	−2.57160e16	−1.21932	−0.609660	−	0.792663i	$-0.708694\pi$
$929$	−2.57160e16	−1.21932	−0.609660	+	0.792663i	$0.708694\pi$
$930$	−6.20544e15	−0.292493
$931$	−4.13794e15	−0.193893
$932$	5.18978e16	2.41747
$933$	2.58272e14	0.0119599
$934$	−3.76049e16	−1.73116
$935$	3.46086e15	0.158387
$936$	−1.90074e15	−0.0864782
$937$	2.62394e16	1.18682	0.593412	−	0.804899i	$-0.297780\pi$
$937$	2.62394e16	1.18682	0.593412	+	0.804899i	$0.297780\pi$
$938$	−4.36833e16	−1.96427
$939$	9.32199e14	0.0416723
$940$	−9.96822e15	−0.443011
$941$	−2.10008e16	−0.927881	−0.463941	−	0.885866i	$-0.653565\pi$
$941$	−2.10008e16	−0.927881	−0.463941	+	0.885866i	$0.653565\pi$
$942$	3.03579e16	1.33350
$943$	−1.04454e14	−0.00456153
$944$	4.08291e15	0.177265
$945$	4.52197e15	0.195188
$946$	−1.19893e16	−0.514510
$947$	−1.77925e16	−0.759122	−0.379561	−	0.925167i	$-0.623925\pi$
$947$	−1.77925e16	−0.759122	−0.379561	+	0.925167i	$0.623925\pi$
$948$	−4.24309e16	−1.79985
$949$	−3.61968e15	−0.152653
$950$	−4.51646e15	−0.189373
$951$	2.00309e16	0.835040
$952$	5.46061e16	2.26328
$953$	−1.08891e15	−0.0448725	−0.0224363	−	0.999748i	$-0.507142\pi$
$953$	−1.08891e15	−0.0448725	−0.0224363	+	0.999748i	$0.507142\pi$
$954$	4.41516e14	0.0180897
$955$	−9.42181e15	−0.383810
$956$	−2.96580e16	−1.20122
$957$	4.29589e15	0.172997
$958$	−7.46656e16	−2.98958
$959$	2.13745e16	0.850930
$960$	6.69450e15	0.264988
$961$	−2.18743e16	−0.860907
$962$	−2.12857e15	−0.0832963
$963$	−1.45885e14	−0.00567630
$964$	−5.52210e15	−0.213639
$965$	9.83385e15	0.378289
$966$	−2.57432e16	−0.984665
$967$	1.66647e16	0.633801	0.316901	−	0.948459i	$-0.397358\pi$
$967$	1.66647e16	0.633801	0.316901	+	0.948459i	$0.397358\pi$
$968$	4.91905e16	1.86023
$969$	−3.52041e15	−0.132377
$970$	−3.43422e16	−1.28406
$971$	1.14441e16	0.425478	0.212739	−	0.977109i	$-0.431762\pi$
$971$	1.14441e16	0.425478	0.212739	+	0.977109i	$0.431762\pi$
$972$	3.67186e15	0.135744
$973$	5.26837e15	0.193667
$974$	4.75740e15	0.173898
$975$	−8.53087e14	−0.0310076
$976$	−1.34650e15	−0.0486668
$977$	3.65010e16	1.31185	0.655925	−	0.754826i	$-0.272279\pi$
$977$	3.65010e16	1.31185	0.655925	+	0.754826i	$0.272279\pi$
$978$	1.08019e16	0.386044
$979$	4.39926e14	0.0156342
$980$	−3.39640e16	−1.20026
$981$	9.11950e15	0.320473
$982$	1.25261e16	0.437726
$983$	−3.58113e16	−1.24444	−0.622222	−	0.782841i	$-0.713770\pi$
$983$	−3.58113e16	−1.24444	−0.622222	+	0.782841i	$0.713770\pi$
$984$	−2.04820e14	−0.00707781
$985$	−3.40523e16	−1.17017
$986$	5.71357e16	1.95247
$987$	−6.09207e15	−0.207024
$988$	−2.16903e15	−0.0732996
$989$	2.69246e16	0.904835
$990$	−3.19928e15	−0.106920
$991$	4.00599e16	1.33139	0.665694	−	0.746224i	$-0.268135\pi$
$991$	4.00599e16	1.33139	0.665694	+	0.746224i	$0.268135\pi$
$992$	4.89124e15	0.161661
$993$	−5.98443e15	−0.196699
$994$	1.84248e16	0.602253
$995$	−2.83652e16	−0.922058
$996$	−1.22999e16	−0.397626
$997$	1.73367e16	0.557370	0.278685	−	0.960383i	$-0.410102\pi$
$997$	1.73367e16	0.557370	0.278685	+	0.960383i	$0.410102\pi$
$998$	2.61022e16	0.834564
$999$	2.16874e15	0.0689600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.2	✓	28	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-79.8853 q^{2} +243.000 q^{3} +4333.66 q^{4} -5377.20 q^{5} -19412.1 q^{6} -58607.4 q^{7} -182591. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-79.8853 q^{2} +243.000 q^{3} +4333.66 q^{4} -5377.20 q^{5} -19412.1 q^{6} -58607.4 q^{7} -182591. q^{8} +59049.0 q^{9} +429560. q^{10} -126129. q^{11} +1.05308e6 q^{12} +176292. q^{13} +4.68187e6 q^{14} -1.30666e6 q^{15} +5.71097e6 q^{16} +5.10282e6 q^{17} -4.71715e6 q^{18} -2.83908e6 q^{19} -2.33030e7 q^{20} -1.42416e7 q^{21} +1.00759e7 q^{22} -2.26275e7 q^{23} -4.43695e7 q^{24} -1.99138e7 q^{25} -1.40831e7 q^{26} +1.43489e7 q^{27} -2.53984e8 q^{28} -1.40162e8 q^{29} +1.04383e8 q^{30} -5.94487e7 q^{31} -8.22767e7 q^{32} -3.06495e7 q^{33} -4.07640e8 q^{34} +3.15144e8 q^{35} +2.55898e8 q^{36} +1.51143e8 q^{37} +2.26800e8 q^{38} +4.28390e7 q^{39} +9.81827e8 q^{40} +4.61623e6 q^{41} +1.13769e9 q^{42} -1.18990e9 q^{43} -5.46602e8 q^{44} -3.17519e8 q^{45} +1.80761e9 q^{46} +4.27766e8 q^{47} +1.38776e9 q^{48} +1.45750e9 q^{49} +1.59082e9 q^{50} +1.23999e9 q^{51} +7.63990e8 q^{52} -9.35982e7 q^{53} -1.14627e9 q^{54} +6.78224e8 q^{55} +1.07012e10 q^{56} -6.89896e8 q^{57} +1.11969e10 q^{58} +7.14924e8 q^{59} -5.66262e9 q^{60} -2.35775e8 q^{61} +4.74908e9 q^{62} -3.46071e9 q^{63} -5.12336e9 q^{64} -9.47959e8 q^{65} +2.44844e9 q^{66} -9.33033e9 q^{67} +2.21139e10 q^{68} -5.49849e9 q^{69} -2.51754e10 q^{70} +3.93536e9 q^{71} -1.07818e10 q^{72} -2.05323e10 q^{73} -1.20741e10 q^{74} -4.83905e9 q^{75} -1.23036e10 q^{76} +7.39212e9 q^{77} -3.42220e9 q^{78} -4.02922e10 q^{79} -3.07090e10 q^{80} +3.48678e9 q^{81} -3.68769e8 q^{82} -1.16799e10 q^{83} -6.17182e10 q^{84} -2.74389e10 q^{85} +9.50558e10 q^{86} -3.40594e10 q^{87} +2.30301e10 q^{88} -3.48789e9 q^{89} +2.53651e10 q^{90} -1.03320e10 q^{91} -9.80600e10 q^{92} -1.44460e10 q^{93} -3.41722e10 q^{94} +1.52663e10 q^{95} -1.99932e10 q^{96} -7.99476e10 q^{97} -1.16433e11 q^{98} -7.44782e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

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