LMFDB - Embedded newform 177.12.a.d.1.4

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			1.4
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)

$f(q)$	$=$	$q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +11438.4 q^{10} -851602. q^{11} +608396. q^{12} -64569.7 q^{13} -4.43745e6 q^{14} -41198.8 q^{15} -3.05340e6 q^{16} +4.48109e6 q^{17} -3.98381e6 q^{18} -8.64046e6 q^{19} -424482. q^{20} +1.59828e7 q^{21} +5.74544e7 q^{22} -8.74923e6 q^{23} -7.47068e6 q^{24} -4.87994e7 q^{25} +4.35627e6 q^{26} +1.43489e7 q^{27} +1.64675e8 q^{28} +1.62922e8 q^{29} +2.77953e6 q^{30} -2.58081e8 q^{31} +2.68964e8 q^{32} -2.06939e8 q^{33} -3.02322e8 q^{34} -1.11513e7 q^{35} +1.47840e8 q^{36} +6.12752e7 q^{37} +5.82939e8 q^{38} -1.56904e7 q^{39} +5.21234e6 q^{40} +1.09619e9 q^{41} -1.07830e9 q^{42} +2.73022e8 q^{43} -2.13215e9 q^{44} -1.00113e7 q^{45} +5.90277e8 q^{46} +2.85354e8 q^{47} -7.41977e8 q^{48} +2.34875e9 q^{49} +3.29231e9 q^{50} +1.08890e9 q^{51} -1.61662e8 q^{52} +3.57388e9 q^{53} -9.68066e8 q^{54} +1.44383e8 q^{55} -2.02209e9 q^{56} -2.09963e9 q^{57} -1.09917e10 q^{58} +7.14924e8 q^{59} -1.03149e8 q^{60} -5.00064e9 q^{61} +1.74117e10 q^{62} +3.88382e9 q^{63} -1.18926e10 q^{64} +1.09473e7 q^{65} +1.39614e10 q^{66} +1.14088e10 q^{67} +1.12192e10 q^{68} -2.12606e9 q^{69} +7.52336e8 q^{70} +1.70442e10 q^{71} -1.81538e9 q^{72} -1.15800e9 q^{73} -4.13400e9 q^{74} -1.18582e10 q^{75} -2.16330e10 q^{76} -5.60123e10 q^{77} +1.05857e9 q^{78} +5.14025e8 q^{79} +5.17682e8 q^{80} +3.48678e9 q^{81} -7.39556e10 q^{82} -4.94656e9 q^{83} +4.00160e10 q^{84} -7.59735e8 q^{85} -1.84197e10 q^{86} +3.95901e10 q^{87} +2.61813e10 q^{88} -6.81005e10 q^{89} +6.75425e8 q^{90} -4.24693e9 q^{91} -2.19053e10 q^{92} -6.27136e10 q^{93} -1.92517e10 q^{94} +1.46493e9 q^{95} +6.53583e10 q^{96} -7.84607e10 q^{97} -1.58461e11 q^{98} -5.02863e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−67.4662	−1.49081	−0.745403	−	0.666614i	$-0.767743\pi$
$2$	−67.4662	−1.49081	−0.745403	+	0.666614i	$0.767743\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	2503.69	1.22250
$5$	−169.543	−0.0242630	−0.0121315	−	0.999926i	$-0.503862\pi$
$5$	−169.543	−0.0242630	−0.0121315	+	0.999926i	$0.503862\pi$
$6$	−16394.3	−0.860718
$7$	65772.9	1.47913	0.739567	−	0.673083i	$-0.235030\pi$
$7$	65772.9	1.47913	0.739567	+	0.673083i	$0.235030\pi$
$8$	−30743.5	−0.331710
$9$	59049.0	0.333333
$10$	11438.4	0.0361714
$11$	−851602.	−1.59433	−0.797163	−	0.603764i	$-0.793667\pi$
$11$	−851602.	−1.59433	−0.797163	+	0.603764i	$0.793667\pi$
$12$	608396.	0.705813
$13$	−64569.7	−0.0482325	−0.0241163	−	0.999709i	$-0.507677\pi$
$13$	−64569.7	−0.0482325	−0.0241163	+	0.999709i	$0.507677\pi$
$14$	−4.43745e6	−2.20510
$15$	−41198.8	−0.0140082
$16$	−3.05340e6	−0.727988
$17$	4.48109e6	0.765446	0.382723	−	0.923863i	$-0.374986\pi$
$17$	4.48109e6	0.765446	0.382723	+	0.923863i	$0.374986\pi$
$18$	−3.98381e6	−0.496935
$19$	−8.64046e6	−0.800557	−0.400278	−	0.916394i	$-0.631087\pi$
$19$	−8.64046e6	−0.800557	−0.400278	+	0.916394i	$0.631087\pi$
$20$	−424482.	−0.0296616
$21$	1.59828e7	0.853979
$22$	5.74544e7	2.37683
$23$	−8.74923e6	−0.283444	−0.141722	−	0.989907i	$-0.545264\pi$
$23$	−8.74923e6	−0.283444	−0.141722	+	0.989907i	$0.545264\pi$
$24$	−7.47068e6	−0.191513
$25$	−4.87994e7	−0.999411
$26$	4.35627e6	0.0719054
$27$	1.43489e7	0.192450
$28$	1.64675e8	1.80825
$29$	1.62922e8	1.47500	0.737499	−	0.675348i	$-0.236007\pi$
$29$	1.62922e8	1.47500	0.737499	+	0.675348i	$0.236007\pi$
$30$	2.77953e6	0.0208835
$31$	−2.58081e8	−1.61907	−0.809536	−	0.587071i	$-0.800281\pi$
$31$	−2.58081e8	−1.61907	−0.809536	+	0.587071i	$0.800281\pi$
$32$	2.68964e8	1.41700
$33$	−2.06939e8	−0.920484
$34$	−3.02322e8	−1.14113
$35$	−1.11513e7	−0.0358882
$36$	1.47840e8	0.407501
$37$	6.12752e7	0.145270	0.0726348	−	0.997359i	$-0.476859\pi$
$37$	6.12752e7	0.145270	0.0726348	+	0.997359i	$0.476859\pi$
$38$	5.82939e8	1.19348
$39$	−1.56904e7	−0.0278471
$40$	5.21234e6	0.00804827
$41$	1.09619e9	1.47766	0.738829	−	0.673893i	$-0.235379\pi$
$41$	1.09619e9	1.47766	0.738829	+	0.673893i	$0.235379\pi$
$42$	−1.07830e9	−1.27312
$43$	2.73022e8	0.283218	0.141609	−	0.989923i	$-0.454772\pi$
$43$	2.73022e8	0.283218	0.141609	+	0.989923i	$0.454772\pi$
$44$	−2.13215e9	−1.94907
$45$	−1.00113e7	−0.00808765
$46$	5.90277e8	0.422560
$47$	2.85354e8	0.181487	0.0907434	−	0.995874i	$-0.471076\pi$
$47$	2.85354e8	0.181487	0.0907434	+	0.995874i	$0.471076\pi$
$48$	−7.41977e8	−0.420304
$49$	2.34875e9	1.18784
$50$	3.29231e9	1.48993
$51$	1.08890e9	0.441930
$52$	−1.61662e8	−0.0589645
$53$	3.57388e9	1.17388	0.586939	−	0.809631i	$-0.300333\pi$
$53$	3.57388e9	1.17388	0.586939	+	0.809631i	$0.300333\pi$
$54$	−9.68066e8	−0.286906
$55$	1.44383e8	0.0386830
$56$	−2.02209e9	−0.490644
$57$	−2.09963e9	−0.462202
$58$	−1.09917e10	−2.19894
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.03149e8	−0.0171251
$61$	−5.00064e9	−0.758073	−0.379037	−	0.925382i	$-0.623745\pi$
$61$	−5.00064e9	−0.758073	−0.379037	+	0.925382i	$0.623745\pi$
$62$	1.74117e10	2.41372
$63$	3.88382e9	0.493045
$64$	−1.18926e10	−1.38448
$65$	1.09473e7	0.00117026
$66$	1.39614e10	1.37226
$67$	1.14088e10	1.03236	0.516178	−	0.856482i	$-0.327354\pi$
$67$	1.14088e10	1.03236	0.516178	+	0.856482i	$0.327354\pi$
$68$	1.12192e10	0.935760
$69$	−2.12606e9	−0.163646
$70$	7.52336e8	0.0535023
$71$	1.70442e10	1.12113	0.560566	−	0.828110i	$-0.310584\pi$
$71$	1.70442e10	1.12113	0.560566	+	0.828110i	$0.310584\pi$
$72$	−1.81538e9	−0.110570
$73$	−1.15800e9	−0.0653779	−0.0326889	−	0.999466i	$-0.510407\pi$
$73$	−1.15800e9	−0.0653779	−0.0326889	+	0.999466i	$0.510407\pi$
$74$	−4.13400e9	−0.216569
$75$	−1.18582e10	−0.577010
$76$	−2.16330e10	−0.978684
$77$	−5.60123e10	−2.35822
$78$	1.05857e9	0.0415146
$79$	5.14025e8	0.0187947	0.00939735	−	0.999956i	$-0.497009\pi$
$79$	5.14025e8	0.0187947	0.00939735	+	0.999956i	$0.497009\pi$
$80$	5.17682e8	0.0176631
$81$	3.48678e9	0.111111
$82$	−7.39556e10	−2.20290
$83$	−4.94656e9	−0.137839	−0.0689197	−	0.997622i	$-0.521955\pi$
$83$	−4.94656e9	−0.137839	−0.0689197	+	0.997622i	$0.521955\pi$
$84$	4.00160e10	1.04399
$85$	−7.59735e8	−0.0185720
$86$	−1.84197e10	−0.422223
$87$	3.95901e10	0.851591
$88$	2.61813e10	0.528854
$89$	−6.81005e10	−1.29272	−0.646361	−	0.763032i	$-0.723710\pi$
$89$	−6.81005e10	−1.29272	−0.646361	+	0.763032i	$0.723710\pi$
$90$	6.75425e8	0.0120571
$91$	−4.24693e9	−0.0713424
$92$	−2.19053e10	−0.346511
$93$	−6.27136e10	−0.934771
$94$	−1.92517e10	−0.270562
$95$	1.46493e9	0.0194239
$96$	6.53583e10	0.818105
$97$	−7.84607e10	−0.927700	−0.463850	−	0.885914i	$-0.653532\pi$
$97$	−7.84607e10	−0.927700	−0.463850	+	0.885914i	$0.653532\pi$
$98$	−1.58461e11	−1.77084
$99$	−5.02863e10	−0.531442
$100$	−1.22178e11	−1.22178
$101$	3.26246e9	0.0308871	0.0154435	−	0.999881i	$-0.495084\pi$
$101$	3.26246e9	0.0308871	0.0154435	+	0.999881i	$0.495084\pi$
$102$	−7.34642e10	−0.658832
$103$	−1.84747e10	−0.157026	−0.0785132	−	0.996913i	$-0.525017\pi$
$103$	−1.84747e10	−0.157026	−0.0785132	+	0.996913i	$0.525017\pi$
$104$	1.98510e9	0.0159992
$105$	−2.70977e9	−0.0207200
$106$	−2.41116e11	−1.75002
$107$	−2.22331e11	−1.53246	−0.766229	−	0.642568i	$-0.777869\pi$
$107$	−2.22331e11	−1.53246	−0.766229	+	0.642568i	$0.777869\pi$
$108$	3.59252e10	0.235271
$109$	−1.79474e10	−0.111726	−0.0558631	−	0.998438i	$-0.517791\pi$
$109$	−1.79474e10	−0.111726	−0.0558631	+	0.998438i	$0.517791\pi$
$110$	−9.74096e9	−0.0576689
$111$	1.48899e10	0.0838715
$112$	−2.00831e11	−1.07679
$113$	9.25443e10	0.472518	0.236259	−	0.971690i	$-0.424079\pi$
$113$	9.25443e10	0.472518	0.236259	+	0.971690i	$0.424079\pi$
$114$	1.41654e11	0.689053
$115$	1.48337e9	0.00687718
$116$	4.07907e11	1.80319
$117$	−3.81277e9	−0.0160775
$118$	−4.82332e10	−0.194086
$119$	2.94734e11	1.13220
$120$	1.26660e9	0.00464667
$121$	4.39915e11	1.54187
$122$	3.37374e11	1.13014
$123$	2.66374e11	0.853126
$124$	−6.46153e11	−1.97932
$125$	1.65520e10	0.0485116
$126$	−2.62027e11	−0.735034
$127$	5.63726e11	1.51408	0.757038	−	0.653370i	$-0.226646\pi$
$127$	5.63726e11	1.51408	0.757038	+	0.653370i	$0.226646\pi$
$128$	2.51512e11	0.646998
$129$	6.63443e10	0.163516
$130$	−7.38573e8	−0.00174464
$131$	2.25503e11	0.510693	0.255346	−	0.966850i	$-0.417811\pi$
$131$	2.25503e11	0.510693	0.255346	+	0.966850i	$0.417811\pi$
$132$	−5.18112e11	−1.12530
$133$	−5.68308e11	−1.18413
$134$	−7.69710e11	−1.53904
$135$	−2.43275e9	−0.00466941
$136$	−1.37765e11	−0.253906
$137$	8.78053e11	1.55438	0.777191	−	0.629265i	$-0.216644\pi$
$137$	8.78053e11	1.55438	0.777191	+	0.629265i	$0.216644\pi$
$138$	1.43437e11	0.243965
$139$	4.95579e11	0.810086	0.405043	−	0.914298i	$-0.367257\pi$
$139$	4.95579e11	0.810086	0.405043	+	0.914298i	$0.367257\pi$
$140$	−2.79194e10	−0.0438734
$141$	6.93409e10	0.104781
$142$	−1.14991e12	−1.67139
$143$	5.49877e10	0.0768984
$144$	−1.80300e11	−0.242663
$145$	−2.76223e10	−0.0357878
$146$	7.81255e10	0.0974658
$147$	5.70745e11	0.685799
$148$	1.53414e11	0.177593
$149$	4.30474e11	0.480200	0.240100	−	0.970748i	$-0.422820\pi$
$149$	4.30474e11	0.480200	0.240100	+	0.970748i	$0.422820\pi$
$150$	8.00031e11	0.860211
$151$	7.89752e11	0.818686	0.409343	−	0.912381i	$-0.365758\pi$
$151$	7.89752e11	0.818686	0.409343	+	0.912381i	$0.365758\pi$
$152$	2.65638e11	0.265553
$153$	2.64604e11	0.255149
$154$	3.77894e12	3.51565
$155$	4.37556e10	0.0392834
$156$	−3.92839e10	−0.0340432
$157$	3.35317e11	0.280548	0.140274	−	0.990113i	$-0.455202\pi$
$157$	3.35317e11	0.280548	0.140274	+	0.990113i	$0.455202\pi$
$158$	−3.46793e10	−0.0280193
$159$	8.68453e11	0.677738
$160$	−4.56009e10	−0.0343806
$161$	−5.75462e11	−0.419251
$162$	−2.35240e11	−0.165645
$163$	5.24082e11	0.356753	0.178376	−	0.983962i	$-0.442916\pi$
$163$	5.24082e11	0.356753	0.178376	+	0.983962i	$0.442916\pi$
$164$	2.74451e12	1.80644
$165$	3.50850e10	0.0223337
$166$	3.33725e11	0.205492
$167$	6.04526e11	0.360143	0.180071	−	0.983654i	$-0.442367\pi$
$167$	6.04526e11	0.360143	0.180071	+	0.983654i	$0.442367\pi$
$168$	−4.91368e11	−0.283274
$169$	−1.78799e12	−0.997674
$170$	5.12564e10	0.0276872
$171$	−5.10211e11	−0.266852
$172$	6.83562e11	0.346235
$173$	−2.60831e12	−1.27969	−0.639846	−	0.768503i	$-0.721002\pi$
$173$	−2.60831e12	−1.27969	−0.639846	+	0.768503i	$0.721002\pi$
$174$	−2.67099e12	−1.26956
$175$	−3.20968e12	−1.47826
$176$	2.60029e12	1.16065
$177$	1.73727e11	0.0751646
$178$	4.59448e12	1.92720
$179$	2.59282e12	1.05458	0.527292	−	0.849684i	$-0.323208\pi$
$179$	2.59282e12	1.05458	0.527292	+	0.849684i	$0.323208\pi$
$180$	−2.50652e10	−0.00988718
$181$	1.19060e12	0.455547	0.227774	−	0.973714i	$-0.426855\pi$
$181$	1.19060e12	0.455547	0.227774	+	0.973714i	$0.426855\pi$
$182$	2.86524e11	0.106358
$183$	−1.21515e12	−0.437674
$184$	2.68982e11	0.0940212
$185$	−1.03887e10	−0.00352467
$186$	4.23105e12	1.39356
$187$	−3.81610e12	−1.22037
$188$	7.14436e11	0.221868
$189$	9.43769e11	0.284660
$190$	−9.88330e10	−0.0289572
$191$	6.53664e12	1.86068	0.930338	−	0.366703i	$-0.119513\pi$
$191$	6.53664e12	1.86068	0.930338	+	0.366703i	$0.119513\pi$
$192$	−2.88991e12	−0.799332
$193$	−1.16867e12	−0.314141	−0.157071	−	0.987587i	$-0.550205\pi$
$193$	−1.16867e12	−0.314141	−0.157071	+	0.987587i	$0.550205\pi$
$194$	5.29344e12	1.38302
$195$	2.66019e9	0.000675652 0
$196$	5.88053e12	1.45214
$197$	−3.62189e12	−0.869704	−0.434852	−	0.900502i	$-0.643199\pi$
$197$	−3.62189e12	−0.869704	−0.434852	+	0.900502i	$0.643199\pi$
$198$	3.39262e12	0.792277
$199$	3.21209e12	0.729618	0.364809	−	0.931082i	$-0.381134\pi$
$199$	3.21209e12	0.729618	0.364809	+	0.931082i	$0.381134\pi$
$200$	1.50027e12	0.331515
$201$	2.77234e12	0.596031
$202$	−2.20105e11	−0.0460467
$203$	1.07159e13	2.18172
$204$	2.72628e12	0.540261
$205$	−1.85850e11	−0.0358523
$206$	1.24642e12	0.234096
$207$	−5.16633e11	−0.0944812
$208$	1.97157e11	0.0351127
$209$	7.35824e12	1.27635
$210$	1.82818e11	0.0308896
$211$	−7.23792e12	−1.19141	−0.595703	−	0.803204i	$-0.703127\pi$
$211$	−7.23792e12	−1.19141	−0.595703	+	0.803204i	$0.703127\pi$
$212$	8.94788e12	1.43507
$213$	4.14175e12	0.647286
$214$	1.49998e13	2.28460
$215$	−4.62888e10	−0.00687171
$216$	−4.41136e11	−0.0638377
$217$	−1.69747e13	−2.39482
$218$	1.21084e12	0.166562
$219$	−2.81393e11	−0.0377459
$220$	3.61489e11	0.0472902
$221$	−2.89342e11	−0.0369194
$222$	−1.00456e12	−0.125036
$223$	1.22787e13	1.49099	0.745497	−	0.666509i	$-0.232212\pi$
$223$	1.22787e13	1.49099	0.745497	+	0.666509i	$0.232212\pi$
$224$	1.76906e13	2.09593
$225$	−2.88155e12	−0.333137
$226$	−6.24361e12	−0.704433
$227$	3.31881e12	0.365460	0.182730	−	0.983163i	$-0.441507\pi$
$227$	3.31881e12	0.365460	0.182730	+	0.983163i	$0.441507\pi$
$228$	−5.25682e12	−0.565043
$229$	8.44412e12	0.886052	0.443026	−	0.896509i	$-0.353905\pi$
$229$	8.44412e12	0.886052	0.443026	+	0.896509i	$0.353905\pi$
$230$	−1.00077e11	−0.0102525
$231$	−1.36110e13	−1.36152
$232$	−5.00881e12	−0.489272
$233$	−3.56568e12	−0.340162	−0.170081	−	0.985430i	$-0.554403\pi$
$233$	−3.56568e12	−0.340162	−0.170081	+	0.985430i	$0.554403\pi$
$234$	2.57233e11	0.0239685
$235$	−4.83796e10	−0.00440340
$236$	1.78995e12	0.159156
$237$	1.24908e11	0.0108511
$238$	−1.98846e13	−1.68789
$239$	4.22044e12	0.350082	0.175041	−	0.984561i	$-0.443994\pi$
$239$	4.22044e12	0.350082	0.175041	+	0.984561i	$0.443994\pi$
$240$	1.25797e11	0.0101978
$241$	8.04748e12	0.637626	0.318813	−	0.947818i	$-0.396716\pi$
$241$	8.04748e12	0.637626	0.318813	+	0.947818i	$0.396716\pi$
$242$	−2.96794e13	−2.29864
$243$	8.47289e11	0.0641500
$244$	−1.25200e13	−0.926747
$245$	−3.98212e11	−0.0288205
$246$	−1.79712e13	−1.27185
$247$	5.57912e11	0.0386129
$248$	7.93431e12	0.537063
$249$	−1.20201e12	−0.0795816
$250$	−1.11670e12	−0.0723214
$251$	−7.29754e12	−0.462350	−0.231175	−	0.972912i	$-0.574257\pi$
$251$	−7.29754e12	−0.462350	−0.231175	+	0.972912i	$0.574257\pi$
$252$	9.72388e12	0.602749
$253$	7.45086e12	0.451902
$254$	−3.80325e13	−2.25720
$255$	−1.84616e11	−0.0107225
$256$	7.38757e12	0.419935
$257$	−2.27868e13	−1.26780	−0.633900	−	0.773415i	$-0.718547\pi$
$257$	−2.27868e13	−1.26780	−0.633900	+	0.773415i	$0.718547\pi$
$258$	−4.47600e12	−0.243771
$259$	4.03024e12	0.214873
$260$	2.74086e10	0.00143065
$261$	9.62040e12	0.491666
$262$	−1.52138e13	−0.761344
$263$	3.57299e12	0.175096	0.0875478	−	0.996160i	$-0.472097\pi$
$263$	3.57299e12	0.175096	0.0875478	+	0.996160i	$0.472097\pi$
$264$	6.36205e12	0.305334
$265$	−6.05925e11	−0.0284817
$266$	3.83416e13	1.76531
$267$	−1.65484e13	−0.746353
$268$	2.85641e13	1.26206
$269$	3.87184e13	1.67602	0.838011	−	0.545653i	$-0.183718\pi$
$269$	3.87184e13	1.67602	0.838011	+	0.545653i	$0.183718\pi$
$270$	1.64128e11	0.00696118
$271$	−3.02431e12	−0.125688	−0.0628442	−	0.998023i	$-0.520017\pi$
$271$	−3.02431e12	−0.125688	−0.0628442	+	0.998023i	$0.520017\pi$
$272$	−1.36826e13	−0.557235
$273$	−1.03200e12	−0.0411896
$274$	−5.92389e13	−2.31728
$275$	4.15577e13	1.59339
$276$	−5.32300e12	−0.200058
$277$	−5.00826e13	−1.84522	−0.922610	−	0.385734i	$-0.873948\pi$
$277$	−5.00826e13	−1.84522	−0.922610	+	0.385734i	$0.873948\pi$
$278$	−3.34348e13	−1.20768
$279$	−1.52394e13	−0.539690
$280$	3.42831e11	0.0119045
$281$	3.16837e13	1.07883	0.539413	−	0.842042i	$-0.318646\pi$
$281$	3.16837e13	1.07883	0.539413	+	0.842042i	$0.318646\pi$
$282$	−4.67817e12	−0.156209
$283$	3.40171e13	1.11397	0.556983	−	0.830524i	$-0.311959\pi$
$283$	3.40171e13	1.11397	0.556983	+	0.830524i	$0.311959\pi$
$284$	4.26735e13	1.37059
$285$	3.55977e11	0.0112144
$286$	−3.70981e12	−0.114641
$287$	7.20994e13	2.18565
$288$	1.58821e13	0.472333
$289$	−1.41917e13	−0.414093
$290$	1.86357e12	0.0533527
$291$	−1.90659e13	−0.535608
$292$	−2.89926e12	−0.0799247
$293$	8.97620e11	0.0242840	0.0121420	−	0.999926i	$-0.496135\pi$
$293$	8.97620e11	0.0242840	0.0121420	+	0.999926i	$0.496135\pi$
$294$	−3.85060e13	−1.02239
$295$	−1.21210e11	−0.00315877
$296$	−1.88382e12	−0.0481875
$297$	−1.22196e13	−0.306828
$298$	−2.90424e13	−0.715886
$299$	5.64935e11	0.0136712
$300$	−2.96894e13	−0.705397
$301$	1.79574e13	0.418918
$302$	−5.32815e13	−1.22050
$303$	7.92777e11	0.0178327
$304$	2.63828e13	0.582796
$305$	8.47820e11	0.0183931
$306$	−1.78518e13	−0.380377
$307$	2.31111e13	0.483682	0.241841	−	0.970316i	$-0.422249\pi$
$307$	2.31111e13	0.483682	0.241841	+	0.970316i	$0.422249\pi$
$308$	−1.40237e14	−2.88294
$309$	−4.48935e12	−0.0906593
$310$	−2.95203e12	−0.0585640
$311$	6.81672e13	1.32860	0.664298	−	0.747468i	$-0.268730\pi$
$311$	6.81672e13	1.32860	0.664298	+	0.747468i	$0.268730\pi$
$312$	4.82379e11	0.00923716
$313$	6.75405e13	1.27078	0.635390	−	0.772191i	$-0.280839\pi$
$313$	6.75405e13	1.27078	0.635390	+	0.772191i	$0.280839\pi$
$314$	−2.26226e13	−0.418243
$315$	−6.58473e11	−0.0119627
$316$	1.28696e12	0.0229766
$317$	−3.94816e13	−0.692737	−0.346368	−	0.938099i	$-0.612585\pi$
$317$	−3.94816e13	−0.692737	−0.346368	+	0.938099i	$0.612585\pi$
$318$	−5.85912e13	−1.01038
$319$	−1.38745e14	−2.35163
$320$	2.01631e12	0.0335917
$321$	−5.40263e13	−0.884765
$322$	3.88242e13	0.625023
$323$	−3.87187e13	−0.612783
$324$	8.72982e12	0.135834
$325$	3.15096e12	0.0482041
$326$	−3.53578e13	−0.531849
$327$	−4.36121e12	−0.0645052
$328$	−3.37007e13	−0.490154
$329$	1.87685e13	0.268443
$330$	−2.36705e12	−0.0332952
$331$	4.14501e13	0.573418	0.286709	−	0.958018i	$-0.407439\pi$
$331$	4.14501e13	0.573418	0.286709	+	0.958018i	$0.407439\pi$
$332$	−1.23846e13	−0.168509
$333$	3.61824e12	0.0484232
$334$	−4.07851e13	−0.536903
$335$	−1.93428e12	−0.0250480
$336$	−4.88020e13	−0.621686
$337$	−3.96138e13	−0.496457	−0.248228	−	0.968702i	$-0.579848\pi$
$337$	−3.96138e13	−0.496457	−0.248228	+	0.968702i	$0.579848\pi$
$338$	1.20629e14	1.48734
$339$	2.24883e13	0.272808
$340$	−1.90214e12	−0.0227043
$341$	2.19782e14	2.58133
$342$	3.44220e13	0.397825
$343$	2.44293e13	0.277839
$344$	−8.39366e12	−0.0939464
$345$	3.60458e11	0.00397054
$346$	1.75973e14	1.90777
$347$	2.47444e12	0.0264037	0.0132019	−	0.999913i	$-0.495798\pi$
$347$	2.47444e12	0.0264037	0.0132019	+	0.999913i	$0.495798\pi$
$348$	9.91213e13	1.04107
$349$	1.14708e14	1.18591	0.592956	−	0.805235i	$-0.297961\pi$
$349$	1.14708e14	1.18591	0.592956	+	0.805235i	$0.297961\pi$
$350$	2.16545e14	2.20381
$351$	−9.26504e11	−0.00928236
$352$	−2.29051e14	−2.25916
$353$	1.25470e14	1.21837	0.609183	−	0.793030i	$-0.291498\pi$
$353$	1.25470e14	1.21837	0.609183	+	0.793030i	$0.291498\pi$
$354$	−1.17207e13	−0.112056
$355$	−2.88972e12	−0.0272020
$356$	−1.70502e14	−1.58036
$357$	7.16204e13	0.653674
$358$	−1.74928e14	−1.57218
$359$	−1.44977e14	−1.28316	−0.641580	−	0.767056i	$-0.721721\pi$
$359$	−1.44977e14	−1.28316	−0.641580	+	0.767056i	$0.721721\pi$
$360$	3.07783e11	0.00268276
$361$	−4.18327e13	−0.359109
$362$	−8.03252e13	−0.679133
$363$	1.06899e14	0.890202
$364$	−1.06330e13	−0.0872164
$365$	1.96329e11	0.00158626
$366$	8.19819e13	0.652487
$367$	−2.36110e14	−1.85119	−0.925594	−	0.378518i	$-0.876434\pi$
$367$	−2.36110e14	−1.85119	−0.925594	+	0.378518i	$0.876434\pi$
$368$	2.67149e13	0.206344
$369$	6.47288e13	0.492552
$370$	7.00889e11	0.00525460
$371$	2.35064e14	1.73632
$372$	−1.57015e14	−1.14276
$373$	−1.59228e14	−1.14188	−0.570940	−	0.820992i	$-0.693421\pi$
$373$	−1.59228e14	−1.14188	−0.570940	+	0.820992i	$0.693421\pi$
$374$	2.57458e14	1.81934
$375$	4.02214e12	0.0280082
$376$	−8.77278e12	−0.0602010
$377$	−1.05198e13	−0.0711429
$378$	−6.36725e13	−0.424372
$379$	2.40271e14	1.57829	0.789144	−	0.614208i	$-0.210525\pi$
$379$	2.40271e14	1.57829	0.789144	+	0.614208i	$0.210525\pi$
$380$	3.66772e12	0.0237458
$381$	1.36986e14	0.874153
$382$	−4.41002e14	−2.77391
$383$	2.44363e14	1.51510	0.757550	−	0.652777i	$-0.226396\pi$
$383$	2.44363e14	1.51510	0.757550	+	0.652777i	$0.226396\pi$
$384$	6.11173e13	0.373545
$385$	9.49647e12	0.0572174
$386$	7.88454e13	0.468324
$387$	1.61217e13	0.0944060
$388$	−1.96441e14	−1.13412
$389$	1.43407e14	0.816295	0.408148	−	0.912916i	$-0.366175\pi$
$389$	1.43407e14	0.816295	0.408148	+	0.912916i	$0.366175\pi$
$390$	−1.79473e11	−0.00100727
$391$	−3.92061e13	−0.216961
$392$	−7.22088e13	−0.394018
$393$	5.47972e13	0.294849
$394$	2.44355e14	1.29656
$395$	−8.71491e10	−0.000456015 0
$396$	−1.25901e14	−0.649690
$397$	1.64826e13	0.0838839	0.0419420	−	0.999120i	$-0.486646\pi$
$397$	1.64826e13	0.0838839	0.0419420	+	0.999120i	$0.486646\pi$
$398$	−2.16708e14	−1.08772
$399$	−1.38099e14	−0.683658
$400$	1.49004e14	0.727559
$401$	−9.03944e13	−0.435359	−0.217679	−	0.976020i	$-0.569849\pi$
$401$	−9.03944e13	−0.435359	−0.217679	+	0.976020i	$0.569849\pi$
$402$	−1.87039e14	−0.888566
$403$	1.66642e13	0.0780919
$404$	8.16817e12	0.0377596
$405$	−5.91158e11	−0.00269588
$406$	−7.22959e14	−3.25252
$407$	−5.21821e13	−0.231607
$408$	−3.34768e13	−0.146593
$409$	3.76497e14	1.62661	0.813305	−	0.581838i	$-0.197666\pi$
$409$	3.76497e14	1.62661	0.813305	+	0.581838i	$0.197666\pi$
$410$	1.25386e13	0.0534489
$411$	2.13367e14	0.897423
$412$	−4.62549e13	−0.191965
$413$	4.70226e13	0.192567
$414$	3.48553e13	0.140853
$415$	8.38652e11	0.00334439
$416$	−1.73669e13	−0.0683455
$417$	1.20426e14	0.467703
$418$	−4.96432e14	−1.90279
$419$	−3.16379e14	−1.19683	−0.598413	−	0.801188i	$-0.704202\pi$
$419$	−3.16379e14	−1.19683	−0.598413	+	0.801188i	$0.704202\pi$
$420$	−6.78441e12	−0.0253303
$421$	−1.16430e14	−0.429056	−0.214528	−	0.976718i	$-0.568821\pi$
$421$	−1.16430e14	−0.429056	−0.214528	+	0.976718i	$0.568821\pi$
$422$	4.88315e14	1.77616
$423$	1.68498e13	0.0604956
$424$	−1.09874e14	−0.389387
$425$	−2.18674e14	−0.764995
$426$	−2.79428e14	−0.964978
$427$	−3.28906e14	−1.12129
$428$	−5.56647e14	−1.87344
$429$	1.33620e13	0.0443973
$430$	3.12293e12	0.0102444
$431$	−1.17999e14	−0.382167	−0.191083	−	0.981574i	$-0.561200\pi$
$431$	−1.17999e14	−0.382167	−0.191083	+	0.981574i	$0.561200\pi$
$432$	−4.38130e13	−0.140101
$433$	−3.75432e14	−1.18535	−0.592676	−	0.805441i	$-0.701929\pi$
$433$	−3.75432e14	−1.18535	−0.592676	+	0.805441i	$0.701929\pi$
$434$	1.14522e15	3.57022
$435$	−6.71221e12	−0.0206621
$436$	−4.49346e13	−0.136586
$437$	7.55974e13	0.226913
$438$	1.89845e13	0.0562719
$439$	−3.21075e13	−0.0939835	−0.0469917	−	0.998895i	$-0.514963\pi$
$439$	−3.21075e13	−0.0939835	−0.0469917	+	0.998895i	$0.514963\pi$
$440$	−4.43884e12	−0.0128316
$441$	1.38691e14	0.395946
$442$	1.95208e13	0.0550397
$443$	4.03275e14	1.12300	0.561502	−	0.827476i	$-0.310224\pi$
$443$	4.03275e14	1.12300	0.561502	+	0.827476i	$0.310224\pi$
$444$	3.72796e13	0.102533
$445$	1.15459e13	0.0313652
$446$	−8.28398e14	−2.22278
$447$	1.04605e14	0.277244
$448$	−7.82212e14	−2.04784
$449$	−5.84948e14	−1.51273	−0.756366	−	0.654148i	$-0.773027\pi$
$449$	−5.84948e14	−1.51273	−0.756366	+	0.654148i	$0.773027\pi$
$450$	1.94408e14	0.496643
$451$	−9.33516e14	−2.35587
$452$	2.31702e14	0.577655
$453$	1.91910e14	0.472668
$454$	−2.23908e14	−0.544831
$455$	7.20036e11	0.00173098
$456$	6.45501e13	0.153317
$457$	4.51440e14	1.05940	0.529701	−	0.848185i	$-0.322304\pi$
$457$	4.51440e14	1.05940	0.529701	+	0.848185i	$0.322304\pi$
$458$	−5.69692e14	−1.32093
$459$	6.42987e13	0.147310
$460$	3.71389e12	0.00840738
$461$	−6.82451e14	−1.52657	−0.763284	−	0.646063i	$-0.776414\pi$
$461$	−6.82451e14	−1.52657	−0.763284	+	0.646063i	$0.776414\pi$
$462$	9.18282e14	2.02976
$463$	−3.08000e14	−0.672751	−0.336376	−	0.941728i	$-0.609201\pi$
$463$	−3.08000e14	−0.672751	−0.336376	+	0.941728i	$0.609201\pi$
$464$	−4.97467e14	−1.07378
$465$	1.06326e13	0.0226803
$466$	2.40563e14	0.507115
$467$	−2.27817e13	−0.0474617	−0.0237308	−	0.999718i	$-0.507554\pi$
$467$	−2.27817e13	−0.0474617	−0.0237308	+	0.999718i	$0.507554\pi$
$468$	−9.54600e12	−0.0196548
$469$	7.50391e14	1.52699
$470$	3.26398e12	0.00656462
$471$	8.14821e13	0.161975
$472$	−2.19793e13	−0.0431850
$473$	−2.32506e14	−0.451542
$474$	−8.42708e12	−0.0161769
$475$	4.21649e14	0.800085
$476$	7.37922e14	1.38412
$477$	2.11034e14	0.391292
$478$	−2.84737e14	−0.521904
$479$	3.10826e14	0.563212	0.281606	−	0.959530i	$-0.409133\pi$
$479$	3.10826e14	0.563212	0.281606	+	0.959530i	$0.409133\pi$
$480$	−1.10810e13	−0.0198496
$481$	−3.95652e12	−0.00700673
$482$	−5.42933e14	−0.950577
$483$	−1.39837e14	−0.242055
$484$	1.10141e15	1.88495
$485$	1.33024e13	0.0225087
$486$	−5.71633e13	−0.0956353
$487$	−2.12017e14	−0.350721	−0.175360	−	0.984504i	$-0.556109\pi$
$487$	−2.12017e14	−0.350721	−0.175360	+	0.984504i	$0.556109\pi$
$488$	1.53737e14	0.251461
$489$	1.27352e14	0.205971
$490$	2.68659e13	0.0429658
$491$	4.60829e14	0.728771	0.364386	−	0.931248i	$-0.381279\pi$
$491$	4.60829e14	0.728771	0.364386	+	0.931248i	$0.381279\pi$
$492$	6.66916e14	1.04295
$493$	7.30069e14	1.12903
$494$	−3.76402e13	−0.0575643
$495$	8.52566e12	0.0128943
$496$	7.88024e14	1.17866
$497$	1.12105e15	1.65831
$498$	8.10953e13	0.118641
$499$	1.37256e15	1.98600	0.993001	−	0.118109i	$-0.0376832\pi$
$499$	1.37256e15	1.98600	0.993001	+	0.118109i	$0.0376832\pi$
$500$	4.14411e13	0.0593056
$501$	1.46900e14	0.207928
$502$	4.92337e14	0.689275
$503$	−2.53209e14	−0.350635	−0.175317	−	0.984512i	$-0.556095\pi$
$503$	−2.53209e14	−0.350635	−0.175317	+	0.984512i	$0.556095\pi$
$504$	−1.19402e14	−0.163548
$505$	−5.53125e11	−0.000749412 0
$506$	−5.02682e14	−0.673698
$507$	−4.34482e14	−0.576007
$508$	1.41140e15	1.85097
$509$	−6.32882e14	−0.821060	−0.410530	−	0.911847i	$-0.634656\pi$
$509$	−6.32882e14	−0.821060	−0.410530	+	0.911847i	$0.634656\pi$
$510$	1.24553e13	0.0159852
$511$	−7.61647e13	−0.0967027
$512$	−1.01351e15	−1.27304
$513$	−1.23981e14	−0.154067
$514$	1.53734e15	1.89004
$515$	3.13225e12	0.00380993
$516$	1.66105e14	0.199899
$517$	−2.43008e14	−0.289349
$518$	−2.71905e14	−0.320335
$519$	−6.33819e14	−0.738830
$520$	−3.36559e11	−0.000388189 0
$521$	1.46198e15	1.66853	0.834263	−	0.551366i	$-0.185893\pi$
$521$	1.46198e15	1.66853	0.834263	+	0.551366i	$0.185893\pi$
$522$	−6.49052e14	−0.732979
$523$	6.47747e14	0.723846	0.361923	−	0.932208i	$-0.382120\pi$
$523$	6.47747e14	0.723846	0.361923	+	0.932208i	$0.382120\pi$
$524$	5.64588e14	0.624324
$525$	−7.79951e14	−0.853476
$526$	−2.41056e14	−0.261034
$527$	−1.15648e15	−1.23931
$528$	6.31869e14	0.670102
$529$	−8.76261e14	−0.919660
$530$	4.08794e13	0.0424607
$531$	4.22156e13	0.0433963
$532$	−1.42287e15	−1.44760
$533$	−7.07805e13	−0.0712712
$534$	1.11646e15	1.11267
$535$	3.76945e13	0.0371819
$536$	−3.50747e14	−0.342443
$537$	6.30056e14	0.608864
$538$	−2.61218e15	−2.49862
$539$	−2.00020e15	−1.89380
$540$	−6.09085e12	−0.00570837
$541$	1.79622e15	1.66638	0.833191	−	0.552985i	$-0.186511\pi$
$541$	1.79622e15	1.66638	0.833191	+	0.552985i	$0.186511\pi$
$542$	2.04039e14	0.187377
$543$	2.89316e14	0.263010
$544$	1.20525e15	1.08464
$545$	3.04284e12	0.00271081
$546$	6.96254e13	0.0614057
$547$	3.15025e14	0.275052	0.137526	−	0.990498i	$-0.456085\pi$
$547$	3.15025e14	0.275052	0.137526	+	0.990498i	$0.456085\pi$
$548$	2.19837e15	1.90024
$549$	−2.95283e14	−0.252691
$550$	−2.80374e15	−2.37543
$551$	−1.40772e15	−1.18082
$552$	6.53627e13	0.0542832
$553$	3.38089e13	0.0277999
$554$	3.37888e15	2.75087
$555$	−2.52447e12	−0.00203497
$556$	1.24077e15	0.990333
$557$	1.05585e15	0.834444	0.417222	−	0.908805i	$-0.363004\pi$
$557$	1.05585e15	0.834444	0.417222	+	0.908805i	$0.363004\pi$
$558$	1.02814e15	0.804574
$559$	−1.76289e13	−0.0136603
$560$	3.40494e13	0.0261262
$561$	−9.27313e14	−0.704581
$562$	−2.13758e15	−1.60832
$563$	2.02103e15	1.50583	0.752916	−	0.658117i	$-0.228647\pi$
$563$	2.02103e15	1.50583	0.752916	+	0.658117i	$0.228647\pi$
$564$	1.73608e14	0.128096
$565$	−1.56902e13	−0.0114647
$566$	−2.29500e15	−1.66071
$567$	2.29336e14	0.164348
$568$	−5.24000e14	−0.371891
$569$	−3.45715e14	−0.242997	−0.121498	−	0.992592i	$-0.538770\pi$
$569$	−3.45715e14	−0.242997	−0.121498	+	0.992592i	$0.538770\pi$
$570$	−2.40164e13	−0.0167185
$571$	1.56621e15	1.07982	0.539911	−	0.841722i	$-0.318458\pi$
$571$	1.56621e15	1.07982	0.539911	+	0.841722i	$0.318458\pi$
$572$	1.37672e14	0.0940086
$573$	1.58840e15	1.07426
$574$	−4.86427e15	−3.25839
$575$	4.26957e14	0.283277
$576$	−7.02248e14	−0.461495
$577$	2.47269e15	1.60954	0.804771	−	0.593585i	$-0.202288\pi$
$577$	2.47269e15	1.60954	0.804771	+	0.593585i	$0.202288\pi$
$578$	9.57463e14	0.617332
$579$	−2.83986e14	−0.181370
$580$	−6.91575e13	−0.0437507
$581$	−3.25349e14	−0.203883
$582$	1.28631e15	0.798488
$583$	−3.04352e15	−1.87154
$584$	3.56009e13	0.0216865
$585$	6.46427e11	0.000390088 0
$586$	−6.05590e13	−0.0362028
$587$	4.42798e14	0.262238	0.131119	−	0.991367i	$-0.458143\pi$
$587$	4.42798e14	0.262238	0.131119	+	0.991367i	$0.458143\pi$
$588$	1.42897e15	0.838392
$589$	2.22993e15	1.29616
$590$	8.17758e12	0.00470911
$591$	−8.80120e14	−0.502124
$592$	−1.87098e14	−0.105755
$593$	2.62869e15	1.47210	0.736052	−	0.676925i	$-0.236688\pi$
$593$	2.62869e15	1.47210	0.736052	+	0.676925i	$0.236688\pi$
$594$	8.24407e14	0.457421
$595$	−4.99700e13	−0.0274704
$596$	1.07777e15	0.587047
$597$	7.80538e14	0.421245
$598$	−3.81140e13	−0.0203811
$599$	1.68909e15	0.894966	0.447483	−	0.894293i	$-0.352321\pi$
$599$	1.68909e15	0.894966	0.447483	+	0.894293i	$0.352321\pi$
$600$	3.64565e14	0.191400
$601$	2.39749e15	1.24723	0.623615	−	0.781731i	$-0.285663\pi$
$601$	2.39749e15	1.24723	0.623615	+	0.781731i	$0.285663\pi$
$602$	−1.21152e15	−0.624525
$603$	6.73679e14	0.344118
$604$	1.97729e15	1.00085
$605$	−7.45843e13	−0.0374104
$606$	−5.34856e13	−0.0265851
$607$	−1.71531e15	−0.844899	−0.422450	−	0.906386i	$-0.638830\pi$
$607$	−1.71531e15	−0.844899	−0.422450	+	0.906386i	$0.638830\pi$
$608$	−2.32398e15	−1.13439
$609$	2.60396e15	1.25962
$610$	−5.71992e13	−0.0274205
$611$	−1.84252e13	−0.00875357
$612$	6.62485e14	0.311920
$613$	−1.32113e15	−0.616473	−0.308237	−	0.951310i	$-0.599739\pi$
$613$	−1.32113e15	−0.616473	−0.308237	+	0.951310i	$0.599739\pi$
$614$	−1.55922e15	−0.721076
$615$	−4.51616e13	−0.0206993
$616$	1.72202e15	0.782247
$617$	1.03999e15	0.468233	0.234116	−	0.972209i	$-0.424780\pi$
$617$	1.03999e15	0.468233	0.234116	+	0.972209i	$0.424780\pi$
$618$	3.02880e14	0.135155
$619$	2.90474e15	1.28472	0.642361	−	0.766402i	$-0.277955\pi$
$619$	2.90474e15	1.28472	0.642361	+	0.766402i	$0.277955\pi$
$620$	1.09550e14	0.0480242
$621$	−1.25542e14	−0.0545488
$622$	−4.59898e15	−1.98068
$623$	−4.47916e15	−1.91211
$624$	4.79092e13	0.0202723
$625$	2.37998e15	0.998234
$626$	−4.55670e15	−1.89449
$627$	1.78805e15	0.736900
$628$	8.39530e14	0.342971
$629$	2.74579e14	0.111196
$630$	4.44247e13	0.0178341
$631$	−5.42978e14	−0.216083	−0.108042	−	0.994146i	$-0.534458\pi$
$631$	−5.42978e14	−0.216083	−0.108042	+	0.994146i	$0.534458\pi$
$632$	−1.58030e13	−0.00623440
$633$	−1.75881e15	−0.687859
$634$	2.66367e15	1.03274
$635$	−9.55756e13	−0.0367360
$636$	2.17434e15	0.828538
$637$	−1.51658e14	−0.0572925
$638$	9.36060e15	3.50582
$639$	1.00645e15	0.373711
$640$	−4.26419e13	−0.0156981
$641$	−4.49603e15	−1.64101	−0.820503	−	0.571642i	$-0.806307\pi$
$641$	−4.49603e15	−1.64101	−0.820503	+	0.571642i	$0.806307\pi$
$642$	3.64495e15	1.31901
$643$	−1.07318e15	−0.385044	−0.192522	−	0.981293i	$-0.561667\pi$
$643$	−1.07318e15	−0.385044	−0.192522	+	0.981293i	$0.561667\pi$
$644$	−1.44078e15	−0.512536
$645$	−1.12482e13	−0.00396738
$646$	2.61220e15	0.913540
$647$	3.03792e15	1.05342	0.526712	−	0.850044i	$-0.323425\pi$
$647$	3.03792e15	1.05342	0.526712	+	0.850044i	$0.323425\pi$
$648$	−1.07196e14	−0.0368567
$649$	−6.08831e14	−0.207564
$650$	−2.12583e14	−0.0718631
$651$	−4.12485e15	−1.38265
$652$	1.31214e15	0.436132
$653$	5.16352e15	1.70186	0.850930	−	0.525279i	$-0.176039\pi$
$653$	5.16352e15	1.70186	0.850930	+	0.525279i	$0.176039\pi$
$654$	2.94235e14	0.0961648
$655$	−3.82323e13	−0.0123909
$656$	−3.34710e15	−1.07572
$657$	−6.83784e13	−0.0217926
$658$	−1.26624e15	−0.400197
$659$	−3.90470e15	−1.22382	−0.611910	−	0.790927i	$-0.709599\pi$
$659$	−3.90470e15	−1.22382	−0.611910	+	0.790927i	$0.709599\pi$
$660$	8.78419e13	0.0273030
$661$	−5.81767e15	−1.79325	−0.896626	−	0.442789i	$-0.853989\pi$
$661$	−5.81767e15	−1.79325	−0.896626	+	0.442789i	$0.853989\pi$
$662$	−2.79648e15	−0.854856
$663$	−7.03102e13	−0.0213154
$664$	1.52075e14	0.0457228
$665$	9.63524e13	0.0287305
$666$	−2.44109e14	−0.0721897
$667$	−1.42544e15	−0.418079
$668$	1.51354e15	0.440276
$669$	2.98373e15	0.860826
$670$	1.30498e14	0.0373417
$671$	4.25855e15	1.20862
$672$	4.29881e15	1.21009
$673$	4.90313e14	0.136896	0.0684480	−	0.997655i	$-0.478195\pi$
$673$	4.90313e14	0.136896	0.0684480	+	0.997655i	$0.478195\pi$
$674$	2.67259e15	0.740121
$675$	−7.00218e14	−0.192337
$676$	−4.47657e15	−1.21966
$677$	−5.37352e15	−1.45218	−0.726091	−	0.687599i	$-0.758665\pi$
$677$	−5.37352e15	−1.45218	−0.726091	+	0.687599i	$0.758665\pi$
$678$	−1.51720e15	−0.406705
$679$	−5.16058e15	−1.37219
$680$	2.33569e13	0.00616051
$681$	8.06471e14	0.210999
$682$	−1.48279e16	−3.84826
$683$	3.66009e15	0.942276	0.471138	−	0.882059i	$-0.343843\pi$
$683$	3.66009e15	0.942276	0.471138	+	0.882059i	$0.343843\pi$
$684$	−1.27741e15	−0.326228
$685$	−1.48867e14	−0.0377139
$686$	−1.64815e15	−0.414204
$687$	2.05192e15	0.511562
$688$	−8.33646e14	−0.206179
$689$	−2.30764e14	−0.0566191
$690$	−2.43187e13	−0.00591931
$691$	−6.87405e15	−1.65991	−0.829953	−	0.557833i	$-0.811633\pi$
$691$	−6.87405e15	−1.65991	−0.829953	+	0.557833i	$0.811633\pi$
$692$	−6.53039e15	−1.56443
$693$	−3.30747e15	−0.786074
$694$	−1.66941e14	−0.0393629
$695$	−8.40216e13	−0.0196551
$696$	−1.21714e15	−0.282481
$697$	4.91211e15	1.13107
$698$	−7.73889e15	−1.76796
$699$	−8.66461e14	−0.196392
$700$	−8.03603e15	−1.80718
$701$	3.87733e15	0.865134	0.432567	−	0.901602i	$-0.357608\pi$
$701$	3.87733e15	0.865134	0.432567	+	0.901602i	$0.357608\pi$
$702$	6.25077e13	0.0138382
$703$	−5.29446e14	−0.116297
$704$	1.01278e16	2.20732
$705$	−1.17562e13	−0.00254231
$706$	−8.46496e15	−1.81635
$707$	2.14581e14	0.0456862
$708$	4.34957e14	0.0918890
$709$	−7.08025e15	−1.48421	−0.742103	−	0.670286i	$-0.766172\pi$
$709$	−7.08025e15	−1.48421	−0.742103	+	0.670286i	$0.766172\pi$
$710$	1.94959e14	0.0405529
$711$	3.03527e13	0.00626490
$712$	2.09365e15	0.428809
$713$	2.25801e15	0.458915
$714$	−4.83195e15	−0.974502
$715$	−9.32275e12	−0.00186578
$716$	6.49162e15	1.28923
$717$	1.02557e15	0.202120
$718$	9.78107e15	1.91294
$719$	2.44004e15	0.473573	0.236787	−	0.971562i	$-0.423906\pi$
$719$	2.44004e15	0.473573	0.236787	+	0.971562i	$0.423906\pi$
$720$	3.05686e13	0.00588771
$721$	−1.21514e15	−0.232263
$722$	2.82229e15	0.535362
$723$	1.95554e15	0.368134
$724$	2.98089e15	0.556908
$725$	−7.95051e15	−1.47413
$726$	−7.21209e15	−1.32712
$727$	1.00123e15	0.182849	0.0914247	−	0.995812i	$-0.470858\pi$
$727$	1.00123e15	0.182849	0.0914247	+	0.995812i	$0.470858\pi$
$728$	1.30566e14	0.0236650
$729$	2.05891e14	0.0370370
$730$	−1.32456e13	−0.00236481
$731$	1.22344e15	0.216788
$732$	−3.04237e15	−0.535058
$733$	3.47124e15	0.605917	0.302958	−	0.953004i	$-0.402026\pi$
$733$	3.47124e15	0.605917	0.302958	+	0.953004i	$0.402026\pi$
$734$	1.59294e16	2.75976
$735$	−9.67656e13	−0.0166395
$736$	−2.35323e15	−0.401640
$737$	−9.71578e15	−1.64591
$738$	−4.36701e15	−0.734300
$739$	−6.59520e15	−1.10074	−0.550369	−	0.834922i	$-0.685513\pi$
$739$	−6.59520e15	−1.10074	−0.550369	+	0.834922i	$0.685513\pi$
$740$	−2.60102e13	−0.00430892
$741$	1.35573e14	0.0222932
$742$	−1.58589e16	−2.58852
$743$	7.66685e15	1.24216	0.621081	−	0.783746i	$-0.286694\pi$
$743$	7.66685e15	1.24216	0.621081	+	0.783746i	$0.286694\pi$
$744$	1.92804e15	0.310073
$745$	−7.29836e13	−0.0116511
$746$	1.07425e16	1.70232
$747$	−2.92089e14	−0.0459465
$748$	−9.55434e15	−1.49191
$749$	−1.46233e16	−2.26671
$750$	−2.71358e14	−0.0417548
$751$	8.14775e15	1.24457	0.622283	−	0.782792i	$-0.286205\pi$
$751$	8.14775e15	1.24457	0.622283	+	0.782792i	$0.286205\pi$
$752$	−8.71299e14	−0.132120
$753$	−1.77330e15	−0.266938
$754$	7.09733e14	0.106060
$755$	−1.33896e14	−0.0198637
$756$	2.36290e15	0.347997
$757$	−5.62091e15	−0.821825	−0.410913	−	0.911675i	$-0.634790\pi$
$757$	−5.62091e15	−0.821825	−0.410913	+	0.911675i	$0.634790\pi$
$758$	−1.62102e16	−2.35292
$759$	1.81056e15	0.260905
$760$	−4.50370e13	−0.00644310
$761$	−8.24946e15	−1.17168	−0.585842	−	0.810426i	$-0.699236\pi$
$761$	−8.24946e15	−1.17168	−0.585842	+	0.810426i	$0.699236\pi$
$762$	−9.24189e15	−1.30319
$763$	−1.18045e15	−0.165258
$764$	1.63657e16	2.27468
$765$	−4.48616e13	−0.00619066
$766$	−1.64862e16	−2.25872
$767$	−4.61624e13	−0.00627934
$768$	1.79518e15	0.242449
$769$	5.54028e15	0.742911	0.371455	−	0.928451i	$-0.378859\pi$
$769$	5.54028e15	0.742911	0.371455	+	0.928451i	$0.378859\pi$
$770$	−6.40691e14	−0.0853001
$771$	−5.53719e15	−0.731965
$772$	−2.92597e15	−0.384039
$773$	9.42666e14	0.122849	0.0614244	−	0.998112i	$-0.480436\pi$
$773$	9.42666e14	0.122849	0.0614244	+	0.998112i	$0.480436\pi$
$774$	−1.08767e15	−0.140741
$775$	1.25942e16	1.61812
$776$	2.41216e15	0.307728
$777$	9.79349e14	0.124057
$778$	−9.67512e15	−1.21694
$779$	−9.47157e15	−1.18295
$780$	6.66030e12	0.000825987 0
$781$	−1.45149e16	−1.78745
$782$	2.64508e15	0.323446
$783$	2.33776e15	0.283864
$784$	−7.17167e15	−0.864733
$785$	−5.68505e13	−0.00680693
$786$	−3.69696e15	−0.439562
$787$	4.74422e15	0.560149	0.280074	−	0.959978i	$-0.409641\pi$
$787$	4.74422e15	0.560149	0.280074	+	0.959978i	$0.409641\pi$
$788$	−9.06809e15	−1.06322
$789$	8.68236e14	0.101091
$790$	5.87962e12	0.000679830 0
$791$	6.08691e15	0.698918
$792$	1.54598e15	0.176285
$793$	3.22889e14	0.0365638
$794$	−1.11202e15	−0.125055
$795$	−1.47240e14	−0.0164439
$796$	8.04207e15	0.891961
$797$	1.86196e15	0.205093	0.102546	−	0.994728i	$-0.467301\pi$
$797$	1.86196e15	0.205093	0.102546	+	0.994728i	$0.467301\pi$
$798$	9.31701e15	1.01920
$799$	1.27869e15	0.138918
$800$	−1.31253e16	−1.41617
$801$	−4.02126e15	−0.430907
$802$	6.09856e15	0.649036
$803$	9.86151e14	0.104234
$804$	6.94108e15	0.728650
$805$	9.75653e13	0.0101723
$806$	−1.12427e15	−0.116420
$807$	9.40857e15	0.967652
$808$	−1.00299e14	−0.0102456
$809$	1.77383e16	1.79968	0.899838	−	0.436225i	$-0.143685\pi$
$809$	1.77383e16	1.79968	0.899838	+	0.436225i	$0.143685\pi$
$810$	3.98832e13	0.00401904
$811$	1.29473e16	1.29587	0.647937	−	0.761694i	$-0.275632\pi$
$811$	1.29473e16	1.29587	0.647937	+	0.761694i	$0.275632\pi$
$812$	2.68292e16	2.66716
$813$	−7.34907e14	−0.0725662
$814$	3.52053e15	0.345282
$815$	−8.88542e13	−0.00865587
$816$	−3.32486e15	−0.321720
$817$	−2.35904e15	−0.226732
$818$	−2.54008e16	−2.42496
$819$	−2.50777e14	−0.0237808
$820$	−4.65311e14	−0.0438296
$821$	−1.79237e16	−1.67702	−0.838512	−	0.544883i	$-0.816574\pi$
$821$	−1.79237e16	−1.67702	−0.838512	+	0.544883i	$0.816574\pi$
$822$	−1.43951e16	−1.33788
$823$	8.64977e15	0.798556	0.399278	−	0.916830i	$-0.369261\pi$
$823$	8.64977e15	0.798556	0.399278	+	0.916830i	$0.369261\pi$
$824$	5.67978e14	0.0520873
$825$	1.00985e16	0.919942
$826$	−3.17244e15	−0.287080
$827$	1.66067e16	1.49281	0.746403	−	0.665494i	$-0.231779\pi$
$827$	1.66067e16	1.49281	0.746403	+	0.665494i	$0.231779\pi$
$828$	−1.29349e15	−0.115504
$829$	1.98415e14	0.0176005	0.00880025	−	0.999961i	$-0.497199\pi$
$829$	1.98415e14	0.0176005	0.00880025	+	0.999961i	$0.497199\pi$
$830$	−5.65806e13	−0.00498584
$831$	−1.21701e16	−1.06534
$832$	7.67903e14	0.0667772
$833$	1.05249e16	0.909226
$834$	−8.12466e15	−0.697255
$835$	−1.02493e14	−0.00873812
$836$	1.84227e16	1.56034
$837$	−3.70317e15	−0.311590
$838$	2.13449e16	1.78423
$839$	2.10750e16	1.75015	0.875077	−	0.483984i	$-0.160811\pi$
$839$	2.10750e16	1.75015	0.875077	+	0.483984i	$0.160811\pi$
$840$	8.33078e13	0.00687305
$841$	1.43432e16	1.17562
$842$	7.85510e15	0.639640
$843$	7.69914e15	0.622860
$844$	−1.81215e16	−1.45650
$845$	3.03141e14	0.0242065
$846$	−1.13679e15	−0.0901872
$847$	2.89345e16	2.28064
$848$	−1.09125e16	−0.854569
$849$	8.26615e15	0.643148
$850$	1.47531e16	1.14046
$851$	−5.36111e14	−0.0411758
$852$	1.03697e16	0.791309
$853$	3.17382e15	0.240637	0.120319	−	0.992735i	$-0.461608\pi$
$853$	3.17382e15	0.240637	0.120319	+	0.992735i	$0.461608\pi$
$854$	2.21901e16	1.67163
$855$	8.65024e13	0.00647462
$856$	6.83523e15	0.508332
$857$	−1.00250e16	−0.740784	−0.370392	−	0.928876i	$-0.620777\pi$
$857$	−1.00250e16	−0.740784	−0.370392	+	0.928876i	$0.620777\pi$
$858$	−9.01484e14	−0.0661878
$859$	−3.59308e15	−0.262123	−0.131061	−	0.991374i	$-0.541839\pi$
$859$	−3.59308e15	−0.262123	−0.131061	+	0.991374i	$0.541839\pi$
$860$	−1.15893e14	−0.00840069
$861$	1.75202e16	1.26189
$862$	7.96093e15	0.569737
$863$	2.13704e16	1.51968	0.759841	−	0.650109i	$-0.225277\pi$
$863$	2.13704e16	1.51968	0.759841	+	0.650109i	$0.225277\pi$
$864$	3.85934e15	0.272702
$865$	4.42219e14	0.0310491
$866$	2.53289e16	1.76713
$867$	−3.44860e15	−0.239077
$868$	−4.24994e16	−2.92768
$869$	−4.37745e14	−0.0299649
$870$	4.52847e14	0.0308032
$871$	−7.36664e14	−0.0497931
$872$	5.51766e14	0.0370608
$873$	−4.63302e15	−0.309233
$874$	−5.10027e15	−0.338283
$875$	1.08867e15	0.0717552
$876$	−7.04520e14	−0.0461446
$877$	−1.44168e16	−0.938362	−0.469181	−	0.883102i	$-0.655451\pi$
$877$	−1.44168e16	−0.938362	−0.469181	+	0.883102i	$0.655451\pi$
$878$	2.16617e15	0.140111
$879$	2.18122e14	0.0140204
$880$	−4.40859e14	−0.0281608
$881$	−2.28978e15	−0.145354	−0.0726769	−	0.997356i	$-0.523154\pi$
$881$	−2.28978e15	−0.145354	−0.0726769	+	0.997356i	$0.523154\pi$
$882$	−9.35696e15	−0.590279
$883$	−1.36279e16	−0.854366	−0.427183	−	0.904165i	$-0.640494\pi$
$883$	−1.36279e16	−0.854366	−0.427183	+	0.904165i	$0.640494\pi$
$884$	−7.24423e14	−0.0451341
$885$	−2.94540e13	−0.00182372
$886$	−2.72075e16	−1.67418
$887$	−2.29093e16	−1.40098	−0.700488	−	0.713664i	$-0.747034\pi$
$887$	−2.29093e16	−1.40098	−0.700488	+	0.713664i	$0.747034\pi$
$888$	−4.57767e14	−0.0278210
$889$	3.70779e16	2.23952
$890$	−7.78960e14	−0.0467595
$891$	−2.96935e15	−0.177147
$892$	3.07421e16	1.82275
$893$	−2.46559e15	−0.145290
$894$	−7.05731e15	−0.413317
$895$	−4.39593e14	−0.0255873
$896$	1.65426e16	0.956998
$897$	1.37279e14	0.00789308
$898$	3.94642e16	2.25519
$899$	−4.20471e16	−2.38813
$900$	−7.21451e15	−0.407261
$901$	1.60149e16	0.898539
$902$	6.29808e16	3.51214
$903$	4.36366e15	0.241862
$904$	−2.84514e15	−0.156739
$905$	−2.01857e14	−0.0110529
$906$	−1.29474e16	−0.704657
$907$	−3.19683e16	−1.72934	−0.864668	−	0.502344i	$-0.832471\pi$
$907$	−3.19683e16	−1.72934	−0.864668	+	0.502344i	$0.832471\pi$
$908$	8.30927e15	0.446777
$909$	1.92645e14	0.0102957
$910$	−4.85781e13	−0.00258055
$911$	4.71409e15	0.248912	0.124456	−	0.992225i	$-0.460281\pi$
$911$	4.71409e15	0.248912	0.124456	+	0.992225i	$0.460281\pi$
$912$	6.41102e15	0.336477
$913$	4.21250e15	0.219761
$914$	−3.04569e16	−1.57936
$915$	2.06020e14	0.0106193
$916$	2.11414e16	1.08320
$917$	1.48320e16	0.755383
$918$	−4.33799e15	−0.219611
$919$	−2.18519e16	−1.09965	−0.549825	−	0.835280i	$-0.685306\pi$
$919$	−2.18519e16	−1.09965	−0.549825	+	0.835280i	$0.685306\pi$
$920$	−4.56039e13	−0.00228123
$921$	5.61600e15	0.279254
$922$	4.60423e16	2.27582
$923$	−1.10054e15	−0.0540750
$924$	−3.40777e16	−1.66446
$925$	−2.99019e15	−0.145184
$926$	2.07796e16	1.00294
$927$	−1.09091e15	−0.0523422
$928$	4.38203e16	2.09007
$929$	2.01713e16	0.956418	0.478209	−	0.878246i	$-0.341286\pi$
$929$	2.01713e16	0.956418	0.478209	+	0.878246i	$0.341286\pi$
$930$	−7.17342e14	−0.0338119
$931$	−2.02942e16	−0.950932
$932$	−8.92736e15	−0.415849
$933$	1.65646e16	0.767066
$934$	1.53699e15	0.0707561
$935$	6.46992e14	0.0296098
$936$	1.17218e14	0.00533308
$937$	−1.57861e16	−0.714015	−0.357007	−	0.934102i	$-0.616203\pi$
$937$	−1.57861e16	−0.714015	−0.357007	+	0.934102i	$0.616203\pi$
$938$	−5.06260e16	−2.27645
$939$	1.64123e16	0.733685
$940$	−1.21127e14	−0.00538318
$941$	−9.22140e15	−0.407431	−0.203715	−	0.979030i	$-0.565302\pi$
$941$	−9.22140e15	−0.407431	−0.203715	+	0.979030i	$0.565302\pi$
$942$	−5.49729e15	−0.241473
$943$	−9.59080e15	−0.418833
$944$	−2.18295e15	−0.0947760
$945$	−1.60009e14	−0.00690668
$946$	1.56863e16	0.673162
$947$	4.52101e16	1.92890	0.964451	−	0.264260i	$-0.0851278\pi$
$947$	4.52101e16	1.92890	0.964451	+	0.264260i	$0.0851278\pi$
$948$	3.12731e14	0.0132655
$949$	7.47714e13	0.00315334
$950$	−2.84471e16	−1.19277
$951$	−9.59402e15	−0.399952
$952$	−9.06117e15	−0.375561
$953$	−1.36142e16	−0.561025	−0.280512	−	0.959850i	$-0.590504\pi$
$953$	−1.36142e16	−0.561025	−0.280512	+	0.959850i	$0.590504\pi$
$954$	−1.42377e16	−0.583341
$955$	−1.10824e15	−0.0451455
$956$	1.05667e16	0.427976
$957$	−3.37150e16	−1.35771
$958$	−2.09703e16	−0.839641
$959$	5.77521e16	2.29914
$960$	4.89962e14	0.0193942
$961$	4.11971e16	1.62139
$962$	2.66931e14	0.0104457
$963$	−1.31284e16	−0.510819
$964$	2.01484e16	0.779501
$965$	1.98138e14	0.00762199
$966$	9.43429e15	0.360857
$967$	−2.03858e16	−0.775322	−0.387661	−	0.921802i	$-0.626717\pi$
$967$	−2.03858e16	−0.775322	−0.387661	+	0.921802i	$0.626717\pi$
$968$	−1.35245e16	−0.511456
$969$	−9.40864e15	−0.353790
$970$	−8.97464e14	−0.0335562
$971$	−6.86008e15	−0.255049	−0.127524	−	0.991835i	$-0.540703\pi$
$971$	−6.86008e15	−0.255049	−0.127524	+	0.991835i	$0.540703\pi$
$972$	2.12135e15	0.0784237
$973$	3.25956e16	1.19823
$974$	1.43040e16	0.522857
$975$	7.65683e14	0.0278307
$976$	1.52690e16	0.551868
$977$	−8.98868e15	−0.323054	−0.161527	−	0.986868i	$-0.551642\pi$
$977$	−8.98868e15	−0.323054	−0.161527	+	0.986868i	$0.551642\pi$
$978$	−8.59195e15	−0.307063
$979$	5.79945e16	2.06102
$980$	−9.96999e14	−0.0352331
$981$	−1.05977e15	−0.0372421
$982$	−3.10904e16	−1.08646
$983$	−3.43270e16	−1.19286	−0.596432	−	0.802664i	$-0.703415\pi$
$983$	−3.43270e16	−1.19286	−0.596432	+	0.802664i	$0.703415\pi$
$984$	−8.18927e15	−0.282991
$985$	6.14065e14	0.0211016
$986$	−4.92550e16	−1.68317
$987$	4.56075e15	0.154986
$988$	1.39684e15	0.0472044
$989$	−2.38873e15	−0.0802764
$990$	−5.75194e14	−0.0192230
$991$	−4.41564e16	−1.46754	−0.733768	−	0.679400i	$-0.762240\pi$
$991$	−4.41564e16	−1.46754	−0.733768	+	0.679400i	$0.762240\pi$
$992$	−6.94144e16	−2.29422
$993$	1.00724e16	0.331063
$994$	−7.56329e16	−2.47221
$995$	−5.44586e14	−0.0177027
$996$	−3.00947e15	−0.0972889
$997$	8.85676e15	0.284742	0.142371	−	0.989813i	$-0.454527\pi$
$997$	8.85676e15	0.284742	0.142371	+	0.989813i	$0.454527\pi$
$998$	−9.26017e16	−2.96074
$999$	8.79232e14	0.0279572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +11438.4 q^{10} -851602. q^{11} +608396. q^{12} -64569.7 q^{13} -4.43745e6 q^{14} -41198.8 q^{15} -3.05340e6 q^{16} +4.48109e6 q^{17} -3.98381e6 q^{18} -8.64046e6 q^{19} -424482. q^{20} +1.59828e7 q^{21} +5.74544e7 q^{22} -8.74923e6 q^{23} -7.47068e6 q^{24} -4.87994e7 q^{25} +4.35627e6 q^{26} +1.43489e7 q^{27} +1.64675e8 q^{28} +1.62922e8 q^{29} +2.77953e6 q^{30} -2.58081e8 q^{31} +2.68964e8 q^{32} -2.06939e8 q^{33} -3.02322e8 q^{34} -1.11513e7 q^{35} +1.47840e8 q^{36} +6.12752e7 q^{37} +5.82939e8 q^{38} -1.56904e7 q^{39} +5.21234e6 q^{40} +1.09619e9 q^{41} -1.07830e9 q^{42} +2.73022e8 q^{43} -2.13215e9 q^{44} -1.00113e7 q^{45} +5.90277e8 q^{46} +2.85354e8 q^{47} -7.41977e8 q^{48} +2.34875e9 q^{49} +3.29231e9 q^{50} +1.08890e9 q^{51} -1.61662e8 q^{52} +3.57388e9 q^{53} -9.68066e8 q^{54} +1.44383e8 q^{55} -2.02209e9 q^{56} -2.09963e9 q^{57} -1.09917e10 q^{58} +7.14924e8 q^{59} -1.03149e8 q^{60} -5.00064e9 q^{61} +1.74117e10 q^{62} +3.88382e9 q^{63} -1.18926e10 q^{64} +1.09473e7 q^{65} +1.39614e10 q^{66} +1.14088e10 q^{67} +1.12192e10 q^{68} -2.12606e9 q^{69} +7.52336e8 q^{70} +1.70442e10 q^{71} -1.81538e9 q^{72} -1.15800e9 q^{73} -4.13400e9 q^{74} -1.18582e10 q^{75} -2.16330e10 q^{76} -5.60123e10 q^{77} +1.05857e9 q^{78} +5.14025e8 q^{79} +5.17682e8 q^{80} +3.48678e9 q^{81} -7.39556e10 q^{82} -4.94656e9 q^{83} +4.00160e10 q^{84} -7.59735e8 q^{85} -1.84197e10 q^{86} +3.95901e10 q^{87} +2.61813e10 q^{88} -6.81005e10 q^{89} +6.75425e8 q^{90} -4.24693e9 q^{91} -2.19053e10 q^{92} -6.27136e10 q^{93} -1.92517e10 q^{94} +1.46493e9 q^{95} +6.53583e10 q^{96} -7.84607e10 q^{97} -1.58461e11 q^{98} -5.02863e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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