LMFDB - Embedded newform 177.12.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-39.1439 q^{2} +243.000 q^{3} -515.752 q^{4} +158.720 q^{5} -9511.98 q^{6} -70159.1 q^{7} +100355. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-39.1439 q^{2} +243.000 q^{3} -515.752 q^{4} +158.720 q^{5} -9511.98 q^{6} -70159.1 q^{7} +100355. q^{8} +59049.0 q^{9} -6212.92 q^{10} +492429. q^{11} -125328. q^{12} +2.38920e6 q^{13} +2.74630e6 q^{14} +38568.9 q^{15} -2.87204e6 q^{16} +4.34922e6 q^{17} -2.31141e6 q^{18} +1.74914e7 q^{19} -81860.1 q^{20} -1.70487e7 q^{21} -1.92756e7 q^{22} +3.13914e6 q^{23} +2.43864e7 q^{24} -4.88029e7 q^{25} -9.35227e7 q^{26} +1.43489e7 q^{27} +3.61847e7 q^{28} -4.79247e7 q^{29} -1.50974e6 q^{30} -6.76298e7 q^{31} -9.31047e7 q^{32} +1.19660e8 q^{33} -1.70246e8 q^{34} -1.11356e7 q^{35} -3.04546e7 q^{36} -2.35146e8 q^{37} -6.84681e8 q^{38} +5.80576e8 q^{39} +1.59284e7 q^{40} -2.65713e8 q^{41} +6.67352e8 q^{42} +5.47895e8 q^{43} -2.53971e8 q^{44} +9.37225e6 q^{45} -1.22878e8 q^{46} -7.16085e8 q^{47} -6.97907e8 q^{48} +2.94498e9 q^{49} +1.91034e9 q^{50} +1.05686e9 q^{51} -1.23224e9 q^{52} -1.02867e7 q^{53} -5.61673e8 q^{54} +7.81582e7 q^{55} -7.04084e9 q^{56} +4.25040e9 q^{57} +1.87596e9 q^{58} +7.14924e8 q^{59} -1.98920e7 q^{60} -9.31011e8 q^{61} +2.64730e9 q^{62} -4.14283e9 q^{63} +9.52643e9 q^{64} +3.79213e8 q^{65} -4.68397e9 q^{66} +7.59551e9 q^{67} -2.24312e9 q^{68} +7.62811e8 q^{69} +4.35893e8 q^{70} +1.44444e9 q^{71} +5.92588e9 q^{72} +1.34828e10 q^{73} +9.20456e9 q^{74} -1.18591e10 q^{75} -9.02121e9 q^{76} -3.45484e10 q^{77} -2.27260e10 q^{78} +2.11165e10 q^{79} -4.55850e8 q^{80} +3.48678e9 q^{81} +1.04010e10 q^{82} -4.40162e10 q^{83} +8.79289e9 q^{84} +6.90307e8 q^{85} -2.14468e10 q^{86} -1.16457e10 q^{87} +4.94179e10 q^{88} -6.64139e10 q^{89} -3.66867e8 q^{90} -1.67624e11 q^{91} -1.61902e9 q^{92} -1.64340e10 q^{93} +2.80304e10 q^{94} +2.77623e9 q^{95} -2.26244e10 q^{96} +6.49449e10 q^{97} -1.15278e11 q^{98} +2.90774e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−39.1439	−0.864967	−0.432483	−	0.901642i	$-0.642363\pi$
$2$	−39.1439	−0.864967	−0.432483	+	0.901642i	$0.642363\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−515.752	−0.251832
$5$	158.720	0.0227141	0.0113571	−	0.999936i	$-0.496385\pi$
$5$	158.720	0.0227141	0.0113571	+	0.999936i	$0.496385\pi$
$6$	−9511.98	−0.499389
$7$	−70159.1	−1.57777	−0.788887	−	0.614538i	$-0.789342\pi$
$7$	−70159.1	−1.57777	−0.788887	+	0.614538i	$0.789342\pi$
$8$	100355.	1.08279
$9$	59049.0	0.333333
$10$	−6212.92	−0.0196470
$11$	492429.	0.921900	0.460950	−	0.887426i	$-0.347509\pi$
$11$	492429.	0.921900	0.460950	+	0.887426i	$0.347509\pi$
$12$	−125328.	−0.145395
$13$	2.38920e6	1.78470	0.892348	−	0.451348i	$-0.149057\pi$
$13$	2.38920e6	1.78470	0.892348	+	0.451348i	$0.149057\pi$
$14$	2.74630e6	1.36472
$15$	38568.9	0.0131140
$16$	−2.87204e6	−0.684748
$17$	4.34922e6	0.742920	0.371460	−	0.928449i	$-0.378857\pi$
$17$	4.34922e6	0.742920	0.371460	+	0.928449i	$0.378857\pi$
$18$	−2.31141e6	−0.288322
$19$	1.74914e7	1.62061	0.810305	−	0.586008i	$-0.199301\pi$
$19$	1.74914e7	1.62061	0.810305	+	0.586008i	$0.199301\pi$
$20$	−81860.1	−0.00572015
$21$	−1.70487e7	−0.910928
$22$	−1.92756e7	−0.797413
$23$	3.13914e6	0.101697	0.0508484	−	0.998706i	$-0.483807\pi$
$23$	3.13914e6	0.101697	0.0508484	+	0.998706i	$0.483807\pi$
$24$	2.43864e7	0.625151
$25$	−4.88029e7	−0.999484
$26$	−9.35227e7	−1.54370
$27$	1.43489e7	0.192450
$28$	3.61847e7	0.397334
$29$	−4.79247e7	−0.433881	−0.216940	−	0.976185i	$-0.569608\pi$
$29$	−4.79247e7	−0.433881	−0.216940	+	0.976185i	$0.569608\pi$
$30$	−1.50974e6	−0.0113432
$31$	−6.76298e7	−0.424276	−0.212138	−	0.977240i	$-0.568043\pi$
$31$	−6.76298e7	−0.424276	−0.212138	+	0.977240i	$0.568043\pi$
$32$	−9.31047e7	−0.490509
$33$	1.19660e8	0.532259
$34$	−1.70246e8	−0.642602
$35$	−1.11356e7	−0.0358378
$36$	−3.04546e7	−0.0839440
$37$	−2.35146e8	−0.557480	−0.278740	−	0.960367i	$-0.589917\pi$
$37$	−2.35146e8	−0.557480	−0.278740	+	0.960367i	$0.589917\pi$
$38$	−6.84681e8	−1.40177
$39$	5.80576e8	1.03039
$40$	1.59284e7	0.0245947
$41$	−2.65713e8	−0.358180	−0.179090	−	0.983833i	$-0.557315\pi$
$41$	−2.65713e8	−0.358180	−0.179090	+	0.983833i	$0.557315\pi$
$42$	6.67352e8	0.787923
$43$	5.47895e8	0.568356	0.284178	−	0.958771i	$-0.408279\pi$
$43$	5.47895e8	0.568356	0.284178	+	0.958771i	$0.408279\pi$
$44$	−2.53971e8	−0.232164
$45$	9.37225e6	0.00757138
$46$	−1.22878e8	−0.0879644
$47$	−7.16085e8	−0.455435	−0.227717	−	0.973727i	$-0.573126\pi$
$47$	−7.16085e8	−0.455435	−0.227717	+	0.973727i	$0.573126\pi$
$48$	−6.97907e8	−0.395340
$49$	2.94498e9	1.48937
$50$	1.91034e9	0.864521
$51$	1.05686e9	0.428925
$52$	−1.23224e9	−0.449444
$53$	−1.02867e7	−0.00337878	−0.00168939	−	0.999999i	$-0.500538\pi$
$53$	−1.02867e7	−0.00337878	−0.00168939	+	0.999999i	$0.500538\pi$
$54$	−5.61673e8	−0.166463
$55$	7.81582e7	0.0209402
$56$	−7.04084e9	−1.70840
$57$	4.25040e9	0.935660
$58$	1.87596e9	0.375293
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.98920e7	−0.00330253
$61$	−9.31011e8	−0.141137	−0.0705685	−	0.997507i	$-0.522481\pi$
$61$	−9.31011e8	−0.141137	−0.0705685	+	0.997507i	$0.522481\pi$
$62$	2.64730e9	0.366985
$63$	−4.14283e9	−0.525925
$64$	9.52643e9	1.10902
$65$	3.79213e8	0.0405378
$66$	−4.68397e9	−0.460387
$67$	7.59551e9	0.687299	0.343649	−	0.939098i	$-0.388337\pi$
$67$	7.59551e9	0.687299	0.343649	+	0.939098i	$0.388337\pi$
$68$	−2.24312e9	−0.187091
$69$	7.62811e8	0.0587147
$70$	4.35893e8	0.0309985
$71$	1.44444e9	0.0950121	0.0475060	−	0.998871i	$-0.484873\pi$
$71$	1.44444e9	0.0950121	0.0475060	+	0.998871i	$0.484873\pi$
$72$	5.92588e9	0.360931
$73$	1.34828e10	0.761212	0.380606	−	0.924737i	$-0.375715\pi$
$73$	1.34828e10	0.761212	0.380606	+	0.924737i	$0.375715\pi$
$74$	9.20456e9	0.482201
$75$	−1.18591e10	−0.577052
$76$	−9.02121e9	−0.408122
$77$	−3.45484e10	−1.45455
$78$	−2.27260e10	−0.891257
$79$	2.11165e10	0.772099	0.386049	−	0.922478i	$-0.373839\pi$
$79$	2.11165e10	0.772099	0.386049	+	0.922478i	$0.373839\pi$
$80$	−4.55850e8	−0.0155535
$81$	3.48678e9	0.111111
$82$	1.04010e10	0.309814
$83$	−4.40162e10	−1.22654	−0.613272	−	0.789872i	$-0.710147\pi$
$83$	−4.40162e10	−1.22654	−0.613272	+	0.789872i	$0.710147\pi$
$84$	8.79289e9	0.229401
$85$	6.90307e8	0.0168748
$86$	−2.14468e10	−0.491609
$87$	−1.16457e10	−0.250501
$88$	4.94179e10	0.998227
$89$	−6.64139e10	−1.26071	−0.630353	−	0.776308i	$-0.717090\pi$
$89$	−6.64139e10	−1.26071	−0.630353	+	0.776308i	$0.717090\pi$
$90$	−3.66867e8	−0.00654899
$91$	−1.67624e11	−2.81585
$92$	−1.61902e9	−0.0256105
$93$	−1.64340e10	−0.244956
$94$	2.80304e10	0.393936
$95$	2.77623e9	0.0368108
$96$	−2.26244e10	−0.283195
$97$	6.49449e10	0.767893	0.383946	−	0.923355i	$-0.374565\pi$
$97$	6.49449e10	0.767893	0.383946	+	0.923355i	$0.374565\pi$
$98$	−1.15278e11	−1.28826
$99$	2.90774e10	0.307300
$100$	2.51702e10	0.251702
$101$	1.33002e11	1.25918	0.629592	−	0.776926i	$-0.283222\pi$
$101$	1.33002e11	1.25918	0.629592	+	0.776926i	$0.283222\pi$
$102$	−4.13697e10	−0.371006
$103$	1.52129e11	1.29303	0.646513	−	0.762903i	$-0.276227\pi$
$103$	1.52129e11	1.29303	0.646513	+	0.762903i	$0.276227\pi$
$104$	2.39769e11	1.93246
$105$	−2.70596e9	−0.0206909
$106$	4.02663e8	0.00292253
$107$	−1.25642e11	−0.866011	−0.433005	−	0.901391i	$-0.642547\pi$
$107$	−1.25642e11	−0.866011	−0.433005	+	0.901391i	$0.642547\pi$
$108$	−7.40048e9	−0.0484651
$109$	−2.26950e10	−0.141281	−0.0706405	−	0.997502i	$-0.522504\pi$
$109$	−2.26950e10	−0.141281	−0.0706405	+	0.997502i	$0.522504\pi$
$110$	−3.05942e9	−0.0181125
$111$	−5.71406e10	−0.321861
$112$	2.01500e11	1.08038
$113$	7.42906e10	0.379317	0.189659	−	0.981850i	$-0.439262\pi$
$113$	7.42906e10	0.379317	0.189659	+	0.981850i	$0.439262\pi$
$114$	−1.66377e11	−0.809315
$115$	4.98244e8	0.00230996
$116$	2.47173e10	0.109265
$117$	1.41080e11	0.594899
$118$	−2.79850e10	−0.112609
$119$	−3.05137e11	−1.17216
$120$	3.87060e9	0.0141998
$121$	−4.28255e10	−0.150101
$122$	3.64435e10	0.122079
$123$	−6.45682e10	−0.206795
$124$	3.48802e10	0.106846
$125$	−1.54960e10	−0.0454165
$126$	1.62167e11	0.454908
$127$	−6.27051e11	−1.68415	−0.842077	−	0.539357i	$-0.818668\pi$
$127$	−6.27051e11	−1.68415	−0.842077	+	0.539357i	$0.818668\pi$
$128$	−1.82224e11	−0.468759
$129$	1.33138e11	0.328141
$130$	−1.48439e10	−0.0350639
$131$	−1.87407e11	−0.424419	−0.212209	−	0.977224i	$-0.568066\pi$
$131$	−1.87407e11	−0.424419	−0.212209	+	0.977224i	$0.568066\pi$
$132$	−6.17150e10	−0.134040
$133$	−1.22718e12	−2.55696
$134$	−2.97318e11	−0.594491
$135$	2.27746e9	0.00437134
$136$	4.36467e11	0.804429
$137$	7.43105e11	1.31549	0.657745	−	0.753241i	$-0.271511\pi$
$137$	7.43105e11	1.31549	0.657745	+	0.753241i	$0.271511\pi$
$138$	−2.98594e10	−0.0507863
$139$	2.42816e11	0.396914	0.198457	−	0.980110i	$-0.436407\pi$
$139$	2.42816e11	0.396914	0.198457	+	0.980110i	$0.436407\pi$
$140$	5.74323e9	0.00902510
$141$	−1.74009e11	−0.262946
$142$	−5.65411e10	−0.0821823
$143$	1.17651e12	1.64531
$144$	−1.69591e11	−0.228249
$145$	−7.60660e9	−0.00985523
$146$	−5.27771e11	−0.658423
$147$	7.15629e11	0.859889
$148$	1.21277e11	0.140391
$149$	1.53014e12	1.70690	0.853448	−	0.521178i	$-0.174507\pi$
$149$	1.53014e12	1.70690	0.853448	+	0.521178i	$0.174507\pi$
$150$	4.64212e11	0.499131
$151$	−1.05358e12	−1.09219	−0.546093	−	0.837725i	$-0.683885\pi$
$151$	−1.05358e12	−1.09219	−0.546093	+	0.837725i	$0.683885\pi$
$152$	1.75535e12	1.75479
$153$	2.56817e11	0.247640
$154$	1.35236e12	1.25814
$155$	−1.07342e10	−0.00963706
$156$	−2.99433e11	−0.259486
$157$	−1.53165e12	−1.28148	−0.640740	−	0.767758i	$-0.721372\pi$
$157$	−1.53165e12	−1.28148	−0.640740	+	0.767758i	$0.721372\pi$
$158$	−8.26583e11	−0.667840
$159$	−2.49967e9	−0.00195074
$160$	−1.47776e10	−0.0111415
$161$	−2.20239e11	−0.160455
$162$	−1.36486e11	−0.0961074
$163$	−5.32648e11	−0.362584	−0.181292	−	0.983429i	$-0.558028\pi$
$163$	−5.32648e11	−0.362584	−0.181292	+	0.983429i	$0.558028\pi$
$164$	1.37042e11	0.0902012
$165$	1.89924e10	0.0120898
$166$	1.72297e12	1.06092
$167$	2.20232e12	1.31202	0.656008	−	0.754754i	$-0.272244\pi$
$167$	2.20232e12	1.31202	0.656008	+	0.754754i	$0.272244\pi$
$168$	−1.71092e12	−0.986347
$169$	3.91612e12	2.18514
$170$	−2.70213e10	−0.0145961
$171$	1.03285e12	0.540204
$172$	−2.82578e11	−0.143130
$173$	2.45988e12	1.20687	0.603434	−	0.797413i	$-0.293799\pi$
$173$	2.45988e12	1.20687	0.603434	+	0.797413i	$0.293799\pi$
$174$	4.55859e11	0.216675
$175$	3.42397e12	1.57696
$176$	−1.41428e12	−0.631270
$177$	1.73727e11	0.0751646
$178$	2.59970e12	1.09047
$179$	−1.26117e12	−0.512957	−0.256478	−	0.966550i	$-0.582562\pi$
$179$	−1.26117e12	−0.512957	−0.256478	+	0.966550i	$0.582562\pi$
$180$	−4.83376e9	−0.00190672
$181$	3.98209e12	1.52363	0.761814	−	0.647796i	$-0.224309\pi$
$181$	3.98209e12	1.52363	0.761814	+	0.647796i	$0.224309\pi$
$182$	6.56147e12	2.43561
$183$	−2.26236e11	−0.0814855
$184$	3.15029e11	0.110117
$185$	−3.73224e10	−0.0126627
$186$	6.43293e11	0.211879
$187$	2.14168e12	0.684898
$188$	3.69322e11	0.114693
$189$	−1.00671e12	−0.303643
$190$	−1.08672e11	−0.0318401
$191$	6.26611e12	1.78367	0.891836	−	0.452360i	$-0.149418\pi$
$191$	6.26611e12	1.78367	0.891836	+	0.452360i	$0.149418\pi$
$192$	2.31492e12	0.640294
$193$	1.42924e12	0.384184	0.192092	−	0.981377i	$-0.438473\pi$
$193$	1.42924e12	0.384184	0.192092	+	0.981377i	$0.438473\pi$
$194$	−2.54220e12	−0.664202
$195$	9.21489e10	0.0234045
$196$	−1.51888e12	−0.375072
$197$	−2.27297e12	−0.545795	−0.272897	−	0.962043i	$-0.587982\pi$
$197$	−2.27297e12	−0.545795	−0.272897	+	0.962043i	$0.587982\pi$
$198$	−1.13821e12	−0.265804
$199$	8.10936e12	1.84202	0.921011	−	0.389537i	$-0.127365\pi$
$199$	8.10936e12	1.84202	0.921011	+	0.389537i	$0.127365\pi$
$200$	−4.89764e12	−1.08223
$201$	1.84571e12	0.396812
$202$	−5.20621e12	−1.08915
$203$	3.36236e12	0.684566
$204$	−5.45078e11	−0.108017
$205$	−4.21739e10	−0.00813575
$206$	−5.95493e12	−1.11842
$207$	1.85363e11	0.0338989
$208$	−6.86189e12	−1.22207
$209$	8.61325e12	1.49404
$210$	1.05922e11	0.0178970
$211$	−8.72185e12	−1.43567	−0.717836	−	0.696212i	$-0.754867\pi$
$211$	−8.72185e12	−1.43567	−0.717836	+	0.696212i	$0.754867\pi$
$212$	5.30540e9	0.000850885 0
$213$	3.50999e11	0.0548552
$214$	4.91811e12	0.749071
$215$	8.69618e10	0.0129097
$216$	1.43999e12	0.208384
$217$	4.74484e12	0.669412
$218$	8.88371e11	0.122203
$219$	3.27633e12	0.439486
$220$	−4.03103e10	−0.00527340
$221$	1.03912e13	1.32589
$222$	2.23671e12	0.278399
$223$	−9.90424e12	−1.20266	−0.601332	−	0.798999i	$-0.705363\pi$
$223$	−9.90424e12	−1.20266	−0.601332	+	0.798999i	$0.705363\pi$
$224$	6.53214e12	0.773912
$225$	−2.88176e12	−0.333161
$226$	−2.90803e12	−0.328097
$227$	9.81507e12	1.08082	0.540408	−	0.841403i	$-0.318270\pi$
$227$	9.81507e12	1.08082	0.540408	+	0.841403i	$0.318270\pi$
$228$	−2.19215e12	−0.235629
$229$	4.48537e12	0.470656	0.235328	−	0.971916i	$-0.424384\pi$
$229$	4.48537e12	0.470656	0.235328	+	0.971916i	$0.424384\pi$
$230$	−1.95032e10	−0.00199804
$231$	−8.39526e12	−0.839785
$232$	−4.80950e12	−0.469804
$233$	−1.92906e13	−1.84030	−0.920150	−	0.391567i	$-0.871933\pi$
$233$	−1.92906e13	−1.84030	−0.920150	+	0.391567i	$0.871933\pi$
$234$	−5.52242e12	−0.514568
$235$	−1.13657e11	−0.0103448
$236$	−3.68724e11	−0.0327857
$237$	5.13131e12	0.445772
$238$	1.19443e13	1.01388
$239$	1.90066e13	1.57658	0.788289	−	0.615306i	$-0.210967\pi$
$239$	1.90066e13	1.57658	0.788289	+	0.615306i	$0.210967\pi$
$240$	−1.10772e11	−0.00897980
$241$	−1.83679e13	−1.45534	−0.727672	−	0.685925i	$-0.759398\pi$
$241$	−1.83679e13	−1.45534	−0.727672	+	0.685925i	$0.759398\pi$
$242$	1.67636e12	0.129832
$243$	8.47289e11	0.0641500
$244$	4.80171e11	0.0355428
$245$	4.67426e11	0.0338298
$246$	2.52746e12	0.178871
$247$	4.17904e13	2.89230
$248$	−6.78701e12	−0.459403
$249$	−1.06959e13	−0.708146
$250$	6.06574e11	0.0392838
$251$	−1.47420e13	−0.934007	−0.467003	−	0.884256i	$-0.654666\pi$
$251$	−1.47420e13	−0.934007	−0.467003	+	0.884256i	$0.654666\pi$
$252$	2.13667e12	0.132445
$253$	1.54580e12	0.0937543
$254$	2.45452e13	1.45674
$255$	1.67745e11	0.00974266
$256$	−1.23772e13	−0.703561
$257$	−2.00386e13	−1.11490	−0.557449	−	0.830211i	$-0.688220\pi$
$257$	−2.00386e13	−1.11490	−0.557449	+	0.830211i	$0.688220\pi$
$258$	−5.21156e12	−0.283831
$259$	1.64977e13	0.879577
$260$	−1.95580e11	−0.0102087
$261$	−2.82991e12	−0.144627
$262$	7.33586e12	0.367108
$263$	1.59440e13	0.781339	0.390670	−	0.920531i	$-0.372243\pi$
$263$	1.59440e13	0.781339	0.390670	+	0.920531i	$0.372243\pi$
$264$	1.20085e13	0.576327
$265$	−1.63271e9	−7.67460e−5 0
$266$	4.80366e13	2.21168
$267$	−1.61386e13	−0.727869
$268$	−3.91740e12	−0.173084
$269$	−6.18550e12	−0.267755	−0.133877	−	0.990998i	$-0.542743\pi$
$269$	−6.18550e12	−0.267755	−0.133877	+	0.990998i	$0.542743\pi$
$270$	−8.91486e10	−0.00378106
$271$	−9.42813e12	−0.391827	−0.195914	−	0.980621i	$-0.562767\pi$
$271$	−9.42813e12	−0.391827	−0.195914	+	0.980621i	$0.562767\pi$
$272$	−1.24911e13	−0.508714
$273$	−4.07327e13	−1.62573
$274$	−2.90881e13	−1.13785
$275$	−2.40320e13	−0.921424
$276$	−3.93421e11	−0.0147862
$277$	−1.50680e13	−0.555160	−0.277580	−	0.960703i	$-0.589532\pi$
$277$	−1.50680e13	−0.555160	−0.277580	+	0.960703i	$0.589532\pi$
$278$	−9.50478e12	−0.343317
$279$	−3.99347e12	−0.141425
$280$	−1.11752e12	−0.0388049
$281$	−3.61256e13	−1.23007	−0.615035	−	0.788500i	$-0.710858\pi$
$281$	−3.61256e13	−1.23007	−0.615035	+	0.788500i	$0.710858\pi$
$282$	6.81138e12	0.227439
$283$	−7.38949e11	−0.0241985	−0.0120993	−	0.999927i	$-0.503851\pi$
$283$	−7.38949e11	−0.0241985	−0.0120993	+	0.999927i	$0.503851\pi$
$284$	−7.44973e11	−0.0239271
$285$	6.74623e11	0.0212527
$286$	−4.60533e13	−1.42314
$287$	1.86422e13	0.565127
$288$	−5.49774e12	−0.163503
$289$	−1.53562e13	−0.448069
$290$	2.97752e11	0.00852445
$291$	1.57816e13	0.443343
$292$	−6.95380e12	−0.191698
$293$	5.28326e13	1.42932	0.714661	−	0.699471i	$-0.246581\pi$
$293$	5.28326e13	1.42932	0.714661	+	0.699471i	$0.246581\pi$
$294$	−2.80125e13	−0.743776
$295$	1.13473e11	0.00295713
$296$	−2.35982e13	−0.603635
$297$	7.06582e12	0.177420
$298$	−5.98958e13	−1.47641
$299$	7.50003e12	0.181498
$300$	6.11636e12	0.145320
$301$	−3.84398e13	−0.896738
$302$	4.12415e13	0.944704
$303$	3.23194e13	0.726990
$304$	−5.02359e13	−1.10971
$305$	−1.47770e11	−0.00320580
$306$	−1.00528e13	−0.214201
$307$	5.30662e13	1.11060	0.555299	−	0.831651i	$-0.312604\pi$
$307$	5.30662e13	1.11060	0.555299	+	0.831651i	$0.312604\pi$
$308$	1.78184e13	0.366302
$309$	3.69673e13	0.746529
$310$	4.20178e11	0.00833574
$311$	4.95431e13	0.965609	0.482804	−	0.875728i	$-0.339618\pi$
$311$	4.95431e13	0.965609	0.482804	+	0.875728i	$0.339618\pi$
$312$	5.82639e13	1.11570
$313$	4.02674e13	0.757634	0.378817	−	0.925472i	$-0.376331\pi$
$313$	4.02674e13	0.757634	0.378817	+	0.925472i	$0.376331\pi$
$314$	5.99549e13	1.10844
$315$	−6.57549e11	−0.0119459
$316$	−1.08909e13	−0.194439
$317$	2.96572e13	0.520360	0.260180	−	0.965560i	$-0.416218\pi$
$317$	2.96572e13	0.520360	0.260180	+	0.965560i	$0.416218\pi$
$318$	9.78470e10	0.00168732
$319$	−2.35995e13	−0.399995
$320$	1.51203e12	0.0251905
$321$	−3.05310e13	−0.499992
$322$	8.62103e12	0.138788
$323$	7.60738e13	1.20398
$324$	−1.79832e12	−0.0279813
$325$	−1.16600e14	−1.78377
$326$	2.08499e13	0.313623
$327$	−5.51488e12	−0.0815687
$328$	−2.66657e13	−0.387835
$329$	5.02399e13	0.718574
$330$	−7.43439e11	−0.0104573
$331$	−5.87214e13	−0.812349	−0.406174	−	0.913796i	$-0.633137\pi$
$331$	−5.87214e13	−0.812349	−0.406174	+	0.913796i	$0.633137\pi$
$332$	2.27015e13	0.308883
$333$	−1.38852e13	−0.185827
$334$	−8.62074e13	−1.13485
$335$	1.20556e12	0.0156114
$336$	4.89645e13	0.623757
$337$	8.21322e13	1.02932	0.514659	−	0.857395i	$-0.327919\pi$
$337$	8.21322e13	1.02932	0.514659	+	0.857395i	$0.327919\pi$
$338$	−1.53292e14	−1.89007
$339$	1.80526e13	0.218999
$340$	−3.56027e11	−0.00424961
$341$	−3.33028e13	−0.391140
$342$	−4.04297e13	−0.467258
$343$	−6.78894e13	−0.772119
$344$	5.49842e13	0.615412
$345$	1.21073e11	0.00133365
$346$	−9.62892e13	−1.04390
$347$	7.99022e13	0.852602	0.426301	−	0.904581i	$-0.359816\pi$
$347$	7.99022e13	0.852602	0.426301	+	0.904581i	$0.359816\pi$
$348$	6.00630e12	0.0630843
$349$	5.57237e13	0.576103	0.288051	−	0.957615i	$-0.406993\pi$
$349$	5.57237e13	0.576103	0.288051	+	0.957615i	$0.406993\pi$
$350$	−1.34028e14	−1.36402
$351$	3.42824e13	0.343465
$352$	−4.58474e13	−0.452200
$353$	2.40830e13	0.233857	0.116928	−	0.993140i	$-0.462695\pi$
$353$	2.40830e13	0.233857	0.116928	+	0.993140i	$0.462695\pi$
$354$	−6.80034e12	−0.0650149
$355$	2.29261e11	0.00215812
$356$	3.42531e13	0.317486
$357$	−7.41484e13	−0.676747
$358$	4.93670e13	0.443691
$359$	−1.66898e14	−1.47717	−0.738587	−	0.674158i	$-0.764507\pi$
$359$	−1.66898e14	−1.47717	−0.738587	+	0.674158i	$0.764507\pi$
$360$	9.40555e11	0.00819824
$361$	1.89457e14	1.62638
$362$	−1.55875e14	−1.31789
$363$	−1.04066e13	−0.0866607
$364$	8.64525e13	0.709121
$365$	2.13999e12	0.0172903
$366$	8.85576e12	0.0704823
$367$	1.58476e13	0.124251	0.0621254	−	0.998068i	$-0.480212\pi$
$367$	1.58476e13	0.124251	0.0621254	+	0.998068i	$0.480212\pi$
$368$	−9.01574e12	−0.0696368
$369$	−1.56901e13	−0.119393
$370$	1.46095e12	0.0109528
$371$	7.21707e11	0.00533095
$372$	8.47589e12	0.0616878
$373$	−3.37056e13	−0.241715	−0.120857	−	0.992670i	$-0.538564\pi$
$373$	−3.37056e13	−0.241715	−0.120857	+	0.992670i	$0.538564\pi$
$374$	−8.38338e13	−0.592414
$375$	−3.76552e12	−0.0262213
$376$	−7.18630e13	−0.493142
$377$	−1.14502e14	−0.774346
$378$	3.94065e13	0.262641
$379$	−7.12872e13	−0.468270	−0.234135	−	0.972204i	$-0.575226\pi$
$379$	−7.12872e13	−0.468270	−0.234135	+	0.972204i	$0.575226\pi$
$380$	−1.43184e12	−0.00927013
$381$	−1.52373e14	−0.972347
$382$	−2.45280e14	−1.54282
$383$	1.55879e14	0.966485	0.483243	−	0.875486i	$-0.339459\pi$
$383$	1.55879e14	0.966485	0.483243	+	0.875486i	$0.339459\pi$
$384$	−4.42803e13	−0.270638
$385$	−5.48351e12	−0.0330388
$386$	−5.59460e13	−0.332307
$387$	3.23526e13	0.189452
$388$	−3.34955e13	−0.193380
$389$	2.37267e13	0.135056	0.0675280	−	0.997717i	$-0.478489\pi$
$389$	2.37267e13	0.135056	0.0675280	+	0.997717i	$0.478489\pi$
$390$	−3.60707e12	−0.0202441
$391$	1.36528e13	0.0755527
$392$	2.95544e14	1.61268
$393$	−4.55400e13	−0.245038
$394$	8.89730e13	0.472094
$395$	3.35161e12	0.0175376
$396$	−1.49967e13	−0.0773880
$397$	2.57979e14	1.31291	0.656457	−	0.754364i	$-0.272054\pi$
$397$	2.57979e14	1.31291	0.656457	+	0.754364i	$0.272054\pi$
$398$	−3.17432e14	−1.59329
$399$	−2.98204e14	−1.47626
$400$	1.40164e14	0.684395
$401$	3.04127e14	1.46474	0.732370	−	0.680907i	$-0.238414\pi$
$401$	3.04127e14	1.46474	0.732370	+	0.680907i	$0.238414\pi$
$402$	−7.22483e13	−0.343229
$403$	−1.61581e14	−0.757204
$404$	−6.85958e13	−0.317103
$405$	5.53422e11	0.00252379
$406$	−1.31616e14	−0.592127
$407$	−1.15793e14	−0.513940
$408$	1.06062e14	0.464437
$409$	2.04430e14	0.883213	0.441606	−	0.897209i	$-0.354409\pi$
$409$	2.04430e14	0.883213	0.441606	+	0.897209i	$0.354409\pi$
$410$	1.65085e12	0.00703715
$411$	1.80575e14	0.759498
$412$	−7.84609e13	−0.325625
$413$	−5.01585e13	−0.205409
$414$	−7.25584e12	−0.0293215
$415$	−6.98625e12	−0.0278599
$416$	−2.22446e14	−0.875409
$417$	5.90043e13	0.229158
$418$	−3.37157e14	−1.29230
$419$	−3.11752e14	−1.17932	−0.589660	−	0.807652i	$-0.700738\pi$
$419$	−3.11752e14	−1.17932	−0.589660	+	0.807652i	$0.700738\pi$
$420$	1.39561e12	0.00521064
$421$	2.19862e14	0.810211	0.405105	−	0.914270i	$-0.367235\pi$
$421$	2.19862e14	0.810211	0.405105	+	0.914270i	$0.367235\pi$
$422$	3.41408e14	1.24181
$423$	−4.22841e13	−0.151812
$424$	−1.03233e12	−0.00365852
$425$	−2.12255e14	−0.742537
$426$	−1.37395e13	−0.0474480
$427$	6.53189e13	0.222682
$428$	6.48000e13	0.218089
$429$	2.85892e14	0.949921
$430$	−3.40403e12	−0.0111665
$431$	5.72745e14	1.85497	0.927484	−	0.373864i	$-0.121967\pi$
$431$	5.72745e14	1.85497	0.927484	+	0.373864i	$0.121967\pi$
$432$	−4.12107e13	−0.131780
$433$	−4.52318e14	−1.42811	−0.714054	−	0.700091i	$-0.753143\pi$
$433$	−4.52318e14	−1.42811	−0.714054	+	0.700091i	$0.753143\pi$
$434$	−1.85732e14	−0.579019
$435$	−1.84840e12	−0.00568992
$436$	1.17050e13	0.0355791
$437$	5.49078e13	0.164811
$438$	−1.28248e14	−0.380141
$439$	2.80722e14	0.821716	0.410858	−	0.911699i	$-0.365229\pi$
$439$	2.80722e14	0.821716	0.410858	+	0.911699i	$0.365229\pi$
$440$	7.84360e12	0.0226739
$441$	1.73898e14	0.496457
$442$	−4.06751e14	−1.14685
$443$	4.29346e14	1.19560	0.597802	−	0.801644i	$-0.296041\pi$
$443$	4.29346e14	1.19560	0.597802	+	0.801644i	$0.296041\pi$
$444$	2.94704e13	0.0810549
$445$	−1.05412e13	−0.0286359
$446$	3.87691e14	1.04027
$447$	3.71824e14	0.985477
$448$	−6.68366e14	−1.74979
$449$	−3.52063e14	−0.910470	−0.455235	−	0.890371i	$-0.650445\pi$
$449$	−3.52063e14	−0.910470	−0.455235	+	0.890371i	$0.650445\pi$
$450$	1.12804e14	0.288174
$451$	−1.30845e14	−0.330206
$452$	−3.83155e13	−0.0955242
$453$	−2.56021e14	−0.630573
$454$	−3.84201e14	−0.934869
$455$	−2.66053e13	−0.0639595
$456$	4.26550e14	1.01313
$457$	−1.86469e14	−0.437590	−0.218795	−	0.975771i	$-0.570213\pi$
$457$	−1.86469e14	−0.437590	−0.218795	+	0.975771i	$0.570213\pi$
$458$	−1.75575e14	−0.407102
$459$	6.24065e13	0.142975
$460$	−2.56970e11	−0.000581721 0
$461$	−2.25969e14	−0.505469	−0.252734	−	0.967536i	$-0.581330\pi$
$461$	−2.25969e14	−0.505469	−0.252734	+	0.967536i	$0.581330\pi$
$462$	3.28623e14	0.726386
$463$	6.99333e14	1.52753	0.763763	−	0.645497i	$-0.223350\pi$
$463$	6.99333e14	1.52753	0.763763	+	0.645497i	$0.223350\pi$
$464$	1.37642e14	0.297099
$465$	−2.60841e12	−0.00556396
$466$	7.55111e14	1.59180
$467$	7.18639e13	0.149716	0.0748580	−	0.997194i	$-0.476150\pi$
$467$	7.18639e13	0.149716	0.0748580	+	0.997194i	$0.476150\pi$
$468$	−7.27623e13	−0.149815
$469$	−5.32894e14	−1.08440
$470$	4.44898e12	0.00894792
$471$	−3.72191e14	−0.739863
$472$	7.17465e13	0.140968
$473$	2.69799e14	0.523968
$474$	−2.00860e14	−0.385578
$475$	−8.53630e14	−1.61977
$476$	1.57375e14	0.295188
$477$	−6.07421e11	−0.00112626
$478$	−7.43992e14	−1.36369
$479$	6.90841e13	0.125179	0.0625897	−	0.998039i	$-0.480064\pi$
$479$	6.90841e13	0.125179	0.0625897	+	0.998039i	$0.480064\pi$
$480$	−3.59095e12	−0.00643253
$481$	−5.61812e14	−0.994931
$482$	7.18992e14	1.25883
$483$	−5.35181e13	−0.0926385
$484$	2.20873e13	0.0378002
$485$	1.03080e13	0.0174420
$486$	−3.31662e13	−0.0554877
$487$	6.50107e14	1.07541	0.537707	−	0.843132i	$-0.319291\pi$
$487$	6.50107e14	1.07541	0.537707	+	0.843132i	$0.319291\pi$
$488$	−9.34320e13	−0.152822
$489$	−1.29433e14	−0.209338
$490$	−1.82969e13	−0.0292617
$491$	1.02957e15	1.62820	0.814102	−	0.580722i	$-0.197230\pi$
$491$	1.02957e15	1.62820	0.814102	+	0.580722i	$0.197230\pi$
$492$	3.33012e13	0.0520777
$493$	−2.08435e14	−0.322339
$494$	−1.63584e15	−2.50174
$495$	4.61516e12	0.00698005
$496$	1.94236e14	0.290522
$497$	−1.01341e14	−0.149908
$498$	4.18681e14	0.612523
$499$	−7.05829e14	−1.02128	−0.510642	−	0.859793i	$-0.670592\pi$
$499$	−7.05829e14	−1.02128	−0.510642	+	0.859793i	$0.670592\pi$
$500$	7.99209e12	0.0114373
$501$	5.35163e14	0.757493
$502$	5.77059e14	0.807885
$503$	−2.56115e14	−0.354659	−0.177330	−	0.984152i	$-0.556746\pi$
$503$	−2.56115e14	−0.354659	−0.177330	+	0.984152i	$0.556746\pi$
$504$	−4.15755e14	−0.569468
$505$	2.11100e13	0.0286013
$506$	−6.05088e13	−0.0810944
$507$	9.51617e14	1.26159
$508$	3.23403e14	0.424124
$509$	1.10840e15	1.43796	0.718982	−	0.695029i	$-0.244609\pi$
$509$	1.10840e15	1.43796	0.718982	+	0.695029i	$0.244609\pi$
$510$	−6.56619e12	−0.00842708
$511$	−9.45944e14	−1.20102
$512$	8.57685e14	1.07732
$513$	2.50982e14	0.311887
$514$	7.84389e14	0.964350
$515$	2.41459e13	0.0293700
$516$	−6.86664e13	−0.0826364
$517$	−3.52621e14	−0.419865
$518$	−6.45784e14	−0.760805
$519$	5.97750e14	0.696785
$520$	3.80561e13	0.0438941
$521$	−2.81370e14	−0.321122	−0.160561	−	0.987026i	$-0.551330\pi$
$521$	−2.81370e14	−0.321122	−0.160561	+	0.987026i	$0.551330\pi$
$522$	1.10774e14	0.125098
$523$	6.77347e14	0.756923	0.378462	−	0.925617i	$-0.376453\pi$
$523$	6.77347e14	0.756923	0.378462	+	0.925617i	$0.376453\pi$
$524$	9.66557e13	0.106882
$525$	8.32025e14	0.910459
$526$	−6.24110e14	−0.675833
$527$	−2.94137e14	−0.315203
$528$	−3.43669e14	−0.364464
$529$	−9.42956e14	−0.989658
$530$	6.39106e10	6.63828e−5 0
$531$	4.22156e13	0.0433963
$532$	6.32920e14	0.643924
$533$	−6.34841e14	−0.639242
$534$	6.31728e14	0.629583
$535$	−1.99418e13	−0.0196707
$536$	7.62250e14	0.744203
$537$	−3.06464e14	−0.296156
$538$	2.42125e14	0.231599
$539$	1.45019e15	1.37305
$540$	−1.17460e12	−0.00110084
$541$	1.38190e15	1.28201	0.641003	−	0.767538i	$-0.278519\pi$
$541$	1.38190e15	1.28201	0.641003	+	0.767538i	$0.278519\pi$
$542$	3.69054e14	0.338918
$543$	9.67648e14	0.879667
$544$	−4.04933e14	−0.364409
$545$	−3.60214e12	−0.00320908
$546$	1.59444e15	1.40620
$547$	−6.01823e13	−0.0525458	−0.0262729	−	0.999655i	$-0.508364\pi$
$547$	−6.01823e13	−0.0525458	−0.0262729	+	0.999655i	$0.508364\pi$
$548$	−3.83258e14	−0.331282
$549$	−5.49753e13	−0.0470457
$550$	9.40706e14	0.797002
$551$	−8.38269e14	−0.703152
$552$	7.65521e13	0.0635759
$553$	−1.48152e15	−1.21820
$554$	5.89822e14	0.480195
$555$	−9.06934e12	−0.00731079
$556$	−1.25233e14	−0.0999556
$557$	−7.65629e14	−0.605083	−0.302541	−	0.953136i	$-0.597835\pi$
$557$	−7.65629e14	−0.605083	−0.302541	+	0.953136i	$0.597835\pi$
$558$	1.56320e14	0.122328
$559$	1.30903e15	1.01434
$560$	3.19820e13	0.0245399
$561$	5.20429e14	0.395426
$562$	1.41410e15	1.06397
$563$	−7.33817e14	−0.546754	−0.273377	−	0.961907i	$-0.588141\pi$
$563$	−7.33817e14	−0.546754	−0.273377	+	0.961907i	$0.588141\pi$
$564$	8.97453e13	0.0662181
$565$	1.17914e13	0.00861586
$566$	2.89254e13	0.0209309
$567$	−2.44630e14	−0.175308
$568$	1.44957e14	0.102878
$569$	−9.71035e14	−0.682523	−0.341261	−	0.939968i	$-0.610854\pi$
$569$	−9.71035e14	−0.682523	−0.341261	+	0.939968i	$0.610854\pi$
$570$	−2.64074e13	−0.0183829
$571$	1.96144e15	1.35231	0.676154	−	0.736761i	$-0.263646\pi$
$571$	1.96144e15	1.35231	0.676154	+	0.736761i	$0.263646\pi$
$572$	−6.06788e14	−0.414342
$573$	1.52267e15	1.02980
$574$	−7.29728e14	−0.488817
$575$	−1.53199e14	−0.101644
$576$	5.62526e14	0.369674
$577$	−1.81907e12	−0.00118408	−0.000592041	−	1.00000i	$-0.500188\pi$
$577$	−1.81907e12	−0.00118408	−0.000592041		1.00000i	$0.500188\pi$
$578$	6.01102e14	0.387565
$579$	3.47305e14	0.221809
$580$	3.92312e12	0.00248186
$581$	3.08814e15	1.93521
$582$	−6.17754e14	−0.383477
$583$	−5.06548e12	−0.00311489
$584$	1.35308e15	0.824235
$585$	2.23922e13	0.0135126
$586$	−2.06807e15	−1.23632
$587$	5.42865e14	0.321501	0.160751	−	0.986995i	$-0.448609\pi$
$587$	5.42865e14	0.321501	0.160751	+	0.986995i	$0.448609\pi$
$588$	−3.69087e14	−0.216548
$589$	−1.18294e15	−0.687586
$590$	−4.44177e12	−0.00255782
$591$	−5.52331e14	−0.315115
$592$	6.75351e14	0.381733
$593$	−1.05930e15	−0.593226	−0.296613	−	0.954998i	$-0.595857\pi$
$593$	−1.05930e15	−0.593226	−0.296613	+	0.954998i	$0.595857\pi$
$594$	−2.76584e14	−0.153462
$595$	−4.84314e13	−0.0266246
$596$	−7.89174e14	−0.429851
$597$	1.97057e15	1.06349
$598$	−2.93581e14	−0.156990
$599$	7.90466e14	0.418828	0.209414	−	0.977827i	$-0.432844\pi$
$599$	7.90466e14	0.418828	0.209414	+	0.977827i	$0.432844\pi$
$600$	−1.19013e15	−0.624829
$601$	1.21619e15	0.632692	0.316346	−	0.948644i	$-0.397544\pi$
$601$	1.21619e15	0.632692	0.316346	+	0.948644i	$0.397544\pi$
$602$	1.50469e15	0.775649
$603$	4.48507e14	0.229100
$604$	5.43389e14	0.275047
$605$	−6.79725e12	−0.00340941
$606$	−1.26511e15	−0.628823
$607$	−1.68034e15	−0.827675	−0.413838	−	0.910351i	$-0.635812\pi$
$607$	−1.68034e15	−0.827675	−0.413838	+	0.910351i	$0.635812\pi$
$608$	−1.62853e15	−0.794924
$609$	8.17053e14	0.395235
$610$	5.78430e12	0.00277291
$611$	−1.71087e15	−0.812813
$612$	−1.32454e14	−0.0623637
$613$	−3.94994e15	−1.84314	−0.921569	−	0.388214i	$-0.873092\pi$
$613$	−3.94994e15	−1.84314	−0.921569	+	0.388214i	$0.873092\pi$
$614$	−2.07722e15	−0.960631
$615$	−1.02483e13	−0.00469718
$616$	−3.46711e15	−1.57498
$617$	−2.85141e15	−1.28378	−0.641892	−	0.766795i	$-0.721850\pi$
$617$	−2.85141e15	−1.28378	−0.641892	+	0.766795i	$0.721850\pi$
$618$	−1.44705e15	−0.645723
$619$	−4.06614e14	−0.179839	−0.0899194	−	0.995949i	$-0.528661\pi$
$619$	−4.06614e14	−0.179839	−0.0899194	+	0.995949i	$0.528661\pi$
$620$	5.53618e12	0.00242692
$621$	4.50432e13	0.0195716
$622$	−1.93931e15	−0.835220
$623$	4.65954e15	1.98911
$624$	−1.66744e15	−0.705561
$625$	2.38050e15	0.998452
$626$	−1.57622e15	−0.655328
$627$	2.09302e15	0.862585
$628$	7.89953e14	0.322718
$629$	−1.02270e15	−0.414163
$630$	2.57390e13	0.0103328
$631$	8.63879e14	0.343789	0.171894	−	0.985115i	$-0.445011\pi$
$631$	8.63879e14	0.343789	0.171894	+	0.985115i	$0.445011\pi$
$632$	2.11915e15	0.836024
$633$	−2.11941e15	−0.828885
$634$	−1.16090e15	−0.450094
$635$	−9.95253e13	−0.0382541
$636$	1.28921e12	0.000491259 0
$637$	7.03614e15	2.65808
$638$	9.23778e14	0.345982
$639$	8.52928e13	0.0316707
$640$	−2.89225e13	−0.0106475
$641$	1.73480e15	0.633184	0.316592	−	0.948562i	$-0.397461\pi$
$641$	1.73480e15	0.633184	0.316592	+	0.948562i	$0.397461\pi$
$642$	1.19510e15	0.432476
$643$	3.12183e15	1.12008	0.560039	−	0.828466i	$-0.310786\pi$
$643$	3.12183e15	1.12008	0.560039	+	0.828466i	$0.310786\pi$
$644$	1.13589e14	0.0404076
$645$	2.11317e13	0.00745343
$646$	−2.97783e15	−1.04141
$647$	4.04414e15	1.40234	0.701168	−	0.712996i	$-0.252662\pi$
$647$	4.04414e15	1.40234	0.701168	+	0.712996i	$0.252662\pi$
$648$	3.49917e14	0.120310
$649$	3.52049e14	0.120021
$650$	4.56418e15	1.54291
$651$	1.15300e15	0.386485
$652$	2.74714e14	0.0913102
$653$	5.64810e15	1.86157	0.930787	−	0.365563i	$-0.119124\pi$
$653$	5.64810e15	1.86157	0.930787	+	0.365563i	$0.119124\pi$
$654$	2.15874e14	0.0705542
$655$	−2.97453e13	−0.00964030
$656$	7.63139e14	0.245263
$657$	7.96148e14	0.253737
$658$	−1.96659e15	−0.621542
$659$	−4.96751e14	−0.155693	−0.0778465	−	0.996965i	$-0.524804\pi$
$659$	−4.96751e14	−0.155693	−0.0778465	+	0.996965i	$0.524804\pi$
$660$	−9.79540e12	−0.00304460
$661$	−5.54252e15	−1.70844	−0.854218	−	0.519914i	$-0.825964\pi$
$661$	−5.54252e15	−1.70844	−0.854218	+	0.519914i	$0.825964\pi$
$662$	2.29859e15	0.702655
$663$	2.52505e15	0.765501
$664$	−4.41726e15	−1.32809
$665$	−1.94778e14	−0.0580791
$666$	5.43520e14	0.160734
$667$	−1.50442e14	−0.0441243
$668$	−1.13585e15	−0.330408
$669$	−2.40673e15	−0.694359
$670$	−4.71903e13	−0.0135033
$671$	−4.58457e14	−0.130114
$672$	1.58731e15	0.446818
$673$	−1.45891e15	−0.407331	−0.203665	−	0.979041i	$-0.565285\pi$
$673$	−1.45891e15	−0.407331	−0.203665	+	0.979041i	$0.565285\pi$
$674$	−3.21498e15	−0.890325
$675$	−7.00269e14	−0.192351
$676$	−2.01975e15	−0.550288
$677$	−2.10073e14	−0.0567717	−0.0283858	−	0.999597i	$-0.509037\pi$
$677$	−2.10073e14	−0.0567717	−0.0283858	+	0.999597i	$0.509037\pi$
$678$	−7.06650e14	−0.189427
$679$	−4.55648e15	−1.21156
$680$	6.92760e13	0.0182719
$681$	2.38506e15	0.624009
$682$	1.30360e15	0.338323
$683$	−1.08298e15	−0.278810	−0.139405	−	0.990235i	$-0.544519\pi$
$683$	−1.08298e15	−0.278810	−0.139405	+	0.990235i	$0.544519\pi$
$684$	−5.32693e14	−0.136041
$685$	1.17946e14	0.0298802
$686$	2.65746e15	0.667857
$687$	1.08995e15	0.271733
$688$	−1.57358e15	−0.389181
$689$	−2.45770e13	−0.00603009
$690$	−4.73928e12	−0.00115357
$691$	2.04378e15	0.493520	0.246760	−	0.969077i	$-0.420634\pi$
$691$	2.04378e15	0.493520	0.246760	+	0.969077i	$0.420634\pi$
$692$	−1.26869e15	−0.303928
$693$	−2.04005e15	−0.484850
$694$	−3.12769e15	−0.737473
$695$	3.85397e13	0.00901555
$696$	−1.16871e15	−0.271241
$697$	−1.15564e15	−0.266099
$698$	−2.18124e15	−0.498310
$699$	−4.68762e15	−1.06250
$700$	−1.76592e15	−0.397129
$701$	−6.80781e15	−1.51900	−0.759501	−	0.650507i	$-0.774557\pi$
$701$	−6.80781e15	−1.51900	−0.759501	+	0.650507i	$0.774557\pi$
$702$	−1.34195e15	−0.297086
$703$	−4.11303e15	−0.903457
$704$	4.69109e15	1.02241
$705$	−2.76186e13	−0.00597258
$706$	−9.42704e14	−0.202278
$707$	−9.33127e15	−1.98671
$708$	−8.95999e13	−0.0189289
$709$	2.71429e15	0.568987	0.284493	−	0.958678i	$-0.408175\pi$
$709$	2.71429e15	0.568987	0.284493	+	0.958678i	$0.408175\pi$
$710$	−8.97419e12	−0.00186670
$711$	1.24691e15	0.257366
$712$	−6.66499e15	−1.36509
$713$	−2.12299e14	−0.0431475
$714$	2.90246e15	0.585364
$715$	1.86736e14	0.0373718
$716$	6.50450e14	0.129179
$717$	4.61860e15	0.910237
$718$	6.53305e15	1.27771
$719$	−5.42045e15	−1.05203	−0.526013	−	0.850477i	$-0.676314\pi$
$719$	−5.42045e15	−1.05203	−0.526013	+	0.850477i	$0.676314\pi$
$720$	−2.69175e13	−0.00518449
$721$	−1.06732e16	−2.04010
$722$	−7.41611e15	−1.40676
$723$	−4.46340e15	−0.840244
$724$	−2.05377e15	−0.383699
$725$	2.33887e15	0.433657
$726$	4.07355e14	0.0749586
$727$	−4.59899e15	−0.839891	−0.419946	−	0.907549i	$-0.637951\pi$
$727$	−4.59899e15	−0.839891	−0.419946	+	0.907549i	$0.637951\pi$
$728$	−1.68220e16	−3.04898
$729$	2.05891e14	0.0370370
$730$	−8.37678e13	−0.0149555
$731$	2.38291e15	0.422243
$732$	1.16682e14	0.0205207
$733$	−8.40465e15	−1.46706	−0.733530	−	0.679657i	$-0.762129\pi$
$733$	−8.40465e15	−1.46706	−0.733530	+	0.679657i	$0.762129\pi$
$734$	−6.20336e14	−0.107473
$735$	1.13585e14	0.0195316
$736$	−2.92269e14	−0.0498832
$737$	3.74025e15	0.633621
$738$	6.14172e14	0.103271
$739$	9.76215e15	1.62930	0.814650	−	0.579953i	$-0.196929\pi$
$739$	9.76215e15	1.62930	0.814650	+	0.579953i	$0.196929\pi$
$740$	1.92491e13	0.00318887
$741$	1.01551e16	1.66987
$742$	−2.82505e13	−0.00461110
$743$	−1.02184e16	−1.65556	−0.827781	−	0.561052i	$-0.810397\pi$
$743$	−1.02184e16	−1.65556	−0.827781	+	0.561052i	$0.810397\pi$
$744$	−1.64924e15	−0.265237
$745$	2.42864e14	0.0387707
$746$	1.31937e15	0.209075
$747$	−2.59911e15	−0.408848
$748$	−1.10458e15	−0.172479
$749$	8.81492e15	1.36637
$750$	1.47397e14	0.0226805
$751$	−8.36434e14	−0.127765	−0.0638825	−	0.997957i	$-0.520348\pi$
$751$	−8.36434e14	−0.127765	−0.0638825	+	0.997957i	$0.520348\pi$
$752$	2.05663e15	0.311858
$753$	−3.58230e15	−0.539249
$754$	4.48205e15	0.669783
$755$	−1.67225e14	−0.0248080
$756$	5.19211e14	0.0764670
$757$	−3.94834e15	−0.577280	−0.288640	−	0.957438i	$-0.593203\pi$
$757$	−3.94834e15	−0.577280	−0.288640	+	0.957438i	$0.593203\pi$
$758$	2.79046e15	0.405038
$759$	3.75630e14	0.0541291
$760$	2.78609e14	0.0398585
$761$	3.51564e15	0.499332	0.249666	−	0.968332i	$-0.419679\pi$
$761$	3.51564e15	0.499332	0.249666	+	0.968332i	$0.419679\pi$
$762$	5.96449e15	0.841048
$763$	1.59226e15	0.222910
$764$	−3.23176e15	−0.449186
$765$	4.07620e13	0.00562493
$766$	−6.10173e15	−0.835978
$767$	1.70810e15	0.232348
$768$	−3.00765e15	−0.406201
$769$	−6.49784e15	−0.871313	−0.435657	−	0.900113i	$-0.643484\pi$
$769$	−6.49784e15	−0.871313	−0.435657	+	0.900113i	$0.643484\pi$
$770$	2.14646e14	0.0285775
$771$	−4.86938e15	−0.643687
$772$	−7.37133e14	−0.0967499
$773$	1.12344e16	1.46408	0.732039	−	0.681263i	$-0.238569\pi$
$773$	1.12344e16	1.46408	0.732039	+	0.681263i	$0.238569\pi$
$774$	−1.26641e15	−0.163870
$775$	3.30053e15	0.424057
$776$	6.51757e15	0.831469
$777$	4.00893e15	0.507824
$778$	−9.28756e14	−0.116819
$779$	−4.64768e15	−0.580471
$780$	−4.75260e13	−0.00589401
$781$	7.11284e14	0.0875916
$782$	−5.34425e14	−0.0653506
$783$	−6.87667e14	−0.0835004
$784$	−8.45810e15	−1.01985
$785$	−2.43104e14	−0.0291077
$786$	1.78261e15	0.211950
$787$	−6.35498e15	−0.750331	−0.375166	−	0.926958i	$-0.622414\pi$
$787$	−6.35498e15	−0.750331	−0.375166	+	0.926958i	$0.622414\pi$
$788$	1.17229e15	0.137449
$789$	3.87438e15	0.451107
$790$	−1.31195e14	−0.0151694
$791$	−5.21216e15	−0.598477
$792$	2.91808e15	0.332742
$793$	−2.22437e15	−0.251887
$794$	−1.00983e16	−1.13563
$795$	−3.96748e11	−4.43093e−5 0
$796$	−4.18242e15	−0.463880
$797$	1.65088e16	1.81842	0.909209	−	0.416340i	$-0.136687\pi$
$797$	1.65088e16	1.81842	0.909209	+	0.416340i	$0.136687\pi$
$798$	1.16729e16	1.27692
$799$	−3.11441e15	−0.338352
$800$	4.54378e15	0.490256
$801$	−3.92168e15	−0.420236
$802$	−1.19047e16	−1.26695
$803$	6.63934e15	0.701761
$804$	−9.51928e14	−0.0999300
$805$	−3.49563e13	−0.00364459
$806$	6.32492e15	0.654956
$807$	−1.50308e15	−0.154588
$808$	1.33474e16	1.36344
$809$	1.16065e16	1.17757	0.588784	−	0.808290i	$-0.299607\pi$
$809$	1.16065e16	1.17757	0.588784	+	0.808290i	$0.299607\pi$
$810$	−2.16631e13	−0.00218300
$811$	−1.31655e16	−1.31772	−0.658859	−	0.752266i	$-0.728961\pi$
$811$	−1.31655e16	−1.31772	−0.658859	+	0.752266i	$0.728961\pi$
$812$	−1.73414e15	−0.172396
$813$	−2.29104e15	−0.226222
$814$	4.53259e15	0.444541
$815$	−8.45417e13	−0.00823577
$816$	−3.03535e15	−0.293706
$817$	9.58343e15	0.921084
$818$	−8.00218e15	−0.763950
$819$	−9.89804e15	−0.938616
$820$	2.17513e13	0.00204884
$821$	1.73884e16	1.62695	0.813473	−	0.581603i	$-0.197574\pi$
$821$	1.73884e16	1.62695	0.813473	+	0.581603i	$0.197574\pi$
$822$	−7.06840e15	−0.656941
$823$	−8.90289e15	−0.821925	−0.410962	−	0.911652i	$-0.634807\pi$
$823$	−8.90289e15	−0.821925	−0.410962	+	0.911652i	$0.634807\pi$
$824$	1.52670e16	1.40008
$825$	−5.83977e15	−0.531985
$826$	1.96340e15	0.177672
$827$	−4.62970e15	−0.416172	−0.208086	−	0.978111i	$-0.566723\pi$
$827$	−4.62970e15	−0.416172	−0.208086	+	0.978111i	$0.566723\pi$
$828$	−9.56014e13	−0.00853684
$829$	1.14604e16	1.01660	0.508299	−	0.861181i	$-0.330275\pi$
$829$	1.14604e16	1.01660	0.508299	+	0.861181i	$0.330275\pi$
$830$	2.73469e14	0.0240979
$831$	−3.66153e15	−0.320522
$832$	2.27605e16	1.97927
$833$	1.28083e16	1.10648
$834$	−2.30966e15	−0.198214
$835$	3.49552e14	0.0298013
$836$	−4.44230e15	−0.376247
$837$	−9.70413e14	−0.0816520
$838$	1.22032e16	1.02007
$839$	7.27881e15	0.604463	0.302232	−	0.953235i	$-0.402268\pi$
$839$	7.27881e15	0.604463	0.302232	+	0.953235i	$0.402268\pi$
$840$	−2.71558e14	−0.0224040
$841$	−9.90373e15	−0.811747
$842$	−8.60625e15	−0.700806
$843$	−8.77852e15	−0.710182
$844$	4.49831e15	0.361548
$845$	6.21566e14	0.0496335
$846$	1.65517e15	0.131312
$847$	3.00460e15	0.236825
$848$	2.95439e13	0.00231361
$849$	−1.79565e14	−0.0139710
$850$	8.30848e15	0.642270
$851$	−7.38157e14	−0.0566939
$852$	−1.81029e14	−0.0138143
$853$	−2.24056e16	−1.69878	−0.849390	−	0.527766i	$-0.823030\pi$
$853$	−2.24056e16	−1.69878	−0.849390	+	0.527766i	$0.823030\pi$
$854$	−2.55684e15	−0.192613
$855$	1.63933e14	0.0122703
$856$	−1.26088e16	−0.937711
$857$	2.08862e16	1.54336	0.771678	−	0.636014i	$-0.219418\pi$
$857$	2.08862e16	1.54336	0.771678	+	0.636014i	$0.219418\pi$
$858$	−1.11909e16	−0.821650
$859$	1.61887e16	1.18100	0.590500	−	0.807038i	$-0.298931\pi$
$859$	1.61887e16	1.18100	0.590500	+	0.807038i	$0.298931\pi$
$860$	−4.48507e13	−0.00325108
$861$	4.53005e15	0.326276
$862$	−2.24195e16	−1.60449
$863$	−2.12574e16	−1.51165	−0.755823	−	0.654776i	$-0.772763\pi$
$863$	−2.12574e16	−1.51165	−0.755823	+	0.654776i	$0.772763\pi$
$864$	−1.33595e15	−0.0943984
$865$	3.90431e14	0.0274129
$866$	1.77055e16	1.23527
$867$	−3.73155e15	−0.258693
$868$	−2.44716e15	−0.168579
$869$	1.03984e16	0.711798
$870$	7.23538e13	0.00492159
$871$	1.81472e16	1.22662
$872$	−2.27756e15	−0.152978
$873$	3.83493e15	0.255964
$874$	−2.14931e15	−0.142556
$875$	1.08718e15	0.0716571
$876$	−1.68977e15	−0.110677
$877$	1.97651e16	1.28647	0.643237	−	0.765667i	$-0.277591\pi$
$877$	1.97651e16	1.28647	0.643237	+	0.765667i	$0.277591\pi$
$878$	−1.09886e16	−0.710757
$879$	1.28383e16	0.825219
$880$	−2.24474e14	−0.0143387
$881$	−8.05942e14	−0.0511607	−0.0255803	−	0.999673i	$-0.508143\pi$
$881$	−8.05942e14	−0.0511607	−0.0255803	+	0.999673i	$0.508143\pi$
$882$	−6.80705e15	−0.429419
$883$	2.51360e16	1.57584	0.787922	−	0.615775i	$-0.211157\pi$
$883$	2.51360e16	1.57584	0.787922	+	0.615775i	$0.211157\pi$
$884$	−5.35926e15	−0.333901
$885$	2.75739e13	0.00170730
$886$	−1.68063e16	−1.03416
$887$	−1.94110e16	−1.18705	−0.593524	−	0.804816i	$-0.702264\pi$
$887$	−1.94110e16	−1.18705	−0.593524	+	0.804816i	$0.702264\pi$
$888$	−5.73436e15	−0.348509
$889$	4.39933e16	2.65722
$890$	4.12624e14	0.0247691
$891$	1.71699e15	0.102433
$892$	5.10814e15	0.302870
$893$	−1.25253e16	−0.738083
$894$	−1.45547e16	−0.852405
$895$	−2.00172e14	−0.0116514
$896$	1.27846e16	0.739596
$897$	1.82251e15	0.104788
$898$	1.37811e16	0.787526
$899$	3.24114e15	0.184085
$900$	1.48628e15	0.0839007
$901$	−4.47392e13	−0.00251016
$902$	5.12178e15	0.285617
$903$	−9.34088e15	−0.517732
$904$	7.45546e15	0.410722
$905$	6.32037e14	0.0346079
$906$	1.00217e16	0.545425
$907$	2.00957e16	1.08708	0.543542	−	0.839382i	$-0.317083\pi$
$907$	2.00957e16	1.08708	0.543542	+	0.839382i	$0.317083\pi$
$908$	−5.06215e15	−0.272184
$909$	7.85361e15	0.419728
$910$	1.04144e15	0.0553229
$911$	7.42610e15	0.392112	0.196056	−	0.980593i	$-0.437187\pi$
$911$	7.42610e15	0.392112	0.196056	+	0.980593i	$0.437187\pi$
$912$	−1.22073e16	−0.640692
$913$	−2.16749e16	−1.13075
$914$	7.29913e15	0.378501
$915$	−3.59081e13	−0.00185087
$916$	−2.31334e15	−0.118526
$917$	1.31483e16	0.669637
$918$	−2.44284e15	−0.123669
$919$	6.17137e15	0.310561	0.155280	−	0.987870i	$-0.450372\pi$
$919$	6.17137e15	0.310561	0.155280	+	0.987870i	$0.450372\pi$
$920$	5.00014e13	0.00250120
$921$	1.28951e16	0.641204
$922$	8.84533e15	0.437214
$923$	3.45106e15	0.169568
$924$	4.32987e15	0.211485
$925$	1.14758e16	0.557192
$926$	−2.73746e16	−1.32126
$927$	8.98307e15	0.431009
$928$	4.46202e15	0.212822
$929$	−7.02023e15	−0.332863	−0.166431	−	0.986053i	$-0.553224\pi$
$929$	−7.02023e15	−0.332863	−0.166431	+	0.986053i	$0.553224\pi$
$930$	1.02103e14	0.00481264
$931$	5.15116e16	2.41369
$932$	9.94918e15	0.463446
$933$	1.20390e16	0.557494
$934$	−2.81304e15	−0.129499
$935$	3.39927e14	0.0155569
$936$	1.41581e16	0.644152
$937$	−2.63747e16	−1.19294	−0.596472	−	0.802634i	$-0.703431\pi$
$937$	−2.63747e16	−1.19294	−0.596472	+	0.802634i	$0.703431\pi$
$938$	2.08596e16	0.937972
$939$	9.78497e15	0.437420
$940$	5.86188e13	0.00260516
$941$	−8.37641e15	−0.370096	−0.185048	−	0.982729i	$-0.559244\pi$
$941$	−8.37641e15	−0.370096	−0.185048	+	0.982729i	$0.559244\pi$
$942$	1.45690e16	0.639957
$943$	−8.34110e14	−0.0364258
$944$	−2.05329e15	−0.0891467
$945$	−1.59784e14	−0.00689698
$946$	−1.05610e16	−0.453215
$947$	−1.64277e16	−0.700895	−0.350447	−	0.936582i	$-0.613970\pi$
$947$	−1.64277e16	−0.700895	−0.350447	+	0.936582i	$0.613970\pi$
$948$	−2.64648e15	−0.112260
$949$	3.22132e16	1.35853
$950$	3.34144e16	1.40105
$951$	7.20669e15	0.300430
$952$	−3.06222e16	−1.26921
$953$	−1.19901e16	−0.494097	−0.247048	−	0.969003i	$-0.579461\pi$
$953$	−1.19901e16	−0.494097	−0.247048	+	0.969003i	$0.579461\pi$
$954$	2.37768e13	0.000974177 0
$955$	9.94557e14	0.0405145
$956$	−9.80268e15	−0.397033
$957$	−5.73468e15	−0.230937
$958$	−2.70423e15	−0.108276
$959$	−5.21356e16	−2.07555
$960$	3.67424e14	0.0145437
$961$	−2.08347e16	−0.819990
$962$	2.19915e16	0.860583
$963$	−7.41902e15	−0.288670
$964$	9.47329e15	0.366502
$965$	2.26848e14	0.00872641
$966$	2.09491e15	0.0801293
$967$	2.13763e16	0.812995	0.406497	−	0.913652i	$-0.366750\pi$
$967$	2.13763e16	0.812995	0.406497	+	0.913652i	$0.366750\pi$
$968$	−4.29777e15	−0.162528
$969$	1.84859e16	0.695121
$970$	−4.03497e14	−0.0150868
$971$	2.09662e16	0.779497	0.389749	−	0.920921i	$-0.372562\pi$
$971$	2.09662e16	0.779497	0.389749	+	0.920921i	$0.372562\pi$
$972$	−4.36991e14	−0.0161550
$973$	−1.70358e16	−0.626240
$974$	−2.54478e16	−0.930198
$975$	−2.83338e16	−1.02986
$976$	2.67391e15	0.0966434
$977$	4.44124e16	1.59619	0.798095	−	0.602532i	$-0.205841\pi$
$977$	4.44124e16	1.59619	0.798095	+	0.602532i	$0.205841\pi$
$978$	5.06653e15	0.181070
$979$	−3.27041e16	−1.16225
$980$	−2.41076e14	−0.00851943
$981$	−1.34012e15	−0.0470937
$982$	−4.03015e16	−1.40834
$983$	2.35985e16	0.820051	0.410025	−	0.912074i	$-0.365520\pi$
$983$	2.35985e16	0.820051	0.410025	+	0.912074i	$0.365520\pi$
$984$	−6.47977e15	−0.223917
$985$	−3.60765e14	−0.0123973
$986$	8.15897e15	0.278813
$987$	1.22083e16	0.414869
$988$	−2.15535e16	−0.728373
$989$	1.71992e15	0.0578000
$990$	−1.80656e14	−0.00603751
$991$	2.85391e16	0.948497	0.474248	−	0.880391i	$-0.342720\pi$
$991$	2.85391e16	0.948497	0.474248	+	0.880391i	$0.342720\pi$
$992$	6.29665e15	0.208111
$993$	−1.42693e16	−0.469010
$994$	3.96687e15	0.129665
$995$	1.28712e15	0.0418399
$996$	5.51646e15	0.178334
$997$	7.94845e15	0.255540	0.127770	−	0.991804i	$-0.459218\pi$
$997$	7.94845e15	0.255540	0.127770	+	0.991804i	$0.459218\pi$
$998$	2.76289e16	0.883377
$999$	−3.37409e15	−0.107287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-39.1439 q^{2} +243.000 q^{3} -515.752 q^{4} +158.720 q^{5} -9511.98 q^{6} -70159.1 q^{7} +100355. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-39.1439 q^{2} +243.000 q^{3} -515.752 q^{4} +158.720 q^{5} -9511.98 q^{6} -70159.1 q^{7} +100355. q^{8} +59049.0 q^{9} -6212.92 q^{10} +492429. q^{11} -125328. q^{12} +2.38920e6 q^{13} +2.74630e6 q^{14} +38568.9 q^{15} -2.87204e6 q^{16} +4.34922e6 q^{17} -2.31141e6 q^{18} +1.74914e7 q^{19} -81860.1 q^{20} -1.70487e7 q^{21} -1.92756e7 q^{22} +3.13914e6 q^{23} +2.43864e7 q^{24} -4.88029e7 q^{25} -9.35227e7 q^{26} +1.43489e7 q^{27} +3.61847e7 q^{28} -4.79247e7 q^{29} -1.50974e6 q^{30} -6.76298e7 q^{31} -9.31047e7 q^{32} +1.19660e8 q^{33} -1.70246e8 q^{34} -1.11356e7 q^{35} -3.04546e7 q^{36} -2.35146e8 q^{37} -6.84681e8 q^{38} +5.80576e8 q^{39} +1.59284e7 q^{40} -2.65713e8 q^{41} +6.67352e8 q^{42} +5.47895e8 q^{43} -2.53971e8 q^{44} +9.37225e6 q^{45} -1.22878e8 q^{46} -7.16085e8 q^{47} -6.97907e8 q^{48} +2.94498e9 q^{49} +1.91034e9 q^{50} +1.05686e9 q^{51} -1.23224e9 q^{52} -1.02867e7 q^{53} -5.61673e8 q^{54} +7.81582e7 q^{55} -7.04084e9 q^{56} +4.25040e9 q^{57} +1.87596e9 q^{58} +7.14924e8 q^{59} -1.98920e7 q^{60} -9.31011e8 q^{61} +2.64730e9 q^{62} -4.14283e9 q^{63} +9.52643e9 q^{64} +3.79213e8 q^{65} -4.68397e9 q^{66} +7.59551e9 q^{67} -2.24312e9 q^{68} +7.62811e8 q^{69} +4.35893e8 q^{70} +1.44444e9 q^{71} +5.92588e9 q^{72} +1.34828e10 q^{73} +9.20456e9 q^{74} -1.18591e10 q^{75} -9.02121e9 q^{76} -3.45484e10 q^{77} -2.27260e10 q^{78} +2.11165e10 q^{79} -4.55850e8 q^{80} +3.48678e9 q^{81} +1.04010e10 q^{82} -4.40162e10 q^{83} +8.79289e9 q^{84} +6.90307e8 q^{85} -2.14468e10 q^{86} -1.16457e10 q^{87} +4.94179e10 q^{88} -6.64139e10 q^{89} -3.66867e8 q^{90} -1.67624e11 q^{91} -1.61902e9 q^{92} -1.64340e10 q^{93} +2.80304e10 q^{94} +2.77623e9 q^{95} -2.26244e10 q^{96} +6.49449e10 q^{97} -1.15278e11 q^{98} +2.90774e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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

Modular forms

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