LMFDB - Embedded newform 177.12.a.d.1.10

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			1.10
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)

$f(q)$	$=$	$q-33.4729 q^{2} +243.000 q^{3} -927.563 q^{4} -11827.5 q^{5} -8133.92 q^{6} +55304.7 q^{7} +99600.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-33.4729 q^{2} +243.000 q^{3} -927.563 q^{4} -11827.5 q^{5} -8133.92 q^{6} +55304.7 q^{7} +99600.8 q^{8} +59049.0 q^{9} +395902. q^{10} +310193. q^{11} -225398. q^{12} +635071. q^{13} -1.85121e6 q^{14} -2.87409e6 q^{15} -1.43428e6 q^{16} +4.94920e6 q^{17} -1.97654e6 q^{18} +7.38988e6 q^{19} +1.09708e7 q^{20} +1.34390e7 q^{21} -1.03831e7 q^{22} +5.49557e7 q^{23} +2.42030e7 q^{24} +9.10623e7 q^{25} -2.12577e7 q^{26} +1.43489e7 q^{27} -5.12986e7 q^{28} -1.08586e8 q^{29} +9.62042e7 q^{30} -1.74859e8 q^{31} -1.55973e8 q^{32} +7.53769e7 q^{33} -1.65664e8 q^{34} -6.54118e8 q^{35} -5.47716e7 q^{36} +2.79905e8 q^{37} -2.47361e8 q^{38} +1.54322e8 q^{39} -1.17803e9 q^{40} +2.62906e8 q^{41} -4.49844e8 q^{42} -6.62017e8 q^{43} -2.87723e8 q^{44} -6.98404e8 q^{45} -1.83953e9 q^{46} +2.01581e9 q^{47} -3.48531e8 q^{48} +1.08128e9 q^{49} -3.04812e9 q^{50} +1.20266e9 q^{51} -5.89068e8 q^{52} +1.32226e9 q^{53} -4.80300e8 q^{54} -3.66881e9 q^{55} +5.50839e9 q^{56} +1.79574e9 q^{57} +3.63469e9 q^{58} +7.14924e8 q^{59} +2.66590e9 q^{60} -1.28279e10 q^{61} +5.85305e9 q^{62} +3.26569e9 q^{63} +8.15828e9 q^{64} -7.51131e9 q^{65} -2.52309e9 q^{66} -3.98567e9 q^{67} -4.59070e9 q^{68} +1.33542e10 q^{69} +2.18952e10 q^{70} +4.51133e9 q^{71} +5.88133e9 q^{72} -1.35618e10 q^{73} -9.36925e9 q^{74} +2.21281e10 q^{75} -6.85458e9 q^{76} +1.71551e10 q^{77} -5.16561e9 q^{78} +3.46284e10 q^{79} +1.69640e10 q^{80} +3.48678e9 q^{81} -8.80025e9 q^{82} +3.01060e10 q^{83} -1.24655e10 q^{84} -5.85369e10 q^{85} +2.21597e10 q^{86} -2.63864e10 q^{87} +3.08955e10 q^{88} +2.22704e10 q^{89} +2.33776e10 q^{90} +3.51224e10 q^{91} -5.09749e10 q^{92} -4.24908e10 q^{93} -6.74752e10 q^{94} -8.74041e10 q^{95} -3.79014e10 q^{96} -8.94449e10 q^{97} -3.61936e10 q^{98} +1.83166e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−33.4729	−0.739654	−0.369827	−	0.929101i	$-0.620583\pi$
$2$	−33.4729	−0.739654	−0.369827	+	0.929101i	$0.620583\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−927.563	−0.452911
$5$	−11827.5	−1.69262	−0.846309	−	0.532692i	$-0.821180\pi$
$5$	−11827.5	−1.69262	−0.846309	+	0.532692i	$0.821180\pi$
$6$	−8133.92	−0.427040
$7$	55304.7	1.24372	0.621860	−	0.783128i	$-0.286377\pi$
$7$	55304.7	1.24372	0.621860	+	0.783128i	$0.286377\pi$
$8$	99600.8	1.07465
$9$	59049.0	0.333333
$10$	395902.	1.25195
$11$	310193.	0.580727	0.290364	−	0.956916i	$-0.406224\pi$
$11$	310193.	0.580727	0.290364	+	0.956916i	$0.406224\pi$
$12$	−225398.	−0.261489
$13$	635071.	0.474388	0.237194	−	0.971462i	$-0.423772\pi$
$13$	635071.	0.474388	0.237194	+	0.971462i	$0.423772\pi$
$14$	−1.85121e6	−0.919923
$15$	−2.87409e6	−0.977233
$16$	−1.43428e6	−0.341960
$17$	4.94920e6	0.845408	0.422704	−	0.906268i	$-0.361081\pi$
$17$	4.94920e6	0.845408	0.422704	+	0.906268i	$0.361081\pi$
$18$	−1.97654e6	−0.246551
$19$	7.38988e6	0.684688	0.342344	−	0.939575i	$-0.388779\pi$
$19$	7.38988e6	0.684688	0.342344	+	0.939575i	$0.388779\pi$
$20$	1.09708e7	0.766606
$21$	1.34390e7	0.718062
$22$	−1.03831e7	−0.429537
$23$	5.49557e7	1.78037	0.890184	−	0.455602i	$-0.150576\pi$
$23$	5.49557e7	1.78037	0.890184	+	0.455602i	$0.150576\pi$
$24$	2.42030e7	0.620451
$25$	9.10623e7	1.86496
$26$	−2.12577e7	−0.350883
$27$	1.43489e7	0.192450
$28$	−5.12986e7	−0.563295
$29$	−1.08586e8	−0.983071	−0.491536	−	0.870857i	$-0.663564\pi$
$29$	−1.08586e8	−0.983071	−0.491536	+	0.870857i	$0.663564\pi$
$30$	9.62042e7	0.722815
$31$	−1.74859e8	−1.09698	−0.548491	−	0.836157i	$-0.684797\pi$
$31$	−1.74859e8	−1.09698	−0.548491	+	0.836157i	$0.684797\pi$
$32$	−1.55973e8	−0.821720
$33$	7.53769e7	0.335283
$34$	−1.65664e8	−0.625310
$35$	−6.54118e8	−2.10514
$36$	−5.47716e7	−0.150970
$37$	2.79905e8	0.663593	0.331796	−	0.943351i	$-0.392345\pi$
$37$	2.79905e8	0.663593	0.331796	+	0.943351i	$0.392345\pi$
$38$	−2.47361e8	−0.506433
$39$	1.54322e8	0.273888
$40$	−1.17803e9	−1.81898
$41$	2.62906e8	0.354397	0.177198	−	0.984175i	$-0.443297\pi$
$41$	2.62906e8	0.354397	0.177198	+	0.984175i	$0.443297\pi$
$42$	−4.49844e8	−0.531118
$43$	−6.62017e8	−0.686741	−0.343370	−	0.939200i	$-0.611569\pi$
$43$	−6.62017e8	−0.686741	−0.343370	+	0.939200i	$0.611569\pi$
$44$	−2.87723e8	−0.263018
$45$	−6.98404e8	−0.564206
$46$	−1.83953e9	−1.31686
$47$	2.01581e9	1.28207	0.641035	−	0.767511i	$-0.278505\pi$
$47$	2.01581e9	1.28207	0.641035	+	0.767511i	$0.278505\pi$
$48$	−3.48531e8	−0.197431
$49$	1.08128e9	0.546840
$50$	−3.04812e9	−1.37942
$51$	1.20266e9	0.488097
$52$	−5.89068e8	−0.214856
$53$	1.32226e9	0.434310	0.217155	−	0.976137i	$-0.430322\pi$
$53$	1.32226e9	0.434310	0.217155	+	0.976137i	$0.430322\pi$
$54$	−4.80300e8	−0.142347
$55$	−3.66881e9	−0.982949
$56$	5.50839e9	1.33657
$57$	1.79574e9	0.395305
$58$	3.63469e9	0.727133
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	2.66590e9	0.442600
$61$	−1.28279e10	−1.94465	−0.972323	−	0.233642i	$-0.924936\pi$
$61$	−1.28279e10	−1.94465	−0.972323	+	0.233642i	$0.924936\pi$
$62$	5.85305e9	0.811387
$63$	3.26569e9	0.414573
$64$	8.15828e9	0.949749
$65$	−7.51131e9	−0.802957
$66$	−2.52309e9	−0.247993
$67$	−3.98567e9	−0.360654	−0.180327	−	0.983607i	$-0.557716\pi$
$67$	−3.98567e9	−0.360654	−0.180327	+	0.983607i	$0.557716\pi$
$68$	−4.59070e9	−0.382895
$69$	1.33542e10	1.02790
$70$	2.18952e10	1.55708
$71$	4.51133e9	0.296745	0.148373	−	0.988932i	$-0.452596\pi$
$71$	4.51133e9	0.296745	0.148373	+	0.988932i	$0.452596\pi$
$72$	5.88133e9	0.358217
$73$	−1.35618e10	−0.765668	−0.382834	−	0.923817i	$-0.625052\pi$
$73$	−1.35618e10	−0.765668	−0.382834	+	0.923817i	$0.625052\pi$
$74$	−9.36925e9	−0.490829
$75$	2.21281e10	1.07673
$76$	−6.85458e9	−0.310103
$77$	1.71551e10	0.722262
$78$	−5.16561e9	−0.202582
$79$	3.46284e10	1.26614	0.633072	−	0.774093i	$-0.281794\pi$
$79$	3.46284e10	1.26614	0.633072	+	0.774093i	$0.281794\pi$
$80$	1.69640e10	0.578807
$81$	3.48678e9	0.111111
$82$	−8.80025e9	−0.262131
$83$	3.01060e10	0.838927	0.419464	−	0.907772i	$-0.362218\pi$
$83$	3.01060e10	0.838927	0.419464	+	0.907772i	$0.362218\pi$
$84$	−1.24655e10	−0.325219
$85$	−5.85369e10	−1.43095
$86$	2.21597e10	0.507951
$87$	−2.63864e10	−0.567576
$88$	3.08955e10	0.624080
$89$	2.22704e10	0.422750	0.211375	−	0.977405i	$-0.432206\pi$
$89$	2.22704e10	0.422750	0.211375	+	0.977405i	$0.432206\pi$
$90$	2.33776e10	0.417317
$91$	3.51224e10	0.590006
$92$	−5.09749e10	−0.806349
$93$	−4.24908e10	−0.633343
$94$	−6.74752e10	−0.948289
$95$	−8.74041e10	−1.15892
$96$	−3.79014e10	−0.474420
$97$	−8.94449e10	−1.05758	−0.528788	−	0.848754i	$-0.677353\pi$
$97$	−8.94449e10	−1.05758	−0.528788	+	0.848754i	$0.677353\pi$
$98$	−3.61936e10	−0.404472
$99$	1.83166e10	0.193576
$100$	−8.44660e10	−0.844660
$101$	−4.57588e10	−0.433219	−0.216609	−	0.976258i	$-0.569500\pi$
$101$	−4.57588e10	−0.433219	−0.216609	+	0.976258i	$0.569500\pi$
$102$	−4.02565e10	−0.361023
$103$	2.53716e10	0.215647	0.107823	−	0.994170i	$-0.465612\pi$
$103$	2.53716e10	0.215647	0.107823	+	0.994170i	$0.465612\pi$
$104$	6.32535e10	0.509802
$105$	−1.58951e11	−1.21540
$106$	−4.42599e10	−0.321239
$107$	5.58310e10	0.384826	0.192413	−	0.981314i	$-0.438369\pi$
$107$	5.58310e10	0.384826	0.192413	+	0.981314i	$0.438369\pi$
$108$	−1.33095e10	−0.0871628
$109$	1.74576e11	1.08677	0.543386	−	0.839483i	$-0.317142\pi$
$109$	1.74576e11	1.08677	0.543386	+	0.839483i	$0.317142\pi$
$110$	1.22806e11	0.727043
$111$	6.80170e10	0.383125
$112$	−7.93226e10	−0.425302
$113$	2.62472e10	0.134014	0.0670071	−	0.997752i	$-0.478655\pi$
$113$	2.62472e10	0.134014	0.0670071	+	0.997752i	$0.478655\pi$
$114$	−6.01088e10	−0.292389
$115$	−6.49990e11	−3.01348
$116$	1.00720e11	0.445244
$117$	3.75003e10	0.158129
$118$	−2.39306e10	−0.0962948
$119$	2.73714e11	1.05145
$120$	−2.86262e11	−1.05019
$121$	−1.89092e11	−0.662756
$122$	4.29386e11	1.43837
$123$	6.38863e10	0.204611
$124$	1.62193e11	0.496836
$125$	−4.99526e11	−1.46404
$126$	−1.09312e11	−0.306641
$127$	8.60866e10	0.231215	0.115607	−	0.993295i	$-0.463119\pi$
$127$	8.60866e10	0.231215	0.115607	+	0.993295i	$0.463119\pi$
$128$	4.63507e10	0.119234
$129$	−1.60870e11	−0.396490
$130$	2.51426e11	0.593911
$131$	3.13858e11	0.710789	0.355395	−	0.934716i	$-0.384346\pi$
$131$	3.13858e11	0.710789	0.355395	+	0.934716i	$0.384346\pi$
$132$	−6.99168e10	−0.151853
$133$	4.08695e11	0.851560
$134$	1.33412e11	0.266759
$135$	−1.69712e11	−0.325744
$136$	4.92945e11	0.908520
$137$	6.14363e10	0.108758	0.0543791	−	0.998520i	$-0.482682\pi$
$137$	6.14363e10	0.108758	0.0543791	+	0.998520i	$0.482682\pi$
$138$	−4.47005e11	−0.760287
$139$	3.91170e11	0.639417	0.319709	−	0.947516i	$-0.396415\pi$
$139$	3.91170e11	0.639417	0.319709	+	0.947516i	$0.396415\pi$
$140$	6.06735e11	0.953443
$141$	4.89843e11	0.740204
$142$	−1.51008e11	−0.219489
$143$	1.96994e11	0.275490
$144$	−8.46930e10	−0.113987
$145$	1.28430e12	1.66396
$146$	4.53952e11	0.566330
$147$	2.62751e11	0.315718
$148$	−2.59630e11	−0.300549
$149$	−1.13502e12	−1.26613	−0.633064	−	0.774099i	$-0.718203\pi$
$149$	−1.13502e12	−1.26613	−0.633064	+	0.774099i	$0.718203\pi$
$150$	−7.40694e11	−0.796410
$151$	−5.95629e11	−0.617451	−0.308726	−	0.951151i	$-0.599903\pi$
$151$	−5.95629e11	−0.617451	−0.308726	+	0.951151i	$0.599903\pi$
$152$	7.36039e11	0.735802
$153$	2.92246e11	0.281803
$154$	−5.74232e11	−0.534224
$155$	2.06815e12	1.85677
$156$	−1.43143e11	−0.124047
$157$	6.19298e11	0.518145	0.259072	−	0.965858i	$-0.416583\pi$
$157$	6.19298e11	0.518145	0.259072	+	0.965858i	$0.416583\pi$
$158$	−1.15911e12	−0.936508
$159$	3.21309e11	0.250749
$160$	1.84477e12	1.39086
$161$	3.03931e12	2.21428
$162$	−1.16713e11	−0.0821838
$163$	−3.02889e11	−0.206183	−0.103091	−	0.994672i	$-0.532873\pi$
$163$	−3.02889e11	−0.206183	−0.103091	+	0.994672i	$0.532873\pi$
$164$	−2.43862e11	−0.160510
$165$	−8.91522e11	−0.567506
$166$	−1.00774e12	−0.620516
$167$	−2.88370e12	−1.71795	−0.858974	−	0.512020i	$-0.828897\pi$
$167$	−2.88370e12	−1.71795	−0.858974	+	0.512020i	$0.828897\pi$
$168$	1.33854e12	0.771667
$169$	−1.38885e12	−0.774956
$170$	1.95940e12	1.05841
$171$	4.36365e11	0.228229
$172$	6.14062e11	0.311033
$173$	3.10578e12	1.52376	0.761881	−	0.647717i	$-0.224276\pi$
$173$	3.10578e12	1.52376	0.761881	+	0.647717i	$0.224276\pi$
$174$	8.83230e11	0.419810
$175$	5.03617e12	2.31948
$176$	−4.44904e11	−0.198585
$177$	1.73727e11	0.0751646
$178$	−7.45456e11	−0.312689
$179$	−5.83860e11	−0.237475	−0.118737	−	0.992926i	$-0.537885\pi$
$179$	−5.83860e11	−0.237475	−0.118737	+	0.992926i	$0.537885\pi$
$180$	6.47813e11	0.255535
$181$	−1.55134e12	−0.593573	−0.296786	−	0.954944i	$-0.595915\pi$
$181$	−1.55134e12	−0.593573	−0.296786	+	0.954944i	$0.595915\pi$
$182$	−1.17565e12	−0.436400
$183$	−3.11717e12	−1.12274
$184$	5.47363e12	1.91328
$185$	−3.31059e12	−1.12321
$186$	1.42229e12	0.468455
$187$	1.53521e12	0.490951
$188$	−1.86979e12	−0.580665
$189$	7.93562e11	0.239354
$190$	2.92567e12	0.857197
$191$	−1.36960e12	−0.389861	−0.194931	−	0.980817i	$-0.562448\pi$
$191$	−1.36960e12	−0.389861	−0.194931	+	0.980817i	$0.562448\pi$
$192$	1.98246e12	0.548338
$193$	3.06839e12	0.824794	0.412397	−	0.911004i	$-0.364692\pi$
$193$	3.06839e12	0.824794	0.412397	+	0.911004i	$0.364692\pi$
$194$	2.99398e12	0.782240
$195$	−1.82525e12	−0.463588
$196$	−1.00296e12	−0.247670
$197$	7.65200e12	1.83743	0.918715	−	0.394921i	$-0.129228\pi$
$197$	7.65200e12	1.83743	0.918715	+	0.394921i	$0.129228\pi$
$198$	−6.13110e11	−0.143179
$199$	7.77276e12	1.76556	0.882782	−	0.469783i	$-0.155668\pi$
$199$	7.77276e12	1.76556	0.882782	+	0.469783i	$0.155668\pi$
$200$	9.06988e12	2.00418
$201$	−9.68519e11	−0.208224
$202$	1.53168e12	0.320432
$203$	−6.00532e12	−1.22267
$204$	−1.11554e12	−0.221065
$205$	−3.10953e12	−0.599859
$206$	−8.49261e11	−0.159504
$207$	3.24508e12	0.593456
$208$	−9.10871e11	−0.162222
$209$	2.29229e12	0.397617
$210$	5.32054e12	0.898979
$211$	7.92113e12	1.30387	0.651934	−	0.758275i	$-0.273958\pi$
$211$	7.92113e12	1.30387	0.651934	+	0.758275i	$0.273958\pi$
$212$	−1.22648e12	−0.196704
$213$	1.09625e12	0.171326
$214$	−1.86883e12	−0.284638
$215$	7.83003e12	1.16239
$216$	1.42916e12	0.206817
$217$	−9.67053e12	−1.36434
$218$	−5.84357e12	−0.803836
$219$	−3.29551e12	−0.442059
$220$	3.40306e12	0.445189
$221$	3.14309e12	0.401051
$222$	−2.27673e12	−0.283380
$223$	1.15651e13	1.40434	0.702171	−	0.712008i	$-0.252214\pi$
$223$	1.15651e13	1.40434	0.702171	+	0.712008i	$0.252214\pi$
$224$	−8.62603e12	−1.02199
$225$	5.37714e12	0.621652
$226$	−8.78570e11	−0.0991242
$227$	3.55430e12	0.391392	0.195696	−	0.980665i	$-0.437303\pi$
$227$	3.55430e12	0.391392	0.195696	+	0.980665i	$0.437303\pi$
$228$	−1.66566e12	−0.179038
$229$	−1.38410e13	−1.45236	−0.726178	−	0.687507i	$-0.758705\pi$
$229$	−1.38410e13	−1.45236	−0.726178	+	0.687507i	$0.758705\pi$
$230$	2.17571e13	2.22894
$231$	4.16869e12	0.416998
$232$	−1.08153e13	−1.05646
$233$	−1.32391e13	−1.26299	−0.631495	−	0.775380i	$-0.717558\pi$
$233$	−1.32391e13	−1.26299	−0.631495	+	0.775380i	$0.717558\pi$
$234$	−1.25524e12	−0.116961
$235$	−2.38421e13	−2.17006
$236$	−6.63137e11	−0.0589640
$237$	8.41469e12	0.731008
$238$	−9.16202e12	−0.777710
$239$	−4.46934e12	−0.370727	−0.185364	−	0.982670i	$-0.559346\pi$
$239$	−4.46934e12	−0.370727	−0.185364	+	0.982670i	$0.559346\pi$
$240$	4.12226e12	0.334175
$241$	5.74664e12	0.455324	0.227662	−	0.973740i	$-0.426892\pi$
$241$	5.74664e12	0.455324	0.227662	+	0.973740i	$0.426892\pi$
$242$	6.32947e12	0.490210
$243$	8.47289e11	0.0641500
$244$	1.18987e13	0.880752
$245$	−1.27889e13	−0.925590
$246$	−2.13846e12	−0.151342
$247$	4.69310e12	0.324808
$248$	−1.74161e13	−1.17887
$249$	7.31577e12	0.484355
$250$	1.67206e13	1.08288
$251$	1.44705e13	0.916809	0.458404	−	0.888744i	$-0.348421\pi$
$251$	1.44705e13	0.916809	0.458404	+	0.888744i	$0.348421\pi$
$252$	−3.02913e12	−0.187765
$253$	1.70469e13	1.03391
$254$	−2.88157e12	−0.171019
$255$	−1.42245e13	−0.826161
$256$	−1.82597e13	−1.03794
$257$	2.67034e13	1.48571	0.742856	−	0.669451i	$-0.233471\pi$
$257$	2.67034e13	1.48571	0.742856	+	0.669451i	$0.233471\pi$
$258$	5.38480e12	0.293265
$259$	1.54801e13	0.825324
$260$	6.96721e12	0.363669
$261$	−6.41190e12	−0.327690
$262$	−1.05057e13	−0.525738
$263$	1.00444e13	0.492230	0.246115	−	0.969241i	$-0.420846\pi$
$263$	1.00444e13	0.492230	0.246115	+	0.969241i	$0.420846\pi$
$264$	7.50760e12	0.360313
$265$	−1.56391e13	−0.735121
$266$	−1.36802e13	−0.629860
$267$	5.41171e12	0.244075
$268$	3.69696e12	0.163344
$269$	−2.88682e13	−1.24963	−0.624816	−	0.780772i	$-0.714826\pi$
$269$	−2.88682e13	−1.24963	−0.624816	+	0.780772i	$0.714826\pi$
$270$	5.68076e12	0.240938
$271$	2.93904e13	1.22145	0.610724	−	0.791844i	$-0.290879\pi$
$271$	2.93904e13	1.22145	0.610724	+	0.791844i	$0.290879\pi$
$272$	−7.09856e12	−0.289096
$273$	8.53474e12	0.340640
$274$	−2.05645e12	−0.0804435
$275$	2.82469e13	1.08303
$276$	−1.23869e13	−0.465546
$277$	−3.79666e13	−1.39882	−0.699412	−	0.714719i	$-0.746555\pi$
$277$	−3.79666e13	−1.39882	−0.699412	+	0.714719i	$0.746555\pi$
$278$	−1.30936e13	−0.472948
$279$	−1.03253e13	−0.365661
$280$	−6.51506e13	−2.26230
$281$	4.86401e13	1.65619	0.828094	−	0.560589i	$-0.189425\pi$
$281$	4.86401e13	1.65619	0.828094	+	0.560589i	$0.189425\pi$
$282$	−1.63965e13	−0.547495
$283$	−2.79496e13	−0.915271	−0.457636	−	0.889140i	$-0.651304\pi$
$283$	−2.79496e13	−0.915271	−0.457636	+	0.889140i	$0.651304\pi$
$284$	−4.18454e12	−0.134399
$285$	−2.12392e13	−0.669100
$286$	−6.59398e12	−0.203767
$287$	1.45400e13	0.440771
$288$	−9.21004e12	−0.273907
$289$	−9.77727e12	−0.285285
$290$	−4.29894e13	−1.23076
$291$	−2.17351e13	−0.610591
$292$	1.25794e13	0.346780
$293$	2.56382e13	0.693610	0.346805	−	0.937937i	$-0.387267\pi$
$293$	2.56382e13	0.693610	0.346805	+	0.937937i	$0.387267\pi$
$294$	−8.79505e12	−0.233522
$295$	−8.45579e12	−0.220360
$296$	2.78788e13	0.713131
$297$	4.45093e12	0.111761
$298$	3.79924e13	0.936498
$299$	3.49007e13	0.844585
$300$	−2.05252e13	−0.487665
$301$	−3.66126e13	−0.854113
$302$	1.99375e13	0.456701
$303$	−1.11194e13	−0.250119
$304$	−1.05992e13	−0.234136
$305$	1.51722e14	3.29154
$306$	−9.78232e12	−0.208437
$307$	−3.77775e13	−0.790628	−0.395314	−	0.918546i	$-0.629364\pi$
$307$	−3.77775e13	−0.790628	−0.395314	+	0.918546i	$0.629364\pi$
$308$	−1.59124e13	−0.327121
$309$	6.16529e12	0.124504
$310$	−6.92271e13	−1.37337
$311$	2.70770e13	0.527738	0.263869	−	0.964559i	$-0.415001\pi$
$311$	2.70770e13	0.527738	0.263869	+	0.964559i	$0.415001\pi$
$312$	1.53706e13	0.294334
$313$	3.66522e13	0.689615	0.344807	−	0.938673i	$-0.387944\pi$
$313$	3.66522e13	0.689615	0.344807	+	0.938673i	$0.387944\pi$
$314$	−2.07297e13	−0.383248
$315$	−3.86250e13	−0.701714
$316$	−3.21200e13	−0.573451
$317$	2.63514e13	0.462358	0.231179	−	0.972911i	$-0.425742\pi$
$317$	2.63514e13	0.462358	0.231179	+	0.972911i	$0.425742\pi$
$318$	−1.07552e13	−0.185468
$319$	−3.36826e13	−0.570896
$320$	−9.64923e13	−1.60756
$321$	1.35669e13	0.222179
$322$	−1.01735e14	−1.63780
$323$	3.65741e13	0.578841
$324$	−3.23421e12	−0.0503235
$325$	5.78310e13	0.884712
$326$	1.01386e13	0.152504
$327$	4.24219e13	0.627448
$328$	2.61857e13	0.380854
$329$	1.11484e14	1.59454
$330$	2.98419e13	0.419758
$331$	6.09860e12	0.0843677	0.0421839	−	0.999110i	$-0.486568\pi$
$331$	6.09860e12	0.0843677	0.0421839	+	0.999110i	$0.486568\pi$
$332$	−2.79252e13	−0.379960
$333$	1.65281e13	0.221198
$334$	9.65260e13	1.27069
$335$	4.71407e13	0.610449
$336$	−1.92754e13	−0.245548
$337$	2.31559e13	0.290200	0.145100	−	0.989417i	$-0.453650\pi$
$337$	2.31559e13	0.290200	0.145100	+	0.989417i	$0.453650\pi$
$338$	4.64887e13	0.573200
$339$	6.37806e12	0.0773732
$340$	5.42966e13	0.648095
$341$	−5.42401e13	−0.637047
$342$	−1.46064e13	−0.168811
$343$	−4.95555e13	−0.563605
$344$	−6.59374e13	−0.738007
$345$	−1.57948e14	−1.73983
$346$	−1.03960e14	−1.12706
$347$	−1.36157e14	−1.45287	−0.726436	−	0.687234i	$-0.758825\pi$
$347$	−1.36157e14	−1.45287	−0.726436	+	0.687234i	$0.758825\pi$
$348$	2.44750e13	0.257062
$349$	1.72629e14	1.78474	0.892369	−	0.451307i	$-0.149042\pi$
$349$	1.72629e14	1.78474	0.892369	+	0.451307i	$0.149042\pi$
$350$	−1.68575e14	−1.71562
$351$	9.11257e12	0.0912960
$352$	−4.83817e13	−0.477195
$353$	1.46540e14	1.42297	0.711485	−	0.702701i	$-0.248023\pi$
$353$	1.46540e14	1.42297	0.711485	+	0.702701i	$0.248023\pi$
$354$	−5.81514e12	−0.0555958
$355$	−5.33579e13	−0.502276
$356$	−2.06572e13	−0.191468
$357$	6.65125e13	0.607055
$358$	1.95435e13	0.175649
$359$	−9.00449e13	−0.796966	−0.398483	−	0.917176i	$-0.630463\pi$
$359$	−9.00449e13	−0.796966	−0.398483	+	0.917176i	$0.630463\pi$
$360$	−6.95616e13	−0.606325
$361$	−6.18799e13	−0.531202
$362$	5.19278e13	0.439039
$363$	−4.59494e13	−0.382642
$364$	−3.25782e13	−0.267220
$365$	1.60402e14	1.29598
$366$	1.04341e14	0.830441
$367$	4.84767e13	0.380076	0.190038	−	0.981777i	$-0.439139\pi$
$367$	4.84767e13	0.380076	0.190038	+	0.981777i	$0.439139\pi$
$368$	−7.88220e13	−0.608814
$369$	1.55244e13	0.118132
$370$	1.10815e14	0.830786
$371$	7.31272e13	0.540160
$372$	3.94129e13	0.286848
$373$	−1.78441e14	−1.27966	−0.639832	−	0.768515i	$-0.720996\pi$
$373$	−1.78441e14	−1.27966	−0.639832	+	0.768515i	$0.720996\pi$
$374$	−5.13879e13	−0.363134
$375$	−1.21385e14	−0.845263
$376$	2.00777e14	1.37778
$377$	−6.89598e13	−0.466357
$378$	−2.65628e13	−0.177039
$379$	−2.86072e14	−1.87914	−0.939570	−	0.342357i	$-0.888775\pi$
$379$	−2.86072e14	−1.87914	−0.939570	+	0.342357i	$0.888775\pi$
$380$	8.10727e13	0.524886
$381$	2.09191e13	0.133492
$382$	4.58445e13	0.288362
$383$	−2.08002e14	−1.28966	−0.644830	−	0.764326i	$-0.723072\pi$
$383$	−2.08002e14	−1.28966	−0.644830	+	0.764326i	$0.723072\pi$
$384$	1.12632e13	0.0688401
$385$	−2.02903e14	−1.22251
$386$	−1.02708e14	−0.610063
$387$	−3.90915e13	−0.228914
$388$	8.29658e13	0.478988
$389$	1.11622e14	0.635372	0.317686	−	0.948196i	$-0.397094\pi$
$389$	1.11622e14	0.635372	0.317686	+	0.948196i	$0.397094\pi$
$390$	6.10965e13	0.342895
$391$	2.71987e14	1.50514
$392$	1.07696e14	0.587662
$393$	7.62675e13	0.410374
$394$	−2.56135e14	−1.35906
$395$	−4.09568e14	−2.14310
$396$	−1.69898e13	−0.0876726
$397$	−2.59151e14	−1.31888	−0.659440	−	0.751757i	$-0.729206\pi$
$397$	−2.59151e14	−1.31888	−0.659440	+	0.751757i	$0.729206\pi$
$398$	−2.60177e14	−1.30591
$399$	9.93129e13	0.491649
$400$	−1.30609e14	−0.637740
$401$	9.88216e13	0.475946	0.237973	−	0.971272i	$-0.423517\pi$
$401$	9.88216e13	0.475946	0.237973	+	0.971272i	$0.423517\pi$
$402$	3.24192e13	0.154013
$403$	−1.11048e14	−0.520395
$404$	4.24442e13	0.196210
$405$	−4.12400e13	−0.188069
$406$	2.01016e14	0.904350
$407$	8.68246e13	0.385366
$408$	1.19786e14	0.524534
$409$	−2.00981e14	−0.868312	−0.434156	−	0.900838i	$-0.642953\pi$
$409$	−2.00981e14	−0.868312	−0.434156	+	0.900838i	$0.642953\pi$
$410$	1.04085e14	0.443688
$411$	1.49290e13	0.0627916
$412$	−2.35337e13	−0.0976688
$413$	3.95387e13	0.161919
$414$	−1.08622e14	−0.438952
$415$	−3.56080e14	−1.41998
$416$	−9.90537e13	−0.389814
$417$	9.50544e13	0.369168
$418$	−7.67297e13	−0.294099
$419$	2.58507e14	0.977903	0.488952	−	0.872311i	$-0.337379\pi$
$419$	2.58507e14	0.977903	0.488952	+	0.872311i	$0.337379\pi$
$420$	1.47437e14	0.550471
$421$	6.18380e13	0.227879	0.113939	−	0.993488i	$-0.463653\pi$
$421$	6.18380e13	0.227879	0.113939	+	0.993488i	$0.463653\pi$
$422$	−2.65144e14	−0.964412
$423$	1.19032e14	0.427357
$424$	1.31698e14	0.466732
$425$	4.50686e14	1.57665
$426$	−3.66948e13	−0.126722
$427$	−7.09441e14	−2.41859
$428$	−5.17867e13	−0.174292
$429$	4.78696e13	0.159054
$430$	−2.62094e14	−0.859766
$431$	4.14707e14	1.34313	0.671563	−	0.740947i	$-0.265623\pi$
$431$	4.14707e14	1.34313	0.671563	+	0.740947i	$0.265623\pi$
$432$	−2.05804e13	−0.0658102
$433$	−1.63951e14	−0.517645	−0.258822	−	0.965925i	$-0.583334\pi$
$433$	−1.63951e14	−0.517645	−0.258822	+	0.965925i	$0.583334\pi$
$434$	3.23701e14	1.00914
$435$	3.12086e14	0.960690
$436$	−1.61930e14	−0.492212
$437$	4.06116e14	1.21900
$438$	1.10310e14	0.326971
$439$	2.29011e14	0.670349	0.335174	−	0.942156i	$-0.391205\pi$
$439$	2.29011e14	0.670349	0.335174	+	0.942156i	$0.391205\pi$
$440$	−3.65417e14	−1.05633
$441$	6.38485e13	0.182280
$442$	−1.05209e14	−0.296639
$443$	−3.12630e14	−0.870582	−0.435291	−	0.900290i	$-0.643354\pi$
$443$	−3.12630e14	−0.870582	−0.435291	+	0.900290i	$0.643354\pi$
$444$	−6.30900e13	−0.173522
$445$	−2.63404e14	−0.715554
$446$	−3.87118e14	−1.03873
$447$	−2.75809e14	−0.731000
$448$	4.51191e14	1.18122
$449$	−3.46003e14	−0.894797	−0.447399	−	0.894335i	$-0.647649\pi$
$449$	−3.46003e14	−0.894797	−0.447399	+	0.894335i	$0.647649\pi$
$450$	−1.79989e14	−0.459807
$451$	8.15517e13	0.205808
$452$	−2.43459e13	−0.0606966
$453$	−1.44738e14	−0.356486
$454$	−1.18973e14	−0.289495
$455$	−4.15411e14	−0.998654
$456$	1.78857e14	0.424815
$457$	6.34100e14	1.48805	0.744027	−	0.668150i	$-0.232913\pi$
$457$	6.34100e14	1.48805	0.744027	+	0.668150i	$0.232913\pi$
$458$	4.63299e14	1.07424
$459$	7.10157e13	0.162699
$460$	6.02907e14	1.36484
$461$	−9.14184e13	−0.204493	−0.102247	−	0.994759i	$-0.532603\pi$
$461$	−9.14184e13	−0.204493	−0.102247	+	0.994759i	$0.532603\pi$
$462$	−1.39538e14	−0.308434
$463$	−4.66339e14	−1.01861	−0.509303	−	0.860587i	$-0.670097\pi$
$463$	−4.66339e14	−1.01861	−0.509303	+	0.860587i	$0.670097\pi$
$464$	1.55743e14	0.336171
$465$	5.02561e14	1.07201
$466$	4.43150e14	0.934175
$467$	−5.25176e14	−1.09411	−0.547056	−	0.837096i	$-0.684252\pi$
$467$	−5.25176e14	−1.09411	−0.547056	+	0.837096i	$0.684252\pi$
$468$	−3.47839e13	−0.0716186
$469$	−2.20426e14	−0.448552
$470$	7.98064e14	1.60509
$471$	1.50489e14	0.299151
$472$	7.12070e13	0.139908
$473$	−2.05353e14	−0.398809
$474$	−2.81664e14	−0.540693
$475$	6.72940e14	1.27691
$476$	−2.53887e14	−0.476214
$477$	7.80782e13	0.144770
$478$	1.49602e14	0.274210
$479$	−3.00365e14	−0.544257	−0.272128	−	0.962261i	$-0.587728\pi$
$479$	−3.00365e14	−0.544257	−0.272128	+	0.962261i	$0.587728\pi$
$480$	4.48280e14	0.803012
$481$	1.77760e14	0.314800
$482$	−1.92357e14	−0.336782
$483$	7.38552e14	1.27841
$484$	1.75395e14	0.300170
$485$	1.05791e15	1.79007
$486$	−2.83612e13	−0.0474488
$487$	4.61971e14	0.764197	0.382098	−	0.924122i	$-0.375202\pi$
$487$	4.61971e14	0.764197	0.382098	+	0.924122i	$0.375202\pi$
$488$	−1.27767e15	−2.08982
$489$	−7.36021e13	−0.119040
$490$	4.28081e14	0.684617
$491$	4.64833e14	0.735104	0.367552	−	0.930003i	$-0.380196\pi$
$491$	4.64833e14	0.735104	0.367552	+	0.930003i	$0.380196\pi$
$492$	−5.92585e13	−0.0926708
$493$	−5.37415e14	−0.831096
$494$	−1.57092e14	−0.240245
$495$	−2.16640e14	−0.327650
$496$	2.50798e14	0.375124
$497$	2.49498e14	0.369068
$498$	−2.44880e14	−0.358255
$499$	−8.26145e14	−1.19537	−0.597686	−	0.801730i	$-0.703913\pi$
$499$	−8.26145e14	−1.19537	−0.597686	+	0.801730i	$0.703913\pi$
$500$	4.63341e14	0.663080
$501$	−7.00740e14	−0.991857
$502$	−4.84371e14	−0.678121
$503$	4.95542e14	0.686210	0.343105	−	0.939297i	$-0.388521\pi$
$503$	4.95542e14	0.686210	0.343105	+	0.939297i	$0.388521\pi$
$504$	3.25265e14	0.445522
$505$	5.41214e14	0.733274
$506$	−5.70609e14	−0.764734
$507$	−3.37490e14	−0.447421
$508$	−7.98508e13	−0.104720
$509$	1.10728e15	1.43651	0.718254	−	0.695781i	$-0.244941\pi$
$509$	1.10728e15	1.43651	0.718254	+	0.695781i	$0.244941\pi$
$510$	4.76134e14	0.611074
$511$	−7.50029e14	−0.952277
$512$	5.16278e14	0.648483
$513$	1.06037e14	0.131768
$514$	−8.93842e14	−1.09891
$515$	−3.00083e14	−0.365007
$516$	1.49217e14	0.179575
$517$	6.25291e14	0.744533
$518$	−5.18163e14	−0.610454
$519$	7.54705e14	0.879744
$520$	−7.48133e14	−0.862900
$521$	1.05195e15	1.20057	0.600287	−	0.799784i	$-0.295053\pi$
$521$	1.05195e15	1.20057	0.600287	+	0.799784i	$0.295053\pi$
$522$	2.14625e14	0.242378
$523$	−7.70218e14	−0.860705	−0.430353	−	0.902661i	$-0.641611\pi$
$523$	−7.70218e14	−0.860705	−0.430353	+	0.902661i	$0.641611\pi$
$524$	−2.91123e14	−0.321925
$525$	1.22379e15	1.33915
$526$	−3.36216e14	−0.364080
$527$	−8.65414e14	−0.927397
$528$	−1.08112e14	−0.114653
$529$	2.06732e15	2.16971
$530$	5.23486e14	0.543735
$531$	4.22156e13	0.0433963
$532$	−3.79090e14	−0.385681
$533$	1.66964e14	0.168122
$534$	−1.81146e14	−0.180531
$535$	−6.60342e14	−0.651363
$536$	−3.96976e14	−0.387577
$537$	−1.41878e14	−0.137106
$538$	9.66304e14	0.924296
$539$	3.35406e14	0.317565
$540$	1.57419e14	0.147533
$541$	−1.63413e14	−0.151601	−0.0758006	−	0.997123i	$-0.524151\pi$
$541$	−1.63413e14	−0.151601	−0.0758006	+	0.997123i	$0.524151\pi$
$542$	−9.83784e14	−0.903449
$543$	−3.76975e14	−0.342699
$544$	−7.71941e14	−0.694689
$545$	−2.06480e15	−1.83949
$546$	−2.85683e14	−0.251956
$547$	8.97921e14	0.783985	0.391993	−	0.919968i	$-0.371786\pi$
$547$	8.97921e14	0.783985	0.391993	+	0.919968i	$0.371786\pi$
$548$	−5.69861e13	−0.0492579
$549$	−7.57473e14	−0.648215
$550$	−9.45506e14	−0.801068
$551$	−8.02438e14	−0.673097
$552$	1.33009e15	1.10463
$553$	1.91511e15	1.57473
$554$	1.27085e15	1.03465
$555$	−8.04473e14	−0.648485
$556$	−3.62835e14	−0.289599
$557$	1.31969e15	1.04296	0.521480	−	0.853264i	$-0.325380\pi$
$557$	1.31969e15	1.04296	0.521480	+	0.853264i	$0.325380\pi$
$558$	3.45617e14	0.270462
$559$	−4.20428e14	−0.325781
$560$	9.38190e14	0.719874
$561$	3.73056e14	0.283451
$562$	−1.62813e15	−1.22501
$563$	−2.48165e15	−1.84903	−0.924517	−	0.381140i	$-0.875532\pi$
$563$	−2.48165e15	−1.84903	−0.924517	+	0.381140i	$0.875532\pi$
$564$	−4.54360e14	−0.335247
$565$	−3.10439e14	−0.226835
$566$	9.35554e14	0.676984
$567$	1.92835e14	0.138191
$568$	4.49332e14	0.318898
$569$	2.23206e15	1.56887	0.784436	−	0.620210i	$-0.212953\pi$
$569$	2.23206e15	1.56887	0.784436	+	0.620210i	$0.212953\pi$
$570$	7.10938e14	0.494903
$571$	1.32952e15	0.916636	0.458318	−	0.888788i	$-0.348452\pi$
$571$	1.32952e15	0.916636	0.458318	+	0.888788i	$0.348452\pi$
$572$	−1.82725e14	−0.124773
$573$	−3.32813e14	−0.225086
$574$	−4.86695e14	−0.326018
$575$	5.00439e15	3.32031
$576$	4.81738e14	0.316583
$577$	−7.60604e14	−0.495098	−0.247549	−	0.968875i	$-0.579625\pi$
$577$	−7.60604e14	−0.495098	−0.247549	+	0.968875i	$0.579625\pi$
$578$	3.27274e14	0.211012
$579$	7.45619e14	0.476195
$580$	−1.19127e15	−0.753628
$581$	1.66501e15	1.04339
$582$	7.27538e14	0.451626
$583$	4.10156e14	0.252216
$584$	−1.35076e15	−0.822827
$585$	−4.43536e14	−0.267652
$586$	−8.58185e14	−0.513032
$587$	2.80832e15	1.66317	0.831586	−	0.555396i	$-0.187433\pi$
$587$	2.80832e15	1.66317	0.831586	+	0.555396i	$0.187433\pi$
$588$	−2.43718e14	−0.142992
$589$	−1.29219e15	−0.751090
$590$	2.83040e14	0.162990
$591$	1.85944e15	1.06084
$592$	−4.01463e14	−0.226922
$593$	−2.39814e15	−1.34299	−0.671497	−	0.741007i	$-0.734349\pi$
$593$	−2.39814e15	−1.34299	−0.671497	+	0.741007i	$0.734349\pi$
$594$	−1.48986e14	−0.0826645
$595$	−3.23736e15	−1.77970
$596$	1.05280e15	0.573444
$597$	1.88878e15	1.01935
$598$	−1.16823e15	−0.624701
$599$	2.55061e15	1.35144	0.675718	−	0.737160i	$-0.263834\pi$
$599$	2.55061e15	1.35144	0.675718	+	0.737160i	$0.263834\pi$
$600$	2.20398e15	1.15711
$601$	−2.73179e15	−1.42114	−0.710571	−	0.703626i	$-0.751563\pi$
$601$	−2.73179e15	−1.42114	−0.710571	+	0.703626i	$0.751563\pi$
$602$	1.22553e15	0.631748
$603$	−2.35350e14	−0.120218
$604$	5.52483e14	0.279651
$605$	2.23649e15	1.12179
$606$	3.72199e14	0.185002
$607$	2.31047e15	1.13806	0.569028	−	0.822318i	$-0.307320\pi$
$607$	2.31047e15	1.13806	0.569028	+	0.822318i	$0.307320\pi$
$608$	−1.15262e15	−0.562622
$609$	−1.45929e15	−0.705906
$610$	−5.07858e15	−2.43460
$611$	1.28018e15	0.608199
$612$	−2.71076e14	−0.127632
$613$	3.16315e15	1.47600	0.738002	−	0.674799i	$-0.235770\pi$
$613$	3.16315e15	1.47600	0.738002	+	0.674799i	$0.235770\pi$
$614$	1.26452e15	0.584792
$615$	−7.55617e14	−0.346329
$616$	1.70866e15	0.776180
$617$	−5.87068e14	−0.264314	−0.132157	−	0.991229i	$-0.542190\pi$
$617$	−5.87068e14	−0.264314	−0.132157	+	0.991229i	$0.542190\pi$
$618$	−2.06370e14	−0.0920897
$619$	2.62487e15	1.16094	0.580469	−	0.814283i	$-0.302869\pi$
$619$	2.62487e15	1.16094	0.580469	+	0.814283i	$0.302869\pi$
$620$	−1.91834e15	−0.840953
$621$	7.88554e14	0.342632
$622$	−9.06346e14	−0.390344
$623$	1.23166e15	0.525782
$624$	−2.21342e14	−0.0936587
$625$	1.46175e15	0.613104
$626$	−1.22686e15	−0.510077
$627$	5.57026e14	0.229564
$628$	−5.74437e14	−0.234674
$629$	1.38531e15	0.561007
$630$	1.29289e15	0.519026
$631$	4.20767e14	0.167448	0.0837240	−	0.996489i	$-0.473319\pi$
$631$	4.20767e14	0.167448	0.0837240	+	0.996489i	$0.473319\pi$
$632$	3.44901e15	1.36066
$633$	1.92484e15	0.752789
$634$	−8.82060e14	−0.341985
$635$	−1.01819e15	−0.391358
$636$	−2.98035e14	−0.113567
$637$	6.86689e14	0.259414
$638$	1.12746e15	0.422266
$639$	2.66390e14	0.0989151
$640$	−5.48215e14	−0.201818
$641$	2.55210e15	0.931492	0.465746	−	0.884919i	$-0.345786\pi$
$641$	2.55210e15	0.931492	0.465746	+	0.884919i	$0.345786\pi$
$642$	−4.54125e14	−0.164336
$643$	−1.91924e15	−0.688604	−0.344302	−	0.938859i	$-0.611884\pi$
$643$	−1.91924e15	−0.688604	−0.344302	+	0.938859i	$0.611884\pi$
$644$	−2.81915e15	−1.00287
$645$	1.90270e15	0.671106
$646$	−1.22424e15	−0.428142
$647$	−1.70129e13	−0.00589935	−0.00294967	−	0.999996i	$-0.500939\pi$
$647$	−1.70129e13	−0.00589935	−0.00294967	+	0.999996i	$0.500939\pi$
$648$	3.47287e14	0.119406
$649$	2.21764e14	0.0756042
$650$	−1.93577e15	−0.654381
$651$	−2.34994e15	−0.787701
$652$	2.80949e14	0.0933824
$653$	3.83593e15	1.26430	0.632148	−	0.774848i	$-0.282174\pi$
$653$	3.83593e15	1.26430	0.632148	+	0.774848i	$0.282174\pi$
$654$	−1.41999e15	−0.464095
$655$	−3.71216e15	−1.20309
$656$	−3.77082e14	−0.121190
$657$	−8.00809e14	−0.255223
$658$	−3.73169e15	−1.17941
$659$	−2.75101e15	−0.862230	−0.431115	−	0.902297i	$-0.641880\pi$
$659$	−2.75101e15	−0.862230	−0.431115	+	0.902297i	$0.641880\pi$
$660$	8.26943e14	0.257030
$661$	1.58002e15	0.487029	0.243515	−	0.969897i	$-0.421700\pi$
$661$	1.58002e15	0.487029	0.243515	+	0.969897i	$0.421700\pi$
$662$	−2.04138e14	−0.0624030
$663$	7.63772e14	0.231547
$664$	2.99859e15	0.901555
$665$	−4.83385e15	−1.44137
$666$	−5.53245e14	−0.163610
$667$	−5.96742e15	−1.75023
$668$	2.67481e15	0.778078
$669$	2.81032e15	0.810797
$670$	−1.57794e15	−0.451521
$671$	−3.97911e15	−1.12931
$672$	−2.09612e15	−0.590046
$673$	−8.65273e14	−0.241585	−0.120793	−	0.992678i	$-0.538544\pi$
$673$	−8.65273e14	−0.241585	−0.120793	+	0.992678i	$0.538544\pi$
$674$	−7.75096e14	−0.214648
$675$	1.30664e15	0.358911
$676$	1.28824e15	0.350987
$677$	−5.04092e15	−1.36230	−0.681148	−	0.732145i	$-0.738519\pi$
$677$	−5.04092e15	−1.36230	−0.681148	+	0.732145i	$0.738519\pi$
$678$	−2.13492e14	−0.0572294
$679$	−4.94672e15	−1.31533
$680$	−5.83032e15	−1.53778
$681$	8.63695e14	0.225970
$682$	1.81558e15	0.471194
$683$	−6.71310e15	−1.72826	−0.864131	−	0.503267i	$-0.832131\pi$
$683$	−6.71310e15	−1.72826	−0.864131	+	0.503267i	$0.832131\pi$
$684$	−4.04756e14	−0.103368
$685$	−7.26640e14	−0.184086
$686$	1.65877e15	0.416873
$687$	−3.36337e15	−0.838518
$688$	9.49520e14	0.234838
$689$	8.39729e14	0.206031
$690$	5.28697e15	1.28688
$691$	−1.18226e15	−0.285484	−0.142742	−	0.989760i	$-0.545592\pi$
$691$	−1.18226e15	−0.285484	−0.142742	+	0.989760i	$0.545592\pi$
$692$	−2.88081e15	−0.690129
$693$	1.01299e15	0.240754
$694$	4.55757e15	1.07462
$695$	−4.62658e15	−1.08229
$696$	−2.62811e15	−0.609947
$697$	1.30118e15	0.299610
$698$	−5.77841e15	−1.32009
$699$	−3.21709e15	−0.729187
$700$	−4.67136e15	−1.05052
$701$	−4.74706e14	−0.105919	−0.0529597	−	0.998597i	$-0.516865\pi$
$701$	−4.74706e14	−0.105919	−0.0529597	+	0.998597i	$0.516865\pi$
$702$	−3.05024e14	−0.0675275
$703$	2.06847e15	0.454354
$704$	2.53064e15	0.551545
$705$	−5.79363e15	−1.25288
$706$	−4.90513e15	−1.05251
$707$	−2.53068e15	−0.538803
$708$	−1.61142e14	−0.0340429
$709$	3.87764e15	0.812855	0.406428	−	0.913683i	$-0.366774\pi$
$709$	3.87764e15	0.812855	0.406428	+	0.913683i	$0.366774\pi$
$710$	1.78605e15	0.371511
$711$	2.04477e15	0.422048
$712$	2.21815e15	0.454309
$713$	−9.60951e15	−1.95303
$714$	−2.22637e15	−0.449011
$715$	−2.32996e15	−0.466299
$716$	5.41567e14	0.107555
$717$	−1.08605e15	−0.214040
$718$	3.01407e15	0.589479
$719$	9.10646e15	1.76742	0.883712	−	0.468032i	$-0.155037\pi$
$719$	9.10646e15	1.76742	0.883712	+	0.468032i	$0.155037\pi$
$720$	1.00171e15	0.192936
$721$	1.40317e15	0.268204
$722$	2.07130e15	0.392906
$723$	1.39643e15	0.262881
$724$	1.43896e15	0.268836
$725$	−9.88809e15	−1.83338
$726$	1.53806e15	0.283023
$727$	−5.94180e15	−1.08512	−0.542562	−	0.840016i	$-0.682546\pi$
$727$	−5.94180e15	−1.08512	−0.542562	+	0.840016i	$0.682546\pi$
$728$	3.49822e15	0.634051
$729$	2.05891e14	0.0370370
$730$	−5.36913e15	−0.958580
$731$	−3.27646e15	−0.580576
$732$	2.89137e15	0.508503
$733$	3.64382e15	0.636040	0.318020	−	0.948084i	$-0.396982\pi$
$733$	3.64382e15	0.636040	0.318020	+	0.948084i	$0.396982\pi$
$734$	−1.62266e15	−0.281125
$735$	−3.10770e15	−0.534390
$736$	−8.57159e15	−1.46296
$737$	−1.23633e15	−0.209441
$738$	−5.19646e14	−0.0873771
$739$	−1.33144e15	−0.222217	−0.111108	−	0.993808i	$-0.535440\pi$
$739$	−1.33144e15	−0.222217	−0.111108	+	0.993808i	$0.535440\pi$
$740$	3.07078e15	0.508714
$741$	1.14042e15	0.187528
$742$	−2.44778e15	−0.399532
$743$	−6.17816e14	−0.100097	−0.0500485	−	0.998747i	$-0.515938\pi$
$743$	−6.17816e14	−0.100097	−0.0500485	+	0.998747i	$0.515938\pi$
$744$	−4.23212e15	−0.680623
$745$	1.34244e16	2.14307
$746$	5.97294e15	0.946508
$747$	1.77773e15	0.279642
$748$	−1.42400e15	−0.222357
$749$	3.08771e15	0.478616
$750$	4.06310e15	0.625203
$751$	−9.61547e15	−1.46876	−0.734380	−	0.678739i	$-0.762527\pi$
$751$	−9.61547e15	−1.46876	−0.734380	+	0.678739i	$0.762527\pi$
$752$	−2.89125e15	−0.438417
$753$	3.51634e15	0.529320
$754$	2.30829e15	0.344943
$755$	7.04482e15	1.04511
$756$	−7.36078e14	−0.108406
$757$	8.96873e15	1.31131	0.655653	−	0.755063i	$-0.272394\pi$
$757$	8.96873e15	1.31131	0.655653	+	0.755063i	$0.272394\pi$
$758$	9.57565e15	1.38991
$759$	4.14239e15	0.596927
$760$	−8.70552e15	−1.24543
$761$	1.26989e16	1.80364	0.901822	−	0.432107i	$-0.142230\pi$
$761$	1.26989e16	1.80364	0.901822	+	0.432107i	$0.142230\pi$
$762$	−7.00222e14	−0.0987378
$763$	9.65486e15	1.35164
$764$	1.27039e15	0.176573
$765$	−3.45654e15	−0.476984
$766$	6.96245e15	0.953903
$767$	4.54027e14	0.0617600
$768$	−4.43710e15	−0.599256
$769$	9.65709e15	1.29495	0.647473	−	0.762089i	$-0.275826\pi$
$769$	9.65709e15	1.29495	0.647473	+	0.762089i	$0.275826\pi$
$770$	6.79175e15	0.904237
$771$	6.48893e15	0.857777
$772$	−2.84613e15	−0.373559
$773$	−6.07111e15	−0.791190	−0.395595	−	0.918425i	$-0.629462\pi$
$773$	−6.07111e15	−0.791190	−0.395595	+	0.918425i	$0.629462\pi$
$774$	1.30851e15	0.169317
$775$	−1.59231e16	−2.04582
$776$	−8.90879e15	−1.13653
$777$	3.76166e15	0.476501
$778$	−3.73633e15	−0.469956
$779$	1.94285e15	0.242651
$780$	1.69303e15	0.209964
$781$	1.39938e15	0.172328
$782$	−9.10420e15	−1.11328
$783$	−1.55809e15	−0.189192
$784$	−1.55086e15	−0.186997
$785$	−7.32476e15	−0.877021
$786$	−2.55290e15	−0.303535
$787$	−4.75214e15	−0.561084	−0.280542	−	0.959842i	$-0.590514\pi$
$787$	−4.75214e15	−0.561084	−0.280542	+	0.959842i	$0.590514\pi$
$788$	−7.09771e15	−0.832193
$789$	2.44079e15	0.284189
$790$	1.37094e16	1.58515
$791$	1.45159e15	0.166676
$792$	1.82435e15	0.208027
$793$	−8.14660e15	−0.922516
$794$	8.67455e15	0.975515
$795$	−3.80030e15	−0.424422
$796$	−7.20972e15	−0.799644
$797$	−5.01714e15	−0.552631	−0.276316	−	0.961067i	$-0.589114\pi$
$797$	−5.01714e15	−0.552631	−0.276316	+	0.961067i	$0.589114\pi$
$798$	−3.32430e15	−0.363650
$799$	9.97667e15	1.08387
$800$	−1.42032e16	−1.53247
$801$	1.31505e15	0.140917
$802$	−3.30785e15	−0.352036
$803$	−4.20676e15	−0.444644
$804$	8.98362e14	0.0943068
$805$	−3.59475e16	−3.74793
$806$	3.71710e15	0.384912
$807$	−7.01498e15	−0.721476
$808$	−4.55762e15	−0.465560
$809$	1.27332e16	1.29188	0.645940	−	0.763388i	$-0.276466\pi$
$809$	1.27332e16	1.29188	0.645940	+	0.763388i	$0.276466\pi$
$810$	1.38043e15	0.139106
$811$	−1.14176e16	−1.14277	−0.571387	−	0.820681i	$-0.693595\pi$
$811$	−1.14176e16	−1.14277	−0.571387	+	0.820681i	$0.693595\pi$
$812$	5.57031e15	0.553759
$813$	7.14187e15	0.705203
$814$	−2.90628e15	−0.285038
$815$	3.58243e15	0.348988
$816$	−1.72495e15	−0.166909
$817$	−4.89223e15	−0.470203
$818$	6.72741e15	0.642251
$819$	2.07394e15	0.196669
$820$	2.88429e15	0.271683
$821$	1.13662e16	1.06348	0.531739	−	0.846908i	$-0.321539\pi$
$821$	1.13662e16	1.06348	0.531739	+	0.846908i	$0.321539\pi$
$822$	−4.99718e14	−0.0464441
$823$	−1.05257e16	−0.971745	−0.485873	−	0.874030i	$-0.661498\pi$
$823$	−1.05257e16	−0.971745	−0.485873	+	0.874030i	$0.661498\pi$
$824$	2.52703e15	0.231745
$825$	6.86399e15	0.625288
$826$	−1.32347e15	−0.119764
$827$	−1.82817e16	−1.64337	−0.821686	−	0.569940i	$-0.806966\pi$
$827$	−1.82817e16	−1.64337	−0.821686	+	0.569940i	$0.806966\pi$
$828$	−3.01001e15	−0.268783
$829$	8.77537e15	0.778423	0.389211	−	0.921148i	$-0.372748\pi$
$829$	8.77537e15	0.778423	0.389211	+	0.921148i	$0.372748\pi$
$830$	1.19190e16	1.05030
$831$	−9.22588e15	−0.807611
$832$	5.18108e15	0.450549
$833$	5.35148e15	0.462303
$834$	−3.18175e15	−0.273057
$835$	3.41071e16	2.90783
$836$	−2.12624e15	−0.180085
$837$	−2.50904e15	−0.211114
$838$	−8.65300e15	−0.723311
$839$	1.66805e16	1.38522	0.692610	−	0.721312i	$-0.256461\pi$
$839$	1.66805e16	1.38522	0.692610	+	0.721312i	$0.256461\pi$
$840$	−1.58316e16	−1.30614
$841$	−4.09582e14	−0.0335709
$842$	−2.06990e15	−0.168552
$843$	1.18195e16	0.956200
$844$	−7.34735e15	−0.590537
$845$	1.64266e16	1.31170
$846$	−3.98434e15	−0.316096
$847$	−1.04577e16	−0.824283
$848$	−1.89650e15	−0.148517
$849$	−6.79175e15	−0.528432
$850$	−1.50858e16	−1.16617
$851$	1.53824e16	1.18144
$852$	−1.01684e15	−0.0775955
$853$	1.59893e16	1.21230	0.606150	−	0.795351i	$-0.292713\pi$
$853$	1.59893e16	1.21230	0.606150	+	0.795351i	$0.292713\pi$
$854$	2.37471e16	1.78892
$855$	−5.16112e15	−0.386305
$856$	5.56081e15	0.413554
$857$	1.32251e16	0.977245	0.488622	−	0.872495i	$-0.337500\pi$
$857$	1.32251e16	0.977245	0.488622	+	0.872495i	$0.337500\pi$
$858$	−1.60234e15	−0.117645
$859$	1.43479e16	1.04671	0.523354	−	0.852115i	$-0.324680\pi$
$859$	1.43479e16	1.04671	0.523354	+	0.852115i	$0.324680\pi$
$860$	−7.26284e15	−0.526460
$861$	3.53321e15	0.254479
$862$	−1.38815e16	−0.993449
$863$	1.05265e16	0.748555	0.374277	−	0.927317i	$-0.377891\pi$
$863$	1.05265e16	0.748555	0.374277	+	0.927317i	$0.377891\pi$
$864$	−2.23804e15	−0.158140
$865$	−3.67337e16	−2.57915
$866$	5.48793e15	0.382878
$867$	−2.37588e15	−0.164710
$868$	8.97003e15	0.617924
$869$	1.07415e16	0.735284
$870$	−1.04464e16	−0.710579
$871$	−2.53118e15	−0.171090
$872$	1.73879e16	1.16790
$873$	−5.28163e15	−0.352525
$874$	−1.35939e16	−0.901636
$875$	−2.76261e16	−1.82085
$876$	3.05679e15	0.200213
$877$	−2.81599e16	−1.83288	−0.916438	−	0.400177i	$-0.868949\pi$
$877$	−2.81599e16	−1.83288	−0.916438	+	0.400177i	$0.868949\pi$
$878$	−7.66566e15	−0.495826
$879$	6.23008e15	0.400456
$880$	5.26212e15	0.336129
$881$	2.10815e16	1.33824	0.669119	−	0.743155i	$-0.266672\pi$
$881$	2.10815e16	1.33824	0.669119	+	0.743155i	$0.266672\pi$
$882$	−2.13720e15	−0.134824
$883$	1.51951e16	0.952621	0.476311	−	0.879277i	$-0.341974\pi$
$883$	1.51951e16	0.952621	0.476311	+	0.879277i	$0.341974\pi$
$884$	−2.91542e15	−0.181641
$885$	−2.05476e15	−0.127225
$886$	1.04646e16	0.643930
$887$	−2.11674e15	−0.129445	−0.0647227	−	0.997903i	$-0.520616\pi$
$887$	−2.11674e15	−0.129445	−0.0647227	+	0.997903i	$0.520616\pi$
$888$	6.77455e15	0.411727
$889$	4.76099e15	0.287566
$890$	8.81691e15	0.529263
$891$	1.08158e15	0.0645252
$892$	−1.07274e16	−0.636042
$893$	1.48966e16	0.877819
$894$	9.23214e15	0.540687
$895$	6.90563e15	0.401954
$896$	2.56341e15	0.148294
$897$	8.48088e15	0.487621
$898$	1.15817e16	0.661841
$899$	1.89873e16	1.07841
$900$	−4.98763e15	−0.281553
$901$	6.54414e15	0.367169
$902$	−2.72978e15	−0.152227
$903$	−8.89687e15	−0.493122
$904$	2.61424e15	0.144019
$905$	1.83485e16	1.00469
$906$	4.84480e15	0.263676
$907$	2.67376e16	1.44638	0.723191	−	0.690648i	$-0.242675\pi$
$907$	2.67376e16	1.44638	0.723191	+	0.690648i	$0.242675\pi$
$908$	−3.29683e15	−0.177266
$909$	−2.70201e15	−0.144406
$910$	1.39050e16	0.738659
$911$	1.85949e16	0.981843	0.490922	−	0.871204i	$-0.336660\pi$
$911$	1.85949e16	0.981843	0.490922	+	0.871204i	$0.336660\pi$
$912$	−2.57560e15	−0.135178
$913$	9.33868e15	0.487188
$914$	−2.12252e16	−1.10065
$915$	3.68684e16	1.90037
$916$	1.28384e16	0.657788
$917$	1.73578e16	0.884023
$918$	−2.37710e15	−0.120341
$919$	−5.99557e15	−0.301714	−0.150857	−	0.988556i	$-0.548203\pi$
$919$	−5.99557e15	−0.301714	−0.150857	+	0.988556i	$0.548203\pi$
$920$	−6.47395e16	−3.23845
$921$	−9.17994e15	−0.456469
$922$	3.06004e15	0.151254
$923$	2.86501e15	0.140772
$924$	−3.86672e15	−0.188863
$925$	2.54888e16	1.23757
$926$	1.56097e16	0.753416
$927$	1.49817e15	0.0718822
$928$	1.69365e16	0.807810
$929$	−2.22513e16	−1.05504	−0.527521	−	0.849542i	$-0.676878\pi$
$929$	−2.22513e16	−1.05504	−0.527521	+	0.849542i	$0.676878\pi$
$930$	−1.68222e16	−0.792915
$931$	7.99054e15	0.374415
$932$	1.22801e16	0.572022
$933$	6.57971e15	0.304690
$934$	1.75792e16	0.809265
$935$	−1.81577e16	−0.830993
$936$	3.73506e15	0.169934
$937$	2.70151e16	1.22191	0.610954	−	0.791666i	$-0.290786\pi$
$937$	2.70151e16	1.22191	0.610954	+	0.791666i	$0.290786\pi$
$938$	7.37832e15	0.331774
$939$	8.90649e15	0.398149
$940$	2.21150e16	0.982843
$941$	2.48372e16	1.09739	0.548694	−	0.836024i	$-0.315125\pi$
$941$	2.48372e16	1.09739	0.548694	+	0.836024i	$0.315125\pi$
$942$	−5.03732e15	−0.221268
$943$	1.44482e16	0.630957
$944$	−1.02540e15	−0.0445194
$945$	−9.38587e15	−0.405135
$946$	6.87377e15	0.294981
$947$	−7.51480e15	−0.320621	−0.160311	−	0.987067i	$-0.551250\pi$
$947$	−7.51480e15	−0.320621	−0.160311	+	0.987067i	$0.551250\pi$
$948$	−7.80515e15	−0.331082
$949$	−8.61268e15	−0.363224
$950$	−2.25253e16	−0.944474
$951$	6.40340e15	0.266942
$952$	2.72622e16	1.12994
$953$	−1.72059e16	−0.709033	−0.354516	−	0.935050i	$-0.615354\pi$
$953$	−1.72059e16	−0.709033	−0.354516	+	0.935050i	$0.615354\pi$
$954$	−2.61351e15	−0.107080
$955$	1.61990e16	0.659886
$956$	4.14559e15	0.167907
$957$	−8.18488e15	−0.329607
$958$	1.00541e16	0.402562
$959$	3.39772e15	0.135265
$960$	−2.34476e16	−0.928126
$961$	5.16728e15	0.203369
$962$	−5.95014e15	−0.232843
$963$	3.29676e15	0.128275
$964$	−5.33037e15	−0.206221
$965$	−3.62915e16	−1.39606
$966$	−2.47215e16	−0.945585
$967$	2.43801e16	0.927236	0.463618	−	0.886035i	$-0.346551\pi$
$967$	2.43801e16	0.927236	0.463618	+	0.886035i	$0.346551\pi$
$968$	−1.88337e16	−0.712232
$969$	8.88750e15	0.334194
$970$	−3.54114e16	−1.32403
$971$	1.42680e16	0.530465	0.265232	−	0.964185i	$-0.414551\pi$
$971$	1.42680e16	0.530465	0.265232	+	0.964185i	$0.414551\pi$
$972$	−7.85913e14	−0.0290543
$973$	2.16335e16	0.795256
$974$	−1.54635e16	−0.565241
$975$	1.40529e16	0.510789
$976$	1.83988e16	0.664990
$977$	−4.63196e16	−1.66473	−0.832366	−	0.554227i	$-0.813014\pi$
$977$	−4.63196e16	−1.66473	−0.832366	+	0.554227i	$0.813014\pi$
$978$	2.46368e15	0.0880481
$979$	6.90813e15	0.245502
$980$	1.18625e16	0.419211
$981$	1.03085e16	0.362257
$982$	−1.55593e16	−0.543723
$983$	2.48936e15	0.0865055	0.0432528	−	0.999064i	$-0.486228\pi$
$983$	2.48936e15	0.0865055	0.0432528	+	0.999064i	$0.486228\pi$
$984$	6.36312e15	0.219886
$985$	−9.05043e16	−3.11007
$986$	1.79888e16	0.614724
$987$	2.70906e16	0.920606
$988$	−4.35314e15	−0.147109
$989$	−3.63816e16	−1.22265
$990$	7.25157e15	0.242348
$991$	1.45625e16	0.483984	0.241992	−	0.970278i	$-0.422199\pi$
$991$	1.45625e16	0.483984	0.241992	+	0.970278i	$0.422199\pi$
$992$	2.72733e16	0.901412
$993$	1.48196e15	0.0487097
$994$	−8.35142e15	−0.272983
$995$	−9.19325e16	−2.98842
$996$	−6.78583e15	−0.219370
$997$	3.41264e16	1.09715	0.548576	−	0.836101i	$-0.315170\pi$
$997$	3.41264e16	1.09715	0.548576	+	0.836101i	$0.315170\pi$
$998$	2.76535e16	0.884163
$999$	4.01634e15	0.127708

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-33.4729 q^{2} +243.000 q^{3} -927.563 q^{4} -11827.5 q^{5} -8133.92 q^{6} +55304.7 q^{7} +99600.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-33.4729 q^{2} +243.000 q^{3} -927.563 q^{4} -11827.5 q^{5} -8133.92 q^{6} +55304.7 q^{7} +99600.8 q^{8} +59049.0 q^{9} +395902. q^{10} +310193. q^{11} -225398. q^{12} +635071. q^{13} -1.85121e6 q^{14} -2.87409e6 q^{15} -1.43428e6 q^{16} +4.94920e6 q^{17} -1.97654e6 q^{18} +7.38988e6 q^{19} +1.09708e7 q^{20} +1.34390e7 q^{21} -1.03831e7 q^{22} +5.49557e7 q^{23} +2.42030e7 q^{24} +9.10623e7 q^{25} -2.12577e7 q^{26} +1.43489e7 q^{27} -5.12986e7 q^{28} -1.08586e8 q^{29} +9.62042e7 q^{30} -1.74859e8 q^{31} -1.55973e8 q^{32} +7.53769e7 q^{33} -1.65664e8 q^{34} -6.54118e8 q^{35} -5.47716e7 q^{36} +2.79905e8 q^{37} -2.47361e8 q^{38} +1.54322e8 q^{39} -1.17803e9 q^{40} +2.62906e8 q^{41} -4.49844e8 q^{42} -6.62017e8 q^{43} -2.87723e8 q^{44} -6.98404e8 q^{45} -1.83953e9 q^{46} +2.01581e9 q^{47} -3.48531e8 q^{48} +1.08128e9 q^{49} -3.04812e9 q^{50} +1.20266e9 q^{51} -5.89068e8 q^{52} +1.32226e9 q^{53} -4.80300e8 q^{54} -3.66881e9 q^{55} +5.50839e9 q^{56} +1.79574e9 q^{57} +3.63469e9 q^{58} +7.14924e8 q^{59} +2.66590e9 q^{60} -1.28279e10 q^{61} +5.85305e9 q^{62} +3.26569e9 q^{63} +8.15828e9 q^{64} -7.51131e9 q^{65} -2.52309e9 q^{66} -3.98567e9 q^{67} -4.59070e9 q^{68} +1.33542e10 q^{69} +2.18952e10 q^{70} +4.51133e9 q^{71} +5.88133e9 q^{72} -1.35618e10 q^{73} -9.36925e9 q^{74} +2.21281e10 q^{75} -6.85458e9 q^{76} +1.71551e10 q^{77} -5.16561e9 q^{78} +3.46284e10 q^{79} +1.69640e10 q^{80} +3.48678e9 q^{81} -8.80025e9 q^{82} +3.01060e10 q^{83} -1.24655e10 q^{84} -5.85369e10 q^{85} +2.21597e10 q^{86} -2.63864e10 q^{87} +3.08955e10 q^{88} +2.22704e10 q^{89} +2.33776e10 q^{90} +3.51224e10 q^{91} -5.09749e10 q^{92} -4.24908e10 q^{93} -6.74752e10 q^{94} -8.74041e10 q^{95} -3.79014e10 q^{96} -8.94449e10 q^{97} -3.61936e10 q^{98} +1.83166e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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