LMFDB - Embedded newform 177.12.a.d.1.19

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			1.19
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)

$f(q)$	$=$	$q+31.7299 q^{2} +243.000 q^{3} -1041.21 q^{4} +1823.69 q^{5} +7710.37 q^{6} -52038.7 q^{7} -98020.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+31.7299 q^{2} +243.000 q^{3} -1041.21 q^{4} +1823.69 q^{5} +7710.37 q^{6} -52038.7 q^{7} -98020.5 q^{8} +59049.0 q^{9} +57865.4 q^{10} -443322. q^{11} -253015. q^{12} +780277. q^{13} -1.65118e6 q^{14} +443156. q^{15} -977779. q^{16} +6.30507e6 q^{17} +1.87362e6 q^{18} -9.72491e6 q^{19} -1.89884e6 q^{20} -1.26454e7 q^{21} -1.40666e7 q^{22} -1.54842e7 q^{23} -2.38190e7 q^{24} -4.55023e7 q^{25} +2.47581e7 q^{26} +1.43489e7 q^{27} +5.41833e7 q^{28} -1.80080e8 q^{29} +1.40613e7 q^{30} +2.28440e8 q^{31} +1.69721e8 q^{32} -1.07727e8 q^{33} +2.00059e8 q^{34} -9.49022e7 q^{35} -6.14825e7 q^{36} -3.90774e8 q^{37} -3.08571e8 q^{38} +1.89607e8 q^{39} -1.78759e8 q^{40} +7.69638e8 q^{41} -4.01237e8 q^{42} +2.12524e8 q^{43} +4.61593e8 q^{44} +1.07687e8 q^{45} -4.91312e8 q^{46} +1.63456e9 q^{47} -2.37600e8 q^{48} +7.30697e8 q^{49} -1.44378e9 q^{50} +1.53213e9 q^{51} -8.12434e8 q^{52} +4.66931e9 q^{53} +4.55290e8 q^{54} -8.08481e8 q^{55} +5.10085e9 q^{56} -2.36315e9 q^{57} -5.71393e9 q^{58} +7.14924e8 q^{59} -4.61419e8 q^{60} +1.49764e9 q^{61} +7.24839e9 q^{62} -3.07283e9 q^{63} +7.38773e9 q^{64} +1.42298e9 q^{65} -3.41818e9 q^{66} +1.66508e8 q^{67} -6.56491e9 q^{68} -3.76266e9 q^{69} -3.01124e9 q^{70} -1.80803e10 q^{71} -5.78801e9 q^{72} +1.81596e10 q^{73} -1.23992e10 q^{74} -1.10571e10 q^{75} +1.01257e10 q^{76} +2.30699e10 q^{77} +6.01623e9 q^{78} +1.92745e10 q^{79} -1.78316e9 q^{80} +3.48678e9 q^{81} +2.44206e10 q^{82} +3.05360e10 q^{83} +1.31665e10 q^{84} +1.14985e10 q^{85} +6.74336e9 q^{86} -4.37595e10 q^{87} +4.34547e10 q^{88} -8.33362e9 q^{89} +3.41689e9 q^{90} -4.06046e10 q^{91} +1.61223e10 q^{92} +5.55109e10 q^{93} +5.18643e10 q^{94} -1.77352e10 q^{95} +4.12422e10 q^{96} +8.42053e10 q^{97} +2.31849e10 q^{98} -2.61777e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	31.7299	0.701139	0.350569	−	0.936537i	$-0.385988\pi$
$2$	31.7299	0.701139	0.350569	+	0.936537i	$0.385988\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1041.21	−0.508404
$5$	1823.69	0.260985	0.130492	−	0.991449i	$-0.458344\pi$
$5$	1823.69	0.260985	0.130492	+	0.991449i	$0.458344\pi$
$6$	7710.37	0.404803
$7$	−52038.7	−1.17027	−0.585136	−	0.810935i	$-0.698959\pi$
$7$	−52038.7	−1.17027	−0.585136	+	0.810935i	$0.698959\pi$
$8$	−98020.5	−1.05760
$9$	59049.0	0.333333
$10$	57865.4	0.182986
$11$	−443322.	−0.829965	−0.414983	−	0.909829i	$-0.636212\pi$
$11$	−443322.	−0.829965	−0.414983	+	0.909829i	$0.636212\pi$
$12$	−253015.	−0.293527
$13$	780277.	0.582855	0.291427	−	0.956593i	$-0.405870\pi$
$13$	780277.	0.582855	0.291427	+	0.956593i	$0.405870\pi$
$14$	−1.65118e6	−0.820523
$15$	443156.	0.150680
$16$	−977779.	−0.233121
$17$	6.30507e6	1.07701	0.538506	−	0.842621i	$-0.318989\pi$
$17$	6.30507e6	1.07701	0.538506	+	0.842621i	$0.318989\pi$
$18$	1.87362e6	0.233713
$19$	−9.72491e6	−0.901034	−0.450517	−	0.892768i	$-0.648760\pi$
$19$	−9.72491e6	−0.901034	−0.450517	+	0.892768i	$0.648760\pi$
$20$	−1.89884e6	−0.132686
$21$	−1.26454e7	−0.675657
$22$	−1.40666e7	−0.581921
$23$	−1.54842e7	−0.501632	−0.250816	−	0.968035i	$-0.580699\pi$
$23$	−1.54842e7	−0.501632	−0.250816	+	0.968035i	$0.580699\pi$
$24$	−2.38190e7	−0.610606
$25$	−4.55023e7	−0.931887
$26$	2.47581e7	0.408662
$27$	1.43489e7	0.192450
$28$	5.41833e7	0.594972
$29$	−1.80080e8	−1.63034	−0.815168	−	0.579224i	$-0.803356\pi$
$29$	−1.80080e8	−1.63034	−0.815168	+	0.579224i	$0.803356\pi$
$30$	1.40613e7	0.105647
$31$	2.28440e8	1.43312	0.716561	−	0.697525i	$-0.245715\pi$
$31$	2.28440e8	1.43312	0.716561	+	0.697525i	$0.245715\pi$
$32$	1.69721e8	0.894151
$33$	−1.07727e8	−0.479181
$34$	2.00059e8	0.755135
$35$	−9.49022e7	−0.305423
$36$	−6.14825e7	−0.169468
$37$	−3.90774e8	−0.926437	−0.463219	−	0.886244i	$-0.653306\pi$
$37$	−3.90774e8	−0.926437	−0.463219	+	0.886244i	$0.653306\pi$
$38$	−3.08571e8	−0.631750
$39$	1.89607e8	0.336511
$40$	−1.78759e8	−0.276018
$41$	7.69638e8	1.03747	0.518735	−	0.854935i	$-0.326403\pi$
$41$	7.69638e8	1.03747	0.518735	+	0.854935i	$0.326403\pi$
$42$	−4.01237e8	−0.473729
$43$	2.12524e8	0.220460	0.110230	−	0.993906i	$-0.464841\pi$
$43$	2.12524e8	0.220460	0.110230	+	0.993906i	$0.464841\pi$
$44$	4.61593e8	0.421958
$45$	1.07687e8	0.0869949
$46$	−4.91312e8	−0.351714
$47$	1.63456e9	1.03959	0.519794	−	0.854291i	$-0.326009\pi$
$47$	1.63456e9	1.03959	0.519794	+	0.854291i	$0.326009\pi$
$48$	−2.37600e8	−0.134592
$49$	7.30697e8	0.369538
$50$	−1.44378e9	−0.653382
$51$	1.53213e9	0.621814
$52$	−8.12434e8	−0.296326
$53$	4.66931e9	1.53368	0.766842	−	0.641836i	$-0.221827\pi$
$53$	4.66931e9	1.53368	0.766842	+	0.641836i	$0.221827\pi$
$54$	4.55290e8	0.134934
$55$	−8.08481e8	−0.216608
$56$	5.10085e9	1.23768
$57$	−2.36315e9	−0.520212
$58$	−5.71393e9	−1.14309
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−4.61419e8	−0.0766061
$61$	1.49764e9	0.227035	0.113517	−	0.993536i	$-0.463788\pi$
$61$	1.49764e9	0.227035	0.113517	+	0.993536i	$0.463788\pi$
$62$	7.24839e9	1.00482
$63$	−3.07283e9	−0.390091
$64$	7.38773e9	0.860045
$65$	1.42298e9	0.152116
$66$	−3.41818e9	−0.335972
$67$	1.66508e8	0.0150669	0.00753345	−	0.999972i	$-0.497602\pi$
$67$	1.66508e8	0.0150669	0.00753345	+	0.999972i	$0.497602\pi$
$68$	−6.56491e9	−0.547558
$69$	−3.76266e9	−0.289618
$70$	−3.01124e9	−0.214144
$71$	−1.80803e10	−1.18928	−0.594641	−	0.803991i	$-0.702706\pi$
$71$	−1.80803e10	−1.18928	−0.594641	+	0.803991i	$0.702706\pi$
$72$	−5.78801e9	−0.352534
$73$	1.81596e10	1.02525	0.512625	−	0.858613i	$-0.328673\pi$
$73$	1.81596e10	1.02525	0.512625	+	0.858613i	$0.328673\pi$
$74$	−1.23992e10	−0.649561
$75$	−1.10571e10	−0.538025
$76$	1.01257e10	0.458089
$77$	2.30699e10	0.971285
$78$	6.01623e9	0.235941
$79$	1.92745e10	0.704749	0.352375	−	0.935859i	$-0.385374\pi$
$79$	1.92745e10	0.704749	0.352375	+	0.935859i	$0.385374\pi$
$80$	−1.78316e9	−0.0608409
$81$	3.48678e9	0.111111
$82$	2.44206e10	0.727410
$83$	3.05360e10	0.850907	0.425453	−	0.904980i	$-0.360115\pi$
$83$	3.05360e10	0.850907	0.425453	+	0.904980i	$0.360115\pi$
$84$	1.31665e10	0.343507
$85$	1.14985e10	0.281084
$86$	6.74336e9	0.154573
$87$	−4.37595e10	−0.941275
$88$	4.34547e10	0.877772
$89$	−8.33362e9	−0.158193	−0.0790967	−	0.996867i	$-0.525204\pi$
$89$	−8.33362e9	−0.158193	−0.0790967	+	0.996867i	$0.525204\pi$
$90$	3.41689e9	0.0609955
$91$	−4.06046e10	−0.682099
$92$	1.61223e10	0.255032
$93$	5.55109e10	0.827413
$94$	5.18643e10	0.728896
$95$	−1.77352e10	−0.235156
$96$	4.12422e10	0.516238
$97$	8.42053e10	0.995623	0.497811	−	0.867285i	$-0.334137\pi$
$97$	8.42053e10	0.995623	0.497811	+	0.867285i	$0.334137\pi$
$98$	2.31849e10	0.259097
$99$	−2.61777e10	−0.276655
$100$	4.73775e10	0.473775
$101$	5.16619e10	0.489106	0.244553	−	0.969636i	$-0.421359\pi$
$101$	5.16619e10	0.489106	0.244553	+	0.969636i	$0.421359\pi$
$102$	4.86144e10	0.435978
$103$	9.70573e10	0.824942	0.412471	−	0.910971i	$-0.364666\pi$
$103$	9.70573e10	0.824942	0.412471	+	0.910971i	$0.364666\pi$
$104$	−7.64831e10	−0.616428
$105$	−2.30612e10	−0.176336
$106$	1.48157e11	1.07533
$107$	4.76546e10	0.328469	0.164234	−	0.986421i	$-0.447485\pi$
$107$	4.76546e10	0.328469	0.164234	+	0.986421i	$0.447485\pi$
$108$	−1.49403e10	−0.0978425
$109$	7.42731e10	0.462366	0.231183	−	0.972910i	$-0.425740\pi$
$109$	7.42731e10	0.462366	0.231183	+	0.972910i	$0.425740\pi$
$110$	−2.56530e10	−0.151872
$111$	−9.49580e10	−0.534879
$112$	5.08823e10	0.272815
$113$	3.03166e10	0.154792	0.0773961	−	0.997000i	$-0.475339\pi$
$113$	3.03166e10	0.154792	0.0773961	+	0.997000i	$0.475339\pi$
$114$	−7.49827e10	−0.364741
$115$	−2.82383e10	−0.130918
$116$	1.87502e11	0.828870
$117$	4.60746e10	0.194285
$118$	2.26845e10	0.0912805
$119$	−3.28107e11	−1.26040
$120$	−4.34383e10	−0.159359
$121$	−8.87769e10	−0.311158
$122$	4.75199e10	0.159183
$123$	1.87022e11	0.598983
$124$	−2.37855e11	−0.728605
$125$	−1.72029e11	−0.504193
$126$	−9.75007e10	−0.273508
$127$	−2.86207e11	−0.768704	−0.384352	−	0.923187i	$-0.625575\pi$
$127$	−2.86207e11	−0.768704	−0.384352	+	0.923187i	$0.625575\pi$
$128$	−1.13177e11	−0.291140
$129$	5.16432e10	0.127283
$130$	4.51510e10	0.106655
$131$	2.74019e11	0.620566	0.310283	−	0.950644i	$-0.399576\pi$
$131$	2.74019e11	0.620566	0.310283	+	0.950644i	$0.399576\pi$
$132$	1.12167e11	0.243618
$133$	5.06072e11	1.05445
$134$	5.28329e9	0.0105640
$135$	2.61679e10	0.0502265
$136$	−6.18026e11	−1.13905
$137$	−6.66596e11	−1.18005	−0.590024	−	0.807386i	$-0.700882\pi$
$137$	−6.66596e11	−1.18005	−0.590024	+	0.807386i	$0.700882\pi$
$138$	−1.19389e11	−0.203062
$139$	1.81154e11	0.296119	0.148059	−	0.988978i	$-0.452697\pi$
$139$	1.81154e11	0.296119	0.148059	+	0.988978i	$0.452697\pi$
$140$	9.88133e10	0.155278
$141$	3.97197e11	0.600207
$142$	−5.73687e11	−0.833852
$143$	−3.45914e11	−0.483749
$144$	−5.77369e10	−0.0777069
$145$	−3.28410e11	−0.425493
$146$	5.76201e11	0.718842
$147$	1.77559e11	0.213353
$148$	4.06878e11	0.471005
$149$	4.69746e10	0.0524009	0.0262005	−	0.999657i	$-0.491659\pi$
$149$	4.69746e10	0.0524009	0.0262005	+	0.999657i	$0.491659\pi$
$150$	−3.50840e11	−0.377230
$151$	1.57217e12	1.62977	0.814885	−	0.579623i	$-0.196800\pi$
$151$	1.57217e12	1.62977	0.814885	+	0.579623i	$0.196800\pi$
$152$	9.53241e11	0.952934
$153$	3.72308e11	0.359004
$154$	7.32006e11	0.681006
$155$	4.16603e11	0.374023
$156$	−1.97421e11	−0.171084
$157$	1.25470e12	1.04977	0.524883	−	0.851175i	$-0.324109\pi$
$157$	1.25470e12	1.04977	0.524883	+	0.851175i	$0.324109\pi$
$158$	6.11579e11	0.494127
$159$	1.13464e12	0.885473
$160$	3.09518e11	0.233360
$161$	8.05777e11	0.587047
$162$	1.10635e11	0.0779043
$163$	5.24687e11	0.357165	0.178582	−	0.983925i	$-0.442849\pi$
$163$	5.24687e11	0.357165	0.178582	+	0.983925i	$0.442849\pi$
$164$	−8.01356e11	−0.527454
$165$	−1.96461e11	−0.125059
$166$	9.68904e11	0.596604
$167$	2.89074e11	0.172214	0.0861071	−	0.996286i	$-0.472557\pi$
$167$	2.89074e11	0.172214	0.0861071	+	0.996286i	$0.472557\pi$
$168$	1.23951e12	0.714576
$169$	−1.18333e12	−0.660280
$170$	3.64845e11	0.197079
$171$	−5.74246e11	−0.300345
$172$	−2.21282e11	−0.112083
$173$	−3.71003e12	−1.82022	−0.910109	−	0.414369i	$-0.864002\pi$
$173$	−3.71003e12	−1.82022	−0.910109	+	0.414369i	$0.864002\pi$
$174$	−1.38849e12	−0.659965
$175$	2.36788e12	1.09056
$176$	4.33471e11	0.193482
$177$	1.73727e11	0.0751646
$178$	−2.64425e11	−0.110916
$179$	2.04322e12	0.831043	0.415522	−	0.909583i	$-0.363599\pi$
$179$	2.04322e12	0.831043	0.415522	+	0.909583i	$0.363599\pi$
$180$	−1.12125e11	−0.0442286
$181$	−7.73103e11	−0.295805	−0.147902	−	0.989002i	$-0.547252\pi$
$181$	−7.73103e11	−0.295805	−0.147902	+	0.989002i	$0.547252\pi$
$182$	−1.28838e12	−0.478246
$183$	3.63926e11	0.131079
$184$	1.51777e12	0.530527
$185$	−7.12649e11	−0.241786
$186$	1.76136e12	0.580131
$187$	−2.79518e12	−0.893883
$188$	−1.70192e12	−0.528531
$189$	−7.46698e11	−0.225219
$190$	−5.62736e11	−0.164877
$191$	5.26945e12	1.49997	0.749984	−	0.661457i	$-0.230061\pi$
$191$	5.26945e12	1.49997	0.749984	+	0.661457i	$0.230061\pi$
$192$	1.79522e12	0.496547
$193$	3.18046e12	0.854918	0.427459	−	0.904035i	$-0.359409\pi$
$193$	3.18046e12	0.854918	0.427459	+	0.904035i	$0.359409\pi$
$194$	2.67183e12	0.698070
$195$	3.45784e11	0.0878243
$196$	−7.60810e11	−0.187875
$197$	−5.18962e12	−1.24615	−0.623077	−	0.782161i	$-0.714117\pi$
$197$	−5.18962e12	−1.24615	−0.623077	+	0.782161i	$0.714117\pi$
$198$	−8.30618e11	−0.193974
$199$	−5.44048e11	−0.123579	−0.0617895	−	0.998089i	$-0.519681\pi$
$199$	−5.44048e11	−0.123579	−0.0617895	+	0.998089i	$0.519681\pi$
$200$	4.46016e12	0.985564
$201$	4.04615e10	0.00869888
$202$	1.63923e12	0.342931
$203$	9.37114e12	1.90794
$204$	−1.59527e12	−0.316133
$205$	1.40358e12	0.270764
$206$	3.07962e12	0.578399
$207$	−9.14326e11	−0.167211
$208$	−7.62939e11	−0.135876
$209$	4.31127e12	0.747827
$210$	−7.31731e11	−0.123636
$211$	4.24001e12	0.697933	0.348966	−	0.937135i	$-0.386533\pi$
$211$	4.24001e12	0.697933	0.348966	+	0.937135i	$0.386533\pi$
$212$	−4.86175e12	−0.779731
$213$	−4.39352e12	−0.686633
$214$	1.51208e12	0.230302
$215$	3.87576e11	0.0575368
$216$	−1.40649e12	−0.203535
$217$	−1.18877e13	−1.67714
$218$	2.35668e12	0.324183
$219$	4.41277e12	0.591928
$220$	8.41800e11	0.110125
$221$	4.91970e12	0.627742
$222$	−3.01301e12	−0.375024
$223$	1.47233e13	1.78784	0.893921	−	0.448225i	$-0.147944\pi$
$223$	1.47233e13	1.78784	0.893921	+	0.448225i	$0.147944\pi$
$224$	−8.83206e12	−1.04640
$225$	−2.68687e12	−0.310629
$226$	9.61943e11	0.108531
$227$	−3.07095e12	−0.338167	−0.169083	−	0.985602i	$-0.554081\pi$
$227$	−3.07095e12	−0.338167	−0.169083	+	0.985602i	$0.554081\pi$
$228$	2.46054e12	0.264478
$229$	1.73696e12	0.182261	0.0911306	−	0.995839i	$-0.470952\pi$
$229$	1.73696e12	0.182261	0.0911306	+	0.995839i	$0.470952\pi$
$230$	−8.95999e11	−0.0917920
$231$	5.60599e12	0.560772
$232$	1.76516e13	1.72425
$233$	−8.97649e12	−0.856345	−0.428173	−	0.903697i	$-0.640842\pi$
$233$	−8.97649e12	−0.856345	−0.428173	+	0.903697i	$0.640842\pi$
$234$	1.46194e12	0.136221
$235$	2.98092e12	0.271317
$236$	−7.44388e11	−0.0661886
$237$	4.68371e12	0.406887
$238$	−1.04108e13	−0.883714
$239$	−1.45199e12	−0.120441	−0.0602205	−	0.998185i	$-0.519180\pi$
$239$	−1.45199e12	−0.120441	−0.0602205	+	0.998185i	$0.519180\pi$
$240$	−4.33308e11	−0.0351265
$241$	1.32929e13	1.05323	0.526617	−	0.850103i	$-0.323460\pi$
$241$	1.32929e13	1.05323	0.526617	+	0.850103i	$0.323460\pi$
$242$	−2.81688e12	−0.218165
$243$	8.47289e11	0.0641500
$244$	−1.55936e12	−0.115426
$245$	1.33256e12	0.0964436
$246$	5.93420e12	0.419970
$247$	−7.58813e12	−0.525172
$248$	−2.23918e13	−1.51567
$249$	7.42024e12	0.491271
$250$	−5.45847e12	−0.353509
$251$	1.27985e13	0.810876	0.405438	−	0.914123i	$-0.367119\pi$
$251$	1.27985e13	0.810876	0.405438	+	0.914123i	$0.367119\pi$
$252$	3.19947e12	0.198324
$253$	6.86449e12	0.416338
$254$	−9.08131e12	−0.538968
$255$	2.79413e12	0.162284
$256$	−1.87212e13	−1.06417
$257$	1.91661e12	0.106635	0.0533176	−	0.998578i	$-0.483020\pi$
$257$	1.91661e12	0.106635	0.0533176	+	0.998578i	$0.483020\pi$
$258$	1.63864e12	0.0892430
$259$	2.03353e13	1.08418
$260$	−1.48162e12	−0.0773365
$261$	−1.06336e13	−0.543445
$262$	8.69460e12	0.435103
$263$	6.84308e12	0.335348	0.167674	−	0.985843i	$-0.446374\pi$
$263$	6.84308e12	0.335348	0.167674	+	0.985843i	$0.446374\pi$
$264$	1.05595e13	0.506782
$265$	8.51536e12	0.400268
$266$	1.60576e13	0.739319
$267$	−2.02507e12	−0.0913330
$268$	−1.73370e11	−0.00766008
$269$	7.41245e12	0.320866	0.160433	−	0.987047i	$-0.448711\pi$
$269$	7.41245e12	0.320866	0.160433	+	0.987047i	$0.448711\pi$
$270$	8.30305e11	0.0352158
$271$	7.82419e12	0.325168	0.162584	−	0.986695i	$-0.448017\pi$
$271$	7.82419e12	0.325168	0.162584	+	0.986695i	$0.448017\pi$
$272$	−6.16497e12	−0.251074
$273$	−9.86691e12	−0.393810
$274$	−2.11511e13	−0.827378
$275$	2.01722e13	0.773434
$276$	3.91773e12	0.147243
$277$	3.55026e13	1.30804	0.654021	−	0.756476i	$-0.273081\pi$
$277$	3.55026e13	1.30804	0.654021	+	0.756476i	$0.273081\pi$
$278$	5.74799e12	0.207620
$279$	1.34892e13	0.477707
$280$	9.30236e12	0.323016
$281$	4.78222e12	0.162834	0.0814170	−	0.996680i	$-0.474055\pi$
$281$	4.78222e12	0.162834	0.0814170	+	0.996680i	$0.474055\pi$
$282$	1.26030e13	0.420828
$283$	−3.81288e13	−1.24861	−0.624307	−	0.781179i	$-0.714619\pi$
$283$	−3.81288e13	−1.24861	−0.624307	+	0.781179i	$0.714619\pi$
$284$	1.88254e13	0.604636
$285$	−4.30965e12	−0.135767
$286$	−1.09758e13	−0.339175
$287$	−4.00509e13	−1.21412
$288$	1.00219e13	0.298050
$289$	5.48200e12	0.159956
$290$	−1.04204e13	−0.298330
$291$	2.04619e13	0.574823
$292$	−1.89079e13	−0.521241
$293$	−5.77895e13	−1.56343	−0.781713	−	0.623639i	$-0.785654\pi$
$293$	−5.77895e13	−1.56343	−0.781713	+	0.623639i	$0.785654\pi$
$294$	5.63394e12	0.149590
$295$	1.30380e12	0.0339773
$296$	3.83038e13	0.979801
$297$	−6.36119e12	−0.159727
$298$	1.49050e12	0.0367403
$299$	−1.20820e13	−0.292379
$300$	1.15127e13	0.273534
$301$	−1.10594e13	−0.257999
$302$	4.98848e13	1.14269
$303$	1.25538e13	0.282385
$304$	9.50882e12	0.210050
$305$	2.73122e12	0.0592526
$306$	1.18133e13	0.251712
$307$	−6.85156e13	−1.43393	−0.716966	−	0.697108i	$-0.754470\pi$
$307$	−6.85156e13	−1.43393	−0.716966	+	0.697108i	$0.754470\pi$
$308$	−2.40207e13	−0.493806
$309$	2.35849e13	0.476280
$310$	1.32188e13	0.262242
$311$	−1.67459e13	−0.326382	−0.163191	−	0.986594i	$-0.552179\pi$
$311$	−1.67459e13	−0.326382	−0.163191	+	0.986594i	$0.552179\pi$
$312$	−1.85854e13	−0.355895
$313$	2.32665e13	0.437761	0.218881	−	0.975752i	$-0.429759\pi$
$313$	2.32665e13	0.437761	0.218881	+	0.975752i	$0.429759\pi$
$314$	3.98116e13	0.736031
$315$	−5.60388e12	−0.101808
$316$	−2.00689e13	−0.358298
$317$	−2.53473e13	−0.444740	−0.222370	−	0.974962i	$-0.571379\pi$
$317$	−2.53473e13	−0.444740	−0.222370	+	0.974962i	$0.571379\pi$
$318$	3.60021e13	0.620839
$319$	7.98336e13	1.35312
$320$	1.34729e13	0.224458
$321$	1.15801e13	0.189642
$322$	2.55672e13	0.411601
$323$	−6.13163e13	−0.970425
$324$	−3.63048e12	−0.0564894
$325$	−3.55044e13	−0.543155
$326$	1.66483e13	0.250422
$327$	1.80484e13	0.266947
$328$	−7.54403e13	−1.09723
$329$	−8.50601e13	−1.21660
$330$	−6.23369e12	−0.0876836
$331$	−9.52814e13	−1.31812	−0.659059	−	0.752092i	$-0.729045\pi$
$331$	−9.52814e13	−1.31812	−0.659059	+	0.752092i	$0.729045\pi$
$332$	−3.17944e13	−0.432605
$333$	−2.30748e13	−0.308812
$334$	9.17231e12	0.120746
$335$	3.03659e11	0.00393223
$336$	1.23644e13	0.157510
$337$	1.35144e13	0.169369	0.0846844	−	0.996408i	$-0.473012\pi$
$337$	1.35144e13	0.169369	0.0846844	+	0.996408i	$0.473012\pi$
$338$	−3.75469e13	−0.462948
$339$	7.36693e12	0.0893693
$340$	−1.19723e13	−0.142904
$341$	−1.01273e14	−1.18944
$342$	−1.82208e13	−0.210583
$343$	6.48730e13	0.737813
$344$	−2.08317e13	−0.233159
$345$	−6.86191e12	−0.0755858
$346$	−1.17719e14	−1.27623
$347$	6.87579e13	0.733686	0.366843	−	0.930283i	$-0.380439\pi$
$347$	6.87579e13	0.733686	0.366843	+	0.930283i	$0.380439\pi$
$348$	4.55629e13	0.478548
$349$	−1.03182e14	−1.06676	−0.533378	−	0.845877i	$-0.679078\pi$
$349$	−1.03182e14	−1.06676	−0.533378	+	0.845877i	$0.679078\pi$
$350$	7.51326e13	0.764635
$351$	1.11961e13	0.112170
$352$	−7.52411e13	−0.742114
$353$	1.08150e13	0.105018	0.0525092	−	0.998620i	$-0.483278\pi$
$353$	1.08150e13	0.105018	0.0525092	+	0.998620i	$0.483278\pi$
$354$	5.51233e12	0.0527008
$355$	−3.29728e13	−0.310384
$356$	8.67706e12	0.0804262
$357$	−7.97301e13	−0.727691
$358$	6.48312e13	0.582677
$359$	−2.15264e13	−0.190525	−0.0952627	−	0.995452i	$-0.530369\pi$
$359$	−2.15264e13	−0.190525	−0.0952627	+	0.995452i	$0.530369\pi$
$360$	−1.05555e13	−0.0920059
$361$	−2.19163e13	−0.188138
$362$	−2.45305e13	−0.207400
$363$	−2.15728e13	−0.179647
$364$	4.22780e13	0.346782
$365$	3.31173e13	0.267574
$366$	1.15473e13	0.0919044
$367$	1.54251e13	0.120939	0.0604693	−	0.998170i	$-0.480740\pi$
$367$	1.54251e13	0.120939	0.0604693	+	0.998170i	$0.480740\pi$
$368$	1.51401e13	0.116941
$369$	4.54464e13	0.345823
$370$	−2.26123e13	−0.169525
$371$	−2.42985e14	−1.79483
$372$	−5.77987e13	−0.420660
$373$	−2.20761e14	−1.58315	−0.791577	−	0.611069i	$-0.790740\pi$
$373$	−2.20761e14	−1.58315	−0.791577	+	0.611069i	$0.790740\pi$
$374$	−8.86908e13	−0.626736
$375$	−4.18031e13	−0.291096
$376$	−1.60220e14	−1.09947
$377$	−1.40513e14	−0.950249
$378$	−2.36927e13	−0.157910
$379$	−3.21113e13	−0.210932	−0.105466	−	0.994423i	$-0.533633\pi$
$379$	−3.21113e13	−0.210932	−0.105466	+	0.994423i	$0.533633\pi$
$380$	1.84661e13	0.119554
$381$	−6.95482e13	−0.443812
$382$	1.67199e14	1.05169
$383$	−1.99474e14	−1.23678	−0.618392	−	0.785870i	$-0.712215\pi$
$383$	−1.99474e14	−1.23678	−0.618392	+	0.785870i	$0.712215\pi$
$384$	−2.75019e13	−0.168090
$385$	4.20723e13	0.253491
$386$	1.00916e14	0.599416
$387$	1.25493e13	0.0734868
$388$	−8.76756e13	−0.506179
$389$	−2.66409e14	−1.51644	−0.758222	−	0.651996i	$-0.773932\pi$
$389$	−2.66409e14	−1.51644	−0.758222	+	0.651996i	$0.773932\pi$
$390$	1.09717e13	0.0615770
$391$	−9.76289e13	−0.540264
$392$	−7.16232e13	−0.390823
$393$	6.65866e13	0.358284
$394$	−1.64666e14	−0.873726
$395$	3.51507e13	0.183929
$396$	2.72566e13	0.140653
$397$	−1.13244e14	−0.576327	−0.288164	−	0.957581i	$-0.593045\pi$
$397$	−1.13244e14	−0.576327	−0.288164	+	0.957581i	$0.593045\pi$
$398$	−1.72626e13	−0.0866461
$399$	1.22975e14	0.608790
$400$	4.44912e13	0.217242
$401$	−2.36341e13	−0.113827	−0.0569136	−	0.998379i	$-0.518126\pi$
$401$	−2.36341e13	−0.113827	−0.0569136	+	0.998379i	$0.518126\pi$
$402$	1.28384e12	0.00609912
$403$	1.78247e14	0.835302
$404$	−5.37910e13	−0.248664
$405$	6.35880e12	0.0289983
$406$	2.97346e14	1.33773
$407$	1.73239e14	0.768911
$408$	−1.50180e14	−0.657631
$409$	3.20954e14	1.38664	0.693321	−	0.720629i	$-0.256147\pi$
$409$	3.20954e14	1.38664	0.693321	+	0.720629i	$0.256147\pi$
$410$	4.45354e13	0.189843
$411$	−1.61983e14	−0.681301
$412$	−1.01057e14	−0.419404
$413$	−3.72037e13	−0.152356
$414$	−2.90115e13	−0.117238
$415$	5.56880e13	0.222074
$416$	1.32429e14	0.521160
$417$	4.40203e13	0.170964
$418$	1.36796e14	0.524330
$419$	3.70709e14	1.40235	0.701174	−	0.712990i	$-0.252659\pi$
$419$	3.70709e14	1.40235	0.701174	+	0.712990i	$0.252659\pi$
$420$	2.40116e13	0.0896501
$421$	5.33573e12	0.0196627	0.00983133	−	0.999952i	$-0.496871\pi$
$421$	5.33573e12	0.0196627	0.00983133	+	0.999952i	$0.496871\pi$
$422$	1.34535e14	0.489348
$423$	9.65189e13	0.346530
$424$	−4.57688e14	−1.62203
$425$	−2.86895e14	−1.00365
$426$	−1.39406e14	−0.481425
$427$	−7.79351e13	−0.265693
$428$	−4.96185e13	−0.166995
$429$	−8.40572e13	−0.279293
$430$	1.22978e13	0.0403413
$431$	4.38169e14	1.41911	0.709557	−	0.704648i	$-0.248895\pi$
$431$	4.38169e14	1.41911	0.709557	+	0.704648i	$0.248895\pi$
$432$	−1.40301e13	−0.0448641
$433$	−1.97721e14	−0.624267	−0.312133	−	0.950038i	$-0.601044\pi$
$433$	−1.97721e14	−0.624267	−0.312133	+	0.950038i	$0.601044\pi$
$434$	−3.77196e14	−1.17591
$435$	−7.98036e13	−0.245658
$436$	−7.73340e13	−0.235069
$437$	1.50583e14	0.451988
$438$	1.40017e14	0.415024
$439$	2.87713e14	0.842180	0.421090	−	0.907019i	$-0.361648\pi$
$439$	2.87713e14	0.842180	0.421090	+	0.907019i	$0.361648\pi$
$440$	7.92477e13	0.229085
$441$	4.31469e13	0.123179
$442$	1.56102e14	0.440134
$443$	5.49354e14	1.52979	0.764895	−	0.644155i	$-0.222791\pi$
$443$	5.49354e14	1.52979	0.764895	+	0.644155i	$0.222791\pi$
$444$	9.88714e13	0.271935
$445$	−1.51979e13	−0.0412861
$446$	4.67170e14	1.25352
$447$	1.14148e13	0.0302537
$448$	−3.84448e14	−1.00649
$449$	−3.18321e14	−0.823210	−0.411605	−	0.911362i	$-0.635032\pi$
$449$	−3.18321e14	−0.823210	−0.411605	+	0.911362i	$0.635032\pi$
$450$	−8.52540e13	−0.217794
$451$	−3.41198e14	−0.861064
$452$	−3.15660e13	−0.0786970
$453$	3.82037e14	0.940948
$454$	−9.74411e13	−0.237102
$455$	−7.40500e13	−0.178017
$456$	2.31637e14	0.550177
$457$	7.42812e13	0.174317	0.0871585	−	0.996194i	$-0.472221\pi$
$457$	7.42812e13	0.174317	0.0871585	+	0.996194i	$0.472221\pi$
$458$	5.51136e13	0.127790
$459$	9.04709e13	0.207271
$460$	2.94021e13	0.0665595
$461$	4.18115e14	0.935279	0.467639	−	0.883919i	$-0.345105\pi$
$461$	4.18115e14	0.935279	0.467639	+	0.883919i	$0.345105\pi$
$462$	1.77878e14	0.393179
$463$	3.81881e14	0.834128	0.417064	−	0.908877i	$-0.363059\pi$
$463$	3.81881e14	0.834128	0.417064	+	0.908877i	$0.363059\pi$
$464$	1.76079e14	0.380065
$465$	1.01235e14	0.215942
$466$	−2.84823e14	−0.600417
$467$	−8.74922e14	−1.82275	−0.911374	−	0.411580i	$-0.864977\pi$
$467$	−8.74922e14	−1.82275	−0.911374	+	0.411580i	$0.864977\pi$
$468$	−4.79734e13	−0.0987753
$469$	−8.66486e12	−0.0176324
$470$	9.45842e13	0.190231
$471$	3.04892e14	0.606082
$472$	−7.00772e13	−0.137688
$473$	−9.42165e13	−0.182974
$474$	1.48614e14	0.285284
$475$	4.42506e14	0.839661
$476$	3.41629e14	0.640792
$477$	2.75718e14	0.511228
$478$	−4.60714e13	−0.0844458
$479$	1.37469e14	0.249092	0.124546	−	0.992214i	$-0.460253\pi$
$479$	1.37469e14	0.249092	0.124546	+	0.992214i	$0.460253\pi$
$480$	7.52128e13	0.134730
$481$	−3.04912e14	−0.539978
$482$	4.21782e14	0.738463
$483$	1.95804e14	0.338932
$484$	9.24356e13	0.158194
$485$	1.53564e14	0.259842
$486$	2.68844e13	0.0449781
$487$	6.78733e14	1.12277	0.561384	−	0.827556i	$-0.310269\pi$
$487$	6.78733e14	1.12277	0.561384	+	0.827556i	$0.310269\pi$
$488$	−1.46799e14	−0.240112
$489$	1.27499e14	0.206209
$490$	4.22821e13	0.0676204
$491$	2.33040e14	0.368538	0.184269	−	0.982876i	$-0.441008\pi$
$491$	2.33040e14	0.368538	0.184269	+	0.982876i	$0.441008\pi$
$492$	−1.94730e14	−0.304526
$493$	−1.13542e15	−1.75589
$494$	−2.40771e14	−0.368218
$495$	−4.77400e13	−0.0722027
$496$	−2.23364e14	−0.334090
$497$	9.40875e14	1.39178
$498$	2.35444e14	0.344449
$499$	−2.66776e14	−0.386006	−0.193003	−	0.981198i	$-0.561823\pi$
$499$	−2.66776e14	−0.386006	−0.193003	+	0.981198i	$0.561823\pi$
$500$	1.79119e14	0.256334
$501$	7.02451e13	0.0994280
$502$	4.06096e14	0.568536
$503$	−2.58819e14	−0.358403	−0.179202	−	0.983812i	$-0.557351\pi$
$503$	−2.58819e14	−0.358403	−0.179202	+	0.983812i	$0.557351\pi$
$504$	3.01200e14	0.412560
$505$	9.42151e13	0.127649
$506$	2.17810e14	0.291910
$507$	−2.87549e14	−0.381213
$508$	2.98002e14	0.390813
$509$	1.20045e15	1.55738	0.778691	−	0.627407i	$-0.215884\pi$
$509$	1.20045e15	1.55738	0.778691	+	0.627407i	$0.215884\pi$
$510$	8.86574e13	0.113783
$511$	−9.44999e14	−1.19982
$512$	−3.62235e14	−0.454994
$513$	−1.39542e14	−0.173404
$514$	6.08137e13	0.0747661
$515$	1.77002e14	0.215297
$516$	−5.37716e13	−0.0647112
$517$	−7.24635e14	−0.862822
$518$	6.45239e14	0.760163
$519$	−9.01536e14	−1.05090
$520$	−1.39481e14	−0.160878
$521$	5.94863e14	0.678906	0.339453	−	0.940623i	$-0.389758\pi$
$521$	5.94863e14	0.678906	0.339453	+	0.940623i	$0.389758\pi$
$522$	−3.37402e14	−0.381031
$523$	−1.47836e15	−1.65204	−0.826019	−	0.563643i	$-0.809399\pi$
$523$	−1.47836e15	−1.65204	−0.826019	+	0.563643i	$0.809399\pi$
$524$	−2.85312e14	−0.315499
$525$	5.75395e14	0.629636
$526$	2.17130e14	0.235125
$527$	1.44033e15	1.54349
$528$	1.05334e14	0.111707
$529$	−7.13049e14	−0.748365
$530$	2.70192e14	0.280643
$531$	4.22156e13	0.0433963
$532$	−5.26928e14	−0.536089
$533$	6.00531e14	0.604694
$534$	−6.42553e13	−0.0640371
$535$	8.69070e13	0.0857253
$536$	−1.63212e13	−0.0159348
$537$	4.96503e14	0.479803
$538$	2.35196e14	0.224972
$539$	−3.23934e14	−0.306703
$540$	−2.72463e13	−0.0255354
$541$	−1.80702e15	−1.67640	−0.838201	−	0.545361i	$-0.816393\pi$
$541$	−1.80702e15	−1.67640	−0.838201	+	0.545361i	$0.816393\pi$
$542$	2.48261e14	0.227988
$543$	−1.87864e14	−0.170783
$544$	1.07010e15	0.963012
$545$	1.35451e14	0.120670
$546$	−3.13076e14	−0.276115
$547$	−2.61646e14	−0.228446	−0.114223	−	0.993455i	$-0.536438\pi$
$547$	−2.61646e14	−0.228446	−0.114223	+	0.993455i	$0.536438\pi$
$548$	6.94068e14	0.599942
$549$	8.84340e13	0.0756783
$550$	6.40062e14	0.542285
$551$	1.75127e15	1.46899
$552$	3.68818e14	0.306300
$553$	−1.00302e15	−0.824749
$554$	1.12650e15	0.917119
$555$	−1.73174e14	−0.139595
$556$	−1.88619e14	−0.150548
$557$	−1.71485e13	−0.0135526	−0.00677629	−	0.999977i	$-0.502157\pi$
$557$	−1.71485e13	−0.0135526	−0.00677629	+	0.999977i	$0.502157\pi$
$558$	4.28010e14	0.334939
$559$	1.65827e14	0.128496
$560$	9.27934e13	0.0712005
$561$	−6.79228e14	−0.516084
$562$	1.51740e14	0.114169
$563$	2.23152e15	1.66266	0.831331	−	0.555778i	$-0.187580\pi$
$563$	2.23152e15	1.66266	0.831331	+	0.555778i	$0.187580\pi$
$564$	−4.13566e14	−0.305148
$565$	5.52880e13	0.0403984
$566$	−1.20983e15	−0.875452
$567$	−1.81448e14	−0.130030
$568$	1.77224e15	1.25779
$569$	1.21180e15	0.851755	0.425878	−	0.904781i	$-0.359965\pi$
$569$	1.21180e15	0.851755	0.425878	+	0.904781i	$0.359965\pi$
$570$	−1.36745e14	−0.0951918
$571$	−4.26898e14	−0.294324	−0.147162	−	0.989112i	$-0.547014\pi$
$571$	−4.26898e14	−0.294324	−0.147162	+	0.989112i	$0.547014\pi$
$572$	3.60170e14	0.245940
$573$	1.28048e15	0.866006
$574$	−1.27081e15	−0.851268
$575$	7.04567e14	0.467465
$576$	4.36238e14	0.286682
$577$	2.37727e15	1.54743	0.773717	−	0.633531i	$-0.218395\pi$
$577$	2.37727e15	1.54743	0.773717	+	0.633531i	$0.218395\pi$
$578$	1.73944e14	0.112152
$579$	7.72852e14	0.493587
$580$	3.41944e14	0.216322
$581$	−1.58905e15	−0.995793
$582$	6.49254e14	0.403031
$583$	−2.07001e15	−1.27290
$584$	−1.78001e15	−1.08430
$585$	8.40256e13	0.0507054
$586$	−1.83366e15	−1.09618
$587$	3.05800e15	1.81104	0.905521	−	0.424302i	$-0.139480\pi$
$587$	3.05800e15	1.81104	0.905521	+	0.424302i	$0.139480\pi$
$588$	−1.84877e14	−0.108469
$589$	−2.22156e15	−1.29129
$590$	4.13694e13	0.0238228
$591$	−1.26108e15	−0.719467
$592$	3.82090e14	0.215972
$593$	−1.64773e15	−0.922754	−0.461377	−	0.887204i	$-0.652645\pi$
$593$	−1.64773e15	−0.922754	−0.461377	+	0.887204i	$0.652645\pi$
$594$	−2.01840e14	−0.111991
$595$	−5.98365e14	−0.328945
$596$	−4.89106e13	−0.0266409
$597$	−1.32204e14	−0.0713484
$598$	−3.83360e14	−0.204998
$599$	−2.26430e15	−1.19974	−0.599869	−	0.800098i	$-0.704781\pi$
$599$	−2.26430e15	−1.19974	−0.599869	+	0.800098i	$0.704781\pi$
$600$	1.08382e15	0.569016
$601$	−3.57425e15	−1.85941	−0.929704	−	0.368307i	$-0.879937\pi$
$601$	−3.57425e15	−1.85941	−0.929704	+	0.368307i	$0.879937\pi$
$602$	−3.50915e14	−0.180893
$603$	9.83214e12	0.00502230
$604$	−1.63696e15	−0.828582
$605$	−1.61901e14	−0.0812074
$606$	3.98333e14	0.197991
$607$	3.14155e15	1.54741	0.773706	−	0.633544i	$-0.218401\pi$
$607$	3.14155e15	1.54741	0.773706	+	0.633544i	$0.218401\pi$
$608$	−1.65052e15	−0.805660
$609$	2.27719e15	1.10155
$610$	8.66614e13	0.0415443
$611$	1.27541e15	0.605929
$612$	−3.87652e14	−0.182519
$613$	3.80047e15	1.77339	0.886695	−	0.462354i	$-0.152995\pi$
$613$	3.80047e15	1.77339	0.886695	+	0.462354i	$0.152995\pi$
$614$	−2.17400e15	−1.00539
$615$	3.41069e14	0.156325
$616$	−2.26132e15	−1.02723
$617$	−1.04144e15	−0.468883	−0.234442	−	0.972130i	$-0.575326\pi$
$617$	−1.04144e15	−0.468883	−0.234442	+	0.972130i	$0.575326\pi$
$618$	7.48348e14	0.333939
$619$	1.05252e15	0.465514	0.232757	−	0.972535i	$-0.425225\pi$
$619$	1.05252e15	0.465514	0.232757	+	0.972535i	$0.425225\pi$
$620$	−4.33772e14	−0.190155
$621$	−2.22181e14	−0.0965392
$622$	−5.31346e14	−0.228839
$623$	4.33670e14	0.185129
$624$	−1.85394e14	−0.0784478
$625$	1.90806e15	0.800300
$626$	7.38245e14	0.306932
$627$	1.04764e15	0.431758
$628$	−1.30641e15	−0.533705
$629$	−2.46386e15	−0.997784
$630$	−1.77811e14	−0.0713813
$631$	−1.55786e15	−0.619966	−0.309983	−	0.950742i	$-0.600323\pi$
$631$	−1.55786e15	−0.619966	−0.309983	+	0.950742i	$0.600323\pi$
$632$	−1.88930e15	−0.745343
$633$	1.03032e15	0.402952
$634$	−8.04269e14	−0.311824
$635$	−5.21951e14	−0.200620
$636$	−1.18140e15	−0.450178
$637$	5.70146e14	0.215387
$638$	2.53312e15	0.948727
$639$	−1.06762e15	−0.396427
$640$	−2.06399e14	−0.0759831
$641$	1.92660e15	0.703189	0.351595	−	0.936152i	$-0.385640\pi$
$641$	1.92660e15	0.703189	0.351595	+	0.936152i	$0.385640\pi$
$642$	3.67435e14	0.132965
$643$	−6.88029e14	−0.246857	−0.123429	−	0.992353i	$-0.539389\pi$
$643$	−6.88029e14	−0.246857	−0.123429	+	0.992353i	$0.539389\pi$
$644$	−8.38985e14	−0.298457
$645$	9.41810e13	0.0332189
$646$	−1.94556e15	−0.680402
$647$	1.09245e15	0.378815	0.189408	−	0.981899i	$-0.439343\pi$
$647$	1.09245e15	0.378815	0.189408	+	0.981899i	$0.439343\pi$
$648$	−3.41776e14	−0.117511
$649$	−3.16942e14	−0.108052
$650$	−1.12655e15	−0.380827
$651$	−2.88872e15	−0.968299
$652$	−5.46311e14	−0.181584
$653$	3.74060e15	1.23287	0.616437	−	0.787404i	$-0.288575\pi$
$653$	3.74060e15	1.23287	0.616437	+	0.787404i	$0.288575\pi$
$654$	5.72673e14	0.187167
$655$	4.99724e14	0.161958
$656$	−7.52536e14	−0.241856
$657$	1.07230e15	0.341750
$658$	−2.69895e15	−0.853007
$659$	3.53097e15	1.10668	0.553342	−	0.832954i	$-0.313352\pi$
$659$	3.53097e15	1.10668	0.553342	+	0.832954i	$0.313352\pi$
$660$	2.04557e14	0.0635804
$661$	3.00196e15	0.925332	0.462666	−	0.886533i	$-0.346893\pi$
$661$	3.00196e15	0.925332	0.462666	+	0.886533i	$0.346893\pi$
$662$	−3.02327e15	−0.924183
$663$	1.19549e15	0.362427
$664$	−2.99315e15	−0.899920
$665$	9.22916e14	0.275197
$666$	−7.32162e14	−0.216520
$667$	2.78840e15	0.817830
$668$	−3.00988e14	−0.0875545
$669$	3.57777e15	1.03221
$670$	9.63506e12	0.00275704
$671$	−6.63936e14	−0.188431
$672$	−2.14619e15	−0.604139
$673$	6.86134e13	0.0191569	0.00957847	−	0.999954i	$-0.496951\pi$
$673$	6.86134e13	0.0191569	0.00957847	+	0.999954i	$0.496951\pi$
$674$	4.28812e14	0.118751
$675$	−6.52908e14	−0.179342
$676$	1.23210e15	0.335689
$677$	3.47540e15	0.939220	0.469610	−	0.882874i	$-0.344395\pi$
$677$	3.47540e15	0.939220	0.469610	+	0.882874i	$0.344395\pi$
$678$	2.33752e14	0.0626603
$679$	−4.38193e15	−1.16515
$680$	−1.12708e15	−0.297274
$681$	−7.46241e14	−0.195241
$682$	−3.21337e15	−0.833963
$683$	−3.88839e15	−1.00105	−0.500525	−	0.865722i	$-0.666860\pi$
$683$	−3.88839e15	−1.00105	−0.500525	+	0.865722i	$0.666860\pi$
$684$	5.97912e14	0.152696
$685$	−1.21566e15	−0.307975
$686$	2.05841e15	0.517309
$687$	4.22081e14	0.105229
$688$	−2.07801e14	−0.0513939
$689$	3.64336e15	0.893915
$690$	−2.17728e14	−0.0529961
$691$	2.20209e15	0.531748	0.265874	−	0.964008i	$-0.414340\pi$
$691$	2.20209e15	0.531748	0.265874	+	0.964008i	$0.414340\pi$
$692$	3.86292e15	0.925407
$693$	1.36226e15	0.323762
$694$	2.18168e15	0.514416
$695$	3.30367e14	0.0772824
$696$	4.28933e15	0.995493
$697$	4.85262e15	1.11737
$698$	−3.27397e15	−0.747945
$699$	−2.18129e15	−0.494411
$700$	−2.46546e15	−0.554446
$701$	−2.64860e15	−0.590974	−0.295487	−	0.955347i	$-0.595482\pi$
$701$	−2.64860e15	−0.590974	−0.295487	+	0.955347i	$0.595482\pi$
$702$	3.55252e14	0.0786471
$703$	3.80024e15	0.834751
$704$	−3.27514e15	−0.713807
$705$	7.24363e14	0.156645
$706$	3.43159e14	0.0736325
$707$	−2.68842e15	−0.572387
$708$	−1.80886e14	−0.0382140
$709$	−6.31638e15	−1.32408	−0.662040	−	0.749469i	$-0.730309\pi$
$709$	−6.31638e15	−1.32408	−0.662040	+	0.749469i	$0.730309\pi$
$710$	−1.04622e15	−0.217623
$711$	1.13814e15	0.234916
$712$	8.16865e14	0.167306
$713$	−3.53721e15	−0.718900
$714$	−2.52983e15	−0.510213
$715$	−6.30839e14	−0.126251
$716$	−2.12743e15	−0.422506
$717$	−3.52833e14	−0.0695366
$718$	−6.83033e14	−0.133585
$719$	8.99398e15	1.74559	0.872797	−	0.488083i	$-0.162304\pi$
$719$	8.99398e15	1.74559	0.872797	+	0.488083i	$0.162304\pi$
$720$	−1.05294e14	−0.0202803
$721$	−5.05073e15	−0.965407
$722$	−6.95402e14	−0.131911
$723$	3.23017e15	0.608085
$724$	8.04964e14	0.150388
$725$	8.19407e15	1.51929
$726$	−6.84503e14	−0.125957
$727$	−9.72835e15	−1.77664	−0.888321	−	0.459223i	$-0.848128\pi$
$727$	−9.72835e15	−1.77664	−0.888321	+	0.459223i	$0.848128\pi$
$728$	3.98008e15	0.721388
$729$	2.05891e14	0.0370370
$730$	1.05081e15	0.187607
$731$	1.33998e15	0.237439
$732$	−3.78924e14	−0.0666410
$733$	−1.55093e15	−0.270719	−0.135360	−	0.990797i	$-0.543219\pi$
$733$	−1.55093e15	−0.270719	−0.135360	+	0.990797i	$0.543219\pi$
$734$	4.89438e14	0.0847948
$735$	3.23812e14	0.0556818
$736$	−2.62799e15	−0.448535
$737$	−7.38168e13	−0.0125050
$738$	1.44201e15	0.242470
$739$	4.95578e15	0.827118	0.413559	−	0.910477i	$-0.364285\pi$
$739$	4.95578e15	0.827118	0.413559	+	0.910477i	$0.364285\pi$
$740$	7.42018e14	0.122925
$741$	−1.84391e15	−0.303208
$742$	−7.70989e15	−1.25842
$743$	4.31572e15	0.699222	0.349611	−	0.936895i	$-0.386314\pi$
$743$	4.31572e15	0.699222	0.349611	+	0.936895i	$0.386314\pi$
$744$	−5.44121e15	−0.875073
$745$	8.56670e13	0.0136758
$746$	−7.00472e15	−1.11001
$747$	1.80312e15	0.283636
$748$	2.91037e15	0.454454
$749$	−2.47988e15	−0.384398
$750$	−1.32641e15	−0.204099
$751$	5.80093e14	0.0886090	0.0443045	−	0.999018i	$-0.485893\pi$
$751$	5.80093e14	0.0886090	0.0443045	+	0.999018i	$0.485893\pi$
$752$	−1.59823e15	−0.242350
$753$	3.11004e15	0.468159
$754$	−4.45845e15	−0.666257
$755$	2.86714e15	0.425345
$756$	7.77471e14	0.114502
$757$	−2.22175e15	−0.324838	−0.162419	−	0.986722i	$-0.551930\pi$
$757$	−2.22175e15	−0.324838	−0.162419	+	0.986722i	$0.551930\pi$
$758$	−1.01889e15	−0.147893
$759$	1.66807e15	0.240373
$760$	1.73841e15	0.248701
$761$	4.37184e15	0.620939	0.310469	−	0.950583i	$-0.399514\pi$
$761$	4.37184e15	0.620939	0.310469	+	0.950583i	$0.399514\pi$
$762$	−2.20676e15	−0.311174
$763$	−3.86507e15	−0.541094
$764$	−5.48661e15	−0.762590
$765$	6.78973e14	0.0936946
$766$	−6.32930e15	−0.867157
$767$	5.57839e14	0.0758812
$768$	−4.54924e15	−0.614401
$769$	−1.74235e15	−0.233636	−0.116818	−	0.993153i	$-0.537269\pi$
$769$	−1.74235e15	−0.233636	−0.116818	+	0.993153i	$0.537269\pi$
$770$	1.33495e15	0.177732
$771$	4.65735e14	0.0615659
$772$	−3.31153e15	−0.434644
$773$	−2.41985e15	−0.315356	−0.157678	−	0.987491i	$-0.550401\pi$
$773$	−2.41985e15	−0.315356	−0.157678	+	0.987491i	$0.550401\pi$
$774$	3.98188e14	0.0515245
$775$	−1.03945e16	−1.33551
$776$	−8.25384e15	−1.05297
$777$	4.94149e15	0.625954
$778$	−8.45314e15	−1.06324
$779$	−7.48466e15	−0.934795
$780$	−3.60035e14	−0.0446503
$781$	8.01541e15	0.987063
$782$	−3.09776e15	−0.378800
$783$	−2.58396e15	−0.313758
$784$	−7.14460e14	−0.0861469
$785$	2.28818e15	0.273973
$786$	2.11279e15	0.251207
$787$	−1.07655e16	−1.27108	−0.635538	−	0.772069i	$-0.719222\pi$
$787$	−1.07655e16	−1.27108	−0.635538	+	0.772069i	$0.719222\pi$
$788$	5.40350e15	0.633550
$789$	1.66287e15	0.193613
$790$	1.11533e15	0.128960
$791$	−1.57764e15	−0.181149
$792$	2.56595e15	0.292591
$793$	1.16857e15	0.132328
$794$	−3.59324e15	−0.404086
$795$	2.06923e15	0.231095
$796$	5.66469e14	0.0628281
$797$	−2.58738e15	−0.284997	−0.142498	−	0.989795i	$-0.545514\pi$
$797$	−2.58738e15	−0.284997	−0.142498	+	0.989795i	$0.545514\pi$
$798$	3.90200e15	0.426846
$799$	1.03060e16	1.11965
$800$	−7.72270e15	−0.833248
$801$	−4.92092e14	−0.0527312
$802$	−7.49910e14	−0.0798086
$803$	−8.05054e15	−0.850921
$804$	−4.21290e13	−0.00442255
$805$	1.46948e15	0.153210
$806$	5.65575e15	0.585663
$807$	1.80122e15	0.185252
$808$	−5.06393e15	−0.517279
$809$	−1.13803e16	−1.15461	−0.577307	−	0.816527i	$-0.695896\pi$
$809$	−1.13803e16	−1.15461	−0.577307	+	0.816527i	$0.695896\pi$
$810$	2.01764e14	0.0203318
$811$	8.98215e15	0.899012	0.449506	−	0.893277i	$-0.351600\pi$
$811$	8.98215e15	0.899012	0.449506	+	0.893277i	$0.351600\pi$
$812$	−9.75734e15	−0.970004
$813$	1.90128e15	0.187736
$814$	5.49685e15	0.539113
$815$	9.56865e14	0.0932146
$816$	−1.49809e15	−0.144958
$817$	−2.06677e15	−0.198642
$818$	1.01838e16	0.972228
$819$	−2.39766e15	−0.227366
$820$	−1.46142e15	−0.137657
$821$	6.30672e15	0.590087	0.295043	−	0.955484i	$-0.404666\pi$
$821$	6.30672e15	0.590087	0.295043	+	0.955484i	$0.404666\pi$
$822$	−5.13971e15	−0.477687
$823$	2.13866e16	1.97443	0.987215	−	0.159396i	$-0.0509546\pi$
$823$	2.13866e16	1.97443	0.987215	+	0.159396i	$0.0509546\pi$
$824$	−9.51360e15	−0.872459
$825$	4.90184e15	0.446542
$826$	−1.18047e15	−0.106823
$827$	−8.24854e15	−0.741476	−0.370738	−	0.928738i	$-0.620895\pi$
$827$	−8.24854e15	−0.741476	−0.370738	+	0.928738i	$0.620895\pi$
$828$	9.52008e14	0.0850107
$829$	8.52629e15	0.756328	0.378164	−	0.925739i	$-0.376556\pi$
$829$	8.52629e15	0.756328	0.378164	+	0.925739i	$0.376556\pi$
$830$	1.76698e15	0.155704
$831$	8.62714e15	0.755199
$832$	5.76447e15	0.501281
$833$	4.60709e15	0.397997
$834$	1.39676e15	0.119870
$835$	5.27181e14	0.0449453
$836$	−4.48895e15	−0.380198
$837$	3.27787e15	0.275804
$838$	1.17626e16	0.983241
$839$	−2.94730e15	−0.244756	−0.122378	−	0.992484i	$-0.539052\pi$
$839$	−2.94730e15	−0.244756	−0.122378	+	0.992484i	$0.539052\pi$
$840$	2.26047e15	0.186493
$841$	2.02284e16	1.65800
$842$	1.69302e14	0.0137863
$843$	1.16208e15	0.0940122
$844$	−4.41475e15	−0.354832
$845$	−2.15802e15	−0.172323
$846$	3.06254e15	0.242965
$847$	4.61983e15	0.364139
$848$	−4.56556e15	−0.357533
$849$	−9.26531e15	−0.720888
$850$	−9.10316e15	−0.703701
$851$	6.05082e15	0.464731
$852$	4.57458e15	0.349087
$853$	−1.10689e16	−0.839237	−0.419618	−	0.907701i	$-0.637836\pi$
$853$	−1.10689e16	−0.839237	−0.419618	+	0.907701i	$0.637836\pi$
$854$	−2.47287e15	−0.186288
$855$	−1.04725e15	−0.0783853
$856$	−4.67113e15	−0.347389
$857$	1.86672e16	1.37939	0.689693	−	0.724102i	$-0.257746\pi$
$857$	1.86672e16	1.37939	0.689693	+	0.724102i	$0.257746\pi$
$858$	−2.66713e15	−0.195823
$859$	−1.61594e16	−1.17886	−0.589432	−	0.807818i	$-0.700649\pi$
$859$	−1.61594e16	−1.17886	−0.589432	+	0.807818i	$0.700649\pi$
$860$	−4.03549e14	−0.0292520
$861$	−9.73238e15	−0.700974
$862$	1.39031e16	0.994996
$863$	8.57698e15	0.609923	0.304961	−	0.952365i	$-0.401356\pi$
$863$	8.57698e15	0.609923	0.304961	+	0.952365i	$0.401356\pi$
$864$	2.43531e15	0.172079
$865$	−6.76592e15	−0.475049
$866$	−6.27368e15	−0.437698
$867$	1.33213e15	0.0923508
$868$	1.23776e16	0.852667
$869$	−8.54483e15	−0.584917
$870$	−2.53216e15	−0.172241
$871$	1.29922e14	0.00878182
$872$	−7.28028e15	−0.488998
$873$	4.97224e15	0.331874
$874$	4.77797e15	0.316906
$875$	8.95216e15	0.590043
$876$	−4.59463e15	−0.300939
$877$	−1.34626e16	−0.876255	−0.438128	−	0.898913i	$-0.644358\pi$
$877$	−1.34626e16	−0.876255	−0.438128	+	0.898913i	$0.644358\pi$
$878$	9.12912e15	0.590485
$879$	−1.40429e16	−0.902644
$880$	7.90516e14	0.0504959
$881$	8.04558e15	0.510728	0.255364	−	0.966845i	$-0.417805\pi$
$881$	8.04558e15	0.510728	0.255364	+	0.966845i	$0.417805\pi$
$882$	1.36905e15	0.0863657
$883$	−1.38620e15	−0.0869047	−0.0434523	−	0.999056i	$-0.513836\pi$
$883$	−1.38620e15	−0.0869047	−0.0434523	+	0.999056i	$0.513836\pi$
$884$	−5.12245e15	−0.319147
$885$	3.16823e14	0.0196168
$886$	1.74310e16	1.07260
$887$	−1.93804e16	−1.18517	−0.592587	−	0.805507i	$-0.701893\pi$
$887$	−1.93804e16	−1.18517	−0.592587	+	0.805507i	$0.701893\pi$
$888$	9.30783e15	0.565688
$889$	1.48938e16	0.899593
$890$	−4.82228e14	−0.0289473
$891$	−1.54577e15	−0.0922184
$892$	−1.53301e16	−0.908946
$893$	−1.58959e16	−0.936704
$894$	3.62192e14	0.0212120
$895$	3.72619e15	0.216890
$896$	5.88956e15	0.340713
$897$	−2.93592e15	−0.168805
$898$	−1.01003e16	−0.577184
$899$	−4.11376e16	−2.33647
$900$	2.79760e15	0.157925
$901$	2.94404e16	1.65180
$902$	−1.08262e16	−0.603725
$903$	−2.68744e15	−0.148956
$904$	−2.97165e15	−0.163708
$905$	−1.40990e15	−0.0772005
$906$	1.21220e16	0.659735
$907$	2.31034e16	1.24979	0.624893	−	0.780710i	$-0.285143\pi$
$907$	2.31034e16	1.24979	0.624893	+	0.780710i	$0.285143\pi$
$908$	3.19751e15	0.171925
$909$	3.05058e15	0.163035
$910$	−2.34960e15	−0.124815
$911$	3.61189e16	1.90715	0.953573	−	0.301161i	$-0.0973743\pi$
$911$	3.61189e16	1.90715	0.953573	+	0.301161i	$0.0973743\pi$
$912$	2.31064e15	0.121272
$913$	−1.35373e16	−0.706223
$914$	2.35694e15	0.122220
$915$	6.63687e14	0.0342095
$916$	−1.80854e15	−0.0926624
$917$	−1.42596e16	−0.726232
$918$	2.87063e15	0.145326
$919$	5.85313e15	0.294546	0.147273	−	0.989096i	$-0.452950\pi$
$919$	5.85313e15	0.294546	0.147273	+	0.989096i	$0.452950\pi$
$920$	2.76793e15	0.138459
$921$	−1.66493e16	−0.827881
$922$	1.32668e16	0.655760
$923$	−1.41077e16	−0.693179
$924$	−5.83702e15	−0.285099
$925$	1.77811e16	0.863335
$926$	1.21171e16	0.584840
$927$	5.73113e15	0.274981
$928$	−3.05634e16	−1.45777
$929$	2.08034e16	0.986390	0.493195	−	0.869919i	$-0.335829\pi$
$929$	2.08034e16	0.986390	0.493195	+	0.869919i	$0.335829\pi$
$930$	3.21216e15	0.151405
$931$	−7.10596e15	−0.332966
$932$	9.34643e15	0.435370
$933$	−4.06926e15	−0.188437
$934$	−2.77612e16	−1.27800
$935$	−5.09753e15	−0.233290
$936$	−4.51625e15	−0.205476
$937$	2.51133e16	1.13589	0.567945	−	0.823067i	$-0.307739\pi$
$937$	2.51133e16	1.13589	0.567945	+	0.823067i	$0.307739\pi$
$938$	−2.74935e14	−0.0123628
$939$	5.65376e15	0.252742
$940$	−3.10377e15	−0.137939
$941$	1.42223e16	0.628386	0.314193	−	0.949359i	$-0.398266\pi$
$941$	1.42223e16	0.628386	0.314193	+	0.949359i	$0.398266\pi$
$942$	9.67421e15	0.424948
$943$	−1.19172e16	−0.520428
$944$	−6.99038e14	−0.0303497
$945$	−1.36174e15	−0.0587787
$946$	−2.98948e15	−0.128291
$947$	3.67105e16	1.56627	0.783133	−	0.621855i	$-0.213620\pi$
$947$	3.67105e16	1.56627	0.783133	+	0.621855i	$0.213620\pi$
$948$	−4.87673e15	−0.206863
$949$	1.41695e16	0.597571
$950$	1.40407e16	0.588719
$951$	−6.15940e15	−0.256771
$952$	3.21612e16	1.33300
$953$	3.72037e16	1.53312	0.766559	−	0.642174i	$-0.221967\pi$
$953$	3.72037e16	1.53312	0.766559	+	0.642174i	$0.221967\pi$
$954$	8.74852e15	0.358442
$955$	9.60982e15	0.391468
$956$	1.51183e15	0.0612327
$957$	1.93996e16	0.781226
$958$	4.36188e15	0.174648
$959$	3.46888e16	1.38098
$960$	3.27391e15	0.129591
$961$	2.67764e16	1.05384
$962$	−9.67483e15	−0.378600
$963$	2.81396e15	0.109490
$964$	−1.38407e16	−0.535469
$965$	5.80016e15	0.223121
$966$	6.21284e15	0.237638
$967$	3.66743e16	1.39481	0.697406	−	0.716676i	$-0.254337\pi$
$967$	3.66743e16	1.39481	0.697406	+	0.716676i	$0.254337\pi$
$968$	8.70195e15	0.329081
$969$	−1.48999e16	−0.560275
$970$	4.87257e15	0.182186
$971$	1.90896e16	0.709725	0.354863	−	0.934918i	$-0.384528\pi$
$971$	1.90896e16	0.709725	0.354863	+	0.934918i	$0.384528\pi$
$972$	−8.82207e14	−0.0326142
$973$	−9.42700e15	−0.346539
$974$	2.15362e16	0.787216
$975$	−8.62757e15	−0.313591
$976$	−1.46436e15	−0.0529266
$977$	3.80992e16	1.36929	0.684646	−	0.728875i	$-0.259957\pi$
$977$	3.80992e16	1.36929	0.684646	+	0.728875i	$0.259957\pi$
$978$	4.04554e15	0.144581
$979$	3.69448e15	0.131295
$980$	−1.38748e15	−0.0490324
$981$	4.38575e15	0.154122
$982$	7.39433e15	0.258396
$983$	−2.80815e16	−0.975835	−0.487917	−	0.872890i	$-0.662243\pi$
$983$	−2.80815e16	−0.975835	−0.487917	+	0.872890i	$0.662243\pi$
$984$	−1.83320e16	−0.633485
$985$	−9.46424e15	−0.325227
$986$	−3.60268e16	−1.23112
$987$	−2.06696e16	−0.702405
$988$	7.90085e15	0.267000
$989$	−3.29076e15	−0.110590
$990$	−1.51479e15	−0.0506241
$991$	−2.53187e16	−0.841464	−0.420732	−	0.907185i	$-0.638227\pi$
$991$	−2.53187e16	−0.841464	−0.420732	+	0.907185i	$0.638227\pi$
$992$	3.87711e16	1.28143
$993$	−2.31534e16	−0.761015
$994$	2.98539e16	0.975834
$995$	−9.92172e14	−0.0322522
$996$	−7.72604e15	−0.249764
$997$	−3.10539e16	−0.998374	−0.499187	−	0.866494i	$-0.666368\pi$
$997$	−3.10539e16	−0.998374	−0.499187	+	0.866494i	$0.666368\pi$
$998$	−8.46479e15	−0.270644
$999$	−5.60718e15	−0.178293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.19	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+31.7299 q^{2} +243.000 q^{3} -1041.21 q^{4} +1823.69 q^{5} +7710.37 q^{6} -52038.7 q^{7} -98020.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+31.7299 q^{2} +243.000 q^{3} -1041.21 q^{4} +1823.69 q^{5} +7710.37 q^{6} -52038.7 q^{7} -98020.5 q^{8} +59049.0 q^{9} +57865.4 q^{10} -443322. q^{11} -253015. q^{12} +780277. q^{13} -1.65118e6 q^{14} +443156. q^{15} -977779. q^{16} +6.30507e6 q^{17} +1.87362e6 q^{18} -9.72491e6 q^{19} -1.89884e6 q^{20} -1.26454e7 q^{21} -1.40666e7 q^{22} -1.54842e7 q^{23} -2.38190e7 q^{24} -4.55023e7 q^{25} +2.47581e7 q^{26} +1.43489e7 q^{27} +5.41833e7 q^{28} -1.80080e8 q^{29} +1.40613e7 q^{30} +2.28440e8 q^{31} +1.69721e8 q^{32} -1.07727e8 q^{33} +2.00059e8 q^{34} -9.49022e7 q^{35} -6.14825e7 q^{36} -3.90774e8 q^{37} -3.08571e8 q^{38} +1.89607e8 q^{39} -1.78759e8 q^{40} +7.69638e8 q^{41} -4.01237e8 q^{42} +2.12524e8 q^{43} +4.61593e8 q^{44} +1.07687e8 q^{45} -4.91312e8 q^{46} +1.63456e9 q^{47} -2.37600e8 q^{48} +7.30697e8 q^{49} -1.44378e9 q^{50} +1.53213e9 q^{51} -8.12434e8 q^{52} +4.66931e9 q^{53} +4.55290e8 q^{54} -8.08481e8 q^{55} +5.10085e9 q^{56} -2.36315e9 q^{57} -5.71393e9 q^{58} +7.14924e8 q^{59} -4.61419e8 q^{60} +1.49764e9 q^{61} +7.24839e9 q^{62} -3.07283e9 q^{63} +7.38773e9 q^{64} +1.42298e9 q^{65} -3.41818e9 q^{66} +1.66508e8 q^{67} -6.56491e9 q^{68} -3.76266e9 q^{69} -3.01124e9 q^{70} -1.80803e10 q^{71} -5.78801e9 q^{72} +1.81596e10 q^{73} -1.23992e10 q^{74} -1.10571e10 q^{75} +1.01257e10 q^{76} +2.30699e10 q^{77} +6.01623e9 q^{78} +1.92745e10 q^{79} -1.78316e9 q^{80} +3.48678e9 q^{81} +2.44206e10 q^{82} +3.05360e10 q^{83} +1.31665e10 q^{84} +1.14985e10 q^{85} +6.74336e9 q^{86} -4.37595e10 q^{87} +4.34547e10 q^{88} -8.33362e9 q^{89} +3.41689e9 q^{90} -4.06046e10 q^{91} +1.61223e10 q^{92} +5.55109e10 q^{93} +5.18643e10 q^{94} -1.77352e10 q^{95} +4.12422e10 q^{96} +8.42053e10 q^{97} +2.31849e10 q^{98} -2.61777e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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