LMFDB - Embedded newform 177.12.a.d.1.26

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			1.26
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +285730. q^{10} +561469. q^{11} +1.05674e6 q^{12} -841746. q^{13} +2.74320e6 q^{14} +868128. q^{15} +5.81083e6 q^{16} -1.34277e6 q^{17} +4.72271e6 q^{18} -1.30792e6 q^{19} +1.55360e7 q^{20} +8.33461e6 q^{21} +4.49060e7 q^{22} +5.35592e7 q^{23} +4.47143e7 q^{24} -3.60651e7 q^{25} -6.73224e7 q^{26} +1.43489e7 q^{27} +1.49156e8 q^{28} +7.22123e7 q^{29} +6.94324e7 q^{30} +1.64321e8 q^{31} +8.78949e7 q^{32} +1.36437e8 q^{33} -1.07394e8 q^{34} +1.22534e8 q^{35} +2.56787e8 q^{36} -2.58614e8 q^{37} -1.04607e8 q^{38} -2.04544e8 q^{39} +6.57382e8 q^{40} -5.88764e8 q^{41} +6.66597e8 q^{42} +6.19956e8 q^{43} +2.44167e9 q^{44} +2.10955e8 q^{45} +4.28363e9 q^{46} -1.16783e9 q^{47} +1.41203e9 q^{48} -8.00919e8 q^{49} -2.88446e9 q^{50} -3.26294e8 q^{51} -3.66051e9 q^{52} -1.57562e9 q^{53} +1.14762e9 q^{54} +2.00587e9 q^{55} +6.31131e9 q^{56} -3.17825e8 q^{57} +5.77550e9 q^{58} +7.14924e8 q^{59} +3.77524e9 q^{60} +7.71700e9 q^{61} +1.31423e10 q^{62} +2.02531e9 q^{63} -4.87079e9 q^{64} -3.00717e9 q^{65} +1.09122e10 q^{66} -3.30544e9 q^{67} -5.83933e9 q^{68} +1.30149e10 q^{69} +9.80020e9 q^{70} -1.03471e10 q^{71} +1.08656e10 q^{72} +2.59913e10 q^{73} -2.06838e10 q^{74} -8.76381e9 q^{75} -5.68777e9 q^{76} +1.92577e10 q^{77} -1.63593e10 q^{78} +4.26792e9 q^{79} +2.07594e10 q^{80} +3.48678e9 q^{81} -4.70890e10 q^{82} -3.07597e10 q^{83} +3.62448e10 q^{84} -4.79711e9 q^{85} +4.95837e10 q^{86} +1.75476e10 q^{87} +1.03316e11 q^{88} -8.23783e10 q^{89} +1.68721e10 q^{90} -2.88709e10 q^{91} +2.32913e11 q^{92} +3.99301e10 q^{93} -9.34021e10 q^{94} -4.67260e9 q^{95} +2.13585e10 q^{96} +1.52034e10 q^{97} -6.40571e10 q^{98} +3.31542e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	79.9794	1.76731	0.883656	−	0.468136i	$-0.155074\pi$
$2$	79.9794	1.76731	0.883656	+	0.468136i	$0.155074\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	4348.71	2.12339
$5$	3572.54	0.511261	0.255630	−	0.966775i	$-0.417717\pi$
$5$	3572.54	0.511261	0.255630	+	0.966775i	$0.417717\pi$
$6$	19435.0	1.02036
$7$	34298.8	0.771329	0.385665	−	0.922639i	$-0.373972\pi$
$7$	34298.8	0.771329	0.385665	+	0.922639i	$0.373972\pi$
$8$	184010.	1.98539
$9$	59049.0	0.333333
$10$	285730.	0.903558
$11$	561469.	1.05115	0.525577	−	0.850746i	$-0.323850\pi$
$11$	561469.	1.05115	0.525577	+	0.850746i	$0.323850\pi$
$12$	1.05674e6	1.22594
$13$	−841746.	−0.628771	−0.314386	−	0.949295i	$-0.601798\pi$
$13$	−841746.	−0.628771	−0.314386	+	0.949295i	$0.601798\pi$
$14$	2.74320e6	1.36318
$15$	868128.	0.295177
$16$	5.81083e6	1.38541
$17$	−1.34277e6	−0.229368	−0.114684	−	0.993402i	$-0.536586\pi$
$17$	−1.34277e6	−0.229368	−0.114684	+	0.993402i	$0.536586\pi$
$18$	4.72271e6	0.589104
$19$	−1.30792e6	−0.121182	−0.0605908	−	0.998163i	$-0.519298\pi$
$19$	−1.30792e6	−0.121182	−0.0605908	+	0.998163i	$0.519298\pi$
$20$	1.55360e7	1.08561
$21$	8.33461e6	0.445327
$22$	4.49060e7	1.85772
$23$	5.35592e7	1.73512	0.867562	−	0.497328i	$-0.165686\pi$
$23$	5.35592e7	1.73512	0.867562	+	0.497328i	$0.165686\pi$
$24$	4.47143e7	1.14626
$25$	−3.60651e7	−0.738612
$26$	−6.73224e7	−1.11123
$27$	1.43489e7	0.192450
$28$	1.49156e8	1.63784
$29$	7.22123e7	0.653766	0.326883	−	0.945065i	$-0.394002\pi$
$29$	7.22123e7	0.653766	0.326883	+	0.945065i	$0.394002\pi$
$30$	6.94324e7	0.521669
$31$	1.64321e8	1.03087	0.515436	−	0.856928i	$-0.327630\pi$
$31$	1.64321e8	1.03087	0.515436	+	0.856928i	$0.327630\pi$
$32$	8.78949e7	0.463062
$33$	1.36437e8	0.606884
$34$	−1.07394e8	−0.405365
$35$	1.22534e8	0.394350
$36$	2.56787e8	0.707798
$37$	−2.58614e8	−0.613115	−0.306558	−	0.951852i	$-0.599177\pi$
$37$	−2.58614e8	−0.613115	−0.306558	+	0.951852i	$0.599177\pi$
$38$	−1.04607e8	−0.214166
$39$	−2.04544e8	−0.363021
$40$	6.57382e8	1.01505
$41$	−5.88764e8	−0.793651	−0.396826	−	0.917894i	$-0.629888\pi$
$41$	−5.88764e8	−0.793651	−0.396826	+	0.917894i	$0.629888\pi$
$42$	6.66597e8	0.787032
$43$	6.19956e8	0.643109	0.321554	−	0.946891i	$-0.395795\pi$
$43$	6.19956e8	0.643109	0.321554	+	0.946891i	$0.395795\pi$
$44$	2.44167e9	2.23201
$45$	2.10955e8	0.170420
$46$	4.28363e9	3.06651
$47$	−1.16783e9	−0.742745	−0.371373	−	0.928484i	$-0.621113\pi$
$47$	−1.16783e9	−0.742745	−0.371373	+	0.928484i	$0.621113\pi$
$48$	1.41203e9	0.799866
$49$	−8.00919e8	−0.405051
$50$	−2.88446e9	−1.30536
$51$	−3.26294e8	−0.132426
$52$	−3.66051e9	−1.33513
$53$	−1.57562e9	−0.517528	−0.258764	−	0.965941i	$-0.583315\pi$
$53$	−1.57562e9	−0.517528	−0.258764	+	0.965941i	$0.583315\pi$
$54$	1.14762e9	0.340119
$55$	2.00587e9	0.537413
$56$	6.31131e9	1.53139
$57$	−3.17825e8	−0.0699642
$58$	5.77550e9	1.15541
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	3.77524e9	0.626776
$61$	7.71700e9	1.16986	0.584930	−	0.811083i	$-0.301122\pi$
$61$	7.71700e9	1.16986	0.584930	+	0.811083i	$0.301122\pi$
$62$	1.31423e10	1.82187
$63$	2.02531e9	0.257110
$64$	−4.87079e9	−0.567034
$65$	−3.00717e9	−0.321466
$66$	1.09122e10	1.07255
$67$	−3.30544e9	−0.299101	−0.149550	−	0.988754i	$-0.547783\pi$
$67$	−3.30544e9	−0.299101	−0.149550	+	0.988754i	$0.547783\pi$
$68$	−5.83933e9	−0.487039
$69$	1.30149e10	1.00177
$70$	9.80020e9	0.696940
$71$	−1.03471e10	−0.680609	−0.340304	−	0.940315i	$-0.610530\pi$
$71$	−1.03471e10	−0.680609	−0.340304	+	0.940315i	$0.610530\pi$
$72$	1.08656e10	0.661796
$73$	2.59913e10	1.46741	0.733705	−	0.679468i	$-0.237789\pi$
$73$	2.59913e10	1.46741	0.733705	+	0.679468i	$0.237789\pi$
$74$	−2.06838e10	−1.08357
$75$	−8.76381e9	−0.426438
$76$	−5.68777e9	−0.257316
$77$	1.92577e10	0.810785
$78$	−1.63593e10	−0.641572
$79$	4.26792e9	0.156051	0.0780257	−	0.996951i	$-0.475138\pi$
$79$	4.26792e9	0.156051	0.0780257	+	0.996951i	$0.475138\pi$
$80$	2.07594e10	0.708305
$81$	3.48678e9	0.111111
$82$	−4.70890e10	−1.40263
$83$	−3.07597e10	−0.857141	−0.428571	−	0.903508i	$-0.640983\pi$
$83$	−3.07597e10	−0.857141	−0.428571	+	0.903508i	$0.640983\pi$
$84$	3.62448e10	0.945605
$85$	−4.79711e9	−0.117267
$86$	4.95837e10	1.13657
$87$	1.75476e10	0.377452
$88$	1.03316e11	2.08695
$89$	−8.23783e10	−1.56375	−0.781876	−	0.623434i	$-0.785737\pi$
$89$	−8.23783e10	−1.56375	−0.781876	+	0.623434i	$0.785737\pi$
$90$	1.68721e10	0.301186
$91$	−2.88709e10	−0.484989
$92$	2.32913e11	3.68435
$93$	3.99301e10	0.595175
$94$	−9.34021e10	−1.31266
$95$	−4.67260e9	−0.0619554
$96$	2.13585e10	0.267349
$97$	1.52034e10	0.179761	0.0898806	−	0.995953i	$-0.471351\pi$
$97$	1.52034e10	0.179761	0.0898806	+	0.995953i	$0.471351\pi$
$98$	−6.40571e10	−0.715853
$99$	3.31542e10	0.350384
$100$	−1.56837e11	−1.56837
$101$	8.95263e10	0.847585	0.423793	−	0.905759i	$-0.360699\pi$
$101$	8.95263e10	0.847585	0.423793	+	0.905759i	$0.360699\pi$
$102$	−2.60968e10	−0.234038
$103$	5.26327e9	0.0447354	0.0223677	−	0.999750i	$-0.492880\pi$
$103$	5.26327e9	0.0447354	0.0223677	+	0.999750i	$0.492880\pi$
$104$	−1.54889e11	−1.24835
$105$	2.97758e10	0.227678
$106$	−1.26017e11	−0.914634
$107$	−7.94295e10	−0.547483	−0.273742	−	0.961803i	$-0.588261\pi$
$107$	−7.94295e10	−0.547483	−0.273742	+	0.961803i	$0.588261\pi$
$108$	6.23993e10	0.408647
$109$	8.71745e10	0.542680	0.271340	−	0.962484i	$-0.412533\pi$
$109$	8.71745e10	0.542680	0.271340	+	0.962484i	$0.412533\pi$
$110$	1.60429e11	0.949778
$111$	−6.28432e10	−0.353982
$112$	1.99304e11	1.06861
$113$	3.06361e11	1.56423	0.782117	−	0.623131i	$-0.214140\pi$
$113$	3.06361e11	1.56423	0.782117	+	0.623131i	$0.214140\pi$
$114$	−2.54194e10	−0.123649
$115$	1.91342e11	0.887101
$116$	3.14031e11	1.38820
$117$	−4.97042e10	−0.209590
$118$	5.71792e10	0.230085
$119$	−4.60555e10	−0.176918
$120$	1.59744e11	0.586040
$121$	2.99358e10	0.104923
$122$	6.17201e11	2.06751
$123$	−1.43070e11	−0.458215
$124$	7.14587e11	2.18895
$125$	−3.03285e11	−0.888884
$126$	1.61983e11	0.454393
$127$	4.86702e10	0.130720	0.0653601	−	0.997862i	$-0.479180\pi$
$127$	4.86702e10	0.130720	0.0653601	+	0.997862i	$0.479180\pi$
$128$	−5.69571e11	−1.46519
$129$	1.50649e11	0.371299
$130$	−2.40512e11	−0.568131
$131$	5.88093e11	1.33184	0.665922	−	0.746021i	$-0.268038\pi$
$131$	5.88093e11	1.33184	0.665922	+	0.746021i	$0.268038\pi$
$132$	5.93325e11	1.28865
$133$	−4.48601e10	−0.0934709
$134$	−2.64367e11	−0.528605
$135$	5.12621e10	0.0983922
$136$	−2.47083e11	−0.455385
$137$	8.79493e10	0.155693	0.0778466	−	0.996965i	$-0.475196\pi$
$137$	8.79493e10	0.155693	0.0778466	+	0.996965i	$0.475196\pi$
$138$	1.04092e12	1.77045
$139$	−1.38697e10	−0.0226719	−0.0113359	−	0.999936i	$-0.503608\pi$
$139$	−1.38697e10	−0.0226719	−0.0113359	+	0.999936i	$0.503608\pi$
$140$	5.32865e11	0.837361
$141$	−2.83782e11	−0.428824
$142$	−8.27555e11	−1.20285
$143$	−4.72614e11	−0.660935
$144$	3.43123e11	0.461803
$145$	2.57982e11	0.334245
$146$	2.07877e12	2.59337
$147$	−1.94623e11	−0.233857
$148$	−1.12464e12	−1.30189
$149$	9.30625e10	0.103813	0.0519063	−	0.998652i	$-0.483470\pi$
$149$	9.30625e10	0.103813	0.0519063	+	0.998652i	$0.483470\pi$
$150$	−7.00925e11	−0.753649
$151$	−8.33215e11	−0.863742	−0.431871	−	0.901935i	$-0.642146\pi$
$151$	−8.33215e11	−0.863742	−0.431871	+	0.901935i	$0.642146\pi$
$152$	−2.40670e11	−0.240592
$153$	−7.92894e10	−0.0764561
$154$	1.54022e12	1.43291
$155$	5.87046e11	0.527045
$156$	−8.89504e11	−0.770837
$157$	1.06013e11	0.0886978	0.0443489	−	0.999016i	$-0.485879\pi$
$157$	1.06013e11	0.0886978	0.0443489	+	0.999016i	$0.485879\pi$
$158$	3.41346e11	0.275791
$159$	−3.82875e11	−0.298795
$160$	3.14008e11	0.236745
$161$	1.83702e12	1.33835
$162$	2.78871e11	0.196368
$163$	−2.01619e12	−1.37246	−0.686230	−	0.727385i	$-0.740735\pi$
$163$	−2.01619e12	−1.37246	−0.686230	+	0.727385i	$0.740735\pi$
$164$	−2.56036e12	−1.68523
$165$	4.87427e11	0.310276
$166$	−2.46014e12	−1.51484
$167$	−2.42962e12	−1.44743	−0.723715	−	0.690099i	$-0.757567\pi$
$167$	−2.42962e12	−1.44743	−0.723715	+	0.690099i	$0.757567\pi$
$168$	1.53365e12	0.884147
$169$	−1.08362e12	−0.604647
$170$	−3.83670e11	−0.207247
$171$	−7.72314e10	−0.0403938
$172$	2.69601e12	1.36557
$173$	2.10687e12	1.03367	0.516837	−	0.856084i	$-0.327109\pi$
$173$	2.10687e12	1.03367	0.516837	+	0.856084i	$0.327109\pi$
$174$	1.40345e12	0.667076
$175$	−1.23699e12	−0.569713
$176$	3.26260e12	1.45628
$177$	1.73727e11	0.0751646
$178$	−6.58857e12	−2.76364
$179$	2.02471e12	0.823514	0.411757	−	0.911294i	$-0.364915\pi$
$179$	2.02471e12	0.823514	0.411757	+	0.911294i	$0.364915\pi$
$180$	9.17383e11	0.361869
$181$	−1.86962e12	−0.715352	−0.357676	−	0.933846i	$-0.616431\pi$
$181$	−1.86962e12	−0.715352	−0.357676	+	0.933846i	$0.616431\pi$
$182$	−2.30908e12	−0.857128
$183$	1.87523e12	0.675419
$184$	9.85540e12	3.44490
$185$	−9.23909e11	−0.313462
$186$	3.19359e12	1.05186
$187$	−7.53925e11	−0.241101
$188$	−5.07854e12	−1.57714
$189$	4.92150e11	0.148442
$190$	−3.73712e11	−0.109495
$191$	−5.41601e12	−1.54168	−0.770842	−	0.637026i	$-0.780164\pi$
$191$	−5.41601e12	−1.54168	−0.770842	+	0.637026i	$0.780164\pi$
$192$	−1.18360e12	−0.327377
$193$	6.88015e11	0.184941	0.0924705	−	0.995715i	$-0.470524\pi$
$193$	6.88015e11	0.184941	0.0924705	+	0.995715i	$0.470524\pi$
$194$	1.21596e12	0.317694
$195$	−7.30743e11	−0.185598
$196$	−3.48297e12	−0.860084
$197$	−3.58885e12	−0.861770	−0.430885	−	0.902407i	$-0.641799\pi$
$197$	−3.58885e12	−0.861770	−0.430885	+	0.902407i	$0.641799\pi$
$198$	2.65165e12	0.619239
$199$	−2.32985e12	−0.529219	−0.264609	−	0.964356i	$-0.585243\pi$
$199$	−2.32985e12	−0.529219	−0.264609	+	0.964356i	$0.585243\pi$
$200$	−6.63632e12	−1.46643
$201$	−8.03222e11	−0.172686
$202$	7.16027e12	1.49795
$203$	2.47680e12	0.504269
$204$	−1.41896e12	−0.281192
$205$	−2.10338e12	−0.405763
$206$	4.20954e11	0.0790614
$207$	3.16262e12	0.578375
$208$	−4.89124e12	−0.871105
$209$	−7.34357e11	−0.127380
$210$	2.38145e12	0.402379
$211$	2.97692e12	0.490021	0.245010	−	0.969520i	$-0.421209\pi$
$211$	2.97692e12	0.490021	0.245010	+	0.969520i	$0.421209\pi$
$212$	−6.85191e12	−1.09892
$213$	−2.51434e12	−0.392950
$214$	−6.35272e12	−0.967574
$215$	2.21482e12	0.328796
$216$	2.64034e12	0.382088
$217$	5.63603e12	0.795142
$218$	6.97217e12	0.959085
$219$	6.31587e12	0.847210
$220$	8.72296e12	1.14114
$221$	1.13027e12	0.144220
$222$	−5.02616e12	−0.625597
$223$	3.54917e12	0.430972	0.215486	−	0.976507i	$-0.430866\pi$
$223$	3.54917e12	0.430972	0.215486	+	0.976507i	$0.430866\pi$
$224$	3.01469e12	0.357173
$225$	−2.12961e12	−0.246204
$226$	2.45026e13	2.76449
$227$	−7.30662e12	−0.804589	−0.402295	−	0.915510i	$-0.631787\pi$
$227$	−7.30662e12	−0.804589	−0.402295	+	0.915510i	$0.631787\pi$
$228$	−1.38213e12	−0.148562
$229$	1.39308e13	1.46177	0.730886	−	0.682499i	$-0.239107\pi$
$229$	1.39308e13	1.46177	0.730886	+	0.682499i	$0.239107\pi$
$230$	1.53035e13	1.56779
$231$	4.67962e12	0.468107
$232$	1.32878e13	1.29798
$233$	−1.29379e13	−1.23426	−0.617129	−	0.786862i	$-0.711704\pi$
$233$	−1.29379e13	−1.23426	−0.617129	+	0.786862i	$0.711704\pi$
$234$	−3.97532e12	−0.370412
$235$	−4.17211e12	−0.379737
$236$	3.10900e12	0.276442
$237$	1.03710e12	0.0900963
$238$	−3.68349e12	−0.312670
$239$	−1.86912e13	−1.55042	−0.775209	−	0.631705i	$-0.782356\pi$
$239$	−1.86912e13	−1.55042	−0.775209	+	0.631705i	$0.782356\pi$
$240$	5.04454e12	0.408940
$241$	2.45800e13	1.94755	0.973773	−	0.227521i	$-0.0730621\pi$
$241$	2.45800e13	1.94755	0.973773	+	0.227521i	$0.0730621\pi$
$242$	2.39424e12	0.185432
$243$	8.47289e11	0.0641500
$244$	3.35590e13	2.48408
$245$	−2.86132e12	−0.207087
$246$	−1.14426e13	−0.809809
$247$	1.10094e12	0.0761954
$248$	3.02367e13	2.04668
$249$	−7.47460e12	−0.494871
$250$	−2.42565e13	−1.57094
$251$	1.55098e13	0.982657	0.491329	−	0.870974i	$-0.336511\pi$
$251$	1.55098e13	0.982657	0.491329	+	0.870974i	$0.336511\pi$
$252$	8.80749e12	0.545945
$253$	3.00718e13	1.82388
$254$	3.89262e12	0.231024
$255$	−1.16570e12	−0.0677041
$256$	−3.55786e13	−2.02241
$257$	1.52741e13	0.849815	0.424907	−	0.905237i	$-0.360307\pi$
$257$	1.52741e13	0.849815	0.424907	+	0.905237i	$0.360307\pi$
$258$	1.20488e13	0.656201
$259$	−8.87014e12	−0.472914
$260$	−1.30773e13	−0.682599
$261$	4.26406e12	0.217922
$262$	4.70353e13	2.35379
$263$	1.10164e13	0.539863	0.269931	−	0.962880i	$-0.412999\pi$
$263$	1.10164e13	0.539863	0.269931	+	0.962880i	$0.412999\pi$
$264$	2.51057e13	1.20490
$265$	−5.62897e12	−0.264592
$266$	−3.58789e12	−0.165192
$267$	−2.00179e13	−0.902833
$268$	−1.43744e13	−0.635109
$269$	5.21846e12	0.225894	0.112947	−	0.993601i	$-0.463971\pi$
$269$	5.21846e12	0.225894	0.112947	+	0.993601i	$0.463971\pi$
$270$	4.09991e12	0.173890
$271$	−4.48531e12	−0.186406	−0.0932032	−	0.995647i	$-0.529711\pi$
$271$	−4.48531e12	−0.186406	−0.0932032	+	0.995647i	$0.529711\pi$
$272$	−7.80261e12	−0.317769
$273$	−7.01562e12	−0.280009
$274$	7.03414e12	0.275158
$275$	−2.02494e13	−0.776395
$276$	5.65979e13	2.12716
$277$	−1.35475e13	−0.499137	−0.249568	−	0.968357i	$-0.580289\pi$
$277$	−1.35475e13	−0.499137	−0.249568	+	0.968357i	$0.580289\pi$
$278$	−1.10929e12	−0.0400683
$279$	9.70302e12	0.343624
$280$	2.25474e13	0.782939
$281$	−3.84766e13	−1.31012	−0.655062	−	0.755575i	$-0.727358\pi$
$281$	−3.84766e13	−1.31012	−0.655062	+	0.755575i	$0.727358\pi$
$282$	−2.26967e13	−0.757866
$283$	1.31918e12	0.0431997	0.0215998	−	0.999767i	$-0.493124\pi$
$283$	1.31918e12	0.0431997	0.0215998	+	0.999767i	$0.493124\pi$
$284$	−4.49965e13	−1.44520
$285$	−1.13544e12	−0.0357700
$286$	−3.77994e13	−1.16808
$287$	−2.01939e13	−0.612166
$288$	5.19011e12	0.154354
$289$	−3.24689e13	−0.947390
$290$	2.06332e13	0.590715
$291$	3.69443e12	0.103785
$292$	1.13028e14	3.11589
$293$	−2.28631e13	−0.618532	−0.309266	−	0.950976i	$-0.600083\pi$
$293$	−2.28631e13	−0.618532	−0.309266	+	0.950976i	$0.600083\pi$
$294$	−1.55659e13	−0.413298
$295$	2.55410e12	0.0665605
$296$	−4.75874e13	−1.21727
$297$	8.05647e12	0.202295
$298$	7.44309e12	0.183469
$299$	−4.50832e13	−1.09100
$300$	−3.81113e13	−0.905496
$301$	2.12637e13	0.496048
$302$	−6.66401e13	−1.52650
$303$	2.17549e13	0.489353
$304$	−7.60010e12	−0.167886
$305$	2.75693e13	0.598104
$306$	−6.34152e12	−0.135122
$307$	−1.45153e13	−0.303783	−0.151892	−	0.988397i	$-0.548536\pi$
$307$	−1.45153e13	−0.303783	−0.151892	+	0.988397i	$0.548536\pi$
$308$	8.37462e13	1.72162
$309$	1.27898e12	0.0258280
$310$	4.69516e13	0.931453
$311$	−5.42173e13	−1.05671	−0.528355	−	0.849023i	$-0.677191\pi$
$311$	−5.42173e13	−1.05671	−0.528355	+	0.849023i	$0.677191\pi$
$312$	−3.76381e13	−0.720738
$313$	5.61660e13	1.05677	0.528384	−	0.849005i	$-0.322798\pi$
$313$	5.61660e13	1.05677	0.528384	+	0.849005i	$0.322798\pi$
$314$	8.47890e12	0.156757
$315$	7.23551e12	0.131450
$316$	1.85600e13	0.331358
$317$	−5.86840e13	−1.02966	−0.514830	−	0.857292i	$-0.672145\pi$
$317$	−5.86840e13	−1.02966	−0.514830	+	0.857292i	$0.672145\pi$
$318$	−3.06222e13	−0.528064
$319$	4.05450e13	0.687208
$320$	−1.74011e13	−0.289902
$321$	−1.93014e13	−0.316090
$322$	1.46923e14	2.36529
$323$	1.75624e12	0.0277952
$324$	1.51630e13	0.235933
$325$	3.03576e13	0.464418
$326$	−1.61254e14	−2.42556
$327$	2.11834e13	0.313316
$328$	−1.08338e14	−1.57571
$329$	−4.00550e13	−0.572901
$330$	3.89841e13	0.548354
$331$	2.77443e13	0.383813	0.191906	−	0.981413i	$-0.438533\pi$
$331$	2.77443e13	0.383813	0.191906	+	0.981413i	$0.438533\pi$
$332$	−1.33765e14	−1.82005
$333$	−1.52709e13	−0.204372
$334$	−1.94319e14	−2.55806
$335$	−1.18088e13	−0.152919
$336$	4.84310e13	0.616960
$337$	8.92104e12	0.111802	0.0559012	−	0.998436i	$-0.482197\pi$
$337$	8.92104e12	0.111802	0.0559012	+	0.998436i	$0.482197\pi$
$338$	−8.66677e13	−1.06860
$339$	7.44457e13	0.903111
$340$	−2.08613e13	−0.249004
$341$	9.22614e13	1.08360
$342$	−6.17692e12	−0.0713886
$343$	−9.52905e13	−1.08376
$344$	1.14078e14	1.27682
$345$	4.64962e13	0.512168
$346$	1.68506e14	1.82683
$347$	−1.23395e13	−0.131670	−0.0658350	−	0.997831i	$-0.520971\pi$
$347$	−1.23395e13	−0.131670	−0.0658350	+	0.997831i	$0.520971\pi$
$348$	7.63094e13	0.801479
$349$	2.06884e13	0.213888	0.106944	−	0.994265i	$-0.465893\pi$
$349$	2.06884e13	0.213888	0.106944	+	0.994265i	$0.465893\pi$
$350$	−9.89336e13	−1.00686
$351$	−1.20781e13	−0.121007
$352$	4.93503e13	0.486749
$353$	7.96972e13	0.773895	0.386947	−	0.922102i	$-0.373529\pi$
$353$	7.96972e13	0.773895	0.386947	+	0.922102i	$0.373529\pi$
$354$	1.38946e13	0.132839
$355$	−3.69654e13	−0.347969
$356$	−3.58240e14	−3.32046
$357$	−1.11915e13	−0.102144
$358$	1.61935e14	1.45541
$359$	−1.58028e14	−1.39867	−0.699335	−	0.714794i	$-0.746520\pi$
$359$	−1.58028e14	−1.39867	−0.699335	+	0.714794i	$0.746520\pi$
$360$	3.88178e13	0.338350
$361$	−1.14780e14	−0.985315
$362$	−1.49531e14	−1.26425
$363$	7.27439e12	0.0605773
$364$	−1.25551e14	−1.02982
$365$	9.28549e13	0.750229
$366$	1.49980e14	1.19368
$367$	−2.16424e14	−1.69685	−0.848423	−	0.529319i	$-0.822448\pi$
$367$	−2.16424e14	−1.69685	−0.848423	+	0.529319i	$0.822448\pi$
$368$	3.11223e14	2.40386
$369$	−3.47659e13	−0.264550
$370$	−7.38937e13	−0.553985
$371$	−5.40418e13	−0.399184
$372$	1.73645e14	1.26379
$373$	−2.24017e14	−1.60651	−0.803254	−	0.595637i	$-0.796900\pi$
$373$	−2.24017e14	−1.60651	−0.803254	+	0.595637i	$0.796900\pi$
$374$	−6.02985e13	−0.426101
$375$	−7.36982e13	−0.513198
$376$	−2.14891e14	−1.47464
$377$	−6.07844e13	−0.411069
$378$	3.93619e13	0.262344
$379$	−1.47661e14	−0.969949	−0.484974	−	0.874528i	$-0.661171\pi$
$379$	−1.47661e14	−0.969949	−0.484974	+	0.874528i	$0.661171\pi$
$380$	−2.03198e13	−0.131556
$381$	1.18269e13	0.0754714
$382$	−4.33169e14	−2.72464
$383$	1.58886e14	0.985125	0.492562	−	0.870277i	$-0.336060\pi$
$383$	1.58886e14	0.985125	0.492562	+	0.870277i	$0.336060\pi$
$384$	−1.38406e14	−0.845927
$385$	6.87990e13	0.414523
$386$	5.50271e13	0.326848
$387$	3.66078e13	0.214370
$388$	6.61152e13	0.381704
$389$	−1.38859e14	−0.790405	−0.395203	−	0.918594i	$-0.629326\pi$
$389$	−1.38859e14	−0.790405	−0.395203	+	0.918594i	$0.629326\pi$
$390$	−5.84444e13	−0.328011
$391$	−7.19178e13	−0.397983
$392$	−1.47377e14	−0.804185
$393$	1.42906e14	0.768941
$394$	−2.87034e14	−1.52302
$395$	1.52473e13	0.0797829
$396$	1.44178e14	0.744004
$397$	−1.52121e14	−0.774179	−0.387090	−	0.922042i	$-0.626520\pi$
$397$	−1.52121e14	−0.774179	−0.387090	+	0.922042i	$0.626520\pi$
$398$	−1.86340e14	−0.935295
$399$	−1.09010e13	−0.0539654
$400$	−2.09568e14	−1.02328
$401$	4.48848e13	0.216175	0.108087	−	0.994141i	$-0.465527\pi$
$401$	4.48848e13	0.216175	0.108087	+	0.994141i	$0.465527\pi$
$402$	−6.42412e13	−0.305190
$403$	−1.38317e14	−0.648183
$404$	3.89324e14	1.79976
$405$	1.24567e13	0.0568068
$406$	1.98093e14	0.891200
$407$	−1.45204e14	−0.644478
$408$	−6.00412e13	−0.262917
$409$	−1.18153e14	−0.510468	−0.255234	−	0.966879i	$-0.582152\pi$
$409$	−1.18153e14	−0.510468	−0.255234	+	0.966879i	$0.582152\pi$
$410$	−1.68227e14	−0.717110
$411$	2.13717e13	0.0898895
$412$	2.28885e13	0.0949909
$413$	2.45210e13	0.100418
$414$	2.52944e14	1.02217
$415$	−1.09890e14	−0.438223
$416$	−7.39852e13	−0.291160
$417$	−3.37035e12	−0.0130896
$418$	−5.87334e13	−0.225121
$419$	−1.87467e14	−0.709165	−0.354582	−	0.935025i	$-0.615377\pi$
$419$	−1.87467e14	−0.709165	−0.354582	+	0.935025i	$0.615377\pi$
$420$	1.29486e14	0.483451
$421$	−2.67548e14	−0.985938	−0.492969	−	0.870047i	$-0.664088\pi$
$421$	−2.67548e14	−0.985938	−0.492969	+	0.870047i	$0.664088\pi$
$422$	2.38093e14	0.866020
$423$	−6.89590e13	−0.247582
$424$	−2.89929e14	−1.02749
$425$	4.84272e13	0.169414
$426$	−2.01096e14	−0.694465
$427$	2.64684e14	0.902348
$428$	−3.45416e14	−1.16252
$429$	−1.14845e14	−0.381591
$430$	1.77140e14	0.581086
$431$	3.55171e14	1.15030	0.575152	−	0.818046i	$-0.304943\pi$
$431$	3.55171e14	1.15030	0.575152	+	0.818046i	$0.304943\pi$
$432$	8.33790e13	0.266622
$433$	−1.83266e14	−0.578628	−0.289314	−	0.957234i	$-0.593427\pi$
$433$	−1.83266e14	−0.578628	−0.289314	+	0.957234i	$0.593427\pi$
$434$	4.50766e14	1.40526
$435$	6.26895e13	0.192976
$436$	3.79097e14	1.15232
$437$	−7.00511e13	−0.210265
$438$	5.05140e14	1.49728
$439$	1.75742e14	0.514424	0.257212	−	0.966355i	$-0.417196\pi$
$439$	1.75742e14	0.514424	0.257212	+	0.966355i	$0.417196\pi$
$440$	3.69100e14	1.06697
$441$	−4.72935e13	−0.135017
$442$	9.03986e13	0.254882
$443$	2.35033e14	0.654499	0.327249	−	0.944938i	$-0.393878\pi$
$443$	2.35033e14	0.654499	0.327249	+	0.944938i	$0.393878\pi$
$444$	−2.73287e14	−0.751644
$445$	−2.94300e14	−0.799485
$446$	2.83860e14	0.761663
$447$	2.26142e13	0.0599363
$448$	−1.67062e14	−0.437370
$449$	−4.79472e13	−0.123996	−0.0619981	−	0.998076i	$-0.519747\pi$
$449$	−4.79472e13	−0.123996	−0.0619981	+	0.998076i	$0.519747\pi$
$450$	−1.70325e14	−0.435120
$451$	−3.30572e14	−0.834249
$452$	1.33227e15	3.32149
$453$	−2.02471e14	−0.498681
$454$	−5.84379e14	−1.42196
$455$	−1.03142e14	−0.247956
$456$	−5.84828e13	−0.138906
$457$	2.63461e14	0.618269	0.309134	−	0.951018i	$-0.399961\pi$
$457$	2.63461e14	0.618269	0.309134	+	0.951018i	$0.399961\pi$
$458$	1.11417e15	2.58341
$459$	−1.92673e13	−0.0441419
$460$	8.32093e14	1.88367
$461$	7.90062e12	0.0176728	0.00883641	−	0.999961i	$-0.497187\pi$
$461$	7.90062e12	0.0176728	0.00883641	+	0.999961i	$0.497187\pi$
$462$	3.74274e14	0.827291
$463$	2.36642e13	0.0516887	0.0258444	−	0.999666i	$-0.491773\pi$
$463$	2.36642e13	0.0516887	0.0258444	+	0.999666i	$0.491773\pi$
$464$	4.19613e14	0.905733
$465$	1.42652e14	0.304289
$466$	−1.03477e15	−2.18132
$467$	−5.01380e14	−1.04454	−0.522269	−	0.852781i	$-0.674914\pi$
$467$	−5.01380e14	−1.04454	−0.522269	+	0.852781i	$0.674914\pi$
$468$	−2.16149e14	−0.445043
$469$	−1.13373e14	−0.230705
$470$	−3.33683e14	−0.671113
$471$	2.57613e13	0.0512097
$472$	1.31553e14	0.258476
$473$	3.48086e14	0.676006
$474$	8.29471e13	0.159228
$475$	4.71702e13	0.0895062
$476$	−2.00282e14	−0.375668
$477$	−9.30387e13	−0.172509
$478$	−1.49491e15	−2.74007
$479$	3.41620e14	0.619010	0.309505	−	0.950898i	$-0.399837\pi$
$479$	3.41620e14	0.619010	0.309505	+	0.950898i	$0.399837\pi$
$480$	7.63040e13	0.136685
$481$	2.17687e14	0.385509
$482$	1.96589e15	3.44192
$483$	4.46395e14	0.772698
$484$	1.30182e14	0.222793
$485$	5.43148e13	0.0919049
$486$	6.77657e13	0.113373
$487$	4.67082e14	0.772652	0.386326	−	0.922362i	$-0.373744\pi$
$487$	4.67082e14	0.772652	0.386326	+	0.922362i	$0.373744\pi$
$488$	1.42000e15	2.32263
$489$	−4.89934e14	−0.792390
$490$	−2.28847e14	−0.365987
$491$	6.11829e14	0.967569	0.483784	−	0.875187i	$-0.339262\pi$
$491$	6.11829e14	0.967569	0.483784	+	0.875187i	$0.339262\pi$
$492$	−6.22168e14	−0.972970
$493$	−9.69647e13	−0.149953
$494$	8.80523e13	0.134661
$495$	1.18445e14	0.179138
$496$	9.54843e14	1.42818
$497$	−3.54893e14	−0.524973
$498$	−5.97815e14	−0.874591
$499$	1.18221e15	1.71057	0.855283	−	0.518160i	$-0.173383\pi$
$499$	1.18221e15	1.71057	0.855283	+	0.518160i	$0.173383\pi$
$500$	−1.31890e15	−1.88745
$501$	−5.90397e14	−0.835674
$502$	1.24047e15	1.73666
$503$	−9.30484e14	−1.28850	−0.644251	−	0.764814i	$-0.722831\pi$
$503$	−9.30484e14	−1.28850	−0.644251	+	0.764814i	$0.722831\pi$
$504$	3.72676e14	0.510463
$505$	3.19837e14	0.433337
$506$	2.40513e15	3.22337
$507$	−2.63321e14	−0.349093
$508$	2.11653e14	0.277571
$509$	1.32830e15	1.72325	0.861627	−	0.507542i	$-0.169446\pi$
$509$	1.32830e15	1.72325	0.861627	+	0.507542i	$0.169446\pi$
$510$	−9.32319e13	−0.119654
$511$	8.91469e14	1.13186
$512$	−1.67908e15	−2.10905
$513$	−1.87672e13	−0.0233214
$514$	1.22162e15	1.50189
$515$	1.88033e13	0.0228715
$516$	6.55130e14	0.788414
$517$	−6.55698e14	−0.780739
$518$	−7.09429e14	−0.835786
$519$	5.11969e14	0.596792
$520$	−5.53349e14	−0.638235
$521$	−5.69906e14	−0.650422	−0.325211	−	0.945641i	$-0.605435\pi$
$521$	−5.69906e14	−0.650422	−0.325211	+	0.945641i	$0.605435\pi$
$522$	3.41038e14	0.385136
$523$	5.33919e14	0.596645	0.298323	−	0.954465i	$-0.403573\pi$
$523$	5.33919e14	0.596645	0.298323	+	0.954465i	$0.403573\pi$
$524$	2.55744e15	2.82803
$525$	−3.00588e14	−0.328924
$526$	8.81086e14	0.954106
$527$	−2.20646e14	−0.236449
$528$	7.92811e14	0.840782
$529$	1.91577e15	2.01066
$530$	−4.50202e14	−0.467616
$531$	4.22156e13	0.0433963
$532$	−1.95084e14	−0.198475
$533$	4.95589e14	0.499025
$534$	−1.60102e15	−1.59559
$535$	−2.83765e14	−0.279907
$536$	−6.08233e14	−0.593832
$537$	4.92004e14	0.475456
$538$	4.17370e14	0.399226
$539$	−4.49691e14	−0.425771
$540$	2.22924e14	0.208925
$541$	−1.12465e15	−1.04336	−0.521679	−	0.853142i	$-0.674694\pi$
$541$	−1.12465e15	−1.04336	−0.521679	+	0.853142i	$0.674694\pi$
$542$	−3.58732e14	−0.329439
$543$	−4.54316e14	−0.413009
$544$	−1.18023e14	−0.106212
$545$	3.11435e14	0.277451
$546$	−5.61106e14	−0.494863
$547$	−4.20520e14	−0.367161	−0.183580	−	0.983005i	$-0.558769\pi$
$547$	−4.20520e14	−0.367161	−0.183580	+	0.983005i	$0.558769\pi$
$548$	3.82466e14	0.330598
$549$	4.55681e14	0.389954
$550$	−1.61954e15	−1.37213
$551$	−9.44480e13	−0.0792244
$552$	2.39486e15	1.98891
$553$	1.46385e14	0.120367
$554$	−1.08352e15	−0.882131
$555$	−2.24510e14	−0.180977
$556$	−6.03155e13	−0.0481413
$557$	−1.70913e15	−1.35074	−0.675369	−	0.737480i	$-0.736016\pi$
$557$	−1.70913e15	−1.35074	−0.675369	+	0.737480i	$0.736016\pi$
$558$	7.76042e14	0.607291
$559$	−5.21845e14	−0.404368
$560$	7.12023e14	0.546336
$561$	−1.83204e14	−0.139200
$562$	−3.07734e15	−2.31540
$563$	−7.02850e14	−0.523680	−0.261840	−	0.965111i	$-0.584329\pi$
$563$	−7.02850e14	−0.523680	−0.261840	+	0.965111i	$0.584329\pi$
$564$	−1.23408e15	−0.910563
$565$	1.09449e15	0.799732
$566$	1.05508e14	0.0763473
$567$	1.19593e14	0.0857032
$568$	−1.90396e15	−1.35127
$569$	−7.52563e14	−0.528963	−0.264481	−	0.964391i	$-0.585201\pi$
$569$	−7.52563e14	−0.528963	−0.264481	+	0.964391i	$0.585201\pi$
$570$	−9.08120e13	−0.0632167
$571$	−7.63440e14	−0.526352	−0.263176	−	0.964748i	$-0.584770\pi$
$571$	−7.63440e14	−0.526352	−0.263176	+	0.964748i	$0.584770\pi$
$572$	−2.05526e15	−1.40342
$573$	−1.31609e15	−0.890092
$574$	−1.61510e15	−1.08189
$575$	−1.93161e15	−1.28158
$576$	−2.87615e14	−0.189011
$577$	4.05246e14	0.263786	0.131893	−	0.991264i	$-0.457894\pi$
$577$	4.05246e14	0.263786	0.131893	+	0.991264i	$0.457894\pi$
$578$	−2.59684e15	−1.67433
$579$	1.67188e14	0.106776
$580$	1.12189e15	0.709734
$581$	−1.05502e15	−0.661138
$582$	2.95478e14	0.183421
$583$	−8.84661e14	−0.544001
$584$	4.78264e15	2.91338
$585$	−1.77571e14	−0.107155
$586$	−1.82857e15	−1.09314
$587$	2.81960e15	1.66985	0.834926	−	0.550363i	$-0.185511\pi$
$587$	2.81960e15	1.66985	0.834926	+	0.550363i	$0.185511\pi$
$588$	−8.46361e14	−0.496570
$589$	−2.14919e14	−0.124923
$590$	2.04275e14	0.117633
$591$	−8.72091e14	−0.497543
$592$	−1.50276e15	−0.849415
$593$	1.71000e14	0.0957622	0.0478811	−	0.998853i	$-0.484753\pi$
$593$	1.71000e14	0.0957622	0.0478811	+	0.998853i	$0.484753\pi$
$594$	6.44352e14	0.357518
$595$	−1.64535e14	−0.0904514
$596$	4.04702e14	0.220435
$597$	−5.66152e14	−0.305545
$598$	−3.60573e15	−1.92813
$599$	1.28350e15	0.680062	0.340031	−	0.940414i	$-0.389562\pi$
$599$	1.28350e15	0.680062	0.340031	+	0.940414i	$0.389562\pi$
$600$	−1.61263e15	−0.846645
$601$	−7.80949e14	−0.406268	−0.203134	−	0.979151i	$-0.565113\pi$
$601$	−7.80949e14	−0.406268	−0.203134	+	0.979151i	$0.565113\pi$
$602$	1.70066e15	0.876672
$603$	−1.95183e14	−0.0997003
$604$	−3.62341e15	−1.83406
$605$	1.06947e14	0.0536430
$606$	1.73994e15	0.864841
$607$	−1.58644e15	−0.781423	−0.390712	−	0.920513i	$-0.627771\pi$
$607$	−1.58644e15	−0.781423	−0.390712	+	0.920513i	$0.627771\pi$
$608$	−1.14960e14	−0.0561145
$609$	6.01861e14	0.291140
$610$	2.20498e15	1.05704
$611$	9.83013e14	0.467017
$612$	−3.44807e14	−0.162346
$613$	−7.34991e14	−0.342965	−0.171482	−	0.985187i	$-0.554856\pi$
$613$	−7.34991e14	−0.342965	−0.171482	+	0.985187i	$0.554856\pi$
$614$	−1.16092e15	−0.536880
$615$	−5.11122e14	−0.234267
$616$	3.54360e15	1.60972
$617$	3.87074e15	1.74271	0.871356	−	0.490652i	$-0.163241\pi$
$617$	3.87074e15	1.74271	0.871356	+	0.490652i	$0.163241\pi$
$618$	1.02292e14	0.0456461
$619$	−1.48567e15	−0.657089	−0.328545	−	0.944488i	$-0.606558\pi$
$619$	−1.48567e15	−0.657089	−0.328545	+	0.944488i	$0.606558\pi$
$620$	2.55289e15	1.11912
$621$	7.68515e14	0.333925
$622$	−4.33627e15	−1.86754
$623$	−2.82548e15	−1.20617
$624$	−1.18857e15	−0.502933
$625$	6.77492e14	0.284161
$626$	4.49213e15	1.86764
$627$	−1.78449e14	−0.0735431
$628$	4.61022e14	0.188340
$629$	3.47259e14	0.140629
$630$	5.78692e14	0.232313
$631$	3.20662e15	1.27611	0.638053	−	0.769993i	$-0.279740\pi$
$631$	3.20662e15	1.27611	0.638053	+	0.769993i	$0.279740\pi$
$632$	7.85339e14	0.309823
$633$	7.23393e14	0.282914
$634$	−4.69351e15	−1.81973
$635$	1.73876e14	0.0668321
$636$	−1.66501e15	−0.634459
$637$	6.74170e14	0.254685
$638$	3.24276e15	1.21451
$639$	−6.10986e14	−0.226870
$640$	−2.03482e15	−0.749093
$641$	1.69427e15	0.618393	0.309196	−	0.950998i	$-0.399940\pi$
$641$	1.69427e15	0.618393	0.309196	+	0.950998i	$0.399940\pi$
$642$	−1.54371e15	−0.558629
$643$	−1.21733e15	−0.436765	−0.218382	−	0.975863i	$-0.570078\pi$
$643$	−1.21733e15	−0.436765	−0.218382	+	0.975863i	$0.570078\pi$
$644$	7.98865e15	2.84185
$645$	5.38201e14	0.189831
$646$	1.40463e14	0.0491228
$647$	−3.53897e15	−1.22717	−0.613584	−	0.789630i	$-0.710273\pi$
$647$	−3.53897e15	−1.22717	−0.613584	+	0.789630i	$0.710273\pi$
$648$	6.41602e14	0.220599
$649$	4.01408e14	0.136848
$650$	2.42798e15	0.820772
$651$	1.36956e15	0.459075
$652$	−8.76782e15	−2.91427
$653$	2.33782e15	0.770530	0.385265	−	0.922806i	$-0.374110\pi$
$653$	2.33782e15	0.770530	0.385265	+	0.922806i	$0.374110\pi$
$654$	1.69424e15	0.553728
$655$	2.10099e15	0.680920
$656$	−3.42120e15	−1.09953
$657$	1.53476e15	0.489137
$658$	−3.20358e15	−1.01250
$659$	1.65395e15	0.518385	0.259192	−	0.965826i	$-0.416544\pi$
$659$	1.65395e15	0.518385	0.259192	+	0.965826i	$0.416544\pi$
$660$	2.11968e15	0.658838
$661$	2.69598e15	0.831015	0.415508	−	0.909590i	$-0.363604\pi$
$661$	2.69598e15	0.831015	0.415508	+	0.909590i	$0.363604\pi$
$662$	2.21897e15	0.678317
$663$	2.74656e14	0.0832655
$664$	−5.66008e15	−1.70176
$665$	−1.60265e14	−0.0477880
$666$	−1.22136e15	−0.361189
$667$	3.86763e15	1.13437
$668$	−1.05657e16	−3.07346
$669$	8.62447e14	0.248822
$670$	−9.44463e14	−0.270255
$671$	4.33285e15	1.22970
$672$	7.32570e14	0.206214
$673$	2.56365e15	0.715775	0.357888	−	0.933765i	$-0.383497\pi$
$673$	2.56365e15	0.715775	0.357888	+	0.933765i	$0.383497\pi$
$674$	7.13500e14	0.197590
$675$	−5.17494e14	−0.142146
$676$	−4.71237e15	−1.28390
$677$	1.34304e15	0.362953	0.181476	−	0.983395i	$-0.441912\pi$
$677$	1.34304e15	0.362953	0.181476	+	0.983395i	$0.441912\pi$
$678$	5.95412e15	1.59608
$679$	5.21458e14	0.138655
$680$	−8.82715e14	−0.232821
$681$	−1.77551e15	−0.464530
$682$	7.37902e15	1.91507
$683$	2.87848e15	0.741053	0.370527	−	0.928822i	$-0.379177\pi$
$683$	2.87848e15	0.741053	0.370527	+	0.928822i	$0.379177\pi$
$684$	−3.35857e14	−0.0857721
$685$	3.14203e14	0.0795998
$686$	−7.62128e15	−1.91534
$687$	3.38517e15	0.843955
$688$	3.60246e15	0.890968
$689$	1.32627e15	0.325407
$690$	3.71874e15	0.905161
$691$	5.82940e15	1.40765	0.703824	−	0.710374i	$-0.251474\pi$
$691$	5.82940e15	1.40765	0.703824	+	0.710374i	$0.251474\pi$
$692$	9.16216e15	2.19490
$693$	1.13715e15	0.270262
$694$	−9.86910e14	−0.232702
$695$	−4.95503e13	−0.0115912
$696$	3.22893e15	0.749389
$697$	7.90575e14	0.182038
$698$	1.65465e15	0.378007
$699$	−3.14391e15	−0.712599
$700$	−5.37930e15	−1.20973
$701$	3.84624e15	0.858197	0.429098	−	0.903258i	$-0.358831\pi$
$701$	3.84624e15	0.858197	0.429098	+	0.903258i	$0.358831\pi$
$702$	−9.66002e14	−0.213857
$703$	3.38246e14	0.0742983
$704$	−2.73480e15	−0.596040
$705$	−1.01382e15	−0.219241
$706$	6.37413e15	1.36771
$707$	3.07065e15	0.653767
$708$	7.55487e14	0.159604
$709$	3.06847e15	0.643231	0.321616	−	0.946870i	$-0.395774\pi$
$709$	3.06847e15	0.643231	0.321616	+	0.946870i	$0.395774\pi$
$710$	−2.95648e15	−0.614969
$711$	2.52016e14	0.0520171
$712$	−1.51584e16	−3.10466
$713$	8.80092e15	1.78869
$714$	−8.95088e14	−0.180520
$715$	−1.68843e15	−0.337910
$716$	8.80488e15	1.74865
$717$	−4.54196e15	−0.895134
$718$	−1.26390e16	−2.47189
$719$	6.87669e15	1.33466	0.667330	−	0.744762i	$-0.267437\pi$
$719$	6.87669e15	1.33466	0.667330	+	0.744762i	$0.267437\pi$
$720$	1.22582e15	0.236102
$721$	1.80524e14	0.0345057
$722$	−9.18001e15	−1.74136
$723$	5.97293e15	1.12442
$724$	−8.13042e15	−1.51898
$725$	−2.60434e15	−0.482880
$726$	5.81802e14	0.107059
$727$	6.86387e15	1.25351	0.626757	−	0.779214i	$-0.284382\pi$
$727$	6.86387e15	1.25351	0.626757	+	0.779214i	$0.284382\pi$
$728$	−5.31252e15	−0.962892
$729$	2.05891e14	0.0370370
$730$	7.42648e15	1.32589
$731$	−8.32460e14	−0.147509
$732$	8.15483e15	1.43418
$733$	−4.45996e15	−0.778501	−0.389251	−	0.921132i	$-0.627266\pi$
$733$	−4.45996e15	−0.778501	−0.389251	+	0.921132i	$0.627266\pi$
$734$	−1.73095e16	−2.99886
$735$	−6.95300e14	−0.119562
$736$	4.70758e15	0.803470
$737$	−1.85590e15	−0.314401
$738$	−2.78056e15	−0.467543
$739$	−2.66547e15	−0.444866	−0.222433	−	0.974948i	$-0.571400\pi$
$739$	−2.66547e15	−0.444866	−0.222433	+	0.974948i	$0.571400\pi$
$740$	−4.01781e15	−0.665603
$741$	2.67528e14	0.0439915
$742$	−4.32223e15	−0.705484
$743$	−5.44547e15	−0.882261	−0.441131	−	0.897443i	$-0.645422\pi$
$743$	−5.44547e15	−0.882261	−0.441131	+	0.897443i	$0.645422\pi$
$744$	7.34752e15	1.18165
$745$	3.32470e14	0.0530754
$746$	−1.79168e16	−2.83920
$747$	−1.81633e15	−0.285714
$748$	−3.27860e15	−0.511953
$749$	−2.72433e15	−0.422290
$750$	−5.89434e15	−0.906981
$751$	1.41234e15	0.215735	0.107868	−	0.994165i	$-0.465598\pi$
$751$	1.41234e15	0.215735	0.107868	+	0.994165i	$0.465598\pi$
$752$	−6.78603e15	−1.02901
$753$	3.76889e15	0.567337
$754$	−4.86150e15	−0.726488
$755$	−2.97670e15	−0.441597
$756$	2.14022e15	0.315202
$757$	1.28316e16	1.87609	0.938045	−	0.346514i	$-0.112635\pi$
$757$	1.28316e16	1.87609	0.938045	+	0.346514i	$0.112635\pi$
$758$	−1.18098e16	−1.71420
$759$	7.30745e15	1.05302
$760$	−8.59804e14	−0.123006
$761$	−1.15160e15	−0.163563	−0.0817813	−	0.996650i	$-0.526061\pi$
$761$	−1.15160e15	−0.163563	−0.0817813	+	0.996650i	$0.526061\pi$
$762$	9.45906e14	0.133382
$763$	2.98998e15	0.418585
$764$	−2.35526e16	−3.27360
$765$	−2.83265e14	−0.0390890
$766$	1.27076e16	1.74102
$767$	−6.01785e14	−0.0818590
$768$	−8.64561e15	−1.16764
$769$	−1.81080e14	−0.0242815	−0.0121407	−	0.999926i	$-0.503865\pi$
$769$	−1.81080e14	−0.0242815	−0.0121407	+	0.999926i	$0.503865\pi$
$770$	5.50251e15	0.732591
$771$	3.71161e15	0.490641
$772$	2.99198e15	0.392702
$773$	1.46772e16	1.91274	0.956368	−	0.292165i	$-0.0943756\pi$
$773$	1.46772e16	1.91274	0.956368	+	0.292165i	$0.0943756\pi$
$774$	2.92787e15	0.378858
$775$	−5.92626e15	−0.761415
$776$	2.79757e15	0.356896
$777$	−2.15544e15	−0.273037
$778$	−1.11058e16	−1.39689
$779$	7.70056e14	0.0961759
$780$	−3.17779e15	−0.394099
$781$	−5.80957e15	−0.715424
$782$	−5.75194e15	−0.703360
$783$	1.03617e15	0.125817
$784$	−4.65400e15	−0.561162
$785$	3.78738e14	0.0453477
$786$	1.14296e16	1.35896
$787$	3.83560e15	0.452869	0.226435	−	0.974026i	$-0.427293\pi$
$787$	3.83560e15	0.452869	0.226435	+	0.974026i	$0.427293\pi$
$788$	−1.56069e16	−1.82988
$789$	2.67699e15	0.311690
$790$	1.21947e15	0.141001
$791$	1.05078e16	1.20654
$792$	6.10069e15	0.695649
$793$	−6.49575e15	−0.735575
$794$	−1.21666e16	−1.36822
$795$	−1.36784e15	−0.152762
$796$	−1.01318e16	−1.12374
$797$	1.05481e16	1.16186	0.580929	−	0.813954i	$-0.302690\pi$
$797$	1.05481e16	1.16186	0.580929	+	0.813954i	$0.302690\pi$
$798$	−8.71856e14	−0.0953738
$799$	1.56812e15	0.170362
$800$	−3.16993e15	−0.342023
$801$	−4.86436e15	−0.521251
$802$	3.58986e15	0.382049
$803$	1.45933e16	1.54247
$804$	−3.49298e15	−0.366681
$805$	6.56282e15	0.684247
$806$	−1.10625e16	−1.14554
$807$	1.26809e15	0.130420
$808$	1.64737e16	1.68279
$809$	5.79101e15	0.587540	0.293770	−	0.955876i	$-0.405090\pi$
$809$	5.79101e15	0.587540	0.293770	+	0.955876i	$0.405090\pi$
$810$	9.96279e14	0.100395
$811$	−1.64492e16	−1.64638	−0.823190	−	0.567767i	$-0.807808\pi$
$811$	−1.64492e16	−1.64638	−0.823190	+	0.567767i	$0.807808\pi$
$812$	1.07709e16	1.07076
$813$	−1.08993e15	−0.107622
$814$	−1.16133e16	−1.13899
$815$	−7.20292e15	−0.701685
$816$	−1.89604e15	−0.183464
$817$	−8.10853e14	−0.0779329
$818$	−9.44985e15	−0.902156
$819$	−1.70480e15	−0.161663
$820$	−9.14701e15	−0.861594
$821$	−1.68942e16	−1.58070	−0.790350	−	0.612655i	$-0.790101\pi$
$821$	−1.68942e16	−1.58070	−0.790350	+	0.612655i	$0.790101\pi$
$822$	1.70930e15	0.158863
$823$	7.50053e15	0.692457	0.346228	−	0.938150i	$-0.387462\pi$
$823$	7.50053e15	0.692457	0.346228	+	0.938150i	$0.387462\pi$
$824$	9.68493e14	0.0888171
$825$	−4.92061e15	−0.448252
$826$	1.96118e15	0.177471
$827$	1.69067e16	1.51977	0.759887	−	0.650055i	$-0.225254\pi$
$827$	1.69067e16	1.51977	0.759887	+	0.650055i	$0.225254\pi$
$828$	1.37533e16	1.22812
$829$	−3.61894e15	−0.321020	−0.160510	−	0.987034i	$-0.551314\pi$
$829$	−3.61894e15	−0.321020	−0.160510	+	0.987034i	$0.551314\pi$
$830$	−8.78897e15	−0.774476
$831$	−3.29204e15	−0.288177
$832$	4.09996e15	0.356535
$833$	1.07545e15	0.0929059
$834$	−2.69559e14	−0.0231334
$835$	−8.67992e15	−0.740014
$836$	−3.19351e15	−0.270479
$837$	2.35783e15	0.198392
$838$	−1.49935e16	−1.25332
$839$	1.98137e16	1.64541	0.822707	−	0.568466i	$-0.192463\pi$
$839$	1.98137e16	1.64541	0.822707	+	0.568466i	$0.192463\pi$
$840$	5.47902e15	0.452030
$841$	−6.98589e15	−0.572590
$842$	−2.13983e16	−1.74246
$843$	−9.34982e15	−0.756401
$844$	1.29458e16	1.04051
$845$	−3.87130e15	−0.309132
$846$	−5.51530e15	−0.437554
$847$	1.02676e15	0.0809302
$848$	−9.15564e15	−0.716988
$849$	3.20562e14	0.0249413
$850$	3.87318e15	0.299408
$851$	−1.38511e16	−1.06383
$852$	−1.09342e16	−0.834387
$853$	2.28015e16	1.72879	0.864397	−	0.502809i	$-0.167700\pi$
$853$	2.28015e16	1.72879	0.864397	+	0.502809i	$0.167700\pi$
$854$	2.11693e16	1.59473
$855$	−2.75912e14	−0.0206518
$856$	−1.46158e16	−1.08697
$857$	−1.99033e15	−0.147072	−0.0735359	−	0.997293i	$-0.523428\pi$
$857$	−1.99033e15	−0.147072	−0.0735359	+	0.997293i	$0.523428\pi$
$858$	−9.18526e15	−0.674390
$859$	−4.83946e15	−0.353049	−0.176524	−	0.984296i	$-0.556485\pi$
$859$	−4.83946e15	−0.353049	−0.176524	+	0.984296i	$0.556485\pi$
$860$	9.63161e15	0.698164
$861$	−4.90711e15	−0.353434
$862$	2.84064e16	2.03295
$863$	1.58331e16	1.12592	0.562960	−	0.826484i	$-0.309663\pi$
$863$	1.58331e16	1.12592	0.562960	+	0.826484i	$0.309663\pi$
$864$	1.26120e15	0.0891162
$865$	7.52688e15	0.528477
$866$	−1.46575e16	−1.02262
$867$	−7.88993e15	−0.546976
$868$	2.45095e16	1.68840
$869$	2.39631e15	0.164034
$870$	5.01387e15	0.341050
$871$	2.78234e15	0.188066
$872$	1.60409e16	1.07743
$873$	8.97746e14	0.0599204
$874$	−5.60265e15	−0.371604
$875$	−1.04023e16	−0.685622
$876$	2.74659e16	1.79896
$877$	2.47298e16	1.60962	0.804808	−	0.593536i	$-0.202268\pi$
$877$	2.47298e16	1.60962	0.804808	+	0.593536i	$0.202268\pi$
$878$	1.40558e16	0.909148
$879$	−5.55572e15	−0.357110
$880$	1.16558e16	0.744537
$881$	1.84220e15	0.116942	0.0584710	−	0.998289i	$-0.481377\pi$
$881$	1.84220e15	0.116942	0.0584710	+	0.998289i	$0.481377\pi$
$882$	−3.78251e15	−0.238618
$883$	1.86832e16	1.17130	0.585648	−	0.810565i	$-0.300840\pi$
$883$	1.86832e16	1.17130	0.585648	+	0.810565i	$0.300840\pi$
$884$	4.91523e15	0.306236
$885$	6.20646e14	0.0384287
$886$	1.87978e16	1.15670
$887$	2.73600e16	1.67316	0.836578	−	0.547848i	$-0.184553\pi$
$887$	2.73600e16	1.67316	0.836578	+	0.547848i	$0.184553\pi$
$888$	−1.15637e16	−0.702793
$889$	1.66933e15	0.100828
$890$	−2.35380e16	−1.41294
$891$	1.95772e15	0.116795
$892$	1.54343e16	0.915124
$893$	1.52742e15	0.0900070
$894$	1.80867e15	0.105926
$895$	7.23336e15	0.421031
$896$	−1.95356e16	−1.13014
$897$	−1.09552e16	−0.629887
$898$	−3.83479e15	−0.219140
$899$	1.18660e16	0.673949
$900$	−9.26104e15	−0.522788
$901$	2.11570e15	0.118704
$902$	−2.64390e16	−1.47438
$903$	5.16709e15	0.286394
$904$	5.63733e16	3.10561
$905$	−6.67928e15	−0.365732
$906$	−1.61935e16	−0.881326
$907$	−6.43997e14	−0.0348372	−0.0174186	−	0.999848i	$-0.505545\pi$
$907$	−6.43997e14	−0.0348372	−0.0174186	+	0.999848i	$0.505545\pi$
$908$	−3.17744e16	−1.70846
$909$	5.28644e15	0.282528
$910$	−8.24927e15	−0.438216
$911$	−1.57513e16	−0.831696	−0.415848	−	0.909434i	$-0.636515\pi$
$911$	−1.57513e16	−0.831696	−0.415848	+	0.909434i	$0.636515\pi$
$912$	−1.84682e15	−0.0969290
$913$	−1.72706e16	−0.900987
$914$	2.10715e16	1.09267
$915$	6.69934e15	0.345316
$916$	6.05809e16	3.10392
$917$	2.01709e16	1.02729
$918$	−1.54099e15	−0.0780126
$919$	−2.79204e16	−1.40503	−0.702516	−	0.711668i	$-0.747940\pi$
$919$	−2.79204e16	−1.40503	−0.702516	+	0.711668i	$0.747940\pi$
$920$	3.52088e16	1.76124
$921$	−3.52721e15	−0.175389
$922$	6.31887e14	0.0312334
$923$	8.70962e15	0.427947
$924$	2.03503e16	0.993976
$925$	9.32692e15	0.452855
$926$	1.89265e15	0.0913501
$927$	3.10791e14	0.0149118
$928$	6.34709e15	0.302734
$929$	−7.89495e15	−0.374337	−0.187169	−	0.982328i	$-0.559931\pi$
$929$	−7.89495e15	−0.374337	−0.187169	+	0.982328i	$0.559931\pi$
$930$	1.14092e16	0.537775
$931$	1.04754e15	0.0490848
$932$	−5.62632e16	−2.62082
$933$	−1.31748e16	−0.610092
$934$	−4.01001e16	−1.84602
$935$	−2.69343e15	−0.123266
$936$	−9.14606e15	−0.416118
$937$	−1.31134e16	−0.593126	−0.296563	−	0.955013i	$-0.595840\pi$
$937$	−1.31134e16	−0.593126	−0.296563	+	0.955013i	$0.595840\pi$
$938$	−9.06748e15	−0.407728
$939$	1.36483e16	0.610126
$940$	−1.81433e16	−0.806330
$941$	−2.58260e16	−1.14107	−0.570537	−	0.821272i	$-0.693265\pi$
$941$	−2.58260e16	−1.14107	−0.570537	+	0.821272i	$0.693265\pi$
$942$	2.06037e15	0.0905036
$943$	−3.15337e16	−1.37708
$944$	4.15430e15	0.180365
$945$	1.75823e15	0.0758928
$946$	2.78397e16	1.19471
$947$	1.15258e15	0.0491751	0.0245875	−	0.999698i	$-0.492173\pi$
$947$	1.15258e15	0.0491751	0.0245875	+	0.999698i	$0.492173\pi$
$948$	4.51007e15	0.191310
$949$	−2.18780e16	−0.922665
$950$	3.77265e15	0.158185
$951$	−1.42602e16	−0.594474
$952$	−8.47465e15	−0.351252
$953$	−2.71230e16	−1.11770	−0.558852	−	0.829267i	$-0.688758\pi$
$953$	−2.71230e16	−1.11770	−0.558852	+	0.829267i	$0.688758\pi$
$954$	−7.44118e15	−0.304878
$955$	−1.93489e16	−0.788203
$956$	−8.12827e16	−3.29215
$957$	9.85243e15	0.396760
$958$	2.73226e16	1.09399
$959$	3.01656e15	0.120091
$960$	−4.22847e15	−0.167375
$961$	1.59307e15	0.0626982
$962$	1.74105e16	0.681315
$963$	−4.69023e15	−0.182494
$964$	1.06891e17	4.13541
$965$	2.45797e15	0.0945530
$966$	3.57024e16	1.36560
$967$	−6.11822e15	−0.232691	−0.116346	−	0.993209i	$-0.537118\pi$
$967$	−6.11822e15	−0.232691	−0.116346	+	0.993209i	$0.537118\pi$
$968$	5.50847e15	0.208313
$969$	4.26766e14	0.0160476
$970$	4.34407e15	0.162425
$971$	−1.74742e16	−0.649668	−0.324834	−	0.945771i	$-0.605308\pi$
$971$	−1.74742e16	−0.649668	−0.324834	+	0.945771i	$0.605308\pi$
$972$	3.68461e15	0.136216
$973$	−4.75716e14	−0.0174875
$974$	3.73570e16	1.36552
$975$	7.37690e15	0.268132
$976$	4.48421e16	1.62074
$977$	4.04578e16	1.45406	0.727030	−	0.686606i	$-0.240900\pi$
$977$	4.04578e16	1.45406	0.727030	+	0.686606i	$0.240900\pi$
$978$	−3.91846e16	−1.40040
$979$	−4.62529e16	−1.64374
$980$	−1.24430e16	−0.439727
$981$	5.14757e15	0.180893
$982$	4.89337e16	1.71000
$983$	−8.70149e15	−0.302377	−0.151189	−	0.988505i	$-0.548310\pi$
$983$	−8.70149e15	−0.302377	−0.151189	+	0.988505i	$0.548310\pi$
$984$	−2.63262e16	−0.909734
$985$	−1.28213e16	−0.440589
$986$	−7.75518e15	−0.265014
$987$	−9.73337e15	−0.330765
$988$	4.78765e15	0.161793
$989$	3.32043e16	1.11587
$990$	9.47315e15	0.316593
$991$	−2.22000e16	−0.737817	−0.368909	−	0.929466i	$-0.620268\pi$
$991$	−2.22000e16	−0.737817	−0.368909	+	0.929466i	$0.620268\pi$
$992$	1.44430e16	0.477357
$993$	6.74186e15	0.221594
$994$	−2.83841e16	−0.927792
$995$	−8.32347e15	−0.270569
$996$	−3.25049e16	−1.05081
$997$	−2.56007e16	−0.823055	−0.411528	−	0.911397i	$-0.635005\pi$
$997$	−2.56007e16	−0.823055	−0.411528	+	0.911397i	$0.635005\pi$
$998$	9.45522e16	3.02311
$999$	−3.71083e15	−0.117994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.26	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.26	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +285730. q^{10} +561469. q^{11} +1.05674e6 q^{12} -841746. q^{13} +2.74320e6 q^{14} +868128. q^{15} +5.81083e6 q^{16} -1.34277e6 q^{17} +4.72271e6 q^{18} -1.30792e6 q^{19} +1.55360e7 q^{20} +8.33461e6 q^{21} +4.49060e7 q^{22} +5.35592e7 q^{23} +4.47143e7 q^{24} -3.60651e7 q^{25} -6.73224e7 q^{26} +1.43489e7 q^{27} +1.49156e8 q^{28} +7.22123e7 q^{29} +6.94324e7 q^{30} +1.64321e8 q^{31} +8.78949e7 q^{32} +1.36437e8 q^{33} -1.07394e8 q^{34} +1.22534e8 q^{35} +2.56787e8 q^{36} -2.58614e8 q^{37} -1.04607e8 q^{38} -2.04544e8 q^{39} +6.57382e8 q^{40} -5.88764e8 q^{41} +6.66597e8 q^{42} +6.19956e8 q^{43} +2.44167e9 q^{44} +2.10955e8 q^{45} +4.28363e9 q^{46} -1.16783e9 q^{47} +1.41203e9 q^{48} -8.00919e8 q^{49} -2.88446e9 q^{50} -3.26294e8 q^{51} -3.66051e9 q^{52} -1.57562e9 q^{53} +1.14762e9 q^{54} +2.00587e9 q^{55} +6.31131e9 q^{56} -3.17825e8 q^{57} +5.77550e9 q^{58} +7.14924e8 q^{59} +3.77524e9 q^{60} +7.71700e9 q^{61} +1.31423e10 q^{62} +2.02531e9 q^{63} -4.87079e9 q^{64} -3.00717e9 q^{65} +1.09122e10 q^{66} -3.30544e9 q^{67} -5.83933e9 q^{68} +1.30149e10 q^{69} +9.80020e9 q^{70} -1.03471e10 q^{71} +1.08656e10 q^{72} +2.59913e10 q^{73} -2.06838e10 q^{74} -8.76381e9 q^{75} -5.68777e9 q^{76} +1.92577e10 q^{77} -1.63593e10 q^{78} +4.26792e9 q^{79} +2.07594e10 q^{80} +3.48678e9 q^{81} -4.70890e10 q^{82} -3.07597e10 q^{83} +3.62448e10 q^{84} -4.79711e9 q^{85} +4.95837e10 q^{86} +1.75476e10 q^{87} +1.03316e11 q^{88} -8.23783e10 q^{89} +1.68721e10 q^{90} -2.88709e10 q^{91} +2.32913e11 q^{92} +3.99301e10 q^{93} -9.34021e10 q^{94} -4.67260e9 q^{95} +2.13585e10 q^{96} +1.52034e10 q^{97} -6.40571e10 q^{98} +3.31542e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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