LMFDB - Embedded newform 177.12.a.b.1.24

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:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
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)

$f(q)$	$=$	$q+65.6908 q^{2} +243.000 q^{3} +2267.28 q^{4} -3292.96 q^{5} +15962.9 q^{6} +54722.4 q^{7} +14404.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+65.6908 q^{2} +243.000 q^{3} +2267.28 q^{4} -3292.96 q^{5} +15962.9 q^{6} +54722.4 q^{7} +14404.6 q^{8} +59049.0 q^{9} -216317. q^{10} -423940. q^{11} +550949. q^{12} -1.58429e6 q^{13} +3.59476e6 q^{14} -800188. q^{15} -3.69714e6 q^{16} -4.57310e6 q^{17} +3.87898e6 q^{18} +1.41446e7 q^{19} -7.46605e6 q^{20} +1.32976e7 q^{21} -2.78490e7 q^{22} -1.71025e7 q^{23} +3.50032e6 q^{24} -3.79846e7 q^{25} -1.04073e8 q^{26} +1.43489e7 q^{27} +1.24071e8 q^{28} +5.00348e7 q^{29} -5.25650e7 q^{30} -1.79132e8 q^{31} -2.72368e8 q^{32} -1.03018e8 q^{33} -3.00411e8 q^{34} -1.80199e8 q^{35} +1.33881e8 q^{36} -5.12362e8 q^{37} +9.29169e8 q^{38} -3.84983e8 q^{39} -4.74337e7 q^{40} +1.65132e8 q^{41} +8.73527e8 q^{42} -8.33134e8 q^{43} -9.61191e8 q^{44} -1.94446e8 q^{45} -1.12348e9 q^{46} +2.33243e9 q^{47} -8.98404e8 q^{48} +1.01722e9 q^{49} -2.49524e9 q^{50} -1.11126e9 q^{51} -3.59203e9 q^{52} +8.94903e8 q^{53} +9.42591e8 q^{54} +1.39602e9 q^{55} +7.88255e8 q^{56} +3.43714e9 q^{57} +3.28682e9 q^{58} -7.14924e8 q^{59} -1.81425e9 q^{60} +7.14313e9 q^{61} -1.17673e10 q^{62} +3.23130e9 q^{63} -1.03204e10 q^{64} +5.21700e9 q^{65} -6.76730e9 q^{66} -1.42596e10 q^{67} -1.03685e10 q^{68} -4.15591e9 q^{69} -1.18374e10 q^{70} -2.36719e10 q^{71} +8.50577e8 q^{72} -1.92843e10 q^{73} -3.36575e10 q^{74} -9.23025e9 q^{75} +3.20697e10 q^{76} -2.31990e10 q^{77} -2.52898e10 q^{78} +2.75591e10 q^{79} +1.21745e10 q^{80} +3.48678e9 q^{81} +1.08477e10 q^{82} +3.14438e10 q^{83} +3.01493e10 q^{84} +1.50590e10 q^{85} -5.47292e10 q^{86} +1.21584e10 q^{87} -6.10669e9 q^{88} -4.56397e10 q^{89} -1.27733e10 q^{90} -8.66963e10 q^{91} -3.87762e10 q^{92} -4.35291e10 q^{93} +1.53219e11 q^{94} -4.65775e10 q^{95} -6.61855e10 q^{96} +1.05631e11 q^{97} +6.68218e10 q^{98} -2.50333e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	65.6908	1.45157	0.725787	−	0.687919i	$-0.241476\pi$
$2$	65.6908	1.45157	0.725787	+	0.687919i	$0.241476\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	2267.28	1.10707
$5$	−3292.96	−0.471249	−0.235625	−	0.971844i	$-0.575714\pi$
$5$	−3292.96	−0.471249	−0.235625	+	0.971844i	$0.575714\pi$
$6$	15962.9	0.838067
$7$	54722.4	1.23063	0.615313	−	0.788283i	$-0.289030\pi$
$7$	54722.4	1.23063	0.615313	+	0.788283i	$0.289030\pi$
$8$	14404.6	0.155420
$9$	59049.0	0.333333
$10$	−216317.	−0.684054
$11$	−423940.	−0.793679	−0.396840	−	0.917888i	$-0.629893\pi$
$11$	−423940.	−0.793679	−0.396840	+	0.917888i	$0.629893\pi$
$12$	550949.	0.639167
$13$	−1.58429e6	−1.18344	−0.591721	−	0.806143i	$-0.701551\pi$
$13$	−1.58429e6	−1.18344	−0.591721	+	0.806143i	$0.701551\pi$
$14$	3.59476e6	1.78635
$15$	−800188.	−0.272076
$16$	−3.69714e6	−0.881466
$17$	−4.57310e6	−0.781163	−0.390581	−	0.920568i	$-0.627726\pi$
$17$	−4.57310e6	−0.781163	−0.390581	+	0.920568i	$0.627726\pi$
$18$	3.87898e6	0.483858
$19$	1.41446e7	1.31053	0.655263	−	0.755401i	$-0.272558\pi$
$19$	1.41446e7	1.31053	0.655263	+	0.755401i	$0.272558\pi$
$20$	−7.46605e6	−0.521706
$21$	1.32976e7	0.710502
$22$	−2.78490e7	−1.15208
$23$	−1.71025e7	−0.554060	−0.277030	−	0.960861i	$-0.589350\pi$
$23$	−1.71025e7	−0.554060	−0.277030	+	0.960861i	$0.589350\pi$
$24$	3.50032e6	0.0897317
$25$	−3.79846e7	−0.777924
$26$	−1.04073e8	−1.71785
$27$	1.43489e7	0.192450
$28$	1.24071e8	1.36239
$29$	5.00348e7	0.452984	0.226492	−	0.974013i	$-0.427274\pi$
$29$	5.00348e7	0.452984	0.226492	+	0.974013i	$0.427274\pi$
$30$	−5.25650e7	−0.394939
$31$	−1.79132e8	−1.12379	−0.561893	−	0.827210i	$-0.689927\pi$
$31$	−1.79132e8	−1.12379	−0.561893	+	0.827210i	$0.689927\pi$
$32$	−2.72368e8	−1.43493
$33$	−1.03018e8	−0.458231
$34$	−3.00411e8	−1.13392
$35$	−1.80199e8	−0.579932
$36$	1.33881e8	0.369023
$37$	−5.12362e8	−1.21470	−0.607348	−	0.794436i	$-0.707767\pi$
$37$	−5.12362e8	−1.21470	−0.607348	+	0.794436i	$0.707767\pi$
$38$	9.29169e8	1.90233
$39$	−3.84983e8	−0.683260
$40$	−4.74337e7	−0.0732415
$41$	1.65132e8	0.222598	0.111299	−	0.993787i	$-0.464499\pi$
$41$	1.65132e8	0.222598	0.111299	+	0.993787i	$0.464499\pi$
$42$	8.73527e8	1.03135
$43$	−8.33134e8	−0.864248	−0.432124	−	0.901814i	$-0.642236\pi$
$43$	−8.33134e8	−0.864248	−0.432124	+	0.901814i	$0.642236\pi$
$44$	−9.61191e8	−0.878658
$45$	−1.94446e8	−0.157083
$46$	−1.12348e9	−0.804260
$47$	2.33243e9	1.48344	0.741720	−	0.670709i	$-0.234010\pi$
$47$	2.33243e9	1.48344	0.741720	+	0.670709i	$0.234010\pi$
$48$	−8.98404e8	−0.508915
$49$	1.01722e9	0.514441
$50$	−2.49524e9	−1.12922
$51$	−1.11126e9	−0.451005
$52$	−3.59203e9	−1.31015
$53$	8.94903e8	0.293940	0.146970	−	0.989141i	$-0.453048\pi$
$53$	8.94903e8	0.293940	0.146970	+	0.989141i	$0.453048\pi$
$54$	9.42591e8	0.279356
$55$	1.39602e9	0.374021
$56$	7.88255e8	0.191264
$57$	3.43714e9	0.756632
$58$	3.28682e9	0.657540
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.81425e9	−0.301207
$61$	7.14313e9	1.08287	0.541433	−	0.840744i	$-0.317882\pi$
$61$	7.14313e9	1.08287	0.541433	+	0.840744i	$0.317882\pi$
$62$	−1.17673e10	−1.63126
$63$	3.23130e9	0.410209
$64$	−1.03204e10	−1.20145
$65$	5.21700e9	0.557696
$66$	−6.76730e9	−0.665157
$67$	−1.42596e10	−1.29031	−0.645157	−	0.764050i	$-0.723208\pi$
$67$	−1.42596e10	−1.29031	−0.645157	+	0.764050i	$0.723208\pi$
$68$	−1.03685e10	−0.864802
$69$	−4.15591e9	−0.319887
$70$	−1.18374e10	−0.841815
$71$	−2.36719e10	−1.55708	−0.778542	−	0.627592i	$-0.784041\pi$
$71$	−2.36719e10	−1.55708	−0.778542	+	0.627592i	$0.784041\pi$
$72$	8.50577e8	0.0518066
$73$	−1.92843e10	−1.08875	−0.544376	−	0.838841i	$-0.683234\pi$
$73$	−1.92843e10	−1.08875	−0.544376	+	0.838841i	$0.683234\pi$
$74$	−3.36575e10	−1.76322
$75$	−9.23025e9	−0.449135
$76$	3.20697e10	1.45084
$77$	−2.31990e10	−0.976723
$78$	−2.52898e10	−0.991803
$79$	2.75591e10	1.00767	0.503833	−	0.863801i	$-0.331923\pi$
$79$	2.75591e10	1.00767	0.503833	+	0.863801i	$0.331923\pi$
$80$	1.21745e10	0.415390
$81$	3.48678e9	0.111111
$82$	1.08477e10	0.323117
$83$	3.14438e10	0.876204	0.438102	−	0.898925i	$-0.355651\pi$
$83$	3.14438e10	0.876204	0.438102	+	0.898925i	$0.355651\pi$
$84$	3.01493e10	0.786576
$85$	1.50590e10	0.368123
$86$	−5.47292e10	−1.25452
$87$	1.21584e10	0.261530
$88$	−6.10669e9	−0.123353
$89$	−4.56397e10	−0.866359	−0.433180	−	0.901308i	$-0.642608\pi$
$89$	−4.56397e10	−0.866359	−0.433180	+	0.901308i	$0.642608\pi$
$90$	−1.27733e10	−0.228018
$91$	−8.66963e10	−1.45637
$92$	−3.87762e10	−0.613384
$93$	−4.35291e10	−0.648818
$94$	1.53219e11	2.15333
$95$	−4.65775e10	−0.617584
$96$	−6.61855e10	−0.828460
$97$	1.05631e11	1.24895	0.624477	−	0.781044i	$-0.285312\pi$
$97$	1.05631e11	1.24895	0.624477	+	0.781044i	$0.285312\pi$
$98$	6.68218e10	0.746750
$99$	−2.50333e10	−0.264560
$100$	−8.61216e10	−0.861216
$101$	−1.21433e11	−1.14966	−0.574829	−	0.818274i	$-0.694931\pi$
$101$	−1.21433e11	−1.14966	−0.574829	+	0.818274i	$0.694931\pi$
$102$	−7.29998e10	−0.654667
$103$	1.03031e11	0.875719	0.437860	−	0.899043i	$-0.355737\pi$
$103$	1.03031e11	0.875719	0.437860	+	0.899043i	$0.355737\pi$
$104$	−2.28211e10	−0.183930
$105$	−4.37882e10	−0.334824
$106$	5.87869e10	0.426676
$107$	1.94561e10	0.134105	0.0670525	−	0.997749i	$-0.478640\pi$
$107$	1.94561e10	0.134105	0.0670525	+	0.997749i	$0.478640\pi$
$108$	3.25330e10	0.213056
$109$	−1.85907e11	−1.15731	−0.578656	−	0.815572i	$-0.696423\pi$
$109$	−1.85907e11	−1.15731	−0.578656	+	0.815572i	$0.696423\pi$
$110$	9.17054e10	0.542919
$111$	−1.24504e11	−0.701305
$112$	−2.02316e11	−1.08476
$113$	−1.19648e11	−0.610908	−0.305454	−	0.952207i	$-0.598808\pi$
$113$	−1.19648e11	−0.610908	−0.305454	+	0.952207i	$0.598808\pi$
$114$	2.25788e11	1.09831
$115$	5.63178e10	0.261101
$116$	1.13443e11	0.501485
$117$	−9.35509e10	−0.394480
$118$	−4.69639e10	−0.188979
$119$	−2.50251e11	−0.961320
$120$	−1.15264e10	−0.0422860
$121$	−1.05586e11	−0.370073
$122$	4.69238e11	1.57186
$123$	4.01271e10	0.128517
$124$	−4.06142e11	−1.24411
$125$	2.85870e11	0.837846
$126$	2.12267e11	0.595449
$127$	−5.18158e11	−1.39169	−0.695843	−	0.718194i	$-0.744969\pi$
$127$	−5.18158e11	−1.39169	−0.695843	+	0.718194i	$0.744969\pi$
$128$	−1.20142e11	−0.309058
$129$	−2.02451e11	−0.498974
$130$	3.42709e11	0.809538
$131$	−6.87809e11	−1.55767	−0.778835	−	0.627229i	$-0.784189\pi$
$131$	−6.87809e11	−1.55767	−0.778835	+	0.627229i	$0.784189\pi$
$132$	−2.33569e11	−0.507294
$133$	7.74026e11	1.61277
$134$	−9.36723e11	−1.87299
$135$	−4.72503e10	−0.0906920
$136$	−6.58737e10	−0.121408
$137$	−4.14368e11	−0.733539	−0.366770	−	0.930312i	$-0.619536\pi$
$137$	−4.14368e11	−0.733539	−0.366770	+	0.930312i	$0.619536\pi$
$138$	−2.73005e11	−0.464340
$139$	8.41544e11	1.37561	0.687805	−	0.725895i	$-0.258574\pi$
$139$	8.41544e11	1.37561	0.687805	+	0.725895i	$0.258574\pi$
$140$	−4.08560e11	−0.642025
$141$	5.66780e11	0.856465
$142$	−1.55503e12	−2.26022
$143$	6.71645e11	0.939273
$144$	−2.18312e11	−0.293822
$145$	−1.64762e11	−0.213468
$146$	−1.26680e12	−1.58041
$147$	2.47184e11	0.297013
$148$	−1.16167e12	−1.34475
$149$	−1.47821e12	−1.64896	−0.824480	−	0.565891i	$-0.808532\pi$
$149$	−1.47821e12	−1.64896	−0.824480	+	0.565891i	$0.808532\pi$
$150$	−6.06342e11	−0.651953
$151$	1.32610e12	1.37469	0.687344	−	0.726332i	$-0.258777\pi$
$151$	1.32610e12	1.37469	0.687344	+	0.726332i	$0.258777\pi$
$152$	2.03747e11	0.203682
$153$	−2.70037e11	−0.260388
$154$	−1.52396e12	−1.41779
$155$	5.89873e11	0.529584
$156$	−8.72864e11	−0.756417
$157$	2.29774e12	1.92244	0.961219	−	0.275786i	$-0.0889382\pi$
$157$	2.29774e12	1.92244	0.961219	+	0.275786i	$0.0889382\pi$
$158$	1.81038e12	1.46270
$159$	2.17462e11	0.169706
$160$	8.96897e11	0.676212
$161$	−9.35892e11	−0.681841
$162$	2.29050e11	0.161286
$163$	1.38533e12	0.943024	0.471512	−	0.881860i	$-0.343708\pi$
$163$	1.38533e12	0.943024	0.471512	+	0.881860i	$0.343708\pi$
$164$	3.74401e11	0.246431
$165$	3.39232e11	0.215941
$166$	2.06557e12	1.27188
$167$	−2.04726e12	−1.21964	−0.609821	−	0.792539i	$-0.708759\pi$
$167$	−2.04726e12	−1.21964	−0.609821	+	0.792539i	$0.708759\pi$
$168$	1.91546e11	0.110426
$169$	7.17821e11	0.400534
$170$	9.89238e11	0.534357
$171$	8.35224e11	0.436842
$172$	−1.88895e12	−0.956782
$173$	4.60082e10	0.0225726	0.0112863	−	0.999936i	$-0.496407\pi$
$173$	4.60082e10	0.0225726	0.0112863	+	0.999936i	$0.496407\pi$
$174$	7.98698e11	0.379631
$175$	−2.07861e12	−0.957334
$176$	1.56737e12	0.699602
$177$	−1.73727e11	−0.0751646
$178$	−2.99811e12	−1.25759
$179$	1.62761e12	0.662003	0.331001	−	0.943630i	$-0.392614\pi$
$179$	1.62761e12	0.662003	0.331001	+	0.943630i	$0.392614\pi$
$180$	−4.40863e11	−0.173902
$181$	−2.10985e12	−0.807270	−0.403635	−	0.914920i	$-0.632253\pi$
$181$	−2.10985e12	−0.807270	−0.403635	+	0.914920i	$0.632253\pi$
$182$	−5.69515e12	−2.11404
$183$	1.73578e12	0.625192
$184$	−2.46355e11	−0.0861119
$185$	1.68719e12	0.572425
$186$	−2.85946e12	−0.941808
$187$	1.93872e12	0.619993
$188$	5.28827e12	1.64227
$189$	7.85207e11	0.236834
$190$	−3.05971e12	−0.896470
$191$	3.22243e12	0.917277	0.458638	−	0.888623i	$-0.348337\pi$
$191$	3.22243e12	0.917277	0.458638	+	0.888623i	$0.348337\pi$
$192$	−2.50785e12	−0.693656
$193$	−4.83971e11	−0.130093	−0.0650465	−	0.997882i	$-0.520720\pi$
$193$	−4.83971e11	−0.130093	−0.0650465	+	0.997882i	$0.520720\pi$
$194$	6.93897e12	1.81295
$195$	1.26773e12	0.321986
$196$	2.30632e12	0.569522
$197$	2.40573e12	0.577674	0.288837	−	0.957378i	$-0.406731\pi$
$197$	2.40573e12	0.577674	0.288837	+	0.957378i	$0.406731\pi$
$198$	−1.64445e12	−0.384028
$199$	4.08030e12	0.926831	0.463415	−	0.886141i	$-0.346624\pi$
$199$	4.08030e12	0.926831	0.463415	+	0.886141i	$0.346624\pi$
$200$	−5.47153e11	−0.120905
$201$	−3.46508e12	−0.744963
$202$	−7.97702e12	−1.66881
$203$	2.73802e12	0.557454
$204$	−2.51954e12	−0.499294
$205$	−5.43773e11	−0.104899
$206$	6.76821e12	1.27117
$207$	−1.00989e12	−0.184687
$208$	5.85735e12	1.04316
$209$	−5.99646e12	−1.04014
$210$	−2.87648e12	−0.486022
$211$	4.57036e11	0.0752311	0.0376155	−	0.999292i	$-0.488024\pi$
$211$	4.57036e11	0.0752311	0.0376155	+	0.999292i	$0.488024\pi$
$212$	2.02900e12	0.325412
$213$	−5.75227e12	−0.898983
$214$	1.27809e12	0.194664
$215$	2.74347e12	0.407276
$216$	2.06690e11	0.0299106
$217$	−9.80254e12	−1.38296
$218$	−1.22124e13	−1.67992
$219$	−4.68610e12	−0.628592
$220$	3.16516e12	0.414067
$221$	7.24513e12	0.924461
$222$	−8.17876e12	−1.01800
$223$	2.19937e12	0.267068	0.133534	−	0.991044i	$-0.457367\pi$
$223$	2.19937e12	0.267068	0.133534	+	0.991044i	$0.457367\pi$
$224$	−1.49047e13	−1.76587
$225$	−2.24295e12	−0.259308
$226$	−7.85980e12	−0.886778
$227$	−1.02690e13	−1.13080	−0.565398	−	0.824818i	$-0.691277\pi$
$227$	−1.02690e13	−1.13080	−0.565398	+	0.824818i	$0.691277\pi$
$228$	7.79295e12	0.837645
$229$	−8.49761e12	−0.891665	−0.445832	−	0.895116i	$-0.647092\pi$
$229$	−8.49761e12	−0.891665	−0.445832	+	0.895116i	$0.647092\pi$
$230$	3.69956e12	0.379007
$231$	−5.63737e12	−0.563911
$232$	7.20731e11	0.0704027
$233$	2.98522e12	0.284786	0.142393	−	0.989810i	$-0.454520\pi$
$233$	2.98522e12	0.284786	0.142393	+	0.989810i	$0.454520\pi$
$234$	−6.14543e12	−0.572618
$235$	−7.68058e12	−0.699071
$236$	−1.62093e12	−0.144128
$237$	6.69687e12	0.581776
$238$	−1.64392e13	−1.39543
$239$	−9.86658e12	−0.818424	−0.409212	−	0.912439i	$-0.634196\pi$
$239$	−9.86658e12	−0.818424	−0.409212	+	0.912439i	$0.634196\pi$
$240$	2.95841e12	0.239826
$241$	1.66839e12	0.132192	0.0660959	−	0.997813i	$-0.478946\pi$
$241$	1.66839e12	0.132192	0.0660959	+	0.997813i	$0.478946\pi$
$242$	−6.93604e12	−0.537189
$243$	8.47289e11	0.0641500
$244$	1.61955e13	1.19881
$245$	−3.34965e12	−0.242430
$246$	2.63598e12	0.186552
$247$	−2.24092e13	−1.55093
$248$	−2.58032e12	−0.174659
$249$	7.64084e12	0.505876
$250$	1.87790e13	1.21620
$251$	5.92217e12	0.375211	0.187606	−	0.982244i	$-0.439927\pi$
$251$	5.92217e12	0.375211	0.187606	+	0.982244i	$0.439927\pi$
$252$	7.32627e12	0.454130
$253$	7.25045e12	0.439746
$254$	−3.40382e13	−2.02014
$255$	3.65934e12	0.212536
$256$	1.32439e13	0.752828
$257$	−1.01898e13	−0.566936	−0.283468	−	0.958982i	$-0.591485\pi$
$257$	−1.01898e13	−0.566936	−0.283468	+	0.958982i	$0.591485\pi$
$258$	−1.32992e13	−0.724298
$259$	−2.80377e13	−1.49484
$260$	1.18284e13	0.617408
$261$	2.95450e12	0.150995
$262$	−4.51827e13	−2.26108
$263$	2.17541e13	1.06607	0.533034	−	0.846094i	$-0.321052\pi$
$263$	2.17541e13	1.06607	0.533034	+	0.846094i	$0.321052\pi$
$264$	−1.48393e12	−0.0712182
$265$	−2.94688e12	−0.138519
$266$	5.08464e13	2.34105
$267$	−1.10905e13	−0.500193
$268$	−3.23305e13	−1.42847
$269$	2.13070e13	0.922328	0.461164	−	0.887315i	$-0.347432\pi$
$269$	2.13070e13	0.922328	0.461164	+	0.887315i	$0.347432\pi$
$270$	−3.10391e12	−0.131646
$271$	3.95348e13	1.64304	0.821520	−	0.570179i	$-0.193126\pi$
$271$	3.95348e13	1.64304	0.821520	+	0.570179i	$0.193126\pi$
$272$	1.69074e13	0.688569
$273$	−2.10672e13	−0.840838
$274$	−2.72202e13	−1.06479
$275$	1.61032e13	0.617422
$276$	−9.42261e12	−0.354137
$277$	−1.88219e13	−0.693466	−0.346733	−	0.937964i	$-0.612709\pi$
$277$	−1.88219e13	−0.693466	−0.346733	+	0.937964i	$0.612709\pi$
$278$	5.52817e13	1.99680
$279$	−1.05776e13	−0.374595
$280$	−2.59569e12	−0.0901329
$281$	−1.75697e12	−0.0598245	−0.0299123	−	0.999553i	$-0.509523\pi$
$281$	−1.75697e12	−0.0598245	−0.0299123	+	0.999553i	$0.509523\pi$
$282$	3.72322e13	1.24322
$283$	−2.11279e13	−0.691879	−0.345940	−	0.938257i	$-0.612440\pi$
$283$	−2.11279e13	−0.691879	−0.345940	+	0.938257i	$0.612440\pi$
$284$	−5.36708e13	−1.72380
$285$	−1.13183e13	−0.356563
$286$	4.41209e13	1.36343
$287$	9.03644e12	0.273934
$288$	−1.60831e13	−0.478311
$289$	−1.33587e13	−0.389784
$290$	−1.08234e13	−0.309865
$291$	2.56683e13	0.721083
$292$	−4.37230e13	−1.20533
$293$	−2.80030e13	−0.757588	−0.378794	−	0.925481i	$-0.623661\pi$
$293$	−2.80030e13	−0.757588	−0.378794	+	0.925481i	$0.623661\pi$
$294$	1.62377e13	0.431136
$295$	2.35421e12	0.0613514
$296$	−7.38037e12	−0.188788
$297$	−6.08308e12	−0.152744
$298$	−9.71045e13	−2.39359
$299$	2.70954e13	0.655698
$300$	−2.09276e13	−0.497223
$301$	−4.55911e13	−1.06357
$302$	8.71127e13	1.99546
$303$	−2.95082e13	−0.663755
$304$	−5.22945e13	−1.15518
$305$	−2.35220e13	−0.510300
$306$	−1.77389e13	−0.377972
$307$	9.18183e13	1.92162	0.960811	−	0.277204i	$-0.0894079\pi$
$307$	9.18183e13	1.92162	0.960811	+	0.277204i	$0.0894079\pi$
$308$	−5.25987e13	−1.08130
$309$	2.50366e13	0.505597
$310$	3.87493e13	0.768730
$311$	−4.13482e13	−0.805887	−0.402943	−	0.915225i	$-0.632013\pi$
$311$	−4.13482e13	−0.805887	−0.402943	+	0.915225i	$0.632013\pi$
$312$	−5.54553e12	−0.106192
$313$	1.00501e14	1.89094	0.945472	−	0.325703i	$-0.105601\pi$
$313$	1.00501e14	1.89094	0.945472	+	0.325703i	$0.105601\pi$
$314$	1.50940e14	2.79056
$315$	−1.06405e13	−0.193311
$316$	6.24842e13	1.11556
$317$	4.01923e13	0.705208	0.352604	−	0.935773i	$-0.385296\pi$
$317$	4.01923e13	0.705208	0.352604	+	0.935773i	$0.385296\pi$
$318$	1.42852e13	0.246342
$319$	−2.12118e13	−0.359524
$320$	3.39845e13	0.566182
$321$	4.72783e12	0.0774256
$322$	−6.14795e13	−0.989744
$323$	−6.46846e13	−1.02373
$324$	7.90551e12	0.123008
$325$	6.01787e13	0.920628
$326$	9.10037e13	1.36887
$327$	−4.51754e13	−0.668174
$328$	2.37866e12	0.0345961
$329$	1.27636e14	1.82556
$330$	2.22844e13	0.313455
$331$	7.37558e13	1.02033	0.510167	−	0.860076i	$-0.329584\pi$
$331$	7.37558e13	1.02033	0.510167	+	0.860076i	$0.329584\pi$
$332$	7.12918e13	0.970019
$333$	−3.02545e13	−0.404899
$334$	−1.34486e14	−1.77040
$335$	4.69562e13	0.608060
$336$	−4.91629e13	−0.626284
$337$	−1.16498e14	−1.46001	−0.730004	−	0.683442i	$-0.760482\pi$
$337$	−1.16498e14	−1.46001	−0.730004	+	0.683442i	$0.760482\pi$
$338$	4.71542e13	0.581405
$339$	−2.90746e13	−0.352708
$340$	3.41430e13	0.407537
$341$	7.59413e13	0.891926
$342$	5.48665e13	0.634109
$343$	−5.25395e13	−0.597542
$344$	−1.20010e13	−0.134321
$345$	1.36852e13	0.150747
$346$	3.02231e12	0.0327658
$347$	−2.09212e13	−0.223241	−0.111620	−	0.993751i	$-0.535604\pi$
$347$	−2.09212e13	−0.223241	−0.111620	+	0.993751i	$0.535604\pi$
$348$	2.75666e13	0.289532
$349$	4.15391e13	0.429455	0.214727	−	0.976674i	$-0.431114\pi$
$349$	4.15391e13	0.429455	0.214727	+	0.976674i	$0.431114\pi$
$350$	−1.36545e14	−1.38964
$351$	−2.27329e13	−0.227753
$352$	1.15468e14	1.13888
$353$	8.50807e13	0.826171	0.413086	−	0.910692i	$-0.364451\pi$
$353$	8.50807e13	0.826171	0.413086	+	0.910692i	$0.364451\pi$
$354$	−1.14122e13	−0.109107
$355$	7.79505e13	0.733775
$356$	−1.03478e14	−0.959120
$357$	−6.08110e13	−0.555018
$358$	1.06919e14	0.960946
$359$	−5.39153e13	−0.477191	−0.238596	−	0.971119i	$-0.576687\pi$
$359$	−5.39153e13	−0.477191	−0.238596	+	0.971119i	$0.576687\pi$
$360$	−2.80091e12	−0.0244138
$361$	8.35792e13	0.717478
$362$	−1.38597e14	−1.17181
$363$	−2.56575e13	−0.213662
$364$	−1.96565e14	−1.61231
$365$	6.35025e13	0.513074
$366$	1.14025e14	0.907514
$367$	1.50539e14	1.18028	0.590139	−	0.807301i	$-0.299073\pi$
$367$	1.50539e14	1.18028	0.590139	+	0.807301i	$0.299073\pi$
$368$	6.32304e13	0.488386
$369$	9.75089e12	0.0741992
$370$	1.10833e14	0.830917
$371$	4.89713e13	0.361730
$372$	−9.86925e13	−0.718287
$373$	5.50202e12	0.0394570	0.0197285	−	0.999805i	$-0.493720\pi$
$373$	5.50202e12	0.0394570	0.0197285	+	0.999805i	$0.493720\pi$
$374$	1.27356e14	0.899966
$375$	6.94665e13	0.483730
$376$	3.35977e13	0.230556
$377$	−7.92697e13	−0.536080
$378$	5.15809e13	0.343782
$379$	2.84797e14	1.87077	0.935383	−	0.353635i	$-0.115055\pi$
$379$	2.84797e14	1.87077	0.935383	+	0.353635i	$0.115055\pi$
$380$	−1.05604e14	−0.683709
$381$	−1.25912e14	−0.803490
$382$	2.11684e14	1.33150
$383$	4.42806e13	0.274549	0.137275	−	0.990533i	$-0.456166\pi$
$383$	4.42806e13	0.274549	0.137275	+	0.990533i	$0.456166\pi$
$384$	−2.91945e13	−0.178435
$385$	7.63934e13	0.460280
$386$	−3.17924e13	−0.188840
$387$	−4.91957e13	−0.288083
$388$	2.39495e14	1.38268
$389$	1.05303e14	0.599402	0.299701	−	0.954033i	$-0.403113\pi$
$389$	1.05303e14	0.599402	0.299701	+	0.954033i	$0.403113\pi$
$390$	8.32783e13	0.467387
$391$	7.82116e13	0.432811
$392$	1.46526e13	0.0799543
$393$	−1.67138e14	−0.899321
$394$	1.58034e14	0.838537
$395$	−9.07509e13	−0.474862
$396$	−5.67574e13	−0.292886
$397$	−1.95091e14	−0.992862	−0.496431	−	0.868076i	$-0.665356\pi$
$397$	−1.95091e14	−0.992862	−0.496431	+	0.868076i	$0.665356\pi$
$398$	2.68038e14	1.34536
$399$	1.88088e14	0.931132
$400$	1.40434e14	0.685714
$401$	3.69126e14	1.77779	0.888895	−	0.458111i	$-0.151474\pi$
$401$	3.69126e14	1.77779	0.888895	+	0.458111i	$0.151474\pi$
$402$	−2.27624e14	−1.08137
$403$	2.83797e14	1.32994
$404$	−2.75322e14	−1.27275
$405$	−1.14818e13	−0.0523610
$406$	1.79863e14	0.809186
$407$	2.17211e14	0.964079
$408$	−1.60073e13	−0.0700950
$409$	6.54475e13	0.282758	0.141379	−	0.989956i	$-0.454846\pi$
$409$	6.54475e13	0.282758	0.141379	+	0.989956i	$0.454846\pi$
$410$	−3.57209e13	−0.152269
$411$	−1.00692e14	−0.423509
$412$	2.33601e14	0.969482
$413$	−3.91224e13	−0.160214
$414$	−6.63403e13	−0.268087
$415$	−1.03543e14	−0.412910
$416$	4.31511e14	1.69816
$417$	2.04495e14	0.794209
$418$	−3.93912e14	−1.50984
$419$	−4.53374e14	−1.71506	−0.857530	−	0.514435i	$-0.828002\pi$
$419$	−4.53374e14	−1.71506	−0.857530	+	0.514435i	$0.828002\pi$
$420$	−9.92801e13	−0.370673
$421$	7.61656e13	0.280677	0.140339	−	0.990104i	$-0.455181\pi$
$421$	7.61656e13	0.280677	0.140339	+	0.990104i	$0.455181\pi$
$422$	3.00231e13	0.109204
$423$	1.37728e14	0.494480
$424$	1.28907e13	0.0456841
$425$	1.73707e14	0.607685
$426$	−3.77871e14	−1.30494
$427$	3.90889e14	1.33260
$428$	4.41124e13	0.148464
$429$	1.63210e14	0.542289
$430$	1.80221e14	0.591192
$431$	4.91853e14	1.59298	0.796490	−	0.604652i	$-0.206688\pi$
$431$	4.91853e14	1.59298	0.796490	+	0.604652i	$0.206688\pi$
$432$	−5.30499e13	−0.169638
$433$	1.20040e14	0.379002	0.189501	−	0.981881i	$-0.439313\pi$
$433$	1.20040e14	0.379002	0.189501	+	0.981881i	$0.439313\pi$
$434$	−6.43936e14	−2.00747
$435$	−4.00372e13	−0.123246
$436$	−4.21503e14	−1.28122
$437$	−2.41908e14	−0.726110
$438$	−3.07833e14	−0.912448
$439$	1.44680e14	0.423500	0.211750	−	0.977324i	$-0.432084\pi$
$439$	1.44680e14	0.423500	0.211750	+	0.977324i	$0.432084\pi$
$440$	2.01091e13	0.0581302
$441$	6.00657e13	0.171480
$442$	4.75938e14	1.34192
$443$	−2.59576e14	−0.722844	−0.361422	−	0.932402i	$-0.617709\pi$
$443$	−2.59576e14	−0.722844	−0.361422	+	0.932402i	$0.617709\pi$
$444$	−2.82285e14	−0.776393
$445$	1.50290e14	0.408271
$446$	1.44479e14	0.387669
$447$	−3.59204e14	−0.952028
$448$	−5.64755e14	−1.47853
$449$	−4.00766e14	−1.03642	−0.518211	−	0.855253i	$-0.673402\pi$
$449$	−4.00766e14	−1.03642	−0.518211	+	0.855253i	$0.673402\pi$
$450$	−1.47341e14	−0.376405
$451$	−7.00062e13	−0.176671
$452$	−2.71276e14	−0.676318
$453$	3.22243e14	0.793676
$454$	−6.74576e14	−1.64143
$455$	2.85487e14	0.686315
$456$	4.95106e13	0.117596
$457$	−5.84780e14	−1.37231	−0.686157	−	0.727454i	$-0.740704\pi$
$457$	−5.84780e14	−1.37231	−0.686157	+	0.727454i	$0.740704\pi$
$458$	−5.58215e14	−1.29432
$459$	−6.56190e13	−0.150335
$460$	1.27688e14	0.289057
$461$	−6.57390e14	−1.47051	−0.735256	−	0.677790i	$-0.762938\pi$
$461$	−6.57390e14	−1.47051	−0.735256	+	0.677790i	$0.762938\pi$
$462$	−3.70323e14	−0.818559
$463$	1.70510e14	0.372438	0.186219	−	0.982508i	$-0.440377\pi$
$463$	1.70510e14	0.372438	0.186219	+	0.982508i	$0.440377\pi$
$464$	−1.84985e14	−0.399290
$465$	1.43339e14	0.305755
$466$	1.96102e14	0.413389
$467$	3.13256e14	0.652615	0.326308	−	0.945264i	$-0.394195\pi$
$467$	3.13256e14	0.652615	0.326308	+	0.945264i	$0.394195\pi$
$468$	−2.12106e14	−0.436717
$469$	−7.80319e14	−1.58789
$470$	−5.04544e14	−1.01475
$471$	5.58350e14	1.10992
$472$	−1.02982e13	−0.0202339
$473$	3.53199e14	0.685935
$474$	4.39922e14	0.844491
$475$	−5.37276e14	−1.01949
$476$	−5.67389e14	−1.06425
$477$	5.28432e13	0.0979801
$478$	−6.48143e14	−1.18800
$479$	4.10567e14	0.743942	0.371971	−	0.928244i	$-0.378682\pi$
$479$	4.10567e14	0.743942	0.371971	+	0.928244i	$0.378682\pi$
$480$	2.17946e14	0.390411
$481$	8.11731e14	1.43752
$482$	1.09598e14	0.191886
$483$	−2.27422e14	−0.393661
$484$	−2.39393e14	−0.409697
$485$	−3.47838e14	−0.588568
$486$	5.56591e13	0.0931186
$487$	6.39035e14	1.05710	0.528549	−	0.848902i	$-0.322736\pi$
$487$	6.39035e14	1.05710	0.528549	+	0.848902i	$0.322736\pi$
$488$	1.02894e14	0.168299
$489$	3.36636e14	0.544455
$490$	−2.20041e14	−0.351905
$491$	−9.78123e14	−1.54684	−0.773420	−	0.633894i	$-0.781455\pi$
$491$	−9.78123e14	−1.54684	−0.773420	+	0.633894i	$0.781455\pi$
$492$	9.09794e13	0.142277
$493$	−2.28814e14	−0.353854
$494$	−1.47208e15	−2.25129
$495$	8.24334e13	0.124674
$496$	6.62275e14	0.990580
$497$	−1.29538e15	−1.91619
$498$	5.01932e14	0.734318
$499$	−3.39503e14	−0.491237	−0.245618	−	0.969367i	$-0.578991\pi$
$499$	−3.39503e14	−0.491237	−0.245618	+	0.969367i	$0.578991\pi$
$500$	6.48148e14	0.927554
$501$	−4.97484e14	−0.704160
$502$	3.89032e14	0.544647
$503$	−5.53348e14	−0.766257	−0.383129	−	0.923695i	$-0.625153\pi$
$503$	−5.53348e14	−0.766257	−0.383129	+	0.923695i	$0.625153\pi$
$504$	4.65457e13	0.0637546
$505$	3.99873e14	0.541775
$506$	4.76288e14	0.638325
$507$	1.74430e14	0.231248
$508$	−1.17481e15	−1.54069
$509$	−1.48683e15	−1.92891	−0.964456	−	0.264245i	$-0.914877\pi$
$509$	−1.48683e15	−1.92891	−0.964456	+	0.264245i	$0.914877\pi$
$510$	2.40385e14	0.308511
$511$	−1.05529e15	−1.33985
$512$	1.11605e15	1.40184
$513$	2.02959e14	0.252211
$514$	−6.69377e14	−0.822950
$515$	−3.39278e14	−0.412682
$516$	−4.59014e14	−0.552399
$517$	−9.88811e14	−1.17738
$518$	−1.84182e15	−2.16987
$519$	1.11800e13	0.0130323
$520$	7.51488e13	0.0866770
$521$	−2.96903e13	−0.0338850	−0.0169425	−	0.999856i	$-0.505393\pi$
$521$	−2.96903e13	−0.0338850	−0.0169425	+	0.999856i	$0.505393\pi$
$522$	1.94084e14	0.219180
$523$	1.24557e15	1.39190	0.695950	−	0.718090i	$-0.254983\pi$
$523$	1.24557e15	1.39190	0.695950	+	0.718090i	$0.254983\pi$
$524$	−1.55945e15	−1.72445
$525$	−5.05102e14	−0.552717
$526$	1.42904e15	1.54748
$527$	8.19188e14	0.877860
$528$	3.80870e14	0.403915
$529$	−6.60313e14	−0.693017
$530$	−1.93583e14	−0.201071
$531$	−4.22156e13	−0.0433963
$532$	1.75493e15	1.78545
$533$	−2.61618e14	−0.263431
$534$	−7.28541e14	−0.726067
$535$	−6.40681e13	−0.0631969
$536$	−2.05404e14	−0.200540
$537$	3.95510e14	0.382207
$538$	1.39967e15	1.33883
$539$	−4.31240e14	−0.408301
$540$	−1.07130e14	−0.100402
$541$	−1.41201e15	−1.30994	−0.654970	−	0.755655i	$-0.727319\pi$
$541$	−1.41201e15	−1.30994	−0.654970	+	0.755655i	$0.727319\pi$
$542$	2.59707e15	2.38500
$543$	−5.12693e14	−0.466077
$544$	1.24557e15	1.12092
$545$	6.12184e14	0.545382
$546$	−1.38392e15	−1.22054
$547$	1.59592e15	1.39342	0.696708	−	0.717355i	$-0.254647\pi$
$547$	1.59592e15	1.39342	0.696708	+	0.717355i	$0.254647\pi$
$548$	−9.39489e14	−0.812079
$549$	4.21795e14	0.360955
$550$	1.05783e15	0.896235
$551$	7.07721e14	0.593647
$552$	−5.98643e13	−0.0497168
$553$	1.50810e15	1.24006
$554$	−1.23643e15	−1.00662
$555$	4.09986e14	0.330489
$556$	1.90801e15	1.52290
$557$	−1.34361e15	−1.06186	−0.530932	−	0.847415i	$-0.678158\pi$
$557$	−1.34361e15	−1.06186	−0.530932	+	0.847415i	$0.678158\pi$
$558$	−6.94848e14	−0.543753
$559$	1.31993e15	1.02279
$560$	6.66219e14	0.511190
$561$	4.71109e14	0.357953
$562$	−1.15417e14	−0.0868398
$563$	4.70726e14	0.350729	0.175365	−	0.984504i	$-0.443890\pi$
$563$	4.70726e14	0.350729	0.175365	+	0.984504i	$0.443890\pi$
$564$	1.28505e15	0.948166
$565$	3.93997e14	0.287890
$566$	−1.38791e15	−1.00431
$567$	1.90805e14	0.136736
$568$	−3.40984e14	−0.242002
$569$	1.52850e15	1.07436	0.537178	−	0.843469i	$-0.319490\pi$
$569$	1.52850e15	1.07436	0.537178	+	0.843469i	$0.319490\pi$
$570$	−7.43510e14	−0.517577
$571$	1.08546e15	0.748371	0.374185	−	0.927354i	$-0.377922\pi$
$571$	1.08546e15	0.748371	0.374185	+	0.927354i	$0.377922\pi$
$572$	1.52281e15	1.03984
$573$	7.83051e14	0.529590
$574$	5.93611e14	0.397636
$575$	6.49632e14	0.431017
$576$	−6.09407e14	−0.400483
$577$	−1.67528e15	−1.09049	−0.545244	−	0.838277i	$-0.683563\pi$
$577$	−1.67528e15	−1.09049	−0.545244	+	0.838277i	$0.683563\pi$
$578$	−8.77540e14	−0.565801
$579$	−1.17605e14	−0.0751092
$580$	−3.73562e14	−0.236324
$581$	1.72068e15	1.07828
$582$	1.68617e15	1.04671
$583$	−3.79386e14	−0.233294
$584$	−2.77783e14	−0.169214
$585$	3.08059e14	0.185899
$586$	−1.83954e15	−1.09970
$587$	−1.70503e15	−1.00977	−0.504884	−	0.863187i	$-0.668465\pi$
$587$	−1.70503e15	−1.00977	−0.504884	+	0.863187i	$0.668465\pi$
$588$	5.60435e14	0.328814
$589$	−2.53375e15	−1.47275
$590$	1.54650e14	0.0890562
$591$	5.84593e14	0.333520
$592$	1.89427e15	1.07071
$593$	−2.76326e15	−1.54746	−0.773732	−	0.633513i	$-0.781612\pi$
$593$	−2.76326e15	−1.54746	−0.773732	+	0.633513i	$0.781612\pi$
$594$	−3.99602e14	−0.221719
$595$	8.24066e14	0.453021
$596$	−3.35150e15	−1.82551
$597$	9.91513e14	0.535106
$598$	1.77992e15	0.951795
$599$	1.78890e15	0.947848	0.473924	−	0.880566i	$-0.342837\pi$
$599$	1.78890e15	0.947848	0.473924	+	0.880566i	$0.342837\pi$
$600$	−1.32958e14	−0.0698044
$601$	−1.61462e15	−0.839966	−0.419983	−	0.907532i	$-0.637964\pi$
$601$	−1.61462e15	−0.839966	−0.419983	+	0.907532i	$0.637964\pi$
$602$	−2.99492e15	−1.54385
$603$	−8.42014e14	−0.430105
$604$	3.00664e15	1.52187
$605$	3.47691e14	0.174397
$606$	−1.93841e15	−0.963490
$607$	4.95610e14	0.244119	0.122060	−	0.992523i	$-0.461050\pi$
$607$	4.95610e14	0.244119	0.122060	+	0.992523i	$0.461050\pi$
$608$	−3.85254e15	−1.88052
$609$	6.65340e14	0.321846
$610$	−1.54518e15	−0.740738
$611$	−3.69525e15	−1.75557
$612$	−6.12249e14	−0.288267
$613$	1.32654e13	0.00618995	0.00309497	−	0.999995i	$-0.499015\pi$
$613$	1.32654e13	0.00618995	0.00309497	+	0.999995i	$0.499015\pi$
$614$	6.03161e15	2.78938
$615$	−1.32137e14	−0.0605635
$616$	−3.34173e14	−0.151802
$617$	−3.18346e15	−1.43328	−0.716640	−	0.697444i	$-0.754321\pi$
$617$	−3.18346e15	−1.43328	−0.716640	+	0.697444i	$0.754321\pi$
$618$	1.64468e15	0.733912
$619$	1.37661e15	0.608854	0.304427	−	0.952536i	$-0.401535\pi$
$619$	1.37661e15	0.608854	0.304427	+	0.952536i	$0.401535\pi$
$620$	1.33741e15	0.586286
$621$	−2.45403e14	−0.106629
$622$	−2.71619e15	−1.16980
$623$	−2.49752e15	−1.06616
$624$	1.42333e15	0.602271
$625$	9.13357e14	0.383090
$626$	6.60202e15	2.74485
$627$	−1.45714e15	−0.600523
$628$	5.20961e15	2.12827
$629$	2.34308e15	0.948875
$630$	−6.98986e14	−0.280605
$631$	1.85383e15	0.737750	0.368875	−	0.929479i	$-0.379743\pi$
$631$	1.85383e15	0.737750	0.368875	+	0.929479i	$0.379743\pi$
$632$	3.96978e14	0.156611
$633$	1.11060e14	0.0434347
$634$	2.64026e15	1.02366
$635$	1.70627e15	0.655831
$636$	4.93046e14	0.187877
$637$	−1.61157e15	−0.608811
$638$	−1.39342e15	−0.521876
$639$	−1.39780e15	−0.519028
$640$	3.95622e14	0.145643
$641$	−1.87439e15	−0.684135	−0.342068	−	0.939675i	$-0.611127\pi$
$641$	−1.87439e15	−0.684135	−0.342068	+	0.939675i	$0.611127\pi$
$642$	3.10575e14	0.112389
$643$	−5.44962e12	−0.00195527	−0.000977633	−	1.00000i	$-0.500311\pi$
$643$	−5.44962e12	−0.00195527	−0.000977633		1.00000i	$0.500311\pi$
$644$	−2.12193e15	−0.754846
$645$	6.66664e14	0.235141
$646$	−4.24918e15	−1.48603
$647$	−7.26249e13	−0.0251833	−0.0125916	−	0.999921i	$-0.504008\pi$
$647$	−7.26249e13	−0.0251833	−0.0125916	+	0.999921i	$0.504008\pi$
$648$	5.02257e13	0.0172689
$649$	3.03085e14	0.103328
$650$	3.95318e15	1.33636
$651$	−2.38202e15	−0.798453
$652$	3.14094e15	1.04399
$653$	−4.01422e15	−1.32306	−0.661529	−	0.749919i	$-0.730092\pi$
$653$	−4.01422e15	−1.32306	−0.661529	+	0.749919i	$0.730092\pi$
$654$	−2.96761e15	−0.969905
$655$	2.26492e15	0.734051
$656$	−6.10516e14	−0.196212
$657$	−1.13872e15	−0.362918
$658$	8.38452e15	2.64994
$659$	3.10192e15	0.972212	0.486106	−	0.873900i	$-0.338417\pi$
$659$	3.10192e15	0.972212	0.486106	+	0.873900i	$0.338417\pi$
$660$	7.69134e14	0.239062
$661$	−6.87250e13	−0.0211839	−0.0105920	−	0.999944i	$-0.503372\pi$
$661$	−6.87250e13	−0.0211839	−0.0105920	+	0.999944i	$0.503372\pi$
$662$	4.84507e15	1.48109
$663$	1.76057e15	0.533738
$664$	4.52935e14	0.136179
$665$	−2.54883e15	−0.760016
$666$	−1.98744e15	−0.587741
$667$	−8.55721e14	−0.250981
$668$	−4.64171e15	−1.35023
$669$	5.34448e14	0.154192
$670$	3.08459e15	0.882644
$671$	−3.02826e15	−0.859448
$672$	−3.62183e15	−1.01952
$673$	−3.54753e15	−0.990474	−0.495237	−	0.868758i	$-0.664919\pi$
$673$	−3.54753e15	−0.990474	−0.495237	+	0.868758i	$0.664919\pi$
$674$	−7.65287e15	−2.11931
$675$	−5.45037e14	−0.149712
$676$	1.62750e15	0.443419
$677$	2.58632e14	0.0698948	0.0349474	−	0.999389i	$-0.488874\pi$
$677$	2.58632e14	0.0698948	0.0349474	+	0.999389i	$0.488874\pi$
$678$	−1.90993e15	−0.511982
$679$	5.78038e15	1.53699
$680$	2.16919e14	0.0572135
$681$	−2.49536e15	−0.652865
$682$	4.98864e15	1.29470
$683$	−1.42258e15	−0.366238	−0.183119	−	0.983091i	$-0.558619\pi$
$683$	−1.42258e15	−0.366238	−0.183119	+	0.983091i	$0.558619\pi$
$684$	1.89369e15	0.483615
$685$	1.36450e15	0.345680
$686$	−3.45136e15	−0.867377
$687$	−2.06492e15	−0.514803
$688$	3.08021e15	0.761805
$689$	−1.41779e15	−0.347861
$690$	8.98994e14	0.218820
$691$	−4.43465e15	−1.07085	−0.535427	−	0.844582i	$-0.679849\pi$
$691$	−4.43465e15	−1.07085	−0.535427	+	0.844582i	$0.679849\pi$
$692$	1.04313e14	0.0249894
$693$	−1.36988e15	−0.325574
$694$	−1.37433e15	−0.324051
$695$	−2.77117e15	−0.648255
$696$	1.75138e14	0.0406470
$697$	−7.55166e14	−0.173885
$698$	2.72874e15	0.623386
$699$	7.25409e14	0.164422
$700$	−4.71278e15	−1.05984
$701$	9.72490e14	0.216988	0.108494	−	0.994097i	$-0.465397\pi$
$701$	9.72490e14	0.216988	0.108494	+	0.994097i	$0.465397\pi$
$702$	−1.49334e15	−0.330601
$703$	−7.24715e15	−1.59189
$704$	4.37522e15	0.953564
$705$	−1.86638e15	−0.403609
$706$	5.58902e15	1.19925
$707$	−6.64510e15	−1.41480
$708$	−3.93887e14	−0.0832125
$709$	−6.28835e15	−1.31820	−0.659102	−	0.752054i	$-0.729063\pi$
$709$	−6.28835e15	−1.31820	−0.659102	+	0.752054i	$0.729063\pi$
$710$	5.12063e15	1.06513
$711$	1.62734e15	0.335888
$712$	−6.57422e14	−0.134649
$713$	3.06361e15	0.622646
$714$	−3.99472e15	−0.805650
$715$	−2.21170e15	−0.442632
$716$	3.69025e15	0.732883
$717$	−2.39758e15	−0.472517
$718$	−3.54174e15	−0.692679
$719$	−3.91950e15	−0.760714	−0.380357	−	0.924840i	$-0.624199\pi$
$719$	−3.91950e15	−0.760714	−0.380357	+	0.924840i	$0.624199\pi$
$720$	7.18893e14	0.138463
$721$	5.63813e15	1.07768
$722$	5.49038e15	1.04147
$723$	4.05420e14	0.0763210
$724$	−4.78361e15	−0.893704
$725$	−1.90055e15	−0.352387
$726$	−1.68546e15	−0.310146
$727$	−2.51753e15	−0.459765	−0.229883	−	0.973218i	$-0.573834\pi$
$727$	−2.51753e15	−0.459765	−0.229883	+	0.973218i	$0.573834\pi$
$728$	−1.24883e15	−0.226349
$729$	2.05891e14	0.0370370
$730$	4.17153e15	0.744765
$731$	3.81000e15	0.675118
$732$	3.93550e15	0.692132
$733$	−4.48714e15	−0.783245	−0.391622	−	0.920126i	$-0.628086\pi$
$733$	−4.48714e15	−0.783245	−0.391622	+	0.920126i	$0.628086\pi$
$734$	9.88900e15	1.71326
$735$	−8.13966e14	−0.139967
$736$	4.65819e15	0.795040
$737$	6.04521e15	1.02410
$738$	6.40544e14	0.107706
$739$	6.83508e15	1.14077	0.570386	−	0.821377i	$-0.306793\pi$
$739$	6.83508e15	1.14077	0.570386	+	0.821377i	$0.306793\pi$
$740$	3.82532e15	0.633714
$741$	−5.44543e15	−0.895430
$742$	3.21696e15	0.525079
$743$	−7.18069e15	−1.16340	−0.581698	−	0.813405i	$-0.697611\pi$
$743$	−7.18069e15	−1.16340	−0.581698	+	0.813405i	$0.697611\pi$
$744$	−6.27019e14	−0.100839
$745$	4.86766e15	0.777072
$746$	3.61432e14	0.0572747
$747$	1.85672e15	0.292068
$748$	4.39562e15	0.686375
$749$	1.06469e15	0.165033
$750$	4.56331e15	0.702171
$751$	2.65375e15	0.405360	0.202680	−	0.979245i	$-0.435035\pi$
$751$	2.65375e15	0.405360	0.202680	+	0.979245i	$0.435035\pi$
$752$	−8.62331e15	−1.30760
$753$	1.43909e15	0.216628
$754$	−5.20729e15	−0.778160
$755$	−4.36680e15	−0.647820
$756$	1.78028e15	0.262192
$757$	−3.05788e15	−0.447088	−0.223544	−	0.974694i	$-0.571763\pi$
$757$	−3.05788e15	−0.447088	−0.223544	+	0.974694i	$0.571763\pi$
$758$	1.87085e16	2.71556
$759$	1.76186e15	0.253888
$760$	−6.70930e14	−0.0959848
$761$	3.38111e15	0.480224	0.240112	−	0.970745i	$-0.422816\pi$
$761$	3.38111e15	0.480224	0.240112	+	0.970745i	$0.422816\pi$
$762$	−8.27128e15	−1.16633
$763$	−1.01733e16	−1.42422
$764$	7.30615e15	1.01549
$765$	8.89220e14	0.122708
$766$	2.90883e15	0.398529
$767$	1.13265e15	0.154071
$768$	3.21826e15	0.434645
$769$	4.90444e15	0.657650	0.328825	−	0.944391i	$-0.393347\pi$
$769$	4.90444e15	0.657650	0.328825	+	0.944391i	$0.393347\pi$
$770$	5.01834e15	0.668131
$771$	−2.47612e15	−0.327321
$772$	−1.09730e15	−0.144022
$773$	6.32644e15	0.824464	0.412232	−	0.911079i	$-0.364749\pi$
$773$	6.32644e15	0.824464	0.412232	+	0.911079i	$0.364749\pi$
$774$	−3.23170e15	−0.418173
$775$	6.80425e15	0.874220
$776$	1.52157e15	0.194112
$777$	−6.81316e15	−0.863044
$778$	6.91744e15	0.870077
$779$	2.33573e15	0.291720
$780$	2.87430e15	0.356461
$781$	1.00355e16	1.23583
$782$	5.13778e15	0.628258
$783$	7.17944e14	0.0871768
$784$	−3.76079e15	−0.453462
$785$	−7.56635e15	−0.905948
$786$	−1.09794e16	−1.30543
$787$	−5.39680e15	−0.637199	−0.318599	−	0.947889i	$-0.603212\pi$
$787$	−5.39680e15	−0.637199	−0.318599	+	0.947889i	$0.603212\pi$
$788$	5.45446e15	0.639525
$789$	5.28625e15	0.615494
$790$	−5.96150e15	−0.689297
$791$	−6.54745e15	−0.751799
$792$	−3.60594e14	−0.0411178
$793$	−1.13168e16	−1.28151
$794$	−1.28157e16	−1.44121
$795$	−7.16091e14	−0.0799740
$796$	9.25118e15	1.02607
$797$	2.79301e15	0.307646	0.153823	−	0.988098i	$-0.450841\pi$
$797$	2.79301e15	0.307646	0.153823	+	0.988098i	$0.450841\pi$
$798$	1.23557e16	1.35161
$799$	−1.06664e16	−1.15881
$800$	1.03458e16	1.11627
$801$	−2.69498e15	−0.288786
$802$	2.42482e16	2.58059
$803$	8.17541e15	0.864120
$804$	−7.85630e15	−0.824726
$805$	3.08185e15	0.321317
$806$	1.86429e16	1.93050
$807$	5.17761e15	0.532506
$808$	−1.74919e15	−0.178680
$809$	1.05905e15	0.107449	0.0537243	−	0.998556i	$-0.482891\pi$
$809$	1.05905e15	0.107449	0.0537243	+	0.998556i	$0.482891\pi$
$810$	−7.54250e14	−0.0760060
$811$	−1.42473e16	−1.42600	−0.712999	−	0.701165i	$-0.752664\pi$
$811$	−1.42473e16	−1.42600	−0.712999	+	0.701165i	$0.752664\pi$
$812$	6.20786e15	0.617141
$813$	9.60695e15	0.948610
$814$	1.42688e16	1.39943
$815$	−4.56184e15	−0.444400
$816$	4.10849e15	0.397545
$817$	−1.17843e16	−1.13262
$818$	4.29930e15	0.410444
$819$	−5.11933e15	−0.485458
$820$	−1.23288e15	−0.116131
$821$	−1.94964e16	−1.82417	−0.912087	−	0.409996i	$-0.865530\pi$
$821$	−1.94964e16	−1.82417	−0.912087	+	0.409996i	$0.865530\pi$
$822$	−6.61450e15	−0.614755
$823$	1.91090e15	0.176417	0.0882083	−	0.996102i	$-0.471886\pi$
$823$	1.91090e15	0.176417	0.0882083	+	0.996102i	$0.471886\pi$
$824$	1.48413e15	0.136104
$825$	3.91308e15	0.356469
$826$	−2.56998e15	−0.232562
$827$	1.22595e16	1.10203	0.551016	−	0.834495i	$-0.314240\pi$
$827$	1.22595e16	1.10203	0.551016	+	0.834495i	$0.314240\pi$
$828$	−2.28970e15	−0.204461
$829$	−2.03207e16	−1.80256	−0.901280	−	0.433237i	$-0.857371\pi$
$829$	−2.03207e16	−1.80256	−0.901280	+	0.433237i	$0.857371\pi$
$830$	−6.80182e15	−0.599370
$831$	−4.57372e15	−0.400373
$832$	1.63505e16	1.42184
$833$	−4.65184e15	−0.401862
$834$	1.34334e16	1.15285
$835$	6.74153e15	0.574755
$836$	−1.35957e16	−1.15150
$837$	−2.57035e15	−0.216273
$838$	−2.97825e16	−2.48954
$839$	−1.16475e16	−0.967260	−0.483630	−	0.875273i	$-0.660682\pi$
$839$	−1.16475e16	−0.967260	−0.483630	+	0.875273i	$0.660682\pi$
$840$	−6.30752e14	−0.0520382
$841$	−9.69703e15	−0.794805
$842$	5.00338e15	0.407424
$843$	−4.26943e14	−0.0345397
$844$	1.03623e15	0.0832860
$845$	−2.36375e15	−0.188751
$846$	9.04743e15	0.717775
$847$	−5.77793e15	−0.455422
$848$	−3.30858e15	−0.259098
$849$	−5.13407e15	−0.399457
$850$	1.14110e16	0.882101
$851$	8.76269e15	0.673015
$852$	−1.30420e16	−0.995237
$853$	2.29365e16	1.73903	0.869516	−	0.493906i	$-0.164431\pi$
$853$	2.29365e16	1.73903	0.869516	+	0.493906i	$0.164431\pi$
$854$	2.56778e16	1.93437
$855$	−2.75036e15	−0.205861
$856$	2.80257e14	0.0208426
$857$	1.30656e16	0.965459	0.482729	−	0.875770i	$-0.339645\pi$
$857$	1.30656e16	0.965459	0.482729	+	0.875770i	$0.339645\pi$
$858$	1.07214e16	0.787174
$859$	2.50105e16	1.82457	0.912283	−	0.409560i	$-0.134318\pi$
$859$	2.50105e16	1.82457	0.912283	+	0.409560i	$0.134318\pi$
$860$	6.22022e15	0.450883
$861$	2.19585e15	0.158156
$862$	3.23102e16	2.31233
$863$	−2.33376e16	−1.65957	−0.829787	−	0.558079i	$-0.811538\pi$
$863$	−2.33376e16	−1.65957	−0.829787	+	0.558079i	$0.811538\pi$
$864$	−3.90819e15	−0.276153
$865$	−1.51503e14	−0.0106373
$866$	7.88550e15	0.550149
$867$	−3.24615e15	−0.225042
$868$	−2.22251e16	−1.53103
$869$	−1.16834e16	−0.799763
$870$	−2.63008e15	−0.178901
$871$	2.25913e16	1.52701
$872$	−2.67792e15	−0.179869
$873$	6.23739e15	0.416318
$874$	−1.58911e16	−1.05400
$875$	1.56435e16	1.03107
$876$	−1.06247e16	−0.695895
$877$	−2.40317e16	−1.56418	−0.782090	−	0.623166i	$-0.785846\pi$
$877$	−2.40317e16	−1.56418	−0.782090	+	0.623166i	$0.785846\pi$
$878$	9.50413e15	0.614741
$879$	−6.80473e15	−0.437393
$880$	−5.16127e15	−0.329687
$881$	−5.43514e15	−0.345019	−0.172510	−	0.985008i	$-0.555188\pi$
$881$	−5.43514e15	−0.345019	−0.172510	+	0.985008i	$0.555188\pi$
$882$	3.94576e15	0.248917
$883$	−2.46537e16	−1.54560	−0.772802	−	0.634647i	$-0.781146\pi$
$883$	−2.46537e16	−1.54560	−0.772802	+	0.634647i	$0.781146\pi$
$884$	1.64267e16	1.02344
$885$	5.72074e14	0.0354213
$886$	−1.70518e16	−1.04926
$887$	−2.43626e16	−1.48986	−0.744928	−	0.667145i	$-0.767516\pi$
$887$	−2.43626e16	−1.48986	−0.744928	+	0.667145i	$0.767516\pi$
$888$	−1.79343e15	−0.108997
$889$	−2.83548e16	−1.71265
$890$	9.87264e15	0.592636
$891$	−1.47819e15	−0.0881866
$892$	4.98659e15	0.295663
$893$	3.29913e16	1.94409
$894$	−2.35964e16	−1.38194
$895$	−5.35966e15	−0.311968
$896$	−6.57446e15	−0.380335
$897$	6.58418e15	0.378567
$898$	−2.63267e16	−1.50444
$899$	−8.96283e15	−0.509057
$900$	−5.08540e15	−0.287072
$901$	−4.09248e15	−0.229615
$902$	−4.59876e15	−0.256451
$903$	−1.10786e16	−0.614050
$904$	−1.72349e15	−0.0949472
$905$	6.94763e15	0.380425
$906$	2.11684e16	1.15208
$907$	5.93642e15	0.321133	0.160566	−	0.987025i	$-0.448668\pi$
$907$	5.93642e15	0.321133	0.160566	+	0.987025i	$0.448668\pi$
$908$	−2.32826e16	−1.25187
$909$	−7.17049e15	−0.383219
$910$	1.87539e16	0.996238
$911$	−2.01807e15	−0.106558	−0.0532789	−	0.998580i	$-0.516967\pi$
$911$	−2.01807e15	−0.106558	−0.0532789	+	0.998580i	$0.516967\pi$
$912$	−1.27076e16	−0.666946
$913$	−1.33303e16	−0.695425
$914$	−3.84147e16	−1.99202
$915$	−5.71585e15	−0.294622
$916$	−1.92664e16	−0.987135
$917$	−3.76386e16	−1.91691
$918$	−4.31056e15	−0.218222
$919$	2.47115e16	1.24355	0.621776	−	0.783195i	$-0.286411\pi$
$919$	2.47115e16	1.24355	0.621776	+	0.783195i	$0.286411\pi$
$920$	8.11236e14	0.0405802
$921$	2.23118e16	1.10945
$922$	−4.31845e16	−2.13456
$923$	3.75032e16	1.84272
$924$	−1.27815e16	−0.624289
$925$	1.94619e16	0.944941
$926$	1.12009e16	0.540622
$927$	6.08390e15	0.291906
$928$	−1.36279e16	−0.650002
$929$	−1.58044e16	−0.749363	−0.374682	−	0.927153i	$-0.622248\pi$
$929$	−1.58044e16	−0.749363	−0.374682	+	0.927153i	$0.622248\pi$
$930$	9.41607e15	0.443827
$931$	1.43881e16	0.674188
$932$	6.76833e15	0.315278
$933$	−1.00476e16	−0.465279
$934$	2.05781e16	0.947320
$935$	−6.38412e15	−0.292171
$936$	−1.34756e15	−0.0613101
$937$	−1.95711e16	−0.885211	−0.442606	−	0.896716i	$-0.645946\pi$
$937$	−1.95711e16	−0.885211	−0.442606	+	0.896716i	$0.645946\pi$
$938$	−5.12598e16	−2.30495
$939$	2.44219e16	1.09174
$940$	−1.74140e16	−0.773920
$941$	1.17821e16	0.520571	0.260286	−	0.965532i	$-0.416183\pi$
$941$	1.17821e16	0.520571	0.260286	+	0.965532i	$0.416183\pi$
$942$	3.66785e16	1.61113
$943$	−2.82418e15	−0.123333
$944$	2.64317e15	0.114757
$945$	−2.58565e15	−0.111608
$946$	2.32019e16	0.995687
$947$	−8.49336e15	−0.362372	−0.181186	−	0.983449i	$-0.557994\pi$
$947$	−8.49336e15	−0.362372	−0.181186	+	0.983449i	$0.557994\pi$
$948$	1.51837e16	0.644066
$949$	3.05520e16	1.28847
$950$	−3.52941e16	−1.47987
$951$	9.76673e15	0.407152
$952$	−3.60477e15	−0.149408
$953$	4.45058e16	1.83403	0.917013	−	0.398858i	$-0.130593\pi$
$953$	4.45058e16	1.83403	0.917013	+	0.398858i	$0.130593\pi$
$954$	3.47131e15	0.142225
$955$	−1.06113e16	−0.432266
$956$	−2.23703e16	−0.906052
$957$	−5.15446e15	−0.207571
$958$	2.69705e16	1.07989
$959$	−2.26752e16	−0.902713
$960$	8.25823e15	0.326885
$961$	6.67978e15	0.262896
$962$	5.33233e16	2.08667
$963$	1.14886e15	0.0447017
$964$	3.78271e15	0.146346
$965$	1.59369e15	0.0613062
$966$	−1.49395e16	−0.571429
$967$	−4.76152e16	−1.81092	−0.905462	−	0.424427i	$-0.860476\pi$
$967$	−4.76152e16	−1.81092	−0.905462	+	0.424427i	$0.860476\pi$
$968$	−1.52093e15	−0.0575167
$969$	−1.57184e16	−0.591053
$970$	−2.28497e16	−0.854351
$971$	2.21700e16	0.824251	0.412125	−	0.911127i	$-0.364787\pi$
$971$	2.21700e16	0.824251	0.412125	+	0.911127i	$0.364787\pi$
$972$	1.92104e15	0.0710186
$973$	4.60513e16	1.69286
$974$	4.19787e16	1.53446
$975$	1.46234e16	0.531525
$976$	−2.64091e16	−0.954509
$977$	−1.14933e16	−0.413071	−0.206536	−	0.978439i	$-0.566219\pi$
$977$	−1.14933e16	−0.413071	−0.206536	+	0.978439i	$0.566219\pi$
$978$	2.21139e16	0.790318
$979$	1.93485e16	0.687612
$980$	−7.59460e15	−0.268387
$981$	−1.09776e16	−0.385771
$982$	−6.42537e16	−2.24535
$983$	−4.38128e15	−0.152250	−0.0761248	−	0.997098i	$-0.524255\pi$
$983$	−4.38128e15	−0.152250	−0.0761248	+	0.997098i	$0.524255\pi$
$984$	5.78015e14	0.0199741
$985$	−7.92197e15	−0.272229
$986$	−1.50310e16	−0.513646
$987$	3.10156e16	1.05399
$988$	−5.08078e16	−1.71699
$989$	1.42487e16	0.478845
$990$	5.41511e15	0.180973
$991$	−3.53889e15	−0.117615	−0.0588074	−	0.998269i	$-0.518730\pi$
$991$	−3.53889e15	−0.117615	−0.0588074	+	0.998269i	$0.518730\pi$
$992$	4.87899e16	1.61256
$993$	1.79227e16	0.589090
$994$	−8.50948e16	−2.78149
$995$	−1.34363e16	−0.436768
$996$	1.73239e16	0.560040
$997$	4.22004e16	1.35673	0.678365	−	0.734725i	$-0.262689\pi$
$997$	4.22004e16	1.35673	0.678365	+	0.734725i	$0.262689\pi$
$998$	−2.23022e16	−0.713067
$999$	−7.35184e15	−0.233768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.24	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.24	✓	27	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)

\(f(q)\)	\(=\)	\(q+65.6908 q^{2} +243.000 q^{3} +2267.28 q^{4} -3292.96 q^{5} +15962.9 q^{6} +54722.4 q^{7} +14404.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+65.6908 q^{2} +243.000 q^{3} +2267.28 q^{4} -3292.96 q^{5} +15962.9 q^{6} +54722.4 q^{7} +14404.6 q^{8} +59049.0 q^{9} -216317. q^{10} -423940. q^{11} +550949. q^{12} -1.58429e6 q^{13} +3.59476e6 q^{14} -800188. q^{15} -3.69714e6 q^{16} -4.57310e6 q^{17} +3.87898e6 q^{18} +1.41446e7 q^{19} -7.46605e6 q^{20} +1.32976e7 q^{21} -2.78490e7 q^{22} -1.71025e7 q^{23} +3.50032e6 q^{24} -3.79846e7 q^{25} -1.04073e8 q^{26} +1.43489e7 q^{27} +1.24071e8 q^{28} +5.00348e7 q^{29} -5.25650e7 q^{30} -1.79132e8 q^{31} -2.72368e8 q^{32} -1.03018e8 q^{33} -3.00411e8 q^{34} -1.80199e8 q^{35} +1.33881e8 q^{36} -5.12362e8 q^{37} +9.29169e8 q^{38} -3.84983e8 q^{39} -4.74337e7 q^{40} +1.65132e8 q^{41} +8.73527e8 q^{42} -8.33134e8 q^{43} -9.61191e8 q^{44} -1.94446e8 q^{45} -1.12348e9 q^{46} +2.33243e9 q^{47} -8.98404e8 q^{48} +1.01722e9 q^{49} -2.49524e9 q^{50} -1.11126e9 q^{51} -3.59203e9 q^{52} +8.94903e8 q^{53} +9.42591e8 q^{54} +1.39602e9 q^{55} +7.88255e8 q^{56} +3.43714e9 q^{57} +3.28682e9 q^{58} -7.14924e8 q^{59} -1.81425e9 q^{60} +7.14313e9 q^{61} -1.17673e10 q^{62} +3.23130e9 q^{63} -1.03204e10 q^{64} +5.21700e9 q^{65} -6.76730e9 q^{66} -1.42596e10 q^{67} -1.03685e10 q^{68} -4.15591e9 q^{69} -1.18374e10 q^{70} -2.36719e10 q^{71} +8.50577e8 q^{72} -1.92843e10 q^{73} -3.36575e10 q^{74} -9.23025e9 q^{75} +3.20697e10 q^{76} -2.31990e10 q^{77} -2.52898e10 q^{78} +2.75591e10 q^{79} +1.21745e10 q^{80} +3.48678e9 q^{81} +1.08477e10 q^{82} +3.14438e10 q^{83} +3.01493e10 q^{84} +1.50590e10 q^{85} -5.47292e10 q^{86} +1.21584e10 q^{87} -6.10669e9 q^{88} -4.56397e10 q^{89} -1.27733e10 q^{90} -8.66963e10 q^{91} -3.87762e10 q^{92} -4.35291e10 q^{93} +1.53219e11 q^{94} -4.65775e10 q^{95} -6.61855e10 q^{96} +1.05631e11 q^{97} +6.68218e10 q^{98} -2.50333e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

Modular forms

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