LMFDB - Embedded newform 177.14.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +O(q^{10})$	\(q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +3.33229e6 q^{10} +6.74053e6 q^{11} -4.13751e6 q^{12} +1.09553e7 q^{13} -3.50432e7 q^{14} +2.06286e7 q^{15} -8.13909e7 q^{16} +1.25092e8 q^{17} -6.25829e7 q^{18} +5.93564e7 q^{19} -1.60603e8 q^{20} -2.16936e8 q^{21} -7.93770e8 q^{22} -2.24559e8 q^{23} -2.16027e8 q^{24} -4.19977e8 q^{25} -1.29011e9 q^{26} -3.87420e8 q^{27} +1.68894e9 q^{28} -3.59989e9 q^{29} -2.42924e9 q^{30} +2.51758e9 q^{31} +7.15710e9 q^{32} -4.91384e9 q^{33} -1.47309e10 q^{34} -8.42065e9 q^{35} +3.01625e9 q^{36} -9.31650e9 q^{37} -6.98985e9 q^{38} -7.98643e9 q^{39} -8.38537e9 q^{40} -2.88329e10 q^{41} +2.55465e10 q^{42} +6.45299e10 q^{43} +3.82565e10 q^{44} -1.50382e10 q^{45} +2.64442e10 q^{46} -3.47238e9 q^{47} +5.93340e10 q^{48} -8.33535e9 q^{49} +4.94568e10 q^{50} -9.11920e10 q^{51} +6.21780e10 q^{52} -6.81644e10 q^{53} +4.56229e10 q^{54} -1.90737e11 q^{55} +8.81827e10 q^{56} -4.32708e10 q^{57} +4.23926e11 q^{58} -4.21805e10 q^{59} +1.17080e11 q^{60} -2.72876e11 q^{61} -2.96473e11 q^{62} +1.58146e11 q^{63} -1.76071e11 q^{64} -3.10004e11 q^{65} +5.78658e11 q^{66} -1.27218e12 q^{67} +7.09972e11 q^{68} +1.63703e11 q^{69} +9.91622e11 q^{70} +2.97964e11 q^{71} +1.57484e11 q^{72} -7.41056e11 q^{73} +1.09712e12 q^{74} +3.06163e11 q^{75} +3.36883e11 q^{76} +2.00584e12 q^{77} +9.40488e11 q^{78} -2.93932e12 q^{79} +2.30313e12 q^{80} +2.82430e11 q^{81} +3.39538e12 q^{82} +3.27472e12 q^{83} -1.23124e12 q^{84} -3.53974e12 q^{85} -7.59909e12 q^{86} +2.62432e12 q^{87} +1.99744e12 q^{88} +1.53034e12 q^{89} +1.77092e12 q^{90} +3.26008e12 q^{91} -1.27450e12 q^{92} -1.83532e12 q^{93} +4.08910e11 q^{94} -1.67961e12 q^{95} -5.21753e12 q^{96} -6.38006e12 q^{97} +9.81577e11 q^{98} +3.58219e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * 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 $

$2$	−117.761	−1.30109	−0.650543	−	0.759470i	$-0.725458\pi$
$2$	−117.761	−1.30109	−0.650543	+	0.759470i	$0.725458\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	5675.60	0.692822
$5$	−28297.1	−0.809911	−0.404955	−	0.914336i	$-0.632713\pi$
$5$	−28297.1	−0.809911	−0.404955	+	0.914336i	$0.632713\pi$
$6$	85847.6	0.751182
$7$	297580.	0.956018	0.478009	−	0.878355i	$-0.341359\pi$
$7$	297580.	0.956018	0.478009	+	0.878355i	$0.341359\pi$
$8$	296333.	0.399664
$9$	531441.	0.333333
$10$	3.33229e6	1.05376
$11$	6.74053e6	1.14721	0.573603	−	0.819133i	$-0.305545\pi$
$11$	6.74053e6	1.14721	0.573603	+	0.819133i	$0.305545\pi$
$12$	−4.13751e6	−0.400001
$13$	1.09553e7	0.629496	0.314748	−	0.949175i	$-0.398080\pi$
$13$	1.09553e7	0.629496	0.314748	+	0.949175i	$0.398080\pi$
$14$	−3.50432e7	−1.24386
$15$	2.06286e7	0.467602
$16$	−8.13909e7	−1.21282
$17$	1.25092e8	1.25693	0.628465	−	0.777838i	$-0.283683\pi$
$17$	1.25092e8	1.25693	0.628465	+	0.777838i	$0.283683\pi$
$18$	−6.25829e7	−0.433695
$19$	5.93564e7	0.289447	0.144723	−	0.989472i	$-0.453771\pi$
$19$	5.93564e7	0.289447	0.144723	+	0.989472i	$0.453771\pi$
$20$	−1.60603e8	−0.561124
$21$	−2.16936e8	−0.551957
$22$	−7.93770e8	−1.49261
$23$	−2.24559e8	−0.316300	−0.158150	−	0.987415i	$-0.550553\pi$
$23$	−2.24559e8	−0.316300	−0.158150	+	0.987415i	$0.550553\pi$
$24$	−2.16027e8	−0.230746
$25$	−4.19977e8	−0.344045
$26$	−1.29011e9	−0.819028
$27$	−3.87420e8	−0.192450
$28$	1.68894e9	0.662351
$29$	−3.59989e9	−1.12383	−0.561917	−	0.827194i	$-0.689936\pi$
$29$	−3.59989e9	−1.12383	−0.561917	+	0.827194i	$0.689936\pi$
$30$	−2.42924e9	−0.608390
$31$	2.51758e9	0.509487	0.254743	−	0.967009i	$-0.418009\pi$
$31$	2.51758e9	0.509487	0.254743	+	0.967009i	$0.418009\pi$
$32$	7.15710e9	1.17832
$33$	−4.91384e9	−0.662340
$34$	−1.47309e10	−1.63537
$35$	−8.42065e9	−0.774289
$36$	3.01625e9	0.230941
$37$	−9.31650e9	−0.596955	−0.298477	−	0.954417i	$-0.596479\pi$
$37$	−9.31650e9	−0.596955	−0.298477	+	0.954417i	$0.596479\pi$
$38$	−6.98985e9	−0.376595
$39$	−7.98643e9	−0.363440
$40$	−8.38537e9	−0.323692
$41$	−2.88329e10	−0.947966	−0.473983	−	0.880534i	$-0.657184\pi$
$41$	−2.88329e10	−0.947966	−0.473983	+	0.880534i	$0.657184\pi$
$42$	2.55465e10	0.718143
$43$	6.45299e10	1.55674	0.778370	−	0.627806i	$-0.216047\pi$
$43$	6.45299e10	1.55674	0.778370	+	0.627806i	$0.216047\pi$
$44$	3.82565e10	0.794810
$45$	−1.50382e10	−0.269970
$46$	2.64442e10	0.411533
$47$	−3.47238e9	−0.0469884	−0.0234942	−	0.999724i	$-0.507479\pi$
$47$	−3.47238e9	−0.0469884	−0.0234942	+	0.999724i	$0.507479\pi$
$48$	5.93340e10	0.700222
$49$	−8.33535e9	−0.0860299
$50$	4.94568e10	0.447632
$51$	−9.11920e10	−0.725689
$52$	6.21780e10	0.436129
$53$	−6.81644e10	−0.422440	−0.211220	−	0.977439i	$-0.567744\pi$
$53$	−6.81644e10	−0.422440	−0.211220	+	0.977439i	$0.567744\pi$
$54$	4.56229e10	0.250394
$55$	−1.90737e11	−0.929134
$56$	8.81827e10	0.382086
$57$	−4.32708e10	−0.167112
$58$	4.23926e11	1.46220
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.17080e11	0.323965
$61$	−2.72876e11	−0.678144	−0.339072	−	0.940760i	$-0.610113\pi$
$61$	−2.72876e11	−0.678144	−0.339072	+	0.940760i	$0.610113\pi$
$62$	−2.96473e11	−0.662886
$63$	1.58146e11	0.318673
$64$	−1.76071e11	−0.320271
$65$	−3.10004e11	−0.509836
$66$	5.78658e11	0.861760
$67$	−1.27218e12	−1.71815	−0.859077	−	0.511847i	$-0.828962\pi$
$67$	−1.27218e12	−1.71815	−0.859077	+	0.511847i	$0.828962\pi$
$68$	7.09972e11	0.870830
$69$	1.63703e11	0.182616
$70$	9.91622e11	1.00742
$71$	2.97964e11	0.276048	0.138024	−	0.990429i	$-0.455925\pi$
$71$	2.97964e11	0.276048	0.138024	+	0.990429i	$0.455925\pi$
$72$	1.57484e11	0.133221
$73$	−7.41056e11	−0.573129	−0.286564	−	0.958061i	$-0.592513\pi$
$73$	−7.41056e11	−0.573129	−0.286564	+	0.958061i	$0.592513\pi$
$74$	1.09712e12	0.776689
$75$	3.06163e11	0.198634
$76$	3.36883e11	0.200535
$77$	2.00584e12	1.09675
$78$	9.40488e11	0.472866
$79$	−2.93932e12	−1.36041	−0.680207	−	0.733020i	$-0.738110\pi$
$79$	−2.93932e12	−1.36041	−0.680207	+	0.733020i	$0.738110\pi$
$80$	2.30313e12	0.982275
$81$	2.82430e11	0.111111
$82$	3.39538e12	1.23338
$83$	3.27472e12	1.09943	0.549714	−	0.835353i	$-0.314737\pi$
$83$	3.27472e12	1.09943	0.549714	+	0.835353i	$0.314737\pi$
$84$	−1.23124e12	−0.382408
$85$	−3.53974e12	−1.01800
$86$	−7.59909e12	−2.02545
$87$	2.62432e12	0.648846
$88$	1.99744e12	0.458497
$89$	1.53034e12	0.326402	0.163201	−	0.986593i	$-0.447818\pi$
$89$	1.53034e12	0.326402	0.163201	+	0.986593i	$0.447818\pi$
$90$	1.77092e12	0.351254
$91$	3.26008e12	0.601810
$92$	−1.27450e12	−0.219139
$93$	−1.83532e12	−0.294152
$94$	4.08910e11	0.0611359
$95$	−1.67961e12	−0.234426
$96$	−5.21753e12	−0.680302
$97$	−6.38006e12	−0.777694	−0.388847	−	0.921302i	$-0.627127\pi$
$97$	−6.38006e12	−0.777694	−0.388847	+	0.921302i	$0.627127\pi$
$98$	9.81577e11	0.111932
$99$	3.58219e12	0.382402
$100$	−2.38362e12	−0.238362
$101$	−9.05475e12	−0.848765	−0.424383	−	0.905483i	$-0.639509\pi$
$101$	−9.05475e12	−0.848765	−0.424383	+	0.905483i	$0.639509\pi$
$102$	1.07388e13	0.944184
$103$	1.75266e13	1.44629	0.723144	−	0.690697i	$-0.242696\pi$
$103$	1.75266e13	1.44629	0.723144	+	0.690697i	$0.242696\pi$
$104$	3.24642e12	0.251587
$105$	6.13865e12	0.447036
$106$	8.02710e12	0.549630
$107$	3.27589e12	0.211026	0.105513	−	0.994418i	$-0.466352\pi$
$107$	3.27589e12	0.211026	0.105513	+	0.994418i	$0.466352\pi$
$108$	−2.19884e12	−0.133334
$109$	−9.70937e12	−0.554522	−0.277261	−	0.960795i	$-0.589427\pi$
$109$	−9.70937e12	−0.554522	−0.277261	+	0.960795i	$0.589427\pi$
$110$	2.24614e13	1.20888
$111$	6.79173e12	0.344652
$112$	−2.42203e13	−1.15948
$113$	2.39339e13	1.08144	0.540721	−	0.841202i	$-0.318151\pi$
$113$	2.39339e13	1.08144	0.540721	+	0.841202i	$0.318151\pi$
$114$	5.09560e12	0.217427
$115$	6.35436e12	0.256174
$116$	−2.04315e13	−0.778617
$117$	5.82210e12	0.209832
$118$	4.96721e12	0.169387
$119$	3.72248e13	1.20165
$120$	6.11294e12	0.186884
$121$	1.09120e13	0.316082
$122$	3.21341e13	0.882323
$123$	2.10192e13	0.547308
$124$	1.42888e13	0.352984
$125$	4.64265e13	1.08856
$126$	−1.86234e13	−0.414620
$127$	−1.10493e13	−0.233674	−0.116837	−	0.993151i	$-0.537275\pi$
$127$	−1.10493e13	−0.233674	−0.116837	+	0.993151i	$0.537275\pi$
$128$	−3.78967e13	−0.761617
$129$	−4.70423e13	−0.898784
$130$	3.65063e13	0.663340
$131$	7.94265e13	1.37310	0.686550	−	0.727083i	$-0.259124\pi$
$131$	7.94265e13	1.37310	0.686550	+	0.727083i	$0.259124\pi$
$132$	−2.78890e13	−0.458884
$133$	1.76632e13	0.276716
$134$	1.49813e14	2.23546
$135$	1.09629e13	0.155867
$136$	3.70689e13	0.502350
$137$	−1.29017e13	−0.166711	−0.0833553	−	0.996520i	$-0.526564\pi$
$137$	−1.29017e13	−0.166711	−0.0833553	+	0.996520i	$0.526564\pi$
$138$	−1.92778e13	−0.237599
$139$	1.05554e14	1.24131	0.620653	−	0.784086i	$-0.286868\pi$
$139$	1.05554e14	1.24131	0.620653	+	0.784086i	$0.286868\pi$
$140$	−4.77922e13	−0.536445
$141$	2.53136e12	0.0271288
$142$	−3.50884e13	−0.359162
$143$	7.38446e13	0.722162
$144$	−4.32545e13	−0.404273
$145$	1.01866e14	0.910205
$146$	8.72673e13	0.745690
$147$	6.07647e12	0.0496694
$148$	−5.28767e13	−0.413584
$149$	−1.53169e14	−1.14672	−0.573362	−	0.819302i	$-0.694361\pi$
$149$	−1.53169e14	−1.14672	−0.573362	+	0.819302i	$0.694361\pi$
$150$	−3.60540e13	−0.258440
$151$	−2.16491e14	−1.48624	−0.743121	−	0.669157i	$-0.766655\pi$
$151$	−2.16491e14	−1.48624	−0.743121	+	0.669157i	$0.766655\pi$
$152$	1.75893e13	0.115682
$153$	6.64790e13	0.418977
$154$	−2.36210e14	−1.42696
$155$	−7.12404e13	−0.412639
$156$	−4.53278e13	−0.251799
$157$	1.48745e14	0.792675	0.396338	−	0.918105i	$-0.370281\pi$
$157$	1.48745e14	0.792675	0.396338	+	0.918105i	$0.370281\pi$
$158$	3.46137e14	1.77001
$159$	4.96919e13	0.243896
$160$	−2.02525e14	−0.954332
$161$	−6.68241e13	−0.302388
$162$	−3.32591e13	−0.144565
$163$	−2.47866e14	−1.03513	−0.517567	−	0.855642i	$-0.673162\pi$
$163$	−2.47866e14	−1.03513	−0.517567	+	0.855642i	$0.673162\pi$
$164$	−1.63644e14	−0.656772
$165$	1.39048e14	0.536436
$166$	−3.85633e14	−1.43045
$167$	4.58344e13	0.163506	0.0817532	−	0.996653i	$-0.473948\pi$
$167$	4.58344e13	0.163506	0.0817532	+	0.996653i	$0.473948\pi$
$168$	−6.42852e13	−0.220598
$169$	−1.82856e14	−0.603735
$170$	4.16843e14	1.32451
$171$	3.15444e13	0.0964823
$172$	3.66246e14	1.07854
$173$	2.10806e14	0.597838	0.298919	−	0.954279i	$-0.403374\pi$
$173$	2.10806e14	0.597838	0.298919	+	0.954279i	$0.403374\pi$
$174$	−3.09042e14	−0.844203
$175$	−1.24977e14	−0.328913
$176$	−5.48618e14	−1.39135
$177$	3.07496e13	0.0751646
$178$	−1.80214e14	−0.424676
$179$	−5.78992e14	−1.31561	−0.657807	−	0.753187i	$-0.728516\pi$
$179$	−5.78992e14	−1.31561	−0.657807	+	0.753187i	$0.728516\pi$
$180$	−8.53511e13	−0.187041
$181$	−8.43273e14	−1.78261	−0.891307	−	0.453400i	$-0.850211\pi$
$181$	−8.43273e14	−1.78261	−0.891307	+	0.453400i	$0.850211\pi$
$182$	−3.83909e14	−0.783006
$183$	1.98927e14	0.391527
$184$	−6.65441e13	−0.126414
$185$	2.63630e14	0.483480
$186$	2.16129e14	0.382717
$187$	8.43186e14	1.44196
$188$	−1.97078e13	−0.0325546
$189$	−1.15288e14	−0.183986
$190$	1.97793e14	0.305008
$191$	5.90563e14	0.880135	0.440068	−	0.897965i	$-0.354954\pi$
$191$	5.90563e14	0.880135	0.440068	+	0.897965i	$0.354954\pi$
$192$	1.28356e14	0.184909
$193$	−7.89365e14	−1.09940	−0.549699	−	0.835363i	$-0.685258\pi$
$193$	−7.89365e14	−1.09940	−0.549699	+	0.835363i	$0.685258\pi$
$194$	7.51321e14	1.01185
$195$	2.25993e14	0.294354
$196$	−4.73081e13	−0.0596034
$197$	−8.09274e14	−0.986428	−0.493214	−	0.869908i	$-0.664178\pi$
$197$	−8.09274e14	−0.986428	−0.493214	+	0.869908i	$0.664178\pi$
$198$	−4.21842e14	−0.497538
$199$	−3.81549e14	−0.435517	−0.217759	−	0.976003i	$-0.569875\pi$
$199$	−3.81549e14	−0.435517	−0.217759	+	0.976003i	$0.569875\pi$
$200$	−1.24453e14	−0.137502
$201$	9.27418e14	0.991976
$202$	1.06629e15	1.10432
$203$	−1.07125e15	−1.07441
$204$	−5.17570e14	−0.502774
$205$	8.15887e14	0.767768
$206$	−2.06394e15	−1.88174
$207$	−1.19340e14	−0.105433
$208$	−8.91663e14	−0.763465
$209$	4.00093e14	0.332055
$210$	−7.22892e14	−0.581632
$211$	4.82454e14	0.376374	0.188187	−	0.982133i	$-0.439739\pi$
$211$	4.82454e14	0.376374	0.188187	+	0.982133i	$0.439739\pi$
$212$	−3.86874e14	−0.292676
$213$	−2.17216e14	−0.159376
$214$	−3.85772e14	−0.274562
$215$	−1.82601e15	−1.26082
$216$	−1.14806e14	−0.0769154
$217$	7.49182e14	0.487079
$218$	1.14338e15	0.721480
$219$	5.40230e14	0.330896
$220$	−1.08255e15	−0.643725
$221$	1.37042e15	0.791233
$222$	−7.99799e14	−0.448422
$223$	−4.81615e14	−0.262252	−0.131126	−	0.991366i	$-0.541859\pi$
$223$	−4.81615e14	−0.262252	−0.131126	+	0.991366i	$0.541859\pi$
$224$	2.12981e15	1.12649
$225$	−2.23193e14	−0.114682
$226$	−2.81847e15	−1.40705
$227$	1.33786e15	0.648996	0.324498	−	0.945886i	$-0.394805\pi$
$227$	1.33786e15	0.648996	0.324498	+	0.945886i	$0.394805\pi$
$228$	−2.45588e14	−0.115779
$229$	1.86755e14	0.0855737	0.0427869	−	0.999084i	$-0.486376\pi$
$229$	1.86755e14	0.0855737	0.0427869	+	0.999084i	$0.486376\pi$
$230$	−7.48294e14	−0.333305
$231$	−1.46226e15	−0.633209
$232$	−1.06677e15	−0.449156
$233$	1.75469e15	0.718434	0.359217	−	0.933254i	$-0.383044\pi$
$233$	1.75469e15	0.718434	0.359217	+	0.933254i	$0.383044\pi$
$234$	−6.85616e14	−0.273009
$235$	9.82582e13	0.0380564
$236$	−2.39400e14	−0.0901978
$237$	2.14276e15	0.785435
$238$	−4.38362e15	−1.56345
$239$	−8.29366e14	−0.287846	−0.143923	−	0.989589i	$-0.545972\pi$
$239$	−8.29366e14	−0.287846	−0.143923	+	0.989589i	$0.545972\pi$
$240$	−1.67898e15	−0.567117
$241$	−3.96498e15	−1.30356	−0.651779	−	0.758409i	$-0.725977\pi$
$241$	−3.96498e15	−1.30356	−0.651779	+	0.758409i	$0.725977\pi$
$242$	−1.28501e15	−0.411249
$243$	−2.05891e14	−0.0641500
$244$	−1.54874e15	−0.469834
$245$	2.35866e14	0.0696765
$246$	−2.47523e15	−0.712095
$247$	6.50268e14	0.182206
$248$	7.46044e14	0.203624
$249$	−2.38727e15	−0.634755
$250$	−5.46722e15	−1.41630
$251$	−3.63989e15	−0.918774	−0.459387	−	0.888236i	$-0.651931\pi$
$251$	−3.63989e15	−0.918774	−0.459387	+	0.888236i	$0.651931\pi$
$252$	8.97574e14	0.220784
$253$	−1.51364e15	−0.362861
$254$	1.30117e15	0.304029
$255$	2.58047e15	0.587743
$256$	5.90512e15	1.31120
$257$	−2.52357e15	−0.546323	−0.273162	−	0.961968i	$-0.588069\pi$
$257$	−2.52357e15	−0.546323	−0.273162	+	0.961968i	$0.588069\pi$
$258$	5.53974e15	1.16939
$259$	−2.77240e15	−0.570699
$260$	−1.75946e15	−0.353226
$261$	−1.91313e15	−0.374611
$262$	−9.35332e15	−1.78652
$263$	7.92683e15	1.47702	0.738512	−	0.674241i	$-0.235529\pi$
$263$	7.92683e15	1.47702	0.738512	+	0.674241i	$0.235529\pi$
$264$	−1.45613e15	−0.264713
$265$	1.92886e15	0.342138
$266$	−2.08004e15	−0.360032
$267$	−1.11562e15	−0.188448
$268$	−7.22038e15	−1.19038
$269$	−1.79820e15	−0.289367	−0.144684	−	0.989478i	$-0.546216\pi$
$269$	−1.79820e15	−0.289367	−0.144684	+	0.989478i	$0.546216\pi$
$270$	−1.29100e15	−0.202797
$271$	−1.92526e15	−0.295249	−0.147625	−	0.989043i	$-0.547163\pi$
$271$	−1.92526e15	−0.295249	−0.147625	+	0.989043i	$0.547163\pi$
$272$	−1.01814e16	−1.52443
$273$	−2.37660e15	−0.347455
$274$	1.51931e15	0.216905
$275$	−2.83086e15	−0.394690
$276$	9.29114e14	0.126520
$277$	−1.51421e15	−0.201404	−0.100702	−	0.994917i	$-0.532109\pi$
$277$	−1.51421e15	−0.201404	−0.100702	+	0.994917i	$0.532109\pi$
$278$	−1.24301e16	−1.61504
$279$	1.33795e15	0.169829
$280$	−2.49532e15	−0.309456
$281$	−6.62527e15	−0.802810	−0.401405	−	0.915901i	$-0.631478\pi$
$281$	−6.62527e15	−0.802810	−0.401405	+	0.915901i	$0.631478\pi$
$282$	−2.98095e14	−0.0352968
$283$	−9.24844e15	−1.07018	−0.535090	−	0.844795i	$-0.679722\pi$
$283$	−9.24844e15	−1.07018	−0.535090	+	0.844795i	$0.679722\pi$
$284$	1.69112e15	0.191252
$285$	1.22444e15	0.135346
$286$	−8.69600e15	−0.939594
$287$	−8.58007e15	−0.906272
$288$	3.80358e15	0.392772
$289$	5.74342e15	0.579875
$290$	−1.19959e16	−1.18425
$291$	4.65107e15	0.449002
$292$	−4.20594e15	−0.397077
$293$	−1.32961e16	−1.22767	−0.613837	−	0.789433i	$-0.710375\pi$
$293$	−1.32961e16	−1.22767	−0.613837	+	0.789433i	$0.710375\pi$
$294$	−7.15570e14	−0.0646241
$295$	1.19359e15	0.105441
$296$	−2.76079e15	−0.238581
$297$	−2.61142e15	−0.220780
$298$	1.80373e16	1.49199
$299$	−2.46011e15	−0.199109
$300$	1.73766e15	0.137618
$301$	1.92028e16	1.48827
$302$	2.54941e16	1.93373
$303$	6.60091e15	0.490035
$304$	−4.83107e15	−0.351047
$305$	7.72162e15	0.549236
$306$	−7.82862e15	−0.545125
$307$	−7.15787e15	−0.487960	−0.243980	−	0.969780i	$-0.578453\pi$
$307$	−7.15787e15	−0.487960	−0.243980	+	0.969780i	$0.578453\pi$
$308$	1.13844e16	0.759853
$309$	−1.27769e16	−0.835015
$310$	8.38932e15	0.536878
$311$	1.06496e16	0.667408	0.333704	−	0.942678i	$-0.391701\pi$
$311$	1.06496e16	0.667408	0.333704	+	0.942678i	$0.391701\pi$
$312$	−2.36664e15	−0.145254
$313$	2.71914e16	1.63453	0.817266	−	0.576261i	$-0.195489\pi$
$313$	2.71914e16	1.63453	0.817266	+	0.576261i	$0.195489\pi$
$314$	−1.75164e16	−1.03134
$315$	−4.47508e15	−0.258096
$316$	−1.66824e16	−0.942525
$317$	−9.02585e14	−0.0499578	−0.0249789	−	0.999688i	$-0.507952\pi$
$317$	−9.02585e14	−0.0499578	−0.0249789	+	0.999688i	$0.507952\pi$
$318$	−5.85175e15	−0.317329
$319$	−2.42651e16	−1.28927
$320$	4.98230e15	0.259391
$321$	−2.38812e15	−0.121836
$322$	7.86926e15	0.393433
$323$	7.42500e15	0.363815
$324$	1.60296e15	0.0769803
$325$	−4.60098e15	−0.216575
$326$	2.91888e16	1.34680
$327$	7.07813e15	0.320153
$328$	−8.54413e15	−0.378868
$329$	−1.03331e15	−0.0449218
$330$	−1.63744e16	−0.697949
$331$	4.49271e16	1.87770	0.938851	−	0.344323i	$-0.111891\pi$
$331$	4.49271e16	1.87770	0.938851	+	0.344323i	$0.111891\pi$
$332$	1.85860e16	0.761708
$333$	−4.95117e15	−0.198985
$334$	−5.39750e15	−0.212736
$335$	3.59990e16	1.39155
$336$	1.76566e16	0.669424
$337$	−7.55357e15	−0.280904	−0.140452	−	0.990087i	$-0.544856\pi$
$337$	−7.55357e15	−0.280904	−0.140452	+	0.990087i	$0.544856\pi$
$338$	2.15333e16	0.785510
$339$	−1.74478e16	−0.624371
$340$	−2.00902e16	−0.705294
$341$	1.69698e16	0.584486
$342$	−3.71469e15	−0.125532
$343$	−3.13126e16	−1.03826
$344$	1.91223e16	0.622173
$345$	−4.63233e15	−0.147902
$346$	−2.48247e16	−0.777838
$347$	−4.10435e15	−0.126213	−0.0631063	−	0.998007i	$-0.520101\pi$
$347$	−4.10435e15	−0.126213	−0.0631063	+	0.998007i	$0.520101\pi$
$348$	1.48946e16	0.449535
$349$	1.63887e16	0.485488	0.242744	−	0.970090i	$-0.421952\pi$
$349$	1.63887e16	0.485488	0.242744	+	0.970090i	$0.421952\pi$
$350$	1.47173e16	0.427944
$351$	−4.24431e15	−0.121147
$352$	4.82426e16	1.35177
$353$	4.19774e16	1.15473	0.577365	−	0.816486i	$-0.304081\pi$
$353$	4.19774e16	1.15473	0.577365	+	0.816486i	$0.304081\pi$
$354$	−3.62110e15	−0.0977955
$355$	−8.43151e15	−0.223574
$356$	8.68559e15	0.226138
$357$	−2.71369e16	−0.693772
$358$	6.81826e16	1.71172
$359$	2.40099e15	0.0591939	0.0295970	−	0.999562i	$-0.490578\pi$
$359$	2.40099e15	0.0591939	0.0295970	+	0.999562i	$0.490578\pi$
$360$	−4.45633e15	−0.107897
$361$	−3.85298e16	−0.916220
$362$	9.93045e16	2.31933
$363$	−7.95485e15	−0.182490
$364$	1.85029e16	0.416947
$365$	2.09697e16	0.464183
$366$	−2.34258e16	−0.509410
$367$	−2.70476e16	−0.577829	−0.288915	−	0.957355i	$-0.593294\pi$
$367$	−2.70476e16	−0.577829	−0.288915	+	0.957355i	$0.593294\pi$
$368$	1.82770e16	0.383614
$369$	−1.53230e16	−0.315989
$370$	−3.10453e16	−0.629049
$371$	−2.02844e16	−0.403860
$372$	−1.04165e16	−0.203795
$373$	−8.72842e16	−1.67814	−0.839070	−	0.544023i	$-0.816900\pi$
$373$	−8.72842e16	−1.67814	−0.839070	+	0.544023i	$0.816900\pi$
$374$	−9.92942e16	−1.87611
$375$	−3.38449e16	−0.628478
$376$	−1.02898e15	−0.0187796
$377$	−3.94379e16	−0.707449
$378$	1.35765e16	0.239381
$379$	2.75110e16	0.476818	0.238409	−	0.971165i	$-0.423374\pi$
$379$	2.75110e16	0.476818	0.238409	+	0.971165i	$0.423374\pi$
$380$	−9.53282e15	−0.162416
$381$	8.05492e15	0.134912
$382$	−6.95452e16	−1.14513
$383$	8.86617e16	1.43530	0.717652	−	0.696402i	$-0.245217\pi$
$383$	8.86617e16	1.43530	0.717652	+	0.696402i	$0.245217\pi$
$384$	2.76267e16	0.439720
$385$	−5.67596e16	−0.888269
$386$	9.29562e16	1.43041
$387$	3.42938e16	0.518913
$388$	−3.62107e16	−0.538804
$389$	2.30974e15	0.0337980	0.0168990	−	0.999857i	$-0.494621\pi$
$389$	2.30974e15	0.0337980	0.0168990	+	0.999857i	$0.494621\pi$
$390$	−2.66131e16	−0.382979
$391$	−2.80905e16	−0.397567
$392$	−2.47004e15	−0.0343831
$393$	−5.79019e16	−0.792759
$394$	9.53008e16	1.28343
$395$	8.31743e16	1.10181
$396$	2.03311e16	0.264937
$397$	8.90985e16	1.14217	0.571087	−	0.820890i	$-0.306522\pi$
$397$	8.90985e16	1.14217	0.571087	+	0.820890i	$0.306522\pi$
$398$	4.49315e16	0.566645
$399$	−1.28765e16	−0.159762
$400$	3.41823e16	0.417264
$401$	−4.54579e16	−0.545973	−0.272986	−	0.962018i	$-0.588011\pi$
$401$	−4.54579e16	−0.545973	−0.272986	+	0.962018i	$0.588011\pi$
$402$	−1.09214e17	−1.29065
$403$	2.75809e16	0.320720
$404$	−5.13912e16	−0.588044
$405$	−7.99194e15	−0.0899901
$406$	1.26152e17	1.39789
$407$	−6.27981e16	−0.684830
$408$	−2.70232e16	−0.290032
$409$	2.24076e16	0.236698	0.118349	−	0.992972i	$-0.462240\pi$
$409$	2.24076e16	0.236698	0.118349	+	0.992972i	$0.462240\pi$
$410$	−9.60795e16	−0.998931
$411$	9.40534e15	0.0962505
$412$	9.94738e16	1.00202
$413$	−1.25521e16	−0.124463
$414$	1.40535e16	0.137178
$415$	−9.26651e16	−0.890438
$416$	7.84083e16	0.741746
$417$	−7.69489e16	−0.716668
$418$	−4.71153e16	−0.432032
$419$	1.54773e16	0.139735	0.0698673	−	0.997556i	$-0.477742\pi$
$419$	1.54773e16	0.139735	0.0698673	+	0.997556i	$0.477742\pi$
$420$	3.48405e16	0.309717
$421$	−1.50058e17	−1.31348	−0.656742	−	0.754115i	$-0.728066\pi$
$421$	−1.50058e17	−1.31348	−0.656742	+	0.754115i	$0.728066\pi$
$422$	−5.68142e16	−0.489695
$423$	−1.84536e15	−0.0156628
$424$	−2.01994e16	−0.168834
$425$	−5.25357e16	−0.432441
$426$	2.55795e16	0.207362
$427$	−8.12025e16	−0.648318
$428$	1.85927e16	0.146203
$429$	−5.38327e16	−0.416940
$430$	2.15032e17	1.64043
$431$	5.05907e16	0.380162	0.190081	−	0.981768i	$-0.439125\pi$
$431$	5.05907e16	0.380162	0.190081	+	0.981768i	$0.439125\pi$
$432$	3.15325e16	0.233407
$433$	−1.65677e17	−1.20807	−0.604033	−	0.796959i	$-0.706441\pi$
$433$	−1.65677e17	−1.20807	−0.604033	+	0.796959i	$0.706441\pi$
$434$	−8.82242e16	−0.633731
$435$	−7.42606e16	−0.525507
$436$	−5.51065e16	−0.384185
$437$	−1.33290e16	−0.0915520
$438$	−6.36179e16	−0.430524
$439$	2.59250e17	1.72862	0.864309	−	0.502961i	$-0.167756\pi$
$439$	2.59250e17	1.72862	0.864309	+	0.502961i	$0.167756\pi$
$440$	−5.65218e16	−0.371342
$441$	−4.42975e15	−0.0286766
$442$	−1.61382e17	−1.02946
$443$	3.12166e17	1.96228	0.981141	−	0.193291i	$-0.0619163\pi$
$443$	3.12166e17	1.96228	0.981141	+	0.193291i	$0.0619163\pi$
$444$	3.85471e16	0.238783
$445$	−4.33041e16	−0.264356
$446$	5.67154e16	0.341212
$447$	1.11660e17	0.662062
$448$	−5.23952e16	−0.306185
$449$	7.88485e16	0.454142	0.227071	−	0.973878i	$-0.427085\pi$
$449$	7.88485e16	0.454142	0.227071	+	0.973878i	$0.427085\pi$
$450$	2.62834e16	0.149211
$451$	−1.94349e17	−1.08751
$452$	1.35839e17	0.749247
$453$	1.57822e17	0.858082
$454$	−1.57547e17	−0.844399
$455$	−9.22508e16	−0.487412
$456$	−1.28226e16	−0.0667888
$457$	2.47908e17	1.27302	0.636511	−	0.771267i	$-0.280377\pi$
$457$	2.47908e17	1.27302	0.636511	+	0.771267i	$0.280377\pi$
$458$	−2.19924e16	−0.111339
$459$	−4.84632e16	−0.241896
$460$	3.60648e16	0.177483
$461$	−1.42944e17	−0.693602	−0.346801	−	0.937939i	$-0.612732\pi$
$461$	−1.42944e17	−0.693602	−0.346801	+	0.937939i	$0.612732\pi$
$462$	1.72197e17	0.823858
$463$	−3.17250e17	−1.49667	−0.748333	−	0.663323i	$-0.769146\pi$
$463$	−3.17250e17	−1.49667	−0.748333	+	0.663323i	$0.769146\pi$
$464$	2.92998e17	1.36301
$465$	5.19342e16	0.238237
$466$	−2.06634e17	−0.934744
$467$	2.64421e17	1.17961	0.589803	−	0.807548i	$-0.299206\pi$
$467$	2.64421e17	1.17961	0.589803	+	0.807548i	$0.299206\pi$
$468$	3.30439e16	0.145376
$469$	−3.78575e17	−1.64259
$470$	−1.15710e16	−0.0495146
$471$	−1.08435e17	−0.457651
$472$	−1.24995e16	−0.0520318
$473$	4.34966e17	1.78590
$474$	−2.52334e17	−1.02192
$475$	−2.49283e16	−0.0995827
$476$	2.11273e17	0.832529
$477$	−3.62254e16	−0.140813
$478$	9.76668e16	0.374512
$479$	3.00162e17	1.13547	0.567734	−	0.823212i	$-0.307820\pi$
$479$	3.00162e17	1.13547	0.567734	+	0.823212i	$0.307820\pi$
$480$	1.47641e17	0.550984
$481$	−1.02065e17	−0.375781
$482$	4.66919e17	1.69604
$483$	4.87148e16	0.174584
$484$	6.19321e16	0.218988
$485$	1.80537e17	0.629863
$486$	2.42459e16	0.0834646
$487$	3.73898e17	1.27003	0.635016	−	0.772499i	$-0.280994\pi$
$487$	3.73898e17	1.27003	0.635016	+	0.772499i	$0.280994\pi$
$488$	−8.08623e16	−0.271030
$489$	1.80694e17	0.597635
$490$	−2.77758e16	−0.0906551
$491$	2.38789e17	0.769102	0.384551	−	0.923104i	$-0.374356\pi$
$491$	2.38789e17	0.769102	0.384551	+	0.923104i	$0.374356\pi$
$492$	1.19296e17	0.379187
$493$	−4.50317e17	−1.41258
$494$	−7.65760e16	−0.237065
$495$	−1.01366e17	−0.309711
$496$	−2.04909e17	−0.617916
$497$	8.86680e16	0.263907
$498$	2.81127e17	0.825870
$499$	−1.66895e17	−0.483937	−0.241969	−	0.970284i	$-0.577793\pi$
$499$	−1.66895e17	−0.483937	−0.241969	+	0.970284i	$0.577793\pi$
$500$	2.63498e17	0.754176
$501$	−3.34133e16	−0.0944005
$502$	4.28636e17	1.19540
$503$	−5.06854e17	−1.39538	−0.697688	−	0.716402i	$-0.745788\pi$
$503$	−5.06854e17	−1.39538	−0.697688	+	0.716402i	$0.745788\pi$
$504$	4.68639e16	0.127362
$505$	2.56223e17	0.687424
$506$	1.78248e17	0.472113
$507$	1.33302e17	0.348566
$508$	−6.27113e16	−0.161894
$509$	2.37315e17	0.604867	0.302434	−	0.953170i	$-0.402201\pi$
$509$	2.37315e17	0.604867	0.302434	+	0.953170i	$0.402201\pi$
$510$	−3.03878e17	−0.764704
$511$	−2.20523e17	−0.547922
$512$	−3.84942e17	−0.944366
$513$	−2.29959e16	−0.0557041
$514$	2.97177e17	0.710813
$515$	−4.95951e17	−1.17136
$516$	−2.66993e17	−0.622698
$517$	−2.34056e16	−0.0539054
$518$	3.26480e17	0.742528
$519$	−1.53678e17	−0.345162
$520$	−9.18644e16	−0.203763
$521$	−3.55489e17	−0.778719	−0.389360	−	0.921086i	$-0.627304\pi$
$521$	−3.55489e17	−0.778719	−0.389360	+	0.921086i	$0.627304\pi$
$522$	2.25291e17	0.487401
$523$	−1.66098e17	−0.354897	−0.177449	−	0.984130i	$-0.556784\pi$
$523$	−1.66098e17	−0.354897	−0.177449	+	0.984130i	$0.556784\pi$
$524$	4.50793e17	0.951314
$525$	9.11079e16	0.189898
$526$	−9.33470e17	−1.92173
$527$	3.14930e17	0.640390
$528$	3.99942e17	0.803299
$529$	−4.53610e17	−0.899955
$530$	−2.27144e17	−0.445151
$531$	−2.24165e16	−0.0433963
$532$	1.00250e17	0.191715
$533$	−3.15873e17	−0.596741
$534$	1.31376e17	0.245187
$535$	−9.26983e16	−0.170912
$536$	−3.76989e17	−0.686685
$537$	4.22086e17	0.759570
$538$	2.11758e17	0.376491
$539$	−5.61846e16	−0.0986940
$540$	6.22209e16	0.107988
$541$	5.99966e17	1.02883	0.514416	−	0.857541i	$-0.328009\pi$
$541$	5.99966e17	1.02883	0.514416	+	0.857541i	$0.328009\pi$
$542$	2.26720e17	0.384144
$543$	6.14746e17	1.02919
$544$	8.95296e17	1.48106
$545$	2.74747e17	0.449113
$546$	2.79870e17	0.452068
$547$	6.07266e17	0.969306	0.484653	−	0.874706i	$-0.338946\pi$
$547$	6.07266e17	0.969306	0.484653	+	0.874706i	$0.338946\pi$
$548$	−7.32249e16	−0.115501
$549$	−1.45018e17	−0.226048
$550$	3.33365e17	0.513526
$551$	−2.13676e17	−0.325290
$552$	4.85107e16	0.0729850
$553$	−8.74682e17	−1.30058
$554$	1.78315e17	0.262044
$555$	−1.92186e17	−0.279137
$556$	5.99083e17	0.860004
$557$	−5.93798e17	−0.842519	−0.421260	−	0.906940i	$-0.638412\pi$
$557$	−5.93798e17	−0.842519	−0.421260	+	0.906940i	$0.638412\pi$
$558$	−1.57558e17	−0.220962
$559$	7.06945e17	0.979962
$560$	6.85364e17	0.939073
$561$	−6.14682e17	−0.832515
$562$	7.80197e17	1.04452
$563$	1.46670e18	1.94106	0.970528	−	0.240989i	$-0.0774718\pi$
$563$	1.46670e18	1.94106	0.970528	+	0.240989i	$0.0774718\pi$
$564$	1.43670e16	0.0187954
$565$	−6.77260e17	−0.875871
$566$	1.08910e18	1.39239
$567$	8.40453e16	0.106224
$568$	8.82965e16	0.110326
$569$	−2.96505e17	−0.366270	−0.183135	−	0.983088i	$-0.558625\pi$
$569$	−2.96505e17	−0.366270	−0.183135	+	0.983088i	$0.558625\pi$
$570$	−1.44191e17	−0.176097
$571$	−9.45165e17	−1.14123	−0.570615	−	0.821218i	$-0.693295\pi$
$571$	−9.45165e17	−1.14123	−0.570615	+	0.821218i	$0.693295\pi$
$572$	4.19113e17	0.500330
$573$	−4.30520e17	−0.508146
$574$	1.01040e18	1.17914
$575$	9.43094e16	0.108821
$576$	−9.35714e16	−0.106757
$577$	5.97695e16	0.0674274	0.0337137	−	0.999432i	$-0.489267\pi$
$577$	5.97695e16	0.0674274	0.0337137	+	0.999432i	$0.489267\pi$
$578$	−6.76349e17	−0.754467
$579$	5.75447e17	0.634738
$580$	5.78153e17	0.630610
$581$	9.74490e17	1.05107
$582$	−5.47713e17	−0.584190
$583$	−4.59464e17	−0.484625
$584$	−2.19599e17	−0.229059
$585$	−1.64749e17	−0.169945
$586$	1.56575e18	1.59731
$587$	−1.05773e18	−1.06716	−0.533578	−	0.845751i	$-0.679153\pi$
$587$	−1.05773e18	−1.06716	−0.533578	+	0.845751i	$0.679153\pi$
$588$	3.44876e16	0.0344120
$589$	1.49435e17	0.147469
$590$	−1.40558e17	−0.137188
$591$	5.89961e17	0.569514
$592$	7.58278e17	0.723998
$593$	−1.24219e18	−1.17309	−0.586545	−	0.809917i	$-0.699512\pi$
$593$	−1.24219e18	−1.17309	−0.586545	+	0.809917i	$0.699512\pi$
$594$	3.07523e17	0.287253
$595$	−1.05335e18	−0.973228
$596$	−8.69324e17	−0.794477
$597$	2.78149e17	0.251446
$598$	2.89705e17	0.259058
$599$	4.08031e17	0.360927	0.180463	−	0.983582i	$-0.442240\pi$
$599$	4.08031e17	0.360927	0.180463	+	0.983582i	$0.442240\pi$
$600$	9.07262e16	0.0793871
$601$	−1.38737e18	−1.20091	−0.600453	−	0.799660i	$-0.705013\pi$
$601$	−1.38737e18	−1.20091	−0.600453	+	0.799660i	$0.705013\pi$
$602$	−2.26134e18	−1.93637
$603$	−6.76088e17	−0.572718
$604$	−1.22872e18	−1.02970
$605$	−3.08778e17	−0.255998
$606$	−7.77329e17	−0.637577
$607$	−1.70509e17	−0.138363	−0.0691816	−	0.997604i	$-0.522039\pi$
$607$	−1.70509e17	−0.138363	−0.0691816	+	0.997604i	$0.522039\pi$
$608$	4.24819e17	0.341060
$609$	7.80944e17	0.620308
$610$	−9.09303e17	−0.714603
$611$	−3.80410e16	−0.0295790
$612$	3.77308e17	0.290277
$613$	2.03409e16	0.0154838	0.00774189	−	0.999970i	$-0.497536\pi$
$613$	2.03409e16	0.0154838	0.00774189	+	0.999970i	$0.497536\pi$
$614$	8.42917e17	0.634878
$615$	−5.94781e17	−0.443271
$616$	5.94398e17	0.438332
$617$	−2.02104e18	−1.47476	−0.737380	−	0.675478i	$-0.763937\pi$
$617$	−2.02104e18	−1.47476	−0.737380	+	0.675478i	$0.763937\pi$
$618$	1.50461e18	1.08643
$619$	−5.19853e17	−0.371442	−0.185721	−	0.982602i	$-0.559462\pi$
$619$	−5.19853e17	−0.371442	−0.185721	+	0.982602i	$0.559462\pi$
$620$	−4.04332e17	−0.285885
$621$	8.69986e16	0.0608719
$622$	−1.25411e18	−0.868354
$623$	4.55397e17	0.312046
$624$	6.50023e17	0.440787
$625$	−8.01069e17	−0.537588
$626$	−3.20208e18	−2.12666
$627$	−2.91668e17	−0.191712
$628$	8.44219e17	0.549183
$629$	−1.16542e18	−0.750331
$630$	5.26988e17	0.335805
$631$	−2.04962e18	−1.29266	−0.646328	−	0.763060i	$-0.723696\pi$
$631$	−2.04962e18	−1.29266	−0.646328	+	0.763060i	$0.723696\pi$
$632$	−8.71018e17	−0.543709
$633$	−3.51709e17	−0.217300
$634$	1.06289e17	0.0649993
$635$	3.12663e17	0.189255
$636$	2.82031e17	0.168976
$637$	−9.13164e16	−0.0541555
$638$	2.85748e18	1.67745
$639$	1.58350e17	0.0920159
$640$	1.07237e18	0.616842
$641$	−1.02725e18	−0.584924	−0.292462	−	0.956277i	$-0.594474\pi$
$641$	−1.02725e18	−0.584924	−0.292462	+	0.956277i	$0.594474\pi$
$642$	2.81227e17	0.158519
$643$	2.56040e18	1.42869	0.714343	−	0.699795i	$-0.246725\pi$
$643$	2.56040e18	1.42869	0.714343	+	0.699795i	$0.246725\pi$
$644$	−3.79267e17	−0.209501
$645$	1.33116e18	0.727935
$646$	−8.74374e17	−0.473354
$647$	−1.82578e17	−0.0978523	−0.0489262	−	0.998802i	$-0.515580\pi$
$647$	−1.82578e17	−0.0978523	−0.0489262	+	0.998802i	$0.515580\pi$
$648$	8.36932e16	0.0444071
$649$	−2.84319e17	−0.149354
$650$	5.41815e17	0.281782
$651$	−5.46154e17	−0.281215
$652$	−1.40679e18	−0.717164
$653$	−5.14885e15	−0.00259881	−0.00129941	−	0.999999i	$-0.500414\pi$
$653$	−5.14885e15	−0.00259881	−0.00129941	+	0.999999i	$0.500414\pi$
$654$	−8.33526e17	−0.416547
$655$	−2.24754e18	−1.11209
$656$	2.34673e18	1.14971
$657$	−3.93827e17	−0.191043
$658$	1.21683e17	0.0584470
$659$	8.96066e17	0.426172	0.213086	−	0.977033i	$-0.431649\pi$
$659$	8.96066e17	0.426172	0.213086	+	0.977033i	$0.431649\pi$
$660$	7.89179e17	0.371655
$661$	−2.05762e18	−0.959523	−0.479762	−	0.877399i	$-0.659277\pi$
$661$	−2.05762e18	−0.959523	−0.479762	+	0.877399i	$0.659277\pi$
$662$	−5.29066e18	−2.44305
$663$	−9.99038e17	−0.456819
$664$	9.70408e17	0.439402
$665$	−4.99819e17	−0.224116
$666$	5.83053e17	0.258896
$667$	8.08386e17	0.355468
$668$	2.60138e17	0.113281
$669$	3.51097e17	0.151411
$670$	−4.23927e18	−1.81053
$671$	−1.83933e18	−0.777971
$672$	−1.55263e18	−0.650381
$673$	−2.65917e18	−1.10319	−0.551593	−	0.834113i	$-0.685980\pi$
$673$	−2.65917e18	−1.10319	−0.551593	+	0.834113i	$0.685980\pi$
$674$	8.89514e17	0.365480
$675$	1.62708e17	0.0662115
$676$	−1.03782e18	−0.418281
$677$	−9.92748e16	−0.0396289	−0.0198145	−	0.999804i	$-0.506308\pi$
$677$	−9.92748e16	−0.0396289	−0.0198145	+	0.999804i	$0.506308\pi$
$678$	2.05467e18	0.812360
$679$	−1.89858e18	−0.743489
$680$	−1.04894e18	−0.406859
$681$	−9.75299e17	−0.374698
$682$	−1.99838e18	−0.760467
$683$	−4.11610e18	−1.55150	−0.775748	−	0.631042i	$-0.782627\pi$
$683$	−4.11610e18	−1.55150	−0.775748	+	0.631042i	$0.782627\pi$
$684$	1.79033e17	0.0668451
$685$	3.65081e17	0.135021
$686$	3.68740e18	1.35087
$687$	−1.36144e17	−0.0494060
$688$	−5.25215e18	−1.88804
$689$	−7.46763e17	−0.265924
$690$	5.45507e17	0.192434
$691$	−5.22830e17	−0.182706	−0.0913530	−	0.995819i	$-0.529119\pi$
$691$	−5.22830e17	−0.182706	−0.0913530	+	0.995819i	$0.529119\pi$
$692$	1.19645e18	0.414195
$693$	1.06599e18	0.365583
$694$	4.83331e17	0.164213
$695$	−2.98687e18	−1.00535
$696$	7.77673e17	0.259320
$697$	−3.60676e18	−1.19153
$698$	−1.92994e18	−0.631662
$699$	−1.27917e18	−0.414788
$700$	−7.09317e17	−0.227878
$701$	9.28005e16	0.0295382	0.0147691	−	0.999891i	$-0.495299\pi$
$701$	9.28005e16	0.0295382	0.0147691	+	0.999891i	$0.495299\pi$
$702$	4.99814e17	0.157622
$703$	−5.52993e17	−0.172787
$704$	−1.18681e18	−0.367417
$705$	−7.16302e16	−0.0219719
$706$	−4.94329e18	−1.50240
$707$	−2.69451e18	−0.811435
$708$	1.74523e17	0.0520757
$709$	1.08498e18	0.320791	0.160395	−	0.987053i	$-0.448723\pi$
$709$	1.08498e18	0.320791	0.160395	+	0.987053i	$0.448723\pi$
$710$	9.92902e17	0.290889
$711$	−1.56208e18	−0.453471
$712$	4.53490e17	0.130451
$713$	−5.65345e17	−0.161151
$714$	3.19566e18	0.902656
$715$	−2.08959e18	−0.584887
$716$	−3.28613e18	−0.911486
$717$	6.04608e17	0.166188
$718$	−2.82743e17	−0.0770163
$719$	−1.43557e18	−0.387514	−0.193757	−	0.981050i	$-0.562067\pi$
$719$	−1.43557e18	−0.387514	−0.193757	+	0.981050i	$0.562067\pi$
$720$	1.22398e18	0.327425
$721$	5.21555e18	1.38268
$722$	4.53730e18	1.19208
$723$	2.89047e18	0.752610
$724$	−4.78608e18	−1.23503
$725$	1.51187e18	0.386649
$726$	9.36769e17	0.237435
$727$	3.01211e18	0.756654	0.378327	−	0.925672i	$-0.376499\pi$
$727$	3.01211e18	0.756654	0.378327	+	0.925672i	$0.376499\pi$
$728$	9.66069e17	0.240522
$729$	1.50095e17	0.0370370
$730$	−2.46941e18	−0.603942
$731$	8.07217e18	1.95671
$732$	1.12903e18	0.271259
$733$	1.04077e18	0.247845	0.123922	−	0.992292i	$-0.460453\pi$
$733$	1.04077e18	0.247845	0.123922	+	0.992292i	$0.460453\pi$
$734$	3.18515e18	0.751805
$735$	−1.71947e17	−0.0402277
$736$	−1.60719e18	−0.372701
$737$	−8.57516e18	−1.97108
$738$	1.80444e18	0.411128
$739$	6.59981e18	1.49054	0.745268	−	0.666765i	$-0.232322\pi$
$739$	6.59981e18	1.49054	0.745268	+	0.666765i	$0.232322\pi$
$740$	1.49626e18	0.334966
$741$	−4.74045e17	−0.105197
$742$	2.38870e18	0.525456
$743$	−6.39379e18	−1.39422	−0.697110	−	0.716964i	$-0.745531\pi$
$743$	−6.39379e18	−1.39422	−0.697110	+	0.716964i	$0.745531\pi$
$744$	−5.43866e17	−0.117562
$745$	4.33423e18	0.928745
$746$	1.02787e19	2.18340
$747$	1.74032e18	0.366476
$748$	4.78559e18	0.999021
$749$	9.74839e17	0.201744
$750$	3.98560e18	0.817704
$751$	−2.96633e18	−0.603336	−0.301668	−	0.953413i	$-0.597543\pi$
$751$	−2.96633e18	−0.603336	−0.301668	+	0.953413i	$0.597543\pi$
$752$	2.82620e17	0.0569885
$753$	2.65348e18	0.530454
$754$	4.64424e18	0.920451
$755$	6.12607e18	1.20372
$756$	−6.54331e17	−0.127469
$757$	−1.36828e18	−0.264272	−0.132136	−	0.991232i	$-0.542184\pi$
$757$	−1.36828e18	−0.264272	−0.132136	+	0.991232i	$0.542184\pi$
$758$	−3.23972e18	−0.620380
$759$	1.10345e18	0.209498
$760$	−4.97725e17	−0.0936917
$761$	3.65930e18	0.682965	0.341482	−	0.939888i	$-0.389071\pi$
$761$	3.65930e18	0.682965	0.341482	+	0.939888i	$0.389071\pi$
$762$	−9.48554e17	−0.175531
$763$	−2.88931e18	−0.530133
$764$	3.35180e18	0.609777
$765$	−1.88116e18	−0.339334
$766$	−1.04409e19	−1.86745
$767$	−4.62101e17	−0.0819534
$768$	−4.30483e18	−0.757022
$769$	8.16747e18	1.42418	0.712092	−	0.702086i	$-0.247748\pi$
$769$	8.16747e18	1.42418	0.712092	+	0.702086i	$0.247748\pi$
$770$	6.68405e18	1.15571
$771$	1.83968e18	0.315420
$772$	−4.48012e18	−0.761688
$773$	−9.87665e18	−1.66511	−0.832555	−	0.553942i	$-0.813123\pi$
$773$	−9.87665e18	−1.66511	−0.832555	+	0.553942i	$0.813123\pi$
$774$	−4.03847e18	−0.675150
$775$	−1.05733e18	−0.175286
$776$	−1.89062e18	−0.310817
$777$	2.02108e18	0.329493
$778$	−2.71997e17	−0.0439740
$779$	−1.71141e18	−0.274386
$780$	1.28264e18	0.203935
$781$	2.00843e18	0.316684
$782$	3.30796e18	0.517268
$783$	1.39467e18	0.216282
$784$	6.78422e17	0.104339
$785$	−4.20906e18	−0.641996
$786$	6.81857e18	1.03145
$787$	−1.02120e17	−0.0153206	−0.00766029	−	0.999971i	$-0.502438\pi$
$787$	−1.02120e17	−0.0153206	−0.00766029	+	0.999971i	$0.502438\pi$
$788$	−4.59312e18	−0.683419
$789$	−5.77866e18	−0.852760
$790$	−9.79467e18	−1.43355
$791$	7.12224e18	1.03388
$792$	1.06152e18	0.152832
$793$	−2.98945e18	−0.426889
$794$	−1.04923e19	−1.48606
$795$	−1.40614e18	−0.197534
$796$	−2.16552e18	−0.301736
$797$	−3.18508e18	−0.440191	−0.220095	−	0.975478i	$-0.570637\pi$
$797$	−3.18508e18	−0.440191	−0.220095	+	0.975478i	$0.570637\pi$
$798$	1.51635e18	0.207864
$799$	−4.34366e17	−0.0590612
$800$	−3.00581e18	−0.405394
$801$	8.13284e17	0.108801
$802$	5.35316e18	0.710357
$803$	−4.99511e18	−0.657497
$804$	5.26366e18	0.687264
$805$	1.89093e18	0.244907
$806$	−3.24795e18	−0.417284
$807$	1.31089e18	0.167066
$808$	−2.68322e18	−0.339221
$809$	3.36804e18	0.422388	0.211194	−	0.977444i	$-0.432265\pi$
$809$	3.36804e18	0.422388	0.211194	+	0.977444i	$0.432265\pi$
$810$	9.41137e17	0.117085
$811$	1.45522e19	1.79595	0.897975	−	0.440046i	$-0.145038\pi$
$811$	1.45522e19	1.79595	0.897975	+	0.440046i	$0.145038\pi$
$812$	−6.08001e18	−0.744372
$813$	1.40351e18	0.170462
$814$	7.39515e18	0.891022
$815$	7.01388e18	0.838366
$816$	7.42221e18	0.880130
$817$	3.83026e18	0.450593
$818$	−2.63874e18	−0.307964
$819$	1.73254e18	0.200603
$820$	4.63065e18	0.531927
$821$	7.95100e18	0.906132	0.453066	−	0.891477i	$-0.350330\pi$
$821$	7.95100e18	0.906132	0.453066	+	0.891477i	$0.350330\pi$
$822$	−1.10758e18	−0.125230
$823$	4.31928e18	0.484521	0.242261	−	0.970211i	$-0.422111\pi$
$823$	4.31928e18	0.484521	0.242261	+	0.970211i	$0.422111\pi$
$824$	5.19370e18	0.578030
$825$	2.06370e18	0.227875
$826$	1.47814e18	0.161937
$827$	4.40647e18	0.478966	0.239483	−	0.970901i	$-0.423022\pi$
$827$	4.40647e18	0.478966	0.239483	+	0.970901i	$0.423022\pi$
$828$	−6.77324e17	−0.0730465
$829$	−5.62494e18	−0.601885	−0.300943	−	0.953642i	$-0.597301\pi$
$829$	−5.62494e18	−0.601885	−0.300943	+	0.953642i	$0.597301\pi$
$830$	1.09123e19	1.15854
$831$	1.10386e18	0.116281
$832$	−1.92891e18	−0.201610
$833$	−1.04268e18	−0.108134
$834$	9.06156e18	0.932446
$835$	−1.29698e18	−0.132426
$836$	2.27077e18	0.230055
$837$	−9.75364e17	−0.0980508
$838$	−1.82262e18	−0.181807
$839$	6.34005e18	0.627538	0.313769	−	0.949499i	$-0.398408\pi$
$839$	6.34005e18	0.627538	0.313769	+	0.949499i	$0.398408\pi$
$840$	1.81909e18	0.178664
$841$	2.69857e18	0.263002
$842$	1.76709e19	1.70895
$843$	4.82982e18	0.463503
$844$	2.73822e18	0.260761
$845$	5.17430e18	0.488971
$846$	2.17311e17	0.0203786
$847$	3.24719e18	0.302180
$848$	5.54797e18	0.512343
$849$	6.74211e18	0.617868
$850$	6.18664e18	0.562642
$851$	2.09210e18	0.188817
$852$	−1.23283e18	−0.110419
$853$	−1.82493e19	−1.62210	−0.811049	−	0.584978i	$-0.801103\pi$
$853$	−1.82493e19	−1.62210	−0.811049	+	0.584978i	$0.801103\pi$
$854$	9.56247e18	0.843517
$855$	−8.92616e17	−0.0781420
$856$	9.70755e17	0.0843393
$857$	3.55069e18	0.306152	0.153076	−	0.988214i	$-0.451082\pi$
$857$	3.55069e18	0.306152	0.153076	+	0.988214i	$0.451082\pi$
$858$	6.33938e18	0.542475
$859$	1.25671e18	0.106728	0.0533642	−	0.998575i	$-0.483006\pi$
$859$	1.25671e18	0.106728	0.0533642	+	0.998575i	$0.483006\pi$
$860$	−1.03637e19	−0.873524
$861$	6.25487e18	0.523237
$862$	−5.95760e18	−0.494623
$863$	1.66156e19	1.36914	0.684568	−	0.728949i	$-0.259991\pi$
$863$	1.66156e19	1.36914	0.684568	+	0.728949i	$0.259991\pi$
$864$	−2.77281e18	−0.226767
$865$	−5.96520e18	−0.484195
$866$	1.95102e19	1.57180
$867$	−4.18695e18	−0.334791
$868$	4.25206e18	0.337459
$869$	−1.98126e19	−1.56067
$870$	8.74499e18	0.683729
$871$	−1.39371e19	−1.08157
$872$	−2.87721e18	−0.221623
$873$	−3.39063e18	−0.259231
$874$	1.56963e18	0.119117
$875$	1.38156e19	1.04068
$876$	3.06613e18	0.229252
$877$	−2.23539e19	−1.65904	−0.829519	−	0.558479i	$-0.811385\pi$
$877$	−2.23539e19	−1.65904	−0.829519	+	0.558479i	$0.811385\pi$
$878$	−3.05295e19	−2.24908
$879$	9.69282e18	0.708798
$880$	1.55243e19	1.12687
$881$	−1.82829e18	−0.131735	−0.0658677	−	0.997828i	$-0.520982\pi$
$881$	−1.82829e18	−0.131735	−0.0658677	+	0.997828i	$0.520982\pi$
$882$	5.21650e17	0.0373107
$883$	9.26249e18	0.657632	0.328816	−	0.944394i	$-0.393350\pi$
$883$	9.26249e18	0.657632	0.328816	+	0.944394i	$0.393350\pi$
$884$	7.77797e18	0.548184
$885$	−8.70125e17	−0.0608766
$886$	−3.67609e19	−2.55310
$887$	1.52083e19	1.04852	0.524261	−	0.851558i	$-0.324342\pi$
$887$	1.52083e19	1.04852	0.524261	+	0.851558i	$0.324342\pi$
$888$	2.01261e18	0.137745
$889$	−3.28804e18	−0.223396
$890$	5.09953e18	0.343950
$891$	1.90372e18	0.127467
$892$	−2.73345e18	−0.181694
$893$	−2.06108e17	−0.0136006
$894$	−1.31492e19	−0.861399
$895$	1.63838e19	1.06553
$896$	−1.12773e19	−0.728119
$897$	1.79342e18	0.114956
$898$	−9.28525e18	−0.590878
$899$	−9.06302e18	−0.572579
$900$	−1.26675e18	−0.0794540
$901$	−8.52682e18	−0.530977
$902$	2.28867e19	1.41495
$903$	−1.39988e19	−0.859254
$904$	7.09240e18	0.432214
$905$	2.38622e19	1.44376
$906$	−1.85852e19	−1.11644
$907$	1.57518e19	0.939467	0.469733	−	0.882808i	$-0.344350\pi$
$907$	1.57518e19	0.939467	0.469733	+	0.882808i	$0.344350\pi$
$908$	7.59315e18	0.449639
$909$	−4.81207e18	−0.282922
$910$	1.08635e19	0.634164
$911$	−3.62535e18	−0.210127	−0.105063	−	0.994466i	$-0.533505\pi$
$911$	−3.62535e18	−0.210127	−0.105063	+	0.994466i	$0.533505\pi$
$912$	3.52185e18	0.202677
$913$	2.20733e19	1.26127
$914$	−2.91939e19	−1.65631
$915$	−5.62906e18	−0.317102
$916$	1.05994e18	0.0592874
$917$	2.36357e19	1.31271
$918$	5.70706e18	0.314728
$919$	−3.56210e19	−1.95054	−0.975270	−	0.221018i	$-0.929062\pi$
$919$	−3.56210e19	−1.95054	−0.975270	+	0.221018i	$0.929062\pi$
$920$	1.88301e18	0.102384
$921$	5.21809e18	0.281724
$922$	1.68332e19	0.902436
$923$	3.26429e18	0.173771
$924$	−8.29921e18	−0.438701
$925$	3.91271e18	0.205379
$926$	3.73596e19	1.94729
$927$	9.31434e18	0.482096
$928$	−2.57648e19	−1.32423
$929$	−1.54882e18	−0.0790494	−0.0395247	−	0.999219i	$-0.512584\pi$
$929$	−1.54882e18	−0.0790494	−0.0395247	+	0.999219i	$0.512584\pi$
$930$	−6.11581e18	−0.309967
$931$	−4.94756e17	−0.0249011
$932$	9.95892e18	0.497747
$933$	−7.76357e18	−0.385328
$934$	−3.11385e19	−1.53477
$935$	−2.38597e19	−1.16786
$936$	1.72528e18	0.0838624
$937$	−2.69360e19	−1.30025	−0.650124	−	0.759828i	$-0.725283\pi$
$937$	−2.69360e19	−1.30025	−0.650124	+	0.759828i	$0.725283\pi$
$938$	4.45812e19	2.13714
$939$	−1.98225e19	−0.943697
$940$	5.57674e17	0.0263663
$941$	5.50527e18	0.258491	0.129246	−	0.991613i	$-0.458744\pi$
$941$	5.50527e18	0.258491	0.129246	+	0.991613i	$0.458744\pi$
$942$	1.27694e19	0.595443
$943$	6.47467e18	0.299841
$944$	3.43311e18	0.157896
$945$	3.26233e18	0.149012
$946$	−5.12219e19	−2.32361
$947$	3.46328e18	0.156032	0.0780158	−	0.996952i	$-0.475142\pi$
$947$	3.46328e18	0.156032	0.0780158	+	0.996952i	$0.475142\pi$
$948$	1.21615e19	0.544167
$949$	−8.11850e18	−0.360783
$950$	2.93557e18	0.129566
$951$	6.57984e17	0.0288431
$952$	1.10309e19	0.480256
$953$	−9.28755e18	−0.401603	−0.200802	−	0.979632i	$-0.564355\pi$
$953$	−9.28755e18	−0.401603	−0.200802	+	0.979632i	$0.564355\pi$
$954$	4.26593e18	0.183210
$955$	−1.67112e19	−0.712831
$956$	−4.70715e18	−0.199426
$957$	1.76893e19	0.744360
$958$	−3.53473e19	−1.47734
$959$	−3.83929e18	−0.159378
$960$	−3.63210e18	−0.149760
$961$	−1.80793e19	−0.740423
$962$	1.20193e19	0.488923
$963$	1.74094e18	0.0703418
$964$	−2.25037e19	−0.903135
$965$	2.23367e19	0.890414
$966$	−5.73669e18	−0.227148
$967$	−2.33632e18	−0.0918882	−0.0459441	−	0.998944i	$-0.514630\pi$
$967$	−2.33632e18	−0.0918882	−0.0459441	+	0.998944i	$0.514630\pi$
$968$	3.23359e18	0.126327
$969$	−5.41283e18	−0.210049
$970$	−2.12602e19	−0.819505
$971$	−7.87518e18	−0.301534	−0.150767	−	0.988569i	$-0.548174\pi$
$971$	−7.87518e18	−0.301534	−0.150767	+	0.988569i	$0.548174\pi$
$972$	−1.16856e18	−0.0444446
$973$	3.14107e19	1.18671
$974$	−4.40305e19	−1.65242
$975$	3.35411e18	0.125040
$976$	2.22097e19	0.822467
$977$	−1.02952e19	−0.378723	−0.189362	−	0.981907i	$-0.560642\pi$
$977$	−1.02952e19	−0.378723	−0.189362	+	0.981907i	$0.560642\pi$
$978$	−2.12787e19	−0.777574
$979$	1.03153e19	0.374450
$980$	1.33868e18	0.0482734
$981$	−5.15996e18	−0.184841
$982$	−2.81199e19	−1.00067
$983$	−3.04604e19	−1.07681	−0.538403	−	0.842687i	$-0.680972\pi$
$983$	−3.04604e19	−1.07681	−0.538403	+	0.842687i	$0.680972\pi$
$984$	6.22867e18	0.218740
$985$	2.29001e19	0.798918
$986$	5.30297e19	1.83789
$987$	7.53282e17	0.0259356
$988$	3.69066e18	0.126236
$989$	−1.44907e19	−0.492396
$990$	1.19369e19	0.402961
$991$	−1.84904e19	−0.620108	−0.310054	−	0.950719i	$-0.600347\pi$
$991$	−1.84904e19	−0.620108	−0.310054	+	0.950719i	$0.600347\pi$
$992$	1.80186e19	0.600337
$993$	−3.27519e19	−1.08409
$994$	−1.04416e19	−0.343365
$995$	1.07967e19	0.352730
$996$	−1.35492e19	−0.439772
$997$	−3.53403e19	−1.13960	−0.569799	−	0.821784i	$-0.692979\pi$
$997$	−3.53403e19	−1.13960	−0.569799	+	0.821784i	$0.692979\pi$
$998$	1.96537e19	0.629644
$999$	3.60940e18	0.114884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.7	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.7	✓	31	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +3.33229e6 q^{10} +6.74053e6 q^{11} -4.13751e6 q^{12} +1.09553e7 q^{13} -3.50432e7 q^{14} +2.06286e7 q^{15} -8.13909e7 q^{16} +1.25092e8 q^{17} -6.25829e7 q^{18} +5.93564e7 q^{19} -1.60603e8 q^{20} -2.16936e8 q^{21} -7.93770e8 q^{22} -2.24559e8 q^{23} -2.16027e8 q^{24} -4.19977e8 q^{25} -1.29011e9 q^{26} -3.87420e8 q^{27} +1.68894e9 q^{28} -3.59989e9 q^{29} -2.42924e9 q^{30} +2.51758e9 q^{31} +7.15710e9 q^{32} -4.91384e9 q^{33} -1.47309e10 q^{34} -8.42065e9 q^{35} +3.01625e9 q^{36} -9.31650e9 q^{37} -6.98985e9 q^{38} -7.98643e9 q^{39} -8.38537e9 q^{40} -2.88329e10 q^{41} +2.55465e10 q^{42} +6.45299e10 q^{43} +3.82565e10 q^{44} -1.50382e10 q^{45} +2.64442e10 q^{46} -3.47238e9 q^{47} +5.93340e10 q^{48} -8.33535e9 q^{49} +4.94568e10 q^{50} -9.11920e10 q^{51} +6.21780e10 q^{52} -6.81644e10 q^{53} +4.56229e10 q^{54} -1.90737e11 q^{55} +8.81827e10 q^{56} -4.32708e10 q^{57} +4.23926e11 q^{58} -4.21805e10 q^{59} +1.17080e11 q^{60} -2.72876e11 q^{61} -2.96473e11 q^{62} +1.58146e11 q^{63} -1.76071e11 q^{64} -3.10004e11 q^{65} +5.78658e11 q^{66} -1.27218e12 q^{67} +7.09972e11 q^{68} +1.63703e11 q^{69} +9.91622e11 q^{70} +2.97964e11 q^{71} +1.57484e11 q^{72} -7.41056e11 q^{73} +1.09712e12 q^{74} +3.06163e11 q^{75} +3.36883e11 q^{76} +2.00584e12 q^{77} +9.40488e11 q^{78} -2.93932e12 q^{79} +2.30313e12 q^{80} +2.82430e11 q^{81} +3.39538e12 q^{82} +3.27472e12 q^{83} -1.23124e12 q^{84} -3.53974e12 q^{85} -7.59909e12 q^{86} +2.62432e12 q^{87} +1.99744e12 q^{88} +1.53034e12 q^{89} +1.77092e12 q^{90} +3.26008e12 q^{91} -1.27450e12 q^{92} -1.83532e12 q^{93} +4.08910e11 q^{94} -1.67961e12 q^{95} -5.21753e12 q^{96} -6.38006e12 q^{97} +9.81577e11 q^{98} +3.58219e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * q^99

Introduction

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