LMFDB - Embedded newform 177.14.a.b.1.8

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			1.8
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)

$f(q)$	$=$	$q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} +O(q^{10})$	\(q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} -4.30817e6 q^{10} -1.79804e6 q^{11} -1.03129e6 q^{12} +6.51184e6 q^{13} +3.88799e7 q^{14} -3.20431e7 q^{15} -7.66965e7 q^{16} +9.76681e7 q^{17} -5.20884e7 q^{18} -6.83663e7 q^{19} +6.21814e7 q^{20} +2.89178e8 q^{21} +1.76232e8 q^{22} +1.72252e8 q^{23} -4.84253e8 q^{24} +7.11324e8 q^{25} -6.38249e8 q^{26} -3.87420e8 q^{27} -5.61168e8 q^{28} -5.74570e8 q^{29} +3.14066e9 q^{30} +3.46020e8 q^{31} +2.07560e9 q^{32} +1.31077e9 q^{33} -9.57281e9 q^{34} -1.74359e10 q^{35} +7.51812e8 q^{36} +2.87382e10 q^{37} +6.70083e9 q^{38} -4.74713e9 q^{39} +2.91979e10 q^{40} -3.40879e10 q^{41} -2.83434e10 q^{42} -5.78702e10 q^{43} -2.54363e9 q^{44} +2.33594e10 q^{45} -1.68830e10 q^{46} -1.12577e11 q^{47} +5.59118e10 q^{48} +6.04647e10 q^{49} -6.97194e10 q^{50} -7.12001e10 q^{51} +9.21208e9 q^{52} -1.23263e11 q^{53} +3.79725e10 q^{54} -7.90325e10 q^{55} -2.63502e11 q^{56} +4.98390e10 q^{57} +5.63157e10 q^{58} -4.21805e10 q^{59} -4.53303e10 q^{60} +5.05675e11 q^{61} -3.39147e10 q^{62} -2.10811e11 q^{63} +4.24861e11 q^{64} +2.86227e11 q^{65} -1.28473e11 q^{66} +1.07434e9 q^{67} +1.38168e11 q^{68} -1.25572e11 q^{69} +1.70896e12 q^{70} +8.42822e11 q^{71} +3.53021e11 q^{72} -6.23496e11 q^{73} -2.81674e12 q^{74} -5.18555e11 q^{75} -9.67155e10 q^{76} +7.13243e11 q^{77} +4.65283e11 q^{78} -2.92796e12 q^{79} -3.37118e12 q^{80} +2.82430e11 q^{81} +3.34107e12 q^{82} +1.48483e12 q^{83} +4.09091e11 q^{84} +4.29299e12 q^{85} +5.67207e12 q^{86} +4.18862e11 q^{87} -1.19439e12 q^{88} +8.15790e12 q^{89} -2.28954e12 q^{90} -2.58311e12 q^{91} +2.43679e11 q^{92} -2.52249e11 q^{93} +1.10341e13 q^{94} -3.00503e12 q^{95} -1.51311e12 q^{96} +1.16685e13 q^{97} -5.92636e12 q^{98} -9.55552e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−98.0136	−1.08291	−0.541454	−	0.840731i	$-0.682126\pi$
$2$	−98.0136	−1.08291	−0.541454	+	0.840731i	$0.682126\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	1414.67	0.172689
$5$	43954.8	1.25806	0.629030	−	0.777381i	$-0.283452\pi$
$5$	43954.8	1.25806	0.629030	+	0.777381i	$0.283452\pi$
$6$	71451.9	0.625217
$7$	−396678.	−1.27439	−0.637193	−	0.770704i	$-0.719905\pi$
$7$	−396678.	−1.27439	−0.637193	+	0.770704i	$0.719905\pi$
$8$	664271.	0.895902
$9$	531441.	0.333333
$10$	−4.30817e6	−1.36236
$11$	−1.79804e6	−0.306018	−0.153009	−	0.988225i	$-0.548896\pi$
$11$	−1.79804e6	−0.306018	−0.153009	+	0.988225i	$0.548896\pi$
$12$	−1.03129e6	−0.0997019
$13$	6.51184e6	0.374172	0.187086	−	0.982343i	$-0.440096\pi$
$13$	6.51184e6	0.374172	0.187086	+	0.982343i	$0.440096\pi$
$14$	3.88799e7	1.38004
$15$	−3.20431e7	−0.726342
$16$	−7.66965e7	−1.14287
$17$	9.76681e7	0.981375	0.490687	−	0.871336i	$-0.336746\pi$
$17$	9.76681e7	0.981375	0.490687	+	0.871336i	$0.336746\pi$
$18$	−5.20884e7	−0.360969
$19$	−6.83663e7	−0.333383	−0.166692	−	0.986009i	$-0.553308\pi$
$19$	−6.83663e7	−0.333383	−0.166692	+	0.986009i	$0.553308\pi$
$20$	6.21814e7	0.217253
$21$	2.89178e8	0.735767
$22$	1.76232e8	0.331389
$23$	1.72252e8	0.242624	0.121312	−	0.992614i	$-0.461290\pi$
$23$	1.72252e8	0.242624	0.121312	+	0.992614i	$0.461290\pi$
$24$	−4.84253e8	−0.517249
$25$	7.11324e8	0.582716
$26$	−6.38249e8	−0.405194
$27$	−3.87420e8	−0.192450
$28$	−5.61168e8	−0.220072
$29$	−5.74570e8	−0.179373	−0.0896863	−	0.995970i	$-0.528586\pi$
$29$	−5.74570e8	−0.179373	−0.0896863	+	0.995970i	$0.528586\pi$
$30$	3.14066e9	0.786561
$31$	3.46020e8	0.0700246	0.0350123	−	0.999387i	$-0.488853\pi$
$31$	3.46020e8	0.0700246	0.0350123	+	0.999387i	$0.488853\pi$
$32$	2.07560e9	0.341718
$33$	1.31077e9	0.176680
$34$	−9.57281e9	−1.06274
$35$	−1.74359e10	−1.60326
$36$	7.51812e8	0.0575629
$37$	2.87382e10	1.84140	0.920701	−	0.390268i	$-0.127618\pi$
$37$	2.87382e10	1.84140	0.920701	+	0.390268i	$0.127618\pi$
$38$	6.70083e9	0.361023
$39$	−4.74713e9	−0.216029
$40$	2.91979e10	1.12710
$41$	−3.40879e10	−1.12074	−0.560370	−	0.828243i	$-0.689341\pi$
$41$	−3.40879e10	−1.12074	−0.560370	+	0.828243i	$0.689341\pi$
$42$	−2.83434e10	−0.796768
$43$	−5.78702e10	−1.39608	−0.698040	−	0.716059i	$-0.745944\pi$
$43$	−5.78702e10	−1.39608	−0.698040	+	0.716059i	$0.745944\pi$
$44$	−2.54363e9	−0.0528459
$45$	2.33594e10	0.419354
$46$	−1.68830e10	−0.262739
$47$	−1.12577e11	−1.52339	−0.761697	−	0.647933i	$-0.775634\pi$
$47$	−1.12577e11	−1.52339	−0.761697	+	0.647933i	$0.775634\pi$
$48$	5.59118e10	0.659835
$49$	6.04647e10	0.624061
$50$	−6.97194e10	−0.631028
$51$	−7.12001e10	−0.566597
$52$	9.21208e9	0.0646154
$53$	−1.23263e11	−0.763906	−0.381953	−	0.924182i	$-0.624748\pi$
$53$	−1.23263e11	−0.763906	−0.381953	+	0.924182i	$0.624748\pi$
$54$	3.79725e10	0.208406
$55$	−7.90325e10	−0.384989
$56$	−2.63502e11	−1.14172
$57$	4.98390e10	0.192479
$58$	5.63157e10	0.194244
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−4.53303e10	−0.125431
$61$	5.05675e11	1.25669	0.628344	−	0.777936i	$-0.283733\pi$
$61$	5.05675e11	1.25669	0.628344	+	0.777936i	$0.283733\pi$
$62$	−3.39147e10	−0.0758302
$63$	−2.10811e11	−0.424796
$64$	4.24861e11	0.772818
$65$	2.86227e11	0.470732
$66$	−1.28473e11	−0.191328
$67$	1.07434e9	0.00145096	0.000725482	−	1.00000i	$-0.499769\pi$
$67$	1.07434e9	0.00145096	0.000725482		1.00000i	$0.499769\pi$
$68$	1.38168e11	0.169472
$69$	−1.25572e11	−0.140079
$70$	1.70896e12	1.73618
$71$	8.42822e11	0.780830	0.390415	−	0.920639i	$-0.372332\pi$
$71$	8.42822e11	0.780830	0.390415	+	0.920639i	$0.372332\pi$
$72$	3.53021e11	0.298634
$73$	−6.23496e11	−0.482208	−0.241104	−	0.970499i	$-0.577510\pi$
$73$	−6.23496e11	−0.482208	−0.241104	+	0.970499i	$0.577510\pi$
$74$	−2.81674e12	−1.99407
$75$	−5.18555e11	−0.336431
$76$	−9.67155e10	−0.0575715
$77$	7.13243e11	0.389985
$78$	4.65283e11	0.233939
$79$	−2.92796e12	−1.35515	−0.677577	−	0.735452i	$-0.736970\pi$
$79$	−2.92796e12	−1.35515	−0.677577	+	0.735452i	$0.736970\pi$
$80$	−3.37118e12	−1.43780
$81$	2.82430e11	0.111111
$82$	3.34107e12	1.21366
$83$	1.48483e12	0.498503	0.249252	−	0.968439i	$-0.419815\pi$
$83$	1.48483e12	0.498503	0.249252	+	0.968439i	$0.419815\pi$
$84$	4.09091e11	0.127059
$85$	4.29299e12	1.23463
$86$	5.67207e12	1.51183
$87$	4.18862e11	0.103561
$88$	−1.19439e12	−0.274162
$89$	8.15790e12	1.73998	0.869988	−	0.493073i	$-0.164126\pi$
$89$	8.15790e12	1.73998	0.869988	+	0.493073i	$0.164126\pi$
$90$	−2.28954e12	−0.454121
$91$	−2.58311e12	−0.476840
$92$	2.43679e11	0.0418984
$93$	−2.52249e11	−0.0404287
$94$	1.10341e13	1.64970
$95$	−3.00503e12	−0.419416
$96$	−1.51311e12	−0.197291
$97$	1.16685e13	1.42233	0.711165	−	0.703026i	$-0.248168\pi$
$97$	1.16685e13	1.42233	0.711165	+	0.703026i	$0.248168\pi$
$98$	−5.92636e12	−0.675801
$99$	−9.55552e11	−0.102006
$100$	1.00629e12	0.100629
$101$	5.07705e12	0.475908	0.237954	−	0.971276i	$-0.423523\pi$
$101$	5.07705e12	0.475908	0.237954	+	0.971276i	$0.423523\pi$
$102$	6.97858e12	0.613572
$103$	2.23272e13	1.84243	0.921217	−	0.389050i	$-0.127197\pi$
$103$	2.23272e13	1.84243	0.921217	+	0.389050i	$0.127197\pi$
$104$	4.32562e12	0.335222
$105$	1.27108e13	0.925640
$106$	1.20815e13	0.827239
$107$	−8.65420e12	−0.557484	−0.278742	−	0.960366i	$-0.589917\pi$
$107$	−8.65420e12	−0.557484	−0.278742	+	0.960366i	$0.589917\pi$
$108$	−5.48071e11	−0.0332340
$109$	2.16117e13	1.23429	0.617145	−	0.786850i	$-0.288289\pi$
$109$	2.16117e13	1.23429	0.617145	+	0.786850i	$0.288289\pi$
$110$	7.74626e12	0.416908
$111$	−2.09502e13	−1.06313
$112$	3.04239e13	1.45645
$113$	−1.90976e12	−0.0862915	−0.0431457	−	0.999069i	$-0.513738\pi$
$113$	−1.90976e12	−0.0862915	−0.0431457	+	0.999069i	$0.513738\pi$
$114$	−4.88490e12	−0.208437
$115$	7.57131e12	0.305235
$116$	−8.12825e11	−0.0309756
$117$	3.46066e12	0.124724
$118$	4.13427e12	0.140983
$119$	−3.87428e13	−1.25065
$120$	−2.12853e13	−0.650731
$121$	−3.12898e13	−0.906353
$122$	−4.95630e13	−1.36088
$123$	2.48501e13	0.647059
$124$	4.89504e11	0.0120925
$125$	−2.23897e13	−0.524968
$126$	2.06624e13	0.460014
$127$	−4.53065e13	−0.958157	−0.479079	−	0.877772i	$-0.659029\pi$
$127$	−4.53065e13	−0.958157	−0.479079	+	0.877772i	$0.659029\pi$
$128$	−5.86455e13	−1.17861
$129$	4.21874e13	0.806027
$130$	−2.80541e13	−0.509759
$131$	−1.12857e13	−0.195103	−0.0975515	−	0.995230i	$-0.531101\pi$
$131$	−1.12857e13	−0.195103	−0.0975515	+	0.995230i	$0.531101\pi$
$132$	1.85430e12	0.0305106
$133$	2.71194e13	0.424859
$134$	−1.05300e11	−0.00157126
$135$	−1.70290e13	−0.242114
$136$	6.48781e13	0.879215
$137$	7.67214e13	0.991363	0.495681	−	0.868504i	$-0.334918\pi$
$137$	7.67214e13	0.991363	0.495681	+	0.868504i	$0.334918\pi$
$138$	1.23077e13	0.151693
$139$	−4.18439e13	−0.492080	−0.246040	−	0.969260i	$-0.579129\pi$
$139$	−4.18439e13	−0.492080	−0.246040	+	0.969260i	$0.579129\pi$
$140$	−2.46660e13	−0.276864
$141$	8.20684e13	0.879533
$142$	−8.26080e13	−0.845567
$143$	−1.17085e13	−0.114503
$144$	−4.07597e13	−0.380956
$145$	−2.52551e13	−0.225662
$146$	6.11111e13	0.522187
$147$	−4.40788e13	−0.360302
$148$	4.06550e13	0.317990
$149$	−8.40108e13	−0.628962	−0.314481	−	0.949264i	$-0.601830\pi$
$149$	−8.40108e13	−0.628962	−0.314481	+	0.949264i	$0.601830\pi$
$150$	5.08254e13	0.364324
$151$	2.33896e14	1.60573	0.802865	−	0.596161i	$-0.203308\pi$
$151$	2.33896e14	1.60573	0.802865	+	0.596161i	$0.203308\pi$
$152$	−4.54138e13	−0.298679
$153$	5.19049e13	0.327125
$154$	−6.99076e13	−0.422318
$155$	1.52093e13	0.0880952
$156$	−6.71561e12	−0.0373057
$157$	1.54696e14	0.824385	0.412192	−	0.911097i	$-0.364763\pi$
$157$	1.54696e14	0.824385	0.412192	+	0.911097i	$0.364763\pi$
$158$	2.86980e14	1.46751
$159$	8.98588e13	0.441041
$160$	9.12325e13	0.429902
$161$	−6.83286e13	−0.309197
$162$	−2.76819e13	−0.120323
$163$	2.14513e14	0.895846	0.447923	−	0.894072i	$-0.352164\pi$
$163$	2.14513e14	0.895846	0.447923	+	0.894072i	$0.352164\pi$
$164$	−4.82230e13	−0.193539
$165$	5.76147e13	0.222274
$166$	−1.45533e14	−0.539833
$167$	4.60772e14	1.64372	0.821862	−	0.569687i	$-0.192936\pi$
$167$	4.60772e14	1.64372	0.821862	+	0.569687i	$0.192936\pi$
$168$	1.92093e14	0.659175
$169$	−2.60471e14	−0.859995
$170$	−4.20771e14	−1.33699
$171$	−3.63327e13	−0.111128
$172$	−8.18671e13	−0.241087
$173$	−1.40439e14	−0.398280	−0.199140	−	0.979971i	$-0.563815\pi$
$173$	−1.40439e14	−0.398280	−0.199140	+	0.979971i	$0.563815\pi$
$174$	−4.10541e13	−0.112147
$175$	−2.82167e14	−0.742606
$176$	1.37903e14	0.349738
$177$	3.07496e13	0.0751646
$178$	−7.99585e14	−1.88423
$179$	−3.25729e14	−0.740136	−0.370068	−	0.929005i	$-0.620666\pi$
$179$	−3.25729e14	−0.740136	−0.370068	+	0.929005i	$0.620666\pi$
$180$	3.30458e13	0.0724176
$181$	−6.48931e13	−0.137179	−0.0685896	−	0.997645i	$-0.521850\pi$
$181$	−6.48931e13	−0.137179	−0.0685896	+	0.997645i	$0.521850\pi$
$182$	2.53179e14	0.516374
$183$	−3.68637e14	−0.725549
$184$	1.14422e14	0.217367
$185$	1.26318e15	2.31660
$186$	2.47238e13	0.0437806
$187$	−1.75611e14	−0.300318
$188$	−1.59259e14	−0.263073
$189$	1.53681e14	0.245256
$190$	2.94534e14	0.454189
$191$	−1.25464e15	−1.86984	−0.934918	−	0.354865i	$-0.884527\pi$
$191$	−1.25464e15	−1.86984	−0.934918	+	0.354865i	$0.884527\pi$
$192$	−3.09724e14	−0.446187
$193$	−1.13796e13	−0.0158490	−0.00792452	−	0.999969i	$-0.502522\pi$
$193$	−1.13796e13	−0.0158490	−0.00792452	+	0.999969i	$0.502522\pi$
$194$	−1.14368e15	−1.54025
$195$	−2.08659e14	−0.271777
$196$	8.55374e13	0.107768
$197$	3.13415e14	0.382022	0.191011	−	0.981588i	$-0.438823\pi$
$197$	3.13415e14	0.382022	0.191011	+	0.981588i	$0.438823\pi$
$198$	9.36571e13	0.110463
$199$	6.90722e14	0.788421	0.394211	−	0.919020i	$-0.371018\pi$
$199$	6.90722e14	0.788421	0.394211	+	0.919020i	$0.371018\pi$
$200$	4.72512e14	0.522056
$201$	−7.83196e11	−0.000837714 0
$202$	−4.97620e14	−0.515364
$203$	2.27919e14	0.228590
$204$	−1.00724e14	−0.0978449
$205$	−1.49833e15	−1.40996
$206$	−2.18837e15	−1.99518
$207$	9.15418e13	0.0808746
$208$	−4.99435e14	−0.427630
$209$	1.22925e14	0.102021
$210$	−1.24583e15	−1.00238
$211$	−1.09845e15	−0.856925	−0.428463	−	0.903560i	$-0.640945\pi$
$211$	−1.09845e15	−0.856925	−0.428463	+	0.903560i	$0.640945\pi$
$212$	−1.74376e14	−0.131918
$213$	−6.14417e14	−0.450812
$214$	8.48230e14	0.603704
$215$	−2.54368e15	−1.75635
$216$	−2.57352e14	−0.172416
$217$	−1.37259e14	−0.0892384
$218$	−2.11824e15	−1.33662
$219$	4.54528e14	0.278403
$220$	−1.11805e14	−0.0664833
$221$	6.35999e14	0.367203
$222$	2.05340e15	1.15128
$223$	−2.02103e14	−0.110050	−0.0550252	−	0.998485i	$-0.517524\pi$
$223$	−2.02103e14	−0.110050	−0.0550252	+	0.998485i	$0.517524\pi$
$224$	−8.23344e14	−0.435481
$225$	3.78026e14	0.194239
$226$	1.87182e14	0.0934457
$227$	3.68958e15	1.78982	0.894908	−	0.446250i	$-0.147241\pi$
$227$	3.68958e15	1.78982	0.894908	+	0.446250i	$0.147241\pi$
$228$	7.05056e13	0.0332389
$229$	−1.70193e15	−0.779848	−0.389924	−	0.920847i	$-0.627499\pi$
$229$	−1.70193e15	−0.779848	−0.389924	+	0.920847i	$0.627499\pi$
$230$	−7.42091e14	−0.330542
$231$	−5.19954e14	−0.225158
$232$	−3.81670e14	−0.160700
$233$	1.44631e13	0.00592172	0.00296086	−	0.999996i	$-0.499058\pi$
$233$	1.44631e13	0.00592172	0.00296086	+	0.999996i	$0.499058\pi$
$234$	−3.39192e14	−0.135065
$235$	−4.94829e15	−1.91652
$236$	−5.96714e13	−0.0224822
$237$	2.13448e15	0.782398
$238$	3.79732e15	1.35434
$239$	−1.24049e15	−0.430534	−0.215267	−	0.976555i	$-0.569062\pi$
$239$	−1.24049e15	−0.430534	−0.215267	+	0.976555i	$0.569062\pi$
$240$	2.45759e15	0.830112
$241$	−5.51883e15	−1.81441	−0.907207	−	0.420685i	$-0.861790\pi$
$241$	−5.51883e15	−1.81441	−0.907207	+	0.420685i	$0.861790\pi$
$242$	3.06682e15	0.981497
$243$	−2.05891e14	−0.0641500
$244$	7.15361e14	0.217016
$245$	2.65771e15	0.785107
$246$	−2.43564e15	−0.700705
$247$	−4.45190e14	−0.124743
$248$	2.29851e14	0.0627352
$249$	−1.08244e15	−0.287811
$250$	2.19449e15	0.568492
$251$	−4.36406e15	−1.10157	−0.550784	−	0.834648i	$-0.685671\pi$
$251$	−4.36406e15	−1.10157	−0.550784	+	0.834648i	$0.685671\pi$
$252$	−2.98227e14	−0.0733574
$253$	−3.09716e14	−0.0742472
$254$	4.44066e15	1.03760
$255$	−3.12959e15	−0.712813
$256$	2.26759e15	0.503506
$257$	−3.31441e15	−0.717531	−0.358766	−	0.933428i	$-0.616802\pi$
$257$	−3.31441e15	−0.717531	−0.358766	+	0.933428i	$0.616802\pi$
$258$	−4.13494e15	−0.872853
$259$	−1.13998e16	−2.34666
$260$	4.04915e14	0.0812901
$261$	−3.05350e14	−0.0597909
$262$	1.10615e15	0.211279
$263$	−9.91017e15	−1.84658	−0.923291	−	0.384101i	$-0.874511\pi$
$263$	−9.91017e15	−1.84658	−0.923291	+	0.384101i	$0.874511\pi$
$264$	8.70707e14	0.158287
$265$	−5.41801e15	−0.961040
$266$	−2.65807e15	−0.460083
$267$	−5.94711e15	−1.00458
$268$	1.51984e12	0.000250565 0
$269$	1.08935e15	0.175299	0.0876495	−	0.996151i	$-0.472064\pi$
$269$	1.08935e15	0.175299	0.0876495	+	0.996151i	$0.472064\pi$
$270$	1.66907e15	0.262187
$271$	−1.62457e13	−0.00249137	−0.00124568	−	0.999999i	$-0.500397\pi$
$271$	−1.62457e13	−0.00249137	−0.00124568	+	0.999999i	$0.500397\pi$
$272$	−7.49081e15	−1.12158
$273$	1.88308e15	0.275304
$274$	−7.51974e15	−1.07355
$275$	−1.27899e15	−0.178322
$276$	−1.77642e14	−0.0241901
$277$	−5.67135e15	−0.754341	−0.377171	−	0.926144i	$-0.623103\pi$
$277$	−5.67135e15	−0.754341	−0.377171	+	0.926144i	$0.623103\pi$
$278$	4.10127e15	0.532877
$279$	1.83889e14	0.0233415
$280$	−1.15822e16	−1.43636
$281$	1.53869e15	0.186449	0.0932243	−	0.995645i	$-0.470283\pi$
$281$	1.53869e15	0.186449	0.0932243	+	0.995645i	$0.470283\pi$
$282$	−8.04382e15	−0.952452
$283$	−6.94777e15	−0.803958	−0.401979	−	0.915649i	$-0.631677\pi$
$283$	−6.94777e15	−0.803958	−0.401979	+	0.915649i	$0.631677\pi$
$284$	1.19231e15	0.134841
$285$	2.19067e15	0.242150
$286$	1.14760e15	0.123997
$287$	1.35219e16	1.42826
$288$	1.10306e15	0.113906
$289$	−3.65514e14	−0.0369035
$290$	2.47535e15	0.244371
$291$	−8.50636e15	−0.821182
$292$	−8.82038e14	−0.0832720
$293$	−3.05245e15	−0.281844	−0.140922	−	0.990021i	$-0.545007\pi$
$293$	−3.05245e15	−0.281844	−0.140922	+	0.990021i	$0.545007\pi$
$294$	4.32032e15	0.390174
$295$	−1.85404e15	−0.163786
$296$	1.90900e16	1.64972
$297$	6.96597e14	0.0588932
$298$	8.23420e15	0.681108
$299$	1.12168e15	0.0907832
$300$	−7.33582e14	−0.0580979
$301$	2.29559e16	1.77915
$302$	−2.29250e16	−1.73886
$303$	−3.70117e15	−0.274766
$304$	5.24346e15	0.381013
$305$	2.22268e16	1.58099
$306$	−5.08738e15	−0.354246
$307$	5.47480e15	0.373223	0.186612	−	0.982434i	$-0.440249\pi$
$307$	5.47480e15	0.373223	0.186612	+	0.982434i	$0.440249\pi$
$308$	1.00900e15	0.0673461
$309$	−1.62765e16	−1.06373
$310$	−1.49072e15	−0.0953990
$311$	1.11347e16	0.697806	0.348903	−	0.937159i	$-0.386554\pi$
$311$	1.11347e16	0.697806	0.348903	+	0.937159i	$0.386554\pi$
$312$	−3.15338e15	−0.193540
$313$	−6.11381e15	−0.367514	−0.183757	−	0.982972i	$-0.558826\pi$
$313$	−6.11381e15	−0.367514	−0.183757	+	0.982972i	$0.558826\pi$
$314$	−1.51623e16	−0.892733
$315$	−9.26617e15	−0.534419
$316$	−4.14208e15	−0.234020
$317$	2.22496e15	0.123151	0.0615753	−	0.998102i	$-0.480388\pi$
$317$	2.22496e15	0.123151	0.0615753	+	0.998102i	$0.480388\pi$
$318$	−8.80738e15	−0.477607
$319$	1.03310e15	0.0548912
$320$	1.86747e16	0.972252
$321$	6.30892e15	0.321864
$322$	6.69714e15	0.334831
$323$	−6.67721e15	−0.327174
$324$	3.99544e14	0.0191876
$325$	4.63202e15	0.218036
$326$	−2.10251e16	−0.970118
$327$	−1.57549e16	−0.712617
$328$	−2.26436e16	−1.00407
$329$	4.46567e16	1.94139
$330$	−5.64703e15	−0.240702
$331$	1.77998e16	0.743934	0.371967	−	0.928246i	$-0.378684\pi$
$331$	1.77998e16	0.743934	0.371967	+	0.928246i	$0.378684\pi$
$332$	2.10053e15	0.0860859
$333$	1.52727e16	0.613801
$334$	−4.51619e16	−1.78000
$335$	4.72225e13	0.00182540
$336$	−2.21790e16	−0.840885
$337$	−8.05639e14	−0.0299603	−0.0149801	−	0.999888i	$-0.504769\pi$
$337$	−8.05639e14	−0.0299603	−0.0149801	+	0.999888i	$0.504769\pi$
$338$	2.55297e16	0.931295
$339$	1.39221e15	0.0498204
$340$	6.07314e15	0.213207
$341$	−6.22158e14	−0.0214288
$342$	3.56110e15	0.120341
$343$	1.44487e16	0.479091
$344$	−3.84415e16	−1.25075
$345$	−5.51948e15	−0.176228
$346$	1.37649e16	0.431300
$347$	−2.01330e16	−0.619108	−0.309554	−	0.950882i	$-0.600180\pi$
$347$	−2.01330e16	−0.619108	−0.309554	+	0.950882i	$0.600180\pi$
$348$	5.92549e14	0.0178838
$349$	−3.93224e15	−0.116486	−0.0582431	−	0.998302i	$-0.518550\pi$
$349$	−3.93224e15	−0.116486	−0.0582431	+	0.998302i	$0.518550\pi$
$350$	2.76562e16	0.804173
$351$	−2.52282e15	−0.0720095
$352$	−3.73200e15	−0.104572
$353$	2.27174e16	0.624918	0.312459	−	0.949931i	$-0.398847\pi$
$353$	2.27174e16	0.624918	0.312459	+	0.949931i	$0.398847\pi$
$354$	−3.01388e15	−0.0813963
$355$	3.70461e16	0.982331
$356$	1.15407e16	0.300474
$357$	2.82435e16	0.722064
$358$	3.19259e16	0.801499
$359$	3.34599e16	0.824917	0.412458	−	0.910976i	$-0.364670\pi$
$359$	3.34599e16	0.824917	0.412458	+	0.910976i	$0.364670\pi$
$360$	1.55170e16	0.375699
$361$	−3.73790e16	−0.888856
$362$	6.36041e15	0.148552
$363$	2.28102e16	0.523283
$364$	−3.65423e15	−0.0823450
$365$	−2.74056e16	−0.606647
$366$	3.61314e16	0.785702
$367$	−2.96174e16	−0.632729	−0.316364	−	0.948638i	$-0.602462\pi$
$367$	−2.96174e16	−0.632729	−0.316364	+	0.948638i	$0.602462\pi$
$368$	−1.32111e16	−0.277287
$369$	−1.81157e16	−0.373580
$370$	−1.23809e17	−2.50866
$371$	4.88958e16	0.973511
$372$	−3.56848e14	−0.00698159
$373$	−3.03136e15	−0.0582814	−0.0291407	−	0.999575i	$-0.509277\pi$
$373$	−3.03136e15	−0.0582814	−0.0291407	+	0.999575i	$0.509277\pi$
$374$	1.72123e16	0.325217
$375$	1.63221e16	0.303091
$376$	−7.47814e16	−1.36481
$377$	−3.74151e15	−0.0671163
$378$	−1.50629e16	−0.265589
$379$	1.68088e16	0.291329	0.145664	−	0.989334i	$-0.453468\pi$
$379$	1.68088e16	0.291329	0.145664	+	0.989334i	$0.453468\pi$
$380$	−4.25111e15	−0.0724285
$381$	3.30285e16	0.553192
$382$	1.22972e17	2.02486
$383$	7.39427e16	1.19702	0.598512	−	0.801114i	$-0.295759\pi$
$383$	7.39427e16	1.19702	0.598512	+	0.801114i	$0.295759\pi$
$384$	4.27525e16	0.680470
$385$	3.13505e16	0.490625
$386$	1.11535e15	0.0171630
$387$	−3.07546e16	−0.465360
$388$	1.65071e16	0.245620
$389$	2.70944e16	0.396467	0.198234	−	0.980155i	$-0.436480\pi$
$389$	2.70944e16	0.396467	0.198234	+	0.980155i	$0.436480\pi$
$390$	2.04514e16	0.294309
$391$	1.68235e16	0.238105
$392$	4.01649e16	0.559098
$393$	8.22726e15	0.112643
$394$	−3.07189e16	−0.413695
$395$	−1.28698e17	−1.70487
$396$	−1.35179e15	−0.0176153
$397$	−1.12309e16	−0.143971	−0.0719854	−	0.997406i	$-0.522934\pi$
$397$	−1.12309e16	−0.143971	−0.0719854	+	0.997406i	$0.522934\pi$
$398$	−6.77002e16	−0.853787
$399$	−1.97701e16	−0.245293
$400$	−5.45560e16	−0.665967
$401$	2.22390e16	0.267101	0.133551	−	0.991042i	$-0.457362\pi$
$401$	2.22390e16	0.267101	0.133551	+	0.991042i	$0.457362\pi$
$402$	7.67638e13	0.000907167 0
$403$	2.25323e15	0.0262013
$404$	7.18234e15	0.0821840
$405$	1.24141e16	0.139785
$406$	−2.23392e16	−0.247542
$407$	−5.16725e16	−0.563502
$408$	−4.72961e16	−0.507615
$409$	−1.55417e17	−1.64172	−0.820858	−	0.571133i	$-0.806504\pi$
$409$	−1.55417e17	−1.64172	−0.820858	+	0.571133i	$0.806504\pi$
$410$	1.46856e17	1.52685
$411$	−5.59299e16	−0.572364
$412$	3.15855e16	0.318168
$413$	1.67321e16	0.165911
$414$	−8.97234e15	−0.0875797
$415$	6.52653e16	0.627147
$416$	1.35159e16	0.127862
$417$	3.05042e16	0.284103
$418$	−1.20484e16	−0.110480
$419$	9.43507e16	0.851832	0.425916	−	0.904763i	$-0.359952\pi$
$419$	9.43507e16	0.851832	0.425916	+	0.904763i	$0.359952\pi$
$420$	1.79815e16	0.159848
$421$	2.00336e17	1.75358	0.876792	−	0.480870i	$-0.159679\pi$
$421$	2.00336e17	1.75358	0.876792	+	0.480870i	$0.159679\pi$
$422$	1.07663e17	0.927971
$423$	−5.98279e16	−0.507798
$424$	−8.18801e16	−0.684384
$425$	6.94736e16	0.571863
$426$	6.02212e16	0.488188
$427$	−2.00590e17	−1.60151
$428$	−1.22428e16	−0.0962713
$429$	8.53553e15	0.0661086
$430$	2.49315e17	1.90197
$431$	9.65868e16	0.725797	0.362899	−	0.931829i	$-0.381787\pi$
$431$	9.65868e16	0.725797	0.362899	+	0.931829i	$0.381787\pi$
$432$	2.97138e16	0.219945
$433$	−6.71250e16	−0.489455	−0.244728	−	0.969592i	$-0.578699\pi$
$433$	−6.71250e16	−0.489455	−0.244728	+	0.969592i	$0.578699\pi$
$434$	1.34532e16	0.0966370
$435$	1.84110e16	0.130286
$436$	3.05734e16	0.213148
$437$	−1.17762e16	−0.0808867
$438$	−4.45500e16	−0.301485
$439$	−1.19945e17	−0.799763	−0.399881	−	0.916567i	$-0.630949\pi$
$439$	−1.19945e17	−0.799763	−0.399881	+	0.916567i	$0.630949\pi$
$440$	−5.24990e16	−0.344912
$441$	3.21334e16	0.208020
$442$	−6.23366e16	−0.397647
$443$	−1.11001e16	−0.0697752	−0.0348876	−	0.999391i	$-0.511107\pi$
$443$	−1.11001e16	−0.0697752	−0.0348876	+	0.999391i	$0.511107\pi$
$444$	−2.96375e16	−0.183591
$445$	3.58579e17	2.18900
$446$	1.98089e16	0.119174
$447$	6.12439e16	0.363131
$448$	−1.68533e17	−0.984869
$449$	−2.25580e17	−1.29927	−0.649635	−	0.760247i	$-0.725078\pi$
$449$	−2.25580e17	−1.29927	−0.649635	+	0.760247i	$0.725078\pi$
$450$	−3.70517e16	−0.210343
$451$	6.12913e16	0.342966
$452$	−2.70167e15	−0.0149016
$453$	−1.70510e17	−0.927069
$454$	−3.61629e17	−1.93821
$455$	−1.13540e17	−0.599894
$456$	3.31066e16	0.172442
$457$	−2.82152e17	−1.44886	−0.724432	−	0.689347i	$-0.757898\pi$
$457$	−2.82152e17	−1.44886	−0.724432	+	0.689347i	$0.757898\pi$
$458$	1.66812e17	0.844504
$459$	−3.78386e16	−0.188866
$460$	1.07109e16	0.0527107
$461$	−1.95029e17	−0.946333	−0.473167	−	0.880973i	$-0.656889\pi$
$461$	−1.95029e17	−0.946333	−0.473167	+	0.880973i	$0.656889\pi$
$462$	5.09626e16	0.243825
$463$	2.97176e17	1.40197	0.700983	−	0.713178i	$-0.252745\pi$
$463$	2.97176e17	1.40197	0.700983	+	0.713178i	$0.252745\pi$
$464$	4.40675e16	0.204999
$465$	−1.10876e16	−0.0508618
$466$	−1.41758e15	−0.00641268
$467$	−3.64073e17	−1.62416	−0.812079	−	0.583548i	$-0.801664\pi$
$467$	−3.64073e17	−1.62416	−0.812079	+	0.583548i	$0.801664\pi$
$468$	4.89568e15	0.0215385
$469$	−4.26168e14	−0.00184909
$470$	4.85000e17	2.07542
$471$	−1.12773e17	−0.475959
$472$	−2.80193e16	−0.116636
$473$	1.04053e17	0.427225
$474$	−2.09208e17	−0.847265
$475$	−4.86306e16	−0.194268
$476$	−5.48082e16	−0.215973
$477$	−6.55071e16	−0.254635
$478$	1.21585e17	0.466229
$479$	−1.29900e17	−0.491392	−0.245696	−	0.969347i	$-0.579016\pi$
$479$	−1.29900e17	−0.491392	−0.245696	+	0.969347i	$0.579016\pi$
$480$	−6.65085e16	−0.248204
$481$	1.87139e17	0.689002
$482$	5.40920e17	1.96484
$483$	4.98116e16	0.178515
$484$	−4.42646e16	−0.156517
$485$	5.12889e17	1.78938
$486$	2.01801e16	0.0694686
$487$	−2.01035e17	−0.682862	−0.341431	−	0.939907i	$-0.610912\pi$
$487$	−2.01035e17	−0.682862	−0.341431	+	0.939907i	$0.610912\pi$
$488$	3.35905e17	1.12587
$489$	−1.56380e17	−0.517217
$490$	−2.60492e17	−0.850198
$491$	−3.03144e17	−0.976382	−0.488191	−	0.872737i	$-0.662343\pi$
$491$	−3.03144e17	−0.976382	−0.488191	+	0.872737i	$0.662343\pi$
$492$	3.51545e16	0.111740
$493$	−5.61172e16	−0.176032
$494$	4.36347e16	0.135085
$495$	−4.20011e16	−0.128330
$496$	−2.65386e16	−0.0800289
$497$	−3.34329e17	−0.995079
$498$	1.06094e17	0.311673
$499$	−6.67583e16	−0.193576	−0.0967880	−	0.995305i	$-0.530857\pi$
$499$	−6.67583e16	−0.193576	−0.0967880	+	0.995305i	$0.530857\pi$
$500$	−3.16739e16	−0.0906561
$501$	−3.35903e17	−0.949004
$502$	4.27737e17	1.19290
$503$	−4.65095e17	−1.28041	−0.640206	−	0.768204i	$-0.721151\pi$
$503$	−4.65095e17	−1.28041	−0.640206	+	0.768204i	$0.721151\pi$
$504$	−1.40036e17	−0.380575
$505$	2.23161e17	0.598721
$506$	3.03564e16	0.0804029
$507$	1.89883e17	0.496518
$508$	−6.40936e16	−0.165463
$509$	3.08399e17	0.786044	0.393022	−	0.919529i	$-0.371430\pi$
$509$	3.08399e17	0.786044	0.393022	+	0.919529i	$0.371430\pi$
$510$	3.06742e17	0.771911
$511$	2.47327e17	0.614520
$512$	2.58169e17	0.633358
$513$	2.64865e16	0.0641596
$514$	3.24857e17	0.777020
$515$	9.81387e17	2.31789
$516$	5.96811e16	0.139192
$517$	2.02417e17	0.466186
$518$	1.11734e18	2.54121
$519$	1.02380e17	0.229947
$520$	1.90132e17	0.421729
$521$	−2.52706e17	−0.553567	−0.276784	−	0.960932i	$-0.589269\pi$
$521$	−2.52706e17	−0.553567	−0.276784	+	0.960932i	$0.589269\pi$
$522$	2.99285e16	0.0647480
$523$	−7.28616e17	−1.55682	−0.778409	−	0.627757i	$-0.783973\pi$
$523$	−7.28616e17	−1.55682	−0.778409	+	0.627757i	$0.783973\pi$
$524$	−1.59655e16	−0.0336921
$525$	2.05699e17	0.428744
$526$	9.71331e17	1.99968
$527$	3.37952e16	0.0687204
$528$	−1.00532e17	−0.201921
$529$	−4.74366e17	−0.941134
$530$	5.31038e17	1.04072
$531$	−2.24165e16	−0.0433963
$532$	3.83650e16	0.0733684
$533$	−2.21975e17	−0.419350
$534$	5.82898e17	1.08786
$535$	−3.80394e17	−0.701349
$536$	7.13654e14	0.00129992
$537$	2.37456e17	0.427318
$538$	−1.06772e17	−0.189833
$539$	−1.08718e17	−0.190974
$540$	−2.40904e16	−0.0418103
$541$	1.03306e17	0.177151	0.0885756	−	0.996069i	$-0.471769\pi$
$541$	1.03306e17	0.177151	0.0885756	+	0.996069i	$0.471769\pi$
$542$	1.59230e15	0.00269792
$543$	4.73071e16	0.0792004
$544$	2.02720e17	0.335354
$545$	9.49939e17	1.55281
$546$	−1.84568e17	−0.298129
$547$	−1.17000e18	−1.86753	−0.933763	−	0.357892i	$-0.883495\pi$
$547$	−1.17000e18	−1.86753	−0.933763	+	0.357892i	$0.883495\pi$
$548$	1.08535e17	0.171197
$549$	2.68736e17	0.418896
$550$	1.25358e17	0.193106
$551$	3.92812e16	0.0597998
$552$	−8.34136e16	−0.125497
$553$	1.16146e18	1.72699
$554$	5.55869e17	0.816882
$555$	−9.20861e17	−1.33749
$556$	−5.91951e16	−0.0849767
$557$	7.54719e16	0.107084	0.0535422	−	0.998566i	$-0.482949\pi$
$557$	7.54719e16	0.107084	0.0535422	+	0.998566i	$0.482949\pi$
$558$	−1.80237e16	−0.0252767
$559$	−3.76842e17	−0.522375
$560$	1.33728e18	1.83231
$561$	1.28021e17	0.173389
$562$	−1.50812e17	−0.201907
$563$	4.98148e17	0.659256	0.329628	−	0.944111i	$-0.393077\pi$
$563$	4.98148e17	0.659256	0.329628	+	0.944111i	$0.393077\pi$
$564$	1.16099e17	0.151885
$565$	−8.39430e16	−0.108560
$566$	6.80975e17	0.870612
$567$	−1.12034e17	−0.141599
$568$	5.59862e17	0.699547
$569$	2.49767e16	0.0308535	0.0154268	−	0.999881i	$-0.495089\pi$
$569$	2.49767e16	0.0308535	0.0154268	+	0.999881i	$0.495089\pi$
$570$	−2.14715e17	−0.262226
$571$	−3.03773e17	−0.366787	−0.183394	−	0.983040i	$-0.558708\pi$
$571$	−3.03773e17	−0.366787	−0.183394	+	0.983040i	$0.558708\pi$
$572$	−1.65637e16	−0.0197735
$573$	9.14635e17	1.07955
$574$	−1.32533e18	−1.54667
$575$	1.22527e17	0.141381
$576$	2.25789e17	0.257606
$577$	−1.35220e18	−1.52545	−0.762724	−	0.646724i	$-0.776139\pi$
$577$	−1.35220e18	−1.52545	−0.762724	+	0.646724i	$0.776139\pi$
$578$	3.58253e16	0.0399631
$579$	8.29570e15	0.00915045
$580$	−3.57276e16	−0.0389692
$581$	−5.88999e17	−0.635286
$582$	8.33739e17	0.889264
$583$	2.21632e17	0.233769
$584$	−4.14170e17	−0.432011
$585$	1.52113e17	0.156911
$586$	2.99182e17	0.305211
$587$	−1.28182e18	−1.29324	−0.646619	−	0.762813i	$-0.723818\pi$
$587$	−1.28182e18	−1.29324	−0.646619	+	0.762813i	$0.723818\pi$
$588$	−6.23567e16	−0.0622201
$589$	−2.36561e16	−0.0233450
$590$	1.81721e17	0.177365
$591$	−2.28479e17	−0.220561
$592$	−2.20412e18	−2.10448
$593$	6.39424e17	0.603856	0.301928	−	0.953331i	$-0.402370\pi$
$593$	6.39424e17	0.603856	0.301928	+	0.953331i	$0.402370\pi$
$594$	−6.82760e16	−0.0637759
$595$	−1.70293e18	−1.57339
$596$	−1.18847e17	−0.108615
$597$	−5.03536e17	−0.455195
$598$	−1.09940e17	−0.0983098
$599$	−7.65253e17	−0.676910	−0.338455	−	0.940983i	$-0.609904\pi$
$599$	−7.65253e17	−0.676910	−0.338455	+	0.940983i	$0.609904\pi$
$600$	−3.44461e17	−0.301409
$601$	1.09286e18	0.945976	0.472988	−	0.881069i	$-0.343175\pi$
$601$	1.09286e18	0.945976	0.472988	+	0.881069i	$0.343175\pi$
$602$	−2.24999e18	−1.92665
$603$	5.70950e14	0.000483655 0
$604$	3.30885e17	0.277292
$605$	−1.37534e18	−1.14025
$606$	3.62765e17	0.297546
$607$	6.43496e17	0.522179	0.261089	−	0.965315i	$-0.415918\pi$
$607$	6.43496e17	0.522179	0.261089	+	0.965315i	$0.415918\pi$
$608$	−1.41901e17	−0.113923
$609$	−1.66153e17	−0.131976
$610$	−2.17853e18	−1.71206
$611$	−7.33081e17	−0.570013
$612$	7.34281e16	0.0564908
$613$	−1.64149e18	−1.24953	−0.624763	−	0.780814i	$-0.714804\pi$
$613$	−1.64149e18	−1.24953	−0.624763	+	0.780814i	$0.714804\pi$
$614$	−5.36605e17	−0.404166
$615$	1.09228e18	0.814040
$616$	4.73787e17	0.349388
$617$	−2.19011e18	−1.59813	−0.799066	−	0.601244i	$-0.794672\pi$
$617$	−2.19011e18	−1.59813	−0.799066	+	0.601244i	$0.794672\pi$
$618$	1.59532e18	1.15192
$619$	2.33506e18	1.66843	0.834216	−	0.551438i	$-0.185921\pi$
$619$	2.33506e18	1.66843	0.834216	+	0.551438i	$0.185921\pi$
$620$	2.15160e16	0.0152131
$621$	−6.67340e16	−0.0466930
$622$	−1.09135e18	−0.755660
$623$	−3.23606e18	−2.21740
$624$	3.64088e17	0.246892
$625$	−1.85245e18	−1.24316
$626$	5.99237e17	0.397984
$627$	−8.96126e16	−0.0589020
$628$	2.18843e17	0.142362
$629$	2.80681e18	1.80711
$630$	9.08210e17	0.578726
$631$	2.95666e17	0.186471	0.0932354	−	0.995644i	$-0.470279\pi$
$631$	2.95666e17	0.186471	0.0932354	+	0.995644i	$0.470279\pi$
$632$	−1.94496e18	−1.21408
$633$	8.00767e17	0.494746
$634$	−2.18076e17	−0.133361
$635$	−1.99144e18	−1.20542
$636$	1.27120e17	0.0761629
$637$	3.93736e17	0.233507
$638$	−1.01258e17	−0.0594421
$639$	4.47910e17	0.260277
$640$	−2.57775e18	−1.48276
$641$	−1.72246e18	−0.980780	−0.490390	−	0.871503i	$-0.663146\pi$
$641$	−1.72246e18	−0.980780	−0.490390	+	0.871503i	$0.663146\pi$
$642$	−6.18360e17	−0.348549
$643$	9.63720e17	0.537749	0.268875	−	0.963175i	$-0.413348\pi$
$643$	9.63720e17	0.537749	0.268875	+	0.963175i	$0.413348\pi$
$644$	−9.66622e16	−0.0533948
$645$	1.85434e18	1.01403
$646$	6.54457e17	0.354299
$647$	1.08203e18	0.579909	0.289955	−	0.957040i	$-0.406360\pi$
$647$	1.08203e18	0.579909	0.289955	+	0.957040i	$0.406360\pi$
$648$	1.87610e17	0.0995446
$649$	7.58423e16	0.0398401
$650$	−4.54001e17	−0.236113
$651$	1.00062e17	0.0515218
$652$	3.03464e17	0.154703
$653$	−8.01051e17	−0.404319	−0.202160	−	0.979353i	$-0.564796\pi$
$653$	−8.01051e17	−0.404319	−0.202160	+	0.979353i	$0.564796\pi$
$654$	1.54420e18	0.771699
$655$	−4.96060e17	−0.245451
$656$	2.61442e18	1.28086
$657$	−3.31351e17	−0.160736
$658$	−4.37697e18	−2.10235
$659$	−1.24626e18	−0.592724	−0.296362	−	0.955076i	$-0.595773\pi$
$659$	−1.24626e18	−0.592724	−0.296362	+	0.955076i	$0.595773\pi$
$660$	8.15056e16	0.0383841
$661$	2.34871e18	1.09527	0.547633	−	0.836719i	$-0.315529\pi$
$661$	2.34871e18	1.09527	0.547633	+	0.836719i	$0.315529\pi$
$662$	−1.74463e18	−0.805611
$663$	−4.63643e17	−0.212005
$664$	9.86327e17	0.446610
$665$	1.19203e18	0.534499
$666$	−1.49693e18	−0.664690
$667$	−9.89709e16	−0.0435201
$668$	6.51838e17	0.283853
$669$	1.47333e17	0.0635377
$670$	−4.62845e15	−0.00197674
$671$	−9.09223e17	−0.384569
$672$	6.00218e17	0.251425
$673$	4.08779e18	1.69586	0.847931	−	0.530106i	$-0.177848\pi$
$673$	4.08779e18	1.69586	0.847931	+	0.530106i	$0.177848\pi$
$674$	7.89636e16	0.0324442
$675$	−2.75581e17	−0.112144
$676$	−3.68480e17	−0.148511
$677$	−3.34933e18	−1.33700	−0.668500	−	0.743712i	$-0.733063\pi$
$677$	−3.34933e18	−1.33700	−0.668500	+	0.743712i	$0.733063\pi$
$678$	−1.36456e17	−0.0539509
$679$	−4.62866e18	−1.81260
$680$	2.85171e18	1.10611
$681$	−2.68970e18	−1.03335
$682$	6.09800e16	0.0232054
$683$	−2.32332e18	−0.875737	−0.437868	−	0.899039i	$-0.644266\pi$
$683$	−2.32332e18	−0.875737	−0.437868	+	0.899039i	$0.644266\pi$
$684$	−5.13986e16	−0.0191905
$685$	3.37227e18	1.24719
$686$	−1.41617e18	−0.518812
$687$	1.24070e18	0.450246
$688$	4.43845e18	1.59553
$689$	−8.02669e17	−0.285833
$690$	5.40984e17	0.190838
$691$	5.87579e17	0.205333	0.102666	−	0.994716i	$-0.467263\pi$
$691$	5.87579e17	0.205333	0.102666	+	0.994716i	$0.467263\pi$
$692$	−1.98675e17	−0.0687785
$693$	3.79047e17	0.129995
$694$	1.97331e18	0.670437
$695$	−1.83924e18	−0.619067
$696$	2.78238e17	0.0927803
$697$	−3.32930e18	−1.09987
$698$	3.85413e17	0.126144
$699$	−1.05436e16	−0.00341891
$700$	−3.99172e17	−0.128240
$701$	−3.77375e18	−1.20117	−0.600587	−	0.799559i	$-0.705066\pi$
$701$	−3.77375e18	−1.20117	−0.600587	+	0.799559i	$0.705066\pi$
$702$	2.47271e17	0.0779797
$703$	−1.96473e18	−0.613893
$704$	−7.63917e17	−0.236496
$705$	3.60730e18	1.10651
$706$	−2.22661e18	−0.676729
$707$	−2.01396e18	−0.606491
$708$	4.35004e16	0.0129801
$709$	5.70959e17	0.168813	0.0844063	−	0.996431i	$-0.473101\pi$
$709$	5.70959e17	0.168813	0.0844063	+	0.996431i	$0.473101\pi$
$710$	−3.63102e18	−1.06377
$711$	−1.55604e18	−0.451718
$712$	5.41905e18	1.55885
$713$	5.96027e16	0.0169896
$714$	−2.76825e18	−0.781928
$715$	−5.14647e17	−0.144052
$716$	−4.60798e17	−0.127813
$717$	9.04318e17	0.248569
$718$	−3.27952e18	−0.893309
$719$	−4.09843e18	−1.10632	−0.553159	−	0.833076i	$-0.686578\pi$
$719$	−4.09843e18	−1.10632	−0.553159	+	0.833076i	$0.686578\pi$
$720$	−1.79158e18	−0.479265
$721$	−8.85670e18	−2.34797
$722$	3.66365e18	0.962548
$723$	4.02323e18	1.04755
$724$	−9.18021e16	−0.0236893
$725$	−4.08705e17	−0.104523
$726$	−2.23571e18	−0.566667
$727$	−6.55964e18	−1.64781	−0.823904	−	0.566729i	$-0.808209\pi$
$727$	−6.55964e18	−1.64781	−0.823904	+	0.566729i	$0.808209\pi$
$728$	−1.71588e18	−0.427202
$729$	1.50095e17	0.0370370
$730$	2.68613e18	0.656943
$731$	−5.65208e18	−1.37008
$732$	−5.21498e17	−0.125294
$733$	8.63234e17	0.205567	0.102783	−	0.994704i	$-0.467225\pi$
$733$	8.63234e17	0.205567	0.102783	+	0.994704i	$0.467225\pi$
$734$	2.90291e18	0.685187
$735$	−1.93747e18	−0.453282
$736$	3.57526e17	0.0829090
$737$	−1.93171e15	−0.000444021 0
$738$	1.77558e18	0.404552
$739$	3.66698e18	0.828171	0.414086	−	0.910238i	$-0.364101\pi$
$739$	3.66698e18	0.828171	0.414086	+	0.910238i	$0.364101\pi$
$740$	1.78698e18	0.400050
$741$	3.24544e17	0.0720203
$742$	−4.79245e18	−1.05422
$743$	−3.20909e18	−0.699769	−0.349885	−	0.936793i	$-0.613779\pi$
$743$	−3.20909e18	−0.699769	−0.349885	+	0.936793i	$0.613779\pi$
$744$	−1.67562e17	−0.0362202
$745$	−3.69268e18	−0.791272
$746$	2.97114e17	0.0631134
$747$	7.89098e17	0.166168
$748$	−2.48431e17	−0.0518616
$749$	3.43294e18	0.710450
$750$	−1.59979e18	−0.328219
$751$	−7.66711e18	−1.55945	−0.779726	−	0.626121i	$-0.784642\pi$
$751$	−7.66711e18	−1.55945	−0.779726	+	0.626121i	$0.784642\pi$
$752$	8.63424e18	1.74104
$753$	3.18140e18	0.635991
$754$	3.66719e17	0.0726807
$755$	1.02809e19	2.02011
$756$	2.17408e17	0.0423529
$757$	3.40955e18	0.658528	0.329264	−	0.944238i	$-0.393199\pi$
$757$	3.40955e18	0.658528	0.329264	+	0.944238i	$0.393199\pi$
$758$	−1.64750e18	−0.315482
$759$	2.25783e17	0.0428667
$760$	−1.99615e18	−0.375756
$761$	6.05897e18	1.13083	0.565417	−	0.824805i	$-0.308715\pi$
$761$	6.05897e18	1.13083	0.565417	+	0.824805i	$0.308715\pi$
$762$	−3.23724e18	−0.599056
$763$	−8.57290e18	−1.57296
$764$	−1.77490e18	−0.322900
$765$	2.28147e18	0.411543
$766$	−7.24739e18	−1.29627
$767$	−2.74673e17	−0.0487131
$768$	−1.65307e18	−0.290699
$769$	7.76829e18	1.35458	0.677289	−	0.735717i	$-0.263155\pi$
$769$	7.76829e18	1.35458	0.677289	+	0.735717i	$0.263155\pi$
$770$	−3.07277e18	−0.531301
$771$	2.41620e18	0.414267
$772$	−1.60983e16	−0.00273695
$773$	6.22741e18	1.04988	0.524941	−	0.851139i	$-0.324087\pi$
$773$	6.22741e18	1.04988	0.524941	+	0.851139i	$0.324087\pi$
$774$	3.01437e18	0.503942
$775$	2.46132e17	0.0408045
$776$	7.75107e18	1.27427
$777$	8.31048e18	1.35484
$778$	−2.65562e18	−0.429337
$779$	2.33046e18	0.373636
$780$	−2.95183e17	−0.0469328
$781$	−1.51543e18	−0.238948
$782$	−1.64894e18	−0.257846
$783$	2.22600e17	0.0345203
$784$	−4.63743e18	−0.713219
$785$	6.79961e18	1.03713
$786$	−8.06383e17	−0.121982
$787$	−2.74400e17	−0.0411670	−0.0205835	−	0.999788i	$-0.506552\pi$
$787$	−2.74400e17	−0.0411670	−0.0205835	+	0.999788i	$0.506552\pi$
$788$	4.43377e17	0.0659710
$789$	7.22451e18	1.06612
$790$	1.26141e19	1.84621
$791$	7.57559e17	0.109969
$792$	−6.34745e17	−0.0913873
$793$	3.29287e18	0.470218
$794$	1.10078e18	0.155907
$795$	3.94973e18	0.554857
$796$	9.77141e17	0.136151
$797$	−1.68707e18	−0.233160	−0.116580	−	0.993181i	$-0.537193\pi$
$797$	−1.68707e18	−0.233160	−0.116580	+	0.993181i	$0.537193\pi$
$798$	1.93774e18	0.265629
$799$	−1.09952e19	−1.49502
$800$	1.47642e18	0.199125
$801$	4.33544e18	0.579992
$802$	−2.17972e18	−0.289246
$803$	1.12107e18	0.147564
$804$	−1.10796e15	−0.000144664 0
$805$	−3.00337e18	−0.388988
$806$	−2.20847e17	−0.0283736
$807$	−7.94140e17	−0.101209
$808$	3.37254e18	0.426367
$809$	8.85570e18	1.11060	0.555300	−	0.831650i	$-0.312604\pi$
$809$	8.85570e18	1.11060	0.555300	+	0.831650i	$0.312604\pi$
$810$	−1.21675e18	−0.151374
$811$	−1.43789e18	−0.177456	−0.0887280	−	0.996056i	$-0.528280\pi$
$811$	−1.43789e18	−0.177456	−0.0887280	+	0.996056i	$0.528280\pi$
$812$	3.22430e17	0.0394749
$813$	1.18431e16	0.00143839
$814$	5.06461e18	0.610221
$815$	9.42886e18	1.12703
$816$	5.46080e18	0.647545
$817$	3.95637e18	0.465430
$818$	1.52330e19	1.77783
$819$	−1.37277e18	−0.158947
$820$	−2.11963e18	−0.243484
$821$	−7.99413e18	−0.911046	−0.455523	−	0.890224i	$-0.650548\pi$
$821$	−7.99413e18	−0.911046	−0.455523	+	0.890224i	$0.650548\pi$
$822$	5.48189e18	0.619817
$823$	1.03119e18	0.115675	0.0578373	−	0.998326i	$-0.481580\pi$
$823$	1.03119e18	0.115675	0.0578373	+	0.998326i	$0.481580\pi$
$824$	1.48313e19	1.65064
$825$	9.32382e17	0.102954
$826$	−1.63997e18	−0.179666
$827$	−5.41749e17	−0.0588860	−0.0294430	−	0.999566i	$-0.509373\pi$
$827$	−5.41749e17	−0.0588860	−0.0294430	+	0.999566i	$0.509373\pi$
$828$	1.29501e17	0.0139661
$829$	3.08642e18	0.330256	0.165128	−	0.986272i	$-0.447196\pi$
$829$	3.08642e18	0.330256	0.165128	+	0.986272i	$0.447196\pi$
$830$	−6.39689e18	−0.679143
$831$	4.13441e18	0.435519
$832$	2.76663e18	0.289167
$833$	5.90547e18	0.612438
$834$	−2.98983e18	−0.307657
$835$	2.02531e19	2.06790
$836$	1.73898e17	0.0176179
$837$	−1.34055e17	−0.0134762
$838$	−9.24766e18	−0.922456
$839$	−5.52405e18	−0.546771	−0.273385	−	0.961905i	$-0.588143\pi$
$839$	−5.52405e18	−0.546771	−0.273385	+	0.961905i	$0.588143\pi$
$840$	8.44341e18	0.829282
$841$	−9.93050e18	−0.967825
$842$	−1.96357e19	−1.89897
$843$	−1.12170e18	−0.107646
$844$	−1.55394e18	−0.147981
$845$	−1.14490e19	−1.08193
$846$	5.86395e18	0.549899
$847$	1.24120e19	1.15504
$848$	9.45385e18	0.873043
$849$	5.06492e18	0.464165
$850$	−6.80936e18	−0.619275
$851$	4.95022e18	0.446768
$852$	−8.69195e17	−0.0778502
$853$	−1.76911e19	−1.57248	−0.786240	−	0.617921i	$-0.787975\pi$
$853$	−1.76911e19	−1.57248	−0.786240	+	0.617921i	$0.787975\pi$
$854$	1.96606e19	1.73428
$855$	−1.59700e18	−0.139805
$856$	−5.74874e18	−0.499451
$857$	−2.92655e18	−0.252337	−0.126168	−	0.992009i	$-0.540268\pi$
$857$	−2.92655e18	−0.252337	−0.126168	+	0.992009i	$0.540268\pi$
$858$	−8.36598e17	−0.0715895
$859$	1.31028e19	1.11278	0.556389	−	0.830922i	$-0.312186\pi$
$859$	1.31028e19	1.11278	0.556389	+	0.830922i	$0.312186\pi$
$860$	−3.59845e18	−0.303302
$861$	−9.85748e18	−0.824604
$862$	−9.46682e18	−0.785972
$863$	9.80759e18	0.808150	0.404075	−	0.914726i	$-0.367593\pi$
$863$	9.80759e18	0.808150	0.404075	+	0.914726i	$0.367593\pi$
$864$	−8.04129e17	−0.0657637
$865$	−6.17298e18	−0.501060
$866$	6.57916e18	0.530035
$867$	2.66459e17	0.0213062
$868$	−1.94175e17	−0.0154105
$869$	5.26458e18	0.414701
$870$	−1.80453e18	−0.141087
$871$	6.99594e15	0.000542911 0
$872$	1.43560e19	1.10580
$873$	6.20114e18	0.474110
$874$	1.15423e18	0.0875928
$875$	8.88150e18	0.669012
$876$	6.43006e17	0.0480771
$877$	−1.77473e19	−1.31715	−0.658574	−	0.752516i	$-0.728840\pi$
$877$	−1.77473e19	−1.31715	−0.658574	+	0.752516i	$0.728840\pi$
$878$	1.17562e19	0.866069
$879$	2.22524e18	0.162723
$880$	6.06152e18	0.439991
$881$	5.68538e17	0.0409653	0.0204826	−	0.999790i	$-0.493480\pi$
$881$	5.68538e17	0.0409653	0.0204826	+	0.999790i	$0.493480\pi$
$882$	−3.14951e18	−0.225267
$883$	−1.31235e19	−0.931765	−0.465882	−	0.884847i	$-0.654263\pi$
$883$	−1.31235e19	−0.931765	−0.465882	+	0.884847i	$0.654263\pi$
$884$	8.99727e17	0.0634119
$885$	1.35159e18	0.0945616
$886$	1.08796e18	0.0755601
$887$	−5.67124e18	−0.390998	−0.195499	−	0.980704i	$-0.562633\pi$
$887$	−5.67124e18	−0.390998	−0.195499	+	0.980704i	$0.562633\pi$
$888$	−1.39166e19	−0.952464
$889$	1.79721e19	1.22106
$890$	−3.51456e19	−2.37048
$891$	−5.07820e17	−0.0340020
$892$	−2.85909e17	−0.0190045
$893$	7.69646e18	0.507874
$894$	−6.00273e18	−0.393238
$895$	−1.43174e19	−0.931136
$896$	2.32634e19	1.50200
$897$	−8.17703e17	−0.0524137
$898$	2.21099e19	1.40699
$899$	−1.98813e17	−0.0125605
$900$	5.34781e17	0.0335429
$901$	−1.20389e19	−0.749678
$902$	−6.00738e18	−0.371401
$903$	−1.67348e19	−1.02719
$904$	−1.26860e18	−0.0773087
$905$	−2.85237e18	−0.172580
$906$	1.67123e19	1.00393
$907$	−2.26476e19	−1.35075	−0.675374	−	0.737475i	$-0.736018\pi$
$907$	−2.26476e19	−1.35075	−0.675374	+	0.737475i	$0.736018\pi$
$908$	5.21952e18	0.309081
$909$	2.69815e18	0.158636
$910$	1.11285e19	0.649630
$911$	3.19163e19	1.84988	0.924939	−	0.380117i	$-0.124116\pi$
$911$	3.19163e19	1.84988	0.924939	+	0.380117i	$0.124116\pi$
$912$	−3.82248e18	−0.219978
$913$	−2.66978e18	−0.152551
$914$	2.76547e19	1.56898
$915$	−1.62034e19	−0.912784
$916$	−2.40766e18	−0.134671
$917$	4.47678e18	0.248637
$918$	3.70870e18	0.204524
$919$	6.67933e18	0.365748	0.182874	−	0.983136i	$-0.441460\pi$
$919$	6.67933e18	0.365748	0.182874	+	0.983136i	$0.441460\pi$
$920$	5.02940e18	0.273461
$921$	−3.99113e18	−0.215481
$922$	1.91155e19	1.02479
$923$	5.48832e18	0.292165
$924$	−7.35562e17	−0.0388823
$925$	2.04422e19	1.07302
$926$	−2.91273e19	−1.51820
$927$	1.18656e19	0.614144
$928$	−1.19258e18	−0.0612949
$929$	−1.94975e19	−0.995123	−0.497561	−	0.867429i	$-0.665771\pi$
$929$	−1.94975e19	−0.995123	−0.497561	+	0.867429i	$0.665771\pi$
$930$	1.08673e18	0.0550786
$931$	−4.13375e18	−0.208052
$932$	2.04605e16	0.00102262
$933$	−8.11718e18	−0.402879
$934$	3.56841e19	1.75881
$935$	−7.71896e18	−0.377819
$936$	2.29881e18	0.111741
$937$	−1.98727e19	−0.959289	−0.479645	−	0.877463i	$-0.659234\pi$
$937$	−1.98727e19	−0.959289	−0.479645	+	0.877463i	$0.659234\pi$
$938$	4.17703e16	0.00200239
$939$	4.45697e18	0.212184
$940$	−7.00018e18	−0.330962
$941$	−4.48542e18	−0.210606	−0.105303	−	0.994440i	$-0.533581\pi$
$941$	−4.48542e18	−0.210606	−0.105303	+	0.994440i	$0.533581\pi$
$942$	1.10533e19	0.515419
$943$	−5.87170e18	−0.271918
$944$	3.23510e18	0.148789
$945$	6.75504e18	0.308547
$946$	−1.01986e19	−0.462646
$947$	−2.27860e18	−0.102658	−0.0513290	−	0.998682i	$-0.516346\pi$
$947$	−2.27860e18	−0.102658	−0.0513290	+	0.998682i	$0.516346\pi$
$948$	3.01958e18	0.135111
$949$	−4.06010e18	−0.180429
$950$	4.76646e18	0.210374
$951$	−1.62199e18	−0.0711010
$952$	−2.57357e19	−1.12046
$953$	9.30159e18	0.402210	0.201105	−	0.979570i	$-0.435547\pi$
$953$	9.30159e18	0.402210	0.201105	+	0.979570i	$0.435547\pi$
$954$	6.42058e18	0.275746
$955$	−5.51476e19	−2.35237
$956$	−1.75488e18	−0.0743484
$957$	−7.53130e17	−0.0316915
$958$	1.27320e19	0.532132
$959$	−3.04337e19	−1.26338
$960$	−1.36139e19	−0.561330
$961$	−2.42978e19	−0.995097
$962$	−1.83421e19	−0.746126
$963$	−4.59920e18	−0.185828
$964$	−7.80730e18	−0.313329
$965$	−5.00186e17	−0.0199390
$966$	−4.88221e18	−0.193315
$967$	−1.83135e19	−0.720277	−0.360139	−	0.932899i	$-0.617271\pi$
$967$	−1.83135e19	−0.720277	−0.360139	+	0.932899i	$0.617271\pi$
$968$	−2.07849e19	−0.812003
$969$	4.86769e18	0.188894
$970$	−5.02701e19	−1.93773
$971$	−1.03164e19	−0.395005	−0.197503	−	0.980302i	$-0.563283\pi$
$971$	−1.03164e19	−0.395005	−0.197503	+	0.980302i	$0.563283\pi$
$972$	−2.91267e17	−0.0110780
$973$	1.65986e19	0.627100
$974$	1.97041e19	0.739476
$975$	−3.37675e18	−0.125883
$976$	−3.87835e19	−1.43623
$977$	4.89176e19	1.79949	0.899747	−	0.436413i	$-0.143751\pi$
$977$	4.89176e19	1.79949	0.899747	+	0.436413i	$0.143751\pi$
$978$	1.53273e19	0.560098
$979$	−1.46682e19	−0.532464
$980$	3.75978e18	0.135579
$981$	1.14854e19	0.411430
$982$	2.97123e19	1.05733
$983$	−1.15301e19	−0.407600	−0.203800	−	0.979013i	$-0.565329\pi$
$983$	−1.15301e19	−0.407600	−0.203800	+	0.979013i	$0.565329\pi$
$984$	1.65072e19	0.579701
$985$	1.37761e19	0.480607
$986$	5.50025e18	0.190626
$987$	−3.25548e19	−1.12086
$988$	−6.29796e17	−0.0215417
$989$	−9.96826e18	−0.338722
$990$	4.11668e18	0.138969
$991$	2.90894e19	0.975565	0.487783	−	0.872965i	$-0.337806\pi$
$991$	2.90894e19	0.975565	0.487783	+	0.872965i	$0.337806\pi$
$992$	7.18199e17	0.0239287
$993$	−1.29761e19	−0.429510
$994$	3.27688e19	1.07758
$995$	3.03606e19	0.991882
$996$	−1.53129e18	−0.0497017
$997$	2.78215e19	0.897144	0.448572	−	0.893747i	$-0.351933\pi$
$997$	2.78215e19	0.897144	0.448572	+	0.893747i	$0.351933\pi$
$998$	6.54322e18	0.209625
$999$	−1.11338e19	−0.354378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.8	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} -4.30817e6 q^{10} -1.79804e6 q^{11} -1.03129e6 q^{12} +6.51184e6 q^{13} +3.88799e7 q^{14} -3.20431e7 q^{15} -7.66965e7 q^{16} +9.76681e7 q^{17} -5.20884e7 q^{18} -6.83663e7 q^{19} +6.21814e7 q^{20} +2.89178e8 q^{21} +1.76232e8 q^{22} +1.72252e8 q^{23} -4.84253e8 q^{24} +7.11324e8 q^{25} -6.38249e8 q^{26} -3.87420e8 q^{27} -5.61168e8 q^{28} -5.74570e8 q^{29} +3.14066e9 q^{30} +3.46020e8 q^{31} +2.07560e9 q^{32} +1.31077e9 q^{33} -9.57281e9 q^{34} -1.74359e10 q^{35} +7.51812e8 q^{36} +2.87382e10 q^{37} +6.70083e9 q^{38} -4.74713e9 q^{39} +2.91979e10 q^{40} -3.40879e10 q^{41} -2.83434e10 q^{42} -5.78702e10 q^{43} -2.54363e9 q^{44} +2.33594e10 q^{45} -1.68830e10 q^{46} -1.12577e11 q^{47} +5.59118e10 q^{48} +6.04647e10 q^{49} -6.97194e10 q^{50} -7.12001e10 q^{51} +9.21208e9 q^{52} -1.23263e11 q^{53} +3.79725e10 q^{54} -7.90325e10 q^{55} -2.63502e11 q^{56} +4.98390e10 q^{57} +5.63157e10 q^{58} -4.21805e10 q^{59} -4.53303e10 q^{60} +5.05675e11 q^{61} -3.39147e10 q^{62} -2.10811e11 q^{63} +4.24861e11 q^{64} +2.86227e11 q^{65} -1.28473e11 q^{66} +1.07434e9 q^{67} +1.38168e11 q^{68} -1.25572e11 q^{69} +1.70896e12 q^{70} +8.42822e11 q^{71} +3.53021e11 q^{72} -6.23496e11 q^{73} -2.81674e12 q^{74} -5.18555e11 q^{75} -9.67155e10 q^{76} +7.13243e11 q^{77} +4.65283e11 q^{78} -2.92796e12 q^{79} -3.37118e12 q^{80} +2.82430e11 q^{81} +3.34107e12 q^{82} +1.48483e12 q^{83} +4.09091e11 q^{84} +4.29299e12 q^{85} +5.67207e12 q^{86} +4.18862e11 q^{87} -1.19439e12 q^{88} +8.15790e12 q^{89} -2.28954e12 q^{90} -2.58311e12 q^{91} +2.43679e11 q^{92} -2.52249e11 q^{93} +1.10341e13 q^{94} -3.00503e12 q^{95} -1.51311e12 q^{96} +1.16685e13 q^{97} -5.92636e12 q^{98} -9.55552e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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

L-functions

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