LMFDB - Embedded newform 177.14.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} -7.05083e6 q^{10} -1.07727e7 q^{11} -1.50728e7 q^{12} +2.00397e7 q^{13} -3.77728e7 q^{14} -3.02524e7 q^{15} +1.91008e8 q^{16} +1.01659e8 q^{17} -9.02948e7 q^{18} -3.33309e8 q^{19} +8.58021e8 q^{20} -1.62069e8 q^{21} +1.83034e9 q^{22} +1.06894e9 q^{23} +1.54628e9 q^{24} +5.01424e8 q^{25} -3.40486e9 q^{26} -3.87420e8 q^{27} +4.59660e9 q^{28} +5.94950e9 q^{29} +5.14006e9 q^{30} -6.31398e9 q^{31} -1.50774e10 q^{32} +7.85331e9 q^{33} -1.72724e10 q^{34} +9.22581e9 q^{35} +1.09880e10 q^{36} -1.05289e10 q^{37} +5.66310e10 q^{38} -1.46089e10 q^{39} -8.80222e10 q^{40} -3.83957e10 q^{41} +2.75364e10 q^{42} +1.84687e10 q^{43} -2.22736e11 q^{44} +2.20540e10 q^{45} -1.81619e11 q^{46} +2.22256e10 q^{47} -1.39245e11 q^{48} -4.74644e10 q^{49} -8.51948e10 q^{50} -7.41094e10 q^{51} +4.14339e11 q^{52} +1.89641e10 q^{53} +6.58249e10 q^{54} -4.47052e11 q^{55} -4.71554e11 q^{56} +2.42982e11 q^{57} -1.01085e12 q^{58} -4.21805e10 q^{59} -6.25497e11 q^{60} +3.61171e11 q^{61} +1.07278e12 q^{62} +1.18148e11 q^{63} +9.96998e11 q^{64} +8.31617e11 q^{65} -1.33432e12 q^{66} -1.10019e12 q^{67} +2.10190e12 q^{68} -7.79257e11 q^{69} -1.56752e12 q^{70} -5.32591e11 q^{71} -1.12724e12 q^{72} +8.30365e11 q^{73} +1.78893e12 q^{74} -3.65538e11 q^{75} -6.89147e12 q^{76} -2.39495e12 q^{77} +2.48214e12 q^{78} -2.73593e12 q^{79} +7.92656e12 q^{80} +2.82430e11 q^{81} +6.52364e12 q^{82} +3.89497e12 q^{83} -3.35092e12 q^{84} +4.21870e12 q^{85} -3.13794e12 q^{86} -4.33718e12 q^{87} +2.28499e13 q^{88} -6.16283e12 q^{89} -3.74710e12 q^{90} +4.45516e12 q^{91} +2.21013e13 q^{92} +4.60289e12 q^{93} -3.77625e12 q^{94} -1.38318e13 q^{95} +1.09914e13 q^{96} -1.11435e13 q^{97} +8.06446e12 q^{98} -5.72506e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−169.906	−1.87721	−0.938605	−	0.344993i	$-0.887881\pi$
$2$	−169.906	−1.87721	−0.938605	+	0.344993i	$0.887881\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	20675.9	2.52392
$5$	41498.5	1.18776	0.593878	−	0.804555i	$-0.297596\pi$
$5$	41498.5	1.18776	0.593878	+	0.804555i	$0.297596\pi$
$6$	123861.	1.08381
$7$	222317.	0.714224	0.357112	−	0.934062i	$-0.383761\pi$
$7$	222317.	0.714224	0.357112	+	0.934062i	$0.383761\pi$
$8$	−2.12109e6	−2.86072
$9$	531441.	0.333333
$10$	−7.05083e6	−2.22967
$11$	−1.07727e7	−1.83346	−0.916732	−	0.399502i	$-0.869183\pi$
$11$	−1.07727e7	−1.83346	−0.916732	+	0.399502i	$0.869183\pi$
$12$	−1.50728e7	−1.45719
$13$	2.00397e7	1.15149	0.575744	−	0.817630i	$-0.304713\pi$
$13$	2.00397e7	1.15149	0.575744	+	0.817630i	$0.304713\pi$
$14$	−3.77728e7	−1.34075
$15$	−3.02524e7	−0.685752
$16$	1.91008e8	2.84625
$17$	1.01659e8	1.02148	0.510738	−	0.859737i	$-0.329372\pi$
$17$	1.01659e8	1.02148	0.510738	+	0.859737i	$0.329372\pi$
$18$	−9.02948e7	−0.625737
$19$	−3.33309e8	−1.62535	−0.812677	−	0.582714i	$-0.801991\pi$
$19$	−3.33309e8	−1.62535	−0.812677	+	0.582714i	$0.801991\pi$
$20$	8.58021e8	2.99780
$21$	−1.62069e8	−0.412358
$22$	1.83034e9	3.44180
$23$	1.06894e9	1.50564	0.752822	−	0.658224i	$-0.228692\pi$
$23$	1.06894e9	1.50564	0.752822	+	0.658224i	$0.228692\pi$
$24$	1.54628e9	1.65163
$25$	5.01424e8	0.410766
$26$	−3.40486e9	−2.16158
$27$	−3.87420e8	−0.192450
$28$	4.59660e9	1.80264
$29$	5.94950e9	1.85735	0.928674	−	0.370897i	$-0.120950\pi$
$29$	5.94950e9	1.85735	0.928674	+	0.370897i	$0.120950\pi$
$30$	5.14006e9	1.28730
$31$	−6.31398e9	−1.27777	−0.638884	−	0.769303i	$-0.720604\pi$
$31$	−6.31398e9	−1.27777	−0.638884	+	0.769303i	$0.720604\pi$
$32$	−1.50774e10	−2.48229
$33$	7.85331e9	1.05855
$34$	−1.72724e10	−1.91752
$35$	9.22581e9	0.848325
$36$	1.09880e10	0.841306
$37$	−1.05289e10	−0.674643	−0.337321	−	0.941390i	$-0.609521\pi$
$37$	−1.05289e10	−0.674643	−0.337321	+	0.941390i	$0.609521\pi$
$38$	5.66310e10	3.05113
$39$	−1.46089e10	−0.664812
$40$	−8.80222e10	−3.39783
$41$	−3.83957e10	−1.26237	−0.631185	−	0.775632i	$-0.717431\pi$
$41$	−3.83957e10	−1.26237	−0.631185	+	0.775632i	$0.717431\pi$
$42$	2.75364e10	0.774082
$43$	1.84687e10	0.445546	0.222773	−	0.974870i	$-0.428489\pi$
$43$	1.84687e10	0.445546	0.222773	+	0.974870i	$0.428489\pi$
$44$	−2.22736e11	−4.62752
$45$	2.20540e10	0.395919
$46$	−1.81619e11	−2.82641
$47$	2.22256e10	0.300758	0.150379	−	0.988628i	$-0.451951\pi$
$47$	2.22256e10	0.300758	0.150379	+	0.988628i	$0.451951\pi$
$48$	−1.39245e11	−1.64328
$49$	−4.74644e10	−0.489884
$50$	−8.51948e10	−0.771095
$51$	−7.41094e10	−0.589749
$52$	4.14339e11	2.90626
$53$	1.89641e10	0.117527	0.0587637	−	0.998272i	$-0.481284\pi$
$53$	1.89641e10	0.117527	0.0587637	+	0.998272i	$0.481284\pi$
$54$	6.58249e10	0.361269
$55$	−4.47052e11	−2.17771
$56$	−4.71554e11	−2.04319
$57$	2.42982e11	0.938399
$58$	−1.01085e12	−3.48663
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−6.25497e11	−1.73078
$61$	3.61171e11	0.897572	0.448786	−	0.893639i	$-0.351857\pi$
$61$	3.61171e11	0.897572	0.448786	+	0.893639i	$0.351857\pi$
$62$	1.07278e12	2.39864
$63$	1.18148e11	0.238075
$64$	9.96998e11	1.81353
$65$	8.31617e11	1.36769
$66$	−1.33432e12	−1.98712
$67$	−1.10019e12	−1.48587	−0.742937	−	0.669362i	$-0.766568\pi$
$67$	−1.10019e12	−1.48587	−0.742937	+	0.669362i	$0.766568\pi$
$68$	2.10190e12	2.57812
$69$	−7.79257e11	−0.869284
$70$	−1.56752e12	−1.59248
$71$	−5.32591e11	−0.493418	−0.246709	−	0.969090i	$-0.579349\pi$
$71$	−5.32591e11	−0.493418	−0.246709	+	0.969090i	$0.579349\pi$
$72$	−1.12724e12	−0.953572
$73$	8.30365e11	0.642200	0.321100	−	0.947045i	$-0.395947\pi$
$73$	8.30365e11	0.642200	0.321100	+	0.947045i	$0.395947\pi$
$74$	1.78893e12	1.26645
$75$	−3.65538e11	−0.237156
$76$	−6.89147e12	−4.10226
$77$	−2.39495e12	−1.30950
$78$	2.48214e12	1.24799
$79$	−2.73593e12	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$79$	−2.73593e12	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$80$	7.92656e12	3.38065
$81$	2.82430e11	0.111111
$82$	6.52364e12	2.36974
$83$	3.89497e12	1.30766	0.653832	−	0.756640i	$-0.273160\pi$
$83$	3.89497e12	1.30766	0.653832	+	0.756640i	$0.273160\pi$
$84$	−3.35092e12	−1.04076
$85$	4.21870e12	1.21326
$86$	−3.13794e12	−0.836383
$87$	−4.33718e12	−1.07234
$88$	2.28499e13	5.24502
$89$	−6.16283e12	−1.31445	−0.657227	−	0.753693i	$-0.728271\pi$
$89$	−6.16283e12	−1.31445	−0.657227	+	0.753693i	$0.728271\pi$
$90$	−3.74710e12	−0.743223
$91$	4.45516e12	0.822420
$92$	2.21013e13	3.80012
$93$	4.60289e12	0.737720
$94$	−3.77625e12	−0.564585
$95$	−1.38318e13	−1.93053
$96$	1.09914e13	1.43315
$97$	−1.11435e13	−1.35833	−0.679164	−	0.733987i	$-0.737657\pi$
$97$	−1.11435e13	−1.35833	−0.679164	+	0.733987i	$0.737657\pi$
$98$	8.06446e12	0.919615
$99$	−5.72506e12	−0.611155
$100$	1.03674e13	1.03674
$101$	−3.08647e12	−0.289316	−0.144658	−	0.989482i	$-0.546208\pi$
$101$	−3.08647e12	−0.289316	−0.144658	+	0.989482i	$0.546208\pi$
$102$	1.25916e13	1.10708
$103$	−1.71321e12	−0.141374	−0.0706869	−	0.997499i	$-0.522519\pi$
$103$	−1.71321e12	−0.141374	−0.0706869	+	0.997499i	$0.522519\pi$
$104$	−4.25060e13	−3.29408
$105$	−6.72561e12	−0.489780
$106$	−3.22211e12	−0.220624
$107$	−2.62326e12	−0.168985	−0.0844923	−	0.996424i	$-0.526927\pi$
$107$	−2.62326e12	−0.168985	−0.0844923	+	0.996424i	$0.526927\pi$
$108$	−8.01028e12	−0.485728
$109$	−8.90261e12	−0.508446	−0.254223	−	0.967146i	$-0.581820\pi$
$109$	−8.90261e12	−0.508446	−0.254223	+	0.967146i	$0.581820\pi$
$110$	7.59566e13	4.08802
$111$	7.67560e12	0.389505
$112$	4.24643e13	2.03286
$113$	2.18781e13	0.988553	0.494277	−	0.869305i	$-0.335433\pi$
$113$	2.18781e13	0.988553	0.494277	+	0.869305i	$0.335433\pi$
$114$	−4.12840e13	−1.76157
$115$	4.43594e13	1.78834
$116$	1.23011e14	4.68779
$117$	1.06499e13	0.383829
$118$	7.16671e12	0.244392
$119$	2.26005e13	0.729562
$120$	6.41682e13	1.96174
$121$	8.15286e13	2.36159
$122$	−6.13651e13	−1.68493
$123$	2.79904e13	0.728830
$124$	−1.30547e14	−3.22498
$125$	−2.98490e13	−0.699866
$126$	−2.00740e13	−0.446916
$127$	−2.92834e13	−0.619295	−0.309647	−	0.950851i	$-0.600211\pi$
$127$	−2.92834e13	−0.619295	−0.309647	+	0.950851i	$0.600211\pi$
$128$	−4.58814e13	−0.922088
$129$	−1.34637e13	−0.257236
$130$	−1.41297e14	−2.56744
$131$	−1.01661e13	−0.175748	−0.0878739	−	0.996132i	$-0.528007\pi$
$131$	−1.01661e13	−0.175748	−0.0878739	+	0.996132i	$0.528007\pi$
$132$	1.62374e14	2.67170
$133$	−7.41000e13	−1.16087
$134$	1.86929e14	2.78930
$135$	−1.60774e13	−0.228584
$136$	−2.15628e14	−2.92215
$137$	1.16359e14	1.50355	0.751774	−	0.659421i	$-0.229199\pi$
$137$	1.16359e14	1.50355	0.751774	+	0.659421i	$0.229199\pi$
$138$	1.32400e14	1.63183
$139$	1.06667e14	1.25440	0.627200	−	0.778858i	$-0.284201\pi$
$139$	1.06667e14	1.25440	0.627200	+	0.778858i	$0.284201\pi$
$140$	1.90752e14	2.14110
$141$	−1.62024e13	−0.173642
$142$	9.04903e13	0.926249
$143$	−2.15882e14	−2.11121
$144$	1.01510e14	0.948749
$145$	2.46895e14	2.20608
$146$	−1.41084e14	−1.20554
$147$	3.46015e13	0.282835
$148$	−2.17696e14	−1.70274
$149$	−2.04918e14	−1.53416	−0.767078	−	0.641554i	$-0.778290\pi$
$149$	−2.04918e14	−1.53416	−0.767078	+	0.641554i	$0.778290\pi$
$150$	6.21070e13	0.445192
$151$	−9.14387e12	−0.0627740	−0.0313870	−	0.999507i	$-0.509992\pi$
$151$	−9.14387e12	−0.0627740	−0.0313870	+	0.999507i	$0.509992\pi$
$152$	7.06978e14	4.64968
$153$	5.40258e13	0.340492
$154$	4.06916e14	2.45822
$155$	−2.62021e14	−1.51768
$156$	−3.02053e14	−1.67793
$157$	−2.59828e14	−1.38464	−0.692322	−	0.721589i	$-0.743412\pi$
$157$	−2.59828e14	−1.38464	−0.692322	+	0.721589i	$0.743412\pi$
$158$	4.64850e14	2.37707
$159$	−1.38248e13	−0.0678545
$160$	−6.25690e14	−2.94835
$161$	2.37643e14	1.07537
$162$	−4.79864e13	−0.208579
$163$	2.09548e14	0.875111	0.437556	−	0.899191i	$-0.355844\pi$
$163$	2.09548e14	0.875111	0.437556	+	0.899191i	$0.355844\pi$
$164$	−7.93866e14	−3.18612
$165$	3.25901e14	1.25730
$166$	−6.61777e14	−2.45476
$167$	−4.71310e14	−1.68132	−0.840658	−	0.541567i	$-0.817831\pi$
$167$	−4.71310e14	−1.68132	−0.840658	+	0.541567i	$0.817831\pi$
$168$	3.43763e14	1.17964
$169$	9.87141e13	0.325923
$170$	−7.16781e14	−2.27755
$171$	−1.77134e14	−0.541785
$172$	3.81859e14	1.12452
$173$	3.58466e14	1.01660	0.508298	−	0.861181i	$-0.330275\pi$
$173$	3.58466e14	1.01660	0.508298	+	0.861181i	$0.330275\pi$
$174$	7.36912e14	2.01301
$175$	1.11475e14	0.293379
$176$	−2.05768e15	−5.21849
$177$	3.07496e13	0.0751646
$178$	1.04710e15	2.46751
$179$	−8.11876e14	−1.84478	−0.922391	−	0.386258i	$-0.873767\pi$
$179$	−8.11876e14	−1.84478	−0.922391	+	0.386258i	$0.873767\pi$
$180$	4.55987e14	0.999267
$181$	1.02697e14	0.217093	0.108546	−	0.994091i	$-0.465380\pi$
$181$	1.02697e14	0.217093	0.108546	+	0.994091i	$0.465380\pi$
$182$	−7.56956e14	−1.54386
$183$	−2.63294e14	−0.518213
$184$	−2.26732e15	−4.30722
$185$	−4.36936e14	−0.801312
$186$	−7.82057e14	−1.38486
$187$	−1.09514e15	−1.87284
$188$	4.59534e14	0.759088
$189$	−8.61300e13	−0.137453
$190$	2.35010e15	3.62400
$191$	7.72970e14	1.15198	0.575991	−	0.817456i	$-0.304616\pi$
$191$	7.72970e14	1.15198	0.575991	+	0.817456i	$0.304616\pi$
$192$	−7.26811e14	−1.04704
$193$	−9.59978e13	−0.133702	−0.0668511	−	0.997763i	$-0.521295\pi$
$193$	−9.59978e13	−0.133702	−0.0668511	+	0.997763i	$0.521295\pi$
$194$	1.89334e15	2.54987
$195$	−6.06249e14	−0.789635
$196$	−9.81370e14	−1.23643
$197$	7.21801e14	0.879806	0.439903	−	0.898045i	$-0.355013\pi$
$197$	7.21801e14	0.879806	0.439903	+	0.898045i	$0.355013\pi$
$198$	9.72720e14	1.14727
$199$	−4.25273e14	−0.485426	−0.242713	−	0.970098i	$-0.578037\pi$
$199$	−4.25273e14	−0.485426	−0.242713	+	0.970098i	$0.578037\pi$
$200$	−1.06357e15	−1.17509
$201$	8.02039e14	0.857869
$202$	5.24408e14	0.543107
$203$	1.32267e15	1.32656
$204$	−1.53228e15	−1.48848
$205$	−1.59336e15	−1.49939
$206$	2.91084e14	0.265388
$207$	5.68079e14	0.501881
$208$	3.82775e15	3.27742
$209$	3.59064e15	2.98003
$210$	1.14272e15	0.919421
$211$	−4.88535e14	−0.381118	−0.190559	−	0.981676i	$-0.561030\pi$
$211$	−4.88535e14	−0.381118	−0.190559	+	0.981676i	$0.561030\pi$
$212$	3.92101e14	0.296630
$213$	3.88259e14	0.284875
$214$	4.45707e14	0.317220
$215$	7.66425e14	0.529200
$216$	8.21755e14	0.550545
$217$	−1.40370e15	−0.912613
$218$	1.51260e15	0.954460
$219$	−6.05336e14	−0.370774
$220$	−9.24321e15	−5.49636
$221$	2.03722e15	1.17622
$222$	−1.30413e15	−0.731183
$223$	2.42274e15	1.31925	0.659623	−	0.751596i	$-0.270716\pi$
$223$	2.42274e15	1.31925	0.659623	+	0.751596i	$0.270716\pi$
$224$	−3.35196e15	−1.77291
$225$	2.66477e14	0.136922
$226$	−3.71722e15	−1.85572
$227$	4.93812e14	0.239548	0.119774	−	0.992801i	$-0.461783\pi$
$227$	4.93812e14	0.239548	0.119774	+	0.992801i	$0.461783\pi$
$228$	5.02388e15	2.36844
$229$	4.26781e14	0.195557	0.0977786	−	0.995208i	$-0.468826\pi$
$229$	4.26781e14	0.195557	0.0977786	+	0.995208i	$0.468826\pi$
$230$	−7.53692e15	−3.35709
$231$	1.74592e15	0.756043
$232$	−1.26194e16	−5.31334
$233$	−1.10492e15	−0.452394	−0.226197	−	0.974082i	$-0.572629\pi$
$233$	−1.10492e15	−0.452394	−0.226197	+	0.974082i	$0.572629\pi$
$234$	−1.80948e15	−0.720528
$235$	9.22328e14	0.357227
$236$	−8.72122e14	−0.328586
$237$	1.99449e15	0.731086
$238$	−3.83995e15	−1.36954
$239$	2.55175e15	0.885629	0.442815	−	0.896613i	$-0.353980\pi$
$239$	2.55175e15	0.885629	0.442815	+	0.896613i	$0.353980\pi$
$240$	−5.77846e15	−1.95182
$241$	−5.07400e14	−0.166817	−0.0834084	−	0.996515i	$-0.526581\pi$
$241$	−5.07400e14	−0.166817	−0.0834084	+	0.996515i	$0.526581\pi$
$242$	−1.38522e16	−4.43321
$243$	−2.05891e14	−0.0641500
$244$	7.46756e15	2.26540
$245$	−1.96970e15	−0.581863
$246$	−4.75573e15	−1.36817
$247$	−6.67940e15	−1.87158
$248$	1.33925e16	3.65533
$249$	−2.83943e15	−0.754980
$250$	5.07152e15	1.31380
$251$	−2.50939e15	−0.633416	−0.316708	−	0.948523i	$-0.602578\pi$
$251$	−2.50939e15	−0.633416	−0.316708	+	0.948523i	$0.602578\pi$
$252$	2.44282e15	0.600881
$253$	−1.15154e16	−2.76055
$254$	4.97542e15	1.16255
$255$	−3.07543e15	−0.700479
$256$	−3.71890e14	−0.0825762
$257$	2.31866e15	0.501963	0.250982	−	0.967992i	$-0.419247\pi$
$257$	2.31866e15	0.501963	0.250982	+	0.967992i	$0.419247\pi$
$258$	2.28756e15	0.482886
$259$	−2.34076e15	−0.481846
$260$	1.71945e16	3.45193
$261$	3.16181e15	0.619116
$262$	1.72727e15	0.329916
$263$	−5.55745e15	−1.03553	−0.517766	−	0.855522i	$-0.673236\pi$
$263$	−5.55745e15	−1.03553	−0.517766	+	0.855522i	$0.673236\pi$
$264$	−1.66576e16	−3.02821
$265$	7.86982e14	0.139594
$266$	1.25900e16	2.17919
$267$	4.49270e15	0.758900
$268$	−2.27475e16	−3.75022
$269$	−4.98044e15	−0.801453	−0.400726	−	0.916198i	$-0.631242\pi$
$269$	−4.98044e15	−0.801453	−0.400726	+	0.916198i	$0.631242\pi$
$270$	2.73164e15	0.429100
$271$	−6.85334e15	−1.05100	−0.525499	−	0.850794i	$-0.676121\pi$
$271$	−6.85334e15	−1.05100	−0.525499	+	0.850794i	$0.676121\pi$
$272$	1.94177e16	2.90737
$273$	−3.24781e15	−0.474825
$274$	−1.97701e16	−2.82247
$275$	−5.40169e15	−0.753126
$276$	−1.61119e16	−2.19400
$277$	6.46709e15	0.860182	0.430091	−	0.902786i	$-0.358481\pi$
$277$	6.46709e15	0.860182	0.430091	+	0.902786i	$0.358481\pi$
$278$	−1.81234e16	−2.35477
$279$	−3.35551e15	−0.425923
$280$	−1.95688e16	−2.42682
$281$	1.61187e16	1.95316	0.976581	−	0.215148i	$-0.0690234\pi$
$281$	1.61187e16	1.95316	0.976581	+	0.215148i	$0.0690234\pi$
$282$	2.75288e15	0.325963
$283$	−1.04420e16	−1.20830	−0.604148	−	0.796872i	$-0.706486\pi$
$283$	−1.04420e16	−1.20830	−0.604148	+	0.796872i	$0.706486\pi$
$284$	−1.10118e16	−1.24535
$285$	1.00834e16	1.11459
$286$	3.66795e16	3.96319
$287$	−8.53599e15	−0.901616
$288$	−8.01276e15	−0.827429
$289$	4.29979e14	0.0434121
$290$	−4.19489e16	−4.14127
$291$	8.12360e15	0.784231
$292$	1.71686e16	1.62086
$293$	6.23910e15	0.576079	0.288040	−	0.957619i	$-0.406997\pi$
$293$	6.23910e15	0.576079	0.288040	+	0.957619i	$0.406997\pi$
$294$	−5.87899e15	−0.530940
$295$	−1.75043e15	−0.154633
$296$	2.23329e16	1.92996
$297$	4.17357e15	0.352850
$298$	3.48167e16	2.87993
$299$	2.14212e16	1.73373
$300$	−7.55784e15	−0.598563
$301$	4.10591e15	0.318219
$302$	1.55360e15	0.117840
$303$	2.25003e15	0.167037
$304$	−6.36647e16	−4.62616
$305$	1.49881e16	1.06610
$306$	−9.17929e15	−0.639175
$307$	−3.51073e15	−0.239330	−0.119665	−	0.992814i	$-0.538182\pi$
$307$	−3.51073e15	−0.239330	−0.119665	+	0.992814i	$0.538182\pi$
$308$	−4.95179e16	−3.30508
$309$	1.24893e15	0.0816222
$310$	4.45188e16	2.84900
$311$	5.47784e15	0.343295	0.171647	−	0.985158i	$-0.445091\pi$
$311$	5.47784e15	0.343295	0.171647	+	0.985158i	$0.445091\pi$
$312$	3.09869e16	1.90184
$313$	1.64788e16	0.990574	0.495287	−	0.868729i	$-0.335063\pi$
$313$	1.64788e16	0.990574	0.495287	+	0.868729i	$0.335063\pi$
$314$	4.41462e16	2.59927
$315$	4.90297e15	0.282775
$316$	−5.65680e16	−3.19598
$317$	5.74438e15	0.317950	0.158975	−	0.987283i	$-0.449181\pi$
$317$	5.74438e15	0.317950	0.158975	+	0.987283i	$0.449181\pi$
$318$	2.34892e15	0.127377
$319$	−6.40922e16	−3.40538
$320$	4.13739e16	2.15403
$321$	1.91236e15	0.0975633
$322$	−4.03769e16	−2.01869
$323$	−3.38838e16	−1.66026
$324$	5.83950e15	0.280435
$325$	1.00484e16	0.472992
$326$	−3.56033e16	−1.64277
$327$	6.49000e15	0.293552
$328$	8.14407e16	3.61128
$329$	4.94111e15	0.214808
$330$	−5.53724e16	−2.36022
$331$	1.62670e16	0.679869	0.339934	−	0.940449i	$-0.389595\pi$
$331$	1.62670e16	0.679869	0.339934	+	0.940449i	$0.389595\pi$
$332$	8.05321e16	3.30044
$333$	−5.59552e15	−0.224881
$334$	8.00782e16	3.15618
$335$	−4.56563e16	−1.76486
$336$	−3.09565e16	−1.17367
$337$	5.00718e16	1.86208	0.931041	−	0.364914i	$-0.118901\pi$
$337$	5.00718e16	1.86208	0.931041	+	0.364914i	$0.118901\pi$
$338$	−1.67721e16	−0.611827
$339$	−1.59491e16	−0.570742
$340$	8.72256e16	3.06218
$341$	6.80187e16	2.34274
$342$	3.00960e16	1.01704
$343$	−3.20921e16	−1.06411
$344$	−3.91739e16	−1.27458
$345$	−3.23380e16	−1.03250
$346$	−6.09054e16	−1.90836
$347$	1.83010e16	0.562774	0.281387	−	0.959594i	$-0.409205\pi$
$347$	1.83010e16	0.562774	0.281387	+	0.959594i	$0.409205\pi$
$348$	−8.96753e16	−2.70650
$349$	−3.68256e16	−1.09090	−0.545449	−	0.838144i	$-0.683641\pi$
$349$	−3.68256e16	−1.09090	−0.545449	+	0.838144i	$0.683641\pi$
$350$	−1.89402e16	−0.550735
$351$	−7.76379e15	−0.221604
$352$	1.62425e17	4.55119
$353$	−5.65039e16	−1.55433	−0.777165	−	0.629297i	$-0.783343\pi$
$353$	−5.65039e16	−1.55433	−0.777165	+	0.629297i	$0.783343\pi$
$354$	−5.22453e15	−0.141100
$355$	−2.21018e16	−0.586060
$356$	−1.27422e17	−3.31757
$357$	−1.64758e16	−0.421213
$358$	1.37942e17	3.46304
$359$	2.96902e16	0.731980	0.365990	−	0.930619i	$-0.380730\pi$
$359$	2.96902e16	0.731980	0.365990	+	0.930619i	$0.380730\pi$
$360$	−4.67786e16	−1.13261
$361$	6.90416e16	1.64178
$362$	−1.74487e16	−0.407529
$363$	−5.94343e16	−1.36347
$364$	9.21145e16	2.07572
$365$	3.44589e16	0.762778
$366$	4.47351e16	0.972796
$367$	2.27563e16	0.486151	0.243076	−	0.970007i	$-0.421844\pi$
$367$	2.27563e16	0.486151	0.243076	+	0.970007i	$0.421844\pi$
$368$	2.04176e17	4.28543
$369$	−2.04050e16	−0.420790
$370$	7.42379e16	1.50423
$371$	4.21603e15	0.0839409
$372$	9.51691e16	1.86195
$373$	8.01528e16	1.54103	0.770516	−	0.637421i	$-0.219999\pi$
$373$	8.01528e16	1.54103	0.770516	+	0.637421i	$0.219999\pi$
$374$	1.86071e17	3.51571
$375$	2.17599e16	0.404068
$376$	−4.71425e16	−0.860382
$377$	1.19226e17	2.13871
$378$	1.46340e16	0.258027
$379$	−2.97541e15	−0.0515694	−0.0257847	−	0.999668i	$-0.508208\pi$
$379$	−2.97541e15	−0.0515694	−0.0257847	+	0.999668i	$0.508208\pi$
$380$	−2.85986e17	−4.87249
$381$	2.13476e16	0.357550
$382$	−1.31332e17	−2.16251
$383$	−3.32467e16	−0.538217	−0.269108	−	0.963110i	$-0.586729\pi$
$383$	−3.32467e16	−0.538217	−0.269108	+	0.963110i	$0.586729\pi$
$384$	3.34476e16	0.532368
$385$	−9.93869e16	−1.55537
$386$	1.63106e16	0.250987
$387$	9.81504e15	0.148515
$388$	−2.30402e17	−3.42831
$389$	4.92225e16	0.720263	0.360131	−	0.932902i	$-0.382732\pi$
$389$	4.92225e16	0.720263	0.360131	+	0.932902i	$0.382732\pi$
$390$	1.03005e17	1.48231
$391$	1.08667e17	1.53798
$392$	1.00676e17	1.40142
$393$	7.41107e15	0.101468
$394$	−1.22638e17	−1.65158
$395$	−1.13537e17	−1.50403
$396$	−1.18371e17	−1.54251
$397$	−9.44825e16	−1.21119	−0.605596	−	0.795772i	$-0.707065\pi$
$397$	−9.44825e16	−1.21119	−0.605596	+	0.795772i	$0.707065\pi$
$398$	7.22563e16	0.911246
$399$	5.40189e16	0.670227
$400$	9.57761e16	1.16914
$401$	3.07168e16	0.368925	0.184462	−	0.982840i	$-0.440946\pi$
$401$	3.07168e16	0.368925	0.184462	+	0.982840i	$0.440946\pi$
$402$	−1.36271e17	−1.61040
$403$	−1.26530e17	−1.47133
$404$	−6.38156e16	−0.730210
$405$	1.17204e16	0.131973
$406$	−2.24729e17	−2.49024
$407$	1.13425e17	1.23693
$408$	1.57193e17	1.68710
$409$	−6.13389e16	−0.647940	−0.323970	−	0.946067i	$-0.605018\pi$
$409$	−6.13389e16	−0.647940	−0.323970	+	0.946067i	$0.605018\pi$
$410$	2.70721e17	2.81467
$411$	−8.48259e16	−0.868074
$412$	−3.54223e16	−0.356816
$413$	−9.37743e15	−0.0929841
$414$	−9.65198e16	−0.942137
$415$	1.61635e17	1.55319
$416$	−3.02147e17	−2.85832
$417$	−7.77606e16	−0.724228
$418$	−6.10069e17	−5.59414
$419$	1.31663e16	0.118870	0.0594350	−	0.998232i	$-0.481070\pi$
$419$	1.31663e16	0.118870	0.0594350	+	0.998232i	$0.481070\pi$
$420$	−1.39058e17	−1.23617
$421$	−1.64531e17	−1.44018	−0.720088	−	0.693883i	$-0.755898\pi$
$421$	−1.64531e17	−1.44018	−0.720088	+	0.693883i	$0.755898\pi$
$422$	8.30049e16	0.715439
$423$	1.18116e16	0.100253
$424$	−4.02246e16	−0.336212
$425$	5.09743e16	0.419588
$426$	−6.59674e16	−0.534770
$427$	8.02944e16	0.641068
$428$	−5.42384e16	−0.426503
$429$	1.57378e17	1.21891
$430$	−1.30220e17	−0.993420
$431$	−1.06355e17	−0.799202	−0.399601	−	0.916689i	$-0.630851\pi$
$431$	−1.06355e17	−0.799202	−0.399601	+	0.916689i	$0.630851\pi$
$432$	−7.40005e16	−0.547760
$433$	1.21678e17	0.887239	0.443619	−	0.896215i	$-0.353694\pi$
$433$	1.21678e17	0.887239	0.443619	+	0.896215i	$0.353694\pi$
$434$	2.38497e17	1.71317
$435$	−1.79987e17	−1.27368
$436$	−1.84070e17	−1.28328
$437$	−3.56287e17	−2.44721
$438$	1.02850e17	0.696022
$439$	−2.38736e17	−1.59184	−0.795920	−	0.605402i	$-0.793012\pi$
$439$	−2.38736e17	−1.59184	−0.795920	+	0.605402i	$0.793012\pi$
$440$	9.48238e17	6.22981
$441$	−2.52245e16	−0.163295
$442$	−3.46134e17	−2.20801
$443$	−2.57387e17	−1.61794	−0.808970	−	0.587850i	$-0.799975\pi$
$443$	−2.57387e17	−1.61794	−0.808970	+	0.587850i	$0.799975\pi$
$444$	1.58700e17	0.983079
$445$	−2.55748e17	−1.56125
$446$	−4.11638e17	−2.47650
$447$	1.49385e17	0.885745
$448$	2.21649e17	1.29527
$449$	2.94292e17	1.69503	0.847516	−	0.530770i	$-0.178097\pi$
$449$	2.94292e17	1.69503	0.847516	+	0.530770i	$0.178097\pi$
$450$	−4.52760e16	−0.257032
$451$	4.13625e17	2.31451
$452$	4.52351e17	2.49503
$453$	6.66588e15	0.0362426
$454$	−8.39014e16	−0.449683
$455$	1.84882e17	0.976835
$456$	−5.15387e17	−2.68449
$457$	−2.48129e17	−1.27416	−0.637078	−	0.770800i	$-0.719857\pi$
$457$	−2.48129e17	−1.27416	−0.637078	+	0.770800i	$0.719857\pi$
$458$	−7.25124e16	−0.367102
$459$	−3.93848e16	−0.196583
$460$	9.17173e17	4.51362
$461$	−2.54644e17	−1.23560	−0.617801	−	0.786335i	$-0.711976\pi$
$461$	−2.54644e17	−1.23560	−0.617801	+	0.786335i	$0.711976\pi$
$462$	−2.96642e17	−1.41925
$463$	3.82962e16	0.180667	0.0903337	−	0.995912i	$-0.471207\pi$
$463$	3.82962e16	0.180667	0.0903337	+	0.995912i	$0.471207\pi$
$464$	1.13640e18	5.28647
$465$	1.91013e17	0.876232
$466$	1.87732e17	0.849238
$467$	−3.09661e16	−0.138142	−0.0690711	−	0.997612i	$-0.522004\pi$
$467$	−3.09661e16	−0.138142	−0.0690711	+	0.997612i	$0.522004\pi$
$468$	2.20197e17	0.968754
$469$	−2.44591e17	−1.06125
$470$	−1.56709e17	−0.670590
$471$	1.89414e17	0.799424
$472$	8.94688e16	0.372433
$473$	−1.98958e17	−0.816892
$474$	−3.38876e17	−1.37240
$475$	−1.67129e17	−0.667641
$476$	4.67286e17	1.84136
$477$	1.00783e16	0.0391758
$478$	−4.33557e17	−1.66251
$479$	4.11777e17	1.55769	0.778846	−	0.627215i	$-0.215805\pi$
$479$	4.11777e17	1.55769	0.778846	+	0.627215i	$0.215805\pi$
$480$	4.56128e17	1.70223
$481$	−2.10997e17	−0.776843
$482$	8.62102e16	0.313150
$483$	−1.73242e17	−0.620864
$484$	1.68568e18	5.96047
$485$	−4.62438e17	−1.61336
$486$	3.49821e16	0.120423
$487$	−3.38591e17	−1.15010	−0.575052	−	0.818117i	$-0.695018\pi$
$487$	−3.38591e17	−1.15010	−0.575052	+	0.818117i	$0.695018\pi$
$488$	−7.66078e17	−2.56770
$489$	−1.52760e17	−0.505246
$490$	3.34663e17	1.09228
$491$	−5.96980e16	−0.192278	−0.0961391	−	0.995368i	$-0.530649\pi$
$491$	−5.96980e16	−0.192278	−0.0961391	+	0.995368i	$0.530649\pi$
$492$	5.78729e17	1.83951
$493$	6.04820e17	1.89724
$494$	1.13487e18	3.51334
$495$	−2.37581e17	−0.725903
$496$	−1.20602e18	−3.63684
$497$	−1.18404e17	−0.352411
$498$	4.82436e17	1.41726
$499$	1.33164e16	0.0386130	0.0193065	−	0.999814i	$-0.493854\pi$
$499$	1.33164e16	0.0386130	0.0193065	+	0.999814i	$0.493854\pi$
$500$	−6.17157e17	−1.76641
$501$	3.43585e17	0.970708
$502$	4.26360e17	1.18906
$503$	−3.31781e17	−0.913397	−0.456699	−	0.889621i	$-0.650968\pi$
$503$	−3.31781e17	−0.913397	−0.456699	+	0.889621i	$0.650968\pi$
$504$	−2.50603e17	−0.681064
$505$	−1.28084e17	−0.343637
$506$	1.95653e18	5.18212
$507$	−7.19626e16	−0.188172
$508$	−6.05462e17	−1.56305
$509$	−5.66799e17	−1.44465	−0.722326	−	0.691552i	$-0.756927\pi$
$509$	−5.66799e17	−1.44465	−0.722326	+	0.691552i	$0.756927\pi$
$510$	5.22533e17	1.31495
$511$	1.84604e17	0.458675
$512$	4.39047e17	1.07710
$513$	1.29131e17	0.312800
$514$	−3.93954e17	−0.942290
$515$	−7.10957e16	−0.167918
$516$	−2.78375e17	−0.649242
$517$	−2.39429e17	−0.551428
$518$	3.97708e17	0.904527
$519$	−2.61322e17	−0.586932
$520$	−1.76394e18	−3.91256
$521$	−2.81915e17	−0.617550	−0.308775	−	0.951135i	$-0.599919\pi$
$521$	−2.81915e17	−0.617550	−0.308775	+	0.951135i	$0.599919\pi$
$522$	−5.37209e17	−1.16221
$523$	−5.36927e17	−1.14724	−0.573620	−	0.819121i	$-0.694462\pi$
$523$	−5.36927e17	−1.14724	−0.573620	+	0.819121i	$0.694462\pi$
$524$	−2.10193e17	−0.443573
$525$	−8.12652e16	−0.169383
$526$	9.44243e17	1.94391
$527$	−6.41873e17	−1.30521
$528$	1.50005e18	3.01290
$529$	6.38596e17	1.26696
$530$	−1.33713e17	−0.262047
$531$	−2.24165e16	−0.0433963
$532$	−1.53209e18	−2.92993
$533$	−7.69437e17	−1.45360
$534$	−7.63336e17	−1.42462
$535$	−1.08861e17	−0.200713
$536$	2.33361e18	4.25066
$537$	5.91857e17	1.06509
$538$	8.46205e17	1.50450
$539$	5.11320e17	0.898185
$540$	−3.32415e17	−0.576927
$541$	−1.11950e18	−1.91974	−0.959868	−	0.280452i	$-0.909516\pi$
$541$	−1.11950e18	−1.91974	−0.959868	+	0.280452i	$0.909516\pi$
$542$	1.16442e18	1.97295
$543$	−7.48658e16	−0.125339
$544$	−1.53276e18	−2.53560
$545$	−3.69445e17	−0.603910
$546$	5.51821e17	0.891345
$547$	8.41696e17	1.34350	0.671750	−	0.740778i	$-0.265543\pi$
$547$	8.41696e17	1.34350	0.671750	+	0.740778i	$0.265543\pi$
$548$	2.40584e18	3.79483
$549$	1.91941e17	0.299191
$550$	9.17779e17	1.41378
$551$	−1.98302e18	−3.01885
$552$	1.65288e18	2.48677
$553$	−6.08243e17	−0.904406
$554$	−1.09880e18	−1.61474
$555$	3.18526e17	0.462637
$556$	2.20545e18	3.16600
$557$	−1.54092e17	−0.218636	−0.109318	−	0.994007i	$-0.534867\pi$
$557$	−1.54092e17	−0.218636	−0.109318	+	0.994007i	$0.534867\pi$
$558$	5.70120e17	0.799547
$559$	3.70108e17	0.513040
$560$	1.76221e18	2.41454
$561$	7.98359e17	1.08128
$562$	−2.73866e18	−3.66650
$563$	3.23193e17	0.427717	0.213859	−	0.976865i	$-0.431397\pi$
$563$	3.23193e17	0.427717	0.213859	+	0.976865i	$0.431397\pi$
$564$	−3.35000e17	−0.438259
$565$	9.07909e17	1.17416
$566$	1.77416e18	2.26822
$567$	6.27888e16	0.0793582
$568$	1.12968e18	1.41153
$569$	−3.00730e17	−0.371490	−0.185745	−	0.982598i	$-0.559470\pi$
$569$	−3.00730e17	−0.371490	−0.185745	+	0.982598i	$0.559470\pi$
$570$	−1.71323e18	−2.09232
$571$	−2.63499e17	−0.318159	−0.159079	−	0.987266i	$-0.550853\pi$
$571$	−2.63499e17	−0.318159	−0.159079	+	0.987266i	$0.550853\pi$
$572$	−4.46356e18	−5.32853
$573$	−5.63495e17	−0.665097
$574$	1.45031e18	1.69252
$575$	5.35992e17	0.618468
$576$	5.29846e17	0.604510
$577$	−8.70812e17	−0.982385	−0.491192	−	0.871051i	$-0.663439\pi$
$577$	−8.70812e17	−0.982385	−0.491192	+	0.871051i	$0.663439\pi$
$578$	−7.30558e16	−0.0814937
$579$	6.99824e16	0.0771931
$580$	5.10479e18	5.56796
$581$	8.65916e17	0.933966
$582$	−1.38025e18	−1.47217
$583$	−2.04295e17	−0.215482
$584$	−1.76128e18	−1.83715
$585$	4.41956e17	0.455896
$586$	−1.06006e18	−1.08142
$587$	−1.15068e18	−1.16093	−0.580467	−	0.814284i	$-0.697130\pi$
$587$	−1.15068e18	−1.16093	−0.580467	+	0.814284i	$0.697130\pi$
$588$	7.15419e17	0.713851
$589$	2.10450e18	2.07683
$590$	2.97408e17	0.290278
$591$	−5.26193e17	−0.507956
$592$	−2.01112e18	−1.92020
$593$	−6.40296e17	−0.604679	−0.302340	−	0.953200i	$-0.597768\pi$
$593$	−6.40296e17	−0.604679	−0.302340	+	0.953200i	$0.597768\pi$
$594$	−7.09113e17	−0.662374
$595$	9.37887e17	0.866543
$596$	−4.23687e18	−3.87208
$597$	3.10024e17	0.280261
$598$	−3.63959e18	−3.25458
$599$	−6.09215e17	−0.538886	−0.269443	−	0.963016i	$-0.586840\pi$
$599$	−6.09215e17	−0.538886	−0.269443	+	0.963016i	$0.586840\pi$
$600$	7.75340e17	0.678436
$601$	−1.59761e18	−1.38289	−0.691443	−	0.722431i	$-0.743025\pi$
$601$	−1.59761e18	−1.38289	−0.691443	+	0.722431i	$0.743025\pi$
$602$	−6.97617e17	−0.597365
$603$	−5.84687e17	−0.495291
$604$	−1.89058e17	−0.158437
$605$	3.38331e18	2.80500
$606$	−3.82294e17	−0.313563
$607$	−1.52598e17	−0.123829	−0.0619145	−	0.998081i	$-0.519721\pi$
$607$	−1.52598e17	−0.123829	−0.0619145	+	0.998081i	$0.519721\pi$
$608$	5.02543e18	4.03460
$609$	−9.64228e17	−0.765891
$610$	−2.54656e18	−2.00129
$611$	4.45393e17	0.346319
$612$	1.11703e18	0.859374
$613$	−5.78338e17	−0.440239	−0.220120	−	0.975473i	$-0.570645\pi$
$613$	−5.78338e17	−0.440239	−0.220120	+	0.975473i	$0.570645\pi$
$614$	5.96492e17	0.449273
$615$	1.16156e18	0.865673
$616$	5.07991e18	3.74612
$617$	1.27830e18	0.932777	0.466388	−	0.884580i	$-0.345555\pi$
$617$	1.27830e18	0.932777	0.466388	+	0.884580i	$0.345555\pi$
$618$	−2.12201e17	−0.153222
$619$	−1.25526e18	−0.896902	−0.448451	−	0.893807i	$-0.648024\pi$
$619$	−1.25526e18	−0.896902	−0.448451	+	0.893807i	$0.648024\pi$
$620$	−5.41753e18	−3.83050
$621$	−4.14129e17	−0.289761
$622$	−9.30717e17	−0.644436
$623$	−1.37010e18	−0.938815
$624$	−2.79043e18	−1.89222
$625$	−1.85078e18	−1.24204
$626$	−2.79984e18	−1.85952
$627$	−2.61757e18	−1.72052
$628$	−5.37218e18	−3.49473
$629$	−1.07036e18	−0.689131
$630$	−8.33043e17	−0.530828
$631$	4.25601e17	0.268418	0.134209	−	0.990953i	$-0.457151\pi$
$631$	4.25601e17	0.268418	0.134209	+	0.990953i	$0.457151\pi$
$632$	5.80316e18	3.62246
$633$	3.56142e17	0.220039
$634$	−9.76003e17	−0.596858
$635$	−1.21522e18	−0.735571
$636$	−2.85841e17	−0.171259
$637$	−9.51171e17	−0.564095
$638$	1.08896e19	6.39262
$639$	−2.83041e17	−0.164473
$640$	−1.90401e18	−1.09522
$641$	−2.52388e18	−1.43712	−0.718558	−	0.695467i	$-0.755197\pi$
$641$	−2.52388e18	−1.43712	−0.718558	+	0.695467i	$0.755197\pi$
$642$	−3.24920e17	−0.183147
$643$	−2.66994e17	−0.148981	−0.0744903	−	0.997222i	$-0.523733\pi$
$643$	−2.66994e17	−0.148981	−0.0744903	+	0.997222i	$0.523733\pi$
$644$	4.91349e18	2.71414
$645$	−5.58724e17	−0.305534
$646$	5.75705e18	3.11666
$647$	−2.91487e18	−1.56222	−0.781108	−	0.624395i	$-0.785345\pi$
$647$	−2.91487e18	−1.56222	−0.781108	+	0.624395i	$0.785345\pi$
$648$	−5.99059e17	−0.317857
$649$	4.54399e17	0.238697
$650$	−1.70728e18	−0.887906
$651$	1.02330e18	0.526897
$652$	4.33259e18	2.20871
$653$	9.19067e17	0.463886	0.231943	−	0.972729i	$-0.425492\pi$
$653$	9.19067e17	0.463886	0.231943	+	0.972729i	$0.425492\pi$
$654$	−1.10269e18	−0.551058
$655$	−4.21877e17	−0.208746
$656$	−7.33389e18	−3.59302
$657$	4.41290e17	0.214067
$658$	−8.39522e17	−0.403240
$659$	−2.20480e17	−0.104861	−0.0524306	−	0.998625i	$-0.516697\pi$
$659$	−2.20480e17	−0.104861	−0.0524306	+	0.998625i	$0.516697\pi$
$660$	6.73830e18	3.17333
$661$	3.51365e18	1.63851	0.819255	−	0.573430i	$-0.194388\pi$
$661$	3.51365e18	1.63851	0.819255	+	0.573430i	$0.194388\pi$
$662$	−2.76385e18	−1.27626
$663$	−1.48513e18	−0.679089
$664$	−8.26159e18	−3.74086
$665$	−3.07504e18	−1.37883
$666$	9.50710e17	0.422149
$667$	6.35966e18	2.79651
$668$	−9.74477e18	−4.24350
$669$	−1.76618e18	−0.761667
$670$	7.75726e18	3.31301
$671$	−3.89079e18	−1.64567
$672$	2.44358e18	1.02359
$673$	−1.15268e18	−0.478200	−0.239100	−	0.970995i	$-0.576852\pi$
$673$	−1.15268e18	−0.478200	−0.239100	+	0.970995i	$0.576852\pi$
$674$	−8.50749e18	−3.49552
$675$	−1.94262e17	−0.0790520
$676$	2.04101e18	0.822604
$677$	−4.04894e18	−1.61627	−0.808136	−	0.588995i	$-0.799524\pi$
$677$	−4.04894e18	−1.61627	−0.808136	+	0.588995i	$0.799524\pi$
$678$	2.70985e18	1.07140
$679$	−2.47738e18	−0.970150
$680$	−8.94825e18	−3.47080
$681$	−3.59989e17	−0.138303
$682$	−1.15568e19	−4.39782
$683$	1.80682e17	0.0681052	0.0340526	−	0.999420i	$-0.489159\pi$
$683$	1.80682e17	0.0681052	0.0340526	+	0.999420i	$0.489159\pi$
$684$	−3.66241e18	−1.36742
$685$	4.82874e18	1.78585
$686$	5.45264e18	1.99756
$687$	−3.11123e17	−0.112905
$688$	3.52768e18	1.26813
$689$	3.80035e17	0.135331
$690$	5.49441e18	1.93822
$691$	5.20396e18	1.81855	0.909277	−	0.416191i	$-0.136635\pi$
$691$	5.20396e18	1.81855	0.909277	+	0.416191i	$0.136635\pi$
$692$	7.41162e18	2.56581
$693$	−1.27278e18	−0.436502
$694$	−3.10945e18	−1.05645
$695$	4.42654e18	1.48992
$696$	9.19957e18	3.06766
$697$	−3.90326e18	−1.28948
$698$	6.25687e18	2.04784
$699$	8.05485e17	0.261190
$700$	2.30485e18	0.740466
$701$	1.05851e18	0.336920	0.168460	−	0.985708i	$-0.446121\pi$
$701$	1.05851e18	0.336920	0.168460	+	0.985708i	$0.446121\pi$
$702$	1.31911e18	0.415997
$703$	3.50939e18	1.09653
$704$	−1.07404e19	−3.32504
$705$	−6.72377e17	−0.206245
$706$	9.60034e18	2.91780
$707$	−6.86173e17	−0.206637
$708$	6.35777e17	0.189709
$709$	−7.68395e17	−0.227187	−0.113594	−	0.993527i	$-0.536236\pi$
$709$	−7.68395e17	−0.227187	−0.113594	+	0.993527i	$0.536236\pi$
$710$	3.75521e18	1.10016
$711$	−1.45399e18	−0.422093
$712$	1.30719e19	3.76028
$713$	−6.74927e18	−1.92387
$714$	2.79932e18	0.790706
$715$	−8.95877e18	−2.50761
$716$	−1.67863e19	−4.65608
$717$	−1.86023e18	−0.511318
$718$	−5.04453e18	−1.37408
$719$	1.35722e18	0.366364	0.183182	−	0.983079i	$-0.441360\pi$
$719$	1.35722e18	0.366364	0.183182	+	0.983079i	$0.441360\pi$
$720$	4.21250e18	1.12688
$721$	−3.80875e17	−0.100973
$722$	−1.17306e19	−3.08196
$723$	3.69895e17	0.0963117
$724$	2.12335e18	0.547924
$725$	2.98322e18	0.762936
$726$	1.00982e19	2.55951
$727$	1.76674e18	0.443813	0.221906	−	0.975068i	$-0.428772\pi$
$727$	1.76674e18	0.443813	0.221906	+	0.975068i	$0.428772\pi$
$728$	−9.44980e18	−2.35271
$729$	1.50095e17	0.0370370
$730$	−5.85477e18	−1.43189
$731$	1.87751e18	0.455114
$732$	−5.44385e18	−1.30793
$733$	−5.71590e18	−1.36116	−0.680580	−	0.732674i	$-0.738272\pi$
$733$	−5.71590e18	−1.36116	−0.680580	+	0.732674i	$0.738272\pi$
$734$	−3.86642e18	−0.912608
$735$	1.43591e18	0.335939
$736$	−1.61169e19	−3.73744
$737$	1.18520e19	2.72430
$738$	3.46693e18	0.789912
$739$	1.38377e18	0.312518	0.156259	−	0.987716i	$-0.450056\pi$
$739$	1.38377e18	0.312518	0.156259	+	0.987716i	$0.450056\pi$
$740$	−9.03406e18	−2.02245
$741$	4.86928e18	1.08055
$742$	−7.16328e17	−0.157575
$743$	−1.50693e18	−0.328598	−0.164299	−	0.986411i	$-0.552536\pi$
$743$	−1.50693e18	−0.328598	−0.164299	+	0.986411i	$0.552536\pi$
$744$	−9.76316e18	−2.11041
$745$	−8.50379e18	−1.82220
$746$	−1.36184e19	−2.89284
$747$	2.06995e18	0.435888
$748$	−2.26431e19	−4.72689
$749$	−5.83194e17	−0.120693
$750$	−3.69714e18	−0.758521
$751$	2.94298e18	0.598587	0.299294	−	0.954161i	$-0.403249\pi$
$751$	2.94298e18	0.598587	0.299294	+	0.954161i	$0.403249\pi$
$752$	4.24527e18	0.856030
$753$	1.82935e18	0.365703
$754$	−2.02572e19	−4.01481
$755$	−3.79457e17	−0.0745603
$756$	−1.78082e18	−0.346919
$757$	1.83281e18	0.353992	0.176996	−	0.984212i	$-0.443362\pi$
$757$	1.83281e18	0.353992	0.176996	+	0.984212i	$0.443362\pi$
$758$	5.05539e17	0.0968066
$759$	8.39471e18	1.59380
$760$	2.93385e19	5.52268
$761$	5.44048e18	1.01540	0.507700	−	0.861534i	$-0.330496\pi$
$761$	5.44048e18	1.01540	0.507700	+	0.861534i	$0.330496\pi$
$762$	−3.62708e18	−0.671196
$763$	−1.97920e18	−0.363145
$764$	1.59819e19	2.90751
$765$	2.24199e18	0.404422
$766$	5.64881e18	1.01035
$767$	−8.45285e17	−0.149911
$768$	2.71108e17	0.0476754
$769$	−5.22162e18	−0.910509	−0.455255	−	0.890361i	$-0.650452\pi$
$769$	−5.22162e18	−0.910509	−0.455255	+	0.890361i	$0.650452\pi$
$770$	1.68864e19	2.91976
$771$	−1.69030e18	−0.289809
$772$	−1.98485e18	−0.337454
$773$	−4.14804e18	−0.699321	−0.349661	−	0.936876i	$-0.613703\pi$
$773$	−4.14804e18	−0.699321	−0.349661	+	0.936876i	$0.613703\pi$
$774$	−1.66763e18	−0.278794
$775$	−3.16598e18	−0.524864
$776$	2.36363e19	3.88579
$777$	1.70641e18	0.278194
$778$	−8.36318e18	−1.35208
$779$	1.27976e19	2.05180
$780$	−1.25348e19	−1.99297
$781$	5.73745e18	0.904664
$782$	−1.84632e19	−2.88711
$783$	−2.30496e18	−0.357447
$784$	−9.06609e18	−1.39433
$785$	−1.07825e19	−1.64462
$786$	−1.25918e18	−0.190477
$787$	−2.74707e17	−0.0412130	−0.0206065	−	0.999788i	$-0.506560\pi$
$787$	−2.74707e17	−0.0412130	−0.0206065	+	0.999788i	$0.506560\pi$
$788$	1.49239e19	2.22056
$789$	4.05138e18	0.597864
$790$	1.92906e19	2.82338
$791$	4.86387e18	0.706049
$792$	1.21434e19	1.74834
$793$	7.23776e18	1.03354
$794$	1.60531e19	2.27366
$795$	−5.73710e17	−0.0805946
$796$	−8.79292e18	−1.22518
$797$	−9.11974e18	−1.26039	−0.630193	−	0.776439i	$-0.717024\pi$
$797$	−9.11974e18	−1.26039	−0.630193	+	0.776439i	$0.717024\pi$
$798$	−9.17812e18	−1.25816
$799$	2.25943e18	0.307216
$800$	−7.56018e18	−1.01964
$801$	−3.27518e18	−0.438151
$802$	−5.21896e18	−0.692549
$803$	−8.94528e18	−1.17745
$804$	1.65829e19	2.16519
$805$	9.86184e18	1.27728
$806$	2.14982e19	2.76200
$807$	3.63074e18	0.462719
$808$	6.54668e18	0.827651
$809$	−1.69025e18	−0.211976	−0.105988	−	0.994367i	$-0.533801\pi$
$809$	−1.69025e18	−0.211976	−0.105988	+	0.994367i	$0.533801\pi$
$810$	−1.99136e18	−0.247741
$811$	−3.21503e18	−0.396780	−0.198390	−	0.980123i	$-0.563571\pi$
$811$	−3.21503e18	−0.396780	−0.198390	+	0.980123i	$0.563571\pi$
$812$	2.73475e19	3.34814
$813$	4.99609e18	0.606794
$814$	−1.92716e19	−2.32198
$815$	8.69591e18	1.03942
$816$	−1.41555e19	−1.67857
$817$	−6.15579e18	−0.724170
$818$	1.04218e19	1.21632
$819$	2.36765e18	0.274140
$820$	−3.29443e19	−3.78434
$821$	5.39563e18	0.614911	0.307455	−	0.951563i	$-0.400523\pi$
$821$	5.39563e18	0.614911	0.307455	+	0.951563i	$0.400523\pi$
$822$	1.44124e19	1.62956
$823$	6.17768e18	0.692989	0.346494	−	0.938052i	$-0.387372\pi$
$823$	6.17768e18	0.692989	0.346494	+	0.938052i	$0.387372\pi$
$824$	3.63388e18	0.404430
$825$	3.93784e18	0.434817
$826$	1.59328e18	0.174551
$827$	7.42446e18	0.807010	0.403505	−	0.914977i	$-0.367792\pi$
$827$	7.42446e18	0.807010	0.403505	+	0.914977i	$0.367792\pi$
$828$	1.17456e19	1.26671
$829$	4.12318e18	0.441192	0.220596	−	0.975365i	$-0.429200\pi$
$829$	4.12318e18	0.441192	0.220596	+	0.975365i	$0.429200\pi$
$830$	−2.74628e19	−2.91566
$831$	−4.71451e18	−0.496626
$832$	1.99795e19	2.08826
$833$	−4.82518e18	−0.500404
$834$	1.32120e19	1.35953
$835$	−1.95586e19	−1.99699
$836$	7.42398e19	7.52135
$837$	2.44617e18	0.245907
$838$	−2.23703e18	−0.223144
$839$	1.29446e19	1.28126	0.640630	−	0.767849i	$-0.278673\pi$
$839$	1.29446e19	1.28126	0.640630	+	0.767849i	$0.278673\pi$
$840$	1.42656e19	1.40112
$841$	2.51359e19	2.44974
$842$	2.79548e19	2.70351
$843$	−1.17505e19	−1.12766
$844$	−1.01009e19	−0.961912
$845$	4.09649e18	0.387118
$846$	−2.00685e18	−0.188195
$847$	1.81252e19	1.68671
$848$	3.62230e18	0.334512
$849$	7.61224e18	0.697610
$850$	−8.66082e18	−0.787655
$851$	−1.12548e19	−1.01577
$852$	8.02762e18	0.719001
$853$	1.06609e19	0.947603	0.473801	−	0.880632i	$-0.342881\pi$
$853$	1.06609e19	0.947603	0.473801	+	0.880632i	$0.342881\pi$
$854$	−1.36425e19	−1.20342
$855$	−7.35079e18	−0.643509
$856$	5.56418e18	0.483417
$857$	−1.58162e19	−1.36373	−0.681864	−	0.731479i	$-0.738830\pi$
$857$	−1.58162e19	−1.36373	−0.681864	+	0.731479i	$0.738830\pi$
$858$	−2.67394e19	−2.28815
$859$	−1.52986e18	−0.129926	−0.0649632	−	0.997888i	$-0.520693\pi$
$859$	−1.52986e18	−0.129926	−0.0649632	+	0.997888i	$0.520693\pi$
$860$	1.58466e19	1.33566
$861$	6.22274e18	0.520548
$862$	1.80704e19	1.50027
$863$	−2.83497e18	−0.233603	−0.116801	−	0.993155i	$-0.537264\pi$
$863$	−2.83497e18	−0.233603	−0.116801	+	0.993155i	$0.537264\pi$
$864$	5.84130e18	0.477716
$865$	1.48758e19	1.20747
$866$	−2.06738e19	−1.66553
$867$	−3.13454e17	−0.0250640
$868$	−2.90229e19	−2.30336
$869$	2.94734e19	2.32168
$870$	3.05808e19	2.39096
$871$	−2.20475e19	−1.71096
$872$	1.88833e19	1.45452
$873$	−5.92210e18	−0.452776
$874$	6.05352e19	4.59392
$875$	−6.63593e18	−0.499861
$876$	−1.25159e19	−0.935805
$877$	−8.45969e18	−0.627852	−0.313926	−	0.949447i	$-0.601644\pi$
$877$	−8.45969e18	−0.627852	−0.313926	+	0.949447i	$0.601644\pi$
$878$	4.05627e19	2.98822
$879$	−4.54830e18	−0.332599
$880$	−8.53906e19	−6.19830
$881$	1.94438e19	1.40100	0.700501	−	0.713651i	$-0.252960\pi$
$881$	1.94438e19	1.40100	0.700501	+	0.713651i	$0.252960\pi$
$882$	4.28579e18	0.306538
$883$	8.34134e18	0.592231	0.296115	−	0.955152i	$-0.404309\pi$
$883$	8.34134e18	0.592231	0.296115	+	0.955152i	$0.404309\pi$
$884$	4.21213e19	2.96867
$885$	1.27606e18	0.0892773
$886$	4.37315e19	3.03721
$887$	−1.84638e19	−1.27297	−0.636486	−	0.771289i	$-0.719612\pi$
$887$	−1.84638e19	−1.27297	−0.636486	+	0.771289i	$0.719612\pi$
$888$	−1.62807e19	−1.11426
$889$	−6.51018e18	−0.442315
$890$	4.34531e19	2.93080
$891$	−3.04253e18	−0.203718
$892$	5.00925e19	3.32967
$893$	−7.40797e18	−0.488838
$894$	−2.53814e19	−1.66273
$895$	−3.36916e19	−2.19115
$896$	−1.02002e19	−0.658577
$897$	−1.56161e19	−1.00097
$898$	−5.00020e19	−3.18193
$899$	−3.75650e19	−2.37326
$900$	5.50967e18	0.345580
$901$	1.92787e18	0.120051
$902$	−7.02773e19	−4.34483
$903$	−2.99321e18	−0.183724
$904$	−4.64055e19	−2.82797
$905$	4.26176e18	0.257853
$906$	−1.13257e18	−0.0680350
$907$	1.60702e19	0.958461	0.479231	−	0.877689i	$-0.340916\pi$
$907$	1.60702e19	0.958461	0.479231	+	0.877689i	$0.340916\pi$
$908$	1.02100e19	0.604601
$909$	−1.64027e18	−0.0964387
$910$	−3.14126e19	−1.83373
$911$	−2.89298e19	−1.67678	−0.838390	−	0.545070i	$-0.816503\pi$
$911$	−2.89298e19	−1.67678	−0.838390	+	0.545070i	$0.816503\pi$
$912$	4.64116e19	2.67091
$913$	−4.19594e19	−2.39756
$914$	4.21585e19	2.39186
$915$	−1.09263e19	−0.615512
$916$	8.82409e18	0.493571
$917$	−2.26009e18	−0.125523
$918$	6.69170e18	0.369028
$919$	−2.54475e19	−1.39346	−0.696731	−	0.717333i	$-0.745363\pi$
$919$	−2.54475e19	−1.39346	−0.696731	+	0.717333i	$0.745363\pi$
$920$	−9.40904e19	−5.11593
$921$	2.55932e18	0.138177
$922$	4.32655e19	2.31948
$923$	−1.06730e19	−0.568164
$924$	3.60985e19	1.90819
$925$	−5.27947e18	−0.277121
$926$	−6.50675e18	−0.339151
$927$	−9.10471e17	−0.0471246
$928$	−8.97030e19	−4.61047
$929$	−3.42006e19	−1.74555	−0.872774	−	0.488125i	$-0.837681\pi$
$929$	−3.42006e19	−1.74555	−0.872774	+	0.488125i	$0.837681\pi$
$930$	−3.24542e19	−1.64487
$931$	1.58203e19	0.796235
$932$	−2.28452e19	−1.14180
$933$	−3.99335e18	−0.198201
$934$	5.26131e18	0.259322
$935$	−4.54468e19	−2.22448
$936$	−2.25895e19	−1.09803
$937$	7.36987e18	0.355756	0.177878	−	0.984053i	$-0.443077\pi$
$937$	7.36987e18	0.355756	0.177878	+	0.984053i	$0.443077\pi$
$938$	4.15573e19	1.99218
$939$	−1.20130e19	−0.571908
$940$	1.90700e19	0.901611
$941$	2.27720e19	1.06922	0.534611	−	0.845098i	$-0.320458\pi$
$941$	2.27720e19	1.06922	0.534611	+	0.845098i	$0.320458\pi$
$942$	−3.21826e19	−1.50069
$943$	−4.10427e19	−1.90068
$944$	−8.05683e18	−0.370550
$945$	−3.57427e18	−0.163260
$946$	3.38042e19	1.53348
$947$	4.25430e18	0.191670	0.0958349	−	0.995397i	$-0.469448\pi$
$947$	4.25430e18	0.191670	0.0958349	+	0.995397i	$0.469448\pi$
$948$	4.12380e19	1.84520
$949$	1.66403e19	0.739486
$950$	2.83961e19	1.25330
$951$	−4.18766e18	−0.183568
$952$	−4.79377e19	−2.08707
$953$	−1.23523e19	−0.534126	−0.267063	−	0.963679i	$-0.586053\pi$
$953$	−1.23523e19	−0.534126	−0.267063	+	0.963679i	$0.586053\pi$
$954$	−1.71236e18	−0.0735412
$955$	3.20771e19	1.36827
$956$	5.27599e19	2.23526
$957$	4.67232e19	1.96610
$958$	−6.99633e19	−2.92411
$959$	2.58686e19	1.07387
$960$	−3.01616e19	−1.24363
$961$	1.54488e19	0.632693
$962$	3.58496e19	1.45830
$963$	−1.39411e18	−0.0563282
$964$	−1.04910e19	−0.421032
$965$	−3.98377e18	−0.158806
$966$	2.94348e19	1.16549
$967$	−5.84975e18	−0.230073	−0.115036	−	0.993361i	$-0.536698\pi$
$967$	−5.84975e18	−0.230073	−0.115036	+	0.993361i	$0.536698\pi$
$968$	−1.72930e20	−6.75584
$969$	2.47013e19	0.958551
$970$	7.85708e19	3.02862
$971$	3.23007e19	1.23677	0.618383	−	0.785877i	$-0.287788\pi$
$971$	3.23007e19	1.23677	0.618383	+	0.785877i	$0.287788\pi$
$972$	−4.25699e18	−0.161909
$973$	2.37139e19	0.895922
$974$	5.75286e19	2.15899
$975$	−7.32527e18	−0.273082
$976$	6.89867e19	2.55471
$977$	3.22016e19	1.18457	0.592287	−	0.805727i	$-0.298225\pi$
$977$	3.22016e19	1.18457	0.592287	+	0.805727i	$0.298225\pi$
$978$	2.59548e19	0.948452
$979$	6.63904e19	2.41000
$980$	−4.07254e19	−1.46857
$981$	−4.73121e18	−0.169482
$982$	1.01430e19	0.360947
$983$	1.37394e19	0.485700	0.242850	−	0.970064i	$-0.421918\pi$
$983$	1.37394e19	0.485700	0.242850	+	0.970064i	$0.421918\pi$
$984$	−5.93703e19	−2.08498
$985$	2.99537e19	1.04500
$986$	−1.02762e20	−3.56151
$987$	−3.60207e18	−0.124020
$988$	−1.38103e20	−4.72370
$989$	1.97420e19	0.670833
$990$	4.03664e19	1.36267
$991$	−6.20738e18	−0.208176	−0.104088	−	0.994568i	$-0.533192\pi$
$991$	−6.20738e18	−0.208176	−0.104088	+	0.994568i	$0.533192\pi$
$992$	9.51985e19	3.17179
$993$	−1.18586e19	−0.392522
$994$	2.01175e19	0.661549
$995$	−1.76482e19	−0.576568
$996$	−5.87079e19	−1.90551
$997$	−2.64598e18	−0.0853234	−0.0426617	−	0.999090i	$-0.513584\pi$
$997$	−2.64598e18	−0.0853234	−0.0426617	+	0.999090i	$0.513584\pi$
$998$	−2.26254e18	−0.0724848
$999$	4.07913e18	0.129835

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} -7.05083e6 q^{10} -1.07727e7 q^{11} -1.50728e7 q^{12} +2.00397e7 q^{13} -3.77728e7 q^{14} -3.02524e7 q^{15} +1.91008e8 q^{16} +1.01659e8 q^{17} -9.02948e7 q^{18} -3.33309e8 q^{19} +8.58021e8 q^{20} -1.62069e8 q^{21} +1.83034e9 q^{22} +1.06894e9 q^{23} +1.54628e9 q^{24} +5.01424e8 q^{25} -3.40486e9 q^{26} -3.87420e8 q^{27} +4.59660e9 q^{28} +5.94950e9 q^{29} +5.14006e9 q^{30} -6.31398e9 q^{31} -1.50774e10 q^{32} +7.85331e9 q^{33} -1.72724e10 q^{34} +9.22581e9 q^{35} +1.09880e10 q^{36} -1.05289e10 q^{37} +5.66310e10 q^{38} -1.46089e10 q^{39} -8.80222e10 q^{40} -3.83957e10 q^{41} +2.75364e10 q^{42} +1.84687e10 q^{43} -2.22736e11 q^{44} +2.20540e10 q^{45} -1.81619e11 q^{46} +2.22256e10 q^{47} -1.39245e11 q^{48} -4.74644e10 q^{49} -8.51948e10 q^{50} -7.41094e10 q^{51} +4.14339e11 q^{52} +1.89641e10 q^{53} +6.58249e10 q^{54} -4.47052e11 q^{55} -4.71554e11 q^{56} +2.42982e11 q^{57} -1.01085e12 q^{58} -4.21805e10 q^{59} -6.25497e11 q^{60} +3.61171e11 q^{61} +1.07278e12 q^{62} +1.18148e11 q^{63} +9.96998e11 q^{64} +8.31617e11 q^{65} -1.33432e12 q^{66} -1.10019e12 q^{67} +2.10190e12 q^{68} -7.79257e11 q^{69} -1.56752e12 q^{70} -5.32591e11 q^{71} -1.12724e12 q^{72} +8.30365e11 q^{73} +1.78893e12 q^{74} -3.65538e11 q^{75} -6.89147e12 q^{76} -2.39495e12 q^{77} +2.48214e12 q^{78} -2.73593e12 q^{79} +7.92656e12 q^{80} +2.82430e11 q^{81} +6.52364e12 q^{82} +3.89497e12 q^{83} -3.35092e12 q^{84} +4.21870e12 q^{85} -3.13794e12 q^{86} -4.33718e12 q^{87} +2.28499e13 q^{88} -6.16283e12 q^{89} -3.74710e12 q^{90} +4.45516e12 q^{91} +2.21013e13 q^{92} +4.60289e12 q^{93} -3.77625e12 q^{94} -1.38318e13 q^{95} +1.09914e13 q^{96} -1.11435e13 q^{97} +8.06446e12 q^{98} -5.72506e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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