LMFDB - Embedded newform 177.14.a.b.1.24

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			1.24
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+96.2584 q^{2} -729.000 q^{3} +1073.68 q^{4} +26611.4 q^{5} -70172.4 q^{6} +274772. q^{7} -685198. q^{8} +531441. q^{9} +O(q^{10})$	\(q+96.2584 q^{2} -729.000 q^{3} +1073.68 q^{4} +26611.4 q^{5} -70172.4 q^{6} +274772. q^{7} -685198. q^{8} +531441. q^{9} +2.56158e6 q^{10} +800651. q^{11} -782714. q^{12} -3.00072e6 q^{13} +2.64491e7 q^{14} -1.93997e7 q^{15} -7.47517e7 q^{16} -1.21012e8 q^{17} +5.11557e7 q^{18} +4.02255e8 q^{19} +2.85722e7 q^{20} -2.00309e8 q^{21} +7.70694e7 q^{22} -6.66039e8 q^{23} +4.99509e8 q^{24} -5.12534e8 q^{25} -2.88844e8 q^{26} -3.87420e8 q^{27} +2.95017e8 q^{28} +4.58053e8 q^{29} -1.86739e9 q^{30} -2.88050e9 q^{31} -1.58233e9 q^{32} -5.83674e8 q^{33} -1.16484e10 q^{34} +7.31207e9 q^{35} +5.70598e8 q^{36} +1.84789e9 q^{37} +3.87204e10 q^{38} +2.18752e9 q^{39} -1.82341e10 q^{40} -1.94423e10 q^{41} -1.92814e10 q^{42} +4.71360e10 q^{43} +8.59644e8 q^{44} +1.41424e10 q^{45} -6.41119e10 q^{46} +4.88308e10 q^{47} +5.44940e10 q^{48} -2.13895e10 q^{49} -4.93357e10 q^{50} +8.82179e10 q^{51} -3.22181e9 q^{52} -1.01733e11 q^{53} -3.72925e10 q^{54} +2.13065e10 q^{55} -1.88273e11 q^{56} -2.93244e11 q^{57} +4.40914e10 q^{58} -4.21805e10 q^{59} -2.08291e10 q^{60} -4.55386e11 q^{61} -2.77273e11 q^{62} +1.46025e11 q^{63} +4.60053e11 q^{64} -7.98534e10 q^{65} -5.61836e10 q^{66} +6.52429e11 q^{67} -1.29928e11 q^{68} +4.85542e11 q^{69} +7.03848e11 q^{70} +1.59803e12 q^{71} -3.64142e11 q^{72} -1.70976e12 q^{73} +1.77875e11 q^{74} +3.73637e11 q^{75} +4.31893e11 q^{76} +2.19996e11 q^{77} +2.10567e11 q^{78} -8.10316e11 q^{79} -1.98925e12 q^{80} +2.82430e11 q^{81} -1.87149e12 q^{82} -1.15126e12 q^{83} -2.15068e11 q^{84} -3.22031e12 q^{85} +4.53723e12 q^{86} -3.33920e11 q^{87} -5.48604e11 q^{88} +2.23377e12 q^{89} +1.36133e12 q^{90} -8.24512e11 q^{91} -7.15114e11 q^{92} +2.09989e12 q^{93} +4.70038e12 q^{94} +1.07046e13 q^{95} +1.15352e12 q^{96} -9.65937e12 q^{97} -2.05892e12 q^{98} +4.25499e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	96.2584	1.06352	0.531758	−	0.846897i	$-0.321532\pi$
$2$	96.2584	1.06352	0.531758	+	0.846897i	$0.321532\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	1073.68	0.131065
$5$	26611.4	0.761664	0.380832	−	0.924644i	$-0.375638\pi$
$5$	26611.4	0.761664	0.380832	+	0.924644i	$0.375638\pi$
$6$	−70172.4	−0.614021
$7$	274772.	0.882744	0.441372	−	0.897324i	$-0.354492\pi$
$7$	274772.	0.882744	0.441372	+	0.897324i	$0.354492\pi$
$8$	−685198.	−0.924126
$9$	531441.	0.333333
$10$	2.56158e6	0.810041
$11$	800651.	0.136267	0.0681335	−	0.997676i	$-0.478296\pi$
$11$	800651.	0.136267	0.0681335	+	0.997676i	$0.478296\pi$
$12$	−782714.	−0.0756702
$13$	−3.00072e6	−0.172422	−0.0862111	−	0.996277i	$-0.527476\pi$
$13$	−3.00072e6	−0.172422	−0.0862111	+	0.996277i	$0.527476\pi$
$14$	2.64491e7	0.938811
$15$	−1.93997e7	−0.439747
$16$	−7.47517e7	−1.11389
$17$	−1.21012e8	−1.21594	−0.607968	−	0.793961i	$-0.708015\pi$
$17$	−1.21012e8	−1.21594	−0.607968	+	0.793961i	$0.708015\pi$
$18$	5.11557e7	0.354505
$19$	4.02255e8	1.96157	0.980783	−	0.195104i	$-0.0625044\pi$
$19$	4.02255e8	1.96157	0.980783	+	0.195104i	$0.0625044\pi$
$20$	2.85722e7	0.0998272
$21$	−2.00309e8	−0.509652
$22$	7.70694e7	0.144922
$23$	−6.66039e8	−0.938142	−0.469071	−	0.883160i	$-0.655411\pi$
$23$	−6.66039e8	−0.938142	−0.469071	+	0.883160i	$0.655411\pi$
$24$	4.99509e8	0.533544
$25$	−5.12534e8	−0.419868
$26$	−2.88844e8	−0.183374
$27$	−3.87420e8	−0.192450
$28$	2.95017e8	0.115696
$29$	4.58053e8	0.142997	0.0714987	−	0.997441i	$-0.477222\pi$
$29$	4.58053e8	0.142997	0.0714987	+	0.997441i	$0.477222\pi$
$30$	−1.86739e9	−0.467678
$31$	−2.88050e9	−0.582932	−0.291466	−	0.956581i	$-0.594143\pi$
$31$	−2.88050e9	−0.582932	−0.291466	+	0.956581i	$0.594143\pi$
$32$	−1.58233e9	−0.260509
$33$	−5.83674e8	−0.0786738
$34$	−1.16484e10	−1.29317
$35$	7.31207e9	0.672354
$36$	5.70598e8	0.0436882
$37$	1.84789e9	0.118404	0.0592018	−	0.998246i	$-0.481144\pi$
$37$	1.84789e9	0.118404	0.0592018	+	0.998246i	$0.481144\pi$
$38$	3.87204e10	2.08615
$39$	2.18752e9	0.0995480
$40$	−1.82341e10	−0.703874
$41$	−1.94423e10	−0.639225	−0.319612	−	0.947548i	$-0.603553\pi$
$41$	−1.94423e10	−0.639225	−0.319612	+	0.947548i	$0.603553\pi$
$42$	−1.92814e10	−0.542023
$43$	4.71360e10	1.13712	0.568562	−	0.822641i	$-0.307500\pi$
$43$	4.71360e10	1.13712	0.568562	+	0.822641i	$0.307500\pi$
$44$	8.59644e8	0.0178598
$45$	1.41424e10	0.253888
$46$	−6.41119e10	−0.997729
$47$	4.88308e10	0.660782	0.330391	−	0.943844i	$-0.392819\pi$
$47$	4.88308e10	0.660782	0.330391	+	0.943844i	$0.392819\pi$
$48$	5.44940e10	0.643103
$49$	−2.13895e10	−0.220763
$50$	−4.93357e10	−0.446536
$51$	8.82179e10	0.702021
$52$	−3.22181e9	−0.0225984
$53$	−1.01733e11	−0.630479	−0.315240	−	0.949012i	$-0.602085\pi$
$53$	−1.01733e11	−0.630479	−0.315240	+	0.949012i	$0.602085\pi$
$54$	−3.72925e10	−0.204674
$55$	2.13065e10	0.103790
$56$	−1.88273e11	−0.815766
$57$	−2.93244e11	−1.13251
$58$	4.40914e10	0.152080
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−2.08291e10	−0.0576353
$61$	−4.55386e11	−1.13171	−0.565855	−	0.824505i	$-0.691454\pi$
$61$	−4.55386e11	−1.13171	−0.565855	+	0.824505i	$0.691454\pi$
$62$	−2.77273e11	−0.619957
$63$	1.46025e11	0.294248
$64$	4.60053e11	0.836831
$65$	−7.98534e10	−0.131328
$66$	−5.61836e10	−0.0836708
$67$	6.52429e11	0.881144	0.440572	−	0.897717i	$-0.354776\pi$
$67$	6.52429e11	0.881144	0.440572	+	0.897717i	$0.354776\pi$
$68$	−1.29928e11	−0.159366
$69$	4.85542e11	0.541637
$70$	7.03848e11	0.715059
$71$	1.59803e12	1.48049	0.740244	−	0.672338i	$-0.234710\pi$
$71$	1.59803e12	1.48049	0.740244	+	0.672338i	$0.234710\pi$
$72$	−3.64142e11	−0.308042
$73$	−1.70976e12	−1.32232	−0.661161	−	0.750244i	$-0.729936\pi$
$73$	−1.70976e12	−1.32232	−0.661161	+	0.750244i	$0.729936\pi$
$74$	1.77875e11	0.125924
$75$	3.73637e11	0.242411
$76$	4.31893e11	0.257092
$77$	2.19996e11	0.120289
$78$	2.10567e11	0.105871
$79$	−8.10316e11	−0.375040	−0.187520	−	0.982261i	$-0.560045\pi$
$79$	−8.10316e11	−0.375040	−0.187520	+	0.982261i	$0.560045\pi$
$80$	−1.98925e12	−0.848408
$81$	2.82430e11	0.111111
$82$	−1.87149e12	−0.679825
$83$	−1.15126e12	−0.386515	−0.193258	−	0.981148i	$-0.561905\pi$
$83$	−1.15126e12	−0.386515	−0.193258	+	0.981148i	$0.561905\pi$
$84$	−2.15068e11	−0.0667974
$85$	−3.22031e12	−0.926135
$86$	4.53723e12	1.20935
$87$	−3.33920e11	−0.0825596
$88$	−5.48604e11	−0.125928
$89$	2.23377e12	0.476435	0.238217	−	0.971212i	$-0.423437\pi$
$89$	2.23377e12	0.476435	0.238217	+	0.971212i	$0.423437\pi$
$90$	1.36133e12	0.270014
$91$	−8.24512e11	−0.152205
$92$	−7.15114e11	−0.122957
$93$	2.09989e12	0.336556
$94$	4.70038e12	0.702752
$95$	1.07046e13	1.49405
$96$	1.15352e12	0.150405
$97$	−9.65937e12	−1.17742	−0.588712	−	0.808343i	$-0.700365\pi$
$97$	−9.65937e12	−1.17742	−0.588712	+	0.808343i	$0.700365\pi$
$98$	−2.05892e12	−0.234785
$99$	4.25499e11	0.0454223
$100$	−5.50298e11	−0.0550298
$101$	1.00932e12	0.0946109	0.0473054	−	0.998880i	$-0.484937\pi$
$101$	1.00932e12	0.0946109	0.0473054	+	0.998880i	$0.484937\pi$
$102$	8.49171e12	0.746610
$103$	−2.47538e12	−0.204268	−0.102134	−	0.994771i	$-0.532567\pi$
$103$	−2.47538e12	−0.204268	−0.102134	+	0.994771i	$0.532567\pi$
$104$	2.05608e12	0.159340
$105$	−5.33050e12	−0.388184
$106$	−9.79270e12	−0.670524
$107$	1.20549e13	0.776549	0.388275	−	0.921544i	$-0.373071\pi$
$107$	1.20549e13	0.776549	0.388275	+	0.921544i	$0.373071\pi$
$108$	−4.15966e11	−0.0252234
$109$	−6.06424e12	−0.346341	−0.173170	−	0.984892i	$-0.555401\pi$
$109$	−6.06424e12	−0.346341	−0.173170	+	0.984892i	$0.555401\pi$
$110$	2.05093e12	0.110382
$111$	−1.34711e12	−0.0683604
$112$	−2.05396e13	−0.983277
$113$	1.10992e13	0.501514	0.250757	−	0.968050i	$-0.419320\pi$
$113$	1.10992e13	0.501514	0.250757	+	0.968050i	$0.419320\pi$
$114$	−2.82272e13	−1.20444
$115$	−1.77243e13	−0.714549
$116$	4.91803e11	0.0187419
$117$	−1.59470e12	−0.0574740
$118$	−4.06023e12	−0.138458
$119$	−3.32507e13	−1.07336
$120$	1.32927e13	0.406382
$121$	−3.38817e13	−0.981431
$122$	−4.38347e13	−1.20359
$123$	1.41735e13	0.369057
$124$	−3.09274e12	−0.0764017
$125$	−4.61239e13	−1.08146
$126$	1.40561e13	0.312937
$127$	−7.69177e12	−0.162668	−0.0813340	−	0.996687i	$-0.525918\pi$
$127$	−7.69177e12	−0.162668	−0.0813340	+	0.996687i	$0.525918\pi$
$128$	5.72464e13	1.15049
$129$	−3.43621e13	−0.656518
$130$	−7.68656e12	−0.139669
$131$	−1.05058e14	−1.81621	−0.908104	−	0.418745i	$-0.862470\pi$
$131$	−1.05058e14	−1.81621	−0.908104	+	0.418745i	$0.862470\pi$
$132$	−6.26680e11	−0.0103113
$133$	1.10528e14	1.73156
$134$	6.28018e13	0.937111
$135$	−1.03098e13	−0.146582
$136$	8.29173e13	1.12368
$137$	−3.61517e13	−0.467138	−0.233569	−	0.972340i	$-0.575040\pi$
$137$	−3.61517e13	−0.467138	−0.233569	+	0.972340i	$0.575040\pi$
$138$	4.67375e13	0.576039
$139$	−1.24371e14	−1.46259	−0.731294	−	0.682062i	$-0.761083\pi$
$139$	−1.24371e14	−1.46259	−0.731294	+	0.682062i	$0.761083\pi$
$140$	7.85084e12	0.0881219
$141$	−3.55977e13	−0.381503
$142$	1.53824e14	1.57452
$143$	−2.40253e12	−0.0234954
$144$	−3.97261e13	−0.371296
$145$	1.21894e13	0.108916
$146$	−1.64579e14	−1.40631
$147$	1.55930e13	0.127458
$148$	1.98405e12	0.0155185
$149$	−1.99209e14	−1.49141	−0.745707	−	0.666274i	$-0.767888\pi$
$149$	−1.99209e14	−1.49141	−0.745707	+	0.666274i	$0.767888\pi$
$150$	3.59657e13	0.257808
$151$	−2.53185e14	−1.73815	−0.869075	−	0.494679i	$-0.835285\pi$
$151$	−2.53185e14	−1.73815	−0.869075	+	0.494679i	$0.835285\pi$
$152$	−2.75624e14	−1.81273
$153$	−6.43108e13	−0.405312
$154$	2.11765e13	0.127929
$155$	−7.66544e13	−0.443998
$156$	2.34870e12	0.0130472
$157$	−3.55630e14	−1.89518	−0.947591	−	0.319486i	$-0.896490\pi$
$157$	−3.55630e14	−1.89518	−0.947591	+	0.319486i	$0.896490\pi$
$158$	−7.79997e13	−0.398861
$159$	7.41637e13	0.364007
$160$	−4.21082e13	−0.198421
$161$	−1.83009e14	−0.828139
$162$	2.71862e13	0.118168
$163$	−6.72918e13	−0.281024	−0.140512	−	0.990079i	$-0.544875\pi$
$163$	−6.72918e13	−0.281024	−0.140512	+	0.990079i	$0.544875\pi$
$164$	−2.08749e13	−0.0837797
$165$	−1.55324e13	−0.0599230
$166$	−1.10819e14	−0.411065
$167$	1.66317e14	0.593306	0.296653	−	0.954985i	$-0.404130\pi$
$167$	1.66317e14	0.593306	0.296653	+	0.954985i	$0.404130\pi$
$168$	1.37251e14	0.470983
$169$	−2.93871e14	−0.970271
$170$	−3.09982e14	−0.984959
$171$	2.13775e14	0.653855
$172$	5.06090e13	0.149037
$173$	1.89764e14	0.538162	0.269081	−	0.963118i	$-0.413280\pi$
$173$	1.89764e14	0.538162	0.269081	+	0.963118i	$0.413280\pi$
$174$	−3.21426e13	−0.0878034
$175$	−1.40830e14	−0.370636
$176$	−5.98500e13	−0.151786
$177$	3.07496e13	0.0751646
$178$	2.15019e14	0.506695
$179$	−3.47584e13	−0.0789795	−0.0394898	−	0.999220i	$-0.512573\pi$
$179$	−3.47584e13	−0.0789795	−0.0394898	+	0.999220i	$0.512573\pi$
$180$	1.51844e13	0.0332757
$181$	2.21852e14	0.468978	0.234489	−	0.972119i	$-0.424658\pi$
$181$	2.21852e14	0.468978	0.234489	+	0.972119i	$0.424658\pi$
$182$	−7.93662e13	−0.161872
$183$	3.31976e14	0.653393
$184$	4.56369e14	0.866962
$185$	4.91750e13	0.0901838
$186$	2.02132e14	0.357932
$187$	−9.68885e13	−0.165692
$188$	5.24288e13	0.0866051
$189$	−1.06452e14	−0.169884
$190$	1.03041e15	1.58895
$191$	1.52559e14	0.227364	0.113682	−	0.993517i	$-0.463735\pi$
$191$	1.52559e14	0.227364	0.113682	+	0.993517i	$0.463735\pi$
$192$	−3.35378e14	−0.483145
$193$	9.50610e13	0.132398	0.0661988	−	0.997806i	$-0.478913\pi$
$193$	9.50610e13	0.132398	0.0661988	+	0.997806i	$0.478913\pi$
$194$	−9.29796e14	−1.25221
$195$	5.82131e13	0.0758221
$196$	−2.29656e13	−0.0289343
$197$	3.91102e14	0.476716	0.238358	−	0.971177i	$-0.423391\pi$
$197$	3.91102e14	0.476716	0.238358	+	0.971177i	$0.423391\pi$
$198$	4.09578e13	0.0483073
$199$	−7.58569e13	−0.0865864	−0.0432932	−	0.999062i	$-0.513785\pi$
$199$	−7.58569e13	−0.0865864	−0.0432932	+	0.999062i	$0.513785\pi$
$200$	3.51187e14	0.388011
$201$	−4.75621e14	−0.508729
$202$	9.71558e13	0.100620
$203$	1.25860e14	0.126230
$204$	9.47179e13	0.0920102
$205$	−5.17389e14	−0.486874
$206$	−2.38276e14	−0.217242
$207$	−3.53960e14	−0.312714
$208$	2.24308e14	0.192059
$209$	3.22066e14	0.267297
$210$	−5.13105e14	−0.412840
$211$	−1.74343e15	−1.36010	−0.680048	−	0.733167i	$-0.738041\pi$
$211$	−1.74343e15	−1.36010	−0.680048	+	0.733167i	$0.738041\pi$
$212$	−1.09229e14	−0.0826335
$213$	−1.16496e15	−0.854761
$214$	1.16039e15	0.825872
$215$	1.25436e15	0.866106
$216$	2.65460e14	0.177848
$217$	−7.91481e14	−0.514579
$218$	−5.83734e14	−0.368339
$219$	1.24642e15	0.763442
$220$	2.28764e13	0.0136032
$221$	3.63123e14	0.209654
$222$	−1.29671e14	−0.0727023
$223$	3.20846e15	1.74709	0.873545	−	0.486744i	$-0.161816\pi$
$223$	3.20846e15	1.74709	0.873545	+	0.486744i	$0.161816\pi$
$224$	−4.34781e14	−0.229963
$225$	−2.72382e14	−0.139956
$226$	1.06839e15	0.533368
$227$	2.46939e14	0.119790	0.0598950	−	0.998205i	$-0.480923\pi$
$227$	2.46939e14	0.119790	0.0598950	+	0.998205i	$0.480923\pi$
$228$	−3.14850e14	−0.148432
$229$	−1.31963e15	−0.604673	−0.302336	−	0.953201i	$-0.597767\pi$
$229$	−1.31963e15	−0.604673	−0.302336	+	0.953201i	$0.597767\pi$
$230$	−1.70611e15	−0.759934
$231$	−1.60377e14	−0.0694488
$232$	−3.13857e14	−0.132148
$233$	−4.02534e15	−1.64812	−0.824060	−	0.566502i	$-0.808296\pi$
$233$	−4.02534e15	−1.64812	−0.824060	+	0.566502i	$0.808296\pi$
$234$	−1.53504e14	−0.0611245
$235$	1.29946e15	0.503294
$236$	−4.52885e13	−0.0170632
$237$	5.90720e14	0.216530
$238$	−3.20066e15	−1.14154
$239$	−3.29132e15	−1.14231	−0.571155	−	0.820842i	$-0.693504\pi$
$239$	−3.29132e15	−1.14231	−0.571155	+	0.820842i	$0.693504\pi$
$240$	1.45016e15	0.489828
$241$	−7.47010e14	−0.245593	−0.122796	−	0.992432i	$-0.539186\pi$
$241$	−7.47010e14	−0.245593	−0.122796	+	0.992432i	$0.539186\pi$
$242$	−3.26140e15	−1.04377
$243$	−2.05891e14	−0.0641500
$244$	−4.88939e14	−0.148327
$245$	−5.69207e14	−0.168148
$246$	1.36432e15	0.392497
$247$	−1.20705e15	−0.338217
$248$	1.97372e15	0.538702
$249$	8.39270e14	0.223155
$250$	−4.43982e15	−1.15015
$251$	3.60776e15	0.910665	0.455332	−	0.890322i	$-0.349520\pi$
$251$	3.60776e15	0.910665	0.455332	+	0.890322i	$0.349520\pi$
$252$	1.56784e14	0.0385655
$253$	−5.33265e14	−0.127838
$254$	−7.40398e14	−0.173000
$255$	2.34760e15	0.534705
$256$	1.74170e15	0.386735
$257$	2.58075e15	0.558703	0.279352	−	0.960189i	$-0.409881\pi$
$257$	2.58075e15	0.558703	0.279352	+	0.960189i	$0.409881\pi$
$258$	−3.30764e15	−0.698217
$259$	5.07748e14	0.104520
$260$	−8.57371e13	−0.0172124
$261$	2.43428e14	0.0476658
$262$	−1.01127e16	−1.93157
$263$	3.88056e15	0.723073	0.361537	−	0.932358i	$-0.382252\pi$
$263$	3.88056e15	0.723073	0.361537	+	0.932358i	$0.382252\pi$
$264$	3.99933e14	0.0727045
$265$	−2.70728e15	−0.480213
$266$	1.06393e16	1.84154
$267$	−1.62842e15	−0.275070
$268$	7.00501e14	0.115487
$269$	−9.84274e15	−1.58389	−0.791947	−	0.610589i	$-0.790933\pi$
$269$	−9.84274e15	−1.58389	−0.791947	+	0.610589i	$0.790933\pi$
$270$	−9.92407e14	−0.155893
$271$	1.07175e16	1.64359	0.821797	−	0.569781i	$-0.192972\pi$
$271$	1.07175e16	1.64359	0.821797	+	0.569781i	$0.192972\pi$
$272$	9.04586e15	1.35442
$273$	6.01069e14	0.0878753
$274$	−3.47991e15	−0.496808
$275$	−4.10361e14	−0.0572141
$276$	5.21318e14	0.0709894
$277$	−9.77368e14	−0.129999	−0.0649995	−	0.997885i	$-0.520705\pi$
$277$	−9.77368e14	−0.129999	−0.0649995	+	0.997885i	$0.520705\pi$
$278$	−1.19717e16	−1.55549
$279$	−1.53082e15	−0.194311
$280$	−5.01022e15	−0.621340
$281$	9.13533e14	0.110696	0.0553481	−	0.998467i	$-0.482373\pi$
$281$	9.13533e14	0.110696	0.0553481	+	0.998467i	$0.482373\pi$
$282$	−3.42658e15	−0.405734
$283$	4.85474e15	0.561765	0.280882	−	0.959742i	$-0.409373\pi$
$283$	4.85474e15	0.561765	0.280882	+	0.959742i	$0.409373\pi$
$284$	1.71577e15	0.194040
$285$	−7.80364e15	−0.862592
$286$	−2.31263e14	−0.0249878
$287$	−5.34220e15	−0.564272
$288$	−8.40917e14	−0.0868365
$289$	4.73936e15	0.478502
$290$	1.17334e15	0.115834
$291$	7.04168e15	0.679786
$292$	−1.83574e15	−0.173310
$293$	6.83364e15	0.630975	0.315488	−	0.948930i	$-0.397832\pi$
$293$	6.83364e15	0.630975	0.315488	+	0.948930i	$0.397832\pi$
$294$	1.50096e15	0.135553
$295$	−1.12249e15	−0.0991602
$296$	−1.26617e15	−0.109420
$297$	−3.10189e14	−0.0262246
$298$	−1.91755e16	−1.58614
$299$	1.99859e15	0.161757
$300$	4.01167e14	0.0317715
$301$	1.29516e16	1.00379
$302$	−2.43712e16	−1.84855
$303$	−7.35796e14	−0.0546236
$304$	−3.00692e16	−2.18496
$305$	−1.21185e16	−0.861983
$306$	−6.19046e15	−0.431056
$307$	−1.03239e16	−0.703789	−0.351895	−	0.936040i	$-0.614462\pi$
$307$	−1.03239e16	−0.703789	−0.351895	+	0.936040i	$0.614462\pi$
$308$	2.36206e14	0.0157656
$309$	1.80455e15	0.117934
$310$	−7.37863e15	−0.472199
$311$	−9.25225e15	−0.579836	−0.289918	−	0.957052i	$-0.593628\pi$
$311$	−9.25225e15	−0.579836	−0.289918	+	0.957052i	$0.593628\pi$
$312$	−1.49889e15	−0.0919949
$313$	6.96286e15	0.418552	0.209276	−	0.977857i	$-0.432889\pi$
$313$	6.96286e15	0.418552	0.209276	+	0.977857i	$0.432889\pi$
$314$	−3.42324e16	−2.01555
$315$	3.88593e15	0.224118
$316$	−8.70021e14	−0.0491545
$317$	−2.38599e16	−1.32064	−0.660319	−	0.750985i	$-0.729579\pi$
$317$	−2.38599e16	−1.32064	−0.660319	+	0.750985i	$0.729579\pi$
$318$	7.13888e15	0.387127
$319$	3.66740e14	0.0194858
$320$	1.22427e16	0.637384
$321$	−8.78802e15	−0.448341
$322$	−1.76161e16	−0.880739
$323$	−4.86777e16	−2.38514
$324$	3.03239e14	0.0145627
$325$	1.53797e15	0.0723945
$326$	−6.47741e15	−0.298873
$327$	4.42083e15	0.199960
$328$	1.33219e16	0.590724
$329$	1.34173e16	0.583301
$330$	−1.49513e15	−0.0637290
$331$	3.12984e15	0.130810	0.0654049	−	0.997859i	$-0.479166\pi$
$331$	3.12984e15	0.130810	0.0654049	+	0.997859i	$0.479166\pi$
$332$	−1.23609e15	−0.0506585
$333$	9.82045e14	0.0394679
$334$	1.60094e16	0.630990
$335$	1.73621e16	0.671136
$336$	1.49734e16	0.567695
$337$	−4.37680e16	−1.62766	−0.813828	−	0.581106i	$-0.802620\pi$
$337$	−4.37680e16	−1.62766	−0.813828	+	0.581106i	$0.802620\pi$
$338$	−2.82875e16	−1.03190
$339$	−8.09134e15	−0.289549
$340$	−3.45759e15	−0.121384
$341$	−2.30628e15	−0.0794343
$342$	2.05776e16	0.695385
$343$	−3.24996e16	−1.07762
$344$	−3.22975e16	−1.05085
$345$	1.29210e16	0.412545
$346$	1.82663e16	0.572344
$347$	−6.03840e16	−1.85687	−0.928433	−	0.371501i	$-0.878843\pi$
$347$	−6.03840e16	−1.85687	−0.928433	+	0.371501i	$0.878843\pi$
$348$	−3.58524e14	−0.0108206
$349$	−1.61733e16	−0.479108	−0.239554	−	0.970883i	$-0.577001\pi$
$349$	−1.61733e16	−0.479108	−0.239554	+	0.970883i	$0.577001\pi$
$350$	−1.35561e16	−0.394177
$351$	1.16254e15	0.0331827
$352$	−1.26690e15	−0.0354988
$353$	1.88247e16	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$353$	1.88247e16	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$354$	2.95991e15	0.0799387
$355$	4.25258e16	1.12764
$356$	2.39836e15	0.0624437
$357$	2.42398e16	0.619705
$358$	−3.34578e15	−0.0839959
$359$	1.69544e15	0.0417992	0.0208996	−	0.999782i	$-0.493347\pi$
$359$	1.69544e15	0.0417992	0.0208996	+	0.999782i	$0.493347\pi$
$360$	−9.69036e15	−0.234625
$361$	1.19756e17	2.84774
$362$	2.13551e16	0.498765
$363$	2.46997e16	0.566630
$364$	−8.85263e14	−0.0199486
$365$	−4.54992e16	−1.00716
$366$	3.19555e16	0.694894
$367$	−6.16808e15	−0.131771	−0.0658856	−	0.997827i	$-0.520987\pi$
$367$	−6.16808e15	−0.131771	−0.0658856	+	0.997827i	$0.520987\pi$
$368$	4.97875e16	1.04498
$369$	−1.03325e16	−0.213075
$370$	4.73351e15	0.0959118
$371$	−2.79535e16	−0.556552
$372$	2.25461e15	0.0441105
$373$	2.34451e16	0.450758	0.225379	−	0.974271i	$-0.427638\pi$
$373$	2.34451e16	0.450758	0.225379	+	0.974271i	$0.427638\pi$
$374$	−9.32633e15	−0.176216
$375$	3.36244e16	0.624383
$376$	−3.34588e16	−0.610646
$377$	−1.37449e15	−0.0246559
$378$	−1.02469e16	−0.180674
$379$	6.96177e16	1.20660	0.603302	−	0.797513i	$-0.293851\pi$
$379$	6.96177e16	1.20660	0.603302	+	0.797513i	$0.293851\pi$
$380$	1.14933e16	0.195818
$381$	5.60730e15	0.0939164
$382$	1.46851e16	0.241805
$383$	5.69170e16	0.921404	0.460702	−	0.887555i	$-0.347598\pi$
$383$	5.69170e16	0.921404	0.460702	+	0.887555i	$0.347598\pi$
$384$	−4.17326e16	−0.664237
$385$	5.85442e15	0.0916197
$386$	9.15042e15	0.140807
$387$	2.50500e16	0.379041
$388$	−1.03711e16	−0.154319
$389$	3.69528e16	0.540723	0.270362	−	0.962759i	$-0.412857\pi$
$389$	3.69528e16	0.540723	0.270362	+	0.962759i	$0.412857\pi$
$390$	5.60350e15	0.0806380
$391$	8.05988e16	1.14072
$392$	1.46561e16	0.204013
$393$	7.65873e16	1.04859
$394$	3.76469e16	0.506995
$395$	−2.15637e16	−0.285655
$396$	4.56850e14	0.00595326
$397$	2.48723e15	0.0318844	0.0159422	−	0.999873i	$-0.494925\pi$
$397$	2.48723e15	0.0318844	0.0159422	+	0.999873i	$0.494925\pi$
$398$	−7.30186e15	−0.0920860
$399$	−8.05751e16	−0.999716
$400$	3.83128e16	0.467685
$401$	7.61054e16	0.914065	0.457032	−	0.889450i	$-0.348912\pi$
$401$	7.61054e16	0.914065	0.457032	+	0.889450i	$0.348912\pi$
$402$	−4.57825e16	−0.541041
$403$	8.64357e15	0.100510
$404$	1.08369e15	0.0124001
$405$	7.51586e15	0.0846293
$406$	1.21151e16	0.134248
$407$	1.47951e15	0.0161345
$408$	−6.04467e16	−0.648756
$409$	−4.94664e16	−0.522527	−0.261264	−	0.965267i	$-0.584139\pi$
$409$	−4.94664e16	−0.522527	−0.261264	+	0.965267i	$0.584139\pi$
$410$	−4.98030e16	−0.517798
$411$	2.63546e16	0.269702
$412$	−2.65777e15	−0.0267723
$413$	−1.15900e16	−0.114923
$414$	−3.40717e16	−0.332576
$415$	−3.06368e16	−0.294395
$416$	4.74814e15	0.0449176
$417$	9.06663e16	0.844426
$418$	3.10015e16	0.284274
$419$	−3.85256e16	−0.347823	−0.173912	−	0.984761i	$-0.555641\pi$
$419$	−3.85256e16	−0.347823	−0.173912	+	0.984761i	$0.555641\pi$
$420$	−5.72326e15	−0.0508772
$421$	1.46879e17	1.28566	0.642831	−	0.766008i	$-0.277760\pi$
$421$	1.46879e17	1.28566	0.642831	+	0.766008i	$0.277760\pi$
$422$	−1.67820e17	−1.44648
$423$	2.59507e16	0.220261
$424$	6.97076e16	0.582642
$425$	6.20228e16	0.510533
$426$	−1.12137e17	−0.909051
$427$	−1.25127e17	−0.999011
$428$	1.29431e16	0.101778
$429$	1.75144e15	0.0135651
$430$	1.20742e17	0.921117
$431$	−5.92705e16	−0.445386	−0.222693	−	0.974889i	$-0.571485\pi$
$431$	−5.92705e16	−0.445386	−0.222693	+	0.974889i	$0.571485\pi$
$432$	2.89603e16	0.214368
$433$	2.37967e17	1.73518	0.867591	−	0.497278i	$-0.165667\pi$
$433$	2.37967e17	1.73518	0.867591	+	0.497278i	$0.165667\pi$
$434$	−7.61867e16	−0.547263
$435$	−8.88610e15	−0.0628827
$436$	−6.51106e15	−0.0453930
$437$	−2.67917e17	−1.84023
$438$	1.19978e17	0.811933
$439$	−1.13299e17	−0.755451	−0.377725	−	0.925918i	$-0.623294\pi$
$439$	−1.13299e17	−0.755451	−0.377725	+	0.925918i	$0.623294\pi$
$440$	−1.45992e16	−0.0959147
$441$	−1.13673e16	−0.0735878
$442$	3.49536e16	0.222971
$443$	1.73104e17	1.08813	0.544067	−	0.839042i	$-0.316884\pi$
$443$	1.73104e17	1.08813	0.544067	+	0.839042i	$0.316884\pi$
$444$	−1.44637e15	−0.00895963
$445$	5.94438e16	0.362883
$446$	3.08841e17	1.85806
$447$	1.45223e17	0.861068
$448$	1.26409e17	0.738707
$449$	1.95401e17	1.12545	0.562725	−	0.826644i	$-0.309753\pi$
$449$	1.95401e17	1.12545	0.562725	+	0.826644i	$0.309753\pi$
$450$	−2.62190e16	−0.148845
$451$	−1.55665e16	−0.0871052
$452$	1.19170e16	0.0657307
$453$	1.84572e17	1.00352
$454$	2.37699e16	0.127399
$455$	−2.19414e16	−0.115929
$456$	2.00930e17	1.04658
$457$	−2.54346e17	−1.30608	−0.653040	−	0.757323i	$-0.726507\pi$
$457$	−2.54346e17	−1.30608	−0.653040	+	0.757323i	$0.726507\pi$
$458$	−1.27025e17	−0.643079
$459$	4.68826e16	0.234007
$460$	−1.90302e16	−0.0936521
$461$	−6.79376e16	−0.329651	−0.164825	−	0.986323i	$-0.552706\pi$
$461$	−6.79376e16	−0.329651	−0.164825	+	0.986323i	$0.552706\pi$
$462$	−1.54377e16	−0.0738599
$463$	1.56009e17	0.735994	0.367997	−	0.929827i	$-0.380044\pi$
$463$	1.56009e17	0.735994	0.367997	+	0.929827i	$0.380044\pi$
$464$	−3.42402e16	−0.159283
$465$	5.58811e16	0.256342
$466$	−3.87473e17	−1.75280
$467$	−2.28289e16	−0.101842	−0.0509209	−	0.998703i	$-0.516216\pi$
$467$	−2.28289e16	−0.101842	−0.0509209	+	0.998703i	$0.516216\pi$
$468$	−1.71220e15	−0.00753281
$469$	1.79269e17	0.777825
$470$	1.25084e17	0.535261
$471$	2.59254e17	1.09418
$472$	2.89020e16	0.120311
$473$	3.77395e16	0.154952
$474$	5.68618e16	0.230283
$475$	−2.06169e17	−0.823598
$476$	−3.57007e16	−0.140680
$477$	−5.40653e16	−0.210160
$478$	−3.16817e17	−1.21486
$479$	3.05783e17	1.15673	0.578365	−	0.815778i	$-0.303691\pi$
$479$	3.05783e17	1.15673	0.578365	+	0.815778i	$0.303691\pi$
$480$	3.06969e16	0.114558
$481$	−5.54499e15	−0.0204154
$482$	−7.19060e16	−0.261192
$483$	1.33413e17	0.478126
$484$	−3.63781e16	−0.128631
$485$	−2.57050e17	−0.896801
$486$	−1.98188e16	−0.0682245
$487$	1.94215e17	0.659695	0.329848	−	0.944034i	$-0.393003\pi$
$487$	1.94215e17	0.659695	0.329848	+	0.944034i	$0.393003\pi$
$488$	3.12029e17	1.04584
$489$	4.90558e16	0.162249
$490$	−5.47909e16	−0.178827
$491$	5.85917e17	1.88715	0.943575	−	0.331158i	$-0.107439\pi$
$491$	5.85917e17	1.88715	0.943575	+	0.331158i	$0.107439\pi$
$492$	1.52178e16	0.0483703
$493$	−5.54299e16	−0.173876
$494$	−1.16189e17	−0.359699
$495$	1.13231e16	0.0345966
$496$	2.15323e17	0.649320
$497$	4.39093e17	1.30689
$498$	8.07868e16	0.237328
$499$	2.11145e17	0.612248	0.306124	−	0.951992i	$-0.400968\pi$
$499$	2.11145e17	0.612248	0.306124	+	0.951992i	$0.400968\pi$
$500$	−4.95224e16	−0.141741
$501$	−1.21245e17	−0.342545
$502$	3.47277e17	0.968506
$503$	−1.22598e17	−0.337513	−0.168756	−	0.985658i	$-0.553975\pi$
$503$	−1.22598e17	−0.337513	−0.168756	+	0.985658i	$0.553975\pi$
$504$	−1.00056e17	−0.271922
$505$	2.68595e16	0.0720617
$506$	−5.13312e16	−0.135957
$507$	2.14232e17	0.560186
$508$	−8.25851e15	−0.0213200
$509$	3.19116e17	0.813361	0.406680	−	0.913570i	$-0.366686\pi$
$509$	3.19116e17	0.813361	0.406680	+	0.913570i	$0.366686\pi$
$510$	2.25977e17	0.568666
$511$	−4.69794e17	−1.16727
$512$	−3.01310e17	−0.739194
$513$	−1.55842e17	−0.377503
$514$	2.48419e17	0.594189
$515$	−6.58735e16	−0.155584
$516$	−3.68940e16	−0.0860463
$517$	3.90964e16	0.0900428
$518$	4.88750e16	0.111159
$519$	−1.38338e17	−0.310708
$520$	5.47154e16	0.121363
$521$	−3.19757e17	−0.700446	−0.350223	−	0.936666i	$-0.613894\pi$
$521$	−3.19757e17	−0.700446	−0.350223	+	0.936666i	$0.613894\pi$
$522$	2.34320e16	0.0506933
$523$	−2.44296e17	−0.521982	−0.260991	−	0.965341i	$-0.584049\pi$
$523$	−2.44296e17	−0.521982	−0.260991	+	0.965341i	$0.584049\pi$
$524$	−1.12799e17	−0.238041
$525$	1.02665e17	0.213987
$526$	3.73537e17	0.769000
$527$	3.48576e17	0.708808
$528$	4.36306e16	0.0876337
$529$	−6.04283e16	−0.119889
$530$	−2.60598e17	−0.510714
$531$	−2.24165e16	−0.0433963
$532$	1.18672e17	0.226946
$533$	5.83409e16	0.110216
$534$	−1.56749e17	−0.292541
$535$	3.20798e17	0.591470
$536$	−4.47043e17	−0.814289
$537$	2.53388e16	0.0455988
$538$	−9.47447e17	−1.68450
$539$	−1.71256e16	−0.0300828
$540$	−1.10695e16	−0.0192118
$541$	−6.99890e17	−1.20018	−0.600092	−	0.799931i	$-0.704869\pi$
$541$	−6.99890e17	−1.20018	−0.600092	+	0.799931i	$0.704869\pi$
$542$	1.03165e18	1.74799
$543$	−1.61730e17	−0.270765
$544$	1.91482e17	0.316763
$545$	−1.61378e17	−0.263795
$546$	5.78579e16	0.0934568
$547$	−7.01054e17	−1.11901	−0.559505	−	0.828827i	$-0.689009\pi$
$547$	−7.01054e17	−1.11901	−0.559505	+	0.828827i	$0.689009\pi$
$548$	−3.88154e16	−0.0612253
$549$	−2.42011e17	−0.377237
$550$	−3.95007e16	−0.0608481
$551$	1.84254e17	0.280499
$552$	−3.32693e17	−0.500541
$553$	−2.22652e17	−0.331065
$554$	−9.40799e16	−0.138256
$555$	−3.58486e16	−0.0520676
$556$	−1.33535e17	−0.191694
$557$	−5.34311e17	−0.758115	−0.379058	−	0.925373i	$-0.623752\pi$
$557$	−5.34311e17	−0.758115	−0.379058	+	0.925373i	$0.623752\pi$
$558$	−1.47354e17	−0.206652
$559$	−1.41442e17	−0.196065
$560$	−5.46590e17	−0.748926
$561$	7.06317e16	0.0956623
$562$	8.79352e16	0.117727
$563$	−7.41989e17	−0.981958	−0.490979	−	0.871171i	$-0.663361\pi$
$563$	−7.41989e17	−0.981958	−0.490979	+	0.871171i	$0.663361\pi$
$564$	−3.82206e16	−0.0500015
$565$	2.95367e17	0.381985
$566$	4.67310e17	0.597445
$567$	7.76036e16	0.0980826
$568$	−1.09497e18	−1.36816
$569$	−6.38522e17	−0.788763	−0.394381	−	0.918947i	$-0.629041\pi$
$569$	−6.38522e17	−0.788763	−0.394381	+	0.918947i	$0.629041\pi$
$570$	−7.51166e17	−0.917380
$571$	1.18316e18	1.42859	0.714294	−	0.699845i	$-0.246748\pi$
$571$	1.18316e18	1.42859	0.714294	+	0.699845i	$0.246748\pi$
$572$	−2.57955e15	−0.00307942
$573$	−1.11216e17	−0.131269
$574$	−5.14232e17	−0.600111
$575$	3.41368e17	0.393896
$576$	2.44491e17	0.278944
$577$	7.66718e17	0.864954	0.432477	−	0.901645i	$-0.357640\pi$
$577$	7.66718e17	0.864954	0.432477	+	0.901645i	$0.357640\pi$
$578$	4.56203e17	0.508894
$579$	−6.92995e16	−0.0764397
$580$	1.30876e16	0.0142750
$581$	−3.16334e17	−0.341194
$582$	6.77821e17	0.722962
$583$	−8.14530e16	−0.0859135
$584$	1.17153e18	1.22199
$585$	−4.24374e16	−0.0437759
$586$	6.57795e17	0.671052
$587$	−8.09141e17	−0.816350	−0.408175	−	0.912904i	$-0.633835\pi$
$587$	−8.09141e17	−0.816350	−0.408175	+	0.912904i	$0.633835\pi$
$588$	1.67419e16	0.0167052
$589$	−1.15870e18	−1.14346
$590$	−1.08049e17	−0.105458
$591$	−2.85113e17	−0.275232
$592$	−1.38133e17	−0.131888
$593$	3.31642e17	0.313194	0.156597	−	0.987663i	$-0.449948\pi$
$593$	3.31642e17	0.313194	0.156597	+	0.987663i	$0.449948\pi$
$594$	−2.98583e16	−0.0278903
$595$	−8.84850e17	−0.817540
$596$	−2.13887e17	−0.195472
$597$	5.52997e16	0.0499907
$598$	1.92381e17	0.172031
$599$	1.94608e18	1.72141	0.860707	−	0.509100i	$-0.170022\pi$
$599$	1.94608e18	1.72141	0.860707	+	0.509100i	$0.170022\pi$
$600$	−2.56015e17	−0.224018
$601$	9.09691e17	0.787426	0.393713	−	0.919233i	$-0.371190\pi$
$601$	9.09691e17	0.787426	0.393713	+	0.919233i	$0.371190\pi$
$602$	1.24670e18	1.06754
$603$	3.46728e17	0.293715
$604$	−2.71840e17	−0.227810
$605$	−9.01640e17	−0.747521
$606$	−7.08266e16	−0.0580930
$607$	−6.11058e17	−0.495857	−0.247928	−	0.968778i	$-0.579750\pi$
$607$	−6.11058e17	−0.495857	−0.247928	+	0.968778i	$0.579750\pi$
$608$	−6.36502e17	−0.511006
$609$	−9.17518e16	−0.0728790
$610$	−1.16650e18	−0.916732
$611$	−1.46527e17	−0.113933
$612$	−6.90493e16	−0.0531221
$613$	−2.08508e18	−1.58720	−0.793598	−	0.608442i	$-0.791795\pi$
$613$	−2.08508e18	−1.58720	−0.793598	+	0.608442i	$0.791795\pi$
$614$	−9.93758e17	−0.748491
$615$	3.77177e17	0.281097
$616$	−1.50741e17	−0.111162
$617$	5.25036e16	0.0383120	0.0191560	−	0.999817i	$-0.493902\pi$
$617$	5.25036e16	0.0383120	0.0191560	+	0.999817i	$0.493902\pi$
$618$	1.73704e17	0.125425
$619$	3.04863e17	0.217829	0.108915	−	0.994051i	$-0.465263\pi$
$619$	3.04863e17	0.217829	0.108915	+	0.994051i	$0.465263\pi$
$620$	−8.23024e16	−0.0581924
$621$	2.58037e17	0.180546
$622$	−8.90607e17	−0.616664
$623$	6.13776e17	0.420570
$624$	−1.63521e17	−0.110885
$625$	−6.01773e17	−0.403843
$626$	6.70234e17	0.445136
$627$	−2.34786e17	−0.154324
$628$	−3.81834e17	−0.248391
$629$	−2.23617e17	−0.143971
$630$	3.74054e17	0.238353
$631$	−3.86042e17	−0.243469	−0.121735	−	0.992563i	$-0.538846\pi$
$631$	−3.86042e17	−0.243469	−0.121735	+	0.992563i	$0.538846\pi$
$632$	5.55227e17	0.346585
$633$	1.27096e18	0.785252
$634$	−2.29672e18	−1.40452
$635$	−2.04689e17	−0.123898
$636$	7.96282e16	0.0477085
$637$	6.41839e16	0.0380645
$638$	3.53018e16	0.0207235
$639$	8.49258e17	0.493496
$640$	1.52341e18	0.876288
$641$	−1.07225e18	−0.610548	−0.305274	−	0.952265i	$-0.598748\pi$
$641$	−1.07225e18	−0.610548	−0.305274	+	0.952265i	$0.598748\pi$
$642$	−8.45921e17	−0.476817
$643$	−1.51704e18	−0.846498	−0.423249	−	0.906013i	$-0.639111\pi$
$643$	−1.51704e18	−0.846498	−0.423249	+	0.906013i	$0.639111\pi$
$644$	−1.96493e17	−0.108540
$645$	−9.14426e17	−0.500047
$646$	−4.68564e18	−2.53663
$647$	1.77716e18	0.952467	0.476233	−	0.879319i	$-0.342002\pi$
$647$	1.77716e18	0.952467	0.476233	+	0.879319i	$0.342002\pi$
$648$	−1.93520e17	−0.102681
$649$	−3.37719e16	−0.0177405
$650$	1.48042e17	0.0769926
$651$	5.76990e17	0.297092
$652$	−7.22500e16	−0.0368323
$653$	−2.38790e18	−1.20526	−0.602629	−	0.798021i	$-0.705880\pi$
$653$	−2.38790e18	−1.20526	−0.602629	+	0.798021i	$0.705880\pi$
$654$	4.25542e17	0.212661
$655$	−2.79575e18	−1.38334
$656$	1.45335e18	0.712024
$657$	−9.08637e17	−0.440774
$658$	1.29153e18	0.620350
$659$	1.97468e18	0.939163	0.469582	−	0.882889i	$-0.344405\pi$
$659$	1.97468e18	0.939163	0.469582	+	0.882889i	$0.344405\pi$
$660$	−1.66769e16	−0.00785379
$661$	3.29575e18	1.53690	0.768450	−	0.639910i	$-0.221029\pi$
$661$	3.29575e18	1.53690	0.768450	+	0.639910i	$0.221029\pi$
$662$	3.01274e17	0.139118
$663$	−2.64717e17	−0.121044
$664$	7.88843e17	0.357189
$665$	2.94132e18	1.31887
$666$	9.45301e16	0.0419747
$667$	−3.05081e17	−0.134152
$668$	1.78571e17	0.0777614
$669$	−2.33897e18	−1.00868
$670$	1.67125e18	0.713763
$671$	−3.64605e17	−0.154215
$672$	3.16955e17	0.132769
$673$	2.77924e18	1.15300	0.576499	−	0.817098i	$-0.304418\pi$
$673$	2.77924e18	1.15300	0.576499	+	0.817098i	$0.304418\pi$
$674$	−4.21304e18	−1.73104
$675$	1.98566e17	0.0808036
$676$	−3.15524e17	−0.127168
$677$	1.33920e18	0.534590	0.267295	−	0.963615i	$-0.413870\pi$
$677$	1.33920e18	0.534590	0.267295	+	0.963615i	$0.413870\pi$
$678$	−7.78860e17	−0.307940
$679$	−2.65412e18	−1.03936
$680$	2.20655e18	0.855866
$681$	−1.80018e17	−0.0691608
$682$	−2.21999e17	−0.0844796
$683$	9.46938e17	0.356933	0.178467	−	0.983946i	$-0.442886\pi$
$683$	9.46938e17	0.356933	0.178467	+	0.983946i	$0.442886\pi$
$684$	2.29526e17	0.0856973
$685$	−9.62050e17	−0.355802
$686$	−3.12836e18	−1.14607
$687$	9.62008e17	0.349108
$688$	−3.52349e18	−1.26663
$689$	3.05273e17	0.108709
$690$	1.24375e18	0.438748
$691$	2.18537e17	0.0763692	0.0381846	−	0.999271i	$-0.487843\pi$
$691$	2.18537e17	0.0763692	0.0381846	+	0.999271i	$0.487843\pi$
$692$	2.03746e17	0.0705340
$693$	1.16915e17	0.0400963
$694$	−5.81247e18	−1.97480
$695$	−3.30969e18	−1.11400
$696$	2.28802e17	0.0762955
$697$	2.35276e18	0.777257
$698$	−1.55682e18	−0.509538
$699$	2.93447e18	0.951543
$700$	−1.51206e17	−0.0485772
$701$	3.52630e18	1.12241	0.561206	−	0.827676i	$-0.310338\pi$
$701$	3.52630e18	1.12241	0.561206	+	0.827676i	$0.310338\pi$
$702$	1.11904e17	0.0352903
$703$	7.43323e17	0.232256
$704$	3.68342e17	0.114032
$705$	−9.47306e17	−0.290577
$706$	1.81204e18	0.550728
$707$	2.77333e17	0.0835171
$708$	3.30153e16	0.00985142
$709$	−6.54909e17	−0.193633	−0.0968167	−	0.995302i	$-0.530866\pi$
$709$	−6.54909e17	−0.193633	−0.0968167	+	0.995302i	$0.530866\pi$
$710$	4.09347e18	1.19926
$711$	−4.30635e17	−0.125013
$712$	−1.53057e18	−0.440286
$713$	1.91853e18	0.546873
$714$	2.33328e18	0.659066
$715$	−6.39347e16	−0.0178956
$716$	−3.73194e16	−0.0103514
$717$	2.39937e18	0.659513
$718$	1.63200e17	0.0444541
$719$	6.15649e18	1.66186	0.830932	−	0.556374i	$-0.187808\pi$
$719$	6.15649e18	1.66186	0.830932	+	0.556374i	$0.187808\pi$
$720$	−1.05717e18	−0.282803
$721$	−6.80165e17	−0.180316
$722$	1.15275e19	3.02861
$723$	5.44570e17	0.141793
$724$	2.38198e17	0.0614664
$725$	−2.34767e17	−0.0600400
$726$	2.37756e18	0.602619
$727$	−5.44794e18	−1.36854	−0.684272	−	0.729227i	$-0.739880\pi$
$727$	−5.44794e18	−1.36854	−0.684272	+	0.729227i	$0.739880\pi$
$728$	5.64954e17	0.140656
$729$	1.50095e17	0.0370370
$730$	−4.37968e18	−1.07113
$731$	−5.70403e18	−1.38267
$732$	3.56437e17	0.0856368
$733$	−4.74592e18	−1.13017	−0.565087	−	0.825032i	$-0.691157\pi$
$733$	−4.74592e18	−1.13017	−0.565087	+	0.825032i	$0.691157\pi$
$734$	−5.93730e17	−0.140141
$735$	4.14952e17	0.0970800
$736$	1.05390e18	0.244395
$737$	5.22368e17	0.120071
$738$	−9.94586e17	−0.226608
$739$	3.79014e18	0.855987	0.427993	−	0.903782i	$-0.359221\pi$
$739$	3.79014e18	0.855987	0.427993	+	0.903782i	$0.359221\pi$
$740$	5.27983e16	0.0118199
$741$	8.79941e17	0.195270
$742$	−2.69076e18	−0.591901
$743$	−4.45105e18	−0.970588	−0.485294	−	0.874351i	$-0.661287\pi$
$743$	−4.45105e18	−0.970588	−0.485294	+	0.874351i	$0.661287\pi$
$744$	−1.43884e18	−0.311020
$745$	−5.30124e18	−1.13596
$746$	2.25678e18	0.479388
$747$	−6.11828e17	−0.128838
$748$	−1.04027e17	−0.0217164
$749$	3.31234e18	0.685494
$750$	3.23663e18	0.664040
$751$	−6.47584e18	−1.31715	−0.658577	−	0.752513i	$-0.728841\pi$
$751$	−6.47584e18	−1.31715	−0.658577	+	0.752513i	$0.728841\pi$
$752$	−3.65019e18	−0.736036
$753$	−2.63006e18	−0.525772
$754$	−1.32306e17	−0.0262220
$755$	−6.73761e18	−1.32389
$756$	−1.14296e17	−0.0222658
$757$	−8.67459e16	−0.0167543	−0.00837714	−	0.999965i	$-0.502667\pi$
$757$	−8.67459e16	−0.0167543	−0.00837714	+	0.999965i	$0.502667\pi$
$758$	6.70129e18	1.28324
$759$	3.88750e17	0.0738072
$760$	−7.33476e18	−1.38069
$761$	6.66613e18	1.24415	0.622076	−	0.782957i	$-0.286290\pi$
$761$	6.66613e18	1.24415	0.622076	+	0.782957i	$0.286290\pi$
$762$	5.39750e17	0.0998815
$763$	−1.66628e18	−0.305730
$764$	1.63800e17	0.0297994
$765$	−1.71140e18	−0.308712
$766$	5.47874e18	0.979927
$767$	1.26572e17	0.0224474
$768$	−1.26970e18	−0.223281
$769$	3.86012e18	0.673100	0.336550	−	0.941666i	$-0.390740\pi$
$769$	3.86012e18	0.673100	0.336550	+	0.941666i	$0.390740\pi$
$770$	5.63537e17	0.0974389
$771$	−1.88137e18	−0.322567
$772$	1.02065e17	0.0173526
$773$	−7.51013e18	−1.26614	−0.633068	−	0.774096i	$-0.718205\pi$
$773$	−7.51013e18	−1.26614	−0.633068	+	0.774096i	$0.718205\pi$
$774$	2.41127e18	0.403116
$775$	1.47636e18	0.244754
$776$	6.61858e18	1.08809
$777$	−3.70148e17	−0.0603447
$778$	3.55702e18	0.575067
$779$	−7.82077e18	−1.25388
$780$	6.25023e16	0.00993760
$781$	1.27946e18	0.201742
$782$	7.75831e18	1.21317
$783$	−1.77459e17	−0.0275199
$784$	1.59890e18	0.245905
$785$	−9.46384e18	−1.44349
$786$	7.37217e18	1.11519
$787$	−1.07288e19	−1.60959	−0.804796	−	0.593552i	$-0.797725\pi$
$787$	−1.07288e19	−1.60959	−0.804796	+	0.593552i	$0.797725\pi$
$788$	4.19919e17	0.0624806
$789$	−2.82893e18	−0.417467
$790$	−2.07568e18	−0.303798
$791$	3.04975e18	0.442708
$792$	−2.91551e17	−0.0419760
$793$	1.36648e18	0.195132
$794$	2.39417e17	0.0339095
$795$	1.97360e18	0.277251
$796$	−8.14461e16	−0.0113484
$797$	1.01221e19	1.39891	0.699457	−	0.714675i	$-0.253425\pi$
$797$	1.01221e19	1.39891	0.699457	+	0.714675i	$0.253425\pi$
$798$	−7.75603e18	−1.06321
$799$	−5.90912e18	−0.803469
$800$	8.11000e17	0.109380
$801$	1.18712e18	0.158812
$802$	7.32578e18	0.972122
$803$	−1.36892e18	−0.180189
$804$	−5.10665e17	−0.0666764
$805$	−4.87013e18	−0.630764
$806$	8.32017e17	0.106894
$807$	7.17536e18	0.914462
$808$	−6.91586e17	−0.0874323
$809$	5.40892e18	0.678336	0.339168	−	0.940726i	$-0.389854\pi$
$809$	5.40892e18	0.678336	0.339168	+	0.940726i	$0.389854\pi$
$810$	7.23465e17	0.0900046
$811$	−6.31087e18	−0.778850	−0.389425	−	0.921058i	$-0.627326\pi$
$811$	−6.31087e18	−0.778850	−0.389425	+	0.921058i	$0.627326\pi$
$812$	1.35133e17	0.0165443
$813$	−7.81308e18	−0.948929
$814$	1.42416e17	0.0171593
$815$	−1.79073e18	−0.214046
$816$	−6.59443e18	−0.781972
$817$	1.89607e19	2.23054
$818$	−4.76156e18	−0.555716
$819$	−4.38179e17	−0.0507349
$820$	−5.55511e17	−0.0638120
$821$	8.15731e17	0.0929644	0.0464822	−	0.998919i	$-0.485199\pi$
$821$	8.15731e17	0.0929644	0.0464822	+	0.998919i	$0.485199\pi$
$822$	2.53685e18	0.286832
$823$	−4.18280e18	−0.469211	−0.234605	−	0.972091i	$-0.575380\pi$
$823$	−4.18280e18	−0.469211	−0.234605	+	0.972091i	$0.575380\pi$
$824$	1.69613e18	0.188769
$825$	2.99153e17	0.0330326
$826$	−1.11564e18	−0.122223
$827$	7.25110e18	0.788166	0.394083	−	0.919075i	$-0.371062\pi$
$827$	7.25110e18	0.788166	0.394083	+	0.919075i	$0.371062\pi$
$828$	−3.80041e17	−0.0409858
$829$	2.21210e18	0.236702	0.118351	−	0.992972i	$-0.462239\pi$
$829$	2.21210e18	0.236702	0.118351	+	0.992972i	$0.462239\pi$
$830$	−2.94905e18	−0.313093
$831$	7.12501e17	0.0750549
$832$	−1.38049e18	−0.144288
$833$	2.58840e18	0.268434
$834$	8.72740e18	0.898060
$835$	4.42593e18	0.451900
$836$	3.45796e17	0.0350331
$837$	1.11597e18	0.112185
$838$	−3.70842e18	−0.369915
$839$	−3.25826e18	−0.322503	−0.161251	−	0.986913i	$-0.551553\pi$
$839$	−3.25826e18	−0.322503	−0.161251	+	0.986913i	$0.551553\pi$
$840$	3.65245e18	0.358731
$841$	−1.00508e19	−0.979552
$842$	1.41384e19	1.36732
$843$	−6.65965e17	−0.0639105
$844$	−1.87189e18	−0.178261
$845$	−7.82033e18	−0.739020
$846$	2.49797e18	0.234251
$847$	−9.30972e18	−0.866352
$848$	7.60475e18	0.702282
$849$	−3.53911e18	−0.324335
$850$	5.97022e18	0.542959
$851$	−1.23077e18	−0.111079
$852$	−1.25080e18	−0.112029
$853$	−1.57798e19	−1.40260	−0.701298	−	0.712868i	$-0.747396\pi$
$853$	−1.57798e19	−1.40260	−0.701298	+	0.712868i	$0.747396\pi$
$854$	−1.20445e19	−1.06246
$855$	5.68885e18	0.498018
$856$	−8.25999e18	−0.717629
$857$	1.39266e19	1.20080	0.600400	−	0.799700i	$-0.295008\pi$
$857$	1.39266e19	1.20080	0.600400	+	0.799700i	$0.295008\pi$
$858$	1.68591e17	0.0144267
$859$	1.55460e19	1.32027	0.660134	−	0.751148i	$-0.270499\pi$
$859$	1.55460e19	1.32027	0.660134	+	0.751148i	$0.270499\pi$
$860$	1.34678e18	0.113516
$861$	3.89447e18	0.325782
$862$	−5.70528e18	−0.473674
$863$	2.21810e19	1.82772	0.913862	−	0.406024i	$-0.133085\pi$
$863$	2.21810e19	1.82772	0.913862	+	0.406024i	$0.133085\pi$
$864$	6.13029e17	0.0501351
$865$	5.04988e18	0.409899
$866$	2.29063e19	1.84539
$867$	−3.45499e18	−0.276263
$868$	−8.49798e17	−0.0674431
$869$	−6.48780e17	−0.0511056
$870$	−8.55362e17	−0.0668767
$871$	−1.95775e18	−0.151929
$872$	4.15520e18	0.320063
$873$	−5.13339e18	−0.392474
$874$	−2.57893e19	−1.95711
$875$	−1.26736e19	−0.954654
$876$	1.33825e18	0.100060
$877$	−1.51503e19	−1.12441	−0.562203	−	0.826999i	$-0.690046\pi$
$877$	−1.51503e19	−1.12441	−0.562203	+	0.826999i	$0.690046\pi$
$878$	−1.09060e19	−0.803433
$879$	−4.98172e18	−0.364294
$880$	−1.59269e18	−0.115610
$881$	−2.48812e17	−0.0179279	−0.00896393	−	0.999960i	$-0.502853\pi$
$881$	−2.48812e17	−0.0179279	−0.00896393	+	0.999960i	$0.502853\pi$
$882$	−1.09420e18	−0.0782617
$883$	1.89485e19	1.34533	0.672667	−	0.739945i	$-0.265149\pi$
$883$	1.89485e19	1.34533	0.672667	+	0.739945i	$0.265149\pi$
$884$	3.89878e17	0.0274783
$885$	8.18292e17	0.0572502
$886$	1.66627e19	1.15725
$887$	−6.97577e18	−0.480937	−0.240469	−	0.970657i	$-0.577301\pi$
$887$	−6.97577e18	−0.480937	−0.240469	+	0.970657i	$0.577301\pi$
$888$	9.23039e17	0.0631736
$889$	−2.11348e18	−0.143594
$890$	5.72197e18	0.385932
$891$	2.26127e17	0.0151408
$892$	3.44486e18	0.228982
$893$	1.96424e19	1.29617
$894$	1.39790e19	0.915759
$895$	−9.24970e17	−0.0601559
$896$	1.57297e19	1.01559
$897$	−1.45697e18	−0.0933902
$898$	1.88090e19	1.19693
$899$	−1.31942e18	−0.0833577
$900$	−2.92451e17	−0.0183433
$901$	1.23110e19	0.766623
$902$	−1.49841e18	−0.0926377
$903$	−9.44174e18	−0.579538
$904$	−7.60517e18	−0.463462
$905$	5.90380e18	0.357204
$906$	1.77666e19	1.06726
$907$	−2.69699e19	−1.60854	−0.804269	−	0.594265i	$-0.797443\pi$
$907$	−2.69699e19	−1.60854	−0.804269	+	0.594265i	$0.797443\pi$
$908$	2.65133e17	0.0157002
$909$	5.36395e17	0.0315370
$910$	−2.11205e18	−0.123292
$911$	−9.51970e18	−0.551764	−0.275882	−	0.961191i	$-0.588970\pi$
$911$	−9.51970e18	−0.551764	−0.275882	+	0.961191i	$0.588970\pi$
$912$	2.19205e19	1.26149
$913$	−9.21759e17	−0.0526693
$914$	−2.44830e19	−1.38904
$915$	8.83437e18	0.497666
$916$	−1.41686e18	−0.0792512
$917$	−2.88670e19	−1.60325
$918$	4.51284e18	0.248870
$919$	−9.85114e18	−0.539431	−0.269715	−	0.962940i	$-0.586930\pi$
$919$	−9.85114e18	−0.539431	−0.269715	+	0.962940i	$0.586930\pi$
$920$	1.21446e19	0.660334
$921$	7.52609e18	0.406333
$922$	−6.53956e18	−0.350588
$923$	−4.79523e18	−0.255269
$924$	−1.72194e17	−0.00910228
$925$	−9.47106e17	−0.0497139
$926$	1.50172e19	0.782741
$927$	−1.31552e18	−0.0680894
$928$	−7.24792e17	−0.0372522
$929$	−1.44492e19	−0.737465	−0.368732	−	0.929536i	$-0.620208\pi$
$929$	−1.44492e19	−0.737465	−0.368732	+	0.929536i	$0.620208\pi$
$930$	5.37902e18	0.272624
$931$	−8.60405e18	−0.433042
$932$	−4.32193e18	−0.216010
$933$	6.74489e18	0.334768
$934$	−2.19748e18	−0.108310
$935$	−2.57834e18	−0.126202
$936$	1.09269e18	0.0531133
$937$	1.16220e19	0.561015	0.280507	−	0.959852i	$-0.409497\pi$
$937$	1.16220e19	0.561015	0.280507	+	0.959852i	$0.409497\pi$
$938$	1.72562e19	0.827229
$939$	−5.07592e18	−0.241651
$940$	1.39521e18	0.0659640
$941$	−2.51421e19	−1.18051	−0.590255	−	0.807217i	$-0.700973\pi$
$941$	−2.51421e19	−1.18051	−0.590255	+	0.807217i	$0.700973\pi$
$942$	2.49554e19	1.16368
$943$	1.29494e19	0.599684
$944$	3.15307e18	0.145016
$945$	−2.83285e18	−0.129395
$946$	3.63274e18	0.164794
$947$	−3.47479e18	−0.156550	−0.0782752	−	0.996932i	$-0.524941\pi$
$947$	−3.47479e18	−0.156550	−0.0782752	+	0.996932i	$0.524941\pi$
$948$	6.34245e17	0.0283794
$949$	5.13051e18	0.227997
$950$	−1.98455e19	−0.875909
$951$	1.73939e19	0.762471
$952$	2.27833e19	0.991920
$953$	1.85841e19	0.803597	0.401799	−	0.915728i	$-0.368385\pi$
$953$	1.85841e19	0.803597	0.401799	+	0.915728i	$0.368385\pi$
$954$	−5.20424e18	−0.223508
$955$	4.05983e18	0.173175
$956$	−3.53383e18	−0.149716
$957$	−2.67354e17	−0.0112502
$958$	2.94342e19	1.23020
$959$	−9.93347e18	−0.412363
$960$	−8.92491e18	−0.367994
$961$	−1.61202e19	−0.660191
$962$	−5.33752e17	−0.0217121
$963$	6.40647e18	0.258850
$964$	−8.02051e17	−0.0321885
$965$	2.52971e18	0.100842
$966$	1.28422e19	0.508495
$967$	−2.10520e19	−0.827983	−0.413991	−	0.910281i	$-0.635866\pi$
$967$	−2.10520e19	−0.827983	−0.413991	+	0.910281i	$0.635866\pi$
$968$	2.32157e19	0.906966
$969$	3.54860e19	1.37706
$970$	−2.47432e19	−0.953762
$971$	−5.24399e18	−0.200788	−0.100394	−	0.994948i	$-0.532010\pi$
$971$	−5.24399e18	−0.200788	−0.100394	+	0.994948i	$0.532010\pi$
$972$	−2.21061e17	−0.00840780
$973$	−3.41736e19	−1.29109
$974$	1.86948e19	0.701596
$975$	−1.12118e18	−0.0417970
$976$	3.40408e19	1.26060
$977$	3.95889e19	1.45633	0.728164	−	0.685403i	$-0.240374\pi$
$977$	3.95889e19	1.45633	0.728164	+	0.685403i	$0.240374\pi$
$978$	4.72203e18	0.172554
$979$	1.78847e18	0.0649223
$980$	−6.11147e17	−0.0220382
$981$	−3.22278e18	−0.115447
$982$	5.63995e19	2.00701
$983$	5.89288e18	0.208319	0.104160	−	0.994561i	$-0.466785\pi$
$983$	5.89288e18	0.208319	0.104160	+	0.994561i	$0.466785\pi$
$984$	−9.71163e18	−0.341055
$985$	1.04078e19	0.363097
$986$	−5.33560e18	−0.184920
$987$	−9.78123e18	−0.336769
$988$	−1.29599e18	−0.0443283
$989$	−3.13944e19	−1.06678
$990$	1.08995e18	0.0367940
$991$	3.13115e19	1.05009	0.525044	−	0.851075i	$-0.324049\pi$
$991$	3.13115e19	1.05009	0.525044	+	0.851075i	$0.324049\pi$
$992$	4.55792e18	0.151859
$993$	−2.28166e18	−0.0755231
$994$	4.22664e19	1.38990
$995$	−2.01866e18	−0.0659498
$996$	9.01109e17	0.0292477
$997$	−2.75575e19	−0.888629	−0.444315	−	0.895871i	$-0.646553\pi$
$997$	−2.75575e19	−0.888629	−0.444315	+	0.895871i	$0.646553\pi$
$998$	2.03245e19	0.651135
$999$	−7.15911e17	−0.0227868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.24	✓	31

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

\(f(q)\)	\(=\)	\(q+96.2584 q^{2} -729.000 q^{3} +1073.68 q^{4} +26611.4 q^{5} -70172.4 q^{6} +274772. q^{7} -685198. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+96.2584 q^{2} -729.000 q^{3} +1073.68 q^{4} +26611.4 q^{5} -70172.4 q^{6} +274772. q^{7} -685198. q^{8} +531441. q^{9} +2.56158e6 q^{10} +800651. q^{11} -782714. q^{12} -3.00072e6 q^{13} +2.64491e7 q^{14} -1.93997e7 q^{15} -7.47517e7 q^{16} -1.21012e8 q^{17} +5.11557e7 q^{18} +4.02255e8 q^{19} +2.85722e7 q^{20} -2.00309e8 q^{21} +7.70694e7 q^{22} -6.66039e8 q^{23} +4.99509e8 q^{24} -5.12534e8 q^{25} -2.88844e8 q^{26} -3.87420e8 q^{27} +2.95017e8 q^{28} +4.58053e8 q^{29} -1.86739e9 q^{30} -2.88050e9 q^{31} -1.58233e9 q^{32} -5.83674e8 q^{33} -1.16484e10 q^{34} +7.31207e9 q^{35} +5.70598e8 q^{36} +1.84789e9 q^{37} +3.87204e10 q^{38} +2.18752e9 q^{39} -1.82341e10 q^{40} -1.94423e10 q^{41} -1.92814e10 q^{42} +4.71360e10 q^{43} +8.59644e8 q^{44} +1.41424e10 q^{45} -6.41119e10 q^{46} +4.88308e10 q^{47} +5.44940e10 q^{48} -2.13895e10 q^{49} -4.93357e10 q^{50} +8.82179e10 q^{51} -3.22181e9 q^{52} -1.01733e11 q^{53} -3.72925e10 q^{54} +2.13065e10 q^{55} -1.88273e11 q^{56} -2.93244e11 q^{57} +4.40914e10 q^{58} -4.21805e10 q^{59} -2.08291e10 q^{60} -4.55386e11 q^{61} -2.77273e11 q^{62} +1.46025e11 q^{63} +4.60053e11 q^{64} -7.98534e10 q^{65} -5.61836e10 q^{66} +6.52429e11 q^{67} -1.29928e11 q^{68} +4.85542e11 q^{69} +7.03848e11 q^{70} +1.59803e12 q^{71} -3.64142e11 q^{72} -1.70976e12 q^{73} +1.77875e11 q^{74} +3.73637e11 q^{75} +4.31893e11 q^{76} +2.19996e11 q^{77} +2.10567e11 q^{78} -8.10316e11 q^{79} -1.98925e12 q^{80} +2.82430e11 q^{81} -1.87149e12 q^{82} -1.15126e12 q^{83} -2.15068e11 q^{84} -3.22031e12 q^{85} +4.53723e12 q^{86} -3.33920e11 q^{87} -5.48604e11 q^{88} +2.23377e12 q^{89} +1.36133e12 q^{90} -8.24512e11 q^{91} -7.15114e11 q^{92} +2.09989e12 q^{93} +4.70038e12 q^{94} +1.07046e13 q^{95} +1.15352e12 q^{96} -9.65937e12 q^{97} -2.05892e12 q^{98} +4.25499e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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