LMFDB - Embedded newform 177.10.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+33.2747 q^{2} -81.0000 q^{3} +595.206 q^{4} -1222.14 q^{5} -2695.25 q^{6} +7343.10 q^{7} +2768.67 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+33.2747 q^{2} -81.0000 q^{3} +595.206 q^{4} -1222.14 q^{5} -2695.25 q^{6} +7343.10 q^{7} +2768.67 q^{8} +6561.00 q^{9} -40666.2 q^{10} -29821.5 q^{11} -48211.7 q^{12} -22797.1 q^{13} +244340. q^{14} +98993.0 q^{15} -212619. q^{16} +633639. q^{17} +218315. q^{18} +943799. q^{19} -727423. q^{20} -594791. q^{21} -992302. q^{22} -2.11142e6 q^{23} -224262. q^{24} -459508. q^{25} -758567. q^{26} -531441. q^{27} +4.37066e6 q^{28} -3.29075e6 q^{29} +3.29396e6 q^{30} -5.35294e6 q^{31} -8.49239e6 q^{32} +2.41554e6 q^{33} +2.10842e7 q^{34} -8.97427e6 q^{35} +3.90515e6 q^{36} +1.22347e6 q^{37} +3.14046e7 q^{38} +1.84657e6 q^{39} -3.38369e6 q^{40} +1.04674e7 q^{41} -1.97915e7 q^{42} -2.91320e7 q^{43} -1.77500e7 q^{44} -8.01844e6 q^{45} -7.02569e7 q^{46} -2.38542e7 q^{47} +1.72221e7 q^{48} +1.35675e7 q^{49} -1.52900e7 q^{50} -5.13248e7 q^{51} -1.35690e7 q^{52} +4.57699e7 q^{53} -1.76835e7 q^{54} +3.64459e7 q^{55} +2.03306e7 q^{56} -7.64477e7 q^{57} -1.09499e8 q^{58} -1.21174e7 q^{59} +5.89213e7 q^{60} -1.05999e8 q^{61} -1.78117e8 q^{62} +4.81781e7 q^{63} -1.73721e8 q^{64} +2.78612e7 q^{65} +8.03765e7 q^{66} -3.01366e8 q^{67} +3.77146e8 q^{68} +1.71025e8 q^{69} -2.98616e8 q^{70} +6.25203e7 q^{71} +1.81652e7 q^{72} +1.58794e8 q^{73} +4.07105e7 q^{74} +3.72201e7 q^{75} +5.61755e8 q^{76} -2.18982e8 q^{77} +6.14439e7 q^{78} -4.83457e8 q^{79} +2.59849e8 q^{80} +4.30467e7 q^{81} +3.48300e8 q^{82} +2.41279e7 q^{83} -3.54024e8 q^{84} -7.74393e8 q^{85} -9.69358e8 q^{86} +2.66550e8 q^{87} -8.25660e7 q^{88} +3.08334e7 q^{89} -2.66811e8 q^{90} -1.67402e8 q^{91} -1.25673e9 q^{92} +4.33588e8 q^{93} -7.93741e8 q^{94} -1.15345e9 q^{95} +6.87884e8 q^{96} -1.35366e9 q^{97} +4.51456e8 q^{98} -1.95659e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	33.2747	1.47055	0.735274	−	0.677770i	$-0.237053\pi$
$2$	33.2747	1.47055	0.735274	+	0.677770i	$0.237053\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	595.206	1.16251
$5$	−1222.14	−0.874490	−0.437245	−	0.899343i	$-0.644046\pi$
$5$	−1222.14	−0.874490	−0.437245	+	0.899343i	$0.644046\pi$
$6$	−2695.25	−0.849022
$7$	7343.10	1.15595	0.577974	−	0.816055i	$-0.303843\pi$
$7$	7343.10	1.15595	0.577974	+	0.816055i	$0.303843\pi$
$8$	2768.67	0.238983
$9$	6561.00	0.333333
$10$	−40666.2	−1.28598
$11$	−29821.5	−0.614133	−0.307067	−	0.951688i	$-0.599347\pi$
$11$	−29821.5	−0.614133	−0.307067	+	0.951688i	$0.599347\pi$
$12$	−48211.7	−0.671177
$13$	−22797.1	−0.221378	−0.110689	−	0.993855i	$-0.535306\pi$
$13$	−22797.1	−0.221378	−0.110689	+	0.993855i	$0.535306\pi$
$14$	244340.	1.69988
$15$	98993.0	0.504887
$16$	−212619.	−0.811077
$17$	633639.	1.84002	0.920008	−	0.391899i	$-0.128182\pi$
$17$	633639.	1.84002	0.920008	+	0.391899i	$0.128182\pi$
$18$	218315.	0.490183
$19$	943799.	1.66145	0.830727	−	0.556680i	$-0.187925\pi$
$19$	943799.	1.66145	0.830727	+	0.556680i	$0.187925\pi$
$20$	−727423.	−1.01661
$21$	−594791.	−0.667387
$22$	−992302.	−0.903113
$23$	−2.11142e6	−1.57326	−0.786628	−	0.617427i	$-0.788175\pi$
$23$	−2.11142e6	−1.57326	−0.786628	+	0.617427i	$0.788175\pi$
$24$	−224262.	−0.137977
$25$	−459508.	−0.235268
$26$	−758567.	−0.325547
$27$	−531441.	−0.192450
$28$	4.37066e6	1.34380
$29$	−3.29075e6	−0.863979	−0.431990	−	0.901879i	$-0.642188\pi$
$29$	−3.29075e6	−0.863979	−0.431990	+	0.901879i	$0.642188\pi$
$30$	3.29396e6	0.742460
$31$	−5.35294e6	−1.04103	−0.520517	−	0.853852i	$-0.674261\pi$
$31$	−5.35294e6	−1.04103	−0.520517	+	0.853852i	$0.674261\pi$
$32$	−8.49239e6	−1.43171
$33$	2.41554e6	0.354570
$34$	2.10842e7	2.70583
$35$	−8.97427e6	−1.01086
$36$	3.90515e6	0.387504
$37$	1.22347e6	0.107321	0.0536605	−	0.998559i	$-0.482911\pi$
$37$	1.22347e6	0.107321	0.0536605	+	0.998559i	$0.482911\pi$
$38$	3.14046e7	2.44325
$39$	1.84657e6	0.127813
$40$	−3.38369e6	−0.208988
$41$	1.04674e7	0.578511	0.289255	−	0.957252i	$-0.406592\pi$
$41$	1.04674e7	0.578511	0.289255	+	0.957252i	$0.406592\pi$
$42$	−1.97915e7	−0.981425
$43$	−2.91320e7	−1.29946	−0.649729	−	0.760166i	$-0.725117\pi$
$43$	−2.91320e7	−1.29946	−0.649729	+	0.760166i	$0.725117\pi$
$44$	−1.77500e7	−0.713938
$45$	−8.01844e6	−0.291497
$46$	−7.02569e7	−2.31355
$47$	−2.38542e7	−0.713057	−0.356528	−	0.934285i	$-0.616040\pi$
$47$	−2.38542e7	−0.713057	−0.356528	+	0.934285i	$0.616040\pi$
$48$	1.72221e7	0.468276
$49$	1.35675e7	0.336216
$50$	−1.52900e7	−0.345973
$51$	−5.13248e7	−1.06233
$52$	−1.35690e7	−0.257355
$53$	4.57699e7	0.796781	0.398391	−	0.917216i	$-0.369569\pi$
$53$	4.57699e7	0.796781	0.398391	+	0.917216i	$0.369569\pi$
$54$	−1.76835e7	−0.283007
$55$	3.64459e7	0.537053
$56$	2.03306e7	0.276252
$57$	−7.64477e7	−0.959241
$58$	−1.09499e8	−1.27052
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	5.89213e7	0.586937
$61$	−1.05999e8	−0.980207	−0.490103	−	0.871664i	$-0.663041\pi$
$61$	−1.05999e8	−0.980207	−0.490103	+	0.871664i	$0.663041\pi$
$62$	−1.78117e8	−1.53089
$63$	4.81781e7	0.385316
$64$	−1.73721e8	−1.29432
$65$	2.78612e7	0.193593
$66$	8.03765e7	0.521412
$67$	−3.01366e8	−1.82708	−0.913540	−	0.406749i	$-0.866663\pi$
$67$	−3.01366e8	−1.82708	−0.913540	+	0.406749i	$0.866663\pi$
$68$	3.77146e8	2.13904
$69$	1.71025e8	0.908320
$70$	−2.98616e8	−1.48653
$71$	6.25203e7	0.291983	0.145992	−	0.989286i	$-0.453363\pi$
$71$	6.25203e7	0.291983	0.145992	+	0.989286i	$0.453363\pi$
$72$	1.81652e7	0.0796609
$73$	1.58794e8	0.654456	0.327228	−	0.944945i	$-0.393886\pi$
$73$	1.58794e8	0.654456	0.327228	+	0.944945i	$0.393886\pi$
$74$	4.07105e7	0.157821
$75$	3.72201e7	0.135832
$76$	5.61755e8	1.93146
$77$	−2.18982e8	−0.709906
$78$	6.14439e7	0.187955
$79$	−4.83457e8	−1.39648	−0.698242	−	0.715862i	$-0.746034\pi$
$79$	−4.83457e8	−1.39648	−0.698242	+	0.715862i	$0.746034\pi$
$80$	2.59849e8	0.709278
$81$	4.30467e7	0.111111
$82$	3.48300e8	0.850728
$83$	2.41279e7	0.0558043	0.0279021	−	0.999611i	$-0.491117\pi$
$83$	2.41279e7	0.0558043	0.0279021	+	0.999611i	$0.491117\pi$
$84$	−3.54024e8	−0.775846
$85$	−7.74393e8	−1.60908
$86$	−9.69358e8	−1.91091
$87$	2.66550e8	0.498819
$88$	−8.25660e7	−0.146767
$89$	3.08334e7	0.0520914	0.0260457	−	0.999661i	$-0.491708\pi$
$89$	3.08334e7	0.0520914	0.0260457	+	0.999661i	$0.491708\pi$
$90$	−2.66811e8	−0.428660
$91$	−1.67402e8	−0.255902
$92$	−1.25673e9	−1.82893
$93$	4.33588e8	0.601041
$94$	−7.93741e8	−1.04858
$95$	−1.15345e9	−1.45292
$96$	6.87884e8	0.826599
$97$	−1.35366e9	−1.55251	−0.776257	−	0.630416i	$-0.782884\pi$
$97$	−1.35366e9	−1.55251	−0.776257	+	0.630416i	$0.782884\pi$
$98$	4.51456e8	0.494422
$99$	−1.95659e8	−0.204711
$100$	−2.73502e8	−0.273502
$101$	−4.41470e7	−0.0422138	−0.0211069	−	0.999777i	$-0.506719\pi$
$101$	−4.41470e7	−0.0422138	−0.0211069	+	0.999777i	$0.506719\pi$
$102$	−1.70782e9	−1.56221
$103$	−1.73960e9	−1.52294	−0.761470	−	0.648200i	$-0.775522\pi$
$103$	−1.73960e9	−1.52294	−0.761470	+	0.648200i	$0.775522\pi$
$104$	−6.31177e7	−0.0529055
$105$	7.26916e8	0.583623
$106$	1.52298e9	1.17171
$107$	1.62889e9	1.20134	0.600670	−	0.799497i	$-0.294901\pi$
$107$	1.62889e9	1.20134	0.600670	+	0.799497i	$0.294901\pi$
$108$	−3.16317e8	−0.223726
$109$	−1.93862e9	−1.31545	−0.657725	−	0.753258i	$-0.728481\pi$
$109$	−1.93862e9	−1.31545	−0.657725	+	0.753258i	$0.728481\pi$
$110$	1.21273e9	0.789762
$111$	−9.91009e7	−0.0619618
$112$	−1.56128e9	−0.937563
$113$	−5.01522e8	−0.289359	−0.144679	−	0.989479i	$-0.546215\pi$
$113$	−5.01522e8	−0.289359	−0.144679	+	0.989479i	$0.546215\pi$
$114$	−2.54378e9	−1.41061
$115$	2.58044e9	1.37580
$116$	−1.95867e9	−1.00439
$117$	−1.49572e8	−0.0737927
$118$	−4.03202e8	−0.191449
$119$	4.65288e9	2.12696
$120$	2.74079e8	0.120659
$121$	−1.46863e9	−0.622840
$122$	−3.52709e9	−1.44144
$123$	−8.47859e8	−0.334003
$124$	−3.18610e9	−1.21021
$125$	2.94857e9	1.08023
$126$	1.60311e9	0.566626
$127$	5.57053e8	0.190011	0.0950057	−	0.995477i	$-0.469713\pi$
$127$	5.57053e8	0.190011	0.0950057	+	0.995477i	$0.469713\pi$
$128$	−1.43241e9	−0.471654
$129$	2.35969e9	0.750242
$130$	9.27073e8	0.284688
$131$	2.71370e8	0.0805084	0.0402542	−	0.999189i	$-0.487183\pi$
$131$	2.71370e8	0.0805084	0.0402542	+	0.999189i	$0.487183\pi$
$132$	1.43775e9	0.412192
$133$	6.93041e9	1.92055
$134$	−1.00279e10	−2.68681
$135$	6.49493e8	0.168296
$136$	1.75434e9	0.439732
$137$	−9.01699e8	−0.218685	−0.109343	−	0.994004i	$-0.534875\pi$
$137$	−9.01699e8	−0.218685	−0.109343	+	0.994004i	$0.534875\pi$
$138$	5.69081e9	1.33573
$139$	4.40010e9	0.999761	0.499880	−	0.866095i	$-0.333377\pi$
$139$	4.40010e9	0.999761	0.499880	+	0.866095i	$0.333377\pi$
$140$	−5.34154e9	−1.17514
$141$	1.93219e9	0.411683
$142$	2.08034e9	0.429376
$143$	6.79844e8	0.135956
$144$	−1.39499e9	−0.270359
$145$	4.02174e9	0.755541
$146$	5.28381e9	0.962409
$147$	−1.09897e9	−0.194115
$148$	7.28216e8	0.124762
$149$	9.19443e9	1.52822	0.764111	−	0.645084i	$-0.223178\pi$
$149$	9.19443e9	1.52822	0.764111	+	0.645084i	$0.223178\pi$
$150$	1.23849e9	0.199748
$151$	3.37031e9	0.527563	0.263781	−	0.964582i	$-0.415030\pi$
$151$	3.37031e9	0.527563	0.263781	+	0.964582i	$0.415030\pi$
$152$	2.61307e9	0.397059
$153$	4.15731e9	0.613339
$154$	−7.28658e9	−1.04395
$155$	6.54202e9	0.910373
$156$	1.09909e9	0.148584
$157$	4.84811e9	0.636830	0.318415	−	0.947951i	$-0.396849\pi$
$157$	4.84811e9	0.636830	0.318415	+	0.947951i	$0.396849\pi$
$158$	−1.60869e10	−2.05360
$159$	−3.70737e9	−0.460022
$160$	1.03789e10	1.25202
$161$	−1.55044e10	−1.81860
$162$	1.43237e9	0.163394
$163$	−8.02089e8	−0.0889976	−0.0444988	−	0.999009i	$-0.514169\pi$
$163$	−8.02089e8	−0.0889976	−0.0444988	+	0.999009i	$0.514169\pi$
$164$	6.23026e9	0.672526
$165$	−2.95212e9	−0.310068
$166$	8.02848e8	0.0820629
$167$	−1.29522e10	−1.28860	−0.644300	−	0.764773i	$-0.722851\pi$
$167$	−1.29522e10	−1.28860	−0.644300	+	0.764773i	$0.722851\pi$
$168$	−1.64678e9	−0.159494
$169$	−1.00848e10	−0.950992
$170$	−2.57677e10	−2.36622
$171$	6.19226e9	0.553818
$172$	−1.73395e10	−1.51064
$173$	−1.23942e10	−1.05199	−0.525994	−	0.850488i	$-0.676307\pi$
$173$	−1.23942e10	−1.05199	−0.525994	+	0.850488i	$0.676307\pi$
$174$	8.86939e9	0.733537
$175$	−3.37421e9	−0.271958
$176$	6.34062e9	0.498109
$177$	9.81506e8	0.0751646
$178$	1.02597e9	0.0766030
$179$	−4.64159e9	−0.337931	−0.168966	−	0.985622i	$-0.554043\pi$
$179$	−4.64159e9	−0.337931	−0.168966	+	0.985622i	$0.554043\pi$
$180$	−4.77262e9	−0.338868
$181$	1.20747e10	0.836227	0.418114	−	0.908395i	$-0.362691\pi$
$181$	1.20747e10	0.836227	0.418114	+	0.908395i	$0.362691\pi$
$182$	−5.57024e9	−0.376316
$183$	8.58592e9	0.565923
$184$	−5.84583e9	−0.375981
$185$	−1.49524e9	−0.0938511
$186$	1.44275e10	0.883860
$187$	−1.88961e10	−1.13002
$188$	−1.41982e10	−0.828937
$189$	−3.90243e9	−0.222462
$190$	−3.83807e10	−2.13659
$191$	2.29459e10	1.24754	0.623771	−	0.781607i	$-0.285600\pi$
$191$	2.29459e10	1.24754	0.623771	+	0.781607i	$0.285600\pi$
$192$	1.40714e10	0.747278
$193$	8.99321e9	0.466559	0.233280	−	0.972410i	$-0.425054\pi$
$193$	8.99321e9	0.466559	0.233280	+	0.972410i	$0.425054\pi$
$194$	−4.50425e10	−2.28305
$195$	−2.25676e9	−0.111771
$196$	8.07549e9	0.390856
$197$	2.70257e10	1.27844	0.639219	−	0.769025i	$-0.279258\pi$
$197$	2.70257e10	1.27844	0.639219	+	0.769025i	$0.279258\pi$
$198$	−6.51049e9	−0.301038
$199$	−4.03112e10	−1.82216	−0.911080	−	0.412230i	$-0.864750\pi$
$199$	−4.03112e10	−1.82216	−0.911080	+	0.412230i	$0.864750\pi$
$200$	−1.27223e9	−0.0562250
$201$	2.44106e10	1.05487
$202$	−1.46898e9	−0.0620775
$203$	−2.41643e10	−0.998715
$204$	−3.05488e10	−1.23498
$205$	−1.27926e10	−0.505902
$206$	−5.78848e10	−2.23956
$207$	−1.38530e10	−0.524419
$208$	4.84710e9	0.179555
$209$	−2.81455e10	−1.02035
$210$	2.41879e10	0.858246
$211$	2.34009e10	0.812759	0.406379	−	0.913704i	$-0.366791\pi$
$211$	2.34009e10	0.812759	0.406379	+	0.913704i	$0.366791\pi$
$212$	2.72426e10	0.926268
$213$	−5.06414e9	−0.168577
$214$	5.42010e10	1.76663
$215$	3.56032e10	1.13636
$216$	−1.47139e9	−0.0459922
$217$	−3.93072e10	−1.20338
$218$	−6.45072e10	−1.93443
$219$	−1.28623e10	−0.377850
$220$	2.16929e10	0.624331
$221$	−1.44451e10	−0.407339
$222$	−3.29755e9	−0.0911178
$223$	5.25145e10	1.42202	0.711012	−	0.703180i	$-0.248237\pi$
$223$	5.25145e10	1.42202	0.711012	+	0.703180i	$0.248237\pi$
$224$	−6.23605e10	−1.65498
$225$	−3.01483e9	−0.0784227
$226$	−1.66880e10	−0.425516
$227$	5.93675e10	1.48400	0.741998	−	0.670402i	$-0.233878\pi$
$227$	5.93675e10	1.48400	0.741998	+	0.670402i	$0.233878\pi$
$228$	−4.55022e10	−1.11513
$229$	1.29521e9	0.0311230	0.0155615	−	0.999879i	$-0.495046\pi$
$229$	1.29521e9	0.0311230	0.0155615	+	0.999879i	$0.495046\pi$
$230$	8.58635e10	2.02317
$231$	1.77376e10	0.409865
$232$	−9.11099e9	−0.206476
$233$	−4.18809e10	−0.930925	−0.465462	−	0.885068i	$-0.654112\pi$
$233$	−4.18809e10	−0.930925	−0.465462	+	0.885068i	$0.654112\pi$
$234$	−4.97696e9	−0.108516
$235$	2.91530e10	0.623560
$236$	−7.21233e9	−0.151346
$237$	3.91600e10	0.806260
$238$	1.54823e11	3.12780
$239$	−2.82303e10	−0.559661	−0.279831	−	0.960049i	$-0.590278\pi$
$239$	−2.82303e10	−0.559661	−0.279831	+	0.960049i	$0.590278\pi$
$240$	−2.10478e10	−0.409502
$241$	9.42595e10	1.79990	0.899950	−	0.435993i	$-0.143603\pi$
$241$	9.42595e10	1.79990	0.899950	+	0.435993i	$0.143603\pi$
$242$	−4.88681e10	−0.915917
$243$	−3.48678e9	−0.0641500
$244$	−6.30913e10	−1.13950
$245$	−1.65814e10	−0.294018
$246$	−2.82123e10	−0.491168
$247$	−2.15159e10	−0.367809
$248$	−1.48205e10	−0.248789
$249$	−1.95436e9	−0.0322186
$250$	9.81127e10	1.58853
$251$	6.70119e10	1.06566	0.532832	−	0.846221i	$-0.321128\pi$
$251$	6.70119e10	1.06566	0.532832	+	0.846221i	$0.321128\pi$
$252$	2.86759e10	0.447935
$253$	6.29657e10	0.966189
$254$	1.85358e10	0.279421
$255$	6.27258e10	0.929000
$256$	4.12821e10	0.600733
$257$	8.43337e10	1.20587	0.602937	−	0.797789i	$-0.293997\pi$
$257$	8.43337e10	1.20587	0.602937	+	0.797789i	$0.293997\pi$
$258$	7.85180e10	1.10327
$259$	8.98405e9	0.124058
$260$	1.65832e10	0.225054
$261$	−2.15906e10	−0.287993
$262$	9.02976e9	0.118391
$263$	−8.29087e10	−1.06856	−0.534280	−	0.845307i	$-0.679417\pi$
$263$	−8.29087e10	−1.06856	−0.534280	+	0.845307i	$0.679417\pi$
$264$	6.68784e9	0.0847361
$265$	−5.59371e10	−0.696777
$266$	2.30607e11	2.82427
$267$	−2.49750e9	−0.0300750
$268$	−1.79375e11	−2.12400
$269$	−2.24386e10	−0.261282	−0.130641	−	0.991430i	$-0.541704\pi$
$269$	−2.24386e10	−0.261282	−0.130641	+	0.991430i	$0.541704\pi$
$270$	2.16117e10	0.247487
$271$	−1.48344e11	−1.67074	−0.835368	−	0.549691i	$-0.814746\pi$
$271$	−1.48344e11	−1.67074	−0.835368	+	0.549691i	$0.814746\pi$
$272$	−1.34724e11	−1.49240
$273$	1.35595e10	0.147745
$274$	−3.00038e10	−0.321587
$275$	1.37032e10	0.144486
$276$	1.01795e11	1.05593
$277$	−1.66355e11	−1.69777	−0.848883	−	0.528581i	$-0.822724\pi$
$277$	−1.66355e11	−1.69777	−0.848883	+	0.528581i	$0.822724\pi$
$278$	1.46412e11	1.47020
$279$	−3.51206e10	−0.347011
$280$	−2.48468e10	−0.241579
$281$	7.65570e10	0.732498	0.366249	−	0.930517i	$-0.380642\pi$
$281$	7.65570e10	0.732498	0.366249	+	0.930517i	$0.380642\pi$
$282$	6.42930e10	0.605400
$283$	1.42902e11	1.32434	0.662170	−	0.749354i	$-0.269636\pi$
$283$	1.42902e11	1.32434	0.662170	+	0.749354i	$0.269636\pi$
$284$	3.72125e10	0.339434
$285$	9.34295e10	0.838846
$286$	2.26216e10	0.199929
$287$	7.68632e10	0.668729
$288$	−5.57186e10	−0.477237
$289$	2.82910e11	2.38566
$290$	1.33822e11	1.11106
$291$	1.09646e11	0.896345
$292$	9.45150e10	0.760813
$293$	−1.62226e11	−1.28592	−0.642962	−	0.765898i	$-0.722295\pi$
$293$	−1.62226e11	−1.28592	−0.642962	+	0.765898i	$0.722295\pi$
$294$	−3.65679e10	−0.285455
$295$	1.48091e10	0.113849
$296$	3.38738e9	0.0256479
$297$	1.58484e10	0.118190
$298$	3.05942e11	2.24733
$299$	4.81343e10	0.348284
$300$	2.21537e10	0.157907
$301$	−2.13919e11	−1.50211
$302$	1.12146e11	0.775807
$303$	3.57590e9	0.0243722
$304$	−2.00670e11	−1.34757
$305$	1.29545e11	0.857180
$306$	1.38333e11	0.901944
$307$	−2.18138e11	−1.40155	−0.700774	−	0.713384i	$-0.747162\pi$
$307$	−2.18138e11	−1.40155	−0.700774	+	0.713384i	$0.747162\pi$
$308$	−1.30340e11	−0.825275
$309$	1.40908e11	0.879270
$310$	2.17684e11	1.33875
$311$	−1.16507e11	−0.706202	−0.353101	−	0.935585i	$-0.614873\pi$
$311$	−1.16507e11	−0.706202	−0.353101	+	0.935585i	$0.614873\pi$
$312$	5.11253e9	0.0305450
$313$	1.14756e11	0.675814	0.337907	−	0.941179i	$-0.390281\pi$
$313$	1.14756e11	0.675814	0.337907	+	0.941179i	$0.390281\pi$
$314$	1.61319e11	0.936490
$315$	−5.88802e10	−0.336955
$316$	−2.87757e11	−1.62343
$317$	−3.51023e11	−1.95240	−0.976200	−	0.216872i	$-0.930415\pi$
$317$	−3.51023e11	−1.95240	−0.976200	+	0.216872i	$0.930415\pi$
$318$	−1.23362e11	−0.676484
$319$	9.81350e10	0.530598
$320$	2.12311e11	1.13187
$321$	−1.31940e11	−0.693594
$322$	−5.15904e11	−2.67434
$323$	5.98028e11	3.05710
$324$	2.56217e10	0.129168
$325$	1.04755e10	0.0520832
$326$	−2.66893e10	−0.130875
$327$	1.57029e11	0.759476
$328$	2.89808e10	0.138254
$329$	−1.75164e11	−0.824256
$330$	−9.82310e10	−0.455970
$331$	2.31178e11	1.05857	0.529285	−	0.848444i	$-0.322460\pi$
$331$	2.31178e11	1.05857	0.529285	+	0.848444i	$0.322460\pi$
$332$	1.43611e10	0.0648732
$333$	8.02717e9	0.0357737
$334$	−4.30979e11	−1.89495
$335$	3.68310e11	1.59776
$336$	1.26464e11	0.541302
$337$	−1.88549e11	−0.796324	−0.398162	−	0.917315i	$-0.630352\pi$
$337$	−1.88549e11	−0.796324	−0.398162	+	0.917315i	$0.630352\pi$
$338$	−3.35569e11	−1.39848
$339$	4.06232e10	0.167061
$340$	−4.60924e11	−1.87057
$341$	1.59633e11	0.639333
$342$	2.06046e11	0.814416
$343$	−1.96693e11	−0.767300
$344$	−8.06569e10	−0.310548
$345$	−2.09016e11	−0.794316
$346$	−4.12413e11	−1.54700
$347$	6.04999e10	0.224012	0.112006	−	0.993708i	$-0.464272\pi$
$347$	6.04999e10	0.224012	0.112006	+	0.993708i	$0.464272\pi$
$348$	1.58653e11	0.579883
$349$	−1.82709e11	−0.659245	−0.329622	−	0.944113i	$-0.606921\pi$
$349$	−1.82709e11	−0.659245	−0.329622	+	0.944113i	$0.606921\pi$
$350$	−1.12276e11	−0.399927
$351$	1.21153e10	0.0426042
$352$	2.53256e11	0.879261
$353$	4.28924e10	0.147026	0.0735130	−	0.997294i	$-0.476579\pi$
$353$	4.28924e10	0.147026	0.0735130	+	0.997294i	$0.476579\pi$
$354$	3.26593e10	0.110533
$355$	−7.64083e10	−0.255336
$356$	1.83522e10	0.0605569
$357$	−3.76883e11	−1.22800
$358$	−1.54448e11	−0.496944
$359$	−7.82389e10	−0.248598	−0.124299	−	0.992245i	$-0.539668\pi$
$359$	−7.82389e10	−0.248598	−0.124299	+	0.992245i	$0.539668\pi$
$360$	−2.22004e10	−0.0696626
$361$	5.68068e11	1.76043
$362$	4.01784e11	1.22971
$363$	1.18959e11	0.359597
$364$	−9.96385e10	−0.297489
$365$	−1.94067e11	−0.572315
$366$	2.85694e11	0.832217
$367$	−8.56690e10	−0.246505	−0.123253	−	0.992375i	$-0.539333\pi$
$367$	−8.56690e10	−0.246505	−0.123253	+	0.992375i	$0.539333\pi$
$368$	4.48928e11	1.27603
$369$	6.86766e10	0.192837
$370$	−4.97538e10	−0.138013
$371$	3.36093e11	0.921038
$372$	2.58074e11	0.698718
$373$	2.10755e11	0.563752	0.281876	−	0.959451i	$-0.409043\pi$
$373$	2.10755e11	0.563752	0.281876	+	0.959451i	$0.409043\pi$
$374$	−6.28761e11	−1.66174
$375$	−2.38834e11	−0.623671
$376$	−6.60444e10	−0.170408
$377$	7.50195e10	0.191266
$378$	−1.29852e11	−0.327142
$379$	−5.11215e11	−1.27270	−0.636351	−	0.771399i	$-0.719557\pi$
$379$	−5.11215e11	−1.27270	−0.636351	+	0.771399i	$0.719557\pi$
$380$	−6.86541e11	−1.68904
$381$	−4.51213e10	−0.109703
$382$	7.63519e11	1.83457
$383$	8.17990e11	1.94247	0.971233	−	0.238132i	$-0.0765350\pi$
$383$	8.17990e11	1.94247	0.971233	+	0.238132i	$0.0765350\pi$
$384$	1.16025e11	0.272309
$385$	2.67626e11	0.620806
$386$	2.99246e11	0.686098
$387$	−1.91135e11	−0.433152
$388$	−8.05705e11	−1.80482
$389$	1.37600e11	0.304681	0.152340	−	0.988328i	$-0.451319\pi$
$389$	1.37600e11	0.304681	0.152340	+	0.988328i	$0.451319\pi$
$390$	−7.50929e10	−0.164364
$391$	−1.33788e12	−2.89482
$392$	3.75641e10	0.0803499
$393$	−2.19810e10	−0.0464815
$394$	8.99273e11	1.88000
$395$	5.90850e11	1.22121
$396$	−1.16457e11	−0.237979
$397$	2.84094e11	0.573991	0.286995	−	0.957932i	$-0.407344\pi$
$397$	2.84094e11	0.573991	0.286995	+	0.957932i	$0.407344\pi$
$398$	−1.34134e12	−2.67957
$399$	−5.61363e11	−1.10883
$400$	9.77001e10	0.190821
$401$	−6.62746e11	−1.27996	−0.639982	−	0.768390i	$-0.721058\pi$
$401$	−6.62746e11	−1.27996	−0.639982	+	0.768390i	$0.721058\pi$
$402$	8.12257e11	1.55123
$403$	1.22032e11	0.230462
$404$	−2.62766e10	−0.0490741
$405$	−5.26090e10	−0.0971655
$406$	−8.04059e11	−1.46866
$407$	−3.64856e10	−0.0659094
$408$	−1.42101e11	−0.253879
$409$	−4.50389e11	−0.795853	−0.397926	−	0.917417i	$-0.630270\pi$
$409$	−4.50389e11	−0.795853	−0.397926	+	0.917417i	$0.630270\pi$
$410$	−4.25670e11	−0.743953
$411$	7.30376e10	0.126258
$412$	−1.03542e12	−1.77044
$413$	−8.89790e10	−0.150492
$414$	−4.60955e11	−0.771183
$415$	−2.94875e10	−0.0488002
$416$	1.93602e11	0.316949
$417$	−3.56408e11	−0.577212
$418$	−9.36534e11	−1.50048
$419$	9.29357e11	1.47306	0.736528	−	0.676407i	$-0.236464\pi$
$419$	9.29357e11	1.47306	0.736528	+	0.676407i	$0.236464\pi$
$420$	4.32665e11	0.678469
$421$	−6.37533e11	−0.989084	−0.494542	−	0.869154i	$-0.664664\pi$
$421$	−6.37533e11	−0.989084	−0.494542	+	0.869154i	$0.664664\pi$
$422$	7.78658e11	1.19520
$423$	−1.56507e11	−0.237686
$424$	1.26722e11	0.190417
$425$	−2.91162e11	−0.432897
$426$	−1.68508e11	−0.247900
$427$	−7.78362e11	−1.13307
$428$	9.69528e11	1.39657
$429$	−5.50674e10	−0.0784940
$430$	1.18469e12	1.67107
$431$	−2.65041e11	−0.369969	−0.184984	−	0.982741i	$-0.559223\pi$
$431$	−2.65041e11	−0.369969	−0.184984	+	0.982741i	$0.559223\pi$
$432$	1.12994e11	0.156092
$433$	−2.08274e11	−0.284733	−0.142367	−	0.989814i	$-0.545471\pi$
$433$	−2.08274e11	−0.284733	−0.142367	+	0.989814i	$0.545471\pi$
$434$	−1.30793e12	−1.76963
$435$	−3.25761e11	−0.436212
$436$	−1.15388e12	−1.52923
$437$	−1.99276e12	−2.61389
$438$	−4.27989e11	−0.555647
$439$	2.97100e11	0.381779	0.190890	−	0.981611i	$-0.438863\pi$
$439$	2.97100e11	0.381779	0.190890	+	0.981611i	$0.438863\pi$
$440$	1.00907e11	0.128346
$441$	8.90166e10	0.112072
$442$	−4.80658e11	−0.599012
$443$	4.93616e11	0.608937	0.304469	−	0.952522i	$-0.401521\pi$
$443$	4.93616e11	0.608937	0.304469	+	0.952522i	$0.401521\pi$
$444$	−5.89855e10	−0.0720314
$445$	−3.76826e10	−0.0455534
$446$	1.74740e12	2.09116
$447$	−7.44749e11	−0.882320
$448$	−1.27565e12	−1.49617
$449$	−2.14905e11	−0.249539	−0.124769	−	0.992186i	$-0.539819\pi$
$449$	−2.14905e11	−0.249539	−0.124769	+	0.992186i	$0.539819\pi$
$450$	−1.00318e11	−0.115324
$451$	−3.12154e11	−0.355283
$452$	−2.98509e11	−0.336383
$453$	−2.72995e11	−0.304589
$454$	1.97544e12	2.18229
$455$	2.04587e11	0.223783
$456$	−2.11659e11	−0.229242
$457$	6.45951e11	0.692750	0.346375	−	0.938096i	$-0.387413\pi$
$457$	6.45951e11	0.692750	0.346375	+	0.938096i	$0.387413\pi$
$458$	4.30978e10	0.0457679
$459$	−3.36742e11	−0.354111
$460$	1.53590e12	1.59938
$461$	−4.25233e11	−0.438503	−0.219252	−	0.975668i	$-0.570362\pi$
$461$	−4.25233e11	−0.438503	−0.219252	+	0.975668i	$0.570362\pi$
$462$	5.90213e11	0.602726
$463$	1.46536e12	1.48194	0.740969	−	0.671539i	$-0.234367\pi$
$463$	1.46536e12	1.48194	0.740969	+	0.671539i	$0.234367\pi$
$464$	6.99675e11	0.700754
$465$	−5.29904e11	−0.525604
$466$	−1.39358e12	−1.36897
$467$	−6.74336e10	−0.0656070	−0.0328035	−	0.999462i	$-0.510444\pi$
$467$	−6.74336e10	−0.0656070	−0.0328035	+	0.999462i	$0.510444\pi$
$468$	−8.90261e10	−0.0857850
$469$	−2.21296e12	−2.11201
$470$	9.70059e11	0.916976
$471$	−3.92697e11	−0.367674
$472$	−3.35490e10	−0.0311129
$473$	8.68760e11	0.798040
$474$	1.30304e12	1.18564
$475$	−4.33683e11	−0.390887
$476$	2.76942e12	2.47262
$477$	3.00297e11	0.265594
$478$	−9.39355e11	−0.823009
$479$	−6.79998e11	−0.590199	−0.295099	−	0.955467i	$-0.595353\pi$
$479$	−6.79998e11	−0.590199	−0.295099	+	0.955467i	$0.595353\pi$
$480$	−8.40688e11	−0.722852
$481$	−2.78915e10	−0.0237585
$482$	3.13646e12	2.64684
$483$	1.25585e12	1.04997
$484$	−8.74135e11	−0.724060
$485$	1.65435e12	1.35766
$486$	−1.16022e11	−0.0943357
$487$	−1.21750e12	−0.980821	−0.490410	−	0.871492i	$-0.663153\pi$
$487$	−1.21750e12	−0.980821	−0.490410	+	0.871492i	$0.663153\pi$
$488$	−2.93476e11	−0.234252
$489$	6.49692e10	0.0513828
$490$	−5.51741e11	−0.432367
$491$	−9.98749e11	−0.775514	−0.387757	−	0.921762i	$-0.626750\pi$
$491$	−9.98749e11	−0.775514	−0.387757	+	0.921762i	$0.626750\pi$
$492$	−5.04651e11	−0.388283
$493$	−2.08514e12	−1.58974
$494$	−7.15935e11	−0.540882
$495$	2.39122e11	0.179018
$496$	1.13814e12	0.844358
$497$	4.59093e11	0.337518
$498$	−6.50306e10	−0.0473790
$499$	−1.86731e12	−1.34823	−0.674116	−	0.738626i	$-0.735475\pi$
$499$	−1.86731e12	−1.34823	−0.674116	+	0.738626i	$0.735475\pi$
$500$	1.75501e12	1.25578
$501$	1.04912e12	0.743973
$502$	2.22980e12	1.56711
$503$	9.42114e11	0.656217	0.328108	−	0.944640i	$-0.393589\pi$
$503$	9.42114e11	0.656217	0.328108	+	0.944640i	$0.393589\pi$
$504$	1.33389e11	0.0920839
$505$	5.39536e10	0.0369155
$506$	2.09517e12	1.42083
$507$	8.16868e11	0.549055
$508$	3.31562e11	0.220891
$509$	−1.88541e12	−1.24502	−0.622508	−	0.782613i	$-0.713886\pi$
$509$	−1.88541e12	−1.24502	−0.622508	+	0.782613i	$0.713886\pi$
$510$	2.08718e12	1.36614
$511$	1.16604e12	0.756517
$512$	2.10704e12	1.35506
$513$	−5.01573e11	−0.319747
$514$	2.80618e12	1.77330
$515$	2.12603e12	1.33180
$516$	1.40450e12	0.872166
$517$	7.11367e11	0.437912
$518$	2.98942e11	0.182433
$519$	1.00393e12	0.607366
$520$	7.71384e10	0.0462653
$521$	−7.90673e11	−0.470140	−0.235070	−	0.971978i	$-0.575532\pi$
$521$	−7.90673e11	−0.470140	−0.235070	+	0.971978i	$0.575532\pi$
$522$	−7.18420e11	−0.423508
$523$	6.50634e11	0.380259	0.190129	−	0.981759i	$-0.439109\pi$
$523$	6.50634e11	0.380259	0.190129	+	0.981759i	$0.439109\pi$
$524$	1.61521e11	0.0935920
$525$	2.73311e11	0.157015
$526$	−2.75876e12	−1.57137
$527$	−3.39183e12	−1.91552
$528$	−5.13590e11	−0.287584
$529$	2.65694e12	1.47513
$530$	−1.86129e12	−1.02464
$531$	−7.95020e10	−0.0433963
$532$	4.12503e12	2.23267
$533$	−2.38626e11	−0.128070
$534$	−8.31037e10	−0.0442267
$535$	−1.99073e12	−1.05056
$536$	−8.34383e11	−0.436641
$537$	3.75969e11	0.195105
$538$	−7.46636e11	−0.384228
$539$	−4.04605e11	−0.206482
$540$	3.86583e11	0.195646
$541$	1.93440e12	0.970862	0.485431	−	0.874275i	$-0.338663\pi$
$541$	1.93440e12	0.970862	0.485431	+	0.874275i	$0.338663\pi$
$542$	−4.93610e12	−2.45690
$543$	−9.78054e11	−0.482796
$544$	−5.38111e12	−2.63437
$545$	2.36926e12	1.15035
$546$	4.51189e11	0.217266
$547$	−4.16068e11	−0.198711	−0.0993554	−	0.995052i	$-0.531678\pi$
$547$	−4.16068e11	−0.198711	−0.0993554	+	0.995052i	$0.531678\pi$
$548$	−5.36697e11	−0.254224
$549$	−6.95460e11	−0.326736
$550$	4.55971e11	0.212474
$551$	−3.10580e12	−1.43546
$552$	4.73512e11	0.217073
$553$	−3.55007e12	−1.61426
$554$	−5.53542e12	−2.49665
$555$	1.21115e11	0.0541849
$556$	2.61897e12	1.16223
$557$	−1.43212e9	−0.000630422 0	−0.000315211	−	1.00000i	$-0.500100\pi$
$557$	−1.43212e9	−0.000630422 0	−0.000315211		1.00000i	$0.500100\pi$
$558$	−1.16863e12	−0.510297
$559$	6.64125e11	0.287671
$560$	1.90810e12	0.819889
$561$	1.53058e12	0.652415
$562$	2.54741e12	1.07717
$563$	−7.08013e11	−0.296998	−0.148499	−	0.988913i	$-0.547444\pi$
$563$	−7.08013e11	−0.296998	−0.148499	+	0.988913i	$0.547444\pi$
$564$	1.15005e12	0.478587
$565$	6.12928e11	0.253041
$566$	4.75502e12	1.94751
$567$	3.16096e11	0.128439
$568$	1.73098e11	0.0697790
$569$	−3.86045e12	−1.54395	−0.771975	−	0.635653i	$-0.780731\pi$
$569$	−3.86045e12	−1.54395	−0.771975	+	0.635653i	$0.780731\pi$
$570$	3.10884e12	1.23356
$571$	8.54976e11	0.336582	0.168291	−	0.985737i	$-0.446175\pi$
$571$	8.54976e11	0.336582	0.168291	+	0.985737i	$0.446175\pi$
$572$	4.04648e11	0.158050
$573$	−1.85862e12	−0.720269
$574$	2.55760e12	0.983398
$575$	9.70214e11	0.370137
$576$	−1.13978e12	−0.431441
$577$	−8.16514e11	−0.306671	−0.153335	−	0.988174i	$-0.549002\pi$
$577$	−8.16514e11	−0.306671	−0.153335	+	0.988174i	$0.549002\pi$
$578$	9.41376e12	3.50823
$579$	−7.28450e11	−0.269368
$580$	2.39377e12	0.878326
$581$	1.77173e11	0.0645068
$582$	3.64844e12	1.31812
$583$	−1.36493e12	−0.489330
$584$	4.39647e11	0.156404
$585$	1.82797e11	0.0645309
$586$	−5.39801e12	−1.89101
$587$	−6.88105e11	−0.239212	−0.119606	−	0.992821i	$-0.538163\pi$
$587$	−6.88105e11	−0.239212	−0.119606	+	0.992821i	$0.538163\pi$
$588$	−6.54115e11	−0.225661
$589$	−5.05210e12	−1.72963
$590$	4.92767e11	0.167420
$591$	−2.18908e12	−0.738106
$592$	−2.60132e11	−0.0870456
$593$	1.01206e12	0.336093	0.168046	−	0.985779i	$-0.446254\pi$
$593$	1.01206e12	0.336093	0.168046	+	0.985779i	$0.446254\pi$
$594$	5.27350e11	0.173804
$595$	−5.68645e12	−1.86001
$596$	5.47258e12	1.77658
$597$	3.26520e12	1.05202
$598$	1.60165e12	0.512169
$599$	−2.62579e11	−0.0833373	−0.0416687	−	0.999131i	$-0.513267\pi$
$599$	−2.62579e11	−0.0833373	−0.0416687	+	0.999131i	$0.513267\pi$
$600$	1.03050e11	0.0324615
$601$	−4.47857e12	−1.40024	−0.700122	−	0.714023i	$-0.746871\pi$
$601$	−4.47857e12	−1.40024	−0.700122	+	0.714023i	$0.746871\pi$
$602$	−7.11810e12	−2.20892
$603$	−1.97726e12	−0.609027
$604$	2.00603e12	0.613298
$605$	1.79486e12	0.544667
$606$	1.18987e11	0.0358404
$607$	−4.13002e12	−1.23482	−0.617408	−	0.786643i	$-0.711817\pi$
$607$	−4.13002e12	−1.23482	−0.617408	+	0.786643i	$0.711817\pi$
$608$	−8.01511e12	−2.37872
$609$	1.95731e12	0.576608
$610$	4.31058e12	1.26053
$611$	5.43806e11	0.157855
$612$	2.47445e12	0.713014
$613$	6.67693e12	1.90987	0.954937	−	0.296809i	$-0.0959225\pi$
$613$	6.67693e12	1.90987	0.954937	+	0.296809i	$0.0959225\pi$
$614$	−7.25847e12	−2.06104
$615$	1.03620e12	0.292082
$616$	−6.06290e11	−0.169655
$617$	3.41841e12	0.949601	0.474801	−	0.880093i	$-0.342520\pi$
$617$	3.41841e12	0.949601	0.474801	+	0.880093i	$0.342520\pi$
$618$	4.68867e12	1.29301
$619$	2.23977e12	0.613190	0.306595	−	0.951840i	$-0.400810\pi$
$619$	2.23977e12	0.613190	0.306595	+	0.951840i	$0.400810\pi$
$620$	3.89385e12	1.05832
$621$	1.12210e12	0.302773
$622$	−3.87673e12	−1.03850
$623$	2.26413e11	0.0602150
$624$	−3.92615e11	−0.103666
$625$	−2.70607e12	−0.709381
$626$	3.81848e12	0.993817
$627$	2.27979e12	0.589102
$628$	2.88562e12	0.740323
$629$	7.75237e11	0.197472
$630$	−1.95922e12	−0.495508
$631$	1.76983e11	0.0444425	0.0222212	−	0.999753i	$-0.492926\pi$
$631$	1.76983e11	0.0444425	0.0222212	+	0.999753i	$0.492926\pi$
$632$	−1.33853e12	−0.333735
$633$	−1.89547e12	−0.469246
$634$	−1.16802e13	−2.87110
$635$	−6.80795e11	−0.166163
$636$	−2.20665e12	−0.534781
$637$	−3.09301e11	−0.0744309
$638$	3.26541e12	0.780270
$639$	4.10195e11	0.0973278
$640$	1.75060e12	0.412456
$641$	−5.42293e12	−1.26874	−0.634371	−	0.773029i	$-0.718741\pi$
$641$	−5.42293e12	−1.26874	−0.634371	+	0.773029i	$0.718741\pi$
$642$	−4.39028e12	−1.01996
$643$	7.75462e12	1.78900	0.894502	−	0.447064i	$-0.147531\pi$
$643$	7.75462e12	1.78900	0.894502	+	0.447064i	$0.147531\pi$
$644$	−9.22830e12	−2.11415
$645$	−2.88386e12	−0.656079
$646$	1.98992e13	4.49562
$647$	−5.81831e12	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$647$	−5.81831e12	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$648$	1.19182e11	0.0265536
$649$	3.61358e11	0.0799533
$650$	3.48568e11	0.0765909
$651$	3.18388e12	0.694772
$652$	−4.77408e11	−0.103461
$653$	1.39312e12	0.299833	0.149917	−	0.988699i	$-0.452099\pi$
$653$	1.39312e12	0.299833	0.149917	+	0.988699i	$0.452099\pi$
$654$	5.22508e12	1.11685
$655$	−3.31651e11	−0.0704037
$656$	−2.22557e12	−0.469217
$657$	1.04185e12	0.218152
$658$	−5.82852e12	−1.21211
$659$	1.30966e12	0.270504	0.135252	−	0.990811i	$-0.456816\pi$
$659$	1.30966e12	0.270504	0.135252	+	0.990811i	$0.456816\pi$
$660$	−1.75712e12	−0.360458
$661$	8.50546e12	1.73297	0.866486	−	0.499202i	$-0.166373\pi$
$661$	8.50546e12	1.73297	0.866486	+	0.499202i	$0.166373\pi$
$662$	7.69237e12	1.55668
$663$	1.17006e12	0.235178
$664$	6.68021e10	0.0133363
$665$	−8.46991e12	−1.67950
$666$	2.67102e11	0.0526069
$667$	6.94815e12	1.35926
$668$	−7.70921e12	−1.49801
$669$	−4.25367e12	−0.821006
$670$	1.22554e13	2.34959
$671$	3.16105e12	0.601977
$672$	5.05120e12	0.955505
$673$	7.37062e12	1.38496	0.692478	−	0.721439i	$-0.256519\pi$
$673$	7.37062e12	1.38496	0.692478	+	0.721439i	$0.256519\pi$
$674$	−6.27392e12	−1.17103
$675$	2.44201e11	0.0452774
$676$	−6.00253e12	−1.10554
$677$	−1.27182e12	−0.232689	−0.116344	−	0.993209i	$-0.537118\pi$
$677$	−1.27182e12	−0.232689	−0.116344	+	0.993209i	$0.537118\pi$
$678$	1.35173e12	0.245672
$679$	−9.94004e12	−1.79463
$680$	−2.14404e12	−0.384541
$681$	−4.80877e12	−0.856785
$682$	5.31173e12	0.940170
$683$	1.72717e12	0.303698	0.151849	−	0.988404i	$-0.451477\pi$
$683$	1.72717e12	0.303698	0.151849	+	0.988404i	$0.451477\pi$
$684$	3.68568e12	0.643820
$685$	1.10200e12	0.191238
$686$	−6.54490e12	−1.12835
$687$	−1.04912e11	−0.0179689
$688$	6.19401e12	1.05396
$689$	−1.04342e12	−0.176390
$690$	−6.95494e12	−1.16808
$691$	−9.94197e12	−1.65890	−0.829452	−	0.558578i	$-0.811347\pi$
$691$	−9.94197e12	−1.65890	−0.829452	+	0.558578i	$0.811347\pi$
$692$	−7.37711e12	−1.22295
$693$	−1.43674e12	−0.236635
$694$	2.01312e12	0.329421
$695$	−5.37752e12	−0.874280
$696$	7.37990e11	0.119209
$697$	6.63255e12	1.06447
$698$	−6.07960e12	−0.969451
$699$	3.39236e12	0.537470
$700$	−2.00835e12	−0.316154
$701$	1.02802e13	1.60795	0.803973	−	0.594665i	$-0.202715\pi$
$701$	1.02802e13	1.60795	0.803973	+	0.594665i	$0.202715\pi$
$702$	4.03134e11	0.0626516
$703$	1.15471e12	0.178309
$704$	5.18062e12	0.794887
$705$	−2.36140e12	−0.360013
$706$	1.42723e12	0.216209
$707$	−3.24176e11	−0.0487970
$708$	5.84199e11	0.0873798
$709$	3.73020e12	0.554401	0.277200	−	0.960812i	$-0.410593\pi$
$709$	3.73020e12	0.554401	0.277200	+	0.960812i	$0.410593\pi$
$710$	−2.54246e12	−0.375485
$711$	−3.17196e12	−0.465495
$712$	8.53675e10	0.0124489
$713$	1.13023e13	1.63781
$714$	−1.25407e13	−1.80584
$715$	−8.30862e11	−0.118892
$716$	−2.76270e12	−0.392849
$717$	2.28666e12	0.323120
$718$	−2.60338e12	−0.365575
$719$	−6.22941e12	−0.869295	−0.434647	−	0.900601i	$-0.643127\pi$
$719$	−6.22941e12	−0.869295	−0.434647	+	0.900601i	$0.643127\pi$
$720$	1.70487e12	0.236426
$721$	−1.27741e13	−1.76044
$722$	1.89023e13	2.58879
$723$	−7.63502e12	−1.03917
$724$	7.18697e12	0.972125
$725$	1.51212e12	0.203267
$726$	3.95831e12	0.528805
$727$	−1.29128e13	−1.71442	−0.857209	−	0.514969i	$-0.827803\pi$
$727$	−1.29128e13	−1.71442	−0.857209	+	0.514969i	$0.827803\pi$
$728$	−4.63480e11	−0.0611561
$729$	2.82430e11	0.0370370
$730$	−6.45754e12	−0.841616
$731$	−1.84592e13	−2.39102
$732$	5.11040e12	0.657892
$733$	−1.19680e13	−1.53128	−0.765640	−	0.643269i	$-0.777578\pi$
$733$	−1.19680e13	−1.53128	−0.765640	+	0.643269i	$0.777578\pi$
$734$	−2.85061e12	−0.362498
$735$	1.34309e12	0.169751
$736$	1.79310e13	2.25245
$737$	8.98719e12	1.12207
$738$	2.28519e12	0.283576
$739$	1.09774e13	1.35394	0.676968	−	0.736012i	$-0.263294\pi$
$739$	1.09774e13	1.35394	0.676968	+	0.736012i	$0.263294\pi$
$740$	−8.89979e11	−0.109103
$741$	1.74279e12	0.212355
$742$	1.11834e13	1.35443
$743$	5.36386e12	0.645696	0.322848	−	0.946451i	$-0.395360\pi$
$743$	5.36386e12	0.645696	0.322848	+	0.946451i	$0.395360\pi$
$744$	1.20046e12	0.143638
$745$	−1.12368e13	−1.33641
$746$	7.01281e12	0.829024
$747$	1.58303e11	0.0186014
$748$	−1.12471e13	−1.31366
$749$	1.19611e13	1.38869
$750$	−7.94713e12	−0.917138
$751$	7.01860e12	0.805138	0.402569	−	0.915390i	$-0.368117\pi$
$751$	7.01860e12	0.805138	0.402569	+	0.915390i	$0.368117\pi$
$752$	5.07185e12	0.578344
$753$	−5.42796e12	−0.615261
$754$	2.49625e12	0.281266
$755$	−4.11898e12	−0.461348
$756$	−2.32275e12	−0.258615
$757$	1.79609e13	1.98791	0.993954	−	0.109801i	$-0.0350212\pi$
$757$	1.79609e13	1.98791	0.993954	+	0.109801i	$0.0350212\pi$
$758$	−1.70105e13	−1.87157
$759$	−5.10022e12	−0.557829
$760$	−3.19353e12	−0.347224
$761$	1.18244e13	1.27805	0.639027	−	0.769185i	$-0.279337\pi$
$761$	1.18244e13	1.27805	0.639027	+	0.769185i	$0.279337\pi$
$762$	−1.50140e12	−0.161324
$763$	−1.42355e13	−1.52059
$764$	1.36576e13	1.45028
$765$	−5.08079e12	−0.536358
$766$	2.72184e13	2.85649
$767$	2.76241e11	0.0288210
$768$	−3.34385e12	−0.346834
$769$	−6.84476e12	−0.705813	−0.352907	−	0.935659i	$-0.614807\pi$
$769$	−6.84476e12	−0.705813	−0.352907	+	0.935659i	$0.614807\pi$
$770$	8.90519e12	0.912925
$771$	−6.83103e12	−0.696212
$772$	5.35281e12	0.542381
$773$	−2.32880e12	−0.234598	−0.117299	−	0.993097i	$-0.537424\pi$
$773$	−2.32880e12	−0.234598	−0.117299	+	0.993097i	$0.537424\pi$
$774$	−6.35996e12	−0.636972
$775$	2.45972e12	0.244922
$776$	−3.74783e12	−0.371024
$777$	−7.27708e11	−0.0716246
$778$	4.57860e12	0.448048
$779$	9.87912e12	0.961169
$780$	−1.34324e12	−0.129935
$781$	−1.86445e12	−0.179317
$782$	−4.45175e13	−4.25697
$783$	1.74884e12	0.166273
$784$	−2.88472e12	−0.272697
$785$	−5.92505e12	−0.556901
$786$	−7.31410e11	−0.0683533
$787$	−8.23251e12	−0.764973	−0.382486	−	0.923961i	$-0.624932\pi$
$787$	−8.23251e12	−0.764973	−0.382486	+	0.923961i	$0.624932\pi$
$788$	1.60859e13	1.48620
$789$	6.71560e12	0.616934
$790$	1.96604e13	1.79585
$791$	−3.68272e12	−0.334484
$792$	−5.41715e11	−0.0489224
$793$	2.41647e12	0.216996
$794$	9.45315e12	0.844081
$795$	4.53091e12	0.402284
$796$	−2.39935e13	−2.11828
$797$	−6.43290e12	−0.564735	−0.282367	−	0.959306i	$-0.591120\pi$
$797$	−6.43290e12	−0.564735	−0.282367	+	0.959306i	$0.591120\pi$
$798$	−1.86792e13	−1.63059
$799$	−1.51149e13	−1.31204
$800$	3.90232e12	0.336836
$801$	2.02298e11	0.0173638
$802$	−2.20527e13	−1.88225
$803$	−4.73547e12	−0.401923
$804$	1.45294e13	1.22629
$805$	1.89485e13	1.59035
$806$	4.06056e12	0.338906
$807$	1.81752e12	0.150851
$808$	−1.22228e11	−0.0100884
$809$	9.69199e12	0.795508	0.397754	−	0.917492i	$-0.369790\pi$
$809$	9.69199e12	0.795508	0.397754	+	0.917492i	$0.369790\pi$
$810$	−1.75055e12	−0.142887
$811$	2.19755e13	1.78379	0.891895	−	0.452242i	$-0.149376\pi$
$811$	2.19755e13	1.78379	0.891895	+	0.452242i	$0.149376\pi$
$812$	−1.43827e13	−1.16102
$813$	1.20159e13	0.964600
$814$	−1.21405e12	−0.0969229
$815$	9.80262e11	0.0778275
$816$	1.09126e13	0.861635
$817$	−2.74947e13	−2.15899
$818$	−1.49866e13	−1.17034
$819$	−1.09832e12	−0.0853005
$820$	−7.61423e12	−0.588117
$821$	1.92611e13	1.47958	0.739789	−	0.672839i	$-0.234925\pi$
$821$	1.92611e13	1.47958	0.739789	+	0.672839i	$0.234925\pi$
$822$	2.43031e12	0.185668
$823$	−3.16275e12	−0.240307	−0.120153	−	0.992755i	$-0.538339\pi$
$823$	−3.16275e12	−0.240307	−0.120153	+	0.992755i	$0.538339\pi$
$824$	−4.81639e12	−0.363956
$825$	−1.10996e12	−0.0834190
$826$	−2.96075e12	−0.221305
$827$	−1.34577e13	−1.00045	−0.500226	−	0.865895i	$-0.666750\pi$
$827$	−1.34577e13	−1.00045	−0.500226	+	0.865895i	$0.666750\pi$
$828$	−8.24541e12	−0.609643
$829$	8.05129e12	0.592066	0.296033	−	0.955178i	$-0.404336\pi$
$829$	8.05129e12	0.592066	0.296033	+	0.955178i	$0.404336\pi$
$830$	−9.81189e11	−0.0717631
$831$	1.34748e13	0.980205
$832$	3.96034e12	0.286535
$833$	8.59692e12	0.618644
$834$	−1.18594e13	−0.848818
$835$	1.58293e13	1.12687
$836$	−1.67524e13	−1.18617
$837$	2.84477e12	0.200347
$838$	3.09241e13	2.16620
$839$	1.60923e12	0.112122	0.0560608	−	0.998427i	$-0.482146\pi$
$839$	1.60923e12	0.112122	0.0560608	+	0.998427i	$0.482146\pi$
$840$	2.01259e12	0.139476
$841$	−3.67814e12	−0.253540
$842$	−2.12137e13	−1.45450
$843$	−6.20112e12	−0.422908
$844$	1.39284e13	0.944842
$845$	1.23250e13	0.831632
$846$	−5.20773e12	−0.349528
$847$	−1.07843e13	−0.719971
$848$	−9.73156e12	−0.646251
$849$	−1.15751e13	−0.764608
$850$	−9.68834e12	−0.636596
$851$	−2.58325e12	−0.168843
$852$	−3.01421e12	−0.195973
$853$	4.39684e11	0.0284361	0.0142180	−	0.999899i	$-0.495474\pi$
$853$	4.39684e11	0.0284361	0.0142180	+	0.999899i	$0.495474\pi$
$854$	−2.58998e13	−1.66623
$855$	−7.56779e12	−0.484308
$856$	4.50987e12	0.287099
$857$	−1.45210e13	−0.919567	−0.459783	−	0.888031i	$-0.652073\pi$
$857$	−1.45210e13	−0.919567	−0.459783	+	0.888031i	$0.652073\pi$
$858$	−1.83235e12	−0.115429
$859$	−3.00853e13	−1.88532	−0.942659	−	0.333757i	$-0.891683\pi$
$859$	−3.00853e13	−1.88532	−0.942659	+	0.333757i	$0.891683\pi$
$860$	2.11913e13	1.32103
$861$	−6.22592e12	−0.386091
$862$	−8.81916e12	−0.544057
$863$	−2.40297e13	−1.47469	−0.737344	−	0.675518i	$-0.763920\pi$
$863$	−2.40297e13	−1.47469	−0.737344	+	0.675518i	$0.763920\pi$
$864$	4.51321e12	0.275533
$865$	1.51474e13	0.919953
$866$	−6.93024e12	−0.418714
$867$	−2.29157e13	−1.37736
$868$	−2.33959e13	−1.39895
$869$	1.44174e13	0.857627
$870$	−1.08396e13	−0.641470
$871$	6.87027e12	0.404476
$872$	−5.36741e12	−0.314370
$873$	−8.88134e12	−0.517505
$874$	−6.63084e13	−3.84385
$875$	2.16516e13	1.24869
$876$	−7.65572e12	−0.439256
$877$	8.54455e12	0.487743	0.243872	−	0.969808i	$-0.421582\pi$
$877$	8.54455e12	0.487743	0.243872	+	0.969808i	$0.421582\pi$
$878$	9.88592e12	0.561425
$879$	1.31403e13	0.742428
$880$	−7.74910e12	−0.435591
$881$	5.82575e10	0.00325807	0.00162904	−	0.999999i	$-0.499481\pi$
$881$	5.82575e10	0.00325807	0.00162904	+	0.999999i	$0.499481\pi$
$882$	2.96200e12	0.164807
$883$	1.99889e13	1.10654	0.553268	−	0.833003i	$-0.313380\pi$
$883$	1.99889e13	1.10654	0.553268	+	0.833003i	$0.313380\pi$
$884$	−8.59784e12	−0.473537
$885$	−1.19953e12	−0.0657307
$886$	1.64249e13	0.895472
$887$	3.41855e13	1.85432	0.927162	−	0.374660i	$-0.122241\pi$
$887$	3.41855e13	1.85432	0.927162	+	0.374660i	$0.122241\pi$
$888$	−2.74378e11	−0.0148078
$889$	4.09050e12	0.219643
$890$	−1.25388e12	−0.0669885
$891$	−1.28372e12	−0.0682370
$892$	3.12569e13	1.65312
$893$	−2.25135e13	−1.18471
$894$	−2.47813e13	−1.29749
$895$	5.67265e12	0.295517
$896$	−1.05184e13	−0.545207
$897$	−3.89888e12	−0.201082
$898$	−7.15090e12	−0.366959
$899$	1.76152e13	0.899431
$900$	−1.79445e12	−0.0911674
$901$	2.90016e13	1.46609
$902$	−1.03868e13	−0.522460
$903$	1.73274e13	0.867241
$904$	−1.38855e12	−0.0691517
$905$	−1.47570e13	−0.731272
$906$	−9.08385e12	−0.447912
$907$	−2.53806e13	−1.24529	−0.622643	−	0.782506i	$-0.713941\pi$
$907$	−2.53806e13	−1.24529	−0.622643	+	0.782506i	$0.713941\pi$
$908$	3.53359e13	1.72516
$909$	−2.89648e11	−0.0140713
$910$	6.80759e12	0.329084
$911$	2.89755e13	1.39379	0.696897	−	0.717172i	$-0.254564\pi$
$911$	2.89755e13	1.39379	0.696897	+	0.717172i	$0.254564\pi$
$912$	1.62542e13	0.778018
$913$	−7.19529e11	−0.0342712
$914$	2.14938e13	1.01872
$915$	−1.04932e13	−0.494893
$916$	7.70919e11	0.0361809
$917$	1.99270e12	0.0930635
$918$	−1.12050e13	−0.520738
$919$	1.24959e13	0.577895	0.288948	−	0.957345i	$-0.406695\pi$
$919$	1.24959e13	0.577895	0.288948	+	0.957345i	$0.406695\pi$
$920$	7.14440e12	0.328791
$921$	1.76691e13	0.809184
$922$	−1.41495e13	−0.644840
$923$	−1.42528e12	−0.0646387
$924$	1.05575e13	0.476473
$925$	−5.62193e11	−0.0252492
$926$	4.87594e13	2.17926
$927$	−1.14135e13	−0.507647
$928$	2.79463e13	1.23697
$929$	3.35765e13	1.47899	0.739494	−	0.673164i	$-0.235065\pi$
$929$	3.35765e13	1.47899	0.739494	+	0.673164i	$0.235065\pi$
$930$	−1.76324e13	−0.772926
$931$	1.28050e13	0.558608
$932$	−2.49278e13	−1.08221
$933$	9.43704e12	0.407726
$934$	−2.24383e12	−0.0964783
$935$	2.30936e13	0.988186
$936$	−4.14115e11	−0.0176352
$937$	−2.67690e13	−1.13450	−0.567249	−	0.823547i	$-0.691992\pi$
$937$	−2.67690e13	−1.13450	−0.567249	+	0.823547i	$0.691992\pi$
$938$	−7.36356e13	−3.10581
$939$	−9.29527e12	−0.390181
$940$	1.73521e13	0.724897
$941$	−1.27689e13	−0.530886	−0.265443	−	0.964127i	$-0.585518\pi$
$941$	−1.27689e13	−0.530886	−0.265443	+	0.964127i	$0.585518\pi$
$942$	−1.30669e13	−0.540683
$943$	−2.21011e13	−0.910146
$944$	2.57638e12	0.105593
$945$	4.76930e12	0.194541
$946$	2.89077e13	1.17356
$947$	1.65573e13	0.668983	0.334492	−	0.942399i	$-0.391435\pi$
$947$	1.65573e13	0.668983	0.334492	+	0.942399i	$0.391435\pi$
$948$	2.33083e13	0.937288
$949$	−3.62004e12	−0.144882
$950$	−1.44307e13	−0.574818
$951$	2.84329e13	1.12722
$952$	1.28823e13	0.508307
$953$	2.27052e13	0.891676	0.445838	−	0.895114i	$-0.352906\pi$
$953$	2.27052e13	0.891676	0.445838	+	0.895114i	$0.352906\pi$
$954$	9.99228e12	0.390568
$955$	−2.80431e13	−1.09096
$956$	−1.68029e13	−0.650613
$957$	−7.94893e12	−0.306341
$958$	−2.26268e13	−0.867915
$959$	−6.62127e12	−0.252789
$960$	−1.71972e13	−0.653486
$961$	2.21433e12	0.0837503
$962$	−9.28082e11	−0.0349381
$963$	1.06872e13	0.400447
$964$	5.61039e13	2.09241
$965$	−1.09909e13	−0.408001
$966$	4.17882e13	1.54403
$967$	−4.78565e13	−1.76004	−0.880019	−	0.474939i	$-0.842470\pi$
$967$	−4.78565e13	−1.76004	−0.880019	+	0.474939i	$0.842470\pi$
$968$	−4.06614e12	−0.148848
$969$	−4.84402e13	−1.76502
$970$	5.50481e13	1.99650
$971$	5.29607e13	1.91191	0.955955	−	0.293514i	$-0.0948248\pi$
$971$	5.29607e13	1.91191	0.955955	+	0.293514i	$0.0948248\pi$
$972$	−2.07536e12	−0.0745752
$973$	3.23104e13	1.15567
$974$	−4.05121e13	−1.44234
$975$	−8.48512e11	−0.0300703
$976$	2.25374e13	0.795023
$977$	1.40423e13	0.493074	0.246537	−	0.969133i	$-0.420707\pi$
$977$	1.40423e13	0.493074	0.246537	+	0.969133i	$0.420707\pi$
$978$	2.16183e12	0.0755609
$979$	−9.19498e11	−0.0319911
$980$	−9.86935e12	−0.341799
$981$	−1.27193e13	−0.438484
$982$	−3.32331e13	−1.14043
$983$	−7.60200e12	−0.259679	−0.129840	−	0.991535i	$-0.541446\pi$
$983$	−7.60200e12	−0.259679	−0.129840	+	0.991535i	$0.541446\pi$
$984$	−2.34744e12	−0.0798210
$985$	−3.30291e13	−1.11798
$986$	−6.93826e13	−2.33778
$987$	1.41883e13	0.475885
$988$	−1.28064e13	−0.427583
$989$	6.15098e13	2.04438
$990$	7.95671e12	0.263254
$991$	−2.87997e13	−0.948542	−0.474271	−	0.880379i	$-0.657288\pi$
$991$	−2.87997e13	−0.948542	−0.474271	+	0.880379i	$0.657288\pi$
$992$	4.54593e13	1.49046
$993$	−1.87254e13	−0.611166
$994$	1.52762e13	0.496336
$995$	4.92657e13	1.59346
$996$	−1.16325e12	−0.0374545
$997$	−4.03019e13	−1.29181	−0.645904	−	0.763419i	$-0.723519\pi$
$997$	−4.03019e13	−1.29181	−0.645904	+	0.763419i	$0.723519\pi$
$998$	−6.21343e13	−1.98264
$999$	−6.50201e11	−0.0206539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.18	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.18	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+33.2747 q^{2} -81.0000 q^{3} +595.206 q^{4} -1222.14 q^{5} -2695.25 q^{6} +7343.10 q^{7} +2768.67 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+33.2747 q^{2} -81.0000 q^{3} +595.206 q^{4} -1222.14 q^{5} -2695.25 q^{6} +7343.10 q^{7} +2768.67 q^{8} +6561.00 q^{9} -40666.2 q^{10} -29821.5 q^{11} -48211.7 q^{12} -22797.1 q^{13} +244340. q^{14} +98993.0 q^{15} -212619. q^{16} +633639. q^{17} +218315. q^{18} +943799. q^{19} -727423. q^{20} -594791. q^{21} -992302. q^{22} -2.11142e6 q^{23} -224262. q^{24} -459508. q^{25} -758567. q^{26} -531441. q^{27} +4.37066e6 q^{28} -3.29075e6 q^{29} +3.29396e6 q^{30} -5.35294e6 q^{31} -8.49239e6 q^{32} +2.41554e6 q^{33} +2.10842e7 q^{34} -8.97427e6 q^{35} +3.90515e6 q^{36} +1.22347e6 q^{37} +3.14046e7 q^{38} +1.84657e6 q^{39} -3.38369e6 q^{40} +1.04674e7 q^{41} -1.97915e7 q^{42} -2.91320e7 q^{43} -1.77500e7 q^{44} -8.01844e6 q^{45} -7.02569e7 q^{46} -2.38542e7 q^{47} +1.72221e7 q^{48} +1.35675e7 q^{49} -1.52900e7 q^{50} -5.13248e7 q^{51} -1.35690e7 q^{52} +4.57699e7 q^{53} -1.76835e7 q^{54} +3.64459e7 q^{55} +2.03306e7 q^{56} -7.64477e7 q^{57} -1.09499e8 q^{58} -1.21174e7 q^{59} +5.89213e7 q^{60} -1.05999e8 q^{61} -1.78117e8 q^{62} +4.81781e7 q^{63} -1.73721e8 q^{64} +2.78612e7 q^{65} +8.03765e7 q^{66} -3.01366e8 q^{67} +3.77146e8 q^{68} +1.71025e8 q^{69} -2.98616e8 q^{70} +6.25203e7 q^{71} +1.81652e7 q^{72} +1.58794e8 q^{73} +4.07105e7 q^{74} +3.72201e7 q^{75} +5.61755e8 q^{76} -2.18982e8 q^{77} +6.14439e7 q^{78} -4.83457e8 q^{79} +2.59849e8 q^{80} +4.30467e7 q^{81} +3.48300e8 q^{82} +2.41279e7 q^{83} -3.54024e8 q^{84} -7.74393e8 q^{85} -9.69358e8 q^{86} +2.66550e8 q^{87} -8.25660e7 q^{88} +3.08334e7 q^{89} -2.66811e8 q^{90} -1.67402e8 q^{91} -1.25673e9 q^{92} +4.33588e8 q^{93} -7.93741e8 q^{94} -1.15345e9 q^{95} +6.87884e8 q^{96} -1.35366e9 q^{97} +4.51456e8 q^{98} -1.95659e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

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