LMFDB - Embedded newform 177.10.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} -14416.7 q^{10} +33314.0 q^{11} -7992.61 q^{12} -72674.0 q^{13} -248479. q^{14} -47254.7 q^{15} -302929. q^{16} -336269. q^{17} -162134. q^{18} +317254. q^{19} +57565.7 q^{20} -814461. q^{21} -823249. q^{22} -1.35598e6 q^{23} -827337. q^{24} -1.61278e6 q^{25} +1.79591e6 q^{26} -531441. q^{27} +992176. q^{28} +2.66208e6 q^{29} +1.16775e6 q^{30} +5.69989e6 q^{31} +2.25633e6 q^{32} -2.69843e6 q^{33} +8.30983e6 q^{34} +5.86605e6 q^{35} +647401. q^{36} -6.10000e6 q^{37} -7.83993e6 q^{38} +5.88659e6 q^{39} +5.95878e6 q^{40} +2.11049e6 q^{41} +2.01268e7 q^{42} -2.57854e7 q^{43} +3.28723e6 q^{44} +3.82763e6 q^{45} +3.35086e7 q^{46} -3.88147e7 q^{47} +2.45372e7 q^{48} +6.07508e7 q^{49} +3.98547e7 q^{50} +2.72378e7 q^{51} -7.17105e6 q^{52} -9.44146e6 q^{53} +1.31329e7 q^{54} +1.94351e7 q^{55} +1.02703e8 q^{56} -2.56976e7 q^{57} -6.57849e7 q^{58} -1.21174e7 q^{59} -4.66282e6 q^{60} -5.09326e7 q^{61} -1.40855e8 q^{62} +6.59713e7 q^{63} +9.93414e7 q^{64} -4.23974e7 q^{65} +6.66831e7 q^{66} -1.19930e8 q^{67} -3.31811e7 q^{68} +1.09834e8 q^{69} -1.44961e8 q^{70} +2.67018e8 q^{71} +6.70143e7 q^{72} -3.11741e8 q^{73} +1.50742e8 q^{74} +1.30635e8 q^{75} +3.13048e7 q^{76} +3.34974e8 q^{77} -1.45468e8 q^{78} +4.14333e8 q^{79} -1.76726e8 q^{80} +4.30467e7 q^{81} -5.21542e7 q^{82} +2.74165e8 q^{83} -8.03662e7 q^{84} -1.96177e8 q^{85} +6.37203e8 q^{86} -2.15629e8 q^{87} +3.40270e8 q^{88} -7.08062e8 q^{89} -9.45878e7 q^{90} -7.30742e8 q^{91} -1.33800e8 q^{92} -4.61691e8 q^{93} +9.59181e8 q^{94} +1.85083e8 q^{95} -1.82763e8 q^{96} -3.69989e8 q^{97} -1.50126e9 q^{98} +2.18573e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−24.7118	−1.09212	−0.546059	−	0.837747i	$-0.683873\pi$
$2$	−24.7118	−1.09212	−0.546059	+	0.837747i	$0.683873\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	98.6742	0.192723
$5$	583.392	0.417441	0.208721	−	0.977975i	$-0.433070\pi$
$5$	583.392	0.417441	0.208721	+	0.977975i	$0.433070\pi$
$6$	2001.66	0.630535
$7$	10055.1	1.58287	0.791433	−	0.611256i	$-0.209336\pi$
$7$	10055.1	1.58287	0.791433	+	0.611256i	$0.209336\pi$
$8$	10214.0	0.881642
$9$	6561.00	0.333333
$10$	−14416.7	−0.455895
$11$	33314.0	0.686055	0.343028	−	0.939325i	$-0.388548\pi$
$11$	33314.0	0.686055	0.343028	+	0.939325i	$0.388548\pi$
$12$	−7992.61	−0.111269
$13$	−72674.0	−0.705722	−0.352861	−	0.935676i	$-0.614791\pi$
$13$	−72674.0	−0.705722	−0.352861	+	0.935676i	$0.614791\pi$
$14$	−248479.	−1.72868
$15$	−47254.7	−0.241010
$16$	−302929.	−1.15558
$17$	−336269.	−0.976489	−0.488244	−	0.872707i	$-0.662362\pi$
$17$	−336269.	−0.976489	−0.488244	+	0.872707i	$0.662362\pi$
$18$	−162134.	−0.364040
$19$	317254.	0.558491	0.279245	−	0.960220i	$-0.409916\pi$
$19$	317254.	0.558491	0.279245	+	0.960220i	$0.409916\pi$
$20$	57565.7	0.0804505
$21$	−814461.	−0.913868
$22$	−823249.	−0.749254
$23$	−1.35598e6	−1.01036	−0.505181	−	0.863014i	$-0.668574\pi$
$23$	−1.35598e6	−1.01036	−0.505181	+	0.863014i	$0.668574\pi$
$24$	−827337.	−0.509016
$25$	−1.61278e6	−0.825743
$26$	1.79591e6	0.770733
$27$	−531441.	−0.192450
$28$	992176.	0.305055
$29$	2.66208e6	0.698925	0.349462	−	0.936950i	$-0.386364\pi$
$29$	2.66208e6	0.698925	0.349462	+	0.936950i	$0.386364\pi$
$30$	1.16775e6	0.263211
$31$	5.69989e6	1.10851	0.554254	−	0.832348i	$-0.313004\pi$
$31$	5.69989e6	1.10851	0.554254	+	0.832348i	$0.313004\pi$
$32$	2.25633e6	0.380389
$33$	−2.69843e6	−0.396094
$34$	8.30983e6	1.06644
$35$	5.86605e6	0.660753
$36$	647401.	0.0642410
$37$	−6.10000e6	−0.535084	−0.267542	−	0.963546i	$-0.586211\pi$
$37$	−6.10000e6	−0.535084	−0.267542	+	0.963546i	$0.586211\pi$
$38$	−7.83993e6	−0.609938
$39$	5.88659e6	0.407449
$40$	5.95878e6	0.368034
$41$	2.11049e6	0.116642	0.0583212	−	0.998298i	$-0.481425\pi$
$41$	2.11049e6	0.116642	0.0583212	+	0.998298i	$0.481425\pi$
$42$	2.01268e7	0.998052
$43$	−2.57854e7	−1.15018	−0.575089	−	0.818091i	$-0.695033\pi$
$43$	−2.57854e7	−1.15018	−0.575089	+	0.818091i	$0.695033\pi$
$44$	3.28723e6	0.132219
$45$	3.82763e6	0.139147
$46$	3.35086e7	1.10343
$47$	−3.88147e7	−1.16026	−0.580130	−	0.814524i	$-0.696998\pi$
$47$	−3.88147e7	−1.16026	−0.580130	+	0.814524i	$0.696998\pi$
$48$	2.45372e7	0.667175
$49$	6.07508e7	1.50546
$50$	3.98547e7	0.901809
$51$	2.72378e7	0.563776
$52$	−7.17105e6	−0.136009
$53$	−9.44146e6	−0.164361	−0.0821803	−	0.996617i	$-0.526188\pi$
$53$	−9.44146e6	−0.164361	−0.0821803	+	0.996617i	$0.526188\pi$
$54$	1.31329e7	0.210178
$55$	1.94351e7	0.286388
$56$	1.02703e8	1.39552
$57$	−2.56976e7	−0.322445
$58$	−6.57849e7	−0.763308
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−4.66282e6	−0.0464481
$61$	−5.09326e7	−0.470990	−0.235495	−	0.971876i	$-0.575671\pi$
$61$	−5.09326e7	−0.470990	−0.235495	+	0.971876i	$0.575671\pi$
$62$	−1.40855e8	−1.21062
$63$	6.59713e7	0.527622
$64$	9.93414e7	0.740151
$65$	−4.23974e7	−0.294598
$66$	6.66831e7	0.432582
$67$	−1.19930e8	−0.727092	−0.363546	−	0.931576i	$-0.618434\pi$
$67$	−1.19930e8	−0.727092	−0.363546	+	0.931576i	$0.618434\pi$
$68$	−3.31811e7	−0.188192
$69$	1.09834e8	0.583333
$70$	−1.44961e8	−0.721621
$71$	2.67018e8	1.24703	0.623517	−	0.781810i	$-0.285703\pi$
$71$	2.67018e8	1.24703	0.623517	+	0.781810i	$0.285703\pi$
$72$	6.70143e7	0.293881
$73$	−3.11741e8	−1.28481	−0.642407	−	0.766363i	$-0.722064\pi$
$73$	−3.11741e8	−1.28481	−0.642407	+	0.766363i	$0.722064\pi$
$74$	1.50742e8	0.584375
$75$	1.30635e8	0.476743
$76$	3.13048e7	0.107634
$77$	3.34974e8	1.08593
$78$	−1.45468e8	−0.444983
$79$	4.14333e8	1.19682	0.598408	−	0.801191i	$-0.295800\pi$
$79$	4.14333e8	1.19682	0.598408	+	0.801191i	$0.295800\pi$
$80$	−1.76726e8	−0.482387
$81$	4.30467e7	0.111111
$82$	−5.21542e7	−0.127387
$83$	2.74165e8	0.634104	0.317052	−	0.948408i	$-0.397307\pi$
$83$	2.74165e8	0.634104	0.317052	+	0.948408i	$0.397307\pi$
$84$	−8.03662e7	−0.176123
$85$	−1.96177e8	−0.407627
$86$	6.37203e8	1.25613
$87$	−2.15629e8	−0.403524
$88$	3.40270e8	0.604855
$89$	−7.08062e8	−1.19623	−0.598117	−	0.801409i	$-0.704084\pi$
$89$	−7.08062e8	−1.19623	−0.598117	+	0.801409i	$0.704084\pi$
$90$	−9.45878e7	−0.151965
$91$	−7.30742e8	−1.11706
$92$	−1.33800e8	−0.194720
$93$	−4.61691e8	−0.639997
$94$	9.59181e8	1.26714
$95$	1.85083e8	0.233137
$96$	−1.82763e8	−0.219618
$97$	−3.69989e8	−0.424342	−0.212171	−	0.977233i	$-0.568053\pi$
$97$	−3.69989e8	−0.424342	−0.212171	+	0.977233i	$0.568053\pi$
$98$	−1.50126e9	−1.64414
$99$	2.18573e8	0.228685
$100$	−1.59140e8	−0.159140
$101$	2.73696e8	0.261711	0.130856	−	0.991401i	$-0.458228\pi$
$101$	2.73696e8	0.261711	0.130856	+	0.991401i	$0.458228\pi$
$102$	−6.73096e8	−0.615710
$103$	1.11582e8	0.0976844	0.0488422	−	0.998807i	$-0.484447\pi$
$103$	1.11582e8	0.0976844	0.0488422	+	0.998807i	$0.484447\pi$
$104$	−7.42295e8	−0.622195
$105$	−4.75150e8	−0.381486
$106$	2.33316e8	0.179501
$107$	1.30638e9	0.963482	0.481741	−	0.876314i	$-0.340005\pi$
$107$	1.30638e9	0.963482	0.481741	+	0.876314i	$0.340005\pi$
$108$	−5.24395e7	−0.0370896
$109$	−1.76066e9	−1.19469	−0.597346	−	0.801984i	$-0.703778\pi$
$109$	−1.76066e9	−1.19469	−0.597346	+	0.801984i	$0.703778\pi$
$110$	−4.80276e8	−0.312769
$111$	4.94100e8	0.308931
$112$	−3.04597e9	−1.82913
$113$	−1.20055e9	−0.692674	−0.346337	−	0.938110i	$-0.612575\pi$
$113$	−1.20055e9	−0.692674	−0.346337	+	0.938110i	$0.612575\pi$
$114$	6.35034e8	0.352148
$115$	−7.91065e8	−0.421767
$116$	2.62679e8	0.134699
$117$	−4.76814e8	−0.235241
$118$	2.99442e8	0.142182
$119$	−3.38121e9	−1.54565
$120$	−4.82661e8	−0.212484
$121$	−1.24813e9	−0.529328
$122$	1.25864e9	0.514377
$123$	−1.70950e8	−0.0673436
$124$	5.62432e8	0.213635
$125$	−2.08032e9	−0.762140
$126$	−1.63027e9	−0.576226
$127$	4.28292e9	1.46091	0.730454	−	0.682961i	$-0.239308\pi$
$127$	4.28292e9	1.46091	0.730454	+	0.682961i	$0.239308\pi$
$128$	−3.61015e9	−1.18872
$129$	2.08861e9	0.664056
$130$	1.04772e9	0.321735
$131$	−5.40976e8	−0.160494	−0.0802468	−	0.996775i	$-0.525571\pi$
$131$	−5.40976e8	−0.160494	−0.0802468	+	0.996775i	$0.525571\pi$
$132$	−2.66265e8	−0.0763365
$133$	3.19001e9	0.884016
$134$	2.96368e9	0.794071
$135$	−3.10038e8	−0.0803366
$136$	−3.43467e9	−0.860914
$137$	−3.01617e9	−0.731498	−0.365749	−	0.930714i	$-0.619187\pi$
$137$	−3.01617e9	−0.731498	−0.365749	+	0.930714i	$0.619187\pi$
$138$	−2.71420e9	−0.637068
$139$	−4.53487e9	−1.03038	−0.515190	−	0.857076i	$-0.672279\pi$
$139$	−4.53487e9	−1.03038	−0.515190	+	0.857076i	$0.672279\pi$
$140$	5.78827e8	0.127342
$141$	3.14399e9	0.669877
$142$	−6.59851e9	−1.36191
$143$	−2.42106e9	−0.484165
$144$	−1.98751e9	−0.385194
$145$	1.55304e9	0.291760
$146$	7.70368e9	1.40317
$147$	−4.92082e9	−0.869179
$148$	−6.01912e8	−0.103123
$149$	−6.01406e7	−0.00999608	−0.00499804	−	0.999988i	$-0.501591\pi$
$149$	−6.01406e7	−0.00999608	−0.00499804	+	0.999988i	$0.501591\pi$
$150$	−3.22823e9	−0.520660
$151$	−1.44002e9	−0.225409	−0.112705	−	0.993629i	$-0.535951\pi$
$151$	−1.44002e9	−0.225409	−0.112705	+	0.993629i	$0.535951\pi$
$152$	3.24044e9	0.492389
$153$	−2.20626e9	−0.325496
$154$	−8.27782e9	−1.18597
$155$	3.32527e9	0.462737
$156$	5.80855e8	0.0785248
$157$	−1.10621e10	−1.45308	−0.726542	−	0.687122i	$-0.758874\pi$
$157$	−1.10621e10	−1.45308	−0.726542	+	0.687122i	$0.758874\pi$
$158$	−1.02389e10	−1.30707
$159$	7.64758e8	0.0948937
$160$	1.31633e9	0.158790
$161$	−1.36344e10	−1.59927
$162$	−1.06376e9	−0.121347
$163$	3.14291e9	0.348729	0.174365	−	0.984681i	$-0.444213\pi$
$163$	3.14291e9	0.348729	0.174365	+	0.984681i	$0.444213\pi$
$164$	2.08251e8	0.0224797
$165$	−1.57424e9	−0.165346
$166$	−6.77512e9	−0.692517
$167$	9.21149e9	0.916444	0.458222	−	0.888838i	$-0.348487\pi$
$167$	9.21149e9	0.916444	0.458222	+	0.888838i	$0.348487\pi$
$168$	−8.31893e9	−0.805704
$169$	−5.32299e9	−0.501956
$170$	4.84789e9	0.445176
$171$	2.08150e9	0.186164
$172$	−2.54435e9	−0.221666
$173$	2.07454e10	1.76082	0.880409	−	0.474215i	$-0.157268\pi$
$173$	2.07454e10	1.76082	0.880409	+	0.474215i	$0.157268\pi$
$174$	5.32857e9	0.440696
$175$	−1.62166e10	−1.30704
$176$	−1.00917e10	−0.792792
$177$	9.81506e8	0.0751646
$178$	1.74975e10	1.30643
$179$	1.59637e10	1.16224	0.581121	−	0.813817i	$-0.302614\pi$
$179$	1.59637e10	1.16224	0.581121	+	0.813817i	$0.302614\pi$
$180$	3.77689e8	0.0268168
$181$	−1.49143e10	−1.03288	−0.516438	−	0.856325i	$-0.672742\pi$
$181$	−1.49143e10	−1.03288	−0.516438	+	0.856325i	$0.672742\pi$
$182$	1.80580e10	1.21997
$183$	4.12554e9	0.271926
$184$	−1.38500e10	−0.890778
$185$	−3.55869e9	−0.223366
$186$	1.14092e10	0.698953
$187$	−1.12025e10	−0.669925
$188$	−3.83001e9	−0.223609
$189$	−5.34368e9	−0.304623
$190$	−4.57375e9	−0.254613
$191$	1.06714e10	0.580190	0.290095	−	0.956998i	$-0.406313\pi$
$191$	1.06714e10	0.580190	0.290095	+	0.956998i	$0.406313\pi$
$192$	−8.04665e9	−0.427326
$193$	−2.65737e10	−1.37862	−0.689309	−	0.724468i	$-0.742086\pi$
$193$	−2.65737e10	−1.37862	−0.689309	+	0.724468i	$0.742086\pi$
$194$	9.14311e9	0.463432
$195$	3.43419e9	0.170086
$196$	5.99454e9	0.290137
$197$	−2.11193e10	−0.999038	−0.499519	−	0.866303i	$-0.666490\pi$
$197$	−2.11193e10	−0.999038	−0.499519	+	0.866303i	$0.666490\pi$
$198$	−5.40133e9	−0.249751
$199$	2.77406e10	1.25394	0.626970	−	0.779043i	$-0.284295\pi$
$199$	2.77406e10	1.25394	0.626970	+	0.779043i	$0.284295\pi$
$200$	−1.64730e10	−0.728010
$201$	9.71429e9	0.419787
$202$	−6.76353e9	−0.285820
$203$	2.67674e10	1.10630
$204$	2.68767e9	0.108653
$205$	1.23124e9	0.0486914
$206$	−2.75739e9	−0.106683
$207$	−8.89656e9	−0.336787
$208$	2.20150e10	0.815519
$209$	1.05690e10	0.383156
$210$	1.17418e10	0.416628
$211$	−2.28234e10	−0.792700	−0.396350	−	0.918100i	$-0.629723\pi$
$211$	−2.28234e10	−0.792700	−0.396350	+	0.918100i	$0.629723\pi$
$212$	−9.31629e8	−0.0316761
$213$	−2.16285e10	−0.719975
$214$	−3.22831e10	−1.05224
$215$	−1.50430e10	−0.480132
$216$	−5.42816e9	−0.169672
$217$	5.73128e10	1.75462
$218$	4.35091e10	1.30474
$219$	2.52510e10	0.741788
$220$	1.91774e9	0.0551935
$221$	2.44380e10	0.689130
$222$	−1.22101e10	−0.337389
$223$	−1.01621e10	−0.275177	−0.137589	−	0.990489i	$-0.543935\pi$
$223$	−1.01621e10	−0.275177	−0.137589	+	0.990489i	$0.543935\pi$
$224$	2.26876e10	0.602105
$225$	−1.05814e10	−0.275248
$226$	2.96679e10	0.756482
$227$	6.52813e10	1.63182	0.815911	−	0.578178i	$-0.196236\pi$
$227$	6.52813e10	1.63182	0.815911	+	0.578178i	$0.196236\pi$
$228$	−2.53569e9	−0.0621425
$229$	−1.14856e10	−0.275990	−0.137995	−	0.990433i	$-0.544066\pi$
$229$	−1.14856e10	−0.275990	−0.137995	+	0.990433i	$0.544066\pi$
$230$	1.95487e10	0.460619
$231$	−2.71329e10	−0.626964
$232$	2.71906e10	0.616201
$233$	−3.31036e10	−0.735823	−0.367911	−	0.929861i	$-0.619927\pi$
$233$	−3.31036e10	−0.735823	−0.367911	+	0.929861i	$0.619927\pi$
$234$	1.17829e10	0.256911
$235$	−2.26442e10	−0.484341
$236$	−1.19567e9	−0.0250904
$237$	−3.35610e10	−0.690982
$238$	8.35559e10	1.68803
$239$	7.69117e9	0.152476	0.0762381	−	0.997090i	$-0.475709\pi$
$239$	7.69117e9	0.152476	0.0762381	+	0.997090i	$0.475709\pi$
$240$	1.43148e10	0.278506
$241$	−9.28482e9	−0.177295	−0.0886475	−	0.996063i	$-0.528254\pi$
$241$	−9.28482e9	−0.177295	−0.0886475	+	0.996063i	$0.528254\pi$
$242$	3.08435e10	0.578089
$243$	−3.48678e9	−0.0641500
$244$	−5.02574e9	−0.0907707
$245$	3.54415e10	0.628442
$246$	4.22449e9	0.0735472
$247$	−2.30561e10	−0.394140
$248$	5.82188e10	0.977307
$249$	−2.22074e10	−0.366100
$250$	5.14085e10	0.832347
$251$	5.11894e10	0.814044	0.407022	−	0.913418i	$-0.366567\pi$
$251$	5.11894e10	0.814044	0.407022	+	0.913418i	$0.366567\pi$
$252$	6.50967e9	0.101685
$253$	−4.51729e10	−0.693164
$254$	−1.05839e11	−1.59549
$255$	1.58903e10	0.235343
$256$	3.83506e10	0.558074
$257$	4.21976e10	0.603377	0.301688	−	0.953407i	$-0.402450\pi$
$257$	4.21976e10	0.603377	0.301688	+	0.953407i	$0.402450\pi$
$258$	−5.16135e10	−0.725227
$259$	−6.13359e10	−0.846966
$260$	−4.18353e9	−0.0567757
$261$	1.74659e10	0.232975
$262$	1.33685e10	0.175278
$263$	−2.08366e10	−0.268550	−0.134275	−	0.990944i	$-0.542871\pi$
$263$	−2.08366e10	−0.268550	−0.134275	+	0.990944i	$0.542871\pi$
$264$	−2.75619e10	−0.349213
$265$	−5.50807e9	−0.0686109
$266$	−7.88310e10	−0.965450
$267$	5.73530e10	0.690646
$268$	−1.18339e10	−0.140127
$269$	3.97522e10	0.462888	0.231444	−	0.972848i	$-0.425655\pi$
$269$	3.97522e10	0.462888	0.231444	+	0.972848i	$0.425655\pi$
$270$	7.66161e9	0.0877371
$271$	−9.42541e10	−1.06155	−0.530773	−	0.847514i	$-0.678098\pi$
$271$	−9.42541e10	−1.06155	−0.530773	+	0.847514i	$0.678098\pi$
$272$	1.01866e11	1.12841
$273$	5.91901e10	0.644937
$274$	7.45350e10	0.798883
$275$	−5.37281e10	−0.566505
$276$	1.08378e10	0.112422
$277$	1.23332e11	1.25868	0.629342	−	0.777129i	$-0.283325\pi$
$277$	1.23332e11	1.25868	0.629342	+	0.777129i	$0.283325\pi$
$278$	1.12065e11	1.12530
$279$	3.73970e10	0.369502
$280$	5.99160e10	0.582548
$281$	9.76161e10	0.933992	0.466996	−	0.884260i	$-0.345336\pi$
$281$	9.76161e10	0.933992	0.466996	+	0.884260i	$0.345336\pi$
$282$	−7.76937e10	−0.731585
$283$	−1.91585e11	−1.77551	−0.887756	−	0.460314i	$-0.847737\pi$
$283$	−1.91585e11	−1.77551	−0.887756	+	0.460314i	$0.847737\pi$
$284$	2.63478e10	0.240332
$285$	−1.49918e10	−0.134602
$286$	5.98288e10	0.528765
$287$	2.12212e10	0.184629
$288$	1.48038e10	0.126796
$289$	−5.51079e9	−0.0464701
$290$	−3.83784e10	−0.318636
$291$	2.99691e10	0.244994
$292$	−3.07607e10	−0.247613
$293$	−1.07936e11	−0.855584	−0.427792	−	0.903877i	$-0.640708\pi$
$293$	−1.07936e11	−0.855584	−0.427792	+	0.903877i	$0.640708\pi$
$294$	1.21602e11	0.949247
$295$	−7.06917e9	−0.0543462
$296$	−6.23056e10	−0.471753
$297$	−1.77044e10	−0.132031
$298$	1.48618e9	0.0109169
$299$	9.85442e10	0.713035
$300$	1.28903e10	0.0918793
$301$	−2.59274e11	−1.82058
$302$	3.55855e10	0.246174
$303$	−2.21694e10	−0.151099
$304$	−9.61054e10	−0.645381
$305$	−2.97137e10	−0.196611
$306$	5.45208e10	0.355480
$307$	−2.31525e11	−1.48756	−0.743781	−	0.668424i	$-0.766969\pi$
$307$	−2.31525e11	−1.48756	−0.743781	+	0.668424i	$0.766969\pi$
$308$	3.30533e10	0.209284
$309$	−9.03811e9	−0.0563981
$310$	−8.21734e10	−0.505363
$311$	1.61621e11	0.979661	0.489831	−	0.871818i	$-0.337059\pi$
$311$	1.61621e11	0.979661	0.489831	+	0.871818i	$0.337059\pi$
$312$	6.01259e10	0.359224
$313$	2.96549e10	0.174641	0.0873206	−	0.996180i	$-0.472170\pi$
$313$	2.96549e10	0.174641	0.0873206	+	0.996180i	$0.472170\pi$
$314$	2.73366e11	1.58694
$315$	3.84871e10	0.220251
$316$	4.08840e10	0.230654
$317$	−2.78281e11	−1.54781	−0.773904	−	0.633303i	$-0.781699\pi$
$317$	−2.78281e11	−1.54781	−0.773904	+	0.633303i	$0.781699\pi$
$318$	−1.88986e10	−0.103635
$319$	8.86845e10	0.479501
$320$	5.79549e10	0.308969
$321$	−1.05817e11	−0.556266
$322$	3.36932e11	1.74659
$323$	−1.06683e11	−0.545360
$324$	4.24760e9	0.0214137
$325$	1.17207e11	0.582745
$326$	−7.76671e10	−0.380854
$327$	1.42613e11	0.689756
$328$	2.15567e10	0.102837
$329$	−3.90284e11	−1.83654
$330$	3.89024e10	0.180577
$331$	−3.77481e11	−1.72850	−0.864249	−	0.503064i	$-0.832206\pi$
$331$	−3.77481e11	−1.72850	−0.864249	+	0.503064i	$0.832206\pi$
$332$	2.70530e10	0.122206
$333$	−4.00221e10	−0.178361
$334$	−2.27633e11	−1.00087
$335$	−6.99659e10	−0.303518
$336$	2.46723e11	1.05605
$337$	−1.60848e11	−0.679331	−0.339665	−	0.940546i	$-0.610314\pi$
$337$	−1.60848e11	−0.679331	−0.339665	+	0.940546i	$0.610314\pi$
$338$	1.31541e11	0.548195
$339$	9.72449e10	0.399915
$340$	−1.93576e10	−0.0785590
$341$	1.89886e11	0.760497
$342$	−5.14378e10	−0.203313
$343$	2.05096e11	0.800079
$344$	−2.63373e11	−1.01405
$345$	6.40763e10	0.243507
$346$	−5.12657e11	−1.92302
$347$	−5.57316e10	−0.206357	−0.103178	−	0.994663i	$-0.532901\pi$
$347$	−5.57316e10	−0.206357	−0.103178	+	0.994663i	$0.532901\pi$
$348$	−2.12770e10	−0.0777684
$349$	−5.47751e10	−0.197637	−0.0988185	−	0.995105i	$-0.531506\pi$
$349$	−5.47751e10	−0.197637	−0.0988185	+	0.995105i	$0.531506\pi$
$350$	4.00742e11	1.42744
$351$	3.86219e10	0.135816
$352$	7.51673e10	0.260968
$353$	−5.18865e10	−0.177856	−0.0889279	−	0.996038i	$-0.528344\pi$
$353$	−5.18865e10	−0.177856	−0.0889279	+	0.996038i	$0.528344\pi$
$354$	−2.42548e10	−0.0820887
$355$	1.55776e11	0.520563
$356$	−6.98674e10	−0.230542
$357$	2.73878e11	0.892381
$358$	−3.94493e11	−1.26931
$359$	4.27875e9	0.0135954	0.00679770	−	0.999977i	$-0.497836\pi$
$359$	4.27875e9	0.0135954	0.00679770	+	0.999977i	$0.497836\pi$
$360$	3.90956e10	0.122678
$361$	−2.22037e11	−0.688088
$362$	3.68559e11	1.12802
$363$	1.01098e11	0.305608
$364$	−7.21054e10	−0.215284
$365$	−1.81867e11	−0.536334
$366$	−1.01950e11	−0.296976
$367$	1.77664e11	0.511214	0.255607	−	0.966781i	$-0.417725\pi$
$367$	1.77664e11	0.511214	0.255607	+	0.966781i	$0.417725\pi$
$368$	4.10764e11	1.16755
$369$	1.38470e10	0.0388808
$370$	8.79417e10	0.243942
$371$	−9.49346e10	−0.260161
$372$	−4.55570e10	−0.123342
$373$	−4.80359e11	−1.28492	−0.642460	−	0.766319i	$-0.722086\pi$
$373$	−4.80359e11	−1.28492	−0.642460	+	0.766319i	$0.722086\pi$
$374$	2.76833e11	0.731638
$375$	1.68506e11	0.440022
$376$	−3.96454e11	−1.02293
$377$	−1.93464e11	−0.493247
$378$	1.32052e11	0.332684
$379$	3.08183e11	0.767243	0.383621	−	0.923490i	$-0.374677\pi$
$379$	3.08183e11	0.767243	0.383621	+	0.923490i	$0.374677\pi$
$380$	1.82630e10	0.0449309
$381$	−3.46916e11	−0.843456
$382$	−2.63709e11	−0.633636
$383$	−2.66534e11	−0.632934	−0.316467	−	0.948604i	$-0.602497\pi$
$383$	−2.66534e11	−0.632934	−0.316467	+	0.948604i	$0.602497\pi$
$384$	2.92422e11	0.686309
$385$	1.95421e11	0.453313
$386$	6.56684e11	1.50561
$387$	−1.69178e11	−0.383393
$388$	−3.65084e10	−0.0817805
$389$	5.77946e11	1.27972	0.639858	−	0.768493i	$-0.278993\pi$
$389$	5.77946e11	1.27972	0.639858	+	0.768493i	$0.278993\pi$
$390$	−8.48651e10	−0.185754
$391$	4.55973e11	0.986607
$392$	6.20511e11	1.32728
$393$	4.38191e10	0.0926610
$394$	5.21897e11	1.09107
$395$	2.41718e11	0.499600
$396$	2.15675e10	0.0440729
$397$	−1.36491e11	−0.275769	−0.137885	−	0.990448i	$-0.544030\pi$
$397$	−1.36491e11	−0.275769	−0.137885	+	0.990448i	$0.544030\pi$
$398$	−6.85521e11	−1.36945
$399$	−2.58391e11	−0.510387
$400$	4.88557e11	0.954213
$401$	−7.29742e11	−1.40935	−0.704676	−	0.709529i	$-0.748908\pi$
$401$	−7.29742e11	−1.40935	−0.704676	+	0.709529i	$0.748908\pi$
$402$	−2.40058e11	−0.458457
$403$	−4.14233e11	−0.782298
$404$	2.70067e10	0.0504378
$405$	2.51131e10	0.0463824
$406$	−6.61472e11	−1.20821
$407$	−2.03215e11	−0.367097
$408$	2.78208e11	0.497049
$409$	5.94538e11	1.05057	0.525285	−	0.850926i	$-0.323959\pi$
$409$	5.94538e11	1.05057	0.525285	+	0.850926i	$0.323959\pi$
$410$	−3.04263e10	−0.0531768
$411$	2.44310e11	0.422331
$412$	1.10102e10	0.0188260
$413$	−1.21841e11	−0.206072
$414$	2.19850e11	0.367812
$415$	1.59946e11	0.264701
$416$	−1.63977e11	−0.268449
$417$	3.67324e11	0.594891
$418$	−2.61179e11	−0.418451
$419$	−1.07046e12	−1.69671	−0.848357	−	0.529425i	$-0.822408\pi$
$419$	−1.07046e12	−1.69671	−0.848357	+	0.529425i	$0.822408\pi$
$420$	−4.68850e10	−0.0735211
$421$	4.16461e11	0.646108	0.323054	−	0.946381i	$-0.395290\pi$
$421$	4.16461e11	0.646108	0.323054	+	0.946381i	$0.395290\pi$
$422$	5.64007e11	0.865722
$423$	−2.54663e11	−0.386754
$424$	−9.64354e10	−0.144907
$425$	5.42328e11	0.806328
$426$	5.34479e11	0.786299
$427$	−5.12131e11	−0.745514
$428$	1.28906e11	0.185685
$429$	1.96106e11	0.279533
$430$	3.71739e11	0.524361
$431$	−9.10399e11	−1.27082	−0.635410	−	0.772175i	$-0.719169\pi$
$431$	−9.10399e11	−1.27082	−0.635410	+	0.772175i	$0.719169\pi$
$432$	1.60989e11	0.222392
$433$	−4.34129e11	−0.593504	−0.296752	−	0.954955i	$-0.595903\pi$
$433$	−4.34129e11	−0.593504	−0.296752	+	0.954955i	$0.595903\pi$
$434$	−1.41630e12	−1.91625
$435$	−1.25796e11	−0.168448
$436$	−1.73732e11	−0.230245
$437$	−4.30189e11	−0.564278
$438$	−6.23998e11	−0.810120
$439$	−3.72886e11	−0.479166	−0.239583	−	0.970876i	$-0.577011\pi$
$439$	−3.72886e11	−0.479166	−0.239583	+	0.970876i	$0.577011\pi$
$440$	1.98511e11	0.252492
$441$	3.98586e11	0.501821
$442$	−6.03908e11	−0.752611
$443$	−1.16812e12	−1.44102	−0.720511	−	0.693444i	$-0.756093\pi$
$443$	−1.16812e12	−1.44102	−0.720511	+	0.693444i	$0.756093\pi$
$444$	4.87549e10	0.0595381
$445$	−4.13078e11	−0.499357
$446$	2.51124e11	0.300526
$447$	4.87139e9	0.00577124
$448$	9.98884e11	1.17156
$449$	−3.08179e11	−0.357844	−0.178922	−	0.983863i	$-0.557261\pi$
$449$	−3.08179e11	−0.357844	−0.178922	+	0.983863i	$0.557261\pi$
$450$	2.61487e11	0.300603
$451$	7.03089e10	0.0800232
$452$	−1.18464e11	−0.133494
$453$	1.16642e11	0.130140
$454$	−1.61322e12	−1.78214
$455$	−4.26309e11	−0.466308
$456$	−2.62476e11	−0.284281
$457$	8.35294e11	0.895811	0.447906	−	0.894081i	$-0.352170\pi$
$457$	8.35294e11	0.895811	0.447906	+	0.894081i	$0.352170\pi$
$458$	2.83830e11	0.301414
$459$	1.78707e11	0.187925
$460$	−7.80577e10	−0.0812841
$461$	−1.21807e12	−1.25608	−0.628041	−	0.778180i	$-0.716143\pi$
$461$	−1.21807e12	−1.25608	−0.628041	+	0.778180i	$0.716143\pi$
$462$	6.70504e11	0.684719
$463$	6.81687e11	0.689399	0.344699	−	0.938713i	$-0.387981\pi$
$463$	6.81687e11	0.689399	0.344699	+	0.938713i	$0.387981\pi$
$464$	−8.06420e11	−0.807664
$465$	−2.69347e11	−0.267161
$466$	8.18049e11	0.803605
$467$	−9.80497e11	−0.953938	−0.476969	−	0.878920i	$-0.658265\pi$
$467$	−9.80497e11	−0.953938	−0.476969	+	0.878920i	$0.658265\pi$
$468$	−4.70492e10	−0.0453363
$469$	−1.20590e12	−1.15089
$470$	5.59578e11	0.528957
$471$	8.96033e11	0.838938
$472$	−1.23767e11	−0.114780
$473$	−8.59012e11	−0.789086
$474$	8.29353e11	0.754635
$475$	−5.11661e11	−0.461170
$476$	−3.33638e11	−0.297882
$477$	−6.19454e10	−0.0547869
$478$	−1.90063e11	−0.166522
$479$	−4.03930e11	−0.350587	−0.175294	−	0.984516i	$-0.556088\pi$
$479$	−4.03930e11	−0.350587	−0.175294	+	0.984516i	$0.556088\pi$
$480$	−1.06622e11	−0.0916775
$481$	4.43311e11	0.377621
$482$	2.29445e11	0.193627
$483$	1.10439e12	0.923337
$484$	−1.23158e11	−0.102014
$485$	−2.15849e11	−0.177138
$486$	8.61648e10	0.0700594
$487$	−1.82775e12	−1.47243	−0.736217	−	0.676745i	$-0.763390\pi$
$487$	−1.82775e12	−1.47243	−0.736217	+	0.676745i	$0.763390\pi$
$488$	−5.20228e11	−0.415245
$489$	−2.54576e11	−0.201339
$490$	−8.75825e11	−0.686333
$491$	1.13125e12	0.878401	0.439201	−	0.898389i	$-0.355262\pi$
$491$	1.13125e12	0.878401	0.439201	+	0.898389i	$0.355262\pi$
$492$	−1.68684e10	−0.0129787
$493$	−8.95176e11	−0.682492
$494$	5.69759e11	0.430447
$495$	1.27514e11	0.0954626
$496$	−1.72666e12	−1.28097
$497$	2.68489e12	1.97389
$498$	5.48784e11	0.399825
$499$	1.24403e12	0.898209	0.449105	−	0.893479i	$-0.351743\pi$
$499$	1.24403e12	0.898209	0.449105	+	0.893479i	$0.351743\pi$
$500$	−2.05274e11	−0.146882
$501$	−7.46131e11	−0.529109
$502$	−1.26498e12	−0.889033
$503$	2.15528e11	0.150123	0.0750616	−	0.997179i	$-0.476085\pi$
$503$	2.15528e11	0.150123	0.0750616	+	0.997179i	$0.476085\pi$
$504$	6.73833e11	0.465174
$505$	1.59672e11	0.109249
$506$	1.11631e12	0.757017
$507$	4.31162e11	0.289804
$508$	4.22613e11	0.281551
$509$	−3.70298e9	−0.00244524	−0.00122262	−	0.999999i	$-0.500389\pi$
$509$	−3.70298e9	−0.00244524	−0.00122262	+	0.999999i	$0.500389\pi$
$510$	−3.92679e11	−0.257023
$511$	−3.13457e12	−2.03369
$512$	9.00684e11	0.579238
$513$	−1.68602e11	−0.107482
$514$	−1.04278e12	−0.658959
$515$	6.50958e10	0.0407775
$516$	2.06092e11	0.127979
$517$	−1.29307e12	−0.796003
$518$	1.51572e12	0.924987
$519$	−1.68038e12	−1.01661
$520$	−4.33049e11	−0.259730
$521$	1.81848e12	1.08128	0.540640	−	0.841254i	$-0.318182\pi$
$521$	1.81848e12	1.08128	0.540640	+	0.841254i	$0.318182\pi$
$522$	−4.31615e11	−0.254436
$523$	−2.89336e12	−1.69101	−0.845503	−	0.533970i	$-0.820700\pi$
$523$	−2.89336e12	−1.69101	−0.845503	+	0.533970i	$0.820700\pi$
$524$	−5.33804e10	−0.0309308
$525$	1.31355e12	0.754620
$526$	5.14910e11	0.293289
$527$	−1.91670e12	−1.08244
$528$	8.17432e11	0.457719
$529$	3.75193e10	0.0208307
$530$	1.36114e11	0.0749312
$531$	−7.95020e10	−0.0433963
$532$	3.14772e11	0.170370
$533$	−1.53378e11	−0.0823172
$534$	−1.41730e12	−0.754268
$535$	7.62133e11	0.402197
$536$	−1.22496e12	−0.641035
$537$	−1.29306e12	−0.671020
$538$	−9.82350e11	−0.505529
$539$	2.02385e12	1.03283
$540$	−3.05928e10	−0.0154827
$541$	1.25468e12	0.629717	0.314858	−	0.949139i	$-0.398043\pi$
$541$	1.25468e12	0.629717	0.314858	+	0.949139i	$0.398043\pi$
$542$	2.32919e12	1.15933
$543$	1.20806e12	0.596331
$544$	−7.58735e11	−0.371446
$545$	−1.02715e12	−0.498713
$546$	−1.46270e12	−0.704348
$547$	3.38178e12	1.61511	0.807555	−	0.589792i	$-0.200790\pi$
$547$	3.38178e12	1.61511	0.807555	+	0.589792i	$0.200790\pi$
$548$	−2.97618e11	−0.140977
$549$	−3.34169e11	−0.156997
$550$	1.32772e12	0.618691
$551$	8.44556e11	0.390343
$552$	1.12185e12	0.514291
$553$	4.16615e12	1.89440
$554$	−3.04776e12	−1.37463
$555$	2.88254e11	0.128960
$556$	−4.47474e11	−0.198578
$557$	4.26701e12	1.87835	0.939173	−	0.343445i	$-0.111594\pi$
$557$	4.26701e12	1.87835	0.939173	+	0.343445i	$0.111594\pi$
$558$	−9.24147e11	−0.403540
$559$	1.87392e12	0.811706
$560$	−1.77699e12	−0.763554
$561$	9.07400e11	0.386781
$562$	−2.41227e12	−1.02003
$563$	1.91024e12	0.801310	0.400655	−	0.916229i	$-0.368783\pi$
$563$	1.91024e12	0.801310	0.400655	+	0.916229i	$0.368783\pi$
$564$	3.10230e11	0.129101
$565$	−7.00393e11	−0.289150
$566$	4.73443e12	1.93907
$567$	4.32838e11	0.175874
$568$	2.72733e12	1.09944
$569$	2.79896e12	1.11942	0.559708	−	0.828690i	$-0.310913\pi$
$569$	2.79896e12	1.11942	0.559708	+	0.828690i	$0.310913\pi$
$570$	3.70474e11	0.147001
$571$	−2.87023e10	−0.0112994	−0.00564969	−	0.999984i	$-0.501798\pi$
$571$	−2.87023e10	−0.0112994	−0.00564969	+	0.999984i	$0.501798\pi$
$572$	−2.38896e11	−0.0933097
$573$	−8.64381e11	−0.334973
$574$	−5.24414e11	−0.201637
$575$	2.18689e12	0.834299
$576$	6.51779e11	0.246717
$577$	−3.08998e12	−1.16055	−0.580276	−	0.814420i	$-0.697055\pi$
$577$	−3.08998e12	−1.16055	−0.580276	+	0.814420i	$0.697055\pi$
$578$	1.36182e11	0.0507508
$579$	2.15247e12	0.795945
$580$	1.53245e11	0.0562288
$581$	2.75675e12	1.00370
$582$	−7.40592e11	−0.267563
$583$	−3.14532e11	−0.112760
$584$	−3.18413e12	−1.13275
$585$	−2.78169e11	−0.0981992
$586$	2.66730e12	0.934399
$587$	−9.98356e11	−0.347067	−0.173534	−	0.984828i	$-0.555519\pi$
$587$	−9.98356e11	−0.347067	−0.173534	+	0.984828i	$0.555519\pi$
$588$	−4.85558e11	−0.167511
$589$	1.80831e12	0.619091
$590$	1.74692e11	0.0593525
$591$	1.71067e12	0.576795
$592$	1.84786e12	0.618333
$593$	2.87076e12	0.953348	0.476674	−	0.879080i	$-0.341842\pi$
$593$	2.87076e12	0.953348	0.476674	+	0.879080i	$0.341842\pi$
$594$	4.37508e11	0.144194
$595$	−1.97257e12	−0.645218
$596$	−5.93433e9	−0.00192648
$597$	−2.24699e12	−0.723963
$598$	−2.43521e12	−0.778719
$599$	−3.72134e12	−1.18108	−0.590539	−	0.807009i	$-0.701085\pi$
$599$	−3.72134e12	−1.18108	−0.590539	+	0.807009i	$0.701085\pi$
$600$	1.33431e12	0.420317
$601$	4.44903e12	1.39101	0.695505	−	0.718521i	$-0.255181\pi$
$601$	4.44903e12	1.39101	0.695505	+	0.718521i	$0.255181\pi$
$602$	6.40712e12	1.98829
$603$	−7.86858e11	−0.242364
$604$	−1.42093e11	−0.0434416
$605$	−7.28148e11	−0.220963
$606$	5.47846e11	0.165018
$607$	1.63535e12	0.488947	0.244474	−	0.969656i	$-0.421385\pi$
$607$	1.63535e12	0.488947	0.244474	+	0.969656i	$0.421385\pi$
$608$	7.15831e11	0.212444
$609$	−2.16816e12	−0.638725
$610$	7.34279e11	0.214722
$611$	2.82082e12	0.818822
$612$	−2.17701e11	−0.0627306
$613$	3.00016e12	0.858168	0.429084	−	0.903265i	$-0.358836\pi$
$613$	3.00016e12	0.858168	0.429084	+	0.903265i	$0.358836\pi$
$614$	5.72140e12	1.62459
$615$	−9.97308e10	−0.0281120
$616$	3.42144e12	0.957405
$617$	2.70641e12	0.751815	0.375907	−	0.926657i	$-0.377331\pi$
$617$	2.70641e12	0.751815	0.375907	+	0.926657i	$0.377331\pi$
$618$	2.23348e11	0.0615934
$619$	−7.12632e12	−1.95100	−0.975500	−	0.219997i	$-0.929395\pi$
$619$	−7.12632e12	−1.95100	−0.975500	+	0.219997i	$0.929395\pi$
$620$	3.28118e11	0.0891800
$621$	7.20621e11	0.194444
$622$	−3.99395e12	−1.06991
$623$	−7.11961e12	−1.89348
$624$	−1.78322e12	−0.470840
$625$	1.93632e12	0.507594
$626$	−7.32826e11	−0.190729
$627$	−8.56088e11	−0.221215
$628$	−1.09155e12	−0.280043
$629$	2.05124e12	0.522503
$630$	−9.51087e11	−0.240540
$631$	−1.93984e12	−0.487117	−0.243558	−	0.969886i	$-0.578315\pi$
$631$	−1.93984e12	−0.487117	−0.243558	+	0.969886i	$0.578315\pi$
$632$	4.23201e12	1.05516
$633$	1.84869e12	0.457665
$634$	6.87683e12	1.69039
$635$	2.49862e12	0.609843
$636$	7.54619e10	0.0182882
$637$	−4.41501e12	−1.06244
$638$	−2.19155e12	−0.523672
$639$	1.75191e12	0.415678
$640$	−2.10613e12	−0.496221
$641$	−5.51853e12	−1.29111	−0.645553	−	0.763715i	$-0.723373\pi$
$641$	−5.51853e12	−1.29111	−0.645553	+	0.763715i	$0.723373\pi$
$642$	2.61493e12	0.607509
$643$	3.98103e12	0.918431	0.459216	−	0.888325i	$-0.348131\pi$
$643$	3.98103e12	0.918431	0.459216	+	0.888325i	$0.348131\pi$
$644$	−1.34537e12	−0.308215
$645$	1.21848e12	0.277204
$646$	2.63633e12	0.595598
$647$	−1.27610e11	−0.0286297	−0.0143148	−	0.999898i	$-0.504557\pi$
$647$	−1.27610e11	−0.0286297	−0.0143148	+	0.999898i	$0.504557\pi$
$648$	4.39681e11	0.0979602
$649$	−4.03677e11	−0.0893168
$650$	−2.89640e12	−0.636427
$651$	−4.64233e12	−1.01303
$652$	3.10124e11	0.0672081
$653$	1.16332e12	0.250375	0.125188	−	0.992133i	$-0.460047\pi$
$653$	1.16332e12	0.250375	0.125188	+	0.992133i	$0.460047\pi$
$654$	−3.52424e12	−0.753295
$655$	−3.15601e11	−0.0669966
$656$	−6.39329e11	−0.134790
$657$	−2.04533e12	−0.428272
$658$	9.64464e12	2.00572
$659$	5.75734e12	1.18915	0.594576	−	0.804040i	$-0.297320\pi$
$659$	5.75734e12	1.18915	0.594576	+	0.804040i	$0.297320\pi$
$660$	−1.55337e11	−0.0318660
$661$	−2.31031e12	−0.470721	−0.235360	−	0.971908i	$-0.575627\pi$
$661$	−2.31031e12	−0.470721	−0.235360	+	0.971908i	$0.575627\pi$
$662$	9.32824e12	1.88773
$663$	−1.97948e12	−0.397869
$664$	2.80033e12	0.559053
$665$	1.86103e12	0.369025
$666$	9.89018e11	0.194792
$667$	−3.60972e12	−0.706167
$668$	9.08936e11	0.176620
$669$	8.23131e11	0.158874
$670$	1.72899e12	0.331478
$671$	−1.69677e12	−0.323125
$672$	−1.83769e12	−0.347625
$673$	2.38685e12	0.448495	0.224248	−	0.974532i	$-0.428008\pi$
$673$	2.38685e12	0.448495	0.224248	+	0.974532i	$0.428008\pi$
$674$	3.97485e12	0.741910
$675$	8.57097e11	0.158914
$676$	−5.25242e11	−0.0967385
$677$	−6.20512e12	−1.13528	−0.567638	−	0.823278i	$-0.692143\pi$
$677$	−6.20512e12	−1.13528	−0.567638	+	0.823278i	$0.692143\pi$
$678$	−2.40310e12	−0.436755
$679$	−3.72027e12	−0.671677
$680$	−2.00376e12	−0.359381
$681$	−5.28779e12	−0.942133
$682$	−4.69242e12	−0.830553
$683$	−9.18735e12	−1.61546	−0.807731	−	0.589551i	$-0.799305\pi$
$683$	−9.18735e12	−1.61546	−0.807731	+	0.589551i	$0.799305\pi$
$684$	2.05391e11	0.0358780
$685$	−1.75961e12	−0.305357
$686$	−5.06829e12	−0.873781
$687$	9.30333e11	0.159343
$688$	7.81112e12	1.32912
$689$	6.86149e11	0.115993
$690$	−1.58344e12	−0.265939
$691$	−9.24435e12	−1.54250	−0.771250	−	0.636532i	$-0.780368\pi$
$691$	−9.24435e12	−1.54250	−0.771250	+	0.636532i	$0.780368\pi$
$692$	2.04704e12	0.339350
$693$	2.19777e12	0.361978
$694$	1.37723e12	0.225366
$695$	−2.64560e12	−0.430123
$696$	−2.20244e12	−0.355764
$697$	−7.09695e11	−0.113900
$698$	1.35359e12	0.215843
$699$	2.68139e12	0.424827
$700$	−1.60016e12	−0.251897
$701$	−1.11505e13	−1.74407	−0.872033	−	0.489447i	$-0.837199\pi$
$701$	−1.11505e13	−1.74407	−0.872033	+	0.489447i	$0.837199\pi$
$702$	−9.54418e11	−0.148328
$703$	−1.93525e12	−0.298839
$704$	3.30945e12	0.507784
$705$	1.83418e12	0.279634
$706$	1.28221e12	0.194240
$707$	2.75203e12	0.414254
$708$	9.68493e10	0.0144859
$709$	5.08517e12	0.755783	0.377892	−	0.925850i	$-0.376649\pi$
$709$	5.08517e12	0.755783	0.377892	+	0.925850i	$0.376649\pi$
$710$	−3.84951e12	−0.568517
$711$	2.71844e12	0.398939
$712$	−7.23217e12	−1.05465
$713$	−7.72891e12	−1.11999
$714$	−6.76803e12	−0.974586
$715$	−1.41243e12	−0.202110
$716$	1.57521e12	0.223991
$717$	−6.22985e11	−0.0880322
$718$	−1.05736e11	−0.0148478
$719$	−1.03787e13	−1.44832	−0.724158	−	0.689634i	$-0.757771\pi$
$719$	−1.03787e13	−1.44832	−0.724158	+	0.689634i	$0.757771\pi$
$720$	−1.15950e12	−0.160796
$721$	1.12196e12	0.154621
$722$	5.48695e12	0.751474
$723$	7.52070e11	0.102361
$724$	−1.47165e12	−0.199059
$725$	−4.29335e12	−0.577132
$726$	−2.49832e12	−0.333760
$727$	5.48173e12	0.727802	0.363901	−	0.931438i	$-0.381445\pi$
$727$	5.48173e12	0.727802	0.363901	+	0.931438i	$0.381445\pi$
$728$	−7.46382e12	−0.984850
$729$	2.82430e11	0.0370370
$730$	4.49426e12	0.585741
$731$	8.67083e12	1.12314
$732$	4.07085e11	0.0524065
$733$	4.00237e12	0.512093	0.256047	−	0.966664i	$-0.417580\pi$
$733$	4.00237e12	0.512093	0.256047	+	0.966664i	$0.417580\pi$
$734$	−4.39041e12	−0.558306
$735$	−2.87076e12	−0.362831
$736$	−3.05953e12	−0.384331
$737$	−3.99533e12	−0.498826
$738$	−3.42183e11	−0.0424625
$739$	−1.25819e13	−1.55184	−0.775920	−	0.630832i	$-0.782714\pi$
$739$	−1.25819e13	−1.55184	−0.775920	+	0.630832i	$0.782714\pi$
$740$	−3.51151e11	−0.0430478
$741$	1.86755e12	0.227557
$742$	2.34601e12	0.284126
$743$	−5.63633e12	−0.678495	−0.339247	−	0.940697i	$-0.610172\pi$
$743$	−5.63633e12	−0.678495	−0.339247	+	0.940697i	$0.610172\pi$
$744$	−4.71573e12	−0.564248
$745$	−3.50856e10	−0.00417278
$746$	1.18705e13	1.40329
$747$	1.79880e12	0.211368
$748$	−1.10539e12	−0.129110
$749$	1.31358e13	1.52506
$750$	−4.16409e12	−0.480556
$751$	−3.92028e12	−0.449715	−0.224857	−	0.974392i	$-0.572192\pi$
$751$	−3.92028e12	−0.449715	−0.224857	+	0.974392i	$0.572192\pi$
$752$	1.17581e13	1.34077
$753$	−4.14634e12	−0.469989
$754$	4.78085e12	0.538684
$755$	−8.40095e11	−0.0940951
$756$	−5.27283e11	−0.0587078
$757$	1.70392e13	1.88590	0.942948	−	0.332940i	$-0.108041\pi$
$757$	1.70392e13	1.88590	0.942948	+	0.332940i	$0.108041\pi$
$758$	−7.61577e12	−0.837920
$759$	3.65901e12	0.400198
$760$	1.89045e12	0.205544
$761$	−1.25446e13	−1.35590	−0.677949	−	0.735109i	$-0.737131\pi$
$761$	−1.25446e13	−1.35590	−0.677949	+	0.735109i	$0.737131\pi$
$762$	8.57294e12	0.921154
$763$	−1.77035e13	−1.89104
$764$	1.05299e12	0.111816
$765$	−1.28712e12	−0.135876
$766$	6.58654e12	0.691239
$767$	8.80617e11	0.0918772
$768$	−3.10640e12	−0.322204
$769$	−1.86068e12	−0.191868	−0.0959342	−	0.995388i	$-0.530584\pi$
$769$	−1.86068e12	−0.191868	−0.0959342	+	0.995388i	$0.530584\pi$
$770$	−4.82921e12	−0.495072
$771$	−3.41800e12	−0.348360
$772$	−2.62214e12	−0.265691
$773$	−3.51001e12	−0.353590	−0.176795	−	0.984248i	$-0.556573\pi$
$773$	−3.51001e12	−0.353590	−0.176795	+	0.984248i	$0.556573\pi$
$774$	4.18069e12	0.418710
$775$	−9.19266e12	−0.915342
$776$	−3.77908e12	−0.374118
$777$	4.96821e12	0.488996
$778$	−1.42821e13	−1.39760
$779$	6.69563e11	0.0651438
$780$	3.38866e11	0.0327795
$781$	8.89543e12	0.855534
$782$	−1.12679e13	−1.07749
$783$	−1.41474e12	−0.134508
$784$	−1.84032e13	−1.73968
$785$	−6.45356e12	−0.606577
$786$	−1.08285e12	−0.101197
$787$	1.24989e12	0.116141	0.0580706	−	0.998312i	$-0.481505\pi$
$787$	1.24989e12	0.116141	0.0580706	+	0.998312i	$0.481505\pi$
$788$	−2.08393e12	−0.192538
$789$	1.68776e12	0.155048
$790$	−5.97330e12	−0.545623
$791$	−1.20717e13	−1.09641
$792$	2.23251e12	0.201618
$793$	3.70148e12	0.332388
$794$	3.37293e12	0.301173
$795$	4.46154e11	0.0396125
$796$	2.73728e12	0.241663
$797$	−5.24321e12	−0.460294	−0.230147	−	0.973156i	$-0.573921\pi$
$797$	−5.24321e12	−0.460294	−0.230147	+	0.973156i	$0.573921\pi$
$798$	6.38531e12	0.557403
$799$	1.30522e13	1.13298
$800$	−3.63896e12	−0.314104
$801$	−4.64559e12	−0.398745
$802$	1.80333e13	1.53918
$803$	−1.03853e13	−0.881454
$804$	9.58550e11	0.0809026
$805$	−7.95422e12	−0.667600
$806$	1.02365e13	0.854363
$807$	−3.21993e12	−0.267249
$808$	2.79554e12	0.230736
$809$	7.17872e12	0.589221	0.294611	−	0.955617i	$-0.404810\pi$
$809$	7.17872e12	0.589221	0.294611	+	0.955617i	$0.404810\pi$
$810$	−6.20591e11	−0.0506550
$811$	5.28665e12	0.429128	0.214564	−	0.976710i	$-0.431167\pi$
$811$	5.28665e12	0.429128	0.214564	+	0.976710i	$0.431167\pi$
$812$	2.64125e12	0.213210
$813$	7.63458e12	0.612883
$814$	5.02181e12	0.400914
$815$	1.83355e12	0.145574
$816$	−8.25111e12	−0.651489
$817$	−8.18051e12	−0.642364
$818$	−1.46921e13	−1.14735
$819$	−4.79440e12	−0.372354
$820$	1.21492e11	0.00938395
$821$	7.85159e12	0.603134	0.301567	−	0.953445i	$-0.402490\pi$
$821$	7.85159e12	0.603134	0.301567	+	0.953445i	$0.402490\pi$
$822$	−6.03734e12	−0.461235
$823$	4.98524e12	0.378780	0.189390	−	0.981902i	$-0.439349\pi$
$823$	4.98524e12	0.378780	0.189390	+	0.981902i	$0.439349\pi$
$824$	1.13970e12	0.0861227
$825$	4.35197e12	0.327072
$826$	3.01091e12	0.225055
$827$	9.30138e12	0.691469	0.345735	−	0.938332i	$-0.387630\pi$
$827$	9.30138e12	0.691469	0.345735	+	0.938332i	$0.387630\pi$
$828$	−8.77861e11	−0.0649066
$829$	−3.32785e12	−0.244719	−0.122360	−	0.992486i	$-0.539046\pi$
$829$	−3.32785e12	−0.244719	−0.122360	+	0.992486i	$0.539046\pi$
$830$	−3.95255e12	−0.289085
$831$	−9.98988e12	−0.726701
$832$	−7.21953e12	−0.522341
$833$	−2.04286e13	−1.47007
$834$	−9.07725e12	−0.649691
$835$	5.37391e12	0.382561
$836$	1.04289e12	0.0738429
$837$	−3.02915e12	−0.213332
$838$	2.64531e13	1.85301
$839$	7.16300e12	0.499075	0.249538	−	0.968365i	$-0.419721\pi$
$839$	7.16300e12	0.499075	0.249538	+	0.968365i	$0.419721\pi$
$840$	−4.85320e12	−0.336334
$841$	−7.42047e12	−0.511504
$842$	−1.02915e13	−0.705627
$843$	−7.90690e12	−0.539240
$844$	−2.25208e12	−0.152771
$845$	−3.10539e12	−0.209537
$846$	6.29319e12	0.422381
$847$	−1.25500e13	−0.837855
$848$	2.86009e12	0.189932
$849$	1.55184e13	1.02509
$850$	−1.34019e13	−0.880606
$851$	8.27145e12	0.540628
$852$	−2.13417e12	−0.138756
$853$	1.95050e13	1.26146	0.630732	−	0.776001i	$-0.282755\pi$
$853$	1.95050e13	1.26146	0.630732	+	0.776001i	$0.282755\pi$
$854$	1.26557e13	0.814190
$855$	1.21433e12	0.0777124
$856$	1.33434e13	0.849446
$857$	−1.86203e13	−1.17916	−0.589581	−	0.807709i	$-0.700707\pi$
$857$	−1.86203e13	−1.17916	−0.589581	+	0.807709i	$0.700707\pi$
$858$	−4.84613e12	−0.305283
$859$	2.15213e13	1.34865	0.674324	−	0.738436i	$-0.264435\pi$
$859$	2.15213e13	1.34865	0.674324	+	0.738436i	$0.264435\pi$
$860$	−1.48435e12	−0.0925324
$861$	−1.71891e12	−0.106596
$862$	2.24976e13	1.38789
$863$	−2.03644e13	−1.24975	−0.624874	−	0.780725i	$-0.714850\pi$
$863$	−2.03644e13	−1.24975	−0.624874	+	0.780725i	$0.714850\pi$
$864$	−1.19911e12	−0.0732059
$865$	1.21027e13	0.735038
$866$	1.07281e13	0.648176
$867$	4.46374e11	0.0268295
$868$	5.65529e12	0.338155
$869$	1.38031e13	0.821082
$870$	3.10865e12	0.183965
$871$	8.71576e12	0.513125
$872$	−1.79834e13	−1.05329
$873$	−2.42750e12	−0.141447
$874$	1.06308e13	0.616258
$875$	−2.09178e13	−1.20637
$876$	2.49162e12	0.142960
$877$	−6.72050e12	−0.383622	−0.191811	−	0.981432i	$-0.561436\pi$
$877$	−6.72050e12	−0.383622	−0.191811	+	0.981432i	$0.561436\pi$
$878$	9.21470e12	0.523306
$879$	8.74283e12	0.493972
$880$	−5.88744e12	−0.330944
$881$	1.12208e13	0.627526	0.313763	−	0.949501i	$-0.398410\pi$
$881$	1.12208e13	0.627526	0.313763	+	0.949501i	$0.398410\pi$
$882$	−9.84979e12	−0.548048
$883$	−5.14531e12	−0.284832	−0.142416	−	0.989807i	$-0.545487\pi$
$883$	−5.14531e12	−0.284832	−0.142416	+	0.989807i	$0.545487\pi$
$884$	2.41140e12	0.132811
$885$	5.72603e11	0.0313768
$886$	2.88664e13	1.57377
$887$	2.87791e13	1.56106	0.780531	−	0.625117i	$-0.214949\pi$
$887$	2.87791e13	1.56106	0.780531	+	0.625117i	$0.214949\pi$
$888$	5.04675e12	0.272366
$889$	4.30651e13	2.31242
$890$	1.02079e13	0.545358
$891$	1.43406e12	0.0762284
$892$	−1.00274e12	−0.0530329
$893$	−1.23141e13	−0.647995
$894$	−1.20381e11	−0.00630288
$895$	9.31312e12	0.485167
$896$	−3.63003e13	−1.88159
$897$	−7.98208e12	−0.411671
$898$	7.61566e12	0.390808
$899$	1.51736e13	0.774763
$900$	−1.04412e12	−0.0530465
$901$	3.17487e12	0.160496
$902$	−1.73746e12	−0.0873948
$903$	2.10012e13	1.05111
$904$	−1.22625e13	−0.610690
$905$	−8.70086e12	−0.431165
$906$	−2.88242e12	−0.142128
$907$	−5.53089e11	−0.0271370	−0.0135685	−	0.999908i	$-0.504319\pi$
$907$	−5.53089e11	−0.0271370	−0.0135685	+	0.999908i	$0.504319\pi$
$908$	6.44158e12	0.314490
$909$	1.79572e12	0.0872371
$910$	1.05349e13	0.509264
$911$	−1.02219e13	−0.491700	−0.245850	−	0.969308i	$-0.579067\pi$
$911$	−1.02219e13	−0.491700	−0.245850	+	0.969308i	$0.579067\pi$
$912$	7.78453e12	0.372611
$913$	9.13352e12	0.435030
$914$	−2.06416e13	−0.978332
$915$	2.40681e12	0.113513
$916$	−1.13333e12	−0.0531897
$917$	−5.43956e12	−0.254040
$918$	−4.41618e12	−0.205237
$919$	−8.14184e12	−0.376533	−0.188266	−	0.982118i	$-0.560287\pi$
$919$	−8.14184e12	−0.376533	−0.188266	+	0.982118i	$0.560287\pi$
$920$	−8.07997e12	−0.371847
$921$	1.87535e13	0.858844
$922$	3.01007e13	1.37179
$923$	−1.94053e13	−0.880060
$924$	−2.67732e12	−0.120830
$925$	9.83795e12	0.441842
$926$	−1.68457e13	−0.752905
$927$	7.32087e11	0.0325615
$928$	6.00654e12	0.265863
$929$	−3.34987e13	−1.47556	−0.737781	−	0.675040i	$-0.764126\pi$
$929$	−3.34987e13	−1.47556	−0.737781	+	0.675040i	$0.764126\pi$
$930$	6.65604e12	0.291772
$931$	1.92735e13	0.840787
$932$	−3.26647e12	−0.141810
$933$	−1.30913e13	−0.565608
$934$	2.42299e13	1.04181
$935$	−6.53542e12	−0.279654
$936$	−4.87019e12	−0.207398
$937$	−2.93698e13	−1.24472	−0.622362	−	0.782730i	$-0.713827\pi$
$937$	−2.93698e13	−1.24472	−0.622362	+	0.782730i	$0.713827\pi$
$938$	2.98000e13	1.25691
$939$	−2.40205e12	−0.100829
$940$	−2.23439e12	−0.0933436
$941$	2.86861e13	1.19267	0.596333	−	0.802737i	$-0.296624\pi$
$941$	2.86861e13	1.19267	0.596333	+	0.802737i	$0.296624\pi$
$942$	−2.21426e13	−0.916220
$943$	−2.86178e12	−0.117851
$944$	3.67070e12	0.150444
$945$	−3.11746e12	−0.127162
$946$	2.12278e13	0.861775
$947$	9.95289e12	0.402137	0.201069	−	0.979577i	$-0.435559\pi$
$947$	9.95289e12	0.402137	0.201069	+	0.979577i	$0.435559\pi$
$948$	−3.31160e12	−0.133168
$949$	2.26554e13	0.906722
$950$	1.26441e13	0.503652
$951$	2.25408e13	0.893627
$952$	−3.45358e13	−1.36271
$953$	−2.34797e12	−0.0922092	−0.0461046	−	0.998937i	$-0.514681\pi$
$953$	−2.34797e12	−0.0922092	−0.0461046	+	0.998937i	$0.514681\pi$
$954$	1.53078e12	0.0598338
$955$	6.22559e12	0.242195
$956$	7.58920e11	0.0293857
$957$	−7.18344e12	−0.276840
$958$	9.98185e12	0.382883
$959$	−3.03278e13	−1.15786
$960$	−4.69435e12	−0.178384
$961$	6.04908e12	0.228788
$962$	−1.09550e13	−0.412407
$963$	8.57118e12	0.321161
$964$	−9.16172e11	−0.0341688
$965$	−1.55029e13	−0.575492
$966$	−2.72915e13	−1.00839
$967$	−4.11035e13	−1.51168	−0.755840	−	0.654756i	$-0.772771\pi$
$967$	−4.11035e13	−1.51168	−0.755840	+	0.654756i	$0.772771\pi$
$968$	−1.27484e13	−0.466678
$969$	8.64131e12	0.314864
$970$	5.33402e12	0.193456
$971$	1.57004e13	0.566793	0.283396	−	0.959003i	$-0.408539\pi$
$971$	1.57004e13	0.566793	0.283396	+	0.959003i	$0.408539\pi$
$972$	−3.44056e11	−0.0123632
$973$	−4.55984e13	−1.63095
$974$	4.51670e13	1.60807
$975$	−9.49377e12	−0.336448
$976$	1.54290e13	0.544267
$977$	−3.32213e13	−1.16652	−0.583258	−	0.812287i	$-0.698223\pi$
$977$	−3.32213e13	−1.16652	−0.583258	+	0.812287i	$0.698223\pi$
$978$	6.29104e12	0.219886
$979$	−2.35883e13	−0.820683
$980$	3.49716e12	0.121115
$981$	−1.15517e13	−0.398231
$982$	−2.79553e13	−0.959318
$983$	1.42131e13	0.485510	0.242755	−	0.970088i	$-0.421949\pi$
$983$	1.42131e13	0.485510	0.242755	+	0.970088i	$0.421949\pi$
$984$	−1.74609e12	−0.0593729
$985$	−1.23208e13	−0.417040
$986$	2.21214e13	0.745362
$987$	3.16130e13	1.06032
$988$	−2.27504e12	−0.0759598
$989$	3.49643e13	1.16210
$990$	−3.15109e12	−0.104256
$991$	5.46920e12	0.180133	0.0900664	−	0.995936i	$-0.471292\pi$
$991$	5.46920e12	0.180133	0.0900664	+	0.995936i	$0.471292\pi$
$992$	1.28608e13	0.421664
$993$	3.05759e13	0.997949
$994$	−6.63485e13	−2.15572
$995$	1.61836e13	0.523446
$996$	−2.19129e12	−0.0705559
$997$	−2.15200e13	−0.689784	−0.344892	−	0.938642i	$-0.612084\pi$
$997$	−2.15200e13	−0.689784	−0.344892	+	0.938642i	$0.612084\pi$
$998$	−3.07422e13	−0.980951
$999$	3.24179e12	0.102977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.5	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-24.7118 q^{2} -81.0000 q^{3} +98.6742 q^{4} +583.392 q^{5} +2001.66 q^{6} +10055.1 q^{7} +10214.0 q^{8} +6561.00 q^{9} -14416.7 q^{10} +33314.0 q^{11} -7992.61 q^{12} -72674.0 q^{13} -248479. q^{14} -47254.7 q^{15} -302929. q^{16} -336269. q^{17} -162134. q^{18} +317254. q^{19} +57565.7 q^{20} -814461. q^{21} -823249. q^{22} -1.35598e6 q^{23} -827337. q^{24} -1.61278e6 q^{25} +1.79591e6 q^{26} -531441. q^{27} +992176. q^{28} +2.66208e6 q^{29} +1.16775e6 q^{30} +5.69989e6 q^{31} +2.25633e6 q^{32} -2.69843e6 q^{33} +8.30983e6 q^{34} +5.86605e6 q^{35} +647401. q^{36} -6.10000e6 q^{37} -7.83993e6 q^{38} +5.88659e6 q^{39} +5.95878e6 q^{40} +2.11049e6 q^{41} +2.01268e7 q^{42} -2.57854e7 q^{43} +3.28723e6 q^{44} +3.82763e6 q^{45} +3.35086e7 q^{46} -3.88147e7 q^{47} +2.45372e7 q^{48} +6.07508e7 q^{49} +3.98547e7 q^{50} +2.72378e7 q^{51} -7.17105e6 q^{52} -9.44146e6 q^{53} +1.31329e7 q^{54} +1.94351e7 q^{55} +1.02703e8 q^{56} -2.56976e7 q^{57} -6.57849e7 q^{58} -1.21174e7 q^{59} -4.66282e6 q^{60} -5.09326e7 q^{61} -1.40855e8 q^{62} +6.59713e7 q^{63} +9.93414e7 q^{64} -4.23974e7 q^{65} +6.66831e7 q^{66} -1.19930e8 q^{67} -3.31811e7 q^{68} +1.09834e8 q^{69} -1.44961e8 q^{70} +2.67018e8 q^{71} +6.70143e7 q^{72} -3.11741e8 q^{73} +1.50742e8 q^{74} +1.30635e8 q^{75} +3.13048e7 q^{76} +3.34974e8 q^{77} -1.45468e8 q^{78} +4.14333e8 q^{79} -1.76726e8 q^{80} +4.30467e7 q^{81} -5.21542e7 q^{82} +2.74165e8 q^{83} -8.03662e7 q^{84} -1.96177e8 q^{85} +6.37203e8 q^{86} -2.15629e8 q^{87} +3.40270e8 q^{88} -7.08062e8 q^{89} -9.45878e7 q^{90} -7.30742e8 q^{91} -1.33800e8 q^{92} -4.61691e8 q^{93} +9.59181e8 q^{94} +1.85083e8 q^{95} -1.82763e8 q^{96} -3.69989e8 q^{97} -1.50126e9 q^{98} +2.18573e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more