LMFDB - Embedded newform 177.10.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +32940.9 q^{10} +70959.2 q^{11} +20523.9 q^{12} -57764.1 q^{13} -142817. q^{14} -165917. q^{15} -68210.6 q^{16} +574690. q^{17} +105512. q^{18} -675543. q^{19} -519016. q^{20} +719343. q^{21} +1.14114e6 q^{22} +325234. q^{23} +996995. q^{24} +2.24265e6 q^{25} -928941. q^{26} -531441. q^{27} +2.25022e6 q^{28} -2.59800e6 q^{29} -2.66822e6 q^{30} +3.69152e6 q^{31} +5.20505e6 q^{32} -5.74770e6 q^{33} +9.24195e6 q^{34} -1.81910e7 q^{35} -1.66244e6 q^{36} -1.59909e7 q^{37} -1.08638e7 q^{38} +4.67889e6 q^{39} -2.52124e7 q^{40} +2.01221e7 q^{41} +1.15682e7 q^{42} -2.99619e7 q^{43} -1.79797e7 q^{44} +1.34393e7 q^{45} +5.23028e6 q^{46} +1.30817e7 q^{47} +5.52506e6 q^{48} +3.85146e7 q^{49} +3.60654e7 q^{50} -4.65499e7 q^{51} +1.46364e7 q^{52} -4.33294e7 q^{53} -8.54643e6 q^{54} +1.45350e8 q^{55} +1.09310e8 q^{56} +5.47190e7 q^{57} -4.17801e7 q^{58} -1.21174e7 q^{59} +4.20403e7 q^{60} +1.48079e8 q^{61} +5.93656e7 q^{62} -5.82668e7 q^{63} +1.18630e8 q^{64} -1.18322e8 q^{65} -9.24323e7 q^{66} +2.62228e7 q^{67} -1.45616e8 q^{68} -2.63439e7 q^{69} -2.92541e8 q^{70} -3.59885e8 q^{71} -8.07566e7 q^{72} -3.34147e8 q^{73} -2.57160e8 q^{74} -1.81654e8 q^{75} +1.71170e8 q^{76} -6.30173e8 q^{77} +7.52442e7 q^{78} -6.43140e8 q^{79} -1.39720e8 q^{80} +4.30467e7 q^{81} +3.23596e8 q^{82} -3.84290e8 q^{83} -1.82268e8 q^{84} +1.17717e9 q^{85} -4.81835e8 q^{86} +2.10438e8 q^{87} -8.73407e8 q^{88} +3.95175e8 q^{89} +2.16125e8 q^{90} +5.12990e8 q^{91} -8.24081e7 q^{92} -2.99013e8 q^{93} +2.10374e8 q^{94} -1.38375e9 q^{95} -4.21609e8 q^{96} -3.41540e8 q^{97} +6.19377e8 q^{98} +4.65564e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	16.0816	0.710714	0.355357	−	0.934731i	$-0.384359\pi$
$2$	16.0816	0.710714	0.355357	+	0.934731i	$0.384359\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−253.381	−0.494885
$5$	2048.36	1.46569	0.732843	−	0.680398i	$-0.238193\pi$
$5$	2048.36	1.46569	0.732843	+	0.680398i	$0.238193\pi$
$6$	−1302.61	−0.410331
$7$	−8880.78	−1.39801	−0.699004	−	0.715118i	$-0.746373\pi$
$7$	−8880.78	−1.39801	−0.699004	+	0.715118i	$0.746373\pi$
$8$	−12308.6	−1.06244
$9$	6561.00	0.333333
$10$	32940.9	1.04168
$11$	70959.2	1.46131	0.730654	−	0.682748i	$-0.239215\pi$
$11$	70959.2	1.46131	0.730654	+	0.682748i	$0.239215\pi$
$12$	20523.9	0.285722
$13$	−57764.1	−0.560936	−0.280468	−	0.959863i	$-0.590490\pi$
$13$	−57764.1	−0.560936	−0.280468	+	0.959863i	$0.590490\pi$
$14$	−142817.	−0.993584
$15$	−165917.	−0.846214
$16$	−68210.6	−0.260203
$17$	574690.	1.66884	0.834418	−	0.551132i	$-0.185804\pi$
$17$	574690.	1.66884	0.834418	+	0.551132i	$0.185804\pi$
$18$	105512.	0.236905
$19$	−675543.	−1.18922	−0.594610	−	0.804015i	$-0.702693\pi$
$19$	−675543.	−1.18922	−0.594610	+	0.804015i	$0.702693\pi$
$20$	−519016.	−0.725347
$21$	719343.	0.807141
$22$	1.14114e6	1.03857
$23$	325234.	0.242337	0.121169	−	0.992632i	$-0.461336\pi$
$23$	325234.	0.242337	0.121169	+	0.992632i	$0.461336\pi$
$24$	996995.	0.613398
$25$	2.24265e6	1.14823
$26$	−928941.	−0.398665
$27$	−531441.	−0.192450
$28$	2.25022e6	0.691854
$29$	−2.59800e6	−0.682101	−0.341050	−	0.940045i	$-0.610783\pi$
$29$	−2.59800e6	−0.682101	−0.341050	+	0.940045i	$0.610783\pi$
$30$	−2.66822e6	−0.601416
$31$	3.69152e6	0.717922	0.358961	−	0.933352i	$-0.383131\pi$
$31$	3.69152e6	0.717922	0.358961	+	0.933352i	$0.383131\pi$
$32$	5.20505e6	0.877506
$33$	−5.74770e6	−0.843687
$34$	9.24195e6	1.18607
$35$	−1.81910e7	−2.04904
$36$	−1.66244e6	−0.164962
$37$	−1.59909e7	−1.40271	−0.701353	−	0.712814i	$-0.747420\pi$
$37$	−1.59909e7	−1.40271	−0.701353	+	0.712814i	$0.747420\pi$
$38$	−1.08638e7	−0.845195
$39$	4.67889e6	0.323856
$40$	−2.52124e7	−1.55720
$41$	2.01221e7	1.11210	0.556052	−	0.831147i	$-0.312316\pi$
$41$	2.01221e7	1.11210	0.556052	+	0.831147i	$0.312316\pi$
$42$	1.15682e7	0.573646
$43$	−2.99619e7	−1.33647	−0.668237	−	0.743948i	$-0.732951\pi$
$43$	−2.99619e7	−1.33647	−0.668237	+	0.743948i	$0.732951\pi$
$44$	−1.79797e7	−0.723180
$45$	1.34393e7	0.488562
$46$	5.23028e6	0.172232
$47$	1.30817e7	0.391041	0.195521	−	0.980700i	$-0.437360\pi$
$47$	1.30817e7	0.391041	0.195521	+	0.980700i	$0.437360\pi$
$48$	5.52506e6	0.150228
$49$	3.85146e7	0.954428
$50$	3.60654e7	0.816067
$51$	−4.65499e7	−0.963503
$52$	1.46364e7	0.277599
$53$	−4.33294e7	−0.754295	−0.377148	−	0.926153i	$-0.623095\pi$
$53$	−4.33294e7	−0.754295	−0.377148	+	0.926153i	$0.623095\pi$
$54$	−8.54643e6	−0.136777
$55$	1.45350e8	2.14182
$56$	1.09310e8	1.48529
$57$	5.47190e7	0.686596
$58$	−4.17801e7	−0.484779
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	4.20403e7	0.418779
$61$	1.48079e8	1.36934	0.684668	−	0.728855i	$-0.259947\pi$
$61$	1.48079e8	1.36934	0.684668	+	0.728855i	$0.259947\pi$
$62$	5.93656e7	0.510238
$63$	−5.82668e7	−0.466003
$64$	1.18630e8	0.883859
$65$	−1.18322e8	−0.822156
$66$	−9.24323e7	−0.599620
$67$	2.62228e7	0.158980	0.0794899	−	0.996836i	$-0.474671\pi$
$67$	2.62228e7	0.158980	0.0794899	+	0.996836i	$0.474671\pi$
$68$	−1.45616e8	−0.825883
$69$	−2.63439e7	−0.139913
$70$	−2.92541e8	−1.45628
$71$	−3.59885e8	−1.68074	−0.840372	−	0.542010i	$-0.817663\pi$
$71$	−3.59885e8	−1.68074	−0.840372	+	0.542010i	$0.817663\pi$
$72$	−8.07566e7	−0.354145
$73$	−3.34147e8	−1.37716	−0.688580	−	0.725160i	$-0.741766\pi$
$73$	−3.34147e8	−1.37716	−0.688580	+	0.725160i	$0.741766\pi$
$74$	−2.57160e8	−0.996922
$75$	−1.81654e8	−0.662934
$76$	1.71170e8	0.588527
$77$	−6.30173e8	−2.04292
$78$	7.52442e7	0.230169
$79$	−6.43140e8	−1.85773	−0.928867	−	0.370413i	$-0.879216\pi$
$79$	−6.43140e8	−1.85773	−0.928867	+	0.370413i	$0.879216\pi$
$80$	−1.39720e8	−0.381376
$81$	4.30467e7	0.111111
$82$	3.23596e8	0.790388
$83$	−3.84290e8	−0.888808	−0.444404	−	0.895826i	$-0.646585\pi$
$83$	−3.84290e8	−0.888808	−0.444404	+	0.895826i	$0.646585\pi$
$84$	−1.82268e8	−0.399442
$85$	1.17717e9	2.44599
$86$	−4.81835e8	−0.949852
$87$	2.10438e8	0.393811
$88$	−8.73407e8	−1.55255
$89$	3.95175e8	0.667628	0.333814	−	0.942639i	$-0.391664\pi$
$89$	3.95175e8	0.667628	0.333814	+	0.942639i	$0.391664\pi$
$90$	2.16125e8	0.347228
$91$	5.12990e8	0.784193
$92$	−8.24081e7	−0.119929
$93$	−2.99013e8	−0.414493
$94$	2.10374e8	0.277918
$95$	−1.38375e9	−1.74302
$96$	−4.21609e8	−0.506628
$97$	−3.41540e8	−0.391714	−0.195857	−	0.980632i	$-0.562749\pi$
$97$	−3.41540e8	−0.391714	−0.195857	+	0.980632i	$0.562749\pi$
$98$	6.19377e8	0.678325
$99$	4.65564e8	0.487103
$100$	−5.68245e8	−0.568245
$101$	−1.26167e9	−1.20643	−0.603213	−	0.797580i	$-0.706113\pi$
$101$	−1.26167e9	−1.20643	−0.603213	+	0.797580i	$0.706113\pi$
$102$	−7.48598e8	−0.684775
$103$	−3.05119e8	−0.267117	−0.133559	−	0.991041i	$-0.542640\pi$
$103$	−3.05119e8	−0.267117	−0.133559	+	0.991041i	$0.542640\pi$
$104$	7.10994e8	0.595958
$105$	1.47347e9	1.18301
$106$	−6.96807e8	−0.536088
$107$	−1.23762e9	−0.912769	−0.456385	−	0.889783i	$-0.650856\pi$
$107$	−1.23762e9	−0.912769	−0.456385	+	0.889783i	$0.650856\pi$
$108$	1.34657e8	0.0952407
$109$	−9.06241e8	−0.614928	−0.307464	−	0.951560i	$-0.599480\pi$
$109$	−9.06241e8	−0.614928	−0.307464	+	0.951560i	$0.599480\pi$
$110$	2.33746e9	1.52222
$111$	1.29527e9	0.809852
$112$	6.05764e8	0.363766
$113$	−1.77528e9	−1.02427	−0.512135	−	0.858905i	$-0.671145\pi$
$113$	−1.77528e9	−1.02427	−0.512135	+	0.858905i	$0.671145\pi$
$114$	8.79970e8	0.487973
$115$	6.66195e8	0.355190
$116$	6.58285e8	0.337562
$117$	−3.78990e8	−0.186979
$118$	−1.94867e8	−0.0925271
$119$	−5.10370e9	−2.33305
$120$	2.04220e9	0.899048
$121$	2.67727e9	1.13542
$122$	2.38136e9	0.973207
$123$	−1.62989e9	−0.642074
$124$	−9.35362e8	−0.355289
$125$	5.93043e8	0.217266
$126$	−9.37024e8	−0.331195
$127$	4.23992e9	1.44624	0.723120	−	0.690722i	$-0.242707\pi$
$127$	4.23992e9	1.44624	0.723120	+	0.690722i	$0.242707\pi$
$128$	−7.57231e8	−0.249335
$129$	2.42691e9	0.771614
$130$	−1.90280e9	−0.584318
$131$	−1.60747e9	−0.476895	−0.238447	−	0.971155i	$-0.576638\pi$
$131$	−1.60747e9	−0.476895	−0.238447	+	0.971155i	$0.576638\pi$
$132$	1.45636e9	0.417528
$133$	5.99935e9	1.66254
$134$	4.21705e8	0.112989
$135$	−1.08858e9	−0.282071
$136$	−7.07362e9	−1.77303
$137$	−6.17427e9	−1.49742	−0.748709	−	0.662899i	$-0.769326\pi$
$137$	−6.17427e9	−1.49742	−0.748709	+	0.662899i	$0.769326\pi$
$138$	−4.23653e8	−0.0994384
$139$	−6.22009e9	−1.41329	−0.706643	−	0.707571i	$-0.749791\pi$
$139$	−6.22009e9	−1.41329	−0.706643	+	0.707571i	$0.749791\pi$
$140$	4.60926e9	1.01404
$141$	−1.05961e9	−0.225768
$142$	−5.78754e9	−1.19453
$143$	−4.09890e9	−0.819700
$144$	−4.47530e8	−0.0867343
$145$	−5.32164e9	−0.999746
$146$	−5.37363e9	−0.978768
$147$	−3.11968e9	−0.551039
$148$	4.05181e9	0.694178
$149$	1.18843e10	1.97531	0.987657	−	0.156630i	$-0.0500630\pi$
$149$	1.18843e10	1.97531	0.987657	+	0.156630i	$0.0500630\pi$
$150$	−2.92130e9	−0.471156
$151$	−7.78951e9	−1.21931	−0.609654	−	0.792667i	$-0.708692\pi$
$151$	−7.78951e9	−1.21931	−0.609654	+	0.792667i	$0.708692\pi$
$152$	8.31497e9	1.26347
$153$	3.77054e9	0.556279
$154$	−1.01342e10	−1.45193
$155$	7.56155e9	1.05225
$156$	−1.18554e9	−0.160272
$157$	9.52831e9	1.25161	0.625803	−	0.779981i	$-0.284771\pi$
$157$	9.52831e9	1.25161	0.625803	+	0.779981i	$0.284771\pi$
$158$	−1.03427e10	−1.32032
$159$	3.50968e9	0.435492
$160$	1.06618e10	1.28615
$161$	−2.88833e9	−0.338789
$162$	6.92261e8	0.0789682
$163$	−6.42572e9	−0.712981	−0.356490	−	0.934299i	$-0.616027\pi$
$163$	−6.42572e9	−0.712981	−0.356490	+	0.934299i	$0.616027\pi$
$164$	−5.09856e9	−0.550364
$165$	−1.17733e10	−1.23658
$166$	−6.18001e9	−0.631688
$167$	1.74275e9	0.173385	0.0866925	−	0.996235i	$-0.472370\pi$
$167$	1.74275e9	0.173385	0.0866925	+	0.996235i	$0.472370\pi$
$168$	−8.85409e9	−0.857535
$169$	−7.26781e9	−0.685351
$170$	1.89308e10	1.73840
$171$	−4.43224e9	−0.396406
$172$	7.59178e9	0.661402
$173$	−1.30581e9	−0.110834	−0.0554168	−	0.998463i	$-0.517649\pi$
$173$	−1.30581e9	−0.110834	−0.0554168	+	0.998463i	$0.517649\pi$
$174$	3.38419e9	0.279887
$175$	−1.99164e10	−1.60524
$176$	−4.84017e9	−0.380237
$177$	9.81506e8	0.0751646
$178$	6.35506e9	0.474493
$179$	−9.50453e9	−0.691978	−0.345989	−	0.938239i	$-0.612456\pi$
$179$	−9.50453e9	−0.691978	−0.345989	+	0.938239i	$0.612456\pi$
$180$	−3.40526e9	−0.241782
$181$	6.40309e9	0.443441	0.221721	−	0.975110i	$-0.428833\pi$
$181$	6.40309e9	0.443441	0.221721	+	0.975110i	$0.428833\pi$
$182$	8.24972e9	0.557337
$183$	−1.19944e10	−0.790587
$184$	−4.00316e9	−0.257468
$185$	−3.27552e10	−2.05593
$186$	−4.80862e9	−0.294586
$187$	4.07796e10	2.43868
$188$	−3.31465e9	−0.193521
$189$	4.71961e9	0.269047
$190$	−2.22530e10	−1.23879
$191$	2.35967e10	1.28293	0.641463	−	0.767154i	$-0.278328\pi$
$191$	2.35967e10	1.28293	0.641463	+	0.767154i	$0.278328\pi$
$192$	−9.60899e9	−0.510296
$193$	−1.82705e9	−0.0947857	−0.0473928	−	0.998876i	$-0.515091\pi$
$193$	−1.82705e9	−0.0947857	−0.0473928	+	0.998876i	$0.515091\pi$
$194$	−5.49253e9	−0.278397
$195$	9.58405e9	0.474672
$196$	−9.75888e9	−0.472332
$197$	1.08956e10	0.515409	0.257705	−	0.966224i	$-0.417034\pi$
$197$	1.08956e10	0.515409	0.257705	+	0.966224i	$0.417034\pi$
$198$	7.48702e9	0.346191
$199$	3.90626e10	1.76572	0.882862	−	0.469633i	$-0.155614\pi$
$199$	3.90626e10	1.76572	0.882862	+	0.469633i	$0.155614\pi$
$200$	−2.76038e10	−1.21993
$201$	−2.12405e9	−0.0917871
$202$	−2.02898e10	−0.857424
$203$	2.30723e10	0.953583
$204$	1.17949e10	0.476824
$205$	4.12172e10	1.63000
$206$	−4.90681e9	−0.189844
$207$	2.13386e9	0.0807791
$208$	3.94013e9	0.145957
$209$	−4.79360e10	−1.73782
$210$	2.36958e10	0.840785
$211$	−1.23713e10	−0.429678	−0.214839	−	0.976649i	$-0.568923\pi$
$211$	−1.23713e10	−0.429678	−0.214839	+	0.976649i	$0.568923\pi$
$212$	1.09789e10	0.373290
$213$	2.91507e10	0.970378
$214$	−1.99030e10	−0.648718
$215$	−6.13726e10	−1.95885
$216$	6.54128e9	0.204466
$217$	−3.27836e10	−1.00366
$218$	−1.45738e10	−0.437038
$219$	2.70659e10	0.795104
$220$	−3.68290e10	−1.05995
$221$	−3.31965e10	−0.936110
$222$	2.08300e10	0.575573
$223$	8.76793e9	0.237424	0.118712	−	0.992929i	$-0.462123\pi$
$223$	8.76793e9	0.237424	0.118712	+	0.992929i	$0.462123\pi$
$224$	−4.62249e10	−1.22676
$225$	1.47140e10	0.382745
$226$	−2.85494e10	−0.727963
$227$	1.40496e10	0.351195	0.175597	−	0.984462i	$-0.443814\pi$
$227$	1.40496e10	0.351195	0.175597	+	0.984462i	$0.443814\pi$
$228$	−1.38648e10	−0.339786
$229$	5.68805e10	1.36680	0.683398	−	0.730046i	$-0.260501\pi$
$229$	5.68805e10	1.36680	0.683398	+	0.730046i	$0.260501\pi$
$230$	1.07135e10	0.252439
$231$	5.10440e10	1.17948
$232$	3.19777e10	0.724689
$233$	−7.66188e10	−1.70307	−0.851537	−	0.524294i	$-0.824329\pi$
$233$	−7.66188e10	−1.70307	−0.851537	+	0.524294i	$0.824329\pi$
$234$	−6.09478e9	−0.132888
$235$	2.67959e10	0.573143
$236$	3.07031e9	0.0644286
$237$	5.20943e10	1.07256
$238$	−8.20757e10	−1.65813
$239$	−2.35739e9	−0.0467348	−0.0233674	−	0.999727i	$-0.507439\pi$
$239$	−2.35739e9	−0.0467348	−0.0233674	+	0.999727i	$0.507439\pi$
$240$	1.13173e10	0.220187
$241$	−6.47507e10	−1.23642	−0.618212	−	0.786011i	$-0.712143\pi$
$241$	−6.47507e10	−1.23642	−0.618212	+	0.786011i	$0.712143\pi$
$242$	4.30548e10	0.806960
$243$	−3.48678e9	−0.0641500
$244$	−3.75205e10	−0.677665
$245$	7.88917e10	1.39889
$246$	−2.62113e10	−0.456331
$247$	3.90222e10	0.667075
$248$	−4.54373e10	−0.762747
$249$	3.11275e10	0.513154
$250$	9.53710e9	0.154414
$251$	7.83882e10	1.24658	0.623288	−	0.781992i	$-0.285796\pi$
$251$	7.83882e10	1.24658	0.623288	+	0.781992i	$0.285796\pi$
$252$	1.47637e10	0.230618
$253$	2.30783e10	0.354129
$254$	6.81848e10	1.02786
$255$	−9.53509e10	−1.41219
$256$	−7.29158e10	−1.06107
$257$	1.12417e11	1.60743	0.803716	−	0.595013i	$-0.202853\pi$
$257$	1.12417e11	1.60743	0.803716	+	0.595013i	$0.202853\pi$
$258$	3.90287e10	0.548397
$259$	1.42012e11	1.96099
$260$	2.99805e10	0.406873
$261$	−1.70455e10	−0.227367
$262$	−2.58508e10	−0.338936
$263$	−3.79023e10	−0.488501	−0.244250	−	0.969712i	$-0.578542\pi$
$263$	−3.79023e10	−0.488501	−0.244250	+	0.969712i	$0.578542\pi$
$264$	7.07460e10	0.896363
$265$	−8.87541e10	−1.10556
$266$	9.64793e10	1.18159
$267$	−3.20092e10	−0.385455
$268$	−6.64436e9	−0.0786768
$269$	−4.07264e10	−0.474232	−0.237116	−	0.971481i	$-0.576202\pi$
$269$	−4.07264e10	−0.474232	−0.237116	+	0.971481i	$0.576202\pi$
$270$	−1.75062e10	−0.200472
$271$	−9.29803e10	−1.04720	−0.523599	−	0.851965i	$-0.675411\pi$
$271$	−9.29803e10	−1.04720	−0.523599	+	0.851965i	$0.675411\pi$
$272$	−3.92000e10	−0.434236
$273$	−4.15522e10	−0.452754
$274$	−9.92923e10	−1.06424
$275$	1.59136e11	1.67793
$276$	6.67506e9	0.0692411
$277$	6.68436e10	0.682183	0.341091	−	0.940030i	$-0.389203\pi$
$277$	6.68436e10	0.682183	0.341091	+	0.940030i	$0.389203\pi$
$278$	−1.00029e11	−1.00444
$279$	2.42201e10	0.239307
$280$	2.23905e11	2.17698
$281$	1.78845e11	1.71119	0.855595	−	0.517647i	$-0.173192\pi$
$281$	1.78845e11	1.71119	0.855595	+	0.517647i	$0.173192\pi$
$282$	−1.70403e10	−0.160456
$283$	8.69585e10	0.805885	0.402943	−	0.915225i	$-0.367987\pi$
$283$	8.69585e10	0.805885	0.402943	+	0.915225i	$0.367987\pi$
$284$	9.11882e10	0.831776
$285$	1.12084e11	1.00633
$286$	−6.59169e10	−0.582572
$287$	−1.78700e11	−1.55473
$288$	3.41504e10	0.292502
$289$	2.11681e11	1.78501
$290$	−8.55806e10	−0.710533
$291$	2.76648e10	0.226156
$292$	8.46666e10	0.681537
$293$	−1.40207e11	−1.11139	−0.555693	−	0.831387i	$-0.687547\pi$
$293$	−1.40207e11	−1.11139	−0.555693	+	0.831387i	$0.687547\pi$
$294$	−5.01696e10	−0.391631
$295$	−2.48207e10	−0.190816
$296$	1.96826e11	1.49028
$297$	−3.77106e10	−0.281229
$298$	1.91119e11	1.40388
$299$	−1.87868e10	−0.135936
$300$	4.60278e10	0.328076
$301$	2.66085e11	1.86840
$302$	−1.25268e11	−0.866580
$303$	1.02196e11	0.696531
$304$	4.60792e10	0.309438
$305$	3.03319e11	2.00702
$306$	6.06365e10	0.395355
$307$	−1.99661e11	−1.28283	−0.641417	−	0.767192i	$-0.721653\pi$
$307$	−1.99661e11	−1.28283	−0.641417	+	0.767192i	$0.721653\pi$
$308$	1.59674e11	1.01101
$309$	2.47147e10	0.154220
$310$	1.21602e11	0.747848
$311$	−1.99334e11	−1.20826	−0.604130	−	0.796886i	$-0.706479\pi$
$311$	−1.99334e11	−1.20826	−0.604130	+	0.796886i	$0.706479\pi$
$312$	−5.75905e10	−0.344077
$313$	−1.31175e11	−0.772508	−0.386254	−	0.922393i	$-0.626231\pi$
$313$	−1.31175e11	−0.772508	−0.386254	+	0.922393i	$0.626231\pi$
$314$	1.53231e11	0.889534
$315$	−1.19351e11	−0.683014
$316$	1.62960e11	0.919366
$317$	8.58630e10	0.477573	0.238786	−	0.971072i	$-0.423250\pi$
$317$	8.58630e10	0.477573	0.238786	+	0.971072i	$0.423250\pi$
$318$	5.64414e10	0.309511
$319$	−1.84352e11	−0.996760
$320$	2.42996e11	1.29546
$321$	1.00247e11	0.526987
$322$	−4.64490e10	−0.240782
$323$	−3.88228e11	−1.98461
$324$	−1.09072e10	−0.0549873
$325$	−1.29544e11	−0.644086
$326$	−1.03336e11	−0.506725
$327$	7.34055e10	0.355029
$328$	−2.47674e11	−1.18154
$329$	−1.16175e11	−0.546679
$330$	−1.89335e11	−0.878855
$331$	−8.30618e10	−0.380343	−0.190171	−	0.981751i	$-0.560904\pi$
$331$	−8.30618e10	−0.380343	−0.190171	+	0.981751i	$0.560904\pi$
$332$	9.73720e10	0.439858
$333$	−1.04917e11	−0.467568
$334$	2.80263e10	0.123227
$335$	5.37136e10	0.233015
$336$	−4.90668e10	−0.210020
$337$	−1.49661e11	−0.632083	−0.316042	−	0.948745i	$-0.602354\pi$
$337$	−1.49661e11	−0.632083	−0.316042	+	0.948745i	$0.602354\pi$
$338$	−1.16878e11	−0.487089
$339$	1.43798e11	0.591362
$340$	−2.98273e11	−1.21048
$341$	2.61947e11	1.04911
$342$	−7.12776e10	−0.281732
$343$	1.63318e10	0.0637104
$344$	3.68788e11	1.41992
$345$	−5.39618e10	−0.205069
$346$	−2.09995e10	−0.0787710
$347$	−2.38151e11	−0.881801	−0.440900	−	0.897556i	$-0.645341\pi$
$347$	−2.38151e11	−0.881801	−0.440900	+	0.897556i	$0.645341\pi$
$348$	−5.33211e10	−0.194891
$349$	2.91117e11	1.05040	0.525199	−	0.850980i	$-0.323991\pi$
$349$	2.91117e11	1.05040	0.525199	+	0.850980i	$0.323991\pi$
$350$	−3.20289e11	−1.14087
$351$	3.06982e10	0.107952
$352$	3.69347e11	1.28231
$353$	4.63430e11	1.58854	0.794270	−	0.607565i	$-0.207854\pi$
$353$	4.63430e11	1.58854	0.794270	+	0.607565i	$0.207854\pi$
$354$	1.57842e10	0.0534205
$355$	−7.37174e11	−2.46344
$356$	−1.00130e11	−0.330399
$357$	4.13399e11	1.34699
$358$	−1.52848e11	−0.491798
$359$	−3.43784e11	−1.09235	−0.546173	−	0.837672i	$-0.683916\pi$
$359$	−3.43784e11	−1.09235	−0.546173	+	0.837672i	$0.683916\pi$
$360$	−1.65418e11	−0.519066
$361$	1.33671e11	0.414242
$362$	1.02972e11	0.315160
$363$	−2.16859e11	−0.655536
$364$	−1.29982e11	−0.388086
$365$	−6.84453e11	−2.01849
$366$	−1.92890e11	−0.561881
$367$	−5.88441e11	−1.69319	−0.846595	−	0.532237i	$-0.821352\pi$
$367$	−5.88441e11	−1.69319	−0.846595	+	0.532237i	$0.821352\pi$
$368$	−2.21844e10	−0.0630568
$369$	1.32021e11	0.370701
$370$	−5.26757e11	−1.46118
$371$	3.84799e11	1.05451
$372$	7.57643e10	0.205126
$373$	−4.80252e11	−1.28463	−0.642317	−	0.766439i	$-0.722027\pi$
$373$	−4.80252e11	−1.28463	−0.642317	+	0.766439i	$0.722027\pi$
$374$	6.55802e11	1.73321
$375$	−4.80365e10	−0.125438
$376$	−1.61017e11	−0.415456
$377$	1.50071e11	0.382615
$378$	7.58990e10	0.191215
$379$	7.91147e10	0.196961	0.0984806	−	0.995139i	$-0.468602\pi$
$379$	7.91147e10	0.196961	0.0984806	+	0.995139i	$0.468602\pi$
$380$	3.50618e11	0.862596
$381$	−3.43433e11	−0.834988
$382$	3.79474e11	0.911793
$383$	5.13977e11	1.22053	0.610266	−	0.792197i	$-0.291063\pi$
$383$	5.13977e11	1.22053	0.610266	+	0.792197i	$0.291063\pi$
$384$	6.13357e10	0.143954
$385$	−1.29082e12	−2.99428
$386$	−2.93819e10	−0.0673655
$387$	−1.96580e11	−0.445492
$388$	8.65400e10	0.193854
$389$	5.24137e11	1.16057	0.580286	−	0.814413i	$-0.302941\pi$
$389$	5.24137e11	1.16057	0.580286	+	0.814413i	$0.302941\pi$
$390$	1.54127e11	0.337356
$391$	1.86909e11	0.404421
$392$	−4.74060e11	−1.01402
$393$	1.30205e11	0.275335
$394$	1.75219e11	0.366309
$395$	−1.31738e12	−2.72286
$396$	−1.17965e11	−0.241060
$397$	1.37630e11	0.278071	0.139036	−	0.990287i	$-0.455600\pi$
$397$	1.37630e11	0.278071	0.139036	+	0.990287i	$0.455600\pi$
$398$	6.28191e11	1.25492
$399$	−4.85947e11	−0.959867
$400$	−1.52972e11	−0.298774
$401$	9.21929e11	1.78052	0.890261	−	0.455450i	$-0.150522\pi$
$401$	9.21929e11	1.78052	0.890261	+	0.455450i	$0.150522\pi$
$402$	−3.41581e10	−0.0652344
$403$	−2.13237e11	−0.402708
$404$	3.19685e11	0.597043
$405$	8.81751e10	0.162854
$406$	3.71040e11	0.677725
$407$	−1.13471e12	−2.04978
$408$	5.72963e11	1.02366
$409$	−2.01994e11	−0.356931	−0.178466	−	0.983946i	$-0.557113\pi$
$409$	−2.01994e11	−0.356931	−0.178466	+	0.983946i	$0.557113\pi$
$410$	6.62840e11	1.15846
$411$	5.00116e11	0.864535
$412$	7.73115e10	0.132192
$413$	1.07612e11	0.182005
$414$	3.43159e10	0.0574108
$415$	−7.87164e11	−1.30271
$416$	−3.00665e11	−0.492225
$417$	5.03827e11	0.815961
$418$	−7.70889e11	−1.23509
$419$	5.01944e11	0.795596	0.397798	−	0.917473i	$-0.369775\pi$
$419$	5.01944e11	0.795596	0.397798	+	0.917473i	$0.369775\pi$
$420$	−3.73350e11	−0.585457
$421$	−7.66121e11	−1.18858	−0.594289	−	0.804251i	$-0.702567\pi$
$421$	−7.66121e11	−1.18858	−0.594289	+	0.804251i	$0.702567\pi$
$422$	−1.98950e11	−0.305379
$423$	8.58287e10	0.130347
$424$	5.33323e11	0.801390
$425$	1.28883e12	1.91622
$426$	4.68791e11	0.689661
$427$	−1.31506e12	−1.91434
$428$	3.13590e11	0.451716
$429$	3.32011e11	0.473254
$430$	−9.86972e11	−1.39218
$431$	−2.97428e11	−0.415177	−0.207589	−	0.978216i	$-0.566562\pi$
$431$	−2.97428e11	−0.415177	−0.207589	+	0.978216i	$0.566562\pi$
$432$	3.62499e10	0.0500761
$433$	1.09804e12	1.50114	0.750569	−	0.660792i	$-0.229779\pi$
$433$	1.09804e12	1.50114	0.750569	+	0.660792i	$0.229779\pi$
$434$	−5.27213e11	−0.713316
$435$	4.31053e11	0.577203
$436$	2.29625e11	0.304319
$437$	−2.19709e11	−0.288192
$438$	4.35264e11	0.565092
$439$	−8.54029e11	−1.09744	−0.548722	−	0.836005i	$-0.684886\pi$
$439$	−8.54029e11	−1.09744	−0.548722	+	0.836005i	$0.684886\pi$
$440$	−1.78905e12	−2.27555
$441$	2.52694e11	0.318143
$442$	−5.33853e11	−0.665307
$443$	−3.63618e11	−0.448568	−0.224284	−	0.974524i	$-0.572004\pi$
$443$	−3.63618e11	−0.448568	−0.224284	+	0.974524i	$0.572004\pi$
$444$	−3.28196e11	−0.400784
$445$	8.09460e11	0.978533
$446$	1.41003e11	0.168741
$447$	−9.62630e11	−1.14045
$448$	−1.05352e12	−1.23564
$449$	−2.76604e11	−0.321181	−0.160590	−	0.987021i	$-0.551340\pi$
$449$	−2.76604e11	−0.321181	−0.160590	+	0.987021i	$0.551340\pi$
$450$	2.36625e11	0.272022
$451$	1.42785e12	1.62513
$452$	4.49823e11	0.506896
$453$	6.30950e11	0.703968
$454$	2.25941e11	0.249599
$455$	1.05079e12	1.14938
$456$	−6.73513e11	−0.729464
$457$	−2.71605e11	−0.291283	−0.145642	−	0.989337i	$-0.546525\pi$
$457$	−2.71605e11	−0.291283	−0.145642	+	0.989337i	$0.546525\pi$
$458$	9.14731e11	0.971402
$459$	−3.05414e11	−0.321168
$460$	−1.68801e11	−0.175778
$461$	5.93856e11	0.612388	0.306194	−	0.951969i	$-0.400944\pi$
$461$	5.93856e11	0.612388	0.306194	+	0.951969i	$0.400944\pi$
$462$	8.20871e11	0.838274
$463$	−1.90507e11	−0.192662	−0.0963310	−	0.995349i	$-0.530711\pi$
$463$	−1.90507e11	−0.192662	−0.0963310	+	0.995349i	$0.530711\pi$
$464$	1.77211e11	0.177485
$465$	−6.12486e11	−0.607516
$466$	−1.23215e12	−1.21040
$467$	−6.17353e11	−0.600631	−0.300315	−	0.953840i	$-0.597092\pi$
$467$	−6.17353e11	−0.600631	−0.300315	+	0.953840i	$0.597092\pi$
$468$	9.60291e10	0.0925330
$469$	−2.32879e11	−0.222255
$470$	4.30922e11	0.407341
$471$	−7.71793e11	−0.722615
$472$	1.49147e11	0.138317
$473$	−2.12607e12	−1.95300
$474$	8.37762e11	0.762286
$475$	−1.51500e12	−1.36550
$476$	1.29318e12	1.15459
$477$	−2.84284e11	−0.251432
$478$	−3.79107e10	−0.0332151
$479$	−2.05297e11	−0.178186	−0.0890928	−	0.996023i	$-0.528397\pi$
$479$	−2.05297e11	−0.178186	−0.0890928	+	0.996023i	$0.528397\pi$
$480$	−8.63607e11	−0.742558
$481$	9.23703e11	0.786828
$482$	−1.04130e12	−0.878745
$483$	2.33954e11	0.195600
$484$	−6.78369e11	−0.561904
$485$	−6.99597e11	−0.574130
$486$	−5.60732e10	−0.0455923
$487$	−1.89086e12	−1.52328	−0.761640	−	0.648001i	$-0.775605\pi$
$487$	−1.89086e12	−1.52328	−0.761640	+	0.648001i	$0.775605\pi$
$488$	−1.82265e12	−1.45483
$489$	5.20484e11	0.411640
$490$	1.26871e12	0.994212
$491$	1.01893e12	0.791187	0.395594	−	0.918426i	$-0.370539\pi$
$491$	1.01893e12	0.791187	0.395594	+	0.918426i	$0.370539\pi$
$492$	4.12983e11	0.317753
$493$	−1.49305e12	−1.13831
$494$	6.27540e11	0.474100
$495$	9.53641e11	0.713940
$496$	−2.51801e11	−0.186805
$497$	3.19606e12	2.34969
$498$	5.00581e11	0.364705
$499$	1.51606e12	1.09462	0.547311	−	0.836929i	$-0.315651\pi$
$499$	1.51606e12	1.09462	0.547311	+	0.836929i	$0.315651\pi$
$500$	−1.50266e11	−0.107522
$501$	−1.41163e11	−0.100104
$502$	1.26061e12	0.885959
$503$	−2.25319e12	−1.56943	−0.784713	−	0.619859i	$-0.787190\pi$
$503$	−2.25319e12	−1.56943	−0.784713	+	0.619859i	$0.787190\pi$
$504$	7.17181e11	0.495098
$505$	−2.58436e12	−1.76824
$506$	3.71137e11	0.251685
$507$	5.88692e11	0.395688
$508$	−1.07432e12	−0.715724
$509$	−1.89541e11	−0.125162	−0.0625812	−	0.998040i	$-0.519933\pi$
$509$	−1.89541e11	−0.125162	−0.0625812	+	0.998040i	$0.519933\pi$
$510$	−1.53340e12	−1.00367
$511$	2.96748e12	1.92528
$512$	−7.84903e11	−0.504779
$513$	3.59011e11	0.228865
$514$	1.80785e12	1.14242
$515$	−6.24993e11	−0.391510
$516$	−6.14934e11	−0.381861
$517$	9.28264e11	0.571431
$518$	2.28378e12	1.39371
$519$	1.05770e11	0.0639898
$520$	1.45637e12	0.873488
$521$	2.48369e11	0.147682	0.0738411	−	0.997270i	$-0.476474\pi$
$521$	2.48369e11	0.147682	0.0738411	+	0.997270i	$0.476474\pi$
$522$	−2.74119e11	−0.161593
$523$	−2.94791e11	−0.172289	−0.0861443	−	0.996283i	$-0.527455\pi$
$523$	−2.94791e11	−0.172289	−0.0861443	+	0.996283i	$0.527455\pi$
$524$	4.07303e11	0.236008
$525$	1.61323e12	0.926787
$526$	−6.09531e11	−0.347184
$527$	2.12148e12	1.19809
$528$	3.92054e11	0.219530
$529$	−1.69538e12	−0.941273
$530$	−1.42731e12	−0.785737
$531$	−7.95020e10	−0.0433963
$532$	−1.52012e12	−0.822766
$533$	−1.16233e12	−0.623819
$534$	−5.14760e11	−0.273948
$535$	−2.53509e12	−1.33783
$536$	−3.22765e11	−0.168906
$537$	7.69867e11	0.399513
$538$	−6.54947e11	−0.337044
$539$	2.73297e12	1.39471
$540$	2.75826e11	0.139593
$541$	2.55667e11	0.128318	0.0641590	−	0.997940i	$-0.479564\pi$
$541$	2.55667e11	0.128318	0.0641590	+	0.997940i	$0.479564\pi$
$542$	−1.49527e12	−0.744259
$543$	−5.18650e11	−0.256021
$544$	2.99129e12	1.46441
$545$	−1.85631e12	−0.901292
$546$	−6.68227e11	−0.321779
$547$	−2.11030e12	−1.00786	−0.503932	−	0.863743i	$-0.668114\pi$
$547$	−2.11030e12	−1.00786	−0.503932	+	0.863743i	$0.668114\pi$
$548$	1.56445e12	0.741051
$549$	9.71548e11	0.456445
$550$	2.55917e12	1.19253
$551$	1.75506e12	0.811167
$552$	3.24256e11	0.148649
$553$	5.71158e12	2.59713
$554$	1.07495e12	0.484837
$555$	2.65317e12	1.18699
$556$	1.57605e12	0.699414
$557$	−4.44566e12	−1.95699	−0.978493	−	0.206279i	$-0.933865\pi$
$557$	−4.44566e12	−1.95699	−0.978493	+	0.206279i	$0.933865\pi$
$558$	3.89498e11	0.170079
$559$	1.73072e12	0.749677
$560$	1.24082e12	0.533167
$561$	−3.30315e12	−1.40798
$562$	2.87612e12	1.21617
$563$	4.54146e12	1.90506	0.952528	−	0.304452i	$-0.0984732\pi$
$563$	4.54146e12	1.90506	0.952528	+	0.304452i	$0.0984732\pi$
$564$	2.68486e11	0.111729
$565$	−3.63641e12	−1.50126
$566$	1.39843e12	0.572754
$567$	−3.82288e11	−0.155334
$568$	4.42967e12	1.78568
$569$	−3.69150e12	−1.47638	−0.738190	−	0.674593i	$-0.764319\pi$
$569$	−3.69150e12	−1.47638	−0.738190	+	0.674593i	$0.764319\pi$
$570$	1.80249e12	0.715216
$571$	2.45410e10	0.00966117	0.00483058	−	0.999988i	$-0.498462\pi$
$571$	2.45410e10	0.00966117	0.00483058	+	0.999988i	$0.498462\pi$
$572$	1.03858e12	0.405658
$573$	−1.91133e12	−0.740697
$574$	−2.87378e12	−1.10497
$575$	7.29384e11	0.278260
$576$	7.78328e11	0.294620
$577$	2.34560e12	0.880974	0.440487	−	0.897759i	$-0.354806\pi$
$577$	2.34560e12	0.880974	0.440487	+	0.897759i	$0.354806\pi$
$578$	3.40418e12	1.26864
$579$	1.47991e11	0.0547245
$580$	1.34840e12	0.494760
$581$	3.41280e12	1.24256
$582$	4.44895e11	0.160733
$583$	−3.07462e12	−1.10226
$584$	4.11287e12	1.46315
$585$	−7.76308e11	−0.274052
$586$	−2.25475e12	−0.789878
$587$	−2.42490e12	−0.842990	−0.421495	−	0.906831i	$-0.638495\pi$
$587$	−2.42490e12	−0.842990	−0.421495	+	0.906831i	$0.638495\pi$
$588$	7.90469e11	0.272701
$589$	−2.49378e12	−0.853767
$590$	−3.99157e11	−0.135616
$591$	−8.82542e11	−0.297572
$592$	1.09075e12	0.364988
$593$	2.29186e12	0.761101	0.380551	−	0.924760i	$-0.375734\pi$
$593$	2.29186e12	0.761101	0.380551	+	0.924760i	$0.375734\pi$
$594$	−6.06448e11	−0.199873
$595$	−1.04542e13	−3.41951
$596$	−3.01127e12	−0.977555
$597$	−3.16407e12	−1.01944
$598$	−3.02123e11	−0.0966113
$599$	−5.21413e12	−1.65486	−0.827430	−	0.561569i	$-0.810198\pi$
$599$	−5.21413e12	−1.65486	−0.827430	+	0.561569i	$0.810198\pi$
$600$	2.23591e12	0.704325
$601$	1.28472e12	0.401674	0.200837	−	0.979625i	$-0.435634\pi$
$601$	1.28472e12	0.401674	0.200837	+	0.979625i	$0.435634\pi$
$602$	4.27907e12	1.32790
$603$	1.72048e11	0.0529933
$604$	1.97372e12	0.603418
$605$	5.48400e12	1.66417
$606$	1.64347e12	0.495034
$607$	1.50667e12	0.450474	0.225237	−	0.974304i	$-0.427684\pi$
$607$	1.50667e12	0.450474	0.225237	+	0.974304i	$0.427684\pi$
$608$	−3.51624e12	−1.04355
$609$	−1.86886e12	−0.550551
$610$	4.87787e12	1.42642
$611$	−7.55650e11	−0.219349
$612$	−9.55385e11	−0.275294
$613$	7.34445e11	0.210081	0.105041	−	0.994468i	$-0.466503\pi$
$613$	7.34445e11	0.210081	0.105041	+	0.994468i	$0.466503\pi$
$614$	−3.21087e12	−0.911728
$615$	−3.33859e12	−0.941078
$616$	7.75653e12	2.17047
$617$	6.90093e11	0.191701	0.0958505	−	0.995396i	$-0.469443\pi$
$617$	6.90093e11	0.191701	0.0958505	+	0.995396i	$0.469443\pi$
$618$	3.97452e11	0.109606
$619$	−2.37314e12	−0.649704	−0.324852	−	0.945765i	$-0.605314\pi$
$619$	−2.37314e12	−0.649704	−0.324852	+	0.945765i	$0.605314\pi$
$620$	−1.91596e12	−0.520742
$621$	−1.72842e11	−0.0466378
$622$	−3.20562e12	−0.858727
$623$	−3.50946e12	−0.933349
$624$	−3.19150e11	−0.0842684
$625$	−3.16540e12	−0.829792
$626$	−2.10951e12	−0.549032
$627$	3.88282e12	1.00333
$628$	−2.41430e12	−0.619401
$629$	−9.18984e12	−2.34089
$630$	−1.91936e12	−0.485427
$631$	3.82877e12	0.961450	0.480725	−	0.876871i	$-0.340374\pi$
$631$	3.82877e12	0.961450	0.480725	+	0.876871i	$0.340374\pi$
$632$	7.91614e12	1.97372
$633$	1.00207e12	0.248075
$634$	1.38082e12	0.339418
$635$	8.68487e12	2.11973
$636$	−8.89288e11	−0.215519
$637$	−2.22476e12	−0.535373
$638$	−2.96468e12	−0.708411
$639$	−2.36121e12	−0.560248
$640$	−1.55108e12	−0.365447
$641$	−8.41400e12	−1.96853	−0.984263	−	0.176708i	$-0.943455\pi$
$641$	−8.41400e12	−1.96853	−0.984263	+	0.176708i	$0.943455\pi$
$642$	1.61214e12	0.374537
$643$	6.56454e12	1.51445	0.757225	−	0.653155i	$-0.226555\pi$
$643$	6.56454e12	1.51445	0.757225	+	0.653155i	$0.226555\pi$
$644$	7.31848e11	0.167662
$645$	4.97118e12	1.13094
$646$	−6.24334e12	−1.41049
$647$	−1.08070e12	−0.242458	−0.121229	−	0.992625i	$-0.538684\pi$
$647$	−1.08070e12	−0.242458	−0.121229	+	0.992625i	$0.538684\pi$
$648$	−5.29844e11	−0.118048
$649$	−8.59839e11	−0.190246
$650$	−2.08329e12	−0.457761
$651$	2.65547e12	0.579464
$652$	1.62816e12	0.352844
$653$	4.48631e12	0.965562	0.482781	−	0.875741i	$-0.339627\pi$
$653$	4.48631e12	0.965562	0.482781	+	0.875741i	$0.339627\pi$
$654$	1.18048e12	0.252324
$655$	−3.29268e12	−0.698978
$656$	−1.37254e12	−0.289373
$657$	−2.19234e12	−0.459054
$658$	−1.86829e12	−0.388532
$659$	−2.37848e12	−0.491264	−0.245632	−	0.969363i	$-0.578995\pi$
$659$	−2.37848e12	−0.491264	−0.245632	+	0.969363i	$0.578995\pi$
$660$	2.98315e12	0.611965
$661$	−7.15743e12	−1.45831	−0.729157	−	0.684347i	$-0.760087\pi$
$661$	−7.15743e12	−1.45831	−0.729157	+	0.684347i	$0.760087\pi$
$662$	−1.33577e12	−0.270315
$663$	2.68892e12	0.540463
$664$	4.73007e12	0.944302
$665$	1.22888e13	2.43676
$666$	−1.68723e12	−0.332307
$667$	−8.44958e11	−0.165298
$668$	−4.41581e11	−0.0858057
$669$	−7.10202e11	−0.137077
$670$	8.63803e11	0.165607
$671$	1.05076e13	2.00102
$672$	3.74422e12	0.708271
$673$	3.34043e12	0.627675	0.313838	−	0.949477i	$-0.398385\pi$
$673$	3.34043e12	0.627675	0.313838	+	0.949477i	$0.398385\pi$
$674$	−2.40679e12	−0.449231
$675$	−1.19183e12	−0.220978
$676$	1.84153e12	0.339170
$677$	1.16108e10	0.00212429	0.00106214	−	0.999999i	$-0.499662\pi$
$677$	1.16108e10	0.00212429	0.00106214	+	0.999999i	$0.499662\pi$
$678$	2.31250e12	0.420290
$679$	3.03315e12	0.547620
$680$	−1.44893e13	−2.59871
$681$	−1.13802e12	−0.202763
$682$	4.21254e12	0.745614
$683$	−2.75359e12	−0.484179	−0.242090	−	0.970254i	$-0.577833\pi$
$683$	−2.75359e12	−0.484179	−0.242090	+	0.970254i	$0.577833\pi$
$684$	1.12305e12	0.196176
$685$	−1.26471e13	−2.19474
$686$	2.62642e11	0.0452799
$687$	−4.60732e12	−0.789120
$688$	2.04372e12	0.347755
$689$	2.50288e12	0.423111
$690$	−8.67793e11	−0.145746
$691$	3.09917e12	0.517124	0.258562	−	0.965995i	$-0.416751\pi$
$691$	3.09917e12	0.517124	0.258562	+	0.965995i	$0.416751\pi$
$692$	3.30867e11	0.0548499
$693$	−4.13457e12	−0.680974
$694$	−3.82986e12	−0.626708
$695$	−1.27410e13	−2.07143
$696$	−2.59019e12	−0.418399
$697$	1.15640e13	1.85592
$698$	4.68164e12	0.746532
$699$	6.20612e12	0.983270
$700$	5.04645e12	0.794411
$701$	2.89435e12	0.452710	0.226355	−	0.974045i	$-0.427319\pi$
$701$	2.89435e12	0.452710	0.226355	+	0.974045i	$0.427319\pi$
$702$	4.93677e11	0.0767231
$703$	1.08026e13	1.66812
$704$	8.41786e12	1.29159
$705$	−2.17047e12	−0.330904
$706$	7.45271e12	1.12900
$707$	1.12046e13	1.68659
$708$	−2.48695e11	−0.0371979
$709$	−3.07176e12	−0.456540	−0.228270	−	0.973598i	$-0.573307\pi$
$709$	−3.07176e12	−0.456540	−0.228270	+	0.973598i	$0.573307\pi$
$710$	−1.18550e13	−1.75080
$711$	−4.21964e12	−0.619245
$712$	−4.86404e12	−0.709312
$713$	1.20061e12	0.173979
$714$	6.64813e12	0.957322
$715$	−8.39601e12	−1.20142
$716$	2.40827e12	0.342450
$717$	1.90949e11	0.0269824
$718$	−5.52860e12	−0.776346
$719$	−7.37377e12	−1.02899	−0.514493	−	0.857495i	$-0.672020\pi$
$719$	−7.37377e12	−1.02899	−0.514493	+	0.857495i	$0.672020\pi$
$720$	−9.16702e11	−0.127125
$721$	2.70970e12	0.373432
$722$	2.14964e12	0.294408
$723$	5.24481e12	0.713850
$724$	−1.62242e12	−0.219453
$725$	−5.82640e12	−0.783212
$726$	−3.48744e12	−0.465899
$727$	1.76907e11	0.0234877	0.0117438	−	0.999931i	$-0.496262\pi$
$727$	1.76907e11	0.0234877	0.0117438	+	0.999931i	$0.496262\pi$
$728$	−6.31418e12	−0.833155
$729$	2.82430e11	0.0370370
$730$	−1.10071e13	−1.43457
$731$	−1.72188e13	−2.23036
$732$	3.03916e12	0.391250
$733$	7.53574e12	0.964180	0.482090	−	0.876122i	$-0.339878\pi$
$733$	7.53574e12	0.964180	0.482090	+	0.876122i	$0.339878\pi$
$734$	−9.46309e12	−1.20337
$735$	−6.39023e12	−0.807650
$736$	1.69286e12	0.212652
$737$	1.86075e12	0.232319
$738$	2.12311e12	0.263463
$739$	9.74013e12	1.20134	0.600669	−	0.799498i	$-0.294901\pi$
$739$	9.74013e12	1.20134	0.600669	+	0.799498i	$0.294901\pi$
$740$	8.29955e12	1.01745
$741$	−3.16079e12	−0.385136
$742$	6.18819e12	0.749456
$743$	−6.04164e12	−0.727286	−0.363643	−	0.931538i	$-0.618467\pi$
$743$	−6.04164e12	−0.727286	−0.363643	+	0.931538i	$0.618467\pi$
$744$	3.68042e12	0.440372
$745$	2.43434e13	2.89519
$746$	−7.72323e12	−0.913007
$747$	−2.52133e12	−0.296269
$748$	−1.03328e13	−1.20687
$749$	1.09910e13	1.27606
$750$	−7.72505e11	−0.0891508
$751$	−1.86477e12	−0.213917	−0.106958	−	0.994264i	$-0.534111\pi$
$751$	−1.86477e12	−0.213917	−0.106958	+	0.994264i	$0.534111\pi$
$752$	−8.92308e11	−0.101750
$753$	−6.34944e12	−0.719711
$754$	2.41339e12	0.271930
$755$	−1.59557e13	−1.78712
$756$	−1.19586e12	−0.133147
$757$	−1.42975e13	−1.58244	−0.791222	−	0.611528i	$-0.790555\pi$
$757$	−1.42975e13	−1.58244	−0.791222	+	0.611528i	$0.790555\pi$
$758$	1.27229e12	0.139983
$759$	−1.86934e12	−0.204457
$760$	1.70320e13	1.85185
$761$	7.40971e11	0.0800885	0.0400442	−	0.999198i	$-0.487250\pi$
$761$	7.40971e11	0.0800885	0.0400442	+	0.999198i	$0.487250\pi$
$762$	−5.52297e12	−0.593437
$763$	8.04813e12	0.859675
$764$	−5.97897e12	−0.634901
$765$	7.72342e12	0.815330
$766$	8.26559e12	0.867449
$767$	6.99949e11	0.0730276
$768$	5.90618e12	0.612606
$769$	−2.78398e12	−0.287076	−0.143538	−	0.989645i	$-0.545848\pi$
$769$	−2.78398e12	−0.287076	−0.143538	+	0.989645i	$0.545848\pi$
$770$	−2.07585e13	−2.12808
$771$	−9.10577e12	−0.928051
$772$	4.62941e11	0.0469080
$773$	7.72432e11	0.0778131	0.0389065	−	0.999243i	$-0.487613\pi$
$773$	7.72432e11	0.0778131	0.0389065	+	0.999243i	$0.487613\pi$
$774$	−3.16132e12	−0.316617
$775$	8.27877e12	0.824343
$776$	4.20388e12	0.416171
$777$	−1.15030e13	−1.13218
$778$	8.42898e12	0.824835
$779$	−1.35933e13	−1.32254
$780$	−2.42842e12	−0.234908
$781$	−2.55372e13	−2.45608
$782$	3.00579e12	0.287428
$783$	1.38069e12	0.131270
$784$	−2.62711e12	−0.248345
$785$	1.95174e13	1.83446
$786$	2.09391e12	0.195685
$787$	−1.05342e12	−0.0978851	−0.0489425	−	0.998802i	$-0.515585\pi$
$787$	−1.05342e12	−0.0978851	−0.0489425	+	0.998802i	$0.515585\pi$
$788$	−2.76074e12	−0.255068
$789$	3.07009e12	0.282036
$790$	−2.11856e13	−1.93517
$791$	1.57659e13	1.43194
$792$	−5.73042e12	−0.517516
$793$	−8.55367e12	−0.768110
$794$	2.21331e12	0.197629
$795$	7.18908e12	0.638295
$796$	−9.89774e12	−0.873831
$797$	−5.36649e12	−0.471116	−0.235558	−	0.971860i	$-0.575692\pi$
$797$	−5.36649e12	−0.471116	−0.235558	+	0.971860i	$0.575692\pi$
$798$	−7.81482e12	−0.682191
$799$	7.51790e12	0.652583
$800$	1.16731e13	1.00758
$801$	2.59274e12	0.222543
$802$	1.48261e13	1.26544
$803$	−2.37108e13	−2.01246
$804$	5.38193e11	0.0454241
$805$	−5.91633e12	−0.496559
$806$	−3.42920e12	−0.286210
$807$	3.29884e12	0.273798
$808$	1.55294e13	1.28175
$809$	6.93954e12	0.569590	0.284795	−	0.958589i	$-0.408075\pi$
$809$	6.93954e12	0.569590	0.284795	+	0.958589i	$0.408075\pi$
$810$	1.41800e12	0.115743
$811$	−1.68670e12	−0.136913	−0.0684565	−	0.997654i	$-0.521807\pi$
$811$	−1.68670e12	−0.136913	−0.0684565	+	0.997654i	$0.521807\pi$
$812$	−5.84609e12	−0.471914
$813$	7.53141e12	0.604601
$814$	−1.82479e13	−1.45681
$815$	−1.31622e13	−1.04501
$816$	3.17520e12	0.250706
$817$	2.02405e13	1.58936
$818$	−3.24840e12	−0.253676
$819$	3.36573e12	0.261398
$820$	−1.04437e13	−0.806661
$821$	2.02395e13	1.55473	0.777365	−	0.629050i	$-0.216556\pi$
$821$	2.02395e13	1.55473	0.777365	+	0.629050i	$0.216556\pi$
$822$	8.04268e12	0.614437
$823$	8.31956e11	0.0632123	0.0316061	−	0.999500i	$-0.489938\pi$
$823$	8.31956e11	0.0632123	0.0316061	+	0.999500i	$0.489938\pi$
$824$	3.75558e12	0.283795
$825$	−1.28901e13	−0.968751
$826$	1.73057e12	0.129354
$827$	1.16197e13	0.863813	0.431906	−	0.901918i	$-0.357841\pi$
$827$	1.16197e13	0.863813	0.431906	+	0.901918i	$0.357841\pi$
$828$	−5.40680e11	−0.0399764
$829$	2.32301e13	1.70827	0.854135	−	0.520051i	$-0.174087\pi$
$829$	2.32301e13	1.70827	0.854135	+	0.520051i	$0.174087\pi$
$830$	−1.26589e13	−0.925857
$831$	−5.41433e12	−0.393858
$832$	−6.85253e12	−0.495788
$833$	2.21340e13	1.59278
$834$	8.10236e12	0.579915
$835$	3.56978e12	0.254128
$836$	1.21461e13	0.860020
$837$	−1.96182e12	−0.138164
$838$	8.07208e12	0.565441
$839$	1.50688e13	1.04990	0.524952	−	0.851132i	$-0.324083\pi$
$839$	1.50688e13	1.04990	0.524952	+	0.851132i	$0.324083\pi$
$840$	−1.81363e13	−1.25688
$841$	−7.75753e12	−0.534738
$842$	−1.23205e13	−0.844739
$843$	−1.44864e13	−0.987955
$844$	3.13465e12	0.212642
$845$	−1.48871e13	−1.00451
$846$	1.38027e12	0.0926395
$847$	−2.37762e13	−1.58733
$848$	2.95553e12	0.196270
$849$	−7.04364e12	−0.465278
$850$	2.07264e13	1.36188
$851$	−5.20079e12	−0.339928
$852$	−7.38625e12	−0.480226
$853$	−2.01905e13	−1.30580	−0.652900	−	0.757444i	$-0.726448\pi$
$853$	−2.01905e13	−1.30580	−0.652900	+	0.757444i	$0.726448\pi$
$854$	−2.11483e13	−1.36055
$855$	−9.07881e12	−0.581007
$856$	1.52334e13	0.969759
$857$	−5.74789e11	−0.0363994	−0.0181997	−	0.999834i	$-0.505793\pi$
$857$	−5.74789e11	−0.0363994	−0.0181997	+	0.999834i	$0.505793\pi$
$858$	5.33927e12	0.336348
$859$	1.93738e13	1.21407	0.607037	−	0.794674i	$-0.292358\pi$
$859$	1.93738e13	1.21407	0.607037	+	0.794674i	$0.292358\pi$
$860$	1.55507e13	0.969407
$861$	1.44747e13	0.897624
$862$	−4.78312e12	−0.295072
$863$	−4.19691e12	−0.257562	−0.128781	−	0.991673i	$-0.541106\pi$
$863$	−4.19691e12	−0.257562	−0.128781	+	0.991673i	$0.541106\pi$
$864$	−2.76618e12	−0.168876
$865$	−2.67476e12	−0.162447
$866$	1.76582e13	1.06688
$867$	−1.71462e13	−1.03058
$868$	8.30674e12	0.496697
$869$	−4.56367e13	−2.71472
$870$	6.93203e12	0.410227
$871$	−1.51474e12	−0.0891775
$872$	1.11545e13	0.653322
$873$	−2.24085e12	−0.130571
$874$	−3.53328e12	−0.204822
$875$	−5.26668e12	−0.303739
$876$	−6.85800e12	−0.393485
$877$	1.32466e13	0.756148	0.378074	−	0.925775i	$-0.376586\pi$
$877$	1.32466e13	0.756148	0.378074	+	0.925775i	$0.376586\pi$
$878$	−1.37342e13	−0.779969
$879$	1.13568e13	0.641659
$880$	−9.91441e12	−0.557308
$881$	2.43165e13	1.35991	0.679955	−	0.733254i	$-0.261999\pi$
$881$	2.43165e13	1.35991	0.679955	+	0.733254i	$0.261999\pi$
$882$	4.06373e12	0.226108
$883$	1.97916e13	1.09562	0.547809	−	0.836604i	$-0.315462\pi$
$883$	1.97916e13	1.09562	0.547809	+	0.836604i	$0.315462\pi$
$884$	8.41137e12	0.463267
$885$	2.01048e12	0.110168
$886$	−5.84757e12	−0.318804
$887$	−5.09160e12	−0.276184	−0.138092	−	0.990419i	$-0.544097\pi$
$887$	−5.09160e12	−0.276184	−0.138092	+	0.990419i	$0.544097\pi$
$888$	−1.59429e13	−0.860416
$889$	−3.76538e13	−2.02186
$890$	1.30174e13	0.695457
$891$	3.05456e12	0.162368
$892$	−2.22163e12	−0.117498
$893$	−8.83722e12	−0.465033
$894$	−1.54807e13	−0.810533
$895$	−1.94687e13	−1.01422
$896$	6.72480e12	0.348573
$897$	1.52173e12	0.0784824
$898$	−4.44823e12	−0.228268
$899$	−9.59058e12	−0.489695
$900$	−3.72825e12	−0.189415
$901$	−2.49010e13	−1.25879
$902$	2.29621e13	1.15500
$903$	−2.15529e13	−1.07872
$904$	2.18512e13	1.08822
$905$	1.31158e13	0.649945
$906$	1.01467e13	0.500320
$907$	3.51115e12	0.172273	0.0861364	−	0.996283i	$-0.472548\pi$
$907$	3.51115e12	0.172273	0.0861364	+	0.996283i	$0.472548\pi$
$908$	−3.55991e12	−0.173801
$909$	−8.27784e12	−0.402142
$910$	1.68984e13	0.816881
$911$	−5.93968e12	−0.285713	−0.142857	−	0.989743i	$-0.545629\pi$
$911$	−5.93968e12	−0.285713	−0.142857	+	0.989743i	$0.545629\pi$
$912$	−3.73242e12	−0.178654
$913$	−2.72689e13	−1.29882
$914$	−4.36786e12	−0.207019
$915$	−2.45689e13	−1.15875
$916$	−1.44125e13	−0.676408
$917$	1.42756e13	0.666703
$918$	−4.91155e12	−0.228258
$919$	−1.16149e12	−0.0537151	−0.0268576	−	0.999639i	$-0.508550\pi$
$919$	−1.16149e12	−0.0537151	−0.0268576	+	0.999639i	$0.508550\pi$
$920$	−8.19991e12	−0.377367
$921$	1.61725e13	0.740645
$922$	9.55016e12	0.435233
$923$	2.07885e13	0.942789
$924$	−1.29336e13	−0.583708
$925$	−3.58620e13	−1.61064
$926$	−3.06366e12	−0.136928
$927$	−2.00189e12	−0.0890391
$928$	−1.35227e13	−0.598548
$929$	−7.37213e12	−0.324730	−0.162365	−	0.986731i	$-0.551912\pi$
$929$	−7.37213e12	−0.324730	−0.162365	+	0.986731i	$0.551912\pi$
$930$	−9.84977e12	−0.431770
$931$	−2.60183e13	−1.13502
$932$	1.94138e13	0.842827
$933$	1.61461e13	0.697589
$934$	−9.92804e12	−0.426877
$935$	8.35312e13	3.57435
$936$	4.66483e12	0.198653
$937$	3.78723e13	1.60507	0.802534	−	0.596606i	$-0.203485\pi$
$937$	3.78723e13	1.60507	0.802534	+	0.596606i	$0.203485\pi$
$938$	−3.74507e12	−0.157960
$939$	1.06252e13	0.446008
$940$	−6.78958e12	−0.283640
$941$	−6.80763e12	−0.283037	−0.141518	−	0.989936i	$-0.545198\pi$
$941$	−6.80763e12	−0.283037	−0.141518	+	0.989936i	$0.545198\pi$
$942$	−1.24117e13	−0.513573
$943$	6.54437e12	0.269504
$944$	8.26533e11	0.0338755
$945$	9.66745e12	0.394338
$946$	−3.41907e13	−1.38803
$947$	−3.21838e12	−0.130036	−0.0650179	−	0.997884i	$-0.520710\pi$
$947$	−3.21838e12	−0.130036	−0.0650179	+	0.997884i	$0.520710\pi$
$948$	−1.31997e13	−0.530796
$949$	1.93017e13	0.772499
$950$	−2.43637e13	−0.970482
$951$	−6.95491e12	−0.275727
$952$	6.28192e13	2.47871
$953$	2.57077e13	1.00959	0.504796	−	0.863239i	$-0.331568\pi$
$953$	2.57077e13	1.00959	0.504796	+	0.863239i	$0.331568\pi$
$954$	−4.57175e12	−0.178696
$955$	4.83345e13	1.88037
$956$	5.97319e11	0.0231284
$957$	1.49325e13	0.575480
$958$	−3.30151e12	−0.126639
$959$	5.48323e13	2.09340
$960$	−1.96827e13	−0.747934
$961$	−1.28123e13	−0.484588
$962$	1.48546e13	0.559209
$963$	−8.12004e12	−0.304256
$964$	1.64066e13	0.611889
$965$	−3.74245e12	−0.138926
$966$	3.76237e12	0.139016
$967$	8.66214e12	0.318571	0.159285	−	0.987233i	$-0.449081\pi$
$967$	8.66214e12	0.318571	0.159285	+	0.987233i	$0.449081\pi$
$968$	−3.29533e13	−1.20631
$969$	3.14465e13	1.14582
$970$	−1.12507e13	−0.408042
$971$	−2.16854e12	−0.0782852	−0.0391426	−	0.999234i	$-0.512463\pi$
$971$	−2.16854e12	−0.0782852	−0.0391426	+	0.999234i	$0.512463\pi$
$972$	8.83486e11	0.0317469
$973$	5.52392e13	1.97579
$974$	−3.04081e13	−1.08262
$975$	1.04931e13	0.371863
$976$	−1.01006e13	−0.356305
$977$	−4.24310e13	−1.48990	−0.744951	−	0.667120i	$-0.767527\pi$
$977$	−4.24310e13	−1.48990	−0.744951	+	0.667120i	$0.767527\pi$
$978$	8.37022e12	0.292558
$979$	2.80413e13	0.975610
$980$	−1.99897e13	−0.692291
$981$	−5.94585e12	−0.204976
$982$	1.63861e13	0.562308
$983$	−5.52491e13	−1.88727	−0.943635	−	0.330987i	$-0.892618\pi$
$983$	−5.52491e13	−1.88727	−0.943635	+	0.330987i	$0.892618\pi$
$984$	2.00616e13	0.682162
$985$	2.23180e13	0.755428
$986$	−2.40106e13	−0.809016
$987$	9.41020e12	0.315625
$988$	−9.88749e12	−0.330126
$989$	−9.74460e12	−0.323878
$990$	1.53361e13	0.507407
$991$	2.15925e13	0.711167	0.355584	−	0.934644i	$-0.384282\pi$
$991$	2.15925e13	0.711167	0.355584	+	0.934644i	$0.384282\pi$
$992$	1.92145e13	0.629981
$993$	6.72801e12	0.219591
$994$	5.13978e13	1.66996
$995$	8.00143e13	2.58800
$996$	−7.88713e12	−0.253952
$997$	3.54323e12	0.113572	0.0567860	−	0.998386i	$-0.481915\pi$
$997$	3.54323e12	0.113572	0.0567860	+	0.998386i	$0.481915\pi$
$998$	2.43807e13	0.777964
$999$	8.49825e12	0.269951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.15	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +32940.9 q^{10} +70959.2 q^{11} +20523.9 q^{12} -57764.1 q^{13} -142817. q^{14} -165917. q^{15} -68210.6 q^{16} +574690. q^{17} +105512. q^{18} -675543. q^{19} -519016. q^{20} +719343. q^{21} +1.14114e6 q^{22} +325234. q^{23} +996995. q^{24} +2.24265e6 q^{25} -928941. q^{26} -531441. q^{27} +2.25022e6 q^{28} -2.59800e6 q^{29} -2.66822e6 q^{30} +3.69152e6 q^{31} +5.20505e6 q^{32} -5.74770e6 q^{33} +9.24195e6 q^{34} -1.81910e7 q^{35} -1.66244e6 q^{36} -1.59909e7 q^{37} -1.08638e7 q^{38} +4.67889e6 q^{39} -2.52124e7 q^{40} +2.01221e7 q^{41} +1.15682e7 q^{42} -2.99619e7 q^{43} -1.79797e7 q^{44} +1.34393e7 q^{45} +5.23028e6 q^{46} +1.30817e7 q^{47} +5.52506e6 q^{48} +3.85146e7 q^{49} +3.60654e7 q^{50} -4.65499e7 q^{51} +1.46364e7 q^{52} -4.33294e7 q^{53} -8.54643e6 q^{54} +1.45350e8 q^{55} +1.09310e8 q^{56} +5.47190e7 q^{57} -4.17801e7 q^{58} -1.21174e7 q^{59} +4.20403e7 q^{60} +1.48079e8 q^{61} +5.93656e7 q^{62} -5.82668e7 q^{63} +1.18630e8 q^{64} -1.18322e8 q^{65} -9.24323e7 q^{66} +2.62228e7 q^{67} -1.45616e8 q^{68} -2.63439e7 q^{69} -2.92541e8 q^{70} -3.59885e8 q^{71} -8.07566e7 q^{72} -3.34147e8 q^{73} -2.57160e8 q^{74} -1.81654e8 q^{75} +1.71170e8 q^{76} -6.30173e8 q^{77} +7.52442e7 q^{78} -6.43140e8 q^{79} -1.39720e8 q^{80} +4.30467e7 q^{81} +3.23596e8 q^{82} -3.84290e8 q^{83} -1.82268e8 q^{84} +1.17717e9 q^{85} -4.81835e8 q^{86} +2.10438e8 q^{87} -8.73407e8 q^{88} +3.95175e8 q^{89} +2.16125e8 q^{90} +5.12990e8 q^{91} -8.24081e7 q^{92} -2.99013e8 q^{93} +2.10374e8 q^{94} -1.38375e9 q^{95} -4.21609e8 q^{96} -3.41540e8 q^{97} +6.19377e8 q^{98} +4.65564e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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