LMFDB - Embedded newform 177.10.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +3356.80 q^{10} -83963.0 q^{11} +40904.4 q^{12} -20968.8 q^{13} +19591.2 q^{14} -102711. q^{15} +251429. q^{16} +236460. q^{17} +17368.6 q^{18} -382997. q^{19} -640348. q^{20} -599447. q^{21} -222271. q^{22} +605458. q^{23} +218071. q^{24} -345212. q^{25} -55509.5 q^{26} -531441. q^{27} -3.73724e6 q^{28} +1.75753e6 q^{29} -271901. q^{30} -2.07730e6 q^{31} +2.04402e6 q^{32} +6.80100e6 q^{33} +625969. q^{34} +9.38420e6 q^{35} -3.31325e6 q^{36} +1.60852e7 q^{37} -1.01389e6 q^{38} +1.69847e6 q^{39} -3.41384e6 q^{40} +3.00304e7 q^{41} -1.58688e6 q^{42} -2.29946e6 q^{43} +4.24007e7 q^{44} +8.31958e6 q^{45} +1.60280e6 q^{46} -6.22537e7 q^{47} -2.03657e7 q^{48} +1.44150e7 q^{49} -913861. q^{50} -1.91533e7 q^{51} +1.05891e7 q^{52} +5.08411e7 q^{53} -1.40686e6 q^{54} -1.06468e8 q^{55} -1.99241e7 q^{56} +3.10228e7 q^{57} +4.65261e6 q^{58} -1.21174e7 q^{59} +5.18682e7 q^{60} +1.27624e8 q^{61} -5.49914e6 q^{62} +4.85552e7 q^{63} -1.23321e8 q^{64} -2.65891e7 q^{65} +1.80039e7 q^{66} +1.93722e7 q^{67} -1.19411e8 q^{68} -4.90421e7 q^{69} +2.48423e7 q^{70} -2.57271e8 q^{71} -1.76637e7 q^{72} -4.11266e8 q^{73} +4.25816e7 q^{74} +2.79622e7 q^{75} +1.93411e8 q^{76} -6.21375e8 q^{77} +4.49627e6 q^{78} +3.74382e7 q^{79} +3.18821e8 q^{80} +4.30467e7 q^{81} +7.94978e7 q^{82} -4.85239e8 q^{83} +3.02716e8 q^{84} +2.99840e8 q^{85} -6.08724e6 q^{86} -1.42360e8 q^{87} +2.26048e8 q^{88} -1.10415e9 q^{89} +2.20240e7 q^{90} -1.55181e8 q^{91} -3.05751e8 q^{92} +1.68262e8 q^{93} -1.64801e8 q^{94} -4.85654e8 q^{95} -1.65565e8 q^{96} -1.73000e8 q^{97} +3.81601e7 q^{98} -5.50881e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.64725	0.116993	0.0584964	−	0.998288i	$-0.481369\pi$
$2$	2.64725	0.116993	0.0584964	+	0.998288i	$0.481369\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−504.992	−0.986313
$5$	1268.04	0.907332	0.453666	−	0.891172i	$-0.350116\pi$
$5$	1268.04	0.907332	0.453666	+	0.891172i	$0.350116\pi$
$6$	−214.427	−0.0675459
$7$	7400.58	1.16500	0.582498	−	0.812832i	$-0.302075\pi$
$7$	7400.58	1.16500	0.582498	+	0.812832i	$0.302075\pi$
$8$	−2692.23	−0.232384
$9$	6561.00	0.333333
$10$	3356.80	0.106151
$11$	−83963.0	−1.72910	−0.864552	−	0.502544i	$-0.832398\pi$
$11$	−83963.0	−1.72910	−0.864552	+	0.502544i	$0.832398\pi$
$12$	40904.4	0.569448
$13$	−20968.8	−0.203623	−0.101812	−	0.994804i	$-0.532464\pi$
$13$	−20968.8	−0.203623	−0.101812	+	0.994804i	$0.532464\pi$
$14$	19591.2	0.136296
$15$	−102711.	−0.523848
$16$	251429.	0.959125
$17$	236460.	0.686655	0.343327	−	0.939216i	$-0.388446\pi$
$17$	236460.	0.686655	0.343327	+	0.939216i	$0.388446\pi$
$18$	17368.6	0.0389976
$19$	−382997.	−0.674225	−0.337112	−	0.941464i	$-0.609450\pi$
$19$	−382997.	−0.674225	−0.337112	+	0.941464i	$0.609450\pi$
$20$	−640348.	−0.894913
$21$	−599447.	−0.672611
$22$	−222271.	−0.202293
$23$	605458.	0.451137	0.225568	−	0.974227i	$-0.427576\pi$
$23$	605458.	0.451137	0.225568	+	0.974227i	$0.427576\pi$
$24$	218071.	0.134167
$25$	−345212.	−0.176749
$26$	−55509.5	−0.0238225
$27$	−531441.	−0.192450
$28$	−3.73724e6	−1.14905
$29$	1.75753e6	0.461436	0.230718	−	0.973021i	$-0.425892\pi$
$29$	1.75753e6	0.461436	0.230718	+	0.973021i	$0.425892\pi$
$30$	−271901.	−0.0612865
$31$	−2.07730e6	−0.403992	−0.201996	−	0.979386i	$-0.564743\pi$
$31$	−2.07730e6	−0.403992	−0.201996	+	0.979386i	$0.564743\pi$
$32$	2.04402e6	0.344595
$33$	6.80100e6	0.998298
$34$	625969.	0.0803337
$35$	9.38420e6	1.05704
$36$	−3.31325e6	−0.328771
$37$	1.60852e7	1.41098	0.705488	−	0.708722i	$-0.250728\pi$
$37$	1.60852e7	1.41098	0.705488	+	0.708722i	$0.250728\pi$
$38$	−1.01389e6	−0.0788795
$39$	1.69847e6	0.117562
$40$	−3.41384e6	−0.210850
$41$	3.00304e7	1.65971	0.829857	−	0.557976i	$-0.188422\pi$
$41$	3.00304e7	1.65971	0.829857	+	0.557976i	$0.188422\pi$
$42$	−1.58688e6	−0.0786907
$43$	−2.29946e6	−0.102570	−0.0512848	−	0.998684i	$-0.516332\pi$
$43$	−2.29946e6	−0.102570	−0.0512848	+	0.998684i	$0.516332\pi$
$44$	4.24007e7	1.70544
$45$	8.31958e6	0.302444
$46$	1.60280e6	0.0527798
$47$	−6.22537e7	−1.86091	−0.930454	−	0.366408i	$-0.880587\pi$
$47$	−6.22537e7	−1.86091	−0.930454	+	0.366408i	$0.880587\pi$
$48$	−2.03657e7	−0.553751
$49$	1.44150e7	0.357218
$50$	−913861.	−0.0206783
$51$	−1.91533e7	−0.396440
$52$	1.05891e7	0.200836
$53$	5.08411e7	0.885062	0.442531	−	0.896753i	$-0.354081\pi$
$53$	5.08411e7	0.885062	0.442531	+	0.896753i	$0.354081\pi$
$54$	−1.40686e6	−0.0225153
$55$	−1.06468e8	−1.56887
$56$	−1.99241e7	−0.270727
$57$	3.10228e7	0.389264
$58$	4.65261e6	0.0539847
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	5.18682e7	0.516678
$61$	1.27624e8	1.18018	0.590088	−	0.807339i	$-0.299093\pi$
$61$	1.27624e8	1.18018	0.590088	+	0.807339i	$0.299093\pi$
$62$	−5.49914e6	−0.0472642
$63$	4.85552e7	0.388332
$64$	−1.23321e8	−0.918810
$65$	−2.65891e7	−0.184754
$66$	1.80039e7	0.116794
$67$	1.93722e7	0.117447	0.0587235	−	0.998274i	$-0.481297\pi$
$67$	1.93722e7	0.117447	0.0587235	+	0.998274i	$0.481297\pi$
$68$	−1.19411e8	−0.677256
$69$	−4.90421e7	−0.260464
$70$	2.48423e7	0.123666
$71$	−2.57271e8	−1.20151	−0.600756	−	0.799432i	$-0.705134\pi$
$71$	−2.57271e8	−1.20151	−0.600756	+	0.799432i	$0.705134\pi$
$72$	−1.76637e7	−0.0774615
$73$	−4.11266e8	−1.69500	−0.847500	−	0.530796i	$-0.821893\pi$
$73$	−4.11266e8	−1.69500	−0.847500	+	0.530796i	$0.821893\pi$
$74$	4.25816e7	0.165074
$75$	2.79622e7	0.102046
$76$	1.93411e8	0.664996
$77$	−6.21375e8	−2.01440
$78$	4.49627e6	0.0137539
$79$	3.74382e7	0.108142	0.0540708	−	0.998537i	$-0.482780\pi$
$79$	3.74382e7	0.108142	0.0540708	+	0.998537i	$0.482780\pi$
$80$	3.18821e8	0.870245
$81$	4.30467e7	0.111111
$82$	7.94978e7	0.194175
$83$	−4.85239e8	−1.12229	−0.561144	−	0.827718i	$-0.689639\pi$
$83$	−4.85239e8	−1.12229	−0.561144	+	0.827718i	$0.689639\pi$
$84$	3.02716e8	0.663405
$85$	2.99840e8	0.623024
$86$	−6.08724e6	−0.0119999
$87$	−1.42360e8	−0.266410
$88$	2.26048e8	0.401817
$89$	−1.10415e9	−1.86540	−0.932701	−	0.360650i	$-0.882555\pi$
$89$	−1.10415e9	−1.86540	−0.932701	+	0.360650i	$0.882555\pi$
$90$	2.20240e7	0.0353838
$91$	−1.55181e8	−0.237221
$92$	−3.05751e8	−0.444962
$93$	1.68262e8	0.233245
$94$	−1.64801e8	−0.217713
$95$	−4.85654e8	−0.611746
$96$	−1.65565e8	−0.198952
$97$	−1.73000e8	−0.198415	−0.0992073	−	0.995067i	$-0.531631\pi$
$97$	−1.73000e8	−0.198415	−0.0992073	+	0.995067i	$0.531631\pi$
$98$	3.81601e7	0.0417919
$99$	−5.50881e8	−0.576368
$100$	1.74329e8	0.174329
$101$	−1.52660e8	−0.145975	−0.0729877	−	0.997333i	$-0.523253\pi$
$101$	−1.52660e8	−0.145975	−0.0729877	+	0.997333i	$0.523253\pi$
$102$	−5.07035e7	−0.0463807
$103$	6.75584e8	0.591441	0.295721	−	0.955274i	$-0.404440\pi$
$103$	6.75584e8	0.591441	0.295721	+	0.955274i	$0.404440\pi$
$104$	5.64527e7	0.0473189
$105$	−7.60120e8	−0.610282
$106$	1.34589e8	0.103546
$107$	1.71946e8	0.126813	0.0634067	−	0.997988i	$-0.479803\pi$
$107$	1.71946e8	0.126813	0.0634067	+	0.997988i	$0.479803\pi$
$108$	2.68373e8	0.189816
$109$	−2.23617e9	−1.51735	−0.758675	−	0.651469i	$-0.774153\pi$
$109$	−2.23617e9	−1.51735	−0.758675	+	0.651469i	$0.774153\pi$
$110$	−2.81847e8	−0.183547
$111$	−1.30290e9	−0.814628
$112$	1.86072e9	1.11738
$113$	1.03949e9	0.599746	0.299873	−	0.953979i	$-0.403056\pi$
$113$	1.03949e9	0.599746	0.299873	+	0.953979i	$0.403056\pi$
$114$	8.21250e7	0.0455411
$115$	7.67741e8	0.409331
$116$	−8.87539e8	−0.455120
$117$	−1.37576e8	−0.0678745
$118$	−3.20776e7	−0.0152312
$119$	1.74995e9	0.799950
$120$	2.76521e8	0.121734
$121$	4.69184e9	1.98980
$122$	3.37851e8	0.138072
$123$	−2.43246e9	−0.958236
$124$	1.04902e9	0.398462
$125$	−2.91437e9	−1.06770
$126$	1.28538e8	0.0454321
$127$	−5.55509e8	−0.189485	−0.0947424	−	0.995502i	$-0.530203\pi$
$127$	−5.55509e8	−0.189485	−0.0947424	+	0.995502i	$0.530203\pi$
$128$	−1.37300e9	−0.452089
$129$	1.86256e8	0.0592185
$130$	−7.03880e7	−0.0216149
$131$	−5.56674e9	−1.65151	−0.825753	−	0.564032i	$-0.809250\pi$
$131$	−5.56674e9	−1.65151	−0.825753	+	0.564032i	$0.809250\pi$
$132$	−3.43445e9	−0.984634
$133$	−2.83440e9	−0.785470
$134$	5.12829e7	0.0137405
$135$	−6.73886e8	−0.174616
$136$	−6.36606e8	−0.159568
$137$	4.06140e9	0.984994	0.492497	−	0.870314i	$-0.336084\pi$
$137$	4.06140e9	0.984994	0.492497	+	0.870314i	$0.336084\pi$
$138$	−1.29826e8	−0.0304724
$139$	−6.88552e9	−1.56448	−0.782240	−	0.622977i	$-0.785923\pi$
$139$	−6.88552e9	−1.56448	−0.782240	+	0.622977i	$0.785923\pi$
$140$	−4.73895e9	−1.04257
$141$	5.04255e9	1.07440
$142$	−6.81060e8	−0.140568
$143$	1.76060e9	0.352086
$144$	1.64963e9	0.319708
$145$	2.22861e9	0.418676
$146$	−1.08872e9	−0.198303
$147$	−1.16762e9	−0.206240
$148$	−8.12292e9	−1.39166
$149$	4.91341e8	0.0816667	0.0408333	−	0.999166i	$-0.486999\pi$
$149$	4.91341e8	0.0816667	0.0408333	+	0.999166i	$0.486999\pi$
$150$	7.40228e7	0.0119386
$151$	−2.31149e9	−0.361822	−0.180911	−	0.983499i	$-0.557905\pi$
$151$	−2.31149e9	−0.361822	−0.180911	+	0.983499i	$0.557905\pi$
$152$	1.03112e9	0.156679
$153$	1.55142e9	0.228885
$154$	−1.64493e9	−0.235670
$155$	−2.63410e9	−0.366555
$156$	−8.57714e8	−0.115953
$157$	−3.56376e9	−0.468123	−0.234061	−	0.972222i	$-0.575202\pi$
$157$	−3.56376e9	−0.468123	−0.234061	+	0.972222i	$0.575202\pi$
$158$	9.91081e7	0.0126518
$159$	−4.11813e9	−0.510991
$160$	2.59188e9	0.312662
$161$	4.48074e9	0.525573
$162$	1.13955e8	0.0129992
$163$	5.02224e9	0.557254	0.278627	−	0.960399i	$-0.410121\pi$
$163$	5.02224e9	0.557254	0.278627	+	0.960399i	$0.410121\pi$
$164$	−1.51651e10	−1.63700
$165$	8.62391e9	0.905788
$166$	−1.28455e9	−0.131300
$167$	9.65049e9	0.960120	0.480060	−	0.877236i	$-0.340615\pi$
$167$	9.65049e9	0.960120	0.480060	+	0.877236i	$0.340615\pi$
$168$	1.61385e9	0.156304
$169$	−1.01648e10	−0.958537
$170$	7.93751e8	0.0728893
$171$	−2.51285e9	−0.224742
$172$	1.16121e9	0.101166
$173$	−1.56297e10	−1.32661	−0.663305	−	0.748349i	$-0.730847\pi$
$173$	−1.56297e10	−1.32661	−0.663305	+	0.748349i	$0.730847\pi$
$174$	−3.76862e8	−0.0311681
$175$	−2.55477e9	−0.205912
$176$	−2.11107e10	−1.65843
$177$	9.81506e8	0.0751646
$178$	−2.92295e9	−0.218239
$179$	8.44559e9	0.614881	0.307441	−	0.951567i	$-0.400527\pi$
$179$	8.44559e9	0.614881	0.307441	+	0.951567i	$0.400527\pi$
$180$	−4.20132e9	−0.298304
$181$	−2.04552e10	−1.41661	−0.708304	−	0.705907i	$-0.750539\pi$
$181$	−2.04552e10	−1.41661	−0.708304	+	0.705907i	$0.750539\pi$
$182$	−4.10803e8	−0.0277531
$183$	−1.03375e10	−0.681375
$184$	−1.63003e9	−0.104837
$185$	2.03966e10	1.28022
$186$	4.45430e8	0.0272880
$187$	−1.98539e10	−1.18730
$188$	3.14376e10	1.83544
$189$	−3.93297e9	−0.224204
$190$	−1.28565e9	−0.0715699
$191$	−1.10483e10	−0.600681	−0.300341	−	0.953832i	$-0.597100\pi$
$191$	−1.10483e10	−0.600681	−0.300341	+	0.953832i	$0.597100\pi$
$192$	9.98897e9	0.530475
$193$	3.46522e9	0.179772	0.0898862	−	0.995952i	$-0.471350\pi$
$193$	3.46522e9	0.179772	0.0898862	+	0.995952i	$0.471350\pi$
$194$	−4.57974e8	−0.0232131
$195$	2.15372e9	0.106668
$196$	−7.27947e9	−0.352328
$197$	2.42596e10	1.14759	0.573795	−	0.818999i	$-0.305471\pi$
$197$	2.42596e10	1.14759	0.573795	+	0.818999i	$0.305471\pi$
$198$	−1.45832e9	−0.0674309
$199$	−3.35206e10	−1.51521	−0.757605	−	0.652713i	$-0.773631\pi$
$199$	−3.35206e10	−1.51521	−0.757605	+	0.652713i	$0.773631\pi$
$200$	9.29390e8	0.0410736
$201$	−1.56915e9	−0.0678080
$202$	−4.04129e8	−0.0170781
$203$	1.30067e10	0.537572
$204$	9.67226e9	0.391014
$205$	3.80795e10	1.50591
$206$	1.78844e9	0.0691944
$207$	3.97241e9	0.150379
$208$	−5.27216e9	−0.195300
$209$	3.21576e10	1.16580
$210$	−2.01223e9	−0.0713986
$211$	2.65185e10	0.921039	0.460520	−	0.887650i	$-0.347663\pi$
$211$	2.65185e10	0.921039	0.460520	+	0.887650i	$0.347663\pi$
$212$	−2.56744e10	−0.872948
$213$	2.08389e10	0.693693
$214$	4.55183e8	0.0148363
$215$	−2.91580e9	−0.0930646
$216$	1.43076e9	0.0447224
$217$	−1.53733e10	−0.470649
$218$	−5.91970e9	−0.177519
$219$	3.33125e10	0.978609
$220$	5.37655e10	1.54740
$221$	−4.95828e9	−0.139819
$222$	−3.44911e9	−0.0953056
$223$	−2.56391e10	−0.694273	−0.347137	−	0.937815i	$-0.612846\pi$
$223$	−2.56391e10	−0.694273	−0.347137	+	0.937815i	$0.612846\pi$
$224$	1.51269e10	0.401452
$225$	−2.26494e9	−0.0589162
$226$	2.75179e9	0.0701660
$227$	3.49072e8	0.00872567	0.00436283	−	0.999990i	$-0.498611\pi$
$227$	3.49072e8	0.00872567	0.00436283	+	0.999990i	$0.498611\pi$
$228$	−1.56663e10	−0.383936
$229$	−4.41360e10	−1.06055	−0.530277	−	0.847824i	$-0.677912\pi$
$229$	−4.41360e10	−1.06055	−0.530277	+	0.847824i	$0.677912\pi$
$230$	2.03240e9	0.0478888
$231$	5.03314e10	1.16301
$232$	−4.73167e9	−0.107231
$233$	−7.72944e9	−0.171809	−0.0859046	−	0.996303i	$-0.527378\pi$
$233$	−7.72944e9	−0.171809	−0.0859046	+	0.996303i	$0.527378\pi$
$234$	−3.64198e8	−0.00794083
$235$	−7.89399e10	−1.68846
$236$	6.11917e9	0.128407
$237$	−3.03249e9	−0.0624356
$238$	4.63254e9	0.0935885
$239$	−5.40150e10	−1.07084	−0.535419	−	0.844587i	$-0.679846\pi$
$239$	−5.40150e10	−1.07084	−0.535419	+	0.844587i	$0.679846\pi$
$240$	−2.58245e10	−0.502436
$241$	3.72961e10	0.712174	0.356087	−	0.934453i	$-0.384111\pi$
$241$	3.72961e10	0.712174	0.356087	+	0.934453i	$0.384111\pi$
$242$	1.24205e10	0.232792
$243$	−3.48678e9	−0.0641500
$244$	−6.44489e10	−1.16402
$245$	1.82788e10	0.324115
$246$	−6.43932e9	−0.112107
$247$	8.03099e9	0.137288
$248$	5.59258e9	0.0938814
$249$	3.93043e10	0.647953
$250$	−7.71506e9	−0.124913
$251$	−3.71733e10	−0.591153	−0.295576	−	0.955319i	$-0.595512\pi$
$251$	−3.71733e10	−0.591153	−0.295576	+	0.955319i	$0.595512\pi$
$252$	−2.45200e10	−0.383017
$253$	−5.08360e10	−0.780063
$254$	−1.47057e9	−0.0221684
$255$	−2.42870e10	−0.359703
$256$	5.95055e10	0.865919
$257$	−2.50707e10	−0.358481	−0.179241	−	0.983805i	$-0.557364\pi$
$257$	−2.50707e10	−0.358481	−0.179241	+	0.983805i	$0.557364\pi$
$258$	4.93067e8	0.00692815
$259$	1.19040e11	1.64378
$260$	1.34273e10	0.182225
$261$	1.15312e10	0.153812
$262$	−1.47365e10	−0.193214
$263$	−3.73057e10	−0.480811	−0.240405	−	0.970673i	$-0.577280\pi$
$263$	−3.73057e10	−0.480811	−0.240405	+	0.970673i	$0.577280\pi$
$264$	−1.83099e10	−0.231989
$265$	6.44683e10	0.803045
$266$	−7.50337e9	−0.0918944
$267$	8.94361e10	1.07699
$268$	−9.78279e9	−0.115839
$269$	−9.05863e10	−1.05482	−0.527409	−	0.849612i	$-0.676836\pi$
$269$	−9.05863e10	−1.05482	−0.527409	+	0.849612i	$0.676836\pi$
$270$	−1.78394e9	−0.0204288
$271$	1.37795e11	1.55193	0.775963	−	0.630778i	$-0.217264\pi$
$271$	1.37795e11	1.55193	0.775963	+	0.630778i	$0.217264\pi$
$272$	5.94530e10	0.658588
$273$	1.25697e10	0.136959
$274$	1.07515e10	0.115237
$275$	2.89850e10	0.305617
$276$	2.47659e10	0.256899
$277$	1.13941e11	1.16284	0.581420	−	0.813603i	$-0.302497\pi$
$277$	1.13941e11	1.16284	0.581420	+	0.813603i	$0.302497\pi$
$278$	−1.82277e10	−0.183033
$279$	−1.36292e10	−0.134664
$280$	−2.52644e10	−0.245639
$281$	−7.38986e9	−0.0707062	−0.0353531	−	0.999375i	$-0.511256\pi$
$281$	−7.38986e9	−0.0707062	−0.0353531	+	0.999375i	$0.511256\pi$
$282$	1.33489e10	0.125697
$283$	1.41655e11	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$283$	1.41655e11	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$284$	1.29920e11	1.18507
$285$	3.93380e10	0.353192
$286$	4.66075e9	0.0411916
$287$	2.22242e11	1.93356
$288$	1.34108e10	0.114865
$289$	−6.26743e10	−0.528505
$290$	5.89968e9	0.0489821
$291$	1.40130e10	0.114555
$292$	2.07686e11	1.67180
$293$	4.52982e10	0.359068	0.179534	−	0.983752i	$-0.442541\pi$
$293$	4.52982e10	0.359068	0.179534	+	0.983752i	$0.442541\pi$
$294$	−3.09097e9	−0.0241286
$295$	−1.53652e10	−0.118125
$296$	−4.33051e10	−0.327889
$297$	4.46214e10	0.332766
$298$	1.30070e9	0.00955442
$299$	−1.26957e10	−0.0918621
$300$	−1.41207e10	−0.100649
$301$	−1.70174e10	−0.119493
$302$	−6.11908e9	−0.0423306
$303$	1.23655e10	0.0842789
$304$	−9.62967e10	−0.646666
$305$	1.61831e11	1.07081
$306$	4.10698e9	0.0267779
$307$	−1.00284e11	−0.644332	−0.322166	−	0.946683i	$-0.604411\pi$
$307$	−1.00284e11	−0.644332	−0.322166	+	0.946683i	$0.604411\pi$
$308$	3.13790e11	1.98683
$309$	−5.47223e10	−0.341469
$310$	−6.97310e9	−0.0428843
$311$	−6.47700e10	−0.392602	−0.196301	−	0.980544i	$-0.562893\pi$
$311$	−6.47700e10	−0.392602	−0.196301	+	0.980544i	$0.562893\pi$
$312$	−4.57267e9	−0.0273196
$313$	−3.40302e10	−0.200408	−0.100204	−	0.994967i	$-0.531950\pi$
$313$	−3.40302e10	−0.200408	−0.100204	+	0.994967i	$0.531950\pi$
$314$	−9.43415e9	−0.0547670
$315$	6.15697e10	0.352346
$316$	−1.89060e10	−0.106661
$317$	1.62420e11	0.903383	0.451692	−	0.892174i	$-0.350821\pi$
$317$	1.62420e11	0.903383	0.451692	+	0.892174i	$0.350821\pi$
$318$	−1.09017e10	−0.0597823
$319$	−1.47567e11	−0.797871
$320$	−1.56375e11	−0.833666
$321$	−1.39276e10	−0.0732157
$322$	1.18616e10	0.0614883
$323$	−9.05637e10	−0.462960
$324$	−2.17383e10	−0.109590
$325$	7.23867e9	0.0359902
$326$	1.32951e10	0.0651948
$327$	1.81130e11	0.876043
$328$	−8.08486e10	−0.385692
$329$	−4.60714e11	−2.16795
$330$	2.28296e10	0.105971
$331$	−1.18427e11	−0.542281	−0.271141	−	0.962540i	$-0.587401\pi$
$331$	−1.18427e11	−0.542281	−0.271141	+	0.962540i	$0.587401\pi$
$332$	2.45042e11	1.10693
$333$	1.05535e11	0.470325
$334$	2.55472e10	0.112327
$335$	2.45646e10	0.106563
$336$	−1.50718e11	−0.645118
$337$	−3.82790e11	−1.61669	−0.808343	−	0.588712i	$-0.799635\pi$
$337$	−3.82790e11	−1.61669	−0.808343	+	0.588712i	$0.799635\pi$
$338$	−2.69088e10	−0.112142
$339$	−8.41987e10	−0.346264
$340$	−1.51417e11	−0.614496
$341$	1.74417e11	0.698544
$342$	−6.65212e9	−0.0262932
$343$	−1.91961e11	−0.748839
$344$	6.19068e9	0.0238356
$345$	−6.21871e10	−0.236327
$346$	−4.13757e10	−0.155204
$347$	3.70788e11	1.37291	0.686457	−	0.727170i	$-0.259165\pi$
$347$	3.70788e11	1.37291	0.686457	+	0.727170i	$0.259165\pi$
$348$	7.18906e10	0.262764
$349$	−2.96796e11	−1.07089	−0.535444	−	0.844571i	$-0.679856\pi$
$349$	−2.96796e11	−1.07089	−0.535444	+	0.844571i	$0.679856\pi$
$350$	−6.76311e9	−0.0240902
$351$	1.11437e10	0.0391874
$352$	−1.71622e11	−0.595841
$353$	−6.71934e8	−0.00230325	−0.00115162	−	0.999999i	$-0.500367\pi$
$353$	−6.71934e8	−0.00230325	−0.00115162	+	0.999999i	$0.500367\pi$
$354$	2.59829e9	0.00879372
$355$	−3.26229e11	−1.09017
$356$	5.57586e11	1.83987
$357$	−1.41746e11	−0.461852
$358$	2.23576e10	0.0719367
$359$	−1.03830e11	−0.329912	−0.164956	−	0.986301i	$-0.552748\pi$
$359$	−1.03830e11	−0.329912	−0.164956	+	0.986301i	$0.552748\pi$
$360$	−2.23982e10	−0.0702833
$361$	−1.76001e11	−0.545421
$362$	−5.41499e10	−0.165733
$363$	−3.80039e11	−1.14881
$364$	7.83652e10	0.233974
$365$	−5.21499e11	−1.53793
$366$	−2.73659e10	−0.0797160
$367$	−1.97639e11	−0.568689	−0.284344	−	0.958722i	$-0.591776\pi$
$367$	−1.97639e11	−0.568689	−0.284344	+	0.958722i	$0.591776\pi$
$368$	1.52230e11	0.432697
$369$	1.97029e11	0.553238
$370$	5.39950e10	0.149777
$371$	3.76254e11	1.03109
$372$	−8.49708e10	−0.230052
$373$	5.84644e11	1.56387	0.781937	−	0.623358i	$-0.214232\pi$
$373$	5.84644e11	1.56387	0.781937	+	0.623358i	$0.214232\pi$
$374$	−5.25583e10	−0.138905
$375$	2.36064e11	0.616438
$376$	1.67601e11	0.432446
$377$	−3.68532e10	−0.0939592
$378$	−1.04115e10	−0.0262302
$379$	−3.90824e11	−0.972982	−0.486491	−	0.873686i	$-0.661723\pi$
$379$	−3.90824e11	−0.972982	−0.486491	+	0.873686i	$0.661723\pi$
$380$	2.45252e11	0.603373
$381$	4.49962e10	0.109399
$382$	−2.92475e10	−0.0702754
$383$	−3.50848e11	−0.833152	−0.416576	−	0.909101i	$-0.636770\pi$
$383$	−3.50848e11	−0.833152	−0.416576	+	0.909101i	$0.636770\pi$
$384$	1.11213e11	0.261014
$385$	−7.87926e11	−1.82773
$386$	9.17329e9	0.0210321
$387$	−1.50868e10	−0.0341898
$388$	8.73637e10	0.195699
$389$	−4.73630e11	−1.04874	−0.524368	−	0.851492i	$-0.675698\pi$
$389$	−4.73630e11	−1.04874	−0.524368	+	0.851492i	$0.675698\pi$
$390$	5.70143e9	0.0124794
$391$	1.43167e11	0.309775
$392$	−3.88085e10	−0.0830118
$393$	4.50906e11	0.953498
$394$	6.42213e10	0.134260
$395$	4.74729e10	0.0981204
$396$	2.78191e11	0.568479
$397$	4.00573e11	0.809327	0.404664	−	0.914466i	$-0.367389\pi$
$397$	4.00573e11	0.809327	0.404664	+	0.914466i	$0.367389\pi$
$398$	−8.87373e10	−0.177269
$399$	2.29587e11	0.453491
$400$	−8.67963e10	−0.169524
$401$	−5.08723e10	−0.0982497	−0.0491249	−	0.998793i	$-0.515643\pi$
$401$	−5.08723e10	−0.0982497	−0.0491249	+	0.998793i	$0.515643\pi$
$402$	−4.15392e9	−0.00793305
$403$	4.35585e10	0.0822622
$404$	7.70922e10	0.143977
$405$	5.45848e10	0.100815
$406$	3.44321e10	0.0628921
$407$	−1.35057e12	−2.43972
$408$	5.15650e10	0.0921265
$409$	−1.01888e12	−1.80040	−0.900201	−	0.435475i	$-0.856581\pi$
$409$	−1.01888e12	−1.80040	−0.900201	+	0.435475i	$0.856581\pi$
$410$	1.00806e11	0.176181
$411$	−3.28974e11	−0.568687
$412$	−3.41164e11	−0.583346
$413$	−8.96755e10	−0.151670
$414$	1.05159e10	0.0175933
$415$	−6.15300e11	−1.01829
$416$	−4.28605e10	−0.0701677
$417$	5.57727e11	0.903253
$418$	8.51292e10	0.136391
$419$	6.31480e11	1.00091	0.500457	−	0.865762i	$-0.333166\pi$
$419$	6.31480e11	1.00091	0.500457	+	0.865762i	$0.333166\pi$
$420$	3.83855e11	0.601929
$421$	1.07466e12	1.66725	0.833627	−	0.552328i	$-0.186260\pi$
$421$	1.07466e12	1.66725	0.833627	+	0.552328i	$0.186260\pi$
$422$	7.02010e10	0.107755
$423$	−4.08447e11	−0.620303
$424$	−1.36876e11	−0.205675
$425$	−8.16290e10	−0.121365
$426$	5.51658e10	0.0811572
$427$	9.44489e11	1.37490
$428$	−8.68313e10	−0.125078
$429$	−1.42609e11	−0.203277
$430$	−7.71884e9	−0.0108879
$431$	8.34208e11	1.16446	0.582232	−	0.813022i	$-0.302179\pi$
$431$	8.34208e11	1.16446	0.582232	+	0.813022i	$0.302179\pi$
$432$	−1.33620e11	−0.184584
$433$	−2.77552e11	−0.379445	−0.189722	−	0.981838i	$-0.560759\pi$
$433$	−2.77552e11	−0.379445	−0.189722	+	0.981838i	$0.560759\pi$
$434$	−4.06968e10	−0.0550626
$435$	−1.80517e11	−0.241723
$436$	1.12925e12	1.49658
$437$	−2.31889e11	−0.304168
$438$	8.81865e10	0.114490
$439$	−1.24198e12	−1.59597	−0.797985	−	0.602677i	$-0.794101\pi$
$439$	−1.24198e12	−1.59597	−0.797985	+	0.602677i	$0.794101\pi$
$440$	2.86636e11	0.364581
$441$	9.45769e10	0.119073
$442$	−1.31258e10	−0.0163578
$443$	1.30548e12	1.61048	0.805238	−	0.592952i	$-0.202038\pi$
$443$	1.30548e12	1.61048	0.805238	+	0.592952i	$0.202038\pi$
$444$	6.57956e11	0.803478
$445$	−1.40010e12	−1.69254
$446$	−6.78729e10	−0.0812250
$447$	−3.97986e10	−0.0471503
$448$	−9.12644e11	−1.07041
$449$	1.24776e11	0.144885	0.0724423	−	0.997373i	$-0.476921\pi$
$449$	1.24776e11	0.144885	0.0724423	+	0.997373i	$0.476921\pi$
$450$	−5.99584e9	−0.00689277
$451$	−2.52144e12	−2.86982
$452$	−5.24934e11	−0.591537
$453$	1.87230e11	0.208898
$454$	9.24079e8	0.00102084
$455$	−1.96775e11	−0.215238
$456$	−8.35205e10	−0.0904589
$457$	−2.00971e11	−0.215532	−0.107766	−	0.994176i	$-0.534370\pi$
$457$	−2.00971e11	−0.215532	−0.107766	+	0.994176i	$0.534370\pi$
$458$	−1.16839e11	−0.124077
$459$	−1.25665e11	−0.132147
$460$	−3.87703e11	−0.403728
$461$	5.94860e11	0.613424	0.306712	−	0.951802i	$-0.400771\pi$
$461$	5.94860e11	0.613424	0.306712	+	0.951802i	$0.400771\pi$
$462$	1.33240e11	0.136064
$463$	−1.77212e12	−1.79217	−0.896086	−	0.443880i	$-0.853602\pi$
$463$	−1.77212e12	−1.79217	−0.896086	+	0.443880i	$0.853602\pi$
$464$	4.41894e11	0.442575
$465$	2.13362e11	0.211630
$466$	−2.04617e10	−0.0201004
$467$	−3.70502e11	−0.360466	−0.180233	−	0.983624i	$-0.557685\pi$
$467$	−3.70502e11	−0.360466	−0.180233	+	0.983624i	$0.557685\pi$
$468$	6.94748e10	0.0669455
$469$	1.43365e11	0.136825
$470$	−2.08973e11	−0.197538
$471$	2.88664e11	0.270271
$472$	3.26227e10	0.0302539
$473$	1.93070e11	0.177353
$474$	−8.02776e9	−0.00730452
$475$	1.32215e11	0.119168
$476$	−8.83708e11	−0.789001
$477$	3.33568e11	0.295021
$478$	−1.42991e11	−0.125280
$479$	1.99610e12	1.73249	0.866247	−	0.499616i	$-0.166526\pi$
$479$	1.99610e12	1.73249	0.866247	+	0.499616i	$0.166526\pi$
$480$	−2.09943e11	−0.180516
$481$	−3.37288e11	−0.287308
$482$	9.87319e10	0.0833193
$483$	−3.62940e11	−0.303440
$484$	−2.36934e12	−1.96256
$485$	−2.19370e11	−0.180028
$486$	−9.23038e9	−0.00750510
$487$	1.94904e12	1.57015	0.785074	−	0.619402i	$-0.212625\pi$
$487$	1.94904e12	1.57015	0.785074	+	0.619402i	$0.212625\pi$
$488$	−3.43592e11	−0.274254
$489$	−4.06801e11	−0.321731
$490$	4.83884e10	0.0379191
$491$	−1.65894e12	−1.28814	−0.644071	−	0.764966i	$-0.722756\pi$
$491$	−1.65894e12	−1.28814	−0.644071	+	0.764966i	$0.722756\pi$
$492$	1.22837e12	0.945120
$493$	4.15586e11	0.316847
$494$	2.12600e10	0.0160617
$495$	−6.98537e11	−0.522957
$496$	−5.22295e11	−0.387479
$497$	−1.90395e12	−1.39976
$498$	1.04048e11	0.0758059
$499$	2.60326e11	0.187960	0.0939800	−	0.995574i	$-0.470041\pi$
$499$	2.60326e11	0.187960	0.0939800	+	0.995574i	$0.470041\pi$
$500$	1.47173e12	1.05309
$501$	−7.81690e11	−0.554325
$502$	−9.84070e10	−0.0691607
$503$	5.42560e10	0.0377913	0.0188956	−	0.999821i	$-0.493985\pi$
$503$	5.42560e10	0.0377913	0.0188956	+	0.999821i	$0.493985\pi$
$504$	−1.30722e11	−0.0902424
$505$	−1.93579e11	−0.132448
$506$	−1.34576e11	−0.0912617
$507$	8.23350e11	0.553412
$508$	2.80528e11	0.186891
$509$	−1.84767e12	−1.22009	−0.610047	−	0.792365i	$-0.708849\pi$
$509$	−1.84767e12	−1.22009	−0.610047	+	0.792365i	$0.708849\pi$
$510$	−6.42938e10	−0.0420827
$511$	−3.04361e12	−1.97467
$512$	8.60500e11	0.553396
$513$	2.03541e11	0.129755
$514$	−6.63682e10	−0.0419398
$515$	8.56664e11	0.536634
$516$	−9.40581e10	−0.0584080
$517$	5.22701e12	3.21770
$518$	3.15129e11	0.192311
$519$	1.26601e12	0.765918
$520$	7.15840e10	0.0429340
$521$	2.95733e12	1.75845	0.879224	−	0.476408i	$-0.158062\pi$
$521$	2.95733e12	1.75845	0.879224	+	0.476408i	$0.158062\pi$
$522$	3.05258e10	0.0179949
$523$	−7.77640e11	−0.454486	−0.227243	−	0.973838i	$-0.572971\pi$
$523$	−7.77640e11	−0.454486	−0.227243	+	0.973838i	$0.572971\pi$
$524$	2.81116e12	1.62890
$525$	2.06936e11	0.118883
$526$	−9.87574e10	−0.0562514
$527$	−4.91200e11	−0.277403
$528$	1.70997e12	0.957493
$529$	−1.43457e12	−0.796475
$530$	1.70663e11	0.0939505
$531$	−7.95020e10	−0.0433963
$532$	1.43135e12	0.774719
$533$	−6.29700e11	−0.337957
$534$	2.36759e11	0.126000
$535$	2.18033e11	0.115062
$536$	−5.21543e10	−0.0272928
$537$	−6.84093e11	−0.355002
$538$	−2.39804e11	−0.123406
$539$	−1.21033e12	−0.617666
$540$	3.40307e11	0.172226
$541$	−2.42887e12	−1.21904	−0.609518	−	0.792772i	$-0.708637\pi$
$541$	−2.42887e12	−1.21904	−0.609518	+	0.792772i	$0.708637\pi$
$542$	3.64777e11	0.181564
$543$	1.65687e12	0.817879
$544$	4.83329e11	0.236618
$545$	−2.83554e12	−1.37674
$546$	3.32750e10	0.0160233
$547$	−1.71049e12	−0.816915	−0.408458	−	0.912777i	$-0.633933\pi$
$547$	−1.71049e12	−0.816915	−0.408458	+	0.912777i	$0.633933\pi$
$548$	−2.05098e12	−0.971512
$549$	8.37338e11	0.393392
$550$	7.67306e10	0.0357550
$551$	−6.73129e11	−0.311112
$552$	1.32032e11	0.0605278
$553$	2.77064e11	0.125985
$554$	3.01629e11	0.136044
$555$	−1.65213e12	−0.739138
$556$	3.47713e12	1.54307
$557$	2.43566e12	1.07218	0.536090	−	0.844161i	$-0.319901\pi$
$557$	2.43566e12	1.07218	0.536090	+	0.844161i	$0.319901\pi$
$558$	−3.60798e10	−0.0157547
$559$	4.82169e10	0.0208856
$560$	2.35946e12	1.01383
$561$	1.60817e12	0.685486
$562$	−1.95628e10	−0.00827212
$563$	3.00333e12	1.25984	0.629920	−	0.776660i	$-0.283088\pi$
$563$	3.00333e12	1.25984	0.629920	+	0.776660i	$0.283088\pi$
$564$	−2.54645e12	−1.05969
$565$	1.31811e12	0.544169
$566$	3.74996e11	0.153586
$567$	3.18571e11	0.129444
$568$	6.92632e11	0.279213
$569$	−1.16306e12	−0.465154	−0.232577	−	0.972578i	$-0.574716\pi$
$569$	−1.16306e12	−0.465154	−0.232577	+	0.972578i	$0.574716\pi$
$570$	1.04137e11	0.0413209
$571$	−1.84040e12	−0.724520	−0.362260	−	0.932077i	$-0.617995\pi$
$571$	−1.84040e12	−0.724520	−0.362260	+	0.932077i	$0.617995\pi$
$572$	−8.89090e11	−0.347267
$573$	8.94910e11	0.346803
$574$	5.88330e11	0.226213
$575$	−2.09011e11	−0.0797378
$576$	−8.09107e11	−0.306270
$577$	1.75431e12	0.658893	0.329447	−	0.944174i	$-0.393138\pi$
$577$	1.75431e12	0.658893	0.329447	+	0.944174i	$0.393138\pi$
$578$	−1.65914e11	−0.0618314
$579$	−2.80683e11	−0.103792
$580$	−1.12543e12	−0.412945
$581$	−3.59105e12	−1.30746
$582$	3.70959e10	0.0134021
$583$	−4.26877e12	−1.53036
$584$	1.10722e12	0.393892
$585$	−1.74451e11	−0.0615847
$586$	1.19915e11	0.0420084
$587$	3.10713e12	1.08016	0.540079	−	0.841614i	$-0.318394\pi$
$587$	3.10713e12	1.08016	0.540079	+	0.841614i	$0.318394\pi$
$588$	5.89637e11	0.203417
$589$	7.95603e11	0.272381
$590$	−4.06756e10	−0.0138197
$591$	−1.96503e12	−0.662561
$592$	4.04430e12	1.35330
$593$	5.13068e12	1.70384	0.851919	−	0.523673i	$-0.175439\pi$
$593$	5.13068e12	1.70384	0.851919	+	0.523673i	$0.175439\pi$
$594$	1.18124e11	0.0389313
$595$	2.21899e12	0.725821
$596$	−2.48123e11	−0.0805489
$597$	2.71517e12	0.874807
$598$	−3.36086e10	−0.0107472
$599$	3.74232e12	1.18774	0.593869	−	0.804562i	$-0.297600\pi$
$599$	3.74232e12	1.18774	0.593869	+	0.804562i	$0.297600\pi$
$600$	−7.52806e10	−0.0237139
$601$	2.89651e12	0.905606	0.452803	−	0.891611i	$-0.350424\pi$
$601$	2.89651e12	0.905606	0.452803	+	0.891611i	$0.350424\pi$
$602$	−4.50492e10	−0.0139798
$603$	1.27101e11	0.0391490
$604$	1.16728e12	0.356870
$605$	5.94942e12	1.80541
$606$	3.27345e10	0.00986003
$607$	4.39157e12	1.31302	0.656509	−	0.754318i	$-0.272033\pi$
$607$	4.39157e12	1.31302	0.656509	+	0.754318i	$0.272033\pi$
$608$	−7.82853e11	−0.232335
$609$	−1.05355e12	−0.310367
$610$	4.28407e11	0.125277
$611$	1.30538e12	0.378925
$612$	−7.83453e11	−0.225752
$613$	4.73516e12	1.35445	0.677225	−	0.735776i	$-0.263182\pi$
$613$	4.73516e12	1.35445	0.677225	+	0.735776i	$0.263182\pi$
$614$	−2.65477e11	−0.0753823
$615$	−3.08444e12	−0.869438
$616$	1.67288e12	0.468115
$617$	−1.27730e12	−0.354822	−0.177411	−	0.984137i	$-0.556772\pi$
$617$	−1.27730e12	−0.354822	−0.177411	+	0.984137i	$0.556772\pi$
$618$	−1.44863e11	−0.0399494
$619$	6.62813e12	1.81461	0.907304	−	0.420475i	$-0.138137\pi$
$619$	6.62813e12	1.81461	0.907304	+	0.420475i	$0.138137\pi$
$620$	1.33020e12	0.361538
$621$	−3.21765e11	−0.0868213
$622$	−1.71462e11	−0.0459316
$623$	−8.17135e12	−2.17319
$624$	4.27045e11	0.112757
$625$	−3.02128e12	−0.792011
$626$	−9.00863e10	−0.0234463
$627$	−2.60477e12	−0.673077
$628$	1.79967e12	0.461716
$629$	3.80352e12	0.968853
$630$	1.62990e11	0.0412220
$631$	−2.91085e12	−0.730949	−0.365474	−	0.930821i	$-0.619093\pi$
$631$	−2.91085e12	−0.730949	−0.365474	+	0.930821i	$0.619093\pi$
$632$	−1.00792e11	−0.0251304
$633$	−2.14800e12	−0.531762
$634$	4.29965e11	0.105689
$635$	−7.04405e11	−0.171926
$636$	2.07962e12	0.503997
$637$	−3.02265e11	−0.0727379
$638$	−3.90648e11	−0.0933452
$639$	−1.68795e12	−0.400504
$640$	−1.74101e12	−0.410195
$641$	1.50835e12	0.352892	0.176446	−	0.984310i	$-0.443540\pi$
$641$	1.50835e12	0.352892	0.176446	+	0.984310i	$0.443540\pi$
$642$	−3.68698e10	−0.00856572
$643$	−4.67324e12	−1.07812	−0.539062	−	0.842266i	$-0.681221\pi$
$643$	−4.67324e12	−1.07812	−0.539062	+	0.842266i	$0.681221\pi$
$644$	−2.26274e12	−0.518379
$645$	2.36180e11	0.0537309
$646$	−2.39745e11	−0.0541630
$647$	−3.96680e12	−0.889960	−0.444980	−	0.895540i	$-0.646789\pi$
$647$	−3.96680e12	−0.889960	−0.444980	+	0.895540i	$0.646789\pi$
$648$	−1.15892e11	−0.0258205
$649$	1.01741e12	0.225110
$650$	1.91625e10	0.00421059
$651$	1.24523e12	0.271729
$652$	−2.53619e12	−0.549627
$653$	6.89985e11	0.148501	0.0742507	−	0.997240i	$-0.476344\pi$
$653$	6.89985e11	0.148501	0.0742507	+	0.997240i	$0.476344\pi$
$654$	4.79495e11	0.102491
$655$	−7.05882e12	−1.49846
$656$	7.55050e12	1.59187
$657$	−2.69831e12	−0.565000
$658$	−1.21962e12	−0.253635
$659$	1.30340e12	0.269212	0.134606	−	0.990899i	$-0.457023\pi$
$659$	1.30340e12	0.269212	0.134606	+	0.990899i	$0.457023\pi$
$660$	−4.35501e12	−0.893390
$661$	−7.17732e11	−0.146237	−0.0731183	−	0.997323i	$-0.523295\pi$
$661$	−7.17732e11	−0.146237	−0.0731183	+	0.997323i	$0.523295\pi$
$662$	−3.13505e11	−0.0634430
$663$	4.01621e11	0.0807245
$664$	1.30637e12	0.260802
$665$	−3.59412e12	−0.712682
$666$	2.79378e11	0.0550247
$667$	1.06411e12	0.208171
$668$	−4.87342e12	−0.946978
$669$	2.07676e12	0.400839
$670$	6.50285e10	0.0124672
$671$	−1.07157e13	−2.04065
$672$	−1.22528e12	−0.231779
$673$	−2.07991e12	−0.390819	−0.195410	−	0.980722i	$-0.562604\pi$
$673$	−2.07991e12	−0.390819	−0.195410	+	0.980722i	$0.562604\pi$
$674$	−1.01334e12	−0.189141
$675$	1.83460e11	0.0340153
$676$	5.13315e12	0.945418
$677$	−2.75692e11	−0.0504400	−0.0252200	−	0.999682i	$-0.508029\pi$
$677$	−2.75692e11	−0.0504400	−0.0252200	+	0.999682i	$0.508029\pi$
$678$	−2.22895e11	−0.0405104
$679$	−1.28030e12	−0.231152
$680$	−8.07238e11	−0.144781
$681$	−2.82748e10	−0.00503777
$682$	4.61724e11	0.0817246
$683$	−2.66370e12	−0.468374	−0.234187	−	0.972192i	$-0.575243\pi$
$683$	−2.66370e12	−0.468374	−0.234187	+	0.972192i	$0.575243\pi$
$684$	1.26897e12	0.221665
$685$	5.15000e12	0.893717
$686$	−5.08167e11	−0.0876089
$687$	3.57502e12	0.612312
$688$	−5.78152e11	−0.0983770
$689$	−1.06608e12	−0.180219
$690$	−1.64624e11	−0.0276486
$691$	−1.07739e13	−1.79772	−0.898861	−	0.438234i	$-0.855604\pi$
$691$	−1.07739e13	−1.79772	−0.898861	+	0.438234i	$0.855604\pi$
$692$	7.89287e12	1.30845
$693$	−4.07684e12	−0.671467
$694$	9.81568e11	0.160621
$695$	−8.73108e12	−1.41950
$696$	3.83265e11	0.0619096
$697$	7.10099e12	1.13965
$698$	−7.85693e11	−0.125286
$699$	6.26084e11	0.0991940
$700$	1.29014e12	0.203093
$701$	−4.43000e12	−0.692903	−0.346452	−	0.938068i	$-0.612614\pi$
$701$	−4.43000e12	−0.692903	−0.346452	+	0.938068i	$0.612614\pi$
$702$	2.95000e10	0.00458464
$703$	−6.16061e12	−0.951315
$704$	1.03544e13	1.58872
$705$	6.39413e12	0.974834
$706$	−1.77877e9	−0.000269463 0
$707$	−1.12977e12	−0.170061
$708$	−4.95653e11	−0.0741358
$709$	−2.47005e12	−0.367112	−0.183556	−	0.983009i	$-0.558761\pi$
$709$	−2.47005e12	−0.367112	−0.183556	+	0.983009i	$0.558761\pi$
$710$	−8.63607e11	−0.127542
$711$	2.45632e11	0.0360472
$712$	2.97262e12	0.433491
$713$	−1.25772e12	−0.182256
$714$	−3.75235e11	−0.0540333
$715$	2.23250e12	0.319459
$716$	−4.26496e12	−0.606465
$717$	4.37521e12	0.618248
$718$	−2.74864e11	−0.0385973
$719$	1.20822e13	1.68604	0.843019	−	0.537884i	$-0.180776\pi$
$719$	1.20822e13	1.68604	0.843019	+	0.537884i	$0.180776\pi$
$720$	2.09178e12	0.290082
$721$	4.99971e12	0.689027
$722$	−4.65917e11	−0.0638104
$723$	−3.02098e12	−0.411174
$724$	1.03297e13	1.39722
$725$	−6.06720e11	−0.0815582
$726$	−1.00606e12	−0.134403
$727$	5.60118e11	0.0743660	0.0371830	−	0.999308i	$-0.488162\pi$
$727$	5.60118e11	0.0743660	0.0371830	+	0.999308i	$0.488162\pi$
$728$	4.17783e11	0.0551264
$729$	2.82430e11	0.0370370
$730$	−1.38054e12	−0.179927
$731$	−5.43732e11	−0.0704298
$732$	5.22036e12	0.672049
$733$	−1.15065e13	−1.47223	−0.736116	−	0.676855i	$-0.763342\pi$
$733$	−1.15065e13	−1.47223	−0.736116	+	0.676855i	$0.763342\pi$
$734$	−5.23198e11	−0.0665325
$735$	−1.48058e12	−0.187128
$736$	1.23756e12	0.155460
$737$	−1.62655e12	−0.203078
$738$	5.21585e11	0.0647249
$739$	−5.25102e12	−0.647654	−0.323827	−	0.946116i	$-0.604970\pi$
$739$	−5.25102e12	−0.647654	−0.323827	+	0.946116i	$0.604970\pi$
$740$	−1.03001e13	−1.26270
$741$	−6.50510e11	−0.0792633
$742$	9.96036e11	0.120631
$743$	7.30377e12	0.879219	0.439610	−	0.898189i	$-0.355117\pi$
$743$	7.30377e12	0.879219	0.439610	+	0.898189i	$0.355117\pi$
$744$	−4.52999e11	−0.0542025
$745$	6.23038e11	0.0740988
$746$	1.54770e12	0.182962
$747$	−3.18365e12	−0.374096
$748$	1.00261e13	1.17105
$749$	1.27250e12	0.147737
$750$	6.24920e11	0.0721188
$751$	−8.33892e12	−0.956599	−0.478300	−	0.878197i	$-0.658747\pi$
$751$	−8.33892e12	−0.956599	−0.478300	+	0.878197i	$0.658747\pi$
$752$	−1.56524e13	−1.78484
$753$	3.01104e12	0.341302
$754$	−9.75596e10	−0.0109926
$755$	−2.93105e12	−0.328293
$756$	1.98612e12	0.221135
$757$	−3.39837e12	−0.376131	−0.188065	−	0.982157i	$-0.560222\pi$
$757$	−3.39837e12	−0.376131	−0.188065	+	0.982157i	$0.560222\pi$
$758$	−1.03461e12	−0.113832
$759$	4.11772e12	0.450369
$760$	1.30749e12	0.142160
$761$	−1.02566e13	−1.10860	−0.554298	−	0.832319i	$-0.687013\pi$
$761$	−1.02566e13	−1.10860	−0.554298	+	0.832319i	$0.687013\pi$
$762$	1.19116e11	0.0127989
$763$	−1.65490e13	−1.76771
$764$	5.57929e12	0.592460
$765$	1.96725e12	0.207675
$766$	−9.28780e11	−0.0974728
$767$	2.54086e11	0.0265095
$768$	−4.81995e12	−0.499939
$769$	3.84432e12	0.396416	0.198208	−	0.980160i	$-0.436488\pi$
$769$	3.84432e12	0.396416	0.198208	+	0.980160i	$0.436488\pi$
$770$	−2.08583e12	−0.213831
$771$	2.03072e12	0.206969
$772$	−1.74991e12	−0.177312
$773$	−5.47346e12	−0.551384	−0.275692	−	0.961246i	$-0.588907\pi$
$773$	−5.47346e12	−0.551384	−0.275692	+	0.961246i	$0.588907\pi$
$774$	−3.99384e10	−0.00399997
$775$	7.17111e11	0.0714050
$776$	4.65756e11	0.0461085
$777$	−9.64225e12	−0.949039
$778$	−1.25382e12	−0.122695
$779$	−1.15016e13	−1.11902
$780$	−1.08761e12	−0.105208
$781$	2.16012e13	2.07754
$782$	3.78998e11	0.0362415
$783$	−9.34023e11	−0.0888034
$784$	3.62435e12	0.342616
$785$	−4.51897e12	−0.424743
$786$	1.19366e12	0.111552
$787$	−1.00323e12	−0.0932208	−0.0466104	−	0.998913i	$-0.514842\pi$
$787$	−1.00323e12	−0.0932208	−0.0466104	+	0.998913i	$0.514842\pi$
$788$	−1.22509e13	−1.13188
$789$	3.02176e12	0.277596
$790$	1.25673e11	0.0114794
$791$	7.69283e12	0.698702
$792$	1.48310e12	0.133939
$793$	−2.67611e12	−0.240312
$794$	1.06041e12	0.0946855
$795$	−5.22193e12	−0.463638
$796$	1.69276e13	1.49447
$797$	7.85435e12	0.689522	0.344761	−	0.938691i	$-0.387960\pi$
$797$	7.85435e12	0.689522	0.344761	+	0.938691i	$0.387960\pi$
$798$	6.07773e11	0.0530552
$799$	−1.47205e13	−1.27780
$800$	−7.05619e11	−0.0609067
$801$	−7.24432e12	−0.621801
$802$	−1.34671e11	−0.0114945
$803$	3.45311e13	2.93083
$804$	7.92406e11	0.0668799
$805$	5.68173e12	0.476869
$806$	1.15310e11	0.00962409
$807$	7.33749e12	0.608999
$808$	4.10996e11	0.0339224
$809$	−2.34330e13	−1.92335	−0.961676	−	0.274188i	$-0.911591\pi$
$809$	−2.34330e13	−1.92335	−0.961676	+	0.274188i	$0.911591\pi$
$810$	1.44499e11	0.0117946
$811$	−5.12210e12	−0.415771	−0.207885	−	0.978153i	$-0.566658\pi$
$811$	−5.12210e12	−0.415771	−0.207885	+	0.978153i	$0.566658\pi$
$812$	−6.56830e12	−0.530214
$813$	−1.11614e13	−0.896005
$814$	−3.57528e12	−0.285430
$815$	6.36838e12	0.505614
$816$	−4.81569e12	−0.380236
$817$	8.80688e11	0.0691549
$818$	−2.69723e12	−0.210634
$819$	−1.01814e12	−0.0790736
$820$	−1.92299e13	−1.48530
$821$	−1.89983e13	−1.45939	−0.729693	−	0.683775i	$-0.760337\pi$
$821$	−1.89983e13	−1.45939	−0.729693	+	0.683775i	$0.760337\pi$
$822$	−8.70875e11	−0.0665323
$823$	4.77442e12	0.362762	0.181381	−	0.983413i	$-0.441943\pi$
$823$	4.77442e12	0.362762	0.181381	+	0.983413i	$0.441943\pi$
$824$	−1.81883e12	−0.137442
$825$	−2.34779e12	−0.176448
$826$	−2.37393e11	−0.0177443
$827$	1.54874e13	1.15134	0.575669	−	0.817683i	$-0.304742\pi$
$827$	1.54874e13	1.15134	0.575669	+	0.817683i	$0.304742\pi$
$828$	−2.00603e12	−0.148321
$829$	2.20968e13	1.62493	0.812465	−	0.583010i	$-0.198125\pi$
$829$	2.20968e13	1.62493	0.812465	+	0.583010i	$0.198125\pi$
$830$	−1.62885e12	−0.119132
$831$	−9.22920e12	−0.671366
$832$	2.58588e12	0.187091
$833$	3.40858e12	0.245285
$834$	1.47644e12	0.105674
$835$	1.22372e13	0.871147
$836$	−1.62393e13	−1.14985
$837$	1.10396e12	0.0777483
$838$	1.67168e12	0.117100
$839$	6.56319e12	0.457284	0.228642	−	0.973511i	$-0.426571\pi$
$839$	6.56319e12	0.457284	0.228642	+	0.973511i	$0.426571\pi$
$840$	2.04642e12	0.141820
$841$	−1.14182e13	−0.787077
$842$	2.84489e12	0.195057
$843$	5.98579e11	0.0408223
$844$	−1.33916e13	−0.908433
$845$	−1.28893e13	−0.869712
$846$	−1.08126e12	−0.0725710
$847$	3.47224e13	2.31811
$848$	1.27829e13	0.848885
$849$	−1.14741e13	−0.757937
$850$	−2.16092e11	−0.0141989
$851$	9.73893e12	0.636544
$852$	−1.05235e13	−0.684199
$853$	1.02788e13	0.664773	0.332386	−	0.943143i	$-0.392146\pi$
$853$	1.02788e13	0.664773	0.332386	+	0.943143i	$0.392146\pi$
$854$	2.50029e12	0.160854
$855$	−3.18638e12	−0.203915
$856$	−4.62918e11	−0.0294694
$857$	1.06746e13	0.675983	0.337992	−	0.941149i	$-0.390252\pi$
$857$	1.06746e13	0.675983	0.337992	+	0.941149i	$0.390252\pi$
$858$	−3.77520e11	−0.0237820
$859$	−2.46494e13	−1.54468	−0.772339	−	0.635211i	$-0.780913\pi$
$859$	−2.46494e13	−1.54468	−0.772339	+	0.635211i	$0.780913\pi$
$860$	1.47246e12	0.0917908
$861$	−1.80016e13	−1.11634
$862$	2.20835e12	0.136234
$863$	1.62899e13	0.999699	0.499850	−	0.866112i	$-0.333389\pi$
$863$	1.62899e13	0.999699	0.499850	+	0.866112i	$0.333389\pi$
$864$	−1.08627e12	−0.0663174
$865$	−1.98190e13	−1.20368
$866$	−7.34748e11	−0.0443923
$867$	5.07662e12	0.305133
$868$	7.76338e12	0.464207
$869$	−3.14342e12	−0.186988
$870$	−4.77874e11	−0.0282798
$871$	−4.06211e11	−0.0239150
$872$	6.02028e12	0.352609
$873$	−1.13505e12	−0.0661382
$874$	−6.13867e11	−0.0355855
$875$	−2.15681e13	−1.24387
$876$	−1.68226e13	−0.965214
$877$	2.73486e13	1.56112	0.780562	−	0.625078i	$-0.214933\pi$
$877$	2.73486e13	1.56112	0.780562	+	0.625078i	$0.214933\pi$
$878$	−3.28783e12	−0.186717
$879$	−3.66915e12	−0.207308
$880$	−2.67692e13	−1.50474
$881$	−8.62622e12	−0.482424	−0.241212	−	0.970472i	$-0.577545\pi$
$881$	−8.62622e12	−0.482424	−0.241212	+	0.970472i	$0.577545\pi$
$882$	2.50368e11	0.0139306
$883$	2.05976e13	1.14023	0.570116	−	0.821564i	$-0.306898\pi$
$883$	2.05976e13	1.14023	0.570116	+	0.821564i	$0.306898\pi$
$884$	2.50389e12	0.137905
$885$	1.24458e12	0.0681993
$886$	3.45593e12	0.188414
$887$	−2.61466e13	−1.41827	−0.709134	−	0.705073i	$-0.750914\pi$
$887$	−2.61466e13	−1.41827	−0.709134	+	0.705073i	$0.750914\pi$
$888$	3.50772e12	0.189307
$889$	−4.11109e12	−0.220749
$890$	−3.70641e12	−0.198015
$891$	−3.61433e12	−0.192123
$892$	1.29475e13	0.684770
$893$	2.38430e13	1.25467
$894$	−1.05357e11	−0.00551625
$895$	1.07093e13	0.557902
$896$	−1.01610e13	−0.526683
$897$	1.02835e12	0.0530366
$898$	3.30313e11	0.0169505
$899$	−3.65092e12	−0.186416
$900$	1.14377e12	0.0581098
$901$	1.20219e13	0.607732
$902$	−6.67487e12	−0.335748
$903$	1.37841e12	0.0689894
$904$	−2.79855e12	−0.139372
$905$	−2.59379e13	−1.28533
$906$	4.95645e11	0.0244396
$907$	−9.64696e12	−0.473323	−0.236662	−	0.971592i	$-0.576053\pi$
$907$	−9.64696e12	−0.473323	−0.236662	+	0.971592i	$0.576053\pi$
$908$	−1.76279e11	−0.00860624
$909$	−1.00160e12	−0.0486585
$910$	−5.20912e11	−0.0251813
$911$	3.40085e13	1.63589	0.817947	−	0.575294i	$-0.195112\pi$
$911$	3.40085e13	1.63589	0.817947	+	0.575294i	$0.195112\pi$
$912$	7.80003e12	0.373353
$913$	4.07421e13	1.94055
$914$	−5.32020e11	−0.0252157
$915$	−1.31083e13	−0.618233
$916$	2.22883e13	1.04604
$917$	−4.11971e13	−1.92400
$918$	−3.32666e11	−0.0154602
$919$	2.17503e13	1.00588	0.502939	−	0.864322i	$-0.332252\pi$
$919$	2.17503e13	1.00588	0.502939	+	0.864322i	$0.332252\pi$
$920$	−2.06694e12	−0.0951221
$921$	8.12302e12	0.372005
$922$	1.57474e12	0.0717662
$923$	5.39465e12	0.244656
$924$	−2.54170e13	−1.14710
$925$	−5.55282e12	−0.249388
$926$	−4.69125e12	−0.209671
$927$	4.43250e12	0.197147
$928$	3.59242e12	0.159009
$929$	1.64442e13	0.724338	0.362169	−	0.932112i	$-0.382036\pi$
$929$	1.64442e13	0.724338	0.362169	+	0.932112i	$0.382036\pi$
$930$	5.64821e11	0.0247593
$931$	−5.52092e12	−0.240845
$932$	3.90330e12	0.169458
$933$	5.24637e12	0.226669
$934$	−9.80811e11	−0.0421720
$935$	−2.51755e13	−1.07727
$936$	3.70386e11	0.0157730
$937$	−3.48954e13	−1.47890	−0.739452	−	0.673209i	$-0.764916\pi$
$937$	−3.48954e13	−1.47890	−0.739452	+	0.673209i	$0.764916\pi$
$938$	3.79523e11	0.0160076
$939$	2.75645e12	0.115706
$940$	3.98640e13	1.66535
$941$	3.27535e13	1.36177	0.680886	−	0.732389i	$-0.261595\pi$
$941$	3.27535e13	1.36177	0.680886	+	0.732389i	$0.261595\pi$
$942$	7.64166e11	0.0316198
$943$	1.81821e13	0.748758
$944$	−3.04666e12	−0.124867
$945$	−4.98715e12	−0.203427
$946$	5.11103e11	0.0207491
$947$	3.21396e12	0.129857	0.0649285	−	0.997890i	$-0.479318\pi$
$947$	3.21396e12	0.129857	0.0649285	+	0.997890i	$0.479318\pi$
$948$	1.53138e12	0.0615810
$949$	8.62374e12	0.345142
$950$	3.50007e11	0.0139418
$951$	−1.31560e13	−0.521569
$952$	−4.71125e12	−0.185896
$953$	1.10804e13	0.435150	0.217575	−	0.976044i	$-0.430185\pi$
$953$	1.10804e13	0.435150	0.217575	+	0.976044i	$0.430185\pi$
$954$	8.83038e11	0.0345153
$955$	−1.40096e13	−0.545017
$956$	2.72771e13	1.05618
$957$	1.19530e13	0.460651
$958$	5.28416e12	0.202689
$959$	3.00568e13	1.14752
$960$	1.26664e13	0.481317
$961$	−2.21244e13	−0.836791
$962$	−8.92884e11	−0.0336130
$963$	1.12814e12	0.0422711
$964$	−1.88342e13	−0.702427
$965$	4.39402e12	0.163113
$966$	−9.60791e11	−0.0355003
$967$	1.09145e13	0.401408	0.200704	−	0.979652i	$-0.435677\pi$
$967$	1.09145e13	0.401408	0.200704	+	0.979652i	$0.435677\pi$
$968$	−1.26315e13	−0.462398
$969$	7.33566e12	0.267290
$970$	−5.80727e11	−0.0210620
$971$	6.96329e11	0.0251379	0.0125689	−	0.999921i	$-0.495999\pi$
$971$	6.96329e11	0.0251379	0.0125689	+	0.999921i	$0.495999\pi$
$972$	1.76080e12	0.0632720
$973$	−5.09569e13	−1.82262
$974$	5.15959e12	0.183696
$975$	−5.86332e11	−0.0207789
$976$	3.20883e13	1.13194
$977$	−1.37974e13	−0.484476	−0.242238	−	0.970217i	$-0.577881\pi$
$977$	−1.37974e13	−0.484476	−0.242238	+	0.970217i	$0.577881\pi$
$978$	−1.07690e12	−0.0376402
$979$	9.27077e13	3.22547
$980$	−9.23062e12	−0.319679
$981$	−1.46715e13	−0.505783
$982$	−4.39162e12	−0.150703
$983$	−1.76354e13	−0.602415	−0.301207	−	0.953559i	$-0.597390\pi$
$983$	−1.76354e13	−0.602415	−0.301207	+	0.953559i	$0.597390\pi$
$984$	6.54874e12	0.222679
$985$	3.07621e13	1.04124
$986$	1.10016e12	0.0370689
$987$	3.73178e13	1.25167
$988$	−4.05558e12	−0.135409
$989$	−1.39223e12	−0.0462729
$990$	−1.84920e12	−0.0611822
$991$	2.80655e13	0.924362	0.462181	−	0.886786i	$-0.347067\pi$
$991$	2.80655e13	0.924362	0.462181	+	0.886786i	$0.347067\pi$
$992$	−4.24604e12	−0.139214
$993$	9.59258e12	0.313086
$994$	−5.04024e12	−0.163762
$995$	−4.25053e13	−1.37480
$996$	−1.98484e13	−0.639084
$997$	−1.61831e12	−0.0518720	−0.0259360	−	0.999664i	$-0.508257\pi$
$997$	−1.61831e12	−0.0518720	−0.0259360	+	0.999664i	$0.508257\pi$
$998$	6.89148e11	0.0219900
$999$	−8.54836e12	−0.271543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.11	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +3356.80 q^{10} -83963.0 q^{11} +40904.4 q^{12} -20968.8 q^{13} +19591.2 q^{14} -102711. q^{15} +251429. q^{16} +236460. q^{17} +17368.6 q^{18} -382997. q^{19} -640348. q^{20} -599447. q^{21} -222271. q^{22} +605458. q^{23} +218071. q^{24} -345212. q^{25} -55509.5 q^{26} -531441. q^{27} -3.73724e6 q^{28} +1.75753e6 q^{29} -271901. q^{30} -2.07730e6 q^{31} +2.04402e6 q^{32} +6.80100e6 q^{33} +625969. q^{34} +9.38420e6 q^{35} -3.31325e6 q^{36} +1.60852e7 q^{37} -1.01389e6 q^{38} +1.69847e6 q^{39} -3.41384e6 q^{40} +3.00304e7 q^{41} -1.58688e6 q^{42} -2.29946e6 q^{43} +4.24007e7 q^{44} +8.31958e6 q^{45} +1.60280e6 q^{46} -6.22537e7 q^{47} -2.03657e7 q^{48} +1.44150e7 q^{49} -913861. q^{50} -1.91533e7 q^{51} +1.05891e7 q^{52} +5.08411e7 q^{53} -1.40686e6 q^{54} -1.06468e8 q^{55} -1.99241e7 q^{56} +3.10228e7 q^{57} +4.65261e6 q^{58} -1.21174e7 q^{59} +5.18682e7 q^{60} +1.27624e8 q^{61} -5.49914e6 q^{62} +4.85552e7 q^{63} -1.23321e8 q^{64} -2.65891e7 q^{65} +1.80039e7 q^{66} +1.93722e7 q^{67} -1.19411e8 q^{68} -4.90421e7 q^{69} +2.48423e7 q^{70} -2.57271e8 q^{71} -1.76637e7 q^{72} -4.11266e8 q^{73} +4.25816e7 q^{74} +2.79622e7 q^{75} +1.93411e8 q^{76} -6.21375e8 q^{77} +4.49627e6 q^{78} +3.74382e7 q^{79} +3.18821e8 q^{80} +4.30467e7 q^{81} +7.94978e7 q^{82} -4.85239e8 q^{83} +3.02716e8 q^{84} +2.99840e8 q^{85} -6.08724e6 q^{86} -1.42360e8 q^{87} +2.26048e8 q^{88} -1.10415e9 q^{89} +2.20240e7 q^{90} -1.55181e8 q^{91} -3.05751e8 q^{92} +1.68262e8 q^{93} -1.64801e8 q^{94} -4.85654e8 q^{95} -1.65565e8 q^{96} -1.73000e8 q^{97} +3.81601e7 q^{98} -5.50881e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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