LMFDB - Embedded newform 289.10.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.8587 q^{2} +204.729 q^{3} -346.654 q^{4} -120.661 q^{5} -2632.54 q^{6} -4525.78 q^{7} +11041.2 q^{8} +22230.9 q^{9} +O(q^{10})$	\(q-12.8587 q^{2} +204.729 q^{3} -346.654 q^{4} -120.661 q^{5} -2632.54 q^{6} -4525.78 q^{7} +11041.2 q^{8} +22230.9 q^{9} +1551.54 q^{10} +57864.7 q^{11} -70970.1 q^{12} +50786.7 q^{13} +58195.5 q^{14} -24702.7 q^{15} +35512.1 q^{16} -285861. q^{18} -815845. q^{19} +41827.5 q^{20} -926557. q^{21} -744065. q^{22} -745187. q^{23} +2.26045e6 q^{24} -1.93857e6 q^{25} -653050. q^{26} +521635. q^{27} +1.56888e6 q^{28} -1.01091e6 q^{29} +317644. q^{30} +1.30750e6 q^{31} -6.10972e6 q^{32} +1.18466e7 q^{33} +546083. q^{35} -7.70645e6 q^{36} +1.57690e7 q^{37} +1.04907e7 q^{38} +1.03975e7 q^{39} -1.33223e6 q^{40} -4.94296e6 q^{41} +1.19143e7 q^{42} -4.64999e6 q^{43} -2.00591e7 q^{44} -2.68240e6 q^{45} +9.58213e6 q^{46} +3.34810e7 q^{47} +7.27035e6 q^{48} -1.98710e7 q^{49} +2.49274e7 q^{50} -1.76054e7 q^{52} +5.09370e7 q^{53} -6.70755e6 q^{54} -6.98199e6 q^{55} -4.99698e7 q^{56} -1.67027e8 q^{57} +1.29989e7 q^{58} +1.72235e8 q^{59} +8.56330e6 q^{60} +4.80961e7 q^{61} -1.68127e7 q^{62} -1.00612e8 q^{63} +6.03807e7 q^{64} -6.12795e6 q^{65} -1.52332e8 q^{66} +2.00253e8 q^{67} -1.52561e8 q^{69} -7.02191e6 q^{70} -1.02425e8 q^{71} +2.45455e8 q^{72} -4.38332e8 q^{73} -2.02769e8 q^{74} -3.96881e8 q^{75} +2.82816e8 q^{76} -2.61883e8 q^{77} -1.33698e8 q^{78} -3.10924e8 q^{79} -4.28491e6 q^{80} -3.30778e8 q^{81} +6.35600e7 q^{82} -8.30705e8 q^{83} +3.21195e8 q^{84} +5.97928e7 q^{86} -2.06962e8 q^{87} +6.38894e8 q^{88} -6.52199e7 q^{89} +3.44921e7 q^{90} -2.29849e8 q^{91} +2.58322e8 q^{92} +2.67683e8 q^{93} -4.30522e8 q^{94} +9.84404e7 q^{95} -1.25084e9 q^{96} -2.25459e8 q^{97} +2.55514e8 q^{98} +1.28639e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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 $

$2$	−12.8587	−0.568279	−0.284139	−	0.958783i	$-0.591708\pi$
$2$	−12.8587	−0.568279	−0.284139	+	0.958783i	$0.591708\pi$
$3$	204.729	1.45926	0.729631	−	0.683841i	$-0.239692\pi$
$3$	204.729	1.45926	0.729631	+	0.683841i	$0.239692\pi$
$4$	−346.654	−0.677059
$5$	−120.661	−0.0863377	−0.0431688	−	0.999068i	$-0.513745\pi$
$5$	−120.661	−0.0863377	−0.0431688	+	0.999068i	$0.513745\pi$
$6$	−2632.54	−0.829268
$7$	−4525.78	−0.712446	−0.356223	−	0.934401i	$-0.615936\pi$
$7$	−4525.78	−0.712446	−0.356223	+	0.934401i	$0.615936\pi$
$8$	11041.2	0.953037
$9$	22230.9	1.12945
$10$	1551.54	0.0490639
$11$	57864.7	1.19165	0.595823	−	0.803116i	$-0.296826\pi$
$11$	57864.7	1.19165	0.595823	+	0.803116i	$0.296826\pi$
$12$	−70970.1	−0.988007
$13$	50786.7	0.493179	0.246590	−	0.969120i	$-0.420690\pi$
$13$	50786.7	0.493179	0.246590	+	0.969120i	$0.420690\pi$
$14$	58195.5	0.404868
$15$	−24702.7	−0.125989
$16$	35512.1	0.135468
$17$	0	0
$17$	0	0
$18$	−285861.	−0.641842
$19$	−815845.	−1.43621	−0.718103	−	0.695937i	$-0.754989\pi$
$19$	−815845.	−1.43621	−0.718103	+	0.695937i	$0.754989\pi$
$20$	41827.5	0.0584557
$21$	−926557.	−1.03965
$22$	−744065.	−0.677187
$23$	−745187.	−0.555252	−0.277626	−	0.960689i	$-0.589548\pi$
$23$	−745187.	−0.555252	−0.277626	+	0.960689i	$0.589548\pi$
$24$	2.26045e6	1.39073
$25$	−1.93857e6	−0.992546
$26$	−653050.	−0.280263
$27$	521635.	0.188899
$28$	1.56888e6	0.482368
$29$	−1.01091e6	−0.265411	−0.132706	−	0.991155i	$-0.542367\pi$
$29$	−1.01091e6	−0.265411	−0.132706	+	0.991155i	$0.542367\pi$
$30$	317644.	0.0715971
$31$	1.30750e6	0.254281	0.127140	−	0.991885i	$-0.459420\pi$
$31$	1.30750e6	0.254281	0.127140	+	0.991885i	$0.459420\pi$
$32$	−6.10972e6	−1.03002
$33$	1.18466e7	1.73892
$34$	0	0
$35$	546083.	0.0615109
$36$	−7.70645e6	−0.764703
$37$	1.57690e7	1.38324	0.691620	−	0.722262i	$-0.256897\pi$
$37$	1.57690e7	1.38324	0.691620	+	0.722262i	$0.256897\pi$
$38$	1.04907e7	0.816165
$39$	1.03975e7	0.719678
$40$	−1.33223e6	−0.0822830
$41$	−4.94296e6	−0.273187	−0.136593	−	0.990627i	$-0.543615\pi$
$41$	−4.94296e6	−0.273187	−0.136593	+	0.990627i	$0.543615\pi$
$42$	1.19143e7	0.590809
$43$	−4.64999e6	−0.207417	−0.103708	−	0.994608i	$-0.533071\pi$
$43$	−4.64999e6	−0.207417	−0.103708	+	0.994608i	$0.533071\pi$
$44$	−2.00591e7	−0.806814
$45$	−2.68240e6	−0.0975140
$46$	9.58213e6	0.315538
$47$	3.34810e7	1.00082	0.500412	−	0.865787i	$-0.333182\pi$
$47$	3.34810e7	1.00082	0.500412	+	0.865787i	$0.333182\pi$
$48$	7.27035e6	0.197683
$49$	−1.98710e7	−0.492421
$50$	2.49274e7	0.564043
$51$	0	0
$52$	−1.76054e7	−0.333912
$53$	5.09370e7	0.886731	0.443366	−	0.896341i	$-0.353784\pi$
$53$	5.09370e7	0.886731	0.443366	+	0.896341i	$0.353784\pi$
$54$	−6.70755e6	−0.107347
$55$	−6.98199e6	−0.102884
$56$	−4.99698e7	−0.678988
$57$	−1.67027e8	−2.09580
$58$	1.29989e7	0.150828
$59$	1.72235e8	1.85049	0.925245	−	0.379371i	$-0.123860\pi$
$59$	1.72235e8	1.85049	0.925245	+	0.379371i	$0.123860\pi$
$60$	8.56330e6	0.0853023
$61$	4.80961e7	0.444760	0.222380	−	0.974960i	$-0.428618\pi$
$61$	4.80961e7	0.444760	0.222380	+	0.974960i	$0.428618\pi$
$62$	−1.68127e7	−0.144502
$63$	−1.00612e8	−0.804671
$64$	6.03807e7	0.449871
$65$	−6.12795e6	−0.0425800
$66$	−1.52332e8	−0.988194
$67$	2.00253e8	1.21407	0.607033	−	0.794677i	$-0.292360\pi$
$67$	2.00253e8	1.21407	0.607033	+	0.794677i	$0.292360\pi$
$68$	0	0
$69$	−1.52561e8	−0.810259
$70$	−7.02191e6	−0.0349554
$71$	−1.02425e8	−0.478347	−0.239174	−	0.970977i	$-0.576876\pi$
$71$	−1.02425e8	−0.478347	−0.239174	+	0.970977i	$0.576876\pi$
$72$	2.45455e8	1.07641
$73$	−4.38332e8	−1.80655	−0.903275	−	0.429063i	$-0.858844\pi$
$73$	−4.38332e8	−1.80655	−0.903275	+	0.429063i	$0.858844\pi$
$74$	−2.02769e8	−0.786066
$75$	−3.96881e8	−1.44839
$76$	2.82816e8	0.972396
$77$	−2.61883e8	−0.848983
$78$	−1.33698e8	−0.408978
$79$	−3.10924e8	−0.898116	−0.449058	−	0.893502i	$-0.648240\pi$
$79$	−3.10924e8	−0.898116	−0.449058	+	0.893502i	$0.648240\pi$
$80$	−4.28491e6	−0.0116960
$81$	−3.30778e8	−0.853795
$82$	6.35600e7	0.155246
$83$	−8.30705e8	−1.92130	−0.960650	−	0.277761i	$-0.910408\pi$
$83$	−8.30705e8	−1.92130	−0.960650	+	0.277761i	$0.910408\pi$
$84$	3.21195e8	0.703902
$85$	0	0
$86$	5.97928e7	0.117871
$87$	−2.06962e8	−0.387305
$88$	6.38894e8	1.13568
$89$	−6.52199e7	−0.110186	−0.0550928	−	0.998481i	$-0.517545\pi$
$89$	−6.52199e7	−0.110186	−0.0550928	+	0.998481i	$0.517545\pi$
$90$	3.44921e7	0.0554151
$91$	−2.29849e8	−0.351364
$92$	2.58322e8	0.375938
$93$	2.67683e8	0.371063
$94$	−4.30522e8	−0.568748
$95$	9.84404e7	0.123999
$96$	−1.25084e9	−1.50307
$97$	−2.25459e8	−0.258580	−0.129290	−	0.991607i	$-0.541270\pi$
$97$	−2.25459e8	−0.258580	−0.129290	+	0.991607i	$0.541270\pi$
$98$	2.55514e8	0.279832
$99$	1.28639e9	1.34590
$100$	6.72012e8	0.672012
$101$	1.79147e9	1.71303	0.856514	−	0.516124i	$-0.172626\pi$
$101$	1.79147e9	1.71303	0.856514	+	0.516124i	$0.172626\pi$
$102$	0	0
$103$	−2.00302e9	−1.75355	−0.876773	−	0.480904i	$-0.840308\pi$
$103$	−2.00302e9	−1.75355	−0.876773	+	0.480904i	$0.840308\pi$
$104$	5.60744e8	0.470018
$105$	1.11799e8	0.0897606
$106$	−6.54983e8	−0.503911
$107$	7.80191e8	0.575405	0.287703	−	0.957720i	$-0.407109\pi$
$107$	7.80191e8	0.575405	0.287703	+	0.957720i	$0.407109\pi$
$108$	−1.80827e8	−0.127896
$109$	−2.15583e9	−1.46284	−0.731418	−	0.681930i	$-0.761141\pi$
$109$	−2.15583e9	−1.46284	−0.731418	+	0.681930i	$0.761141\pi$
$110$	8.97793e7	0.0584668
$111$	3.22838e9	2.01851
$112$	−1.60720e8	−0.0965136
$113$	1.13163e9	0.652904	0.326452	−	0.945214i	$-0.394147\pi$
$113$	1.13163e9	0.652904	0.326452	+	0.945214i	$0.394147\pi$
$114$	2.14775e9	1.19100
$115$	8.99147e7	0.0479392
$116$	3.50435e8	0.179699
$117$	1.12904e9	0.557021
$118$	−2.21471e9	−1.05159
$119$	0	0
$120$	−2.72747e8	−0.120073
$121$	9.90381e8	0.420018
$122$	−6.18452e8	−0.252747
$123$	−1.01197e9	−0.398651
$124$	−4.53250e8	−0.172163
$125$	4.69574e8	0.172032
$126$	1.29374e9	0.457278
$127$	−3.66984e9	−1.25179	−0.625894	−	0.779908i	$-0.715266\pi$
$127$	−3.66984e9	−1.25179	−0.625894	+	0.779908i	$0.715266\pi$
$128$	2.35176e9	0.774369
$129$	−9.51988e8	−0.302676
$130$	7.87974e7	0.0241973
$131$	−1.90644e9	−0.565591	−0.282796	−	0.959180i	$-0.591262\pi$
$131$	−1.90644e9	−0.565591	−0.282796	+	0.959180i	$0.591262\pi$
$132$	−4.10667e9	−1.17735
$133$	3.69233e9	1.02322
$134$	−2.57499e9	−0.689928
$135$	−6.29408e7	−0.0163091
$136$	0	0
$137$	2.68382e9	0.650895	0.325448	−	0.945560i	$-0.394485\pi$
$137$	2.68382e9	0.650895	0.325448	+	0.945560i	$0.394485\pi$
$138$	1.96174e9	0.460453
$139$	−4.34137e9	−0.986415	−0.493208	−	0.869912i	$-0.664176\pi$
$139$	−4.34137e9	−0.986415	−0.493208	+	0.869912i	$0.664176\pi$
$140$	−1.89302e8	−0.0416465
$141$	6.85453e9	1.46047
$142$	1.31705e9	0.271835
$143$	2.93876e9	0.587695
$144$	7.89467e8	0.153004
$145$	1.21976e8	0.0229150
$146$	5.63637e9	1.02662
$147$	−4.06816e9	−0.718571
$148$	−5.46640e9	−0.936535
$149$	−7.27303e9	−1.20886	−0.604432	−	0.796657i	$-0.706600\pi$
$149$	−7.27303e9	−1.20886	−0.604432	+	0.796657i	$0.706600\pi$
$150$	5.10336e9	0.823087
$151$	4.35149e9	0.681149	0.340574	−	0.940218i	$-0.389379\pi$
$151$	4.35149e9	0.681149	0.340574	+	0.940218i	$0.389379\pi$
$152$	−9.00788e9	−1.36876
$153$	0	0
$154$	3.36747e9	0.482459
$155$	−1.57764e8	−0.0219540
$156$	−3.60434e9	−0.487265
$157$	−8.25994e9	−1.08500	−0.542498	−	0.840057i	$-0.682522\pi$
$157$	−8.25994e9	−1.08500	−0.542498	+	0.840057i	$0.682522\pi$
$158$	3.99808e9	0.510381
$159$	1.04283e10	1.29397
$160$	7.37202e8	0.0889296
$161$	3.37255e9	0.395587
$162$	4.25336e9	0.485194
$163$	−5.06011e9	−0.561456	−0.280728	−	0.959787i	$-0.590576\pi$
$163$	−5.06011e9	−0.561456	−0.280728	+	0.959787i	$0.590576\pi$
$164$	1.71350e9	0.184964
$165$	−1.42942e9	−0.150135
$166$	1.06818e10	1.09183
$167$	1.45710e9	0.144966	0.0724829	−	0.997370i	$-0.476908\pi$
$167$	1.45710e9	0.144966	0.0724829	+	0.997370i	$0.476908\pi$
$168$	−1.02303e10	−0.990822
$169$	−8.02521e9	−0.756774
$170$	0	0
$171$	−1.81370e10	−1.62212
$172$	1.61194e9	0.140433
$173$	−9.29522e9	−0.788955	−0.394477	−	0.918906i	$-0.629074\pi$
$173$	−9.29522e9	−0.788955	−0.394477	+	0.918906i	$0.629074\pi$
$174$	2.66125e9	0.220097
$175$	8.77352e9	0.707135
$176$	2.05490e9	0.161430
$177$	3.52614e10	2.70035
$178$	8.38642e8	0.0626162
$179$	5.29738e9	0.385676	0.192838	−	0.981231i	$-0.438231\pi$
$179$	5.29738e9	0.385676	0.192838	+	0.981231i	$0.438231\pi$
$180$	9.29864e8	0.0660227
$181$	−2.03955e10	−1.41248	−0.706238	−	0.707975i	$-0.749609\pi$
$181$	−2.03955e10	−1.41248	−0.706238	+	0.707975i	$0.749609\pi$
$182$	2.95556e9	0.199673
$183$	9.84666e9	0.649021
$184$	−8.22773e9	−0.529176
$185$	−1.90270e9	−0.119426
$186$	−3.44205e9	−0.210867
$187$	0	0
$188$	−1.16063e10	−0.677617
$189$	−2.36081e9	−0.134580
$190$	−1.26581e9	−0.0704658
$191$	−1.13020e9	−0.0614478	−0.0307239	−	0.999528i	$-0.509781\pi$
$191$	−1.13020e9	−0.0614478	−0.0307239	+	0.999528i	$0.509781\pi$
$192$	1.23617e10	0.656481
$193$	−3.57356e10	−1.85393	−0.926966	−	0.375146i	$-0.877592\pi$
$193$	−3.57356e10	−1.85393	−0.926966	+	0.375146i	$0.877592\pi$
$194$	2.89910e9	0.146945
$195$	−1.25457e9	−0.0621354
$196$	6.88835e9	0.333398
$197$	−3.55928e10	−1.68370	−0.841848	−	0.539715i	$-0.818532\pi$
$197$	−3.55928e10	−1.68370	−0.841848	+	0.539715i	$0.818532\pi$
$198$	−1.65412e10	−0.764848
$199$	3.12374e10	1.41200	0.706001	−	0.708211i	$-0.250497\pi$
$199$	3.12374e10	1.41200	0.706001	+	0.708211i	$0.250497\pi$
$200$	−2.14040e10	−0.945933
$201$	4.09976e10	1.77164
$202$	−2.30360e10	−0.973477
$203$	4.57513e9	0.189091
$204$	0	0
$205$	5.96420e8	0.0235863
$206$	2.57562e10	0.996503
$207$	−1.65662e10	−0.627128
$208$	1.80354e9	0.0668100
$209$	−4.72087e10	−1.71145
$210$	−1.43759e9	−0.0510091
$211$	−2.89353e10	−1.00498	−0.502489	−	0.864583i	$-0.667582\pi$
$211$	−2.89353e10	−1.00498	−0.502489	+	0.864583i	$0.667582\pi$
$212$	−1.76575e10	−0.600370
$213$	−2.09693e10	−0.698034
$214$	−1.00322e10	−0.326991
$215$	5.61071e8	0.0179079
$216$	5.75946e9	0.180028
$217$	−5.91745e9	−0.181161
$218$	2.77211e10	0.831298
$219$	−8.97391e10	−2.63623
$220$	2.42034e9	0.0696585
$221$	0	0
$222$	−4.15127e10	−1.14708
$223$	−5.45398e10	−1.47687	−0.738434	−	0.674326i	$-0.764434\pi$
$223$	−5.45398e10	−1.47687	−0.738434	+	0.674326i	$0.764434\pi$
$224$	2.76512e10	0.733834
$225$	−4.30961e10	−1.12103
$226$	−1.45512e10	−0.371032
$227$	9.17512e9	0.229348	0.114674	−	0.993403i	$-0.463418\pi$
$227$	9.17512e9	0.229348	0.114674	+	0.993403i	$0.463418\pi$
$228$	5.79006e10	1.41898
$229$	2.94750e10	0.708263	0.354131	−	0.935196i	$-0.384777\pi$
$229$	2.94750e10	0.708263	0.354131	+	0.935196i	$0.384777\pi$
$230$	−1.15619e9	−0.0272428
$231$	−5.36150e10	−1.23889
$232$	−1.11616e10	−0.252947
$233$	5.54557e10	1.23266	0.616332	−	0.787487i	$-0.288618\pi$
$233$	5.54557e10	1.23266	0.616332	+	0.787487i	$0.288618\pi$
$234$	−1.45179e10	−0.316543
$235$	−4.03984e9	−0.0864089
$236$	−5.97059e10	−1.25289
$237$	−6.36552e10	−1.31059
$238$	0	0
$239$	−6.16221e10	−1.22165	−0.610823	−	0.791767i	$-0.709161\pi$
$239$	−6.16221e10	−1.22165	−0.610823	+	0.791767i	$0.709161\pi$
$240$	−8.77245e8	−0.0170675
$241$	−4.49410e10	−0.858157	−0.429078	−	0.903267i	$-0.641162\pi$
$241$	−4.49410e10	−0.858157	−0.429078	+	0.903267i	$0.641162\pi$
$242$	−1.27350e10	−0.238687
$243$	−7.79871e10	−1.43481
$244$	−1.66727e10	−0.301128
$245$	2.39764e9	0.0425145
$246$	1.30126e10	0.226545
$247$	−4.14341e10	−0.708307
$248$	1.44363e10	0.242339
$249$	−1.70069e11	−2.80368
$250$	−6.03810e9	−0.0977621
$251$	3.67666e10	0.584685	0.292343	−	0.956314i	$-0.405565\pi$
$251$	3.67666e10	0.584685	0.292343	+	0.956314i	$0.405565\pi$
$252$	3.48777e10	0.544810
$253$	−4.31201e10	−0.661663
$254$	4.71893e10	0.711365
$255$	0	0
$256$	−6.11554e10	−0.889929
$257$	1.06275e11	1.51962	0.759808	−	0.650148i	$-0.225293\pi$
$257$	1.06275e11	1.51962	0.759808	+	0.650148i	$0.225293\pi$
$258$	1.22413e10	0.172004
$259$	−7.13671e10	−0.985484
$260$	2.12428e9	0.0288292
$261$	−2.24734e10	−0.299769
$262$	2.45143e10	0.321414
$263$	−4.15683e10	−0.535749	−0.267875	−	0.963454i	$-0.586321\pi$
$263$	−4.15683e10	−0.535749	−0.267875	+	0.963454i	$0.586321\pi$
$264$	1.30800e11	1.65726
$265$	−6.14609e9	−0.0765583
$266$	−4.74785e10	−0.581474
$267$	−1.33524e10	−0.160790
$268$	−6.94185e10	−0.821994
$269$	−1.92950e10	−0.224678	−0.112339	−	0.993670i	$-0.535834\pi$
$269$	−1.92950e10	−0.224678	−0.112339	+	0.993670i	$0.535834\pi$
$270$	8.09336e8	0.00926813
$271$	−5.51694e10	−0.621350	−0.310675	−	0.950516i	$-0.600555\pi$
$271$	−5.51694e10	−0.621350	−0.310675	+	0.950516i	$0.600555\pi$
$272$	0	0
$273$	−4.70568e10	−0.512732
$274$	−3.45104e10	−0.369890
$275$	−1.12175e11	−1.18276
$276$	5.28860e10	0.548593
$277$	1.49538e11	1.52613	0.763066	−	0.646320i	$-0.223693\pi$
$277$	1.49538e11	1.52613	0.763066	+	0.646320i	$0.223693\pi$
$278$	5.58243e10	0.560559
$279$	2.90669e10	0.287197
$280$	6.02939e9	0.0586222
$281$	−8.27561e10	−0.791811	−0.395906	−	0.918291i	$-0.629569\pi$
$281$	−8.27561e10	−0.791811	−0.395906	+	0.918291i	$0.629569\pi$
$282$	−8.81402e10	−0.829952
$283$	−5.14641e10	−0.476942	−0.238471	−	0.971150i	$-0.576646\pi$
$283$	−5.14641e10	−0.476942	−0.238471	+	0.971150i	$0.576646\pi$
$284$	3.55060e10	0.323869
$285$	2.01536e10	0.180947
$286$	−3.77886e10	−0.333975
$287$	2.23707e10	0.194631
$288$	−1.35825e11	−1.16336
$289$	0	0
$290$	−1.56846e9	−0.0130221
$291$	−4.61579e10	−0.377336
$292$	1.51949e11	1.22314
$293$	1.21927e11	0.966484	0.483242	−	0.875487i	$-0.339459\pi$
$293$	1.21927e11	0.966484	0.483242	+	0.875487i	$0.339459\pi$
$294$	5.23112e10	0.408349
$295$	−2.07819e10	−0.159767
$296$	1.74109e11	1.31828
$297$	3.01843e10	0.225101
$298$	9.35216e10	0.686972
$299$	−3.78456e10	−0.273839
$300$	1.37580e11	0.980642
$301$	2.10448e10	0.147773
$302$	−5.59545e10	−0.387082
$303$	3.66766e11	2.49976
$304$	−2.89724e10	−0.194560
$305$	−5.80330e9	−0.0383995
$306$	0	0
$307$	9.71611e10	0.624266	0.312133	−	0.950038i	$-0.398957\pi$
$307$	9.71611e10	0.624266	0.312133	+	0.950038i	$0.398957\pi$
$308$	9.07828e10	0.574811
$309$	−4.10076e11	−2.55889
$310$	2.02863e9	0.0124760
$311$	2.23120e11	1.35244	0.676218	−	0.736701i	$-0.263618\pi$
$311$	2.23120e11	1.35244	0.676218	+	0.736701i	$0.263618\pi$
$312$	1.14801e11	0.685880
$313$	−1.59734e10	−0.0940694	−0.0470347	−	0.998893i	$-0.514977\pi$
$313$	−1.59734e10	−0.0940694	−0.0470347	+	0.998893i	$0.514977\pi$
$314$	1.06212e11	0.616581
$315$	1.21399e10	0.0694734
$316$	1.07783e11	0.608078
$317$	2.02194e11	1.12461	0.562305	−	0.826930i	$-0.309915\pi$
$317$	2.02194e11	1.12461	0.562305	+	0.826930i	$0.309915\pi$
$318$	−1.34094e11	−0.735338
$319$	−5.84958e10	−0.316276
$320$	−7.28557e9	−0.0388409
$321$	1.59728e11	0.839667
$322$	−4.33666e10	−0.224804
$323$	0	0
$324$	1.14665e11	0.578069
$325$	−9.84534e10	−0.489503
$326$	6.50663e10	0.319064
$327$	−4.41361e11	−2.13466
$328$	−5.45760e10	−0.260357
$329$	−1.51527e11	−0.713033
$330$	1.83804e10	0.0853184
$331$	−3.68035e11	−1.68524	−0.842622	−	0.538505i	$-0.818989\pi$
$331$	−3.68035e11	−1.68524	−0.842622	+	0.538505i	$0.818989\pi$
$332$	2.87967e11	1.30083
$333$	3.50560e11	1.56230
$334$	−1.87364e10	−0.0823811
$335$	−2.41626e10	−0.104820
$336$	−3.29040e10	−0.140839
$337$	1.35639e11	0.572862	0.286431	−	0.958101i	$-0.407531\pi$
$337$	1.35639e11	0.572862	0.286431	+	0.958101i	$0.407531\pi$
$338$	1.03194e11	0.430059
$339$	2.31676e11	0.952759
$340$	0	0
$341$	7.56581e10	0.303013
$342$	2.33218e11	0.921817
$343$	2.72563e11	1.06327
$344$	−5.13413e10	−0.197676
$345$	1.84081e10	0.0699559
$346$	1.19524e11	0.448346
$347$	−1.52215e11	−0.563603	−0.281802	−	0.959473i	$-0.590932\pi$
$347$	−1.52215e11	−0.563603	−0.281802	+	0.959473i	$0.590932\pi$
$348$	7.17441e10	0.262228
$349$	1.78457e11	0.643903	0.321951	−	0.946756i	$-0.395661\pi$
$349$	1.78457e11	0.643903	0.321951	+	0.946756i	$0.395661\pi$
$350$	−1.12816e11	−0.401850
$351$	2.64921e10	0.0931612
$352$	−3.53537e11	−1.22742
$353$	2.96867e11	1.01760	0.508798	−	0.860886i	$-0.330090\pi$
$353$	2.96867e11	1.01760	0.508798	+	0.860886i	$0.330090\pi$
$354$	−4.53416e11	−1.53455
$355$	1.23587e10	0.0412994
$356$	2.26088e10	0.0746022
$357$	0	0
$358$	−6.81173e10	−0.219171
$359$	−1.67133e11	−0.531052	−0.265526	−	0.964104i	$-0.585546\pi$
$359$	−1.67133e11	−0.531052	−0.265526	+	0.964104i	$0.585546\pi$
$360$	−2.96168e10	−0.0929345
$361$	3.42916e11	1.06269
$362$	2.62259e11	0.802680
$363$	2.02760e11	0.612917
$364$	7.96782e10	0.237894
$365$	5.28893e10	0.155973
$366$	−1.26615e11	−0.368825
$367$	−3.22425e11	−0.927752	−0.463876	−	0.885900i	$-0.653542\pi$
$367$	−3.22425e11	−0.927752	−0.463876	+	0.885900i	$0.653542\pi$
$368$	−2.64632e10	−0.0752188
$369$	−1.09887e11	−0.308550
$370$	2.44662e10	0.0678671
$371$	−2.30530e11	−0.631748
$372$	−9.27934e10	−0.251231
$373$	−3.84623e10	−0.102883	−0.0514417	−	0.998676i	$-0.516382\pi$
$373$	−3.84623e10	−0.102883	−0.0514417	+	0.998676i	$0.516382\pi$
$374$	0	0
$375$	9.61353e10	0.251040
$376$	3.69669e11	0.953823
$377$	−5.13406e10	−0.130895
$378$	3.03569e10	0.0764793
$379$	−9.81716e10	−0.244405	−0.122202	−	0.992505i	$-0.538996\pi$
$379$	−9.81716e10	−0.244405	−0.122202	+	0.992505i	$0.538996\pi$
$380$	−3.41248e10	−0.0839544
$381$	−7.51323e11	−1.82669
$382$	1.45329e10	0.0349195
$383$	−3.91752e11	−0.930286	−0.465143	−	0.885236i	$-0.653997\pi$
$383$	−3.91752e11	−0.930286	−0.465143	+	0.885236i	$0.653997\pi$
$384$	4.81473e11	1.13001
$385$	3.15989e10	0.0732992
$386$	4.59513e11	1.05355
$387$	−1.03374e11	−0.234267
$388$	7.81562e10	0.175074
$389$	4.40744e11	0.975917	0.487959	−	0.872867i	$-0.337742\pi$
$389$	4.40744e11	0.975917	0.487959	+	0.872867i	$0.337742\pi$
$390$	1.61321e10	0.0353102
$391$	0	0
$392$	−2.19398e11	−0.469295
$393$	−3.90304e11	−0.825346
$394$	4.57676e11	0.956809
$395$	3.75163e10	0.0775413
$396$	−4.45932e11	−0.911255
$397$	−3.38508e11	−0.683930	−0.341965	−	0.939713i	$-0.611092\pi$
$397$	−3.38508e11	−0.683930	−0.341965	+	0.939713i	$0.611092\pi$
$398$	−4.01671e11	−0.802411
$399$	7.55927e11	1.49315
$400$	−6.88426e10	−0.134458
$401$	−1.71912e11	−0.332014	−0.166007	−	0.986125i	$-0.553087\pi$
$401$	−1.71912e11	−0.332014	−0.166007	+	0.986125i	$0.553087\pi$
$402$	−5.27175e11	−1.00679
$403$	6.64036e10	0.125406
$404$	−6.21022e11	−1.15982
$405$	3.99118e10	0.0737147
$406$	−5.88302e10	−0.107457
$407$	9.12471e11	1.64833
$408$	0	0
$409$	1.81166e11	0.320126	0.160063	−	0.987107i	$-0.448830\pi$
$409$	1.81166e11	0.320126	0.160063	+	0.987107i	$0.448830\pi$
$410$	−7.66918e9	−0.0134036
$411$	5.49456e11	0.949827
$412$	6.94354e11	1.18725
$413$	−7.79496e11	−1.31837
$414$	2.13020e11	0.356384
$415$	1.00233e11	0.165881
$416$	−3.10292e11	−0.507985
$417$	−8.88803e11	−1.43944
$418$	6.07041e11	0.972579
$419$	5.34687e11	0.847493	0.423747	−	0.905781i	$-0.360715\pi$
$419$	5.34687e11	0.847493	0.423747	+	0.905781i	$0.360715\pi$
$420$	−3.87556e10	−0.0607732
$421$	−4.75293e10	−0.0737381	−0.0368691	−	0.999320i	$-0.511738\pi$
$421$	−4.75293e10	−0.0737381	−0.0368691	+	0.999320i	$0.511738\pi$
$422$	3.72070e11	0.571108
$423$	7.44314e11	1.13038
$424$	5.62404e11	0.845088
$425$	0	0
$426$	2.69638e11	0.396678
$427$	−2.17672e11	−0.316867
$428$	−2.70456e11	−0.389583
$429$	6.01649e11	0.857601
$430$	−7.21463e9	−0.0101767
$431$	−8.44046e11	−1.17820	−0.589099	−	0.808061i	$-0.700517\pi$
$431$	−8.44046e11	−1.17820	−0.589099	+	0.808061i	$0.700517\pi$
$432$	1.85244e10	0.0255898
$433$	−2.09001e10	−0.0285728	−0.0142864	−	0.999898i	$-0.504548\pi$
$433$	−2.09001e10	−0.0285728	−0.0142864	+	0.999898i	$0.504548\pi$
$434$	7.60906e10	0.102950
$435$	2.49721e10	0.0334390
$436$	7.47328e11	0.990426
$437$	6.07957e11	0.797456
$438$	1.15393e12	1.49811
$439$	−1.18658e12	−1.52478	−0.762389	−	0.647119i	$-0.775974\pi$
$439$	−1.18658e12	−1.52478	−0.762389	+	0.647119i	$0.775974\pi$
$440$	−7.70893e10	−0.0980522
$441$	−4.41750e11	−0.556164
$442$	0	0
$443$	4.19386e11	0.517366	0.258683	−	0.965962i	$-0.416712\pi$
$443$	4.19386e11	0.517366	0.258683	+	0.965962i	$0.416712\pi$
$444$	−1.11913e12	−1.36665
$445$	7.86947e9	0.00951318
$446$	7.01310e11	0.839273
$447$	−1.48900e12	−1.76405
$448$	−2.73270e11	−0.320509
$449$	−6.83486e11	−0.793636	−0.396818	−	0.917897i	$-0.629886\pi$
$449$	−6.83486e11	−0.793636	−0.396818	+	0.917897i	$0.629886\pi$
$450$	5.54160e11	0.637057
$451$	−2.86023e11	−0.325542
$452$	−3.92283e11	−0.442055
$453$	8.90876e11	0.993975
$454$	−1.17980e11	−0.130334
$455$	2.77337e10	0.0303359
$456$	−1.84417e12	−1.99738
$457$	−1.13726e12	−1.21966	−0.609829	−	0.792533i	$-0.708762\pi$
$457$	−1.13726e12	−1.21966	−0.609829	+	0.792533i	$0.708762\pi$
$458$	−3.79010e11	−0.402491
$459$	0	0
$460$	−3.11693e10	−0.0324577
$461$	4.01702e11	0.414238	0.207119	−	0.978316i	$-0.433591\pi$
$461$	4.01702e11	0.414238	0.207119	+	0.978316i	$0.433591\pi$
$462$	6.89418e11	0.704035
$463$	−1.71828e12	−1.73772	−0.868859	−	0.495059i	$-0.835146\pi$
$463$	−1.71828e12	−1.73772	−0.868859	+	0.495059i	$0.835146\pi$
$464$	−3.58994e10	−0.0359547
$465$	−3.22988e10	−0.0320367
$466$	−7.13087e11	−0.700497
$467$	−1.25508e12	−1.22108	−0.610542	−	0.791984i	$-0.709048\pi$
$467$	−1.25508e12	−1.22108	−0.610542	+	0.791984i	$0.709048\pi$
$468$	−3.91385e11	−0.377136
$469$	−9.06300e11	−0.864956
$470$	5.19470e10	0.0491044
$471$	−1.69105e12	−1.58330
$472$	1.90167e12	1.76359
$473$	−2.69071e11	−0.247167
$474$	8.18522e11	0.744780
$475$	1.58157e12	1.42550
$476$	0	0
$477$	1.13238e12	1.00152
$478$	7.92379e11	0.694236
$479$	1.10403e12	0.958235	0.479118	−	0.877751i	$-0.340957\pi$
$479$	1.10403e12	0.958235	0.479118	+	0.877751i	$0.340957\pi$
$480$	1.50927e11	0.129772
$481$	8.00857e11	0.682185
$482$	5.77883e11	0.487672
$483$	6.90459e11	0.577266
$484$	−3.43320e11	−0.284377
$485$	2.72040e10	0.0223252
$486$	1.00281e12	0.815372
$487$	1.20949e12	0.974370	0.487185	−	0.873299i	$-0.338024\pi$
$487$	1.20949e12	0.974370	0.487185	+	0.873299i	$0.338024\pi$
$488$	5.31037e11	0.423872
$489$	−1.03595e12	−0.819312
$490$	−3.08305e10	−0.0241601
$491$	8.42274e11	0.654014	0.327007	−	0.945022i	$-0.393960\pi$
$491$	8.42274e11	0.654014	0.327007	+	0.945022i	$0.393960\pi$
$492$	3.50803e11	0.269910
$493$	0	0
$494$	5.32788e11	0.402516
$495$	−1.55216e11	−0.116202
$496$	4.64320e10	0.0344469
$497$	4.63552e11	0.340796
$498$	2.18687e12	1.59327
$499$	1.70715e12	1.23259	0.616297	−	0.787514i	$-0.288632\pi$
$499$	1.70715e12	1.23259	0.616297	+	0.787514i	$0.288632\pi$
$500$	−1.62780e11	−0.116476
$501$	2.98311e11	0.211543
$502$	−4.72771e11	−0.332264
$503$	1.31164e12	0.913605	0.456803	−	0.889568i	$-0.348995\pi$
$503$	1.31164e12	0.913605	0.456803	+	0.889568i	$0.348995\pi$
$504$	−1.11088e12	−0.766881
$505$	−2.16160e11	−0.147899
$506$	5.54467e11	0.376009
$507$	−1.64299e12	−1.10433
$508$	1.27217e12	0.847534
$509$	−2.27732e12	−1.50382	−0.751908	−	0.659268i	$-0.770866\pi$
$509$	−2.27732e12	−1.50382	−0.751908	+	0.659268i	$0.770866\pi$
$510$	0	0
$511$	1.98379e12	1.28707
$512$	−4.17721e11	−0.268641
$513$	−4.25574e11	−0.271298
$514$	−1.36656e12	−0.863566
$515$	2.41685e11	0.151397
$516$	3.30010e11	0.204929
$517$	1.93737e12	1.19263
$518$	9.17688e11	0.560030
$519$	−1.90300e12	−1.15129
$520$	−6.76597e10	−0.0405803
$521$	3.20184e12	1.90384	0.951919	−	0.306351i	$-0.0991081\pi$
$521$	3.20184e12	1.90384	0.951919	+	0.306351i	$0.0991081\pi$
$522$	2.88978e11	0.170352
$523$	2.74758e11	0.160580	0.0802902	−	0.996772i	$-0.474415\pi$
$523$	2.74758e11	0.160580	0.0802902	+	0.996772i	$0.474415\pi$
$524$	6.60876e11	0.382939
$525$	1.79619e12	1.03190
$526$	5.34514e11	0.304455
$527$	0	0
$528$	4.20697e11	0.235568
$529$	−1.24585e12	−0.691695
$530$	7.90307e10	0.0435065
$531$	3.82894e12	2.09003
$532$	−1.27996e12	−0.692779
$533$	−2.51037e11	−0.134730
$534$	1.71694e11	0.0913735
$535$	−9.41383e10	−0.0496791
$536$	2.21102e12	1.15705
$537$	1.08453e12	0.562802
$538$	2.48109e11	0.127680
$539$	−1.14983e12	−0.586791
$540$	2.18187e10	0.0110422
$541$	7.68673e11	0.385793	0.192896	−	0.981219i	$-0.438212\pi$
$541$	7.68673e11	0.385793	0.192896	+	0.981219i	$0.438212\pi$
$542$	7.09406e11	0.353100
$543$	−4.17555e12	−2.06117
$544$	0	0
$545$	2.60124e11	0.126298
$546$	6.05089e11	0.291375
$547$	−3.26534e12	−1.55950	−0.779750	−	0.626091i	$-0.784654\pi$
$547$	−3.26534e12	−1.55950	−0.779750	+	0.626091i	$0.784654\pi$
$548$	−9.30358e11	−0.440694
$549$	1.06922e12	0.502333
$550$	1.44242e12	0.672139
$551$	8.24742e11	0.381185
$552$	−1.68446e12	−0.772207
$553$	1.40717e12	0.639859
$554$	−1.92286e12	−0.867269
$555$	−3.89538e11	−0.174274
$556$	1.50495e12	0.667861
$557$	−1.66914e12	−0.734760	−0.367380	−	0.930071i	$-0.619745\pi$
$557$	−1.66914e12	−0.734760	−0.367380	+	0.930071i	$0.619745\pi$
$558$	−3.73762e11	−0.163208
$559$	−2.36158e11	−0.102294
$560$	1.93926e10	0.00833276
$561$	0	0
$562$	1.06413e12	0.449970
$563$	−1.13172e12	−0.474734	−0.237367	−	0.971420i	$-0.576284\pi$
$563$	−1.13172e12	−0.474734	−0.237367	+	0.971420i	$0.576284\pi$
$564$	−2.37615e12	−0.988822
$565$	−1.36543e11	−0.0563703
$566$	6.61761e11	0.271036
$567$	1.49703e12	0.608283
$568$	−1.13089e12	−0.455883
$569$	−2.09042e12	−0.836042	−0.418021	−	0.908437i	$-0.637276\pi$
$569$	−2.09042e12	−0.836042	−0.418021	+	0.908437i	$0.637276\pi$
$570$	−2.59149e11	−0.102828
$571$	6.27130e11	0.246885	0.123443	−	0.992352i	$-0.460607\pi$
$571$	6.27130e11	0.246885	0.123443	+	0.992352i	$0.460607\pi$
$572$	−1.01873e12	−0.397904
$573$	−2.31385e11	−0.0896685
$574$	−2.87658e11	−0.110605
$575$	1.44459e12	0.551113
$576$	1.34232e12	0.508106
$577$	1.42436e12	0.534968	0.267484	−	0.963562i	$-0.413808\pi$
$577$	1.42436e12	0.534968	0.267484	+	0.963562i	$0.413808\pi$
$578$	0	0
$579$	−7.31612e12	−2.70537
$580$	−4.22837e10	−0.0155148
$581$	3.75958e12	1.36882
$582$	5.93530e11	0.214432
$583$	2.94746e12	1.05667
$584$	−4.83969e12	−1.72171
$585$	−1.36230e11	−0.0480919
$586$	−1.56782e12	−0.549233
$587$	3.09625e12	1.07638	0.538189	−	0.842824i	$-0.319109\pi$
$587$	3.09625e12	1.07638	0.538189	+	0.842824i	$0.319109\pi$
$588$	1.41024e12	0.486515
$589$	−1.06672e12	−0.365200
$590$	2.67228e11	0.0907922
$591$	−7.28687e12	−2.45695
$592$	5.59992e11	0.187385
$593$	−1.01140e12	−0.335874	−0.167937	−	0.985798i	$-0.553711\pi$
$593$	−1.01140e12	−0.335874	−0.167937	+	0.985798i	$0.553711\pi$
$594$	−3.88130e11	−0.127920
$595$	0	0
$596$	2.52123e12	0.818472
$597$	6.39519e12	2.06048
$598$	4.86645e11	0.155617
$599$	−1.80697e12	−0.573495	−0.286747	−	0.958006i	$-0.592574\pi$
$599$	−1.80697e12	−0.573495	−0.286747	+	0.958006i	$0.592574\pi$
$600$	−4.38202e12	−1.38037
$601$	−1.41403e12	−0.442102	−0.221051	−	0.975262i	$-0.570949\pi$
$601$	−1.41403e12	−0.442102	−0.221051	+	0.975262i	$0.570949\pi$
$602$	−2.70609e11	−0.0839765
$603$	4.45181e12	1.37122
$604$	−1.50846e12	−0.461178
$605$	−1.19500e11	−0.0362634
$606$	−4.71613e12	−1.42056
$607$	−1.19074e12	−0.356015	−0.178008	−	0.984029i	$-0.556965\pi$
$607$	−1.19074e12	−0.356015	−0.178008	+	0.984029i	$0.556965\pi$
$608$	4.98458e12	1.47932
$609$	9.36662e11	0.275934
$610$	7.46228e10	0.0218216
$611$	1.70039e12	0.493586
$612$	0	0
$613$	−3.81378e11	−0.109090	−0.0545448	−	0.998511i	$-0.517371\pi$
$613$	−3.81378e11	−0.109090	−0.0545448	+	0.998511i	$0.517371\pi$
$614$	−1.24936e12	−0.354757
$615$	1.22104e11	0.0344186
$616$	−2.89149e12	−0.809112
$617$	2.00413e12	0.556727	0.278364	−	0.960476i	$-0.410208\pi$
$617$	2.00413e12	0.556727	0.278364	+	0.960476i	$0.410208\pi$
$618$	5.27303e12	1.45416
$619$	−1.20173e12	−0.329003	−0.164501	−	0.986377i	$-0.552601\pi$
$619$	−1.20173e12	−0.329003	−0.164501	+	0.986377i	$0.552601\pi$
$620$	5.46894e10	0.0148642
$621$	−3.88716e11	−0.104887
$622$	−2.86903e12	−0.768561
$623$	2.95171e11	0.0785013
$624$	3.69237e11	0.0974933
$625$	3.72960e12	0.977693
$626$	2.05397e11	0.0534576
$627$	−9.66498e12	−2.49745
$628$	2.86334e12	0.734607
$629$	0	0
$630$	−1.56104e11	−0.0394803
$631$	9.59070e11	0.240834	0.120417	−	0.992723i	$-0.461577\pi$
$631$	9.59070e11	0.240834	0.120417	+	0.992723i	$0.461577\pi$
$632$	−3.43297e12	−0.855939
$633$	−5.92389e12	−1.46653
$634$	−2.59995e12	−0.639092
$635$	4.42805e11	0.108076
$636$	−3.61501e12	−0.876097
$637$	−1.00918e12	−0.242852
$638$	7.52179e11	0.179733
$639$	−2.27700e12	−0.540268
$640$	−2.83764e11	−0.0668572
$641$	1.76987e12	0.414077	0.207038	−	0.978333i	$-0.433617\pi$
$641$	1.76987e12	0.414077	0.207038	+	0.978333i	$0.433617\pi$
$642$	−2.05389e12	−0.477165
$643$	7.53766e12	1.73895	0.869475	−	0.493977i	$-0.164457\pi$
$643$	7.53766e12	1.73895	0.869475	+	0.493977i	$0.164457\pi$
$644$	−1.16911e12	−0.267836
$645$	1.14867e11	0.0261323
$646$	0	0
$647$	−5.30405e12	−1.18998	−0.594989	−	0.803734i	$-0.702843\pi$
$647$	−5.30405e12	−1.18998	−0.594989	+	0.803734i	$0.702843\pi$
$648$	−3.65217e12	−0.813698
$649$	9.96632e12	2.20513
$650$	1.26598e12	0.278174
$651$	−1.21147e12	−0.264362
$652$	1.75411e12	0.380139
$653$	−3.41486e11	−0.0734959	−0.0367480	−	0.999325i	$-0.511700\pi$
$653$	−3.41486e11	−0.0734959	−0.0367480	+	0.999325i	$0.511700\pi$
$654$	5.67532e12	1.21308
$655$	2.30032e11	0.0488318
$656$	−1.75535e11	−0.0370080
$657$	−9.74452e12	−2.04040
$658$	1.94844e12	0.405202
$659$	−1.73640e12	−0.358646	−0.179323	−	0.983790i	$-0.557391\pi$
$659$	−1.73640e12	−0.358646	−0.179323	+	0.983790i	$0.557391\pi$
$660$	4.95513e11	0.101650
$661$	−7.10034e12	−1.44668	−0.723340	−	0.690492i	$-0.757394\pi$
$661$	−7.10034e12	−1.44668	−0.723340	+	0.690492i	$0.757394\pi$
$662$	4.73244e12	0.957689
$663$	0	0
$664$	−9.17195e12	−1.83107
$665$	−4.45519e11	−0.0883423
$666$	−4.50775e12	−0.887821
$667$	7.53314e11	0.147370
$668$	−5.05111e11	−0.0981505
$669$	−1.11659e13	−2.15514
$670$	3.10700e11	0.0595668
$671$	2.78307e12	0.529996
$672$	5.66100e12	1.07086
$673$	−8.55362e11	−0.160725	−0.0803623	−	0.996766i	$-0.525608\pi$
$673$	−8.55362e11	−0.160725	−0.0803623	+	0.996766i	$0.525608\pi$
$674$	−1.74414e12	−0.325545
$675$	−1.01122e12	−0.187491
$676$	2.78197e12	0.512381
$677$	1.00796e13	1.84415	0.922073	−	0.387017i	$-0.126494\pi$
$677$	1.00796e13	1.84415	0.922073	+	0.387017i	$0.126494\pi$
$678$	−2.97905e12	−0.541433
$679$	1.02038e12	0.184224
$680$	0	0
$681$	1.87841e12	0.334679
$682$	−9.72864e11	−0.172196
$683$	−4.29728e12	−0.755614	−0.377807	−	0.925884i	$-0.623322\pi$
$683$	−4.29728e12	−0.755614	−0.377807	+	0.925884i	$0.623322\pi$
$684$	6.28727e12	1.09827
$685$	−3.23831e11	−0.0561968
$686$	−3.50480e12	−0.604233
$687$	6.03439e12	1.03354
$688$	−1.65131e11	−0.0280983
$689$	2.58692e12	0.437318
$690$	−2.36705e11	−0.0397544
$691$	7.79682e12	1.30097	0.650484	−	0.759520i	$-0.274566\pi$
$691$	7.79682e12	1.30097	0.650484	+	0.759520i	$0.274566\pi$
$692$	3.22223e12	0.534169
$693$	−5.82190e12	−0.958882
$694$	1.95728e12	0.320284
$695$	5.23832e11	0.0851648
$696$	−2.28510e12	−0.369116
$697$	0	0
$698$	−2.29473e12	−0.365916
$699$	1.13534e13	1.79878
$700$	−3.04138e12	−0.478772
$701$	−2.38474e12	−0.373000	−0.186500	−	0.982455i	$-0.559714\pi$
$701$	−2.38474e12	−0.373000	−0.186500	+	0.982455i	$0.559714\pi$
$702$	−3.40654e11	−0.0529416
$703$	−1.28651e13	−1.98662
$704$	3.49391e12	0.536087
$705$	−8.27071e11	−0.126093
$706$	−3.81732e12	−0.578279
$707$	−8.10781e12	−1.22044
$708$	−1.22235e13	−1.82830
$709$	−5.62327e12	−0.835759	−0.417880	−	0.908502i	$-0.637227\pi$
$709$	−5.62327e12	−0.835759	−0.417880	+	0.908502i	$0.637227\pi$
$710$	−1.58916e11	−0.0234696
$711$	−6.91214e12	−1.01438
$712$	−7.20104e11	−0.105011
$713$	−9.74332e11	−0.141190
$714$	0	0
$715$	−3.54592e11	−0.0507402
$716$	−1.83636e12	−0.261125
$717$	−1.26158e13	−1.78270
$718$	2.14911e12	0.301786
$719$	−1.53363e12	−0.214013	−0.107006	−	0.994258i	$-0.534126\pi$
$719$	−1.53363e12	−0.214013	−0.107006	+	0.994258i	$0.534126\pi$
$720$	−9.52576e10	−0.0132100
$721$	9.06521e12	1.24931
$722$	−4.40944e12	−0.603902
$723$	−9.20073e12	−1.25228
$724$	7.07019e12	0.956329
$725$	1.95971e12	0.263433
$726$	−2.60722e12	−0.348308
$727$	−1.19798e12	−0.159054	−0.0795268	−	0.996833i	$-0.525341\pi$
$727$	−1.19798e12	−0.159054	−0.0795268	+	0.996833i	$0.525341\pi$
$728$	−2.53780e12	−0.334863
$729$	−9.45552e12	−1.23997
$730$	−6.80087e11	−0.0886364
$731$	0	0
$732$	−3.41338e12	−0.439426
$733$	−8.71100e12	−1.11455	−0.557276	−	0.830328i	$-0.688153\pi$
$733$	−8.71100e12	−1.11455	−0.557276	+	0.830328i	$0.688153\pi$
$734$	4.14597e12	0.527222
$735$	4.90866e11	0.0620398
$736$	4.55288e12	0.571921
$737$	1.15876e13	1.44674
$738$	1.41300e12	0.175343
$739$	1.05005e13	1.29512	0.647560	−	0.762015i	$-0.275790\pi$
$739$	1.05005e13	1.29512	0.647560	+	0.762015i	$0.275790\pi$
$740$	6.59580e11	0.0808583
$741$	−8.48276e12	−1.03361
$742$	2.96431e12	0.359009
$743$	1.33088e13	1.60210	0.801051	−	0.598596i	$-0.204274\pi$
$743$	1.33088e13	1.60210	0.801051	+	0.598596i	$0.204274\pi$
$744$	2.95553e12	0.353637
$745$	8.77568e11	0.104370
$746$	4.94575e11	0.0584665
$747$	−1.84673e13	−2.17001
$748$	0	0
$749$	−3.53097e12	−0.409945
$750$	−1.23617e12	−0.142661
$751$	9.18538e12	1.05370	0.526850	−	0.849958i	$-0.323373\pi$
$751$	9.18538e12	1.05370	0.526850	+	0.849958i	$0.323373\pi$
$752$	1.18898e12	0.135580
$753$	7.52719e12	0.853209
$754$	6.60172e11	0.0743851
$755$	−5.25053e11	−0.0588088
$756$	8.18383e11	0.0911189
$757$	1.11837e13	1.23781	0.618903	−	0.785467i	$-0.287577\pi$
$757$	1.11837e13	1.23781	0.618903	+	0.785467i	$0.287577\pi$
$758$	1.26236e12	0.138890
$759$	−8.82792e12	−0.965541
$760$	1.08690e12	0.118175
$761$	4.29799e12	0.464553	0.232276	−	0.972650i	$-0.425383\pi$
$761$	4.29799e12	0.464553	0.232276	+	0.972650i	$0.425383\pi$
$762$	9.66102e12	1.03807
$763$	9.75681e12	1.04219
$764$	3.91790e11	0.0416038
$765$	0	0
$766$	5.03741e12	0.528662
$767$	8.74723e12	0.912623
$768$	−1.25203e13	−1.29864
$769$	−9.88894e12	−1.01972	−0.509860	−	0.860257i	$-0.670303\pi$
$769$	−9.88894e12	−1.01972	−0.509860	+	0.860257i	$0.670303\pi$
$770$	−4.06321e11	−0.0416544
$771$	2.17577e13	2.21752
$772$	1.23879e13	1.25522
$773$	−1.06695e13	−1.07482	−0.537409	−	0.843322i	$-0.680597\pi$
$773$	−1.06695e13	−1.07482	−0.537409	+	0.843322i	$0.680597\pi$
$774$	1.32925e12	0.133129
$775$	−2.53467e12	−0.252385
$776$	−2.48933e12	−0.246436
$777$	−1.46109e13	−1.43808
$778$	−5.66738e12	−0.554593
$779$	4.03269e12	0.392352
$780$	4.34902e11	0.0420693
$781$	−5.92679e12	−0.570020
$782$	0	0
$783$	−5.27324e11	−0.0501360
$784$	−7.05659e11	−0.0667072
$785$	9.96649e11	0.0936761
$786$	5.01879e12	0.469027
$787$	1.39379e13	1.29513	0.647563	−	0.762012i	$-0.275788\pi$
$787$	1.39379e13	1.29513	0.647563	+	0.762012i	$0.275788\pi$
$788$	1.23384e13	1.13996
$789$	−8.51023e12	−0.781799
$790$	−4.82410e11	−0.0440651
$791$	−5.12148e12	−0.465159
$792$	1.42032e13	1.28269
$793$	2.44264e12	0.219346
$794$	4.35277e12	0.388663
$795$	−1.25828e12	−0.111719
$796$	−1.08286e13	−0.956009
$797$	5.24283e11	0.0460260	0.0230130	−	0.999735i	$-0.492674\pi$
$797$	5.24283e11	0.0460260	0.0230130	+	0.999735i	$0.492674\pi$
$798$	−9.72023e12	−0.848523
$799$	0	0
$800$	1.18441e13	1.02234
$801$	−1.44990e12	−0.124449
$802$	2.21056e12	0.188677
$803$	−2.53639e13	−2.15277
$804$	−1.42120e13	−1.19951
$805$	−4.06934e11	−0.0341541
$806$	−8.53863e11	−0.0712657
$807$	−3.95025e12	−0.327864
$808$	1.97800e13	1.63258
$809$	−5.77660e12	−0.474137	−0.237069	−	0.971493i	$-0.576187\pi$
$809$	−5.77660e12	−0.474137	−0.237069	+	0.971493i	$0.576187\pi$
$810$	−5.13214e11	−0.0418905
$811$	−4.16550e11	−0.0338122	−0.0169061	−	0.999857i	$-0.505382\pi$
$811$	−4.16550e11	−0.0338122	−0.0169061	+	0.999857i	$0.505382\pi$
$812$	−1.58599e12	−0.128026
$813$	−1.12948e13	−0.906714
$814$	−1.17332e13	−0.936712
$815$	6.10556e11	0.0484748
$816$	0	0
$817$	3.79367e12	0.297893
$818$	−2.32956e12	−0.181921
$819$	−5.10976e12	−0.396847
$820$	−2.06752e11	−0.0159693
$821$	1.00996e13	0.775822	0.387911	−	0.921697i	$-0.373197\pi$
$821$	1.00996e13	0.775822	0.387911	+	0.921697i	$0.373197\pi$
$822$	−7.06528e12	−0.539767
$823$	4.79075e12	0.364003	0.182001	−	0.983298i	$-0.441742\pi$
$823$	4.79075e12	0.364003	0.182001	+	0.983298i	$0.441742\pi$
$824$	−2.21156e13	−1.67120
$825$	−2.29654e13	−1.72596
$826$	1.00233e13	0.749204
$827$	2.02121e13	1.50258	0.751288	−	0.659975i	$-0.229433\pi$
$827$	2.02121e13	1.50258	0.751288	+	0.659975i	$0.229433\pi$
$828$	5.74275e12	0.424603
$829$	9.90972e12	0.728729	0.364364	−	0.931256i	$-0.381286\pi$
$829$	9.90972e12	0.728729	0.364364	+	0.931256i	$0.381286\pi$
$830$	−1.28887e12	−0.0942665
$831$	3.06147e13	2.22703
$832$	3.06654e12	0.221867
$833$	0	0
$834$	1.14288e13	0.818003
$835$	−1.75815e11	−0.0125160
$836$	1.63651e13	1.15875
$837$	6.82038e11	0.0480335
$838$	−6.87537e12	−0.481613
$839$	−8.45160e12	−0.588857	−0.294429	−	0.955673i	$-0.595129\pi$
$839$	−8.45160e12	−0.588857	−0.294429	+	0.955673i	$0.595129\pi$
$840$	1.23439e12	0.0855452
$841$	−1.34852e13	−0.929557
$842$	6.11165e11	0.0419038
$843$	−1.69426e13	−1.15546
$844$	1.00305e13	0.680430
$845$	9.68327e11	0.0653381
$846$	−9.57090e12	−0.642371
$847$	−4.48224e12	−0.299240
$848$	1.80888e12	0.120124
$849$	−1.05362e13	−0.695984
$850$	0	0
$851$	−1.17509e13	−0.768047
$852$	7.26911e12	0.472610
$853$	−8.99345e12	−0.581642	−0.290821	−	0.956778i	$-0.593928\pi$
$853$	−8.99345e12	−0.581642	−0.290821	+	0.956778i	$0.593928\pi$
$854$	2.79898e12	0.180069
$855$	2.18842e12	0.140050
$856$	8.61421e12	0.548383
$857$	1.72593e12	0.109297	0.0546486	−	0.998506i	$-0.482596\pi$
$857$	1.72593e12	0.109297	0.0546486	+	0.998506i	$0.482596\pi$
$858$	−7.73642e12	−0.487357
$859$	−4.15450e12	−0.260345	−0.130173	−	0.991491i	$-0.541553\pi$
$859$	−4.15450e12	−0.260345	−0.130173	+	0.991491i	$0.541553\pi$
$860$	−1.94497e11	−0.0121247
$861$	4.57993e12	0.284018
$862$	1.08533e13	0.669545
$863$	−3.76231e11	−0.0230890	−0.0115445	−	0.999933i	$-0.503675\pi$
$863$	−3.76231e11	−0.0230890	−0.0115445	+	0.999933i	$0.503675\pi$
$864$	−3.18704e12	−0.194570
$865$	1.12157e12	0.0681165
$866$	2.68748e11	0.0162373
$867$	0	0
$868$	2.05131e12	0.122657
$869$	−1.79916e13	−1.07024
$870$	−3.21109e11	−0.0190027
$871$	1.01702e13	0.598752
$872$	−2.38029e13	−1.39414
$873$	−5.01216e12	−0.292052
$874$	−7.81753e12	−0.453177
$875$	−2.12519e12	−0.122563
$876$	3.11085e13	1.78488
$877$	−1.91957e13	−1.09574	−0.547869	−	0.836564i	$-0.684561\pi$
$877$	−1.91957e13	−1.09574	−0.547869	+	0.836564i	$0.684561\pi$
$878$	1.52579e13	0.866500
$879$	2.49619e13	1.41035
$880$	−2.47945e11	−0.0139375
$881$	1.22362e12	0.0684312	0.0342156	−	0.999414i	$-0.489107\pi$
$881$	1.22362e12	0.0684312	0.0342156	+	0.999414i	$0.489107\pi$
$882$	5.68032e12	0.316056
$883$	1.57603e13	0.872451	0.436225	−	0.899837i	$-0.356315\pi$
$883$	1.57603e13	0.872451	0.436225	+	0.899837i	$0.356315\pi$
$884$	0	0
$885$	−4.25466e12	−0.233142
$886$	−5.39276e12	−0.294008
$887$	−3.84466e12	−0.208546	−0.104273	−	0.994549i	$-0.533252\pi$
$887$	−3.84466e12	−0.208546	−0.104273	+	0.994549i	$0.533252\pi$
$888$	3.56451e13	1.92372
$889$	1.66089e13	0.891831
$890$	−1.01191e11	−0.00540614
$891$	−1.91404e13	−1.01742
$892$	1.89064e13	0.999926
$893$	−2.73153e13	−1.43739
$894$	1.91466e13	1.00247
$895$	−6.39185e11	−0.0332984
$896$	−1.06435e13	−0.551696
$897$	−7.74809e12	−0.399603
$898$	8.78874e12	0.451007
$899$	−1.32176e12	−0.0674891
$900$	1.49395e13	0.759003
$901$	0	0
$902$	3.67788e12	0.184998
$903$	4.30848e12	0.215640
$904$	1.24945e13	0.622242
$905$	2.46093e12	0.121950
$906$	−1.14555e13	−0.564855
$907$	−3.00858e13	−1.47614	−0.738072	−	0.674722i	$-0.764264\pi$
$907$	−3.00858e13	−1.47614	−0.738072	+	0.674722i	$0.764264\pi$
$908$	−3.18059e12	−0.155282
$909$	3.98261e13	1.93478
$910$	−3.56620e11	−0.0172393
$911$	3.25658e13	1.56650	0.783249	−	0.621709i	$-0.213561\pi$
$911$	3.25658e13	1.56650	0.783249	+	0.621709i	$0.213561\pi$
$912$	−5.93148e12	−0.283914
$913$	−4.80685e13	−2.28951
$914$	1.46237e13	0.693105
$915$	−1.18810e12	−0.0560350
$916$	−1.02176e13	−0.479536
$917$	8.62813e12	0.402953
$918$	0	0
$919$	1.18128e13	0.546304	0.273152	−	0.961971i	$-0.411934\pi$
$919$	1.18128e13	0.546304	0.273152	+	0.961971i	$0.411934\pi$
$920$	9.92763e11	0.0456878
$921$	1.98917e13	0.910968
$922$	−5.16535e12	−0.235402
$923$	−5.20182e12	−0.235911
$924$	1.85859e13	0.838801
$925$	−3.05693e13	−1.37293
$926$	2.20948e13	0.987509
$927$	−4.45289e13	−1.98054
$928$	6.17635e12	0.273379
$929$	−3.31944e13	−1.46216	−0.731078	−	0.682293i	$-0.760983\pi$
$929$	−3.31944e13	−1.46216	−0.731078	+	0.682293i	$0.760983\pi$
$930$	4.15320e11	0.0182058
$931$	1.62116e13	0.707217
$932$	−1.92239e13	−0.834586
$933$	4.56791e13	1.97356
$934$	1.61387e13	0.693916
$935$	0	0
$936$	1.24659e13	0.530862
$937$	−7.61249e12	−0.322625	−0.161313	−	0.986903i	$-0.551573\pi$
$937$	−7.61249e12	−0.322625	−0.161313	+	0.986903i	$0.551573\pi$
$938$	1.16538e13	0.491536
$939$	−3.27022e12	−0.137272
$940$	1.40043e12	0.0585039
$941$	8.99657e12	0.374045	0.187022	−	0.982356i	$-0.440116\pi$
$941$	8.99657e12	0.374045	0.187022	+	0.982356i	$0.440116\pi$
$942$	2.17447e13	0.899754
$943$	3.68343e12	0.151687
$944$	6.11642e12	0.250682
$945$	2.84856e11	0.0116194
$946$	3.45989e12	0.140460
$947$	4.12752e12	0.166769	0.0833843	−	0.996517i	$-0.473427\pi$
$947$	4.12752e12	0.166769	0.0833843	+	0.996517i	$0.473427\pi$
$948$	2.20663e13	0.887345
$949$	−2.22614e13	−0.890953
$950$	−2.03369e13	−0.810081
$951$	4.13950e13	1.64110
$952$	0	0
$953$	1.80381e13	0.708389	0.354195	−	0.935172i	$-0.384755\pi$
$953$	1.80381e13	0.708389	0.354195	+	0.935172i	$0.384755\pi$
$954$	−1.45609e13	−0.569141
$955$	1.36371e11	0.00530526
$956$	2.13615e13	0.827127
$957$	−1.19758e13	−0.461530
$958$	−1.41964e13	−0.544545
$959$	−1.21464e13	−0.463728
$960$	−1.49157e12	−0.0566790
$961$	−2.47301e13	−0.935341
$962$	−1.02980e13	−0.387672
$963$	1.73444e13	0.649890
$964$	1.55790e13	0.581023
$965$	4.31188e12	0.160064
$966$	−8.87839e12	−0.328048
$967$	−3.92827e12	−0.144472	−0.0722358	−	0.997388i	$-0.523013\pi$
$967$	−3.92827e12	−0.144472	−0.0722358	+	0.997388i	$0.523013\pi$
$968$	1.09350e13	0.400293
$969$	0	0
$970$	−3.49808e11	−0.0126869
$971$	3.04563e13	1.09949	0.549744	−	0.835333i	$-0.314725\pi$
$971$	3.04563e13	1.09949	0.549744	+	0.835333i	$0.314725\pi$
$972$	2.70346e13	0.971451
$973$	1.96481e13	0.702768
$974$	−1.55525e13	−0.553714
$975$	−2.01563e13	−0.714314
$976$	1.70799e12	0.0602506
$977$	1.55251e13	0.545140	0.272570	−	0.962136i	$-0.412126\pi$
$977$	1.55251e13	0.545140	0.272570	+	0.962136i	$0.412126\pi$
$978$	1.33210e13	0.465598
$979$	−3.77393e12	−0.131302
$980$	−8.31152e11	−0.0287848
$981$	−4.79261e13	−1.65220
$982$	−1.08305e13	−0.371662
$983$	−4.00675e13	−1.36868	−0.684339	−	0.729164i	$-0.739909\pi$
$983$	−4.00675e13	−1.36868	−0.684339	+	0.729164i	$0.739909\pi$
$984$	−1.11733e13	−0.379930
$985$	4.29464e12	0.145366
$986$	0	0
$987$	−3.10221e13	−1.04050
$988$	1.43633e13	0.479566
$989$	3.46511e12	0.115169
$990$	1.99588e12	0.0660352
$991$	−2.48607e12	−0.0818808	−0.0409404	−	0.999162i	$-0.513035\pi$
$991$	−2.48607e12	−0.0818808	−0.0409404	+	0.999162i	$0.513035\pi$
$992$	−7.98845e12	−0.261915
$993$	−7.53473e13	−2.45921
$994$	−5.96067e12	−0.193667
$995$	−3.76912e12	−0.121909
$996$	5.89552e13	1.89826
$997$	2.45995e13	0.788494	0.394247	−	0.919005i	$-0.371006\pi$
$997$	2.45995e13	0.788494	0.394247	+	0.919005i	$0.371006\pi$
$998$	−2.19517e13	−0.700457
$999$	8.22569e12	0.261293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.10		24
17.8	even	8		17.10.c.a.13.8	yes	24
17.15	even	8		17.10.c.a.4.5	✓	24
17.16	even	2	inner	289.10.a.f.1.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.5	✓	24	17.15	even	8
17.10.c.a.13.8	yes	24	17.8	even	8
289.10.a.f.1.9		24	17.16	even	2	inner
289.10.a.f.1.10		24	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-12.8587 q^{2} +204.729 q^{3} -346.654 q^{4} -120.661 q^{5} -2632.54 q^{6} -4525.78 q^{7} +11041.2 q^{8} +22230.9 q^{9} +O(q^{10})\)	\(q-12.8587 q^{2} +204.729 q^{3} -346.654 q^{4} -120.661 q^{5} -2632.54 q^{6} -4525.78 q^{7} +11041.2 q^{8} +22230.9 q^{9} +1551.54 q^{10} +57864.7 q^{11} -70970.1 q^{12} +50786.7 q^{13} +58195.5 q^{14} -24702.7 q^{15} +35512.1 q^{16} -285861. q^{18} -815845. q^{19} +41827.5 q^{20} -926557. q^{21} -744065. q^{22} -745187. q^{23} +2.26045e6 q^{24} -1.93857e6 q^{25} -653050. q^{26} +521635. q^{27} +1.56888e6 q^{28} -1.01091e6 q^{29} +317644. q^{30} +1.30750e6 q^{31} -6.10972e6 q^{32} +1.18466e7 q^{33} +546083. q^{35} -7.70645e6 q^{36} +1.57690e7 q^{37} +1.04907e7 q^{38} +1.03975e7 q^{39} -1.33223e6 q^{40} -4.94296e6 q^{41} +1.19143e7 q^{42} -4.64999e6 q^{43} -2.00591e7 q^{44} -2.68240e6 q^{45} +9.58213e6 q^{46} +3.34810e7 q^{47} +7.27035e6 q^{48} -1.98710e7 q^{49} +2.49274e7 q^{50} -1.76054e7 q^{52} +5.09370e7 q^{53} -6.70755e6 q^{54} -6.98199e6 q^{55} -4.99698e7 q^{56} -1.67027e8 q^{57} +1.29989e7 q^{58} +1.72235e8 q^{59} +8.56330e6 q^{60} +4.80961e7 q^{61} -1.68127e7 q^{62} -1.00612e8 q^{63} +6.03807e7 q^{64} -6.12795e6 q^{65} -1.52332e8 q^{66} +2.00253e8 q^{67} -1.52561e8 q^{69} -7.02191e6 q^{70} -1.02425e8 q^{71} +2.45455e8 q^{72} -4.38332e8 q^{73} -2.02769e8 q^{74} -3.96881e8 q^{75} +2.82816e8 q^{76} -2.61883e8 q^{77} -1.33698e8 q^{78} -3.10924e8 q^{79} -4.28491e6 q^{80} -3.30778e8 q^{81} +6.35600e7 q^{82} -8.30705e8 q^{83} +3.21195e8 q^{84} +5.97928e7 q^{86} -2.06962e8 q^{87} +6.38894e8 q^{88} -6.52199e7 q^{89} +3.44921e7 q^{90} -2.29849e8 q^{91} +2.58322e8 q^{92} +2.67683e8 q^{93} -4.30522e8 q^{94} +9.84404e7 q^{95} -1.25084e9 q^{96} -2.25459e8 q^{97} +2.55514e8 q^{98} +1.28639e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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