LMFDB - Embedded newform 47.16.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,16,Mod(1,47)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	47.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:	$67.0659473970$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+180.170 q^{2} +4814.12 q^{3} -306.823 q^{4} +234624. q^{5} +867360. q^{6} -3.90024e6 q^{7} -5.95909e6 q^{8} +8.82688e6 q^{9} +O(q^{10})$	\(q+180.170 q^{2} +4814.12 q^{3} -306.823 q^{4} +234624. q^{5} +867360. q^{6} -3.90024e6 q^{7} -5.95909e6 q^{8} +8.82688e6 q^{9} +4.22722e7 q^{10} -6.01049e7 q^{11} -1.47708e6 q^{12} +2.37923e8 q^{13} -7.02706e8 q^{14} +1.12951e9 q^{15} -1.06359e9 q^{16} -3.07237e9 q^{17} +1.59034e9 q^{18} -5.20091e9 q^{19} -7.19880e7 q^{20} -1.87762e10 q^{21} -1.08291e10 q^{22} +1.30603e10 q^{23} -2.86878e10 q^{24} +2.45309e10 q^{25} +4.28666e10 q^{26} -2.65837e10 q^{27} +1.19668e9 q^{28} -9.06607e10 q^{29} +2.03503e11 q^{30} +1.73938e11 q^{31} +3.63980e9 q^{32} -2.89353e11 q^{33} -5.53548e11 q^{34} -9.15090e11 q^{35} -2.70829e9 q^{36} -6.88388e11 q^{37} -9.37048e11 q^{38} +1.14539e12 q^{39} -1.39814e12 q^{40} +2.09803e12 q^{41} -3.38291e12 q^{42} +1.48362e11 q^{43} +1.84416e10 q^{44} +2.07100e12 q^{45} +2.35307e12 q^{46} +5.06623e11 q^{47} -5.12027e12 q^{48} +1.04643e13 q^{49} +4.41972e12 q^{50} -1.47908e13 q^{51} -7.30002e10 q^{52} +5.94921e12 q^{53} -4.78959e12 q^{54} -1.41021e13 q^{55} +2.32419e13 q^{56} -2.50378e13 q^{57} -1.63343e13 q^{58} +2.12217e13 q^{59} -3.46559e11 q^{60} -4.28821e13 q^{61} +3.13384e13 q^{62} -3.44269e13 q^{63} +3.55076e13 q^{64} +5.58225e13 q^{65} -5.21326e13 q^{66} -3.83429e13 q^{67} +9.42672e11 q^{68} +6.28739e13 q^{69} -1.64872e14 q^{70} -4.66251e13 q^{71} -5.26001e13 q^{72} -5.86765e13 q^{73} -1.24027e14 q^{74} +1.18095e14 q^{75} +1.59576e12 q^{76} +2.34424e14 q^{77} +2.06365e14 q^{78} +1.69712e14 q^{79} -2.49545e14 q^{80} -2.54633e14 q^{81} +3.78001e14 q^{82} -2.46874e14 q^{83} +5.76097e12 q^{84} -7.20851e14 q^{85} +2.67303e13 q^{86} -4.36452e14 q^{87} +3.58170e14 q^{88} +2.00232e14 q^{89} +3.73131e14 q^{90} -9.27957e14 q^{91} -4.00720e12 q^{92} +8.37358e14 q^{93} +9.12782e13 q^{94} -1.22026e15 q^{95} +1.75225e13 q^{96} +7.04024e14 q^{97} +1.88535e15 q^{98} -5.30539e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 473 q^{2} - 1745 q^{3} + 352357 q^{4} - 204476 q^{5} - 747008 q^{6} - 8691077 q^{7} - 17976447 q^{8} + 89941305 q^{9}+O(q^{10}) $ 26 * q - 473 * q^2 - 1745 * q^3 + 352357 * q^4 - 204476 * q^5 - 747008 * q^6 - 8691077 * q^7 - 17976447 * q^8 + 89941305 * q^9	\( 26 q - 473 q^{2} - 1745 q^{3} + 352357 q^{4} - 204476 q^{5} - 747008 q^{6} - 8691077 q^{7} - 17976447 q^{8} + 89941305 q^{9} - 51585280 q^{10} + 3001662 q^{11} + 512888508 q^{12} - 508793550 q^{13} - 942073166 q^{14} + 434322614 q^{15} + 7184267409 q^{16} - 4325904793 q^{17} - 9157469975 q^{18} - 4303587332 q^{19} - 32919037912 q^{20} - 45132645408 q^{21} - 50162299142 q^{22} - 13266095576 q^{23} - 110793074064 q^{24} + 65244286550 q^{25} + 10349295428 q^{26} - 77660429552 q^{27} - 239645313896 q^{28} - 66416799998 q^{29} + 507306134084 q^{30} + 103672859796 q^{31} + 368590250641 q^{32} + 570965925392 q^{33} - 100184286950 q^{34} + 581363635284 q^{35} + 2931853687289 q^{36} - 560172981803 q^{37} + 2624915279530 q^{38} - 1035242881236 q^{39} + 241463579696 q^{40} - 228932453550 q^{41} + 2858157268962 q^{42} - 2794438909830 q^{43} + 1064714773938 q^{44} - 3913841787756 q^{45} - 9400875205784 q^{46} + 13172201132038 q^{47} + 15759485913912 q^{48} + 1120374064245 q^{49} - 7441418685467 q^{50} - 42740308387651 q^{51} - 44596665749220 q^{52} - 28744292825331 q^{53} - 95850311037158 q^{54} - 39514788196568 q^{55} - 49201538022872 q^{56} - 40736796192480 q^{57} - 63400902535764 q^{58} - 10165773170481 q^{59} - 167491035794256 q^{60} - 46855749858739 q^{61} + 31884013995940 q^{62} - 37101898831500 q^{63} + 112051931566497 q^{64} + 52029013079708 q^{65} - 354971424918056 q^{66} + 13467823312288 q^{67} - 437586159999366 q^{68} + 59943985913034 q^{69} - 441355039314724 q^{70} - 307074659343603 q^{71} - 11\!\cdots\!83 q^{72}+ \cdots - 34\!\cdots\!42 q^{99}+O(q^{100}) \) 26 * q - 473 * q^2 - 1745 * q^3 + 352357 * q^4 - 204476 * q^5 - 747008 * q^6 - 8691077 * q^7 - 17976447 * q^8 + 89941305 * q^9 - 51585280 * q^10 + 3001662 * q^11 + 512888508 * q^12 - 508793550 * q^13 - 942073166 * q^14 + 434322614 * q^15 + 7184267409 * q^16 - 4325904793 * q^17 - 9157469975 * q^18 - 4303587332 * q^19 - 32919037912 * q^20 - 45132645408 * q^21 - 50162299142 * q^22 - 13266095576 * q^23 - 110793074064 * q^24 + 65244286550 * q^25 + 10349295428 * q^26 - 77660429552 * q^27 - 239645313896 * q^28 - 66416799998 * q^29 + 507306134084 * q^30 + 103672859796 * q^31 + 368590250641 * q^32 + 570965925392 * q^33 - 100184286950 * q^34 + 581363635284 * q^35 + 2931853687289 * q^36 - 560172981803 * q^37 + 2624915279530 * q^38 - 1035242881236 * q^39 + 241463579696 * q^40 - 228932453550 * q^41 + 2858157268962 * q^42 - 2794438909830 * q^43 + 1064714773938 * q^44 - 3913841787756 * q^45 - 9400875205784 * q^46 + 13172201132038 * q^47 + 15759485913912 * q^48 + 1120374064245 * q^49 - 7441418685467 * q^50 - 42740308387651 * q^51 - 44596665749220 * q^52 - 28744292825331 * q^53 - 95850311037158 * q^54 - 39514788196568 * q^55 - 49201538022872 * q^56 - 40736796192480 * q^57 - 63400902535764 * q^58 - 10165773170481 * q^59 - 167491035794256 * q^60 - 46855749858739 * q^61 + 31884013995940 * q^62 - 37101898831500 * q^63 + 112051931566497 * q^64 + 52029013079708 * q^65 - 354971424918056 * q^66 + 13467823312288 * q^67 - 437586159999366 * q^68 + 59943985913034 * q^69 - 441355039314724 * q^70 - 307074659343603 * q^71 - 1133879864100483 * q^72 - 487321498781430 * q^73 - 466623577082946 * q^74 - 884794971698755 * q^75 - 449968444781650 * q^76 - 796649959838384 * q^77 - 1093393795219952 * q^78 - 1035453802803531 * q^79 - 2167251026769280 * q^80 - 1039682728268070 * q^81 - 991772458272898 * q^82 - 1863772921617340 * q^83 - 3523568074865964 * q^84 - 1683039147983738 * q^85 - 2592833967137750 * q^86 - 2998549636473296 * q^87 - 3673206314818526 * q^88 - 2071643237231455 * q^89 - 3623510242236052 * q^90 - 2115409445432896 * q^91 - 2075443749084868 * q^92 - 2937586548722292 * q^93 - 239632735978999 * q^94 - 4926569981598120 * q^95 - 9268187425786600 * q^96 - 5317102893236637 * q^97 - 2530592027590081 * q^98 - 3419492458359442 * 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 $

$2$	180.170	0.995307	0.497654	−	0.867376i	$-0.334195\pi$
$2$	180.170	0.995307	0.497654	+	0.867376i	$0.334195\pi$
$3$	4814.12	1.27089	0.635445	−	0.772146i	$-0.280817\pi$
$3$	4814.12	1.27089	0.635445	+	0.772146i	$0.280817\pi$
$4$	−306.823	−0.00936348
$5$	234624.	1.34307	0.671533	−	0.740975i	$-0.265636\pi$
$5$	234624.	1.34307	0.671533	+	0.740975i	$0.265636\pi$
$6$	867360.	1.26493
$7$	−3.90024e6	−1.79001	−0.895006	−	0.446054i	$-0.852829\pi$
$7$	−3.90024e6	−1.79001	−0.895006	+	0.446054i	$0.852829\pi$
$8$	−5.95909e6	−1.00463
$9$	8.82688e6	0.615160
$10$	4.22722e7	1.33676
$11$	−6.01049e7	−0.929961	−0.464981	−	0.885321i	$-0.653939\pi$
$11$	−6.01049e7	−0.929961	−0.464981	+	0.885321i	$0.653939\pi$
$12$	−1.47708e6	−0.0119000
$13$	2.37923e8	1.05163	0.525813	−	0.850600i	$-0.323761\pi$
$13$	2.37923e8	1.05163	0.525813	+	0.850600i	$0.323761\pi$
$14$	−7.02706e8	−1.78161
$15$	1.12951e9	1.70689
$16$	−1.06359e9	−0.990549
$17$	−3.07237e9	−1.81596	−0.907980	−	0.419014i	$-0.862376\pi$
$17$	−3.07237e9	−1.81596	−0.907980	+	0.419014i	$0.862376\pi$
$18$	1.59034e9	0.612274
$19$	−5.20091e9	−1.33483	−0.667417	−	0.744684i	$-0.732600\pi$
$19$	−5.20091e9	−1.33483	−0.667417	+	0.744684i	$0.732600\pi$
$20$	−7.19880e7	−0.0125758
$21$	−1.87762e10	−2.27491
$22$	−1.08291e10	−0.925597
$23$	1.30603e10	0.799824	0.399912	−	0.916553i	$-0.369041\pi$
$23$	1.30603e10	0.799824	0.399912	+	0.916553i	$0.369041\pi$
$24$	−2.86878e10	−1.27677
$25$	2.45309e10	0.803827
$26$	4.28666e10	1.04669
$27$	−2.65837e10	−0.489089
$28$	1.19668e9	0.0167607
$29$	−9.06607e10	−0.975965	−0.487982	−	0.872853i	$-0.662267\pi$
$29$	−9.06607e10	−0.975965	−0.487982	+	0.872853i	$0.662267\pi$
$30$	2.03503e11	1.69888
$31$	1.73938e11	1.13548	0.567742	−	0.823206i	$-0.307817\pi$
$31$	1.73938e11	1.13548	0.567742	+	0.823206i	$0.307817\pi$
$32$	3.63980e9	0.0187264
$33$	−2.89353e11	−1.18188
$34$	−5.53548e11	−1.80744
$35$	−9.15090e11	−2.40410
$36$	−2.70829e9	−0.00576005
$37$	−6.88388e11	−1.19212	−0.596061	−	0.802939i	$-0.703268\pi$
$37$	−6.88388e11	−1.19212	−0.596061	+	0.802939i	$0.703268\pi$
$38$	−9.37048e11	−1.32857
$39$	1.14539e12	1.33650
$40$	−1.39814e12	−1.34928
$41$	2.09803e12	1.68241	0.841205	−	0.540716i	$-0.181847\pi$
$41$	2.09803e12	1.68241	0.841205	+	0.540716i	$0.181847\pi$
$42$	−3.38291e12	−2.26423
$43$	1.48362e11	0.0832354	0.0416177	−	0.999134i	$-0.486749\pi$
$43$	1.48362e11	0.0832354	0.0416177	+	0.999134i	$0.486749\pi$
$44$	1.84416e10	0.00870768
$45$	2.07100e12	0.826201
$46$	2.35307e12	0.796071
$47$	5.06623e11	0.145865
$47$	5.06623e11	0.145865
$48$	−5.12027e12	−1.25888
$49$	1.04643e13	2.20414
$50$	4.41972e12	0.800055
$51$	−1.47908e13	−2.30788
$52$	−7.30002e10	−0.00984689
$53$	5.94921e12	0.695650	0.347825	−	0.937560i	$-0.386920\pi$
$53$	5.94921e12	0.695650	0.347825	+	0.937560i	$0.386920\pi$
$54$	−4.78959e12	−0.486793
$55$	−1.41021e13	−1.24900
$56$	2.32419e13	1.79829
$57$	−2.50378e13	−1.69643
$58$	−1.63343e13	−0.971385
$59$	2.12217e13	1.11017	0.555086	−	0.831793i	$-0.312686\pi$
$59$	2.12217e13	1.11017	0.555086	+	0.831793i	$0.312686\pi$
$60$	−3.46559e11	−0.0159824
$61$	−4.28821e13	−1.74704	−0.873520	−	0.486789i	$-0.838168\pi$
$61$	−4.28821e13	−1.74704	−0.873520	+	0.486789i	$0.838168\pi$
$62$	3.13384e13	1.13016
$63$	−3.44269e13	−1.10114
$64$	3.55076e13	1.00919
$65$	5.58225e13	1.41240
$66$	−5.21326e13	−1.17633
$67$	−3.83429e13	−0.772900	−0.386450	−	0.922310i	$-0.626299\pi$
$67$	−3.83429e13	−0.772900	−0.386450	+	0.922310i	$0.626299\pi$
$68$	9.42672e11	0.0170037
$69$	6.28739e13	1.01649
$70$	−1.64872e14	−2.39282
$71$	−4.66251e13	−0.608390	−0.304195	−	0.952610i	$-0.598388\pi$
$71$	−4.66251e13	−0.608390	−0.304195	+	0.952610i	$0.598388\pi$
$72$	−5.26001e13	−0.618007
$73$	−5.86765e13	−0.621645	−0.310822	−	0.950468i	$-0.600604\pi$
$73$	−5.86765e13	−0.621645	−0.310822	+	0.950468i	$0.600604\pi$
$74$	−1.24027e14	−1.18653
$75$	1.18095e14	1.02158
$76$	1.59576e12	0.0124987
$77$	2.34424e14	1.66464
$78$	2.06365e14	1.33023
$79$	1.69712e14	0.994283	0.497141	−	0.867670i	$-0.334383\pi$
$79$	1.69712e14	0.994283	0.497141	+	0.867670i	$0.334383\pi$
$80$	−2.49545e14	−1.33037
$81$	−2.54633e14	−1.23674
$82$	3.78001e14	1.67452
$83$	−2.46874e14	−0.998594	−0.499297	−	0.866431i	$-0.666408\pi$
$83$	−2.46874e14	−0.998594	−0.499297	+	0.866431i	$0.666408\pi$
$84$	5.76097e12	0.0213011
$85$	−7.20851e14	−2.43895
$86$	2.67303e13	0.0828448
$87$	−4.36452e14	−1.24034
$88$	3.58170e14	0.934264
$89$	2.00232e14	0.479852	0.239926	−	0.970791i	$-0.422877\pi$
$89$	2.00232e14	0.479852	0.239926	+	0.970791i	$0.422877\pi$
$90$	3.73131e14	0.822324
$91$	−9.27957e14	−1.88242
$92$	−4.00720e12	−0.00748914
$93$	8.37358e14	1.44308
$94$	9.12782e13	0.145180
$95$	−1.22026e15	−1.79277
$96$	1.75225e13	0.0237991
$97$	7.04024e14	0.884707	0.442354	−	0.896841i	$-0.354144\pi$
$97$	7.04024e14	0.884707	0.442354	+	0.896841i	$0.354144\pi$
$98$	1.88535e15	2.19380
$99$	−5.30539e14	−0.572076
$100$	−7.52662e12	−0.00752662
$101$	−1.14921e15	−1.06657	−0.533287	−	0.845934i	$-0.679043\pi$
$101$	−1.14921e15	−1.06657	−0.533287	+	0.845934i	$0.679043\pi$
$102$	−2.66485e15	−2.29705
$103$	6.42568e14	0.514802	0.257401	−	0.966305i	$-0.417134\pi$
$103$	6.42568e14	0.514802	0.257401	+	0.966305i	$0.417134\pi$
$104$	−1.41780e15	−1.05649
$105$	−4.40536e15	−3.05535
$106$	1.07187e15	0.692385
$107$	−3.53157e14	−0.212613	−0.106307	−	0.994333i	$-0.533902\pi$
$107$	−3.53157e14	−0.212613	−0.106307	+	0.994333i	$0.533902\pi$
$108$	8.15649e12	0.00457957
$109$	−2.22595e15	−1.16631	−0.583157	−	0.812359i	$-0.698183\pi$
$109$	−2.22595e15	−1.16631	−0.583157	+	0.812359i	$0.698183\pi$
$110$	−2.54077e15	−1.24314
$111$	−3.31399e15	−1.51505
$112$	4.14827e15	1.77309
$113$	−2.24821e15	−0.898978	−0.449489	−	0.893286i	$-0.648394\pi$
$113$	−2.24821e15	−0.898978	−0.449489	+	0.893286i	$0.648394\pi$
$114$	−4.51106e15	−1.68847
$115$	3.06426e15	1.07422
$116$	2.78168e13	0.00913843
$117$	2.10012e15	0.646919
$118$	3.82351e15	1.10496
$119$	1.19830e16	3.25059
$120$	−6.73084e15	−1.71479
$121$	−5.64646e14	−0.135172
$122$	−7.72607e15	−1.73884
$123$	1.01002e16	2.13816
$124$	−5.33681e13	−0.0106321
$125$	−1.40463e15	−0.263473
$126$	−6.20270e15	−1.09598
$127$	−9.30446e15	−1.54940	−0.774700	−	0.632329i	$-0.782099\pi$
$127$	−9.30446e15	−1.54940	−0.774700	+	0.632329i	$0.782099\pi$
$128$	6.27813e15	0.985725
$129$	7.14231e14	0.105783
$130$	1.00575e16	1.40578
$131$	6.83071e15	0.901428	0.450714	−	0.892668i	$-0.351169\pi$
$131$	6.83071e15	0.901428	0.450714	+	0.892668i	$0.351169\pi$
$132$	8.87799e13	0.0110665
$133$	2.02848e16	2.38937
$134$	−6.90823e15	−0.769273
$135$	−6.23718e15	−0.656878
$136$	1.83085e16	1.82436
$137$	−3.66474e15	−0.345652	−0.172826	−	0.984952i	$-0.555290\pi$
$137$	−3.66474e15	−0.345652	−0.172826	+	0.984952i	$0.555290\pi$
$138$	1.13280e16	1.01172
$139$	2.09750e16	1.77456	0.887282	−	0.461228i	$-0.152591\pi$
$139$	2.09750e16	1.77456	0.887282	+	0.461228i	$0.152591\pi$
$140$	2.80770e14	0.0225108
$141$	2.43895e15	0.185378
$142$	−8.40044e15	−0.605535
$143$	−1.43004e16	−0.977972
$144$	−9.38821e15	−0.609346
$145$	−2.12712e16	−1.31079
$146$	−1.05717e16	−0.618728
$147$	5.03764e16	2.80122
$148$	2.11213e14	0.0111624
$149$	−2.97020e16	−1.49241	−0.746207	−	0.665714i	$-0.768127\pi$
$149$	−2.97020e16	−1.49241	−0.746207	+	0.665714i	$0.768127\pi$
$150$	2.12771e16	1.01678
$151$	8.13080e15	0.369663	0.184832	−	0.982770i	$-0.440826\pi$
$151$	8.13080e15	0.369663	0.184832	+	0.982770i	$0.440826\pi$
$152$	3.09927e16	1.34101
$153$	−2.71194e16	−1.11711
$154$	4.22361e16	1.65683
$155$	4.08100e16	1.52503
$156$	−3.51432e14	−0.0125143
$157$	2.49755e16	0.847747	0.423873	−	0.905721i	$-0.360670\pi$
$157$	2.49755e16	0.847747	0.423873	+	0.905721i	$0.360670\pi$
$158$	3.05770e16	0.989617
$159$	2.86403e16	0.884094
$160$	8.53985e14	0.0251507
$161$	−5.09383e16	−1.43169
$162$	−4.58773e16	−1.23093
$163$	−3.67828e15	−0.0942404	−0.0471202	−	0.998889i	$-0.515004\pi$
$163$	−3.67828e15	−0.0942404	−0.0471202	+	0.998889i	$0.515004\pi$
$164$	−6.43722e14	−0.0157532
$165$	−6.78891e16	−1.58734
$166$	−4.44792e16	−0.993908
$167$	−5.82020e15	−0.124327	−0.0621634	−	0.998066i	$-0.519800\pi$
$167$	−5.82020e15	−0.124327	−0.0621634	+	0.998066i	$0.519800\pi$
$168$	1.11889e17	2.28543
$169$	5.42156e15	0.105919
$170$	−1.29876e17	−2.42751
$171$	−4.59078e16	−0.821138
$172$	−4.55207e13	−0.000779373 0
$173$	1.44079e16	0.236186	0.118093	−	0.993003i	$-0.462322\pi$
$173$	1.44079e16	0.236186	0.118093	+	0.993003i	$0.462322\pi$
$174$	−7.86355e16	−1.23452
$175$	−9.56762e16	−1.43886
$176$	6.39272e16	0.921172
$177$	1.02164e17	1.41090
$178$	3.60757e16	0.477600
$179$	7.05036e16	0.894980	0.447490	−	0.894289i	$-0.352318\pi$
$179$	7.05036e16	0.894980	0.447490	+	0.894289i	$0.352318\pi$
$180$	−6.35429e14	−0.00773612
$181$	1.56223e15	0.0182455	0.00912273	−	0.999958i	$-0.497096\pi$
$181$	1.56223e15	0.0182455	0.00912273	+	0.999958i	$0.497096\pi$
$182$	−1.67190e17	−1.87359
$183$	−2.06440e17	−2.22029
$184$	−7.78275e16	−0.803525
$185$	−1.61512e17	−1.60110
$186$	1.50867e17	1.43630
$187$	1.84664e17	1.68877
$188$	−1.55443e14	−0.00136580
$189$	1.03683e17	0.875474
$190$	−2.19854e17	−1.78436
$191$	1.40409e17	1.09559	0.547793	−	0.836614i	$-0.315468\pi$
$191$	1.40409e17	1.09559	0.547793	+	0.836614i	$0.315468\pi$
$192$	1.70938e17	1.28257
$193$	1.16974e17	0.844133	0.422067	−	0.906565i	$-0.361305\pi$
$193$	1.16974e17	0.844133	0.422067	+	0.906565i	$0.361305\pi$
$194$	1.26844e17	0.880555
$195$	2.68736e17	1.79501
$196$	−3.21069e15	−0.0206385
$197$	−5.73688e16	−0.354959	−0.177480	−	0.984124i	$-0.556794\pi$
$197$	−5.73688e16	−0.354959	−0.177480	+	0.984124i	$0.556794\pi$
$198$	−9.55871e16	−0.569391
$199$	8.86370e16	0.508413	0.254207	−	0.967150i	$-0.418186\pi$
$199$	8.86370e16	0.508413	0.254207	+	0.967150i	$0.418186\pi$
$200$	−1.46181e17	−0.807546
$201$	−1.84587e17	−0.982271
$202$	−2.07054e17	−1.06157
$203$	3.53599e17	1.74699
$204$	4.53814e15	0.0216098
$205$	4.92247e17	2.25959
$206$	1.15771e17	0.512386
$207$	1.15282e17	0.492020
$208$	−2.53054e17	−1.04169
$209$	3.12600e17	1.24134
$210$	−7.93712e17	−3.04101
$211$	−2.13991e16	−0.0791183	−0.0395591	−	0.999217i	$-0.512595\pi$
$211$	−2.13991e16	−0.0791183	−0.0395591	+	0.999217i	$0.512595\pi$
$212$	−1.82535e15	−0.00651370
$213$	−2.24459e17	−0.773197
$214$	−6.36283e16	−0.211615
$215$	3.48092e16	0.111791
$216$	1.58415e17	0.491351
$217$	−6.78399e17	−2.03253
$218$	−4.01048e17	−1.16084
$219$	−2.82476e17	−0.790042
$220$	4.32683e15	0.0116950
$221$	−7.30987e17	−1.90971
$222$	−5.97080e17	−1.50794
$223$	−4.53830e16	−0.110817	−0.0554086	−	0.998464i	$-0.517646\pi$
$223$	−4.53830e16	−0.110817	−0.0554086	+	0.998464i	$0.517646\pi$
$224$	−1.41961e16	−0.0335204
$225$	2.16531e17	0.494483
$226$	−4.05060e17	−0.894760
$227$	−3.43232e17	−0.733490	−0.366745	−	0.930322i	$-0.619528\pi$
$227$	−3.43232e17	−0.733490	−0.366745	+	0.930322i	$0.619528\pi$
$228$	7.68217e15	0.0158845
$229$	−6.64182e17	−1.32899	−0.664494	−	0.747294i	$-0.731353\pi$
$229$	−6.64182e17	−1.32899	−0.664494	+	0.747294i	$0.731353\pi$
$230$	5.52087e17	1.06918
$231$	1.12854e18	2.11558
$232$	5.40255e17	0.980481
$233$	−6.33365e16	−0.111297	−0.0556487	−	0.998450i	$-0.517723\pi$
$233$	−6.33365e16	−0.111297	−0.0556487	+	0.998450i	$0.517723\pi$
$234$	3.78378e17	0.643883
$235$	1.18866e17	0.195906
$236$	−6.51130e15	−0.0103951
$237$	8.17016e17	1.26362
$238$	2.15897e18	3.23533
$239$	−6.12106e17	−0.888878	−0.444439	−	0.895809i	$-0.646597\pi$
$239$	−6.12106e17	−0.888878	−0.444439	+	0.895809i	$0.646597\pi$
$240$	−1.20134e18	−1.69076
$241$	−3.91411e17	−0.533956	−0.266978	−	0.963703i	$-0.586025\pi$
$241$	−3.91411e17	−0.533956	−0.266978	+	0.963703i	$0.586025\pi$
$242$	−1.01732e17	−0.134537
$243$	−8.44389e17	−1.08267
$244$	1.31572e16	0.0163584
$245$	2.45518e18	2.96031
$246$	1.81974e18	2.12812
$247$	−1.23742e18	−1.40375
$248$	−1.03651e18	−1.14074
$249$	−1.18848e18	−1.26910
$250$	−2.53072e17	−0.262237
$251$	1.29546e18	1.30278	0.651391	−	0.758743i	$-0.274186\pi$
$251$	1.29546e18	1.30278	0.651391	+	0.758743i	$0.274186\pi$
$252$	1.05630e16	0.0103105
$253$	−7.84989e17	−0.743806
$254$	−1.67638e18	−1.54213
$255$	−3.47027e18	−3.09964
$256$	−3.23832e16	−0.0280880
$257$	−7.89605e17	−0.665138	−0.332569	−	0.943079i	$-0.607915\pi$
$257$	−7.89605e17	−0.665138	−0.332569	+	0.943079i	$0.607915\pi$
$258$	1.28683e17	0.105287
$259$	2.68488e18	2.13391
$260$	−1.71276e16	−0.0132250
$261$	−8.00251e17	−0.600375
$262$	1.23069e18	0.897198
$263$	1.86316e18	1.32003	0.660013	−	0.751254i	$-0.270551\pi$
$263$	1.86316e18	1.32003	0.660013	+	0.751254i	$0.270551\pi$
$264$	1.72428e18	1.18735
$265$	1.39583e18	0.934303
$266$	3.65471e18	2.37816
$267$	9.63939e17	0.609839
$268$	1.17645e16	0.00723704
$269$	−1.37324e18	−0.821494	−0.410747	−	0.911749i	$-0.634732\pi$
$269$	−1.37324e18	−0.821494	−0.410747	+	0.911749i	$0.634732\pi$
$270$	−1.12375e18	−0.653796
$271$	2.67188e18	1.51198	0.755992	−	0.654581i	$-0.227155\pi$
$271$	2.67188e18	1.51198	0.755992	+	0.654581i	$0.227155\pi$
$272$	3.26775e18	1.79880
$273$	−4.46730e18	−2.39235
$274$	−6.60276e17	−0.344030
$275$	−1.47443e18	−0.747528
$276$	−1.92911e16	−0.00951787
$277$	−2.74291e18	−1.31709	−0.658543	−	0.752544i	$-0.728827\pi$
$277$	−2.74291e18	−1.31709	−0.658543	+	0.752544i	$0.728827\pi$
$278$	3.77907e18	1.76624
$279$	1.53533e18	0.698505
$280$	5.45310e18	2.41523
$281$	−5.62434e17	−0.242535	−0.121267	−	0.992620i	$-0.538696\pi$
$281$	−5.62434e17	−0.242535	−0.121267	+	0.992620i	$0.538696\pi$
$282$	4.39425e17	0.184508
$283$	−7.42103e17	−0.303435	−0.151717	−	0.988424i	$-0.548480\pi$
$283$	−7.42103e17	−0.303435	−0.151717	+	0.988424i	$0.548480\pi$
$284$	1.43056e16	0.00569665
$285$	−5.87448e18	−2.27841
$286$	−2.57649e18	−0.973383
$287$	−8.18280e18	−3.01153
$288$	3.21281e16	0.0115197
$289$	6.57701e18	2.29771
$290$	−3.83243e18	−1.30463
$291$	3.38926e18	1.12436
$292$	1.80033e16	0.00582076
$293$	2.69850e18	0.850385	0.425192	−	0.905103i	$-0.360206\pi$
$293$	2.69850e18	0.850385	0.425192	+	0.905103i	$0.360206\pi$
$294$	9.07632e18	2.78808
$295$	4.97912e18	1.49103
$296$	4.10216e18	1.19764
$297$	1.59781e18	0.454834
$298$	−5.35141e18	−1.48541
$299$	3.10735e18	0.841117
$300$	−3.62341e16	−0.00956550
$301$	−5.78645e17	−0.148992
$302$	1.46493e18	0.367929
$303$	−5.53246e18	−1.35550
$304$	5.53166e18	1.32222
$305$	−1.00612e19	−2.34639
$306$	−4.88610e18	−1.11186
$307$	−2.80311e18	−0.622446	−0.311223	−	0.950337i	$-0.600739\pi$
$307$	−2.80311e18	−0.622446	−0.311223	+	0.950337i	$0.600739\pi$
$308$	−7.19265e16	−0.0155868
$309$	3.09340e18	0.654256
$310$	7.35273e18	1.51787
$311$	3.20251e18	0.645339	0.322670	−	0.946512i	$-0.395420\pi$
$311$	3.20251e18	0.645339	0.322670	+	0.946512i	$0.395420\pi$
$312$	−6.82549e18	−1.34269
$313$	−8.15335e18	−1.56586	−0.782931	−	0.622108i	$-0.786276\pi$
$313$	−8.15335e18	−1.56586	−0.782931	+	0.622108i	$0.786276\pi$
$314$	4.49983e18	0.843769
$315$	−8.07739e18	−1.47891
$316$	−5.20716e16	−0.00930995
$317$	−7.25488e18	−1.26673	−0.633367	−	0.773851i	$-0.718328\pi$
$317$	−7.25488e18	−1.26673	−0.633367	+	0.773851i	$0.718328\pi$
$318$	5.16011e18	0.879945
$319$	5.44916e18	0.907610
$320$	8.33094e18	1.35541
$321$	−1.70014e18	−0.270208
$322$	−9.17755e18	−1.42498
$323$	1.59791e19	2.42401
$324$	7.81273e16	0.0115802
$325$	5.83646e18	0.845326
$326$	−6.62714e17	−0.0937982
$327$	−1.07160e19	−1.48226
$328$	−1.25023e19	−1.69019
$329$	−1.97595e18	−0.261100
$330$	−1.22316e19	−1.57989
$331$	−1.81924e17	−0.0229710	−0.0114855	−	0.999934i	$-0.503656\pi$
$331$	−1.81924e17	−0.0229710	−0.0114855	+	0.999934i	$0.503656\pi$
$332$	7.57464e16	0.00935032
$333$	−6.07632e18	−0.733346
$334$	−1.04862e18	−0.123743
$335$	−8.99616e18	−1.03806
$336$	1.99703e19	2.25341
$337$	7.73619e18	0.853695	0.426848	−	0.904324i	$-0.359624\pi$
$337$	7.73619e18	0.853695	0.426848	+	0.904324i	$0.359624\pi$
$338$	9.76801e17	0.105422
$339$	−1.08232e19	−1.14250
$340$	2.21173e17	0.0228371
$341$	−1.04545e19	−1.05596
$342$	−8.27121e18	−0.817284
$343$	−2.22967e19	−2.15543
$344$	−8.84099e17	−0.0836205
$345$	1.47517e19	1.36521
$346$	2.59587e18	0.235078
$347$	−5.75296e18	−0.509824	−0.254912	−	0.966964i	$-0.582046\pi$
$347$	−5.75296e18	−0.509824	−0.254912	+	0.966964i	$0.582046\pi$
$348$	1.33913e17	0.0116139
$349$	4.64835e18	0.394555	0.197278	−	0.980348i	$-0.436790\pi$
$349$	4.64835e18	0.394555	0.197278	+	0.980348i	$0.436790\pi$
$350$	−1.72380e19	−1.43211
$351$	−6.32488e18	−0.514339
$352$	−2.18770e17	−0.0174148
$353$	1.92611e18	0.150097	0.0750483	−	0.997180i	$-0.476089\pi$
$353$	1.92611e18	0.150097	0.0750483	+	0.997180i	$0.476089\pi$
$354$	1.84068e19	1.40428
$355$	−1.09394e19	−0.817109
$356$	−6.14356e16	−0.00449309
$357$	5.76875e19	4.13114
$358$	1.27026e19	0.890780
$359$	−1.41904e19	−0.974512	−0.487256	−	0.873259i	$-0.662002\pi$
$359$	−1.41904e19	−0.974512	−0.487256	+	0.873259i	$0.662002\pi$
$360$	−1.23413e19	−0.830024
$361$	1.18684e19	0.781784
$362$	2.81466e17	0.0181598
$363$	−2.71827e18	−0.171788
$364$	2.84718e17	0.0176261
$365$	−1.37669e19	−0.834910
$366$	−3.71942e19	−2.20987
$367$	−1.41207e19	−0.821978	−0.410989	−	0.911640i	$-0.634817\pi$
$367$	−1.41207e19	−0.821978	−0.410989	+	0.911640i	$0.634817\pi$
$368$	−1.38909e19	−0.792265
$369$	1.85190e19	1.03495
$370$	−2.90997e19	−1.59358
$371$	−2.32034e19	−1.24522
$372$	−2.56920e17	−0.0135122
$373$	5.07053e18	0.261359	0.130679	−	0.991425i	$-0.458284\pi$
$373$	5.07053e18	0.261359	0.130679	+	0.991425i	$0.458284\pi$
$374$	3.32709e19	1.68085
$375$	−6.76206e18	−0.334846
$376$	−3.01901e18	−0.146540
$377$	−2.15703e19	−1.02635
$378$	1.86805e19	0.871366
$379$	3.66780e19	1.67730	0.838651	−	0.544669i	$-0.183345\pi$
$379$	3.66780e19	1.67730	0.838651	+	0.544669i	$0.183345\pi$
$380$	3.74403e17	0.0167866
$381$	−4.47928e19	−1.96912
$382$	2.52976e19	1.09044
$383$	−4.42549e19	−1.87056	−0.935278	−	0.353914i	$-0.884850\pi$
$383$	−4.42549e19	−1.87056	−0.935278	+	0.353914i	$0.884850\pi$
$384$	3.02237e19	1.25275
$385$	5.50014e19	2.23572
$386$	2.10753e19	0.840172
$387$	1.30957e18	0.0512031
$388$	−2.16011e17	−0.00828394
$389$	−9.07305e18	−0.341296	−0.170648	−	0.985332i	$-0.554586\pi$
$389$	−9.07305e18	−0.341296	−0.170648	+	0.985332i	$0.554586\pi$
$390$	4.84182e19	1.78659
$391$	−4.01260e19	−1.45245
$392$	−6.23577e19	−2.21434
$393$	3.28839e19	1.14562
$394$	−1.03361e19	−0.353294
$395$	3.98186e19	1.33539
$396$	1.62781e17	0.00535662
$397$	−3.01876e18	−0.0974764	−0.0487382	−	0.998812i	$-0.515520\pi$
$397$	−3.01876e18	−0.0974764	−0.0487382	+	0.998812i	$0.515520\pi$
$398$	1.59697e19	0.506028
$399$	9.76535e19	3.03663
$400$	−2.60909e19	−0.796230
$401$	9.54747e18	0.285960	0.142980	−	0.989726i	$-0.454332\pi$
$401$	9.54747e18	0.285960	0.142980	+	0.989726i	$0.454332\pi$
$402$	−3.32571e19	−0.977661
$403$	4.13838e19	1.19411
$404$	3.52605e17	0.00998685
$405$	−5.97431e19	−1.66102
$406$	6.37078e19	1.73879
$407$	4.13755e19	1.10863
$408$	8.81394e19	2.31856
$409$	3.52511e18	0.0910432	0.0455216	−	0.998963i	$-0.485505\pi$
$409$	3.52511e18	0.0910432	0.0455216	+	0.998963i	$0.485505\pi$
$410$	8.86881e19	2.24898
$411$	−1.76425e19	−0.439286
$412$	−1.97154e17	−0.00482034
$413$	−8.27697e19	−1.98722
$414$	2.07703e19	0.489711
$415$	−5.79225e19	−1.34118
$416$	8.65994e17	0.0196931
$417$	1.00976e20	2.25527
$418$	5.63212e19	1.23552
$419$	−3.78807e19	−0.816230	−0.408115	−	0.912930i	$-0.633814\pi$
$419$	−3.78807e19	−0.816230	−0.408115	+	0.912930i	$0.633814\pi$
$420$	1.35166e18	0.0286087
$421$	−2.44640e19	−0.508641	−0.254321	−	0.967120i	$-0.581852\pi$
$421$	−2.44640e19	−0.508641	−0.254321	+	0.967120i	$0.581852\pi$
$422$	−3.85547e18	−0.0787470
$423$	4.47190e18	0.0897304
$424$	−3.54519e19	−0.698868
$425$	−7.53678e19	−1.45972
$426$	−4.04408e19	−0.769569
$427$	1.67251e20	3.12722
$428$	1.08357e17	0.00199080
$429$	−6.88437e19	−1.24289
$430$	6.27156e18	0.111266
$431$	−2.52136e19	−0.439597	−0.219799	−	0.975545i	$-0.570540\pi$
$431$	−2.52136e19	−0.439597	−0.219799	+	0.975545i	$0.570540\pi$
$432$	2.82743e19	0.484466
$433$	5.52023e19	0.929605	0.464802	−	0.885415i	$-0.346125\pi$
$433$	5.52023e19	0.929605	0.464802	+	0.885415i	$0.346125\pi$
$434$	−1.22227e20	−2.02299
$435$	−1.02402e20	−1.66586
$436$	6.82970e17	0.0109208
$437$	−6.79255e19	−1.06763
$438$	−5.08936e19	−0.786335
$439$	−6.34750e19	−0.964093	−0.482047	−	0.876146i	$-0.660106\pi$
$439$	−6.34750e19	−0.964093	−0.482047	+	0.876146i	$0.660106\pi$
$440$	8.40354e19	1.25478
$441$	9.23671e19	1.35590
$442$	−1.31702e20	−1.90075
$443$	7.69211e19	1.09148	0.545742	−	0.837953i	$-0.316248\pi$
$443$	7.69211e19	1.09148	0.545742	+	0.837953i	$0.316248\pi$
$444$	1.01681e18	0.0141862
$445$	4.69791e19	0.644473
$446$	−8.17666e18	−0.110297
$447$	−1.42989e20	−1.89669
$448$	−1.38488e20	−1.80646
$449$	5.79880e19	0.743858	0.371929	−	0.928261i	$-0.378696\pi$
$449$	5.79880e19	0.743858	0.371929	+	0.928261i	$0.378696\pi$
$450$	3.90123e19	0.492162
$451$	−1.26102e20	−1.56458
$452$	6.89803e17	0.00841757
$453$	3.91427e19	0.469801
$454$	−6.18401e19	−0.730048
$455$	−2.17721e20	−2.52822
$456$	1.49203e20	1.70428
$457$	−1.13881e20	−1.27962	−0.639809	−	0.768534i	$-0.720987\pi$
$457$	−1.13881e20	−1.27962	−0.639809	+	0.768534i	$0.720987\pi$
$458$	−1.19666e20	−1.32275
$459$	8.16749e19	0.888165
$460$	−9.40185e17	−0.0100584
$461$	−3.09739e19	−0.326016	−0.163008	−	0.986625i	$-0.552120\pi$
$461$	−3.09739e19	−0.326016	−0.163008	+	0.986625i	$0.552120\pi$
$462$	2.03330e20	2.10565
$463$	1.59580e20	1.62600	0.813000	−	0.582263i	$-0.197833\pi$
$463$	1.59580e20	1.62600	0.813000	+	0.582263i	$0.197833\pi$
$464$	9.64262e19	0.966741
$465$	1.96464e20	1.93815
$466$	−1.14113e19	−0.110775
$467$	4.92548e18	0.0470514	0.0235257	−	0.999723i	$-0.492511\pi$
$467$	4.92548e18	0.0470514	0.0235257	+	0.999723i	$0.492511\pi$
$468$	−6.44364e17	−0.00605742
$469$	1.49546e20	1.38350
$470$	2.14161e19	0.194987
$471$	1.20235e20	1.07739
$472$	−1.26462e20	−1.11531
$473$	−8.91726e18	−0.0774057
$474$	1.47202e20	1.25769
$475$	−1.27583e20	−1.07298
$476$	−3.67664e18	−0.0304368
$477$	5.25130e19	0.427936
$478$	−1.10283e20	−0.884707
$479$	−7.94886e18	−0.0627752	−0.0313876	−	0.999507i	$-0.509993\pi$
$479$	−7.94886e18	−0.0627752	−0.0313876	+	0.999507i	$0.509993\pi$
$480$	4.11119e18	0.0319638
$481$	−1.63784e20	−1.25367
$482$	−7.05205e19	−0.531450
$483$	−2.45223e20	−1.81953
$484$	1.73246e17	0.00126568
$485$	1.65181e20	1.18822
$486$	−1.52134e20	−1.07759
$487$	1.46156e20	1.01941	0.509705	−	0.860349i	$-0.329754\pi$
$487$	1.46156e20	1.01941	0.509705	+	0.860349i	$0.329754\pi$
$488$	2.55538e20	1.75512
$489$	−1.77077e19	−0.119769
$490$	4.42349e20	2.94642
$491$	−2.19332e20	−1.43877	−0.719385	−	0.694612i	$-0.755576\pi$
$491$	−2.19332e20	−1.43877	−0.719385	+	0.694612i	$0.755576\pi$
$492$	−3.09896e18	−0.0200206
$493$	2.78543e20	1.77231
$494$	−2.22945e20	−1.39716
$495$	−1.24477e20	−0.768335
$496$	−1.84999e20	−1.12475
$497$	1.81849e20	1.08903
$498$	−2.14128e20	−1.26315
$499$	−1.16262e20	−0.675590	−0.337795	−	0.941220i	$-0.609681\pi$
$499$	−1.16262e20	−0.675590	−0.337795	+	0.941220i	$0.609681\pi$
$500$	4.30972e17	0.00246703
$501$	−2.80192e19	−0.158006
$502$	2.33403e20	1.29667
$503$	−2.10274e20	−1.15087	−0.575434	−	0.817848i	$-0.695167\pi$
$503$	−2.10274e20	−1.15087	−0.575434	+	0.817848i	$0.695167\pi$
$504$	2.05153e20	1.10624
$505$	−2.69633e20	−1.43248
$506$	−1.41431e20	−0.740315
$507$	2.61000e19	0.134611
$508$	2.85482e18	0.0145078
$509$	5.98425e18	0.0299658	0.0149829	−	0.999888i	$-0.495231\pi$
$509$	5.98425e18	0.0299658	0.0149829	+	0.999888i	$0.495231\pi$
$510$	−6.25237e20	−3.08509
$511$	2.28852e20	1.11275
$512$	−2.11556e20	−1.01368
$513$	1.38260e20	0.652852
$514$	−1.42263e20	−0.662017
$515$	1.50762e20	0.691413
$516$	−2.19142e17	−0.000990497 0
$517$	−3.04505e19	−0.135649
$518$	4.83734e20	2.12390
$519$	6.93613e19	0.300167
$520$	−3.32651e20	−1.41894
$521$	−7.91564e18	−0.0332815	−0.0166407	−	0.999862i	$-0.505297\pi$
$521$	−7.91564e18	−0.0332815	−0.0166407	+	0.999862i	$0.505297\pi$
$522$	−1.44181e20	−0.597558
$523$	2.97135e18	0.0121392	0.00606961	−	0.999982i	$-0.498068\pi$
$523$	2.97135e18	0.0121392	0.00606961	+	0.999982i	$0.498068\pi$
$524$	−2.09582e18	−0.00844051
$525$	−4.60597e20	−1.82863
$526$	3.35686e20	1.31383
$527$	−5.34401e20	−2.06199
$528$	3.07754e20	1.17071
$529$	−9.60637e19	−0.360281
$530$	2.51486e20	0.929919
$531$	1.87321e20	0.682933
$532$	−6.22384e18	−0.0223728
$533$	4.99169e20	1.76927
$534$	1.73673e20	0.606977
$535$	−8.28592e19	−0.285553
$536$	2.28488e20	0.776476
$537$	3.39413e20	1.13742
$538$	−2.47417e20	−0.817639
$539$	−6.28956e20	−2.04977
$540$	1.91371e18	0.00615067
$541$	3.66835e20	1.16276	0.581381	−	0.813631i	$-0.302512\pi$
$541$	3.66835e20	1.16276	0.581381	+	0.813631i	$0.302512\pi$
$542$	4.81392e20	1.50489
$543$	7.52075e18	0.0231880
$544$	−1.11828e19	−0.0340063
$545$	−5.22260e20	−1.56644
$546$	−8.04873e20	−2.38113
$547$	3.07138e19	0.0896250	0.0448125	−	0.998995i	$-0.485731\pi$
$547$	3.07138e19	0.0896250	0.0448125	+	0.998995i	$0.485731\pi$
$548$	1.12443e18	0.00323651
$549$	−3.78515e20	−1.07471
$550$	−2.65647e20	−0.744020
$551$	4.71518e20	1.30275
$552$	−3.74671e20	−1.02119
$553$	−6.61918e20	−1.77978
$554$	−4.94190e20	−1.31090
$555$	−7.77541e20	−2.03482
$556$	−6.43561e18	−0.0166161
$557$	6.47516e20	1.64944	0.824720	−	0.565541i	$-0.191332\pi$
$557$	6.47516e20	1.64944	0.824720	+	0.565541i	$0.191332\pi$
$558$	2.76620e20	0.695227
$559$	3.52986e19	0.0875325
$560$	9.73284e20	2.38138
$561$	8.88997e20	2.14624
$562$	−1.01334e20	−0.241397
$563$	−5.41061e20	−1.27184	−0.635921	−	0.771754i	$-0.719380\pi$
$563$	−5.41061e20	−1.27184	−0.635921	+	0.771754i	$0.719380\pi$
$564$	−7.48324e17	−0.00173579
$565$	−5.27485e20	−1.20739
$566$	−1.33705e20	−0.302011
$567$	9.93131e20	2.21378
$568$	2.77843e20	0.611205
$569$	6.55773e20	1.42368	0.711838	−	0.702343i	$-0.247863\pi$
$569$	6.55773e20	1.42368	0.711838	+	0.702343i	$0.247863\pi$
$570$	−1.05840e21	−2.26772
$571$	2.23044e20	0.471649	0.235824	−	0.971796i	$-0.424221\pi$
$571$	2.23044e20	0.471649	0.235824	+	0.971796i	$0.424221\pi$
$572$	4.38767e18	0.00915723
$573$	6.75949e20	1.39237
$574$	−1.47429e21	−2.99740
$575$	3.20380e20	0.642920
$576$	3.13422e20	0.620812
$577$	−6.54201e20	−1.27907	−0.639533	−	0.768764i	$-0.720872\pi$
$577$	−6.54201e20	−1.27907	−0.639533	+	0.768764i	$0.720872\pi$
$578$	1.18498e21	2.28692
$579$	5.63129e20	1.07280
$580$	6.52648e18	0.0122735
$581$	9.62866e20	1.78749
$582$	6.10642e20	1.11909
$583$	−3.57577e20	−0.646927
$584$	3.49658e20	0.624521
$585$	4.92738e20	0.868855
$586$	4.86189e20	0.846394
$587$	−5.39137e20	−0.926645	−0.463322	−	0.886190i	$-0.653343\pi$
$587$	−5.39137e20	−0.926645	−0.463322	+	0.886190i	$0.653343\pi$
$588$	−1.54566e19	−0.0262292
$589$	−9.04635e20	−1.51568
$590$	8.97087e20	1.48404
$591$	−2.76180e20	−0.451114
$592$	7.32165e20	1.18085
$593$	−1.08907e20	−0.173438	−0.0867191	−	0.996233i	$-0.527638\pi$
$593$	−1.08907e20	−0.173438	−0.0867191	+	0.996233i	$0.527638\pi$
$594$	2.87878e20	0.452699
$595$	2.81149e21	4.36576
$596$	9.11326e18	0.0139742
$597$	4.26710e20	0.646137
$598$	5.59851e20	0.837169
$599$	−8.73348e20	−1.28969	−0.644846	−	0.764313i	$-0.723078\pi$
$599$	−8.73348e20	−1.28969	−0.644846	+	0.764313i	$0.723078\pi$
$600$	−7.03736e20	−1.02630
$601$	−5.48793e20	−0.790405	−0.395203	−	0.918594i	$-0.629326\pi$
$601$	−5.48793e20	−0.790405	−0.395203	+	0.918594i	$0.629326\pi$
$602$	−1.04254e20	−0.148293
$603$	−3.38448e20	−0.475458
$604$	−2.49471e18	−0.00346134
$605$	−1.32479e20	−0.181545
$606$	−9.96783e20	−1.34914
$607$	5.95274e20	0.795796	0.397898	−	0.917430i	$-0.369740\pi$
$607$	5.95274e20	0.795796	0.397898	+	0.917430i	$0.369740\pi$
$608$	−1.89303e19	−0.0249966
$609$	1.70227e21	2.22023
$610$	−1.81272e21	−2.33538
$611$	1.20537e20	0.153396
$612$	8.32085e18	0.0104600
$613$	7.25946e20	0.901469	0.450734	−	0.892658i	$-0.351162\pi$
$613$	7.25946e20	0.901469	0.450734	+	0.892658i	$0.351162\pi$
$614$	−5.05035e20	−0.619525
$615$	2.36974e21	2.87169
$616$	−1.39695e21	−1.67234
$617$	−9.60340e20	−1.13576	−0.567879	−	0.823112i	$-0.692236\pi$
$617$	−9.60340e20	−1.13576	−0.567879	+	0.823112i	$0.692236\pi$
$618$	5.57338e20	0.651186
$619$	6.93617e19	0.0800645	0.0400323	−	0.999198i	$-0.487254\pi$
$619$	6.93617e19	0.0800645	0.0400323	+	0.999198i	$0.487254\pi$
$620$	−1.25214e19	−0.0142796
$621$	−3.47191e20	−0.391185
$622$	5.76996e20	0.642311
$623$	−7.80951e20	−0.858941
$624$	−1.21823e21	−1.32387
$625$	−1.07818e21	−1.15769
$626$	−1.46899e21	−1.55851
$627$	1.50490e21	1.57761
$628$	−7.66304e18	−0.00793786
$629$	2.11498e21	2.16484
$630$	−1.45530e21	−1.47197
$631$	−1.39925e21	−1.39854	−0.699270	−	0.714858i	$-0.746491\pi$
$631$	−1.39925e21	−1.39854	−0.699270	+	0.714858i	$0.746491\pi$
$632$	−1.01133e21	−0.998883
$633$	−1.03018e20	−0.100551
$634$	−1.30711e21	−1.26079
$635$	−2.18305e21	−2.08095
$636$	−8.78748e18	−0.00827820
$637$	2.48970e21	2.31794
$638$	9.81774e20	0.903351
$639$	−4.11554e20	−0.374258
$640$	1.47300e21	1.32389
$641$	−1.45323e21	−1.29092	−0.645459	−	0.763795i	$-0.723334\pi$
$641$	−1.45323e21	−1.29092	−0.645459	+	0.763795i	$0.723334\pi$
$642$	−3.06315e20	−0.268940
$643$	1.95831e21	1.69941	0.849707	−	0.527256i	$-0.176779\pi$
$643$	1.95831e21	1.69941	0.849707	+	0.527256i	$0.176779\pi$
$644$	1.56290e19	0.0134057
$645$	1.67576e20	0.142074
$646$	2.87895e21	2.41263
$647$	1.82367e20	0.151065	0.0755327	−	0.997143i	$-0.475934\pi$
$647$	1.82367e20	0.151065	0.0755327	+	0.997143i	$0.475934\pi$
$648$	1.51738e21	1.24246
$649$	−1.27553e21	−1.03242
$650$	1.05155e21	0.841359
$651$	−3.26590e21	−2.58312
$652$	1.12858e18	0.000882419 0
$653$	−2.51396e21	−1.94316	−0.971581	−	0.236705i	$-0.923932\pi$
$653$	−2.51396e21	−1.94316	−0.971581	+	0.236705i	$0.923932\pi$
$654$	−1.93070e21	−1.47530
$655$	1.60265e21	1.21068
$656$	−2.23145e21	−1.66651
$657$	−5.17930e20	−0.382411
$658$	−3.56007e20	−0.259875
$659$	−8.59521e20	−0.620320	−0.310160	−	0.950684i	$-0.600383\pi$
$659$	−8.59521e20	−0.620320	−0.310160	+	0.950684i	$0.600383\pi$
$660$	2.08299e19	0.0148630
$661$	7.65820e20	0.540276	0.270138	−	0.962822i	$-0.412931\pi$
$661$	7.65820e20	0.540276	0.270138	+	0.962822i	$0.412931\pi$
$662$	−3.27773e19	−0.0228632
$663$	−3.51906e21	−2.42703
$664$	1.47114e21	1.00321
$665$	4.75930e21	3.20908
$666$	−1.09477e21	−0.729905
$667$	−1.18406e21	−0.780600
$668$	1.78577e18	0.00116413
$669$	−2.18480e20	−0.140836
$670$	−1.62084e21	−1.03318
$671$	2.57743e21	1.62468
$672$	−6.83418e19	−0.0426007
$673$	−1.91881e21	−1.18282	−0.591409	−	0.806371i	$-0.701428\pi$
$673$	−1.91881e21	−1.18282	−0.591409	+	0.806371i	$0.701428\pi$
$674$	1.39383e21	0.849689
$675$	−6.52121e20	−0.393143
$676$	−1.66346e18	−0.000991771 0
$677$	−1.66545e21	−0.982014	−0.491007	−	0.871156i	$-0.663371\pi$
$677$	−1.66545e21	−0.982014	−0.491007	+	0.871156i	$0.663371\pi$
$678$	−1.95001e21	−1.13714
$679$	−2.74586e21	−1.58364
$680$	4.29561e21	2.45024
$681$	−1.65236e21	−0.932185
$682$	−1.88359e21	−1.05100
$683$	3.52667e20	0.194630	0.0973149	−	0.995254i	$-0.468975\pi$
$683$	3.52667e20	0.194630	0.0973149	+	0.995254i	$0.468975\pi$
$684$	1.40856e19	0.00768871
$685$	−8.59837e20	−0.464234
$686$	−4.01719e21	−2.14531
$687$	−3.19745e21	−1.68900
$688$	−1.57796e20	−0.0824487
$689$	1.41546e21	0.731564
$690$	2.65782e21	1.35880
$691$	−3.62341e20	−0.183245	−0.0916226	−	0.995794i	$-0.529205\pi$
$691$	−3.62341e20	−0.183245	−0.0916226	+	0.995794i	$0.529205\pi$
$692$	−4.42066e18	−0.00221153
$693$	2.06923e21	1.02402
$694$	−1.03651e21	−0.507431
$695$	4.92124e21	2.38336
$696$	2.60085e21	1.24608
$697$	−6.44590e21	−3.05519
$698$	8.37492e20	0.392704
$699$	−3.04910e20	−0.141447
$700$	2.93556e19	0.0134727
$701$	3.01589e21	1.36940	0.684701	−	0.728824i	$-0.259933\pi$
$701$	3.01589e21	1.36940	0.684701	+	0.728824i	$0.259933\pi$
$702$	−1.13955e21	−0.511925
$703$	3.58025e21	1.59128
$704$	−2.13418e21	−0.938505
$705$	5.72235e20	0.248975
$706$	3.47027e20	0.149392
$707$	4.48221e21	1.90918
$708$	−3.13462e19	−0.0132110
$709$	5.82215e20	0.242793	0.121397	−	0.992604i	$-0.461263\pi$
$709$	5.82215e20	0.242793	0.121397	+	0.992604i	$0.461263\pi$
$710$	−1.97095e21	−0.813274
$711$	1.49803e21	0.611643
$712$	−1.19320e21	−0.482072
$713$	2.27168e21	0.908188
$714$	1.03935e22	4.11175
$715$	−3.35521e21	−1.31348
$716$	−2.16321e19	−0.00838013
$717$	−2.94675e21	−1.12967
$718$	−2.55669e21	−0.969938
$719$	2.71826e21	1.02053	0.510264	−	0.860018i	$-0.329548\pi$
$719$	2.71826e21	1.02053	0.510264	+	0.860018i	$0.329548\pi$
$720$	−2.20270e21	−0.818393
$721$	−2.50617e21	−0.921501
$722$	2.13832e21	0.778115
$723$	−1.88430e21	−0.678599
$724$	−4.79327e17	−0.000170841 0
$725$	−2.22398e21	−0.784507
$726$	−4.89751e20	−0.170982
$727$	2.02302e20	0.0699026	0.0349513	−	0.999389i	$-0.488872\pi$
$727$	2.02302e20	0.0699026	0.0349513	+	0.999389i	$0.488872\pi$
$728$	5.52978e21	1.89113
$729$	−4.11284e20	−0.139215
$730$	−2.48038e21	−0.830992
$731$	−4.55821e20	−0.151152
$732$	6.33404e19	0.0207897
$733$	−3.94905e21	−1.28296	−0.641479	−	0.767140i	$-0.721679\pi$
$733$	−3.94905e21	−1.28296	−0.641479	+	0.767140i	$0.721679\pi$
$734$	−2.54412e21	−0.818121
$735$	1.18195e22	3.76223
$736$	4.75369e19	0.0149778
$737$	2.30459e21	0.718767
$738$	3.33657e21	1.03010
$739$	2.60362e21	0.795690	0.397845	−	0.917453i	$-0.369758\pi$
$739$	2.60362e21	0.795690	0.397845	+	0.917453i	$0.369758\pi$
$740$	4.95557e19	0.0149919
$741$	−5.95708e21	−1.78401
$742$	−4.18055e21	−1.23938
$743$	3.39054e21	0.995069	0.497535	−	0.867444i	$-0.334239\pi$
$743$	3.39054e21	0.995069	0.497535	+	0.867444i	$0.334239\pi$
$744$	−4.98989e21	−1.44975
$745$	−6.96881e21	−2.00441
$746$	9.13556e20	0.260132
$747$	−2.17912e21	−0.614295
$748$	−5.66592e19	−0.0158128
$749$	1.37740e21	0.380580
$750$	−1.21832e21	−0.333274
$751$	4.83722e21	1.31007	0.655037	−	0.755597i	$-0.272653\pi$
$751$	4.83722e21	1.31007	0.655037	+	0.755597i	$0.272653\pi$
$752$	−5.38841e20	−0.144486
$753$	6.23651e21	1.65569
$754$	−3.88632e21	−1.02153
$755$	1.90768e21	0.496482
$756$	−3.18123e19	−0.00819749
$757$	−3.18474e21	−0.812559	−0.406279	−	0.913749i	$-0.633174\pi$
$757$	−3.18474e21	−0.812559	−0.406279	+	0.913749i	$0.633174\pi$
$758$	6.60826e21	1.66943
$759$	−3.77903e21	−0.945295
$760$	7.27163e21	1.80107
$761$	2.18602e21	0.536129	0.268064	−	0.963401i	$-0.413616\pi$
$761$	2.18602e21	0.536129	0.268064	+	0.963401i	$0.413616\pi$
$762$	−8.07032e21	−1.95987
$763$	8.68172e21	2.08772
$764$	−4.30808e19	−0.0102585
$765$	−6.36286e21	−1.50035
$766$	−7.97340e21	−1.86178
$767$	5.04913e21	1.16749
$768$	−1.55897e20	−0.0356967
$769$	4.58999e21	1.04079	0.520396	−	0.853925i	$-0.325784\pi$
$769$	4.58999e21	1.04079	0.520396	+	0.853925i	$0.325784\pi$
$770$	9.90960e21	2.22523
$771$	−3.80126e21	−0.845317
$772$	−3.58904e19	−0.00790403
$773$	−3.16446e21	−0.690165	−0.345082	−	0.938572i	$-0.612149\pi$
$773$	−3.16446e21	−0.690165	−0.345082	+	0.938572i	$0.612149\pi$
$774$	2.35945e20	0.0509628
$775$	4.26684e21	0.912733
$776$	−4.19534e21	−0.888800
$777$	1.29253e22	2.71197
$778$	−1.63469e21	−0.339695
$779$	−1.09116e22	−2.24574
$780$	−8.24544e19	−0.0168075
$781$	2.80240e21	0.565780
$782$	−7.22950e21	−1.44563
$783$	2.41010e21	0.477333
$784$	−1.11298e22	−2.18331
$785$	5.85984e21	1.13858
$786$	5.92469e21	1.14024
$787$	−4.26997e21	−0.813981	−0.406991	−	0.913432i	$-0.633422\pi$
$787$	−4.26997e21	−0.813981	−0.406991	+	0.913432i	$0.633422\pi$
$788$	1.76020e19	0.00332366
$789$	8.96950e21	1.67761
$790$	7.17411e21	1.32912
$791$	8.76857e21	1.60918
$792$	3.16153e21	0.574722
$793$	−1.02027e22	−1.83723
$794$	−5.43889e20	−0.0970190
$795$	6.71969e21	1.18740
$796$	−2.71958e19	−0.00476052
$797$	−6.53999e21	−1.13407	−0.567035	−	0.823694i	$-0.691909\pi$
$797$	−6.53999e21	−1.13407	−0.567035	+	0.823694i	$0.691909\pi$
$798$	1.75942e22	3.02238
$799$	−1.55653e21	−0.264885
$800$	8.92875e19	0.0150527
$801$	1.76742e21	0.295186
$802$	1.72017e21	0.284618
$803$	3.52674e21	0.578106
$804$	5.66356e19	0.00919748
$805$	−1.19514e22	−1.92286
$806$	7.45612e21	1.18850
$807$	−6.61095e21	−1.04403
$808$	6.84827e21	1.07151
$809$	−8.33601e21	−1.29224	−0.646122	−	0.763234i	$-0.723610\pi$
$809$	−8.33601e21	−1.29224	−0.646122	+	0.763234i	$0.723610\pi$
$810$	−1.07639e22	−1.65323
$811$	−1.17600e22	−1.78959	−0.894793	−	0.446481i	$-0.852677\pi$
$811$	−1.17600e22	−1.78959	−0.894793	+	0.446481i	$0.852677\pi$
$812$	−1.08492e20	−0.0163579
$813$	1.28628e22	1.92156
$814$	7.45462e21	1.10342
$815$	−8.63012e20	−0.126571
$816$	1.57313e22	2.28607
$817$	−7.71615e20	−0.111105
$818$	6.35118e20	0.0906160
$819$	−8.19097e21	−1.15799
$820$	−1.51033e20	−0.0211576
$821$	3.90866e21	0.542568	0.271284	−	0.962499i	$-0.412552\pi$
$821$	3.90866e21	0.542568	0.271284	+	0.962499i	$0.412552\pi$
$822$	−3.17865e21	−0.437224
$823$	−3.47555e21	−0.473723	−0.236861	−	0.971543i	$-0.576119\pi$
$823$	−3.47555e21	−0.473723	−0.236861	+	0.971543i	$0.576119\pi$
$824$	−3.82912e21	−0.517183
$825$	−7.09806e21	−0.950026
$826$	−1.49126e22	−1.97789
$827$	2.76385e21	0.363265	0.181632	−	0.983367i	$-0.441862\pi$
$827$	2.76385e21	0.363265	0.181632	+	0.983367i	$0.441862\pi$
$828$	−3.53711e19	−0.00460702
$829$	−3.29495e21	−0.425295	−0.212647	−	0.977129i	$-0.568209\pi$
$829$	−3.29495e21	−0.425295	−0.212647	+	0.977129i	$0.568209\pi$
$830$	−1.04359e22	−1.33488
$831$	−1.32047e22	−1.67387
$832$	8.44809e21	1.06129
$833$	−3.21502e22	−4.00263
$834$	1.81929e22	2.24469
$835$	−1.36556e21	−0.166979
$836$	−9.59129e19	−0.0116233
$837$	−4.62391e21	−0.555353
$838$	−6.82496e21	−0.812400
$839$	5.21358e21	0.615066	0.307533	−	0.951537i	$-0.400497\pi$
$839$	5.21358e21	0.615066	0.307533	+	0.951537i	$0.400497\pi$
$840$	2.62519e22	3.06949
$841$	−4.09820e20	−0.0474923
$842$	−4.40767e21	−0.506254
$843$	−2.70763e21	−0.308235
$844$	6.56572e18	0.000740823 0
$845$	1.27203e21	0.142256
$846$	8.05702e20	0.0893093
$847$	2.20225e21	0.241959
$848$	−6.32755e21	−0.689075
$849$	−3.57257e21	−0.385632
$850$	−1.35790e22	−1.45287
$851$	−8.99056e21	−0.953488
$852$	6.88691e19	0.00723982
$853$	−9.08836e20	−0.0947039	−0.0473519	−	0.998878i	$-0.515078\pi$
$853$	−9.08836e20	−0.0947039	−0.0473519	+	0.998878i	$0.515078\pi$
$854$	3.01335e22	3.11255
$855$	−1.07711e22	−1.10284
$856$	2.10449e21	0.213597
$857$	3.21966e21	0.323932	0.161966	−	0.986796i	$-0.448216\pi$
$857$	3.21966e21	0.323932	0.161966	+	0.986796i	$0.448216\pi$
$858$	−1.24036e22	−1.23706
$859$	−6.23925e21	−0.616856	−0.308428	−	0.951248i	$-0.599803\pi$
$859$	−6.23925e21	−0.616856	−0.308428	+	0.951248i	$0.599803\pi$
$860$	−1.06802e19	−0.00104675
$861$	−3.93930e22	−3.82733
$862$	−4.54273e21	−0.437534
$863$	−1.21687e22	−1.16189	−0.580945	−	0.813943i	$-0.697317\pi$
$863$	−1.21687e22	−1.16189	−0.580945	+	0.813943i	$0.697317\pi$
$864$	−9.67595e19	−0.00915884
$865$	3.38044e21	0.317214
$866$	9.94580e21	0.925242
$867$	3.16625e22	2.92013
$868$	2.08148e20	0.0190316
$869$	−1.02005e22	−0.924645
$870$	−1.84498e22	−1.65805
$871$	−9.12266e21	−0.812803
$872$	1.32646e22	1.17171
$873$	6.21434e21	0.544237
$874$	−1.22381e22	−1.06262
$875$	5.47839e21	0.471621
$876$	8.66700e19	0.00739755
$877$	1.86875e22	1.58144	0.790722	−	0.612176i	$-0.209706\pi$
$877$	1.86875e22	1.58144	0.790722	+	0.612176i	$0.209706\pi$
$878$	−1.14363e22	−0.959569
$879$	1.29909e22	1.08074
$880$	1.49989e22	1.23720
$881$	−1.87256e22	−1.53149	−0.765747	−	0.643141i	$-0.777631\pi$
$881$	−1.87256e22	−1.53149	−0.765747	+	0.643141i	$0.777631\pi$
$882$	1.66418e22	1.34954
$883$	−1.98293e21	−0.159442	−0.0797208	−	0.996817i	$-0.525403\pi$
$883$	−1.98293e21	−0.159442	−0.0797208	+	0.996817i	$0.525403\pi$
$884$	2.24283e20	0.0178816
$885$	2.39701e22	1.89494
$886$	1.38589e22	1.08636
$887$	7.94501e21	0.617543	0.308772	−	0.951136i	$-0.400082\pi$
$887$	7.94501e21	0.617543	0.308772	+	0.951136i	$0.400082\pi$
$888$	1.97483e22	1.52206
$889$	3.62896e22	2.77344
$890$	8.46422e21	0.641449
$891$	1.53047e22	1.15012
$892$	1.39245e19	0.00103764
$893$	−2.63490e21	−0.194706
$894$	−2.57624e22	−1.88779
$895$	1.65418e22	1.20202
$896$	−2.44862e22	−1.76446
$897$	1.49592e22	1.06897
$898$	1.04477e22	0.740368
$899$	−1.57693e22	−1.10819
$900$	−6.64366e19	−0.00463008
$901$	−1.82782e22	−1.26327
$902$	−2.27197e22	−1.55723
$903$	−2.78567e21	−0.189353
$904$	1.33973e22	0.903138
$905$	3.66536e20	0.0245049
$906$	7.05233e21	0.467597
$907$	1.06120e22	0.697816	0.348908	−	0.937157i	$-0.386553\pi$
$907$	1.06120e22	0.697816	0.348908	+	0.937157i	$0.386553\pi$
$908$	1.05311e20	0.00686802
$909$	−1.01440e22	−0.656114
$910$	−3.92268e22	−2.51636
$911$	−2.18995e22	−1.39331	−0.696653	−	0.717408i	$-0.745328\pi$
$911$	−2.18995e22	−1.39331	−0.696653	+	0.717408i	$0.745328\pi$
$912$	2.66301e22	1.68039
$913$	1.48383e22	0.928654
$914$	−2.05180e22	−1.27361
$915$	−4.84358e22	−2.98200
$916$	2.03786e20	0.0124440
$917$	−2.66414e22	−1.61357
$918$	1.47154e22	0.883997
$919$	2.12109e22	1.26384	0.631920	−	0.775034i	$-0.282267\pi$
$919$	2.12109e22	1.26384	0.631920	+	0.775034i	$0.282267\pi$
$920$	−1.82602e22	−1.07919
$921$	−1.34945e22	−0.791060
$922$	−5.58057e21	−0.324487
$923$	−1.10932e22	−0.639800
$924$	−3.46263e20	−0.0198092
$925$	−1.68867e22	−0.958259
$926$	2.87515e22	1.61837
$927$	5.67187e21	0.316686
$928$	−3.29987e20	−0.0182763
$929$	1.71579e22	0.942639	0.471320	−	0.881962i	$-0.343778\pi$
$929$	1.71579e22	0.942639	0.471320	+	0.881962i	$0.343778\pi$
$930$	3.53969e22	1.92905
$931$	−5.44239e22	−2.94217
$932$	1.94331e19	0.00104213
$933$	1.54173e22	0.820155
$934$	8.87423e20	0.0468306
$935$	4.33267e22	2.26813
$936$	−1.25148e22	−0.649912
$937$	−2.54808e22	−1.31270	−0.656351	−	0.754456i	$-0.727901\pi$
$937$	−2.54808e22	−1.31270	−0.656351	+	0.754456i	$0.727901\pi$
$938$	2.69437e22	1.37701
$939$	−3.92513e22	−1.99004
$940$	−3.64708e19	−0.00183437
$941$	1.40263e22	0.699874	0.349937	−	0.936773i	$-0.386203\pi$
$941$	1.40263e22	0.699874	0.349937	+	0.936773i	$0.386203\pi$
$942$	2.16627e22	1.07234
$943$	2.74009e22	1.34563
$944$	−2.25713e22	−1.09968
$945$	2.43265e22	1.17582
$946$	−1.60662e21	−0.0770424
$947$	3.23077e22	1.53702	0.768512	−	0.639835i	$-0.220997\pi$
$947$	3.23077e22	1.53702	0.768512	+	0.639835i	$0.220997\pi$
$948$	−2.50679e20	−0.0118319
$949$	−1.39605e22	−0.653739
$950$	−2.29866e22	−1.06794
$951$	−3.49259e22	−1.60988
$952$	−7.14075e22	−3.26563
$953$	9.67873e20	0.0439159	0.0219579	−	0.999759i	$-0.493010\pi$
$953$	9.67873e20	0.0439159	0.0219579	+	0.999759i	$0.493010\pi$
$954$	9.46126e21	0.425928
$955$	3.29434e22	1.47144
$956$	1.87808e20	0.00832299
$957$	2.62329e22	1.15347
$958$	−1.43214e21	−0.0624807
$959$	1.42934e22	0.618722
$960$	4.01062e22	1.72257
$961$	6.78910e21	0.289326
$962$	−2.95089e22	−1.24778
$963$	−3.11728e21	−0.130791
$964$	1.20094e20	0.00499969
$965$	2.74450e22	1.13373
$966$	−4.41819e22	−1.81099
$967$	1.97099e20	0.00801652	0.00400826	−	0.999992i	$-0.498724\pi$
$967$	1.97099e20	0.00801652	0.00400826	+	0.999992i	$0.498724\pi$
$968$	3.36477e21	0.135797
$969$	7.69254e22	3.08064
$970$	2.97606e22	1.18264
$971$	1.25685e21	0.0495607	0.0247804	−	0.999693i	$-0.492111\pi$
$971$	1.25685e21	0.0495607	0.0247804	+	0.999693i	$0.492111\pi$
$972$	2.59078e20	0.0101376
$973$	−8.18076e22	−3.17649
$974$	2.63329e22	1.01463
$975$	2.80974e22	1.07432
$976$	4.56092e22	1.73053
$977$	2.75196e22	1.03617	0.518087	−	0.855328i	$-0.326644\pi$
$977$	2.75196e22	1.03617	0.518087	+	0.855328i	$0.326644\pi$
$978$	−3.19039e21	−0.119207
$979$	−1.20349e22	−0.446244
$980$	−7.53304e20	−0.0277188
$981$	−1.96482e22	−0.717471
$982$	−3.95170e22	−1.43202
$983$	−2.15241e22	−0.774058	−0.387029	−	0.922067i	$-0.626499\pi$
$983$	−2.15241e22	−0.774058	−0.387029	+	0.922067i	$0.626499\pi$
$984$	−6.01877e22	−2.14805
$985$	−1.34601e22	−0.476734
$986$	5.01850e22	1.76400
$987$	−9.51247e21	−0.331829
$988$	3.79668e20	0.0131440
$989$	1.93765e21	0.0665737
$990$	−2.24270e22	−0.764730
$991$	1.98051e22	0.670231	0.335116	−	0.942177i	$-0.391225\pi$
$991$	1.98051e22	0.670231	0.335116	+	0.942177i	$0.391225\pi$
$992$	6.33100e20	0.0212635
$993$	−8.75806e20	−0.0291937
$994$	3.27637e22	1.08392
$995$	2.07964e22	0.682833
$996$	3.64652e20	0.0118832
$997$	5.83484e22	1.88719	0.943594	−	0.331104i	$-0.107421\pi$
$997$	5.83484e22	1.88719	0.943594	+	0.331104i	$0.107421\pi$
$998$	−2.09469e22	−0.672420
$999$	1.82999e22	0.583053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.16.a.a.1.20	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.16.a.a.1.20	✓	26	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:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q+180.170 q^{2} +4814.12 q^{3} -306.823 q^{4} +234624. q^{5} +867360. q^{6} -3.90024e6 q^{7} -5.95909e6 q^{8} +8.82688e6 q^{9} +O(q^{10})\)	\(q+180.170 q^{2} +4814.12 q^{3} -306.823 q^{4} +234624. q^{5} +867360. q^{6} -3.90024e6 q^{7} -5.95909e6 q^{8} +8.82688e6 q^{9} +4.22722e7 q^{10} -6.01049e7 q^{11} -1.47708e6 q^{12} +2.37923e8 q^{13} -7.02706e8 q^{14} +1.12951e9 q^{15} -1.06359e9 q^{16} -3.07237e9 q^{17} +1.59034e9 q^{18} -5.20091e9 q^{19} -7.19880e7 q^{20} -1.87762e10 q^{21} -1.08291e10 q^{22} +1.30603e10 q^{23} -2.86878e10 q^{24} +2.45309e10 q^{25} +4.28666e10 q^{26} -2.65837e10 q^{27} +1.19668e9 q^{28} -9.06607e10 q^{29} +2.03503e11 q^{30} +1.73938e11 q^{31} +3.63980e9 q^{32} -2.89353e11 q^{33} -5.53548e11 q^{34} -9.15090e11 q^{35} -2.70829e9 q^{36} -6.88388e11 q^{37} -9.37048e11 q^{38} +1.14539e12 q^{39} -1.39814e12 q^{40} +2.09803e12 q^{41} -3.38291e12 q^{42} +1.48362e11 q^{43} +1.84416e10 q^{44} +2.07100e12 q^{45} +2.35307e12 q^{46} +5.06623e11 q^{47} -5.12027e12 q^{48} +1.04643e13 q^{49} +4.41972e12 q^{50} -1.47908e13 q^{51} -7.30002e10 q^{52} +5.94921e12 q^{53} -4.78959e12 q^{54} -1.41021e13 q^{55} +2.32419e13 q^{56} -2.50378e13 q^{57} -1.63343e13 q^{58} +2.12217e13 q^{59} -3.46559e11 q^{60} -4.28821e13 q^{61} +3.13384e13 q^{62} -3.44269e13 q^{63} +3.55076e13 q^{64} +5.58225e13 q^{65} -5.21326e13 q^{66} -3.83429e13 q^{67} +9.42672e11 q^{68} +6.28739e13 q^{69} -1.64872e14 q^{70} -4.66251e13 q^{71} -5.26001e13 q^{72} -5.86765e13 q^{73} -1.24027e14 q^{74} +1.18095e14 q^{75} +1.59576e12 q^{76} +2.34424e14 q^{77} +2.06365e14 q^{78} +1.69712e14 q^{79} -2.49545e14 q^{80} -2.54633e14 q^{81} +3.78001e14 q^{82} -2.46874e14 q^{83} +5.76097e12 q^{84} -7.20851e14 q^{85} +2.67303e13 q^{86} -4.36452e14 q^{87} +3.58170e14 q^{88} +2.00232e14 q^{89} +3.73131e14 q^{90} -9.27957e14 q^{91} -4.00720e12 q^{92} +8.37358e14 q^{93} +9.12782e13 q^{94} -1.22026e15 q^{95} +1.75225e13 q^{96} +7.04024e14 q^{97} +1.88535e15 q^{98} -5.30539e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 473 q^{2} - 1745 q^{3} + 352357 q^{4} - 204476 q^{5} - 747008 q^{6} - 8691077 q^{7} - 17976447 q^{8} + 89941305 q^{9}+O(q^{10}) \) 26 * q - 473 * q^2 - 1745 * q^3 + 352357 * q^4 - 204476 * q^5 - 747008 * q^6 - 8691077 * q^7 - 17976447 * q^8 + 89941305 * q^9	\( 26 q - 473 q^{2} - 1745 q^{3} + 352357 q^{4} - 204476 q^{5} - 747008 q^{6} - 8691077 q^{7} - 17976447 q^{8} + 89941305 q^{9} - 51585280 q^{10} + 3001662 q^{11} + 512888508 q^{12} - 508793550 q^{13} - 942073166 q^{14} + 434322614 q^{15} + 7184267409 q^{16} - 4325904793 q^{17} - 9157469975 q^{18} - 4303587332 q^{19} - 32919037912 q^{20} - 45132645408 q^{21} - 50162299142 q^{22} - 13266095576 q^{23} - 110793074064 q^{24} + 65244286550 q^{25} + 10349295428 q^{26} - 77660429552 q^{27} - 239645313896 q^{28} - 66416799998 q^{29} + 507306134084 q^{30} + 103672859796 q^{31} + 368590250641 q^{32} + 570965925392 q^{33} - 100184286950 q^{34} + 581363635284 q^{35} + 2931853687289 q^{36} - 560172981803 q^{37} + 2624915279530 q^{38} - 1035242881236 q^{39} + 241463579696 q^{40} - 228932453550 q^{41} + 2858157268962 q^{42} - 2794438909830 q^{43} + 1064714773938 q^{44} - 3913841787756 q^{45} - 9400875205784 q^{46} + 13172201132038 q^{47} + 15759485913912 q^{48} + 1120374064245 q^{49} - 7441418685467 q^{50} - 42740308387651 q^{51} - 44596665749220 q^{52} - 28744292825331 q^{53} - 95850311037158 q^{54} - 39514788196568 q^{55} - 49201538022872 q^{56} - 40736796192480 q^{57} - 63400902535764 q^{58} - 10165773170481 q^{59} - 167491035794256 q^{60} - 46855749858739 q^{61} + 31884013995940 q^{62} - 37101898831500 q^{63} + 112051931566497 q^{64} + 52029013079708 q^{65} - 354971424918056 q^{66} + 13467823312288 q^{67} - 437586159999366 q^{68} + 59943985913034 q^{69} - 441355039314724 q^{70} - 307074659343603 q^{71} - 11\!\cdots\!83 q^{72}+ \cdots - 34\!\cdots\!42 q^{99}+O(q^{100}) \) 26 * q - 473 * q^2 - 1745 * q^3 + 352357 * q^4 - 204476 * q^5 - 747008 * q^6 - 8691077 * q^7 - 17976447 * q^8 + 89941305 * q^9 - 51585280 * q^10 + 3001662 * q^11 + 512888508 * q^12 - 508793550 * q^13 - 942073166 * q^14 + 434322614 * q^15 + 7184267409 * q^16 - 4325904793 * q^17 - 9157469975 * q^18 - 4303587332 * q^19 - 32919037912 * q^20 - 45132645408 * q^21 - 50162299142 * q^22 - 13266095576 * q^23 - 110793074064 * q^24 + 65244286550 * q^25 + 10349295428 * q^26 - 77660429552 * q^27 - 239645313896 * q^28 - 66416799998 * q^29 + 507306134084 * q^30 + 103672859796 * q^31 + 368590250641 * q^32 + 570965925392 * q^33 - 100184286950 * q^34 + 581363635284 * q^35 + 2931853687289 * q^36 - 560172981803 * q^37 + 2624915279530 * q^38 - 1035242881236 * q^39 + 241463579696 * q^40 - 228932453550 * q^41 + 2858157268962 * q^42 - 2794438909830 * q^43 + 1064714773938 * q^44 - 3913841787756 * q^45 - 9400875205784 * q^46 + 13172201132038 * q^47 + 15759485913912 * q^48 + 1120374064245 * q^49 - 7441418685467 * q^50 - 42740308387651 * q^51 - 44596665749220 * q^52 - 28744292825331 * q^53 - 95850311037158 * q^54 - 39514788196568 * q^55 - 49201538022872 * q^56 - 40736796192480 * q^57 - 63400902535764 * q^58 - 10165773170481 * q^59 - 167491035794256 * q^60 - 46855749858739 * q^61 + 31884013995940 * q^62 - 37101898831500 * q^63 + 112051931566497 * q^64 + 52029013079708 * q^65 - 354971424918056 * q^66 + 13467823312288 * q^67 - 437586159999366 * q^68 + 59943985913034 * q^69 - 441355039314724 * q^70 - 307074659343603 * q^71 - 1133879864100483 * q^72 - 487321498781430 * q^73 - 466623577082946 * q^74 - 884794971698755 * q^75 - 449968444781650 * q^76 - 796649959838384 * q^77 - 1093393795219952 * q^78 - 1035453802803531 * q^79 - 2167251026769280 * q^80 - 1039682728268070 * q^81 - 991772458272898 * q^82 - 1863772921617340 * q^83 - 3523568074865964 * q^84 - 1683039147983738 * q^85 - 2592833967137750 * q^86 - 2998549636473296 * q^87 - 3673206314818526 * q^88 - 2071643237231455 * q^89 - 3623510242236052 * q^90 - 2115409445432896 * q^91 - 2075443749084868 * q^92 - 2937586548722292 * q^93 - 239632735978999 * q^94 - 4926569981598120 * q^95 - 9268187425786600 * q^96 - 5317102893236637 * q^97 - 2530592027590081 * q^98 - 3419492458359442 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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