LMFDB - Embedded newform 23.14.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,14,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	23.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:	$24.6631136589$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 91997 x^{12} + 766599 x^{11} + 3278769040 x^{10} - 30986318669 x^{9} + \cdots - 45\!\cdots\!18 $ x^14 - 6x^13 - 91997x^12 + 766599x^11 + 3278769040x^10 - 30986318669x^9 - 56829440072404x^8 + 496745885608086x^7 + 489413218263943745x^6 - 2739731727714726112x^5 - 1876344541617480126605x^4 + 570635039214955094451x^3 + 2228700241007939520815870x^2 - 899908554608774434140317*x - 453423216458424113690611218
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{4}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-72.0951$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+77.0951 q^{2} -2221.44 q^{3} -2248.35 q^{4} -42257.5 q^{5} -171262. q^{6} -355522. q^{7} -804900. q^{8} +3.34048e6 q^{9} +O(q^{10})$	\(q+77.0951 q^{2} -2221.44 q^{3} -2248.35 q^{4} -42257.5 q^{5} -171262. q^{6} -355522. q^{7} -804900. q^{8} +3.34048e6 q^{9} -3.25785e6 q^{10} -4.93802e6 q^{11} +4.99458e6 q^{12} -1.79427e7 q^{13} -2.74090e7 q^{14} +9.38727e7 q^{15} -4.36353e7 q^{16} +1.12535e8 q^{17} +2.57535e8 q^{18} -1.54138e8 q^{19} +9.50098e7 q^{20} +7.89771e8 q^{21} -3.80697e8 q^{22} +1.48036e8 q^{23} +1.78804e9 q^{24} +5.64997e8 q^{25} -1.38329e9 q^{26} -3.87900e9 q^{27} +7.99338e8 q^{28} -6.25861e9 q^{29} +7.23712e9 q^{30} -3.75042e9 q^{31} +3.22967e9 q^{32} +1.09695e10 q^{33} +8.67588e9 q^{34} +1.50235e10 q^{35} -7.51058e9 q^{36} -1.27183e10 q^{37} -1.18833e10 q^{38} +3.98586e10 q^{39} +3.40131e10 q^{40} +4.64987e10 q^{41} +6.08875e10 q^{42} -2.40041e10 q^{43} +1.11024e10 q^{44} -1.41161e11 q^{45} +1.14128e10 q^{46} -1.14101e11 q^{47} +9.69333e10 q^{48} +2.95067e10 q^{49} +4.35585e10 q^{50} -2.49990e11 q^{51} +4.03415e10 q^{52} -1.00225e11 q^{53} -2.99052e11 q^{54} +2.08669e11 q^{55} +2.86159e11 q^{56} +3.42409e11 q^{57} -4.82508e11 q^{58} -3.80706e11 q^{59} -2.11059e11 q^{60} +1.53125e11 q^{61} -2.89139e11 q^{62} -1.18761e12 q^{63} +6.06452e11 q^{64} +7.58214e11 q^{65} +8.45697e11 q^{66} -6.35196e11 q^{67} -2.53018e11 q^{68} -3.28853e11 q^{69} +1.15824e12 q^{70} +1.63175e11 q^{71} -2.68875e12 q^{72} +1.26234e12 q^{73} -9.80518e11 q^{74} -1.25511e12 q^{75} +3.46557e11 q^{76} +1.75557e12 q^{77} +3.07290e12 q^{78} -3.10270e12 q^{79} +1.84392e12 q^{80} +3.29116e12 q^{81} +3.58482e12 q^{82} +2.16644e12 q^{83} -1.77568e12 q^{84} -4.75545e12 q^{85} -1.85060e12 q^{86} +1.39031e13 q^{87} +3.97461e12 q^{88} -7.35506e12 q^{89} -1.08828e13 q^{90} +6.37901e12 q^{91} -3.32837e11 q^{92} +8.33135e12 q^{93} -8.79666e12 q^{94} +6.51351e12 q^{95} -7.17453e12 q^{96} -1.94707e12 q^{97} +2.27482e12 q^{98} -1.64954e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) $ 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * 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 $

$2$	77.0951	0.851788	0.425894	−	0.904773i	$-0.359960\pi$
$2$	77.0951	0.851788	0.425894	+	0.904773i	$0.359960\pi$
$3$	−2221.44	−1.75933	−0.879664	−	0.475595i	$-0.842233\pi$
$3$	−2221.44	−1.75933	−0.879664	+	0.475595i	$0.842233\pi$
$4$	−2248.35	−0.274457
$5$	−42257.5	−1.20948	−0.604741	−	0.796422i	$-0.706723\pi$
$5$	−42257.5	−1.20948	−0.604741	+	0.796422i	$0.706723\pi$
$6$	−171262.	−1.49858
$7$	−355522.	−1.14217	−0.571083	−	0.820893i	$-0.693476\pi$
$7$	−355522.	−1.14217	−0.571083	+	0.820893i	$0.693476\pi$
$8$	−804900.	−1.08557
$9$	3.34048e6	2.09524
$10$	−3.25785e6	−1.03022
$11$	−4.93802e6	−0.840428	−0.420214	−	0.907425i	$-0.638045\pi$
$11$	−4.93802e6	−0.840428	−0.420214	+	0.907425i	$0.638045\pi$
$12$	4.99458e6	0.482860
$13$	−1.79427e7	−1.03099	−0.515496	−	0.856892i	$-0.672392\pi$
$13$	−1.79427e7	−1.03099	−0.515496	+	0.856892i	$0.672392\pi$
$14$	−2.74090e7	−0.972883
$15$	9.38727e7	2.12788
$16$	−4.36353e7	−0.650216
$17$	1.12535e8	1.13076	0.565378	−	0.824832i	$-0.308730\pi$
$17$	1.12535e8	1.13076	0.565378	+	0.824832i	$0.308730\pi$
$18$	2.57535e8	1.78470
$19$	−1.54138e8	−0.751644	−0.375822	−	0.926692i	$-0.622640\pi$
$19$	−1.54138e8	−0.751644	−0.375822	+	0.926692i	$0.622640\pi$
$20$	9.50098e7	0.331951
$21$	7.89771e8	2.00944
$22$	−3.80697e8	−0.715867
$23$	1.48036e8	0.208514
$23$	1.48036e8	0.208514
$24$	1.78804e9	1.90987
$25$	5.64997e8	0.462845
$26$	−1.38329e9	−0.878187
$27$	−3.87900e9	−1.92688
$28$	7.99338e8	0.313475
$29$	−6.25861e9	−1.95385	−0.976924	−	0.213588i	$-0.931485\pi$
$29$	−6.25861e9	−1.95385	−0.976924	+	0.213588i	$0.931485\pi$
$30$	7.23712e9	1.81250
$31$	−3.75042e9	−0.758978	−0.379489	−	0.925196i	$-0.623900\pi$
$31$	−3.75042e9	−0.758978	−0.379489	+	0.925196i	$0.623900\pi$
$32$	3.22967e9	0.531721
$33$	1.09695e10	1.47859
$34$	8.67588e9	0.963165
$35$	1.50235e10	1.38143
$36$	−7.51058e9	−0.575052
$37$	−1.27183e10	−0.814926	−0.407463	−	0.913222i	$-0.633586\pi$
$37$	−1.27183e10	−0.814926	−0.407463	+	0.913222i	$0.633586\pi$
$38$	−1.18833e10	−0.640241
$39$	3.98586e10	1.81386
$40$	3.40131e10	1.31297
$41$	4.64987e10	1.52878	0.764391	−	0.644753i	$-0.223040\pi$
$41$	4.64987e10	1.52878	0.764391	+	0.644753i	$0.223040\pi$
$42$	6.08875e10	1.71162
$43$	−2.40041e10	−0.579082	−0.289541	−	0.957166i	$-0.593503\pi$
$43$	−2.40041e10	−0.579082	−0.289541	+	0.957166i	$0.593503\pi$
$44$	1.11024e10	0.230661
$45$	−1.41161e11	−2.53415
$46$	1.14128e10	0.177610
$47$	−1.14101e11	−1.54403	−0.772014	−	0.635605i	$-0.780751\pi$
$47$	−1.14101e11	−1.54403	−0.772014	+	0.635605i	$0.780751\pi$
$48$	9.69333e10	1.14394
$49$	2.95067e10	0.304541
$50$	4.35585e10	0.394246
$51$	−2.49990e11	−1.98937
$52$	4.03415e10	0.282963
$53$	−1.00225e11	−0.621128	−0.310564	−	0.950552i	$-0.600518\pi$
$53$	−1.00225e11	−0.621128	−0.310564	+	0.950552i	$0.600518\pi$
$54$	−2.99052e11	−1.64129
$55$	2.08669e11	1.01648
$56$	2.86159e11	1.23990
$57$	3.42409e11	1.32239
$58$	−4.82508e11	−1.66426
$59$	−3.80706e11	−1.17504	−0.587519	−	0.809210i	$-0.699895\pi$
$59$	−3.80706e11	−1.17504	−0.587519	+	0.809210i	$0.699895\pi$
$60$	−2.11059e11	−0.584010
$61$	1.53125e11	0.380541	0.190270	−	0.981732i	$-0.439064\pi$
$61$	1.53125e11	0.380541	0.190270	+	0.981732i	$0.439064\pi$
$62$	−2.89139e11	−0.646489
$63$	−1.18761e12	−2.39311
$64$	6.06452e11	1.10313
$65$	7.58214e11	1.24697
$66$	8.45697e11	1.25944
$67$	−6.35196e11	−0.857870	−0.428935	−	0.903335i	$-0.641111\pi$
$67$	−6.35196e11	−0.857870	−0.428935	+	0.903335i	$0.641111\pi$
$68$	−2.53018e11	−0.310344
$69$	−3.28853e11	−0.366845
$70$	1.15824e12	1.17668
$71$	1.63175e11	0.151173	0.0755865	−	0.997139i	$-0.475917\pi$
$71$	1.63175e11	0.151173	0.0755865	+	0.997139i	$0.475917\pi$
$72$	−2.68875e12	−2.27452
$73$	1.26234e12	0.976288	0.488144	−	0.872763i	$-0.337674\pi$
$73$	1.26234e12	0.976288	0.488144	+	0.872763i	$0.337674\pi$
$74$	−9.80518e11	−0.694144
$75$	−1.25511e12	−0.814297
$76$	3.46557e11	0.206294
$77$	1.75557e12	0.959908
$78$	3.07290e12	1.54502
$79$	−3.10270e12	−1.43603	−0.718016	−	0.696027i	$-0.754950\pi$
$79$	−3.10270e12	−1.43603	−0.718016	+	0.696027i	$0.754950\pi$
$80$	1.84392e12	0.786425
$81$	3.29116e12	1.29478
$82$	3.58482e12	1.30220
$83$	2.16644e12	0.727341	0.363671	−	0.931528i	$-0.381523\pi$
$83$	2.16644e12	0.727341	0.363671	+	0.931528i	$0.381523\pi$
$84$	−1.77568e12	−0.551506
$85$	−4.75545e12	−1.36763
$86$	−1.85060e12	−0.493255
$87$	1.39031e13	3.43746
$88$	3.97461e12	0.912341
$89$	−7.35506e12	−1.56874	−0.784370	−	0.620293i	$-0.787014\pi$
$89$	−7.35506e12	−1.56874	−0.784370	+	0.620293i	$0.787014\pi$
$90$	−1.08828e13	−2.15856
$91$	6.37901e12	1.17756
$92$	−3.32837e11	−0.0572282
$93$	8.33135e12	1.33529
$94$	−8.79666e12	−1.31518
$95$	6.51351e12	0.909099
$96$	−7.17453e12	−0.935471
$97$	−1.94707e12	−0.237337	−0.118669	−	0.992934i	$-0.537863\pi$
$97$	−1.94707e12	−0.237337	−0.118669	+	0.992934i	$0.537863\pi$
$98$	2.27482e12	0.259404
$99$	−1.64954e13	−1.76090
$100$	−1.27031e12	−0.127031
$101$	5.09502e12	0.477592	0.238796	−	0.971070i	$-0.423247\pi$
$101$	5.09502e12	0.477592	0.238796	+	0.971070i	$0.423247\pi$
$102$	−1.92730e13	−1.69452
$103$	1.76525e13	1.45668	0.728340	−	0.685216i	$-0.240292\pi$
$103$	1.76525e13	1.45668	0.728340	+	0.685216i	$0.240292\pi$
$104$	1.44421e13	1.11921
$105$	−3.33738e13	−2.43038
$106$	−7.72682e12	−0.529070
$107$	6.70690e12	0.432043	0.216022	−	0.976389i	$-0.430692\pi$
$107$	6.70690e12	0.432043	0.216022	+	0.976389i	$0.430692\pi$
$108$	8.72135e12	0.528846
$109$	−7.05716e12	−0.403049	−0.201524	−	0.979484i	$-0.564590\pi$
$109$	−7.05716e12	−0.403049	−0.201524	+	0.979484i	$0.564590\pi$
$110$	1.60873e13	0.865828
$111$	2.82530e13	1.43372
$112$	1.55133e13	0.742654
$113$	4.16692e13	1.88281	0.941403	−	0.337284i	$-0.109508\pi$
$113$	4.16692e13	1.88281	0.941403	+	0.337284i	$0.109508\pi$
$114$	2.63981e13	1.12640
$115$	−6.25563e12	−0.252194
$116$	1.40715e13	0.536247
$117$	−5.99373e13	−2.16017
$118$	−2.93506e13	−1.00088
$119$	−4.00086e13	−1.29151
$120$	−7.55581e13	−2.30995
$121$	−1.01386e13	−0.293680
$122$	1.18052e13	0.324140
$123$	−1.03294e14	−2.68963
$124$	8.43227e12	0.208307
$125$	2.77085e13	0.649679
$126$	−9.15592e13	−2.03842
$127$	−1.08456e12	−0.0229365	−0.0114683	−	0.999934i	$-0.503651\pi$
$127$	−1.08456e12	−0.0229365	−0.0114683	+	0.999934i	$0.503651\pi$
$128$	2.02970e13	0.407912
$129$	5.33237e13	1.01880
$130$	5.84545e13	1.06215
$131$	1.00078e14	1.73012	0.865059	−	0.501670i	$-0.167281\pi$
$131$	1.00078e14	1.73012	0.865059	+	0.501670i	$0.167281\pi$
$132$	−2.46634e13	−0.405809
$133$	5.47995e13	0.858501
$134$	−4.89705e13	−0.730723
$135$	1.63917e14	2.33053
$136$	−9.05792e13	−1.22751
$137$	−4.53383e13	−0.585843	−0.292921	−	0.956137i	$-0.594627\pi$
$137$	−4.53383e13	−0.585843	−0.292921	+	0.956137i	$0.594627\pi$
$138$	−2.53530e13	−0.312475
$139$	−2.23344e13	−0.262650	−0.131325	−	0.991339i	$-0.541923\pi$
$139$	−2.23344e13	−0.262650	−0.131325	+	0.991339i	$0.541923\pi$
$140$	−3.37780e13	−0.379142
$141$	2.53470e14	2.71645
$142$	1.25800e13	0.128767
$143$	8.86014e13	0.866475
$144$	−1.45763e14	−1.36236
$145$	2.64473e14	2.36314
$146$	9.73202e13	0.831590
$147$	−6.55474e13	−0.535788
$148$	2.85952e13	0.223662
$149$	−1.66323e14	−1.24521	−0.622603	−	0.782538i	$-0.713925\pi$
$149$	−1.66323e14	−1.24521	−0.622603	+	0.782538i	$0.713925\pi$
$150$	−9.67626e13	−0.693609
$151$	−1.47583e14	−1.01318	−0.506590	−	0.862187i	$-0.669094\pi$
$151$	−1.47583e14	−1.01318	−0.506590	+	0.862187i	$0.669094\pi$
$152$	1.24066e14	0.815960
$153$	3.75921e14	2.36920
$154$	1.35346e14	0.817638
$155$	1.58484e14	0.917970
$156$	−8.96162e13	−0.497825
$157$	−6.38748e13	−0.340394	−0.170197	−	0.985410i	$-0.554440\pi$
$157$	−6.38748e13	−0.340394	−0.170197	+	0.985410i	$0.554440\pi$
$158$	−2.39203e14	−1.22320
$159$	2.22643e14	1.09277
$160$	−1.36478e14	−0.643106
$161$	−5.26300e13	−0.238158
$162$	2.53732e14	1.10288
$163$	−2.69848e14	−1.12694	−0.563470	−	0.826137i	$-0.690534\pi$
$163$	−2.69848e14	−1.12694	−0.563470	+	0.826137i	$0.690534\pi$
$164$	−1.04545e14	−0.419585
$165$	−4.63546e14	−1.78833
$166$	1.67021e14	0.619541
$167$	−4.02645e14	−1.43637	−0.718183	−	0.695854i	$-0.755026\pi$
$167$	−4.02645e14	−1.43637	−0.718183	+	0.695854i	$0.755026\pi$
$168$	−6.35686e14	−2.18139
$169$	1.90648e13	0.0629462
$170$	−3.66621e14	−1.16493
$171$	−5.14897e14	−1.57487
$172$	5.39696e13	0.158933
$173$	−1.81296e14	−0.514150	−0.257075	−	0.966391i	$-0.582759\pi$
$173$	−1.81296e14	−0.514150	−0.257075	+	0.966391i	$0.582759\pi$
$174$	1.07186e15	2.92799
$175$	−2.00869e14	−0.528646
$176$	2.15472e14	0.546460
$177$	8.45717e14	2.06728
$178$	−5.67039e14	−1.33623
$179$	−3.72587e14	−0.846610	−0.423305	−	0.905987i	$-0.639130\pi$
$179$	−3.72587e14	−0.846610	−0.423305	+	0.905987i	$0.639130\pi$
$180$	3.17379e14	0.695515
$181$	−3.92973e14	−0.830715	−0.415357	−	0.909658i	$-0.636343\pi$
$181$	−3.92973e14	−0.830715	−0.415357	+	0.909658i	$0.636343\pi$
$182$	4.91790e14	1.00304
$183$	−3.40158e14	−0.669496
$184$	−1.19154e14	−0.226356
$185$	5.37444e14	0.985637
$186$	6.42306e14	1.13739
$187$	−5.55700e14	−0.950319
$188$	2.56540e14	0.423769
$189$	1.37907e15	2.20082
$190$	5.02159e14	0.774360
$191$	1.23203e14	0.183614	0.0918071	−	0.995777i	$-0.470736\pi$
$191$	1.23203e14	0.183614	0.0918071	+	0.995777i	$0.470736\pi$
$192$	−1.34720e15	−1.94077
$193$	8.26333e14	1.15089	0.575443	−	0.817842i	$-0.304830\pi$
$193$	8.26333e14	1.15089	0.575443	+	0.817842i	$0.304830\pi$
$194$	−1.50110e14	−0.202161
$195$	−1.68433e15	−2.19382
$196$	−6.63414e13	−0.0835834
$197$	−1.86230e14	−0.226997	−0.113498	−	0.993538i	$-0.536206\pi$
$197$	−1.86230e14	−0.226997	−0.113498	+	0.993538i	$0.536206\pi$
$198$	−1.27171e15	−1.49991
$199$	−1.39857e15	−1.59639	−0.798196	−	0.602398i	$-0.794212\pi$
$199$	−1.39857e15	−1.59639	−0.798196	+	0.602398i	$0.794212\pi$
$200$	−4.54766e14	−0.502450
$201$	1.41105e15	1.50928
$202$	3.92801e14	0.406807
$203$	2.22507e15	2.23162
$204$	5.62065e14	0.545997
$205$	−1.96492e15	−1.84903
$206$	1.36092e15	1.24078
$207$	4.94512e14	0.436887
$208$	7.82934e14	0.670368
$209$	7.61138e14	0.631703
$210$	−2.57295e15	−2.07017
$211$	6.18228e14	0.482295	0.241147	−	0.970489i	$-0.422476\pi$
$211$	6.18228e14	0.482295	0.241147	+	0.970489i	$0.422476\pi$
$212$	2.25340e14	0.170473
$213$	−3.62484e14	−0.265963
$214$	5.17069e14	0.368009
$215$	1.01435e15	0.700389
$216$	3.12220e15	2.09176
$217$	1.33336e15	0.866879
$218$	−5.44072e14	−0.343312
$219$	−2.80422e15	−1.71761
$220$	−4.69161e14	−0.278981
$221$	−2.01918e15	−1.16580
$222$	2.17817e15	1.22123
$223$	3.66559e14	0.199601	0.0998003	−	0.995007i	$-0.468180\pi$
$223$	3.66559e14	0.199601	0.0998003	+	0.995007i	$0.468180\pi$
$224$	−1.14822e15	−0.607313
$225$	1.88736e15	0.969771
$226$	3.21249e15	1.60375
$227$	−2.33054e15	−1.13054	−0.565272	−	0.824904i	$-0.691229\pi$
$227$	−2.33054e15	−1.13054	−0.565272	+	0.824904i	$0.691229\pi$
$228$	−7.69857e14	−0.362939
$229$	1.55598e15	0.712972	0.356486	−	0.934301i	$-0.383975\pi$
$229$	1.55598e15	0.712972	0.356486	+	0.934301i	$0.383975\pi$
$230$	−4.82278e14	−0.214816
$231$	−3.89991e15	−1.68879
$232$	5.03755e15	2.12103
$233$	−2.84240e15	−1.16378	−0.581891	−	0.813267i	$-0.697687\pi$
$233$	−2.84240e15	−1.16378	−0.581891	+	0.813267i	$0.697687\pi$
$234$	−4.62087e15	−1.84001
$235$	4.82165e15	1.86747
$236$	8.55962e14	0.322497
$237$	6.89248e15	2.52645
$238$	−3.08446e15	−1.10009
$239$	−4.23368e15	−1.46937	−0.734686	−	0.678407i	$-0.762670\pi$
$239$	−4.23368e15	−1.46937	−0.734686	+	0.678407i	$0.762670\pi$
$240$	−4.09616e15	−1.38358
$241$	8.76284e14	0.288094	0.144047	−	0.989571i	$-0.453988\pi$
$241$	8.76284e14	0.288094	0.144047	+	0.989571i	$0.453988\pi$
$242$	−7.81640e14	−0.250154
$243$	−1.12674e15	−0.351063
$244$	−3.44278e14	−0.104442
$245$	−1.24688e15	−0.368337
$246$	−7.96347e15	−2.29100
$247$	2.76566e15	0.774940
$248$	3.01872e15	0.823922
$249$	−4.81261e15	−1.27963
$250$	2.13619e15	0.553388
$251$	−3.57369e15	−0.902064	−0.451032	−	0.892508i	$-0.648944\pi$
$251$	−3.57369e15	−0.902064	−0.451032	+	0.892508i	$0.648944\pi$
$252$	2.67017e15	0.656805
$253$	−7.31005e14	−0.175241
$254$	−8.36139e13	−0.0195371
$255$	1.05639e16	2.40611
$256$	−3.40326e15	−0.755675
$257$	−1.86343e15	−0.403411	−0.201706	−	0.979446i	$-0.564648\pi$
$257$	−1.86343e15	−0.403411	−0.201706	+	0.979446i	$0.564648\pi$
$258$	4.11099e15	0.867798
$259$	4.52163e15	0.930779
$260$	−1.70473e15	−0.342239
$261$	−2.09068e16	−4.09377
$262$	7.71553e15	1.47369
$263$	−8.14355e15	−1.51740	−0.758702	−	0.651438i	$-0.774166\pi$
$263$	−8.14355e15	−1.51740	−0.758702	+	0.651438i	$0.774166\pi$
$264$	−8.82937e15	−1.60511
$265$	4.23525e15	0.751243
$266$	4.22477e15	0.731261
$267$	1.63388e16	2.75993
$268$	1.42814e15	0.235448
$269$	1.16660e16	1.87730	0.938649	−	0.344874i	$-0.112078\pi$
$269$	1.16660e16	1.87730	0.938649	+	0.344874i	$0.112078\pi$
$270$	1.26372e16	1.98512
$271$	−7.55725e15	−1.15895	−0.579473	−	0.814991i	$-0.696742\pi$
$271$	−7.55725e15	−1.15895	−0.579473	+	0.814991i	$0.696742\pi$
$272$	−4.91049e15	−0.735236
$273$	−1.41706e16	−2.07172
$274$	−3.49536e15	−0.499014
$275$	−2.78997e15	−0.388988
$276$	7.39378e14	0.100683
$277$	6.06275e15	0.806402	0.403201	−	0.915112i	$-0.367898\pi$
$277$	6.06275e15	0.806402	0.403201	+	0.915112i	$0.367898\pi$
$278$	−1.72187e15	−0.223723
$279$	−1.25282e16	−1.59024
$280$	−1.20924e16	−1.49963
$281$	4.20287e15	0.509278	0.254639	−	0.967036i	$-0.418043\pi$
$281$	4.20287e15	0.509278	0.254639	+	0.967036i	$0.418043\pi$
$282$	1.95413e16	2.31384
$283$	4.99883e15	0.578438	0.289219	−	0.957263i	$-0.406604\pi$
$283$	4.99883e15	0.578438	0.289219	+	0.957263i	$0.406604\pi$
$284$	−3.66875e14	−0.0414905
$285$	−1.44694e16	−1.59940
$286$	6.83073e15	0.738053
$287$	−1.65313e16	−1.74612
$288$	1.07887e16	1.11408
$289$	2.75951e15	0.278610
$290$	2.03896e16	2.01290
$291$	4.32531e15	0.417555
$292$	−2.83818e15	−0.267949
$293$	−1.30695e16	−1.20676	−0.603379	−	0.797454i	$-0.706180\pi$
$293$	−1.30695e16	−1.20676	−0.603379	+	0.797454i	$0.706180\pi$
$294$	−5.05338e15	−0.456378
$295$	1.60877e16	1.42119
$296$	1.02370e16	0.884657
$297$	1.91546e16	1.61941
$298$	−1.28227e16	−1.06065
$299$	−2.65616e15	−0.214977
$300$	2.82192e15	0.223489
$301$	8.53397e15	0.661407
$302$	−1.13779e16	−0.863015
$303$	−1.13183e16	−0.840241
$304$	6.72587e15	0.488731
$305$	−6.47067e15	−0.460257
$306$	2.89816e16	2.01806
$307$	2.74663e16	1.87241	0.936204	−	0.351457i	$-0.114314\pi$
$307$	2.74663e16	1.87241	0.936204	+	0.351457i	$0.114314\pi$
$308$	−3.94715e15	−0.263453
$309$	−3.92140e16	−2.56278
$310$	1.22183e16	0.781916
$311$	−5.93397e15	−0.371880	−0.185940	−	0.982561i	$-0.559533\pi$
$311$	−5.93397e15	−0.371880	−0.185940	+	0.982561i	$0.559533\pi$
$312$	−3.20822e16	−1.96906
$313$	1.69137e16	1.01672	0.508359	−	0.861145i	$-0.330252\pi$
$313$	1.69137e16	1.01672	0.508359	+	0.861145i	$0.330252\pi$
$314$	−4.92444e15	−0.289944
$315$	5.01857e16	2.89442
$316$	6.97597e15	0.394129
$317$	5.45014e15	0.301664	0.150832	−	0.988559i	$-0.451805\pi$
$317$	5.45014e15	0.301664	0.150832	+	0.988559i	$0.451805\pi$
$318$	1.71647e16	0.930807
$319$	3.09051e16	1.64207
$320$	−2.56272e16	−1.33422
$321$	−1.48990e16	−0.760106
$322$	−4.05751e15	−0.202860
$323$	−1.73459e16	−0.849926
$324$	−7.39968e15	−0.355361
$325$	−1.01376e16	−0.477190
$326$	−2.08040e16	−0.959913
$327$	1.56771e16	0.709095
$328$	−3.74268e16	−1.65960
$329$	4.05656e16	1.76354
$330$	−3.57371e16	−1.52328
$331$	−3.63136e15	−0.151771	−0.0758853	−	0.997117i	$-0.524178\pi$
$331$	−3.63136e15	−0.151771	−0.0758853	+	0.997117i	$0.524178\pi$
$332$	−4.87091e15	−0.199624
$333$	−4.24853e16	−1.70746
$334$	−3.10419e16	−1.22348
$335$	2.68418e16	1.03758
$336$	−3.44619e16	−1.30657
$337$	3.40078e15	0.126469	0.0632345	−	0.997999i	$-0.479858\pi$
$337$	3.40078e15	0.126469	0.0632345	+	0.997999i	$0.479858\pi$
$338$	1.46980e15	0.0536168
$339$	−9.25658e16	−3.31247
$340$	1.06919e16	0.375355
$341$	1.85197e16	0.637867
$342$	−3.96960e16	−1.34146
$343$	2.39559e16	0.794329
$344$	1.93209e16	0.628632
$345$	1.38965e16	0.443693
$346$	−1.39771e16	−0.437947
$347$	−1.35371e16	−0.416279	−0.208140	−	0.978099i	$-0.566741\pi$
$347$	−1.35371e16	−0.416279	−0.208140	+	0.978099i	$0.566741\pi$
$348$	−3.12591e16	−0.943435
$349$	3.95386e15	0.117127	0.0585633	−	0.998284i	$-0.481348\pi$
$349$	3.95386e15	0.117127	0.0585633	+	0.998284i	$0.481348\pi$
$350$	−1.54860e16	−0.450294
$351$	6.95996e16	1.98660
$352$	−1.59482e16	−0.446873
$353$	−3.08295e15	−0.0848069	−0.0424035	−	0.999101i	$-0.513501\pi$
$353$	−3.08295e15	−0.0848069	−0.0424035	+	0.999101i	$0.513501\pi$
$354$	6.52006e16	1.76088
$355$	−6.89538e15	−0.182841
$356$	1.65368e16	0.430552
$357$	8.88768e16	2.27219
$358$	−2.87246e16	−0.721132
$359$	−6.96398e16	−1.71689	−0.858447	−	0.512902i	$-0.828570\pi$
$359$	−6.96398e16	−1.71689	−0.858447	+	0.512902i	$0.828570\pi$
$360$	1.13620e17	2.75099
$361$	−1.82944e16	−0.435031
$362$	−3.02963e16	−0.707593
$363$	2.25224e16	0.516680
$364$	−1.43423e16	−0.323191
$365$	−5.33434e16	−1.18080
$366$	−2.62245e16	−0.570269
$367$	−1.04043e16	−0.222272	−0.111136	−	0.993805i	$-0.535449\pi$
$367$	−1.04043e16	−0.222272	−0.111136	+	0.993805i	$0.535449\pi$
$368$	−6.45959e15	−0.135579
$369$	1.55328e17	3.20316
$370$	4.14343e16	0.839554
$371$	3.56320e16	0.709431
$372$	−1.87318e16	−0.366480
$373$	7.41326e16	1.42528	0.712642	−	0.701527i	$-0.247498\pi$
$373$	7.41326e16	1.42528	0.712642	+	0.701527i	$0.247498\pi$
$374$	−4.28417e16	−0.809471
$375$	−6.15529e16	−1.14300
$376$	9.18402e16	1.67615
$377$	1.12296e17	2.01440
$378$	1.06319e17	1.87463
$379$	−6.84279e16	−1.18598	−0.592991	−	0.805209i	$-0.702053\pi$
$379$	−6.84279e16	−1.18598	−0.592991	+	0.805209i	$0.702053\pi$
$380$	−1.46447e16	−0.249509
$381$	2.40928e15	0.0403529
$382$	9.49838e15	0.156400
$383$	−4.97045e16	−0.804644	−0.402322	−	0.915498i	$-0.631797\pi$
$383$	−4.97045e16	−0.804644	−0.402322	+	0.915498i	$0.631797\pi$
$384$	−4.50886e16	−0.717652
$385$	−7.41863e16	−1.16099
$386$	6.37062e16	0.980312
$387$	−8.01852e16	−1.21331
$388$	4.37771e15	0.0651389
$389$	2.19773e16	0.321589	0.160795	−	0.986988i	$-0.448594\pi$
$389$	2.19773e16	0.321589	0.160795	+	0.986988i	$0.448594\pi$
$390$	−1.29853e17	−1.86867
$391$	1.66592e16	0.235779
$392$	−2.37499e16	−0.330600
$393$	−2.22318e17	−3.04385
$394$	−1.43574e16	−0.193353
$395$	1.31113e17	1.73685
$396$	3.70874e16	0.483290
$397$	3.90103e16	0.500082	0.250041	−	0.968235i	$-0.419556\pi$
$397$	3.90103e16	0.500082	0.250041	+	0.968235i	$0.419556\pi$
$398$	−1.07823e17	−1.35979
$399$	−1.21734e17	−1.51039
$400$	−2.46538e16	−0.300950
$401$	−3.98639e16	−0.478786	−0.239393	−	0.970923i	$-0.576948\pi$
$401$	−3.98639e16	−0.478786	−0.239393	+	0.970923i	$0.576948\pi$
$402$	1.08785e17	1.28558
$403$	6.72927e16	0.782501
$404$	−1.14554e16	−0.131078
$405$	−1.39076e17	−1.56601
$406$	1.71542e17	1.90086
$407$	6.28033e16	0.684886
$408$	2.01217e17	2.15960
$409$	2.63039e16	0.277855	0.138927	−	0.990303i	$-0.455635\pi$
$409$	2.63039e16	0.277855	0.138927	+	0.990303i	$0.455635\pi$
$410$	−1.51486e17	−1.57499
$411$	1.00716e17	1.03069
$412$	−3.96890e16	−0.399796
$413$	1.35349e17	1.34209
$414$	3.81244e16	0.372135
$415$	−9.15482e16	−0.879706
$416$	−5.79490e16	−0.548200
$417$	4.96146e16	0.462088
$418$	5.86800e16	0.538077
$419$	1.34029e17	1.21007	0.605033	−	0.796201i	$-0.293160\pi$
$419$	1.34029e17	1.21007	0.605033	+	0.796201i	$0.293160\pi$
$420$	7.50360e16	0.667036
$421$	3.03968e16	0.266069	0.133034	−	0.991111i	$-0.457528\pi$
$421$	3.03968e16	0.266069	0.133034	+	0.991111i	$0.457528\pi$
$422$	4.76623e16	0.410813
$423$	−3.81154e17	−3.23510
$424$	8.06707e16	0.674276
$425$	6.35818e16	0.523365
$426$	−2.79457e16	−0.226544
$427$	−5.44391e16	−0.434640
$428$	−1.50795e16	−0.118577
$429$	−1.96823e17	−1.52441
$430$	7.82016e16	0.596583
$431$	5.36691e16	0.403294	0.201647	−	0.979458i	$-0.435371\pi$
$431$	5.36691e16	0.403294	0.201647	+	0.979458i	$0.435371\pi$
$432$	1.69261e17	1.25289
$433$	−1.91538e17	−1.39664	−0.698319	−	0.715787i	$-0.746068\pi$
$433$	−1.91538e17	−1.39664	−0.698319	+	0.715787i	$0.746068\pi$
$434$	1.02795e17	0.738397
$435$	−5.87512e17	−4.15754
$436$	1.58670e16	0.110620
$437$	−2.28180e16	−0.156729
$438$	−2.16191e17	−1.46304
$439$	1.49311e17	0.995568	0.497784	−	0.867301i	$-0.334147\pi$
$439$	1.49311e17	0.995568	0.497784	+	0.867301i	$0.334147\pi$
$440$	−1.67957e17	−1.10346
$441$	9.85666e16	0.638086
$442$	−1.55669e17	−0.993016
$443$	8.15078e16	0.512360	0.256180	−	0.966629i	$-0.417536\pi$
$443$	8.15078e16	0.512360	0.256180	+	0.966629i	$0.417536\pi$
$444$	−6.35226e16	−0.393495
$445$	3.10807e17	1.89736
$446$	2.82599e16	0.170017
$447$	3.69477e17	2.19073
$448$	−2.15607e17	−1.25996
$449$	2.97496e17	1.71348	0.856741	−	0.515747i	$-0.172485\pi$
$449$	2.97496e17	1.71348	0.856741	+	0.515747i	$0.172485\pi$
$450$	1.45506e17	0.826039
$451$	−2.29612e17	−1.28483
$452$	−9.36871e16	−0.516749
$453$	3.27848e17	1.78252
$454$	−1.79673e17	−0.962985
$455$	−2.69561e17	−1.42424
$456$	−2.75605e17	−1.43554
$457$	5.90270e16	0.303107	0.151553	−	0.988449i	$-0.451572\pi$
$457$	5.90270e16	0.303107	0.151553	+	0.988449i	$0.451572\pi$
$458$	1.19958e17	0.607301
$459$	−4.36522e17	−2.17883
$460$	1.40649e16	0.0692165
$461$	−2.09832e17	−1.01816	−0.509079	−	0.860720i	$-0.670014\pi$
$461$	−2.09832e17	−1.01816	−0.509079	+	0.860720i	$0.670014\pi$
$462$	−3.00664e17	−1.43849
$463$	3.00565e17	1.41795	0.708977	−	0.705231i	$-0.249157\pi$
$463$	3.00565e17	1.41795	0.708977	+	0.705231i	$0.249157\pi$
$464$	2.73096e17	1.27042
$465$	−3.52063e17	−1.61501
$466$	−2.19135e17	−0.991296
$467$	4.19991e16	0.187362	0.0936808	−	0.995602i	$-0.470137\pi$
$467$	4.19991e16	0.187362	0.0936808	+	0.995602i	$0.470137\pi$
$468$	1.34760e17	0.592875
$469$	2.25826e17	0.979829
$470$	3.71725e17	1.59069
$471$	1.41894e17	0.598865
$472$	3.06430e17	1.27558
$473$	1.18533e17	0.486677
$474$	5.31376e17	2.15200
$475$	−8.70877e16	−0.347895
$476$	8.99533e16	0.354464
$477$	−3.34799e17	−1.30141
$478$	−3.26396e17	−1.25159
$479$	−3.77672e17	−1.42868	−0.714338	−	0.699801i	$-0.753272\pi$
$479$	−3.77672e17	−1.42868	−0.714338	+	0.699801i	$0.753272\pi$
$480$	3.03178e17	1.13144
$481$	2.28200e17	0.840182
$482$	6.75572e16	0.245395
$483$	1.16914e17	0.418998
$484$	2.27952e16	0.0806026
$485$	8.22786e16	0.287055
$486$	−8.68665e16	−0.299031
$487$	−2.22797e17	−0.756783	−0.378391	−	0.925646i	$-0.623523\pi$
$487$	−2.22797e17	−0.756783	−0.378391	+	0.925646i	$0.623523\pi$
$488$	−1.23250e17	−0.413103
$489$	5.99453e17	1.98266
$490$	−9.61283e16	−0.313745
$491$	−1.70140e17	−0.547994	−0.273997	−	0.961731i	$-0.588346\pi$
$491$	−1.70140e17	−0.547994	−0.273997	+	0.961731i	$0.588346\pi$
$492$	2.32242e17	0.738188
$493$	−7.04311e17	−2.20933
$494$	2.13218e17	0.660084
$495$	6.97055e17	2.12977
$496$	1.63651e17	0.493500
$497$	−5.80123e16	−0.172665
$498$	−3.71029e17	−1.08998
$499$	−1.67941e17	−0.486971	−0.243485	−	0.969905i	$-0.578291\pi$
$499$	−1.67941e17	−0.486971	−0.243485	+	0.969905i	$0.578291\pi$
$500$	−6.22985e16	−0.178309
$501$	8.94453e17	2.52704
$502$	−2.75514e17	−0.768368
$503$	−2.28744e17	−0.629735	−0.314867	−	0.949136i	$-0.601960\pi$
$503$	−2.28744e17	−0.629735	−0.314867	+	0.949136i	$0.601960\pi$
$504$	9.55910e17	2.59788
$505$	−2.15303e17	−0.577638
$506$	−5.63568e16	−0.149269
$507$	−4.23514e16	−0.110743
$508$	2.43846e15	0.00629509
$509$	1.58719e17	0.404542	0.202271	−	0.979330i	$-0.435168\pi$
$509$	1.58719e17	0.404542	0.202271	+	0.979330i	$0.435168\pi$
$510$	8.14428e17	2.04949
$511$	−4.48789e17	−1.11508
$512$	−4.28647e17	−1.05159
$513$	5.97902e17	1.44833
$514$	−1.43661e17	−0.343621
$515$	−7.45951e17	−1.76183
$516$	−1.19890e17	−0.279615
$517$	5.63436e17	1.29764
$518$	3.48596e17	0.792827
$519$	4.02740e17	0.904558
$520$	−6.10286e17	−1.35367
$521$	−2.64796e17	−0.580050	−0.290025	−	0.957019i	$-0.593664\pi$
$521$	−2.64796e17	−0.580050	−0.290025	+	0.957019i	$0.593664\pi$
$522$	−1.61181e18	−3.48703
$523$	1.88202e17	0.402128	0.201064	−	0.979578i	$-0.435560\pi$
$523$	1.88202e17	0.402128	0.201064	+	0.979578i	$0.435560\pi$
$524$	−2.25011e17	−0.474843
$525$	4.46218e17	0.930062
$526$	−6.27827e17	−1.29251
$527$	−4.22053e17	−0.858220
$528$	−4.78659e17	−0.961403
$529$	2.19146e16	0.0434783
$530$	3.26517e17	0.639900
$531$	−1.27174e18	−2.46198
$532$	−1.23209e17	−0.235622
$533$	−8.34312e17	−1.57616
$534$	1.25964e18	2.35088
$535$	−2.83417e17	−0.522548
$536$	5.11269e17	0.931276
$537$	8.27681e17	1.48946
$538$	8.99393e17	1.59906
$539$	−1.45705e17	−0.255945
$540$	−3.68543e17	−0.639629
$541$	−6.30668e17	−1.08148	−0.540740	−	0.841190i	$-0.681856\pi$
$541$	−6.30668e17	−1.08148	−0.540740	+	0.841190i	$0.681856\pi$
$542$	−5.82627e17	−0.987177
$543$	8.72967e17	1.46150
$544$	3.63451e17	0.601246
$545$	2.98218e17	0.487480
$546$	−1.09248e18	−1.76467
$547$	6.23439e16	0.0995121	0.0497561	−	0.998761i	$-0.484156\pi$
$547$	6.23439e16	0.0995121	0.0497561	+	0.998761i	$0.484156\pi$
$548$	1.01936e17	0.160789
$549$	5.11510e17	0.797323
$550$	−2.15093e17	−0.331336
$551$	9.64691e17	1.46860
$552$	2.64694e17	0.398235
$553$	1.10308e18	1.64019
$554$	4.67408e17	0.686883
$555$	−1.19390e18	−1.73406
$556$	5.02156e16	0.0720862
$557$	−6.04028e17	−0.857034	−0.428517	−	0.903534i	$-0.640964\pi$
$557$	−6.04028e17	−0.857034	−0.428517	+	0.903534i	$0.640964\pi$
$558$	−9.65865e17	−1.35455
$559$	4.30697e17	0.597029
$560$	−6.55554e17	−0.898227
$561$	1.23445e18	1.67192
$562$	3.24021e17	0.433797
$563$	5.16655e17	0.683747	0.341874	−	0.939746i	$-0.388938\pi$
$563$	5.16655e17	0.683747	0.341874	+	0.939746i	$0.388938\pi$
$564$	−5.69889e17	−0.745549
$565$	−1.76084e18	−2.27722
$566$	3.85385e17	0.492707
$567$	−1.17008e18	−1.47885
$568$	−1.31339e17	−0.164109
$569$	−8.60002e17	−1.06236	−0.531178	−	0.847261i	$-0.678250\pi$
$569$	−8.60002e17	−1.06236	−0.531178	+	0.847261i	$0.678250\pi$
$570$	−1.11552e18	−1.36235
$571$	6.17603e16	0.0745718	0.0372859	−	0.999305i	$-0.488129\pi$
$571$	6.17603e16	0.0745718	0.0372859	+	0.999305i	$0.488129\pi$
$572$	−1.99207e17	−0.237810
$573$	−2.73689e17	−0.323038
$574$	−1.27448e18	−1.48733
$575$	8.36398e16	0.0965099
$576$	2.02584e18	2.31132
$577$	4.20228e17	0.474070	0.237035	−	0.971501i	$-0.423824\pi$
$577$	4.20228e17	0.474070	0.237035	+	0.971501i	$0.423824\pi$
$578$	2.12745e17	0.237316
$579$	−1.83565e18	−2.02479
$580$	−5.94629e17	−0.648581
$581$	−7.70215e17	−0.830744
$582$	3.33460e17	0.355668
$583$	4.94911e17	0.522014
$584$	−1.01606e18	−1.05983
$585$	2.53280e18	2.61269
$586$	−1.00760e18	−1.02790
$587$	1.31889e18	1.33064	0.665322	−	0.746556i	$-0.268294\pi$
$587$	1.31889e18	1.33064	0.665322	+	0.746556i	$0.268294\pi$
$588$	1.47374e17	0.147051
$589$	5.78084e17	0.570482
$590$	1.24028e18	1.21055
$591$	4.13699e17	0.399362
$592$	5.54967e17	0.529878
$593$	5.46702e17	0.516292	0.258146	−	0.966106i	$-0.416889\pi$
$593$	5.46702e17	0.516292	0.258146	+	0.966106i	$0.416889\pi$
$594$	1.47672e18	1.37939
$595$	1.69066e18	1.56206
$596$	3.73952e17	0.341755
$597$	3.10684e18	2.80858
$598$	−2.04777e17	−0.183115
$599$	1.29309e18	1.14381	0.571905	−	0.820320i	$-0.306204\pi$
$599$	1.29309e18	1.14381	0.571905	+	0.820320i	$0.306204\pi$
$600$	1.01024e18	0.883974
$601$	6.46414e17	0.559534	0.279767	−	0.960068i	$-0.409743\pi$
$601$	6.46414e17	0.559534	0.279767	+	0.960068i	$0.409743\pi$
$602$	6.57927e17	0.563379
$603$	−2.12186e18	−1.79744
$604$	3.31819e17	0.278075
$605$	4.28434e17	0.355201
$606$	−8.72584e17	−0.715707
$607$	−2.61804e17	−0.212446	−0.106223	−	0.994342i	$-0.533876\pi$
$607$	−2.61804e17	−0.212446	−0.106223	+	0.994342i	$0.533876\pi$
$608$	−4.97816e17	−0.399665
$609$	−4.94287e18	−3.92615
$610$	−4.98857e17	−0.392041
$611$	2.04729e18	1.59188
$612$	−8.45202e17	−0.650244
$613$	−2.11033e16	−0.0160641	−0.00803205	−	0.999968i	$-0.502557\pi$
$613$	−2.11033e16	−0.0160641	−0.00803205	+	0.999968i	$0.502557\pi$
$614$	2.11751e18	1.59489
$615$	4.36496e18	3.25306
$616$	−1.41306e18	−1.04204
$617$	−9.02060e17	−0.658236	−0.329118	−	0.944289i	$-0.606751\pi$
$617$	−9.02060e17	−0.658236	−0.329118	+	0.944289i	$0.606751\pi$
$618$	−3.02320e18	−2.18294
$619$	−1.48463e18	−1.06079	−0.530393	−	0.847752i	$-0.677956\pi$
$619$	−1.48463e18	−1.06079	−0.530393	+	0.847752i	$0.677956\pi$
$620$	−3.56327e17	−0.251943
$621$	−5.74231e17	−0.401783
$622$	−4.57480e17	−0.316763
$623$	2.61488e18	1.79176
$624$	−1.73924e18	−1.17940
$625$	−1.86059e18	−1.24862
$626$	1.30396e18	0.866028
$627$	−1.69083e18	−1.11137
$628$	1.43613e17	0.0934235
$629$	−1.43125e18	−0.921482
$630$	3.86907e18	2.46543
$631$	3.95787e17	0.249615	0.124808	−	0.992181i	$-0.460169\pi$
$631$	3.95787e17	0.249615	0.124808	+	0.992181i	$0.460169\pi$
$632$	2.49736e18	1.55891
$633$	−1.37336e18	−0.848515
$634$	4.20179e17	0.256953
$635$	4.58307e16	0.0277413
$636$	−5.00580e17	−0.299918
$637$	−5.29429e17	−0.313980
$638$	2.38263e18	1.39869
$639$	5.45084e17	0.316743
$640$	−8.57701e17	−0.493362
$641$	−1.08034e18	−0.615156	−0.307578	−	0.951523i	$-0.599518\pi$
$641$	−1.08034e18	−0.615156	−0.307578	+	0.951523i	$0.599518\pi$
$642$	−1.14864e18	−0.647449
$643$	−1.29773e18	−0.724125	−0.362063	−	0.932154i	$-0.617927\pi$
$643$	−1.29773e18	−0.724125	−0.362063	+	0.932154i	$0.617927\pi$
$644$	1.18331e17	0.0653641
$645$	−2.25333e18	−1.23221
$646$	−1.33729e18	−0.723957
$647$	−2.18430e18	−1.17067	−0.585335	−	0.810792i	$-0.699037\pi$
$647$	−2.18430e18	−1.17067	−0.585335	+	0.810792i	$0.699037\pi$
$648$	−2.64905e18	−1.40557
$649$	1.87994e18	0.987535
$650$	−7.81556e17	−0.406465
$651$	−2.96198e18	−1.52512
$652$	6.06714e17	0.309296
$653$	−7.50432e17	−0.378770	−0.189385	−	0.981903i	$-0.560649\pi$
$653$	−7.50432e17	−0.378770	−0.189385	+	0.981903i	$0.560649\pi$
$654$	1.20862e18	0.603999
$655$	−4.22906e18	−2.09255
$656$	−2.02898e18	−0.994040
$657$	4.21683e18	2.04555
$658$	3.12740e18	1.50216
$659$	−1.43200e18	−0.681064	−0.340532	−	0.940233i	$-0.610607\pi$
$659$	−1.43200e18	−0.681064	−0.340532	+	0.940233i	$0.610607\pi$
$660$	1.04221e18	0.490819
$661$	3.21075e18	1.49726	0.748629	−	0.662990i	$-0.230713\pi$
$661$	3.21075e18	1.49726	0.748629	+	0.662990i	$0.230713\pi$
$662$	−2.79960e17	−0.129276
$663$	4.48549e18	2.05103
$664$	−1.74376e18	−0.789578
$665$	−2.31569e18	−1.03834
$666$	−3.27541e18	−1.45440
$667$	−9.26498e17	−0.407405
$668$	9.05287e17	0.394221
$669$	−8.14289e17	−0.351163
$670$	2.06937e18	0.883796
$671$	−7.56133e17	−0.319817
$672$	2.55070e18	1.06846
$673$	8.87852e17	0.368335	0.184167	−	0.982895i	$-0.441041\pi$
$673$	8.87852e17	0.368335	0.184167	+	0.982895i	$0.441041\pi$
$674$	2.62183e17	0.107725
$675$	−2.19162e18	−0.891848
$676$	−4.28644e16	−0.0172760
$677$	1.39743e18	0.557831	0.278916	−	0.960316i	$-0.410025\pi$
$677$	1.39743e18	0.557831	0.278916	+	0.960316i	$0.410025\pi$
$678$	−7.13637e18	−2.82153
$679$	6.92227e17	0.271079
$680$	3.82766e18	1.48465
$681$	5.17715e18	1.98900
$682$	1.42778e18	0.543327
$683$	−3.95474e18	−1.49068	−0.745338	−	0.666686i	$-0.767712\pi$
$683$	−3.95474e18	−1.49068	−0.745338	+	0.666686i	$0.767712\pi$
$684$	1.15767e18	0.432235
$685$	1.91588e18	0.708566
$686$	1.84688e18	0.676600
$687$	−3.45651e18	−1.25435
$688$	1.04742e18	0.376529
$689$	1.79830e18	0.640379
$690$	1.07135e18	0.377932
$691$	6.80585e17	0.237834	0.118917	−	0.992904i	$-0.462058\pi$
$691$	6.80585e17	0.237834	0.118917	+	0.992904i	$0.462058\pi$
$692$	4.07618e17	0.141112
$693$	5.86447e18	2.01123
$694$	−1.04365e18	−0.354582
$695$	9.43797e17	0.317671
$696$	−1.11906e19	−3.73159
$697$	5.23272e18	1.72868
$698$	3.04823e17	0.0997671
$699$	6.31423e18	2.04747
$700$	4.51623e17	0.145091
$701$	−5.29067e18	−1.68401	−0.842003	−	0.539474i	$-0.818623\pi$
$701$	−5.29067e18	−1.68401	−0.842003	+	0.539474i	$0.818623\pi$
$702$	5.36579e18	1.69216
$703$	1.96038e18	0.612534
$704$	−2.99467e18	−0.927101
$705$	−1.07110e19	−3.28550
$706$	−2.37680e17	−0.0722375
$707$	−1.81139e18	−0.545488
$708$	−1.90147e18	−0.567379
$709$	3.80884e16	0.0112614	0.00563070	−	0.999984i	$-0.498208\pi$
$709$	3.80884e16	0.0112614	0.00563070	+	0.999984i	$0.498208\pi$
$710$	−5.31599e17	−0.155742
$711$	−1.03645e19	−3.00883
$712$	5.92008e18	1.70297
$713$	−5.55197e17	−0.158258
$714$	6.85196e18	1.93543
$715$	−3.74408e18	−1.04799
$716$	8.37707e17	0.232358
$717$	9.40488e18	2.58511
$718$	−5.36888e18	−1.46243
$719$	1.92850e18	0.520574	0.260287	−	0.965531i	$-0.416183\pi$
$719$	1.92850e18	0.520574	0.260287	+	0.965531i	$0.416183\pi$
$720$	6.15959e18	1.64775
$721$	−6.27584e18	−1.66377
$722$	−1.41041e18	−0.370555
$723$	−1.94661e18	−0.506852
$724$	8.83541e17	0.227995
$725$	−3.53609e18	−0.904329
$726$	1.73637e18	0.440102
$727$	2.92567e18	0.734938	0.367469	−	0.930036i	$-0.380224\pi$
$727$	2.92567e18	0.734938	0.367469	+	0.930036i	$0.380224\pi$
$728$	−5.13447e18	−1.27832
$729$	−2.74417e18	−0.677146
$730$	−4.11251e18	−1.00579
$731$	−2.70129e18	−0.654800
$732$	7.64794e17	0.183748
$733$	8.28489e18	1.97293	0.986463	−	0.163985i	$-0.0524349\pi$
$733$	8.28489e18	1.97293	0.986463	+	0.163985i	$0.0524349\pi$
$734$	−8.02122e17	−0.189329
$735$	2.76987e18	0.648025
$736$	4.78107e17	0.110871
$737$	3.13661e18	0.720978
$738$	1.19750e19	2.72842
$739$	−6.14772e18	−1.38843	−0.694217	−	0.719766i	$-0.744249\pi$
$739$	−6.14772e18	−1.38843	−0.694217	+	0.719766i	$0.744249\pi$
$740$	−1.20836e18	−0.270515
$741$	−6.14374e18	−1.36337
$742$	2.74705e18	0.604285
$743$	−1.78922e18	−0.390155	−0.195077	−	0.980788i	$-0.562496\pi$
$743$	−1.78922e18	−0.390155	−0.195077	+	0.980788i	$0.562496\pi$
$744$	−6.70590e18	−1.44955
$745$	7.02839e18	1.50605
$746$	5.71526e18	1.21404
$747$	7.23694e18	1.52395
$748$	1.24941e18	0.260822
$749$	−2.38445e18	−0.493465
$750$	−4.74543e18	−0.973592
$751$	3.11967e18	0.634525	0.317262	−	0.948338i	$-0.397236\pi$
$751$	3.11967e18	0.634525	0.317262	+	0.948338i	$0.397236\pi$
$752$	4.97885e18	1.00395
$753$	7.93874e18	1.58703
$754$	8.65748e18	1.71584
$755$	6.23651e18	1.22542
$756$	−3.10063e18	−0.604029
$757$	9.05493e18	1.74889	0.874444	−	0.485127i	$-0.161226\pi$
$757$	9.05493e18	1.74889	0.874444	+	0.485127i	$0.161226\pi$
$758$	−5.27545e18	−1.01021
$759$	1.62388e18	0.308307
$760$	−5.24272e18	−0.986889
$761$	1.13343e18	0.211540	0.105770	−	0.994391i	$-0.466269\pi$
$761$	1.13343e18	0.211540	0.105770	+	0.994391i	$0.466269\pi$
$762$	1.85744e17	0.0343721
$763$	2.50897e18	0.460348
$764$	−2.77005e17	−0.0503942
$765$	−1.58855e19	−2.86551
$766$	−3.83197e18	−0.685386
$767$	6.83089e18	1.21146
$768$	7.56014e18	1.32948
$769$	−8.22510e18	−1.43423	−0.717117	−	0.696953i	$-0.754539\pi$
$769$	−8.22510e18	−1.43423	−0.717117	+	0.696953i	$0.754539\pi$
$770$	−5.71939e18	−0.988918
$771$	4.13950e18	0.709733
$772$	−1.85789e18	−0.315869
$773$	−4.33818e18	−0.731376	−0.365688	−	0.930738i	$-0.619166\pi$
$773$	−4.33818e18	−0.731376	−0.365688	+	0.930738i	$0.619166\pi$
$774$	−6.18188e18	−1.03349
$775$	−2.11898e18	−0.351290
$776$	1.56720e18	0.257646
$777$	−1.00445e19	−1.63755
$778$	1.69434e18	0.273926
$779$	−7.16723e18	−1.14910
$780$	3.78696e18	0.602110
$781$	−8.05762e17	−0.127050
$782$	1.28434e18	0.200834
$783$	2.42771e19	3.76483
$784$	−1.28753e18	−0.198018
$785$	2.69919e18	0.411700
$786$	−1.71396e19	−2.59271
$787$	−1.32575e19	−1.98895	−0.994476	−	0.104960i	$-0.966529\pi$
$787$	−1.32575e19	−1.98895	−0.994476	+	0.104960i	$0.966529\pi$
$788$	4.18711e17	0.0623008
$789$	1.80904e19	2.66961
$790$	1.01081e19	1.47943
$791$	−1.48143e19	−2.15048
$792$	1.32771e19	1.91157
$793$	−2.74747e18	−0.392335
$794$	3.00750e18	0.425964
$795$	−9.40836e18	−1.32168
$796$	3.14448e18	0.438141
$797$	−1.59976e18	−0.221093	−0.110547	−	0.993871i	$-0.535260\pi$
$797$	−1.59976e18	−0.221093	−0.110547	+	0.993871i	$0.535260\pi$
$798$	−9.38509e18	−1.28653
$799$	−1.28404e19	−1.74592
$800$	1.82475e18	0.246104
$801$	−2.45695e19	−3.28688
$802$	−3.07331e18	−0.407824
$803$	−6.23346e18	−0.820500
$804$	−3.17254e18	−0.414231
$805$	2.22401e18	0.288048
$806$	5.18793e18	0.666525
$807$	−2.59154e19	−3.30278
$808$	−4.10098e18	−0.518458
$809$	−1.79527e18	−0.225146	−0.112573	−	0.993643i	$-0.535909\pi$
$809$	−1.79527e18	−0.225146	−0.112573	+	0.993643i	$0.535909\pi$
$810$	−1.07221e19	−1.33391
$811$	−1.43008e18	−0.176492	−0.0882461	−	0.996099i	$-0.528126\pi$
$811$	−1.43008e18	−0.176492	−0.0882461	+	0.996099i	$0.528126\pi$
$812$	−5.00274e18	−0.612483
$813$	1.67880e19	2.03897
$814$	4.84182e18	0.583378
$815$	1.14031e19	1.36301
$816$	1.09084e19	1.29352
$817$	3.69995e18	0.435263
$818$	2.02790e18	0.236673
$819$	2.13090e19	2.46728
$820$	4.41783e18	0.507480
$821$	−1.10267e19	−1.25665	−0.628324	−	0.777952i	$-0.716259\pi$
$821$	−1.10267e19	−1.25665	−0.628324	+	0.777952i	$0.716259\pi$
$822$	7.76473e18	0.877930
$823$	2.44365e18	0.274120	0.137060	−	0.990563i	$-0.456235\pi$
$823$	2.44365e18	0.274120	0.137060	+	0.990563i	$0.456235\pi$
$824$	−1.42085e19	−1.58132
$825$	6.19775e18	0.684358
$826$	1.04348e19	1.14317
$827$	−1.13040e19	−1.22870	−0.614351	−	0.789033i	$-0.710582\pi$
$827$	−1.13040e19	−1.22870	−0.614351	+	0.789033i	$0.710582\pi$
$828$	−1.11184e18	−0.119907
$829$	−1.91514e18	−0.204926	−0.102463	−	0.994737i	$-0.532672\pi$
$829$	−1.91514e18	−0.204926	−0.102463	+	0.994737i	$0.532672\pi$
$830$	−7.05792e18	−0.749323
$831$	−1.34681e19	−1.41873
$832$	−1.08814e19	−1.13732
$833$	3.32053e18	0.344362
$834$	3.82504e18	0.393601
$835$	1.70148e19	1.73726
$836$	−1.71131e18	−0.173375
$837$	1.45479e19	1.46246
$838$	1.03330e19	1.03072
$839$	9.40046e18	0.930458	0.465229	−	0.885190i	$-0.345972\pi$
$839$	9.40046e18	0.930458	0.465229	+	0.885190i	$0.345972\pi$
$840$	2.68625e19	2.63835
$841$	2.89095e19	2.81752
$842$	2.34344e18	0.226634
$843$	−9.33644e18	−0.895988
$844$	−1.38999e18	−0.132369
$845$	−8.05633e17	−0.0761322
$846$	−2.93851e19	−2.75562
$847$	3.60451e18	0.335432
$848$	4.37333e18	0.403868
$849$	−1.11046e19	−1.01766
$850$	4.90184e18	0.445796
$851$	−1.88277e18	−0.169924
$852$	8.14991e17	0.0729954
$853$	−9.20242e18	−0.817962	−0.408981	−	0.912543i	$-0.634116\pi$
$853$	−9.20242e18	−0.817962	−0.408981	+	0.912543i	$0.634116\pi$
$854$	−4.19699e18	−0.370221
$855$	2.17583e19	1.90478
$856$	−5.39838e18	−0.469012
$857$	−1.22311e19	−1.05461	−0.527304	−	0.849677i	$-0.676797\pi$
$857$	−1.22311e19	−1.05461	−0.527304	+	0.849677i	$0.676797\pi$
$858$	−1.51741e19	−1.29848
$859$	7.24076e18	0.614934	0.307467	−	0.951559i	$-0.400519\pi$
$859$	7.24076e18	0.614934	0.307467	+	0.951559i	$0.400519\pi$
$860$	−2.28062e18	−0.192227
$861$	3.67233e19	3.07200
$862$	4.13762e18	0.343521
$863$	1.56242e19	1.28744	0.643720	−	0.765261i	$-0.277390\pi$
$863$	1.56242e19	1.28744	0.643720	+	0.765261i	$0.277390\pi$
$864$	−1.25279e19	−1.02456
$865$	7.66114e18	0.621855
$866$	−1.47666e19	−1.18964
$867$	−6.13009e18	−0.490166
$868$	−2.99786e18	−0.237921
$869$	1.53212e19	1.20688
$870$	−4.52943e19	−3.54135
$871$	1.13971e19	0.884458
$872$	5.68030e18	0.437536
$873$	−6.50417e18	−0.497278
$874$	−1.75916e18	−0.133500
$875$	−9.85099e18	−0.742040
$876$	6.30486e18	0.471410
$877$	2.01707e19	1.49701	0.748503	−	0.663131i	$-0.230773\pi$
$877$	2.01707e19	1.49701	0.748503	+	0.663131i	$0.230773\pi$
$878$	1.15111e19	0.848013
$879$	2.90332e19	2.12309
$880$	−9.10532e18	−0.660934
$881$	−1.26100e19	−0.908598	−0.454299	−	0.890849i	$-0.650110\pi$
$881$	−1.26100e19	−0.908598	−0.454299	+	0.890849i	$0.650110\pi$
$882$	7.59900e18	0.543514
$883$	−2.47520e19	−1.75738	−0.878692	−	0.477390i	$-0.841583\pi$
$883$	−2.47520e19	−1.75738	−0.878692	+	0.477390i	$0.841583\pi$
$884$	4.53982e18	0.319962
$885$	−3.57379e19	−2.50033
$886$	6.28385e18	0.436422
$887$	2.36466e18	0.163029	0.0815147	−	0.996672i	$-0.474024\pi$
$887$	2.36466e18	0.163029	0.0815147	+	0.996672i	$0.474024\pi$
$888$	−2.27408e19	−1.55640
$889$	3.85583e17	0.0261973
$890$	2.39617e19	1.61615
$891$	−1.62518e19	−1.08817
$892$	−8.24153e17	−0.0547818
$893$	1.75874e19	1.16056
$894$	2.84848e19	1.86603
$895$	1.57446e19	1.02396
$896$	−7.21602e18	−0.465903
$897$	5.90051e18	0.378215
$898$	2.29355e19	1.45952
$899$	2.34724e19	1.48293
$900$	−4.24346e18	−0.266160
$901$	−1.12788e19	−0.702344
$902$	−1.77019e19	−1.09440
$903$	−1.89577e19	−1.16363
$904$	−3.35395e19	−2.04391
$905$	1.66061e19	1.00473
$906$	2.52754e19	1.51833
$907$	1.83193e19	1.09260	0.546301	−	0.837589i	$-0.316035\pi$
$907$	1.83193e19	1.09260	0.546301	+	0.837589i	$0.316035\pi$
$908$	5.23986e18	0.310286
$909$	1.70198e19	1.00067
$910$	−2.07819e19	−1.21315
$911$	1.36705e19	0.792346	0.396173	−	0.918176i	$-0.370338\pi$
$911$	1.36705e19	0.792346	0.396173	+	0.918176i	$0.370338\pi$
$912$	−1.49411e19	−0.859839
$913$	−1.06979e19	−0.611278
$914$	4.55069e18	0.258183
$915$	1.43742e19	0.809743
$916$	−3.49838e18	−0.195680
$917$	−3.55799e19	−1.97608
$918$	−3.36537e19	−1.85590
$919$	−5.74839e18	−0.314772	−0.157386	−	0.987537i	$-0.550307\pi$
$919$	−5.74839e18	−0.314772	−0.157386	+	0.987537i	$0.550307\pi$
$920$	5.03516e18	0.273774
$921$	−6.10148e19	−3.29418
$922$	−1.61770e19	−0.867254
$923$	−2.92780e18	−0.155858
$924$	8.76836e18	0.463501
$925$	−7.18580e18	−0.377185
$926$	2.31721e19	1.20780
$927$	5.89678e19	3.05209
$928$	−2.02132e19	−1.03890
$929$	2.38779e18	0.121869	0.0609347	−	0.998142i	$-0.480592\pi$
$929$	2.38779e18	0.121869	0.0609347	+	0.998142i	$0.480592\pi$
$930$	−2.71423e19	−1.37565
$931$	−4.54811e18	−0.228906
$932$	6.39071e18	0.319408
$933$	1.31820e19	0.654259
$934$	3.23792e18	0.159592
$935$	2.34825e19	1.14939
$936$	4.82435e19	2.34501
$937$	−3.72084e19	−1.79611	−0.898057	−	0.439879i	$-0.855021\pi$
$937$	−3.72084e19	−1.79611	−0.898057	+	0.439879i	$0.855021\pi$
$938$	1.74101e19	0.834607
$939$	−3.75728e19	−1.78874
$940$	−1.08408e19	−0.512541
$941$	−3.04184e19	−1.42825	−0.714124	−	0.700019i	$-0.753175\pi$
$941$	−3.04184e19	−1.42825	−0.714124	+	0.700019i	$0.753175\pi$
$942$	1.09394e19	0.510106
$943$	6.88348e18	0.318773
$944$	1.66122e19	0.764029
$945$	−5.82760e19	−2.66185
$946$	9.13828e18	0.414545
$947$	3.34337e19	1.50629	0.753147	−	0.657853i	$-0.228535\pi$
$947$	3.34337e19	1.50629	0.753147	+	0.657853i	$0.228535\pi$
$948$	−1.54967e19	−0.693402
$949$	−2.26498e19	−1.00655
$950$	−6.71403e18	−0.296333
$951$	−1.21072e19	−0.530725
$952$	3.22029e19	1.40202
$953$	−1.80874e19	−0.782120	−0.391060	−	0.920365i	$-0.627891\pi$
$953$	−1.80874e19	−0.782120	−0.391060	+	0.920365i	$0.627891\pi$
$954$	−2.58113e19	−1.10853
$955$	−5.20628e18	−0.222078
$956$	9.51880e18	0.403279
$957$	−6.86540e19	−2.88894
$958$	−2.91166e19	−1.21693
$959$	1.61187e19	0.669129
$960$	5.69293e19	2.34732
$961$	−1.03519e19	−0.423952
$962$	1.75931e19	0.715657
$963$	2.24043e19	0.905233
$964$	−1.97019e18	−0.0790694
$965$	−3.49188e19	−1.39198
$966$	9.01353e18	0.356897
$967$	1.42612e19	0.560897	0.280448	−	0.959869i	$-0.409517\pi$
$967$	1.42612e19	0.560897	0.280448	+	0.959869i	$0.409517\pi$
$968$	8.16059e18	0.318810
$969$	3.85330e19	1.49530
$970$	6.34327e18	0.244510
$971$	−1.50749e19	−0.577203	−0.288602	−	0.957449i	$-0.593190\pi$
$971$	−1.50749e19	−0.577203	−0.288602	+	0.957449i	$0.593190\pi$
$972$	2.53332e18	0.0963516
$973$	7.94036e18	0.299990
$974$	−1.71766e19	−0.644618
$975$	2.25200e19	0.839534
$976$	−6.68164e18	−0.247434
$977$	−3.05018e18	−0.112205	−0.0561024	−	0.998425i	$-0.517867\pi$
$977$	−3.05018e18	−0.112205	−0.0561024	+	0.998425i	$0.517867\pi$
$978$	4.62148e19	1.68880
$979$	3.63194e19	1.31841
$980$	2.80342e18	0.101093
$981$	−2.35743e19	−0.844482
$982$	−1.31169e19	−0.466775
$983$	3.97735e18	0.140603	0.0703016	−	0.997526i	$-0.477604\pi$
$983$	3.97735e18	0.140603	0.0703016	+	0.997526i	$0.477604\pi$
$984$	8.31415e19	2.91978
$985$	7.86963e18	0.274548
$986$	−5.42989e19	−1.88188
$987$	−9.01141e19	−3.10264
$988$	−6.21816e18	−0.212688
$989$	−3.55346e18	−0.120747
$990$	5.37395e19	1.81411
$991$	1.22079e19	0.409415	0.204707	−	0.978823i	$-0.434376\pi$
$991$	1.22079e19	0.409415	0.204707	+	0.978823i	$0.434376\pi$
$992$	−1.21126e19	−0.403565
$993$	8.06686e18	0.267014
$994$	−4.47246e18	−0.147074
$995$	5.91001e19	1.93081
$996$	1.08204e19	0.351204
$997$	−2.29170e19	−0.738992	−0.369496	−	0.929232i	$-0.620470\pi$
$997$	−2.29170e19	−0.738992	−0.369496	+	0.929232i	$0.620470\pi$
$998$	−1.29474e19	−0.414796
$999$	4.93343e19	1.57026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.a.b.1.10	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.a.b.1.10	✓	14	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q+77.0951 q^{2} -2221.44 q^{3} -2248.35 q^{4} -42257.5 q^{5} -171262. q^{6} -355522. q^{7} -804900. q^{8} +3.34048e6 q^{9} +O(q^{10})\)	\(q+77.0951 q^{2} -2221.44 q^{3} -2248.35 q^{4} -42257.5 q^{5} -171262. q^{6} -355522. q^{7} -804900. q^{8} +3.34048e6 q^{9} -3.25785e6 q^{10} -4.93802e6 q^{11} +4.99458e6 q^{12} -1.79427e7 q^{13} -2.74090e7 q^{14} +9.38727e7 q^{15} -4.36353e7 q^{16} +1.12535e8 q^{17} +2.57535e8 q^{18} -1.54138e8 q^{19} +9.50098e7 q^{20} +7.89771e8 q^{21} -3.80697e8 q^{22} +1.48036e8 q^{23} +1.78804e9 q^{24} +5.64997e8 q^{25} -1.38329e9 q^{26} -3.87900e9 q^{27} +7.99338e8 q^{28} -6.25861e9 q^{29} +7.23712e9 q^{30} -3.75042e9 q^{31} +3.22967e9 q^{32} +1.09695e10 q^{33} +8.67588e9 q^{34} +1.50235e10 q^{35} -7.51058e9 q^{36} -1.27183e10 q^{37} -1.18833e10 q^{38} +3.98586e10 q^{39} +3.40131e10 q^{40} +4.64987e10 q^{41} +6.08875e10 q^{42} -2.40041e10 q^{43} +1.11024e10 q^{44} -1.41161e11 q^{45} +1.14128e10 q^{46} -1.14101e11 q^{47} +9.69333e10 q^{48} +2.95067e10 q^{49} +4.35585e10 q^{50} -2.49990e11 q^{51} +4.03415e10 q^{52} -1.00225e11 q^{53} -2.99052e11 q^{54} +2.08669e11 q^{55} +2.86159e11 q^{56} +3.42409e11 q^{57} -4.82508e11 q^{58} -3.80706e11 q^{59} -2.11059e11 q^{60} +1.53125e11 q^{61} -2.89139e11 q^{62} -1.18761e12 q^{63} +6.06452e11 q^{64} +7.58214e11 q^{65} +8.45697e11 q^{66} -6.35196e11 q^{67} -2.53018e11 q^{68} -3.28853e11 q^{69} +1.15824e12 q^{70} +1.63175e11 q^{71} -2.68875e12 q^{72} +1.26234e12 q^{73} -9.80518e11 q^{74} -1.25511e12 q^{75} +3.46557e11 q^{76} +1.75557e12 q^{77} +3.07290e12 q^{78} -3.10270e12 q^{79} +1.84392e12 q^{80} +3.29116e12 q^{81} +3.58482e12 q^{82} +2.16644e12 q^{83} -1.77568e12 q^{84} -4.75545e12 q^{85} -1.85060e12 q^{86} +1.39031e13 q^{87} +3.97461e12 q^{88} -7.35506e12 q^{89} -1.08828e13 q^{90} +6.37901e12 q^{91} -3.32837e11 q^{92} +8.33135e12 q^{93} -8.79666e12 q^{94} +6.51351e12 q^{95} -7.17453e12 q^{96} -1.94707e12 q^{97} +2.27482e12 q^{98} -1.64954e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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