LMFDB - Embedded newform 23.14.a.b.1.13

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			1.13
Root			$-154.604$ 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)

$f(q)$	$=$	$q+159.604 q^{2} -1789.05 q^{3} +17281.5 q^{4} +24592.6 q^{5} -285540. q^{6} -77186.8 q^{7} +1.45072e6 q^{8} +1.60638e6 q^{9} +O(q^{10})$	\(q+159.604 q^{2} -1789.05 q^{3} +17281.5 q^{4} +24592.6 q^{5} -285540. q^{6} -77186.8 q^{7} +1.45072e6 q^{8} +1.60638e6 q^{9} +3.92509e6 q^{10} +5.97442e6 q^{11} -3.09175e7 q^{12} +4.52310e6 q^{13} -1.23193e7 q^{14} -4.39974e7 q^{15} +8.99715e7 q^{16} +1.13802e8 q^{17} +2.56385e8 q^{18} +3.74050e8 q^{19} +4.24998e8 q^{20} +1.38091e8 q^{21} +9.53543e8 q^{22} +1.48036e8 q^{23} -2.59542e9 q^{24} -6.15906e8 q^{25} +7.21905e8 q^{26} -2.15667e7 q^{27} -1.33390e9 q^{28} +4.46863e9 q^{29} -7.02218e9 q^{30} -4.02926e9 q^{31} +2.47551e9 q^{32} -1.06885e10 q^{33} +1.81633e10 q^{34} -1.89823e9 q^{35} +2.77606e10 q^{36} +1.36275e9 q^{37} +5.96999e10 q^{38} -8.09205e9 q^{39} +3.56771e10 q^{40} -2.90819e10 q^{41} +2.20399e10 q^{42} -5.83765e10 q^{43} +1.03247e11 q^{44} +3.95050e10 q^{45} +2.36272e10 q^{46} -3.78464e10 q^{47} -1.60964e11 q^{48} -9.09312e10 q^{49} -9.83012e10 q^{50} -2.03598e11 q^{51} +7.81659e10 q^{52} +2.57775e11 q^{53} -3.44213e9 q^{54} +1.46927e11 q^{55} -1.11977e11 q^{56} -6.69193e11 q^{57} +7.13212e11 q^{58} +5.98301e10 q^{59} -7.60342e11 q^{60} -5.45363e10 q^{61} -6.43087e11 q^{62} -1.23991e11 q^{63} -3.41945e11 q^{64} +1.11235e11 q^{65} -1.70594e12 q^{66} +5.79636e11 q^{67} +1.96667e12 q^{68} -2.64844e11 q^{69} -3.02965e11 q^{70} -1.99260e12 q^{71} +2.33041e12 q^{72} +1.98891e12 q^{73} +2.17501e11 q^{74} +1.10189e12 q^{75} +6.46414e12 q^{76} -4.61146e11 q^{77} -1.29152e12 q^{78} -1.73332e12 q^{79} +2.21264e12 q^{80} -2.52250e12 q^{81} -4.64159e12 q^{82} -2.01188e12 q^{83} +2.38642e12 q^{84} +2.79869e12 q^{85} -9.31713e12 q^{86} -7.99460e12 q^{87} +8.66723e12 q^{88} +5.86100e12 q^{89} +6.30517e12 q^{90} -3.49123e11 q^{91} +2.55828e12 q^{92} +7.20856e12 q^{93} -6.04045e12 q^{94} +9.19886e12 q^{95} -4.42881e12 q^{96} -5.72699e12 q^{97} -1.45130e13 q^{98} +9.59718e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	159.604	1.76339	0.881697	−	0.471816i	$-0.156401\pi$
$2$	159.604	1.76339	0.881697	+	0.471816i	$0.156401\pi$
$3$	−1789.05	−1.41688	−0.708442	−	0.705769i	$-0.750602\pi$
$3$	−1789.05	−1.41688	−0.708442	+	0.705769i	$0.750602\pi$
$4$	17281.5	2.10956
$5$	24592.6	0.703882	0.351941	−	0.936022i	$-0.385522\pi$
$5$	24592.6	0.703882	0.351941	+	0.936022i	$0.385522\pi$
$6$	−285540.	−2.49853
$7$	−77186.8	−0.247974	−0.123987	−	0.992284i	$-0.539568\pi$
$7$	−77186.8	−0.247974	−0.123987	+	0.992284i	$0.539568\pi$
$8$	1.45072e6	1.95659
$9$	1.60638e6	1.00756
$10$	3.92509e6	1.24122
$11$	5.97442e6	1.01682	0.508409	−	0.861116i	$-0.330234\pi$
$11$	5.97442e6	1.01682	0.508409	+	0.861116i	$0.330234\pi$
$12$	−3.09175e7	−2.98900
$13$	4.52310e6	0.259899	0.129949	−	0.991521i	$-0.458519\pi$
$13$	4.52310e6	0.259899	0.129949	+	0.991521i	$0.458519\pi$
$14$	−1.23193e7	−0.437276
$15$	−4.39974e7	−0.997319
$16$	8.99715e7	1.34068
$17$	1.13802e8	1.14349	0.571745	−	0.820432i	$-0.306267\pi$
$17$	1.13802e8	1.14349	0.571745	+	0.820432i	$0.306267\pi$
$18$	2.56385e8	1.77673
$19$	3.74050e8	1.82402	0.912012	−	0.410163i	$-0.134528\pi$
$19$	3.74050e8	1.82402	0.912012	+	0.410163i	$0.134528\pi$
$20$	4.24998e8	1.48488
$21$	1.38091e8	0.351350
$22$	9.53543e8	1.79305
$23$	1.48036e8	0.208514
$23$	1.48036e8	0.208514
$24$	−2.59542e9	−2.77226
$25$	−6.15906e8	−0.504550
$26$	7.21905e8	0.458304
$27$	−2.15667e7	−0.0107132
$28$	−1.33390e9	−0.523115
$29$	4.46863e9	1.39504	0.697521	−	0.716564i	$-0.254286\pi$
$29$	4.46863e9	1.39504	0.697521	+	0.716564i	$0.254286\pi$
$30$	−7.02218e9	−1.75867
$31$	−4.02926e9	−0.815407	−0.407704	−	0.913114i	$-0.633670\pi$
$31$	−4.02926e9	−0.815407	−0.407704	+	0.913114i	$0.633670\pi$
$32$	2.47551e9	0.407558
$33$	−1.06885e10	−1.44071
$34$	1.81633e10	2.01642
$35$	−1.89823e9	−0.174544
$36$	2.77606e10	2.12551
$37$	1.36275e9	0.0873185	0.0436593	−	0.999046i	$-0.486098\pi$
$37$	1.36275e9	0.0873185	0.0436593	+	0.999046i	$0.486098\pi$
$38$	5.96999e10	3.21647
$39$	−8.09205e9	−0.368246
$40$	3.56771e10	1.37721
$41$	−2.90819e10	−0.956154	−0.478077	−	0.878318i	$-0.658666\pi$
$41$	−2.90819e10	−0.956154	−0.478077	+	0.878318i	$0.658666\pi$
$42$	2.20399e10	0.619569
$43$	−5.83765e10	−1.40829	−0.704146	−	0.710055i	$-0.748670\pi$
$43$	−5.83765e10	−1.40829	−0.704146	+	0.710055i	$0.748670\pi$
$44$	1.03247e11	2.14504
$45$	3.95050e10	0.709204
$46$	2.36272e10	0.367693
$47$	−3.78464e10	−0.512140	−0.256070	−	0.966658i	$-0.582428\pi$
$47$	−3.78464e10	−0.512140	−0.256070	+	0.966658i	$0.582428\pi$
$48$	−1.60964e11	−1.89959
$49$	−9.09312e10	−0.938509
$50$	−9.83012e10	−0.889721
$51$	−2.03598e11	−1.62019
$52$	7.81659e10	0.548271
$53$	2.57775e11	1.59753	0.798763	−	0.601646i	$-0.205488\pi$
$53$	2.57775e11	1.59753	0.798763	+	0.601646i	$0.205488\pi$
$54$	−3.44213e9	−0.0188916
$55$	1.46927e11	0.715720
$56$	−1.11977e11	−0.485183
$57$	−6.69193e11	−2.58443
$58$	7.13212e11	2.46001
$59$	5.98301e10	0.184664	0.0923318	−	0.995728i	$-0.470568\pi$
$59$	5.98301e10	0.184664	0.0923318	+	0.995728i	$0.470568\pi$
$60$	−7.60342e11	−2.10390
$61$	−5.45363e10	−0.135532	−0.0677660	−	0.997701i	$-0.521587\pi$
$61$	−5.45363e10	−0.135532	−0.0677660	+	0.997701i	$0.521587\pi$
$62$	−6.43087e11	−1.43788
$63$	−1.23991e11	−0.249849
$64$	−3.41945e11	−0.621995
$65$	1.11235e11	0.182938
$66$	−1.70594e12	−2.54055
$67$	5.79636e11	0.782832	0.391416	−	0.920214i	$-0.371985\pi$
$67$	5.79636e11	0.782832	0.391416	+	0.920214i	$0.371985\pi$
$68$	1.96667e12	2.41226
$69$	−2.64844e11	−0.295441
$70$	−3.02965e11	−0.307790
$71$	−1.99260e12	−1.84604	−0.923019	−	0.384754i	$-0.874286\pi$
$71$	−1.99260e12	−1.84604	−0.923019	+	0.384754i	$0.874286\pi$
$72$	2.33041e12	1.97138
$73$	1.98891e12	1.53822	0.769108	−	0.639118i	$-0.220701\pi$
$73$	1.98891e12	1.53822	0.769108	+	0.639118i	$0.220701\pi$
$74$	2.17501e11	0.153977
$75$	1.10189e12	0.714889
$76$	6.46414e12	3.84789
$77$	−4.61146e11	−0.252144
$78$	−1.29152e12	−0.649363
$79$	−1.73332e12	−0.802237	−0.401118	−	0.916026i	$-0.631378\pi$
$79$	−1.73332e12	−0.802237	−0.401118	+	0.916026i	$0.631378\pi$
$80$	2.21264e12	0.943681
$81$	−2.52250e12	−0.992382
$82$	−4.64159e12	−1.68608
$83$	−2.01188e12	−0.675452	−0.337726	−	0.941244i	$-0.609658\pi$
$83$	−2.01188e12	−0.675452	−0.337726	+	0.941244i	$0.609658\pi$
$84$	2.38642e12	0.741194
$85$	2.79869e12	0.804881
$86$	−9.31713e12	−2.48337
$87$	−7.99460e12	−1.97661
$88$	8.66723e12	1.98950
$89$	5.86100e12	1.25008	0.625038	−	0.780594i	$-0.285083\pi$
$89$	5.86100e12	1.25008	0.625038	+	0.780594i	$0.285083\pi$
$90$	6.30517e12	1.25061
$91$	−3.49123e11	−0.0644481
$92$	2.55828e12	0.439873
$93$	7.20856e12	1.15534
$94$	−6.04045e12	−0.903105
$95$	9.19886e12	1.28390
$96$	−4.42881e12	−0.577462
$97$	−5.72699e12	−0.698088	−0.349044	−	0.937106i	$-0.613494\pi$
$97$	−5.72699e12	−0.698088	−0.349044	+	0.937106i	$0.613494\pi$
$98$	−1.45130e13	−1.65496
$99$	9.59718e12	1.02451
$100$	−1.06438e13	−1.06438
$101$	1.40164e13	1.31386	0.656928	−	0.753953i	$-0.271855\pi$
$101$	1.40164e13	1.31386	0.656928	+	0.753953i	$0.271855\pi$
$102$	−3.24950e13	−2.85704
$103$	−1.68607e12	−0.139134	−0.0695669	−	0.997577i	$-0.522162\pi$
$103$	−1.68607e12	−0.139134	−0.0695669	+	0.997577i	$0.522162\pi$
$104$	6.56176e12	0.508515
$105$	3.39602e12	0.247309
$106$	4.11420e13	2.81707
$107$	−5.91542e11	−0.0381058	−0.0190529	−	0.999818i	$-0.506065\pi$
$107$	−5.91542e11	−0.0381058	−0.0190529	+	0.999818i	$0.506065\pi$
$108$	−3.72705e11	−0.0226001
$109$	−1.71391e13	−0.978851	−0.489425	−	0.872045i	$-0.662793\pi$
$109$	−1.71391e13	−0.978851	−0.489425	+	0.872045i	$0.662793\pi$
$110$	2.34501e13	1.26210
$111$	−2.43804e12	−0.123720
$112$	−6.94462e12	−0.332454
$113$	1.97993e13	0.894624	0.447312	−	0.894378i	$-0.352381\pi$
$113$	1.97993e13	0.894624	0.447312	+	0.894378i	$0.352381\pi$
$114$	−1.06806e14	−4.55737
$115$	3.64059e12	0.146770
$116$	7.72247e13	2.94292
$117$	7.26580e12	0.261864
$118$	9.54913e12	0.325635
$119$	−8.78402e12	−0.283555
$120$	−6.38281e13	−1.95134
$121$	1.17098e12	0.0339192
$122$	−8.70422e12	−0.238996
$123$	5.20290e13	1.35476
$124$	−6.96318e13	−1.72015
$125$	−4.51670e13	−1.05903
$126$	−1.97895e13	−0.440582
$127$	−4.39208e13	−0.928851	−0.464426	−	0.885612i	$-0.653739\pi$
$127$	−4.39208e13	−0.928851	−0.464426	+	0.885612i	$0.653739\pi$
$128$	−7.48553e13	−1.50438
$129$	1.04438e14	1.99539
$130$	1.77535e13	0.322592
$131$	6.20408e13	1.07254	0.536270	−	0.844046i	$-0.319833\pi$
$131$	6.20408e13	1.07254	0.536270	+	0.844046i	$0.319833\pi$
$132$	−1.84714e14	−3.03927
$133$	−2.88717e13	−0.452310
$134$	9.25123e13	1.38044
$135$	−5.30381e11	−0.00754082
$136$	1.65095e14	2.23734
$137$	8.34719e13	1.07859	0.539296	−	0.842117i	$-0.318691\pi$
$137$	8.34719e13	1.07859	0.539296	+	0.842117i	$0.318691\pi$
$138$	−4.22702e13	−0.520979
$139$	−7.36446e12	−0.0866053	−0.0433026	−	0.999062i	$-0.513788\pi$
$139$	−7.36446e12	−0.0866053	−0.0433026	+	0.999062i	$0.513788\pi$
$140$	−3.28042e13	−0.368211
$141$	6.77091e13	0.725643
$142$	−3.18027e14	−3.25529
$143$	2.70229e13	0.264270
$144$	1.44528e14	1.35082
$145$	1.09895e14	0.981945
$146$	3.17439e14	2.71248
$147$	1.62680e14	1.32976
$148$	2.35505e13	0.184204
$149$	1.63879e14	1.22691	0.613456	−	0.789729i	$-0.289779\pi$
$149$	1.63879e14	1.22691	0.613456	+	0.789729i	$0.289779\pi$
$150$	1.75866e14	1.26063
$151$	−2.20115e14	−1.51112	−0.755561	−	0.655078i	$-0.772636\pi$
$151$	−2.20115e14	−1.51112	−0.755561	+	0.655078i	$0.772636\pi$
$152$	5.42643e14	3.56887
$153$	1.82809e14	1.15214
$154$	−7.36009e13	−0.444630
$155$	−9.90901e13	−0.573951
$156$	−1.39843e14	−0.776837
$157$	1.53865e14	0.819957	0.409978	−	0.912095i	$-0.365536\pi$
$157$	1.53865e14	0.819957	0.409978	+	0.912095i	$0.365536\pi$
$158$	−2.76645e14	−1.41466
$159$	−4.61173e14	−2.26351
$160$	6.08792e13	0.286873
$161$	−1.14264e13	−0.0517061
$162$	−4.02602e14	−1.74996
$163$	−4.26584e14	−1.78150	−0.890748	−	0.454498i	$-0.849819\pi$
$163$	−4.26584e14	−1.78150	−0.890748	+	0.454498i	$0.849819\pi$
$164$	−5.02579e14	−2.01706
$165$	−2.62859e14	−1.01409
$166$	−3.21105e14	−1.19109
$167$	1.27574e14	0.455099	0.227549	−	0.973767i	$-0.426929\pi$
$167$	1.27574e14	0.455099	0.227549	+	0.973767i	$0.426929\pi$
$168$	2.00332e14	0.687448
$169$	−2.82417e14	−0.932453
$170$	4.46683e14	1.41932
$171$	6.00865e14	1.83782
$172$	−1.00883e15	−2.97088
$173$	4.52009e14	1.28188	0.640940	−	0.767591i	$-0.278545\pi$
$173$	4.52009e14	1.28188	0.640940	+	0.767591i	$0.278545\pi$
$174$	−1.27597e15	−3.48555
$175$	4.75398e13	0.125115
$176$	5.37528e14	1.36323
$177$	−1.07039e14	−0.261647
$178$	9.35440e14	2.20438
$179$	−6.82855e14	−1.55161	−0.775807	−	0.630971i	$-0.782657\pi$
$179$	−6.82855e14	−1.55161	−0.775807	+	0.630971i	$0.782657\pi$
$180$	6.82707e14	1.49611
$181$	−1.37422e14	−0.290500	−0.145250	−	0.989395i	$-0.546399\pi$
$181$	−1.37422e14	−0.290500	−0.145250	+	0.989395i	$0.546399\pi$
$182$	−5.57216e13	−0.113647
$183$	9.75681e13	0.192033
$184$	2.14759e14	0.407977
$185$	3.35137e13	0.0614619
$186$	1.15052e15	2.03732
$187$	6.79901e14	1.16272
$188$	−6.54043e14	−1.08039
$189$	1.66466e12	0.00265659
$190$	1.46818e15	2.26402
$191$	−9.35926e14	−1.39484	−0.697420	−	0.716662i	$-0.745669\pi$
$191$	−9.35926e14	−1.39484	−0.697420	+	0.716662i	$0.745669\pi$
$192$	6.11758e14	0.881295
$193$	3.65669e14	0.509291	0.254646	−	0.967034i	$-0.418041\pi$
$193$	3.65669e14	0.509291	0.254646	+	0.967034i	$0.418041\pi$
$194$	−9.14051e14	−1.23100
$195$	−1.99005e14	−0.259202
$196$	−1.57143e15	−1.97984
$197$	−1.07626e15	−1.31186	−0.655929	−	0.754823i	$-0.727723\pi$
$197$	−1.07626e15	−1.31186	−0.655929	+	0.754823i	$0.727723\pi$
$198$	1.53175e15	1.80661
$199$	3.37635e14	0.385392	0.192696	−	0.981259i	$-0.438277\pi$
$199$	3.37635e14	0.385392	0.192696	+	0.981259i	$0.438277\pi$
$200$	−8.93510e14	−0.987198
$201$	−1.03700e15	−1.10918
$202$	2.23708e15	2.31685
$203$	−3.44919e14	−0.345934
$204$	−3.51847e15	−3.41789
$205$	−7.15200e14	−0.673019
$206$	−2.69103e14	−0.245348
$207$	2.37802e14	0.210091
$208$	4.06950e14	0.348441
$209$	2.23473e15	1.85470
$210$	5.42019e14	0.436103
$211$	1.04209e15	0.812961	0.406480	−	0.913660i	$-0.366756\pi$
$211$	1.04209e15	0.812961	0.406480	+	0.913660i	$0.366756\pi$
$212$	4.45474e15	3.37007
$213$	3.56486e15	2.61562
$214$	−9.44125e13	−0.0671955
$215$	−1.43563e15	−0.991272
$216$	−3.12873e13	−0.0209613
$217$	3.11006e14	0.202200
$218$	−2.73548e15	−1.72610
$219$	−3.55827e15	−2.17948
$220$	2.53911e15	1.50985
$221$	5.14738e14	0.297191
$222$	−3.89121e14	−0.218168
$223$	3.85434e14	0.209879	0.104939	−	0.994479i	$-0.466535\pi$
$223$	3.85434e14	0.209879	0.104939	+	0.994479i	$0.466535\pi$
$224$	−1.91077e14	−0.101064
$225$	−9.89378e14	−0.508365
$226$	3.16005e15	1.57757
$227$	1.43175e14	0.0694541	0.0347271	−	0.999397i	$-0.488944\pi$
$227$	1.43175e14	0.0694541	0.0347271	+	0.999397i	$0.488944\pi$
$228$	−1.15647e16	−5.45201
$229$	−3.99114e15	−1.82880	−0.914400	−	0.404811i	$-0.867337\pi$
$229$	−3.99114e15	−1.82880	−0.914400	+	0.404811i	$0.867337\pi$
$230$	5.81054e14	0.258813
$231$	8.25014e14	0.357259
$232$	6.48275e15	2.72953
$233$	2.39447e15	0.980385	0.490192	−	0.871614i	$-0.336927\pi$
$233$	2.39447e15	0.980385	0.490192	+	0.871614i	$0.336927\pi$
$234$	1.15965e15	0.461769
$235$	−9.30742e14	−0.360486
$236$	1.03395e15	0.389559
$237$	3.10100e15	1.13668
$238$	−1.40197e15	−0.500020
$239$	2.80271e15	0.972730	0.486365	−	0.873756i	$-0.338323\pi$
$239$	2.80271e15	0.972730	0.486365	+	0.873756i	$0.338323\pi$
$240$	−3.95852e15	−1.33709
$241$	−4.20395e15	−1.38212	−0.691062	−	0.722796i	$-0.742857\pi$
$241$	−4.20395e15	−1.38212	−0.691062	+	0.722796i	$0.742857\pi$
$242$	1.86894e14	0.0598129
$243$	4.54727e15	1.41680
$244$	−9.42469e14	−0.285913
$245$	−2.23624e15	−0.660599
$246$	8.30404e15	2.38897
$247$	1.69186e15	0.474062
$248$	−5.84535e15	−1.59542
$249$	3.59936e15	0.957037
$250$	−7.20885e15	−1.86748
$251$	−1.08711e14	−0.0274407	−0.0137204	−	0.999906i	$-0.504367\pi$
$251$	−1.08711e14	−0.0274407	−0.0137204	+	0.999906i	$0.504367\pi$
$252$	−2.14275e15	−0.527071
$253$	8.84429e14	0.212021
$254$	−7.00995e15	−1.63793
$255$	−5.00700e15	−1.14042
$256$	−9.14600e15	−2.03082
$257$	−1.43670e14	−0.0311030	−0.0155515	−	0.999879i	$-0.504950\pi$
$257$	−1.43670e14	−0.0311030	−0.0155515	+	0.999879i	$0.504950\pi$
$258$	1.66688e16	3.51865
$259$	−1.05187e14	−0.0216527
$260$	1.92230e15	0.385918
$261$	7.17831e15	1.40559
$262$	9.90197e15	1.89131
$263$	−7.22757e15	−1.34673	−0.673364	−	0.739311i	$-0.735151\pi$
$263$	−7.22757e15	−1.34673	−0.673364	+	0.739311i	$0.735151\pi$
$264$	−1.55061e16	−2.81889
$265$	6.33936e15	1.12447
$266$	−4.60804e15	−0.797602
$267$	−1.04856e16	−1.77121
$268$	1.00170e16	1.65143
$269$	−5.12612e14	−0.0824895	−0.0412447	−	0.999149i	$-0.513132\pi$
$269$	−5.12612e14	−0.0824895	−0.0412447	+	0.999149i	$0.513132\pi$
$270$	−8.46511e13	−0.0132974
$271$	−1.50444e15	−0.230714	−0.115357	−	0.993324i	$-0.536801\pi$
$271$	−1.50444e15	−0.230714	−0.115357	+	0.993324i	$0.536801\pi$
$272$	1.02389e16	1.53305
$273$	6.24599e14	0.0913154
$274$	1.33225e16	1.90198
$275$	−3.67968e15	−0.513036
$276$	−4.57690e15	−0.623250
$277$	−1.32858e16	−1.76714	−0.883568	−	0.468303i	$-0.844865\pi$
$277$	−1.32858e16	−1.76714	−0.883568	+	0.468303i	$0.844865\pi$
$278$	−1.17540e15	−0.152719
$279$	−6.47252e15	−0.821573
$280$	−2.75380e15	−0.341512
$281$	−1.09358e16	−1.32513	−0.662565	−	0.749004i	$-0.730532\pi$
$281$	−1.09358e16	−1.32513	−0.662565	+	0.749004i	$0.730532\pi$
$282$	1.08067e16	1.27959
$283$	2.62759e15	0.304051	0.152025	−	0.988377i	$-0.451420\pi$
$283$	2.62759e15	0.304051	0.152025	+	0.988377i	$0.451420\pi$
$284$	−3.44351e16	−3.89433
$285$	−1.64572e16	−1.81913
$286$	4.31296e15	0.466012
$287$	2.24474e15	0.237101
$288$	3.97660e15	0.410639
$289$	3.04633e15	0.307568
$290$	1.75398e16	1.73156
$291$	1.02459e16	0.989109
$292$	3.43714e16	3.24496
$293$	−5.35427e15	−0.494380	−0.247190	−	0.968967i	$-0.579507\pi$
$293$	−5.35427e15	−0.494380	−0.247190	+	0.968967i	$0.579507\pi$
$294$	2.59645e16	2.34489
$295$	1.47138e15	0.129981
$296$	1.97698e15	0.170847
$297$	−1.28848e14	−0.0108934
$298$	2.61559e16	2.16353
$299$	6.69580e14	0.0541926
$300$	1.90423e16	1.50810
$301$	4.50589e15	0.349220
$302$	−3.51313e16	−2.66470
$303$	−2.50761e16	−1.86158
$304$	3.36538e16	2.44543
$305$	−1.34119e15	−0.0953985
$306$	2.91771e16	2.03167
$307$	8.36816e15	0.570467	0.285234	−	0.958458i	$-0.407929\pi$
$307$	8.36816e15	0.570467	0.285234	+	0.958458i	$0.407929\pi$
$308$	−7.96931e15	−0.531913
$309$	3.01646e15	0.197137
$310$	−1.58152e16	−1.01210
$311$	2.00432e16	1.25610	0.628052	−	0.778172i	$-0.283853\pi$
$311$	2.00432e16	1.25610	0.628052	+	0.778172i	$0.283853\pi$
$312$	−1.17393e16	−0.720507
$313$	−1.45668e16	−0.875639	−0.437819	−	0.899063i	$-0.644249\pi$
$313$	−1.45668e16	−0.875639	−0.437819	+	0.899063i	$0.644249\pi$
$314$	2.45574e16	1.44591
$315$	−3.04927e15	−0.175864
$316$	−2.99544e16	−1.69237
$317$	2.13000e16	1.17895	0.589474	−	0.807787i	$-0.299335\pi$
$317$	2.13000e16	1.17895	0.589474	+	0.807787i	$0.299335\pi$
$318$	−7.36051e16	−3.99146
$319$	2.66975e16	1.41850
$320$	−8.40933e15	−0.437811
$321$	1.05830e15	0.0539915
$322$	−1.82370e15	−0.0911783
$323$	4.25676e16	2.08575
$324$	−4.35926e16	−2.09349
$325$	−2.78580e15	−0.131132
$326$	−6.80845e16	−3.14148
$327$	3.06628e16	1.38692
$328$	−4.21898e16	−1.87080
$329$	2.92124e15	0.126997
$330$	−4.19534e16	−1.78824
$331$	8.68760e15	0.363093	0.181547	−	0.983382i	$-0.441890\pi$
$331$	8.68760e15	0.363093	0.181547	+	0.983382i	$0.441890\pi$
$332$	−3.47683e16	−1.42491
$333$	2.18910e15	0.0879788
$334$	2.03614e16	0.802519
$335$	1.42548e16	0.551021
$336$	1.24243e16	0.471048
$337$	1.70522e16	0.634143	0.317072	−	0.948402i	$-0.397300\pi$
$337$	1.70522e16	0.634143	0.317072	+	0.948402i	$0.397300\pi$
$338$	−4.50749e16	−1.64428
$339$	−3.54220e16	−1.26758
$340$	4.83656e16	1.69794
$341$	−2.40725e16	−0.829121
$342$	9.59006e16	3.24079
$343$	1.44972e16	0.480700
$344$	−8.46881e16	−2.75545
$345$	−6.51320e15	−0.207955
$346$	7.21425e16	2.26046
$347$	4.08101e16	1.25495	0.627475	−	0.778637i	$-0.284088\pi$
$347$	4.08101e16	1.25495	0.627475	+	0.778637i	$0.284088\pi$
$348$	−1.38159e17	−4.16978
$349$	−1.68976e15	−0.0500563	−0.0250282	−	0.999687i	$-0.507968\pi$
$349$	−1.68976e15	−0.0500563	−0.0250282	+	0.999687i	$0.507968\pi$
$350$	7.58756e15	0.220628
$351$	−9.75482e13	−0.00278434
$352$	1.47897e16	0.414412
$353$	−6.84019e15	−0.188162	−0.0940812	−	0.995565i	$-0.529991\pi$
$353$	−6.84019e15	−0.188162	−0.0940812	+	0.995565i	$0.529991\pi$
$354$	−1.70839e16	−0.461387
$355$	−4.90032e16	−1.29939
$356$	1.01287e17	2.63711
$357$	1.57151e16	0.401765
$358$	−1.08986e17	−2.73611
$359$	−4.18175e16	−1.03097	−0.515483	−	0.856900i	$-0.672387\pi$
$359$	−4.18175e16	−1.03097	−0.515483	+	0.856900i	$0.672387\pi$
$360$	5.73109e16	1.38762
$361$	9.78601e16	2.32707
$362$	−2.19332e16	−0.512267
$363$	−2.09495e15	−0.0480596
$364$	−6.03338e15	−0.135957
$365$	4.89126e16	1.08272
$366$	1.55723e16	0.338630
$367$	1.01051e16	0.215879	0.107940	−	0.994157i	$-0.465575\pi$
$367$	1.01051e16	0.215879	0.107940	+	0.994157i	$0.465575\pi$
$368$	1.33190e16	0.279551
$369$	−4.67165e16	−0.963383
$370$	5.34893e15	0.108382
$371$	−1.98968e16	−0.396145
$372$	1.24575e17	2.43725
$373$	−5.64081e15	−0.108451	−0.0542256	−	0.998529i	$-0.517269\pi$
$373$	−5.64081e15	−0.108451	−0.0542256	+	0.998529i	$0.517269\pi$
$374$	1.08515e17	2.05033
$375$	8.08061e16	1.50052
$376$	−5.49047e16	−1.00205
$377$	2.02120e16	0.362570
$378$	2.65687e14	0.00468462
$379$	3.24996e16	0.563278	0.281639	−	0.959520i	$-0.409122\pi$
$379$	3.24996e16	0.563278	0.281639	+	0.959520i	$0.409122\pi$
$380$	1.58970e17	2.70846
$381$	7.85765e16	1.31607
$382$	−1.49378e17	−2.45965
$383$	−9.13623e16	−1.47902	−0.739511	−	0.673144i	$-0.764943\pi$
$383$	−9.13623e16	−1.47902	−0.739511	+	0.673144i	$0.764943\pi$
$384$	1.33920e17	2.13153
$385$	−1.13408e16	−0.177480
$386$	5.83624e16	0.898081
$387$	−9.37747e16	−1.41894
$388$	−9.89710e16	−1.47266
$389$	2.71690e16	0.397558	0.198779	−	0.980044i	$-0.436302\pi$
$389$	2.71690e16	0.397558	0.198779	+	0.980044i	$0.436302\pi$
$390$	−3.17620e16	−0.457075
$391$	1.68468e16	0.238434
$392$	−1.31916e17	−1.83628
$393$	−1.10994e17	−1.51967
$394$	−1.71776e17	−2.31332
$395$	−4.26269e16	−0.564680
$396$	1.65854e17	2.16126
$397$	7.57003e16	0.970419	0.485209	−	0.874398i	$-0.338743\pi$
$397$	7.57003e16	0.970419	0.485209	+	0.874398i	$0.338743\pi$
$398$	5.38880e16	0.679597
$399$	5.16529e16	0.640872
$400$	−5.54140e16	−0.676441
$401$	1.10089e15	0.0132222	0.00661112	−	0.999978i	$-0.497896\pi$
$401$	1.10089e15	0.0132222	0.00661112	+	0.999978i	$0.497896\pi$
$402$	−1.65509e17	−1.95593
$403$	−1.82247e16	−0.211923
$404$	2.42225e17	2.77166
$405$	−6.20349e16	−0.698519
$406$	−5.50506e16	−0.610018
$407$	8.14167e15	0.0887871
$408$	−2.95364e17	−3.17005
$409$	−1.08103e17	−1.14192	−0.570962	−	0.820977i	$-0.693429\pi$
$409$	−1.08103e17	−1.14192	−0.570962	+	0.820977i	$0.693429\pi$
$410$	−1.14149e17	−1.18680
$411$	−1.49335e17	−1.52824
$412$	−2.91378e16	−0.293511
$413$	−4.61809e15	−0.0457918
$414$	3.79541e16	0.370473
$415$	−4.94774e16	−0.475438
$416$	1.11970e16	0.105924
$417$	1.31754e16	0.122710
$418$	3.56672e17	3.27057
$419$	7.78588e16	0.702938	0.351469	−	0.936200i	$-0.385682\pi$
$419$	7.78588e16	0.702938	0.351469	+	0.936200i	$0.385682\pi$
$420$	5.86884e16	0.521713
$421$	1.00628e17	0.880814	0.440407	−	0.897798i	$-0.354834\pi$
$421$	1.00628e17	0.880814	0.440407	+	0.897798i	$0.354834\pi$
$422$	1.66322e17	1.43357
$423$	−6.07956e16	−0.516012
$424$	3.73960e17	3.12570
$425$	−7.00914e16	−0.576948
$426$	5.68967e17	4.61237
$427$	4.20948e15	0.0336084
$428$	−1.02227e16	−0.0803864
$429$	−4.83453e16	−0.374440
$430$	−2.29133e17	−1.74800
$431$	−4.66185e16	−0.350313	−0.175156	−	0.984541i	$-0.556043\pi$
$431$	−4.66185e16	−0.350313	−0.175156	+	0.984541i	$0.556043\pi$
$432$	−1.94039e15	−0.0143630
$433$	1.22748e17	0.895044	0.447522	−	0.894273i	$-0.352307\pi$
$433$	1.22748e17	0.895044	0.447522	+	0.894273i	$0.352307\pi$
$434$	4.96379e16	0.356558
$435$	−1.96608e17	−1.39130
$436$	−2.96190e17	−2.06494
$437$	5.53728e16	0.380335
$438$	−5.67915e17	−3.84327
$439$	−7.48727e16	−0.499234	−0.249617	−	0.968345i	$-0.580305\pi$
$439$	−7.48727e16	−0.499234	−0.249617	+	0.968345i	$0.580305\pi$
$440$	2.13150e17	1.40037
$441$	−1.46070e17	−0.945605
$442$	8.21543e16	0.524065
$443$	1.68648e17	1.06012	0.530062	−	0.847959i	$-0.322169\pi$
$443$	1.68648e17	1.06012	0.530062	+	0.847959i	$0.322169\pi$
$444$	−4.21329e16	−0.260995
$445$	1.44137e17	0.879906
$446$	6.15169e16	0.370099
$447$	−2.93189e17	−1.73839
$448$	2.63937e16	0.154239
$449$	−2.76617e17	−1.59323	−0.796613	−	0.604490i	$-0.793377\pi$
$449$	−2.76617e17	−1.59323	−0.796613	+	0.604490i	$0.793377\pi$
$450$	−1.57909e17	−0.896448
$451$	−1.73747e17	−0.972234
$452$	3.42162e17	1.88726
$453$	3.93797e17	2.14109
$454$	2.28513e16	0.122475
$455$	−8.58586e15	−0.0453638
$456$	−9.70815e17	−5.05667
$457$	1.94213e17	0.997296	0.498648	−	0.866805i	$-0.333830\pi$
$457$	1.94213e17	0.997296	0.498648	+	0.866805i	$0.333830\pi$
$458$	−6.37003e17	−3.22490
$459$	−2.45433e15	−0.0122504
$460$	6.29149e16	0.309619
$461$	2.76804e17	1.34313	0.671563	−	0.740947i	$-0.265623\pi$
$461$	2.76804e17	1.34313	0.671563	+	0.740947i	$0.265623\pi$
$462$	1.31676e17	0.629989
$463$	2.80534e16	0.132345	0.0661727	−	0.997808i	$-0.478921\pi$
$463$	2.80534e16	0.132345	0.0661727	+	0.997808i	$0.478921\pi$
$464$	4.02049e17	1.87031
$465$	1.77277e17	0.813221
$466$	3.82168e17	1.72880
$467$	−4.45631e17	−1.98800	−0.993998	−	0.109399i	$-0.965108\pi$
$467$	−4.45631e17	−1.98800	−0.993998	+	0.109399i	$0.965108\pi$
$468$	1.25564e17	0.552417
$469$	−4.47402e16	−0.194122
$470$	−1.48550e17	−0.635679
$471$	−2.75272e17	−1.16178
$472$	8.67969e16	0.361311
$473$	−3.48766e17	−1.43198
$474$	4.94932e17	2.00441
$475$	−2.30379e17	−0.920312
$476$	−1.51801e17	−0.598177
$477$	4.14084e17	1.60960
$478$	4.47325e17	1.71531
$479$	1.60032e16	0.0605377	0.0302689	−	0.999542i	$-0.490364\pi$
$479$	1.60032e16	0.0605377	0.0302689	+	0.999542i	$0.490364\pi$
$480$	−1.08916e17	−0.406465
$481$	6.16387e15	0.0226940
$482$	−6.70968e17	−2.43723
$483$	2.04424e16	0.0732616
$484$	2.02363e16	0.0715546
$485$	−1.40842e17	−0.491371
$486$	7.25763e17	2.49838
$487$	−9.36406e15	−0.0318072	−0.0159036	−	0.999874i	$-0.505062\pi$
$487$	−9.36406e15	−0.0318072	−0.0159036	+	0.999874i	$0.505062\pi$
$488$	−7.91171e16	−0.265180
$489$	7.63180e17	2.52417
$490$	−3.56913e17	−1.16490
$491$	−4.44265e16	−0.143091	−0.0715454	−	0.997437i	$-0.522793\pi$
$491$	−4.44265e16	−0.143091	−0.0715454	+	0.997437i	$0.522793\pi$
$492$	8.99139e17	2.85794
$493$	5.08539e17	1.59522
$494$	2.70028e17	0.835957
$495$	2.36020e17	0.721131
$496$	−3.62519e17	−1.09320
$497$	1.53802e17	0.457769
$498$	5.74472e17	1.68763
$499$	3.26869e16	0.0947809	0.0473904	−	0.998876i	$-0.484910\pi$
$499$	3.26869e16	0.0947809	0.0473904	+	0.998876i	$0.484910\pi$
$500$	−7.80554e17	−2.23408
$501$	−2.28237e17	−0.644823
$502$	−1.73508e16	−0.0483888
$503$	2.25171e17	0.619899	0.309950	−	0.950753i	$-0.399688\pi$
$503$	2.25171e17	0.619899	0.309950	+	0.950753i	$0.399688\pi$
$504$	−1.79877e17	−0.488852
$505$	3.44700e17	0.924800
$506$	1.41159e17	0.373877
$507$	5.05258e17	1.32118
$508$	−7.59018e17	−1.95947
$509$	−4.19212e17	−1.06848	−0.534242	−	0.845332i	$-0.679403\pi$
$509$	−4.19212e17	−1.06848	−0.534242	+	0.845332i	$0.679403\pi$
$510$	−7.99138e17	−2.01102
$511$	−1.53518e17	−0.381438
$512$	−8.46526e17	−2.07676
$513$	−8.06701e15	−0.0195411
$514$	−2.29304e16	−0.0548468
$515$	−4.14648e16	−0.0979338
$516$	1.80485e18	4.20939
$517$	−2.26110e17	−0.520753
$518$	−1.67882e16	−0.0381823
$519$	−8.08667e17	−1.81628
$520$	1.61371e17	0.357935
$521$	−6.89688e16	−0.151080	−0.0755401	−	0.997143i	$-0.524068\pi$
$521$	−6.89688e16	−0.151080	−0.0755401	+	0.997143i	$0.524068\pi$
$522$	1.14569e18	2.47861
$523$	−7.64614e17	−1.63373	−0.816867	−	0.576826i	$-0.804291\pi$
$523$	−7.64614e17	−1.63373	−0.816867	+	0.576826i	$0.804291\pi$
$524$	1.07216e18	2.26259
$525$	−8.50512e16	−0.177274
$526$	−1.15355e18	−2.37481
$527$	−4.58538e17	−0.932410
$528$	−9.61664e17	−1.93154
$529$	2.19146e16	0.0434783
$530$	1.01179e18	1.98288
$531$	9.61097e16	0.186060
$532$	−4.98946e17	−0.954176
$533$	−1.31540e17	−0.248503
$534$	−1.67355e18	−3.12335
$535$	−1.45476e16	−0.0268220
$536$	8.40891e17	1.53168
$537$	1.22166e18	2.19846
$538$	−8.18150e16	−0.145461
$539$	−5.43261e17	−0.954293
$540$	−9.16579e15	−0.0159078
$541$	8.48215e17	1.45453	0.727267	−	0.686355i	$-0.240790\pi$
$541$	8.48215e17	1.45453	0.727267	+	0.686355i	$0.240790\pi$
$542$	−2.40114e17	−0.406839
$543$	2.45856e17	0.411605
$544$	2.81718e17	0.466038
$545$	−4.21496e17	−0.688995
$546$	9.96887e16	0.161025
$547$	9.83470e16	0.156980	0.0784898	−	0.996915i	$-0.474990\pi$
$547$	9.83470e16	0.156980	0.0784898	+	0.996915i	$0.474990\pi$
$548$	1.44252e18	2.27535
$549$	−8.76059e16	−0.136557
$550$	−5.87293e17	−0.904685
$551$	1.67149e18	2.54459
$552$	−3.84215e17	−0.578056
$553$	1.33789e17	0.198934
$554$	−2.12047e18	−3.11616
$555$	−5.99577e16	−0.0870844
$556$	−1.27269e17	−0.182699
$557$	−8.64678e17	−1.22686	−0.613431	−	0.789749i	$-0.710211\pi$
$557$	−8.64678e17	−1.22686	−0.613431	+	0.789749i	$0.710211\pi$
$558$	−1.03304e18	−1.44876
$559$	−2.64042e17	−0.366013
$560$	−1.70786e17	−0.234008
$561$	−1.21638e18	−1.64744
$562$	−1.74540e18	−2.33673
$563$	−8.30144e17	−1.09862	−0.549312	−	0.835618i	$-0.685110\pi$
$563$	−8.30144e17	−1.09862	−0.549312	+	0.835618i	$0.685110\pi$
$564$	1.17012e18	1.53079
$565$	4.86917e17	0.629709
$566$	4.19375e17	0.536161
$567$	1.94704e17	0.246085
$568$	−2.89071e18	−3.61194
$569$	−1.75088e17	−0.216285	−0.108143	−	0.994135i	$-0.534490\pi$
$569$	−1.75088e17	−0.216285	−0.108143	+	0.994135i	$0.534490\pi$
$570$	−2.62664e18	−3.20785
$571$	1.06029e18	1.28023	0.640116	−	0.768278i	$-0.278886\pi$
$571$	1.06029e18	1.28023	0.640116	+	0.768278i	$0.278886\pi$
$572$	4.66996e17	0.557492
$573$	1.67442e18	1.97633
$574$	3.58270e17	0.418103
$575$	−9.11762e16	−0.105206
$576$	−5.49294e17	−0.626698
$577$	5.79143e17	0.653346	0.326673	−	0.945138i	$-0.394072\pi$
$577$	5.79143e17	0.653346	0.326673	+	0.945138i	$0.394072\pi$
$578$	4.86207e17	0.542363
$579$	−6.54201e17	−0.721607
$580$	1.89916e18	2.07147
$581$	1.55291e17	0.167494
$582$	1.63528e18	1.74419
$583$	1.54006e18	1.62439
$584$	2.88537e18	3.00966
$585$	1.78685e17	0.184321
$586$	−8.54564e17	−0.871787
$587$	−1.20221e18	−1.21292	−0.606460	−	0.795114i	$-0.707411\pi$
$587$	−1.20221e18	−1.21292	−0.606460	+	0.795114i	$0.707411\pi$
$588$	2.81136e18	2.80520
$589$	−1.50714e18	−1.48732
$590$	2.34838e17	0.229208
$591$	1.92548e18	1.85875
$592$	1.22609e17	0.117066
$593$	1.11099e18	1.04920	0.524598	−	0.851350i	$-0.324216\pi$
$593$	1.11099e18	1.04920	0.524598	+	0.851350i	$0.324216\pi$
$594$	−2.05648e16	−0.0192093
$595$	−2.16022e17	−0.199590
$596$	2.83208e18	2.58825
$597$	−6.04046e17	−0.546055
$598$	1.06868e17	0.0955629
$599$	−4.33254e16	−0.0383237	−0.0191619	−	0.999816i	$-0.506100\pi$
$599$	−4.33254e16	−0.0383237	−0.0191619	+	0.999816i	$0.506100\pi$
$600$	1.59853e18	1.39875
$601$	−3.17694e17	−0.274995	−0.137498	−	0.990502i	$-0.543906\pi$
$601$	−3.17694e17	−0.274995	−0.137498	+	0.990502i	$0.543906\pi$
$602$	7.19160e17	0.615812
$603$	9.31114e17	0.788751
$604$	−3.80392e18	−3.18780
$605$	2.87975e16	0.0238751
$606$	−4.00225e18	−3.28270
$607$	1.05134e18	0.853130	0.426565	−	0.904457i	$-0.359724\pi$
$607$	1.05134e18	0.853130	0.426565	+	0.904457i	$0.359724\pi$
$608$	9.25962e17	0.743396
$609$	6.17078e17	0.490148
$610$	−2.14060e17	−0.168225
$611$	−1.71183e17	−0.133104
$612$	3.15922e18	2.43050
$613$	−2.46254e18	−1.87452	−0.937259	−	0.348634i	$-0.886646\pi$
$613$	−2.46254e18	−1.87452	−0.937259	+	0.348634i	$0.886646\pi$
$614$	1.33559e18	1.00596
$615$	1.27953e18	0.953590
$616$	−6.68996e17	−0.493343
$617$	−6.35362e17	−0.463626	−0.231813	−	0.972760i	$-0.574466\pi$
$617$	−6.35362e17	−0.463626	−0.231813	+	0.972760i	$0.574466\pi$
$618$	4.81439e17	0.347629
$619$	−7.74637e17	−0.553489	−0.276745	−	0.960944i	$-0.589256\pi$
$619$	−7.74637e17	−0.553489	−0.276745	+	0.960944i	$0.589256\pi$
$620$	−1.71243e18	−1.21078
$621$	−3.19264e15	−0.00223386
$622$	3.19899e18	2.21501
$623$	−4.52392e17	−0.309986
$624$	−7.28054e17	−0.493701
$625$	−3.58937e17	−0.240879
$626$	−2.32492e18	−1.54410
$627$	−3.99804e18	−2.62790
$628$	2.65901e18	1.72975
$629$	1.55084e17	0.0998478
$630$	−4.86676e17	−0.310118
$631$	−1.59250e18	−1.00436	−0.502179	−	0.864764i	$-0.667468\pi$
$631$	−1.59250e18	−1.00436	−0.502179	+	0.864764i	$0.667468\pi$
$632$	−2.51457e18	−1.56965
$633$	−1.86435e18	−1.15187
$634$	3.39957e18	2.07895
$635$	−1.08013e18	−0.653801
$636$	−7.96976e18	−4.77501
$637$	−4.11291e17	−0.243917
$638$	4.26103e18	2.50138
$639$	−3.20087e18	−1.86000
$640$	−1.84089e18	−1.05891
$641$	1.78381e18	1.01571	0.507856	−	0.861442i	$-0.330438\pi$
$641$	1.78381e18	1.01571	0.507856	+	0.861442i	$0.330438\pi$
$642$	1.68909e17	0.0952082
$643$	3.17832e18	1.77348	0.886739	−	0.462271i	$-0.152965\pi$
$643$	3.17832e18	1.77348	0.886739	+	0.462271i	$0.152965\pi$
$644$	−1.97466e17	−0.109077
$645$	2.56841e18	1.40452
$646$	6.79397e18	3.67800
$647$	−4.00878e17	−0.214850	−0.107425	−	0.994213i	$-0.534261\pi$
$647$	−4.00878e17	−0.214850	−0.107425	+	0.994213i	$0.534261\pi$
$648$	−3.65945e18	−1.94168
$649$	3.57450e17	0.187769
$650$	−4.44626e17	−0.231237
$651$	−5.56405e17	−0.286494
$652$	−7.37201e18	−3.75817
$653$	−2.79058e17	−0.140850	−0.0704252	−	0.997517i	$-0.522436\pi$
$653$	−2.79058e17	−0.140850	−0.0704252	+	0.997517i	$0.522436\pi$
$654$	4.89391e18	2.44568
$655$	1.52575e18	0.754942
$656$	−2.61654e18	−1.28190
$657$	3.19495e18	1.54985
$658$	4.66243e17	0.223946
$659$	−6.48421e17	−0.308391	−0.154195	−	0.988040i	$-0.549279\pi$
$659$	−6.48421e17	−0.308391	−0.154195	+	0.988040i	$0.549279\pi$
$660$	−4.54260e18	−2.13929
$661$	3.01510e18	1.40602	0.703012	−	0.711178i	$-0.251838\pi$
$661$	3.01510e18	1.40602	0.703012	+	0.711178i	$0.251838\pi$
$662$	1.38658e18	0.640276
$663$	−9.20891e17	−0.421086
$664$	−2.91868e18	−1.32158
$665$	−7.10031e17	−0.318373
$666$	3.49389e17	0.155141
$667$	6.61518e17	0.290886
$668$	2.20467e18	0.960058
$669$	−6.89561e17	−0.297374
$670$	2.27512e18	0.971668
$671$	−3.25823e17	−0.137811
$672$	3.41845e17	0.143196
$673$	2.81842e18	1.16925	0.584625	−	0.811303i	$-0.301242\pi$
$673$	2.81842e18	1.16925	0.584625	+	0.811303i	$0.301242\pi$
$674$	2.72161e18	1.11824
$675$	1.32831e16	0.00540535
$676$	−4.88059e18	−1.96706
$677$	6.74941e16	0.0269426	0.0134713	−	0.999909i	$-0.495712\pi$
$677$	6.74941e16	0.0269426	0.0134713	+	0.999909i	$0.495712\pi$
$678$	−5.65350e18	−2.23524
$679$	4.42048e17	0.173107
$680$	4.06013e18	1.57482
$681$	−2.56147e17	−0.0984085
$682$	−3.84207e18	−1.46207
$683$	−4.06284e18	−1.53142	−0.765711	−	0.643184i	$-0.777613\pi$
$683$	−4.06284e18	−1.53142	−0.765711	+	0.643184i	$0.777613\pi$
$684$	1.03839e19	3.87698
$685$	2.05279e18	0.759201
$686$	2.31382e18	0.847663
$687$	7.14035e18	2.59120
$688$	−5.25222e18	−1.88807
$689$	1.16594e18	0.415195
$690$	−1.03953e18	−0.366707
$691$	−4.60003e18	−1.60751	−0.803754	−	0.594962i	$-0.797167\pi$
$691$	−4.60003e18	−1.60751	−0.803754	+	0.594962i	$0.797167\pi$
$692$	7.81139e18	2.70420
$693$	−7.40775e17	−0.254051
$694$	6.51347e18	2.21297
$695$	−1.81111e17	−0.0609599
$696$	−1.15980e19	−3.86742
$697$	−3.30958e18	−1.09335
$698$	−2.69692e17	−0.0882690
$699$	−4.28383e18	−1.38909
$700$	8.21560e17	0.263938
$701$	3.57379e18	1.13753	0.568764	−	0.822501i	$-0.307422\pi$
$701$	3.57379e18	1.13753	0.568764	+	0.822501i	$0.307422\pi$
$702$	−1.55691e16	−0.00490990
$703$	5.09738e17	0.159271
$704$	−2.04293e18	−0.632456
$705$	1.66515e18	0.510767
$706$	−1.09172e18	−0.331804
$707$	−1.08188e18	−0.325802
$708$	−1.84980e18	−0.551960
$709$	5.96637e18	1.76404	0.882022	−	0.471209i	$-0.156182\pi$
$709$	5.96637e18	1.76404	0.882022	+	0.471209i	$0.156182\pi$
$710$	−7.82112e18	−2.29134
$711$	−2.78437e18	−0.808303
$712$	8.50269e18	2.44589
$713$	−5.96476e17	−0.170024
$714$	2.50819e18	0.708471
$715$	6.64563e17	0.186015
$716$	−1.18008e19	−3.27322
$717$	−5.01419e18	−1.37825
$718$	−6.67425e18	−1.81800
$719$	−4.81807e17	−0.130058	−0.0650288	−	0.997883i	$-0.520714\pi$
$719$	−4.81807e17	−0.130058	−0.0650288	+	0.997883i	$0.520714\pi$
$720$	3.55433e18	0.950816
$721$	1.30142e17	0.0345016
$722$	1.56189e19	4.10353
$723$	7.52108e18	1.95831
$724$	−2.37487e18	−0.612828
$725$	−2.75226e18	−0.703869
$726$	−3.34362e17	−0.0847480
$727$	−1.41311e18	−0.354978	−0.177489	−	0.984123i	$-0.556797\pi$
$727$	−1.41311e18	−0.354978	−0.177489	+	0.984123i	$0.556797\pi$
$728$	−5.06482e17	−0.126098
$729$	−4.11361e18	−1.01506
$730$	7.80666e18	1.90927
$731$	−6.64336e18	−1.61037
$732$	1.68612e18	0.405105
$733$	−6.38028e18	−1.51937	−0.759686	−	0.650290i	$-0.774647\pi$
$733$	−6.38028e18	−1.51937	−0.759686	+	0.650290i	$0.774647\pi$
$734$	1.61282e18	0.380680
$735$	4.00074e18	0.935993
$736$	3.66464e17	0.0849817
$737$	3.46299e18	0.795998
$738$	−7.45615e18	−1.69882
$739$	−2.02496e18	−0.457327	−0.228663	−	0.973506i	$-0.573436\pi$
$739$	−2.02496e18	−0.457327	−0.228663	+	0.973506i	$0.573436\pi$
$740$	5.79167e17	0.129658
$741$	−3.02683e18	−0.671690
$742$	−3.17562e18	−0.698559
$743$	4.19060e18	0.913796	0.456898	−	0.889519i	$-0.348960\pi$
$743$	4.19060e18	0.913796	0.456898	+	0.889519i	$0.348960\pi$
$744$	1.04576e19	2.26052
$745$	4.03022e18	0.863602
$746$	−9.00297e17	−0.191242
$747$	−3.23184e18	−0.680559
$748$	1.17497e19	2.45283
$749$	4.56592e16	0.00944923
$750$	1.28970e19	2.64600
$751$	−1.65251e18	−0.336113	−0.168057	−	0.985777i	$-0.553749\pi$
$751$	−1.65251e18	−0.336113	−0.168057	+	0.985777i	$0.553749\pi$
$752$	−3.40510e18	−0.686616
$753$	1.94490e17	0.0388803
$754$	3.22593e18	0.639353
$755$	−5.41321e18	−1.06365
$756$	2.87679e16	0.00560424
$757$	−2.70389e18	−0.522235	−0.261118	−	0.965307i	$-0.584091\pi$
$757$	−2.70389e18	−0.522235	−0.261118	+	0.965307i	$0.584091\pi$
$758$	5.18707e18	0.993281
$759$	−1.58229e18	−0.300410
$760$	1.33450e19	2.51206
$761$	−9.78515e18	−1.82628	−0.913140	−	0.407647i	$-0.866350\pi$
$761$	−9.78515e18	−1.82628	−0.913140	+	0.407647i	$0.866350\pi$
$762$	1.25411e19	2.32076
$763$	1.32291e18	0.242729
$764$	−1.61742e19	−2.94250
$765$	4.49575e18	0.810967
$766$	−1.45818e19	−2.60810
$767$	2.70617e17	0.0479938
$768$	1.63627e19	2.87744
$769$	7.31370e18	1.27531	0.637655	−	0.770322i	$-0.279905\pi$
$769$	7.31370e18	1.27531	0.637655	+	0.770322i	$0.279905\pi$
$770$	−1.81004e18	−0.312967
$771$	2.57034e17	0.0440693
$772$	6.31932e18	1.07438
$773$	3.33538e18	0.562314	0.281157	−	0.959662i	$-0.409282\pi$
$773$	3.33538e18	0.562314	0.281157	+	0.959662i	$0.409282\pi$
$774$	−1.49668e19	−2.50215
$775$	2.48165e18	0.411414
$776$	−8.30828e18	−1.36587
$777$	1.88184e17	0.0306794
$778$	4.33628e18	0.701051
$779$	−1.08781e19	−1.74405
$780$	−3.43910e18	−0.546802
$781$	−1.19046e19	−1.87708
$782$	2.68882e18	0.420453
$783$	−9.63735e16	−0.0149454
$784$	−8.18122e18	−1.25824
$785$	3.78393e18	0.577153
$786$	−1.77151e19	−2.67977
$787$	1.07124e19	1.60713	0.803565	−	0.595216i	$-0.202934\pi$
$787$	1.07124e19	1.60713	0.803565	+	0.595216i	$0.202934\pi$
$788$	−1.85994e19	−2.76744
$789$	1.29305e19	1.90816
$790$	−6.80343e18	−0.995754
$791$	−1.52825e18	−0.221843
$792$	1.39229e19	2.00454
$793$	−2.46673e17	−0.0352246
$794$	1.20821e19	1.71123
$795$	−1.13414e19	−1.59324
$796$	5.83484e18	0.813007
$797$	5.61938e18	0.776621	0.388311	−	0.921529i	$-0.373059\pi$
$797$	5.61938e18	0.776621	0.388311	+	0.921529i	$0.373059\pi$
$798$	8.24402e18	1.13011
$799$	−4.30700e18	−0.585627
$800$	−1.52468e18	−0.205633
$801$	9.41498e18	1.25953
$802$	1.75706e17	0.0233160
$803$	1.18826e19	1.56409
$804$	−1.79209e19	−2.33989
$805$	−2.81006e17	−0.0363950
$806$	−2.90875e18	−0.373704
$807$	9.17088e17	0.116878
$808$	2.03339e19	2.57068
$809$	3.09483e18	0.388124	0.194062	−	0.980989i	$-0.437834\pi$
$809$	3.09483e18	0.388124	0.194062	+	0.980989i	$0.437834\pi$
$810$	−9.90103e18	−1.23177
$811$	−6.13123e18	−0.756679	−0.378340	−	0.925667i	$-0.623505\pi$
$811$	−6.13123e18	−0.756679	−0.378340	+	0.925667i	$0.623505\pi$
$812$	−5.96073e18	−0.729768
$813$	2.69151e18	0.326895
$814$	1.29944e18	0.156567
$815$	−1.04908e19	−1.25396
$816$	−1.83180e19	−2.17216
$817$	−2.18357e19	−2.56876
$818$	−1.72537e19	−2.01366
$819$	−5.60824e17	−0.0649354
$820$	−1.23597e19	−1.41977
$821$	−1.17627e19	−1.34053	−0.670267	−	0.742120i	$-0.733820\pi$
$821$	−1.17627e19	−1.34053	−0.670267	+	0.742120i	$0.733820\pi$
$822$	−2.38346e19	−2.69489
$823$	8.04590e18	0.902559	0.451280	−	0.892383i	$-0.350968\pi$
$823$	8.04590e18	0.902559	0.451280	+	0.892383i	$0.350968\pi$
$824$	−2.44602e18	−0.272228
$825$	6.58314e18	0.726913
$826$	−7.37067e17	−0.0807489
$827$	−1.32331e19	−1.43839	−0.719194	−	0.694810i	$-0.755489\pi$
$827$	−1.32331e19	−1.43839	−0.719194	+	0.694810i	$0.755489\pi$
$828$	4.10957e18	0.443199
$829$	−9.28421e18	−0.993437	−0.496719	−	0.867912i	$-0.665462\pi$
$829$	−9.28421e18	−0.993437	−0.496719	+	0.867912i	$0.665462\pi$
$830$	−7.89680e18	−0.838385
$831$	2.37690e19	2.50383
$832$	−1.54665e18	−0.161656
$833$	−1.03482e19	−1.07317
$834$	2.10285e18	0.216386
$835$	3.13738e18	0.320336
$836$	3.86195e19	3.91260
$837$	8.68979e16	0.00873562
$838$	1.24266e19	1.23956
$839$	−6.30892e18	−0.624457	−0.312228	−	0.950007i	$-0.601075\pi$
$839$	−6.30892e18	−0.624457	−0.312228	+	0.950007i	$0.601075\pi$
$840$	4.92669e18	0.483882
$841$	9.70802e18	0.946143
$842$	1.60606e19	1.55322
$843$	1.95647e19	1.87756
$844$	1.80089e19	1.71499
$845$	−6.94537e18	−0.656337
$846$	−9.70324e18	−0.909933
$847$	−9.03844e16	−0.00841108
$848$	2.31924e19	2.14177
$849$	−4.70089e18	−0.430805
$850$	−1.11869e19	−1.01739
$851$	2.01737e17	0.0182072
$852$	6.16062e19	5.51781
$853$	2.10844e19	1.87410	0.937048	−	0.349199i	$-0.113546\pi$
$853$	2.10844e19	1.87410	0.937048	+	0.349199i	$0.113546\pi$
$854$	6.71851e17	0.0592648
$855$	1.47768e19	1.29361
$856$	−8.58163e17	−0.0745574
$857$	1.93706e18	0.167020	0.0835099	−	0.996507i	$-0.473387\pi$
$857$	1.93706e18	0.167020	0.0835099	+	0.996507i	$0.473387\pi$
$858$	−7.71611e18	−0.660284
$859$	1.88527e19	1.60110	0.800548	−	0.599268i	$-0.204542\pi$
$859$	1.88527e19	1.60110	0.800548	+	0.599268i	$0.204542\pi$
$860$	−2.48099e19	−2.09115
$861$	−4.01595e18	−0.335945
$862$	−7.44051e18	−0.617739
$863$	1.63690e19	1.34882	0.674408	−	0.738359i	$-0.264399\pi$
$863$	1.63690e19	1.34882	0.674408	+	0.738359i	$0.264399\pi$
$864$	−5.33885e16	−0.00436625
$865$	1.11161e19	0.902292
$866$	1.95912e19	1.57832
$867$	−5.45004e18	−0.435788
$868$	5.37465e18	0.426552
$869$	−1.03556e19	−0.815729
$870$	−3.13795e19	−2.45341
$871$	2.62175e18	0.203457
$872$	−2.48641e19	−1.91521
$873$	−9.19970e18	−0.703366
$874$	8.83773e18	0.670681
$875$	3.48630e18	0.262611
$876$	−6.14922e19	−4.59773
$877$	−7.47570e18	−0.554823	−0.277411	−	0.960751i	$-0.589476\pi$
$877$	−7.47570e18	−0.554823	−0.277411	+	0.960751i	$0.589476\pi$
$878$	−1.19500e19	−0.880347
$879$	9.57906e18	0.700479
$880$	1.32192e19	0.959552
$881$	2.19867e19	1.58423	0.792113	−	0.610375i	$-0.208981\pi$
$881$	2.19867e19	1.58423	0.792113	+	0.610375i	$0.208981\pi$
$882$	−2.33134e19	−1.66747
$883$	8.45677e18	0.600427	0.300213	−	0.953872i	$-0.402942\pi$
$883$	8.45677e18	0.600427	0.300213	+	0.953872i	$0.402942\pi$
$884$	8.89544e18	0.626943
$885$	−2.63237e18	−0.184169
$886$	2.69169e19	1.86942
$887$	2.01765e19	1.39105	0.695523	−	0.718504i	$-0.255173\pi$
$887$	2.01765e19	1.39105	0.695523	+	0.718504i	$0.255173\pi$
$888$	−3.53692e18	−0.242070
$889$	3.39011e18	0.230331
$890$	2.30049e19	1.55162
$891$	−1.50705e19	−1.00907
$892$	6.66088e18	0.442751
$893$	−1.41564e19	−0.934156
$894$	−4.67941e19	−3.06547
$895$	−1.67932e19	−1.09215
$896$	5.77784e18	0.373047
$897$	−1.19791e18	−0.0767847
$898$	−4.41492e19	−2.80948
$899$	−1.80053e19	−1.13753
$900$	−1.70979e19	−1.07243
$901$	2.93353e19	1.82675
$902$	−2.77308e19	−1.71443
$903$	−8.06127e18	−0.494804
$904$	2.87233e19	1.75041
$905$	−3.37958e18	−0.204478
$906$	6.28516e19	3.77558
$907$	1.96424e19	1.17152	0.585758	−	0.810486i	$-0.300797\pi$
$907$	1.96424e19	1.17152	0.585758	+	0.810486i	$0.300797\pi$
$908$	2.47427e18	0.146518
$909$	2.25156e19	1.32379
$910$	−1.37034e18	−0.0799943
$911$	2.26142e19	1.31073	0.655363	−	0.755314i	$-0.272516\pi$
$911$	2.26142e19	1.31073	0.655363	+	0.755314i	$0.272516\pi$
$912$	−6.02084e19	−3.46490
$913$	−1.20198e19	−0.686812
$914$	3.09973e19	1.75863
$915$	2.39946e18	0.135169
$916$	−6.89729e19	−3.85796
$917$	−4.78873e18	−0.265962
$918$	−3.91722e17	−0.0216023
$919$	3.46167e19	1.89555	0.947775	−	0.318939i	$-0.103327\pi$
$919$	3.46167e19	1.89555	0.947775	+	0.318939i	$0.103327\pi$
$920$	5.28149e18	0.287168
$921$	−1.49711e19	−0.808286
$922$	4.41792e19	2.36846
$923$	−9.01272e18	−0.479783
$924$	1.42575e19	0.753660
$925$	−8.39329e17	−0.0440566
$926$	4.47744e18	0.233377
$927$	−2.70846e18	−0.140186
$928$	1.10621e19	0.568561
$929$	−2.22275e19	−1.13446	−0.567229	−	0.823560i	$-0.691984\pi$
$929$	−2.22275e19	−1.13446	−0.567229	+	0.823560i	$0.691984\pi$
$930$	2.82942e19	1.43403
$931$	−3.40128e19	−1.71186
$932$	4.13801e19	2.06818
$933$	−3.58584e19	−1.77975
$934$	−7.11246e19	−3.50562
$935$	1.67206e19	0.818418
$936$	1.05407e19	0.512360
$937$	−7.71930e18	−0.372624	−0.186312	−	0.982491i	$-0.559653\pi$
$937$	−7.71930e18	−0.372624	−0.186312	+	0.982491i	$0.559653\pi$
$938$	−7.14073e18	−0.342314
$939$	2.60607e19	1.24068
$940$	−1.60846e19	−0.760467
$941$	2.99071e18	0.140424	0.0702121	−	0.997532i	$-0.477632\pi$
$941$	2.99071e18	0.140424	0.0702121	+	0.997532i	$0.477632\pi$
$942$	−4.39345e19	−2.04868
$943$	−4.30516e18	−0.199372
$944$	5.38300e18	0.247575
$945$	4.09384e16	0.00186993
$946$	−5.56645e19	−2.52514
$947$	2.15766e19	0.972094	0.486047	−	0.873933i	$-0.338438\pi$
$947$	2.15766e19	0.972094	0.486047	+	0.873933i	$0.338438\pi$
$948$	5.35899e19	2.39789
$949$	8.99605e18	0.399780
$950$	−3.67695e19	−1.62287
$951$	−3.81068e19	−1.67043
$952$	−1.27432e19	−0.554802
$953$	1.34621e19	0.582114	0.291057	−	0.956706i	$-0.405993\pi$
$953$	1.34621e19	0.582114	0.291057	+	0.956706i	$0.405993\pi$
$954$	6.60896e19	2.83837
$955$	−2.30169e19	−0.981803
$956$	4.84351e19	2.05203
$957$	−4.77631e19	−2.00986
$958$	2.55418e18	0.106752
$959$	−6.44293e18	−0.267462
$960$	1.50447e19	0.620328
$961$	−8.18258e18	−0.335111
$962$	9.83780e17	0.0400184
$963$	−9.50239e17	−0.0383939
$964$	−7.26506e19	−2.91567
$965$	8.99277e18	0.358481
$966$	3.26270e18	0.129189
$967$	−3.75122e19	−1.47537	−0.737683	−	0.675147i	$-0.764080\pi$
$967$	−3.75122e19	−1.47537	−0.737683	+	0.675147i	$0.764080\pi$
$968$	1.69877e18	0.0663660
$969$	−7.61556e19	−2.95527
$970$	−2.24789e19	−0.866481
$971$	4.29736e19	1.64542	0.822711	−	0.568460i	$-0.192461\pi$
$971$	4.29736e19	1.64542	0.822711	+	0.568460i	$0.192461\pi$
$972$	7.85836e19	2.98883
$973$	5.68439e17	0.0214758
$974$	−1.49454e18	−0.0560887
$975$	4.98394e18	0.185799
$976$	−4.90671e18	−0.181705
$977$	1.83224e19	0.674014	0.337007	−	0.941502i	$-0.390585\pi$
$977$	1.83224e19	0.674014	0.337007	+	0.941502i	$0.390585\pi$
$978$	1.21807e20	4.45111
$979$	3.50161e19	1.27110
$980$	−3.86455e19	−1.39357
$981$	−2.75319e19	−0.986252
$982$	−7.09065e18	−0.252326
$983$	−3.67210e19	−1.29812	−0.649062	−	0.760735i	$-0.724838\pi$
$983$	−3.67210e19	−1.29812	−0.649062	+	0.760735i	$0.724838\pi$
$984$	7.54797e19	2.65071
$985$	−2.64680e19	−0.923393
$986$	8.11650e19	2.81299
$987$	−5.22625e18	−0.179940
$988$	2.92379e19	1.00006
$989$	−8.64181e18	−0.293649
$990$	3.76697e19	1.27164
$991$	−1.83094e19	−0.614037	−0.307018	−	0.951704i	$-0.599331\pi$
$991$	−1.83094e19	−0.614037	−0.307018	+	0.951704i	$0.599331\pi$
$992$	−9.97447e18	−0.332326
$993$	−1.55426e19	−0.514461
$994$	2.45475e19	0.807227
$995$	8.30333e18	0.271270
$996$	6.22023e19	2.01893
$997$	8.15930e18	0.263108	0.131554	−	0.991309i	$-0.458003\pi$
$997$	8.15930e18	0.263108	0.131554	+	0.991309i	$0.458003\pi$
$998$	5.21697e18	0.167136
$999$	−2.93901e16	−0.000935460 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.a.b.1.13	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+159.604 q^{2} -1789.05 q^{3} +17281.5 q^{4} +24592.6 q^{5} -285540. q^{6} -77186.8 q^{7} +1.45072e6 q^{8} +1.60638e6 q^{9} +O(q^{10})\)	\(q+159.604 q^{2} -1789.05 q^{3} +17281.5 q^{4} +24592.6 q^{5} -285540. q^{6} -77186.8 q^{7} +1.45072e6 q^{8} +1.60638e6 q^{9} +3.92509e6 q^{10} +5.97442e6 q^{11} -3.09175e7 q^{12} +4.52310e6 q^{13} -1.23193e7 q^{14} -4.39974e7 q^{15} +8.99715e7 q^{16} +1.13802e8 q^{17} +2.56385e8 q^{18} +3.74050e8 q^{19} +4.24998e8 q^{20} +1.38091e8 q^{21} +9.53543e8 q^{22} +1.48036e8 q^{23} -2.59542e9 q^{24} -6.15906e8 q^{25} +7.21905e8 q^{26} -2.15667e7 q^{27} -1.33390e9 q^{28} +4.46863e9 q^{29} -7.02218e9 q^{30} -4.02926e9 q^{31} +2.47551e9 q^{32} -1.06885e10 q^{33} +1.81633e10 q^{34} -1.89823e9 q^{35} +2.77606e10 q^{36} +1.36275e9 q^{37} +5.96999e10 q^{38} -8.09205e9 q^{39} +3.56771e10 q^{40} -2.90819e10 q^{41} +2.20399e10 q^{42} -5.83765e10 q^{43} +1.03247e11 q^{44} +3.95050e10 q^{45} +2.36272e10 q^{46} -3.78464e10 q^{47} -1.60964e11 q^{48} -9.09312e10 q^{49} -9.83012e10 q^{50} -2.03598e11 q^{51} +7.81659e10 q^{52} +2.57775e11 q^{53} -3.44213e9 q^{54} +1.46927e11 q^{55} -1.11977e11 q^{56} -6.69193e11 q^{57} +7.13212e11 q^{58} +5.98301e10 q^{59} -7.60342e11 q^{60} -5.45363e10 q^{61} -6.43087e11 q^{62} -1.23991e11 q^{63} -3.41945e11 q^{64} +1.11235e11 q^{65} -1.70594e12 q^{66} +5.79636e11 q^{67} +1.96667e12 q^{68} -2.64844e11 q^{69} -3.02965e11 q^{70} -1.99260e12 q^{71} +2.33041e12 q^{72} +1.98891e12 q^{73} +2.17501e11 q^{74} +1.10189e12 q^{75} +6.46414e12 q^{76} -4.61146e11 q^{77} -1.29152e12 q^{78} -1.73332e12 q^{79} +2.21264e12 q^{80} -2.52250e12 q^{81} -4.64159e12 q^{82} -2.01188e12 q^{83} +2.38642e12 q^{84} +2.79869e12 q^{85} -9.31713e12 q^{86} -7.99460e12 q^{87} +8.66723e12 q^{88} +5.86100e12 q^{89} +6.30517e12 q^{90} -3.49123e11 q^{91} +2.55828e12 q^{92} +7.20856e12 q^{93} -6.04045e12 q^{94} +9.19886e12 q^{95} -4.42881e12 q^{96} -5.72699e12 q^{97} -1.45130e13 q^{98} +9.59718e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) 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

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Groups

Database

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