LMFDB - Embedded newform 23.14.a.b.1.6

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			1.6
Root			$37.0185$ 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)

$f(q)$	$=$	$q-32.0185 q^{2} +511.530 q^{3} -7166.81 q^{4} -62645.6 q^{5} -16378.4 q^{6} -516700. q^{7} +491767. q^{8} -1.33266e6 q^{9} +O(q^{10})$	\(q-32.0185 q^{2} +511.530 q^{3} -7166.81 q^{4} -62645.6 q^{5} -16378.4 q^{6} -516700. q^{7} +491767. q^{8} -1.33266e6 q^{9} +2.00582e6 q^{10} +2.85439e6 q^{11} -3.66604e6 q^{12} +1.15006e7 q^{13} +1.65440e7 q^{14} -3.20451e7 q^{15} +4.29649e7 q^{16} -8.05620e7 q^{17} +4.26698e7 q^{18} -3.82250e8 q^{19} +4.48969e8 q^{20} -2.64308e8 q^{21} -9.13935e7 q^{22} +1.48036e8 q^{23} +2.51553e8 q^{24} +2.70376e9 q^{25} -3.68231e8 q^{26} -1.49724e9 q^{27} +3.70310e9 q^{28} +3.69952e9 q^{29} +1.02604e9 q^{30} -1.91754e9 q^{31} -5.40423e9 q^{32} +1.46011e9 q^{33} +2.57948e9 q^{34} +3.23690e10 q^{35} +9.55093e9 q^{36} -9.74919e9 q^{37} +1.22391e10 q^{38} +5.88289e9 q^{39} -3.08070e10 q^{40} -2.00398e10 q^{41} +8.46275e9 q^{42} -3.06550e10 q^{43} -2.04569e10 q^{44} +8.34852e10 q^{45} -4.73989e9 q^{46} +5.09263e10 q^{47} +2.19778e10 q^{48} +1.70090e11 q^{49} -8.65706e10 q^{50} -4.12099e10 q^{51} -8.24224e10 q^{52} -1.36451e11 q^{53} +4.79394e10 q^{54} -1.78815e11 q^{55} -2.54096e11 q^{56} -1.95532e11 q^{57} -1.18453e11 q^{58} -4.59495e9 q^{59} +2.29661e11 q^{60} -2.49239e11 q^{61} +6.13968e10 q^{62} +6.88586e11 q^{63} -1.78933e11 q^{64} -7.20460e11 q^{65} -4.67505e10 q^{66} +4.16945e11 q^{67} +5.77373e11 q^{68} +7.57248e10 q^{69} -1.03641e12 q^{70} -1.95420e12 q^{71} -6.55358e11 q^{72} +1.27673e12 q^{73} +3.12155e11 q^{74} +1.38306e12 q^{75} +2.73951e12 q^{76} -1.47487e12 q^{77} -1.88361e11 q^{78} -1.18557e12 q^{79} -2.69156e12 q^{80} +1.35881e12 q^{81} +6.41644e11 q^{82} +1.35576e12 q^{83} +1.89424e12 q^{84} +5.04685e12 q^{85} +9.81529e11 q^{86} +1.89242e12 q^{87} +1.40370e12 q^{88} +7.69900e12 q^{89} -2.67308e12 q^{90} -5.94235e12 q^{91} -1.06095e12 q^{92} -9.80880e11 q^{93} -1.63058e12 q^{94} +2.39463e13 q^{95} -2.76442e12 q^{96} -9.67989e12 q^{97} -5.44604e12 q^{98} -3.80393e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−32.0185	−0.353758	−0.176879	−	0.984233i	$-0.556600\pi$
$2$	−32.0185	−0.353758	−0.176879	+	0.984233i	$0.556600\pi$
$3$	511.530	0.405119	0.202560	−	0.979270i	$-0.435074\pi$
$3$	511.530	0.405119	0.202560	+	0.979270i	$0.435074\pi$
$4$	−7166.81	−0.874855
$5$	−62645.6	−1.79302	−0.896510	−	0.443023i	$-0.853906\pi$
$5$	−62645.6	−1.79302	−0.896510	+	0.443023i	$0.853906\pi$
$6$	−16378.4	−0.143314
$7$	−516700.	−1.65998	−0.829988	−	0.557782i	$-0.811653\pi$
$7$	−516700.	−1.65998	−0.829988	+	0.557782i	$0.811653\pi$
$8$	491767.	0.663245
$9$	−1.33266e6	−0.835878
$10$	2.00582e6	0.634296
$11$	2.85439e6	0.485804	0.242902	−	0.970051i	$-0.421901\pi$
$11$	2.85439e6	0.485804	0.242902	+	0.970051i	$0.421901\pi$
$12$	−3.66604e6	−0.354421
$13$	1.15006e7	0.660827	0.330413	−	0.943836i	$-0.392812\pi$
$13$	1.15006e7	0.660827	0.330413	+	0.943836i	$0.392812\pi$
$14$	1.65440e7	0.587230
$15$	−3.20451e7	−0.726387
$16$	4.29649e7	0.640227
$17$	−8.05620e7	−0.809492	−0.404746	−	0.914429i	$-0.632640\pi$
$17$	−8.05620e7	−0.809492	−0.404746	+	0.914429i	$0.632640\pi$
$18$	4.26698e7	0.295699
$19$	−3.82250e8	−1.86401	−0.932007	−	0.362441i	$-0.881943\pi$
$19$	−3.82250e8	−1.86401	−0.932007	+	0.362441i	$0.881943\pi$
$20$	4.48969e8	1.56863
$21$	−2.64308e8	−0.672488
$22$	−9.13935e7	−0.171857
$23$	1.48036e8	0.208514
$23$	1.48036e8	0.208514
$24$	2.51553e8	0.268694
$25$	2.70376e9	2.21492
$26$	−3.68231e8	−0.233773
$27$	−1.49724e9	−0.743750
$28$	3.70310e9	1.45224
$29$	3.69952e9	1.15494	0.577469	−	0.816413i	$-0.304040\pi$
$29$	3.69952e9	1.15494	0.577469	+	0.816413i	$0.304040\pi$
$30$	1.02604e9	0.256965
$31$	−1.91754e9	−0.388055	−0.194028	−	0.980996i	$-0.562155\pi$
$31$	−1.91754e9	−0.388055	−0.194028	+	0.980996i	$0.562155\pi$
$32$	−5.40423e9	−0.889731
$33$	1.46011e9	0.196809
$34$	2.57948e9	0.286364
$35$	3.23690e10	2.97637
$36$	9.55093e9	0.731272
$37$	−9.74919e9	−0.624680	−0.312340	−	0.949970i	$-0.601113\pi$
$37$	−9.74919e9	−0.624680	−0.312340	+	0.949970i	$0.601113\pi$
$38$	1.22391e10	0.659410
$39$	5.88289e9	0.267714
$40$	−3.08070e10	−1.18921
$41$	−2.00398e10	−0.658867	−0.329434	−	0.944179i	$-0.606858\pi$
$41$	−2.00398e10	−0.658867	−0.329434	+	0.944179i	$0.606858\pi$
$42$	8.46275e9	0.237898
$43$	−3.06550e10	−0.739532	−0.369766	−	0.929125i	$-0.620562\pi$
$43$	−3.06550e10	−0.739532	−0.369766	+	0.929125i	$0.620562\pi$
$44$	−2.04569e10	−0.425008
$45$	8.34852e10	1.49875
$46$	−4.73989e9	−0.0737637
$47$	5.09263e10	0.689137	0.344569	−	0.938761i	$-0.388025\pi$
$47$	5.09263e10	0.689137	0.344569	+	0.938761i	$0.388025\pi$
$48$	2.19778e10	0.259368
$49$	1.70090e11	1.75552
$50$	−8.65706e10	−0.783547
$51$	−4.12099e10	−0.327941
$52$	−8.24224e10	−0.578128
$53$	−1.36451e11	−0.845636	−0.422818	−	0.906215i	$-0.638959\pi$
$53$	−1.36451e11	−0.845636	−0.422818	+	0.906215i	$0.638959\pi$
$54$	4.79394e10	0.263108
$55$	−1.78815e11	−0.871057
$56$	−2.54096e11	−1.10097
$57$	−1.95532e11	−0.755148
$58$	−1.18453e11	−0.408569
$59$	−4.59495e9	−0.0141822	−0.00709108	−	0.999975i	$-0.502257\pi$
$59$	−4.59495e9	−0.0141822	−0.00709108	+	0.999975i	$0.502257\pi$
$60$	2.29661e11	0.635484
$61$	−2.49239e11	−0.619400	−0.309700	−	0.950834i	$-0.600229\pi$
$61$	−2.49239e11	−0.619400	−0.309700	+	0.950834i	$0.600229\pi$
$62$	6.13968e10	0.137278
$63$	6.88586e11	1.38754
$64$	−1.78933e11	−0.325477
$65$	−7.20460e11	−1.18488
$66$	−4.67505e10	−0.0696227
$67$	4.16945e11	0.563110	0.281555	−	0.959545i	$-0.409150\pi$
$67$	4.16945e11	0.563110	0.281555	+	0.959545i	$0.409150\pi$
$68$	5.77373e11	0.708188
$69$	7.57248e10	0.0844732
$70$	−1.03641e12	−1.05292
$71$	−1.95420e12	−1.81047	−0.905234	−	0.424913i	$-0.860305\pi$
$71$	−1.95420e12	−1.81047	−0.905234	+	0.424913i	$0.860305\pi$
$72$	−6.55358e11	−0.554392
$73$	1.27673e12	0.987417	0.493709	−	0.869627i	$-0.335641\pi$
$73$	1.27673e12	0.987417	0.493709	+	0.869627i	$0.335641\pi$
$74$	3.12155e11	0.220986
$75$	1.38306e12	0.897308
$76$	2.73951e12	1.63074
$77$	−1.47487e12	−0.806423
$78$	−1.88361e11	−0.0947059
$79$	−1.18557e12	−0.548721	−0.274360	−	0.961627i	$-0.588466\pi$
$79$	−1.18557e12	−0.548721	−0.274360	+	0.961627i	$0.588466\pi$
$80$	−2.69156e12	−1.14794
$81$	1.35881e12	0.534571
$82$	6.41644e11	0.233080
$83$	1.35576e12	0.455173	0.227586	−	0.973758i	$-0.426917\pi$
$83$	1.35576e12	0.455173	0.227586	+	0.973758i	$0.426917\pi$
$84$	1.89424e12	0.588330
$85$	5.04685e12	1.45144
$86$	9.81529e11	0.261615
$87$	1.89242e12	0.467888
$88$	1.40370e12	0.322207
$89$	7.69900e12	1.64210	0.821049	−	0.570857i	$-0.193389\pi$
$89$	7.69900e12	1.64210	0.821049	+	0.570857i	$0.193389\pi$
$90$	−2.67308e12	−0.530194
$91$	−5.94235e12	−1.09696
$92$	−1.06095e12	−0.182420
$93$	−9.80880e11	−0.157209
$94$	−1.63058e12	−0.243788
$95$	2.39463e13	3.34221
$96$	−2.76442e12	−0.360447
$97$	−9.67989e12	−1.17992	−0.589962	−	0.807431i	$-0.700857\pi$
$97$	−9.67989e12	−1.17992	−0.589962	+	0.807431i	$0.700857\pi$
$98$	−5.44604e12	−0.621028
$99$	−3.80393e12	−0.406073
$100$	−1.93774e13	−1.93774
$101$	−1.19941e13	−1.12429	−0.562144	−	0.827039i	$-0.690023\pi$
$101$	−1.19941e13	−1.12429	−0.562144	+	0.827039i	$0.690023\pi$
$102$	1.31948e12	0.116012
$103$	−1.20863e12	−0.0997362	−0.0498681	−	0.998756i	$-0.515880\pi$
$103$	−1.20863e12	−0.0997362	−0.0498681	+	0.998756i	$0.515880\pi$
$104$	5.65560e12	0.438290
$105$	1.65577e13	1.20578
$106$	4.36896e12	0.299151
$107$	−4.92503e12	−0.317259	−0.158630	−	0.987338i	$-0.550708\pi$
$107$	−4.92503e12	−0.317259	−0.158630	+	0.987338i	$0.550708\pi$
$108$	1.07304e13	0.650673
$109$	6.21119e11	0.0354734	0.0177367	−	0.999843i	$-0.494354\pi$
$109$	6.21119e11	0.0354734	0.0177367	+	0.999843i	$0.494354\pi$
$110$	5.72540e12	0.308144
$111$	−4.98701e12	−0.253070
$112$	−2.22000e13	−1.06276
$113$	−2.15698e13	−0.974623	−0.487312	−	0.873228i	$-0.662022\pi$
$113$	−2.15698e13	−0.974623	−0.487312	+	0.873228i	$0.662022\pi$
$114$	6.26066e12	0.267140
$115$	−9.27379e12	−0.373871
$116$	−2.65138e13	−1.01040
$117$	−1.53263e13	−0.552371
$118$	1.47123e11	0.00501706
$119$	4.16264e13	1.34374
$120$	−1.57587e13	−0.481773
$121$	−2.63752e13	−0.763994
$122$	7.98026e12	0.219118
$123$	−1.02509e13	−0.266920
$124$	1.37427e13	0.339492
$125$	−9.29072e13	−2.17838
$126$	−2.20475e13	−0.490853
$127$	1.57930e13	0.333995	0.166998	−	0.985957i	$-0.446593\pi$
$127$	1.57930e13	0.333995	0.166998	+	0.985957i	$0.446593\pi$
$128$	5.00006e13	1.00487
$129$	−1.56810e13	−0.299599
$130$	2.30681e13	0.419159
$131$	1.03906e14	1.79629	0.898143	−	0.439703i	$-0.144916\pi$
$131$	1.03906e14	1.79629	0.898143	+	0.439703i	$0.144916\pi$
$132$	−1.04643e13	−0.172179
$133$	1.97509e14	3.09422
$134$	−1.33500e13	−0.199205
$135$	9.37954e13	1.33356
$136$	−3.96177e13	−0.536892
$137$	−3.27499e13	−0.423182	−0.211591	−	0.977358i	$-0.567864\pi$
$137$	−3.27499e13	−0.423182	−0.211591	+	0.977358i	$0.567864\pi$
$138$	−2.42460e12	−0.0298831
$139$	1.36060e14	1.60005	0.800025	−	0.599966i	$-0.204819\pi$
$139$	1.36060e14	1.60005	0.800025	+	0.599966i	$0.204819\pi$
$140$	−2.31983e14	−2.60389
$141$	2.60503e13	0.279183
$142$	6.25708e13	0.640468
$143$	3.28271e13	0.321032
$144$	−5.72576e13	−0.535152
$145$	−2.31759e14	−2.07083
$146$	−4.08791e13	−0.349307
$147$	8.70063e13	0.711194
$148$	6.98706e13	0.546504
$149$	−9.19889e13	−0.688691	−0.344346	−	0.938843i	$-0.611899\pi$
$149$	−9.19889e13	−0.688691	−0.344346	+	0.938843i	$0.611899\pi$
$150$	−4.42834e13	−0.317430
$151$	1.19372e14	0.819506	0.409753	−	0.912196i	$-0.365615\pi$
$151$	1.19372e14	0.819506	0.409753	+	0.912196i	$0.365615\pi$
$152$	−1.87978e14	−1.23630
$153$	1.07362e14	0.676636
$154$	4.72230e13	0.285279
$155$	1.20125e14	0.695791
$156$	−4.21616e13	−0.234211
$157$	3.52279e14	1.87732	0.938661	−	0.344842i	$-0.112067\pi$
$157$	3.52279e14	1.87732	0.938661	+	0.344842i	$0.112067\pi$
$158$	3.79602e13	0.194114
$159$	−6.97988e13	−0.342584
$160$	3.38551e14	1.59531
$161$	−7.64902e13	−0.346129
$162$	−4.35070e13	−0.189109
$163$	−1.08905e14	−0.454809	−0.227405	−	0.973800i	$-0.573024\pi$
$163$	−1.08905e14	−0.454809	−0.227405	+	0.973800i	$0.573024\pi$
$164$	1.43621e14	0.576413
$165$	−9.14693e13	−0.352882
$166$	−4.34095e13	−0.161021
$167$	−4.25908e14	−1.51935	−0.759677	−	0.650300i	$-0.774643\pi$
$167$	−4.25908e14	−1.51935	−0.759677	+	0.650300i	$0.774643\pi$
$168$	−1.29978e14	−0.446025
$169$	−1.70612e14	−0.563308
$170$	−1.61593e14	−0.513457
$171$	5.09409e14	1.55809
$172$	2.19699e14	0.646983
$173$	6.33486e13	0.179654	0.0898272	−	0.995957i	$-0.471369\pi$
$173$	6.33486e13	0.179654	0.0898272	+	0.995957i	$0.471369\pi$
$174$	−6.05924e13	−0.165519
$175$	−1.39704e15	−3.67672
$176$	1.22639e14	0.311025
$177$	−2.35045e12	−0.00574547
$178$	−2.46511e14	−0.580906
$179$	2.27033e14	0.515875	0.257937	−	0.966162i	$-0.416957\pi$
$179$	2.27033e14	0.515875	0.257937	+	0.966162i	$0.416957\pi$
$180$	−5.98323e14	−1.31119
$181$	2.30783e14	0.487857	0.243929	−	0.969793i	$-0.421564\pi$
$181$	2.30783e14	0.487857	0.243929	+	0.969793i	$0.421564\pi$
$182$	1.90265e14	0.388057
$183$	−1.27493e14	−0.250931
$184$	7.27991e13	0.138296
$185$	6.10744e14	1.12006
$186$	3.14063e13	0.0556139
$187$	−2.29956e14	−0.393254
$188$	−3.64979e14	−0.602895
$189$	7.73624e14	1.23461
$190$	−7.66724e14	−1.18234
$191$	−3.75613e14	−0.559788	−0.279894	−	0.960031i	$-0.590299\pi$
$191$	−3.75613e14	−0.559788	−0.279894	+	0.960031i	$0.590299\pi$
$192$	−9.15296e13	−0.131857
$193$	3.79143e14	0.528056	0.264028	−	0.964515i	$-0.414949\pi$
$193$	3.79143e14	0.528056	0.264028	+	0.964515i	$0.414949\pi$
$194$	3.09936e14	0.417408
$195$	−3.68537e14	−0.480016
$196$	−1.21901e15	−1.53582
$197$	2.98520e14	0.363867	0.181934	−	0.983311i	$-0.441764\pi$
$197$	2.98520e14	0.363867	0.181934	+	0.983311i	$0.441764\pi$
$198$	1.21796e14	0.143652
$199$	1.43180e15	1.63432	0.817159	−	0.576412i	$-0.195548\pi$
$199$	1.43180e15	1.63432	0.817159	+	0.576412i	$0.195548\pi$
$200$	1.32962e15	1.46904
$201$	2.13280e14	0.228127
$202$	3.84032e14	0.397726
$203$	−1.91155e15	−1.91717
$204$	2.95344e14	0.286901
$205$	1.25540e15	1.18136
$206$	3.86987e13	0.0352825
$207$	−1.97282e14	−0.174293
$208$	4.94121e14	0.423079
$209$	−1.09109e15	−0.905545
$210$	−5.30154e14	−0.426556
$211$	1.71864e15	1.34076	0.670378	−	0.742020i	$-0.266132\pi$
$211$	1.71864e15	1.34076	0.670378	+	0.742020i	$0.266132\pi$
$212$	9.77919e14	0.739809
$213$	−9.99635e14	−0.733456
$214$	1.57692e14	0.112233
$215$	1.92040e15	1.32600
$216$	−7.36293e14	−0.493289
$217$	9.90794e14	0.644162
$218$	−1.98873e13	−0.0125490
$219$	6.53086e14	0.400022
$220$	1.28153e15	0.762049
$221$	−9.26509e14	−0.534934
$222$	1.59677e14	0.0895255
$223$	−3.20442e15	−1.74489	−0.872446	−	0.488711i	$-0.837467\pi$
$223$	−3.20442e15	−1.74489	−0.872446	+	0.488711i	$0.837467\pi$
$224$	2.79237e15	1.47693
$225$	−3.60320e15	−1.85141
$226$	6.90634e14	0.344781
$227$	8.71567e14	0.422798	0.211399	−	0.977400i	$-0.432198\pi$
$227$	8.71567e14	0.422798	0.211399	+	0.977400i	$0.432198\pi$
$228$	1.40134e15	0.660645
$229$	7.20983e14	0.330365	0.165183	−	0.986263i	$-0.447179\pi$
$229$	7.20983e14	0.330365	0.165183	+	0.986263i	$0.447179\pi$
$230$	2.96933e14	0.132260
$231$	−7.54438e14	−0.326697
$232$	1.81930e15	0.766007
$233$	−5.97350e14	−0.244577	−0.122288	−	0.992495i	$-0.539023\pi$
$233$	−5.97350e14	−0.244577	−0.122288	+	0.992495i	$0.539023\pi$
$234$	4.90727e14	0.195406
$235$	−3.19030e15	−1.23564
$236$	3.29311e13	0.0124073
$237$	−6.06455e14	−0.222297
$238$	−1.33282e15	−0.475358
$239$	−3.68853e15	−1.28017	−0.640085	−	0.768304i	$-0.721101\pi$
$239$	−3.68853e15	−1.28017	−0.640085	+	0.768304i	$0.721101\pi$
$240$	−1.37681e15	−0.465053
$241$	5.85513e15	1.92498	0.962489	−	0.271319i	$-0.0874600\pi$
$241$	5.85513e15	1.92498	0.962489	+	0.271319i	$0.0874600\pi$
$242$	8.44494e14	0.270269
$243$	3.08215e15	0.960315
$244$	1.78625e15	0.541886
$245$	−1.06554e16	−3.14768
$246$	3.28220e14	0.0944251
$247$	−4.39609e15	−1.23179
$248$	−9.42983e14	−0.257376
$249$	6.93513e14	0.184399
$250$	2.97475e15	0.770621
$251$	−7.72967e13	−0.0195111	−0.00975555	−	0.999952i	$-0.503105\pi$
$251$	−7.72967e13	−0.0195111	−0.00975555	+	0.999952i	$0.503105\pi$
$252$	−4.93497e15	−1.21389
$253$	4.22553e14	0.101297
$254$	−5.05669e14	−0.118154
$255$	2.58162e15	0.588005
$256$	−1.35127e14	−0.0300041
$257$	−5.40278e15	−1.16964	−0.584820	−	0.811163i	$-0.698835\pi$
$257$	−5.40278e15	−1.16964	−0.584820	+	0.811163i	$0.698835\pi$
$258$	5.02082e14	0.105985
$259$	5.03741e15	1.03695
$260$	5.16340e15	1.03659
$261$	−4.93021e15	−0.965388
$262$	−3.32691e15	−0.635451
$263$	−4.51997e15	−0.842216	−0.421108	−	0.907011i	$-0.638359\pi$
$263$	−4.51997e15	−0.842216	−0.421108	+	0.907011i	$0.638359\pi$
$264$	7.18032e14	0.130532
$265$	8.54805e15	1.51624
$266$	−6.32394e15	−1.09460
$267$	3.93827e15	0.665246
$268$	−2.98817e15	−0.492639
$269$	−3.30186e14	−0.0531336	−0.0265668	−	0.999647i	$-0.508457\pi$
$269$	−3.30186e14	−0.0531336	−0.0265668	+	0.999647i	$0.508457\pi$
$270$	−3.00319e15	−0.471757
$271$	6.69790e15	1.02716	0.513580	−	0.858042i	$-0.328319\pi$
$271$	6.69790e15	1.02716	0.513580	+	0.858042i	$0.328319\pi$
$272$	−3.46134e15	−0.518258
$273$	−3.03969e15	−0.444398
$274$	1.04861e15	0.149704
$275$	7.71760e15	1.07602
$276$	−5.42706e14	−0.0739018
$277$	−1.06589e16	−1.41773	−0.708863	−	0.705346i	$-0.750792\pi$
$277$	−1.06589e16	−1.41773	−0.708863	+	0.705346i	$0.750792\pi$
$278$	−4.35644e15	−0.566031
$279$	2.55543e15	0.324367
$280$	1.59180e16	1.97406
$281$	−1.50104e16	−1.81886	−0.909432	−	0.415853i	$-0.863483\pi$
$281$	−1.50104e16	−1.81886	−0.909432	+	0.415853i	$0.863483\pi$
$282$	−8.34093e14	−0.0987632
$283$	1.16727e16	1.35071	0.675353	−	0.737495i	$-0.263991\pi$
$283$	1.16727e16	1.35071	0.675353	+	0.737495i	$0.263991\pi$
$284$	1.40054e16	1.58390
$285$	1.22492e16	1.35400
$286$	−1.05108e15	−0.113568
$287$	1.03546e16	1.09370
$288$	7.20200e15	0.743707
$289$	−3.41434e15	−0.344723
$290$	7.42057e15	0.732572
$291$	−4.95155e15	−0.478010
$292$	−9.15009e15	−0.863847
$293$	6.60463e15	0.609830	0.304915	−	0.952380i	$-0.401372\pi$
$293$	6.60463e15	0.609830	0.304915	+	0.952380i	$0.401372\pi$
$294$	−2.78581e15	−0.251591
$295$	2.87853e14	0.0254289
$296$	−4.79433e15	−0.414316
$297$	−4.27371e15	−0.361317
$298$	2.94535e15	0.243630
$299$	1.70250e15	0.137792
$300$	−9.91211e15	−0.785015
$301$	1.58395e16	1.22760
$302$	−3.82212e15	−0.289907
$303$	−6.13532e15	−0.455471
$304$	−1.64233e16	−1.19339
$305$	1.56137e16	1.11060
$306$	−3.43757e15	−0.239366
$307$	−1.06953e16	−0.729110	−0.364555	−	0.931182i	$-0.618779\pi$
$307$	−1.06953e16	−0.729110	−0.364555	+	0.931182i	$0.618779\pi$
$308$	1.05701e16	0.705503
$309$	−6.18252e14	−0.0404051
$310$	−3.84624e15	−0.246142
$311$	−2.46294e16	−1.54351	−0.771757	−	0.635917i	$-0.780622\pi$
$311$	−2.46294e16	−1.54351	−0.771757	+	0.635917i	$0.780622\pi$
$312$	2.89301e15	0.177560
$313$	3.09147e16	1.85835	0.929175	−	0.369641i	$-0.120519\pi$
$313$	3.09147e16	1.85835	0.929175	+	0.369641i	$0.120519\pi$
$314$	−1.12794e16	−0.664118
$315$	−4.31369e16	−2.48788
$316$	8.49676e15	0.480051
$317$	7.77912e15	0.430571	0.215286	−	0.976551i	$-0.430932\pi$
$317$	7.77912e15	0.430571	0.215286	+	0.976551i	$0.430932\pi$
$318$	2.23485e15	0.121192
$319$	1.05599e16	0.561074
$320$	1.12094e16	0.583587
$321$	−2.51930e15	−0.128528
$322$	2.44910e15	0.122446
$323$	3.07948e16	1.50890
$324$	−9.73832e15	−0.467672
$325$	3.10948e16	1.46368
$326$	3.48699e15	0.160893
$327$	3.17721e14	0.0143710
$328$	−9.85489e15	−0.436990
$329$	−2.63136e16	−1.14395
$330$	2.92871e15	0.124835
$331$	−2.83019e16	−1.18286	−0.591431	−	0.806356i	$-0.701437\pi$
$331$	−2.83019e16	−1.18286	−0.591431	+	0.806356i	$0.701437\pi$
$332$	−9.71650e15	−0.398210
$333$	1.29924e16	0.522156
$334$	1.36370e16	0.537484
$335$	−2.61198e16	−1.00967
$336$	−1.13560e16	−0.430545
$337$	3.46570e16	1.28883	0.644416	−	0.764675i	$-0.277101\pi$
$337$	3.46570e16	1.28883	0.644416	+	0.764675i	$0.277101\pi$
$338$	5.46275e15	0.199275
$339$	−1.10336e16	−0.394839
$340$	−3.61699e16	−1.26980
$341$	−5.47341e15	−0.188519
$342$	−1.63105e16	−0.551186
$343$	−3.78231e16	−1.25414
$344$	−1.50751e16	−0.490491
$345$	−4.74382e15	−0.151462
$346$	−2.02833e15	−0.0635542
$347$	−2.26774e16	−0.697353	−0.348676	−	0.937243i	$-0.613369\pi$
$347$	−2.26774e16	−0.697353	−0.348676	+	0.937243i	$0.613369\pi$
$348$	−1.35626e16	−0.409334
$349$	−4.93290e16	−1.46129	−0.730646	−	0.682756i	$-0.760781\pi$
$349$	−4.93290e16	−1.46129	−0.730646	+	0.682756i	$0.760781\pi$
$350$	4.47310e16	1.30067
$351$	−1.72191e16	−0.491490
$352$	−1.54258e16	−0.432235
$353$	3.83604e16	1.05523	0.527615	−	0.849484i	$-0.323086\pi$
$353$	3.83604e16	1.05523	0.527615	+	0.849484i	$0.323086\pi$
$354$	7.52581e13	0.00203251
$355$	1.22422e17	3.24621
$356$	−5.51773e16	−1.43660
$357$	2.12932e16	0.544373
$358$	−7.26926e15	−0.182495
$359$	−4.24811e16	−1.04733	−0.523663	−	0.851926i	$-0.675435\pi$
$359$	−4.24811e16	−1.04733	−0.523663	+	0.851926i	$0.675435\pi$
$360$	4.10553e16	0.994037
$361$	1.04062e17	2.47455
$362$	−7.38932e15	−0.172583
$363$	−1.34917e16	−0.309509
$364$	4.25877e16	0.959677
$365$	−7.99815e16	−1.77046
$366$	4.08214e15	0.0887689
$367$	2.44935e15	0.0523265	0.0261633	−	0.999658i	$-0.491671\pi$
$367$	2.44935e15	0.0523265	0.0261633	+	0.999658i	$0.491671\pi$
$368$	6.36035e15	0.133496
$369$	2.67062e16	0.550733
$370$	−1.95551e16	−0.396232
$371$	7.05043e16	1.40373
$372$	7.02978e15	0.137535
$373$	−1.96267e16	−0.377346	−0.188673	−	0.982040i	$-0.560419\pi$
$373$	−1.96267e16	−0.377346	−0.188673	+	0.982040i	$0.560419\pi$
$374$	7.36284e15	0.139117
$375$	−4.75248e16	−0.882505
$376$	2.50438e16	0.457067
$377$	4.25466e16	0.763214
$378$	−2.47703e16	−0.436752
$379$	−4.56625e16	−0.791416	−0.395708	−	0.918376i	$-0.629501\pi$
$379$	−4.56625e16	−0.791416	−0.395708	+	0.918376i	$0.629501\pi$
$380$	−1.71618e17	−2.92395
$381$	8.07859e15	0.135308
$382$	1.20266e16	0.198030
$383$	−5.21651e16	−0.844478	−0.422239	−	0.906485i	$-0.638756\pi$
$383$	−5.21651e16	−0.844478	−0.422239	+	0.906485i	$0.638756\pi$
$384$	2.55768e16	0.407093
$385$	9.23938e16	1.44593
$386$	−1.21396e16	−0.186804
$387$	4.08527e16	0.618159
$388$	6.93739e16	1.03226
$389$	2.68501e16	0.392892	0.196446	−	0.980515i	$-0.437060\pi$
$389$	2.68501e16	0.392892	0.196446	+	0.980515i	$0.437060\pi$
$390$	1.18000e16	0.169810
$391$	−1.19261e16	−0.168791
$392$	8.36447e16	1.16434
$393$	5.31508e16	0.727710
$394$	−9.55818e15	−0.128721
$395$	7.42707e16	0.983867
$396$	2.72621e16	0.355255
$397$	−1.39302e17	−1.78574	−0.892870	−	0.450314i	$-0.851312\pi$
$397$	−1.39302e17	−1.78574	−0.892870	+	0.450314i	$0.851312\pi$
$398$	−4.58441e16	−0.578154
$399$	1.01032e17	1.25353
$400$	1.16167e17	1.41805
$401$	1.03506e16	0.124316	0.0621578	−	0.998066i	$-0.480202\pi$
$401$	1.03506e16	0.124316	0.0621578	+	0.998066i	$0.480202\pi$
$402$	−6.82892e15	−0.0807017
$403$	−2.20528e16	−0.256437
$404$	8.59592e16	0.983589
$405$	−8.51233e16	−0.958497
$406$	6.12049e16	0.678214
$407$	−2.78280e16	−0.303472
$408$	−2.02657e16	−0.217505
$409$	1.04252e16	0.110125	0.0550623	−	0.998483i	$-0.482464\pi$
$409$	1.04252e16	0.110125	0.0550623	+	0.998483i	$0.482464\pi$
$410$	−4.01962e16	−0.417917
$411$	−1.67526e16	−0.171439
$412$	8.66205e15	0.0872547
$413$	2.37421e15	0.0235420
$414$	6.31666e15	0.0616575
$415$	−8.49325e16	−0.816134
$416$	−6.21517e16	−0.587958
$417$	6.95987e16	0.648211
$418$	3.49351e16	0.320344
$419$	−9.75000e16	−0.880265	−0.440133	−	0.897933i	$-0.645069\pi$
$419$	−9.75000e16	−0.880265	−0.440133	+	0.897933i	$0.645069\pi$
$420$	−1.18666e17	−1.05489
$421$	5.78052e16	0.505980	0.252990	−	0.967469i	$-0.418586\pi$
$421$	5.78052e16	0.505980	0.252990	+	0.967469i	$0.418586\pi$
$422$	−5.50285e16	−0.474304
$423$	−6.78674e16	−0.576035
$424$	−6.71020e16	−0.560864
$425$	−2.17821e17	−1.79296
$426$	3.20068e16	0.259466
$427$	1.28782e17	1.02819
$428$	3.52968e16	0.277556
$429$	1.67921e16	0.130056
$430$	−6.14885e16	−0.469082
$431$	−3.46127e16	−0.260095	−0.130048	−	0.991508i	$-0.541513\pi$
$431$	−3.46127e16	−0.260095	−0.130048	+	0.991508i	$0.541513\pi$
$432$	−6.43287e16	−0.476169
$433$	2.26499e17	1.65156	0.825781	−	0.563991i	$-0.190735\pi$
$433$	2.26499e17	1.65156	0.825781	+	0.563991i	$0.190735\pi$
$434$	−3.17238e16	−0.227878
$435$	−1.18552e17	−0.838933
$436$	−4.45144e15	−0.0310341
$437$	−5.65867e16	−0.388674
$438$	−2.09109e16	−0.141511
$439$	−1.51805e17	−1.01220	−0.506102	−	0.862474i	$-0.668914\pi$
$439$	−1.51805e17	−1.01220	−0.506102	+	0.862474i	$0.668914\pi$
$440$	−8.79353e16	−0.577724
$441$	−2.26673e17	−1.46740
$442$	2.96655e16	0.189237
$443$	6.50527e16	0.408922	0.204461	−	0.978875i	$-0.434456\pi$
$443$	6.50527e16	0.408922	0.204461	+	0.978875i	$0.434456\pi$
$444$	3.57409e16	0.221399
$445$	−4.82308e17	−2.94432
$446$	1.02601e17	0.617270
$447$	−4.70551e16	−0.279002
$448$	9.24547e16	0.540284
$449$	2.38710e17	1.37490	0.687448	−	0.726234i	$-0.258731\pi$
$449$	2.38710e17	1.37490	0.687448	+	0.726234i	$0.258731\pi$
$450$	1.15369e17	0.654950
$451$	−5.72014e16	−0.320080
$452$	1.54587e17	0.852654
$453$	6.10624e16	0.331998
$454$	−2.79063e16	−0.149568
$455$	3.72262e17	1.96686
$456$	−9.61563e16	−0.500848
$457$	−7.50478e16	−0.385374	−0.192687	−	0.981260i	$-0.561720\pi$
$457$	−7.50478e16	−0.385374	−0.192687	+	0.981260i	$0.561720\pi$
$458$	−2.30848e16	−0.116869
$459$	1.20621e17	0.602059
$460$	6.64635e16	0.327083
$461$	1.84833e17	0.896857	0.448428	−	0.893819i	$-0.351984\pi$
$461$	1.84833e17	0.896857	0.448428	+	0.893819i	$0.351984\pi$
$462$	2.41560e16	0.115572
$463$	1.44950e17	0.683819	0.341909	−	0.939733i	$-0.388926\pi$
$463$	1.44950e17	0.683819	0.341909	+	0.939733i	$0.388926\pi$
$464$	1.58950e17	0.739422
$465$	6.14478e16	0.281878
$466$	1.91263e16	0.0865211
$467$	8.64140e16	0.385500	0.192750	−	0.981248i	$-0.438259\pi$
$467$	8.64140e16	0.385500	0.192750	+	0.981248i	$0.438259\pi$
$468$	1.09841e17	0.483244
$469$	−2.15436e17	−0.934748
$470$	1.02149e17	0.437117
$471$	1.80201e17	0.760539
$472$	−2.25964e15	−0.00940625
$473$	−8.75015e16	−0.359268
$474$	1.94178e16	0.0786395
$475$	−1.03351e18	−4.12865
$476$	−2.98329e17	−1.17557
$477$	1.81843e17	0.706849
$478$	1.18101e17	0.452870
$479$	−1.60626e17	−0.607625	−0.303812	−	0.952732i	$-0.598260\pi$
$479$	−1.60626e17	−0.607625	−0.303812	+	0.952732i	$0.598260\pi$
$480$	1.73179e17	0.646289
$481$	−1.12121e17	−0.412805
$482$	−1.87473e17	−0.680977
$483$	−3.91270e16	−0.140223
$484$	1.89026e17	0.668384
$485$	6.06402e17	2.11563
$486$	−9.86861e16	−0.339719
$487$	−9.60789e14	−0.00326355	−0.00163177	−	0.999999i	$-0.500519\pi$
$487$	−9.60789e14	−0.00326355	−0.00163177	+	0.999999i	$0.500519\pi$
$488$	−1.22567e17	−0.410814
$489$	−5.57083e16	−0.184252
$490$	3.41170e17	1.11352
$491$	−4.20283e17	−1.35367	−0.676835	−	0.736135i	$-0.736649\pi$
$491$	−4.20283e17	−1.35367	−0.676835	+	0.736135i	$0.736649\pi$
$492$	7.34666e16	0.233516
$493$	−2.98041e17	−0.934913
$494$	1.40756e17	0.435756
$495$	2.38300e17	0.728098
$496$	−8.23869e16	−0.248443
$497$	1.00974e18	3.00533
$498$	−2.22053e16	−0.0652327
$499$	−1.72288e17	−0.499576	−0.249788	−	0.968301i	$-0.580361\pi$
$499$	−1.72288e17	−0.499576	−0.249788	+	0.968301i	$0.580361\pi$
$500$	6.65848e17	1.90577
$501$	−2.17865e17	−0.615520
$502$	2.47493e15	0.00690221
$503$	1.59288e17	0.438523	0.219261	−	0.975666i	$-0.429635\pi$
$503$	1.59288e17	0.438523	0.219261	+	0.975666i	$0.429635\pi$
$504$	3.38624e17	0.920278
$505$	7.51375e17	2.01587
$506$	−1.35295e16	−0.0358347
$507$	−8.72732e16	−0.228207
$508$	−1.13185e17	−0.292198
$509$	−4.66557e17	−1.18916	−0.594579	−	0.804037i	$-0.702681\pi$
$509$	−4.66557e17	−1.18916	−0.594579	+	0.804037i	$0.702681\pi$
$510$	−8.26596e16	−0.208011
$511$	−6.59687e17	−1.63909
$512$	−4.05278e17	−0.994257
$513$	5.72320e17	1.38636
$514$	1.72989e17	0.413770
$515$	7.57155e16	0.178829
$516$	1.12383e17	0.262105
$517$	1.45364e17	0.334786
$518$	−1.61291e17	−0.366831
$519$	3.24047e16	0.0727814
$520$	−3.54298e17	−0.785863
$521$	−1.47020e17	−0.322055	−0.161028	−	0.986950i	$-0.551481\pi$
$521$	−1.47020e17	−0.322055	−0.161028	+	0.986950i	$0.551481\pi$
$522$	1.57858e17	0.341514
$523$	−3.08717e17	−0.659630	−0.329815	−	0.944046i	$-0.606986\pi$
$523$	−3.08717e17	−0.659630	−0.329815	+	0.944046i	$0.606986\pi$
$524$	−7.44672e17	−1.57149
$525$	−7.14626e17	−1.48951
$526$	1.44723e17	0.297941
$527$	1.54481e17	0.314127
$528$	6.27334e16	0.126002
$529$	2.19146e16	0.0434783
$530$	−2.73696e17	−0.536383
$531$	6.12350e15	0.0118546
$532$	−1.41551e18	−2.70699
$533$	−2.30469e17	−0.435397
$534$	−1.26098e17	−0.235336
$535$	3.08531e17	0.568852
$536$	2.05040e17	0.373480
$537$	1.16134e17	0.208991
$538$	1.05721e16	0.0187964
$539$	4.85505e17	0.852838
$540$	−6.72214e17	−1.16667
$541$	7.35026e17	1.26044	0.630218	−	0.776418i	$-0.282966\pi$
$541$	7.35026e17	1.26044	0.630218	+	0.776418i	$0.282966\pi$
$542$	−2.14457e17	−0.363366
$543$	1.18052e17	0.197640
$544$	4.35375e17	0.720230
$545$	−3.89103e16	−0.0636045
$546$	9.73264e16	0.157209
$547$	3.22910e16	0.0515423	0.0257712	−	0.999668i	$-0.491796\pi$
$547$	3.22910e16	0.0515423	0.0257712	+	0.999668i	$0.491796\pi$
$548$	2.34713e17	0.370223
$549$	3.32150e17	0.517743
$550$	−2.47106e17	−0.380651
$551$	−1.41414e18	−2.15282
$552$	3.72389e16	0.0560265
$553$	6.12585e17	0.910862
$554$	3.41281e17	0.501532
$555$	3.12414e17	0.453760
$556$	−9.75115e17	−1.39981
$557$	2.80391e17	0.397837	0.198918	−	0.980016i	$-0.436257\pi$
$557$	2.80391e17	0.397837	0.198918	+	0.980016i	$0.436257\pi$
$558$	−8.18211e16	−0.114747
$559$	−3.52550e17	−0.488702
$560$	1.39073e18	1.90555
$561$	−1.17629e17	−0.159315
$562$	4.80610e17	0.643438
$563$	5.71018e16	0.0755693	0.0377847	−	0.999286i	$-0.487970\pi$
$563$	5.71018e16	0.0755693	0.0377847	+	0.999286i	$0.487970\pi$
$564$	−1.86698e17	−0.244245
$565$	1.35125e18	1.74752
$566$	−3.73744e17	−0.477823
$567$	−7.02096e17	−0.887374
$568$	−9.61013e17	−1.20078
$569$	−9.13946e17	−1.12899	−0.564496	−	0.825436i	$-0.690929\pi$
$569$	−9.13946e17	−1.12899	−0.564496	+	0.825436i	$0.690929\pi$
$570$	−3.92202e17	−0.478987
$571$	−6.83601e17	−0.825406	−0.412703	−	0.910866i	$-0.635415\pi$
$571$	−6.83601e17	−0.825406	−0.412703	+	0.910866i	$0.635415\pi$
$572$	−2.35266e17	−0.280857
$573$	−1.92137e17	−0.226781
$574$	−3.31538e17	−0.386906
$575$	4.00254e17	0.461843
$576$	2.38457e17	0.272059
$577$	9.14491e16	0.103166	0.0515830	−	0.998669i	$-0.483573\pi$
$577$	9.14491e16	0.103166	0.0515830	+	0.998669i	$0.483573\pi$
$578$	1.09322e17	0.121949
$579$	1.93943e17	0.213926
$580$	1.66097e18	1.81167
$581$	−7.00523e17	−0.755575
$582$	1.58541e17	0.169100
$583$	−3.89485e17	−0.410814
$584$	6.27854e17	0.654900
$585$	9.60128e17	0.990412
$586$	−2.11470e17	−0.215732
$587$	1.06378e18	1.07325	0.536627	−	0.843820i	$-0.319698\pi$
$587$	1.06378e18	1.07325	0.536627	+	0.843820i	$0.319698\pi$
$588$	−6.23558e17	−0.622192
$589$	7.32980e17	0.723340
$590$	−9.21663e15	−0.00899568
$591$	1.52702e17	0.147410
$592$	−4.18873e17	−0.399937
$593$	−1.56887e17	−0.148161	−0.0740803	−	0.997252i	$-0.523602\pi$
$593$	−1.56887e17	−0.148161	−0.0740803	+	0.997252i	$0.523602\pi$
$594$	1.36838e17	0.127819
$595$	−2.60771e18	−2.40935
$596$	6.59267e17	0.602505
$597$	7.32408e17	0.662094
$598$	−5.45115e16	−0.0487450
$599$	8.92458e17	0.789429	0.394715	−	0.918804i	$-0.370843\pi$
$599$	8.92458e17	0.789429	0.394715	+	0.918804i	$0.370843\pi$
$600$	6.80141e17	0.595136
$601$	1.11807e18	0.967795	0.483898	−	0.875125i	$-0.339221\pi$
$601$	1.11807e18	0.967795	0.483898	+	0.875125i	$0.339221\pi$
$602$	−5.07157e17	−0.434275
$603$	−5.55647e17	−0.470691
$604$	−8.55517e17	−0.716949
$605$	1.65229e18	1.36986
$606$	1.96444e17	0.161126
$607$	9.15812e17	0.743156	0.371578	−	0.928402i	$-0.378817\pi$
$607$	9.15812e17	0.743156	0.371578	+	0.928402i	$0.378817\pi$
$608$	2.06576e18	1.65847
$609$	−9.77813e17	−0.776682
$610$	−4.99928e17	−0.392883
$611$	5.85681e17	0.455400
$612$	−7.69442e17	−0.591959
$613$	−9.19606e17	−0.700017	−0.350009	−	0.936747i	$-0.613821\pi$
$613$	−9.19606e17	−0.700017	−0.350009	+	0.936747i	$0.613821\pi$
$614$	3.42447e17	0.257929
$615$	6.42176e17	0.478593
$616$	−7.25290e17	−0.534856
$617$	2.12536e18	1.55088	0.775441	−	0.631420i	$-0.217528\pi$
$617$	2.12536e18	1.55088	0.775441	+	0.631420i	$0.217528\pi$
$618$	1.97955e16	0.0142936
$619$	2.29975e17	0.164321	0.0821603	−	0.996619i	$-0.473818\pi$
$619$	2.29975e17	0.164321	0.0821603	+	0.996619i	$0.473818\pi$
$620$	−8.60916e17	−0.608716
$621$	−2.21645e17	−0.155083
$622$	7.88596e17	0.546031
$623$	−3.97808e18	−2.72584
$624$	2.52758e17	0.171397
$625$	2.51973e18	1.69096
$626$	−9.89845e17	−0.657406
$627$	−5.58126e17	−0.366854
$628$	−2.52472e18	−1.64238
$629$	7.85415e17	0.505673
$630$	1.38118e18	0.880109
$631$	−1.22318e16	−0.00771435	−0.00385717	−	0.999993i	$-0.501228\pi$
$631$	−1.22318e16	−0.00771435	−0.00385717	+	0.999993i	$0.501228\pi$
$632$	−5.83024e17	−0.363936
$633$	8.79138e17	0.543166
$634$	−2.49076e17	−0.152318
$635$	−9.89361e17	−0.598861
$636$	5.00235e17	0.299711
$637$	1.95614e18	1.16009
$638$	−3.38112e17	−0.198484
$639$	2.60429e18	1.51333
$640$	−3.13232e18	−1.80175
$641$	9.38815e17	0.534568	0.267284	−	0.963618i	$-0.413874\pi$
$641$	9.38815e17	0.534568	0.267284	+	0.963618i	$0.413874\pi$
$642$	8.06643e16	0.0454678
$643$	−9.83813e17	−0.548960	−0.274480	−	0.961593i	$-0.588506\pi$
$643$	−9.83813e17	−0.548960	−0.274480	+	0.961593i	$0.588506\pi$
$644$	5.48191e17	0.302812
$645$	9.82344e17	0.537187
$646$	−9.86005e17	−0.533787
$647$	8.38861e17	0.449585	0.224793	−	0.974407i	$-0.427830\pi$
$647$	8.38861e17	0.449585	0.224793	+	0.974407i	$0.427830\pi$
$648$	6.68216e17	0.354552
$649$	−1.31158e16	−0.00688975
$650$	−9.95611e17	−0.517789
$651$	5.06821e17	0.260962
$652$	7.80504e17	0.397892
$653$	2.92986e18	1.47881	0.739403	−	0.673263i	$-0.235108\pi$
$653$	2.92986e18	1.47881	0.739403	+	0.673263i	$0.235108\pi$
$654$	−1.01730e16	−0.00508384
$655$	−6.50923e18	−3.22078
$656$	−8.61007e17	−0.421824
$657$	−1.70145e18	−0.825361
$658$	8.42524e17	0.404682
$659$	1.81390e18	0.862697	0.431349	−	0.902185i	$-0.358038\pi$
$659$	1.81390e18	0.862697	0.431349	+	0.902185i	$0.358038\pi$
$660$	6.55543e17	0.308721
$661$	−1.99014e17	−0.0928056	−0.0464028	−	0.998923i	$-0.514776\pi$
$661$	−1.99014e17	−0.0928056	−0.0464028	+	0.998923i	$0.514776\pi$
$662$	9.06186e17	0.418447
$663$	−4.73937e17	−0.216712
$664$	6.66719e17	0.301891
$665$	−1.23730e19	−5.54799
$666$	−4.15996e17	−0.184717
$667$	5.47662e17	0.240821
$668$	3.05241e18	1.32922
$669$	−1.63916e18	−0.706889
$670$	8.36317e17	0.357178
$671$	−7.11425e17	−0.300907
$672$	1.42838e18	0.598333
$673$	−1.08637e18	−0.450691	−0.225345	−	0.974279i	$-0.572351\pi$
$673$	−1.08637e18	−0.450691	−0.225345	+	0.974279i	$0.572351\pi$
$674$	−1.10967e18	−0.455935
$675$	−4.04818e18	−1.64735
$676$	1.22274e18	0.492813
$677$	−4.22974e18	−1.68845	−0.844223	−	0.535993i	$-0.819937\pi$
$677$	−4.22974e18	−1.68845	−0.844223	+	0.535993i	$0.819937\pi$
$678$	3.53280e17	0.139677
$679$	5.00160e18	1.95864
$680$	2.48187e18	0.962658
$681$	4.45833e17	0.171284
$682$	1.75251e17	0.0666901
$683$	2.44790e18	0.922697	0.461349	−	0.887219i	$-0.347366\pi$
$683$	2.44790e18	0.922697	0.461349	+	0.887219i	$0.347366\pi$
$684$	−3.65084e18	−1.36310
$685$	2.05164e18	0.758773
$686$	1.21104e18	0.443662
$687$	3.68805e17	0.133837
$688$	−1.31709e18	−0.473468
$689$	−1.56926e18	−0.558819
$690$	1.51890e17	0.0535810
$691$	−1.62419e18	−0.567583	−0.283791	−	0.958886i	$-0.591592\pi$
$691$	−1.62419e18	−0.567583	−0.283791	+	0.958886i	$0.591592\pi$
$692$	−4.54008e17	−0.157171
$693$	1.96549e18	0.674071
$694$	7.26098e17	0.246694
$695$	−8.52354e18	−2.86892
$696$	9.30628e17	0.310324
$697$	1.61444e18	0.533347
$698$	1.57944e18	0.516944
$699$	−3.05562e17	−0.0990828
$700$	1.00123e19	3.21660
$701$	−9.62866e17	−0.306478	−0.153239	−	0.988189i	$-0.548970\pi$
$701$	−9.62866e17	−0.306478	−0.153239	+	0.988189i	$0.548970\pi$
$702$	5.51331e17	0.173868
$703$	3.72663e18	1.16441
$704$	−5.10745e17	−0.158118
$705$	−1.63194e18	−0.500581
$706$	−1.22824e18	−0.373296
$707$	6.19734e18	1.86629
$708$	1.68453e16	0.00502645
$709$	−3.29145e18	−0.973165	−0.486583	−	0.873635i	$-0.661757\pi$
$709$	−3.29145e18	−0.973165	−0.486583	+	0.873635i	$0.661757\pi$
$710$	−3.91978e18	−1.14837
$711$	1.57996e18	0.458664
$712$	3.78611e18	1.08911
$713$	−2.83865e17	−0.0809151
$714$	−6.81776e17	−0.192577
$715$	−2.05647e18	−0.575618
$716$	−1.62710e18	−0.451315
$717$	−1.88680e18	−0.518621
$718$	1.36018e18	0.370500
$719$	9.12365e17	0.246281	0.123140	−	0.992389i	$-0.460703\pi$
$719$	9.12365e17	0.246281	0.123140	+	0.992389i	$0.460703\pi$
$720$	3.58693e18	0.959538
$721$	6.24501e17	0.165560
$722$	−3.33191e18	−0.875391
$723$	2.99508e18	0.779846
$724$	−1.65398e18	−0.426804
$725$	1.00026e19	2.55810
$726$	4.31984e17	0.109491
$727$	4.79816e18	1.20532	0.602658	−	0.798000i	$-0.294108\pi$
$727$	4.79816e18	1.20532	0.602658	+	0.798000i	$0.294108\pi$
$728$	−2.92225e18	−0.727551
$729$	−5.89763e17	−0.145529
$730$	2.56089e18	0.626315
$731$	2.46963e18	0.598645
$732$	9.13719e17	0.219528
$733$	1.52244e18	0.362548	0.181274	−	0.983433i	$-0.441978\pi$
$733$	1.52244e18	0.362548	0.181274	+	0.983433i	$0.441978\pi$
$734$	−7.84247e16	−0.0185109
$735$	−5.45056e18	−1.27519
$736$	−8.00019e17	−0.185522
$737$	1.19013e18	0.273561
$738$	−8.55094e17	−0.194826
$739$	−2.54897e15	−0.000575674 0	−0.000287837	−	1.00000i	$-0.500092\pi$
$739$	−2.54897e15	−0.000575674 0	−0.000287837		1.00000i	$0.500092\pi$
$740$	−4.37709e18	−0.979894
$741$	−2.24873e18	−0.499022
$742$	−2.25744e18	−0.496583
$743$	3.37469e18	0.735880	0.367940	−	0.929850i	$-0.380063\pi$
$743$	3.37469e18	0.735880	0.367940	+	0.929850i	$0.380063\pi$
$744$	−4.82364e17	−0.104268
$745$	5.76270e18	1.23484
$746$	6.28418e17	0.133489
$747$	−1.80677e18	−0.380469
$748$	1.64805e18	0.344041
$749$	2.54476e18	0.526642
$750$	1.52167e18	0.312193
$751$	−8.39300e18	−1.70709	−0.853547	−	0.521016i	$-0.825553\pi$
$751$	−8.39300e18	−1.70709	−0.853547	+	0.521016i	$0.825553\pi$
$752$	2.18804e18	0.441204
$753$	−3.95396e16	−0.00790432
$754$	−1.36228e18	−0.269993
$755$	−7.47813e18	−1.46939
$756$	−5.54442e18	−1.08010
$757$	−5.75060e17	−0.111068	−0.0555341	−	0.998457i	$-0.517686\pi$
$757$	−5.75060e17	−0.111068	−0.0555341	+	0.998457i	$0.517686\pi$
$758$	1.46205e18	0.279970
$759$	2.16148e17	0.0410374
$760$	1.17760e19	2.21671
$761$	−2.08311e17	−0.0388788	−0.0194394	−	0.999811i	$-0.506188\pi$
$761$	−2.08311e17	−0.0388788	−0.0194394	+	0.999811i	$0.506188\pi$
$762$	−2.58665e17	−0.0478663
$763$	−3.20932e17	−0.0588849
$764$	2.69195e18	0.489734
$765$	−6.72574e18	−1.21322
$766$	1.67025e18	0.298741
$767$	−5.28445e16	−0.00937195
$768$	−6.91213e16	−0.0121553
$769$	4.57108e18	0.797071	0.398536	−	0.917153i	$-0.369519\pi$
$769$	4.57108e18	0.797071	0.398536	+	0.917153i	$0.369519\pi$
$770$	−2.95831e18	−0.511511
$771$	−2.76369e18	−0.473844
$772$	−2.71724e18	−0.461973
$773$	9.32114e18	1.57146	0.785728	−	0.618572i	$-0.212289\pi$
$773$	9.32114e18	1.57146	0.785728	+	0.618572i	$0.212289\pi$
$774$	−1.30805e18	−0.218679
$775$	−5.18458e18	−0.859513
$776$	−4.76025e18	−0.782579
$777$	2.57679e18	0.420090
$778$	−8.59701e17	−0.138989
$779$	7.66020e18	1.22814
$780$	2.64123e18	0.419945
$781$	−5.57807e18	−0.879533
$782$	3.81855e17	0.0597111
$783$	−5.53907e18	−0.858985
$784$	7.30791e18	1.12393
$785$	−2.20687e19	−3.36608
$786$	−1.70181e18	−0.257433
$787$	9.07837e18	1.36198	0.680992	−	0.732290i	$-0.261549\pi$
$787$	9.07837e18	1.36198	0.680992	+	0.732290i	$0.261549\pi$
$788$	−2.13944e18	−0.318331
$789$	−2.31210e18	−0.341198
$790$	−2.37804e18	−0.348051
$791$	1.11451e19	1.61785
$792$	−1.87065e18	−0.269326
$793$	−2.86639e18	−0.409316
$794$	4.46024e18	0.631720
$795$	4.37258e18	0.614259
$796$	−1.02614e19	−1.42979
$797$	−2.38228e18	−0.329241	−0.164620	−	0.986357i	$-0.552640\pi$
$797$	−2.38228e18	−0.329241	−0.164620	+	0.986357i	$0.552640\pi$
$798$	−3.23488e18	−0.443445
$799$	−4.10272e18	−0.557851
$800$	−1.46117e19	−1.97069
$801$	−1.02601e19	−1.37259
$802$	−3.31410e17	−0.0439777
$803$	3.64429e18	0.479692
$804$	−1.52854e18	−0.199578
$805$	4.79177e18	0.620616
$806$	7.06099e17	0.0907168
$807$	−1.68900e17	−0.0215254
$808$	−5.89828e18	−0.745679
$809$	6.48368e18	0.813123	0.406562	−	0.913623i	$-0.366728\pi$
$809$	6.48368e18	0.813123	0.406562	+	0.913623i	$0.366728\pi$
$810$	2.72552e18	0.339076
$811$	−7.88245e18	−0.972805	−0.486402	−	0.873735i	$-0.661691\pi$
$811$	−7.88245e18	−0.972805	−0.486402	+	0.873735i	$0.661691\pi$
$812$	1.36997e19	1.67724
$813$	3.42618e18	0.416122
$814$	8.91013e17	0.107356
$815$	6.82243e18	0.815483
$816$	−1.77058e18	−0.209956
$817$	1.17179e19	1.37850
$818$	−3.33801e17	−0.0389575
$819$	7.91913e18	0.916921
$820$	−8.99724e18	−1.03352
$821$	−5.49484e18	−0.626216	−0.313108	−	0.949718i	$-0.601370\pi$
$821$	−5.49484e18	−0.626216	−0.313108	+	0.949718i	$0.601370\pi$
$822$	5.36393e17	0.0606480
$823$	−1.29471e19	−1.45236	−0.726178	−	0.687507i	$-0.758705\pi$
$823$	−1.29471e19	−1.45236	−0.726178	+	0.687507i	$0.758705\pi$
$824$	−5.94366e17	−0.0661495
$825$	3.94779e18	0.435916
$826$	−7.60188e16	−0.00832819
$827$	1.22409e17	0.0133054	0.00665270	−	0.999978i	$-0.497882\pi$
$827$	1.22409e17	0.0133054	0.00665270	+	0.999978i	$0.497882\pi$
$828$	1.41388e18	0.152481
$829$	7.37755e18	0.789419	0.394710	−	0.918806i	$-0.370845\pi$
$829$	7.37755e18	0.789419	0.394710	+	0.918806i	$0.370845\pi$
$830$	2.71941e18	0.288714
$831$	−5.45233e18	−0.574349
$832$	−2.05783e18	−0.215084
$833$	−1.37028e19	−1.42108
$834$	−2.22845e18	−0.229310
$835$	2.66813e19	2.72423
$836$	7.81965e18	0.792221
$837$	2.87102e18	0.288616
$838$	3.12181e18	0.311401
$839$	−1.87237e18	−0.185327	−0.0926634	−	0.995697i	$-0.529538\pi$
$839$	−1.87237e18	−0.185327	−0.0926634	+	0.995697i	$0.529538\pi$
$840$	8.14253e18	0.799731
$841$	3.42584e18	0.333882
$842$	−1.85084e18	−0.178994
$843$	−7.67825e18	−0.736857
$844$	−1.23172e19	−1.17297
$845$	1.06881e19	1.01002
$846$	2.17301e18	0.203777
$847$	1.36281e19	1.26821
$848$	−5.86260e18	−0.541399
$849$	5.97096e18	0.547197
$850$	6.97430e18	0.634275
$851$	−1.44323e18	−0.130255
$852$	7.16419e18	0.641667
$853$	1.84258e19	1.63779	0.818896	−	0.573942i	$-0.194586\pi$
$853$	1.84258e19	1.63779	0.818896	+	0.573942i	$0.194586\pi$
$854$	−4.12340e18	−0.363730
$855$	−3.19122e19	−2.79368
$856$	−2.42196e18	−0.210421
$857$	−1.90656e19	−1.64390	−0.821950	−	0.569560i	$-0.807114\pi$
$857$	−1.90656e19	−1.64390	−0.821950	+	0.569560i	$0.807114\pi$
$858$	−5.37657e17	−0.0460085
$859$	−1.11720e19	−0.948802	−0.474401	−	0.880309i	$-0.657335\pi$
$859$	−1.11720e19	−0.948802	−0.474401	+	0.880309i	$0.657335\pi$
$860$	−1.37632e19	−1.16005
$861$	5.29667e18	0.443080
$862$	1.10825e18	0.0920109
$863$	−1.40194e19	−1.15521	−0.577603	−	0.816318i	$-0.696012\pi$
$863$	−1.40194e19	−1.15521	−0.577603	+	0.816318i	$0.696012\pi$
$864$	8.09142e18	0.661737
$865$	−3.96851e18	−0.322124
$866$	−7.25216e18	−0.584253
$867$	−1.74654e18	−0.139654
$868$	−7.10084e18	−0.563548
$869$	−3.38408e18	−0.266571
$870$	3.79585e18	0.296779
$871$	4.79511e18	0.372118
$872$	3.05446e17	0.0235276
$873$	1.29000e19	0.986273
$874$	1.81182e18	0.137496
$875$	4.80052e19	3.61606
$876$	−4.68055e18	−0.349961
$877$	9.49326e17	0.0704560	0.0352280	−	0.999379i	$-0.488784\pi$
$877$	9.49326e17	0.0704560	0.0352280	+	0.999379i	$0.488784\pi$
$878$	4.86059e18	0.358075
$879$	3.37846e18	0.247054
$880$	−7.68277e18	−0.557674
$881$	4.53351e18	0.326656	0.163328	−	0.986572i	$-0.447777\pi$
$881$	4.53351e18	0.326656	0.163328	+	0.986572i	$0.447777\pi$
$882$	7.25772e18	0.519104
$883$	1.89007e19	1.34194	0.670972	−	0.741483i	$-0.265877\pi$
$883$	1.89007e19	1.34194	0.670972	+	0.741483i	$0.265877\pi$
$884$	6.64012e18	0.467989
$885$	1.47245e17	0.0103017
$886$	−2.08289e18	−0.144660
$887$	2.33421e19	1.60930	0.804649	−	0.593751i	$-0.202353\pi$
$887$	2.33421e19	1.60930	0.804649	+	0.593751i	$0.202353\pi$
$888$	−2.45244e18	−0.167847
$889$	−8.16025e18	−0.554424
$890$	1.54428e19	1.04158
$891$	3.87857e18	0.259697
$892$	2.29655e19	1.52653
$893$	−1.94666e19	−1.28456
$894$	1.50663e18	0.0986993
$895$	−1.42226e19	−0.924974
$896$	−2.58353e19	−1.66806
$897$	8.70878e17	0.0558222
$898$	−7.64315e18	−0.486381
$899$	−7.09399e18	−0.448180
$900$	2.58234e19	1.61971
$901$	1.09928e19	0.684535
$902$	1.83150e18	0.113231
$903$	8.10237e18	0.497326
$904$	−1.06073e19	−0.646414
$905$	−1.44575e19	−0.874738
$906$	−1.95513e18	−0.117447
$907$	7.33375e18	0.437400	0.218700	−	0.975792i	$-0.429818\pi$
$907$	7.33375e18	0.437400	0.218700	+	0.975792i	$0.429818\pi$
$908$	−6.24636e18	−0.369887
$909$	1.59840e19	0.939768
$910$	−1.19193e19	−0.695794
$911$	5.10958e18	0.296153	0.148076	−	0.988976i	$-0.452692\pi$
$911$	5.10958e18	0.296153	0.148076	+	0.988976i	$0.452692\pi$
$912$	−8.40102e18	−0.483466
$913$	3.86988e18	0.221125
$914$	2.40292e18	0.136329
$915$	7.98687e18	0.449925
$916$	−5.16715e18	−0.289022
$917$	−5.36881e19	−2.98179
$918$	−3.86210e18	−0.212983
$919$	1.18519e19	0.648990	0.324495	−	0.945887i	$-0.394806\pi$
$919$	1.18519e19	0.648990	0.324495	+	0.945887i	$0.394806\pi$
$920$	−4.56054e18	−0.247968
$921$	−5.47096e18	−0.295377
$922$	−5.91808e18	−0.317270
$923$	−2.24745e19	−1.19641
$924$	5.40692e18	0.285813
$925$	−2.63595e19	−1.38362
$926$	−4.64108e18	−0.241906
$927$	1.61070e18	0.0833673
$928$	−1.99931e19	−1.02758
$929$	1.76450e19	0.900577	0.450288	−	0.892883i	$-0.351321\pi$
$929$	1.76450e19	0.900577	0.450288	+	0.892883i	$0.351321\pi$
$930$	−1.96747e18	−0.0997168
$931$	−6.50170e19	−3.27231
$932$	4.28110e18	0.213969
$933$	−1.25987e19	−0.625308
$934$	−2.76685e18	−0.136374
$935$	1.44057e19	0.705113
$936$	−7.53699e18	−0.366357
$937$	2.83709e19	1.36951	0.684755	−	0.728773i	$-0.259909\pi$
$937$	2.83709e19	1.36951	0.684755	+	0.728773i	$0.259909\pi$
$938$	6.89794e18	0.330675
$939$	1.58138e19	0.752853
$940$	2.28643e19	1.08100
$941$	−2.71116e19	−1.27298	−0.636492	−	0.771283i	$-0.719615\pi$
$941$	−2.71116e19	−1.27298	−0.636492	+	0.771283i	$0.719615\pi$
$942$	−5.76978e18	−0.269047
$943$	−2.96661e18	−0.137383
$944$	−1.97421e17	−0.00907980
$945$	−4.84641e19	−2.21367
$946$	2.80167e18	0.127094
$947$	1.95984e19	0.882970	0.441485	−	0.897269i	$-0.354452\pi$
$947$	1.95984e19	0.882970	0.441485	+	0.897269i	$0.354452\pi$
$948$	4.34635e18	0.194478
$949$	1.46831e19	0.652512
$950$	3.30916e19	1.46054
$951$	3.97925e18	0.174433
$952$	2.04705e19	0.891227
$953$	1.94142e19	0.839490	0.419745	−	0.907642i	$-0.362119\pi$
$953$	1.94142e19	0.839490	0.419745	+	0.907642i	$0.362119\pi$
$954$	−5.82234e18	−0.250054
$955$	2.35305e19	1.00371
$956$	2.64350e19	1.11996
$957$	5.40170e18	0.227302
$958$	5.14301e18	0.214952
$959$	1.69219e19	0.702471
$960$	5.73392e18	0.236423
$961$	−2.07406e19	−0.849413
$962$	3.58996e18	0.146033
$963$	6.56339e18	0.265190
$964$	−4.19626e19	−1.68408
$965$	−2.37516e19	−0.946816
$966$	1.25279e18	0.0496052
$967$	−2.74080e19	−1.07796	−0.538982	−	0.842317i	$-0.681191\pi$
$967$	−2.74080e19	−1.07796	−0.538982	+	0.842317i	$0.681191\pi$
$968$	−1.29704e19	−0.506716
$969$	1.57525e19	0.611286
$970$	−1.94161e19	−0.748421
$971$	−7.43591e18	−0.284714	−0.142357	−	0.989815i	$-0.545468\pi$
$971$	−7.43591e18	−0.284714	−0.142357	+	0.989815i	$0.545468\pi$
$972$	−2.20892e19	−0.840136
$973$	−7.03022e19	−2.65604
$974$	3.07631e16	0.00115451
$975$	1.59059e19	0.592965
$976$	−1.07085e19	−0.396557
$977$	2.75313e19	1.01277	0.506387	−	0.862307i	$-0.330981\pi$
$977$	2.75313e19	1.01277	0.506387	+	0.862307i	$0.330981\pi$
$978$	1.78370e18	0.0651807
$979$	2.19760e19	0.797738
$980$	7.63653e19	2.75376
$981$	−8.27740e17	−0.0296514
$982$	1.34569e19	0.478872
$983$	1.64486e19	0.581474	0.290737	−	0.956803i	$-0.406099\pi$
$983$	1.64486e19	0.581474	0.290737	+	0.956803i	$0.406099\pi$
$984$	−5.04107e18	−0.177033
$985$	−1.87010e19	−0.652422
$986$	9.54284e18	0.330733
$987$	−1.34602e19	−0.463437
$988$	3.15060e19	1.07764
$989$	−4.53805e18	−0.154203
$990$	−7.63001e18	−0.257570
$991$	1.37491e19	0.461100	0.230550	−	0.973060i	$-0.425947\pi$
$991$	1.37491e19	0.461100	0.230550	+	0.973060i	$0.425947\pi$
$992$	1.03628e19	0.345265
$993$	−1.44773e19	−0.479200
$994$	−3.23303e19	−1.06316
$995$	−8.96958e19	−2.93037
$996$	−4.97028e18	−0.161323
$997$	2.09895e19	0.676837	0.338418	−	0.940996i	$-0.390108\pi$
$997$	2.09895e19	0.676837	0.338418	+	0.940996i	$0.390108\pi$
$998$	5.51641e18	0.176729
$999$	1.45969e19	0.464605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.a.b.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.a.b.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-32.0185 q^{2} +511.530 q^{3} -7166.81 q^{4} -62645.6 q^{5} -16378.4 q^{6} -516700. q^{7} +491767. q^{8} -1.33266e6 q^{9} +O(q^{10})\)	\(q-32.0185 q^{2} +511.530 q^{3} -7166.81 q^{4} -62645.6 q^{5} -16378.4 q^{6} -516700. q^{7} +491767. q^{8} -1.33266e6 q^{9} +2.00582e6 q^{10} +2.85439e6 q^{11} -3.66604e6 q^{12} +1.15006e7 q^{13} +1.65440e7 q^{14} -3.20451e7 q^{15} +4.29649e7 q^{16} -8.05620e7 q^{17} +4.26698e7 q^{18} -3.82250e8 q^{19} +4.48969e8 q^{20} -2.64308e8 q^{21} -9.13935e7 q^{22} +1.48036e8 q^{23} +2.51553e8 q^{24} +2.70376e9 q^{25} -3.68231e8 q^{26} -1.49724e9 q^{27} +3.70310e9 q^{28} +3.69952e9 q^{29} +1.02604e9 q^{30} -1.91754e9 q^{31} -5.40423e9 q^{32} +1.46011e9 q^{33} +2.57948e9 q^{34} +3.23690e10 q^{35} +9.55093e9 q^{36} -9.74919e9 q^{37} +1.22391e10 q^{38} +5.88289e9 q^{39} -3.08070e10 q^{40} -2.00398e10 q^{41} +8.46275e9 q^{42} -3.06550e10 q^{43} -2.04569e10 q^{44} +8.34852e10 q^{45} -4.73989e9 q^{46} +5.09263e10 q^{47} +2.19778e10 q^{48} +1.70090e11 q^{49} -8.65706e10 q^{50} -4.12099e10 q^{51} -8.24224e10 q^{52} -1.36451e11 q^{53} +4.79394e10 q^{54} -1.78815e11 q^{55} -2.54096e11 q^{56} -1.95532e11 q^{57} -1.18453e11 q^{58} -4.59495e9 q^{59} +2.29661e11 q^{60} -2.49239e11 q^{61} +6.13968e10 q^{62} +6.88586e11 q^{63} -1.78933e11 q^{64} -7.20460e11 q^{65} -4.67505e10 q^{66} +4.16945e11 q^{67} +5.77373e11 q^{68} +7.57248e10 q^{69} -1.03641e12 q^{70} -1.95420e12 q^{71} -6.55358e11 q^{72} +1.27673e12 q^{73} +3.12155e11 q^{74} +1.38306e12 q^{75} +2.73951e12 q^{76} -1.47487e12 q^{77} -1.88361e11 q^{78} -1.18557e12 q^{79} -2.69156e12 q^{80} +1.35881e12 q^{81} +6.41644e11 q^{82} +1.35576e12 q^{83} +1.89424e12 q^{84} +5.04685e12 q^{85} +9.81529e11 q^{86} +1.89242e12 q^{87} +1.40370e12 q^{88} +7.69900e12 q^{89} -2.67308e12 q^{90} -5.94235e12 q^{91} -1.06095e12 q^{92} -9.80880e11 q^{93} -1.63058e12 q^{94} +2.39463e13 q^{95} -2.76442e12 q^{96} -9.67989e12 q^{97} -5.44604e12 q^{98} -3.80393e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) 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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