LMFDB - Embedded newform 29.16.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	29.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:	$41.3811164790$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 381613 x^{14} - 3733354 x^{13} + 57580338072 x^{12} + 1053633121552 x^{11} + \cdots + 56\!\cdots\!24 $ x^16 - 381613x^14 - 3733354x^13 + 57580338072x^12 + 1053633121552x^11 - 4368708806733008x^10 - 112027323561555872x^9 + 175073374072500887552x^8 + 5628322450139411218432x^7 - 3559766404200168515698688x^6 - 136592485261791822734163968x^5 + 31960388770880055093699280896x^4 + 1389289310261686682407697121280x^3 - 81097743966968601971743751405568x^2 - 3651876483524920831899376851877888x + 5681589407398948985967076414849024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{7}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-51.1693$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.1693 q^{2} -694.438 q^{3} -30904.4 q^{4} +52528.3 q^{5} -29978.4 q^{6} +2.43575e6 q^{7} -2.74869e6 q^{8} -1.38667e7 q^{9} +O(q^{10})$	\(q+43.1693 q^{2} -694.438 q^{3} -30904.4 q^{4} +52528.3 q^{5} -29978.4 q^{6} +2.43575e6 q^{7} -2.74869e6 q^{8} -1.38667e7 q^{9} +2.26761e6 q^{10} -1.14577e7 q^{11} +2.14612e7 q^{12} +3.67166e8 q^{13} +1.05150e8 q^{14} -3.64777e7 q^{15} +8.94017e8 q^{16} -7.57642e8 q^{17} -5.98614e8 q^{18} +4.84395e7 q^{19} -1.62336e9 q^{20} -1.69148e9 q^{21} -4.94622e8 q^{22} -1.31554e9 q^{23} +1.90880e9 q^{24} -2.77584e10 q^{25} +1.58503e10 q^{26} +1.95940e10 q^{27} -7.52754e10 q^{28} +1.72499e10 q^{29} -1.57472e9 q^{30} -2.04844e11 q^{31} +1.28663e11 q^{32} +7.95669e9 q^{33} -3.27069e10 q^{34} +1.27946e11 q^{35} +4.28541e11 q^{36} -2.18341e11 q^{37} +2.09110e9 q^{38} -2.54974e11 q^{39} -1.44384e11 q^{40} -2.07419e12 q^{41} -7.30199e10 q^{42} -2.63516e12 q^{43} +3.54094e11 q^{44} -7.28392e11 q^{45} -5.67910e10 q^{46} +2.71687e12 q^{47} -6.20839e11 q^{48} +1.18531e12 q^{49} -1.19831e12 q^{50} +5.26136e11 q^{51} -1.13471e13 q^{52} +1.25942e12 q^{53} +8.45858e11 q^{54} -6.01855e11 q^{55} -6.69513e12 q^{56} -3.36383e10 q^{57} +7.44665e11 q^{58} -2.79795e13 q^{59} +1.12732e12 q^{60} -2.57758e13 q^{61} -8.84295e12 q^{62} -3.37757e13 q^{63} -2.37408e13 q^{64} +1.92866e13 q^{65} +3.43485e11 q^{66} -2.02279e13 q^{67} +2.34145e13 q^{68} +9.13562e11 q^{69} +5.52333e12 q^{70} -1.74311e13 q^{71} +3.81152e13 q^{72} +2.24376e13 q^{73} -9.42565e12 q^{74} +1.92765e13 q^{75} -1.49700e12 q^{76} -2.79082e13 q^{77} -1.10071e13 q^{78} -1.06698e13 q^{79} +4.69612e13 q^{80} +1.85365e14 q^{81} -8.95411e13 q^{82} +2.91603e14 q^{83} +5.22741e13 q^{84} -3.97977e13 q^{85} -1.13758e14 q^{86} -1.19790e13 q^{87} +3.14938e13 q^{88} -1.94582e13 q^{89} -3.14442e13 q^{90} +8.94325e14 q^{91} +4.06560e13 q^{92} +1.42251e14 q^{93} +1.17285e14 q^{94} +2.54445e12 q^{95} -8.93487e13 q^{96} -8.54834e14 q^{97} +5.11692e13 q^{98} +1.58881e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * 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 $

$2$	43.1693	0.238479	0.119239	−	0.992866i	$-0.461954\pi$
$2$	43.1693	0.238479	0.119239	+	0.992866i	$0.461954\pi$
$3$	−694.438	−0.183326	−0.0916630	−	0.995790i	$-0.529218\pi$
$3$	−694.438	−0.183326	−0.0916630	+	0.995790i	$0.529218\pi$
$4$	−30904.4	−0.943128
$5$	52528.3	0.300690	0.150345	−	0.988634i	$-0.451962\pi$
$5$	52528.3	0.300690	0.150345	+	0.988634i	$0.451962\pi$
$6$	−29978.4	−0.0437194
$7$	2.43575e6	1.11789	0.558943	−	0.829206i	$-0.311207\pi$
$7$	2.43575e6	1.11789	0.558943	+	0.829206i	$0.311207\pi$
$8$	−2.74869e6	−0.463395
$9$	−1.38667e7	−0.966392
$10$	2.26761e6	0.0717081
$11$	−1.14577e7	−0.177277	−0.0886387	−	0.996064i	$-0.528252\pi$
$11$	−1.14577e7	−0.177277	−0.0886387	+	0.996064i	$0.528252\pi$
$12$	2.14612e7	0.172900
$13$	3.67166e8	1.62288	0.811442	−	0.584433i	$-0.198683\pi$
$13$	3.67166e8	1.62288	0.811442	+	0.584433i	$0.198683\pi$
$14$	1.05150e8	0.266592
$15$	−3.64777e7	−0.0551242
$16$	8.94017e8	0.832618
$17$	−7.57642e8	−0.447814	−0.223907	−	0.974611i	$-0.571881\pi$
$17$	−7.57642e8	−0.447814	−0.223907	+	0.974611i	$0.571881\pi$
$18$	−5.98614e8	−0.230464
$19$	4.84395e7	0.0124322	0.00621610	−	0.999981i	$-0.498021\pi$
$19$	4.84395e7	0.0124322	0.00621610	+	0.999981i	$0.498021\pi$
$20$	−1.62336e9	−0.283589
$21$	−1.69148e9	−0.204938
$22$	−4.94622e8	−0.0422769
$23$	−1.31554e9	−0.0805648	−0.0402824	−	0.999188i	$-0.512826\pi$
$23$	−1.31554e9	−0.0805648	−0.0402824	+	0.999188i	$0.512826\pi$
$24$	1.90880e9	0.0849524
$25$	−2.77584e10	−0.909586
$26$	1.58503e10	0.387024
$27$	1.95940e10	0.360491
$28$	−7.52754e10	−1.05431
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−1.57472e9	−0.0131460
$31$	−2.04844e11	−1.33724	−0.668620	−	0.743604i	$-0.733115\pi$
$31$	−2.04844e11	−1.33724	−0.668620	+	0.743604i	$0.733115\pi$
$32$	1.28663e11	0.661957
$33$	7.95669e9	0.0324996
$34$	−3.27069e10	−0.106794
$35$	1.27946e11	0.336137
$36$	4.28541e11	0.911431
$37$	−2.18341e11	−0.378114	−0.189057	−	0.981966i	$-0.560543\pi$
$37$	−2.18341e11	−0.378114	−0.189057	+	0.981966i	$0.560543\pi$
$38$	2.09110e9	0.00296482
$39$	−2.54974e11	−0.297517
$40$	−1.44384e11	−0.139338
$41$	−2.07419e12	−1.66329	−0.831646	−	0.555306i	$-0.812601\pi$
$41$	−2.07419e12	−1.66329	−0.831646	+	0.555306i	$0.812601\pi$
$42$	−7.30199e10	−0.0488733
$43$	−2.63516e12	−1.47841	−0.739203	−	0.673483i	$-0.764798\pi$
$43$	−2.63516e12	−1.47841	−0.739203	+	0.673483i	$0.764798\pi$
$44$	3.54094e11	0.167195
$45$	−7.28392e11	−0.290584
$46$	−5.67910e10	−0.0192130
$47$	2.71687e12	0.782230	0.391115	−	0.920342i	$-0.372089\pi$
$47$	2.71687e12	0.782230	0.391115	+	0.920342i	$0.372089\pi$
$48$	−6.20839e11	−0.152641
$49$	1.18531e12	0.249668
$50$	−1.19831e12	−0.216917
$51$	5.26136e11	0.0820959
$52$	−1.13471e13	−1.53059
$53$	1.25942e12	0.147266	0.0736329	−	0.997285i	$-0.476541\pi$
$53$	1.25942e12	0.147266	0.0736329	+	0.997285i	$0.476541\pi$
$54$	8.45858e11	0.0859695
$55$	−6.01855e11	−0.0533055
$56$	−6.69513e12	−0.518023
$57$	−3.36383e10	−0.00227915
$58$	7.44665e11	0.0442844
$59$	−2.79795e13	−1.46369	−0.731846	−	0.681470i	$-0.761341\pi$
$59$	−2.79795e13	−1.46369	−0.731846	+	0.681470i	$0.761341\pi$
$60$	1.12732e12	0.0519892
$61$	−2.57758e13	−1.05012	−0.525060	−	0.851065i	$-0.675957\pi$
$61$	−2.57758e13	−1.05012	−0.525060	+	0.851065i	$0.675957\pi$
$62$	−8.84295e12	−0.318904
$63$	−3.37757e13	−1.08032
$64$	−2.37408e13	−0.674755
$65$	1.92866e13	0.487984
$66$	3.43485e11	0.00775047
$67$	−2.02279e13	−0.407746	−0.203873	−	0.978997i	$-0.565353\pi$
$67$	−2.02279e13	−0.407746	−0.203873	+	0.978997i	$0.565353\pi$
$68$	2.34145e13	0.422346
$69$	9.13562e11	0.0147696
$70$	5.52333e12	0.0801615
$71$	−1.74311e13	−0.227450	−0.113725	−	0.993512i	$-0.536278\pi$
$71$	−1.74311e13	−0.227450	−0.113725	+	0.993512i	$0.536278\pi$
$72$	3.81152e13	0.447821
$73$	2.24376e13	0.237714	0.118857	−	0.992911i	$-0.462077\pi$
$73$	2.24376e13	0.237714	0.118857	+	0.992911i	$0.462077\pi$
$74$	−9.42565e12	−0.0901723
$75$	1.92765e13	0.166751
$76$	−1.49700e12	−0.0117252
$77$	−2.79082e13	−0.198176
$78$	−1.10071e13	−0.0709516
$79$	−1.06698e13	−0.0625108	−0.0312554	−	0.999511i	$-0.509951\pi$
$79$	−1.06698e13	−0.0625108	−0.0312554	+	0.999511i	$0.509951\pi$
$80$	4.69612e13	0.250360
$81$	1.85365e14	0.900304
$82$	−8.95411e13	−0.396660
$83$	2.91603e14	1.17952	0.589762	−	0.807577i	$-0.299222\pi$
$83$	2.91603e14	1.17952	0.589762	+	0.807577i	$0.299222\pi$
$84$	5.22741e13	0.193282
$85$	−3.97977e13	−0.134653
$86$	−1.13758e14	−0.352569
$87$	−1.19790e13	−0.0340428
$88$	3.14938e13	0.0821495
$89$	−1.94582e13	−0.0466312	−0.0233156	−	0.999728i	$-0.507422\pi$
$89$	−1.94582e13	−0.0466312	−0.0233156	+	0.999728i	$0.507422\pi$
$90$	−3.14442e13	−0.0692981
$91$	8.94325e14	1.81420
$92$	4.06560e13	0.0759829
$93$	1.42251e14	0.245151
$94$	1.17285e14	0.186545
$95$	2.54445e12	0.00373823
$96$	−8.93487e13	−0.121354
$97$	−8.54834e14	−1.07422	−0.537111	−	0.843512i	$-0.680484\pi$
$97$	−8.54834e14	−1.07422	−0.537111	+	0.843512i	$0.680484\pi$
$98$	5.11692e13	0.0595406
$99$	1.58881e14	0.171319
$100$	8.57856e14	0.857856
$101$	9.73252e14	0.903264	0.451632	−	0.892204i	$-0.350842\pi$
$101$	9.73252e14	0.903264	0.451632	+	0.892204i	$0.350842\pi$
$102$	2.27129e13	0.0195782
$103$	1.56541e15	1.25415	0.627076	−	0.778958i	$-0.284252\pi$
$103$	1.56541e15	1.25415	0.627076	+	0.778958i	$0.284252\pi$
$104$	−1.00923e15	−0.752037
$105$	−8.88505e13	−0.0616226
$106$	5.43684e13	0.0351198
$107$	1.09111e14	0.0656884	0.0328442	−	0.999460i	$-0.489543\pi$
$107$	1.09111e14	0.0656884	0.0328442	+	0.999460i	$0.489543\pi$
$108$	−6.05540e14	−0.339989
$109$	1.69680e15	0.889061	0.444531	−	0.895764i	$-0.353371\pi$
$109$	1.69680e15	0.889061	0.444531	+	0.895764i	$0.353371\pi$
$110$	−2.59817e13	−0.0127122
$111$	1.51625e14	0.0693183
$112$	2.17760e15	0.930771
$113$	−4.32464e15	−1.72926	−0.864632	−	0.502406i	$-0.832448\pi$
$113$	−4.32464e15	−1.72926	−0.864632	+	0.502406i	$0.832448\pi$
$114$	−1.45214e12	−0.000543529 0
$115$	−6.91031e13	−0.0242250
$116$	−5.33097e14	−0.175134
$117$	−5.09137e15	−1.56834
$118$	−1.20785e15	−0.349060
$119$	−1.84543e15	−0.500604
$120$	1.00266e14	0.0255443
$121$	−4.04597e15	−0.968573
$122$	−1.11272e15	−0.250431
$123$	1.44039e15	0.304925
$124$	6.33057e15	1.26119
$125$	−3.06114e15	−0.574193
$126$	−1.45807e15	−0.257632
$127$	5.15941e14	0.0859157	0.0429578	−	0.999077i	$-0.486322\pi$
$127$	5.15941e14	0.0859157	0.0429578	+	0.999077i	$0.486322\pi$
$128$	−5.24091e15	−0.822872
$129$	1.82996e15	0.271030
$130$	8.32590e14	0.116374
$131$	8.52258e15	1.12470	0.562350	−	0.826899i	$-0.309897\pi$
$131$	8.52258e15	1.12470	0.562350	+	0.826899i	$0.309897\pi$
$132$	−2.45897e14	−0.0306513
$133$	1.17987e14	0.0138978
$134$	−8.73225e14	−0.0972389
$135$	1.02924e15	0.108396
$136$	2.08253e15	0.207515
$137$	−1.73240e16	−1.63397	−0.816987	−	0.576656i	$-0.804357\pi$
$137$	−1.73240e16	−1.63397	−0.816987	+	0.576656i	$0.804357\pi$
$138$	3.94378e13	0.00352225
$139$	−3.26517e15	−0.276245	−0.138123	−	0.990415i	$-0.544107\pi$
$139$	−3.26517e15	−0.276245	−0.138123	+	0.990415i	$0.544107\pi$
$140$	−3.95409e15	−0.317020
$141$	−1.88670e15	−0.143403
$142$	−7.52487e14	−0.0542421
$143$	−4.20689e15	−0.287701
$144$	−1.23970e16	−0.804635
$145$	9.06107e14	0.0558367
$146$	9.68616e14	0.0566898
$147$	−8.23128e14	−0.0457707
$148$	6.74772e15	0.356610
$149$	3.58034e16	1.79898	0.899492	−	0.436938i	$-0.143937\pi$
$149$	3.58034e16	1.79898	0.899492	+	0.436938i	$0.143937\pi$
$150$	8.32152e14	0.0397666
$151$	−1.69680e16	−0.771441	−0.385721	−	0.922616i	$-0.626047\pi$
$151$	−1.69680e16	−0.771441	−0.385721	+	0.922616i	$0.626047\pi$
$152$	−1.33145e14	−0.00576102
$153$	1.05060e16	0.432763
$154$	−1.20478e15	−0.0472608
$155$	−1.07601e16	−0.402094
$156$	7.87983e15	0.280597
$157$	−4.78131e15	−0.162293	−0.0811465	−	0.996702i	$-0.525858\pi$
$157$	−4.78131e15	−0.162293	−0.0811465	+	0.996702i	$0.525858\pi$
$158$	−4.60610e14	−0.0149075
$159$	−8.74591e14	−0.0269977
$160$	6.75846e15	0.199044
$161$	−3.20433e15	−0.0900622
$162$	8.00206e15	0.214704
$163$	−4.31243e16	−1.10488	−0.552440	−	0.833552i	$-0.686303\pi$
$163$	−4.31243e16	−1.10488	−0.552440	+	0.833552i	$0.686303\pi$
$164$	6.41015e16	1.56870
$165$	4.17951e14	0.00977229
$166$	1.25883e16	0.281292
$167$	−2.67826e15	−0.0572110	−0.0286055	−	0.999591i	$-0.509107\pi$
$167$	−2.67826e15	−0.0572110	−0.0286055	+	0.999591i	$0.509107\pi$
$168$	4.64935e15	0.0949671
$169$	8.36251e16	1.63375
$170$	−1.71804e15	−0.0321119
$171$	−6.71695e14	−0.0120144
$172$	8.14381e16	1.39433
$173$	1.19035e16	0.195132	0.0975662	−	0.995229i	$-0.468894\pi$
$173$	1.19035e16	0.195132	0.0975662	+	0.995229i	$0.468894\pi$
$174$	−5.17124e14	−0.00811849
$175$	−6.76124e16	−1.01681
$176$	−1.02434e16	−0.147604
$177$	1.94300e16	0.268333
$178$	−8.39995e14	−0.0111206
$179$	1.28056e17	1.62556	0.812778	−	0.582573i	$-0.197954\pi$
$179$	1.28056e17	1.62556	0.812778	+	0.582573i	$0.197954\pi$
$180$	2.25105e16	0.274058
$181$	−8.91293e16	−1.04095	−0.520476	−	0.853876i	$-0.674246\pi$
$181$	−8.91293e16	−1.04095	−0.520476	+	0.853876i	$0.674246\pi$
$182$	3.86074e16	0.432648
$183$	1.78997e16	0.192514
$184$	3.61602e15	0.0373333
$185$	−1.14691e16	−0.113695
$186$	6.14089e15	0.0584634
$187$	8.68086e15	0.0793873
$188$	−8.39632e16	−0.737743
$189$	4.77260e16	0.402988
$190$	1.09842e14	0.000891490 0
$191$	−1.92861e17	−1.50485	−0.752426	−	0.658677i	$-0.771116\pi$
$191$	−1.92861e17	−1.50485	−0.752426	+	0.658677i	$0.771116\pi$
$192$	1.64865e16	0.123700
$193$	2.98483e16	0.215397	0.107699	−	0.994184i	$-0.465652\pi$
$193$	2.98483e16	0.215397	0.107699	+	0.994184i	$0.465652\pi$
$194$	−3.69026e16	−0.256179
$195$	−1.33934e16	−0.0894603
$196$	−3.66314e16	−0.235469
$197$	−2.30889e17	−1.42859	−0.714294	−	0.699846i	$-0.753252\pi$
$197$	−2.30889e17	−1.42859	−0.714294	+	0.699846i	$0.753252\pi$
$198$	6.85876e15	0.0408561
$199$	−1.30435e17	−0.748165	−0.374082	−	0.927395i	$-0.622042\pi$
$199$	−1.30435e17	−0.748165	−0.374082	+	0.927395i	$0.622042\pi$
$200$	7.62992e16	0.421498
$201$	1.40470e16	0.0747505
$202$	4.20146e16	0.215410
$203$	4.20164e16	0.207586
$204$	−1.62599e16	−0.0774270
$205$	−1.08953e17	−0.500135
$206$	6.75778e16	0.299089
$207$	1.82422e16	0.0778571
$208$	3.28253e17	1.35124
$209$	−5.55007e14	−0.00220395
$210$	−3.83561e15	−0.0146957
$211$	−3.86871e17	−1.43037	−0.715184	−	0.698936i	$-0.753657\pi$
$211$	−3.86871e17	−1.43037	−0.715184	+	0.698936i	$0.753657\pi$
$212$	−3.89217e16	−0.138891
$213$	1.21048e16	0.0416975
$214$	4.71023e15	0.0156653
$215$	−1.38421e17	−0.444541
$216$	−5.38578e16	−0.167050
$217$	−4.98948e17	−1.49488
$218$	7.32496e16	0.212022
$219$	−1.55815e16	−0.0435792
$220$	1.86000e16	0.0502739
$221$	−2.78181e17	−0.726750
$222$	6.54553e15	0.0165309
$223$	−4.18877e17	−1.02282	−0.511411	−	0.859336i	$-0.670877\pi$
$223$	−4.18877e17	−1.02282	−0.511411	+	0.859336i	$0.670877\pi$
$224$	3.13391e17	0.739992
$225$	3.84916e17	0.879016
$226$	−1.86692e17	−0.412393
$227$	1.66413e17	0.355626	0.177813	−	0.984064i	$-0.443098\pi$
$227$	1.66413e17	0.355626	0.177813	+	0.984064i	$0.443098\pi$
$228$	1.03957e15	0.00214953
$229$	5.44302e17	1.08912	0.544558	−	0.838723i	$-0.316698\pi$
$229$	5.44302e17	1.08912	0.544558	+	0.838723i	$0.316698\pi$
$230$	−2.98313e15	−0.00577715
$231$	1.93805e16	0.0363308
$232$	−4.74146e16	−0.0860503
$233$	−1.10061e18	−1.93403	−0.967017	−	0.254712i	$-0.918019\pi$
$233$	−1.10061e18	−1.93403	−0.967017	+	0.254712i	$0.918019\pi$
$234$	−2.19791e17	−0.374016
$235$	1.42713e17	0.235209
$236$	8.64689e17	1.38045
$237$	7.40955e15	0.0114599
$238$	−7.96658e16	−0.119384
$239$	−2.60010e17	−0.377577	−0.188788	−	0.982018i	$-0.560456\pi$
$239$	−2.60010e17	−0.377577	−0.188788	+	0.982018i	$0.560456\pi$
$240$	−3.26116e16	−0.0458974
$241$	1.09202e18	1.48971	0.744853	−	0.667228i	$-0.232519\pi$
$241$	1.09202e18	1.48971	0.744853	+	0.667228i	$0.232519\pi$
$242$	−1.74662e17	−0.230984
$243$	−4.09876e17	−0.525540
$244$	7.96587e17	0.990397
$245$	6.22626e16	0.0750726
$246$	6.21808e16	0.0727182
$247$	1.77854e16	0.0201760
$248$	5.63052e17	0.619671
$249$	−2.02501e17	−0.216238
$250$	−1.32147e17	−0.136933
$251$	1.60288e18	1.61194	0.805970	−	0.591957i	$-0.201644\pi$
$251$	1.60288e18	1.61194	0.805970	+	0.591957i	$0.201644\pi$
$252$	1.04382e18	1.01888
$253$	1.50731e16	0.0142823
$254$	2.22728e16	0.0204891
$255$	2.76370e16	0.0246854
$256$	5.51693e17	0.478517
$257$	1.34727e17	0.113490	0.0567449	−	0.998389i	$-0.481928\pi$
$257$	1.34727e17	0.113490	0.0567449	+	0.998389i	$0.481928\pi$
$258$	7.89979e16	0.0646350
$259$	−5.31825e17	−0.422689
$260$	−5.96042e17	−0.460232
$261$	−2.39198e17	−0.179454
$262$	3.67914e17	0.268217
$263$	−9.06569e17	−0.642292	−0.321146	−	0.947030i	$-0.604068\pi$
$263$	−9.06569e17	−0.642292	−0.321146	+	0.947030i	$0.604068\pi$
$264$	−2.18705e16	−0.0150601
$265$	6.61553e16	0.0442813
$266$	5.09340e15	0.00331433
$267$	1.35125e16	0.00854872
$268$	6.25132e17	0.384557
$269$	4.59879e17	0.275107	0.137554	−	0.990494i	$-0.456076\pi$
$269$	4.59879e17	0.275107	0.137554	+	0.990494i	$0.456076\pi$
$270$	4.44315e16	0.0258501
$271$	−1.46905e18	−0.831320	−0.415660	−	0.909520i	$-0.636449\pi$
$271$	−1.46905e18	−0.831320	−0.415660	+	0.909520i	$0.636449\pi$
$272$	−6.77345e17	−0.372858
$273$	−6.21054e17	−0.332590
$274$	−7.47867e17	−0.389668
$275$	3.18048e17	0.161249
$276$	−2.82331e16	−0.0139296
$277$	1.78395e17	0.0856613	0.0428307	−	0.999082i	$-0.486362\pi$
$277$	1.78395e17	0.0856613	0.0428307	+	0.999082i	$0.486362\pi$
$278$	−1.40955e17	−0.0658786
$279$	2.84050e18	1.29230
$280$	−3.51684e17	−0.155764
$281$	1.33805e18	0.577001	0.288500	−	0.957480i	$-0.406843\pi$
$281$	1.33805e18	0.577001	0.288500	+	0.957480i	$0.406843\pi$
$282$	−8.14474e16	−0.0341987
$283$	2.99614e18	1.22508	0.612538	−	0.790441i	$-0.290149\pi$
$283$	2.99614e18	1.22508	0.612538	+	0.790441i	$0.290149\pi$
$284$	5.38697e17	0.214515
$285$	−1.76696e15	−0.000685316 0
$286$	−1.81609e17	−0.0686106
$287$	−5.05220e18	−1.85937
$288$	−1.78413e18	−0.639710
$289$	−2.28840e18	−0.799463
$290$	3.91160e16	0.0133159
$291$	5.93630e17	0.196933
$292$	−6.93421e17	−0.224195
$293$	3.31060e18	1.04328	0.521639	−	0.853166i	$-0.325321\pi$
$293$	3.31060e18	1.04328	0.521639	+	0.853166i	$0.325321\pi$
$294$	−3.55339e16	−0.0109153
$295$	−1.46971e18	−0.440117
$296$	6.00154e17	0.175216
$297$	−2.24503e17	−0.0639069
$298$	1.54561e18	0.429020
$299$	−4.83022e17	−0.130747
$300$	−5.95728e17	−0.157267
$301$	−6.41859e18	−1.65269
$302$	−7.32496e17	−0.183973
$303$	−6.75863e17	−0.165592
$304$	4.33058e16	0.0103513
$305$	−1.35396e18	−0.315760
$306$	4.53535e17	0.103205
$307$	3.74757e18	0.832171	0.416085	−	0.909326i	$-0.363402\pi$
$307$	3.74757e18	0.832171	0.416085	+	0.909326i	$0.363402\pi$
$308$	8.62486e17	0.186905
$309$	−1.08708e18	−0.229919
$310$	−4.64505e17	−0.0958910
$311$	−3.05820e18	−0.616258	−0.308129	−	0.951345i	$-0.599703\pi$
$311$	−3.05820e18	−0.616258	−0.308129	+	0.951345i	$0.599703\pi$
$312$	7.00846e17	0.137868
$313$	3.94380e17	0.0757413	0.0378706	−	0.999283i	$-0.487943\pi$
$313$	3.94380e17	0.0757413	0.0378706	+	0.999283i	$0.487943\pi$
$314$	−2.06406e17	−0.0387035
$315$	−1.77418e18	−0.324840
$316$	3.29745e17	0.0589557
$317$	−4.33172e18	−0.756337	−0.378169	−	0.925737i	$-0.623446\pi$
$317$	−4.33172e18	−0.756337	−0.378169	+	0.925737i	$0.623446\pi$
$318$	−3.77555e16	−0.00643838
$319$	−1.97644e17	−0.0329196
$320$	−1.24707e18	−0.202892
$321$	−7.57706e16	−0.0120424
$322$	−1.38329e17	−0.0214779
$323$	−3.66999e16	−0.00556731
$324$	−5.72859e18	−0.849102
$325$	−1.01919e19	−1.47615
$326$	−1.86165e18	−0.263491
$327$	−1.17832e18	−0.162988
$328$	5.70130e18	0.770762
$329$	6.61761e18	0.874444
$330$	1.80427e16	0.00233048
$331$	1.43216e19	1.80834	0.904172	−	0.427169i	$-0.140489\pi$
$331$	1.43216e19	1.80834	0.904172	+	0.427169i	$0.140489\pi$
$332$	−9.01183e18	−1.11244
$333$	3.02767e18	0.365407
$334$	−1.15619e17	−0.0136436
$335$	−1.06254e18	−0.122605
$336$	−1.51221e18	−0.170635
$337$	5.16567e18	0.570036	0.285018	−	0.958522i	$-0.408000\pi$
$337$	5.16567e18	0.570036	0.285018	+	0.958522i	$0.408000\pi$
$338$	3.61004e18	0.389616
$339$	3.00319e18	0.317019
$340$	1.22992e18	0.126995
$341$	2.34704e18	0.237063
$342$	−2.89966e16	−0.00286518
$343$	−8.67674e18	−0.838785
$344$	7.24325e18	0.685086
$345$	4.79878e16	0.00444107
$346$	5.13866e17	0.0465350
$347$	6.45748e18	0.572258	0.286129	−	0.958191i	$-0.407631\pi$
$347$	6.45748e18	0.572258	0.286129	+	0.958191i	$0.407631\pi$
$348$	3.70203e17	0.0321067
$349$	1.07299e19	0.910765	0.455382	−	0.890296i	$-0.349503\pi$
$349$	1.07299e19	0.910765	0.455382	+	0.890296i	$0.349503\pi$
$350$	−2.91878e18	−0.242488
$351$	7.19424e18	0.585035
$352$	−1.47419e18	−0.117350
$353$	1.91637e19	1.49338	0.746689	−	0.665173i	$-0.231642\pi$
$353$	1.91637e19	1.49338	0.746689	+	0.665173i	$0.231642\pi$
$354$	8.38780e17	0.0639917
$355$	−9.15624e17	−0.0683919
$356$	6.01343e17	0.0439792
$357$	1.28154e18	0.0917739
$358$	5.52809e18	0.387661
$359$	1.11622e19	0.766551	0.383275	−	0.923634i	$-0.374796\pi$
$359$	1.11622e19	0.766551	0.383275	+	0.923634i	$0.374796\pi$
$360$	2.00213e18	0.134655
$361$	−1.51788e19	−0.999845
$362$	−3.84765e18	−0.248245
$363$	2.80968e18	0.177565
$364$	−2.76386e19	−1.71102
$365$	1.17861e18	0.0714782
$366$	7.72719e17	0.0459106
$367$	−3.31582e19	−1.93017	−0.965086	−	0.261935i	$-0.915640\pi$
$367$	−3.31582e19	−1.93017	−0.965086	+	0.261935i	$0.915640\pi$
$368$	−1.17611e18	−0.0670797
$369$	2.87620e19	1.60739
$370$	−4.95113e17	−0.0271139
$371$	3.06764e18	0.164626
$372$	−4.39619e18	−0.231209
$373$	1.16128e19	0.598578	0.299289	−	0.954162i	$-0.403251\pi$
$373$	1.16128e19	0.598578	0.299289	+	0.954162i	$0.403251\pi$
$374$	3.74747e17	0.0189322
$375$	2.12577e18	0.105264
$376$	−7.46784e18	−0.362482
$377$	6.33357e18	0.301362
$378$	2.06030e18	0.0961040
$379$	−1.42430e19	−0.651339	−0.325670	−	0.945484i	$-0.605590\pi$
$379$	−1.42430e19	−0.651339	−0.325670	+	0.945484i	$0.605590\pi$
$380$	−7.86347e16	−0.00352563
$381$	−3.58290e17	−0.0157506
$382$	−8.32566e18	−0.358875
$383$	2.64192e19	1.11668	0.558340	−	0.829612i	$-0.311438\pi$
$383$	2.64192e19	1.11668	0.558340	+	0.829612i	$0.311438\pi$
$384$	3.63949e18	0.150854
$385$	−1.46597e18	−0.0595894
$386$	1.28853e18	0.0513677
$387$	3.65409e19	1.42872
$388$	2.64181e19	1.01313
$389$	4.04435e19	1.52134	0.760671	−	0.649138i	$-0.224870\pi$
$389$	4.04435e19	1.52134	0.760671	+	0.649138i	$0.224870\pi$
$390$	−5.78182e17	−0.0213344
$391$	9.96709e17	0.0360780
$392$	−3.25807e18	−0.115695
$393$	−5.91841e18	−0.206187
$394$	−9.96733e18	−0.340688
$395$	−5.60469e17	−0.0187963
$396$	−4.91011e18	−0.161576
$397$	−4.01544e19	−1.29659	−0.648297	−	0.761387i	$-0.724519\pi$
$397$	−4.01544e19	−1.29659	−0.648297	+	0.761387i	$0.724519\pi$
$398$	−5.63080e18	−0.178422
$399$	−8.19344e16	−0.00254783
$400$	−2.48164e19	−0.757337
$401$	−2.58661e19	−0.774727	−0.387364	−	0.921927i	$-0.626614\pi$
$401$	−2.58661e19	−0.774727	−0.387364	+	0.921927i	$0.626614\pi$
$402$	6.06401e17	0.0178264
$403$	−7.52116e19	−2.17019
$404$	−3.00778e19	−0.851894
$405$	9.73689e18	0.270712
$406$	1.81382e18	0.0495049
$407$	2.50170e18	0.0670312
$408$	−1.44619e18	−0.0380429
$409$	2.84354e19	0.734402	0.367201	−	0.930142i	$-0.380316\pi$
$409$	2.84354e19	0.734402	0.367201	+	0.930142i	$0.380316\pi$
$410$	−4.70344e18	−0.119272
$411$	1.20305e19	0.299550
$412$	−4.83782e19	−1.18283
$413$	−6.81510e19	−1.63624
$414$	7.87501e17	0.0185673
$415$	1.53174e19	0.354671
$416$	4.72408e19	1.07428
$417$	2.26746e18	0.0506429
$418$	−2.39593e16	−0.000525596 0
$419$	−1.75184e19	−0.377477	−0.188738	−	0.982027i	$-0.560440\pi$
$419$	−1.75184e19	−0.377477	−0.188738	+	0.982027i	$0.560440\pi$
$420$	2.74587e18	0.0581180
$421$	1.75992e19	0.365913	0.182956	−	0.983121i	$-0.441433\pi$
$421$	1.75992e19	0.365913	0.182956	+	0.983121i	$0.441433\pi$
$422$	−1.67009e19	−0.341113
$423$	−3.76739e19	−0.755941
$424$	−3.46176e18	−0.0682423
$425$	2.10309e19	0.407325
$426$	5.22556e17	0.00994399
$427$	−6.27835e19	−1.17391
$428$	−3.37200e18	−0.0619525
$429$	2.92143e18	0.0527431
$430$	−5.97552e18	−0.106014
$431$	3.90632e18	0.0681064	0.0340532	−	0.999420i	$-0.489158\pi$
$431$	3.90632e18	0.0681064	0.0340532	+	0.999420i	$0.489158\pi$
$432$	1.75173e19	0.300151
$433$	2.58056e19	0.434565	0.217283	−	0.976109i	$-0.430281\pi$
$433$	2.58056e19	0.434565	0.217283	+	0.976109i	$0.430281\pi$
$434$	−2.15392e19	−0.356498
$435$	−6.29235e17	−0.0102363
$436$	−5.24386e19	−0.838498
$437$	−6.37242e16	−0.00100160
$438$	−6.72644e17	−0.0103927
$439$	8.76336e19	1.33103	0.665513	−	0.746386i	$-0.268213\pi$
$439$	8.76336e19	1.33103	0.665513	+	0.746386i	$0.268213\pi$
$440$	1.65432e18	0.0247015
$441$	−1.64364e19	−0.241277
$442$	−1.20089e19	−0.173315
$443$	4.94528e19	0.701718	0.350859	−	0.936428i	$-0.385890\pi$
$443$	4.94528e19	0.701718	0.350859	+	0.936428i	$0.385890\pi$
$444$	−4.68587e18	−0.0653760
$445$	−1.02210e18	−0.0140215
$446$	−1.80826e19	−0.243922
$447$	−2.48632e19	−0.329801
$448$	−5.78267e19	−0.754299
$449$	8.07507e19	1.03585	0.517927	−	0.855425i	$-0.326704\pi$
$449$	8.07507e19	1.03585	0.517927	+	0.855425i	$0.326704\pi$
$450$	1.66165e19	0.209627
$451$	2.37655e19	0.294864
$452$	1.33650e20	1.63092
$453$	1.17832e19	0.141425
$454$	7.18394e18	0.0848094
$455$	4.69774e19	0.545511
$456$	9.24613e16	0.00105615
$457$	3.19676e19	0.359202	0.179601	−	0.983740i	$-0.442519\pi$
$457$	3.19676e19	0.359202	0.179601	+	0.983740i	$0.442519\pi$
$458$	2.34971e19	0.259731
$459$	−1.48452e19	−0.161433
$460$	2.13559e18	0.0228473
$461$	−9.20117e19	−0.968470	−0.484235	−	0.874938i	$-0.660902\pi$
$461$	−9.20117e19	−0.968470	−0.484235	+	0.874938i	$0.660902\pi$
$462$	8.36643e17	0.00866414
$463$	−7.12244e19	−0.725724	−0.362862	−	0.931843i	$-0.618200\pi$
$463$	−7.12244e19	−0.725724	−0.362862	+	0.931843i	$0.618200\pi$
$464$	1.54217e19	0.154613
$465$	7.47222e18	0.0737144
$466$	−4.75126e19	−0.461226
$467$	1.76019e20	1.68144	0.840721	−	0.541469i	$-0.182132\pi$
$467$	1.76019e20	1.68144	0.840721	+	0.541469i	$0.182132\pi$
$468$	1.57346e20	1.47915
$469$	−4.92701e19	−0.455814
$470$	6.16080e18	0.0560923
$471$	3.32033e18	0.0297525
$472$	7.69070e19	0.678267
$473$	3.01930e19	0.262088
$474$	3.19865e17	0.00273294
$475$	−1.34460e18	−0.0113082
$476$	5.70318e19	0.472134
$477$	−1.74640e19	−0.142317
$478$	−1.12244e19	−0.0900440
$479$	−9.66868e19	−0.763573	−0.381787	−	0.924250i	$-0.624691\pi$
$479$	−9.66868e19	−0.763573	−0.381787	+	0.924250i	$0.624691\pi$
$480$	−4.69334e18	−0.0364899
$481$	−8.01676e19	−0.613636
$482$	4.71415e19	0.355264
$483$	2.22521e18	0.0165108
$484$	1.25038e20	0.913488
$485$	−4.49030e19	−0.323007
$486$	−1.76941e19	−0.125330
$487$	−4.43555e19	−0.309371	−0.154686	−	0.987964i	$-0.549436\pi$
$487$	−4.43555e19	−0.309371	−0.154686	+	0.987964i	$0.549436\pi$
$488$	7.08499e19	0.486620
$489$	2.99472e19	0.202554
$490$	2.68783e18	0.0179032
$491$	−9.87427e19	−0.647730	−0.323865	−	0.946103i	$-0.604982\pi$
$491$	−9.87427e19	−0.647730	−0.323865	+	0.946103i	$0.604982\pi$
$492$	−4.45145e19	−0.287583
$493$	−1.30692e19	−0.0831569
$494$	7.67782e17	0.00481156
$495$	8.34572e18	0.0515140
$496$	−1.83134e20	−1.11341
$497$	−4.24577e19	−0.254263
$498$	−8.74181e18	−0.0515681
$499$	3.99640e19	0.232228	0.116114	−	0.993236i	$-0.462956\pi$
$499$	3.99640e19	0.232228	0.116114	+	0.993236i	$0.462956\pi$
$500$	9.46026e19	0.541537
$501$	1.85989e18	0.0104883
$502$	6.91953e19	0.384414
$503$	−2.00453e20	−1.09712	−0.548559	−	0.836112i	$-0.684823\pi$
$503$	−2.00453e20	−1.09712	−0.548559	+	0.836112i	$0.684823\pi$
$504$	9.28391e19	0.500613
$505$	5.11233e19	0.271602
$506$	6.50696e17	0.00340603
$507$	−5.80725e19	−0.299510
$508$	−1.59449e19	−0.0810295
$509$	1.74773e20	0.875165	0.437582	−	0.899178i	$-0.355835\pi$
$509$	1.74773e20	0.875165	0.437582	+	0.899178i	$0.355835\pi$
$510$	1.19307e18	0.00588695
$511$	5.46524e19	0.265737
$512$	1.95550e20	0.936988
$513$	9.49123e17	0.00448170
$514$	5.81608e18	0.0270649
$515$	8.22286e19	0.377110
$516$	−5.65537e19	−0.255616
$517$	−3.11292e19	−0.138672
$518$	−2.29585e19	−0.100802
$519$	−8.26626e18	−0.0357729
$520$	−5.30130e19	−0.226130
$521$	9.00276e19	0.378524	0.189262	−	0.981927i	$-0.439391\pi$
$521$	9.00276e19	0.378524	0.189262	+	0.981927i	$0.439391\pi$
$522$	−1.03260e19	−0.0427961
$523$	−3.48342e20	−1.42313	−0.711564	−	0.702622i	$-0.752013\pi$
$523$	−3.48342e20	−1.42313	−0.711564	+	0.702622i	$0.752013\pi$
$524$	−2.63385e20	−1.06074
$525$	4.69526e19	0.186408
$526$	−3.91360e19	−0.153173
$527$	1.55198e20	0.598835
$528$	7.11341e18	0.0270597
$529$	−2.64905e20	−0.993509
$530$	2.85588e18	0.0105602
$531$	3.87982e20	1.41450
$532$	−3.64631e18	−0.0131074
$533$	−7.61571e20	−2.69933
$534$	5.83325e17	0.00203869
$535$	5.73140e18	0.0197518
$536$	5.56003e19	0.188948
$537$	−8.89270e19	−0.298007
$538$	1.98527e19	0.0656072
$539$	−1.35810e19	−0.0442605
$540$	−3.18080e19	−0.102231
$541$	−3.63676e20	−1.15275	−0.576374	−	0.817186i	$-0.695533\pi$
$541$	−3.63676e20	−1.15275	−0.576374	+	0.817186i	$0.695533\pi$
$542$	−6.34181e19	−0.198252
$543$	6.18948e19	0.190834
$544$	−9.74807e19	−0.296433
$545$	8.91300e19	0.267331
$546$	−2.68104e19	−0.0793157
$547$	−5.46902e20	−1.59589	−0.797947	−	0.602727i	$-0.794081\pi$
$547$	−5.46902e20	−1.59589	−0.797947	+	0.602727i	$0.794081\pi$
$548$	5.35389e20	1.54105
$549$	3.57425e20	1.01483
$550$	1.37299e19	0.0384545
$551$	8.35576e17	0.00230860
$552$	−2.51110e18	−0.00684417
$553$	−2.59891e19	−0.0698799
$554$	7.70119e18	0.0204284
$555$	7.96459e18	0.0208433
$556$	1.00908e20	0.260534
$557$	−1.61014e20	−0.410156	−0.205078	−	0.978746i	$-0.565745\pi$
$557$	−1.61014e20	−0.410156	−0.205078	+	0.978746i	$0.565745\pi$
$558$	1.22622e20	0.308186
$559$	−9.67542e20	−2.39928
$560$	1.14386e20	0.279873
$561$	−6.02833e18	−0.0145538
$562$	5.77629e19	0.137602
$563$	2.44069e20	0.573719	0.286860	−	0.957973i	$-0.407389\pi$
$563$	2.44069e20	0.573719	0.286860	+	0.957973i	$0.407389\pi$
$564$	5.83073e19	0.135248
$565$	−2.27166e20	−0.519972
$566$	1.29341e20	0.292155
$567$	4.51502e20	1.00644
$568$	4.79126e19	0.105399
$569$	−6.47873e19	−0.140653	−0.0703263	−	0.997524i	$-0.522404\pi$
$569$	−6.47873e19	−0.140653	−0.0703263	+	0.997524i	$0.522404\pi$
$570$	−7.62785e16	−0.000163433 0
$571$	−3.45253e20	−0.730074	−0.365037	−	0.930993i	$-0.618944\pi$
$571$	−3.45253e20	−0.730074	−0.365037	+	0.930993i	$0.618944\pi$
$572$	1.30012e20	0.271339
$573$	1.33930e20	0.275878
$574$	−2.18100e20	−0.443421
$575$	3.65172e19	0.0732806
$576$	3.29206e20	0.652078
$577$	7.04822e20	1.37804	0.689019	−	0.724744i	$-0.258042\pi$
$577$	7.04822e20	1.37804	0.689019	+	0.724744i	$0.258042\pi$
$578$	−9.87887e19	−0.190655
$579$	−2.07278e19	−0.0394879
$580$	−2.80027e19	−0.0526611
$581$	7.10273e20	1.31857
$582$	2.56266e19	0.0469643
$583$	−1.44301e19	−0.0261069
$584$	−6.16741e19	−0.110156
$585$	−2.67441e20	−0.471584
$586$	1.42916e20	0.248800
$587$	−1.24278e20	−0.213603	−0.106801	−	0.994280i	$-0.534061\pi$
$587$	−1.24278e20	−0.213603	−0.106801	+	0.994280i	$0.534061\pi$
$588$	2.54383e19	0.0431676
$589$	−9.92253e18	−0.0166248
$590$	−6.34465e19	−0.104959
$591$	1.60338e20	0.261897
$592$	−1.95201e20	−0.314825
$593$	7.05632e20	1.12375	0.561873	−	0.827223i	$-0.310081\pi$
$593$	7.05632e20	1.12375	0.561873	+	0.827223i	$0.310081\pi$
$594$	−9.69162e18	−0.0152405
$595$	−9.69372e19	−0.150527
$596$	−1.10648e21	−1.69667
$597$	9.05793e19	0.137158
$598$	−2.08517e19	−0.0311805
$599$	1.79279e20	0.264745	0.132372	−	0.991200i	$-0.457741\pi$
$599$	1.79279e20	0.264745	0.132372	+	0.991200i	$0.457741\pi$
$600$	−5.29851e19	−0.0772715
$601$	5.87361e20	0.845954	0.422977	−	0.906140i	$-0.360985\pi$
$601$	5.87361e20	0.845954	0.422977	+	0.906140i	$0.360985\pi$
$602$	−2.77086e20	−0.394131
$603$	2.80494e20	0.394043
$604$	5.24385e20	0.727568
$605$	−2.12528e20	−0.291240
$606$	−2.91765e19	−0.0394902
$607$	−6.98904e19	−0.0934335	−0.0467167	−	0.998908i	$-0.514876\pi$
$607$	−6.98904e19	−0.0934335	−0.0467167	+	0.998908i	$0.514876\pi$
$608$	6.23239e18	0.00822958
$609$	−2.91778e19	−0.0380560
$610$	−5.84495e19	−0.0753021
$611$	9.97542e20	1.26947
$612$	−3.24681e20	−0.408151
$613$	−2.65290e20	−0.329433	−0.164716	−	0.986341i	$-0.552671\pi$
$613$	−2.65290e20	−0.329433	−0.164716	+	0.986341i	$0.552671\pi$
$614$	1.61780e20	0.198455
$615$	7.56615e19	0.0916878
$616$	7.67110e19	0.0918337
$617$	1.27670e21	1.50990	0.754952	−	0.655780i	$-0.227660\pi$
$617$	1.27670e21	1.50990	0.754952	+	0.655780i	$0.227660\pi$
$618$	−4.69286e19	−0.0548308
$619$	3.78774e19	0.0437220	0.0218610	−	0.999761i	$-0.493041\pi$
$619$	3.78774e19	0.0437220	0.0218610	+	0.999761i	$0.493041\pi$
$620$	3.32534e20	0.379226
$621$	−2.57767e19	−0.0290429
$622$	−1.32020e20	−0.146965
$623$	−4.73952e19	−0.0521284
$624$	−2.27951e20	−0.247718
$625$	6.86321e20	0.736932
$626$	1.70251e19	0.0180627
$627$	3.85418e17	0.000404041 0
$628$	1.47764e20	0.153063
$629$	1.65425e20	0.169325
$630$	−7.65902e19	−0.0774674
$631$	−9.62356e20	−0.961868	−0.480934	−	0.876757i	$-0.659702\pi$
$631$	−9.62356e20	−0.961868	−0.480934	+	0.876757i	$0.659702\pi$
$632$	2.93281e19	0.0289672
$633$	2.68658e20	0.262224
$634$	−1.86997e20	−0.180371
$635$	2.71015e19	0.0258340
$636$	2.70287e19	0.0254623
$637$	4.35207e20	0.405182
$638$	−8.53217e18	−0.00785063
$639$	2.41711e20	0.219806
$640$	−2.75296e20	−0.247429
$641$	−8.19634e20	−0.728089	−0.364045	−	0.931382i	$-0.618604\pi$
$641$	−8.19634e20	−0.728089	−0.364045	+	0.931382i	$0.618604\pi$
$642$	−3.27096e18	−0.00287186
$643$	−5.37717e20	−0.466629	−0.233314	−	0.972401i	$-0.574957\pi$
$643$	−5.37717e20	−0.466629	−0.233314	+	0.972401i	$0.574957\pi$
$644$	9.90278e19	0.0849402
$645$	9.61245e19	0.0814960
$646$	−1.58431e18	−0.00132769
$647$	−2.01975e21	−1.67307	−0.836537	−	0.547911i	$-0.815423\pi$
$647$	−2.01975e21	−1.67307	−0.836537	+	0.547911i	$0.815423\pi$
$648$	−5.09511e20	−0.417197
$649$	3.20581e20	0.259479
$650$	−4.39978e20	−0.352031
$651$	3.46488e20	0.274051
$652$	1.33273e21	1.04204
$653$	1.16246e21	0.898525	0.449262	−	0.893400i	$-0.351687\pi$
$653$	1.16246e21	0.898525	0.449262	+	0.893400i	$0.351687\pi$
$654$	−5.08673e19	−0.0388692
$655$	4.47677e20	0.338185
$656$	−1.85436e21	−1.38489
$657$	−3.11135e20	−0.229725
$658$	2.85678e20	0.208537
$659$	−1.40047e21	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$659$	−1.40047e21	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$660$	−1.29165e19	−0.00921652
$661$	1.81218e21	1.27847	0.639235	−	0.769012i	$-0.279251\pi$
$661$	1.81218e21	1.27847	0.639235	+	0.769012i	$0.279251\pi$
$662$	6.18253e20	0.431252
$663$	1.93179e20	0.133232
$664$	−8.01528e20	−0.546586
$665$	6.19764e18	0.00417892
$666$	1.30702e20	0.0871418
$667$	−2.26929e19	−0.0149605
$668$	8.27701e19	0.0539572
$669$	2.90884e20	0.187510
$670$	−4.58690e19	−0.0292387
$671$	2.95333e20	0.186163
$672$	−2.17631e20	−0.135660
$673$	−1.81208e21	−1.11703	−0.558515	−	0.829495i	$-0.688629\pi$
$673$	−1.81208e21	−1.11703	−0.558515	+	0.829495i	$0.688629\pi$
$674$	2.22998e20	0.135942
$675$	−5.43896e20	−0.327897
$676$	−2.58439e21	−1.54084
$677$	−2.82560e20	−0.166608	−0.0833041	−	0.996524i	$-0.526547\pi$
$677$	−2.82560e20	−0.166608	−0.0833041	+	0.996524i	$0.526547\pi$
$678$	1.29646e20	0.0756024
$679$	−2.08216e21	−1.20086
$680$	1.09392e20	0.0623975
$681$	−1.15564e20	−0.0651956
$682$	1.01320e20	0.0565344
$683$	1.77601e20	0.0980143	0.0490072	−	0.998798i	$-0.484394\pi$
$683$	1.77601e20	0.0980143	0.0490072	+	0.998798i	$0.484394\pi$
$684$	2.07583e19	0.0113311
$685$	−9.10003e20	−0.491319
$686$	−3.74569e20	−0.200033
$687$	−3.77984e20	−0.199663
$688$	−2.35588e21	−1.23095
$689$	4.62417e20	0.238995
$690$	2.07160e18	0.00105910
$691$	−3.11441e21	−1.57503	−0.787517	−	0.616293i	$-0.788634\pi$
$691$	−3.11441e21	−1.57503	−0.787517	+	0.616293i	$0.788634\pi$
$692$	−3.67871e20	−0.184035
$693$	3.86993e20	0.191516
$694$	2.78765e20	0.136472
$695$	−1.71514e20	−0.0830640
$696$	3.29265e19	0.0157753
$697$	1.57149e21	0.744845
$698$	4.63204e20	0.217198
$699$	7.64306e20	0.354559
$700$	2.08952e21	0.958984
$701$	−9.50953e20	−0.431791	−0.215896	−	0.976416i	$-0.569267\pi$
$701$	−9.50953e20	−0.431791	−0.215896	+	0.976416i	$0.569267\pi$
$702$	3.10571e20	0.139519
$703$	−1.05764e19	−0.00470080
$704$	2.72016e20	0.119619
$705$	−9.91051e19	−0.0431199
$706$	8.27285e20	0.356139
$707$	2.37060e21	1.00975
$708$	−6.00473e20	−0.253072
$709$	2.24986e21	0.938230	0.469115	−	0.883137i	$-0.344573\pi$
$709$	2.24986e21	0.938230	0.469115	+	0.883137i	$0.344573\pi$
$710$	−3.95269e19	−0.0163100
$711$	1.47955e20	0.0604099
$712$	5.34845e19	0.0216087
$713$	2.69480e20	0.107735
$714$	5.53230e19	0.0218861
$715$	−2.20981e20	−0.0865086
$716$	−3.95749e21	−1.53311
$717$	1.80561e20	0.0692196
$718$	4.81864e20	0.182806
$719$	3.93394e21	1.47694	0.738468	−	0.674289i	$-0.235550\pi$
$719$	3.93394e21	1.47694	0.738468	+	0.674289i	$0.235550\pi$
$720$	−6.51195e20	−0.241945
$721$	3.81296e21	1.40200
$722$	−6.55257e20	−0.238442
$723$	−7.58337e20	−0.273102
$724$	2.75449e21	0.981752
$725$	−4.78828e20	−0.168906
$726$	1.21292e20	0.0423454
$727$	4.95570e21	1.71237	0.856183	−	0.516673i	$-0.172830\pi$
$727$	4.95570e21	1.71237	0.856183	+	0.516673i	$0.172830\pi$
$728$	−2.45823e21	−0.840691
$729$	−2.37515e21	−0.803959
$730$	5.08798e19	0.0170460
$731$	1.99651e21	0.662050
$732$	−5.53180e20	−0.181566
$733$	−1.29373e20	−0.0420306	−0.0210153	−	0.999779i	$-0.506690\pi$
$733$	−1.29373e20	−0.0420306	−0.0210153	+	0.999779i	$0.506690\pi$
$734$	−1.43142e21	−0.460305
$735$	−4.32375e19	−0.0137628
$736$	−1.69262e20	−0.0533304
$737$	2.31766e20	0.0722842
$738$	1.24164e21	0.383329
$739$	8.61649e20	0.263328	0.131664	−	0.991294i	$-0.457968\pi$
$739$	8.61649e20	0.263328	0.131664	+	0.991294i	$0.457968\pi$
$740$	3.54446e20	0.107229
$741$	−1.23508e19	−0.00369879
$742$	1.32428e20	0.0392599
$743$	−1.73621e21	−0.509549	−0.254775	−	0.967000i	$-0.582001\pi$
$743$	−1.73621e21	−0.509549	−0.254775	+	0.967000i	$0.582001\pi$
$744$	−3.91005e20	−0.113602
$745$	1.88069e21	0.540936
$746$	5.01317e20	0.142748
$747$	−4.04357e21	−1.13988
$748$	−2.68277e20	−0.0748724
$749$	2.65766e20	0.0734321
$750$	9.17680e19	0.0251034
$751$	1.51988e21	0.411632	0.205816	−	0.978591i	$-0.434015\pi$
$751$	1.51988e21	0.411632	0.205816	+	0.978591i	$0.434015\pi$
$752$	2.42893e21	0.651299
$753$	−1.11310e21	−0.295510
$754$	2.73416e20	0.0718685
$755$	−8.91299e20	−0.231964
$756$	−1.47494e21	−0.380069
$757$	−1.52254e21	−0.388462	−0.194231	−	0.980956i	$-0.562221\pi$
$757$	−1.52254e21	−0.388462	−0.194231	+	0.980956i	$0.562221\pi$
$758$	−6.14860e20	−0.155331
$759$	−1.04673e19	−0.00261832
$760$	−6.99391e18	−0.00173228
$761$	5.09798e21	1.25030	0.625148	−	0.780506i	$-0.285039\pi$
$761$	5.09798e21	1.25030	0.625148	+	0.780506i	$0.285039\pi$
$762$	−1.54671e19	−0.00375618
$763$	4.13298e21	0.993869
$764$	5.96025e21	1.41927
$765$	5.51861e20	0.130127
$766$	1.14050e21	0.266305
$767$	−1.02731e22	−2.37540
$768$	−3.83117e20	−0.0877247
$769$	7.07991e20	0.160539	0.0802694	−	0.996773i	$-0.474422\pi$
$769$	7.07991e20	0.160539	0.0802694	+	0.996773i	$0.474422\pi$
$770$	−6.32849e19	−0.0142108
$771$	−9.35597e19	−0.0208056
$772$	−9.22445e20	−0.203147
$773$	3.99256e21	0.870774	0.435387	−	0.900243i	$-0.356611\pi$
$773$	3.99256e21	0.870774	0.435387	+	0.900243i	$0.356611\pi$
$774$	1.57744e21	0.340719
$775$	5.68612e21	1.21634
$776$	2.34968e21	0.497789
$777$	3.69320e20	0.0774899
$778$	1.74592e21	0.362808
$779$	−1.00473e20	−0.0206784
$780$	4.13914e20	0.0843725
$781$	1.99720e20	0.0403218
$782$	4.30272e19	0.00860385
$783$	3.37994e20	0.0669415
$784$	1.05969e21	0.207878
$785$	−2.51154e20	−0.0487998
$786$	−2.55494e20	−0.0491712
$787$	−3.21137e21	−0.612181	−0.306090	−	0.952002i	$-0.599021\pi$
$787$	−3.21137e21	−0.612181	−0.306090	+	0.952002i	$0.599021\pi$
$788$	7.13550e21	1.34734
$789$	6.29556e20	0.117749
$790$	−2.41951e19	−0.00448253
$791$	−1.05337e22	−1.93312
$792$	−4.36714e20	−0.0793886
$793$	−9.46401e21	−1.70422
$794$	−1.73344e21	−0.309210
$795$	−4.59408e19	−0.00811792
$796$	4.03103e21	0.705615
$797$	−5.85333e21	−1.01500	−0.507500	−	0.861652i	$-0.669430\pi$
$797$	−5.85333e21	−1.01500	−0.507500	+	0.861652i	$0.669430\pi$
$798$	−3.53705e18	−0.000607603 0
$799$	−2.05842e21	−0.350294
$800$	−3.57148e21	−0.602107
$801$	2.69820e20	0.0450640
$802$	−1.11662e21	−0.184756
$803$	−2.57084e20	−0.0421414
$804$	−4.34115e20	−0.0704993
$805$	−1.68318e20	−0.0270808
$806$	−3.24683e21	−0.517544
$807$	−3.19358e20	−0.0504343
$808$	−2.67517e21	−0.418568
$809$	6.41682e21	0.994732	0.497366	−	0.867541i	$-0.334301\pi$
$809$	6.41682e21	0.994732	0.497366	+	0.867541i	$0.334301\pi$
$810$	4.20335e20	0.0645591
$811$	−1.22537e21	−0.186471	−0.0932357	−	0.995644i	$-0.529721\pi$
$811$	−1.22537e21	−0.186471	−0.0932357	+	0.995644i	$0.529721\pi$
$812$	−1.29849e21	−0.195780
$813$	1.02017e21	0.152403
$814$	1.07997e20	0.0159855
$815$	−2.26525e21	−0.332226
$816$	4.70374e20	0.0683545
$817$	−1.27646e20	−0.0183798
$818$	1.22753e21	0.175139
$819$	−1.24013e22	−1.75323
$820$	3.36714e21	0.471691
$821$	1.26391e22	1.75446	0.877230	−	0.480071i	$-0.159389\pi$
$821$	1.26391e22	1.75446	0.877230	+	0.480071i	$0.159389\pi$
$822$	5.19347e20	0.0714364
$823$	−7.70128e21	−1.04970	−0.524849	−	0.851196i	$-0.675878\pi$
$823$	−7.70128e21	−1.04970	−0.524849	+	0.851196i	$0.675878\pi$
$824$	−4.30284e21	−0.581168
$825$	−2.20865e20	−0.0295612
$826$	−2.94203e21	−0.390209
$827$	−1.18556e22	−1.55824	−0.779119	−	0.626876i	$-0.784333\pi$
$827$	−1.18556e22	−1.55824	−0.779119	+	0.626876i	$0.784333\pi$
$828$	−5.63763e20	−0.0734292
$829$	1.38940e22	1.79336	0.896681	−	0.442677i	$-0.145971\pi$
$829$	1.38940e22	1.79336	0.896681	+	0.442677i	$0.145971\pi$
$830$	6.61243e20	0.0845815
$831$	−1.23884e20	−0.0157040
$832$	−8.71683e21	−1.09505
$833$	−8.98045e20	−0.111805
$834$	9.78846e19	0.0120773
$835$	−1.40684e20	−0.0172027
$836$	1.71522e19	0.00207861
$837$	−4.01370e21	−0.482063
$838$	−7.56259e20	−0.0900203
$839$	−1.09260e22	−1.28898	−0.644488	−	0.764614i	$-0.722930\pi$
$839$	−1.09260e22	−1.28898	−0.644488	+	0.764614i	$0.722930\pi$
$840$	2.44223e20	0.0285556
$841$	2.97558e20	0.0344828
$842$	7.59746e20	0.0872625
$843$	−9.29196e20	−0.105779
$844$	1.19560e22	1.34902
$845$	4.39269e21	0.491253
$846$	−1.62636e21	−0.180276
$847$	−9.85497e21	−1.08275
$848$	1.12594e21	0.122616
$849$	−2.08063e21	−0.224588
$850$	9.07890e20	0.0971384
$851$	2.87237e20	0.0304627
$852$	−3.74092e20	−0.0393261
$853$	9.24945e21	0.963825	0.481912	−	0.876219i	$-0.339942\pi$
$853$	9.24945e21	0.963825	0.481912	+	0.876219i	$0.339942\pi$
$854$	−2.71032e21	−0.279954
$855$	−3.52830e19	−0.00361260
$856$	−2.99912e20	−0.0304397
$857$	−1.36929e21	−0.137765	−0.0688826	−	0.997625i	$-0.521943\pi$
$857$	−1.36929e21	−0.137765	−0.0688826	+	0.997625i	$0.521943\pi$
$858$	1.26116e20	0.0125781
$859$	3.58229e21	0.354170	0.177085	−	0.984196i	$-0.443333\pi$
$859$	3.58229e21	0.354170	0.177085	+	0.984196i	$0.443333\pi$
$860$	4.27780e21	0.419259
$861$	3.50844e21	0.340871
$862$	1.68633e20	0.0162419
$863$	9.94939e21	0.949983	0.474991	−	0.879990i	$-0.342451\pi$
$863$	9.94939e21	0.949983	0.474991	+	0.879990i	$0.342451\pi$
$864$	2.52102e21	0.238629
$865$	6.25271e20	0.0586743
$866$	1.11401e21	0.103635
$867$	1.58915e21	0.146562
$868$	1.54197e22	1.40986
$869$	1.22252e20	0.0110818
$870$	−2.71637e19	−0.00244115
$871$	−7.42700e21	−0.661725
$872$	−4.66398e21	−0.411987
$873$	1.18537e22	1.03812
$874$	−2.75093e18	−0.000238860 0
$875$	−7.45616e21	−0.641882
$876$	4.81538e20	0.0411008
$877$	−5.94386e21	−0.503005	−0.251502	−	0.967857i	$-0.580925\pi$
$877$	−5.94386e21	−0.503005	−0.251502	+	0.967857i	$0.580925\pi$
$878$	3.78308e21	0.317422
$879$	−2.29901e21	−0.191260
$880$	−5.38069e20	−0.0443831
$881$	−1.42928e22	−1.16896	−0.584478	−	0.811409i	$-0.698701\pi$
$881$	−1.42928e22	−1.16896	−0.584478	+	0.811409i	$0.698701\pi$
$882$	−7.09546e20	−0.0575395
$883$	−8.76464e20	−0.0704740	−0.0352370	−	0.999379i	$-0.511219\pi$
$883$	−8.76464e20	−0.0704740	−0.0352370	+	0.999379i	$0.511219\pi$
$884$	8.59701e21	0.685418
$885$	1.02063e21	0.0806849
$886$	2.13484e21	0.167345
$887$	4.44570e21	0.345552	0.172776	−	0.984961i	$-0.444726\pi$
$887$	4.44570e21	0.345552	0.172776	+	0.984961i	$0.444726\pi$
$888$	−4.16770e20	−0.0321217
$889$	1.25670e21	0.0960439
$890$	−4.41235e19	−0.00334384
$891$	−2.12386e21	−0.159604
$892$	1.29452e22	0.964652
$893$	1.31604e20	0.00972485
$894$	−1.07333e21	−0.0786505
$895$	6.72656e21	0.488788
$896$	−1.27656e22	−0.919876
$897$	3.35429e20	0.0239694
$898$	3.48595e21	0.247029
$899$	−3.53353e21	−0.248319
$900$	−1.18956e22	−0.829024
$901$	−9.54191e20	−0.0659477
$902$	1.02594e21	0.0703189
$903$	4.45732e21	0.302981
$904$	1.18871e22	0.801332
$905$	−4.68181e21	−0.313004
$906$	5.08673e20	0.0337270
$907$	1.92033e22	1.26276	0.631382	−	0.775472i	$-0.282488\pi$
$907$	1.92033e22	1.26276	0.631382	+	0.775472i	$0.282488\pi$
$908$	−5.14290e21	−0.335401
$909$	−1.34958e22	−0.872907
$910$	2.02798e21	0.130093
$911$	−2.68156e21	−0.170608	−0.0853040	−	0.996355i	$-0.527186\pi$
$911$	−2.68156e21	−0.170608	−0.0853040	+	0.996355i	$0.527186\pi$
$912$	−3.00732e19	−0.00189766
$913$	−3.34111e21	−0.209103
$914$	1.38002e21	0.0856622
$915$	9.40242e20	0.0578871
$916$	−1.68213e22	−1.02717
$917$	2.07589e22	1.25729
$918$	−6.40858e20	−0.0384983
$919$	3.32379e22	1.98047	0.990233	−	0.139426i	$-0.0445256\pi$
$919$	3.32379e22	1.98047	0.990233	+	0.139426i	$0.0445256\pi$
$920$	1.89943e20	0.0112257
$921$	−2.60246e21	−0.152559
$922$	−3.97208e21	−0.230960
$923$	−6.40010e21	−0.369125
$924$	−5.98943e20	−0.0342646
$925$	6.06080e21	0.343928
$926$	−3.07471e21	−0.173070
$927$	−2.17071e22	−1.21200
$928$	2.21943e21	0.122922
$929$	−9.11238e21	−0.500627	−0.250313	−	0.968165i	$-0.580534\pi$
$929$	−9.11238e21	−0.500627	−0.250313	+	0.968165i	$0.580534\pi$
$930$	3.22570e20	0.0175793
$931$	5.74161e19	0.00310392
$932$	3.40137e22	1.82404
$933$	2.12373e21	0.112976
$934$	7.59860e21	0.400988
$935$	4.55991e20	0.0238709
$936$	1.39946e22	0.726762
$937$	2.11853e22	1.09141	0.545705	−	0.837977i	$-0.316262\pi$
$937$	2.11853e22	1.09141	0.545705	+	0.837977i	$0.316262\pi$
$938$	−2.12696e21	−0.108702
$939$	−2.73873e20	−0.0138853
$940$	−4.41045e21	−0.221832
$941$	4.12363e20	0.0205759	0.0102879	−	0.999947i	$-0.496725\pi$
$941$	4.12363e20	0.0205759	0.0102879	+	0.999947i	$0.496725\pi$
$942$	1.43336e20	0.00709535
$943$	2.72867e21	0.134003
$944$	−2.50141e22	−1.21870
$945$	2.50697e21	0.121174
$946$	1.30341e21	0.0625025
$947$	−7.76252e21	−0.369299	−0.184649	−	0.982804i	$-0.559115\pi$
$947$	−7.76252e21	−0.369299	−0.184649	+	0.982804i	$0.559115\pi$
$948$	−2.28988e20	−0.0108081
$949$	8.23833e21	0.385783
$950$	−5.80455e19	−0.00269676
$951$	3.00811e21	0.138656
$952$	5.07251e21	0.231978
$953$	2.92068e22	1.32522	0.662608	−	0.748966i	$-0.269450\pi$
$953$	2.92068e22	1.32522	0.662608	+	0.748966i	$0.269450\pi$
$954$	−7.53908e20	−0.0339395
$955$	−1.01306e22	−0.452493
$956$	8.03544e21	0.356103
$957$	1.37252e20	0.00603502
$958$	−4.17390e21	−0.182096
$959$	−4.21970e22	−1.82660
$960$	8.66010e20	0.0371954
$961$	1.84956e22	0.788212
$962$	−3.46078e21	−0.146339
$963$	−1.51300e21	−0.0634807
$964$	−3.37481e22	−1.40498
$965$	1.56788e21	0.0647677
$966$	9.60606e19	0.00393747
$967$	1.14028e22	0.463783	0.231891	−	0.972742i	$-0.425509\pi$
$967$	1.14028e22	0.463783	0.231891	+	0.972742i	$0.425509\pi$
$968$	1.11211e22	0.448832
$969$	2.54858e19	0.00102063
$970$	−1.93843e21	−0.0770304
$971$	1.21668e22	0.479769	0.239884	−	0.970801i	$-0.422890\pi$
$971$	1.21668e22	0.479769	0.239884	+	0.970801i	$0.422890\pi$
$972$	1.26670e22	0.495652
$973$	−7.95313e21	−0.308810
$974$	−1.91480e21	−0.0737786
$975$	7.07767e21	0.270617
$976$	−2.30440e22	−0.874349
$977$	−4.57667e22	−1.72322	−0.861609	−	0.507573i	$-0.830543\pi$
$977$	−4.57667e22	−1.72322	−0.861609	+	0.507573i	$0.830543\pi$
$978$	1.29280e21	0.0483047
$979$	2.22946e20	0.00826667
$980$	−1.92419e21	−0.0708030
$981$	−2.35289e22	−0.859181
$982$	−4.26265e21	−0.154470
$983$	−1.82387e22	−0.655909	−0.327954	−	0.944694i	$-0.606359\pi$
$983$	−1.82387e22	−0.655909	−0.327954	+	0.944694i	$0.606359\pi$
$984$	−3.95920e21	−0.141301
$985$	−1.21282e22	−0.429562
$986$	−5.64190e20	−0.0198312
$987$	−4.59552e21	−0.160308
$988$	−5.49646e20	−0.0190286
$989$	3.46666e21	0.119107
$990$	3.60279e20	0.0122850
$991$	−8.03876e21	−0.272042	−0.136021	−	0.990706i	$-0.543432\pi$
$991$	−8.03876e21	−0.272042	−0.136021	+	0.990706i	$0.543432\pi$
$992$	−2.63558e22	−0.885196
$993$	−9.94546e21	−0.331517
$994$	−1.83287e21	−0.0606364
$995$	−6.85155e21	−0.224965
$996$	6.25816e21	0.203940
$997$	5.51080e21	0.178238	0.0891192	−	0.996021i	$-0.471595\pi$
$997$	5.51080e21	0.178238	0.0891192	+	0.996021i	$0.471595\pi$
$998$	1.72522e21	0.0553816
$999$	−4.27818e21	−0.136307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.9	✓	16	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+43.1693 q^{2} -694.438 q^{3} -30904.4 q^{4} +52528.3 q^{5} -29978.4 q^{6} +2.43575e6 q^{7} -2.74869e6 q^{8} -1.38667e7 q^{9} +O(q^{10})\)	\(q+43.1693 q^{2} -694.438 q^{3} -30904.4 q^{4} +52528.3 q^{5} -29978.4 q^{6} +2.43575e6 q^{7} -2.74869e6 q^{8} -1.38667e7 q^{9} +2.26761e6 q^{10} -1.14577e7 q^{11} +2.14612e7 q^{12} +3.67166e8 q^{13} +1.05150e8 q^{14} -3.64777e7 q^{15} +8.94017e8 q^{16} -7.57642e8 q^{17} -5.98614e8 q^{18} +4.84395e7 q^{19} -1.62336e9 q^{20} -1.69148e9 q^{21} -4.94622e8 q^{22} -1.31554e9 q^{23} +1.90880e9 q^{24} -2.77584e10 q^{25} +1.58503e10 q^{26} +1.95940e10 q^{27} -7.52754e10 q^{28} +1.72499e10 q^{29} -1.57472e9 q^{30} -2.04844e11 q^{31} +1.28663e11 q^{32} +7.95669e9 q^{33} -3.27069e10 q^{34} +1.27946e11 q^{35} +4.28541e11 q^{36} -2.18341e11 q^{37} +2.09110e9 q^{38} -2.54974e11 q^{39} -1.44384e11 q^{40} -2.07419e12 q^{41} -7.30199e10 q^{42} -2.63516e12 q^{43} +3.54094e11 q^{44} -7.28392e11 q^{45} -5.67910e10 q^{46} +2.71687e12 q^{47} -6.20839e11 q^{48} +1.18531e12 q^{49} -1.19831e12 q^{50} +5.26136e11 q^{51} -1.13471e13 q^{52} +1.25942e12 q^{53} +8.45858e11 q^{54} -6.01855e11 q^{55} -6.69513e12 q^{56} -3.36383e10 q^{57} +7.44665e11 q^{58} -2.79795e13 q^{59} +1.12732e12 q^{60} -2.57758e13 q^{61} -8.84295e12 q^{62} -3.37757e13 q^{63} -2.37408e13 q^{64} +1.92866e13 q^{65} +3.43485e11 q^{66} -2.02279e13 q^{67} +2.34145e13 q^{68} +9.13562e11 q^{69} +5.52333e12 q^{70} -1.74311e13 q^{71} +3.81152e13 q^{72} +2.24376e13 q^{73} -9.42565e12 q^{74} +1.92765e13 q^{75} -1.49700e12 q^{76} -2.79082e13 q^{77} -1.10071e13 q^{78} -1.06698e13 q^{79} +4.69612e13 q^{80} +1.85365e14 q^{81} -8.95411e13 q^{82} +2.91603e14 q^{83} +5.22741e13 q^{84} -3.97977e13 q^{85} -1.13758e14 q^{86} -1.19790e13 q^{87} +3.14938e13 q^{88} -1.94582e13 q^{89} -3.14442e13 q^{90} +8.94325e14 q^{91} +4.06560e13 q^{92} +1.42251e14 q^{93} +1.17285e14 q^{94} +2.54445e12 q^{95} -8.93487e13 q^{96} -8.54834e14 q^{97} +5.11692e13 q^{98} +1.58881e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more