LMFDB - Embedded newform 1.54.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,54,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 54, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 54);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 54 $
Character orbit:	$[\chi]$	$=$	1.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:	$17.7903107608$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2315873743412x^{2} - 421178019174503472x + 612167648493870378955584 $ x^4 - x^3 - 2315873743412x^2 - 421178019174503472x + 612167648493870378955584
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-708531.$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} +O(q^{10})$	\(q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} -1.92700e25 q^{10} +4.70740e27 q^{11} -1.15021e28 q^{12} -5.49891e29 q^{13} +2.76633e30 q^{14} +1.48027e30 q^{15} -6.21955e31 q^{16} -1.83884e32 q^{17} -1.99134e33 q^{18} -8.16294e33 q^{19} -3.98062e32 q^{20} -2.12502e35 q^{21} -4.00779e35 q^{22} +8.36591e35 q^{23} +5.99457e36 q^{24} -1.10510e37 q^{25} +4.68167e37 q^{26} +2.62013e37 q^{27} +5.71444e37 q^{28} -7.80382e38 q^{29} -1.26027e38 q^{30} -3.24461e39 q^{31} -2.96069e39 q^{32} +3.07868e40 q^{33} +1.56555e40 q^{34} -7.35423e39 q^{35} -4.11353e40 q^{36} -2.65824e40 q^{37} +6.94977e41 q^{38} -3.59634e42 q^{39} +2.07459e41 q^{40} +5.60775e41 q^{41} +1.80920e43 q^{42} +2.91200e42 q^{43} -8.27894e42 q^{44} +5.29393e42 q^{45} -7.12258e43 q^{46} -3.43769e43 q^{47} -4.06764e44 q^{48} +4.38874e44 q^{49} +9.40861e44 q^{50} -1.20262e45 q^{51} +9.67099e44 q^{52} +5.37279e45 q^{53} -2.23073e45 q^{54} +1.06546e45 q^{55} -2.97820e46 q^{56} -5.33864e46 q^{57} +6.64402e46 q^{58} +1.17524e47 q^{59} -2.60336e45 q^{60} -6.10529e46 q^{61} +2.76240e47 q^{62} -7.59978e47 q^{63} +8.12275e47 q^{64} -1.24461e47 q^{65} -2.62113e48 q^{66} +5.08562e47 q^{67} +3.23399e47 q^{68} +5.47138e48 q^{69} +6.26125e47 q^{70} -2.80926e48 q^{71} +2.14386e49 q^{72} -1.95202e49 q^{73} +2.26317e48 q^{74} -7.22745e49 q^{75} +1.43562e49 q^{76} -1.52954e50 q^{77} +3.06185e50 q^{78} +1.95888e50 q^{79} -1.40772e49 q^{80} -2.82006e50 q^{81} -4.77433e49 q^{82} -9.78793e49 q^{83} +3.73730e50 q^{84} -4.16200e49 q^{85} -2.47922e50 q^{86} -5.10376e51 q^{87} +4.31475e51 q^{88} +4.98452e50 q^{89} -4.50715e50 q^{90} +1.78672e52 q^{91} -1.47132e51 q^{92} -2.12201e52 q^{93} +2.92678e51 q^{94} -1.84758e51 q^{95} -1.93632e52 q^{96} -1.99451e52 q^{97} -3.73649e52 q^{98} +1.10104e53 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!12 q^{9}+O(q^{10}) $ 4 * q - 68476320 * q^2 - 1048411007280 * q^3 + 7829639419798528 * q^4 - 4563895793294313000 * q^5 + 365243285516994476928 * q^6 - 224841770748445429600 * q^7 + 139144349902380051824640 * q^8 + 11374560253581116395684212 * q^9	$ 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 20\!\cdots\!84 q^{99}+O(q^{100}) $ 4 * q - 68476320 * q^2 - 1048411007280 * q^3 + 7829639419798528 * q^4 - 4563895793294313000 * q^5 + 365243285516994476928 * q^6 - 224841770748445429600 * q^7 + 139144349902380051824640 * q^8 + 11374560253581116395684212 * q^9 + 239691034935725362703784000 * q^10 + 2482225436399137396212828528 * q^11 - 36954074065409878778429091840 * q^12 + 38846785417115118418757458040 * q^13 - 2318389217831653006768429089024 * q^14 + 10885572770546350531014554412000 * q^15 - 158675761303426594387641091751936 * q^16 - 869470789827683332623267869375160 * q^17 - 6763457530054882037574097250222880 * q^18 - 25573430606481293737377136094590960 * q^19 - 137124186244908431721319713321216000 * q^20 - 456430072728043514442750337944104832 * q^21 - 930239272324579210970924539473171840 * q^22 + 692283403499940921426611559815316960 * q^23 + 8087484160806183674287697801240248320 * q^24 + 36481255519181820020535795184467437500 * q^25 + 88199592302469577023283184091414497088 * q^26 + 85289145712610214901983766257673297440 * q^27 - 5693966184427848677134093343909109760 * q^28 - 1403448065249545071892827367228561632840 * q^29 - 5799093432823921615312476874120821216000 * q^30 - 3964172885133396823441211087460727887232 * q^31 + 3478175004061909463146496356345215713280 * q^32 + 26488618539649572306469337360654123586240 * q^33 + 149997773608319010417738024908146242937536 * q^34 + 61365948170559642529868826584708753304000 * q^35 + 74373890656883085418751005021443502838784 * q^36 - 283737807523680188930907412534612515795880 * q^37 - 2149858349100743242412726210681586741479040 * q^38 - 3695759405159081384443679869760359201600416 * q^39 - 530824655589569872286083924732862423040000 * q^40 + 816268439352205816307560932682632884757288 * q^41 + 34473336675516302350057635130637873086909440 * q^42 + 45680017888765970285202819125021276867644400 * q^43 + 36450257868828743991533939202628376274333696 * q^44 - 52785302554790432865174172783106255610789000 * q^45 - 286598377899888278123152881845505043619242752 * q^46 - 450331332464449690190061856166374876708223040 * q^47 - 307327868606734954261884348178650744005591040 * q^48 + 61256589204322440136838991964906594854806628 * q^49 + 521470775015683964723409941128468604170500000 * q^50 + 4823104417223604238685131462744139603812556448 * q^51 + 6480873745173555872757727943119261362842777600 * q^52 + 3894630980633224571473003534722579109607488920 * q^53 - 9094643349894867160783307676594158361928776960 * q^54 - 25220087960941681699071033843031097345513916000 * q^55 - 41708301235969326798480993683317763265335132160 * q^56 - 78794438935790744156133212572387836678302205120 * q^57 + 23153390818000102952173078969301145284748805440 * q^58 + 161352440713620380366889082872890081870684067120 * q^59 + 406305479737925709888509415210821103661353984000 * q^60 + 65647964430669998286897420448040378258467279928 * q^61 + 397783228528983419561799088374192602352940661760 * q^62 - 302986559547633524951279897150694105228921738720 * q^63 - 1033735951572319175631379922707833053066697900032 * q^64 - 3420620126550512806970332375686936386825214798000 * q^65 - 658347942888276364671353073747068107649649237504 * q^66 - 1114206317023626852397290701407230552884994982960 * q^67 + 2848472333882807118405541680155589548651324344320 * q^68 + 775291276168249766930956334518267852448076104064 * q^69 + 33179725699094578918821931009364962909309028928000 * q^70 + 3568565136657140046536067623675232742954247775648 * q^71 + 26402495617891679740981292232213348882933665464320 * q^72 - 70697396612705842206652346649767546611106446705240 * q^73 - 2477665041456578897595255396512213772982320606144 * q^74 - 214147644415917420957952976584023331338227237250000 * q^75 + 45189859364823457604586927205450004182295006842880 * q^76 - 161023821416166064076421008340115759390173471196800 * q^77 + 512081797195935502825354508308769411884974336211200 * q^78 - 156417020870005797258130007144678737115075518344640 * q^79 + 1135588155590291950317639086884448883835074772992000 * q^80 - 498743339483968532647094896032944674900788125971356 * q^81 + 1595344511843776298585510858680959074676233895092160 * q^82 - 2616078236644862619515249170129703738064518568891120 * q^83 - 769036580140824400081375315496419857132807898497024 * q^84 - 2322985242765977498040783878693923846942012787106000 * q^85 - 771473689440649042704510533443081756253708267624832 * q^86 - 4553516071908987502170780484180858967295593004331680 * q^87 + 5676678682320308097974311975312643702936459537940480 * q^88 - 377838445322199523132380916699165405584669879895320 * q^89 + 20963916598038401334962666668658272688885372614152000 * q^90 + 12668228612190081366491587480915595422042752342094528 * q^91 + 8910978937854086377493208678167975007758313267978240 * q^92 - 9941509412818307372855389204673554966584205049372160 * q^93 - 37159704993639903541096652460057479885138542709712384 * q^94 - 17088387525725080516970439013001314242158750454180000 * q^95 - 115890361493294838169648124263288994270902966699425792 * q^96 + 10362822344952442405677621761316902058987153293434760 * q^97 - 88214006056362955165305640276151180685109758813947040 * q^98 + 200357011548750056817277275156798035565052172823063984 * 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 $

$2$	−8.51381e7	−0.897075	−0.448538	−	0.893764i	$-0.648055\pi$
$2$	−8.51381e7	−0.897075	−0.448538	+	0.893764i	$0.648055\pi$
$3$	6.54009e12	1.48549	0.742746	−	0.669573i	$-0.233523\pi$
$3$	6.54009e12	1.48549	0.742746	+	0.669573i	$0.233523\pi$
$4$	−1.75871e15	−0.195256
$5$	2.26338e17	0.0679285	0.0339643	−	0.999423i	$-0.489187\pi$
$5$	2.26338e17	0.0679285	0.0339643	+	0.999423i	$0.489187\pi$
$6$	−5.56810e20	−1.33260
$7$	−3.24923e22	−1.30822	−0.654112	−	0.756398i	$-0.726957\pi$
$7$	−3.24923e22	−1.30822	−0.654112	+	0.756398i	$0.726957\pi$
$8$	9.16589e23	1.07223
$9$	2.33895e25	1.20669
$10$	−1.92700e25	−0.0609370
$11$	4.70740e27	1.19090	0.595449	−	0.803393i	$-0.296974\pi$
$11$	4.70740e27	1.19090	0.595449	+	0.803393i	$0.296974\pi$
$12$	−1.15021e28	−0.290051
$13$	−5.49891e29	−1.66256	−0.831282	−	0.555852i	$-0.812392\pi$
$13$	−5.49891e29	−1.66256	−0.831282	+	0.555852i	$0.812392\pi$
$14$	2.76633e30	1.17357
$15$	1.48027e30	0.100907
$16$	−6.21955e31	−0.766619
$17$	−1.83884e32	−0.454620	−0.227310	−	0.973823i	$-0.572993\pi$
$17$	−1.83884e32	−0.454620	−0.227310	+	0.973823i	$0.572993\pi$
$18$	−1.99134e33	−1.08249
$19$	−8.16294e33	−1.05895	−0.529476	−	0.848325i	$-0.677611\pi$
$19$	−8.16294e33	−1.05895	−0.529476	+	0.848325i	$0.677611\pi$
$20$	−3.98062e32	−0.0132634
$21$	−2.12502e35	−1.94336
$22$	−4.00779e35	−1.06833
$23$	8.36591e35	0.686635	0.343317	−	0.939219i	$-0.388449\pi$
$23$	8.36591e35	0.686635	0.343317	+	0.939219i	$0.388449\pi$
$24$	5.99457e36	1.59280
$25$	−1.10510e37	−0.995386
$26$	4.68167e37	1.49144
$27$	2.62013e37	0.307032
$28$	5.71444e37	0.255438
$29$	−7.80382e38	−1.37645	−0.688224	−	0.725498i	$-0.741610\pi$
$29$	−7.80382e38	−1.37645	−0.688224	+	0.725498i	$0.741610\pi$
$30$	−1.26027e38	−0.0905214
$31$	−3.24461e39	−0.977413	−0.488707	−	0.872448i	$-0.662531\pi$
$31$	−3.24461e39	−0.977413	−0.488707	+	0.872448i	$0.662531\pi$
$32$	−2.96069e39	−0.384519
$33$	3.07868e40	1.76907
$34$	1.56555e40	0.407828
$35$	−7.35423e39	−0.0888657
$36$	−4.11353e40	−0.235613
$37$	−2.65824e40	−0.0736628	−0.0368314	−	0.999321i	$-0.511726\pi$
$37$	−2.65824e40	−0.0736628	−0.0368314	+	0.999321i	$0.511726\pi$
$38$	6.94977e41	0.949960
$39$	−3.59634e42	−2.46972
$40$	2.07459e41	0.0728353
$41$	5.60775e41	0.102333	0.0511666	−	0.998690i	$-0.483706\pi$
$41$	5.60775e41	0.102333	0.0511666	+	0.998690i	$0.483706\pi$
$42$	1.80920e43	1.74334
$43$	2.91200e42	0.150410	0.0752050	−	0.997168i	$-0.476039\pi$
$43$	2.91200e42	0.150410	0.0752050	+	0.997168i	$0.476039\pi$
$44$	−8.27894e42	−0.232530
$45$	5.29393e42	0.0819684
$46$	−7.12258e43	−0.615963
$47$	−3.43769e43	−0.168141	−0.0840705	−	0.996460i	$-0.526792\pi$
$47$	−3.43769e43	−0.168141	−0.0840705	+	0.996460i	$0.526792\pi$
$48$	−4.06764e44	−1.13881
$49$	4.38874e44	0.711448
$50$	9.40861e44	0.892936
$51$	−1.20262e45	−0.675334
$52$	9.67099e44	0.324625
$53$	5.37279e45	1.08865	0.544327	−	0.838873i	$-0.316785\pi$
$53$	5.37279e45	1.08865	0.544327	+	0.838873i	$0.316785\pi$
$54$	−2.23073e45	−0.275430
$55$	1.06546e45	0.0808959
$56$	−2.97820e46	−1.40272
$57$	−5.33864e46	−1.57307
$58$	6.64402e46	1.23478
$59$	1.17524e47	1.38851	0.694256	−	0.719728i	$-0.255733\pi$
$59$	1.17524e47	1.38851	0.694256	+	0.719728i	$0.255733\pi$
$60$	−2.60336e45	−0.0197027
$61$	−6.10529e46	−0.298171	−0.149086	−	0.988824i	$-0.547633\pi$
$61$	−6.10529e46	−0.298171	−0.149086	+	0.988824i	$0.547633\pi$
$62$	2.76240e47	0.876813
$63$	−7.59978e47	−1.57862
$64$	8.12275e47	1.11156
$65$	−1.24461e47	−0.112935
$66$	−2.62113e48	−1.58699
$67$	5.08562e47	0.206710	0.103355	−	0.994645i	$-0.467042\pi$
$67$	5.08562e47	0.206710	0.103355	+	0.994645i	$0.467042\pi$
$68$	3.23399e47	0.0887671
$69$	5.47138e48	1.01999
$70$	6.26125e47	0.0797192
$71$	−2.80926e48	−0.245610	−0.122805	−	0.992431i	$-0.539189\pi$
$71$	−2.80926e48	−0.245610	−0.122805	+	0.992431i	$0.539189\pi$
$72$	2.14386e49	1.29385
$73$	−1.95202e49	−0.817389	−0.408695	−	0.912671i	$-0.634016\pi$
$73$	−1.95202e49	−0.817389	−0.408695	+	0.912671i	$0.634016\pi$
$74$	2.26317e48	0.0660811
$75$	−7.22745e49	−1.47864
$76$	1.43562e49	0.206767
$77$	−1.52954e50	−1.55796
$78$	3.06185e50	2.21553
$79$	1.95888e50	1.01132	0.505662	−	0.862732i	$-0.331248\pi$
$79$	1.95888e50	1.01132	0.505662	+	0.862732i	$0.331248\pi$
$80$	−1.40772e49	−0.0520753
$81$	−2.82006e50	−0.750594
$82$	−4.77433e49	−0.0918005
$83$	−9.78793e49	−0.136496	−0.0682482	−	0.997668i	$-0.521741\pi$
$83$	−9.78793e49	−0.136496	−0.0682482	+	0.997668i	$0.521741\pi$
$84$	3.73730e50	0.379452
$85$	−4.16200e49	−0.0308816
$86$	−2.47922e50	−0.134929
$87$	−5.10376e51	−2.04470
$88$	4.31475e51	1.27692
$89$	4.98452e50	0.109342	0.0546712	−	0.998504i	$-0.482589\pi$
$89$	4.98452e50	0.109342	0.0546712	+	0.998504i	$0.482589\pi$
$90$	−4.50715e50	−0.0735318
$91$	1.78672e52	2.17500
$92$	−1.47132e51	−0.134069
$93$	−2.12201e52	−1.45194
$94$	2.92678e51	0.150835
$95$	−1.84758e51	−0.0719330
$96$	−1.93632e52	−0.571200
$97$	−1.99451e52	−0.447079	−0.223540	−	0.974695i	$-0.571761\pi$
$97$	−1.99451e52	−0.447079	−0.223540	+	0.974695i	$0.571761\pi$
$98$	−3.73649e52	−0.638223
$99$	1.10104e53	1.43704
$100$	1.94355e52	0.194355
$101$	1.70262e52	0.130798	0.0653990	−	0.997859i	$-0.479168\pi$
$101$	1.70262e52	0.130798	0.0653990	+	0.997859i	$0.479168\pi$
$102$	1.02389e53	0.605825
$103$	1.87090e53	0.854799	0.427400	−	0.904063i	$-0.359430\pi$
$103$	1.87090e53	0.854799	0.427400	+	0.904063i	$0.359430\pi$
$104$	−5.04024e53	−1.78266
$105$	−4.80973e52	−0.132009
$106$	−4.57429e53	−0.976604
$107$	1.10378e54	1.83743	0.918716	−	0.394918i	$-0.129227\pi$
$107$	1.10378e54	1.83743	0.918716	+	0.394918i	$0.129227\pi$
$108$	−4.60804e52	−0.0599497
$109$	−1.44235e54	−1.46984	−0.734919	−	0.678155i	$-0.762780\pi$
$109$	−1.44235e54	−1.46984	−0.734919	+	0.678155i	$0.762780\pi$
$110$	−9.07114e52	−0.0725697
$111$	−1.73851e53	−0.109426
$112$	2.02087e54	1.00291
$113$	1.79503e53	0.0703869	0.0351935	−	0.999381i	$-0.488795\pi$
$113$	1.79503e53	0.0703869	0.0351935	+	0.999381i	$0.488795\pi$
$114$	4.54521e54	1.41116
$115$	1.89352e53	0.0466421
$116$	1.37246e54	0.268760
$117$	−1.28617e55	−2.00619
$118$	−1.00058e55	−1.24560
$119$	5.97481e54	0.594744
$120$	1.35680e54	0.108196
$121$	6.53486e54	0.418238
$122$	5.19793e54	0.267482
$123$	3.66752e54	0.152015
$124$	5.70633e54	0.190846
$125$	−5.01411e54	−0.135544
$126$	6.47031e55	1.41614
$127$	−4.95049e55	−0.878719	−0.439359	−	0.898311i	$-0.644794\pi$
$127$	−4.95049e55	−0.878719	−0.439359	+	0.898311i	$0.644794\pi$
$128$	−4.24880e55	−0.612636
$129$	1.90447e55	0.223433
$130$	1.05964e55	0.101312
$131$	−1.71039e56	−1.33477	−0.667386	−	0.744712i	$-0.732587\pi$
$131$	−1.71039e56	−1.33477	−0.667386	+	0.744712i	$0.732587\pi$
$132$	−5.41450e55	−0.345421
$133$	2.65233e56	1.38535
$134$	−4.32979e55	−0.185434
$135$	5.93034e54	0.0208562
$136$	−1.68546e56	−0.487459
$137$	4.96948e56	1.18363	0.591815	−	0.806074i	$-0.298412\pi$
$137$	4.96948e56	1.18363	0.591815	+	0.806074i	$0.298412\pi$
$138$	−4.65823e56	−0.915008
$139$	9.49018e56	1.53951	0.769755	−	0.638340i	$-0.220379\pi$
$139$	9.49018e56	1.53951	0.769755	+	0.638340i	$0.220379\pi$
$140$	1.29339e55	0.0173515
$141$	−2.24828e56	−0.249772
$142$	2.39175e56	0.220331
$143$	−2.58856e57	−1.97994
$144$	−1.45472e57	−0.925069
$145$	−1.76630e56	−0.0935001
$146$	1.66191e57	0.733260
$147$	2.87027e57	1.05685
$148$	4.67507e55	0.0143831
$149$	3.22647e57	0.830407	0.415204	−	0.909728i	$-0.363710\pi$
$149$	3.22647e57	0.830407	0.415204	+	0.909728i	$0.363710\pi$
$150$	6.15331e57	1.32645
$151$	−7.49843e57	−1.35544	−0.677721	−	0.735319i	$-0.737032\pi$
$151$	−7.49843e57	−1.35544	−0.677721	+	0.735319i	$0.737032\pi$
$152$	−7.48206e57	−1.13545
$153$	−4.30096e57	−0.548583
$154$	1.30222e58	1.39761
$155$	−7.34379e56	−0.0663942
$156$	6.32491e57	0.482228
$157$	−2.71453e58	−1.74725	−0.873624	−	0.486602i	$-0.838236\pi$
$157$	−2.71453e58	−1.74725	−0.873624	+	0.486602i	$0.838236\pi$
$158$	−1.66775e58	−0.907233
$159$	3.51385e58	1.61719
$160$	−6.70116e56	−0.0261198
$161$	−2.71827e58	−0.898272
$162$	2.40094e58	0.673339
$163$	5.10046e58	1.21517	0.607586	−	0.794254i	$-0.292138\pi$
$163$	5.10046e58	1.21517	0.607586	+	0.794254i	$0.292138\pi$
$164$	−9.86239e56	−0.0199811
$165$	6.96821e57	0.120170
$166$	8.33325e57	0.122448
$167$	−1.89473e58	−0.237444	−0.118722	−	0.992928i	$-0.537880\pi$
$167$	−1.89473e58	−0.237444	−0.118722	+	0.992928i	$0.537880\pi$
$168$	−1.94777e59	−2.08373
$169$	1.92986e59	1.76412
$170$	3.54344e57	0.0277031
$171$	−1.90927e59	−1.27782
$172$	−5.12135e57	−0.0293684
$173$	−3.74302e59	−1.84078	−0.920388	−	0.391006i	$-0.872127\pi$
$173$	−3.74302e59	−1.84078	−0.920388	+	0.391006i	$0.872127\pi$
$174$	4.34525e59	1.83425
$175$	3.59072e59	1.30219
$176$	−2.92779e59	−0.912965
$177$	7.68620e59	2.06262
$178$	−4.24373e58	−0.0980883
$179$	−3.52065e59	−0.701483	−0.350741	−	0.936472i	$-0.614070\pi$
$179$	−3.52065e59	−0.701483	−0.350741	+	0.936472i	$0.614070\pi$
$180$	−9.31048e57	−0.0160048
$181$	3.15641e58	0.0468501	0.0234251	−	0.999726i	$-0.492543\pi$
$181$	3.15641e58	0.0468501	0.0234251	+	0.999726i	$0.492543\pi$
$182$	−1.52118e60	−1.95114
$183$	−3.99292e59	−0.442931
$184$	7.66810e59	0.736233
$185$	−6.01660e57	−0.00500380
$186$	1.80664e60	1.30250
$187$	−8.65616e59	−0.541406
$188$	6.04590e58	0.0328305
$189$	−8.51339e59	−0.401666
$190$	1.57300e59	0.0645294
$191$	−2.50150e60	−0.892927	−0.446464	−	0.894802i	$-0.647317\pi$
$191$	−2.50150e60	−0.892927	−0.446464	+	0.894802i	$0.647317\pi$
$192$	5.31235e60	1.65122
$193$	1.82350e60	0.493899	0.246949	−	0.969028i	$-0.420572\pi$
$193$	1.82350e60	0.493899	0.246949	+	0.969028i	$0.420572\pi$
$194$	1.69808e60	0.401064
$195$	−8.13987e59	−0.167765
$196$	−7.71851e59	−0.138914
$197$	−4.11846e60	−0.647709	−0.323855	−	0.946107i	$-0.604979\pi$
$197$	−4.11846e60	−0.647709	−0.323855	+	0.946107i	$0.604979\pi$
$198$	−9.37401e60	−1.28913
$199$	2.79044e60	0.335789	0.167895	−	0.985805i	$-0.446303\pi$
$199$	2.79044e60	0.335789	0.167895	+	0.985805i	$0.446303\pi$
$200$	−1.01292e61	−1.06729
$201$	3.32604e60	0.307066
$202$	−1.44958e60	−0.117336
$203$	2.53564e61	1.80070
$204$	2.11506e60	0.131863
$205$	1.26925e59	0.00695133
$206$	−1.59285e61	−0.766819
$207$	1.95675e61	0.828553
$208$	3.42008e61	1.27455
$209$	−3.84262e61	−1.26110
$210$	4.09491e60	0.118422
$211$	−9.61153e60	−0.245080	−0.122540	−	0.992464i	$-0.539104\pi$
$211$	−9.61153e60	−0.245080	−0.122540	+	0.992464i	$0.539104\pi$
$212$	−9.44918e60	−0.212566
$213$	−1.83728e61	−0.364852
$214$	−9.39735e61	−1.64832
$215$	6.59095e59	0.0102171
$216$	2.40158e61	0.329210
$217$	1.05425e62	1.27867
$218$	1.22799e62	1.31856
$219$	−1.27664e62	−1.21423
$220$	−1.87384e60	−0.0157954
$221$	1.01116e62	0.755834
$222$	1.48014e61	0.0981629
$223$	−8.79461e61	−0.517771	−0.258885	−	0.965908i	$-0.583355\pi$
$223$	−8.79461e61	−0.517771	−0.258885	+	0.965908i	$0.583355\pi$
$224$	9.61994e61	0.503037
$225$	−2.58477e62	−1.20112
$226$	−1.52825e61	−0.0631424
$227$	3.14689e62	1.15664	0.578318	−	0.815811i	$-0.303709\pi$
$227$	3.14689e62	1.15664	0.578318	+	0.815811i	$0.303709\pi$
$228$	9.38911e61	0.307150
$229$	−4.50545e61	−0.131250	−0.0656248	−	0.997844i	$-0.520904\pi$
$229$	−4.50545e61	−0.131250	−0.0656248	+	0.997844i	$0.520904\pi$
$230$	−1.61211e61	−0.0418414
$231$	−1.00033e63	−2.31434
$232$	−7.15289e62	−1.47588
$233$	6.26152e62	1.15278	0.576392	−	0.817173i	$-0.304460\pi$
$233$	6.26152e62	1.15278	0.576392	+	0.817173i	$0.304460\pi$
$234$	1.09502e63	1.79971
$235$	−7.78080e60	−0.0114216
$236$	−2.06691e62	−0.271115
$237$	1.28113e63	1.50231
$238$	−5.08684e62	−0.533530
$239$	1.59379e63	1.49585	0.747923	−	0.663785i	$-0.231051\pi$
$239$	1.59379e63	1.49585	0.747923	+	0.663785i	$0.231051\pi$
$240$	−9.20662e61	−0.0773574
$241$	−1.86546e63	−1.40390	−0.701948	−	0.712228i	$-0.747686\pi$
$241$	−1.86546e63	−1.40390	−0.701948	+	0.712228i	$0.747686\pi$
$242$	−5.56365e62	−0.375191
$243$	−2.35221e63	−1.42203
$244$	1.07374e62	0.0582197
$245$	9.93337e61	0.0483276
$246$	−3.12245e62	−0.136369
$247$	4.48873e63	1.76058
$248$	−2.97398e63	−1.04802
$249$	−6.40139e62	−0.202764
$250$	4.26892e62	0.121593
$251$	−1.23471e62	−0.0316382	−0.0158191	−	0.999875i	$-0.505036\pi$
$251$	−1.23471e62	−0.0316382	−0.0158191	+	0.999875i	$0.505036\pi$
$252$	1.33658e63	0.308234
$253$	3.93817e63	0.817712
$254$	4.21475e63	0.788277
$255$	−2.72198e62	−0.0458744
$256$	−3.69897e63	−0.561982
$257$	−2.57030e63	−0.352174	−0.176087	−	0.984375i	$-0.556344\pi$
$257$	−2.57030e63	−0.352174	−0.176087	+	0.984375i	$0.556344\pi$
$258$	−1.62143e63	−0.200436
$259$	8.63722e62	0.0963674
$260$	2.18891e62	0.0220513
$261$	−1.82527e64	−1.66094
$262$	1.45620e64	1.19739
$263$	−1.92105e64	−1.42794	−0.713972	−	0.700174i	$-0.753106\pi$
$263$	−1.92105e64	−1.42794	−0.713972	+	0.700174i	$0.753106\pi$
$264$	2.82188e64	1.89686
$265$	1.21607e63	0.0739506
$266$	−2.25814e64	−1.24276
$267$	3.25992e63	0.162427
$268$	−8.94411e62	−0.0403613
$269$	1.72508e64	0.705301	0.352651	−	0.935755i	$-0.385280\pi$
$269$	1.72508e64	0.705301	0.352651	+	0.935755i	$0.385280\pi$
$270$	−5.04898e62	−0.0187096
$271$	−1.11722e64	−0.375365	−0.187682	−	0.982230i	$-0.560098\pi$
$271$	−1.11722e64	−0.375365	−0.187682	+	0.982230i	$0.560098\pi$
$272$	1.14368e64	0.348520
$273$	1.16853e65	3.23095
$274$	−4.23092e64	−1.06180
$275$	−5.20214e64	−1.18540
$276$	−9.62256e63	−0.199159
$277$	−1.05957e64	−0.199258	−0.0996291	−	0.995025i	$-0.531766\pi$
$277$	−1.05957e64	−0.199258	−0.0996291	+	0.995025i	$0.531766\pi$
$278$	−8.07976e64	−1.38106
$279$	−7.58899e64	−1.17943
$280$	−6.74080e63	−0.0952848
$281$	5.57080e64	0.716473	0.358237	−	0.933631i	$-0.383378\pi$
$281$	5.57080e64	0.716473	0.358237	+	0.933631i	$0.383378\pi$
$282$	1.91414e64	0.224064
$283$	1.04527e65	1.11401	0.557003	−	0.830511i	$-0.311951\pi$
$283$	1.04527e65	1.11401	0.557003	+	0.830511i	$0.311951\pi$
$284$	4.94067e63	0.0479568
$285$	−1.20834e64	−0.106856
$286$	2.20385e65	1.77616
$287$	−1.82208e64	−0.133875
$288$	−6.92490e64	−0.463994
$289$	−1.29790e65	−0.793321
$290$	1.50379e64	0.0838766
$291$	−1.30442e65	−0.664132
$292$	3.43304e64	0.159600
$293$	2.53583e65	1.07678	0.538392	−	0.842694i	$-0.319032\pi$
$293$	2.53583e65	1.07678	0.538392	+	0.842694i	$0.319032\pi$
$294$	−2.44369e65	−0.948075
$295$	2.66002e64	0.0943196
$296$	−2.43651e64	−0.0789838
$297$	1.23340e65	0.365643
$298$	−2.74695e65	−0.744938
$299$	−4.60034e65	−1.14157
$300$	1.27110e65	0.288713
$301$	−9.46174e64	−0.196770
$302$	6.38402e65	1.21593
$303$	1.11353e65	0.194300
$304$	5.07699e65	0.811813
$305$	−1.38186e64	−0.0202543
$306$	3.66176e65	0.492121
$307$	−1.14760e66	−1.41457	−0.707284	−	0.706930i	$-0.750080\pi$
$307$	−1.14760e66	−1.41457	−0.707284	+	0.706930i	$0.750080\pi$
$308$	2.69001e65	0.304201
$309$	1.22358e66	1.26980
$310$	6.25236e64	0.0595606
$311$	3.98992e65	0.348991	0.174496	−	0.984658i	$-0.444171\pi$
$311$	3.98992e65	0.348991	0.174496	+	0.984658i	$0.444171\pi$
$312$	−3.29636e66	−2.64812
$313$	−1.04506e66	−0.771291	−0.385645	−	0.922647i	$-0.626021\pi$
$313$	−1.04506e66	−0.771291	−0.385645	+	0.922647i	$0.626021\pi$
$314$	2.31110e66	1.56741
$315$	−1.72012e65	−0.107233
$316$	−3.44510e65	−0.197467
$317$	1.24693e66	0.657312	0.328656	−	0.944450i	$-0.393404\pi$
$317$	1.24693e66	0.657312	0.328656	+	0.944450i	$0.393404\pi$
$318$	−2.99163e66	−1.45074
$319$	−3.67357e66	−1.63921
$320$	1.83849e65	0.0755067
$321$	7.21880e66	2.72949
$322$	2.31429e66	0.805817
$323$	1.50104e66	0.481420
$324$	4.95966e65	0.146558
$325$	6.07685e66	1.65489
$326$	−4.34243e66	−1.09010
$327$	−9.43312e66	−2.18343
$328$	5.14000e65	0.109725
$329$	1.11698e66	0.219966
$330$	−5.93260e65	−0.107802
$331$	−7.02324e66	−1.17787	−0.588933	−	0.808182i	$-0.700452\pi$
$331$	−7.02324e66	−1.17787	−0.588933	+	0.808182i	$0.700452\pi$
$332$	1.72141e65	0.0266517
$333$	−6.21749e65	−0.0888879
$334$	1.61314e66	0.213005
$335$	1.15107e65	0.0140415
$336$	1.32167e67	1.48981
$337$	7.44919e66	0.776098	0.388049	−	0.921639i	$-0.373149\pi$
$337$	7.44919e66	0.776098	0.388049	+	0.921639i	$0.373149\pi$
$338$	−1.64304e67	−1.58254
$339$	1.17396e66	0.104559
$340$	7.31974e64	0.00602982
$341$	−1.52737e67	−1.16400
$342$	1.62552e67	1.14630
$343$	5.78362e66	0.377490
$344$	2.66910e66	0.161275
$345$	1.23838e66	0.0692864
$346$	3.18674e67	1.65131
$347$	−1.68736e67	−0.809985	−0.404993	−	0.914320i	$-0.632726\pi$
$347$	−1.68736e67	−0.809985	−0.404993	+	0.914320i	$0.632726\pi$
$348$	8.97603e66	0.399240
$349$	−1.94835e67	−0.803143	−0.401571	−	0.915828i	$-0.631536\pi$
$349$	−1.94835e67	−0.803143	−0.401571	+	0.915828i	$0.631536\pi$
$350$	−3.05707e67	−1.16816
$351$	−1.44079e67	−0.510459
$352$	−1.39371e67	−0.457923
$353$	4.86893e67	1.48390	0.741948	−	0.670457i	$-0.233902\pi$
$353$	4.86893e67	1.48390	0.741948	+	0.670457i	$0.233902\pi$
$354$	−6.54388e67	−1.85033
$355$	−6.35842e65	−0.0166839
$356$	−8.76632e65	−0.0213497
$357$	3.90758e67	0.883487
$358$	2.99741e67	0.629283
$359$	3.23986e67	0.631719	0.315860	−	0.948806i	$-0.397707\pi$
$359$	3.23986e67	0.631719	0.315860	+	0.948806i	$0.397707\pi$
$360$	4.85236e66	0.0878894
$361$	7.21254e66	0.121380
$362$	−2.68730e66	−0.0420281
$363$	4.27385e67	0.621290
$364$	−3.14232e67	−0.424682
$365$	−4.41816e66	−0.0555240
$366$	3.39949e67	0.397343
$367$	−4.09627e67	−0.445388	−0.222694	−	0.974888i	$-0.571485\pi$
$367$	−4.09627e67	−0.445388	−0.222694	+	0.974888i	$0.571485\pi$
$368$	−5.20323e67	−0.526387
$369$	1.31162e67	0.123484
$370$	5.12242e65	0.00448879
$371$	−1.74574e68	−1.42420
$372$	3.73199e67	0.283500
$373$	−1.54943e68	−1.09619	−0.548097	−	0.836415i	$-0.684648\pi$
$373$	−1.54943e68	−1.09619	−0.548097	+	0.836415i	$0.684648\pi$
$374$	7.36969e67	0.485682
$375$	−3.27927e67	−0.201349
$376$	−3.15095e67	−0.180287
$377$	4.29125e68	2.28843
$378$	7.24814e67	0.360324
$379$	1.05294e68	0.488049	0.244025	−	0.969769i	$-0.421532\pi$
$379$	1.05294e68	0.488049	0.244025	+	0.969769i	$0.421532\pi$
$380$	3.24936e66	0.0140453
$381$	−3.23767e68	−1.30533
$382$	2.12973e68	0.801023
$383$	8.24887e67	0.289486	0.144743	−	0.989469i	$-0.453764\pi$
$383$	8.24887e67	0.289486	0.144743	+	0.989469i	$0.453764\pi$
$384$	−2.77875e68	−0.910065
$385$	−3.46193e67	−0.105830
$386$	−1.55250e68	−0.443064
$387$	6.81102e67	0.181498
$388$	3.50775e67	0.0872948
$389$	1.89075e68	0.439510	0.219755	−	0.975555i	$-0.429474\pi$
$389$	1.89075e68	0.439510	0.219755	+	0.975555i	$0.429474\pi$
$390$	6.93013e67	0.150498
$391$	−1.53836e68	−0.312158
$392$	4.02267e68	0.762840
$393$	−1.11861e69	−1.98279
$394$	3.50638e68	0.581044
$395$	4.43369e67	0.0686977
$396$	−1.93640e68	−0.280591
$397$	−1.41885e69	−1.92304	−0.961518	−	0.274743i	$-0.911407\pi$
$397$	−1.41885e69	−1.92304	−0.961518	+	0.274743i	$0.911407\pi$
$398$	−2.37573e68	−0.301228
$399$	1.73464e69	2.05792
$400$	6.87323e68	0.763082
$401$	1.07913e69	1.12137	0.560686	−	0.828028i	$-0.310537\pi$
$401$	1.07913e69	1.12137	0.560686	+	0.828028i	$0.310537\pi$
$402$	−2.83172e68	−0.275461
$403$	1.78419e69	1.62501
$404$	−2.99441e67	−0.0255391
$405$	−6.38286e67	−0.0509867
$406$	−2.15879e69	−1.61537
$407$	−1.25134e68	−0.0877249
$408$	−1.10231e69	−0.724116
$409$	−1.89009e69	−1.16363	−0.581814	−	0.813322i	$-0.697657\pi$
$409$	−1.89009e69	−1.16363	−0.581814	+	0.813322i	$0.697657\pi$
$410$	−1.08061e67	−0.00623587
$411$	3.25008e69	1.75827
$412$	−3.29037e68	−0.166905
$413$	−3.81863e69	−1.81648
$414$	−1.66594e69	−0.743274
$415$	−2.21538e67	−0.00927200
$416$	1.62806e69	0.639288
$417$	6.20666e69	2.28693
$418$	3.27153e69	1.13131
$419$	−5.52165e69	−1.79225	−0.896123	−	0.443807i	$-0.853628\pi$
$419$	−5.52165e69	−1.79225	−0.896123	+	0.443807i	$0.853628\pi$
$420$	8.45891e67	0.0257756
$421$	−1.18435e69	−0.338847	−0.169424	−	0.985543i	$-0.554191\pi$
$421$	−1.18435e69	−0.338847	−0.169424	+	0.985543i	$0.554191\pi$
$422$	8.18307e68	0.219855
$423$	−8.04059e68	−0.202894
$424$	4.92464e69	1.16729
$425$	2.03210e69	0.452522
$426$	1.56423e69	0.327300
$427$	1.98375e69	0.390075
$428$	−1.94122e69	−0.358769
$429$	−1.69294e70	−2.94119
$430$	−5.61141e67	−0.00916554
$431$	2.27553e69	0.349490	0.174745	−	0.984614i	$-0.444090\pi$
$431$	2.27553e69	0.349490	0.174745	+	0.984614i	$0.444090\pi$
$432$	−1.62960e69	−0.235376
$433$	1.18575e70	1.61088	0.805440	−	0.592677i	$-0.201929\pi$
$433$	1.18575e70	1.61088	0.805440	+	0.592677i	$0.201929\pi$
$434$	−8.97567e69	−1.14707
$435$	−1.15517e69	−0.138894
$436$	2.53668e69	0.286994
$437$	−6.82905e69	−0.727113
$438$	1.08691e70	1.08925
$439$	−1.92587e69	−0.181684	−0.0908422	−	0.995865i	$-0.528956\pi$
$439$	−1.92587e69	−0.181684	−0.0908422	+	0.995865i	$0.528956\pi$
$440$	9.76590e68	0.0867394
$441$	1.02650e70	0.858495
$442$	−8.60885e69	−0.678040
$443$	−1.15476e69	−0.0856626	−0.0428313	−	0.999082i	$-0.513638\pi$
$443$	−1.15476e69	−0.0856626	−0.0428313	+	0.999082i	$0.513638\pi$
$444$	3.05754e68	0.0213660
$445$	1.12819e68	0.00742746
$446$	7.48756e69	0.464479
$447$	2.11014e70	1.23356
$448$	−2.63926e70	−1.45417
$449$	1.26244e70	0.655664	0.327832	−	0.944736i	$-0.393682\pi$
$449$	1.26244e70	0.655664	0.327832	+	0.944736i	$0.393682\pi$
$450$	2.20063e70	1.07749
$451$	2.63979e69	0.121868
$452$	−3.15693e68	−0.0137435
$453$	−4.90404e70	−2.01350
$454$	−2.67921e70	−1.03759
$455$	4.04403e69	0.147745
$456$	−4.89333e70	−1.68669
$457$	1.89960e70	0.617848	0.308924	−	0.951087i	$-0.400031\pi$
$457$	1.89960e70	0.617848	0.308924	+	0.951087i	$0.400031\pi$
$458$	3.83586e69	0.117741
$459$	−4.81800e69	−0.139583
$460$	−3.33015e68	−0.00910714
$461$	4.91287e70	1.26841	0.634206	−	0.773164i	$-0.281327\pi$
$461$	4.91287e70	1.26841	0.634206	+	0.773164i	$0.281327\pi$
$462$	8.51664e70	2.07614
$463$	−1.61924e70	−0.372748	−0.186374	−	0.982479i	$-0.559674\pi$
$463$	−1.61924e70	−0.372748	−0.186374	+	0.982479i	$0.559674\pi$
$464$	4.85363e70	1.05521
$465$	−4.80290e69	−0.0986281
$466$	−5.33094e70	−1.03413
$467$	9.60677e68	0.0176068	0.00880339	−	0.999961i	$-0.497198\pi$
$467$	9.60677e68	0.0176068	0.00880339	+	0.999961i	$0.497198\pi$
$468$	2.26200e70	0.391721
$469$	−1.65243e70	−0.270423
$470$	6.62442e68	0.0102460
$471$	−1.77533e71	−2.59552
$472$	1.07722e71	1.48881
$473$	1.37079e70	0.179123
$474$	−1.09073e71	−1.34769
$475$	9.02087e70	1.05407
$476$	−1.05080e70	−0.116127
$477$	1.25667e71	1.31366
$478$	−1.35692e71	−1.34189
$479$	−7.16104e70	−0.670016	−0.335008	−	0.942215i	$-0.608739\pi$
$479$	−7.16104e70	−0.670016	−0.335008	+	0.942215i	$0.608739\pi$
$480$	−4.38261e69	−0.0388008
$481$	1.46174e70	0.122469
$482$	1.58822e71	1.25940
$483$	−1.77778e71	−1.33438
$484$	−1.14929e70	−0.0816635
$485$	−4.51432e69	−0.0303694
$486$	2.00263e71	1.27567
$487$	8.84962e70	0.533835	0.266918	−	0.963719i	$-0.413995\pi$
$487$	8.84962e70	0.533835	0.266918	+	0.963719i	$0.413995\pi$
$488$	−5.59604e70	−0.319710
$489$	3.33574e71	1.80513
$490$	−8.45708e69	−0.0433535
$491$	−3.37986e71	−1.64149	−0.820747	−	0.571292i	$-0.806442\pi$
$491$	−3.37986e71	−1.64149	−0.820747	+	0.571292i	$0.806442\pi$
$492$	−6.45009e69	−0.0296818
$493$	1.43500e71	0.625760
$494$	−3.82162e71	−1.57937
$495$	2.49206e70	0.0976160
$496$	2.01801e71	0.749304
$497$	9.12793e70	0.321313
$498$	5.45002e70	0.181895
$499$	−5.44978e71	−1.72470	−0.862352	−	0.506310i	$-0.831009\pi$
$499$	−5.44978e71	−1.72470	−0.862352	+	0.506310i	$0.831009\pi$
$500$	8.81836e69	0.0264657
$501$	−1.23917e71	−0.352722
$502$	1.05121e70	0.0283818
$503$	5.30455e71	1.35862	0.679308	−	0.733853i	$-0.262280\pi$
$503$	5.30455e71	1.35862	0.679308	+	0.733853i	$0.262280\pi$
$504$	−6.96587e71	−1.69265
$505$	3.85367e69	0.00888492
$506$	−3.35288e71	−0.733549
$507$	1.26214e72	2.62058
$508$	8.70647e70	0.171575
$509$	−5.04965e71	−0.944582	−0.472291	−	0.881443i	$-0.656573\pi$
$509$	−5.04965e71	−0.944582	−0.472291	+	0.881443i	$0.656573\pi$
$510$	2.31744e70	0.0411528
$511$	6.34256e71	1.06933
$512$	6.97622e71	1.11678
$513$	−2.13880e71	−0.325132
$514$	2.18831e71	0.315926
$515$	4.23455e70	0.0580652
$516$	−3.34941e70	−0.0436266
$517$	−1.61826e71	−0.200239
$518$	−7.35356e70	−0.0864488
$519$	−2.44797e72	−2.73446
$520$	−1.14080e71	−0.121093
$521$	−1.71481e72	−1.72989	−0.864943	−	0.501870i	$-0.832646\pi$
$521$	−1.71481e72	−1.72989	−0.864943	+	0.501870i	$0.832646\pi$
$522$	1.55400e72	1.48999
$523$	−1.17717e72	−1.07287	−0.536433	−	0.843943i	$-0.680228\pi$
$523$	−1.17717e72	−1.07287	−0.536433	+	0.843943i	$0.680228\pi$
$524$	3.00808e71	0.260622
$525$	2.34836e72	1.93439
$526$	1.63554e72	1.28097
$527$	5.96633e71	0.444351
$528$	−1.91480e72	−1.35620
$529$	−7.84598e71	−0.528533
$530$	−1.03534e71	−0.0663392
$531$	2.74884e72	1.67550
$532$	−4.66467e71	−0.270497
$533$	−3.08365e71	−0.170135
$534$	−2.77543e71	−0.145709
$535$	2.49827e71	0.124814
$536$	4.66142e71	0.221641
$537$	−2.30253e72	−1.04205
$538$	−1.46870e72	−0.632708
$539$	2.06595e72	0.847263
$540$	−1.04297e70	−0.00407229
$541$	3.05901e72	1.13724	0.568621	−	0.822600i	$-0.307477\pi$
$541$	3.05901e72	1.13724	0.568621	+	0.822600i	$0.307477\pi$
$542$	9.51181e71	0.336730
$543$	2.06432e71	0.0695955
$544$	5.44424e71	0.174810
$545$	−3.26459e71	−0.0998439
$546$	−9.94865e72	−2.89841
$547$	−3.46128e72	−0.960667	−0.480333	−	0.877086i	$-0.659484\pi$
$547$	−3.46128e72	−0.960667	−0.480333	+	0.877086i	$0.659484\pi$
$548$	−8.73986e71	−0.231111
$549$	−1.42800e72	−0.359799
$550$	4.42901e72	1.06340
$551$	6.37021e72	1.45759
$552$	5.01501e72	1.09367
$553$	−6.36485e72	−1.32304
$554$	9.02098e71	0.178750
$555$	−3.93491e70	−0.00743311
$556$	−1.66905e72	−0.300598
$557$	9.15984e72	1.57299	0.786493	−	0.617599i	$-0.211894\pi$
$557$	9.15984e72	1.57299	0.786493	+	0.617599i	$0.211894\pi$
$558$	6.46112e72	1.05804
$559$	−1.60128e72	−0.250066
$560$	4.57400e71	0.0681261
$561$	−5.66120e72	−0.804254
$562$	−4.74287e72	−0.642730
$563$	2.99024e72	0.386575	0.193288	−	0.981142i	$-0.438085\pi$
$563$	2.99024e72	0.386575	0.193288	+	0.981142i	$0.438085\pi$
$564$	3.95407e71	0.0487695
$565$	4.06282e70	0.00478128
$566$	−8.89922e72	−0.999347
$567$	9.16301e72	0.981944
$568$	−2.57494e72	−0.263352
$569$	−1.95493e73	−1.90834	−0.954169	−	0.299270i	$-0.903257\pi$
$569$	−1.95493e73	−1.90834	−0.954169	+	0.299270i	$0.903257\pi$
$570$	1.02875e72	0.0958579
$571$	6.21208e72	0.552561	0.276280	−	0.961077i	$-0.410898\pi$
$571$	6.21208e72	0.552561	0.276280	+	0.961077i	$0.410898\pi$
$572$	4.55252e72	0.386595
$573$	−1.63600e73	−1.32644
$574$	1.55129e72	0.120096
$575$	−9.24517e72	−0.683466
$576$	1.89987e73	1.34131
$577$	3.44976e72	0.232611	0.116305	−	0.993213i	$-0.462895\pi$
$577$	3.44976e72	0.232611	0.116305	+	0.993213i	$0.462895\pi$
$578$	1.10501e73	0.711669
$579$	1.19259e73	0.733682
$580$	3.10640e71	0.0182564
$581$	3.18032e72	0.178568
$582$	1.11056e73	0.595777
$583$	2.52919e73	1.29647
$584$	−1.78920e73	−0.876433
$585$	−2.91109e72	−0.136278
$586$	−2.15896e73	−0.965957
$587$	−3.91303e73	−1.67341	−0.836707	−	0.547650i	$-0.815522\pi$
$587$	−3.91303e73	−1.67341	−0.836707	+	0.547650i	$0.815522\pi$
$588$	−5.04797e72	−0.206356
$589$	2.64856e73	1.03503
$590$	−2.26469e72	−0.0846118
$591$	−2.69351e73	−0.962167
$592$	1.65331e72	0.0564713
$593$	3.03919e73	0.992679	0.496340	−	0.868128i	$-0.334677\pi$
$593$	3.03919e73	0.992679	0.496340	+	0.868128i	$0.334677\pi$
$594$	−1.05009e73	−0.328010
$595$	1.35233e72	0.0404001
$596$	−5.67442e72	−0.162142
$597$	1.82497e73	0.498812
$598$	3.91664e73	1.02408
$599$	−4.69569e73	−1.17460	−0.587298	−	0.809371i	$-0.699808\pi$
$599$	−4.69569e73	−1.17460	−0.587298	+	0.809371i	$0.699808\pi$
$600$	−6.62460e73	−1.58545
$601$	3.32571e73	0.761572	0.380786	−	0.924663i	$-0.375653\pi$
$601$	3.32571e73	0.761572	0.380786	+	0.924663i	$0.375653\pi$
$602$	8.05554e72	0.176517
$603$	1.18950e73	0.249434
$604$	1.31875e73	0.264658
$605$	1.47909e72	0.0284103
$606$	−9.48037e72	−0.174301
$607$	−4.03134e73	−0.709495	−0.354747	−	0.934962i	$-0.615433\pi$
$607$	−4.03134e73	−0.709495	−0.354747	+	0.934962i	$0.615433\pi$
$608$	2.41679e73	0.407188
$609$	1.65833e74	2.67493
$610$	1.17649e72	0.0181697
$611$	1.89036e73	0.279545
$612$	7.56414e72	0.107114
$613$	−1.16967e74	−1.58621	−0.793103	−	0.609087i	$-0.791536\pi$
$613$	−1.16967e74	−1.58621	−0.793103	+	0.609087i	$0.791536\pi$
$614$	9.77045e73	1.26897
$615$	8.30098e71	0.0103262
$616$	−1.40196e74	−1.67050
$617$	−8.47254e73	−0.967067	−0.483534	−	0.875326i	$-0.660647\pi$
$617$	−8.47254e73	−0.967067	−0.483534	+	0.875326i	$0.660647\pi$
$618$	−1.04174e74	−1.13910
$619$	−4.01420e73	−0.420529	−0.210265	−	0.977644i	$-0.567433\pi$
$619$	−4.01420e73	−0.420529	−0.210265	+	0.977644i	$0.567433\pi$
$620$	1.29156e72	0.0129639
$621$	2.19198e73	0.210818
$622$	−3.39694e73	−0.313071
$623$	−1.61958e73	−0.143044
$624$	2.23676e74	1.89334
$625$	1.21556e74	0.986178
$626$	8.89748e73	0.691906
$627$	−2.51311e74	−1.87336
$628$	4.77407e73	0.341160
$629$	4.88808e72	0.0334886
$630$	1.46447e73	0.0961961
$631$	1.79458e74	1.13028	0.565139	−	0.824996i	$-0.308823\pi$
$631$	1.79458e74	1.13028	0.565139	+	0.824996i	$0.308823\pi$
$632$	1.79549e74	1.08438
$633$	−6.28603e73	−0.364064
$634$	−1.06161e74	−0.589658
$635$	−1.12048e73	−0.0596900
$636$	−6.17984e73	−0.315765
$637$	−2.41333e74	−1.18283
$638$	3.12760e74	1.47050
$639$	−6.57073e73	−0.296374
$640$	−9.61665e72	−0.0416154
$641$	9.16136e73	0.380384	0.190192	−	0.981747i	$-0.439089\pi$
$641$	9.16136e73	0.380384	0.190192	+	0.981747i	$0.439089\pi$
$642$	−6.14595e74	−2.44856
$643$	2.41149e74	0.921924	0.460962	−	0.887420i	$-0.347504\pi$
$643$	2.41149e74	0.921924	0.460962	+	0.887420i	$0.347504\pi$
$644$	4.78065e73	0.175393
$645$	4.31054e72	0.0151775
$646$	−1.27795e74	−0.431870
$647$	−2.73867e74	−0.888334	−0.444167	−	0.895944i	$-0.646500\pi$
$647$	−2.73867e74	−0.888334	−0.444167	+	0.895944i	$0.646500\pi$
$648$	−2.58483e74	−0.804813
$649$	5.53234e74	1.65358
$650$	−5.17371e74	−1.48456
$651$	6.89488e74	1.89946
$652$	−8.97021e73	−0.237269
$653$	2.24596e74	0.570430	0.285215	−	0.958464i	$-0.407935\pi$
$653$	2.24596e74	0.570430	0.285215	+	0.958464i	$0.407935\pi$
$654$	8.03117e74	1.95870
$655$	−3.87127e73	−0.0906690
$656$	−3.48777e73	−0.0784505
$657$	−4.56568e74	−0.986333
$658$	−9.50979e73	−0.197326
$659$	−7.20835e74	−1.43672	−0.718361	−	0.695671i	$-0.755107\pi$
$659$	−7.20835e74	−1.43672	−0.718361	+	0.695671i	$0.755107\pi$
$660$	−1.22551e73	−0.0234639
$661$	2.05504e73	0.0377992	0.0188996	−	0.999821i	$-0.493984\pi$
$661$	2.05504e73	0.0377992	0.0188996	+	0.999821i	$0.493984\pi$
$662$	5.97945e74	1.05663
$663$	6.61310e74	1.12278
$664$	−8.97150e73	−0.146356
$665$	6.00322e73	0.0941045
$666$	5.29345e73	0.0797392
$667$	−6.52861e74	−0.945118
$668$	3.33228e73	0.0463624
$669$	−5.75175e74	−0.769144
$670$	−9.79996e72	−0.0125963
$671$	−2.87400e74	−0.355092
$672$	6.29153e74	0.747258
$673$	−8.58844e73	−0.0980652	−0.0490326	−	0.998797i	$-0.515614\pi$
$673$	−8.58844e73	−0.0980652	−0.0490326	+	0.998797i	$0.515614\pi$
$674$	−6.34209e74	−0.696218
$675$	−2.89551e74	−0.305615
$676$	−3.39405e74	−0.344454
$677$	−1.28702e75	−1.25599	−0.627993	−	0.778219i	$-0.716123\pi$
$677$	−1.28702e75	−1.25599	−0.627993	+	0.778219i	$0.716123\pi$
$678$	−9.99489e73	−0.0937975
$679$	6.48060e74	0.584879
$680$	−3.81484e73	−0.0331123
$681$	2.05810e75	1.71817
$682$	1.30037e75	1.04420
$683$	2.32106e75	1.79283	0.896414	−	0.443218i	$-0.146163\pi$
$683$	2.32106e75	1.79283	0.896414	+	0.443218i	$0.146163\pi$
$684$	3.35785e74	0.249503
$685$	1.12478e74	0.0804022
$686$	−4.92406e74	−0.338637
$687$	−2.94661e74	−0.194970
$688$	−1.81113e74	−0.115307
$689$	−2.95445e75	−1.80995
$690$	−1.05433e74	−0.0621551
$691$	4.45634e74	0.252819	0.126410	−	0.991978i	$-0.459655\pi$
$691$	4.45634e74	0.252819	0.126410	+	0.991978i	$0.459655\pi$
$692$	6.58289e74	0.359422
$693$	−3.57752e75	−1.87997
$694$	1.43659e75	0.726618
$695$	2.14799e74	0.104577
$696$	−4.67805e75	−2.19240
$697$	−1.03118e74	−0.0465226
$698$	1.65879e75	0.720480
$699$	4.09509e75	1.71245
$700$	−6.31503e74	−0.254260
$701$	−1.68252e75	−0.652276	−0.326138	−	0.945322i	$-0.605747\pi$
$701$	−1.68252e75	−0.652276	−0.326138	+	0.945322i	$0.605747\pi$
$702$	1.22666e75	0.457920
$703$	2.16991e74	0.0780054
$704$	3.82370e75	1.32376
$705$	−5.08871e73	−0.0169667
$706$	−4.14531e75	−1.33117
$707$	−5.53220e74	−0.171113
$708$	−1.35178e75	−0.402739
$709$	4.03690e75	1.15857	0.579286	−	0.815124i	$-0.303331\pi$
$709$	4.03690e75	1.15857	0.579286	+	0.815124i	$0.303331\pi$
$710$	5.41344e73	0.0149667
$711$	4.58173e75	1.22035
$712$	4.56876e74	0.117241
$713$	−2.71442e75	−0.671126
$714$	−3.32684e75	−0.792555
$715$	−5.85888e74	−0.134495
$716$	6.19179e74	0.136969
$717$	1.04235e76	2.22207
$718$	−2.75836e75	−0.566700
$719$	−2.29058e75	−0.453555	−0.226778	−	0.973947i	$-0.572819\pi$
$719$	−2.29058e75	−0.453555	−0.226778	+	0.973947i	$0.572819\pi$
$720$	−3.29259e74	−0.0628386
$721$	−6.07898e75	−1.11827
$722$	−6.14062e74	−0.108887
$723$	−1.22003e76	−2.08548
$724$	−5.55120e73	−0.00914776
$725$	8.62400e75	1.37010
$726$	−3.63868e75	−0.557344
$727$	−1.58967e75	−0.234772	−0.117386	−	0.993086i	$-0.537451\pi$
$727$	−1.58967e75	−0.234772	−0.117386	+	0.993086i	$0.537451\pi$
$728$	1.63769e76	2.33211
$729$	−9.91746e75	−1.36182
$730$	3.76154e74	0.0498092
$731$	−5.35470e74	−0.0683793
$732$	7.02237e74	0.0864849
$733$	8.19933e74	0.0973919	0.0486959	−	0.998814i	$-0.484493\pi$
$733$	8.19933e74	0.0973919	0.0486959	+	0.998814i	$0.484493\pi$
$734$	3.48749e75	0.399546
$735$	6.49651e74	0.0717903
$736$	−2.47689e75	−0.264024
$737$	2.39400e75	0.246170
$738$	−1.11669e75	−0.110774
$739$	−5.66664e75	−0.542310	−0.271155	−	0.962536i	$-0.587406\pi$
$739$	−5.66664e75	−0.542310	−0.271155	+	0.962536i	$0.587406\pi$
$740$	1.05814e73	0.000977022 0
$741$	2.93567e76	2.61532
$742$	1.48629e76	1.27762
$743$	−1.25772e76	−1.04323	−0.521615	−	0.853181i	$-0.674670\pi$
$743$	−1.25772e76	−1.04323	−0.521615	+	0.853181i	$0.674670\pi$
$744$	−1.94501e76	−1.55682
$745$	7.30272e74	0.0564083
$746$	1.31915e76	0.983369
$747$	−2.28935e75	−0.164708
$748$	1.52237e75	0.105713
$749$	−3.58642e76	−2.40377
$750$	2.79191e75	0.180625
$751$	−5.86096e75	−0.366025	−0.183012	−	0.983111i	$-0.558585\pi$
$751$	−5.86096e75	−0.366025	−0.183012	+	0.983111i	$0.558585\pi$
$752$	2.13809e75	0.128900
$753$	−8.07512e74	−0.0469983
$754$	−3.65349e76	−2.05290
$755$	−1.69718e75	−0.0920732
$756$	1.49726e75	0.0784276
$757$	3.11946e76	1.57775	0.788877	−	0.614551i	$-0.210663\pi$
$757$	3.11946e76	1.57775	0.788877	+	0.614551i	$0.210663\pi$
$758$	−8.96451e75	−0.437817
$759$	2.57560e76	1.21470
$760$	−1.69347e75	−0.0771291
$761$	7.11505e75	0.312957	0.156478	−	0.987681i	$-0.449986\pi$
$761$	7.11505e75	0.312957	0.156478	+	0.987681i	$0.449986\pi$
$762$	2.75649e76	1.17098
$763$	4.68653e76	1.92288
$764$	4.39941e75	0.174349
$765$	−9.73470e74	−0.0372644
$766$	−7.02293e75	−0.259691
$767$	−6.46257e76	−2.30849
$768$	−2.41916e76	−0.834819
$769$	2.10631e76	0.702223	0.351112	−	0.936334i	$-0.385804\pi$
$769$	2.10631e76	0.702223	0.351112	+	0.936334i	$0.385804\pi$
$770$	2.94742e75	0.0949374
$771$	−1.68100e76	−0.523151
$772$	−3.20701e75	−0.0964366
$773$	3.92297e75	0.113988	0.0569938	−	0.998375i	$-0.481848\pi$
$773$	3.92297e75	0.113988	0.0569938	+	0.998375i	$0.481848\pi$
$774$	−5.79877e75	−0.162817
$775$	3.58562e76	0.972903
$776$	−1.82814e76	−0.479374
$777$	5.64882e75	0.143153
$778$	−1.60975e76	−0.394274
$779$	−4.57757e75	−0.108366
$780$	1.43157e75	0.0327570
$781$	−1.32243e76	−0.292497
$782$	1.30973e76	0.280029
$783$	−2.04470e76	−0.422613
$784$	−2.72960e76	−0.545410
$785$	−6.14402e75	−0.118688
$786$	9.52365e76	1.77871
$787$	−2.38560e76	−0.430792	−0.215396	−	0.976527i	$-0.569104\pi$
$787$	−2.38560e76	−0.430792	−0.215396	+	0.976527i	$0.569104\pi$
$788$	7.24317e75	0.126469
$789$	−1.25638e77	−2.12120
$790$	−3.77476e75	−0.0616270
$791$	−5.83244e75	−0.0920818
$792$	1.00920e77	1.54084
$793$	3.35725e76	0.495729
$794$	1.20798e77	1.72511
$795$	7.95318e75	0.109853
$796$	−4.90758e75	−0.0655648
$797$	9.89205e76	1.27832	0.639162	−	0.769072i	$-0.279281\pi$
$797$	9.89205e76	1.27832	0.639162	+	0.769072i	$0.279281\pi$
$798$	−1.47684e77	−1.84611
$799$	6.32137e75	0.0764402
$800$	3.27186e76	0.382745
$801$	1.16586e76	0.131942
$802$	−9.18754e76	−1.00596
$803$	−9.18894e76	−0.973427
$804$	−5.84953e75	−0.0599564
$805$	−6.15248e75	−0.0610182
$806$	−1.51902e77	−1.45776
$807$	1.12822e77	1.04772
$808$	1.56060e76	0.140246
$809$	1.59609e77	1.38810	0.694050	−	0.719927i	$-0.255825\pi$
$809$	1.59609e77	1.38810	0.694050	+	0.719927i	$0.255825\pi$
$810$	5.43424e75	0.0457389
$811$	−2.38631e77	−1.94390	−0.971952	−	0.235181i	$-0.924432\pi$
$811$	−2.38631e77	−1.94390	−0.971952	+	0.235181i	$0.924432\pi$
$812$	−4.45944e76	−0.351598
$813$	−7.30673e76	−0.557601
$814$	1.06537e76	0.0786959
$815$	1.15443e76	0.0825448
$816$	7.47976e76	0.517724
$817$	−2.37705e76	−0.159277
$818$	1.60918e77	1.04386
$819$	4.17905e77	2.62455
$820$	−2.23223e74	−0.00135729
$821$	−2.72431e77	−1.60385	−0.801924	−	0.597425i	$-0.796190\pi$
$821$	−2.72431e77	−1.60385	−0.801924	+	0.597425i	$0.796190\pi$
$822$	−2.76706e77	−1.57730
$823$	2.80427e77	1.54784	0.773918	−	0.633286i	$-0.218294\pi$
$823$	2.80427e77	1.54784	0.773918	+	0.633286i	$0.218294\pi$
$824$	1.71485e77	0.916545
$825$	−3.40225e77	−1.76091
$826$	3.25111e77	1.62952
$827$	3.27438e77	1.58940	0.794700	−	0.607002i	$-0.207628\pi$
$827$	3.27438e77	1.58940	0.794700	+	0.607002i	$0.207628\pi$
$828$	−3.44135e76	−0.161780
$829$	−1.12060e77	−0.510216	−0.255108	−	0.966913i	$-0.582111\pi$
$829$	−1.12060e77	−0.510216	−0.255108	+	0.966913i	$0.582111\pi$
$830$	1.88613e75	0.00831768
$831$	−6.92969e76	−0.295996
$832$	−4.46663e77	−1.84804
$833$	−8.07019e76	−0.323438
$834$	−5.28423e77	−2.05155
$835$	−4.28850e75	−0.0161292
$836$	6.75805e76	0.246238
$837$	−8.50131e76	−0.300097
$838$	4.70103e77	1.60778
$839$	−2.49923e77	−0.828159	−0.414079	−	0.910241i	$-0.635896\pi$
$839$	−2.49923e77	−0.828159	−0.414079	+	0.910241i	$0.635896\pi$
$840$	−4.40854e76	−0.141545
$841$	2.87560e77	0.894611
$842$	1.00833e77	0.303972
$843$	3.64335e77	1.06432
$844$	1.69039e76	0.0478533
$845$	4.36799e76	0.119834
$846$	6.84560e76	0.182011
$847$	−2.12332e77	−0.547149
$848$	−3.34164e77	−0.834583
$849$	6.83615e77	1.65485
$850$	−1.73009e77	−0.405946
$851$	−2.22386e76	−0.0505794
$852$	3.23124e76	0.0712394
$853$	−7.69577e77	−1.64476	−0.822381	−	0.568937i	$-0.807355\pi$
$853$	−7.69577e77	−1.64476	−0.822381	+	0.568937i	$0.807355\pi$
$854$	−1.68892e77	−0.349926
$855$	−4.32141e76	−0.0868007
$856$	1.01171e78	1.97016
$857$	−4.56317e77	−0.861539	−0.430769	−	0.902462i	$-0.641758\pi$
$857$	−4.56317e77	−0.861539	−0.430769	+	0.902462i	$0.641758\pi$
$858$	1.44134e78	2.63847
$859$	−5.50005e77	−0.976219	−0.488110	−	0.872782i	$-0.662313\pi$
$859$	−5.50005e77	−0.976219	−0.488110	+	0.872782i	$0.662313\pi$
$860$	−1.15916e75	−0.00199495
$861$	−1.19166e77	−0.198870
$862$	−1.93734e77	−0.313519
$863$	2.27402e77	0.356868	0.178434	−	0.983952i	$-0.442897\pi$
$863$	2.27402e77	0.356868	0.178434	+	0.983952i	$0.442897\pi$
$864$	−7.75738e76	−0.118060
$865$	−8.47188e76	−0.125041
$866$	−1.00952e78	−1.44508
$867$	−8.48839e77	−1.17847
$868$	−1.85412e77	−0.249669
$869$	9.22123e77	1.20438
$870$	9.83494e76	0.124598
$871$	−2.79654e77	−0.343668
$872$	−1.32204e78	−1.57601
$873$	−4.66505e77	−0.539484
$874$	5.81412e77	0.652276
$875$	1.62920e77	0.177321
$876$	2.24524e77	0.237085
$877$	1.67020e78	1.71111	0.855556	−	0.517711i	$-0.173216\pi$
$877$	1.67020e78	1.71111	0.855556	+	0.517711i	$0.173216\pi$
$878$	1.63965e77	0.162985
$879$	1.65846e78	1.59955
$880$	−6.62670e76	−0.0620164
$881$	1.51231e78	1.37334	0.686672	−	0.726967i	$-0.259071\pi$
$881$	1.51231e78	1.37334	0.686672	+	0.726967i	$0.259071\pi$
$882$	−8.73946e77	−0.770135
$883$	−7.53014e77	−0.643938	−0.321969	−	0.946750i	$-0.604345\pi$
$883$	−7.53014e77	−0.643938	−0.321969	+	0.946750i	$0.604345\pi$
$884$	−1.77834e77	−0.147581
$885$	1.73968e77	0.140111
$886$	9.83137e76	0.0768458
$887$	−2.01497e78	−1.52859	−0.764296	−	0.644865i	$-0.776914\pi$
$887$	−2.01497e78	−1.52859	−0.764296	+	0.644865i	$0.776914\pi$
$888$	−1.59350e77	−0.117330
$889$	1.60853e78	1.14956
$890$	−9.60516e75	−0.00666299
$891$	−1.32751e78	−0.893881
$892$	1.54671e77	0.101098
$893$	2.80617e77	0.178053
$894$	−1.79653e78	−1.10660
$895$	−7.96855e76	−0.0476507
$896$	1.38053e78	0.801464
$897$	−3.00867e78	−1.69580
$898$	−1.07481e78	−0.588180
$899$	2.53204e78	1.34536
$900$	4.54586e77	0.234525
$901$	−9.87972e77	−0.494923
$902$	−2.24746e77	−0.109325
$903$	−6.18806e77	−0.292300
$904$	1.64530e77	0.0754713
$905$	7.14414e75	0.00318246
$906$	4.17520e78	1.80626
$907$	8.47265e77	0.355980	0.177990	−	0.984032i	$-0.443040\pi$
$907$	8.47265e77	0.355980	0.177990	+	0.984032i	$0.443040\pi$
$908$	−5.53447e77	−0.225840
$909$	3.98234e77	0.157832
$910$	−3.44301e77	−0.132538
$911$	−5.35967e77	−0.200402	−0.100201	−	0.994967i	$-0.531949\pi$
$911$	−5.35967e77	−0.200402	−0.100201	+	0.994967i	$0.531949\pi$
$912$	3.32039e78	1.20594
$913$	−4.60756e77	−0.162553
$914$	−1.61728e78	−0.554256
$915$	−9.03748e76	−0.0300877
$916$	7.92378e76	0.0256273
$917$	5.55746e78	1.74618
$918$	4.10196e77	0.125216
$919$	−5.43292e78	−1.61129	−0.805643	−	0.592402i	$-0.798180\pi$
$919$	−5.43292e78	−1.61129	−0.805643	+	0.592402i	$0.798180\pi$
$920$	1.73558e77	0.0500112
$921$	−7.50541e78	−2.10133
$922$	−4.18272e78	−1.13786
$923$	1.54479e78	0.408342
$924$	1.75929e78	0.451888
$925$	2.93762e77	0.0733229
$926$	1.37859e78	0.334383
$927$	4.37594e78	1.03147
$928$	2.31047e78	0.529271
$929$	−1.48878e78	−0.331446	−0.165723	−	0.986172i	$-0.552996\pi$
$929$	−1.48878e78	−0.331446	−0.165723	+	0.986172i	$0.552996\pi$
$930$	4.08910e77	0.0884768
$931$	−3.58250e78	−0.753390
$932$	−1.10122e78	−0.225088
$933$	2.60945e78	0.518423
$934$	−8.17902e76	−0.0157946
$935$	−1.95922e77	−0.0367769
$936$	−1.17889e79	−2.15111
$937$	5.58551e78	0.990749	0.495374	−	0.868680i	$-0.335031\pi$
$937$	5.58551e78	0.990749	0.495374	+	0.868680i	$0.335031\pi$
$938$	1.40685e78	0.242590
$939$	−6.83481e78	−1.14575
$940$	1.36842e76	0.00223013
$941$	9.38809e78	1.48748	0.743742	−	0.668467i	$-0.233049\pi$
$941$	9.38809e78	1.48748	0.743742	+	0.668467i	$0.233049\pi$
$942$	1.51148e79	2.32838
$943$	4.69139e77	0.0702655
$944$	−7.30950e78	−1.06446
$945$	−1.92690e77	−0.0272846
$946$	−1.16707e78	−0.160687
$947$	7.56797e78	1.01322	0.506611	−	0.862174i	$-0.330898\pi$
$947$	7.56797e78	1.01322	0.506611	+	0.862174i	$0.330898\pi$
$948$	−2.25313e78	−0.293335
$949$	1.07340e79	1.35896
$950$	−7.68020e78	−0.945577
$951$	8.15503e78	0.976431
$952$	5.47645e78	0.637705
$953$	−1.45966e79	−1.65306	−0.826530	−	0.562892i	$-0.809689\pi$
$953$	−1.45966e79	−1.65306	−0.826530	+	0.562892i	$0.809689\pi$
$954$	−1.06990e79	−1.17845
$955$	−5.66184e77	−0.0606552
$956$	−2.80301e78	−0.292073
$957$	−2.40254e79	−2.43503
$958$	6.09677e78	0.601055
$959$	−1.61470e79	−1.54845
$960$	1.20239e78	0.112165
$961$	−4.92178e77	−0.0446634
$962$	−1.24450e78	−0.109864
$963$	2.58168e79	2.21721
$964$	3.28080e78	0.274119
$965$	4.12728e77	0.0335498
$966$	1.51356e79	1.19704
$967$	1.29544e78	0.0996821	0.0498411	−	0.998757i	$-0.484129\pi$
$967$	1.29544e78	0.0996821	0.0498411	+	0.998757i	$0.484129\pi$
$968$	5.98978e78	0.448450
$969$	9.81691e78	0.715146
$970$	3.84341e77	0.0272436
$971$	−1.09632e79	−0.756185	−0.378092	−	0.925768i	$-0.623420\pi$
$971$	−1.09632e79	−0.756185	−0.378092	+	0.925768i	$0.623420\pi$
$972$	4.13685e78	0.277660
$973$	−3.08357e79	−2.01402
$974$	−7.53440e78	−0.478891
$975$	3.97431e79	2.45833
$976$	3.79722e78	0.228584
$977$	2.12309e79	1.24384	0.621918	−	0.783083i	$-0.286354\pi$
$977$	2.12309e79	1.24384	0.621918	+	0.783083i	$0.286354\pi$
$978$	−2.83999e79	−1.61933
$979$	2.34641e78	0.130216
$980$	−1.74699e77	−0.00943625
$981$	−3.37359e79	−1.77363
$982$	2.87755e79	1.47254
$983$	−1.67774e79	−0.835710	−0.417855	−	0.908514i	$-0.637218\pi$
$983$	−1.67774e79	−0.835710	−0.417855	+	0.908514i	$0.637218\pi$
$984$	3.36160e78	0.162996
$985$	−9.32164e77	−0.0439979
$986$	−1.22173e79	−0.561354
$987$	7.30517e78	0.326758
$988$	−7.89437e78	−0.343763
$989$	2.43615e78	0.103277
$990$	−2.12169e78	−0.0875689
$991$	1.19328e79	0.479502	0.239751	−	0.970834i	$-0.422934\pi$
$991$	1.19328e79	0.479502	0.239751	+	0.970834i	$0.422934\pi$
$992$	9.60629e78	0.375834
$993$	−4.59326e79	−1.74971
$994$	−7.77134e78	−0.288242
$995$	6.31583e77	0.0228097
$996$	1.12582e78	0.0395909
$997$	−2.54279e79	−0.870739	−0.435370	−	0.900252i	$-0.643382\pi$
$997$	−2.54279e79	−0.870739	−0.435370	+	0.900252i	$0.643382\pi$
$998$	4.63984e79	1.54719
$999$	−6.96493e77	−0.0226168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.54.a.a.1.2	✓	4
3.2	odd	2		9.54.a.b.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.54.a.a.1.2	✓	4	1.1	even	1	trivial
9.54.a.b.1.3		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 54 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} +O(q^{10})\)	\(q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} -1.92700e25 q^{10} +4.70740e27 q^{11} -1.15021e28 q^{12} -5.49891e29 q^{13} +2.76633e30 q^{14} +1.48027e30 q^{15} -6.21955e31 q^{16} -1.83884e32 q^{17} -1.99134e33 q^{18} -8.16294e33 q^{19} -3.98062e32 q^{20} -2.12502e35 q^{21} -4.00779e35 q^{22} +8.36591e35 q^{23} +5.99457e36 q^{24} -1.10510e37 q^{25} +4.68167e37 q^{26} +2.62013e37 q^{27} +5.71444e37 q^{28} -7.80382e38 q^{29} -1.26027e38 q^{30} -3.24461e39 q^{31} -2.96069e39 q^{32} +3.07868e40 q^{33} +1.56555e40 q^{34} -7.35423e39 q^{35} -4.11353e40 q^{36} -2.65824e40 q^{37} +6.94977e41 q^{38} -3.59634e42 q^{39} +2.07459e41 q^{40} +5.60775e41 q^{41} +1.80920e43 q^{42} +2.91200e42 q^{43} -8.27894e42 q^{44} +5.29393e42 q^{45} -7.12258e43 q^{46} -3.43769e43 q^{47} -4.06764e44 q^{48} +4.38874e44 q^{49} +9.40861e44 q^{50} -1.20262e45 q^{51} +9.67099e44 q^{52} +5.37279e45 q^{53} -2.23073e45 q^{54} +1.06546e45 q^{55} -2.97820e46 q^{56} -5.33864e46 q^{57} +6.64402e46 q^{58} +1.17524e47 q^{59} -2.60336e45 q^{60} -6.10529e46 q^{61} +2.76240e47 q^{62} -7.59978e47 q^{63} +8.12275e47 q^{64} -1.24461e47 q^{65} -2.62113e48 q^{66} +5.08562e47 q^{67} +3.23399e47 q^{68} +5.47138e48 q^{69} +6.26125e47 q^{70} -2.80926e48 q^{71} +2.14386e49 q^{72} -1.95202e49 q^{73} +2.26317e48 q^{74} -7.22745e49 q^{75} +1.43562e49 q^{76} -1.52954e50 q^{77} +3.06185e50 q^{78} +1.95888e50 q^{79} -1.40772e49 q^{80} -2.82006e50 q^{81} -4.77433e49 q^{82} -9.78793e49 q^{83} +3.73730e50 q^{84} -4.16200e49 q^{85} -2.47922e50 q^{86} -5.10376e51 q^{87} +4.31475e51 q^{88} +4.98452e50 q^{89} -4.50715e50 q^{90} +1.78672e52 q^{91} -1.47132e51 q^{92} -2.12201e52 q^{93} +2.92678e51 q^{94} -1.84758e51 q^{95} -1.93632e52 q^{96} -1.99451e52 q^{97} -3.73649e52 q^{98} +1.10104e53 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!12 q^{9}+O(q^{10}) \) 4 * q - 68476320 * q^2 - 1048411007280 * q^3 + 7829639419798528 * q^4 - 4563895793294313000 * q^5 + 365243285516994476928 * q^6 - 224841770748445429600 * q^7 + 139144349902380051824640 * q^8 + 11374560253581116395684212 * q^9	\( 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 20\!\cdots\!84 q^{99}+O(q^{100}) \) 4 * q - 68476320 * q^2 - 1048411007280 * q^3 + 7829639419798528 * q^4 - 4563895793294313000 * q^5 + 365243285516994476928 * q^6 - 224841770748445429600 * q^7 + 139144349902380051824640 * q^8 + 11374560253581116395684212 * q^9 + 239691034935725362703784000 * q^10 + 2482225436399137396212828528 * q^11 - 36954074065409878778429091840 * q^12 + 38846785417115118418757458040 * q^13 - 2318389217831653006768429089024 * q^14 + 10885572770546350531014554412000 * q^15 - 158675761303426594387641091751936 * q^16 - 869470789827683332623267869375160 * q^17 - 6763457530054882037574097250222880 * q^18 - 25573430606481293737377136094590960 * q^19 - 137124186244908431721319713321216000 * q^20 - 456430072728043514442750337944104832 * q^21 - 930239272324579210970924539473171840 * q^22 + 692283403499940921426611559815316960 * q^23 + 8087484160806183674287697801240248320 * q^24 + 36481255519181820020535795184467437500 * q^25 + 88199592302469577023283184091414497088 * q^26 + 85289145712610214901983766257673297440 * q^27 - 5693966184427848677134093343909109760 * q^28 - 1403448065249545071892827367228561632840 * q^29 - 5799093432823921615312476874120821216000 * q^30 - 3964172885133396823441211087460727887232 * q^31 + 3478175004061909463146496356345215713280 * q^32 + 26488618539649572306469337360654123586240 * q^33 + 149997773608319010417738024908146242937536 * q^34 + 61365948170559642529868826584708753304000 * q^35 + 74373890656883085418751005021443502838784 * q^36 - 283737807523680188930907412534612515795880 * q^37 - 2149858349100743242412726210681586741479040 * q^38 - 3695759405159081384443679869760359201600416 * q^39 - 530824655589569872286083924732862423040000 * q^40 + 816268439352205816307560932682632884757288 * q^41 + 34473336675516302350057635130637873086909440 * q^42 + 45680017888765970285202819125021276867644400 * q^43 + 36450257868828743991533939202628376274333696 * q^44 - 52785302554790432865174172783106255610789000 * q^45 - 286598377899888278123152881845505043619242752 * q^46 - 450331332464449690190061856166374876708223040 * q^47 - 307327868606734954261884348178650744005591040 * q^48 + 61256589204322440136838991964906594854806628 * q^49 + 521470775015683964723409941128468604170500000 * q^50 + 4823104417223604238685131462744139603812556448 * q^51 + 6480873745173555872757727943119261362842777600 * q^52 + 3894630980633224571473003534722579109607488920 * q^53 - 9094643349894867160783307676594158361928776960 * q^54 - 25220087960941681699071033843031097345513916000 * q^55 - 41708301235969326798480993683317763265335132160 * q^56 - 78794438935790744156133212572387836678302205120 * q^57 + 23153390818000102952173078969301145284748805440 * q^58 + 161352440713620380366889082872890081870684067120 * q^59 + 406305479737925709888509415210821103661353984000 * q^60 + 65647964430669998286897420448040378258467279928 * q^61 + 397783228528983419561799088374192602352940661760 * q^62 - 302986559547633524951279897150694105228921738720 * q^63 - 1033735951572319175631379922707833053066697900032 * q^64 - 3420620126550512806970332375686936386825214798000 * q^65 - 658347942888276364671353073747068107649649237504 * q^66 - 1114206317023626852397290701407230552884994982960 * q^67 + 2848472333882807118405541680155589548651324344320 * q^68 + 775291276168249766930956334518267852448076104064 * q^69 + 33179725699094578918821931009364962909309028928000 * q^70 + 3568565136657140046536067623675232742954247775648 * q^71 + 26402495617891679740981292232213348882933665464320 * q^72 - 70697396612705842206652346649767546611106446705240 * q^73 - 2477665041456578897595255396512213772982320606144 * q^74 - 214147644415917420957952976584023331338227237250000 * q^75 + 45189859364823457604586927205450004182295006842880 * q^76 - 161023821416166064076421008340115759390173471196800 * q^77 + 512081797195935502825354508308769411884974336211200 * q^78 - 156417020870005797258130007144678737115075518344640 * q^79 + 1135588155590291950317639086884448883835074772992000 * q^80 - 498743339483968532647094896032944674900788125971356 * q^81 + 1595344511843776298585510858680959074676233895092160 * q^82 - 2616078236644862619515249170129703738064518568891120 * q^83 - 769036580140824400081375315496419857132807898497024 * q^84 - 2322985242765977498040783878693923846942012787106000 * q^85 - 771473689440649042704510533443081756253708267624832 * q^86 - 4553516071908987502170780484180858967295593004331680 * q^87 + 5676678682320308097974311975312643702936459537940480 * q^88 - 377838445322199523132380916699165405584669879895320 * q^89 + 20963916598038401334962666668658272688885372614152000 * q^90 + 12668228612190081366491587480915595422042752342094528 * q^91 + 8910978937854086377493208678167975007758313267978240 * q^92 - 9941509412818307372855389204673554966584205049372160 * q^93 - 37159704993639903541096652460057479885138542709712384 * q^94 - 17088387525725080516970439013001314242158750454180000 * q^95 - 115890361493294838169648124263288994270902966699425792 * q^96 + 10362822344952442405677621761316902058987153293434760 * q^97 - 88214006056362955165305640276151180685109758813947040 * q^98 + 200357011548750056817277275156798035565052172823063984 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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