LMFDB - Embedded newform 1.54.a.a.1.1

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			1.1
Root			$-1.26509e6$ 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)

$f(q)$	$=$	$q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +O(q^{10})$	\(q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +7.42585e26 q^{10} +2.25708e27 q^{11} -6.06954e28 q^{12} +1.44397e29 q^{13} -3.53851e30 q^{14} +3.19082e31 q^{15} -6.90335e31 q^{16} -6.08256e32 q^{17} -2.22657e33 q^{18} +5.84282e33 q^{19} -5.46287e34 q^{20} -1.52047e35 q^{21} -3.12758e35 q^{22} +9.54096e35 q^{23} +9.79021e35 q^{24} +1.76167e37 q^{25} -2.00088e37 q^{26} +1.97365e37 q^{27} +2.60313e38 q^{28} -4.38838e37 q^{29} -4.42145e39 q^{30} +8.43957e38 q^{31} +1.10468e40 q^{32} -1.34390e40 q^{33} +8.42846e40 q^{34} -1.36849e41 q^{35} +1.63799e41 q^{36} +1.19964e41 q^{37} -8.09626e41 q^{38} -8.59760e41 q^{39} +8.81165e41 q^{40} -8.08650e42 q^{41} +2.10688e43 q^{42} +1.66354e43 q^{43} +2.30083e43 q^{44} -8.61111e43 q^{45} -1.32207e44 q^{46} -7.16487e42 q^{47} +4.11035e44 q^{48} +3.52310e43 q^{49} -2.44110e45 q^{50} +3.62164e45 q^{51} +1.47196e45 q^{52} +3.19144e45 q^{53} -2.73484e45 q^{54} -1.20957e46 q^{55} -4.19887e45 q^{56} -3.47889e46 q^{57} +6.08088e45 q^{58} +3.07882e46 q^{59} +3.25267e47 q^{60} -2.46965e47 q^{61} -1.16945e47 q^{62} +4.10330e47 q^{63} -9.08937e47 q^{64} -7.73825e47 q^{65} +1.86221e48 q^{66} +1.37146e48 q^{67} -6.20045e48 q^{68} -5.68081e48 q^{69} +1.89629e49 q^{70} +1.40028e49 q^{71} -2.64209e48 q^{72} -1.59560e49 q^{73} -1.66231e49 q^{74} -1.04892e50 q^{75} +5.95606e49 q^{76} +5.76375e49 q^{77} +1.19135e50 q^{78} -1.73480e50 q^{79} +3.69950e50 q^{80} -4.28973e50 q^{81} +1.12053e51 q^{82} -1.32890e51 q^{83} -1.54994e51 q^{84} +3.25964e51 q^{85} -2.30513e51 q^{86} +2.61290e50 q^{87} -3.71125e50 q^{88} -6.74530e51 q^{89} +1.19322e52 q^{90} +3.68737e51 q^{91} +9.72588e51 q^{92} -5.02503e51 q^{93} +9.92819e50 q^{94} -3.13117e52 q^{95} -6.57744e52 q^{96} +4.44346e52 q^{97} -4.88188e51 q^{98} +3.62679e52 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.38568e8	−1.46005	−0.730024	−	0.683421i	$-0.760491\pi$
$2$	−1.38568e8	−1.46005	−0.730024	+	0.683421i	$0.760491\pi$
$3$	−5.95414e12	−1.35240	−0.676201	−	0.736718i	$-0.736375\pi$
$3$	−5.95414e12	−1.35240	−0.676201	+	0.736718i	$0.736375\pi$
$4$	1.01938e16	1.13174
$5$	−5.35900e18	−1.60834	−0.804172	−	0.594397i	$-0.797391\pi$
$5$	−5.35900e18	−1.60834	−0.804172	+	0.594397i	$0.797391\pi$
$6$	8.25051e20	1.97457
$7$	2.55363e22	1.02816	0.514080	−	0.857742i	$-0.328134\pi$
$7$	2.55363e22	1.02816	0.514080	+	0.857742i	$0.328134\pi$
$8$	−1.64427e23	−0.192348
$9$	1.60685e25	0.828989
$10$	7.42585e26	2.34826
$11$	2.25708e27	0.571006	0.285503	−	0.958378i	$-0.407839\pi$
$11$	2.25708e27	0.571006	0.285503	+	0.958378i	$0.407839\pi$
$12$	−6.06954e28	−1.53057
$13$	1.44397e29	0.436576	0.218288	−	0.975884i	$-0.429953\pi$
$13$	1.44397e29	0.436576	0.218288	+	0.975884i	$0.429953\pi$
$14$	−3.53851e30	−1.50116
$15$	3.19082e31	2.17513
$16$	−6.90335e31	−0.850903
$17$	−6.08256e32	−1.50380	−0.751899	−	0.659278i	$-0.770862\pi$
$17$	−6.08256e32	−1.50380	−0.751899	+	0.659278i	$0.770862\pi$
$18$	−2.22657e33	−1.21036
$19$	5.84282e33	0.757970	0.378985	−	0.925403i	$-0.376273\pi$
$19$	5.84282e33	0.757970	0.378985	+	0.925403i	$0.376273\pi$
$20$	−5.46287e34	−1.82023
$21$	−1.52047e35	−1.39048
$22$	−3.12758e35	−0.833696
$23$	9.54096e35	0.783077	0.391538	−	0.920162i	$-0.371943\pi$
$23$	9.54096e35	0.783077	0.391538	+	0.920162i	$0.371943\pi$
$24$	9.79021e35	0.260132
$25$	1.76167e37	1.58677
$26$	−2.00088e37	−0.637422
$27$	1.97365e37	0.231276
$28$	2.60313e38	1.16361
$29$	−4.38838e37	−0.0774029	−0.0387015	−	0.999251i	$-0.512322\pi$
$29$	−4.38838e37	−0.0774029	−0.0387015	+	0.999251i	$0.512322\pi$
$30$	−4.42145e39	−3.17579
$31$	8.43957e38	0.254235	0.127118	−	0.991888i	$-0.459427\pi$
$31$	8.43957e38	0.254235	0.127118	+	0.991888i	$0.459427\pi$
$32$	1.10468e40	1.43471
$33$	−1.34390e40	−0.772229
$34$	8.42846e40	2.19562
$35$	−1.36849e41	−1.65363
$36$	1.63799e41	0.938200
$37$	1.19964e41	0.332433	0.166216	−	0.986089i	$-0.446845\pi$
$37$	1.19964e41	0.332433	0.166216	+	0.986089i	$0.446845\pi$
$38$	−8.09626e41	−1.10667
$39$	−8.59760e41	−0.590426
$40$	8.81165e41	0.309362
$41$	−8.08650e42	−1.47567	−0.737834	−	0.674983i	$-0.764151\pi$
$41$	−8.08650e42	−1.47567	−0.737834	+	0.674983i	$0.764151\pi$
$42$	2.10688e43	2.03017
$43$	1.66354e43	0.859249	0.429624	−	0.903008i	$-0.358646\pi$
$43$	1.66354e43	0.859249	0.429624	+	0.903008i	$0.358646\pi$
$44$	2.30083e43	0.646231
$45$	−8.61111e43	−1.33330
$46$	−1.32207e44	−1.14333
$47$	−7.16487e42	−0.0350441	−0.0175220	−	0.999846i	$-0.505578\pi$
$47$	−7.16487e42	−0.0350441	−0.0175220	+	0.999846i	$0.505578\pi$
$48$	4.11035e44	1.15076
$49$	3.52310e43	0.0571122
$50$	−2.44110e45	−2.31676
$51$	3.62164e45	2.03374
$52$	1.47196e45	0.494091
$53$	3.19144e45	0.646660	0.323330	−	0.946286i	$-0.395198\pi$
$53$	3.19144e45	0.646660	0.323330	+	0.946286i	$0.395198\pi$
$54$	−2.73484e45	−0.337674
$55$	−1.20957e46	−0.918374
$56$	−4.19887e45	−0.197765
$57$	−3.47889e46	−1.02508
$58$	6.08088e45	0.113012
$59$	3.07882e46	0.363752	0.181876	−	0.983321i	$-0.441783\pi$
$59$	3.07882e46	0.363752	0.181876	+	0.983321i	$0.441783\pi$
$60$	3.25267e47	2.46168
$61$	−2.46965e47	−1.20613	−0.603066	−	0.797691i	$-0.706054\pi$
$61$	−2.46965e47	−1.20613	−0.603066	+	0.797691i	$0.706054\pi$
$62$	−1.16945e47	−0.371195
$63$	4.10330e47	0.852333
$64$	−9.08937e47	−1.24384
$65$	−7.73825e47	−0.702164
$66$	1.86221e48	1.12749
$67$	1.37146e48	0.557445	0.278723	−	0.960372i	$-0.410089\pi$
$67$	1.37146e48	0.557445	0.278723	+	0.960372i	$0.410089\pi$
$68$	−6.20045e48	−1.70191
$69$	−5.68081e48	−1.05903
$70$	1.89629e49	2.41439
$71$	1.40028e49	1.22424	0.612122	−	0.790763i	$-0.290316\pi$
$71$	1.40028e49	1.22424	0.612122	+	0.790763i	$0.290316\pi$
$72$	−2.64209e48	−0.159455
$73$	−1.59560e49	−0.668140	−0.334070	−	0.942548i	$-0.608422\pi$
$73$	−1.59560e49	−0.668140	−0.334070	+	0.942548i	$0.608422\pi$
$74$	−1.66231e49	−0.485368
$75$	−1.04892e50	−2.14595
$76$	5.95606e49	0.857825
$77$	5.76375e49	0.587085
$78$	1.19135e50	0.862050
$79$	−1.73480e50	−0.895635	−0.447818	−	0.894125i	$-0.647799\pi$
$79$	−1.73480e50	−0.895635	−0.447818	+	0.894125i	$0.647799\pi$
$80$	3.69950e50	1.36854
$81$	−4.28973e50	−1.14177
$82$	1.12053e51	2.15455
$83$	−1.32890e51	−1.85320	−0.926600	−	0.376048i	$-0.877283\pi$
$83$	−1.32890e51	−1.85320	−0.926600	+	0.376048i	$0.877283\pi$
$84$	−1.54994e51	−1.57367
$85$	3.25964e51	2.41862
$86$	−2.30513e51	−1.25454
$87$	2.61290e50	0.104680
$88$	−3.71125e50	−0.109832
$89$	−6.74530e51	−1.47967	−0.739837	−	0.672786i	$-0.765098\pi$
$89$	−6.74530e51	−1.47967	−0.739837	+	0.672786i	$0.765098\pi$
$90$	1.19322e52	1.94668
$91$	3.68737e51	0.448870
$92$	9.72588e51	0.886240
$93$	−5.02503e51	−0.343828
$94$	9.92819e50	0.0511661
$95$	−3.13117e52	−1.21908
$96$	−6.57744e52	−1.94030
$97$	4.44346e52	0.996025	0.498012	−	0.867170i	$-0.334063\pi$
$97$	4.44346e52	0.996025	0.498012	+	0.867170i	$0.334063\pi$
$98$	−4.88188e51	−0.0833866
$99$	3.62679e52	0.473357
$100$	1.79581e53	1.79581
$101$	1.33654e53	1.02675	0.513377	−	0.858163i	$-0.328394\pi$
$101$	1.33654e53	1.02675	0.513377	+	0.858163i	$0.328394\pi$
$102$	−5.01842e53	−2.96936
$103$	7.98514e52	0.364835	0.182417	−	0.983221i	$-0.441608\pi$
$103$	7.98514e52	0.364835	0.182417	+	0.983221i	$0.441608\pi$
$104$	−2.37428e52	−0.0839747
$105$	8.14819e53	2.23638
$106$	−4.42230e53	−0.944155
$107$	−1.04658e54	−1.74222	−0.871108	−	0.491092i	$-0.836598\pi$
$107$	−1.04658e54	−1.74222	−0.871108	+	0.491092i	$0.836598\pi$
$108$	2.01190e53	0.261745
$109$	−5.02767e53	−0.512348	−0.256174	−	0.966631i	$-0.582462\pi$
$109$	−5.02767e53	−0.512348	−0.256174	+	0.966631i	$0.582462\pi$
$110$	1.67607e54	1.34087
$111$	−7.14279e53	−0.449582
$112$	−1.76286e54	−0.874864
$113$	3.92048e54	1.53731	0.768654	−	0.639665i	$-0.220927\pi$
$113$	3.92048e54	1.53731	0.768654	+	0.639665i	$0.220927\pi$
$114$	4.82062e54	1.49666
$115$	−5.11300e54	−1.25946
$116$	−4.47344e53	−0.0876001
$117$	2.32024e54	0.361916
$118$	−4.26625e54	−0.531096
$119$	−1.55326e55	−1.54615
$120$	−5.24658e54	−0.418382
$121$	−1.05303e55	−0.673952
$122$	3.42214e55	1.76101
$123$	4.81481e55	1.99569
$124$	8.60314e54	0.287728
$125$	−3.49109e55	−0.943726
$126$	−5.68585e55	−1.24445
$127$	2.95271e55	0.524110	0.262055	−	0.965053i	$-0.415600\pi$
$127$	2.95271e55	0.524110	0.262055	+	0.965053i	$0.415600\pi$
$128$	2.64483e55	0.381359
$129$	−9.90494e55	−1.16205
$130$	1.07227e56	1.02519
$131$	−1.59227e55	−0.124259	−0.0621296	−	0.998068i	$-0.519789\pi$
$131$	−1.59227e55	−0.124259	−0.0621296	+	0.998068i	$0.519789\pi$
$132$	−1.36994e56	−0.873963
$133$	1.49204e56	0.779314
$134$	−1.90041e56	−0.813897
$135$	−1.05768e56	−0.371971
$136$	1.00014e56	0.289253
$137$	1.20350e56	0.286650	0.143325	−	0.989676i	$-0.454221\pi$
$137$	1.20350e56	0.286650	0.143325	+	0.989676i	$0.454221\pi$
$138$	7.87178e56	1.54624
$139$	1.03961e57	1.68647	0.843235	−	0.537546i	$-0.180648\pi$
$139$	1.03961e57	1.68647	0.843235	+	0.537546i	$0.180648\pi$
$140$	−1.39502e57	−1.87149
$141$	4.26606e55	0.0473937
$142$	−1.94033e57	−1.78745
$143$	3.25916e56	0.249287
$144$	−1.10926e57	−0.705389
$145$	2.35173e56	0.124490
$146$	2.21098e57	0.975516
$147$	−2.09770e56	−0.0772386
$148$	1.22289e57	0.376228
$149$	−5.27498e57	−1.35764	−0.678820	−	0.734305i	$-0.737508\pi$
$149$	−5.27498e57	−1.35764	−0.678820	+	0.734305i	$0.737508\pi$
$150$	1.45347e58	3.13319
$151$	−1.14345e57	−0.206695	−0.103347	−	0.994645i	$-0.532955\pi$
$151$	−1.14345e57	−0.206695	−0.103347	+	0.994645i	$0.532955\pi$
$152$	−9.60717e56	−0.145794
$153$	−9.77375e57	−1.24663
$154$	−7.98670e57	−0.857173
$155$	−4.52277e57	−0.408897
$156$	−8.76424e57	−0.668209
$157$	2.71579e58	1.74806	0.874030	−	0.485873i	$-0.161498\pi$
$157$	2.71579e58	1.74806	0.874030	+	0.485873i	$0.161498\pi$
$158$	2.40387e58	1.30767
$159$	−1.90023e58	−0.874544
$160$	−5.92000e58	−2.30750
$161$	2.43641e58	0.805128
$162$	5.94419e58	1.66703
$163$	−1.18765e58	−0.282955	−0.141478	−	0.989941i	$-0.545185\pi$
$163$	−1.18765e58	−0.282955	−0.141478	+	0.989941i	$0.545185\pi$
$164$	−8.24323e58	−1.67007
$165$	7.20194e58	1.24201
$166$	1.84142e59	2.70576
$167$	−1.03522e59	−1.29732	−0.648661	−	0.761078i	$-0.724671\pi$
$167$	−1.03522e59	−1.29732	−0.648661	+	0.761078i	$0.724671\pi$
$168$	2.50006e58	0.267457
$169$	−8.85445e58	−0.809402
$170$	−4.51681e59	−3.53131
$171$	9.38852e58	0.628348
$172$	1.69578e59	0.972447
$173$	1.05509e59	0.518881	0.259441	−	0.965759i	$-0.416462\pi$
$173$	1.05509e59	0.518881	0.259441	+	0.965759i	$0.416462\pi$
$174$	−3.62064e58	−0.152838
$175$	4.49865e59	1.63145
$176$	−1.55814e59	−0.485871
$177$	−1.83317e59	−0.491939
$178$	9.34681e59	2.16040
$179$	−8.35545e58	−0.166481	−0.0832405	−	0.996529i	$-0.526527\pi$
$179$	−8.35545e58	−0.166481	−0.0832405	+	0.996529i	$0.526527\pi$
$180$	−8.77801e59	−1.50895
$181$	−7.95749e59	−1.18112	−0.590559	−	0.806994i	$-0.701093\pi$
$181$	−7.95749e59	−1.18112	−0.590559	+	0.806994i	$0.701093\pi$
$182$	−5.10951e59	−0.655371
$183$	1.47046e60	1.63117
$184$	−1.56879e59	−0.150624
$185$	−6.42885e59	−0.534666
$186$	6.96308e59	0.502005
$187$	−1.37288e60	−0.858678
$188$	−7.30373e58	−0.0396608
$189$	5.03998e59	0.237789
$190$	4.33879e60	1.77991
$191$	−3.99509e60	−1.42607	−0.713037	−	0.701126i	$-0.752681\pi$
$191$	−3.99509e60	−1.42607	−0.713037	+	0.701126i	$0.752681\pi$
$192$	5.41194e60	1.68217
$193$	−2.31728e60	−0.627638	−0.313819	−	0.949483i	$-0.601609\pi$
$193$	−2.31728e60	−0.627638	−0.313819	+	0.949483i	$0.601609\pi$
$194$	−6.15720e60	−1.45424
$195$	4.60746e60	0.949607
$196$	3.59139e59	0.0646362
$197$	6.97303e60	1.09665	0.548323	−	0.836267i	$-0.315267\pi$
$197$	6.97303e60	1.09665	0.548323	+	0.836267i	$0.315267\pi$
$198$	−5.02555e60	−0.691125
$199$	−7.01618e60	−0.844295	−0.422148	−	0.906527i	$-0.638724\pi$
$199$	−7.01618e60	−0.844295	−0.422148	+	0.906527i	$0.638724\pi$
$200$	−2.89666e60	−0.305213
$201$	−8.16589e60	−0.753890
$202$	−1.85202e61	−1.49911
$203$	−1.12063e60	−0.0795826
$204$	3.69183e61	2.30167
$205$	4.33356e61	2.37338
$206$	−1.10648e61	−0.532676
$207$	1.53309e61	0.649161
$208$	−9.96823e60	−0.371484
$209$	1.31877e61	0.432805
$210$	−1.12908e62	−3.26522
$211$	7.11365e60	0.181388	0.0906938	−	0.995879i	$-0.471092\pi$
$211$	7.11365e60	0.181388	0.0906938	+	0.995879i	$0.471092\pi$
$212$	3.25329e61	0.731852
$213$	−8.33744e61	−1.65567
$214$	1.45022e62	2.54372
$215$	−8.91491e61	−1.38197
$216$	−3.24522e60	−0.0444856
$217$	2.15516e61	0.261394
$218$	6.96673e61	0.748052
$219$	9.50040e61	0.903593
$220$	−1.23301e62	−1.03936
$221$	−8.78304e61	−0.656522
$222$	9.89761e61	0.656412
$223$	−1.07039e62	−0.630176	−0.315088	−	0.949062i	$-0.602034\pi$
$223$	−1.07039e62	−0.630176	−0.315088	+	0.949062i	$0.602034\pi$
$224$	2.82096e62	1.47511
$225$	2.83073e62	1.31541
$226$	−5.43252e62	−2.24454
$227$	2.87663e62	1.05730	0.528651	−	0.848840i	$-0.322698\pi$
$227$	2.87663e62	1.05730	0.528651	+	0.848840i	$0.322698\pi$
$228$	−3.54632e62	−1.16012
$229$	−5.16513e62	−1.50467	−0.752334	−	0.658782i	$-0.771072\pi$
$229$	−5.16513e62	−1.50467	−0.752334	+	0.658782i	$0.771072\pi$
$230$	7.08497e62	1.83887
$231$	−3.43182e62	−0.793975
$232$	7.21569e60	0.0148883
$233$	−1.10244e62	−0.202965	−0.101483	−	0.994837i	$-0.532359\pi$
$233$	−1.10244e62	−0.202965	−0.101483	+	0.994837i	$0.532359\pi$
$234$	−3.21511e62	−0.528415
$235$	3.83965e61	0.0563629
$236$	3.13849e62	0.411673
$237$	1.03292e63	1.21126
$238$	2.15232e63	2.25745
$239$	4.32058e61	0.0405507	0.0202753	−	0.999794i	$-0.493546\pi$
$239$	4.32058e61	0.0405507	0.0202753	+	0.999794i	$0.493546\pi$
$240$	−2.20274e63	−1.85082
$241$	−2.12916e63	−1.60235	−0.801175	−	0.598431i	$-0.795791\pi$
$241$	−2.12916e63	−1.60235	−0.801175	+	0.598431i	$0.795791\pi$
$242$	1.45916e63	0.984003
$243$	2.17161e63	1.31285
$244$	−2.51752e63	−1.36503
$245$	−1.88803e62	−0.0918561
$246$	−6.67178e63	−2.91381
$247$	8.43686e62	0.330911
$248$	−1.38769e62	−0.0489017
$249$	7.91244e63	2.50627
$250$	4.83753e63	1.37789
$251$	−2.49739e63	−0.639930	−0.319965	−	0.947429i	$-0.603671\pi$
$251$	−2.49739e63	−0.639930	−0.319965	+	0.947429i	$0.603671\pi$
$252$	4.18283e63	0.964620
$253$	2.15347e63	0.447141
$254$	−4.09150e63	−0.765226
$255$	−1.94084e64	−3.27095
$256$	4.52210e63	0.687038
$257$	3.80580e63	0.521457	0.260728	−	0.965412i	$-0.416037\pi$
$257$	3.80580e63	0.521457	0.260728	+	0.965412i	$0.416037\pi$
$258$	1.37250e64	1.69665
$259$	3.06343e63	0.341794
$260$	−7.88823e63	−0.794668
$261$	−7.05146e62	−0.0641661
$262$	2.20638e63	0.181425
$263$	−1.69696e64	−1.26137	−0.630687	−	0.776037i	$-0.717227\pi$
$263$	−1.69696e64	−1.26137	−0.630687	+	0.776037i	$0.717227\pi$
$264$	2.20973e63	0.148537
$265$	−1.71029e64	−1.04005
$266$	−2.06749e64	−1.13784
$267$	4.01625e64	2.00111
$268$	1.39805e64	0.630884
$269$	6.10982e63	0.249800	0.124900	−	0.992169i	$-0.460139\pi$
$269$	6.10982e63	0.249800	0.124900	+	0.992169i	$0.460139\pi$
$270$	1.46560e64	0.543096
$271$	−9.96186e63	−0.334699	−0.167350	−	0.985898i	$-0.553521\pi$
$271$	−9.96186e63	−0.334699	−0.167350	+	0.985898i	$0.553521\pi$
$272$	4.19900e64	1.27959
$273$	−2.19551e64	−0.607052
$274$	−1.66767e64	−0.418523
$275$	3.97622e64	0.906055
$276$	−5.79092e64	−1.19855
$277$	2.47062e64	0.464615	0.232307	−	0.972642i	$-0.425372\pi$
$277$	2.47062e64	0.464615	0.232307	+	0.972642i	$0.425372\pi$
$278$	−1.44056e65	−2.46233
$279$	1.35611e64	0.210758
$280$	2.25017e64	0.318074
$281$	−1.25270e64	−0.161113	−0.0805564	−	0.996750i	$-0.525670\pi$
$281$	−1.25270e64	−0.161113	−0.0805564	+	0.996750i	$0.525670\pi$
$282$	−5.91138e63	−0.0691971
$283$	−2.70393e64	−0.288174	−0.144087	−	0.989565i	$-0.546025\pi$
$283$	−2.70393e64	−0.288174	−0.144087	+	0.989565i	$0.546025\pi$
$284$	1.42742e65	1.38553
$285$	1.86434e65	1.64868
$286$	−4.51614e64	−0.363972
$287$	−2.06500e65	−1.51722
$288$	1.77506e65	1.18936
$289$	2.06371e65	1.26141
$290$	−3.25874e64	−0.181762
$291$	−2.64569e65	−1.34702
$292$	−1.62652e65	−0.756161
$293$	−6.85669e64	−0.291154	−0.145577	−	0.989347i	$-0.546504\pi$
$293$	−6.85669e64	−0.291154	−0.145577	+	0.989347i	$0.546504\pi$
$294$	2.90674e64	0.112772
$295$	−1.64994e65	−0.585039
$296$	−1.97253e64	−0.0639429
$297$	4.45469e64	0.132060
$298$	7.30942e65	1.98222
$299$	1.37769e65	0.341872
$300$	−1.06925e66	−2.42866
$301$	4.24807e65	0.883445
$302$	1.58446e65	0.301784
$303$	−7.95796e65	−1.38858
$304$	−4.03350e65	−0.644959
$305$	1.32349e66	1.93987
$306$	1.35433e66	1.82014
$307$	−1.46437e66	−1.80502	−0.902512	−	0.430664i	$-0.858279\pi$
$307$	−1.46437e66	−1.80502	−0.902512	+	0.430664i	$0.858279\pi$
$308$	5.87547e65	0.664429
$309$	−4.75446e65	−0.493403
$310$	6.26710e65	0.597010
$311$	2.08500e66	1.82371	0.911856	−	0.410511i	$-0.134650\pi$
$311$	2.08500e66	1.82371	0.911856	+	0.410511i	$0.134650\pi$
$312$	1.41368e65	0.113567
$313$	−1.88530e66	−1.39141	−0.695706	−	0.718327i	$-0.744908\pi$
$313$	−1.88530e66	−1.39141	−0.695706	+	0.718327i	$0.744908\pi$
$314$	−3.76322e66	−2.55225
$315$	−2.19896e66	−1.37084
$316$	−1.76842e66	−1.01363
$317$	1.84865e66	0.974503	0.487252	−	0.873262i	$-0.337999\pi$
$317$	1.84865e66	0.974503	0.487252	+	0.873262i	$0.337999\pi$
$318$	2.63310e66	1.27688
$319$	−9.90492e64	−0.0441975
$320$	4.87100e66	2.00052
$321$	6.23147e66	2.35617
$322$	−3.37608e66	−1.17553
$323$	−3.55393e66	−1.13983
$324$	−4.37288e66	−1.29218
$325$	2.54380e66	0.692745
$326$	1.64570e66	0.413129
$327$	2.99354e66	0.692899
$328$	1.32964e66	0.283842
$329$	−1.82964e65	−0.0360309
$330$	−9.97957e66	−1.81339
$331$	1.90131e66	0.318867	0.159434	−	0.987209i	$-0.449033\pi$
$331$	1.90131e66	0.318867	0.159434	+	0.987209i	$0.449033\pi$
$332$	−1.35466e67	−2.09734
$333$	1.92763e66	0.275583
$334$	1.43449e67	1.89415
$335$	−7.34968e66	−0.896564
$336$	1.04963e67	1.18317
$337$	−9.17803e66	−0.956218	−0.478109	−	0.878300i	$-0.658678\pi$
$337$	−9.17803e66	−0.956218	−0.478109	+	0.878300i	$0.658678\pi$
$338$	1.22694e67	1.18177
$339$	−2.33431e67	−2.07906
$340$	3.32282e67	2.73726
$341$	1.90488e66	0.145170
$342$	−1.30095e67	−0.917419
$343$	−1.48530e67	−0.969439
$344$	−2.73531e66	−0.165275
$345$	3.04435e67	1.70329
$346$	−1.46202e67	−0.757592
$347$	1.14278e67	0.548569	0.274285	−	0.961649i	$-0.411559\pi$
$347$	1.14278e67	0.548569	0.274285	+	0.961649i	$0.411559\pi$
$348$	2.66354e66	0.118470
$349$	2.72467e67	1.12316	0.561578	−	0.827424i	$-0.310195\pi$
$349$	2.72467e67	1.12316	0.561578	+	0.827424i	$0.310195\pi$
$350$	−6.23368e67	−2.38200
$351$	2.84990e66	0.100970
$352$	2.49336e67	0.819227
$353$	−3.17343e67	−0.967163	−0.483582	−	0.875299i	$-0.660664\pi$
$353$	−3.17343e67	−0.967163	−0.483582	+	0.875299i	$0.660664\pi$
$354$	2.54018e67	0.718255
$355$	−7.50409e67	−1.96900
$356$	−6.87604e67	−1.67461
$357$	9.24833e67	2.09101
$358$	1.15780e67	0.243070
$359$	3.93676e67	0.767601	0.383801	−	0.923416i	$-0.374615\pi$
$359$	3.93676e67	0.767601	0.383801	+	0.923416i	$0.374615\pi$
$360$	1.41590e67	0.256458
$361$	−2.52826e67	−0.425482
$362$	1.10265e68	1.72449
$363$	6.26989e67	0.911454
$364$	3.75884e67	0.508004
$365$	8.55081e67	1.07460
$366$	−2.03759e68	−2.38159
$367$	−1.53609e68	−1.67020	−0.835098	−	0.550101i	$-0.814589\pi$
$367$	−1.53609e68	−1.67020	−0.835098	+	0.550101i	$0.814589\pi$
$368$	−6.58645e67	−0.666322
$369$	−1.29938e68	−1.22331
$370$	8.90831e67	0.780638
$371$	8.14977e67	0.664870
$372$	−5.12243e67	−0.389124
$373$	−1.29701e68	−0.917611	−0.458805	−	0.888537i	$-0.651722\pi$
$373$	−1.29701e68	−0.917611	−0.458805	+	0.888537i	$0.651722\pi$
$374$	1.90237e68	1.25371
$375$	2.07864e68	1.27630
$376$	1.17810e66	0.00674068
$377$	−6.33670e66	−0.0337922
$378$	−6.98379e67	−0.347183
$379$	1.95972e68	0.908354	0.454177	−	0.890911i	$-0.349933\pi$
$379$	1.95972e68	0.908354	0.454177	+	0.890911i	$0.349933\pi$
$380$	−3.19185e68	−1.37968
$381$	−1.75808e68	−0.708807
$382$	5.53590e68	2.08214
$383$	−7.90039e67	−0.277256	−0.138628	−	0.990345i	$-0.544269\pi$
$383$	−7.90039e67	−0.277256	−0.138628	+	0.990345i	$0.544269\pi$
$384$	−1.57477e68	−0.515750
$385$	−3.08880e68	−0.944235
$386$	3.21100e68	0.916382
$387$	2.67306e68	0.712308
$388$	4.52958e68	1.12724
$389$	−2.30262e68	−0.535252	−0.267626	−	0.963523i	$-0.586239\pi$
$389$	−2.30262e68	−0.535252	−0.267626	+	0.963523i	$0.586239\pi$
$390$	−6.38445e68	−1.38647
$391$	−5.80334e68	−1.17759
$392$	−5.79293e66	−0.0109854
$393$	9.48062e67	0.168048
$394$	−9.66236e68	−1.60116
$395$	9.29679e68	1.44049
$396$	3.69708e68	0.535718
$397$	4.76387e68	0.645671	0.322835	−	0.946455i	$-0.395364\pi$
$397$	4.76387e68	0.645671	0.322835	+	0.946455i	$0.395364\pi$
$398$	9.72217e68	1.23271
$399$	−8.88382e68	−1.05394
$400$	−1.21614e69	−1.35019
$401$	−5.31851e68	−0.552668	−0.276334	−	0.961062i	$-0.589120\pi$
$401$	−5.31851e68	−0.552668	−0.276334	+	0.961062i	$0.589120\pi$
$402$	1.13153e69	1.10072
$403$	1.21865e68	0.110993
$404$	1.36245e69	1.16202
$405$	2.29887e69	1.83635
$406$	1.55283e68	0.116194
$407$	2.70767e68	0.189821
$408$	−5.95495e68	−0.391187
$409$	−2.07340e69	−1.27649	−0.638243	−	0.769835i	$-0.720338\pi$
$409$	−2.07340e69	−1.27649	−0.638243	+	0.769835i	$0.720338\pi$
$410$	−6.00491e69	−3.46525
$411$	−7.16581e68	−0.387666
$412$	8.13991e68	0.412898
$413$	7.86217e68	0.373995
$414$	−2.12436e69	−0.947807
$415$	7.12157e69	2.98058
$416$	1.59513e69	0.626359
$417$	−6.18998e69	−2.28078
$418$	−1.82739e69	−0.631916
$419$	4.81874e69	1.56409	0.782045	−	0.623221i	$-0.214176\pi$
$419$	4.81874e69	1.56409	0.782045	+	0.623221i	$0.214176\pi$
$420$	8.30612e69	2.53100
$421$	−4.17794e68	−0.119533	−0.0597664	−	0.998212i	$-0.519036\pi$
$421$	−4.17794e68	−0.119533	−0.0597664	+	0.998212i	$0.519036\pi$
$422$	−9.85723e68	−0.264835
$423$	−1.15129e68	−0.0290512
$424$	−5.24759e68	−0.124384
$425$	−1.07154e70	−2.38618
$426$	1.15530e70	2.41736
$427$	−6.30658e69	−1.24010
$428$	−1.06686e70	−1.97174
$429$	−1.94055e69	−0.337137
$430$	1.23532e70	2.01774
$431$	2.97872e69	0.457490	0.228745	−	0.973486i	$-0.426538\pi$
$431$	2.97872e69	0.457490	0.228745	+	0.973486i	$0.426538\pi$
$432$	−1.36248e69	−0.196794
$433$	2.69910e69	0.366682	0.183341	−	0.983049i	$-0.441309\pi$
$433$	2.69910e69	0.366682	0.183341	+	0.983049i	$0.441309\pi$
$434$	−2.98635e69	−0.381648
$435$	−1.40025e69	−0.168361
$436$	−5.12512e69	−0.579845
$437$	5.57460e69	0.593548
$438$	−1.31645e70	−1.31929
$439$	−3.57805e68	−0.0337549	−0.0168774	−	0.999858i	$-0.505373\pi$
$439$	−3.57805e68	−0.0337549	−0.0168774	+	0.999858i	$0.505373\pi$
$440$	1.98886e69	0.176648
$441$	5.66109e68	0.0473454
$442$	1.21705e70	0.958554
$443$	−9.79799e69	−0.726839	−0.363419	−	0.931626i	$-0.618391\pi$
$443$	−9.79799e69	−0.726839	−0.363419	+	0.931626i	$0.618391\pi$
$444$	−7.28123e69	−0.508811
$445$	3.61481e70	2.37983
$446$	1.48321e70	0.920088
$447$	3.14079e70	1.83607
$448$	−2.32109e70	−1.27887
$449$	−2.01028e70	−1.04407	−0.522033	−	0.852925i	$-0.674826\pi$
$449$	−2.01028e70	−1.04407	−0.522033	+	0.852925i	$0.674826\pi$
$450$	−3.92248e70	−1.92057
$451$	−1.82519e70	−0.842615
$452$	3.99647e70	1.73983
$453$	6.80827e69	0.279534
$454$	−3.98608e70	−1.54371
$455$	−1.97606e70	−0.721937
$456$	5.72024e69	0.197172
$457$	−3.35756e70	−1.09205	−0.546027	−	0.837768i	$-0.683860\pi$
$457$	−3.35756e70	−1.09205	−0.546027	+	0.837768i	$0.683860\pi$
$458$	7.15720e70	2.19689
$459$	−1.20048e70	−0.347793
$460$	−5.21210e70	−1.42538
$461$	4.09546e70	1.05737	0.528686	−	0.848817i	$-0.322685\pi$
$461$	4.09546e70	1.05737	0.528686	+	0.848817i	$0.322685\pi$
$462$	4.75539e70	1.15924
$463$	1.86380e69	0.0429045	0.0214523	−	0.999770i	$-0.493171\pi$
$463$	1.86380e69	0.0429045	0.0214523	+	0.999770i	$0.493171\pi$
$464$	3.02945e69	0.0658624
$465$	2.69292e70	0.552993
$466$	1.52762e70	0.296339
$467$	4.04901e69	0.0742081	0.0371040	−	0.999311i	$-0.488187\pi$
$467$	4.04901e69	0.0742081	0.0371040	+	0.999311i	$0.488187\pi$
$468$	2.36521e70	0.409596
$469$	3.50222e70	0.573143
$470$	−5.32052e69	−0.0822926
$471$	−1.61702e71	−2.36408
$472$	−5.06241e69	−0.0699672
$473$	3.75474e70	0.490636
$474$	−1.43130e71	−1.76850
$475$	1.02931e71	1.20272
$476$	−1.58337e71	−1.74984
$477$	5.12816e70	0.536074
$478$	−5.98694e69	−0.0592059
$479$	−1.14957e71	−1.07558	−0.537790	−	0.843079i	$-0.680741\pi$
$479$	−1.14957e71	−1.07558	−0.537790	+	0.843079i	$0.680741\pi$
$480$	3.52485e71	3.12067
$481$	1.73224e70	0.145132
$482$	2.95033e71	2.33951
$483$	−1.45067e71	−1.08886
$484$	−1.07344e71	−0.762739
$485$	−2.38125e71	−1.60195
$486$	−3.00915e71	−1.91682
$487$	2.40380e71	1.45004	0.725022	−	0.688726i	$-0.241830\pi$
$487$	2.40380e71	1.45004	0.725022	+	0.688726i	$0.241830\pi$
$488$	4.06077e70	0.231998
$489$	7.07145e70	0.382669
$490$	2.61620e70	0.134114
$491$	4.81194e70	0.233701	0.116850	−	0.993150i	$-0.462720\pi$
$491$	4.81194e70	0.233701	0.116850	+	0.993150i	$0.462720\pi$
$492$	4.90813e71	2.25861
$493$	2.66926e70	0.116398
$494$	−1.16908e71	−0.483146
$495$	−1.94360e71	−0.761321
$496$	−5.82613e70	−0.216329
$497$	3.57580e71	1.25872
$498$	−1.09641e72	−3.65928
$499$	4.07670e69	0.0129016	0.00645082	−	0.999979i	$-0.497947\pi$
$499$	4.07670e69	0.0129016	0.00645082	+	0.999979i	$0.497947\pi$
$500$	−3.55875e71	−1.06805
$501$	6.16386e71	1.75450
$502$	3.46057e71	0.934329
$503$	−2.27736e71	−0.583284	−0.291642	−	0.956527i	$-0.594202\pi$
$503$	−2.27736e71	−0.583284	−0.291642	+	0.956527i	$0.594202\pi$
$504$	−6.74694e70	−0.163945
$505$	−7.16254e71	−1.65137
$506$	−2.98401e71	−0.652848
$507$	5.27206e71	1.09464
$508$	3.00994e71	0.593157
$509$	3.77057e71	0.705319	0.352659	−	0.935752i	$-0.385277\pi$
$509$	3.77057e71	0.705319	0.352659	+	0.935752i	$0.385277\pi$
$510$	2.68937e72	4.77575
$511$	−4.07457e71	−0.686954
$512$	−8.64842e71	−1.38447
$513$	1.15317e71	0.175300
$514$	−5.27361e71	−0.761352
$515$	−4.27924e71	−0.586779
$516$	−1.00969e72	−1.31514
$517$	−1.61717e70	−0.0200104
$518$	−4.24492e71	−0.499035
$519$	−6.28215e71	−0.701736
$520$	1.27238e71	0.135060
$521$	1.53660e72	1.55011	0.775055	−	0.631894i	$-0.217722\pi$
$521$	1.53660e72	1.55011	0.775055	+	0.631894i	$0.217722\pi$
$522$	9.77106e70	0.0936857
$523$	−5.24951e71	−0.478436	−0.239218	−	0.970966i	$-0.576891\pi$
$523$	−5.24951e71	−0.478436	−0.239218	+	0.970966i	$0.576891\pi$
$524$	−1.62314e71	−0.140629
$525$	−2.67856e72	−2.20638
$526$	2.35144e72	1.84167
$527$	−5.13342e71	−0.382318
$528$	9.27738e71	0.657092
$529$	−5.74185e71	−0.386791
$530$	2.36991e72	1.51853
$531$	4.94719e71	0.301546
$532$	1.52096e72	0.881981
$533$	−1.16767e72	−0.644241
$534$	−5.56522e72	−2.92172
$535$	5.60862e72	2.80208
$536$	−2.25506e71	−0.107224
$537$	4.97495e71	0.225149
$538$	−8.46624e71	−0.364721
$539$	7.95192e70	0.0326114
$540$	−1.07818e72	−0.420975
$541$	−4.62761e72	−1.72040	−0.860200	−	0.509956i	$-0.829662\pi$
$541$	−4.62761e72	−1.72040	−0.860200	+	0.509956i	$0.829662\pi$
$542$	1.38039e72	0.488677
$543$	4.73799e72	1.59735
$544$	−6.71930e72	−2.15751
$545$	2.69433e72	0.824031
$546$	3.04227e72	0.886325
$547$	1.78991e72	0.496782	0.248391	−	0.968660i	$-0.420098\pi$
$547$	1.78991e72	0.496782	0.248391	+	0.968660i	$0.420098\pi$
$548$	1.22683e72	0.324413
$549$	−3.96835e72	−0.999869
$550$	−5.50976e72	−1.32288
$551$	−2.56405e71	−0.0586691
$552$	9.34080e71	0.203703
$553$	−4.43004e72	−0.920856
$554$	−3.42349e72	−0.678360
$555$	3.82782e72	0.723083
$556$	1.05976e73	1.90865
$557$	2.84794e72	0.489067	0.244533	−	0.969641i	$-0.421365\pi$
$557$	2.84794e72	0.489067	0.244533	+	0.969641i	$0.421365\pi$
$558$	−1.87913e72	−0.307717
$559$	2.40210e72	0.375127
$560$	9.44718e72	1.40708
$561$	8.17432e72	1.16128
$562$	1.73584e72	0.235232
$563$	−8.39092e72	−1.08477	−0.542385	−	0.840130i	$-0.682478\pi$
$563$	−8.39092e72	−1.08477	−0.542385	+	0.840130i	$0.682478\pi$
$564$	4.34874e71	0.0536374
$565$	−2.10099e73	−2.47252
$566$	3.74678e72	0.420748
$567$	−1.09544e73	−1.17392
$568$	−2.30244e72	−0.235481
$569$	6.11471e72	0.596899	0.298450	−	0.954425i	$-0.403531\pi$
$569$	6.11471e72	0.596899	0.298450	+	0.954425i	$0.403531\pi$
$570$	−2.58337e73	−2.40715
$571$	−1.26705e73	−1.12703	−0.563515	−	0.826106i	$-0.690551\pi$
$571$	−1.26705e73	−1.12703	−0.563515	+	0.826106i	$0.690551\pi$
$572$	3.32233e72	0.282129
$573$	2.37873e73	1.92862
$574$	2.86142e73	2.21522
$575$	1.68080e73	1.24256
$576$	−1.46052e73	−1.03113
$577$	1.54639e73	1.04270	0.521350	−	0.853343i	$-0.325429\pi$
$577$	1.54639e73	1.04270	0.521350	+	0.853343i	$0.325429\pi$
$578$	−2.85964e73	−1.84172
$579$	1.37974e73	0.848819
$580$	2.39732e72	0.140891
$581$	−3.39352e73	−1.90539
$582$	3.66608e73	1.96672
$583$	7.20333e72	0.369247
$584$	2.62359e72	0.128516
$585$	−1.24342e73	−0.582086
$586$	9.50116e72	0.425099
$587$	−2.89131e73	−1.23647	−0.618237	−	0.785992i	$-0.712153\pi$
$587$	−2.89131e73	−1.23647	−0.618237	+	0.785992i	$0.712153\pi$
$588$	−2.13836e72	−0.0874141
$589$	4.93109e72	0.192702
$590$	2.28628e73	0.854185
$591$	−4.15183e73	−1.48310
$592$	−8.28150e72	−0.282868
$593$	−1.35508e73	−0.442606	−0.221303	−	0.975205i	$-0.571031\pi$
$593$	−1.35508e73	−0.442606	−0.221303	+	0.975205i	$0.571031\pi$
$594$	−6.17276e72	−0.192814
$595$	8.32393e73	2.48673
$596$	−5.37722e73	−1.53650
$597$	4.17753e73	1.14183
$598$	−1.90903e73	−0.499150
$599$	−1.38679e73	−0.346897	−0.173448	−	0.984843i	$-0.555491\pi$
$599$	−1.38679e73	−0.346897	−0.173448	+	0.984843i	$0.555491\pi$
$600$	1.72471e73	0.412770
$601$	−4.98700e73	−1.14200	−0.571000	−	0.820950i	$-0.693444\pi$
$601$	−4.98700e73	−1.14200	−0.571000	+	0.820950i	$0.693444\pi$
$602$	−5.88645e73	−1.28987
$603$	2.20374e73	0.462116
$604$	−1.16561e73	−0.233925
$605$	5.64320e73	1.08395
$606$	1.10272e74	2.02740
$607$	4.33744e73	0.763367	0.381683	−	0.924293i	$-0.375344\pi$
$607$	4.33744e73	0.763367	0.381683	+	0.924293i	$0.375344\pi$
$608$	6.45446e73	1.08747
$609$	6.67239e72	0.107628
$610$	−1.83392e74	−2.83231
$611$	−1.03459e72	−0.0152994
$612$	−9.96318e73	−1.41086
$613$	1.11056e74	1.50605	0.753027	−	0.657990i	$-0.228593\pi$
$613$	1.11056e74	1.50605	0.753027	+	0.657990i	$0.228593\pi$
$614$	2.02914e74	2.63542
$615$	−2.58026e74	−3.20976
$616$	−9.47717e72	−0.112925
$617$	6.32555e73	0.722007	0.361004	−	0.932564i	$-0.382434\pi$
$617$	6.32555e73	0.722007	0.361004	+	0.932564i	$0.382434\pi$
$618$	6.58815e73	0.720392
$619$	−2.98152e73	−0.312345	−0.156173	−	0.987730i	$-0.549916\pi$
$619$	−2.98152e73	−0.312345	−0.156173	+	0.987730i	$0.549916\pi$
$620$	−4.61043e73	−0.462766
$621$	1.88305e73	0.181107
$622$	−2.88914e74	−2.66271
$623$	−1.72250e74	−1.52134
$624$	5.93522e73	0.502395
$625$	−8.49672e72	−0.0689336
$626$	2.61242e74	2.03153
$627$	−7.85214e73	−0.585326
$628$	2.76843e74	1.97835
$629$	−7.29685e73	−0.499912
$630$	3.04705e74	2.00150
$631$	2.66754e74	1.68009	0.840046	−	0.542515i	$-0.182528\pi$
$631$	2.66754e74	1.68009	0.840046	+	0.542515i	$0.182528\pi$
$632$	2.85248e73	0.172274
$633$	−4.23557e73	−0.245309
$634$	−2.56163e74	−1.42282
$635$	−1.58236e74	−0.842949
$636$	−1.93706e74	−0.989757
$637$	5.08726e72	0.0249338
$638$	1.37250e73	0.0645305
$639$	2.25003e74	1.01488
$640$	−1.41736e74	−0.613356
$641$	−7.34082e72	−0.0304794	−0.0152397	−	0.999884i	$-0.504851\pi$
$641$	−7.34082e72	−0.0304794	−0.0152397	+	0.999884i	$0.504851\pi$
$642$	−8.63481e74	−3.44013
$643$	−2.35192e74	−0.899150	−0.449575	−	0.893243i	$-0.648425\pi$
$643$	−2.35192e74	−0.899150	−0.449575	+	0.893243i	$0.648425\pi$
$644$	2.48363e74	0.911196
$645$	5.30806e74	1.86897
$646$	4.92459e74	1.66421
$647$	1.32555e74	0.429963	0.214981	−	0.976618i	$-0.431031\pi$
$647$	1.32555e74	0.429963	0.214981	+	0.976618i	$0.431031\pi$
$648$	7.05348e73	0.219617
$649$	6.94914e73	0.207705
$650$	−3.52488e74	−1.01144
$651$	−1.28321e74	−0.353510
$652$	−1.21067e74	−0.320232
$653$	−8.70965e73	−0.221208	−0.110604	−	0.993865i	$-0.535279\pi$
$653$	−8.70965e73	−0.221208	−0.110604	+	0.993865i	$0.535279\pi$
$654$	−4.14809e74	−1.01167
$655$	8.53300e73	0.199852
$656$	5.58239e74	1.25565
$657$	−2.56388e74	−0.553880
$658$	2.53530e73	0.0526069
$659$	2.94646e74	0.587270	0.293635	−	0.955918i	$-0.405135\pi$
$659$	2.94646e74	0.587270	0.293635	+	0.955918i	$0.405135\pi$
$660$	7.34153e74	1.40563
$661$	−1.59089e73	−0.0292618	−0.0146309	−	0.999893i	$-0.504657\pi$
$661$	−1.59089e73	−0.0292618	−0.0146309	+	0.999893i	$0.504657\pi$
$662$	−2.63460e74	−0.465562
$663$	5.22954e74	0.887881
$664$	2.18507e74	0.356460
$665$	−7.99585e74	−1.25340
$666$	−2.67108e74	−0.402364
$667$	−4.18693e73	−0.0606124
$668$	−1.05529e75	−1.46823
$669$	6.37323e74	0.852251
$670$	1.01843e75	1.30903
$671$	−5.57420e74	−0.688708
$672$	−1.67964e75	−1.99494
$673$	−1.05609e75	−1.20587	−0.602935	−	0.797790i	$-0.706002\pi$
$673$	−1.05609e75	−1.20587	−0.602935	+	0.797790i	$0.706002\pi$
$674$	1.27178e75	1.39612
$675$	3.47692e74	0.366982
$676$	−9.02607e74	−0.916033
$677$	−1.20175e75	−1.17277	−0.586386	−	0.810032i	$-0.699450\pi$
$677$	−1.20175e75	−1.17277	−0.586386	+	0.810032i	$0.699450\pi$
$678$	3.23460e75	3.03552
$679$	1.13470e75	1.02407
$680$	−5.35974e74	−0.465219
$681$	−1.71278e75	−1.42990
$682$	−2.63955e74	−0.211955
$683$	1.42292e75	1.09909	0.549543	−	0.835466i	$-0.314802\pi$
$683$	1.42292e75	1.09909	0.549543	+	0.835466i	$0.314802\pi$
$684$	9.57049e74	0.711127
$685$	−6.44957e74	−0.461031
$686$	2.05815e75	1.41543
$687$	3.07539e75	2.03491
$688$	−1.14840e75	−0.731138
$689$	4.60835e74	0.282316
$690$	−4.21849e75	−2.48689
$691$	−1.83314e75	−1.03998	−0.519992	−	0.854171i	$-0.674065\pi$
$691$	−1.83314e75	−1.03998	−0.519992	+	0.854171i	$0.674065\pi$
$692$	1.07554e75	0.587239
$693$	9.26148e74	0.486687
$694$	−1.58352e75	−0.800938
$695$	−5.57127e75	−2.71242
$696$	−4.29632e73	−0.0201350
$697$	4.91866e75	2.21911
$698$	−3.77551e75	−1.63986
$699$	6.56406e74	0.274490
$700$	4.58584e75	1.84638
$701$	−1.33614e75	−0.517992	−0.258996	−	0.965878i	$-0.583392\pi$
$701$	−1.33614e75	−0.517992	−0.258996	+	0.965878i	$0.583392\pi$
$702$	−3.94904e74	−0.147420
$703$	7.00925e74	0.251974
$704$	−2.05154e75	−0.710240
$705$	−2.28618e74	−0.0762253
$706$	4.39736e75	1.41211
$707$	3.41304e75	1.05567
$708$	−1.86870e75	−0.556747
$709$	−2.59964e75	−0.746084	−0.373042	−	0.927815i	$-0.621685\pi$
$709$	−2.59964e75	−0.746084	−0.373042	+	0.927815i	$0.621685\pi$
$710$	1.03982e76	2.87484
$711$	−2.78756e75	−0.742471
$712$	1.10911e75	0.284613
$713$	8.05216e74	0.199086
$714$	−1.28152e76	−3.05297
$715$	−1.74658e75	−0.400940
$716$	−8.51739e74	−0.188413
$717$	−2.57253e74	−0.0548408
$718$	−5.45508e75	−1.12074
$719$	5.36453e75	1.06222	0.531112	−	0.847302i	$-0.321774\pi$
$719$	5.36453e75	1.06222	0.531112	+	0.847302i	$0.321774\pi$
$720$	5.94454e75	1.13451
$721$	2.03911e75	0.375108
$722$	3.50336e75	0.621225
$723$	1.26773e76	2.16702
$724$	−8.11172e75	−1.33672
$725$	−7.73087e74	−0.122821
$726$	−8.68805e75	−1.33077
$727$	−4.93191e75	−0.728373	−0.364186	−	0.931326i	$-0.618653\pi$
$727$	−4.93191e75	−0.728373	−0.364186	+	0.931326i	$0.618653\pi$
$728$	−6.06304e74	−0.0863394
$729$	−4.61515e75	−0.633733
$730$	−1.18487e76	−1.56897
$731$	−1.01186e76	−1.29214
$732$	1.49896e76	1.84607
$733$	−9.00902e75	−1.07010	−0.535048	−	0.844822i	$-0.679706\pi$
$733$	−9.00902e75	−1.07010	−0.535048	+	0.844822i	$0.679706\pi$
$734$	2.12853e76	2.43857
$735$	1.12416e75	0.124226
$736$	1.05397e76	1.12349
$737$	3.09550e75	0.318305
$738$	1.80052e76	1.78609
$739$	4.93120e75	0.471927	0.235964	−	0.971762i	$-0.424175\pi$
$739$	4.93120e75	0.471927	0.235964	+	0.971762i	$0.424175\pi$
$740$	−6.55345e75	−0.605103
$741$	−5.02342e75	−0.447525
$742$	−1.12929e76	−0.970742
$743$	−1.49779e76	−1.24236	−0.621181	−	0.783667i	$-0.713347\pi$
$743$	−1.49779e76	−1.24236	−0.621181	+	0.783667i	$0.713347\pi$
$744$	8.26252e74	0.0661347
$745$	2.82686e76	2.18355
$746$	1.79723e76	1.33976
$747$	−2.13534e76	−1.53628
$748$	−1.39949e76	−0.971801
$749$	−2.67258e76	−1.79128
$750$	−2.88033e76	−1.86345
$751$	4.11227e75	0.256817	0.128408	−	0.991721i	$-0.459013\pi$
$751$	4.11227e75	0.256817	0.128408	+	0.991721i	$0.459013\pi$
$752$	4.94616e74	0.0298191
$753$	1.48698e76	0.865442
$754$	8.78062e74	0.0493383
$755$	6.12777e75	0.332436
$756$	5.13767e75	0.269115
$757$	3.57142e76	1.80634	0.903172	−	0.429278i	$-0.141232\pi$
$757$	3.57142e76	1.80634	0.903172	+	0.429278i	$0.141232\pi$
$758$	−2.71554e76	−1.32624
$759$	−1.28220e76	−0.604715
$760$	5.14848e75	0.234487
$761$	2.38006e76	1.04687	0.523437	−	0.852064i	$-0.324649\pi$
$761$	2.38006e76	1.04687	0.523437	+	0.852064i	$0.324649\pi$
$762$	2.43614e76	1.03489
$763$	−1.28388e76	−0.526775
$764$	−4.07252e76	−1.61395
$765$	5.23775e76	2.00501
$766$	1.09474e76	0.404807
$767$	4.44572e75	0.158805
$768$	−2.69252e76	−0.929151
$769$	2.37124e76	0.790546	0.395273	−	0.918564i	$-0.370650\pi$
$769$	2.37124e76	0.790546	0.395273	+	0.918564i	$0.370650\pi$
$770$	4.28008e76	1.37863
$771$	−2.26603e76	−0.705219
$772$	−2.36219e76	−0.710324
$773$	−6.25079e76	−1.81626	−0.908131	−	0.418686i	$-0.862491\pi$
$773$	−6.25079e76	−1.81626	−0.908131	+	0.418686i	$0.862491\pi$
$774$	−3.70399e76	−1.04000
$775$	1.48677e76	0.403412
$776$	−7.30625e75	−0.191584
$777$	−1.82401e76	−0.462242
$778$	3.19069e76	0.781494
$779$	−4.72479e76	−1.11851
$780$	4.69676e76	1.07471
$781$	3.16054e76	0.699051
$782$	8.04156e76	1.71934
$783$	−8.66113e74	−0.0179014
$784$	−2.43212e75	−0.0485970
$785$	−1.45540e77	−2.81148
$786$	−1.31371e76	−0.245359
$787$	−1.33252e76	−0.240627	−0.120314	−	0.992736i	$-0.538390\pi$
$787$	−1.33252e76	−0.240627	−0.120314	+	0.992736i	$0.538390\pi$
$788$	7.10818e76	1.24112
$789$	1.01039e77	1.70588
$790$	−1.28824e77	−2.10318
$791$	1.00115e77	1.58060
$792$	−5.96342e75	−0.0910496
$793$	−3.56610e76	−0.526568
$794$	−6.60118e76	−0.942710
$795$	1.01833e77	1.40657
$796$	−7.15217e76	−0.955524
$797$	−2.10248e76	−0.271698	−0.135849	−	0.990730i	$-0.543376\pi$
$797$	−2.10248e76	−0.271698	−0.135849	+	0.990730i	$0.543376\pi$
$798$	1.23101e77	1.53881
$799$	4.35807e75	0.0526993
$800$	1.94609e77	2.27655
$801$	−1.08387e77	−1.22663
$802$	7.36975e76	0.806922
$803$	−3.60139e76	−0.381512
$804$	−8.32416e76	−0.853208
$805$	−1.30567e77	−1.29492
$806$	−1.68866e76	−0.162055
$807$	−3.63787e76	−0.337830
$808$	−2.19764e76	−0.197495
$809$	1.17401e77	1.02103	0.510514	−	0.859870i	$-0.329455\pi$
$809$	1.17401e77	1.02103	0.510514	+	0.859870i	$0.329455\pi$
$810$	−3.18549e77	−2.68116
$811$	9.03233e75	0.0735779	0.0367889	−	0.999323i	$-0.488287\pi$
$811$	9.03233e75	0.0735779	0.0367889	+	0.999323i	$0.488287\pi$
$812$	−1.14235e76	−0.0900669
$813$	5.93143e76	0.452647
$814$	−3.75196e76	−0.277148
$815$	6.36464e76	0.455090
$816$	−2.50014e77	−1.73051
$817$	9.71975e76	0.651285
$818$	2.87307e77	1.86373
$819$	5.92505e76	0.372108
$820$	4.41755e77	2.68605
$821$	8.19852e76	0.482660	0.241330	−	0.970443i	$-0.422416\pi$
$821$	8.19852e76	0.482660	0.241330	+	0.970443i	$0.422416\pi$
$822$	9.92951e76	0.566010
$823$	1.15061e76	0.0635088	0.0317544	−	0.999496i	$-0.489891\pi$
$823$	1.15061e76	0.0635088	0.0317544	+	0.999496i	$0.489891\pi$
$824$	−1.31297e76	−0.0701754
$825$	−2.36750e77	−1.22535
$826$	−1.08944e77	−0.546051
$827$	4.29383e76	0.208425	0.104212	−	0.994555i	$-0.466768\pi$
$827$	4.29383e76	0.208425	0.104212	+	0.994555i	$0.466768\pi$
$828$	1.56280e77	0.734683
$829$	−1.25368e77	−0.570808	−0.285404	−	0.958407i	$-0.592128\pi$
$829$	−1.25368e77	−0.570808	−0.285404	+	0.958407i	$0.592128\pi$
$830$	−9.86820e77	−4.35180
$831$	−1.47104e77	−0.628345
$832$	−1.31248e77	−0.543031
$833$	−2.14295e76	−0.0858853
$834$	8.57732e77	3.33005
$835$	5.54776e77	2.08654
$836$	1.34433e77	0.489823
$837$	1.66568e76	0.0587985
$838$	−6.67722e77	−2.28365
$839$	−1.07457e77	−0.356075	−0.178038	−	0.984024i	$-0.556975\pi$
$839$	−1.07457e77	−0.356075	−0.178038	+	0.984024i	$0.556975\pi$
$840$	−1.33978e77	−0.430163
$841$	−3.19510e77	−0.994009
$842$	5.78928e76	0.174524
$843$	7.45875e76	0.217889
$844$	7.25153e76	0.205284
$845$	4.74510e77	1.30180
$846$	1.59531e76	0.0424161
$847$	−2.68906e77	−0.692930
$848$	−2.20316e77	−0.550245
$849$	1.60996e77	0.389727
$850$	1.48481e78	3.48394
$851$	1.14457e77	0.260320
$852$	−8.49904e77	−1.87379
$853$	−7.22678e77	−1.54453	−0.772263	−	0.635303i	$-0.780875\pi$
$853$	−7.22678e77	−1.54453	−0.772263	+	0.635303i	$0.780875\pi$
$854$	8.73889e77	1.81060
$855$	−5.03131e77	−1.01060
$856$	1.72086e77	0.335113
$857$	−6.80686e77	−1.28515	−0.642577	−	0.766221i	$-0.722135\pi$
$857$	−6.80686e77	−1.28515	−0.642577	+	0.766221i	$0.722135\pi$
$858$	2.68897e77	0.492236
$859$	4.28760e77	0.761019	0.380510	−	0.924777i	$-0.375749\pi$
$859$	4.28760e77	0.761019	0.380510	+	0.924777i	$0.375749\pi$
$860$	−9.08770e77	−1.56403
$861$	1.22953e78	2.05189
$862$	−4.12755e77	−0.667958
$863$	6.31202e77	0.990564	0.495282	−	0.868732i	$-0.335065\pi$
$863$	6.31202e77	0.990564	0.495282	+	0.868732i	$0.335065\pi$
$864$	2.18026e77	0.331814
$865$	−5.65423e77	−0.834539
$866$	−3.74009e77	−0.535374
$867$	−1.22876e78	−1.70593
$868$	2.19693e77	0.295831
$869$	−3.91558e77	−0.511413
$870$	1.94030e77	0.245815
$871$	1.98036e77	0.243367
$872$	8.26685e76	0.0985493
$873$	7.13996e77	0.825693
$874$	−7.72460e77	−0.866609
$875$	−8.91497e77	−0.970301
$876$	9.68454e77	1.02263
$877$	−8.46824e77	−0.867569	−0.433785	−	0.901017i	$-0.642822\pi$
$877$	−8.46824e77	−0.867569	−0.433785	+	0.901017i	$0.642822\pi$
$878$	4.95802e76	0.0492837
$879$	4.08257e77	0.393757
$880$	8.35008e77	0.781447
$881$	1.78575e78	1.62166	0.810830	−	0.585281i	$-0.199016\pi$
$881$	1.78575e78	1.62166	0.810830	+	0.585281i	$0.199016\pi$
$882$	−7.84445e76	−0.0691265
$883$	8.63389e77	0.738325	0.369163	−	0.929365i	$-0.379645\pi$
$883$	8.63389e77	0.738325	0.369163	+	0.929365i	$0.379645\pi$
$884$	−8.95327e77	−0.743013
$885$	9.82396e77	0.791207
$886$	1.35768e78	1.06122
$887$	1.09908e78	0.833785	0.416893	−	0.908956i	$-0.363119\pi$
$887$	1.09908e78	0.833785	0.416893	+	0.908956i	$0.363119\pi$
$888$	1.17447e77	0.0864764
$889$	7.54014e77	0.538869
$890$	−5.00896e78	−3.47466
$891$	−9.68227e77	−0.651956
$892$	−1.09113e78	−0.713197
$893$	−4.18630e76	−0.0265624
$894$	−4.35213e78	−2.68076
$895$	4.47769e77	0.267759
$896$	6.75393e77	0.392097
$897$	−8.20293e77	−0.462348
$898$	2.78560e78	1.52439
$899$	−3.70360e76	−0.0196785
$900$	2.88560e78	1.48871
$901$	−1.94121e78	−0.972446
$902$	2.52912e78	1.23026
$903$	−2.52936e78	−1.19477
$904$	−6.44633e77	−0.295699
$905$	4.26442e78	1.89964
$906$	−9.43407e77	−0.408133
$907$	−1.67275e78	−0.702812	−0.351406	−	0.936223i	$-0.614296\pi$
$907$	−1.67275e78	−0.702812	−0.351406	+	0.936223i	$0.614296\pi$
$908$	2.93238e78	1.19659
$909$	2.14762e78	0.851168
$910$	2.73819e78	1.05406
$911$	−3.79500e78	−1.41898	−0.709488	−	0.704718i	$-0.751074\pi$
$911$	−3.79500e78	−1.41898	−0.709488	+	0.704718i	$0.751074\pi$
$912$	2.40160e78	0.872243
$913$	−2.99943e78	−1.05819
$914$	4.65249e78	1.59445
$915$	−7.88021e78	−2.62349
$916$	−5.26524e78	−1.70289
$917$	−4.06609e77	−0.127758
$918$	1.66348e78	0.507794
$919$	2.27887e78	0.675863	0.337932	−	0.941171i	$-0.390273\pi$
$919$	2.27887e78	0.675863	0.337932	+	0.941171i	$0.390273\pi$
$920$	8.40716e77	0.242254
$921$	8.71904e78	2.44112
$922$	−5.67499e78	−1.54382
$923$	2.02196e78	0.534475
$924$	−3.49833e78	−0.898574
$925$	2.11336e78	0.527494
$926$	−2.58263e77	−0.0626427
$927$	1.28309e78	0.302444
$928$	−4.84777e77	−0.111051
$929$	−1.94979e78	−0.434082	−0.217041	−	0.976162i	$-0.569641\pi$
$929$	−1.94979e78	−0.434082	−0.217041	+	0.976162i	$0.569641\pi$
$930$	−3.73151e78	−0.807397
$931$	2.05848e77	0.0432893
$932$	−1.12380e78	−0.229704
$933$	−1.24144e79	−2.46639
$934$	−5.61062e77	−0.108347
$935$	7.35727e78	1.38105
$936$	−3.81511e77	−0.0696141
$937$	7.29807e78	1.29452	0.647260	−	0.762269i	$-0.275915\pi$
$937$	7.29807e78	1.29452	0.647260	+	0.762269i	$0.275915\pi$
$938$	−4.85295e78	−0.836816
$939$	1.12253e79	1.88175
$940$	3.91407e77	0.0637883
$941$	−8.24697e78	−1.30668	−0.653341	−	0.757064i	$-0.726633\pi$
$941$	−8.24697e78	−1.30668	−0.653341	+	0.757064i	$0.726633\pi$
$942$	2.24067e79	3.45167
$943$	−7.71529e78	−1.15556
$944$	−2.12541e78	−0.309518
$945$	−2.70093e78	−0.382446
$946$	−5.20286e78	−0.716353
$947$	1.41218e79	1.89067	0.945335	−	0.326100i	$-0.105734\pi$
$947$	1.41218e79	1.89067	0.945335	+	0.326100i	$0.105734\pi$
$948$	1.05294e79	1.37083
$949$	−2.30400e78	−0.291694
$950$	−1.42629e79	−1.75603
$951$	−1.10071e79	−1.31792
$952$	2.55398e78	0.297399
$953$	−1.39912e79	−1.58451	−0.792253	−	0.610192i	$-0.791092\pi$
$953$	−1.39912e79	−1.58451	−0.792253	+	0.610192i	$0.791092\pi$
$954$	−7.10598e78	−0.782694
$955$	2.14097e79	2.29362
$956$	4.40432e77	0.0458929
$957$	5.89753e77	0.0597728
$958$	1.59293e79	1.57040
$959$	3.07330e78	0.294722
$960$	−2.90026e79	−2.70551
$961$	−1.03074e79	−0.935365
$962$	−2.40032e78	−0.211900
$963$	−1.68169e79	−1.44428
$964$	−2.17043e79	−1.81344
$965$	1.24183e79	1.00946
$966$	2.01016e79	1.58978
$967$	4.89301e78	0.376508	0.188254	−	0.982120i	$-0.439717\pi$
$967$	4.89301e78	0.376508	0.188254	+	0.982120i	$0.439717\pi$
$968$	1.73147e78	0.129634
$969$	2.11606e79	1.54151
$970$	3.29964e79	2.33892
$971$	−5.58018e78	−0.384892	−0.192446	−	0.981308i	$-0.561642\pi$
$971$	−5.58018e78	−0.384892	−0.192446	+	0.981308i	$0.561642\pi$
$972$	2.21370e79	1.48581
$973$	2.65478e79	1.73396
$974$	−3.33089e79	−2.11713
$975$	−1.51461e79	−0.936869
$976$	1.70488e79	1.02630
$977$	−2.57199e79	−1.50683	−0.753414	−	0.657546i	$-0.771594\pi$
$977$	−2.57199e79	−1.50683	−0.753414	+	0.657546i	$0.771594\pi$
$978$	−9.79875e78	−0.558716
$979$	−1.52247e79	−0.844903
$980$	−1.92462e78	−0.103957
$981$	−8.07871e78	−0.424730
$982$	−6.66779e78	−0.341215
$983$	3.41218e79	1.69967	0.849833	−	0.527051i	$-0.176702\pi$
$983$	3.41218e79	1.69967	0.849833	+	0.527051i	$0.176702\pi$
$984$	−7.91685e78	−0.383869
$985$	−3.73685e79	−1.76378
$986$	−3.69873e78	−0.169947
$987$	1.08940e78	0.0487283
$988$	8.60038e78	0.374506
$989$	1.58718e79	0.672858
$990$	2.69320e79	1.11157
$991$	−2.88433e79	−1.15902	−0.579512	−	0.814964i	$-0.696757\pi$
$991$	−2.88433e79	−1.15902	−0.579512	+	0.814964i	$0.696757\pi$
$992$	9.32306e78	0.364753
$993$	−1.13206e79	−0.431237
$994$	−4.95490e79	−1.83779
$995$	3.75997e79	1.35792
$996$	8.06580e79	2.83645
$997$	−3.11454e79	−1.06653	−0.533264	−	0.845949i	$-0.679035\pi$
$997$	−3.11454e79	−1.06653	−0.533264	+	0.845949i	$0.679035\pi$
$998$	−5.64900e77	−0.0188370
$999$	2.36766e78	0.0768837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.54.a.a.1.1	✓	4
3.2	odd	2		9.54.a.b.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.54.a.a.1.1	✓	4	1.1	even	1	trivial
9.54.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +O(q^{10})\)	\(q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +7.42585e26 q^{10} +2.25708e27 q^{11} -6.06954e28 q^{12} +1.44397e29 q^{13} -3.53851e30 q^{14} +3.19082e31 q^{15} -6.90335e31 q^{16} -6.08256e32 q^{17} -2.22657e33 q^{18} +5.84282e33 q^{19} -5.46287e34 q^{20} -1.52047e35 q^{21} -3.12758e35 q^{22} +9.54096e35 q^{23} +9.79021e35 q^{24} +1.76167e37 q^{25} -2.00088e37 q^{26} +1.97365e37 q^{27} +2.60313e38 q^{28} -4.38838e37 q^{29} -4.42145e39 q^{30} +8.43957e38 q^{31} +1.10468e40 q^{32} -1.34390e40 q^{33} +8.42846e40 q^{34} -1.36849e41 q^{35} +1.63799e41 q^{36} +1.19964e41 q^{37} -8.09626e41 q^{38} -8.59760e41 q^{39} +8.81165e41 q^{40} -8.08650e42 q^{41} +2.10688e43 q^{42} +1.66354e43 q^{43} +2.30083e43 q^{44} -8.61111e43 q^{45} -1.32207e44 q^{46} -7.16487e42 q^{47} +4.11035e44 q^{48} +3.52310e43 q^{49} -2.44110e45 q^{50} +3.62164e45 q^{51} +1.47196e45 q^{52} +3.19144e45 q^{53} -2.73484e45 q^{54} -1.20957e46 q^{55} -4.19887e45 q^{56} -3.47889e46 q^{57} +6.08088e45 q^{58} +3.07882e46 q^{59} +3.25267e47 q^{60} -2.46965e47 q^{61} -1.16945e47 q^{62} +4.10330e47 q^{63} -9.08937e47 q^{64} -7.73825e47 q^{65} +1.86221e48 q^{66} +1.37146e48 q^{67} -6.20045e48 q^{68} -5.68081e48 q^{69} +1.89629e49 q^{70} +1.40028e49 q^{71} -2.64209e48 q^{72} -1.59560e49 q^{73} -1.66231e49 q^{74} -1.04892e50 q^{75} +5.95606e49 q^{76} +5.76375e49 q^{77} +1.19135e50 q^{78} -1.73480e50 q^{79} +3.69950e50 q^{80} -4.28973e50 q^{81} +1.12053e51 q^{82} -1.32890e51 q^{83} -1.54994e51 q^{84} +3.25964e51 q^{85} -2.30513e51 q^{86} +2.61290e50 q^{87} -3.71125e50 q^{88} -6.74530e51 q^{89} +1.19322e52 q^{90} +3.68737e51 q^{91} +9.72588e51 q^{92} -5.02503e51 q^{93} +9.92819e50 q^{94} -3.13117e52 q^{95} -6.57744e52 q^{96} +4.44346e52 q^{97} -4.88188e51 q^{98} +3.62679e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!12 q^{9}+O(q^{10}) \) 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

Properties

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