LMFDB - Embedded newform 1.54.a.a.1.4

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			1.4
Root			$1.52611e6$ 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)

$f(q)$	$=$	$q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} +O(q^{10})$	\(q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} -6.22689e26 q^{10} -9.74180e26 q^{11} +1.03998e28 q^{12} +4.82001e29 q^{13} -2.14945e30 q^{14} -6.47150e30 q^{15} -9.09771e31 q^{16} +5.02736e32 q^{17} -2.27399e33 q^{18} -1.38519e34 q^{19} -3.72202e34 q^{20} -2.23389e34 q^{21} -1.26047e35 q^{22} -5.29051e35 q^{23} -2.21535e35 q^{24} +1.20588e37 q^{25} +6.23649e37 q^{26} -4.96979e37 q^{27} -1.28480e38 q^{28} -3.32225e38 q^{29} -8.37331e38 q^{30} +2.69343e39 q^{31} -1.02874e40 q^{32} -1.30998e39 q^{33} +6.50477e40 q^{34} +7.99492e40 q^{35} -1.35924e41 q^{36} +2.08872e41 q^{37} -1.79226e42 q^{38} +6.48148e41 q^{39} +7.92857e41 q^{40} +2.96475e42 q^{41} -2.89037e42 q^{42} +1.06838e43 q^{43} -7.53423e42 q^{44} +8.45814e43 q^{45} -6.84525e43 q^{46} -2.94705e44 q^{47} -1.22337e44 q^{48} -3.40898e44 q^{49} +1.56026e45 q^{50} +6.76030e44 q^{51} +3.72776e45 q^{52} -5.52073e45 q^{53} -6.43028e45 q^{54} +4.68833e45 q^{55} +2.73685e45 q^{56} -1.86266e46 q^{57} -4.29858e46 q^{58} +1.07917e47 q^{59} -5.00501e46 q^{60} +3.62994e46 q^{61} +3.48496e47 q^{62} +2.91965e47 q^{63} -5.11611e47 q^{64} -2.31967e48 q^{65} -1.69495e47 q^{66} +7.15705e47 q^{67} +3.88812e48 q^{68} -7.11416e47 q^{69} +1.03444e49 q^{70} -9.79077e48 q^{71} +2.89542e48 q^{72} -2.48596e49 q^{73} +2.70254e49 q^{74} +1.62155e49 q^{75} -1.07129e50 q^{76} +1.61836e49 q^{77} +8.38622e49 q^{78} -2.29029e50 q^{79} +4.37835e50 q^{80} +2.73832e50 q^{81} +3.83601e50 q^{82} -8.70995e50 q^{83} -1.72767e50 q^{84} -2.41946e51 q^{85} +1.38235e51 q^{86} -4.46744e50 q^{87} +1.60493e50 q^{88} +2.82739e51 q^{89} +1.09438e52 q^{90} -8.00725e51 q^{91} -4.09163e51 q^{92} +3.62186e51 q^{93} -3.81311e52 q^{94} +6.66634e52 q^{95} -1.38335e52 q^{96} -5.70641e52 q^{97} -4.41079e52 q^{98} +1.71212e52 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.29387e8	1.36332	0.681659	−	0.731670i	$-0.261259\pi$
$2$	1.29387e8	1.36332	0.681659	+	0.731670i	$0.261259\pi$
$3$	1.34470e12	0.305431	0.152715	−	0.988270i	$-0.451198\pi$
$3$	1.34470e12	0.305431	0.152715	+	0.988270i	$0.451198\pi$
$4$	7.73392e15	0.858638
$5$	−4.81259e18	−1.44435	−0.722177	−	0.691708i	$-0.756858\pi$
$5$	−4.81259e18	−1.44435	−0.722177	+	0.691708i	$0.756858\pi$
$6$	1.73988e20	0.416400
$7$	−1.66125e22	−0.668863	−0.334432	−	0.942420i	$-0.608544\pi$
$7$	−1.66125e22	−0.668863	−0.334432	+	0.942420i	$0.608544\pi$
$8$	−1.64746e23	−0.192722
$9$	−1.75750e25	−0.906712
$10$	−6.22689e26	−1.96912
$11$	−9.74180e26	−0.246452	−0.123226	−	0.992379i	$-0.539324\pi$
$11$	−9.74180e26	−0.246452	−0.123226	+	0.992379i	$0.539324\pi$
$12$	1.03998e28	0.262254
$13$	4.82001e29	1.45730	0.728650	−	0.684886i	$-0.240148\pi$
$13$	4.82001e29	1.45730	0.728650	+	0.684886i	$0.240148\pi$
$14$	−2.14945e30	−0.911873
$15$	−6.47150e30	−0.441150
$16$	−9.09771e31	−1.12138
$17$	5.02736e32	1.24292	0.621460	−	0.783446i	$-0.286540\pi$
$17$	5.02736e32	1.24292	0.621460	+	0.783446i	$0.286540\pi$
$18$	−2.27399e33	−1.23614
$19$	−1.38519e34	−1.79696	−0.898479	−	0.439017i	$-0.855327\pi$
$19$	−1.38519e34	−1.79696	−0.898479	+	0.439017i	$0.855327\pi$
$20$	−3.72202e34	−1.24018
$21$	−2.23389e34	−0.204291
$22$	−1.26047e35	−0.335993
$23$	−5.29051e35	−0.434220	−0.217110	−	0.976147i	$-0.569663\pi$
$23$	−5.29051e35	−0.434220	−0.217110	+	0.976147i	$0.569663\pi$
$24$	−2.21535e35	−0.0588633
$25$	1.20588e37	1.08616
$26$	6.23649e37	1.98676
$27$	−4.96979e37	−0.582369
$28$	−1.28480e38	−0.574311
$29$	−3.32225e38	−0.585984	−0.292992	−	0.956115i	$-0.594651\pi$
$29$	−3.32225e38	−0.585984	−0.292992	+	0.956115i	$0.594651\pi$
$30$	−8.37331e38	−0.601429
$31$	2.69343e39	0.811374	0.405687	−	0.914012i	$-0.367032\pi$
$31$	2.69343e39	0.811374	0.405687	+	0.914012i	$0.367032\pi$
$32$	−1.02874e40	−1.33607
$33$	−1.30998e39	−0.0752742
$34$	6.50477e40	1.69450
$35$	7.99492e40	0.966075
$36$	−1.35924e41	−0.778537
$37$	2.08872e41	0.578808	0.289404	−	0.957207i	$-0.406543\pi$
$37$	2.08872e41	0.578808	0.289404	+	0.957207i	$0.406543\pi$
$38$	−1.79226e42	−2.44983
$39$	6.48148e41	0.445105
$40$	7.92857e41	0.278359
$41$	2.96475e42	0.541022	0.270511	−	0.962717i	$-0.412807\pi$
$41$	2.96475e42	0.541022	0.270511	+	0.962717i	$0.412807\pi$
$42$	−2.89037e42	−0.278514
$43$	1.06838e43	0.551837	0.275919	−	0.961181i	$-0.411018\pi$
$43$	1.06838e43	0.551837	0.275919	+	0.961181i	$0.411018\pi$
$44$	−7.53423e42	−0.211613
$45$	8.45814e43	1.30961
$46$	−6.84525e43	−0.591980
$47$	−2.94705e44	−1.44143	−0.720716	−	0.693230i	$-0.756187\pi$
$47$	−2.94705e44	−1.44143	−0.720716	+	0.693230i	$0.756187\pi$
$48$	−1.22337e44	−0.342504
$49$	−3.40898e44	−0.552622
$50$	1.56026e45	1.48078
$51$	6.76030e44	0.379626
$52$	3.72776e45	1.25129
$53$	−5.52073e45	−1.11863	−0.559314	−	0.828956i	$-0.688936\pi$
$53$	−5.52073e45	−1.11863	−0.559314	+	0.828956i	$0.688936\pi$
$54$	−6.43028e45	−0.793954
$55$	4.68833e45	0.355965
$56$	2.73685e45	0.128905
$57$	−1.86266e46	−0.548846
$58$	−4.29858e46	−0.798883
$59$	1.07917e47	1.27501	0.637503	−	0.770448i	$-0.279967\pi$
$59$	1.07917e47	1.27501	0.637503	+	0.770448i	$0.279967\pi$
$60$	−5.00501e46	−0.378788
$61$	3.62994e46	0.177280	0.0886398	−	0.996064i	$-0.471748\pi$
$61$	3.62994e46	0.177280	0.0886398	+	0.996064i	$0.471748\pi$
$62$	3.48496e47	1.10616
$63$	2.91965e47	0.606466
$64$	−5.11611e47	−0.700117
$65$	−2.31967e48	−2.10486
$66$	−1.69495e47	−0.102623
$67$	7.15705e47	0.290905	0.145453	−	0.989365i	$-0.453536\pi$
$67$	7.15705e47	0.290905	0.145453	+	0.989365i	$0.453536\pi$
$68$	3.88812e48	1.06722
$69$	−7.11416e47	−0.132624
$70$	1.03444e49	1.31707
$71$	−9.79077e48	−0.855994	−0.427997	−	0.903780i	$-0.640781\pi$
$71$	−9.79077e48	−0.855994	−0.427997	+	0.903780i	$0.640781\pi$
$72$	2.89542e48	0.174743
$73$	−2.48596e49	−1.04097	−0.520485	−	0.853871i	$-0.674249\pi$
$73$	−2.48596e49	−1.04097	−0.520485	+	0.853871i	$0.674249\pi$
$74$	2.70254e49	0.789100
$75$	1.62155e49	0.331747
$76$	−1.07129e50	−1.54294
$77$	1.61836e49	0.164843
$78$	8.38622e49	0.606819
$79$	−2.29029e50	−1.18242	−0.591210	−	0.806517i	$-0.701350\pi$
$79$	−2.29029e50	−1.18242	−0.591210	+	0.806517i	$0.701350\pi$
$80$	4.37835e50	1.61967
$81$	2.73832e50	0.728839
$82$	3.83601e50	0.737586
$83$	−8.70995e50	−1.21464	−0.607318	−	0.794459i	$-0.707755\pi$
$83$	−8.70995e50	−1.21464	−0.607318	+	0.794459i	$0.707755\pi$
$84$	−1.72767e50	−0.175412
$85$	−2.41946e51	−1.79522
$86$	1.38235e51	0.752330
$87$	−4.46744e50	−0.178978
$88$	1.60493e50	0.0474968
$89$	2.82739e51	0.620227	0.310114	−	0.950700i	$-0.399633\pi$
$89$	2.82739e51	0.620227	0.310114	+	0.950700i	$0.399633\pi$
$90$	1.09438e52	1.78542
$91$	−8.00725e51	−0.974734
$92$	−4.09163e51	−0.372837
$93$	3.62186e51	0.247819
$94$	−3.81311e52	−1.96513
$95$	6.66634e52	2.59544
$96$	−1.38335e52	−0.408079
$97$	−5.70641e52	−1.27912	−0.639561	−	0.768740i	$-0.720884\pi$
$97$	−5.70641e52	−1.27912	−0.639561	+	0.768740i	$0.720884\pi$
$98$	−4.41079e52	−0.753400
$99$	1.71212e52	0.223461
$100$	9.32617e52	0.932617
$101$	2.16630e52	0.166418	0.0832092	−	0.996532i	$-0.473483\pi$
$101$	2.16630e52	0.166418	0.0832092	+	0.996532i	$0.473483\pi$
$102$	8.74698e52	0.517552
$103$	1.64434e53	0.751284	0.375642	−	0.926765i	$-0.377422\pi$
$103$	1.64434e53	0.751284	0.375642	+	0.926765i	$0.377422\pi$
$104$	−7.94079e52	−0.280854
$105$	1.07508e53	0.295069
$106$	−7.14313e53	−1.52505
$107$	−6.28499e53	−1.04625	−0.523124	−	0.852257i	$-0.675234\pi$
$107$	−6.28499e53	−1.04625	−0.523124	+	0.852257i	$0.675234\pi$
$108$	−3.84359e53	−0.500044
$109$	1.11123e54	1.13240	0.566201	−	0.824267i	$-0.308412\pi$
$109$	1.11123e54	1.13240	0.566201	+	0.824267i	$0.308412\pi$
$110$	6.06611e53	0.485293
$111$	2.80871e53	0.176786
$112$	1.51136e54	0.750049
$113$	3.22273e53	0.126371	0.0631853	−	0.998002i	$-0.479874\pi$
$113$	3.22273e53	0.126371	0.0631853	+	0.998002i	$0.479874\pi$
$114$	−2.41005e54	−0.748253
$115$	2.54610e54	0.627167
$116$	−2.56940e54	−0.503148
$117$	−8.47118e54	−1.32135
$118$	1.39631e55	1.73824
$119$	−8.35170e54	−0.831344
$120$	1.06616e54	0.0850194
$121$	−1.46757e55	−0.939261
$122$	4.69669e54	0.241689
$123$	3.98670e54	0.165245
$124$	2.08308e55	0.696676
$125$	−4.60355e54	−0.124445
$126$	3.77766e55	0.826807
$127$	1.88562e55	0.334700	0.167350	−	0.985898i	$-0.446479\pi$
$127$	1.88562e55	0.334700	0.167350	+	0.985898i	$0.446479\pi$
$128$	2.64645e55	0.381593
$129$	1.43665e55	0.168548
$130$	−3.00137e56	−2.86959
$131$	−7.70511e55	−0.601298	−0.300649	−	0.953735i	$-0.597203\pi$
$131$	−7.70511e55	−0.601298	−0.300649	+	0.953735i	$0.597203\pi$
$132$	−1.01313e55	−0.0646332
$133$	2.30114e56	1.20192
$134$	9.26033e55	0.396597
$135$	2.39176e56	0.841147
$136$	−8.28239e55	−0.239538
$137$	2.23996e56	0.533513	0.266757	−	0.963764i	$-0.414048\pi$
$137$	2.23996e56	0.533513	0.266757	+	0.963764i	$0.414048\pi$
$138$	−9.20483e55	−0.180809
$139$	−4.13628e56	−0.670993	−0.335496	−	0.942042i	$-0.608904\pi$
$139$	−4.13628e56	−0.670993	−0.335496	+	0.942042i	$0.608904\pi$
$140$	6.18321e56	0.829509
$141$	−3.96291e56	−0.440258
$142$	−1.26680e57	−1.16699
$143$	−4.69556e56	−0.359155
$144$	1.59892e57	1.01677
$145$	1.59886e57	0.846369
$146$	−3.21652e57	−1.41917
$147$	−4.58406e56	−0.168788
$148$	1.61540e57	0.496986
$149$	−2.00904e57	−0.517073	−0.258536	−	0.966001i	$-0.583240\pi$
$149$	−2.00904e57	−0.517073	−0.258536	+	0.966001i	$0.583240\pi$
$150$	2.09808e57	0.452276
$151$	1.00882e58	1.82358	0.911790	−	0.410656i	$-0.134700\pi$
$151$	1.00882e58	1.82358	0.911790	+	0.410656i	$0.134700\pi$
$152$	2.28205e57	0.346313
$153$	−8.83559e57	−1.12697
$154$	2.09395e57	0.224733
$155$	−1.29624e58	−1.17191
$156$	5.01272e57	0.382183
$157$	−6.27576e57	−0.403948	−0.201974	−	0.979391i	$-0.564736\pi$
$157$	−6.27576e57	−0.403948	−0.201974	+	0.979391i	$0.564736\pi$
$158$	−2.96334e58	−1.61202
$159$	−7.42374e57	−0.341664
$160$	4.95090e58	1.92977
$161$	8.78886e57	0.290433
$162$	3.54304e58	0.993639
$163$	9.18357e55	0.00218796	0.00109398	−	0.999999i	$-0.499652\pi$
$163$	9.18357e55	0.00218796	0.00109398	+	0.999999i	$0.499652\pi$
$164$	2.29291e58	0.464542
$165$	6.30441e57	0.108723
$166$	−1.12696e59	−1.65594
$167$	−3.13517e58	−0.392893	−0.196447	−	0.980515i	$-0.562940\pi$
$167$	−3.13517e58	−0.392893	−0.196447	+	0.980515i	$0.562940\pi$
$168$	3.68025e57	0.0393715
$169$	1.22930e59	1.12372
$170$	−3.13048e59	−2.44745
$171$	2.43447e59	1.62932
$172$	8.26275e58	0.473828
$173$	−4.28978e58	−0.210966	−0.105483	−	0.994421i	$-0.533639\pi$
$173$	−4.28978e58	−0.210966	−0.105483	+	0.994421i	$0.533639\pi$
$174$	−5.78031e58	−0.244004
$175$	−2.00327e59	−0.726492
$176$	8.86280e58	0.276367
$177$	1.45117e59	0.389426
$178$	3.65829e59	0.845567
$179$	1.12342e59	0.223840	0.111920	−	0.993717i	$-0.464300\pi$
$179$	1.12342e59	0.223840	0.111920	+	0.993717i	$0.464300\pi$
$180$	6.54146e59	1.12448
$181$	−6.03513e59	−0.895786	−0.447893	−	0.894087i	$-0.647825\pi$
$181$	−6.03513e59	−0.895786	−0.447893	+	0.894087i	$0.647825\pi$
$182$	−1.03604e60	−1.32887
$183$	4.88119e58	0.0541467
$184$	8.71592e58	0.0836837
$185$	−1.00522e60	−0.836004
$186$	4.68624e59	0.337856
$187$	−4.89755e59	−0.306321
$188$	−2.27922e60	−1.23767
$189$	8.25606e59	0.389525
$190$	8.62540e60	3.53842
$191$	−1.23426e60	−0.440577	−0.220289	−	0.975435i	$-0.570700\pi$
$191$	−1.23426e60	−0.440577	−0.220289	+	0.975435i	$0.570700\pi$
$192$	−6.87964e59	−0.213837
$193$	4.53607e60	1.22860	0.614301	−	0.789072i	$-0.289438\pi$
$193$	4.53607e60	1.22860	0.614301	+	0.789072i	$0.289438\pi$
$194$	−7.38338e60	−1.74385
$195$	−3.11927e60	−0.642889
$196$	−2.63648e60	−0.474502
$197$	−2.14130e60	−0.336761	−0.168381	−	0.985722i	$-0.553854\pi$
$197$	−2.14130e60	−0.336761	−0.168381	+	0.985722i	$0.553854\pi$
$198$	2.21527e60	0.304649
$199$	9.14306e59	0.110023	0.0550117	−	0.998486i	$-0.482480\pi$
$199$	9.14306e59	0.110023	0.0550117	+	0.998486i	$0.482480\pi$
$200$	−1.98664e60	−0.209327
$201$	9.62411e59	0.0888515
$202$	2.80292e60	0.226881
$203$	5.51910e60	0.391943
$204$	5.22836e60	0.325961
$205$	−1.42681e61	−0.781428
$206$	2.12756e61	1.02424
$207$	9.29807e60	0.393712
$208$	−4.38510e61	−1.63419
$209$	1.34942e61	0.442864
$210$	1.39102e61	0.402273
$211$	6.72523e61	1.71483	0.857417	−	0.514623i	$-0.172068\pi$
$211$	6.72523e61	1.71483	0.857417	+	0.514623i	$0.172068\pi$
$212$	−4.26969e61	−0.960497
$213$	−1.31657e61	−0.261447
$214$	−8.13199e61	−1.42637
$215$	−5.14167e61	−0.797049
$216$	8.18755e60	0.112235
$217$	−4.47447e61	−0.542698
$218$	1.43779e62	1.54383
$219$	−3.34288e61	−0.317944
$220$	3.62592e61	0.305645
$221$	2.42319e62	1.81131
$222$	3.63412e61	0.241015
$223$	−1.36676e62	−0.804660	−0.402330	−	0.915495i	$-0.631799\pi$
$223$	−1.36676e62	−0.804660	−0.402330	+	0.915495i	$0.631799\pi$
$224$	1.70899e62	0.893651
$225$	−2.11934e62	−0.984834
$226$	4.16981e61	0.172283
$227$	−4.41921e62	−1.62427	−0.812137	−	0.583467i	$-0.801696\pi$
$227$	−4.41921e62	−1.62427	−0.812137	+	0.583467i	$0.801696\pi$
$228$	−1.44057e62	−0.471260
$229$	−1.20175e62	−0.350087	−0.175043	−	0.984561i	$-0.556007\pi$
$229$	−1.20175e62	−0.350087	−0.175043	+	0.984561i	$0.556007\pi$
$230$	3.29434e62	0.855029
$231$	2.17621e61	0.0503481
$232$	5.47329e61	0.112932
$233$	3.74033e62	0.688618	0.344309	−	0.938856i	$-0.388113\pi$
$233$	3.74033e62	0.688618	0.344309	+	0.938856i	$0.388113\pi$
$234$	−1.09606e63	−1.80142
$235$	1.41829e63	2.08194
$236$	8.34623e62	1.09477
$237$	−3.07975e62	−0.361148
$238$	−1.08061e63	−1.13339
$239$	−2.03152e62	−0.190668	−0.0953339	−	0.995445i	$-0.530392\pi$
$239$	−2.03152e62	−0.190668	−0.0953339	+	0.995445i	$0.530392\pi$
$240$	5.88758e62	0.494697
$241$	2.85110e62	0.214566	0.107283	−	0.994229i	$-0.465785\pi$
$241$	2.85110e62	0.214566	0.107283	+	0.994229i	$0.465785\pi$
$242$	−1.89885e63	−1.28051
$243$	1.33153e63	0.804979
$244$	2.80737e62	0.152219
$245$	1.64060e63	0.798182
$246$	5.15829e62	0.225282
$247$	−6.67661e63	−2.61871
$248$	−4.43733e62	−0.156370
$249$	−1.17123e63	−0.370987
$250$	−5.95642e62	−0.169658
$251$	7.65328e63	1.96107	0.980537	−	0.196336i	$-0.0629045\pi$
$251$	7.65328e63	1.96107	0.980537	+	0.196336i	$0.0629045\pi$
$252$	2.25804e63	0.520735
$253$	5.15390e62	0.107014
$254$	2.43976e63	0.456302
$255$	−3.25346e63	−0.548315
$256$	8.03236e63	1.22035
$257$	−3.77322e63	−0.516993	−0.258496	−	0.966012i	$-0.583227\pi$
$257$	−3.77322e63	−0.516993	−0.258496	+	0.966012i	$0.583227\pi$
$258$	1.85885e63	0.229785
$259$	−3.46989e63	−0.387143
$260$	−1.79402e64	−1.80731
$261$	5.83887e63	0.531319
$262$	−9.96945e63	−0.819761
$263$	−2.00429e64	−1.48982	−0.744911	−	0.667164i	$-0.767508\pi$
$263$	−2.00429e64	−1.48982	−0.744911	+	0.667164i	$0.767508\pi$
$264$	2.15815e62	0.0145070
$265$	2.65690e64	1.61570
$266$	2.97739e64	1.63860
$267$	3.80200e63	0.189437
$268$	5.53521e63	0.249782
$269$	−3.27370e64	−1.33846	−0.669228	−	0.743058i	$-0.733375\pi$
$269$	−3.27370e64	−1.33846	−0.669228	+	0.743058i	$0.733375\pi$
$270$	3.09463e64	1.14675
$271$	1.33847e64	0.449699	0.224849	−	0.974394i	$-0.427811\pi$
$271$	1.33847e64	0.449699	0.224849	+	0.974394i	$0.427811\pi$
$272$	−4.57374e64	−1.39379
$273$	−1.07674e64	−0.297714
$274$	2.89823e64	0.727348
$275$	−1.17474e64	−0.267687
$276$	−5.50203e63	−0.113876
$277$	4.06188e64	0.763858	0.381929	−	0.924192i	$-0.375260\pi$
$277$	4.06188e64	0.763858	0.381929	+	0.924192i	$0.375260\pi$
$278$	−5.35183e64	−0.914777
$279$	−4.73371e64	−0.735682
$280$	−1.31713e64	−0.186184
$281$	7.96754e64	1.02472	0.512362	−	0.858770i	$-0.328771\pi$
$281$	7.96754e64	1.02472	0.512362	+	0.858770i	$0.328771\pi$
$282$	−5.12750e64	−0.600212
$283$	4.10609e64	0.437611	0.218806	−	0.975768i	$-0.429784\pi$
$283$	4.10609e64	0.437611	0.218806	+	0.975768i	$0.429784\pi$
$284$	−7.57210e64	−0.734988
$285$	8.96424e64	0.792729
$286$	−6.07546e64	−0.489643
$287$	−4.92519e64	−0.361870
$288$	1.80801e65	1.21144
$289$	8.91397e64	0.544852
$290$	2.06873e65	1.15387
$291$	−7.67342e64	−0.390683
$292$	−1.92262e65	−0.893816
$293$	1.54719e65	0.656980	0.328490	−	0.944507i	$-0.393460\pi$
$293$	1.54719e65	0.656980	0.328490	+	0.944507i	$0.393460\pi$
$294$	−5.93120e64	−0.230112
$295$	−5.19361e65	−1.84156
$296$	−3.44109e64	−0.111549
$297$	4.84147e64	0.143526
$298$	−2.59944e65	−0.704935
$299$	−2.55003e65	−0.632788
$300$	1.25409e65	0.284850
$301$	−1.77484e65	−0.369104
$302$	1.30529e66	2.48612
$303$	2.91302e64	0.0508293
$304$	1.26020e66	2.01507
$305$	−1.74694e65	−0.256055
$306$	−1.14321e66	−1.53642
$307$	−5.91230e64	−0.0728769	−0.0364384	−	0.999336i	$-0.511601\pi$
$307$	−5.91230e64	−0.0728769	−0.0364384	+	0.999336i	$0.511601\pi$
$308$	1.25162e65	0.141540
$309$	2.21114e65	0.229465
$310$	−1.67717e66	−1.59769
$311$	6.42175e63	0.00561699	0.00280849	−	0.999996i	$-0.499106\pi$
$311$	6.42175e63	0.00561699	0.00280849	+	0.999996i	$0.499106\pi$
$312$	−1.06780e65	−0.0857815
$313$	1.94924e66	1.43860	0.719302	−	0.694698i	$-0.244462\pi$
$313$	1.94924e66	1.43860	0.719302	+	0.694698i	$0.244462\pi$
$314$	−8.12005e65	−0.550710
$315$	−1.40511e66	−0.875952
$316$	−1.77129e66	−1.01527
$317$	3.17927e66	1.67593	0.837967	−	0.545721i	$-0.183744\pi$
$317$	3.17927e66	1.67593	0.837967	+	0.545721i	$0.183744\pi$
$318$	−9.60539e65	−0.465797
$319$	3.23647e65	0.144417
$320$	2.46217e66	1.01122
$321$	−8.45145e65	−0.319557
$322$	1.13717e66	0.395953
$323$	−6.96383e66	−2.23348
$324$	2.11780e66	0.625808
$325$	5.81235e66	1.58286
$326$	1.18824e64	0.00298289
$327$	1.49427e66	0.345871
$328$	−4.88431e65	−0.104267
$329$	4.89579e66	0.964121
$330$	8.15711e65	0.148224
$331$	−9.10692e66	−1.52732	−0.763659	−	0.645620i	$-0.776599\pi$
$331$	−9.10692e66	−1.52732	−0.763659	+	0.645620i	$0.776599\pi$
$332$	−6.73621e66	−1.04293
$333$	−3.67093e66	−0.524812
$334$	−4.05651e66	−0.535638
$335$	−3.44440e66	−0.420171
$336$	2.03233e66	0.229088
$337$	6.75654e66	0.703934	0.351967	−	0.936012i	$-0.385513\pi$
$337$	6.75654e66	0.703934	0.351967	+	0.936012i	$0.385513\pi$
$338$	1.59056e67	1.53199
$339$	4.33362e65	0.0385975
$340$	−1.87119e67	−1.54144
$341$	−2.62389e66	−0.199965
$342$	3.14990e67	2.22129
$343$	1.59110e67	1.03849
$344$	−1.76012e66	−0.106351
$345$	3.42375e66	0.191556
$346$	−5.55043e66	−0.287614
$347$	−3.44317e67	−1.65283	−0.826413	−	0.563064i	$-0.809622\pi$
$347$	−3.44317e67	−1.65283	−0.826413	+	0.563064i	$0.809622\pi$
$348$	−3.45508e66	−0.153677
$349$	3.11481e66	0.128398	0.0641989	−	0.997937i	$-0.479551\pi$
$349$	3.11481e66	0.128398	0.0641989	+	0.997937i	$0.479551\pi$
$350$	−2.59198e67	−0.990440
$351$	−2.39544e67	−0.848686
$352$	1.00218e67	0.329279
$353$	−8.64866e66	−0.263584	−0.131792	−	0.991277i	$-0.542073\pi$
$353$	−8.64866e66	−0.263584	−0.131792	+	0.991277i	$0.542073\pi$
$354$	1.87763e67	0.530912
$355$	4.71190e67	1.23636
$356$	2.18668e67	0.532550
$357$	−1.12306e67	−0.253918
$358$	1.45357e67	0.305166
$359$	−5.93891e67	−1.15799	−0.578993	−	0.815332i	$-0.696554\pi$
$359$	−5.93891e67	−1.15799	−0.578993	+	0.815332i	$0.696554\pi$
$360$	−1.39345e67	−0.252391
$361$	1.32453e68	2.22906
$362$	−7.80870e67	−1.22124
$363$	−1.97344e67	−0.286879
$364$	−6.19274e67	−0.836944
$365$	1.19639e68	1.50353
$366$	6.31565e66	0.0738192
$367$	1.25080e66	0.0136000	0.00679999	−	0.999977i	$-0.497835\pi$
$367$	1.25080e66	0.0136000	0.00679999	+	0.999977i	$0.497835\pi$
$368$	4.81315e67	0.486925
$369$	−5.21055e67	−0.490551
$370$	−1.30062e68	−1.13974
$371$	9.17132e67	0.748209
$372$	2.80112e67	0.212786
$373$	−2.22554e68	−1.57453	−0.787267	−	0.616613i	$-0.788504\pi$
$373$	−2.22554e68	−1.57453	−0.787267	+	0.616613i	$0.788504\pi$
$374$	−6.33682e67	−0.417613
$375$	−6.19041e66	−0.0380094
$376$	4.85516e67	0.277796
$377$	−1.60133e68	−0.853955
$378$	1.06823e68	0.531047
$379$	1.79817e68	0.833474	0.416737	−	0.909027i	$-0.363174\pi$
$379$	1.79817e68	0.833474	0.416737	+	0.909027i	$0.363174\pi$
$380$	5.15569e68	2.22855
$381$	2.53560e67	0.102228
$382$	−1.59698e68	−0.600647
$383$	−7.96579e67	−0.279551	−0.139776	−	0.990183i	$-0.544638\pi$
$383$	−7.96579e67	−0.279551	−0.139776	+	0.990183i	$0.544638\pi$
$384$	3.55869e67	0.116550
$385$	−7.78849e67	−0.238092
$386$	5.86911e68	1.67498
$387$	−1.87768e68	−0.500357
$388$	−4.41329e68	−1.09830
$389$	−4.61806e68	−1.07348	−0.536741	−	0.843747i	$-0.680345\pi$
$389$	−4.61806e68	−1.07348	−0.536741	+	0.843747i	$0.680345\pi$
$390$	−4.03595e68	−0.876462
$391$	−2.65973e68	−0.539701
$392$	5.61617e67	0.106502
$393$	−1.03611e68	−0.183655
$394$	−2.77057e68	−0.459113
$395$	1.10222e69	1.70783
$396$	1.32414e68	0.191872
$397$	9.49592e68	1.28703	0.643515	−	0.765434i	$-0.277475\pi$
$397$	9.49592e68	1.28703	0.643515	+	0.765434i	$0.277475\pi$
$398$	1.18300e68	0.149997
$399$	3.09435e68	0.367103
$400$	−1.09707e69	−1.21800
$401$	−4.54047e68	−0.471818	−0.235909	−	0.971775i	$-0.575807\pi$
$401$	−4.54047e68	−0.471818	−0.235909	+	0.971775i	$0.575807\pi$
$402$	1.24524e68	0.121133
$403$	1.29824e69	1.18242
$404$	1.67540e68	0.142893
$405$	−1.31784e69	−1.05270
$406$	7.14102e68	0.534343
$407$	−2.03479e68	−0.142649
$408$	−1.11374e68	−0.0731624
$409$	−4.09199e68	−0.251923	−0.125961	−	0.992035i	$-0.540202\pi$
$409$	−4.09199e68	−0.251923	−0.125961	+	0.992035i	$0.540202\pi$
$410$	−1.84611e69	−1.06534
$411$	3.01208e68	0.162951
$412$	1.27172e69	0.645080
$413$	−1.79278e69	−0.852805
$414$	1.20305e69	0.536755
$415$	4.19174e69	1.75437
$416$	−4.95853e69	−1.94706
$417$	−5.56207e68	−0.204942
$418$	1.74598e69	0.603765
$419$	−3.39626e69	−1.10238	−0.551188	−	0.834381i	$-0.685825\pi$
$419$	−3.39626e69	−1.10238	−0.551188	+	0.834381i	$0.685825\pi$
$420$	8.31457e68	0.253358
$421$	−5.62917e69	−1.61053	−0.805264	−	0.592916i	$-0.797977\pi$
$421$	−5.62917e69	−1.61053	−0.805264	+	0.592916i	$0.797977\pi$
$422$	8.70160e69	2.33786
$423$	5.17945e69	1.30696
$424$	9.09521e68	0.215584
$425$	6.06239e69	1.35001
$426$	−1.70347e69	−0.356435
$427$	−6.03024e68	−0.118576
$428$	−4.86076e69	−0.898348
$429$	−6.31413e68	−0.109697
$430$	−6.65267e69	−1.08663
$431$	−4.87848e69	−0.749267	−0.374633	−	0.927173i	$-0.622231\pi$
$431$	−4.87848e69	−0.749267	−0.374633	+	0.927173i	$0.622231\pi$
$432$	4.52137e69	0.653056
$433$	−1.12249e70	−1.52494	−0.762469	−	0.647025i	$-0.776013\pi$
$433$	−1.12249e70	−1.52494	−0.762469	+	0.647025i	$0.776013\pi$
$434$	−5.78940e69	−0.739870
$435$	2.15000e69	0.258507
$436$	8.59415e69	0.972323
$437$	7.32834e69	0.780274
$438$	−4.32526e69	−0.433460
$439$	−1.69286e68	−0.0159702	−0.00798509	−	0.999968i	$-0.502542\pi$
$439$	−1.69286e68	−0.0159702	−0.00798509	+	0.999968i	$0.502542\pi$
$440$	−7.72385e68	−0.0686022
$441$	5.99129e69	0.501069
$442$	3.13531e70	2.46939
$443$	−1.39750e69	−0.103670	−0.0518351	−	0.998656i	$-0.516507\pi$
$443$	−1.39750e69	−0.103670	−0.0518351	+	0.998656i	$0.516507\pi$
$444$	2.17223e69	0.151795
$445$	−1.36071e70	−0.895828
$446$	−1.76841e70	−1.09701
$447$	−2.70156e69	−0.157930
$448$	8.49914e69	0.468282
$449$	1.04380e70	0.542110	0.271055	−	0.962564i	$-0.412627\pi$
$449$	1.04380e70	0.542110	0.271055	+	0.962564i	$0.412627\pi$
$450$	−2.74215e70	−1.34264
$451$	−2.88820e69	−0.133336
$452$	2.49244e69	0.108506
$453$	1.35656e70	0.556978
$454$	−5.71790e70	−2.21440
$455$	3.85356e70	1.40786
$456$	3.06867e69	0.105775
$457$	3.06454e70	0.996751	0.498376	−	0.866961i	$-0.333930\pi$
$457$	3.06454e70	0.996751	0.498376	+	0.866961i	$0.333930\pi$
$458$	−1.55492e70	−0.477280
$459$	−2.49849e70	−0.723838
$460$	1.96914e70	0.538509
$461$	−1.38267e70	−0.356979	−0.178489	−	0.983942i	$-0.557121\pi$
$461$	−1.38267e70	−0.356979	−0.178489	+	0.983942i	$0.557121\pi$
$462$	2.81574e69	0.0686405
$463$	−2.87526e69	−0.0661882	−0.0330941	−	0.999452i	$-0.510536\pi$
$463$	−2.87526e69	−0.0661882	−0.0330941	+	0.999452i	$0.510536\pi$
$464$	3.02249e70	0.657110
$465$	−1.74305e70	−0.357938
$466$	4.83952e70	0.938805
$467$	−3.27527e69	−0.0600275	−0.0300137	−	0.999549i	$-0.509555\pi$
$467$	−3.27527e69	−0.0600275	−0.0300137	+	0.999549i	$0.509555\pi$
$468$	−6.55154e70	−1.13456
$469$	−1.18897e70	−0.194576
$470$	1.83510e71	2.83835
$471$	−8.43903e69	−0.123378
$472$	−1.77790e70	−0.245722
$473$	−1.04079e70	−0.136002
$474$	−3.98482e70	−0.492359
$475$	−1.67037e71	−1.95178
$476$	−6.45914e70	−0.713823
$477$	9.70269e70	1.01427
$478$	−2.62854e70	−0.259941
$479$	−1.92415e71	−1.80032	−0.900158	−	0.435564i	$-0.856549\pi$
$479$	−1.92415e71	−1.80032	−0.900158	+	0.435564i	$0.856549\pi$
$480$	6.65749e70	0.589410
$481$	1.00677e71	0.843497
$482$	3.68897e70	0.292522
$483$	1.18184e70	0.0887074
$484$	−1.13501e71	−0.806485
$485$	2.74626e71	1.84751
$486$	1.72283e71	1.09744
$487$	−1.33015e71	−0.802388	−0.401194	−	0.915993i	$-0.631405\pi$
$487$	−1.33015e71	−0.802388	−0.401194	+	0.915993i	$0.631405\pi$
$488$	−5.98020e69	−0.0341657
$489$	1.23492e68	0.000668272 0
$490$	2.12273e71	1.08818
$491$	3.09725e71	1.50424	0.752120	−	0.659027i	$-0.229032\pi$
$491$	3.09725e71	1.50424	0.752120	+	0.659027i	$0.229032\pi$
$492$	3.08328e70	0.141886
$493$	−1.67022e71	−0.728332
$494$	−8.63870e71	−3.57013
$495$	−8.23975e70	−0.322757
$496$	−2.45041e71	−0.909858
$497$	1.62649e71	0.572543
$498$	−1.51542e71	−0.505774
$499$	4.41016e71	1.39569	0.697847	−	0.716247i	$-0.254142\pi$
$499$	4.41016e71	1.39569	0.697847	+	0.716247i	$0.254142\pi$
$500$	−3.56035e70	−0.106853
$501$	−4.21587e70	−0.120002
$502$	9.90238e71	2.67357
$503$	−6.61525e71	−1.69432	−0.847158	−	0.531341i	$-0.821688\pi$
$503$	−6.61525e71	−1.69432	−0.847158	+	0.531341i	$0.821688\pi$
$504$	−4.81002e70	−0.116879
$505$	−1.04255e71	−0.240367
$506$	6.66851e70	0.145895
$507$	1.65304e71	0.343220
$508$	1.45832e71	0.287386
$509$	−3.73962e71	−0.699530	−0.349765	−	0.936837i	$-0.613739\pi$
$509$	−3.73962e71	−0.699530	−0.349765	+	0.936837i	$0.613739\pi$
$510$	−4.20956e71	−0.747528
$511$	4.12980e71	0.696267
$512$	8.00916e71	1.28213
$513$	6.88408e71	1.04649
$514$	−4.88208e71	−0.704826
$515$	−7.91351e71	−1.08512
$516$	1.11109e71	0.144722
$517$	2.87096e71	0.355244
$518$	−4.48960e71	−0.527800
$519$	−5.76847e70	−0.0644356
$520$	3.82158e71	0.405653
$521$	−8.23378e71	−0.830614	−0.415307	−	0.909681i	$-0.636326\pi$
$521$	−8.23378e71	−0.830614	−0.415307	+	0.909681i	$0.636326\pi$
$522$	7.55476e71	0.724357
$523$	−1.56757e71	−0.142867	−0.0714336	−	0.997445i	$-0.522757\pi$
$523$	−1.56757e71	−0.142867	−0.0714336	+	0.997445i	$0.522757\pi$
$524$	−5.95907e71	−0.516297
$525$	−2.69380e71	−0.221893
$526$	−2.59331e72	−2.03110
$527$	1.35408e72	1.00847
$528$	1.19178e71	0.0844109
$529$	−1.20459e72	−0.811453
$530$	3.43770e72	2.20271
$531$	−1.89665e72	−1.15606
$532$	1.77969e72	1.03201
$533$	1.42901e72	0.788432
$534$	4.91931e71	0.258262
$535$	3.02471e72	1.51115
$536$	−1.17910e71	−0.0560639
$537$	1.51067e71	0.0683678
$538$	−4.23576e72	−1.82474
$539$	3.32096e71	0.136195
$540$	1.84976e72	0.722240
$541$	−3.10699e72	−1.15508	−0.577541	−	0.816362i	$-0.695987\pi$
$541$	−3.10699e72	−1.15508	−0.577541	+	0.816362i	$0.695987\pi$
$542$	1.73181e72	0.613082
$543$	−8.11545e71	−0.273601
$544$	−5.17184e72	−1.66063
$545$	−5.34788e72	−1.63559
$546$	−1.39316e72	−0.405879
$547$	6.13544e72	1.70287	0.851435	−	0.524460i	$-0.175733\pi$
$547$	6.13544e72	1.70287	0.851435	+	0.524460i	$0.175733\pi$
$548$	1.73237e72	0.458094
$549$	−6.37963e71	−0.160742
$550$	−1.51997e72	−0.364942
$551$	4.60194e72	1.05299
$552$	1.17203e71	0.0255596
$553$	3.80474e72	0.790877
$554$	5.25556e72	1.04138
$555$	−1.35172e72	−0.255341
$556$	−3.19897e72	−0.576140
$557$	3.45443e72	0.593217	0.296608	−	0.954999i	$-0.404144\pi$
$557$	3.45443e72	0.593217	0.296608	+	0.954999i	$0.404144\pi$
$558$	−6.12483e72	−1.00297
$559$	5.14959e72	0.804193
$560$	−7.27355e72	−1.08334
$561$	−6.58575e71	−0.0935598
$562$	1.03090e73	1.39702
$563$	−7.65255e72	−0.989313	−0.494656	−	0.869089i	$-0.664706\pi$
$563$	−7.65255e72	−0.989313	−0.494656	+	0.869089i	$0.664706\pi$
$564$	−3.06488e72	−0.378022
$565$	−1.55097e72	−0.182524
$566$	5.31277e72	0.596603
$567$	−4.54904e72	−0.487493
$568$	1.61299e72	0.164969
$569$	−1.06701e73	−1.04158	−0.520789	−	0.853686i	$-0.674362\pi$
$569$	−1.06701e73	−1.04158	−0.520789	+	0.853686i	$0.674362\pi$
$570$	1.15986e73	1.08074
$571$	4.28488e72	0.381137	0.190569	−	0.981674i	$-0.438967\pi$
$571$	4.28488e72	0.381137	0.190569	+	0.981674i	$0.438967\pi$
$572$	−3.63151e72	−0.308384
$573$	−1.65971e72	−0.134566
$574$	−6.37257e72	−0.493344
$575$	−6.37971e72	−0.471632
$576$	8.99157e72	0.634804
$577$	−2.73962e73	−1.84727	−0.923636	−	0.383271i	$-0.874798\pi$
$577$	−2.73962e73	−1.84727	−0.923636	+	0.383271i	$0.874798\pi$
$578$	1.15336e73	0.742806
$579$	6.09966e72	0.375253
$580$	1.23655e73	0.726724
$581$	1.44694e73	0.812425
$582$	−9.92845e72	−0.532626
$583$	5.37818e72	0.275689
$584$	4.09553e72	0.200618
$585$	4.07683e73	1.90850
$586$	2.00187e73	0.895673
$587$	−1.81383e72	−0.0775689	−0.0387844	−	0.999248i	$-0.512349\pi$
$587$	−1.81383e72	−0.0775689	−0.0387844	+	0.999248i	$0.512349\pi$
$588$	−3.54528e72	−0.144928
$589$	−3.73091e73	−1.45800
$590$	−6.71988e73	−2.51063
$591$	−2.87941e72	−0.102857
$592$	−1.90026e73	−0.649063
$593$	4.87506e72	0.159232	0.0796161	−	0.996826i	$-0.474631\pi$
$593$	4.87506e72	0.159232	0.0796161	+	0.996826i	$0.474631\pi$
$594$	6.26425e72	0.195672
$595$	4.01933e73	1.20075
$596$	−1.55377e73	−0.443978
$597$	1.22947e72	0.0336045
$598$	−3.29942e73	−0.862692
$599$	−1.49187e73	−0.373181	−0.186590	−	0.982438i	$-0.559744\pi$
$599$	−1.49187e73	−0.373181	−0.186590	+	0.982438i	$0.559744\pi$
$600$	−2.67144e72	−0.0639349
$601$	7.02936e73	1.60969	0.804845	−	0.593485i	$-0.202248\pi$
$601$	7.02936e73	1.60969	0.804845	+	0.593485i	$0.202248\pi$
$602$	−2.29643e73	−0.503206
$603$	−1.25785e73	−0.263767
$604$	7.80214e73	1.56579
$605$	7.06281e73	1.35663
$606$	3.76909e72	0.0692966
$607$	−9.09644e73	−1.60093	−0.800463	−	0.599382i	$-0.795413\pi$
$607$	−9.09644e73	−1.60093	−0.800463	+	0.599382i	$0.795413\pi$
$608$	1.42500e74	2.40087
$609$	7.42154e72	0.119712
$610$	−2.26032e73	−0.349084
$611$	−1.42048e74	−2.10060
$612$	−6.83338e73	−0.967660
$613$	−1.39239e73	−0.188825	−0.0944125	−	0.995533i	$-0.530097\pi$
$613$	−1.39239e73	−0.188825	−0.0944125	+	0.995533i	$0.530097\pi$
$614$	−7.64978e72	−0.0993544
$615$	−1.91864e73	−0.238672
$616$	−2.66619e72	−0.0317689
$617$	1.12495e73	0.128403	0.0642015	−	0.997937i	$-0.479550\pi$
$617$	1.12495e73	0.128403	0.0642015	+	0.997937i	$0.479550\pi$
$618$	2.86094e73	0.312834
$619$	1.38480e74	1.45072	0.725360	−	0.688369i	$-0.241673\pi$
$619$	1.38480e74	1.45072	0.725360	+	0.688369i	$0.241673\pi$
$620$	−1.00250e74	−1.00625
$621$	2.62927e73	0.252876
$622$	8.30895e71	0.00765774
$623$	−4.69701e73	−0.414847
$624$	−5.89666e73	−0.499131
$625$	−1.11725e74	−0.906417
$626$	2.52208e74	1.96127
$627$	1.81457e73	0.135264
$628$	−4.85362e73	−0.346845
$629$	1.05007e74	0.719412
$630$	−1.81803e74	−1.19420
$631$	−8.85014e73	−0.557406	−0.278703	−	0.960377i	$-0.589905\pi$
$631$	−8.85014e73	−0.557406	−0.278703	+	0.960377i	$0.589905\pi$
$632$	3.77317e73	0.227878
$633$	9.04343e73	0.523763
$634$	4.11358e74	2.28483
$635$	−9.07471e73	−0.483425
$636$	−5.74146e73	−0.293365
$637$	−1.64313e74	−0.805337
$638$	4.18759e73	0.196887
$639$	1.72073e74	0.776140
$640$	−1.27363e74	−0.551155
$641$	1.61877e74	0.672122	0.336061	−	0.941840i	$-0.390905\pi$
$641$	1.61877e74	0.672122	0.336061	+	0.941840i	$0.390905\pi$
$642$	−1.09351e74	−0.435657
$643$	−1.44296e74	−0.551648	−0.275824	−	0.961208i	$-0.588951\pi$
$643$	−1.44296e74	−0.551648	−0.275824	+	0.961208i	$0.588951\pi$
$644$	6.79723e73	0.249377
$645$	−6.91401e73	−0.243443
$646$	−9.01032e74	−3.04494
$647$	3.96918e72	0.0128747	0.00643735	−	0.999979i	$-0.497951\pi$
$647$	3.96918e72	0.0128747	0.00643735	+	0.999979i	$0.497951\pi$
$648$	−4.51129e73	−0.140463
$649$	−1.05131e74	−0.314228
$650$	7.52045e74	2.15794
$651$	−6.01683e73	−0.165757
$652$	7.10250e71	0.00187867
$653$	1.24882e74	0.317175	0.158588	−	0.987345i	$-0.449306\pi$
$653$	1.24882e74	0.317175	0.158588	+	0.987345i	$0.449306\pi$
$654$	1.93340e74	0.471532
$655$	3.70815e74	0.868487
$656$	−2.69724e74	−0.606691
$657$	4.36908e74	0.943860
$658$	6.33454e74	1.31440
$659$	−1.41749e74	−0.282524	−0.141262	−	0.989972i	$-0.545116\pi$
$659$	−1.41749e74	−0.282524	−0.141262	+	0.989972i	$0.545116\pi$
$660$	4.87578e73	0.0933533
$661$	3.68248e74	0.677333	0.338666	−	0.940906i	$-0.390024\pi$
$661$	3.68248e74	0.677333	0.338666	+	0.940906i	$0.390024\pi$
$662$	−1.17832e75	−2.08222
$663$	3.25847e74	0.553230
$664$	1.43493e74	0.234087
$665$	−1.10745e75	−1.73600
$666$	−4.74972e74	−0.715486
$667$	1.75764e74	0.254446
$668$	−2.42471e74	−0.337353
$669$	−1.83788e74	−0.245768
$670$	−4.45662e74	−0.572826
$671$	−3.53622e73	−0.0436910
$672$	2.29809e74	0.272949
$673$	1.04283e75	1.19073	0.595366	−	0.803455i	$-0.297007\pi$
$673$	1.04283e75	1.19073	0.595366	+	0.803455i	$0.297007\pi$
$674$	8.74211e74	0.959686
$675$	−5.99296e74	−0.632545
$676$	9.50730e74	0.964872
$677$	−1.67343e75	−1.63309	−0.816543	−	0.577285i	$-0.804112\pi$
$677$	−1.67343e75	−1.63309	−0.816543	+	0.577285i	$0.804112\pi$
$678$	5.60716e73	0.0526206
$679$	9.47978e74	0.855558
$680$	3.98598e74	0.345978
$681$	−5.94252e74	−0.496103
$682$	−3.39498e74	−0.272616
$683$	−1.24036e74	−0.0958078	−0.0479039	−	0.998852i	$-0.515254\pi$
$683$	−1.24036e74	−0.0958078	−0.0479039	+	0.998852i	$0.515254\pi$
$684$	1.88280e75	1.39900
$685$	−1.07800e75	−0.770582
$686$	2.05868e75	1.41579
$687$	−1.61600e74	−0.106927
$688$	−9.71979e74	−0.618819
$689$	−2.66100e75	−1.63018
$690$	4.42991e74	0.261152
$691$	2.95439e75	1.67610	0.838049	−	0.545595i	$-0.183696\pi$
$691$	2.95439e75	1.67610	0.838049	+	0.545595i	$0.183696\pi$
$692$	−3.31768e74	−0.181144
$693$	−2.84427e74	−0.149465
$694$	−4.45503e75	−2.25333
$695$	1.99062e75	0.969151
$696$	7.35995e73	0.0344929
$697$	1.49048e75	0.672448
$698$	4.03017e74	0.175047
$699$	5.02963e74	0.210325
$700$	−1.54931e75	−0.623793
$701$	−6.43274e74	−0.249384	−0.124692	−	0.992196i	$-0.539794\pi$
$701$	−6.43274e74	−0.249384	−0.124692	+	0.992196i	$0.539794\pi$
$702$	−3.09940e75	−1.15703
$703$	−2.89327e75	−1.04009
$704$	4.98401e74	0.172545
$705$	1.90718e75	0.635889
$706$	−1.11903e75	−0.359349
$707$	−3.59876e74	−0.111311
$708$	1.12232e75	0.334376
$709$	5.30581e75	1.52274	0.761372	−	0.648315i	$-0.224526\pi$
$709$	5.30581e75	1.52274	0.761372	+	0.648315i	$0.224526\pi$
$710$	6.09660e75	1.68555
$711$	4.02518e75	1.07211
$712$	−4.65803e74	−0.119531
$713$	−1.42496e75	−0.352315
$714$	−1.45309e75	−0.346171
$715$	2.25978e75	0.518747
$716$	8.68847e74	0.192198
$717$	−2.73179e74	−0.0582358
$718$	−7.68420e75	−1.57870
$719$	−7.52021e75	−1.48907	−0.744534	−	0.667585i	$-0.767328\pi$
$719$	−7.52021e75	−1.48907	−0.744534	+	0.667585i	$0.767328\pi$
$720$	−7.69497e75	−1.46857
$721$	−2.73165e75	−0.502506
$722$	1.71378e76	3.03891
$723$	3.83388e74	0.0655351
$724$	−4.66752e75	−0.769156
$725$	−4.00624e75	−0.636472
$726$	−2.55339e75	−0.391108
$727$	−9.24803e75	−1.36580	−0.682900	−	0.730512i	$-0.739282\pi$
$727$	−9.24803e75	−1.36580	−0.682900	+	0.730512i	$0.739282\pi$
$728$	1.31917e75	0.187853
$729$	−3.51724e75	−0.482973
$730$	1.54798e76	2.04979
$731$	5.37112e75	0.685890
$732$	3.77507e74	0.0464924
$733$	1.08537e76	1.28921	0.644603	−	0.764517i	$-0.277023\pi$
$733$	1.08537e76	1.28921	0.644603	+	0.764517i	$0.277023\pi$
$734$	1.61838e74	0.0185411
$735$	2.20612e75	0.243790
$736$	5.44255e75	0.580150
$737$	−6.97226e74	−0.0716943
$738$	−6.74179e75	−0.668778
$739$	−3.55012e75	−0.339755	−0.169877	−	0.985465i	$-0.554337\pi$
$739$	−3.55012e75	−0.339755	−0.169877	+	0.985465i	$0.554337\pi$
$740$	−7.77425e75	−0.717824
$741$	−8.97806e75	−0.799834
$742$	1.18665e76	1.02005
$743$	−1.21666e75	−0.100917	−0.0504586	−	0.998726i	$-0.516068\pi$
$743$	−1.21666e75	−0.100917	−0.0504586	+	0.998726i	$0.516068\pi$
$744$	−5.96689e74	−0.0477601
$745$	9.66867e75	0.746837
$746$	−2.87957e76	−2.14659
$747$	1.53078e76	1.10133
$748$	−3.78773e75	−0.263018
$749$	1.04410e76	0.699797
$750$	−8.00961e74	−0.0518189
$751$	−1.83232e76	−1.14431	−0.572153	−	0.820147i	$-0.693892\pi$
$751$	−1.83232e76	−1.14431	−0.572153	+	0.820147i	$0.693892\pi$
$752$	2.68114e76	1.61639
$753$	1.02914e76	0.598972
$754$	−2.07192e76	−1.16421
$755$	−4.85504e76	−2.63390
$756$	6.38517e75	0.334461
$757$	1.67987e76	0.849639	0.424819	−	0.905278i	$-0.360338\pi$
$757$	1.67987e76	0.849639	0.424819	+	0.905278i	$0.360338\pi$
$758$	2.32661e76	1.13629
$759$	6.93047e74	0.0326855
$760$	−1.09826e76	−0.500199
$761$	−6.65143e74	−0.0292565	−0.0146282	−	0.999893i	$-0.504656\pi$
$761$	−6.65143e74	−0.0292565	−0.0146282	+	0.999893i	$0.504656\pi$
$762$	3.28075e75	0.139369
$763$	−1.84603e76	−0.757422
$764$	−9.54566e75	−0.378296
$765$	4.25221e76	1.62775
$766$	−1.03067e76	−0.381117
$767$	5.20162e76	1.85807
$768$	1.08011e76	0.372732
$769$	1.78455e75	0.0594952	0.0297476	−	0.999557i	$-0.490530\pi$
$769$	1.78455e75	0.0594952	0.0297476	+	0.999557i	$0.490530\pi$
$770$	−1.00773e76	−0.324595
$771$	−5.07386e75	−0.157906
$772$	3.50816e76	1.05492
$773$	−6.01277e76	−1.74710	−0.873550	−	0.486735i	$-0.838188\pi$
$773$	−6.01277e76	−1.74710	−0.873550	+	0.486735i	$0.838188\pi$
$774$	−2.42948e76	−0.682147
$775$	3.24795e76	0.881282
$776$	9.40111e75	0.246515
$777$	−4.66597e75	−0.118246
$778$	−5.97519e76	−1.46350
$779$	−4.10673e76	−0.972194
$780$	−2.41242e76	−0.552008
$781$	9.53797e75	0.210962
$782$	−3.44135e76	−0.735784
$783$	1.65109e76	0.341259
$784$	3.10139e76	0.619699
$785$	3.02027e76	0.583444
$786$	−1.34059e76	−0.250380
$787$	7.06315e75	0.127546	0.0637732	−	0.997964i	$-0.479687\pi$
$787$	7.06315e75	0.127546	0.0637732	+	0.997964i	$0.479687\pi$
$788$	−1.65606e76	−0.289156
$789$	−2.69518e76	−0.455037
$790$	1.42614e77	2.32832
$791$	−5.35377e75	−0.0845246
$792$	−2.82066e75	−0.0430659
$793$	1.74963e76	0.258350
$794$	1.22865e77	1.75463
$795$	3.57274e76	0.493484
$796$	7.07117e75	0.0944702
$797$	−5.54535e76	−0.716612	−0.358306	−	0.933604i	$-0.616645\pi$
$797$	−5.54535e76	−0.716612	−0.358306	+	0.933604i	$0.616645\pi$
$798$	4.00370e76	0.500478
$799$	−1.48159e77	−1.79159
$800$	−1.24054e77	−1.45119
$801$	−4.96915e76	−0.562367
$802$	−5.87479e76	−0.643238
$803$	2.42177e76	0.256550
$804$	7.44321e75	0.0762912
$805$	−4.22972e76	−0.419489
$806$	1.67976e77	1.61201
$807$	−4.40216e76	−0.408806
$808$	−3.56890e75	−0.0320725
$809$	7.38311e76	0.642101	0.321050	−	0.947062i	$-0.395964\pi$
$809$	7.38311e76	0.642101	0.321050	+	0.947062i	$0.395964\pi$
$810$	−1.70512e77	−1.43517
$811$	1.49559e77	1.21832	0.609159	−	0.793048i	$-0.291507\pi$
$811$	1.49559e77	1.21832	0.609159	+	0.793048i	$0.291507\pi$
$812$	4.26842e76	0.336537
$813$	1.79984e76	0.137352
$814$	−2.63276e76	−0.194475
$815$	−4.41968e74	−0.00316019
$816$	−6.15032e76	−0.425705
$817$	−1.47990e77	−0.991628
$818$	−5.29453e76	−0.343451
$819$	1.40728e77	0.883803
$820$	−1.10348e77	−0.670963
$821$	2.15004e77	1.26576	0.632881	−	0.774249i	$-0.281872\pi$
$821$	2.15004e77	1.26576	0.632881	+	0.774249i	$0.281872\pi$
$822$	3.89725e76	0.222155
$823$	2.98860e77	1.64958	0.824788	−	0.565442i	$-0.191294\pi$
$823$	2.98860e77	1.64958	0.824788	+	0.565442i	$0.191294\pi$
$824$	−2.70898e76	−0.144789
$825$	−1.57968e76	−0.0817598
$826$	−2.31963e77	−1.16264
$827$	−1.03100e77	−0.500451	−0.250226	−	0.968188i	$-0.580505\pi$
$827$	−1.03100e77	−0.500451	−0.250226	+	0.968188i	$0.580505\pi$
$828$	7.19106e76	0.338056
$829$	−1.73661e77	−0.790692	−0.395346	−	0.918532i	$-0.629375\pi$
$829$	−1.73661e77	−0.790692	−0.395346	+	0.918532i	$0.629375\pi$
$830$	5.42359e77	2.39176
$831$	5.46202e76	0.233306
$832$	−2.46597e77	−1.02028
$833$	−1.71382e77	−0.686866
$834$	−7.19662e76	−0.279401
$835$	1.50883e77	0.567477
$836$	1.04363e77	0.380260
$837$	−1.33858e77	−0.472519
$838$	−4.39434e77	−1.50289
$839$	1.10592e77	0.366464	0.183232	−	0.983070i	$-0.441344\pi$
$839$	1.10592e77	0.366464	0.183232	+	0.983070i	$0.441344\pi$
$840$	−1.77115e76	−0.0568664
$841$	−2.11062e77	−0.656623
$842$	−7.28344e77	−2.19566
$843$	1.07140e77	0.312982
$844$	5.20124e77	1.47242
$845$	−5.91611e77	−1.62306
$846$	6.70155e77	1.78181
$847$	2.43800e77	0.628237
$848$	5.02260e77	1.25441
$849$	5.52147e76	0.133660
$850$	7.84397e77	1.84049
$851$	−1.10504e77	−0.251330
$852$	−1.01822e77	−0.224488
$853$	4.30141e77	0.919309	0.459655	−	0.888098i	$-0.347973\pi$
$853$	4.30141e77	0.919309	0.459655	+	0.888098i	$0.347973\pi$
$854$	−7.80238e76	−0.161657
$855$	−1.17161e78	−2.35332
$856$	1.03543e77	0.201635
$857$	4.39078e77	0.828992	0.414496	−	0.910051i	$-0.363958\pi$
$857$	4.39078e77	0.828992	0.414496	+	0.910051i	$0.363958\pi$
$858$	−8.16969e76	−0.149552
$859$	2.05806e77	0.365291	0.182646	−	0.983179i	$-0.441534\pi$
$859$	2.05806e77	0.365291	0.182646	+	0.983179i	$0.441534\pi$
$860$	−3.97652e77	−0.684376
$861$	−6.62291e76	−0.110526
$862$	−6.31214e77	−1.02149
$863$	−4.32424e77	−0.678615	−0.339307	−	0.940676i	$-0.610193\pi$
$863$	−4.32424e77	−0.678615	−0.339307	+	0.940676i	$0.610193\pi$
$864$	5.11261e77	0.778088
$865$	2.06449e77	0.304710
$866$	−1.45236e78	−2.07898
$867$	1.19866e77	0.166414
$868$	−3.46052e77	−0.465981
$869$	2.23115e77	0.291410
$870$	2.78183e77	0.352428
$871$	3.44971e77	0.423937
$872$	−1.83071e77	−0.218239
$873$	1.00290e78	1.15980
$874$	9.48195e77	1.06376
$875$	7.64765e76	0.0832367
$876$	−2.58535e77	−0.272999
$877$	3.01916e77	0.309313	0.154656	−	0.987968i	$-0.450573\pi$
$877$	3.01916e77	0.309313	0.154656	+	0.987968i	$0.450573\pi$
$878$	−2.19034e76	−0.0217725
$879$	2.08051e77	0.200662
$880$	−4.26530e77	−0.399171
$881$	−9.08145e77	−0.824696	−0.412348	−	0.911026i	$-0.635291\pi$
$881$	−9.08145e77	−0.824696	−0.412348	+	0.911026i	$0.635291\pi$
$882$	7.75198e77	0.683117
$883$	−1.16332e78	−0.994812	−0.497406	−	0.867518i	$-0.665714\pi$
$883$	−1.16332e78	−0.994812	−0.497406	+	0.867518i	$0.665714\pi$
$884$	1.87408e78	1.55526
$885$	−6.98386e77	−0.562470
$886$	−1.80819e77	−0.141336
$887$	7.38531e77	0.560264	0.280132	−	0.959962i	$-0.409622\pi$
$887$	7.38531e77	0.560264	0.280132	+	0.959962i	$0.409622\pi$
$888$	−4.62725e76	−0.0340705
$889$	−3.13249e77	−0.223868
$890$	−1.76059e78	−1.22130
$891$	−2.66762e77	−0.179624
$892$	−1.05704e78	−0.690911
$893$	4.08221e78	2.59019
$894$	−3.49548e77	−0.215309
$895$	−5.40658e77	−0.323305
$896$	−4.39643e77	−0.255233
$897$	−3.42903e77	−0.193273
$898$	1.35054e78	0.739069
$899$	−8.94826e77	−0.475452
$900$	−1.63908e78	−0.845615
$901$	−2.77547e78	−1.39037
$902$	−3.73696e77	−0.181780
$903$	−2.38664e77	−0.112736
$904$	−5.30934e76	−0.0243544
$905$	2.90446e78	1.29383
$906$	1.75522e78	0.759338
$907$	−2.54346e78	−1.06864	−0.534321	−	0.845281i	$-0.679433\pi$
$907$	−2.54346e78	−1.06864	−0.534321	+	0.845281i	$0.679433\pi$
$908$	−3.41778e78	−1.39466
$909$	−3.80727e77	−0.150894
$910$	4.98602e78	1.91936
$911$	4.02246e78	1.50403	0.752013	−	0.659149i	$-0.229083\pi$
$911$	4.02246e78	1.50403	0.752013	+	0.659149i	$0.229083\pi$
$912$	1.69460e78	0.615465
$913$	8.48506e77	0.299350
$914$	3.96514e78	1.35889
$915$	−2.34912e77	−0.0782070
$916$	−9.29427e77	−0.300598
$917$	1.28001e78	0.402186
$918$	−3.23273e78	−0.986822
$919$	−4.43829e78	−1.31630	−0.658150	−	0.752887i	$-0.728661\pi$
$919$	−4.43829e78	−1.31630	−0.658150	+	0.752887i	$0.728661\pi$
$920$	−4.19461e77	−0.120869
$921$	−7.95029e76	−0.0222588
$922$	−1.78900e78	−0.486676
$923$	−4.71916e78	−1.24744
$924$	1.68306e77	0.0432308
$925$	2.51874e78	0.628678
$926$	−3.72023e77	−0.0902357
$927$	−2.88992e78	−0.681198
$928$	3.41773e78	0.782919
$929$	−8.06660e78	−1.79587	−0.897934	−	0.440131i	$-0.854932\pi$
$929$	−8.06660e78	−1.79587	−0.897934	+	0.440131i	$0.854932\pi$
$930$	−2.25529e78	−0.487984
$931$	4.72207e78	0.993039
$932$	2.89274e78	0.591273
$933$	8.63535e75	0.00171560
$934$	−4.23779e77	−0.0818366
$935$	2.35699e78	0.442436
$936$	1.39560e78	0.254654
$937$	8.82372e76	0.0156514	0.00782569	−	0.999969i	$-0.497509\pi$
$937$	8.82372e76	0.0156514	0.00782569	+	0.999969i	$0.497509\pi$
$938$	−1.53837e78	−0.265269
$939$	2.62115e78	0.439394
$940$	1.09690e79	1.78763
$941$	1.02741e79	1.62787	0.813937	−	0.580954i	$-0.197320\pi$
$941$	1.02741e79	1.62787	0.813937	+	0.580954i	$0.197320\pi$
$942$	−1.09190e78	−0.168204
$943$	−1.56850e78	−0.234923
$944$	−9.81799e78	−1.42977
$945$	−3.97331e78	−0.562612
$946$	−1.34666e78	−0.185413
$947$	1.04239e79	1.39558	0.697792	−	0.716301i	$-0.254166\pi$
$947$	1.04239e79	1.39558	0.697792	+	0.716301i	$0.254166\pi$
$948$	−2.38186e78	−0.310095
$949$	−1.19824e79	−1.51701
$950$	−2.16125e79	−2.66090
$951$	4.27517e78	0.511882
$952$	1.37591e78	0.160218
$953$	1.23008e79	1.39306	0.696532	−	0.717526i	$-0.254725\pi$
$953$	1.23008e79	1.39306	0.696532	+	0.717526i	$0.254725\pi$
$954$	1.25541e79	1.38278
$955$	5.93998e78	0.636349
$956$	−1.57116e78	−0.163714
$957$	4.35209e77	0.0441095
$958$	−2.48961e79	−2.45440
$959$	−3.72113e78	−0.356847
$960$	3.31089e78	0.308857
$961$	−3.76513e78	−0.341672
$962$	1.30263e79	1.14996
$963$	1.10459e79	0.948646
$964$	2.20502e78	0.184235
$965$	−2.18302e79	−1.77454
$966$	1.52915e78	0.120936
$967$	−1.31832e79	−1.01442	−0.507211	−	0.861822i	$-0.669324\pi$
$967$	−1.31832e79	−1.01442	−0.507211	+	0.861822i	$0.669324\pi$
$968$	2.41777e78	0.181016
$969$	−9.36428e78	−0.682173
$970$	3.55332e79	2.51874
$971$	5.52826e77	0.0381311	0.0190655	−	0.999818i	$-0.493931\pi$
$971$	5.52826e77	0.0381311	0.0190655	+	0.999818i	$0.493931\pi$
$972$	1.02979e79	0.691185
$973$	6.87140e78	0.448802
$974$	−1.72105e79	−1.09391
$975$	7.81588e78	0.483455
$976$	−3.30241e78	−0.198798
$977$	−1.64164e78	−0.0961772	−0.0480886	−	0.998843i	$-0.515313\pi$
$977$	−1.64164e78	−0.0961772	−0.0480886	+	0.998843i	$0.515313\pi$
$978$	1.59783e76	0.000911067 0
$979$	−2.75439e78	−0.152856
$980$	1.26883e79	0.685349
$981$	−1.95299e79	−1.02676
$982$	4.00746e79	2.05076
$983$	9.35921e77	0.0466198	0.0233099	−	0.999728i	$-0.492580\pi$
$983$	9.35921e77	0.0466198	0.0233099	+	0.999728i	$0.492580\pi$
$984$	−6.56795e77	−0.0318463
$985$	1.03052e79	0.486402
$986$	−2.16105e79	−0.992948
$987$	6.58338e78	0.294472
$988$	−5.16364e79	−2.24852
$989$	−5.65226e78	−0.239619
$990$	−1.06612e79	−0.440021
$991$	−1.55923e79	−0.626553	−0.313277	−	0.949662i	$-0.601427\pi$
$991$	−1.55923e79	−0.626553	−0.313277	+	0.949662i	$0.601427\pi$
$992$	−2.77084e79	−1.08406
$993$	−1.22461e79	−0.466490
$994$	2.10448e79	0.780558
$995$	−4.40018e78	−0.158913
$996$	−9.05819e78	−0.318544
$997$	3.05684e79	1.04677	0.523385	−	0.852097i	$-0.324669\pi$
$997$	3.05684e79	1.04677	0.523385	+	0.852097i	$0.324669\pi$
$998$	5.70620e79	1.90278
$999$	−1.03805e79	−0.337080

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} +O(q^{10})\)	\(q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} -6.22689e26 q^{10} -9.74180e26 q^{11} +1.03998e28 q^{12} +4.82001e29 q^{13} -2.14945e30 q^{14} -6.47150e30 q^{15} -9.09771e31 q^{16} +5.02736e32 q^{17} -2.27399e33 q^{18} -1.38519e34 q^{19} -3.72202e34 q^{20} -2.23389e34 q^{21} -1.26047e35 q^{22} -5.29051e35 q^{23} -2.21535e35 q^{24} +1.20588e37 q^{25} +6.23649e37 q^{26} -4.96979e37 q^{27} -1.28480e38 q^{28} -3.32225e38 q^{29} -8.37331e38 q^{30} +2.69343e39 q^{31} -1.02874e40 q^{32} -1.30998e39 q^{33} +6.50477e40 q^{34} +7.99492e40 q^{35} -1.35924e41 q^{36} +2.08872e41 q^{37} -1.79226e42 q^{38} +6.48148e41 q^{39} +7.92857e41 q^{40} +2.96475e42 q^{41} -2.89037e42 q^{42} +1.06838e43 q^{43} -7.53423e42 q^{44} +8.45814e43 q^{45} -6.84525e43 q^{46} -2.94705e44 q^{47} -1.22337e44 q^{48} -3.40898e44 q^{49} +1.56026e45 q^{50} +6.76030e44 q^{51} +3.72776e45 q^{52} -5.52073e45 q^{53} -6.43028e45 q^{54} +4.68833e45 q^{55} +2.73685e45 q^{56} -1.86266e46 q^{57} -4.29858e46 q^{58} +1.07917e47 q^{59} -5.00501e46 q^{60} +3.62994e46 q^{61} +3.48496e47 q^{62} +2.91965e47 q^{63} -5.11611e47 q^{64} -2.31967e48 q^{65} -1.69495e47 q^{66} +7.15705e47 q^{67} +3.88812e48 q^{68} -7.11416e47 q^{69} +1.03444e49 q^{70} -9.79077e48 q^{71} +2.89542e48 q^{72} -2.48596e49 q^{73} +2.70254e49 q^{74} +1.62155e49 q^{75} -1.07129e50 q^{76} +1.61836e49 q^{77} +8.38622e49 q^{78} -2.29029e50 q^{79} +4.37835e50 q^{80} +2.73832e50 q^{81} +3.83601e50 q^{82} -8.70995e50 q^{83} -1.72767e50 q^{84} -2.41946e51 q^{85} +1.38235e51 q^{86} -4.46744e50 q^{87} +1.60493e50 q^{88} +2.82739e51 q^{89} +1.09438e52 q^{90} -8.00725e51 q^{91} -4.09163e51 q^{92} +3.62186e51 q^{93} -3.81311e52 q^{94} +6.66634e52 q^{95} -1.38335e52 q^{96} -5.70641e52 q^{97} -4.41079e52 q^{98} +1.71212e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!12 q^{9}+O(q^{10}) \) 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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