LMFDB - Embedded newform 1.54.a.a.1.3

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			1.3
Root			$447512.$ 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)

$f(q)$	$=$	$q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +O(q^{10})$	\(q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +1.39065e26 q^{10} -3.50807e27 q^{11} +2.48436e28 q^{12} -3.76599e28 q^{13} +6.03245e29 q^{14} -1.60314e31 q^{15} +6.35303e31 q^{16} -5.80067e32 q^{17} -2.71559e32 q^{18} -9.40144e33 q^{19} -4.48772e34 q^{20} -6.95421e34 q^{21} -9.06556e34 q^{22} -5.69353e35 q^{23} +1.33543e36 q^{24} +1.78568e37 q^{25} -9.73207e35 q^{26} +8.90492e37 q^{27} -1.94671e38 q^{28} -2.46957e38 q^{29} -4.14284e38 q^{30} -4.25695e39 q^{31} +5.67942e39 q^{32} +1.04508e40 q^{33} -1.49901e40 q^{34} +1.25620e41 q^{35} +8.76338e40 q^{36} -5.85991e41 q^{37} -2.42952e41 q^{38} +1.12191e41 q^{39} -2.41231e42 q^{40} +5.37725e42 q^{41} -1.79711e42 q^{42} +1.54488e43 q^{43} +2.92552e43 q^{44} -5.65495e43 q^{45} -1.47132e43 q^{46} -1.14085e44 q^{47} -1.89261e44 q^{48} -7.19501e43 q^{49} +4.61455e44 q^{50} +1.72806e45 q^{51} +3.14060e44 q^{52} +8.51129e44 q^{53} +2.30121e45 q^{54} -1.88782e46 q^{55} -1.04643e46 q^{56} +2.80075e46 q^{57} -6.38187e45 q^{58} -9.48774e46 q^{59} +1.33692e47 q^{60} +3.37366e47 q^{61} -1.10008e47 q^{62} -2.45304e47 q^{63} -4.25463e47 q^{64} -2.02661e47 q^{65} +2.70069e47 q^{66} -3.70994e48 q^{67} +4.83740e48 q^{68} +1.69614e48 q^{69} +3.24628e48 q^{70} +2.16582e48 q^{71} +4.71061e48 q^{72} -1.03616e49 q^{73} -1.51432e49 q^{74} -5.31966e49 q^{75} +7.84022e49 q^{76} -8.18910e49 q^{77} +2.89925e48 q^{78} +5.02034e49 q^{79} +3.41879e50 q^{80} -6.15963e49 q^{81} +1.38959e50 q^{82} -3.18305e50 q^{83} +5.79939e50 q^{84} -3.12155e51 q^{85} +3.99229e50 q^{86} +7.35702e50 q^{87} +1.57257e51 q^{88} +3.04162e51 q^{89} -1.46135e51 q^{90} -8.79117e50 q^{91} +4.74806e51 q^{92} +1.26817e52 q^{93} -2.94817e51 q^{94} -5.05925e52 q^{95} -1.69194e52 q^{96} +4.29374e52 q^{97} -1.85933e51 q^{98} +3.68643e52 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.58420e7	0.272290	0.136145	−	0.990689i	$-0.456529\pi$
$2$	2.58420e7	0.272290	0.136145	+	0.990689i	$0.456529\pi$
$3$	−2.97907e12	−0.676654	−0.338327	−	0.941029i	$-0.609861\pi$
$3$	−2.97907e12	−0.676654	−0.338327	+	0.941029i	$0.609861\pi$
$4$	−8.33939e15	−0.925858
$5$	5.38136e18	1.61505	0.807527	−	0.589831i	$-0.200806\pi$
$5$	5.38136e18	1.61505	0.807527	+	0.589831i	$0.200806\pi$
$6$	−7.69850e19	−0.184246
$7$	2.33436e22	0.939874	0.469937	−	0.882700i	$-0.344277\pi$
$7$	2.33436e22	0.939874	0.469937	+	0.882700i	$0.344277\pi$
$8$	−4.48271e23	−0.524392
$9$	−1.05084e25	−0.542139
$10$	1.39065e26	0.439763
$11$	−3.50807e27	−0.887487	−0.443744	−	0.896154i	$-0.646350\pi$
$11$	−3.50807e27	−0.887487	−0.443744	+	0.896154i	$0.646350\pi$
$12$	2.48436e28	0.626486
$13$	−3.76599e28	−0.113862	−0.0569312	−	0.998378i	$-0.518132\pi$
$13$	−3.76599e28	−0.113862	−0.0569312	+	0.998378i	$0.518132\pi$
$14$	6.03245e29	0.255918
$15$	−1.60314e31	−1.09283
$16$	6.35303e31	0.783072
$17$	−5.80067e32	−1.43411	−0.717053	−	0.697018i	$-0.754510\pi$
$17$	−5.80067e32	−1.43411	−0.717053	+	0.697018i	$0.754510\pi$
$18$	−2.71559e32	−0.147619
$19$	−9.40144e33	−1.21962	−0.609809	−	0.792548i	$-0.708754\pi$
$19$	−9.40144e33	−1.21962	−0.609809	+	0.792548i	$0.708754\pi$
$20$	−4.48772e34	−1.49531
$21$	−6.95421e34	−0.635970
$22$	−9.06556e34	−0.241654
$23$	−5.69353e35	−0.467298	−0.233649	−	0.972321i	$-0.575067\pi$
$23$	−5.69353e35	−0.467298	−0.233649	+	0.972321i	$0.575067\pi$
$24$	1.33543e36	0.354832
$25$	1.78568e37	1.60840
$26$	−9.73207e35	−0.0310035
$27$	8.90492e37	1.04349
$28$	−1.94671e38	−0.870190
$29$	−2.46957e38	−0.435587	−0.217794	−	0.975995i	$-0.569886\pi$
$29$	−2.46957e38	−0.435587	−0.217794	+	0.975995i	$0.569886\pi$
$30$	−4.14284e38	−0.297567
$31$	−4.25695e39	−1.28237	−0.641185	−	0.767386i	$-0.721557\pi$
$31$	−4.25695e39	−1.28237	−0.641185	+	0.767386i	$0.721557\pi$
$32$	5.67942e39	0.737614
$33$	1.04508e40	0.600522
$34$	−1.49901e40	−0.390493
$35$	1.25620e41	1.51795
$36$	8.76338e40	0.501944
$37$	−5.85991e41	−1.62385	−0.811924	−	0.583764i	$-0.801580\pi$
$37$	−5.85991e41	−1.62385	−0.811924	+	0.583764i	$0.801580\pi$
$38$	−2.42952e41	−0.332090
$39$	1.12191e41	0.0770454
$40$	−2.41231e42	−0.846920
$41$	5.37725e42	0.981269	0.490634	−	0.871366i	$-0.336765\pi$
$41$	5.37725e42	0.981269	0.490634	+	0.871366i	$0.336765\pi$
$42$	−1.79711e42	−0.173168
$43$	1.54488e43	0.797961	0.398981	−	0.916959i	$-0.369364\pi$
$43$	1.54488e43	0.797961	0.398981	+	0.916959i	$0.369364\pi$
$44$	2.92552e43	0.821687
$45$	−5.65495e43	−0.875583
$46$	−1.47132e43	−0.127241
$47$	−1.14085e44	−0.557999	−0.279000	−	0.960291i	$-0.590003\pi$
$47$	−1.14085e44	−0.557999	−0.279000	+	0.960291i	$0.590003\pi$
$48$	−1.89261e44	−0.529869
$49$	−7.19501e43	−0.116637
$50$	4.61455e44	0.437950
$51$	1.72806e45	0.970395
$52$	3.14060e44	0.105420
$53$	8.51129e44	0.172459	0.0862293	−	0.996275i	$-0.472518\pi$
$53$	8.51129e44	0.172459	0.0862293	+	0.996275i	$0.472518\pi$
$54$	2.30121e45	0.284133
$55$	−1.88782e46	−1.43334
$56$	−1.04643e46	−0.492862
$57$	2.80075e46	0.825260
$58$	−6.38187e45	−0.118606
$59$	−9.48774e46	−1.12095	−0.560473	−	0.828173i	$-0.689380\pi$
$59$	−9.48774e46	−1.12095	−0.560473	+	0.828173i	$0.689380\pi$
$60$	1.33692e47	1.01181
$61$	3.37366e47	1.64764	0.823818	−	0.566854i	$-0.191840\pi$
$61$	3.37366e47	1.64764	0.823818	+	0.566854i	$0.191840\pi$
$62$	−1.10008e47	−0.349176
$63$	−2.45304e47	−0.509542
$64$	−4.25463e47	−0.582227
$65$	−2.02661e47	−0.183894
$66$	2.70069e47	0.163516
$67$	−3.70994e48	−1.50794	−0.753971	−	0.656908i	$-0.771864\pi$
$67$	−3.70994e48	−1.50794	−0.753971	+	0.656908i	$0.771864\pi$
$68$	4.83740e48	1.32778
$69$	1.69614e48	0.316199
$70$	3.24628e48	0.413321
$71$	2.16582e48	0.189355	0.0946774	−	0.995508i	$-0.469818\pi$
$71$	2.16582e48	0.189355	0.0946774	+	0.995508i	$0.469818\pi$
$72$	4.71061e48	0.284293
$73$	−1.03616e49	−0.433882	−0.216941	−	0.976185i	$-0.569608\pi$
$73$	−1.03616e49	−0.433882	−0.216941	+	0.976185i	$0.569608\pi$
$74$	−1.51432e49	−0.442157
$75$	−5.31966e49	−1.08833
$76$	7.84022e49	1.12919
$77$	−8.18910e49	−0.834126
$78$	2.89925e48	0.0209787
$79$	5.02034e49	0.259188	0.129594	−	0.991567i	$-0.458633\pi$
$79$	5.02034e49	0.259188	0.129594	+	0.991567i	$0.458633\pi$
$80$	3.41879e50	1.26470
$81$	−6.15963e49	−0.163946
$82$	1.38959e50	0.267189
$83$	−3.18305e50	−0.443889	−0.221944	−	0.975059i	$-0.571240\pi$
$83$	−3.18305e50	−0.443889	−0.221944	+	0.975059i	$0.571240\pi$
$84$	5.79939e50	0.588818
$85$	−3.12155e51	−2.31616
$86$	3.99229e50	0.217277
$87$	7.35702e50	0.294742
$88$	1.57257e51	0.465391
$89$	3.04162e51	0.667222	0.333611	−	0.942711i	$-0.391733\pi$
$89$	3.04162e51	0.667222	0.333611	+	0.942711i	$0.391733\pi$
$90$	−1.46135e51	−0.238412
$91$	−8.79117e50	−0.107016
$92$	4.74806e51	0.432652
$93$	1.26817e52	0.867721
$94$	−2.94817e51	−0.151938
$95$	−5.05925e52	−1.96975
$96$	−1.69194e52	−0.499110
$97$	4.29374e52	0.962465	0.481232	−	0.876593i	$-0.340189\pi$
$97$	4.29374e52	0.962465	0.481232	+	0.876593i	$0.340189\pi$
$98$	−1.85933e51	−0.0317590
$99$	3.68643e52	0.481141
$100$	−1.48915e53	−1.48915
$101$	2.40879e53	1.85047	0.925236	−	0.379392i	$-0.123867\pi$
$101$	2.40879e53	1.85047	0.925236	+	0.379392i	$0.123867\pi$
$102$	4.46565e52	0.264229
$103$	5.77425e52	0.263821	0.131910	−	0.991262i	$-0.457889\pi$
$103$	5.77425e52	0.263821	0.131910	+	0.991262i	$0.457889\pi$
$104$	1.68818e52	0.0597084
$105$	−3.74231e53	−1.02713
$106$	2.19949e52	0.0469587
$107$	−2.30554e53	−0.383797	−0.191899	−	0.981415i	$-0.561465\pi$
$107$	−2.30554e53	−0.383797	−0.191899	+	0.981415i	$0.561465\pi$
$108$	−7.42616e53	−0.966128
$109$	5.84013e53	0.595142	0.297571	−	0.954700i	$-0.403824\pi$
$109$	5.84013e53	0.595142	0.297571	+	0.954700i	$0.403824\pi$
$110$	−4.87850e53	−0.390284
$111$	1.74571e54	1.09878
$112$	1.48303e54	0.735989
$113$	−4.64679e53	−0.182211	−0.0911055	−	0.995841i	$-0.529040\pi$
$113$	−4.64679e53	−0.182211	−0.0911055	+	0.995841i	$0.529040\pi$
$114$	7.23770e53	0.224710
$115$	−3.06389e54	−0.754711
$116$	2.05947e54	0.403292
$117$	3.95745e53	0.0617292
$118$	−2.45182e54	−0.305222
$119$	−1.35408e55	−1.34788
$120$	7.18642e54	0.573072
$121$	−3.31816e54	−0.212366
$122$	8.71823e54	0.448634
$123$	−1.60192e55	−0.663980
$124$	3.55003e55	1.18729
$125$	3.63487e55	0.982593
$126$	−6.33915e54	−0.138743
$127$	1.05751e54	0.0187709	0.00938545	−	0.999956i	$-0.497012\pi$
$127$	1.05751e54	0.0187709	0.00938545	+	0.999956i	$0.497012\pi$
$128$	−6.21504e55	−0.896149
$129$	−4.60231e55	−0.539944
$130$	−5.23717e54	−0.0500724
$131$	9.48285e55	0.740031	0.370015	−	0.929026i	$-0.379352\pi$
$131$	9.48285e55	0.740031	0.370015	+	0.929026i	$0.379352\pi$
$132$	−8.71531e55	−0.555998
$133$	−2.19463e56	−1.14629
$134$	−9.58722e55	−0.410597
$135$	4.79206e56	1.68530
$136$	2.60027e56	0.752034
$137$	1.67624e56	0.399248	0.199624	−	0.979873i	$-0.436028\pi$
$137$	1.67624e56	0.399248	0.199624	+	0.979873i	$0.436028\pi$
$138$	4.38317e55	0.0860978
$139$	−6.36794e55	−0.103301	−0.0516507	−	0.998665i	$-0.516448\pi$
$139$	−6.36794e55	−0.103301	−0.0516507	+	0.998665i	$0.516448\pi$
$140$	−1.04760e57	−1.40540
$141$	3.39865e56	0.377573
$142$	5.59692e55	0.0515594
$143$	1.32113e56	0.101051
$144$	−6.67603e56	−0.424534
$145$	−1.32897e57	−0.703496
$146$	−2.67765e56	−0.118142
$147$	2.14344e56	0.0789227
$148$	4.88681e57	1.50345
$149$	5.30162e55	0.0136450	0.00682249	−	0.999977i	$-0.497828\pi$
$149$	5.30162e55	0.0136450	0.00682249	+	0.999977i	$0.497828\pi$
$150$	−1.37471e57	−0.296341
$151$	−3.81438e56	−0.0689500	−0.0344750	−	0.999406i	$-0.510976\pi$
$151$	−3.81438e56	−0.0689500	−0.0344750	+	0.999406i	$0.510976\pi$
$152$	4.21439e57	0.639557
$153$	6.09558e57	0.777485
$154$	−2.11623e57	−0.227124
$155$	−2.29082e58	−2.07110
$156$	−9.35606e56	−0.0713331
$157$	−2.25055e57	−0.144860	−0.0724298	−	0.997374i	$-0.523075\pi$
$157$	−2.25055e57	−0.144860	−0.0724298	+	0.997374i	$0.523075\pi$
$158$	1.29736e57	0.0705744
$159$	−2.53557e57	−0.116695
$160$	3.05630e58	1.19129
$161$	−1.32907e58	−0.439201
$162$	−1.59177e57	−0.0446409
$163$	5.68137e58	1.35357	0.676786	−	0.736180i	$-0.263372\pi$
$163$	5.68137e58	1.35357	0.676786	+	0.736180i	$0.263372\pi$
$164$	−4.48430e58	−0.908516
$165$	5.62394e58	0.969875
$166$	−8.22564e57	−0.120866
$167$	−5.90727e58	−0.740288	−0.370144	−	0.928974i	$-0.620692\pi$
$167$	−5.90727e58	−0.740288	−0.370144	+	0.928974i	$0.620692\pi$
$168$	3.11737e58	0.333497
$169$	−1.07977e59	−0.987035
$170$	−8.06670e58	−0.630666
$171$	9.87942e58	0.661202
$172$	−1.28834e59	−0.738799
$173$	5.53658e58	0.272282	0.136141	−	0.990689i	$-0.456530\pi$
$173$	5.53658e58	0.272282	0.136141	+	0.990689i	$0.456530\pi$
$174$	1.90120e58	0.0802552
$175$	4.16842e59	1.51169
$176$	−2.22869e59	−0.694966
$177$	2.82646e59	0.758492
$178$	7.86016e58	0.181678
$179$	−7.91775e59	−1.57760	−0.788799	−	0.614651i	$-0.789297\pi$
$179$	−7.91775e59	−1.57760	−0.788799	+	0.614651i	$0.789297\pi$
$180$	4.71589e59	0.810666
$181$	6.76480e59	1.00409	0.502045	−	0.864841i	$-0.332581\pi$
$181$	6.76480e59	1.00409	0.502045	+	0.864841i	$0.332581\pi$
$182$	−2.27181e58	−0.0291394
$183$	−1.00504e60	−1.11488
$184$	2.55224e59	0.245047
$185$	−3.15343e60	−2.62260
$186$	3.27721e59	0.236272
$187$	2.03491e60	1.27275
$188$	9.51396e59	0.516628
$189$	2.07873e60	0.980754
$190$	−1.30741e60	−0.536342
$191$	5.29979e59	0.189180	0.0945899	−	0.995516i	$-0.469846\pi$
$191$	5.29979e59	0.189180	0.0945899	+	0.995516i	$0.469846\pi$
$192$	1.26748e60	0.393966
$193$	−9.36608e59	−0.253682	−0.126841	−	0.991923i	$-0.540484\pi$
$193$	−9.36608e59	−0.253682	−0.126841	+	0.991923i	$0.540484\pi$
$194$	1.10959e60	0.262069
$195$	6.03741e59	0.124432
$196$	6.00020e59	0.107989
$197$	−1.14277e61	−1.79723	−0.898615	−	0.438737i	$-0.855426\pi$
$197$	−1.14277e61	−1.79723	−0.898615	+	0.438737i	$0.855426\pi$
$198$	9.52646e59	0.131010
$199$	7.32212e59	0.0881110	0.0440555	−	0.999029i	$-0.485972\pi$
$199$	7.32212e59	0.0881110	0.0440555	+	0.999029i	$0.485972\pi$
$200$	−8.00468e60	−0.843430
$201$	1.10521e61	1.02035
$202$	6.22480e60	0.503865
$203$	−5.76487e60	−0.409397
$204$	−1.44109e61	−0.898448
$205$	2.89369e61	1.58480
$206$	1.49218e60	0.0718357
$207$	5.98300e60	0.253341
$208$	−2.39254e60	−0.0891624
$209$	3.29809e61	1.08240
$210$	−9.67088e60	−0.279676
$211$	−7.50377e61	−1.91335	−0.956676	−	0.291156i	$-0.905960\pi$
$211$	−7.50377e61	−1.91335	−0.956676	+	0.291156i	$0.905960\pi$
$212$	−7.09790e60	−0.159672
$213$	−6.45212e60	−0.128128
$214$	−5.95797e60	−0.104504
$215$	8.31358e61	1.28875
$216$	−3.99182e61	−0.547200
$217$	−9.93724e61	−1.20527
$218$	1.50921e61	0.162051
$219$	3.08679e61	0.293588
$220$	1.57433e62	1.32707
$221$	2.18452e61	0.163291
$222$	4.51125e61	0.299188
$223$	−1.22197e61	−0.0719419	−0.0359710	−	0.999353i	$-0.511452\pi$
$223$	−1.22197e61	−0.0719419	−0.0359710	+	0.999353i	$0.511452\pi$
$224$	1.32578e62	0.693264
$225$	−1.87647e62	−0.871975
$226$	−1.20082e61	−0.0496142
$227$	−5.02981e61	−0.184870	−0.0924350	−	0.995719i	$-0.529465\pi$
$227$	−5.02981e61	−0.184870	−0.0924350	+	0.995719i	$0.529465\pi$
$228$	−2.33565e62	−0.764073
$229$	−3.41310e62	−0.994281	−0.497140	−	0.867670i	$-0.665617\pi$
$229$	−3.41310e62	−0.994281	−0.497140	+	0.867670i	$0.665617\pi$
$230$	−7.91771e61	−0.205500
$231$	2.43959e62	0.564415
$232$	1.10704e62	0.228418
$233$	5.82407e62	1.07225	0.536123	−	0.844140i	$-0.319888\pi$
$233$	5.82407e62	1.07225	0.536123	+	0.844140i	$0.319888\pi$
$234$	1.02269e61	0.0168082
$235$	−6.13930e62	−0.901198
$236$	7.91219e62	1.03784
$237$	−1.49559e62	−0.175381
$238$	−3.49923e62	−0.367014
$239$	1.01634e63	0.953879	0.476939	−	0.878936i	$-0.341746\pi$
$239$	1.01634e63	0.953879	0.476939	+	0.878936i	$0.341746\pi$
$240$	−1.01848e63	−0.855766
$241$	2.10470e63	1.58394	0.791970	−	0.610560i	$-0.209056\pi$
$241$	2.10470e63	1.58394	0.791970	+	0.610560i	$0.209056\pi$
$242$	−8.57480e61	−0.0578252
$243$	−1.54256e63	−0.932560
$244$	−2.81343e63	−1.52548
$245$	−3.87189e62	−0.188374
$246$	−4.13968e62	−0.180795
$247$	3.54057e62	0.138868
$248$	1.90826e63	0.672464
$249$	9.48252e62	0.300359
$250$	9.39324e62	0.267550
$251$	−3.46671e63	−0.888309	−0.444154	−	0.895950i	$-0.646496\pi$
$251$	−3.46671e63	−0.888309	−0.444154	+	0.895950i	$0.646496\pi$
$252$	2.04569e63	0.471764
$253$	1.99733e63	0.414721
$254$	2.73281e61	0.00511113
$255$	9.29929e63	1.56724
$256$	2.22614e63	0.338215
$257$	−7.98120e63	−1.09355	−0.546777	−	0.837278i	$-0.684146\pi$
$257$	−7.98120e63	−1.09355	−0.546777	+	0.837278i	$0.684146\pi$
$258$	−1.18933e63	−0.147021
$259$	−1.36791e64	−1.52621
$260$	1.69007e63	0.170259
$261$	2.59513e63	0.236149
$262$	2.45056e63	0.201503
$263$	−6.73466e63	−0.500597	−0.250299	−	0.968169i	$-0.580529\pi$
$263$	−6.73466e63	−0.500597	−0.250299	+	0.968169i	$0.580529\pi$
$264$	−4.68478e63	−0.314909
$265$	4.58023e63	0.278530
$266$	−5.67137e63	−0.312122
$267$	−9.06119e63	−0.451478
$268$	3.09386e64	1.39614
$269$	1.44464e64	0.590640	0.295320	−	0.955398i	$-0.404574\pi$
$269$	1.44464e64	0.590640	0.295320	+	0.955398i	$0.404574\pi$
$270$	1.23836e64	0.458890
$271$	2.71685e64	0.912810	0.456405	−	0.889772i	$-0.349137\pi$
$271$	2.71685e64	0.912810	0.456405	+	0.889772i	$0.349137\pi$
$272$	−3.68518e64	−1.12301
$273$	2.61895e63	0.0724130
$274$	4.33175e63	0.108711
$275$	−6.26429e64	−1.42743
$276$	−1.41448e64	−0.292756
$277$	2.80661e64	0.527798	0.263899	−	0.964550i	$-0.414991\pi$
$277$	2.80661e64	0.527798	0.263899	+	0.964550i	$0.414991\pi$
$278$	−1.64560e63	−0.0281279
$279$	4.47338e64	0.695223
$280$	−5.63119e64	−0.795998
$281$	−2.78031e64	−0.357582	−0.178791	−	0.983887i	$-0.557219\pi$
$281$	−2.78031e64	−0.357582	−0.178791	+	0.983887i	$0.557219\pi$
$282$	8.78280e63	0.102809
$283$	−6.35233e64	−0.677006	−0.338503	−	0.940965i	$-0.609920\pi$
$283$	−6.35233e64	−0.677006	−0.338503	+	0.940965i	$0.609920\pi$
$284$	−1.80616e64	−0.175316
$285$	1.50718e65	1.33284
$286$	3.41408e63	0.0275153
$287$	1.25524e65	0.922269
$288$	−5.96816e64	−0.399889
$289$	1.72874e65	1.05666
$290$	−3.43432e64	−0.191555
$291$	−1.27913e65	−0.651256
$292$	8.64095e64	0.401713
$293$	−1.18763e65	−0.504300	−0.252150	−	0.967688i	$-0.581138\pi$
$293$	−1.18763e65	−0.504300	−0.252150	+	0.967688i	$0.581138\pi$
$294$	5.53908e63	0.0214899
$295$	−5.10569e65	−1.81039
$296$	2.62683e65	0.851532
$297$	−3.12391e65	−0.926089
$298$	1.37005e63	0.00371539
$299$	2.14418e64	0.0532076
$300$	4.43627e65	1.00764
$301$	3.60632e65	0.749983
$302$	−9.85711e63	−0.0187744
$303$	−7.17594e65	−1.25213
$304$	−5.97276e65	−0.955048
$305$	1.81549e66	2.66102
$306$	1.57522e65	0.211701
$307$	−1.02441e65	−0.126271	−0.0631357	−	0.998005i	$-0.520110\pi$
$307$	−1.02441e65	−0.126271	−0.0631357	+	0.998005i	$0.520110\pi$
$308$	6.82921e65	0.772283
$309$	−1.72019e65	−0.178515
$310$	−5.91993e65	−0.563938
$311$	−2.08869e66	−1.82694	−0.913469	−	0.406909i	$-0.866607\pi$
$311$	−2.08869e66	−1.82694	−0.913469	+	0.406909i	$0.866607\pi$
$312$	−5.02920e64	−0.0404020
$313$	8.41675e65	0.621183	0.310591	−	0.950543i	$-0.399473\pi$
$313$	8.41675e65	0.621183	0.310591	+	0.950543i	$0.399473\pi$
$314$	−5.81587e64	−0.0394438
$315$	−1.32007e66	−0.822938
$316$	−4.18666e65	−0.239972
$317$	1.89204e66	0.997378	0.498689	−	0.866781i	$-0.333815\pi$
$317$	1.89204e66	0.997378	0.498689	+	0.866781i	$0.333815\pi$
$318$	−6.55242e64	−0.0317748
$319$	8.66344e65	0.386578
$320$	−2.28957e66	−0.940328
$321$	6.86835e65	0.259698
$322$	−3.43460e65	−0.119590
$323$	5.45346e66	1.74906
$324$	5.13676e65	0.151791
$325$	−6.72484e65	−0.183136
$326$	1.46818e66	0.368564
$327$	−1.73981e66	−0.402705
$328$	−2.41046e66	−0.514569
$329$	−2.66314e66	−0.524449
$330$	1.45334e66	0.264087
$331$	−3.72579e66	−0.624850	−0.312425	−	0.949942i	$-0.601141\pi$
$331$	−3.72579e66	−0.624850	−0.312425	+	0.949942i	$0.601141\pi$
$332$	2.65447e66	0.410978
$333$	6.15784e66	0.880351
$334$	−1.52656e66	−0.201573
$335$	−1.99645e67	−2.43540
$336$	−4.41803e66	−0.498010
$337$	9.36606e66	0.975808	0.487904	−	0.872897i	$-0.337762\pi$
$337$	9.36606e66	0.975808	0.487904	+	0.872897i	$0.337762\pi$
$338$	−2.79034e66	−0.268760
$339$	1.38431e66	0.123294
$340$	2.60318e67	2.14443
$341$	1.49337e67	1.13809
$342$	2.55304e66	0.180039
$343$	−1.60796e67	−1.04950
$344$	−6.92526e66	−0.418444
$345$	9.12754e66	0.510679
$346$	1.43076e66	0.0741397
$347$	−2.74862e67	−1.31942	−0.659711	−	0.751520i	$-0.729321\pi$
$347$	−2.74862e67	−1.31942	−0.659711	+	0.751520i	$0.729321\pi$
$348$	−6.13531e66	−0.272889
$349$	1.18632e67	0.489024	0.244512	−	0.969646i	$-0.421372\pi$
$349$	1.18632e67	0.489024	0.244512	+	0.969646i	$0.421372\pi$
$350$	1.07720e67	0.411618
$351$	−3.35358e66	−0.118815
$352$	−1.99238e67	−0.654623
$353$	−2.74837e67	−0.837618	−0.418809	−	0.908074i	$-0.637552\pi$
$353$	−2.74837e67	−0.837618	−0.418809	+	0.908074i	$0.637552\pi$
$354$	7.30414e66	0.206530
$355$	1.16551e67	0.305818
$356$	−2.53653e67	−0.617753
$357$	4.03391e67	0.912049
$358$	−2.04610e67	−0.429564
$359$	3.20694e67	0.625299	0.312649	−	0.949869i	$-0.398784\pi$
$359$	3.20694e67	0.625299	0.312649	+	0.949869i	$0.398784\pi$
$360$	2.53495e67	0.459149
$361$	2.89659e67	0.487468
$362$	1.74816e67	0.273404
$363$	9.88503e66	0.143699
$364$	7.33130e66	0.0990819
$365$	−5.57595e67	−0.700742
$366$	−2.59722e67	−0.303570
$367$	6.14979e67	0.668666	0.334333	−	0.942455i	$-0.391489\pi$
$367$	6.14979e67	0.668666	0.334333	+	0.942455i	$0.391489\pi$
$368$	−3.61712e67	−0.365928
$369$	−5.65063e67	−0.531984
$370$	−8.14909e67	−0.714107
$371$	1.98684e67	0.162089
$372$	−1.05758e68	−0.803387
$373$	1.08656e68	0.768723	0.384362	−	0.923183i	$-0.374422\pi$
$373$	1.08656e68	0.768723	0.384362	+	0.923183i	$0.374422\pi$
$374$	5.25863e67	0.346557
$375$	−1.08285e68	−0.664876
$376$	5.11408e67	0.292610
$377$	9.30038e66	0.0495970
$378$	5.37185e67	0.267049
$379$	−2.80807e68	−1.30158	−0.650788	−	0.759259i	$-0.725561\pi$
$379$	−2.80807e68	−1.30158	−0.650788	+	0.759259i	$0.725561\pi$
$380$	4.21911e68	1.82371
$381$	−3.15039e66	−0.0127014
$382$	1.36957e67	0.0515117
$383$	4.61965e68	1.62122	0.810610	−	0.585586i	$-0.199136\pi$
$383$	4.61965e68	1.62122	0.810610	+	0.585586i	$0.199136\pi$
$384$	1.85150e68	0.606383
$385$	−4.40685e68	−1.34716
$386$	−2.42038e67	−0.0690749
$387$	−1.62343e68	−0.432606
$388$	−3.58072e68	−0.891106
$389$	−3.34377e68	−0.777271	−0.388636	−	0.921392i	$-0.627053\pi$
$389$	−3.34377e68	−0.777271	−0.388636	+	0.921392i	$0.627053\pi$
$390$	1.56019e67	0.0338817
$391$	3.30263e68	0.670155
$392$	3.22531e67	0.0611633
$393$	−2.82500e68	−0.500745
$394$	−2.95315e68	−0.489368
$395$	2.70163e68	0.418603
$396$	−3.07425e68	−0.445469
$397$	2.89097e68	0.391827	0.195914	−	0.980621i	$-0.437233\pi$
$397$	2.89097e68	0.391827	0.195914	+	0.980621i	$0.437233\pi$
$398$	1.89218e67	0.0239917
$399$	6.53796e68	0.775640
$400$	1.13445e69	1.25949
$401$	4.66806e67	0.0485077	0.0242538	−	0.999706i	$-0.492279\pi$
$401$	4.66806e67	0.0485077	0.0242538	+	0.999706i	$0.492279\pi$
$402$	2.85610e68	0.277832
$403$	1.60316e68	0.146014
$404$	−2.00878e69	−1.71327
$405$	−3.31472e68	−0.264782
$406$	−1.48976e68	−0.111475
$407$	2.05570e69	1.44114
$408$	−7.74637e68	−0.508867
$409$	−5.42643e68	−0.334077	−0.167039	−	0.985950i	$-0.553420\pi$
$409$	−5.42643e68	−0.334077	−0.167039	+	0.985950i	$0.553420\pi$
$410$	7.47788e68	0.431525
$411$	−4.99364e68	−0.270153
$412$	−4.81537e68	−0.244261
$413$	−2.21478e69	−1.05355
$414$	1.54613e68	0.0689820
$415$	−1.71291e69	−0.716904
$416$	−2.13886e68	−0.0839864
$417$	1.89705e68	0.0698994
$418$	8.52293e68	0.294725
$419$	2.80482e69	0.910403	0.455202	−	0.890388i	$-0.349567\pi$
$419$	2.80482e69	0.910403	0.455202	+	0.890388i	$0.349567\pi$
$420$	3.12086e69	0.950972
$421$	4.47945e69	1.28159	0.640795	−	0.767712i	$-0.278605\pi$
$421$	4.47945e69	1.28159	0.640795	+	0.767712i	$0.278605\pi$
$422$	−1.93913e69	−0.520986
$423$	1.19885e69	0.302513
$424$	−3.81536e68	−0.0904359
$425$	−1.03581e70	−2.30661
$426$	−1.66736e68	−0.0348879
$427$	7.87535e69	1.54857
$428$	1.92268e69	0.355342
$429$	−3.93575e68	−0.0683768
$430$	2.14840e69	0.350914
$431$	−1.07297e70	−1.64793	−0.823967	−	0.566638i	$-0.808244\pi$
$431$	−1.07297e70	−1.64793	−0.823967	+	0.566638i	$0.808244\pi$
$432$	5.65733e69	0.817131
$433$	−1.28857e70	−1.75057	−0.875286	−	0.483606i	$-0.839327\pi$
$433$	−1.28857e70	−1.75057	−0.875286	+	0.483606i	$0.839327\pi$
$434$	−2.56798e69	−0.328182
$435$	3.95908e69	0.476024
$436$	−4.87031e69	−0.551017
$437$	5.35274e69	0.569925
$438$	7.97689e68	0.0799410
$439$	2.10965e69	0.199022	0.0995111	−	0.995036i	$-0.468272\pi$
$439$	2.10965e69	0.199022	0.0995111	+	0.995036i	$0.468272\pi$
$440$	8.46254e69	0.751631
$441$	7.56081e68	0.0632333
$442$	5.64525e68	0.0444624
$443$	1.77505e70	1.31678	0.658389	−	0.752678i	$-0.271238\pi$
$443$	1.77505e70	1.31678	0.658389	+	0.752678i	$0.271238\pi$
$444$	−1.45581e70	−1.01732
$445$	1.63681e70	1.07760
$446$	−3.15782e68	−0.0195891
$447$	−1.57939e68	−0.00923293
$448$	−9.93183e69	−0.547220
$449$	−7.87557e69	−0.409029	−0.204515	−	0.978864i	$-0.565562\pi$
$449$	−7.87557e69	−0.409029	−0.204515	+	0.978864i	$0.565562\pi$
$450$	−4.84916e69	−0.237430
$451$	−1.88638e70	−0.870863
$452$	3.87514e69	0.168702
$453$	1.13633e69	0.0466553
$454$	−1.29980e69	−0.0503382
$455$	−4.73084e69	−0.172837
$456$	−1.25549e70	−0.432759
$457$	3.48981e70	1.13507	0.567536	−	0.823349i	$-0.307897\pi$
$457$	3.48981e70	1.13507	0.567536	+	0.823349i	$0.307897\pi$
$458$	−8.82014e69	−0.270733
$459$	−5.16545e70	−1.49648
$460$	2.55510e70	0.698756
$461$	4.79728e70	1.23857	0.619286	−	0.785166i	$-0.287422\pi$
$461$	4.79728e70	1.23857	0.619286	+	0.785166i	$0.287422\pi$
$462$	6.30438e69	0.153684
$463$	−5.09571e70	−1.17303	−0.586514	−	0.809939i	$-0.699500\pi$
$463$	−5.09571e70	−1.17303	−0.586514	+	0.809939i	$0.699500\pi$
$464$	−1.56893e70	−0.341096
$465$	6.82449e70	1.40142
$466$	1.50506e70	0.291962
$467$	8.74085e70	1.60198	0.800989	−	0.598680i	$-0.204308\pi$
$467$	8.74085e70	1.60198	0.800989	+	0.598680i	$0.204308\pi$
$468$	−3.30028e69	−0.0571525
$469$	−8.66033e70	−1.41727
$470$	−1.58652e70	−0.245387
$471$	6.70453e69	0.0980199
$472$	4.25307e70	0.587814
$473$	−5.41956e70	−0.708181
$474$	−3.86491e69	−0.0477544
$475$	−1.67879e71	−1.96163
$476$	1.12922e71	1.24795
$477$	−8.94402e69	−0.0934966
$478$	2.62642e70	0.259732
$479$	−9.38882e70	−0.878455	−0.439228	−	0.898376i	$-0.644748\pi$
$479$	−9.38882e70	−0.878455	−0.439228	+	0.898376i	$0.644748\pi$
$480$	−9.10491e70	−0.806089
$481$	2.20683e70	0.184895
$482$	5.43897e70	0.431291
$483$	3.95940e70	0.297187
$484$	2.76715e70	0.196621
$485$	2.31062e71	1.55443
$486$	−3.98629e70	−0.253927
$487$	3.27176e71	1.97362	0.986810	−	0.161885i	$-0.0517573\pi$
$487$	3.27176e71	1.97362	0.986810	+	0.161885i	$0.0517573\pi$
$488$	−1.51232e71	−0.864006
$489$	−1.69252e71	−0.915900
$490$	−1.00057e70	−0.0512924
$491$	−2.76660e71	−1.34365	−0.671826	−	0.740709i	$-0.734490\pi$
$491$	−2.76660e71	−1.34365	−0.671826	+	0.740709i	$0.734490\pi$
$492$	1.33590e71	0.614751
$493$	1.43252e71	0.624679
$494$	9.14954e69	0.0378125
$495$	1.98380e71	0.777069
$496$	−2.70445e71	−1.00419
$497$	5.05580e70	0.177970
$498$	2.45047e70	0.0817848
$499$	−4.81364e71	−1.52338	−0.761692	−	0.647939i	$-0.775631\pi$
$499$	−4.81364e71	−1.52338	−0.761692	+	0.647939i	$0.775631\pi$
$500$	−3.03126e71	−0.909742
$501$	1.75981e71	0.500919
$502$	−8.95868e70	−0.241877
$503$	−4.97279e71	−1.27364	−0.636822	−	0.771011i	$-0.719751\pi$
$503$	−4.97279e71	−1.27364	−0.636822	+	0.771011i	$0.719751\pi$
$504$	1.09963e71	0.267200
$505$	1.29626e72	2.98861
$506$	5.16150e70	0.112924
$507$	3.21670e71	0.667882
$508$	−8.81898e69	−0.0173792
$509$	−4.86664e71	−0.910349	−0.455174	−	0.890402i	$-0.650423\pi$
$509$	−4.86664e71	−0.910349	−0.455174	+	0.890402i	$0.650423\pi$
$510$	2.40312e71	0.426743
$511$	−2.41877e71	−0.407794
$512$	6.17329e71	0.988241
$513$	−8.37190e71	−1.27267
$514$	−2.06250e71	−0.297764
$515$	3.10733e71	0.426084
$516$	3.83805e71	0.499912
$517$	4.00217e71	0.495217
$518$	−3.53496e71	−0.415572
$519$	−1.64938e71	−0.184241
$520$	9.08471e70	0.0964323
$521$	−1.04553e72	−1.05472	−0.527358	−	0.849643i	$-0.676817\pi$
$521$	−1.04553e72	−1.05472	−0.527358	+	0.849643i	$0.676817\pi$
$522$	6.70634e70	0.0643009
$523$	−2.01240e71	−0.183408	−0.0917042	−	0.995786i	$-0.529231\pi$
$523$	−2.01240e71	−0.183408	−0.0917042	+	0.995786i	$0.529231\pi$
$524$	−7.90812e71	−0.685163
$525$	−1.24180e72	−1.02289
$526$	−1.74037e71	−0.136308
$527$	2.46931e72	1.83906
$528$	6.63941e71	0.470252
$529$	−1.16032e72	−0.781633
$530$	1.18362e71	0.0758409
$531$	9.97011e71	0.607708
$532$	1.83019e72	1.06130
$533$	−2.02506e71	−0.111730
$534$	−2.34159e71	−0.122933
$535$	−1.24069e72	−0.619853
$536$	1.66306e72	0.790752
$537$	2.35875e72	1.06749
$538$	3.73323e71	0.160825
$539$	2.52406e71	0.103514
$540$	−3.99628e72	−1.56035
$541$	−2.67923e72	−0.996053	−0.498026	−	0.867162i	$-0.665942\pi$
$541$	−2.67923e72	−0.996053	−0.498026	+	0.867162i	$0.665942\pi$
$542$	7.02090e71	0.248549
$543$	−2.01528e72	−0.679422
$544$	−3.29444e72	−1.05782
$545$	3.14278e72	0.961186
$546$	6.76788e70	0.0197173
$547$	3.99196e72	1.10795	0.553977	−	0.832532i	$-0.313110\pi$
$547$	3.99196e72	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$548$	−1.39789e72	−0.369647
$549$	−3.54519e72	−0.893248
$550$	−1.61882e72	−0.388675
$551$	2.32175e72	0.531250
$552$	−7.60330e71	−0.165812
$553$	1.17193e72	0.243604
$554$	7.25284e71	0.143714
$555$	9.39427e72	1.77459
$556$	5.31047e71	0.0956425
$557$	−4.75050e72	−0.815786	−0.407893	−	0.913030i	$-0.633736\pi$
$557$	−4.75050e72	−0.815786	−0.407893	+	0.913030i	$0.633736\pi$
$558$	1.15601e72	0.189302
$559$	−5.81801e71	−0.0908577
$560$	7.98070e72	1.18866
$561$	−6.06215e72	−0.861213
$562$	−7.18488e71	−0.0973660
$563$	2.08122e72	0.269058	0.134529	−	0.990910i	$-0.457048\pi$
$563$	2.08122e72	0.269058	0.134529	+	0.990910i	$0.457048\pi$
$564$	−2.83427e72	−0.349579
$565$	−2.50061e72	−0.294280
$566$	−1.64157e72	−0.184342
$567$	−1.43788e72	−0.154089
$568$	−9.70874e71	−0.0992961
$569$	−8.16033e72	−0.796586	−0.398293	−	0.917258i	$-0.630397\pi$
$569$	−8.16033e72	−0.796586	−0.398293	+	0.917258i	$0.630397\pi$
$570$	3.89487e72	0.362918
$571$	−5.30282e72	−0.471683	−0.235841	−	0.971792i	$-0.575785\pi$
$571$	−5.30282e72	−0.471683	−0.235841	+	0.971792i	$0.575785\pi$
$572$	−1.10175e72	−0.0935592
$573$	−1.57884e72	−0.128009
$574$	3.24380e72	0.251124
$575$	−1.01668e73	−0.751601
$576$	4.47094e72	0.315648
$577$	2.14077e73	1.44348	0.721740	−	0.692164i	$-0.243343\pi$
$577$	2.14077e73	1.44348	0.721740	+	0.692164i	$0.243343\pi$
$578$	4.46741e72	0.287718
$579$	2.79022e72	0.171655
$580$	1.10828e73	0.651338
$581$	−7.43039e72	−0.417200
$582$	−3.30554e72	−0.177330
$583$	−2.98582e72	−0.153055
$584$	4.64481e72	0.227524
$585$	2.12965e72	0.0996959
$586$	−3.06907e72	−0.137316
$587$	−1.26033e73	−0.538981	−0.269490	−	0.963003i	$-0.586855\pi$
$587$	−1.26033e73	−0.538981	−0.269490	+	0.963003i	$0.586855\pi$
$588$	−1.78750e72	−0.0730713
$589$	4.00214e73	1.56400
$590$	−1.31941e73	−0.492950
$591$	3.40439e73	1.21610
$592$	−3.72282e73	−1.27159
$593$	−3.38540e73	−1.10576	−0.552880	−	0.833261i	$-0.686471\pi$
$593$	−3.38540e73	−1.10576	−0.552880	+	0.833261i	$0.686471\pi$
$594$	−8.07281e72	−0.252164
$595$	−7.28681e73	−2.17690
$596$	−4.42123e71	−0.0126333
$597$	−2.18131e72	−0.0596207
$598$	5.54098e71	0.0144879
$599$	4.50976e73	1.12809	0.564043	−	0.825745i	$-0.309245\pi$
$599$	4.50976e73	1.12809	0.564043	+	0.825745i	$0.309245\pi$
$600$	2.38465e73	0.570710
$601$	5.21159e73	1.19343	0.596714	−	0.802454i	$-0.296473\pi$
$601$	5.21159e73	1.19343	0.596714	+	0.802454i	$0.296473\pi$
$602$	9.31944e72	0.204213
$603$	3.89856e73	0.817514
$604$	3.18096e72	0.0638379
$605$	−1.78562e73	−0.342983
$606$	−1.85441e73	−0.340942
$607$	1.40353e72	0.0247015	0.0123507	−	0.999924i	$-0.496069\pi$
$607$	1.40353e72	0.0247015	0.0123507	+	0.999924i	$0.496069\pi$
$608$	−5.33947e73	−0.899607
$609$	1.71739e73	0.277020
$610$	4.69159e73	0.724569
$611$	4.29641e72	0.0635351
$612$	−5.08334e73	−0.719841
$613$	9.09089e73	1.23283	0.616416	−	0.787421i	$-0.288584\pi$
$613$	9.09089e73	1.23283	0.616416	+	0.787421i	$0.288584\pi$
$614$	−2.64727e72	−0.0343824
$615$	−8.62049e73	−1.07236
$616$	3.67093e73	0.437409
$617$	−1.15906e74	−1.32297	−0.661486	−	0.749957i	$-0.730074\pi$
$617$	−1.15906e74	−1.32297	−0.661486	+	0.749957i	$0.730074\pi$
$618$	−4.44531e72	−0.0486079
$619$	−1.53802e74	−1.61124	−0.805621	−	0.592432i	$-0.798168\pi$
$619$	−1.53802e74	−1.61124	−0.805621	+	0.592432i	$0.798168\pi$
$620$	1.91040e74	1.91754
$621$	−5.07004e73	−0.487623
$622$	−5.39760e73	−0.497457
$623$	7.10024e73	0.627104
$624$	7.12755e72	0.0603321
$625$	−2.64476e72	−0.0214568
$626$	2.17506e73	0.169142
$627$	−9.82523e73	−0.732407
$628$	1.87682e73	0.134119
$629$	3.39914e74	2.32877
$630$	−3.41133e73	−0.224078
$631$	−1.90940e74	−1.20259	−0.601297	−	0.799025i	$-0.705349\pi$
$631$	−1.90940e74	−1.20259	−0.601297	+	0.799025i	$0.705349\pi$
$632$	−2.25047e73	−0.135916
$633$	2.23542e74	1.29468
$634$	4.88941e73	0.271576
$635$	5.69083e72	0.0303160
$636$	2.11451e73	0.108043
$637$	2.70963e72	0.0132805
$638$	2.23881e73	0.105261
$639$	−2.27593e73	−0.102657
$640$	−3.34454e74	−1.44733
$641$	−2.13596e74	−0.886860	−0.443430	−	0.896309i	$-0.646239\pi$
$641$	−2.13596e74	−0.886860	−0.443430	+	0.896309i	$0.646239\pi$
$642$	1.77492e73	0.0707132
$643$	1.06521e74	0.407235	0.203617	−	0.979051i	$-0.434730\pi$
$643$	1.06521e74	0.407235	0.203617	+	0.979051i	$0.434730\pi$
$644$	1.10837e74	0.406638
$645$	−2.47667e74	−0.872038
$646$	1.40928e74	0.476252
$647$	−3.74264e74	−1.21399	−0.606995	−	0.794706i	$-0.707625\pi$
$647$	−3.74264e74	−1.21399	−0.606995	+	0.794706i	$0.707625\pi$
$648$	2.76118e73	0.0859721
$649$	3.32836e74	0.994824
$650$	−1.73783e73	−0.0498660
$651$	2.96037e74	0.815549
$652$	−4.73791e74	−1.25322
$653$	−5.40144e73	−0.137186	−0.0685930	−	0.997645i	$-0.521851\pi$
$653$	−5.40144e73	−0.137186	−0.0685930	+	0.997645i	$0.521851\pi$
$654$	−4.49603e73	−0.109653
$655$	5.10306e74	1.19519
$656$	3.41618e74	0.768404
$657$	1.08884e74	0.235224
$658$	−6.88210e73	−0.142802
$659$	7.60313e74	1.51541	0.757703	−	0.652599i	$-0.226322\pi$
$659$	7.60313e74	1.51541	0.757703	+	0.652599i	$0.226322\pi$
$660$	−4.69002e74	−0.897967
$661$	−2.63286e72	−0.00484272	−0.00242136	−	0.999997i	$-0.500771\pi$
$661$	−2.63286e72	−0.00484272	−0.00242136	+	0.999997i	$0.500771\pi$
$662$	−9.62818e73	−0.170140
$663$	−6.50784e73	−0.110491
$664$	1.42687e74	0.232772
$665$	−1.18101e75	−1.85131
$666$	1.59131e74	0.239711
$667$	1.40606e74	0.203549
$668$	4.92630e74	0.685401
$669$	3.64033e73	0.0486798
$670$	−5.15923e74	−0.663136
$671$	−1.18351e75	−1.46226
$672$	−3.94958e74	−0.469100
$673$	−6.59799e74	−0.753378	−0.376689	−	0.926340i	$-0.622937\pi$
$673$	−6.59799e74	−0.753378	−0.376689	+	0.926340i	$0.622937\pi$
$674$	2.42038e74	0.265703
$675$	1.59013e75	1.67835
$676$	9.00460e74	0.913855
$677$	−9.68261e74	−0.944915	−0.472457	−	0.881354i	$-0.656633\pi$
$677$	−9.68261e74	−0.944915	−0.472457	+	0.881354i	$0.656633\pi$
$678$	3.57734e73	0.0335717
$679$	1.00231e75	0.904596
$680$	1.39930e75	1.21457
$681$	1.49841e74	0.125093
$682$	3.85916e74	0.309890
$683$	−2.38917e75	−1.84543	−0.922715	−	0.385483i	$-0.874035\pi$
$683$	−2.38917e75	−1.84543	−0.922715	+	0.385483i	$0.874035\pi$
$684$	−8.23883e74	−0.612180
$685$	9.02047e74	0.644806
$686$	−4.15530e74	−0.285768
$687$	1.01679e75	0.672784
$688$	9.81470e74	0.624861
$689$	−3.20534e73	−0.0196365
$690$	2.35874e74	0.139053
$691$	−2.74982e74	−0.156004	−0.0780020	−	0.996953i	$-0.524854\pi$
$691$	−2.74982e74	−0.156004	−0.0780020	+	0.996953i	$0.524854\pi$
$692$	−4.61717e74	−0.252095
$693$	8.60544e74	0.452212
$694$	−7.10298e74	−0.359265
$695$	−3.42681e74	−0.166837
$696$	−3.29794e74	−0.154560
$697$	−3.11916e75	−1.40724
$698$	3.06570e74	0.133156
$699$	−1.73503e75	−0.725540
$700$	−3.47621e75	−1.39961
$701$	5.35713e74	0.207685	0.103842	−	0.994594i	$-0.466886\pi$
$701$	5.35713e74	0.207685	0.103842	+	0.994594i	$0.466886\pi$
$702$	−8.66633e73	−0.0323520
$703$	5.50916e75	1.98047
$704$	1.49255e75	0.516719
$705$	1.82894e75	0.609800
$706$	−7.10235e74	−0.228075
$707$	5.62298e75	1.73921
$708$	−2.35709e75	−0.702256
$709$	−3.32161e75	−0.953287	−0.476644	−	0.879097i	$-0.658147\pi$
$709$	−3.32161e75	−0.953287	−0.476644	+	0.879097i	$0.658147\pi$
$710$	3.01190e74	0.0832711
$711$	−5.27559e74	−0.140516
$712$	−1.36347e75	−0.349885
$713$	2.42371e75	0.599249
$714$	1.04244e75	0.248342
$715$	7.10950e74	0.163203
$716$	6.60292e75	1.46063
$717$	−3.02773e75	−0.645446
$718$	8.28737e74	0.170262
$719$	−6.15825e75	−1.21939	−0.609694	−	0.792637i	$-0.708708\pi$
$719$	−6.15825e75	−1.21939	−0.609694	+	0.792637i	$0.708708\pi$
$720$	−3.59261e75	−0.685645
$721$	1.34792e75	0.247958
$722$	7.48536e74	0.132732
$723$	−6.27004e75	−1.07178
$724$	−5.64143e75	−0.929645
$725$	−4.40987e75	−0.700597
$726$	2.55449e74	0.0391277
$727$	1.07750e76	1.59131	0.795657	−	0.605747i	$-0.207126\pi$
$727$	1.07750e76	1.59131	0.795657	+	0.605747i	$0.207126\pi$
$728$	3.94082e74	0.0561184
$729$	5.78933e75	0.794967
$730$	−1.44094e75	−0.190805
$731$	−8.96136e75	−1.14436
$732$	8.38139e75	1.03222
$733$	−1.46870e75	−0.174453	−0.0872263	−	0.996189i	$-0.527800\pi$
$733$	−1.46870e75	−0.174453	−0.0872263	+	0.996189i	$0.527800\pi$
$734$	1.58923e75	0.182071
$735$	1.15346e75	0.127464
$736$	−3.23359e75	−0.344686
$737$	1.30147e76	1.33828
$738$	−1.46024e75	−0.144854
$739$	−7.45777e75	−0.713726	−0.356863	−	0.934157i	$-0.616154\pi$
$739$	−7.45777e75	−0.713726	−0.356863	+	0.934157i	$0.616154\pi$
$740$	2.62977e76	2.42816
$741$	−1.05476e75	−0.0939660
$742$	5.13440e74	0.0441353
$743$	−2.17472e76	−1.80385	−0.901923	−	0.431897i	$-0.857845\pi$
$743$	−2.17472e76	−1.80385	−0.901923	+	0.431897i	$0.857845\pi$
$744$	−5.68485e75	−0.455026
$745$	2.85299e74	0.0220374
$746$	2.80789e75	0.209316
$747$	3.34488e75	0.240649
$748$	−1.69699e76	−1.17839
$749$	−5.38195e75	−0.360721
$750$	−2.79831e75	−0.181039
$751$	8.74960e75	0.546424	0.273212	−	0.961954i	$-0.411914\pi$
$751$	8.74960e75	0.546424	0.273212	+	0.961954i	$0.411914\pi$
$752$	−7.24783e75	−0.436953
$753$	1.03276e76	0.601078
$754$	2.40341e74	0.0135047
$755$	−2.05265e75	−0.111358
$756$	−1.73353e76	−0.908039
$757$	2.13811e76	1.08141	0.540705	−	0.841212i	$-0.318158\pi$
$757$	2.13811e76	1.08141	0.540705	+	0.841212i	$0.318158\pi$
$758$	−7.25663e75	−0.354406
$759$	−5.95018e75	−0.280623
$760$	2.26791e76	1.03292
$761$	−2.22724e76	−0.979658	−0.489829	−	0.871819i	$-0.662941\pi$
$761$	−2.22724e76	−0.979658	−0.489829	+	0.871819i	$0.662941\pi$
$762$	−8.14123e73	−0.00345847
$763$	1.36330e76	0.559358
$764$	−4.41970e75	−0.175154
$765$	3.28025e76	1.25568
$766$	1.19381e76	0.441442
$767$	3.57307e75	0.127633
$768$	−6.63181e75	−0.228855
$769$	−1.21344e75	−0.0404548	−0.0202274	−	0.999795i	$-0.506439\pi$
$769$	−1.21344e75	−0.0404548	−0.0202274	+	0.999795i	$0.506439\pi$
$770$	−1.13882e76	−0.366817
$771$	2.37765e76	0.739958
$772$	7.81074e75	0.234873
$773$	8.70709e75	0.252998	0.126499	−	0.991967i	$-0.459626\pi$
$773$	8.70709e75	0.252998	0.126499	+	0.991967i	$0.459626\pi$
$774$	−4.19527e75	−0.117794
$775$	−7.60154e76	−2.06256
$776$	−1.92476e76	−0.504709
$777$	4.07510e76	1.03272
$778$	−8.64098e75	−0.211643
$779$	−5.05539e76	−1.19677
$780$	−5.03483e75	−0.115207
$781$	−7.59785e75	−0.168050
$782$	8.53465e75	0.182476
$783$	−2.19914e76	−0.454533
$784$	−4.57101e75	−0.0913349
$785$	−1.21110e76	−0.233956
$786$	−7.30038e75	−0.136348
$787$	7.21858e76	1.30353	0.651766	−	0.758420i	$-0.274029\pi$
$787$	7.21858e76	1.30353	0.651766	+	0.758420i	$0.274029\pi$
$788$	9.53000e76	1.66398
$789$	2.00630e76	0.338731
$790$	6.98155e75	0.113981
$791$	−1.08473e76	−0.171255
$792$	−1.65252e76	−0.252307
$793$	−1.27052e76	−0.187604
$794$	7.47084e75	0.106691
$795$	−1.36448e76	−0.188468
$796$	−6.10620e75	−0.0815783
$797$	−7.22104e76	−0.933155	−0.466578	−	0.884480i	$-0.654513\pi$
$797$	−7.22104e76	−0.933155	−0.466578	+	0.884480i	$0.654513\pi$
$798$	1.68954e76	0.211199
$799$	6.61767e76	0.800231
$800$	1.01416e77	1.18638
$801$	−3.19626e76	−0.361727
$802$	1.20632e75	0.0132082
$803$	3.63493e76	0.385065
$804$	−9.21682e76	−0.944704
$805$	−7.15223e76	−0.709334
$806$	4.14289e75	0.0397580
$807$	−4.30366e76	−0.399659
$808$	−1.07979e77	−0.970372
$809$	−1.58042e77	−1.37447	−0.687235	−	0.726435i	$-0.741176\pi$
$809$	−1.58042e77	−1.37447	−0.687235	+	0.726435i	$0.741176\pi$
$810$	−8.56590e75	−0.0720974
$811$	1.16585e77	0.949707	0.474853	−	0.880065i	$-0.342501\pi$
$811$	1.16585e77	0.949707	0.474853	+	0.880065i	$0.342501\pi$
$812$	4.80755e76	0.379044
$813$	−8.09369e76	−0.617656
$814$	5.31234e76	0.392409
$815$	3.05735e77	2.18609
$816$	1.09784e77	0.759889
$817$	−1.45241e77	−0.973208
$818$	−1.40230e76	−0.0909658
$819$	9.23812e75	0.0580177
$820$	−2.41316e77	−1.46730
$821$	2.60575e77	1.53405	0.767023	−	0.641619i	$-0.221737\pi$
$821$	2.60575e77	1.53405	0.767023	+	0.641619i	$0.221737\pi$
$822$	−1.29046e76	−0.0735598
$823$	3.34341e76	0.184541	0.0922707	−	0.995734i	$-0.470588\pi$
$823$	3.34341e76	0.184541	0.0922707	+	0.995734i	$0.470588\pi$
$824$	−2.58843e76	−0.138345
$825$	1.86617e77	0.965878
$826$	−5.72343e76	−0.286870
$827$	−1.56452e77	−0.759426	−0.379713	−	0.925104i	$-0.623977\pi$
$827$	−1.56452e77	−0.759426	−0.379713	+	0.925104i	$0.623977\pi$
$828$	−4.98945e76	−0.234557
$829$	2.97591e77	1.35495	0.677477	−	0.735544i	$-0.263073\pi$
$829$	2.97591e77	1.35495	0.677477	+	0.735544i	$0.263073\pi$
$830$	−4.42651e76	−0.195206
$831$	−8.36107e76	−0.357137
$832$	1.60229e76	0.0662937
$833$	4.17359e76	0.167269
$834$	4.90236e75	0.0190329
$835$	−3.17891e77	−1.19560
$836$	−2.75041e77	−1.00214
$837$	−3.79078e77	−1.33815
$838$	7.24822e76	0.247893
$839$	2.75386e77	0.912535	0.456267	−	0.889843i	$-0.349186\pi$
$839$	2.75386e77	0.912535	0.456267	+	0.889843i	$0.349186\pi$
$840$	1.67757e77	0.538616
$841$	−2.60448e77	−0.810264
$842$	1.15758e77	0.348964
$843$	8.28273e76	0.241959
$844$	6.25769e77	1.77149
$845$	−5.81062e77	−1.59411
$846$	3.09806e76	0.0823713
$847$	−7.74579e76	−0.199598
$848$	5.40725e76	0.135048
$849$	1.89240e77	0.458099
$850$	−2.67675e77	−0.628067
$851$	3.33636e77	0.758821
$852$	5.38068e76	0.118628
$853$	6.83575e77	1.46096	0.730478	−	0.682936i	$-0.239297\pi$
$853$	6.83575e77	1.46096	0.730478	+	0.682936i	$0.239297\pi$
$854$	2.03515e77	0.421660
$855$	5.31647e77	1.06788
$856$	1.03350e77	0.201260
$857$	−6.22171e77	−1.17467	−0.587337	−	0.809342i	$-0.699824\pi$
$857$	−6.22171e77	−1.17467	−0.587337	+	0.809342i	$0.699824\pi$
$858$	−1.01708e76	−0.0186183
$859$	−4.11261e77	−0.729960	−0.364980	−	0.931015i	$-0.618924\pi$
$859$	−4.11261e77	−0.729960	−0.364980	+	0.931015i	$0.618924\pi$
$860$	−6.93302e77	−1.19320
$861$	−3.73945e77	−0.624057
$862$	−2.77277e77	−0.448716
$863$	−3.72761e77	−0.584984	−0.292492	−	0.956268i	$-0.594484\pi$
$863$	−3.72761e77	−0.584984	−0.292492	+	0.956268i	$0.594484\pi$
$864$	5.05747e77	0.769697
$865$	2.97943e77	0.439751
$866$	−3.32993e77	−0.476663
$867$	−5.15002e77	−0.714995
$868$	8.28706e77	1.11591
$869$	−1.76117e77	−0.230026
$870$	1.02311e77	0.129616
$871$	1.39716e77	0.171698
$872$	−2.61796e77	−0.312087
$873$	−4.51204e77	−0.521790
$874$	1.38325e77	0.155185
$875$	8.48510e77	0.923514
$876$	−2.57420e77	−0.271821
$877$	4.87970e77	0.499924	0.249962	−	0.968256i	$-0.419582\pi$
$877$	4.87970e77	0.499924	0.249962	+	0.968256i	$0.419582\pi$
$878$	5.45177e76	0.0541917
$879$	3.53803e77	0.341237
$880$	−1.19934e78	−1.12241
$881$	1.30154e78	1.18194	0.590970	−	0.806693i	$-0.298745\pi$
$881$	1.30154e78	1.18194	0.590970	+	0.806693i	$0.298745\pi$
$882$	1.95387e76	0.0172178
$883$	3.47958e77	0.297556	0.148778	−	0.988871i	$-0.452466\pi$
$883$	3.47958e77	0.297556	0.148778	+	0.988871i	$0.452466\pi$
$884$	−1.82176e77	−0.151184
$885$	1.52102e78	1.22501
$886$	4.58710e77	0.358545
$887$	−1.85101e78	−1.40421	−0.702107	−	0.712071i	$-0.747757\pi$
$887$	−1.85101e78	−1.40421	−0.702107	+	0.712071i	$0.747757\pi$
$888$	−7.82549e77	−0.576193
$889$	2.46861e76	0.0176423
$890$	4.22984e77	0.293419
$891$	2.16084e77	0.145500
$892$	1.01905e77	0.0666080
$893$	1.07256e78	0.680546
$894$	−4.08146e75	−0.00251403
$895$	−4.26082e78	−2.54790
$896$	−1.45081e78	−0.842267
$897$	−6.38764e76	−0.0360032
$898$	−2.03521e77	−0.111374
$899$	1.05128e78	0.558584
$900$	1.56486e78	0.807325
$901$	−4.93712e77	−0.247324
$902$	−4.87478e77	−0.237127
$903$	−1.07435e78	−0.507479
$904$	2.08302e77	0.0955499
$905$	3.64038e78	1.62166
$906$	2.93650e76	0.0127038
$907$	1.94140e78	0.815686	0.407843	−	0.913052i	$-0.366281\pi$
$907$	1.94140e78	0.815686	0.407843	+	0.913052i	$0.366281\pi$
$908$	4.19456e77	0.171163
$909$	−2.53126e78	−1.00321
$910$	−1.22254e77	−0.0470617
$911$	6.52188e75	0.00243857	0.00121929	−	0.999999i	$-0.499612\pi$
$911$	6.52188e75	0.00243857	0.00121929	+	0.999999i	$0.499612\pi$
$912$	1.77933e78	0.646237
$913$	1.11664e78	0.393946
$914$	9.01838e77	0.309068
$915$	−5.40846e78	−1.80059
$916$	2.84632e78	0.920563
$917$	2.21364e78	0.695536
$918$	−1.33486e78	−0.407477
$919$	1.20106e78	0.356208	0.178104	−	0.984012i	$-0.443004\pi$
$919$	1.20106e78	0.356208	0.178104	+	0.984012i	$0.443004\pi$
$920$	1.37345e78	0.395764
$921$	3.05177e77	0.0854421
$922$	1.23971e78	0.337250
$923$	−8.15645e76	−0.0215604
$924$	−2.03447e78	−0.522568
$925$	−1.04639e79	−2.61179
$926$	−1.31683e78	−0.319404
$927$	−6.06782e77	−0.143027
$928$	−1.40257e78	−0.321295
$929$	−1.35743e78	−0.302205	−0.151103	−	0.988518i	$-0.548282\pi$
$929$	−1.35743e78	−0.302205	−0.151103	+	0.988518i	$0.548282\pi$
$930$	1.76359e78	0.381591
$931$	6.76434e77	0.142252
$932$	−4.85692e78	−0.992748
$933$	6.22235e78	1.23621
$934$	2.25881e78	0.436202
$935$	1.09506e79	2.05556
$936$	−1.77401e77	−0.0323703
$937$	−7.78543e77	−0.138097	−0.0690483	−	0.997613i	$-0.521996\pi$
$937$	−7.78543e77	−0.138097	−0.0690483	+	0.997613i	$0.521996\pi$
$938$	−2.23800e78	−0.385909
$939$	−2.50741e78	−0.420326
$940$	5.11980e78	0.834382
$941$	−8.40474e77	−0.133168	−0.0665839	−	0.997781i	$-0.521210\pi$
$941$	−8.40474e77	−0.133168	−0.0665839	+	0.997781i	$0.521210\pi$
$942$	1.73259e77	0.0266898
$943$	−3.06155e78	−0.458545
$944$	−6.02759e78	−0.877780
$945$	1.11864e79	1.58397
$946$	−1.40052e78	−0.192830
$947$	6.73558e78	0.901780	0.450890	−	0.892579i	$-0.351107\pi$
$947$	6.73558e78	0.901780	0.450890	+	0.892579i	$0.351107\pi$
$948$	1.24723e78	0.162378
$949$	3.90217e77	0.0494028
$950$	−4.33834e78	−0.534132
$951$	−5.63651e78	−0.674880
$952$	6.06996e78	0.706817
$953$	−1.66845e79	−1.88952	−0.944758	−	0.327768i	$-0.893704\pi$
$953$	−1.66845e79	−1.88952	−0.944758	+	0.327768i	$0.893704\pi$
$954$	−2.31131e77	−0.0254582
$955$	2.85201e78	0.305535
$956$	−8.47563e78	−0.883157
$957$	−2.58090e78	−0.261580
$958$	−2.42626e78	−0.239194
$959$	3.91296e78	0.375242
$960$	6.82077e78	0.636277
$961$	7.10190e78	0.644473
$962$	5.70290e77	0.0503450
$963$	2.42275e78	0.208072
$964$	−1.75519e79	−1.46650
$965$	−5.04022e78	−0.409709
$966$	1.02319e78	0.0809211
$967$	2.07490e79	1.59660	0.798301	−	0.602259i	$-0.205733\pi$
$967$	2.07490e79	1.59660	0.798301	+	0.602259i	$0.205733\pi$
$968$	1.48744e78	0.111363
$969$	−1.62462e79	−1.18351
$970$	5.97110e78	0.423256
$971$	−7.04775e78	−0.486117	−0.243059	−	0.970012i	$-0.578151\pi$
$971$	−7.04775e78	−0.486117	−0.243059	+	0.970012i	$0.578151\pi$
$972$	1.28640e79	0.863418
$973$	−1.48651e78	−0.0970904
$974$	8.45487e78	0.537396
$975$	2.00338e78	0.123920
$976$	2.14330e79	1.29022
$977$	1.67318e79	0.980247	0.490123	−	0.871653i	$-0.336952\pi$
$977$	1.67318e79	0.980247	0.490123	+	0.871653i	$0.336952\pi$
$978$	−4.37380e78	−0.249390
$979$	−1.06702e79	−0.592151
$980$	3.22892e78	0.174408
$981$	−6.13705e78	−0.322650
$982$	−7.14945e78	−0.365863
$983$	−5.74735e78	−0.286286	−0.143143	−	0.989702i	$-0.545721\pi$
$983$	−5.74735e78	−0.286286	−0.143143	+	0.989702i	$0.545721\pi$
$984$	7.18093e78	0.348185
$985$	−6.14966e79	−2.90262
$986$	3.70191e78	0.170094
$987$	7.93368e78	0.354871
$988$	−2.95262e78	−0.128573
$989$	−8.79585e78	−0.372886
$990$	5.12653e78	0.211588
$991$	2.54858e79	1.02411	0.512055	−	0.858953i	$-0.328885\pi$
$991$	2.54858e79	1.02411	0.512055	+	0.858953i	$0.328885\pi$
$992$	−2.41770e79	−0.945894
$993$	1.10994e79	0.422808
$994$	1.30652e78	0.0484593
$995$	3.94029e78	0.142304
$996$	−7.90784e78	−0.278090
$997$	4.70743e79	1.61199	0.805994	−	0.591924i	$-0.201631\pi$
$997$	4.70743e79	1.61199	0.805994	+	0.591924i	$0.201631\pi$
$998$	−1.24394e79	−0.414802
$999$	−5.21820e79	−1.69448

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +O(q^{10})\)	\(q+2.58420e7 q^{2} -2.97907e12 q^{3} -8.33939e15 q^{4} +5.38136e18 q^{5} -7.69850e19 q^{6} +2.33436e22 q^{7} -4.48271e23 q^{8} -1.05084e25 q^{9} +1.39065e26 q^{10} -3.50807e27 q^{11} +2.48436e28 q^{12} -3.76599e28 q^{13} +6.03245e29 q^{14} -1.60314e31 q^{15} +6.35303e31 q^{16} -5.80067e32 q^{17} -2.71559e32 q^{18} -9.40144e33 q^{19} -4.48772e34 q^{20} -6.95421e34 q^{21} -9.06556e34 q^{22} -5.69353e35 q^{23} +1.33543e36 q^{24} +1.78568e37 q^{25} -9.73207e35 q^{26} +8.90492e37 q^{27} -1.94671e38 q^{28} -2.46957e38 q^{29} -4.14284e38 q^{30} -4.25695e39 q^{31} +5.67942e39 q^{32} +1.04508e40 q^{33} -1.49901e40 q^{34} +1.25620e41 q^{35} +8.76338e40 q^{36} -5.85991e41 q^{37} -2.42952e41 q^{38} +1.12191e41 q^{39} -2.41231e42 q^{40} +5.37725e42 q^{41} -1.79711e42 q^{42} +1.54488e43 q^{43} +2.92552e43 q^{44} -5.65495e43 q^{45} -1.47132e43 q^{46} -1.14085e44 q^{47} -1.89261e44 q^{48} -7.19501e43 q^{49} +4.61455e44 q^{50} +1.72806e45 q^{51} +3.14060e44 q^{52} +8.51129e44 q^{53} +2.30121e45 q^{54} -1.88782e46 q^{55} -1.04643e46 q^{56} +2.80075e46 q^{57} -6.38187e45 q^{58} -9.48774e46 q^{59} +1.33692e47 q^{60} +3.37366e47 q^{61} -1.10008e47 q^{62} -2.45304e47 q^{63} -4.25463e47 q^{64} -2.02661e47 q^{65} +2.70069e47 q^{66} -3.70994e48 q^{67} +4.83740e48 q^{68} +1.69614e48 q^{69} +3.24628e48 q^{70} +2.16582e48 q^{71} +4.71061e48 q^{72} -1.03616e49 q^{73} -1.51432e49 q^{74} -5.31966e49 q^{75} +7.84022e49 q^{76} -8.18910e49 q^{77} +2.89925e48 q^{78} +5.02034e49 q^{79} +3.41879e50 q^{80} -6.15963e49 q^{81} +1.38959e50 q^{82} -3.18305e50 q^{83} +5.79939e50 q^{84} -3.12155e51 q^{85} +3.99229e50 q^{86} +7.35702e50 q^{87} +1.57257e51 q^{88} +3.04162e51 q^{89} -1.46135e51 q^{90} -8.79117e50 q^{91} +4.74806e51 q^{92} +1.26817e52 q^{93} -2.94817e51 q^{94} -5.05925e52 q^{95} -1.69194e52 q^{96} +4.29374e52 q^{97} -1.85933e51 q^{98} +3.68643e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!12 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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