LMFDB - Embedded newform 1.60.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,60,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, 60, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 60);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 60 $
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:	$22.0458005510$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 23\!\cdots\!36 $ x^5 - x^4 - 3976283494919360x^3 + 9065173660301515822976x^2 + 2677795447191606098169599438848*x - 23358185771581696169459363194340724736
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{13}\cdot 5^{3}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-5.61966e7$ 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)

$f(q)$	$=$	$q+1.25878e9 q^{2} +2.00976e14 q^{3} +1.00806e18 q^{4} -4.05126e20 q^{5} +2.52984e23 q^{6} +2.66317e24 q^{7} +5.43293e26 q^{8} +2.62609e28 q^{9} +O(q^{10})$	\(q+1.25878e9 q^{2} +2.00976e14 q^{3} +1.00806e18 q^{4} -4.05126e20 q^{5} +2.52984e23 q^{6} +2.66317e24 q^{7} +5.43293e26 q^{8} +2.62609e28 q^{9} -5.09964e29 q^{10} +7.79706e30 q^{11} +2.02597e32 q^{12} +1.35975e32 q^{13} +3.35235e33 q^{14} -8.14206e34 q^{15} +1.02776e35 q^{16} -2.91767e36 q^{17} +3.30567e37 q^{18} -6.13079e36 q^{19} -4.08393e38 q^{20} +5.35234e38 q^{21} +9.81478e39 q^{22} -2.47627e39 q^{23} +1.09189e41 q^{24} -9.34524e39 q^{25} +1.71162e41 q^{26} +2.43795e42 q^{27} +2.68465e42 q^{28} -4.74630e42 q^{29} -1.02491e44 q^{30} +1.04997e43 q^{31} -1.83814e44 q^{32} +1.56702e45 q^{33} -3.67270e45 q^{34} -1.07892e45 q^{35} +2.64727e46 q^{36} -7.35159e45 q^{37} -7.71730e45 q^{38} +2.73277e46 q^{39} -2.20102e47 q^{40} -6.31455e47 q^{41} +6.73741e47 q^{42} -5.26596e47 q^{43} +7.85993e48 q^{44} -1.06390e49 q^{45} -3.11707e48 q^{46} +3.33197e49 q^{47} +2.06556e49 q^{48} -6.54821e49 q^{49} -1.17636e49 q^{50} -5.86381e50 q^{51} +1.37071e50 q^{52} +7.06726e50 q^{53} +3.06884e51 q^{54} -3.15879e51 q^{55} +1.44688e51 q^{56} -1.23214e51 q^{57} -5.97454e51 q^{58} +2.46009e52 q^{59} -8.20771e52 q^{60} +5.32529e52 q^{61} +1.32169e52 q^{62} +6.99375e52 q^{63} -2.90628e53 q^{64} -5.50869e52 q^{65} +1.97253e54 q^{66} -2.99074e53 q^{67} -2.94120e54 q^{68} -4.97670e53 q^{69} -1.35812e54 q^{70} -4.94138e54 q^{71} +1.42674e55 q^{72} +7.41825e54 q^{73} -9.25403e54 q^{74} -1.87817e54 q^{75} -6.18022e54 q^{76} +2.07649e55 q^{77} +3.43995e55 q^{78} -6.76516e55 q^{79} -4.16374e55 q^{80} +1.18892e56 q^{81} -7.94862e56 q^{82} +4.29546e56 q^{83} +5.39550e56 q^{84} +1.18202e57 q^{85} -6.62869e56 q^{86} -9.53891e56 q^{87} +4.23609e57 q^{88} -4.87740e56 q^{89} -1.33921e58 q^{90} +3.62124e56 q^{91} -2.49623e57 q^{92} +2.11019e57 q^{93} +4.19421e58 q^{94} +2.48374e57 q^{95} -3.69423e58 q^{96} -9.59338e57 q^{97} -8.24274e58 q^{98} +2.04758e59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) $ 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9	$ 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 23\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9 - 816306987485763512638039118160 * q^10 + 4258478353252041879297428322660 * q^11 - 44182708253273060258139543308544 * q^12 - 845614914312482778669168084611378 * q^13 + 6292067851730037636066126264146880 * q^14 - 40513800156133976678914677598869720 * q^15 + 694835480494500010980166187386081280 * q^16 - 3408789133052869460614097222783941254 * q^17 + 9695472609892683802181177716078279752 * q^18 + 64613555538305267315990967466483855900 * q^19 + 167758871278751870059053885614959950720 * q^20 + 3416027528563001630003898902298902729760 * q^21 + 16748450439811023159371198583524768270112 * q^22 + 26762219406239912352813565493381233364712 * q^23 + 432715559082166564545012957137471770368000 * q^24 + 626328164486171817149625807278273965801475 * q^25 + 2749973149308040923633652135036287227445360 * q^26 + 4216422593373619915288217358331953848770680 * q^27 - 5611228561379710656820495758490486062705152 * q^28 - 17549046108593766297328008399864666159350850 * q^29 - 150145537158572429445793395106337059707760320 * q^30 - 358583623042201488230225328552738568224907040 * q^31 - 1074522626525330530995966308544265757955293184 * q^32 + 751114060128814067949775005681101561535832944 * q^33 + 1313186147384734516654444992913422917722864080 * q^34 + 8788755903389357061227741366680412802419085840 * q^35 + 50365332867541870766115057156818159463301788480 * q^36 + 12289654705391014078883644083969663074775614326 * q^37 - 45794685161100120795332322131326257673964677920 * q^38 - 9221768768351520041372477942735049607434903480 * q^39 - 623280493607240105129626720516519294122185241600 * q^40 - 1264600318837995850108850617547077064258140834590 * q^41 - 1891447371005345295768856102377155889725040492288 * q^42 + 1362401402875616509759331175816257798295684833092 * q^43 + 10077075627927391677990061115125884792646469172480 * q^44 + 10049700882739433416170827255242789411985618900430 * q^45 + 35794385229187598114442404877782400066811275005760 * q^46 + 58116315089138636393563553286549713195469724328016 * q^47 - 140681680096635395071164158203106499934517556953088 * q^48 - 172418318747588613327122588406220961507566908720435 * q^49 - 233848387346081992883910872998391056418422012487400 * q^50 - 465020225697129855978502466718810564745463254433640 * q^51 - 992097542005695911104987622381229757223139868049024 * q^52 + 2268101788488183861226576340546566132432064315777382 * q^53 + 4267182630237865543673874484672773145843435829054400 * q^54 + 900686393182056151569568156583842171451592208829880 * q^55 + 13057990199329560708452108630914154838760821091430400 * q^56 - 1461399454110401384802692435956966006781083287581040 * q^57 - 19935384508052610930909349257749128471453923297265680 * q^58 - 21931653365540795176945573682489794310901322601489100 * q^59 - 156464057876025038631690397519755203816227736824450560 * q^60 - 55594140754072322694181208673989737469003346813960290 * q^61 + 183475769536335462614566613996468524195162017418651392 * q^62 + 182010153390148596243930899005933467643747025172792792 * q^63 + 442992326944585087629292186411036974187652719990538240 * q^64 + 108239432655103548226552811908240865218465397888070180 * q^65 + 1851519511613271584553254669645963732036891556451969920 * q^66 + 251728958220345096328034657219059743090559333983657196 * q^67 - 5807349046062465910161766073979061475602982250739804032 * q^68 - 1186914917838620759227364067219409346615803888683557280 * q^69 - 5752977156560799367346480182820409713199133658156760960 * q^70 - 6369597660991167158573967320963521000612243175546832840 * q^71 + 505582168407192977842217602799461333023468587718935040 * q^72 + 12498734118021895660608582328454257591891310584798516162 * q^73 + 30430803441235884517255321866854090380478491767252508080 * q^74 + 71252573634955902069214955355612845417141504756757611700 * q^75 + 44485052481827577410579765985045990814357967613276332800 * q^76 + 17284905559091020495400324815223194592508822902892800352 * q^77 - 201581338752116742909455308452046241693931223329795704256 * q^78 - 195027743716001656833247333265450397879290980351117845200 * q^79 - 206704704480779086536260387174822452768748287935918120960 * q^80 - 272827015213405140901132899770256322932509539084953805395 * q^81 - 900520634877949974377918733125010085392642066824246973168 * q^82 + 1340753017495815214930655712848265601901866175919407282652 * q^83 + 1757594637692279239094128738775127192473269576864397076480 * q^84 + 2489371886919081358504761029214476055227000571885198923340 * q^85 - 1480724029310290822922398160933917869023473589220972227040 * q^86 + 2732195656620738105781600070679866258015898732907716552840 * q^87 - 766253667564296029168711510940105999694943299571114997760 * q^88 + 4137994032714609594535072901976334293523151283735651174450 * q^89 - 27581529153974409588805844338613259043100774320772297131920 * q^90 + 2026135516273811264299668018701283385599128389353986522960 * q^91 - 40220109586116561836814028008941466356622877640185075490304 * q^92 + 35686922849658258124721404138853435620012609371542349362304 * q^93 - 11288243726815211032514455546739674300124940708563708661120 * q^94 + 87101339446452871712134322546432797479691690743389226486600 * q^95 + 35374905257632352454877863276046463006859953360328478556160 * q^96 + 116502743099592096760799908821840050224405365201122277495466 * q^97 - 100197653381373748947470486612022288330601696851398709875352 * q^98 + 233753058124724467227621750953596851247855288092335837370420 * 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 $

$2$	1.25878e9	1.65792	0.828962	−	0.559305i	$-0.188932\pi$
$2$	1.25878e9	1.65792	0.828962	+	0.559305i	$0.188932\pi$
$3$	2.00976e14	1.69070	0.845351	−	0.534211i	$-0.179391\pi$
$3$	2.00976e14	1.69070	0.845351	+	0.534211i	$0.179391\pi$
$4$	1.00806e18	1.74871
$5$	−4.05126e20	−0.972691	−0.486346	−	0.873767i	$-0.661670\pi$
$5$	−4.05126e20	−0.972691	−0.486346	+	0.873767i	$0.661670\pi$
$6$	2.52984e23	2.80306
$7$	2.66317e24	0.312613	0.156307	−	0.987709i	$-0.450041\pi$
$7$	2.66317e24	0.312613	0.156307	+	0.987709i	$0.450041\pi$
$8$	5.43293e26	1.24131
$9$	2.62609e28	1.85847
$10$	−5.09964e29	−1.61265
$11$	7.79706e30	1.48199	0.740997	−	0.671508i	$-0.234353\pi$
$11$	7.79706e30	1.48199	0.740997	+	0.671508i	$0.234353\pi$
$12$	2.02597e32	2.95655
$13$	1.35975e32	0.187124	0.0935620	−	0.995613i	$-0.470175\pi$
$13$	1.35975e32	0.187124	0.0935620	+	0.995613i	$0.470175\pi$
$14$	3.35235e33	0.518289
$15$	−8.14206e34	−1.64453
$16$	1.02776e35	0.309281
$17$	−2.91767e36	−1.46823	−0.734113	−	0.679027i	$-0.762402\pi$
$17$	−2.91767e36	−1.46823	−0.734113	+	0.679027i	$0.762402\pi$
$18$	3.30567e37	3.08121
$19$	−6.13079e36	−0.115954	−0.0579769	−	0.998318i	$-0.518465\pi$
$19$	−6.13079e36	−0.115954	−0.0579769	+	0.998318i	$0.518465\pi$
$20$	−4.08393e38	−1.70096
$21$	5.35234e38	0.528536
$22$	9.81478e39	2.45703
$23$	−2.47627e39	−0.167042	−0.0835211	−	0.996506i	$-0.526617\pi$
$23$	−2.47627e39	−0.167042	−0.0835211	+	0.996506i	$0.526617\pi$
$24$	1.09189e41	2.09868
$25$	−9.34524e39	−0.0538716
$26$	1.71162e41	0.310237
$27$	2.43795e42	1.45142
$28$	2.68465e42	0.546670
$29$	−4.74630e42	−0.343253	−0.171626	−	0.985162i	$-0.554902\pi$
$29$	−4.74630e42	−0.343253	−0.171626	+	0.985162i	$0.554902\pi$
$30$	−1.02491e44	−2.72651
$31$	1.04997e43	0.106172	0.0530858	−	0.998590i	$-0.483094\pi$
$31$	1.04997e43	0.106172	0.0530858	+	0.998590i	$0.483094\pi$
$32$	−1.83814e44	−0.728543
$33$	1.56702e45	2.50561
$34$	−3.67270e45	−2.43421
$35$	−1.07892e45	−0.304076
$36$	2.64727e46	3.24993
$37$	−7.35159e45	−0.402189	−0.201095	−	0.979572i	$-0.564450\pi$
$37$	−7.35159e45	−0.402189	−0.201095	+	0.979572i	$0.564450\pi$
$38$	−7.71730e45	−0.192243
$39$	2.73277e46	0.316371
$40$	−2.20102e47	−1.20741
$41$	−6.31455e47	−1.67193	−0.835965	−	0.548782i	$-0.815092\pi$
$41$	−6.31455e47	−1.67193	−0.835965	+	0.548782i	$0.815092\pi$
$42$	6.73741e47	0.876272
$43$	−5.26596e47	−0.342104	−0.171052	−	0.985262i	$-0.554717\pi$
$43$	−5.26596e47	−0.342104	−0.171052	+	0.985262i	$0.554717\pi$
$44$	7.85993e48	2.59158
$45$	−1.06390e49	−1.80772
$46$	−3.11707e48	−0.276943
$47$	3.33197e49	1.56969	0.784845	−	0.619692i	$-0.212742\pi$
$47$	3.33197e49	1.56969	0.784845	+	0.619692i	$0.212742\pi$
$48$	2.06556e49	0.522902
$49$	−6.54821e49	−0.902273
$50$	−1.17636e49	−0.0893151
$51$	−5.86381e50	−2.48233
$52$	1.37071e50	0.327226
$53$	7.06726e50	0.961863	0.480931	−	0.876758i	$-0.340299\pi$
$53$	7.06726e50	0.961863	0.480931	+	0.876758i	$0.340299\pi$
$54$	3.06884e51	2.40635
$55$	−3.15879e51	−1.44152
$56$	1.44688e51	0.388049
$57$	−1.23214e51	−0.196043
$58$	−5.97454e51	−0.569087
$59$	2.46009e52	1.41519	0.707597	−	0.706616i	$-0.249779\pi$
$59$	2.46009e52	1.41519	0.707597	+	0.706616i	$0.249779\pi$
$60$	−8.20771e52	−2.87581
$61$	5.32529e52	1.14581	0.572906	−	0.819621i	$-0.305816\pi$
$61$	5.32529e52	1.14581	0.572906	+	0.819621i	$0.305816\pi$
$62$	1.32169e52	0.176025
$63$	6.99375e52	0.580983
$64$	−2.90628e53	−1.51715
$65$	−5.50869e52	−0.182014
$66$	1.97253e54	4.15411
$67$	−2.99074e53	−0.404178	−0.202089	−	0.979367i	$-0.564773\pi$
$67$	−2.99074e53	−0.404178	−0.202089	+	0.979367i	$0.564773\pi$
$68$	−2.94120e54	−2.56750
$69$	−4.97670e53	−0.282418
$70$	−1.35812e54	−0.504135
$71$	−4.94138e54	−1.20705	−0.603527	−	0.797342i	$-0.706239\pi$
$71$	−4.94138e54	−1.20705	−0.603527	+	0.797342i	$0.706239\pi$
$72$	1.42674e55	2.30694
$73$	7.41825e54	0.798504	0.399252	−	0.916841i	$-0.369270\pi$
$73$	7.41825e54	0.798504	0.399252	+	0.916841i	$0.369270\pi$
$74$	−9.25403e54	−0.666799
$75$	−1.87817e54	−0.0910809
$76$	−6.18022e54	−0.202770
$77$	2.07649e55	0.463291
$78$	3.43995e55	0.524519
$79$	−6.76516e55	−0.708400	−0.354200	−	0.935170i	$-0.615247\pi$
$79$	−6.76516e55	−0.708400	−0.354200	+	0.935170i	$0.615247\pi$
$80$	−4.16374e55	−0.300835
$81$	1.18892e56	0.595449
$82$	−7.94862e56	−2.77193
$83$	4.29546e56	1.04763	0.523813	−	0.851833i	$-0.324509\pi$
$83$	4.29546e56	1.04763	0.523813	+	0.851833i	$0.324509\pi$
$84$	5.39550e56	0.924257
$85$	1.18202e57	1.42813
$86$	−6.62869e56	−0.567183
$87$	−9.53891e56	−0.580338
$88$	4.23609e57	1.83961
$89$	−4.87740e56	−0.151769	−0.0758845	−	0.997117i	$-0.524178\pi$
$89$	−4.87740e56	−0.151769	−0.0758845	+	0.997117i	$0.524178\pi$
$90$	−1.33921e58	−2.99706
$91$	3.62124e56	0.0584974
$92$	−2.49623e57	−0.292109
$93$	2.11019e57	0.179505
$94$	4.19421e58	2.60243
$95$	2.48374e57	0.112787
$96$	−3.69423e58	−1.23175
$97$	−9.59338e57	−0.235616	−0.117808	−	0.993036i	$-0.537587\pi$
$97$	−9.59338e57	−0.235616	−0.117808	+	0.993036i	$0.537587\pi$
$98$	−8.24274e58	−1.49590
$99$	2.04758e59	2.75425
$100$	−9.42060e57	−0.0942060
$101$	2.04672e59	1.52608	0.763040	−	0.646351i	$-0.223706\pi$
$101$	2.04672e59	1.52608	0.763040	+	0.646351i	$0.223706\pi$
$102$	−7.38125e59	−4.11552
$103$	1.04146e59	0.435456	0.217728	−	0.976009i	$-0.430135\pi$
$103$	1.04146e59	0.435456	0.217728	+	0.976009i	$0.430135\pi$
$104$	7.38741e58	0.232278
$105$	−2.16837e59	−0.514102
$106$	8.89612e59	1.59470
$107$	−1.19773e60	−1.62756	−0.813779	−	0.581175i	$-0.802593\pi$
$107$	−1.19773e60	−1.62756	−0.813779	+	0.581175i	$0.802593\pi$
$108$	2.45761e60	2.53812
$109$	2.38792e60	1.87905	0.939526	−	0.342478i	$-0.111266\pi$
$109$	2.38792e60	1.87905	0.939526	+	0.342478i	$0.111266\pi$
$110$	−3.97622e60	−2.38994
$111$	−1.47749e60	−0.679982
$112$	2.73711e59	0.0966854
$113$	−1.74667e60	−0.474674	−0.237337	−	0.971427i	$-0.576275\pi$
$113$	−1.74667e60	−0.474674	−0.237337	+	0.971427i	$0.576275\pi$
$114$	−1.55099e60	−0.325025
$115$	1.00320e60	0.162480
$116$	−4.78457e60	−0.600250
$117$	3.57083e60	0.347765
$118$	3.09670e61	2.34628
$119$	−7.77026e60	−0.458987
$120$	−4.42352e61	−2.04137
$121$	3.31140e61	1.19631
$122$	6.70336e61	1.89967
$123$	−1.26907e62	−2.82674
$124$	1.05844e61	0.185664
$125$	7.40642e61	1.02509
$126$	8.80358e61	0.963226
$127$	−1.13188e62	−0.980826	−0.490413	−	0.871490i	$-0.663154\pi$
$127$	−1.13188e62	−0.980826	−0.490413	+	0.871490i	$0.663154\pi$
$128$	−2.59875e62	−1.78678
$129$	−1.05833e62	−0.578396
$130$	−6.93423e61	−0.301765
$131$	1.46816e62	0.509646	0.254823	−	0.966988i	$-0.417983\pi$
$131$	1.46816e62	0.509646	0.254823	+	0.966988i	$0.417983\pi$
$132$	1.57966e63	4.38159
$133$	−1.63273e61	−0.0362487
$134$	−3.76469e62	−0.670096
$135$	−9.87677e62	−1.41179
$136$	−1.58515e63	−1.82252
$137$	1.25262e63	1.16028	0.580139	−	0.814517i	$-0.302998\pi$
$137$	1.25262e63	1.16028	0.580139	+	0.814517i	$0.302998\pi$
$138$	−6.26456e62	−0.468228
$139$	−5.27386e62	−0.318560	−0.159280	−	0.987233i	$-0.550917\pi$
$139$	−5.27386e62	−0.318560	−0.159280	+	0.987233i	$0.550917\pi$
$140$	−1.08762e63	−0.531742
$141$	6.69646e63	2.65388
$142$	−6.22011e63	−2.00121
$143$	1.06020e63	0.277317
$144$	2.69900e63	0.574791
$145$	1.92285e63	0.333879
$146$	9.33794e63	1.32386
$147$	−1.31603e64	−1.52547
$148$	−7.41087e63	−0.703313
$149$	9.39911e63	0.731293	0.365647	−	0.930754i	$-0.380848\pi$
$149$	9.39911e63	0.731293	0.365647	+	0.930754i	$0.380848\pi$
$150$	−2.36420e63	−0.151005
$151$	1.88603e64	0.990211	0.495105	−	0.868833i	$-0.335129\pi$
$151$	1.88603e64	0.990211	0.495105	+	0.868833i	$0.335129\pi$
$152$	−3.33081e63	−0.143934
$153$	−7.66207e64	−2.72866
$154$	2.61385e64	0.768102
$155$	−4.25372e63	−0.103272
$156$	2.75480e64	0.553242
$157$	4.92576e64	0.819282	0.409641	−	0.912247i	$-0.365654\pi$
$157$	4.92576e64	0.819282	0.409641	+	0.912247i	$0.365654\pi$
$158$	−8.51584e64	−1.17447
$159$	1.42035e65	1.62622
$160$	7.44680e64	0.708647
$161$	−6.59472e63	−0.0522196
$162$	1.49659e65	0.987209
$163$	−8.13744e64	−0.447665	−0.223833	−	0.974628i	$-0.571857\pi$
$163$	−8.13744e64	−0.447665	−0.223833	+	0.974628i	$0.571857\pi$
$164$	−6.36546e65	−2.92373
$165$	−6.34841e65	−2.43719
$166$	5.40704e65	1.73688
$167$	4.38132e65	1.17888	0.589439	−	0.807813i	$-0.299349\pi$
$167$	4.38132e65	1.17888	0.589439	+	0.807813i	$0.299349\pi$
$168$	2.90789e65	0.656075
$169$	−5.09540e65	−0.964985
$170$	1.48791e66	2.36773
$171$	−1.61000e65	−0.215497
$172$	−5.30843e65	−0.598242
$173$	−5.55515e65	−0.527637	−0.263819	−	0.964572i	$-0.584982\pi$
$173$	−5.55515e65	−0.527637	−0.263819	+	0.964572i	$0.584982\pi$
$174$	−1.20074e66	−0.962156
$175$	−2.48880e64	−0.0168410
$176$	8.01353e65	0.458353
$177$	4.94418e66	2.39267
$178$	−6.13957e65	−0.251621
$179$	−1.41303e66	−0.490893	−0.245446	−	0.969410i	$-0.578935\pi$
$179$	−1.41303e66	−0.490893	−0.245446	+	0.969410i	$0.578935\pi$
$180$	−1.07248e67	−3.16118
$181$	−2.80750e65	−0.0702752	−0.0351376	−	0.999382i	$-0.511187\pi$
$181$	−2.80750e65	−0.0702752	−0.0351376	+	0.999382i	$0.511187\pi$
$182$	4.55835e65	0.0969843
$183$	1.07026e67	1.93723
$184$	−1.34534e66	−0.207351
$185$	2.97832e66	0.391206
$186$	2.65627e66	0.297605
$187$	−2.27492e67	−2.17590
$188$	3.35884e67	2.74494
$189$	6.49268e66	0.453734
$190$	3.12648e66	0.186993
$191$	3.97971e66	0.203876	0.101938	−	0.994791i	$-0.467496\pi$
$191$	3.97971e66	0.203876	0.101938	+	0.994791i	$0.467496\pi$
$192$	−5.84093e67	−2.56505
$193$	5.02510e66	0.189323	0.0946616	−	0.995510i	$-0.469823\pi$
$193$	5.02510e66	0.189323	0.0946616	+	0.995510i	$0.469823\pi$
$194$	−1.20759e67	−0.390634
$195$	−1.10711e67	−0.307731
$196$	−6.60101e67	−1.57782
$197$	−1.09574e66	−0.0225400	−0.0112700	−	0.999936i	$-0.503587\pi$
$197$	−1.09574e66	−0.0225400	−0.0112700	+	0.999936i	$0.503587\pi$
$198$	2.57745e68	4.56633
$199$	−8.25782e67	−1.26096	−0.630478	−	0.776208i	$-0.717141\pi$
$199$	−8.25782e67	−1.26096	−0.630478	+	0.776208i	$0.717141\pi$
$200$	−5.07720e66	−0.0668712
$201$	−6.01068e67	−0.683344
$202$	2.57636e68	2.53012
$203$	−1.26402e67	−0.107305
$204$	−5.91110e68	−4.34088
$205$	2.55819e68	1.62627
$206$	1.31097e68	0.721953
$207$	−6.50291e67	−0.310443
$208$	1.39750e67	0.0578739
$209$	−4.78021e67	−0.171843
$210$	−2.72950e68	−0.852342
$211$	4.55772e68	1.23713	0.618565	−	0.785734i	$-0.287714\pi$
$211$	4.55772e68	1.23713	0.618565	+	0.785734i	$0.287714\pi$
$212$	7.12425e68	1.68202
$213$	−9.93099e68	−2.04077
$214$	−1.50767e69	−2.69837
$215$	2.13338e68	0.332762
$216$	1.32452e69	1.80166
$217$	2.79626e67	0.0331907
$218$	3.00587e69	3.11532
$219$	1.49089e69	1.35003
$220$	−3.18426e69	−2.52081
$221$	−3.96729e68	−0.274740
$222$	−1.85984e69	−1.12736
$223$	−1.12231e69	−0.595824	−0.297912	−	0.954593i	$-0.596290\pi$
$223$	−1.12231e69	−0.595824	−0.297912	+	0.954593i	$0.596290\pi$
$224$	−4.89529e68	−0.227752
$225$	−2.45415e68	−0.100119
$226$	−2.19867e69	−0.786974
$227$	3.72597e69	1.17078	0.585392	−	0.810750i	$-0.300941\pi$
$227$	3.72597e69	1.17078	0.585392	+	0.810750i	$0.300941\pi$
$228$	−1.24208e69	−0.342823
$229$	2.90625e69	0.704996	0.352498	−	0.935813i	$-0.385332\pi$
$229$	2.90625e69	0.704996	0.352498	+	0.935813i	$0.385332\pi$
$230$	1.26281e69	0.269380
$231$	4.17325e69	0.783287
$232$	−2.57863e69	−0.426082
$233$	2.52938e69	0.368141	0.184070	−	0.982913i	$-0.441073\pi$
$233$	2.52938e69	0.368141	0.184070	+	0.982913i	$0.441073\pi$
$234$	4.49488e69	0.576568
$235$	−1.34987e70	−1.52682
$236$	2.47992e70	2.47477
$237$	−1.35963e70	−1.19769
$238$	−9.78104e69	−0.760965
$239$	−2.82462e70	−1.94188	−0.970940	−	0.239322i	$-0.923075\pi$
$239$	−2.82462e70	−1.94188	−0.970940	+	0.239322i	$0.923075\pi$
$240$	−8.36811e69	−0.508622
$241$	7.56182e69	0.406559	0.203279	−	0.979121i	$-0.434840\pi$
$241$	7.56182e69	0.406559	0.203279	+	0.979121i	$0.434840\pi$
$242$	4.16832e70	1.98339
$243$	−1.05547e70	−0.444695
$244$	5.36823e70	2.00369
$245$	2.65285e70	0.877633
$246$	−1.59748e71	−4.68651
$247$	−8.33632e68	−0.0216977
$248$	5.70443e69	0.131792
$249$	8.63285e70	1.77122
$250$	9.32304e70	1.69952
$251$	−5.62006e70	−0.910680	−0.455340	−	0.890318i	$-0.650482\pi$
$251$	−5.62006e70	−0.910680	−0.455340	+	0.890318i	$0.650482\pi$
$252$	7.05014e70	1.01597
$253$	−1.93076e70	−0.247556
$254$	−1.42479e71	−1.62614
$255$	2.37558e71	2.41454
$256$	−1.59589e71	−1.44519
$257$	−1.57080e71	−1.26792	−0.633962	−	0.773364i	$-0.718572\pi$
$257$	−1.57080e71	−1.26792	−0.633962	+	0.773364i	$0.718572\pi$
$258$	−1.33221e71	−0.958937
$259$	−1.95786e70	−0.125730
$260$	−5.55311e70	−0.318290
$261$	−1.24642e71	−0.637926
$262$	1.84808e71	0.844955
$263$	2.94951e71	1.20519	0.602595	−	0.798047i	$-0.294133\pi$
$263$	2.94951e71	1.20519	0.602595	+	0.798047i	$0.294133\pi$
$264$	8.51351e71	3.11023
$265$	−2.86313e71	−0.935596
$266$	−2.05525e70	−0.0600976
$267$	−9.80240e70	−0.256596
$268$	−3.01486e71	−0.706791
$269$	5.24635e71	1.10196	0.550979	−	0.834519i	$-0.314255\pi$
$269$	5.24635e71	1.10196	0.550979	+	0.834519i	$0.314255\pi$
$270$	−1.24327e72	−2.34063
$271$	−2.35272e71	−0.397170	−0.198585	−	0.980084i	$-0.563635\pi$
$271$	−2.35272e71	−0.397170	−0.198585	+	0.980084i	$0.563635\pi$
$272$	−2.99867e71	−0.454095
$273$	7.27783e70	0.0989017
$274$	1.57677e72	1.92365
$275$	−7.28654e70	−0.0798375
$276$	−5.01683e71	−0.493868
$277$	−2.69582e71	−0.238527	−0.119264	−	0.992863i	$-0.538053\pi$
$277$	−2.69582e71	−0.238527	−0.119264	+	0.992863i	$0.538053\pi$
$278$	−6.63862e71	−0.528149
$279$	2.75733e71	0.197317
$280$	−5.86170e71	−0.377452
$281$	−2.72521e72	−1.57966	−0.789831	−	0.613325i	$-0.789832\pi$
$281$	−2.72521e72	−1.57966	−0.789831	+	0.613325i	$0.789832\pi$
$282$	8.42936e72	4.39993
$283$	9.41566e71	0.442742	0.221371	−	0.975190i	$-0.428947\pi$
$283$	9.41566e71	0.442742	0.221371	+	0.975190i	$0.428947\pi$
$284$	−4.98123e72	−2.11079
$285$	4.99172e71	0.190690
$286$	1.33456e72	0.459770
$287$	−1.68167e72	−0.522668
$288$	−4.82714e72	−1.35398
$289$	4.56380e72	1.15569
$290$	2.42044e72	0.553546
$291$	−1.92804e72	−0.398357
$292$	7.47807e72	1.39635
$293$	−3.41955e72	−0.577264	−0.288632	−	0.957440i	$-0.593200\pi$
$293$	−3.41955e72	−0.577264	−0.288632	+	0.957440i	$0.593200\pi$
$294$	−1.65659e73	−2.52912
$295$	−9.96645e72	−1.37655
$296$	−3.99407e72	−0.499240
$297$	1.90088e73	2.15100
$298$	1.18314e73	1.21243
$299$	−3.36710e71	−0.0312576
$300$	−1.89331e72	−0.159274
$301$	−1.40242e72	−0.106946
$302$	2.37409e73	1.64169
$303$	4.11341e73	2.58015
$304$	−6.30099e71	−0.0358623
$305$	−2.15741e73	−1.11452
$306$	−9.64486e73	−4.52391
$307$	−2.53220e73	−1.07874	−0.539368	−	0.842070i	$-0.681337\pi$
$307$	−2.53220e73	−1.07874	−0.539368	+	0.842070i	$0.681337\pi$
$308$	2.09324e73	0.810163
$309$	2.09308e73	0.736227
$310$	−5.35449e72	−0.171218
$311$	2.94213e73	0.855520	0.427760	−	0.903892i	$-0.359303\pi$
$311$	2.94213e73	0.855520	0.427760	+	0.903892i	$0.359303\pi$
$312$	1.48469e73	0.392713
$313$	−6.09875e72	−0.146785	−0.0733927	−	0.997303i	$-0.523383\pi$
$313$	−6.09875e72	−0.146785	−0.0733927	+	0.997303i	$0.523383\pi$
$314$	6.20044e73	1.35831
$315$	−2.83335e73	−0.565117
$316$	−6.81971e73	−1.23879
$317$	−4.68192e73	−0.774776	−0.387388	−	0.921917i	$-0.626623\pi$
$317$	−4.68192e73	−0.774776	−0.387388	+	0.921917i	$0.626623\pi$
$318$	1.78791e74	2.69615
$319$	−3.70072e73	−0.508699
$320$	1.17741e74	1.47572
$321$	−2.40714e74	−2.75171
$322$	−8.30130e72	−0.0865761
$323$	1.78876e73	0.170246
$324$	1.19851e74	1.04127
$325$	−1.27072e72	−0.0100807
$326$	−1.02432e74	−0.742195
$327$	4.79915e74	3.17692
$328$	−3.43065e74	−2.07538
$329$	8.87361e73	0.490706
$330$	−7.99125e74	−4.04067
$331$	−1.18420e74	−0.547645	−0.273823	−	0.961780i	$-0.588288\pi$
$331$	−1.18420e74	−0.547645	−0.273823	+	0.961780i	$0.588288\pi$
$332$	4.33010e74	1.83200
$333$	−1.93060e74	−0.747458
$334$	5.51511e74	1.95449
$335$	1.21163e74	0.393140
$336$	5.50094e73	0.163466
$337$	4.43546e74	1.20742	0.603708	−	0.797206i	$-0.293689\pi$
$337$	4.43546e74	1.20742	0.603708	+	0.797206i	$0.293689\pi$
$338$	−6.41398e74	−1.59987
$339$	−3.51038e74	−0.802532
$340$	1.19156e75	2.49739
$341$	8.18671e73	0.157346
$342$	−2.02664e74	−0.357278
$343$	−3.67669e74	−0.594676
$344$	−2.86096e74	−0.424657
$345$	2.01619e74	0.274706
$346$	−6.99270e74	−0.874783
$347$	−3.30123e74	−0.379277	−0.189639	−	0.981854i	$-0.560732\pi$
$347$	−3.30123e74	−0.379277	−0.189639	+	0.981854i	$0.560732\pi$
$348$	−9.61583e74	−1.01484
$349$	−2.57241e74	−0.249453	−0.124727	−	0.992191i	$-0.539805\pi$
$349$	−2.57241e74	−0.249453	−0.124727	+	0.992191i	$0.539805\pi$
$350$	−3.13285e73	−0.0279211
$351$	3.31500e74	0.271596
$352$	−1.43321e75	−1.07970
$353$	5.86179e74	0.406141	0.203070	−	0.979164i	$-0.434908\pi$
$353$	5.86179e74	0.406141	0.203070	+	0.979164i	$0.434908\pi$
$354$	6.22363e75	3.96687
$355$	2.00188e75	1.17409
$356$	−4.91673e74	−0.265400
$357$	−1.56164e75	−0.776010
$358$	−1.77869e75	−0.813863
$359$	6.82502e74	0.287619	0.143809	−	0.989605i	$-0.454065\pi$
$359$	6.82502e74	0.287619	0.143809	+	0.989605i	$0.454065\pi$
$360$	−5.78009e75	−2.24394
$361$	−2.75793e75	−0.986555
$362$	−3.53403e74	−0.116511
$363$	6.65512e75	2.02260
$364$	3.65045e74	0.102295
$365$	−3.00533e75	−0.776698
$366$	1.34722e76	3.21177
$367$	−5.95804e75	−1.31055	−0.655277	−	0.755389i	$-0.727448\pi$
$367$	−5.95804e75	−1.31055	−0.655277	+	0.755389i	$0.727448\pi$
$368$	−2.54501e74	−0.0516630
$369$	−1.65826e76	−3.10724
$370$	3.74905e75	0.648590
$371$	1.88214e75	0.300691
$372$	2.12721e75	0.313902
$373$	6.82715e75	0.930741	0.465370	−	0.885116i	$-0.345921\pi$
$373$	6.82715e75	0.930741	0.465370	+	0.885116i	$0.345921\pi$
$374$	−2.86363e76	−3.60748
$375$	1.48851e76	1.73312
$376$	1.81023e76	1.94847
$377$	−6.45377e74	−0.0642308
$378$	8.17285e75	0.752256
$379$	1.45662e76	1.24019	0.620097	−	0.784525i	$-0.287093\pi$
$379$	1.45662e76	1.24019	0.620097	+	0.784525i	$0.287093\pi$
$380$	2.50377e75	0.197232
$381$	−2.27481e76	−1.65829
$382$	5.00957e75	0.338011
$383$	2.09671e76	1.30971	0.654854	−	0.755756i	$-0.272730\pi$
$383$	2.09671e76	1.30971	0.654854	+	0.755756i	$0.272730\pi$
$384$	−5.22286e76	−3.02091
$385$	−8.41241e75	−0.450639
$386$	6.32549e75	0.313884
$387$	−1.38289e76	−0.635792
$388$	−9.67074e75	−0.412025
$389$	2.84944e76	1.12524	0.562621	−	0.826715i	$-0.309793\pi$
$389$	2.84944e76	1.12524	0.562621	+	0.826715i	$0.309793\pi$
$390$	−1.39361e76	−0.510195
$391$	7.22492e75	0.245256
$392$	−3.55759e76	−1.12000
$393$	2.95064e76	0.861660
$394$	−1.37930e75	−0.0373697
$395$	2.74074e76	0.689055
$396$	2.06409e77	4.81639
$397$	−7.03399e76	−1.52364	−0.761819	−	0.647790i	$-0.775693\pi$
$397$	−7.03399e76	−1.52364	−0.761819	+	0.647790i	$0.775693\pi$
$398$	−1.03948e77	−2.09057
$399$	−3.28140e75	−0.0612857
$400$	−9.60469e74	−0.0166615
$401$	−3.74569e76	−0.603633	−0.301816	−	0.953366i	$-0.597593\pi$
$401$	−3.74569e76	−0.603633	−0.301816	+	0.953366i	$0.597593\pi$
$402$	−7.56611e76	−1.13293
$403$	1.42770e75	0.0198673
$404$	2.06322e77	2.66867
$405$	−4.81662e76	−0.579188
$406$	−1.59112e76	−0.177904
$407$	−5.73208e76	−0.596042
$408$	−3.18577e77	−3.08134
$409$	−1.57475e77	−1.41701	−0.708507	−	0.705703i	$-0.750631\pi$
$409$	−1.57475e77	−1.41701	−0.708507	+	0.705703i	$0.750631\pi$
$410$	3.22019e77	2.69624
$411$	2.51746e77	1.96168
$412$	1.04986e77	0.761488
$413$	6.55163e76	0.442408
$414$	−8.18572e76	−0.514691
$415$	−1.74020e77	−1.01902
$416$	−2.49941e76	−0.136328
$417$	−1.05992e77	−0.538591
$418$	−6.01723e76	−0.284902
$419$	1.83449e77	0.809474	0.404737	−	0.914433i	$-0.367363\pi$
$419$	1.83449e77	0.809474	0.404737	+	0.914433i	$0.367363\pi$
$420$	−2.18586e77	−0.899017
$421$	−3.33082e77	−1.27711	−0.638557	−	0.769574i	$-0.720468\pi$
$421$	−3.33082e77	−1.27711	−0.638557	+	0.769574i	$0.720468\pi$
$422$	5.73716e77	2.05107
$423$	8.75006e77	2.91723
$424$	3.83959e77	1.19397
$425$	2.72663e76	0.0790957
$426$	−1.25009e78	−3.38344
$427$	1.41822e77	0.358196
$428$	−1.20738e78	−2.84613
$429$	2.13075e77	0.468860
$430$	2.68545e77	0.551694
$431$	−7.84833e77	−1.50556	−0.752780	−	0.658272i	$-0.771288\pi$
$431$	−7.84833e77	−1.50556	−0.752780	+	0.658272i	$0.771288\pi$
$432$	2.50563e77	0.448897
$433$	−6.03006e77	−1.00909	−0.504543	−	0.863386i	$-0.668339\pi$
$433$	−6.03006e77	−1.00909	−0.504543	+	0.863386i	$0.668339\pi$
$434$	3.51988e76	0.0550276
$435$	3.86446e77	0.564490
$436$	2.40718e78	3.28592
$437$	1.51815e76	0.0193692
$438$	1.87670e78	2.23825
$439$	4.29376e77	0.478779	0.239389	−	0.970924i	$-0.423053\pi$
$439$	4.29376e77	0.478779	0.239389	+	0.970924i	$0.423053\pi$
$440$	−1.71615e78	−1.78937
$441$	−1.71962e78	−1.67685
$442$	−4.99395e77	−0.455499
$443$	1.51168e78	1.28988	0.644942	−	0.764231i	$-0.276881\pi$
$443$	1.51168e78	1.28988	0.644942	+	0.764231i	$0.276881\pi$
$444$	−1.48941e78	−1.18909
$445$	1.97596e77	0.147624
$446$	−1.41274e78	−0.987832
$447$	1.88899e78	1.23640
$448$	−7.73993e77	−0.474281
$449$	9.96470e77	0.571738	0.285869	−	0.958269i	$-0.407718\pi$
$449$	9.96470e77	0.571738	0.285869	+	0.958269i	$0.407718\pi$
$450$	−3.08923e77	−0.165990
$451$	−4.92349e78	−2.47779
$452$	−1.76075e78	−0.830068
$453$	3.79046e78	1.67415
$454$	4.69017e78	1.94107
$455$	−1.46706e77	−0.0568999
$456$	−6.69413e77	−0.243350
$457$	−4.29393e77	−0.146328	−0.0731640	−	0.997320i	$-0.523310\pi$
$457$	−4.29393e77	−0.146328	−0.0731640	+	0.997320i	$0.523310\pi$
$458$	3.65833e78	1.16883
$459$	−7.11313e78	−2.13102
$460$	1.01129e78	0.284131
$461$	3.37402e78	0.889141	0.444570	−	0.895744i	$-0.353356\pi$
$461$	3.37402e78	0.889141	0.444570	+	0.895744i	$0.353356\pi$
$462$	5.25320e78	1.29863
$463$	−5.49470e78	−1.27440	−0.637199	−	0.770700i	$-0.719907\pi$
$463$	−5.49470e78	−1.27440	−0.637199	+	0.770700i	$0.719907\pi$
$464$	−4.87807e77	−0.106162
$465$	−8.54895e77	−0.174603
$466$	3.18393e78	0.610349
$467$	−1.25571e78	−0.225965	−0.112982	−	0.993597i	$-0.536040\pi$
$467$	−1.25571e78	−0.225965	−0.112982	+	0.993597i	$0.536040\pi$
$468$	3.59962e78	0.608141
$469$	−7.96487e77	−0.126351
$470$	−1.69918e79	−2.53136
$471$	9.89959e78	1.38516
$472$	1.33655e79	1.75669
$473$	−4.10590e78	−0.506997
$474$	−1.71148e79	−1.98568
$475$	5.72937e76	0.00624662
$476$	−7.83292e78	−0.802636
$477$	1.85593e79	1.78760
$478$	−3.55558e79	−3.21949
$479$	1.64131e79	1.39731	0.698654	−	0.715460i	$-0.253783\pi$
$479$	1.64131e79	1.39731	0.698654	+	0.715460i	$0.253783\pi$
$480$	1.49663e79	1.19811
$481$	−9.99631e77	−0.0752592
$482$	9.51866e78	0.674044
$483$	−1.32538e78	−0.0882877
$484$	3.33810e79	2.09200
$485$	3.88653e78	0.229182
$486$	−1.32861e79	−0.737271
$487$	−1.57188e79	−0.820947	−0.410473	−	0.911873i	$-0.634637\pi$
$487$	−1.57188e79	−0.820947	−0.410473	+	0.911873i	$0.634637\pi$
$488$	2.89319e79	1.42230
$489$	−1.63543e79	−0.756869
$490$	3.33935e79	1.45505
$491$	9.03820e78	0.370833	0.185416	−	0.982660i	$-0.440637\pi$
$491$	9.03820e78	0.370833	0.185416	+	0.982660i	$0.440637\pi$
$492$	−1.27931e80	−4.94315
$493$	1.38481e79	0.503972
$494$	−1.04936e78	−0.0359732
$495$	−8.29529e79	−2.67903
$496$	1.07912e78	0.0328369
$497$	−1.31598e79	−0.377341
$498$	1.08669e80	2.93655
$499$	4.86147e79	1.23823	0.619115	−	0.785300i	$-0.287491\pi$
$499$	4.86147e79	1.23823	0.619115	+	0.785300i	$0.287491\pi$
$500$	7.46614e79	1.79259
$501$	8.80539e79	1.99313
$502$	−7.07441e79	−1.50984
$503$	−5.22741e79	−1.05204	−0.526018	−	0.850473i	$-0.676316\pi$
$503$	−5.22741e79	−1.05204	−0.526018	+	0.850473i	$0.676316\pi$
$504$	3.79965e79	0.721179
$505$	−8.29178e79	−1.48440
$506$	−2.43040e79	−0.410428
$507$	−1.02405e80	−1.63150
$508$	−1.14101e80	−1.71518
$509$	1.28179e80	1.81821	0.909104	−	0.416569i	$-0.136767\pi$
$509$	1.28179e80	1.81821	0.909104	+	0.416569i	$0.136767\pi$
$510$	2.99033e80	4.00313
$511$	1.97561e79	0.249623
$512$	−5.10799e79	−0.609237
$513$	−1.49465e79	−0.168298
$514$	−1.97729e80	−2.10212
$515$	−4.21923e79	−0.423565
$516$	−1.06687e80	−1.01145
$517$	2.59796e80	2.32627
$518$	−2.46451e79	−0.208450
$519$	−1.11645e80	−0.892078
$520$	−2.99283e79	−0.225935
$521$	7.71085e79	0.550034	0.275017	−	0.961439i	$-0.411317\pi$
$521$	7.71085e79	0.550034	0.275017	+	0.961439i	$0.411317\pi$
$522$	−1.56897e80	−1.05763
$523$	−1.72723e80	−1.10040	−0.550201	−	0.835032i	$-0.685449\pi$
$523$	−1.72723e80	−1.10040	−0.550201	+	0.835032i	$0.685449\pi$
$524$	1.47999e80	0.891224
$525$	−5.00189e78	−0.0284731
$526$	3.71279e80	1.99811
$527$	−3.06348e79	−0.155884
$528$	1.61053e80	0.774938
$529$	−2.13625e80	−0.972097
$530$	−3.60405e80	−1.55115
$531$	6.46042e80	2.63010
$532$	−1.64590e79	−0.0633885
$533$	−8.58619e79	−0.312858
$534$	−1.23391e80	−0.425417
$535$	4.85230e80	1.58311
$536$	−1.62485e80	−0.501709
$537$	−2.83985e80	−0.829954
$538$	6.60399e80	1.82696
$539$	−5.10568e80	−1.33716
$540$	−9.95641e80	−2.46881
$541$	−7.96457e79	−0.187001	−0.0935003	−	0.995619i	$-0.529806\pi$
$541$	−7.96457e79	−0.187001	−0.0935003	+	0.995619i	$0.529806\pi$
$542$	−2.96155e80	−0.658477
$543$	−5.64241e79	−0.118814
$544$	5.36309e80	1.06967
$545$	−9.67410e80	−1.82774
$546$	9.16118e79	0.163972
$547$	2.46062e80	0.417271	0.208635	−	0.977993i	$-0.433098\pi$
$547$	2.46062e80	0.417271	0.208635	+	0.977993i	$0.433098\pi$
$548$	1.26272e81	2.02899
$549$	1.39847e81	2.12946
$550$	−9.17214e79	−0.132364
$551$	2.90985e79	0.0398014
$552$	−2.70380e80	−0.350568
$553$	−1.80168e80	−0.221455
$554$	−3.39344e80	−0.395460
$555$	5.98571e80	0.661413
$556$	−5.31638e80	−0.557070
$557$	5.11029e80	0.507828	0.253914	−	0.967227i	$-0.418282\pi$
$557$	5.11029e80	0.507828	0.253914	+	0.967227i	$0.418282\pi$
$558$	3.47087e80	0.327137
$559$	−7.16038e79	−0.0640159
$560$	−1.10888e80	−0.0940450
$561$	−4.57205e81	−3.67880
$562$	−3.43044e81	−2.61896
$563$	5.95243e80	0.431218	0.215609	−	0.976480i	$-0.430826\pi$
$563$	5.95243e80	0.431218	0.215609	+	0.976480i	$0.430826\pi$
$564$	6.75045e81	4.64087
$565$	7.07619e80	0.461711
$566$	1.18522e81	0.734033
$567$	3.16630e80	0.186145
$568$	−2.68462e81	−1.49833
$569$	−1.31747e81	−0.698120	−0.349060	−	0.937100i	$-0.613499\pi$
$569$	−1.31747e81	−0.698120	−0.349060	+	0.937100i	$0.613499\pi$
$570$	6.28347e80	0.316149
$571$	−4.52346e80	−0.216125	−0.108063	−	0.994144i	$-0.534465\pi$
$571$	−4.52346e80	−0.216125	−0.108063	+	0.994144i	$0.534465\pi$
$572$	1.06875e81	0.484947
$573$	7.99825e80	0.344694
$574$	−2.11685e81	−0.866543
$575$	2.31413e79	0.00899883
$576$	−7.63217e81	−2.81958
$577$	4.44759e81	1.56113	0.780563	−	0.625077i	$-0.214932\pi$
$577$	4.44759e81	1.56113	0.780563	+	0.625077i	$0.214932\pi$
$578$	5.74482e81	1.91604
$579$	1.00992e81	0.320089
$580$	1.93835e81	0.583858
$581$	1.14396e81	0.327502
$582$	−2.42698e81	−0.660446
$583$	5.51039e81	1.42548
$584$	4.03028e81	0.991189
$585$	−1.44663e81	−0.338268
$586$	−4.30446e81	−0.957060
$587$	−8.24445e80	−0.174316	−0.0871581	−	0.996194i	$-0.527779\pi$
$587$	−8.24445e80	−0.174316	−0.0871581	+	0.996194i	$0.527779\pi$
$588$	−1.32664e82	−2.66762
$589$	−6.43716e79	−0.0123110
$590$	−1.25456e82	−2.28221
$591$	−2.20218e80	−0.0381085
$592$	−7.55569e80	−0.124390
$593$	−1.00937e81	−0.158103	−0.0790513	−	0.996871i	$-0.525189\pi$
$593$	−1.00937e81	−0.158103	−0.0790513	+	0.996871i	$0.525189\pi$
$594$	2.39279e82	3.56619
$595$	3.14794e81	0.446453
$596$	9.47490e81	1.27882
$597$	−1.65962e82	−2.13190
$598$	−4.23843e80	−0.0518227
$599$	9.57967e81	1.11496	0.557480	−	0.830190i	$-0.311768\pi$
$599$	9.57967e81	1.11496	0.557480	+	0.830190i	$0.311768\pi$
$600$	−1.02040e81	−0.113059
$601$	−3.89987e81	−0.411390	−0.205695	−	0.978616i	$-0.565945\pi$
$601$	−3.89987e81	−0.411390	−0.205695	+	0.978616i	$0.565945\pi$
$602$	−1.76533e81	−0.177309
$603$	−7.85398e81	−0.751154
$604$	1.90123e82	1.73159
$605$	−1.34153e82	−1.16364
$606$	5.17787e82	4.27769
$607$	−1.83298e82	−1.44242	−0.721208	−	0.692718i	$-0.756413\pi$
$607$	−1.83298e82	−1.44242	−0.721208	+	0.692718i	$0.756413\pi$
$608$	1.12693e81	0.0844773
$609$	−2.54038e81	−0.181421
$610$	−2.71571e82	−1.84779
$611$	4.53064e81	0.293727
$612$	−7.72386e82	−4.77164
$613$	2.18098e82	1.28401	0.642003	−	0.766702i	$-0.278104\pi$
$613$	2.18098e82	1.28401	0.642003	+	0.766702i	$0.278104\pi$
$614$	−3.18747e82	−1.78846
$615$	5.14134e82	2.74954
$616$	1.12814e82	0.575087
$617$	7.94496e81	0.386082	0.193041	−	0.981191i	$-0.438165\pi$
$617$	7.94496e81	0.386082	0.193041	+	0.981191i	$0.438165\pi$
$618$	2.63473e82	1.22061
$619$	−1.42782e82	−0.630666	−0.315333	−	0.948981i	$-0.602116\pi$
$619$	−1.42782e82	−0.630666	−0.315333	+	0.948981i	$0.602116\pi$
$620$	−4.28802e81	−0.180593
$621$	−6.03701e81	−0.242449
$622$	3.70349e82	1.41839
$623$	−1.29894e81	−0.0474450
$624$	2.80864e81	0.0978476
$625$	−2.83842e82	−0.943226
$626$	−7.67698e81	−0.243359
$627$	−9.60707e81	−0.290535
$628$	4.96548e82	1.43269
$629$	2.14495e82	0.590505
$630$	−3.56656e82	−0.936922
$631$	−6.26495e82	−1.57055	−0.785274	−	0.619148i	$-0.787478\pi$
$631$	−6.26495e82	−1.57055	−0.785274	+	0.619148i	$0.787478\pi$
$632$	−3.67546e82	−0.879342
$633$	9.15992e82	2.09162
$634$	−5.89351e82	−1.28452
$635$	4.58556e82	0.954041
$636$	1.43180e83	2.84380
$637$	−8.90391e81	−0.168837
$638$	−4.65838e82	−0.843384
$639$	−1.29765e83	−2.24328
$640$	1.05282e83	1.73798
$641$	7.02735e82	1.10785	0.553923	−	0.832568i	$-0.313130\pi$
$641$	7.02735e82	1.10785	0.553923	+	0.832568i	$0.313130\pi$
$642$	−3.03006e83	−4.56213
$643$	−9.72512e81	−0.139853	−0.0699264	−	0.997552i	$-0.522276\pi$
$643$	−9.72512e81	−0.139853	−0.0699264	+	0.997552i	$0.522276\pi$
$644$	−6.64790e81	−0.0913170
$645$	4.28758e82	0.562601
$646$	2.25165e82	0.282255
$647$	−9.49018e82	−1.13658	−0.568288	−	0.822830i	$-0.692394\pi$
$647$	−9.49018e82	−1.13658	−0.568288	+	0.822830i	$0.692394\pi$
$648$	6.45932e82	0.739135
$649$	1.91814e83	2.09731
$650$	−1.59955e81	−0.0167130
$651$	5.61982e81	0.0561155
$652$	−8.20306e82	−0.782838
$653$	−1.74041e83	−1.58749	−0.793746	−	0.608249i	$-0.791872\pi$
$653$	−1.74041e83	−1.58749	−0.793746	+	0.608249i	$0.791872\pi$
$654$	6.04107e83	5.26708
$655$	−5.94788e82	−0.495728
$656$	−6.48986e82	−0.517097
$657$	1.94810e83	1.48400
$658$	1.11699e83	0.813553
$659$	2.27995e82	0.158784	0.0793918	−	0.996843i	$-0.474702\pi$
$659$	2.27995e82	0.158784	0.0793918	+	0.996843i	$0.474702\pi$
$660$	−6.39960e83	−4.26194
$661$	−2.21921e83	−1.41337	−0.706685	−	0.707528i	$-0.749810\pi$
$661$	−2.21921e83	−1.41337	−0.706685	+	0.707528i	$0.749810\pi$
$662$	−1.49065e83	−0.907954
$663$	−7.97331e82	−0.464504
$664$	2.33369e83	1.30043
$665$	6.61463e81	0.0352588
$666$	−2.43019e83	−1.23923
$667$	1.17531e82	0.0573377
$668$	4.41665e83	2.06152
$669$	−2.25557e83	−1.00736
$670$	1.52517e83	0.651797
$671$	4.15216e83	1.69809
$672$	−9.83836e82	−0.385061
$673$	−3.98624e83	−1.49320	−0.746602	−	0.665271i	$-0.768316\pi$
$673$	−3.98624e83	−1.49320	−0.746602	+	0.665271i	$0.768316\pi$
$674$	5.58326e83	2.00180
$675$	−2.27832e82	−0.0781905
$676$	−5.13649e83	−1.68748
$677$	2.34092e83	0.736242	0.368121	−	0.929778i	$-0.380001\pi$
$677$	2.34092e83	0.736242	0.368121	+	0.929778i	$0.380001\pi$
$678$	−4.41879e83	−1.33054
$679$	−2.55488e82	−0.0736568
$680$	6.42185e83	1.77275
$681$	7.48831e83	1.97945
$682$	1.03053e83	0.260867
$683$	−4.81642e83	−1.16765	−0.583827	−	0.811878i	$-0.698445\pi$
$683$	−4.81642e83	−1.16765	−0.583827	+	0.811878i	$0.698445\pi$
$684$	−1.62298e83	−0.376842
$685$	−5.07469e83	−1.12859
$686$	−4.62814e83	−0.985927
$687$	5.84087e83	1.19194
$688$	−5.41216e82	−0.105806
$689$	9.60970e82	0.179988
$690$	2.53794e83	0.455442
$691$	−8.07164e83	−1.38790	−0.693952	−	0.720021i	$-0.744132\pi$
$691$	−8.07164e83	−1.38790	−0.693952	+	0.720021i	$0.744132\pi$
$692$	−5.59994e83	−0.922686
$693$	5.45307e83	0.861014
$694$	−4.15552e83	−0.628813
$695$	2.13658e83	0.309861
$696$	−5.18242e83	−0.720378
$697$	1.84238e84	2.45477
$698$	−3.23809e83	−0.413575
$699$	5.08344e83	0.622416
$700$	−2.50887e82	−0.0294500
$701$	−8.56706e83	−0.964163	−0.482082	−	0.876126i	$-0.660119\pi$
$701$	−8.56706e83	−0.964163	−0.482082	+	0.876126i	$0.660119\pi$
$702$	4.17285e83	0.450285
$703$	4.50710e82	0.0466354
$704$	−2.26604e84	−2.24841
$705$	−2.71291e84	−2.58141
$706$	7.37870e83	0.673351
$707$	5.45076e83	0.477073
$708$	4.98405e84	4.18409
$709$	2.41227e84	1.94250	0.971252	−	0.238055i	$-0.0765100\pi$
$709$	2.41227e84	1.94250	0.971252	+	0.238055i	$0.0765100\pi$
$710$	2.51993e84	1.94655
$711$	−1.77659e84	−1.31654
$712$	−2.64986e83	−0.188392
$713$	−2.60001e82	−0.0177351
$714$	−1.96575e84	−1.28657
$715$	−4.29516e83	−0.269744
$716$	−1.42442e84	−0.858430
$717$	−5.67681e84	−3.28314
$718$	8.59119e83	0.476850
$719$	1.36154e84	0.725315	0.362658	−	0.931922i	$-0.381869\pi$
$719$	1.36154e84	0.725315	0.362658	+	0.931922i	$0.381869\pi$
$720$	−1.09344e84	−0.559094
$721$	2.77359e83	0.136129
$722$	−3.47163e84	−1.63563
$723$	1.51974e84	0.687370
$724$	−2.83014e83	−0.122891
$725$	4.43553e82	0.0184916
$726$	8.37732e84	3.35332
$727$	6.66201e83	0.256059	0.128030	−	0.991770i	$-0.459135\pi$
$727$	6.66201e83	0.256059	0.128030	+	0.991770i	$0.459135\pi$
$728$	1.96740e83	0.0726133
$729$	−3.80124e84	−1.34730
$730$	−3.78304e84	−1.28771
$731$	1.53643e84	0.502286
$732$	1.07889e85	3.38765
$733$	5.58371e84	1.68405	0.842026	−	0.539437i	$-0.181363\pi$
$733$	5.58371e84	1.68405	0.842026	+	0.539437i	$0.181363\pi$
$734$	−7.49986e84	−2.17280
$735$	5.33159e84	1.48382
$736$	4.55173e83	0.121697
$737$	−2.33190e84	−0.598990
$738$	−2.08738e85	−5.15156
$739$	1.57406e84	0.373258	0.186629	−	0.982430i	$-0.440244\pi$
$739$	1.57406e84	0.373258	0.186629	+	0.982430i	$0.440244\pi$
$740$	3.00234e84	0.684106
$741$	−1.67540e83	−0.0366844
$742$	2.36919e84	0.498523
$743$	1.90142e84	0.384510	0.192255	−	0.981345i	$-0.438420\pi$
$743$	1.90142e84	0.384510	0.192255	+	0.981345i	$0.438420\pi$
$744$	1.14645e84	0.222820
$745$	−3.80782e84	−0.711323
$746$	8.59387e84	1.54310
$747$	1.12803e85	1.94699
$748$	−2.29327e85	−3.80503
$749$	−3.18975e84	−0.508796
$750$	1.87371e85	2.87339
$751$	−7.50454e84	−1.10649	−0.553243	−	0.833020i	$-0.686610\pi$
$751$	−7.50454e84	−1.10649	−0.553243	+	0.833020i	$0.686610\pi$
$752$	3.42447e84	0.485476
$753$	−1.12950e85	−1.53969
$754$	−8.12387e83	−0.106490
$755$	−7.64078e84	−0.963169
$756$	6.54504e84	0.793450
$757$	2.08215e84	0.242764	0.121382	−	0.992606i	$-0.461267\pi$
$757$	2.08215e84	0.242764	0.121382	+	0.992606i	$0.461267\pi$
$758$	1.83356e85	2.05615
$759$	−3.88036e84	−0.418543
$760$	1.34940e84	0.140004
$761$	1.47227e84	0.146940	0.0734702	−	0.997297i	$-0.476593\pi$
$761$	1.47227e84	0.146940	0.0734702	+	0.997297i	$0.476593\pi$
$762$	−2.86349e85	−2.74931
$763$	6.35945e84	0.587416
$764$	4.01180e84	0.356521
$765$	3.10411e85	2.65414
$766$	2.63929e85	2.17139
$767$	3.34510e84	0.264817
$768$	−3.20736e85	−2.44338
$769$	−1.22435e84	−0.0897589	−0.0448794	−	0.998992i	$-0.514290\pi$
$769$	−1.22435e84	−0.0897589	−0.0448794	+	0.998992i	$0.514290\pi$
$770$	−1.05894e85	−0.747126
$771$	−3.15693e85	−2.14368
$772$	5.06562e84	0.331072
$773$	1.68623e85	1.06077	0.530385	−	0.847757i	$-0.322047\pi$
$773$	1.68623e85	1.06077	0.530385	+	0.847757i	$0.322047\pi$
$774$	−1.74076e85	−1.05409
$775$	−9.81226e82	−0.00571964
$776$	−5.21202e84	−0.292472
$777$	−3.93482e84	−0.212571
$778$	3.58681e85	1.86556
$779$	3.87131e84	0.193867
$780$	−1.11604e85	−0.538133
$781$	−3.85282e85	−1.78885
$782$	9.09458e84	0.406615
$783$	−1.15712e85	−0.498204
$784$	−6.73000e84	−0.279056
$785$	−1.99555e85	−0.796908
$786$	3.71420e85	1.42857
$787$	1.38493e85	0.513066	0.256533	−	0.966535i	$-0.417420\pi$
$787$	1.38493e85	0.513066	0.256533	+	0.966535i	$0.417420\pi$
$788$	−1.10458e84	−0.0394160
$789$	5.92781e85	2.03762
$790$	3.44999e85	1.14240
$791$	−4.65167e84	−0.148389
$792$	1.11244e86	3.41887
$793$	7.24105e84	0.214409
$794$	−8.85423e85	−2.52607
$795$	−5.75421e85	−1.58181
$796$	−8.32441e85	−2.20505
$797$	5.79219e85	1.47850	0.739251	−	0.673430i	$-0.235180\pi$
$797$	5.79219e85	1.47850	0.739251	+	0.673430i	$0.235180\pi$
$798$	−4.13056e84	−0.101607
$799$	−9.72158e85	−2.30466
$800$	1.71779e84	0.0392478
$801$	−1.28085e85	−0.282059
$802$	−4.71500e85	−1.00078
$803$	5.78406e85	1.18338
$804$	−6.05914e85	−1.19497
$805$	2.67169e84	0.0507935
$806$	1.79716e84	0.0329384
$807$	1.05439e86	1.86308
$808$	1.11197e86	1.89433
$809$	6.11552e85	1.00451	0.502253	−	0.864721i	$-0.332505\pi$
$809$	6.11552e85	1.00451	0.502253	+	0.864721i	$0.332505\pi$
$810$	−6.06307e85	−0.960250
$811$	5.35716e85	0.818125	0.409062	−	0.912506i	$-0.365856\pi$
$811$	5.35716e85	0.818125	0.409062	+	0.912506i	$0.365856\pi$
$812$	−1.27421e85	−0.187646
$813$	−4.72840e85	−0.671496
$814$	−7.21542e85	−0.988193
$815$	3.29669e85	0.435440
$816$	−6.02661e85	−0.767739
$817$	3.22845e84	0.0396683
$818$	−1.98226e86	−2.34930
$819$	9.50973e84	0.108716
$820$	2.57882e86	2.84388
$821$	−1.37690e86	−1.46480	−0.732399	−	0.680876i	$-0.761599\pi$
$821$	−1.37690e86	−1.46480	−0.732399	+	0.680876i	$0.761599\pi$
$822$	3.16893e86	3.25232
$823$	−1.30297e86	−1.29015	−0.645076	−	0.764119i	$-0.723174\pi$
$823$	−1.30297e86	−1.29015	−0.645076	+	0.764119i	$0.723174\pi$
$824$	5.65818e85	0.540535
$825$	−1.46442e85	−0.134981
$826$	8.24706e85	0.733479
$827$	−4.49004e85	−0.385335	−0.192667	−	0.981264i	$-0.561714\pi$
$827$	−4.49004e85	−0.385335	−0.192667	+	0.981264i	$0.561714\pi$
$828$	−6.55534e85	−0.542876
$829$	5.72698e85	0.457686	0.228843	−	0.973463i	$-0.426506\pi$
$829$	5.72698e85	0.457686	0.228843	+	0.973463i	$0.426506\pi$
$830$	−2.19053e86	−1.68945
$831$	−5.41795e85	−0.403278
$832$	−3.95181e85	−0.283895
$833$	1.91055e86	1.32474
$834$	−1.33420e86	−0.892942
$835$	−1.77499e86	−1.14668
$836$	−4.81876e85	−0.300504
$837$	2.55978e85	0.154100
$838$	2.30922e86	1.34205
$839$	2.09389e86	1.17483	0.587415	−	0.809286i	$-0.300146\pi$
$839$	2.09389e86	1.17483	0.587415	+	0.809286i	$0.300146\pi$
$840$	−1.17806e86	−0.638159
$841$	−1.68670e86	−0.882178
$842$	−4.19277e86	−2.11736
$843$	−5.47702e86	−2.67074
$844$	4.59447e86	2.16338
$845$	2.06428e86	0.938632
$846$	1.10144e87	4.83654
$847$	8.81884e85	0.373982
$848$	7.26347e85	0.297486
$849$	1.89232e86	0.748545
$850$	3.43223e85	0.131135
$851$	1.82045e85	0.0671825
$852$	−1.00111e87	−3.56872
$853$	−1.65015e86	−0.568232	−0.284116	−	0.958790i	$-0.591700\pi$
$853$	−1.65015e86	−0.568232	−0.284116	+	0.958790i	$0.591700\pi$
$854$	1.78522e86	0.593862
$855$	6.52254e85	0.209612
$856$	−6.50716e86	−2.02030
$857$	1.41058e86	0.423121	0.211560	−	0.977365i	$-0.432145\pi$
$857$	1.41058e86	0.423121	0.211560	+	0.977365i	$0.432145\pi$
$858$	2.68215e86	0.777334
$859$	2.96519e86	0.830337	0.415169	−	0.909744i	$-0.363723\pi$
$859$	2.96519e86	0.830337	0.415169	+	0.909744i	$0.363723\pi$
$860$	2.15058e86	0.581905
$861$	−3.37976e86	−0.883675
$862$	−9.87932e86	−2.49610
$863$	4.87041e86	1.18918	0.594590	−	0.804029i	$-0.297315\pi$
$863$	4.87041e86	1.18918	0.594590	+	0.804029i	$0.297315\pi$
$864$	−4.48130e86	−1.05742
$865$	2.25054e86	0.513228
$866$	−7.59051e86	−1.67299
$867$	9.17214e86	1.95392
$868$	2.81881e85	0.0580409
$869$	−5.27483e86	−1.04985
$870$	4.86450e86	0.935881
$871$	−4.06666e85	−0.0756314
$872$	1.29734e87	2.33248
$873$	−2.51931e86	−0.437887
$874$	1.91101e85	0.0321126
$875$	1.97246e86	0.320457
$876$	1.50291e87	2.36082
$877$	−1.13902e87	−1.72998	−0.864992	−	0.501786i	$-0.832677\pi$
$877$	−1.13902e87	−1.72998	−0.864992	+	0.501786i	$0.832677\pi$
$878$	5.40490e86	0.793779
$879$	−6.87248e86	−0.975981
$880$	−3.24649e86	−0.445836
$881$	1.02118e87	1.35617	0.678084	−	0.734985i	$-0.262811\pi$
$881$	1.02118e87	1.35617	0.678084	+	0.734985i	$0.262811\pi$
$882$	−2.16462e87	−2.78009
$883$	6.55825e86	0.814605	0.407302	−	0.913293i	$-0.366470\pi$
$883$	6.55825e86	0.814605	0.407302	+	0.913293i	$0.366470\pi$
$884$	−3.99929e86	−0.480442
$885$	−2.00302e87	−2.32733
$886$	1.90287e87	2.13853
$887$	3.31163e86	0.359994	0.179997	−	0.983667i	$-0.442391\pi$
$887$	3.31163e86	0.359994	0.179997	+	0.983667i	$0.442391\pi$
$888$	−8.02711e86	−0.844067
$889$	−3.01440e86	−0.306619
$890$	2.48730e86	0.244750
$891$	9.27008e86	0.882452
$892$	−1.13136e87	−1.04193
$893$	−2.04276e86	−0.182012
$894$	2.37783e87	2.04986
$895$	5.72455e86	0.477487
$896$	−6.92092e86	−0.558570
$897$	−6.76705e85	−0.0528473
$898$	1.25434e87	0.947898
$899$	−4.98349e85	−0.0364437
$900$	−2.47394e86	−0.175079
$901$	−2.06199e87	−1.41223
$902$	−6.19758e87	−4.10799
$903$	−2.81852e86	−0.180814
$904$	−9.48950e86	−0.589216
$905$	1.13739e86	0.0683561
$906$	4.77135e87	2.77562
$907$	2.14918e87	1.21020	0.605101	−	0.796149i	$-0.293133\pi$
$907$	2.14918e87	1.21020	0.605101	+	0.796149i	$0.293133\pi$
$908$	3.75602e87	2.04736
$909$	5.37487e87	2.83618
$910$	−1.84670e86	−0.0943358
$911$	−3.84694e87	−1.90249	−0.951247	−	0.308432i	$-0.900196\pi$
$911$	−3.84694e87	−1.90249	−0.951247	+	0.308432i	$0.900196\pi$
$912$	−1.26635e86	−0.0606325
$913$	3.34920e87	1.55258
$914$	−5.40511e86	−0.242601
$915$	−4.33588e87	−1.88432
$916$	2.92969e87	1.23284
$917$	3.90995e86	0.159322
$918$	−8.95386e87	−3.53306
$919$	−2.17929e87	−0.832738	−0.416369	−	0.909196i	$-0.636698\pi$
$919$	−2.17929e87	−0.832738	−0.416369	+	0.909196i	$0.636698\pi$
$920$	5.45031e86	0.201688
$921$	−5.08910e87	−1.82382
$922$	4.24715e87	1.47413
$923$	−6.71903e86	−0.225869
$924$	4.20690e87	1.36974
$925$	6.87024e85	0.0216666
$926$	−6.91661e87	−2.11285
$927$	2.73497e87	0.809284
$928$	8.72437e86	0.250074
$929$	7.27755e86	0.202079	0.101040	−	0.994882i	$-0.467783\pi$
$929$	7.27755e86	0.202079	0.101040	+	0.994882i	$0.467783\pi$
$930$	−1.07612e87	−0.289478
$931$	4.01456e86	0.104622
$932$	2.54977e87	0.643772
$933$	5.91297e87	1.44643
$934$	−1.58066e87	−0.374633
$935$	9.21631e87	2.11648
$936$	1.94000e87	0.431683
$937$	−5.04758e87	−1.08834	−0.544171	−	0.838974i	$-0.683156\pi$
$937$	−5.04758e87	−1.08834	−0.544171	+	0.838974i	$0.683156\pi$
$938$	−1.00260e87	−0.209481
$939$	−1.22570e87	−0.248170
$940$	−1.36075e88	−2.66998
$941$	5.36600e87	1.02037	0.510184	−	0.860065i	$-0.329577\pi$
$941$	5.36600e87	1.02037	0.510184	+	0.860065i	$0.329577\pi$
$942$	1.24614e88	2.29649
$943$	1.56365e87	0.279283
$944$	2.52838e87	0.437693
$945$	−2.63036e87	−0.441343
$946$	−5.16843e87	−0.840562
$947$	−3.04783e87	−0.480471	−0.240235	−	0.970715i	$-0.577225\pi$
$947$	−3.04783e87	−0.480471	−0.240235	+	0.970715i	$0.577225\pi$
$948$	−1.37060e88	−2.09442
$949$	1.00870e87	0.149419
$950$	7.21200e85	0.0103564
$951$	−9.40954e87	−1.30991
$952$	−4.22153e87	−0.569744
$953$	1.26501e88	1.65522	0.827608	−	0.561306i	$-0.189701\pi$
$953$	1.26501e88	1.65522	0.827608	+	0.561306i	$0.189701\pi$
$954$	2.33621e88	2.96370
$955$	−1.61228e87	−0.198309
$956$	−2.84740e88	−3.39579
$957$	−7.43755e87	−0.860058
$958$	2.06604e88	2.31663
$959$	3.33594e87	0.362718
$960$	2.36631e88	2.49500
$961$	−9.66978e87	−0.988728
$962$	−1.25831e87	−0.124774
$963$	−3.14534e88	−3.02477
$964$	7.62279e87	0.710954
$965$	−2.03580e87	−0.184153
$966$	−1.66836e87	−0.146374
$967$	1.77625e87	0.151155	0.0755776	−	0.997140i	$-0.475920\pi$
$967$	1.77625e87	0.151155	0.0755776	+	0.997140i	$0.475920\pi$
$968$	1.79906e88	1.48499
$969$	3.59498e87	0.287836
$970$	4.89228e87	0.379966
$971$	2.22991e88	1.68004	0.840021	−	0.542554i	$-0.182543\pi$
$971$	2.22991e88	1.68004	0.840021	+	0.542554i	$0.182543\pi$
$972$	−1.06399e88	−0.777644
$973$	−1.40452e87	−0.0995862
$974$	−1.97865e88	−1.36107
$975$	−2.55383e86	−0.0170434
$976$	5.47314e87	0.354378
$977$	−1.69730e88	−1.06627	−0.533137	−	0.846029i	$-0.678987\pi$
$977$	−1.69730e88	−1.06627	−0.533137	+	0.846029i	$0.678987\pi$
$978$	−2.05864e88	−1.25483
$979$	−3.80294e87	−0.224921
$980$	2.67424e88	1.53473
$981$	6.27091e88	3.49217
$982$	1.13771e88	0.614812
$983$	−1.49460e88	−0.783785	−0.391893	−	0.920011i	$-0.628179\pi$
$983$	−1.49460e88	−0.783785	−0.391893	+	0.920011i	$0.628179\pi$
$984$	−6.89477e88	−3.50885
$985$	4.43914e86	0.0219245
$986$	1.74317e88	0.835548
$987$	1.78338e88	0.829638
$988$	−8.40354e86	−0.0379431
$989$	1.30399e87	0.0571458
$990$	−1.04419e89	−4.44163
$991$	−1.20694e88	−0.498326	−0.249163	−	0.968462i	$-0.580156\pi$
$991$	−1.20694e88	−0.498326	−0.249163	+	0.968462i	$0.580156\pi$
$992$	−1.93000e87	−0.0773506
$993$	−2.37996e88	−0.925905
$994$	−1.65652e88	−0.625603
$995$	3.34546e88	1.22652
$996$	8.70246e88	3.09736
$997$	2.24931e88	0.777216	0.388608	−	0.921403i	$-0.372956\pi$
$997$	2.24931e88	0.777216	0.388608	+	0.921403i	$0.372956\pi$
$998$	6.11952e88	2.05289
$999$	−1.79228e88	−0.583746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.60.a.a.1.5	✓	5
3.2	odd	2		9.60.a.c.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.60.a.a.1.5	✓	5	1.1	even	1	trivial
9.60.a.c.1.1		5	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:	\( k \)	\(=\)	\( 60 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.25878e9 q^{2} +2.00976e14 q^{3} +1.00806e18 q^{4} -4.05126e20 q^{5} +2.52984e23 q^{6} +2.66317e24 q^{7} +5.43293e26 q^{8} +2.62609e28 q^{9} +O(q^{10})\)	\(q+1.25878e9 q^{2} +2.00976e14 q^{3} +1.00806e18 q^{4} -4.05126e20 q^{5} +2.52984e23 q^{6} +2.66317e24 q^{7} +5.43293e26 q^{8} +2.62609e28 q^{9} -5.09964e29 q^{10} +7.79706e30 q^{11} +2.02597e32 q^{12} +1.35975e32 q^{13} +3.35235e33 q^{14} -8.14206e34 q^{15} +1.02776e35 q^{16} -2.91767e36 q^{17} +3.30567e37 q^{18} -6.13079e36 q^{19} -4.08393e38 q^{20} +5.35234e38 q^{21} +9.81478e39 q^{22} -2.47627e39 q^{23} +1.09189e41 q^{24} -9.34524e39 q^{25} +1.71162e41 q^{26} +2.43795e42 q^{27} +2.68465e42 q^{28} -4.74630e42 q^{29} -1.02491e44 q^{30} +1.04997e43 q^{31} -1.83814e44 q^{32} +1.56702e45 q^{33} -3.67270e45 q^{34} -1.07892e45 q^{35} +2.64727e46 q^{36} -7.35159e45 q^{37} -7.71730e45 q^{38} +2.73277e46 q^{39} -2.20102e47 q^{40} -6.31455e47 q^{41} +6.73741e47 q^{42} -5.26596e47 q^{43} +7.85993e48 q^{44} -1.06390e49 q^{45} -3.11707e48 q^{46} +3.33197e49 q^{47} +2.06556e49 q^{48} -6.54821e49 q^{49} -1.17636e49 q^{50} -5.86381e50 q^{51} +1.37071e50 q^{52} +7.06726e50 q^{53} +3.06884e51 q^{54} -3.15879e51 q^{55} +1.44688e51 q^{56} -1.23214e51 q^{57} -5.97454e51 q^{58} +2.46009e52 q^{59} -8.20771e52 q^{60} +5.32529e52 q^{61} +1.32169e52 q^{62} +6.99375e52 q^{63} -2.90628e53 q^{64} -5.50869e52 q^{65} +1.97253e54 q^{66} -2.99074e53 q^{67} -2.94120e54 q^{68} -4.97670e53 q^{69} -1.35812e54 q^{70} -4.94138e54 q^{71} +1.42674e55 q^{72} +7.41825e54 q^{73} -9.25403e54 q^{74} -1.87817e54 q^{75} -6.18022e54 q^{76} +2.07649e55 q^{77} +3.43995e55 q^{78} -6.76516e55 q^{79} -4.16374e55 q^{80} +1.18892e56 q^{81} -7.94862e56 q^{82} +4.29546e56 q^{83} +5.39550e56 q^{84} +1.18202e57 q^{85} -6.62869e56 q^{86} -9.53891e56 q^{87} +4.23609e57 q^{88} -4.87740e56 q^{89} -1.33921e58 q^{90} +3.62124e56 q^{91} -2.49623e57 q^{92} +2.11019e57 q^{93} +4.19421e58 q^{94} +2.48374e57 q^{95} -3.69423e58 q^{96} -9.59338e57 q^{97} -8.24274e58 q^{98} +2.04758e59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) \) 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 23\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9 - 816306987485763512638039118160 * q^10 + 4258478353252041879297428322660 * q^11 - 44182708253273060258139543308544 * q^12 - 845614914312482778669168084611378 * q^13 + 6292067851730037636066126264146880 * q^14 - 40513800156133976678914677598869720 * q^15 + 694835480494500010980166187386081280 * q^16 - 3408789133052869460614097222783941254 * q^17 + 9695472609892683802181177716078279752 * q^18 + 64613555538305267315990967466483855900 * q^19 + 167758871278751870059053885614959950720 * q^20 + 3416027528563001630003898902298902729760 * q^21 + 16748450439811023159371198583524768270112 * q^22 + 26762219406239912352813565493381233364712 * q^23 + 432715559082166564545012957137471770368000 * q^24 + 626328164486171817149625807278273965801475 * q^25 + 2749973149308040923633652135036287227445360 * q^26 + 4216422593373619915288217358331953848770680 * q^27 - 5611228561379710656820495758490486062705152 * q^28 - 17549046108593766297328008399864666159350850 * q^29 - 150145537158572429445793395106337059707760320 * q^30 - 358583623042201488230225328552738568224907040 * q^31 - 1074522626525330530995966308544265757955293184 * q^32 + 751114060128814067949775005681101561535832944 * q^33 + 1313186147384734516654444992913422917722864080 * q^34 + 8788755903389357061227741366680412802419085840 * q^35 + 50365332867541870766115057156818159463301788480 * q^36 + 12289654705391014078883644083969663074775614326 * q^37 - 45794685161100120795332322131326257673964677920 * q^38 - 9221768768351520041372477942735049607434903480 * q^39 - 623280493607240105129626720516519294122185241600 * q^40 - 1264600318837995850108850617547077064258140834590 * q^41 - 1891447371005345295768856102377155889725040492288 * q^42 + 1362401402875616509759331175816257798295684833092 * q^43 + 10077075627927391677990061115125884792646469172480 * q^44 + 10049700882739433416170827255242789411985618900430 * q^45 + 35794385229187598114442404877782400066811275005760 * q^46 + 58116315089138636393563553286549713195469724328016 * q^47 - 140681680096635395071164158203106499934517556953088 * q^48 - 172418318747588613327122588406220961507566908720435 * q^49 - 233848387346081992883910872998391056418422012487400 * q^50 - 465020225697129855978502466718810564745463254433640 * q^51 - 992097542005695911104987622381229757223139868049024 * q^52 + 2268101788488183861226576340546566132432064315777382 * q^53 + 4267182630237865543673874484672773145843435829054400 * q^54 + 900686393182056151569568156583842171451592208829880 * q^55 + 13057990199329560708452108630914154838760821091430400 * q^56 - 1461399454110401384802692435956966006781083287581040 * q^57 - 19935384508052610930909349257749128471453923297265680 * q^58 - 21931653365540795176945573682489794310901322601489100 * q^59 - 156464057876025038631690397519755203816227736824450560 * q^60 - 55594140754072322694181208673989737469003346813960290 * q^61 + 183475769536335462614566613996468524195162017418651392 * q^62 + 182010153390148596243930899005933467643747025172792792 * q^63 + 442992326944585087629292186411036974187652719990538240 * q^64 + 108239432655103548226552811908240865218465397888070180 * q^65 + 1851519511613271584553254669645963732036891556451969920 * q^66 + 251728958220345096328034657219059743090559333983657196 * q^67 - 5807349046062465910161766073979061475602982250739804032 * q^68 - 1186914917838620759227364067219409346615803888683557280 * q^69 - 5752977156560799367346480182820409713199133658156760960 * q^70 - 6369597660991167158573967320963521000612243175546832840 * q^71 + 505582168407192977842217602799461333023468587718935040 * q^72 + 12498734118021895660608582328454257591891310584798516162 * q^73 + 30430803441235884517255321866854090380478491767252508080 * q^74 + 71252573634955902069214955355612845417141504756757611700 * q^75 + 44485052481827577410579765985045990814357967613276332800 * q^76 + 17284905559091020495400324815223194592508822902892800352 * q^77 - 201581338752116742909455308452046241693931223329795704256 * q^78 - 195027743716001656833247333265450397879290980351117845200 * q^79 - 206704704480779086536260387174822452768748287935918120960 * q^80 - 272827015213405140901132899770256322932509539084953805395 * q^81 - 900520634877949974377918733125010085392642066824246973168 * q^82 + 1340753017495815214930655712848265601901866175919407282652 * q^83 + 1757594637692279239094128738775127192473269576864397076480 * q^84 + 2489371886919081358504761029214476055227000571885198923340 * q^85 - 1480724029310290822922398160933917869023473589220972227040 * q^86 + 2732195656620738105781600070679866258015898732907716552840 * q^87 - 766253667564296029168711510940105999694943299571114997760 * q^88 + 4137994032714609594535072901976334293523151283735651174450 * q^89 - 27581529153974409588805844338613259043100774320772297131920 * q^90 + 2026135516273811264299668018701283385599128389353986522960 * q^91 - 40220109586116561836814028008941466356622877640185075490304 * q^92 + 35686922849658258124721404138853435620012609371542349362304 * q^93 - 11288243726815211032514455546739674300124940708563708661120 * q^94 + 87101339446452871712134322546432797479691690743389226486600 * q^95 + 35374905257632352454877863276046463006859953360328478556160 * q^96 + 116502743099592096760799908821840050224405365201122277495466 * q^97 - 100197653381373748947470486612022288330601696851398709875352 * q^98 + 233753058124724467227621750953596851247855288092335837370420 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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