LMFDB - Embedded newform 1.60.a.a.1.4

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			1.4
Root			$-3.26158e7$ 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)

$f(q)$	$=$	$q+6.92842e8 q^{2} -1.03284e14 q^{3} -9.64308e16 q^{4} +3.87033e20 q^{5} -7.15597e22 q^{6} -7.47157e23 q^{7} -4.66207e26 q^{8} -3.46273e27 q^{9} +O(q^{10})$	\(q+6.92842e8 q^{2} -1.03284e14 q^{3} -9.64308e16 q^{4} +3.87033e20 q^{5} -7.15597e22 q^{6} -7.47157e23 q^{7} -4.66207e26 q^{8} -3.46273e27 q^{9} +2.68153e29 q^{10} +4.64881e30 q^{11} +9.95979e30 q^{12} +1.02949e33 q^{13} -5.17661e32 q^{14} -3.99744e34 q^{15} -2.67420e35 q^{16} +2.49454e36 q^{17} -2.39912e36 q^{18} +3.24421e37 q^{19} -3.73219e37 q^{20} +7.71696e37 q^{21} +3.22089e39 q^{22} +2.77809e40 q^{23} +4.81519e40 q^{24} -2.36780e40 q^{25} +7.13271e41 q^{26} +1.81709e42 q^{27} +7.20489e40 q^{28} -1.27852e43 q^{29} -2.76960e43 q^{30} -1.14110e44 q^{31} +8.34708e43 q^{32} -4.80150e44 q^{33} +1.72832e45 q^{34} -2.89174e44 q^{35} +3.33914e44 q^{36} +2.85266e46 q^{37} +2.24773e46 q^{38} -1.06330e47 q^{39} -1.80438e47 q^{40} -2.41356e47 q^{41} +5.34663e46 q^{42} +1.26598e48 q^{43} -4.48289e47 q^{44} -1.34019e48 q^{45} +1.92478e49 q^{46} -1.54116e49 q^{47} +2.76203e49 q^{48} -7.20163e49 q^{49} -1.64051e49 q^{50} -2.57647e50 q^{51} -9.92742e49 q^{52} +3.50384e50 q^{53} +1.25896e51 q^{54} +1.79924e51 q^{55} +3.48330e50 q^{56} -3.35077e51 q^{57} -8.85809e51 q^{58} +3.68928e51 q^{59} +3.85477e51 q^{60} -9.17858e51 q^{61} -7.90602e52 q^{62} +2.58720e51 q^{63} +2.11989e53 q^{64} +3.98445e53 q^{65} -3.32668e53 q^{66} +4.08228e53 q^{67} -2.40550e53 q^{68} -2.86934e54 q^{69} -2.00352e53 q^{70} -3.75256e52 q^{71} +1.61435e54 q^{72} -2.19258e54 q^{73} +1.97644e55 q^{74} +2.44557e54 q^{75} -3.12842e54 q^{76} -3.47339e54 q^{77} -7.36697e55 q^{78} +1.38224e56 q^{79} -1.03500e56 q^{80} -1.38748e56 q^{81} -1.67221e56 q^{82} +1.05696e56 q^{83} -7.44152e54 q^{84} +9.65467e56 q^{85} +8.77123e56 q^{86} +1.32051e57 q^{87} -2.16731e57 q^{88} -3.89442e57 q^{89} -9.28540e56 q^{90} -7.69187e56 q^{91} -2.67894e57 q^{92} +1.17858e58 q^{93} -1.06778e58 q^{94} +1.25562e58 q^{95} -8.62123e57 q^{96} +7.21075e58 q^{97} -4.98959e58 q^{98} -1.60976e58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.92842e8	0.912535	0.456267	−	0.889843i	$-0.349186\pi$
$2$	6.92842e8	0.912535	0.456267	+	0.889843i	$0.349186\pi$
$3$	−1.03284e14	−0.868875	−0.434438	−	0.900702i	$-0.643053\pi$
$3$	−1.03284e14	−0.868875	−0.434438	+	0.900702i	$0.643053\pi$
$4$	−9.64308e16	−0.167281
$5$	3.87033e20	0.929250	0.464625	−	0.885508i	$-0.346189\pi$
$5$	3.87033e20	0.929250	0.464625	+	0.885508i	$0.346189\pi$
$6$	−7.15597e22	−0.792879
$7$	−7.47157e23	−0.0877040	−0.0438520	−	0.999038i	$-0.513963\pi$
$7$	−7.47157e23	−0.0877040	−0.0438520	+	0.999038i	$0.513963\pi$
$8$	−4.66207e26	−1.06518
$9$	−3.46273e27	−0.245056
$10$	2.68153e29	0.847973
$11$	4.64881e30	0.883604	0.441802	−	0.897113i	$-0.354339\pi$
$11$	4.64881e30	0.883604	0.441802	+	0.897113i	$0.354339\pi$
$12$	9.95979e30	0.145346
$13$	1.02949e33	1.41674	0.708372	−	0.705839i	$-0.249430\pi$
$13$	1.02949e33	1.41674	0.708372	+	0.705839i	$0.249430\pi$
$14$	−5.17661e32	−0.0800329
$15$	−3.99744e34	−0.807402
$16$	−2.67420e35	−0.804736
$17$	2.49454e36	1.25530	0.627649	−	0.778497i	$-0.284017\pi$
$17$	2.49454e36	1.25530	0.627649	+	0.778497i	$0.284017\pi$
$18$	−2.39912e36	−0.223622
$19$	3.24421e37	0.613590	0.306795	−	0.951776i	$-0.400743\pi$
$19$	3.24421e37	0.613590	0.306795	+	0.951776i	$0.400743\pi$
$20$	−3.73219e37	−0.155446
$21$	7.71696e37	0.0762039
$22$	3.22089e39	0.806319
$23$	2.77809e40	1.87403	0.937013	−	0.349294i	$-0.113579\pi$
$23$	2.77809e40	1.87403	0.937013	+	0.349294i	$0.113579\pi$
$24$	4.81519e40	0.925512
$25$	−2.36780e40	−0.136494
$26$	7.13271e41	1.29283
$27$	1.81709e42	1.08180
$28$	7.20489e40	0.0146712
$29$	−1.27852e43	−0.924624	−0.462312	−	0.886717i	$-0.652980\pi$
$29$	−1.27852e43	−0.924624	−0.462312	+	0.886717i	$0.652980\pi$
$30$	−2.76960e43	−0.736783
$31$	−1.14110e44	−1.15386	−0.576931	−	0.816793i	$-0.695750\pi$
$31$	−1.14110e44	−1.15386	−0.576931	+	0.816793i	$0.695750\pi$
$32$	8.34708e43	0.330834
$33$	−4.80150e44	−0.767742
$34$	1.72832e45	1.14550
$35$	−2.89174e44	−0.0814990
$36$	3.33914e44	0.0409931
$37$	2.85266e46	1.56063	0.780313	−	0.625390i	$-0.215060\pi$
$37$	2.85266e46	1.56063	0.780313	+	0.625390i	$0.215060\pi$
$38$	2.24773e46	0.559922
$39$	−1.06330e47	−1.23097
$40$	−1.80438e47	−0.989822
$41$	−2.41356e47	−0.639049	−0.319524	−	0.947578i	$-0.603523\pi$
$41$	−2.41356e47	−0.639049	−0.319524	+	0.947578i	$0.603523\pi$
$42$	5.34663e46	0.0695387
$43$	1.26598e48	0.822445	0.411223	−	0.911535i	$-0.365102\pi$
$43$	1.26598e48	0.822445	0.411223	+	0.911535i	$0.365102\pi$
$44$	−4.48289e47	−0.147810
$45$	−1.34019e48	−0.227718
$46$	1.92478e49	1.71011
$47$	−1.54116e49	−0.726038	−0.363019	−	0.931782i	$-0.618254\pi$
$47$	−1.54116e49	−0.726038	−0.363019	+	0.931782i	$0.618254\pi$
$48$	2.76203e49	0.699216
$49$	−7.20163e49	−0.992308
$50$	−1.64051e49	−0.124556
$51$	−2.57647e50	−1.09070
$52$	−9.92742e49	−0.236994
$53$	3.50384e50	0.476876	0.238438	−	0.971158i	$-0.423365\pi$
$53$	3.50384e50	0.476876	0.238438	+	0.971158i	$0.423365\pi$
$54$	1.25896e51	0.987178
$55$	1.79924e51	0.821089
$56$	3.48330e50	0.0934209
$57$	−3.35077e51	−0.533133
$58$	−8.85809e51	−0.843751
$59$	3.68928e51	0.212230	0.106115	−	0.994354i	$-0.466159\pi$
$59$	3.68928e51	0.212230	0.106115	+	0.994354i	$0.466159\pi$
$60$	3.85477e51	0.135063
$61$	−9.17858e51	−0.197490	−0.0987450	−	0.995113i	$-0.531483\pi$
$61$	−9.17858e51	−0.197490	−0.0987450	+	0.995113i	$0.531483\pi$
$62$	−7.90602e52	−1.05294
$63$	2.58720e51	0.0214924
$64$	2.11989e53	1.10663
$65$	3.98445e53	1.31651
$66$	−3.32668e53	−0.700591
$67$	4.08228e53	0.551691	0.275845	−	0.961202i	$-0.411042\pi$
$67$	4.08228e53	0.551691	0.275845	+	0.961202i	$0.411042\pi$
$68$	−2.40550e53	−0.209987
$69$	−2.86934e54	−1.62830
$70$	−2.00352e53	−0.0743706
$71$	−3.75256e52	−0.00916657	−0.00458329	−	0.999989i	$-0.501459\pi$
$71$	−3.75256e52	−0.00916657	−0.00458329	+	0.999989i	$0.501459\pi$
$72$	1.61435e54	0.261029
$73$	−2.19258e54	−0.236010	−0.118005	−	0.993013i	$-0.537650\pi$
$73$	−2.19258e54	−0.236010	−0.118005	+	0.993013i	$0.537650\pi$
$74$	1.97644e55	1.42412
$75$	2.44557e54	0.118597
$76$	−3.12842e54	−0.102642
$77$	−3.47339e54	−0.0774956
$78$	−7.36697e55	−1.12331
$79$	1.38224e56	1.44739	0.723694	−	0.690121i	$-0.242443\pi$
$79$	1.38224e56	1.44739	0.723694	+	0.690121i	$0.242443\pi$
$80$	−1.03500e56	−0.747801
$81$	−1.38748e56	−0.694892
$82$	−1.67221e56	−0.583154
$83$	1.05696e56	0.257783	0.128892	−	0.991659i	$-0.458858\pi$
$83$	1.05696e56	0.257783	0.128892	+	0.991659i	$0.458858\pi$
$84$	−7.44152e54	−0.0127474
$85$	9.65467e56	1.16649
$86$	8.77123e56	0.750510
$87$	1.32051e57	0.803383
$88$	−2.16731e57	−0.941201
$89$	−3.89442e57	−1.21182	−0.605909	−	0.795534i	$-0.707190\pi$
$89$	−3.89442e57	−1.21182	−0.605909	+	0.795534i	$0.707190\pi$
$90$	−9.28540e56	−0.207800
$91$	−7.69187e56	−0.124254
$92$	−2.67894e57	−0.313489
$93$	1.17858e58	1.00256
$94$	−1.06778e58	−0.662535
$95$	1.25562e58	0.570179
$96$	−8.62123e57	−0.287454
$97$	7.21075e58	1.77098	0.885492	−	0.464655i	$-0.153822\pi$
$97$	7.21075e58	1.77098	0.885492	+	0.464655i	$0.153822\pi$
$98$	−4.98959e58	−0.905515
$99$	−1.60976e58	−0.216532
$100$	2.28329e57	0.0228329
$101$	1.38211e58	0.103053	0.0515267	−	0.998672i	$-0.483591\pi$
$101$	1.38211e58	0.103053	0.0515267	+	0.998672i	$0.483591\pi$
$102$	−1.78508e59	−0.995299
$103$	1.89666e59	0.793034	0.396517	−	0.918027i	$-0.370219\pi$
$103$	1.89666e59	0.793034	0.396517	+	0.918027i	$0.370219\pi$
$104$	−4.79954e59	−1.50909
$105$	2.98672e58	0.0708124
$106$	2.42760e59	0.435166
$107$	8.57892e59	1.16577	0.582883	−	0.812556i	$-0.301925\pi$
$107$	8.57892e59	1.16577	0.582883	+	0.812556i	$0.301925\pi$
$108$	−1.75224e59	−0.180964
$109$	1.17707e60	0.926233	0.463117	−	0.886297i	$-0.346731\pi$
$109$	1.17707e60	0.926233	0.463117	+	0.886297i	$0.346731\pi$
$110$	1.24659e60	0.749272
$111$	−2.94635e60	−1.35599
$112$	1.99804e59	0.0705786
$113$	−7.22546e60	−1.96359	−0.981796	−	0.189938i	$-0.939171\pi$
$113$	−7.22546e60	−1.96359	−0.981796	+	0.189938i	$0.939171\pi$
$114$	−2.32155e60	−0.486503
$115$	1.07521e61	1.74144
$116$	1.23288e60	0.154672
$117$	−3.56483e60	−0.347181
$118$	2.55609e60	0.193667
$119$	−1.86381e60	−0.110095
$120$	1.86364e61	0.860032
$121$	−6.06869e60	−0.219244
$122$	−6.35930e60	−0.180217
$123$	2.49283e61	0.555254
$124$	1.10037e61	0.193019
$125$	−7.63036e61	−1.05609
$126$	1.79252e60	0.0196125
$127$	−1.53871e62	−1.33336	−0.666680	−	0.745344i	$-0.732285\pi$
$127$	−1.53871e62	−1.33336	−0.666680	+	0.745344i	$0.732285\pi$
$128$	9.87572e61	0.679008
$129$	−1.30756e62	−0.714602
$130$	2.76059e62	1.20136
$131$	1.44734e62	0.502421	0.251210	−	0.967933i	$-0.419171\pi$
$131$	1.44734e62	0.502421	0.251210	+	0.967933i	$0.419171\pi$
$132$	4.63012e61	0.128428
$133$	−2.42394e61	−0.0538143
$134$	2.82837e62	0.503437
$135$	7.03275e62	1.00526
$136$	−1.16297e63	−1.33712
$137$	−2.88977e62	−0.267674	−0.133837	−	0.991003i	$-0.542730\pi$
$137$	−2.88977e62	−0.267674	−0.133837	+	0.991003i	$0.542730\pi$
$138$	−1.98800e63	−1.48588
$139$	5.60982e61	0.0338854	0.0169427	−	0.999856i	$-0.494607\pi$
$139$	5.60982e61	0.0338854	0.0169427	+	0.999856i	$0.494607\pi$
$140$	2.78853e61	0.0136332
$141$	1.59177e63	0.630837
$142$	−2.59993e61	−0.00836481
$143$	4.78589e63	1.25184
$144$	9.26002e62	0.197205
$145$	−4.94827e63	−0.859207
$146$	−1.51911e63	−0.215367
$147$	7.43816e63	0.862192
$148$	−2.75084e63	−0.261063
$149$	−4.37262e62	−0.0340210	−0.0170105	−	0.999855i	$-0.505415\pi$
$149$	−4.37262e62	−0.0340210	−0.0170105	+	0.999855i	$0.505415\pi$
$150$	1.69439e63	0.108224
$151$	−2.73644e63	−0.143670	−0.0718349	−	0.997417i	$-0.522885\pi$
$151$	−2.73644e63	−0.143670	−0.0718349	+	0.997417i	$0.522885\pi$
$152$	−1.51248e64	−0.653586
$153$	−8.63791e63	−0.307618
$154$	−2.40651e63	−0.0707175
$155$	−4.41643e64	−1.07223
$156$	1.02535e64	0.205918
$157$	9.42454e64	1.56755	0.783773	−	0.621047i	$-0.213292\pi$
$157$	9.42454e64	1.56755	0.783773	+	0.621047i	$0.213292\pi$
$158$	9.57675e64	1.32079
$159$	−3.61891e64	−0.414346
$160$	3.23059e64	0.307428
$161$	−2.07567e64	−0.164360
$162$	−9.61302e64	−0.634113
$163$	−9.60370e64	−0.528329	−0.264164	−	0.964478i	$-0.585096\pi$
$163$	−9.60370e64	−0.528329	−0.264164	+	0.964478i	$0.585096\pi$
$164$	2.32741e64	0.106901
$165$	−1.85834e65	−0.713424
$166$	7.32307e64	0.235236
$167$	−3.29003e65	−0.885245	−0.442623	−	0.896708i	$-0.645952\pi$
$167$	−3.29003e65	−0.885245	−0.442623	+	0.896708i	$0.645952\pi$
$168$	−3.59770e64	−0.0811711
$169$	5.31813e65	1.00717
$170$	6.68916e65	1.06446
$171$	−1.12338e65	−0.150364
$172$	−1.22079e65	−0.137579
$173$	−1.32471e65	−0.125823	−0.0629114	−	0.998019i	$-0.520039\pi$
$173$	−1.32471e65	−0.125823	−0.0629114	+	0.998019i	$0.520039\pi$
$174$	9.14902e65	0.733115
$175$	1.76912e64	0.0119711
$176$	−1.24318e66	−0.711068
$177$	−3.81045e65	−0.184402
$178$	−2.69822e66	−1.10583
$179$	3.36648e66	1.16953	0.584766	−	0.811202i	$-0.301186\pi$
$179$	3.36648e66	1.16953	0.584766	+	0.811202i	$0.301186\pi$
$180$	1.29236e65	0.0380928
$181$	−2.06923e66	−0.517952	−0.258976	−	0.965884i	$-0.583385\pi$
$181$	−2.06923e66	−0.517952	−0.258976	+	0.965884i	$0.583385\pi$
$182$	−5.32925e65	−0.113386
$183$	9.48003e65	0.171594
$184$	−1.29517e67	−1.99618
$185$	1.10407e67	1.45021
$186$	8.16568e66	0.914873
$187$	1.15966e67	1.10919
$188$	1.48615e66	0.121452
$189$	−1.35765e66	−0.0948780
$190$	8.69944e66	0.520308
$191$	−1.71430e67	−0.878217	−0.439108	−	0.898434i	$-0.644706\pi$
$191$	−1.71430e67	−0.878217	−0.439108	+	0.898434i	$0.644706\pi$
$192$	−2.18951e67	−0.961527
$193$	−4.57672e67	−1.72430	−0.862152	−	0.506650i	$-0.830884\pi$
$193$	−4.57672e67	−1.72430	−0.862152	+	0.506650i	$0.830884\pi$
$194$	4.99591e67	1.61608
$195$	−4.11531e67	−1.14388
$196$	6.94459e66	0.165994
$197$	2.68332e67	0.551974	0.275987	−	0.961161i	$-0.410995\pi$
$197$	2.68332e67	0.551974	0.275987	+	0.961161i	$0.410995\pi$
$198$	−1.11531e67	−0.197593
$199$	9.84849e67	1.50385	0.751924	−	0.659250i	$-0.229126\pi$
$199$	9.84849e67	1.50385	0.751924	+	0.659250i	$0.229126\pi$
$200$	1.10389e67	0.145392
$201$	−4.21635e67	−0.479351
$202$	9.57584e66	0.0940397
$203$	9.55251e66	0.0810932
$204$	2.48451e67	0.182453
$205$	−9.34126e67	−0.593836
$206$	1.31409e68	0.723671
$207$	−9.61979e67	−0.459241
$208$	−2.75305e68	−1.14011
$209$	1.50817e68	0.542171
$210$	2.06932e67	0.0646188
$211$	−3.01598e68	−0.818646	−0.409323	−	0.912390i	$-0.634235\pi$
$211$	−3.01598e68	−0.818646	−0.409323	+	0.912390i	$0.634235\pi$
$212$	−3.37878e67	−0.0797722
$213$	3.87581e66	0.00796461
$214$	5.94384e68	1.06380
$215$	4.89975e68	0.764257
$216$	−8.47143e68	−1.15231
$217$	8.52581e67	0.101198
$218$	8.15523e68	0.845220
$219$	2.26459e68	0.205063
$220$	−1.73502e68	−0.137352
$221$	2.56809e69	1.77844
$222$	−2.04135e69	−1.23739
$223$	−3.24546e69	−1.72299	−0.861494	−	0.507767i	$-0.830471\pi$
$223$	−3.24546e69	−1.72299	−0.861494	+	0.507767i	$0.830471\pi$
$224$	−6.23658e67	−0.0290155
$225$	8.19906e67	0.0334487
$226$	−5.00610e69	−1.79185
$227$	4.06034e69	1.27585	0.637926	−	0.770098i	$-0.279793\pi$
$227$	4.06034e69	1.27585	0.637926	+	0.770098i	$0.279793\pi$
$228$	3.23117e68	0.0891829
$229$	−1.33796e69	−0.324560	−0.162280	−	0.986745i	$-0.551885\pi$
$229$	−1.33796e69	−0.324560	−0.162280	+	0.986745i	$0.551885\pi$
$230$	7.44953e69	1.58912
$231$	3.58747e68	0.0673341
$232$	5.96053e69	0.984894
$233$	1.30041e69	0.189270	0.0946348	−	0.995512i	$-0.469832\pi$
$233$	1.30041e69	0.189270	0.0946348	+	0.995512i	$0.469832\pi$
$234$	−2.46987e69	−0.316815
$235$	−5.96478e69	−0.674671
$236$	−3.55760e68	−0.0355020
$237$	−1.42764e70	−1.25760
$238$	−1.29133e69	−0.100465
$239$	1.00216e70	0.688968	0.344484	−	0.938792i	$-0.388054\pi$
$239$	1.00216e70	0.688968	0.344484	+	0.938792i	$0.388054\pi$
$240$	1.06899e70	0.649746
$241$	−8.59826e69	−0.462283	−0.231142	−	0.972920i	$-0.574246\pi$
$241$	−8.59826e69	−0.462283	−0.231142	+	0.972920i	$0.574246\pi$
$242$	−4.20465e69	−0.200067
$243$	−1.13458e70	−0.478023
$244$	8.85097e68	0.0330363
$245$	−2.78727e70	−0.922102
$246$	1.72713e70	0.506688
$247$	3.33987e70	0.869300
$248$	5.31990e70	1.22908
$249$	−1.09167e70	−0.223982
$250$	−5.28664e70	−0.963716
$251$	4.07048e70	0.659586	0.329793	−	0.944053i	$-0.393021\pi$
$251$	4.07048e70	0.659586	0.329793	+	0.944053i	$0.393021\pi$
$252$	−2.49486e68	−0.00359526
$253$	1.29148e71	1.65590
$254$	−1.06608e71	−1.21674
$255$	−9.97177e70	−1.01353
$256$	−5.37802e70	−0.487016
$257$	2.69905e70	0.217863	0.108932	−	0.994049i	$-0.465257\pi$
$257$	2.69905e70	0.217863	0.108932	+	0.994049i	$0.465257\pi$
$258$	−9.05931e70	−0.652099
$259$	−2.13138e70	−0.136873
$260$	−3.84223e70	−0.220227
$261$	4.42715e70	0.226584
$262$	1.00278e71	0.458476
$263$	6.00409e69	0.0245331	0.0122666	−	0.999925i	$-0.496095\pi$
$263$	6.00409e69	0.0245331	0.0122666	+	0.999925i	$0.496095\pi$
$264$	2.23849e71	0.817786
$265$	1.35610e71	0.443137
$266$	−1.67940e70	−0.0491074
$267$	4.02232e71	1.05292
$268$	−3.93657e70	−0.0922873
$269$	−4.29641e71	−0.902430	−0.451215	−	0.892415i	$-0.649009\pi$
$269$	−4.29641e71	−0.902430	−0.451215	+	0.892415i	$0.649009\pi$
$270$	4.87258e71	0.917335
$271$	−9.26809e71	−1.56457	−0.782287	−	0.622918i	$-0.785947\pi$
$271$	−9.26809e71	−1.56457	−0.782287	+	0.622918i	$0.785947\pi$
$272$	−6.67088e71	−1.01018
$273$	7.94450e70	0.107961
$274$	−2.00215e71	−0.244262
$275$	−1.10075e71	−0.120607
$276$	2.76692e71	0.272382
$277$	1.16877e72	1.03413	0.517067	−	0.855945i	$-0.327024\pi$
$277$	1.16877e72	1.03413	0.517067	+	0.855945i	$0.327024\pi$
$278$	3.88672e70	0.0309216
$279$	3.95132e71	0.282760
$280$	1.34815e71	0.0868114
$281$	−2.43176e72	−1.40957	−0.704783	−	0.709423i	$-0.748955\pi$
$281$	−2.43176e72	−1.40957	−0.704783	+	0.709423i	$0.748955\pi$
$282$	1.10285e72	0.575660
$283$	1.52233e72	0.715831	0.357915	−	0.933754i	$-0.383488\pi$
$283$	1.52233e72	0.715831	0.357915	+	0.933754i	$0.383488\pi$
$284$	3.61863e69	0.00153339
$285$	−1.29686e72	−0.495414
$286$	3.31586e72	1.14235
$287$	1.80331e71	0.0560471
$288$	−2.89037e71	−0.0810728
$289$	2.27372e72	0.575772
$290$	−3.42837e72	−0.784056
$291$	−7.44758e72	−1.53876
$292$	2.11432e71	0.0394799
$293$	−4.64053e72	−0.783380	−0.391690	−	0.920097i	$-0.628110\pi$
$293$	−4.64053e72	−0.783380	−0.391690	+	0.920097i	$0.628110\pi$
$294$	5.15347e72	0.786780
$295$	1.42787e72	0.197215
$296$	−1.32993e73	−1.66235
$297$	8.44733e72	0.955881
$298$	−3.02954e71	−0.0310453
$299$	2.86001e73	2.65502
$300$	−2.35828e71	−0.0198389
$301$	−9.45884e71	−0.0721317
$302$	−1.89592e72	−0.131104
$303$	−1.42750e72	−0.0895405
$304$	−8.67566e72	−0.493778
$305$	−3.55241e72	−0.183518
$306$	−5.98470e72	−0.280712
$307$	9.50693e72	0.405003	0.202501	−	0.979282i	$-0.435093\pi$
$307$	9.50693e72	0.405003	0.202501	+	0.979282i	$0.435093\pi$
$308$	3.34942e71	0.0129635
$309$	−1.95896e73	−0.689048
$310$	−3.05989e73	−0.978444
$311$	−3.66965e73	−1.06707	−0.533536	−	0.845778i	$-0.679137\pi$
$311$	−3.66965e73	−1.06707	−0.533536	+	0.845778i	$0.679137\pi$
$312$	4.95717e73	1.31121
$313$	−2.59653e73	−0.624937	−0.312468	−	0.949928i	$-0.601156\pi$
$313$	−2.59653e73	−0.624937	−0.312468	+	0.949928i	$0.601156\pi$
$314$	6.52972e73	1.43044
$315$	1.00133e72	0.0199718
$316$	−1.33291e73	−0.242120
$317$	9.43841e73	1.56189	0.780945	−	0.624599i	$-0.214738\pi$
$317$	9.43841e73	1.56189	0.780945	+	0.624599i	$0.214738\pi$
$318$	−2.50734e73	−0.378105
$319$	−5.94358e73	−0.817001
$320$	8.20467e73	1.02834
$321$	−8.86069e73	−1.01291
$322$	−1.43811e73	−0.149984
$323$	8.09281e73	0.770238
$324$	1.33795e73	0.116242
$325$	−2.43762e73	−0.193378
$326$	−6.65384e73	−0.482118
$327$	−1.21573e74	−0.804781
$328$	1.12522e74	0.680704
$329$	1.15148e73	0.0636765
$330$	−1.28753e74	−0.651024
$331$	2.42184e73	0.112000	0.0560002	−	0.998431i	$-0.482165\pi$
$331$	2.42184e73	0.112000	0.0560002	+	0.998431i	$0.482165\pi$
$332$	−1.01924e73	−0.0431222
$333$	−9.87798e73	−0.382440
$334$	−2.27947e74	−0.807817
$335$	1.57997e74	0.512659
$336$	−2.06367e73	−0.0613240
$337$	4.16269e74	1.13316	0.566581	−	0.824006i	$-0.308266\pi$
$337$	4.16269e74	1.13316	0.566581	+	0.824006i	$0.308266\pi$
$338$	3.68462e74	0.919073
$339$	7.46277e74	1.70612
$340$	−9.31008e73	−0.195131
$341$	−5.30476e74	−1.01956
$342$	−7.78328e73	−0.137212
$343$	1.08032e74	0.174733
$344$	−5.90209e74	−0.876055
$345$	−1.11053e75	−1.51309
$346$	−9.17812e73	−0.114818
$347$	3.03466e74	0.348651	0.174326	−	0.984688i	$-0.444225\pi$
$347$	3.03466e74	0.348651	0.174326	+	0.984688i	$0.444225\pi$
$348$	−1.27337e74	−0.134390
$349$	−7.65470e74	−0.742297	−0.371149	−	0.928573i	$-0.621036\pi$
$349$	−7.65470e74	−0.742297	−0.371149	+	0.928573i	$0.621036\pi$
$350$	1.22572e73	0.0109241
$351$	1.87067e75	1.53263
$352$	3.88040e74	0.292327
$353$	3.52861e73	0.0244484	0.0122242	−	0.999925i	$-0.496109\pi$
$353$	3.52861e73	0.0244484	0.0122242	+	0.999925i	$0.496109\pi$
$354$	−2.64004e74	−0.168273
$355$	−1.45237e73	−0.00851804
$356$	3.75542e74	0.202714
$357$	1.92502e74	0.0956585
$358$	2.33244e75	1.06724
$359$	−1.13038e75	−0.476363	−0.238182	−	0.971221i	$-0.576551\pi$
$359$	−1.13038e75	−0.476363	−0.238182	+	0.971221i	$0.576551\pi$
$360$	6.24807e74	0.242561
$361$	−1.74303e75	−0.623507
$362$	−1.43365e75	−0.472650
$363$	6.26801e74	0.190495
$364$	7.41733e73	0.0207853
$365$	−8.48599e74	−0.219312
$366$	6.56816e74	0.156586
$367$	−1.14489e75	−0.251834	−0.125917	−	0.992041i	$-0.540187\pi$
$367$	−1.14489e75	−0.251834	−0.125917	+	0.992041i	$0.540187\pi$
$368$	−7.42916e75	−1.50810
$369$	8.35750e74	0.156602
$370$	7.64947e75	1.32337
$371$	−2.61791e74	−0.0418240
$372$	−1.13651e75	−0.167709
$373$	−9.11728e75	−1.24295	−0.621476	−	0.783433i	$-0.713467\pi$
$373$	−9.11728e75	−1.24295	−0.621476	+	0.783433i	$0.713467\pi$
$374$	8.03463e75	1.01217
$375$	7.88097e75	0.917608
$376$	7.18498e75	0.773364
$377$	−1.31621e76	−1.30996
$378$	−9.40639e74	−0.0865795
$379$	1.17838e76	1.00330	0.501648	−	0.865072i	$-0.332727\pi$
$379$	1.17838e76	1.00330	0.501648	+	0.865072i	$0.332727\pi$
$380$	−1.21080e75	−0.0953799
$381$	1.58925e76	1.15852
$382$	−1.18774e76	−0.801403
$383$	8.81216e75	0.550451	0.275225	−	0.961380i	$-0.411247\pi$
$383$	8.81216e75	0.550451	0.275225	+	0.961380i	$0.411247\pi$
$384$	−1.02001e76	−0.589973
$385$	−1.34432e75	−0.0720128
$386$	−3.17094e76	−1.57349
$387$	−4.38374e75	−0.201545
$388$	−6.95339e75	−0.296251
$389$	−2.99716e76	−1.18358	−0.591789	−	0.806093i	$-0.701578\pi$
$389$	−2.99716e76	−1.18358	−0.591789	+	0.806093i	$0.701578\pi$
$390$	−2.85126e76	−1.04383
$391$	6.93005e76	2.35246
$392$	3.35745e76	1.05699
$393$	−1.49488e76	−0.436541
$394$	1.85912e76	0.503695
$395$	5.34973e76	1.34498
$396$	1.55230e75	0.0362217
$397$	−7.53563e76	−1.63230	−0.816149	−	0.577841i	$-0.803895\pi$
$397$	−7.53563e76	−1.63230	−0.816149	+	0.577841i	$0.803895\pi$
$398$	6.82345e76	1.37231
$399$	2.50355e75	0.0467579
$400$	6.33196e75	0.109842
$401$	2.27678e74	0.00366913	0.00183456	−	0.999998i	$-0.499416\pi$
$401$	2.27678e74	0.00366913	0.00183456	+	0.999998i	$0.499416\pi$
$402$	−2.92127e76	−0.437424
$403$	−1.17475e77	−1.63473
$404$	−1.33278e75	−0.0172388
$405$	−5.36999e76	−0.645729
$406$	6.61838e75	0.0740004
$407$	1.32615e77	1.37898
$408$	1.20117e77	1.16179
$409$	−1.56193e77	−1.40548	−0.702740	−	0.711447i	$-0.748040\pi$
$409$	−1.56193e77	−1.40548	−0.702740	+	0.711447i	$0.748040\pi$
$410$	−6.47201e76	−0.541896
$411$	2.98468e76	0.232575
$412$	−1.82897e76	−0.132659
$413$	−2.75647e75	−0.0186134
$414$	−6.66499e76	−0.419073
$415$	4.09078e76	0.239545
$416$	8.59321e76	0.468708
$417$	−5.79407e75	−0.0294422
$418$	1.04493e77	0.494750
$419$	3.54180e77	1.56282	0.781411	−	0.624016i	$-0.214500\pi$
$419$	3.54180e77	1.56282	0.781411	+	0.624016i	$0.214500\pi$
$420$	−2.88011e75	−0.0118456
$421$	−6.31905e76	−0.242287	−0.121144	−	0.992635i	$-0.538656\pi$
$421$	−6.31905e76	−0.242287	−0.121144	+	0.992635i	$0.538656\pi$
$422$	−2.08960e77	−0.747042
$423$	5.33661e76	0.177920
$424$	−1.63351e77	−0.507961
$425$	−5.90657e76	−0.171341
$426$	2.68532e75	0.00726798
$427$	6.85784e75	0.0173207
$428$	−8.27272e76	−0.195010
$429$	−4.94307e77	−1.08769
$430$	3.39475e77	0.697411
$431$	−3.24391e77	−0.622285	−0.311142	−	0.950363i	$-0.600712\pi$
$431$	−3.24391e77	−0.622285	−0.311142	+	0.950363i	$0.600712\pi$
$432$	−4.85926e77	−0.870562
$433$	2.56630e77	0.429451	0.214726	−	0.976674i	$-0.431114\pi$
$433$	2.56630e77	0.429451	0.214726	+	0.976674i	$0.431114\pi$
$434$	5.90704e76	0.0923470
$435$	5.11079e77	0.746543
$436$	−1.13506e77	−0.154941
$437$	9.01273e77	1.14988
$438$	1.56900e77	0.187127
$439$	6.93858e77	0.773690	0.386845	−	0.922145i	$-0.373565\pi$
$439$	6.93858e77	0.773690	0.386845	+	0.922145i	$0.373565\pi$
$440$	−8.38820e77	−0.874611
$441$	2.49373e77	0.243171
$442$	1.77928e78	1.62288
$443$	−6.61525e77	−0.564464	−0.282232	−	0.959346i	$-0.591075\pi$
$443$	−6.61525e77	−0.564464	−0.282232	+	0.959346i	$0.591075\pi$
$444$	2.84119e77	0.226831
$445$	−1.50727e78	−1.12608
$446$	−2.24859e78	−1.57229
$447$	4.51623e76	0.0295600
$448$	−1.58389e77	−0.0970563
$449$	−5.52670e77	−0.317102	−0.158551	−	0.987351i	$-0.550682\pi$
$449$	−5.52670e77	−0.317102	−0.158551	+	0.987351i	$0.550682\pi$
$450$	5.68065e76	0.0305231
$451$	−1.12202e78	−0.564666
$452$	6.96757e77	0.328471
$453$	2.82631e77	0.124831
$454$	2.81318e78	1.16426
$455$	−2.97701e77	−0.115463
$456$	1.56215e78	0.567885
$457$	−1.03722e78	−0.353464	−0.176732	−	0.984259i	$-0.556553\pi$
$457$	−1.03722e78	−0.353464	−0.176732	+	0.984259i	$0.556553\pi$
$458$	−9.26993e77	−0.296172
$459$	4.53281e78	1.35798
$460$	−1.03684e78	−0.291309
$461$	−3.77107e78	−0.993774	−0.496887	−	0.867815i	$-0.665524\pi$
$461$	−3.77107e78	−0.993774	−0.496887	+	0.867815i	$0.665524\pi$
$462$	2.48555e77	0.0614447
$463$	−3.38674e78	−0.785495	−0.392747	−	0.919646i	$-0.628475\pi$
$463$	−3.38674e78	−0.785495	−0.392747	+	0.919646i	$0.628475\pi$
$464$	3.41900e78	0.744078
$465$	4.56148e78	0.931631
$466$	9.00979e77	0.172715
$467$	1.56624e78	0.281844	0.140922	−	0.990021i	$-0.454993\pi$
$467$	1.56624e78	0.281844	0.140922	+	0.990021i	$0.454993\pi$
$468$	3.43760e77	0.0580767
$469$	−3.05010e77	−0.0483855
$470$	−4.13265e78	−0.615661
$471$	−9.73408e78	−1.36200
$472$	−1.71997e78	−0.226064
$473$	5.88530e78	0.726716
$474$	−9.89128e78	−1.14760
$475$	−7.68165e77	−0.0837516
$476$	1.79729e77	0.0184167
$477$	−1.21328e78	−0.116861
$478$	6.94339e78	0.628707
$479$	−1.69803e78	−0.144560	−0.0722800	−	0.997384i	$-0.523028\pi$
$479$	−1.69803e78	−0.144560	−0.0722800	+	0.997384i	$0.523028\pi$
$480$	−3.33670e78	−0.267116
$481$	2.93677e79	2.21101
$482$	−5.95724e78	−0.421849
$483$	2.14384e78	0.142808
$484$	5.85209e77	0.0366752
$485$	2.79080e79	1.64569
$486$	−7.86083e78	−0.436213
$487$	−1.96778e79	−1.02772	−0.513858	−	0.857875i	$-0.671784\pi$
$487$	−1.96778e79	−1.02772	−0.513858	+	0.857875i	$0.671784\pi$
$488$	4.27912e78	0.210363
$489$	9.91911e78	0.459052
$490$	−1.93114e79	−0.841450
$491$	−2.71958e79	−1.11583	−0.557915	−	0.829898i	$-0.688399\pi$
$491$	−2.71958e79	−1.11583	−0.557915	+	0.829898i	$0.688399\pi$
$492$	−2.40385e78	−0.0928832
$493$	−3.18930e79	−1.16068
$494$	2.31400e79	0.793267
$495$	−6.23029e78	−0.201213
$496$	3.05153e79	0.928555
$497$	2.80375e76	0.000803945 0
$498$	−7.56358e78	−0.204391
$499$	−6.54096e79	−1.66600	−0.833000	−	0.553273i	$-0.813379\pi$
$499$	−6.54096e79	−1.66600	−0.833000	+	0.553273i	$0.813379\pi$
$500$	7.35802e78	0.176663
$501$	3.39808e79	0.769168
$502$	2.82020e79	0.601895
$503$	5.77167e79	1.16157	0.580786	−	0.814056i	$-0.302745\pi$
$503$	5.77167e79	1.16157	0.580786	+	0.814056i	$0.302745\pi$
$504$	−1.20617e78	−0.0228933
$505$	5.34922e78	0.0957623
$506$	8.94794e79	1.51106
$507$	−5.49279e79	−0.875101
$508$	1.48379e79	0.223046
$509$	−4.64283e79	−0.658580	−0.329290	−	0.944229i	$-0.606809\pi$
$509$	−4.64283e79	−0.658580	−0.329290	+	0.944229i	$0.606809\pi$
$510$	−6.90886e79	−0.924881
$511$	1.63820e78	0.0206990
$512$	−9.41908e79	−1.12343
$513$	5.89504e79	0.663781
$514$	1.87002e79	0.198808
$515$	7.34070e79	0.736927
$516$	1.26089e79	0.119539
$517$	−7.16454e79	−0.641531
$518$	−1.47671e79	−0.124901
$519$	1.36821e79	0.109324
$520$	−1.85758e80	−1.40233
$521$	9.43942e79	0.673337	0.336669	−	0.941623i	$-0.390700\pi$
$521$	9.43942e79	0.673337	0.336669	+	0.941623i	$0.390700\pi$
$522$	3.06732e79	0.206766
$523$	1.03084e78	0.00656739	0.00328369	−	0.999995i	$-0.498955\pi$
$523$	1.03084e78	0.00656739	0.00328369	+	0.999995i	$0.498955\pi$
$524$	−1.39568e79	−0.0840453
$525$	−1.82722e78	−0.0104014
$526$	4.15989e78	0.0223873
$527$	−2.84652e80	−1.44844
$528$	1.28401e80	0.617830
$529$	5.52023e80	2.51197
$530$	9.39562e79	0.404378
$531$	−1.27750e79	−0.0520082
$532$	2.33742e78	0.00900210
$533$	−2.48472e80	−0.905369
$534$	2.78684e80	0.960825
$535$	3.32032e80	1.08329
$536$	−1.90319e80	−0.587652
$537$	−3.47705e80	−1.01618
$538$	−2.97673e80	−0.823499
$539$	−3.34790e80	−0.876808
$540$	−6.78173e79	−0.168161
$541$	−1.44420e80	−0.339085	−0.169542	−	0.985523i	$-0.554229\pi$
$541$	−1.44420e80	−0.339085	−0.169542	+	0.985523i	$0.554229\pi$
$542$	−6.42132e80	−1.42773
$543$	2.13719e80	0.450036
$544$	2.08221e80	0.415295
$545$	4.55564e80	0.860702
$546$	5.50428e79	0.0985185
$547$	5.62958e80	0.954662	0.477331	−	0.878724i	$-0.341604\pi$
$547$	5.62958e80	0.954662	0.477331	+	0.878724i	$0.341604\pi$
$548$	2.78662e79	0.0447767
$549$	3.17829e79	0.0483960
$550$	−7.62643e79	−0.110058
$551$	−4.14778e80	−0.567340
$552$	1.33771e81	1.73443
$553$	−1.03275e80	−0.126942
$554$	8.09775e80	0.943684
$555$	−1.14033e81	−1.26005
$556$	−5.40960e78	−0.00566838
$557$	−1.07909e81	−1.07233	−0.536166	−	0.844113i	$-0.680128\pi$
$557$	−1.07909e81	−1.07233	−0.536166	+	0.844113i	$0.680128\pi$
$558$	2.73764e80	0.258029
$559$	1.30331e81	1.16519
$560$	7.73308e79	0.0655852
$561$	−1.19775e81	−0.963745
$562$	−1.68483e81	−1.28628
$563$	1.75793e81	1.27351	0.636756	−	0.771065i	$-0.280276\pi$
$563$	1.75793e81	1.27351	0.636756	+	0.771065i	$0.280276\pi$
$564$	−1.53496e80	−0.105527
$565$	−2.79649e81	−1.82467
$566$	1.05474e81	0.653220
$567$	1.03666e80	0.0609448
$568$	1.74947e79	0.00976408
$569$	1.15567e81	0.612380	0.306190	−	0.951970i	$-0.400946\pi$
$569$	1.15567e81	0.612380	0.306190	+	0.951970i	$0.400946\pi$
$570$	−8.98516e80	−0.452082
$571$	8.43971e80	0.403239	0.201619	−	0.979464i	$-0.435380\pi$
$571$	8.43971e80	0.403239	0.201619	+	0.979464i	$0.435380\pi$
$572$	−4.61507e80	−0.209409
$573$	1.77060e81	0.763061
$574$	1.24941e80	0.0511449
$575$	−6.57797e80	−0.255794
$576$	−7.34061e80	−0.271187
$577$	−7.28689e80	−0.255773	−0.127887	−	0.991789i	$-0.540819\pi$
$577$	−7.28689e80	−0.255773	−0.127887	+	0.991789i	$0.540819\pi$
$578$	1.57533e81	0.525412
$579$	4.72704e81	1.49821
$580$	4.77166e80	0.143729
$581$	−7.89715e79	−0.0226086
$582$	−5.15999e81	−1.40417
$583$	1.62887e81	0.421370
$584$	1.02220e81	0.251394
$585$	−1.37971e81	−0.322618
$586$	−3.21515e81	−0.714862
$587$	5.13026e81	1.08471	0.542357	−	0.840148i	$-0.317532\pi$
$587$	5.13026e81	1.08471	0.542357	+	0.840148i	$0.317532\pi$
$588$	−7.17267e80	−0.144228
$589$	−3.70197e81	−0.707998
$590$	9.89289e80	0.179965
$591$	−2.77145e81	−0.479597
$592$	−7.62856e81	−1.25589
$593$	−6.47695e81	−1.01451	−0.507256	−	0.861796i	$-0.669340\pi$
$593$	−6.47695e81	−1.01451	−0.507256	+	0.861796i	$0.669340\pi$
$594$	5.85266e81	0.872275
$595$	−7.21355e80	−0.102305
$596$	4.21655e79	0.00569106
$597$	−1.01719e82	−1.30666
$598$	1.98153e82	2.42279
$599$	9.11251e81	1.06059	0.530294	−	0.847814i	$-0.322081\pi$
$599$	9.11251e81	1.06059	0.530294	+	0.847814i	$0.322081\pi$
$600$	−1.14014e81	−0.126327
$601$	1.84804e82	1.94946	0.974730	−	0.223386i	$-0.0717110\pi$
$601$	1.84804e82	1.94946	0.974730	+	0.223386i	$0.0717110\pi$
$602$	−6.55348e80	−0.0658227
$603$	−1.41358e81	−0.135195
$604$	2.63877e80	0.0240332
$605$	−2.34878e81	−0.203732
$606$	−9.89034e80	−0.0817088
$607$	−2.33831e82	−1.84008	−0.920039	−	0.391827i	$-0.871843\pi$
$607$	−2.33831e82	−1.84008	−0.920039	+	0.391827i	$0.871843\pi$
$608$	2.70797e81	0.202997
$609$	−9.86625e80	−0.0704599
$610$	−2.46126e81	−0.167466
$611$	−1.58660e82	−1.02861
$612$	8.32960e80	0.0514585
$613$	2.82036e81	0.166043	0.0830214	−	0.996548i	$-0.473543\pi$
$613$	2.82036e81	0.166043	0.0830214	+	0.996548i	$0.473543\pi$
$614$	6.58680e81	0.369579
$615$	9.64806e81	0.515969
$616$	1.61932e81	0.0825471
$617$	−2.69137e82	−1.30786	−0.653929	−	0.756556i	$-0.726881\pi$
$617$	−2.69137e82	−1.30786	−0.653929	+	0.756556i	$0.726881\pi$
$618$	−1.35725e82	−0.628780
$619$	1.45072e82	0.640779	0.320389	−	0.947286i	$-0.396186\pi$
$619$	1.45072e82	0.640779	0.320389	+	0.947286i	$0.396186\pi$
$620$	4.25880e81	0.179363
$621$	5.04806e82	2.02732
$622$	−2.54249e82	−0.973739
$623$	2.90974e81	0.106281
$624$	2.84347e82	0.990610
$625$	−2.54245e82	−0.844875
$626$	−1.79899e82	−0.570276
$627$	−1.55771e82	−0.471079
$628$	−9.08816e81	−0.262220
$629$	7.11606e82	1.95905
$630$	6.93765e80	0.0182249
$631$	3.24958e82	0.814632	0.407316	−	0.913287i	$-0.366465\pi$
$631$	3.24958e82	0.814632	0.407316	+	0.913287i	$0.366465\pi$
$632$	−6.44411e82	−1.54173
$633$	3.11503e82	0.711301
$634$	6.53933e82	1.42528
$635$	−5.95532e82	−1.23903
$636$	3.48975e81	0.0693121
$637$	−7.41398e82	−1.40585
$638$	−4.11796e82	−0.745542
$639$	1.29941e80	0.00224632
$640$	3.82223e82	0.630968
$641$	3.40514e81	0.0536812	0.0268406	−	0.999640i	$-0.491455\pi$
$641$	3.40514e81	0.0536812	0.0268406	+	0.999640i	$0.491455\pi$
$642$	−6.13905e82	−0.924311
$643$	2.29625e82	0.330213	0.165107	−	0.986276i	$-0.447203\pi$
$643$	2.29625e82	0.330213	0.165107	+	0.986276i	$0.447203\pi$
$644$	2.00159e81	0.0274942
$645$	−5.06068e82	−0.664044
$646$	5.60704e82	0.702869
$647$	−3.49095e82	−0.418088	−0.209044	−	0.977906i	$-0.567035\pi$
$647$	−3.49095e82	−0.418088	−0.209044	+	0.977906i	$0.567035\pi$
$648$	6.46852e82	0.740188
$649$	1.71508e82	0.187527
$650$	−1.68888e82	−0.176464
$651$	−8.80583e81	−0.0879288
$652$	9.26092e81	0.0883792
$653$	2.13154e83	1.94426	0.972131	−	0.234437i	$-0.0753248\pi$
$653$	2.13154e83	1.94426	0.972131	+	0.234437i	$0.0753248\pi$
$654$	−8.42307e82	−0.734391
$655$	5.60168e82	0.466874
$656$	6.45432e82	0.514266
$657$	7.59230e81	0.0578356
$658$	7.97797e81	0.0581070
$659$	−8.26273e82	−0.575445	−0.287722	−	0.957714i	$-0.592898\pi$
$659$	−8.26273e82	−0.575445	−0.287722	+	0.957714i	$0.592898\pi$
$660$	1.79201e82	0.119342
$661$	−5.66974e82	−0.361094	−0.180547	−	0.983566i	$-0.557787\pi$
$661$	−5.66974e82	−0.361094	−0.180547	+	0.983566i	$0.557787\pi$
$662$	1.67795e82	0.102204
$663$	−2.65244e83	−1.54524
$664$	−4.92763e82	−0.274587
$665$	−9.38143e81	−0.0500070
$666$	−6.84388e82	−0.348990
$667$	−3.55184e83	−1.73277
$668$	3.17260e82	0.148085
$669$	3.35205e83	1.49706
$670$	1.09467e83	0.467819
$671$	−4.26695e82	−0.174503
$672$	6.44141e81	0.0252108
$673$	8.50409e81	0.0318554	0.0159277	−	0.999873i	$-0.494930\pi$
$673$	8.50409e81	0.0318554	0.0159277	+	0.999873i	$0.494930\pi$
$674$	2.88409e83	1.03405
$675$	−4.30252e82	−0.147659
$676$	−5.12831e82	−0.168479
$677$	3.74663e83	1.17835	0.589177	−	0.808004i	$-0.299452\pi$
$677$	3.74663e83	1.17835	0.589177	+	0.808004i	$0.299452\pi$
$678$	5.17052e83	1.55689
$679$	−5.38756e82	−0.155322
$680$	−4.50108e83	−1.24252
$681$	−4.19370e83	−1.10856
$682$	−3.67536e83	−0.930381
$683$	4.72123e83	1.14458	0.572288	−	0.820053i	$-0.306056\pi$
$683$	4.72123e83	1.14458	0.572288	+	0.820053i	$0.306056\pi$
$684$	1.08329e82	0.0251530
$685$	−1.11843e83	−0.248736
$686$	7.48491e82	0.159450
$687$	1.38190e83	0.282002
$688$	−3.38547e83	−0.661852
$689$	3.60715e83	0.675612
$690$	−7.69419e83	−1.38075
$691$	5.74414e83	0.987694	0.493847	−	0.869549i	$-0.335590\pi$
$691$	5.74414e83	0.987694	0.493847	+	0.869549i	$0.335590\pi$
$692$	1.27743e82	0.0210477
$693$	1.20274e82	0.0189907
$694$	2.10254e83	0.318156
$695$	2.17119e82	0.0314880
$696$	−6.15630e83	−0.855750
$697$	−6.02071e83	−0.802196
$698$	−5.30349e83	−0.677372
$699$	−1.34312e83	−0.164452
$700$	−1.70597e81	−0.00200254
$701$	−5.67798e83	−0.639017	−0.319508	−	0.947583i	$-0.603518\pi$
$701$	−5.67798e83	−0.639017	−0.319508	+	0.947583i	$0.603518\pi$
$702$	1.29608e84	1.39858
$703$	9.25463e83	0.957584
$704$	9.85497e83	0.977827
$705$	6.16068e83	0.586205
$706$	2.44477e82	0.0223100
$707$	−1.03265e82	−0.00903819
$708$	3.67444e82	0.0308468
$709$	−1.74026e83	−0.140136	−0.0700681	−	0.997542i	$-0.522322\pi$
$709$	−1.74026e83	−0.140136	−0.0700681	+	0.997542i	$0.522322\pi$
$710$	−1.00626e82	−0.00777300
$711$	−4.78633e83	−0.354690
$712$	1.81561e84	1.29081
$713$	−3.17008e84	−2.16237
$714$	1.33374e83	0.0872917
$715$	1.85230e84	1.16327
$716$	−3.24633e83	−0.195640
$717$	−1.03508e84	−0.598628
$718$	−7.83174e83	−0.434698
$719$	−2.89395e84	−1.54166	−0.770831	−	0.637040i	$-0.780158\pi$
$719$	−2.89395e84	−1.54166	−0.770831	+	0.637040i	$0.780158\pi$
$720$	3.58393e83	0.183253
$721$	−1.41710e83	−0.0695523
$722$	−1.20764e84	−0.568972
$723$	8.88066e83	0.401666
$724$	1.99537e83	0.0866435
$725$	3.02727e83	0.126206
$726$	4.34274e83	0.173834
$727$	1.08709e84	0.417830	0.208915	−	0.977934i	$-0.433007\pi$
$727$	1.08709e84	0.417830	0.208915	+	0.977934i	$0.433007\pi$
$728$	3.58601e83	0.132354
$729$	3.13240e84	1.11023
$730$	−5.87945e83	−0.200130
$731$	3.15803e84	1.03241
$732$	−9.14167e82	−0.0287044
$733$	−3.02062e84	−0.911021	−0.455511	−	0.890230i	$-0.650543\pi$
$733$	−3.02062e84	−0.911021	−0.455511	+	0.890230i	$0.650543\pi$
$734$	−7.93228e83	−0.229808
$735$	2.87881e84	0.801192
$736$	2.31890e84	0.619992
$737$	1.89777e84	0.487476
$738$	5.79042e83	0.142905
$739$	−5.50898e84	−1.30635	−0.653176	−	0.757206i	$-0.726564\pi$
$739$	−5.50898e84	−1.30635	−0.653176	+	0.757206i	$0.726564\pi$
$740$	−1.06466e84	−0.242592
$741$	−3.44957e84	−0.755314
$742$	−1.81380e83	−0.0381658
$743$	3.77858e84	0.764115	0.382057	−	0.924139i	$-0.375216\pi$
$743$	3.77858e84	0.764115	0.382057	+	0.924139i	$0.375216\pi$
$744$	−5.49462e84	−1.06791
$745$	−1.69235e83	−0.0316140
$746$	−6.31683e84	−1.13424
$747$	−3.65997e83	−0.0631713
$748$	−1.11827e84	−0.185545
$749$	−6.40980e83	−0.102242
$750$	5.46027e84	0.837349
$751$	1.32327e85	1.95106	0.975530	−	0.219865i	$-0.0705617\pi$
$751$	1.32327e85	1.95106	0.975530	+	0.219865i	$0.0705617\pi$
$752$	4.12135e84	0.584270
$753$	−4.20417e84	−0.573098
$754$	−9.11928e84	−1.19538
$755$	−1.05909e84	−0.133505
$756$	1.30920e83	0.0158713
$757$	−1.84701e82	−0.00215348	−0.00107674	−	0.999999i	$-0.500343\pi$
$757$	−1.84701e82	−0.00215348	−0.00107674	+	0.999999i	$0.500343\pi$
$758$	8.16432e84	0.915543
$759$	−1.33390e85	−1.43877
$760$	−5.85378e84	−0.607345
$761$	1.43924e85	1.43643	0.718216	−	0.695820i	$-0.244959\pi$
$761$	1.43924e85	1.43643	0.718216	+	0.695820i	$0.244959\pi$
$762$	1.10110e85	1.05719
$763$	−8.79455e83	−0.0812344
$764$	1.65311e84	0.146909
$765$	−3.34315e84	−0.285854
$766$	6.10544e84	0.502306
$767$	3.79806e84	0.300676
$768$	5.55465e84	0.423156
$769$	−1.22496e85	−0.898039	−0.449019	−	0.893522i	$-0.648227\pi$
$769$	−1.22496e85	−0.898039	−0.449019	+	0.893522i	$0.648227\pi$
$770$	−9.31399e83	−0.0657142
$771$	−2.78770e84	−0.189296
$772$	4.41337e84	0.288443
$773$	−8.47270e84	−0.533000	−0.266500	−	0.963835i	$-0.585867\pi$
$773$	−8.47270e84	−0.533000	−0.266500	+	0.963835i	$0.585867\pi$
$774$	−3.03724e84	−0.183917
$775$	2.70190e84	0.157496
$776$	−3.36171e85	−1.88642
$777$	2.20138e84	0.118926
$778$	−2.07656e85	−1.08006
$779$	−7.83010e84	−0.392114
$780$	3.96843e84	0.191350
$781$	−1.74450e83	−0.00809962
$782$	4.80143e85	2.14670
$783$	−2.32318e85	−1.00026
$784$	1.92586e85	0.798546
$785$	3.64761e85	1.45664
$786$	−1.03571e85	−0.398359
$787$	1.24322e85	0.460568	0.230284	−	0.973123i	$-0.426034\pi$
$787$	1.24322e85	0.460568	0.230284	+	0.973123i	$0.426034\pi$
$788$	−2.58755e84	−0.0923346
$789$	−6.20129e83	−0.0213162
$790$	3.70652e85	1.22734
$791$	5.39855e84	0.172215
$792$	7.50481e84	0.230647
$793$	−9.44922e84	−0.279793
$794$	−5.22100e85	−1.48953
$795$	−1.40064e85	−0.385031
$796$	−9.49698e84	−0.251565
$797$	1.49621e85	0.381919	0.190960	−	0.981598i	$-0.438840\pi$
$797$	1.49621e85	0.381919	0.190960	+	0.981598i	$0.438840\pi$
$798$	1.73456e84	0.0426682
$799$	−3.84447e85	−0.911394
$800$	−1.97642e84	−0.0451570
$801$	1.34853e85	0.296963
$802$	1.57745e83	0.00334820
$803$	−1.01929e85	−0.208539
$804$	4.06586e84	0.0801861
$805$	−8.03353e84	−0.152731
$806$	−8.13914e85	−1.49175
$807$	4.43752e85	0.784099
$808$	−6.44350e84	−0.109771
$809$	9.07918e85	1.49130	0.745651	−	0.666337i	$-0.232139\pi$
$809$	9.07918e85	1.49130	0.745651	+	0.666337i	$0.232139\pi$
$810$	−3.72055e85	−0.589250
$811$	−8.14581e85	−1.24400	−0.621998	−	0.783019i	$-0.713679\pi$
$811$	−8.14581e85	−1.24400	−0.621998	+	0.783019i	$0.713679\pi$
$812$	−9.21156e83	−0.0135653
$813$	9.57248e85	1.35942
$814$	9.18810e85	1.25836
$815$	−3.71694e85	−0.490949
$816$	6.88997e85	0.877724
$817$	4.10711e85	0.504644
$818$	−1.08217e86	−1.28255
$819$	2.66349e84	0.0304492
$820$	9.00785e84	0.0993373
$821$	1.56347e85	0.166329	0.0831644	−	0.996536i	$-0.473497\pi$
$821$	1.56347e85	0.166329	0.0831644	+	0.996536i	$0.473497\pi$
$822$	2.06791e85	0.212233
$823$	−2.10191e85	−0.208123	−0.104061	−	0.994571i	$-0.533184\pi$
$823$	−2.10191e85	−0.208123	−0.104061	+	0.994571i	$0.533184\pi$
$824$	−8.84238e85	−0.844727
$825$	1.13690e85	0.104793
$826$	−1.90980e84	−0.0169854
$827$	4.67868e85	0.401524	0.200762	−	0.979640i	$-0.435658\pi$
$827$	4.67868e85	0.401524	0.200762	+	0.979640i	$0.435658\pi$
$828$	9.27644e84	0.0768221
$829$	−2.94227e85	−0.235139	−0.117569	−	0.993065i	$-0.537510\pi$
$829$	−2.94227e85	−0.235139	−0.117569	+	0.993065i	$0.537510\pi$
$830$	2.83427e85	0.218593
$831$	−1.20716e86	−0.898534
$832$	2.18240e86	1.56782
$833$	−1.79647e86	−1.24564
$834$	−4.01438e84	−0.0268670
$835$	−1.27335e86	−0.822614
$836$	−1.45434e85	−0.0906947
$837$	−2.07349e86	−1.24825
$838$	2.45390e86	1.42613
$839$	−8.27969e85	−0.464554	−0.232277	−	0.972650i	$-0.574618\pi$
$839$	−8.27969e85	−0.464554	−0.232277	+	0.972650i	$0.574618\pi$
$840$	−1.39243e85	−0.0754283
$841$	−2.77372e85	−0.145071
$842$	−4.37811e85	−0.221095
$843$	2.51163e86	1.22474
$844$	2.90833e85	0.136944
$845$	2.05829e86	0.935908
$846$	3.69742e85	0.162358
$847$	4.53427e84	0.0192285
$848$	−9.36994e85	−0.383760
$849$	−1.57233e86	−0.621968
$850$	−4.09232e85	−0.156355
$851$	7.92495e86	2.92465
$852$	−3.73748e83	−0.00133233
$853$	1.96043e86	0.675080	0.337540	−	0.941311i	$-0.390405\pi$
$853$	1.96043e86	0.675080	0.337540	+	0.941311i	$0.390405\pi$
$854$	4.75140e84	0.0158057
$855$	−4.34786e85	−0.139725
$856$	−3.99956e86	−1.24176
$857$	−4.95329e86	−1.48580	−0.742898	−	0.669405i	$-0.766549\pi$
$857$	−4.95329e86	−1.48580	−0.742898	+	0.669405i	$0.766549\pi$
$858$	−3.42477e86	−0.992559
$859$	−4.22920e86	−1.18429	−0.592147	−	0.805830i	$-0.701720\pi$
$859$	−4.22920e86	−1.18429	−0.592147	+	0.805830i	$0.701720\pi$
$860$	−4.72487e85	−0.127846
$861$	−1.86253e85	−0.0486980
$862$	−2.24752e86	−0.567856
$863$	4.05433e86	0.989921	0.494961	−	0.868915i	$-0.335182\pi$
$863$	4.05433e86	0.989921	0.494961	+	0.868915i	$0.335182\pi$
$864$	1.51674e86	0.357896
$865$	−5.12705e85	−0.116921
$866$	1.77804e86	0.391889
$867$	−2.34840e86	−0.500274
$868$	−8.22150e84	−0.0169285
$869$	6.42578e86	1.27892
$870$	3.54097e86	0.681247
$871$	4.20265e86	0.781605
$872$	−5.48758e86	−0.986609
$873$	−2.49689e86	−0.433989
$874$	6.24440e86	1.04931
$875$	5.70108e85	0.0926231
$876$	−2.18376e85	−0.0343031
$877$	−9.27906e86	−1.40934	−0.704670	−	0.709535i	$-0.748905\pi$
$877$	−9.27906e86	−1.40934	−0.704670	+	0.709535i	$0.748905\pi$
$878$	4.80734e86	0.706019
$879$	4.79294e86	0.680660
$880$	−4.81153e86	−0.660760
$881$	9.83973e86	1.30675	0.653377	−	0.757033i	$-0.273352\pi$
$881$	9.83973e86	1.30675	0.653377	+	0.757033i	$0.273352\pi$
$882$	1.72776e86	0.221902
$883$	−9.21451e86	−1.14454	−0.572270	−	0.820065i	$-0.693937\pi$
$883$	−9.21451e86	−1.14454	−0.572270	+	0.820065i	$0.693937\pi$
$884$	−2.47643e86	−0.297498
$885$	−1.47477e86	−0.171355
$886$	−4.58332e86	−0.515093
$887$	−2.01047e86	−0.218550	−0.109275	−	0.994012i	$-0.534853\pi$
$887$	−2.01047e86	−0.218550	−0.109275	+	0.994012i	$0.534853\pi$
$888$	1.37361e87	1.44438
$889$	1.14966e86	0.116941
$890$	−1.04430e87	−1.02759
$891$	−6.45012e86	−0.614010
$892$	3.12962e86	0.288223
$893$	−4.99984e86	−0.445490
$894$	3.12904e85	0.0269745
$895$	1.30294e87	1.08679
$896$	−7.37871e85	−0.0595517
$897$	−2.95394e87	−2.30688
$898$	−3.82913e86	−0.289366
$899$	1.45891e87	1.06689
$900$	−7.90641e84	−0.00559533
$901$	8.74044e86	0.598621
$902$	−7.77381e86	−0.515277
$903$	9.76951e85	0.0626735
$904$	3.36856e87	2.09159
$905$	−8.00858e86	−0.481307
$906$	1.95819e86	0.113913
$907$	1.04265e87	0.587118	0.293559	−	0.955941i	$-0.405160\pi$
$907$	1.04265e87	0.587118	0.293559	+	0.955941i	$0.405160\pi$
$908$	−3.91542e86	−0.213425
$909$	−4.78587e85	−0.0252538
$910$	−2.06260e86	−0.105364
$911$	−8.82970e86	−0.436671	−0.218335	−	0.975874i	$-0.570063\pi$
$911$	−8.82970e86	−0.436671	−0.218335	+	0.975874i	$0.570063\pi$
$912$	8.96060e86	0.429032
$913$	4.91361e86	0.227779
$914$	−7.18633e86	−0.322548
$915$	3.66908e86	0.159454
$916$	1.29020e86	0.0542927
$917$	−1.08139e86	−0.0440643
$918$	3.14052e87	1.23920
$919$	−4.47608e86	−0.171037	−0.0855186	−	0.996337i	$-0.527255\pi$
$919$	−4.47608e86	−0.171037	−0.0855186	+	0.996337i	$0.527255\pi$
$920$	−5.01272e87	−1.85495
$921$	−9.81917e86	−0.351897
$922$	−2.61276e87	−0.906853
$923$	−3.86321e85	−0.0129867
$924$	−3.45942e85	−0.0112637
$925$	−6.75452e86	−0.213017
$926$	−2.34648e87	−0.716791
$927$	−6.56763e86	−0.194337
$928$	−1.06719e87	−0.305897
$929$	3.23475e87	0.898208	0.449104	−	0.893480i	$-0.351743\pi$
$929$	3.23475e87	0.898208	0.449104	+	0.893480i	$0.351743\pi$
$930$	3.16039e87	0.850146
$931$	−2.33636e87	−0.608870
$932$	−1.25400e86	−0.0316612
$933$	3.79018e87	0.927152
$934$	1.08515e87	0.257193
$935$	4.48828e87	1.03071
$936$	1.66195e87	0.369812
$937$	4.49837e87	0.969923	0.484962	−	0.874535i	$-0.338834\pi$
$937$	4.49837e87	0.969923	0.484962	+	0.874535i	$0.338834\pi$
$938$	−2.11324e86	−0.0441534
$939$	2.68181e87	0.542992
$940$	5.75188e86	0.112860
$941$	−6.41416e86	−0.121968	−0.0609840	−	0.998139i	$-0.519424\pi$
$941$	−6.41416e86	−0.121968	−0.0609840	+	0.998139i	$0.519424\pi$
$942$	−6.74418e87	−1.24287
$943$	−6.70509e87	−1.19759
$944$	−9.86585e86	−0.170789
$945$	−5.25456e86	−0.0881654
$946$	4.07758e87	0.663153
$947$	−4.17909e87	−0.658806	−0.329403	−	0.944189i	$-0.606847\pi$
$947$	−4.17909e87	−0.658806	−0.329403	+	0.944189i	$0.606847\pi$
$948$	1.37668e87	0.210372
$949$	−2.25723e87	−0.334366
$950$	−5.32217e86	−0.0764263
$951$	−9.74840e87	−1.35709
$952$	8.68922e86	0.117271
$953$	1.20950e88	1.58258	0.791290	−	0.611441i	$-0.209410\pi$
$953$	1.20950e88	1.58258	0.791290	+	0.611441i	$0.209410\pi$
$954$	−8.40614e86	−0.106640
$955$	−6.63489e87	−0.816083
$956$	−9.66392e86	−0.115251
$957$	6.13879e87	0.709872
$958$	−1.17647e87	−0.131916
$959$	2.15911e86	0.0234761
$960$	−8.47414e87	−0.893499
$961$	3.24108e87	0.331398
$962$	2.03472e88	2.01762
$963$	−2.97065e87	−0.285678
$964$	8.29137e86	0.0773311
$965$	−1.77134e88	−1.60231
$966$	1.48534e87	0.130317
$967$	−4.94615e87	−0.420907	−0.210454	−	0.977604i	$-0.567494\pi$
$967$	−4.94615e87	−0.420907	−0.210454	+	0.977604i	$0.567494\pi$
$968$	2.82927e87	0.233535
$969$	−8.35861e87	−0.669241
$970$	1.93358e88	1.50175
$971$	1.84748e88	1.39191	0.695955	−	0.718085i	$-0.254981\pi$
$971$	1.84748e88	1.39191	0.695955	+	0.718085i	$0.254981\pi$
$972$	1.09408e87	0.0799641
$973$	−4.19142e85	−0.00297189
$974$	−1.36336e88	−0.937826
$975$	2.51768e87	0.168021
$976$	2.45453e87	0.158927
$977$	2.10891e88	1.32486	0.662429	−	0.749125i	$-0.269526\pi$
$977$	2.10891e88	1.32486	0.662429	+	0.749125i	$0.269526\pi$
$978$	6.87238e87	0.418900
$979$	−1.81044e88	−1.07077
$980$	2.68778e87	0.154250
$981$	−4.07587e87	−0.226979
$982$	−1.88424e88	−1.01823
$983$	−2.64046e88	−1.38468	−0.692342	−	0.721569i	$-0.743421\pi$
$983$	−2.64046e88	−1.38468	−0.692342	+	0.721569i	$0.743421\pi$
$984$	−1.16217e88	−0.591447
$985$	1.03853e88	0.512922
$986$	−2.20968e88	−1.05916
$987$	−1.18930e87	−0.0553269
$988$	−3.22067e87	−0.145417
$989$	3.51701e88	1.54128
$990$	−4.31661e87	−0.183613
$991$	5.37825e87	0.222059	0.111030	−	0.993817i	$-0.464585\pi$
$991$	5.37825e87	0.222059	0.111030	+	0.993817i	$0.464585\pi$
$992$	−9.52486e87	−0.381737
$993$	−2.50138e87	−0.0973144
$994$	1.94256e85	0.000733628 0
$995$	3.81169e88	1.39745
$996$	1.05271e87	0.0374678
$997$	−1.80703e88	−0.624392	−0.312196	−	0.950018i	$-0.601065\pi$
$997$	−1.80703e88	−0.624392	−0.312196	+	0.950018i	$0.601065\pi$
$998$	−4.53185e88	−1.52028
$999$	5.18354e88	1.68828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.60.a.a.1.4	✓	5
3.2	odd	2		9.60.a.c.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.60.a.a.1.4	✓	5	1.1	even	1	trivial
9.60.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+6.92842e8 q^{2} -1.03284e14 q^{3} -9.64308e16 q^{4} +3.87033e20 q^{5} -7.15597e22 q^{6} -7.47157e23 q^{7} -4.66207e26 q^{8} -3.46273e27 q^{9} +O(q^{10})\)	\(q+6.92842e8 q^{2} -1.03284e14 q^{3} -9.64308e16 q^{4} +3.87033e20 q^{5} -7.15597e22 q^{6} -7.47157e23 q^{7} -4.66207e26 q^{8} -3.46273e27 q^{9} +2.68153e29 q^{10} +4.64881e30 q^{11} +9.95979e30 q^{12} +1.02949e33 q^{13} -5.17661e32 q^{14} -3.99744e34 q^{15} -2.67420e35 q^{16} +2.49454e36 q^{17} -2.39912e36 q^{18} +3.24421e37 q^{19} -3.73219e37 q^{20} +7.71696e37 q^{21} +3.22089e39 q^{22} +2.77809e40 q^{23} +4.81519e40 q^{24} -2.36780e40 q^{25} +7.13271e41 q^{26} +1.81709e42 q^{27} +7.20489e40 q^{28} -1.27852e43 q^{29} -2.76960e43 q^{30} -1.14110e44 q^{31} +8.34708e43 q^{32} -4.80150e44 q^{33} +1.72832e45 q^{34} -2.89174e44 q^{35} +3.33914e44 q^{36} +2.85266e46 q^{37} +2.24773e46 q^{38} -1.06330e47 q^{39} -1.80438e47 q^{40} -2.41356e47 q^{41} +5.34663e46 q^{42} +1.26598e48 q^{43} -4.48289e47 q^{44} -1.34019e48 q^{45} +1.92478e49 q^{46} -1.54116e49 q^{47} +2.76203e49 q^{48} -7.20163e49 q^{49} -1.64051e49 q^{50} -2.57647e50 q^{51} -9.92742e49 q^{52} +3.50384e50 q^{53} +1.25896e51 q^{54} +1.79924e51 q^{55} +3.48330e50 q^{56} -3.35077e51 q^{57} -8.85809e51 q^{58} +3.68928e51 q^{59} +3.85477e51 q^{60} -9.17858e51 q^{61} -7.90602e52 q^{62} +2.58720e51 q^{63} +2.11989e53 q^{64} +3.98445e53 q^{65} -3.32668e53 q^{66} +4.08228e53 q^{67} -2.40550e53 q^{68} -2.86934e54 q^{69} -2.00352e53 q^{70} -3.75256e52 q^{71} +1.61435e54 q^{72} -2.19258e54 q^{73} +1.97644e55 q^{74} +2.44557e54 q^{75} -3.12842e54 q^{76} -3.47339e54 q^{77} -7.36697e55 q^{78} +1.38224e56 q^{79} -1.03500e56 q^{80} -1.38748e56 q^{81} -1.67221e56 q^{82} +1.05696e56 q^{83} -7.44152e54 q^{84} +9.65467e56 q^{85} +8.77123e56 q^{86} +1.32051e57 q^{87} -2.16731e57 q^{88} -3.89442e57 q^{89} -9.28540e56 q^{90} -7.69187e56 q^{91} -2.67894e57 q^{92} +1.17858e58 q^{93} -1.06778e58 q^{94} +1.25562e58 q^{95} -8.62123e57 q^{96} +7.21075e58 q^{97} -4.98959e58 q^{98} -1.60976e58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more