LMFDB - Embedded newform 1.60.a.a.1.3

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			1.3
Root			$9.74166e6$ 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)

$f(q)$	$=$	$q-3.23738e8 q^{2} -8.24972e12 q^{3} -4.71654e17 q^{4} -7.71676e20 q^{5} +2.67075e21 q^{6} -4.97804e24 q^{7} +3.39315e26 q^{8} -1.40623e28 q^{9} +O(q^{10})$	\(q-3.23738e8 q^{2} -8.24972e12 q^{3} -4.71654e17 q^{4} -7.71676e20 q^{5} +2.67075e21 q^{6} -4.97804e24 q^{7} +3.39315e26 q^{8} -1.40623e28 q^{9} +2.49821e29 q^{10} -5.41469e30 q^{11} +3.89102e30 q^{12} -5.16559e32 q^{13} +1.61158e33 q^{14} +6.36611e33 q^{15} +1.62041e35 q^{16} -9.94078e35 q^{17} +4.55251e36 q^{18} -3.90272e37 q^{19} +3.63964e38 q^{20} +4.10675e37 q^{21} +1.75294e39 q^{22} +2.19671e40 q^{23} -2.79925e39 q^{24} +4.22011e41 q^{25} +1.67230e41 q^{26} +2.32582e41 q^{27} +2.34792e42 q^{28} -1.47397e43 q^{29} -2.06095e42 q^{30} -9.00895e43 q^{31} -2.48061e44 q^{32} +4.46697e43 q^{33} +3.21821e44 q^{34} +3.84144e45 q^{35} +6.63256e45 q^{36} -4.57851e45 q^{37} +1.26346e46 q^{38} +4.26147e45 q^{39} -2.61841e47 q^{40} +1.81556e46 q^{41} -1.32951e46 q^{42} -1.81438e48 q^{43} +2.55386e48 q^{44} +1.08516e49 q^{45} -7.11158e48 q^{46} +9.84593e48 q^{47} -1.33679e48 q^{48} -4.77936e49 q^{49} -1.36621e50 q^{50} +8.20087e48 q^{51} +2.43637e50 q^{52} -4.04855e50 q^{53} -7.52957e49 q^{54} +4.17839e51 q^{55} -1.68912e51 q^{56} +3.21964e50 q^{57} +4.77181e51 q^{58} -2.73608e52 q^{59} -3.00260e51 q^{60} -2.82665e52 q^{61} +2.91654e52 q^{62} +7.00029e52 q^{63} -1.31036e52 q^{64} +3.98616e53 q^{65} -1.44613e52 q^{66} -7.96736e53 q^{67} +4.68861e53 q^{68} -1.81222e53 q^{69} -1.24362e54 q^{70} -2.85479e54 q^{71} -4.77156e54 q^{72} +1.64698e55 q^{73} +1.48224e54 q^{74} -3.48148e54 q^{75} +1.84074e55 q^{76} +2.69546e55 q^{77} -1.37960e54 q^{78} -1.63561e56 q^{79} -1.25043e56 q^{80} +1.96787e56 q^{81} -5.87766e54 q^{82} -4.71355e55 q^{83} -1.93697e55 q^{84} +7.67106e56 q^{85} +5.87385e56 q^{86} +1.21599e56 q^{87} -1.83729e57 q^{88} +1.35054e57 q^{89} -3.51306e57 q^{90} +2.57145e57 q^{91} -1.03609e58 q^{92} +7.43213e56 q^{93} -3.18751e57 q^{94} +3.01164e58 q^{95} +2.04643e57 q^{96} +1.09114e58 q^{97} +1.54726e58 q^{98} +7.61432e58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.23738e8	−0.426392	−0.213196	−	0.977009i	$-0.568387\pi$
$2$	−3.23738e8	−0.426392	−0.213196	+	0.977009i	$0.568387\pi$
$3$	−8.24972e12	−0.0694005	−0.0347002	−	0.999398i	$-0.511048\pi$
$3$	−8.24972e12	−0.0694005	−0.0347002	+	0.999398i	$0.511048\pi$
$4$	−4.71654e17	−0.818190
$5$	−7.71676e20	−1.85276	−0.926381	−	0.376587i	$-0.877098\pi$
$5$	−7.71676e20	−1.85276	−0.926381	+	0.376587i	$0.877098\pi$
$6$	2.67075e21	0.0295918
$7$	−4.97804e24	−0.584341	−0.292171	−	0.956366i	$-0.594378\pi$
$7$	−4.97804e24	−0.584341	−0.292171	+	0.956366i	$0.594378\pi$
$8$	3.39315e26	0.775262
$9$	−1.40623e28	−0.995184
$10$	2.49821e29	0.790003
$11$	−5.41469e30	−1.02918	−0.514588	−	0.857438i	$-0.672055\pi$
$11$	−5.41469e30	−1.02918	−0.514588	+	0.857438i	$0.672055\pi$
$12$	3.89102e30	0.0567828
$13$	−5.16559e32	−0.710872	−0.355436	−	0.934701i	$-0.615668\pi$
$13$	−5.16559e32	−0.710872	−0.355436	+	0.934701i	$0.615668\pi$
$14$	1.61158e33	0.249159
$15$	6.36611e33	0.128583
$16$	1.62041e35	0.487624
$17$	−9.94078e35	−0.500239	−0.250119	−	0.968215i	$-0.580470\pi$
$17$	−9.94078e35	−0.500239	−0.250119	+	0.968215i	$0.580470\pi$
$18$	4.55251e36	0.424338
$19$	−3.90272e37	−0.738136	−0.369068	−	0.929402i	$-0.620323\pi$
$19$	−3.90272e37	−0.738136	−0.369068	+	0.929402i	$0.620323\pi$
$20$	3.63964e38	1.51591
$21$	4.10675e37	0.0405536
$22$	1.75294e39	0.438833
$23$	2.19671e40	1.48184	0.740920	−	0.671594i	$-0.234390\pi$
$23$	2.19671e40	1.48184	0.740920	+	0.671594i	$0.234390\pi$
$24$	−2.79925e39	−0.0538035
$25$	4.22011e41	2.43273
$26$	1.67230e41	0.303110
$27$	2.32582e41	0.138467
$28$	2.34792e42	0.478102
$29$	−1.47397e43	−1.06598	−0.532989	−	0.846122i	$-0.678931\pi$
$29$	−1.47397e43	−1.06598	−0.532989	+	0.846122i	$0.678931\pi$
$30$	−2.06095e42	−0.0548266
$31$	−9.00895e43	−0.910970	−0.455485	−	0.890243i	$-0.650534\pi$
$31$	−9.00895e43	−0.910970	−0.455485	+	0.890243i	$0.650534\pi$
$32$	−2.48061e44	−0.983181
$33$	4.46697e43	0.0714253
$34$	3.21821e44	0.213298
$35$	3.84144e45	1.08265
$36$	6.63256e45	0.814249
$37$	−4.57851e45	−0.250480	−0.125240	−	0.992126i	$-0.539970\pi$
$37$	−4.57851e45	−0.250480	−0.125240	+	0.992126i	$0.539970\pi$
$38$	1.26346e46	0.314736
$39$	4.26147e45	0.0493348
$40$	−2.61841e47	−1.43638
$41$	1.81556e46	0.0480714	0.0240357	−	0.999711i	$-0.492348\pi$
$41$	1.81556e46	0.0480714	0.0240357	+	0.999711i	$0.492348\pi$
$42$	−1.32951e46	−0.0172917
$43$	−1.81438e48	−1.17872	−0.589359	−	0.807871i	$-0.700620\pi$
$43$	−1.81438e48	−1.17872	−0.589359	+	0.807871i	$0.700620\pi$
$44$	2.55386e48	0.842061
$45$	1.08516e49	1.84384
$46$	−7.11158e48	−0.631845
$47$	9.84593e48	0.463842	0.231921	−	0.972735i	$-0.425499\pi$
$47$	9.84593e48	0.463842	0.231921	+	0.972735i	$0.425499\pi$
$48$	−1.33679e48	−0.0338414
$49$	−4.77936e49	−0.658545
$50$	−1.36621e50	−1.03730
$51$	8.20087e48	0.0347168
$52$	2.43637e50	0.581628
$53$	−4.04855e50	−0.551013	−0.275506	−	0.961299i	$-0.588846\pi$
$53$	−4.04855e50	−0.551013	−0.275506	+	0.961299i	$0.588846\pi$
$54$	−7.52957e49	−0.0590411
$55$	4.17839e51	1.90682
$56$	−1.68912e51	−0.453017
$57$	3.21964e50	0.0512270
$58$	4.77181e51	0.454524
$59$	−2.73608e52	−1.57396	−0.786980	−	0.616978i	$-0.788357\pi$
$59$	−2.73608e52	−1.57396	−0.786980	+	0.616978i	$0.788357\pi$
$60$	−3.00260e51	−0.105205
$61$	−2.82665e52	−0.608194	−0.304097	−	0.952641i	$-0.598355\pi$
$61$	−2.82665e52	−0.608194	−0.304097	+	0.952641i	$0.598355\pi$
$62$	2.91654e52	0.388430
$63$	7.00029e52	0.581527
$64$	−1.31036e52	−0.0684039
$65$	3.98616e53	1.31708
$66$	−1.44613e52	−0.0304552
$67$	−7.96736e53	−1.07673	−0.538366	−	0.842711i	$-0.680958\pi$
$67$	−7.96736e53	−1.07673	−0.538366	+	0.842711i	$0.680958\pi$
$68$	4.68861e53	0.409290
$69$	−1.81222e53	−0.102840
$70$	−1.24362e54	−0.461632
$71$	−2.85479e54	−0.697354	−0.348677	−	0.937243i	$-0.613369\pi$
$71$	−2.85479e54	−0.697354	−0.348677	+	0.937243i	$0.613369\pi$
$72$	−4.77156e54	−0.771528
$73$	1.64698e55	1.77282	0.886410	−	0.462902i	$-0.153192\pi$
$73$	1.64698e55	1.77282	0.886410	+	0.462902i	$0.153192\pi$
$74$	1.48224e54	0.106803
$75$	−3.48148e54	−0.168833
$76$	1.84074e55	0.603936
$77$	2.69546e55	0.601390
$78$	−1.37960e54	−0.0210360
$79$	−1.63561e56	−1.71270	−0.856349	−	0.516397i	$-0.827273\pi$
$79$	−1.63561e56	−1.71270	−0.856349	+	0.516397i	$0.827273\pi$
$80$	−1.25043e56	−0.903452
$81$	1.96787e56	0.985574
$82$	−5.87766e54	−0.0204973
$83$	−4.71355e55	−0.114959	−0.0574797	−	0.998347i	$-0.518306\pi$
$83$	−4.71355e55	−0.114959	−0.0574797	+	0.998347i	$0.518306\pi$
$84$	−1.93697e55	−0.0331805
$85$	7.67106e56	0.926823
$86$	5.87385e56	0.502596
$87$	1.21599e56	0.0739793
$88$	−1.83729e57	−0.797881
$89$	1.35054e57	0.420244	0.210122	−	0.977675i	$-0.432614\pi$
$89$	1.35054e57	0.420244	0.210122	+	0.977675i	$0.432614\pi$
$90$	−3.51306e57	−0.786198
$91$	2.57145e57	0.415392
$92$	−1.03609e58	−1.21243
$93$	7.43213e56	0.0632218
$94$	−3.18751e57	−0.197779
$95$	3.01164e58	1.36759
$96$	2.04643e57	0.0682332
$97$	1.09114e58	0.267987	0.133994	−	0.990982i	$-0.457220\pi$
$97$	1.09114e58	0.267987	0.133994	+	0.990982i	$0.457220\pi$
$98$	1.54726e58	0.280798
$99$	7.61432e58	1.02422
$100$	−1.99043e59	−1.99043
$101$	−7.05413e58	−0.525972	−0.262986	−	0.964800i	$-0.584707\pi$
$101$	−7.05413e58	−0.525972	−0.262986	+	0.964800i	$0.584707\pi$
$102$	−2.65493e57	−0.0148030
$103$	1.13759e59	0.475648	0.237824	−	0.971308i	$-0.423566\pi$
$103$	1.13759e59	0.475648	0.237824	+	0.971308i	$0.423566\pi$
$104$	−1.75276e59	−0.551112
$105$	−3.16908e58	−0.0751361
$106$	1.31067e59	0.234948
$107$	8.55072e59	1.16193	0.580967	−	0.813927i	$-0.302675\pi$
$107$	8.55072e59	1.16193	0.580967	+	0.813927i	$0.302675\pi$
$108$	−1.09698e59	−0.113292
$109$	8.25998e59	0.649976	0.324988	−	0.945718i	$-0.394640\pi$
$109$	8.25998e59	0.649976	0.324988	+	0.945718i	$0.394640\pi$
$110$	−1.35270e60	−0.813052
$111$	3.77715e58	0.0173834
$112$	−8.06647e59	−0.284939
$113$	2.15843e60	0.586577	0.293288	−	0.956024i	$-0.405250\pi$
$113$	2.15843e60	0.586577	0.293288	+	0.956024i	$0.405250\pi$
$114$	−1.04232e59	−0.0218428
$115$	−1.69515e61	−2.74550
$116$	6.95205e60	0.872172
$117$	7.26402e60	0.707448
$118$	8.85772e60	0.671124
$119$	4.94856e60	0.292310
$120$	2.16012e60	0.0996852
$121$	1.63876e60	0.0592034
$122$	9.15095e60	0.259329
$123$	−1.49779e59	−0.00333618
$124$	4.24911e61	0.745347
$125$	−1.91791e62	−2.65451
$126$	−2.26626e61	−0.247958
$127$	2.24486e61	0.194527	0.0972633	−	0.995259i	$-0.468991\pi$
$127$	2.24486e61	0.194527	0.0972633	+	0.995259i	$0.468991\pi$
$128$	1.47239e62	1.01235
$129$	1.49682e61	0.0818035
$130$	−1.29047e62	−0.561591
$131$	2.32590e62	0.807399	0.403699	−	0.914892i	$-0.367724\pi$
$131$	2.32590e62	0.807399	0.403699	+	0.914892i	$0.367724\pi$
$132$	−2.10687e61	−0.0584395
$133$	1.94279e62	0.431324
$134$	2.57934e62	0.459110
$135$	−1.79478e62	−0.256546
$136$	−3.37305e62	−0.387816
$137$	−4.33788e62	−0.401810	−0.200905	−	0.979611i	$-0.564388\pi$
$137$	−4.33788e62	−0.401810	−0.200905	+	0.979611i	$0.564388\pi$
$138$	5.86686e61	0.0438503
$139$	−3.58922e62	−0.216802	−0.108401	−	0.994107i	$-0.534573\pi$
$139$	−3.58922e62	−0.216802	−0.108401	+	0.994107i	$0.534573\pi$
$140$	−1.81183e63	−0.885810
$141$	−8.12262e61	−0.0321909
$142$	9.24205e62	0.297346
$143$	2.79701e63	0.731612
$144$	−2.27867e63	−0.485276
$145$	1.13743e64	1.97500
$146$	−5.33191e63	−0.755916
$147$	3.94284e62	0.0457033
$148$	2.15947e63	0.204940
$149$	−2.37342e63	−0.184663	−0.0923313	−	0.995728i	$-0.529432\pi$
$149$	−2.37342e63	−0.184663	−0.0923313	+	0.995728i	$0.529432\pi$
$150$	1.12709e63	0.0719888
$151$	−3.15470e64	−1.65630	−0.828150	−	0.560507i	$-0.810606\pi$
$151$	−3.15470e64	−1.65630	−0.828150	+	0.560507i	$0.810606\pi$
$152$	−1.32425e64	−0.572249
$153$	1.39790e64	0.497829
$154$	−8.72623e63	−0.256428
$155$	6.95199e64	1.68781
$156$	−2.00994e63	−0.0403652
$157$	−7.08856e64	−1.17901	−0.589506	−	0.807764i	$-0.700678\pi$
$157$	−7.08856e64	−1.17901	−0.589506	+	0.807764i	$0.700678\pi$
$158$	5.29510e64	0.730281
$159$	3.33995e63	0.0382406
$160$	1.91422e65	1.82160
$161$	−1.09353e65	−0.865900
$162$	−6.37076e64	−0.420241
$163$	−1.42919e65	−0.786243	−0.393122	−	0.919486i	$-0.628605\pi$
$163$	−1.42919e65	−0.786243	−0.393122	+	0.919486i	$0.628605\pi$
$164$	−8.56317e63	−0.0393316
$165$	−3.44705e64	−0.132334
$166$	1.52596e64	0.0490178
$167$	−3.84006e64	−0.103324	−0.0516621	−	0.998665i	$-0.516452\pi$
$167$	−3.84006e64	−0.103324	−0.0516621	+	0.998665i	$0.516452\pi$
$168$	1.39348e64	0.0314396
$169$	−2.61196e65	−0.494662
$170$	−2.48341e65	−0.395190
$171$	5.48814e65	0.734581
$172$	8.55762e65	0.964415
$173$	1.60962e66	1.52885	0.764423	−	0.644715i	$-0.223024\pi$
$173$	1.60962e66	1.52885	0.764423	+	0.644715i	$0.223024\pi$
$174$	−3.93661e64	−0.0315442
$175$	−2.10079e66	−1.42154
$176$	−8.77402e65	−0.501851
$177$	2.25719e65	0.109234
$178$	−4.37221e65	−0.179189
$179$	1.29253e66	0.449030	0.224515	−	0.974471i	$-0.427920\pi$
$179$	1.29253e66	0.449030	0.224515	+	0.974471i	$0.427920\pi$
$180$	−5.11818e66	−1.50861
$181$	7.40860e65	0.185446	0.0927231	−	0.995692i	$-0.470443\pi$
$181$	7.40860e65	0.185446	0.0927231	+	0.995692i	$0.470443\pi$
$182$	−8.32478e65	−0.177120
$183$	2.33191e65	0.0422089
$184$	7.45376e66	1.14881
$185$	3.53313e66	0.464080
$186$	−2.40607e65	−0.0269573
$187$	5.38263e66	0.514834
$188$	−4.64388e66	−0.379511
$189$	−1.15780e66	−0.0809118
$190$	−9.74982e66	−0.583130
$191$	1.84854e67	0.946989	0.473494	−	0.880797i	$-0.342992\pi$
$191$	1.84854e67	0.946989	0.473494	+	0.880797i	$0.342992\pi$
$192$	1.08101e65	0.00474726
$193$	−4.21306e67	−1.58729	−0.793647	−	0.608379i	$-0.791820\pi$
$193$	−4.21306e67	−1.58729	−0.793647	+	0.608379i	$0.791820\pi$
$194$	−3.53244e66	−0.114268
$195$	−3.28847e66	−0.0914057
$196$	2.25421e67	0.538815
$197$	5.58072e66	0.114799	0.0573993	−	0.998351i	$-0.481719\pi$
$197$	5.58072e66	0.114799	0.0573993	+	0.998351i	$0.481719\pi$
$198$	−2.46505e67	−0.436719
$199$	−5.98440e67	−0.913808	−0.456904	−	0.889516i	$-0.651042\pi$
$199$	−5.98440e67	−0.913808	−0.456904	+	0.889516i	$0.651042\pi$
$200$	1.43195e68	1.88600
$201$	6.57285e66	0.0747257
$202$	2.28369e67	0.224270
$203$	7.33749e67	0.622895
$204$	−3.86797e66	−0.0284049
$205$	−1.40102e67	−0.0890649
$206$	−3.68280e67	−0.202813
$207$	−3.08908e68	−1.47470
$208$	−8.37038e67	−0.346638
$209$	2.11321e68	0.759672
$210$	1.02595e67	0.0320374
$211$	−4.69123e68	−1.27337	−0.636685	−	0.771124i	$-0.719695\pi$
$211$	−4.69123e68	−1.27337	−0.636685	+	0.771124i	$0.719695\pi$
$212$	1.90952e68	0.450833
$213$	2.35512e67	0.0483967
$214$	−2.76820e68	−0.495439
$215$	1.40012e69	2.18388
$216$	7.89186e67	0.107348
$217$	4.48469e68	0.532318
$218$	−2.67407e68	−0.277145
$219$	−1.35871e68	−0.123034
$220$	−1.97075e69	−1.56014
$221$	5.13500e68	0.355605
$222$	−1.22281e67	−0.00741216
$223$	1.78943e69	0.949997	0.474998	−	0.879987i	$-0.342449\pi$
$223$	1.78943e69	0.949997	0.474998	+	0.879987i	$0.342449\pi$
$224$	1.23486e69	0.574513
$225$	−5.93446e69	−2.42101
$226$	−6.98768e68	−0.250112
$227$	3.77818e68	0.118719	0.0593595	−	0.998237i	$-0.481094\pi$
$227$	3.77818e68	0.118719	0.0593595	+	0.998237i	$0.481094\pi$
$228$	−1.51856e68	−0.0419134
$229$	2.57281e69	0.624110	0.312055	−	0.950064i	$-0.398983\pi$
$229$	2.57281e69	0.624110	0.312055	+	0.950064i	$0.398983\pi$
$230$	5.48784e69	1.17066
$231$	−2.22368e68	−0.0417368
$232$	−5.00140e69	−0.826412
$233$	9.08473e69	1.32225	0.661123	−	0.750277i	$-0.270080\pi$
$233$	9.08473e69	1.32225	0.661123	+	0.750277i	$0.270080\pi$
$234$	−2.35164e69	−0.301650
$235$	−7.59787e69	−0.859389
$236$	1.29048e70	1.28780
$237$	1.34933e69	0.118862
$238$	−1.60204e69	−0.124639
$239$	−1.60292e70	−1.10198	−0.550992	−	0.834511i	$-0.685750\pi$
$239$	−1.60292e70	−1.10198	−0.550992	+	0.834511i	$0.685750\pi$
$240$	1.03157e69	0.0627000
$241$	−2.77243e70	−1.49059	−0.745294	−	0.666736i	$-0.767691\pi$
$241$	−2.77243e70	−1.49059	−0.745294	+	0.666736i	$0.767691\pi$
$242$	−5.30529e68	−0.0252439
$243$	−4.90992e69	−0.206866
$244$	1.33320e70	0.497618
$245$	3.68812e70	1.22013
$246$	4.84891e67	0.00142252
$247$	2.01599e70	0.524720
$248$	−3.05687e70	−0.706240
$249$	3.88855e68	0.00797824
$250$	6.20902e70	1.13186
$251$	5.84246e70	0.946719	0.473360	−	0.880869i	$-0.343041\pi$
$251$	5.84246e70	0.946719	0.473360	+	0.880869i	$0.343041\pi$
$252$	−3.30172e70	−0.475799
$253$	−1.18945e71	−1.52507
$254$	−7.26746e69	−0.0829446
$255$	−6.32841e69	−0.0643220
$256$	−4.01133e70	−0.363253
$257$	1.26421e70	0.102045	0.0510224	−	0.998698i	$-0.483752\pi$
$257$	1.26421e70	0.102045	0.0510224	+	0.998698i	$0.483752\pi$
$258$	−4.84577e69	−0.0348804
$259$	2.27920e70	0.146366
$260$	−1.88009e71	−1.07762
$261$	2.07275e71	1.06084
$262$	−7.52983e70	−0.344268
$263$	9.45182e70	0.386208	0.193104	−	0.981178i	$-0.438145\pi$
$263$	9.45182e70	0.386208	0.193104	+	0.981178i	$0.438145\pi$
$264$	1.51571e70	0.0553733
$265$	3.12417e71	1.02090
$266$	−6.28957e70	−0.183913
$267$	−1.11416e70	−0.0291651
$268$	3.75784e71	0.880971
$269$	−6.14377e71	−1.29045	−0.645227	−	0.763991i	$-0.723237\pi$
$269$	−6.14377e71	−1.29045	−0.645227	+	0.763991i	$0.723237\pi$
$270$	5.81039e70	0.109389
$271$	3.10484e71	0.524137	0.262068	−	0.965049i	$-0.415595\pi$
$271$	3.10484e71	0.524137	0.262068	+	0.965049i	$0.415595\pi$
$272$	−1.61081e71	−0.243928
$273$	−2.12138e70	−0.0288284
$274$	1.40434e71	0.171329
$275$	−2.28506e72	−2.50371
$276$	8.54743e70	0.0841429
$277$	2.42201e71	0.214300	0.107150	−	0.994243i	$-0.465827\pi$
$277$	2.42201e71	0.214300	0.107150	+	0.994243i	$0.465827\pi$
$278$	1.16197e71	0.0924426
$279$	1.26687e72	0.906583
$280$	1.30346e72	0.839334
$281$	4.41465e71	0.255894	0.127947	−	0.991781i	$-0.459161\pi$
$281$	4.41465e71	0.255894	0.127947	+	0.991781i	$0.459161\pi$
$282$	2.62960e70	0.0137259
$283$	−4.82991e71	−0.227111	−0.113556	−	0.993532i	$-0.536224\pi$
$283$	−4.82991e71	−0.227111	−0.113556	+	0.993532i	$0.536224\pi$
$284$	1.34647e72	0.570568
$285$	−2.48452e71	−0.0949115
$286$	−9.05499e71	−0.311954
$287$	−9.03794e70	−0.0280901
$288$	3.48831e72	0.978445
$289$	−2.96080e72	−0.749761
$290$	−3.68229e72	−0.842126
$291$	−9.00160e70	−0.0185984
$292$	−7.76806e72	−1.45050
$293$	−3.92066e72	−0.661857	−0.330929	−	0.943656i	$-0.607362\pi$
$293$	−3.92066e72	−0.661857	−0.330929	+	0.943656i	$0.607362\pi$
$294$	−1.27645e71	−0.0194875
$295$	2.11136e73	2.91617
$296$	−1.55356e72	−0.194188
$297$	−1.25936e72	−0.142507
$298$	7.68366e71	0.0787387
$299$	−1.13473e73	−1.05340
$300$	1.64205e72	0.138137
$301$	9.03208e72	0.688773
$302$	1.02130e73	0.706233
$303$	5.81946e71	0.0365027
$304$	−6.32401e72	−0.359933
$305$	2.18126e73	1.12684
$306$	−4.52555e72	−0.212270
$307$	−3.54986e73	−1.51227	−0.756136	−	0.654415i	$-0.772915\pi$
$307$	−3.54986e73	−1.51227	−0.756136	+	0.654415i	$0.772915\pi$
$308$	−1.27132e73	−0.492051
$309$	−9.38477e71	−0.0330102
$310$	−2.25062e73	−0.719669
$311$	3.81419e73	1.10910	0.554551	−	0.832150i	$-0.312890\pi$
$311$	3.81419e73	1.10910	0.554551	+	0.832150i	$0.312890\pi$
$312$	1.44598e72	0.0382474
$313$	−4.16185e73	−1.00168	−0.500840	−	0.865540i	$-0.666975\pi$
$313$	−4.16185e73	−1.00168	−0.500840	+	0.865540i	$0.666975\pi$
$314$	2.29484e73	0.502722
$315$	−5.40195e73	−1.07743
$316$	7.71443e73	1.40131
$317$	1.46541e73	0.242499	0.121250	−	0.992622i	$-0.461310\pi$
$317$	1.46541e73	0.242499	0.121250	+	0.992622i	$0.461310\pi$
$318$	−1.08127e72	−0.0163055
$319$	7.98110e73	1.09708
$320$	1.01117e73	0.126736
$321$	−7.05411e72	−0.0806387
$322$	3.54018e73	0.369213
$323$	3.87961e73	0.369244
$324$	−9.28156e73	−0.806387
$325$	−2.17994e74	−1.72936
$326$	4.62685e73	0.335248
$327$	−6.81425e72	−0.0451086
$328$	6.16047e72	0.0372679
$329$	−4.90135e73	−0.271042
$330$	1.11594e73	0.0564262
$331$	−1.50576e74	−0.696353	−0.348177	−	0.937429i	$-0.613199\pi$
$331$	−1.50576e74	−0.696353	−0.348177	+	0.937429i	$0.613199\pi$
$332$	2.22317e73	0.0940586
$333$	6.43845e73	0.249274
$334$	1.24318e73	0.0440567
$335$	6.14822e74	1.99493
$336$	6.65462e72	0.0197749
$337$	−2.34878e74	−0.639381	−0.319691	−	0.947522i	$-0.603579\pi$
$337$	−2.34878e74	−0.639381	−0.319691	+	0.947522i	$0.603579\pi$
$338$	8.45590e73	0.210920
$339$	−1.78065e73	−0.0407087
$340$	−3.61809e74	−0.758317
$341$	4.87807e74	0.937549
$342$	−1.77672e74	−0.313220
$343$	5.99198e74	0.969157
$344$	−6.15647e74	−0.913815
$345$	1.39845e74	0.190539
$346$	−5.21096e74	−0.651888
$347$	−1.16630e75	−1.33996	−0.669980	−	0.742379i	$-0.733697\pi$
$347$	−1.16630e75	−1.33996	−0.669980	+	0.742379i	$0.733697\pi$
$348$	−5.73525e73	−0.0605291
$349$	1.43487e74	0.139144	0.0695718	−	0.997577i	$-0.477837\pi$
$349$	1.43487e74	0.139144	0.0695718	+	0.997577i	$0.477837\pi$
$350$	6.80106e74	0.606135
$351$	−1.20142e74	−0.0984320
$352$	1.34317e75	1.01187
$353$	−1.70914e75	−1.18419	−0.592097	−	0.805866i	$-0.701700\pi$
$353$	−1.70914e75	−1.18419	−0.592097	+	0.805866i	$0.701700\pi$
$354$	−7.30738e73	−0.0465763
$355$	2.20297e75	1.29203
$356$	−6.36987e74	−0.343840
$357$	−4.08243e73	−0.0202865
$358$	−4.18441e74	−0.191463
$359$	2.00456e75	0.844757	0.422379	−	0.906420i	$-0.361195\pi$
$359$	2.00456e75	0.844757	0.422379	+	0.906420i	$0.361195\pi$
$360$	3.68210e75	1.42946
$361$	−1.27239e75	−0.455155
$362$	−2.39845e74	−0.0790728
$363$	−1.35193e73	−0.00410875
$364$	−1.21284e75	−0.339869
$365$	−1.27094e76	−3.28461
$366$	−7.54928e73	−0.0179976
$367$	3.69368e75	0.812476	0.406238	−	0.913767i	$-0.366840\pi$
$367$	3.69368e75	0.812476	0.406238	+	0.913767i	$0.366840\pi$
$368$	3.55957e75	0.722581
$369$	−2.55310e74	−0.0478399
$370$	−1.14381e75	−0.197880
$371$	2.01539e75	0.321980
$372$	−3.50540e74	−0.0517274
$373$	2.06268e75	0.281203	0.140602	−	0.990066i	$-0.455096\pi$
$373$	2.06268e75	0.281203	0.140602	+	0.990066i	$0.455096\pi$
$374$	−1.74256e75	−0.219521
$375$	1.58223e75	0.184224
$376$	3.34087e75	0.359599
$377$	7.61393e75	0.757773
$378$	3.74825e74	0.0345001
$379$	1.63106e76	1.38872	0.694359	−	0.719629i	$-0.255688\pi$
$379$	1.63106e76	1.38872	0.694359	+	0.719629i	$0.255688\pi$
$380$	−1.42045e76	−1.11895
$381$	−1.85195e74	−0.0135002
$382$	−5.98443e75	−0.403788
$383$	−1.67919e76	−1.04891	−0.524453	−	0.851440i	$-0.675730\pi$
$383$	−1.67919e76	−1.04891	−0.524453	+	0.851440i	$0.675730\pi$
$384$	−1.21468e75	−0.0702574
$385$	−2.08002e76	−1.11423
$386$	1.36393e76	0.676809
$387$	2.55145e76	1.17304
$388$	−5.14641e75	−0.219265
$389$	−9.77054e75	−0.385838	−0.192919	−	0.981215i	$-0.561796\pi$
$389$	−9.77054e75	−0.385838	−0.192919	+	0.981215i	$0.561796\pi$
$390$	1.06460e75	0.0389747
$391$	−2.18370e76	−0.741273
$392$	−1.62171e76	−0.510545
$393$	−1.91880e75	−0.0560339
$394$	−1.80669e75	−0.0489492
$395$	1.26216e77	3.17322
$396$	−3.59133e76	−0.838006
$397$	−2.20390e76	−0.477388	−0.238694	−	0.971095i	$-0.576719\pi$
$397$	−2.20390e76	−0.477388	−0.238694	+	0.971095i	$0.576719\pi$
$398$	1.93738e76	0.389640
$399$	−1.60275e75	−0.0299341
$400$	6.83831e76	1.18626
$401$	−8.57114e76	−1.38127	−0.690636	−	0.723202i	$-0.742669\pi$
$401$	−8.57114e76	−1.38127	−0.690636	+	0.723202i	$0.742669\pi$
$402$	−2.12788e75	−0.0318625
$403$	4.65365e76	0.647583
$404$	3.32711e76	0.430345
$405$	−1.51856e77	−1.82603
$406$	−2.37543e76	−0.265597
$407$	2.47912e76	0.257788
$408$	2.78268e75	0.0269146
$409$	−1.18117e77	−1.06286	−0.531428	−	0.847104i	$-0.678344\pi$
$409$	−1.18117e77	−1.06286	−0.531428	+	0.847104i	$0.678344\pi$
$410$	4.53565e75	0.0379766
$411$	3.57863e75	0.0278858
$412$	−5.36547e76	−0.389171
$413$	1.36203e77	0.919730
$414$	1.00005e77	0.628801
$415$	3.63733e76	0.212992
$416$	1.28138e77	0.698915
$417$	2.96100e75	0.0150462
$418$	−6.84126e76	−0.323918
$419$	8.82341e76	0.389334	0.194667	−	0.980869i	$-0.437637\pi$
$419$	8.82341e76	0.389334	0.194667	+	0.980869i	$0.437637\pi$
$420$	1.49471e76	0.0614756
$421$	4.95671e76	0.190052	0.0950258	−	0.995475i	$-0.469707\pi$
$421$	4.95671e76	0.190052	0.0950258	+	0.995475i	$0.469707\pi$
$422$	1.51873e77	0.542955
$423$	−1.38457e77	−0.461608
$424$	−1.37373e77	−0.427179
$425$	−4.19512e77	−1.21694
$426$	−7.62444e75	−0.0206360
$427$	1.40712e77	0.355393
$428$	−4.03298e77	−0.950682
$429$	−2.30746e76	−0.0507742
$430$	−4.53271e77	−0.931191
$431$	8.16025e77	1.56540	0.782698	−	0.622402i	$-0.213843\pi$
$431$	8.16025e77	1.56540	0.782698	+	0.622402i	$0.213843\pi$
$432$	3.76878e76	0.0675197
$433$	5.70929e77	0.955408	0.477704	−	0.878521i	$-0.341469\pi$
$433$	5.70929e77	0.955408	0.477704	+	0.878521i	$0.341469\pi$
$434$	−1.45187e77	−0.226976
$435$	−9.38347e76	−0.137066
$436$	−3.89585e77	−0.531804
$437$	−8.57314e77	−1.09380
$438$	4.39868e76	0.0524609
$439$	1.20511e78	1.34376	0.671881	−	0.740659i	$-0.265487\pi$
$439$	1.20511e78	1.34376	0.671881	+	0.740659i	$0.265487\pi$
$440$	1.41779e78	1.47828
$441$	6.72090e77	0.655373
$442$	−1.66240e77	−0.151627
$443$	−9.08891e77	−0.775536	−0.387768	−	0.921757i	$-0.626754\pi$
$443$	−9.08891e77	−0.775536	−0.387768	+	0.921757i	$0.626754\pi$
$444$	−1.78151e76	−0.0142230
$445$	−1.04218e78	−0.778613
$446$	−5.79308e77	−0.405071
$447$	1.95800e76	0.0128157
$448$	6.52302e76	0.0399712
$449$	−2.07903e78	−1.19287	−0.596435	−	0.802661i	$-0.703417\pi$
$449$	−2.07903e78	−1.19287	−0.596435	+	0.802661i	$0.703417\pi$
$450$	1.92121e78	1.03230
$451$	−9.83071e76	−0.0494740
$452$	−1.01803e78	−0.479931
$453$	2.60254e77	0.114948
$454$	−1.22314e77	−0.0506208
$455$	−1.98433e78	−0.769622
$456$	1.09247e77	0.0397143
$457$	1.64014e78	0.558923	0.279462	−	0.960157i	$-0.409844\pi$
$457$	1.64014e78	0.558923	0.279462	+	0.960157i	$0.409844\pi$
$458$	−8.32918e77	−0.266116
$459$	−2.31205e77	−0.0692664
$460$	7.99523e78	2.24634
$461$	2.32024e78	0.611441	0.305721	−	0.952121i	$-0.401103\pi$
$461$	2.32024e78	0.611441	0.305721	+	0.952121i	$0.401103\pi$
$462$	7.19890e76	0.0177962
$463$	1.52939e78	0.354713	0.177357	−	0.984147i	$-0.443245\pi$
$463$	1.52939e78	0.354713	0.177357	+	0.984147i	$0.443245\pi$
$464$	−2.38844e78	−0.519797
$465$	−5.73520e77	−0.117135
$466$	−2.94108e78	−0.563796
$467$	−7.17147e78	−1.29051	−0.645254	−	0.763968i	$-0.723248\pi$
$467$	−7.17147e78	−1.29051	−0.645254	+	0.763968i	$0.723248\pi$
$468$	−3.42611e78	−0.578827
$469$	3.96619e78	0.629179
$470$	2.45972e78	0.366437
$471$	5.84787e77	0.0818240
$472$	−9.28391e78	−1.22023
$473$	9.82433e78	1.21311
$474$	−4.36831e77	−0.0506818
$475$	−1.64699e79	−1.79569
$476$	−2.33401e78	−0.239165
$477$	5.69321e78	0.548359
$478$	5.18928e78	0.469877
$479$	1.52757e79	1.30048	0.650241	−	0.759728i	$-0.274668\pi$
$479$	1.52757e79	1.30048	0.650241	+	0.759728i	$0.274668\pi$
$480$	−1.57918e78	−0.126420
$481$	2.36507e78	0.178059
$482$	8.97542e78	0.635575
$483$	9.02133e77	0.0600939
$484$	−7.72928e77	−0.0484397
$485$	−8.42006e78	−0.496517
$486$	1.58953e78	0.0882060
$487$	4.49651e78	0.234840	0.117420	−	0.993082i	$-0.462538\pi$
$487$	4.49651e78	0.234840	0.117420	+	0.993082i	$0.462538\pi$
$488$	−9.59125e78	−0.471509
$489$	1.17905e78	0.0545656
$490$	−1.19398e79	−0.520253
$491$	1.13413e79	0.465326	0.232663	−	0.972557i	$-0.425256\pi$
$491$	1.13413e79	0.465326	0.232663	+	0.972557i	$0.425256\pi$
$492$	7.06438e76	0.00272963
$493$	1.46524e79	0.533243
$494$	−6.52652e78	−0.223737
$495$	−5.87579e79	−1.89763
$496$	−1.45982e79	−0.444211
$497$	1.42113e79	0.407493
$498$	−1.25887e77	−0.00340186
$499$	−2.74327e79	−0.698719	−0.349359	−	0.936989i	$-0.613601\pi$
$499$	−2.74327e79	−0.698719	−0.349359	+	0.936989i	$0.613601\pi$
$500$	9.04592e79	2.17189
$501$	3.16795e77	0.00717075
$502$	−1.89143e79	−0.403674
$503$	−5.28271e79	−1.06317	−0.531583	−	0.847006i	$-0.678403\pi$
$503$	−5.28271e79	−1.06317	−0.531583	+	0.847006i	$0.678403\pi$
$504$	2.37530e79	0.450836
$505$	5.44350e79	0.974502
$506$	3.85070e79	0.650279
$507$	2.15479e78	0.0343297
$508$	−1.05880e79	−0.159160
$509$	1.13708e80	1.61294	0.806470	−	0.591275i	$-0.201375\pi$
$509$	1.13708e80	1.61294	0.806470	+	0.591275i	$0.201375\pi$
$510$	2.04875e78	0.0274264
$511$	−8.19875e79	−1.03593
$512$	−7.18915e79	−0.857459
$513$	−9.07704e78	−0.102207
$514$	−4.09272e78	−0.0435111
$515$	−8.77847e79	−0.881263
$516$	−7.05980e78	−0.0669308
$517$	−5.33127e79	−0.477375
$518$	−7.37865e78	−0.0624093
$519$	−1.32789e79	−0.106103
$520$	1.35256e80	1.02108
$521$	−1.18992e80	−0.848797	−0.424398	−	0.905476i	$-0.639514\pi$
$521$	−1.18992e80	−0.848797	−0.424398	+	0.905476i	$0.639514\pi$
$522$	−6.71027e79	−0.452335
$523$	2.64671e80	1.68619	0.843097	−	0.537762i	$-0.180730\pi$
$523$	2.64671e80	1.68619	0.843097	+	0.537762i	$0.180730\pi$
$524$	−1.09702e80	−0.660606
$525$	1.73309e79	0.0986558
$526$	−3.05992e79	−0.164676
$527$	8.95559e79	0.455702
$528$	7.23833e78	0.0348287
$529$	2.62796e80	1.19585
$530$	−1.01141e80	−0.435302
$531$	3.84756e80	1.56638
$532$	−9.16327e79	−0.352905
$533$	−9.37844e78	−0.0341726
$534$	3.60695e78	0.0124358
$535$	−6.59838e80	−2.15279
$536$	−2.70344e80	−0.834749
$537$	−1.06630e79	−0.0311629
$538$	1.98897e80	0.550240
$539$	2.58788e80	0.677759
$540$	8.46516e79	0.209903
$541$	−1.23574e80	−0.290141	−0.145071	−	0.989421i	$-0.546341\pi$
$541$	−1.23574e80	−0.290141	−0.145071	+	0.989421i	$0.546341\pi$
$542$	−1.00515e80	−0.223488
$543$	−6.11189e78	−0.0128701
$544$	2.46591e80	0.491825
$545$	−6.37403e80	−1.20425
$546$	6.86771e78	0.0122922
$547$	−6.88700e80	−1.16789	−0.583947	−	0.811792i	$-0.698493\pi$
$547$	−6.88700e80	−1.16789	−0.583947	+	0.811792i	$0.698493\pi$
$548$	2.04598e80	0.328757
$549$	3.97493e80	0.605265
$550$	7.39762e80	1.06756
$551$	5.75250e80	0.786837
$552$	−6.14914e79	−0.0797282
$553$	8.14214e80	1.00080
$554$	−7.84097e79	−0.0913760
$555$	−2.91473e79	−0.0322074
$556$	1.69287e80	0.177385
$557$	−1.64679e81	−1.63648	−0.818239	−	0.574878i	$-0.805049\pi$
$557$	−1.64679e81	−1.63648	−0.818239	+	0.574878i	$0.805049\pi$
$558$	−4.10134e80	−0.386560
$559$	9.37237e80	0.837917
$560$	6.22470e80	0.527924
$561$	−4.44052e79	−0.0357297
$562$	−1.42919e80	−0.109111
$563$	−8.28386e80	−0.600116	−0.300058	−	0.953921i	$-0.597006\pi$
$563$	−8.28386e80	−0.600116	−0.300058	+	0.953921i	$0.597006\pi$
$564$	3.83107e79	0.0263382
$565$	−1.66561e81	−1.08679
$566$	1.56363e80	0.0968385
$567$	−9.79616e80	−0.575912
$568$	−9.68673e80	−0.540632
$569$	1.62848e80	0.0862919	0.0431460	−	0.999069i	$-0.486262\pi$
$569$	1.62848e80	0.0862919	0.0431460	+	0.999069i	$0.486262\pi$
$570$	8.04334e79	0.0404695
$571$	2.39641e81	1.14497	0.572487	−	0.819914i	$-0.305979\pi$
$571$	2.39641e81	1.14497	0.572487	+	0.819914i	$0.305979\pi$
$572$	−1.31922e81	−0.598598
$573$	−1.52500e80	−0.0657215
$574$	2.92593e79	0.0119774
$575$	9.27035e81	3.60491
$576$	1.84267e80	0.0680744
$577$	−3.77209e81	−1.32402	−0.662012	−	0.749493i	$-0.730297\pi$
$577$	−3.77209e81	−1.32402	−0.662012	+	0.749493i	$0.730297\pi$
$578$	9.58525e80	0.319692
$579$	3.47566e80	0.110159
$580$	−5.36473e81	−1.61593
$581$	2.34643e80	0.0671755
$582$	2.91416e79	0.00793023
$583$	2.19217e81	0.567089
$584$	5.58846e81	1.37440
$585$	−5.60547e81	−1.31073
$586$	1.26927e81	0.282211
$587$	−8.21302e81	−1.73652	−0.868258	−	0.496113i	$-0.834760\pi$
$587$	−8.21302e81	−1.73652	−0.868258	+	0.496113i	$0.834760\pi$
$588$	−1.85966e80	−0.0373940
$589$	3.51594e81	0.672420
$590$	−6.83529e81	−1.24343
$591$	−4.60394e79	−0.00796707
$592$	−7.41907e80	−0.122140
$593$	7.94731e81	1.24482	0.622410	−	0.782691i	$-0.286154\pi$
$593$	7.94731e81	1.24482	0.622410	+	0.782691i	$0.286154\pi$
$594$	4.07703e80	0.0607637
$595$	−3.81869e81	−0.541581
$596$	1.11943e81	0.151089
$597$	4.93697e80	0.0634187
$598$	3.67355e81	0.449160
$599$	5.80570e81	0.675715	0.337857	−	0.941197i	$-0.390298\pi$
$599$	5.80570e81	0.675715	0.337857	+	0.941197i	$0.390298\pi$
$600$	−1.18132e81	−0.130889
$601$	−7.35889e81	−0.776274	−0.388137	−	0.921602i	$-0.626881\pi$
$601$	−7.35889e81	−0.776274	−0.388137	+	0.921602i	$0.626881\pi$
$602$	−2.92403e81	−0.293687
$603$	1.12040e82	1.07155
$604$	1.48793e82	1.35517
$605$	−1.26459e81	−0.109690
$606$	−1.88398e80	−0.0155645
$607$	−1.69742e82	−1.33574	−0.667870	−	0.744278i	$-0.732794\pi$
$607$	−1.69742e82	−1.33574	−0.667870	+	0.744278i	$0.732794\pi$
$608$	9.68112e81	0.725722
$609$	−6.05323e80	−0.0432292
$610$	−7.06157e81	−0.480475
$611$	−5.08601e81	−0.329732
$612$	−6.59328e81	−0.407319
$613$	−1.34842e82	−0.793852	−0.396926	−	0.917851i	$-0.629923\pi$
$613$	−1.34842e82	−0.793852	−0.396926	+	0.917851i	$0.629923\pi$
$614$	1.14923e82	0.644820
$615$	1.15581e80	0.00618115
$616$	9.14609e81	0.466235
$617$	−3.18225e82	−1.54640	−0.773199	−	0.634163i	$-0.781345\pi$
$617$	−3.18225e82	−1.54640	−0.773199	+	0.634163i	$0.781345\pi$
$618$	3.03821e80	0.0140753
$619$	3.44849e82	1.52319	0.761596	−	0.648053i	$-0.224416\pi$
$619$	3.44849e82	1.52319	0.761596	+	0.648053i	$0.224416\pi$
$620$	−3.27893e82	−1.38095
$621$	5.10915e81	0.205185
$622$	−1.23480e82	−0.472912
$623$	−6.72304e81	−0.245566
$624$	6.90533e80	0.0240569
$625$	7.47935e82	2.48544
$626$	1.34735e82	0.427108
$627$	−1.74334e81	−0.0527216
$628$	3.34335e82	0.964656
$629$	4.55140e81	0.125300
$630$	1.74882e82	0.459408
$631$	−4.48510e82	−1.12436	−0.562181	−	0.827014i	$-0.690038\pi$
$631$	−4.48510e82	−1.12436	−0.562181	+	0.827014i	$0.690038\pi$
$632$	−5.54987e82	−1.32779
$633$	3.87014e81	0.0883725
$634$	−4.74409e81	−0.103400
$635$	−1.73230e82	−0.360412
$636$	−1.57530e81	−0.0312880
$637$	2.46882e82	0.468141
$638$	−2.58379e82	−0.467786
$639$	4.01450e82	0.693995
$640$	−1.13621e83	−1.87564
$641$	3.38457e82	0.533570	0.266785	−	0.963756i	$-0.414039\pi$
$641$	3.38457e82	0.533570	0.266785	+	0.963756i	$0.414039\pi$
$642$	2.28368e81	0.0343837
$643$	−3.04533e82	−0.437936	−0.218968	−	0.975732i	$-0.570269\pi$
$643$	−3.04533e82	−0.437936	−0.218968	+	0.975732i	$0.570269\pi$
$644$	5.15769e82	0.708470
$645$	−1.15506e82	−0.151563
$646$	−1.25598e82	−0.157443
$647$	−1.22434e83	−1.46631	−0.733157	−	0.680060i	$-0.761954\pi$
$647$	−1.22434e83	−1.46631	−0.733157	+	0.680060i	$0.761954\pi$
$648$	6.67729e82	0.764078
$649$	1.48150e83	1.61988
$650$	7.05729e82	0.737384
$651$	−3.69975e81	−0.0369431
$652$	6.74086e82	0.643296
$653$	9.26564e82	0.845156	0.422578	−	0.906327i	$-0.361125\pi$
$653$	9.26564e82	0.845156	0.422578	+	0.906327i	$0.361125\pi$
$654$	2.20603e81	0.0192340
$655$	−1.79484e83	−1.49592
$656$	2.94195e81	0.0234408
$657$	−2.31604e83	−1.76428
$658$	1.58675e82	0.115570
$659$	1.42910e83	0.995275	0.497638	−	0.867385i	$-0.334201\pi$
$659$	1.42910e83	0.995275	0.497638	+	0.867385i	$0.334201\pi$
$660$	1.62582e82	0.108274
$661$	1.00439e83	0.639674	0.319837	−	0.947473i	$-0.396372\pi$
$661$	1.00439e83	0.639674	0.319837	+	0.947473i	$0.396372\pi$
$662$	4.87472e82	0.296920
$663$	−4.23623e81	−0.0246792
$664$	−1.59938e82	−0.0891236
$665$	−1.49921e83	−0.799140
$666$	−2.08437e82	−0.106288
$667$	−3.23788e83	−1.57961
$668$	1.81118e82	0.0845389
$669$	−1.47623e82	−0.0659302
$670$	−1.99041e83	−0.850622
$671$	1.53054e83	0.625939
$672$	−1.01872e82	−0.0398715
$673$	2.95487e83	1.10686	0.553432	−	0.832894i	$-0.313318\pi$
$673$	2.95487e83	1.10686	0.553432	+	0.832894i	$0.313318\pi$
$674$	7.60389e82	0.272627
$675$	9.81523e82	0.336852
$676$	1.23194e83	0.404727
$677$	−8.74198e81	−0.0274944	−0.0137472	−	0.999906i	$-0.504376\pi$
$677$	−8.74198e81	−0.0274944	−0.0137472	+	0.999906i	$0.504376\pi$
$678$	5.76464e81	0.0173579
$679$	−5.43174e82	−0.156596
$680$	2.60290e83	0.718531
$681$	−3.11690e81	−0.00823915
$682$	−1.57922e83	−0.399763
$683$	3.28450e83	0.796267	0.398134	−	0.917327i	$-0.369658\pi$
$683$	3.28450e83	0.796267	0.398134	+	0.917327i	$0.369658\pi$
$684$	−2.58850e83	−0.601027
$685$	3.34744e83	0.744459
$686$	−1.93983e83	−0.413241
$687$	−2.12250e82	−0.0433135
$688$	−2.94005e83	−0.574771
$689$	2.09132e83	0.391699
$690$	−4.52731e82	−0.0812442
$691$	−6.66760e83	−1.14648	−0.573241	−	0.819387i	$-0.694314\pi$
$691$	−6.66760e83	−1.14648	−0.573241	+	0.819387i	$0.694314\pi$
$692$	−7.59185e83	−1.25089
$693$	−3.79044e83	−0.598494
$694$	3.77577e83	0.571349
$695$	2.76971e83	0.401682
$696$	4.12602e82	0.0573533
$697$	−1.80481e82	−0.0240472
$698$	−4.64523e82	−0.0593297
$699$	−7.49465e82	−0.0917646
$700$	9.90847e83	1.16309
$701$	2.68462e83	0.302135	0.151068	−	0.988523i	$-0.451729\pi$
$701$	2.68462e83	0.302135	0.151068	+	0.988523i	$0.451729\pi$
$702$	3.88947e82	0.0419706
$703$	1.78687e83	0.184889
$704$	7.09518e82	0.0703996
$705$	6.26803e82	0.0596420
$706$	5.53313e83	0.504931
$707$	3.51158e83	0.307347
$708$	−1.06461e83	−0.0893738
$709$	−7.40264e83	−0.596105	−0.298053	−	0.954549i	$-0.596337\pi$
$709$	−7.40264e83	−0.596105	−0.298053	+	0.954549i	$0.596337\pi$
$710$	−7.13187e83	−0.550912
$711$	2.30005e84	1.70445
$712$	4.58258e83	0.325799
$713$	−1.97900e84	−1.34991
$714$	1.32164e82	0.00864998
$715$	−2.15838e84	−1.35550
$716$	−6.09627e83	−0.367392
$717$	1.32237e83	0.0764782
$718$	−6.48951e83	−0.360198
$719$	1.09772e84	0.584773	0.292387	−	0.956300i	$-0.405551\pi$
$719$	1.09772e84	0.584773	0.292387	+	0.956300i	$0.405551\pi$
$720$	1.75840e84	0.899101
$721$	−5.66295e83	−0.277941
$722$	4.11922e83	0.194074
$723$	2.28718e83	0.103448
$724$	−3.49430e83	−0.151730
$725$	−6.22032e84	−2.59323
$726$	4.37672e81	0.00175194
$727$	4.10850e84	1.57913	0.789566	−	0.613666i	$-0.210306\pi$
$727$	4.10850e84	1.57913	0.789566	+	0.613666i	$0.210306\pi$
$728$	8.72533e83	0.322037
$729$	−2.74018e84	−0.971217
$730$	4.11451e84	1.40053
$731$	1.80364e84	0.589640
$732$	−1.09985e83	−0.0345349
$733$	4.99365e84	1.50609	0.753045	−	0.657969i	$-0.228584\pi$
$733$	4.99365e84	1.50609	0.753045	+	0.657969i	$0.228584\pi$
$734$	−1.19579e84	−0.346433
$735$	−3.04260e83	−0.0846774
$736$	−5.44917e84	−1.45692
$737$	4.31408e84	1.10815
$738$	8.26536e82	0.0203986
$739$	−1.62337e83	−0.0384951	−0.0192476	−	0.999815i	$-0.506127\pi$
$739$	−1.62337e83	−0.0384951	−0.0192476	+	0.999815i	$0.506127\pi$
$740$	−1.66641e84	−0.379706
$741$	−1.66313e83	−0.0364158
$742$	−6.52458e83	−0.137290
$743$	−3.18863e84	−0.644814	−0.322407	−	0.946601i	$-0.604492\pi$
$743$	−3.18863e84	−0.644814	−0.322407	+	0.946601i	$0.604492\pi$
$744$	2.52183e83	0.0490134
$745$	1.83151e84	0.342136
$746$	−6.67767e83	−0.119903
$747$	6.62835e83	0.114406
$748$	−2.53874e84	−0.421232
$749$	−4.25659e84	−0.678966
$750$	−5.12227e83	−0.0785516
$751$	−1.31852e85	−1.94405	−0.972026	−	0.234872i	$-0.924533\pi$
$751$	−1.31852e85	−1.94405	−0.972026	+	0.234872i	$0.924533\pi$
$752$	1.59544e84	0.226181
$753$	−4.81987e83	−0.0657028
$754$	−2.46492e84	−0.323108
$755$	2.43441e85	3.06873
$756$	5.46083e83	0.0662012
$757$	8.93658e84	1.04194	0.520970	−	0.853575i	$-0.325570\pi$
$757$	8.93658e84	1.04194	0.520970	+	0.853575i	$0.325570\pi$
$758$	−5.28038e84	−0.592138
$759$	9.81263e83	0.105841
$760$	1.02189e85	1.06024
$761$	−5.17623e83	−0.0516614	−0.0258307	−	0.999666i	$-0.508223\pi$
$761$	−5.17623e83	−0.0516614	−0.0258307	+	0.999666i	$0.508223\pi$
$762$	5.99546e82	0.00575640
$763$	−4.11185e84	−0.379808
$764$	−8.71872e84	−0.774817
$765$	−1.07873e85	−0.922359
$766$	5.43618e84	0.447245
$767$	1.41334e85	1.11888
$768$	3.30924e83	0.0252099
$769$	−2.04223e85	−1.49719	−0.748596	−	0.663026i	$-0.769272\pi$
$769$	−2.04223e85	−1.49719	−0.748596	+	0.663026i	$0.769272\pi$
$770$	6.73382e84	0.475100
$771$	−1.04294e83	−0.00708196
$772$	1.98711e85	1.29871
$773$	−1.06063e85	−0.667221	−0.333611	−	0.942711i	$-0.608267\pi$
$773$	−1.06063e85	−0.667221	−0.333611	+	0.942711i	$0.608267\pi$
$774$	−8.26001e84	−0.500175
$775$	−3.80188e85	−2.21614
$776$	3.70240e84	0.207760
$777$	−1.88028e83	−0.0101579
$778$	3.16310e84	0.164518
$779$	−7.08563e83	−0.0354833
$780$	1.55102e84	0.0747872
$781$	1.54578e85	0.717700
$782$	7.06947e84	0.316073
$783$	−3.42819e84	−0.147602
$784$	−7.74453e84	−0.321123
$785$	5.47007e85	2.18443
$786$	6.21190e83	0.0238924
$787$	−6.47255e84	−0.239784	−0.119892	−	0.992787i	$-0.538255\pi$
$787$	−6.47255e84	−0.239784	−0.119892	+	0.992787i	$0.538255\pi$
$788$	−2.63217e84	−0.0939270
$789$	−7.79749e83	−0.0268030
$790$	−4.08610e85	−1.35304
$791$	−1.07448e85	−0.342761
$792$	2.58365e85	0.794038
$793$	1.46013e85	0.432348
$794$	7.13487e84	0.203555
$795$	−2.57735e84	−0.0708507
$796$	2.82257e85	0.747668
$797$	3.83924e85	0.979997	0.489998	−	0.871723i	$-0.336997\pi$
$797$	3.83924e85	0.979997	0.489998	+	0.871723i	$0.336997\pi$
$798$	5.18872e83	0.0127636
$799$	−9.78762e84	−0.232032
$800$	−1.04684e86	−2.39181
$801$	−1.89917e85	−0.418220
$802$	2.77480e85	0.588964
$803$	−8.91790e85	−1.82454
$804$	−3.10011e84	−0.0611398
$805$	8.43851e85	1.60431
$806$	−1.50657e85	−0.276124
$807$	5.06844e84	0.0895582
$808$	−2.39357e85	−0.407766
$809$	−5.32062e85	−0.873938	−0.436969	−	0.899476i	$-0.643948\pi$
$809$	−5.32062e85	−0.873938	−0.436969	+	0.899476i	$0.643948\pi$
$810$	4.91616e85	0.778607
$811$	3.55627e85	0.543100	0.271550	−	0.962424i	$-0.412464\pi$
$811$	3.55627e85	0.543100	0.271550	+	0.962424i	$0.412464\pi$
$812$	−3.46076e85	−0.509646
$813$	−2.56140e84	−0.0363753
$814$	−8.02587e84	−0.109919
$815$	1.10287e86	1.45672
$816$	1.32888e84	0.0169288
$817$	7.08104e85	0.870054
$818$	3.82389e85	0.453193
$819$	−3.61606e85	−0.413391
$820$	6.60799e84	0.0728720
$821$	1.58053e84	0.0168144	0.00840719	−	0.999965i	$-0.497324\pi$
$821$	1.58053e84	0.0168144	0.00840719	+	0.999965i	$0.497324\pi$
$822$	−1.15854e84	−0.0118903
$823$	−1.35395e84	−0.0134063	−0.00670315	−	0.999978i	$-0.502134\pi$
$823$	−1.35395e84	−0.0134063	−0.00670315	+	0.999978i	$0.502134\pi$
$824$	3.86000e85	0.368752
$825$	1.88511e85	0.173758
$826$	−4.40941e85	−0.392166
$827$	−2.09737e86	−1.79996	−0.899980	−	0.435930i	$-0.856419\pi$
$827$	−2.09737e86	−1.79996	−0.899980	+	0.435930i	$0.856419\pi$
$828$	1.45698e86	1.20659
$829$	−2.20814e86	−1.76469	−0.882345	−	0.470603i	$-0.844037\pi$
$829$	−2.20814e86	−1.76469	−0.882345	+	0.470603i	$0.844037\pi$
$830$	−1.17754e85	−0.0908183
$831$	−1.99809e84	−0.0148725
$832$	6.76877e84	0.0486264
$833$	4.75106e85	0.329430
$834$	−9.58590e83	−0.00641556
$835$	2.96328e85	0.191435
$836$	−9.96703e85	−0.621556
$837$	−2.09532e85	−0.126139
$838$	−2.85647e85	−0.166009
$839$	1.14299e86	0.641307	0.320654	−	0.947197i	$-0.396097\pi$
$839$	1.14299e86	0.641307	0.320654	+	0.947197i	$0.396097\pi$
$840$	−1.07532e85	−0.0582502
$841$	2.60617e85	0.136308
$842$	−1.60468e85	−0.0810365
$843$	−3.64196e84	−0.0177591
$844$	2.21264e86	1.04186
$845$	2.01558e86	0.916490
$846$	4.48237e85	0.196826
$847$	−8.15782e84	−0.0345950
$848$	−6.56032e85	−0.268687
$849$	3.98454e84	0.0157616
$850$	1.35812e86	0.518896
$851$	−1.00577e86	−0.371171
$852$	−1.11080e85	−0.0395977
$853$	−2.96557e86	−1.02120	−0.510601	−	0.859818i	$-0.670577\pi$
$853$	−2.96557e86	−1.02120	−0.510601	+	0.859818i	$0.670577\pi$
$854$	−4.55538e85	−0.151537
$855$	−4.23506e86	−1.36100
$856$	2.90139e86	0.900803
$857$	4.75436e86	1.42612	0.713062	−	0.701101i	$-0.247308\pi$
$857$	4.75436e86	1.42612	0.713062	+	0.701101i	$0.247308\pi$
$858$	7.47012e84	0.0216497
$859$	2.70859e86	0.758481	0.379240	−	0.925298i	$-0.376185\pi$
$859$	2.70859e86	0.758481	0.379240	+	0.925298i	$0.376185\pi$
$860$	−6.60371e86	−1.78683
$861$	7.45605e83	0.00194947
$862$	−2.64179e86	−0.667472
$863$	6.38040e86	1.55786	0.778932	−	0.627109i	$-0.215762\pi$
$863$	6.38040e86	1.55786	0.778932	+	0.627109i	$0.215762\pi$
$864$	−5.76945e85	−0.136138
$865$	−1.24211e87	−2.83259
$866$	−1.84831e86	−0.407379
$867$	2.44258e85	0.0520338
$868$	−2.11523e86	−0.435537
$869$	8.85633e86	1.76267
$870$	3.03779e85	0.0584439
$871$	4.11561e86	0.765418
$872$	2.80273e86	0.503901
$873$	−1.53440e86	−0.266697
$874$	2.77545e86	0.466387
$875$	9.54746e86	1.55114
$876$	6.40844e85	0.100666
$877$	−1.05932e87	−1.60894	−0.804469	−	0.593995i	$-0.797550\pi$
$877$	−1.05932e87	−1.60894	−0.804469	+	0.593995i	$0.797550\pi$
$878$	−3.90139e86	−0.572970
$879$	3.23444e85	0.0459332
$880$	6.77070e86	0.929811
$881$	−3.34361e86	−0.444045	−0.222022	−	0.975042i	$-0.571266\pi$
$881$	−3.34361e86	−0.444045	−0.222022	+	0.975042i	$0.571266\pi$
$882$	−2.17581e86	−0.279446
$883$	1.56798e87	1.94761	0.973803	−	0.227394i	$-0.0730204\pi$
$883$	1.56798e87	1.94761	0.973803	+	0.227394i	$0.0730204\pi$
$884$	−2.42194e86	−0.290953
$885$	−1.74182e86	−0.202384
$886$	2.94243e86	0.330682
$887$	−1.35049e87	−1.46806	−0.734032	−	0.679115i	$-0.762364\pi$
$887$	−1.35049e87	−1.46806	−0.734032	+	0.679115i	$0.762364\pi$
$888$	1.28164e85	0.0134767
$889$	−1.11750e86	−0.113670
$890$	3.37393e86	0.331994
$891$	−1.06554e87	−1.01433
$892$	−8.43994e86	−0.777278
$893$	−3.84260e86	−0.342379
$894$	−6.33881e84	−0.00546450
$895$	−9.97413e86	−0.831947
$896$	−7.32964e86	−0.591557
$897$	9.36120e85	0.0731063
$898$	6.73061e86	0.508630
$899$	1.32789e87	0.971074
$900$	2.79901e87	1.98085
$901$	4.02458e86	0.275638
$902$	3.18258e85	0.0210953
$903$	−7.45122e85	−0.0478012
$904$	7.32389e86	0.454750
$905$	−5.71703e86	−0.343588
$906$	−8.42543e85	−0.0490129
$907$	−2.09556e87	−1.18001	−0.590003	−	0.807401i	$-0.700873\pi$
$907$	−2.09556e87	−1.18001	−0.590003	+	0.807401i	$0.700873\pi$
$908$	−1.78200e86	−0.0971346
$909$	9.91975e86	0.523439
$910$	6.42403e86	0.328161
$911$	1.73916e87	0.860096	0.430048	−	0.902806i	$-0.358497\pi$
$911$	1.73916e87	0.860096	0.430048	+	0.902806i	$0.358497\pi$
$912$	5.21714e85	0.0249795
$913$	2.55224e86	0.118313
$914$	−5.30975e86	−0.238320
$915$	−1.79948e86	−0.0782031
$916$	−1.21348e87	−0.510641
$917$	−1.15784e87	−0.471797
$918$	7.48498e85	0.0295346
$919$	2.15988e87	0.825320	0.412660	−	0.910885i	$-0.364600\pi$
$919$	2.15988e87	0.825320	0.412660	+	0.910885i	$0.364600\pi$
$920$	−5.75188e87	−2.12848
$921$	2.92854e86	0.104952
$922$	−7.51149e86	−0.260714
$923$	1.47467e87	0.495729
$924$	1.04881e86	0.0341486
$925$	−1.93218e87	−0.609350
$926$	−4.95120e86	−0.151247
$927$	−1.59971e87	−0.473357
$928$	3.65634e87	1.04805
$929$	3.13437e87	0.870336	0.435168	−	0.900349i	$-0.356689\pi$
$929$	3.13437e87	0.870336	0.435168	+	0.900349i	$0.356689\pi$
$930$	1.85670e86	0.0499454
$931$	1.86525e87	0.486096
$932$	−4.28485e87	−1.08185
$933$	−3.14660e86	−0.0769722
$934$	2.32168e87	0.550262
$935$	−4.15364e87	−0.953864
$936$	2.46479e87	0.548457
$937$	3.43491e87	0.740624	0.370312	−	0.928907i	$-0.379251\pi$
$937$	3.43491e87	0.740624	0.370312	+	0.928907i	$0.379251\pi$
$938$	−1.28401e87	−0.268277
$939$	3.43341e86	0.0695170
$940$	3.58357e87	0.703143
$941$	6.94454e87	1.32053	0.660267	−	0.751031i	$-0.270443\pi$
$941$	6.94454e87	1.32053	0.660267	+	0.751031i	$0.270443\pi$
$942$	−1.89318e86	−0.0348891
$943$	3.98826e86	0.0712341
$944$	−4.43356e87	−0.767501
$945$	8.93449e86	0.149910
$946$	−3.18051e87	−0.517260
$947$	−2.62366e87	−0.413603	−0.206801	−	0.978383i	$-0.566305\pi$
$947$	−2.62366e87	−0.413603	−0.206801	+	0.978383i	$0.566305\pi$
$948$	−6.36419e86	−0.0972517
$949$	−8.50764e87	−1.26025
$950$	5.33195e87	0.765666
$951$	−1.20892e86	−0.0168296
$952$	1.67912e87	0.226617
$953$	−7.56122e86	−0.0989353	−0.0494676	−	0.998776i	$-0.515752\pi$
$953$	−7.56122e86	−0.0989353	−0.0494676	+	0.998776i	$0.515752\pi$
$954$	−1.84311e87	−0.233816
$955$	−1.42647e88	−1.75455
$956$	7.56026e87	0.901632
$957$	−6.58419e86	−0.0761378
$958$	−4.94534e87	−0.554515
$959$	2.15942e87	0.234794
$960$	−8.34188e85	−0.00879554
$961$	−1.66391e87	−0.170133
$962$	−7.65664e86	−0.0759231
$963$	−1.20243e88	−1.15634
$964$	1.30763e88	1.21958
$965$	3.25112e88	2.94088
$966$	−2.92055e86	−0.0256235
$967$	1.62324e87	0.138134	0.0690671	−	0.997612i	$-0.477998\pi$
$967$	1.62324e87	0.138134	0.0690671	+	0.997612i	$0.477998\pi$
$968$	5.56056e86	0.0458982
$969$	−3.20057e86	−0.0256257
$970$	2.72590e87	0.211711
$971$	−1.28331e88	−0.966859	−0.483430	−	0.875383i	$-0.660609\pi$
$971$	−1.28331e88	−0.966859	−0.483430	+	0.875383i	$0.660609\pi$
$972$	2.31578e87	0.169256
$973$	1.78673e87	0.126686
$974$	−1.45569e87	−0.100134
$975$	1.79839e87	0.120018
$976$	−4.58033e87	−0.296570
$977$	7.50188e87	0.471281	0.235641	−	0.971840i	$-0.424281\pi$
$977$	7.50188e87	0.471281	0.235641	+	0.971840i	$0.424281\pi$
$978$	−3.81702e86	−0.0232664
$979$	−7.31275e87	−0.432505
$980$	−1.73952e88	−0.998296
$981$	−1.16155e88	−0.646845
$982$	−3.67160e87	−0.198411
$983$	2.00914e88	1.05361	0.526807	−	0.849985i	$-0.323389\pi$
$983$	2.00914e88	1.05361	0.526807	+	0.849985i	$0.323389\pi$
$984$	−5.08222e85	−0.00258641
$985$	−4.30650e87	−0.212694
$986$	−4.74355e87	−0.227371
$987$	4.04348e86	0.0188104
$988$	−9.50849e87	−0.429321
$989$	−3.98567e88	−1.74667
$990$	1.90222e88	0.809136
$991$	−9.16723e87	−0.378500	−0.189250	−	0.981929i	$-0.560606\pi$
$991$	−9.16723e87	−0.378500	−0.189250	+	0.981929i	$0.560606\pi$
$992$	2.23477e88	0.895648
$993$	1.24221e87	0.0483272
$994$	−4.60073e87	−0.173752
$995$	4.61802e88	1.69307
$996$	−1.83405e86	−0.00652771
$997$	4.97874e88	1.72033	0.860167	−	0.510013i	$-0.170359\pi$
$997$	4.97874e88	1.72033	0.860167	+	0.510013i	$0.170359\pi$
$998$	8.88101e87	0.297928
$999$	−1.06488e87	−0.0346832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.60.a.a.1.3	✓	5
3.2	odd	2		9.60.a.c.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.60.a.a.1.3	✓	5	1.1	even	1	trivial
9.60.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-3.23738e8 q^{2} -8.24972e12 q^{3} -4.71654e17 q^{4} -7.71676e20 q^{5} +2.67075e21 q^{6} -4.97804e24 q^{7} +3.39315e26 q^{8} -1.40623e28 q^{9} +O(q^{10})\)	\(q-3.23738e8 q^{2} -8.24972e12 q^{3} -4.71654e17 q^{4} -7.71676e20 q^{5} +2.67075e21 q^{6} -4.97804e24 q^{7} +3.39315e26 q^{8} -1.40623e28 q^{9} +2.49821e29 q^{10} -5.41469e30 q^{11} +3.89102e30 q^{12} -5.16559e32 q^{13} +1.61158e33 q^{14} +6.36611e33 q^{15} +1.62041e35 q^{16} -9.94078e35 q^{17} +4.55251e36 q^{18} -3.90272e37 q^{19} +3.63964e38 q^{20} +4.10675e37 q^{21} +1.75294e39 q^{22} +2.19671e40 q^{23} -2.79925e39 q^{24} +4.22011e41 q^{25} +1.67230e41 q^{26} +2.32582e41 q^{27} +2.34792e42 q^{28} -1.47397e43 q^{29} -2.06095e42 q^{30} -9.00895e43 q^{31} -2.48061e44 q^{32} +4.46697e43 q^{33} +3.21821e44 q^{34} +3.84144e45 q^{35} +6.63256e45 q^{36} -4.57851e45 q^{37} +1.26346e46 q^{38} +4.26147e45 q^{39} -2.61841e47 q^{40} +1.81556e46 q^{41} -1.32951e46 q^{42} -1.81438e48 q^{43} +2.55386e48 q^{44} +1.08516e49 q^{45} -7.11158e48 q^{46} +9.84593e48 q^{47} -1.33679e48 q^{48} -4.77936e49 q^{49} -1.36621e50 q^{50} +8.20087e48 q^{51} +2.43637e50 q^{52} -4.04855e50 q^{53} -7.52957e49 q^{54} +4.17839e51 q^{55} -1.68912e51 q^{56} +3.21964e50 q^{57} +4.77181e51 q^{58} -2.73608e52 q^{59} -3.00260e51 q^{60} -2.82665e52 q^{61} +2.91654e52 q^{62} +7.00029e52 q^{63} -1.31036e52 q^{64} +3.98616e53 q^{65} -1.44613e52 q^{66} -7.96736e53 q^{67} +4.68861e53 q^{68} -1.81222e53 q^{69} -1.24362e54 q^{70} -2.85479e54 q^{71} -4.77156e54 q^{72} +1.64698e55 q^{73} +1.48224e54 q^{74} -3.48148e54 q^{75} +1.84074e55 q^{76} +2.69546e55 q^{77} -1.37960e54 q^{78} -1.63561e56 q^{79} -1.25043e56 q^{80} +1.96787e56 q^{81} -5.87766e54 q^{82} -4.71355e55 q^{83} -1.93697e55 q^{84} +7.67106e56 q^{85} +5.87385e56 q^{86} +1.21599e56 q^{87} -1.83729e57 q^{88} +1.35054e57 q^{89} -3.51306e57 q^{90} +2.57145e57 q^{91} -1.03609e58 q^{92} +7.43213e56 q^{93} -3.18751e57 q^{94} +3.01164e58 q^{95} +2.04643e57 q^{96} +1.09114e58 q^{97} +1.54726e58 q^{98} +7.61432e58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) \) 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

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Groups

Database

Properties

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