LMFDB - Embedded newform 1.60.a.a.1.2

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			1.2
Root			$2.35709e7$ 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)

$f(q)$	$=$	$q-6.55640e8 q^{2} +1.58783e14 q^{3} -1.46597e17 q^{4} +7.23713e20 q^{5} -1.04104e23 q^{6} +1.08717e25 q^{7} +4.74066e26 q^{8} +1.10817e28 q^{9} +O(q^{10})$	\(q-6.55640e8 q^{2} +1.58783e14 q^{3} -1.46597e17 q^{4} +7.23713e20 q^{5} -1.04104e23 q^{6} +1.08717e25 q^{7} +4.74066e26 q^{8} +1.10817e28 q^{9} -4.74495e29 q^{10} -2.58746e30 q^{11} -2.32772e31 q^{12} -5.56960e32 q^{13} -7.12795e33 q^{14} +1.14913e35 q^{15} -2.26309e35 q^{16} +1.35524e35 q^{17} -7.26557e36 q^{18} +4.79817e37 q^{19} -1.06094e38 q^{20} +1.72625e39 q^{21} +1.69644e39 q^{22} -3.11625e39 q^{23} +7.52736e40 q^{24} +3.50288e41 q^{25} +3.65165e41 q^{26} -4.84086e41 q^{27} -1.59377e42 q^{28} +1.44322e43 q^{29} -7.53417e43 q^{30} -1.86617e43 q^{31} -1.24903e44 q^{32} -4.10845e44 q^{33} -8.88552e43 q^{34} +7.86802e45 q^{35} -1.62454e45 q^{36} +1.60698e46 q^{37} -3.14587e46 q^{38} -8.84357e46 q^{39} +3.43087e47 q^{40} -6.72686e47 q^{41} -1.13180e48 q^{42} +1.54440e48 q^{43} +3.79316e47 q^{44} +8.01994e48 q^{45} +2.04314e48 q^{46} +4.96944e48 q^{47} -3.59339e49 q^{48} +4.56203e49 q^{49} -2.29663e50 q^{50} +2.15190e49 q^{51} +8.16489e49 q^{52} +3.89245e50 q^{53} +3.17386e50 q^{54} -1.87258e51 q^{55} +5.15392e51 q^{56} +7.61868e51 q^{57} -9.46232e51 q^{58} -2.34464e52 q^{59} -1.68460e52 q^{60} -7.62724e51 q^{61} +1.22353e52 q^{62} +1.20477e53 q^{63} +2.12350e53 q^{64} -4.03079e53 q^{65} +2.69366e53 q^{66} +2.92761e53 q^{67} -1.98675e52 q^{68} -4.94807e53 q^{69} -5.15859e54 q^{70} +2.90747e54 q^{71} +5.25343e54 q^{72} -6.77367e54 q^{73} -1.05360e55 q^{74} +5.56197e55 q^{75} -7.03400e54 q^{76} -2.81302e55 q^{77} +5.79820e55 q^{78} -1.07018e56 q^{79} -1.63782e56 q^{80} -2.33453e56 q^{81} +4.41039e56 q^{82} +5.08183e56 q^{83} -2.53064e56 q^{84} +9.80807e55 q^{85} -1.01257e57 q^{86} +2.29159e57 q^{87} -1.22663e57 q^{88} +3.31938e57 q^{89} -5.25819e57 q^{90} -6.05512e57 q^{91} +4.56834e56 q^{92} -2.96315e57 q^{93} -3.25816e57 q^{94} +3.47250e58 q^{95} -1.98325e58 q^{96} +7.26288e58 q^{97} -2.99105e58 q^{98} -2.86734e58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.55640e8	−0.863536	−0.431768	−	0.901985i	$-0.642110\pi$
$2$	−6.55640e8	−0.863536	−0.431768	+	0.901985i	$0.642110\pi$
$3$	1.58783e14	1.33576	0.667878	−	0.744271i	$-0.267203\pi$
$3$	1.58783e14	1.33576	0.667878	+	0.744271i	$0.267203\pi$
$4$	−1.46597e17	−0.254306
$5$	7.23713e20	1.73761	0.868803	−	0.495159i	$-0.164890\pi$
$5$	7.23713e20	1.73761	0.868803	+	0.495159i	$0.164890\pi$
$6$	−1.04104e23	−1.15347
$7$	1.08717e25	1.27617	0.638083	−	0.769968i	$-0.279728\pi$
$7$	1.08717e25	1.27617	0.638083	+	0.769968i	$0.279728\pi$
$8$	4.74066e26	1.08314
$9$	1.10817e28	0.784243
$10$	−4.74495e29	−1.50048
$11$	−2.58746e30	−0.491802	−0.245901	−	0.969295i	$-0.579084\pi$
$11$	−2.58746e30	−0.491802	−0.245901	+	0.969295i	$0.579084\pi$
$12$	−2.32772e31	−0.339691
$13$	−5.56960e32	−0.766469	−0.383235	−	0.923651i	$-0.625190\pi$
$13$	−5.56960e32	−0.766469	−0.383235	+	0.923651i	$0.625190\pi$
$14$	−7.12795e33	−1.10201
$15$	1.14913e35	2.32102
$16$	−2.26309e35	−0.681022
$17$	1.35524e35	0.0681984	0.0340992	−	0.999418i	$-0.489144\pi$
$17$	1.35524e35	0.0681984	0.0340992	+	0.999418i	$0.489144\pi$
$18$	−7.26557e36	−0.677222
$19$	4.79817e37	0.907496	0.453748	−	0.891130i	$-0.350087\pi$
$19$	4.79817e37	0.907496	0.453748	+	0.891130i	$0.350087\pi$
$20$	−1.06094e38	−0.441883
$21$	1.72625e39	1.70465
$22$	1.69644e39	0.424688
$23$	−3.11625e39	−0.210214	−0.105107	−	0.994461i	$-0.533518\pi$
$23$	−3.11625e39	−0.210214	−0.105107	+	0.994461i	$0.533518\pi$
$24$	7.52736e40	1.44681
$25$	3.50288e41	2.01927
$26$	3.65165e41	0.661874
$27$	−4.84086e41	−0.288198
$28$	−1.59377e42	−0.324537
$29$	1.44322e43	1.04374	0.521869	−	0.853026i	$-0.325235\pi$
$29$	1.44322e43	1.04374	0.521869	+	0.853026i	$0.325235\pi$
$30$	−7.53417e43	−2.00428
$31$	−1.86617e43	−0.188704	−0.0943518	−	0.995539i	$-0.530078\pi$
$31$	−1.86617e43	−0.188704	−0.0943518	+	0.995539i	$0.530078\pi$
$32$	−1.24903e44	−0.495051
$33$	−4.10845e44	−0.656927
$34$	−8.88552e43	−0.0588918
$35$	7.86802e45	2.21747
$36$	−1.62454e45	−0.199438
$37$	1.60698e46	0.879141	0.439571	−	0.898208i	$-0.355131\pi$
$37$	1.60698e46	0.879141	0.439571	+	0.898208i	$0.355131\pi$
$38$	−3.14587e46	−0.783655
$39$	−8.84357e46	−1.02382
$40$	3.43087e47	1.88207
$41$	−6.72686e47	−1.78110	−0.890550	−	0.454885i	$-0.849681\pi$
$41$	−6.72686e47	−1.78110	−0.890550	+	0.454885i	$0.849681\pi$
$42$	−1.13180e48	−1.47202
$43$	1.54440e48	1.00332	0.501660	−	0.865065i	$-0.332723\pi$
$43$	1.54440e48	1.00332	0.501660	+	0.865065i	$0.332723\pi$
$44$	3.79316e47	0.125068
$45$	8.01994e48	1.36270
$46$	2.04314e48	0.181527
$47$	4.96944e48	0.234110	0.117055	−	0.993125i	$-0.462655\pi$
$47$	4.96944e48	0.234110	0.117055	+	0.993125i	$0.462655\pi$
$48$	−3.59339e49	−0.909680
$49$	4.56203e49	0.628599
$50$	−2.29663e50	−1.74371
$51$	2.15190e49	0.0910964
$52$	8.16489e49	0.194918
$53$	3.89245e50	0.529768	0.264884	−	0.964280i	$-0.414666\pi$
$53$	3.89245e50	0.529768	0.264884	+	0.964280i	$0.414666\pi$
$54$	3.17386e50	0.248870
$55$	−1.87258e51	−0.854557
$56$	5.15392e51	1.38226
$57$	7.61868e51	1.21219
$58$	−9.46232e51	−0.901305
$59$	−2.34464e52	−1.34878	−0.674390	−	0.738375i	$-0.735593\pi$
$59$	−2.34464e52	−1.34878	−0.674390	+	0.738375i	$0.735593\pi$
$60$	−1.68460e52	−0.590248
$61$	−7.62724e51	−0.164111	−0.0820554	−	0.996628i	$-0.526148\pi$
$61$	−7.62724e51	−0.164111	−0.0820554	+	0.996628i	$0.526148\pi$
$62$	1.22353e52	0.162952
$63$	1.20477e53	1.00082
$64$	2.12350e53	1.10852
$65$	−4.03079e53	−1.33182
$66$	2.69366e53	0.567280
$67$	2.92761e53	0.395646	0.197823	−	0.980238i	$-0.436613\pi$
$67$	2.92761e53	0.395646	0.197823	+	0.980238i	$0.436613\pi$
$68$	−1.98675e52	−0.0173433
$69$	−4.94807e53	−0.280794
$70$	−5.15859e54	−1.91487
$71$	2.90747e54	0.710223	0.355111	−	0.934824i	$-0.384443\pi$
$71$	2.90747e54	0.710223	0.355111	+	0.934824i	$0.384443\pi$
$72$	5.25343e54	0.849444
$73$	−6.77367e54	−0.729121	−0.364561	−	0.931180i	$-0.618781\pi$
$73$	−6.77367e54	−0.729121	−0.364561	+	0.931180i	$0.618781\pi$
$74$	−1.05360e55	−0.759170
$75$	5.56197e55	2.69725
$76$	−7.03400e54	−0.230782
$77$	−2.81302e55	−0.627620
$78$	5.79820e55	0.884101
$79$	−1.07018e56	−1.12062	−0.560308	−	0.828284i	$-0.689317\pi$
$79$	−1.07018e56	−1.12062	−0.560308	+	0.828284i	$0.689317\pi$
$80$	−1.63782e56	−1.18335
$81$	−2.33453e56	−1.16921
$82$	4.41039e56	1.53804
$83$	5.08183e56	1.23941	0.619707	−	0.784834i	$-0.287252\pi$
$83$	5.08183e56	1.23941	0.619707	+	0.784834i	$0.287252\pi$
$84$	−2.53064e56	−0.433502
$85$	9.80807e55	0.118502
$86$	−1.01257e57	−0.866403
$87$	2.29159e57	1.39418
$88$	−1.22663e57	−0.532689
$89$	3.31938e57	1.03289	0.516443	−	0.856322i	$-0.327256\pi$
$89$	3.31938e57	1.03289	0.516443	+	0.856322i	$0.327256\pi$
$90$	−5.25819e57	−1.17674
$91$	−6.05512e57	−0.978142
$92$	4.56834e56	0.0534586
$93$	−2.96315e57	−0.252062
$94$	−3.25816e57	−0.202163
$95$	3.47250e58	1.57687
$96$	−1.98325e58	−0.661267
$97$	7.26288e58	1.78379	0.891893	−	0.452246i	$-0.149377\pi$
$97$	7.26288e58	1.78379	0.891893	+	0.452246i	$0.149377\pi$
$98$	−2.99105e58	−0.542817
$99$	−2.86734e58	−0.385692
$100$	−5.13513e58	−0.513513
$101$	2.72416e58	0.203120	0.101560	−	0.994829i	$-0.467617\pi$
$101$	2.72416e58	0.203120	0.101560	+	0.994829i	$0.467617\pi$
$102$	−1.41087e58	−0.0786650
$103$	−4.07754e59	−1.70490	−0.852452	−	0.522805i	$-0.824886\pi$
$103$	−4.07754e59	−1.70490	−0.852452	+	0.522805i	$0.824886\pi$
$104$	−2.64035e59	−0.830192
$105$	1.24931e60	2.96200
$106$	−2.55205e59	−0.457473
$107$	4.45535e59	0.605425	0.302713	−	0.953082i	$-0.402108\pi$
$107$	4.45535e59	0.605425	0.302713	+	0.953082i	$0.402108\pi$
$108$	7.09658e58	0.0732906
$109$	−1.92062e60	−1.51133	−0.755664	−	0.654959i	$-0.772686\pi$
$109$	−1.92062e60	−1.51133	−0.755664	+	0.654959i	$0.772686\pi$
$110$	1.22774e60	0.737941
$111$	2.55161e60	1.17432
$112$	−2.46037e60	−0.869097
$113$	1.02620e60	0.278881	0.139440	−	0.990230i	$-0.455470\pi$
$113$	1.02620e60	0.278881	0.139440	+	0.990230i	$0.455470\pi$
$114$	−4.99511e60	−1.04677
$115$	−2.25527e60	−0.365268
$116$	−2.11572e60	−0.265429
$117$	−6.17204e60	−0.601098
$118$	1.53724e61	1.16472
$119$	1.47339e60	0.0870325
$120$	5.44764e61	2.51398
$121$	−2.09852e61	−0.758131
$122$	5.00072e60	0.141716
$123$	−1.06811e62	−2.37912
$124$	2.73575e60	0.0479885
$125$	1.27964e62	1.77109
$126$	−7.89895e61	−0.864247
$127$	−1.57917e62	−1.36842	−0.684212	−	0.729284i	$-0.739853\pi$
$127$	−1.57917e62	−1.36842	−0.684212	+	0.729284i	$0.739853\pi$
$128$	−6.72229e61	−0.462193
$129$	2.45224e62	1.34019
$130$	2.64274e62	1.15007
$131$	−2.72028e62	−0.944300	−0.472150	−	0.881518i	$-0.656522\pi$
$131$	−2.72028e62	−0.944300	−0.472150	+	0.881518i	$0.656522\pi$
$132$	6.02289e61	0.167060
$133$	5.21645e62	1.15811
$134$	−1.91946e62	−0.341654
$135$	−3.50339e62	−0.500775
$136$	6.42475e61	0.0738683
$137$	−4.95801e62	−0.459251	−0.229626	−	0.973279i	$-0.573750\pi$
$137$	−4.95801e62	−0.459251	−0.229626	+	0.973279i	$0.573750\pi$
$138$	3.24415e62	0.242476
$139$	−5.52437e62	−0.333692	−0.166846	−	0.985983i	$-0.553358\pi$
$139$	−5.52437e62	−0.333692	−0.166846	+	0.985983i	$0.553358\pi$
$140$	−1.15343e63	−0.563916
$141$	7.89062e62	0.312714
$142$	−1.90626e63	−0.613303
$143$	1.44111e63	0.376951
$144$	−2.50787e63	−0.534087
$145$	1.04448e64	1.81361
$146$	4.44109e63	0.629622
$147$	7.24372e63	0.839654
$148$	−2.35579e63	−0.223571
$149$	−1.36260e64	−1.06016	−0.530081	−	0.847947i	$-0.677838\pi$
$149$	−1.36260e64	−1.06016	−0.530081	+	0.847947i	$0.677838\pi$
$150$	−3.64665e64	−2.32917
$151$	−1.02852e63	−0.0540000	−0.0270000	−	0.999635i	$-0.508595\pi$
$151$	−1.02852e63	−0.0540000	−0.0270000	+	0.999635i	$0.508595\pi$
$152$	2.27465e64	0.982943
$153$	1.50184e63	0.0534842
$154$	1.84433e64	0.541973
$155$	−1.35057e64	−0.327892
$156$	1.29645e64	0.260363
$157$	−2.81384e64	−0.468015	−0.234007	−	0.972235i	$-0.575184\pi$
$157$	−2.81384e64	−0.468015	−0.234007	+	0.972235i	$0.575184\pi$
$158$	7.01651e64	0.967692
$159$	6.18056e64	0.707640
$160$	−9.03942e64	−0.860203
$161$	−3.38790e64	−0.268267
$162$	1.53061e65	1.00965
$163$	−1.02410e65	−0.563387	−0.281693	−	0.959504i	$-0.590896\pi$
$163$	−1.02410e65	−0.563387	−0.281693	+	0.959504i	$0.590896\pi$
$164$	9.86140e64	0.452945
$165$	−2.97334e65	−1.14148
$166$	−3.33185e65	−1.07028
$167$	−1.89739e65	−0.510529	−0.255264	−	0.966871i	$-0.582162\pi$
$167$	−1.89739e65	−0.510529	−0.255264	+	0.966871i	$0.582162\pi$
$168$	8.18355e65	1.84637
$169$	−2.17825e65	−0.412525
$170$	−6.43056e64	−0.102331
$171$	5.31717e65	0.711697
$172$	−2.26405e65	−0.255150
$173$	7.44337e65	0.706984	0.353492	−	0.935438i	$-0.384994\pi$
$173$	7.44337e65	0.706984	0.353492	+	0.935438i	$0.384994\pi$
$174$	−1.50246e66	−1.20392
$175$	3.80824e66	2.57692
$176$	5.85565e65	0.334928
$177$	−3.72288e66	−1.80164
$178$	−2.17632e66	−0.891934
$179$	−3.24427e66	−1.12707	−0.563537	−	0.826091i	$-0.690560\pi$
$179$	−3.24427e66	−1.12707	−0.563537	+	0.826091i	$0.690560\pi$
$180$	−1.17570e66	−0.346544
$181$	2.66375e66	0.666770	0.333385	−	0.942791i	$-0.391809\pi$
$181$	2.66375e66	0.666770	0.333385	+	0.942791i	$0.391809\pi$
$182$	3.96998e66	0.844660
$183$	−1.21108e66	−0.219212
$184$	−1.47731e66	−0.227690
$185$	1.16299e67	1.52760
$186$	1.94276e66	0.217664
$187$	−3.50664e65	−0.0335401
$188$	−7.28507e65	−0.0595356
$189$	−5.26286e66	−0.367789
$190$	−2.27671e67	−1.36168
$191$	−5.19175e66	−0.265968	−0.132984	−	0.991118i	$-0.542456\pi$
$191$	−5.19175e66	−0.265968	−0.132984	+	0.991118i	$0.542456\pi$
$192$	3.37175e67	1.48071
$193$	4.45977e67	1.68024	0.840121	−	0.542399i	$-0.182484\pi$
$193$	4.45977e67	1.68024	0.840121	+	0.542399i	$0.182484\pi$
$194$	−4.76183e67	−1.54036
$195$	−6.40020e67	−1.77899
$196$	−6.68782e66	−0.159856
$197$	2.05470e67	0.422663	0.211331	−	0.977414i	$-0.432220\pi$
$197$	2.05470e67	0.422663	0.211331	+	0.977414i	$0.432220\pi$
$198$	1.87994e67	0.333059
$199$	−8.18192e67	−1.24936	−0.624682	−	0.780879i	$-0.714772\pi$
$199$	−8.18192e67	−1.24936	−0.624682	+	0.780879i	$0.714772\pi$
$200$	1.66059e68	2.18715
$201$	4.64855e67	0.528486
$202$	−1.78607e67	−0.175401
$203$	1.56903e68	1.33198
$204$	−3.15463e66	−0.0231664
$205$	−4.86831e68	−3.09485
$206$	2.67340e68	1.47225
$207$	−3.45332e67	−0.164859
$208$	1.26045e68	0.521983
$209$	−1.24151e68	−0.446308
$210$	−8.19096e68	−2.55779
$211$	4.28352e68	1.16270	0.581351	−	0.813653i	$-0.302524\pi$
$211$	4.28352e68	1.16270	0.581351	+	0.813653i	$0.302524\pi$
$212$	−5.70624e67	−0.134723
$213$	4.61658e68	0.948684
$214$	−2.92111e68	−0.522806
$215$	1.11770e69	1.74337
$216$	−2.29489e68	−0.312159
$217$	−2.02885e68	−0.240817
$218$	1.25923e69	1.30509
$219$	−1.07554e69	−0.973928
$220$	2.74515e68	0.217319
$221$	−7.54816e67	−0.0522720
$222$	−1.67293e69	−1.01407
$223$	−1.66903e69	−0.886076	−0.443038	−	0.896503i	$-0.646099\pi$
$223$	−1.66903e69	−0.886076	−0.443038	+	0.896503i	$0.646099\pi$
$224$	−1.35792e69	−0.631767
$225$	3.88177e69	1.58360
$226$	−6.72818e68	−0.240823
$227$	3.77482e69	1.18613	0.593066	−	0.805154i	$-0.297917\pi$
$227$	3.77482e69	1.18613	0.593066	+	0.805154i	$0.297917\pi$
$228$	−1.11688e69	−0.308268
$229$	−6.77671e69	−1.64389	−0.821944	−	0.569569i	$-0.807110\pi$
$229$	−6.77671e69	−1.64389	−0.821944	+	0.569569i	$0.807110\pi$
$230$	1.47864e69	0.315422
$231$	−4.46660e69	−0.838348
$232$	6.84181e69	1.13051
$233$	8.16171e69	1.18791	0.593953	−	0.804500i	$-0.297567\pi$
$233$	8.16171e69	1.18791	0.593953	+	0.804500i	$0.297567\pi$
$234$	4.04663e69	0.519070
$235$	3.59644e69	0.406791
$236$	3.43718e69	0.343003
$237$	−1.69926e70	−1.49687
$238$	−9.66011e68	−0.0751557
$239$	5.21276e69	0.358368	0.179184	−	0.983816i	$-0.442654\pi$
$239$	5.21276e69	0.358368	0.179184	+	0.983816i	$0.442654\pi$
$240$	−2.60059e70	−1.58066
$241$	−9.20131e69	−0.494706	−0.247353	−	0.968925i	$-0.579561\pi$
$241$	−9.20131e69	−0.494706	−0.247353	+	0.968925i	$0.579561\pi$
$242$	1.37587e70	0.654673
$243$	−3.02280e70	−1.27357
$244$	1.11813e69	0.0417344
$245$	3.30160e70	1.09226
$246$	7.00296e70	2.05445
$247$	−2.67239e70	−0.695568
$248$	−8.84685e69	−0.204392
$249$	8.06908e70	1.65555
$250$	−8.38980e70	−1.52940
$251$	−2.03203e70	−0.329272	−0.164636	−	0.986354i	$-0.552645\pi$
$251$	−2.03203e70	−0.329272	−0.164636	+	0.986354i	$0.552645\pi$
$252$	−1.76616e70	−0.254516
$253$	8.06318e69	0.103383
$254$	1.03537e71	1.18168
$255$	1.55736e70	0.158290
$256$	−7.83372e70	−0.709397
$257$	−2.26975e71	−1.83211	−0.916055	−	0.401053i	$-0.868644\pi$
$257$	−2.26975e71	−1.83211	−0.916055	+	0.401053i	$0.868644\pi$
$258$	−1.60779e71	−1.15730
$259$	1.74706e71	1.12193
$260$	5.90903e70	0.338690
$261$	1.59933e71	0.818545
$262$	1.78352e71	0.815437
$263$	−9.72811e70	−0.397497	−0.198749	−	0.980051i	$-0.563688\pi$
$263$	−9.72811e70	−0.397497	−0.198749	+	0.980051i	$0.563688\pi$
$264$	−1.94768e71	−0.711543
$265$	2.81702e71	0.920527
$266$	−3.42011e71	−1.00007
$267$	5.27062e71	1.37968
$268$	−4.29180e70	−0.100615
$269$	−3.85798e71	−0.810340	−0.405170	−	0.914241i	$-0.632788\pi$
$269$	−3.85798e71	−0.810340	−0.405170	+	0.914241i	$0.632788\pi$
$270$	2.29696e71	0.432437
$271$	4.86572e71	0.821398	0.410699	−	0.911771i	$-0.365285\pi$
$271$	4.86572e71	0.821398	0.410699	+	0.911771i	$0.365285\pi$
$272$	−3.06703e70	−0.0464447
$273$	−9.61450e71	−1.30656
$274$	3.25067e71	0.396580
$275$	−9.06357e71	−0.993081
$276$	7.25375e70	0.0714076
$277$	−1.75710e72	−1.55469	−0.777344	−	0.629076i	$-0.783433\pi$
$277$	−1.75710e72	−1.55469	−0.777344	+	0.629076i	$0.783433\pi$
$278$	3.62199e71	0.288155
$279$	−2.06802e71	−0.147990
$280$	3.72996e72	2.40183
$281$	3.44814e71	0.199870	0.0999351	−	0.994994i	$-0.468136\pi$
$281$	3.44814e71	0.199870	0.0999351	+	0.994994i	$0.468136\pi$
$282$	−5.17340e71	−0.270040
$283$	1.33526e72	0.627863	0.313932	−	0.949446i	$-0.398354\pi$
$283$	1.33526e72	0.627863	0.313932	+	0.949446i	$0.398354\pi$
$284$	−4.26228e71	−0.180614
$285$	5.51374e72	2.10631
$286$	−9.44850e71	−0.325511
$287$	−7.31327e72	−2.27298
$288$	−1.38414e72	−0.388240
$289$	−3.93063e72	−0.995349
$290$	−6.84800e72	−1.56611
$291$	1.15322e73	2.38270
$292$	9.93003e71	0.185420
$293$	7.74487e72	1.30743	0.653716	−	0.756740i	$-0.273209\pi$
$293$	7.74487e72	1.30743	0.653716	+	0.756740i	$0.273209\pi$
$294$	−4.74927e72	−0.725071
$295$	−1.69684e73	−2.34365
$296$	7.61812e72	0.952232
$297$	1.25255e72	0.141736
$298$	8.93372e72	0.915488
$299$	1.73562e72	0.161122
$300$	−8.15371e72	−0.685928
$301$	1.67903e73	1.28040
$302$	6.74340e71	0.0466310
$303$	4.32551e72	0.271318
$304$	−1.08587e73	−0.618025
$305$	−5.51993e72	−0.285160
$306$	−9.84663e71	−0.0461855
$307$	1.91212e73	0.814577	0.407288	−	0.913300i	$-0.366474\pi$
$307$	1.91212e73	0.814577	0.407288	+	0.913300i	$0.366474\pi$
$308$	4.12382e72	0.159608
$309$	−6.47444e73	−2.27734
$310$	8.85486e72	0.283147
$311$	1.53350e73	0.445914	0.222957	−	0.974828i	$-0.428429\pi$
$311$	1.53350e73	0.445914	0.222957	+	0.974828i	$0.428429\pi$
$312$	−4.19243e73	−1.10893
$313$	−9.46132e72	−0.227716	−0.113858	−	0.993497i	$-0.536321\pi$
$313$	−9.46132e72	−0.227716	−0.113858	+	0.993497i	$0.536321\pi$
$314$	1.84486e73	0.404147
$315$	8.71907e73	1.73904
$316$	1.56885e73	0.284979
$317$	−5.08207e73	−0.840993	−0.420496	−	0.907294i	$-0.638144\pi$
$317$	−5.08207e73	−0.840993	−0.420496	+	0.907294i	$0.638144\pi$
$318$	−4.05222e73	−0.611072
$319$	−3.73428e73	−0.513312
$320$	1.53680e74	1.92616
$321$	7.07434e73	0.808700
$322$	2.22124e73	0.231658
$323$	6.50269e72	0.0618898
$324$	3.42236e73	0.297336
$325$	−1.95096e74	−1.54771
$326$	6.71438e73	0.486505
$327$	−3.04961e74	−2.01876
$328$	−3.18897e74	−1.92918
$329$	5.40264e73	0.298763
$330$	1.94944e74	0.985708
$331$	2.90945e74	1.34551	0.672753	−	0.739867i	$-0.265112\pi$
$331$	2.90945e74	1.34551	0.672753	+	0.739867i	$0.265112\pi$
$332$	−7.44983e73	−0.315190
$333$	1.78080e74	0.689461
$334$	1.24400e74	0.440860
$335$	2.11875e74	0.687476
$336$	−3.90665e74	−1.16090
$337$	−4.42174e73	−0.120368	−0.0601840	−	0.998187i	$-0.519169\pi$
$337$	−4.42174e73	−0.120368	−0.0601840	+	0.998187i	$0.519169\pi$
$338$	1.42815e74	0.356230
$339$	1.62943e74	0.372517
$340$	−1.43784e73	−0.0301358
$341$	4.82864e73	0.0928048
$342$	−3.48615e74	−0.614576
$343$	−2.93040e74	−0.473970
$344$	7.32146e74	1.08673
$345$	−3.58098e74	−0.487909
$346$	−4.88017e74	−0.610506
$347$	1.08045e75	1.24133	0.620663	−	0.784078i	$-0.286864\pi$
$347$	1.08045e75	1.24133	0.620663	+	0.784078i	$0.286864\pi$
$348$	−3.35941e74	−0.354548
$349$	−3.17015e74	−0.307419	−0.153709	−	0.988116i	$-0.549122\pi$
$349$	−3.17015e74	−0.307419	−0.153709	+	0.988116i	$0.549122\pi$
$350$	−2.49683e75	−2.22527
$351$	2.69616e74	0.220895
$352$	3.23183e74	0.243467
$353$	−6.44178e74	−0.446326	−0.223163	−	0.974781i	$-0.571638\pi$
$353$	−6.44178e74	−0.446326	−0.223163	+	0.974781i	$0.571638\pi$
$354$	2.44087e75	1.55578
$355$	2.10418e75	1.23409
$356$	−4.86613e74	−0.262669
$357$	2.33949e74	0.116254
$358$	2.12707e75	0.973268
$359$	−3.30229e75	−1.39164	−0.695822	−	0.718214i	$-0.744960\pi$
$359$	−3.30229e75	−1.39164	−0.695822	+	0.718214i	$0.744960\pi$
$360$	3.80198e75	1.47600
$361$	−4.93274e74	−0.176452
$362$	−1.74646e75	−0.575779
$363$	−3.33209e75	−1.01268
$364$	8.87665e74	0.248747
$365$	−4.90219e75	−1.26693
$366$	7.94029e74	0.189297
$367$	5.43152e75	1.19474	0.597368	−	0.801967i	$-0.296213\pi$
$367$	5.43152e75	1.19474	0.597368	+	0.801967i	$0.296213\pi$
$368$	7.05233e74	0.143160
$369$	−7.45448e75	−1.39682
$370$	−7.62502e75	−1.31914
$371$	4.23178e75	0.676071
$372$	4.34391e74	0.0641009
$373$	5.16798e75	0.704547	0.352274	−	0.935897i	$-0.385409\pi$
$373$	5.16798e75	0.704547	0.352274	+	0.935897i	$0.385409\pi$
$374$	2.29910e74	0.0289631
$375$	2.03184e76	2.36574
$376$	2.35584e75	0.253574
$377$	−8.03815e75	−0.799993
$378$	3.45054e75	0.317599
$379$	1.10163e75	0.0937950	0.0468975	−	0.998900i	$-0.485067\pi$
$379$	1.10163e75	0.0937950	0.0468975	+	0.998900i	$0.485067\pi$
$380$	−5.09059e75	−0.401007
$381$	−2.50746e76	−1.82788
$382$	3.40392e75	0.229673
$383$	3.09321e76	1.93217	0.966084	−	0.258228i	$-0.0831384\pi$
$383$	3.09321e76	1.93217	0.966084	+	0.258228i	$0.0831384\pi$
$384$	−1.06739e76	−0.617377
$385$	−2.03582e76	−1.09056
$386$	−2.92400e76	−1.45095
$387$	1.71145e76	0.786847
$388$	−1.06472e76	−0.453628
$389$	1.22185e76	0.482507	0.241254	−	0.970462i	$-0.422441\pi$
$389$	1.22185e76	0.482507	0.241254	+	0.970462i	$0.422441\pi$
$390$	4.19623e76	1.53622
$391$	−4.22328e74	−0.0143362
$392$	2.16270e76	0.680859
$393$	−4.31934e76	−1.26135
$394$	−1.34714e76	−0.364984
$395$	−7.74501e76	−1.94719
$396$	4.20345e75	0.0980838
$397$	8.16439e76	1.76850	0.884248	−	0.467018i	$-0.154672\pi$
$397$	8.16439e76	1.76850	0.884248	+	0.467018i	$0.154672\pi$
$398$	5.36439e76	1.07887
$399$	8.28284e76	1.54696
$400$	−7.92731e76	−1.37517
$401$	8.81919e76	1.42125	0.710623	−	0.703573i	$-0.248413\pi$
$401$	8.81919e76	1.42125	0.710623	+	0.703573i	$0.248413\pi$
$402$	−3.04777e76	−0.456367
$403$	1.03938e76	0.144636
$404$	−3.99355e75	−0.0516546
$405$	−1.68953e77	−2.03162
$406$	−1.02872e77	−1.15021
$407$	−4.15799e76	−0.432363
$408$	1.02014e76	0.0986700
$409$	−9.51763e76	−0.856428	−0.428214	−	0.903677i	$-0.640857\pi$
$409$	−9.51763e76	−0.856428	−0.428214	+	0.903677i	$0.640857\pi$
$410$	3.19186e77	2.67251
$411$	−7.87248e76	−0.613448
$412$	5.97757e76	0.433568
$413$	−2.54903e77	−1.72127
$414$	2.26413e76	0.142361
$415$	3.67778e77	2.15361
$416$	6.95661e76	0.379441
$417$	−8.77176e76	−0.445731
$418$	8.13983e76	0.385403
$419$	3.31477e77	1.46265	0.731324	−	0.682030i	$-0.238903\pi$
$419$	3.31477e77	1.46265	0.731324	+	0.682030i	$0.238903\pi$
$420$	−1.83145e77	−0.753255
$421$	−2.10408e77	−0.806752	−0.403376	−	0.915034i	$-0.632163\pi$
$421$	−2.10408e77	−0.806752	−0.403376	+	0.915034i	$0.632163\pi$
$422$	−2.80844e77	−1.00403
$423$	5.50696e76	0.183599
$424$	1.84528e77	0.573811
$425$	4.74725e76	0.137711
$426$	−3.02681e77	−0.819223
$427$	−8.29214e76	−0.209433
$428$	−6.53143e76	−0.153963
$429$	2.28824e77	0.503514
$430$	−7.32808e77	−1.50547
$431$	4.43348e77	0.850482	0.425241	−	0.905080i	$-0.360189\pi$
$431$	4.43348e77	0.850482	0.425241	+	0.905080i	$0.360189\pi$
$432$	1.09553e77	0.196270
$433$	−1.00421e78	−1.68047	−0.840236	−	0.542220i	$-0.817584\pi$
$433$	−1.00421e78	−1.68047	−0.840236	+	0.542220i	$0.817584\pi$
$434$	1.33019e77	0.207954
$435$	1.65845e78	2.42253
$436$	2.81557e77	0.384340
$437$	−1.49523e77	−0.190768
$438$	7.05169e77	0.841022
$439$	−5.00093e77	−0.557631	−0.278816	−	0.960345i	$-0.589942\pi$
$439$	−5.00093e77	−0.557631	−0.278816	+	0.960345i	$0.589942\pi$
$440$	−8.87726e77	−0.925603
$441$	5.05548e77	0.492974
$442$	4.94887e76	0.0451387
$443$	−1.24372e78	−1.06124	−0.530618	−	0.847611i	$-0.678040\pi$
$443$	−1.24372e78	−1.06124	−0.530618	+	0.847611i	$0.678040\pi$
$444$	−3.74059e77	−0.298636
$445$	2.40228e78	1.79475
$446$	1.09428e78	0.765158
$447$	−2.16357e78	−1.41612
$448$	2.30861e78	1.41465
$449$	−2.77078e78	−1.58977	−0.794886	−	0.606759i	$-0.792469\pi$
$449$	−2.77078e78	−1.58977	−0.794886	+	0.606759i	$0.792469\pi$
$450$	−2.54504e78	−1.36749
$451$	1.74055e78	0.875948
$452$	−1.50439e77	−0.0709211
$453$	−1.63312e77	−0.0721309
$454$	−2.47492e78	−1.02427
$455$	−4.38217e78	−1.69962
$456$	3.61175e78	1.31297
$457$	1.86231e78	0.634636	0.317318	−	0.948319i	$-0.397218\pi$
$457$	1.86231e78	0.634636	0.317318	+	0.948319i	$0.397218\pi$
$458$	4.44308e78	1.41956
$459$	−6.56055e76	−0.0196547
$460$	3.30617e77	0.0928899
$461$	3.95029e78	1.04100	0.520501	−	0.853861i	$-0.325745\pi$
$461$	3.95029e78	1.04100	0.520501	+	0.853861i	$0.325745\pi$
$462$	2.92848e78	0.723943
$463$	3.19378e78	0.740739	0.370370	−	0.928884i	$-0.379231\pi$
$463$	3.19378e78	0.740739	0.370370	+	0.928884i	$0.379231\pi$
$464$	−3.26613e78	−0.710809
$465$	−2.14447e78	−0.437984
$466$	−5.35114e78	−1.02580
$467$	−5.82978e78	−1.04907	−0.524535	−	0.851389i	$-0.675761\pi$
$467$	−5.82978e78	−1.04907	−0.524535	+	0.851389i	$0.675761\pi$
$468$	9.04805e77	0.152863
$469$	3.18282e78	0.504910
$470$	−2.35797e78	−0.351279
$471$	−4.46790e78	−0.625153
$472$	−1.11151e79	−1.46091
$473$	−3.99607e78	−0.493435
$474$	1.11410e79	1.29260
$475$	1.68074e79	1.83248
$476$	−2.15995e77	−0.0221329
$477$	4.31349e78	0.415467
$478$	−3.41769e78	−0.309464
$479$	2.24826e78	0.191403	0.0957017	−	0.995410i	$-0.469491\pi$
$479$	2.24826e78	0.191403	0.0957017	+	0.995410i	$0.469491\pi$
$480$	−1.43531e79	−1.14902
$481$	−8.95021e78	−0.673835
$482$	6.03274e78	0.427196
$483$	−5.37942e78	−0.358340
$484$	3.07637e78	0.192797
$485$	5.25624e79	3.09952
$486$	1.98187e79	1.09978
$487$	−3.09514e79	−1.61650	−0.808251	−	0.588838i	$-0.799586\pi$
$487$	−3.09514e79	−1.61650	−0.808251	+	0.588838i	$0.799586\pi$
$488$	−3.61581e78	−0.177755
$489$	−1.62609e79	−0.752547
$490$	−2.16466e79	−0.943202
$491$	−2.38917e79	−0.980262	−0.490131	−	0.871649i	$-0.663051\pi$
$491$	−2.38917e79	−0.980262	−0.490131	+	0.871649i	$0.663051\pi$
$492$	1.56582e79	0.605023
$493$	1.95592e78	0.0711813
$494$	1.75212e79	0.600647
$495$	−2.07513e79	−0.670181
$496$	4.22329e78	0.128511
$497$	3.16093e79	0.906362
$498$	−5.29041e79	−1.42963
$499$	1.08643e79	0.276717	0.138358	−	0.990382i	$-0.455817\pi$
$499$	1.08643e79	0.276717	0.138358	+	0.990382i	$0.455817\pi$
$500$	−1.87591e79	−0.450399
$501$	−3.01273e79	−0.681941
$502$	1.33228e79	0.284338
$503$	5.40902e79	1.08859	0.544293	−	0.838895i	$-0.316798\pi$
$503$	5.40902e79	1.08859	0.544293	+	0.838895i	$0.316798\pi$
$504$	5.71140e79	1.08403
$505$	1.97151e79	0.352942
$506$	−5.28654e78	−0.0892752
$507$	−3.45869e79	−0.551032
$508$	2.31503e79	0.347998
$509$	4.74617e79	0.673238	0.336619	−	0.941641i	$-0.390717\pi$
$509$	4.74617e79	0.673238	0.336619	+	0.941641i	$0.390717\pi$
$510$	−1.02106e79	−0.136689
$511$	−7.36416e79	−0.930480
$512$	9.01123e79	1.07478
$513$	−2.32273e79	−0.261539
$514$	1.48814e80	1.58209
$515$	−2.95097e80	−2.96245
$516$	−3.59492e79	−0.340819
$517$	−1.28582e79	−0.115136
$518$	−1.14544e80	−0.968827
$519$	1.18188e80	0.944358
$520$	−1.91086e80	−1.44255
$521$	1.73445e79	0.123723	0.0618613	−	0.998085i	$-0.480296\pi$
$521$	1.73445e79	0.123723	0.0618613	+	0.998085i	$0.480296\pi$
$522$	−1.04858e80	−0.706843
$523$	1.18403e80	0.754335	0.377167	−	0.926145i	$-0.376898\pi$
$523$	1.18403e80	0.754335	0.377167	+	0.926145i	$0.376898\pi$
$524$	3.98786e79	0.240141
$525$	6.04684e80	3.44214
$526$	6.37814e79	0.343253
$527$	−2.52911e78	−0.0128693
$528$	9.29778e79	0.447382
$529$	−2.10046e80	−0.955810
$530$	−1.84695e80	−0.794908
$531$	−2.59825e80	−1.05777
$532$	−7.64718e79	−0.294516
$533$	3.74659e80	1.36516
$534$	−3.45563e80	−1.19141
$535$	3.22440e80	1.05199
$536$	1.38788e80	0.428539
$537$	−5.15135e80	−1.50549
$538$	2.52944e80	0.699758
$539$	−1.18041e80	−0.309146
$540$	5.13588e79	0.127350
$541$	7.98203e79	0.187411	0.0937053	−	0.995600i	$-0.470129\pi$
$541$	7.98203e79	0.187411	0.0937053	+	0.995600i	$0.470129\pi$
$542$	−3.19016e80	−0.709306
$543$	4.22959e80	0.890641
$544$	−1.69275e79	−0.0337617
$545$	−1.38997e81	−2.62609
$546$	6.30365e80	1.12826
$547$	−1.05852e79	−0.0179504	−0.00897518	−	0.999960i	$-0.502857\pi$
$547$	−1.05852e79	−0.0179504	−0.00897518	+	0.999960i	$0.502857\pi$
$548$	7.26831e79	0.116790
$549$	−8.45225e79	−0.128703
$550$	5.94243e80	0.857561
$551$	6.92482e80	0.947188
$552$	−2.34571e80	−0.304139
$553$	−1.16347e81	−1.43009
$554$	1.15202e81	1.34253
$555$	1.84663e81	2.04050
$556$	8.09858e79	0.0848599
$557$	−4.29933e80	−0.427241	−0.213620	−	0.976917i	$-0.568526\pi$
$557$	−4.29933e80	−0.427241	−0.213620	+	0.976917i	$0.568526\pi$
$558$	1.35588e80	0.127794
$559$	−8.60167e80	−0.769014
$560$	−1.78060e81	−1.51015
$561$	−5.56796e79	−0.0448014
$562$	−2.26074e80	−0.172595
$563$	−1.67492e78	−0.00121338	−0.000606690	−	1.00000i	$-0.500193\pi$
$563$	−1.67492e78	−0.00121338	−0.000606690		1.00000i	$0.500193\pi$
$564$	−1.15674e80	−0.0795251
$565$	7.42675e80	0.484585
$566$	−8.75447e80	−0.542182
$567$	−2.53804e81	−1.49210
$568$	1.37833e81	0.769269
$569$	3.30406e81	1.75080	0.875399	−	0.483401i	$-0.160599\pi$
$569$	3.30406e81	1.75080	0.875399	+	0.483401i	$0.160599\pi$
$570$	−3.61502e81	−1.81888
$571$	5.82486e80	0.278305	0.139152	−	0.990271i	$-0.455562\pi$
$571$	5.82486e80	0.278305	0.139152	+	0.990271i	$0.455562\pi$
$572$	−2.11263e80	−0.0958609
$573$	−8.24361e80	−0.355268
$574$	4.79487e81	1.96280
$575$	−1.09158e81	−0.424478
$576$	2.35319e81	0.869347
$577$	−4.10666e81	−1.44146	−0.720730	−	0.693216i	$-0.756193\pi$
$577$	−4.10666e81	−1.44146	−0.720730	+	0.693216i	$0.756193\pi$
$578$	2.57707e81	0.859519
$579$	7.08136e81	2.24439
$580$	−1.53118e81	−0.461211
$581$	5.52483e81	1.58170
$582$	−7.56098e81	−2.05755
$583$	−1.00716e81	−0.260541
$584$	−3.21117e81	−0.789739
$585$	−4.46678e81	−1.04447
$586$	−5.07784e81	−1.12901
$587$	−4.15508e80	−0.0878528	−0.0439264	−	0.999035i	$-0.513987\pi$
$587$	−4.15508e80	−0.0878528	−0.0439264	+	0.999035i	$0.513987\pi$
$588$	−1.06191e81	−0.213529
$589$	−8.95418e80	−0.171248
$590$	1.11252e82	2.02382
$591$	3.26251e81	0.564574
$592$	−3.63672e81	−0.598715
$593$	−5.04161e80	−0.0789689	−0.0394845	−	0.999220i	$-0.512572\pi$
$593$	−5.04161e80	−0.0789689	−0.0394845	+	0.999220i	$0.512572\pi$
$594$	−8.21225e80	−0.122394
$595$	1.06631e81	0.151228
$596$	1.99753e81	0.269606
$597$	−1.29915e82	−1.66885
$598$	−1.13794e81	−0.139135
$599$	1.04485e82	1.21608	0.608041	−	0.793906i	$-0.291956\pi$
$599$	1.04485e82	1.21608	0.608041	+	0.793906i	$0.291956\pi$
$600$	2.63674e82	2.92150
$601$	−1.04932e82	−1.10690	−0.553452	−	0.832881i	$-0.686690\pi$
$601$	−1.04932e82	−1.10690	−0.553452	+	0.832881i	$0.686690\pi$
$602$	−1.10084e82	−1.10567
$603$	3.24428e81	0.310283
$604$	1.50779e80	0.0137325
$605$	−1.51872e82	−1.31733
$606$	−2.83597e81	−0.234293
$607$	1.83220e82	1.44180	0.720902	−	0.693037i	$-0.243728\pi$
$607$	1.83220e82	1.44180	0.720902	+	0.693037i	$0.243728\pi$
$608$	−5.99308e81	−0.449257
$609$	2.49136e82	1.77920
$610$	3.61908e81	0.246246
$611$	−2.76778e81	−0.179438
$612$	−2.20165e80	−0.0136013
$613$	7.20904e81	0.424418	0.212209	−	0.977224i	$-0.431934\pi$
$613$	7.20904e81	0.424418	0.212209	+	0.977224i	$0.431934\pi$
$614$	−1.25366e82	−0.703416
$615$	−7.73005e82	−4.13396
$616$	−1.33356e82	−0.679800
$617$	−1.07578e82	−0.522772	−0.261386	−	0.965234i	$-0.584180\pi$
$617$	−1.07578e82	−0.522772	−0.261386	+	0.965234i	$0.584180\pi$
$618$	4.24490e82	1.96656
$619$	1.25527e82	0.554449	0.277224	−	0.960805i	$-0.410585\pi$
$619$	1.25527e82	0.554449	0.277224	+	0.960805i	$0.410585\pi$
$620$	1.97990e81	0.0833850
$621$	1.50853e81	0.0605832
$622$	−1.00542e82	−0.385063
$623$	3.60875e82	1.31813
$624$	2.00138e82	0.697241
$625$	3.18436e82	1.05819
$626$	6.20321e81	0.196641
$627$	−1.97131e82	−0.596158
$628$	4.12502e81	0.119019
$629$	2.17785e81	0.0599561
$630$	−5.71657e82	−1.50172
$631$	5.54665e82	1.39048	0.695239	−	0.718778i	$-0.255298\pi$
$631$	5.54665e82	1.39048	0.695239	+	0.718778i	$0.255298\pi$
$632$	−5.07335e82	−1.21378
$633$	6.80150e82	1.55308
$634$	3.33200e82	0.726227
$635$	−1.14287e83	−2.37778
$636$	−9.06054e81	−0.179957
$637$	−2.54086e82	−0.481802
$638$	2.44834e82	0.443264
$639$	3.22196e82	0.556987
$640$	−4.86501e82	−0.803108
$641$	−2.80336e82	−0.441944	−0.220972	−	0.975280i	$-0.570923\pi$
$641$	−2.80336e82	−0.441944	−0.220972	+	0.975280i	$0.570923\pi$
$642$	−4.63822e82	−0.698342
$643$	−3.52192e82	−0.506473	−0.253236	−	0.967404i	$-0.581495\pi$
$643$	−3.52192e82	−0.506473	−0.253236	+	0.967404i	$0.581495\pi$
$644$	4.96658e81	0.0682220
$645$	1.77472e83	2.32872
$646$	−4.26342e81	−0.0534440
$647$	−1.31942e82	−0.158018	−0.0790088	−	0.996874i	$-0.525176\pi$
$647$	−1.31942e82	−0.158018	−0.0790088	+	0.996874i	$0.525176\pi$
$648$	−1.10672e83	−1.26641
$649$	6.06666e82	0.663332
$650$	1.27913e83	1.33650
$651$	−3.22147e82	−0.321673
$652$	1.50130e82	0.143273
$653$	−1.65618e82	−0.151066	−0.0755332	−	0.997143i	$-0.524066\pi$
$653$	−1.65618e82	−0.151066	−0.0755332	+	0.997143i	$0.524066\pi$
$654$	1.99945e83	1.74328
$655$	−1.96870e83	−1.64082
$656$	1.52235e83	1.21297
$657$	−7.50635e82	−0.571809
$658$	−3.54219e82	−0.257993
$659$	−9.65525e81	−0.0672425	−0.0336212	−	0.999435i	$-0.510704\pi$
$659$	−9.65525e81	−0.0672425	−0.0336212	+	0.999435i	$0.510704\pi$
$660$	4.35884e82	0.290285
$661$	−2.85133e83	−1.81595	−0.907976	−	0.419022i	$-0.862373\pi$
$661$	−2.85133e83	−1.81595	−0.907976	+	0.419022i	$0.862373\pi$
$662$	−1.90755e83	−1.16189
$663$	−1.19852e82	−0.0698226
$664$	2.40912e83	1.34246
$665$	3.77521e83	2.01235
$666$	−1.16756e83	−0.595374
$667$	−4.49743e82	−0.219408
$668$	2.78152e82	0.129831
$669$	−2.65014e83	−1.18358
$670$	−1.38914e83	−0.593660
$671$	1.97352e82	0.0807100
$672$	−2.15614e83	−0.843886
$673$	2.49097e83	0.933091	0.466546	−	0.884497i	$-0.345498\pi$
$673$	2.49097e83	0.933091	0.466546	+	0.884497i	$0.345498\pi$
$674$	2.89907e82	0.103942
$675$	−1.69569e83	−0.581951
$676$	3.19326e82	0.104908
$677$	−1.42903e82	−0.0449445	−0.0224722	−	0.999747i	$-0.507154\pi$
$677$	−1.42903e82	−0.0449445	−0.0224722	+	0.999747i	$0.507154\pi$
$678$	−1.06832e83	−0.321681
$679$	7.89602e83	2.27641
$680$	4.64967e82	0.128354
$681$	5.99377e83	1.58438
$682$	−3.16584e82	−0.0801402
$683$	2.48288e83	0.601928	0.300964	−	0.953635i	$-0.402692\pi$
$683$	2.48288e83	0.601928	0.300964	+	0.953635i	$0.402692\pi$
$684$	−7.79484e82	−0.180989
$685$	−3.58817e83	−0.797998
$686$	1.92129e83	0.409290
$687$	−1.07603e84	−2.19583
$688$	−3.49510e83	−0.683284
$689$	−2.16794e83	−0.406051
$690$	2.34783e83	0.421327
$691$	5.53022e82	0.0950912	0.0475456	−	0.998869i	$-0.484860\pi$
$691$	5.53022e82	0.0950912	0.0475456	+	0.998869i	$0.484860\pi$
$692$	−1.09118e83	−0.179790
$693$	−3.11730e83	−0.492207
$694$	−7.08387e83	−1.07193
$695$	−3.99805e83	−0.579825
$696$	1.08636e84	1.51009
$697$	−9.11653e82	−0.121468
$698$	2.07848e83	0.265467
$699$	1.29594e84	1.58675
$700$	−5.58278e83	−0.655328
$701$	3.90202e83	0.439145	0.219572	−	0.975596i	$-0.429534\pi$
$701$	3.90202e83	0.439145	0.219572	+	0.975596i	$0.429534\pi$
$702$	−1.76771e83	−0.190751
$703$	7.71055e83	0.797817
$704$	−5.49447e83	−0.545170
$705$	5.71054e83	0.543373
$706$	4.22349e83	0.385418
$707$	2.96164e83	0.259215
$708$	5.45765e83	0.458168
$709$	−1.40891e84	−1.13454	−0.567270	−	0.823532i	$-0.692001\pi$
$709$	−1.40891e84	−1.13454	−0.567270	+	0.823532i	$0.692001\pi$
$710$	−1.37958e84	−1.06568
$711$	−1.18593e84	−0.878835
$712$	1.57361e84	1.11876
$713$	5.81543e82	0.0396681
$714$	−1.53386e83	−0.100390
$715$	1.04295e84	0.654992
$716$	4.75601e83	0.286622
$717$	8.27698e83	0.478693
$718$	2.16511e84	1.20173
$719$	−3.73873e84	−1.99169	−0.995845	−	0.0910630i	$-0.970974\pi$
$719$	−3.73873e84	−1.99169	−0.995845	+	0.0910630i	$0.970974\pi$
$720$	−1.81498e84	−0.928033
$721$	−4.43300e84	−2.17574
$722$	3.23410e83	0.152372
$723$	−1.46101e84	−0.660806
$724$	−3.90499e83	−0.169564
$725$	5.05542e84	2.10759
$726$	2.18465e84	0.874484
$727$	4.53192e84	1.74188	0.870938	−	0.491392i	$-0.163512\pi$
$727$	4.53192e84	1.74188	0.870938	+	0.491392i	$0.163512\pi$
$728$	−2.87052e84	−1.05946
$729$	−1.50092e84	−0.531979
$730$	3.21407e84	1.09404
$731$	2.09304e83	0.0684249
$732$	1.77541e83	0.0557469
$733$	−5.45127e84	−1.64411	−0.822054	−	0.569409i	$-0.807172\pi$
$733$	−5.45127e84	−1.64411	−0.822054	+	0.569409i	$0.807172\pi$
$734$	−3.56112e84	−1.03170
$735$	5.24237e84	1.45899
$736$	3.89230e83	0.104066
$737$	−7.57508e83	−0.194579
$738$	4.88745e84	1.20620
$739$	7.25178e84	1.71963	0.859813	−	0.510609i	$-0.170580\pi$
$739$	7.25178e84	1.71963	0.859813	+	0.510609i	$0.170580\pi$
$740$	−1.70491e84	−0.388478
$741$	−4.24330e84	−0.929108
$742$	−2.77452e84	−0.583812
$743$	1.87471e84	0.379108	0.189554	−	0.981870i	$-0.439296\pi$
$743$	1.87471e84	0.379108	0.189554	+	0.981870i	$0.439296\pi$
$744$	−1.40473e84	−0.273018
$745$	−9.86128e84	−1.84214
$746$	−3.38833e84	−0.608402
$747$	5.63151e84	0.972001
$748$	5.14065e82	0.00852945
$749$	4.84375e84	0.772623
$750$	−1.33216e85	−2.04291
$751$	5.00370e83	0.0737756	0.0368878	−	0.999319i	$-0.488256\pi$
$751$	5.00370e83	0.0737756	0.0368878	+	0.999319i	$0.488256\pi$
$752$	−1.12463e84	−0.159434
$753$	−3.22652e84	−0.439827
$754$	5.27013e84	0.690823
$755$	−7.44355e83	−0.0938307
$756$	7.71522e83	0.0935309
$757$	1.39411e85	1.62543	0.812714	−	0.582663i	$-0.197989\pi$
$757$	1.39411e85	1.62543	0.812714	+	0.582663i	$0.197989\pi$
$758$	−7.22273e83	−0.0809953
$759$	1.28030e84	0.138095
$760$	1.64619e85	1.70797
$761$	4.02373e84	0.401588	0.200794	−	0.979633i	$-0.435648\pi$
$761$	4.02373e84	0.401588	0.200794	+	0.979633i	$0.435648\pi$
$762$	1.64399e85	1.57844
$763$	−2.08804e85	−1.92870
$764$	7.61097e83	0.0676372
$765$	1.08690e84	0.0929343
$766$	−2.02803e85	−1.66850
$767$	1.30587e85	1.03380
$768$	−1.24386e85	−0.947581
$769$	−1.19509e85	−0.876143	−0.438072	−	0.898940i	$-0.644338\pi$
$769$	−1.19509e85	−0.876143	−0.438072	+	0.898940i	$0.644338\pi$
$770$	1.33477e85	0.941734
$771$	−3.60398e85	−2.44725
$772$	−6.53791e84	−0.427296
$773$	2.46928e85	1.55337	0.776685	−	0.629889i	$-0.216900\pi$
$773$	2.46928e85	1.55337	0.776685	+	0.629889i	$0.216900\pi$
$774$	−1.12209e85	−0.679471
$775$	−6.53695e84	−0.381044
$776$	3.44308e85	1.93209
$777$	2.77404e85	1.49862
$778$	−8.01092e84	−0.416662
$779$	−3.22766e85	−1.61634
$780$	9.38254e84	0.452407
$781$	−7.52298e84	−0.349289
$782$	2.76895e83	0.0123799
$783$	−6.98643e84	−0.300804
$784$	−1.03243e85	−0.428090
$785$	−2.03641e85	−0.813225
$786$	2.83193e85	1.08922
$787$	2.95880e85	1.09613	0.548064	−	0.836437i	$-0.315365\pi$
$787$	2.95880e85	1.09613	0.548064	+	0.836437i	$0.315365\pi$
$788$	−3.01213e84	−0.107486
$789$	−1.54466e85	−0.530959
$790$	5.07794e85	1.68147
$791$	1.11566e85	0.355898
$792$	−1.35931e85	−0.417758
$793$	4.24806e84	0.125786
$794$	−5.35290e85	−1.52716
$795$	4.47295e85	1.22960
$796$	1.19945e85	0.317721
$797$	2.78567e85	0.711065	0.355532	−	0.934664i	$-0.384300\pi$
$797$	2.78567e85	0.711065	0.355532	+	0.934664i	$0.384300\pi$
$798$	−5.43056e85	−1.33585
$799$	6.73480e83	0.0159659
$800$	−4.37521e85	−0.999642
$801$	3.67843e85	0.810034
$802$	−5.78221e85	−1.22730
$803$	1.75266e85	0.358583
$804$	−6.81465e84	−0.134397
$805$	−2.45187e85	−0.466143
$806$	−6.81458e84	−0.124898
$807$	−6.12581e85	−1.08242
$808$	1.29143e85	0.220007
$809$	−3.79734e85	−0.623732	−0.311866	−	0.950126i	$-0.600954\pi$
$809$	−3.79734e85	−0.623732	−0.311866	+	0.950126i	$0.600954\pi$
$810$	1.10772e86	1.75437
$811$	1.37244e85	0.209594	0.104797	−	0.994494i	$-0.466581\pi$
$811$	1.37244e85	0.209594	0.104797	+	0.994494i	$0.466581\pi$
$812$	−2.30016e85	−0.338731
$813$	7.72594e85	1.09719
$814$	2.72615e85	0.373361
$815$	−7.41152e85	−0.978944
$816$	−4.86993e84	−0.0620387
$817$	7.41028e85	0.910509
$818$	6.24013e85	0.739557
$819$	−6.71008e85	−0.767101
$820$	7.13682e85	0.787039
$821$	5.67502e85	0.603732	0.301866	−	0.953350i	$-0.402390\pi$
$821$	5.67502e85	0.603732	0.301866	+	0.953350i	$0.402390\pi$
$822$	5.16151e85	0.529734
$823$	−3.36239e85	−0.332930	−0.166465	−	0.986047i	$-0.553235\pi$
$823$	−3.36239e85	−0.332930	−0.166465	+	0.986047i	$0.553235\pi$
$824$	−1.93302e86	−1.84665
$825$	−1.43914e86	−1.32651
$826$	1.67124e86	1.48638
$827$	1.72236e86	1.47812	0.739061	−	0.673638i	$-0.235269\pi$
$827$	1.72236e86	1.47812	0.739061	+	0.673638i	$0.235269\pi$
$828$	5.06248e84	0.0419245
$829$	1.06995e86	0.855080	0.427540	−	0.903996i	$-0.359380\pi$
$829$	1.06995e86	0.855080	0.427540	+	0.903996i	$0.359380\pi$
$830$	−2.41130e86	−1.85972
$831$	−2.78998e86	−2.07668
$832$	−1.18270e86	−0.849644
$833$	6.18266e84	0.0428694
$834$	5.75111e85	0.384905
$835$	−1.37316e86	−0.887097
$836$	1.82002e85	0.113499
$837$	9.03385e84	0.0543841
$838$	−2.17330e86	−1.26305
$839$	2.77617e86	1.55764	0.778822	−	0.627245i	$-0.215817\pi$
$839$	2.77617e86	1.55764	0.778822	+	0.627245i	$0.215817\pi$
$840$	5.92254e86	3.20826
$841$	1.70911e85	0.0893898
$842$	1.37952e86	0.696659
$843$	5.47506e85	0.266978
$844$	−6.27953e85	−0.295682
$845$	−1.57643e86	−0.716805
$846$	−3.61058e85	−0.158545
$847$	−2.28146e86	−0.967501
$848$	−8.80895e85	−0.360784
$849$	2.12016e86	0.838672
$850$	−3.11249e85	−0.118918
$851$	−5.00774e85	−0.184807
$852$	−6.76778e85	−0.241256
$853$	−2.60122e86	−0.895737	−0.447869	−	0.894099i	$-0.647817\pi$
$853$	−2.60122e86	−0.895737	−0.447869	+	0.894099i	$0.647817\pi$
$854$	5.43665e85	0.180853
$855$	3.84810e86	1.23665
$856$	2.11213e86	0.655759
$857$	1.69052e86	0.507091	0.253545	−	0.967323i	$-0.418403\pi$
$857$	1.69052e86	0.507091	0.253545	+	0.967323i	$0.418403\pi$
$858$	−1.50026e86	−0.434803
$859$	3.14436e86	0.880509	0.440254	−	0.897873i	$-0.354888\pi$
$859$	3.14436e86	0.880509	0.440254	+	0.897873i	$0.354888\pi$
$860$	−1.63852e86	−0.443351
$861$	−1.16122e87	−3.03615
$862$	−2.90676e86	−0.734422
$863$	1.46329e86	0.357282	0.178641	−	0.983914i	$-0.442830\pi$
$863$	1.46329e86	0.357282	0.178641	+	0.983914i	$0.442830\pi$
$864$	6.04640e85	0.142673
$865$	5.38686e86	1.22846
$866$	6.58400e86	1.45115
$867$	−6.24117e86	−1.32954
$868$	2.97424e85	0.0612412
$869$	2.76905e86	0.551121
$870$	−1.08735e87	−2.09194
$871$	−1.63056e86	−0.303250
$872$	−9.10498e86	−1.63698
$873$	8.04848e86	1.39892
$874$	9.80331e85	0.164735
$875$	1.39119e87	2.26021
$876$	1.57672e86	0.247676
$877$	5.57754e86	0.847139	0.423570	−	0.905864i	$-0.360777\pi$
$877$	5.57754e86	0.847139	0.423570	+	0.905864i	$0.360777\pi$
$878$	3.27881e86	0.481535
$879$	1.22975e87	1.74641
$880$	4.23781e86	0.581972
$881$	−8.88813e86	−1.18038	−0.590189	−	0.807265i	$-0.700947\pi$
$881$	−8.88813e86	−1.18038	−0.590189	+	0.807265i	$0.700947\pi$
$882$	−3.31457e86	−0.425701
$883$	−1.03961e87	−1.29131	−0.645654	−	0.763630i	$-0.723415\pi$
$883$	−1.03961e87	−1.29131	−0.645654	+	0.763630i	$0.723415\pi$
$884$	1.10654e85	0.0132931
$885$	−2.69430e87	−3.13054
$886$	8.15431e86	0.916415
$887$	1.24157e87	1.34967	0.674833	−	0.737971i	$-0.264216\pi$
$887$	1.24157e87	1.34967	0.674833	+	0.737971i	$0.264216\pi$
$888$	1.20963e87	1.27195
$889$	−1.71684e87	−1.74633
$890$	−1.57503e87	−1.54983
$891$	6.04050e86	0.575017
$892$	2.44676e86	0.225334
$893$	2.38442e86	0.212454
$894$	1.41852e87	1.22287
$895$	−2.34792e87	−1.95841
$896$	−7.30830e86	−0.589834
$897$	2.75588e86	0.215220
$898$	1.81663e87	1.37282
$899$	−2.69329e86	−0.196957
$900$	−5.69058e86	−0.402719
$901$	5.27523e85	0.0361293
$902$	−1.14117e87	−0.756413
$903$	2.66601e87	1.71031
$904$	4.86487e86	0.302066
$905$	1.92779e87	1.15858
$906$	1.07074e86	0.0622876
$907$	−1.22203e87	−0.688122	−0.344061	−	0.938947i	$-0.611803\pi$
$907$	−1.22203e87	−0.688122	−0.344061	+	0.938947i	$0.611803\pi$
$908$	−5.53378e86	−0.301640
$909$	3.01882e86	0.159295
$910$	2.87312e87	1.46769
$911$	1.00822e87	0.498611	0.249306	−	0.968425i	$-0.419798\pi$
$911$	1.00822e87	0.498611	0.249306	+	0.968425i	$0.419798\pi$
$912$	−1.72417e87	−0.825530
$913$	−1.31490e87	−0.609546
$914$	−1.22101e87	−0.548031
$915$	−8.76471e86	−0.380904
$916$	9.93448e86	0.418051
$917$	−2.95742e87	−1.20508
$918$	4.30135e85	0.0169725
$919$	−3.55829e86	−0.135967	−0.0679835	−	0.997686i	$-0.521657\pi$
$919$	−3.55829e86	−0.135967	−0.0679835	+	0.997686i	$0.521657\pi$
$920$	−1.06914e87	−0.395636
$921$	3.03612e87	1.08808
$922$	−2.58996e87	−0.898942
$923$	−1.61935e87	−0.544364
$924$	6.54793e86	0.213197
$925$	5.62904e87	1.77522
$926$	−2.09397e87	−0.639655
$927$	−4.51859e87	−1.33706
$928$	−1.80263e87	−0.516704
$929$	3.60367e87	1.00065	0.500324	−	0.865838i	$-0.333214\pi$
$929$	3.60367e87	1.00065	0.500324	+	0.865838i	$0.333214\pi$
$930$	1.40600e87	0.378215
$931$	2.18894e87	0.570451
$932$	−1.19649e87	−0.302091
$933$	2.43493e87	0.595633
$934$	3.82224e87	0.905909
$935$	−2.53780e86	−0.0582794
$936$	−2.92595e87	−0.651073
$937$	−4.13844e87	−0.892316	−0.446158	−	0.894954i	$-0.647208\pi$
$937$	−4.13844e87	−0.892316	−0.446158	+	0.894954i	$0.647208\pi$
$938$	−2.08678e87	−0.436007
$939$	−1.50230e87	−0.304173
$940$	−5.27230e86	−0.103449
$941$	6.38918e87	1.21493	0.607465	−	0.794346i	$-0.292186\pi$
$941$	6.38918e87	1.21493	0.607465	+	0.794346i	$0.292186\pi$
$942$	2.92933e87	0.539842
$943$	2.09626e87	0.374412
$944$	5.30611e87	0.918549
$945$	−3.80880e87	−0.639072
$946$	2.61998e87	0.426098
$947$	3.09168e87	0.487383	0.243692	−	0.969853i	$-0.421641\pi$
$947$	3.09168e87	0.487383	0.243692	+	0.969853i	$0.421641\pi$
$948$	2.49107e87	0.380663
$949$	3.77266e87	0.558849
$950$	−1.10196e88	−1.58241
$951$	−8.06946e87	−1.12336
$952$	6.98482e86	0.0942682
$953$	−1.26538e88	−1.65569	−0.827845	−	0.560957i	$-0.810433\pi$
$953$	−1.26538e88	−1.65569	−0.827845	+	0.560957i	$0.810433\pi$
$954$	−2.82809e87	−0.358770
$955$	−3.75733e87	−0.462147
$956$	−7.64177e86	−0.0911352
$957$	−5.92940e87	−0.685660
$958$	−1.47405e87	−0.165284
$959$	−5.39022e87	−0.586081
$960$	2.44018e88	2.57288
$961$	−9.43177e87	−0.964391
$962$	5.86811e87	0.581880
$963$	4.93727e87	0.474801
$964$	1.34889e87	0.125807
$965$	3.22759e88	2.91960
$966$	3.52696e87	0.309439
$967$	2.19059e87	0.186415	0.0932073	−	0.995647i	$-0.470288\pi$
$967$	2.19059e87	0.186415	0.0932073	+	0.995647i	$0.470288\pi$
$968$	−9.94835e87	−0.821161
$969$	1.03252e87	0.0826696
$970$	−3.44620e88	−2.67654
$971$	2.13221e88	1.60643	0.803217	−	0.595686i	$-0.203120\pi$
$971$	2.13221e88	1.60643	0.803217	+	0.595686i	$0.203120\pi$
$972$	4.43135e87	0.323878
$973$	−6.00595e87	−0.425846
$974$	2.02930e88	1.39591
$975$	−3.09779e88	−2.06736
$976$	1.72611e87	0.111763
$977$	6.88952e87	0.432812	0.216406	−	0.976303i	$-0.430566\pi$
$977$	6.88952e87	0.432812	0.216406	+	0.976303i	$0.430566\pi$
$978$	1.06613e88	0.649851
$979$	−8.58878e87	−0.507975
$980$	−4.84006e87	−0.277767
$981$	−2.12836e88	−1.18525
$982$	1.56643e88	0.846491
$983$	4.93080e87	0.258576	0.129288	−	0.991607i	$-0.458731\pi$
$983$	4.93080e87	0.258576	0.129288	+	0.991607i	$0.458731\pi$
$984$	−5.06355e88	−2.57691
$985$	1.48701e88	0.734421
$986$	−1.28238e87	−0.0614676
$987$	8.57848e87	0.399075
$988$	3.91765e87	0.176887
$989$	−4.81272e87	−0.210912
$990$	1.36054e88	0.578725
$991$	4.59414e87	0.189684	0.0948421	−	0.995492i	$-0.469765\pi$
$991$	4.59414e87	0.189684	0.0948421	+	0.995492i	$0.469765\pi$
$992$	2.33090e87	0.0934179
$993$	4.61972e88	1.79727
$994$	−2.07243e88	−0.782676
$995$	−5.92136e88	−2.17090
$996$	−1.18291e88	−0.421017
$997$	3.03646e88	1.04921	0.524603	−	0.851347i	$-0.324214\pi$
$997$	3.03646e88	1.04921	0.524603	+	0.851347i	$0.324214\pi$
$998$	−7.12306e87	−0.238955
$999$	−7.77915e87	−0.253367

Twists

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

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

\(f(q)\)	\(=\)	\(q-6.55640e8 q^{2} +1.58783e14 q^{3} -1.46597e17 q^{4} +7.23713e20 q^{5} -1.04104e23 q^{6} +1.08717e25 q^{7} +4.74066e26 q^{8} +1.10817e28 q^{9} +O(q^{10})\)	\(q-6.55640e8 q^{2} +1.58783e14 q^{3} -1.46597e17 q^{4} +7.23713e20 q^{5} -1.04104e23 q^{6} +1.08717e25 q^{7} +4.74066e26 q^{8} +1.10817e28 q^{9} -4.74495e29 q^{10} -2.58746e30 q^{11} -2.32772e31 q^{12} -5.56960e32 q^{13} -7.12795e33 q^{14} +1.14913e35 q^{15} -2.26309e35 q^{16} +1.35524e35 q^{17} -7.26557e36 q^{18} +4.79817e37 q^{19} -1.06094e38 q^{20} +1.72625e39 q^{21} +1.69644e39 q^{22} -3.11625e39 q^{23} +7.52736e40 q^{24} +3.50288e41 q^{25} +3.65165e41 q^{26} -4.84086e41 q^{27} -1.59377e42 q^{28} +1.44322e43 q^{29} -7.53417e43 q^{30} -1.86617e43 q^{31} -1.24903e44 q^{32} -4.10845e44 q^{33} -8.88552e43 q^{34} +7.86802e45 q^{35} -1.62454e45 q^{36} +1.60698e46 q^{37} -3.14587e46 q^{38} -8.84357e46 q^{39} +3.43087e47 q^{40} -6.72686e47 q^{41} -1.13180e48 q^{42} +1.54440e48 q^{43} +3.79316e47 q^{44} +8.01994e48 q^{45} +2.04314e48 q^{46} +4.96944e48 q^{47} -3.59339e49 q^{48} +4.56203e49 q^{49} -2.29663e50 q^{50} +2.15190e49 q^{51} +8.16489e49 q^{52} +3.89245e50 q^{53} +3.17386e50 q^{54} -1.87258e51 q^{55} +5.15392e51 q^{56} +7.61868e51 q^{57} -9.46232e51 q^{58} -2.34464e52 q^{59} -1.68460e52 q^{60} -7.62724e51 q^{61} +1.22353e52 q^{62} +1.20477e53 q^{63} +2.12350e53 q^{64} -4.03079e53 q^{65} +2.69366e53 q^{66} +2.92761e53 q^{67} -1.98675e52 q^{68} -4.94807e53 q^{69} -5.15859e54 q^{70} +2.90747e54 q^{71} +5.25343e54 q^{72} -6.77367e54 q^{73} -1.05360e55 q^{74} +5.56197e55 q^{75} -7.03400e54 q^{76} -2.81302e55 q^{77} +5.79820e55 q^{78} -1.07018e56 q^{79} -1.63782e56 q^{80} -2.33453e56 q^{81} +4.41039e56 q^{82} +5.08183e56 q^{83} -2.53064e56 q^{84} +9.80807e55 q^{85} -1.01257e57 q^{86} +2.29159e57 q^{87} -1.22663e57 q^{88} +3.31938e57 q^{89} -5.25819e57 q^{90} -6.05512e57 q^{91} +4.56834e56 q^{92} -2.96315e57 q^{93} -3.25816e57 q^{94} +3.47250e58 q^{95} -1.98325e58 q^{96} +7.26288e58 q^{97} -2.99105e58 q^{98} -2.86734e58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) \) 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

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