LMFDB - Embedded newform 1.60.a.a.1.1

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			1.1
Root			$5.54999e7$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.42193e9 q^{2} -1.64208e14 q^{3} +1.44544e18 q^{4} +2.46018e20 q^{5} +2.33493e23 q^{6} -6.31094e24 q^{7} -1.23563e27 q^{8} +1.28340e28 q^{9} +O(q^{10})$	\(q-1.42193e9 q^{2} -1.64208e14 q^{3} +1.44544e18 q^{4} +2.46018e20 q^{5} +2.33493e23 q^{6} -6.31094e24 q^{7} -1.23563e27 q^{8} +1.28340e28 q^{9} -3.49822e29 q^{10} -1.85237e29 q^{11} -2.37353e32 q^{12} -9.37557e32 q^{13} +8.97374e33 q^{14} -4.03982e34 q^{15} +9.23746e35 q^{16} -2.12710e36 q^{17} -1.82491e37 q^{18} +2.93477e37 q^{19} +3.55604e38 q^{20} +1.03631e39 q^{21} +2.63395e38 q^{22} -1.73933e40 q^{23} +2.02901e41 q^{24} -1.12947e41 q^{25} +1.33315e42 q^{26} +2.12883e41 q^{27} -9.12207e42 q^{28} +2.89914e41 q^{29} +5.74436e43 q^{30} -1.46222e44 q^{31} -6.01215e44 q^{32} +3.04175e43 q^{33} +3.02460e45 q^{34} -1.55260e45 q^{35} +1.85507e46 q^{36} -2.03766e46 q^{37} -4.17306e46 q^{38} +1.53955e47 q^{39} -3.03987e47 q^{40} +2.62740e47 q^{41} -1.47356e48 q^{42} +8.93006e47 q^{43} -2.67749e47 q^{44} +3.15739e48 q^{45} +2.47321e49 q^{46} +2.53928e49 q^{47} -1.51687e50 q^{48} -3.27466e49 q^{49} +1.60604e50 q^{50} +3.49288e50 q^{51} -1.35518e51 q^{52} +1.22660e51 q^{53} -3.02706e50 q^{54} -4.55717e49 q^{55} +7.79798e51 q^{56} -4.81914e51 q^{57} -4.12239e50 q^{58} +5.85329e50 q^{59} -5.83931e52 q^{60} -6.37747e52 q^{61} +2.07918e53 q^{62} -8.09944e52 q^{63} +3.22385e53 q^{64} -2.30656e53 q^{65} -4.32517e52 q^{66} +6.46551e53 q^{67} -3.07460e54 q^{68} +2.85612e54 q^{69} +2.20770e54 q^{70} -1.44338e54 q^{71} -1.58580e55 q^{72} -2.42309e54 q^{73} +2.89742e55 q^{74} +1.85469e55 q^{75} +4.24203e55 q^{76} +1.16902e54 q^{77} -2.18913e56 q^{78} +4.97858e54 q^{79} +2.27258e56 q^{80} -2.16306e56 q^{81} -3.73599e56 q^{82} +3.44463e56 q^{83} +1.49792e57 q^{84} -5.23306e56 q^{85} -1.26980e57 q^{86} -4.76063e55 q^{87} +2.28885e56 q^{88} +3.85023e57 q^{89} -4.48960e57 q^{90} +5.91687e57 q^{91} -2.51409e58 q^{92} +2.40109e58 q^{93} -3.61069e58 q^{94} +7.22007e57 q^{95} +9.87245e58 q^{96} -2.95516e58 q^{97} +4.65635e58 q^{98} -2.37733e57 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) $ 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9	$ 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 23\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9 - 816306987485763512638039118160 * q^10 + 4258478353252041879297428322660 * q^11 - 44182708253273060258139543308544 * q^12 - 845614914312482778669168084611378 * q^13 + 6292067851730037636066126264146880 * q^14 - 40513800156133976678914677598869720 * q^15 + 694835480494500010980166187386081280 * q^16 - 3408789133052869460614097222783941254 * q^17 + 9695472609892683802181177716078279752 * q^18 + 64613555538305267315990967466483855900 * q^19 + 167758871278751870059053885614959950720 * q^20 + 3416027528563001630003898902298902729760 * q^21 + 16748450439811023159371198583524768270112 * q^22 + 26762219406239912352813565493381233364712 * q^23 + 432715559082166564545012957137471770368000 * q^24 + 626328164486171817149625807278273965801475 * q^25 + 2749973149308040923633652135036287227445360 * q^26 + 4216422593373619915288217358331953848770680 * q^27 - 5611228561379710656820495758490486062705152 * q^28 - 17549046108593766297328008399864666159350850 * q^29 - 150145537158572429445793395106337059707760320 * q^30 - 358583623042201488230225328552738568224907040 * q^31 - 1074522626525330530995966308544265757955293184 * q^32 + 751114060128814067949775005681101561535832944 * q^33 + 1313186147384734516654444992913422917722864080 * q^34 + 8788755903389357061227741366680412802419085840 * q^35 + 50365332867541870766115057156818159463301788480 * q^36 + 12289654705391014078883644083969663074775614326 * q^37 - 45794685161100120795332322131326257673964677920 * q^38 - 9221768768351520041372477942735049607434903480 * q^39 - 623280493607240105129626720516519294122185241600 * q^40 - 1264600318837995850108850617547077064258140834590 * q^41 - 1891447371005345295768856102377155889725040492288 * q^42 + 1362401402875616509759331175816257798295684833092 * q^43 + 10077075627927391677990061115125884792646469172480 * q^44 + 10049700882739433416170827255242789411985618900430 * q^45 + 35794385229187598114442404877782400066811275005760 * q^46 + 58116315089138636393563553286549713195469724328016 * q^47 - 140681680096635395071164158203106499934517556953088 * q^48 - 172418318747588613327122588406220961507566908720435 * q^49 - 233848387346081992883910872998391056418422012487400 * q^50 - 465020225697129855978502466718810564745463254433640 * q^51 - 992097542005695911104987622381229757223139868049024 * q^52 + 2268101788488183861226576340546566132432064315777382 * q^53 + 4267182630237865543673874484672773145843435829054400 * q^54 + 900686393182056151569568156583842171451592208829880 * q^55 + 13057990199329560708452108630914154838760821091430400 * q^56 - 1461399454110401384802692435956966006781083287581040 * q^57 - 19935384508052610930909349257749128471453923297265680 * q^58 - 21931653365540795176945573682489794310901322601489100 * q^59 - 156464057876025038631690397519755203816227736824450560 * q^60 - 55594140754072322694181208673989737469003346813960290 * q^61 + 183475769536335462614566613996468524195162017418651392 * q^62 + 182010153390148596243930899005933467643747025172792792 * q^63 + 442992326944585087629292186411036974187652719990538240 * q^64 + 108239432655103548226552811908240865218465397888070180 * q^65 + 1851519511613271584553254669645963732036891556451969920 * q^66 + 251728958220345096328034657219059743090559333983657196 * q^67 - 5807349046062465910161766073979061475602982250739804032 * q^68 - 1186914917838620759227364067219409346615803888683557280 * q^69 - 5752977156560799367346480182820409713199133658156760960 * q^70 - 6369597660991167158573967320963521000612243175546832840 * q^71 + 505582168407192977842217602799461333023468587718935040 * q^72 + 12498734118021895660608582328454257591891310584798516162 * q^73 + 30430803441235884517255321866854090380478491767252508080 * q^74 + 71252573634955902069214955355612845417141504756757611700 * q^75 + 44485052481827577410579765985045990814357967613276332800 * q^76 + 17284905559091020495400324815223194592508822902892800352 * q^77 - 201581338752116742909455308452046241693931223329795704256 * q^78 - 195027743716001656833247333265450397879290980351117845200 * q^79 - 206704704480779086536260387174822452768748287935918120960 * q^80 - 272827015213405140901132899770256322932509539084953805395 * q^81 - 900520634877949974377918733125010085392642066824246973168 * q^82 + 1340753017495815214930655712848265601901866175919407282652 * q^83 + 1757594637692279239094128738775127192473269576864397076480 * q^84 + 2489371886919081358504761029214476055227000571885198923340 * q^85 - 1480724029310290822922398160933917869023473589220972227040 * q^86 + 2732195656620738105781600070679866258015898732907716552840 * q^87 - 766253667564296029168711510940105999694943299571114997760 * q^88 + 4137994032714609594535072901976334293523151283735651174450 * q^89 - 27581529153974409588805844338613259043100774320772297131920 * q^90 + 2026135516273811264299668018701283385599128389353986522960 * q^91 - 40220109586116561836814028008941466356622877640185075490304 * q^92 + 35686922849658258124721404138853435620012609371542349362304 * q^93 - 11288243726815211032514455546739674300124940708563708661120 * q^94 + 87101339446452871712134322546432797479691690743389226486600 * q^95 + 35374905257632352454877863276046463006859953360328478556160 * q^96 + 116502743099592096760799908821840050224405365201122277495466 * q^97 - 100197653381373748947470486612022288330601696851398709875352 * q^98 + 233753058124724467227621750953596851247855288092335837370420 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.42193e9	−1.87281	−0.936407	−	0.350915i	$-0.885871\pi$
$2$	−1.42193e9	−1.87281	−0.936407	+	0.350915i	$0.885871\pi$
$3$	−1.64208e14	−1.38140	−0.690698	−	0.723144i	$-0.742696\pi$
$3$	−1.64208e14	−1.38140	−0.690698	+	0.723144i	$0.742696\pi$
$4$	1.44544e18	2.50744
$5$	2.46018e20	0.590679	0.295340	−	0.955392i	$-0.404567\pi$
$5$	2.46018e20	0.590679	0.295340	+	0.955392i	$0.404567\pi$
$6$	2.33493e23	2.58710
$7$	−6.31094e24	−0.740801	−0.370401	−	0.928872i	$-0.620780\pi$
$7$	−6.31094e24	−0.740801	−0.370401	+	0.928872i	$0.620780\pi$
$8$	−1.23563e27	−2.82315
$9$	1.28340e28	0.908253
$10$	−3.49822e29	−1.10623
$11$	−1.85237e29	−0.0352082	−0.0176041	−	0.999845i	$-0.505604\pi$
$11$	−1.85237e29	−0.0352082	−0.0176041	+	0.999845i	$0.505604\pi$
$12$	−2.37353e32	−3.46376
$13$	−9.37557e32	−1.29024	−0.645118	−	0.764083i	$-0.723192\pi$
$13$	−9.37557e32	−1.29024	−0.645118	+	0.764083i	$0.723192\pi$
$14$	8.97374e33	1.38738
$15$	−4.03982e34	−0.815962
$16$	9.23746e35	2.77980
$17$	−2.12710e36	−1.07040	−0.535199	−	0.844726i	$-0.679763\pi$
$17$	−2.12710e36	−1.07040	−0.535199	+	0.844726i	$0.679763\pi$
$18$	−1.82491e37	−1.70099
$19$	2.93477e37	0.555064	0.277532	−	0.960716i	$-0.410484\pi$
$19$	2.93477e37	0.555064	0.277532	+	0.960716i	$0.410484\pi$
$20$	3.55604e38	1.48109
$21$	1.03631e39	1.02334
$22$	2.63395e38	0.0659385
$23$	−1.73933e40	−1.17330	−0.586652	−	0.809839i	$-0.699554\pi$
$23$	−1.73933e40	−1.17330	−0.586652	+	0.809839i	$0.699554\pi$
$24$	2.02901e41	3.89988
$25$	−1.12947e41	−0.651098
$26$	1.33315e42	2.41637
$27$	2.12883e41	0.126739
$28$	−9.12207e42	−1.85751
$29$	2.89914e41	0.0209666	0.0104833	−	0.999945i	$-0.496663\pi$
$29$	2.89914e41	0.0209666	0.0104833	+	0.999945i	$0.496663\pi$
$30$	5.74436e43	1.52815
$31$	−1.46222e44	−1.47857	−0.739287	−	0.673390i	$-0.764837\pi$
$31$	−1.46222e44	−1.47857	−0.739287	+	0.673390i	$0.764837\pi$
$32$	−6.01215e44	−2.38290
$33$	3.04175e43	0.0486365
$34$	3.02460e45	2.00466
$35$	−1.55260e45	−0.437576
$36$	1.85507e46	2.27739
$37$	−2.03766e46	−1.11476	−0.557379	−	0.830258i	$-0.688193\pi$
$37$	−2.03766e46	−1.11476	−0.557379	+	0.830258i	$0.688193\pi$
$38$	−4.17306e46	−1.03953
$39$	1.53955e47	1.78232
$40$	−3.03987e47	−1.66758
$41$	2.62740e47	0.695669	0.347835	−	0.937556i	$-0.386917\pi$
$41$	2.62740e47	0.695669	0.347835	+	0.937556i	$0.386917\pi$
$42$	−1.47356e48	−1.91653
$43$	8.93006e47	0.580143	0.290071	−	0.957005i	$-0.406321\pi$
$43$	8.93006e47	0.580143	0.290071	+	0.957005i	$0.406321\pi$
$44$	−2.67749e47	−0.0882824
$45$	3.15739e48	0.536486
$46$	2.47321e49	2.19738
$47$	2.53928e49	1.19626	0.598128	−	0.801401i	$-0.295911\pi$
$47$	2.53928e49	1.19626	0.598128	+	0.801401i	$0.295911\pi$
$48$	−1.51687e50	−3.84000
$49$	−3.27466e49	−0.451213
$50$	1.60604e50	1.21939
$51$	3.49288e50	1.47864
$52$	−1.35518e51	−3.23518
$53$	1.22660e51	1.66942	0.834710	−	0.550690i	$-0.185635\pi$
$53$	1.22660e51	1.66942	0.834710	+	0.550690i	$0.185635\pi$
$54$	−3.02706e50	−0.237359
$55$	−4.55717e49	−0.0207968
$56$	7.79798e51	2.09139
$57$	−4.81914e51	−0.766763
$58$	−4.12239e50	−0.0392666
$59$	5.85329e50	0.0336717	0.0168359	−	0.999858i	$-0.494641\pi$
$59$	5.85329e50	0.0336717	0.0168359	+	0.999858i	$0.494641\pi$
$60$	−5.83931e52	−2.04597
$61$	−6.37747e52	−1.37220	−0.686102	−	0.727506i	$-0.740680\pi$
$61$	−6.37747e52	−1.37220	−0.686102	+	0.727506i	$0.740680\pi$
$62$	2.07918e53	2.76910
$63$	−8.09944e52	−0.672835
$64$	3.22385e53	1.68293
$65$	−2.30656e53	−0.762115
$66$	−4.32517e52	−0.0910871
$67$	6.46551e53	0.873767	0.436884	−	0.899518i	$-0.356082\pi$
$67$	6.46551e53	0.873767	0.436884	+	0.899518i	$0.356082\pi$
$68$	−3.07460e54	−2.68395
$69$	2.85612e54	1.62080
$70$	2.20770e54	0.819499
$71$	−1.44338e54	−0.352580	−0.176290	−	0.984338i	$-0.556410\pi$
$71$	−1.44338e54	−0.352580	−0.176290	+	0.984338i	$0.556410\pi$
$72$	−1.58580e55	−2.56413
$73$	−2.42309e54	−0.260822	−0.130411	−	0.991460i	$-0.541630\pi$
$73$	−2.42309e54	−0.260822	−0.130411	+	0.991460i	$0.541630\pi$
$74$	2.89742e55	2.08773
$75$	1.85469e55	0.899424
$76$	4.24203e55	1.39179
$77$	1.16902e54	0.0260823
$78$	−2.18913e56	−3.33796
$79$	4.97858e54	0.0521322	0.0260661	−	0.999660i	$-0.491702\pi$
$79$	4.97858e54	0.0521322	0.0260661	+	0.999660i	$0.491702\pi$
$80$	2.27258e56	1.64197
$81$	−2.16306e56	−1.08333
$82$	−3.73599e56	−1.30286
$83$	3.44463e56	0.840116	0.420058	−	0.907497i	$-0.362010\pi$
$83$	3.44463e56	0.840116	0.420058	+	0.907497i	$0.362010\pi$
$84$	1.49792e57	2.56596
$85$	−5.23306e56	−0.632262
$86$	−1.26980e57	−1.08650
$87$	−4.76063e55	−0.0289632
$88$	2.28885e56	0.0993981
$89$	3.85023e57	1.19807	0.599034	−	0.800724i	$-0.295551\pi$
$89$	3.85023e57	1.19807	0.599034	+	0.800724i	$0.295551\pi$
$90$	−4.48960e57	−1.00474
$91$	5.91687e57	0.955808
$92$	−2.51409e58	−2.94198
$93$	2.40109e58	2.04250
$94$	−3.61069e58	−2.24037
$95$	7.22007e57	0.327865
$96$	9.87245e58	3.29172
$97$	−2.95516e58	−0.725797	−0.362899	−	0.931829i	$-0.618213\pi$
$97$	−2.95516e58	−0.725797	−0.362899	+	0.931829i	$0.618213\pi$
$98$	4.65635e58	0.845039
$99$	−2.37733e57	−0.0319780
$100$	−1.63259e59	−1.63259
$101$	6.95950e57	0.0518916	0.0259458	−	0.999663i	$-0.491740\pi$
$101$	6.95950e57	0.0518916	0.0259458	+	0.999663i	$0.491740\pi$
$102$	−4.96665e59	−2.76922
$103$	9.43331e58	0.394426	0.197213	−	0.980361i	$-0.436811\pi$
$103$	9.43331e58	0.394426	0.197213	+	0.980361i	$0.436811\pi$
$104$	1.15847e60	3.64252
$105$	2.54951e59	0.604466
$106$	−1.74415e60	−3.12651
$107$	4.79536e59	0.651627	0.325814	−	0.945434i	$-0.394362\pi$
$107$	4.79536e59	0.651627	0.325814	+	0.945434i	$0.394362\pi$
$108$	3.07710e59	0.317790
$109$	8.62112e59	0.678394	0.339197	−	0.940715i	$-0.389845\pi$
$109$	8.62112e59	0.678394	0.339197	+	0.940715i	$0.389845\pi$
$110$	6.48000e58	0.0389485
$111$	3.34600e60	1.53992
$112$	−5.82971e60	−2.05928
$113$	−3.86899e60	−1.05144	−0.525719	−	0.850658i	$-0.676204\pi$
$113$	−3.86899e60	−1.05144	−0.525719	+	0.850658i	$0.676204\pi$
$114$	6.85250e60	1.43601
$115$	−4.27906e60	−0.693046
$116$	4.19053e59	0.0525725
$117$	−1.20326e61	−1.17186
$118$	−8.32299e59	−0.0630609
$119$	1.34240e61	0.792952
$120$	4.99172e61	2.30358
$121$	−2.76458e61	−0.998760
$122$	9.06835e61	2.56988
$123$	−4.31441e61	−0.960994
$124$	−2.11355e62	−3.70743
$125$	−7.04644e61	−0.975269
$126$	1.15169e62	1.26010
$127$	2.00091e62	1.73388	0.866939	−	0.498414i	$-0.166084\pi$
$127$	2.00091e62	1.73388	0.866939	+	0.498414i	$0.166084\pi$
$128$	−1.11834e62	−0.768918
$129$	−1.46639e62	−0.801406
$130$	3.27978e62	1.42730
$131$	1.11788e62	0.388053	0.194026	−	0.980996i	$-0.437845\pi$
$131$	1.11788e62	0.388053	0.194026	+	0.980996i	$0.437845\pi$
$132$	4.39666e61	0.121953
$133$	−1.85212e62	−0.411192
$134$	−9.19353e62	−1.63640
$135$	5.23731e61	0.0748621
$136$	2.62831e63	3.02189
$137$	2.78939e62	0.258376	0.129188	−	0.991620i	$-0.458763\pi$
$137$	2.78939e62	0.258376	0.129188	+	0.991620i	$0.458763\pi$
$138$	−4.06122e63	−3.03545
$139$	2.28698e63	1.38142	0.690710	−	0.723132i	$-0.257298\pi$
$139$	2.28698e63	1.38142	0.690710	+	0.723132i	$0.257298\pi$
$140$	−2.24419e63	−1.09719
$141$	−4.16971e63	−1.65250
$142$	2.05239e63	0.660317
$143$	1.73671e62	0.0454269
$144$	1.18553e64	2.52476
$145$	7.13242e61	0.0123846
$146$	3.44547e63	0.488472
$147$	5.37726e63	0.623304
$148$	−2.94531e64	−2.79518
$149$	1.95296e64	1.51949	0.759745	−	0.650221i	$-0.225324\pi$
$149$	1.95296e64	1.51949	0.759745	+	0.650221i	$0.225324\pi$
$150$	−2.63725e64	−1.68445
$151$	3.23263e64	1.69721	0.848607	−	0.529024i	$-0.177442\pi$
$151$	3.23263e64	1.69721	0.848607	+	0.529024i	$0.177442\pi$
$152$	−3.62629e64	−1.56703
$153$	−2.72992e64	−0.972192
$154$	−1.66227e63	−0.0488473
$155$	−3.59733e64	−0.873363
$156$	2.22532e65	4.46906
$157$	1.75281e64	0.291538	0.145769	−	0.989319i	$-0.453434\pi$
$157$	1.75281e64	0.291538	0.145769	+	0.989319i	$0.453434\pi$
$158$	−7.07922e63	−0.0976340
$159$	−2.01418e65	−2.30613
$160$	−1.47910e65	−1.40753
$161$	1.09768e65	0.869185
$162$	3.07573e65	2.02888
$163$	−3.13298e65	−1.72355	−0.861774	−	0.507292i	$-0.830646\pi$
$163$	−3.13298e65	−1.72355	−0.861774	+	0.507292i	$0.830646\pi$
$164$	3.79775e65	1.74435
$165$	7.48325e63	0.0287286
$166$	−4.89804e65	−1.57338
$167$	1.87971e65	0.505772	0.252886	−	0.967496i	$-0.418620\pi$
$167$	1.87971e65	0.505772	0.252886	+	0.967496i	$0.418620\pi$
$168$	−1.28049e66	−2.88904
$169$	3.50984e65	0.664706
$170$	7.44107e65	1.18411
$171$	3.76648e65	0.504139
$172$	1.29078e66	1.45467
$173$	−1.53152e65	−0.145466	−0.0727330	−	0.997351i	$-0.523172\pi$
$173$	−1.53152e65	−0.145466	−0.0727330	+	0.997351i	$0.523172\pi$
$174$	6.76931e64	0.0542428
$175$	7.12805e65	0.482334
$176$	−1.71112e65	−0.0978718
$177$	−9.61158e64	−0.0465140
$178$	−5.47478e66	−2.24376
$179$	−4.89309e66	−1.69988	−0.849941	−	0.526878i	$-0.823363\pi$
$179$	−4.89309e66	−1.69988	−0.849941	+	0.526878i	$0.823363\pi$
$180$	4.56381e66	1.34520
$181$	2.49289e66	0.624002	0.312001	−	0.950082i	$-0.399001\pi$
$181$	2.49289e66	0.624002	0.312001	+	0.950082i	$0.399001\pi$
$182$	−8.41340e66	−1.79005
$183$	1.04723e67	1.89556
$184$	2.14916e67	3.31241
$185$	−5.01300e66	−0.658464
$186$	−3.41419e67	−3.82522
$187$	3.94019e65	0.0376868
$188$	3.67037e67	2.99953
$189$	−1.34349e66	−0.0938885
$190$	−1.02665e67	−0.614030
$191$	9.18865e66	0.470725	0.235362	−	0.971908i	$-0.424372\pi$
$191$	9.18865e66	0.470725	0.235362	+	0.971908i	$0.424372\pi$
$192$	−5.29383e67	−2.32479
$193$	−6.86206e66	−0.258532	−0.129266	−	0.991610i	$-0.541262\pi$
$193$	−6.86206e66	−0.258532	−0.129266	+	0.991610i	$0.541262\pi$
$194$	4.20205e67	1.35928
$195$	3.78756e67	1.05278
$196$	−4.73332e67	−1.13139
$197$	−2.65331e67	−0.545800	−0.272900	−	0.962042i	$-0.587983\pi$
$197$	−2.65331e67	−0.545800	−0.272900	+	0.962042i	$0.587983\pi$
$198$	3.38041e66	0.0598888
$199$	−4.85073e67	−0.740699	−0.370349	−	0.928892i	$-0.620762\pi$
$199$	−4.85073e67	−0.740699	−0.370349	+	0.928892i	$0.620762\pi$
$200$	1.39561e68	1.83815
$201$	−1.06169e68	−1.20702
$202$	−9.89595e66	−0.0971834
$203$	−1.82963e66	−0.0155321
$204$	5.04874e68	3.70760
$205$	6.46388e67	0.410917
$206$	−1.34136e68	−0.738687
$207$	−2.23225e68	−1.06566
$208$	−8.66065e68	−3.58659
$209$	−5.43629e66	−0.0195428
$210$	−3.62523e68	−1.13205
$211$	1.87935e67	0.0510124	0.0255062	−	0.999675i	$-0.491880\pi$
$211$	1.87935e67	0.0510124	0.0255062	+	0.999675i	$0.491880\pi$
$212$	1.77298e69	4.18596
$213$	2.37014e68	0.487053
$214$	−6.81868e68	−1.22038
$215$	2.19695e68	0.342678
$216$	−2.63045e68	−0.357803
$217$	9.22799e68	1.09533
$218$	−1.22587e69	−1.27051
$219$	3.97891e68	0.360299
$220$	−6.58711e67	−0.0521466
$221$	1.99428e69	1.38107
$222$	−4.75780e69	−2.88399
$223$	−9.19286e68	−0.488042	−0.244021	−	0.969770i	$-0.578467\pi$
$223$	−9.19286e68	−0.488042	−0.244021	+	0.969770i	$0.578467\pi$
$224$	3.79423e69	1.76525
$225$	−1.44956e69	−0.591362
$226$	5.50146e69	1.96915
$227$	−3.67098e69	−1.15350	−0.576752	−	0.816919i	$-0.695680\pi$
$227$	−3.67098e69	−1.15350	−0.576752	+	0.816919i	$0.695680\pi$
$228$	−6.96577e69	−1.92261
$229$	4.99969e68	0.121282	0.0606410	−	0.998160i	$-0.480686\pi$
$229$	4.99969e68	0.121282	0.0606410	+	0.998160i	$0.480686\pi$
$230$	6.08454e69	1.29795
$231$	−1.91963e68	−0.0360300
$232$	−3.58227e68	−0.0591919
$233$	−6.24576e69	−0.909046	−0.454523	−	0.890735i	$-0.650190\pi$
$233$	−6.24576e69	−0.909046	−0.454523	+	0.890735i	$0.650190\pi$
$234$	1.71095e70	2.19468
$235$	6.24709e69	0.706603
$236$	8.46056e68	0.0844297
$237$	−8.17524e68	−0.0720152
$238$	−1.90881e70	−1.48505
$239$	7.76076e69	0.533539	0.266770	−	0.963760i	$-0.414044\pi$
$239$	7.76076e69	0.533539	0.266770	+	0.963760i	$0.414044\pi$
$240$	−3.73177e70	−2.26821
$241$	−1.26377e70	−0.679462	−0.339731	−	0.940523i	$-0.610336\pi$
$241$	−1.26377e70	−0.679462	−0.339731	+	0.940523i	$0.610336\pi$
$242$	3.93106e70	1.87049
$243$	3.25111e70	1.36977
$244$	−9.21824e70	−3.44071
$245$	−8.05625e69	−0.266522
$246$	6.13481e70	1.79976
$247$	−2.75152e70	−0.716163
$248$	1.80676e71	4.17423
$249$	−5.65637e70	−1.16053
$250$	1.00196e71	1.82650
$251$	−6.71368e70	−1.08789	−0.543946	−	0.839120i	$-0.683070\pi$
$251$	−6.71368e70	−1.08789	−0.543946	+	0.839120i	$0.683070\pi$
$252$	−1.17072e71	−1.68709
$253$	3.22188e69	0.0413099
$254$	−2.84517e71	−3.24723
$255$	8.59311e70	0.873404
$256$	−2.68217e70	−0.242888
$257$	1.99205e71	1.60795	0.803977	−	0.594661i	$-0.202714\pi$
$257$	1.99205e71	1.60795	0.803977	+	0.594661i	$0.202714\pi$
$258$	2.08511e71	1.50089
$259$	1.28595e71	0.825814
$260$	−3.33399e71	−1.91095
$261$	3.72075e69	0.0190430
$262$	−1.58955e71	−0.726751
$263$	−9.75645e70	−0.398655	−0.199328	−	0.979933i	$-0.563876\pi$
$263$	−9.75645e70	−0.398655	−0.199328	+	0.979933i	$0.563876\pi$
$264$	−3.75848e70	−0.137308
$265$	3.01766e71	0.986092
$266$	2.63359e71	0.770087
$267$	−6.32240e71	−1.65501
$268$	9.34549e71	2.19092
$269$	5.47919e71	1.15086	0.575432	−	0.817850i	$-0.304834\pi$
$269$	5.47919e71	1.15086	0.575432	+	0.817850i	$0.304834\pi$
$270$	−7.44711e70	−0.140203
$271$	4.44087e71	0.749677	0.374839	−	0.927090i	$-0.377698\pi$
$271$	4.44087e71	0.749677	0.374839	+	0.927090i	$0.377698\pi$
$272$	−1.96490e72	−2.97549
$273$	−9.71598e71	−1.32035
$274$	−3.96634e71	−0.483891
$275$	2.09221e70	0.0229240
$276$	4.12834e72	4.06404
$277$	−1.63500e72	−1.44665	−0.723325	−	0.690507i	$-0.757387\pi$
$277$	−1.63500e72	−1.44665	−0.723325	+	0.690507i	$0.757387\pi$
$278$	−3.25194e72	−2.58714
$279$	−1.87661e72	−1.34292
$280$	1.91844e72	1.23534
$281$	1.36625e72	0.791944	0.395972	−	0.918263i	$-0.370408\pi$
$281$	1.36625e72	0.791944	0.395972	+	0.918263i	$0.370408\pi$
$282$	5.92906e72	3.09483
$283$	2.35491e72	1.10732	0.553661	−	0.832742i	$-0.313230\pi$
$283$	2.35491e72	1.10732	0.553661	+	0.832742i	$0.313230\pi$
$284$	−2.08631e72	−0.884072
$285$	−1.18559e72	−0.452911
$286$	−2.46948e71	−0.0850762
$287$	−1.65814e72	−0.515353
$288$	−7.71597e72	−2.16427
$289$	5.75573e71	0.145752
$290$	−1.01418e71	−0.0231940
$291$	4.85262e72	1.00261
$292$	−3.50242e72	−0.653995
$293$	3.23554e71	0.0546200	0.0273100	−	0.999627i	$-0.491306\pi$
$293$	3.23554e71	0.0546200	0.0273100	+	0.999627i	$0.491306\pi$
$294$	−7.64612e72	−1.16733
$295$	1.44001e71	0.0198892
$296$	2.51779e73	3.14712
$297$	−3.94339e70	−0.00446226
$298$	−2.77698e73	−2.84572
$299$	1.63072e73	1.51384
$300$	2.68084e73	2.25525
$301$	−5.63570e72	−0.429770
$302$	−4.59659e73	−3.17857
$303$	−1.14281e72	−0.0716828
$304$	2.71099e73	1.54297
$305$	−1.56897e73	−0.810532
$306$	3.88176e73	1.82074
$307$	−7.55894e72	−0.322017	−0.161008	−	0.986953i	$-0.551475\pi$
$307$	−7.55894e72	−0.322017	−0.161008	+	0.986953i	$0.551475\pi$
$308$	1.68975e72	0.0653997
$309$	−1.54903e73	−0.544859
$310$	5.11517e73	1.63565
$311$	4.75210e71	0.0138183	0.00690914	−	0.999976i	$-0.497801\pi$
$311$	4.75210e71	0.0138183	0.00690914	+	0.999976i	$0.497801\pi$
$312$	−1.90231e74	−5.03177
$313$	4.85436e73	1.16835	0.584176	−	0.811627i	$-0.301418\pi$
$313$	4.85436e73	1.16835	0.584176	+	0.811627i	$0.301418\pi$
$314$	−2.49239e73	−0.545997
$315$	−1.99261e73	−0.397430
$316$	7.19623e72	0.130718
$317$	5.69481e73	0.942391	0.471195	−	0.882029i	$-0.343823\pi$
$317$	5.69481e73	0.942391	0.471195	+	0.882029i	$0.343823\pi$
$318$	2.86404e74	4.31895
$319$	−5.37030e70	−0.000738199 0
$320$	7.93126e73	0.994072
$321$	−7.87437e73	−0.900155
$322$	−1.56083e74	−1.62782
$323$	−6.24256e73	−0.594140
$324$	−3.12657e74	−2.71638
$325$	1.05895e74	0.840069
$326$	4.45489e74	3.22789
$327$	−1.41566e74	−0.937131
$328$	−3.24649e74	−1.96398
$329$	−1.60252e74	−0.886188
$330$	−1.06407e73	−0.0538033
$331$	1.34777e74	0.623288	0.311644	−	0.950199i	$-0.399120\pi$
$331$	1.34777e74	0.623288	0.311644	+	0.950199i	$0.399120\pi$
$332$	4.97900e74	2.10654
$333$	−2.61512e74	−1.01248
$334$	−2.67282e74	−0.947217
$335$	1.59063e74	0.516116
$336$	9.57286e74	2.84468
$337$	−2.02155e74	−0.550303	−0.275151	−	0.961401i	$-0.588728\pi$
$337$	−2.02155e74	−0.550303	−0.275151	+	0.961401i	$0.588728\pi$
$338$	−4.99077e74	−1.24487
$339$	6.35320e74	1.45245
$340$	−7.56406e74	−1.58536
$341$	2.70858e73	0.0520580
$342$	−5.35568e74	−0.944158
$343$	6.64675e74	1.07506
$344$	−1.10342e75	−1.63783
$345$	7.02657e74	0.957370
$346$	2.17772e74	0.272431
$347$	1.04939e75	1.20564	0.602818	−	0.797879i	$-0.294045\pi$
$347$	1.04939e75	1.20564	0.602818	+	0.797879i	$0.294045\pi$
$348$	−6.88120e73	−0.0726234
$349$	−7.51505e74	−0.728755	−0.364378	−	0.931251i	$-0.618718\pi$
$349$	−7.51505e74	−0.728755	−0.364378	+	0.931251i	$0.618718\pi$
$350$	−1.01356e75	−0.903323
$351$	−1.99590e74	−0.163523
$352$	1.11367e74	0.0838977
$353$	−2.22200e75	−1.53954	−0.769770	−	0.638321i	$-0.779629\pi$
$353$	−2.22200e75	−1.53954	−0.769770	+	0.638321i	$0.779629\pi$
$354$	1.36670e74	0.0871120
$355$	−3.55096e74	−0.208262
$356$	5.56527e75	3.00408
$357$	−2.20433e75	−1.09538
$358$	6.95766e75	3.18356
$359$	−3.15427e74	−0.132927	−0.0664635	−	0.997789i	$-0.521172\pi$
$359$	−3.15427e74	−0.132927	−0.0664635	+	0.997789i	$0.521172\pi$
$360$	−3.90136e75	−1.51458
$361$	−1.93423e75	−0.691904
$362$	−3.54473e75	−1.16864
$363$	4.53967e75	1.37968
$364$	8.55246e75	2.39663
$365$	−5.96123e74	−0.154062
$366$	−1.48910e76	−3.55002
$367$	−2.41055e75	−0.530233	−0.265116	−	0.964216i	$-0.585410\pi$
$367$	−2.41055e75	−0.530233	−0.265116	+	0.964216i	$0.585410\pi$
$368$	−1.60670e76	−3.26155
$369$	3.37200e75	0.631843
$370$	7.12817e75	1.23318
$371$	−7.74101e75	−1.23671
$372$	3.47063e76	5.12143
$373$	6.47651e75	0.882938	0.441469	−	0.897276i	$-0.354457\pi$
$373$	6.47651e75	0.882938	0.441469	+	0.897276i	$0.354457\pi$
$374$	−5.60269e74	−0.0705804
$375$	1.15708e76	1.34723
$376$	−3.13761e76	−3.37721
$377$	−2.71811e74	−0.0270519
$378$	1.91036e75	0.175836
$379$	3.32994e75	0.283517	0.141759	−	0.989901i	$-0.454724\pi$
$379$	3.32994e75	0.283517	0.141759	+	0.989901i	$0.454724\pi$
$380$	1.04362e76	0.822100
$381$	−3.28567e76	−2.39517
$382$	−1.30657e76	−0.881581
$383$	2.22332e76	1.38880	0.694398	−	0.719591i	$-0.255671\pi$
$383$	2.22332e76	1.38880	0.694398	+	0.719591i	$0.255671\pi$
$384$	1.83641e76	1.06218
$385$	2.87600e74	0.0154063
$386$	9.75740e75	0.484182
$387$	1.14608e76	0.526916
$388$	−4.27151e76	−1.81989
$389$	−1.38935e76	−0.548653	−0.274327	−	0.961637i	$-0.588455\pi$
$389$	−1.38935e76	−0.548653	−0.274327	+	0.961637i	$0.588455\pi$
$390$	−5.38566e76	−1.97167
$391$	3.69973e76	1.25590
$392$	4.04627e76	1.27384
$393$	−1.83565e76	−0.536054
$394$	3.77283e76	1.02218
$395$	1.22482e75	0.0307934
$396$	−3.43628e75	−0.0801827
$397$	−2.17609e76	−0.471364	−0.235682	−	0.971830i	$-0.575732\pi$
$397$	−2.17609e76	−0.471364	−0.235682	+	0.971830i	$0.575732\pi$
$398$	6.89743e76	1.38719
$399$	3.04133e76	0.568019
$400$	−1.04335e77	−1.80992
$401$	−1.16224e77	−1.87300	−0.936499	−	0.350671i	$-0.885954\pi$
$401$	−1.16224e77	−1.87300	−0.936499	+	0.350671i	$0.885954\pi$
$402$	1.50965e77	2.26052
$403$	1.37092e77	1.90771
$404$	1.00595e76	0.130115
$405$	−5.32152e76	−0.639900
$406$	2.60162e75	0.0290888
$407$	3.77450e75	0.0392486
$408$	−4.31590e77	−4.17443
$409$	4.02114e76	0.361836	0.180918	−	0.983498i	$-0.442093\pi$
$409$	4.02114e76	0.361836	0.180918	+	0.983498i	$0.442093\pi$
$410$	−9.19122e76	−0.769572
$411$	−4.58041e76	−0.356920
$412$	1.36353e77	0.988999
$413$	−3.69397e75	−0.0249441
$414$	3.17411e77	1.99578
$415$	8.47442e76	0.496239
$416$	5.63674e77	3.07450
$417$	−3.75541e77	−1.90829
$418$	7.73006e75	0.0366001
$419$	−1.98426e77	−0.875557	−0.437778	−	0.899083i	$-0.644235\pi$
$419$	−1.98426e77	−0.875557	−0.437778	+	0.899083i	$0.644235\pi$
$420$	3.68515e77	1.51566
$421$	−1.57509e77	−0.603927	−0.301963	−	0.953320i	$-0.597642\pi$
$421$	−1.57509e77	−0.603927	−0.301963	+	0.953320i	$0.597642\pi$
$422$	−2.67232e76	−0.0955368
$423$	3.25890e77	1.08650
$424$	−1.51563e78	−4.71302
$425$	2.40251e77	0.696934
$426$	−3.37019e77	−0.912159
$427$	4.02478e77	1.01653
$428$	6.93139e77	1.63391
$429$	−2.85181e76	−0.0627525
$430$	−3.12393e77	−0.641773
$431$	−1.55654e77	−0.298594	−0.149297	−	0.988792i	$-0.547701\pi$
$431$	−1.55654e77	−0.298594	−0.149297	+	0.988792i	$0.547701\pi$
$432$	1.96650e77	0.352309
$433$	1.11740e78	1.86989	0.934946	−	0.354789i	$-0.115447\pi$
$433$	1.11740e78	1.86989	0.934946	+	0.354789i	$0.115447\pi$
$434$	−1.31216e78	−2.05135
$435$	−1.17120e76	−0.0171080
$436$	1.24613e78	1.70103
$437$	−5.10453e77	−0.651259
$438$	−5.65775e77	−0.674773
$439$	3.27856e77	0.365578	0.182789	−	0.983152i	$-0.441487\pi$
$439$	3.27856e77	0.365578	0.182789	+	0.983152i	$0.441487\pi$
$440$	5.63098e76	0.0587124
$441$	−4.20269e77	−0.409816
$442$	−2.83574e78	−2.58648
$443$	1.54152e78	1.31534	0.657672	−	0.753304i	$-0.271541\pi$
$443$	1.54152e78	1.31534	0.657672	+	0.753304i	$0.271541\pi$
$444$	4.83644e78	3.86125
$445$	9.47226e77	0.707674
$446$	1.30716e78	0.914012
$447$	−3.20692e78	−2.09902
$448$	−2.03455e78	−1.24672
$449$	−2.79348e78	−1.60280	−0.801398	−	0.598132i	$-0.795910\pi$
$449$	−2.79348e78	−1.60280	−0.801398	+	0.598132i	$0.795910\pi$
$450$	2.06119e78	1.10751
$451$	−4.86693e76	−0.0244933
$452$	−5.59239e78	−2.63641
$453$	−5.30825e78	−2.34452
$454$	5.21989e78	2.16030
$455$	1.45566e78	0.564576
$456$	5.95467e78	2.16469
$457$	5.45392e78	1.85858	0.929290	−	0.369351i	$-0.120420\pi$
$457$	5.45392e78	1.85858	0.929290	+	0.369351i	$0.120420\pi$
$458$	−7.10924e77	−0.227139
$459$	−4.52824e77	−0.135661
$460$	−6.18512e78	−1.73777
$461$	−1.71684e78	−0.452430	−0.226215	−	0.974077i	$-0.572635\pi$
$461$	−1.71684e78	−0.452430	−0.226215	+	0.974077i	$0.572635\pi$
$462$	2.72959e77	0.0674775
$463$	5.84613e78	1.35590	0.677952	−	0.735106i	$-0.262868\pi$
$463$	5.84613e78	1.35590	0.677952	+	0.735106i	$0.262868\pi$
$464$	2.67807e77	0.0582830
$465$	5.90711e78	1.20646
$466$	8.88107e78	1.70247
$467$	−2.20699e78	−0.397148	−0.198574	−	0.980086i	$-0.563631\pi$
$467$	−2.20699e78	−0.397148	−0.198574	+	0.980086i	$0.563631\pi$
$468$	−1.73923e79	−2.93836
$469$	−4.08034e78	−0.647288
$470$	−8.88295e78	−1.32334
$471$	−2.87826e78	−0.402730
$472$	−7.23249e77	−0.0950603
$473$	−1.65418e77	−0.0204258
$474$	1.16247e78	0.134871
$475$	−3.31475e78	−0.361401
$476$	1.94036e79	1.98828
$477$	1.57422e79	1.51626
$478$	−1.10353e79	−0.999220
$479$	−1.40796e79	−1.19865	−0.599326	−	0.800505i	$-0.704565\pi$
$479$	−1.40796e79	−1.19865	−0.599326	+	0.800505i	$0.704565\pi$
$480$	2.42880e79	1.94435
$481$	1.91042e79	1.43830
$482$	1.79700e79	1.27251
$483$	−1.80248e79	−1.20069
$484$	−3.99603e79	−2.50433
$485$	−7.27023e78	−0.428713
$486$	−4.62287e79	−2.56532
$487$	−2.26249e79	−1.18163	−0.590816	−	0.806806i	$-0.701194\pi$
$487$	−2.26249e79	−1.18163	−0.590816	+	0.806806i	$0.701194\pi$
$488$	7.88019e79	3.87393
$489$	5.14461e79	2.38090
$490$	1.14555e79	0.499147
$491$	2.61865e78	0.107442	0.0537210	−	0.998556i	$-0.482892\pi$
$491$	2.61865e78	0.107442	0.0537210	+	0.998556i	$0.482892\pi$
$492$	−6.23621e79	−2.40963
$493$	−6.16678e77	−0.0224427
$494$	3.91248e79	1.34124
$495$	−5.84866e77	−0.0188887
$496$	−1.35072e80	−4.11014
$497$	9.10905e78	0.261192
$498$	8.04299e79	2.17346
$499$	2.62064e79	0.667485	0.333743	−	0.942664i	$-0.391688\pi$
$499$	2.62064e79	0.667485	0.333743	+	0.942664i	$0.391688\pi$
$500$	−1.01852e80	−2.44543
$501$	−3.08664e79	−0.698671
$502$	9.54642e79	2.03742
$503$	−5.52525e79	−1.11198	−0.555989	−	0.831190i	$-0.687660\pi$
$503$	−5.52525e79	−1.11198	−0.555989	+	0.831190i	$0.687660\pi$
$504$	1.00079e80	1.89951
$505$	1.71216e78	0.0306513
$506$	−4.58131e78	−0.0773659
$507$	−5.76345e79	−0.918222
$508$	2.89220e80	4.34759
$509$	−4.32837e79	−0.613974	−0.306987	−	0.951714i	$-0.599321\pi$
$509$	−4.32837e79	−0.613974	−0.306987	+	0.951714i	$0.599321\pi$
$510$	−1.22188e80	−1.63572
$511$	1.52920e79	0.193217
$512$	1.02607e80	1.22380
$513$	6.24764e78	0.0703483
$514$	−2.83257e80	−3.01140
$515$	2.32076e79	0.232979
$516$	−2.11957e80	−2.00947
$517$	−4.70370e78	−0.0421181
$518$	−1.82854e80	−1.54660
$519$	2.51488e79	0.200946
$520$	2.85005e80	2.15156
$521$	2.41170e80	1.72033	0.860164	−	0.510018i	$-0.170361\pi$
$521$	2.41170e80	1.72033	0.860164	+	0.510018i	$0.170361\pi$
$522$	−5.29067e78	−0.0356640
$523$	−2.16416e80	−1.37876	−0.689380	−	0.724400i	$-0.742117\pi$
$523$	−2.16416e80	−1.37876	−0.689380	+	0.724400i	$0.742117\pi$
$524$	1.61582e80	0.973017
$525$	−1.17048e80	−0.666294
$526$	1.38730e80	0.746607
$527$	3.11030e80	1.58266
$528$	2.80980e79	0.135200
$529$	8.27693e79	0.376640
$530$	−4.29092e80	−1.84677
$531$	7.51209e78	0.0305824
$532$	−2.67712e80	−1.03104
$533$	−2.46334e80	−0.897577
$534$	8.99004e80	3.09952
$535$	1.17974e80	0.384903
$536$	−7.98897e80	−2.46677
$537$	8.03486e80	2.34821
$538$	−7.79105e80	−2.15536
$539$	6.06589e78	0.0158864
$540$	7.57021e79	0.187712
$541$	−3.15606e80	−0.741012	−0.370506	−	0.928830i	$-0.620816\pi$
$541$	−3.15606e80	−0.741012	−0.370506	+	0.928830i	$0.620816\pi$
$542$	−6.31463e80	−1.40401
$543$	−4.09354e80	−0.861993
$544$	1.27885e81	2.55065
$545$	2.12095e80	0.400713
$546$	1.38155e81	2.47277
$547$	−7.77150e80	−1.31789	−0.658945	−	0.752191i	$-0.728997\pi$
$547$	−7.77150e80	−1.31789	−0.658945	+	0.752191i	$0.728997\pi$
$548$	4.03190e80	0.647862
$549$	−8.18483e80	−1.24631
$550$	−2.97498e79	−0.0429324
$551$	8.50833e78	0.0116378
$552$	−3.52911e81	−4.57575
$553$	−3.14195e79	−0.0386196
$554$	2.32486e81	2.70931
$555$	8.23177e80	0.909599
$556$	3.30569e81	3.46382
$557$	−1.16000e81	−1.15274	−0.576368	−	0.817191i	$-0.695530\pi$
$557$	−1.16000e81	−1.15274	−0.576368	+	0.817191i	$0.695530\pi$
$558$	2.66842e81	2.51504
$559$	−8.37244e80	−0.748520
$560$	−1.43421e81	−1.21637
$561$	−6.47011e79	−0.0520604
$562$	−1.94272e81	−1.48316
$563$	2.67395e81	1.93712	0.968558	−	0.248786i	$-0.0800316\pi$
$563$	2.67395e81	1.93712	0.968558	+	0.248786i	$0.0800316\pi$
$564$	−6.02706e81	−4.14354
$565$	−9.51842e80	−0.621063
$566$	−3.34852e81	−2.07381
$567$	1.36509e81	0.802532
$568$	1.78348e81	0.995386
$569$	8.26000e80	0.437691	0.218846	−	0.975759i	$-0.429771\pi$
$569$	8.26000e80	0.437691	0.218846	+	0.975759i	$0.429771\pi$
$570$	1.68584e81	0.848219
$571$	1.96473e81	0.938722	0.469361	−	0.883006i	$-0.344484\pi$
$571$	1.96473e81	0.938722	0.469361	+	0.883006i	$0.344484\pi$
$572$	2.51030e80	0.113905
$573$	−1.50885e81	−0.650257
$574$	2.35776e81	0.965160
$575$	1.96453e81	0.763935
$576$	4.13748e81	1.52853
$577$	−1.98064e81	−0.695215	−0.347607	−	0.937640i	$-0.613006\pi$
$577$	−1.98064e81	−0.695215	−0.347607	+	0.937640i	$0.613006\pi$
$578$	−8.18428e80	−0.272966
$579$	1.12681e81	0.357135
$580$	1.03095e80	0.0310535
$581$	−2.17389e81	−0.622359
$582$	−6.90011e81	−1.87771
$583$	−2.27212e80	−0.0587773
$584$	2.99404e81	0.736340
$585$	−2.96023e81	−0.692193
$586$	−4.60072e80	−0.102293
$587$	−2.18290e81	−0.461540	−0.230770	−	0.973008i	$-0.574124\pi$
$587$	−2.18290e81	−0.461540	−0.230770	+	0.973008i	$0.574124\pi$
$588$	7.77250e81	1.56289
$589$	−4.29129e81	−0.820704
$590$	−2.04761e80	−0.0372488
$591$	4.35695e81	0.753966
$592$	−1.88228e82	−3.09880
$593$	8.01746e81	1.25581	0.627904	−	0.778290i	$-0.283913\pi$
$593$	8.01746e81	1.25581	0.627904	+	0.778290i	$0.283913\pi$
$594$	5.60725e79	0.00835698
$595$	3.30255e81	0.468381
$596$	2.82288e82	3.81002
$597$	7.96531e81	1.02320
$598$	−2.31878e82	−2.83514
$599$	−3.31265e81	−0.385553	−0.192776	−	0.981243i	$-0.561749\pi$
$599$	−3.31265e81	−0.385553	−0.192776	+	0.981243i	$0.561749\pi$
$600$	−2.29171e82	−2.53921
$601$	−1.30012e82	−1.37147	−0.685733	−	0.727853i	$-0.740518\pi$
$601$	−1.30012e82	−1.37147	−0.685733	+	0.727853i	$0.740518\pi$
$602$	8.01360e81	0.804880
$603$	8.29781e81	0.793602
$604$	4.67257e82	4.25565
$605$	−6.80137e81	−0.589947
$606$	1.62500e81	0.134249
$607$	6.65424e80	0.0523639	0.0261820	−	0.999657i	$-0.491665\pi$
$607$	6.65424e80	0.0523639	0.0261820	+	0.999657i	$0.491665\pi$
$608$	−1.76443e82	−1.32266
$609$	3.00441e80	0.0214560
$610$	2.23098e82	1.51798
$611$	−2.38072e82	−1.54345
$612$	−3.94593e82	−2.43771
$613$	1.87920e82	1.10634	0.553169	−	0.833069i	$-0.313418\pi$
$613$	1.87920e82	1.10634	0.553169	+	0.833069i	$0.313418\pi$
$614$	1.07483e82	0.603078
$615$	−1.06142e82	−0.567639
$616$	−1.44448e81	−0.0736342
$617$	−2.20328e80	−0.0107068	−0.00535338	−	0.999986i	$-0.501704\pi$
$617$	−2.20328e80	−0.0107068	−0.00535338	+	0.999986i	$0.501704\pi$
$618$	2.20262e82	1.02042
$619$	−1.34870e82	−0.595719	−0.297859	−	0.954610i	$-0.596273\pi$
$619$	−1.34870e82	−0.595719	−0.297859	+	0.954610i	$0.596273\pi$
$620$	−5.19972e82	−2.18990
$621$	−3.70274e81	−0.148703
$622$	−6.75717e80	−0.0258791
$623$	−2.42986e82	−0.887531
$624$	1.42215e83	4.95450
$625$	2.25774e81	0.0750264
$626$	−6.90258e82	−2.18811
$627$	8.92684e80	0.0269964
$628$	2.53358e82	0.731014
$629$	4.33431e82	1.19323
$630$	2.83336e82	0.744312
$631$	7.15154e82	1.79281	0.896403	−	0.443239i	$-0.146171\pi$
$631$	7.15154e82	1.79281	0.896403	+	0.443239i	$0.146171\pi$
$632$	−6.15168e81	−0.147177
$633$	−3.08605e81	−0.0704683
$634$	−8.09765e82	−1.76492
$635$	4.92261e82	1.02417
$636$	−2.91137e83	−5.78247
$637$	3.07018e82	0.582171
$638$	7.63621e79	0.00138251
$639$	−1.85242e82	−0.320232
$640$	−2.75132e82	−0.454184
$641$	−2.99840e82	−0.472692	−0.236346	−	0.971669i	$-0.575950\pi$
$641$	−2.99840e82	−0.472692	−0.236346	+	0.971669i	$0.575950\pi$
$642$	1.11968e83	1.68582
$643$	5.90345e81	0.0848951	0.0424475	−	0.999099i	$-0.486484\pi$
$643$	5.90345e81	0.0848951	0.0424475	+	0.999099i	$0.486484\pi$
$644$	1.58663e83	2.17942
$645$	−3.60758e82	−0.473374
$646$	8.87652e82	1.11271
$647$	−3.93898e82	−0.471746	−0.235873	−	0.971784i	$-0.575795\pi$
$647$	−3.93898e82	−0.471746	−0.235873	+	0.971784i	$0.575795\pi$
$648$	2.67274e83	3.05840
$649$	−1.08425e80	−0.00118552
$650$	−1.50575e83	−1.57329
$651$	−1.51531e83	−1.51308
$652$	−4.52853e83	−4.32169
$653$	6.47496e82	0.590607	0.295303	−	0.955404i	$-0.404579\pi$
$653$	6.47496e82	0.590607	0.295303	+	0.955404i	$0.404579\pi$
$654$	2.01298e83	1.75507
$655$	2.75018e82	0.229215
$656$	2.42705e83	1.93382
$657$	−3.10978e82	−0.236893
$658$	2.27869e83	1.65967
$659$	−1.27657e83	−0.889044	−0.444522	−	0.895768i	$-0.646627\pi$
$659$	−1.27657e83	−0.889044	−0.444522	+	0.895768i	$0.646627\pi$
$660$	1.08166e82	0.0720350
$661$	2.81059e83	1.79000	0.895002	−	0.446062i	$-0.147174\pi$
$661$	2.81059e83	1.79000	0.895002	+	0.446062i	$0.147174\pi$
$662$	−1.91644e83	−1.16730
$663$	−3.27477e83	−1.90780
$664$	−4.25629e83	−2.37177
$665$	−4.55654e82	−0.242883
$666$	3.71853e83	1.89619
$667$	−5.04256e81	−0.0246002
$668$	2.71700e83	1.26819
$669$	1.50954e83	0.674179
$670$	−2.26177e83	−0.966590
$671$	1.18135e82	0.0483129
$672$	−6.23044e83	−2.43851
$673$	−2.82753e83	−1.05916	−0.529581	−	0.848260i	$-0.677651\pi$
$673$	−2.82753e83	−1.05916	−0.529581	+	0.848260i	$0.677651\pi$
$674$	2.87451e83	1.03062
$675$	−2.40446e82	−0.0825195
$676$	5.07326e83	1.66671
$677$	5.84082e83	1.83700	0.918498	−	0.395425i	$-0.129403\pi$
$677$	5.84082e83	1.83700	0.918498	+	0.395425i	$0.129403\pi$
$678$	−9.03384e83	−2.72017
$679$	1.86499e83	0.537672
$680$	6.46612e83	1.78497
$681$	6.02805e83	1.59344
$682$	−3.85142e82	−0.0974950
$683$	−4.16662e83	−1.01012	−0.505060	−	0.863084i	$-0.668530\pi$
$683$	−4.16662e83	−1.01012	−0.505060	+	0.863084i	$0.668530\pi$
$684$	5.44421e83	1.26410
$685$	6.86241e82	0.152618
$686$	−9.45125e83	−2.01339
$687$	−8.20991e82	−0.167538
$688$	8.24910e83	1.61268
$689$	−1.15001e84	−2.15394
$690$	−9.99132e83	−1.79298
$691$	6.93132e83	1.19183	0.595914	−	0.803048i	$-0.296790\pi$
$691$	6.93132e83	1.19183	0.595914	+	0.803048i	$0.296790\pi$
$692$	−2.21371e83	−0.364747
$693$	1.50032e82	0.0236893
$694$	−1.49216e84	−2.25793
$695$	5.62638e83	0.815976
$696$	5.88238e82	0.0817675
$697$	−5.58875e83	−0.744643
$698$	1.06859e84	1.36482
$699$	1.02561e84	1.25575
$700$	1.03032e84	1.20942
$701$	−6.90202e82	−0.0776774	−0.0388387	−	0.999245i	$-0.512366\pi$
$701$	−6.90202e82	−0.0776774	−0.0388387	+	0.999245i	$0.512366\pi$
$702$	2.83804e83	0.306249
$703$	−5.98006e83	−0.618762
$704$	−5.97178e82	−0.0592530
$705$	−1.02582e84	−0.976099
$706$	3.15954e84	2.88327
$707$	−4.39210e82	−0.0384414
$708$	−1.38929e83	−0.116631
$709$	−1.62009e84	−1.30460	−0.652299	−	0.757962i	$-0.726195\pi$
$709$	−1.62009e84	−1.30460	−0.652299	+	0.757962i	$0.726195\pi$
$710$	5.04924e83	0.390036
$711$	6.38949e82	0.0473492
$712$	−4.75746e84	−3.38232
$713$	2.54328e84	1.73482
$714$	3.13442e84	2.05145
$715$	4.27261e82	0.0268327
$716$	−7.07266e84	−4.26235
$717$	−1.27438e84	−0.737028
$718$	4.48517e83	0.248948
$719$	2.70431e84	1.44064	0.720319	−	0.693643i	$-0.243996\pi$
$719$	2.70431e84	1.44064	0.720319	+	0.693643i	$0.243996\pi$
$720$	2.91662e84	1.49132
$721$	−5.95330e83	−0.292192
$722$	2.75035e84	1.29581
$723$	2.07521e84	0.938606
$724$	3.60332e84	1.56464
$725$	−3.27451e82	−0.0136513
$726$	−6.45512e84	−2.58389
$727$	−3.36956e84	−1.29511	−0.647557	−	0.762017i	$-0.724209\pi$
$727$	−3.36956e84	−1.29511	−0.647557	+	0.762017i	$0.724209\pi$
$728$	−7.31105e84	−2.69839
$729$	−2.28211e84	−0.808861
$730$	8.47648e83	0.288530
$731$	−1.89951e84	−0.620983
$732$	1.51371e85	4.75298
$733$	−4.13834e84	−1.24813	−0.624063	−	0.781374i	$-0.714519\pi$
$733$	−4.13834e84	−1.24813	−0.624063	+	0.781374i	$0.714519\pi$
$734$	3.42764e84	0.993028
$735$	1.32290e84	0.368173
$736$	1.04571e85	2.79586
$737$	−1.19765e83	−0.0307638
$738$	−4.79476e84	−1.18333
$739$	−1.38714e82	−0.00328934	−0.00164467	−	0.999999i	$-0.500524\pi$
$739$	−1.38714e82	−0.00328934	−0.00164467	+	0.999999i	$0.500524\pi$
$740$	−7.24599e84	−1.65106
$741$	4.51822e84	0.989305
$742$	1.10072e85	2.31613
$743$	1.47222e84	0.297716	0.148858	−	0.988859i	$-0.452440\pi$
$743$	1.47222e84	0.297716	0.148858	+	0.988859i	$0.452440\pi$
$744$	−2.96686e85	−5.76627
$745$	4.80463e84	0.897531
$746$	−9.20917e84	−1.65358
$747$	4.42083e84	0.763038
$748$	5.69530e83	0.0944973
$749$	−3.02632e84	−0.482727
$750$	−1.64530e85	−2.52312
$751$	2.68915e84	0.396494	0.198247	−	0.980152i	$-0.436475\pi$
$751$	2.68915e84	0.396494	0.198247	+	0.980152i	$0.436475\pi$
$752$	2.34565e85	3.32535
$753$	1.10244e85	1.50281
$754$	3.86498e83	0.0506632
$755$	7.95286e84	1.00251
$756$	−1.94194e84	−0.235419
$757$	−1.64478e85	−1.91770	−0.958850	−	0.283915i	$-0.908367\pi$
$757$	−1.64478e85	−1.91770	−0.958850	+	0.283915i	$0.908367\pi$
$758$	−4.73495e84	−0.530975
$759$	−5.29060e83	−0.0570653
$760$	−8.92133e84	−0.925611
$761$	7.57979e84	0.756502	0.378251	−	0.925703i	$-0.376526\pi$
$761$	7.57979e84	0.756502	0.378251	+	0.925703i	$0.376526\pi$
$762$	4.67200e85	4.48571
$763$	−5.44074e84	−0.502555
$764$	1.32816e85	1.18031
$765$	−6.71609e84	−0.574254
$766$	−3.16142e85	−2.60096
$767$	−5.48779e83	−0.0434444
$768$	4.40434e84	0.335525
$769$	−2.70374e84	−0.198216	−0.0991078	−	0.995077i	$-0.531599\pi$
$769$	−2.70374e84	−0.198216	−0.0991078	+	0.995077i	$0.531599\pi$
$770$	−4.08949e83	−0.0288531
$771$	−3.27111e85	−2.22122
$772$	−9.91868e84	−0.648252
$773$	−6.61906e84	−0.416391	−0.208195	−	0.978087i	$-0.566759\pi$
$773$	−6.61906e84	−0.416391	−0.208195	+	0.978087i	$0.566759\pi$
$774$	−1.62965e85	−0.986816
$775$	1.65154e85	0.962697
$776$	3.65149e85	2.04903
$777$	−2.11164e85	−1.14078
$778$	1.97556e85	1.02753
$779$	7.71083e84	0.386141
$780$	5.47468e85	2.63978
$781$	2.67367e83	0.0124137
$782$	−5.26077e85	−2.35207
$783$	6.17179e82	0.00265729
$784$	−3.02495e85	−1.25428
$785$	4.31223e84	0.172206
$786$	2.61017e85	1.00393
$787$	3.14052e84	0.116345	0.0581724	−	0.998307i	$-0.481473\pi$
$787$	3.14052e84	0.116345	0.0581724	+	0.998307i	$0.481473\pi$
$788$	−3.83519e85	−1.36856
$789$	1.60209e85	0.550700
$790$	−1.74161e84	−0.0576704
$791$	2.44170e85	0.778907
$792$	2.93750e84	0.0902786
$793$	5.97924e85	1.77046
$794$	3.09426e85	0.882778
$795$	−4.95525e85	−1.36218
$796$	−7.01144e85	−1.85726
$797$	2.74800e85	0.701449	0.350725	−	0.936479i	$-0.385935\pi$
$797$	2.74800e85	0.701449	0.350725	+	0.936479i	$0.385935\pi$
$798$	−4.32457e85	−1.06379
$799$	−5.40131e85	−1.28047
$800$	6.79057e85	1.55150
$801$	4.94137e85	1.08815
$802$	1.65263e86	3.50778
$803$	4.48846e83	0.00918309
$804$	−1.53461e86	−3.02652
$805$	2.70049e85	0.513409
$806$	−1.94935e86	−3.57279
$807$	−8.99728e85	−1.58980
$808$	−8.59936e84	−0.146498
$809$	1.02903e85	0.169024	0.0845119	−	0.996422i	$-0.473067\pi$
$809$	1.02903e85	0.169024	0.0845119	+	0.996422i	$0.473067\pi$
$810$	7.56685e85	1.19841
$811$	9.82250e85	1.50005	0.750027	−	0.661407i	$-0.230041\pi$
$811$	9.82250e85	1.50005	0.750027	+	0.661407i	$0.230041\pi$
$812$	−2.64462e84	−0.0389458
$813$	−7.29228e85	−1.03560
$814$	−5.36710e84	−0.0735054
$815$	−7.70770e85	−1.01806
$816$	3.22653e86	4.11033
$817$	2.62077e85	0.322016
$818$	−5.71781e85	−0.677652
$819$	7.59368e85	0.868115
$820$	9.34314e85	1.03035
$821$	1.25320e86	1.33321	0.666603	−	0.745413i	$-0.267748\pi$
$821$	1.25320e86	1.33321	0.666603	+	0.745413i	$0.267748\pi$
$822$	6.51305e85	0.668445
$823$	−1.58233e86	−1.56676	−0.783378	−	0.621546i	$-0.786505\pi$
$823$	−1.58233e86	−1.56676	−0.783378	+	0.621546i	$0.786505\pi$
$824$	−1.16561e86	−1.11352
$825$	−3.43558e84	−0.0316671
$826$	5.25259e84	0.0467156
$827$	−2.03076e86	−1.74280	−0.871398	−	0.490576i	$-0.836786\pi$
$827$	−2.03076e86	−1.74280	−0.871398	+	0.490576i	$0.836786\pi$
$828$	−3.22657e86	−2.67206
$829$	−6.59368e85	−0.526950	−0.263475	−	0.964666i	$-0.584869\pi$
$829$	−6.59368e85	−0.526950	−0.263475	+	0.964666i	$0.584869\pi$
$830$	−1.20501e86	−0.929364
$831$	2.68480e86	1.99840
$832$	−3.02255e86	−2.17138
$833$	6.96554e85	0.482978
$834$	5.33995e86	3.57387
$835$	4.62442e85	0.298749
$836$	−7.85783e84	−0.0490024
$837$	−3.11282e85	−0.187393
$838$	2.82148e86	1.63976
$839$	3.14600e85	0.176515	0.0882573	−	0.996098i	$-0.471870\pi$
$839$	3.14600e85	0.176515	0.0882573	+	0.996098i	$0.471870\pi$
$840$	−3.15024e86	−1.70650
$841$	−1.91113e86	−0.999560
$842$	2.23968e86	1.13104
$843$	−2.24350e86	−1.09399
$844$	2.71649e85	0.127910
$845$	8.63484e85	0.392628
$846$	−4.63395e86	−2.03482
$847$	1.74471e86	0.739883
$848$	1.13307e87	4.64065
$849$	−3.86695e86	−1.52965
$850$	−3.41621e86	−1.30523
$851$	3.54415e86	1.30795
$852$	3.42589e86	1.22125
$853$	−8.87150e85	−0.305492	−0.152746	−	0.988265i	$-0.548812\pi$
$853$	−8.87150e85	−0.305492	−0.152746	+	0.988265i	$0.548812\pi$
$854$	−5.72298e86	−1.90377
$855$	9.26621e85	0.297784
$856$	−5.92528e86	−1.83964
$857$	−3.27258e86	−0.981648	−0.490824	−	0.871259i	$-0.663304\pi$
$857$	−3.27258e86	−0.981648	−0.490824	+	0.871259i	$0.663304\pi$
$858$	4.05509e85	0.117524
$859$	1.26296e86	0.353664	0.176832	−	0.984241i	$-0.443415\pi$
$859$	1.26296e86	0.353664	0.176832	+	0.984241i	$0.443415\pi$
$860$	3.17556e86	0.859244
$861$	2.72280e86	0.711906
$862$	2.21330e86	0.559211
$863$	4.16687e86	1.01740	0.508700	−	0.860944i	$-0.330126\pi$
$863$	4.16687e86	1.01740	0.508700	+	0.860944i	$0.330126\pi$
$864$	−1.27989e86	−0.302006
$865$	−3.76781e85	−0.0859238
$866$	−1.58887e87	−3.50196
$867$	−9.45139e85	−0.201341
$868$	1.33385e87	2.74647
$869$	−9.22219e83	−0.00183548
$870$	1.66537e85	0.0320401
$871$	−6.06178e86	−1.12737
$872$	−1.06525e87	−1.91521
$873$	−3.79265e86	−0.659207
$874$	7.25831e86	1.21969
$875$	4.44697e86	0.722481
$876$	5.75127e86	0.903425
$877$	1.19187e87	1.81026	0.905128	−	0.425139i	$-0.139775\pi$
$877$	1.19187e87	1.81026	0.905128	+	0.425139i	$0.139775\pi$
$878$	−4.66191e86	−0.684660
$879$	−5.31302e85	−0.0754517
$880$	−4.20967e85	−0.0578108
$881$	5.33978e86	0.709143	0.354572	−	0.935029i	$-0.384627\pi$
$881$	5.33978e86	0.709143	0.354572	+	0.935029i	$0.384627\pi$
$882$	5.97595e86	0.767509
$883$	−3.28934e85	−0.0408571	−0.0204286	−	0.999791i	$-0.506503\pi$
$883$	−3.28934e85	−0.0408571	−0.0204286	+	0.999791i	$0.506503\pi$
$884$	2.88261e87	3.46293
$885$	−2.36462e85	−0.0274748
$886$	−2.19194e87	−2.46340
$887$	6.82023e86	0.741400	0.370700	−	0.928753i	$-0.379118\pi$
$887$	6.82023e86	0.741400	0.370700	+	0.928753i	$0.379118\pi$
$888$	−4.13442e87	−4.34742
$889$	−1.26276e87	−1.28446
$890$	−1.34689e87	−1.32534
$891$	4.00680e85	0.0381421
$892$	−1.32877e87	−1.22373
$893$	7.45221e86	0.663999
$894$	4.56003e87	3.93107
$895$	−1.20379e87	−1.00409
$896$	7.05778e86	0.569616
$897$	−2.67778e87	−2.09121
$898$	3.97214e87	3.00174
$899$	−4.23919e85	−0.0310007
$900$	−2.09526e87	−1.48280
$901$	−2.60911e87	−1.78694
$902$	6.92045e85	0.0458714
$903$	9.25429e86	0.593683
$904$	4.78064e87	2.96837
$905$	6.13297e86	0.368585
$906$	7.54799e87	4.39086
$907$	−1.50909e87	−0.849767	−0.424883	−	0.905248i	$-0.639685\pi$
$907$	−1.50909e87	−0.849767	−0.424883	+	0.905248i	$0.639685\pi$
$908$	−5.30617e87	−2.89234
$909$	8.93179e85	0.0471307
$910$	−2.06985e87	−1.05735
$911$	3.87850e87	1.91810	0.959051	−	0.283234i	$-0.0914073\pi$
$911$	3.87850e87	1.91810	0.959051	+	0.283234i	$0.0914073\pi$
$912$	−4.45166e87	−2.13145
$913$	−6.38075e85	−0.0295790
$914$	−7.75513e87	−3.48078
$915$	2.57638e87	1.11967
$916$	7.22674e86	0.304107
$917$	−7.05485e86	−0.287470
$918$	6.43887e86	0.254068
$919$	−2.15450e87	−0.823263	−0.411632	−	0.911350i	$-0.635041\pi$
$919$	−2.15450e87	−0.823263	−0.411632	+	0.911350i	$0.635041\pi$
$920$	5.28733e87	1.95657
$921$	1.24124e87	0.444833
$922$	2.44123e87	0.847319
$923$	1.35325e87	0.454911
$924$	−2.77471e86	−0.0903429
$925$	2.30148e87	0.725816
$926$	−8.31282e87	−2.53936
$927$	1.21067e87	0.358239
$928$	−1.74301e86	−0.0499614
$929$	5.54912e87	1.54085	0.770426	−	0.637530i	$-0.220044\pi$
$929$	5.54912e87	1.54085	0.770426	+	0.637530i	$0.220044\pi$
$930$	−8.39953e87	−2.25948
$931$	−9.61038e86	−0.250452
$932$	−9.02786e87	−2.27937
$933$	−7.80334e85	−0.0190885
$934$	3.13819e87	0.743784
$935$	9.69357e85	0.0222608
$936$	1.48678e88	3.30833
$937$	3.57990e86	0.0771885	0.0385942	−	0.999255i	$-0.487712\pi$
$937$	3.57990e86	0.0771885	0.0385942	+	0.999255i	$0.487712\pi$
$938$	5.80198e87	1.21225
$939$	−7.97125e87	−1.61396
$940$	9.02978e87	1.77176
$941$	−4.47034e87	−0.850054	−0.425027	−	0.905181i	$-0.639735\pi$
$941$	−4.47034e87	−0.850054	−0.425027	+	0.905181i	$0.639735\pi$
$942$	4.09270e87	0.754238
$943$	−4.56991e87	−0.816231
$944$	5.40695e86	0.0936006
$945$	−3.30523e86	−0.0554580
$946$	2.35214e86	0.0382537
$947$	−9.93580e86	−0.156631	−0.0783156	−	0.996929i	$-0.524954\pi$
$947$	−9.93580e86	−0.156631	−0.0783156	+	0.996929i	$0.524954\pi$
$948$	−1.18168e87	−0.180573
$949$	2.27178e87	0.336522
$950$	4.71336e87	0.676837
$951$	−9.35135e87	−1.30181
$952$	−1.65871e88	−2.23862
$953$	1.00705e88	1.31768	0.658842	−	0.752281i	$-0.271047\pi$
$953$	1.00705e88	1.31768	0.658842	+	0.752281i	$0.271047\pi$
$954$	−2.23843e88	−2.83967
$955$	2.26057e87	0.278047
$956$	1.12177e88	1.33782
$957$	8.81847e84	0.00101974
$958$	2.00203e88	2.24485
$959$	−1.76037e87	−0.191406
$960$	−1.30238e88	−1.37321
$961$	1.16009e88	1.18618
$962$	−2.71649e88	−2.69367
$963$	6.15434e87	0.591843
$964$	−1.82670e88	−1.70371
$965$	−1.68819e87	−0.152709
$966$	2.56301e88	2.24867
$967$	−3.35222e87	−0.285267	−0.142633	−	0.989776i	$-0.545557\pi$
$967$	−3.35222e87	−0.285267	−0.142633	+	0.989776i	$0.545557\pi$
$968$	3.41600e88	2.81965
$969$	1.02508e88	0.820742
$970$	1.03378e88	0.802901
$971$	−1.60573e88	−1.20978	−0.604889	−	0.796309i	$-0.706783\pi$
$971$	−1.60573e88	−1.20978	−0.604889	+	0.796309i	$0.706783\pi$
$972$	4.69928e88	3.43460
$973$	−1.44330e88	−1.02336
$974$	3.21711e88	2.21298
$975$	−1.73888e88	−1.16047
$976$	−5.89117e88	−3.81445
$977$	6.18037e87	0.388262	0.194131	−	0.980976i	$-0.437811\pi$
$977$	6.18037e87	0.388262	0.194131	+	0.980976i	$0.437811\pi$
$978$	−7.31530e88	−4.45899
$979$	−7.13206e86	−0.0421819
$980$	−1.16448e88	−0.668288
$981$	1.10643e88	0.616154
$982$	−3.72355e87	−0.201219
$983$	4.68900e87	0.245896	0.122948	−	0.992413i	$-0.460765\pi$
$983$	4.68900e87	0.245896	0.122948	+	0.992413i	$0.460765\pi$
$984$	5.33101e88	2.71303
$985$	−6.52761e87	−0.322393
$986$	8.76876e86	0.0420309
$987$	2.63148e88	1.22418
$988$	−3.97715e88	−1.79573
$989$	−1.55323e88	−0.680683
$990$	8.31641e86	0.0353751
$991$	3.12613e88	1.29073	0.645363	−	0.763876i	$-0.276706\pi$
$991$	3.12613e88	1.29073	0.645363	+	0.763876i	$0.276706\pi$
$992$	8.79110e88	3.52329
$993$	−2.21314e88	−0.861007
$994$	−1.29525e88	−0.489164
$995$	−1.19337e88	−0.437516
$996$	−8.17594e88	−2.90996
$997$	2.03910e88	0.704581	0.352290	−	0.935891i	$-0.385403\pi$
$997$	2.03910e88	0.704581	0.352290	+	0.935891i	$0.385403\pi$
$998$	−3.72638e88	−1.25008
$999$	−4.33783e87	−0.141283

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 60 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.42193e9 q^{2} -1.64208e14 q^{3} +1.44544e18 q^{4} +2.46018e20 q^{5} +2.33493e23 q^{6} -6.31094e24 q^{7} -1.23563e27 q^{8} +1.28340e28 q^{9} +O(q^{10})\)	\(q-1.42193e9 q^{2} -1.64208e14 q^{3} +1.44544e18 q^{4} +2.46018e20 q^{5} +2.33493e23 q^{6} -6.31094e24 q^{7} -1.23563e27 q^{8} +1.28340e28 q^{9} -3.49822e29 q^{10} -1.85237e29 q^{11} -2.37353e32 q^{12} -9.37557e32 q^{13} +8.97374e33 q^{14} -4.03982e34 q^{15} +9.23746e35 q^{16} -2.12710e36 q^{17} -1.82491e37 q^{18} +2.93477e37 q^{19} +3.55604e38 q^{20} +1.03631e39 q^{21} +2.63395e38 q^{22} -1.73933e40 q^{23} +2.02901e41 q^{24} -1.12947e41 q^{25} +1.33315e42 q^{26} +2.12883e41 q^{27} -9.12207e42 q^{28} +2.89914e41 q^{29} +5.74436e43 q^{30} -1.46222e44 q^{31} -6.01215e44 q^{32} +3.04175e43 q^{33} +3.02460e45 q^{34} -1.55260e45 q^{35} +1.85507e46 q^{36} -2.03766e46 q^{37} -4.17306e46 q^{38} +1.53955e47 q^{39} -3.03987e47 q^{40} +2.62740e47 q^{41} -1.47356e48 q^{42} +8.93006e47 q^{43} -2.67749e47 q^{44} +3.15739e48 q^{45} +2.47321e49 q^{46} +2.53928e49 q^{47} -1.51687e50 q^{48} -3.27466e49 q^{49} +1.60604e50 q^{50} +3.49288e50 q^{51} -1.35518e51 q^{52} +1.22660e51 q^{53} -3.02706e50 q^{54} -4.55717e49 q^{55} +7.79798e51 q^{56} -4.81914e51 q^{57} -4.12239e50 q^{58} +5.85329e50 q^{59} -5.83931e52 q^{60} -6.37747e52 q^{61} +2.07918e53 q^{62} -8.09944e52 q^{63} +3.22385e53 q^{64} -2.30656e53 q^{65} -4.32517e52 q^{66} +6.46551e53 q^{67} -3.07460e54 q^{68} +2.85612e54 q^{69} +2.20770e54 q^{70} -1.44338e54 q^{71} -1.58580e55 q^{72} -2.42309e54 q^{73} +2.89742e55 q^{74} +1.85469e55 q^{75} +4.24203e55 q^{76} +1.16902e54 q^{77} -2.18913e56 q^{78} +4.97858e54 q^{79} +2.27258e56 q^{80} -2.16306e56 q^{81} -3.73599e56 q^{82} +3.44463e56 q^{83} +1.49792e57 q^{84} -5.23306e56 q^{85} -1.26980e57 q^{86} -4.76063e55 q^{87} +2.28885e56 q^{88} +3.85023e57 q^{89} -4.48960e57 q^{90} +5.91687e57 q^{91} -2.51409e58 q^{92} +2.40109e58 q^{93} -3.61069e58 q^{94} +7.22007e57 q^{95} +9.87245e58 q^{96} -2.95516e58 q^{97} +4.65635e58 q^{98} -2.37733e57 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 32\!\cdots\!85 q^{9}+O(q^{10}) \) 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9	\( 5 q - 449691864 q^{2} + 84016631749932 q^{3} + 17\!\cdots\!40 q^{4}+ \cdots + 23\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 449691864 * q^2 + 84016631749932 * q^3 + 1738819379139544640 * q^4 + 179961612150086058390 * q^5 + 313484324816744176606560 * q^6 + 1498777546338193415604856 * q^7 - 345163648945131266751137280 * q^8 + 32651506629679703293856326185 * q^9 - 816306987485763512638039118160 * q^10 + 4258478353252041879297428322660 * q^11 - 44182708253273060258139543308544 * q^12 - 845614914312482778669168084611378 * q^13 + 6292067851730037636066126264146880 * q^14 - 40513800156133976678914677598869720 * q^15 + 694835480494500010980166187386081280 * q^16 - 3408789133052869460614097222783941254 * q^17 + 9695472609892683802181177716078279752 * q^18 + 64613555538305267315990967466483855900 * q^19 + 167758871278751870059053885614959950720 * q^20 + 3416027528563001630003898902298902729760 * q^21 + 16748450439811023159371198583524768270112 * q^22 + 26762219406239912352813565493381233364712 * q^23 + 432715559082166564545012957137471770368000 * q^24 + 626328164486171817149625807278273965801475 * q^25 + 2749973149308040923633652135036287227445360 * q^26 + 4216422593373619915288217358331953848770680 * q^27 - 5611228561379710656820495758490486062705152 * q^28 - 17549046108593766297328008399864666159350850 * q^29 - 150145537158572429445793395106337059707760320 * q^30 - 358583623042201488230225328552738568224907040 * q^31 - 1074522626525330530995966308544265757955293184 * q^32 + 751114060128814067949775005681101561535832944 * q^33 + 1313186147384734516654444992913422917722864080 * q^34 + 8788755903389357061227741366680412802419085840 * q^35 + 50365332867541870766115057156818159463301788480 * q^36 + 12289654705391014078883644083969663074775614326 * q^37 - 45794685161100120795332322131326257673964677920 * q^38 - 9221768768351520041372477942735049607434903480 * q^39 - 623280493607240105129626720516519294122185241600 * q^40 - 1264600318837995850108850617547077064258140834590 * q^41 - 1891447371005345295768856102377155889725040492288 * q^42 + 1362401402875616509759331175816257798295684833092 * q^43 + 10077075627927391677990061115125884792646469172480 * q^44 + 10049700882739433416170827255242789411985618900430 * q^45 + 35794385229187598114442404877782400066811275005760 * q^46 + 58116315089138636393563553286549713195469724328016 * q^47 - 140681680096635395071164158203106499934517556953088 * q^48 - 172418318747588613327122588406220961507566908720435 * q^49 - 233848387346081992883910872998391056418422012487400 * q^50 - 465020225697129855978502466718810564745463254433640 * q^51 - 992097542005695911104987622381229757223139868049024 * q^52 + 2268101788488183861226576340546566132432064315777382 * q^53 + 4267182630237865543673874484672773145843435829054400 * q^54 + 900686393182056151569568156583842171451592208829880 * q^55 + 13057990199329560708452108630914154838760821091430400 * q^56 - 1461399454110401384802692435956966006781083287581040 * q^57 - 19935384508052610930909349257749128471453923297265680 * q^58 - 21931653365540795176945573682489794310901322601489100 * q^59 - 156464057876025038631690397519755203816227736824450560 * q^60 - 55594140754072322694181208673989737469003346813960290 * q^61 + 183475769536335462614566613996468524195162017418651392 * q^62 + 182010153390148596243930899005933467643747025172792792 * q^63 + 442992326944585087629292186411036974187652719990538240 * q^64 + 108239432655103548226552811908240865218465397888070180 * q^65 + 1851519511613271584553254669645963732036891556451969920 * q^66 + 251728958220345096328034657219059743090559333983657196 * q^67 - 5807349046062465910161766073979061475602982250739804032 * q^68 - 1186914917838620759227364067219409346615803888683557280 * q^69 - 5752977156560799367346480182820409713199133658156760960 * q^70 - 6369597660991167158573967320963521000612243175546832840 * q^71 + 505582168407192977842217602799461333023468587718935040 * q^72 + 12498734118021895660608582328454257591891310584798516162 * q^73 + 30430803441235884517255321866854090380478491767252508080 * q^74 + 71252573634955902069214955355612845417141504756757611700 * q^75 + 44485052481827577410579765985045990814357967613276332800 * q^76 + 17284905559091020495400324815223194592508822902892800352 * q^77 - 201581338752116742909455308452046241693931223329795704256 * q^78 - 195027743716001656833247333265450397879290980351117845200 * q^79 - 206704704480779086536260387174822452768748287935918120960 * q^80 - 272827015213405140901132899770256322932509539084953805395 * q^81 - 900520634877949974377918733125010085392642066824246973168 * q^82 + 1340753017495815214930655712848265601901866175919407282652 * q^83 + 1757594637692279239094128738775127192473269576864397076480 * q^84 + 2489371886919081358504761029214476055227000571885198923340 * q^85 - 1480724029310290822922398160933917869023473589220972227040 * q^86 + 2732195656620738105781600070679866258015898732907716552840 * q^87 - 766253667564296029168711510940105999694943299571114997760 * q^88 + 4137994032714609594535072901976334293523151283735651174450 * q^89 - 27581529153974409588805844338613259043100774320772297131920 * q^90 + 2026135516273811264299668018701283385599128389353986522960 * q^91 - 40220109586116561836814028008941466356622877640185075490304 * q^92 + 35686922849658258124721404138853435620012609371542349362304 * q^93 - 11288243726815211032514455546739674300124940708563708661120 * q^94 + 87101339446452871712134322546432797479691690743389226486600 * q^95 + 35374905257632352454877863276046463006859953360328478556160 * q^96 + 116502743099592096760799908821840050224405365201122277495466 * q^97 - 100197653381373748947470486612022288330601696851398709875352 * q^98 + 233753058124724467227621750953596851247855288092335837370420 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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